LMFDB - Embedded newform 1050.3.q.b.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(199,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1050.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.22986704741655040229376.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 31x^{12} + 880x^{8} - 2511x^{4} + 6561 $ x^16 - 31x^12 + 880x^8 - 2511*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Root			$-1.25838 + 0.337183i$ of defining polynomial
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.b.649.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.98615 + 0.440173i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.98615 + 0.440173i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(2.76860 - 4.79536i) q^{11} +(1.73205 + 3.00000i) q^{12} +3.50434 q^{13} +(8.24500 - 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-4.06994 + 7.04933i) q^{17} +(3.67423 + 2.12132i) q^{18} +(15.3628 - 8.86974i) q^{19} +(5.38992 - 10.8604i) q^{21} +7.83078i q^{22} +(10.3316 - 5.96495i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-4.29192 + 2.47794i) q^{26} +5.19615 q^{27} +(-6.22374 + 12.5405i) q^{28} +8.52374 q^{29} +(-6.68072 - 3.85711i) q^{31} +(4.89898 + 2.82843i) q^{32} +(4.79536 + 8.30580i) q^{33} -11.5115i q^{34} -6.00000 q^{36} +(-24.2950 + 14.0267i) q^{37} +(-12.5437 + 21.7263i) q^{38} +(-3.03484 + 5.25650i) q^{39} -3.14207i q^{41} +(1.07820 + 17.1125i) q^{42} +43.1943i q^{43} +(-5.53720 - 9.59071i) q^{44} +(-8.43572 + 14.6111i) q^{46} +(9.35524 + 16.2037i) q^{47} +6.92820 q^{48} +(48.6125 - 6.15023i) q^{49} +(-7.04933 - 12.2098i) q^{51} +(3.50434 - 6.06969i) q^{52} +(2.44037 + 1.40895i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} +30.7257i q^{57} +(-10.4394 + 6.02720i) q^{58} +(26.1612 + 15.1042i) q^{59} +(-41.0095 + 23.6769i) q^{61} +10.9096 q^{62} +(11.6228 + 17.4903i) q^{63} -8.00000 q^{64} +(-11.7462 - 6.78166i) q^{66} +(-5.70032 - 3.29108i) q^{67} +(8.13987 + 14.0987i) q^{68} +20.6632i q^{69} -97.7751 q^{71} +(7.34847 - 4.24264i) q^{72} +(-30.5806 + 52.9672i) q^{73} +(19.8368 - 34.3583i) q^{74} -35.4790i q^{76} +(-17.2311 + 34.7197i) q^{77} -8.58383i q^{78} +(61.5670 + 106.637i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(2.22178 + 3.84823i) q^{82} +89.5815 q^{83} +(-13.4209 - 20.1960i) q^{84} +(-30.5430 - 52.9020i) q^{86} +(-7.38178 + 12.7856i) q^{87} +(13.5633 + 7.83078i) q^{88} +(102.290 - 59.0573i) q^{89} +(-24.4818 + 1.54251i) q^{91} -23.8598i q^{92} +(11.5713 - 6.68072i) q^{93} +(-22.9156 - 13.2303i) q^{94} +(-8.48528 + 4.89898i) q^{96} -65.1965 q^{97} +(-55.1890 + 41.9067i) q^{98} -16.6116 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) $ 16 * q + 16 * q^4 - 24 * q^9	$ 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 32 q^{14} - 32 q^{16} - 144 q^{19} - 144 q^{26} + 48 q^{29} + 192 q^{31} - 96 q^{36} + 24 q^{39} + 16 q^{44} + 64 q^{46} + 528 q^{49} + 48 q^{51} + 80 q^{56} - 624 q^{59} - 408 q^{61} - 128 q^{64} - 72 q^{66} - 128 q^{71} + 32 q^{74} + 288 q^{79} - 72 q^{81} + 352 q^{86} + 672 q^{89} - 592 q^{91} - 72 q^{94} + 48 q^{99}+O(q^{100}) $ 16 * q + 16 * q^4 - 24 * q^9 - 8 * q^11 + 32 * q^14 - 32 * q^16 - 144 * q^19 - 144 * q^26 + 48 * q^29 + 192 * q^31 - 96 * q^36 + 24 * q^39 + 16 * q^44 + 64 * q^46 + 528 * q^49 + 48 * q^51 + 80 * q^56 - 624 * q^59 - 408 * q^61 - 128 * q^64 - 72 * q^66 - 128 * q^71 + 32 * q^74 + 288 * q^79 - 72 * q^81 + 352 * q^86 + 672 * q^89 - 592 * q^91 - 72 * q^94 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	0.408248i
$7$	−6.98615	+	0.440173i	−0.998021	+	0.0628819i
$7$	−6.98615	+	0.440173i	−0.998021	+	0.0628819i
$8$			2.82843i			0.353553i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	2.76860	−	4.79536i	0.251691	−	0.435942i	−0.712301	−	0.701875i	$-0.752347\pi$
$11$	2.76860	−	4.79536i	0.251691	−	0.435942i	0.963991	+	0.265933i	$0.0856800\pi$
$12$	1.73205	+	3.00000i	0.144338	+	0.250000i
$13$	3.50434			0.269564			0.134782	−	0.990875i	$-0.456967\pi$
$13$	3.50434			0.269564			0.134782	+	0.990875i	$0.456967\pi$
$14$	8.24500	−	5.47905i	0.588928	−	0.391361i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−4.06994	+	7.04933i	−0.239408	+	0.414667i	−0.960545	−	0.278126i	$-0.910287\pi$
$17$	−4.06994	+	7.04933i	−0.239408	+	0.414667i	0.721137	+	0.692793i	$0.243620\pi$
$18$	3.67423	+	2.12132i	0.204124	+	0.117851i
$19$	15.3628	−	8.86974i	0.808571	−	0.466828i	−0.0378887	−	0.999282i	$-0.512063\pi$
$19$	15.3628	−	8.86974i	0.808571	−	0.466828i	0.846459	+	0.532454i	$0.178730\pi$
$20$		0			0
$21$	5.38992	−	10.8604i	0.256663	−	0.517163i
$22$			7.83078i			0.355945i
$23$	10.3316	−	5.96495i	0.449200	−	0.259346i	−0.258292	−	0.966067i	$-0.583160\pi$
$23$	10.3316	−	5.96495i	0.449200	−	0.259346i	0.707492	+	0.706721i	$0.249826\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$		0			0
$26$	−4.29192	+	2.47794i	−0.165074	+	0.0953054i
$27$	5.19615			0.192450
$28$	−6.22374	+	12.5405i	−0.222277	+	0.447876i
$29$	8.52374			0.293922			0.146961	−	0.989142i	$-0.453051\pi$
$29$	8.52374			0.293922			0.146961	+	0.989142i	$0.453051\pi$
$30$		0			0
$31$	−6.68072	−	3.85711i	−0.215507	−	0.124423i	0.388361	−	0.921507i	$-0.373041\pi$
$31$	−6.68072	−	3.85711i	−0.215507	−	0.124423i	−0.603868	+	0.797084i	$0.706375\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$	4.79536	+	8.30580i	0.145314	+	0.251691i
$34$		−	11.5115i		−	0.338574i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−24.2950	+	14.0267i	−0.656621	+	0.379100i	−0.790988	−	0.611831i	$-0.790433\pi$
$37$	−24.2950	+	14.0267i	−0.656621	+	0.379100i	0.134367	+	0.990932i	$0.457100\pi$
$38$	−12.5437	+	21.7263i	−0.330098	+	0.571746i
$39$	−3.03484	+	5.25650i	−0.0778165	+	0.134782i
$40$		0			0
$41$		−	3.14207i		−	0.0766358i	−0.999266	−	0.0383179i	$-0.987800\pi$
$41$		−	3.14207i		−	0.0766358i	0.999266	−	0.0383179i	$-0.0121999\pi$
$42$	1.07820	+	17.1125i	0.0256714	+	0.407440i
$43$			43.1943i			1.00452i	0.864717	+	0.502260i	$0.167498\pi$
$43$			43.1943i			1.00452i	−0.864717	+	0.502260i	$0.832502\pi$
$44$	−5.53720	−	9.59071i	−0.125845	−	0.217971i
$45$		0			0
$46$	−8.43572	+	14.6111i	−0.183385	+	0.317632i
$47$	9.35524	+	16.2037i	0.199048	+	0.344761i	0.948220	−	0.317615i	$-0.102882\pi$
$47$	9.35524	+	16.2037i	0.199048	+	0.344761i	−0.749172	+	0.662375i	$0.769548\pi$
$48$	6.92820			0.144338
$49$	48.6125	−	6.15023i	0.992092	−	0.125515i
$50$		0			0
$51$	−7.04933	−	12.2098i	−0.138222	−	0.239408i
$52$	3.50434	−	6.06969i	0.0673911	−	0.116725i
$53$	2.44037	+	1.40895i	0.0460448	+	0.0265840i	0.522846	−	0.852427i	$-0.324870\pi$
$53$	2.44037	+	1.40895i	0.0460448	+	0.0265840i	−0.476801	+	0.879011i	$0.658204\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$		0			0
$56$	−1.24500	−	19.7598i	−0.0222321	−	0.352854i
$57$			30.7257i			0.539047i
$58$	−10.4394	+	6.02720i	−0.179990	+	0.103917i
$59$	26.1612	+	15.1042i	0.443411	+	0.256003i	0.705043	−	0.709164i	$-0.250928\pi$
$59$	26.1612	+	15.1042i	0.443411	+	0.256003i	−0.261633	+	0.965168i	$0.584261\pi$
$60$		0			0
$61$	−41.0095	+	23.6769i	−0.672288	+	0.388145i	−0.796943	−	0.604055i	$-0.793551\pi$
$61$	−41.0095	+	23.6769i	−0.672288	+	0.388145i	0.124655	+	0.992200i	$0.460218\pi$
$62$	10.9096			0.175961
$63$	11.6228	+	17.4903i	0.184489	+	0.277624i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−11.7462	−	6.78166i	−0.177972	−	0.102752i
$67$	−5.70032	−	3.29108i	−0.0850794	−	0.0491206i	0.456857	−	0.889540i	$-0.348975\pi$
$67$	−5.70032	−	3.29108i	−0.0850794	−	0.0491206i	−0.541936	+	0.840420i	$0.682309\pi$
$68$	8.13987	+	14.0987i	0.119704	+	0.207333i
$69$			20.6632i			0.299467i
$70$		0			0
$71$	−97.7751			−1.37711			−0.688557	−	0.725182i	$-0.741755\pi$
$71$	−97.7751			−1.37711			−0.688557	+	0.725182i	$0.741755\pi$
$72$	7.34847	−	4.24264i	0.102062	−	0.0589256i
$73$	−30.5806	+	52.9672i	−0.418913	+	0.725578i	−0.995830	−	0.0912244i	$-0.970922\pi$
