LMFDB - Embedded newform 1950.2.i.d.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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
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			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1950.601
Dual form			1950.2.i.d.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.50000 + 4.33013i) q^{11} +1.00000 q^{12} +(1.00000 - 3.46410i) q^{13} +2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +1.00000 q^{18} +(1.00000 - 1.73205i) q^{19} +2.00000 q^{21} +(2.50000 - 4.33013i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.50000 + 0.866025i) q^{26} +1.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(-2.50000 - 4.33013i) q^{29} -11.0000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.50000 - 4.33013i) q^{33} +2.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(1.50000 + 2.59808i) q^{37} -2.00000 q^{38} +(-3.50000 + 0.866025i) q^{39} +(1.00000 + 1.73205i) q^{41} +(-1.00000 - 1.73205i) q^{42} +(-5.50000 + 9.52628i) q^{43} -5.00000 q^{44} +(-0.500000 + 0.866025i) q^{46} -9.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +2.00000 q^{51} +(2.50000 + 2.59808i) q^{52} -6.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.00000 + 1.73205i) q^{56} -2.00000 q^{57} +(-2.50000 + 4.33013i) q^{58} +(7.50000 - 12.9904i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(5.50000 + 9.52628i) q^{62} +(-1.00000 - 1.73205i) q^{63} +1.00000 q^{64} -5.00000 q^{66} +(8.00000 + 13.8564i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(-0.500000 + 0.866025i) q^{69} +(-0.500000 + 0.866025i) q^{72} +6.00000 q^{73} +(1.50000 - 2.59808i) q^{74} +(1.00000 + 1.73205i) q^{76} -10.0000 q^{77} +(2.50000 + 2.59808i) q^{78} -11.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} -6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +11.0000 q^{86} +(-2.50000 + 4.33013i) q^{87} +(2.50000 + 4.33013i) q^{88} +(-1.00000 - 1.73205i) q^{89} +(5.00000 + 5.19615i) q^{91} +1.00000 q^{92} +(5.50000 + 9.52628i) q^{93} +(4.50000 + 7.79423i) q^{94} +1.00000 q^{96} +(-1.00000 + 1.73205i) q^{97} +(1.50000 - 2.59808i) q^{98} -5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - q^3 - q^4 - q^6 - 2 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9} + 5 q^{11} + 2 q^{12} + 2 q^{13} + 4 q^{14} - q^{16} - 2 q^{17} + 2 q^{18} + 2 q^{19} + 4 q^{21} + 5 q^{22} - q^{23} - q^{24} - 7 q^{26} + 2 q^{27} - 2 q^{28} - 5 q^{29} - 22 q^{31} - q^{32} + 5 q^{33} + 4 q^{34} - q^{36} + 3 q^{37} - 4 q^{38} - 7 q^{39} + 2 q^{41} - 2 q^{42} - 11 q^{43} - 10 q^{44} - q^{46} - 18 q^{47} - q^{48} + 3 q^{49} + 4 q^{51} + 5 q^{52} - 12 q^{53} - q^{54} - 2 q^{56} - 4 q^{57} - 5 q^{58} + 15 q^{59} - 10 q^{61} + 11 q^{62} - 2 q^{63} + 2 q^{64} - 10 q^{66} + 16 q^{67} - 2 q^{68} - q^{69} - q^{72} + 12 q^{73} + 3 q^{74} + 2 q^{76} - 20 q^{77} + 5 q^{78} - 22 q^{79} - q^{81} + 2 q^{82} - 12 q^{83} - 2 q^{84} + 22 q^{86} - 5 q^{87} + 5 q^{88} - 2 q^{89} + 10 q^{91} + 2 q^{92} + 11 q^{93} + 9 q^{94} + 2 q^{96} - 2 q^{97} + 3 q^{98} - 10 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^3 - q^4 - q^6 - 2 * q^7 + 2 * q^8 - q^9 + 5 * q^11 + 2 * q^12 + 2 * q^13 + 4 * q^14 - q^16 - 2 * q^17 + 2 * q^18 + 2 * q^19 + 4 * q^21 + 5 * q^22 - q^23 - q^24 - 7 * q^26 + 2 * q^27 - 2 * q^28 - 5 * q^29 - 22 * q^31 - q^32 + 5 * q^33 + 4 * q^34 - q^36 + 3 * q^37 - 4 * q^38 - 7 * q^39 + 2 * q^41 - 2 * q^42 - 11 * q^43 - 10 * q^44 - q^46 - 18 * q^47 - q^48 + 3 * q^49 + 4 * q^51 + 5 * q^52 - 12 * q^53 - q^54 - 2 * q^56 - 4 * q^57 - 5 * q^58 + 15 * q^59 - 10 * q^61 + 11 * q^62 - 2 * q^63 + 2 * q^64 - 10 * q^66 + 16 * q^67 - 2 * q^68 - q^69 - q^72 + 12 * q^73 + 3 * q^74 + 2 * q^76 - 20 * q^77 + 5 * q^78 - 22 * q^79 - q^81 + 2 * q^82 - 12 * q^83 - 2 * q^84 + 22 * q^86 - 5 * q^87 + 5 * q^88 - 2 * q^89 + 10 * q^91 + 2 * q^92 + 11 * q^93 + 9 * q^94 + 2 * q^96 - 2 * q^97 + 3 * q^98 - 10 * q^99

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
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	−0.990766	−	0.135583i	$-0.956709\pi$
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	0.612801	+	0.790237i	$0.290043\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	0.945979	+	0.324227i	$0.105104\pi$
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	−0.192201	+	0.981356i	$0.561563\pi$
$12$	1.00000			0.288675
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$14$	2.00000			0.534522
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	1.00000			0.235702
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$	2.50000	−	4.33013i	0.533002	−	0.923186i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	0.809177	−	0.587565i	$-0.199913\pi$
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	−0.913434	+	0.406986i	$0.866580\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	−3.50000	+	0.866025i	−0.686406	+	0.169842i
$27$	1.00000			0.192450
$28$	−1.00000	−	1.73205i	−0.188982	−	0.327327i
$29$	−2.50000	−	4.33013i	−0.464238	−	0.804084i	0.534928	−	0.844897i	$-0.320339\pi$
$29$	−2.50000	−	4.33013i	−0.464238	−	0.804084i	−0.999167	+	0.0408130i	$0.987005\pi$
$30$		0			0
$31$	−11.0000			−1.97566			−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−11.0000			−1.97566			−0.987829	+	0.155543i	$0.950287\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.50000	−	4.33013i	0.435194	−	0.753778i
$34$	2.00000			0.342997
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	0.962580	−	0.270998i	$-0.0873538\pi$
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	−0.715981	+	0.698119i	$0.754020\pi$
$38$	−2.00000			−0.324443
$39$	−3.50000	+	0.866025i	−0.560449	+	0.138675i
$40$		0			0
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	0.933486	−	0.358614i	$-0.116751\pi$
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	−0.777312	+	0.629115i	$0.783417\pi$
$42$	−1.00000	−	1.73205i	−0.154303	−	0.267261i
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	0.0522047	+	0.998636i	$0.483375\pi$
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	−0.890947	+	0.454108i	$0.849958\pi$
$44$	−5.00000			−0.753778
$45$		0			0
$46$	−0.500000	+	0.866025i	−0.0737210	+	0.127688i
$47$	−9.00000			−1.31278			−0.656392	−	0.754420i	$-0.727918\pi$
$47$	−9.00000			−1.31278			−0.656392	+	0.754420i	$0.727918\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$		0			0
$51$	2.00000			0.280056
$52$	2.50000	+	2.59808i	0.346688	+	0.360288i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	−1.00000	+	1.73205i	−0.133631	+	0.231455i
$57$	−2.00000			−0.264906
$58$	−2.50000	+	4.33013i	−0.328266	+	0.568574i
$59$	7.50000	−	12.9904i	0.976417	−	1.69120i	0.301239	−	0.953549i	$-0.402600\pi$
$59$	7.50000	−	12.9904i	0.976417	−	1.69120i	0.675178	−	0.737655i	$-0.264067\pi$
$60$		0			0
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	0.345207	+	0.938527i	$0.387809\pi$
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	−0.985391	+	0.170305i	$0.945525\pi$
$62$	5.50000	+	9.52628i	0.698501	+	1.20984i
$63$	−1.00000	−	1.73205i	−0.125988	−	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	−5.00000			−0.615457
$67$	8.00000	+	13.8564i	0.977356	+	1.69283i	0.671932	+	0.740613i	$0.265465\pi$
$67$	8.00000	+	13.8564i	0.977356	+	1.69283i	0.305424	+	0.952217i	$0.401202\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$	−0.500000	+	0.866025i	−0.0601929	+	0.104257i
$70$		0			0
