LMFDB - Embedded newform 1050.2.i.p.751.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(151,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1050.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			751.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1050.751
Dual form			1050.2.i.p.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.50000 + 4.33013i) q^{11} +(-0.500000 + 0.866025i) q^{12} +5.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.50000 - 6.06218i) q^{19} +(-2.50000 - 0.866025i) q^{21} +5.00000 q^{22} +(0.500000 - 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{26} +1.00000 q^{27} +(-2.50000 - 0.866025i) q^{28} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.50000 - 4.33013i) q^{33} -4.00000 q^{34} +1.00000 q^{36} +(0.500000 - 0.866025i) q^{37} +(-3.50000 - 6.06218i) q^{38} +(-2.50000 - 4.33013i) q^{39} +5.00000 q^{41} +(-2.00000 + 1.73205i) q^{42} -12.0000 q^{43} +(2.50000 - 4.33013i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(-5.50000 + 9.52628i) q^{47} +1.00000 q^{48} +(1.00000 - 6.92820i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(-2.50000 - 4.33013i) q^{52} +(-4.50000 - 7.79423i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.00000 + 1.73205i) q^{56} -7.00000 q^{57} +(-2.00000 - 3.46410i) q^{59} +(-2.00000 + 3.46410i) q^{61} +2.00000 q^{62} +(0.500000 + 2.59808i) q^{63} +1.00000 q^{64} +(-2.50000 - 4.33013i) q^{66} +(-6.00000 - 10.3923i) q^{67} +(-2.00000 + 3.46410i) q^{68} -1.00000 q^{69} +2.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(5.00000 + 8.66025i) q^{73} +(-0.500000 - 0.866025i) q^{74} -7.00000 q^{76} +(12.5000 + 4.33013i) q^{77} -5.00000 q^{78} +(6.00000 - 10.3923i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(2.50000 - 4.33013i) q^{82} +12.0000 q^{83} +(0.500000 + 2.59808i) q^{84} +(-6.00000 + 10.3923i) q^{86} +(-2.50000 - 4.33013i) q^{88} +(-7.00000 + 12.1244i) q^{89} +(10.0000 - 8.66025i) q^{91} -1.00000 q^{92} +(1.00000 - 1.73205i) q^{93} +(5.50000 + 9.52628i) q^{94} +(0.500000 - 0.866025i) q^{96} +8.00000 q^{97} +(-5.50000 - 4.33013i) q^{98} -5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} + 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 - 2 * q^6 + 4 * q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} + 4 q^{7} - 2 q^{8} - q^{9} + 5 q^{11} - q^{12} + 10 q^{13} - q^{14} - q^{16} - 4 q^{17} + q^{18} + 7 q^{19} - 5 q^{21} + 10 q^{22} + q^{23} + q^{24} + 5 q^{26} + 2 q^{27} - 5 q^{28} + 2 q^{31} + q^{32} + 5 q^{33} - 8 q^{34} + 2 q^{36} + q^{37} - 7 q^{38} - 5 q^{39} + 10 q^{41} - 4 q^{42} - 24 q^{43} + 5 q^{44} - q^{46} - 11 q^{47} + 2 q^{48} + 2 q^{49} - 4 q^{51} - 5 q^{52} - 9 q^{53} + q^{54} - 4 q^{56} - 14 q^{57} - 4 q^{59} - 4 q^{61} + 4 q^{62} + q^{63} + 2 q^{64} - 5 q^{66} - 12 q^{67} - 4 q^{68} - 2 q^{69} + 4 q^{71} + q^{72} + 10 q^{73} - q^{74} - 14 q^{76} + 25 q^{77} - 10 q^{78} + 12 q^{79} - q^{81} + 5 q^{82} + 24 q^{83} + q^{84} - 12 q^{86} - 5 q^{88} - 14 q^{89} + 20 q^{91} - 2 q^{92} + 2 q^{93} + 11 q^{94} + q^{96} + 16 q^{97} - 11 q^{98} - 10 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 - 2 * q^6 + 4 * q^7 - 2 * q^8 - q^9 + 5 * q^11 - q^12 + 10 * q^13 - q^14 - q^16 - 4 * q^17 + q^18 + 7 * q^19 - 5 * q^21 + 10 * q^22 + q^23 + q^24 + 5 * q^26 + 2 * q^27 - 5 * q^28 + 2 * q^31 + q^32 + 5 * q^33 - 8 * q^34 + 2 * q^36 + q^37 - 7 * q^38 - 5 * q^39 + 10 * q^41 - 4 * q^42 - 24 * q^43 + 5 * q^44 - q^46 - 11 * q^47 + 2 * q^48 + 2 * q^49 - 4 * q^51 - 5 * q^52 - 9 * q^53 + q^54 - 4 * q^56 - 14 * q^57 - 4 * q^59 - 4 * q^61 + 4 * q^62 + q^63 + 2 * q^64 - 5 * q^66 - 12 * q^67 - 4 * q^68 - 2 * q^69 + 4 * q^71 + q^72 + 10 * q^73 - q^74 - 14 * q^76 + 25 * q^77 - 10 * q^78 + 12 * q^79 - q^81 + 5 * q^82 + 24 * q^83 + q^84 - 12 * q^86 - 5 * q^88 - 14 * q^89 + 20 * q^91 - 2 * q^92 + 2 * q^93 + 11 * q^94 + q^96 + 16 * q^97 - 11 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.00000			−0.408248
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	0.945979	+	0.324227i	$0.105104\pi$
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	−0.192201	+	0.981356i	$0.561563\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	5.00000			1.38675			0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000			1.38675			0.693375	+	0.720577i	$0.256123\pi$
$14$	−0.500000	−	2.59808i	−0.133631	−	0.694365i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	0.917663	−	0.397360i	$-0.130073\pi$
$20$		0			0
$21$	−2.50000	−	0.866025i	−0.545545	−	0.188982i
$22$	5.00000			1.06600
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	2.50000	−	4.33013i	0.490290	−	0.849208i
$27$	1.00000			0.192450
$28$	−2.50000	−	0.866025i	−0.472456	−	0.163663i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.50000	−	4.33013i	0.435194	−	0.753778i
$34$	−4.00000			−0.685994
$35$		0			0
$36$	1.00000			0.166667
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−3.50000	−	6.06218i	−0.567775	−	0.983415i
$39$	−2.50000	−	4.33013i	−0.400320	−	0.693375i
$40$		0			0
$41$	5.00000			0.780869			0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000			0.780869			0.390434	+	0.920631i	$0.372325\pi$
$42$	−2.00000	+	1.73205i	−0.308607	+	0.267261i
$43$	−12.0000			−1.82998			−0.914991	−	0.403473i	$-0.867803\pi$
$43$	−12.0000			−1.82998			−0.914991	+	0.403473i	$0.867803\pi$
$44$	2.50000	−	4.33013i	0.376889	−	0.652791i
$45$		0			0
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	−5.50000	+	9.52628i	−0.802257	+	1.38955i	0.115870	+	0.993264i	$0.463035\pi$
$47$	−5.50000	+	9.52628i	−0.802257	+	1.38955i	−0.918127	+	0.396286i	$0.870299\pi$
$48$	1.00000			0.144338
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	−0.989828	−	0.142269i	$-0.954560\pi$
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	0.371706	−	0.928351i	$-0.378773\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	−2.00000	+	1.73205i	−0.267261	+	0.231455i
$57$	−7.00000			−0.927173
$58$		0			0
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	0.705965	−	0.708247i	$-0.250514\pi$
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	−0.966342	+	0.257260i	$0.917180\pi$
$60$		0			0
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	−0.965187	−	0.261562i	$-0.915762\pi$
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	0.709113	+	0.705095i	$0.249096\pi$
$62$	2.00000			0.254000
$63$	0.500000	+	2.59808i	0.0629941	+	0.327327i
$64$	1.00000			0.125000
$65$		0			0
$66$	−2.50000	−	4.33013i	−0.307729	−	0.533002i
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$	−2.00000	+	3.46410i	−0.242536	+	0.420084i
$69$	−1.00000			−0.120386
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	0.994850	+	0.101361i	$0.0323196\pi$
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	−0.409644	+	0.912245i	$0.634347\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$		0			0
$76$	−7.00000			−0.802955
$77$	12.5000	+	4.33013i	1.42451	+	0.493464i
$78$	−5.00000			−0.566139
$79$	6.00000	−	10.3923i	0.675053	−	1.16923i	−0.301401	−	0.953498i	$-0.597454\pi$
$79$	6.00000	−	10.3923i	0.675053	−	1.16923i	0.976453	−	0.215728i	$-0.0692125\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.50000	−	4.33013i	0.276079	−	0.478183i
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$	0.500000	+	2.59808i	0.0545545	+	0.283473i
$85$		0			0
$86$	−6.00000	+	10.3923i	−0.646997	+	1.12063i
$87$		0			0
