LMFDB - Embedded newform 1050.3.p.c.451.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(451,1050)]

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, 0, 1]))

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

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

chi := DirichletCharacter("1050.451");

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.p (of order $6$, degree $2$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.151613669376.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 12x^{6} + 95x^{4} - 588x^{2} + 2401 $ x^8 - 12x^6 + 95x^4 - 588*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.4
Root			$-2.56149 + 0.662382i$ of defining polynomial
Character	$\chi$	$=$	1050.451
Dual form			1050.3.p.c.901.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(0.440173 + 6.98615i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(0.440173 + 6.98615i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(2.76860 - 4.79536i) q^{11} +(3.00000 - 1.73205i) q^{12} +3.50434i q^{13} +(-8.24500 + 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(7.04933 + 4.06994i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-15.3628 + 8.86974i) q^{19} +(5.38992 - 10.8604i) q^{21} +7.83078 q^{22} +(5.96495 + 10.3316i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-4.29192 + 2.47794i) q^{26} -5.19615i q^{27} +(-12.5405 - 6.22374i) q^{28} -8.52374 q^{29} +(-6.68072 - 3.85711i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-8.30580 + 4.79536i) q^{33} +11.5115i q^{34} -6.00000 q^{36} +(14.0267 + 24.2950i) q^{37} +(-21.7263 - 12.5437i) q^{38} +(3.03484 - 5.25650i) q^{39} -3.14207i q^{41} +(17.1125 - 1.07820i) q^{42} -43.1943 q^{43} +(5.53720 + 9.59071i) q^{44} +(-8.43572 + 14.6111i) q^{46} +(16.2037 - 9.35524i) q^{47} +6.92820i q^{48} +(-48.6125 + 6.15023i) q^{49} +(-7.04933 - 12.2098i) q^{51} +(-6.06969 - 3.50434i) q^{52} +(-1.40895 + 2.44037i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} +30.7257 q^{57} +(-6.02720 - 10.4394i) q^{58} +(-26.1612 - 15.1042i) q^{59} +(-41.0095 + 23.6769i) q^{61} -10.9096i q^{62} +(-17.4903 + 11.6228i) q^{63} +8.00000 q^{64} +(-11.7462 - 6.78166i) q^{66} +(-3.29108 + 5.70032i) q^{67} +(-14.0987 + 8.13987i) q^{68} -20.6632i q^{69} -97.7751 q^{71} +(-4.24264 - 7.34847i) q^{72} +(-52.9672 - 30.5806i) q^{73} +(-19.8368 + 34.3583i) q^{74} -35.4790i q^{76} +(34.7197 + 17.2311i) q^{77} +8.58383 q^{78} +(-61.5670 - 106.637i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(3.84823 - 2.22178i) q^{82} +89.5815i q^{83} +(13.4209 + 20.1960i) q^{84} +(-30.5430 - 52.9020i) q^{86} +(12.7856 + 7.38178i) q^{87} +(-7.83078 + 13.5633i) q^{88} +(-102.290 + 59.0573i) q^{89} +(-24.4818 + 1.54251i) q^{91} -23.8598 q^{92} +(6.68072 + 11.5713i) q^{93} +(22.9156 + 13.2303i) q^{94} +(-8.48528 + 4.89898i) q^{96} +65.1965i q^{97} +(-41.9067 - 55.1890i) q^{98} +16.6116 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9}+O(q^{10}) $ 8 * q - 12 * q^3 - 8 * q^4 + 12 * q^9	$ 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} + 24 q^{12} - 16 q^{14} - 16 q^{16} - 24 q^{17} + 72 q^{19} + 24 q^{22} + 60 q^{23} - 72 q^{26} - 24 q^{29} + 96 q^{31} + 12 q^{33} - 48 q^{36} - 24 q^{37} - 180 q^{38} - 12 q^{39} + 12 q^{42} - 112 q^{43} - 8 q^{44} + 32 q^{46} + 84 q^{47} - 264 q^{49} + 24 q^{51} + 24 q^{52} + 44 q^{53} + 40 q^{56} - 144 q^{57} + 104 q^{58} + 312 q^{59} - 204 q^{61} + 64 q^{64} - 36 q^{66} + 120 q^{67} + 48 q^{68} - 64 q^{71} + 84 q^{73} - 16 q^{74} + 228 q^{77} + 144 q^{78} - 144 q^{79} - 36 q^{81} - 60 q^{82} + 176 q^{86} + 36 q^{87} - 24 q^{88} - 336 q^{89} - 296 q^{91} - 240 q^{92} - 96 q^{93} + 36 q^{94} - 24 q^{99}+O(q^{100}) $ 8 * q - 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 + 24 * q^12 - 16 * q^14 - 16 * q^16 - 24 * q^17 + 72 * q^19 + 24 * q^22 + 60 * q^23 - 72 * q^26 - 24 * q^29 + 96 * q^31 + 12 * q^33 - 48 * q^36 - 24 * q^37 - 180 * q^38 - 12 * q^39 + 12 * q^42 - 112 * q^43 - 8 * q^44 + 32 * q^46 + 84 * q^47 - 264 * q^49 + 24 * q^51 + 24 * q^52 + 44 * q^53 + 40 * q^56 - 144 * q^57 + 104 * q^58 + 312 * q^59 - 204 * q^61 + 64 * q^64 - 36 * q^66 + 120 * q^67 + 48 * q^68 - 64 * q^71 + 84 * q^73 - 16 * q^74 + 228 * q^77 + 144 * q^78 - 144 * q^79 - 36 * q^81 - 60 * q^82 + 176 * q^86 + 36 * q^87 - 24 * q^88 - 336 * q^89 - 296 * q^91 - 240 * q^92 - 96 * q^93 + 36 * q^94 - 24 * 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 $

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	0.408248i
$7$	0.440173	+	6.98615i	0.0628819	+	0.998021i
$7$	0.440173	+	6.98615i	0.0628819	+	0.998021i
$8$	−2.82843			−0.353553
$9$	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	$0.0856800\pi$
$12$	3.00000	−	1.73205i	0.250000	−	0.144338i
$13$			3.50434i			0.269564i	0.990875	+	0.134782i	$0.0430335\pi$
$13$			3.50434i			0.269564i	−0.990875	+	0.134782i	$0.956967\pi$
$14$	−8.24500	+	5.47905i	−0.588928	+	0.391361i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	7.04933	+	4.06994i	0.414667	+	0.239408i	0.692793	−	0.721137i	$-0.256380\pi$
$17$	7.04933	+	4.06994i	0.414667	+	0.239408i	−0.278126	+	0.960545i	$0.589713\pi$
$18$	−2.12132	+	3.67423i	−0.117851	+	0.204124i
$19$	−15.3628	+	8.86974i	−0.808571	+	0.466828i	−0.846459	−	0.532454i	$-0.821270\pi$
$19$	−15.3628	+	8.86974i	−0.808571	+	0.466828i	0.0378887	+	0.999282i	$0.487937\pi$
$20$		0			0
$21$	5.38992	−	10.8604i	0.256663	−	0.517163i
$22$	7.83078			0.355945
$23$	5.96495	+	10.3316i	0.259346	+	0.449200i	0.966067	−	0.258292i	$-0.0831597\pi$
$23$	5.96495	+	10.3316i	0.259346	+	0.449200i	−0.706721	+	0.707492i	$0.749826\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$		0			0
$26$	−4.29192	+	2.47794i	−0.165074	+	0.0953054i
$27$		−	5.19615i		−	0.192450i
$28$	−12.5405	−	6.22374i	−0.447876	−	0.222277i
