LMFDB - Embedded newform 950.2.e.a.201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(201,950)]

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([0, 4]))

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

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

chi := DirichletCharacter("950.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	950.201
Dual form			950.2.e.a.501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} -3.00000 q^{11} +1.00000 q^{12} +(3.00000 + 5.19615i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} -2.00000 q^{18} +(3.50000 + 2.59808i) q^{19} +(1.00000 - 1.73205i) q^{21} +(1.50000 - 2.59808i) q^{22} +(-4.00000 - 6.92820i) q^{23} +(-0.500000 + 0.866025i) q^{24} -6.00000 q^{26} -5.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(1.00000 + 1.73205i) q^{29} -8.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +(1.00000 + 1.73205i) q^{34} +(1.00000 - 1.73205i) q^{36} -8.00000 q^{37} +(-4.00000 + 1.73205i) q^{38} -6.00000 q^{39} +(-2.50000 + 4.33013i) q^{41} +(1.00000 + 1.73205i) q^{42} +(1.50000 + 2.59808i) q^{44} +8.00000 q^{46} +(-3.00000 - 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{48} -3.00000 q^{49} +(1.00000 + 1.73205i) q^{51} +(3.00000 - 5.19615i) q^{52} +(3.00000 + 5.19615i) q^{53} +(2.50000 - 4.33013i) q^{54} -2.00000 q^{56} +(-4.00000 + 1.73205i) q^{57} -2.00000 q^{58} +(-2.50000 + 4.33013i) q^{59} +(-7.00000 - 12.1244i) q^{61} +(4.00000 - 6.92820i) q^{62} +(-2.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(1.50000 + 2.59808i) q^{66} +(-2.50000 - 4.33013i) q^{67} -2.00000 q^{68} +8.00000 q^{69} +(3.00000 - 5.19615i) q^{71} +(1.00000 + 1.73205i) q^{72} +(-4.50000 + 7.79423i) q^{73} +(4.00000 - 6.92820i) q^{74} +(0.500000 - 4.33013i) q^{76} +6.00000 q^{77} +(3.00000 - 5.19615i) q^{78} +(-4.00000 + 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.50000 - 4.33013i) q^{82} +11.0000 q^{83} -2.00000 q^{84} -2.00000 q^{87} -3.00000 q^{88} +(-7.00000 - 12.1244i) q^{89} +(-6.00000 - 10.3923i) q^{91} +(-4.00000 + 6.92820i) q^{92} +(4.00000 - 6.92820i) q^{93} +6.00000 q^{94} +1.00000 q^{96} +(-7.50000 + 12.9904i) q^{97} +(1.50000 - 2.59808i) q^{98} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 - q^3 - q^4 - q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9} - 6 q^{11} + 2 q^{12} + 6 q^{13} + 2 q^{14} - q^{16} + 2 q^{17} - 4 q^{18} + 7 q^{19} + 2 q^{21} + 3 q^{22} - 8 q^{23} - q^{24} - 12 q^{26} - 10 q^{27} + 2 q^{28} + 2 q^{29} - 16 q^{31} - q^{32} + 3 q^{33} + 2 q^{34} + 2 q^{36} - 16 q^{37} - 8 q^{38} - 12 q^{39} - 5 q^{41} + 2 q^{42} + 3 q^{44} + 16 q^{46} - 6 q^{47} - q^{48} - 6 q^{49} + 2 q^{51} + 6 q^{52} + 6 q^{53} + 5 q^{54} - 4 q^{56} - 8 q^{57} - 4 q^{58} - 5 q^{59} - 14 q^{61} + 8 q^{62} - 4 q^{63} + 2 q^{64} + 3 q^{66} - 5 q^{67} - 4 q^{68} + 16 q^{69} + 6 q^{71} + 2 q^{72} - 9 q^{73} + 8 q^{74} + q^{76} + 12 q^{77} + 6 q^{78} - 8 q^{79} - q^{81} - 5 q^{82} + 22 q^{83} - 4 q^{84} - 4 q^{87} - 6 q^{88} - 14 q^{89} - 12 q^{91} - 8 q^{92} + 8 q^{93} + 12 q^{94} + 2 q^{96} - 15 q^{97} + 3 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^3 - q^4 - q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9 - 6 * q^11 + 2 * q^12 + 6 * q^13 + 2 * q^14 - q^16 + 2 * q^17 - 4 * q^18 + 7 * q^19 + 2 * q^21 + 3 * q^22 - 8 * q^23 - q^24 - 12 * q^26 - 10 * q^27 + 2 * q^28 + 2 * q^29 - 16 * q^31 - q^32 + 3 * q^33 + 2 * q^34 + 2 * q^36 - 16 * q^37 - 8 * q^38 - 12 * q^39 - 5 * q^41 + 2 * q^42 + 3 * q^44 + 16 * q^46 - 6 * q^47 - q^48 - 6 * q^49 + 2 * q^51 + 6 * q^52 + 6 * q^53 + 5 * q^54 - 4 * q^56 - 8 * q^57 - 4 * q^58 - 5 * q^59 - 14 * q^61 + 8 * q^62 - 4 * q^63 + 2 * q^64 + 3 * q^66 - 5 * q^67 - 4 * q^68 + 16 * q^69 + 6 * q^71 + 2 * q^72 - 9 * q^73 + 8 * q^74 + q^76 + 12 * q^77 + 6 * q^78 - 8 * q^79 - q^81 - 5 * q^82 + 22 * q^83 - 4 * q^84 - 4 * q^87 - 6 * q^88 - 14 * q^89 - 12 * q^91 - 8 * q^92 + 8 * q^93 + 12 * q^94 + 2 * q^96 - 15 * q^97 + 3 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$	1.00000			0.353553
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$		0			0
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	1.00000			0.288675
$13$	3.00000	+	5.19615i	0.832050	+	1.44115i	0.896410	+	0.443227i	$0.146166\pi$
$13$	3.00000	+	5.19615i	0.832050	+	1.44115i	−0.0643593	+	0.997927i	$0.520500\pi$
$14$	1.00000	−	1.73205i	0.267261	−	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$	−2.00000			−0.471405
$19$	3.50000	+	2.59808i	0.802955	+	0.596040i
$19$	3.50000	+	2.59808i	0.802955	+	0.596040i
$20$		0			0
$21$	1.00000	−	1.73205i	0.218218	−	0.377964i
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	−0.894795	−	0.446476i	$-0.852679\pi$
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	0.0607377	−	0.998154i	$-0.480655\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	−6.00000			−1.17670
$27$	−5.00000			−0.962250
$28$	1.00000	+	1.73205i	0.188982	+	0.327327i
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	0.943811	−	0.330487i	$-0.107213\pi$
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	−0.758115	+	0.652121i	$0.773880\pi$
$30$		0			0
$31$	−8.00000			−1.43684			−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000			−1.43684			−0.718421	+	0.695608i	$0.755135\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$	1.00000	+	1.73205i	0.171499	+	0.297044i
$35$		0			0
$36$	1.00000	−	1.73205i	0.166667	−	0.288675i
$37$	−8.00000			−1.31519			−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000			−1.31519			−0.657596	+	0.753371i	$0.728427\pi$
$38$	−4.00000	+	1.73205i	−0.648886	+	0.280976i
$39$	−6.00000			−0.960769
$40$		0			0
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	−0.992507	−	0.122189i	$-0.961009\pi$
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	0.602072	+	0.798441i	$0.294342\pi$
$42$	1.00000	+	1.73205i	0.154303	+	0.267261i
$43$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$43$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$		0			0
$46$	8.00000			1.17954
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−3.00000			−0.428571
$50$		0			0
$51$	1.00000	+	1.73205i	0.140028	+	0.242536i
$52$	3.00000	−	5.19615i	0.416025	−	0.720577i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$	2.50000	−	4.33013i	0.340207	−	0.589256i
$55$		0			0
$56$	−2.00000			−0.267261
$57$	−4.00000	+	1.73205i	−0.529813	+	0.229416i
$58$	−2.00000			−0.262613
$59$	−2.50000	+	4.33013i	−0.325472	+	0.563735i	−0.981608	−	0.190909i	$-0.938857\pi$
$59$	−2.50000	+	4.33013i	−0.325472	+	0.563735i	0.656136	+	0.754643i	$0.272190\pi$
$60$		0			0
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.0640184	−	0.997949i	$-0.520392\pi$
$62$	4.00000	−	6.92820i	0.508001	−	0.879883i
$63$	−2.00000	−	3.46410i	−0.251976	−	0.436436i
$64$	1.00000			0.125000
$65$		0			0
$66$	1.50000	+	2.59808i	0.184637	+	0.319801i
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	0.671932	−	0.740613i	$-0.265465\pi$
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−2.00000			−0.242536
$69$	8.00000			0.963087
$70$		0			0
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$	1.00000	+	1.73205i	0.117851	+	0.204124i
$73$	−4.50000	+	7.79423i	−0.526685	+	0.912245i	0.472831	+	0.881153i	$0.343232\pi$
$73$	−4.50000	+	7.79423i	−0.526685	+	0.912245i	−0.999517	+	0.0310925i	$0.990101\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$		0			0