$71$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$71$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	6.00000			0.702247			0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000			0.702247			0.351123	+	0.936329i	$0.385800\pi$
$74$	1.50000	−	2.59808i	0.174371	−	0.302020i
$75$		0			0
$76$	1.00000	+	1.73205i	0.114708	+	0.198680i
$77$	−10.0000			−1.13961
$78$	2.50000	+	2.59808i	0.283069	+	0.294174i
$79$	−11.0000			−1.23760			−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000			−1.23760			−0.618798	+	0.785550i	$0.712380\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.00000	−	1.73205i	0.110432	−	0.191273i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	−1.00000	+	1.73205i	−0.109109	+	0.188982i
$85$		0			0
$86$	11.0000			1.18616
$87$	−2.50000	+	4.33013i	−0.268028	+	0.464238i
$88$	2.50000	+	4.33013i	0.266501	+	0.461593i
$89$	−1.00000	−	1.73205i	−0.106000	−	0.183597i	0.808146	−	0.588982i	$-0.200471\pi$
$89$	−1.00000	−	1.73205i	−0.106000	−	0.183597i	−0.914146	+	0.405385i	$0.867138\pi$
$90$		0			0
$91$	5.00000	+	5.19615i	0.524142	+	0.544705i
$92$	1.00000			0.104257
$93$	5.50000	+	9.52628i	0.570323	+	0.987829i
$94$	4.50000	+	7.79423i	0.464140	+	0.803913i
$95$		0			0
$96$	1.00000			0.102062
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$	1.50000	−	2.59808i	0.151523	−	0.262445i
$99$	−5.00000			−0.502519
$100$		0			0
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	0.811976	−	0.583691i	$-0.198392\pi$
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	−0.911479	+	0.411346i	$0.865059\pi$
$102$	−1.00000	−	1.73205i	−0.0990148	−	0.171499i
$103$	−10.0000			−0.985329			−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000			−0.985329			−0.492665	+	0.870219i	$0.663977\pi$
$104$	1.00000	−	3.46410i	0.0980581	−	0.339683i
$105$		0			0
$106$	3.00000	+	5.19615i	0.291386	+	0.504695i
$107$	5.00000	+	8.66025i	0.483368	+	0.837218i	0.999818	−	0.0190994i	$-0.00607989\pi$
$107$	5.00000	+	8.66025i	0.483368	+	0.837218i	−0.516449	+	0.856318i	$0.672747\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	1.50000	−	2.59808i	0.142374	−	0.246598i
$112$	2.00000			0.188982
$113$	5.50000	−	9.52628i	0.517396	−	0.896157i	−0.482399	−	0.875951i	$-0.660235\pi$
$113$	5.50000	−	9.52628i	0.517396	−	0.896157i	0.999796	−	0.0202056i	$-0.00643208\pi$
$114$	1.00000	+	1.73205i	0.0936586	+	0.162221i
$115$		0			0
$116$	5.00000			0.464238
$117$	2.50000	+	2.59808i	0.231125	+	0.240192i
$118$	−15.0000			−1.38086
$119$	−2.00000	−	3.46410i	−0.183340	−	0.317554i
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$	10.0000			0.905357
$123$	1.00000	−	1.73205i	0.0901670	−	0.156174i
$124$	5.50000	−	9.52628i	0.493915	−	0.855485i
$125$		0			0
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	1.00000	+	1.73205i	0.0887357	+	0.153695i	0.906977	−	0.421180i	$-0.138384\pi$
$127$	1.00000	+	1.73205i	0.0887357	+	0.153695i	−0.818241	+	0.574875i	$0.805051\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	11.0000			0.968496
$130$		0			0
$131$	−1.00000			−0.0873704			−0.0436852	−	0.999045i	$-0.513910\pi$
$131$	−1.00000			−0.0873704			−0.0436852	+	0.999045i	$0.513910\pi$
$132$	2.50000	+	4.33013i	0.217597	+	0.376889i
$133$	2.00000	+	3.46410i	0.173422	+	0.300376i
$134$	8.00000	−	13.8564i	0.691095	−	1.19701i
$135$		0			0
$136$	−1.00000	+	1.73205i	−0.0857493	+	0.148522i
$137$	−5.50000	+	9.52628i	−0.469897	+	0.813885i	−0.999408	−	0.0344182i	$-0.989042\pi$
$137$	−5.50000	+	9.52628i	−0.469897	+	0.813885i	0.529511	+	0.848303i	$0.322376\pi$
$138$	1.00000			0.0851257
$139$	−1.00000	+	1.73205i	−0.0848189	+	0.146911i	−0.905314	−	0.424743i	$-0.860365\pi$
$139$	−1.00000	+	1.73205i	−0.0848189	+	0.146911i	0.820495	+	0.571654i	$0.193698\pi$
$140$		0			0
$141$	4.50000	+	7.79423i	0.378968	+	0.656392i
$142$		0			0
$143$	17.5000	−	4.33013i	1.46342	−	0.362103i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−3.00000	−	5.19615i	−0.248282	−	0.430037i
$147$	1.50000	−	2.59808i	0.123718	−	0.214286i
$148$	−3.00000			−0.246598
$149$	−8.50000	+	14.7224i	−0.696347	+	1.20611i	0.273377	+	0.961907i	$0.411859\pi$
$149$	−8.50000	+	14.7224i	−0.696347	+	1.20611i	−0.969724	+	0.244202i	$0.921474\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	−1.00000	−	1.73205i	−0.0808452	−	0.140028i
$154$	5.00000	+	8.66025i	0.402911	+	0.697863i
$155$		0			0
$156$	1.00000	−	3.46410i	0.0800641	−	0.277350i
$157$	7.00000			0.558661			0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000			0.558661			0.279330	+	0.960195i	$0.409888\pi$
$158$	5.50000	+	9.52628i	0.437557	+	0.757870i
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$		0			0
$161$	2.00000			0.157622
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−7.50000	+	12.9904i	−0.587445	+	1.01749i	0.407120	+	0.913375i	$0.366533\pi$
$163$	−7.50000	+	12.9904i	−0.587445	+	1.01749i	−0.994566	+	0.104111i	$0.966800\pi$
$164$	−2.00000			−0.156174
$165$		0			0
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	0.918208	−	0.396098i	$-0.129636\pi$
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	−0.802135	+	0.597143i	$0.796303\pi$
$168$	2.00000			0.154303
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$		0			0
$171$	1.00000	+	1.73205i	0.0764719	+	0.132453i
$172$	−5.50000	−	9.52628i	−0.419371	−	0.726372i
$173$	10.0000	−	17.3205i	0.760286	−	1.31685i	−0.182417	−	0.983221i	$-0.558392\pi$
$173$	10.0000	−	17.3205i	0.760286	−	1.31685i	0.942703	−	0.333633i	$-0.108275\pi$
$174$	5.00000			0.379049
$175$		0			0
$176$	2.50000	−	4.33013i	0.188445	−	0.326396i
$177$	−15.0000			−1.12747
$178$	−1.00000	+	1.73205i	−0.0749532	+	0.129823i
$179$	6.50000	+	11.2583i	0.485833	+	0.841487i	0.999867	−	0.0162823i	$-0.00518305\pi$
$179$	6.50000	+	11.2583i	0.485833	+	0.841487i	−0.514035	+	0.857769i	$0.671850\pi$
$180$		0			0
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	2.00000	−	6.92820i	0.148250	−	0.513553i
$183$	10.0000			0.739221
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$		0			0
$186$	5.50000	−	9.52628i	0.403280	−	0.698501i
$187$	−10.0000			−0.731272
$188$	4.50000	−	7.79423i	0.328196	−	0.568453i
$189$	−1.00000	+	1.73205i	−0.0727393	+	0.125988i
$190$		0			0
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	−0.929267	−	0.369410i	$-0.879560\pi$
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	0.784552	+	0.620063i	$0.212893\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−12.0000	−	20.7846i	−0.863779	−	1.49611i	−0.868255	−	0.496119i	$-0.834758\pi$
$193$	−12.0000	−	20.7846i	−0.863779	−	1.49611i	0.00447566	−	0.999990i	$-0.498575\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	−3.00000			−0.214286
$197$	−4.00000	−	6.92820i	−0.284988	−	0.493614i	0.687618	−	0.726073i	$-0.258656\pi$
$197$	−4.00000	−	6.92820i	−0.284988	−	0.493614i	−0.972606	+	0.232458i	$0.925323\pi$
$198$	2.50000	+	4.33013i	0.177667	+	0.307729i
$199$	−12.0000	+	20.7846i	−0.850657	+	1.47338i	0.0299585	+	0.999551i	$0.490462\pi$
$199$	−12.0000	+	20.7846i	−0.850657	+	1.47338i	−0.880616	+	0.473831i	$0.842871\pi$
$200$		0			0
$201$	8.00000	−	13.8564i	0.564276	−	0.977356i
$202$	−1.00000	+	1.73205i	−0.0703598	+	0.121867i
$203$	10.0000			0.701862
$204$	−1.00000	+	1.73205i	−0.0700140	+	0.121268i
$205$		0			0
$206$	5.00000	+	8.66025i	0.348367	+	0.603388i
$207$	1.00000			0.0695048
$208$	−3.50000	+	0.866025i	−0.242681	+	0.0600481i
$209$	10.0000			0.691714
$210$		0			0
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	0.926620	−	0.375999i	$-0.122700\pi$
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	−0.788935	+	0.614477i	$0.789367\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$		0			0
