LMFDB - Embedded newform 1950.2.z.e.1849.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(1699,1950)]

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, 3, 4]))

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

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

chi := DirichletCharacter("1950.1699");

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.z (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1849.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.1849
Dual form			1950.2.z.e.1699.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.50000 + 4.33013i) q^{11} -1.00000i q^{12} +(3.46410 + 1.00000i) q^{13} -2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +1.00000i q^{18} +(-1.00000 + 1.73205i) q^{19} +2.00000 q^{21} +(-4.33013 - 2.50000i) q^{22} +(0.866025 - 0.500000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.50000 + 0.866025i) q^{26} -1.00000i q^{27} +(1.73205 - 1.00000i) q^{28} +(2.50000 + 4.33013i) q^{29} -11.0000 q^{31} +(0.866025 + 0.500000i) q^{32} +(4.33013 + 2.50000i) q^{33} -2.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(2.59808 - 1.50000i) q^{37} -2.00000i q^{38} +(3.50000 - 0.866025i) q^{39} +(1.00000 + 1.73205i) q^{41} +(-1.73205 + 1.00000i) q^{42} +(-9.52628 - 5.50000i) q^{43} +5.00000 q^{44} +(-0.500000 + 0.866025i) q^{46} +9.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-1.50000 - 2.59808i) q^{49} +2.00000 q^{51} +(2.59808 - 2.50000i) q^{52} -6.00000i q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.00000 + 1.73205i) q^{56} +2.00000i q^{57} +(-4.33013 - 2.50000i) q^{58} +(-7.50000 + 12.9904i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(9.52628 - 5.50000i) q^{62} +(1.73205 - 1.00000i) q^{63} -1.00000 q^{64} -5.00000 q^{66} +(13.8564 - 8.00000i) q^{67} +(1.73205 - 1.00000i) q^{68} +(0.500000 - 0.866025i) q^{69} +(0.866025 + 0.500000i) q^{72} +6.00000i q^{73} +(-1.50000 + 2.59808i) q^{74} +(1.00000 + 1.73205i) q^{76} +10.0000i q^{77} +(-2.59808 + 2.50000i) q^{78} +11.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.73205 - 1.00000i) q^{82} -6.00000i q^{83} +(1.00000 - 1.73205i) q^{84} +11.0000 q^{86} +(4.33013 + 2.50000i) q^{87} +(-4.33013 + 2.50000i) q^{88} +(1.00000 + 1.73205i) q^{89} +(5.00000 + 5.19615i) q^{91} -1.00000i q^{92} +(-9.52628 + 5.50000i) q^{93} +(-4.50000 - 7.79423i) q^{94} +1.00000 q^{96} +(1.73205 + 1.00000i) q^{97} +(2.59808 + 1.50000i) q^{98} +5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9} + 10 q^{11} - 8 q^{14} - 2 q^{16} - 4 q^{19} + 8 q^{21} + 2 q^{24} - 14 q^{26} + 10 q^{29} - 44 q^{31} - 8 q^{34} - 2 q^{36} + 14 q^{39} + 4 q^{41} + 20 q^{44} - 2 q^{46} - 6 q^{49} + 8 q^{51} + 2 q^{54} - 4 q^{56} - 30 q^{59} - 20 q^{61} - 4 q^{64} - 20 q^{66} + 2 q^{69} - 6 q^{74} + 4 q^{76} + 44 q^{79} - 2 q^{81} + 4 q^{84} + 44 q^{86} + 4 q^{89} + 20 q^{91} - 18 q^{94} + 4 q^{96} + 20 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9 + 10 * q^11 - 8 * q^14 - 2 * q^16 - 4 * q^19 + 8 * q^21 + 2 * q^24 - 14 * q^26 + 10 * q^29 - 44 * q^31 - 8 * q^34 - 2 * q^36 + 14 * q^39 + 4 * q^41 + 20 * q^44 - 2 * q^46 - 6 * q^49 + 8 * q^51 + 2 * q^54 - 4 * q^56 - 30 * q^59 - 20 * q^61 - 4 * q^64 - 20 * q^66 + 2 * q^69 - 6 * q^74 + 4 * q^76 + 44 * q^79 - 2 * q^81 + 4 * q^84 + 44 * q^86 + 4 * q^89 + 20 * q^91 - 18 * q^94 + 4 * q^96 + 20 * 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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	0.790237	−	0.612801i	$-0.209957\pi$
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	−0.135583	+	0.990766i	$0.543291\pi$
$8$			1.00000i			0.353553i
$9$	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	$0.561563\pi$
$12$		−	1.00000i		−	0.288675i
$13$	3.46410	+	1.00000i	0.960769	+	0.277350i
$13$	3.46410	+	1.00000i	0.960769	+	0.277350i
$14$	−2.00000			−0.534522
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	0.695113	−	0.718900i	$-0.255354\pi$
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	−0.275029	+	0.961436i	$0.588688\pi$
$18$			1.00000i			0.235702i
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$	−4.33013	−	2.50000i	−0.923186	−	0.533002i
$23$	0.866025	−	0.500000i	0.180579	−	0.104257i	−0.406986	−	0.913434i	$-0.633420\pi$
$23$	0.866025	−	0.500000i	0.180579	−	0.104257i	0.587565	+	0.809177i	$0.300087\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	−3.50000	+	0.866025i	−0.686406	+	0.169842i
$27$		−	1.00000i		−	0.192450i
$28$	1.73205	−	1.00000i	0.327327	−	0.188982i
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	0.999167	−	0.0408130i	$-0.0129948\pi$
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	−0.534928	+	0.844897i	$0.679661\pi$
$30$		0			0
$31$	−11.0000			−1.97566			−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−11.0000			−1.97566			−0.987829	+	0.155543i	$0.950287\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	4.33013	+	2.50000i	0.753778	+	0.435194i
$34$	−2.00000			−0.342997
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	−0.270998	−	0.962580i	$-0.587354\pi$
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	0.698119	+	0.715981i	$0.254020\pi$
$38$		−	2.00000i		−	0.324443i
$39$	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	$0.783417\pi$
$42$	−1.73205	+	1.00000i	−0.267261	+	0.154303i
$43$	−9.52628	−	5.50000i	−1.45274	−	0.838742i	−0.454108	−	0.890947i	$-0.650042\pi$
$43$	−9.52628	−	5.50000i	−1.45274	−	0.838742i	−0.998636	+	0.0522047i	$0.983375\pi$
$44$	5.00000			0.753778
$45$		0			0
$46$	−0.500000	+	0.866025i	−0.0737210	+	0.127688i
$47$			9.00000i			1.31278i	0.754420	+	0.656392i	$0.227918\pi$
$47$			9.00000i			1.31278i	−0.754420	+	0.656392i	$0.772082\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$		0			0
$51$	2.00000			0.280056
$52$	2.59808	−	2.50000i	0.360288	−	0.346688i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	−1.00000	+	1.73205i	−0.133631	+	0.231455i
$57$			2.00000i			0.264906i
$58$	−4.33013	−	2.50000i	−0.568574	−	0.328266i
$59$	−7.50000	+	12.9904i	−0.976417	+	1.69120i	−0.301239	+	0.953549i	$0.597400\pi$
$59$	−7.50000	+	12.9904i	−0.976417	+	1.69120i	−0.675178	+	0.737655i	$0.735933\pi$
$60$		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	$0.945525\pi$
$62$	9.52628	−	5.50000i	1.20984	−	0.698501i
$63$	1.73205	−	1.00000i	0.218218	−	0.125988i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−5.00000			−0.615457
$67$	13.8564	−	8.00000i	1.69283	−	0.977356i	0.740613	−	0.671932i	$-0.234535\pi$
$67$	13.8564	−	8.00000i	1.69283	−	0.977356i	0.952217	−	0.305424i	$-0.0987981\pi$
$68$	1.73205	−	1.00000i	0.210042	−	0.121268i
$69$	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	$0.166667\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			6.00000i			0.702247i	0.936329	+	0.351123i	$0.114200\pi$
$73$			6.00000i			0.702247i	−0.936329	+	0.351123i	$0.885800\pi$
$74$	−1.50000	+	2.59808i	−0.174371	+	0.302020i
$75$		0			0
$76$	1.00000	+	1.73205i	0.114708	+	0.198680i
$77$			10.0000i			1.13961i
$78$	−2.59808	+	2.50000i	−0.294174	+	0.283069i