$76$	0.500000	−	4.33013i	0.0573539	−	0.496700i
$77$	6.00000			0.683763
$78$	3.00000	−	5.19615i	0.339683	−	0.588348i
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.50000	−	4.33013i	−0.276079	−	0.478183i
$83$	11.0000			1.20741			0.603703	−	0.797209i	$-0.293691\pi$
$83$	11.0000			1.20741			0.603703	+	0.797209i	$0.293691\pi$
$84$	−2.00000			−0.218218
$85$		0			0
$86$		0			0
$87$	−2.00000			−0.214423
$88$	−3.00000			−0.319801
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	−0.951584	−	0.307389i	$-0.900545\pi$
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	0.209585	−	0.977790i	$-0.432789\pi$
$90$		0			0
$91$	−6.00000	−	10.3923i	−0.628971	−	1.08941i
$92$	−4.00000	+	6.92820i	−0.417029	+	0.722315i
$93$	4.00000	−	6.92820i	0.414781	−	0.718421i
$94$	6.00000			0.618853
$95$		0			0
$96$	1.00000			0.102062
$97$	−7.50000	+	12.9904i	−0.761510	+	1.31897i	0.180563	+	0.983563i	$0.442208\pi$
$97$	−7.50000	+	12.9904i	−0.761510	+	1.31897i	−0.942072	+	0.335410i	$0.891125\pi$
$98$	1.50000	−	2.59808i	0.151523	−	0.262445i
$99$	−3.00000	−	5.19615i	−0.301511	−	0.522233i
$100$		0			0
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	0.999996	−	0.00286291i	$-0.000911295\pi$
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	−0.502477	+	0.864590i	$0.667578\pi$
$102$	−2.00000			−0.198030
$103$	−6.00000			−0.591198			−0.295599	−	0.955312i	$-0.595519\pi$
$103$	−6.00000			−0.591198			−0.295599	+	0.955312i	$0.595519\pi$
$104$	3.00000	+	5.19615i	0.294174	+	0.509525i
$105$		0			0
$106$	−6.00000			−0.582772
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$	2.50000	+	4.33013i	0.240563	+	0.416667i
$109$	4.00000	−	6.92820i	0.383131	−	0.663602i	−0.608377	−	0.793648i	$-0.708179\pi$
$109$	4.00000	−	6.92820i	0.383131	−	0.663602i	0.991508	+	0.130046i	$0.0415126\pi$
$110$		0			0
$111$	4.00000	−	6.92820i	0.379663	−	0.657596i
$112$	1.00000	−	1.73205i	0.0944911	−	0.163663i
$113$	13.0000			1.22294			0.611469	−	0.791269i	$-0.290579\pi$
$113$	13.0000			1.22294			0.611469	+	0.791269i	$0.290579\pi$
$114$	0.500000	−	4.33013i	0.0468293	−	0.405554i
$115$		0			0
$116$	1.00000	−	1.73205i	0.0928477	−	0.160817i
$117$	−6.00000	+	10.3923i	−0.554700	+	0.960769i
$118$	−2.50000	−	4.33013i	−0.230144	−	0.398621i
$119$	−2.00000	+	3.46410i	−0.183340	+	0.317554i
$120$		0			0
$121$	−2.00000			−0.181818
$122$	14.0000			1.26750
$123$	−2.50000	−	4.33013i	−0.225417	−	0.390434i
$124$	4.00000	+	6.92820i	0.359211	+	0.622171i
$125$		0			0
$126$	4.00000			0.356348
$127$	3.00000	+	5.19615i	0.266207	+	0.461084i	0.967879	−	0.251416i	$-0.0808962\pi$
$127$	3.00000	+	5.19615i	0.266207	+	0.461084i	−0.701672	+	0.712500i	$0.747563\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	−3.50000	+	6.06218i	−0.305796	+	0.529655i	−0.977438	−	0.211221i	$-0.932256\pi$
$131$	−3.50000	+	6.06218i	−0.305796	+	0.529655i	0.671642	+	0.740876i	$0.265589\pi$
$132$	−3.00000			−0.261116
$133$	−7.00000	−	5.19615i	−0.606977	−	0.450564i
$134$	5.00000			0.431934
$135$		0			0
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$	−4.00000	+	6.92820i	−0.340503	+	0.589768i
$139$	−4.50000	−	7.79423i	−0.381685	−	0.661098i	0.609618	−	0.792695i	$-0.291323\pi$
$139$	−4.50000	−	7.79423i	−0.381685	−	0.661098i	−0.991303	+	0.131597i	$0.957989\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$	3.00000	+	5.19615i	0.251754	+	0.436051i
$143$	−9.00000	−	15.5885i	−0.752618	−	1.30357i
$144$	−2.00000			−0.166667
$145$		0			0
$146$	−4.50000	−	7.79423i	−0.372423	−	0.645055i
$147$	1.50000	−	2.59808i	0.123718	−	0.214286i
$148$	4.00000	+	6.92820i	0.328798	+	0.569495i
$149$	−2.00000	+	3.46410i	−0.163846	+	0.283790i	−0.936245	−	0.351348i	$-0.885723\pi$
$149$	−2.00000	+	3.46410i	−0.163846	+	0.283790i	0.772399	+	0.635138i	$0.219057\pi$
$150$		0			0
$151$	12.0000			0.976546			0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000			0.976546			0.488273	+	0.872691i	$0.337627\pi$
$152$	3.50000	+	2.59808i	0.283887	+	0.210732i
$153$	4.00000			0.323381
$154$	−3.00000	+	5.19615i	−0.241747	+	0.418718i
$155$		0			0
$156$	3.00000	+	5.19615i	0.240192	+	0.416025i
$157$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$157$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$158$	−4.00000	−	6.92820i	−0.318223	−	0.551178i
$159$	−6.00000			−0.475831
$160$		0			0
$161$	8.00000	+	13.8564i	0.630488	+	1.09204i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−3.00000			−0.234978			−0.117489	−	0.993074i	$-0.537485\pi$
$163$	−3.00000			−0.234978			−0.117489	+	0.993074i	$0.537485\pi$
$164$	5.00000			0.390434
$165$		0			0
$166$	−5.50000	+	9.52628i	−0.426883	+	0.739383i
$167$	4.00000	+	6.92820i	0.309529	+	0.536120i	0.978259	−	0.207385i	$-0.0664952\pi$
$167$	4.00000	+	6.92820i	0.309529	+	0.536120i	−0.668730	+	0.743505i	$0.733162\pi$
$168$	1.00000	−	1.73205i	0.0771517	−	0.133631i
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$		0			0
$171$	−1.00000	+	8.66025i	−0.0764719	+	0.662266i
$172$		0			0
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	0.289412	+	0.957205i	$0.406540\pi$
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	−0.973670	+	0.227964i	$0.926793\pi$
$174$	1.00000	−	1.73205i	0.0758098	−	0.131306i
$175$		0			0
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	−2.50000	−	4.33013i	−0.187912	−	0.325472i
$178$	14.0000			1.04934
$179$	3.00000			0.224231			0.112115	−	0.993695i	$-0.464237\pi$
$179$	3.00000			0.224231			0.112115	+	0.993695i	$0.464237\pi$
$180$		0			0
$181$	8.00000	+	13.8564i	0.594635	+	1.02994i	0.993598	+	0.112972i	$0.0360369\pi$
$181$	8.00000	+	13.8564i	0.594635	+	1.02994i	−0.398963	+	0.916967i	$0.630630\pi$
$182$	12.0000			0.889499
$183$	14.0000			1.03491
$184$	−4.00000	−	6.92820i	−0.294884	−	0.510754i
$185$		0			0
$186$	4.00000	+	6.92820i	0.293294	+	0.508001i
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$	−3.00000	+	5.19615i	−0.218797	+	0.378968i
$189$	10.0000			0.727393
$190$		0			0
$191$	−4.00000			−0.289430			−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000			−0.289430			−0.144715	+	0.989473i	$0.546227\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	−0.628037	−	0.778183i	$-0.716141\pi$
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	0.987945	+	0.154805i	$0.0494748\pi$
$194$	−7.50000	−	12.9904i	−0.538469	−	0.932655i
$195$		0			0
$196$	1.50000	+	2.59808i	0.107143	+	0.185577i
$197$	−8.00000			−0.569976			−0.284988	−	0.958531i	$-0.591990\pi$
$197$	−8.00000			−0.569976			−0.284988	+	0.958531i	$0.591990\pi$
$198$	6.00000			0.426401
$199$	11.0000	+	19.0526i	0.779769	+	1.35060i	0.932075	+	0.362267i	$0.117997\pi$
$199$	11.0000	+	19.0526i	0.779769	+	1.35060i	−0.152305	+	0.988334i	$0.548670\pi$
$200$		0			0
$201$	5.00000			0.352673
$202$	−10.0000			−0.703598
$203$	−2.00000	−	3.46410i	−0.140372	−	0.243132i
$204$	1.00000	−	1.73205i	0.0700140	−	0.121268i
$205$		0			0
$206$	3.00000	−	5.19615i	0.209020	−	0.362033i
$207$	8.00000	−	13.8564i	0.556038	−	0.963087i
$208$	−6.00000			−0.416025
$209$	−10.5000	−	7.79423i	−0.726300	−	0.539138i
$210$		0			0
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$	3.00000	+	5.19615i	0.205557	+	0.356034i
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$		0			0
$216$	−5.00000			−0.340207
$217$	16.0000			1.08615
$218$	4.00000	+	6.92820i	0.270914	+	0.469237i
$219$	−4.50000	−	7.79423i	−0.304082	−	0.526685i
$220$		0			0
$221$	12.0000			0.807207
