LMFDB - Embedded newform 1050.3.q.b.199.8

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			199.8
Root			$-0.596002 - 2.22431i$ of defining polynomial
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.b.649.8

$q$-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	$-0.543033\pi$
$13$	−3.50434			−0.269564			−0.134782	+	0.990875i	$0.543033\pi$
$14$	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	−0.721137	−	0.692793i	$-0.756380\pi$
$17$	4.06994	−	7.04933i	0.239408	−	0.414667i	0.960545	+	0.278126i	$0.0897133\pi$
$18$	−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	−0.707492	−	0.706721i	$-0.750174\pi$
$23$	−10.3316	+	5.96495i	−0.449200	+	0.259346i	0.258292	+	0.966067i	$0.416840\pi$
$24$	−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	−0.134367	−	0.990932i	$-0.542900\pi$
$37$	24.2950	−	14.0267i	0.656621	−	0.379100i	0.790988	+	0.611831i	$0.209567\pi$
$38$	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	$-0.832502\pi$
$43$		−	43.1943i		−	1.00452i	0.864717	−	0.502260i	$-0.167498\pi$
$44$	−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	0.749172	−	0.662375i	$-0.230452\pi$
$47$	−9.35524	−	16.2037i	−0.199048	−	0.344761i	−0.948220	+	0.317615i	$0.897118\pi$
$48$	−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	0.476801	−	0.879011i	$-0.341796\pi$
$53$	−2.44037	−	1.40895i	−0.0460448	−	0.0265840i	−0.522846	+	0.852427i	$0.675130\pi$
$54$	−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	0.541936	−	0.840420i	$-0.317691\pi$
$67$	5.70032	+	3.29108i	0.0850794	+	0.0491206i	−0.456857	+	0.889540i	$0.651025\pi$
$68$	−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	−0.576918	−	0.816802i	$-0.695745\pi$
$73$	30.5806	−	52.9672i	0.418913	−	0.725578i	0.995830	+	0.0912244i	$0.0290781\pi$
$74$	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	$-0.681443\pi$
$83$	−89.5815			−1.07930			−0.539648	+	0.841891i	$0.681443\pi$
$84$	−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	$-0.390904\pi$
$97$	65.1965			0.672128			0.336064	+	0.941839i	$0.390904\pi$
$98$	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	$-0.845066\pi$
$103$	−87.2421	−	151.108i	−0.847011	−	1.46707i	0.0368520	−	0.999321i	$-0.488267\pi$
$104$			9.91176i			0.0953054i
$105$		0			0
$106$	−3.98511			−0.0375954
$107$	52.3741	−	30.2382i	0.489477	−	0.282600i	−0.234880	−	0.972024i	$-0.575470\pi$
$107$	52.3741	−	30.2382i	0.489477	−	0.282600i	0.724358	+	0.689424i	$0.242136\pi$
$108$	−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	$0.106463\pi$
$113$			74.1876i			0.656527i	−0.944586	+	0.328264i	$0.893537\pi$
$114$	−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	$-0.797209\pi$
$127$		−	151.093i		−	1.18971i	0.803833	−	0.594855i	$-0.202791\pi$
$128$	−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	0.858889	−	0.512161i	$-0.171155\pi$
$137$	115.736	+	66.8203i	0.844789	+	0.487739i	−0.0141000	+	0.999901i	$0.504488\pi$
$138$	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	−0.938554	−	0.345132i	$-0.887834\pi$
$157$	−26.7503	+	46.3329i	−0.170384	+	0.295114i	0.768170	+	0.640246i	$0.221168\pi$
$158$	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	0.159655	−	0.987173i	$-0.448962\pi$
$163$	178.387	−	102.992i	1.09440	−	0.631852i	0.934744	+	0.355321i	$0.115628\pi$
$164$	−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	$-0.364477\pi$
$167$	137.945			0.826020			0.413010	+	0.910727i	$0.364477\pi$
$168$	−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	$0.0533544\pi$
$173$	110.283	+	191.016i	0.637475	+	1.10414i	−0.348510	+	0.937305i	$0.613312\pi$
$174$		−	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	0.779613	−	0.626262i	$-0.215416\pi$
$193$	121.023	+	69.8724i	0.627060	+	0.362033i	−0.152552	+	0.988295i	$0.548749\pi$