$29$	−8.52374			−0.293922			−0.146961	−	0.989142i	$-0.546949\pi$
$29$	−8.52374			−0.293922			−0.146961	+	0.989142i	$0.546949\pi$
$30$		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	$0.706375\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	−8.30580	+	4.79536i	−0.251691	+	0.145314i
$34$			11.5115i			0.338574i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	14.0267	+	24.2950i	0.379100	+	0.656621i	0.990932	−	0.134367i	$-0.0429002\pi$
$37$	14.0267	+	24.2950i	0.379100	+	0.656621i	−0.611831	+	0.790988i	$0.709567\pi$
$38$	−21.7263	−	12.5437i	−0.571746	−	0.330098i
$39$	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	$-0.0121999\pi$
$42$	17.1125	−	1.07820i	0.407440	−	0.0256714i
$43$	−43.1943			−1.00452			−0.502260	−	0.864717i	$-0.667498\pi$
$43$	−43.1943			−1.00452			−0.502260	+	0.864717i	$0.667498\pi$
$44$	5.53720	+	9.59071i	0.125845	+	0.217971i
$45$		0			0
$46$	−8.43572	+	14.6111i	−0.183385	+	0.317632i
$47$	16.2037	−	9.35524i	0.344761	−	0.199048i	−0.317615	−	0.948220i	$-0.602882\pi$
$47$	16.2037	−	9.35524i	0.344761	−	0.199048i	0.662375	+	0.749172i	$0.269548\pi$
$48$			6.92820i			0.144338i
$49$	−48.6125	+	6.15023i	−0.992092	+	0.125515i
$50$		0			0
$51$	−7.04933	−	12.2098i	−0.138222	−	0.239408i
$52$	−6.06969	−	3.50434i	−0.116725	−	0.0673911i
$53$	−1.40895	+	2.44037i	−0.0265840	+	0.0460448i	−0.879011	−	0.476801i	$-0.841796\pi$
$53$	−1.40895	+	2.44037i	−0.0265840	+	0.0460448i	0.852427	+	0.522846i	$0.175130\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$		0			0
$56$	−1.24500	−	19.7598i	−0.0222321	−	0.352854i
$57$	30.7257			0.539047
$58$	−6.02720	−	10.4394i	−0.103917	−	0.179990i
$59$	−26.1612	−	15.1042i	−0.443411	−	0.256003i	0.261633	−	0.965168i	$-0.415739\pi$
$59$	−26.1612	−	15.1042i	−0.443411	−	0.256003i	−0.705043	+	0.709164i	$0.749072\pi$
$60$		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	$0.460218\pi$
$62$		−	10.9096i		−	0.175961i
$63$	−17.4903	+	11.6228i	−0.277624	+	0.184489i
$64$	8.00000			0.125000
$65$		0			0
$66$	−11.7462	−	6.78166i	−0.177972	−	0.102752i
$67$	−3.29108	+	5.70032i	−0.0491206	+	0.0850794i	−0.889540	−	0.456857i	$-0.848975\pi$
$67$	−3.29108	+	5.70032i	−0.0491206	+	0.0850794i	0.840420	+	0.541936i	$0.182309\pi$
$68$	−14.0987	+	8.13987i	−0.207333	+	0.119704i
$69$		−	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	$0.741755\pi$
$72$	−4.24264	−	7.34847i	−0.0589256	−	0.102062i
$73$	−52.9672	−	30.5806i	−0.725578	−	0.418913i	0.0912244	−	0.995830i	$-0.470922\pi$
$73$	−52.9672	−	30.5806i	−0.725578	−	0.418913i	−0.816802	+	0.576918i	$0.804255\pi$
$74$	−19.8368	+	34.3583i	−0.268064	+	0.464301i
$75$		0			0
$76$		−	35.4790i		−	0.466828i
$77$	34.7197	+	17.2311i	0.450906	+	0.223780i
$78$	8.58383			0.110049
$79$	−61.5670	−	106.637i	−0.779329	−	1.34984i	−0.932329	−	0.361612i	$-0.882227\pi$
$79$	−61.5670	−	106.637i	−0.779329	−	1.34984i	0.152999	−	0.988226i	$-0.451107\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	3.84823	−	2.22178i	0.0469296	−	0.0270948i
$83$			89.5815i			1.07930i	0.841891	+	0.539648i	$0.181443\pi$
$83$			89.5815i			1.07930i	−0.841891	+	0.539648i	$0.818557\pi$
$84$	13.4209	+	20.1960i	0.159772	+	0.240429i
$85$		0			0
$86$	−30.5430	−	52.9020i	−0.355151	−	0.615140i
$87$	12.7856	+	7.38178i	0.146961	+	0.0848480i
$88$	−7.83078	+	13.5633i	−0.0889862	+	0.154129i
$89$	−102.290	+	59.0573i	−1.14933	+	0.663566i	−0.948724	−	0.316107i	$-0.897624\pi$
$89$	−102.290	+	59.0573i	−1.14933	+	0.663566i	−0.200606	+	0.979672i	$0.564291\pi$
$90$		0			0
$91$	−24.4818	+	1.54251i	−0.269031	+	0.0169507i
$92$	−23.8598			−0.259346
$93$	6.68072	+	11.5713i	0.0718357	+	0.124423i
$94$	22.9156	+	13.2303i	0.243783	+	0.140748i
$95$		0			0
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$			65.1965i			0.672128i	0.941839	+	0.336064i	$0.109096\pi$
$97$			65.1965i			0.672128i	−0.941839	+	0.336064i	$0.890904\pi$
$98$	−41.9067	−	55.1890i	−0.427619	−	0.563153i
$99$	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	$0.909530\pi$
$102$	9.96926	−	17.2673i	0.0977379	−	0.169287i
$103$	−151.108	+	87.2421i	−1.46707	+	0.847011i	−0.999321	−	0.0368520i	$-0.988267\pi$
$103$	−151.108	+	87.2421i	−1.46707	+	0.847011i	−0.467746	+	0.883863i	$0.654934\pi$
$104$		−	9.91176i		−	0.0953054i
$105$		0			0
$106$	−3.98511			−0.0375954
$107$	30.2382	+	52.3741i	0.282600	+	0.489477i	0.972024	−	0.234880i	$-0.0754698\pi$
$107$	30.2382	+	52.3741i	0.282600	+	0.489477i	−0.689424	+	0.724358i	$0.742136\pi$
$108$	9.00000	+	5.19615i	0.0833333	+	0.0481125i
$109$	50.4057	−	87.3052i	0.462437	−	0.800965i	−0.536644	−	0.843808i	$-0.680308\pi$
$109$	50.4057	−	87.3052i	0.462437	−	0.800965i	0.999082	+	0.0428435i	$0.0136417\pi$
$110$		0			0
$111$		−	48.5899i		−	0.437747i
$112$	23.3204	−	15.4971i	0.208218	−	0.138367i
$113$	74.1876			0.656527			0.328264	−	0.944586i	$-0.393537\pi$
$113$	74.1876			0.656527			0.328264	+	0.944586i	$0.393537\pi$
$114$	21.7263	+	37.6311i	0.190582	+	0.330098i
$115$		0			0
$116$	8.52374	−	14.7636i	0.0734805	−	0.127272i
$117$	−9.10453	+	5.25650i	−0.0778165	+	0.0449274i
$118$		−	42.7211i		−	0.362043i
$119$	−25.3302	+	51.0392i	−0.212859	+	0.428901i
$120$		0			0
$121$	45.1697	+	78.2362i	0.373303	+	0.646580i
$122$	−57.9963	−	33.4842i	−0.475379	−	0.274460i
$123$	−2.72111	+	4.71310i	−0.0221228	+	0.0383179i
$124$	13.3614	−	7.71423i	0.107754	−	0.0622115i
$125$		0			0
$126$	−26.6025	−	13.2026i	−0.211131	−	0.104782i
$127$	151.093			1.18971			0.594855	−	0.803833i	$-0.297209\pi$
$127$	151.093			1.18971			0.594855	+	0.803833i	$0.297209\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	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	$0.641238\pi$
$132$		−	19.1814i		−	0.145314i
$133$	−68.7276	−	103.423i	−0.516749	−	0.777615i
$134$	−9.30859			−0.0694671
$135$		0			0
$136$	−19.9385	−	11.5115i	−0.146607	−	0.0846435i
