LMFDB - Embedded newform 441.2.u.c.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			127.1
Character	$\chi$	$=$	441.127
Dual form			441.2.u.c.316.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72952 - 0.832892i) q^{2} +(1.05054 + 1.31734i) q^{4} +(0.379489 + 1.66265i) q^{5} +(0.548424 + 2.58829i) q^{7} +(0.134579 + 0.589630i) q^{8} +O(q^{10})$	\(q+(-1.72952 - 0.832892i) q^{2} +(1.05054 + 1.31734i) q^{4} +(0.379489 + 1.66265i) q^{5} +(0.548424 + 2.58829i) q^{7} +(0.134579 + 0.589630i) q^{8} +(0.728476 - 3.19166i) q^{10} +(-0.764724 - 0.368272i) q^{11} +(-4.30823 - 2.07473i) q^{13} +(1.20726 - 4.93327i) q^{14} +(1.00821 - 4.41726i) q^{16} +(-2.33202 + 2.92427i) q^{17} -7.35258 q^{19} +(-1.79161 + 2.24661i) q^{20} +(1.01587 + 1.27386i) q^{22} +(-3.45324 - 4.33023i) q^{23} +(1.88444 - 0.907501i) q^{25} +(5.72313 + 7.17657i) q^{26} +(-2.83351 + 3.44157i) q^{28} +(-1.10254 + 1.38254i) q^{29} +3.51987 q^{31} +(-4.66865 + 5.85430i) q^{32} +(6.46888 - 3.11525i) q^{34} +(-4.09530 + 1.89407i) q^{35} +(-4.51351 + 5.65977i) q^{37} +(12.7164 + 6.12390i) q^{38} +(-0.929278 + 0.447517i) q^{40} +(-1.53512 - 6.72580i) q^{41} +(-1.44419 + 6.32742i) q^{43} +(-0.318237 - 1.39429i) q^{44} +(2.36583 + 10.3654i) q^{46} +(-2.34814 - 1.13080i) q^{47} +(-6.39846 + 2.83896i) q^{49} -4.01503 q^{50} +(-1.79285 - 7.85500i) q^{52} +(6.09269 + 7.63999i) q^{53} +(0.322103 - 1.41122i) q^{55} +(-1.45233 + 0.671697i) q^{56} +(3.05836 - 1.47283i) q^{58} +(0.338394 - 1.48260i) q^{59} +(-5.74677 + 7.20622i) q^{61} +(-6.08768 - 2.93167i) q^{62} +(4.78620 - 2.30491i) q^{64} +(1.81463 - 7.95042i) q^{65} +8.27010 q^{67} -6.30215 q^{68} +(8.66045 + 0.135123i) q^{70} +(3.77637 + 4.73542i) q^{71} +(2.95146 - 1.42135i) q^{73} +(12.5202 - 6.02940i) q^{74} +(-7.72420 - 9.68585i) q^{76} +(0.533800 - 2.18129i) q^{77} -6.53165 q^{79} +7.72697 q^{80} +(-2.94685 + 12.9110i) q^{82} +(-10.0390 + 4.83453i) q^{83} +(-5.74702 - 2.76762i) q^{85} +(7.76781 - 9.74053i) q^{86} +(0.114228 - 0.500466i) q^{88} +(-7.65927 + 3.68851i) q^{89} +(3.00727 - 12.2888i) q^{91} +(2.07660 - 9.09819i) q^{92} +(3.11931 + 3.91149i) q^{94} +(-2.79023 - 12.2248i) q^{95} +8.74589 q^{97} +(13.4308 + 0.419204i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) $ 24 * q - q^2 - 3 * q^4 - 3 * q^8	$ 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) $ 24 * q - q^2 - 3 * q^4 - 3 * q^8 - 30 * q^10 - 9 * q^11 + 21 * q^14 - 29 * q^16 - 5 * q^17 + 26 * q^19 + 13 * q^20 + 11 * q^22 - 4 * q^23 - 28 * q^25 + 22 * q^26 - 7 * q^28 - 6 * q^29 + 36 * q^31 - 14 * q^32 + 46 * q^34 + 7 * q^35 - 22 * q^37 + 45 * q^38 + 35 * q^40 + 11 * q^41 + 6 * q^43 - 82 * q^44 - 16 * q^46 - 29 * q^47 - 42 * q^49 + 48 * q^50 - 50 * q^52 - 28 * q^53 + 23 * q^55 - 21 * q^56 + 39 * q^58 + 15 * q^59 - 32 * q^61 + 8 * q^62 + 29 * q^64 + 21 * q^65 - 34 * q^67 + 22 * q^68 - 24 * q^71 - 15 * q^73 - 6 * q^74 + 7 * q^76 + 21 * q^77 - 34 * q^79 - 8 * q^80 + 14 * q^82 - 14 * q^83 + 20 * q^85 + 100 * q^86 - 108 * q^88 - 10 * q^89 + 84 * q^91 + 21 * q^92 + 99 * q^94 - 18 * q^95 - 64 * q^97 - 91 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{3}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.72952	−	0.832892i	−1.22295	−	0.588944i	−0.292821	−	0.956167i	$-0.594594\pi$
$2$	−1.72952	−	0.832892i	−1.22295	−	0.588944i	−0.930133	+	0.367224i	$0.880308\pi$
$3$		0			0
$3$		0			0
$4$	1.05054	+	1.31734i	0.525272	+	0.658670i
$5$	0.379489	+	1.66265i	0.169713	+	0.743561i	0.986113	+	0.166074i	$0.0531092\pi$
$5$	0.379489	+	1.66265i	0.169713	+	0.743561i	−0.816400	+	0.577486i	$0.804034\pi$
$6$		0			0
$7$	0.548424	+	2.58829i	0.207285	+	0.978281i
$7$	0.548424	+	2.58829i	0.207285	+	0.978281i
$8$	0.134579	+	0.589630i	0.0475809	+	0.208466i
$9$		0			0
$10$	0.728476	−	3.19166i	0.230364	−	1.00929i
$11$	−0.764724	−	0.368272i	−0.230573	−	0.111038i	0.315031	−	0.949082i	$-0.397985\pi$
$11$	−0.764724	−	0.368272i	−0.230573	−	0.111038i	−0.545603	+	0.838043i	$0.683700\pi$
$12$		0			0
$13$	−4.30823	−	2.07473i	−1.19489	−	0.575427i	−0.272673	−	0.962107i	$-0.587908\pi$
$13$	−4.30823	−	2.07473i	−1.19489	−	0.575427i	−0.922214	+	0.386680i	$0.873622\pi$
$14$	1.20726	−	4.93327i	0.322653	−	1.31847i
$15$		0			0
$16$	1.00821	−	4.41726i	0.252053	−	1.10431i
$17$	−2.33202	+	2.92427i	−0.565599	+	0.709239i	−0.979582	−	0.201046i	$-0.935566\pi$
$17$	−2.33202	+	2.92427i	−0.565599	+	0.709239i	0.413983	+	0.910285i	$0.364137\pi$
$18$		0			0
$19$	−7.35258			−1.68680			−0.843399	−	0.537288i	$-0.819449\pi$
$19$	−7.35258			−1.68680			−0.843399	+	0.537288i	$0.819449\pi$
$20$	−1.79161	+	2.24661i	−0.400616	+	0.502356i
$21$		0			0
$22$	1.01587	+	1.27386i	0.216585	+	0.271589i
$23$	−3.45324	−	4.33023i	−0.720051	−	0.902916i	0.278290	−	0.960497i	$-0.410233\pi$
$23$	−3.45324	−	4.33023i	−0.720051	−	0.902916i	−0.998341	+	0.0575815i	$0.981661\pi$
$24$		0			0
$25$	1.88444	−	0.907501i	0.376889	−	0.181500i
$26$	5.72313	+	7.17657i	1.12240	+	1.40744i
$27$		0			0
$28$	−2.83351	+	3.44157i	−0.535483	+	0.650395i
$29$	−1.10254	+	1.38254i	−0.204736	+	0.256731i	−0.873590	−	0.486663i	$-0.838214\pi$
$29$	−1.10254	+	1.38254i	−0.204736	+	0.256731i	0.668854	+	0.743394i	$0.266785\pi$
$30$		0			0
$31$	3.51987			0.632187			0.316094	−	0.948728i	$-0.397629\pi$
$31$	3.51987			0.632187			0.316094	+	0.948728i	$0.397629\pi$
$32$	−4.66865	+	5.85430i	−0.825309	+	1.03490i
$33$		0			0
$34$	6.46888	−	3.11525i	1.10940	−	0.534260i
$35$	−4.09530	+	1.89407i	−0.692232	+	0.320155i
$36$		0			0
$37$	−4.51351	+	5.65977i	−0.742017	+	0.930460i	−0.999357	−	0.0358611i	$-0.988583\pi$
$37$	−4.51351	+	5.65977i	−0.742017	+	0.930460i	0.257340	+	0.966321i	$0.417154\pi$
$38$	12.7164	+	6.12390i	2.06288	+	0.993428i
$39$		0			0
$40$	−0.929278	+	0.447517i	−0.146932	+	0.0707586i
$41$	−1.53512	−	6.72580i	−0.239745	−	1.05039i	−0.941245	−	0.337723i	$-0.890343\pi$
$41$	−1.53512	−	6.72580i	−0.239745	−	1.05039i	0.701500	−	0.712669i	$-0.252514\pi$
$42$		0			0
$43$	−1.44419	+	6.32742i	−0.220237	+	0.964922i	0.737062	+	0.675825i	$0.236212\pi$
$43$	−1.44419	+	6.32742i	−0.220237	+	0.964922i	−0.957300	+	0.289098i	$0.906645\pi$
$44$	−0.318237	−	1.39429i	−0.0479760	−	0.210197i
$45$		0			0
$46$	2.36583	+	10.3654i	0.348823	+	1.52829i
$47$	−2.34814	−	1.13080i	−0.342511	−	0.164945i	0.254718	−	0.967015i	$-0.418017\pi$
$47$	−2.34814	−	1.13080i	−0.342511	−	0.164945i	−0.597229	+	0.802071i	$0.703732\pi$
$48$		0			0
$49$	−6.39846	+	2.83896i	−0.914066	+	0.405565i
$50$	−4.01503			−0.567811
$51$		0			0
$52$	−1.79285	−	7.85500i	−0.248624	−	1.08929i
$53$	6.09269	+	7.63999i	0.836895	+	1.04943i	0.998045	+	0.0625030i	$0.0199083\pi$
$53$	6.09269	+	7.63999i	0.836895	+	1.04943i	−0.161150	+	0.986930i	$0.551520\pi$
$54$		0			0
$55$	0.322103	−	1.41122i	0.0434323	−	0.190289i
$56$	−1.45233	+	0.671697i	−0.194075	+	0.0897593i
$57$		0			0
$58$	3.05836	−	1.47283i	0.401582	−	0.193392i
$59$	0.338394	−	1.48260i	0.0440551	−	0.193018i	−0.948112	−	0.317937i	$-0.897010\pi$
$59$	0.338394	−	1.48260i	0.0440551	−	0.193018i	0.992167	+	0.124919i	$0.0398671\pi$
$60$		0			0
$61$	−5.74677	+	7.20622i	−0.735798	+	0.922662i	−0.999116	−	0.0420473i	$-0.986612\pi$
$61$	−5.74677	+	7.20622i	−0.735798	+	0.922662i	0.263317	+	0.964709i	$0.415183\pi$
$62$	−6.08768	−	2.93167i	−0.773136	−	0.372322i
$63$		0			0
$64$	4.78620	−	2.30491i	0.598275	−	0.288114i
$65$	1.81463	−	7.95042i	0.225077	−	0.986128i
$66$		0			0
$67$	8.27010			1.01035			0.505177	−	0.863016i	$-0.331427\pi$
$67$	8.27010			1.01035			0.505177	+	0.863016i	$0.331427\pi$
$68$	−6.30215			−0.764248
$69$		0			0
$70$	8.66045	+	0.135123i	1.03512	+	0.0161502i
