LMFDB - Embedded newform 1050.2.o.g.949.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(499,1050)]

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, 3, 2]))

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

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

chi := DirichletCharacter("1050.499");

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			949.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1050.949
Dual form			1050.2.o.g.499.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.50000 - 4.33013i) q^{11} +(0.866025 - 0.500000i) q^{12} -5.00000i q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.46410 - 2.00000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-3.50000 - 6.06218i) q^{19} +(-2.50000 + 0.866025i) q^{21} +5.00000i q^{22} +(0.866025 - 0.500000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{26} +1.00000i q^{27} +(0.866025 + 2.50000i) q^{28} +(1.00000 - 1.73205i) q^{31} +(0.866025 + 0.500000i) q^{32} +(4.33013 - 2.50000i) q^{33} +4.00000 q^{34} +1.00000 q^{36} +(-0.866025 + 0.500000i) q^{37} +(6.06218 + 3.50000i) q^{38} +(2.50000 - 4.33013i) q^{39} +5.00000 q^{41} +(1.73205 - 2.00000i) q^{42} +12.0000i q^{43} +(-2.50000 - 4.33013i) q^{44} +(-0.500000 + 0.866025i) q^{46} +(9.52628 - 5.50000i) q^{47} -1.00000i q^{48} +(-1.00000 - 6.92820i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(-4.33013 - 2.50000i) q^{52} +(7.79423 + 4.50000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.00000 - 1.73205i) q^{56} -7.00000i q^{57} +(2.00000 - 3.46410i) q^{59} +(-2.00000 - 3.46410i) q^{61} +2.00000i q^{62} +(-2.59808 - 0.500000i) q^{63} -1.00000 q^{64} +(-2.50000 + 4.33013i) q^{66} +(-10.3923 - 6.00000i) q^{67} +(-3.46410 + 2.00000i) q^{68} +1.00000 q^{69} +2.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-8.66025 - 5.00000i) q^{73} +(0.500000 - 0.866025i) q^{74} -7.00000 q^{76} +(4.33013 + 12.5000i) q^{77} +5.00000i q^{78} +(-6.00000 - 10.3923i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.33013 + 2.50000i) q^{82} -12.0000i q^{83} +(-0.500000 + 2.59808i) q^{84} +(-6.00000 - 10.3923i) q^{86} +(4.33013 + 2.50000i) q^{88} +(7.00000 + 12.1244i) q^{89} +(10.0000 + 8.66025i) q^{91} -1.00000i q^{92} +(1.73205 - 1.00000i) q^{93} +(-5.50000 + 9.52628i) q^{94} +(0.500000 + 0.866025i) q^{96} +8.00000i q^{97} +(4.33013 + 5.50000i) q^{98} +5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 4 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9} + 10 q^{11} + 2 q^{14} - 2 q^{16} - 14 q^{19} - 10 q^{21} - 2 q^{24} + 10 q^{26} + 4 q^{31} + 16 q^{34} + 4 q^{36} + 10 q^{39} + 20 q^{41} - 10 q^{44} - 2 q^{46} - 4 q^{49} - 8 q^{51} - 2 q^{54} - 8 q^{56} + 8 q^{59} - 8 q^{61} - 4 q^{64} - 10 q^{66} + 4 q^{69} + 8 q^{71} + 2 q^{74} - 28 q^{76} - 24 q^{79} - 2 q^{81} - 2 q^{84} - 24 q^{86} + 28 q^{89} + 40 q^{91} - 22 q^{94} + 2 q^{96} + 20 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 4 * q^6 + 2 * q^9 + 10 * q^11 + 2 * q^14 - 2 * q^16 - 14 * q^19 - 10 * q^21 - 2 * q^24 + 10 * q^26 + 4 * q^31 + 16 * q^34 + 4 * q^36 + 10 * q^39 + 20 * q^41 - 10 * q^44 - 2 * q^46 - 4 * q^49 - 8 * q^51 - 2 * q^54 - 8 * q^56 + 8 * q^59 - 8 * q^61 - 4 * q^64 - 10 * q^66 + 4 * q^69 + 8 * q^71 + 2 * q^74 - 28 * q^76 - 24 * q^79 - 2 * q^81 - 2 * q^84 - 24 * q^86 + 28 * q^89 + 40 * q^91 - 22 * q^94 + 2 * q^96 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.00000			−0.408248
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	−0.192201	−	0.981356i	$-0.561563\pi$
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	0.945979	−	0.324227i	$-0.105104\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$		−	5.00000i		−	1.38675i	−0.720577	−	0.693375i	$-0.756123\pi$
$13$		−	5.00000i		−	1.38675i	0.720577	−	0.693375i	$-0.243877\pi$
$14$	0.500000	−	2.59808i	0.133631	−	0.694365i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.46410	−	2.00000i	−0.840168	−	0.485071i	0.0171533	−	0.999853i	$-0.494540\pi$
$17$	−3.46410	−	2.00000i	−0.840168	−	0.485071i	−0.857321	+	0.514782i	$0.827873\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$20$		0			0
$21$	−2.50000	+	0.866025i	−0.545545	+	0.188982i
$22$			5.00000i			1.06600i
$23$	0.866025	−	0.500000i	0.180579	−	0.104257i	−0.406986	−	0.913434i	$-0.633420\pi$
$23$	0.866025	−	0.500000i	0.180579	−	0.104257i	0.587565	+	0.809177i	$0.300087\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	2.50000	+	4.33013i	0.490290	+	0.849208i
$27$			1.00000i			0.192450i
$28$	0.866025	+	2.50000i	0.163663	+	0.472456i
$29$		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	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	4.33013	−	2.50000i	0.753778	−	0.435194i
$34$	4.00000			0.685994
$35$		0			0
$36$	1.00000			0.166667
$37$	−0.866025	+	0.500000i	−0.142374	+	0.0821995i	−0.569495	−	0.821995i	$-0.692861\pi$
$37$	−0.866025	+	0.500000i	−0.142374	+	0.0821995i	0.427121	+	0.904194i	$0.359528\pi$
$38$	6.06218	+	3.50000i	0.983415	+	0.567775i
$39$	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	$0.372325\pi$
$42$	1.73205	−	2.00000i	0.267261	−	0.308607i
$43$			12.0000i			1.82998i	0.403473	+	0.914991i	$0.367803\pi$
$43$			12.0000i			1.82998i	−0.403473	+	0.914991i	$0.632197\pi$
$44$	−2.50000	−	4.33013i	−0.376889	−	0.652791i
$45$		0			0
$46$	−0.500000	+	0.866025i	−0.0737210	+	0.127688i
$47$	9.52628	−	5.50000i	1.38955	−	0.802257i	0.396286	−	0.918127i	$-0.370299\pi$
$47$	9.52628	−	5.50000i	1.38955	−	0.802257i	0.993264	+	0.115870i	$0.0369655\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$		0			0
$51$	−2.00000	−	3.46410i	−0.280056	−	0.485071i
$52$	−4.33013	−	2.50000i	−0.600481	−	0.346688i
$53$	7.79423	+	4.50000i	1.07062	+	0.618123i	0.928351	−	0.371706i	$-0.121227\pi$
$53$	7.79423	+	4.50000i	1.07062	+	0.618123i	0.142269	+	0.989828i	$0.454560\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	−2.00000	−	1.73205i	−0.267261	−	0.231455i
$57$		−	7.00000i		−	0.927173i
$58$		0			0
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	0.709113	−	0.705095i	$-0.249096\pi$
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	−0.965187	+	0.261562i	$0.915762\pi$
$62$			2.00000i			0.254000i
$63$	−2.59808	−	0.500000i	−0.327327	−	0.0629941i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−2.50000	+	4.33013i	−0.307729	+	0.533002i
$67$	−10.3923	−	6.00000i	−1.26962	−	0.733017i	−0.294706	−	0.955588i	$-0.595222\pi$
$67$	−10.3923	−	6.00000i	−1.26962	−	0.733017i	−0.974916	+	0.222571i	$0.928555\pi$
$68$	−3.46410	+	2.00000i	−0.420084	+	0.242536i
$69$	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	$0.462134\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−8.66025	−	5.00000i	−1.01361	−	0.585206i	−0.101361	−	0.994850i	$-0.532320\pi$
$73$	−8.66025	−	5.00000i	−1.01361	−	0.585206i	−0.912245	+	0.409644i	$0.865653\pi$
$74$	0.500000	−	0.866025i	0.0581238	−	0.100673i
$75$		0			0
$76$	−7.00000			−0.802955
$77$	4.33013	+	12.5000i	0.493464	+	1.42451i
$78$			5.00000i			0.566139i
$79$	−6.00000	−	10.3923i	−0.675053	−	1.16923i	−0.976453	−	0.215728i	$-0.930788\pi$
$79$	−6.00000	−	10.3923i	−0.675053	−	1.16923i	0.301401	−	0.953498i	$-0.402546\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.33013	+	2.50000i	−0.478183	+	0.276079i
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$	−0.500000	+	2.59808i	−0.0545545	+	0.283473i
