LMFDB - Embedded newform 950.2.j.e.349.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(49,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.j (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:	$7.58578819202$
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 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	950.349
Dual form			950.2.j.e.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} -4.00000i q^{7} +1.00000i q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} -4.00000i q^{7} +1.00000i q^{8} +(-1.00000 + 1.73205i) q^{9} +3.00000 q^{11} +1.00000i q^{12} +(1.73205 + 1.00000i) q^{13} +(2.00000 + 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.19615 + 3.00000i) q^{17} -2.00000i q^{18} +(3.50000 - 2.59808i) q^{19} +(2.00000 + 3.46410i) q^{21} +(-2.59808 + 1.50000i) q^{22} +(-5.19615 - 3.00000i) q^{23} +(-0.500000 - 0.866025i) q^{24} -2.00000 q^{26} -5.00000i q^{27} +(-3.46410 - 2.00000i) q^{28} +2.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.59808 + 1.50000i) q^{33} +(3.00000 - 5.19615i) q^{34} +(1.00000 + 1.73205i) q^{36} -10.0000i q^{37} +(-1.73205 + 4.00000i) q^{38} -2.00000 q^{39} +(-4.50000 - 7.79423i) q^{41} +(-3.46410 - 2.00000i) q^{42} +(3.46410 - 2.00000i) q^{43} +(1.50000 - 2.59808i) q^{44} +6.00000 q^{46} +(0.866025 + 0.500000i) q^{48} -9.00000 q^{49} +(3.00000 - 5.19615i) q^{51} +(1.73205 - 1.00000i) q^{52} +(5.19615 + 3.00000i) q^{53} +(2.50000 + 4.33013i) q^{54} +4.00000 q^{56} +(-1.73205 + 4.00000i) q^{57} +(-4.50000 - 7.79423i) q^{59} +(2.00000 - 3.46410i) q^{61} +(-1.73205 + 1.00000i) q^{62} +(6.92820 + 4.00000i) q^{63} -1.00000 q^{64} +(1.50000 - 2.59808i) q^{66} +(6.06218 + 3.50000i) q^{67} +6.00000i q^{68} +6.00000 q^{69} +(3.00000 + 5.19615i) q^{71} +(-1.73205 - 1.00000i) q^{72} +(0.866025 - 0.500000i) q^{73} +(5.00000 + 8.66025i) q^{74} +(-0.500000 - 4.33013i) q^{76} -12.0000i q^{77} +(1.73205 - 1.00000i) q^{78} +(-2.00000 - 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(7.79423 + 4.50000i) q^{82} -3.00000i q^{83} +4.00000 q^{84} +(-2.00000 + 3.46410i) q^{86} +3.00000i q^{88} +(3.00000 - 5.19615i) q^{89} +(4.00000 - 6.92820i) q^{91} +(-5.19615 + 3.00000i) q^{92} +(-1.73205 + 1.00000i) q^{93} -1.00000 q^{96} +(14.7224 - 8.50000i) q^{97} +(7.79423 - 4.50000i) q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 2 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 2 * q^6 - 4 * q^9	$ 4 q + 2 q^{4} + 2 q^{6} - 4 q^{9} + 12 q^{11} + 8 q^{14} - 2 q^{16} + 14 q^{19} + 8 q^{21} - 2 q^{24} - 8 q^{26} + 8 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} - 18 q^{41} + 6 q^{44} + 24 q^{46} - 36 q^{49} + 12 q^{51} + 10 q^{54} + 16 q^{56} - 18 q^{59} + 8 q^{61} - 4 q^{64} + 6 q^{66} + 24 q^{69} + 12 q^{71} + 20 q^{74} - 2 q^{76} - 8 q^{79} - 2 q^{81} + 16 q^{84} - 8 q^{86} + 12 q^{89} + 16 q^{91} - 4 q^{96} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^6 - 4 * q^9 + 12 * q^11 + 8 * q^14 - 2 * q^16 + 14 * q^19 + 8 * q^21 - 2 * q^24 - 8 * q^26 + 8 * q^31 + 12 * q^34 + 4 * q^36 - 8 * q^39 - 18 * q^41 + 6 * q^44 + 24 * q^46 - 36 * q^49 + 12 * q^51 + 10 * q^54 + 16 * q^56 - 18 * q^59 + 8 * q^61 - 4 * q^64 + 6 * q^66 + 24 * q^69 + 12 * q^71 + 20 * q^74 - 2 * q^76 - 8 * q^79 - 2 * q^81 + 16 * q^84 - 8 * q^86 + 12 * q^89 + 16 * q^91 - 4 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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	−0.728714	−	0.684819i	$-0.759881\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i	0.228714	+	0.973494i	$0.426548\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$		−	4.00000i		−	1.51186i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$		−	4.00000i		−	1.51186i	0.654654	−	0.755929i	$-0.272814\pi$
$8$			1.00000i			0.353553i
$9$	−1.00000	+	1.73205i	−0.333333	+	0.577350i
$10$		0			0
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$			1.00000i			0.288675i
$13$	1.73205	+	1.00000i	0.480384	+	0.277350i	0.720577	−	0.693375i	$-0.243877\pi$
$13$	1.73205	+	1.00000i	0.480384	+	0.277350i	−0.240192	+	0.970725i	$0.577210\pi$
$14$	2.00000	+	3.46410i	0.534522	+	0.925820i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.19615	+	3.00000i	−1.26025	+	0.727607i	−0.973123	−	0.230285i	$-0.926034\pi$
$17$	−5.19615	+	3.00000i	−1.26025	+	0.727607i	−0.287129	+	0.957892i	$0.592701\pi$
$18$		−	2.00000i		−	0.471405i
$19$	3.50000	−	2.59808i	0.802955	−	0.596040i
$19$	3.50000	−	2.59808i	0.802955	−	0.596040i
$20$		0			0
$21$	2.00000	+	3.46410i	0.436436	+	0.755929i
$22$	−2.59808	+	1.50000i	−0.553912	+	0.319801i
$23$	−5.19615	−	3.00000i	−1.08347	−	0.625543i	−0.151642	−	0.988436i	$-0.548456\pi$
$23$	−5.19615	−	3.00000i	−1.08347	−	0.625543i	−0.931831	+	0.362892i	$0.881789\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	−2.00000			−0.392232
$27$		−	5.00000i		−	0.962250i
$28$	−3.46410	−	2.00000i	−0.654654	−	0.377964i
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$		0			0
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−2.59808	+	1.50000i	−0.452267	+	0.261116i
$34$	3.00000	−	5.19615i	0.514496	−	0.891133i
$35$		0			0
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$		−	10.0000i		−	1.64399i	−0.569495	−	0.821995i	$-0.692861\pi$
$37$		−	10.0000i		−	1.64399i	0.569495	−	0.821995i	$-0.307139\pi$
$38$	−1.73205	+	4.00000i	−0.280976	+	0.648886i
$39$	−2.00000			−0.320256
$40$		0			0
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$	−3.46410	−	2.00000i	−0.534522	−	0.308607i
$43$	3.46410	−	2.00000i	0.528271	−	0.304997i	−0.212041	−	0.977261i	$-0.568011\pi$
$43$	3.46410	−	2.00000i	0.528271	−	0.304997i	0.740312	+	0.672264i	$0.234678\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$		0			0
$46$	6.00000			0.884652
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−9.00000			−1.28571
$50$		0			0
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$	1.73205	−	1.00000i	0.240192	−	0.138675i
$53$	5.19615	+	3.00000i	0.713746	+	0.412082i	0.812447	−	0.583036i	$-0.198135\pi$
$53$	5.19615	+	3.00000i	0.713746	+	0.412082i	−0.0987002	+	0.995117i	$0.531468\pi$
$54$	2.50000	+	4.33013i	0.340207	+	0.589256i
$55$		0			0
$56$	4.00000			0.534522
$57$	−1.73205	+	4.00000i	−0.229416	+	0.529813i
$58$		0			0
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	−0.994769	−	0.102151i	$-0.967427\pi$
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	0.408919	−	0.912571i	$-0.365906\pi$
$60$		0			0
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$	−1.73205	+	1.00000i	−0.219971	+	0.127000i
$63$	6.92820	+	4.00000i	0.872872	+	0.503953i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	1.50000	−	2.59808i	0.184637	−	0.319801i
$67$	6.06218	+	3.50000i	0.740613	+	0.427593i	0.822292	−	0.569066i	$-0.192695\pi$
$67$	6.06218	+	3.50000i	0.740613	+	0.427593i	−0.0816792	+	0.996659i	$0.526028\pi$
$68$			6.00000i			0.727607i
$69$	6.00000			0.722315
$70$		0			0
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$	−1.73205	−	1.00000i	−0.204124	−	0.117851i
$73$	0.866025	−	0.500000i	0.101361	−	0.0585206i	−0.448463	−	0.893801i	$-0.648028\pi$
$73$	0.866025	−	0.500000i	0.101361	−	0.0585206i	0.549823	+	0.835281i	$0.314695\pi$
$74$	5.00000	+	8.66025i	0.581238	+	1.00673i
$75$		0			0
$76$	−0.500000	−	4.33013i	−0.0573539	−	0.496700i
$77$		−	12.0000i		−	1.36753i
$78$	1.73205	−	1.00000i	0.196116	−	0.113228i
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.79423	+	4.50000i	0.860729	+	0.496942i