$79$	11.0000			1.23760			0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000			1.23760			0.618798	+	0.785550i	$0.287620\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.73205	−	1.00000i	−0.191273	−	0.110432i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$	1.00000	−	1.73205i	0.109109	−	0.188982i
$85$		0			0
$86$	11.0000			1.18616
$87$	4.33013	+	2.50000i	0.464238	+	0.268028i
$88$	−4.33013	+	2.50000i	−0.461593	+	0.266501i
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	0.914146	−	0.405385i	$-0.132862\pi$
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	−0.808146	+	0.588982i	$0.799529\pi$
$90$		0			0
$91$	5.00000	+	5.19615i	0.524142	+	0.544705i
$92$		−	1.00000i		−	0.104257i
$93$	−9.52628	+	5.50000i	−0.987829	+	0.570323i
$94$	−4.50000	−	7.79423i	−0.464140	−	0.803913i
$95$		0			0
$96$	1.00000			0.102062
$97$	1.73205	+	1.00000i	0.175863	+	0.101535i	0.585348	−	0.810782i	$-0.300958\pi$
$97$	1.73205	+	1.00000i	0.175863	+	0.101535i	−0.409484	+	0.912317i	$0.634291\pi$
$98$	2.59808	+	1.50000i	0.262445	+	0.151523i
$99$	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	$0.865059\pi$
$102$	−1.73205	+	1.00000i	−0.171499	+	0.0990148i
$103$		−	10.0000i		−	0.985329i	−0.870219	−	0.492665i	$-0.836023\pi$
$103$		−	10.0000i		−	0.985329i	0.870219	−	0.492665i	$-0.163977\pi$
$104$	−1.00000	+	3.46410i	−0.0980581	+	0.339683i
$105$		0			0
$106$	3.00000	+	5.19615i	0.291386	+	0.504695i
$107$	8.66025	−	5.00000i	0.837218	−	0.483368i	−0.0190994	−	0.999818i	$-0.506080\pi$
$107$	8.66025	−	5.00000i	0.837218	−	0.483368i	0.856318	+	0.516449i	$0.172747\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	1.50000	−	2.59808i	0.142374	−	0.246598i
$112$		−	2.00000i		−	0.188982i
$113$	9.52628	+	5.50000i	0.896157	+	0.517396i	0.875951	−	0.482399i	$-0.160235\pi$
$113$	9.52628	+	5.50000i	0.896157	+	0.517396i	0.0202056	+	0.999796i	$0.493568\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$		0			0
$116$	5.00000			0.464238
$117$	2.59808	−	2.50000i	0.240192	−	0.231125i
$118$		−	15.0000i		−	1.38086i
$119$	2.00000	+	3.46410i	0.183340	+	0.317554i
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$		−	10.0000i		−	0.905357i
$123$	1.73205	+	1.00000i	0.156174	+	0.0901670i
$124$	−5.50000	+	9.52628i	−0.493915	+	0.855485i
$125$		0			0
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	1.73205	−	1.00000i	0.153695	−	0.0887357i	−0.421180	−	0.906977i	$-0.638384\pi$
$127$	1.73205	−	1.00000i	0.153695	−	0.0887357i	0.574875	+	0.818241i	$0.305051\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−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	$0.513910\pi$
$132$	4.33013	−	2.50000i	0.376889	−	0.217597i
$133$	−3.46410	+	2.00000i	−0.300376	+	0.173422i
$134$	−8.00000	+	13.8564i	−0.691095	+	1.19701i
$135$		0			0
$136$	−1.00000	+	1.73205i	−0.0857493	+	0.148522i
$137$	9.52628	+	5.50000i	0.813885	+	0.469897i	0.848303	−	0.529511i	$-0.177624\pi$
$137$	9.52628	+	5.50000i	0.813885	+	0.469897i	−0.0344182	+	0.999408i	$0.510958\pi$
$138$			1.00000i			0.0851257i
$139$	1.00000	−	1.73205i	0.0848189	−	0.146911i	−0.820495	−	0.571654i	$-0.806302\pi$
$139$	1.00000	−	1.73205i	0.0848189	−	0.146911i	0.905314	+	0.424743i	$0.139635\pi$
$140$		0			0
$141$	4.50000	+	7.79423i	0.378968	+	0.656392i
$142$		0			0
$143$	4.33013	+	17.5000i	0.362103	+	1.46342i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−3.00000	−	5.19615i	−0.248282	−	0.430037i
$147$	−2.59808	−	1.50000i	−0.214286	−	0.123718i
$148$		−	3.00000i		−	0.246598i
$149$	8.50000	−	14.7224i	0.696347	−	1.20611i	−0.273377	−	0.961907i	$-0.588141\pi$
$149$	8.50000	−	14.7224i	0.696347	−	1.20611i	0.969724	−	0.244202i	$-0.0785259\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	−1.73205	−	1.00000i	−0.140488	−	0.0811107i
$153$	1.73205	−	1.00000i	0.140028	−	0.0808452i
$154$	−5.00000	−	8.66025i	−0.402911	−	0.697863i
$155$		0			0
$156$	1.00000	−	3.46410i	0.0800641	−	0.277350i
$157$		−	7.00000i		−	0.558661i	−0.960195	−	0.279330i	$-0.909888\pi$
$157$		−	7.00000i		−	0.558661i	0.960195	−	0.279330i	$-0.0901125\pi$
$158$	−9.52628	+	5.50000i	−0.757870	+	0.437557i
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$		0			0
$161$	2.00000			0.157622
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	−12.9904	−	7.50000i	−1.01749	−	0.587445i	−0.104111	−	0.994566i	$-0.533200\pi$
$163$	−12.9904	−	7.50000i	−1.01749	−	0.587445i	−0.913375	+	0.407120i	$0.866533\pi$
$164$	2.00000			0.156174
$165$		0			0
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$	2.59808	−	1.50000i	0.201045	−	0.116073i	−0.396098	−	0.918208i	$-0.629636\pi$
$167$	2.59808	−	1.50000i	0.201045	−	0.116073i	0.597143	+	0.802135i	$0.296303\pi$
$168$			2.00000i			0.154303i
$169$	11.0000	+	6.92820i	0.846154	+	0.532939i
$170$		0			0
$171$	1.00000	+	1.73205i	0.0764719	+	0.132453i
$172$	−9.52628	+	5.50000i	−0.726372	+	0.419371i
$173$	17.3205	+	10.0000i	1.31685	+	0.760286i	0.983221	−	0.182417i	$-0.0583922\pi$
$173$	17.3205	+	10.0000i	1.31685	+	0.760286i	0.333633	+	0.942703i	$0.391725\pi$
$174$	−5.00000			−0.379049
$175$		0			0
$176$	2.50000	−	4.33013i	0.188445	−	0.326396i
$177$			15.0000i			1.12747i
$178$	−1.73205	−	1.00000i	−0.129823	−	0.0749532i
$179$	−6.50000	−	11.2583i	−0.485833	−	0.841487i	0.514035	−	0.857769i	$-0.328150\pi$
$179$	−6.50000	−	11.2583i	−0.485833	−	0.841487i	−0.999867	+	0.0162823i	$0.994817\pi$
$180$		0			0
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	−6.92820	−	2.00000i	−0.513553	−	0.148250i
$183$			10.0000i			0.739221i
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$		0			0
$186$	5.50000	−	9.52628i	0.403280	−	0.698501i
$187$			10.0000i			0.731272i
$188$	7.79423	+	4.50000i	0.568453	+	0.328196i
$189$	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	$0.212893\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	20.7846	−	12.0000i	1.49611	−	0.863779i	0.496119	−	0.868255i	$-0.334758\pi$
$193$	20.7846	−	12.0000i	1.49611	−	0.863779i	0.999990	+	0.00447566i	$0.00142465\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	−3.00000			−0.214286
$197$	−6.92820	+	4.00000i	−0.493614	+	0.284988i	−0.726073	−	0.687618i	$-0.758656\pi$
$197$	−6.92820	+	4.00000i	−0.493614	+	0.284988i	0.232458	+	0.972606i	$0.425323\pi$
$198$	−4.33013	+	2.50000i	−0.307729	+	0.177667i
$199$	12.0000	−	20.7846i	0.850657	−	1.47338i	−0.0299585	−	0.999551i	$-0.509538\pi$
$199$	12.0000	−	20.7846i	0.850657	−	1.47338i	0.880616	−	0.473831i	$-0.157129\pi$
$200$		0			0
$201$	8.00000	−	13.8564i	0.564276	−	0.977356i
$202$	1.73205	+	1.00000i	0.121867	+	0.0703598i
$203$			10.0000i			0.701862i
$204$	1.00000	−	1.73205i	0.0700140	−	0.121268i
$205$		0			0
$206$	5.00000	+	8.66025i	0.348367	+	0.603388i
$207$		−	1.00000i		−	0.0695048i
$208$	−0.866025	−	3.50000i	−0.0600481	−	0.242681i
$209$	−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	$0.789367\pi$
$212$	−5.19615	−	3.00000i	−0.356873	−	0.206041i
$213$		0			0
$214$	−5.00000	+	8.66025i	−0.341793	+	0.592003i
$215$		0			0
$216$	1.00000			0.0680414
$217$	−19.0526	−	11.0000i	−1.29337	−	0.746729i