$85$		0			0
$86$	−6.00000	−	10.3923i	−0.646997	−	1.12063i
$87$		0			0
$88$	4.33013	+	2.50000i	0.461593	+	0.266501i
$89$	7.00000	+	12.1244i	0.741999	+	1.28518i	0.951584	+	0.307389i	$0.0994552\pi$
$89$	7.00000	+	12.1244i	0.741999	+	1.28518i	−0.209585	+	0.977790i	$0.567211\pi$
$90$		0			0
$91$	10.0000	+	8.66025i	1.04828	+	0.907841i
$92$		−	1.00000i		−	0.104257i
$93$	1.73205	−	1.00000i	0.179605	−	0.103695i
$94$	−5.50000	+	9.52628i	−0.567282	+	0.982561i
$95$		0			0
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$			8.00000i			0.812277i	0.913812	+	0.406138i	$0.133125\pi$
$97$			8.00000i			0.812277i	−0.913812	+	0.406138i	$0.866875\pi$
$98$	4.33013	+	5.50000i	0.437409	+	0.555584i
$99$	5.00000			0.502519
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	3.46410	+	2.00000i	0.342997	+	0.198030i
$103$	6.92820	−	4.00000i	0.682656	−	0.394132i	−0.118199	−	0.992990i	$-0.537712\pi$
$103$	6.92820	−	4.00000i	0.682656	−	0.394132i	0.800855	+	0.598858i	$0.204379\pi$
$104$	5.00000			0.490290
$105$		0			0
$106$	−9.00000			−0.874157
$107$	1.73205	−	1.00000i	0.167444	−	0.0966736i	−0.413936	−	0.910306i	$-0.635846\pi$
$107$	1.73205	−	1.00000i	0.167444	−	0.0966736i	0.581380	+	0.813632i	$0.302513\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$		0			0
$111$	−1.00000			−0.0949158
$112$	2.59808	+	0.500000i	0.245495	+	0.0472456i
$113$		−	14.0000i		−	1.31701i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$		−	14.0000i		−	1.31701i	0.752577	−	0.658505i	$-0.228811\pi$
$114$	3.50000	+	6.06218i	0.327805	+	0.567775i
$115$		0			0
$116$		0			0
$117$	4.33013	−	2.50000i	0.400320	−	0.231125i
$118$			4.00000i			0.368230i
$119$	10.0000	−	3.46410i	0.916698	−	0.317554i
$120$		0			0
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	3.46410	+	2.00000i	0.313625	+	0.181071i
$123$	4.33013	+	2.50000i	0.390434	+	0.225417i
$124$	−1.00000	−	1.73205i	−0.0898027	−	0.155543i
$125$		0			0
$126$	2.50000	−	0.866025i	0.222718	−	0.0771517i
$127$		−	9.00000i		−	0.798621i	−0.916816	−	0.399310i	$-0.869250\pi$
$127$		−	9.00000i		−	0.798621i	0.916816	−	0.399310i	$-0.130750\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−6.00000	+	10.3923i	−0.528271	+	0.914991i
$130$		0			0
$131$	4.50000	+	7.79423i	0.393167	+	0.680985i	0.992865	−	0.119241i	$-0.0380462\pi$
$131$	4.50000	+	7.79423i	0.393167	+	0.680985i	−0.599699	+	0.800226i	$0.704713\pi$
$132$		−	5.00000i		−	0.435194i
$133$	18.1865	+	3.50000i	1.57697	+	0.303488i
$134$	12.0000			1.03664
$135$		0			0
$136$	2.00000	−	3.46410i	0.171499	−	0.297044i
$137$	−1.73205	−	1.00000i	−0.147979	−	0.0854358i	0.424182	−	0.905577i	$-0.360562\pi$
$137$	−1.73205	−	1.00000i	−0.147979	−	0.0854358i	−0.572161	+	0.820141i	$0.693895\pi$
$138$	−0.866025	+	0.500000i	−0.0737210	+	0.0425628i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	11.0000			0.926367
$142$	−1.73205	+	1.00000i	−0.145350	+	0.0839181i
$143$	−21.6506	−	12.5000i	−1.81052	−	1.04530i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$		0			0
$146$	10.0000			0.827606
$147$	2.59808	−	6.50000i	0.214286	−	0.536111i
$148$			1.00000i			0.0821995i
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	0.999953	−	0.00974235i	$-0.00310113\pi$
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	−0.508413	+	0.861113i	$0.669768\pi$
$150$		0			0
$151$	−7.00000	+	12.1244i	−0.569652	+	0.986666i	0.426948	+	0.904276i	$0.359589\pi$
$151$	−7.00000	+	12.1244i	−0.569652	+	0.986666i	−0.996600	+	0.0823900i	$0.973745\pi$
$152$	6.06218	−	3.50000i	0.491708	−	0.283887i
$153$		−	4.00000i		−	0.323381i
$154$	−10.0000	−	8.66025i	−0.805823	−	0.697863i
$155$		0			0
$156$	−2.50000	−	4.33013i	−0.200160	−	0.346688i
$157$	9.52628	+	5.50000i	0.760280	+	0.438948i	0.829396	−	0.558661i	$-0.188685\pi$
$157$	9.52628	+	5.50000i	0.760280	+	0.438948i	−0.0691164	+	0.997609i	$0.522018\pi$
$158$	10.3923	+	6.00000i	0.826767	+	0.477334i
$159$	4.50000	+	7.79423i	0.356873	+	0.618123i
$160$		0			0
$161$	−0.500000	+	2.59808i	−0.0394055	+	0.204757i
$162$		−	1.00000i		−	0.0785674i
$163$	−20.7846	+	12.0000i	−1.62798	+	0.939913i	−0.643280	+	0.765631i	$0.722427\pi$
$163$	−20.7846	+	12.0000i	−1.62798	+	0.939913i	−0.984696	+	0.174282i	$0.944240\pi$
$164$	2.50000	−	4.33013i	0.195217	−	0.338126i
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$		−	11.0000i		−	0.851206i	−0.904910	−	0.425603i	$-0.860062\pi$
$167$		−	11.0000i		−	0.851206i	0.904910	−	0.425603i	$-0.139938\pi$
$168$	−0.866025	−	2.50000i	−0.0668153	−	0.192879i
$169$	−12.0000			−0.923077
$170$		0			0
$171$	3.50000	−	6.06218i	0.267652	−	0.463586i
$172$	10.3923	+	6.00000i	0.792406	+	0.457496i
$173$	−11.2583	+	6.50000i	−0.855955	+	0.494186i	−0.862656	−	0.505792i	$-0.831200\pi$
$173$	−11.2583	+	6.50000i	−0.855955	+	0.494186i	0.00670064	+	0.999978i	$0.497867\pi$
$174$		0			0
$175$		0			0
$176$	−5.00000			−0.376889
$177$	3.46410	−	2.00000i	0.260378	−	0.150329i
$178$	−12.1244	−	7.00000i	−0.908759	−	0.524672i
$179$	−11.5000	+	19.9186i	−0.859550	+	1.48878i	0.0128080	+	0.999918i	$0.495923\pi$
$179$	−11.5000	+	19.9186i	−0.859550	+	1.48878i	−0.872358	+	0.488867i	$0.837410\pi$
$180$		0			0
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$	−12.9904	−	2.50000i	−0.962911	−	0.185312i
$183$		−	4.00000i		−	0.295689i
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$		0			0
$186$	−1.00000	+	1.73205i	−0.0733236	+	0.127000i
$187$	−17.3205	+	10.0000i	−1.26660	+	0.731272i
$188$		−	11.0000i		−	0.802257i
$189$	−2.00000	−	1.73205i	−0.145479	−	0.125988i
$190$		0			0
$191$	−7.00000	−	12.1244i	−0.506502	−	0.877288i	−0.999972	−	0.00752447i	$-0.997605\pi$
$191$	−7.00000	−	12.1244i	−0.506502	−	0.877288i	0.493469	−	0.869763i	$-0.335728\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−8.66025	−	5.00000i	−0.623379	−	0.359908i	0.154805	−	0.987945i	$-0.450525\pi$
$193$	−8.66025	−	5.00000i	−0.623379	−	0.359908i	−0.778183	+	0.628037i	$0.783859\pi$
$194$	−4.00000	−	6.92820i	−0.287183	−	0.497416i
$195$		0			0
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$			3.00000i			0.213741i	0.994273	+	0.106871i	$0.0340831\pi$
$197$			3.00000i			0.213741i	−0.994273	+	0.106871i	$0.965917\pi$
$198$	−4.33013	+	2.50000i	−0.307729	+	0.177667i
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$		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
$207$	0.866025	+	0.500000i	0.0601929	+	0.0347524i
$208$	−4.33013	+	2.50000i	−0.300240	+	0.173344i
$209$	−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	$0.301030\pi$
$212$	7.79423	−	4.50000i	0.535310	−	0.309061i
$213$	1.73205	+	1.00000i	0.118678	+	0.0685189i
$214$	−1.00000	+	1.73205i	−0.0683586	+	0.118401i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	1.73205	+	5.00000i	0.117579	+	0.339422i
$218$		−	2.00000i		−	0.135457i
$219$	−5.00000	−	8.66025i	−0.337869	−	0.585206i
$220$		0			0
$221$	−10.0000	+	17.3205i	−0.672673	+	1.16510i
$222$	0.866025	−	0.500000i	0.0581238	−	0.0335578i
$223$		−	12.0000i		−	0.803579i	−0.915732	−	0.401790i	$-0.868388\pi$
$223$		−	12.0000i		−	0.803579i	0.915732	−	0.401790i	$-0.131612\pi$
$224$	−2.50000	+	0.866025i	−0.167038	+	0.0578638i
$225$		0			0
$226$	7.00000	+	12.1244i	0.465633	+	0.806500i
$227$	−10.3923	−	6.00000i	−0.689761	−	0.398234i	0.113761	−	0.993508i	$-0.463710\pi$