$83$		−	3.00000i		−	0.329293i	−0.986353	−	0.164646i	$-0.947352\pi$
$83$		−	3.00000i		−	0.329293i	0.986353	−	0.164646i	$-0.0526483\pi$
$84$	4.00000			0.436436
$85$		0			0
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$		0			0
$88$			3.00000i			0.319801i
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$	4.00000	−	6.92820i	0.419314	−	0.726273i
$92$	−5.19615	+	3.00000i	−0.541736	+	0.312772i
$93$	−1.73205	+	1.00000i	−0.179605	+	0.103695i
$94$		0			0
$95$		0			0
$96$	−1.00000			−0.102062
$97$	14.7224	−	8.50000i	1.49484	−	0.863044i	0.494854	−	0.868976i	$-0.335222\pi$
$97$	14.7224	−	8.50000i	1.49484	−	0.863044i	0.999982	+	0.00593185i	$0.00188818\pi$
$98$	7.79423	−	4.50000i	0.787336	−	0.454569i
$99$	−3.00000	+	5.19615i	−0.301511	+	0.522233i
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$			6.00000i			0.594089i
$103$		−	2.00000i		−	0.197066i	−0.995134	−	0.0985329i	$-0.968585\pi$
$103$		−	2.00000i		−	0.197066i	0.995134	−	0.0985329i	$-0.0314150\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$		0			0
$106$	−6.00000			−0.582772
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	−4.33013	−	2.50000i	−0.416667	−	0.240563i
$109$	−8.00000	−	13.8564i	−0.766261	−	1.32720i	−0.939577	−	0.342337i	$-0.888782\pi$
$109$	−8.00000	−	13.8564i	−0.766261	−	1.32720i	0.173316	−	0.984866i	$-0.444552\pi$
$110$		0			0
$111$	5.00000	+	8.66025i	0.474579	+	0.821995i
$112$	−3.46410	+	2.00000i	−0.327327	+	0.188982i
$113$		−	15.0000i		−	1.41108i	−0.708669	−	0.705541i	$-0.750704\pi$
$113$		−	15.0000i		−	1.41108i	0.708669	−	0.705541i	$-0.249296\pi$
$114$	−0.500000	−	4.33013i	−0.0468293	−	0.405554i
$115$		0			0
$116$		0			0
$117$	−3.46410	+	2.00000i	−0.320256	+	0.184900i
$118$	7.79423	+	4.50000i	0.717517	+	0.414259i
$119$	12.0000	+	20.7846i	1.10004	+	1.90532i
$120$		0			0
$121$	−2.00000			−0.181818
$122$			4.00000i			0.362143i
$123$	7.79423	+	4.50000i	0.702782	+	0.405751i
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$		0			0
$126$	−8.00000			−0.712697
$127$	−1.73205	−	1.00000i	−0.153695	−	0.0887357i	0.421180	−	0.906977i	$-0.361616\pi$
$127$	−1.73205	−	1.00000i	−0.153695	−	0.0887357i	−0.574875	+	0.818241i	$0.694949\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−2.00000	+	3.46410i	−0.176090	+	0.304997i
$130$		0			0
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	0.599699	−	0.800226i	$-0.295287\pi$
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	−0.992865	+	0.119241i	$0.961954\pi$
$132$			3.00000i			0.261116i
$133$	−10.3923	−	14.0000i	−0.901127	−	1.21395i
$134$	−7.00000			−0.604708
$135$		0			0
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	−7.79423	−	4.50000i	−0.665906	−	0.384461i	0.128618	−	0.991694i	$-0.458946\pi$
$137$	−7.79423	−	4.50000i	−0.665906	−	0.384461i	−0.794524	+	0.607233i	$0.792279\pi$
$138$	−5.19615	+	3.00000i	−0.442326	+	0.255377i
$139$	5.50000	−	9.52628i	0.466504	−	0.808008i	−0.532764	−	0.846264i	$-0.678847\pi$
$139$	5.50000	−	9.52628i	0.466504	−	0.808008i	0.999268	+	0.0382553i	$0.0121800\pi$
$140$		0			0
$141$		0			0
$142$	−5.19615	−	3.00000i	−0.436051	−	0.251754i
$143$	5.19615	+	3.00000i	0.434524	+	0.250873i
$144$	2.00000			0.166667
$145$		0			0
$146$	−0.500000	+	0.866025i	−0.0413803	+	0.0716728i
$147$	7.79423	−	4.50000i	0.642857	−	0.371154i
$148$	−8.66025	−	5.00000i	−0.711868	−	0.410997i
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$		0			0
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$	2.59808	+	3.50000i	0.210732	+	0.283887i
$153$		−	12.0000i		−	0.970143i
$154$	6.00000	+	10.3923i	0.483494	+	0.837436i
$155$		0			0
$156$	−1.00000	+	1.73205i	−0.0800641	+	0.138675i
$157$	−13.8564	+	8.00000i	−1.10586	+	0.638470i	−0.937754	−	0.347299i	$-0.887099\pi$
$157$	−13.8564	+	8.00000i	−1.10586	+	0.638470i	−0.168107	+	0.985769i	$0.553765\pi$
$158$	3.46410	+	2.00000i	0.275589	+	0.159111i
$159$	−6.00000			−0.475831
$160$		0			0
$161$	−12.0000	+	20.7846i	−0.945732	+	1.63806i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$			19.0000i			1.48819i	0.668071	+	0.744097i	$0.267120\pi$
$163$			19.0000i			1.48819i	−0.668071	+	0.744097i	$0.732880\pi$
$164$	−9.00000			−0.702782
$165$		0			0
$166$	1.50000	+	2.59808i	0.116423	+	0.201650i
$167$	20.7846	+	12.0000i	1.60836	+	0.928588i	0.989737	+	0.142901i	$0.0456431\pi$
$167$	20.7846	+	12.0000i	1.60836	+	0.928588i	0.618624	+	0.785687i	$0.287690\pi$
$168$	−3.46410	+	2.00000i	−0.267261	+	0.154303i
$169$	−4.50000	−	7.79423i	−0.346154	−	0.599556i
$170$		0			0
$171$	1.00000	+	8.66025i	0.0764719	+	0.662266i
$172$		−	4.00000i		−	0.304997i
$173$	−5.19615	+	3.00000i	−0.395056	+	0.228086i	−0.684349	−	0.729155i	$-0.739913\pi$
$173$	−5.19615	+	3.00000i	−0.395056	+	0.228086i	0.289292	+	0.957241i	$0.406580\pi$
$174$		0			0
$175$		0			0
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$	7.79423	+	4.50000i	0.585850	+	0.338241i
$178$			6.00000i			0.449719i
$179$	−9.00000			−0.672692			−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000			−0.672692			−0.336346	+	0.941739i	$0.609191\pi$
$180$		0			0
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	−0.900794	−	0.434246i	$-0.857015\pi$
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	0.826465	+	0.562988i	$0.190348\pi$
$182$			8.00000i			0.592999i
$183$			4.00000i			0.295689i
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$		0			0
$186$	1.00000	−	1.73205i	0.0733236	−	0.127000i
$187$	−15.5885	+	9.00000i	−1.13994	+	0.658145i
$188$		0			0
$189$	−20.0000			−1.45479
$190$		0			0
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−1.73205	+	1.00000i	−0.124676	+	0.0719816i	−0.561041	−	0.827788i	$-0.689599\pi$
$193$	−1.73205	+	1.00000i	−0.124676	+	0.0719816i	0.436365	+	0.899770i	$0.356266\pi$
$194$	−8.50000	+	14.7224i	−0.610264	+	1.05701i
$195$		0			0
$196$	−4.50000	+	7.79423i	−0.321429	+	0.556731i
$197$			18.0000i			1.28245i	0.767354	+	0.641223i	$0.221573\pi$
$197$			18.0000i			1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$		−	6.00000i		−	0.426401i
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	−0.987022	−	0.160585i	$-0.948662\pi$
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	0.632581	+	0.774494i	$0.281995\pi$
$200$		0			0
$201$	−7.00000			−0.493742
$202$		0			0
$203$		0			0
$204$	−3.00000	−	5.19615i	−0.210042	−	0.363803i
$205$		0			0
$206$	1.00000	+	1.73205i	0.0696733	+	0.120678i
$207$	10.3923	−	6.00000i	0.722315	−	0.417029i
$208$		−	2.00000i		−	0.138675i
$209$	10.5000	−	7.79423i	0.726300	−	0.539138i
$210$		0			0
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	−0.972346	−	0.233544i	$-0.924968\pi$
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	0.283918	−	0.958849i	$-0.408366\pi$
$212$	5.19615	−	3.00000i	0.356873	−	0.206041i
$213$	−5.19615	−	3.00000i	−0.356034	−	0.205557i
$214$		0			0
$215$		0			0
$216$	5.00000			0.340207
$217$		−	8.00000i		−	0.543075i
$218$	13.8564	+	8.00000i	0.938474	+	0.541828i
$219$	−0.500000	+	0.866025i	−0.0337869	+	0.0585206i
$220$		0			0
$221$	−12.0000			−0.807207
$222$	−8.66025	−	5.00000i	−0.581238	−	0.335578i
$223$	−12.1244	+	7.00000i	−0.811907	+	0.468755i	−0.847618	−	0.530607i	$-0.821964\pi$
$223$	−12.1244	+	7.00000i	−0.811907	+	0.468755i	0.0357107	+	0.999362i	$0.488630\pi$
$224$	2.00000	−	3.46410i	0.133631	−	0.231455i
$225$		0			0
$226$	7.50000	+	12.9904i	0.498893	+	0.864107i
$227$			3.00000i			0.199117i	0.995032	+	0.0995585i	$0.0317430\pi$
$227$			3.00000i			0.199117i	−0.995032	+	0.0995585i	$0.968257\pi$