$71$	3.77637	+	4.73542i	0.448172	+	0.561990i	0.953677	−	0.300834i	$-0.0972649\pi$
$71$	3.77637	+	4.73542i	0.448172	+	0.561990i	−0.505504	+	0.862824i	$0.668694\pi$
$72$		0			0
$73$	2.95146	−	1.42135i	0.345442	−	0.166356i	−0.253115	−	0.967436i	$-0.581455\pi$
$73$	2.95146	−	1.42135i	0.345442	−	0.166356i	0.598557	+	0.801080i	$0.295741\pi$
$74$	12.5202	−	6.02940i	1.45544	−	0.700903i
$75$		0			0
$76$	−7.72420	−	9.68585i	−0.886027	−	1.11104i
$77$	0.533800	−	2.18129i	0.0608322	−	0.248581i
$78$		0			0
$79$	−6.53165			−0.734869			−0.367434	−	0.930049i	$-0.619764\pi$
$79$	−6.53165			−0.734869			−0.367434	+	0.930049i	$0.619764\pi$
$80$	7.72697			0.863901
$81$		0			0
$82$	−2.94685	+	12.9110i	−0.325425	+	1.42578i
$83$	−10.0390	+	4.83453i	−1.10192	+	0.530659i	−0.894263	−	0.447542i	$-0.852299\pi$
$83$	−10.0390	+	4.83453i	−1.10192	+	0.530659i	−0.207661	+	0.978201i	$0.566585\pi$
$84$		0			0
$85$	−5.74702	−	2.76762i	−0.623352	−	0.300190i
$86$	7.76781	−	9.74053i	0.837625	−	1.05035i
$87$		0			0
$88$	0.114228	−	0.500466i	0.0121768	−	0.0533498i
$89$	−7.65927	+	3.68851i	−0.811881	+	0.390981i	−0.793289	−	0.608846i	$-0.791633\pi$
$89$	−7.65927	+	3.68851i	−0.811881	+	0.390981i	−0.0185924	+	0.999827i	$0.505918\pi$
$90$		0			0
$91$	3.00727	−	12.2888i	0.315248	−	1.28821i
$92$	2.07660	−	9.09819i	0.216501	−	0.948552i
$93$		0			0
$94$	3.11931	+	3.91149i	0.321732	+	0.403440i
$95$	−2.79023	−	12.2248i	−0.286271	−	1.25424i
$96$		0			0
$97$	8.74589			0.888010			0.444005	−	0.896024i	$-0.353557\pi$
$97$	8.74589			0.888010			0.444005	+	0.896024i	$0.353557\pi$
$98$	13.4308	+	0.419204i	1.35672	+	0.0423460i
$99$		0			0
$100$	3.17518	+	1.52909i	0.317518	+	0.152909i
$101$	−3.33834	−	14.6262i	−0.332177	−	1.45536i	−0.814906	−	0.579593i	$-0.803212\pi$
$101$	−3.33834	−	14.6262i	−0.332177	−	1.45536i	0.482729	−	0.875770i	$-0.339646\pi$
$102$		0			0
$103$	−2.79142	−	12.2300i	−0.275047	−	1.20506i	−0.903971	−	0.427593i	$-0.859362\pi$
$103$	−2.79142	−	12.2300i	−0.275047	−	1.20506i	0.628924	−	0.777467i	$-0.283496\pi$
$104$	0.643527	−	2.81948i	0.0631030	−	0.276472i
$105$		0			0
$106$	−4.17413	−	18.2880i	−0.405427	−	1.77629i
$107$	−3.90233	+	1.87926i	−0.377252	+	0.181675i	−0.612894	−	0.790165i	$-0.709995\pi$
$107$	−3.90233	+	1.87926i	−0.377252	+	0.181675i	0.235642	+	0.971840i	$0.424281\pi$
$108$		0			0
$109$	17.8245	+	8.58382i	1.70728	+	0.822181i	0.992418	+	0.122912i	$0.0392232\pi$
$109$	17.8245	+	8.58382i	1.70728	+	0.822181i	0.714858	+	0.699269i	$0.246491\pi$
$110$	−1.73248	+	2.17246i	−0.165186	+	0.207136i
$111$		0			0
$112$	11.9861	+	0.187010i	1.13258	+	0.0176708i
$113$	5.63229	−	2.71237i	0.529842	−	0.255158i	−0.149782	−	0.988719i	$-0.547857\pi$
$113$	5.63229	−	2.71237i	0.529842	−	0.255158i	0.679624	+	0.733561i	$0.262143\pi$
$114$		0			0
$115$	5.88920	−	7.38482i	0.549171	−	0.688638i
$116$	−2.97953			−0.276643
$117$		0			0
$118$	−1.82010	+	2.28234i	−0.167554	+	0.210106i
$119$	−8.84778	−	4.43221i	−0.811075	−	0.406300i
$120$		0			0
$121$	−6.40921	−	8.03689i	−0.582655	−	0.730627i
$122$	15.9411	−	7.67685i	1.44324	−	0.695029i
$123$		0			0
$124$	3.69778	+	4.63686i	0.332070	+	0.416403i
$125$	7.54051	+	9.45551i	0.674444	+	0.845726i
$126$		0			0
$127$	1.61953	−	2.03082i	0.143710	−	0.180206i	−0.704767	−	0.709439i	$-0.748949\pi$
$127$	1.61953	−	2.03082i	0.143710	−	0.180206i	0.848477	+	0.529232i	$0.177520\pi$
$128$	4.77832			0.422347
$129$		0			0
$130$	−9.76028	+	12.2390i	−0.856033	+	1.07343i
$131$	−0.240817	+	1.05509i	−0.0210403	+	0.0921837i	−0.984358	−	0.176180i	$-0.943626\pi$
$131$	−0.240817	+	1.05509i	−0.0210403	+	0.0921837i	0.963318	+	0.268364i	$0.0864830\pi$
$132$		0			0
$133$	−4.03233	−	19.0306i	−0.349647	−	1.65016i
$134$	−14.3033	−	6.88810i	−1.23562	−	0.595042i
$135$		0			0
$136$	−2.03808	−	0.981487i	−0.174764	−	0.0841618i
$137$	−4.52743	+	19.8360i	−0.386804	+	1.69470i	0.288761	+	0.957401i	$0.406757\pi$
$137$	−4.52743	+	19.8360i	−0.386804	+	1.69470i	−0.675566	+	0.737300i	$0.736100\pi$
$138$		0			0
$139$	1.20279	+	5.26975i	0.102019	+	0.446974i	0.999976	+	0.00689160i	$0.00219368\pi$
$139$	1.20279	+	5.26975i	0.102019	+	0.446974i	−0.897957	+	0.440083i	$0.854949\pi$
$140$	−6.79742	−	3.40510i	−0.574487	−	0.287784i
$141$		0			0
$142$	−2.58721	−	11.3353i	−0.217114	−	0.951236i
$143$	2.53054	+	3.17319i	0.211614	+	0.265356i
$144$		0			0
$145$	−2.71708	−	1.30848i	−0.225641	−	0.108663i
$146$	−6.28843			−0.520434
$147$		0			0
$148$	−12.1975			−1.00263
$149$	19.8142	+	9.54202i	1.62324	+	0.781713i	1.00000		0.000314763i	$-0.000100192\pi$
$149$	19.8142	+	9.54202i	1.62324	+	0.781713i	0.623244	+	0.782028i	$0.285814\pi$
$150$		0			0
$151$	−11.5130	−	14.4368i	−0.936911	−	1.17485i	−0.984394	−	0.175977i	$-0.943692\pi$
$151$	−11.5130	−	14.4368i	−0.936911	−	1.17485i	0.0474836	−	0.998872i	$-0.484880\pi$
$152$	−0.989504	−	4.33530i	−0.0802594	−	0.351639i
$153$		0			0
$154$	−2.74000	+	3.32799i	−0.220795	+	0.268177i
$155$	1.33575	+	5.85232i	0.107290	+	0.470069i
$156$		0			0
$157$	−4.05997	+	17.7879i	−0.324021	+	1.41963i	0.506306	+	0.862354i	$0.331011\pi$
$157$	−4.05997	+	17.7879i	−0.324021	+	1.41963i	−0.830327	+	0.557276i	$0.811847\pi$
$158$	11.2966	+	5.44016i	0.898710	+	0.432796i
$159$		0			0
$160$	−11.5054	−	5.54070i	−0.909580	−	0.438030i
$161$	9.31404	−	11.3128i	0.734049	−	0.891573i
$162$		0			0
$163$	−0.434287	+	1.90273i	−0.0340160	+	0.149034i	−0.989084	−	0.147353i	$-0.952925\pi$
$163$	−0.434287	+	1.90273i	−0.0340160	+	0.149034i	0.955068	+	0.296387i	$0.0957818\pi$
$164$	7.24745	−	9.08802i	0.565931	−	0.709655i
$165$		0			0
$166$	21.3893			1.66013
$167$	−11.3737	+	14.2622i	−0.880126	+	1.10364i	0.113790	+	0.993505i	$0.463701\pi$
$167$	−11.3737	+	14.2622i	−0.880126	+	1.10364i	−0.993916	+	0.110139i	$0.964870\pi$
$168$		0			0
$169$	6.15093	+	7.71303i	0.473149	+	0.593310i
$170$	7.63444	+	9.57329i	0.585535	+	0.734238i
$171$		0			0
$172$	−9.85255	+	4.74474i	−0.751250	+	0.361783i
$173$	14.5869	+	18.2915i	1.10903	+	1.39067i	0.911958	+	0.410283i	$0.134570\pi$
$173$	14.5869	+	18.2915i	1.10903	+	1.39067i	0.197067	+	0.980390i	$0.436858\pi$
$174$		0			0
$175$	3.38235	+	4.37979i	0.255681	+	0.331081i
$176$	−2.39775	+	3.00669i	−0.180737	+	0.226638i
$177$		0			0
$178$	16.3190			1.22316
$179$	−7.68874	+	9.64138i	−0.574683	+	0.720630i	−0.981196	−	0.193015i	$-0.938173\pi$
$179$	−7.68874	+	9.64138i	−0.574683	+	0.720630i	0.406512	+	0.913645i	$0.366745\pi$
$180$		0			0
$181$	−1.51832	+	0.731185i	−0.112856	+	0.0543486i	−0.489460	−	0.872026i	$-0.662806\pi$
$181$	−1.51832	+	0.731185i	−0.112856	+	0.0543486i	0.376604	+	0.926374i	$0.377092\pi$
$182$	−15.4363	+	18.7489i	−1.14422	+	1.38976i
$183$		0			0
$184$	2.08850	−	2.61890i	0.153966	−	0.193068i
$185$	−11.1231	−	5.35658i	−0.817783	−	0.393824i
$186$		0			0
$187$	2.86028	−	1.37744i	0.209164	−	0.100728i
$188$	−0.977169	−	4.28126i	−0.0712674	−	0.312243i
$189$		0			0
$190$	−5.35617	+	23.4669i	−0.388578	+	1.70247i
$191$	−5.32472	−	23.3291i	−0.385283	−	1.68803i	−0.680616	−	0.732640i	$-0.738288\pi$
$191$	−5.32472	−	23.3291i	−0.385283	−	1.68803i	0.295333	−	0.955394i	$-0.404569\pi$
$192$		0			0
$193$	0.295293	+	1.29376i	0.0212556	+	0.0931270i	0.984443	−	0.175704i	$-0.0562200\pi$
$193$	0.295293	+	1.29376i	0.0212556	+	0.0931270i	−0.963188	+	0.268830i	$0.913363\pi$
$194$	−15.1262	−	7.28438i	−1.08600	−	0.522988i
$195$		0			0
$196$	−10.4617	−	5.44650i	−0.747267	−	0.389036i
$197$	8.00346			0.570223			0.285112	−	0.958494i	$-0.407969\pi$
$197$	8.00346			0.570223			0.285112	+	0.958494i	$0.407969\pi$
$198$		0			0
$199$	0.268260	+	1.17533i	0.0190165	+	0.0833166i	0.983546	−	0.180659i	$-0.0578232\pi$
$199$	0.268260	+	1.17533i	0.0190165	+	0.0833166i	−0.964529	+	0.263976i	$0.914966\pi$
