LMFDB - Embedded newform 441.2.bb.f.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, 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:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			109.2
Character	$\chi$	$=$	441.109
Dual form			441.2.bb.f.352.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.970582 + 0.900568i) q^{2} +(-0.0184545 + 0.246258i) q^{4} +(-0.843767 + 2.14988i) q^{5} +(-0.921217 - 2.48019i) q^{7} +(-1.85490 - 2.32597i) q^{8} +O(q^{10})$	\(q+(-0.970582 + 0.900568i) q^{2} +(-0.0184545 + 0.246258i) q^{4} +(-0.843767 + 2.14988i) q^{5} +(-0.921217 - 2.48019i) q^{7} +(-1.85490 - 2.32597i) q^{8} +(-1.11717 - 2.84651i) q^{10} +(-3.02845 - 0.934154i) q^{11} +(-0.953861 - 4.17914i) q^{13} +(3.12770 + 1.57761i) q^{14} +(3.40664 + 0.513468i) q^{16} +(0.187439 - 0.127794i) q^{17} +(-0.255542 - 0.442611i) q^{19} +(-0.513855 - 0.247459i) q^{20} +(3.78063 - 1.82066i) q^{22} +(3.09568 + 2.11060i) q^{23} +(-0.244797 - 0.227138i) q^{25} +(4.68940 + 3.19718i) q^{26} +(0.627768 - 0.181086i) q^{28} +(-4.64086 - 2.23492i) q^{29} +(-0.230978 + 0.400066i) q^{31} +(1.14732 - 0.782232i) q^{32} +(-0.0668380 + 0.292836i) q^{34} +(6.10942 + 0.112196i) q^{35} +(-0.656391 - 8.75893i) q^{37} +(0.646625 + 0.199457i) q^{38} +(6.56566 - 2.02524i) q^{40} +(-6.46643 - 8.10865i) q^{41} +(-4.80563 + 6.02607i) q^{43} +(0.285931 - 0.728541i) q^{44} +(-4.90535 + 0.739362i) q^{46} +(-0.749318 + 0.695265i) q^{47} +(-5.30272 + 4.56959i) q^{49} +0.442148 q^{50} +(1.04675 - 0.157772i) q^{52} +(0.933904 - 12.4621i) q^{53} +(4.56363 - 5.72261i) q^{55} +(-4.06009 + 6.74322i) q^{56} +(6.51703 - 2.01024i) q^{58} +(0.475918 + 1.21262i) q^{59} +(0.332035 + 4.43070i) q^{61} +(-0.136103 - 0.596308i) q^{62} +(-1.94234 + 8.50995i) q^{64} +(9.78950 + 1.47553i) q^{65} +(-4.62087 + 8.00359i) q^{67} +(0.0280112 + 0.0485168i) q^{68} +(-6.03073 + 5.39305i) q^{70} +(-0.267146 + 0.128651i) q^{71} +(-11.8541 - 10.9990i) q^{73} +(8.52510 + 7.91013i) q^{74} +(0.113712 - 0.0547610i) q^{76} +(0.472980 + 8.37171i) q^{77} +(3.09458 + 5.35997i) q^{79} +(-3.97831 + 6.89063i) q^{80} +(13.5786 + 2.04664i) q^{82} +(2.90716 - 12.7371i) q^{83} +(0.116587 + 0.510801i) q^{85} +(-0.762630 - 10.1766i) q^{86} +(3.44466 + 8.77684i) q^{88} +(2.90690 - 0.896660i) q^{89} +(-9.48636 + 6.21565i) q^{91} +(-0.576881 + 0.723386i) q^{92} +(0.101140 - 1.34962i) q^{94} +(1.16718 - 0.175924i) q^{95} +2.15843 q^{97} +(1.03149 - 9.21062i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) $ 72 * q + 14 * q^4 - 28 * q^7	$ 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55} + 56 q^{58} + 112 q^{61} + 38 q^{64} - 36 q^{67} - 14 q^{70} - 28 q^{73} + 56 q^{76} + 62 q^{79} - 70 q^{82} - 100 q^{85} - 262 q^{88} - 154 q^{91} - 294 q^{94} + 56 q^{97}+O(q^{100}) $ 72 * q + 14 * q^4 - 28 * q^7 + 42 * q^13 - 26 * q^16 + 28 * q^19 + 8 * q^22 - 24 * q^25 - 28 * q^28 + 28 * q^31 + 28 * q^34 - 106 * q^37 + 70 * q^40 - 2 * q^43 + 60 * q^46 + 28 * q^49 + 70 * q^52 - 42 * q^55 + 56 * q^58 + 112 * q^61 + 38 * q^64 - 36 * q^67 - 14 * q^70 - 28 * q^73 + 56 * q^76 + 62 * q^79 - 70 * q^82 - 100 * q^85 - 262 * q^88 - 154 * q^91 - 294 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{20}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.970582	+	0.900568i	−0.686305	+	0.636798i	−0.944199	−	0.329375i	$-0.893162\pi$
$2$	−0.970582	+	0.900568i	−0.686305	+	0.636798i	0.257894	+	0.966173i	$0.416971\pi$
$3$		0			0
$3$		0			0
$4$	−0.0184545	+	0.246258i	−0.00922724	+	0.123129i
$5$	−0.843767	+	2.14988i	−0.377344	+	0.961457i	0.608464	+	0.793581i	$0.291786\pi$
$5$	−0.843767	+	2.14988i	−0.377344	+	0.961457i	−0.985808	+	0.167876i	$0.946309\pi$
$6$		0			0
$7$	−0.921217	−	2.48019i	−0.348187	−	0.937425i
$7$	−0.921217	−	2.48019i	−0.348187	−	0.937425i
$8$	−1.85490	−	2.32597i	−0.655805	−	0.822354i
$9$		0			0
$10$	−1.11717	−	2.84651i	−0.353281	−	0.900145i
$11$	−3.02845	−	0.934154i	−0.913113	−	0.281658i	−0.197621	−	0.980279i	$-0.563321\pi$
$11$	−3.02845	−	0.934154i	−0.913113	−	0.281658i	−0.715492	+	0.698621i	$0.753798\pi$
$12$		0			0
$13$	−0.953861	−	4.17914i	−0.264553	−	1.15908i	−0.916251	−	0.400605i	$-0.868800\pi$
$13$	−0.953861	−	4.17914i	−0.264553	−	1.15908i	0.651697	−	0.758479i	$-0.274057\pi$
$14$	3.12770	+	1.57761i	0.835913	+	0.421634i
$15$		0			0
$16$	3.40664	+	0.513468i	0.851660	+	0.128367i
$17$	0.187439	−	0.127794i	0.0454607	−	0.0309946i	−0.540376	−	0.841423i	$-0.681718\pi$
$17$	0.187439	−	0.127794i	0.0454607	−	0.0309946i	0.585837	+	0.810429i	$0.300766\pi$
$18$		0			0
$19$	−0.255542	−	0.442611i	−0.0586253	−	0.101542i	0.835223	−	0.549911i	$-0.185338\pi$
$19$	−0.255542	−	0.442611i	−0.0586253	−	0.101542i	−0.893849	+	0.448369i	$0.852005\pi$
$20$	−0.513855	−	0.247459i	−0.114901	−	0.0553336i
$21$		0			0
$22$	3.78063	−	1.82066i	0.806033	−	0.388165i
$23$	3.09568	+	2.11060i	0.645494	+	0.440090i	0.841312	−	0.540550i	$-0.181784\pi$
$23$	3.09568	+	2.11060i	0.645494	+	0.440090i	−0.195818	+	0.980640i	$0.562736\pi$
$24$		0			0
$25$	−0.244797	−	0.227138i	−0.0489593	−	0.0454276i
$26$	4.68940	+	3.19718i	0.919667	+	0.627018i
$27$		0			0
$28$	0.627768	−	0.181086i	0.118637	−	0.0342221i
$29$	−4.64086	−	2.23492i	−0.861786	−	0.415014i	−0.0498473	−	0.998757i	$-0.515873\pi$
$29$	−4.64086	−	2.23492i	−0.861786	−	0.415014i	−0.811939	+	0.583742i	$0.801588\pi$
$30$		0			0
$31$	−0.230978	+	0.400066i	−0.0414849	+	0.0718540i	−0.886022	−	0.463643i	$-0.846542\pi$
$31$	−0.230978	+	0.400066i	−0.0414849	+	0.0718540i	0.844537	+	0.535497i	$0.179876\pi$
$32$	1.14732	−	0.782232i	0.202820	−	0.138280i
$33$		0			0
$34$	−0.0668380	+	0.292836i	−0.0114626	+	0.0502210i
$35$	6.10942	+	0.112196i	1.03268	+	0.0189646i
$36$		0			0
$37$	−0.656391	−	8.75893i	−0.107910	−	1.43996i	−0.743915	−	0.668274i	$-0.767033\pi$
$37$	−0.656391	−	8.75893i	−0.107910	−	1.43996i	0.636005	−	0.771685i	$-0.280586\pi$
$38$	0.646625	+	0.199457i	0.104896	+	0.0323563i
$39$		0			0
$40$	6.56566	−	2.02524i	1.03812	−	0.320218i
$41$	−6.46643	−	8.10865i	−1.00989	−	1.26636i	−0.963577	−	0.267431i	$-0.913825\pi$
$41$	−6.46643	−	8.10865i	−1.00989	−	1.26636i	−0.0463099	−	0.998927i	$-0.514746\pi$
$42$		0			0
$43$	−4.80563	+	6.02607i	−0.732851	+	0.918967i	−0.998988	−	0.0449685i	$-0.985681\pi$
$43$	−4.80563	+	6.02607i	−0.732851	+	0.918967i	0.266137	+	0.963935i	$0.414253\pi$
$44$	0.285931	−	0.728541i	0.0431058	−	0.109832i
$45$		0			0
$46$	−4.90535	+	0.739362i	−0.723254	+	0.109013i
$47$	−0.749318	+	0.695265i	−0.109299	+	0.101415i	−0.732930	−	0.680305i	$-0.761848\pi$
$47$	−0.749318	+	0.695265i	−0.109299	+	0.101415i	0.623630	+	0.781719i	$0.285657\pi$
$48$		0			0
$49$	−5.30272	+	4.56959i	−0.757531	+	0.652799i
$50$	0.442148			0.0625292
$51$		0			0
$52$	1.04675	−	0.157772i	0.145158	−	0.0218790i
$53$	0.933904	−	12.4621i	0.128282	−	1.71180i	−0.447574	−	0.894247i	$-0.647712\pi$
$53$	0.933904	−	12.4621i	0.128282	−	1.71180i	0.575855	−	0.817552i	$-0.304669\pi$
$54$		0			0
$55$	4.56363	−	5.72261i	0.615360	−	0.771637i
$56$	−4.06009	+	6.74322i	−0.542552	+	0.901101i
$57$		0			0
$58$	6.51703	−	2.01024i	0.855728	−	0.263957i
$59$	0.475918	+	1.21262i	0.0619593	+	0.157870i	0.958501	−	0.285090i	$-0.0920236\pi$
$59$	0.475918	+	1.21262i	0.0619593	+	0.157870i	−0.896541	+	0.442960i	$0.853928\pi$
$60$		0			0
$61$	0.332035	+	4.43070i	0.0425127	+	0.567293i	0.977269	+	0.212003i	$0.0679987\pi$
$61$	0.332035	+	4.43070i	0.0425127	+	0.567293i	−0.934756	+	0.355290i	$0.884382\pi$
$62$	−0.136103	−	0.596308i	−0.0172852	−	0.0757312i
$63$		0			0
$64$	−1.94234	+	8.50995i	−0.242793	+	1.06374i
$65$	9.78950	+	1.47553i	1.21424	+	0.183017i
$66$		0			0
$67$	−4.62087	+	8.00359i	−0.564530	+	0.977794i	0.432564	+	0.901603i	$0.357609\pi$
$67$	−4.62087	+	8.00359i	−0.564530	+	0.977794i	−0.997093	+	0.0761905i	$0.975724\pi$
$68$	0.0280112	+	0.0485168i	0.00339685	+	0.00588352i
$69$		0			0
$70$	−6.03073	+	5.39305i	−0.720810	+	0.644593i