$228$	2.59808	+	3.50000i	0.172062	+	0.231793i
$229$	16.0000			1.05731			0.528655	−	0.848837i	$-0.322697\pi$
$229$	16.0000			1.05731			0.528655	+	0.848837i	$0.322697\pi$
$230$		0			0
$231$	6.00000	+	10.3923i	0.394771	+	0.683763i
$232$		0			0
$233$	−2.59808	+	1.50000i	−0.170206	+	0.0982683i	−0.582683	−	0.812700i	$-0.697997\pi$
$233$	−2.59808	+	1.50000i	−0.170206	+	0.0982683i	0.412477	+	0.910968i	$0.364664\pi$
$234$	2.00000	−	3.46410i	0.130744	−	0.226455i
$235$		0			0
$236$	−9.00000			−0.585850
$237$	3.46410	+	2.00000i	0.225018	+	0.129914i
$238$	−20.7846	−	12.0000i	−1.34727	−	0.777844i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	−0.935242	−	0.354010i	$-0.884818\pi$
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	0.774202	+	0.632938i	$0.218151\pi$
$242$	1.73205	−	1.00000i	0.111340	−	0.0642824i
$243$	13.8564	+	8.00000i	0.888889	+	0.513200i
$244$	−2.00000	−	3.46410i	−0.128037	−	0.221766i
$245$		0			0
$246$	−9.00000			−0.573819
$247$	8.66025	−	1.00000i	0.551039	−	0.0636285i
$248$			2.00000i			0.127000i
$249$	1.50000	+	2.59808i	0.0950586	+	0.164646i
$250$		0			0
$251$	1.50000	−	2.59808i	0.0946792	−	0.163989i	−0.814795	−	0.579748i	$-0.803151\pi$
$251$	1.50000	−	2.59808i	0.0946792	−	0.163989i	0.909475	+	0.415759i	$0.136484\pi$
$252$	6.92820	−	4.00000i	0.436436	−	0.251976i
$253$	−15.5885	−	9.00000i	−0.980038	−	0.565825i
$254$	2.00000			0.125491
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.59808	−	1.50000i	−0.162064	−	0.0935674i	0.416775	−	0.909010i	$-0.363160\pi$
$257$	−2.59808	−	1.50000i	−0.162064	−	0.0935674i	−0.578838	+	0.815442i	$0.696494\pi$
$258$		−	4.00000i		−	0.249029i
$259$	−40.0000			−2.48548
$260$		0			0
$261$		0			0
$262$	7.79423	+	4.50000i	0.481529	+	0.278011i
$263$	10.3923	−	6.00000i	0.640817	−	0.369976i	−0.144112	−	0.989561i	$-0.546033\pi$
$263$	10.3923	−	6.00000i	0.640817	−	0.369976i	0.784929	+	0.619586i	$0.212699\pi$
$264$	−1.50000	−	2.59808i	−0.0923186	−	0.159901i
$265$		0			0
$266$	16.0000	+	6.92820i	0.981023	+	0.424795i
$267$			6.00000i			0.367194i
$268$	6.06218	−	3.50000i	0.370306	−	0.213797i
$269$	6.00000	+	10.3923i	0.365826	+	0.633630i	0.988908	−	0.148527i	$-0.0474530\pi$
$269$	6.00000	+	10.3923i	0.365826	+	0.633630i	−0.623082	+	0.782157i	$0.714120\pi$
$270$		0			0
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$	5.19615	+	3.00000i	0.315063	+	0.181902i
$273$			8.00000i			0.484182i
$274$	9.00000			0.543710
$275$		0			0
$276$	3.00000	−	5.19615i	0.180579	−	0.312772i
$277$			8.00000i			0.480673i	0.970690	+	0.240337i	$0.0772579\pi$
$277$			8.00000i			0.480673i	−0.970690	+	0.240337i	$0.922742\pi$
$278$			11.0000i			0.659736i
$279$	−2.00000	+	3.46410i	−0.119737	+	0.207390i
$280$		0			0
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	0.110717	+	0.993852i	$0.464685\pi$
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	−0.916060	+	0.401042i	$0.868648\pi$
$282$		0			0
$283$	−4.33013	+	2.50000i	−0.257399	+	0.148610i	−0.623148	−	0.782104i	$-0.714146\pi$
$283$	−4.33013	+	2.50000i	−0.257399	+	0.148610i	0.365748	+	0.930714i	$0.380813\pi$
$284$	6.00000			0.356034
$285$		0			0
$286$	−6.00000			−0.354787
$287$	−31.1769	+	18.0000i	−1.84032	+	1.06251i
$288$	−1.73205	+	1.00000i	−0.102062	+	0.0589256i
$289$	9.50000	−	16.4545i	0.558824	−	0.967911i
$290$		0			0
$291$	−8.50000	+	14.7224i	−0.498279	+	0.863044i
$292$		−	1.00000i		−	0.0585206i
$293$		−	24.0000i		−	1.40209i	−0.713115	−	0.701047i	$-0.752716\pi$
$293$		−	24.0000i		−	1.40209i	0.713115	−	0.701047i	$-0.247284\pi$
$294$	−4.50000	+	7.79423i	−0.262445	+	0.454569i
$295$		0			0
$296$	10.0000			0.581238
$297$		−	15.0000i		−	0.870388i
$298$	−15.5885	−	9.00000i	−0.903015	−	0.521356i
$299$	−6.00000	−	10.3923i	−0.346989	−	0.601003i
$300$		0			0
$301$	−8.00000	−	13.8564i	−0.461112	−	0.798670i
$302$	8.66025	−	5.00000i	0.498342	−	0.287718i
$303$		0			0
$304$	−4.00000	−	1.73205i	−0.229416	−	0.0993399i
$305$		0			0
$306$	6.00000	+	10.3923i	0.342997	+	0.594089i
$307$	−6.06218	+	3.50000i	−0.345987	+	0.199756i	−0.662916	−	0.748694i	$-0.730681\pi$
$307$	−6.06218	+	3.50000i	−0.345987	+	0.199756i	0.316929	+	0.948449i	$0.397348\pi$
$308$	−10.3923	−	6.00000i	−0.592157	−	0.341882i
$309$	1.00000	+	1.73205i	0.0568880	+	0.0985329i
$310$		0			0
$311$	−30.0000			−1.70114			−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000			−1.70114			−0.850572	+	0.525859i	$0.823744\pi$
$312$		−	2.00000i		−	0.113228i
$313$	−16.4545	−	9.50000i	−0.930062	−	0.536972i	−0.0432311	−	0.999065i	$-0.513765\pi$
$313$	−16.4545	−	9.50000i	−0.930062	−	0.536972i	−0.886831	+	0.462093i	$0.847098\pi$
$314$	8.00000	−	13.8564i	0.451466	−	0.781962i
$315$		0			0
$316$	−4.00000			−0.225018
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.869184	−	0.494489i	$-0.164645\pi$
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.00635137	+	0.999980i	$0.497978\pi$
$318$	5.19615	−	3.00000i	0.291386	−	0.168232i
$319$		0			0
$320$		0			0
$321$		0			0
$322$		−	24.0000i		−	1.33747i
$323$	−10.3923	+	24.0000i	−0.578243	+	1.33540i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−9.50000	−	16.4545i	−0.526156	−	0.911330i
$327$	13.8564	+	8.00000i	0.766261	+	0.442401i
$328$	7.79423	−	4.50000i	0.430364	−	0.248471i
$329$		0			0
$330$		0			0
$331$	5.00000			0.274825			0.137412	−	0.990514i	$-0.456121\pi$
$331$	5.00000			0.274825			0.137412	+	0.990514i	$0.456121\pi$
$332$	−2.59808	−	1.50000i	−0.142588	−	0.0823232i
$333$	17.3205	+	10.0000i	0.949158	+	0.547997i
$334$	−24.0000			−1.31322
$335$		0			0
$336$	2.00000	−	3.46410i	0.109109	−	0.188982i
$337$	9.52628	−	5.50000i	0.518930	−	0.299604i	−0.217567	−	0.976045i	$-0.569812\pi$
$337$	9.52628	−	5.50000i	0.518930	−	0.299604i	0.736497	+	0.676441i	$0.236479\pi$
$338$	7.79423	+	4.50000i	0.423950	+	0.244768i
$339$	7.50000	+	12.9904i	0.407344	+	0.705541i
$340$		0			0
$341$	6.00000			0.324918
$342$	−5.19615	−	7.00000i	−0.280976	−	0.378517i
$343$			8.00000i			0.431959i
$344$	2.00000	+	3.46410i	0.107833	+	0.186772i
$345$		0			0
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	−7.79423	+	4.50000i	−0.418416	+	0.241573i	−0.694399	−	0.719590i	$-0.744330\pi$
$347$	−7.79423	+	4.50000i	−0.418416	+	0.241573i	0.275983	+	0.961162i	$0.410997\pi$
$348$		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	−	8.66025i	0.266880	−	0.462250i
$352$	2.59808	+	1.50000i	0.138478	+	0.0799503i
$353$		−	3.00000i		−	0.159674i	−0.996808	−	0.0798369i	$-0.974560\pi$
$353$		−	3.00000i		−	0.159674i	0.996808	−	0.0798369i	$-0.0254400\pi$
$354$	−9.00000			−0.478345
$355$		0			0
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$	−20.7846	−	12.0000i	−1.10004	−	0.635107i
$358$	7.79423	−	4.50000i	0.411938	−	0.237832i
$359$	−3.00000	−	5.19615i	−0.158334	−	0.274242i	0.775934	−	0.630814i	$-0.217279\pi$
$359$	−3.00000	−	5.19615i	−0.158334	−	0.274242i	−0.934268	+	0.356572i	$0.883946\pi$
$360$		0			0
$361$	5.50000	−	18.1865i	0.289474	−	0.957186i
$362$		−	2.00000i		−	0.105118i
$363$	1.73205	−	1.00000i	0.0909091	−	0.0524864i
$364$	−4.00000	−	6.92820i	−0.209657	−	0.363137i
$365$		0			0
$366$	−2.00000	−	3.46410i	−0.104542	−	0.181071i
$367$	19.0526	+	11.0000i	0.994535	+	0.574195i	0.906627	−	0.421933i	$-0.138648\pi$
$367$	19.0526	+	11.0000i	0.994535	+	0.574195i	0.0879086	+	0.996129i	$0.471982\pi$
$368$			6.00000i			0.312772i
$369$	18.0000			0.937043
$370$		0			0
$371$	12.0000	−	20.7846i	0.623009	−	1.07908i
$372$			2.00000i			0.103695i