$88$	−2.50000	−	4.33013i	−0.266501	−	0.461593i
$89$	−7.00000	+	12.1244i	−0.741999	+	1.28518i	0.209585	+	0.977790i	$0.432789\pi$
$89$	−7.00000	+	12.1244i	−0.741999	+	1.28518i	−0.951584	+	0.307389i	$0.900545\pi$
$90$		0			0
$91$	10.0000	−	8.66025i	1.04828	−	0.907841i
$92$	−1.00000			−0.104257
$93$	1.00000	−	1.73205i	0.103695	−	0.179605i
$94$	5.50000	+	9.52628i	0.567282	+	0.982561i
$95$		0			0
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$	−5.50000	−	4.33013i	−0.555584	−	0.437409i
$99$	−5.00000			−0.502519
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$	2.00000	+	3.46410i	0.198030	+	0.342997i
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	−0.598858	−	0.800855i	$-0.704379\pi$
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	0.992990	+	0.118199i	$0.0377120\pi$
$104$	−5.00000			−0.490290
$105$		0			0
$106$	−9.00000			−0.874157
$107$	−1.00000	+	1.73205i	−0.0966736	+	0.167444i	−0.910306	−	0.413936i	$-0.864154\pi$
$107$	−1.00000	+	1.73205i	−0.0966736	+	0.167444i	0.813632	+	0.581380i	$0.197487\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$		0			0
$111$	−1.00000			−0.0949158
$112$	0.500000	+	2.59808i	0.0472456	+	0.245495i
$113$	14.0000			1.31701			0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000			1.31701			0.658505	+	0.752577i	$0.271189\pi$
$114$	−3.50000	+	6.06218i	−0.327805	+	0.567775i
$115$		0			0
$116$		0			0
$117$	−2.50000	+	4.33013i	−0.231125	+	0.400320i
$118$	−4.00000			−0.368230
$119$	−10.0000	−	3.46410i	−0.916698	−	0.317554i
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$	2.00000	+	3.46410i	0.181071	+	0.313625i
$123$	−2.50000	−	4.33013i	−0.225417	−	0.390434i
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$		0			0
$126$	2.50000	+	0.866025i	0.222718	+	0.0771517i
$127$	−9.00000			−0.798621			−0.399310	−	0.916816i	$-0.630750\pi$
$127$	−9.00000			−0.798621			−0.399310	+	0.916816i	$0.630750\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	6.00000	+	10.3923i	0.528271	+	0.914991i
$130$		0			0
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	−0.599699	−	0.800226i	$-0.704713\pi$
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	0.992865	+	0.119241i	$0.0380462\pi$
$132$	−5.00000			−0.435194
$133$	−3.50000	−	18.1865i	−0.303488	−	1.57697i
$134$	−12.0000			−1.03664
$135$		0			0
$136$	2.00000	+	3.46410i	0.171499	+	0.297044i
$137$	−1.00000	−	1.73205i	−0.0854358	−	0.147979i	0.820141	−	0.572161i	$-0.193895\pi$
$137$	−1.00000	−	1.73205i	−0.0854358	−	0.147979i	−0.905577	+	0.424182i	$0.860562\pi$
$138$	−0.500000	+	0.866025i	−0.0425628	+	0.0737210i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		0			0
$141$	11.0000			0.926367
$142$	1.00000	−	1.73205i	0.0839181	−	0.145350i
$143$	12.5000	+	21.6506i	1.04530	+	1.81052i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$		0			0
$146$	10.0000			0.827606
$147$	−6.50000	+	2.59808i	−0.536111	+	0.214286i
$148$	−1.00000			−0.0821995
$149$	−6.00000	+	10.3923i	−0.491539	+	0.851371i	−0.999953	−	0.00974235i	$-0.996899\pi$
$149$	−6.00000	+	10.3923i	−0.491539	+	0.851371i	0.508413	+	0.861113i	$0.330232\pi$
$150$		0			0
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	−0.996600	−	0.0823900i	$-0.973745\pi$
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	0.426948	−	0.904276i	$-0.359589\pi$
$152$	−3.50000	+	6.06218i	−0.283887	+	0.491708i
$153$	4.00000			0.323381
$154$	10.0000	−	8.66025i	0.805823	−	0.697863i
$155$		0			0
$156$	−2.50000	+	4.33013i	−0.200160	+	0.346688i
$157$	5.50000	+	9.52628i	0.438948	+	0.760280i	0.997609	−	0.0691164i	$-0.0220180\pi$
$157$	5.50000	+	9.52628i	0.438948	+	0.760280i	−0.558661	+	0.829396i	$0.688685\pi$
$158$	−6.00000	−	10.3923i	−0.477334	−	0.826767i
$159$	−4.50000	+	7.79423i	−0.356873	+	0.618123i
$160$		0			0
$161$	−0.500000	−	2.59808i	−0.0394055	−	0.204757i
$162$	−1.00000			−0.0785674
$163$	−12.0000	+	20.7846i	−0.939913	+	1.62798i	−0.174282	+	0.984696i	$0.555760\pi$
$163$	−12.0000	+	20.7846i	−0.939913	+	1.62798i	−0.765631	+	0.643280i	$0.777573\pi$
$164$	−2.50000	−	4.33013i	−0.195217	−	0.338126i
$165$		0			0
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$	−11.0000			−0.851206			−0.425603	−	0.904910i	$-0.639938\pi$
$167$	−11.0000			−0.851206			−0.425603	+	0.904910i	$0.639938\pi$
$168$	2.50000	+	0.866025i	0.192879	+	0.0668153i
$169$	12.0000			0.923077
$170$		0			0
$171$	3.50000	+	6.06218i	0.267652	+	0.463586i
$172$	6.00000	+	10.3923i	0.457496	+	0.792406i
$173$	−6.50000	+	11.2583i	−0.494186	+	0.855955i	−0.999978	−	0.00670064i	$-0.997867\pi$
$173$	−6.50000	+	11.2583i	−0.494186	+	0.855955i	0.505792	+	0.862656i	$0.331200\pi$
$174$		0			0
$175$		0			0
$176$	−5.00000			−0.376889
$177$	−2.00000	+	3.46410i	−0.150329	+	0.260378i
$178$	7.00000	+	12.1244i	0.524672	+	0.908759i
$179$	11.5000	+	19.9186i	0.859550	+	1.48878i	0.872358	+	0.488867i	$0.162590\pi$
$179$	11.5000	+	19.9186i	0.859550	+	1.48878i	−0.0128080	+	0.999918i	$0.504077\pi$
$180$		0			0
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$	−2.50000	−	12.9904i	−0.185312	−	0.962911i
$183$	4.00000			0.295689
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$		0			0
$186$	−1.00000	−	1.73205i	−0.0733236	−	0.127000i
$187$	10.0000	−	17.3205i	0.731272	−	1.26660i
$188$	11.0000			0.802257
$189$	2.00000	−	1.73205i	0.145479	−	0.125988i
$190$		0			0
$191$	−7.00000	+	12.1244i	−0.506502	+	0.877288i	0.493469	+	0.869763i	$0.335728\pi$
$191$	−7.00000	+	12.1244i	−0.506502	+	0.877288i	−0.999972	+	0.00752447i	$0.997605\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	0.987945	−	0.154805i	$-0.0494748\pi$
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	−0.628037	+	0.778183i	$0.716141\pi$
$194$	4.00000	−	6.92820i	0.287183	−	0.497416i
$195$		0			0
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	3.00000			0.213741			0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000			0.213741			0.106871	+	0.994273i	$0.465917\pi$
$198$	−2.50000	+	4.33013i	−0.177667	+	0.307729i
$199$	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	$0.788052\pi$
$200$		0			0
$201$	−6.00000	+	10.3923i	−0.423207	+	0.733017i
$202$		0			0
$203$		0			0
$204$	4.00000			0.280056
$205$		0			0
$206$	−4.00000	−	6.92820i	−0.278693	−	0.482711i
$207$	0.500000	+	0.866025i	0.0347524	+	0.0601929i
$208$	−2.50000	+	4.33013i	−0.173344	+	0.300240i
$209$	35.0000			2.42100
$210$		0			0
$211$	17.0000			1.17033			0.585164	−	0.810915i	$-0.301030\pi$
$211$	17.0000			1.17033			0.585164	+	0.810915i	$0.301030\pi$
$212$	−4.50000	+	7.79423i	−0.309061	+	0.535310i
$213$	−1.00000	−	1.73205i	−0.0685189	−	0.118678i
$214$	1.00000	+	1.73205i	0.0683586	+	0.118401i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	5.00000	+	1.73205i	0.339422	+	0.117579i
$218$	2.00000			0.135457
$219$	5.00000	−	8.66025i	0.337869	−	0.585206i
$220$		0			0
$221$	−10.0000	−	17.3205i	−0.672673	−	1.16510i
$222$	−0.500000	+	0.866025i	−0.0335578	+	0.0581238i
$223$	12.0000			0.803579			0.401790	−	0.915732i	$-0.368388\pi$
$223$	12.0000			0.803579			0.401790	+	0.915732i	$0.368388\pi$
$224$	2.50000	+	0.866025i	0.167038	+	0.0578638i
$225$		0			0
$226$	7.00000	−	12.1244i	0.465633	−	0.806500i
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$	3.50000	+	6.06218i	0.231793	+	0.401478i
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	−0.982592	−	0.185776i	$-0.940520\pi$
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	0.652183	+	0.758062i	$0.273853\pi$