$218$	−1.73205	+	1.00000i	−0.117309	+	0.0677285i
$219$	3.00000	+	5.19615i	0.202721	+	0.351123i
$220$		0			0
$221$	5.00000	+	5.19615i	0.336336	+	0.349531i
$222$			3.00000i			0.201347i
$223$	−22.5167	+	13.0000i	−1.50783	+	0.870544i	−0.507869	+	0.861435i	$0.669566\pi$
$223$	−22.5167	+	13.0000i	−1.50783	+	0.870544i	−0.999959	+	0.00910984i	$0.997100\pi$
$224$	1.00000	+	1.73205i	0.0668153	+	0.115728i
$225$		0			0
$226$	−11.0000			−0.731709
$227$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$227$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$228$	1.73205	+	1.00000i	0.114708	+	0.0662266i
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$		0			0
$231$	5.00000	+	8.66025i	0.328976	+	0.569803i
$232$	−4.33013	+	2.50000i	−0.284287	+	0.164133i
$233$		−	1.00000i		−	0.0655122i	−0.999463	−	0.0327561i	$-0.989572\pi$
$233$		−	1.00000i		−	0.0655122i	0.999463	−	0.0327561i	$-0.0104285\pi$
$234$	−1.00000	+	3.46410i	−0.0653720	+	0.226455i
$235$		0			0
$236$	7.50000	+	12.9904i	0.488208	+	0.845602i
$237$	9.52628	−	5.50000i	0.618798	−	0.357263i
$238$	−3.46410	−	2.00000i	−0.224544	−	0.129641i
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$		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	$0.0942799\pi$
$242$		−	14.0000i		−	0.899954i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	5.00000	+	8.66025i	0.320092	+	0.554416i
$245$		0			0
$246$	−2.00000			−0.127515
$247$	−5.19615	+	5.00000i	−0.330623	+	0.318142i
$248$		−	11.0000i		−	0.698501i
$249$	−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	$0.877269\pi$
$252$		−	2.00000i		−	0.125988i
$253$	4.33013	+	2.50000i	0.272233	+	0.157174i
$254$	−1.00000	+	1.73205i	−0.0627456	+	0.108679i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−14.7224	+	8.50000i	−0.918360	+	0.530215i	−0.883112	−	0.469163i	$-0.844556\pi$
$257$	−14.7224	+	8.50000i	−0.918360	+	0.530215i	−0.0352486	+	0.999379i	$0.511222\pi$
$258$	9.52628	−	5.50000i	0.593080	−	0.342415i
$259$	6.00000			0.372822
$260$		0			0
$261$	5.00000			0.309492
$262$	0.866025	−	0.500000i	0.0535032	−	0.0308901i
$263$	−18.1865	+	10.5000i	−1.12143	+	0.647458i	−0.941766	−	0.336270i	$-0.890834\pi$
$263$	−18.1865	+	10.5000i	−1.12143	+	0.647458i	−0.179664	+	0.983728i	$0.557501\pi$
$264$	−2.50000	+	4.33013i	−0.153864	+	0.266501i
$265$		0			0
$266$	2.00000	−	3.46410i	0.122628	−	0.212398i
$267$	1.73205	+	1.00000i	0.106000	+	0.0611990i
$268$		−	16.0000i		−	0.977356i
$269$	7.00000	−	12.1244i	0.426798	−	0.739235i	−0.569789	−	0.821791i	$-0.692975\pi$
$269$	7.00000	−	12.1244i	0.426798	−	0.739235i	0.996586	+	0.0825561i	$0.0263084\pi$
$270$		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	$0.704131\pi$
$272$		−	2.00000i		−	0.121268i
$273$	6.92820	+	2.00000i	0.419314	+	0.121046i
$274$	−11.0000			−0.664534
$275$		0			0
$276$	−0.500000	−	0.866025i	−0.0300965	−	0.0521286i
$277$	9.52628	+	5.50000i	0.572379	+	0.330463i	0.758099	−	0.652140i	$-0.226128\pi$
$277$	9.52628	+	5.50000i	0.572379	+	0.330463i	−0.185720	+	0.982603i	$0.559462\pi$
$278$			2.00000i			0.119952i
$279$	−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	$0.596411\pi$
$282$	−7.79423	−	4.50000i	−0.464140	−	0.267971i
$283$	−16.4545	+	9.50000i	−0.978117	+	0.564716i	−0.901701	−	0.432360i	$-0.857681\pi$
$283$	−16.4545	+	9.50000i	−0.978117	+	0.564716i	−0.0764162	+	0.997076i	$0.524348\pi$
$284$		0			0
$285$		0			0
$286$	−12.5000	−	12.9904i	−0.739140	−	0.768137i
$287$			4.00000i			0.236113i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$		0			0
$291$	2.00000			0.117242
$292$	5.19615	+	3.00000i	0.304082	+	0.175562i
$293$	5.19615	+	3.00000i	0.303562	+	0.175262i	0.644042	−	0.764990i	$-0.277256\pi$
$293$	5.19615	+	3.00000i	0.303562	+	0.175262i	−0.340480	+	0.940252i	$0.610589\pi$
$294$	3.00000			0.174964
$295$		0			0
$296$	1.50000	+	2.59808i	0.0871857	+	0.151010i
$297$	4.33013	−	2.50000i	0.251259	−	0.145065i
$298$			17.0000i			0.984784i
$299$	3.50000	−	0.866025i	0.202410	−	0.0500835i
$300$		0			0
$301$	−11.0000	−	19.0526i	−0.634029	−	1.09817i
$302$	−6.92820	+	4.00000i	−0.398673	+	0.230174i
$303$	−1.73205	−	1.00000i	−0.0995037	−	0.0574485i
$304$	2.00000			0.114708
$305$		0			0
$306$	−1.00000	+	1.73205i	−0.0571662	+	0.0990148i
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	8.66025	+	5.00000i	0.493464	+	0.284901i
$309$	−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	$0.308085\pi$
$312$	0.866025	+	3.50000i	0.0490290	+	0.198148i
$313$		−	20.0000i		−	1.13047i	−0.824931	−	0.565233i	$-0.808786\pi$
$313$		−	20.0000i		−	1.13047i	0.824931	−	0.565233i	$-0.191214\pi$
$314$	3.50000	+	6.06218i	0.197516	+	0.342108i
$315$		0			0
$316$	5.50000	−	9.52628i	0.309399	−	0.535895i
$317$			16.0000i			0.898650i	0.893368	+	0.449325i	$0.148335\pi$
$317$			16.0000i			0.898650i	−0.893368	+	0.449325i	$0.851665\pi$
$318$	5.19615	+	3.00000i	0.291386	+	0.168232i
$319$	−12.5000	+	21.6506i	−0.699866	+	1.21220i
$320$		0			0
$321$	5.00000	−	8.66025i	0.279073	−	0.483368i
$322$	−1.73205	+	1.00000i	−0.0965234	+	0.0557278i
$323$	−3.46410	+	2.00000i	−0.192748	+	0.111283i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	15.0000			0.830773
$327$	1.73205	−	1.00000i	0.0957826	−	0.0553001i
$328$	−1.73205	+	1.00000i	−0.0956365	+	0.0552158i
$329$	−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	$-0.112833\pi$
$332$	−5.19615	−	3.00000i	−0.285176	−	0.164646i
$333$		−	3.00000i		−	0.164399i
$334$	−1.50000	+	2.59808i	−0.0820763	+	0.142160i
$335$		0			0
$336$	−1.00000	−	1.73205i	−0.0545545	−	0.0944911i
$337$		−	2.00000i		−	0.108947i	−0.998515	−	0.0544735i	$-0.982652\pi$
$337$		−	2.00000i		−	0.108947i	0.998515	−	0.0544735i	$-0.0173480\pi$
$338$	−12.9904	−	0.500000i	−0.706584	−	0.0271964i
$339$	11.0000			0.597438
$340$		0			0
$341$	−27.5000	−	47.6314i	−1.48921	−	2.57938i
$342$	−1.73205	−	1.00000i	−0.0936586	−	0.0540738i
$343$		−	20.0000i		−	1.07990i
$344$	5.50000	−	9.52628i	0.296540	−	0.513623i
$345$		0			0
$346$	−20.0000			−1.07521
$347$	−29.4449	−	17.0000i	−1.58068	−	0.912608i	−0.994760	−	0.102241i	$-0.967399\pi$
$347$	−29.4449	−	17.0000i	−1.58068	−	0.912608i	−0.585923	−	0.810366i	$-0.699268\pi$
$348$	4.33013	−	2.50000i	0.232119	−	0.134014i
$349$	10.0000	+	17.3205i	0.535288	+	0.927146i	0.999149	+	0.0412379i	$0.0131301\pi$
$349$	10.0000	+	17.3205i	0.535288	+	0.927146i	−0.463862	+	0.885908i	$0.653537\pi$
$350$		0			0
$351$	1.00000	−	3.46410i	0.0533761	−	0.184900i
$352$			5.00000i			0.266501i
$353$	15.5885	−	9.00000i	0.829690	−	0.479022i	−0.0240566	−	0.999711i	$-0.507658\pi$
$353$	15.5885	−	9.00000i	0.829690	−	0.479022i	0.853746	+	0.520689i	$0.174325\pi$
$354$	−7.50000	−	12.9904i	−0.398621	−	0.690431i
$355$		0			0
$356$	2.00000			0.106000
$357$	3.46410	+	2.00000i	0.183340	+	0.105851i
$358$	11.2583	+	6.50000i	0.595021	+	0.343536i
$359$	−12.0000			−0.633336			−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000			−0.633336			−0.316668	+	0.948536i	$0.602564\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	13.8564	−	8.00000i	0.728277	−	0.420471i