$373$			4.00000i			0.207112i	0.994624	+	0.103556i	$0.0330221\pi$
$373$			4.00000i			0.207112i	−0.994624	+	0.103556i	$0.966978\pi$
$374$	9.00000	−	15.5885i	0.465379	−	0.806060i
$375$		0			0
$376$		0			0
$377$		0			0
$378$	17.3205	−	10.0000i	0.890871	−	0.514344i
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$		0			0
$381$	2.00000			0.102463
$382$	−10.3923	+	6.00000i	−0.531717	+	0.306987i
$383$	31.1769	−	18.0000i	1.59307	−	0.919757i	0.600289	−	0.799783i	$-0.295052\pi$
$383$	31.1769	−	18.0000i	1.59307	−	0.919757i	0.992777	−	0.119974i	$-0.0382810\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$		0			0
$386$	1.00000	−	1.73205i	0.0508987	−	0.0881591i
$387$			8.00000i			0.406663i
$388$		−	17.0000i		−	0.863044i
$389$	−18.0000	+	31.1769i	−0.912636	+	1.58073i	−0.102311	+	0.994753i	$0.532624\pi$
$389$	−18.0000	+	31.1769i	−0.912636	+	1.58073i	−0.810326	+	0.585980i	$0.800710\pi$
$390$		0			0
$391$	36.0000			1.82060
$392$		−	9.00000i		−	0.454569i
$393$	7.79423	+	4.50000i	0.393167	+	0.226995i
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$		0			0
$396$	3.00000	+	5.19615i	0.150756	+	0.261116i
$397$	−8.66025	+	5.00000i	−0.434646	+	0.250943i	−0.701324	−	0.712843i	$-0.747407\pi$
$397$	−8.66025	+	5.00000i	−0.434646	+	0.250943i	0.266678	+	0.963786i	$0.414074\pi$
$398$		−	10.0000i		−	0.501255i
$399$	16.0000	+	6.92820i	0.801002	+	0.346844i
$400$		0			0
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$	6.06218	−	3.50000i	0.302354	−	0.174564i
$403$	3.46410	+	2.00000i	0.172559	+	0.0996271i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	30.0000i		−	1.48704i
$408$	5.19615	+	3.00000i	0.257248	+	0.148522i
$409$	2.50000	−	4.33013i	0.123617	−	0.214111i	−0.797574	−	0.603220i	$-0.793884\pi$
$409$	2.50000	−	4.33013i	0.123617	−	0.214111i	0.921192	+	0.389109i	$0.127217\pi$
$410$		0			0
$411$	9.00000			0.443937
$412$	−1.73205	−	1.00000i	−0.0853320	−	0.0492665i
$413$	−31.1769	+	18.0000i	−1.53412	+	0.885722i
$414$	−6.00000	+	10.3923i	−0.294884	+	0.510754i
$415$		0			0
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$			11.0000i			0.538672i
$418$	−5.19615	+	12.0000i	−0.254152	+	0.586939i
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	0.961761	−	0.273890i	$-0.0883103\pi$
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	−0.718076	+	0.695965i	$0.754977\pi$
$422$	17.3205	+	10.0000i	0.843149	+	0.486792i
$423$		0			0
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$		0			0
$426$	6.00000			0.290701
$427$	−13.8564	−	8.00000i	−0.670559	−	0.387147i
$428$		0			0
$429$	−6.00000			−0.289683
$430$		0			0
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	−0.237460	−	0.971397i	$-0.576315\pi$
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	0.959985	−	0.280052i	$-0.0903517\pi$
$432$	−4.33013	+	2.50000i	−0.208333	+	0.120281i
$433$	22.5167	+	13.0000i	1.08208	+	0.624740i	0.931457	−	0.363851i	$-0.118538\pi$
$433$	22.5167	+	13.0000i	1.08208	+	0.624740i	0.150624	+	0.988591i	$0.451872\pi$
$434$	4.00000	+	6.92820i	0.192006	+	0.332564i
$435$		0			0
$436$	−16.0000			−0.766261
$437$	−25.9808	+	3.00000i	−1.24283	+	0.143509i
$438$		−	1.00000i		−	0.0477818i
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	0.983310	−	0.181938i	$-0.0582371\pi$
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	−0.649218	+	0.760602i	$0.724904\pi$
$440$		0			0
$441$	9.00000	−	15.5885i	0.428571	−	0.742307i
$442$	10.3923	−	6.00000i	0.494312	−	0.285391i
$443$	7.79423	+	4.50000i	0.370315	+	0.213801i	0.673596	−	0.739100i	$-0.264749\pi$
$443$	7.79423	+	4.50000i	0.370315	+	0.213801i	−0.303281	+	0.952901i	$0.598082\pi$
$444$	10.0000			0.474579
$445$		0			0
$446$	7.00000	−	12.1244i	0.331460	−	0.574105i
$447$	−15.5885	−	9.00000i	−0.737309	−	0.425685i
$448$			4.00000i			0.188982i
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$	−13.5000	−	23.3827i	−0.635690	−	1.10105i
$452$	−12.9904	−	7.50000i	−0.611016	−	0.352770i
$453$	8.66025	−	5.00000i	0.406894	−	0.234920i
$454$	−1.50000	−	2.59808i	−0.0703985	−	0.121934i
$455$		0			0
$456$	−4.00000	−	1.73205i	−0.187317	−	0.0811107i
$457$			5.00000i			0.233890i	0.993138	+	0.116945i	$0.0373101\pi$
$457$			5.00000i			0.233890i	−0.993138	+	0.116945i	$0.962690\pi$
$458$	−13.8564	+	8.00000i	−0.647467	+	0.373815i
$459$	15.0000	+	25.9808i	0.700140	+	1.21268i
$460$		0			0
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	0.787668	−	0.616100i	$-0.211288\pi$
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	−0.927392	+	0.374091i	$0.877955\pi$
$462$	−10.3923	−	6.00000i	−0.483494	−	0.279145i
$463$			34.0000i			1.58011i	0.613033	+	0.790057i	$0.289949\pi$
$463$			34.0000i			1.58011i	−0.613033	+	0.790057i	$0.710051\pi$
$464$		0			0
$465$		0			0
$466$	1.50000	−	2.59808i	0.0694862	−	0.120354i
$467$		−	27.0000i		−	1.24941i	−0.780860	−	0.624705i	$-0.785219\pi$
$467$		−	27.0000i		−	1.24941i	0.780860	−	0.624705i	$-0.214781\pi$
$468$			4.00000i			0.184900i
$469$	14.0000	−	24.2487i	0.646460	−	1.11970i
$470$		0			0
$471$	8.00000	−	13.8564i	0.368621	−	0.638470i
$472$	7.79423	−	4.50000i	0.358758	−	0.207129i
$473$	10.3923	−	6.00000i	0.477839	−	0.275880i
$474$	−4.00000			−0.183726
$475$		0			0
$476$	24.0000			1.10004
$477$	−10.3923	+	6.00000i	−0.475831	+	0.274721i
$478$	−10.3923	+	6.00000i	−0.475333	+	0.274434i
$479$	18.0000	−	31.1769i	0.822441	−	1.42451i	−0.0814184	−	0.996680i	$-0.525945\pi$
$479$	18.0000	−	31.1769i	0.822441	−	1.42451i	0.903859	−	0.427830i	$-0.140722\pi$
$480$		0			0
$481$	10.0000	−	17.3205i	0.455961	−	0.789747i
$482$		−	5.00000i		−	0.227744i
$483$		−	24.0000i		−	1.09204i
$484$	−1.00000	+	1.73205i	−0.0454545	+	0.0787296i
$485$		0			0
$486$	−16.0000			−0.725775
$487$			2.00000i			0.0906287i	0.998973	+	0.0453143i	$0.0144289\pi$
$487$			2.00000i			0.0906287i	−0.998973	+	0.0453143i	$0.985571\pi$
$488$	3.46410	+	2.00000i	0.156813	+	0.0905357i
$489$	−9.50000	−	16.4545i	−0.429605	−	0.744097i
$490$		0			0
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$	7.79423	−	4.50000i	0.351391	−	0.202876i
$493$		0			0
$494$	−7.00000	+	5.19615i	−0.314945	+	0.233786i
$495$		0			0
$496$	−1.00000	−	1.73205i	−0.0449013	−	0.0777714i
$497$	20.7846	−	12.0000i	0.932317	−	0.538274i
$498$	−2.59808	−	1.50000i	−0.116423	−	0.0672166i
$499$	−12.5000	−	21.6506i	−0.559577	−	0.969216i	−0.997532	−	0.0702185i	$-0.977630\pi$
$499$	−12.5000	−	21.6506i	−0.559577	−	0.969216i	0.437955	−	0.898997i	$-0.355703\pi$
$500$		0			0
$501$	−24.0000			−1.07224
$502$			3.00000i			0.133897i
$503$	5.19615	+	3.00000i	0.231685	+	0.133763i	0.611349	−	0.791361i	$-0.290627\pi$
$503$	5.19615	+	3.00000i	0.231685	+	0.133763i	−0.379664	+	0.925124i	$0.623960\pi$
$504$	−4.00000	+	6.92820i	−0.178174	+	0.308607i
$505$		0			0
$506$	18.0000			0.800198
$507$	7.79423	+	4.50000i	0.346154	+	0.199852i
$508$	−1.73205	+	1.00000i	−0.0768473	+	0.0443678i
$509$	−12.0000	+	20.7846i	−0.531891	+	0.921262i	0.467416	+	0.884037i	$0.345185\pi$
$509$	−12.0000	+	20.7846i	−0.531891	+	0.921262i	−0.999307	+	0.0372243i	$0.988148\pi$
$510$		0			0
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$		−	1.00000i		−	0.0441942i
$513$	−12.9904	−	17.5000i	−0.573539	−	0.772644i
$514$	3.00000			0.132324
$515$		0			0
$516$	2.00000	+	3.46410i	0.0880451	+	0.152499i
$517$		0			0
$518$	34.6410	−	20.0000i	1.52204	−	0.878750i
$519$	3.00000	−	5.19615i	0.131685	−	0.228086i
$520$		0			0
$521$	9.00000			0.394297			0.197149	−	0.980374i	$-0.436832\pi$
$521$	9.00000			0.394297			0.197149	+	0.980374i	$0.436832\pi$