$73$	−30.5806	+	52.9672i	−0.418913	+	0.725578i	0.576918	+	0.816802i	$0.304255\pi$
$74$	19.8368	−	34.3583i	0.268064	−	0.464301i
$75$		0			0
$76$		−	35.4790i		−	0.466828i
$77$	−17.2311	+	34.7197i	−0.223780	+	0.450906i
$78$		−	8.58383i		−	0.110049i
$79$	61.5670	+	106.637i	0.779329	+	1.34984i	0.932329	+	0.361612i	$0.117773\pi$
$79$	61.5670	+	106.637i	0.779329	+	1.34984i	−0.152999	+	0.988226i	$0.548893\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	2.22178	+	3.84823i	0.0270948	+	0.0469296i
$83$	89.5815			1.07930			0.539648	−	0.841891i	$-0.318557\pi$
$83$	89.5815			1.07930			0.539648	+	0.841891i	$0.318557\pi$
$84$	−13.4209	−	20.1960i	−0.159772	−	0.240429i
$85$		0			0
$86$	−30.5430	−	52.9020i	−0.355151	−	0.615140i
$87$	−7.38178	+	12.7856i	−0.0848480	+	0.146961i
$88$	13.5633	+	7.83078i	0.154129	+	0.0889862i
$89$	102.290	−	59.0573i	1.14933	−	0.663566i	0.200606	−	0.979672i	$-0.435709\pi$
$89$	102.290	−	59.0573i	1.14933	−	0.663566i	0.948724	+	0.316107i	$0.102376\pi$
$90$		0			0
$91$	−24.4818	+	1.54251i	−0.269031	+	0.0169507i
$92$		−	23.8598i		−	0.259346i
$93$	11.5713	−	6.68072i	0.124423	−	0.0718357i
$94$	−22.9156	−	13.2303i	−0.243783	−	0.140748i
$95$		0			0
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$	−65.1965			−0.672128			−0.336064	−	0.941839i	$-0.609096\pi$
$97$	−65.1965			−0.672128			−0.336064	+	0.941839i	$0.609096\pi$
$98$	−55.1890	+	41.9067i	−0.563153	+	0.427619i
$99$	−16.6116			−0.167794
$100$		0			0
$101$	−120.895	−	69.7987i	−1.19698	−	0.691076i	−0.237099	−	0.971486i	$-0.576196\pi$
$101$	−120.895	−	69.7987i	−1.19698	−	0.691076i	−0.959881	+	0.280409i	$0.909530\pi$
$102$	17.2673	+	9.96926i	0.169287	+	0.0977379i
$103$	87.2421	+	151.108i	0.847011	+	1.46707i	0.883863	+	0.467746i	$0.154934\pi$
$103$	87.2421	+	151.108i	0.847011	+	1.46707i	−0.0368520	+	0.999321i	$0.511733\pi$
$104$			9.91176i			0.0953054i
$105$		0			0
$106$	−3.98511			−0.0375954
$107$	−52.3741	+	30.2382i	−0.489477	+	0.282600i	−0.724358	−	0.689424i	$-0.757864\pi$
$107$	−52.3741	+	30.2382i	−0.489477	+	0.282600i	0.234880	+	0.972024i	$0.424530\pi$
$108$	5.19615	−	9.00000i	0.0481125	−	0.0833333i
$109$	−50.4057	+	87.3052i	−0.462437	+	0.800965i	−0.999082	−	0.0428435i	$-0.986358\pi$
$109$	−50.4057	+	87.3052i	−0.462437	+	0.800965i	0.536644	+	0.843808i	$0.319692\pi$
$110$		0			0
$111$		−	48.5899i		−	0.437747i
$112$	15.4971	+	23.3204i	0.138367	+	0.208218i
$113$		−	74.1876i		−	0.656527i	−0.944586	−	0.328264i	$-0.893537\pi$
$113$		−	74.1876i		−	0.656527i	0.944586	−	0.328264i	$-0.106463\pi$
$114$	−21.7263	−	37.6311i	−0.190582	−	0.330098i
$115$		0			0
$116$	8.52374	−	14.7636i	0.0734805	−	0.127272i
$117$	−5.25650	−	9.10453i	−0.0449274	−	0.0778165i
$118$	−42.7211			−0.362043
$119$	25.3302	−	51.0392i	0.212859	−	0.428901i
$120$		0			0
$121$	45.1697	+	78.2362i	0.373303	+	0.646580i
$122$	33.4842	−	57.9963i	0.274460	−	0.475379i
$123$	4.71310	+	2.72111i	0.0383179	+	0.0221228i
$124$	−13.3614	+	7.71423i	−0.107754	+	0.0622115i
$125$		0			0
$126$	−26.6025	−	13.2026i	−0.211131	−	0.104782i
$127$			151.093i			1.18971i	0.803833	+	0.594855i	$0.202791\pi$
$127$			151.093i			1.18971i	−0.803833	+	0.594855i	$0.797209\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$	−64.7915	−	37.4074i	−0.502260	−	0.289980i
$130$		0			0
$131$	−186.820	+	107.861i	−1.42611	+	0.823363i	−0.996811	−	0.0798009i	$-0.974572\pi$
$131$	−186.820	+	107.861i	−1.42611	+	0.823363i	−0.429296	+	0.903164i	$0.641238\pi$
$132$	19.1814			0.145314
$133$	−103.423	+	68.7276i	−0.777615	+	0.516749i
$134$	9.30859			0.0694671
$135$		0			0
$136$	−19.9385	−	11.5115i	−0.146607	−	0.0846435i
$137$	−115.736	−	66.8203i	−0.844789	−	0.487739i	0.0141000	−	0.999901i	$-0.495512\pi$
$137$	−115.736	−	66.8203i	−0.844789	−	0.487739i	−0.858889	+	0.512161i	$0.828845\pi$
$138$	−14.6111	−	25.3072i	−0.105877	−	0.183385i
$139$			193.762i			1.39397i	0.717085	+	0.696986i	$0.245476\pi$
$139$			193.762i			1.39397i	−0.717085	+	0.696986i	$0.754524\pi$
$140$		0			0
$141$	−32.4075			−0.229840
$142$	119.750	−	69.1374i	0.843306	−	0.486883i
$143$	9.70210	−	16.8045i	0.0678469	−	0.117514i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$		−	86.4950i		−	0.592432i
$147$	−32.8743	+	78.2450i	−0.223635	+	0.532279i
$148$			56.1068i			0.379100i
$149$	33.0032	+	57.1632i	0.221498	+	0.383646i	0.955263	−	0.295758i	$-0.0955721\pi$
$149$	33.0032	+	57.1632i	0.221498	+	0.383646i	−0.733765	+	0.679403i	$0.762239\pi$
$150$		0			0
$151$	−17.4410	+	30.2087i	−0.115503	+	0.200057i	−0.917981	−	0.396625i	$-0.870181\pi$
$151$	−17.4410	+	30.2087i	−0.115503	+	0.200057i	0.802478	+	0.596682i	$0.203515\pi$
$152$	25.0874	+	43.4527i	0.165049	+	0.285873i
$153$	24.4196			0.159605
$154$	−3.44690	−	54.7070i	−0.0223825	−	0.355240i
$155$		0			0
$156$	6.06969	+	10.5130i	0.0389082	+	0.0673911i
$157$	26.7503	−	46.3329i	0.170384	−	0.295114i	−0.768170	−	0.640246i	$-0.778832\pi$
$157$	26.7503	−	46.3329i	0.170384	−	0.295114i	0.938554	+	0.345132i	$0.112166\pi$
$158$	−150.808	−	87.0689i	−0.954480	−	0.551069i
$159$	−4.22685	+	2.44037i	−0.0265840	+	0.0153483i
$160$		0			0
$161$	−69.5525	+	46.2197i	−0.432003	+	0.287079i
$162$		−	12.7279i		−	0.0785674i
$163$	−178.387	+	102.992i	−1.09440	+	0.631852i	−0.934744	−	0.355321i	$-0.884372\pi$
$163$	−178.387	+	102.992i	−1.09440	+	0.631852i	−0.159655	+	0.987173i	$0.551038\pi$
$164$	−5.44222	−	3.14207i	−0.0331843	−	0.0191589i
$165$		0			0
$166$	−109.714	+	63.3437i	−0.660931	+	0.381589i
$167$	−137.945			−0.826020			−0.413010	−	0.910727i	$-0.635523\pi$
$167$	−137.945			−0.826020			−0.413010	+	0.910727i	$0.635523\pi$
$168$	30.7179	+	15.2450i	0.182845	+	0.0907440i
$169$	−156.720			−0.927335
$170$		0			0
$171$	−46.0885	−	26.6092i	−0.269524	−	0.155609i
$172$	74.8148	+	43.1943i	0.434970	+	0.251130i
$173$	−110.283	−	191.016i	−0.637475	−	1.10414i	−0.985985	−	0.166834i	$-0.946646\pi$
$173$	−110.283	−	191.016i	−0.637475	−	1.10414i	0.348510	−	0.937305i	$-0.386688\pi$
$174$		−	20.8788i		−	0.119993i
$175$		0			0
$176$	−22.1488			−0.125845
$177$	−45.3126	+	26.1612i	−0.256003	+	0.147804i
$178$	−83.5197	+	144.660i	−0.469212	+	0.812699i
$179$	−36.6501	+	63.4798i	−0.204749	+	0.354636i	−0.950053	−	0.312089i	$-0.898971\pi$
$179$	−36.6501	+	63.4798i	−0.204749	+	0.354636i	0.745304	+	0.666725i	$0.232305\pi$
$180$		0			0
$181$			61.4619i			0.339568i	0.985481	+	0.169784i	$0.0543071\pi$
$181$			61.4619i			0.339568i	−0.985481	+	0.169784i	$0.945693\pi$
$182$	28.8932	−	19.2004i	0.158754	−	0.105497i
$183$		−	82.0191i		−	0.448192i
$184$	16.8714	+	29.2222i	0.0916926	+	0.158816i
$185$		0			0
$186$	−9.44796	+	16.3643i	−0.0507955	+	0.0879804i
$187$	22.5360	+	39.0336i	0.120514	+	0.208736i
$188$	37.4210			0.199048
$189$	−36.3011	+	2.28721i	−0.192069	+	0.0121016i
$190$		0			0
$191$	179.931	+	311.650i	0.942048	+	1.63168i	0.761556	+	0.648099i	$0.224436\pi$
$191$	179.931	+	311.650i	0.942048	+	1.63168i	0.180492	+	0.983577i	$0.442231\pi$
$192$	6.92820	−	12.0000i	0.0360844	−	0.0625000i
$193$	−121.023	−	69.8724i	−0.627060	−	0.362033i	0.152552	−	0.988295i	$-0.451251\pi$
$193$	−121.023	−	69.8724i	−0.627060	−	0.362033i	−0.779613	+	0.626262i	$0.784584\pi$
$194$	79.8490	−	46.1009i	0.411593	−	0.237633i
$195$		0			0
$196$	37.9600	−	90.3495i	0.193673	−	0.460967i
$197$			248.343i			1.26062i	0.776342	+	0.630311i	$0.217073\pi$
$197$			248.343i			1.26062i	−0.776342	+	0.630311i	$0.782927\pi$
$198$	20.3450	−	11.7462i	0.102752	−	0.0593241i
$199$	106.170	+	61.2973i	0.533518	+	0.308026i	0.742448	−	0.669904i	$-0.233665\pi$
$199$	106.170	+	61.2973i	0.533518	+	0.308026i	−0.208930	+	0.977931i	$0.566998\pi$
$200$		0			0
$201$	9.87325	−	5.70032i	0.0491206	−	0.0283598i
$202$	197.421			0.977329
$203$	−59.5481	+	3.75192i	−0.293341	+	0.0184824i
$204$	−28.1973			−0.138222
$205$		0			0
$206$	−213.699	−	123.379i	−1.03737	−	0.598927i