$222$	4.00000	+	6.92820i	0.268462	+	0.464991i
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	0.463409	+	0.886145i	$0.346626\pi$
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	−0.999128	+	0.0417488i	$0.986707\pi$
$224$	1.00000	+	1.73205i	0.0668153	+	0.115728i
$225$		0			0
$226$	−6.50000	+	11.2583i	−0.432374	+	0.748893i
$227$	7.00000			0.464606			0.232303	−	0.972643i	$-0.425374\pi$
$227$	7.00000			0.464606			0.232303	+	0.972643i	$0.425374\pi$
$228$	3.50000	+	2.59808i	0.231793	+	0.172062i
$229$	−24.0000			−1.58596			−0.792982	−	0.609245i	$-0.791473\pi$
$229$	−24.0000			−1.58596			−0.792982	+	0.609245i	$0.791473\pi$
$230$		0			0
$231$	−3.00000	+	5.19615i	−0.197386	+	0.341882i
$232$	1.00000	+	1.73205i	0.0656532	+	0.113715i
$233$	5.50000	−	9.52628i	0.360317	−	0.624087i	−0.627696	−	0.778459i	$-0.716002\pi$
$233$	5.50000	−	9.52628i	0.360317	−	0.624087i	0.988013	+	0.154371i	$0.0493352\pi$
$234$	−6.00000	−	10.3923i	−0.392232	−	0.679366i
$235$		0			0
$236$	5.00000			0.325472
$237$	−4.00000	−	6.92820i	−0.259828	−	0.450035i
$238$	−2.00000	−	3.46410i	−0.129641	−	0.224544i
$239$	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
$241$	9.50000	+	16.4545i	0.611949	+	1.05993i	0.990912	+	0.134515i	$0.0429475\pi$
$241$	9.50000	+	16.4545i	0.611949	+	1.05993i	−0.378963	+	0.925412i	$0.623719\pi$
$242$	1.00000	−	1.73205i	0.0642824	−	0.111340i
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	−7.00000	+	12.1244i	−0.448129	+	0.776182i
$245$		0			0
$246$	5.00000			0.318788
$247$	−3.00000	+	25.9808i	−0.190885	+	1.65312i
$248$	−8.00000			−0.508001
$249$	−5.50000	+	9.52628i	−0.348548	+	0.603703i
$250$		0			0
$251$	8.50000	+	14.7224i	0.536515	+	0.929272i	0.999088	+	0.0426905i	$0.0135929\pi$
$251$	8.50000	+	14.7224i	0.536515	+	0.929272i	−0.462573	+	0.886581i	$0.653074\pi$
$252$	−2.00000	+	3.46410i	−0.125988	+	0.218218i
$253$	12.0000	+	20.7846i	0.754434	+	1.30672i
$254$	−6.00000			−0.376473
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$		0			0
$259$	16.0000			0.994192
$260$		0			0
$261$	−2.00000	+	3.46410i	−0.123797	+	0.214423i
$262$	−3.50000	−	6.06218i	−0.216231	−	0.374523i
$263$	−13.0000	+	22.5167i	−0.801614	+	1.38844i	0.116939	+	0.993139i	$0.462692\pi$
$263$	−13.0000	+	22.5167i	−0.801614	+	1.38844i	−0.918553	+	0.395298i	$0.870641\pi$
$264$	1.50000	−	2.59808i	0.0923186	−	0.159901i
$265$		0			0
$266$	8.00000	−	3.46410i	0.490511	−	0.212398i
$267$	14.0000			0.856786
$268$	−2.50000	+	4.33013i	−0.152712	+	0.264505i
$269$	14.0000	−	24.2487i	0.853595	−	1.47847i	−0.0243472	−	0.999704i	$-0.507751\pi$
$269$	14.0000	−	24.2487i	0.853595	−	1.47847i	0.877942	−	0.478766i	$-0.158916\pi$
$270$		0			0
$271$	11.0000	−	19.0526i	0.668202	−	1.15736i	−0.310204	−	0.950670i	$-0.600397\pi$
$271$	11.0000	−	19.0526i	0.668202	−	1.15736i	0.978406	−	0.206691i	$-0.0662693\pi$
$272$	1.00000	+	1.73205i	0.0606339	+	0.105021i
$273$	12.0000			0.726273
$274$	3.00000			0.181237
$275$		0			0
$276$	−4.00000	−	6.92820i	−0.240772	−	0.417029i
$277$	14.0000			0.841178			0.420589	−	0.907251i	$-0.361823\pi$
$277$	14.0000			0.841178			0.420589	+	0.907251i	$0.361823\pi$
$278$	9.00000			0.539784
$279$	−8.00000	−	13.8564i	−0.478947	−	0.829561i
$280$		0			0
$281$	−3.50000	−	6.06218i	−0.208792	−	0.361639i	0.742542	−	0.669800i	$-0.233620\pi$
$281$	−3.50000	−	6.06218i	−0.208792	−	0.361639i	−0.951334	+	0.308160i	$0.900287\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$	−14.5000	+	25.1147i	−0.861936	+	1.49292i	0.00812260	+	0.999967i	$0.497414\pi$
$283$	−14.5000	+	25.1147i	−0.861936	+	1.49292i	−0.870058	+	0.492949i	$0.835919\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$	18.0000			1.06436
$287$	5.00000	−	8.66025i	0.295141	−	0.511199i
$288$	1.00000	−	1.73205i	0.0589256	−	0.102062i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	−7.50000	−	12.9904i	−0.439658	−	0.761510i
$292$	9.00000			0.526685
$293$	−22.0000			−1.28525			−0.642627	−	0.766179i	$-0.722155\pi$
$293$	−22.0000			−1.28525			−0.642627	+	0.766179i	$0.722155\pi$
$294$	1.50000	+	2.59808i	0.0874818	+	0.151523i
$295$		0			0
$296$	−8.00000			−0.464991
$297$	15.0000			0.870388
$298$	−2.00000	−	3.46410i	−0.115857	−	0.200670i
$299$	24.0000	−	41.5692i	1.38796	−	2.40401i
$300$		0			0
$301$		0			0
$302$	−6.00000	+	10.3923i	−0.345261	+	0.598010i
$303$	−10.0000			−0.574485
$304$	−4.00000	+	1.73205i	−0.229416	+	0.0993399i
$305$		0			0
$306$	−2.00000	+	3.46410i	−0.114332	+	0.198030i
$307$	−2.50000	+	4.33013i	−0.142683	+	0.247133i	−0.928506	−	0.371318i	$-0.878906\pi$
$307$	−2.50000	+	4.33013i	−0.142683	+	0.247133i	0.785823	+	0.618451i	$0.212239\pi$
$308$	−3.00000	−	5.19615i	−0.170941	−	0.296078i
$309$	3.00000	−	5.19615i	0.170664	−	0.295599i
$310$		0			0
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$	−6.00000			−0.339683
$313$	6.50000	+	11.2583i	0.367402	+	0.636358i	0.989158	−	0.146852i	$-0.0469141\pi$
$313$	6.50000	+	11.2583i	0.367402	+	0.636358i	−0.621757	+	0.783210i	$0.713581\pi$
$314$		0			0
$315$		0			0
$316$	8.00000			0.450035
$317$	−15.0000	−	25.9808i	−0.842484	−	1.45922i	−0.887788	−	0.460252i	$-0.847759\pi$
$317$	−15.0000	−	25.9808i	−0.842484	−	1.45922i	0.0453045	−	0.998973i	$-0.485574\pi$
$318$	3.00000	−	5.19615i	0.168232	−	0.291386i
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$		0			0
$321$	−6.00000	+	10.3923i	−0.334887	+	0.580042i
$322$	−16.0000			−0.891645
$323$	8.00000	−	3.46410i	0.445132	−	0.192748i
$324$	1.00000			0.0555556
$325$		0			0
$326$	1.50000	−	2.59808i	0.0830773	−	0.143894i
$327$	4.00000	+	6.92820i	0.221201	+	0.383131i
$328$	−2.50000	+	4.33013i	−0.138039	+	0.239091i
$329$	6.00000	+	10.3923i	0.330791	+	0.572946i
$330$		0			0
$331$	−17.0000			−0.934405			−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000			−0.934405			−0.467202	+	0.884150i	$0.654738\pi$
$332$	−5.50000	−	9.52628i	−0.301852	−	0.522823i
$333$	−8.00000	−	13.8564i	−0.438397	−	0.759326i
$334$	−8.00000			−0.437741
$335$		0			0
$336$	1.00000	+	1.73205i	0.0545545	+	0.0944911i
$337$	9.50000	−	16.4545i	0.517498	−	0.896333i	−0.482295	−	0.876009i	$-0.660197\pi$
$337$	9.50000	−	16.4545i	0.517498	−	0.896333i	0.999793	−	0.0203242i	$-0.00646983\pi$
$338$	−11.5000	−	19.9186i	−0.625518	−	1.08343i
$339$	−6.50000	+	11.2583i	−0.353032	+	0.611469i
$340$		0			0
$341$	24.0000			1.29967
$342$	−7.00000	−	5.19615i	−0.378517	−	0.280976i
$343$	20.0000			1.07990
$344$		0			0
$345$		0			0
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	−13.5000	+	23.3827i	−0.724718	+	1.25525i	0.234372	+	0.972147i	$0.424697\pi$
$347$	−13.5000	+	23.3827i	−0.724718	+	1.25525i	−0.959090	+	0.283101i	$0.908637\pi$
$348$	1.00000	+	1.73205i	0.0536056	+	0.0928477i
$349$	16.0000			0.856460			0.428230	−	0.903670i	$-0.359137\pi$
$349$	16.0000			0.856460			0.428230	+	0.903670i	$0.359137\pi$
$350$		0			0
$351$	−15.0000	−	25.9808i	−0.800641	−	1.38675i
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	21.0000			1.11772			0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000			1.11772			0.558859	+	0.829263i	$0.311239\pi$
$354$	5.00000			0.265747
$355$		0			0
$356$	−7.00000	+	12.1244i	−0.370999	+	0.642590i
$357$	−2.00000	−	3.46410i	−0.105851	−	0.183340i
$358$	−1.50000	+	2.59808i	−0.0792775	+	0.137313i
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	0.353529	+	0.935423i	$0.384981\pi$
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	−0.986865	+	0.161546i	$0.948352\pi$