$194$	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	$-0.782927\pi$
$197$		−	248.343i		−	1.26062i	0.776342	−	0.630311i	$-0.217073\pi$
$198$	−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	$-0.455793\pi$
$223$	61.7420			0.276870			0.138435	+	0.990372i	$0.455793\pi$
$224$	−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	−0.999036	−	0.0438940i	$-0.986024\pi$
$227$	−104.762	+	181.452i	−0.461505	+	0.799350i	0.537531	+	0.843244i	$0.319357\pi$
$228$	−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	−0.963809	−	0.266592i	$-0.914102\pi$
$233$	−283.057	+	163.423i	−1.21484	+	0.701387i	−0.251029	+	0.967980i	$0.580769\pi$
$234$	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	0.712226	−	0.701950i	$-0.247687\pi$
$257$	−64.7109	−	112.083i	−0.251793	−	0.436119i	−0.964020	+	0.265831i	$0.914354\pi$
$258$	−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	0.199323	−	0.979934i	$-0.436126\pi$
$263$	−144.561	−	83.4625i	−0.549663	−	0.317348i	−0.748986	+	0.662586i	$0.769459\pi$
$264$	−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	0.993771	−	0.111438i	$-0.0355458\pi$
$277$	386.179	+	222.961i	1.39415	+	0.804912i	0.400377	+	0.916350i	$0.368879\pi$
$278$	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	−0.608891	−	0.793254i	$-0.708385\pi$
$283$	108.257	−	187.506i	0.382533	−	0.662566i	0.991424	+	0.130688i	$0.0417185\pi$
$284$	−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	$-0.727241\pi$
$293$	−383.704			−1.30957			−0.654786	+	0.755815i	$0.727241\pi$
$294$	−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	$-0.489046\pi$
$307$	21.1264			0.0688155			0.0344078	+	0.999408i	$0.489046\pi$
$308$	−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	0.863750	−	0.503921i	$-0.168110\pi$
$313$	−1.41903	−	2.45782i	−0.00453363	−	0.00785247i	−0.868283	+	0.496069i	$0.834776\pi$
$314$			75.6613i			0.240960i
$315$		0			0
$316$	246.268			0.779329
$317$	−268.338	+	154.925i	−0.846493	+	0.488723i	−0.859466	−	0.511193i	$-0.829204\pi$
$317$	−268.338	+	154.925i	−0.846493	+	0.488723i	0.0129730	+	0.999916i	$0.495870\pi$
$318$	−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	$0.0741014\pi$
$337$			155.491i			0.461399i	−0.973025	+	0.230699i	$0.925899\pi$
$338$	−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	0.976681	−	0.214697i	$-0.0688763\pi$
$347$	443.844	+	256.253i	1.27909	+	0.738482i	0.302408	+	0.953179i	$0.402210\pi$
$348$	−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	$0.478716\pi$
$353$	−293.231	+	507.890i	−0.830682	+	1.43878i	−0.897498	+	0.441018i	$0.854618\pi$
$354$	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	$0.578522\pi$
$367$	−353.019	+	611.446i	−0.961904	+	1.66607i	−0.717713	+	0.696339i	$0.754811\pi$
$368$	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	−0.439332	−	0.898325i	$-0.644785\pi$
$373$	44.3770	−	25.6211i	0.118973	−	0.0686892i	0.558306	+	0.829635i	$0.311452\pi$
$374$	−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	$-0.926258\pi$
$383$	−262.540	−	454.732i	−0.685482	−	1.18729i	0.287803	−	0.957690i	$-0.407075\pi$
$384$			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	0.746485	−	0.665402i	$-0.231740\pi$
$397$	−80.5960	−	139.596i	−0.203013	−	0.351628i	−0.949498	+	0.313774i	$0.898407\pi$
$398$	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	$-0.500879\pi$
$433$	−2.39222			−0.00552477			−0.00276238	+	0.999996i	$0.500879\pi$
$434$	−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	−0.757491	−	0.652846i	$-0.773575\pi$
$443$	−252.889	+	146.005i	−0.570855	+	0.329583i	0.186636	+	0.982429i	$0.440242\pi$
$444$	−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	−0.416293	−	0.909231i	$-0.636671\pi$