$200$	0.788697	+	0.988995i	0.0557693	+	0.0699325i
$201$		0			0
$202$	−6.40834	+	28.0768i	−0.450889	+	1.97547i
$203$	−4.18306	−	2.09546i	−0.293593	−	0.147073i
$204$		0			0
$205$	10.6001	−	5.10474i	0.740343	−	0.356530i
$206$	−5.35847	+	23.4770i	−0.373342	+	1.63572i
$207$		0			0
$208$	−13.5082	+	16.9388i	−0.936627	+	1.17449i
$209$	5.62269	+	2.70775i	0.388930	+	0.187299i
$210$		0			0
$211$	−9.17731	+	4.41956i	−0.631792	+	0.304255i	−0.722236	−	0.691647i	$-0.756886\pi$
$211$	−9.17731	+	4.41956i	−0.631792	+	0.304255i	0.0904442	+	0.995902i	$0.471171\pi$
$212$	−3.66383	+	16.0523i	−0.251633	+	1.10248i
$213$		0			0
$214$	8.31436			0.568358
$215$	−11.0684			−0.754855
$216$		0			0
$217$	1.93038	+	9.11043i	0.131043	+	0.618456i
$218$	−23.6784	−	29.6917i	−1.60370	−	2.01098i
$219$		0			0
$220$	2.19745	−	1.05823i	0.148152	−	0.0713461i
$221$	16.1140	−	7.76008i	1.08394	−	0.521999i
$222$		0			0
$223$	5.90233	+	7.40129i	0.395249	+	0.495627i	0.939143	−	0.343527i	$-0.111622\pi$
$223$	5.90233	+	7.40129i	0.395249	+	0.495627i	−0.543893	+	0.839154i	$0.683050\pi$
$224$	−17.7130	−	8.87317i	−1.18350	−	0.592864i
$225$		0			0
$226$	−12.0003			−0.798246
$227$	−9.57460			−0.635488			−0.317744	−	0.948176i	$-0.602925\pi$
$227$	−9.57460			−0.635488			−0.317744	+	0.948176i	$0.602925\pi$
$228$		0			0
$229$	1.87134	−	8.19889i	0.123662	−	0.541798i	−0.874704	−	0.484657i	$-0.838944\pi$
$229$	1.87134	−	8.19889i	0.123662	−	0.541798i	0.998366	−	0.0571410i	$-0.0181985\pi$
$230$	−16.3362	+	7.86711i	−1.07718	+	0.518742i
$231$		0			0
$232$	−0.963563	−	0.464028i	−0.0632610	−	0.0304649i
$233$	−9.03763	+	11.3328i	−0.592075	+	0.742438i	−0.984119	−	0.177508i	$-0.943196\pi$
$233$	−9.03763	+	11.3328i	−0.592075	+	0.742438i	0.392045	+	0.919946i	$0.371768\pi$
$234$		0			0
$235$	0.989040	−	4.33327i	0.0645179	−	0.282671i
$236$	2.30859	−	1.11176i	0.150276	−	0.0723692i
$237$		0			0
$238$	11.6108	+	15.0348i	0.752619	+	0.974564i
$239$	4.90124	−	21.4737i	0.317035	−	1.38902i	−0.525691	−	0.850676i	$-0.676193\pi$
$239$	4.90124	−	21.4737i	0.317035	−	1.38902i	0.842725	−	0.538344i	$-0.180950\pi$
$240$		0			0
$241$	4.17155	+	5.23096i	0.268713	+	0.336956i	0.897820	−	0.440364i	$-0.145150\pi$
$241$	4.17155	+	5.23096i	0.268713	+	0.336956i	−0.629106	+	0.777319i	$0.716579\pi$
$242$	4.39098	+	19.2381i	0.282263	+	1.23667i
$243$		0			0
$244$	−15.5303			−0.994224
$245$	−7.14834	−	9.56106i	−0.456691	−	0.610834i
$246$		0			0
$247$	31.6766	+	15.2546i	2.01553	+	0.970629i
$248$	0.473701	+	2.07542i	0.0300801	+	0.131789i
$249$		0			0
$250$	−5.16604	−	22.6339i	−0.326729	−	1.43149i
$251$	4.31107	−	18.8881i	0.272113	−	1.19220i	−0.635402	−	0.772182i	$-0.719165\pi$
$251$	4.31107	−	18.8881i	0.272113	−	1.19220i	0.907514	−	0.420021i	$-0.137977\pi$
$252$		0			0
$253$	1.04608	+	4.58316i	0.0657663	+	0.288141i
$254$	−4.49245	+	2.16345i	−0.281882	+	0.135747i
$255$		0			0
$256$	−17.8366	−	8.58964i	−1.11479	−	0.536853i
$257$	2.55552	−	3.20453i	0.159409	−	0.199893i	−0.695712	−	0.718321i	$-0.744911\pi$
$257$	2.55552	−	3.20453i	0.159409	−	0.199893i	0.855121	+	0.518428i	$0.173483\pi$
$258$		0			0
$259$	−17.1244	−	8.57832i	−1.06406	−	0.533031i
$260$	12.3798	−	5.96178i	0.767760	−	0.369734i
$261$		0			0
$262$	1.29527	−	1.62422i	0.0800223	−	0.100345i
$263$	25.1062			1.54812			0.774059	−	0.633114i	$-0.218224\pi$
$263$	25.1062			1.54812			0.774059	+	0.633114i	$0.218224\pi$
$264$		0			0
$265$	−10.3905	+	13.0293i	−0.638285	+	0.800384i
$266$	−8.87644	+	36.2722i	−0.544249	+	2.22399i
$267$		0			0
$268$	8.68811	+	10.8945i	0.530710	+	0.665490i
$269$	−16.6686	+	8.02717i	−1.01630	+	0.489425i	−0.866440	−	0.499282i	$-0.833597\pi$
$269$	−16.6686	+	8.02717i	−1.01630	+	0.489425i	−0.149862	+	0.988707i	$0.547883\pi$
$270$		0			0
$271$	11.5297	+	14.4577i	0.700377	+	0.878244i	0.997052	−	0.0767341i	$-0.0244492\pi$
$271$	11.5297	+	14.4577i	0.700377	+	0.878244i	−0.296675	+	0.954978i	$0.595878\pi$
$272$	10.5661	+	13.2494i	0.640662	+	0.803365i
$273$		0			0
$274$	24.3515	−	30.5358i	1.47113	−	1.84474i
$275$	−1.77529			−0.107054
$276$		0			0
$277$	6.43749	−	8.07236i	0.386791	−	0.485021i	−0.549873	−	0.835248i	$-0.685324\pi$
$277$	6.43749	−	8.07236i	0.386791	−	0.485021i	0.936665	+	0.350227i	$0.113896\pi$
$278$	2.30889	−	10.1159i	0.138478	−	0.606712i
$279$		0			0
$280$	−1.66794	−	2.15981i	−0.0996785	−	0.129073i
$281$	−12.8743	−	6.19994i	−0.768017	−	0.369858i	0.00849169	−	0.999964i	$-0.497297\pi$
$281$	−12.8743	−	6.19994i	−0.768017	−	0.369858i	−0.776509	+	0.630106i	$0.783011\pi$
$282$		0			0
$283$	−6.17411	−	2.97329i	−0.367013	−	0.176744i	0.241282	−	0.970455i	$-0.422432\pi$
$283$	−6.17411	−	2.97329i	−0.367013	−	0.176744i	−0.608295	+	0.793711i	$0.708146\pi$
$284$	−2.27091	+	9.94952i	−0.134754	+	0.590395i
$285$		0			0
$286$	−1.73368	−	7.59576i	−0.102515	−	0.449147i
$287$	16.5664	−	7.66191i	0.977884	−	0.452268i
$288$		0			0
$289$	0.669860	+	2.93485i	0.0394035	+	0.172638i
$290$	3.60942	+	4.52606i	0.211952	+	0.265780i
$291$		0			0
$292$	4.97303	+	2.39489i	0.291025	+	0.140150i
$293$	19.0363			1.11211			0.556057	−	0.831144i	$-0.312314\pi$
$293$	19.0363			1.11211			0.556057	+	0.831144i	$0.312314\pi$
$294$		0			0
$295$	2.59346			0.150997
$296$	−3.94459	−	1.89962i	−0.229275	−	0.110413i
$297$		0			0
$298$	−26.3216	−	33.0062i	−1.52477	−	1.91200i
$299$	5.89329	+	25.8202i	0.340818	+	1.49322i
$300$		0			0
$301$	−17.1692	−	0.267879i	−0.989617	−	0.0154403i
$302$	7.88757	+	34.5577i	0.453879	+	1.98857i
$303$		0			0
$304$	−7.41295	+	32.4782i	−0.425162	+	1.86275i
$305$	−14.1623	−	6.82019i	−0.810930	−	0.390523i
$306$		0			0
$307$	−14.2185	−	6.84726i	−0.811492	−	0.390794i	−0.0183505	−	0.999832i	$-0.505841\pi$
$307$	−14.2185	−	6.84726i	−0.811492	−	0.390794i	−0.793141	+	0.609038i	$0.791556\pi$
$308$	3.43429	−	1.58835i	0.195687	−	0.0905045i
$309$		0			0
$310$	2.56414	−	11.2342i	0.145633	−	0.638061i
$311$	1.52122	−	1.90755i	0.0862604	−	0.108167i	−0.736828	−	0.676080i	$-0.763677\pi$
$311$	1.52122	−	1.90755i	0.0862604	−	0.108167i	0.823089	+	0.567913i	$0.192249\pi$
$312$		0			0
$313$	7.20689			0.407357			0.203679	−	0.979038i	$-0.434710\pi$
$313$	7.20689			0.407357			0.203679	+	0.979038i	$0.434710\pi$
$314$	21.8372	−	27.3830i	1.23234	−	1.54531i
$315$		0			0
$316$	−6.86179	−	8.60441i	−0.386006	−	0.484036i
$317$	14.8607	+	18.6347i	0.834657	+	1.04663i	0.998193	+	0.0600897i	$0.0191387\pi$
$317$	14.8607	+	18.6347i	0.834657	+	1.04663i	−0.163536	+	0.986537i	$0.552290\pi$
$318$		0			0
$319$	1.35228	−	0.651226i	0.0757134	−	0.0364616i
$320$	5.64858	+	7.08309i	0.315765	+	0.395957i
$321$		0			0
$322$	−25.5311	+	11.8081i	−1.42279	+	0.658039i
$323$	17.1464	−	21.5009i	0.954051	−	1.19634i
$324$		0			0
$325$	−10.0014			−0.554780
$326$	2.33588	−	2.92910i	0.129372	−	0.162228i
$327$		0			0
$328$	3.75914	−	1.81030i	0.207564	−	0.0999574i
$329$	1.63907	−	6.69782i	0.0903650	−	0.369263i
$330$		0			0
$331$	14.5439	−	18.2375i	0.799405	−	1.00242i	−0.200337	−	0.979727i	$-0.564204\pi$
$331$	14.5439	−	18.2375i	0.799405	−	1.00242i	0.999742	−	0.0226955i	$-0.00722483\pi$
$332$	−16.9151	−	8.14590i	−0.928338	−	0.447064i
$333$		0			0
$334$	31.5500	−	15.1937i	1.72634	−	0.831360i
$335$	3.13842	+	13.7503i	0.171470	+	0.751260i
$336$		0			0
$337$	0.751763	−	3.29369i	0.0409511	−	0.179419i	−0.950316	−	0.311286i	$-0.899240\pi$
$337$	0.751763	−	3.29369i	0.0409511	−	0.179419i	0.991267	+	0.131868i	$0.0420974\pi$
$338$	−4.21403	−	18.4629i	−0.229213	−	1.00425i
$339$		0			0
$340$	−2.39160	−	10.4783i	−0.129703	−	0.568264i
$341$	−2.69173	−	1.29627i	−0.145765	−	0.0701968i
$342$		0			0
$343$	−10.8571	−	15.0041i	−0.586228	−	0.810146i
$344$	−3.92520			−0.211632