$360$		0			0
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$	−16.0000			−0.840941
$363$	1.00000	−	1.73205i	0.0524864	−	0.0909091i
$364$	−6.00000	+	10.3923i	−0.314485	+	0.544705i
$365$		0			0
$366$	−7.00000	+	12.1244i	−0.365896	+	0.633750i
$367$	−14.0000	−	24.2487i	−0.730794	−	1.26577i	−0.956544	−	0.291587i	$-0.905817\pi$
$367$	−14.0000	−	24.2487i	−0.730794	−	1.26577i	0.225750	−	0.974185i	$-0.427517\pi$
$368$	8.00000			0.417029
$369$	−10.0000			−0.520579
$370$		0			0
$371$	−6.00000	−	10.3923i	−0.311504	−	0.539542i
$372$	−8.00000			−0.414781
$373$	24.0000			1.24267			0.621336	−	0.783544i	$-0.286590\pi$
$373$	24.0000			1.24267			0.621336	+	0.783544i	$0.286590\pi$
$374$	−3.00000	−	5.19615i	−0.155126	−	0.268687i
$375$		0			0
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	−6.00000	+	10.3923i	−0.309016	+	0.535231i
$378$	−5.00000	+	8.66025i	−0.257172	+	0.445435i
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$	−6.00000			−0.307389
$382$	2.00000	−	3.46410i	0.102329	−	0.177239i
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	−0.779143	−	0.626846i	$-0.784346\pi$
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	0.932436	+	0.361335i	$0.117679\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$		0			0
$386$	5.00000	+	8.66025i	0.254493	+	0.440795i
$387$		0			0
$388$	15.0000			0.761510
$389$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$389$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$	−3.00000			−0.151523
$393$	−3.50000	−	6.06218i	−0.176552	−	0.305796i
$394$	4.00000	−	6.92820i	0.201517	−	0.349038i
$395$		0			0
$396$	−3.00000	+	5.19615i	−0.150756	+	0.261116i
$397$	8.00000	−	13.8564i	0.401508	−	0.695433i	−0.592400	−	0.805644i	$-0.701819\pi$
$397$	8.00000	−	13.8564i	0.401508	−	0.695433i	0.993908	+	0.110211i	$0.0351527\pi$
$398$	−22.0000			−1.10276
$399$	8.00000	−	3.46410i	0.400501	−	0.173422i
$400$		0			0
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$	−2.50000	+	4.33013i	−0.124689	+	0.215967i
$403$	−24.0000	−	41.5692i	−1.19553	−	2.07071i
$404$	5.00000	−	8.66025i	0.248759	−	0.430864i
$405$		0			0
$406$	4.00000			0.198517
$407$	24.0000			1.18964
$408$	1.00000	+	1.73205i	0.0495074	+	0.0857493i
$409$	9.50000	+	16.4545i	0.469745	+	0.813622i	0.999402	−	0.0345902i	$-0.0110126\pi$
$409$	9.50000	+	16.4545i	0.469745	+	0.813622i	−0.529657	+	0.848212i	$0.677679\pi$
$410$		0			0
$411$	3.00000			0.147979
$412$	3.00000	+	5.19615i	0.147799	+	0.255996i
$413$	5.00000	−	8.66025i	0.246034	−	0.426143i
$414$	8.00000	+	13.8564i	0.393179	+	0.681005i
$415$		0			0
$416$	3.00000	−	5.19615i	0.147087	−	0.254762i
$417$	9.00000			0.440732
$418$	12.0000	−	5.19615i	0.586939	−	0.254152i
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$		0			0
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	−0.751935	−	0.659237i	$-0.770879\pi$
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	0.946883	+	0.321577i	$0.104213\pi$
$422$	2.00000	+	3.46410i	0.0973585	+	0.168630i
$423$	6.00000	−	10.3923i	0.291730	−	0.505291i
$424$	3.00000	+	5.19615i	0.145693	+	0.252347i
$425$		0			0
$426$	−6.00000			−0.290701
$427$	14.0000	+	24.2487i	0.677507	+	1.17348i
$428$	−6.00000	−	10.3923i	−0.290021	−	0.502331i
$429$	18.0000			0.869048
$430$		0			0
$431$	3.00000	+	5.19615i	0.144505	+	0.250290i	0.929188	−	0.369607i	$-0.120508\pi$
$431$	3.00000	+	5.19615i	0.144505	+	0.250290i	−0.784683	+	0.619897i	$0.787174\pi$
$432$	2.50000	−	4.33013i	0.120281	−	0.208333i
$433$	15.0000	+	25.9808i	0.720854	+	1.24856i	0.960658	+	0.277734i	$0.0895835\pi$
$433$	15.0000	+	25.9808i	0.720854	+	1.24856i	−0.239804	+	0.970821i	$0.577083\pi$
$434$	−8.00000	+	13.8564i	−0.384012	+	0.665129i
$435$		0			0
$436$	−8.00000			−0.383131
$437$	4.00000	−	34.6410i	0.191346	−	1.65710i
$438$	9.00000			0.430037
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$		0			0
$441$	−3.00000	−	5.19615i	−0.142857	−	0.247436i
$442$	−6.00000	+	10.3923i	−0.285391	+	0.494312i
$443$	−4.50000	−	7.79423i	−0.213801	−	0.370315i	0.739100	−	0.673596i	$-0.235251\pi$
$443$	−4.50000	−	7.79423i	−0.213801	−	0.370315i	−0.952901	+	0.303281i	$0.901918\pi$
$444$	−8.00000			−0.379663
$445$		0			0
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$	−2.00000	−	3.46410i	−0.0945968	−	0.163846i
$448$	−2.00000			−0.0944911
$449$	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
$451$	7.50000	−	12.9904i	0.353161	−	0.611693i
$452$	−6.50000	−	11.2583i	−0.305734	−	0.529547i
$453$	−6.00000	+	10.3923i	−0.281905	+	0.488273i
$454$	−3.50000	+	6.06218i	−0.164263	+	0.284512i
$455$		0			0
$456$	−4.00000	+	1.73205i	−0.187317	+	0.0811107i
$457$	−13.0000			−0.608114			−0.304057	−	0.952654i	$-0.598341\pi$
$457$	−13.0000			−0.608114			−0.304057	+	0.952654i	$0.598341\pi$
$458$	12.0000	−	20.7846i	0.560723	−	0.971201i
$459$	−5.00000	+	8.66025i	−0.233380	+	0.404226i
$460$		0			0
$461$	11.0000	−	19.0526i	0.512321	−	0.887366i	−0.487577	−	0.873080i	$-0.662119\pi$
$461$	11.0000	−	19.0526i	0.512321	−	0.887366i	0.999898	−	0.0142861i	$-0.00454755\pi$
$462$	−3.00000	−	5.19615i	−0.139573	−	0.241747i
$463$	−34.0000			−1.58011			−0.790057	−	0.613033i	$-0.789949\pi$
$463$	−34.0000			−1.58011			−0.790057	+	0.613033i	$0.789949\pi$
$464$	−2.00000			−0.0928477
$465$		0			0
$466$	5.50000	+	9.52628i	0.254783	+	0.441296i
$467$	−7.00000			−0.323921			−0.161961	−	0.986797i	$-0.551782\pi$
$467$	−7.00000			−0.323921			−0.161961	+	0.986797i	$0.551782\pi$
$468$	12.0000			0.554700
$469$	5.00000	+	8.66025i	0.230879	+	0.399893i
$470$		0			0
$471$		0			0
$472$	−2.50000	+	4.33013i	−0.115072	+	0.199310i
$473$		0			0
$474$	8.00000			0.367452
$475$		0			0
$476$	4.00000			0.183340
$477$	−6.00000	+	10.3923i	−0.274721	+	0.475831i
$478$	−6.00000	+	10.3923i	−0.274434	+	0.475333i
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	0.695773	−	0.718262i	$-0.255062\pi$
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	−0.969920	+	0.243426i	$0.921729\pi$
$480$		0			0
$481$	−24.0000	−	41.5692i	−1.09431	−	1.89539i
$482$	−19.0000			−0.865426
$483$	−16.0000			−0.728025
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$		0			0
$486$	16.0000			0.725775
$487$	−4.00000			−0.181257			−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000			−0.181257			−0.0906287	+	0.995885i	$0.528888\pi$
$488$	−7.00000	−	12.1244i	−0.316875	−	0.548844i
$489$	1.50000	−	2.59808i	0.0678323	−	0.117489i
$490$		0			0
$491$	−10.0000	+	17.3205i	−0.451294	+	0.781664i	−0.998467	−	0.0553560i	$-0.982371\pi$
$491$	−10.0000	+	17.3205i	−0.451294	+	0.781664i	0.547173	+	0.837020i	$0.315704\pi$
$492$	−2.50000	+	4.33013i	−0.112709	+	0.195217i
$493$	4.00000			0.180151
$494$	−21.0000	−	15.5885i	−0.944835	−	0.701358i
$495$		0			0
$496$	4.00000	−	6.92820i	0.179605	−	0.311086i
$497$	−6.00000	+	10.3923i	−0.269137	+	0.466159i
$498$	−5.50000	−	9.52628i	−0.246461	−	0.426883i
$499$	−16.5000	+	28.5788i	−0.738641	+	1.27936i	0.214466	+	0.976732i	$0.431199\pi$
$499$	−16.5000	+	28.5788i	−0.738641	+	1.27936i	−0.953107	+	0.302633i	$0.902134\pi$
$500$		0			0
$501$	−8.00000			−0.357414
$502$	−17.0000			−0.758747
$503$	2.00000	+	3.46410i	0.0891756	+	0.154457i	0.907163	−	0.420780i	$-0.138243\pi$
$503$	2.00000	+	3.46410i	0.0891756	+	0.154457i	−0.817987	+	0.575236i	$0.804910\pi$
$504$	−2.00000	−	3.46410i	−0.0890871	−	0.154303i
$505$		0			0
$506$	−24.0000			−1.06693
$507$	−11.5000	−	19.9186i	−0.510733	−	0.884615i