$230$		0			0
$231$	−2.50000	−	12.9904i	−0.164488	−	0.854704i
$232$		0			0
$233$	−7.00000	+	12.1244i	−0.458585	+	0.794293i	−0.998886	−	0.0471787i	$-0.984977\pi$
$233$	−7.00000	+	12.1244i	−0.458585	+	0.794293i	0.540301	+	0.841472i	$0.318310\pi$
$234$	2.50000	+	4.33013i	0.163430	+	0.283069i
$235$		0			0
$236$	−2.00000	+	3.46410i	−0.130189	+	0.225494i
$237$	−12.0000			−0.779484
$238$	−8.00000	+	6.92820i	−0.518563	+	0.449089i
$239$	−22.0000			−1.42306			−0.711531	−	0.702655i	$-0.751998\pi$
$239$	−22.0000			−1.42306			−0.711531	+	0.702655i	$0.751998\pi$
$240$		0			0
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	0.516695	−	0.856170i	$-0.327162\pi$
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	−0.999812	+	0.0193858i	$0.993829\pi$
$242$	7.00000	+	12.1244i	0.449977	+	0.779383i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	4.00000			0.256074
$245$		0			0
$246$	−5.00000			−0.318788
$247$	17.5000	−	30.3109i	1.11350	−	1.92864i
$248$	−1.00000	−	1.73205i	−0.0635001	−	0.109985i
$249$	−6.00000	−	10.3923i	−0.380235	−	0.658586i
$250$		0			0
$251$	1.00000			0.0631194			0.0315597	−	0.999502i	$-0.489953\pi$
$251$	1.00000			0.0631194			0.0315597	+	0.999502i	$0.489953\pi$
$252$	2.00000	−	1.73205i	0.125988	−	0.109109i
$253$	5.00000			0.314347
$254$	−4.50000	+	7.79423i	−0.282355	+	0.489053i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−8.00000	+	13.8564i	−0.499026	+	0.864339i	−0.999999	−	0.00112398i	$-0.999642\pi$
$257$	−8.00000	+	13.8564i	−0.499026	+	0.864339i	0.500973	+	0.865463i	$0.332976\pi$
$258$	12.0000			0.747087
$259$	−0.500000	−	2.59808i	−0.0310685	−	0.161437i
$260$		0			0
$261$		0			0
$262$	−4.50000	−	7.79423i	−0.278011	−	0.481529i
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$	−2.50000	+	4.33013i	−0.153864	+	0.266501i
$265$		0			0
$266$	−17.5000	−	6.06218i	−1.07299	−	0.371696i
$267$	14.0000			0.856786
$268$	−6.00000	+	10.3923i	−0.366508	+	0.634811i
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	0.956176	+	0.292791i	$0.0945841\pi$
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	−0.224523	+	0.974469i	$0.572083\pi$
$270$		0			0
$271$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$271$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$272$	4.00000			0.242536
$273$	−12.5000	−	4.33013i	−0.756534	−	0.262071i
$274$	−2.00000			−0.120824
$275$		0			0
$276$	0.500000	+	0.866025i	0.0300965	+	0.0521286i
$277$	7.00000	+	12.1244i	0.420589	+	0.728482i	0.995997	−	0.0893846i	$-0.0284900\pi$
$277$	7.00000	+	12.1244i	0.420589	+	0.728482i	−0.575408	+	0.817867i	$0.695157\pi$
$278$	−2.00000	+	3.46410i	−0.119952	+	0.207763i
$279$	−2.00000			−0.119737
$280$		0			0
$281$	7.00000			0.417585			0.208792	−	0.977960i	$-0.433047\pi$
$281$	7.00000			0.417585			0.208792	+	0.977960i	$0.433047\pi$
$282$	5.50000	−	9.52628i	0.327520	−	0.567282i
$283$	−5.00000	−	8.66025i	−0.297219	−	0.514799i	0.678280	−	0.734804i	$-0.262726\pi$
$283$	−5.00000	−	8.66025i	−0.297219	−	0.514799i	−0.975499	+	0.220005i	$0.929393\pi$
$284$	−1.00000	−	1.73205i	−0.0593391	−	0.102778i
$285$		0			0
$286$	25.0000			1.47828
$287$	10.0000	−	8.66025i	0.590281	−	0.511199i
$288$	−1.00000			−0.0589256
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$	−4.00000	−	6.92820i	−0.234484	−	0.406138i
$292$	5.00000	−	8.66025i	0.292603	−	0.506803i
$293$	−9.00000			−0.525786			−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000			−0.525786			−0.262893	+	0.964825i	$0.584677\pi$
$294$	−1.00000	+	6.92820i	−0.0583212	+	0.404061i
$295$		0			0
$296$	−0.500000	+	0.866025i	−0.0290619	+	0.0503367i
$297$	2.50000	+	4.33013i	0.145065	+	0.251259i
$298$	6.00000	+	10.3923i	0.347571	+	0.602010i
$299$	2.50000	−	4.33013i	0.144579	−	0.250418i
$300$		0			0
$301$	−24.0000	+	20.7846i	−1.38334	+	1.19800i
$302$	−14.0000			−0.805609
$303$		0			0
$304$	3.50000	+	6.06218i	0.200739	+	0.347690i
$305$		0			0
$306$	2.00000	−	3.46410i	0.114332	−	0.198030i
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$	−2.50000	−	12.9904i	−0.142451	−	0.740196i
$309$	−8.00000			−0.455104
$310$		0			0
$311$	−4.00000	−	6.92820i	−0.226819	−	0.392862i	0.730044	−	0.683400i	$-0.239499\pi$
$311$	−4.00000	−	6.92820i	−0.226819	−	0.392862i	−0.956864	+	0.290537i	$0.906166\pi$
$312$	2.50000	+	4.33013i	0.141535	+	0.245145i
$313$	8.00000	−	13.8564i	0.452187	−	0.783210i	−0.546335	−	0.837567i	$-0.683977\pi$
$313$	8.00000	−	13.8564i	0.452187	−	0.783210i	0.998522	+	0.0543564i	$0.0173107\pi$
$314$	11.0000			0.620766
$315$		0			0
$316$	−12.0000			−0.675053
$317$	−11.0000	+	19.0526i	−0.617822	+	1.07010i	0.372061	+	0.928208i	$0.378651\pi$
$317$	−11.0000	+	19.0526i	−0.617822	+	1.07010i	−0.989882	+	0.141890i	$0.954682\pi$
$318$	4.50000	+	7.79423i	0.252347	+	0.437079i
$319$		0			0
$320$		0			0
$321$	2.00000			0.111629
$322$	−2.50000	−	0.866025i	−0.139320	−	0.0482617i
$323$	−28.0000			−1.55796
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	12.0000	+	20.7846i	0.664619	+	1.15115i
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$	−5.00000			−0.276079
$329$	5.50000	+	28.5788i	0.303225	+	1.57560i
$330$		0			0
$331$	−15.5000	+	26.8468i	−0.851957	+	1.47563i	0.0274825	+	0.999622i	$0.491251\pi$
$331$	−15.5000	+	26.8468i	−0.851957	+	1.47563i	−0.879440	+	0.476011i	$0.842082\pi$
$332$	−6.00000	−	10.3923i	−0.329293	−	0.570352i
$333$	0.500000	+	0.866025i	0.0273998	+	0.0474579i
$334$	−5.50000	+	9.52628i	−0.300947	+	0.521255i
$335$		0			0
$336$	2.00000	−	1.73205i	0.109109	−	0.0944911i
$337$	16.0000			0.871576			0.435788	−	0.900049i	$-0.356470\pi$
$337$	16.0000			0.871576			0.435788	+	0.900049i	$0.356470\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$	−7.00000	−	12.1244i	−0.380188	−	0.658505i
$340$		0			0
$341$	−5.00000	+	8.66025i	−0.270765	+	0.468979i
$342$	7.00000			0.378517
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	12.0000			0.646997
$345$		0			0
$346$	6.50000	+	11.2583i	0.349442	+	0.605252i
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	0.516667	−	0.856186i	$-0.327172\pi$
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	−0.999813	+	0.0193540i	$0.993839\pi$
$348$		0			0
$349$	−4.00000			−0.214115			−0.107058	−	0.994253i	$-0.534143\pi$
$349$	−4.00000			−0.214115			−0.107058	+	0.994253i	$0.534143\pi$
$350$		0			0
$351$	5.00000			0.266880
$352$	−2.50000	+	4.33013i	−0.133250	+	0.230797i
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	0.985719	+	0.168397i	$0.0538590\pi$
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	−0.347024	+	0.937856i	$0.612808\pi$
$354$	2.00000	+	3.46410i	0.106299	+	0.184115i
$355$		0			0
$356$	14.0000			0.741999
$357$	2.00000	+	10.3923i	0.105851	+	0.550019i
$358$	23.0000			1.21559
$359$	10.0000	−	17.3205i	0.527780	−	0.914141i	−0.471696	−	0.881761i	$-0.656358\pi$
$359$	10.0000	−	17.3205i	0.527780	−	0.914141i	0.999476	−	0.0323801i	$-0.0103087\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$	10.0000	−	17.3205i	0.525588	−	0.910346i
$363$	14.0000			0.734809
$364$	−12.5000	−	4.33013i	−0.655178	−	0.226960i
$365$		0			0
$366$	2.00000	−	3.46410i	0.104542	−	0.181071i
$367$	3.50000	+	6.06218i	0.182699	+	0.316443i	0.942799	−	0.333363i	$-0.108183\pi$
$367$	3.50000	+	6.06218i	0.182699	+	0.316443i	−0.760100	+	0.649806i	$0.774850\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$	−2.50000	+	4.33013i	−0.130145	+	0.225417i
$370$		0			0