$137$	−66.8203	+	115.736i	−0.487739	+	0.844789i	−0.999901	−	0.0141000i	$-0.995512\pi$
$137$	−66.8203	+	115.736i	−0.487739	+	0.844789i	0.512161	+	0.858889i	$0.328845\pi$
$138$	25.3072	−	14.6111i	0.183385	−	0.105877i
$139$		−	193.762i		−	1.39397i	−0.717085	−	0.696986i	$-0.754524\pi$
$139$		−	193.762i		−	1.39397i	0.717085	−	0.696986i	$-0.245476\pi$
$140$		0			0
$141$	−32.4075			−0.229840
$142$	−69.1374	−	119.750i	−0.486883	−	0.843306i
$143$	16.8045	+	9.70210i	0.117514	+	0.0678469i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$		0			0
$146$		−	86.4950i		−	0.592432i
$147$	78.2450	+	32.8743i	0.532279	+	0.223635i
$148$	−56.1068			−0.379100
$149$	−33.0032	−	57.1632i	−0.221498	−	0.383646i	0.733765	−	0.679403i	$-0.237761\pi$
$149$	−33.0032	−	57.1632i	−0.221498	−	0.383646i	−0.955263	+	0.295758i	$0.904428\pi$
$150$		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	$0.203515\pi$
$152$	43.4527	−	25.0874i	0.285873	−	0.165049i
$153$			24.4196i			0.159605i
$154$	3.44690	+	54.7070i	0.0223825	+	0.355240i
$155$		0			0
$156$	6.06969	+	10.5130i	0.0389082	+	0.0673911i
$157$	−46.3329	−	26.7503i	−0.295114	−	0.170384i	0.345132	−	0.938554i	$-0.387834\pi$
$157$	−46.3329	−	26.7503i	−0.295114	−	0.170384i	−0.640246	+	0.768170i	$0.721168\pi$
$158$	87.0689	−	150.808i	0.551069	−	0.954480i
$159$	4.22685	−	2.44037i	0.0265840	−	0.0153483i
$160$		0			0
$161$	−69.5525	+	46.2197i	−0.432003	+	0.287079i
$162$	−12.7279			−0.0785674
$163$	−102.992	−	178.387i	−0.631852	−	1.09440i	−0.987173	−	0.159655i	$-0.948962\pi$
$163$	−102.992	−	178.387i	−0.631852	−	1.09440i	0.355321	−	0.934744i	$-0.384372\pi$
$164$	5.44222	+	3.14207i	0.0331843	+	0.0191589i
$165$		0			0
$166$	−109.714	+	63.3437i	−0.660931	+	0.381589i
$167$			137.945i			0.826020i	0.910727	+	0.413010i	$0.135523\pi$
$167$			137.945i			0.826020i	−0.910727	+	0.413010i	$0.864477\pi$
$168$	−15.2450	+	30.7179i	−0.0907440	+	0.182845i
$169$	156.720			0.927335
$170$		0			0
$171$	−46.0885	−	26.6092i	−0.269524	−	0.155609i
$172$	43.1943	−	74.8148i	0.251130	−	0.434970i
$173$	191.016	−	110.283i	1.10414	−	0.637475i	0.166834	−	0.985985i	$-0.446646\pi$
$173$	191.016	−	110.283i	1.10414	−	0.637475i	0.937305	+	0.348510i	$0.113312\pi$
$174$			20.8788i			0.119993i
$175$		0			0
$176$	−22.1488			−0.125845
$177$	26.1612	+	45.3126i	0.147804	+	0.256003i
$178$	−144.660	−	83.5197i	−0.812699	−	0.469212i
$179$	36.6501	−	63.4798i	0.204749	−	0.354636i	−0.745304	−	0.666725i	$-0.767695\pi$
$179$	36.6501	−	63.4798i	0.204749	−	0.354636i	0.950053	+	0.312089i	$0.101029\pi$
$180$		0			0
$181$			61.4619i			0.339568i	0.985481	+	0.169784i	$0.0543071\pi$
$181$			61.4619i			0.339568i	−0.985481	+	0.169784i	$0.945693\pi$
$182$	−19.2004	−	28.8932i	−0.105497	−	0.158754i
$183$	82.0191			0.448192
$184$	−16.8714	−	29.2222i	−0.0916926	−	0.158816i
$185$		0			0
$186$	−9.44796	+	16.3643i	−0.0507955	+	0.0879804i
$187$	39.0336	−	22.5360i	0.208736	−	0.120514i
$188$			37.4210i			0.199048i
$189$	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	$0.442231\pi$
$192$	−12.0000	−	6.92820i	−0.0625000	−	0.0360844i
$193$	69.8724	−	121.023i	0.362033	−	0.627060i	−0.626262	−	0.779613i	$-0.715416\pi$
$193$	69.8724	−	121.023i	0.362033	−	0.627060i	0.988295	+	0.152552i	$0.0487493\pi$
$194$	−79.8490	+	46.1009i	−0.411593	+	0.237633i
$195$		0			0
$196$	37.9600	−	90.3495i	0.193673	−	0.460967i
$197$	248.343			1.26062			0.630311	−	0.776342i	$-0.282927\pi$
$197$	248.343			1.26062			0.630311	+	0.776342i	$0.282927\pi$
$198$	11.7462	+	20.3450i	0.0593241	+	0.102752i
$199$	−106.170	−	61.2973i	−0.533518	−	0.308026i	0.208930	−	0.977931i	$-0.433002\pi$
$199$	−106.170	−	61.2973i	−0.533518	−	0.308026i	−0.742448	+	0.669904i	$0.766335\pi$
$200$		0			0
$201$	9.87325	−	5.70032i	0.0491206	−	0.0283598i
$202$		−	197.421i		−	0.977329i
$203$	−3.75192	−	59.5481i	−0.0184824	−	0.293341i
$204$	28.1973			0.138222
$205$		0			0
$206$	−213.699	−	123.379i	−1.03737	−	0.598927i
$207$	−17.8949	+	30.9948i	−0.0864486	+	0.149733i
$208$	12.1394	−	7.00867i	0.0583624	−	0.0336955i
$209$			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	$0.184837\pi$
$212$	−2.81790	−	4.88074i	−0.0132920	−	0.0230224i
$213$	146.663	+	84.6757i	0.688557	+	0.397538i
$214$	−42.7632	+	74.0681i	−0.199828	+	0.346113i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	24.0057	−	48.3703i	0.110625	−	0.222904i
$218$	142.569			0.653985
$219$	52.9672	+	91.7418i	0.241859	+	0.418913i
$220$		0			0
$221$	−14.2624	+	24.7032i	−0.0645358	+	0.111779i
$222$	59.5103	−	34.3583i	0.268064	−	0.154767i
$223$		−	61.7420i		−	0.276870i	−0.990372	−	0.138435i	$-0.955793\pi$
$223$		−	61.7420i		−	0.276870i	0.990372	−	0.138435i	$-0.0442072\pi$
$224$	35.4700	+	17.6034i	0.158348	+	0.0785866i
$225$		0			0
$226$	52.4586	+	90.8609i	0.232118	+	0.402039i
$227$	−181.452	−	104.762i	−0.799350	−	0.461505i	0.0438940	−	0.999036i	$-0.486024\pi$
$227$	−181.452	−	104.762i	−0.799350	−	0.461505i	−0.843244	+	0.537531i	$0.819357\pi$
$228$	−30.7257	+	53.2184i	−0.134762	+	0.233414i
$229$	−93.3568	+	53.8996i	−0.407671	+	0.235369i	−0.689789	−	0.724011i	$-0.742297\pi$
$229$	−93.3568	+	53.8996i	−0.407671	+	0.235369i	0.282117	+	0.959380i	$0.408963\pi$
$230$		0			0
$231$	−37.1571	−	55.9148i	−0.160853	−	0.242055i
$232$	24.1088			0.103917
$233$	163.423	+	283.057i	0.701387	+	1.21484i	0.967980	+	0.251029i	$0.0807689\pi$
$233$	163.423	+	283.057i	0.701387	+	1.21484i	−0.266592	+	0.963809i	$0.585898\pi$
$234$	−12.8758	−	7.43382i	−0.0550246	−	0.0317685i
$235$		0			0
$236$	52.3224	−	30.2084i	0.221705	−	0.128002i
$237$			213.274i			0.899892i
$238$	−80.4211	+	5.06706i	−0.337904	+	0.0212902i
$239$	−9.20117			−0.0384986			−0.0192493	−	0.999815i	$-0.506128\pi$
$239$	−9.20117			−0.0384986			−0.0192493	+	0.999815i	$0.506128\pi$
$240$		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	$0.434517\pi$
