LMFDB - Embedded newform 1183.2.e.e.170.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.e.508.1

$q$-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 + 1.50000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 1.50000i) q^{5} -1.73205 q^{6} +(-2.59808 - 0.500000i) q^{7} -1.73205 q^{8} +(1.00000 - 1.73205i) q^{9} +(1.50000 + 2.59808i) q^{10} +(2.59808 + 4.50000i) q^{11} +(0.500000 - 0.866025i) q^{12} +(3.00000 - 3.46410i) q^{14} +1.73205 q^{15} +(2.50000 - 4.33013i) q^{16} +(3.00000 + 5.19615i) q^{17} +(1.73205 + 3.00000i) q^{18} +(0.866025 - 1.50000i) q^{19} -1.73205 q^{20} +(-0.866025 - 2.50000i) q^{21} -9.00000 q^{22} +(-0.866025 - 1.50000i) q^{24} +(1.00000 + 1.73205i) q^{25} +5.00000 q^{27} +(0.866025 + 2.50000i) q^{28} +3.00000 q^{29} +(-1.50000 + 2.59808i) q^{30} +(0.866025 + 1.50000i) q^{31} +(2.59808 + 4.50000i) q^{32} +(-2.59808 + 4.50000i) q^{33} -10.3923 q^{34} +(-3.00000 + 3.46410i) q^{35} -2.00000 q^{36} +(1.50000 + 2.59808i) q^{38} +(-1.50000 + 2.59808i) q^{40} -5.19615 q^{41} +(4.50000 + 0.866025i) q^{42} -11.0000 q^{43} +(2.59808 - 4.50000i) q^{44} +(-1.73205 - 3.00000i) q^{45} +(-4.33013 + 7.50000i) q^{47} +5.00000 q^{48} +(6.50000 + 2.59808i) q^{49} -3.46410 q^{50} +(-3.00000 + 5.19615i) q^{51} +(4.50000 + 7.79423i) q^{53} +(-4.33013 + 7.50000i) q^{54} +9.00000 q^{55} +(4.50000 + 0.866025i) q^{56} +1.73205 q^{57} +(-2.59808 + 4.50000i) q^{58} +(-1.73205 - 3.00000i) q^{59} +(-0.866025 - 1.50000i) q^{60} +(-3.50000 + 6.06218i) q^{61} -3.00000 q^{62} +(-3.46410 + 4.00000i) q^{63} +1.00000 q^{64} +(-4.50000 - 7.79423i) q^{66} +(4.33013 + 7.50000i) q^{67} +(3.00000 - 5.19615i) q^{68} +(-2.59808 - 7.50000i) q^{70} -1.73205 q^{71} +(-1.73205 + 3.00000i) q^{72} +(4.33013 + 7.50000i) q^{73} +(-1.00000 + 1.73205i) q^{75} -1.73205 q^{76} +(-4.50000 - 12.9904i) q^{77} +(2.50000 - 4.33013i) q^{79} +(-4.33013 - 7.50000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} +3.46410 q^{83} +(-1.73205 + 2.00000i) q^{84} +10.3923 q^{85} +(9.52628 - 16.5000i) q^{86} +(1.50000 + 2.59808i) q^{87} +(-4.50000 - 7.79423i) q^{88} +(3.46410 - 6.00000i) q^{89} +6.00000 q^{90} +(-0.866025 + 1.50000i) q^{93} +(-7.50000 - 12.9904i) q^{94} +(-1.50000 - 2.59808i) q^{95} +(-2.59808 + 4.50000i) q^{96} +5.19615 q^{97} +(-9.52628 + 7.50000i) q^{98} +10.3923 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 2 q^{4} + 4 q^{9} + 6 q^{10} + 2 q^{12} + 12 q^{14} + 10 q^{16} + 12 q^{17} - 36 q^{22} + 4 q^{25} + 20 q^{27} + 12 q^{29} - 6 q^{30} - 12 q^{35} - 8 q^{36} + 6 q^{38} - 6 q^{40} + 18 q^{42}+ \cdots - 6 q^{95}+O(q^{100}) $ 4 * q + 2 * q^3 - 2 * q^4 + 4 * q^9 + 6 * q^10 + 2 * q^12 + 12 * q^14 + 10 * q^16 + 12 * q^17 - 36 * q^22 + 4 * q^25 + 20 * q^27 + 12 * q^29 - 6 * q^30 - 12 * q^35 - 8 * q^36 + 6 * q^38 - 6 * q^40 + 18 * q^42 - 44 * q^43 + 20 * q^48 + 26 * q^49 - 12 * q^51 + 18 * q^53 + 36 * q^55 + 18 * q^56 - 14 * q^61 - 12 * q^62 + 4 * q^64 - 18 * q^66 + 12 * q^68 - 4 * q^75 - 18 * q^77 + 10 * q^79 - 2 * q^81 + 18 * q^82 + 6 * q^87 - 18 * q^88 + 24 * q^90 - 30 * q^94 - 6 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	+	1.50000i	−0.612372	+	1.06066i	0.378467	+	0.925615i	$0.376451\pi$
$2$	−0.866025	+	1.50000i	−0.612372	+	1.06066i	−0.990839	+	0.135045i	$0.956882\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.866025	−	1.50000i	0.387298	−	0.670820i	−0.604787	−	0.796387i	$-0.706742\pi$
$5$	0.866025	−	1.50000i	0.387298	−	0.670820i	0.992085	+	0.125567i	$0.0400750\pi$
$6$	−1.73205			−0.707107
$7$	−2.59808	−	0.500000i	−0.981981	−	0.188982i
$7$	−2.59808	−	0.500000i	−0.981981	−	0.188982i
$8$	−1.73205			−0.612372
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	2.59808	+	4.50000i	0.783349	+	1.35680i	0.929980	+	0.367610i	$0.119824\pi$
$11$	2.59808	+	4.50000i	0.783349	+	1.35680i	−0.146631	+	0.989191i	$0.546843\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$		0			0
$13$		0			0
$14$	3.00000	−	3.46410i	0.801784	−	0.925820i
$15$	1.73205			0.447214
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$	1.73205	+	3.00000i	0.408248	+	0.707107i
$19$	0.866025	−	1.50000i	0.198680	−	0.344124i	−0.749421	−	0.662094i	$-0.769668\pi$
$19$	0.866025	−	1.50000i	0.198680	−	0.344124i	0.948101	+	0.317970i	$0.103001\pi$
$20$	−1.73205			−0.387298
$21$	−0.866025	−	2.50000i	−0.188982	−	0.545545i
$22$	−9.00000			−1.91881
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−0.866025	−	1.50000i	−0.176777	−	0.306186i
$25$	1.00000	+	1.73205i	0.200000	+	0.346410i
$26$		0			0
$27$	5.00000			0.962250
$28$	0.866025	+	2.50000i	0.163663	+	0.472456i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$	−1.50000	+	2.59808i	−0.273861	+	0.474342i
$31$	0.866025	+	1.50000i	0.155543	+	0.269408i	0.933257	−	0.359211i	$-0.116954\pi$
$31$	0.866025	+	1.50000i	0.155543	+	0.269408i	−0.777714	+	0.628619i	$0.783621\pi$
$32$	2.59808	+	4.50000i	0.459279	+	0.795495i
$33$	−2.59808	+	4.50000i	−0.452267	+	0.783349i
$34$	−10.3923			−1.78227
$35$	−3.00000	+	3.46410i	−0.507093	+	0.585540i
$36$	−2.00000			−0.333333
$37$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$37$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$38$	1.50000	+	2.59808i	0.243332	+	0.421464i
$39$		0			0
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$	−5.19615			−0.811503			−0.405751	−	0.913984i	$-0.632990\pi$
$41$	−5.19615			−0.811503			−0.405751	+	0.913984i	$0.632990\pi$
$42$	4.50000	+	0.866025i	0.694365	+	0.133631i
$43$	−11.0000			−1.67748			−0.838742	−	0.544529i	$-0.816708\pi$
$43$	−11.0000			−1.67748			−0.838742	+	0.544529i	$0.816708\pi$
$44$	2.59808	−	4.50000i	0.391675	−	0.678401i
$45$	−1.73205	−	3.00000i	−0.258199	−	0.447214i
$46$		0			0
$47$	−4.33013	+	7.50000i	−0.631614	+	1.09399i	0.355608	+	0.934635i	$0.384274\pi$
$47$	−4.33013	+	7.50000i	−0.631614	+	1.09399i	−0.987222	+	0.159352i	$0.949059\pi$
$48$	5.00000			0.721688
$49$	6.50000	+	2.59808i	0.928571	+	0.371154i
$50$	−3.46410			−0.489898
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$		0			0
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	0.989828	+	0.142269i	$0.0454398\pi$
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	−0.371706	+	0.928351i	$0.621227\pi$
$54$	−4.33013	+	7.50000i	−0.589256	+	1.02062i
$55$	9.00000			1.21356
$56$	4.50000	+	0.866025i	0.601338	+	0.115728i
$57$	1.73205			0.229416
$58$	−2.59808	+	4.50000i	−0.341144	+	0.590879i
$59$	−1.73205	−	3.00000i	−0.225494	−	0.390567i	0.730974	−	0.682406i	$-0.239066\pi$
$59$	−1.73205	−	3.00000i	−0.225494	−	0.390567i	−0.956467	+	0.291839i	$0.905733\pi$
$60$	−0.866025	−	1.50000i	−0.111803	−	0.193649i
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$	−3.00000			−0.381000
$63$	−3.46410	+	4.00000i	−0.436436	+	0.503953i
$64$	1.00000			0.125000
$65$		0			0
$66$	−4.50000	−	7.79423i	−0.553912	−	0.959403i
$67$	4.33013	+	7.50000i	0.529009	+	0.916271i	0.999428	+	0.0338274i	$0.0107696\pi$
$67$	4.33013	+	7.50000i	0.529009	+	0.916271i	−0.470418	+	0.882443i	$0.655897\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$		0			0
$70$	−2.59808	−	7.50000i	−0.310530	−	0.896421i
$71$	−1.73205			−0.205557			−0.102778	−	0.994704i	$-0.532773\pi$
$71$	−1.73205			−0.205557			−0.102778	+	0.994704i	$0.532773\pi$
$72$	−1.73205	+	3.00000i	−0.204124	+	0.353553i
$73$	4.33013	+	7.50000i	0.506803	+	0.877809i	0.999969	+	0.00787336i	$0.00250619\pi$
$73$	4.33013	+	7.50000i	0.506803	+	0.877809i	−0.493166	+	0.869935i	$0.664160\pi$
$74$		0			0
$75$	−1.00000	+	1.73205i	−0.115470	+	0.200000i
$76$	−1.73205			−0.198680
$77$	−4.50000	−	12.9904i	−0.512823	−	1.48039i
$78$		0			0
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	−0.690426	−	0.723403i	$-0.742577\pi$
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	0.971698	+	0.236225i	$0.0759104\pi$