$345$		0			0
$346$	−9.99358	−	43.7847i	−0.537258	−	2.35388i
$347$	−9.22999	−	11.5740i	−0.495492	−	0.621327i	0.469714	−	0.882819i	$-0.344357\pi$
$347$	−9.22999	−	11.5740i	−0.495492	−	0.621327i	−0.965206	+	0.261491i	$0.915786\pi$
$348$		0			0
$349$	1.11494	−	4.88489i	0.0596816	−	0.261482i	−0.936281	−	0.351252i	$-0.885756\pi$
$349$	1.11494	−	4.88489i	0.0596816	−	0.261482i	0.995963	+	0.0897699i	$0.0286132\pi$
$350$	−2.20194	−	10.3921i	−0.117699	−	0.555479i
$351$		0			0
$352$	5.72620	−	2.75759i	0.305208	−	0.146980i
$353$	0.438983	−	1.92331i	0.0233647	−	0.102367i	−0.961901	−	0.273398i	$-0.911852\pi$
$353$	0.438983	−	1.92331i	0.0233647	−	0.102367i	0.985266	+	0.171030i	$0.0547096\pi$
$354$		0			0
$355$	−6.44026	+	8.07583i	−0.341813	+	0.428620i
$356$	−12.9054	−	6.21492i	−0.683986	−	0.329390i
$357$		0			0
$358$	21.3280	−	10.2710i	1.12722	−	0.542841i
$359$	0.832046	−	3.64543i	0.0439137	−	0.192399i	−0.948213	−	0.317634i	$-0.897112\pi$
$359$	0.832046	−	3.64543i	0.0439137	−	0.192399i	0.992127	+	0.125236i	$0.0399687\pi$
$360$		0			0
$361$	35.0604			1.84528
$362$	3.23496			0.170026
$363$		0			0
$364$	19.3477	−	8.94828i	1.01410	−	0.469017i
$365$	3.48325	+	4.36786i	0.182322	+	0.228624i
$366$		0			0
$367$	−24.8686	+	11.9761i	−1.29813	+	0.625146i	−0.949985	−	0.312295i	$-0.898902\pi$
$367$	−24.8686	+	11.9761i	−1.29813	+	0.625146i	−0.348144	+	0.937441i	$0.613188\pi$
$368$	−22.6093	+	10.8881i	−1.17859	+	0.567581i
$369$		0			0
$370$	14.7761	+	18.5286i	0.768171	+	0.963256i
$371$	−16.4331	+	19.9596i	−0.853165	+	1.03625i
$372$		0			0
$373$	−0.357662			−0.0185190			−0.00925951	−	0.999957i	$-0.502947\pi$
$373$	−0.357662			−0.0185190			−0.00925951	+	0.999957i	$0.502947\pi$
$374$	−6.09416			−0.315122
$375$		0			0
$376$	0.350746	−	1.53672i	0.0180883	−	0.0792501i
$377$	7.61837	−	3.66881i	0.392366	−	0.188953i
$378$		0			0
$379$	34.5705	+	16.6483i	1.77577	+	0.855165i	0.961562	+	0.274588i	$0.0885416\pi$
$379$	34.5705	+	16.6483i	1.77577	+	0.855165i	0.814206	+	0.580576i	$0.197173\pi$
$380$	13.1729	−	16.5183i	0.675757	−	0.847373i
$381$		0			0
$382$	−10.2214	+	44.7830i	−0.522974	+	2.29130i
$383$	10.8375	−	5.21908i	0.553772	−	0.266683i	−0.136000	−	0.990709i	$-0.543425\pi$
$383$	10.8375	−	5.21908i	0.553772	−	0.266683i	0.689773	+	0.724026i	$0.257711\pi$
$384$		0			0
$385$	3.82930	+	0.0597458i	0.195159	+	0.00304493i
$386$	0.566850	−	2.48353i	0.0288519	−	0.126408i
$387$		0			0
$388$	9.18794	+	11.5213i	0.466447	+	0.584906i
$389$	−6.43489	−	28.1931i	−0.326262	−	1.42945i	−0.826196	−	0.563383i	$-0.809500\pi$
$389$	−6.43489	−	28.1931i	−0.326262	−	1.42945i	0.499934	−	0.866063i	$-0.333357\pi$
$390$		0			0
$391$	20.7158			1.04764
$392$	−2.53503	−	3.39066i	−0.128039	−	0.171254i
$393$		0			0
$394$	−13.8421	−	6.66602i	−0.697357	−	0.335829i
$395$	−2.47869	−	10.8599i	−0.124717	−	0.546419i
$396$		0			0
$397$	−2.91957	−	12.7915i	−0.146529	−	0.641985i	−0.993834	−	0.110878i	$-0.964634\pi$
$397$	−2.91957	−	12.7915i	−0.146529	−	0.641985i	0.847305	−	0.531106i	$-0.178224\pi$
$398$	0.514958	−	2.25618i	0.0258125	−	0.113092i
$399$		0			0
$400$	−2.10875	−	9.23903i	−0.105437	−	0.461951i
$401$	−1.95915	+	0.943476i	−0.0978352	+	0.0471149i	−0.482161	−	0.876082i	$-0.660148\pi$
$401$	−1.95915	+	0.943476i	−0.0978352	+	0.0471149i	0.384326	+	0.923197i	$0.374434\pi$
$402$		0			0
$403$	−15.1644	−	7.30279i	−0.755392	−	0.363778i
$404$	15.7606	−	19.7632i	0.784120	−	0.983256i
$405$		0			0
$406$	5.48938	+	7.10818i	0.272433	+	0.352773i
$407$	5.53592	−	2.66596i	0.274405	−	0.132147i
$408$		0			0
$409$	−12.9886	+	16.2871i	−0.642243	+	0.805347i	−0.991282	−	0.131761i	$-0.957937\pi$
$409$	−12.9886	+	16.2871i	−0.642243	+	0.805347i	0.349038	+	0.937108i	$0.386508\pi$
$410$	−22.5848			−1.11538
$411$		0			0
$412$	13.1786	−	16.5254i	0.649262	−	0.814149i
$413$	4.02298	+	0.0627676i	0.197958	+	0.00308859i
$414$		0			0
$415$	−11.8478	−	14.8567i	−0.581587	−	0.729288i
$416$	32.2597	−	15.5355i	1.58166	−	0.761689i
$417$		0			0
$418$	−7.46929	−	9.36619i	−0.365335	−	0.458115i
$419$	6.60492	+	8.28231i	0.322671	+	0.404617i	0.916539	−	0.399946i	$-0.130971\pi$
$419$	6.60492	+	8.28231i	0.322671	+	0.404617i	−0.593867	+	0.804563i	$0.702400\pi$
$420$		0			0
$421$	−3.40296	+	4.26718i	−0.165850	+	0.207970i	−0.857811	−	0.513966i	$-0.828176\pi$
$421$	−3.40296	+	4.26718i	−0.165850	+	0.207970i	0.691960	+	0.721935i	$0.256747\pi$
$422$	19.5533			0.951841
$423$		0			0
$424$	−3.68482	+	4.62062i	−0.178951	+	0.224397i
$425$	−1.74080	+	7.62693i	−0.0844411	+	0.369961i
$426$		0			0
$427$	−21.8034	−	10.9222i	−1.05514	−	0.528564i
$428$	−6.57519	−	3.16644i	−0.317824	−	0.153056i
$429$		0			0
$430$	19.1429	+	9.21874i	0.923153	+	0.444567i
$431$	6.48502	−	28.4127i	0.312372	−	1.36859i	−0.538236	−	0.842794i	$-0.680909\pi$
$431$	6.48502	−	28.4127i	0.312372	−	1.36859i	0.850609	−	0.525799i	$-0.176234\pi$
$432$		0			0
$433$	2.04553	+	8.96207i	0.0983021	+	0.430690i	0.999999	−	0.00167989i	$-0.000534727\pi$
$433$	2.04553	+	8.96207i	0.0983021	+	0.430690i	−0.901696	+	0.432370i	$0.857678\pi$
$434$	4.24938	−	17.3645i	0.203977	−	0.833520i
$435$		0			0
$436$	7.41759	+	32.4986i	0.355238	+	1.55640i
$437$	25.3903	+	31.8384i	1.21458	+	1.52304i
$438$		0			0
$439$	−5.94174	−	2.86139i	−0.283584	−	0.136567i	0.286685	−	0.958025i	$-0.407447\pi$
$439$	−5.94174	−	2.86139i	−0.283584	−	0.136567i	−0.570269	+	0.821458i	$0.693161\pi$
$440$	0.875449			0.0417354
$441$		0			0
$442$	−34.3327			−1.63304
$443$	−31.0729	−	14.9639i	−1.47632	−	0.710958i	−0.489383	−	0.872069i	$-0.662778\pi$
$443$	−31.0729	−	14.9639i	−1.47632	−	0.710958i	−0.986936	+	0.161111i	$0.948492\pi$
$444$		0			0
$445$	−9.03932	−	11.3349i	−0.428505	−	0.537328i
$446$	−4.04371	−	17.7167i	−0.191475	−	0.838908i
$447$		0			0
$448$	8.59063	+	11.1240i	0.405869	+	0.525559i
$449$	6.68747	+	29.2997i	0.315601	+	1.38274i	0.845181	+	0.534480i	$0.179492\pi$
$449$	6.68747	+	29.2997i	0.315601	+	1.38274i	−0.529580	+	0.848260i	$0.677650\pi$
$450$		0			0
$451$	−1.30298	+	5.70872i	−0.0613548	+	0.268813i
$452$	9.49008	+	4.57018i	0.446376	+	0.214963i
$453$		0			0
$454$	16.5594	+	7.97460i	0.777173	+	0.374267i
$455$	21.5732	+	0.336590i	1.01137	+	0.0157796i
$456$		0			0
$457$	−4.26515	+	18.6868i	−0.199515	+	0.874133i	0.771711	+	0.635973i	$0.219401\pi$
$457$	−4.26515	+	18.6868i	−0.199515	+	0.874133i	−0.971226	+	0.238159i	$0.923456\pi$
$458$	−10.0653	+	12.6215i	−0.470321	+	0.589764i
$459$		0			0
$460$	15.9152			0.742049
$461$	−23.2739	+	29.1846i	−1.08397	+	1.35926i	−0.155511	+	0.987834i	$0.549702\pi$
$461$	−23.2739	+	29.1846i	−1.08397	+	1.35926i	−0.928463	+	0.371426i	$0.878869\pi$
$462$		0			0
$463$	−7.60213	−	9.53277i	−0.353301	−	0.443025i	0.573145	−	0.819454i	$-0.305723\pi$
$463$	−7.60213	−	9.53277i	−0.353301	−	0.443025i	−0.926446	+	0.376429i	$0.877152\pi$
$464$	4.99543	+	6.26407i	0.231907	+	0.290802i
$465$		0			0
$466$	25.0698	−	12.0730i	1.16133	−	0.559269i
$467$	−7.63902	−	9.57903i	−0.353492	−	0.443265i	0.573014	−	0.819546i	$-0.305774\pi$
$467$	−7.63902	−	9.57903i	−0.353492	−	0.443265i	−0.926506	+	0.376281i	$0.877203\pi$
$468$		0			0
$469$	4.53552	+	21.4054i	0.209431	+	0.988410i
$470$	−5.31971	+	6.67070i	−0.245380	+	0.307696i
$471$		0			0
$472$	0.919726			0.0423338
$473$	3.43462	−	4.30687i	0.157924	−	0.198030i
$474$		0			0
$475$	−13.8555	+	6.67247i	−0.635735	+	0.306154i
$476$	−3.45625	−	16.3118i	−0.158417	−	0.747649i
$477$		0			0
$478$	−26.3621	+	33.0570i	−1.20577	+	1.51199i
$479$	23.5102	+	11.3219i	1.07421	+	0.517311i	0.885461	−	0.464715i	$-0.153843\pi$
$479$	23.5102	+	11.3219i	1.07421	+	0.517311i	0.188747	+	0.982026i	$0.439557\pi$
$480$		0			0
$481$	31.1877	−	15.0192i	1.42204	−	0.684818i