$227$	−10.3923	−	6.00000i	−0.689761	−	0.398234i	−0.803523	+	0.595274i	$0.797043\pi$
$228$	−6.06218	−	3.50000i	−0.401478	−	0.231793i
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	0.982592	−	0.185776i	$-0.0594799\pi$
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	−0.652183	+	0.758062i	$0.726147\pi$
$230$		0			0
$231$	−2.50000	+	12.9904i	−0.164488	+	0.854704i
$232$		0			0
$233$	−12.1244	+	7.00000i	−0.794293	+	0.458585i	−0.841472	−	0.540301i	$-0.818310\pi$
$233$	−12.1244	+	7.00000i	−0.794293	+	0.458585i	0.0471787	+	0.998886i	$0.484977\pi$
$234$	−2.50000	+	4.33013i	−0.163430	+	0.283069i
$235$		0			0
$236$	−2.00000	−	3.46410i	−0.130189	−	0.225494i
$237$		−	12.0000i		−	0.779484i
$238$	−6.92820	+	8.00000i	−0.449089	+	0.518563i
$239$	22.0000			1.42306			0.711531	−	0.702655i	$-0.248002\pi$
$239$	22.0000			1.42306			0.711531	+	0.702655i	$0.248002\pi$
$240$		0			0
$241$	−7.50000	+	12.9904i	−0.483117	+	0.836784i	−0.999812	−	0.0193858i	$-0.993829\pi$
$241$	−7.50000	+	12.9904i	−0.483117	+	0.836784i	0.516695	+	0.856170i	$0.327162\pi$
$242$	12.1244	+	7.00000i	0.779383	+	0.449977i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−4.00000			−0.256074
$245$		0			0
$246$	−5.00000			−0.318788
$247$	−30.3109	+	17.5000i	−1.92864	+	1.11350i
$248$	1.73205	+	1.00000i	0.109985	+	0.0635001i
$249$	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	$0.489953\pi$
$252$	−1.73205	+	2.00000i	−0.109109	+	0.125988i
$253$		−	5.00000i		−	0.314347i
$254$	4.50000	+	7.79423i	0.282355	+	0.489053i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	13.8564	−	8.00000i	0.864339	−	0.499026i	−0.00112398	−	0.999999i	$-0.500358\pi$
$257$	13.8564	−	8.00000i	0.864339	−	0.499026i	0.865463	+	0.500973i	$0.167024\pi$
$258$		−	12.0000i		−	0.747087i
$259$	0.500000	−	2.59808i	0.0310685	−	0.161437i
$260$		0			0
$261$		0			0
$262$	−7.79423	−	4.50000i	−0.481529	−	0.278011i
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$	2.50000	+	4.33013i	0.153864	+	0.266501i
$265$		0			0
$266$	−17.5000	+	6.06218i	−1.07299	+	0.371696i
$267$			14.0000i			0.856786i
$268$	−10.3923	+	6.00000i	−0.634811	+	0.366508i
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	0.224523	+	0.974469i	$0.427917\pi$
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	−0.956176	+	0.292791i	$0.905416\pi$
$270$		0			0
$271$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$			4.00000i			0.242536i
$273$	4.33013	+	12.5000i	0.262071	+	0.756534i
$274$	2.00000			0.120824
$275$		0			0
$276$	0.500000	−	0.866025i	0.0300965	−	0.0521286i
$277$	12.1244	+	7.00000i	0.728482	+	0.420589i	0.817867	−	0.575408i	$-0.195157\pi$
$277$	12.1244	+	7.00000i	0.728482	+	0.420589i	−0.0893846	+	0.995997i	$0.528490\pi$
$278$	−3.46410	+	2.00000i	−0.207763	+	0.119952i
$279$	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	$0.433047\pi$
$282$	−9.52628	+	5.50000i	−0.567282	+	0.327520i
$283$	8.66025	+	5.00000i	0.514799	+	0.297219i	0.734804	−	0.678280i	$-0.237274\pi$
$283$	8.66025	+	5.00000i	0.514799	+	0.297219i	−0.220005	+	0.975499i	$0.570607\pi$
$284$	1.00000	−	1.73205i	0.0593391	−	0.102778i
$285$		0			0
$286$	25.0000			1.47828
$287$	−8.66025	+	10.0000i	−0.511199	+	0.590281i
$288$			1.00000i			0.0589256i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$		0			0
$291$	−4.00000	+	6.92820i	−0.234484	+	0.406138i
$292$	−8.66025	+	5.00000i	−0.506803	+	0.292603i
$293$			9.00000i			0.525786i	0.964825	+	0.262893i	$0.0846766\pi$
$293$			9.00000i			0.525786i	−0.964825	+	0.262893i	$0.915323\pi$
$294$	1.00000	+	6.92820i	0.0583212	+	0.404061i
$295$		0			0
$296$	−0.500000	−	0.866025i	−0.0290619	−	0.0503367i
$297$	4.33013	+	2.50000i	0.251259	+	0.145065i
$298$	−10.3923	−	6.00000i	−0.602010	−	0.347571i
$299$	−2.50000	−	4.33013i	−0.144579	−	0.250418i
$300$		0			0
$301$	−24.0000	−	20.7846i	−1.38334	−	1.19800i
$302$		−	14.0000i		−	0.805609i
$303$		0			0
$304$	−3.50000	+	6.06218i	−0.200739	+	0.347690i
$305$		0			0
$306$	2.00000	+	3.46410i	0.114332	+	0.198030i
$307$		−	8.00000i		−	0.456584i	−0.973593	−	0.228292i	$-0.926686\pi$
$307$		−	8.00000i		−	0.456584i	0.973593	−	0.228292i	$-0.0733141\pi$
$308$	12.9904	+	2.50000i	0.740196	+	0.142451i
$309$	8.00000			0.455104
$310$		0			0
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	−0.956864	−	0.290537i	$-0.906166\pi$
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	0.730044	+	0.683400i	$0.239499\pi$
$312$	4.33013	+	2.50000i	0.245145	+	0.141535i
$313$	13.8564	−	8.00000i	0.783210	−	0.452187i	−0.0543564	−	0.998522i	$-0.517311\pi$
$313$	13.8564	−	8.00000i	0.783210	−	0.452187i	0.837567	+	0.546335i	$0.183977\pi$
$314$	−11.0000			−0.620766
$315$		0			0
$316$	−12.0000			−0.675053
$317$	19.0526	−	11.0000i	1.07010	−	0.617822i	0.141890	−	0.989882i	$-0.454682\pi$
$317$	19.0526	−	11.0000i	1.07010	−	0.617822i	0.928208	+	0.372061i	$0.121349\pi$
$318$	−7.79423	−	4.50000i	−0.437079	−	0.252347i
$319$		0			0
$320$		0			0
$321$	2.00000			0.111629
$322$	−0.866025	−	2.50000i	−0.0482617	−	0.139320i
$323$			28.0000i			1.55796i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$		0			0
$326$	12.0000	−	20.7846i	0.664619	−	1.15115i
$327$	−1.73205	+	1.00000i	−0.0957826	+	0.0553001i
$328$			5.00000i			0.276079i
$329$	−5.50000	+	28.5788i	−0.303225	+	1.57560i
$330$		0			0
$331$	−15.5000	−	26.8468i	−0.851957	−	1.47563i	−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−15.5000	−	26.8468i	−0.851957	−	1.47563i	0.0274825	−	0.999622i	$-0.491251\pi$
$332$	−10.3923	−	6.00000i	−0.570352	−	0.329293i
$333$	−0.866025	−	0.500000i	−0.0474579	−	0.0273998i
$334$	5.50000	+	9.52628i	0.300947	+	0.521255i
$335$		0			0
$336$	2.00000	+	1.73205i	0.109109	+	0.0944911i
$337$			16.0000i			0.871576i	0.900049	+	0.435788i	$0.143530\pi$
$337$			16.0000i			0.871576i	−0.900049	+	0.435788i	$0.856470\pi$
$338$	10.3923	−	6.00000i	0.565267	−	0.326357i
$339$	7.00000	−	12.1244i	0.380188	−	0.658505i
$340$		0			0
$341$	−5.00000	−	8.66025i	−0.270765	−	0.468979i
$342$			7.00000i			0.378517i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$	−12.0000			−0.646997
$345$		0			0
$346$	6.50000	−	11.2583i	0.349442	−	0.605252i
$347$	−15.5885	−	9.00000i	−0.836832	−	0.483145i	0.0193540	−	0.999813i	$-0.493839\pi$
$347$	−15.5885	−	9.00000i	−0.836832	−	0.483145i	−0.856186	+	0.516667i	$0.827172\pi$
$348$		0			0
$349$	4.00000			0.214115			0.107058	−	0.994253i	$-0.465857\pi$
$349$	4.00000			0.214115			0.107058	+	0.994253i	$0.465857\pi$
$350$		0			0
$351$	5.00000			0.266880
$352$	4.33013	−	2.50000i	0.230797	−	0.133250i
$353$	−20.7846	−	12.0000i	−1.10625	−	0.638696i	−0.168397	−	0.985719i	$-0.553859\pi$
$353$	−20.7846	−	12.0000i	−1.10625	−	0.638696i	−0.937856	+	0.347024i	$0.887192\pi$
$354$	−2.00000	+	3.46410i	−0.106299	+	0.184115i
$355$		0			0
$356$	14.0000			0.741999
$357$	10.3923	+	2.00000i	0.550019	+	0.105851i
$358$		−	23.0000i		−	1.21559i
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	−0.999476	−	0.0323801i	$-0.989691\pi$
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	0.471696	−	0.881761i	$-0.343642\pi$
$360$		0			0
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$	−17.3205	+	10.0000i	−0.910346	+	0.525588i
$363$		−	14.0000i		−	0.734809i
$364$	12.5000	−	4.33013i	0.655178	−	0.226960i
$365$		0			0
$366$	2.00000	+	3.46410i	0.104542	+	0.181071i