$363$			14.0000i			0.734809i
$364$	7.00000	−	1.73205i	0.366900	−	0.0907841i
$365$		0			0
$366$	−5.00000	−	8.66025i	−0.261354	−	0.452679i
$367$	−13.8564	+	8.00000i	−0.723299	+	0.417597i	−0.815966	−	0.578101i	$-0.803794\pi$
$367$	−13.8564	+	8.00000i	−0.723299	+	0.417597i	0.0926670	+	0.995697i	$0.470461\pi$
$368$	−0.866025	−	0.500000i	−0.0451447	−	0.0260643i
$369$	2.00000			0.104116
$370$		0			0
$371$	6.00000	−	10.3923i	0.311504	−	0.539542i
$372$			11.0000i			0.570323i
$373$	−16.4545	−	9.50000i	−0.851981	−	0.491891i	0.00933789	−	0.999956i	$-0.497028\pi$
$373$	−16.4545	−	9.50000i	−0.851981	−	0.491891i	−0.861319	+	0.508065i	$0.830361\pi$
$374$	−5.00000	−	8.66025i	−0.258544	−	0.447811i
$375$		0			0
$376$	−9.00000			−0.464140
$377$	4.33013	+	17.5000i	0.223013	+	0.901296i
$378$			2.00000i			0.102869i
$379$	−1.00000	−	1.73205i	−0.0513665	−	0.0889695i	0.839199	−	0.543825i	$-0.183024\pi$
$379$	−1.00000	−	1.73205i	−0.0513665	−	0.0889695i	−0.890565	+	0.454855i	$0.849691\pi$
$380$		0			0
$381$	1.00000	−	1.73205i	0.0512316	−	0.0887357i
$382$		−	4.00000i		−	0.204658i
$383$	26.8468	+	15.5000i	1.37181	+	0.792013i	0.991155	−	0.132706i	$-0.0423665\pi$
$383$	26.8468	+	15.5000i	1.37181	+	0.792013i	0.380651	+	0.924719i	$0.375700\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$		0			0
$386$	−12.0000	+	20.7846i	−0.610784	+	1.05791i
$387$	−9.52628	+	5.50000i	−0.484248	+	0.279581i
$388$	1.73205	−	1.00000i	0.0879316	−	0.0507673i
$389$	−5.00000			−0.253510			−0.126755	−	0.991934i	$-0.540456\pi$
$389$	−5.00000			−0.253510			−0.126755	+	0.991934i	$0.540456\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$	2.59808	−	1.50000i	0.131223	−	0.0757614i
$393$	−0.866025	+	0.500000i	−0.0436852	+	0.0252217i
$394$	4.00000	−	6.92820i	0.201517	−	0.349038i
$395$		0			0
$396$	2.50000	−	4.33013i	0.125630	−	0.217597i
$397$	−2.59808	−	1.50000i	−0.130394	−	0.0752828i	0.433384	−	0.901209i	$-0.357319\pi$
$397$	−2.59808	−	1.50000i	−0.130394	−	0.0752828i	−0.563778	+	0.825926i	$0.690653\pi$
$398$			24.0000i			1.20301i
$399$	−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	$-0.522283\pi$
$402$			16.0000i			0.798007i
$403$	−38.1051	−	11.0000i	−1.89815	−	0.547949i
$404$	−2.00000			−0.0995037
$405$		0			0
$406$	−5.00000	−	8.66025i	−0.248146	−	0.429801i
$407$	12.9904	+	7.50000i	0.643909	+	0.371761i
$408$			2.00000i			0.0990148i
$409$	15.0000	−	25.9808i	0.741702	−	1.28467i	−0.210017	−	0.977698i	$-0.567352\pi$
$409$	15.0000	−	25.9808i	0.741702	−	1.28467i	0.951720	−	0.306968i	$-0.0993146\pi$
$410$		0			0
$411$	11.0000			0.542590
$412$	−8.66025	−	5.00000i	−0.426660	−	0.246332i
$413$	−25.9808	+	15.0000i	−1.27843	+	0.738102i
$414$	0.500000	+	0.866025i	0.0245737	+	0.0425628i
$415$		0			0
$416$	2.50000	+	2.59808i	0.122573	+	0.127381i
$417$		−	2.00000i		−	0.0979404i
$418$	8.66025	−	5.00000i	0.423587	−	0.244558i
$419$	−2.00000	−	3.46410i	−0.0977064	−	0.169232i	0.813029	−	0.582224i	$-0.197817\pi$
$419$	−2.00000	−	3.46410i	−0.0977064	−	0.169232i	−0.910735	+	0.412991i	$0.864484\pi$
$420$		0			0
$421$	−16.0000			−0.779792			−0.389896	−	0.920859i	$-0.627489\pi$
$421$	−16.0000			−0.779792			−0.389896	+	0.920859i	$0.627489\pi$
$422$	−3.46410	−	2.00000i	−0.168630	−	0.0973585i
$423$	7.79423	+	4.50000i	0.378968	+	0.218797i
$424$	6.00000			0.291386
$425$		0			0
$426$		0			0
$427$	−17.3205	+	10.0000i	−0.838198	+	0.483934i
$428$		−	10.0000i		−	0.483368i
$429$	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	$-0.580241\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	24.2487	+	14.0000i	1.16532	+	0.672797i	0.952573	−	0.304311i	$-0.0984260\pi$
$433$	24.2487	+	14.0000i	1.16532	+	0.672797i	0.212746	+	0.977108i	$0.431759\pi$
$434$	22.0000			1.05603
$435$		0			0
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$			2.00000i			0.0956730i
$438$	−5.19615	−	3.00000i	−0.248282	−	0.143346i
$439$	−2.00000	−	3.46410i	−0.0954548	−	0.165333i	0.814344	−	0.580383i	$-0.197097\pi$
$439$	−2.00000	−	3.46410i	−0.0954548	−	0.165333i	−0.909798	+	0.415051i	$0.863764\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	−6.92820	−	2.00000i	−0.329541	−	0.0951303i
$443$		−	20.0000i		−	0.950229i	−0.879924	−	0.475114i	$-0.842407\pi$
$443$		−	20.0000i		−	0.950229i	0.879924	−	0.475114i	$-0.157593\pi$
$444$	−1.50000	−	2.59808i	−0.0711868	−	0.123299i
$445$		0			0
$446$	13.0000	−	22.5167i	0.615568	−	1.06619i
$447$		−	17.0000i		−	0.804072i
$448$	−1.73205	−	1.00000i	−0.0818317	−	0.0472456i
$449$	6.00000	−	10.3923i	0.283158	−	0.490443i	−0.689003	−	0.724758i	$-0.741951\pi$
$449$	6.00000	−	10.3923i	0.283158	−	0.490443i	0.972161	+	0.234315i	$0.0752847\pi$
$450$		0			0
$451$	−5.00000	+	8.66025i	−0.235441	+	0.407795i
$452$	9.52628	−	5.50000i	0.448078	−	0.258698i
$453$	6.92820	−	4.00000i	0.325515	−	0.187936i
$454$		0			0
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	32.9090	−	19.0000i	1.53942	−	0.888783i	0.540544	−	0.841316i	$-0.318219\pi$
$457$	32.9090	−	19.0000i	1.53942	−	0.888783i	0.998873	−	0.0474665i	$-0.0151147\pi$
$458$	8.66025	−	5.00000i	0.404667	−	0.233635i
$459$	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	$-0.195881\pi$
$462$	−8.66025	−	5.00000i	−0.402911	−	0.232621i
$463$		−	14.0000i		−	0.650635i	−0.945605	−	0.325318i	$-0.894529\pi$
$463$		−	14.0000i		−	0.650635i	0.945605	−	0.325318i	$-0.105471\pi$
$464$	2.50000	−	4.33013i	0.116060	−	0.201021i
$465$		0			0
$466$	0.500000	+	0.866025i	0.0231621	+	0.0401179i
$467$			6.00000i			0.277647i	0.990317	+	0.138823i	$0.0443321\pi$
$467$			6.00000i			0.277647i	−0.990317	+	0.138823i	$0.955668\pi$
$468$	−0.866025	−	3.50000i	−0.0400320	−	0.161788i
$469$	32.0000			1.47762
$470$		0			0
$471$	−3.50000	−	6.06218i	−0.161271	−	0.279330i
$472$	−12.9904	−	7.50000i	−0.597931	−	0.345215i
$473$		−	55.0000i		−	2.52890i
$474$	−5.50000	+	9.52628i	−0.252623	+	0.437557i
$475$		0			0
$476$	4.00000			0.183340
$477$	−5.19615	−	3.00000i	−0.237915	−	0.137361i
$478$	−17.3205	+	10.0000i	−0.792222	+	0.457389i
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	−0.998392	−	0.0566937i	$-0.981944\pi$
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	0.450098	−	0.892979i	$-0.351389\pi$
$480$		0			0
$481$	10.5000	−	2.59808i	0.478759	−	0.118462i
$482$			7.00000i			0.318841i
$483$	1.73205	−	1.00000i	0.0788110	−	0.0455016i
$484$	7.00000	+	12.1244i	0.318182	+	0.551107i
$485$		0			0
$486$	1.00000			0.0453609
$487$	−1.73205	−	1.00000i	−0.0784867	−	0.0453143i	0.460243	−	0.887793i	$-0.347762\pi$
$487$	−1.73205	−	1.00000i	−0.0784867	−	0.0453143i	−0.538730	+	0.842479i	$0.681096\pi$
$488$	−8.66025	−	5.00000i	−0.392031	−	0.226339i
$489$	−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	$0.715757\pi$
$492$	1.73205	−	1.00000i	0.0780869	−	0.0450835i
$493$			10.0000i			0.450377i
$494$	2.00000	−	6.92820i	0.0899843	−	0.311715i
$495$		0			0
$496$	5.50000	+	9.52628i	0.246957	+	0.427743i
$497$		0			0
$498$	5.19615	+	3.00000i	0.232845	+	0.134433i
$499$	−28.0000			−1.25345			−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000			−1.25345			−0.626726	+	0.779240i	$0.715605\pi$