$457$	74.4808	−	43.0015i	0.162978	−	0.0940952i	0.579270	+	0.815135i	$0.303338\pi$
$458$	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	$-0.974540\pi$
$463$		−	73.9873i		−	0.159800i	0.996803	−	0.0798999i	$-0.0254601\pi$
$464$	−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	0.521210	−	0.853429i	$-0.325481\pi$
$467$	−223.453	−	387.032i	−0.478486	−	0.828762i	−0.999696	+	0.0246667i	$0.992148\pi$
$468$	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	0.998882	−	0.0472773i	$-0.0150545\pi$
$487$	709.744	+	409.771i	1.45738	+	0.841418i	0.458498	+	0.888696i	$0.348388\pi$
$488$	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	$-0.461903\pi$
$503$	120.116			0.238800			0.119400	+	0.992846i	$0.461903\pi$
$504$	−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	$-0.936816\pi$
$523$	−345.682	−	598.739i	−0.660960	−	1.14482i	0.319404	−	0.947619i	$-0.396517\pi$
$524$			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	$-0.905970\pi$
$547$		−	318.491i		−	0.582251i	0.956685	−	0.291126i	$-0.0940297\pi$
$548$	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	−0.0208114	−	0.999783i	$-0.506625\pi$
$557$	−499.660	−	288.479i	−0.897055	−	0.517915i	−0.876244	+	0.481869i	$0.839958\pi$
$558$	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	−0.663542	−	0.748139i	$-0.730947\pi$
$563$	177.985	−	308.279i	0.316137	−	0.547565i	0.979678	+	0.200574i	$0.0642808\pi$
$564$	−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	−0.872931	−	0.487844i	$-0.837783\pi$
$577$	−8.06639	+	13.9714i	−0.0139799	+	0.0242139i	0.858951	+	0.512058i	$0.171117\pi$
$578$	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	$-0.555735\pi$
$587$	−204.516			−0.348409			−0.174205	+	0.984709i	$0.555735\pi$
$588$	−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	$0.0309871\pi$
$593$	345.011	+	597.577i	0.581806	+	1.00772i	−0.413459	+	0.910523i	$0.635680\pi$
$594$			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	0.569164	−	0.822224i	$-0.307267\pi$
$607$	−259.483	−	449.438i	−0.427485	−	0.740425i	−0.996649	+	0.0817986i	$0.973934\pi$
$608$	−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	0.407184	−	0.913346i	$-0.366511\pi$
$613$	−110.465	−	63.7771i	−0.180204	−	0.104041i	−0.587389	+	0.809305i	$0.699844\pi$
$614$	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	$-0.870983\pi$
$617$		−	486.581i		−	0.788624i	0.918977	−	0.394312i	$-0.129017\pi$
$618$	−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	$-0.176730\pi$
$643$	1092.83			1.69958			0.849788	+	0.527124i	$0.176730\pi$
$644$	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	−0.993487	−	0.113948i	$-0.963650\pi$
$647$	−257.546	+	446.083i	−0.398062	+	0.689463i	0.595425	+	0.803411i	$0.296984\pi$
$648$	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	−0.920753	−	0.390145i	$-0.872425\pi$
$653$	−681.245	+	393.317i	−1.04325	+	0.602323i	−0.122501	+	0.992468i	$0.539091\pi$
$654$	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	$0.165788\pi$
$673$			669.779i			0.995213i	−0.867403	+	0.497607i	$0.834212\pi$
$674$	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	$-0.932638\pi$
$677$	−454.099	−	786.522i	−0.670751	−	1.16178i	0.306940	−	0.951729i	$-0.400695\pi$
$678$	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	0.0182177	−	0.999834i	$-0.494201\pi$
$683$	−572.733	−	330.668i	−0.838555	−	0.484140i	−0.856773	+	0.515694i	$0.827534\pi$
$684$	−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	$-0.420978\pi$
$727$	357.267			0.491426			0.245713	+	0.969343i	$0.420978\pi$
$728$	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	0.680732	−	0.732532i	$-0.261662\pi$
$733$	−215.521	−	373.293i	−0.294026	−	0.509267i	−0.974758	+	0.223265i	$0.928328\pi$
$734$			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	$-0.659494\pi$