$367$	6.06218	+	3.50000i	0.316443	+	0.182699i	0.649806	−	0.760100i	$-0.274850\pi$
$367$	6.06218	+	3.50000i	0.316443	+	0.182699i	−0.333363	+	0.942799i	$0.608183\pi$
$368$	−0.866025	−	0.500000i	−0.0451447	−	0.0260643i
$369$	2.50000	+	4.33013i	0.130145	+	0.225417i
$370$		0			0
$371$	−22.5000	+	7.79423i	−1.16814	+	0.404656i
$372$		−	2.00000i		−	0.103695i
$373$	−19.0526	+	11.0000i	−0.986504	+	0.569558i	−0.904227	−	0.427051i	$-0.859552\pi$
$373$	−19.0526	+	11.0000i	−0.986504	+	0.569558i	−0.0822766	+	0.996610i	$0.526219\pi$
$374$	10.0000	−	17.3205i	0.517088	−	0.895622i
$375$		0			0
$376$	5.50000	+	9.52628i	0.283641	+	0.491280i
$377$		0			0
$378$	2.59808	+	0.500000i	0.133631	+	0.0257172i
$379$	−1.00000			−0.0513665			−0.0256833	−	0.999670i	$-0.508176\pi$
$379$	−1.00000			−0.0513665			−0.0256833	+	0.999670i	$0.508176\pi$
$380$		0			0
$381$	4.50000	−	7.79423i	0.230542	−	0.399310i
$382$	12.1244	+	7.00000i	0.620336	+	0.358151i
$383$	18.1865	−	10.5000i	0.929288	−	0.536525i	0.0427020	−	0.999088i	$-0.486403\pi$
$383$	18.1865	−	10.5000i	0.929288	−	0.536525i	0.886586	+	0.462563i	$0.153070\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	10.0000			0.508987
$387$	−10.3923	+	6.00000i	−0.528271	+	0.304997i
$388$	6.92820	+	4.00000i	0.351726	+	0.203069i
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	−0.542445	−	0.840091i	$-0.682501\pi$
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	0.998763	+	0.0497253i	$0.0158346\pi$
$390$		0			0
$391$	−4.00000			−0.202289
$392$	6.92820	−	1.00000i	0.349927	−	0.0505076i
$393$			9.00000i			0.453990i
$394$	−1.50000	−	2.59808i	−0.0755689	−	0.130889i
$395$		0			0
$396$	2.50000	−	4.33013i	0.125630	−	0.217597i
$397$	12.1244	−	7.00000i	0.608504	−	0.351320i	−0.163876	−	0.986481i	$-0.552400\pi$
$397$	12.1244	−	7.00000i	0.608504	−	0.351320i	0.772380	+	0.635161i	$0.219066\pi$
$398$		−	4.00000i		−	0.200502i
$399$	14.0000	+	12.1244i	0.700877	+	0.606977i
$400$		0			0
$401$	10.5000	+	18.1865i	0.524345	+	0.908192i	0.999598	+	0.0283431i	$0.00902310\pi$
$401$	10.5000	+	18.1865i	0.524345	+	0.908192i	−0.475253	+	0.879849i	$0.657644\pi$
$402$	10.3923	+	6.00000i	0.518321	+	0.299253i
$403$	−8.66025	−	5.00000i	−0.431398	−	0.249068i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			5.00000i			0.247841i
$408$	3.46410	−	2.00000i	0.171499	−	0.0990148i
$409$	5.00000	−	8.66025i	0.247234	−	0.428222i	−0.715523	−	0.698589i	$-0.753812\pi$
$409$	5.00000	−	8.66025i	0.247234	−	0.428222i	0.962757	+	0.270367i	$0.0871450\pi$
$410$		0			0
$411$	−1.00000	−	1.73205i	−0.0493264	−	0.0854358i
$412$		−	8.00000i		−	0.394132i
$413$	3.46410	+	10.0000i	0.170457	+	0.492068i
$414$	−1.00000			−0.0491473
$415$		0			0
$416$	2.50000	−	4.33013i	0.122573	−	0.212302i
$417$	3.46410	+	2.00000i	0.169638	+	0.0979404i
$418$	30.3109	−	17.5000i	1.48255	−	0.855953i
$419$	−15.0000			−0.732798			−0.366399	−	0.930458i	$-0.619409\pi$
$419$	−15.0000			−0.732798			−0.366399	+	0.930458i	$0.619409\pi$
$420$		0			0
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$	−14.7224	+	8.50000i	−0.716677	+	0.413774i
$423$	9.52628	+	5.50000i	0.463184	+	0.267419i
$424$	−4.50000	+	7.79423i	−0.218539	+	0.378521i
$425$		0			0
$426$	−2.00000			−0.0969003
$427$	10.3923	+	2.00000i	0.502919	+	0.0967868i
$428$		−	2.00000i		−	0.0966736i
$429$	−12.5000	−	21.6506i	−0.603506	−	1.04530i
$430$		0			0
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$			24.0000i			1.15337i	0.816968	+	0.576683i	$0.195653\pi$
$433$			24.0000i			1.15337i	−0.816968	+	0.576683i	$0.804347\pi$
$434$	−4.00000	−	3.46410i	−0.192006	−	0.166282i
$435$		0			0
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	−6.06218	−	3.50000i	−0.289993	−	0.167428i
$438$	8.66025	+	5.00000i	0.413803	+	0.238909i
$439$	−20.0000	−	34.6410i	−0.954548	−	1.65333i	−0.735399	−	0.677634i	$-0.763005\pi$
$439$	−20.0000	−	34.6410i	−0.954548	−	1.65333i	−0.219149	−	0.975691i	$-0.570328\pi$
$440$		0			0
$441$	5.50000	−	4.33013i	0.261905	−	0.206197i
$442$		−	20.0000i		−	0.951303i
$443$	−24.2487	+	14.0000i	−1.15209	+	0.665160i	−0.949396	−	0.314082i	$-0.898303\pi$
$443$	−24.2487	+	14.0000i	−1.15209	+	0.665160i	−0.202695	+	0.979242i	$0.564970\pi$
$444$	−0.500000	+	0.866025i	−0.0237289	+	0.0410997i
$445$		0			0
$446$	6.00000	+	10.3923i	0.284108	+	0.492090i
$447$			12.0000i			0.567581i
$448$	1.73205	−	2.00000i	0.0818317	−	0.0944911i
$449$	29.0000			1.36859			0.684297	−	0.729203i	$-0.260109\pi$
$449$	29.0000			1.36859			0.684297	+	0.729203i	$0.260109\pi$
$450$		0			0
$451$	12.5000	−	21.6506i	0.588602	−	1.01949i
$452$	−12.1244	−	7.00000i	−0.570282	−	0.329252i
$453$	−12.1244	+	7.00000i	−0.569652	+	0.328889i
$454$	12.0000			0.563188
$455$		0			0
$456$	7.00000			0.327805
$457$	12.1244	−	7.00000i	0.567153	−	0.327446i	−0.188858	−	0.982004i	$-0.560479\pi$
$457$	12.1244	−	7.00000i	0.567153	−	0.327446i	0.756012	+	0.654558i	$0.227145\pi$
$458$	−8.66025	−	5.00000i	−0.404667	−	0.233635i
$459$	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	$0.529693\pi$
$462$	−4.33013	−	12.5000i	−0.201456	−	0.581553i
$463$		−	19.0000i		−	0.883005i	−0.897260	−	0.441502i	$-0.854446\pi$
$463$		−	19.0000i		−	0.883005i	0.897260	−	0.441502i	$-0.145554\pi$
$464$		0			0
$465$		0			0
$466$	7.00000	−	12.1244i	0.324269	−	0.561650i
$467$	17.3205	−	10.0000i	0.801498	−	0.462745i	−0.0424970	−	0.999097i	$-0.513531\pi$
$467$	17.3205	−	10.0000i	0.801498	−	0.462745i	0.843995	+	0.536352i	$0.180198\pi$
$468$		−	5.00000i		−	0.231125i
$469$	30.0000	−	10.3923i	1.38527	−	0.479872i
$470$		0			0
$471$	5.50000	+	9.52628i	0.253427	+	0.438948i
$472$	3.46410	+	2.00000i	0.159448	+	0.0920575i
$473$	51.9615	+	30.0000i	2.38919	+	1.37940i
$474$	6.00000	+	10.3923i	0.275589	+	0.477334i
$475$		0			0
$476$	2.00000	−	10.3923i	0.0916698	−	0.476331i
$477$			9.00000i			0.412082i
$478$	−19.0526	+	11.0000i	−0.871444	+	0.503128i
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	−0.583803	−	0.811895i	$-0.698436\pi$
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	0.995023	+	0.0996406i	$0.0317693\pi$
$480$		0			0
$481$	2.50000	+	4.33013i	0.113990	+	0.197437i
$482$		−	15.0000i		−	0.683231i
$483$	−1.73205	+	2.00000i	−0.0788110	+	0.0910032i
$484$	−14.0000			−0.636364
$485$		0			0
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$	3.46410	−	2.00000i	0.156813	−	0.0905357i
$489$	−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	$0.801800\pi$
$492$	4.33013	−	2.50000i	0.195217	−	0.112709i
$493$		0			0
$494$	17.5000	−	30.3109i	0.787362	−	1.36375i
$495$		0			0
$496$	−2.00000			−0.0898027
$497$	−3.46410	+	4.00000i	−0.155386	+	0.179425i
$498$			12.0000i			0.537733i
$499$	20.0000	+	34.6410i	0.895323	+	1.55074i	0.833404	+	0.552664i	$0.186389\pi$
$499$	20.0000	+	34.6410i	0.895323	+	1.55074i	0.0619186	+	0.998081i	$0.480278\pi$
$500$		0			0
$501$	5.50000	−	9.52628i	0.245722	−	0.425603i
$502$	−0.866025	+	0.500000i	−0.0386526	+	0.0223161i
$503$		−	20.0000i		−	0.891756i	−0.895094	−	0.445878i	$-0.852892\pi$
$503$		−	20.0000i		−	0.891756i	0.895094	−	0.445878i	$-0.147108\pi$
$504$	0.500000	−	2.59808i	0.0222718	−	0.115728i
$505$		0			0
$506$	2.50000	+	4.33013i	0.111139	+	0.192498i
$507$	−10.3923	−	6.00000i	−0.461538	−	0.266469i
$508$	−7.79423	−	4.50000i	−0.345813	−	0.199655i
$509$	−5.00000	−	8.66025i	−0.221621	−	0.383859i	0.733679	−	0.679496i	$-0.237801\pi$
