LMFDB - Embedded newform 225.3.r.b.217.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,3,Mod(28,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("225.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	225.r (of order $20$, degree $8$, 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:	$6.13080594811$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			217.2
Character	$\chi$	$=$	225.217
Dual form			225.3.r.b.28.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.51991 + 2.98300i) q^{2} +(-4.23700 - 5.83172i) q^{4} +(-3.83005 + 3.21415i) q^{5} +(-3.58606 - 3.58606i) q^{7} +(10.6092 - 1.68033i) q^{8} +O(q^{10})$	\(q+(-1.51991 + 2.98300i) q^{2} +(-4.23700 - 5.83172i) q^{4} +(-3.83005 + 3.21415i) q^{5} +(-3.58606 - 3.58606i) q^{7} +(10.6092 - 1.68033i) q^{8} +(-3.76645 - 16.3102i) q^{10} +(-2.52268 - 7.76402i) q^{11} +(8.08027 + 15.8584i) q^{13} +(16.1477 - 5.24671i) q^{14} +(-2.20252 + 6.77867i) q^{16} +(-4.14599 - 26.1767i) q^{17} +(7.05272 - 9.70724i) q^{19} +(34.9719 + 8.71745i) q^{20} +(26.9943 + 4.27548i) q^{22} +(29.8372 + 15.2028i) q^{23} +(4.33852 - 24.6207i) q^{25} -59.5869 q^{26} +(-5.71879 + 36.1070i) q^{28} +(-23.3243 - 32.1031i) q^{29} +(-9.95722 - 7.23434i) q^{31} +(13.5082 + 13.5082i) q^{32} +(84.3867 + 27.4189i) q^{34} +(25.2609 + 2.20865i) q^{35} +(-29.4467 + 15.0038i) q^{37} +(18.2371 + 35.7924i) q^{38} +(-35.2328 + 40.5352i) q^{40} +(-6.99156 + 21.5178i) q^{41} +(-8.95040 + 8.95040i) q^{43} +(-34.5890 + 47.6077i) q^{44} +(-90.6999 + 65.8973i) q^{46} +(46.2544 + 7.32597i) q^{47} -23.2804i q^{49} +(66.8492 + 50.3631i) q^{50} +(58.2459 - 114.314i) q^{52} +(10.1740 - 64.2359i) q^{53} +(34.6167 + 21.6283i) q^{55} +(-44.0709 - 32.0194i) q^{56} +(131.214 - 20.7823i) q^{58} +(-82.9473 - 26.9512i) q^{59} +(-24.5238 - 75.4766i) q^{61} +(36.7141 - 18.7068i) q^{62} +(-87.9409 + 28.5737i) q^{64} +(-81.9191 - 34.7673i) q^{65} +(-17.6154 - 111.219i) q^{67} +(-135.089 + 135.089i) q^{68} +(-44.9828 + 71.9962i) q^{70} +(25.0631 - 18.2094i) q^{71} +(-63.6499 - 32.4313i) q^{73} -110.644i q^{74} -86.4923 q^{76} +(-18.7957 + 36.8887i) q^{77} +(-4.19556 - 5.77470i) q^{79} +(-13.3519 - 33.0419i) q^{80} +(-53.5610 - 53.5610i) q^{82} +(16.9166 - 2.67933i) q^{83} +(100.015 + 86.9323i) q^{85} +(-13.0952 - 40.3029i) q^{86} +(-39.8097 - 78.1309i) q^{88} +(1.13062 - 0.367359i) q^{89} +(27.8929 - 85.8456i) q^{91} +(-37.7615 - 238.417i) q^{92} +(-92.1560 + 126.842i) q^{94} +(4.18824 + 59.8477i) q^{95} +(82.1151 + 13.0058i) q^{97} +(69.4452 + 35.3841i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{2} - 4 q^{5} - 4 q^{7} + 12 q^{8}+O(q^{10}) $ 80 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 + 12 * q^8	$ 80 q - 4 q^{2} - 4 q^{5} - 4 q^{7} + 12 q^{8} - 4 q^{10} + 32 q^{13} + 80 q^{16} + 100 q^{17} - 100 q^{19} + 244 q^{20} - 100 q^{22} + 96 q^{23} - 16 q^{25} + 40 q^{26} + 196 q^{28} - 200 q^{29} - 636 q^{32} + 100 q^{34} - 260 q^{35} - 184 q^{37} + 564 q^{38} - 948 q^{40} - 160 q^{41} - 472 q^{43} + 700 q^{44} + 288 q^{47} - 16 q^{50} + 620 q^{52} - 304 q^{53} + 604 q^{55} + 1272 q^{58} - 800 q^{59} - 240 q^{61} - 1212 q^{62} + 100 q^{64} - 272 q^{65} - 80 q^{67} - 104 q^{68} - 260 q^{70} - 116 q^{73} + 88 q^{77} + 200 q^{79} + 164 q^{80} - 168 q^{82} + 1264 q^{83} - 212 q^{85} - 212 q^{88} + 1500 q^{89} + 1504 q^{92} - 200 q^{94} + 784 q^{95} - 260 q^{97} + 92 q^{98}+O(q^{100}) $ 80 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 + 12 * q^8 - 4 * q^10 + 32 * q^13 + 80 * q^16 + 100 * q^17 - 100 * q^19 + 244 * q^20 - 100 * q^22 + 96 * q^23 - 16 * q^25 + 40 * q^26 + 196 * q^28 - 200 * q^29 - 636 * q^32 + 100 * q^34 - 260 * q^35 - 184 * q^37 + 564 * q^38 - 948 * q^40 - 160 * q^41 - 472 * q^43 + 700 * q^44 + 288 * q^47 - 16 * q^50 + 620 * q^52 - 304 * q^53 + 604 * q^55 + 1272 * q^58 - 800 * q^59 - 240 * q^61 - 1212 * q^62 + 100 * q^64 - 272 * q^65 - 80 * q^67 - 104 * q^68 - 260 * q^70 - 116 * q^73 + 88 * q^77 + 200 * q^79 + 164 * q^80 - 168 * q^82 + 1264 * q^83 - 212 * q^85 - 212 * q^88 + 1500 * q^89 + 1504 * q^92 - 200 * q^94 + 784 * q^95 - 260 * q^97 + 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−1.51991	+	2.98300i	−0.759957	+	1.49150i	0.107618	+	0.994192i	$0.465678\pi$
$2$	−1.51991	+	2.98300i	−0.759957	+	1.49150i	−0.867575	+	0.497306i	$0.834322\pi$
$3$		0			0
$3$		0			0
$4$	−4.23700	−	5.83172i	−1.05925	−	1.45793i
$5$	−3.83005	+	3.21415i	−0.766009	+	0.642829i
$5$	−3.83005	+	3.21415i	−0.766009	+	0.642829i
$6$		0			0
$7$	−3.58606	−	3.58606i	−0.512294	−	0.512294i	0.402935	−	0.915229i	$-0.367990\pi$
$7$	−3.58606	−	3.58606i	−0.512294	−	0.512294i	−0.915229	+	0.402935i	$0.867990\pi$
$8$	10.6092	−	1.68033i	1.32615	−	0.210041i
$9$		0			0
$10$	−3.76645	−	16.3102i	−0.376645	−	1.63102i
$11$	−2.52268	−	7.76402i	−0.229335	−	0.705820i	−0.997823	−	0.0659554i	$-0.978990\pi$
$11$	−2.52268	−	7.76402i	−0.229335	−	0.705820i	0.768488	−	0.639864i	$-0.221010\pi$
$12$		0			0
$13$	8.08027	+	15.8584i	0.621559	+	1.21988i	0.960292	+	0.278996i	$0.0900017\pi$
$13$	8.08027	+	15.8584i	0.621559	+	1.21988i	−0.338733	+	0.940883i	$0.609998\pi$
$14$	16.1477	−	5.24671i	1.15341	−	0.374765i
$15$		0			0
$16$	−2.20252	+	6.77867i	−0.137658	+	0.423667i
$17$	−4.14599	−	26.1767i	−0.243882	−	1.53981i	−0.740630	−	0.671913i	$-0.765473\pi$
$17$	−4.14599	−	26.1767i	−0.243882	−	1.53981i	0.496748	−	0.867895i	$-0.334527\pi$
$18$		0			0
$19$	7.05272	−	9.70724i	0.371196	−	0.510907i	−0.582029	−	0.813168i	$-0.697741\pi$
$19$	7.05272	−	9.70724i	0.371196	−	0.510907i	0.953225	+	0.302260i	$0.0977412\pi$
$20$	34.9719	+	8.71745i	1.74860	+	0.435872i
$21$		0			0
$22$	26.9943	+	4.27548i	1.22701	+	0.194340i
$23$	29.8372	+	15.2028i	1.29727	+	0.660992i	0.959890	−	0.280377i	$-0.0904594\pi$
$23$	29.8372	+	15.2028i	1.29727	+	0.660992i	0.337380	+	0.941369i	$0.390459\pi$
$24$		0			0
$25$	4.33852	−	24.6207i	0.173541	−	0.984827i
$26$	−59.5869			−2.29181
$27$		0			0
$28$	−5.71879	+	36.1070i	−0.204243	+	1.28954i
$29$	−23.3243	−	32.1031i	−0.804285	−	1.10700i	−0.992180	−	0.124814i	$-0.960167\pi$
$29$	−23.3243	−	32.1031i	−0.804285	−	1.10700i	0.187895	−	0.982189i	$-0.439833\pi$
$30$		0			0
$31$	−9.95722	−	7.23434i	−0.321201	−	0.233366i	0.415487	−	0.909599i	$-0.363611\pi$
$31$	−9.95722	−	7.23434i	−0.321201	−	0.233366i	−0.736688	+	0.676233i	$0.763611\pi$
$32$	13.5082	+	13.5082i	0.422131	+	0.422131i
$33$		0			0
$34$	84.3867	+	27.4189i	2.48196	+	0.806438i
$35$	25.2609	+	2.20865i	0.721740	+	0.0631043i
$36$		0			0
$37$	−29.4467	+	15.0038i	−0.795857	+	0.405509i	−0.804128	−	0.594456i	$-0.797367\pi$
$37$	−29.4467	+	15.0038i	−0.795857	+	0.405509i	0.00827090	+	0.999966i	$0.497367\pi$
$38$	18.2371	+	35.7924i	0.479925	+	0.941906i
$39$		0			0
$40$	−35.2328	+	40.5352i	−0.880820	+	1.01338i
$41$	−6.99156	+	21.5178i	−0.170526	+	0.524824i	−0.999401	−	0.0346093i	$-0.988981\pi$
$41$	−6.99156	+	21.5178i	−0.170526	+	0.524824i	0.828875	+	0.559434i	$0.188981\pi$
$42$		0			0
$43$	−8.95040	+	8.95040i	−0.208149	+	0.208149i	−0.803480	−	0.595331i	$-0.797021\pi$
$43$	−8.95040	+	8.95040i	−0.208149	+	0.208149i	0.595331	+	0.803480i	$0.297021\pi$
$44$	−34.5890	+	47.6077i	−0.786114	+	1.08199i
$45$		0			0
$46$	−90.6999	+	65.8973i	−1.97174	+	1.43255i
$47$	46.2544	+	7.32597i	0.984136	+	0.155872i	0.627706	−	0.778450i	$-0.283994\pi$
$47$	46.2544	+	7.32597i	0.984136	+	0.155872i	0.356429	+	0.934322i	$0.383994\pi$
$48$		0			0
$49$		−	23.2804i		−	0.475109i
$50$	66.8492	+	50.3631i	1.33698	+	1.00726i
$51$		0			0
$52$	58.2459	−	114.314i	1.12011	−	2.19835i
$53$	10.1740	−	64.2359i	0.191962	−	1.21200i	−0.683951	−	0.729528i	$-0.739740\pi$
$53$	10.1740	−	64.2359i	0.191962	−	1.21200i	0.875913	−	0.482470i	$-0.160260\pi$
$54$		0			0
$55$	34.6167	+	21.6283i	0.629394	+	0.393241i
$56$	−44.0709	−	32.0194i	−0.786980	−	0.571775i
$57$		0			0
$58$	131.214	−	20.7823i	2.26232	−	0.358316i
$59$	−82.9473	−	26.9512i	−1.40589	−	0.456800i	−0.494796	−	0.869009i	$-0.664757\pi$