$482$	−2.85795	−	12.5215i	−0.130176	−	0.570338i
$483$		0			0
$484$	3.85417	−	16.8862i	0.175189	−	0.767555i
$485$	3.31897	+	14.5414i	0.150707	+	0.660290i
$486$		0			0
$487$	−1.92264	−	8.42364i	−0.0871231	−	0.381711i	0.912503	−	0.409071i	$-0.134147\pi$
$487$	−1.92264	−	8.42364i	−0.0871231	−	0.381711i	−0.999626	+	0.0273597i	$0.991290\pi$
$488$	−5.02240	−	2.41866i	−0.227353	−	0.109488i
$489$		0			0
$490$	4.39986	+	22.4898i	0.198765	+	1.01599i
$491$	29.2836			1.32155			0.660775	−	0.750584i	$-0.270228\pi$
$491$	29.2836			1.32155			0.660775	+	0.750584i	$0.270228\pi$
$492$		0			0
$493$	−1.47176	−	6.44822i	−0.0662849	−	0.290413i
$494$	−42.0797	−	52.7663i	−1.89326	−	2.37407i
$495$		0			0
$496$	3.54877	−	15.5482i	0.159344	−	0.698133i
$497$	−10.1856	+	12.3713i	−0.456885	+	0.554930i
$498$		0			0
$499$	−9.06254	+	4.36429i	−0.405695	+	0.195372i	−0.625592	−	0.780151i	$-0.715142\pi$
$499$	−9.06254	+	4.36429i	−0.405695	+	0.195372i	0.219897	+	0.975523i	$0.429428\pi$
$500$	−4.53448	+	19.8668i	−0.202788	+	0.888472i
$501$		0			0
$502$	−23.1878	+	29.0766i	−1.03492	+	1.29775i
$503$	−26.9341	−	12.9708i	−1.20093	−	0.578338i	−0.276991	−	0.960873i	$-0.589337\pi$
$503$	−26.9341	−	12.9708i	−1.20093	−	0.578338i	−0.923941	+	0.382534i	$0.875051\pi$
$504$		0			0
$505$	23.0514	−	11.1010i	1.02578	−	0.493987i
$506$	2.00807	−	8.79793i	0.0892696	−	0.391116i
$507$		0			0
$508$	4.37666			0.194183
$509$	−7.61998			−0.337750			−0.168875	−	0.985637i	$-0.554013\pi$
$509$	−7.61998			−0.337750			−0.168875	+	0.985637i	$0.554013\pi$
$510$		0			0
$511$	5.29750	+	6.85972i	0.234348	+	0.303456i
$512$	17.7360	+	22.2402i	0.783827	+	0.982887i
$513$		0			0
$514$	−7.08885	+	3.41381i	−0.312676	+	0.150577i
$515$	19.2750	−	9.28233i	0.849356	−	0.409028i
$516$		0			0
$517$	1.37923	+	1.72951i	0.0606587	+	0.0760636i
$518$	22.4722	+	29.0991i	0.987371	+	1.27854i
$519$		0			0
$520$	4.93202			0.216283
$521$	−14.1829			−0.621364			−0.310682	−	0.950514i	$-0.600558\pi$
$521$	−14.1829			−0.621364			−0.310682	+	0.950514i	$0.600558\pi$
$522$		0			0
$523$	−7.21101	+	31.5935i	−0.315316	+	1.38149i	0.530352	+	0.847778i	$0.322060\pi$
$523$	−7.21101	+	31.5935i	−0.315316	+	1.38149i	−0.845667	+	0.533710i	$0.820797\pi$
$524$	−1.64290	+	0.791180i	−0.0717705	+	0.0345629i
$525$		0			0
$526$	−43.4217	−	20.9108i	−1.89328	−	0.911754i
$527$	−8.20842	+	10.2930i	−0.357564	+	0.448372i
$528$		0			0
$529$	−1.70803	+	7.48336i	−0.0742620	+	0.325363i
$530$	28.8226	−	13.8802i	1.25197	−	0.602919i
$531$		0			0
$532$	20.8336	−	25.3044i	0.903252	−	1.09709i
$533$	−7.34059	+	32.1612i	−0.317956	+	1.39306i
$534$		0			0
$535$	−4.60545	−	5.77505i	−0.199111	−	0.249677i
$536$	1.11298	+	4.87630i	0.0480736	+	0.210624i
$537$		0			0
$538$	35.5144			1.53113
$539$	5.93856	+	0.185355i	0.255792	+	0.00798382i
$540$		0			0
$541$	−2.24320	−	1.08027i	−0.0964429	−	0.0464445i	0.385040	−	0.922900i	$-0.374188\pi$
$541$	−2.24320	−	1.08027i	−0.0964429	−	0.0464445i	−0.481483	+	0.876455i	$0.659902\pi$
$542$	−7.89902	−	34.6079i	−0.339292	−	1.48653i
$543$		0			0
$544$	−6.23213	−	27.3048i	−0.267201	−	1.17068i
$545$	−7.50770	+	32.8934i	−0.321595	+	1.40900i
$546$		0			0
$547$	4.19310	+	18.3711i	0.179284	+	0.785494i	0.981962	+	0.189081i	$0.0605508\pi$
$547$	4.19310	+	18.3711i	0.179284	+	0.785494i	−0.802678	+	0.596413i	$0.796592\pi$
$548$	−30.8870	+	14.8744i	−1.31943	+	0.635402i
$549$		0			0
$550$	3.07039	+	1.47862i	0.130922	+	0.0630486i
$551$	8.10648	−	10.1652i	0.345348	−	0.433052i
$552$		0			0
$553$	−3.58211	−	16.9058i	−0.152327	−	0.718908i
$554$	−17.8572	+	8.59956i	−0.758678	+	0.365360i
$555$		0			0
$556$	−5.67847	+	7.12058i	−0.240821	+	0.301980i
$557$	11.9484			0.506268			0.253134	−	0.967431i	$-0.418539\pi$
$557$	11.9484			0.506268			0.253134	+	0.967431i	$0.418539\pi$
$558$		0			0
$559$	19.3496	−	24.2636i	0.818401	−	1.02624i
$560$	4.23765	+	19.9996i	0.179073	+	0.845138i
$561$		0			0
$562$	17.1025	+	21.4458i	0.721424	+	0.904637i
$563$	−32.9781	+	15.8814i	−1.38986	+	0.669322i	−0.971078	−	0.238764i	$-0.923258\pi$
$563$	−32.9781	+	15.8814i	−1.38986	+	0.669322i	−0.418784	+	0.908086i	$0.637544\pi$
$564$		0			0
$565$	6.64712	+	8.33523i	0.279647	+	0.350666i
$566$	8.20180	+	10.2847i	0.344747	+	0.432299i
$567$		0			0
$568$	−2.28392	+	2.86395i	−0.0958313	+	0.120169i
$569$	9.20674			0.385967			0.192983	−	0.981202i	$-0.438184\pi$
$569$	9.20674			0.385967			0.192983	+	0.981202i	$0.438184\pi$
$570$		0			0
$571$	−26.6529	+	33.4216i	−1.11539	+	1.39865i	−0.208117	+	0.978104i	$0.566734\pi$
$571$	−26.6529	+	33.4216i	−1.11539	+	1.39865i	−0.907270	+	0.420548i	$0.861838\pi$
$572$	−1.52174	+	6.66716i	−0.0636269	+	0.278768i
$573$		0			0
$574$	−35.0334	−	0.546601i	−1.46227	−	0.0228147i
$575$	−10.4371	−	5.02626i	−0.435259	−	0.209610i
$576$		0			0
$577$	−28.3736	−	13.6640i	−1.18121	−	0.568840i	−0.262945	−	0.964811i	$-0.584694\pi$
$577$	−28.3736	−	13.6640i	−1.18121	−	0.568840i	−0.918263	+	0.395971i	$0.870408\pi$
$578$	1.28588	−	5.63379i	0.0534854	−	0.234335i
$579$		0			0
$580$	−1.13070	−	4.95393i	−0.0469498	−	0.205701i
$581$	−18.0188	−	23.3325i	−0.747545	−	0.967994i
$582$		0			0
$583$	−1.84563	−	8.08624i	−0.0764383	−	0.334898i
$584$	1.23527	+	1.54898i	0.0511160	+	0.0640974i
$585$		0			0
$586$	−32.9237	−	15.8552i	−1.36006	−	0.654972i
$587$	−5.48837			−0.226529			−0.113265	−	0.993565i	$-0.536131\pi$
$587$	−5.48837			−0.226529			−0.113265	+	0.993565i	$0.536131\pi$
$588$		0			0
$589$	−25.8801			−1.06637
$590$	−4.48544	−	2.16008i	−0.184663	−	0.0889289i
$591$		0			0
$592$	20.4501	+	25.6436i	0.840493	+	1.05394i
$593$	−4.34016	−	19.0155i	−0.178229	−	0.780871i	−0.982448	−	0.186538i	$-0.940273\pi$
$593$	−4.34016	−	19.0155i	−0.178229	−	0.780871i	0.804219	−	0.594333i	$-0.202584\pi$
$594$		0			0
$595$	4.01159	−	16.3928i	0.164459	−	0.672038i
$596$	8.24561	+	36.1264i	0.337753	+	1.47979i
$597$		0			0
$598$	11.3129	−	49.5649i	0.462618	−	2.02686i
$599$	−11.5659	−	5.56985i	−0.472570	−	0.227578i	0.182412	−	0.983222i	$-0.441610\pi$
$599$	−11.5659	−	5.56985i	−0.472570	−	0.227578i	−0.654982	+	0.755644i	$0.727324\pi$
$600$		0			0
$601$	14.2243	+	6.85008i	0.580223	+	0.279421i	0.700886	−	0.713273i	$-0.252788\pi$
$601$	14.2243	+	6.85008i	0.580223	+	0.279421i	−0.120664	+	0.992693i	$0.538502\pi$
$602$	29.4713	+	14.7634i	1.20116	+	0.601711i
$603$		0			0
$604$	6.92330	−	30.3329i	0.281705	−	1.23423i
$605$	10.9303	−	13.7062i	0.444381	−	0.557236i
$606$		0			0
$607$	−20.0139			−0.812340			−0.406170	−	0.913798i	$-0.633136\pi$
$607$	−20.0139			−0.812340			−0.406170	+	0.913798i	$0.633136\pi$
$608$	34.3266	−	43.0442i	1.39213	−	1.74567i
$609$		0			0
$610$	18.8134	+	23.5913i	0.761733	+	0.955183i
$611$	7.77020	+	9.74352i	0.314349	+	0.394181i
$612$		0			0
$613$	33.0445	−	15.9134i	1.33465	−	0.642736i	0.375818	−	0.926694i	$-0.377362\pi$
$613$	33.0445	−	15.9134i	1.33465	−	0.642736i	0.958837	+	0.283958i	$0.0916475\pi$
$614$	18.8881	+	23.6849i	0.762261	+	0.955846i
$615$		0			0
$616$	1.35799	+	0.0211878i	0.0547152	+	0.000853681i
$617$	−4.47971	+	5.61738i	−0.180346	+	0.226147i	−0.863785	−	0.503861i	$-0.831912\pi$
$617$	−4.47971	+	5.61738i	−0.180346	+	0.226147i	0.683438	+	0.730008i	$0.260484\pi$
$618$		0			0
$619$	−4.08243			−0.164087			−0.0820433	−	0.996629i	$-0.526145\pi$
$619$	−4.08243			−0.164087			−0.0820433	+	0.996629i	$0.526145\pi$
$620$	−6.30622	+	7.90775i	−0.253264	+	0.317583i
$621$		0			0
$622$	−4.21975	+	2.03213i	−0.169197	+	0.0814809i
$623$	−13.7474	−	17.8015i	−0.550780	−	0.713203i
$624$		0			0
$625$	−6.33929	+	7.94922i	−0.253572	+	0.317969i
$626$	−12.4644	−	6.00256i	−0.498179	−	0.239910i
$627$		0			0
$628$	−27.6979	+	13.3386i	−1.10527	+	0.532268i