$207$	−30.9948	−	17.8949i	−0.149733	−	0.0864486i
$208$	−7.00867	−	12.1394i	−0.0336955	−	0.0583624i
$209$		−	98.2271i		−	0.469986i
$210$		0			0
$211$	352.829			1.67218			0.836088	−	0.548596i	$-0.184837\pi$
$211$	352.829			1.67218			0.836088	+	0.548596i	$0.184837\pi$
$212$	4.88074	−	2.81790i	0.0230224	−	0.0132920i
$213$	84.6757	−	146.663i	0.397538	−	0.688557i
$214$	42.7632	−	74.0681i	0.199828	−	0.346113i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	48.3703	+	24.0057i	0.222904	+	0.110625i
$218$		−	142.569i		−	0.653985i
$219$	−52.9672	−	91.7418i	−0.241859	−	0.418913i
$220$		0			0
$221$	−14.2624	+	24.7032i	−0.0645358	+	0.111779i
$222$	34.3583	+	59.5103i	0.154767	+	0.268064i
$223$	−61.7420			−0.276870			−0.138435	−	0.990372i	$-0.544207\pi$
$223$	−61.7420			−0.276870			−0.138435	+	0.990372i	$0.544207\pi$
$224$	−35.4700	−	17.6034i	−0.158348	−	0.0785866i
$225$		0			0
$226$	52.4586	+	90.8609i	0.232118	+	0.402039i
$227$	104.762	−	181.452i	0.461505	−	0.799350i	−0.537531	−	0.843244i	$-0.680643\pi$
$227$	104.762	−	181.452i	0.461505	−	0.799350i	0.999036	+	0.0438940i	$0.0139764\pi$
$228$	53.2184	+	30.7257i	0.233414	+	0.134762i
$229$	93.3568	−	53.8996i	0.407671	−	0.235369i	−0.282117	−	0.959380i	$-0.591037\pi$
$229$	93.3568	−	53.8996i	0.407671	−	0.235369i	0.689789	+	0.724011i	$0.257703\pi$
$230$		0			0
$231$	−37.1571	−	55.9148i	−0.160853	−	0.242055i
$232$			24.1088i			0.103917i
$233$	283.057	−	163.423i	1.21484	−	0.701387i	0.251029	−	0.967980i	$-0.419231\pi$
$233$	283.057	−	163.423i	1.21484	−	0.701387i	0.963809	+	0.266592i	$0.0858978\pi$
$234$	12.8758	+	7.43382i	0.0550246	+	0.0317685i
$235$		0			0
$236$	52.3224	−	30.2084i	0.221705	−	0.128002i
$237$	−213.274			−0.899892
$238$	5.06706	+	80.4211i	0.0212902	+	0.337904i
$239$	9.20117			0.0384986			0.0192493	−	0.999815i	$-0.493872\pi$
$239$	9.20117			0.0384986			0.0192493	+	0.999815i	$0.493872\pi$
$240$		0			0
$241$	278.156	+	160.593i	1.15417	+	0.666362i	0.949900	−	0.312553i	$-0.101184\pi$
$241$	278.156	+	160.593i	1.15417	+	0.666362i	0.204272	+	0.978914i	$0.434517\pi$
$242$	−110.643	−	63.8796i	−0.457201	−	0.263965i
$243$	−7.79423	−	13.5000i	−0.0320750	−	0.0555556i
$244$			94.7075i			0.388145i
$245$		0			0
$246$	−7.69646			−0.0312864
$247$	53.8365	−	31.0825i	0.217962	−	0.125840i
$248$	10.9096	−	18.8959i	0.0439902	−	0.0761932i
$249$	−77.5799	+	134.372i	−0.311566	+	0.539648i
$250$		0			0
$251$		−	19.2394i		−	0.0766511i	−0.999265	−	0.0383255i	$-0.987798\pi$
$251$		−	19.2394i		−	0.0766511i	0.999265	−	0.0383255i	$-0.0122024\pi$
$252$	41.9169	−	2.64104i	0.166337	−	0.0104803i
$253$		−	66.0583i		−	0.261100i
$254$	−106.839	−	185.051i	−0.420626	−	0.728546i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	64.7109	+	112.083i	0.251793	+	0.436119i	0.964020	−	0.265831i	$-0.0856464\pi$
$257$	64.7109	+	112.083i	0.251793	+	0.436119i	−0.712226	+	0.701950i	$0.752313\pi$
$258$	105.804			0.410093
$259$	163.554	−	108.687i	0.631483	−	0.419640i
$260$		0			0
$261$	−12.7856	−	22.1453i	−0.0489870	−	0.0848480i
$262$	152.538	−	264.203i	0.582206	−	1.00841i
$263$	144.561	+	83.4625i	0.549663	+	0.317348i	0.748986	−	0.662586i	$-0.230541\pi$
$263$	144.561	+	83.4625i	0.549663	+	0.317348i	−0.199323	+	0.979934i	$0.563874\pi$
$264$	−23.4924	+	13.5633i	−0.0889862	+	0.0513762i
$265$		0			0
$266$	78.0688	−	157.305i	0.293492	−	0.591371i
$267$			204.581i			0.766220i
$268$	−11.4006	+	6.58217i	−0.0425397	+	0.0245603i
$269$	−181.081	−	104.547i	−0.673162	−	0.388650i	0.124112	−	0.992268i	$-0.460392\pi$
$269$	−181.081	−	104.547i	−0.673162	−	0.388650i	−0.797274	+	0.603618i	$0.793725\pi$
$270$		0			0
$271$	123.029	−	71.0308i	0.453981	−	0.262106i	−0.255529	−	0.966801i	$-0.582250\pi$
$271$	123.029	−	71.0308i	0.453981	−	0.262106i	0.709510	+	0.704695i	$0.248916\pi$
$272$	32.5595			0.119704
$273$	18.8881	−	38.0586i	0.0691871	−	0.139409i
$274$	188.996			0.689768
$275$		0			0
$276$	35.7897	+	20.6632i	0.129673	+	0.0748667i
$277$	−386.179	−	222.961i	−1.39415	−	0.804912i	−0.400377	−	0.916350i	$-0.631121\pi$
$277$	−386.179	−	222.961i	−1.39415	−	0.804912i	−0.993771	+	0.111438i	$0.964454\pi$
$278$	−137.010	−	237.309i	−0.492843	−	0.853630i
$279$			23.1427i			0.0829487i
$280$		0			0
$281$	482.012			1.71534			0.857672	−	0.514196i	$-0.171910\pi$
$281$	482.012			1.71534			0.857672	+	0.514196i	$0.171910\pi$
$282$	39.6909	−	22.9156i	0.140748	−	0.0812609i
$283$	−108.257	+	187.506i	−0.382533	+	0.662566i	−0.991424	−	0.130688i	$-0.958281\pi$
$283$	−108.257	+	187.506i	−0.382533	+	0.662566i	0.608891	+	0.793254i	$0.291615\pi$
$284$	−97.7751	+	169.351i	−0.344278	+	0.596308i
$285$		0			0
$286$			27.4417i			0.0959500i
$287$	1.38305	+	21.9509i	0.00481900	+	0.0764841i
$288$		−	16.9706i		−	0.0589256i
$289$	111.371	+	192.901i	0.385368	+	0.667476i
$290$		0			0
$291$	56.4618	−	97.7947i	0.194027	−	0.336064i
$292$	61.1612	+	105.934i	0.209456	+	0.362789i
$293$	383.704			1.30957			0.654786	−	0.755815i	$-0.272759\pi$
$293$	383.704			1.30957			0.654786	+	0.755815i	$0.272759\pi$
$294$	−15.0649	−	119.076i	−0.0512412	−	0.405020i
$295$		0			0
$296$	−39.6735	−	68.7166i	−0.134032	−	0.232151i
$297$	14.3861	−	24.9174i	0.0484379	−	0.0838970i
$298$	−80.8410	−	46.6736i	−0.271278	−	0.156623i
$299$	36.2054	−	20.9032i	0.121088	−	0.0699104i
$300$		0			0
$301$	−19.0130	−	301.762i	−0.0631661	−	1.00253i
$302$		−	49.3305i		−	0.163346i
$303$	209.396	−	120.895i	0.691076	−	0.398993i
$304$	−61.4514	−	35.4790i	−0.202143	−	0.116707i
$305$		0			0
$306$	−29.9078	+	17.2673i	−0.0977379	+	0.0564290i
$307$	−21.1264			−0.0688155			−0.0344078	−	0.999408i	$-0.510954\pi$
$307$	−21.1264			−0.0688155			−0.0344078	+	0.999408i	$0.510954\pi$
$308$	42.9053	+	64.5648i	0.139303	+	0.209626i
$309$	−302.216			−0.978044
$310$		0			0
$311$	75.0288	+	43.3179i	0.241250	+	0.139286i	0.615751	−	0.787941i	$-0.288853\pi$
$311$	75.0288	+	43.3179i	0.241250	+	0.139286i	−0.374501	+	0.927226i	$0.622186\pi$
$312$	−14.8676	−	8.58383i	−0.0476527	−	0.0275123i
$313$	1.41903	+	2.45782i	0.00453363	+	0.00785247i	0.868283	−	0.496069i	$-0.165224\pi$
$313$	1.41903	+	2.45782i	0.00453363	+	0.00785247i	−0.863750	+	0.503921i	$0.831890\pi$
$314$			75.6613i			0.240960i
$315$		0			0
$316$	246.268			0.779329
$317$	268.338	−	154.925i	0.846493	−	0.488723i	−0.0129730	−	0.999916i	$-0.504130\pi$
$317$	268.338	−	154.925i	0.846493	−	0.488723i	0.859466	+	0.511193i	$0.170796\pi$
$318$	3.45121	−	5.97767i	0.0108529	−	0.0187977i
$319$	23.5988	−	40.8744i	0.0739776	−	0.128133i
$320$		0			0
$321$		−	104.748i		−	0.326318i
$322$	52.5018	−	105.788i	0.163049	−	0.328535i
$323$			144.397i			0.447050i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	145.652	−	252.278i	0.446787	−	0.773857i
$327$	−87.3052	−	151.217i	−0.266988	−	0.462437i
$328$	8.88711			0.0270948
$329$	−72.4895	−	109.084i	−0.220333	−	0.331562i
$330$		0			0
$331$	208.295	+	360.777i	0.629289	+	1.08996i	0.987695	+	0.156394i	$0.0499871\pi$
$331$	208.295	+	360.777i	0.629289	+	1.08996i	−0.358406	+	0.933566i	$0.616680\pi$
$332$	89.5815	−	155.160i	0.269824	−	0.467349i
$333$	72.8849	+	42.0801i	0.218874	+	0.126367i
$334$	168.948	−	97.5421i	0.505832	−	0.292042i
$335$		0			0
$336$	−48.4014	+	3.04961i	−0.144052	+	0.00907622i
$337$		−	155.491i		−	0.461399i	−0.973025	−	0.230699i	$-0.925899\pi$
$337$		−	155.491i		−	0.461399i	0.973025	−	0.230699i	$-0.0741014\pi$
$338$	191.942	−	110.818i	0.567874	−	0.327862i
$339$	111.281	+	64.2483i	0.328264	+	0.189523i
$340$		0			0
$341$	−36.9925	+	21.3576i	−0.108482	+	0.0626323i
$342$	75.2622			0.220065
$343$	−336.907	+	64.3643i	−0.982236	+	0.187651i
$344$	−122.172			−0.355151
$345$		0			0
$346$	270.138	+	155.964i	0.780744	+	0.450763i
$347$	−443.844	−	256.253i	−1.27909	−	0.738482i	−0.302408	−	0.953179i	$-0.597790\pi$
$347$	−443.844	−	256.253i	−1.27909	−	0.738482i	−0.976681	+	0.214697i	$0.931124\pi$
$348$	14.7636	+	25.5712i	0.0424240	+	0.0734805i