$59$	−82.9473	−	26.9512i	−1.40589	−	0.456800i	−0.911089	+	0.412209i	$0.864757\pi$
$60$		0			0
$61$	−24.5238	−	75.4766i	−0.402030	−	1.23732i	−0.923350	−	0.383960i	$-0.874560\pi$
$61$	−24.5238	−	75.4766i	−0.402030	−	1.23732i	0.521319	−	0.853362i	$-0.325440\pi$
$62$	36.7141	−	18.7068i	0.592163	−	0.301722i
$63$		0			0
$64$	−87.9409	+	28.5737i	−1.37408	+	0.446465i
$65$	−81.9191	−	34.7673i	−1.26029	−	0.534882i
$66$		0			0
$67$	−17.6154	−	111.219i	−0.262917	−	1.65999i	−0.666843	−	0.745199i	$-0.732355\pi$
$67$	−17.6154	−	111.219i	−0.262917	−	1.65999i	0.403926	−	0.914792i	$-0.367645\pi$
$68$	−135.089	+	135.089i	−1.98660	+	1.98660i
$69$		0			0
$70$	−44.9828	+	71.9962i	−0.642611	+	1.02852i
$71$	25.0631	−	18.2094i	0.353002	−	0.256471i	−0.397125	−	0.917764i	$-0.629992\pi$
$71$	25.0631	−	18.2094i	0.353002	−	0.256471i	0.750127	+	0.661293i	$0.229992\pi$
$72$		0			0
$73$	−63.6499	−	32.4313i	−0.871917	−	0.444264i	−0.0400230	−	0.999199i	$-0.512743\pi$
$73$	−63.6499	−	32.4313i	−0.871917	−	0.444264i	−0.831894	+	0.554935i	$0.812743\pi$
$74$		−	110.644i		−	1.49519i
$75$		0			0
$76$	−86.4923			−1.13806
$77$	−18.7957	+	36.8887i	−0.244101	+	0.479074i
$78$		0			0
$79$	−4.19556	−	5.77470i	−0.0531084	−	0.0730975i	0.781637	−	0.623734i	$-0.214385\pi$
$79$	−4.19556	−	5.77470i	−0.0531084	−	0.0730975i	−0.834745	+	0.550636i	$0.814385\pi$
$80$	−13.3519	−	33.0419i	−0.166899	−	0.413023i
$81$		0			0
$82$	−53.5610	−	53.5610i	−0.653183	−	0.653183i
$83$	16.9166	−	2.67933i	0.203815	−	0.0322811i	−0.0536920	−	0.998558i	$-0.517099\pi$
$83$	16.9166	−	2.67933i	0.203815	−	0.0322811i	0.257507	+	0.966276i	$0.417099\pi$
$84$		0			0
$85$	100.015	+	86.9323i	1.17665	+	1.02273i
$86$	−13.0952	−	40.3029i	−0.152270	−	0.468638i
$87$		0			0
$88$	−39.8097	−	78.1309i	−0.452383	−	0.887851i
$89$	1.13062	−	0.367359i	0.0127035	−	0.00412763i	−0.302658	−	0.953099i	$-0.597874\pi$
$89$	1.13062	−	0.367359i	0.0127035	−	0.00412763i	0.315362	+	0.948971i	$0.397874\pi$
$90$		0			0
$91$	27.8929	−	85.8456i	0.306516	−	0.943358i
$92$	−37.7615	−	238.417i	−0.410451	−	2.59148i
$93$		0			0
$94$	−92.1560	+	126.842i	−0.980383	+	1.34938i
$95$	4.18824	+	59.8477i	0.0440868	+	0.629976i
$96$		0			0
$97$	82.1151	+	13.0058i	0.846548	+	0.134080i	0.564615	−	0.825354i	$-0.309025\pi$
$97$	82.1151	+	13.0058i	0.846548	+	0.134080i	0.281932	+	0.959434i	$0.409025\pi$
$98$	69.4452	+	35.3841i	0.708625	+	0.361062i
$99$		0			0
$100$	−161.963	+	79.0166i	−1.61963	+	0.790166i
$101$	−20.1616			−0.199620			−0.0998099	−	0.995007i	$-0.531823\pi$
$101$	−20.1616			−0.199620			−0.0998099	+	0.995007i	$0.531823\pi$
$102$		0			0
$103$	−16.6494	+	105.120i	−0.161644	+	1.02058i	0.764832	+	0.644230i	$0.222822\pi$
$103$	−16.6494	+	105.120i	−0.161644	+	1.02058i	−0.926476	+	0.376353i	$0.877178\pi$
$104$	112.372	+	154.667i	1.08050	+	1.48719i
$105$		0			0
$106$	176.152	+	127.982i	1.66181	+	1.20738i
$107$	−150.099	−	150.099i	−1.40279	−	1.40279i	−0.791075	−	0.611719i	$-0.790478\pi$
$107$	−150.099	−	150.099i	−1.40279	−	1.40279i	−0.611719	−	0.791075i	$-0.709522\pi$
$108$		0			0
$109$	66.6825	+	21.6664i	0.611766	+	0.198775i	0.598481	−	0.801137i	$-0.295771\pi$
$109$	66.6825	+	21.6664i	0.611766	+	0.198775i	0.0132847	+	0.999912i	$0.495771\pi$
$110$	−117.131	+	70.3884i	−1.06483	+	0.639894i
$111$		0			0
$112$	32.2071	−	16.4103i	0.287563	−	0.146521i
$113$	12.8863	+	25.2908i	0.114038	+	0.223812i	0.940970	−	0.338490i	$-0.109916\pi$
$113$	12.8863	+	25.2908i	0.114038	+	0.223812i	−0.826932	+	0.562302i	$0.809916\pi$
$114$		0			0
$115$	−163.142	+	37.6737i	−1.41863	+	0.327597i
$116$	−88.3916	+	272.041i	−0.761996	+	2.34518i
$117$		0			0
$118$	206.468	−	206.468i	1.74973	−	1.74973i
$119$	−79.0036	+	108.739i	−0.663896	+	0.913774i
$120$		0			0
$121$	43.9750	−	31.9497i	0.363430	−	0.264047i
$122$	262.421	+	41.5634i	2.15099	+	0.340683i
$123$		0			0
$124$			88.7196i			0.715481i
$125$	62.5177	+	108.243i	0.500142	+	0.865943i
$126$		0			0
$127$	−75.5353	+	148.246i	−0.594766	+	1.16729i	0.375855	+	0.926679i	$0.377349\pi$
$127$	−75.5353	+	148.246i	−0.594766	+	1.16729i	−0.970621	+	0.240615i	$0.922651\pi$
$128$	36.4734	−	230.284i	0.284948	−	1.79909i
$129$		0			0
$130$	228.221	−	191.521i	1.75554	−	1.47324i
$131$	97.4968	+	70.8356i	0.744251	+	0.540730i	0.894039	−	0.447988i	$-0.147859\pi$
$131$	97.4968	+	70.8356i	0.744251	+	0.540730i	−0.149789	+	0.988718i	$0.547859\pi$
$132$		0			0
$133$	−60.1022	+	9.51926i	−0.451896	+	0.0715734i
$134$	358.541	+	116.497i	2.67568	+	0.869381i
$135$		0			0
$136$	−87.9710	−	270.747i	−0.646846	−	1.99079i
$137$	−197.518	+	100.641i	−1.44174	+	0.734603i	−0.987697	−	0.156377i	$-0.950018\pi$
$137$	−197.518	+	100.641i	−1.44174	+	0.734603i	−0.454042	+	0.890980i	$0.650018\pi$
$138$		0			0
$139$	−6.03287	+	1.96020i	−0.0434019	+	0.0141021i	−0.330637	−	0.943758i	$-0.607264\pi$
$139$	−6.03287	+	1.96020i	−0.0434019	+	0.0141021i	0.287236	+	0.957860i	$0.407264\pi$
$140$	−94.1501	−	156.673i	−0.672501	−	1.11909i
$141$		0			0
$142$	16.2249	+	102.440i	0.114260	+	0.721409i
$143$	102.741	−	102.741i	0.718470	−	0.718470i
$144$		0			0
$145$	192.517	+	47.9887i	1.32770	+	0.330957i
$146$	193.485	−	140.575i	1.32524	−	0.962841i
$147$		0			0
$148$	212.264	+	108.154i	1.43422	+	0.730769i
$149$		−	114.482i		−	0.768336i	−0.923263	−	0.384168i	$-0.874488\pi$
$149$		−	114.482i		−	0.768336i	0.923263	−	0.384168i	$-0.125512\pi$
$150$		0			0
$151$	−17.3173			−0.114684			−0.0573421	−	0.998355i	$-0.518263\pi$
$151$	−17.3173			−0.114684			−0.0573421	+	0.998355i	$0.518263\pi$
$152$	58.5122	−	114.837i	0.384949	−	0.755505i
$153$		0			0
$154$	−81.4711	−	112.135i	−0.529033	−	0.728151i
$155$	61.3888	−	4.29609i	0.396057	−	0.0277167i
$156$		0			0
$157$	−5.55440	−	5.55440i	−0.0353783	−	0.0353783i	0.689196	−	0.724575i	$-0.257964\pi$
$157$	−5.55440	−	5.55440i	−0.0353783	−	0.0353783i	−0.724575	+	0.689196i	$0.757964\pi$
$158$	23.6028	−	3.73832i	0.149385	−	0.0236602i
$159$		0			0
$160$	−95.1544	−	8.31969i	−0.594715	−	0.0519981i
$161$	−52.4798	−	161.516i	−0.325961	−	1.00321i
$162$		0			0
$163$	6.93150	+	13.6038i	0.0425245	+	0.0834591i	0.911291	−	0.411763i	$-0.135087\pi$
$163$	6.93150	+	13.6038i	0.0425245	+	0.0834591i	−0.868767	+	0.495222i	$0.835087\pi$
$164$	155.109	−	50.3980i	0.945787	−	0.307305i
$165$		0			0
$166$	−17.7194	+	54.5347i	−0.106743	+	0.328522i
$167$	35.4877	+	224.061i	0.212501	+	1.34168i	0.831165	+	0.556025i	$0.187674\pi$
$167$	35.4877	+	224.061i	0.212501	+	1.34168i	−0.618664	+	0.785656i	$0.712326\pi$
$168$		0			0
$169$	−86.8631	+	119.557i	−0.513983	+	0.707437i
$170$	−411.333	+	166.216i	−2.41961	+	0.977738i
$171$		0			0
$172$	90.1191	+	14.2735i	0.523948	+	0.0829853i
$173$	4.00151	+	2.03887i	0.0231301	+	0.0117854i	0.465517	−	0.885039i	$-0.345868\pi$
$173$	4.00151	+	2.03887i	0.0231301	+	0.0117854i	−0.442387	+	0.896824i	$0.645868\pi$
$174$		0			0
$175$	−103.849	+	72.7330i	−0.593425	+	0.415617i
$176$	58.1860			0.330602
$177$		0			0
$178$	−0.622605	+	3.93098i	−0.00349778	+	0.0220841i
$179$	111.815	+	153.900i	0.624664	+	0.859776i	0.997682	−	0.0680483i	$-0.0216772\pi$
$179$	111.815	+	153.900i	0.624664	+	0.859776i	−0.373018	+	0.927824i	$0.621677\pi$
$180$		0			0
$181$	−178.031	−	129.347i	−0.983596	−	0.714624i	−0.0250865	−	0.999685i	$-0.507986\pi$
$181$	−178.031	−	129.347i	−0.983596	−	0.714624i	−0.958509	+	0.285061i	$0.907986\pi$
$182$	213.682	+	213.682i	1.17408	+	1.17408i
$183$		0			0
$184$	342.094	+	111.153i	1.85921	+	0.604092i
$185$	64.5577	−	152.111i	0.348960	−	0.822224i
$186$		0			0
$187$	−192.778	+	98.2251i	−1.03090	+	0.525268i
$188$	−153.257	−	300.783i	−0.815194	−	1.59991i
$189$		0			0
$190$	−184.891	−	78.4698i	−0.973112	−	0.412999i
$191$	36.4604	−	112.214i	0.190892	−	0.587506i	−0.809108	−	0.587660i	$-0.800049\pi$
$191$	36.4604	−	112.214i	0.190892	−	0.587506i	1.00000		0.000154600i	$4.92108e-5\pi$
$192$		0			0
$193$	63.8407	−	63.8407i	0.330781	−	0.330781i	−0.522102	−	0.852883i	$-0.674852\pi$
$193$	63.8407	−	63.8407i	0.330781	−	0.330781i	0.852883	+	0.522102i	$0.174852\pi$