$500$		0			0
$501$	1.50000	−	2.59808i	0.0670151	−	0.116073i
$502$		−	25.0000i		−	1.11580i
$503$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$503$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$504$	1.00000	+	1.73205i	0.0445435	+	0.0771517i
$505$		0			0
$506$	−5.00000			−0.222277
$507$	12.9904	+	0.500000i	0.576923	+	0.0222058i
$508$		−	2.00000i		−	0.0887357i
$509$	14.5000	+	25.1147i	0.642701	+	1.11319i	0.984827	+	0.173537i	$0.0555197\pi$
$509$	14.5000	+	25.1147i	0.642701	+	1.11319i	−0.342126	+	0.939654i	$0.611147\pi$
$510$		0			0
$511$	−6.00000	+	10.3923i	−0.265424	+	0.459728i
$512$		−	1.00000i		−	0.0441942i
$513$	1.73205	+	1.00000i	0.0764719	+	0.0441511i
$514$	8.50000	−	14.7224i	0.374919	−	0.649379i
$515$		0			0
$516$	−5.50000	+	9.52628i	−0.242124	+	0.419371i
$517$	−38.9711	+	22.5000i	−1.71395	+	0.989549i
$518$	−5.19615	+	3.00000i	−0.228306	+	0.131812i
$519$	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	$0.370988\pi$
$522$	−4.33013	+	2.50000i	−0.189525	+	0.109422i
$523$	26.8468	−	15.5000i	1.17393	−	0.677768i	0.219326	−	0.975652i	$-0.429614\pi$
$523$	26.8468	−	15.5000i	1.17393	−	0.677768i	0.954602	+	0.297884i	$0.0962809\pi$
$524$	−0.500000	+	0.866025i	−0.0218426	+	0.0378325i
$525$		0			0
$526$	10.5000	−	18.1865i	0.457822	−	0.792971i
$527$	−19.0526	−	11.0000i	−0.829943	−	0.479168i
$528$		−	5.00000i		−	0.217597i
$529$	−11.0000	+	19.0526i	−0.478261	+	0.828372i
$530$		0			0
$531$	7.50000	+	12.9904i	0.325472	+	0.563735i
$532$			4.00000i			0.173422i
$533$	1.73205	+	7.00000i	0.0750234	+	0.303204i
$534$	−2.00000			−0.0865485
$535$		0			0
$536$	8.00000	+	13.8564i	0.345547	+	0.598506i
$537$	−11.2583	−	6.50000i	−0.485833	−	0.280496i
$538$			14.0000i			0.603583i
$539$	7.50000	−	12.9904i	0.323048	−	0.559535i
$540$		0			0
$541$		0			0			−	1.00000i	$-0.5\pi$
$541$		0			0				1.00000i	$0.5\pi$
$542$	−11.2583	−	6.50000i	−0.483587	−	0.279199i
$543$	−13.8564	+	8.00000i	−0.594635	+	0.343313i
$544$	1.00000	+	1.73205i	0.0428746	+	0.0742611i
$545$		0			0
$546$	−7.00000	+	1.73205i	−0.299572	+	0.0741249i
$547$		−	12.0000i		−	0.513083i	−0.966533	−	0.256541i	$-0.917417\pi$
$547$		−	12.0000i		−	0.513083i	0.966533	−	0.256541i	$-0.0825830\pi$
$548$	9.52628	−	5.50000i	0.406942	−	0.234948i
$549$	5.00000	+	8.66025i	0.213395	+	0.369611i
$550$		0			0
$551$	−10.0000			−0.426014
$552$	0.866025	+	0.500000i	0.0368605	+	0.0212814i
$553$	19.0526	+	11.0000i	0.810197	+	0.467768i
$554$	−11.0000			−0.467345
$555$		0			0
$556$	−1.00000	−	1.73205i	−0.0424094	−	0.0734553i
$557$	22.5167	−	13.0000i	0.954062	−	0.550828i	0.0597213	−	0.998215i	$-0.480979\pi$
$557$	22.5167	−	13.0000i	0.954062	−	0.550828i	0.894340	+	0.447387i	$0.147645\pi$
$558$		−	11.0000i		−	0.465667i
$559$	−27.5000	−	28.5788i	−1.16313	−	1.20876i
$560$		0			0
$561$	5.00000	+	8.66025i	0.211100	+	0.365636i
$562$	8.66025	−	5.00000i	0.365311	−	0.210912i
$563$	10.3923	+	6.00000i	0.437983	+	0.252870i	0.702742	−	0.711445i	$-0.251959\pi$
$563$	10.3923	+	6.00000i	0.437983	+	0.252870i	−0.264758	+	0.964315i	$0.585292\pi$
$564$	9.00000			0.378968
$565$		0			0
$566$	9.50000	−	16.4545i	0.399315	−	0.691633i
$567$		−	2.00000i		−	0.0839921i
$568$		0			0
$569$	−11.0000	−	19.0526i	−0.461144	−	0.798725i	0.537874	−	0.843025i	$-0.319228\pi$
$569$	−11.0000	−	19.0526i	−0.461144	−	0.798725i	−0.999018	+	0.0443003i	$0.985894\pi$
$570$		0			0
$571$	−16.0000			−0.669579			−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000			−0.669579			−0.334790	+	0.942293i	$0.608665\pi$
$572$	17.3205	+	5.00000i	0.724207	+	0.209061i
$573$			4.00000i			0.167102i
$574$	−2.00000	−	3.46410i	−0.0834784	−	0.144589i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$		−	22.0000i		−	0.915872i	−0.888985	−	0.457936i	$-0.848589\pi$
$577$		−	22.0000i		−	0.915872i	0.888985	−	0.457936i	$-0.151411\pi$
$578$	11.2583	+	6.50000i	0.468285	+	0.270364i
$579$	12.0000	−	20.7846i	0.498703	−	0.863779i
$580$		0			0
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	−1.73205	+	1.00000i	−0.0717958	+	0.0414513i
$583$	25.9808	−	15.0000i	1.07601	−	0.621237i
$584$	−6.00000			−0.248282
$585$		0			0
$586$	−6.00000			−0.247858
$587$	−15.5885	+	9.00000i	−0.643404	+	0.371470i	−0.785925	−	0.618322i	$-0.787813\pi$
$587$	−15.5885	+	9.00000i	−0.643404	+	0.371470i	0.142520	+	0.989792i	$0.454479\pi$
$588$	−2.59808	+	1.50000i	−0.107143	+	0.0618590i
$589$	11.0000	−	19.0526i	0.453247	−	0.785047i
$590$		0			0
$591$	−4.00000	+	6.92820i	−0.164538	+	0.284988i
$592$	−2.59808	−	1.50000i	−0.106780	−	0.0616496i
$593$		−	31.0000i		−	1.27302i	−0.771270	−	0.636509i	$-0.780378\pi$
$593$		−	31.0000i		−	1.27302i	0.771270	−	0.636509i	$-0.219622\pi$
$594$	−2.50000	+	4.33013i	−0.102576	+	0.177667i
$595$		0			0
$596$	−8.50000	−	14.7224i	−0.348174	−	0.603054i
$597$		−	24.0000i		−	0.982255i
$598$	−2.59808	+	2.50000i	−0.106243	+	0.102233i
$599$	−42.0000			−1.71607			−0.858037	−	0.513588i	$-0.828316\pi$
$599$	−42.0000			−1.71607			−0.858037	+	0.513588i	$0.828316\pi$
$600$		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	$0.813845\pi$
$602$	19.0526	+	11.0000i	0.776524	+	0.448327i
$603$		−	16.0000i		−	0.651570i
$604$	4.00000	−	6.92820i	0.162758	−	0.281905i
$605$		0			0
$606$	2.00000			0.0812444
$607$	−15.5885	−	9.00000i	−0.632716	−	0.365299i	0.149087	−	0.988824i	$-0.452366\pi$
$607$	−15.5885	−	9.00000i	−0.632716	−	0.365299i	−0.781803	+	0.623525i	$0.785700\pi$
$608$	−1.73205	+	1.00000i	−0.0702439	+	0.0405554i
$609$	5.00000	+	8.66025i	0.202610	+	0.350931i
$610$		0			0
$611$	−9.00000	+	31.1769i	−0.364101	+	1.26128i
$612$		−	2.00000i		−	0.0808452i
$613$	25.1147	−	14.5000i	1.01437	−	0.585649i	0.101905	−	0.994794i	$-0.467506\pi$
$613$	25.1147	−	14.5000i	1.01437	−	0.585649i	0.912470	+	0.409145i	$0.134173\pi$
$614$		0			0
$615$		0			0
$616$	−10.0000			−0.402911
$617$	−35.5070	−	20.5000i	−1.42946	−	0.825299i	−0.432382	−	0.901691i	$-0.642327\pi$
$617$	−35.5070	−	20.5000i	−1.42946	−	0.825299i	−0.997078	+	0.0763917i	$0.975660\pi$
$618$	8.66025	+	5.00000i	0.348367	+	0.201129i
$619$	10.0000			0.401934			0.200967	−	0.979598i	$-0.435592\pi$
$619$	10.0000			0.401934			0.200967	+	0.979598i	$0.435592\pi$
$620$		0			0
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$	−17.3205	+	10.0000i	−0.694489	+	0.400963i
$623$			4.00000i			0.160257i
$624$	−2.50000	−	2.59808i	−0.100080	−	0.104006i
$625$		0			0
$626$	10.0000	+	17.3205i	0.399680	+	0.692267i
$627$	−8.66025	+	5.00000i	−0.345857	+	0.199681i
$628$	−6.06218	−	3.50000i	−0.241907	−	0.139665i
$629$	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	$0.873514\pi$
$632$			11.0000i			0.437557i
$633$	3.46410	+	2.00000i	0.137686	+	0.0794929i
$634$	−8.00000	−	13.8564i	−0.317721	−	0.550308i
$635$		0			0
$636$	−6.00000			−0.237915
$637$	−2.59808	−	10.5000i	−0.102940	−	0.416025i
$638$		−	25.0000i		−	0.989759i
$639$		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	$-0.0351782\pi$
$642$			10.0000i			0.394669i
$643$	6.92820	+	4.00000i	0.273222	+	0.157745i	0.630351	−	0.776310i	$-0.282911\pi$