$80$	−4.33013	−	7.50000i	−0.484123	−	0.838525i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.50000	−	7.79423i	0.496942	−	0.860729i
$83$	3.46410			0.380235			0.190117	−	0.981761i	$-0.439113\pi$
$83$	3.46410			0.380235			0.190117	+	0.981761i	$0.439113\pi$
$84$	−1.73205	+	2.00000i	−0.188982	+	0.218218i
$85$	10.3923			1.12720
$86$	9.52628	−	16.5000i	1.02725	−	1.77924i
$87$	1.50000	+	2.59808i	0.160817	+	0.278543i
$88$	−4.50000	−	7.79423i	−0.479702	−	0.830868i
$89$	3.46410	−	6.00000i	0.367194	−	0.635999i	−0.621932	−	0.783072i	$-0.713652\pi$
$89$	3.46410	−	6.00000i	0.367194	−	0.635999i	0.989126	+	0.147073i	$0.0469852\pi$
$90$	6.00000			0.632456
$91$		0			0
$92$		0			0
$93$	−0.866025	+	1.50000i	−0.0898027	+	0.155543i
$94$	−7.50000	−	12.9904i	−0.773566	−	1.33986i
$95$	−1.50000	−	2.59808i	−0.153897	−	0.266557i
$96$	−2.59808	+	4.50000i	−0.265165	+	0.459279i
$97$	5.19615			0.527589			0.263795	−	0.964579i	$-0.415026\pi$
$97$	5.19615			0.527589			0.263795	+	0.964579i	$0.415026\pi$
$98$	−9.52628	+	7.50000i	−0.962300	+	0.757614i
$99$	10.3923			1.04447
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$	−5.19615	−	9.00000i	−0.514496	−	0.891133i
$103$	−6.50000	+	11.2583i	−0.640464	+	1.10932i	0.344865	+	0.938652i	$0.387925\pi$
$103$	−6.50000	+	11.2583i	−0.640464	+	1.10932i	−0.985329	+	0.170664i	$0.945409\pi$
$104$		0			0
$105$	−4.50000	−	0.866025i	−0.439155	−	0.0845154i
$106$	−15.5885			−1.51408
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$	−2.50000	−	4.33013i	−0.240563	−	0.416667i
$109$	2.59808	+	4.50000i	0.248851	+	0.431022i	0.963207	−	0.268760i	$-0.0866139\pi$
$109$	2.59808	+	4.50000i	0.248851	+	0.431022i	−0.714357	+	0.699782i	$0.753281\pi$
$110$	−7.79423	+	13.5000i	−0.743151	+	1.28717i
$111$		0			0
$112$	−8.66025	+	10.0000i	−0.818317	+	0.944911i
$113$	15.0000			1.41108			0.705541	−	0.708669i	$-0.250704\pi$
$113$	15.0000			1.41108			0.705541	+	0.708669i	$0.250704\pi$
$114$	−1.50000	+	2.59808i	−0.140488	+	0.243332i
$115$		0			0
$116$	−1.50000	−	2.59808i	−0.139272	−	0.241225i
$117$		0			0
$118$	6.00000			0.552345
$119$	−5.19615	−	15.0000i	−0.476331	−	1.37505i
$120$	−3.00000			−0.273861
$121$	−8.00000	+	13.8564i	−0.727273	+	1.25967i
$122$	−6.06218	−	10.5000i	−0.548844	−	0.950625i
$123$	−2.59808	−	4.50000i	−0.234261	−	0.405751i
$124$	0.866025	−	1.50000i	0.0777714	−	0.134704i
$125$	12.1244			1.08444
$126$	−3.00000	−	8.66025i	−0.267261	−	0.771517i
$127$	−13.0000			−1.15356			−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000			−1.15356			−0.576782	+	0.816898i	$0.695692\pi$
$128$	−6.06218	+	10.5000i	−0.535826	+	0.928078i
$129$	−5.50000	−	9.52628i	−0.484248	−	0.838742i
$130$		0			0
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	0.326546	+	0.945181i	$0.394115\pi$
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	−0.981824	+	0.189794i	$0.939218\pi$
$132$	5.19615			0.452267
$133$	−3.00000	+	3.46410i	−0.260133	+	0.300376i
$134$	−15.0000			−1.29580
$135$	4.33013	−	7.50000i	0.372678	−	0.645497i
$136$	−5.19615	−	9.00000i	−0.445566	−	0.771744i
$137$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$137$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$138$		0			0
$139$	−13.0000			−1.10265			−0.551323	−	0.834292i	$-0.685877\pi$
$139$	−13.0000			−1.10265			−0.551323	+	0.834292i	$0.685877\pi$
$140$	4.50000	+	0.866025i	0.380319	+	0.0731925i
$141$	−8.66025			−0.729325
$142$	1.50000	−	2.59808i	0.125877	−	0.218026i
$143$		0			0
$144$	−5.00000	−	8.66025i	−0.416667	−	0.721688i
$145$	2.59808	−	4.50000i	0.215758	−	0.373705i
$146$	−15.0000			−1.24141
$147$	1.00000	+	6.92820i	0.0824786	+	0.571429i
$148$		0			0
$149$	9.52628	−	16.5000i	0.780423	−	1.35173i	−0.151272	−	0.988492i	$-0.548337\pi$
$149$	9.52628	−	16.5000i	0.780423	−	1.35173i	0.931695	−	0.363241i	$-0.118330\pi$
$150$	−1.73205	−	3.00000i	−0.141421	−	0.244949i
$151$	6.06218	+	10.5000i	0.493333	+	0.854478i	0.999970	−	0.00768132i	$-0.00244506\pi$
$151$	6.06218	+	10.5000i	0.493333	+	0.854478i	−0.506637	+	0.862159i	$0.669112\pi$
$152$	−1.50000	+	2.59808i	−0.121666	+	0.210732i
$153$	12.0000			0.970143
$154$	23.3827	+	4.50000i	1.88423	+	0.362620i
$155$	3.00000			0.240966
$156$		0			0
$157$	−11.5000	−	19.9186i	−0.917800	−	1.58968i	−0.802749	−	0.596316i	$-0.796630\pi$
$157$	−11.5000	−	19.9186i	−0.917800	−	1.58968i	−0.115050	−	0.993360i	$-0.536703\pi$
$158$	4.33013	+	7.50000i	0.344486	+	0.596668i
$159$	−4.50000	+	7.79423i	−0.356873	+	0.618123i
$160$	9.00000			0.711512
$161$		0			0
$162$	1.73205			0.136083
$163$	6.06218	−	10.5000i	0.474826	−	0.822423i	−0.524758	−	0.851251i	$-0.675844\pi$
$163$	6.06218	−	10.5000i	0.474826	−	0.822423i	0.999584	+	0.0288280i	$0.00917751\pi$
$164$	2.59808	+	4.50000i	0.202876	+	0.351391i
$165$	4.50000	+	7.79423i	0.350325	+	0.606780i
$166$	−3.00000	+	5.19615i	−0.232845	+	0.403300i
$167$	1.73205			0.134030			0.0670151	−	0.997752i	$-0.478652\pi$
$167$	1.73205			0.134030			0.0670151	+	0.997752i	$0.478652\pi$
$168$	1.50000	+	4.33013i	0.115728	+	0.334077i
$169$		0			0
$170$	−9.00000	+	15.5885i	−0.690268	+	1.19558i
$171$	−1.73205	−	3.00000i	−0.132453	−	0.229416i
$172$	5.50000	+	9.52628i	0.419371	+	0.726372i
$173$	7.50000	−	12.9904i	0.570214	−	0.987640i	−0.426329	−	0.904568i	$-0.640193\pi$
$173$	7.50000	−	12.9904i	0.570214	−	0.987640i	0.996544	−	0.0830722i	$-0.0264732\pi$
$174$	−5.19615			−0.393919
$175$	−1.73205	−	5.00000i	−0.130931	−	0.377964i
$176$	25.9808			1.95837
$177$	1.73205	−	3.00000i	0.130189	−	0.225494i
$178$	6.00000	+	10.3923i	0.449719	+	0.778936i
$179$	1.50000	+	2.59808i	0.112115	+	0.194189i	0.916623	−	0.399753i	$-0.130904\pi$
$179$	1.50000	+	2.59808i	0.112115	+	0.194189i	−0.804508	+	0.593942i	$0.797571\pi$
$180$	−1.73205	+	3.00000i	−0.129099	+	0.223607i
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	−7.00000			−0.517455
$184$		0			0
$185$		0			0
$186$	−1.50000	−	2.59808i	−0.109985	−	0.190500i
$187$	−15.5885	+	27.0000i	−1.13994	+	1.97444i
$188$	8.66025			0.631614
$189$	−12.9904	−	2.50000i	−0.944911	−	0.181848i
$190$	5.19615			0.376969
$191$	7.50000	−	12.9904i	0.542681	−	0.939951i	−0.456068	−	0.889945i	$-0.650743\pi$
$191$	7.50000	−	12.9904i	0.542681	−	0.939951i	0.998749	−	0.0500060i	$-0.0159241\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−0.866025	−	1.50000i	−0.0623379	−	0.107972i	0.833172	−	0.553014i	$-0.186522\pi$
$193$	−0.866025	−	1.50000i	−0.0623379	−	0.107972i	−0.895510	+	0.445041i	$0.853189\pi$
$194$	−4.50000	+	7.79423i	−0.323081	+	0.559593i
$195$		0			0
$196$	−1.00000	−	6.92820i	−0.0714286	−	0.494872i
$197$	22.5167			1.60425			0.802123	−	0.597159i	$-0.203704\pi$
$197$	22.5167			1.60425			0.802123	+	0.597159i	$0.203704\pi$
$198$	−9.00000	+	15.5885i	−0.639602	+	1.10782i
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	0.928166	−	0.372168i	$-0.121385\pi$
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	−0.786389	+	0.617731i	$0.788052\pi$
$200$	−1.73205	−	3.00000i	−0.122474	−	0.212132i
$201$	−4.33013	+	7.50000i	−0.305424	+	0.529009i
$202$	15.5885			1.09680
$203$	−7.79423	−	1.50000i	−0.547048	−	0.105279i
$204$	6.00000			0.420084
$205$	−4.50000	+	7.79423i	−0.314294	+	0.544373i
$206$	−11.2583	−	19.5000i	−0.784405	−	1.35863i
$207$		0			0
$208$		0			0
$209$	9.00000			0.622543
$210$	5.19615	−	6.00000i	0.358569	−	0.414039i
$211$	13.0000			0.894957			0.447478	−	0.894295i	$-0.352322\pi$
$211$	13.0000			0.894957			0.447478	+	0.894295i	$0.352322\pi$
$212$	4.50000	−	7.79423i	0.309061	−	0.535310i
$213$	−0.866025	−	1.50000i	−0.0593391	−	0.102778i
$214$		0			0
$215$	−9.52628	+	16.5000i	−0.649687	+	1.12529i
$216$	−8.66025			−0.589256
$217$	−1.50000	−	4.33013i	−0.101827	−	0.293948i
$218$	−9.00000			−0.609557
$219$	−4.33013	+	7.50000i	−0.292603	+	0.506803i
$220$	−4.50000	−	7.79423i	−0.303390	−	0.525487i
$221$		0			0
$222$		0			0