$508$	3.00000	−	5.19615i	0.133103	−	0.230542i
$509$	−6.00000	−	10.3923i	−0.265945	−	0.460631i	0.701866	−	0.712309i	$-0.252351\pi$
$509$	−6.00000	−	10.3923i	−0.265945	−	0.460631i	−0.967811	+	0.251679i	$0.919017\pi$
$510$		0			0
$511$	9.00000	−	15.5885i	0.398137	−	0.689593i
$512$	1.00000			0.0441942
$513$	−17.5000	−	12.9904i	−0.772644	−	0.573539i
$514$	−3.00000			−0.132324
$515$		0			0
$516$		0			0
$517$	9.00000	+	15.5885i	0.395820	+	0.685580i
$518$	−8.00000	+	13.8564i	−0.351500	+	0.608816i
$519$	−9.00000	−	15.5885i	−0.395056	−	0.684257i
$520$		0			0
$521$	21.0000			0.920027			0.460013	−	0.887912i	$-0.347845\pi$
$521$	21.0000			0.920027			0.460013	+	0.887912i	$0.347845\pi$
$522$	−2.00000	−	3.46410i	−0.0875376	−	0.151620i
$523$	4.00000	+	6.92820i	0.174908	+	0.302949i	0.940129	−	0.340818i	$-0.110704\pi$
$523$	4.00000	+	6.92820i	0.174908	+	0.302949i	−0.765222	+	0.643767i	$0.777371\pi$
$524$	7.00000			0.305796
$525$		0			0
$526$	−13.0000	−	22.5167i	−0.566827	−	0.981773i
$527$	−8.00000	+	13.8564i	−0.348485	+	0.603595i
$528$	1.50000	+	2.59808i	0.0652791	+	0.113067i
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$		0			0
$531$	−10.0000			−0.433963
$532$	−1.00000	+	8.66025i	−0.0433555	+	0.375470i
$533$	−30.0000			−1.29944
$534$	−7.00000	+	12.1244i	−0.302920	+	0.524672i
$535$		0			0
$536$	−2.50000	−	4.33013i	−0.107984	−	0.187033i
$537$	−1.50000	+	2.59808i	−0.0647298	+	0.112115i
$538$	14.0000	+	24.2487i	0.603583	+	1.04544i
$539$	9.00000			0.387657
$540$		0			0
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$	11.0000	+	19.0526i	0.472490	+	0.818377i
$543$	−16.0000			−0.686626
$544$	−2.00000			−0.0857493
$545$		0			0
$546$	−6.00000	+	10.3923i	−0.256776	+	0.444750i
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	0.767752	−	0.640747i	$-0.221375\pi$
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	−0.938779	+	0.344519i	$0.888042\pi$
$548$	−1.50000	+	2.59808i	−0.0640768	+	0.110984i
$549$	14.0000	−	24.2487i	0.597505	−	1.03491i
$550$		0			0
$551$	−1.00000	+	8.66025i	−0.0426014	+	0.368939i
$552$	8.00000			0.340503
$553$	8.00000	−	13.8564i	0.340195	−	0.589234i
$554$	−7.00000	+	12.1244i	−0.297402	+	0.515115i
$555$		0			0
$556$	−4.50000	+	7.79423i	−0.190843	+	0.330549i
$557$	−20.0000	−	34.6410i	−0.847427	−	1.46779i	−0.883497	−	0.468438i	$-0.844817\pi$
$557$	−20.0000	−	34.6410i	−0.847427	−	1.46779i	0.0360693	−	0.999349i	$-0.488516\pi$
$558$	16.0000			0.677334
$559$		0			0
$560$		0			0
$561$	−3.00000	−	5.19615i	−0.126660	−	0.219382i
$562$	7.00000			0.295277
$563$	23.0000			0.969334			0.484667	−	0.874699i	$-0.338941\pi$
$563$	23.0000			0.969334			0.484667	+	0.874699i	$0.338941\pi$
$564$	−3.00000	−	5.19615i	−0.126323	−	0.218797i
$565$		0			0
$566$	−14.5000	−	25.1147i	−0.609480	−	1.05565i
$567$	1.00000	−	1.73205i	0.0419961	−	0.0727393i
$568$	3.00000	−	5.19615i	0.125877	−	0.218026i
$569$	34.0000			1.42535			0.712677	−	0.701492i	$-0.247483\pi$
$569$	34.0000			1.42535			0.712677	+	0.701492i	$0.247483\pi$
$570$		0			0
$571$	−29.0000			−1.21361			−0.606806	−	0.794850i	$-0.707550\pi$
$571$	−29.0000			−1.21361			−0.606806	+	0.794850i	$0.707550\pi$
$572$	−9.00000	+	15.5885i	−0.376309	+	0.651786i
$573$	2.00000	−	3.46410i	0.0835512	−	0.144715i
$574$	5.00000	+	8.66025i	0.208696	+	0.361472i
$575$		0			0
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$	−7.00000			−0.291414			−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000			−0.291414			−0.145707	+	0.989328i	$0.546546\pi$
$578$	−13.0000			−0.540729
$579$	5.00000	+	8.66025i	0.207793	+	0.359908i
$580$		0			0
$581$	−22.0000			−0.912714
$582$	15.0000			0.621770
$583$	−9.00000	−	15.5885i	−0.372742	−	0.645608i
$584$	−4.50000	+	7.79423i	−0.186211	+	0.322527i
$585$		0			0
$586$	11.0000	−	19.0526i	0.454406	−	0.787054i
$587$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$587$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$588$	−3.00000			−0.123718
$589$	−28.0000	−	20.7846i	−1.15372	−	0.856415i
$590$		0			0
$591$	4.00000	−	6.92820i	0.164538	−	0.284988i
$592$	4.00000	−	6.92820i	0.164399	−	0.284747i
$593$	−6.50000	−	11.2583i	−0.266923	−	0.462324i	0.701143	−	0.713021i	$-0.252674\pi$
$593$	−6.50000	−	11.2583i	−0.266923	−	0.462324i	−0.968066	+	0.250697i	$0.919340\pi$
$594$	−7.50000	+	12.9904i	−0.307729	+	0.533002i
$595$		0			0
$596$	4.00000			0.163846
$597$	−22.0000			−0.900400
$598$	24.0000	+	41.5692i	0.981433	+	1.69989i
$599$	−24.0000	−	41.5692i	−0.980613	−	1.69847i	−0.660006	−	0.751260i	$-0.729446\pi$
$599$	−24.0000	−	41.5692i	−0.980613	−	1.69847i	−0.320607	−	0.947212i	$-0.603887\pi$
$600$		0			0
$601$	−37.0000			−1.50926			−0.754631	−	0.656150i	$-0.772184\pi$
$601$	−37.0000			−1.50926			−0.754631	+	0.656150i	$0.772184\pi$
$602$		0			0
$603$	5.00000	−	8.66025i	0.203616	−	0.352673i
$604$	−6.00000	−	10.3923i	−0.244137	−	0.422857i
$605$		0			0
$606$	5.00000	−	8.66025i	0.203111	−	0.351799i
$607$	14.0000			0.568242			0.284121	−	0.958788i	$-0.408298\pi$
$607$	14.0000			0.568242			0.284121	+	0.958788i	$0.408298\pi$
$608$	0.500000	−	4.33013i	0.0202777	−	0.175610i
$609$	4.00000			0.162088
$610$		0			0
$611$	18.0000	−	31.1769i	0.728202	−	1.26128i
$612$	−2.00000	−	3.46410i	−0.0808452	−	0.140028i
$613$	−17.0000	+	29.4449i	−0.686624	+	1.18927i	0.286300	+	0.958140i	$0.407575\pi$
$613$	−17.0000	+	29.4449i	−0.686624	+	1.18927i	−0.972924	+	0.231127i	$0.925759\pi$
$614$	−2.50000	−	4.33013i	−0.100892	−	0.174750i
$615$		0			0
$616$	6.00000			0.241747
$617$	9.50000	+	16.4545i	0.382456	+	0.662433i	0.991413	−	0.130771i	$-0.0417452\pi$
$617$	9.50000	+	16.4545i	0.382456	+	0.662433i	−0.608957	+	0.793203i	$0.708412\pi$
$618$	3.00000	+	5.19615i	0.120678	+	0.209020i
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$		0			0
$621$	20.0000	+	34.6410i	0.802572	+	1.39010i
$622$	12.0000	−	20.7846i	0.481156	−	0.833387i
$623$	14.0000	+	24.2487i	0.560898	+	0.971504i
$624$	3.00000	−	5.19615i	0.120096	−	0.208013i
$625$		0			0
$626$	−13.0000			−0.519584
$627$	12.0000	−	5.19615i	0.479234	−	0.207514i
$628$		0			0
$629$	−8.00000	+	13.8564i	−0.318981	+	0.552491i
$630$		0			0
$631$	15.0000	+	25.9808i	0.597141	+	1.03428i	0.993241	+	0.116071i	$0.0370299\pi$
$631$	15.0000	+	25.9808i	0.597141	+	1.03428i	−0.396100	+	0.918207i	$0.629637\pi$
$632$	−4.00000	+	6.92820i	−0.159111	+	0.275589i
$633$	2.00000	+	3.46410i	0.0794929	+	0.137686i
$634$	30.0000			1.19145
$635$		0			0
$636$	3.00000	+	5.19615i	0.118958	+	0.206041i
$637$	−9.00000	−	15.5885i	−0.356593	−	0.617637i
$638$	6.00000			0.237542
$639$	12.0000			0.474713
$640$		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	$0.302789\pi$
$642$	−6.00000	−	10.3923i	−0.236801	−	0.410152i
$643$	−2.50000	+	4.33013i	−0.0985904	+	0.170764i	−0.911101	−	0.412182i	$-0.864767\pi$
$643$	−2.50000	+	4.33013i	−0.0985904	+	0.170764i	0.812511	+	0.582946i	$0.198100\pi$
$644$	8.00000	−	13.8564i	0.315244	−	0.546019i
$645$		0			0
$646$	−1.00000	+	8.66025i	−0.0393445	+	0.340733i
$647$	−6.00000			−0.235884			−0.117942	−	0.993020i	$-0.537630\pi$
$647$	−6.00000			−0.235884			−0.117942	+	0.993020i	$0.537630\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	7.50000	−	12.9904i	0.294401	−	0.509917i
$650$		0			0
$651$	−8.00000	+	13.8564i	−0.313545	+	0.543075i
$652$	1.50000	+	2.59808i	0.0587445	+	0.101749i
$653$	36.0000			1.40879			0.704394	−	0.709809i	$-0.251219\pi$
$653$	36.0000			1.40879			0.704394	+	0.709809i	$0.251219\pi$