$509$	−5.00000	−	8.66025i	−0.221621	−	0.383859i	−0.955300	+	0.295637i	$0.904468\pi$
$510$		0			0
$511$	25.0000	−	8.66025i	1.10593	−	0.383107i
$512$		−	1.00000i		−	0.0441942i
$513$	6.06218	−	3.50000i	0.267652	−	0.154529i
$514$	−8.00000	+	13.8564i	−0.352865	+	0.611180i
$515$		0			0
$516$	6.00000	+	10.3923i	0.264135	+	0.457496i
$517$		−	55.0000i		−	2.41890i
$518$	0.866025	+	2.50000i	0.0380510	+	0.109844i
$519$	−13.0000			−0.570637
$520$		0			0
$521$	16.5000	−	28.5788i	0.722878	−	1.25206i	−0.236963	−	0.971519i	$-0.576152\pi$
$521$	16.5000	−	28.5788i	0.722878	−	1.25206i	0.959841	−	0.280543i	$-0.0905145\pi$
$522$		0			0
$523$	−19.0526	+	11.0000i	−0.833110	+	0.480996i	−0.854916	−	0.518766i	$-0.826392\pi$
$523$	−19.0526	+	11.0000i	−0.833110	+	0.480996i	0.0218062	+	0.999762i	$0.493058\pi$
$524$	9.00000			0.393167
$525$		0			0
$526$		0			0
$527$	−6.92820	+	4.00000i	−0.301797	+	0.174243i
$528$	−4.33013	−	2.50000i	−0.188445	−	0.108799i
$529$	−11.0000	+	19.0526i	−0.478261	+	0.828372i
$530$		0			0
$531$	4.00000			0.173585
$532$	12.1244	−	14.0000i	0.525657	−	0.606977i
$533$		−	25.0000i		−	1.08287i
$534$	−7.00000	−	12.1244i	−0.302920	−	0.524672i
$535$		0			0
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$	−19.9186	+	11.5000i	−0.859550	+	0.496262i
$538$		−	24.0000i		−	1.03471i
$539$	−32.5000	−	12.9904i	−1.39987	−	0.559535i
$540$		0			0
$541$	−1.00000	−	1.73205i	−0.0429934	−	0.0744667i	0.843728	−	0.536771i	$-0.180356\pi$
$541$	−1.00000	−	1.73205i	−0.0429934	−	0.0744667i	−0.886721	+	0.462304i	$0.847023\pi$
$542$		0			0
$543$	17.3205	+	10.0000i	0.743294	+	0.429141i
$544$	−2.00000	−	3.46410i	−0.0857493	−	0.148522i
$545$		0			0
$546$	−10.0000	−	8.66025i	−0.427960	−	0.370625i
$547$		−	28.0000i		−	1.19719i	−0.801050	−	0.598597i	$-0.795725\pi$
$547$		−	28.0000i		−	1.19719i	0.801050	−	0.598597i	$-0.204275\pi$
$548$	−1.73205	+	1.00000i	−0.0739895	+	0.0427179i
$549$	2.00000	−	3.46410i	0.0853579	−	0.147844i
$550$		0			0
$551$		0			0
$552$			1.00000i			0.0425628i
$553$	31.1769	+	6.00000i	1.32578	+	0.255146i
$554$	−14.0000			−0.594803
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	32.0429	+	18.5000i	1.35770	+	0.783870i	0.989314	−	0.145802i	$-0.0465761\pi$
$557$	32.0429	+	18.5000i	1.35770	+	0.783870i	0.368389	+	0.929672i	$0.379909\pi$
$558$	−1.73205	+	1.00000i	−0.0733236	+	0.0423334i
$559$	60.0000			2.53773
$560$		0			0
$561$	−20.0000			−0.844401
$562$	−6.06218	+	3.50000i	−0.255718	+	0.147639i
$563$	15.5885	+	9.00000i	0.656975	+	0.379305i	0.791123	−	0.611656i	$-0.209497\pi$
$563$	15.5885	+	9.00000i	0.656975	+	0.379305i	−0.134148	+	0.990961i	$0.542830\pi$
$564$	5.50000	−	9.52628i	0.231592	−	0.401129i
$565$		0			0
$566$	−10.0000			−0.420331
$567$	−0.866025	−	2.50000i	−0.0363696	−	0.104990i
$568$			2.00000i			0.0839181i
$569$	19.5000	+	33.7750i	0.817483	+	1.41592i	0.907532	+	0.419984i	$0.137964\pi$
$569$	19.5000	+	33.7750i	0.817483	+	1.41592i	−0.0900490	+	0.995937i	$0.528702\pi$
$570$		0			0
$571$	−20.0000	+	34.6410i	−0.836974	+	1.44968i	0.0554391	+	0.998462i	$0.482344\pi$
$571$	−20.0000	+	34.6410i	−0.836974	+	1.44968i	−0.892413	+	0.451219i	$0.850989\pi$
$572$	−21.6506	+	12.5000i	−0.905259	+	0.522651i
$573$		−	14.0000i		−	0.584858i
$574$	2.50000	−	12.9904i	0.104348	−	0.542208i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	22.5167	+	13.0000i	0.937381	+	0.541197i	0.889138	−	0.457639i	$-0.151305\pi$
$577$	22.5167	+	13.0000i	0.937381	+	0.541197i	0.0482425	+	0.998836i	$0.484638\pi$
$578$	0.866025	+	0.500000i	0.0360219	+	0.0207973i
$579$	−5.00000	−	8.66025i	−0.207793	−	0.359908i
$580$		0			0
$581$	24.0000	+	20.7846i	0.995688	+	0.862291i
$582$		−	8.00000i		−	0.331611i
$583$	38.9711	−	22.5000i	1.61402	−	0.931855i
$584$	5.00000	−	8.66025i	0.206901	−	0.358364i
$585$		0			0
$586$	−4.50000	−	7.79423i	−0.185893	−	0.321977i
$587$			30.0000i			1.23823i	0.785299	+	0.619116i	$0.212509\pi$
$587$			30.0000i			1.23823i	−0.785299	+	0.619116i	$0.787491\pi$
$588$	−4.33013	−	5.50000i	−0.178571	−	0.226816i
$589$	−14.0000			−0.576860
$590$		0			0
$591$	−1.50000	+	2.59808i	−0.0617018	+	0.106871i
$592$	0.866025	+	0.500000i	0.0355934	+	0.0205499i
$593$	31.1769	−	18.0000i	1.28028	−	0.739171i	0.303383	−	0.952869i	$-0.401884\pi$
$593$	31.1769	−	18.0000i	1.28028	−	0.739171i	0.976900	+	0.213697i	$0.0685507\pi$
$594$	−5.00000			−0.205152
$595$		0			0
$596$	12.0000			0.491539
$597$	−3.46410	+	2.00000i	−0.141776	+	0.0818546i
$598$	4.33013	+	2.50000i	0.177072	+	0.102233i
$599$	−5.00000	+	8.66025i	−0.204294	+	0.353848i	−0.949908	−	0.312531i	$-0.898823\pi$
$599$	−5.00000	+	8.66025i	−0.204294	+	0.353848i	0.745613	+	0.666379i	$0.232157\pi$
$600$		0			0
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$	31.1769	+	6.00000i	1.27068	+	0.244542i
$603$		−	12.0000i		−	0.488678i
$604$	7.00000	+	12.1244i	0.284826	+	0.493333i
$605$		0			0
$606$		0			0
$607$	23.3827	−	13.5000i	0.949074	−	0.547948i	0.0562808	−	0.998415i	$-0.482076\pi$
$607$	23.3827	−	13.5000i	0.949074	−	0.547948i	0.892793	+	0.450467i	$0.148742\pi$
$608$		−	7.00000i		−	0.283887i
$609$		0			0
$610$		0			0
$611$	−27.5000	−	47.6314i	−1.11253	−	1.92696i
$612$	−3.46410	−	2.00000i	−0.140028	−	0.0808452i
$613$	37.2391	+	21.5000i	1.50407	+	0.868377i	0.999989	+	0.00472215i	$0.00150311\pi$
$613$	37.2391	+	21.5000i	1.50407	+	0.868377i	0.504084	+	0.863655i	$0.331830\pi$
$614$	4.00000	+	6.92820i	0.161427	+	0.279600i
$615$		0			0
$616$	−12.5000	+	4.33013i	−0.503639	+	0.174466i
$617$			8.00000i			0.322068i	0.986949	+	0.161034i	$0.0514829\pi$
$617$			8.00000i			0.322068i	−0.986949	+	0.161034i	$0.948517\pi$
$618$	−6.92820	+	4.00000i	−0.278693	+	0.160904i
$619$	12.5000	−	21.6506i	0.502417	−	0.870212i	−0.497579	−	0.867419i	$-0.665777\pi$
$619$	12.5000	−	21.6506i	0.502417	−	0.870212i	0.999996	−	0.00279365i	$-0.000889247\pi$
$620$		0			0
$621$	0.500000	+	0.866025i	0.0200643	+	0.0347524i
$622$		−	8.00000i		−	0.320771i
$623$	−36.3731	−	7.00000i	−1.45726	−	0.280449i
$624$	−5.00000			−0.200160
$625$		0			0
$626$	−8.00000	+	13.8564i	−0.319744	+	0.553813i
$627$	−30.3109	−	17.5000i	−1.21050	−	0.698883i
$628$	9.52628	−	5.50000i	0.380140	−	0.219474i
$629$	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	$0.461894\pi$
$632$	10.3923	−	6.00000i	0.413384	−	0.238667i
$633$	14.7224	+	8.50000i	0.585164	+	0.337845i
$634$	−11.0000	+	19.0526i	−0.436866	+	0.756674i
$635$		0			0
$636$	9.00000			0.356873
$637$	−34.6410	+	5.00000i	−1.37253	+	0.198107i
$638$		0			0
$639$	1.00000	+	1.73205i	0.0395594	+	0.0685189i
$640$		0			0
$641$	−10.5000	+	18.1865i	−0.414725	+	0.718325i	−0.995400	−	0.0958109i	$-0.969456\pi$
$641$	−10.5000	+	18.1865i	−0.414725	+	0.718325i	0.580674	+	0.814136i	$0.302789\pi$
$642$	−1.73205	+	1.00000i	−0.0683586	+	0.0394669i
$643$			34.0000i			1.34083i	0.741987	+	0.670415i	$0.233884\pi$
$643$			34.0000i			1.34083i	−0.741987	+	0.670415i	$0.766116\pi$
$644$	2.00000	+	1.73205i	0.0788110	+	0.0682524i
$645$		0			0
$646$	−14.0000	−	24.2487i	−0.550823	−	0.954053i
$647$	−19.9186	−	11.5000i	−0.783080	−	0.452112i	0.0544405	−	0.998517i	$-0.482662\pi$
$647$	−19.9186	−	11.5000i	−0.783080	−	0.452112i	−0.837521	+	0.546405i	$0.815996\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−10.0000	−	17.3205i	−0.392534	−	0.679889i