$349$			269.185i			0.771305i	0.922644	+	0.385652i	$0.126024\pi$
$349$			269.185i			0.771305i	−0.922644	+	0.385652i	$0.873976\pi$
$350$		0			0
$351$	18.2091			0.0518777
$352$	27.1266	−	15.6616i	0.0770643	−	0.0444931i
$353$	293.231	−	507.890i	0.830682	−	1.43878i	−0.0668166	−	0.997765i	$-0.521284\pi$
$353$	293.231	−	507.890i	0.830682	−	1.43878i	0.897498	−	0.441018i	$-0.145382\pi$
$354$	36.9976	−	64.0816i	0.104513	−	0.181022i
$355$		0			0
$356$		−	236.229i		−	0.663566i
$357$	54.6221	+	82.1966i	0.153003	+	0.230242i
$358$		−	103.662i		−	0.289559i
$359$	44.4221	+	76.9413i	0.123738	+	0.214321i	0.921239	−	0.388997i	$-0.127178\pi$
$359$	44.4221	+	76.9413i	0.123738	+	0.214321i	−0.797501	+	0.603318i	$0.793845\pi$
$360$		0			0
$361$	−23.1554	+	40.1064i	−0.0641424	+	0.111098i
$362$	−43.4601	−	75.2751i	−0.120056	−	0.207942i
$363$	−156.472			−0.431054
$364$	−21.8101	+	43.9462i	−0.0599178	+	0.120731i
$365$		0			0
$366$	57.9963	+	100.452i	0.158460	+	0.274460i
$367$	353.019	−	611.446i	0.961904	−	1.66607i	0.244191	−	0.969727i	$-0.421478\pi$
$367$	353.019	−	611.446i	0.961904	−	1.66607i	0.717713	−	0.696339i	$-0.245189\pi$
$368$	−41.3264	−	23.8598i	−0.112300	−	0.0648365i
$369$	−8.16333	+	4.71310i	−0.0221228	+	0.0127726i
$370$		0			0
$371$	−17.6690	−	8.76894i	−0.0476253	−	0.0236360i
$372$		−	26.7229i		−	0.0718357i
$373$	−44.3770	+	25.6211i	−0.118973	+	0.0686892i	−0.558306	−	0.829635i	$-0.688548\pi$
$373$	−44.3770	+	25.6211i	−0.118973	+	0.0686892i	0.439332	+	0.898325i	$0.355215\pi$
$374$	−55.2018	−	31.8708i	−0.147598	−	0.0852160i
$375$		0			0
$376$	−45.8311	+	26.4606i	−0.121891	+	0.0703740i
$377$	29.8701			0.0792309
$378$	42.8423	−	28.4700i	0.113339	−	0.0753174i
$379$	194.724			0.513784			0.256892	−	0.966440i	$-0.417302\pi$
$379$	194.724			0.513784			0.256892	+	0.966440i	$0.417302\pi$
$380$		0			0
$381$	−226.640	−	130.851i	−0.594855	−	0.343440i
$382$	−440.740	−	254.461i	−1.15377	−	0.666129i
$383$	262.540	+	454.732i	0.685482	+	1.18729i	0.973285	+	0.229600i	$0.0737418\pi$
$383$	262.540	+	454.732i	0.685482	+	1.18729i	−0.287803	+	0.957690i	$0.592925\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	197.629			0.511993
$387$	112.222	−	64.7915i	0.289980	−	0.167420i
$388$	−65.1965	+	112.924i	−0.168032	+	0.291040i
$389$	−201.765	+	349.467i	−0.518675	+	0.898372i	0.481089	+	0.876672i	$0.340241\pi$
$389$	−201.765	+	349.467i	−0.518675	+	0.898372i	−0.999765	+	0.0217005i	$0.993092\pi$
$390$		0			0
$391$			97.1079i			0.248358i
$392$	17.3955	+	137.497i	0.0443762	+	0.350757i
$393$		−	373.640i		−	0.950738i
$394$	−175.605	−	304.156i	−0.445697	−	0.771971i
$395$		0			0
$396$	−16.6116	+	28.7721i	−0.0419485	+	0.0726569i
$397$	80.5960	+	139.596i	0.203013	+	0.351628i	0.949498	−	0.313774i	$-0.101593\pi$
$397$	80.5960	+	139.596i	0.203013	+	0.351628i	−0.746485	+	0.665402i	$0.768260\pi$
$398$	−173.375			−0.435615
$399$	−13.5246	−	214.654i	−0.0338963	−	0.537980i
$400$		0			0
$401$	212.506	+	368.071i	0.529940	+	0.917883i	0.999390	+	0.0349237i	$0.0111188\pi$
$401$	212.506	+	368.071i	0.529940	+	0.917883i	−0.469450	+	0.882959i	$0.655548\pi$
$402$	−8.06147	+	13.9629i	−0.0200534	+	0.0347335i
$403$	−23.4115	−	13.5166i	−0.0580930	−	0.0335400i
$404$	−241.790	+	139.597i	−0.598490	+	0.345538i
$405$		0			0
$406$	70.2782	−	46.7020i	0.173099	−	0.115030i
$407$			155.337i			0.381664i
$408$	34.5345	−	19.9385i	0.0846435	−	0.0488689i
$409$	−373.605	−	215.701i	−0.913460	−	0.527386i	−0.0319171	−	0.999491i	$-0.510161\pi$
$409$	−373.605	−	215.701i	−0.913460	−	0.527386i	−0.881543	+	0.472104i	$0.843495\pi$
$410$		0			0
$411$	200.461	−	115.736i	0.487739	−	0.281596i
$412$	348.969			0.847011
$413$	−189.415	−	94.0046i	−0.458631	−	0.227614i
$414$	50.6143			0.122257
$415$		0			0
$416$	17.1677	+	9.91176i	0.0412684	+	0.0238263i
$417$	−290.643	−	167.803i	−0.696986	−	0.402405i
$418$	69.4570	+	120.303i	0.166165	+	0.287806i
$419$		−	585.412i		−	1.39716i	−0.715530	−	0.698582i	$-0.753815\pi$
$419$		−	585.412i		−	1.39716i	0.715530	−	0.698582i	$-0.246185\pi$
$420$		0			0
$421$	400.267			0.950754			0.475377	−	0.879782i	$-0.342312\pi$
$421$	400.267			0.950754			0.475377	+	0.879782i	$0.342312\pi$
$422$	−432.126	+	249.488i	−1.02399	+	0.591203i
$423$	28.0657	−	48.6112i	0.0663492	−	0.114920i
$424$	−3.98511	+	6.90241i	−0.00939885	+	0.0162793i
$425$		0			0
$426$			239.499i			0.562204i
$427$	276.077	−	183.461i	0.646550	−	0.429652i
$428$			120.953i			0.282600i
$429$	16.8045	+	29.1063i	0.0391714	+	0.0678469i
$430$		0			0
$431$	−197.631	+	342.307i	−0.458541	+	0.794216i	−0.998884	−	0.0472289i	$-0.984961\pi$
$431$	−197.631	+	342.307i	−0.458541	+	0.794216i	0.540344	+	0.841445i	$0.318294\pi$
$432$	−10.3923	−	18.0000i	−0.0240563	−	0.0416667i
$433$	2.39222			0.00552477			0.00276238	−	0.999996i	$-0.499121\pi$
$433$	2.39222			0.00552477			0.00276238	+	0.999996i	$0.499121\pi$
$434$	−76.2158	+	4.80210i	−0.175613	+	0.0110647i
$435$		0			0
$436$	100.811	+	174.610i	0.231219	+	0.400482i
$437$	105.815	−	183.277i	0.242140	−	0.419399i
$438$	129.743	+	74.9069i	0.296216	+	0.171020i
$439$	350.264	−	202.225i	0.797867	−	0.460649i	−0.0448578	−	0.998993i	$-0.514283\pi$
$439$	350.264	−	202.225i	0.797867	−	0.460649i	0.842725	+	0.538345i	$0.180950\pi$
$440$		0			0
$441$	−88.8975	−	117.074i	−0.201582	−	0.265473i
$442$		−	40.3402i		−	0.0912674i
$443$	252.889	−	146.005i	0.570855	−	0.329583i	−0.186636	−	0.982429i	$-0.559758\pi$
$443$	252.889	−	146.005i	0.570855	−	0.329583i	0.757491	+	0.652846i	$0.226425\pi$
$444$	−84.1603	−	48.5899i	−0.189550	−	0.109437i
$445$		0			0
$446$	75.6182	−	43.6582i	0.169547	−	0.0978883i
$447$	−114.326			−0.255764
$448$	55.8892	−	3.52139i	0.124753	−	0.00786024i
$449$	−125.680			−0.279911			−0.139956	−	0.990158i	$-0.544696\pi$
$449$	−125.680			−0.279911			−0.139956	+	0.990158i	$0.544696\pi$
$450$		0			0
$451$	−15.0673	−	8.69913i	−0.0334087	−	0.0192885i
$452$	−128.497	−	74.1876i	−0.284285	−	0.164132i
$453$	−30.2087	−	52.3229i	−0.0666858	−	0.115503i
$454$			296.310i			0.652666i
$455$		0			0
$456$	−86.9054			−0.190582
$457$	−74.4808	+	43.0015i	−0.162978	+	0.0940952i	−0.579270	−	0.815135i	$-0.696662\pi$
$457$	−74.4808	+	43.0015i	−0.162978	+	0.0940952i	0.416293	+	0.909231i	$0.363329\pi$
$458$	−76.2255	+	132.026i	−0.166431	+	0.288267i
$459$	−21.1480	+	36.6294i	−0.0460741	+	0.0798027i
$460$		0			0
$461$		−	131.449i		−	0.285138i	−0.989785	−	0.142569i	$-0.954464\pi$
$461$		−	131.449i		−	0.285138i	0.989785	−	0.142569i	$-0.0455362\pi$
$462$	85.0456	+	42.2073i	0.184081	+	0.0913578i
$463$			73.9873i			0.159800i	0.996803	+	0.0798999i	$0.0254601\pi$
$463$			73.9873i			0.159800i	−0.996803	+	0.0798999i	$0.974540\pi$
$464$	−17.0475	−	29.5271i	−0.0367403	−	0.0636360i
$465$		0			0
$466$	−231.115	+	400.303i	−0.495956	+	0.859020i
$467$	223.453	+	387.032i	0.478486	+	0.828762i	0.999696	−	0.0246667i	$-0.00785244\pi$
$467$	223.453	+	387.032i	0.478486	+	0.828762i	−0.521210	+	0.853429i	$0.674519\pi$
$468$	−21.0260			−0.0449274
$469$	41.2719	+	20.4829i	0.0879999	+	0.0436735i
$470$		0			0
$471$	46.3329	+	80.2509i	0.0983713	+	0.170384i
$472$	−42.7211	+	73.9951i	−0.0905108	+	0.156769i
$473$	207.132	+	119.588i	0.437912	+	0.252828i
$474$	261.207	−	150.808i	0.551069	−	0.318160i
$475$		0			0
$476$	−63.0722	−	94.9124i	−0.132505	−	0.199396i
$477$		−	8.45370i		−	0.0177226i
$478$	−11.2691	+	6.50621i	−0.0235755	+	0.0136113i
$479$	−513.818	−	296.653i	−1.07269	−	0.619318i	−0.143775	−	0.989610i	$-0.545924\pi$
$479$	−513.818	−	296.653i	−1.07269	−	0.619318i	−0.928915	+	0.370293i	$0.879257\pi$
$480$		0			0
$481$	−85.1377	+	49.1543i	−0.177002	+	0.102192i
$482$	−454.226			−0.942378
$483$	−9.09539	−	144.356i	−0.0188310	−	0.298874i
$484$	180.679			0.373303
$485$		0			0
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	−709.744	−	409.771i	−1.45738	−	0.841418i	−0.458498	−	0.888696i	$-0.651612\pi$