$522$		0			0
$523$	−24.2487	−	14.0000i	−1.06032	−	0.612177i	−0.134801	−	0.990873i	$-0.543039\pi$
$523$	−24.2487	−	14.0000i	−1.06032	−	0.612177i	−0.925521	+	0.378695i	$0.876373\pi$
$524$	−9.00000			−0.393167
$525$		0			0
$526$	−6.00000	+	10.3923i	−0.261612	+	0.453126i
$527$	−10.3923	+	6.00000i	−0.452696	+	0.261364i
$528$	2.59808	+	1.50000i	0.113067	+	0.0652791i
$529$	6.50000	+	11.2583i	0.282609	+	0.489493i
$530$		0			0
$531$	18.0000			0.781133
$532$	−17.3205	+	2.00000i	−0.750939	+	0.0867110i
$533$		−	18.0000i		−	0.779667i
$534$	−3.00000	−	5.19615i	−0.129823	−	0.224860i
$535$		0			0
$536$	−3.50000	+	6.06218i	−0.151177	+	0.261846i
$537$	7.79423	−	4.50000i	0.336346	−	0.194189i
$538$	−10.3923	−	6.00000i	−0.448044	−	0.258678i
$539$	−27.0000			−1.16297
$540$		0			0
$541$	−22.0000	+	38.1051i	−0.945854	+	1.63827i	−0.191821	+	0.981430i	$0.561439\pi$
$541$	−22.0000	+	38.1051i	−0.945854	+	1.63827i	−0.754032	+	0.656837i	$0.771894\pi$
$542$	−13.8564	−	8.00000i	−0.595184	−	0.343629i
$543$		−	2.00000i		−	0.0858282i
$544$	−6.00000			−0.257248
$545$		0			0
$546$	−4.00000	−	6.92820i	−0.171184	−	0.296500i
$547$	3.46410	+	2.00000i	0.148114	+	0.0855138i	0.572226	−	0.820096i	$-0.306080\pi$
$547$	3.46410	+	2.00000i	0.148114	+	0.0855138i	−0.424111	+	0.905610i	$0.639413\pi$
$548$	−7.79423	+	4.50000i	−0.332953	+	0.192230i
$549$	4.00000	+	6.92820i	0.170716	+	0.295689i
$550$		0			0
$551$		0			0
$552$			6.00000i			0.255377i
$553$	−13.8564	+	8.00000i	−0.589234	+	0.340195i
$554$	−4.00000	−	6.92820i	−0.169944	−	0.294351i
$555$		0			0
$556$	−5.50000	−	9.52628i	−0.233252	−	0.404004i
$557$	−20.7846	−	12.0000i	−0.880672	−	0.508456i	−0.00979220	−	0.999952i	$-0.503117\pi$
$557$	−20.7846	−	12.0000i	−0.880672	−	0.508456i	−0.870880	+	0.491496i	$0.836450\pi$
$558$		−	4.00000i		−	0.169334i
$559$	8.00000			0.338364
$560$		0			0
$561$	9.00000	−	15.5885i	0.379980	−	0.658145i
$562$		−	27.0000i		−	1.13893i
$563$			21.0000i			0.885044i	0.896758	+	0.442522i	$0.145916\pi$
$563$			21.0000i			0.885044i	−0.896758	+	0.442522i	$0.854084\pi$
$564$		0			0
$565$		0			0
$566$	2.50000	−	4.33013i	0.105083	−	0.182009i
$567$	−3.46410	+	2.00000i	−0.145479	+	0.0839921i
$568$	−5.19615	+	3.00000i	−0.218026	+	0.125877i
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000			0.251533			0.125767	+	0.992060i	$0.459861\pi$
$570$		0			0
$571$	−7.00000			−0.292941			−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000			−0.292941			−0.146470	+	0.989215i	$0.546791\pi$
$572$	5.19615	−	3.00000i	0.217262	−	0.125436i
$573$	−10.3923	+	6.00000i	−0.434145	+	0.250654i
$574$	18.0000	−	31.1769i	0.751305	−	1.30130i
$575$		0			0
$576$	1.00000	−	1.73205i	0.0416667	−	0.0721688i
$577$			11.0000i			0.457936i	0.973434	+	0.228968i	$0.0735351\pi$
$577$			11.0000i			0.457936i	−0.973434	+	0.228968i	$0.926465\pi$
$578$			19.0000i			0.790296i
$579$	1.00000	−	1.73205i	0.0415586	−	0.0719816i
$580$		0			0
$581$	−12.0000			−0.497844
$582$		−	17.0000i		−	0.704673i
$583$	15.5885	+	9.00000i	0.645608	+	0.372742i
$584$	0.500000	+	0.866025i	0.0206901	+	0.0358364i
$585$		0			0
$586$	12.0000	+	20.7846i	0.495715	+	0.858604i
$587$	−10.3923	+	6.00000i	−0.428936	+	0.247647i	−0.698893	−	0.715226i	$-0.746324\pi$
$587$	−10.3923	+	6.00000i	−0.428936	+	0.247647i	0.269957	+	0.962872i	$0.412990\pi$
$588$		−	9.00000i		−	0.371154i
$589$	7.00000	−	5.19615i	0.288430	−	0.214104i
$590$		0			0
$591$	−9.00000	−	15.5885i	−0.370211	−	0.641223i
$592$	−8.66025	+	5.00000i	−0.355934	+	0.205499i
$593$	−18.1865	−	10.5000i	−0.746831	−	0.431183i	0.0777165	−	0.996976i	$-0.475237\pi$
$593$	−18.1865	−	10.5000i	−0.746831	−	0.431183i	−0.824548	+	0.565792i	$0.808570\pi$
$594$	7.50000	+	12.9904i	0.307729	+	0.533002i
$595$		0			0
$596$	18.0000			0.737309
$597$		−	10.0000i		−	0.409273i
$598$	10.3923	+	6.00000i	0.424973	+	0.245358i
$599$	−3.00000	+	5.19615i	−0.122577	+	0.212309i	−0.920783	−	0.390075i	$-0.872449\pi$
$599$	−3.00000	+	5.19615i	−0.122577	+	0.212309i	0.798206	+	0.602384i	$0.205782\pi$
$600$		0			0
$601$	−13.0000			−0.530281			−0.265141	−	0.964210i	$-0.585418\pi$
$601$	−13.0000			−0.530281			−0.265141	+	0.964210i	$0.585418\pi$
$602$	13.8564	+	8.00000i	0.564745	+	0.326056i
$603$	−12.1244	+	7.00000i	−0.493742	+	0.285062i
$604$	−5.00000	+	8.66025i	−0.203447	+	0.352381i
$605$		0			0
$606$		0			0
$607$			20.0000i			0.811775i	0.913923	+	0.405887i	$0.133038\pi$
$607$			20.0000i			0.811775i	−0.913923	+	0.405887i	$0.866962\pi$
$608$	4.33013	−	0.500000i	0.175610	−	0.0202777i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−10.3923	−	6.00000i	−0.420084	−	0.242536i
$613$	−1.73205	+	1.00000i	−0.0699569	+	0.0403896i	−0.534570	−	0.845124i	$-0.679527\pi$
$613$	−1.73205	+	1.00000i	−0.0699569	+	0.0403896i	0.464614	+	0.885514i	$0.346193\pi$
$614$	3.50000	−	6.06218i	0.141249	−	0.244650i
$615$		0			0
$616$	12.0000			0.483494
$617$	−2.59808	−	1.50000i	−0.104595	−	0.0603877i	0.446790	−	0.894639i	$-0.352567\pi$
$617$	−2.59808	−	1.50000i	−0.104595	−	0.0603877i	−0.551385	+	0.834251i	$0.685900\pi$
$618$	−1.73205	−	1.00000i	−0.0696733	−	0.0402259i
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$		0			0
$621$	−15.0000	+	25.9808i	−0.601929	+	1.04257i
$622$	25.9808	−	15.0000i	1.04173	−	0.601445i
$623$	−20.7846	−	12.0000i	−0.832718	−	0.480770i
$624$	1.00000	+	1.73205i	0.0400320	+	0.0693375i
$625$		0			0
$626$	19.0000			0.759393
$627$	−5.19615	+	12.0000i	−0.207514	+	0.479234i
$628$			16.0000i			0.638470i
$629$	30.0000	+	51.9615i	1.19618	+	2.07184i
$630$		0			0
$631$	14.0000	−	24.2487i	0.557331	−	0.965326i	−0.440387	−	0.897808i	$-0.645159\pi$
$631$	14.0000	−	24.2487i	0.557331	−	0.965326i	0.997718	−	0.0675178i	$-0.0215080\pi$
$632$	3.46410	−	2.00000i	0.137795	−	0.0795557i
$633$	17.3205	+	10.0000i	0.688428	+	0.397464i
$634$	−18.0000			−0.714871
$635$		0			0
$636$	−3.00000	+	5.19615i	−0.118958	+	0.206041i
$637$	−15.5885	−	9.00000i	−0.617637	−	0.356593i
$638$		0			0
$639$	−12.0000			−0.474713
$640$		0			0
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	0.937451	+	0.348117i	$0.113179\pi$
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	−0.167247	+	0.985915i	$0.553488\pi$
$642$		0			0
$643$	37.2391	−	21.5000i	1.46857	−	0.847877i	0.469187	−	0.883099i	$-0.344547\pi$
$643$	37.2391	−	21.5000i	1.46857	−	0.847877i	0.999380	+	0.0352216i	$0.0112137\pi$
$644$	12.0000	+	20.7846i	0.472866	+	0.819028i
$645$		0			0
$646$	−3.00000	−	25.9808i	−0.118033	−	1.02220i
$647$			18.0000i			0.707653i	0.935311	+	0.353827i	$0.115120\pi$
$647$			18.0000i			0.707653i	−0.935311	+	0.353827i	$0.884880\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−13.5000	−	23.3827i	−0.529921	−	0.917851i
$650$		0			0
$651$	4.00000	+	6.92820i	0.156772	+	0.271538i
$652$	16.4545	+	9.50000i	0.644407	+	0.372049i
$653$			12.0000i			0.469596i	0.972044	+	0.234798i	$0.0754429\pi$
$653$			12.0000i			0.469596i	−0.972044	+	0.234798i	$0.924557\pi$
$654$	−16.0000			−0.625650
$655$		0			0
$656$	−4.50000	+	7.79423i	−0.175695	+	0.304314i
$657$			2.00000i			0.0780274i
$658$		0			0
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$		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	$-0.117053\pi$
$662$	−4.33013	+	2.50000i	−0.168295	+	0.0971653i
$663$	10.3923	−	6.00000i	0.403604	−	0.233021i
$664$	3.00000			0.116423
$665$		0			0
$666$	−20.0000			−0.774984
$667$		0			0
$668$	20.7846	−	12.0000i	0.804181	−	0.464294i
$669$	7.00000	−	12.1244i	0.270636	−	0.468755i
$670$		0			0