$194$	−163.604	+	225.182i	−0.843319	+	1.16073i
$195$		0			0
$196$	−135.765	+	98.6388i	−0.692677	+	0.503259i
$197$	−84.0087	−	13.3057i	−0.426440	−	0.0675415i	−0.0604744	−	0.998170i	$-0.519261\pi$
$197$	−84.0087	−	13.3057i	−0.426440	−	0.0675415i	−0.365966	+	0.930628i	$0.619261\pi$
$198$		0			0
$199$		−	112.218i		−	0.563909i	−0.959428	−	0.281954i	$-0.909017\pi$
$199$		−	112.218i		−	0.563909i	0.959428	−	0.281954i	$-0.0909827\pi$
$200$	4.65726	−	268.495i	0.0232863	−	1.34248i
$201$		0			0
$202$	30.6439	−	60.1420i	0.151702	−	0.297733i
$203$	−31.4814	+	198.766i	−0.155081	+	0.979142i
$204$		0			0
$205$	−42.3834	−	104.886i	−0.206748	−	0.511639i
$206$	−288.267	−	209.438i	−1.39936	−	1.01669i
$207$		0			0
$208$	−125.296	+	19.8449i	−0.602385	+	0.0954084i
$209$	−93.1590	−	30.2692i	−0.445737	−	0.144829i
$210$		0			0
$211$	31.2858	+	96.2878i	0.148274	+	0.456340i	0.997417	−	0.0718220i	$-0.0228813\pi$
$211$	31.2858	+	96.2878i	0.148274	+	0.456340i	−0.849144	+	0.528162i	$0.822881\pi$
$212$	−417.713	+	212.835i	−1.97034	+	1.00394i
$213$		0			0
$214$	675.882	−	219.607i	3.15833	−	1.02620i
$215$	5.51255	−	63.0484i	0.0256398	−	0.293248i
$216$		0			0
$217$	9.76439	+	61.6499i	0.0449972	+	0.284101i
$218$	−165.982	+	165.982i	−0.761388	+	0.761388i
$219$		0			0
$220$	−20.5406	−	293.514i	−0.0933664	−	1.33415i
$221$	381.621	−	277.264i	1.72679	−	1.25459i
$222$		0			0
$223$	164.504	+	83.8191i	0.737688	+	0.375871i	0.782108	−	0.623142i	$-0.214144\pi$
$223$	164.504	+	83.8191i	0.737688	+	0.375871i	−0.0444209	+	0.999013i	$0.514144\pi$
$224$		−	96.8824i		−	0.432511i
$225$		0			0
$226$	−95.0283			−0.420479
$227$	−98.2222	+	192.772i	−0.432697	+	0.849216i	0.566978	+	0.823733i	$0.308112\pi$
$227$	−98.2222	+	192.772i	−0.432697	+	0.849216i	−0.999675	+	0.0254830i	$0.991888\pi$
$228$		0			0
$229$	−0.628163	−	0.864593i	−0.00274307	−	0.00377551i	0.807643	−	0.589671i	$-0.200743\pi$
$229$	−0.628163	−	0.864593i	−0.00274307	−	0.00377551i	−0.810386	+	0.585896i	$0.800743\pi$
$230$	135.581	−	543.913i	0.589483	−	2.36484i
$231$		0			0
$232$	−301.395	−	301.395i	−1.29912	−	1.29912i
$233$	412.482	−	65.3308i	1.77031	−	0.280390i	0.815750	−	0.578405i	$-0.196325\pi$
$233$	412.482	−	65.3308i	1.77031	−	0.280390i	0.954561	+	0.298016i	$0.0963248\pi$
$234$		0			0
$235$	−200.703	+	120.610i	−0.854056	+	0.513232i
$236$	194.275	+	597.918i	0.823200	+	2.53355i
$237$		0			0
$238$	−204.290	−	400.941i	−0.858361	−	1.68463i
$239$	−70.0752	+	22.7688i	−0.293202	+	0.0952670i	−0.451925	−	0.892056i	$-0.649262\pi$
$239$	−70.0752	+	22.7688i	−0.293202	+	0.0952670i	0.158723	+	0.987323i	$0.449262\pi$
$240$		0			0
$241$	14.6723	−	45.1568i	0.0608811	−	0.187373i	−0.915990	−	0.401200i	$-0.868593\pi$
$241$	14.6723	−	45.1568i	0.0608811	−	0.187373i	0.976871	+	0.213828i	$0.0685931\pi$
$242$	28.4677	+	179.738i	0.117635	+	0.742719i
$243$		0			0
$244$	−336.252	+	462.811i	−1.37808	+	1.89676i
$245$	74.8265	+	89.1648i	0.305414	+	0.363938i
$246$		0			0
$247$	210.929	+	33.4079i	0.853965	+	0.135255i
$248$	−117.794	−	60.0190i	−0.474975	−	0.242012i
$249$		0			0
$250$	−417.910	+	21.9704i	−1.67164	+	0.0878816i
$251$	−94.4412			−0.376260			−0.188130	−	0.982144i	$-0.560243\pi$
$251$	−94.4412			−0.376260			−0.188130	+	0.982144i	$0.560243\pi$
$252$		0			0
$253$	42.7651	−	270.008i	0.169032	−	1.06723i
$254$	−327.411	−	450.643i	−1.28902	−	1.77419i
$255$		0			0
$256$	332.272	+	241.410i	1.29794	+	0.943007i
$257$	−232.079	−	232.079i	−0.903031	−	0.903031i	0.0926660	−	0.995697i	$-0.470461\pi$
$257$	−232.079	−	232.079i	−0.903031	−	0.903031i	−0.995697	+	0.0926660i	$0.970461\pi$
$258$		0			0
$259$	159.402	+	51.7930i	0.615453	+	0.199973i
$260$	144.338	+	625.039i	0.555144	+	2.40400i
$261$		0			0
$262$	−359.489	+	183.169i	−1.37210	+	0.699118i
$263$	20.4201	+	40.0768i	0.0776431	+	0.152383i	0.926564	−	0.376136i	$-0.122747\pi$
$263$	20.4201	+	40.0768i	0.0776431	+	0.152383i	−0.848921	+	0.528519i	$0.822747\pi$
$264$		0			0
$265$	167.497	+	278.727i	0.632063	+	1.05180i
$266$	62.9542	−	193.753i	0.236670	−	0.728396i
$267$		0			0
$268$	−573.964	+	573.964i	−2.14166	+	2.14166i
$269$	59.8116	−	82.3236i	0.222348	−	0.306036i	−0.683240	−	0.730194i	$-0.739430\pi$
$269$	59.8116	−	82.3236i	0.222348	−	0.306036i	0.905588	+	0.424158i	$0.139430\pi$
$270$		0			0
$271$	238.788	−	173.490i	0.881137	−	0.640183i	−0.0524153	−	0.998625i	$-0.516692\pi$
$271$	238.788	−	173.490i	0.881137	−	0.640183i	0.933552	+	0.358442i	$0.116692\pi$
$272$	186.575	+	29.5506i	0.685938	+	0.108642i
$273$		0			0
$274$		−	742.161i		−	2.70862i
$275$	−202.100	+	28.4258i	−0.734909	+	0.103367i
$276$		0			0
$277$	228.565	−	448.584i	0.825145	−	1.61944i	0.0407548	−	0.999169i	$-0.487024\pi$
$277$	228.565	−	448.584i	0.825145	−	1.61944i	0.784390	−	0.620268i	$-0.212976\pi$
$278$	3.32217	−	20.9754i	0.0119502	−	0.0754509i
$279$		0			0
$280$	271.709	−	19.0146i	0.970388	−	0.0679094i
$281$	8.79106	+	6.38708i	0.0312849	+	0.0227298i	0.603318	−	0.797501i	$-0.293845\pi$
$281$	8.79106	+	6.38708i	0.0312849	+	0.0227298i	−0.572033	+	0.820231i	$0.693845\pi$
$282$		0			0
$283$	−155.546	+	24.6361i	−0.549632	+	0.0870532i	−0.425073	−	0.905159i	$-0.639752\pi$
$283$	−155.546	+	24.6361i	−0.549632	+	0.0870532i	−0.124559	+	0.992212i	$0.539752\pi$
$284$	−212.385	−	69.0080i	−0.747834	−	0.242986i
$285$		0			0
$286$	150.319	+	462.634i	0.525591	+	1.61760i
$287$	102.236	−	52.0920i	0.356224	−	0.181505i
$288$		0			0
$289$	−393.177	+	127.751i	−1.36047	+	0.442045i
$290$	−435.759	+	501.339i	−1.50262	+	1.72876i
$291$		0			0
$292$	80.5543	+	508.600i	0.275871	+	1.74178i
$293$	−170.980	+	170.980i	−0.583549	+	0.583549i	−0.935877	−	0.352328i	$-0.885390\pi$
$293$	−170.980	+	170.980i	−0.583549	+	0.583549i	0.352328	+	0.935877i	$0.385390\pi$
$294$		0			0
$295$	404.317	−	163.380i	1.37057	−	0.553832i
$296$	−287.194	+	208.659i	−0.970249	+	0.704927i
$297$		0			0
$298$	341.500	+	174.003i	1.14597	+	0.583902i
$299$			596.014i			1.99336i
$300$		0			0
$301$	64.1934			0.213267
$302$	26.3208	−	51.6575i	0.0871551	−	0.171051i
$303$		0			0
$304$	50.2684	+	69.1885i	0.165357	+	0.227594i
$305$	336.521	+	210.256i	1.10335	+	0.689363i
$306$		0			0
$307$	−15.9029	−	15.9029i	−0.0518008	−	0.0518008i	0.680732	−	0.732533i	$-0.261662\pi$
$307$	−15.9029	−	15.9029i	−0.0518008	−	0.0518008i	−0.732533	+	0.680732i	$0.761662\pi$
$308$	294.762	−	46.6858i	0.957021	−	0.151577i
$309$		0			0
$310$	−80.4905	+	189.652i	−0.259647	+	0.611782i
$311$	−83.1955	−	256.049i	−0.267510	−	0.823310i	−0.991105	−	0.133085i	$-0.957512\pi$
$311$	−83.1955	−	256.049i	−0.267510	−	0.823310i	0.723595	−	0.690225i	$-0.242488\pi$
$312$		0			0
$313$	45.8839	+	90.0523i	0.146594	+	0.287707i	0.952614	−	0.304181i	$-0.0983828\pi$
$313$	45.8839	+	90.0523i	0.146594	+	0.287707i	−0.806020	+	0.591888i	$0.798383\pi$
$314$	25.0109	−	8.12655i	0.0796527	−	0.0258807i
$315$		0			0
$316$	−15.8999	+	48.9348i	−0.0503160	+	0.154857i
$317$	20.1030	+	126.926i	0.0634165	+	0.400396i	0.998894	+	0.0470107i	$0.0149695\pi$
$317$	20.1030	+	126.926i	0.0634165	+	0.400396i	−0.935478	+	0.353385i	$0.885030\pi$
$318$		0			0
$319$	−190.409	+	262.076i	−0.596894	+	0.821555i
$320$	244.978	−	392.094i	0.765555	−	1.22529i
$321$		0			0
$322$	561.567	+	88.9435i	1.74400	+	0.276222i
$323$	−283.344	−	144.371i	−0.877227	−	0.446970i
$324$		0			0
$325$	425.501	−	130.140i	1.30923	−	0.400430i
$326$	−51.1155			−0.156796
$327$		0			0
$328$	−38.0177	+	240.034i	−0.115908	+	0.731811i
$329$	−139.600	−	192.142i	−0.424315	−	0.584019i
$330$		0			0
$331$	315.837	+	229.469i	0.954191	+	0.693260i	0.951794	−	0.306737i	$-0.0992372\pi$
$331$	315.837	+	229.469i	0.954191	+	0.693260i	0.00239645	+	0.999997i	$0.499237\pi$
$332$	−87.3009	−	87.3009i	−0.262955	−	0.262955i
$333$		0			0
$334$	−722.311	−	234.693i	−2.16261	−	0.702674i
$335$	424.943	+	369.357i	1.26849	+	1.10256i
$336$		0			0
$337$	−242.809	+	123.717i	−0.720501	+	0.367114i	−0.775478	−	0.631374i	$-0.782491\pi$
$337$	−242.809	+	123.717i	−0.720501	+	0.367114i	0.0549775	+	0.998488i	$0.482491\pi$