$487$	−709.744	−	409.771i	−1.45738	−	0.841418i	−0.998882	+	0.0472773i	$0.984946\pi$
$488$	−66.9683	−	115.993i	−0.137230	−	0.237690i
$489$		−	356.774i		−	0.729600i
$490$		0			0
$491$	554.724			1.12978			0.564892	−	0.825165i	$-0.308918\pi$
$491$	554.724			1.12978			0.564892	+	0.825165i	$0.308918\pi$
$492$	9.42620	−	5.44222i	0.0191589	−	0.0110614i
$493$	−34.6911	+	60.0867i	−0.0703673	+	0.121880i
$494$	−43.9574	+	76.1364i	−0.0889825	+	0.154122i
$495$		0			0
$496$			30.8569i			0.0622115i
$497$	683.071	−	43.0380i	1.37439	−	0.0865955i
$498$		−	219.429i		−	0.440620i
$499$	317.394	+	549.742i	0.636060	+	1.10169i	0.986290	+	0.165024i	$0.0527701\pi$
$499$	317.394	+	549.742i	0.636060	+	1.10169i	−0.350230	+	0.936664i	$0.613897\pi$
$500$		0			0
$501$	119.464	−	206.918i	0.238451	−	0.413010i
$502$	13.6043	+	23.5634i	0.0271003	+	0.0469390i
$503$	−120.116			−0.238800			−0.119400	−	0.992846i	$-0.538097\pi$
$503$	−120.116			−0.238800			−0.119400	+	0.992846i	$0.538097\pi$
$504$	−49.4700	+	32.8743i	−0.0981547	+	0.0652268i
$505$		0			0
$506$	46.7103	+	80.9046i	0.0923128	+	0.159890i
$507$	135.723	−	235.079i	0.267699	−	0.463668i
$508$	261.701	+	151.093i	0.515160	+	0.297428i
$509$	−51.1082	+	29.5073i	−0.100409	+	0.0579712i	−0.549364	−	0.835583i	$-0.685130\pi$
$509$	−51.1082	+	29.5073i	−0.100409	+	0.0579712i	0.448955	+	0.893555i	$0.351796\pi$
$510$		0			0
$511$	190.326	−	383.497i	0.372458	−	0.750484i
$512$		−	22.6274i		−	0.0441942i
$513$	79.8277	−	46.0885i	0.155609	−	0.0898412i
$514$	−158.509	−	91.5150i	−0.308383	−	0.178045i
$515$		0			0
$516$	−129.583	+	74.8148i	−0.251130	+	0.144990i
$517$	103.604			0.200394
$518$	−123.459	+	248.764i	−0.238338	+	0.480239i
$519$	382.032			0.736093
$520$		0			0
$521$	−841.241	−	485.691i	−1.61467	−	0.932228i	−0.988269	−	0.152725i	$-0.951195\pi$
$521$	−841.241	−	485.691i	−1.61467	−	0.932228i	−0.626398	−	0.779504i	$-0.715471\pi$
$522$	31.3182	+	18.0816i	0.0599966	+	0.0346391i
$523$	345.682	+	598.739i	0.660960	+	1.14482i	0.980364	+	0.197197i	$0.0631840\pi$
$523$	345.682	+	598.739i	0.660960	+	1.14482i	−0.319404	+	0.947619i	$0.603483\pi$
$524$			431.442i			0.823363i
$525$		0			0
$526$	−236.068			−0.448798
$527$	54.3802	−	31.3964i	0.103188	−	0.0595757i
$528$	19.1814	−	33.2232i	0.0363285	−	0.0629227i
$529$	−193.339	+	334.872i	−0.365479	+	0.633029i
$530$		0			0
$531$		−	90.6251i		−	0.170669i
$532$	15.6169	+	247.861i	0.0293551	+	0.465905i
$533$		−	11.0109i		−	0.0206583i
$534$	−144.660	−	250.559i	−0.270900	−	0.469212i
$535$		0			0
$536$	9.30859	−	16.1229i	0.0173668	−	0.0300801i
$537$	−63.4798	−	109.950i	−0.118212	−	0.204749i
$538$	295.703			0.549635
$539$	105.096	−	250.142i	0.194983	−	0.464085i
$540$		0			0
$541$	−270.888	−	469.192i	−0.500717	−	0.867267i	−1.00000		0.000828025i	$-0.999736\pi$
$541$	−270.888	−	469.192i	−0.500717	−	0.867267i	0.499283	−	0.866439i	$-0.333597\pi$
$542$	−100.453	+	173.989i	−0.185337	+	0.321013i
$543$	−92.1928	−	53.2275i	−0.169784	−	0.0980249i
$544$	−39.8771	+	23.0230i	−0.0733034	+	0.0423217i
$545$		0			0
$546$	3.77837	+	59.9679i	0.00692010	+	0.109831i
$547$			318.491i			0.582251i	0.956685	+	0.291126i	$0.0940297\pi$
$547$			318.491i			0.582251i	−0.956685	+	0.291126i	$0.905970\pi$
$548$	−231.472	+	133.641i	−0.422395	+	0.243870i
$549$	123.029	+	71.0306i	0.224096	+	0.129382i
$550$		0			0
$551$	130.949	−	75.6034i	0.237657	−	0.137211i
$552$	−58.4444			−0.105877
$553$	−477.055	−	717.883i	−0.862667	−	1.29816i
$554$	630.628			1.13832
$555$		0			0
$556$	335.606	+	193.762i	0.603607	+	0.348493i
$557$	499.660	+	288.479i	0.897055	+	0.517915i	0.876244	−	0.481869i	$-0.160042\pi$
$557$	499.660	+	288.479i	0.897055	+	0.517915i	0.0208114	+	0.999783i	$0.493375\pi$
$558$	−16.3643	−	28.3439i	−0.0293268	−	0.0507955i
$559$			151.367i			0.270783i
$560$		0			0
$561$	−78.0672			−0.139157
$562$	−590.342	+	340.834i	−1.05043	+	0.606466i
$563$	−177.985	+	308.279i	−0.316137	+	0.547565i	−0.979678	−	0.200574i	$-0.935719\pi$
$563$	−177.985	+	308.279i	−0.316137	+	0.547565i	0.663542	+	0.748139i	$0.269053\pi$
$564$	−32.4075	+	56.1314i	−0.0574601	+	0.0995238i
$565$		0			0
$566$		−	306.196i		−	0.540983i
$567$	28.0068	−	56.4324i	0.0493948	−	0.0995281i
$568$		−	276.550i		−	0.486883i
$569$	−186.085	−	322.308i	−0.327038	−	0.566447i	0.654885	−	0.755729i	$-0.272717\pi$
$569$	−186.085	−	322.308i	−0.327038	−	0.566447i	−0.981923	+	0.189282i	$0.939384\pi$
$570$		0			0
$571$	82.9355	−	143.649i	0.145246	−	0.251574i	−0.784219	−	0.620485i	$-0.786936\pi$
$571$	82.9355	−	143.649i	0.145246	−	0.251574i	0.929465	+	0.368911i	$0.120269\pi$
$572$	−19.4042	−	33.6091i	−0.0339234	−	0.0587571i
$573$	−623.300			−1.08778
$574$	−17.2155	−	25.9063i	−0.0299922	−	0.0451330i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	8.06639	−	13.9714i	0.0139799	−	0.0242139i	−0.858951	−	0.512058i	$-0.828883\pi$
$577$	8.06639	−	13.9714i	0.0139799	−	0.0242139i	0.872931	+	0.487844i	$0.162217\pi$
$578$	−272.803	−	157.503i	−0.471977	−	0.272496i
$579$	209.617	−	121.023i	0.362033	−	0.209020i
$580$		0			0
$581$	−625.830	+	39.4314i	−1.07716	+	0.0678681i
$582$			159.698i			0.274395i
$583$	13.5128	−	7.80164i	0.0231781	−	0.0133819i
$584$	−149.814	−	86.4950i	−0.256530	−	0.148108i
$585$		0			0
$586$	−469.940	+	271.320i	−0.801945	+	0.463003i
$587$	204.516			0.348409			0.174205	−	0.984709i	$-0.444265\pi$
$587$	204.516			0.348409			0.174205	+	0.984709i	$0.444265\pi$
$588$	102.650	+	135.185i	0.174575	+	0.229906i
$589$	−136.846			−0.232337
$590$		0			0
$591$	−372.514	−	215.071i	−0.630311	−	0.363910i
$592$	97.1799	+	56.1068i	0.164155	+	0.0947751i
$593$	−345.011	−	597.577i	−0.581806	−	1.00772i	−0.995265	−	0.0971952i	$-0.969013\pi$
$593$	−345.011	−	597.577i	−0.581806	−	1.00772i	0.413459	−	0.910523i	$-0.364320\pi$
$594$			40.6899i			0.0685016i
$595$		0			0
$596$	132.013			0.221498
$597$	−183.892	+	106.170i	−0.308026	+	0.177839i
$598$	−29.5616	+	51.2022i	−0.0494341	+	0.0856224i
$599$	−477.775	+	827.531i	−0.797622	+	1.38152i	0.123539	+	0.992340i	$0.460575\pi$
$599$	−477.775	+	827.531i	−0.797622	+	1.38152i	−0.921161	+	0.389182i	$0.872758\pi$
$600$		0			0
$601$			587.954i			0.978293i	0.872202	+	0.489146i	$0.162692\pi$
$601$			587.954i			0.978293i	−0.872202	+	0.489146i	$0.837308\pi$
$602$	236.664	+	356.137i	0.393130	+	0.591590i
$603$			19.7465i			0.0327471i
$604$	34.8820	+	60.4173i	0.0577516	+	0.100029i
$605$		0			0
$606$	−170.971	+	296.131i	−0.282131	+	0.488665i
$607$	259.483	+	449.438i	0.427485	+	0.740425i	0.996649	−	0.0817986i	$-0.0260664\pi$
$607$	259.483	+	449.438i	0.427485	+	0.740425i	−0.569164	+	0.822224i	$0.692733\pi$
$608$	100.350			0.165049
$609$	45.9423	−	92.5714i	0.0754389	−	0.152006i
$610$		0			0
$611$	32.7839	+	56.7834i	0.0536561	+	0.0929351i
$612$	24.4196	−	42.2960i	0.0399013	−	0.0691111i
$613$	110.465	+	63.7771i	0.180204	+	0.104041i	0.587389	−	0.809305i	$-0.300156\pi$
$613$	110.465	+	63.7771i	0.180204	+	0.104041i	−0.407184	+	0.913346i	$0.633489\pi$
$614$	25.8744	−	14.9386i	0.0421407	−	0.0243300i
$615$		0			0
$616$	−98.2022	−	48.7368i	−0.159419	−	0.0791182i
$617$			486.581i			0.788624i	0.918977	+	0.394312i	$0.129017\pi$
$617$			486.581i			0.788624i	−0.918977	+	0.394312i	$0.870983\pi$
$618$	370.137	−	213.699i	0.598927	−	0.345791i
$619$	−370.662	−	214.002i	−0.598808	−	0.345722i	0.169765	−	0.985485i	$-0.445699\pi$
$619$	−370.662	−	214.002i	−0.598808	−	0.345722i	−0.768572	+	0.639763i	$0.779033\pi$
$620$		0			0
$621$	53.6846	−	30.9948i	0.0864486	−	0.0499111i
$622$	−122.522			−0.196980
$623$	−688.620	+	457.609i	−1.10533	+	0.734524i
$624$	24.2787			0.0389082
$625$		0			0
$626$	−3.47589	−	2.00680i	−0.00555254	−	0.00320576i
$627$	147.341	+	85.0671i	0.234993	+	0.135673i
$628$	−53.5006	−	92.6658i	−0.0851921	−	0.147557i
$629$		−	228.351i		−	0.363038i
$630$		0			0
$631$	−64.4987			−0.102217			−0.0511083	−	0.998693i	$-0.516275\pi$