$214$	5.00000	−	8.66025i	0.341793	−	0.592003i
$215$		0			0
$216$	1.00000			0.0680414
$217$	11.0000	−	19.0526i	0.746729	−	1.29337i
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$	−3.00000	−	5.19615i	−0.202721	−	0.351123i
$220$		0			0
$221$	5.00000	+	5.19615i	0.336336	+	0.349531i
$222$	−3.00000			−0.201347
$223$	13.0000	+	22.5167i	0.870544	+	1.50783i	0.861435	+	0.507869i	$0.169566\pi$
$223$	13.0000	+	22.5167i	0.870544	+	1.50783i	0.00910984	+	0.999959i	$0.497100\pi$
$224$	−1.00000	−	1.73205i	−0.0668153	−	0.115728i
$225$		0			0
$226$	−11.0000			−0.731709
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$	1.00000	−	1.73205i	0.0662266	−	0.114708i
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$		0			0
$231$	5.00000	+	8.66025i	0.328976	+	0.569803i
$232$	−2.50000	−	4.33013i	−0.164133	−	0.284287i
$233$	−1.00000			−0.0655122			−0.0327561	−	0.999463i	$-0.510428\pi$
$233$	−1.00000			−0.0655122			−0.0327561	+	0.999463i	$0.510428\pi$
$234$	1.00000	−	3.46410i	0.0653720	−	0.226455i
$235$		0			0
$236$	7.50000	+	12.9904i	0.488208	+	0.845602i
$237$	5.50000	+	9.52628i	0.357263	+	0.618798i
$238$	−2.00000	+	3.46410i	−0.129641	+	0.224544i
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$		0			0
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	−0.731001	−	0.682376i	$-0.760947\pi$
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	0.956456	+	0.291877i	$0.0942799\pi$
$242$	14.0000			0.899954
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−5.00000	−	8.66025i	−0.320092	−	0.554416i
$245$		0			0
$246$	−2.00000			−0.127515
$247$	−5.00000	−	5.19615i	−0.318142	−	0.330623i
$248$	−11.0000			−0.698501
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$		0			0
$251$	−12.5000	+	21.6506i	−0.788993	+	1.36658i	0.137591	+	0.990489i	$0.456064\pi$
$251$	−12.5000	+	21.6506i	−0.788993	+	1.36658i	−0.926584	+	0.376087i	$0.877269\pi$
$252$	2.00000			0.125988
$253$	2.50000	−	4.33013i	0.157174	−	0.272233i
$254$	1.00000	−	1.73205i	0.0627456	−	0.108679i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.50000	−	14.7224i	−0.530215	−	0.918360i	−0.999379	−	0.0352486i	$-0.988778\pi$
$257$	−8.50000	−	14.7224i	−0.530215	−	0.918360i	0.469163	−	0.883112i	$-0.344556\pi$
$258$	−5.50000	−	9.52628i	−0.342415	−	0.593080i
$259$	−6.00000			−0.372822
$260$		0			0
$261$	5.00000			0.309492
$262$	0.500000	+	0.866025i	0.0308901	+	0.0535032i
$263$	10.5000	+	18.1865i	0.647458	+	1.12143i	0.983728	+	0.179664i	$0.0575011\pi$
$263$	10.5000	+	18.1865i	0.647458	+	1.12143i	−0.336270	+	0.941766i	$0.609166\pi$
$264$	2.50000	−	4.33013i	0.153864	−	0.266501i
$265$		0			0
$266$	2.00000	−	3.46410i	0.122628	−	0.212398i
$267$	−1.00000	+	1.73205i	−0.0611990	+	0.106000i
$268$	−16.0000			−0.977356
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	−0.996586	−	0.0825561i	$-0.973692\pi$
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	0.569789	+	0.821791i	$0.307025\pi$
$270$		0			0
$271$	6.50000	+	11.2583i	0.394847	+	0.683895i	0.993082	−	0.117426i	$-0.0374643\pi$
$271$	6.50000	+	11.2583i	0.394847	+	0.683895i	−0.598235	+	0.801321i	$0.704131\pi$
$272$	2.00000			0.121268
$273$	2.00000	−	6.92820i	0.121046	−	0.419314i
$274$	11.0000			0.664534
$275$		0			0
$276$	−0.500000	−	0.866025i	−0.0300965	−	0.0521286i
$277$	−5.50000	+	9.52628i	−0.330463	+	0.572379i	−0.982603	−	0.185720i	$-0.940538\pi$
$277$	−5.50000	+	9.52628i	−0.330463	+	0.572379i	0.652140	+	0.758099i	$0.273872\pi$
$278$	2.00000			0.119952
$279$	5.50000	−	9.52628i	0.329276	−	0.570323i
$280$		0			0
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$	4.50000	−	7.79423i	0.267971	−	0.464140i
$283$	9.50000	+	16.4545i	0.564716	+	0.978117i	0.997076	+	0.0764162i	$0.0243478\pi$
$283$	9.50000	+	16.4545i	0.564716	+	0.978117i	−0.432360	+	0.901701i	$0.642319\pi$
$284$		0			0
$285$		0			0
$286$	−12.5000	−	12.9904i	−0.739140	−	0.768137i
$287$	−4.00000			−0.236113
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	2.00000			0.117242
$292$	−3.00000	+	5.19615i	−0.175562	+	0.304082i
$293$	3.00000	−	5.19615i	0.175262	−	0.303562i	−0.764990	−	0.644042i	$-0.777256\pi$
$293$	3.00000	−	5.19615i	0.175262	−	0.303562i	0.940252	+	0.340480i	$0.110589\pi$
$294$	−3.00000			−0.174964
$295$		0			0
$296$	1.50000	+	2.59808i	0.0871857	+	0.151010i
$297$	2.50000	+	4.33013i	0.145065	+	0.251259i
$298$	17.0000			0.984784
$299$	−3.50000	+	0.866025i	−0.202410	+	0.0500835i
$300$		0			0
$301$	−11.0000	−	19.0526i	−0.634029	−	1.09817i
$302$	−4.00000	−	6.92820i	−0.230174	−	0.398673i
$303$	−1.00000	+	1.73205i	−0.0574485	+	0.0995037i
$304$	−2.00000			−0.114708
$305$		0			0
$306$	−1.00000	+	1.73205i	−0.0571662	+	0.0990148i
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	5.00000	−	8.66025i	0.284901	−	0.493464i
$309$	5.00000	+	8.66025i	0.284440	+	0.492665i
$310$		0			0
$311$	20.0000			1.13410			0.567048	−	0.823685i	$-0.308085\pi$
$311$	20.0000			1.13410			0.567048	+	0.823685i	$0.308085\pi$
$312$	−3.50000	+	0.866025i	−0.198148	+	0.0490290i
$313$	−20.0000			−1.13047			−0.565233	−	0.824931i	$-0.691214\pi$
$313$	−20.0000			−1.13047			−0.565233	+	0.824931i	$0.691214\pi$
$314$	−3.50000	−	6.06218i	−0.197516	−	0.342108i
$315$		0			0
$316$	5.50000	−	9.52628i	0.309399	−	0.535895i
$317$	−16.0000			−0.898650			−0.449325	−	0.893368i	$-0.648335\pi$
$317$	−16.0000			−0.898650			−0.449325	+	0.893368i	$0.648335\pi$
$318$	3.00000	−	5.19615i	0.168232	−	0.291386i
$319$	12.5000	−	21.6506i	0.699866	−	1.21220i
$320$		0			0
$321$	5.00000	−	8.66025i	0.279073	−	0.483368i
$322$	−1.00000	−	1.73205i	−0.0557278	−	0.0965234i
$323$	2.00000	+	3.46410i	0.111283	+	0.192748i
$324$	1.00000			0.0555556
$325$		0			0
$326$	15.0000			0.830773
$327$	1.00000	+	1.73205i	0.0553001	+	0.0957826i
$328$	1.00000	+	1.73205i	0.0552158	+	0.0956365i
$329$	9.00000	−	15.5885i	0.496186	−	0.859419i
$330$		0			0
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$	−3.00000			−0.164399
$334$	1.50000	−	2.59808i	0.0820763	−	0.142160i
$335$		0			0
$336$	−1.00000	−	1.73205i	−0.0545545	−	0.0944911i
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$	−0.500000	+	12.9904i	−0.0271964	+	0.706584i
$339$	−11.0000			−0.597438
$340$		0			0
$341$	−27.5000	−	47.6314i	−1.48921	−	2.57938i
$342$	1.00000	−	1.73205i	0.0540738	−	0.0936586i
$343$	−20.0000			−1.07990
$344$	−5.50000	+	9.52628i	−0.296540	+	0.513623i
$345$		0			0
$346$	−20.0000			−1.07521
$347$	17.0000	−	29.4449i	0.912608	−	1.58068i	0.102241	−	0.994760i	$-0.467399\pi$
$347$	17.0000	−	29.4449i	0.912608	−	1.58068i	0.810366	−	0.585923i	$-0.199268\pi$
$348$	−2.50000	−	4.33013i	−0.134014	−	0.232119i
$349$	−10.0000	−	17.3205i	−0.535288	−	0.927146i	−0.999149	−	0.0412379i	$-0.986870\pi$
$349$	−10.0000	−	17.3205i	−0.535288	−	0.927146i	0.463862	−	0.885908i	$-0.346463\pi$
$350$		0			0
$351$	1.00000	−	3.46410i	0.0533761	−	0.184900i
$352$	−5.00000			−0.266501
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	0.520689	−	0.853746i	$-0.325675\pi$
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	−0.999711	+	0.0240566i	$0.992342\pi$
$354$	7.50000	+	12.9904i	0.398621	+	0.690431i
$355$		0			0
$356$	2.00000			0.106000
$357$	−2.00000	+	3.46410i	−0.105851	+	0.183340i
$358$	6.50000	−	11.2583i	0.343536	−	0.595021i
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	8.00000	+	13.8564i	0.420471	+	0.728277i
$363$	14.0000			0.734809
$364$	−7.00000	+	1.73205i	−0.366900	+	0.0907841i
$365$		0			0