$629$	−6.02504	−	26.3974i	−0.240234	−	1.05253i
$630$		0			0
$631$	−1.02514	+	4.49144i	−0.0408103	+	0.178802i	−0.991225	−	0.132183i	$-0.957801\pi$
$631$	−1.02514	+	4.49144i	−0.0408103	+	0.178802i	0.950415	+	0.310984i	$0.100659\pi$
$632$	−0.879025	−	3.85126i	−0.0349657	−	0.153195i
$633$		0			0
$634$	−10.1811	−	44.6063i	−0.404343	−	1.77154i
$635$	3.99114	+	1.92203i	0.158384	+	0.0762735i
$636$		0			0
$637$	33.4561	+	1.04424i	1.32558	+	0.0413742i
$638$	−2.88120			−0.114068
$639$		0			0
$640$	1.81332	+	7.94468i	0.0716778	+	0.314041i
$641$	12.2968	+	15.4197i	0.485696	+	0.609043i	0.962936	−	0.269729i	$-0.0869343\pi$
$641$	12.2968	+	15.4197i	0.485696	+	0.609043i	−0.477240	+	0.878773i	$0.658363\pi$
$642$		0			0
$643$	7.61618	−	33.3687i	0.300353	−	1.31593i	−0.569244	−	0.822169i	$-0.692764\pi$
$643$	7.61618	−	33.3687i	0.300353	−	1.31593i	0.869597	−	0.493763i	$-0.164379\pi$
$644$	24.6876	+	0.385183i	0.972828	+	0.0151783i
$645$		0			0
$646$	−47.5629	+	22.9051i	−1.87134	+	0.901189i
$647$	−5.89412	+	25.8238i	−0.231722	+	1.01524i	0.716489	+	0.697598i	$0.245748\pi$
$647$	−5.89412	+	25.8238i	−0.231722	+	1.01524i	−0.948211	+	0.317641i	$0.897109\pi$
$648$		0			0
$649$	−0.804777	+	1.00916i	−0.0315903	+	0.0396129i
$650$	17.2977	+	8.33012i	0.678470	+	0.326734i
$651$		0			0
$652$	−2.96279	+	1.42680i	−0.116032	+	0.0558779i
$653$	−3.97946	+	17.4351i	−0.155728	+	0.682290i	0.835429	+	0.549598i	$0.185219\pi$
$653$	−3.97946	+	17.4351i	−0.155728	+	0.682290i	−0.991157	+	0.132692i	$0.957638\pi$
$654$		0			0
$655$	−1.84564			−0.0721150
$656$	−31.2573			−1.22039
$657$		0			0
$658$	−8.41336	+	10.2188i	−0.327987	+	0.398371i
$659$	1.29650	+	1.62575i	0.0505043	+	0.0633304i	0.806442	−	0.591313i	$-0.201390\pi$
$659$	1.29650	+	1.62575i	0.0505043	+	0.0633304i	−0.755938	+	0.654643i	$0.772819\pi$
$660$		0			0
$661$	21.1878	−	10.2035i	0.824109	−	0.396870i	0.0262062	−	0.999657i	$-0.491657\pi$
$661$	21.1878	−	10.2035i	0.824109	−	0.396870i	0.797902	+	0.602787i	$0.205943\pi$
$662$	−40.3438	+	19.4285i	−1.56801	+	0.755112i
$663$		0			0
$664$	−4.20163	−	5.26867i	−0.163055	−	0.204464i
$665$	30.1110	−	13.9263i	1.16766	−	0.540037i
$666$		0			0
$667$	9.79403			0.379226
$668$	−30.7368			−1.18924
$669$		0			0
$670$	6.02457	−	26.3954i	0.232749	−	1.01974i
$671$	7.04854	−	3.39440i	0.272106	−	0.131039i
$672$		0			0
$673$	7.12665	+	3.43202i	0.274712	+	0.132294i	0.566168	−	0.824290i	$-0.308425\pi$
$673$	7.12665	+	3.43202i	0.274712	+	0.132294i	−0.291456	+	0.956584i	$0.594140\pi$
$674$	−4.04347	+	5.07036i	−0.155749	+	0.195303i
$675$		0			0
$676$	−3.69885	+	16.2057i	−0.142264	+	0.623298i
$677$	16.9579	−	8.16648i	0.651744	−	0.313863i	−0.0786370	−	0.996903i	$-0.525057\pi$
$677$	16.9579	−	8.16648i	0.651744	−	0.313863i	0.730381	+	0.683040i	$0.239343\pi$
$678$		0			0
$679$	4.79645	+	22.6369i	0.184071	+	0.868723i
$680$	0.858442	−	3.76108i	0.0329197	−	0.144231i
$681$		0			0
$682$	3.57574	+	4.48384i	0.136922	+	0.171695i
$683$	1.70367	+	7.46426i	0.0651891	+	0.285612i	0.997007	−	0.0773147i	$-0.0246346\pi$
$683$	1.70367	+	7.46426i	0.0651891	+	0.285612i	−0.931818	+	0.362927i	$0.881777\pi$
$684$		0			0
$685$	−34.6984			−1.32576
$686$	6.28075	+	34.9927i	0.239800	+	1.33603i
$687$		0			0
$688$	26.4938	+	12.7587i	1.01007	+	0.486422i
$689$	−10.3977	−	45.5555i	−0.396122	−	1.73553i
$690$		0			0
$691$	5.03661	+	22.0668i	0.191602	+	0.839461i	0.975750	+	0.218888i	$0.0702429\pi$
$691$	5.03661	+	22.0668i	0.191602	+	0.839461i	−0.784148	+	0.620573i	$0.786900\pi$
$692$	−8.77184	+	38.4319i	−0.333455	+	1.46096i
$693$		0			0
$694$	6.32351	+	27.7051i	0.240037	+	1.05167i
$695$	−8.30531	+	3.99963i	−0.315038	+	0.151715i
$696$		0			0
$697$	23.2480	+	11.1956i	0.880579	+	0.424065i
$698$	−5.99690	+	7.51988i	−0.226986	+	0.284632i
$699$		0			0
$700$	−2.21637	+	9.05686i	−0.0837709	+	0.342317i
$701$	−27.8493	+	13.4115i	−1.05185	+	0.506546i	−0.878216	−	0.478264i	$-0.841266\pi$
$701$	−27.8493	+	13.4115i	−1.05185	+	0.506546i	−0.173637	+	0.984810i	$0.555552\pi$
$702$		0			0
$703$	33.1860	−	41.6139i	1.25163	−	1.56950i
$704$	−4.50895			−0.169937
$705$		0			0
$706$	−2.36114	+	2.96077i	−0.0888626	+	0.111430i
$707$	36.0260	−	16.6619i	1.35490	−	0.626637i
$708$		0			0
$709$	−26.8805	−	33.7071i	−1.00952	−	1.26590i	−0.963712	−	0.266945i	$-0.913986\pi$
$709$	−26.8805	−	33.7071i	−1.00952	−	1.26590i	−0.0458061	−	0.998950i	$-0.514586\pi$
$710$	17.8648	−	8.60325i	0.670455	−	0.322874i
$711$		0			0
$712$	−3.20563	−	4.01974i	−0.120136	−	0.150646i
$713$	−12.1550	−	15.2418i	−0.455207	−	0.570812i
$714$		0			0
$715$	−4.31561	+	5.41160i	−0.161394	+	0.202382i
$716$	−20.7783			−0.776523
$717$		0			0
$718$	−4.47529	+	5.61184i	−0.167016	+	0.209432i
$719$	0.884282	−	3.87429i	0.0329781	−	0.144487i	−0.955758	−	0.294153i	$-0.904963\pi$
$719$	0.884282	−	3.87429i	0.0329781	−	0.144487i	0.988737	+	0.149666i	$0.0478198\pi$
$720$		0			0
$721$	30.1239	−	13.9322i	1.12187	−	0.518864i
$722$	−60.6376	−	29.2015i	−2.25670	−	1.08677i
$723$		0			0
$724$	−2.55828	−	1.23200i	−0.0950778	−	0.0457871i
$725$	−0.823015	+	3.60587i	−0.0305660	+	0.133918i
$726$		0			0
$727$	−1.09142	−	4.78182i	−0.0404785	−	0.177348i	0.950648	−	0.310273i	$-0.100420\pi$
$727$	−1.09142	−	4.78182i	−0.0404785	−	0.177348i	−0.991126	+	0.132925i	$0.957563\pi$
$728$	7.65054	+	0.119366i	0.283548	+	0.00442399i
$729$		0			0
$730$	−2.38639	−	10.4555i	−0.0883243	−	0.386974i
$731$	−15.1352	−	18.9789i	−0.559794	−	0.701960i
$732$		0			0
$733$	−11.4558	−	5.51682i	−0.423130	−	0.203768i	0.210187	−	0.977661i	$-0.432593\pi$
$733$	−11.4558	−	5.51682i	−0.423130	−	0.203768i	−0.633317	+	0.773893i	$0.718307\pi$
$734$	52.9854			1.95573
$735$		0			0
$736$	41.4725			1.52870
$737$	−6.32435	−	3.04564i	−0.232960	−	0.112188i
$738$		0			0
$739$	−22.7887	−	28.5761i	−0.838295	−	1.05119i	−0.997949	−	0.0640154i	$-0.979609\pi$
$739$	−22.7887	−	28.5761i	−0.838295	−	1.05119i	0.159654	−	0.987173i	$-0.448962\pi$
$740$	−4.62881	−	20.2802i	−0.170159	−	0.745514i
$741$		0			0
$742$	45.0455	−	20.8334i	1.65367	−	0.764819i
$743$	−2.33772	−	10.2422i	−0.0857624	−	0.375750i	0.913773	−	0.406225i	$-0.133155\pi$
$743$	−2.33772	−	10.2422i	−0.0857624	−	0.375750i	−0.999536	+	0.0304752i	$0.990298\pi$
$744$		0			0
$745$	−8.34578	+	36.5652i	−0.305766	+	1.33965i
$746$	0.618582	+	0.297893i	0.0226479	+	0.0109067i
$747$		0			0
$748$	4.81940	+	2.32090i	0.176215	+	0.0848606i
$749$	−7.00420	−	9.06971i	−0.255928	−	0.331400i
$750$		0			0
$751$	−7.83396	+	34.3228i	−0.285865	+	1.25246i	0.604277	+	0.796774i	$0.293462\pi$
$751$	−7.83396	+	34.3228i	−0.285865	+	1.25246i	−0.890142	+	0.455683i	$0.849395\pi$
$752$	−7.36247	+	9.23225i	−0.268482	+	0.336665i
$753$		0			0
$754$	−16.2318			−0.591128
$755$	19.6343	−	24.6206i	0.714566	−	0.896037i
$756$		0			0
$757$	−14.5859	−	18.2902i	−0.530134	−	0.664767i	0.442592	−	0.896723i	$-0.354059\pi$
$757$	−14.5859	−	18.2902i	−0.530134	−	0.664767i	−0.972726	+	0.231956i	$0.925488\pi$
$758$	−45.9241	−	57.5870i	−1.66804	−	2.09165i
$759$		0			0
$760$	6.83259	−	3.29040i	0.247844	−	0.119355i
$761$	3.60769	+	4.52391i	0.130779	+	0.163991i	0.842909	−	0.538056i	$-0.180841\pi$
$761$	3.60769	+	4.52391i	0.130779	+	0.163991i	−0.712130	+	0.702047i	$0.752270\pi$
$762$		0			0
$763$	−12.4420	+	50.8425i	−0.450432	+	1.84062i
$764$	25.1385	−	31.5227i	0.909480	−	1.14045i
$765$		0			0
$766$	−23.0906			−0.834299
$767$	−4.53387	+	5.68530i	−0.163709	+	0.205284i
$768$		0			0
$769$	−41.0184	+	19.7534i	−1.47916	+	0.712327i	−0.987377	−	0.158389i	$-0.949370\pi$
$769$	−41.0184	+	19.7534i	−1.47916	+	0.712327i	−0.491786	+	0.870716i	$0.663656\pi$
$770$	−6.57309	−	3.29273i	−0.236878	−	0.118662i