$338$	−224.613	−	440.828i	−0.664536	−	1.30423i
$339$		0			0
$340$	83.2012	−	951.593i	0.244709	−	2.79880i
$341$	−31.0487	+	95.5580i	−0.0910518	+	0.280229i
$342$		0			0
$343$	−259.202	+	259.202i	−0.755690	+	0.755690i
$344$	−79.9168	+	109.996i	−0.232316	+	0.319756i
$345$		0			0
$346$	−12.1639	+	8.83759i	−0.0351558	+	0.0255422i
$347$	−162.867	−	25.7956i	−0.469357	−	0.0743389i	−0.0827242	−	0.996572i	$-0.526362\pi$
$347$	−162.867	−	25.7956i	−0.469357	−	0.0743389i	−0.386633	+	0.922234i	$0.626362\pi$
$348$		0			0
$349$		−	504.026i		−	1.44420i	−0.691789	−	0.722100i	$-0.743177\pi$
$349$		−	504.026i		−	1.44420i	0.691789	−	0.722100i	$-0.256823\pi$
$350$	−59.1204	−	420.330i	−0.168915	−	1.20094i
$351$		0			0
$352$	70.8010	−	138.955i	0.201139	−	0.394758i
$353$	−2.03030	+	12.8188i	−0.00575157	+	0.0363140i	−0.990397	−	0.138251i	$-0.955852\pi$
$353$	−2.03030	+	12.8188i	−0.00575157	+	0.0363140i	0.984646	+	0.174565i	$0.0558519\pi$
$354$		0			0
$355$	−37.4652	+	150.300i	−0.105536	+	0.423379i
$356$	−6.93275	−	5.03694i	−0.0194740	−	0.0141487i
$357$		0			0
$358$	−629.032	+	99.6288i	−1.75707	+	0.278293i
$359$	−43.0843	−	13.9989i	−0.120012	−	0.0389942i	0.248395	−	0.968659i	$-0.420097\pi$
$359$	−43.0843	−	13.9989i	−0.120012	−	0.0389942i	−0.368407	+	0.929664i	$0.620097\pi$
$360$		0			0
$361$	67.0655	+	206.406i	0.185777	+	0.571763i
$362$	656.433	−	334.469i	1.81335	−	0.923949i
$363$		0			0
$364$	−618.810	+	201.064i	−1.70003	+	0.552372i
$365$	348.021	−	80.3670i	0.953482	−	0.220184i
$366$		0			0
$367$	−54.4774	−	343.957i	−0.148440	−	0.937212i	−0.943666	−	0.330899i	$-0.892648\pi$
$367$	−54.4774	−	343.957i	−0.148440	−	0.937212i	0.795226	−	0.606313i	$-0.207352\pi$
$368$	−168.772	+	168.772i	−0.458620	+	0.458620i
$369$		0			0
$370$	355.626	+	423.772i	0.961151	+	1.14533i
$371$	−266.838	+	193.869i	−0.719240	+	0.522558i
$372$		0			0
$373$	−535.377	−	272.788i	−1.43533	−	0.731336i	−0.448602	−	0.893732i	$-0.648078\pi$
$373$	−535.377	−	272.788i	−1.43533	−	0.731336i	−0.986726	+	0.162396i	$0.948078\pi$
$374$		−	724.349i		−	1.93676i
$375$		0			0
$376$	503.031			1.33785
$377$	320.638	−	629.288i	0.850499	−	1.66920i
$378$		0			0
$379$	−126.752	−	174.459i	−0.334437	−	0.460313i	0.608369	−	0.793654i	$-0.291824\pi$
$379$	−126.752	−	174.459i	−0.334437	−	0.460313i	−0.942806	+	0.333341i	$0.891824\pi$
$380$	331.270	−	277.999i	0.871762	−	0.731576i
$381$		0			0
$382$	279.316	+	279.316i	0.731194	+	0.731194i
$383$	−68.3267	+	10.8219i	−0.178399	+	0.0282556i	−0.244995	−	0.969524i	$-0.578786\pi$
$383$	−68.3267	+	10.8219i	−0.178399	+	0.0282556i	0.0665959	+	0.997780i	$0.478786\pi$
$384$		0			0
$385$	−46.5772	−	201.698i	−0.120980	−	0.523890i
$386$	93.4043	+	287.469i	0.241980	+	0.744738i
$387$		0			0
$388$	−272.075	−	533.978i	−0.701225	−	1.37623i
$389$	199.223	−	64.7314i	0.512140	−	0.166405i	−0.0415350	−	0.999137i	$-0.513225\pi$
$389$	199.223	−	64.7314i	0.512140	−	0.166405i	0.553675	+	0.832733i	$0.313225\pi$
$390$		0			0
$391$	274.255	−	844.071i	0.701420	−	2.15875i
$392$	−39.1186	−	246.985i	−0.0997924	−	0.630065i
$393$		0			0
$394$	167.377	−	230.374i	0.424814	−	0.584707i
$395$	34.6299	+	8.63220i	0.0876707	+	0.0218537i
$396$		0			0
$397$	−328.529	−	52.0338i	−0.827528	−	0.131068i	−0.271718	−	0.962377i	$-0.587592\pi$
$397$	−328.529	−	52.0338i	−0.827528	−	0.131068i	−0.555810	+	0.831309i	$0.687592\pi$
$398$	334.746	+	170.561i	0.841069	+	0.428546i
$399$		0			0
$400$	157.340	+	83.6370i	0.393349	+	0.209092i
$401$	143.082			0.356813			0.178406	−	0.983957i	$-0.442906\pi$
$401$	143.082			0.356813			0.178406	+	0.983957i	$0.442906\pi$
$402$		0			0
$403$	34.2682	−	216.361i	0.0850329	−	0.536876i
$404$	85.4246	+	117.577i	0.211447	+	0.291032i
$405$		0			0
$406$	−545.069	−	396.016i	−1.34253	−	0.975408i
$407$	190.775	+	190.775i	0.468734	+	0.468734i
$408$		0			0
$409$	711.765	+	231.266i	1.74026	+	0.565444i	0.994868	−	0.101186i	$-0.0322637\pi$
$409$	711.765	+	231.266i	1.74026	+	0.565444i	0.745389	+	0.666630i	$0.232264\pi$
$410$	377.294	+	32.9882i	0.920229	+	0.0804590i
$411$		0			0
$412$	683.574	−	348.299i	1.65916	−	0.845385i
$413$	200.805	+	394.102i	0.486211	+	0.954243i
$414$		0			0
$415$	−56.1798	+	64.6346i	−0.135373	+	0.155746i
$416$	−105.069	+	323.369i	−0.252569	+	0.777329i
$417$		0			0
$418$	231.886	−	231.886i	0.554752	−	0.554752i
$419$	91.4003	−	125.802i	0.218139	−	0.300243i	−0.685897	−	0.727699i	$-0.740590\pi$
$419$	91.4003	−	125.802i	0.218139	−	0.300243i	0.904036	+	0.427456i	$0.140590\pi$
$420$		0			0
$421$	−440.152	+	319.789i	−1.04549	+	0.759595i	−0.971350	−	0.237653i	$-0.923622\pi$
$421$	−440.152	+	319.789i	−1.04549	+	0.759595i	−0.0741422	+	0.997248i	$0.523622\pi$
$422$	−334.778	−	53.0236i	−0.793312	−	0.125648i
$423$		0			0
$424$		−	698.585i		−	1.64761i
$425$	−662.476	−	11.4912i	−1.55877	−	0.0270381i
$426$		0			0
$427$	−182.720	+	358.608i	−0.427915	+	0.839831i
$428$	−239.367	+	1511.30i	−0.559269	+	3.53109i
$429$		0			0
$430$	179.695	+	112.272i	0.417894	+	0.261098i
$431$	−100.126	−	72.7461i	−0.232312	−	0.168784i	0.465539	−	0.885027i	$-0.345860\pi$
$431$	−100.126	−	72.7461i	−0.232312	−	0.168784i	−0.697851	+	0.716243i	$0.745860\pi$
$432$		0			0
$433$	702.066	−	111.196i	1.62140	−	0.256804i	0.721343	−	0.692578i	$-0.243525\pi$
$433$	702.066	−	111.196i	1.62140	−	0.256804i	0.900056	+	0.435774i	$0.143525\pi$
$434$	−198.743	−	64.5754i	−0.457932	−	0.148791i
$435$		0			0
$436$	−156.181	−	480.674i	−0.358212	−	1.10246i
$437$	358.011	−	182.416i	0.819247	−	0.417427i
$438$		0			0
$439$	315.182	−	102.409i	0.717955	−	0.233278i	0.0728185	−	0.997345i	$-0.476801\pi$
$439$	315.182	−	102.409i	0.717955	−	0.233278i	0.645136	+	0.764068i	$0.276801\pi$
$440$	403.597	+	171.291i	0.917266	+	0.389297i
$441$		0			0
$442$	247.047	+	1559.79i	0.558929	+	3.52894i
$443$	−374.913	+	374.913i	−0.846305	+	0.846305i	−0.989670	−	0.143365i	$-0.954208\pi$
$443$	−374.913	+	374.913i	−0.846305	+	0.846305i	0.143365	+	0.989670i	$0.454208\pi$
$444$		0			0
$445$	−3.14956	+	5.04097i	−0.00707767	+	0.0113280i
$446$	−500.065	+	363.318i	−1.12122	+	0.814615i
$447$		0			0
$448$	417.828	+	212.894i	0.932653	+	0.475210i
$449$		−	841.171i		−	1.87343i	−0.350089	−	0.936716i	$-0.613849\pi$
$449$		−	841.171i		−	1.87343i	0.350089	−	0.936716i	$-0.386151\pi$
$450$		0			0
$451$	184.702			0.409539
$452$	92.8896	−	182.306i	0.205508	−	0.403332i
$453$		0			0
$454$	−425.749	−	585.993i	−0.937773	−	1.29073i
$455$	169.089	+	418.445i	0.371625	+	0.919658i
$456$		0			0
$457$	−275.400	−	275.400i	−0.602626	−	0.602626i	0.338383	−	0.941009i	$-0.390120\pi$
$457$	−275.400	−	275.400i	−0.602626	−	0.602626i	−0.941009	+	0.338383i	$0.890120\pi$
$458$	3.53383	−	0.559704i	0.00771579	−	0.00122206i
$459$		0			0
$460$	910.934	+	791.776i	1.98029	+	1.72125i
$461$	54.8017	+	168.662i	0.118876	+	0.365862i	0.992736	−	0.120316i	$-0.0383907\pi$
$461$	54.8017	+	168.662i	0.118876	+	0.365862i	−0.873860	+	0.486178i	$0.838391\pi$
$462$		0			0
$463$	341.485	+	670.202i	0.737548	+	1.44752i	0.888451	+	0.458971i	$0.151782\pi$
$463$	341.485	+	670.202i	0.737548	+	1.44752i	−0.150903	+	0.988549i	$0.548218\pi$
$464$	268.989	−	87.3997i	0.579717	−	0.188361i
$465$		0			0
$466$	−432.056	+	1329.73i	−0.927158	+	2.85350i
$467$	114.260	+	721.406i	0.244667	+	1.54477i	0.737924	+	0.674883i	$0.235806\pi$
$467$	114.260	+	721.406i	0.244667	+	1.54477i	−0.493257	+	0.869883i	$0.664194\pi$
$468$		0			0
$469$	−335.669	+	462.009i	−0.715713	+	0.985094i
$470$	−54.7266	−	782.013i	−0.116440	−	1.66386i
$471$		0			0
$472$	−925.289	−	146.551i	−1.96036	−	0.310490i
$473$	92.0701	+	46.9121i	0.194651	+	0.0991799i
$474$		0			0
$475$	−208.400	−	215.758i	−0.438738	−	0.454227i
$476$	968.874			2.03545
$477$		0			0
$478$	38.5889	−	243.641i	0.0807299	−	0.509709i
$479$	−237.475	−	326.857i	−0.495773	−	0.682373i	0.485667	−	0.874144i	$-0.338577\pi$
$479$	−237.475	−	326.857i	−0.495773	−	0.682373i	−0.981440	+	0.191771i	$0.938577\pi$
$480$		0			0
$481$	−475.875	−	345.743i	−0.989344	−	0.718801i
$482$	112.402	+	112.402i	0.233199	+	0.233199i