$671$	6.00000	−	10.3923i	0.231627	−	0.401190i
$672$			4.00000i			0.154303i
$673$		−	14.0000i		−	0.539660i	−0.962908	−	0.269830i	$-0.913032\pi$
$673$		−	14.0000i		−	0.539660i	0.962908	−	0.269830i	$-0.0869676\pi$
$674$	−5.50000	+	9.52628i	−0.211852	+	0.366939i
$675$		0			0
$676$	−9.00000			−0.346154
$677$		−	42.0000i		−	1.61419i	−0.590421	−	0.807096i	$-0.701038\pi$
$677$		−	42.0000i		−	1.61419i	0.590421	−	0.807096i	$-0.298962\pi$
$678$	−12.9904	−	7.50000i	−0.498893	−	0.288036i
$679$	−34.0000	−	58.8897i	−1.30480	−	2.25998i
$680$		0			0
$681$	−1.50000	−	2.59808i	−0.0574801	−	0.0995585i
$682$	−5.19615	+	3.00000i	−0.198971	+	0.114876i
$683$			36.0000i			1.37750i	0.724998	+	0.688751i	$0.241841\pi$
$683$			36.0000i			1.37750i	−0.724998	+	0.688751i	$0.758159\pi$
$684$	8.00000	+	3.46410i	0.305888	+	0.132453i
$685$		0			0
$686$	−4.00000	−	6.92820i	−0.152721	−	0.264520i
$687$	−13.8564	+	8.00000i	−0.528655	+	0.305219i
$688$	−3.46410	−	2.00000i	−0.132068	−	0.0762493i
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$		0			0
$691$	44.0000			1.67384			0.836919	−	0.547326i	$-0.184354\pi$
$691$	44.0000			1.67384			0.836919	+	0.547326i	$0.184354\pi$
$692$			6.00000i			0.228086i
$693$	20.7846	+	12.0000i	0.789542	+	0.455842i
$694$	4.50000	−	7.79423i	0.170818	−	0.295865i
$695$		0			0
$696$		0			0
$697$	46.7654	+	27.0000i	1.77136	+	1.02270i
$698$	−3.46410	+	2.00000i	−0.131118	+	0.0757011i
$699$	1.50000	−	2.59808i	0.0567352	−	0.0982683i
$700$		0			0
$701$	12.0000	+	20.7846i	0.453234	+	0.785024i	0.998585	−	0.0531839i	$-0.0169370\pi$
$701$	12.0000	+	20.7846i	0.453234	+	0.785024i	−0.545351	+	0.838208i	$0.683604\pi$
$702$			10.0000i			0.377426i
$703$	−25.9808	−	35.0000i	−0.979883	−	1.32005i
$704$	−3.00000			−0.113067
$705$		0			0
$706$	1.50000	+	2.59808i	0.0564532	+	0.0977799i
$707$		0			0
$708$	7.79423	−	4.50000i	0.292925	−	0.169120i
$709$	7.00000	−	12.1244i	0.262891	−	0.455340i	−0.704118	−	0.710083i	$-0.748658\pi$
$709$	7.00000	−	12.1244i	0.262891	−	0.455340i	0.967009	+	0.254743i	$0.0819909\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$	5.19615	+	3.00000i	0.194734	+	0.112430i
$713$	−10.3923	−	6.00000i	−0.389195	−	0.224702i
$714$	24.0000			0.898177
$715$		0			0
$716$	−4.50000	+	7.79423i	−0.168173	+	0.291284i
$717$	−10.3923	+	6.00000i	−0.388108	+	0.224074i
$718$	5.19615	+	3.00000i	0.193919	+	0.111959i
$719$	15.0000	+	25.9808i	0.559406	+	0.968919i	0.997546	+	0.0700124i	$0.0223039\pi$
$719$	15.0000	+	25.9808i	0.559406	+	0.968919i	−0.438141	+	0.898906i	$0.644363\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$	4.33013	+	18.5000i	0.161151	+	0.688499i
$723$		−	5.00000i		−	0.185952i
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$		0			0
$726$	−1.00000	+	1.73205i	−0.0371135	+	0.0642824i
$727$	27.7128	−	16.0000i	1.02781	−	0.593407i	0.111454	−	0.993770i	$-0.464449\pi$
$727$	27.7128	−	16.0000i	1.02781	−	0.593407i	0.916357	+	0.400362i	$0.131116\pi$
$728$	6.92820	+	4.00000i	0.256776	+	0.148250i
$729$	−13.0000			−0.481481
$730$		0			0
$731$	−12.0000	+	20.7846i	−0.443836	+	0.768747i
$732$	3.46410	+	2.00000i	0.128037	+	0.0739221i
$733$			22.0000i			0.812589i	0.913742	+	0.406294i	$0.133179\pi$
$733$			22.0000i			0.812589i	−0.913742	+	0.406294i	$0.866821\pi$
$734$	−22.0000			−0.812035
$735$		0			0
$736$	−3.00000	−	5.19615i	−0.110581	−	0.191533i
$737$	18.1865	+	10.5000i	0.669910	+	0.386772i
$738$	−15.5885	+	9.00000i	−0.573819	+	0.331295i
$739$	17.5000	+	30.3109i	0.643748	+	1.11500i	0.984589	+	0.174883i	$0.0559548\pi$
$739$	17.5000	+	30.3109i	0.643748	+	1.11500i	−0.340841	+	0.940121i	$0.610712\pi$
$740$		0			0
$741$	−7.00000	+	5.19615i	−0.257151	+	0.190885i
$742$			24.0000i			0.881068i
$743$	15.5885	−	9.00000i	0.571885	−	0.330178i	−0.186017	−	0.982547i	$-0.559558\pi$
$743$	15.5885	−	9.00000i	0.571885	−	0.330178i	0.757902	+	0.652369i	$0.226225\pi$
$744$	−1.00000	−	1.73205i	−0.0366618	−	0.0635001i
$745$		0			0
$746$	−2.00000	−	3.46410i	−0.0732252	−	0.126830i
$747$	5.19615	+	3.00000i	0.190117	+	0.109764i
$748$			18.0000i			0.658145i
$749$		0			0
$750$		0			0
$751$	−19.0000	+	32.9090i	−0.693320	+	1.20087i	0.277424	+	0.960748i	$0.410519\pi$
$751$	−19.0000	+	32.9090i	−0.693320	+	1.20087i	−0.970744	+	0.240118i	$0.922814\pi$
$752$		0			0
$753$			3.00000i			0.109326i
$754$		0			0
$755$		0			0
$756$	−10.0000	+	17.3205i	−0.363696	+	0.629941i
$757$	−8.66025	+	5.00000i	−0.314762	+	0.181728i	−0.649056	−	0.760741i	$-0.724836\pi$
$757$	−8.66025	+	5.00000i	−0.314762	+	0.181728i	0.334293	+	0.942469i	$0.391502\pi$
$758$	−24.2487	+	14.0000i	−0.880753	+	0.508503i
$759$	18.0000			0.653359
$760$		0			0
$761$	−39.0000			−1.41375			−0.706874	−	0.707339i	$-0.749895\pi$
$761$	−39.0000			−1.41375			−0.706874	+	0.707339i	$0.749895\pi$
$762$	−1.73205	+	1.00000i	−0.0627456	+	0.0362262i
$763$	−55.4256	+	32.0000i	−2.00654	+	1.15848i
$764$	6.00000	−	10.3923i	0.217072	−	0.375980i
$765$		0			0
$766$	−18.0000	+	31.1769i	−0.650366	+	1.12647i
$767$		−	18.0000i		−	0.649942i
$768$		−	1.00000i		−	0.0360844i
$769$	1.00000	−	1.73205i	0.0360609	−	0.0624593i	−0.847432	−	0.530904i	$-0.821852\pi$
$769$	1.00000	−	1.73205i	0.0360609	−	0.0624593i	0.883493	+	0.468445i	$0.155186\pi$
$770$		0			0
$771$	3.00000			0.108042
$772$			2.00000i			0.0719816i
$773$	−41.5692	−	24.0000i	−1.49514	−	0.863220i	−0.495156	−	0.868804i	$-0.664889\pi$
$773$	−41.5692	−	24.0000i	−1.49514	−	0.863220i	−0.999984	+	0.00558380i	$0.998223\pi$
$774$	−4.00000	−	6.92820i	−0.143777	−	0.249029i
$775$		0			0
$776$	8.50000	+	14.7224i	0.305132	+	0.528505i
$777$	34.6410	−	20.0000i	1.24274	−	0.717496i
$778$		−	36.0000i		−	1.29066i
$779$	−36.0000	−	15.5885i	−1.28983	−	0.558514i
$780$		0			0
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$	−31.1769	+	18.0000i	−1.11488	+	0.643679i
$783$		0			0
$784$	4.50000	+	7.79423i	0.160714	+	0.278365i
$785$		0			0
$786$	−9.00000			−0.321019
$787$		−	7.00000i		−	0.249523i	−0.992187	−	0.124762i	$-0.960183\pi$
$787$		−	7.00000i		−	0.249523i	0.992187	−	0.124762i	$-0.0398166\pi$
$788$	15.5885	+	9.00000i	0.555316	+	0.320612i
$789$	−6.00000	+	10.3923i	−0.213606	+	0.369976i
$790$		0			0
$791$	−60.0000			−2.13335
$792$	−5.19615	−	3.00000i	−0.184637	−	0.106600i
$793$	6.92820	−	4.00000i	0.246028	−	0.142044i
$794$	5.00000	−	8.66025i	0.177443	−	0.307341i
$795$		0			0
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$			6.00000i			0.212531i	0.994338	+	0.106265i	$0.0338893\pi$
$797$			6.00000i			0.212531i	−0.994338	+	0.106265i	$0.966111\pi$
$798$	−17.3205	+	2.00000i	−0.613139	+	0.0707992i
$799$		0			0
$800$		0			0
$801$	6.00000	+	10.3923i	0.212000	+	0.367194i
$802$	−23.3827	−	13.5000i	−0.825671	−	0.476702i
$803$	2.59808	−	1.50000i	0.0916841	−	0.0529339i
$804$	−3.50000	+	6.06218i	−0.123435	+	0.213797i
$805$		0			0
$806$	−4.00000			−0.140894
$807$	−10.3923	−	6.00000i	−0.365826	−	0.211210i
$808$		0			0
$809$	−45.0000			−1.58212			−0.791058	−	0.611741i	$-0.790469\pi$
$809$	−45.0000			−1.58212			−0.791058	+	0.611741i	$0.790469\pi$
$810$		0			0
$811$	8.00000	−	13.8564i	0.280918	−	0.486564i	−0.690693	−	0.723148i	$-0.742694\pi$
$811$	8.00000	−	13.8564i	0.280918	−	0.486564i	0.971611	+	0.236584i	$0.0760278\pi$
$812$		0			0
$813$	−13.8564	−	8.00000i	−0.485965	−	0.280572i
$814$	15.0000	+	25.9808i	0.525750	+	0.910625i
$815$		0			0
$816$	−6.00000			−0.210042
$817$	6.92820	−	16.0000i	0.242387	−	0.559769i
$818$			5.00000i			0.174821i
$819$	8.00000	+	13.8564i	0.279543	+	0.484182i