$242$	−63.8796	+	110.643i	−0.263965	+	0.457201i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		−	94.7075i		−	0.388145i
$245$		0			0
$246$	−7.69646			−0.0312864
$247$	−31.0825	−	53.8365i	−0.125840	−	0.217962i
$248$	18.8959	+	10.9096i	0.0761932	+	0.0439902i
$249$	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	$-0.0122024\pi$
$252$	−2.64104	−	41.9169i	−0.0104803	−	0.166337i
$253$	66.0583			0.261100
$254$	106.839	+	185.051i	0.420626	+	0.728546i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	112.083	−	64.7109i	0.436119	−	0.251793i	−0.265831	−	0.964020i	$-0.585646\pi$
$257$	112.083	−	64.7109i	0.436119	−	0.251793i	0.701950	+	0.712226i	$0.252313\pi$
$258$			105.804i			0.410093i
$259$	−163.554	+	108.687i	−0.631483	+	0.419640i
$260$		0			0
$261$	−12.7856	−	22.1453i	−0.0489870	−	0.0848480i
$262$	−264.203	−	152.538i	−1.00841	−	0.582206i
$263$	−83.4625	+	144.561i	−0.317348	+	0.549663i	−0.979934	−	0.199323i	$-0.936126\pi$
$263$	−83.4625	+	144.561i	−0.317348	+	0.549663i	0.662586	+	0.748986i	$0.269459\pi$
$264$	23.4924	−	13.5633i	0.0889862	−	0.0513762i
$265$		0			0
$266$	78.0688	−	157.305i	0.293492	−	0.591371i
$267$	204.581			0.766220
$268$	−6.58217	−	11.4006i	−0.0245603	−	0.0425397i
$269$	181.081	+	104.547i	0.673162	+	0.388650i	0.797274	−	0.603618i	$-0.206275\pi$
$269$	181.081	+	104.547i	0.673162	+	0.388650i	−0.124112	+	0.992268i	$0.539608\pi$
$270$		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	$0.248916\pi$
$272$		−	32.5595i		−	0.119704i
$273$	38.0586	+	18.8881i	0.139409	+	0.0691871i
$274$	−188.996			−0.689768
$275$		0			0
$276$	35.7897	+	20.6632i	0.129673	+	0.0748667i
$277$	−222.961	+	386.179i	−0.804912	+	1.39415i	0.111438	+	0.993771i	$0.464454\pi$
$277$	−222.961	+	386.179i	−0.804912	+	1.39415i	−0.916350	+	0.400377i	$0.868879\pi$
$278$	237.309	−	137.010i	0.853630	−	0.492843i
$279$		−	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	$0.171910\pi$
$282$	−22.9156	−	39.6909i	−0.0812609	−	0.140748i
$283$	−187.506	−	108.257i	−0.662566	−	0.382533i	0.130688	−	0.991424i	$-0.458281\pi$
$283$	−187.506	−	108.257i	−0.662566	−	0.382533i	−0.793254	+	0.608891i	$0.791615\pi$
$284$	97.7751	−	169.351i	0.344278	−	0.596308i
$285$		0			0
$286$			27.4417i			0.0959500i
$287$	21.9509	−	1.38305i	0.0764841	−	0.00481900i
$288$	16.9706			0.0589256
$289$	−111.371	−	192.901i	−0.385368	−	0.667476i
$290$		0			0
$291$	56.4618	−	97.7947i	0.194027	−	0.336064i
$292$	105.934	−	61.1612i	0.362789	−	0.209456i
$293$			383.704i			1.30957i	0.755815	+	0.654786i	$0.227241\pi$
$293$			383.704i			1.30957i	−0.755815	+	0.654786i	$0.772759\pi$
$294$	15.0649	+	119.076i	0.0512412	+	0.405020i
$295$		0			0
$296$	−39.6735	−	68.7166i	−0.134032	−	0.232151i
$297$	−24.9174	−	14.3861i	−0.0838970	−	0.0484379i
$298$	46.6736	−	80.8410i	0.156623	−	0.271278i
$299$	−36.2054	+	20.9032i	−0.121088	+	0.0699104i
$300$		0			0
$301$	−19.0130	−	301.762i	−0.0631661	−	1.00253i
$302$	−49.3305			−0.163346
$303$	120.895	+	209.396i	0.398993	+	0.691076i
$304$	61.4514	+	35.4790i	0.202143	+	0.116707i
$305$		0			0
$306$	−29.9078	+	17.2673i	−0.0977379	+	0.0564290i
$307$			21.1264i			0.0688155i	0.999408	+	0.0344078i	$0.0109545\pi$
$307$			21.1264i			0.0688155i	−0.999408	+	0.0344078i	$0.989046\pi$
$308$	−64.5648	+	42.9053i	−0.209626	+	0.139303i
$309$	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	$0.622186\pi$
$312$	−8.58383	+	14.8676i	−0.0275123	+	0.0476527i
$313$	−2.45782	+	1.41903i	−0.00785247	+	0.00453363i	−0.503921	−	0.863750i	$-0.668110\pi$
$313$	−2.45782	+	1.41903i	−0.00785247	+	0.00453363i	0.496069	+	0.868283i	$0.334776\pi$
$314$		−	75.6613i		−	0.240960i
$315$		0			0
$316$	246.268			0.779329
$317$	−154.925	−	268.338i	−0.488723	−	0.846493i	0.511193	−	0.859466i	$-0.329204\pi$
$317$	−154.925	−	268.338i	−0.488723	−	0.846493i	−0.999916	+	0.0129730i	$0.995870\pi$
$318$	5.97767	+	3.45121i	0.0187977	+	0.0108529i
$319$	−23.5988	+	40.8744i	−0.0739776	+	0.128133i
$320$		0			0
$321$		−	104.748i		−	0.326318i
$322$	−105.788	−	52.5018i	−0.328535	−	0.163049i
$323$	−144.397			−0.447050
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	145.652	−	252.278i	0.446787	−	0.773857i
$327$	−151.217	+	87.3052i	−0.462437	+	0.266988i
$328$			8.88711i			0.0270948i
$329$	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	$0.616680\pi$
$332$	−155.160	−	89.5815i	−0.467349	−	0.269824i
$333$	−42.0801	+	72.8849i	−0.126367	+	0.218874i
$334$	−168.948	+	97.5421i	−0.505832	+	0.292042i
$335$		0			0
$336$	−48.4014	+	3.04961i	−0.144052	+	0.00907622i
$337$	−155.491			−0.461399			−0.230699	−	0.973025i	$-0.574101\pi$
$337$	−155.491			−0.461399			−0.230699	+	0.973025i	$0.574101\pi$
$338$	110.818	+	191.942i	0.327862	+	0.567874i
$339$	−111.281	−	64.2483i	−0.328264	−	0.189523i
$340$		0			0
$341$	−36.9925	+	21.3576i	−0.108482	+	0.0626323i
$342$		−	75.2622i		−	0.220065i
$343$	−64.3643	−	336.907i	−0.187651	−	0.982236i
$344$	122.172			0.355151
$345$		0			0
$346$	270.138	+	155.964i	0.780744	+	0.450763i
$347$	−256.253	+	443.844i	−0.738482	+	1.27909i	0.214697	+	0.976681i	$0.431124\pi$
$347$	−256.253	+	443.844i	−0.738482	+	1.27909i	−0.953179	+	0.302408i	$0.902210\pi$
$348$	−25.5712	+	14.7636i	−0.0734805	+	0.0424240i
$349$		−	269.185i		−	0.771305i	−0.922644	−	0.385652i	$-0.873976\pi$
$349$		−	269.185i		−	0.771305i	0.922644	−	0.385652i	$-0.126024\pi$
$350$		0			0
$351$	18.2091			0.0518777
$352$	−15.6616	−	27.1266i	−0.0444931	−	0.0770643i
$353$	507.890	+	293.231i	1.43878	+	0.830682i	0.997765	−	0.0668166i	$-0.0212843\pi$
$353$	507.890	+	293.231i	1.43878	+	0.830682i	0.441018	+	0.897498i	$0.354618\pi$
$354$	−36.9976	+	64.0816i	−0.104513	+	0.181022i
$355$		0			0
$356$		−	236.229i		−	0.663566i
$357$	82.1966	−	54.6221i	0.230242	−	0.153003i
$358$	103.662			0.289559