$223$	5.19615			0.347960			0.173980	−	0.984749i	$-0.444337\pi$
$223$	5.19615			0.347960			0.173980	+	0.984749i	$0.444337\pi$
$224$	−4.50000	−	12.9904i	−0.300669	−	0.867956i
$225$	4.00000			0.266667
$226$	−12.9904	+	22.5000i	−0.864107	+	1.49668i
$227$	8.66025	+	15.0000i	0.574801	+	0.995585i	0.996063	+	0.0886460i	$0.0282540\pi$
$227$	8.66025	+	15.0000i	0.574801	+	0.995585i	−0.421262	+	0.906939i	$0.638413\pi$
$228$	−0.866025	−	1.50000i	−0.0573539	−	0.0993399i
$229$	6.06218	−	10.5000i	0.400600	−	0.693860i	−0.593198	−	0.805056i	$-0.702135\pi$
$229$	6.06218	−	10.5000i	0.400600	−	0.693860i	0.993798	+	0.111197i	$0.0354684\pi$
$230$		0			0
$231$	9.00000	−	10.3923i	0.592157	−	0.683763i
$232$	−5.19615			−0.341144
$233$	1.50000	−	2.59808i	0.0982683	−	0.170206i	−0.812700	−	0.582683i	$-0.802003\pi$
$233$	1.50000	−	2.59808i	0.0982683	−	0.170206i	0.910968	+	0.412477i	$0.135336\pi$
$234$		0			0
$235$	7.50000	+	12.9904i	0.489246	+	0.847399i
$236$	−1.73205	+	3.00000i	−0.112747	+	0.195283i
$237$	5.00000			0.324785
$238$	27.0000	+	5.19615i	1.75015	+	0.336817i
$239$	10.3923			0.672222			0.336111	−	0.941822i	$-0.390888\pi$
$239$	10.3923			0.672222			0.336111	+	0.941822i	$0.390888\pi$
$240$	4.33013	−	7.50000i	0.279508	−	0.484123i
$241$	−3.46410	−	6.00000i	−0.223142	−	0.386494i	0.732618	−	0.680640i	$-0.238298\pi$
$241$	−3.46410	−	6.00000i	−0.223142	−	0.386494i	−0.955761	+	0.294146i	$0.904965\pi$
$242$	−13.8564	−	24.0000i	−0.890724	−	1.54278i
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$	7.00000			0.448129
$245$	9.52628	−	7.50000i	0.608612	−	0.479157i
$246$	9.00000			0.573819
$247$		0			0
$248$	−1.50000	−	2.59808i	−0.0952501	−	0.164978i
$249$	1.73205	+	3.00000i	0.109764	+	0.190117i
$250$	−10.5000	+	18.1865i	−0.664078	+	1.15022i
$251$	−3.00000			−0.189358			−0.0946792	−	0.995508i	$-0.530183\pi$
$251$	−3.00000			−0.189358			−0.0946792	+	0.995508i	$0.530183\pi$
$252$	5.19615	+	1.00000i	0.327327	+	0.0629941i
$253$		0			0
$254$	11.2583	−	19.5000i	0.706410	−	1.22354i
$255$	5.19615	+	9.00000i	0.325396	+	0.563602i
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	15.0000	−	25.9808i	0.935674	−	1.62064i	0.162247	−	0.986750i	$-0.448126\pi$
$257$	15.0000	−	25.9808i	0.935674	−	1.62064i	0.773427	−	0.633885i	$-0.218541\pi$
$258$	19.0526			1.18616
$259$		0			0
$260$		0			0
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$	−12.9904	−	22.5000i	−0.802548	−	1.39005i
$263$	−1.50000	−	2.59808i	−0.0924940	−	0.160204i	0.816066	−	0.577959i	$-0.196151\pi$
$263$	−1.50000	−	2.59808i	−0.0924940	−	0.160204i	−0.908560	+	0.417755i	$0.862817\pi$
$264$	4.50000	−	7.79423i	0.276956	−	0.479702i
$265$	15.5885			0.957591
$266$	−2.59808	−	7.50000i	−0.159298	−	0.459855i
$267$	6.92820			0.423999
$268$	4.33013	−	7.50000i	0.264505	−	0.458135i
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	0.942871	−	0.333157i	$-0.108114\pi$
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	−0.759958	+	0.649972i	$0.774781\pi$
$270$	7.50000	+	12.9904i	0.456435	+	0.790569i
$271$	8.66025	−	15.0000i	0.526073	−	0.911185i	−0.473466	−	0.880812i	$-0.656997\pi$
$271$	8.66025	−	15.0000i	0.526073	−	0.911185i	0.999539	−	0.0303728i	$-0.00966946\pi$
$272$	30.0000			1.81902
$273$		0			0
$274$		0			0
$275$	−5.19615	+	9.00000i	−0.313340	+	0.542720i
$276$		0			0
$277$	−5.00000	−	8.66025i	−0.300421	−	0.520344i	0.675810	−	0.737075i	$-0.263794\pi$
$277$	−5.00000	−	8.66025i	−0.300421	−	0.520344i	−0.976231	+	0.216731i	$0.930460\pi$
$278$	11.2583	−	19.5000i	0.675230	−	1.16953i
$279$	3.46410			0.207390
$280$	5.19615	−	6.00000i	0.310530	−	0.358569i
$281$	6.92820			0.413302			0.206651	−	0.978415i	$-0.433744\pi$
$281$	6.92820			0.413302			0.206651	+	0.978415i	$0.433744\pi$
$282$	7.50000	−	12.9904i	0.446619	−	0.773566i
$283$	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	$0.642319\pi$
$284$	0.866025	+	1.50000i	0.0513892	+	0.0890086i
$285$	1.50000	−	2.59808i	0.0888523	−	0.153897i
$286$		0			0
$287$	13.5000	+	2.59808i	0.796880	+	0.153360i
$288$	10.3923			0.612372
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	4.50000	+	7.79423i	0.264249	+	0.457693i
$291$	2.59808	+	4.50000i	0.152302	+	0.263795i
$292$	4.33013	−	7.50000i	0.253402	−	0.438904i
$293$	−25.9808			−1.51781			−0.758906	−	0.651200i	$-0.774266\pi$
$293$	−25.9808			−1.51781			−0.758906	+	0.651200i	$0.774266\pi$
$294$	−11.2583	−	4.50000i	−0.656599	−	0.262445i
$295$	−6.00000			−0.349334
$296$		0			0
$297$	12.9904	+	22.5000i	0.753778	+	1.30558i
$298$	16.5000	+	28.5788i	0.955819	+	1.65553i
$299$		0			0
$300$	2.00000			0.115470
$301$	28.5788	+	5.50000i	1.64726	+	0.317015i
$302$	−21.0000			−1.20841
$303$	4.50000	−	7.79423i	0.258518	−	0.447767i
$304$	−4.33013	−	7.50000i	−0.248350	−	0.430155i
$305$	6.06218	+	10.5000i	0.347119	+	0.601228i
$306$	−10.3923	+	18.0000i	−0.594089	+	1.02899i
$307$	−24.2487			−1.38395			−0.691974	−	0.721923i	$-0.743259\pi$
$307$	−24.2487			−1.38395			−0.691974	+	0.721923i	$0.743259\pi$
$308$	−9.00000	+	10.3923i	−0.512823	+	0.592157i
$309$	−13.0000			−0.739544
$310$	−2.59808	+	4.50000i	−0.147561	+	0.255583i
$311$	−7.50000	−	12.9904i	−0.425286	−	0.736617i	0.571161	−	0.820838i	$-0.306493\pi$
$311$	−7.50000	−	12.9904i	−0.425286	−	0.736617i	−0.996447	+	0.0842210i	$0.973160\pi$
$312$		0			0
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	0.462093	+	0.886831i	$0.347098\pi$
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	−0.999065	+	0.0432311i	$0.986235\pi$
$314$	39.8372			2.24814
$315$	3.00000	+	8.66025i	0.169031	+	0.487950i
$316$	−5.00000			−0.281272
$317$	−2.59808	+	4.50000i	−0.145922	+	0.252745i	−0.929717	−	0.368275i	$-0.879948\pi$
$317$	−2.59808	+	4.50000i	−0.145922	+	0.252745i	0.783794	+	0.621021i	$0.213282\pi$
$318$	−7.79423	−	13.5000i	−0.437079	−	0.757042i
$319$	7.79423	+	13.5000i	0.436393	+	0.755855i
$320$	0.866025	−	1.50000i	0.0484123	−	0.0838525i
$321$		0			0
$322$		0			0
$323$	10.3923			0.578243
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	10.5000	+	18.1865i	0.581541	+	1.00726i
$327$	−2.59808	+	4.50000i	−0.143674	+	0.248851i
$328$	9.00000			0.496942
$329$	15.0000	−	17.3205i	0.826977	−	0.954911i
$330$	−15.5885			−0.858116
$331$	−16.4545	+	28.5000i	−0.904420	+	1.56650i	−0.0827265	+	0.996572i	$0.526363\pi$
$331$	−16.4545	+	28.5000i	−0.904420	+	1.56650i	−0.821694	+	0.569929i	$0.806971\pi$
$332$	−1.73205	−	3.00000i	−0.0950586	−	0.164646i
$333$		0			0
$334$	−1.50000	+	2.59808i	−0.0820763	+	0.142160i
$335$	15.0000			0.819538
$336$	−12.9904	−	2.50000i	−0.708683	−	0.136386i
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$		0			0
$339$	7.50000	+	12.9904i	0.407344	+	0.705541i
$340$	−5.19615	−	9.00000i	−0.281801	−	0.488094i
$341$	−4.50000	+	7.79423i	−0.243689	+	0.422081i
$342$	6.00000			0.324443
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$	19.0526			1.02725
$345$		0			0
$346$	12.9904	+	22.5000i	0.698367	+	1.20961i
$347$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$347$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$348$	1.50000	−	2.59808i	0.0804084	−	0.139272i
$349$	5.19615			0.278144			0.139072	−	0.990282i	$-0.455588\pi$
$349$	5.19615			0.278144			0.139072	+	0.990282i	$0.455588\pi$
$350$	9.00000	+	1.73205i	0.481070	+	0.0925820i
$351$		0			0
$352$	−13.5000	+	23.3827i	−0.719552	+	1.24630i
$353$	0.866025	+	1.50000i	0.0460939	+	0.0798369i	0.888152	−	0.459550i	$-0.151989\pi$
$353$	0.866025	+	1.50000i	0.0460939	+	0.0798369i	−0.842058	+	0.539387i	$0.818656\pi$
$354$	3.00000	+	5.19615i	0.159448	+	0.276172i
$355$	−1.50000	+	2.59808i	−0.0796117	+	0.137892i
$356$	−6.92820			−0.367194
$357$	10.3923	−	12.0000i	0.550019	−	0.635107i
$358$	−5.19615			−0.274625
$359$	9.52628	−	16.5000i	0.502778	−	0.870837i	−0.497217	−	0.867626i	$-0.665645\pi$
$359$	9.52628	−	16.5000i	0.502778	−	0.870837i	0.999995	−	0.00321050i	$-0.00102194\pi$