$650$		0			0
$651$	−1.00000	+	5.19615i	−0.0391931	+	0.203653i
$652$			24.0000i			0.939913i
$653$	−16.4545	+	9.50000i	−0.643914	+	0.371764i	−0.786121	−	0.618073i	$-0.787914\pi$
$653$	−16.4545	+	9.50000i	−0.643914	+	0.371764i	0.142207	+	0.989837i	$0.454580\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$		0			0
$656$	−2.50000	−	4.33013i	−0.0976086	−	0.169063i
$657$		−	10.0000i		−	0.390137i
$658$	−9.52628	−	27.5000i	−0.371373	−	1.07206i
$659$	20.0000			0.779089			0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000			0.779089			0.389545	+	0.921008i	$0.372632\pi$
$660$		0			0
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	−0.155235	−	0.987878i	$-0.549613\pi$
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	0.933144	−	0.359502i	$-0.117053\pi$
$662$	26.8468	+	15.5000i	1.04343	+	0.602425i
$663$	−17.3205	+	10.0000i	−0.672673	+	0.388368i
$664$	12.0000			0.465690
$665$		0			0
$666$	1.00000			0.0387492
$667$		0			0
$668$	−9.52628	−	5.50000i	−0.368583	−	0.212801i
$669$	6.00000	−	10.3923i	0.231973	−	0.401790i
$670$		0			0
$671$	−20.0000			−0.772091
$672$	−2.59808	−	0.500000i	−0.100223	−	0.0192879i
$673$		−	4.00000i		−	0.154189i	−0.997024	−	0.0770943i	$-0.975436\pi$
$673$		−	4.00000i		−	0.154189i	0.997024	−	0.0770943i	$-0.0245643\pi$
$674$	−8.00000	−	13.8564i	−0.308148	−	0.533729i
$675$		0			0
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	−28.5788	+	16.5000i	−1.09837	+	0.634147i	−0.935793	−	0.352549i	$-0.885315\pi$
$677$	−28.5788	+	16.5000i	−1.09837	+	0.634147i	−0.162581	+	0.986695i	$0.551982\pi$
$678$			14.0000i			0.537667i
$679$	−16.0000	−	13.8564i	−0.614024	−	0.531760i
$680$		0			0
$681$	−6.00000	−	10.3923i	−0.229920	−	0.398234i
$682$	8.66025	+	5.00000i	0.331618	+	0.191460i
$683$	3.46410	+	2.00000i	0.132550	+	0.0765279i	0.564809	−	0.825222i	$-0.308950\pi$
$683$	3.46410	+	2.00000i	0.132550	+	0.0765279i	−0.432259	+	0.901750i	$0.642283\pi$
$684$	−3.50000	−	6.06218i	−0.133826	−	0.231793i
$685$		0			0
$686$	−18.5000	−	0.866025i	−0.706333	−	0.0330650i
$687$			10.0000i			0.381524i
$688$	10.3923	−	6.00000i	0.396203	−	0.228748i
$689$	22.5000	−	38.9711i	0.857182	−	1.48468i
$690$		0			0
$691$	−14.0000	−	24.2487i	−0.532585	−	0.922464i	−0.999276	−	0.0380440i	$-0.987887\pi$
$691$	−14.0000	−	24.2487i	−0.532585	−	0.922464i	0.466691	−	0.884420i	$-0.345446\pi$
$692$			13.0000i			0.494186i
$693$	−8.66025	+	10.0000i	−0.328976	+	0.379869i
$694$	18.0000			0.683271
$695$		0			0
$696$		0			0
$697$	−17.3205	−	10.0000i	−0.656061	−	0.378777i
$698$	−3.46410	+	2.00000i	−0.131118	+	0.0757011i
$699$	−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	$0.308281\pi$
$702$	−4.33013	+	2.50000i	−0.163430	+	0.0943564i
$703$	6.06218	+	3.50000i	0.228639	+	0.132005i
$704$	−2.50000	+	4.33013i	−0.0942223	+	0.163198i
$705$		0			0
$706$	24.0000			0.903252
$707$		0			0
$708$		−	4.00000i		−	0.150329i
$709$	14.0000	+	24.2487i	0.525781	+	0.910679i	0.999549	+	0.0300298i	$0.00956021\pi$
$709$	14.0000	+	24.2487i	0.525781	+	0.910679i	−0.473768	+	0.880650i	$0.657106\pi$
$710$		0			0
$711$	6.00000	−	10.3923i	0.225018	−	0.389742i
$712$	−12.1244	+	7.00000i	−0.454379	+	0.262336i
$713$		−	2.00000i		−	0.0749006i
$714$	−10.0000	+	3.46410i	−0.374241	+	0.129641i
$715$		0			0
$716$	11.5000	+	19.9186i	0.429775	+	0.744392i
$717$	19.0526	+	11.0000i	0.711531	+	0.410803i
$718$	17.3205	+	10.0000i	0.646396	+	0.373197i
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$		0			0
$721$	−4.00000	+	20.7846i	−0.148968	+	0.774059i
$722$		−	30.0000i		−	1.11648i
$723$	−12.9904	+	7.50000i	−0.483117	+	0.278928i
$724$	10.0000	−	17.3205i	0.371647	−	0.643712i
$725$		0			0
$726$	7.00000	+	12.1244i	0.259794	+	0.449977i
$727$			3.00000i			0.111264i	0.998451	+	0.0556319i	$0.0177173\pi$
$727$			3.00000i			0.111264i	−0.998451	+	0.0556319i	$0.982283\pi$
$728$	−8.66025	+	10.0000i	−0.320970	+	0.370625i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	24.0000	−	41.5692i	0.887672	−	1.53749i
$732$	−3.46410	−	2.00000i	−0.128037	−	0.0739221i
$733$	7.79423	−	4.50000i	0.287886	−	0.166211i	−0.349102	−	0.937085i	$-0.613513\pi$
$733$	7.79423	−	4.50000i	0.287886	−	0.166211i	0.636988	+	0.770873i	$0.280180\pi$
$734$	−7.00000			−0.258375
$735$		0			0
$736$	1.00000			0.0368605
$737$	−51.9615	+	30.0000i	−1.91403	+	1.10506i
$738$	−4.33013	−	2.50000i	−0.159394	−	0.0920263i
$739$	−7.50000	+	12.9904i	−0.275892	+	0.477859i	−0.970360	−	0.241665i	$-0.922307\pi$
$739$	−7.50000	+	12.9904i	−0.275892	+	0.477859i	0.694468	+	0.719524i	$0.255640\pi$
$740$		0			0
$741$	−35.0000			−1.28576
$742$	15.5885	−	18.0000i	0.572270	−	0.660801i
$743$			15.0000i			0.550297i	0.961402	+	0.275148i	$0.0887270\pi$
$743$			15.0000i			0.550297i	−0.961402	+	0.275148i	$0.911273\pi$
$744$	1.00000	+	1.73205i	0.0366618	+	0.0635001i
$745$		0			0
$746$	11.0000	−	19.0526i	0.402739	−	0.697564i
$747$	10.3923	−	6.00000i	0.380235	−	0.219529i
$748$			20.0000i			0.731272i
$749$	−1.00000	+	5.19615i	−0.0365392	+	0.189863i
$750$		0			0
$751$	25.0000	+	43.3013i	0.912263	+	1.58009i	0.810860	+	0.585240i	$0.199000\pi$
$751$	25.0000	+	43.3013i	0.912263	+	1.58009i	0.101403	+	0.994845i	$0.467667\pi$
$752$	−9.52628	−	5.50000i	−0.347388	−	0.200564i
$753$	0.866025	+	0.500000i	0.0315597	+	0.0182210i
$754$		0			0
$755$		0			0
$756$	−2.50000	+	0.866025i	−0.0909241	+	0.0314970i
$757$			34.0000i			1.23575i	0.786276	+	0.617876i	$0.212006\pi$
$757$			34.0000i			1.23575i	−0.786276	+	0.617876i	$0.787994\pi$
$758$	0.866025	−	0.500000i	0.0314555	−	0.0181608i
$759$	2.50000	−	4.33013i	0.0907443	−	0.157174i
$760$		0			0
$761$	18.5000	+	32.0429i	0.670624	+	1.16156i	0.977727	+	0.209879i	$0.0673071\pi$
$761$	18.5000	+	32.0429i	0.670624	+	1.16156i	−0.307103	+	0.951676i	$0.599360\pi$
$762$			9.00000i			0.326036i
$763$	−1.73205	−	5.00000i	−0.0627044	−	0.181012i
$764$	−14.0000			−0.506502
$765$		0			0
$766$	−10.5000	+	18.1865i	−0.379380	+	0.657106i
$767$	−17.3205	−	10.0000i	−0.625407	−	0.361079i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	5.00000			0.180305			0.0901523	−	0.995928i	$-0.471265\pi$
$769$	5.00000			0.180305			0.0901523	+	0.995928i	$0.471265\pi$
$770$		0			0
$771$	16.0000			0.576226
$772$	−8.66025	+	5.00000i	−0.311689	+	0.179954i
$773$	4.33013	+	2.50000i	0.155744	+	0.0899188i	0.575846	−	0.817558i	$-0.304673\pi$
$773$	4.33013	+	2.50000i	0.155744	+	0.0899188i	−0.420103	+	0.907477i	$0.638006\pi$
$774$	6.00000	−	10.3923i	0.215666	−	0.373544i
$775$		0			0
$776$	−8.00000			−0.287183
$777$	1.73205	−	2.00000i	0.0621370	−	0.0717496i
$778$			18.0000i			0.645331i
$779$	−17.5000	−	30.3109i	−0.627003	−	1.08600i
$780$		0			0
$781$	5.00000	−	8.66025i	0.178914	−	0.309888i
$782$	3.46410	−	2.00000i	0.123876	−	0.0715199i
$783$		0			0
$784$	−5.50000	+	4.33013i	−0.196429	+	0.154647i
$785$		0			0
$786$	−4.50000	−	7.79423i	−0.160510	−	0.278011i
$787$	1.73205	+	1.00000i	0.0617409	+	0.0356462i	0.530553	−	0.847652i	$-0.321984\pi$
$787$	1.73205	+	1.00000i	0.0617409	+	0.0356462i	−0.468812	+	0.883298i	$0.655318\pi$
$788$	2.59808	+	1.50000i	0.0925526	+	0.0534353i
$789$		0			0
$790$		0			0
$791$	28.0000	+	24.2487i	0.995565	+	0.862185i
$792$			5.00000i			0.177667i
$793$	−17.3205	+	10.0000i	−0.615069	+	0.355110i
$794$	−7.00000	+	12.1244i	−0.248421	+	0.430277i
$795$		0			0