$654$	−8.00000			−0.312825
$655$		0			0
$656$	−2.50000	−	4.33013i	−0.0976086	−	0.169063i
$657$	−18.0000			−0.702247
$658$	−12.0000			−0.467809
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	0.958902	−	0.283738i	$-0.0915745\pi$
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	−0.725175	+	0.688565i	$0.758241\pi$
$660$		0			0
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	0.996682	−	0.0813955i	$-0.0259377\pi$
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	−0.568831	+	0.822454i	$0.692604\pi$
$662$	8.50000	−	14.7224i	0.330362	−	0.572204i
$663$	−6.00000	+	10.3923i	−0.233021	+	0.403604i
$664$	11.0000			0.426883
$665$		0			0
$666$	16.0000			0.619987
$667$	8.00000	−	13.8564i	0.309761	−	0.536522i
$668$	4.00000	−	6.92820i	0.154765	−	0.268060i
$669$	−8.00000	−	13.8564i	−0.309298	−	0.535720i
$670$		0			0
$671$	21.0000	+	36.3731i	0.810696	+	1.40417i
$672$	−2.00000			−0.0771517
$673$	−26.0000			−1.00223			−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000			−1.00223			−0.501113	+	0.865382i	$0.667076\pi$
$674$	9.50000	+	16.4545i	0.365926	+	0.633803i
$675$		0			0
$676$	23.0000			0.884615
$677$	2.00000			0.0768662			0.0384331	−	0.999261i	$-0.487763\pi$
$677$	2.00000			0.0768662			0.0384331	+	0.999261i	$0.487763\pi$
$678$	−6.50000	−	11.2583i	−0.249631	−	0.432374i
$679$	15.0000	−	25.9808i	0.575647	−	0.997050i
$680$		0			0
$681$	−3.50000	+	6.06218i	−0.134120	+	0.232303i
$682$	−12.0000	+	20.7846i	−0.459504	+	0.795884i
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$	8.00000	−	3.46410i	0.305888	−	0.132453i
$685$		0			0
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$	12.0000	−	20.7846i	0.457829	−	0.792982i
$688$		0			0
$689$	−18.0000	+	31.1769i	−0.685745	+	1.18775i
$690$		0			0
$691$	28.0000			1.06517			0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000			1.06517			0.532585	+	0.846376i	$0.321221\pi$
$692$	18.0000			0.684257
$693$	6.00000	+	10.3923i	0.227921	+	0.394771i
$694$	−13.5000	−	23.3827i	−0.512453	−	0.887595i
$695$		0			0
$696$	−2.00000			−0.0758098
$697$	5.00000	+	8.66025i	0.189389	+	0.328031i
$698$	−8.00000	+	13.8564i	−0.302804	+	0.524473i
$699$	5.50000	+	9.52628i	0.208029	+	0.360317i
$700$		0			0
$701$	21.0000	−	36.3731i	0.793159	−	1.37379i	−0.130843	−	0.991403i	$-0.541768\pi$
$701$	21.0000	−	36.3731i	0.793159	−	1.37379i	0.924002	−	0.382389i	$-0.124898\pi$
$702$	30.0000			1.13228
$703$	−28.0000	−	20.7846i	−1.05604	−	0.783906i
$704$	−3.00000			−0.113067
$705$		0			0
$706$	−10.5000	+	18.1865i	−0.395173	+	0.684459i
$707$	−10.0000	−	17.3205i	−0.376089	−	0.651405i
$708$	−2.50000	+	4.33013i	−0.0939558	+	0.162736i
$709$	−10.0000	−	17.3205i	−0.375558	−	0.650485i	0.614852	−	0.788642i	$-0.289216\pi$
$709$	−10.0000	−	17.3205i	−0.375558	−	0.650485i	−0.990410	+	0.138157i	$0.955882\pi$
$710$		0			0
$711$	−16.0000			−0.600047
$712$	−7.00000	−	12.1244i	−0.262336	−	0.454379i
$713$	32.0000	+	55.4256i	1.19841	+	2.07571i
$714$	4.00000			0.149696
$715$		0			0
$716$	−1.50000	−	2.59808i	−0.0560576	−	0.0970947i
$717$	−6.00000	+	10.3923i	−0.224074	+	0.388108i
$718$	−12.0000	−	20.7846i	−0.447836	−	0.775675i
$719$	−25.0000	+	43.3013i	−0.932343	+	1.61486i	−0.153037	+	0.988220i	$0.548906\pi$
$719$	−25.0000	+	43.3013i	−0.932343	+	1.61486i	−0.779305	+	0.626644i	$0.784428\pi$
$720$		0			0
$721$	12.0000			0.446903
$722$	−18.5000	−	4.33013i	−0.688499	−	0.161151i
$723$	−19.0000			−0.706618
$724$	8.00000	−	13.8564i	0.297318	−	0.514969i
$725$		0			0
$726$	1.00000	+	1.73205i	0.0371135	+	0.0642824i
$727$	4.00000	−	6.92820i	0.148352	−	0.256953i	−0.782267	−	0.622944i	$-0.785937\pi$
$727$	4.00000	−	6.92820i	0.148352	−	0.256953i	0.930618	+	0.365991i	$0.119270\pi$
$728$	−6.00000	−	10.3923i	−0.222375	−	0.385164i
$729$	13.0000			0.481481
$730$		0			0
$731$		0			0
$732$	−7.00000	−	12.1244i	−0.258727	−	0.448129i
$733$		0			0			−	1.00000i	$-0.5\pi$
$733$		0			0				1.00000i	$0.5\pi$
$734$	28.0000			1.03350
$735$		0			0
$736$	−4.00000	+	6.92820i	−0.147442	+	0.255377i
$737$	7.50000	+	12.9904i	0.276266	+	0.478507i
$738$	5.00000	−	8.66025i	0.184053	−	0.318788i
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	−0.908337	−	0.418238i	$-0.862648\pi$
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	0.816373	+	0.577524i	$0.195981\pi$
$740$		0			0
$741$	−21.0000	−	15.5885i	−0.771454	−	0.572656i
$742$	12.0000			0.440534
$743$	2.00000	−	3.46410i	0.0733729	−	0.127086i	−0.827005	−	0.562195i	$-0.809957\pi$
$743$	2.00000	−	3.46410i	0.0733729	−	0.127086i	0.900378	+	0.435110i	$0.143290\pi$
$744$	4.00000	−	6.92820i	0.146647	−	0.254000i
$745$		0			0
$746$	−12.0000	+	20.7846i	−0.439351	+	0.760979i
$747$	11.0000	+	19.0526i	0.402469	+	0.697097i
$748$	6.00000			0.219382
$749$	−24.0000			−0.876941
$750$		0			0
$751$	19.0000	+	32.9090i	0.693320	+	1.20087i	0.970744	+	0.240118i	$0.0771860\pi$
$751$	19.0000	+	32.9090i	0.693320	+	1.20087i	−0.277424	+	0.960748i	$0.589481\pi$
$752$	6.00000			0.218797
$753$	−17.0000			−0.619514
$754$	−6.00000	−	10.3923i	−0.218507	−	0.378465i
$755$		0			0
$756$	−5.00000	−	8.66025i	−0.181848	−	0.314970i
$757$	17.0000	−	29.4449i	0.617876	−	1.07019i	−0.371997	−	0.928234i	$-0.621327\pi$
$757$	17.0000	−	29.4449i	0.617876	−	1.07019i	0.989873	−	0.141958i	$-0.0453398\pi$
$758$	14.0000	−	24.2487i	0.508503	−	0.880753i
$759$	−24.0000			−0.871145
$760$		0			0
$761$	−3.00000			−0.108750			−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000			−0.108750			−0.0543750	+	0.998521i	$0.517317\pi$
$762$	3.00000	−	5.19615i	0.108679	−	0.188237i
$763$	−8.00000	+	13.8564i	−0.289619	+	0.501636i
$764$	2.00000	+	3.46410i	0.0723575	+	0.125327i
$765$		0			0
$766$	3.00000	+	5.19615i	0.108394	+	0.187745i
$767$	−30.0000			−1.08324
$768$	1.00000			0.0360844
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.825518	+	0.564376i	$0.190883\pi$
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.0760054	+	0.997107i	$0.475783\pi$
$770$		0			0
$771$	−3.00000			−0.108042
$772$	−10.0000			−0.359908
$773$	15.0000	+	25.9808i	0.539513	+	0.934463i	0.998930	+	0.0462427i	$0.0147248\pi$
$773$	15.0000	+	25.9808i	0.539513	+	0.934463i	−0.459418	+	0.888220i	$0.651942\pi$
$774$		0			0
$775$		0			0
$776$	−7.50000	+	12.9904i	−0.269234	+	0.466328i
$777$	−8.00000	+	13.8564i	−0.286998	+	0.497096i
$778$		0			0
$779$	−20.0000	+	8.66025i	−0.716574	+	0.310286i
$780$		0			0
$781$	−9.00000	+	15.5885i	−0.322045	+	0.557799i
$782$	8.00000	−	13.8564i	0.286079	−	0.495504i
$783$	−5.00000	−	8.66025i	−0.178685	−	0.309492i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$		0			0
$786$	7.00000			0.249682
$787$	1.00000			0.0356462			0.0178231	−	0.999841i	$-0.494326\pi$
$787$	1.00000			0.0356462			0.0178231	+	0.999841i	$0.494326\pi$
$788$	4.00000	+	6.92820i	0.142494	+	0.246807i
$789$	−13.0000	−	22.5167i	−0.462812	−	0.801614i
$790$		0			0
$791$	−26.0000			−0.924454
$792$	−3.00000	−	5.19615i	−0.106600	−	0.184637i
$793$	42.0000	−	72.7461i	1.49146	−	2.58329i
$794$	8.00000	+	13.8564i	0.283909	+	0.491745i
$795$		0			0
$796$	11.0000	−	19.0526i	0.389885	−	0.675300i
$797$	28.0000			0.991811			0.495905	−	0.868377i	$-0.334836\pi$
$797$	28.0000			0.991811			0.495905	+	0.868377i	$0.334836\pi$
$798$	−1.00000	+	8.66025i	−0.0353996	+	0.306570i
$799$	−12.0000			−0.424529
$800$		0			0
$801$	14.0000	−	24.2487i	0.494666	−	0.856786i
$802$	1.50000	+	2.59808i	0.0529668	+	0.0917413i