$360$	3.00000	+	5.19615i	0.158114	+	0.273861i
$361$	8.00000	+	13.8564i	0.421053	+	0.729285i
$362$	1.73205	−	3.00000i	0.0910346	−	0.157676i
$363$	−16.0000			−0.839782
$364$		0			0
$365$	15.0000			0.785136
$366$	6.06218	−	10.5000i	0.316875	−	0.548844i
$367$	−11.5000	−	19.9186i	−0.600295	−	1.03974i	−0.992776	−	0.119982i	$-0.961716\pi$
$367$	−11.5000	−	19.9186i	−0.600295	−	1.03974i	0.392481	−	0.919760i	$-0.371617\pi$
$368$		0			0
$369$	−5.19615	+	9.00000i	−0.270501	+	0.468521i
$370$		0			0
$371$	−7.79423	−	22.5000i	−0.404656	−	1.16814i
$372$	1.73205			0.0898027
$373$	−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	$0.330361\pi$
$374$	−27.0000	−	46.7654i	−1.39614	−	2.41818i
$375$	6.06218	+	10.5000i	0.313050	+	0.542218i
$376$	7.50000	−	12.9904i	0.386783	−	0.669928i
$377$		0			0
$378$	15.0000	−	17.3205i	0.771517	−	0.890871i
$379$	−1.73205			−0.0889695			−0.0444847	−	0.999010i	$-0.514165\pi$
$379$	−1.73205			−0.0889695			−0.0444847	+	0.999010i	$0.514165\pi$
$380$	−1.50000	+	2.59808i	−0.0769484	+	0.133278i
$381$	−6.50000	−	11.2583i	−0.333005	−	0.576782i
$382$	12.9904	+	22.5000i	0.664646	+	1.15120i
$383$	7.79423	−	13.5000i	0.398266	−	0.689818i	−0.595246	−	0.803544i	$-0.702945\pi$
$383$	7.79423	−	13.5000i	0.398266	−	0.689818i	0.993512	+	0.113726i	$0.0362786\pi$
$384$	−12.1244			−0.618718
$385$	−23.3827	−	4.50000i	−1.19169	−	0.229341i
$386$	3.00000			0.152696
$387$	−11.0000	+	19.0526i	−0.559161	+	0.968496i
$388$	−2.59808	−	4.50000i	−0.131897	−	0.228453i
$389$	1.50000	+	2.59808i	0.0760530	+	0.131728i	0.901544	−	0.432688i	$-0.142435\pi$
$389$	1.50000	+	2.59808i	0.0760530	+	0.131728i	−0.825491	+	0.564416i	$0.809102\pi$
$390$		0			0
$391$		0			0
$392$	−11.2583	−	4.50000i	−0.568632	−	0.227284i
$393$	−15.0000			−0.756650
$394$	−19.5000	+	33.7750i	−0.982396	+	1.70156i
$395$	−4.33013	−	7.50000i	−0.217872	−	0.377366i
$396$	−5.19615	−	9.00000i	−0.261116	−	0.452267i
$397$	18.1865	−	31.5000i	0.912756	−	1.58094i	0.102602	−	0.994722i	$-0.467283\pi$
$397$	18.1865	−	31.5000i	0.912756	−	1.58094i	0.810154	−	0.586217i	$-0.199383\pi$
$398$	−6.92820			−0.347279
$399$	−4.50000	−	0.866025i	−0.225282	−	0.0433555i
$400$	10.0000			0.500000
$401$	3.46410	−	6.00000i	0.172989	−	0.299626i	−0.766475	−	0.642275i	$-0.777991\pi$
$401$	3.46410	−	6.00000i	0.172989	−	0.299626i	0.939463	+	0.342649i	$0.111324\pi$
$402$	−7.50000	−	12.9904i	−0.374066	−	0.647901i
$403$		0			0
$404$	−4.50000	+	7.79423i	−0.223883	+	0.387777i
$405$	−1.73205			−0.0860663
$406$	9.00000	−	10.3923i	0.446663	−	0.515761i
$407$		0			0
$408$	5.19615	−	9.00000i	0.257248	−	0.445566i
$409$	−3.46410	−	6.00000i	−0.171289	−	0.296681i	0.767582	−	0.640951i	$-0.221460\pi$
$409$	−3.46410	−	6.00000i	−0.171289	−	0.296681i	−0.938871	+	0.344270i	$0.888126\pi$
$410$	−7.79423	−	13.5000i	−0.384930	−	0.666717i
$411$		0			0
$412$	13.0000			0.640464
$413$	3.00000	+	8.66025i	0.147620	+	0.426143i
$414$		0			0
$415$	3.00000	−	5.19615i	0.147264	−	0.255069i
$416$		0			0
$417$	−6.50000	−	11.2583i	−0.318306	−	0.551323i
$418$	−7.79423	+	13.5000i	−0.381228	+	0.660307i
$419$	21.0000			1.02592			0.512959	−	0.858413i	$-0.328549\pi$
$419$	21.0000			1.02592			0.512959	+	0.858413i	$0.328549\pi$
$420$	1.50000	+	4.33013i	0.0731925	+	0.211289i
$421$		0			0			−	1.00000i	$-0.5\pi$
$421$		0			0				1.00000i	$0.5\pi$
$422$	−11.2583	+	19.5000i	−0.548047	+	0.949245i
$423$	8.66025	+	15.0000i	0.421076	+	0.729325i
$424$	−7.79423	−	13.5000i	−0.378521	−	0.655618i
$425$	−6.00000	+	10.3923i	−0.291043	+	0.504101i
$426$	3.00000			0.145350
$427$	12.1244	−	14.0000i	0.586739	−	0.677507i
$428$		0			0
$429$		0			0
$430$	−16.5000	−	28.5788i	−0.795701	−	1.37819i
$431$	−16.4545	−	28.5000i	−0.792585	−	1.37280i	−0.924362	−	0.381517i	$-0.875402\pi$
$431$	−16.4545	−	28.5000i	−0.792585	−	1.37280i	0.131777	−	0.991279i	$-0.457932\pi$
$432$	12.5000	−	21.6506i	0.601407	−	1.04167i
$433$	−19.0000			−0.913082			−0.456541	−	0.889702i	$-0.650912\pi$
$433$	−19.0000			−0.913082			−0.456541	+	0.889702i	$0.650912\pi$
$434$	7.79423	+	1.50000i	0.374135	+	0.0720023i
$435$	5.19615			0.249136
$436$	2.59808	−	4.50000i	0.124425	−	0.215511i
$437$		0			0
$438$	−7.50000	−	12.9904i	−0.358364	−	0.620704i
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$	−15.5885			−0.743151
$441$	11.0000	−	8.66025i	0.523810	−	0.412393i
$442$		0			0
$443$	−7.50000	+	12.9904i	−0.356336	+	0.617192i	−0.987346	−	0.158583i	$-0.949307\pi$
$443$	−7.50000	+	12.9904i	−0.356336	+	0.617192i	0.631010	+	0.775775i	$0.282641\pi$
$444$		0			0
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$	−4.50000	+	7.79423i	−0.213081	+	0.369067i
$447$	19.0526			0.901155
$448$	−2.59808	−	0.500000i	−0.122748	−	0.0236228i
$449$	1.73205			0.0817405			0.0408703	−	0.999164i	$-0.486987\pi$
$449$	1.73205			0.0817405			0.0408703	+	0.999164i	$0.486987\pi$
$450$	−3.46410	+	6.00000i	−0.163299	+	0.282843i
$451$	−13.5000	−	23.3827i	−0.635690	−	1.10105i
$452$	−7.50000	−	12.9904i	−0.352770	−	0.611016i
$453$	−6.06218	+	10.5000i	−0.284826	+	0.493333i
$454$	−30.0000			−1.40797
$455$		0			0
$456$	−3.00000			−0.140488
$457$	−17.3205	+	30.0000i	−0.810219	+	1.40334i	0.102491	+	0.994734i	$0.467319\pi$
$457$	−17.3205	+	30.0000i	−0.810219	+	1.40334i	−0.912710	+	0.408607i	$0.866015\pi$
$458$	10.5000	+	18.1865i	0.490633	+	0.849801i
$459$	15.0000	+	25.9808i	0.700140	+	1.21268i
$460$		0			0
$461$	−29.4449			−1.37138			−0.685692	−	0.727892i	$-0.740500\pi$
$461$	−29.4449			−1.37138			−0.685692	+	0.727892i	$0.740500\pi$
$462$	7.79423	+	22.5000i	0.362620	+	1.04679i
$463$	24.2487			1.12693			0.563467	−	0.826139i	$-0.309467\pi$
$463$	24.2487			1.12693			0.563467	+	0.826139i	$0.309467\pi$
$464$	7.50000	−	12.9904i	0.348179	−	0.603063i
$465$	1.50000	+	2.59808i	0.0695608	+	0.120483i
$466$	2.59808	+	4.50000i	0.120354	+	0.208458i
$467$	−10.5000	+	18.1865i	−0.485882	+	0.841572i	−0.999868	−	0.0162260i	$-0.994835\pi$
$467$	−10.5000	+	18.1865i	−0.485882	+	0.841572i	0.513986	+	0.857798i	$0.328168\pi$
$468$		0			0
$469$	−7.50000	−	21.6506i	−0.346318	−	0.999733i
$470$	−25.9808			−1.19840
$471$	11.5000	−	19.9186i	0.529892	−	0.917800i
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	−28.5788	−	49.5000i	−1.31406	−	2.27601i
$474$	−4.33013	+	7.50000i	−0.198889	+	0.344486i
$475$	3.46410			0.158944
$476$	−10.3923	+	12.0000i	−0.476331	+	0.550019i
$477$	18.0000			0.824163
$478$	−9.00000	+	15.5885i	−0.411650	+	0.712999i
$479$	−14.7224	−	25.5000i	−0.672685	−	1.16512i	−0.977140	−	0.212598i	$-0.931808\pi$
$479$	−14.7224	−	25.5000i	−0.672685	−	1.16512i	0.304455	−	0.952527i	$-0.401526\pi$
$480$	4.50000	+	7.79423i	0.205396	+	0.355756i
$481$		0			0
$482$	12.0000			0.546585
$483$		0			0
$484$	16.0000			0.727273
$485$	4.50000	−	7.79423i	0.204334	−	0.353918i
$486$	13.8564	+	24.0000i	0.628539	+	1.08866i
$487$	12.1244	+	21.0000i	0.549407	+	0.951601i	0.998315	+	0.0580230i	$0.0184797\pi$
$487$	12.1244	+	21.0000i	0.549407	+	0.951601i	−0.448908	+	0.893578i	$0.648187\pi$
$488$	6.06218	−	10.5000i	0.274422	−	0.475313i
$489$	12.1244			0.548282
$490$	3.00000	+	20.7846i	0.135526	+	0.938953i
$491$	27.0000			1.21849			0.609246	−	0.792981i	$-0.291472\pi$
$491$	27.0000			1.21849			0.609246	+	0.792981i	$0.291472\pi$
$492$	−2.59808	+	4.50000i	−0.117130	+	0.202876i
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$		0			0
$495$	9.00000	−	15.5885i	0.404520	−	0.700649i
$496$	8.66025			0.388857
$497$	4.50000	+	0.866025i	0.201853	+	0.0388465i
$498$	−6.00000			−0.268866
$499$	0.866025	−	1.50000i	0.0387686	−	0.0671492i	−0.845990	−	0.533199i	$-0.820990\pi$
$499$	0.866025	−	1.50000i	0.0387686	−	0.0671492i	0.884759	+	0.466049i	$0.154323\pi$
$500$	−6.06218	−	10.5000i	−0.271109	−	0.469574i
$501$	0.866025	+	1.50000i	0.0386912	+	0.0670151i
$502$	2.59808	−	4.50000i	0.115958	−	0.200845i