$371$	−22.5000	−	7.79423i	−1.16814	−	0.404656i
$372$	−2.00000			−0.103695
$373$	−11.0000	+	19.0526i	−0.569558	+	0.986504i	0.427051	+	0.904227i	$0.359552\pi$
$373$	−11.0000	+	19.0526i	−0.569558	+	0.986504i	−0.996610	+	0.0822766i	$0.973781\pi$
$374$	−10.0000	−	17.3205i	−0.517088	−	0.895622i
$375$		0			0
$376$	5.50000	−	9.52628i	0.283641	−	0.491280i
$377$		0			0
$378$	−0.500000	−	2.59808i	−0.0257172	−	0.133631i
$379$	1.00000			0.0513665			0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000			0.0513665			0.0256833	+	0.999670i	$0.491824\pi$
$380$		0			0
$381$	4.50000	+	7.79423i	0.230542	+	0.399310i
$382$	7.00000	+	12.1244i	0.358151	+	0.620336i
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	−0.462563	−	0.886586i	$-0.653070\pi$
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	0.999088	−	0.0427020i	$-0.0135966\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	10.0000			0.508987
$387$	6.00000	−	10.3923i	0.304997	−	0.528271i
$388$	−4.00000	−	6.92820i	−0.203069	−	0.351726i
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	0.542445	−	0.840091i	$-0.317499\pi$
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	−0.998763	+	0.0497253i	$0.984165\pi$
$390$		0			0
$391$	−4.00000			−0.202289
$392$	−1.00000	+	6.92820i	−0.0505076	+	0.349927i
$393$	−9.00000			−0.453990
$394$	1.50000	−	2.59808i	0.0755689	−	0.130889i
$395$		0			0
$396$	2.50000	+	4.33013i	0.125630	+	0.217597i
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	−0.986481	−	0.163876i	$-0.947600\pi$
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	0.635161	+	0.772380i	$0.280934\pi$
$398$	4.00000			0.200502
$399$	−14.0000	+	12.1244i	−0.700877	+	0.606977i
$400$		0			0
$401$	10.5000	−	18.1865i	0.524345	−	0.908192i	−0.475253	−	0.879849i	$-0.657644\pi$
$401$	10.5000	−	18.1865i	0.524345	−	0.908192i	0.999598	−	0.0283431i	$-0.00902310\pi$
$402$	6.00000	+	10.3923i	0.299253	+	0.518321i
$403$	5.00000	+	8.66025i	0.249068	+	0.431398i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5.00000			0.247841
$408$	2.00000	−	3.46410i	0.0990148	−	0.171499i
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$		0			0
$411$	−1.00000	+	1.73205i	−0.0493264	+	0.0854358i
$412$	−8.00000			−0.394132
$413$	−10.0000	−	3.46410i	−0.492068	−	0.170457i
$414$	1.00000			0.0491473
$415$		0			0
$416$	2.50000	+	4.33013i	0.122573	+	0.212302i
$417$	2.00000	+	3.46410i	0.0979404	+	0.169638i
$418$	17.5000	−	30.3109i	0.855953	−	1.48255i
$419$	15.0000			0.732798			0.366399	−	0.930458i	$-0.380591\pi$
$419$	15.0000			0.732798			0.366399	+	0.930458i	$0.380591\pi$
$420$		0			0
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$	8.50000	−	14.7224i	0.413774	−	0.716677i
$423$	−5.50000	−	9.52628i	−0.267419	−	0.463184i
$424$	4.50000	+	7.79423i	0.218539	+	0.378521i
$425$		0			0
$426$	−2.00000			−0.0969003
$427$	2.00000	+	10.3923i	0.0967868	+	0.502919i
$428$	2.00000			0.0966736
$429$	12.5000	−	21.6506i	0.603506	−	1.04530i
$430$		0			0
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−24.0000			−1.15337			−0.576683	−	0.816968i	$-0.695653\pi$
$433$	−24.0000			−1.15337			−0.576683	+	0.816968i	$0.695653\pi$
$434$	4.00000	−	3.46410i	0.192006	−	0.166282i
$435$		0			0
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$	−3.50000	−	6.06218i	−0.167428	−	0.289993i
$438$	−5.00000	−	8.66025i	−0.238909	−	0.413803i
$439$	20.0000	−	34.6410i	0.954548	−	1.65333i	0.219149	−	0.975691i	$-0.429672\pi$
$439$	20.0000	−	34.6410i	0.954548	−	1.65333i	0.735399	−	0.677634i	$-0.236995\pi$
$440$		0			0
$441$	5.50000	+	4.33013i	0.261905	+	0.206197i
$442$	−20.0000			−0.951303
$443$	−14.0000	+	24.2487i	−0.665160	+	1.15209i	0.314082	+	0.949396i	$0.398303\pi$
$443$	−14.0000	+	24.2487i	−0.665160	+	1.15209i	−0.979242	+	0.202695i	$0.935030\pi$
$444$	0.500000	+	0.866025i	0.0237289	+	0.0410997i
$445$		0			0
$446$	6.00000	−	10.3923i	0.284108	−	0.492090i
$447$	12.0000			0.567581
$448$	2.00000	−	1.73205i	0.0944911	−	0.0818317i
$449$	−29.0000			−1.36859			−0.684297	−	0.729203i	$-0.739891\pi$
$449$	−29.0000			−1.36859			−0.684297	+	0.729203i	$0.739891\pi$
$450$		0			0
$451$	12.5000	+	21.6506i	0.588602	+	1.01949i
$452$	−7.00000	−	12.1244i	−0.329252	−	0.570282i
$453$	−7.00000	+	12.1244i	−0.328889	+	0.569652i
$454$	−12.0000			−0.563188
$455$		0			0
$456$	7.00000			0.327805
$457$	−7.00000	+	12.1244i	−0.327446	+	0.567153i	−0.982004	−	0.188858i	$-0.939521\pi$
$457$	−7.00000	+	12.1244i	−0.327446	+	0.567153i	0.654558	+	0.756012i	$0.272855\pi$
$458$	5.00000	+	8.66025i	0.233635	+	0.404667i
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$		0			0
$461$	−4.00000			−0.186299			−0.0931493	−	0.995652i	$-0.529693\pi$
$461$	−4.00000			−0.186299			−0.0931493	+	0.995652i	$0.529693\pi$
$462$	−12.5000	−	4.33013i	−0.581553	−	0.201456i
$463$	19.0000			0.883005			0.441502	−	0.897260i	$-0.354446\pi$
$463$	19.0000			0.883005			0.441502	+	0.897260i	$0.354446\pi$
$464$		0			0
$465$		0			0
$466$	7.00000	+	12.1244i	0.324269	+	0.561650i
$467$	−10.0000	+	17.3205i	−0.462745	+	0.801498i	−0.999097	−	0.0424970i	$-0.986469\pi$
$467$	−10.0000	+	17.3205i	−0.462745	+	0.801498i	0.536352	+	0.843995i	$0.319802\pi$
$468$	5.00000			0.231125
$469$	−30.0000	−	10.3923i	−1.38527	−	0.479872i
$470$		0			0
$471$	5.50000	−	9.52628i	0.253427	−	0.438948i
$472$	2.00000	+	3.46410i	0.0920575	+	0.159448i
$473$	−30.0000	−	51.9615i	−1.37940	−	2.38919i
$474$	−6.00000	+	10.3923i	−0.275589	+	0.477334i
$475$		0			0
$476$	2.00000	+	10.3923i	0.0916698	+	0.476331i
$477$	9.00000			0.412082
$478$	−11.0000	+	19.0526i	−0.503128	+	0.871444i
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	0.583803	−	0.811895i	$-0.301564\pi$
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	−0.995023	+	0.0996406i	$0.968231\pi$
$480$		0			0
$481$	2.50000	−	4.33013i	0.113990	−	0.197437i
$482$	−15.0000			−0.683231
$483$	−2.00000	+	1.73205i	−0.0910032	+	0.0788110i
$484$	14.0000			0.636364
$485$		0			0
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$487$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$488$	2.00000	−	3.46410i	0.0905357	−	0.156813i
$489$	24.0000			1.08532
$490$		0			0
$491$	−36.0000			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$492$	−2.50000	+	4.33013i	−0.112709	+	0.195217i
$493$		0			0
$494$	−17.5000	−	30.3109i	−0.787362	−	1.36375i
$495$		0			0
$496$	−2.00000			−0.0898027
$497$	4.00000	−	3.46410i	0.179425	−	0.155386i
$498$	−12.0000			−0.537733
$499$	−20.0000	+	34.6410i	−0.895323	+	1.55074i	−0.0619186	+	0.998081i	$0.519722\pi$
$499$	−20.0000	+	34.6410i	−0.895323	+	1.55074i	−0.833404	+	0.552664i	$0.813611\pi$
$500$		0			0
$501$	5.50000	+	9.52628i	0.245722	+	0.425603i
$502$	0.500000	−	0.866025i	0.0223161	−	0.0386526i
$503$	20.0000			0.891756			0.445878	−	0.895094i	$-0.352892\pi$
$503$	20.0000			0.891756			0.445878	+	0.895094i	$0.352892\pi$
$504$	−0.500000	−	2.59808i	−0.0222718	−	0.115728i
$505$		0			0
$506$	2.50000	−	4.33013i	0.111139	−	0.192498i
$507$	−6.00000	−	10.3923i	−0.266469	−	0.461538i
$508$	4.50000	+	7.79423i	0.199655	+	0.345813i
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	−0.733679	−	0.679496i	$-0.762199\pi$
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	0.955300	+	0.295637i	$0.0955319\pi$
$510$		0			0
$511$	25.0000	+	8.66025i	1.10593	+	0.383107i
$512$	−1.00000			−0.0441942
$513$	3.50000	−	6.06218i	0.154529	−	0.267652i
$514$	8.00000	+	13.8564i	0.352865	+	0.611180i
$515$		0			0