$771$		0			0
$772$	−1.39411	+	1.74815i	−0.0501750	+	0.0629174i
$773$	1.08468	+	0.522355i	0.0390133	+	0.0187878i	0.453289	−	0.891364i	$-0.350251\pi$
$773$	1.08468	+	0.522355i	0.0390133	+	0.0187878i	−0.414275	+	0.910152i	$0.635965\pi$
$774$		0			0
$775$	6.63300	−	3.19428i	0.238264	−	0.114742i
$776$	1.17701	+	5.15684i	0.0422524	+	0.185120i
$777$		0			0
$778$	−12.3525	+	54.1200i	−0.442860	+	1.94030i
$779$	11.2871	+	49.4519i	0.404402	+	1.77180i
$780$		0			0
$781$	−1.14396	−	5.01201i	−0.0409341	−	0.179344i
$782$	−35.8284	−	17.2540i	−1.28122	−	0.617003i
$783$		0			0
$784$	6.08940	+	31.1259i	0.217479	+	1.11164i
$785$	−31.1158			−1.11057
$786$		0			0
$787$	−5.78556	−	25.3482i	−0.206233	−	0.903566i	−0.967047	−	0.254596i	$-0.918057\pi$
$787$	−5.78556	−	25.3482i	−0.206233	−	0.903566i	0.760814	−	0.648970i	$-0.224800\pi$
$788$	8.40799	+	10.5433i	0.299522	+	0.375589i
$789$		0			0
$790$	−4.75815	+	20.8468i	−0.169287	+	0.741697i
$791$	10.1093	+	13.0905i	0.359444	+	0.465444i
$792$		0			0
$793$	39.7094	−	19.1230i	1.41012	−	0.679078i
$794$	−5.60446	+	24.5547i	−0.198895	+	0.871415i
$795$		0			0
$796$	−1.26648	+	1.58812i	−0.0448893	+	0.0562895i
$797$	−32.9615	−	15.8734i	−1.16755	−	0.562265i	−0.253293	−	0.967390i	$-0.581514\pi$
$797$	−32.9615	−	15.8734i	−1.16755	−	0.562265i	−0.914261	+	0.405125i	$0.867228\pi$
$798$		0			0
$799$	8.78269	−	4.22952i	0.310709	−	0.149630i
$800$	−3.48503	+	15.2689i	−0.123214	+	0.539838i
$801$		0			0
$802$	4.17419			0.147396
$803$	−2.78049			−0.0981214
$804$		0			0
$805$	22.3438	+	11.1929i	0.787516	+	0.394499i
$806$	20.1447	+	25.2606i	0.709565	+	0.889767i
$807$		0			0
$808$	8.17479	−	3.93677i	0.287588	−	0.138495i
$809$	−24.1715	+	11.6404i	−0.849823	+	0.409253i	−0.807512	−	0.589851i	$-0.799186\pi$
$809$	−24.1715	+	11.6404i	−0.849823	+	0.409253i	−0.0423114	+	0.999104i	$0.513472\pi$
$810$		0			0
$811$	22.8545	+	28.6586i	0.802529	+	1.00634i	0.999663	+	0.0259630i	$0.00826520\pi$
$811$	22.8545	+	28.6586i	0.802529	+	1.00634i	−0.197134	+	0.980377i	$0.563163\pi$
$812$	−1.63405	−	7.71189i	−0.0573438	−	0.270634i
$813$		0			0
$814$	−11.7949			−0.413412
$815$	−3.32839			−0.116589
$816$		0			0
$817$	10.6185	−	46.5228i	0.371496	−	1.62763i
$818$	36.0294	−	17.3508i	1.25974	−	0.606658i
$819$		0			0
$820$	17.8605	+	8.60118i	0.623717	+	0.300366i
$821$	0.728230	−	0.913171i	0.0254154	−	0.0318699i	−0.768961	−	0.639295i	$-0.779226\pi$
$821$	0.728230	−	0.913171i	0.0254154	−	0.0318699i	0.794377	+	0.607425i	$0.207798\pi$
$822$		0			0
$823$	0.290129	−	1.27114i	0.0101133	−	0.0443092i	−0.969620	−	0.244618i	$-0.921337\pi$
$823$	0.290129	−	1.27114i	0.0101133	−	0.0443092i	0.979733	+	0.200309i	$0.0641946\pi$
$824$	6.83552	−	3.29181i	0.238127	−	0.114676i
$825$		0			0
$826$	−6.90553	−	3.45926i	−0.240274	−	0.120363i
$827$	−11.4445	+	50.1417i	−0.397965	+	1.74360i	0.237426	+	0.971406i	$0.423696\pi$
$827$	−11.4445	+	50.1417i	−0.397965	+	1.74360i	−0.635390	+	0.772191i	$0.719161\pi$
$828$		0			0
$829$	7.29642	+	9.14942i	0.253415	+	0.317773i	0.892224	−	0.451593i	$-0.149144\pi$
$829$	7.29642	+	9.14942i	0.253415	+	0.317773i	−0.638809	+	0.769365i	$0.720573\pi$
$830$	8.11701	+	35.5629i	0.281745	+	1.23441i
$831$		0			0
$832$	−25.4021			−0.880659
$833$	6.61951	−	25.3313i	0.229353	−	0.877679i
$834$		0			0
$835$	−28.0293	−	13.4982i	−0.969995	−	0.467125i
$836$	2.33986	+	10.2516i	0.0809258	+	0.354559i
$837$		0			0
$838$	−4.52506	−	19.8256i	−0.156316	−	0.684863i
$839$	−7.16001	+	31.3701i	−0.247191	+	1.08301i	0.687117	+	0.726547i	$0.258876\pi$
$839$	−7.16001	+	31.3701i	−0.247191	+	1.08301i	−0.934308	+	0.356468i	$0.883981\pi$
$840$		0			0
$841$	5.75729	+	25.2243i	0.198527	+	0.869804i
$842$	9.43958	−	4.54586i	0.325309	−	0.156661i
$843$		0			0
$844$	−15.4632	−	7.44670i	−0.532266	−	0.256326i
$845$	−10.4899	+	13.1539i	−0.360862	+	0.452507i
$846$		0			0
$847$	17.2868	−	20.9965i	0.593983	−	0.721448i
$848$	39.8905	−	19.2103i	1.36985	−	0.659683i
$849$		0			0
$850$	9.36315	−	11.7410i	0.321153	−	0.402714i
$851$	40.0944			1.37442
$852$		0			0
$853$	0.364773	−	0.457411i	0.0124896	−	0.0156615i	−0.775547	−	0.631289i	$-0.782526\pi$
$853$	0.364773	−	0.457411i	0.0124896	−	0.0156615i	0.788037	+	0.615628i	$0.211098\pi$
$854$	28.6124	+	37.0501i	0.979096	+	1.26783i
$855$		0			0
$856$	−1.63324	−	2.04802i	−0.0558230	−	0.0699999i
$857$	5.02053	−	2.41776i	0.171498	−	0.0825891i	−0.346165	−	0.938174i	$-0.612516\pi$
$857$	5.02053	−	2.41776i	0.171498	−	0.0825891i	0.517663	+	0.855584i	$0.326802\pi$
$858$		0			0
$859$	20.3193	+	25.4796i	0.693285	+	0.869351i	0.996502	−	0.0835701i	$-0.0266322\pi$
$859$	20.3193	+	25.4796i	0.693285	+	0.869351i	−0.303217	+	0.952921i	$0.598061\pi$
$860$	−11.6278	−	14.5808i	−0.396504	−	0.497201i
$861$		0			0
$862$	−34.8807	+	43.7390i	−1.18804	+	1.48976i
$863$	−7.32156			−0.249229			−0.124614	−	0.992205i	$-0.539769\pi$
$863$	−7.32156			−0.249229			−0.124614	+	0.992205i	$0.539769\pi$
$864$		0			0
$865$	−24.8767	+	31.1944i	−0.845834	+	1.06064i
$866$	3.92665	−	17.2038i	0.133433	−	0.584608i
$867$		0			0
$868$	−9.97359	+	12.1139i	−0.338526	+	0.411172i
$869$	4.99491	+	2.40542i	0.169441	+	0.0815984i
$870$		0			0
$871$	−35.6295	−	17.1583i	−1.20726	−	0.581385i
$872$	−2.66247	+	11.6651i	−0.0901627	+	0.395029i
$873$		0			0
$874$	−17.3950	−	76.2124i	−0.588394	−	2.57792i
$875$	−20.3382	+	24.7026i	−0.687556	+	0.835102i
$876$		0			0
$877$	5.03455	+	22.0578i	0.170005	+	0.744839i	0.985995	+	0.166774i	$0.0533350\pi$
$877$	5.03455	+	22.0578i	0.170005	+	0.744839i	−0.815990	+	0.578065i	$0.803808\pi$
$878$	7.89312	+	9.89766i	0.266380	+	0.334030i
$879$		0			0
$880$	−5.90900	−	2.84562i	−0.199192	−	0.0959259i
$881$	42.4237			1.42929			0.714645	−	0.699487i	$-0.246588\pi$
$881$	42.4237			1.42929			0.714645	+	0.699487i	$0.246588\pi$
$882$		0			0
$883$	−5.35721			−0.180285			−0.0901423	−	0.995929i	$-0.528732\pi$
$883$	−5.35721			−0.180285			−0.0901423	+	0.995929i	$0.528732\pi$
$884$	27.1511	+	13.0753i	0.913190	+	0.439769i
$885$		0			0
$886$	41.2778	+	51.7608i	1.38676	+	1.73894i
$887$	−1.07143	−	4.69422i	−0.0359749	−	0.157617i	0.953750	−	0.300601i	$-0.0971872\pi$
$887$	−1.07143	−	4.69422i	−0.0359749	−	0.157617i	−0.989725	+	0.142984i	$0.954330\pi$
$888$		0			0
$889$	6.14453	+	3.07805i	0.206081	+	0.103234i
$890$	6.19288	+	27.1328i	0.207586	+	0.909493i
$891$		0			0
$892$	−3.54936	+	15.5507i	−0.118841	+	0.520678i
$893$	17.2649	+	8.31433i	0.577747	+	0.278228i
$894$		0			0
$895$	−18.9480	−	9.12490i	−0.633363	−	0.305012i
$896$	2.62054	+	12.3677i	0.0875461	+	0.413174i
$897$		0			0
$898$	12.8374	−	56.2443i	0.428390	−	1.87690i
$899$	−3.88078	+	4.86635i	−0.129431	+	0.162302i
$900$		0			0
$901$	−36.5497			−1.21765
$902$	7.00827	−	8.78809i	0.233350	−	0.292611i
$903$		0			0
$904$	2.35729	+	2.95594i	0.0784021	+	0.0983132i
$905$	−1.79189	−	2.24696i	−0.0595646	−	0.0746916i
$906$		0			0
$907$	−9.20684	+	4.43378i	−0.305708	+	0.147221i	−0.580448	−	0.814297i	$-0.697123\pi$
$907$	−9.20684	+	4.43378i	−0.305708	+	0.147221i	0.274740	+	0.961519i	$0.411408\pi$
$908$	−10.0585	−	12.6130i	−0.333804	−	0.418577i
$909$		0			0
$910$	−37.0308	−	18.5502i	−1.22756	−	0.614935i
$911$	31.4359	−	39.4194i	1.04152	−	1.30602i	0.0908324	−	0.995866i	$-0.471047\pi$
$911$	31.4359	−	39.4194i	1.04152	−	1.30602i	0.950686	−	0.310156i	$-0.100381\pi$
$912$		0			0
$913$	9.45748			0.312997
$914$	22.9408	−	28.7668i	0.758813	−	0.951521i
$915$		0			0
$916$	12.7667	−	6.14810i	0.421822	−	0.203139i
$917$	−2.86295	−	0.0446685i	−0.0945428	−	0.00147508i
$918$		0			0
$919$	−4.10050	+	5.14187i	−0.135263	+	0.169615i	−0.844850	−	0.535004i	$-0.820310\pi$