$503$	−9.00000			−0.401290			−0.200645	−	0.979664i	$-0.564304\pi$
$503$	−9.00000			−0.401290			−0.200645	+	0.979664i	$0.564304\pi$
$504$	6.00000	−	6.92820i	0.267261	−	0.308607i
$505$	−15.5885			−0.693677
$506$		0			0
$507$		0			0
$508$	6.50000	+	11.2583i	0.288391	+	0.499508i
$509$	−3.46410	+	6.00000i	−0.153544	+	0.265945i	−0.932528	−	0.361098i	$-0.882402\pi$
$509$	−3.46410	+	6.00000i	−0.153544	+	0.265945i	0.778984	+	0.627044i	$0.215735\pi$
$510$	−18.0000			−0.797053
$511$	−7.50000	−	21.6506i	−0.331780	−	0.957768i
$512$	8.66025			0.382733
$513$	4.33013	−	7.50000i	0.191180	−	0.331133i
$514$	25.9808	+	45.0000i	1.14596	+	1.98486i
$515$	11.2583	+	19.5000i	0.496101	+	0.859273i
$516$	−5.50000	+	9.52628i	−0.242124	+	0.419371i
$517$	−45.0000			−1.97910
$518$		0			0
$519$	15.0000			0.658427
$520$		0			0
$521$	−19.5000	−	33.7750i	−0.854311	−	1.47971i	−0.877283	−	0.479973i	$-0.840646\pi$
$521$	−19.5000	−	33.7750i	−0.854311	−	1.47971i	0.0229727	−	0.999736i	$-0.492687\pi$
$522$	5.19615	+	9.00000i	0.227429	+	0.393919i
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	−0.818980	−	0.573822i	$-0.805460\pi$
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	0.906434	+	0.422347i	$0.138794\pi$
$524$	15.0000			0.655278
$525$	3.46410	−	4.00000i	0.151186	−	0.174574i
$526$	5.19615			0.226563
$527$	−5.19615	+	9.00000i	−0.226348	+	0.392046i
$528$	12.9904	+	22.5000i	0.565334	+	0.979187i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−13.5000	+	23.3827i	−0.586403	+	1.01568i
$531$	−6.92820			−0.300658
$532$	4.50000	+	0.866025i	0.195100	+	0.0375470i
$533$		0			0
$534$	−6.00000	+	10.3923i	−0.259645	+	0.449719i
$535$		0			0
$536$	−7.50000	−	12.9904i	−0.323951	−	0.561099i
$537$	−1.50000	+	2.59808i	−0.0647298	+	0.112115i
$538$	−10.3923			−0.448044
$539$	5.19615	+	36.0000i	0.223814	+	1.55063i
$540$	−8.66025			−0.372678
$541$	6.06218	−	10.5000i	0.260633	−	0.451430i	−0.705777	−	0.708434i	$-0.749402\pi$
$541$	6.06218	−	10.5000i	0.260633	−	0.451430i	0.966410	+	0.257004i	$0.0827353\pi$
$542$	15.0000	+	25.9808i	0.644305	+	1.11597i
$543$	−1.00000	−	1.73205i	−0.0429141	−	0.0743294i
$544$	−15.5885	+	27.0000i	−0.668350	+	1.15762i
$545$	9.00000			0.385518
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$		0			0
$549$	7.00000	+	12.1244i	0.298753	+	0.517455i
$550$	−9.00000	−	15.5885i	−0.383761	−	0.664694i
$551$	2.59808	−	4.50000i	0.110682	−	0.191706i
$552$		0			0
$553$	−8.66025	+	10.0000i	−0.368271	+	0.425243i
$554$	17.3205			0.735878
$555$		0			0
$556$	6.50000	+	11.2583i	0.275661	+	0.477460i
$557$	−7.79423	−	13.5000i	−0.330252	−	0.572013i	0.652309	−	0.757953i	$-0.273800\pi$
$557$	−7.79423	−	13.5000i	−0.330252	−	0.572013i	−0.982561	+	0.185940i	$0.940467\pi$
$558$	−3.00000	+	5.19615i	−0.127000	+	0.219971i
$559$		0			0
$560$	7.50000	+	21.6506i	0.316933	+	0.914906i
$561$	−31.1769			−1.31629
$562$	−6.00000	+	10.3923i	−0.253095	+	0.438373i
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	−0.943560	−	0.331202i	$-0.892546\pi$
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	0.184950	−	0.982748i	$-0.440788\pi$
$564$	4.33013	+	7.50000i	0.182331	+	0.315807i
$565$	12.9904	−	22.5000i	0.546509	−	0.946582i
$566$	−32.9090			−1.38327
$567$	0.866025	+	2.50000i	0.0363696	+	0.104990i
$568$	3.00000			0.125877
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	−0.922032	−	0.387113i	$-0.873472\pi$
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	0.796266	+	0.604947i	$0.206806\pi$
$570$	2.59808	+	4.50000i	0.108821	+	0.188484i
$571$	−11.5000	−	19.9186i	−0.481260	−	0.833567i	0.518509	−	0.855072i	$-0.326487\pi$
$571$	−11.5000	−	19.9186i	−0.481260	−	0.833567i	−0.999769	+	0.0215055i	$0.993154\pi$
$572$		0			0
$573$	15.0000			0.626634
$574$	−15.5885	+	18.0000i	−0.650650	+	0.751305i
$575$		0			0
$576$	1.00000	−	1.73205i	0.0416667	−	0.0721688i
$577$	−7.79423	−	13.5000i	−0.324478	−	0.562012i	0.656929	−	0.753953i	$-0.271855\pi$
$577$	−7.79423	−	13.5000i	−0.324478	−	0.562012i	−0.981407	+	0.191940i	$0.938522\pi$
$578$	−16.4545	−	28.5000i	−0.684416	−	1.18544i
$579$	0.866025	−	1.50000i	0.0359908	−	0.0623379i
$580$	−5.19615			−0.215758
$581$	−9.00000	−	1.73205i	−0.373383	−	0.0718576i
$582$	−9.00000			−0.373062
$583$	−23.3827	+	40.5000i	−0.968412	+	1.67734i
$584$	−7.50000	−	12.9904i	−0.310352	−	0.537546i
$585$		0			0
$586$	22.5000	−	38.9711i	0.929466	−	1.60988i
$587$	−15.5885			−0.643404			−0.321702	−	0.946841i	$-0.604255\pi$
$587$	−15.5885			−0.643404			−0.321702	+	0.946841i	$0.604255\pi$
$588$	5.50000	−	4.33013i	0.226816	−	0.178571i
$589$	3.00000			0.123613
$590$	5.19615	−	9.00000i	0.213922	−	0.370524i
$591$	11.2583	+	19.5000i	0.463106	+	0.802123i
$592$		0			0
$593$	2.59808	−	4.50000i	0.106690	−	0.184793i	−0.807737	−	0.589543i	$-0.799308\pi$
$593$	2.59808	−	4.50000i	0.106690	−	0.184793i	0.914428	+	0.404750i	$0.132641\pi$
$594$	−45.0000			−1.84637
$595$	−27.0000	−	5.19615i	−1.10689	−	0.213021i
$596$	−19.0526			−0.780423
$597$	−2.00000	+	3.46410i	−0.0818546	+	0.141776i
$598$		0			0
$599$	−4.50000	−	7.79423i	−0.183865	−	0.318464i	0.759328	−	0.650708i	$-0.225528\pi$
$599$	−4.50000	−	7.79423i	−0.183865	−	0.318464i	−0.943193	+	0.332244i	$0.892194\pi$
$600$	1.73205	−	3.00000i	0.0707107	−	0.122474i
$601$	19.0000			0.775026			0.387513	−	0.921864i	$-0.373334\pi$
$601$	19.0000			0.775026			0.387513	+	0.921864i	$0.373334\pi$
$602$	−33.0000	+	38.1051i	−1.34498	+	1.55305i
$603$	17.3205			0.705346
$604$	6.06218	−	10.5000i	0.246667	−	0.427239i
$605$	13.8564	+	24.0000i	0.563343	+	0.975739i
$606$	7.79423	+	13.5000i	0.316619	+	0.548400i
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.0134214	−	0.999910i	$-0.495728\pi$
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.859237	−	0.511578i	$-0.170939\pi$
$608$	9.00000			0.364998
$609$	−2.59808	−	7.50000i	−0.105279	−	0.303915i
$610$	−21.0000			−0.850265
$611$		0			0
$612$	−6.00000	−	10.3923i	−0.242536	−	0.420084i
$613$	18.1865	+	31.5000i	0.734547	+	1.27227i	0.954922	+	0.296858i	$0.0959387\pi$
$613$	18.1865	+	31.5000i	0.734547	+	1.27227i	−0.220375	+	0.975415i	$0.570728\pi$
$614$	21.0000	−	36.3731i	0.847491	−	1.46790i
$615$	−9.00000			−0.362915
$616$	7.79423	+	22.5000i	0.314038	+	0.906551i
$617$	−43.3013			−1.74324			−0.871622	−	0.490179i	$-0.836931\pi$
$617$	−43.3013			−1.74324			−0.871622	+	0.490179i	$0.836931\pi$
$618$	11.2583	−	19.5000i	0.452876	−	0.784405i
$619$	9.52628	+	16.5000i	0.382893	+	0.663191i	0.991475	−	0.130301i	$-0.0415943\pi$
$619$	9.52628	+	16.5000i	0.382893	+	0.663191i	−0.608581	+	0.793492i	$0.708261\pi$
$620$	−1.50000	−	2.59808i	−0.0602414	−	0.104341i
$621$		0			0
$622$	25.9808			1.04173
$623$	−12.0000	+	13.8564i	−0.480770	+	0.555145i
$624$		0			0
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	−16.4545	−	28.5000i	−0.657653	−	1.13909i
$627$	4.50000	+	7.79423i	0.179713	+	0.311272i
$628$	−11.5000	+	19.9186i	−0.458900	+	0.794838i
$629$		0			0
$630$	−15.5885	−	3.00000i	−0.621059	−	0.119523i
$631$	−46.7654			−1.86170			−0.930850	−	0.365401i	$-0.880932\pi$
$631$	−46.7654			−1.86170			−0.930850	+	0.365401i	$0.880932\pi$
$632$	−4.33013	+	7.50000i	−0.172243	+	0.298334i
$633$	6.50000	+	11.2583i	0.258352	+	0.447478i
$634$	−4.50000	−	7.79423i	−0.178718	−	0.309548i
$635$	−11.2583	+	19.5000i	−0.446773	+	0.773834i
$636$	9.00000			0.356873
$637$		0			0
$638$	−27.0000			−1.06894
$639$	−1.73205	+	3.00000i	−0.0685189	+	0.118678i
$640$	10.5000	+	18.1865i	0.415049	+	0.718886i
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	0.993899	+	0.110291i	$0.0351782\pi$
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	−0.401435	+	0.915888i	$0.631488\pi$
$642$		0			0
$643$	5.19615			0.204916			0.102458	−	0.994737i	$-0.467329\pi$
$643$	5.19615			0.204916			0.102458	+	0.994737i	$0.467329\pi$
$644$		0			0