$483$		0			0
$484$	−372.644	−	121.079i	−0.769925	−	0.250164i
$485$	−356.307	+	214.117i	−0.734654	+	0.441479i
$486$		0			0
$487$	−167.213	+	85.1992i	−0.343353	+	0.174947i	−0.617160	−	0.786838i	$-0.711717\pi$
$487$	−167.213	+	85.1992i	−0.343353	+	0.174947i	0.273807	+	0.961785i	$0.411717\pi$
$488$	−387.003	−	759.537i	−0.793040	−	1.55643i
$489$		0			0
$490$	−379.708	+	87.6844i	−0.774915	+	0.178948i
$491$	145.170	−	446.788i	0.295662	−	0.909955i	−0.687336	−	0.726340i	$-0.741220\pi$
$491$	145.170	−	446.788i	0.295662	−	0.909955i	0.982998	−	0.183615i	$-0.0587800\pi$
$492$		0			0
$493$	−743.652	+	743.652i	−1.50842	+	1.50842i
$494$	−420.250	+	578.425i	−0.850709	+	1.17090i
$495$		0			0
$496$	70.9702	−	51.5629i	0.143085	−	0.103957i
$497$	−155.178	−	24.5778i	−0.312230	−	0.0494523i
$498$		0			0
$499$			808.726i			1.62069i	0.585951	+	0.810347i	$0.300721\pi$
$499$			808.726i			1.62069i	−0.585951	+	0.810347i	$0.699279\pi$
$500$	366.356	−	823.211i	0.732711	−	1.64642i
$501$		0			0
$502$	143.542	−	281.718i	0.285941	−	0.561191i
$503$	65.3761	−	412.768i	0.129972	−	0.820613i	−0.833444	−	0.552604i	$-0.813634\pi$
$503$	65.3761	−	412.768i	0.129972	−	0.820613i	0.963416	−	0.268009i	$-0.0863658\pi$
$504$		0			0
$505$	77.2198	−	64.8023i	0.152911	−	0.128321i
$506$	740.435	+	537.958i	1.46331	+	1.06316i
$507$		0			0
$508$	1184.57	−	187.618i	2.33184	−	0.369327i
$509$	518.069	+	168.331i	1.01782	+	0.330709i	0.769963	−	0.638088i	$-0.220274\pi$
$509$	518.069	+	168.331i	1.01782	+	0.330709i	0.247855	+	0.968797i	$0.420274\pi$
$510$		0			0
$511$	111.952	+	344.553i	0.219084	+	0.674272i
$512$	−394.180	+	200.845i	−0.769884	+	0.392275i
$513$		0			0
$514$	1045.03	−	339.551i	2.03313	−	0.660605i
$515$	−274.103	−	456.128i	−0.532239	−	0.885686i
$516$		0			0
$517$	−59.8061	−	377.601i	−0.115679	−	0.730369i
$518$	−396.776	+	396.776i	−0.765977	+	0.765977i
$519$		0			0
$520$	−927.515	−	231.202i	−1.78368	−	0.444618i
$521$	−93.2392	+	67.7422i	−0.178962	+	0.130023i	−0.673660	−	0.739042i	$-0.735279\pi$
$521$	−93.2392	+	67.7422i	−0.178962	+	0.130023i	0.494698	+	0.869065i	$0.335279\pi$
$522$		0			0
$523$	444.646	+	226.559i	0.850184	+	0.433190i	0.824083	−	0.566469i	$-0.191691\pi$
$523$	444.646	+	226.559i	0.850184	+	0.433190i	0.0261007	+	0.999659i	$0.491691\pi$
$524$		−	868.705i		−	1.65783i
$525$		0			0
$526$	−150.586			−0.286285
$527$	−148.089	+	290.641i	−0.281004	+	0.551501i
$528$		0			0
$529$	348.195	+	479.249i	0.658213	+	0.905952i
$530$	−1086.02	+	76.0017i	−2.04910	+	0.143399i
$531$		0			0
$532$	310.167	+	310.167i	0.583020	+	0.583020i
$533$	−397.732	+	62.9946i	−0.746214	+	0.118189i
$534$		0			0
$535$	1057.33	+	92.4459i	1.97631	+	0.172796i
$536$	−373.770	−	1150.35i	−0.697332	−	2.14617i
$537$		0			0
$538$	154.663	+	303.542i	0.287477	+	0.564205i
$539$	−180.749	+	58.7289i	−0.335342	+	0.108959i
$540$		0			0
$541$	105.130	−	323.556i	0.194325	−	0.598070i	−0.805659	−	0.592379i	$-0.798189\pi$
$541$	105.130	−	323.556i	0.194325	−	0.598070i	0.999984	−	0.00569041i	$-0.00181132\pi$
$542$	154.582	+	975.993i	0.285207	+	1.80073i
$543$		0			0
$544$	297.596	−	409.605i	0.547051	−	0.752951i
$545$	−325.036	+	131.344i	−0.596396	+	0.240998i
$546$		0			0
$547$	−791.804	−	125.409i	−1.44754	−	0.229268i	−0.617323	−	0.786710i	$-0.711783\pi$
$547$	−791.804	−	125.409i	−1.44754	−	0.229268i	−0.830216	+	0.557442i	$0.811783\pi$
$548$	1423.79	+	725.459i	2.59816	+	1.32383i
$549$		0			0
$550$	222.380	−	646.069i	0.404328	−	1.17467i
$551$	−476.132			−0.864123
$552$		0			0
$553$	−5.66287	+	35.7540i	−0.0102403	+	0.0646545i
$554$	990.726	+	1363.62i	1.78831	+	2.46140i
$555$		0			0
$556$	36.9926	+	26.8767i	0.0665334	+	0.0483393i
$557$	−570.324	−	570.324i	−1.02392	−	1.02392i	−0.999707	−	0.0242138i	$-0.992292\pi$
$557$	−570.324	−	570.324i	−1.02392	−	1.02392i	−0.0242138	−	0.999707i	$-0.507708\pi$
$558$		0			0
$559$	−214.261	−	69.6176i	−0.383293	−	0.124540i
$560$	−70.6095	+	166.371i	−0.126088	+	0.297091i
$561$		0			0
$562$	−32.4143	+	16.5159i	−0.0576767	+	0.0293877i
$563$	−334.231	−	655.966i	−0.593662	−	1.16513i	−0.971006	−	0.239054i	$-0.923163\pi$
$563$	−334.231	−	655.966i	−0.593662	−	1.16513i	0.377345	−	0.926073i	$-0.376837\pi$
$564$		0			0
$565$	−130.643	−	55.4464i	−0.231227	−	0.0981352i
$566$	162.927	−	501.438i	0.287857	−	0.885932i
$567$		0			0
$568$	235.301	−	235.301i	0.414263	−	0.414263i
$569$	−59.8729	+	82.4080i	−0.105225	+	0.144829i	−0.858382	−	0.513011i	$-0.828530\pi$
$569$	−59.8729	+	82.4080i	−0.105225	+	0.144829i	0.753157	+	0.657841i	$0.228530\pi$
$570$		0			0
$571$	71.2359	−	51.7559i	0.124756	−	0.0906408i	−0.523657	−	0.851929i	$-0.675433\pi$
$571$	71.2359	−	51.7559i	0.124756	−	0.0906408i	0.648414	+	0.761288i	$0.275433\pi$
$572$	−1034.47	−	163.844i	−1.80852	−	0.286441i
$573$		0			0
$574$			384.146i			0.669243i
$575$	503.753	−	668.654i	0.876091	−	1.16288i
$576$		0			0
$577$	−310.098	+	608.602i	−0.537432	+	1.05477i	0.449447	+	0.893307i	$0.351621\pi$
$577$	−310.098	+	608.602i	−0.537432	+	1.05477i	−0.986879	+	0.161463i	$0.948379\pi$
$578$	216.514	−	1367.02i	0.374592	−	2.36508i
$579$		0			0
$580$	−535.837	−	1326.03i	−0.923857	−	2.28627i
$581$	−70.2724	−	51.0559i	−0.120951	−	0.0878758i
$582$		0			0
$583$	−524.394	+	83.0559i	−0.899475	+	0.142463i
$584$	−729.768	−	237.116i	−1.24960	−	0.406021i
$585$		0			0
$586$	−250.158	−	769.907i	−0.426891	−	1.31383i
$587$	767.583	−	391.103i	1.30764	−	0.666274i	0.345391	−	0.938459i	$-0.387746\pi$
$587$	767.583	−	391.103i	1.30764	−	0.666274i	0.962245	+	0.272185i	$0.0877462\pi$
$588$		0			0
$589$	−140.451	+	45.6353i	−0.238457	+	0.0774793i
$590$	−127.164	+	1454.40i	−0.215531	+	2.46509i
$591$		0			0
$592$	−36.8491	−	232.656i	−0.0622451	−	0.393000i
$593$	−319.789	+	319.789i	−0.539274	+	0.539274i	−0.923316	−	0.384042i	$-0.874532\pi$
$593$	−319.789	+	319.789i	−0.539274	+	0.539274i	0.384042	+	0.923316i	$0.374532\pi$
$594$		0			0
$595$	−46.9161	−	670.405i	−0.0788505	−	1.12673i
$596$	−667.628	+	485.060i	−1.12018	+	0.813859i
$597$		0			0
$598$	−1777.91	−	905.889i	−2.97309	−	1.51486i
$599$			901.516i			1.50503i	0.658572	+	0.752517i	$0.271161\pi$
$599$			901.516i			1.50503i	−0.658572	+	0.752517i	$0.728839\pi$
$600$		0			0
$601$	−149.364			−0.248525			−0.124263	−	0.992249i	$-0.539657\pi$
$601$	−149.364			−0.248525			−0.124263	+	0.992249i	$0.539657\pi$
$602$	−97.5683	+	191.489i	−0.162074	+	0.318087i
$603$		0			0
$604$	73.3734	+	100.990i	0.121479	+	0.167202i
$605$	−65.7352	+	263.711i	−0.108653	+	0.435886i
$606$		0			0
$607$	337.242	+	337.242i	0.555588	+	0.555588i	0.928048	−	0.372460i	$-0.121486\pi$
$607$	337.242	+	337.242i	0.555588	+	0.555588i	−0.372460	+	0.928048i	$0.621486\pi$
$608$	226.397	−	35.8578i	0.372363	−	0.0589766i
$609$		0			0
$610$	−1138.67	+	684.269i	−1.86668	+	1.12175i
$611$	257.569	+	792.717i	0.421554	+	1.29741i
$612$		0			0
$613$	−303.580	−	595.809i	−0.495236	−	0.971955i	−0.994423	−	0.105461i	$-0.966368\pi$
$613$	−303.580	−	595.809i	−0.495236	−	0.971955i	0.499188	−	0.866494i	$-0.333632\pi$
$614$	71.6091	−	23.2672i	0.116627	−	0.0378945i
$615$		0			0
$616$	−137.422	+	422.942i	−0.223088	+	0.686594i
$617$	−26.8370	−	169.442i	−0.0434959	−	0.274623i	0.956349	−	0.292227i	$-0.0943962\pi$
$617$	−26.8370	−	169.442i	−0.0434959	−	0.274623i	−0.999845	+	0.0176041i	$0.994396\pi$
$618$		0			0
$619$	−89.3476	+	122.976i	−0.144342	+	0.198669i	−0.875066	−	0.484003i	$-0.839182\pi$
$619$	−89.3476	+	122.976i	−0.144342	+	0.198669i	0.730725	+	0.682672i	$0.239182\pi$
$620$	−285.158	−	339.800i	−0.459932	−	0.548065i
$621$		0			0
$622$	890.244	+	141.001i	1.43126	+	0.226689i
$623$	−5.37183	−	2.73708i	−0.00862251	−	0.00439339i
$624$		0			0
$625$	−587.355	−	213.634i	−0.939767	−	0.341815i
$626$	−338.365			−0.540520
$627$		0			0
$628$	−8.85776	+	55.9257i	−0.0141047	+	0.0890536i
$629$	514.837	+	708.613i	0.818501	+	1.12657i
$630$		0			0
$631$	18.5290	+	13.4621i	0.0293644	+	0.0213345i	0.602371	−	0.798216i	$-0.294223\pi$
$631$	18.5290	+	13.4621i	0.0293644	+	0.0213345i	−0.573006	+	0.819551i	$0.694223\pi$