$366$	−5.00000	−	8.66025i	−0.261354	−	0.452679i
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	0.578101	−	0.815966i	$-0.303794\pi$
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	−0.995697	+	0.0926670i	$0.970461\pi$
$368$	−0.500000	+	0.866025i	−0.0260643	+	0.0451447i
$369$	−2.00000			−0.104116
$370$		0			0
$371$	6.00000	−	10.3923i	0.311504	−	0.539542i
$372$	−11.0000			−0.570323
$373$	−9.50000	+	16.4545i	−0.491891	+	0.851981i	−0.999956	−	0.00933789i	$-0.997028\pi$
$373$	−9.50000	+	16.4545i	−0.491891	+	0.851981i	0.508065	+	0.861319i	$0.330361\pi$
$374$	5.00000	+	8.66025i	0.258544	+	0.447811i
$375$		0			0
$376$	−9.00000			−0.464140
$377$	−17.5000	+	4.33013i	−0.901296	+	0.223013i
$378$	2.00000			0.102869
$379$	1.00000	+	1.73205i	0.0513665	+	0.0889695i	0.890565	−	0.454855i	$-0.150309\pi$
$379$	1.00000	+	1.73205i	0.0513665	+	0.0889695i	−0.839199	+	0.543825i	$0.816976\pi$
$380$		0			0
$381$	1.00000	−	1.73205i	0.0512316	−	0.0887357i
$382$	4.00000			0.204658
$383$	15.5000	−	26.8468i	0.792013	−	1.37181i	−0.132706	−	0.991155i	$-0.542367\pi$
$383$	15.5000	−	26.8468i	0.792013	−	1.37181i	0.924719	−	0.380651i	$-0.124300\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$		0			0
$386$	−12.0000	+	20.7846i	−0.610784	+	1.05791i
$387$	−5.50000	−	9.52628i	−0.279581	−	0.484248i
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	5.00000			0.253510			0.126755	−	0.991934i	$-0.459544\pi$
$389$	5.00000			0.253510			0.126755	+	0.991934i	$0.459544\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$	1.50000	+	2.59808i	0.0757614	+	0.131223i
$393$	0.500000	+	0.866025i	0.0252217	+	0.0436852i
$394$	−4.00000	+	6.92820i	−0.201517	+	0.349038i
$395$		0			0
$396$	2.50000	−	4.33013i	0.125630	−	0.217597i
$397$	1.50000	−	2.59808i	0.0752828	−	0.130394i	−0.825926	−	0.563778i	$-0.809347\pi$
$397$	1.50000	−	2.59808i	0.0752828	−	0.130394i	0.901209	+	0.433384i	$0.142681\pi$
$398$	24.0000			1.20301
$399$	2.00000	−	3.46410i	0.100125	−	0.173422i
$400$		0			0
$401$	−18.0000	−	31.1769i	−0.898877	−	1.55690i	−0.828932	−	0.559350i	$-0.811051\pi$
$401$	−18.0000	−	31.1769i	−0.898877	−	1.55690i	−0.0699455	−	0.997551i	$-0.522283\pi$
$402$	−16.0000			−0.798007
$403$	−11.0000	+	38.1051i	−0.547949	+	1.89815i
$404$	2.00000			0.0995037
$405$		0			0
$406$	−5.00000	−	8.66025i	−0.248146	−	0.429801i
$407$	−7.50000	+	12.9904i	−0.371761	+	0.643909i
$408$	2.00000			0.0990148
$409$	−15.0000	+	25.9808i	−0.741702	+	1.28467i	0.210017	+	0.977698i	$0.432648\pi$
$409$	−15.0000	+	25.9808i	−0.741702	+	1.28467i	−0.951720	+	0.306968i	$0.900685\pi$
$410$		0			0
$411$	11.0000			0.542590
$412$	5.00000	−	8.66025i	0.246332	−	0.426660i
$413$	15.0000	+	25.9808i	0.738102	+	1.27843i
$414$	−0.500000	−	0.866025i	−0.0245737	−	0.0425628i
$415$		0			0
$416$	2.50000	+	2.59808i	0.122573	+	0.127381i
$417$	2.00000			0.0979404
$418$	−5.00000	−	8.66025i	−0.244558	−	0.423587i
$419$	2.00000	+	3.46410i	0.0977064	+	0.169232i	0.910735	−	0.412991i	$-0.135516\pi$
$419$	2.00000	+	3.46410i	0.0977064	+	0.169232i	−0.813029	+	0.582224i	$0.802183\pi$
$420$		0			0
$421$	−16.0000			−0.779792			−0.389896	−	0.920859i	$-0.627489\pi$
$421$	−16.0000			−0.779792			−0.389896	+	0.920859i	$0.627489\pi$
$422$	2.00000	−	3.46410i	0.0973585	−	0.168630i
$423$	4.50000	−	7.79423i	0.218797	−	0.378968i
$424$	−6.00000			−0.291386
$425$		0			0
$426$		0			0
$427$	−10.0000	−	17.3205i	−0.483934	−	0.838198i
$428$	−10.0000			−0.483368
$429$	−12.5000	−	12.9904i	−0.603506	−	0.627182i
$430$		0			0
$431$	−20.0000	−	34.6410i	−0.963366	−	1.66860i	−0.713942	−	0.700205i	$-0.753092\pi$
$431$	−20.0000	−	34.6410i	−0.963366	−	1.66860i	−0.249424	−	0.968394i	$-0.580241\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	14.0000	−	24.2487i	0.672797	−	1.16532i	−0.304311	−	0.952573i	$-0.598426\pi$
$433$	14.0000	−	24.2487i	0.672797	−	1.16532i	0.977108	−	0.212746i	$-0.0682406\pi$
$434$	−22.0000			−1.05603
$435$		0			0
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$	−2.00000			−0.0956730
$438$	−3.00000	+	5.19615i	−0.143346	+	0.248282i
$439$	2.00000	+	3.46410i	0.0954548	+	0.165333i	0.909798	−	0.415051i	$-0.136236\pi$
$439$	2.00000	+	3.46410i	0.0954548	+	0.165333i	−0.814344	+	0.580383i	$0.802903\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	2.00000	−	6.92820i	0.0951303	−	0.329541i
$443$	−20.0000			−0.950229			−0.475114	−	0.879924i	$-0.657593\pi$
$443$	−20.0000			−0.950229			−0.475114	+	0.879924i	$0.657593\pi$
$444$	1.50000	+	2.59808i	0.0711868	+	0.123299i
$445$		0			0
$446$	13.0000	−	22.5167i	0.615568	−	1.06619i
$447$	17.0000			0.804072
$448$	−1.00000	+	1.73205i	−0.0472456	+	0.0818317i
$449$	−6.00000	+	10.3923i	−0.283158	+	0.490443i	−0.972161	−	0.234315i	$-0.924715\pi$
$449$	−6.00000	+	10.3923i	−0.283158	+	0.490443i	0.689003	+	0.724758i	$0.258049\pi$
$450$		0			0
$451$	−5.00000	+	8.66025i	−0.235441	+	0.407795i
$452$	5.50000	+	9.52628i	0.258698	+	0.448078i
$453$	−4.00000	−	6.92820i	−0.187936	−	0.325515i
$454$		0			0
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	19.0000	+	32.9090i	0.888783	+	1.53942i	0.841316	+	0.540544i	$0.181781\pi$
$457$	19.0000	+	32.9090i	0.888783	+	1.53942i	0.0474665	+	0.998873i	$0.484885\pi$
$458$	−5.00000	−	8.66025i	−0.233635	−	0.404667i
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$		0			0
$461$	19.5000	−	33.7750i	0.908206	−	1.57306i	0.0916500	−	0.995791i	$-0.470786\pi$
$461$	19.5000	−	33.7750i	0.908206	−	1.57306i	0.816556	−	0.577267i	$-0.195881\pi$
$462$	5.00000	−	8.66025i	0.232621	−	0.402911i
$463$	−14.0000			−0.650635			−0.325318	−	0.945605i	$-0.605471\pi$
$463$	−14.0000			−0.650635			−0.325318	+	0.945605i	$0.605471\pi$
$464$	−2.50000	+	4.33013i	−0.116060	+	0.201021i
$465$		0			0
$466$	0.500000	+	0.866025i	0.0231621	+	0.0401179i
$467$	−6.00000			−0.277647			−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000			−0.277647			−0.138823	+	0.990317i	$0.544332\pi$
$468$	−3.50000	+	0.866025i	−0.161788	+	0.0400320i
$469$	−32.0000			−1.47762
$470$		0			0
$471$	−3.50000	−	6.06218i	−0.161271	−	0.279330i
$472$	7.50000	−	12.9904i	0.345215	−	0.597931i
$473$	−55.0000			−2.52890
$474$	5.50000	−	9.52628i	0.252623	−	0.437557i
$475$		0			0
$476$	4.00000			0.183340
$477$	3.00000	−	5.19615i	0.137361	−	0.237915i
$478$	10.0000	+	17.3205i	0.457389	+	0.792222i
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$		0			0
$481$	10.5000	−	2.59808i	0.478759	−	0.118462i
$482$	−7.00000			−0.318841
$483$	−1.00000	−	1.73205i	−0.0455016	−	0.0788110i
$484$	−7.00000	−	12.1244i	−0.318182	−	0.551107i
$485$		0			0
$486$	1.00000			0.0453609
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	−0.842479	−	0.538730i	$-0.818904\pi$
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	0.887793	+	0.460243i	$0.152238\pi$
$488$	−5.00000	+	8.66025i	−0.226339	+	0.392031i
$489$	15.0000			0.678323
$490$		0			0
$491$	8.00000	+	13.8564i	0.361035	+	0.625331i	0.988131	−	0.153611i	$-0.0490902\pi$
$491$	8.00000	+	13.8564i	0.361035	+	0.625331i	−0.627096	+	0.778942i	$0.715757\pi$
$492$	1.00000	+	1.73205i	0.0450835	+	0.0780869i
$493$	10.0000			0.450377
$494$	−2.00000	+	6.92820i	−0.0899843	+	0.311715i
$495$		0			0
$496$	5.50000	+	9.52628i	0.246957	+	0.427743i
$497$		0			0
$498$	3.00000	−	5.19615i	0.134433	−	0.232845i
$499$	28.0000			1.25345			0.626726	−	0.779240i	$-0.284395\pi$
$499$	28.0000			1.25345			0.626726	+	0.779240i	$0.284395\pi$
$500$		0			0
$501$	1.50000	−	2.59808i	0.0670151	−	0.116073i
$502$	25.0000			1.11580