$820$		0			0
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	−0.979246	−	0.202674i	$-0.935037\pi$
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	0.665144	+	0.746715i	$0.268370\pi$
$822$	−7.79423	+	4.50000i	−0.271855	+	0.156956i
$823$	12.1244	+	7.00000i	0.422628	+	0.244005i	0.696201	−	0.717847i	$-0.254872\pi$
$823$	12.1244	+	7.00000i	0.422628	+	0.244005i	−0.273573	+	0.961851i	$0.588205\pi$
$824$	2.00000			0.0696733
$825$		0			0
$826$	18.0000	−	31.1769i	0.626300	−	1.08478i
$827$	33.7750	+	19.5000i	1.17447	+	0.678081i	0.954729	−	0.297477i	$-0.0961450\pi$
$827$	33.7750	+	19.5000i	1.17447	+	0.678081i	0.219742	+	0.975558i	$0.429478\pi$
$828$		−	12.0000i		−	0.417029i
$829$	−44.0000			−1.52818			−0.764092	−	0.645108i	$-0.776812\pi$
$829$	−44.0000			−1.52818			−0.764092	+	0.645108i	$0.776812\pi$
$830$		0			0
$831$	−4.00000	−	6.92820i	−0.138758	−	0.240337i
$832$	−1.73205	−	1.00000i	−0.0600481	−	0.0346688i
$833$	46.7654	−	27.0000i	1.62032	−	0.935495i
$834$	−5.50000	−	9.52628i	−0.190449	−	0.329868i
$835$		0			0
$836$	−1.50000	−	12.9904i	−0.0518786	−	0.449282i
$837$		−	10.0000i		−	0.345651i
$838$	−10.3923	+	6.00000i	−0.358996	+	0.207267i
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	0.743670	−	0.668546i	$-0.233083\pi$
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	−0.950813	+	0.309764i	$0.899750\pi$
$840$		0			0
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	−8.66025	−	5.00000i	−0.298452	−	0.172311i
$843$		−	27.0000i		−	0.929929i
$844$	−20.0000			−0.688428
$845$		0			0
$846$		0			0
$847$			8.00000i			0.274883i
$848$		−	6.00000i		−	0.206041i
$849$	2.50000	−	4.33013i	0.0857998	−	0.148610i
$850$		0			0
$851$	−30.0000	+	51.9615i	−1.02839	+	1.78122i
$852$	−5.19615	+	3.00000i	−0.178017	+	0.102778i
$853$	19.0526	−	11.0000i	0.652347	−	0.376633i	−0.137008	−	0.990570i	$-0.543749\pi$
$853$	19.0526	−	11.0000i	0.652347	−	0.376633i	0.789355	+	0.613937i	$0.210415\pi$
$854$	16.0000			0.547509
$855$		0			0
$856$		0			0
$857$	−2.59808	+	1.50000i	−0.0887486	+	0.0512390i	−0.543718	−	0.839268i	$-0.682984\pi$
$857$	−2.59808	+	1.50000i	−0.0887486	+	0.0512390i	0.454969	+	0.890507i	$0.349650\pi$
$858$	5.19615	−	3.00000i	0.177394	−	0.102418i
$859$	−21.5000	+	37.2391i	−0.733571	+	1.27058i	0.221777	+	0.975097i	$0.428814\pi$
$859$	−21.5000	+	37.2391i	−0.733571	+	1.27058i	−0.955348	+	0.295484i	$0.904519\pi$
$860$		0			0
$861$	18.0000	−	31.1769i	0.613438	−	1.06251i
$862$			30.0000i			1.02180i
$863$		−	18.0000i		−	0.612727i	−0.951915	−	0.306364i	$-0.900888\pi$
$863$		−	18.0000i		−	0.612727i	0.951915	−	0.306364i	$-0.0991123\pi$
$864$	2.50000	−	4.33013i	0.0850517	−	0.147314i
$865$		0			0
$866$	−26.0000			−0.883516
$867$			19.0000i			0.645274i
$868$	−6.92820	−	4.00000i	−0.235159	−	0.135769i
$869$	−6.00000	−	10.3923i	−0.203536	−	0.352535i
$870$		0			0
$871$	7.00000	+	12.1244i	0.237186	+	0.410818i
$872$	13.8564	−	8.00000i	0.469237	−	0.270914i
$873$			34.0000i			1.15073i
$874$	21.0000	−	15.5885i	0.710336	−	0.527287i
$875$		0			0
$876$	0.500000	+	0.866025i	0.0168934	+	0.0292603i
$877$	17.3205	−	10.0000i	0.584872	−	0.337676i	−0.178195	−	0.983995i	$-0.557026\pi$
$877$	17.3205	−	10.0000i	0.584872	−	0.337676i	0.763067	+	0.646319i	$0.223693\pi$
$878$	−12.1244	−	7.00000i	−0.409177	−	0.236239i
$879$	12.0000	+	20.7846i	0.404750	+	0.701047i
$880$		0			0
$881$	−9.00000			−0.303218			−0.151609	−	0.988441i	$-0.548445\pi$
$881$	−9.00000			−0.303218			−0.151609	+	0.988441i	$0.548445\pi$
$882$			18.0000i			0.606092i
$883$	−16.4545	−	9.50000i	−0.553737	−	0.319700i	0.196891	−	0.980425i	$-0.436916\pi$
$883$	−16.4545	−	9.50000i	−0.553737	−	0.319700i	−0.750628	+	0.660725i	$0.770249\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$		0			0
$886$	−9.00000			−0.302361
$887$	−41.5692	−	24.0000i	−1.39576	−	0.805841i	−0.401813	−	0.915722i	$-0.631620\pi$
$887$	−41.5692	−	24.0000i	−1.39576	−	0.805841i	−0.993945	+	0.109881i	$0.964953\pi$
$888$	−8.66025	+	5.00000i	−0.290619	+	0.167789i
$889$	−4.00000	+	6.92820i	−0.134156	+	0.232364i
$890$		0			0
$891$	−1.50000	−	2.59808i	−0.0502519	−	0.0870388i
$892$			14.0000i			0.468755i
$893$		0			0
$894$	18.0000			0.602010
$895$		0			0
$896$	−2.00000	−	3.46410i	−0.0668153	−	0.115728i
$897$	10.3923	+	6.00000i	0.346989	+	0.200334i
$898$	7.79423	−	4.50000i	0.260097	−	0.150167i
$899$		0			0
$900$		0			0
$901$	−36.0000			−1.19933
$902$	23.3827	+	13.5000i	0.778558	+	0.449501i
$903$	13.8564	+	8.00000i	0.461112	+	0.266223i
$904$	15.0000			0.498893
$905$		0			0
$906$	−5.00000	+	8.66025i	−0.166114	+	0.287718i
$907$	14.7224	−	8.50000i	0.488850	−	0.282238i	−0.235247	−	0.971936i	$-0.575590\pi$
$907$	14.7224	−	8.50000i	0.488850	−	0.282238i	0.724097	+	0.689698i	$0.242257\pi$
$908$	2.59808	+	1.50000i	0.0862202	+	0.0497792i
$909$		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	$0.334445\pi$
$912$	4.33013	−	0.500000i	0.143385	−	0.0165567i
$913$		−	9.00000i		−	0.297857i
$914$	−2.50000	−	4.33013i	−0.0826927	−	0.143228i
$915$		0			0
$916$	8.00000	−	13.8564i	0.264327	−	0.457829i
$917$	−31.1769	+	18.0000i	−1.02955	+	0.594412i
$918$	−25.9808	−	15.0000i	−0.857493	−	0.495074i
$919$	10.0000			0.329870			0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$		0			0
$921$	3.50000	−	6.06218i	0.115329	−	0.199756i
$922$	5.19615	+	3.00000i	0.171126	+	0.0987997i
$923$			12.0000i			0.394985i
$924$	12.0000			0.394771
$925$		0			0
$926$	−17.0000	−	29.4449i	−0.558655	−	0.967618i
$927$	3.46410	+	2.00000i	0.113776	+	0.0656886i
$928$		0			0
$929$	−1.50000	−	2.59808i	−0.0492134	−	0.0852401i	0.840369	−	0.542014i	$-0.182338\pi$
$929$	−1.50000	−	2.59808i	−0.0492134	−	0.0852401i	−0.889583	+	0.456774i	$0.849005\pi$
$930$		0			0
$931$	−31.5000	+	23.3827i	−1.03237	+	0.766337i
$932$			3.00000i			0.0982683i
$933$	25.9808	−	15.0000i	0.850572	−	0.491078i
$934$	13.5000	+	23.3827i	0.441733	+	0.765105i
$935$		0			0
$936$	−2.00000	−	3.46410i	−0.0653720	−	0.113228i
$937$	−30.3109	−	17.5000i	−0.990214	−	0.571700i	−0.0848755	−	0.996392i	$-0.527049\pi$
$937$	−30.3109	−	17.5000i	−0.990214	−	0.571700i	−0.905338	+	0.424691i	$0.860383\pi$
$938$			28.0000i			0.914232i
$939$	19.0000			0.620042
$940$		0			0
$941$	21.0000	−	36.3731i	0.684580	−	1.18573i	−0.288988	−	0.957333i	$-0.593319\pi$
$941$	21.0000	−	36.3731i	0.684580	−	1.18573i	0.973568	−	0.228395i	$-0.0733479\pi$
$942$			16.0000i			0.521308i
$943$			54.0000i			1.75848i
$944$	−4.50000	+	7.79423i	−0.146463	+	0.253681i
$945$		0			0
$946$	−6.00000	+	10.3923i	−0.195077	+	0.337883i
$947$	51.9615	−	30.0000i	1.68852	−	0.974869i	0.732872	−	0.680367i	$-0.238179\pi$
$947$	51.9615	−	30.0000i	1.68852	−	0.974869i	0.955651	−	0.294502i	$-0.0951539\pi$
$948$	3.46410	−	2.00000i	0.112509	−	0.0649570i
$949$	2.00000			0.0649227
$950$		0			0
$951$	−18.0000			−0.583690
$952$	−20.7846	+	12.0000i	−0.673633	+	0.388922i
$953$	12.9904	−	7.50000i	0.420800	−	0.242949i	−0.274620	−	0.961553i	$-0.588552\pi$
$953$	12.9904	−	7.50000i	0.420800	−	0.242949i	0.695419	+	0.718604i	$0.255219\pi$
$954$	6.00000	−	10.3923i	0.194257	−	0.336463i
$955$		0			0
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$		0			0
$958$			36.0000i			1.16311i
$959$	−18.0000	+	31.1769i	−0.581250	+	1.00676i
$960$		0			0
$961$	−27.0000			−0.870968
$962$			20.0000i			0.644826i
$963$		0			0
$964$	2.50000	+	4.33013i	0.0805196	+	0.139464i
$965$		0			0
$966$	12.0000	+	20.7846i	0.386094	+	0.668734i