$516$	6.00000	−	10.3923i	0.264135	−	0.457496i
$517$	−55.0000			−2.41890
$518$	−2.50000	−	0.866025i	−0.109844	−	0.0380510i
$519$	13.0000			0.570637
$520$		0			0
$521$	16.5000	+	28.5788i	0.722878	+	1.25206i	0.959841	+	0.280543i	$0.0905145\pi$
$521$	16.5000	+	28.5788i	0.722878	+	1.25206i	−0.236963	+	0.971519i	$0.576152\pi$
$522$		0			0
$523$	−11.0000	+	19.0526i	−0.480996	+	0.833110i	−0.999762	−	0.0218062i	$-0.993058\pi$
$523$	−11.0000	+	19.0526i	−0.480996	+	0.833110i	0.518766	+	0.854916i	$0.326392\pi$
$524$	−9.00000			−0.393167
$525$		0			0
$526$		0			0
$527$	4.00000	−	6.92820i	0.174243	−	0.301797i
$528$	2.50000	+	4.33013i	0.108799	+	0.188445i
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$		0			0
$531$	4.00000			0.173585
$532$	−14.0000	+	12.1244i	−0.606977	+	0.525657i
$533$	25.0000			1.08287
$534$	7.00000	−	12.1244i	0.302920	−	0.524672i
$535$		0			0
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$	11.5000	−	19.9186i	0.496262	−	0.859550i
$538$	24.0000			1.03471
$539$	32.5000	−	12.9904i	1.39987	−	0.559535i
$540$		0			0
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	−0.886721	−	0.462304i	$-0.847023\pi$
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	0.843728	+	0.536771i	$0.180356\pi$
$542$		0			0
$543$	−10.0000	−	17.3205i	−0.429141	−	0.743294i
$544$	2.00000	−	3.46410i	0.0857493	−	0.148522i
$545$		0			0
$546$	−10.0000	+	8.66025i	−0.427960	+	0.370625i
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	−1.00000	+	1.73205i	−0.0427179	+	0.0739895i
$549$	−2.00000	−	3.46410i	−0.0853579	−	0.147844i
$550$		0			0
$551$		0			0
$552$	1.00000			0.0425628
$553$	−6.00000	−	31.1769i	−0.255146	−	1.32578i
$554$	14.0000			0.594803
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	18.5000	+	32.0429i	0.783870	+	1.35770i	0.929672	+	0.368389i	$0.120091\pi$
$557$	18.5000	+	32.0429i	0.783870	+	1.35770i	−0.145802	+	0.989314i	$0.546576\pi$
$558$	−1.00000	+	1.73205i	−0.0423334	+	0.0733236i
$559$	−60.0000			−2.53773
$560$		0			0
$561$	−20.0000			−0.844401
$562$	3.50000	−	6.06218i	0.147639	−	0.255718i
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	0.611656	−	0.791123i	$-0.290503\pi$
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	−0.990961	+	0.134148i	$0.957170\pi$
$564$	−5.50000	−	9.52628i	−0.231592	−	0.401129i
$565$		0			0
$566$	−10.0000			−0.420331
$567$	−2.50000	−	0.866025i	−0.104990	−	0.0363696i
$568$	−2.00000			−0.0839181
$569$	−19.5000	+	33.7750i	−0.817483	+	1.41592i	0.0900490	+	0.995937i	$0.471298\pi$
$569$	−19.5000	+	33.7750i	−0.817483	+	1.41592i	−0.907532	+	0.419984i	$0.862036\pi$
$570$		0			0
$571$	−20.0000	−	34.6410i	−0.836974	−	1.44968i	−0.892413	−	0.451219i	$-0.850989\pi$
$571$	−20.0000	−	34.6410i	−0.836974	−	1.44968i	0.0554391	−	0.998462i	$-0.482344\pi$
$572$	12.5000	−	21.6506i	0.522651	−	0.905259i
$573$	14.0000			0.584858
$574$	−2.50000	−	12.9904i	−0.104348	−	0.542208i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	13.0000	+	22.5167i	0.541197	+	0.937381i	0.998836	+	0.0482425i	$0.0153620\pi$
$577$	13.0000	+	22.5167i	0.541197	+	0.937381i	−0.457639	+	0.889138i	$0.651305\pi$
$578$	−0.500000	−	0.866025i	−0.0207973	−	0.0360219i
$579$	5.00000	−	8.66025i	0.207793	−	0.359908i
$580$		0			0
$581$	24.0000	−	20.7846i	0.995688	−	0.862291i
$582$	−8.00000			−0.331611
$583$	22.5000	−	38.9711i	0.931855	−	1.61402i
$584$	−5.00000	−	8.66025i	−0.206901	−	0.358364i
$585$		0			0
$586$	−4.50000	+	7.79423i	−0.185893	+	0.321977i
$587$	30.0000			1.23823			0.619116	−	0.785299i	$-0.287491\pi$
$587$	30.0000			1.23823			0.619116	+	0.785299i	$0.287491\pi$
$588$	5.50000	+	4.33013i	0.226816	+	0.178571i
$589$	14.0000			0.576860
$590$		0			0
$591$	−1.50000	−	2.59808i	−0.0617018	−	0.106871i
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	18.0000	−	31.1769i	0.739171	−	1.28028i	−0.213697	−	0.976900i	$-0.568551\pi$
$593$	18.0000	−	31.1769i	0.739171	−	1.28028i	0.952869	−	0.303383i	$-0.0981160\pi$
$594$	5.00000			0.205152
$595$		0			0
$596$	12.0000			0.491539
$597$	2.00000	−	3.46410i	0.0818546	−	0.141776i
$598$	−2.50000	−	4.33013i	−0.102233	−	0.177072i
$599$	5.00000	+	8.66025i	0.204294	+	0.353848i	0.949908	−	0.312531i	$-0.101177\pi$
$599$	5.00000	+	8.66025i	0.204294	+	0.353848i	−0.745613	+	0.666379i	$0.767843\pi$
$600$		0			0
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$	6.00000	+	31.1769i	0.244542	+	1.27068i
$603$	12.0000			0.488678
$604$	−7.00000	+	12.1244i	−0.284826	+	0.493333i
$605$		0			0
$606$		0			0
$607$	−13.5000	+	23.3827i	−0.547948	+	0.949074i	0.450467	+	0.892793i	$0.351258\pi$
$607$	−13.5000	+	23.3827i	−0.547948	+	0.949074i	−0.998415	+	0.0562808i	$0.982076\pi$
$608$	7.00000			0.283887
$609$		0			0
$610$		0			0
$611$	−27.5000	+	47.6314i	−1.11253	+	1.92696i
$612$	−2.00000	−	3.46410i	−0.0808452	−	0.140028i
$613$	−21.5000	−	37.2391i	−0.868377	−	1.50407i	−0.863655	−	0.504084i	$-0.831830\pi$
$613$	−21.5000	−	37.2391i	−0.868377	−	1.50407i	−0.00472215	−	0.999989i	$-0.501503\pi$
$614$	−4.00000	+	6.92820i	−0.161427	+	0.279600i
$615$		0			0
$616$	−12.5000	−	4.33013i	−0.503639	−	0.174466i
$617$	8.00000			0.322068			0.161034	−	0.986949i	$-0.448517\pi$
$617$	8.00000			0.322068			0.161034	+	0.986949i	$0.448517\pi$
$618$	−4.00000	+	6.92820i	−0.160904	+	0.278693i
$619$	−12.5000	−	21.6506i	−0.502417	−	0.870212i	−0.999996	−	0.00279365i	$-0.999111\pi$
$619$	−12.5000	−	21.6506i	−0.502417	−	0.870212i	0.497579	−	0.867419i	$-0.334223\pi$
$620$		0			0
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$	−8.00000			−0.320771
$623$	7.00000	+	36.3731i	0.280449	+	1.45726i
$624$	5.00000			0.200160
$625$		0			0
$626$	−8.00000	−	13.8564i	−0.319744	−	0.553813i
$627$	−17.5000	−	30.3109i	−0.698883	−	1.21050i
$628$	5.50000	−	9.52628i	0.219474	−	0.380140i
$629$	−4.00000			−0.159490
$630$		0			0
$631$	6.00000			0.238856			0.119428	−	0.992843i	$-0.461894\pi$
$631$	6.00000			0.238856			0.119428	+	0.992843i	$0.461894\pi$
$632$	−6.00000	+	10.3923i	−0.238667	+	0.413384i
$633$	−8.50000	−	14.7224i	−0.337845	−	0.585164i
$634$	11.0000	+	19.0526i	0.436866	+	0.756674i
$635$		0			0
$636$	9.00000			0.356873
$637$	5.00000	−	34.6410i	0.198107	−	1.37253i
$638$		0			0
$639$	−1.00000	+	1.73205i	−0.0395594	+	0.0685189i
$640$		0			0
$641$	−10.5000	−	18.1865i	−0.414725	−	0.718325i	0.580674	−	0.814136i	$-0.302789\pi$
$641$	−10.5000	−	18.1865i	−0.414725	−	0.718325i	−0.995400	+	0.0958109i	$0.969456\pi$
$642$	1.00000	−	1.73205i	0.0394669	−	0.0683586i
$643$	−34.0000			−1.34083			−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000			−1.34083			−0.670415	+	0.741987i	$0.733884\pi$
$644$	−2.00000	+	1.73205i	−0.0788110	+	0.0682524i
$645$		0			0
$646$	−14.0000	+	24.2487i	−0.550823	+	0.954053i
$647$	−11.5000	−	19.9186i	−0.452112	−	0.783080i	0.546405	−	0.837521i	$-0.315996\pi$
$647$	−11.5000	−	19.9186i	−0.452112	−	0.783080i	−0.998517	+	0.0544405i	$0.982662\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	10.0000	−	17.3205i	0.392534	−	0.679889i
$650$		0			0
$651$	−1.00000	−	5.19615i	−0.0391931	−	0.203653i
$652$	24.0000			0.939913
$653$	−9.50000	+	16.4545i	−0.371764	+	0.643914i	−0.989837	−	0.142207i	$-0.954580\pi$
$653$	−9.50000	+	16.4545i	−0.371764	+	0.643914i	0.618073	+	0.786121i	$0.287914\pi$
$654$	−1.00000	−	1.73205i	−0.0391031	−	0.0677285i
$655$		0			0
$656$	−2.50000	+	4.33013i	−0.0976086	+	0.169063i
$657$	−10.0000			−0.390137
$658$	27.5000	+	9.52628i	1.07206	+	0.371373i