$503$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$503$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$504$	−1.00000	−	1.73205i	−0.0445435	−	0.0771517i
$505$		0			0
$506$	−5.00000			−0.222277
$507$	−0.500000	+	12.9904i	−0.0222058	+	0.576923i
$508$	−2.00000			−0.0887357
$509$	−14.5000	−	25.1147i	−0.642701	−	1.11319i	−0.984827	−	0.173537i	$-0.944480\pi$
$509$	−14.5000	−	25.1147i	−0.642701	−	1.11319i	0.342126	−	0.939654i	$-0.388853\pi$
$510$		0			0
$511$	−6.00000	+	10.3923i	−0.265424	+	0.459728i
$512$	1.00000			0.0441942
$513$	1.00000	−	1.73205i	0.0441511	−	0.0764719i
$514$	−8.50000	+	14.7224i	−0.374919	+	0.649379i
$515$		0			0
$516$	−5.50000	+	9.52628i	−0.242124	+	0.419371i
$517$	−22.5000	−	38.9711i	−0.989549	−	1.71395i
$518$	3.00000	+	5.19615i	0.131812	+	0.228306i
$519$	−20.0000			−0.877903
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	−2.50000	−	4.33013i	−0.109422	−	0.189525i
$523$	−15.5000	−	26.8468i	−0.677768	−	1.17393i	−0.975652	−	0.219326i	$-0.929614\pi$
$523$	−15.5000	−	26.8468i	−0.677768	−	1.17393i	0.297884	−	0.954602i	$-0.403719\pi$
$524$	0.500000	−	0.866025i	0.0218426	−	0.0378325i
$525$		0			0
$526$	10.5000	−	18.1865i	0.457822	−	0.792971i
$527$	11.0000	−	19.0526i	0.479168	−	0.829943i
$528$	−5.00000			−0.217597
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$		0			0
$531$	7.50000	+	12.9904i	0.325472	+	0.563735i
$532$	−4.00000			−0.173422
$533$	7.00000	−	1.73205i	0.303204	−	0.0750234i
$534$	2.00000			0.0865485
$535$		0			0
$536$	8.00000	+	13.8564i	0.345547	+	0.598506i
$537$	6.50000	−	11.2583i	0.280496	−	0.485833i
$538$	14.0000			0.603583
$539$	−7.50000	+	12.9904i	−0.323048	+	0.559535i
$540$		0			0
$541$		0			0			−	1.00000i	$-0.5\pi$
$541$		0			0				1.00000i	$0.5\pi$
$542$	6.50000	−	11.2583i	0.279199	−	0.483587i
$543$	8.00000	+	13.8564i	0.343313	+	0.594635i
$544$	−1.00000	−	1.73205i	−0.0428746	−	0.0742611i
$545$		0			0
$546$	−7.00000	+	1.73205i	−0.299572	+	0.0741249i
$547$	12.0000			0.513083			0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000			0.513083			0.256541	+	0.966533i	$0.417417\pi$
$548$	−5.50000	−	9.52628i	−0.234948	−	0.406942i
$549$	−5.00000	−	8.66025i	−0.213395	−	0.369611i
$550$		0			0
$551$	−10.0000			−0.426014
$552$	−0.500000	+	0.866025i	−0.0212814	+	0.0368605i
$553$	11.0000	−	19.0526i	0.467768	−	0.810197i
$554$	11.0000			0.467345
$555$		0			0
$556$	−1.00000	−	1.73205i	−0.0424094	−	0.0734553i
$557$	13.0000	+	22.5167i	0.550828	+	0.954062i	0.998215	+	0.0597213i	$0.0190212\pi$
$557$	13.0000	+	22.5167i	0.550828	+	0.954062i	−0.447387	+	0.894340i	$0.647645\pi$
$558$	−11.0000			−0.465667
$559$	27.5000	+	28.5788i	1.16313	+	1.20876i
$560$		0			0
$561$	5.00000	+	8.66025i	0.211100	+	0.365636i
$562$	5.00000	+	8.66025i	0.210912	+	0.365311i
$563$	6.00000	−	10.3923i	0.252870	−	0.437983i	−0.711445	−	0.702742i	$-0.751959\pi$
$563$	6.00000	−	10.3923i	0.252870	−	0.437983i	0.964315	+	0.264758i	$0.0852922\pi$
$564$	−9.00000			−0.378968
$565$		0			0
$566$	9.50000	−	16.4545i	0.399315	−	0.691633i
$567$	2.00000			0.0839921
$568$		0			0
$569$	11.0000	+	19.0526i	0.461144	+	0.798725i	0.999018	−	0.0443003i	$-0.0141058\pi$
$569$	11.0000	+	19.0526i	0.461144	+	0.798725i	−0.537874	+	0.843025i	$0.680772\pi$
$570$		0			0
$571$	−16.0000			−0.669579			−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000			−0.669579			−0.334790	+	0.942293i	$0.608665\pi$
$572$	−5.00000	+	17.3205i	−0.209061	+	0.724207i
$573$	4.00000			0.167102
$574$	2.00000	+	3.46410i	0.0834784	+	0.144589i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	22.0000			0.915872			0.457936	−	0.888985i	$-0.348589\pi$
$577$	22.0000			0.915872			0.457936	+	0.888985i	$0.348589\pi$
$578$	6.50000	−	11.2583i	0.270364	−	0.468285i
$579$	−12.0000	+	20.7846i	−0.498703	+	0.863779i
$580$		0			0
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	−1.00000	−	1.73205i	−0.0414513	−	0.0717958i
$583$	−15.0000	−	25.9808i	−0.621237	−	1.07601i
$584$	6.00000			0.248282
$585$		0			0
$586$	−6.00000			−0.247858
$587$	−9.00000	−	15.5885i	−0.371470	−	0.643404i	0.618322	−	0.785925i	$-0.287813\pi$
$587$	−9.00000	−	15.5885i	−0.371470	−	0.643404i	−0.989792	+	0.142520i	$0.954479\pi$
$588$	1.50000	+	2.59808i	0.0618590	+	0.107143i
$589$	−11.0000	+	19.0526i	−0.453247	+	0.785047i
$590$		0			0
$591$	−4.00000	+	6.92820i	−0.164538	+	0.284988i
$592$	1.50000	−	2.59808i	0.0616496	−	0.106780i
$593$	−31.0000			−1.27302			−0.636509	−	0.771270i	$-0.719622\pi$
$593$	−31.0000			−1.27302			−0.636509	+	0.771270i	$0.719622\pi$
$594$	2.50000	−	4.33013i	0.102576	−	0.177667i
$595$		0			0
$596$	−8.50000	−	14.7224i	−0.348174	−	0.603054i
$597$	24.0000			0.982255
$598$	2.50000	+	2.59808i	0.102233	+	0.106243i
$599$	42.0000			1.71607			0.858037	−	0.513588i	$-0.171684\pi$
$599$	42.0000			1.71607			0.858037	+	0.513588i	$0.171684\pi$
$600$		0			0
$601$	1.50000	+	2.59808i	0.0611863	+	0.105978i	0.894996	−	0.446074i	$-0.147178\pi$
$601$	1.50000	+	2.59808i	0.0611863	+	0.105978i	−0.833810	+	0.552052i	$0.813845\pi$
$602$	−11.0000	+	19.0526i	−0.448327	+	0.776524i
$603$	−16.0000			−0.651570
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$		0			0
$606$	2.00000			0.0812444
$607$	9.00000	−	15.5885i	0.365299	−	0.632716i	−0.623525	−	0.781803i	$-0.714300\pi$
$607$	9.00000	−	15.5885i	0.365299	−	0.632716i	0.988824	+	0.149087i	$0.0476335\pi$
$608$	1.00000	+	1.73205i	0.0405554	+	0.0702439i
$609$	−5.00000	−	8.66025i	−0.202610	−	0.350931i
$610$		0			0
$611$	−9.00000	+	31.1769i	−0.364101	+	1.26128i
$612$	2.00000			0.0808452
$613$	−14.5000	−	25.1147i	−0.585649	−	1.01437i	−0.994794	−	0.101905i	$-0.967506\pi$
$613$	−14.5000	−	25.1147i	−0.585649	−	1.01437i	0.409145	−	0.912470i	$-0.365827\pi$
$614$		0			0
$615$		0			0
$616$	−10.0000			−0.402911
$617$	20.5000	−	35.5070i	0.825299	−	1.42946i	−0.0763917	−	0.997078i	$-0.524340\pi$
$617$	20.5000	−	35.5070i	0.825299	−	1.42946i	0.901691	−	0.432382i	$-0.142327\pi$
$618$	5.00000	−	8.66025i	0.201129	−	0.348367i
$619$	−10.0000			−0.401934			−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000			−0.401934			−0.200967	+	0.979598i	$0.564408\pi$
$620$		0			0
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$	−10.0000	−	17.3205i	−0.400963	−	0.694489i
$623$	4.00000			0.160257
$624$	2.50000	+	2.59808i	0.100080	+	0.104006i
$625$		0			0
$626$	10.0000	+	17.3205i	0.399680	+	0.692267i
$627$	−5.00000	−	8.66025i	−0.199681	−	0.345857i
$628$	−3.50000	+	6.06218i	−0.139665	+	0.241907i
$629$	−6.00000			−0.239236
$630$		0			0
$631$	−20.0000	+	34.6410i	−0.796187	+	1.37904i	0.125895	+	0.992044i	$0.459820\pi$
$631$	−20.0000	+	34.6410i	−0.796187	+	1.37904i	−0.922082	+	0.386994i	$0.873514\pi$
$632$	−11.0000			−0.437557
$633$	2.00000	−	3.46410i	0.0794929	−	0.137686i
$634$	8.00000	+	13.8564i	0.317721	+	0.550308i
$635$		0			0
$636$	−6.00000			−0.237915
$637$	10.5000	−	2.59808i	0.416025	−	0.102940i
$638$	−25.0000			−0.989759
$639$		0			0
$640$		0			0
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$	−10.0000			−0.394669
$643$	4.00000	−	6.92820i	0.157745	−	0.273222i	−0.776310	−	0.630351i	$-0.782911\pi$
$643$	4.00000	−	6.92820i	0.157745	−	0.273222i	0.934055	+	0.357129i	$0.116244\pi$
$644$	−1.00000	+	1.73205i	−0.0394055	+	0.0682524i
$645$		0			0
$646$	2.00000	−	3.46410i	0.0786889	−	0.136293i
$647$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$647$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	75.0000			2.94401
$650$		0			0
$651$	−22.0000			−0.862248
$652$	−7.50000	−	12.9904i	−0.293723	−	0.508743i