$632$	−54.2149	−	54.2149i	−0.0857830	−	0.0857830i
$633$		0			0
$634$	−409.173	−	132.948i	−0.645384	−	0.209698i
$635$	−187.182	−	810.572i	−0.294775	−	1.27649i
$636$		0			0
$637$	369.190	−	188.112i	0.579576	−	0.295309i
$638$	−492.366	−	966.323i	−0.771734	−	1.51461i
$639$		0			0
$640$	600.472	+	999.229i	0.938237	+	1.56130i
$641$	130.156	−	400.579i	0.203052	−	0.624929i	−0.796736	−	0.604327i	$-0.793442\pi$
$641$	130.156	−	400.579i	0.203052	−	0.624929i	0.999788	−	0.0206013i	$-0.00655807\pi$
$642$		0			0
$643$	−153.151	+	153.151i	−0.238182	+	0.238182i	−0.816097	−	0.577915i	$-0.803867\pi$
$643$	−153.151	+	153.151i	−0.238182	+	0.238182i	0.577915	+	0.816097i	$0.303867\pi$
$644$	−719.561	+	990.391i	−1.11733	+	1.53787i
$645$		0			0
$646$	861.318	−	625.784i	1.33331	−	0.968706i
$647$	1003.06	+	158.869i	1.55032	+	0.245546i	0.872105	−	0.489318i	$-0.162754\pi$
$647$	1003.06	+	158.869i	1.55032	+	0.245546i	0.678214	+	0.734864i	$0.262754\pi$
$648$		0			0
$649$			711.993i			1.09706i
$650$	−258.519	+	1467.07i	−0.397721	+	2.25703i
$651$		0			0
$652$	49.9651	−	98.0620i	0.0766336	−	0.150402i
$653$	104.253	−	658.227i	0.159652	−	1.00800i	−0.769592	−	0.638537i	$-0.779540\pi$
$653$	104.253	−	658.227i	0.159652	−	1.00800i	0.929244	−	0.369467i	$-0.120460\pi$
$654$		0			0
$655$	−601.094	+	42.0655i	−0.917700	+	0.0642222i
$656$	−130.463	−	94.7869i	−0.198877	−	0.144492i
$657$		0			0
$658$	785.339	−	124.386i	1.19352	−	0.189036i
$659$	−838.448	−	272.428i	−1.27230	−	0.413396i	−0.406440	−	0.913678i	$-0.633230\pi$
$659$	−838.448	−	272.428i	−1.27230	−	0.413396i	−0.865863	+	0.500281i	$0.833230\pi$
$660$		0			0
$661$	304.897	+	938.378i	0.461267	+	1.41963i	0.863617	+	0.504148i	$0.168193\pi$
$661$	304.897	+	938.378i	0.461267	+	1.41963i	−0.402350	+	0.915486i	$0.631807\pi$
$662$	−1164.55	+	593.368i	−1.75914	+	0.896327i
$663$		0			0
$664$	174.969	−	56.8510i	0.263508	−	0.0856190i
$665$	199.598	−	229.637i	0.300147	−	0.345318i
$666$		0			0
$667$	−207.873	−	1312.46i	−0.311654	−	1.96771i
$668$	1156.30	−	1156.30i	1.73099	−	1.73099i
$669$		0			0
$670$	−1747.67	+	706.214i	−2.60846	+	1.05405i
$671$	−524.136	+	380.807i	−0.781127	+	0.567522i
$672$		0			0
$673$	−864.100	−	440.281i	−1.28395	−	0.654207i	−0.327158	−	0.944970i	$-0.606091\pi$
$673$	−864.100	−	440.281i	−1.28395	−	0.654207i	−0.956795	+	0.290763i	$0.906091\pi$
$674$		−	912.338i		−	1.35362i
$675$		0			0
$676$	1065.26			1.57583
$677$	37.6719	−	73.9352i	0.0556453	−	0.109210i	−0.861509	−	0.507742i	$-0.830480\pi$
$677$	37.6719	−	73.9352i	0.0556453	−	0.109210i	0.917154	+	0.398532i	$0.130480\pi$
$678$		0			0
$679$	−247.830	−	341.109i	−0.364993	−	0.502370i
$680$	1207.15	+	754.221i	1.77523	+	1.10915i
$681$		0			0
$682$	−237.858	−	237.858i	−0.348765	−	0.348765i
$683$	−468.040	+	74.1303i	−0.685272	+	0.108536i	−0.489356	−	0.872084i	$-0.662768\pi$
$683$	−468.040	+	74.1303i	−0.685272	+	0.108536i	−0.195916	+	0.980621i	$0.562768\pi$
$684$		0			0
$685$	433.031	−	1020.31i	0.632161	−	1.48951i
$686$	−379.234	−	1167.16i	−0.552819	−	1.70140i
$687$		0			0
$688$	−40.9584	−	80.3853i	−0.0595325	−	0.116839i
$689$	1100.89	−	357.700i	1.59781	−	0.519158i
$690$		0			0
$691$	159.311	−	490.310i	0.230552	−	0.709566i	−0.767128	−	0.641494i	$-0.778315\pi$
$691$	159.311	−	490.310i	0.230552	−	0.709566i	0.997680	−	0.0680726i	$-0.0216850\pi$
$692$	−5.06425	−	31.9744i	−0.00731828	−	0.0462058i
$693$		0			0
$694$	324.492	−	446.625i	0.467568	−	0.643552i
$695$	16.8058	−	26.8982i	0.0241810	−	0.0387024i
$696$		0			0
$697$	592.252	+	93.8036i	0.849717	+	0.134582i
$698$	1503.51	+	766.075i	2.15402	+	1.09753i
$699$		0			0
$700$	864.168	+	297.451i	1.23453	+	0.424931i
$701$	503.480			0.718232			0.359116	−	0.933293i	$-0.383078\pi$
$701$	503.480			0.718232			0.359116	+	0.933293i	$0.383078\pi$
$702$		0			0
$703$	−62.0335	+	391.664i	−0.0882411	+	0.557133i
$704$	443.694	+	610.692i	0.630247	+	0.867461i
$705$		0			0
$706$	−35.1526	−	25.5399i	−0.0497913	−	0.0361755i
$707$	72.3007	+	72.3007i	0.102264	+	0.102264i
$708$		0			0
$709$	514.565	+	167.192i	0.725762	+	0.235814i	0.648519	−	0.761198i	$-0.275389\pi$
$709$	514.565	+	167.192i	0.725762	+	0.235814i	0.0772422	+	0.997012i	$0.475389\pi$
$710$	−391.400	−	340.201i	−0.551267	−	0.479156i
$711$		0			0
$712$	11.3776	−	5.79718i	0.0159798	−	0.00814211i
$713$	−187.113	−	367.230i	−0.262431	−	0.515049i
$714$		0			0
$715$	−63.2782	+	723.729i	−0.0885010	+	1.01221i
$716$	423.743	−	1304.15i	0.591819	−	1.82143i
$717$		0			0
$718$	107.243	−	107.243i	0.149364	−	0.149364i
$719$	129.983	−	178.907i	0.180784	−	0.248827i	−0.709002	−	0.705207i	$-0.750854\pi$
$719$	129.983	−	178.907i	0.180784	−	0.248827i	0.889785	+	0.456380i	$0.150854\pi$
$720$		0			0
$721$	436.672	−	317.261i	0.605648	−	0.440029i
$722$	−717.644	−	113.664i	−0.993966	−	0.157429i
$723$		0			0
$724$			1586.27i			2.19098i
$725$	−891.592	+	434.979i	−1.22978	+	0.599971i
$726$		0			0
$727$	323.090	−	634.099i	0.444415	−	0.872213i	−0.554776	−	0.832000i	$-0.687196\pi$
$727$	323.090	−	634.099i	0.444415	−	0.872213i	0.999191	−	0.0402135i	$-0.0128038\pi$
$728$	151.672	−	957.620i	0.208341	−	1.31541i
$729$		0			0
$730$	−289.227	+	1160.30i	−0.396202	+	1.58945i
$731$	271.401	+	197.184i	0.371273	+	0.269746i
$732$		0			0
$733$	822.224	−	130.227i	1.12172	−	0.177664i	0.432096	−	0.901828i	$-0.357774\pi$
$733$	822.224	−	130.227i	1.12172	−	0.177664i	0.689628	+	0.724164i	$0.257774\pi$
$734$	1108.82	+	360.278i	1.51066	+	0.490843i
$735$		0			0
$736$	197.684	+	608.410i	0.268593	+	0.826643i
$737$	−819.071	+	417.338i	−1.11136	+	0.566265i
$738$		0			0
$739$	−823.615	+	267.609i	−1.11450	+	0.362123i	−0.807666	−	0.589640i	$-0.799270\pi$
$739$	−823.615	+	267.609i	−1.11450	+	0.362123i	−0.306834	+	0.951763i	$0.599270\pi$
$740$	−1160.60	+	268.013i	−1.56838	+	0.362180i
$741$		0			0
$742$	−172.741	−	1090.64i	−0.232804	−	1.46987i
$743$	82.9751	−	82.9751i	0.111676	−	0.111676i	−0.649061	−	0.760737i	$-0.724838\pi$
$743$	82.9751	−	82.9751i	0.111676	−	0.111676i	0.760737	+	0.649061i	$0.224838\pi$
$744$		0			0
$745$	367.962	+	438.472i	0.493909	+	0.588553i
$746$	1627.45	−	1182.41i	2.18157	−	1.58501i
$747$		0			0
$748$	1389.62	+	708.047i	1.85778	+	0.946587i
$749$			1076.53i			1.43729i
$750$		0			0
$751$	−707.803			−0.942481			−0.471241	−	0.882005i	$-0.656194\pi$
$751$	−707.803			−0.942481			−0.471241	+	0.882005i	$0.656194\pi$
$752$	−151.537	+	297.408i	−0.201512	+	0.395489i
$753$		0			0
$754$	1389.82	+	1912.92i	1.84326	+	2.53704i
$755$	66.3262	−	55.6604i	0.0878492	−	0.0737224i
$756$		0			0
$757$	149.107	+	149.107i	0.196971	+	0.196971i	0.798700	−	0.601729i	$-0.205521\pi$
$757$	149.107	+	149.107i	0.196971	+	0.196971i	−0.601729	+	0.798700i	$0.705521\pi$
$758$	713.061	−	112.938i	0.940714	−	0.148994i
$759$		0			0
$760$	144.998	+	627.897i	0.190786	+	0.826180i
$761$	208.495	+	641.681i	0.273975	+	0.843208i	0.989489	+	0.144610i	$0.0461926\pi$
$761$	208.495	+	641.681i	0.273975	+	0.843208i	−0.715514	+	0.698598i	$0.753807\pi$
$762$		0			0
$763$	−161.430	−	316.824i	−0.211573	−	0.415235i
$764$	−808.881	+	262.821i	−1.05875	+	0.344007i
$765$		0			0
$766$	71.5690	−	220.267i	0.0934321	−	0.287554i
$767$	−242.833	−	1533.19i	−0.316601	−	1.99894i
$768$		0			0
$769$	595.027	−	818.985i	0.773768	−	1.06500i	−0.222175	−	0.975007i	$-0.571315\pi$
$769$	595.027	−	818.985i	0.773768	−	1.06500i	0.995942	−	0.0899931i	$-0.0286845\pi$
$770$	672.457	+	167.623i	0.873321	+	0.217693i
$771$		0			0
$772$	−642.794	−	101.809i	−0.832635	−	0.131876i
$773$	−896.098	−	456.585i	−1.15925	−	0.590666i	−0.234826	−	0.972037i	$-0.575452\pi$
$773$	−896.098	−	456.585i	−1.15925	−	0.590666i	−0.924422	+	0.381371i	$0.875452\pi$
$774$		0			0
$775$	−221.314	+	213.767i	−0.285566	+	0.275828i
$776$	893.027			1.15081
$777$		0			0
$778$	−109.708	+	692.667i	−0.141012	+	0.890317i
$779$	159.569	+	219.628i	0.204838	+	0.281936i
$780$		0			0
$781$	−204.605	−	148.654i	−0.261978	−	0.190338i
$782$	2101.02	+	2101.02i	2.68672	+	2.68672i
$783$		0			0