$803$	13.5000	−	23.3827i	0.476405	−	0.825157i
$804$	−2.50000	−	4.33013i	−0.0881682	−	0.152712i
$805$		0			0
$806$	48.0000			1.69073
$807$	14.0000	+	24.2487i	0.492823	+	0.853595i
$808$	5.00000	+	8.66025i	0.175899	+	0.304667i
$809$	−51.0000			−1.79306			−0.896532	−	0.442978i	$-0.853922\pi$
$809$	−51.0000			−1.79306			−0.896532	+	0.442978i	$0.853922\pi$
$810$		0			0
$811$	−10.0000	−	17.3205i	−0.351147	−	0.608205i	0.635303	−	0.772263i	$-0.280875\pi$
$811$	−10.0000	−	17.3205i	−0.351147	−	0.608205i	−0.986451	+	0.164057i	$0.947542\pi$
$812$	−2.00000	+	3.46410i	−0.0701862	+	0.121566i
$813$	11.0000	+	19.0526i	0.385787	+	0.668202i
$814$	−12.0000	+	20.7846i	−0.420600	+	0.728500i
$815$		0			0
$816$	−2.00000			−0.0700140
$817$		0			0
$818$	−19.0000			−0.664319
$819$	12.0000	−	20.7846i	0.419314	−	0.726273i
$820$		0			0
$821$	7.00000	+	12.1244i	0.244302	+	0.423143i	0.961935	−	0.273278i	$-0.0881079\pi$
$821$	7.00000	+	12.1244i	0.244302	+	0.423143i	−0.717633	+	0.696421i	$0.754775\pi$
$822$	−1.50000	+	2.59808i	−0.0523185	+	0.0906183i
$823$	1.00000	+	1.73205i	0.0348578	+	0.0603755i	0.882928	−	0.469508i	$-0.155569\pi$
$823$	1.00000	+	1.73205i	0.0348578	+	0.0603755i	−0.848070	+	0.529884i	$0.822235\pi$
$824$	−6.00000			−0.209020
$825$		0			0
$826$	5.00000	+	8.66025i	0.173972	+	0.301329i
$827$	13.5000	+	23.3827i	0.469441	+	0.813096i	0.999390	−	0.0349341i	$-0.0111221\pi$
$827$	13.5000	+	23.3827i	0.469441	+	0.813096i	−0.529949	+	0.848030i	$0.677789\pi$
$828$	−16.0000			−0.556038
$829$	48.0000			1.66711			0.833554	−	0.552437i	$-0.186302\pi$
$829$	48.0000			1.66711			0.833554	+	0.552437i	$0.186302\pi$
$830$		0			0
$831$	−7.00000	+	12.1244i	−0.242827	+	0.420589i
$832$	3.00000	+	5.19615i	0.104006	+	0.180144i
$833$	−3.00000	+	5.19615i	−0.103944	+	0.180036i
$834$	−4.50000	+	7.79423i	−0.155822	+	0.269892i
$835$		0			0
$836$	−1.50000	+	12.9904i	−0.0518786	+	0.449282i
$837$	40.0000			1.38260
$838$	−14.0000	+	24.2487i	−0.483622	+	0.837658i
$839$	−21.0000	+	36.3731i	−0.725001	+	1.25574i	0.233973	+	0.972243i	$0.424827\pi$
$839$	−21.0000	+	36.3731i	−0.725001	+	1.25574i	−0.958974	+	0.283495i	$0.908506\pi$
$840$		0			0
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$	4.00000	+	6.92820i	0.137849	+	0.238762i
$843$	7.00000			0.241093
$844$	−4.00000			−0.137686
$845$		0			0
$846$	6.00000	+	10.3923i	0.206284	+	0.357295i
$847$	4.00000			0.137442
$848$	−6.00000			−0.206041
$849$	−14.5000	−	25.1147i	−0.497639	−	0.861936i
$850$		0			0
$851$	32.0000	+	55.4256i	1.09695	+	1.89997i
$852$	3.00000	−	5.19615i	0.102778	−	0.178017i
$853$	−5.00000	+	8.66025i	−0.171197	+	0.296521i	−0.938839	−	0.344358i	$-0.888097\pi$
$853$	−5.00000	+	8.66025i	−0.171197	+	0.296521i	0.767642	+	0.640879i	$0.221430\pi$
$854$	−28.0000			−0.958140
$855$		0			0
$856$	12.0000			0.410152
$857$	−7.50000	+	12.9904i	−0.256195	+	0.443743i	−0.965219	−	0.261441i	$-0.915802\pi$
$857$	−7.50000	+	12.9904i	−0.256195	+	0.443743i	0.709024	+	0.705184i	$0.249136\pi$
$858$	−9.00000	+	15.5885i	−0.307255	+	0.532181i
$859$	−11.5000	−	19.9186i	−0.392375	−	0.679613i	0.600387	−	0.799709i	$-0.295013\pi$
$859$	−11.5000	−	19.9186i	−0.392375	−	0.679613i	−0.992762	+	0.120096i	$0.961680\pi$
$860$		0			0
$861$	5.00000	+	8.66025i	0.170400	+	0.295141i
$862$	−6.00000			−0.204361
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$	2.50000	+	4.33013i	0.0850517	+	0.147314i
$865$		0			0
$866$	−30.0000			−1.01944
$867$	−13.0000			−0.441503
$868$	−8.00000	−	13.8564i	−0.271538	−	0.470317i
$869$	12.0000	−	20.7846i	0.407072	−	0.705070i
$870$		0			0
$871$	15.0000	−	25.9808i	0.508256	−	0.880325i
$872$	4.00000	−	6.92820i	0.135457	−	0.234619i
$873$	−30.0000			−1.01535
$874$	28.0000	+	20.7846i	0.947114	+	0.703050i
$875$		0			0
$876$	−4.50000	+	7.79423i	−0.152041	+	0.263343i
$877$	−19.0000	+	32.9090i	−0.641584	+	1.11126i	0.343495	+	0.939155i	$0.388389\pi$
$877$	−19.0000	+	32.9090i	−0.641584	+	1.11126i	−0.985079	+	0.172102i	$0.944944\pi$
$878$	4.00000	+	6.92820i	0.134993	+	0.233816i
$879$	11.0000	−	19.0526i	0.371021	−	0.642627i
$880$		0			0
$881$	35.0000			1.17918			0.589590	−	0.807703i	$-0.299289\pi$
$881$	35.0000			1.17918			0.589590	+	0.807703i	$0.299289\pi$
$882$	6.00000			0.202031
$883$	11.5000	+	19.9186i	0.387006	+	0.670314i	0.992045	−	0.125882i	$-0.0401760\pi$
$883$	11.5000	+	19.9186i	0.387006	+	0.670314i	−0.605039	+	0.796196i	$0.706843\pi$
$884$	−6.00000	−	10.3923i	−0.201802	−	0.349531i
$885$		0			0
$886$	9.00000			0.302361
$887$	2.00000	+	3.46410i	0.0671534	+	0.116313i	0.897647	−	0.440715i	$-0.145275\pi$
$887$	2.00000	+	3.46410i	0.0671534	+	0.116313i	−0.830494	+	0.557028i	$0.811942\pi$
$888$	4.00000	−	6.92820i	0.134231	−	0.232495i
$889$	−6.00000	−	10.3923i	−0.201234	−	0.348547i
$890$		0			0
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$	16.0000			0.535720
$893$	3.00000	−	25.9808i	0.100391	−	0.869413i
$894$	4.00000			0.133780
$895$		0			0
$896$	1.00000	−	1.73205i	0.0334077	−	0.0578638i
$897$	24.0000	+	41.5692i	0.801337	+	1.38796i
$898$	−14.5000	+	25.1147i	−0.483871	+	0.838090i
$899$	−8.00000	−	13.8564i	−0.266815	−	0.462137i
$900$		0			0
$901$	12.0000			0.399778
$902$	7.50000	+	12.9904i	0.249723	+	0.432532i
$903$		0			0
$904$	13.0000			0.432374
$905$		0			0
$906$	−6.00000	−	10.3923i	−0.199337	−	0.345261i
$907$	23.5000	−	40.7032i	0.780305	−	1.35153i	−0.151460	−	0.988463i	$-0.548397\pi$
$907$	23.5000	−	40.7032i	0.780305	−	1.35153i	0.931764	−	0.363064i	$-0.118269\pi$
$908$	−3.50000	−	6.06218i	−0.116152	−	0.201180i
$909$	−10.0000	+	17.3205i	−0.331679	+	0.574485i
$910$		0			0
$911$	−32.0000			−1.06021			−0.530104	−	0.847933i	$-0.677847\pi$
$911$	−32.0000			−1.06021			−0.530104	+	0.847933i	$0.677847\pi$
$912$	0.500000	−	4.33013i	0.0165567	−	0.143385i
$913$	−33.0000			−1.09214
$914$	6.50000	−	11.2583i	0.215001	−	0.372392i
$915$		0			0
$916$	12.0000	+	20.7846i	0.396491	+	0.686743i
$917$	7.00000	−	12.1244i	0.231160	−	0.400381i
$918$	−5.00000	−	8.66025i	−0.165025	−	0.285831i
$919$	14.0000			0.461817			0.230909	−	0.972975i	$-0.425830\pi$
$919$	14.0000			0.461817			0.230909	+	0.972975i	$0.425830\pi$
$920$		0			0
$921$	−2.50000	−	4.33013i	−0.0823778	−	0.142683i
$922$	11.0000	+	19.0526i	0.362266	+	0.627463i
$923$	36.0000			1.18495
$924$	6.00000			0.197386
$925$		0			0
$926$	17.0000	−	29.4449i	0.558655	−	0.967618i
$927$	−6.00000	−	10.3923i	−0.197066	−	0.341328i
$928$	1.00000	−	1.73205i	0.0328266	−	0.0568574i
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	−0.554984	−	0.831861i	$-0.687276\pi$
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	0.997905	+	0.0646999i	$0.0206090\pi$
$930$		0			0
$931$	−10.5000	−	7.79423i	−0.344124	−	0.255446i
$932$	−11.0000			−0.360317
$933$	12.0000	−	20.7846i	0.392862	−	0.680458i
$934$	3.50000	−	6.06218i	0.114523	−	0.198361i
$935$		0			0
$936$	−6.00000	+	10.3923i	−0.196116	+	0.339683i
$937$	17.5000	+	30.3109i	0.571700	+	0.990214i	0.996392	+	0.0848755i	$0.0270492\pi$
$937$	17.5000	+	30.3109i	0.571700	+	0.990214i	−0.424691	+	0.905338i	$0.639617\pi$
$938$	−10.0000			−0.326512
$939$	−13.0000			−0.424239
$940$		0			0
$941$	−19.0000	−	32.9090i	−0.619382	−	1.07280i	−0.989599	−	0.143856i	$-0.954050\pi$
$941$	−19.0000	−	32.9090i	−0.619382	−	1.07280i	0.370216	−	0.928946i	$-0.379284\pi$
$942$		0			0
$943$	40.0000			1.30258
$944$	−2.50000	−	4.33013i	−0.0813681	−	0.140934i
$945$		0			0
$946$		0			0