$645$	−19.0526			−0.750194
$646$	−9.00000	+	15.5885i	−0.354100	+	0.613320i
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	0.763908	−	0.645325i	$-0.223278\pi$
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	−0.940822	+	0.338902i	$0.889945\pi$
$648$	0.866025	+	1.50000i	0.0340207	+	0.0589256i
$649$	9.00000	−	15.5885i	0.353281	−	0.611900i
$650$		0			0
$651$	3.00000	−	3.46410i	0.117579	−	0.135769i
$652$	−12.1244			−0.474826
$653$	15.0000	−	25.9808i	0.586995	−	1.01671i	−0.407628	−	0.913148i	$-0.633644\pi$
$653$	15.0000	−	25.9808i	0.586995	−	1.01671i	0.994623	−	0.103558i	$-0.0330227\pi$
$654$	−4.50000	−	7.79423i	−0.175964	−	0.304778i
$655$	12.9904	+	22.5000i	0.507576	+	0.879148i
$656$	−12.9904	+	22.5000i	−0.507189	+	0.878477i
$657$	17.3205			0.675737
$658$	12.9904	+	37.5000i	0.506418	+	1.46190i
$659$	15.0000			0.584317			0.292159	−	0.956370i	$-0.405627\pi$
$659$	15.0000			0.584317			0.292159	+	0.956370i	$0.405627\pi$
$660$	4.50000	−	7.79423i	0.175162	−	0.303390i
$661$	−18.1865	−	31.5000i	−0.707374	−	1.22521i	−0.965828	−	0.259184i	$-0.916546\pi$
$661$	−18.1865	−	31.5000i	−0.707374	−	1.22521i	0.258454	−	0.966024i	$-0.416787\pi$
$662$	−28.5000	−	49.3634i	−1.10768	−	1.91856i
$663$		0			0
$664$	−6.00000			−0.232845
$665$	2.59808	+	7.50000i	0.100749	+	0.290838i
$666$		0			0
$667$		0			0
$668$	−0.866025	−	1.50000i	−0.0335075	−	0.0580367i
$669$	2.59808	+	4.50000i	0.100447	+	0.173980i
$670$	−12.9904	+	22.5000i	−0.501862	+	0.869251i
$671$	−36.3731			−1.40417
$672$	9.00000	−	10.3923i	0.347183	−	0.400892i
$673$	1.00000			0.0385472			0.0192736	−	0.999814i	$-0.493865\pi$
$673$	1.00000			0.0385472			0.0192736	+	0.999814i	$0.493865\pi$
$674$	19.0526	−	33.0000i	0.733877	−	1.27111i
$675$	5.00000	+	8.66025i	0.192450	+	0.333333i
$676$		0			0
$677$	−13.5000	+	23.3827i	−0.518847	+	0.898670i	0.480913	+	0.876768i	$0.340305\pi$
$677$	−13.5000	+	23.3827i	−0.518847	+	0.898670i	−0.999760	+	0.0219013i	$0.993028\pi$
$678$	−25.9808			−0.997785
$679$	−13.5000	−	2.59808i	−0.518082	−	0.0997050i
$680$	−18.0000			−0.690268
$681$	−8.66025	+	15.0000i	−0.331862	+	0.574801i
$682$	−7.79423	−	13.5000i	−0.298456	−	0.516942i
$683$	12.1244	+	21.0000i	0.463926	+	0.803543i	0.999152	−	0.0411658i	$-0.0131072\pi$
$683$	12.1244	+	21.0000i	0.463926	+	0.803543i	−0.535227	+	0.844708i	$0.679774\pi$
$684$	−1.73205	+	3.00000i	−0.0662266	+	0.114708i
$685$		0			0
$686$	28.5000	−	14.7224i	1.08814	−	0.562105i
$687$	12.1244			0.462573
$688$	−27.5000	+	47.6314i	−1.04843	+	1.81593i
$689$		0			0
$690$		0			0
$691$	15.5885	−	27.0000i	0.593013	−	1.02713i	−0.400811	−	0.916161i	$-0.631272\pi$
$691$	15.5885	−	27.0000i	0.593013	−	1.02713i	0.993824	−	0.110968i	$-0.0353950\pi$
$692$	−15.0000			−0.570214
$693$	−27.0000	−	5.19615i	−1.02565	−	0.197386i
$694$		0			0
$695$	−11.2583	+	19.5000i	−0.427053	+	0.739677i
$696$	−2.59808	−	4.50000i	−0.0984798	−	0.170572i
$697$	−15.5885	−	27.0000i	−0.590455	−	1.02270i
$698$	−4.50000	+	7.79423i	−0.170328	+	0.295016i
$699$	3.00000			0.113470
$700$	−3.46410	+	4.00000i	−0.130931	+	0.151186i
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$		0			0
$703$		0			0
$704$	2.59808	+	4.50000i	0.0979187	+	0.169600i
$705$	−7.50000	+	12.9904i	−0.282466	+	0.489246i
$706$	−3.00000			−0.112906
$707$	7.79423	+	22.5000i	0.293132	+	0.846200i
$708$	−3.46410			−0.130189
$709$	−6.06218	+	10.5000i	−0.227670	+	0.394336i	−0.957117	−	0.289701i	$-0.906444\pi$
$709$	−6.06218	+	10.5000i	−0.227670	+	0.394336i	0.729447	+	0.684037i	$0.239777\pi$
$710$	−2.59808	−	4.50000i	−0.0975041	−	0.168882i
$711$	−5.00000	−	8.66025i	−0.187515	−	0.324785i
$712$	−6.00000	+	10.3923i	−0.224860	+	0.389468i
$713$		0			0
$714$	9.00000	+	25.9808i	0.336817	+	0.972306i
$715$		0			0
$716$	1.50000	−	2.59808i	0.0560576	−	0.0970947i
$717$	5.19615	+	9.00000i	0.194054	+	0.336111i
$718$	16.5000	+	28.5788i	0.615775	+	1.06655i
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	−0.971311	−	0.237814i	$-0.923569\pi$
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	0.691608	+	0.722273i	$0.256903\pi$
$720$	−17.3205			−0.645497
$721$	22.5167	−	26.0000i	0.838564	−	0.968291i
$722$	−27.7128			−1.03136
$723$	3.46410	−	6.00000i	0.128831	−	0.223142i
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$	3.00000	+	5.19615i	0.111417	+	0.192980i
$726$	13.8564	−	24.0000i	0.514259	−	0.890724i
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−12.9904	+	22.5000i	−0.480796	+	0.832762i
$731$	−33.0000	−	57.1577i	−1.22055	−	2.11405i
$732$	3.50000	+	6.06218i	0.129364	+	0.224065i
$733$	25.1147	−	43.5000i	0.927634	−	1.60671i	0.140365	−	0.990100i	$-0.455173\pi$
$733$	25.1147	−	43.5000i	0.927634	−	1.60671i	0.787269	−	0.616609i	$-0.211494\pi$
$734$	39.8372			1.47042
$735$	11.2583	+	4.50000i	0.415270	+	0.165985i
$736$		0			0
$737$	−22.5000	+	38.9711i	−0.828798	+	1.43552i
$738$	−9.00000	−	15.5885i	−0.331295	−	0.573819i
$739$	19.9186	+	34.5000i	0.732717	+	1.26910i	0.955718	+	0.294285i	$0.0950814\pi$
$739$	19.9186	+	34.5000i	0.732717	+	1.26910i	−0.223001	+	0.974818i	$0.571585\pi$
$740$		0			0
$741$		0			0
$742$	40.5000	+	7.79423i	1.48680	+	0.286135i
$743$	−1.73205			−0.0635428			−0.0317714	−	0.999495i	$-0.510115\pi$
$743$	−1.73205			−0.0635428			−0.0317714	+	0.999495i	$0.510115\pi$
$744$	1.50000	−	2.59808i	0.0549927	−	0.0952501i
$745$	−16.5000	−	28.5788i	−0.604513	−	1.04705i
$746$	−16.4545	−	28.5000i	−0.602441	−	1.04346i
$747$	3.46410	−	6.00000i	0.126745	−	0.219529i
$748$	31.1769			1.13994
$749$		0			0
$750$	−21.0000			−0.766812
$751$	10.0000	−	17.3205i	0.364905	−	0.632034i	−0.623856	−	0.781540i	$-0.714435\pi$
$751$	10.0000	−	17.3205i	0.364905	−	0.632034i	0.988761	+	0.149505i	$0.0477681\pi$
$752$	21.6506	+	37.5000i	0.789517	+	1.36748i
$753$	−1.50000	−	2.59808i	−0.0546630	−	0.0946792i
$754$		0			0
$755$	21.0000			0.764268
$756$	4.33013	+	12.5000i	0.157485	+	0.454621i
$757$	−17.0000			−0.617876			−0.308938	−	0.951082i	$-0.599973\pi$
$757$	−17.0000			−0.617876			−0.308938	+	0.951082i	$0.599973\pi$
$758$	1.50000	−	2.59808i	0.0544825	−	0.0943664i
$759$		0			0
$760$	2.59808	+	4.50000i	0.0942421	+	0.163232i
$761$	14.7224	−	25.5000i	0.533688	−	0.924374i	−0.465538	−	0.885028i	$-0.654139\pi$
$761$	14.7224	−	25.5000i	0.533688	−	0.924374i	0.999226	−	0.0393463i	$-0.0125276\pi$
$762$	22.5167			0.815693
$763$	−4.50000	−	12.9904i	−0.162911	−	0.470283i
$764$	−15.0000			−0.542681
$765$	10.3923	−	18.0000i	0.375735	−	0.650791i
$766$	13.5000	+	23.3827i	0.487775	+	0.844851i
$767$		0			0
$768$	9.50000	−	16.4545i	0.342802	−	0.593750i
$769$	−19.0526			−0.687053			−0.343526	−	0.939143i	$-0.611621\pi$
$769$	−19.0526			−0.687053			−0.343526	+	0.939143i	$0.611621\pi$
$770$	27.0000	−	31.1769i	0.973012	−	1.12354i
$771$	30.0000			1.08042
$772$	−0.866025	+	1.50000i	−0.0311689	+	0.0539862i
$773$	6.92820	+	12.0000i	0.249190	+	0.431610i	0.963301	−	0.268422i	$-0.0865023\pi$
$773$	6.92820	+	12.0000i	0.249190	+	0.431610i	−0.714111	+	0.700032i	$0.753169\pi$
$774$	−19.0526	−	33.0000i	−0.684830	−	1.18616i
$775$	−1.73205	+	3.00000i	−0.0622171	+	0.107763i
$776$	−9.00000			−0.323081
$777$		0			0
$778$	−5.19615			−0.186291
$779$	−4.50000	+	7.79423i	−0.161229	+	0.279257i
$780$		0			0
$781$	−4.50000	−	7.79423i	−0.161023	−	0.278899i
$782$		0			0
$783$	15.0000			0.536056
$784$	27.5000	−	21.6506i	0.982143	−	0.773237i
$785$	−39.8372			−1.42185
$786$	12.9904	−	22.5000i	0.463352	−	0.802548i
$787$	−15.5885	−	27.0000i	−0.555668	−	0.962446i	−0.997851	−	0.0655211i	$-0.979129\pi$
$787$	−15.5885	−	27.0000i	−0.555668	−	0.962446i	0.442183	−	0.896925i	$-0.354204\pi$
$788$	−11.2583	−	19.5000i	−0.401061	−	0.694659i
$789$	1.50000	−	2.59808i	0.0534014	−	0.0924940i
$790$	15.0000			0.533676
$791$	−38.9711	−	7.50000i	−1.38565	−	0.266669i
$792$	−18.0000			−0.639602
$793$		0			0