$967$	−29.4449	+	17.0000i	−0.946883	+	0.546683i	−0.892111	−	0.451816i	$-0.850776\pi$
$967$	−29.4449	+	17.0000i	−0.946883	+	0.546683i	−0.0547717	+	0.998499i	$0.517443\pi$
$968$		−	2.00000i		−	0.0642824i
$969$	−3.00000	−	25.9808i	−0.0963739	−	0.834622i
$970$		0			0
$971$	−10.5000	−	18.1865i	−0.336961	−	0.583634i	0.646899	−	0.762576i	$-0.276066\pi$
$971$	−10.5000	−	18.1865i	−0.336961	−	0.583634i	−0.983860	+	0.178942i	$0.942732\pi$
$972$	13.8564	−	8.00000i	0.444444	−	0.256600i
$973$	−38.1051	−	22.0000i	−1.22159	−	0.705288i
$974$	−1.00000	−	1.73205i	−0.0320421	−	0.0554985i
$975$		0			0
$976$	−4.00000			−0.128037
$977$			33.0000i			1.05576i	0.849318	+	0.527882i	$0.177014\pi$
$977$			33.0000i			1.05576i	−0.849318	+	0.527882i	$0.822986\pi$
$978$	16.4545	+	9.50000i	0.526156	+	0.303777i
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$		0			0
$981$	32.0000			1.02168
$982$		0			0
$983$	−20.7846	+	12.0000i	−0.662926	+	0.382741i	−0.793391	−	0.608712i	$-0.791686\pi$
$983$	−20.7846	+	12.0000i	−0.662926	+	0.382741i	0.130465	+	0.991453i	$0.458353\pi$
$984$	−4.50000	+	7.79423i	−0.143455	+	0.248471i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	3.46410	−	8.00000i	0.110208	−	0.254514i
$989$	−24.0000			−0.763156
$990$		0			0
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	0.795474	−	0.605988i	$-0.207222\pi$
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	−0.922538	+	0.385906i	$0.873889\pi$
$992$	1.73205	+	1.00000i	0.0549927	+	0.0317500i
$993$	−4.33013	+	2.50000i	−0.137412	+	0.0793351i
$994$	−12.0000	+	20.7846i	−0.380617	+	0.659248i
$995$		0			0
$996$	3.00000			0.0950586
$997$	3.46410	+	2.00000i	0.109709	+	0.0633406i	0.553851	−	0.832616i	$-0.313158\pi$
$997$	3.46410	+	2.00000i	0.109709	+	0.0633406i	−0.444141	+	0.895957i	$0.646491\pi$
$998$	21.6506	+	12.5000i	0.685339	+	0.395681i
$999$	−50.0000			−1.58193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.j.e.349.1		4
5.2	odd	4		950.2.e.d.501.1		2
5.3	odd	4		38.2.c.a.7.1	✓	2
5.4	even	2	inner	950.2.j.e.349.2		4
15.8	even	4		342.2.g.b.235.1		2
19.11	even	3	inner	950.2.j.e.49.2		4
20.3	even	4		304.2.i.c.273.1		2
40.3	even	4		1216.2.i.d.577.1		2
40.13	odd	4		1216.2.i.h.577.1		2
60.23	odd	4		2736.2.s.m.577.1		2
95.3	even	36		722.2.e.i.595.1		6
95.8	even	12		722.2.c.b.429.1		2
95.13	even	36		722.2.e.i.423.1		6
95.18	even	4		722.2.c.b.653.1		2
95.23	odd	36		722.2.e.j.245.1		6
95.28	odd	36		722.2.e.j.415.1		6
95.33	even	36		722.2.e.i.99.1		6
95.43	odd	36		722.2.e.j.99.1		6
95.48	even	36		722.2.e.i.415.1		6
95.49	even	6	inner	950.2.j.e.49.1		4
95.53	even	36		722.2.e.i.245.1		6
95.63	odd	36		722.2.e.j.423.1		6
95.68	odd	12		38.2.c.a.11.1	yes	2
95.73	odd	36		722.2.e.j.595.1		6
95.78	even	36		722.2.e.i.389.1		6
95.83	odd	12		722.2.a.c.1.1		1
95.87	odd	12		950.2.e.d.201.1		2
95.88	even	12		722.2.a.d.1.1		1
95.93	odd	36		722.2.e.j.389.1		6
285.68	even	12		342.2.g.b.163.1		2
285.83	even	12		6498.2.a.s.1.1		1
285.278	odd	12		6498.2.a.e.1.1		1
380.83	even	12		5776.2.a.g.1.1		1
380.163	even	12		304.2.i.c.49.1		2
380.183	odd	12		5776.2.a.n.1.1		1
760.163	even	12		1216.2.i.d.961.1		2
760.733	odd	12		1216.2.i.h.961.1		2
1140.923	odd	12		2736.2.s.m.1873.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.a.7.1	✓	2	5.3	odd	4
38.2.c.a.11.1	yes	2	95.68	odd	12
304.2.i.c.49.1		2	380.163	even	12
304.2.i.c.273.1		2	20.3	even	4
342.2.g.b.163.1		2	285.68	even	12
342.2.g.b.235.1		2	15.8	even	4
722.2.a.c.1.1		1	95.83	odd	12
722.2.a.d.1.1		1	95.88	even	12
722.2.c.b.429.1		2	95.8	even	12
722.2.c.b.653.1		2	95.18	even	4
722.2.e.i.99.1		6	95.33	even	36
722.2.e.i.245.1		6	95.53	even	36
722.2.e.i.389.1		6	95.78	even	36
722.2.e.i.415.1		6	95.48	even	36
722.2.e.i.423.1		6	95.13	even	36
722.2.e.i.595.1		6	95.3	even	36
722.2.e.j.99.1		6	95.43	odd	36
722.2.e.j.245.1		6	95.23	odd	36
722.2.e.j.389.1		6	95.93	odd	36
722.2.e.j.415.1		6	95.28	odd	36
722.2.e.j.423.1		6	95.63	odd	36
722.2.e.j.595.1		6	95.73	odd	36
950.2.e.d.201.1		2	95.87	odd	12
950.2.e.d.501.1		2	5.2	odd	4
950.2.j.e.49.1		4	95.49	even	6	inner
950.2.j.e.49.2		4	19.11	even	3	inner
950.2.j.e.349.1		4	1.1	even	1	trivial
950.2.j.e.349.2		4	5.4	even	2	inner
1216.2.i.d.577.1		2	40.3	even	4
1216.2.i.d.961.1		2	760.163	even	12
1216.2.i.h.577.1		2	40.13	odd	4
1216.2.i.h.961.1		2	760.733	odd	12
2736.2.s.m.577.1		2	60.23	odd	4
2736.2.s.m.1873.1		2	1140.923	odd	12
5776.2.a.g.1.1		1	380.83	even	12
5776.2.a.n.1.1		1	380.183	odd	12
6498.2.a.e.1.1		1	285.278	odd	12
6498.2.a.s.1.1		1	285.83	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} -4.00000i q^{7} +1.00000i q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} -4.00000i q^{7} +1.00000i q^{8} +(-1.00000 + 1.73205i) q^{9} +3.00000 q^{11} +1.00000i q^{12} +(1.73205 + 1.00000i) q^{13} +(2.00000 + 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.19615 + 3.00000i) q^{17} -2.00000i q^{18} +(3.50000 - 2.59808i) q^{19} +(2.00000 + 3.46410i) q^{21} +(-2.59808 + 1.50000i) q^{22} +(-5.19615 - 3.00000i) q^{23} +(-0.500000 - 0.866025i) q^{24} -2.00000 q^{26} -5.00000i q^{27} +(-3.46410 - 2.00000i) q^{28} +2.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.59808 + 1.50000i) q^{33} +(3.00000 - 5.19615i) q^{34} +(1.00000 + 1.73205i) q^{36} -10.0000i q^{37} +(-1.73205 + 4.00000i) q^{38} -2.00000 q^{39} +(-4.50000 - 7.79423i) q^{41} +(-3.46410 - 2.00000i) q^{42} +(3.46410 - 2.00000i) q^{43} +(1.50000 - 2.59808i) q^{44} +6.00000 q^{46} +(0.866025 + 0.500000i) q^{48} -9.00000 q^{49} +(3.00000 - 5.19615i) q^{51} +(1.73205 - 1.00000i) q^{52} +(5.19615 + 3.00000i) q^{53} +(2.50000 + 4.33013i) q^{54} +4.00000 q^{56} +(-1.73205 + 4.00000i) q^{57} +(-4.50000 - 7.79423i) q^{59} +(2.00000 - 3.46410i) q^{61} +(-1.73205 + 1.00000i) q^{62} +(6.92820 + 4.00000i) q^{63} -1.00000 q^{64} +(1.50000 - 2.59808i) q^{66} +(6.06218 + 3.50000i) q^{67} +6.00000i q^{68} +6.00000 q^{69} +(3.00000 + 5.19615i) q^{71} +(-1.73205 - 1.00000i) q^{72} +(0.866025 - 0.500000i) q^{73} +(5.00000 + 8.66025i) q^{74} +(-0.500000 - 4.33013i) q^{76} -12.0000i q^{77} +(1.73205 - 1.00000i) q^{78} +(-2.00000 - 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(7.79423 + 4.50000i) q^{82} -3.00000i q^{83} +4.00000 q^{84} +(-2.00000 + 3.46410i) q^{86} +3.00000i q^{88} +(3.00000 - 5.19615i) q^{89} +(4.00000 - 6.92820i) q^{91} +(-5.19615 + 3.00000i) q^{92} +(-1.73205 + 1.00000i) q^{93} -1.00000 q^{96} +(14.7224 - 8.50000i) q^{97} +(7.79423 - 4.50000i) q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 2 * q^6 - 4 * q^9	\( 4 q + 2 q^{4} + 2 q^{6} - 4 q^{9} + 12 q^{11} + 8 q^{14} - 2 q^{16} + 14 q^{19} + 8 q^{21} - 2 q^{24} - 8 q^{26} + 8 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} - 18 q^{41} + 6 q^{44} + 24 q^{46} - 36 q^{49} + 12 q^{51} + 10 q^{54} + 16 q^{56} - 18 q^{59} + 8 q^{61} - 4 q^{64} + 6 q^{66} + 24 q^{69} + 12 q^{71} + 20 q^{74} - 2 q^{76} - 8 q^{79} - 2 q^{81} + 16 q^{84} - 8 q^{86} + 12 q^{89} + 16 q^{91} - 4 q^{96} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^6 - 4 * q^9 + 12 * q^11 + 8 * q^14 - 2 * q^16 + 14 * q^19 + 8 * q^21 - 2 * q^24 - 8 * q^26 + 8 * q^31 + 12 * q^34 + 4 * q^36 - 8 * q^39 - 18 * q^41 + 6 * q^44 + 24 * q^46 - 36 * q^49 + 12 * q^51 + 10 * q^54 + 16 * q^56 - 18 * q^59 + 8 * q^61 - 4 * q^64 + 6 * q^66 + 24 * q^69 + 12 * q^71 + 20 * q^74 - 2 * q^76 - 8 * q^79 - 2 * q^81 + 16 * q^84 - 8 * q^86 + 12 * q^89 + 16 * q^91 - 4 * q^96 - 12 * q^99

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