$71$	−0.267146	+	0.128651i	−0.0317044	+	0.0152680i	−0.449669	−	0.893195i	$-0.648458\pi$
$71$	−0.267146	+	0.128651i	−0.0317044	+	0.0152680i	0.417964	+	0.908463i	$0.362744\pi$
$72$		0			0
$73$	−11.8541	−	10.9990i	−1.38742	−	1.28734i	−0.913538	−	0.406754i	$-0.866661\pi$
$73$	−11.8541	−	10.9990i	−1.38742	−	1.28734i	−0.473886	−	0.880586i	$-0.657149\pi$
$74$	8.52510	+	7.91013i	0.991022	+	0.919534i
$75$		0			0
$76$	0.113712	−	0.0547610i	0.0130437	−	0.00628151i
$77$	0.472980	+	8.37171i	0.0539011	+	0.954045i
$78$		0			0
$79$	3.09458	+	5.35997i	0.348167	+	0.603044i	0.985924	−	0.167194i	$-0.0534708\pi$
$79$	3.09458	+	5.35997i	0.348167	+	0.603044i	−0.637757	+	0.770238i	$0.720137\pi$
$80$	−3.97831	+	6.89063i	−0.444788	+	0.770396i
$81$		0			0
$82$	13.5786	+	2.04664i	1.49950	+	0.226014i
$83$	2.90716	−	12.7371i	0.319102	−	1.39808i	−0.520030	−	0.854148i	$-0.674079\pi$
$83$	2.90716	−	12.7371i	0.319102	−	1.39808i	0.839132	−	0.543928i	$-0.183064\pi$
$84$		0			0
$85$	0.116587	+	0.510801i	0.0126456	+	0.0554041i
$86$	−0.762630	−	10.1766i	−0.0822365	−	1.09737i
$87$		0			0
$88$	3.44466	+	8.77684i	0.367202	+	0.935614i
$89$	2.90690	−	0.896660i	0.308131	−	0.0950457i	−0.136834	−	0.990594i	$-0.543693\pi$
$89$	2.90690	−	0.896660i	0.308131	−	0.0950457i	0.444964	+	0.895548i	$0.353216\pi$
$90$		0			0
$91$	−9.48636	+	6.21565i	−0.994440	+	0.651577i
$92$	−0.576881	+	0.723386i	−0.0601440	+	0.0754182i
$93$		0			0
$94$	0.101140	−	1.34962i	0.0104318	−	0.139203i
$95$	1.16718	−	0.175924i	0.119750	−	0.0180494i
$96$		0			0
$97$	2.15843			0.219156			0.109578	−	0.993978i	$-0.465050\pi$
$97$	2.15843			0.219156			0.109578	+	0.993978i	$0.465050\pi$
$98$	1.03149	−	9.21062i	0.104196	−	0.930413i
$99$		0			0
$100$	0.0604521	−	0.0560914i	0.00604521	−	0.00560914i
$101$	−17.6999	+	2.66782i	−1.76120	+	0.265458i	−0.948399	−	0.317080i	$-0.897298\pi$
$101$	−17.6999	+	2.66782i	−1.76120	+	0.265458i	−0.812803	+	0.582539i	$0.802059\pi$
$102$		0			0
$103$	−4.20944	+	10.7255i	−0.414769	+	1.05681i	0.558979	+	0.829182i	$0.311193\pi$
$103$	−4.20944	+	10.7255i	−0.414769	+	1.05681i	−0.973747	+	0.227631i	$0.926902\pi$
$104$	−7.95122	+	9.97052i	−0.779682	+	0.977690i
$105$		0			0
$106$	10.3165	+	12.9365i	1.00203	+	1.25651i
$107$	5.62711	−	1.73573i	0.543993	−	0.167800i	−0.0105656	−	0.999944i	$-0.503363\pi$
$107$	5.62711	−	1.73573i	0.543993	−	0.167800i	0.554559	+	0.832144i	$0.312887\pi$
$108$		0			0
$109$	3.34859	+	1.03290i	0.320737	+	0.0989343i	0.450943	−	0.892553i	$-0.351088\pi$
$109$	3.34859	+	1.03290i	0.320737	+	0.0989343i	−0.130206	+	0.991487i	$0.541564\pi$
$110$	0.724226	+	9.66412i	0.0690522	+	0.921438i
$111$		0			0
$112$	−1.86475	−	8.92214i	−0.176203	−	0.843063i
$113$	−4.45339	+	19.5116i	−0.418939	+	1.83549i	0.119506	+	0.992833i	$0.461869\pi$
$113$	−4.45339	+	19.5116i	−0.418939	+	1.83549i	−0.538446	+	0.842660i	$0.680988\pi$
$114$		0			0
$115$	−7.14957	+	4.87450i	−0.666701	+	0.454549i
$116$	0.636012	−	1.10160i	0.0590522	−	0.102281i
$117$		0			0
$118$	−1.55396	−	0.748350i	−0.143054	−	0.0688912i
$119$	−0.489626	−	0.347160i	−0.0448839	−	0.0318241i
$120$		0			0
$121$	−0.789744	−	0.538439i	−0.0717949	−	0.0489490i
$122$	−4.31241	−	4.00133i	−0.390428	−	0.362264i
$123$		0			0
$124$	−0.0942568	−	0.0642632i	−0.00846451	−	0.00577101i
$125$	−9.70921	+	4.67571i	−0.868419	+	0.418208i
$126$		0			0
$127$	6.38116	+	3.07300i	0.566236	+	0.272685i	0.695023	−	0.718987i	$-0.255394\pi$
$127$	6.38116	+	3.07300i	0.566236	+	0.272685i	−0.128787	+	0.991672i	$0.541108\pi$
$128$	−4.38998	−	7.60367i	−0.388023	−	0.672076i
$129$		0			0
$130$	−10.8303	+	7.38399i	−0.949882	+	0.647618i
$131$	−17.4825	−	2.63506i	−1.52745	−	0.230226i	−0.669056	−	0.743212i	$-0.733301\pi$
$131$	−17.4825	−	2.63506i	−1.52745	−	0.230226i	−0.858397	+	0.512986i	$0.828539\pi$
$132$		0			0
$133$	−0.862351	+	1.04153i	−0.0747754	+	0.0903124i
$134$	−2.72284	−	11.9295i	−0.235218	−	1.03056i
$135$		0			0
$136$	−0.644925	−	0.198933i	−0.0553019	−	0.0170584i
$137$	−0.0122594	−	0.0312364i	−0.00104739	−	0.00266870i	0.930349	−	0.366675i	$-0.119504\pi$
$137$	−0.0122594	−	0.0312364i	−0.00104739	−	0.00266870i	−0.931396	+	0.364006i	$0.881409\pi$
$138$		0			0
$139$	−12.6171	−	15.8213i	−1.07017	−	1.34195i	−0.936400	−	0.350935i	$-0.885864\pi$
$139$	−12.6171	−	15.8213i	−1.07017	−	1.34195i	−0.133768	−	0.991013i	$-0.542708\pi$
$140$	−0.140375	+	1.50242i	−0.0118639	+	0.126978i
$141$		0			0
$142$	0.143428	−	0.365449i	0.0120362	−	0.0306678i
$143$	−1.01524	+	13.5474i	−0.0848982	+	1.13289i
$144$		0			0
$145$	8.72062	−	8.09156i	0.724208	−	0.671967i
$146$	21.4108			1.77197
$147$		0			0
$148$	2.16907			0.178296
$149$	−0.721137	+	0.669117i	−0.0590778	+	0.0548162i	−0.709159	−	0.705048i	$-0.750925\pi$
$149$	−0.721137	+	0.669117i	−0.0590778	+	0.0548162i	0.650081	+	0.759865i	$0.274735\pi$
$150$		0			0
$151$	−0.431799	+	5.76196i	−0.0351393	+	0.468901i	0.951682	+	0.307086i	$0.0993539\pi$
$151$	−0.431799	+	5.76196i	−0.0351393	+	0.468901i	−0.986821	+	0.161815i	$0.948265\pi$
$152$	−0.555495	+	1.41538i	−0.0450566	+	0.114802i
$153$		0			0
$154$	−7.99836	−	7.69947i	−0.644526	−	0.620441i
$155$	−0.665204	−	0.834139i	−0.0534304	−	0.0669996i
$156$		0			0
$157$	−4.39083	−	11.1877i	−0.350426	−	0.892872i	−0.992049	−	0.125851i	$-0.959834\pi$
$157$	−4.39083	−	11.1877i	−0.350426	−	0.892872i	0.641623	−	0.767020i	$-0.278261\pi$
$158$	−7.83056	−	2.41541i	−0.622966	−	0.192160i
$159$		0			0
$160$	0.713634	+	3.12664i	0.0564177	+	0.247182i
$161$	2.38290	−	9.62221i	0.187799	−	0.758336i
$162$		0			0
$163$	19.3613	+	2.91824i	1.51649	+	0.228574i	0.853912	−	0.520418i	$-0.174224\pi$
$163$	19.3613	+	2.91824i	1.51649	+	0.228574i	0.662579	+	0.748992i	$0.269462\pi$
$164$	2.11615	−	1.44277i	0.165244	−	0.112661i
$165$		0			0
$166$	8.64898	+	14.9805i	0.671291	+	1.16271i
$167$	15.1813	+	7.31092i	1.17476	+	0.565736i	0.916381	−	0.400307i	$-0.131097\pi$
$167$	15.1813	+	7.31092i	1.17476	+	0.565736i	0.258381	+	0.966043i	$0.416811\pi$
$168$		0			0
$169$	−4.84275	+	2.33214i	−0.372519	+	0.179396i
$170$	−0.573168	−	0.390779i	−0.0439600	−	0.0299714i
$171$		0			0
$172$	−1.39528	−	1.29463i	−0.106389	−	0.0987148i
$173$	7.26824	+	4.95540i	0.552594	+	0.376752i	0.807187	−	0.590296i	$-0.200989\pi$
$173$	7.26824	+	4.95540i	0.552594	+	0.376752i	−0.254593	+	0.967048i	$0.581941\pi$
$174$		0			0
$175$	−0.337835	+	0.816386i	−0.0255380	+	0.0617130i
$176$	−9.83719	−	4.73734i	−0.741506	−	0.357091i
$177$		0			0
$178$	−2.01388	+	3.48814i	−0.150947	+	0.261447i
$179$	10.7221	−	7.31021i	0.801408	−	0.546391i	−0.0919356	−	0.995765i	$-0.529305\pi$
$179$	10.7221	−	7.31021i	0.801408	−	0.546391i	0.893344	+	0.449374i	$0.148353\pi$
$180$		0			0
$181$	3.67681	−	16.1091i	0.273295	−	1.19738i	−0.632802	−	0.774313i	$-0.718095\pi$
$181$	3.67681	−	16.1091i	0.273295	−	1.19738i	0.906097	−	0.423070i	$-0.139047\pi$
$182$	3.60966	−	14.5759i	0.267566	−	1.08044i
$183$		0			0
$184$	−0.832984	−	11.1154i	−0.0614084	−	0.819438i
$185$	19.3845	+	5.97933i	1.42518	+	0.439609i
$186$		0			0
$187$	−0.687030	+	0.211921i	−0.0502406	+	0.0154972i
$188$	−0.157386	−	0.197356i	−0.0114786	−	0.0143937i
$189$		0			0
$190$	−0.974411	+	1.22187i	−0.0706912	+	0.0886440i
$191$	−3.10844	+	7.92018i	−0.224919	+	0.573084i	−0.998134	−	0.0610595i	$-0.980552\pi$
$191$	−3.10844	+	7.92018i	−0.224919	+	0.573084i	0.773215	+	0.634144i	$0.218647\pi$
$192$		0			0
$193$	−7.58922	+	1.14389i	−0.546284	+	0.0823391i	−0.416385	−	0.909188i	$-0.636703\pi$
$193$	−7.58922	+	1.14389i	−0.546284	+	0.0823391i	−0.129899	+	0.991527i	$0.541465\pi$
$194$	−2.09494	+	1.94382i	−0.150408	+	0.139558i
$195$		0			0
$196$	−1.02744	−	1.39017i	−0.0733885	−	0.0992975i
$197$	27.0692			1.92860			0.964301	−	0.264810i	$-0.0853092\pi$
$197$	27.0692			1.92860			0.964301	+	0.264810i	$0.0853092\pi$
$198$		0			0
$199$	−3.16039	+	0.476353i	−0.224034	+	0.0337677i	−0.260100	−	0.965582i	$-0.583756\pi$
$199$	−3.16039	+	0.476353i	−0.224034	+	0.0337677i	0.0360657	+	0.999349i	$0.488517\pi$