$794$	31.5000	+	54.5596i	1.11789	+	1.93625i
$795$	7.79423	+	13.5000i	0.276433	+	0.478796i
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	33.0000			1.16892			0.584460	−	0.811423i	$-0.301306\pi$
$797$	33.0000			1.16892			0.584460	+	0.811423i	$0.301306\pi$
$798$	5.19615	−	6.00000i	0.183942	−	0.212398i
$799$	−51.9615			−1.83827
$800$	−5.19615	+	9.00000i	−0.183712	+	0.318198i
$801$	−6.92820	−	12.0000i	−0.244796	−	0.423999i
$802$	6.00000	+	10.3923i	0.211867	+	0.366965i
$803$	−22.5000	+	38.9711i	−0.794008	+	1.37526i
$804$	8.66025			0.305424
$805$		0			0
$806$		0			0
$807$	−3.00000	+	5.19615i	−0.105605	+	0.182913i
$808$	7.79423	+	13.5000i	0.274200	+	0.474928i
$809$	10.5000	+	18.1865i	0.369160	+	0.639404i	0.989434	−	0.144981i	$-0.0463120\pi$
$809$	10.5000	+	18.1865i	0.369160	+	0.639404i	−0.620274	+	0.784385i	$0.712979\pi$
$810$	1.50000	−	2.59808i	0.0527046	−	0.0912871i
$811$	−3.46410			−0.121641			−0.0608205	−	0.998149i	$-0.519372\pi$
$811$	−3.46410			−0.121641			−0.0608205	+	0.998149i	$0.519372\pi$
$812$	2.59808	+	7.50000i	0.0911746	+	0.263198i
$813$	17.3205			0.607457
$814$		0			0
$815$	−10.5000	−	18.1865i	−0.367799	−	0.637046i
$816$	15.0000	+	25.9808i	0.525105	+	0.909509i
$817$	−9.52628	+	16.5000i	−0.333282	+	0.577262i
$818$	12.0000			0.419570
$819$		0			0
$820$	9.00000			0.314294
$821$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$821$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$822$		0			0
$823$	16.0000	+	27.7128i	0.557725	+	0.966008i	0.997686	+	0.0679910i	$0.0216589\pi$
$823$	16.0000	+	27.7128i	0.557725	+	0.966008i	−0.439961	+	0.898017i	$0.645008\pi$
$824$	11.2583	−	19.5000i	0.392203	−	0.679315i
$825$	−10.3923			−0.361814
$826$	−15.5885	−	3.00000i	−0.542392	−	0.104383i
$827$	−10.3923			−0.361376			−0.180688	−	0.983540i	$-0.557832\pi$
$827$	−10.3923			−0.361376			−0.180688	+	0.983540i	$0.557832\pi$
$828$		0			0
$829$	3.50000	+	6.06218i	0.121560	+	0.210548i	0.920383	−	0.391018i	$-0.127877\pi$
$829$	3.50000	+	6.06218i	0.121560	+	0.210548i	−0.798823	+	0.601566i	$0.794544\pi$
$830$	5.19615	+	9.00000i	0.180361	+	0.312395i
$831$	5.00000	−	8.66025i	0.173448	−	0.300421i
$832$		0			0
$833$	6.00000	+	41.5692i	0.207888	+	1.44029i
$834$	22.5167			0.779688
$835$	1.50000	−	2.59808i	0.0519096	−	0.0899101i
$836$	−4.50000	−	7.79423i	−0.155636	−	0.269569i
$837$	4.33013	+	7.50000i	0.149671	+	0.259238i
$838$	−18.1865	+	31.5000i	−0.628243	+	1.08815i
$839$	1.73205			0.0597970			0.0298985	−	0.999553i	$-0.490482\pi$
$839$	1.73205			0.0597970			0.0298985	+	0.999553i	$0.490482\pi$
$840$	7.79423	+	1.50000i	0.268926	+	0.0517549i
$841$	−20.0000			−0.689655
$842$		0			0
$843$	3.46410	+	6.00000i	0.119310	+	0.206651i
$844$	−6.50000	−	11.2583i	−0.223739	−	0.387528i
$845$		0			0
$846$	−30.0000			−1.03142
$847$	27.7128	−	32.0000i	0.952224	−	1.09953i
$848$	45.0000			1.54531
$849$	−9.50000	+	16.4545i	−0.326039	+	0.564716i
$850$	−10.3923	−	18.0000i	−0.356453	−	0.617395i
$851$		0			0
$852$	−0.866025	+	1.50000i	−0.0296695	+	0.0513892i
$853$	−41.5692			−1.42330			−0.711651	−	0.702533i	$-0.752052\pi$
$853$	−41.5692			−1.42330			−0.711651	+	0.702533i	$0.752052\pi$
$854$	10.5000	+	30.3109i	0.359303	+	1.03722i
$855$	−6.00000			−0.205196
$856$		0			0
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	−0.997176	−	0.0751033i	$-0.976071\pi$
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	0.433546	−	0.901131i	$-0.357262\pi$
$858$		0			0
$859$	14.5000	−	25.1147i	0.494734	−	0.856904i	−0.505248	−	0.862974i	$-0.668599\pi$
$859$	14.5000	−	25.1147i	0.494734	−	0.856904i	0.999982	+	0.00607046i	$0.00193230\pi$
$860$	19.0526			0.649687
$861$	4.50000	+	12.9904i	0.153360	+	0.442711i
$862$	57.0000			1.94143
$863$	0.866025	−	1.50000i	0.0294798	−	0.0510606i	−0.850909	−	0.525313i	$-0.823948\pi$
$863$	0.866025	−	1.50000i	0.0294798	−	0.0510606i	0.880389	+	0.474252i	$0.157282\pi$
$864$	12.9904	+	22.5000i	0.441942	+	0.765466i
$865$	−12.9904	−	22.5000i	−0.441686	−	0.765023i
$866$	16.4545	−	28.5000i	0.559146	−	0.968469i
$867$	−19.0000			−0.645274
$868$	−3.00000	+	3.46410i	−0.101827	+	0.117579i
$869$	25.9808			0.881337
$870$	−4.50000	+	7.79423i	−0.152564	+	0.264249i
$871$		0			0
$872$	−4.50000	−	7.79423i	−0.152389	−	0.263946i
$873$	5.19615	−	9.00000i	0.175863	−	0.304604i
$874$		0			0
$875$	−31.5000	−	6.06218i	−1.06489	−	0.204939i
$876$	8.66025			0.292603
$877$	−0.866025	+	1.50000i	−0.0292436	+	0.0506514i	−0.880277	−	0.474460i	$-0.842643\pi$
$877$	−0.866025	+	1.50000i	−0.0292436	+	0.0506514i	0.851033	+	0.525112i	$0.175977\pi$
$878$	6.92820	+	12.0000i	0.233816	+	0.404980i
$879$	−12.9904	−	22.5000i	−0.438155	−	0.758906i
$880$	22.5000	−	38.9711i	0.758475	−	1.31372i
$881$	33.0000			1.11180			0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000			1.11180			0.555899	+	0.831250i	$0.312374\pi$
$882$	3.46410	+	24.0000i	0.116642	+	0.808122i
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$		0			0
$885$	−3.00000	−	5.19615i	−0.100844	−	0.174667i
$886$	−12.9904	−	22.5000i	−0.436420	−	0.755902i
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	−0.994077	−	0.108678i	$-0.965338\pi$
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	0.591156	+	0.806557i	$0.298672\pi$
$888$		0			0
$889$	33.7750	+	6.50000i	1.13278	+	0.218003i
$890$	20.7846			0.696702
$891$	2.59808	−	4.50000i	0.0870388	−	0.150756i
$892$	−2.59808	−	4.50000i	−0.0869900	−	0.150671i
$893$	7.50000	+	12.9904i	0.250978	+	0.434707i
$894$	−16.5000	+	28.5788i	−0.551843	+	0.955819i
$895$	5.19615			0.173688
$896$	21.0000	−	24.2487i	0.701561	−	0.810093i
$897$		0			0
$898$	−1.50000	+	2.59808i	−0.0500556	+	0.0866989i
$899$	2.59808	+	4.50000i	0.0866507	+	0.150083i
$900$	−2.00000	−	3.46410i	−0.0666667	−	0.115470i
$901$	−27.0000	+	46.7654i	−0.899500	+	1.55798i
$902$	46.7654			1.55712
$903$	9.52628	+	27.5000i	0.317015	+	0.915143i
$904$	−25.9808			−0.864107
$905$	−1.73205	+	3.00000i	−0.0575753	+	0.0997234i
$906$	−10.5000	−	18.1865i	−0.348839	−	0.604207i
$907$	−14.5000	−	25.1147i	−0.481465	−	0.833921i	0.518309	−	0.855193i	$-0.326562\pi$
$907$	−14.5000	−	25.1147i	−0.481465	−	0.833921i	−0.999774	+	0.0212722i	$0.993228\pi$
$908$	8.66025	−	15.0000i	0.287401	−	0.497792i
$909$	−18.0000			−0.597022
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	4.33013	−	7.50000i	0.143385	−	0.248350i
$913$	9.00000	+	15.5885i	0.297857	+	0.515903i
$914$	−30.0000	−	51.9615i	−0.992312	−	1.71873i
$915$	−6.06218	+	10.5000i	−0.200409	+	0.347119i
$916$	−12.1244			−0.400600
$917$	25.9808	−	30.0000i	0.857960	−	0.990687i
$918$	−51.9615			−1.71499
$919$	23.5000	−	40.7032i	0.775193	−	1.34267i	−0.159492	−	0.987199i	$-0.550986\pi$
$919$	23.5000	−	40.7032i	0.775193	−	1.34267i	0.934686	−	0.355475i	$-0.115681\pi$
$920$		0			0
$921$	−12.1244	−	21.0000i	−0.399511	−	0.691974i
$922$	25.5000	−	44.1673i	0.839798	−	1.45457i
$923$		0			0
$924$	−13.5000	−	2.59808i	−0.444117	−	0.0854704i
$925$		0			0
$926$	−21.0000	+	36.3731i	−0.690103	+	1.19529i
$927$	13.0000	+	22.5167i	0.426976	+	0.739544i
$928$	7.79423	+	13.5000i	0.255858	+	0.443159i
$929$	23.3827	−	40.5000i	0.767161	−	1.32876i	−0.171935	−	0.985108i	$-0.555002\pi$
$929$	23.3827	−	40.5000i	0.767161	−	1.32876i	0.939096	−	0.343654i	$-0.111665\pi$
$930$	−5.19615			−0.170389
$931$	9.52628	−	7.50000i	0.312211	−	0.245803i
$932$	−3.00000			−0.0982683
$933$	7.50000	−	12.9904i	0.245539	−	0.425286i
$934$	−18.1865	−	31.5000i	−0.595082	−	1.03071i
$935$	27.0000	+	46.7654i	0.882994	+	1.52939i
$936$		0			0
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$	38.9711	+	7.50000i	1.27245	+	0.244884i
$939$	−19.0000			−0.620042
$940$	7.50000	−	12.9904i	0.244623	−	0.423700i
$941$	2.59808	+	4.50000i	0.0846949	+	0.146696i	0.905261	−	0.424856i	$-0.139675\pi$
$941$	2.59808	+	4.50000i	0.0846949	+	0.146696i	−0.820566	+	0.571551i	$0.806342\pi$