$653$	17.0000	+	29.4449i	0.665261	+	1.15227i	0.979214	+	0.202828i	$0.0650132\pi$
$653$	17.0000	+	29.4449i	0.665261	+	1.15227i	−0.313953	+	0.949439i	$0.601653\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$		0			0
$656$	1.00000	−	1.73205i	0.0390434	−	0.0676252i
$657$	−3.00000	+	5.19615i	−0.117041	+	0.202721i
$658$	−18.0000			−0.701713
$659$	19.5000	−	33.7750i	0.759612	−	1.31569i	−0.183436	−	0.983032i	$-0.558722\pi$
$659$	19.5000	−	33.7750i	0.759612	−	1.31569i	0.943049	−	0.332655i	$-0.107945\pi$
$660$		0			0
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	−0.989051	−	0.147573i	$-0.952854\pi$
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	0.366723	−	0.930330i	$-0.380480\pi$
$662$	−28.0000			−1.08825
$663$	2.00000	−	6.92820i	0.0776736	−	0.269069i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	1.50000	+	2.59808i	0.0581238	+	0.100673i
$667$	−2.50000	+	4.33013i	−0.0968004	+	0.167663i
$668$	−3.00000			−0.116073
$669$	13.0000	−	22.5167i	0.502609	−	0.870544i
$670$		0			0
$671$	−50.0000			−1.93023
$672$	−1.00000	+	1.73205i	−0.0385758	+	0.0668153i
$673$	4.00000	+	6.92820i	0.154189	+	0.267063i	0.932763	−	0.360489i	$-0.117390\pi$
$673$	4.00000	+	6.92820i	0.154189	+	0.267063i	−0.778575	+	0.627552i	$0.784057\pi$
$674$	−1.00000	−	1.73205i	−0.0385186	−	0.0667161i
$675$		0			0
$676$	11.5000	−	6.06218i	0.442308	−	0.233161i
$677$	4.00000			0.153732			0.0768662	−	0.997041i	$-0.475509\pi$
$677$	4.00000			0.153732			0.0768662	+	0.997041i	$0.475509\pi$
$678$	5.50000	+	9.52628i	0.211226	+	0.365855i
$679$	−2.00000	−	3.46410i	−0.0767530	−	0.132940i
$680$		0			0
$681$		0			0
$682$	−27.5000	+	47.6314i	−1.05303	+	1.82390i
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$	−2.00000			−0.0764719
$685$		0			0
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$	−5.00000	−	8.66025i	−0.190762	−	0.330409i
$688$	11.0000			0.419371
$689$	−6.00000	+	20.7846i	−0.228582	+	0.791831i
$690$		0			0
$691$	15.0000	+	25.9808i	0.570627	+	0.988355i	0.996502	+	0.0835727i	$0.0266331\pi$
$691$	15.0000	+	25.9808i	0.570627	+	0.988355i	−0.425875	+	0.904782i	$0.640034\pi$
$692$	10.0000	+	17.3205i	0.380143	+	0.658427i
$693$	5.00000	−	8.66025i	0.189934	−	0.328976i
$694$	−34.0000			−1.29062
$695$		0			0
$696$	−2.50000	+	4.33013i	−0.0947623	+	0.164133i
$697$	−4.00000			−0.151511
$698$	−10.0000	+	17.3205i	−0.378506	+	0.655591i
$699$	0.500000	+	0.866025i	0.0189117	+	0.0327561i
$700$		0			0
$701$	13.0000			0.491003			0.245502	−	0.969396i	$-0.421047\pi$
$701$	13.0000			0.491003			0.245502	+	0.969396i	$0.421047\pi$
$702$	−3.50000	+	0.866025i	−0.132099	+	0.0326860i
$703$	6.00000			0.226294
$704$	2.50000	+	4.33013i	0.0942223	+	0.163198i
$705$		0			0
$706$	−9.00000	+	15.5885i	−0.338719	+	0.586679i
$707$	4.00000			0.150435
$708$	7.50000	−	12.9904i	0.281867	−	0.488208i
$709$	4.00000	−	6.92820i	0.150223	−	0.260194i	−0.781086	−	0.624423i	$-0.785334\pi$
$709$	4.00000	−	6.92820i	0.150223	−	0.260194i	0.931309	+	0.364229i	$0.118667\pi$
$710$		0			0
$711$	5.50000	−	9.52628i	0.206266	−	0.357263i
$712$	−1.00000	−	1.73205i	−0.0374766	−	0.0649113i
$713$	5.50000	+	9.52628i	0.205977	+	0.356762i
$714$	4.00000			0.149696
$715$		0			0
$716$	−13.0000			−0.485833
$717$	10.0000	+	17.3205i	0.373457	+	0.646846i
$718$	−6.00000	−	10.3923i	−0.223918	−	0.387837i
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	−0.998224	−	0.0595683i	$-0.981028\pi$
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	0.550700	+	0.834703i	$0.314361\pi$
$720$		0			0
$721$	10.0000	−	17.3205i	0.372419	−	0.645049i
$722$	7.50000	−	12.9904i	0.279121	−	0.483452i
$723$	−7.00000			−0.260333
$724$	8.00000	−	13.8564i	0.297318	−	0.514969i
$725$		0			0
$726$	−7.00000	−	12.1244i	−0.259794	−	0.449977i
$727$	40.0000			1.48352			0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000			1.48352			0.741759	+	0.670667i	$0.233992\pi$
$728$	5.00000	+	5.19615i	0.185312	+	0.192582i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−11.0000	−	19.0526i	−0.406850	−	0.704684i
$732$	−5.00000	+	8.66025i	−0.184805	+	0.320092i
$733$	−6.00000			−0.221615			−0.110808	−	0.993842i	$-0.535344\pi$
$733$	−6.00000			−0.221615			−0.110808	+	0.993842i	$0.535344\pi$
$734$	−8.00000	+	13.8564i	−0.295285	+	0.511449i
$735$		0			0
$736$	1.00000			0.0368605
$737$	−40.0000	+	69.2820i	−1.47342	+	2.55204i
$738$	1.00000	+	1.73205i	0.0368105	+	0.0637577i
$739$	−22.0000	−	38.1051i	−0.809283	−	1.40172i	−0.913361	−	0.407150i	$-0.866523\pi$
$739$	−22.0000	−	38.1051i	−0.809283	−	1.40172i	0.104078	−	0.994569i	$-0.466811\pi$
$740$		0			0
$741$	−2.00000	+	6.92820i	−0.0734718	+	0.254514i
$742$	−12.0000			−0.440534
$743$	25.5000	+	44.1673i	0.935504	+	1.62034i	0.773732	+	0.633513i	$0.218388\pi$
$743$	25.5000	+	44.1673i	0.935504	+	1.62034i	0.161772	+	0.986828i	$0.448279\pi$
$744$	5.50000	+	9.52628i	0.201640	+	0.349250i
$745$		0			0
$746$	19.0000			0.695639
$747$	3.00000	−	5.19615i	0.109764	−	0.190117i
$748$	5.00000	−	8.66025i	0.182818	−	0.316650i
$749$	−20.0000			−0.730784
$750$		0			0
$751$	11.5000	+	19.9186i	0.419641	+	0.726839i	0.995903	−	0.0904254i	$-0.0288227\pi$
$751$	11.5000	+	19.9186i	0.419641	+	0.726839i	−0.576262	+	0.817265i	$0.695489\pi$
$752$	4.50000	+	7.79423i	0.164098	+	0.284226i
$753$	25.0000			0.911051
$754$	12.5000	+	12.9904i	0.455223	+	0.473082i
$755$		0			0
$756$	−1.00000	−	1.73205i	−0.0363696	−	0.0629941i
$757$	5.00000	+	8.66025i	0.181728	+	0.314762i	0.942469	−	0.334293i	$-0.108498\pi$
$757$	5.00000	+	8.66025i	0.181728	+	0.314762i	−0.760741	+	0.649056i	$0.775164\pi$
$758$	1.00000	−	1.73205i	0.0363216	−	0.0629109i
$759$	−5.00000			−0.181489
$760$		0			0
$761$	−10.0000	+	17.3205i	−0.362500	+	0.627868i	−0.988372	−	0.152058i	$-0.951410\pi$
$761$	−10.0000	+	17.3205i	−0.362500	+	0.627868i	0.625872	+	0.779926i	$0.284743\pi$
$762$	−2.00000			−0.0724524
$763$	2.00000	−	3.46410i	0.0724049	−	0.125409i
$764$	−2.00000	−	3.46410i	−0.0723575	−	0.125327i
$765$		0			0
$766$	−31.0000			−1.12008
$767$	−37.5000	−	38.9711i	−1.35405	−	1.40717i
$768$	1.00000			0.0360844
$769$	−21.5000	−	37.2391i	−0.775310	−	1.34288i	−0.934620	−	0.355647i	$-0.884260\pi$
$769$	−21.5000	−	37.2391i	−0.775310	−	1.34288i	0.159310	−	0.987229i	$-0.449073\pi$
$770$		0			0
$771$	−8.50000	+	14.7224i	−0.306120	+	0.530215i
$772$	24.0000			0.863779
$773$	16.0000	−	27.7128i	0.575480	−	0.996761i	−0.420509	−	0.907288i	$-0.638149\pi$
$773$	16.0000	−	27.7128i	0.575480	−	0.996761i	0.995989	−	0.0894724i	$-0.0285181\pi$
$774$	−5.50000	+	9.52628i	−0.197693	+	0.342415i
$775$		0			0
$776$	−1.00000	+	1.73205i	−0.0358979	+	0.0621770i
$777$	3.00000	+	5.19615i	0.107624	+	0.186411i
$778$	−2.50000	−	4.33013i	−0.0896293	−	0.155243i
$779$	4.00000			0.143315
$780$		0			0
$781$		0			0
$782$	−1.00000	−	1.73205i	−0.0357599	−	0.0619380i
$783$	−2.50000	−	4.33013i	−0.0893427	−	0.154746i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$		0			0
$786$	0.500000	−	0.866025i	0.0178344	−	0.0308901i
$787$	−15.5000	+	26.8468i	−0.552515	+	0.956985i	0.445577	+	0.895244i	$0.352999\pi$
$787$	−15.5000	+	26.8468i	−0.552515	+	0.956985i	−0.998092	+	0.0617409i	$0.980335\pi$
$788$	8.00000			0.284988
$789$	10.5000	−	18.1865i	0.373810	−	0.647458i
$790$		0			0
$791$	11.0000	+	19.0526i	0.391115	+	0.677431i
$792$	−5.00000			−0.177667
$793$	25.0000	+	25.9808i	0.887776	+	0.922604i
$794$	−3.00000			−0.106466
$795$		0			0
$796$	−12.0000	−	20.7846i	−0.425329	−	0.736691i
$797$	6.00000	−	10.3923i	0.212531	−	0.368114i	−0.739975	−	0.672634i	$-0.765163\pi$