$200$	−0.0742432	+	0.990706i	−0.00524979	+	0.0700535i
$201$		0			0
$202$	14.7766	−	18.5293i	1.03968	−	1.30371i
$203$	−1.26779	+	13.5691i	−0.0889817	+	0.952363i
$204$		0			0
$205$	22.8888	−	7.06026i	1.59862	−	0.493110i
$206$	−5.57342	−	14.2008i	−0.388319	−	0.989420i
$207$		0			0
$208$	−1.10361	−	14.7266i	−0.0765213	−	1.02111i
$209$	0.360429	+	1.57914i	0.0249314	+	0.109232i
$210$		0			0
$211$	1.57498	−	6.90043i	0.108426	−	0.475045i	−0.891338	−	0.453339i	$-0.850233\pi$
$211$	1.57498	−	6.90043i	0.108426	−	0.475045i	0.999764	−	0.0217068i	$-0.00691003\pi$
$212$	3.05165	+	0.459963i	0.209588	+	0.0315904i
$213$		0			0
$214$	−3.89842	+	6.75227i	−0.266491	+	0.461576i
$215$	−8.90051	−	15.4161i	−0.607010	−	1.05137i
$216$		0			0
$217$	1.20502	+	0.204323i	0.0818022	+	0.0138703i
$218$	−4.18028	+	2.01312i	−0.283124	+	0.136346i
$219$		0			0
$220$	1.32502	+	1.22944i	0.0893328	+	0.0828887i
$221$	−0.712860	−	0.661437i	−0.0479521	−	0.0444931i
$222$		0			0
$223$	−7.79320	+	3.75301i	−0.521872	+	0.251320i	−0.676224	−	0.736696i	$-0.736385\pi$
$223$	−7.79320	+	3.75301i	−0.521872	+	0.251320i	0.154353	+	0.988016i	$0.450671\pi$
$224$	−2.99702	−	2.12498i	−0.200247	−	0.141981i
$225$		0			0
$226$	−13.2491	−	22.9481i	−0.881318	−	1.52649i
$227$	14.5392	−	25.1827i	0.965001	−	1.67143i	0.255390	−	0.966838i	$-0.417796\pi$
$227$	14.5392	−	25.1827i	0.965001	−	1.67143i	0.709611	−	0.704593i	$-0.248871\pi$
$228$		0			0
$229$	9.61539	+	1.44929i	0.635403	+	0.0957715i	0.458841	−	0.888518i	$-0.348265\pi$
$229$	9.61539	+	1.44929i	0.635403	+	0.0957715i	0.176561	+	0.984290i	$0.443503\pi$
$230$	2.54943	−	11.1698i	0.168104	−	0.736513i
$231$		0			0
$232$	3.40997	+	14.9400i	0.223875	+	0.980862i
$233$	0.722120	+	9.63602i	0.0473077	+	0.631277i	0.969586	+	0.244751i	$0.0787061\pi$
$233$	0.722120	+	9.63602i	0.0473077	+	0.631277i	−0.922278	+	0.386526i	$0.873675\pi$
$234$		0			0
$235$	−0.862489	−	2.19759i	−0.0562626	−	0.143355i
$236$	−0.307400	+	0.0948204i	−0.0200100	+	0.00617228i
$237$		0			0
$238$	0.787863	−	0.103995i	0.0510696	−	0.00674098i
$239$	−0.780063	+	0.978167i	−0.0504581	+	0.0632724i	−0.806420	−	0.591343i	$-0.798598\pi$
$239$	−0.780063	+	0.978167i	−0.0504581	+	0.0632724i	0.755962	+	0.654615i	$0.227169\pi$
$240$		0			0
$241$	0.787984	−	10.5149i	0.0507585	−	0.677326i	−0.912556	−	0.408951i	$-0.865895\pi$
$241$	0.787984	−	10.5149i	0.0507585	−	0.677326i	0.963315	−	0.268374i	$-0.0864864\pi$
$242$	1.25141	−	0.188620i	0.0804438	−	0.0121250i
$243$		0			0
$244$	−1.09722			−0.0702425
$245$	−5.34983	−	15.2559i	−0.341788	−	0.974664i
$246$		0			0
$247$	−1.60598	+	1.49013i	−0.102186	+	0.0948149i
$248$	1.35898	−	0.204833i	0.0862954	−	0.0130069i
$249$		0			0
$250$	5.21279	−	13.2820i	0.329686	−	0.840025i
$251$	−15.5477	+	19.4962i	−0.981362	+	1.23059i	−0.00831898	+	0.999965i	$0.502648\pi$
$251$	−15.5477	+	19.4962i	−0.981362	+	1.23059i	−0.973043	+	0.230624i	$0.925923\pi$
$252$		0			0
$253$	−7.40350	−	9.28369i	−0.465454	−	0.583661i
$254$	−8.96088	+	2.76407i	−0.562256	+	0.173433i
$255$		0			0
$256$	−5.57355	−	1.71921i	−0.348347	−	0.107451i
$257$	−1.02258	−	13.6454i	−0.0637869	−	0.851177i	−0.933719	−	0.358006i	$-0.883457\pi$
$257$	−1.02258	−	13.6454i	−0.0637869	−	0.851177i	0.869932	−	0.493171i	$-0.164162\pi$
$258$		0			0
$259$	−21.1192	+	9.69686i	−1.31228	+	0.602533i
$260$	−0.544021	+	2.38351i	−0.0337387	+	0.147819i
$261$		0			0
$262$	19.3412	−	13.1866i	1.19491	−	0.814673i
$263$	−12.2261	+	21.1763i	−0.753896	+	1.30579i	0.192026	+	0.981390i	$0.438494\pi$
$263$	−12.2261	+	21.1763i	−0.753896	+	1.30579i	−0.945922	+	0.324396i	$0.894839\pi$
$264$		0			0
$265$	26.0040	+	12.5229i	1.59741	+	0.769274i
$266$	−0.100989	−	1.78750i	−0.00619205	−	0.109599i
$267$		0			0
$268$	−1.88567	−	1.28563i	−0.115186	−	0.0785323i
$269$	7.18978	+	6.67114i	0.438368	+	0.406746i	0.868241	−	0.496143i	$-0.165251\pi$
$269$	7.18978	+	6.67114i	0.438368	+	0.406746i	−0.429872	+	0.902890i	$0.641441\pi$
$270$		0			0
$271$	−2.62331	−	1.78854i	−0.159355	−	0.108646i	0.481017	−	0.876711i	$-0.340267\pi$
$271$	−2.62331	−	1.78854i	−0.159355	−	0.108646i	−0.640372	+	0.768065i	$0.721220\pi$
$272$	0.704156	−	0.339104i	0.0426958	−	0.0205612i
$273$		0			0
$274$	0.0400292	+	0.0192771i	0.00241825	+	0.00116457i
$275$	0.529173	+	0.916554i	0.0319103	+	0.0552703i
$276$		0			0
$277$	14.6073	−	9.95910i	0.877669	−	0.598384i	−0.0384638	−	0.999260i	$-0.512246\pi$
$277$	14.6073	−	9.95910i	0.877669	−	0.598384i	0.916133	+	0.400876i	$0.131294\pi$
$278$	26.4941	+	3.99334i	1.58901	+	0.239505i
$279$		0			0
$280$	−11.0714	−	14.4184i	−0.661641	−	0.861665i
$281$	0.893808	+	3.91603i	0.0533201	+	0.233611i	0.994565	−	0.104113i	$-0.0332003\pi$
$281$	0.893808	+	3.91603i	0.0533201	+	0.233611i	−0.941245	+	0.337723i	$0.890343\pi$
$282$		0			0
$283$	−21.5989	−	6.66239i	−1.28392	−	0.396038i	−0.423629	−	0.905836i	$-0.639244\pi$
$283$	−21.5989	−	6.66239i	−1.28392	−	0.396038i	−0.860294	+	0.509798i	$0.829720\pi$
$284$	−0.0267512	−	0.0681610i	−0.00158739	−	0.00404461i
$285$		0			0
$286$	−11.2150	−	14.0631i	−0.663155	−	0.831570i
$287$	−14.1540	+	23.5078i	−0.835486	+	1.38762i
$288$		0			0
$289$	−6.19200	+	15.7769i	−0.364235	+	0.928056i
$290$	−1.17708	+	15.7070i	−0.0691205	+	0.922349i
$291$		0			0
$292$	2.92736	−	2.71620i	0.171311	−	0.158953i
$293$	−15.8015			−0.923132			−0.461566	−	0.887106i	$-0.652712\pi$
$293$	−15.8015			−0.923132			−0.461566	+	0.887106i	$0.652712\pi$
$294$		0			0
$295$	−3.00856			−0.175165
$296$	−19.1555	+	17.7737i	−1.11339	+	1.03307i
$297$		0			0
$298$	0.0973365	−	1.29887i	0.00563855	−	0.0752412i
$299$	5.86764	−	14.9505i	0.339334	−	0.864609i
$300$		0			0
$301$	19.3728	+	6.36757i	1.11663	+	0.367021i
$302$	−4.76994	−	5.98131i	−0.274479	−	0.344186i
$303$		0			0
$304$	−0.643271	−	1.63903i	−0.0368941	−	0.0940048i
$305$	−9.80565	−	3.02464i	−0.561470	−	0.173190i
$306$		0			0
$307$	−0.126973	−	0.556307i	−0.00724675	−	0.0317501i	0.971175	−	0.238366i	$-0.0766119\pi$
$307$	−0.126973	−	0.556307i	−0.00724675	−	0.0317501i	−0.978422	+	0.206616i	$0.933755\pi$
$308$	−2.07033	−	0.0380203i	−0.117968	−	0.00216641i
$309$		0			0
$310$	1.39683	+	0.210539i	0.0793348	+	0.0119578i
$311$	21.9095	−	14.9377i	1.24237	−	0.847037i	0.249755	−	0.968309i	$-0.419650\pi$
$311$	21.9095	−	14.9377i	1.24237	−	0.847037i	0.992619	+	0.121272i	$0.0386974\pi$
$312$		0			0
$313$	8.83331	+	15.2997i	0.499288	+	0.864792i	1.00000		0.000822038i	$-0.000261663\pi$
$313$	8.83331	+	15.2997i	0.499288	+	0.864792i	−0.500712	+	0.865614i	$0.666928\pi$
$314$	14.3369	+	6.90429i	0.809078	+	0.389631i
$315$		0			0
$316$	−1.37704	+	0.663149i	−0.0774648	+	0.0373051i
$317$	1.43757	+	0.980121i	0.0807422	+	0.0550491i	0.603018	−	0.797727i	$-0.293965\pi$
$317$	1.43757	+	0.980121i	0.0807422	+	0.0550491i	−0.522276	+	0.852776i	$0.674917\pi$
$318$		0			0
$319$	11.9669	+	11.1036i	0.670016	+	0.621684i
$320$	−16.6565	−	11.3562i	−0.931128	−	0.634832i
$321$		0			0
$322$	6.35265	+	11.4851i	0.354019	+	0.640040i
$323$	−0.104462	−	0.0503060i	−0.00581239	−	0.00279910i
$324$		0			0
$325$	−0.715739	+	1.23970i	−0.0397021	+	0.0687660i
$326$	−21.4197	+	14.6037i	−1.18633	+	0.808826i
$327$		0			0
$328$	−6.86589	+	30.0814i	−0.379105	+	1.66097i
$329$	2.41468	+	1.21796i	0.133125	+	0.0671484i
$330$		0			0
$331$	1.03403	+	13.7981i	0.0568352	+	0.758413i	0.950707	+	0.310090i	$0.100359\pi$
$331$	1.03403	+	13.7981i	0.0568352	+	0.758413i	−0.893872	+	0.448323i	$0.852022\pi$
$332$	3.08296	+	0.950966i	0.169199	+	0.0521911i
$333$		0			0
$334$	−21.3186	+	6.57593i	−1.16650	+	0.359819i
$335$	−13.3078	−	16.6875i	−0.727085	−	0.911736i
$336$		0			0
$337$	14.6917	−	18.4228i	0.800305	−	1.00355i	−0.199415	−	0.979915i	$-0.563904\pi$
$337$	14.6917	−	18.4228i	0.800305	−	1.00355i	0.999721	−	0.0236362i	$-0.00752434\pi$
$338$	2.60003	−	6.62476i	0.141423	−	0.360339i
$339$		0			0
$340$	−0.127940	+	0.0192839i	−0.00693854	+	0.00104582i
$341$	1.07323	−	0.995812i	0.0581187	−	0.0539262i