$942$	19.9186	+	34.5000i	0.648983	+	1.12407i
$943$		0			0
$944$	−17.3205			−0.563735
$945$	−15.0000	+	17.3205i	−0.487950	+	0.563436i
$946$	99.0000			3.21877
$947$	19.0526	−	33.0000i	0.619125	−	1.07236i	−0.370521	−	0.928824i	$-0.620821\pi$
$947$	19.0526	−	33.0000i	0.619125	−	1.07236i	0.989646	−	0.143532i	$-0.0458459\pi$
$948$	−2.50000	−	4.33013i	−0.0811962	−	0.140636i
$949$		0			0
$950$	−3.00000	+	5.19615i	−0.0973329	+	0.168585i
$951$	−5.19615			−0.168497
$952$	9.00000	+	25.9808i	0.291692	+	0.842041i
$953$	57.0000			1.84641			0.923206	−	0.384307i	$-0.125559\pi$
$953$	57.0000			1.84641			0.923206	+	0.384307i	$0.125559\pi$
$954$	−15.5885	+	27.0000i	−0.504695	+	0.874157i
$955$	−12.9904	−	22.5000i	−0.420359	−	0.728083i
$956$	−5.19615	−	9.00000i	−0.168056	−	0.291081i
$957$	−7.79423	+	13.5000i	−0.251952	+	0.436393i
$958$	51.0000			1.64774
$959$		0			0
$960$	1.73205			0.0559017
$961$	14.0000	−	24.2487i	0.451613	−	0.782216i
$962$		0			0
$963$		0			0
$964$	−3.46410	+	6.00000i	−0.111571	+	0.193247i
$965$	−3.00000			−0.0965734
$966$		0			0
$967$	−10.3923			−0.334194			−0.167097	−	0.985940i	$-0.553439\pi$
$967$	−10.3923			−0.334194			−0.167097	+	0.985940i	$0.553439\pi$
$968$	13.8564	−	24.0000i	0.445362	−	0.771389i
$969$	5.19615	+	9.00000i	0.166924	+	0.289122i
$970$	7.79423	+	13.5000i	0.250258	+	0.433459i
$971$	−10.5000	+	18.1865i	−0.336961	+	0.583634i	−0.983860	−	0.178942i	$-0.942732\pi$
$971$	−10.5000	+	18.1865i	−0.336961	+	0.583634i	0.646899	+	0.762576i	$0.276066\pi$
$972$	−16.0000			−0.513200
$973$	33.7750	+	6.50000i	1.08278	+	0.208380i
$974$	−42.0000			−1.34577
$975$		0			0
$976$	17.5000	+	30.3109i	0.560161	+	0.970228i
$977$	−9.52628	−	16.5000i	−0.304773	−	0.527882i	0.672438	−	0.740153i	$-0.265247\pi$
$977$	−9.52628	−	16.5000i	−0.304773	−	0.527882i	−0.977211	+	0.212272i	$0.931914\pi$
$978$	−10.5000	+	18.1865i	−0.335753	+	0.581541i
$979$	36.0000			1.15056
$980$	−11.2583	−	4.50000i	−0.359634	−	0.143747i
$981$	10.3923			0.331801
$982$	−23.3827	+	40.5000i	−0.746171	+	1.29241i
$983$	−18.1865	−	31.5000i	−0.580060	−	1.00469i	−0.995472	−	0.0950602i	$-0.969696\pi$
$983$	−18.1865	−	31.5000i	−0.580060	−	1.00469i	0.415411	−	0.909634i	$-0.363638\pi$
$984$	4.50000	+	7.79423i	0.143455	+	0.248471i
$985$	19.5000	−	33.7750i	0.621322	−	1.07616i
$986$	−31.1769			−0.992875
$987$	22.5000	+	4.33013i	0.716183	+	0.137829i
$988$		0			0
$989$		0			0
$990$	15.5885	+	27.0000i	0.495434	+	0.858116i
$991$	−29.5000	−	51.0955i	−0.937098	−	1.62310i	−0.770849	−	0.637018i	$-0.780168\pi$
$991$	−29.5000	−	51.0955i	−0.937098	−	1.62310i	−0.166250	−	0.986084i	$-0.553166\pi$
$992$	−4.50000	+	7.79423i	−0.142875	+	0.247467i
$993$	−32.9090			−1.04433
$994$	−5.19615	+	6.00000i	−0.164812	+	0.190308i
$995$	6.92820			0.219639
$996$	1.73205	−	3.00000i	0.0548821	−	0.0950586i
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	0.849756	−	0.527176i	$-0.176749\pi$
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	−0.881426	+	0.472322i	$0.843416\pi$
$998$	1.50000	+	2.59808i	0.0474817	+	0.0822407i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.e.170.1		4
7.2	even	3		8281.2.a.s.1.2		2
7.4	even	3	inner	1183.2.e.e.508.1		4
7.5	odd	6		8281.2.a.w.1.2		2
13.2	odd	12		91.2.u.a.30.1	yes	2
13.7	odd	12		91.2.k.a.23.1	yes	2
13.12	even	2	inner	1183.2.e.e.170.2		4
39.2	even	12		819.2.do.c.667.1		2
39.20	even	12		819.2.bm.a.478.1		2
91.2	odd	12		637.2.q.c.589.1		2
91.12	odd	6		8281.2.a.w.1.1		2
91.20	even	12		637.2.k.b.569.1		2
91.25	even	6	inner	1183.2.e.e.508.2		4
91.33	even	12		637.2.q.b.491.1		2
91.41	even	12		637.2.u.a.30.1		2
91.46	odd	12		91.2.u.a.88.1	yes	2
91.51	even	6		8281.2.a.s.1.1		2
91.54	even	12		637.2.q.b.589.1		2
91.59	even	12		637.2.u.a.361.1		2
91.67	odd	12		91.2.k.a.4.1	✓	2
91.72	odd	12		637.2.q.c.491.1		2
91.80	even	12		637.2.k.b.459.1		2
273.137	even	12		819.2.do.c.361.1		2
273.158	even	12		819.2.bm.a.550.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.a.4.1	✓	2	91.67	odd	12
91.2.k.a.23.1	yes	2	13.7	odd	12
91.2.u.a.30.1	yes	2	13.2	odd	12
91.2.u.a.88.1	yes	2	91.46	odd	12
637.2.k.b.459.1		2	91.80	even	12
637.2.k.b.569.1		2	91.20	even	12
637.2.q.b.491.1		2	91.33	even	12
637.2.q.b.589.1		2	91.54	even	12
637.2.q.c.491.1		2	91.72	odd	12
637.2.q.c.589.1		2	91.2	odd	12
637.2.u.a.30.1		2	91.41	even	12
637.2.u.a.361.1		2	91.59	even	12
819.2.bm.a.478.1		2	39.20	even	12
819.2.bm.a.550.1		2	273.158	even	12
819.2.do.c.361.1		2	273.137	even	12
819.2.do.c.667.1		2	39.2	even	12
1183.2.e.e.170.1		4	1.1	even	1	trivial
1183.2.e.e.170.2		4	13.12	even	2	inner
1183.2.e.e.508.1		4	7.4	even	3	inner
1183.2.e.e.508.2		4	91.25	even	6	inner
8281.2.a.s.1.1		2	91.51	even	6
8281.2.a.s.1.2		2	7.2	even	3
8281.2.a.w.1.1		2	91.12	odd	6
8281.2.a.w.1.2		2	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 1.50000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 1.50000i) q^{5} -1.73205 q^{6} +(-2.59808 - 0.500000i) q^{7} -1.73205 q^{8} +(1.00000 - 1.73205i) q^{9} +(1.50000 + 2.59808i) q^{10} +(2.59808 + 4.50000i) q^{11} +(0.500000 - 0.866025i) q^{12} +(3.00000 - 3.46410i) q^{14} +1.73205 q^{15} +(2.50000 - 4.33013i) q^{16} +(3.00000 + 5.19615i) q^{17} +(1.73205 + 3.00000i) q^{18} +(0.866025 - 1.50000i) q^{19} -1.73205 q^{20} +(-0.866025 - 2.50000i) q^{21} -9.00000 q^{22} +(-0.866025 - 1.50000i) q^{24} +(1.00000 + 1.73205i) q^{25} +5.00000 q^{27} +(0.866025 + 2.50000i) q^{28} +3.00000 q^{29} +(-1.50000 + 2.59808i) q^{30} +(0.866025 + 1.50000i) q^{31} +(2.59808 + 4.50000i) q^{32} +(-2.59808 + 4.50000i) q^{33} -10.3923 q^{34} +(-3.00000 + 3.46410i) q^{35} -2.00000 q^{36} +(1.50000 + 2.59808i) q^{38} +(-1.50000 + 2.59808i) q^{40} -5.19615 q^{41} +(4.50000 + 0.866025i) q^{42} -11.0000 q^{43} +(2.59808 - 4.50000i) q^{44} +(-1.73205 - 3.00000i) q^{45} +(-4.33013 + 7.50000i) q^{47} +5.00000 q^{48} +(6.50000 + 2.59808i) q^{49} -3.46410 q^{50} +(-3.00000 + 5.19615i) q^{51} +(4.50000 + 7.79423i) q^{53} +(-4.33013 + 7.50000i) q^{54} +9.00000 q^{55} +(4.50000 + 0.866025i) q^{56} +1.73205 q^{57} +(-2.59808 + 4.50000i) q^{58} +(-1.73205 - 3.00000i) q^{59} +(-0.866025 - 1.50000i) q^{60} +(-3.50000 + 6.06218i) q^{61} -3.00000 q^{62} +(-3.46410 + 4.00000i) q^{63} +1.00000 q^{64} +(-4.50000 - 7.79423i) q^{66} +(4.33013 + 7.50000i) q^{67} +(3.00000 - 5.19615i) q^{68} +(-2.59808 - 7.50000i) q^{70} -1.73205 q^{71} +(-1.73205 + 3.00000i) q^{72} +(4.33013 + 7.50000i) q^{73} +(-1.00000 + 1.73205i) q^{75} -1.73205 q^{76} +(-4.50000 - 12.9904i) q^{77} +(2.50000 - 4.33013i) q^{79} +(-4.33013 - 7.50000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} +3.46410 q^{83} +(-1.73205 + 2.00000i) q^{84} +10.3923 q^{85} +(9.52628 - 16.5000i) q^{86} +(1.50000 + 2.59808i) q^{87} +(-4.50000 - 7.79423i) q^{88} +(3.46410 - 6.00000i) q^{89} +6.00000 q^{90} +(-0.866025 + 1.50000i) q^{93} +(-7.50000 - 12.9904i) q^{94} +(-1.50000 - 2.59808i) q^{95} +(-2.59808 + 4.50000i) q^{96} +5.19615 q^{97} +(-9.52628 + 7.50000i) q^{98} +10.3923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 2 q^{4} + 4 q^{9} + 6 q^{10} + 2 q^{12} + 12 q^{14} + 10 q^{16} + 12 q^{17} - 36 q^{22} + 4 q^{25} + 20 q^{27} + 12 q^{29} - 6 q^{30} - 12 q^{35} - 8 q^{36} + 6 q^{38} - 6 q^{40} + 18 q^{42}+ \cdots - 6 q^{95}+O(q^{100}) \) 4 * q + 2 * q^3 - 2 * q^4 + 4 * q^9 + 6 * q^10 + 2 * q^12 + 12 * q^14 + 10 * q^16 + 12 * q^17 - 36 * q^22 + 4 * q^25 + 20 * q^27 + 12 * q^29 - 6 * q^30 - 12 * q^35 - 8 * q^36 + 6 * q^38 - 6 * q^40 + 18 * q^42 - 44 * q^43 + 20 * q^48 + 26 * q^49 - 12 * q^51 + 18 * q^53 + 36 * q^55 + 18 * q^56 - 14 * q^61 - 12 * q^62 + 4 * q^64 - 18 * q^66 + 12 * q^68 - 4 * q^75 - 18 * q^77 + 10 * q^79 - 2 * q^81 + 18 * q^82 + 6 * q^87 - 18 * q^88 + 24 * q^90 - 30 * q^94 - 6 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more