$359$	−44.4221	−	76.9413i	−0.123738	−	0.214321i	0.797501	−	0.603318i	$-0.206155\pi$
$359$	−44.4221	−	76.9413i	−0.123738	−	0.214321i	−0.921239	+	0.388997i	$0.872822\pi$
$360$		0			0
$361$	−23.1554	+	40.1064i	−0.0641424	+	0.111098i
$362$	−75.2751	+	43.4601i	−0.207942	+	0.120056i
$363$		−	156.472i		−	0.431054i
$364$	21.8101	−	43.9462i	0.0599178	−	0.120731i
$365$		0			0
$366$	57.9963	+	100.452i	0.158460	+	0.274460i
$367$	−611.446	−	353.019i	−1.66607	−	0.961904i	−0.969727	−	0.244191i	$-0.921478\pi$
$367$	−611.446	−	353.019i	−1.66607	−	0.961904i	−0.696339	−	0.717713i	$-0.745189\pi$
$368$	23.8598	−	41.3264i	0.0648365	−	0.112300i
$369$	8.16333	−	4.71310i	0.0221228	−	0.0127726i
$370$		0			0
$371$	−17.6690	−	8.76894i	−0.0476253	−	0.0236360i
$372$	−26.7229			−0.0718357
$373$	−25.6211	−	44.3770i	−0.0686892	−	0.118973i	0.829635	−	0.558306i	$-0.188548\pi$
$373$	−25.6211	−	44.3770i	−0.0686892	−	0.118973i	−0.898325	+	0.439332i	$0.855215\pi$
$374$	55.2018	+	31.8708i	0.147598	+	0.0852160i
$375$		0			0
$376$	−45.8311	+	26.4606i	−0.121891	+	0.0703740i
$377$		−	29.8701i		−	0.0792309i
$378$	28.4700	+	42.8423i	0.0753174	+	0.113339i
$379$	−194.724			−0.513784			−0.256892	−	0.966440i	$-0.582698\pi$
$379$	−194.724			−0.513784			−0.256892	+	0.966440i	$0.582698\pi$
$380$		0			0
$381$	−226.640	−	130.851i	−0.594855	−	0.343440i
$382$	−254.461	+	440.740i	−0.666129	+	1.15377i
$383$	−454.732	+	262.540i	−1.18729	+	0.685482i	−0.957690	−	0.287803i	$-0.907075\pi$
$383$	−454.732	+	262.540i	−1.18729	+	0.685482i	−0.229600	+	0.973285i	$0.573742\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	197.629			0.511993
$387$	−64.7915	−	112.222i	−0.167420	−	0.289980i
$388$	−112.924	−	65.1965i	−0.291040	−	0.168032i
$389$	201.765	−	349.467i	0.518675	−	0.898372i	−0.481089	−	0.876672i	$-0.659759\pi$
$389$	201.765	−	349.467i	0.518675	−	0.898372i	0.999765	−	0.0217005i	$-0.00690803\pi$
$390$		0			0
$391$			97.1079i			0.248358i
$392$	137.497	−	17.3955i	0.350757	−	0.0443762i
$393$	373.640			0.950738
$394$	175.605	+	304.156i	0.445697	+	0.771971i
$395$		0			0
$396$	−16.6116	+	28.7721i	−0.0419485	+	0.0726569i
$397$	139.596	−	80.5960i	0.351628	−	0.203013i	−0.313774	−	0.949498i	$-0.601593\pi$
$397$	139.596	−	80.5960i	0.351628	−	0.203013i	0.665402	+	0.746485i	$0.268260\pi$
$398$		−	173.375i		−	0.435615i
$399$	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	$0.655548\pi$
$402$	13.9629	+	8.06147i	0.0347335	+	0.0200534i
$403$	13.5166	−	23.4115i	0.0335400	−	0.0580930i
$404$	241.790	−	139.597i	0.598490	−	0.345538i
$405$		0			0
$406$	70.2782	−	46.7020i	0.173099	−	0.115030i
$407$	155.337			0.381664
$408$	19.9385	+	34.5345i	0.0488689	+	0.0846435i
$409$	373.605	+	215.701i	0.913460	+	0.527386i	0.881543	−	0.472104i	$-0.156505\pi$
$409$	373.605	+	215.701i	0.913460	+	0.527386i	0.0319171	+	0.999491i	$0.489839\pi$
$410$		0			0
$411$	200.461	−	115.736i	0.487739	−	0.281596i
$412$		−	348.969i		−	0.847011i
$413$	94.0046	−	189.415i	0.227614	−	0.458631i
$414$	−50.6143			−0.122257
$415$		0			0
$416$	17.1677	+	9.91176i	0.0412684	+	0.0238263i
$417$	−167.803	+	290.643i	−0.402405	+	0.696986i
$418$	−120.303	+	69.4570i	−0.287806	+	0.166165i
$419$			585.412i			1.39716i	0.715530	+	0.698582i	$0.246185\pi$
$419$			585.412i			1.39716i	−0.715530	+	0.698582i	$0.753815\pi$
$420$		0			0
$421$	400.267			0.950754			0.475377	−	0.879782i	$-0.342312\pi$
$421$	400.267			0.950754			0.475377	+	0.879782i	$0.342312\pi$
$422$	249.488	+	432.126i	0.591203	+	1.02399i
$423$	48.6112	+	28.0657i	0.114920	+	0.0663492i
$424$	3.98511	−	6.90241i	0.00939885	−	0.0162793i
$425$		0			0
$426$			239.499i			0.562204i
$427$	−183.461	−	276.077i	−0.429652	−	0.646550i
$428$	−120.953			−0.282600
$429$	−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	$0.318294\pi$
$432$	−18.0000	+	10.3923i	−0.0416667	+	0.0240563i
$433$			2.39222i			0.00552477i	0.999996	+	0.00276238i	$0.000879295\pi$
$433$			2.39222i			0.00552477i	−0.999996	+	0.00276238i	$0.999121\pi$
$434$	76.2158	−	4.80210i	0.175613	−	0.0110647i
$435$		0			0
$436$	100.811	+	174.610i	0.231219	+	0.400482i
$437$	−183.277	−	105.815i	−0.419399	−	0.242140i
$438$	−74.9069	+	129.743i	−0.171020	+	0.296216i
$439$	−350.264	+	202.225i	−0.797867	+	0.460649i	−0.842725	−	0.538345i	$-0.819050\pi$
$439$	−350.264	+	202.225i	−0.797867	+	0.460649i	0.0448578	+	0.998993i	$0.485717\pi$
$440$		0			0
$441$	−88.8975	−	117.074i	−0.201582	−	0.265473i
$442$	−40.3402			−0.0912674
$443$	146.005	+	252.889i	0.329583	+	0.570855i	0.982429	−	0.186636i	$-0.0597584\pi$
$443$	146.005	+	252.889i	0.329583	+	0.570855i	−0.652846	+	0.757491i	$0.726425\pi$
$444$	84.1603	+	48.5899i	0.189550	+	0.109437i
$445$		0			0
$446$	75.6182	−	43.6582i	0.169547	−	0.0978883i
$447$			114.326i			0.255764i
$448$	3.52139	+	55.8892i	0.00786024	+	0.124753i
$449$	125.680			0.279911			0.139956	−	0.990158i	$-0.455304\pi$
$449$	125.680			0.279911			0.139956	+	0.990158i	$0.455304\pi$
$450$		0			0
$451$	−15.0673	−	8.69913i	−0.0334087	−	0.0192885i
$452$	−74.1876	+	128.497i	−0.164132	+	0.284285i
$453$	52.3229	−	30.2087i	0.115503	−	0.0666858i
$454$		−	296.310i		−	0.652666i
$455$		0			0
$456$	−86.9054			−0.190582
$457$	43.0015	+	74.4808i	0.0940952	+	0.162978i	0.909231	−	0.416293i	$-0.136671\pi$
$457$	43.0015	+	74.4808i	0.0940952	+	0.162978i	−0.815135	+	0.579270i	$0.803338\pi$
$458$	−132.026	−	76.2255i	−0.288267	−	0.166431i
$459$	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	$-0.0455362\pi$
$462$	42.2073	−	85.0456i	0.0913578	−	0.184081i
$463$	−73.9873			−0.159800			−0.0798999	−	0.996803i	$-0.525460\pi$
$463$	−73.9873			−0.159800			−0.0798999	+	0.996803i	$0.525460\pi$
$464$	17.0475	+	29.5271i	0.0367403	+	0.0636360i
$465$		0			0
$466$	−231.115	+	400.303i	−0.495956	+	0.859020i
$467$	387.032	−	223.453i	0.828762	−	0.478486i	−0.0246667	−	0.999696i	$-0.507852\pi$