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$			54.0000i			1.91278i	0.292096	+	0.956389i	$0.405647\pi$
$797$			54.0000i			1.91278i	−0.292096	+	0.956389i	$0.594353\pi$
$798$	−18.1865	−	3.50000i	−0.643796	−	0.123899i
$799$	−44.0000			−1.55661
$800$		0			0
$801$	−7.00000	+	12.1244i	−0.247333	+	0.428393i
$802$	−18.1865	−	10.5000i	−0.642189	−	0.370768i
$803$	−43.3013	+	25.0000i	−1.52807	+	0.882231i
$804$	−12.0000			−0.423207
$805$		0			0
$806$	10.0000			0.352235
$807$	−20.7846	+	12.0000i	−0.731653	+	0.422420i
$808$		0			0
$809$	12.5000	−	21.6506i	0.439477	−	0.761196i	−0.558173	−	0.829725i	$-0.688497\pi$
$809$	12.5000	−	21.6506i	0.439477	−	0.761196i	0.997649	+	0.0685291i	$0.0218306\pi$
$810$		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
$817$	72.7461	−	42.0000i	2.54507	−	1.46939i
$818$			10.0000i			0.349642i
$819$	−2.50000	+	12.9904i	−0.0873571	+	0.453921i
$820$		0			0
$821$	−5.00000	−	8.66025i	−0.174501	−	0.302245i	0.765487	−	0.643451i	$-0.222498\pi$
$821$	−5.00000	−	8.66025i	−0.174501	−	0.302245i	−0.939989	+	0.341206i	$0.889165\pi$
$822$	1.73205	+	1.00000i	0.0604122	+	0.0348790i
$823$	−34.6410	−	20.0000i	−1.20751	−	0.697156i	−0.245295	−	0.969448i	$-0.578885\pi$
$823$	−34.6410	−	20.0000i	−1.20751	−	0.697156i	−0.962215	+	0.272292i	$0.912218\pi$
$824$	4.00000	+	6.92820i	0.139347	+	0.241355i
$825$		0			0
$826$	−8.00000	−	6.92820i	−0.278356	−	0.241063i
$827$			6.00000i			0.208640i	0.994544	+	0.104320i	$0.0332667\pi$
$827$			6.00000i			0.208640i	−0.994544	+	0.104320i	$0.966733\pi$
$828$	0.866025	−	0.500000i	0.0300965	−	0.0173762i
$829$	−26.0000	+	45.0333i	−0.903017	+	1.56407i	−0.0794606	+	0.996838i	$0.525320\pi$
$829$	−26.0000	+	45.0333i	−0.903017	+	1.56407i	−0.823557	+	0.567234i	$0.808014\pi$
$830$		0			0
$831$	7.00000	+	12.1244i	0.242827	+	0.420589i
$832$			5.00000i			0.173344i
$833$	−10.3923	+	26.0000i	−0.360072	+	0.900847i
$834$	−4.00000			−0.138509
$835$		0			0
$836$	−17.5000	+	30.3109i	−0.605250	+	1.04832i
$837$	1.73205	+	1.00000i	0.0598684	+	0.0345651i
$838$	12.9904	−	7.50000i	0.448745	−	0.259083i
$839$	−12.0000			−0.414286			−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000			−0.414286			−0.207143	+	0.978311i	$0.566417\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	−8.66025	+	5.00000i	−0.298452	+	0.172311i
$843$	6.06218	+	3.50000i	0.208792	+	0.120546i
$844$	8.50000	−	14.7224i	0.292582	−	0.506767i
$845$		0			0
$846$	−11.0000			−0.378188
$847$	36.3731	+	7.00000i	1.24979	+	0.240523i
$848$		−	9.00000i		−	0.309061i
$849$	5.00000	+	8.66025i	0.171600	+	0.297219i
$850$		0			0
$851$	−0.500000	+	0.866025i	−0.0171398	+	0.0296870i
$852$	1.73205	−	1.00000i	0.0593391	−	0.0342594i
$853$		−	11.0000i		−	0.376633i	−0.982108	−	0.188316i	$-0.939697\pi$
$853$		−	11.0000i		−	0.376633i	0.982108	−	0.188316i	$-0.0603030\pi$
$854$	−10.0000	+	3.46410i	−0.342193	+	0.118539i
$855$		0			0
$856$	1.00000	+	1.73205i	0.0341793	+	0.0592003i
$857$	1.73205	+	1.00000i	0.0591657	+	0.0341593i	0.529291	−	0.848440i	$-0.322458\pi$
$857$	1.73205	+	1.00000i	0.0591657	+	0.0341593i	−0.470125	+	0.882600i	$0.655791\pi$
$858$	21.6506	+	12.5000i	0.739140	+	0.426743i
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	0.829887	−	0.557931i	$-0.188405\pi$
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	−0.898126	+	0.439738i	$0.855071\pi$
$860$		0			0
$861$	−12.5000	+	4.33013i	−0.425999	+	0.147570i
$862$		−	12.0000i		−	0.408722i
$863$	38.9711	−	22.5000i	1.32659	−	0.765909i	0.341822	−	0.939765i	$-0.388956\pi$
$863$	38.9711	−	22.5000i	1.32659	−	0.765909i	0.984771	+	0.173856i	$0.0556227\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	−12.0000	−	20.7846i	−0.407777	−	0.706290i
$867$		−	1.00000i		−	0.0339618i
$868$	5.19615	+	1.00000i	0.176369	+	0.0339422i
$869$	−60.0000			−2.03536
$870$		0			0
$871$	−30.0000	+	51.9615i	−1.01651	+	1.76065i
$872$	−1.73205	−	1.00000i	−0.0586546	−	0.0338643i
$873$	−6.92820	+	4.00000i	−0.234484	+	0.135379i
$874$	7.00000			0.236779
$875$		0			0
$876$	−10.0000			−0.337869
$877$	32.0429	−	18.5000i	1.08201	−	0.624701i	0.150574	−	0.988599i	$-0.451888\pi$
$877$	32.0429	−	18.5000i	1.08201	−	0.624701i	0.931439	+	0.363898i	$0.118554\pi$
$878$	34.6410	+	20.0000i	1.16908	+	0.674967i
$879$	−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	$0.483907\pi$
$882$	−2.59808	+	6.50000i	−0.0874818	+	0.218866i
$883$		−	50.0000i		−	1.68263i	−0.540542	−	0.841317i	$-0.681781\pi$
$883$		−	50.0000i		−	1.68263i	0.540542	−	0.841317i	$-0.318219\pi$
$884$	10.0000	+	17.3205i	0.336336	+	0.582552i
$885$		0			0
$886$	14.0000	−	24.2487i	0.470339	−	0.814651i
$887$	38.1051	−	22.0000i	1.27944	−	0.738688i	0.302698	−	0.953086i	$-0.402113\pi$
$887$	38.1051	−	22.0000i	1.27944	−	0.738688i	0.976746	+	0.214399i	$0.0687792\pi$
$888$		−	1.00000i		−	0.0335578i
$889$	18.0000	+	15.5885i	0.603701	+	0.522820i
$890$		0			0
$891$	2.50000	+	4.33013i	0.0837532	+	0.145065i
$892$	−10.3923	−	6.00000i	−0.347960	−	0.200895i
$893$	−66.6840	−	38.5000i	−2.23149	−	1.28835i
$894$	−6.00000	−	10.3923i	−0.200670	−	0.347571i
$895$		0			0
$896$	−0.500000	+	2.59808i	−0.0167038	+	0.0867956i
$897$		−	5.00000i		−	0.166945i
$898$	−25.1147	+	14.5000i	−0.838090	+	0.483871i
$899$		0			0
$900$		0			0
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$			25.0000i			0.832409i
$903$	−10.3923	−	30.0000i	−0.345834	−	0.998337i
$904$	14.0000			0.465633
$905$		0			0
$906$	7.00000	−	12.1244i	0.232559	−	0.402805i
$907$	−15.5885	−	9.00000i	−0.517606	−	0.298840i	0.218348	−	0.975871i	$-0.429933\pi$
$907$	−15.5885	−	9.00000i	−0.517606	−	0.298840i	−0.735955	+	0.677031i	$0.763266\pi$
$908$	−10.3923	+	6.00000i	−0.344881	+	0.199117i
$909$		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	$0.334445\pi$
$912$	−6.06218	+	3.50000i	−0.200739	+	0.115897i
$913$	−51.9615	−	30.0000i	−1.71968	−	0.992855i
$914$	−7.00000	+	12.1244i	−0.231539	+	0.401038i
$915$		0			0
$916$	10.0000			0.330409
$917$	−23.3827	−	4.50000i	−0.772164	−	0.148603i
$918$			4.00000i			0.132020i
$919$	14.0000	+	24.2487i	0.461817	+	0.799891i	0.999052	−	0.0435419i	$-0.0138642\pi$
$919$	14.0000	+	24.2487i	0.461817	+	0.799891i	−0.537234	+	0.843433i	$0.680531\pi$
$920$		0			0
$921$	4.00000	−	6.92820i	0.131804	−	0.228292i
$922$	3.46410	−	2.00000i	0.114084	−	0.0658665i
$923$		−	10.0000i		−	0.329154i
$924$	10.0000	+	8.66025i	0.328976	+	0.284901i
$925$		0			0
$926$	9.50000	+	16.4545i	0.312189	+	0.540728i
$927$	6.92820	+	4.00000i	0.227552	+	0.131377i
$928$		0			0
$929$	9.50000	+	16.4545i	0.311685	+	0.539854i	0.978727	−	0.205166i	$-0.0657733\pi$
$929$	9.50000	+	16.4545i	0.311685	+	0.539854i	−0.667042	+	0.745020i	$0.732440\pi$
$930$		0			0
$931$	−38.5000	+	30.3109i	−1.26179	+	0.993399i
$932$			14.0000i			0.458585i
$933$	−6.92820	+	4.00000i	−0.226819	+	0.130954i
$934$	−10.0000	+	17.3205i	−0.327210	+	0.566744i
$935$		0			0
$936$	2.50000	+	4.33013i	0.0817151	+	0.141535i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	−20.7846	+	24.0000i	−0.678642	+	0.783628i
$939$	16.0000			0.522140
$940$		0			0
$941$	3.00000	−	5.19615i	0.0977972	−	0.169390i	−0.812975	−	0.582298i	$-0.802154\pi$
$941$	3.00000	−	5.19615i	0.0977972	−	0.169390i	0.910773	+	0.412908i	$0.135487\pi$
$942$	−9.52628	−	5.50000i	−0.310383	−	0.179200i
$943$	4.33013	−	2.50000i	0.141008	−	0.0814112i