$643$	6.92820	+	4.00000i	0.273222	+	0.157745i	−0.357129	+	0.934055i	$0.616244\pi$
$644$	1.00000	−	1.73205i	0.0394055	−	0.0682524i
$645$		0			0
$646$	2.00000	−	3.46410i	0.0786889	−	0.136293i
$647$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$647$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−75.0000			−2.94401
$650$		0			0
$651$	−22.0000			−0.862248
$652$	−12.9904	+	7.50000i	−0.508743	+	0.293723i
$653$	−29.4449	+	17.0000i	−1.15227	+	0.665261i	−0.949439	−	0.313953i	$-0.898347\pi$
$653$	−29.4449	+	17.0000i	−1.15227	+	0.665261i	−0.202828	+	0.979214i	$0.565013\pi$
$654$	−1.00000	+	1.73205i	−0.0391031	+	0.0677285i
$655$		0			0
$656$	1.00000	−	1.73205i	0.0390434	−	0.0676252i
$657$	5.19615	+	3.00000i	0.202721	+	0.117041i
$658$		−	18.0000i		−	0.701713i
$659$	−19.5000	+	33.7750i	−0.759612	+	1.31569i	0.183436	+	0.983032i	$0.441278\pi$
$659$	−19.5000	+	33.7750i	−0.759612	+	1.31569i	−0.943049	+	0.332655i	$0.892055\pi$
$660$		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	$-0.380480\pi$
$662$			28.0000i			1.08825i
$663$	6.92820	+	2.00000i	0.269069	+	0.0776736i
$664$	6.00000			0.232845
$665$		0			0
$666$	1.50000	+	2.59808i	0.0581238	+	0.100673i
$667$	4.33013	+	2.50000i	0.167663	+	0.0968004i
$668$		−	3.00000i		−	0.116073i
$669$	−13.0000	+	22.5167i	−0.502609	+	0.870544i
$670$		0			0
$671$	−50.0000			−1.93023
$672$	1.73205	+	1.00000i	0.0668153	+	0.0385758i
$673$	−6.92820	+	4.00000i	−0.267063	+	0.154189i	−0.627552	−	0.778575i	$-0.715943\pi$
$673$	−6.92820	+	4.00000i	−0.267063	+	0.154189i	0.360489	+	0.932763i	$0.382610\pi$
$674$	1.00000	+	1.73205i	0.0385186	+	0.0667161i
$675$		0			0
$676$	11.5000	−	6.06218i	0.442308	−	0.233161i
$677$		−	4.00000i		−	0.153732i	−0.997041	−	0.0768662i	$-0.975509\pi$
$677$		−	4.00000i		−	0.153732i	0.997041	−	0.0768662i	$-0.0244914\pi$
$678$	−9.52628	+	5.50000i	−0.365855	+	0.211226i
$679$	2.00000	+	3.46410i	0.0767530	+	0.132940i
$680$		0			0
$681$		0			0
$682$	47.6314	+	27.5000i	1.82390	+	1.05303i
$683$	−10.3923	−	6.00000i	−0.397650	−	0.229584i	0.287819	−	0.957685i	$-0.407070\pi$
$683$	−10.3923	−	6.00000i	−0.397650	−	0.229584i	−0.685470	+	0.728101i	$0.740403\pi$
$684$	2.00000			0.0764719
$685$		0			0
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$	−8.66025	+	5.00000i	−0.330409	+	0.190762i
$688$			11.0000i			0.419371i
$689$	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	$0.640034\pi$
$692$	17.3205	−	10.0000i	0.658427	−	0.380143i
$693$	8.66025	+	5.00000i	0.328976	+	0.189934i
$694$	34.0000			1.29062
$695$		0			0
$696$	−2.50000	+	4.33013i	−0.0947623	+	0.164133i
$697$			4.00000i			0.151511i
$698$	−17.3205	−	10.0000i	−0.655591	−	0.378506i
$699$	−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	$0.421047\pi$
$702$	0.866025	+	3.50000i	0.0326860	+	0.132099i
$703$			6.00000i			0.226294i
$704$	−2.50000	−	4.33013i	−0.0942223	−	0.163198i
$705$		0			0
$706$	−9.00000	+	15.5885i	−0.338719	+	0.586679i
$707$		−	4.00000i		−	0.150435i
$708$	12.9904	+	7.50000i	0.488208	+	0.281867i
$709$	−4.00000	+	6.92820i	−0.150223	+	0.260194i	−0.931309	−	0.364229i	$-0.881333\pi$
$709$	−4.00000	+	6.92820i	−0.150223	+	0.260194i	0.781086	+	0.624423i	$0.214666\pi$
$710$		0			0
$711$	5.50000	−	9.52628i	0.206266	−	0.357263i
$712$	−1.73205	+	1.00000i	−0.0649113	+	0.0374766i
$713$	−9.52628	+	5.50000i	−0.356762	+	0.205977i
$714$	−4.00000			−0.149696
$715$		0			0
$716$	−13.0000			−0.485833
$717$	17.3205	−	10.0000i	0.646846	−	0.373457i
$718$	10.3923	−	6.00000i	0.387837	−	0.223918i
$719$	12.0000	−	20.7846i	0.447524	−	0.775135i	−0.550700	−	0.834703i	$-0.685639\pi$
$719$	12.0000	−	20.7846i	0.447524	−	0.775135i	0.998224	+	0.0595683i	$0.0189724\pi$
$720$		0			0
$721$	10.0000	−	17.3205i	0.372419	−	0.645049i
$722$	−12.9904	−	7.50000i	−0.483452	−	0.279121i
$723$		−	7.00000i		−	0.260333i
$724$	−8.00000	+	13.8564i	−0.297318	+	0.514969i
$725$		0			0
$726$	−7.00000	−	12.1244i	−0.259794	−	0.449977i
$727$		−	40.0000i		−	1.48352i	−0.670667	−	0.741759i	$-0.733992\pi$
$727$		−	40.0000i		−	1.48352i	0.670667	−	0.741759i	$-0.266008\pi$
$728$	−5.19615	+	5.00000i	−0.192582	+	0.185312i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−11.0000	−	19.0526i	−0.406850	−	0.704684i
$732$	8.66025	+	5.00000i	0.320092	+	0.184805i
$733$		−	6.00000i		−	0.221615i	−0.993842	−	0.110808i	$-0.964656\pi$
$733$		−	6.00000i		−	0.221615i	0.993842	−	0.110808i	$-0.0353437\pi$
$734$	8.00000	−	13.8564i	0.295285	−	0.511449i
$735$		0			0
$736$	1.00000			0.0368605
$737$	69.2820	+	40.0000i	2.55204	+	1.47342i
$738$	−1.73205	+	1.00000i	−0.0637577	+	0.0368105i
$739$	22.0000	+	38.1051i	0.809283	+	1.40172i	0.913361	+	0.407150i	$0.133477\pi$
$739$	22.0000	+	38.1051i	0.809283	+	1.40172i	−0.104078	+	0.994569i	$0.533189\pi$
$740$		0			0
$741$	−2.00000	+	6.92820i	−0.0734718	+	0.254514i
$742$			12.0000i			0.440534i
$743$	−44.1673	+	25.5000i	−1.62034	+	0.935504i	−0.633513	+	0.773732i	$0.718388\pi$
$743$	−44.1673	+	25.5000i	−1.62034	+	0.935504i	−0.986828	+	0.161772i	$0.948279\pi$
$744$	−5.50000	−	9.52628i	−0.201640	−	0.349250i
$745$		0			0
$746$	19.0000			0.695639
$747$	−5.19615	−	3.00000i	−0.190117	−	0.109764i
$748$	8.66025	+	5.00000i	0.316650	+	0.182818i
$749$	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	$0.695489\pi$
$752$	7.79423	−	4.50000i	0.284226	−	0.164098i
$753$			25.0000i			0.911051i
$754$	−12.5000	−	12.9904i	−0.455223	−	0.473082i
$755$		0			0
$756$	−1.00000	−	1.73205i	−0.0363696	−	0.0629941i
$757$	8.66025	−	5.00000i	0.314762	−	0.181728i	−0.334293	−	0.942469i	$-0.608498\pi$
$757$	8.66025	−	5.00000i	0.314762	−	0.181728i	0.649056	+	0.760741i	$0.275164\pi$
$758$	1.73205	+	1.00000i	0.0629109	+	0.0363216i
$759$	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	$0.284743\pi$
$762$			2.00000i			0.0724524i
$763$	3.46410	+	2.00000i	0.125409	+	0.0724049i
$764$	2.00000	+	3.46410i	0.0723575	+	0.125327i
$765$		0			0
$766$	−31.0000			−1.12008
$767$	−38.9711	+	37.5000i	−1.40717	+	1.35405i
$768$			1.00000i			0.0360844i
$769$	21.5000	+	37.2391i	0.775310	+	1.34288i	0.934620	+	0.355647i	$0.115740\pi$
$769$	21.5000	+	37.2391i	0.775310	+	1.34288i	−0.159310	+	0.987229i	$0.550927\pi$
$770$		0			0
$771$	−8.50000	+	14.7224i	−0.306120	+	0.530215i
$772$		−	24.0000i		−	0.863779i
$773$	27.7128	+	16.0000i	0.996761	+	0.575480i	0.907288	−	0.420509i	$-0.138149\pi$
$773$	27.7128	+	16.0000i	0.996761	+	0.575480i	0.0894724	+	0.995989i	$0.471482\pi$
$774$	5.50000	−	9.52628i	0.197693	−	0.342415i
$775$		0			0
$776$	−1.00000	+	1.73205i	−0.0358979	+	0.0621770i
$777$	5.19615	−	3.00000i	0.186411	−	0.107624i
$778$	4.33013	−	2.50000i	0.155243	−	0.0896293i
$779$	−4.00000			−0.143315
$780$		0			0
$781$		0			0
$782$	−1.73205	+	1.00000i	−0.0619380	+	0.0357599i
$783$	4.33013	−	2.50000i	0.154746	−	0.0893427i
$784$	−1.50000	+	2.59808i	−0.0535714	+	0.0927884i
$785$		0			0
$786$	0.500000	−	0.866025i	0.0178344	−	0.0308901i
$787$	26.8468	+	15.5000i	0.956985	+	0.552515i	0.895244	−	0.445577i	$-0.147001\pi$
$787$	26.8468	+	15.5000i	0.956985	+	0.552515i	0.0617409	+	0.998092i	$0.480335\pi$