$467$	387.032	−	223.453i	0.828762	−	0.478486i	0.853429	+	0.521210i	$0.174519\pi$
$468$		−	21.0260i		−	0.0449274i
$469$	−41.2719	−	20.4829i	−0.0879999	−	0.0436735i
$470$		0			0
$471$	46.3329	+	80.2509i	0.0983713	+	0.170384i
$472$	73.9951	+	42.7211i	0.156769	+	0.0905108i
$473$	−119.588	+	207.132i	−0.252828	+	0.437912i
$474$	−261.207	+	150.808i	−0.551069	+	0.318160i
$475$		0			0
$476$	−63.0722	−	94.9124i	−0.132505	−	0.199396i
$477$	−8.45370			−0.0177226
$478$	−6.50621	−	11.2691i	−0.0136113	−	0.0235755i
$479$	513.818	+	296.653i	1.07269	+	0.619318i	0.928915	−	0.370293i	$-0.120743\pi$
$479$	513.818	+	296.653i	1.07269	+	0.619318i	0.143775	+	0.989610i	$0.454076\pi$
$480$		0			0
$481$	−85.1377	+	49.1543i	−0.177002	+	0.102192i
$482$			454.226i			0.942378i
$483$	144.356	−	9.09539i	0.298874	−	0.0188310i
$484$	−180.679			−0.373303
$485$		0			0
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	−409.771	+	709.744i	−0.841418	+	1.45738i	0.0472773	+	0.998882i	$0.484946\pi$
$487$	−409.771	+	709.744i	−0.841418	+	1.45738i	−0.888696	+	0.458498i	$0.848388\pi$
$488$	115.993	−	66.9683i	0.237690	−	0.137230i
$489$			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	$0.308918\pi$
$492$	−5.44222	−	9.42620i	−0.0110614	−	0.0191589i
$493$	−60.0867	−	34.6911i	−0.121880	−	0.0703673i
$494$	43.9574	−	76.1364i	0.0889825	−	0.154122i
$495$		0			0
$496$			30.8569i			0.0622115i
$497$	−43.0380	−	683.071i	−0.0865955	−	1.37439i
$498$	219.429			0.440620
$499$	−317.394	−	549.742i	−0.636060	−	1.10169i	−0.986290	−	0.165024i	$-0.947230\pi$
$499$	−317.394	−	549.742i	−0.636060	−	1.10169i	0.350230	−	0.936664i	$-0.386103\pi$
$500$		0			0
$501$	119.464	−	206.918i	0.238451	−	0.413010i
$502$	23.5634	−	13.6043i	0.0469390	−	0.0271003i
$503$		−	120.116i		−	0.238800i	−0.992846	−	0.119400i	$-0.961903\pi$
$503$		−	120.116i		−	0.238800i	0.992846	−	0.119400i	$-0.0380970\pi$
$504$	49.4700	−	32.8743i	0.0981547	−	0.0652268i
$505$		0			0
$506$	46.7103	+	80.9046i	0.0923128	+	0.159890i
$507$	−235.079	−	135.723i	−0.463668	−	0.267699i
$508$	−151.093	+	261.701i	−0.297428	+	0.515160i
$509$	51.1082	−	29.5073i	0.100409	−	0.0579712i	−0.448955	−	0.893555i	$-0.648204\pi$
$509$	51.1082	−	29.5073i	0.100409	−	0.0579712i	0.549364	+	0.835583i	$0.314870\pi$
$510$		0			0
$511$	190.326	−	383.497i	0.372458	−	0.750484i
$512$	−22.6274			−0.0441942
$513$	46.0885	+	79.8277i	0.0898412	+	0.155609i
$514$	158.509	+	91.5150i	0.308383	+	0.178045i
$515$		0			0
$516$	−129.583	+	74.8148i	−0.251130	+	0.144990i
$517$		−	103.604i		−	0.200394i
$518$	−248.764	−	123.459i	−0.480239	−	0.238338i
$519$	−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	$-0.715471\pi$
$522$	18.0816	−	31.3182i	0.0346391	−	0.0599966i
$523$	−598.739	+	345.682i	−1.14482	+	0.660960i	−0.947619	−	0.319404i	$-0.896517\pi$
$523$	−598.739	+	345.682i	−1.14482	+	0.660960i	−0.197197	+	0.980364i	$0.563184\pi$
$524$		−	431.442i		−	0.823363i
$525$		0			0
$526$	−236.068			−0.448798
$527$	−31.3964	−	54.3802i	−0.0595757	−	0.103188i
$528$	33.2232	+	19.1814i	0.0629227	+	0.0363285i
$529$	193.339	−	334.872i	0.365479	−	0.633029i
$530$		0			0
$531$		−	90.6251i		−	0.170669i
$532$	247.861	−	15.6169i	0.465905	−	0.0293551i
$533$	11.0109			0.0206583
$534$	144.660	+	250.559i	0.270900	+	0.469212i
$535$		0			0
$536$	9.30859	−	16.1229i	0.0173668	−	0.0300801i
$537$	−109.950	+	63.4798i	−0.204749	+	0.118212i
$538$			295.703i			0.549635i
$539$	−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	$-0.333597\pi$
$542$	173.989	+	100.453i	0.321013	+	0.185337i
$543$	53.2275	−	92.1928i	0.0980249	−	0.169784i
$544$	39.8771	−	23.0230i	0.0733034	−	0.0423217i
$545$		0			0
$546$	3.77837	+	59.9679i	0.00692010	+	0.109831i
$547$	318.491			0.582251			0.291126	−	0.956685i	$-0.405970\pi$
$547$	318.491			0.582251			0.291126	+	0.956685i	$0.405970\pi$
$548$	−133.641	−	231.472i	−0.243870	−	0.422395i
$549$	−123.029	−	71.0306i	−0.224096	−	0.129382i
$550$		0			0
$551$	130.949	−	75.6034i	0.237657	−	0.137211i
$552$			58.4444i			0.105877i
$553$	717.883	−	477.055i	1.29816	−	0.862667i
$554$	−630.628			−1.13832
$555$		0			0
$556$	335.606	+	193.762i	0.603607	+	0.348493i
$557$	288.479	−	499.660i	0.517915	−	0.897055i	−0.481869	−	0.876244i	$-0.660042\pi$
$557$	288.479	−	499.660i	0.517915	−	0.897055i	0.999783	−	0.0208114i	$-0.00662495\pi$
$558$	28.3439	−	16.3643i	0.0507955	−	0.0293268i
$559$		−	151.367i		−	0.270783i
$560$		0			0
$561$	−78.0672			−0.139157
$562$	340.834	+	590.342i	0.606466	+	1.05043i
$563$	−308.279	−	177.985i	−0.547565	−	0.316137i	0.200574	−	0.979678i	$-0.435719\pi$
$563$	−308.279	−	177.985i	−0.547565	−	0.316137i	−0.748139	+	0.663542i	$0.769053\pi$
$564$	32.4075	−	56.1314i	0.0574601	−	0.0995238i
$565$		0			0
$566$		−	306.196i		−	0.540983i
$567$	−56.4324	−	28.0068i	−0.0995281	−	0.0493948i
$568$	276.550			0.486883
$569$	186.085	+	322.308i	0.327038	+	0.566447i	0.981923	−	0.189282i	$-0.0606161\pi$
$569$	186.085	+	322.308i	0.327038	+	0.566447i	−0.654885	+	0.755729i	$0.727283\pi$
$570$		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	$0.120269\pi$
$572$	−33.6091	+	19.4042i	−0.0587571	+	0.0339234i
$573$		−	623.300i		−	1.08778i
$574$	17.2155	+	25.9063i	0.0299922	+	0.0451330i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−13.9714	−	8.06639i	−0.0242139	−	0.0139799i	0.487844	−	0.872931i	$-0.337783\pi$
$577$	−13.9714	−	8.06639i	−0.0242139	−	0.0139799i	−0.512058	+	0.858951i	$0.671117\pi$
$578$	157.503	−	272.803i	0.272496	−	0.471977i
$579$	−209.617	+	121.023i	−0.362033	+	0.209020i
$580$		0			0
$581$	−625.830	+	39.4314i	−1.07716	+	0.0678681i
$582$	159.698			0.274395
$583$	7.80164	+	13.5128i	0.0133819	+	0.0231781i
$584$	149.814	+	86.4950i	0.256530	+	0.148108i
$585$		0			0
$586$	−469.940	+	271.320i	−0.801945	+	0.463003i
$587$		−	204.516i		−	0.348409i	−0.984709	−	0.174205i	$-0.944265\pi$