$944$	−4.00000			−0.130189
$945$		0			0
$946$	−60.0000			−1.95077
$947$	36.3731	−	21.0000i	1.18197	−	0.682408i	0.225497	−	0.974244i	$-0.427599\pi$
$947$	36.3731	−	21.0000i	1.18197	−	0.682408i	0.956469	+	0.291835i	$0.0942660\pi$
$948$	−10.3923	−	6.00000i	−0.337526	−	0.194871i
$949$	−25.0000	+	43.3013i	−0.811534	+	1.40562i
$950$		0			0
$951$	22.0000			0.713399
$952$	3.46410	+	10.0000i	0.112272	+	0.324102i
$953$			12.0000i			0.388718i	0.980930	+	0.194359i	$0.0622627\pi$
$953$			12.0000i			0.388718i	−0.980930	+	0.194359i	$0.937737\pi$
$954$	−4.50000	−	7.79423i	−0.145693	−	0.252347i
$955$		0			0
$956$	11.0000	−	19.0526i	0.355765	−	0.616204i
$957$		0			0
$958$			18.0000i			0.581554i
$959$	5.00000	−	1.73205i	0.161458	−	0.0559308i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	−4.33013	−	2.50000i	−0.139609	−	0.0806032i
$963$	1.73205	+	1.00000i	0.0558146	+	0.0322245i
$964$	7.50000	+	12.9904i	0.241559	+	0.418392i
$965$		0			0
$966$	0.500000	−	2.59808i	0.0160872	−	0.0835917i
$967$		−	4.00000i		−	0.128631i	−0.997930	−	0.0643157i	$-0.979514\pi$
$967$		−	4.00000i		−	0.128631i	0.997930	−	0.0643157i	$-0.0204865\pi$
$968$	12.1244	−	7.00000i	0.389692	−	0.224989i
$969$	−14.0000	+	24.2487i	−0.449745	+	0.778981i
$970$		0			0
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	0.720224	−	0.693742i	$-0.244039\pi$
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	−0.960910	+	0.276861i	$0.910706\pi$
$972$			1.00000i			0.0320750i
$973$	−6.92820	+	8.00000i	−0.222108	+	0.256468i
$974$		0			0
$975$		0			0
$976$	−2.00000	+	3.46410i	−0.0640184	+	0.110883i
$977$	−25.9808	−	15.0000i	−0.831198	−	0.479893i	0.0230645	−	0.999734i	$-0.492658\pi$
$977$	−25.9808	−	15.0000i	−0.831198	−	0.479893i	−0.854263	+	0.519841i	$0.825991\pi$
$978$	20.7846	−	12.0000i	0.664619	−	0.383718i
$979$	70.0000			2.23721
$980$		0			0
$981$	−2.00000			−0.0638551
$982$	31.1769	−	18.0000i	0.994895	−	0.574403i
$983$	21.6506	+	12.5000i	0.690548	+	0.398688i	0.803817	−	0.594876i	$-0.202799\pi$
$983$	21.6506	+	12.5000i	0.690548	+	0.398688i	−0.113269	+	0.993564i	$0.536132\pi$
$984$	−2.50000	+	4.33013i	−0.0796971	+	0.138039i
$985$		0			0
$986$		0			0
$987$	−19.0526	+	22.0000i	−0.606450	+	0.700268i
$988$			35.0000i			1.11350i
$989$	6.00000	+	10.3923i	0.190789	+	0.330456i
$990$		0			0
$991$	19.0000	−	32.9090i	0.603555	−	1.04539i	−0.388723	−	0.921355i	$-0.627084\pi$
$991$	19.0000	−	32.9090i	0.603555	−	1.04539i	0.992278	−	0.124033i	$-0.0395829\pi$
$992$	1.73205	−	1.00000i	0.0549927	−	0.0317500i
$993$		−	31.0000i		−	0.983755i
$994$	1.00000	−	5.19615i	0.0317181	−	0.164812i
$995$		0			0
$996$	−6.00000	−	10.3923i	−0.190117	−	0.329293i
$997$	−19.0526	−	11.0000i	−0.603401	−	0.348373i	0.166978	−	0.985961i	$-0.446599\pi$
$997$	−19.0526	−	11.0000i	−0.603401	−	0.348373i	−0.770378	+	0.637587i	$0.779933\pi$
$998$	−34.6410	−	20.0000i	−1.09654	−	0.633089i
$999$	−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.o.g.949.1		4
5.2	odd	4		210.2.i.b.151.1	yes	2
5.3	odd	4		1050.2.i.p.151.1		2
5.4	even	2	inner	1050.2.o.g.949.2		4
7.2	even	3	inner	1050.2.o.g.499.2		4
15.2	even	4		630.2.k.g.361.1		2
20.7	even	4		1680.2.bg.d.1201.1		2
35.2	odd	12		210.2.i.b.121.1	✓	2
35.3	even	12		7350.2.a.a.1.1		1
35.9	even	6	inner	1050.2.o.g.499.1		4
35.12	even	12		1470.2.i.e.961.1		2
35.17	even	12		1470.2.a.o.1.1		1
35.18	odd	12		7350.2.a.u.1.1		1
35.23	odd	12		1050.2.i.p.751.1		2
35.27	even	4		1470.2.i.e.361.1		2
35.32	odd	12		1470.2.a.l.1.1		1
105.2	even	12		630.2.k.g.541.1		2
105.17	odd	12		4410.2.a.u.1.1		1
105.32	even	12		4410.2.a.j.1.1		1
140.107	even	12		1680.2.bg.d.961.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.i.b.121.1	✓	2	35.2	odd	12
210.2.i.b.151.1	yes	2	5.2	odd	4
630.2.k.g.361.1		2	15.2	even	4
630.2.k.g.541.1		2	105.2	even	12
1050.2.i.p.151.1		2	5.3	odd	4
1050.2.i.p.751.1		2	35.23	odd	12
1050.2.o.g.499.1		4	35.9	even	6	inner
1050.2.o.g.499.2		4	7.2	even	3	inner
1050.2.o.g.949.1		4	1.1	even	1	trivial
1050.2.o.g.949.2		4	5.4	even	2	inner
1470.2.a.l.1.1		1	35.32	odd	12
1470.2.a.o.1.1		1	35.17	even	12
1470.2.i.e.361.1		2	35.27	even	4
1470.2.i.e.961.1		2	35.12	even	12
1680.2.bg.d.961.1		2	140.107	even	12
1680.2.bg.d.1201.1		2	20.7	even	4
4410.2.a.j.1.1		1	105.32	even	12
4410.2.a.u.1.1		1	105.17	odd	12
7350.2.a.a.1.1		1	35.3	even	12
7350.2.a.u.1.1		1	35.18	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.50000 - 4.33013i) q^{11} +(0.866025 - 0.500000i) q^{12} -5.00000i q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.46410 - 2.00000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-3.50000 - 6.06218i) q^{19} +(-2.50000 + 0.866025i) q^{21} +5.00000i q^{22} +(0.866025 - 0.500000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{26} +1.00000i q^{27} +(0.866025 + 2.50000i) q^{28} +(1.00000 - 1.73205i) q^{31} +(0.866025 + 0.500000i) q^{32} +(4.33013 - 2.50000i) q^{33} +4.00000 q^{34} +1.00000 q^{36} +(-0.866025 + 0.500000i) q^{37} +(6.06218 + 3.50000i) q^{38} +(2.50000 - 4.33013i) q^{39} +5.00000 q^{41} +(1.73205 - 2.00000i) q^{42} +12.0000i q^{43} +(-2.50000 - 4.33013i) q^{44} +(-0.500000 + 0.866025i) q^{46} +(9.52628 - 5.50000i) q^{47} -1.00000i q^{48} +(-1.00000 - 6.92820i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(-4.33013 - 2.50000i) q^{52} +(7.79423 + 4.50000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.00000 - 1.73205i) q^{56} -7.00000i q^{57} +(2.00000 - 3.46410i) q^{59} +(-2.00000 - 3.46410i) q^{61} +2.00000i q^{62} +(-2.59808 - 0.500000i) q^{63} -1.00000 q^{64} +(-2.50000 + 4.33013i) q^{66} +(-10.3923 - 6.00000i) q^{67} +(-3.46410 + 2.00000i) q^{68} +1.00000 q^{69} +2.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-8.66025 - 5.00000i) q^{73} +(0.500000 - 0.866025i) q^{74} -7.00000 q^{76} +(4.33013 + 12.5000i) q^{77} +5.00000i q^{78} +(-6.00000 - 10.3923i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.33013 + 2.50000i) q^{82} -12.0000i q^{83} +(-0.500000 + 2.59808i) q^{84} +(-6.00000 - 10.3923i) q^{86} +(4.33013 + 2.50000i) q^{88} +(7.00000 + 12.1244i) q^{89} +(10.0000 + 8.66025i) q^{91} -1.00000i q^{92} +(1.73205 - 1.00000i) q^{93} +(-5.50000 + 9.52628i) q^{94} +(0.500000 + 0.866025i) q^{96} +8.00000i q^{97} +(4.33013 + 5.50000i) q^{98} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 4 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9} + 10 q^{11} + 2 q^{14} - 2 q^{16} - 14 q^{19} - 10 q^{21} - 2 q^{24} + 10 q^{26} + 4 q^{31} + 16 q^{34} + 4 q^{36} + 10 q^{39} + 20 q^{41} - 10 q^{44} - 2 q^{46} - 4 q^{49} - 8 q^{51} - 2 q^{54} - 8 q^{56} + 8 q^{59} - 8 q^{61} - 4 q^{64} - 10 q^{66} + 4 q^{69} + 8 q^{71} + 2 q^{74} - 28 q^{76} - 24 q^{79} - 2 q^{81} - 2 q^{84} - 24 q^{86} + 28 q^{89} + 40 q^{91} - 22 q^{94} + 2 q^{96} + 20 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 4 * q^6 + 2 * q^9 + 10 * q^11 + 2 * q^14 - 2 * q^16 - 14 * q^19 - 10 * q^21 - 2 * q^24 + 10 * q^26 + 4 * q^31 + 16 * q^34 + 4 * q^36 + 10 * q^39 + 20 * q^41 - 10 * q^44 - 2 * q^46 - 4 * q^49 - 8 * q^51 - 2 * q^54 - 8 * q^56 + 8 * q^59 - 8 * q^61 - 4 * q^64 - 10 * q^66 + 4 * q^69 + 8 * q^71 + 2 * q^74 - 28 * q^76 - 24 * q^79 - 2 * q^81 - 2 * q^84 - 24 * q^86 + 28 * q^89 + 40 * q^91 - 22 * q^94 + 2 * q^96 + 20 * q^99

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