$631$	−64.4987			−0.102217			−0.0511083	+	0.998693i	$0.516275\pi$
$632$	−301.616	+	174.138i	−0.477240	+	0.275535i
$633$	−305.559	+	529.244i	−0.482716	+	0.836088i
$634$	−219.097	+	379.488i	−0.345579	+	0.598561i
$635$		0			0
$636$			9.76149i			0.0153483i
$637$	170.354	−	21.5525i	0.267432	−	0.0338343i
$638$			66.7476i			0.104620i
$639$	146.663	+	254.027i	0.229519	+	0.397538i
$640$		0			0
$641$	−352.662	+	610.829i	−0.550175	+	0.952932i	0.448086	+	0.893990i	$0.352106\pi$
$641$	−352.662	+	610.829i	−0.550175	+	0.952932i	−0.998261	+	0.0589413i	$0.981228\pi$
$642$	74.0681	+	128.290i	0.115371	+	0.199828i
$643$	−1092.83			−1.69958			−0.849788	−	0.527124i	$-0.823270\pi$
$643$	−1092.83			−1.69958			−0.849788	+	0.527124i	$0.823270\pi$
$644$	10.5025	+	166.688i	0.0163082	+	0.258833i
$645$		0			0
$646$	−102.104	−	176.850i	−0.158056	−	0.273761i
$647$	257.546	−	446.083i	0.398062	−	0.689463i	−0.595425	−	0.803411i	$-0.703016\pi$
$647$	257.546	−	446.083i	0.398062	−	0.689463i	0.993487	+	0.113948i	$0.0363496\pi$
$648$	−22.0454	−	12.7279i	−0.0340207	−	0.0196419i
$649$	144.860	−	83.6349i	0.223205	−	0.128867i
$650$		0			0
$651$	−77.8984	+	51.7659i	−0.119660	+	0.0795175i
$652$			411.967i			0.631852i
$653$	681.245	−	393.317i	1.04325	−	0.602323i	0.122501	−	0.992468i	$-0.460909\pi$
$653$	681.245	−	393.317i	1.04325	−	0.602323i	0.920753	+	0.390145i	$0.127575\pi$
$654$	213.853	+	123.468i	0.326993	+	0.188789i
$655$		0			0
$656$	−10.8844	+	6.28413i	−0.0165921	+	0.00957947i
$657$	183.484			0.279275
$658$	165.915	+	82.3420i	0.252151	+	0.125140i
$659$	819.425			1.24344			0.621719	−	0.783241i	$-0.286435\pi$
$659$	819.425			1.24344			0.621719	+	0.783241i	$0.286435\pi$
$660$		0			0
$661$	−889.453	−	513.526i	−1.34562	−	0.776892i	−0.357991	−	0.933725i	$-0.616538\pi$
$661$	−889.453	−	513.526i	−1.34562	−	0.776892i	−0.987625	+	0.156833i	$0.949872\pi$
$662$	−510.216	−	294.573i	−0.770718	−	0.444974i
$663$	−24.7032	−	42.7873i	−0.0372598	−	0.0645358i
$664$			253.375i			0.381589i
$665$		0			0
$666$	−119.021			−0.178710
$667$	88.0639	−	50.8437i	0.132030	−	0.0762275i
$668$	−137.945	+	238.928i	−0.206505	+	0.357677i
$669$	53.4701	−	92.6130i	0.0799254	−	0.138435i
$670$		0			0
$671$			262.207i			0.390771i
$672$	57.1230	−	37.9600i	0.0850045	−	0.0564881i
$673$		−	669.779i		−	0.995213i	−0.867403	−	0.497607i	$-0.834212\pi$
$673$		−	669.779i		−	0.995213i	0.867403	−	0.497607i	$-0.165788\pi$
$674$	109.949	+	190.437i	0.163129	+	0.282548i
$675$		0			0
$676$	−156.720	+	271.446i	−0.231834	+	0.401548i
$677$	454.099	+	786.522i	0.670751	+	1.16178i	0.977691	+	0.210047i	$0.0673616\pi$
$677$	454.099	+	786.522i	0.670751	+	1.16178i	−0.306940	+	0.951729i	$0.599305\pi$
$678$	−181.722			−0.268026
$679$	455.472	−	28.6977i	0.670798	−	0.0422647i
$680$		0			0
$681$	181.452	+	314.285i	0.266450	+	0.461505i
$682$	30.2042	−	52.3153i	0.0442877	−	0.0767086i
$683$	572.733	+	330.668i	0.838555	+	0.484140i	0.856773	−	0.515694i	$-0.172466\pi$
$683$	572.733	+	330.668i	0.838555	+	0.484140i	−0.0182177	+	0.999834i	$0.505799\pi$
$684$	−92.1770	+	53.2184i	−0.134762	+	0.0778047i
$685$		0			0
$686$	367.112	−	317.059i	0.535149	−	0.462185i
$687$			186.714i			0.271781i
$688$	149.630	−	86.3887i	0.217485	−	0.125565i
$689$	8.55188	+	4.93743i	0.0124120	+	0.00716608i
$690$		0			0
$691$	−239.610	+	138.339i	−0.346759	+	0.200201i	−0.663257	−	0.748392i	$-0.730826\pi$
$691$	−239.610	+	138.339i	−0.346759	+	0.200201i	0.316498	+	0.948593i	$0.397493\pi$
$692$	−441.133			−0.637475
$693$	116.051	−	7.31198i	0.167462	−	0.0105512i
$694$	724.794			1.04437
$695$		0			0
$696$	−36.1632	−	20.8788i	−0.0519586	−	0.0299983i
$697$	22.1495	+	12.7880i	0.0317783	+	0.0183472i
$698$	−190.343	−	329.683i	−0.272697	−	0.472326i
$699$			566.115i			0.809892i
$700$		0			0
$701$	−415.967			−0.593391			−0.296696	−	0.954972i	$-0.595885\pi$
$701$	−415.967			−0.593391			−0.296696	+	0.954972i	$0.595885\pi$
$702$	−22.3015	+	12.8758i	−0.0317685	+	0.0183415i
$703$	−248.827	+	430.980i	−0.353950	+	0.613059i
$704$	−22.1488	+	38.3629i	−0.0314614	+	0.0544927i
$705$		0			0
$706$			829.382i			1.17476i
$707$	875.313	+	434.409i	1.23807	+	0.614440i
$708$			104.645i			0.147804i
$709$	136.620	+	236.632i	0.192693	+	0.333755i	0.946142	−	0.323752i	$-0.104944\pi$
$709$	136.620	+	236.632i	0.192693	+	0.333755i	−0.753449	+	0.657507i	$0.771611\pi$
$710$		0			0
$711$	184.701	−	319.912i	0.259776	−	0.449946i
$712$	167.039	+	289.321i	0.234606	+	0.406349i
$713$	−92.0300			−0.129074
$714$	−125.020	−	62.0462i	−0.175098	−	0.0868994i
$715$		0			0
$716$	73.3002	+	126.960i	0.102375	+	0.177318i
$717$	−7.96845	+	13.8018i	−0.0111136	+	0.0192493i
$718$	−108.811	−	62.8223i	−0.151548	−	0.0874962i
$719$	−361.463	+	208.691i	−0.502731	+	0.290252i	−0.729840	−	0.683617i	$-0.760406\pi$
$719$	−361.463	+	208.691i	−0.502731	+	0.290252i	0.227110	+	0.973869i	$0.427072\pi$
$720$		0			0
$721$	−676.000	−	1017.26i	−0.937587	−	1.41090i
$722$		−	65.4934i		−	0.0907111i
$723$	−481.779	+	278.156i	−0.666362	+	0.384724i
$724$	106.455	+	61.4619i	0.147037	+	0.0848921i
$725$		0			0
$726$	191.639	−	110.643i	0.263965	−	0.152400i
$727$	−357.267			−0.491426			−0.245713	−	0.969343i	$-0.579022\pi$
$727$	−357.267			−0.491426			−0.245713	+	0.969343i	$0.579022\pi$
$728$	−4.36289	−	69.2450i	−0.00599298	−	0.0951167i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−304.491	−	175.798i	−0.416541	−	0.240490i
$732$	−142.061	−	82.0191i	−0.194073	−	0.112048i
$733$	215.521	+	373.293i	0.294026	+	0.509267i	0.974758	−	0.223265i	$-0.0716716\pi$
$733$	215.521	+	373.293i	0.294026	+	0.509267i	−0.680732	+	0.732532i	$0.738338\pi$
$734$			998.488i			1.36034i
$735$		0			0
$736$	67.4858			0.0916926
$737$	−31.5638	+	18.2234i	−0.0428274	+	0.0247264i
$738$	6.66533	−	11.5447i	0.00903161	−	0.0156432i
$739$	159.512	−	276.282i	0.215848	−	0.373860i	−0.737687	−	0.675143i	$-0.764082\pi$
$739$	159.512	−	276.282i	0.215848	−	0.373860i	0.953535	+	0.301284i	$0.0974151\pi$
$740$		0			0
$741$			107.673i			0.145308i
$742$	27.8406	−	1.75414i	0.0375210	−	0.00236407i
$743$			1303.33i			1.75414i	0.480360	+	0.877072i	$0.340506\pi$
$743$			1303.33i			1.75414i	−0.480360	+	0.877072i	$0.659494\pi$
$744$	18.8959	+	32.7287i	0.0253977	+	0.0439902i
$745$		0			0
$746$	36.2337	−	62.7585i	0.0485706	−	0.0841267i
$747$	−134.372	−	232.740i	−0.179883	−	0.311566i
$748$	90.1442			0.120514
$749$	352.583	−	234.302i	0.470738	−	0.312820i
$750$		0			0
$751$	−614.473	−	1064.30i	−0.818206	−	1.41717i	−0.907003	−	0.421124i	$-0.861636\pi$
$751$	−614.473	−	1064.30i	−0.818206	−	1.41717i	0.0887971	−	0.996050i	$-0.471698\pi$
$752$	37.4210	−	64.8150i	0.0497619	−	0.0861901i
$753$	28.8591	+	16.6618i	0.0383255	+	0.0221273i
$754$	−36.5832	+	21.1213i	−0.0485188	+	0.0280124i
$755$		0			0
$756$	−32.3395	+	65.1625i	−0.0427771	+	0.0861938i
$757$			1206.22i			1.59342i	0.604359	+	0.796712i	$0.293429\pi$
$757$			1206.22i			1.59342i	−0.604359	+	0.796712i	$0.706571\pi$
$758$	−238.487	+	137.691i	−0.314627	+	0.181650i
$759$	99.0874	+	57.2082i	0.130550	+	0.0753731i
$760$		0			0
$761$	−204.456	+	118.043i	−0.268667	+	0.155115i	−0.628282	−	0.777986i	$-0.716242\pi$
$761$	−204.456	+	118.043i	−0.268667	+	0.155115i	0.359614	+	0.933101i	$0.382908\pi$
$762$	370.101			0.485697
$763$	313.712	−	632.114i	0.411156	−	0.828459i
$764$	719.725			0.942048
$765$		0			0
$766$	−643.088	−	371.287i	−0.839540	−	0.484709i
$767$	91.6777	+	52.9301i	0.119528	+	0.0690093i
$768$	−13.8564	−	24.0000i	−0.0180422	−	0.0312500i
$769$		−	1341.44i		−	1.74440i	−0.489149	−	0.872200i	$-0.662693\pi$
$769$		−	1341.44i		−	1.74440i	0.489149	−	0.872200i	$-0.337307\pi$
$770$		0			0
$771$	−224.165			−0.290746
$772$	−242.045	+	139.745i	−0.313530	+	0.181017i
$773$	−90.0279	+	155.933i	−0.116466	+	0.201724i	−0.918365	−	0.395735i	$-0.870490\pi$
$773$	−90.0279	+	155.933i	−0.116466	+	0.201724i	0.801899	+	0.597460i	$0.203823\pi$