$587$		−	204.516i		−	0.348409i	0.984709	−	0.174205i	$-0.0557354\pi$
$588$	−135.185	+	102.650i	−0.229906	+	0.174575i
$589$	136.846			0.232337
$590$		0			0
$591$	−372.514	−	215.071i	−0.630311	−	0.363910i
$592$	56.1068	−	97.1799i	0.0947751	−	0.164155i
$593$	597.577	−	345.011i	1.00772	−	0.581806i	0.0971952	−	0.995265i	$-0.469013\pi$
$593$	597.577	−	345.011i	1.00772	−	0.581806i	0.910523	+	0.413459i	$0.135680\pi$
$594$		−	40.6899i		−	0.0685016i
$595$		0			0
$596$	132.013			0.221498
$597$	106.170	+	183.892i	0.177839	+	0.308026i
$598$	−51.2022	−	29.5616i	−0.0856224	−	0.0494341i
$599$	477.775	−	827.531i	0.797622	−	1.38152i	−0.123539	−	0.992340i	$-0.539425\pi$
$599$	477.775	−	827.531i	0.797622	−	1.38152i	0.921161	−	0.389182i	$-0.127242\pi$
$600$		0			0
$601$			587.954i			0.978293i	0.872202	+	0.489146i	$0.162692\pi$
$601$			587.954i			0.978293i	−0.872202	+	0.489146i	$0.837308\pi$
$602$	356.137	−	236.664i	0.591590	−	0.393130i
$603$	−19.7465			−0.0327471
$604$	−34.8820	−	60.4173i	−0.0577516	−	0.100029i
$605$		0			0
$606$	−170.971	+	296.131i	−0.282131	+	0.488665i
$607$	449.438	−	259.483i	0.740425	−	0.427485i	−0.0817986	−	0.996649i	$-0.526066\pi$
$607$	449.438	−	259.483i	0.740425	−	0.427485i	0.822224	+	0.569164i	$0.192733\pi$
$608$			100.350i			0.165049i
$609$	−45.9423	+	92.5714i	−0.0754389	+	0.152006i
$610$		0			0
$611$	32.7839	+	56.7834i	0.0536561	+	0.0929351i
$612$	−42.2960	−	24.4196i	−0.0691111	−	0.0399013i
$613$	−63.7771	+	110.465i	−0.104041	+	0.180204i	−0.913346	−	0.407184i	$-0.866511\pi$
$613$	−63.7771	+	110.465i	−0.104041	+	0.180204i	0.809305	+	0.587389i	$0.199844\pi$
$614$	−25.8744	+	14.9386i	−0.0421407	+	0.0243300i
$615$		0			0
$616$	−98.2022	−	48.7368i	−0.159419	−	0.0791182i
$617$	486.581			0.788624			0.394312	−	0.918977i	$-0.370983\pi$
$617$	486.581			0.788624			0.394312	+	0.918977i	$0.370983\pi$
$618$	213.699	+	370.137i	0.345791	+	0.598927i
$619$	370.662	+	214.002i	0.598808	+	0.345722i	0.768572	−	0.639763i	$-0.220967\pi$
$619$	370.662	+	214.002i	0.598808	+	0.345722i	−0.169765	+	0.985485i	$0.554301\pi$
$620$		0			0
$621$	53.6846	−	30.9948i	0.0864486	−	0.0499111i
$622$			122.522i			0.196980i
$623$	−457.609	−	688.620i	−0.734524	−	1.10533i
$624$	−24.2787			−0.0389082
$625$		0			0
$626$	−3.47589	−	2.00680i	−0.00555254	−	0.00320576i
$627$	85.0671	−	147.341i	0.135673	−	0.234993i
$628$	92.6658	−	53.5006i	0.147557	−	0.0851921i
$629$			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	$0.516275\pi$
$632$	174.138	+	301.616i	0.275535	+	0.477240i
$633$	−529.244	−	305.559i	−0.836088	−	0.482716i
$634$	219.097	−	379.488i	0.345579	−	0.598561i
$635$		0			0
$636$			9.76149i			0.0153483i
$637$	−21.5525	−	170.354i	−0.0338343	−	0.267432i
$638$	−66.7476			−0.104620
$639$	−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	$0.981228\pi$
$642$	128.290	−	74.0681i	0.199828	−	0.115371i
$643$		−	1092.83i		−	1.69958i	−0.527124	−	0.849788i	$-0.676730\pi$
$643$		−	1092.83i		−	1.69958i	0.527124	−	0.849788i	$-0.323270\pi$
$644$	−10.5025	−	166.688i	−0.0163082	−	0.258833i
$645$		0			0
$646$	−102.104	−	176.850i	−0.158056	−	0.273761i
$647$	−446.083	−	257.546i	−0.689463	−	0.398062i	0.113948	−	0.993487i	$-0.463650\pi$
$647$	−446.083	−	257.546i	−0.689463	−	0.398062i	−0.803411	+	0.595425i	$0.796984\pi$
$648$	12.7279	−	22.0454i	0.0196419	−	0.0340207i
$649$	−144.860	+	83.6349i	−0.223205	+	0.128867i
$650$		0			0
$651$	−77.8984	+	51.7659i	−0.119660	+	0.0795175i
$652$	411.967			0.631852
$653$	393.317	+	681.245i	0.602323	+	1.04325i	0.992468	+	0.122501i	$0.0390915\pi$
$653$	393.317	+	681.245i	0.602323	+	1.04325i	−0.390145	+	0.920753i	$0.627575\pi$
$654$	−213.853	−	123.468i	−0.326993	−	0.188789i
$655$		0			0
$656$	−10.8844	+	6.28413i	−0.0165921	+	0.00957947i
$657$		−	183.484i		−	0.279275i
$658$	−82.3420	+	165.915i	−0.125140	+	0.252151i
$659$	−819.425			−1.24344			−0.621719	−	0.783241i	$-0.713565\pi$
$659$	−819.425			−1.24344			−0.621719	+	0.783241i	$0.713565\pi$
$660$		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	$0.949872\pi$
$662$	−294.573	+	510.216i	−0.444974	+	0.770718i
$663$	42.7873	−	24.7032i	0.0645358	−	0.0372598i
$664$		−	253.375i		−	0.381589i
$665$		0			0
$666$	−119.021			−0.178710
$667$	−50.8437	−	88.0639i	−0.0762275	−	0.132030i
$668$	−238.928	−	137.945i	−0.357677	−	0.206505i
$669$	−53.4701	+	92.6130i	−0.0799254	+	0.138435i
$670$		0			0
$671$			262.207i			0.390771i
$672$	−37.9600	−	57.1230i	−0.0564881	−	0.0850045i
$673$	669.779			0.995213			0.497607	−	0.867403i	$-0.334212\pi$
$673$	669.779			0.995213			0.497607	+	0.867403i	$0.334212\pi$
$674$	−109.949	−	190.437i	−0.163129	−	0.282548i
$675$		0			0
$676$	−156.720	+	271.446i	−0.231834	+	0.401548i
$677$	786.522	−	454.099i	1.16178	−	0.670751i	0.210047	−	0.977691i	$-0.432638\pi$
$677$	786.522	−	454.099i	1.16178	−	0.670751i	0.951729	+	0.306940i	$0.0993051\pi$
$678$		−	181.722i		−	0.268026i
$679$	−455.472	+	28.6977i	−0.670798	+	0.0422647i
$680$		0			0
$681$	181.452	+	314.285i	0.266450	+	0.461505i
$682$	−52.3153	−	30.2042i	−0.0767086	−	0.0442877i
$683$	−330.668	+	572.733i	−0.484140	+	0.838555i	−0.999834	−	0.0182177i	$-0.994201\pi$
$683$	−330.668	+	572.733i	−0.484140	+	0.838555i	0.515694	+	0.856773i	$0.327534\pi$
$684$	92.1770	−	53.2184i	0.134762	−	0.0778047i
$685$		0			0
$686$	367.112	−	317.059i	0.535149	−	0.462185i
$687$	186.714			0.271781
$688$	86.3887	+	149.630i	0.125565	+	0.217485i
$689$	−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	$0.397493\pi$
$692$			441.133i			0.637475i
$693$	7.31198	+	116.051i	0.0105512	+	0.167462i
$694$	−724.794			−1.04437
$695$		0			0
$696$	−36.1632	−	20.8788i	−0.0519586	−	0.0299983i
$697$	12.7880	−	22.1495i	0.0183472	−	0.0317783i
$698$	329.683	−	190.343i	0.472326	−	0.272697i
$699$		−	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	$0.595885\pi$