$342$		0			0
$343$	16.2184	+	8.94218i	0.875713	+	0.482832i
$344$	22.9304			1.23632
$345$		0			0
$346$	−11.5171	+	1.73592i	−0.619163	+	0.0933238i
$347$	−0.585825	+	7.81729i	−0.0314487	+	0.419654i	0.959154	+	0.282884i	$0.0912912\pi$
$347$	−0.585825	+	7.81729i	−0.0314487	+	0.419654i	−0.990603	+	0.136770i	$0.956328\pi$
$348$		0			0
$349$	5.52700	−	6.93065i	0.295854	−	0.370989i	−0.611581	−	0.791182i	$-0.709466\pi$
$349$	5.52700	−	6.93065i	0.295854	−	0.370989i	0.907435	+	0.420193i	$0.138038\pi$
$350$	−0.407315	−	1.09661i	−0.0217719	−	0.0586164i
$351$		0			0
$352$	−4.20534	+	1.29718i	−0.224146	+	0.0691397i
$353$	−9.65322	−	24.5960i	−0.513789	−	1.30911i	−0.918772	−	0.394789i	$-0.870818\pi$
$353$	−9.65322	−	24.5960i	−0.513789	−	1.30911i	0.404983	−	0.914324i	$-0.367277\pi$
$354$		0			0
$355$	−0.0511751	−	0.682884i	−0.00271609	−	0.0362437i
$356$	0.167164	+	0.732394i	0.00885969	+	0.0388168i
$357$		0			0
$358$	−3.82334	+	16.7511i	−0.202070	+	0.885325i
$359$	−32.0694	−	4.83368i	−1.69256	−	0.255112i	−0.769187	−	0.639024i	$-0.779338\pi$
$359$	−32.0694	−	4.83368i	−1.69256	−	0.255112i	−0.923370	+	0.383912i	$0.874577\pi$
$360$		0			0
$361$	9.36940	−	16.2283i	0.493126	−	0.854120i
$362$	10.9387	+	18.9464i	0.574927	+	0.995803i
$363$		0			0
$364$	−1.35559	−	2.45080i	−0.0710521	−	0.128457i
$365$	33.6488	−	16.2044i	1.76126	−	0.848178i
$366$		0			0
$367$	15.6895	+	14.5577i	0.818984	+	0.759906i	0.973647	−	0.228061i	$-0.0732386\pi$
$367$	15.6895	+	14.5577i	0.818984	+	0.759906i	−0.154663	+	0.987967i	$0.549429\pi$
$368$	9.46214	+	8.77959i	0.493248	+	0.457668i
$369$		0			0
$370$	−24.1991	+	11.6537i	−1.25805	+	0.605845i
$371$	−31.7687	+	9.16402i	−1.64935	+	0.475772i
$372$		0			0
$373$	−14.1494	−	24.5075i	−0.732627	−	1.26895i	−0.955756	−	0.294159i	$-0.904960\pi$
$373$	−14.1494	−	24.5075i	−0.732627	−	1.26895i	0.223129	−	0.974789i	$-0.428373\pi$
$374$	0.475970	−	0.824404i	0.0246118	−	0.0426289i
$375$		0			0
$376$	3.00707	+	0.453243i	0.155078	+	0.0233742i
$377$	−4.91331	+	21.5266i	−0.253048	+	1.10868i
$378$		0			0
$379$	2.62909	+	11.5188i	0.135047	+	0.591681i	0.996482	+	0.0838118i	$0.0267095\pi$
$379$	2.62909	+	11.5188i	0.135047	+	0.591681i	−0.861434	+	0.507869i	$0.830433\pi$
$380$	0.0217830	+	0.290674i	0.00111744	+	0.0149113i
$381$		0			0
$382$	−4.11567	−	10.4865i	−0.210576	−	0.536539i
$383$	14.1750	−	4.37240i	0.724307	−	0.223419i	0.0893867	−	0.995997i	$-0.471509\pi$
$383$	14.1750	−	4.37240i	0.724307	−	0.223419i	0.634920	+	0.772578i	$0.281033\pi$
$384$		0			0
$385$	−18.3973	−	6.04692i	−0.937612	−	0.308179i
$386$	6.33581	−	7.94485i	0.322484	−	0.404382i
$387$		0			0
$388$	−0.0398328	+	0.531532i	−0.00202220	+	0.0269844i
$389$	4.48051	−	0.675329i	0.227171	−	0.0342405i	−0.0344702	−	0.999406i	$-0.510974\pi$
$389$	4.48051	−	0.675329i	0.227171	−	0.0342405i	0.261641	+	0.965165i	$0.415736\pi$
$390$		0			0
$391$	0.849974			0.0429850
$392$	20.4647	+	3.85782i	1.03362	+	0.194849i
$393$		0			0
$394$	−26.2729	+	24.3777i	−1.32361	+	1.22813i
$395$	−14.1344	+	2.13042i	−0.711179	+	0.107193i
$396$		0			0
$397$	−7.02228	+	17.8925i	−0.352438	+	0.897998i	0.639211	+	0.769032i	$0.279261\pi$
$397$	−7.02228	+	17.8925i	−0.352438	+	0.897998i	−0.991649	+	0.128967i	$0.958834\pi$
$398$	2.63843	−	3.30849i	0.132253	−	0.165840i
$399$		0			0
$400$	−0.717306	−	0.899473i	−0.0358653	−	0.0449736i
$401$	−12.5962	+	3.88542i	−0.629025	+	0.194029i	−0.592845	−	0.805317i	$-0.701995\pi$
$401$	−12.5962	+	3.88542i	−0.629025	+	0.194029i	−0.0361803	+	0.999345i	$0.511519\pi$
$402$		0			0
$403$	1.89225	+	0.583683i	0.0942598	+	0.0290753i
$404$	−0.330331	−	4.40796i	−0.0164346	−	0.219304i
$405$		0			0
$406$	−10.9894	−	14.3116i	−0.545394	−	0.710274i
$407$	−6.19434	+	27.1392i	−0.307042	+	1.34524i
$408$		0			0
$409$	−13.6927	+	9.33552i	−0.677060	+	0.461612i	−0.852396	−	0.522897i	$-0.824851\pi$
$409$	−13.6927	+	9.33552i	−0.677060	+	0.461612i	0.175336	+	0.984509i	$0.443899\pi$
$410$	−15.8572	+	27.4655i	−0.783132	+	1.35642i
$411$		0			0
$412$	−2.56355	−	1.23454i	−0.126297	−	0.0608215i
$413$	2.56911	−	2.29746i	0.126418	−	0.113050i
$414$		0			0
$415$	24.9303	+	16.9972i	1.22378	+	0.834359i
$416$	−4.36344	−	4.04869i	−0.213935	−	0.198503i
$417$		0			0
$418$	−1.77195	−	1.20810i	−0.0866689	−	0.0590899i
$419$	30.5610	−	14.7174i	1.49300	−	0.718991i	0.503564	−	0.863958i	$-0.332022\pi$
$419$	30.5610	−	14.7174i	1.49300	−	0.718991i	0.989436	+	0.144967i	$0.0463076\pi$
$420$		0			0
$421$	−0.978083	−	0.471020i	−0.0476688	−	0.0229561i	0.409897	−	0.912132i	$-0.365564\pi$
$421$	−0.978083	−	0.471020i	−0.0476688	−	0.0229561i	−0.457566	+	0.889176i	$0.651279\pi$
$422$	4.68566	+	8.11581i	0.228095	+	0.395071i
$423$		0			0
$424$	−30.7187	+	20.9437i	−1.49183	+	1.01711i
$425$	−0.0749114	−	0.0112911i	−0.00363373	−	0.000547697i
$426$		0			0
$427$	10.6831	−	4.90515i	0.516992	−	0.237377i
$428$	0.323593	+	1.41775i	0.0156414	+	0.0685297i
$429$		0			0
$430$	22.5220	+	6.94710i	1.08611	+	0.335019i
$431$	4.29893	+	10.9535i	0.207072	+	0.527611i	0.996247	−	0.0865577i	$-0.0275867\pi$
$431$	4.29893	+	10.9535i	0.207072	+	0.527611i	−0.789175	+	0.614169i	$0.789491\pi$
$432$		0			0
$433$	−7.28877	−	9.13983i	−0.350276	−	0.439232i	0.575215	−	0.818002i	$-0.304919\pi$
$433$	−7.28877	−	9.13983i	−0.350276	−	0.439232i	−0.925491	+	0.378770i	$0.876347\pi$
$434$	−1.35358	+	0.886893i	−0.0649739	+	0.0425722i
$435$		0			0
$436$	−0.316157	+	0.805556i	−0.0151412	+	0.0385791i
$437$	0.143099	−	1.90953i	0.00684537	−	0.0913451i
$438$		0			0
$439$	0.821196	−	0.761958i	0.0391935	−	0.0363663i	−0.660333	−	0.750973i	$-0.729585\pi$
$439$	0.821196	−	0.761958i	0.0391935	−	0.0363663i	0.699526	+	0.714607i	$0.253394\pi$
$440$	−21.7757			−1.03811
$441$		0			0
$442$	1.28756			0.0612429
$443$	28.0052	−	25.9851i	1.33057	−	1.23459i	0.379656	−	0.925128i	$-0.376042\pi$
$443$	28.0052	−	25.9851i	1.33057	−	1.23459i	0.950913	−	0.309460i	$-0.100148\pi$
$444$		0			0
$445$	−0.525032	+	7.00607i	−0.0248889	+	0.332119i
$446$	4.18410	−	10.6609i	0.198123	−	0.504809i
$447$		0			0
$448$	22.8956	−	3.02213i	1.08172	−	0.142782i
$449$	−19.7516	−	24.7677i	−0.932134	−	1.16886i	−0.985396	−	0.170279i	$-0.945533\pi$
$449$	−19.7516	−	24.7677i	−0.932134	−	1.16886i	0.0532618	−	0.998581i	$-0.483038\pi$
$450$		0			0
$451$	12.0086	+	30.5973i	0.565461	+	1.44077i
$452$	−4.72269	−	1.45676i	−0.222137	−	0.0685201i
$453$		0			0
$454$	8.56720	+	37.5354i	0.402079	+	1.76162i
$455$	−5.35865	−	25.6391i	−0.251218	−	1.20198i
$456$		0			0
$457$	37.2733	+	5.61805i	1.74357	+	0.262801i	0.942125	−	0.335262i	$-0.108825\pi$
$457$	37.2733	+	5.61805i	1.74357	+	0.262801i	0.801449	+	0.598064i	$0.204063\pi$
$458$	−10.6377	+	7.25266i	−0.497067	+	0.338895i
$459$		0			0
$460$	−1.06844	−	1.85060i	−0.0498164	−	0.0862845i
$461$	16.9687	+	8.17171i	0.790313	+	0.380595i	0.785082	−	0.619392i	$-0.212621\pi$
$461$	16.9687	+	8.17171i	0.790313	+	0.380595i	0.00523072	+	0.999986i	$0.498335\pi$
$462$		0			0
$463$	−19.6150	+	9.44609i	−0.911587	+	0.438997i	−0.830060	−	0.557674i	$-0.811694\pi$
$463$	−19.6150	+	9.44609i	−0.911587	+	0.438997i	−0.0815270	+	0.996671i	$0.525980\pi$
$464$	−14.6622	−	9.99651i	−0.680675	−	0.464076i
$465$		0			0
$466$	−9.37877	−	8.70223i	−0.434463	−	0.403123i
$467$	−20.8916	−	14.2436i	−0.966746	−	0.659116i	−0.0265133	−	0.999648i	$-0.508440\pi$
$467$	−20.8916	−	14.2436i	−0.966746	−	0.659116i	−0.940233	+	0.340532i	$0.889393\pi$
$468$		0			0
$469$	24.1073	+	4.08762i	1.11317	+	0.188749i
$470$	2.81619	+	1.35621i	0.129901	+	0.0625572i
$471$		0			0
$472$	1.93774	−	3.35626i	0.0891915	−	0.154484i
$473$	20.1829	−	13.7605i	0.928010	−	0.632707i
$474$		0			0
$475$	−0.0379781	+	0.166393i	−0.00174255	+	0.00763463i
$476$	0.0945266	−	0.114168i	0.00433262	−	0.00523286i
$477$		0			0
$478$	−0.123792	−	1.65189i	−0.00566212	−	0.0755557i
$479$	18.7346	+	5.77886i	0.856005	+	0.264043i	0.691538	−	0.722340i	$-0.256933\pi$