$788$			8.00000i			0.284988i
$789$	−10.5000	+	18.1865i	−0.373810	+	0.647458i
$790$		0			0
$791$	11.0000	+	19.0526i	0.391115	+	0.677431i
$792$			5.00000i			0.177667i
$793$	−25.9808	+	25.0000i	−0.922604	+	0.887776i
$794$	3.00000			0.106466
$795$		0			0
$796$	−12.0000	−	20.7846i	−0.425329	−	0.736691i
$797$	−10.3923	−	6.00000i	−0.368114	−	0.212531i	0.304520	−	0.952506i	$-0.401504\pi$
$797$	−10.3923	−	6.00000i	−0.368114	−	0.212531i	−0.672634	+	0.739975i	$0.734837\pi$
$798$		−	4.00000i		−	0.141598i
$799$	−9.00000	+	15.5885i	−0.318397	+	0.551480i
$800$		0			0
$801$	2.00000			0.0706665
$802$	31.1769	+	18.0000i	1.10090	+	0.635602i
$803$	−25.9808	+	15.0000i	−0.916841	+	0.529339i
$804$	−8.00000	−	13.8564i	−0.282138	−	0.488678i
$805$		0			0
$806$	38.5000	−	9.52628i	1.35610	−	0.335549i
$807$		−	14.0000i		−	0.492823i
$808$	1.73205	−	1.00000i	0.0609333	−	0.0351799i
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	−0.999491	−	0.0319002i	$-0.989844\pi$
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	0.472119	−	0.881535i	$-0.343489\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	8.66025	+	5.00000i	0.303915	+	0.175466i
$813$	11.2583	+	6.50000i	0.394847	+	0.227965i
$814$	−15.0000			−0.525750
$815$		0			0
$816$	−1.00000	−	1.73205i	−0.0350070	−	0.0606339i
$817$	19.0526	−	11.0000i	0.666565	−	0.384841i
$818$			30.0000i			1.04893i
$819$	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	$0.484068\pi$
$822$	−9.52628	+	5.50000i	−0.332267	+	0.191835i
$823$	−1.73205	−	1.00000i	−0.0603755	−	0.0348578i	0.469508	−	0.882928i	$-0.344431\pi$
$823$	−1.73205	−	1.00000i	−0.0603755	−	0.0348578i	−0.529884	+	0.848070i	$0.677765\pi$
$824$	10.0000			0.348367
$825$		0			0
$826$	15.0000	−	25.9808i	0.521917	−	0.903986i
$827$		−	50.0000i		−	1.73867i	−0.494223	−	0.869335i	$-0.664547\pi$
$827$		−	50.0000i		−	1.73867i	0.494223	−	0.869335i	$-0.335453\pi$
$828$	−0.866025	−	0.500000i	−0.0300965	−	0.0173762i
$829$	7.00000	+	12.1244i	0.243120	+	0.421096i	0.961601	−	0.274450i	$-0.0884958\pi$
$829$	7.00000	+	12.1244i	0.243120	+	0.421096i	−0.718481	+	0.695546i	$0.755162\pi$
$830$		0			0
$831$	11.0000			0.381586
$832$	−3.46410	−	1.00000i	−0.120096	−	0.0346688i
$833$		−	6.00000i		−	0.207888i
$834$	1.00000	+	1.73205i	0.0346272	+	0.0599760i
$835$		0			0
$836$	−5.00000	+	8.66025i	−0.172929	+	0.299521i
$837$			11.0000i			0.380216i
$838$	3.46410	+	2.00000i	0.119665	+	0.0690889i
$839$	−27.0000	+	46.7654i	−0.932144	+	1.61452i	−0.152493	+	0.988304i	$0.548730\pi$
$839$	−27.0000	+	46.7654i	−0.932144	+	1.61452i	−0.779650	+	0.626215i	$0.784603\pi$
$840$		0			0
$841$	2.00000	−	3.46410i	0.0689655	−	0.119452i
$842$	13.8564	−	8.00000i	0.477523	−	0.275698i
$843$	−8.66025	+	5.00000i	−0.298275	+	0.172209i
$844$	4.00000			0.137686
$845$		0			0
$846$	−9.00000			−0.309426
$847$	−24.2487	+	14.0000i	−0.833196	+	0.481046i
$848$	−5.19615	+	3.00000i	−0.178437	+	0.103020i
$849$	−9.50000	+	16.4545i	−0.326039	+	0.564716i
$850$		0			0
$851$	1.50000	−	2.59808i	0.0514193	−	0.0890609i
$852$		0			0
$853$			49.0000i			1.67773i	0.544341	+	0.838864i	$0.316780\pi$
$853$			49.0000i			1.67773i	−0.544341	+	0.838864i	$0.683220\pi$
$854$	10.0000	−	17.3205i	0.342193	−	0.592696i
$855$		0			0
$856$	5.00000	+	8.66025i	0.170896	+	0.296001i
$857$		−	25.0000i		−	0.853984i	−0.904255	−	0.426992i	$-0.859573\pi$
$857$		−	25.0000i		−	0.853984i	0.904255	−	0.426992i	$-0.140427\pi$
$858$	−17.3205	−	5.00000i	−0.591312	−	0.170697i
$859$	50.0000			1.70598			0.852989	−	0.521929i	$-0.174787\pi$
$859$	50.0000			1.70598			0.852989	+	0.521929i	$0.174787\pi$
$860$		0			0
$861$	2.00000	+	3.46410i	0.0681598	+	0.118056i
$862$	34.6410	+	20.0000i	1.17988	+	0.681203i
$863$		−	39.0000i		−	1.32758i	−0.747921	−	0.663788i	$-0.768948\pi$
$863$		−	39.0000i		−	1.32758i	0.747921	−	0.663788i	$-0.231052\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	−28.0000			−0.951479
$867$	−11.2583	−	6.50000i	−0.382353	−	0.220752i
$868$	−19.0526	+	11.0000i	−0.646686	+	0.373364i
$869$	27.5000	+	47.6314i	0.932874	+	1.61578i
$870$		0			0
$871$	56.0000	−	13.8564i	1.89749	−	0.469506i
$872$			2.00000i			0.0677285i
$873$	1.73205	−	1.00000i	0.0586210	−	0.0338449i
$874$	−1.00000	−	1.73205i	−0.0338255	−	0.0585875i
$875$		0			0
$876$	6.00000			0.202721
$877$	16.4545	+	9.50000i	0.555628	+	0.320792i	0.751389	−	0.659860i	$-0.229384\pi$
$877$	16.4545	+	9.50000i	0.555628	+	0.320792i	−0.195761	+	0.980652i	$0.562718\pi$
$878$	3.46410	+	2.00000i	0.116908	+	0.0674967i
$879$	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	$0.735272\pi$
$882$	2.59808	−	1.50000i	0.0874818	−	0.0505076i
$883$			1.00000i			0.0336527i	0.999858	+	0.0168263i	$0.00535624\pi$
$883$			1.00000i			0.0336527i	−0.999858	+	0.0168263i	$0.994644\pi$
$884$	7.00000	−	1.73205i	0.235435	−	0.0582552i
$885$		0			0
$886$	10.0000	+	17.3205i	0.335957	+	0.581894i
$887$	2.59808	−	1.50000i	0.0872349	−	0.0503651i	−0.455748	−	0.890109i	$-0.650628\pi$
$887$	2.59808	−	1.50000i	0.0872349	−	0.0503651i	0.542983	+	0.839744i	$0.317295\pi$
$888$	2.59808	+	1.50000i	0.0871857	+	0.0503367i
$889$	4.00000			0.134156
$890$		0			0
$891$	2.50000	−	4.33013i	0.0837532	−	0.145065i
$892$			26.0000i			0.870544i
$893$	−15.5885	−	9.00000i	−0.521648	−	0.301174i
$894$	8.50000	+	14.7224i	0.284283	+	0.492392i
$895$		0			0
$896$	2.00000			0.0668153
$897$	2.59808	−	2.50000i	0.0867472	−	0.0834726i
$898$			12.0000i			0.400445i
$899$	−27.5000	−	47.6314i	−0.917176	−	1.58860i
$900$		0			0
$901$	6.00000	−	10.3923i	0.199889	−	0.346218i
$902$		−	10.0000i		−	0.332964i
$903$	−19.0526	−	11.0000i	−0.634029	−	0.366057i
$904$	−5.50000	+	9.52628i	−0.182927	+	0.316839i
$905$		0			0
$906$	−4.00000	+	6.92820i	−0.132891	+	0.230174i
$907$	16.4545	−	9.50000i	0.546362	−	0.315442i	−0.201291	−	0.979531i	$-0.564514\pi$
$907$	16.4545	−	9.50000i	0.546362	−	0.315442i	0.747653	+	0.664089i	$0.231180\pi$
$908$		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	$0.596381\pi$
$912$	1.73205	−	1.00000i	0.0573539	−	0.0331133i
$913$	25.9808	−	15.0000i	0.859838	−	0.496428i
$914$	−19.0000	+	32.9090i	−0.628464	+	1.08853i
$915$		0			0
$916$	−5.00000	+	8.66025i	−0.165205	+	0.286143i
$917$	−1.73205	−	1.00000i	−0.0571974	−	0.0330229i
$918$			2.00000i			0.0660098i
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	−0.967274	−	0.253735i	$-0.918341\pi$
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	0.703378	+	0.710816i	$0.251674\pi$
$920$		0			0
$921$		0			0
$922$			39.0000i			1.28440i
$923$		0			0
$924$	10.0000			0.328976
$925$		0			0
$926$	7.00000	+	12.1244i	0.230034	+	0.398431i
$927$	−8.66025	−	5.00000i	−0.284440	−	0.164222i
$928$			5.00000i			0.164133i
$929$	−8.00000	+	13.8564i	−0.262471	+	0.454614i	−0.966898	−	0.255163i	$-0.917871\pi$
$929$	−8.00000	+	13.8564i	−0.262471	+	0.454614i	0.704427	+	0.709777i	$0.251204\pi$
$930$		0			0
$931$	6.00000			0.196642
$932$	−0.866025	−	0.500000i	−0.0283676	−	0.0163780i
$933$	17.3205	−	10.0000i	0.567048	−	0.327385i
$934$	−3.00000	−	5.19615i	−0.0981630	−	0.170023i