$659$	−20.0000			−0.779089			−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000			−0.779089			−0.389545	+	0.921008i	$0.627368\pi$
$660$		0			0
$661$	20.0000	+	34.6410i	0.777910	+	1.34738i	0.933144	+	0.359502i	$0.117053\pi$
$661$	20.0000	+	34.6410i	0.777910	+	1.34738i	−0.155235	+	0.987878i	$0.549613\pi$
$662$	15.5000	+	26.8468i	0.602425	+	1.04343i
$663$	−10.0000	+	17.3205i	−0.388368	+	0.672673i
$664$	−12.0000			−0.465690
$665$		0			0
$666$	1.00000			0.0387492
$667$		0			0
$668$	5.50000	+	9.52628i	0.212801	+	0.368583i
$669$	−6.00000	−	10.3923i	−0.231973	−	0.401790i
$670$		0			0
$671$	−20.0000			−0.772091
$672$	−0.500000	−	2.59808i	−0.0192879	−	0.100223i
$673$	4.00000			0.154189			0.0770943	−	0.997024i	$-0.475436\pi$
$673$	4.00000			0.154189			0.0770943	+	0.997024i	$0.475436\pi$
$674$	8.00000	−	13.8564i	0.308148	−	0.533729i
$675$		0			0
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	16.5000	−	28.5788i	0.634147	−	1.09837i	−0.352549	−	0.935793i	$-0.614685\pi$
$677$	16.5000	−	28.5788i	0.634147	−	1.09837i	0.986695	−	0.162581i	$-0.0519817\pi$
$678$	−14.0000			−0.537667
$679$	16.0000	−	13.8564i	0.614024	−	0.531760i
$680$		0			0
$681$	−6.00000	+	10.3923i	−0.229920	+	0.398234i
$682$	5.00000	+	8.66025i	0.191460	+	0.331618i
$683$	−2.00000	−	3.46410i	−0.0765279	−	0.132550i	0.825222	−	0.564809i	$-0.191050\pi$
$683$	−2.00000	−	3.46410i	−0.0765279	−	0.132550i	−0.901750	+	0.432259i	$0.857717\pi$
$684$	3.50000	−	6.06218i	0.133826	−	0.231793i
$685$		0			0
$686$	−18.5000	+	0.866025i	−0.706333	+	0.0330650i
$687$	10.0000			0.381524
$688$	6.00000	−	10.3923i	0.228748	−	0.396203i
$689$	−22.5000	−	38.9711i	−0.857182	−	1.48468i
$690$		0			0
$691$	−14.0000	+	24.2487i	−0.532585	+	0.922464i	0.466691	+	0.884420i	$0.345446\pi$
$691$	−14.0000	+	24.2487i	−0.532585	+	0.922464i	−0.999276	+	0.0380440i	$0.987887\pi$
$692$	13.0000			0.494186
$693$	−10.0000	+	8.66025i	−0.379869	+	0.328976i
$694$	−18.0000			−0.683271
$695$		0			0
$696$		0			0
$697$	−10.0000	−	17.3205i	−0.378777	−	0.656061i
$698$	−2.00000	+	3.46410i	−0.0757011	+	0.131118i
$699$	14.0000			0.529529
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	2.50000	−	4.33013i	0.0943564	−	0.163430i
$703$	−3.50000	−	6.06218i	−0.132005	−	0.228639i
$704$	2.50000	+	4.33013i	0.0942223	+	0.163198i
$705$		0			0
$706$	24.0000			0.903252
$707$		0			0
$708$	4.00000			0.150329
$709$	−14.0000	+	24.2487i	−0.525781	+	0.910679i	0.473768	+	0.880650i	$0.342894\pi$
$709$	−14.0000	+	24.2487i	−0.525781	+	0.910679i	−0.999549	+	0.0300298i	$0.990440\pi$
$710$		0			0
$711$	6.00000	+	10.3923i	0.225018	+	0.389742i
$712$	7.00000	−	12.1244i	0.262336	−	0.454379i
$713$	2.00000			0.0749006
$714$	10.0000	+	3.46410i	0.374241	+	0.129641i
$715$		0			0
$716$	11.5000	−	19.9186i	0.429775	−	0.744392i
$717$	11.0000	+	19.0526i	0.410803	+	0.711531i
$718$	−10.0000	−	17.3205i	−0.373197	−	0.646396i
$719$	3.00000	−	5.19615i	0.111881	−	0.193784i	−0.804648	−	0.593753i	$-0.797646\pi$
$719$	3.00000	−	5.19615i	0.111881	−	0.193784i	0.916529	+	0.399969i	$0.130979\pi$
$720$		0			0
$721$	−4.00000	−	20.7846i	−0.148968	−	0.774059i
$722$	−30.0000			−1.11648
$723$	−7.50000	+	12.9904i	−0.278928	+	0.483117i
$724$	−10.0000	−	17.3205i	−0.371647	−	0.643712i
$725$		0			0
$726$	7.00000	−	12.1244i	0.259794	−	0.449977i
$727$	3.00000			0.111264			0.0556319	−	0.998451i	$-0.482283\pi$
$727$	3.00000			0.111264			0.0556319	+	0.998451i	$0.482283\pi$
$728$	−10.0000	+	8.66025i	−0.370625	+	0.320970i
$729$	1.00000			0.0370370
$730$		0			0
$731$	24.0000	+	41.5692i	0.887672	+	1.53749i
$732$	−2.00000	−	3.46410i	−0.0739221	−	0.128037i
$733$	4.50000	−	7.79423i	0.166211	−	0.287886i	−0.770873	−	0.636988i	$-0.780180\pi$
$733$	4.50000	−	7.79423i	0.166211	−	0.287886i	0.937085	+	0.349102i	$0.113513\pi$
$734$	7.00000			0.258375
$735$		0			0
$736$	1.00000			0.0368605
$737$	30.0000	−	51.9615i	1.10506	−	1.91403i
$738$	2.50000	+	4.33013i	0.0920263	+	0.159394i
$739$	7.50000	+	12.9904i	0.275892	+	0.477859i	0.970360	−	0.241665i	$-0.0776935\pi$
$739$	7.50000	+	12.9904i	0.275892	+	0.477859i	−0.694468	+	0.719524i	$0.744360\pi$
$740$		0			0
$741$	−35.0000			−1.28576
$742$	−18.0000	+	15.5885i	−0.660801	+	0.572270i
$743$	−15.0000			−0.550297			−0.275148	−	0.961402i	$-0.588727\pi$
$743$	−15.0000			−0.550297			−0.275148	+	0.961402i	$0.588727\pi$
$744$	−1.00000	+	1.73205i	−0.0366618	+	0.0635001i
$745$		0			0
$746$	11.0000	+	19.0526i	0.402739	+	0.697564i
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$	−20.0000			−0.731272
$749$	1.00000	+	5.19615i	0.0365392	+	0.189863i
$750$		0			0
$751$	25.0000	−	43.3013i	0.912263	−	1.58009i	0.101403	−	0.994845i	$-0.467667\pi$
$751$	25.0000	−	43.3013i	0.912263	−	1.58009i	0.810860	−	0.585240i	$-0.199000\pi$
$752$	−5.50000	−	9.52628i	−0.200564	−	0.347388i
$753$	−0.500000	−	0.866025i	−0.0182210	−	0.0315597i
$754$		0			0
$755$		0			0
$756$	−2.50000	−	0.866025i	−0.0909241	−	0.0314970i
$757$	34.0000			1.23575			0.617876	−	0.786276i	$-0.287994\pi$
$757$	34.0000			1.23575			0.617876	+	0.786276i	$0.287994\pi$
$758$	0.500000	−	0.866025i	0.0181608	−	0.0314555i
$759$	−2.50000	−	4.33013i	−0.0907443	−	0.157174i
$760$		0			0
$761$	18.5000	−	32.0429i	0.670624	−	1.16156i	−0.307103	−	0.951676i	$-0.599360\pi$
$761$	18.5000	−	32.0429i	0.670624	−	1.16156i	0.977727	−	0.209879i	$-0.0673071\pi$
$762$	9.00000			0.326036
$763$	5.00000	+	1.73205i	0.181012	+	0.0627044i
$764$	14.0000			0.506502
$765$		0			0
$766$	−10.5000	−	18.1865i	−0.379380	−	0.657106i
$767$	−10.0000	−	17.3205i	−0.361079	−	0.625407i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−5.00000			−0.180305			−0.0901523	−	0.995928i	$-0.528735\pi$
$769$	−5.00000			−0.180305			−0.0901523	+	0.995928i	$0.528735\pi$
$770$		0			0
$771$	16.0000			0.576226
$772$	5.00000	−	8.66025i	0.179954	−	0.311689i
$773$	−2.50000	−	4.33013i	−0.0899188	−	0.155744i	0.817558	−	0.575846i	$-0.195327\pi$
$773$	−2.50000	−	4.33013i	−0.0899188	−	0.155744i	−0.907477	+	0.420103i	$0.861994\pi$
$774$	−6.00000	−	10.3923i	−0.215666	−	0.373544i
$775$		0			0
$776$	−8.00000			−0.287183
$777$	−2.00000	+	1.73205i	−0.0717496	+	0.0621370i
$778$	−18.0000			−0.645331
$779$	17.5000	−	30.3109i	0.627003	−	1.08600i
$780$		0			0
$781$	5.00000	+	8.66025i	0.178914	+	0.309888i
$782$	−2.00000	+	3.46410i	−0.0715199	+	0.123876i
$783$		0			0
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$		0			0
$786$	−4.50000	+	7.79423i	−0.160510	+	0.278011i
$787$	1.00000	+	1.73205i	0.0356462	+	0.0617409i	0.883298	−	0.468812i	$-0.155318\pi$
$787$	1.00000	+	1.73205i	0.0356462	+	0.0617409i	−0.847652	+	0.530553i	$0.821984\pi$
$788$	−1.50000	−	2.59808i	−0.0534353	−	0.0925526i
$789$		0			0
$790$		0			0
$791$	28.0000	−	24.2487i	0.995565	−	0.862185i
$792$	5.00000			0.177667
$793$	−10.0000	+	17.3205i	−0.355110	+	0.615069i
$794$	7.00000	+	12.1244i	0.248421	+	0.430277i
$795$		0			0
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	54.0000			1.91278			0.956389	−	0.292096i	$-0.0943526\pi$
$797$	54.0000			1.91278			0.956389	+	0.292096i	$0.0943526\pi$
$798$	3.50000	+	18.1865i	0.123899	+	0.643796i
$799$	44.0000			1.55661
$800$		0			0
$801$	−7.00000	−	12.1244i	−0.247333	−	0.428393i
$802$	−10.5000	−	18.1865i	−0.370768	−	0.642189i
$803$	−25.0000	+	43.3013i	−0.882231	+	1.52807i
$804$	12.0000			0.423207
$805$		0			0
$806$	10.0000			0.352235
$807$	12.0000	−	20.7846i	0.422420	−	0.731653i