$784$	157.810	+	51.2755i	0.201288	+	0.0654025i
$785$	39.1262	+	3.42095i	0.0498423	+	0.00435790i
$786$		0			0
$787$	1024.64	−	522.079i	1.30195	−	0.663379i	0.340994	−	0.940065i	$-0.389236\pi$
$787$	1024.64	−	522.079i	1.30195	−	0.663379i	0.960960	+	0.276686i	$0.0892363\pi$
$788$	278.350	+	546.292i	0.353236	+	0.693264i
$789$		0			0
$790$	−78.3843	+	90.1808i	−0.0992207	+	0.114153i
$791$	44.4832	−	136.905i	0.0562366	−	0.173079i
$792$		0			0
$793$	998.781	−	998.781i	1.25950	−	1.25950i
$794$	654.552	−	900.913i	0.824372	−	1.13465i
$795$		0			0
$796$	−654.424	+	475.467i	−0.822141	+	0.597320i
$797$	−58.1783	−	9.21454i	−0.0729966	−	0.0115615i	0.119829	−	0.992795i	$-0.461765\pi$
$797$	−58.1783	−	9.21454i	−0.0729966	−	0.0115615i	−0.192826	+	0.981233i	$0.561765\pi$
$798$		0			0
$799$		−	1241.16i		−	1.55339i
$800$	391.186	−	273.975i	0.488983	−	0.342469i
$801$		0			0
$802$	−217.472	+	426.813i	−0.271162	+	0.532186i
$803$	−91.2283	+	575.993i	−0.113609	+	0.717301i
$804$		0			0
$805$	720.137	+	449.937i	0.894580	+	0.558928i
$806$	593.320	+	431.072i	0.736129	+	0.534829i
$807$		0			0
$808$	−213.898	+	33.8781i	−0.264725	+	0.0419283i
$809$	−890.150	−	289.227i	−1.10031	−	0.357512i	−0.298088	−	0.954538i	$-0.596349\pi$
$809$	−890.150	−	289.227i	−1.10031	−	0.357512i	−0.802222	+	0.597026i	$0.796349\pi$
$810$		0			0
$811$	354.720	+	1091.71i	0.437385	+	1.34613i	0.890622	+	0.454744i	$0.150269\pi$
$811$	354.720	+	1091.71i	0.437385	+	1.34613i	−0.453237	+	0.891390i	$0.649731\pi$
$812$	1292.53	−	658.579i	1.59179	−	0.811058i
$813$		0			0
$814$	−859.042	+	279.120i	−1.05533	+	0.342899i
$815$	−70.2727	−	29.8245i	−0.0862242	−	0.0365944i
$816$		0			0
$817$	23.7590	+	150.008i	0.0290808	+	0.183609i
$818$	−1771.69	+	1771.69i	−2.16588	+	2.16588i
$819$		0			0
$820$	−432.088	+	691.570i	−0.526937	+	0.843378i
$821$	598.631	−	434.931i	0.729149	−	0.529758i	−0.160145	−	0.987093i	$-0.551196\pi$
$821$	598.631	−	434.931i	0.729149	−	0.529758i	0.889294	+	0.457336i	$0.151196\pi$
$822$		0			0
$823$	−645.845	−	329.074i	−0.784744	−	0.399847i	0.0152280	−	0.999884i	$-0.495153\pi$
$823$	−645.845	−	329.074i	−0.784744	−	0.399847i	−0.799972	+	0.600037i	$0.795153\pi$
$824$			1143.21i			1.38739i
$825$		0			0
$826$	−1480.81			−1.79275
$827$	−240.680	+	472.361i	−0.291028	+	0.571175i	−0.989512	−	0.144451i	$-0.953858\pi$
$827$	−240.680	+	472.361i	−0.291028	+	0.571175i	0.698484	+	0.715626i	$0.253858\pi$
$828$		0			0
$829$	718.610	+	989.082i	0.866840	+	1.19310i	0.979895	+	0.199514i	$0.0639363\pi$
$829$	718.610	+	989.082i	0.866840	+	1.19310i	−0.113055	+	0.993589i	$0.536064\pi$
$830$	−107.416	−	265.823i	−0.129417	−	0.320269i
$831$		0			0
$832$	−1163.72	−	1163.72i	−1.39870	−	1.39870i
$833$	−609.404	+	96.5200i	−0.731577	+	0.115870i
$834$		0			0
$835$	−856.084	−	744.100i	−1.02525	−	0.891138i
$836$	218.193	+	671.528i	0.260996	+	0.803263i
$837$		0			0
$838$	236.346	+	463.855i	0.282036	+	0.553526i
$839$	1186.02	−	385.361i	1.41361	−	0.459310i	0.500043	−	0.866000i	$-0.333317\pi$
$839$	1186.02	−	385.361i	1.41361	−	0.459310i	0.913566	+	0.406691i	$0.133317\pi$
$840$		0			0
$841$	−226.704	+	697.723i	−0.269565	+	0.829635i
$842$	−284.938	−	1799.03i	−0.338406	−	2.13661i
$843$		0			0
$844$	428.966	−	590.421i	0.508254	−	0.699551i
$845$	−51.5834	−	737.099i	−0.0610455	−	0.872307i
$846$		0			0
$847$	−272.270	−	43.1234i	−0.321453	−	0.0509131i
$848$	413.025	+	210.447i	0.487058	+	0.248169i
$849$		0			0
$850$	1041.18	−	1958.70i	1.22492	−	2.30435i
$851$	−1106.71			−1.30048
$852$		0			0
$853$	203.770	−	1286.55i	0.238887	−	1.50827i	−0.518372	−	0.855155i	$-0.673462\pi$
$853$	203.770	−	1286.55i	0.238887	−	1.50827i	0.757258	−	0.653115i	$-0.226538\pi$
$854$	−792.008	−	1090.11i	−0.927410	−	1.27647i
$855$		0			0
$856$	−1844.64	−	1340.21i	−2.15496	−	1.56567i
$857$	230.040	+	230.040i	0.268424	+	0.268424i	0.828465	−	0.560041i	$-0.189215\pi$
$857$	230.040	+	230.040i	0.268424	+	0.268424i	−0.560041	+	0.828465i	$0.689215\pi$
$858$		0			0
$859$	−200.365	−	65.1026i	−0.233254	−	0.0757889i	0.190058	−	0.981773i	$-0.439133\pi$
$859$	−200.365	−	65.1026i	−0.233254	−	0.0757889i	−0.423312	+	0.905984i	$0.639133\pi$
$860$	−391.037	+	234.988i	−0.454695	+	0.273242i
$861$		0			0
$862$	369.185	−	188.109i	0.428289	−	0.218224i
$863$	404.297	+	793.477i	0.468478	+	0.919440i	0.997489	+	0.0708248i	$0.0225631\pi$
$863$	404.297	+	793.477i	0.468478	+	0.919440i	−0.529011	+	0.848615i	$0.677437\pi$
$864$		0			0
$865$	−21.8792	+	5.05247i	−0.0252939	+	0.00584101i
$866$	−735.381	+	2263.27i	−0.849169	+	2.61347i
$867$		0			0
$868$	318.154	−	318.154i	0.366537	−	0.366537i
$869$	−34.2508	+	47.1422i	−0.0394140	+	0.0542488i
$870$		0			0
$871$	1621.43	−	1178.04i	1.86157	−	1.35251i
$872$	743.853	+	117.815i	0.853042	+	0.135109i
$873$		0			0
$874$			1345.20i			1.53913i
$875$	163.973	−	612.358i	0.187398	−	0.699838i
$876$		0			0
$877$	−355.726	+	698.152i	−0.405617	+	0.796068i	−0.999967	−	0.00813824i	$-0.997409\pi$
$877$	−355.726	+	698.152i	−0.405617	+	0.796068i	0.594350	+	0.804207i	$0.297409\pi$
$878$	−173.564	+	1095.84i	−0.197681	+	1.24811i
$879$		0			0
$880$	−222.855	+	187.018i	−0.253244	+	0.212521i
$881$	−1064.05	−	773.077i	−1.20777	−	0.877499i	−0.212747	−	0.977107i	$-0.568241\pi$
$881$	−1064.05	−	773.077i	−1.20777	−	0.877499i	−0.995027	+	0.0996082i	$0.968241\pi$
$882$		0			0
$883$	−306.337	+	48.5191i	−0.346928	+	0.0549480i	−0.327467	−	0.944863i	$-0.606195\pi$
$883$	−306.337	+	48.5191i	−0.346928	+	0.0549480i	−0.0194609	+	0.999811i	$0.506195\pi$
$884$	−3233.85	−	1050.74i	−3.65821	−	1.18862i
$885$		0			0
$886$	−548.530	−	1688.20i	−0.619108	−	1.90542i
$887$	57.9184	−	29.5109i	0.0652970	−	0.0332705i	−0.421037	−	0.907043i	$-0.638334\pi$
$887$	57.9184	−	29.5109i	0.0652970	−	0.0332705i	0.486334	+	0.873773i	$0.338334\pi$
$888$		0			0
$889$	802.494	−	260.746i	0.902693	−	0.293303i
$890$	−10.2501	−	17.0570i	−0.0115170	−	0.0191651i
$891$		0			0
$892$	−208.194	−	1314.49i	−0.233401	−	1.47364i
$893$	397.334	−	397.334i	0.444943	−	0.444943i
$894$		0			0
$895$	−922.913	−	230.054i	−1.03119	−	0.257044i
$896$	−956.608	+	695.016i	−1.06764	+	0.775688i
$897$		0			0
$898$	2509.21	+	1278.51i	2.79422	+	1.42373i
$899$			488.393i			0.543263i
$900$		0			0
$901$	−1723.67			−1.91306
$902$	−280.731	+	550.966i	−0.311232	+	0.610827i
$903$		0			0
$904$	179.210	+	246.661i	0.198241	+	0.272855i
$905$	1097.61	−	76.8124i	1.21283	−	0.0848755i
$906$		0			0
$907$	867.106	+	867.106i	0.956016	+	0.956016i	0.999073	−	0.0430568i	$-0.0137096\pi$
$907$	867.106	+	867.106i	0.956016	+	0.956016i	−0.0430568	+	0.999073i	$0.513710\pi$
$908$	1540.36	−	243.969i	1.69643	−	0.268688i
$909$		0			0
$910$	−1505.22	−	131.607i	−1.65409	−	0.144623i
$911$	59.9615	+	184.542i	0.0658194	+	0.202571i	0.978557	−	0.205974i	$-0.0660362\pi$
$911$	59.9615	+	184.542i	0.0658194	+	0.202571i	−0.912738	+	0.408545i	$0.866036\pi$
$912$		0			0
$913$	−63.4777	−	124.582i	−0.0695265	−	0.136454i
$914$	1240.10	−	402.933i	1.35678	−	0.440846i
$915$		0			0
$916$	−2.38054	+	7.32655i	−0.00259884	+	0.00799842i
$917$	−95.6088	−	603.650i	−0.104263	−	0.658288i
$918$		0			0
$919$	318.962	−	439.013i	0.347075	−	0.477707i	−0.599416	−	0.800437i	$-0.704601\pi$
$919$	318.962	−	439.013i	0.347075	−	0.477707i	0.946491	+	0.322730i	$0.104601\pi$
$920$	−1667.50	+	673.818i	−1.81250	+	0.732411i
$921$		0			0
$922$	−586.413	−	92.8788i	−0.636023	−	0.100736i
$923$	491.290	+	250.325i	0.532275	+	0.271208i
$924$		0			0
$925$	241.650	+	790.092i	0.261243	+	0.854153i
$926$	−2518.24			−2.71948
$927$		0			0
$928$	118.586	−	748.724i	0.127787	−	0.806814i
$929$	−6.29997	−	8.67117i	−0.00678145	−	0.00933387i	0.805613	−	0.592442i	$-0.201836\pi$
$929$	−6.29997	−	8.67117i	−0.00678145	−	0.00933387i	−0.812394	+	0.583109i	$0.801836\pi$
$930$		0			0
$931$	−225.988	−	164.190i	−0.242737	−	0.176359i
$932$	−2128.68	−	2128.68i	−2.28399	−	2.28399i
$933$		0			0
$934$	−2325.62	−	755.639i	−2.48995	−	0.809035i
$935$	422.637	−	995.822i	0.452019	−	1.06505i
$936$		0			0