$479$	18.7346	+	5.77886i	0.856005	+	0.264043i	0.164467	+	0.986383i	$0.447410\pi$
$480$		0			0
$481$	−35.9787	+	11.0980i	−1.64049	+	0.506023i
$482$	8.70460	+	10.9152i	0.396484	+	0.497175i
$483$		0			0
$484$	0.147169	−	0.184544i	0.00668950	−	0.00838837i
$485$	−1.82122	+	4.64038i	−0.0826972	+	0.210709i
$486$		0			0
$487$	33.1341	−	4.99417i	1.50145	−	0.226307i	0.653721	−	0.756736i	$-0.273207\pi$
$487$	33.1341	−	4.99417i	1.50145	−	0.226307i	0.847730	+	0.530428i	$0.177969\pi$
$488$	9.68977	−	8.99079i	0.438635	−	0.406994i
$489$		0			0
$490$	18.9314	+	9.98920i	0.855235	+	0.451266i
$491$	3.69190			0.166613			0.0833064	−	0.996524i	$-0.473452\pi$
$491$	3.69190			0.166613			0.0833064	+	0.996524i	$0.473452\pi$
$492$		0			0
$493$	−1.15549	+	0.174162i	−0.0520406	+	0.00784386i
$494$	0.216770	−	2.89259i	0.00975293	−	0.130144i
$495$		0			0
$496$	−0.992281	+	1.24428i	−0.0445547	+	0.0558699i
$497$	0.565178	+	0.544058i	0.0253517	+	0.0244044i
$498$		0			0
$499$	−31.0729	+	9.58473i	−1.39102	+	0.429072i	−0.897634	−	0.440741i	$-0.854716\pi$
$499$	−31.0729	+	9.58473i	−1.39102	+	0.429072i	−0.493382	+	0.869813i	$0.664239\pi$
$500$	−0.972252	−	2.47726i	−0.0434804	−	0.110786i
$501$		0			0
$502$	−2.46734	−	32.9244i	−0.110123	−	1.46949i
$503$	4.31696	+	18.9138i	0.192484	+	0.843326i	0.975267	+	0.221032i	$0.0709424\pi$
$503$	4.31696	+	18.9138i	0.192484	+	0.843326i	−0.782783	+	0.622295i	$0.786200\pi$
$504$		0			0
$505$	9.19905	−	40.3037i	0.409352	−	1.79349i
$506$	15.5463	+	2.34323i	0.691117	+	0.104169i
$507$		0			0
$508$	−0.874513	+	1.51470i	−0.0388002	+	0.0672040i
$509$	8.15626	+	14.1271i	0.361520	+	0.626171i	0.988211	−	0.153097i	$-0.0489246\pi$
$509$	8.15626	+	14.1271i	0.361520	+	0.626171i	−0.626691	+	0.779268i	$0.715591\pi$
$510$		0			0
$511$	−16.3595	+	39.5331i	−0.723702	+	1.74884i
$512$	22.7788	−	10.9697i	1.00669	−	0.484796i
$513$		0			0
$514$	13.2811	+	12.3231i	0.585805	+	0.543547i
$515$	−19.5067	−	18.0996i	−0.859570	−	0.797564i
$516$		0			0
$517$	2.91876	−	1.40560i	0.128367	−	0.0618182i
$518$	11.7652	−	28.4308i	0.516933	−	1.24918i
$519$		0			0
$520$	−14.7265	−	25.5070i	−0.645799	−	1.11856i
$521$	8.79223	−	15.2286i	0.385195	−	0.667177i	−0.606601	−	0.795006i	$-0.707468\pi$
$521$	8.79223	−	15.2286i	0.385195	−	0.667177i	0.991796	+	0.127829i	$0.0408009\pi$
$522$		0			0
$523$	−22.3495	−	3.36864i	−0.977273	−	0.147300i	−0.359063	−	0.933313i	$-0.616904\pi$
$523$	−22.3495	−	3.36864i	−0.977273	−	0.147300i	−0.618210	+	0.786013i	$0.712142\pi$
$524$	0.971535	−	4.25657i	0.0424417	−	0.185949i
$525$		0			0
$526$	−7.20423	−	31.5638i	−0.314119	−	1.37625i
$527$	0.00783162	+	0.104506i	0.000341151	+	0.00455234i
$528$		0			0
$529$	−3.27424	−	8.34262i	−0.142358	−	0.362723i
$530$	−36.5167	+	11.2639i	−1.58619	+	0.489274i
$531$		0			0
$532$	−0.240572	−	0.231582i	−0.0104301	−	0.0100403i
$533$	−27.7191	+	34.7586i	−1.20065	+	1.50556i
$534$		0			0
$535$	−1.01635	+	13.5622i	−0.0439404	+	0.586345i
$536$	27.1873	−	4.09783i	1.17431	−	0.176999i
$537$		0			0
$538$	−12.9861			−0.559870
$539$	20.3277	−	8.88524i	0.875577	−	0.382714i
$540$		0			0
$541$	−14.1738	+	13.1514i	−0.609380	+	0.565422i	−0.923325	−	0.384019i	$-0.874540\pi$
$541$	−14.1738	+	13.1514i	−0.609380	+	0.565422i	0.313945	+	0.949441i	$0.398349\pi$
$542$	4.15684	−	0.626543i	0.178552	−	0.0269123i
$543$		0			0
$544$	0.115089	−	0.293242i	0.00493440	−	0.0125727i
$545$	−5.04606	+	6.32755i	−0.216149	+	0.271043i
$546$		0			0
$547$	−14.1440	−	17.7360i	−0.604754	−	0.758338i	0.381356	−	0.924428i	$-0.375457\pi$
$547$	−14.1440	−	17.7360i	−0.604754	−	0.758338i	−0.986111	+	0.166090i	$0.946886\pi$
$548$	0.00791845	−	0.00244252i	0.000338259	−	0.000104339i
$549$		0			0
$550$	−1.33903	−	0.413035i	−0.0570962	−	0.0176119i
$551$	0.196732	+	2.62521i	0.00838108	+	0.111838i
$552$		0			0
$553$	10.4430	−	12.6129i	0.444081	−	0.536353i
$554$	−5.20875	+	22.8210i	−0.221298	+	0.969572i
$555$		0			0
$556$	4.12897	−	2.81508i	0.175107	−	0.119386i
$557$	18.4901	−	32.0258i	0.783451	−	1.35698i	−0.146469	−	0.989215i	$-0.546791\pi$
$557$	18.4901	−	32.0258i	0.783451	−	1.35698i	0.929920	−	0.367762i	$-0.119876\pi$
$558$		0			0
$559$	29.7677	+	14.3354i	1.25904	+	0.606321i
$560$	20.7550	+	3.51920i	0.877058	+	0.148714i
$561$		0			0
$562$	−4.39416	−	2.99589i	−0.185357	−	0.126374i
$563$	13.7521	+	12.7601i	0.579581	+	0.537772i	0.914559	−	0.404454i	$-0.132538\pi$
$563$	13.7521	+	12.7601i	0.579581	+	0.537772i	−0.334978	+	0.942226i	$0.608729\pi$
$564$		0			0
$565$	−38.1900	−	26.0375i	−1.60666	−	1.09541i
$566$	26.9635	−	12.9849i	1.13336	−	0.545797i
$567$		0			0
$568$	0.794766	+	0.382739i	0.0333476	+	0.0160594i
$569$	8.68718	+	15.0466i	0.364186	+	0.630788i	0.988645	−	0.150269i	$-0.0480141\pi$
$569$	8.68718	+	15.0466i	0.364186	+	0.630788i	−0.624460	+	0.781057i	$0.714681\pi$
$570$		0			0
$571$	24.6498	−	16.8059i	1.03156	−	0.703306i	0.0757011	−	0.997131i	$-0.475881\pi$
$571$	24.6498	−	16.8059i	1.03156	−	0.703306i	0.955859	+	0.293825i	$0.0949281\pi$
$572$	−3.31741	−	0.500019i	−0.138708	−	0.0209069i
$573$		0			0
$574$	−7.43276	−	35.5629i	−0.310237	−	1.48437i
$575$	−0.278415	−	1.21981i	−0.0116107	−	0.0508698i
$576$		0			0
$577$	7.55136	+	2.32929i	0.314367	+	0.0969694i	0.447924	−	0.894072i	$-0.352164\pi$
$577$	7.55136	+	2.32929i	0.314367	+	0.0969694i	−0.133557	+	0.991041i	$0.542640\pi$
$578$	−8.19838	−	20.8891i	−0.341008	−	0.868873i
$579$		0			0
$580$	1.83168	+	2.29685i	0.0760562	+	0.0953714i
$581$	−34.2685	+	4.52331i	−1.42170	+	0.187659i
$582$		0			0
$583$	−14.4698	+	36.8684i	−0.599277	+	1.52693i
$584$	−3.59519	+	47.9745i	−0.148770	+	1.98520i
$585$		0			0
$586$	15.3366	−	14.2303i	0.633550	−	0.587849i
$587$	−21.5330			−0.888764			−0.444382	−	0.895838i	$-0.646577\pi$
$587$	−21.5330			−0.888764			−0.444382	+	0.895838i	$0.646577\pi$
$588$		0			0
$589$	0.236098			0.00972826
$590$	2.92005	−	2.70941i	0.120217	−	0.111545i
$591$		0			0
$592$	2.26135	−	30.1756i	0.0929408	−	1.24021i
$593$	−9.68980	+	24.6892i	−0.397912	+	1.01386i	0.581778	+	0.813348i	$0.302357\pi$
$593$	−9.68980	+	24.6892i	−0.397912	+	1.01386i	−0.979690	+	0.200517i	$0.935738\pi$
$594$		0			0
$595$	1.15948	−	0.759717i	0.0475342	−	0.0311454i
$596$	−0.151467	−	0.189934i	−0.00620434	−	0.00777999i
$597$		0			0
$598$	7.76892	+	19.7949i	0.317695	+	0.809473i
$599$	17.1151	+	5.27932i	0.699305	+	0.215707i	0.623967	−	0.781451i	$-0.285520\pi$
$599$	17.1151	+	5.27932i	0.699305	+	0.215707i	0.0753386	+	0.997158i	$0.475996\pi$
$600$		0			0
$601$	2.00401	+	8.78013i	0.0817451	+	0.358149i	0.999213	−	0.0396606i	$-0.0126277\pi$
$601$	2.00401	+	8.78013i	0.0817451	+	0.358149i	−0.917468	+	0.397809i	$0.869771\pi$
$602$	−24.5374	+	11.2663i	−1.00007	+	0.459181i
$603$		0			0
$604$	−1.41096	−	0.212668i	−0.0574111	−	0.00865333i
$605$	1.82394	−	1.24354i	0.0741537	−	0.0505572i
$606$		0			0
$607$	5.90754	+	10.2322i	0.239780	+	0.415311i	0.960651	−	0.277758i	$-0.0895914\pi$
$607$	5.90754	+	10.2322i	0.239780	+	0.415311i	−0.720871	+	0.693069i	$0.756258\pi$
$608$	−0.639414	−	0.307925i	−0.0259316	−	0.0124880i
$609$		0			0
$610$	12.2411	−	5.89499i	0.495627	−	0.238681i
$611$	3.62035	+	2.46832i	0.146464	+	0.0998573i
$612$		0			0
$613$	3.44220	+	3.19390i	0.139029	+	0.129000i	0.746622	−	0.665248i	$-0.231674\pi$
$613$	3.44220	+	3.19390i	0.139029	+	0.129000i	−0.607593	+	0.794249i	$0.707865\pi$
$614$	0.624230	+	0.425593i	0.0251919	+	0.0171755i
$615$		0			0
$616$	18.5950	−	16.6288i	0.749213	−	0.669993i
$617$	−16.5171	−	7.95420i	−0.664952	−	0.320224i	0.0707850	−	0.997492i	$-0.477450\pi$
$617$	−16.5171	−	7.95420i	−0.664952	−	0.320224i	−0.735737	+	0.677268i	$0.763164\pi$
$618$		0			0
$619$	20.6650	−	35.7928i	0.830596	−	1.43863i	−0.0669701	−	0.997755i	$-0.521333\pi$
$619$	20.6650	−	35.7928i	0.830596	−	1.43863i	0.897566	−	0.440880i	$-0.145333\pi$
$620$	0.217689	−	0.148418i	0.00874261	−	0.00596061i
$621$		0			0
$622$	−7.81260	+	34.2292i	−0.313257	+	1.37247i
$623$	−4.90177	−	6.38365i	−0.196385	−	0.255756i