$919$	−4.10050	+	5.14187i	−0.135263	+	0.169615i	0.709587	+	0.704618i	$0.248882\pi$
$920$	5.14688	+	2.47861i	0.169688	+	0.0817172i
$921$		0			0
$922$	64.5602	−	31.0906i	2.12618	−	1.02391i
$923$	−6.44473	−	28.2362i	−0.212131	−	0.929406i
$924$		0			0
$925$	−3.36922	+	14.7615i	−0.110779	+	0.485356i
$926$	5.20825	+	22.8188i	0.171154	+	0.749874i
$927$		0			0
$928$	−2.94643	−	12.9092i	−0.0967213	−	0.423764i
$929$	41.3217	+	19.8995i	1.35572	+	0.652881i	0.963678	−	0.267065i	$-0.0860540\pi$
$929$	41.3217	+	19.8995i	1.35572	+	0.652881i	0.392044	+	0.919947i	$0.371768\pi$
$930$		0			0
$931$	47.0452	−	20.8736i	1.54184	−	0.684106i
$932$	−24.4236			−0.800022
$933$		0			0
$934$	5.23353	+	22.9296i	0.171246	+	0.750279i
$935$	3.37565	+	4.23293i	0.110395	+	0.138431i
$936$		0			0
$937$	6.31975	−	27.6886i	0.206457	−	0.904548i	−0.760445	−	0.649402i	$-0.775019\pi$
$937$	6.31975	−	27.6886i	0.206457	−	0.904548i	0.966903	−	0.255146i	$-0.0821235\pi$
$938$	9.98413	−	40.7986i	0.325993	−	1.33212i
$939$		0			0
$940$	6.74742	−	3.24938i	0.220076	−	0.105983i
$941$	8.49332	−	37.2117i	0.276874	−	1.21307i	−0.624847	−	0.780748i	$-0.714839\pi$
$941$	8.49332	−	37.2117i	0.276874	−	1.21307i	0.901721	−	0.432318i	$-0.142304\pi$
$942$		0			0
$943$	−23.8231	+	29.8732i	−0.775787	+	0.972807i
$944$	−6.20785	−	2.98954i	−0.202048	−	0.0973014i
$945$		0			0
$946$	−9.52739	+	4.58815i	−0.309762	+	0.149174i
$947$	−4.80345	+	21.0453i	−0.156091	+	0.683880i	0.834950	+	0.550325i	$0.185496\pi$
$947$	−4.80345	+	21.0453i	−0.156091	+	0.683880i	−0.991041	+	0.133554i	$0.957361\pi$
$948$		0			0
$949$	−15.6645			−0.508490
$950$	29.5208			0.957782
$951$		0			0
$952$	1.42264	−	5.81340i	0.0461080	−	0.188413i
$953$	20.4721	+	25.6712i	0.663157	+	0.831572i	0.993683	−	0.112225i	$-0.0357977\pi$
$953$	20.4721	+	25.6712i	0.663157	+	0.831572i	−0.330526	+	0.943797i	$0.607226\pi$
$954$		0			0
$955$	36.7675	−	17.7063i	1.18977	−	0.572962i
$956$	33.4372	−	16.1025i	1.08143	−	0.520792i
$957$		0			0
$958$	−31.2314	−	39.1629i	−1.00904	−	1.26530i
$959$	−53.8241	−	0.839779i	−1.73807	−	0.0271179i
$960$		0			0
$961$	−18.6105			−0.600340
$962$	−66.4491			−2.14241
$963$		0			0
$964$	−2.50856	+	10.9907i	−0.0807951	+	0.353987i
$965$	−2.03901	+	0.981938i	−0.0656382	+	0.0316097i
$966$		0			0
$967$	−14.4193	−	6.94395i	−0.463692	−	0.223302i	0.187426	−	0.982279i	$-0.439986\pi$
$967$	−14.4193	−	6.94395i	−0.463692	−	0.223302i	−0.651118	+	0.758976i	$0.725700\pi$
$968$	3.87625	−	4.86066i	0.124587	−	0.156228i
$969$		0			0
$970$	6.37117	−	27.9139i	0.204566	−	0.896261i
$971$	−5.06814	+	2.44069i	−0.162644	+	0.0783253i	−0.513435	−	0.858129i	$-0.671627\pi$
$971$	−5.06814	+	2.44069i	−0.162644	+	0.0783253i	0.350791	+	0.936454i	$0.385913\pi$
$972$		0			0
$973$	−12.9800	+	6.00321i	−0.416119	+	0.192454i
$974$	−3.69074	+	16.1702i	−0.118259	+	0.518126i
$975$		0			0
$976$	26.0378	+	32.6503i	0.833449	+	1.04511i
$977$	−8.49746	−	37.2298i	−0.271858	−	1.19109i	−0.907818	−	0.419365i	$-0.862253\pi$
$977$	−8.49746	−	37.2298i	−0.271858	−	1.19109i	0.635960	−	0.771722i	$-0.280604\pi$
$978$		0			0
$979$	7.21560			0.230612
$980$	5.08552	−	19.4611i	0.162451	−	0.621662i
$981$		0			0
$982$	−50.6465	−	24.3901i	−1.61619	−	0.778318i
$983$	−5.59361	−	24.5072i	−0.178408	−	0.781659i	−0.982365	−	0.186971i	$-0.940133\pi$
$983$	−5.59361	−	24.5072i	−0.178408	−	0.781659i	0.803957	−	0.594688i	$-0.202724\pi$
$984$		0			0
$985$	3.03723	+	13.3070i	0.0967742	+	0.423996i
$986$	−2.82523	+	12.3781i	−0.0899736	+	0.394200i
$987$		0			0
$988$	13.1821	+	57.7545i	0.419378	+	1.83741i
$989$	32.3863	−	15.5964i	1.02983	−	0.495938i
$990$		0			0
$991$	−3.04498	−	1.46639i	−0.0967271	−	0.0465813i	0.384895	−	0.922961i	$-0.374238\pi$
$991$	−3.04498	−	1.46639i	−0.0967271	−	0.0465813i	−0.481622	+	0.876379i	$0.659952\pi$
$992$	−16.4330	+	20.6064i	−0.521749	+	0.654253i
$993$		0			0
$994$	27.9201	−	12.9130i	0.885572	−	0.409575i
$995$	−1.85236	+	0.892048i	−0.0587236	+	0.0282798i
$996$		0			0
$997$	17.8842	−	22.4261i	0.566398	−	0.710240i	−0.413328	−	0.910582i	$-0.635634\pi$
$997$	17.8842	−	22.4261i	0.566398	−	0.710240i	0.979726	+	0.200342i	$0.0642052\pi$
$998$	19.3088			0.611210
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.c.127.1		24
3.2	odd	2		147.2.i.a.127.4	yes	24
49.22	even	7	inner	441.2.u.c.316.1		24
147.62	even	14		7203.2.a.b.1.3		12
147.71	odd	14		147.2.i.a.22.4	✓	24
147.134	odd	14		7203.2.a.a.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.a.22.4	✓	24	147.71	odd	14
147.2.i.a.127.4	yes	24	3.2	odd	2
441.2.u.c.127.1		24	1.1	even	1	trivial
441.2.u.c.316.1		24	49.22	even	7	inner
7203.2.a.a.1.3		12	147.134	odd	14
7203.2.a.b.1.3		12	147.62	even	14

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72952 - 0.832892i) q^{2} +(1.05054 + 1.31734i) q^{4} +(0.379489 + 1.66265i) q^{5} +(0.548424 + 2.58829i) q^{7} +(0.134579 + 0.589630i) q^{8} +O(q^{10})\)	\(q+(-1.72952 - 0.832892i) q^{2} +(1.05054 + 1.31734i) q^{4} +(0.379489 + 1.66265i) q^{5} +(0.548424 + 2.58829i) q^{7} +(0.134579 + 0.589630i) q^{8} +(0.728476 - 3.19166i) q^{10} +(-0.764724 - 0.368272i) q^{11} +(-4.30823 - 2.07473i) q^{13} +(1.20726 - 4.93327i) q^{14} +(1.00821 - 4.41726i) q^{16} +(-2.33202 + 2.92427i) q^{17} -7.35258 q^{19} +(-1.79161 + 2.24661i) q^{20} +(1.01587 + 1.27386i) q^{22} +(-3.45324 - 4.33023i) q^{23} +(1.88444 - 0.907501i) q^{25} +(5.72313 + 7.17657i) q^{26} +(-2.83351 + 3.44157i) q^{28} +(-1.10254 + 1.38254i) q^{29} +3.51987 q^{31} +(-4.66865 + 5.85430i) q^{32} +(6.46888 - 3.11525i) q^{34} +(-4.09530 + 1.89407i) q^{35} +(-4.51351 + 5.65977i) q^{37} +(12.7164 + 6.12390i) q^{38} +(-0.929278 + 0.447517i) q^{40} +(-1.53512 - 6.72580i) q^{41} +(-1.44419 + 6.32742i) q^{43} +(-0.318237 - 1.39429i) q^{44} +(2.36583 + 10.3654i) q^{46} +(-2.34814 - 1.13080i) q^{47} +(-6.39846 + 2.83896i) q^{49} -4.01503 q^{50} +(-1.79285 - 7.85500i) q^{52} +(6.09269 + 7.63999i) q^{53} +(0.322103 - 1.41122i) q^{55} +(-1.45233 + 0.671697i) q^{56} +(3.05836 - 1.47283i) q^{58} +(0.338394 - 1.48260i) q^{59} +(-5.74677 + 7.20622i) q^{61} +(-6.08768 - 2.93167i) q^{62} +(4.78620 - 2.30491i) q^{64} +(1.81463 - 7.95042i) q^{65} +8.27010 q^{67} -6.30215 q^{68} +(8.66045 + 0.135123i) q^{70} +(3.77637 + 4.73542i) q^{71} +(2.95146 - 1.42135i) q^{73} +(12.5202 - 6.02940i) q^{74} +(-7.72420 - 9.68585i) q^{76} +(0.533800 - 2.18129i) q^{77} -6.53165 q^{79} +7.72697 q^{80} +(-2.94685 + 12.9110i) q^{82} +(-10.0390 + 4.83453i) q^{83} +(-5.74702 - 2.76762i) q^{85} +(7.76781 - 9.74053i) q^{86} +(0.114228 - 0.500466i) q^{88} +(-7.65927 + 3.68851i) q^{89} +(3.00727 - 12.2888i) q^{91} +(2.07660 - 9.09819i) q^{92} +(3.11931 + 3.91149i) q^{94} +(-2.79023 - 12.2248i) q^{95} +8.74589 q^{97} +(13.4308 + 0.419204i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) \) 24 * q - q^2 - 3 * q^4 - 3 * q^8	\( 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) \) 24 * q - q^2 - 3 * q^4 - 3 * q^8 - 30 * q^10 - 9 * q^11 + 21 * q^14 - 29 * q^16 - 5 * q^17 + 26 * q^19 + 13 * q^20 + 11 * q^22 - 4 * q^23 - 28 * q^25 + 22 * q^26 - 7 * q^28 - 6 * q^29 + 36 * q^31 - 14 * q^32 + 46 * q^34 + 7 * q^35 - 22 * q^37 + 45 * q^38 + 35 * q^40 + 11 * q^41 + 6 * q^43 - 82 * q^44 - 16 * q^46 - 29 * q^47 - 42 * q^49 + 48 * q^50 - 50 * q^52 - 28 * q^53 + 23 * q^55 - 21 * q^56 + 39 * q^58 + 15 * q^59 - 32 * q^61 + 8 * q^62 + 29 * q^64 + 21 * q^65 - 34 * q^67 + 22 * q^68 - 24 * q^71 - 15 * q^73 - 6 * q^74 + 7 * q^76 + 21 * q^77 - 34 * q^79 - 8 * q^80 + 14 * q^82 - 14 * q^83 + 20 * q^85 + 100 * q^86 - 108 * q^88 - 10 * q^89 + 84 * q^91 + 21 * q^92 + 99 * q^94 - 18 * q^95 - 64 * q^97 - 91 * q^98

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