$947$	−26.0000	+	45.0333i	−0.844886	+	1.46339i	0.0408333	+	0.999166i	$0.486999\pi$
$947$	−26.0000	+	45.0333i	−0.844886	+	1.46339i	−0.885720	+	0.464220i	$0.846335\pi$
$948$	−4.00000	+	6.92820i	−0.129914	+	0.225018i
$949$	−54.0000			−1.75291
$950$		0			0
$951$	30.0000			0.972817
$952$	−2.00000	+	3.46410i	−0.0648204	+	0.112272i
$953$	−3.50000	+	6.06218i	−0.113376	+	0.196373i	−0.917129	−	0.398589i	$-0.869500\pi$
$953$	−3.50000	+	6.06218i	−0.113376	+	0.196373i	0.803753	+	0.594963i	$0.202833\pi$
$954$	−6.00000	−	10.3923i	−0.194257	−	0.336463i
$955$		0			0
$956$	−6.00000	−	10.3923i	−0.194054	−	0.336111i
$957$	6.00000			0.193952
$958$	12.0000			0.387702
$959$	3.00000	+	5.19615i	0.0968751	+	0.167793i
$960$		0			0
$961$	33.0000			1.06452
$962$	48.0000			1.54758
$963$	12.0000	+	20.7846i	0.386695	+	0.669775i
$964$	9.50000	−	16.4545i	0.305974	−	0.529963i
$965$		0			0
$966$	8.00000	−	13.8564i	0.257396	−	0.445823i
$967$	−27.0000	+	46.7654i	−0.868261	+	1.50387i	−0.00448958	+	0.999990i	$0.501429\pi$
$967$	−27.0000	+	46.7654i	−0.868261	+	1.50387i	−0.863772	+	0.503883i	$0.831904\pi$
$968$	−2.00000			−0.0642824
$969$	−1.00000	+	8.66025i	−0.0321246	+	0.278207i
$970$		0			0
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	0.720224	+	0.693742i	$0.244039\pi$
$972$	−8.00000	+	13.8564i	−0.256600	+	0.444444i
$973$	9.00000	+	15.5885i	0.288527	+	0.499743i
$974$	2.00000	−	3.46410i	0.0640841	−	0.110997i
$975$		0			0
$976$	14.0000			0.448129
$977$	−33.0000			−1.05576			−0.527882	−	0.849318i	$-0.677014\pi$
$977$	−33.0000			−1.05576			−0.527882	+	0.849318i	$0.677014\pi$
$978$	1.50000	+	2.59808i	0.0479647	+	0.0830773i
$979$	21.0000	+	36.3731i	0.671163	+	1.16249i
$980$		0			0
$981$	16.0000			0.510841
$982$	−10.0000	−	17.3205i	−0.319113	−	0.552720i
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	−0.422027	−	0.906583i	$-0.638681\pi$
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	0.996138	−	0.0878058i	$-0.0279855\pi$
$984$	−2.50000	−	4.33013i	−0.0796971	−	0.138039i
$985$		0			0
$986$	−2.00000	+	3.46410i	−0.0636930	+	0.110319i
$987$	−12.0000			−0.381964
$988$	24.0000	−	10.3923i	0.763542	−	0.330623i
$989$		0			0
$990$		0			0
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	0.491698	+	0.870766i	$0.336377\pi$
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	−0.999954	+	0.00956046i	$0.996957\pi$
$992$	4.00000	+	6.92820i	0.127000	+	0.219971i
$993$	8.50000	−	14.7224i	0.269739	−	0.467202i
$994$	−6.00000	−	10.3923i	−0.190308	−	0.329624i
$995$		0			0
$996$	11.0000			0.348548
$997$	1.00000	+	1.73205i	0.0316703	+	0.0548546i	0.881426	−	0.472322i	$-0.156584\pi$
$997$	1.00000	+	1.73205i	0.0316703	+	0.0548546i	−0.849756	+	0.527176i	$0.823251\pi$
$998$	−16.5000	−	28.5788i	−0.522298	−	0.904647i
$999$	40.0000			1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.e.a.201.1		2
5.2	odd	4		950.2.j.a.49.1		4
5.3	odd	4		950.2.j.a.49.2		4
5.4	even	2		190.2.e.b.11.1	✓	2
15.14	odd	2		1710.2.l.b.1531.1		2
19.7	even	3	inner	950.2.e.a.501.1		2
20.19	odd	2		1520.2.q.e.961.1		2
95.7	odd	12		950.2.j.a.349.2		4
95.49	even	6		3610.2.a.a.1.1		1
95.64	even	6		190.2.e.b.121.1	yes	2
95.83	odd	12		950.2.j.a.349.1		4
95.84	odd	6		3610.2.a.i.1.1		1
285.254	odd	6		1710.2.l.b.1261.1		2
380.159	odd	6		1520.2.q.e.881.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.e.b.11.1	✓	2	5.4	even	2
190.2.e.b.121.1	yes	2	95.64	even	6
950.2.e.a.201.1		2	1.1	even	1	trivial
950.2.e.a.501.1		2	19.7	even	3	inner
950.2.j.a.49.1		4	5.2	odd	4
950.2.j.a.49.2		4	5.3	odd	4
950.2.j.a.349.1		4	95.83	odd	12
950.2.j.a.349.2		4	95.7	odd	12
1520.2.q.e.881.1		2	380.159	odd	6
1520.2.q.e.961.1		2	20.19	odd	2
1710.2.l.b.1261.1		2	285.254	odd	6
1710.2.l.b.1531.1		2	15.14	odd	2
3610.2.a.a.1.1		1	95.49	even	6
3610.2.a.i.1.1		1	95.84	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} -3.00000 q^{11} +1.00000 q^{12} +(3.00000 + 5.19615i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} -2.00000 q^{18} +(3.50000 + 2.59808i) q^{19} +(1.00000 - 1.73205i) q^{21} +(1.50000 - 2.59808i) q^{22} +(-4.00000 - 6.92820i) q^{23} +(-0.500000 + 0.866025i) q^{24} -6.00000 q^{26} -5.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(1.00000 + 1.73205i) q^{29} -8.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +(1.00000 + 1.73205i) q^{34} +(1.00000 - 1.73205i) q^{36} -8.00000 q^{37} +(-4.00000 + 1.73205i) q^{38} -6.00000 q^{39} +(-2.50000 + 4.33013i) q^{41} +(1.00000 + 1.73205i) q^{42} +(1.50000 + 2.59808i) q^{44} +8.00000 q^{46} +(-3.00000 - 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{48} -3.00000 q^{49} +(1.00000 + 1.73205i) q^{51} +(3.00000 - 5.19615i) q^{52} +(3.00000 + 5.19615i) q^{53} +(2.50000 - 4.33013i) q^{54} -2.00000 q^{56} +(-4.00000 + 1.73205i) q^{57} -2.00000 q^{58} +(-2.50000 + 4.33013i) q^{59} +(-7.00000 - 12.1244i) q^{61} +(4.00000 - 6.92820i) q^{62} +(-2.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(1.50000 + 2.59808i) q^{66} +(-2.50000 - 4.33013i) q^{67} -2.00000 q^{68} +8.00000 q^{69} +(3.00000 - 5.19615i) q^{71} +(1.00000 + 1.73205i) q^{72} +(-4.50000 + 7.79423i) q^{73} +(4.00000 - 6.92820i) q^{74} +(0.500000 - 4.33013i) q^{76} +6.00000 q^{77} +(3.00000 - 5.19615i) q^{78} +(-4.00000 + 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.50000 - 4.33013i) q^{82} +11.0000 q^{83} -2.00000 q^{84} -2.00000 q^{87} -3.00000 q^{88} +(-7.00000 - 12.1244i) q^{89} +(-6.00000 - 10.3923i) q^{91} +(-4.00000 + 6.92820i) q^{92} +(4.00000 - 6.92820i) q^{93} +6.00000 q^{94} +1.00000 q^{96} +(-7.50000 + 12.9904i) q^{97} +(1.50000 - 2.59808i) q^{98} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 - q^3 - q^4 - q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9} - 6 q^{11} + 2 q^{12} + 6 q^{13} + 2 q^{14} - q^{16} + 2 q^{17} - 4 q^{18} + 7 q^{19} + 2 q^{21} + 3 q^{22} - 8 q^{23} - q^{24} - 12 q^{26} - 10 q^{27} + 2 q^{28} + 2 q^{29} - 16 q^{31} - q^{32} + 3 q^{33} + 2 q^{34} + 2 q^{36} - 16 q^{37} - 8 q^{38} - 12 q^{39} - 5 q^{41} + 2 q^{42} + 3 q^{44} + 16 q^{46} - 6 q^{47} - q^{48} - 6 q^{49} + 2 q^{51} + 6 q^{52} + 6 q^{53} + 5 q^{54} - 4 q^{56} - 8 q^{57} - 4 q^{58} - 5 q^{59} - 14 q^{61} + 8 q^{62} - 4 q^{63} + 2 q^{64} + 3 q^{66} - 5 q^{67} - 4 q^{68} + 16 q^{69} + 6 q^{71} + 2 q^{72} - 9 q^{73} + 8 q^{74} + q^{76} + 12 q^{77} + 6 q^{78} - 8 q^{79} - q^{81} - 5 q^{82} + 22 q^{83} - 4 q^{84} - 4 q^{87} - 6 q^{88} - 14 q^{89} - 12 q^{91} - 8 q^{92} + 8 q^{93} + 12 q^{94} + 2 q^{96} - 15 q^{97} + 3 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 - q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9 - 6 * q^11 + 2 * q^12 + 6 * q^13 + 2 * q^14 - q^16 + 2 * q^17 - 4 * q^18 + 7 * q^19 + 2 * q^21 + 3 * q^22 - 8 * q^23 - q^24 - 12 * q^26 - 10 * q^27 + 2 * q^28 + 2 * q^29 - 16 * q^31 - q^32 + 3 * q^33 + 2 * q^34 + 2 * q^36 - 16 * q^37 - 8 * q^38 - 12 * q^39 - 5 * q^41 + 2 * q^42 + 3 * q^44 + 16 * q^46 - 6 * q^47 - q^48 - 6 * q^49 + 2 * q^51 + 6 * q^52 + 6 * q^53 + 5 * q^54 - 4 * q^56 - 8 * q^57 - 4 * q^58 - 5 * q^59 - 14 * q^61 + 8 * q^62 - 4 * q^63 + 2 * q^64 + 3 * q^66 - 5 * q^67 - 4 * q^68 + 16 * q^69 + 6 * q^71 + 2 * q^72 - 9 * q^73 + 8 * q^74 + q^76 + 12 * q^77 + 6 * q^78 - 8 * q^79 - q^81 - 5 * q^82 + 22 * q^83 - 4 * q^84 - 4 * q^87 - 6 * q^88 - 14 * q^89 - 12 * q^91 - 8 * q^92 + 8 * q^93 + 12 * q^94 + 2 * q^96 - 15 * q^97 + 3 * q^98 - 6 * q^99

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