$624$		0			0
$625$	−1.98470	−	26.4839i	−0.0793878	−	1.05936i
$626$	−22.3519	−	6.89465i	−0.893361	−	0.275566i
$627$		0			0
$628$	2.83608	−	0.874814i	0.113172	−	0.0349089i
$629$	−1.24237	−	1.55789i	−0.0495366	−	0.0621170i
$630$		0			0
$631$	−5.73657	+	7.19343i	−0.228369	+	0.286366i	−0.882793	−	0.469762i	$-0.844340\pi$
$631$	−5.73657	+	7.19343i	−0.228369	+	0.286366i	0.654424	+	0.756128i	$0.272911\pi$
$632$	6.72699	−	17.1401i	0.267585	−	0.681796i
$633$		0			0
$634$	−2.27795	+	0.343345i	−0.0904689	+	0.0136360i
$635$	−11.9908	+	11.1258i	−0.475841	+	0.441516i
$636$		0			0
$637$	24.1550	+	17.8020i	0.957057	+	0.705342i
$638$	−21.6144			−0.855722
$639$		0			0
$640$	20.0511	−	3.02222i	0.792590	−	0.119464i
$641$	−1.28174	+	17.1037i	−0.0506258	+	0.675554i	0.912942	+	0.408089i	$0.133805\pi$
$641$	−1.28174	+	17.1037i	−0.0506258	+	0.675554i	−0.963568	+	0.267464i	$0.913814\pi$
$642$		0			0
$643$	20.7569	−	26.0284i	0.818574	−	1.02646i	−0.180506	−	0.983574i	$-0.557773\pi$
$643$	20.7569	−	26.0284i	0.818574	−	1.02646i	0.999080	−	0.0428856i	$-0.0136551\pi$
$644$	2.32557	+	0.764381i	0.0916403	+	0.0301208i
$645$		0			0
$646$	0.146692	−	0.0452486i	0.00577154	−	0.00178028i
$647$	−1.74626	−	4.44940i	−0.0686526	−	0.174924i	0.892430	−	0.451187i	$-0.148999\pi$
$647$	−1.74626	−	4.44940i	−0.0686526	−	0.174924i	−0.961082	+	0.276263i	$0.910904\pi$
$648$		0			0
$649$	−0.308522	−	4.11694i	−0.0121106	−	0.161604i
$650$	−0.421748	−	1.84780i	−0.0165423	−	0.0724766i
$651$		0			0
$652$	−1.07594	+	4.71401i	−0.0421371	+	0.184615i
$653$	−18.0422	−	2.71943i	−0.706046	−	0.106419i	−0.213803	−	0.976877i	$-0.568585\pi$
$653$	−18.0422	−	2.71943i	−0.706046	−	0.106419i	−0.492244	+	0.870458i	$0.663823\pi$
$654$		0			0
$655$	20.4162	−	35.3619i	0.797728	−	1.38171i
$656$	−17.8653	−	30.9436i	−0.697522	−	1.20814i
$657$		0			0
$658$	−3.44050	+	0.992448i	−0.134125	+	0.0386897i
$659$	−15.0258	+	7.23603i	−0.585321	+	0.281876i	−0.703016	−	0.711174i	$-0.748164\pi$
$659$	−15.0258	+	7.23603i	−0.585321	+	0.281876i	0.117695	+	0.993050i	$0.462449\pi$
$660$		0			0
$661$	−22.9543	−	21.2984i	−0.892818	−	0.828414i	0.0930981	−	0.995657i	$-0.470323\pi$
$661$	−22.9543	−	21.2984i	−0.892818	−	0.828414i	−0.985916	+	0.167243i	$0.946513\pi$
$662$	−13.4297	−	12.4610i	−0.521962	−	0.484310i
$663$		0			0
$664$	−35.0185	+	16.8640i	−1.35898	+	0.654451i
$665$	−1.51155	−	2.73277i	−0.0586154	−	0.105972i
$666$		0			0
$667$	−9.64960	−	16.7136i	−0.373634	−	0.647153i
$668$	−2.08053	+	3.60359i	−0.0804983	+	0.139427i
$669$		0			0
$670$	27.9446	+	4.21197i	1.07959	+	0.162722i
$671$	3.13340	−	13.7283i	0.120964	−	0.529976i
$672$		0			0
$673$	−7.01194	−	30.7213i	−0.270290	−	1.18422i	−0.909671	−	0.415329i	$-0.863666\pi$
$673$	−7.01194	−	30.7213i	−0.270290	−	1.18422i	0.639381	−	0.768890i	$-0.279191\pi$
$674$	2.33149	+	31.1116i	0.0898058	+	1.19837i
$675$		0			0
$676$	−0.484939	−	1.23560i	−0.0186515	−	0.0475232i
$677$	−9.76627	+	3.01250i	−0.375348	+	0.115780i	−0.476689	−	0.879072i	$-0.658163\pi$
$677$	−9.76627	+	3.01250i	−0.375348	+	0.115780i	0.101340	+	0.994852i	$0.467687\pi$
$678$		0			0
$679$	−1.98839	−	5.35333i	−0.0763073	−	0.205442i
$680$	0.971849	−	1.21866i	0.0372687	−	0.0467335i
$681$		0			0
$682$	−0.144861	+	1.93303i	−0.00554701	+	0.0740197i
$683$	−16.2086	+	2.44305i	−0.620205	+	0.0934808i	−0.451626	−	0.892207i	$-0.649156\pi$
$683$	−16.2086	+	2.44305i	−0.620205	+	0.0934808i	−0.168579	+	0.985688i	$0.553918\pi$
$684$		0			0
$685$	0.0774987			0.00296107
$686$	−23.7943	+	5.92669i	−0.908472	+	0.226282i
$687$		0			0
$688$	−19.4652	+	18.0611i	−0.742105	+	0.688573i
$689$	−52.9716	+	7.98418i	−2.01806	+	0.304173i
$690$		0			0
$691$	−4.70701	+	11.9933i	−0.179063	+	0.456246i	−0.992020	−	0.126078i	$-0.959761\pi$
$691$	−4.70701	+	11.9933i	−0.179063	+	0.456246i	0.812957	+	0.582324i	$0.197856\pi$
$692$	−1.35444	+	1.69841i	−0.0514880	+	0.0645640i
$693$		0			0
$694$	−6.47141	−	8.11490i	−0.245652	−	0.308037i
$695$	44.6599	−	13.7758i	1.69405	−	0.522544i
$696$		0			0
$697$	−2.24830	−	0.693509i	−0.0851604	−	0.0262685i
$698$	0.877109	+	11.7042i	0.0331991	+	0.443011i
$699$		0			0
$700$	−0.194807	−	0.0982606i	−0.00736301	−	0.00371390i
$701$	−1.47713	+	6.47171i	−0.0557903	+	0.244433i	−0.995132	−	0.0985490i	$-0.968580\pi$
$701$	−1.47713	+	6.47171i	−0.0557903	+	0.244433i	0.939342	+	0.342982i	$0.111437\pi$
$702$		0			0
$703$	−3.70906	+	2.52880i	−0.139890	+	0.0953754i
$704$	13.8319	−	23.9575i	0.521309	−	0.902934i
$705$		0			0
$706$	31.5196	+	15.1790i	1.18626	+	0.571271i
$707$	22.9221	+	41.4414i	0.862076	+	1.55857i
$708$		0			0
$709$	−22.4585	−	15.3120i	−0.843447	−	0.575053i	0.0626917	−	0.998033i	$-0.480032\pi$
$709$	−22.4585	−	15.3120i	−0.843447	−	0.575053i	−0.906139	+	0.422980i	$0.860984\pi$
$710$	0.664653	+	0.616708i	0.0249440	+	0.0231446i
$711$		0			0
$712$	−7.47760	−	5.09814i	−0.280235	−	0.191061i
$713$	−1.55941	+	0.750974i	−0.0584005	+	0.0281242i
$714$		0			0
$715$	−28.2687	−	13.6135i	−1.05719	−	0.509115i
$716$	1.60233	+	2.77531i	0.0598817	+	0.103718i
$717$		0			0
$718$	35.4790	−	24.1892i	1.32406	−	0.902732i
$719$	9.48182	+	1.42915i	0.353612	+	0.0532984i	0.323446	−	0.946246i	$-0.395158\pi$
$719$	9.48182	+	1.42915i	0.353612	+	0.0532984i	0.0301656	+	0.999545i	$0.490397\pi$
$720$		0			0
$721$	30.4791	+	0.559730i	1.13510	+	0.0208454i
$722$	5.52090	+	24.1886i	0.205467	+	0.900208i
$723$		0			0
$724$	3.89915	+	1.20273i	0.144911	+	0.0446990i
$725$	0.628431	+	1.60122i	0.0233394	+	0.0594677i
$726$		0			0
$727$	−27.6459	−	34.6669i	−1.02533	−	1.28572i	−0.957625	−	0.288017i	$-0.907004\pi$
$727$	−27.6459	−	34.6669i	−1.02533	−	1.28572i	−0.0677043	−	0.997705i	$-0.521567\pi$
$728$	32.0536	+	10.5356i	1.18799	+	0.390474i
$729$		0			0
$730$	−18.0657	+	46.0307i	−0.668643	+	1.70367i
$731$	−0.130669	+	1.74365i	−0.00483295	+	0.0644913i
$732$		0			0
$733$	−12.0771	+	11.2059i	−0.446076	+	0.413898i	−0.870963	−	0.491348i	$-0.836504\pi$
$733$	−12.0771	+	11.2059i	−0.446076	+	0.413898i	0.424887	+	0.905246i	$0.360314\pi$
$734$	−28.3381			−1.04598
$735$		0			0
$736$	5.20273			0.191775
$737$	21.4707	−	19.9219i	0.790883	−	0.733832i
$738$		0			0
$739$	1.25799	−	16.7867i	0.0462759	−	0.617509i	−0.925064	−	0.379812i	$-0.875989\pi$
$739$	1.25799	−	16.7867i	0.0462759	−	0.617509i	0.971339	−	0.237697i	$-0.0763924\pi$
$740$	−1.83019	+	4.66325i	−0.0672791	+	0.171424i
$741$		0			0
$742$	22.5813	−	37.5043i	0.828985	−	1.37683i
$743$	−28.7192	−	36.0128i	−1.05361	−	1.32118i	−0.944991	−	0.327096i	$-0.893930\pi$
$743$	−28.7192	−	36.0128i	−1.05361	−	1.32118i	−0.108615	−	0.994084i	$-0.534641\pi$
$744$		0			0
$745$	−0.830052	−	2.11494i	−0.0304108	−	0.0774854i
$746$	35.8038	+	11.0440i	1.31087	+	0.404350i
$747$		0			0
$748$	−0.0395084	−	0.173098i	−0.00144457	−	0.00632907i
$749$	−9.48875	−	12.3573i	−0.346711	−	0.451527i
$750$		0			0
$751$	28.7964	+	4.34035i	1.05079	+	0.158382i	0.651660	−	0.758511i	$-0.274073\pi$
$751$	28.7964	+	4.34035i	1.05079	+	0.158382i	0.399134	+	0.916893i	$0.369311\pi$
$752$	−2.90965	+	1.98377i	−0.106104	+	0.0723405i
$753$		0			0
$754$	−14.6174	−	25.3181i	−0.532334	−	0.922030i
$755$	−12.0232	−	5.79007i	−0.437569	−	0.210722i
$756$		0			0
$757$	19.8709	−	9.56934i	0.722222	−	0.347804i	−0.0363980	−	0.999337i	$-0.511588\pi$
$757$	19.8709	−	9.56934i	0.722222	−	0.347804i	0.758620	+	0.651534i	$0.225874\pi$
$758$	−12.9252	−	8.81226i	−0.469465	−	0.320076i
$759$		0			0
$760$	−2.57419	−	2.38850i	−0.0933757	−	0.0866400i
$761$	28.5822	+	19.4870i	1.03611	+	0.706405i	0.956889	−	0.290453i	$-0.0938059\pi$
$761$	28.5822	+	19.4870i	1.03611	+	0.706405i	0.0792160	+	0.996857i	$0.474758\pi$
$762$		0			0
$763$	−0.522979	−	9.25669i	−0.0189331	−	0.335115i
$764$	−1.89304	−	0.911642i	−0.0684879	−	0.0329820i
$765$		0			0
$766$	−9.82031	+	17.0093i	−0.354822	+	0.614570i
$767$	4.61375	−	3.14560i	0.166593	−	0.113581i
$768$		0			0
$769$	−10.4938	+	45.9765i	−0.378417	+	1.65796i	0.323900	+	0.946091i	$0.395006\pi$