$797$	6.00000	−	10.3923i	0.212531	−	0.368114i	0.952506	+	0.304520i	$0.0984960\pi$
$798$	−4.00000			−0.141598
$799$	9.00000	−	15.5885i	0.318397	−	0.551480i
$800$		0			0
$801$	2.00000			0.0706665
$802$	−18.0000	+	31.1769i	−0.635602	+	1.10090i
$803$	15.0000	+	25.9808i	0.529339	+	0.916841i
$804$	8.00000	+	13.8564i	0.282138	+	0.488678i
$805$		0			0
$806$	38.5000	−	9.52628i	1.35610	−	0.335549i
$807$	14.0000			0.492823
$808$	−1.00000	−	1.73205i	−0.0351799	−	0.0609333i
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	0.999491	+	0.0319002i	$0.0101559\pi$
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	−0.472119	+	0.881535i	$0.656511\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	−5.00000	+	8.66025i	−0.175466	+	0.303915i
$813$	6.50000	−	11.2583i	0.227965	−	0.394847i
$814$	15.0000			0.525750
$815$		0			0
$816$	−1.00000	−	1.73205i	−0.0350070	−	0.0606339i
$817$	11.0000	+	19.0526i	0.384841	+	0.666565i
$818$	30.0000			1.04893
$819$	−7.00000	+	1.73205i	−0.244600	+	0.0605228i
$820$		0			0
$821$	25.5000	+	44.1673i	0.889956	+	1.54145i	0.839926	+	0.542702i	$0.182599\pi$
$821$	25.5000	+	44.1673i	0.889956	+	1.54145i	0.0500305	+	0.998748i	$0.484068\pi$
$822$	−5.50000	−	9.52628i	−0.191835	−	0.332267i
$823$	−1.00000	+	1.73205i	−0.0348578	+	0.0603755i	−0.882928	−	0.469508i	$-0.844431\pi$
$823$	−1.00000	+	1.73205i	−0.0348578	+	0.0603755i	0.848070	+	0.529884i	$0.177765\pi$
$824$	−10.0000			−0.348367
$825$		0			0
$826$	15.0000	−	25.9808i	0.521917	−	0.903986i
$827$	50.0000			1.73867			0.869335	−	0.494223i	$-0.164547\pi$
$827$	50.0000			1.73867			0.869335	+	0.494223i	$0.164547\pi$
$828$	−0.500000	+	0.866025i	−0.0173762	+	0.0300965i
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	0.718481	−	0.695546i	$-0.244838\pi$
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	−0.961601	+	0.274450i	$0.911504\pi$
$830$		0			0
$831$	11.0000			0.381586
$832$	1.00000	−	3.46410i	0.0346688	−	0.120096i
$833$	−6.00000			−0.207888
$834$	−1.00000	−	1.73205i	−0.0346272	−	0.0599760i
$835$		0			0
$836$	−5.00000	+	8.66025i	−0.172929	+	0.299521i
$837$	−11.0000			−0.380216
$838$	2.00000	−	3.46410i	0.0690889	−	0.119665i
$839$	27.0000	−	46.7654i	0.932144	−	1.61452i	0.152493	−	0.988304i	$-0.451270\pi$
$839$	27.0000	−	46.7654i	0.932144	−	1.61452i	0.779650	−	0.626215i	$-0.215397\pi$
$840$		0			0
$841$	2.00000	−	3.46410i	0.0689655	−	0.119452i
$842$	8.00000	+	13.8564i	0.275698	+	0.477523i
$843$	5.00000	+	8.66025i	0.172209	+	0.298275i
$844$	−4.00000			−0.137686
$845$		0			0
$846$	−9.00000			−0.309426
$847$	−14.0000	−	24.2487i	−0.481046	−	0.833196i
$848$	3.00000	+	5.19615i	0.103020	+	0.178437i
$849$	9.50000	−	16.4545i	0.326039	−	0.564716i
$850$		0			0
$851$	1.50000	−	2.59808i	0.0514193	−	0.0890609i
$852$		0			0
$853$	49.0000			1.67773			0.838864	−	0.544341i	$-0.183220\pi$
$853$	49.0000			1.67773			0.838864	+	0.544341i	$0.183220\pi$
$854$	−10.0000	+	17.3205i	−0.342193	+	0.592696i
$855$		0			0
$856$	5.00000	+	8.66025i	0.170896	+	0.296001i
$857$	25.0000			0.853984			0.426992	−	0.904255i	$-0.359573\pi$
$857$	25.0000			0.853984			0.426992	+	0.904255i	$0.359573\pi$
$858$	−5.00000	+	17.3205i	−0.170697	+	0.591312i
$859$	−50.0000			−1.70598			−0.852989	−	0.521929i	$-0.825213\pi$
$859$	−50.0000			−1.70598			−0.852989	+	0.521929i	$0.825213\pi$
$860$		0			0
$861$	2.00000	+	3.46410i	0.0681598	+	0.118056i
$862$	−20.0000	+	34.6410i	−0.681203	+	1.17988i
$863$	−39.0000			−1.32758			−0.663788	−	0.747921i	$-0.731052\pi$
$863$	−39.0000			−1.32758			−0.663788	+	0.747921i	$0.731052\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	−28.0000			−0.951479
$867$	6.50000	−	11.2583i	0.220752	−	0.382353i
$868$	11.0000	+	19.0526i	0.373364	+	0.646686i
$869$	−27.5000	−	47.6314i	−0.932874	−	1.61578i
$870$		0			0
$871$	56.0000	−	13.8564i	1.89749	−	0.469506i
$872$	−2.00000			−0.0677285
$873$	−1.00000	−	1.73205i	−0.0338449	−	0.0586210i
$874$	1.00000	+	1.73205i	0.0338255	+	0.0585875i
$875$		0			0
$876$	6.00000			0.202721
$877$	−9.50000	+	16.4545i	−0.320792	+	0.555628i	−0.980652	−	0.195761i	$-0.937282\pi$
$877$	−9.50000	+	16.4545i	−0.320792	+	0.555628i	0.659860	+	0.751389i	$0.270616\pi$
$878$	2.00000	−	3.46410i	0.0674967	−	0.116908i
$879$	−6.00000			−0.202375
$880$		0			0
$881$	9.00000	+	15.5885i	0.303218	+	0.525188i	0.976863	−	0.213866i	$-0.0686057\pi$
$881$	9.00000	+	15.5885i	0.303218	+	0.525188i	−0.673645	+	0.739055i	$0.735272\pi$
$882$	1.50000	+	2.59808i	0.0505076	+	0.0874818i
$883$	1.00000			0.0336527			0.0168263	−	0.999858i	$-0.494644\pi$
$883$	1.00000			0.0336527			0.0168263	+	0.999858i	$0.494644\pi$
$884$	−7.00000	+	1.73205i	−0.235435	+	0.0582552i
$885$		0			0
$886$	10.0000	+	17.3205i	0.335957	+	0.581894i
$887$	1.50000	+	2.59808i	0.0503651	+	0.0872349i	0.890109	−	0.455748i	$-0.150628\pi$
$887$	1.50000	+	2.59808i	0.0503651	+	0.0872349i	−0.839744	+	0.542983i	$0.817295\pi$
$888$	1.50000	−	2.59808i	0.0503367	−	0.0871857i
$889$	−4.00000			−0.134156
$890$		0			0
$891$	2.50000	−	4.33013i	0.0837532	−	0.145065i
$892$	−26.0000			−0.870544
$893$	−9.00000	+	15.5885i	−0.301174	+	0.521648i
$894$	−8.50000	−	14.7224i	−0.284283	−	0.492392i
$895$		0			0
$896$	2.00000			0.0668153
$897$	2.50000	+	2.59808i	0.0834726	+	0.0867472i
$898$	12.0000			0.400445
$899$	27.5000	+	47.6314i	0.917176	+	1.58860i
$900$		0			0
$901$	6.00000	−	10.3923i	0.199889	−	0.346218i
$902$	10.0000			0.332964
$903$	−11.0000	+	19.0526i	−0.366057	+	0.634029i
$904$	5.50000	−	9.52628i	0.182927	−	0.316839i
$905$		0			0
$906$	−4.00000	+	6.92820i	−0.132891	+	0.230174i
$907$	9.50000	+	16.4545i	0.315442	+	0.546362i	0.979531	−	0.201291i	$-0.0645138\pi$
$907$	9.50000	+	16.4545i	0.315442	+	0.546362i	−0.664089	+	0.747653i	$0.731180\pi$
$908$		0			0
$909$	2.00000			0.0663358
$910$		0			0
$911$	−18.0000			−0.596367			−0.298183	−	0.954509i	$-0.596381\pi$
$911$	−18.0000			−0.596367			−0.298183	+	0.954509i	$0.596381\pi$
$912$	1.00000	+	1.73205i	0.0331133	+	0.0573539i
$913$	−15.0000	−	25.9808i	−0.496428	−	0.859838i
$914$	19.0000	−	32.9090i	0.628464	−	1.08853i
$915$		0			0
$916$	−5.00000	+	8.66025i	−0.165205	+	0.286143i
$917$	1.00000	−	1.73205i	0.0330229	−	0.0571974i
$918$	2.00000			0.0660098
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$		0			0
$921$		0			0
$922$	−39.0000			−1.28440
$923$		0			0
$924$	−10.0000			−0.328976
$925$		0			0
$926$	7.00000	+	12.1244i	0.230034	+	0.398431i
$927$	5.00000	−	8.66025i	0.164222	−	0.284440i
$928$	5.00000			0.164133
$929$	8.00000	−	13.8564i	0.262471	−	0.454614i	−0.704427	−	0.709777i	$-0.748796\pi$
$929$	8.00000	−	13.8564i	0.262471	−	0.454614i	0.966898	+	0.255163i	$0.0821291\pi$
$930$		0			0
$931$	6.00000			0.196642
$932$	0.500000	−	0.866025i	0.0163780	−	0.0283676i
$933$	−10.0000	−	17.3205i	−0.327385	−	0.567048i
$934$	3.00000	+	5.19615i	0.0981630	+	0.170023i
$935$		0			0
$936$	2.50000	+	2.59808i	0.0817151	+	0.0849208i
$937$	50.0000			1.63343			0.816714	−	0.577042i	$-0.195793\pi$
$937$	50.0000			1.63343			0.816714	+	0.577042i	$0.195793\pi$
$938$	16.0000	+	27.7128i	0.522419	+	0.904855i
$939$	10.0000	+	17.3205i	0.326338	+	0.565233i
$940$		0			0
$941$	−50.0000			−1.62995			−0.814977	−	0.579494i	$-0.803250\pi$
$941$	−50.0000			−1.62995			−0.814977	+	0.579494i	$0.803250\pi$
$942$	−3.50000	+	6.06218i	−0.114036	+	0.197516i
$943$	1.00000	−	1.73205i	0.0325645	−	0.0564033i
$944$	−15.0000			−0.488208
$945$		0			0
$946$	27.5000	+	47.6314i	0.894102	+	1.54863i
$947$	4.00000	+	6.92820i	0.129983	+	0.225136i	0.923670	−	0.383190i	$-0.125175\pi$