$774$	−91.6290	+	158.706i	−0.118384	+	0.205047i
$775$		0			0
$776$		−	184.403i		−	0.237633i
$777$	21.3880	+	339.456i	0.0275264	+	0.436881i
$778$		−	570.677i		−	0.733518i
$779$	−27.8693	−	48.2711i	−0.0357758	−	0.0619654i
$780$		0			0
$781$	−270.700	+	468.866i	−0.346607	+	0.600341i
$782$	−68.6657	−	118.932i	−0.0878078	−	0.152087i
$783$	44.2907			0.0565654
$784$	−118.530	−	156.098i	−0.151186	−	0.199105i
$785$		0			0
$786$	264.203	+	457.614i	0.336137	+	0.582206i
$787$	584.386	−	1012.19i	0.742549	−	1.28613i	−0.208783	−	0.977962i	$-0.566950\pi$
$787$	584.386	−	1012.19i	0.742549	−	1.28613i	0.951331	−	0.308170i	$-0.0997166\pi$
$788$	430.142	+	248.343i	0.545866	+	0.315156i
$789$	−250.387	+	144.561i	−0.317348	+	0.183221i
$790$		0			0
$791$	32.6554	+	518.285i	0.0412837	+	0.655228i
$792$		−	46.9847i		−	0.0593241i
$793$	−143.711	+	82.9717i	−0.181225	+	0.104630i
$794$	−197.419	−	113.980i	−0.248639	−	0.143552i
$795$		0			0
$796$	212.340	−	122.595i	0.266759	−	0.154013i
$797$	−1242.38			−1.55883			−0.779413	−	0.626510i	$-0.784483\pi$
$797$	−1242.38			−1.55883			−0.779413	+	0.626510i	$0.784483\pi$
$798$	168.348	+	253.333i	0.210962	+	0.317460i
$799$	−152.301			−0.190614
$800$		0			0
$801$	−306.871	−	177.172i	−0.383110	−	0.221189i
$802$	−520.531	−	300.529i	−0.649041	−	0.374724i
$803$	169.331	+	293.290i	0.210873	+	0.365243i
$804$		−	22.8013i		−	0.0283598i
$805$		0			0
$806$	38.2308			0.0474327
$807$	313.641	−	181.081i	0.388650	−	0.224387i
$808$	197.421	−	341.942i	0.244332	−	0.423196i
$809$	−44.8275	+	77.6435i	−0.0554110	+	0.0959747i	−0.892400	−	0.451244i	$-0.850980\pi$
$809$	−44.8275	+	77.6435i	−0.0554110	+	0.0959747i	0.836989	+	0.547219i	$0.184314\pi$
$810$		0			0
$811$		−	234.127i		−	0.288689i	−0.989527	−	0.144345i	$-0.953893\pi$
$811$		−	234.127i		−	0.288689i	0.989527	−	0.144345i	$-0.0461074\pi$
$812$	−53.0496	+	106.892i	−0.0653320	+	0.131641i
$813$			246.058i			0.302654i
$814$	−109.840	−	190.249i	−0.134939	−	0.233721i
$815$		0			0
$816$	−28.1973	+	48.8392i	−0.0345556	+	0.0598520i
$817$	383.123	+	663.588i	0.468938	+	0.812225i
$818$	610.095			0.745837
$819$	40.7303	+	61.2918i	0.0497317	+	0.0748374i
$820$		0			0
$821$	−331.873	−	574.821i	−0.404231	−	0.700148i	0.590001	−	0.807403i	$-0.299127\pi$
$821$	−331.873	−	574.821i	−0.404231	−	0.700148i	−0.994232	+	0.107255i	$0.965794\pi$
$822$	−163.676	+	283.494i	−0.199119	+	0.344884i
$823$	745.037	+	430.147i	0.905269	+	0.522657i	0.878906	−	0.476995i	$-0.158274\pi$
$823$	745.037	+	430.147i	0.905269	+	0.522657i	0.0263632	+	0.999652i	$0.491607\pi$
$824$	−427.398	+	246.758i	−0.518686	+	0.299464i
$825$		0			0
$826$	298.456	−	18.8047i	0.361327	−	0.0227660i
$827$			703.661i			0.850860i	0.904991	+	0.425430i	$0.139877\pi$
$827$			703.661i			0.850860i	−0.904991	+	0.425430i	$0.860123\pi$
$828$	−61.9896	+	35.7897i	−0.0748667	+	0.0432243i
$829$	−1282.06	−	740.196i	−1.54651	−	0.892878i	−0.998404	−	0.0564693i	$-0.982016\pi$
$829$	−1282.06	−	740.196i	−1.54651	−	0.892878i	−0.548106	−	0.836409i	$-0.684651\pi$
$830$		0			0
$831$	668.882	−	386.179i	0.804912	−	0.464716i
$832$	−28.0347			−0.0336955
$833$	−154.495	+	367.717i	−0.185468	+	0.441437i
$834$	474.618			0.569086
$835$		0			0
$836$	−170.134	−	98.2271i	−0.203510	−	0.117496i
$837$	−34.7140	−	20.0422i	−0.0414743	−	0.0239452i
$838$	413.949	+	716.980i	0.493972	+	0.855585i
$839$		−	1377.82i		−	1.64222i	−0.570769	−	0.821111i	$-0.693355\pi$
$839$		−	1377.82i		−	1.64222i	0.570769	−	0.821111i	$-0.306645\pi$
$840$		0			0
$841$	−768.346			−0.913610
$842$	−490.225	+	283.032i	−0.582215	+	0.336142i
$843$	−417.435	+	723.018i	−0.495177	+	0.857672i
$844$	352.829	−	611.118i	0.418044	−	0.724073i
$845$		0			0
$846$			79.3818i			0.0938319i
$847$	−350.000	−	526.687i	−0.413223	−	0.621827i
$848$		−	11.2716i		−	0.0132920i
$849$	−187.506	−	324.770i	−0.220855	−	0.382533i
$850$		0			0
$851$	−167.337	+	289.837i	−0.196636	+	0.340584i
$852$	−169.351	−	293.325i	−0.198769	−	0.344278i
$853$	383.511			0.449602			0.224801	−	0.974405i	$-0.427827\pi$
$853$	383.511			0.449602			0.224801	+	0.974405i	$0.427827\pi$
$854$	−208.397	+	419.909i	−0.244024	+	0.491697i
$855$		0			0
$856$	−85.5265	−	148.136i	−0.0999141	−	0.173056i
$857$	164.125	−	284.273i	0.191512	−	0.331708i	−0.754240	−	0.656599i	$-0.771994\pi$
$857$	164.125	−	284.273i	0.191512	−	0.331708i	0.945751	+	0.324891i	$0.105328\pi$
$858$	−41.1625	−	23.7652i	−0.0479750	−	0.0276984i
$859$	168.842	−	97.4811i	0.196557	−	0.113482i	−0.398492	−	0.917172i	$-0.630466\pi$
$859$	168.842	−	97.4811i	0.196557	−	0.113482i	0.595048	+	0.803690i	$0.297133\pi$
$860$		0			0
$861$	−34.1242	−	16.9355i	−0.0396332	−	0.0196696i
$862$		−	558.985i		−	0.648474i
$863$	−463.984	+	267.881i	−0.537641	+	0.310407i	−0.744122	−	0.668043i	$-0.767132\pi$
$863$	−463.984	+	267.881i	−0.537641	+	0.310407i	0.206481	+	0.978451i	$0.433799\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$		0			0
$866$	−2.92986	+	1.69156i	−0.00338321	+	0.00195330i
$867$	−385.801			−0.444984
$868$	89.9493	−	59.7741i	0.103628	−	0.0688641i
$869$	681.818			0.784601
$870$		0			0
$871$	−19.9758	−	11.5331i	−0.0229344	−	0.0132412i
$872$	−246.936	−	142.569i	−0.283184	−	0.163496i
$873$	97.7947	+	169.385i	0.112021	+	0.194027i
$874$			299.291i			0.342438i
$875$		0			0
$876$	−211.869			−0.241859
$877$	−1045.48	+	603.606i	−1.19210	+	0.688262i	−0.958784	−	0.284138i	$-0.908293\pi$
$877$	−1045.48	+	603.606i	−1.19210	+	0.688262i	−0.233321	+	0.972400i	$0.574959\pi$
$878$	−285.989	+	495.348i	−0.325728	+	0.564177i
$879$	−332.298	+	575.557i	−0.378041	+	0.654786i
$880$		0			0
$881$			629.491i			0.714519i	0.934005	+	0.357259i	$0.116289\pi$
$881$			629.491i			0.714519i	−0.934005	+	0.357259i	$0.883711\pi$
$882$	191.660	+	80.5253i	0.217302	+	0.0912985i
$883$			177.196i			0.200675i	0.994953	+	0.100337i	$0.0319922\pi$
$883$			177.196i			0.200675i	−0.994953	+	0.100337i	$0.968008\pi$
$884$	28.5248	+	49.4065i	0.0322679	+	0.0558897i
$885$		0			0
$886$	−206.483	+	357.639i	−0.233051	+	0.403655i
$887$	−636.205	−	1101.94i	−0.717255	−	1.24232i	−0.962083	−	0.272755i	$-0.912065\pi$
$887$	−636.205	−	1101.94i	−0.717255	−	1.24232i	0.244829	−	0.969566i	$-0.421268\pi$
$888$	137.433			0.154767
$889$	−66.5072	−	1055.56i	−0.0748112	−	1.18736i
$890$		0			0
$891$	24.9174	+	43.1582i	0.0279657	+	0.0484379i
$892$	−61.7420	+	106.940i	−0.0692175	+	0.119888i
$893$	287.446	+	165.957i	0.321888	+	0.185842i
$894$	140.021	−	80.8410i	0.156623	−	0.0904261i
$895$		0			0
$896$	−65.9600	+	43.8324i	−0.0736161	+	0.0489201i
$897$			72.4108i			0.0807255i
$898$	153.926	−	88.8693i	0.171410	−	0.0989636i
$899$	−56.9447	−	32.8770i	−0.0633423	−	0.0365707i
$900$		0			0
$901$	−19.8643	+	11.4687i	−0.0220470	+	0.0127288i
$902$	24.6048			0.0272781
$903$	469.109	+	232.814i	0.519500	+	0.257823i
$904$	209.834			0.232118
$905$		0			0
$906$	73.9958	+	42.7215i	0.0816731	+	0.0471540i
$907$	155.255	+	89.6364i	0.171174	+	0.0988273i	0.583139	−	0.812372i	$-0.301824\pi$
$907$	155.255	+	89.6364i	0.171174	+	0.0988273i	−0.411965	+	0.911200i	$0.635158\pi$
$908$	−209.523	−	362.905i	−0.230752	−	0.399675i
$909$			418.792i			0.460718i
$910$		0			0
$911$	684.893			0.751803			0.375902	−	0.926660i	$-0.377333\pi$
$911$	684.893			0.751803			0.375902	+	0.926660i	$0.377333\pi$
$912$	106.437	−	61.4514i	0.116707	−	0.0673809i
$913$	248.015	−	429.575i	0.271649	−	0.470510i
$914$	60.8133	−	105.332i	0.0665353	−	0.115243i
$915$		0			0
$916$		−	215.598i		−	0.235369i
$917$	1257.67	−	835.763i	1.37151	−	0.911410i
$918$		−	59.8156i		−	0.0651586i
$919$	470.376	+	814.715i	0.511835	+	0.886523i	0.999906	+	0.0137197i	$0.00436726\pi$
$919$	470.376	+	814.715i	0.511835	+	0.886523i	−0.488071	+	0.872804i	$0.662299\pi$
$920$		0			0
$921$	18.2960	−	31.6896i	0.0198653	−	0.0344078i
$922$	92.9481	+	160.991i	0.100811	+	0.174611i
$923$	−342.637			−0.371221