$769$	−10.4938	+	45.9765i	−0.378417	+	1.65796i	−0.702317	+	0.711864i	$0.747851\pi$
$770$	23.3017	−	10.6990i	0.839736	−	0.385564i
$771$		0			0
$772$	−0.141637	−	1.89002i	−0.00509763	−	0.0680231i
$773$	32.4590	+	10.0123i	1.16747	+	0.360116i	0.817100	−	0.576496i	$-0.195580\pi$
$773$	32.4590	+	10.0123i	1.16747	+	0.360116i	0.350368	+	0.936612i	$0.386057\pi$
$774$		0			0
$775$	0.147413	−	0.0454709i	0.00529523	−	0.00163336i
$776$	−4.00367	−	5.02045i	−0.143724	−	0.180224i
$777$		0			0
$778$	−3.74052	+	4.69047i	−0.134104	+	0.168161i
$779$	−1.93653	+	4.93421i	−0.0693836	+	0.176786i
$780$		0			0
$781$	0.929219	−	0.140057i	0.0332501	−	0.00501164i
$782$	−0.824969	+	0.765459i	−0.0295008	+	0.0273728i
$783$		0			0
$784$	−20.4108	+	12.8442i	−0.728957	+	0.458721i
$785$	27.7570			0.990689
$786$		0			0
$787$	−9.49720	+	1.43147i	−0.338539	+	0.0510265i	−0.316112	−	0.948722i	$-0.602377\pi$
$787$	−9.49720	+	1.43147i	−0.338539	+	0.0510265i	−0.0224270	+	0.999748i	$0.507139\pi$
$788$	−0.499548	+	6.66601i	−0.0177957	+	0.237467i
$789$		0			0
$790$	11.8000	−	14.7967i	0.419826	−	0.526445i
$791$	52.4950	−	6.92913i	1.86651	−	0.246371i
$792$		0			0
$793$	18.1998	−	5.61389i	0.646293	−	0.199355i
$794$	−9.29770	−	23.6902i	−0.329963	−	0.840733i
$795$		0			0
$796$	−0.0589822	−	0.787063i	−0.00209057	−	0.0278967i
$797$	−2.88666	−	12.6473i	−0.102251	−	0.447990i	−0.999972	−	0.00742666i	$-0.997636\pi$
$797$	−2.88666	−	12.6473i	−0.102251	−	0.447990i	0.897722	−	0.440563i	$-0.145221\pi$
$798$		0			0
$799$	−0.0516009	+	0.226078i	−0.00182551	+	0.00799807i
$800$	−0.458536	−	0.0691131i	−0.0162117	−	0.00244352i
$801$		0			0
$802$	8.72657	−	15.1149i	0.308146	−	0.533725i
$803$	25.6249	+	44.3837i	0.904284	+	1.56627i
$804$		0			0
$805$	18.6760	+	13.2419i	0.658243	+	0.466714i
$806$	−2.36223	+	1.13759i	−0.0832060	+	0.0400699i
$807$		0			0
$808$	39.0367	+	36.2208i	1.37331	+	1.27424i
$809$	3.39818	+	3.15305i	0.119474	+	0.110855i	0.737647	−	0.675186i	$-0.235937\pi$
$809$	3.39818	+	3.15305i	0.119474	+	0.110855i	−0.618174	+	0.786042i	$0.712127\pi$
$810$		0			0
$811$	−49.7355	+	23.9514i	−1.74645	+	0.841046i	−0.766383	+	0.642384i	$0.777945\pi$
$811$	−49.7355	+	23.9514i	−1.74645	+	0.841046i	−0.980068	+	0.198662i	$0.936340\pi$
$812$	−3.31810	−	0.562615i	−0.116442	−	0.0197439i
$813$		0			0
$814$	−18.4286	−	31.9192i	−0.645921	−	1.11877i
$815$	−22.6103	+	39.1621i	−0.792003	+	1.37179i
$816$		0			0
$817$	3.89524	+	0.587113i	0.136277	+	0.0205405i
$818$	4.88260	−	21.3921i	0.170716	−	0.747956i
$819$		0			0
$820$	1.31624	+	5.76684i	0.0459653	+	0.201387i
$821$	−0.990124	−	13.2123i	−0.0345556	−	0.461112i	−0.987463	−	0.157851i	$-0.949544\pi$
$821$	−0.990124	−	13.2123i	−0.0345556	−	0.461112i	0.952907	−	0.303261i	$-0.0980755\pi$
$822$		0			0
$823$	−3.51588	−	8.95832i	−0.122556	−	0.312268i	0.856408	−	0.516299i	$-0.172691\pi$
$823$	−3.51588	−	8.95832i	−0.122556	−	0.312268i	−0.978964	+	0.204032i	$0.934595\pi$
$824$	32.7552	−	10.1036i	1.14108	−	0.351977i
$825$		0			0
$826$	−0.424514	+	4.54353i	−0.0147707	+	0.158089i
$827$	3.43877	−	4.31208i	0.119578	−	0.149946i	−0.718440	−	0.695589i	$-0.755143\pi$
$827$	3.43877	−	4.31208i	0.119578	−	0.149946i	0.838017	+	0.545644i	$0.183715\pi$
$828$		0			0
$829$	−1.37184	+	18.3060i	−0.0476461	+	0.635793i	0.921353	+	0.388728i	$0.127085\pi$
$829$	−1.37184	+	18.3060i	−0.0476461	+	0.635793i	−0.968999	+	0.247066i	$0.920534\pi$
$830$	−39.5040	+	5.95427i	−1.37120	+	0.206676i
$831$		0			0
$832$	37.4170			1.29720
$833$	−0.409971	+	1.53418i	−0.0142047	+	0.0531561i
$834$		0			0
$835$	−28.5271	+	26.4693i	−0.987220	+	0.916007i
$836$	−0.395528	+	0.0596162i	−0.0136796	+	0.00206187i
$837$		0			0
$838$	−16.4079	+	41.8066i	−0.566801	+	1.44419i
$839$	24.9648	−	31.3048i	0.861880	−	1.08076i	−0.134081	−	0.990970i	$-0.542808\pi$
$839$	24.9648	−	31.3048i	0.861880	−	1.08076i	0.995960	−	0.0897925i	$-0.0286204\pi$
$840$		0			0
$841$	−1.53849	−	1.92920i	−0.0530513	−	0.0665242i
$842$	1.37349	−	0.423667i	0.0473337	−	0.0146005i
$843$		0			0
$844$	1.67022	+	0.515195i	0.0574914	+	0.0177337i
$845$	−0.927687	−	12.3791i	−0.0319134	−	0.425855i
$846$		0			0
$847$	−0.607906	+	2.45474i	−0.0208879	+	0.0843458i
$848$	9.58036	−	41.9743i	0.328991	−	1.44140i
$849$		0			0
$850$	0.0828760	−	0.0565039i	0.00284262	−	0.00193807i
$851$	16.4546	−	28.5002i	0.564057	−	0.976975i
$852$		0			0
$853$	−0.325109	−	0.156564i	−0.0111315	−	0.00536065i	0.428310	−	0.903632i	$-0.359109\pi$
$853$	−0.325109	−	0.156564i	−0.0111315	−	0.00536065i	−0.439441	+	0.898271i	$0.644824\pi$
$854$	−5.95141	+	14.3817i	−0.203653	+	0.492132i
$855$		0			0
$856$	−14.4750	−	9.86887i	−0.494744	−	0.337311i
$857$	−32.2142	−	29.8904i	−1.10042	−	1.02104i	−0.999659	−	0.0261264i	$-0.991683\pi$
$857$	−32.2142	−	29.8904i	−1.10042	−	1.02104i	−0.100758	−	0.994911i	$-0.532127\pi$
$858$		0			0
$859$	−41.9562	−	28.6052i	−1.43153	−	0.975998i	−0.997164	−	0.0752606i	$-0.976021\pi$
$859$	−41.9562	−	28.6052i	−1.43153	−	0.975998i	−0.434363	−	0.900738i	$-0.643026\pi$
$860$	3.96060	−	1.90732i	0.135055	−	0.0650392i
$861$		0			0
$862$	−14.0368	−	6.75978i	−0.478096	−	0.230239i
$863$	−17.2125	−	29.8129i	−0.585920	−	1.01484i	−0.994760	−	0.102238i	$-0.967400\pi$
$863$	−17.2125	−	29.8129i	−0.585920	−	1.01484i	0.408840	−	0.912606i	$-0.365934\pi$
$864$		0			0
$865$	−16.7862	+	11.4447i	−0.570749	+	0.389130i
$866$	15.3054	+	2.30692i	0.520098	+	0.0783922i
$867$		0			0
$868$	−0.0725542	+	0.292976i	−0.00246265	+	0.00994424i
$869$	−4.36475	−	19.1232i	−0.148064	−	0.648711i
$870$		0			0
$871$	37.8558	+	11.6770i	1.28269	+	0.395659i
$872$	−3.80879	−	9.70465i	−0.128982	−	0.328641i
$873$		0			0
$874$	1.58077	+	1.98222i	0.0534704	+	0.0670497i
$875$	20.5410	+	19.7734i	0.694411	+	0.668462i
$876$		0			0
$877$	−8.64743	+	22.0333i	−0.292003	+	0.744011i	0.707308	+	0.706905i	$0.249909\pi$
$877$	−8.64743	+	22.0333i	−0.292003	+	0.744011i	−0.999311	+	0.0371062i	$0.988186\pi$
$878$	−0.110842	+	1.47909i	−0.00374074	+	0.0499167i
$879$		0			0
$880$	18.4850	−	17.1516i	0.623130	−	0.578180i
$881$	−26.8509			−0.904628			−0.452314	−	0.891859i	$-0.649401\pi$
$881$	−26.8509			−0.904628			−0.452314	+	0.891859i	$0.649401\pi$
$882$		0			0
$883$	−38.3596			−1.29090			−0.645451	−	0.763802i	$-0.723331\pi$
$883$	−38.3596			−1.29090			−0.645451	+	0.763802i	$0.723331\pi$
$884$	0.176040	−	0.163341i	0.00592085	−	0.00549375i
$885$		0			0
$886$	−3.78005	+	50.4412i	−0.126993	+	1.69461i
$887$	−8.88693	+	22.6435i	−0.298394	+	0.760295i	0.700517	+	0.713636i	$0.252953\pi$
$887$	−8.88693	+	22.6435i	−0.298394	+	0.760295i	−0.998911	+	0.0466596i	$0.985142\pi$
$888$		0			0
$889$	1.74321	−	18.6574i	0.0584654	−	0.625750i
$890$	−5.79985	−	7.27279i	−0.194412	−	0.243784i
$891$		0			0
$892$	−0.780389	−	1.98840i	−0.0261293	−	0.0665765i
$893$	0.499214	+	0.153987i	0.0167056	+	0.00515298i
$894$		0			0
$895$	6.66914	+	29.2194i	0.222925	+	0.976697i
$896$	−14.8144	+	17.8926i	−0.494916	+	0.597751i
$897$		0			0
$898$	41.4755	+	6.25143i	1.38406	+	0.208613i
$899$	1.96605	−	1.34043i	0.0655716	−	0.0447059i
$900$		0			0
$901$	−1.41753	−	2.45523i	−0.0472247	−	0.0817956i
$902$	−39.2102	−	18.8827i	−1.30556	−	0.628724i
$903$		0			0
$904$	53.6438	−	25.8335i	1.78417	−	0.859210i
$905$	31.5304	+	21.4971i	1.04811	+	0.714587i
$906$		0			0
$907$	−2.75779	−	2.55886i	−0.0915710	−	0.0849655i	0.633059	−	0.774103i	$-0.281799\pi$
$907$	−2.75779	−	2.55886i	−0.0915710	−	0.0849655i	−0.724630	+	0.689138i	$0.757989\pi$
$908$	5.93311	+	4.04513i	0.196897	+	0.134242i
$909$		0			0
$910$	28.2908	+	20.0590i	0.937831	+	0.664950i
$911$	1.64045	+	0.789997i	0.0543504	+	0.0261738i	0.460862	−	0.887472i	$-0.347540\pi$
$911$	1.64045	+	0.789997i	0.0543504	+	0.0261738i	−0.406511	+	0.913646i	$0.633255\pi$
$912$		0			0
$913$	−20.7026	+	35.8579i	−0.685155	+	1.18672i
$914$	−41.2363	+	28.1144i	−1.36397	+	0.929942i
$915$		0			0
$916$	−0.534345	+	2.34112i	−0.0176553	+	0.0773527i