$947$	4.00000	+	6.92820i	0.129983	+	0.225136i	−0.793687	+	0.608326i	$0.791841\pi$
$948$	−11.0000			−0.357263
$949$	6.00000	−	20.7846i	0.194768	−	0.674697i
$950$		0			0
$951$	8.00000	+	13.8564i	0.259418	+	0.449325i
$952$	−2.00000	−	3.46410i	−0.0648204	−	0.112272i
$953$	−25.5000	+	44.1673i	−0.826026	+	1.43072i	0.0751066	+	0.997176i	$0.476070\pi$
$953$	−25.5000	+	44.1673i	−0.826026	+	1.43072i	−0.901133	+	0.433544i	$0.857263\pi$
$954$	−6.00000			−0.194257
$955$		0			0
$956$	10.0000	−	17.3205i	0.323423	−	0.560185i
$957$	−25.0000			−0.808135
$958$	12.0000	−	20.7846i	0.387702	−	0.671520i
$959$	−11.0000	−	19.0526i	−0.355209	−	0.615239i
$960$		0			0
$961$	90.0000			2.90323
$962$	−7.50000	−	7.79423i	−0.241810	−	0.251296i
$963$	−10.0000			−0.322245
$964$	3.50000	+	6.06218i	0.112727	+	0.195250i
$965$		0			0
$966$	−1.00000	+	1.73205i	−0.0321745	+	0.0557278i
$967$	−20.0000			−0.643157			−0.321578	−	0.946883i	$-0.604213\pi$
$967$	−20.0000			−0.643157			−0.321578	+	0.946883i	$0.604213\pi$
$968$	−7.00000	+	12.1244i	−0.224989	+	0.389692i
$969$	2.00000	−	3.46410i	0.0642493	−	0.111283i
$970$		0			0
$971$	−24.0000	+	41.5692i	−0.770197	+	1.33402i	0.167258	+	0.985913i	$0.446509\pi$
$971$	−24.0000	+	41.5692i	−0.770197	+	1.33402i	−0.937455	+	0.348107i	$0.886825\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−2.00000	−	3.46410i	−0.0641171	−	0.111054i
$974$	−2.00000			−0.0640841
$975$		0			0
$976$	10.0000			0.320092
$977$	−10.5000	−	18.1865i	−0.335925	−	0.581839i	0.647737	−	0.761864i	$-0.275715\pi$
$977$	−10.5000	−	18.1865i	−0.335925	−	0.581839i	−0.983662	+	0.180025i	$0.942382\pi$
$978$	−7.50000	−	12.9904i	−0.239824	−	0.415387i
$979$	5.00000	−	8.66025i	0.159801	−	0.276783i
$980$		0			0
$981$	1.00000	−	1.73205i	0.0319275	−	0.0553001i
$982$	8.00000	−	13.8564i	0.255290	−	0.442176i
$983$	3.00000			0.0956851			0.0478426	−	0.998855i	$-0.484765\pi$
$983$	3.00000			0.0956851			0.0478426	+	0.998855i	$0.484765\pi$
$984$	1.00000	−	1.73205i	0.0318788	−	0.0552158i
$985$		0			0
$986$	−5.00000	−	8.66025i	−0.159232	−	0.275799i
$987$	−18.0000			−0.572946
$988$	7.00000	−	1.73205i	0.222700	−	0.0551039i
$989$	11.0000			0.349780
$990$		0			0
$991$	8.50000	+	14.7224i	0.270011	+	0.467673i	0.968864	−	0.247592i	$-0.0796392\pi$
$991$	8.50000	+	14.7224i	0.270011	+	0.467673i	−0.698853	+	0.715265i	$0.746306\pi$
$992$	5.50000	−	9.52628i	0.174625	−	0.302460i
$993$	−28.0000			−0.888553
$994$		0			0
$995$		0			0
$996$	−6.00000			−0.190117
$997$	−1.00000	+	1.73205i	−0.0316703	+	0.0548546i	−0.881426	−	0.472322i	$-0.843416\pi$
$997$	−1.00000	+	1.73205i	−0.0316703	+	0.0548546i	0.849756	+	0.527176i	$0.176749\pi$
$998$	−14.0000	−	24.2487i	−0.443162	−	0.767580i
$999$	1.50000	+	2.59808i	0.0474579	+	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.i.d.601.1		2
5.2	odd	4		1950.2.z.e.1849.2		4
5.3	odd	4		1950.2.z.e.1849.1		4
5.4	even	2		390.2.i.f.211.1	yes	2
13.9	even	3	inner	1950.2.i.d.451.1		2
15.14	odd	2		1170.2.i.a.991.1		2
65.9	even	6		390.2.i.f.61.1	✓	2
65.22	odd	12		1950.2.z.e.1699.1		4
65.24	odd	12		5070.2.b.h.1351.1		2
65.29	even	6		5070.2.a.d.1.1		1
65.48	odd	12		1950.2.z.e.1699.2		4
65.49	even	6		5070.2.a.p.1.1		1
65.54	odd	12		5070.2.b.h.1351.2		2
195.74	odd	6		1170.2.i.a.451.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.f.61.1	✓	2	65.9	even	6
390.2.i.f.211.1	yes	2	5.4	even	2
1170.2.i.a.451.1		2	195.74	odd	6
1170.2.i.a.991.1		2	15.14	odd	2
1950.2.i.d.451.1		2	13.9	even	3	inner
1950.2.i.d.601.1		2	1.1	even	1	trivial
1950.2.z.e.1699.1		4	65.22	odd	12
1950.2.z.e.1699.2		4	65.48	odd	12
1950.2.z.e.1849.1		4	5.3	odd	4
1950.2.z.e.1849.2		4	5.2	odd	4
5070.2.a.d.1.1		1	65.29	even	6
5070.2.a.p.1.1		1	65.49	even	6
5070.2.b.h.1351.1		2	65.24	odd	12
5070.2.b.h.1351.2		2	65.54	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.50000 + 4.33013i) q^{11} +1.00000 q^{12} +(1.00000 - 3.46410i) q^{13} +2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +1.00000 q^{18} +(1.00000 - 1.73205i) q^{19} +2.00000 q^{21} +(2.50000 - 4.33013i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.50000 + 0.866025i) q^{26} +1.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(-2.50000 - 4.33013i) q^{29} -11.0000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.50000 - 4.33013i) q^{33} +2.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(1.50000 + 2.59808i) q^{37} -2.00000 q^{38} +(-3.50000 + 0.866025i) q^{39} +(1.00000 + 1.73205i) q^{41} +(-1.00000 - 1.73205i) q^{42} +(-5.50000 + 9.52628i) q^{43} -5.00000 q^{44} +(-0.500000 + 0.866025i) q^{46} -9.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +2.00000 q^{51} +(2.50000 + 2.59808i) q^{52} -6.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.00000 + 1.73205i) q^{56} -2.00000 q^{57} +(-2.50000 + 4.33013i) q^{58} +(7.50000 - 12.9904i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(5.50000 + 9.52628i) q^{62} +(-1.00000 - 1.73205i) q^{63} +1.00000 q^{64} -5.00000 q^{66} +(8.00000 + 13.8564i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(-0.500000 + 0.866025i) q^{69} +(-0.500000 + 0.866025i) q^{72} +6.00000 q^{73} +(1.50000 - 2.59808i) q^{74} +(1.00000 + 1.73205i) q^{76} -10.0000 q^{77} +(2.50000 + 2.59808i) q^{78} -11.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} -6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +11.0000 q^{86} +(-2.50000 + 4.33013i) q^{87} +(2.50000 + 4.33013i) q^{88} +(-1.00000 - 1.73205i) q^{89} +(5.00000 + 5.19615i) q^{91} +1.00000 q^{92} +(5.50000 + 9.52628i) q^{93} +(4.50000 + 7.79423i) q^{94} +1.00000 q^{96} +(-1.00000 + 1.73205i) q^{97} +(1.50000 - 2.59808i) q^{98} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - q^3 - q^4 - q^6 - 2 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9} + 5 q^{11} + 2 q^{12} + 2 q^{13} + 4 q^{14} - q^{16} - 2 q^{17} + 2 q^{18} + 2 q^{19} + 4 q^{21} + 5 q^{22} - q^{23} - q^{24} - 7 q^{26} + 2 q^{27} - 2 q^{28} - 5 q^{29} - 22 q^{31} - q^{32} + 5 q^{33} + 4 q^{34} - q^{36} + 3 q^{37} - 4 q^{38} - 7 q^{39} + 2 q^{41} - 2 q^{42} - 11 q^{43} - 10 q^{44} - q^{46} - 18 q^{47} - q^{48} + 3 q^{49} + 4 q^{51} + 5 q^{52} - 12 q^{53} - q^{54} - 2 q^{56} - 4 q^{57} - 5 q^{58} + 15 q^{59} - 10 q^{61} + 11 q^{62} - 2 q^{63} + 2 q^{64} - 10 q^{66} + 16 q^{67} - 2 q^{68} - q^{69} - q^{72} + 12 q^{73} + 3 q^{74} + 2 q^{76} - 20 q^{77} + 5 q^{78} - 22 q^{79} - q^{81} + 2 q^{82} - 12 q^{83} - 2 q^{84} + 22 q^{86} - 5 q^{87} + 5 q^{88} - 2 q^{89} + 10 q^{91} + 2 q^{92} + 11 q^{93} + 9 q^{94} + 2 q^{96} - 2 q^{97} + 3 q^{98} - 10 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 - q^6 - 2 * q^7 + 2 * q^8 - q^9 + 5 * q^11 + 2 * q^12 + 2 * q^13 + 4 * q^14 - q^16 - 2 * q^17 + 2 * q^18 + 2 * q^19 + 4 * q^21 + 5 * q^22 - q^23 - q^24 - 7 * q^26 + 2 * q^27 - 2 * q^28 - 5 * q^29 - 22 * q^31 - q^32 + 5 * q^33 + 4 * q^34 - q^36 + 3 * q^37 - 4 * q^38 - 7 * q^39 + 2 * q^41 - 2 * q^42 - 11 * q^43 - 10 * q^44 - q^46 - 18 * q^47 - q^48 + 3 * q^49 + 4 * q^51 + 5 * q^52 - 12 * q^53 - q^54 - 2 * q^56 - 4 * q^57 - 5 * q^58 + 15 * q^59 - 10 * q^61 + 11 * q^62 - 2 * q^63 + 2 * q^64 - 10 * q^66 + 16 * q^67 - 2 * q^68 - q^69 - q^72 + 12 * q^73 + 3 * q^74 + 2 * q^76 - 20 * q^77 + 5 * q^78 - 22 * q^79 - q^81 + 2 * q^82 - 12 * q^83 - 2 * q^84 + 22 * q^86 - 5 * q^87 + 5 * q^88 - 2 * q^89 + 10 * q^91 + 2 * q^92 + 11 * q^93 + 9 * q^94 + 2 * q^96 - 2 * q^97 + 3 * q^98 - 10 * q^99

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