$743$		−	1303.33i		−	1.75414i	0.480360	−	0.877072i	$-0.340506\pi$
$744$	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	$-0.706571\pi$
$757$		−	1206.22i		−	1.59342i	0.604359	−	0.796712i	$-0.293429\pi$
$758$	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	−0.801899	−	0.597460i	$-0.796177\pi$
$773$	90.0279	−	155.933i	0.116466	−	0.201724i	0.918365	+	0.395735i	$0.129510\pi$
$774$	−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	$0.433050\pi$
$787$	−584.386	+	1012.19i	−0.742549	+	1.28613i	−0.951331	+	0.308170i	$0.900283\pi$
$788$	−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	$-0.215517\pi$
$797$	1242.38			1.55883			0.779413	+	0.626510i	$0.215517\pi$
$798$	−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	−0.0263632	−	0.999652i	$-0.508393\pi$
$823$	−745.037	−	430.147i	−0.905269	−	0.522657i	−0.878906	+	0.476995i	$0.841726\pi$
$824$	−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	$-0.860123\pi$
$827$		−	703.661i		−	0.850860i	0.904991	−	0.425430i	$-0.139877\pi$
$828$	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	$-0.572173\pi$
$853$	−383.511			−0.449602			−0.224801	+	0.974405i	$0.572173\pi$
$854$	−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	−0.945751	−	0.324891i	$-0.894672\pi$
$857$	−164.125	+	284.273i	−0.191512	+	0.331708i	0.754240	+	0.656599i	$0.228006\pi$
$858$	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	−0.206481	−	0.978451i	$-0.566201\pi$
$863$	463.984	−	267.881i	0.537641	−	0.310407i	0.744122	+	0.668043i	$0.232868\pi$
$864$	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	0.233321	−	0.972400i	$-0.425041\pi$
$877$	1045.48	−	603.606i	1.19210	−	0.688262i	0.958784	+	0.284138i	$0.0917072\pi$
$878$	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	$-0.968008\pi$
$883$		−	177.196i		−	0.200675i	0.994953	−	0.100337i	$-0.0319922\pi$
$884$	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	$0.0879350\pi$
$887$	636.205	+	1101.94i	0.717255	+	1.24232i	−0.244829	+	0.969566i	$0.578732\pi$
$888$	−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	0.411965	−	0.911200i	$-0.364842\pi$
$907$	−155.255	−	89.6364i	−0.171174	−	0.0988273i	−0.583139	+	0.812372i	$0.698176\pi$
$908$	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	$-0.346851\pi$
$937$	867.253			0.925564			0.462782	+	0.886472i	$0.346851\pi$
$938$	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	−0.801568	−	0.597903i	$-0.796001\pi$
$947$	−648.272	+	374.280i	−0.684553	+	0.395227i	0.117015	+	0.993130i	$0.462667\pi$
$948$	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	$0.00361244\pi$
$953$			21.6304i			0.0226972i	−0.999936	+	0.0113486i	$0.996388\pi$
$954$	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	$-0.924745\pi$
$967$		−	452.988i		−	0.468447i	0.972183	−	0.234224i	$-0.0752548\pi$
$968$	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	0.920845	−	0.389929i	$-0.127500\pi$
$977$	1019.58	+	588.653i	1.04358	+	0.602511i	0.122734	+	0.992440i	$0.460834\pi$
$978$	−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	−0.586475	−	0.809967i	$-0.699485\pi$
$983$	401.275	−	695.029i	0.408215	−	0.707049i	0.994690	+	0.102918i	$0.0328181\pi$
$984$	−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	−0.999329	−	0.0366170i	$-0.988342\pi$
$997$	−466.550	+	808.088i	−0.467953	+	0.810519i	0.531376	+	0.847136i	$0.321675\pi$
$998$	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.199.8		16
5.2	odd	4		1050.3.p.c.451.4	✓	8
5.3	odd	4		1050.3.p.d.451.1	yes	8
5.4	even	2	inner	1050.3.q.b.199.1		16
7.5	odd	6	inner	1050.3.q.b.649.1		16
35.12	even	12		1050.3.p.c.901.4	yes	8
35.19	odd	6	inner	1050.3.q.b.649.8		16
35.33	even	12		1050.3.p.d.901.1	yes	8

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