$808$		0			0
$809$	−12.5000	−	21.6506i	−0.439477	−	0.761196i	0.558173	−	0.829725i	$-0.311503\pi$
$809$	−12.5000	−	21.6506i	−0.439477	−	0.761196i	−0.997649	+	0.0685291i	$0.978169\pi$
$810$		0			0
$811$	21.0000			0.737410			0.368705	−	0.929547i	$-0.379801\pi$
$811$	21.0000			0.737410			0.368705	+	0.929547i	$0.379801\pi$
$812$		0			0
$813$		0			0
$814$	2.50000	−	4.33013i	0.0876250	−	0.151771i
$815$		0			0
$816$	−2.00000	−	3.46410i	−0.0700140	−	0.121268i
$817$	−42.0000	+	72.7461i	−1.46939	+	2.54507i
$818$	−10.0000			−0.349642
$819$	2.50000	+	12.9904i	0.0873571	+	0.453921i
$820$		0			0
$821$	−5.00000	+	8.66025i	−0.174501	+	0.302245i	−0.939989	−	0.341206i	$-0.889165\pi$
$821$	−5.00000	+	8.66025i	−0.174501	+	0.302245i	0.765487	+	0.643451i	$0.222498\pi$
$822$	1.00000	+	1.73205i	0.0348790	+	0.0604122i
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$	−4.00000	+	6.92820i	−0.139347	+	0.241355i
$825$		0			0
$826$	−8.00000	+	6.92820i	−0.278356	+	0.241063i
$827$	6.00000			0.208640			0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000			0.208640			0.104320	+	0.994544i	$0.466733\pi$
$828$	0.500000	−	0.866025i	0.0173762	−	0.0300965i
$829$	26.0000	+	45.0333i	0.903017	+	1.56407i	0.823557	+	0.567234i	$0.191986\pi$
$829$	26.0000	+	45.0333i	0.903017	+	1.56407i	0.0794606	+	0.996838i	$0.474680\pi$
$830$		0			0
$831$	7.00000	−	12.1244i	0.242827	−	0.420589i
$832$	5.00000			0.173344
$833$	−26.0000	+	10.3923i	−0.900847	+	0.360072i
$834$	4.00000			0.138509
$835$		0			0
$836$	−17.5000	−	30.3109i	−0.605250	−	1.04832i
$837$	1.00000	+	1.73205i	0.0345651	+	0.0598684i
$838$	7.50000	−	12.9904i	0.259083	−	0.448745i
$839$	12.0000			0.414286			0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000			0.414286			0.207143	+	0.978311i	$0.433583\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	5.00000	−	8.66025i	0.172311	−	0.298452i
$843$	−3.50000	−	6.06218i	−0.120546	−	0.208792i
$844$	−8.50000	−	14.7224i	−0.292582	−	0.506767i
$845$		0			0
$846$	−11.0000			−0.378188
$847$	7.00000	+	36.3731i	0.240523	+	1.24979i
$848$	9.00000			0.309061
$849$	−5.00000	+	8.66025i	−0.171600	+	0.297219i
$850$		0			0
$851$	−0.500000	−	0.866025i	−0.0171398	−	0.0296870i
$852$	−1.00000	+	1.73205i	−0.0342594	+	0.0593391i
$853$	11.0000			0.376633			0.188316	−	0.982108i	$-0.439697\pi$
$853$	11.0000			0.376633			0.188316	+	0.982108i	$0.439697\pi$
$854$	10.0000	+	3.46410i	0.342193	+	0.118539i
$855$		0			0
$856$	1.00000	−	1.73205i	0.0341793	−	0.0592003i
$857$	1.00000	+	1.73205i	0.0341593	+	0.0591657i	0.882600	−	0.470125i	$-0.155791\pi$
$857$	1.00000	+	1.73205i	0.0341593	+	0.0591657i	−0.848440	+	0.529291i	$0.822458\pi$
$858$	−12.5000	−	21.6506i	−0.426743	−	0.739140i
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	−0.829887	−	0.557931i	$-0.811595\pi$
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	0.898126	+	0.439738i	$0.144929\pi$
$860$		0			0
$861$	−12.5000	−	4.33013i	−0.425999	−	0.147570i
$862$	−12.0000			−0.408722
$863$	22.5000	−	38.9711i	0.765909	−	1.32659i	−0.173856	−	0.984771i	$-0.555623\pi$
$863$	22.5000	−	38.9711i	0.765909	−	1.32659i	0.939765	−	0.341822i	$-0.111044\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	−12.0000	+	20.7846i	−0.407777	+	0.706290i
$867$	−1.00000			−0.0339618
$868$	−1.00000	−	5.19615i	−0.0339422	−	0.176369i
$869$	60.0000			2.03536
$870$		0			0
$871$	−30.0000	−	51.9615i	−1.01651	−	1.76065i
$872$	−1.00000	−	1.73205i	−0.0338643	−	0.0586546i
$873$	−4.00000	+	6.92820i	−0.135379	+	0.234484i
$874$	−7.00000			−0.236779
$875$		0			0
$876$	−10.0000			−0.337869
$877$	−18.5000	+	32.0429i	−0.624701	+	1.08201i	0.363898	+	0.931439i	$0.381446\pi$
$877$	−18.5000	+	32.0429i	−0.624701	+	1.08201i	−0.988599	+	0.150574i	$0.951888\pi$
$878$	−20.0000	−	34.6410i	−0.674967	−	1.16908i
$879$	4.50000	+	7.79423i	0.151781	+	0.262893i
$880$		0			0
$881$	3.00000			0.101073			0.0505363	−	0.998722i	$-0.483907\pi$
$881$	3.00000			0.101073			0.0505363	+	0.998722i	$0.483907\pi$
$882$	6.50000	−	2.59808i	0.218866	−	0.0874818i
$883$	50.0000			1.68263			0.841317	−	0.540542i	$-0.181781\pi$
$883$	50.0000			1.68263			0.841317	+	0.540542i	$0.181781\pi$
$884$	−10.0000	+	17.3205i	−0.336336	+	0.582552i
$885$		0			0
$886$	14.0000	+	24.2487i	0.470339	+	0.814651i
$887$	−22.0000	+	38.1051i	−0.738688	+	1.27944i	0.214399	+	0.976746i	$0.431221\pi$
$887$	−22.0000	+	38.1051i	−0.738688	+	1.27944i	−0.953086	+	0.302698i	$0.902113\pi$
$888$	1.00000			0.0335578
$889$	−18.0000	+	15.5885i	−0.603701	+	0.522820i
$890$		0			0
$891$	2.50000	−	4.33013i	0.0837532	−	0.145065i
$892$	−6.00000	−	10.3923i	−0.200895	−	0.347960i
$893$	38.5000	+	66.6840i	1.28835	+	2.23149i
$894$	6.00000	−	10.3923i	0.200670	−	0.347571i
$895$		0			0
$896$	−0.500000	−	2.59808i	−0.0167038	−	0.0867956i
$897$	−5.00000			−0.166945
$898$	−14.5000	+	25.1147i	−0.483871	+	0.838090i
$899$		0			0
$900$		0			0
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$	25.0000			0.832409
$903$	30.0000	+	10.3923i	0.998337	+	0.345834i
$904$	−14.0000			−0.465633
$905$		0			0
$906$	7.00000	+	12.1244i	0.232559	+	0.402805i
$907$	−9.00000	−	15.5885i	−0.298840	−	0.517606i	0.677031	−	0.735955i	$-0.263266\pi$
$907$	−9.00000	−	15.5885i	−0.298840	−	0.517606i	−0.975871	+	0.218348i	$0.929933\pi$
$908$	−6.00000	+	10.3923i	−0.199117	+	0.344881i
$909$		0			0
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	3.50000	−	6.06218i	0.115897	−	0.200739i
$913$	30.0000	+	51.9615i	0.992855	+	1.71968i
$914$	7.00000	+	12.1244i	0.231539	+	0.401038i
$915$		0			0
$916$	10.0000			0.330409
$917$	−4.50000	−	23.3827i	−0.148603	−	0.772164i
$918$	−4.00000			−0.132020
$919$	−14.0000	+	24.2487i	−0.461817	+	0.799891i	−0.999052	−	0.0435419i	$-0.986136\pi$
$919$	−14.0000	+	24.2487i	−0.461817	+	0.799891i	0.537234	+	0.843433i	$0.319469\pi$
$920$		0			0
$921$	4.00000	+	6.92820i	0.131804	+	0.228292i
$922$	−2.00000	+	3.46410i	−0.0658665	+	0.114084i
$923$	10.0000			0.329154
$924$	−10.0000	+	8.66025i	−0.328976	+	0.284901i
$925$		0			0
$926$	9.50000	−	16.4545i	0.312189	−	0.540728i
$927$	4.00000	+	6.92820i	0.131377	+	0.227552i
$928$		0			0
$929$	−9.50000	+	16.4545i	−0.311685	+	0.539854i	−0.978727	−	0.205166i	$-0.934227\pi$
$929$	−9.50000	+	16.4545i	−0.311685	+	0.539854i	0.667042	+	0.745020i	$0.267560\pi$
$930$		0			0
$931$	−38.5000	−	30.3109i	−1.26179	−	0.993399i
$932$	14.0000			0.458585
$933$	−4.00000	+	6.92820i	−0.130954	+	0.226819i
$934$	10.0000	+	17.3205i	0.327210	+	0.566744i
$935$		0			0
$936$	2.50000	−	4.33013i	0.0817151	−	0.141535i
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$	−24.0000	+	20.7846i	−0.783628	+	0.678642i
$939$	−16.0000			−0.522140
$940$		0			0
$941$	3.00000	+	5.19615i	0.0977972	+	0.169390i	0.910773	−	0.412908i	$-0.135487\pi$
$941$	3.00000	+	5.19615i	0.0977972	+	0.169390i	−0.812975	+	0.582298i	$0.802154\pi$
$942$	−5.50000	−	9.52628i	−0.179200	−	0.310383i
$943$	2.50000	−	4.33013i	0.0814112	−	0.141008i
$944$	4.00000			0.130189
$945$		0			0
$946$	−60.0000			−1.95077
$947$	−21.0000	+	36.3731i	−0.682408	+	1.18197i	0.291835	+	0.956469i	$0.405734\pi$
$947$	−21.0000	+	36.3731i	−0.682408	+	1.18197i	−0.974244	+	0.225497i	$0.927599\pi$
$948$	6.00000	+	10.3923i	0.194871	+	0.337526i
$949$	25.0000	+	43.3013i	0.811534	+	1.40562i
$950$		0			0
$951$	22.0000			0.713399
$952$	10.0000	+	3.46410i	0.324102	+	0.112272i
$953$	−12.0000			−0.388718			−0.194359	−	0.980930i	$-0.562263\pi$