$917$	9.56971	+	45.7874i	0.316020	+	1.51203i
$918$		0			0
$919$	0.680110	+	9.07544i	0.0224348	+	0.299371i	0.997123	+	0.0758021i	$0.0241517\pi$
$919$	0.680110	+	9.07544i	0.0224348	+	0.299371i	−0.974688	+	0.223569i	$0.928229\pi$
$920$	24.5996	+	7.58799i	0.811026	+	0.250168i
$921$		0			0
$922$	−23.8287	+	7.35019i	−0.784757	+	0.242066i
$923$	0.792469	+	0.993725i	0.0260844	+	0.0327089i
$924$		0			0
$925$	−1.82880	+	2.29325i	−0.0601307	+	0.0754015i
$926$	10.5311	−	26.8329i	0.346074	−	0.881783i
$927$		0			0
$928$	−7.07280	+	1.06605i	−0.232176	+	0.0349949i
$929$	8.97763	−	8.33002i	0.294547	−	0.273299i	−0.519031	−	0.854755i	$-0.673707\pi$
$929$	8.97763	−	8.33002i	0.294547	−	0.273299i	0.813578	+	0.581456i	$0.197517\pi$
$930$		0			0
$931$	3.37762	+	1.17932i	0.110697	+	0.0386507i
$932$	−2.38627			−0.0781650
$933$		0			0
$934$	33.1043	−	4.98967i	1.08321	−	0.163267i
$935$	0.124089	−	1.65585i	0.00405813	−	0.0541520i
$936$		0			0
$937$	22.2908	−	27.9518i	0.728208	−	0.913144i	−0.270563	−	0.962702i	$-0.587210\pi$
$937$	22.2908	−	27.9518i	0.728208	−	0.913144i	0.998771	+	0.0495582i	$0.0157813\pi$
$938$	−27.0793	+	17.7429i	−0.884169	+	0.579325i
$939$		0			0
$940$	0.557090	−	0.171840i	0.0181703	−	0.00560479i
$941$	12.4382	+	31.6920i	0.405473	+	1.03313i	0.977131	+	0.212637i	$0.0682053\pi$
$941$	12.4382	+	31.6920i	0.405473	+	1.03313i	−0.571658	+	0.820492i	$0.693700\pi$
$942$		0			0
$943$	−2.90390	−	38.7498i	−0.0945639	−	1.26187i
$944$	0.998641	+	4.37533i	0.0325030	+	0.142405i
$945$		0			0
$946$	−7.19691	+	31.5317i	−0.233992	+	1.02518i
$947$	12.1588	+	1.83264i	0.395107	+	0.0595527i	0.343591	−	0.939119i	$-0.388357\pi$
$947$	12.1588	+	1.83264i	0.395107	+	0.0595527i	0.0515157	+	0.998672i	$0.483595\pi$
$948$		0			0
$949$	−34.6593	+	60.0317i	−1.12509	+	1.94871i
$950$	−0.112987	−	0.195700i	−0.00366579	−	0.00634934i
$951$		0			0
$952$	0.100724	+	1.78280i	0.00326447	+	0.0577809i
$953$	14.9520	−	7.20053i	0.484344	−	0.233248i	−0.175744	−	0.984436i	$-0.556233\pi$
$953$	14.9520	−	7.20053i	0.484344	−	0.233248i	0.660088	+	0.751188i	$0.270519\pi$
$954$		0			0
$955$	−14.4047	−	13.3656i	−0.466124	−	0.432500i
$956$	−0.226486	−	0.210148i	−0.00732508	−	0.00679668i
$957$		0			0
$958$	−23.3877	+	11.2629i	−0.755622	+	0.363889i
$959$	−0.0661787	+	0.0591811i	−0.00213702	+	0.00191106i
$960$		0			0
$961$	15.3933	+	26.6620i	0.496558	+	0.860064i
$962$	24.9258	−	43.1727i	0.803639	−	1.39194i
$963$		0			0
$964$	2.57484	+	0.388095i	0.0829300	+	0.0124997i
$965$	3.94430	−	17.2811i	0.126972	−	0.556299i
$966$		0			0
$967$	−7.86836	−	34.4735i	−0.253029	−	1.10859i	−0.928537	−	0.371240i	$-0.878933\pi$
$967$	−7.86836	−	34.4735i	−0.253029	−	1.10859i	0.675507	−	0.737353i	$-0.263925\pi$
$968$	0.212504	+	2.83567i	0.00683014	+	0.0911418i
$969$		0			0
$970$	−2.41134	−	6.14400i	−0.0774235	−	0.197272i
$971$	11.0147	−	3.39760i	0.353480	−	0.109034i	−0.112930	−	0.993603i	$-0.536023\pi$
$971$	11.0147	−	3.39760i	0.353480	−	0.109034i	0.466410	+	0.884569i	$0.345547\pi$
$972$		0			0
$973$	−27.6169	+	45.8677i	−0.885357	+	1.47045i
$974$	−27.6618	+	34.6868i	−0.886341	+	1.11144i
$975$		0			0
$976$	−1.14390	+	15.2643i	−0.0366154	+	0.488598i
$977$	−18.4833	+	2.78591i	−0.591334	+	0.0891292i	−0.437891	−	0.899028i	$-0.644274\pi$
$977$	−18.4833	+	2.78591i	−0.591334	+	0.0891292i	−0.153443	+	0.988157i	$0.549036\pi$
$978$		0			0
$979$	−9.64102			−0.308128
$980$	3.85561	−	1.03590i	0.123163	−	0.0330906i
$981$		0			0
$982$	−3.58329	+	3.32480i	−0.114347	+	0.106099i
$983$	−46.0375	+	6.93904i	−1.46837	+	0.221321i	−0.834024	−	0.551729i	$-0.813968\pi$
$983$	−46.0375	+	6.93904i	−1.46837	+	0.221321i	−0.634345	+	0.773050i	$0.718730\pi$
$984$		0			0
$985$	−22.8401	+	58.1956i	−0.727746	+	1.85427i
$986$	0.964652	−	1.20963i	0.0307208	−	0.0385226i
$987$		0			0
$988$	−0.337319	−	0.422985i	−0.0107316	−	0.0134570i
$989$	−27.5953	+	8.51202i	−0.877480	+	0.270667i
$990$		0			0
$991$	25.2827	+	7.79868i	0.803131	+	0.247733i	0.669031	−	0.743235i	$-0.266709\pi$
$991$	25.2827	+	7.79868i	0.803131	+	0.247733i	0.134100	+	0.990968i	$0.457186\pi$
$992$	0.0479377	+	0.639684i	0.00152202	+	0.0203100i
$993$		0			0
$994$	−1.03851	−	0.0190717i	−0.0329396	−	0.000604917i
$995$	1.64253	−	7.19641i	0.0520718	−	0.228141i
$996$		0			0
$997$	−7.38906	+	5.03777i	−0.234014	+	0.159548i	−0.674650	−	0.738138i	$-0.735705\pi$
$997$	−7.38906	+	5.03777i	−0.234014	+	0.159548i	0.440636	+	0.897686i	$0.354753\pi$
$998$	21.5271	−	37.2861i	0.681429	−	1.18027i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.f.109.2	✓	72
3.2	odd	2	inner	441.2.bb.f.109.5	yes	72
49.9	even	21	inner	441.2.bb.f.352.2	yes	72
147.107	odd	42	inner	441.2.bb.f.352.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bb.f.109.2	✓	72	1.1	even	1	trivial
441.2.bb.f.109.5	yes	72	3.2	odd	2	inner
441.2.bb.f.352.2	yes	72	49.9	even	21	inner
441.2.bb.f.352.5	yes	72	147.107	odd	42	inner

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.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.970582 + 0.900568i) q^{2} +(-0.0184545 + 0.246258i) q^{4} +(-0.843767 + 2.14988i) q^{5} +(-0.921217 - 2.48019i) q^{7} +(-1.85490 - 2.32597i) q^{8} +O(q^{10})\)	\(q+(-0.970582 + 0.900568i) q^{2} +(-0.0184545 + 0.246258i) q^{4} +(-0.843767 + 2.14988i) q^{5} +(-0.921217 - 2.48019i) q^{7} +(-1.85490 - 2.32597i) q^{8} +(-1.11717 - 2.84651i) q^{10} +(-3.02845 - 0.934154i) q^{11} +(-0.953861 - 4.17914i) q^{13} +(3.12770 + 1.57761i) q^{14} +(3.40664 + 0.513468i) q^{16} +(0.187439 - 0.127794i) q^{17} +(-0.255542 - 0.442611i) q^{19} +(-0.513855 - 0.247459i) q^{20} +(3.78063 - 1.82066i) q^{22} +(3.09568 + 2.11060i) q^{23} +(-0.244797 - 0.227138i) q^{25} +(4.68940 + 3.19718i) q^{26} +(0.627768 - 0.181086i) q^{28} +(-4.64086 - 2.23492i) q^{29} +(-0.230978 + 0.400066i) q^{31} +(1.14732 - 0.782232i) q^{32} +(-0.0668380 + 0.292836i) q^{34} +(6.10942 + 0.112196i) q^{35} +(-0.656391 - 8.75893i) q^{37} +(0.646625 + 0.199457i) q^{38} +(6.56566 - 2.02524i) q^{40} +(-6.46643 - 8.10865i) q^{41} +(-4.80563 + 6.02607i) q^{43} +(0.285931 - 0.728541i) q^{44} +(-4.90535 + 0.739362i) q^{46} +(-0.749318 + 0.695265i) q^{47} +(-5.30272 + 4.56959i) q^{49} +0.442148 q^{50} +(1.04675 - 0.157772i) q^{52} +(0.933904 - 12.4621i) q^{53} +(4.56363 - 5.72261i) q^{55} +(-4.06009 + 6.74322i) q^{56} +(6.51703 - 2.01024i) q^{58} +(0.475918 + 1.21262i) q^{59} +(0.332035 + 4.43070i) q^{61} +(-0.136103 - 0.596308i) q^{62} +(-1.94234 + 8.50995i) q^{64} +(9.78950 + 1.47553i) q^{65} +(-4.62087 + 8.00359i) q^{67} +(0.0280112 + 0.0485168i) q^{68} +(-6.03073 + 5.39305i) q^{70} +(-0.267146 + 0.128651i) q^{71} +(-11.8541 - 10.9990i) q^{73} +(8.52510 + 7.91013i) q^{74} +(0.113712 - 0.0547610i) q^{76} +(0.472980 + 8.37171i) q^{77} +(3.09458 + 5.35997i) q^{79} +(-3.97831 + 6.89063i) q^{80} +(13.5786 + 2.04664i) q^{82} +(2.90716 - 12.7371i) q^{83} +(0.116587 + 0.510801i) q^{85} +(-0.762630 - 10.1766i) q^{86} +(3.44466 + 8.77684i) q^{88} +(2.90690 - 0.896660i) q^{89} +(-9.48636 + 6.21565i) q^{91} +(-0.576881 + 0.723386i) q^{92} +(0.101140 - 1.34962i) q^{94} +(1.16718 - 0.175924i) q^{95} +2.15843 q^{97} +(1.03149 - 9.21062i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) \) 72 * q + 14 * q^4 - 28 * q^7	\( 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55} + 56 q^{58} + 112 q^{61} + 38 q^{64} - 36 q^{67} - 14 q^{70} - 28 q^{73} + 56 q^{76} + 62 q^{79} - 70 q^{82} - 100 q^{85} - 262 q^{88} - 154 q^{91} - 294 q^{94} + 56 q^{97}+O(q^{100}) \) 72 * q + 14 * q^4 - 28 * q^7 + 42 * q^13 - 26 * q^16 + 28 * q^19 + 8 * q^22 - 24 * q^25 - 28 * q^28 + 28 * q^31 + 28 * q^34 - 106 * q^37 + 70 * q^40 - 2 * q^43 + 60 * q^46 + 28 * q^49 + 70 * q^52 - 42 * q^55 + 56 * q^58 + 112 * q^61 + 38 * q^64 - 36 * q^67 - 14 * q^70 - 28 * q^73 + 56 * q^76 + 62 * q^79 - 70 * q^82 - 100 * q^85 - 262 * q^88 - 154 * q^91 - 294 * q^94 + 56 * q^97

Introduction

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