$924$	−134.004	+	8.44315i	−0.145026	+	0.00913761i
$925$		0			0
$926$	−52.3169	−	90.6156i	−0.0564978	−	0.0978570i
$927$	261.726	−	453.324i	0.282337	−	0.489022i
$928$	41.7576	+	24.1088i	0.0449975	+	0.0259793i
$929$	−5.55322	+	3.20616i	−0.00597764	+	0.00345119i	−0.502986	−	0.864295i	$-0.667765\pi$
$929$	−5.55322	+	3.20616i	−0.00597764	+	0.00345119i	0.497008	+	0.867746i	$0.334432\pi$
$930$		0			0
$931$	692.275	−	525.665i	0.743582	−	0.564624i
$932$		−	653.693i		−	0.701387i
$933$	−129.954	+	75.0288i	−0.139286	+	0.0804167i
$934$	−547.346	−	316.010i	−0.586023	−	0.338341i
$935$		0			0
$936$	25.7515	−	14.8676i	0.0275123	−	0.0158842i
$937$	−867.253			−0.925564			−0.462782	−	0.886472i	$-0.653149\pi$
$937$	−867.253			−0.925564			−0.462782	+	0.886472i	$0.653149\pi$
$938$	−65.0312	+	4.09739i	−0.0693296	+	0.00436822i
$939$	−4.91565			−0.00523498
$940$		0			0
$941$	−500.609	−	289.026i	−0.531996	−	0.307148i	0.209833	−	0.977737i	$-0.432708\pi$
$941$	−500.609	−	289.026i	−0.531996	−	0.307148i	−0.741829	+	0.670589i	$0.766041\pi$
$942$	−113.492	−	65.5246i	−0.120480	−	0.0695590i
$943$	−18.7423	−	32.4626i	−0.0198752	−	0.0344248i
$944$		−	120.833i		−	0.128002i
$945$		0			0
$946$	−338.246			−0.357553
$947$	648.272	−	374.280i	0.684553	−	0.395227i	−0.117015	−	0.993130i	$-0.537333\pi$
$947$	648.272	−	374.280i	0.684553	−	0.395227i	0.801568	+	0.597903i	$0.203999\pi$
$948$	−213.274	+	369.402i	−0.224973	+	0.389665i
$949$	−107.165	+	185.615i	−0.112924	+	0.195590i
$950$		0			0
$951$			536.677i			0.564329i
$952$	144.361	+	71.6447i	0.151639	+	0.0752571i
$953$		−	21.6304i		−	0.0226972i	−0.999936	−	0.0113486i	$-0.996388\pi$
$953$		−	21.6304i		−	0.0226972i	0.999936	−	0.0113486i	$-0.00361244\pi$
$954$	5.97767	+	10.3536i	0.00626590	+	0.0108529i
$955$		0			0
$956$	9.20117	−	15.9369i	0.00962466	−	0.0166704i
$957$	40.8744	+	70.7965i	0.0427110	+	0.0739776i
$958$	839.062			0.875847
$959$	837.962	+	415.872i	0.873787	+	0.433652i
$960$		0			0
$961$	−450.745	−	780.714i	−0.469038	−	0.812397i
$962$	69.5147	−	120.403i	0.0722606	−	0.125159i
$963$	157.122	+	90.7146i	0.163159	+	0.0941999i
$964$	556.311	−	321.186i	0.577086	−	0.333181i
$965$		0			0
$966$	113.215	+	170.368i	0.117200	+	0.176365i
$967$			452.988i			0.468447i	0.972183	+	0.234224i	$0.0752548\pi$
$967$			452.988i			0.468447i	−0.972183	+	0.234224i	$0.924745\pi$
$968$	−221.285	+	127.759i	−0.228601	+	0.131983i
$969$	−216.596	−	125.052i	−0.223525	−	0.129052i
$970$		0			0
$971$	1137.95	−	656.994i	1.17193	−	0.676616i	0.217798	−	0.975994i	$-0.430112\pi$
$971$	1137.95	−	656.994i	1.17193	−	0.676616i	0.954135	+	0.299378i	$0.0967791\pi$
$972$	−31.1769			−0.0320750
$973$	−85.2889	−	1353.65i	−0.0876556	−	1.39121i
$974$	1159.01			1.18995
$975$		0			0
$976$	164.038	+	94.7075i	0.168072	+	0.0970364i
$977$	−1019.58	−	588.653i	−1.04358	−	0.602511i	−0.122734	−	0.992440i	$-0.539166\pi$
$977$	−1019.58	−	588.653i	−1.04358	−	0.602511i	−0.920845	+	0.389929i	$0.872500\pi$
$978$	252.278	+	436.957i	0.257952	+	0.446787i
$979$		−	654.025i		−	0.668054i
$980$		0			0
$981$	302.434			0.308292
$982$	−679.395	+	392.249i	−0.691848	+	0.399439i
$983$	−401.275	+	695.029i	−0.408215	+	0.707049i	−0.994690	−	0.102918i	$-0.967182\pi$
$983$	−401.275	+	695.029i	−0.408215	+	0.707049i	0.586475	+	0.809967i	$0.300515\pi$
$984$	−7.69646	+	13.3307i	−0.00782161	+	0.0135474i
$985$		0			0
$986$		−	98.1212i		−	0.0995144i
$987$	226.404	−	14.2649i	0.229386	−	0.0144528i
$988$		−	124.330i		−	0.125840i
$989$	257.652	+	446.267i	0.260518	+	0.451230i
$990$		0			0
$991$	91.7946	−	158.993i	0.0926283	−	0.160437i	−0.815988	−	0.578069i	$-0.803807\pi$
$991$	91.7946	−	158.993i	0.0926283	−	0.160437i	0.908616	+	0.417632i	$0.137140\pi$
$992$	−21.8191	−	37.7918i	−0.0219951	−	0.0380966i
$993$	−721.554			−0.726640
$994$	−806.155	+	535.715i	−0.811021	+	0.538948i
$995$		0			0
$996$	155.160	+	268.745i	0.155783	+	0.269824i
$997$	466.550	−	808.088i	0.467953	−	0.810519i	−0.531376	−	0.847136i	$-0.678325\pi$
$997$	466.550	−	808.088i	0.467953	−	0.810519i	0.999329	+	0.0366170i	$0.0116582\pi$
$998$	−777.453	−	448.862i	−0.779011	−	0.449762i
$999$	−126.240	+	72.8849i	−0.126367	+	0.0729579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.b.199.1		16
5.2	odd	4		1050.3.p.d.451.1	yes	8
5.3	odd	4		1050.3.p.c.451.4	✓	8
5.4	even	2	inner	1050.3.q.b.199.8		16
7.5	odd	6	inner	1050.3.q.b.649.8		16
35.12	even	12		1050.3.p.d.901.1	yes	8
35.19	odd	6	inner	1050.3.q.b.649.1		16
35.33	even	12		1050.3.p.c.901.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.c.451.4	✓	8	5.3	odd	4
1050.3.p.c.901.4	yes	8	35.33	even	12
1050.3.p.d.451.1	yes	8	5.2	odd	4
1050.3.p.d.901.1	yes	8	35.12	even	12
1050.3.q.b.199.1		16	1.1	even	1	trivial
1050.3.q.b.199.8		16	5.4	even	2	inner
1050.3.q.b.649.1		16	35.19	odd	6	inner
1050.3.q.b.649.8		16	7.5	odd	6	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.98615 + 0.440173i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.98615 + 0.440173i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(2.76860 - 4.79536i) q^{11} +(1.73205 + 3.00000i) q^{12} +3.50434 q^{13} +(8.24500 - 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-4.06994 + 7.04933i) q^{17} +(3.67423 + 2.12132i) q^{18} +(15.3628 - 8.86974i) q^{19} +(5.38992 - 10.8604i) q^{21} +7.83078i q^{22} +(10.3316 - 5.96495i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-4.29192 + 2.47794i) q^{26} +5.19615 q^{27} +(-6.22374 + 12.5405i) q^{28} +8.52374 q^{29} +(-6.68072 - 3.85711i) q^{31} +(4.89898 + 2.82843i) q^{32} +(4.79536 + 8.30580i) q^{33} -11.5115i q^{34} -6.00000 q^{36} +(-24.2950 + 14.0267i) q^{37} +(-12.5437 + 21.7263i) q^{38} +(-3.03484 + 5.25650i) q^{39} -3.14207i q^{41} +(1.07820 + 17.1125i) q^{42} +43.1943i q^{43} +(-5.53720 - 9.59071i) q^{44} +(-8.43572 + 14.6111i) q^{46} +(9.35524 + 16.2037i) q^{47} +6.92820 q^{48} +(48.6125 - 6.15023i) q^{49} +(-7.04933 - 12.2098i) q^{51} +(3.50434 - 6.06969i) q^{52} +(2.44037 + 1.40895i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} +30.7257i q^{57} +(-10.4394 + 6.02720i) q^{58} +(26.1612 + 15.1042i) q^{59} +(-41.0095 + 23.6769i) q^{61} +10.9096 q^{62} +(11.6228 + 17.4903i) q^{63} -8.00000 q^{64} +(-11.7462 - 6.78166i) q^{66} +(-5.70032 - 3.29108i) q^{67} +(8.13987 + 14.0987i) q^{68} +20.6632i q^{69} -97.7751 q^{71} +(7.34847 - 4.24264i) q^{72} +(-30.5806 + 52.9672i) q^{73} +(19.8368 - 34.3583i) q^{74} -35.4790i q^{76} +(-17.2311 + 34.7197i) q^{77} -8.58383i q^{78} +(61.5670 + 106.637i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(2.22178 + 3.84823i) q^{82} +89.5815 q^{83} +(-13.4209 - 20.1960i) q^{84} +(-30.5430 - 52.9020i) q^{86} +(-7.38178 + 12.7856i) q^{87} +(13.5633 + 7.83078i) q^{88} +(102.290 - 59.0573i) q^{89} +(-24.4818 + 1.54251i) q^{91} -23.8598i q^{92} +(11.5713 - 6.68072i) q^{93} +(-22.9156 - 13.2303i) q^{94} +(-8.48528 + 4.89898i) q^{96} -65.1965 q^{97} +(-55.1890 + 41.9067i) q^{98} -16.6116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 16 * q + 16 * q^4 - 24 * q^9	\( 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 32 q^{14} - 32 q^{16} - 144 q^{19} - 144 q^{26} + 48 q^{29} + 192 q^{31} - 96 q^{36} + 24 q^{39} + 16 q^{44} + 64 q^{46} + 528 q^{49} + 48 q^{51} + 80 q^{56} - 624 q^{59} - 408 q^{61} - 128 q^{64} - 72 q^{66} - 128 q^{71} + 32 q^{74} + 288 q^{79} - 72 q^{81} + 352 q^{86} + 672 q^{89} - 592 q^{91} - 72 q^{94} + 48 q^{99}+O(q^{100}) \) 16 * q + 16 * q^4 - 24 * q^9 - 8 * q^11 + 32 * q^14 - 32 * q^16 - 144 * q^19 - 144 * q^26 + 48 * q^29 + 192 * q^31 - 96 * q^36 + 24 * q^39 + 16 * q^44 + 64 * q^46 + 528 * q^49 + 48 * q^51 + 80 * q^56 - 624 * q^59 - 408 * q^61 - 128 * q^64 - 72 * q^66 - 128 * q^71 + 32 * q^74 + 288 * q^79 - 72 * q^81 + 352 * q^86 + 672 * q^89 - 592 * q^91 - 72 * q^94 + 48 * q^99

Introduction

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