$935$		0			0
$936$	2.50000	+	2.59808i	0.0817151	+	0.0849208i
$937$		−	50.0000i		−	1.63343i	−0.577042	−	0.816714i	$-0.695793\pi$
$937$		−	50.0000i		−	1.63343i	0.577042	−	0.816714i	$-0.304207\pi$
$938$	−27.7128	+	16.0000i	−0.904855	+	0.522419i
$939$	−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	$0.803250\pi$
$942$	6.06218	+	3.50000i	0.197516	+	0.114036i
$943$	1.73205	+	1.00000i	0.0564033	+	0.0325645i
$944$	15.0000			0.488208
$945$		0			0
$946$	27.5000	+	47.6314i	0.894102	+	1.54863i
$947$	6.92820	−	4.00000i	0.225136	−	0.129983i	−0.383190	−	0.923670i	$-0.625175\pi$
$947$	6.92820	−	4.00000i	0.225136	−	0.129983i	0.608326	+	0.793687i	$0.291841\pi$
$948$		−	11.0000i		−	0.357263i
$949$	−6.00000	+	20.7846i	−0.194768	+	0.674697i
$950$		0			0
$951$	8.00000	+	13.8564i	0.259418	+	0.449325i
$952$	−3.46410	+	2.00000i	−0.112272	+	0.0648204i
$953$	−44.1673	−	25.5000i	−1.43072	−	0.826026i	−0.433544	−	0.901133i	$-0.642737\pi$
$953$	−44.1673	−	25.5000i	−1.43072	−	0.826026i	−0.997176	+	0.0751066i	$0.976070\pi$
$954$	6.00000			0.194257
$955$		0			0
$956$	10.0000	−	17.3205i	0.323423	−	0.560185i
$957$			25.0000i			0.808135i
$958$	20.7846	+	12.0000i	0.671520	+	0.387702i
$959$	11.0000	+	19.0526i	0.355209	+	0.615239i
$960$		0			0
$961$	90.0000			2.90323
$962$	−7.79423	+	7.50000i	−0.251296	+	0.241810i
$963$		−	10.0000i		−	0.322245i
$964$	−3.50000	−	6.06218i	−0.112727	−	0.195250i
$965$		0			0
$966$	−1.00000	+	1.73205i	−0.0321745	+	0.0557278i
$967$			20.0000i			0.643157i	0.946883	+	0.321578i	$0.104213\pi$
$967$			20.0000i			0.643157i	−0.946883	+	0.321578i	$0.895787\pi$
$968$	−12.1244	−	7.00000i	−0.389692	−	0.224989i
$969$	−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	$0.886825\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	3.46410	−	2.00000i	0.111054	−	0.0641171i
$974$	2.00000			0.0640841
$975$		0			0
$976$	10.0000			0.320092
$977$	−18.1865	+	10.5000i	−0.581839	+	0.335925i	−0.761864	−	0.647737i	$-0.775715\pi$
$977$	−18.1865	+	10.5000i	−0.581839	+	0.335925i	0.180025	+	0.983662i	$0.442382\pi$
$978$	12.9904	−	7.50000i	0.415387	−	0.239824i
$979$	−5.00000	+	8.66025i	−0.159801	+	0.276783i
$980$		0			0
$981$	1.00000	−	1.73205i	0.0319275	−	0.0553001i
$982$	−13.8564	−	8.00000i	−0.442176	−	0.255290i
$983$			3.00000i			0.0956851i	0.998855	+	0.0478426i	$0.0152346\pi$
$983$			3.00000i			0.0956851i	−0.998855	+	0.0478426i	$0.984765\pi$
$984$	−1.00000	+	1.73205i	−0.0318788	+	0.0552158i
$985$		0			0
$986$	−5.00000	−	8.66025i	−0.159232	−	0.275799i
$987$			18.0000i			0.572946i
$988$	1.73205	+	7.00000i	0.0551039	+	0.222700i
$989$	−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	$0.746306\pi$
$992$	−9.52628	−	5.50000i	−0.302460	−	0.174625i
$993$		−	28.0000i		−	0.888553i
$994$		0			0
$995$		0			0
$996$	−6.00000			−0.190117
$997$	1.73205	+	1.00000i	0.0548546	+	0.0316703i	0.527176	−	0.849756i	$-0.323251\pi$
$997$	1.73205	+	1.00000i	0.0548546	+	0.0316703i	−0.472322	+	0.881426i	$0.656584\pi$
$998$	24.2487	−	14.0000i	0.767580	−	0.443162i
$999$	−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.z.e.1849.1		4
5.2	odd	4		1950.2.i.d.601.1		2
5.3	odd	4		390.2.i.f.211.1	yes	2
5.4	even	2	inner	1950.2.z.e.1849.2		4
13.9	even	3	inner	1950.2.z.e.1699.2		4
15.8	even	4		1170.2.i.a.991.1		2
65.3	odd	12		5070.2.a.d.1.1		1
65.9	even	6	inner	1950.2.z.e.1699.1		4
65.22	odd	12		1950.2.i.d.451.1		2
65.23	odd	12		5070.2.a.p.1.1		1
65.28	even	12		5070.2.b.h.1351.2		2
65.48	odd	12		390.2.i.f.61.1	✓	2
65.63	even	12		5070.2.b.h.1351.1		2
195.113	even	12		1170.2.i.a.451.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.f.61.1	✓	2	65.48	odd	12
390.2.i.f.211.1	yes	2	5.3	odd	4
1170.2.i.a.451.1		2	195.113	even	12
1170.2.i.a.991.1		2	15.8	even	4
1950.2.i.d.451.1		2	65.22	odd	12
1950.2.i.d.601.1		2	5.2	odd	4
1950.2.z.e.1699.1		4	65.9	even	6	inner
1950.2.z.e.1699.2		4	13.9	even	3	inner
1950.2.z.e.1849.1		4	1.1	even	1	trivial
1950.2.z.e.1849.2		4	5.4	even	2	inner
5070.2.a.d.1.1		1	65.3	odd	12
5070.2.a.p.1.1		1	65.23	odd	12
5070.2.b.h.1351.1		2	65.63	even	12
5070.2.b.h.1351.2		2	65.28	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.z (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.50000 + 4.33013i) q^{11} -1.00000i q^{12} +(3.46410 + 1.00000i) q^{13} -2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +1.00000i q^{18} +(-1.00000 + 1.73205i) q^{19} +2.00000 q^{21} +(-4.33013 - 2.50000i) q^{22} +(0.866025 - 0.500000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.50000 + 0.866025i) q^{26} -1.00000i q^{27} +(1.73205 - 1.00000i) q^{28} +(2.50000 + 4.33013i) q^{29} -11.0000 q^{31} +(0.866025 + 0.500000i) q^{32} +(4.33013 + 2.50000i) q^{33} -2.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(2.59808 - 1.50000i) q^{37} -2.00000i q^{38} +(3.50000 - 0.866025i) q^{39} +(1.00000 + 1.73205i) q^{41} +(-1.73205 + 1.00000i) q^{42} +(-9.52628 - 5.50000i) q^{43} +5.00000 q^{44} +(-0.500000 + 0.866025i) q^{46} +9.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-1.50000 - 2.59808i) q^{49} +2.00000 q^{51} +(2.59808 - 2.50000i) q^{52} -6.00000i q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.00000 + 1.73205i) q^{56} +2.00000i q^{57} +(-4.33013 - 2.50000i) q^{58} +(-7.50000 + 12.9904i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(9.52628 - 5.50000i) q^{62} +(1.73205 - 1.00000i) q^{63} -1.00000 q^{64} -5.00000 q^{66} +(13.8564 - 8.00000i) q^{67} +(1.73205 - 1.00000i) q^{68} +(0.500000 - 0.866025i) q^{69} +(0.866025 + 0.500000i) q^{72} +6.00000i q^{73} +(-1.50000 + 2.59808i) q^{74} +(1.00000 + 1.73205i) q^{76} +10.0000i q^{77} +(-2.59808 + 2.50000i) q^{78} +11.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.73205 - 1.00000i) q^{82} -6.00000i q^{83} +(1.00000 - 1.73205i) q^{84} +11.0000 q^{86} +(4.33013 + 2.50000i) q^{87} +(-4.33013 + 2.50000i) q^{88} +(1.00000 + 1.73205i) q^{89} +(5.00000 + 5.19615i) q^{91} -1.00000i q^{92} +(-9.52628 + 5.50000i) q^{93} +(-4.50000 - 7.79423i) q^{94} +1.00000 q^{96} +(1.73205 + 1.00000i) q^{97} +(2.59808 + 1.50000i) q^{98} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9} + 10 q^{11} - 8 q^{14} - 2 q^{16} - 4 q^{19} + 8 q^{21} + 2 q^{24} - 14 q^{26} + 10 q^{29} - 44 q^{31} - 8 q^{34} - 2 q^{36} + 14 q^{39} + 4 q^{41} + 20 q^{44} - 2 q^{46} - 6 q^{49} + 8 q^{51} + 2 q^{54} - 4 q^{56} - 30 q^{59} - 20 q^{61} - 4 q^{64} - 20 q^{66} + 2 q^{69} - 6 q^{74} + 4 q^{76} + 44 q^{79} - 2 q^{81} + 4 q^{84} + 44 q^{86} + 4 q^{89} + 20 q^{91} - 18 q^{94} + 4 q^{96} + 20 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9 + 10 * q^11 - 8 * q^14 - 2 * q^16 - 4 * q^19 + 8 * q^21 + 2 * q^24 - 14 * q^26 + 10 * q^29 - 44 * q^31 - 8 * q^34 - 2 * q^36 + 14 * q^39 + 4 * q^41 + 20 * q^44 - 2 * q^46 - 6 * q^49 + 8 * q^51 + 2 * q^54 - 4 * q^56 - 30 * q^59 - 20 * q^61 - 4 * q^64 - 20 * q^66 + 2 * q^69 - 6 * q^74 + 4 * q^76 + 44 * q^79 - 2 * q^81 + 4 * q^84 + 44 * q^86 + 4 * q^89 + 20 * q^91 - 18 * q^94 + 4 * q^96 + 20 * q^99

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