$953$	−12.0000			−0.388718			−0.194359	+	0.980930i	$0.562263\pi$
$954$	4.50000	−	7.79423i	0.145693	−	0.252347i
$955$		0			0
$956$	11.0000	+	19.0526i	0.355765	+	0.616204i
$957$		0			0
$958$	−18.0000			−0.581554
$959$	−5.00000	−	1.73205i	−0.161458	−	0.0559308i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−2.50000	−	4.33013i	−0.0806032	−	0.139609i
$963$	−1.00000	−	1.73205i	−0.0322245	−	0.0558146i
$964$	−7.50000	+	12.9904i	−0.241559	+	0.418392i
$965$		0			0
$966$	0.500000	+	2.59808i	0.0160872	+	0.0835917i
$967$	−4.00000			−0.128631			−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000			−0.128631			−0.0643157	+	0.997930i	$0.520486\pi$
$968$	7.00000	−	12.1244i	0.224989	−	0.389692i
$969$	14.0000	+	24.2487i	0.449745	+	0.778981i
$970$		0			0
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	0.720224	+	0.693742i	$0.244039\pi$
$972$	1.00000			0.0320750
$973$	−8.00000	+	6.92820i	−0.256468	+	0.222108i
$974$		0			0
$975$		0			0
$976$	−2.00000	−	3.46410i	−0.0640184	−	0.110883i
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	0.519841	−	0.854263i	$-0.325991\pi$
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	−0.999734	+	0.0230645i	$0.992658\pi$
$978$	12.0000	−	20.7846i	0.383718	−	0.664619i
$979$	−70.0000			−2.23721
$980$		0			0
$981$	−2.00000			−0.0638551
$982$	−18.0000	+	31.1769i	−0.574403	+	0.994895i
$983$	−12.5000	−	21.6506i	−0.398688	−	0.690548i	0.594876	−	0.803817i	$-0.297201\pi$
$983$	−12.5000	−	21.6506i	−0.398688	−	0.690548i	−0.993564	+	0.113269i	$0.963868\pi$
$984$	2.50000	+	4.33013i	0.0796971	+	0.138039i
$985$		0			0
$986$		0			0
$987$	22.0000	−	19.0526i	0.700268	−	0.606450i
$988$	−35.0000			−1.11350
$989$	−6.00000	+	10.3923i	−0.190789	+	0.330456i
$990$		0			0
$991$	19.0000	+	32.9090i	0.603555	+	1.04539i	0.992278	+	0.124033i	$0.0395829\pi$
$991$	19.0000	+	32.9090i	0.603555	+	1.04539i	−0.388723	+	0.921355i	$0.627084\pi$
$992$	−1.00000	+	1.73205i	−0.0317500	+	0.0549927i
$993$	31.0000			0.983755
$994$	−1.00000	−	5.19615i	−0.0317181	−	0.164812i
$995$		0			0
$996$	−6.00000	+	10.3923i	−0.190117	+	0.329293i
$997$	−11.0000	−	19.0526i	−0.348373	−	0.603401i	0.637587	−	0.770378i	$-0.279933\pi$
$997$	−11.0000	−	19.0526i	−0.348373	−	0.603401i	−0.985961	+	0.166978i	$0.946599\pi$
$998$	20.0000	+	34.6410i	0.633089	+	1.09654i
$999$	0.500000	−	0.866025i	0.0158193	−	0.0273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.i.p.751.1		2
5.2	odd	4		1050.2.o.g.499.2		4
5.3	odd	4		1050.2.o.g.499.1		4
5.4	even	2		210.2.i.b.121.1	✓	2
7.2	even	3		7350.2.a.u.1.1		1
7.4	even	3	inner	1050.2.i.p.151.1		2
7.5	odd	6		7350.2.a.a.1.1		1
15.14	odd	2		630.2.k.g.541.1		2
20.19	odd	2		1680.2.bg.d.961.1		2
35.4	even	6		210.2.i.b.151.1	yes	2
35.9	even	6		1470.2.a.l.1.1		1
35.18	odd	12		1050.2.o.g.949.2		4
35.19	odd	6		1470.2.a.o.1.1		1
35.24	odd	6		1470.2.i.e.361.1		2
35.32	odd	12		1050.2.o.g.949.1		4
35.34	odd	2		1470.2.i.e.961.1		2
105.44	odd	6		4410.2.a.j.1.1		1
105.74	odd	6		630.2.k.g.361.1		2
105.89	even	6		4410.2.a.u.1.1		1
140.39	odd	6		1680.2.bg.d.1201.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.i.b.121.1	✓	2	5.4	even	2
210.2.i.b.151.1	yes	2	35.4	even	6
630.2.k.g.361.1		2	105.74	odd	6
630.2.k.g.541.1		2	15.14	odd	2
1050.2.i.p.151.1		2	7.4	even	3	inner
1050.2.i.p.751.1		2	1.1	even	1	trivial
1050.2.o.g.499.1		4	5.3	odd	4
1050.2.o.g.499.2		4	5.2	odd	4
1050.2.o.g.949.1		4	35.32	odd	12
1050.2.o.g.949.2		4	35.18	odd	12
1470.2.a.l.1.1		1	35.9	even	6
1470.2.a.o.1.1		1	35.19	odd	6
1470.2.i.e.361.1		2	35.24	odd	6
1470.2.i.e.961.1		2	35.34	odd	2
1680.2.bg.d.961.1		2	20.19	odd	2
1680.2.bg.d.1201.1		2	140.39	odd	6
4410.2.a.j.1.1		1	105.44	odd	6
4410.2.a.u.1.1		1	105.89	even	6
7350.2.a.a.1.1		1	7.5	odd	6
7350.2.a.u.1.1		1	7.2	even	3

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.50000 + 4.33013i) q^{11} +(-0.500000 + 0.866025i) q^{12} +5.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.50000 - 6.06218i) q^{19} +(-2.50000 - 0.866025i) q^{21} +5.00000 q^{22} +(0.500000 - 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{26} +1.00000 q^{27} +(-2.50000 - 0.866025i) q^{28} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.50000 - 4.33013i) q^{33} -4.00000 q^{34} +1.00000 q^{36} +(0.500000 - 0.866025i) q^{37} +(-3.50000 - 6.06218i) q^{38} +(-2.50000 - 4.33013i) q^{39} +5.00000 q^{41} +(-2.00000 + 1.73205i) q^{42} -12.0000 q^{43} +(2.50000 - 4.33013i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(-5.50000 + 9.52628i) q^{47} +1.00000 q^{48} +(1.00000 - 6.92820i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(-2.50000 - 4.33013i) q^{52} +(-4.50000 - 7.79423i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.00000 + 1.73205i) q^{56} -7.00000 q^{57} +(-2.00000 - 3.46410i) q^{59} +(-2.00000 + 3.46410i) q^{61} +2.00000 q^{62} +(0.500000 + 2.59808i) q^{63} +1.00000 q^{64} +(-2.50000 - 4.33013i) q^{66} +(-6.00000 - 10.3923i) q^{67} +(-2.00000 + 3.46410i) q^{68} -1.00000 q^{69} +2.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(5.00000 + 8.66025i) q^{73} +(-0.500000 - 0.866025i) q^{74} -7.00000 q^{76} +(12.5000 + 4.33013i) q^{77} -5.00000 q^{78} +(6.00000 - 10.3923i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(2.50000 - 4.33013i) q^{82} +12.0000 q^{83} +(0.500000 + 2.59808i) q^{84} +(-6.00000 + 10.3923i) q^{86} +(-2.50000 - 4.33013i) q^{88} +(-7.00000 + 12.1244i) q^{89} +(10.0000 - 8.66025i) q^{91} -1.00000 q^{92} +(1.00000 - 1.73205i) q^{93} +(5.50000 + 9.52628i) q^{94} +(0.500000 - 0.866025i) q^{96} +8.00000 q^{97} +(-5.50000 - 4.33013i) q^{98} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} + 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 - 2 * q^6 + 4 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} + 4 q^{7} - 2 q^{8} - q^{9} + 5 q^{11} - q^{12} + 10 q^{13} - q^{14} - q^{16} - 4 q^{17} + q^{18} + 7 q^{19} - 5 q^{21} + 10 q^{22} + q^{23} + q^{24} + 5 q^{26} + 2 q^{27} - 5 q^{28} + 2 q^{31} + q^{32} + 5 q^{33} - 8 q^{34} + 2 q^{36} + q^{37} - 7 q^{38} - 5 q^{39} + 10 q^{41} - 4 q^{42} - 24 q^{43} + 5 q^{44} - q^{46} - 11 q^{47} + 2 q^{48} + 2 q^{49} - 4 q^{51} - 5 q^{52} - 9 q^{53} + q^{54} - 4 q^{56} - 14 q^{57} - 4 q^{59} - 4 q^{61} + 4 q^{62} + q^{63} + 2 q^{64} - 5 q^{66} - 12 q^{67} - 4 q^{68} - 2 q^{69} + 4 q^{71} + q^{72} + 10 q^{73} - q^{74} - 14 q^{76} + 25 q^{77} - 10 q^{78} + 12 q^{79} - q^{81} + 5 q^{82} + 24 q^{83} + q^{84} - 12 q^{86} - 5 q^{88} - 14 q^{89} + 20 q^{91} - 2 q^{92} + 2 q^{93} + 11 q^{94} + q^{96} + 16 q^{97} - 11 q^{98} - 10 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 2 * q^6 + 4 * q^7 - 2 * q^8 - q^9 + 5 * q^11 - q^12 + 10 * q^13 - q^14 - q^16 - 4 * q^17 + q^18 + 7 * q^19 - 5 * q^21 + 10 * q^22 + q^23 + q^24 + 5 * q^26 + 2 * q^27 - 5 * q^28 + 2 * q^31 + q^32 + 5 * q^33 - 8 * q^34 + 2 * q^36 + q^37 - 7 * q^38 - 5 * q^39 + 10 * q^41 - 4 * q^42 - 24 * q^43 + 5 * q^44 - q^46 - 11 * q^47 + 2 * q^48 + 2 * q^49 - 4 * q^51 - 5 * q^52 - 9 * q^53 + q^54 - 4 * q^56 - 14 * q^57 - 4 * q^59 - 4 * q^61 + 4 * q^62 + q^63 + 2 * q^64 - 5 * q^66 - 12 * q^67 - 4 * q^68 - 2 * q^69 + 4 * q^71 + q^72 + 10 * q^73 - q^74 - 14 * q^76 + 25 * q^77 - 10 * q^78 + 12 * q^79 - q^81 + 5 * q^82 + 24 * q^83 + q^84 - 12 * q^86 - 5 * q^88 - 14 * q^89 + 20 * q^91 - 2 * q^92 + 2 * q^93 + 11 * q^94 + q^96 + 16 * q^97 - 11 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more