$937$	−240.296	+	122.437i	−0.256453	+	0.130669i	−0.577491	−	0.816397i	$-0.695968\pi$
$937$	−240.296	+	122.437i	−0.256453	+	0.130669i	0.321038	+	0.947066i	$0.395968\pi$
$938$	−867.984	−	1703.51i	−0.925356	−	1.81611i
$939$		0			0
$940$	1553.74	+	659.423i	1.65292	+	0.701514i
$941$	−247.068	+	760.397i	−0.262559	+	0.808073i	0.729687	+	0.683781i	$0.239666\pi$
$941$	−247.068	+	760.397i	−0.262559	+	0.808073i	−0.992246	+	0.124292i	$0.960334\pi$
$942$		0			0
$943$	−535.739	+	535.739i	−0.568122	+	0.568122i
$944$	365.387	−	502.912i	0.387062	−	0.532745i
$945$		0			0
$946$	−279.877	+	203.343i	−0.295853	+	0.214950i
$947$	1164.88	+	184.500i	1.23008	+	0.194825i	0.737443	−	0.675410i	$-0.236033\pi$
$947$	1164.88	+	184.500i	1.23008	+	0.194825i	0.492636	+	0.870235i	$0.336033\pi$
$948$		0			0
$949$		−	1271.44i		−	1.33977i
$950$	960.355	−	293.725i	1.01090	−	0.309184i
$951$		0			0
$952$	−655.445	+	1286.38i	−0.688493	+	1.35124i
$953$	−181.717	+	1147.31i	−0.190679	+	1.20390i	0.687723	+	0.725973i	$0.258610\pi$
$953$	−181.717	+	1147.31i	−0.190679	+	1.20390i	−0.878401	+	0.477924i	$0.841390\pi$
$954$		0			0
$955$	221.026	+	546.972i	0.231441	+	0.572746i
$956$	429.690	+	312.188i	0.449466	+	0.326556i
$957$		0			0
$958$	1335.95	−	211.594i	1.39452	−	0.220871i
$959$	1069.22	+	347.409i	1.11493	+	0.362262i
$960$		0			0
$961$	−250.155	−	769.898i	−0.260307	−	0.801142i
$962$	1754.64	−	894.033i	1.82395	−	0.929349i
$963$		0			0
$964$	−325.509	+	105.764i	−0.337665	+	0.109714i
$965$	−39.3194	+	449.706i	−0.0407455	+	0.466017i
$966$		0			0
$967$	175.279	+	1106.67i	0.181261	+	1.14444i	0.895674	+	0.444711i	$0.146694\pi$
$967$	175.279	+	1106.67i	0.181261	+	1.14444i	−0.714413	+	0.699724i	$0.753306\pi$
$968$	412.852	−	412.852i	0.426500	−	0.426500i
$969$		0			0
$970$	−97.1558	−	1388.30i	−0.100161	−	1.43124i
$971$	806.422	−	585.900i	0.830507	−	0.603399i	−0.0891956	−	0.996014i	$-0.528430\pi$
$971$	806.422	−	585.900i	0.830507	−	0.603399i	0.919703	+	0.392615i	$0.128430\pi$
$972$		0			0
$973$	28.6636	+	14.6048i	0.0294590	+	0.0150101i
$974$		−	628.291i		−	0.645063i
$975$		0			0
$976$	565.646			0.579555
$977$	−9.63744	+	18.9145i	−0.00986432	+	0.0193598i	−0.895886	−	0.444284i	$-0.853458\pi$
$977$	−9.63744	+	18.9145i	−0.00986432	+	0.0193598i	0.886022	+	0.463644i	$0.153458\pi$
$978$		0			0
$979$	−5.70437	−	7.85139i	−0.00582673	−	0.00801980i
$980$	202.945	−	814.159i	0.207087	−	0.830774i
$981$		0			0
$982$	1112.12	+	1112.12i	1.13251	+	1.13251i
$983$	836.347	−	132.464i	0.850810	−	0.134755i	0.284224	−	0.958758i	$-0.408264\pi$
$983$	836.347	−	132.464i	0.850810	−	0.134755i	0.566586	+	0.824003i	$0.308264\pi$
$984$		0			0
$985$	364.524	−	219.055i	0.370075	−	0.222391i
$986$	−1088.03	−	3348.60i	−1.10347	−	3.39614i
$987$		0			0
$988$	−698.881	−	1371.63i	−0.707370	−	1.38829i
$989$	−403.126	+	130.984i	−0.407610	+	0.132441i
$990$		0			0
$991$	−359.275	+	1105.74i	−0.362538	+	1.11578i	0.588970	+	0.808155i	$0.299534\pi$
$991$	−359.275	+	1105.74i	−0.362538	+	1.11578i	−0.951508	+	0.307623i	$0.900466\pi$
$992$	−36.7811	−	232.227i	−0.0370778	−	0.234100i
$993$		0			0
$994$	309.173	−	425.540i	0.311039	−	0.428108i
$995$	360.685	+	429.800i	0.362497	+	0.431960i
$996$		0			0
$997$	496.275	+	78.6022i	0.497768	+	0.0788387i	0.400270	−	0.916397i	$-0.368916\pi$
$997$	496.275	+	78.6022i	0.497768	+	0.0788387i	0.0974975	+	0.995236i	$0.468916\pi$
$998$	−2412.43	−	1229.19i	−2.41726	−	1.23166i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.3.r.b.217.2		80
3.2	odd	2		75.3.k.a.67.9	yes	80
15.2	even	4		375.3.k.b.268.9		80
15.8	even	4		375.3.k.c.268.2		80
15.14	odd	2		375.3.k.a.232.2		80
25.3	odd	20	inner	225.3.r.b.28.2		80
75.29	odd	10		375.3.k.b.7.9		80
75.47	even	20		375.3.k.a.118.2		80
75.53	even	20		75.3.k.a.28.9	✓	80
75.71	odd	10		375.3.k.c.7.2		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.28.9	✓	80	75.53	even	20
75.3.k.a.67.9	yes	80	3.2	odd	2
225.3.r.b.28.2		80	25.3	odd	20	inner
225.3.r.b.217.2		80	1.1	even	1	trivial
375.3.k.a.118.2		80	75.47	even	20
375.3.k.a.232.2		80	15.14	odd	2
375.3.k.b.7.9		80	75.29	odd	10
375.3.k.b.268.9		80	15.2	even	4
375.3.k.c.7.2		80	75.71	odd	10
375.3.k.c.268.2		80	15.8	even	4

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.r (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.51991 + 2.98300i) q^{2} +(-4.23700 - 5.83172i) q^{4} +(-3.83005 + 3.21415i) q^{5} +(-3.58606 - 3.58606i) q^{7} +(10.6092 - 1.68033i) q^{8} +O(q^{10})\)	\(q+(-1.51991 + 2.98300i) q^{2} +(-4.23700 - 5.83172i) q^{4} +(-3.83005 + 3.21415i) q^{5} +(-3.58606 - 3.58606i) q^{7} +(10.6092 - 1.68033i) q^{8} +(-3.76645 - 16.3102i) q^{10} +(-2.52268 - 7.76402i) q^{11} +(8.08027 + 15.8584i) q^{13} +(16.1477 - 5.24671i) q^{14} +(-2.20252 + 6.77867i) q^{16} +(-4.14599 - 26.1767i) q^{17} +(7.05272 - 9.70724i) q^{19} +(34.9719 + 8.71745i) q^{20} +(26.9943 + 4.27548i) q^{22} +(29.8372 + 15.2028i) q^{23} +(4.33852 - 24.6207i) q^{25} -59.5869 q^{26} +(-5.71879 + 36.1070i) q^{28} +(-23.3243 - 32.1031i) q^{29} +(-9.95722 - 7.23434i) q^{31} +(13.5082 + 13.5082i) q^{32} +(84.3867 + 27.4189i) q^{34} +(25.2609 + 2.20865i) q^{35} +(-29.4467 + 15.0038i) q^{37} +(18.2371 + 35.7924i) q^{38} +(-35.2328 + 40.5352i) q^{40} +(-6.99156 + 21.5178i) q^{41} +(-8.95040 + 8.95040i) q^{43} +(-34.5890 + 47.6077i) q^{44} +(-90.6999 + 65.8973i) q^{46} +(46.2544 + 7.32597i) q^{47} -23.2804i q^{49} +(66.8492 + 50.3631i) q^{50} +(58.2459 - 114.314i) q^{52} +(10.1740 - 64.2359i) q^{53} +(34.6167 + 21.6283i) q^{55} +(-44.0709 - 32.0194i) q^{56} +(131.214 - 20.7823i) q^{58} +(-82.9473 - 26.9512i) q^{59} +(-24.5238 - 75.4766i) q^{61} +(36.7141 - 18.7068i) q^{62} +(-87.9409 + 28.5737i) q^{64} +(-81.9191 - 34.7673i) q^{65} +(-17.6154 - 111.219i) q^{67} +(-135.089 + 135.089i) q^{68} +(-44.9828 + 71.9962i) q^{70} +(25.0631 - 18.2094i) q^{71} +(-63.6499 - 32.4313i) q^{73} -110.644i q^{74} -86.4923 q^{76} +(-18.7957 + 36.8887i) q^{77} +(-4.19556 - 5.77470i) q^{79} +(-13.3519 - 33.0419i) q^{80} +(-53.5610 - 53.5610i) q^{82} +(16.9166 - 2.67933i) q^{83} +(100.015 + 86.9323i) q^{85} +(-13.0952 - 40.3029i) q^{86} +(-39.8097 - 78.1309i) q^{88} +(1.13062 - 0.367359i) q^{89} +(27.8929 - 85.8456i) q^{91} +(-37.7615 - 238.417i) q^{92} +(-92.1560 + 126.842i) q^{94} +(4.18824 + 59.8477i) q^{95} +(82.1151 + 13.0058i) q^{97} +(69.4452 + 35.3841i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{2} - 4 q^{5} - 4 q^{7} + 12 q^{8}+O(q^{10}) \) 80 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 + 12 * q^8	\( 80 q - 4 q^{2} - 4 q^{5} - 4 q^{7} + 12 q^{8} - 4 q^{10} + 32 q^{13} + 80 q^{16} + 100 q^{17} - 100 q^{19} + 244 q^{20} - 100 q^{22} + 96 q^{23} - 16 q^{25} + 40 q^{26} + 196 q^{28} - 200 q^{29} - 636 q^{32} + 100 q^{34} - 260 q^{35} - 184 q^{37} + 564 q^{38} - 948 q^{40} - 160 q^{41} - 472 q^{43} + 700 q^{44} + 288 q^{47} - 16 q^{50} + 620 q^{52} - 304 q^{53} + 604 q^{55} + 1272 q^{58} - 800 q^{59} - 240 q^{61} - 1212 q^{62} + 100 q^{64} - 272 q^{65} - 80 q^{67} - 104 q^{68} - 260 q^{70} - 116 q^{73} + 88 q^{77} + 200 q^{79} + 164 q^{80} - 168 q^{82} + 1264 q^{83} - 212 q^{85} - 212 q^{88} + 1500 q^{89} + 1504 q^{92} - 200 q^{94} + 784 q^{95} - 260 q^{97} + 92 q^{98}+O(q^{100}) \) 80 * q - 4 * q^2 - 4 * q^5 - 4 * q^7 + 12 * q^8 - 4 * q^10 + 32 * q^13 + 80 * q^16 + 100 * q^17 - 100 * q^19 + 244 * q^20 - 100 * q^22 + 96 * q^23 - 16 * q^25 + 40 * q^26 + 196 * q^28 - 200 * q^29 - 636 * q^32 + 100 * q^34 - 260 * q^35 - 184 * q^37 + 564 * q^38 - 948 * q^40 - 160 * q^41 - 472 * q^43 + 700 * q^44 + 288 * q^47 - 16 * q^50 + 620 * q^52 - 304 * q^53 + 604 * q^55 + 1272 * q^58 - 800 * q^59 - 240 * q^61 - 1212 * q^62 + 100 * q^64 - 272 * q^65 - 80 * q^67 - 104 * q^68 - 260 * q^70 - 116 * q^73 + 88 * q^77 + 200 * q^79 + 164 * q^80 - 168 * q^82 + 1264 * q^83 - 212 * q^85 - 212 * q^88 + 1500 * q^89 + 1504 * q^92 - 200 * q^94 + 784 * q^95 - 260 * q^97 + 92 * q^98

Introduction

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