$702$	12.8758	+	22.3015i	0.0183415	+	0.0317685i
$703$	−430.980	−	248.827i	−0.613059	−	0.353950i
$704$	22.1488	−	38.3629i	0.0314614	−	0.0544927i
$705$		0			0
$706$			829.382i			1.17476i
$707$	434.409	−	875.313i	0.614440	−	1.23807i
$708$	−104.645			−0.147804
$709$	−136.620	−	236.632i	−0.192693	−	0.333755i	0.753449	−	0.657507i	$-0.228389\pi$
$709$	−136.620	−	236.632i	−0.192693	−	0.333755i	−0.946142	+	0.323752i	$0.895056\pi$
$710$		0			0
$711$	184.701	−	319.912i	0.259776	−	0.449946i
$712$	289.321	−	167.039i	0.406349	−	0.234606i
$713$		−	92.0300i		−	0.129074i
$714$	125.020	+	62.0462i	0.175098	+	0.0868994i
$715$		0			0
$716$	73.3002	+	126.960i	0.102375	+	0.177318i
$717$	13.8018	+	7.96845i	0.0192493	+	0.0111136i
$718$	62.8223	−	108.811i	0.0874962	−	0.151548i
$719$	361.463	−	208.691i	0.502731	−	0.290252i	−0.227110	−	0.973869i	$-0.572928\pi$
$719$	361.463	−	208.691i	0.502731	−	0.290252i	0.729840	+	0.683617i	$0.239594\pi$
$720$		0			0
$721$	−676.000	−	1017.26i	−0.937587	−	1.41090i
$722$	−65.4934			−0.0907111
$723$	−278.156	−	481.779i	−0.384724	−	0.666362i
$724$	−106.455	−	61.4619i	−0.147037	−	0.0848921i
$725$		0			0
$726$	191.639	−	110.643i	0.263965	−	0.152400i
$727$			357.267i			0.491426i	0.969343	+	0.245713i	$0.0790221\pi$
$727$			357.267i			0.491426i	−0.969343	+	0.245713i	$0.920978\pi$
$728$	69.2450	−	4.36289i	0.0951167	−	0.00599298i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−304.491	−	175.798i	−0.416541	−	0.240490i
$732$	−82.0191	+	142.061i	−0.112048	+	0.194073i
$733$	−373.293	+	215.521i	−0.509267	+	0.294026i	−0.732532	−	0.680732i	$-0.761662\pi$
$733$	−373.293	+	215.521i	−0.509267	+	0.294026i	0.223265	+	0.974758i	$0.428328\pi$
$734$		−	998.488i		−	1.36034i
$735$		0			0
$736$	67.4858			0.0916926
$737$	18.2234	+	31.5638i	0.0247264	+	0.0428274i
$738$	11.5447	+	6.66533i	0.0156432	+	0.00903161i
$739$	−159.512	+	276.282i	−0.215848	+	0.373860i	−0.953535	−	0.301284i	$-0.902585\pi$
$739$	−159.512	+	276.282i	−0.215848	+	0.373860i	0.737687	+	0.675143i	$0.235918\pi$
$740$		0			0
$741$			107.673i			0.145308i
$742$	−1.75414	−	27.8406i	−0.00236407	−	0.0375210i
$743$	−1303.33			−1.75414			−0.877072	−	0.480360i	$-0.840506\pi$
$743$	−1303.33			−1.75414			−0.877072	+	0.480360i	$0.840506\pi$
$744$	−18.8959	−	32.7287i	−0.0253977	−	0.0439902i
$745$		0			0
$746$	36.2337	−	62.7585i	0.0485706	−	0.0841267i
$747$	−232.740	+	134.372i	−0.311566	+	0.179883i
$748$			90.1442i			0.120514i
$749$	−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	$-0.471698\pi$
$752$	−64.8150	−	37.4210i	−0.0861901	−	0.0497619i
$753$	−16.6618	+	28.8591i	−0.0221273	+	0.0383255i
$754$	36.5832	−	21.1213i	0.0485188	−	0.0280124i
$755$		0			0
$756$	−32.3395	+	65.1625i	−0.0427771	+	0.0861938i
$757$	1206.22			1.59342			0.796712	−	0.604359i	$-0.206571\pi$
$757$	1206.22			1.59342			0.796712	+	0.604359i	$0.206571\pi$
$758$	−137.691	−	238.487i	−0.181650	−	0.314627i
$759$	−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	$0.382908\pi$
$762$		−	370.101i		−	0.485697i
$763$	632.114	+	313.712i	0.828459	+	0.411156i
$764$	−719.725			−0.942048
$765$		0			0
$766$	−643.088	−	371.287i	−0.839540	−	0.484709i
$767$	52.9301	−	91.6777i	0.0690093	−	0.119528i
$768$	24.0000	−	13.8564i	0.0312500	−	0.0180422i
$769$			1341.44i			1.74440i	0.489149	+	0.872200i	$0.337307\pi$
$769$			1341.44i			1.74440i	−0.489149	+	0.872200i	$0.662693\pi$
$770$		0			0
$771$	−224.165			−0.290746
$772$	139.745	+	242.045i	0.181017	+	0.313530i
$773$	−155.933	−	90.0279i	−0.201724	−	0.116466i	0.395735	−	0.918365i	$-0.370490\pi$
$773$	−155.933	−	90.0279i	−0.201724	−	0.116466i	−0.597460	+	0.801899i	$0.703823\pi$
$774$	91.6290	−	158.706i	0.118384	−	0.205047i
$775$		0			0
$776$		−	184.403i		−	0.237633i
$777$	339.456	−	21.3880i	0.436881	−	0.0275264i
$778$	570.677			0.733518
$779$	27.8693	+	48.2711i	0.0357758	+	0.0619654i
$780$		0			0
$781$	−270.700	+	468.866i	−0.346607	+	0.600341i
$782$	−118.932	+	68.6657i	−0.152087	+	0.0878078i
$783$			44.2907i			0.0565654i
$784$	118.530	+	156.098i	0.151186	+	0.199105i
$785$		0			0
$786$	264.203	+	457.614i	0.336137	+	0.582206i
$787$	−1012.19	−	584.386i	−1.28613	−	0.742549i	−0.308170	−	0.951331i	$-0.599717\pi$
$787$	−1012.19	−	584.386i	−1.28613	−	0.742549i	−0.977962	+	0.208783i	$0.933050\pi$
$788$	−248.343	+	430.142i	−0.315156	+	0.545866i
$789$	250.387	−	144.561i	0.317348	−	0.183221i
$790$		0			0
$791$	32.6554	+	518.285i	0.0412837	+	0.655228i
$792$	−46.9847			−0.0593241
$793$	−82.9717	−	143.711i	−0.104630	−	0.181225i
$794$	197.419	+	113.980i	0.248639	+	0.143552i
$795$		0			0
$796$	212.340	−	122.595i	0.266759	−	0.154013i
$797$			1242.38i			1.55883i	0.626510	+	0.779413i	$0.284483\pi$
$797$			1242.38i			1.55883i	−0.626510	+	0.779413i	$0.715517\pi$
$798$	−253.333	+	168.348i	−0.317460	+	0.210962i
$799$	152.301			0.190614
$800$		0			0
$801$	−306.871	−	177.172i	−0.383110	−	0.221189i
$802$	−300.529	+	520.531i	−0.374724	+	0.649041i
$803$	−293.290	+	169.331i	−0.365243	+	0.210873i
$804$			22.8013i			0.0283598i
$805$		0			0
$806$	38.2308			0.0474327
$807$	−181.081	−	313.641i	−0.224387	−	0.388650i
$808$	341.942	+	197.421i	0.423196	+	0.244332i
$809$	44.8275	−	77.6435i	0.0554110	−	0.0959747i	−0.836989	−	0.547219i	$-0.815686\pi$
$809$	44.8275	−	77.6435i	0.0554110	−	0.0959747i	0.892400	+	0.451244i	$0.149020\pi$
$810$		0			0
$811$		−	234.127i		−	0.288689i	−0.989527	−	0.144345i	$-0.953893\pi$
$811$		−	234.127i		−	0.288689i	0.989527	−	0.144345i	$-0.0461074\pi$
$812$	106.892	+	53.0496i	0.131641	+	0.0653320i
$813$	−246.058			−0.302654
$814$	109.840	+	190.249i	0.134939	+	0.233721i
$815$		0			0
$816$	−28.1973	+	48.8392i	−0.0345556	+	0.0598520i
$817$	663.588	−	383.123i	0.812225	−	0.468938i
$818$			610.095i			0.745837i
$819$	−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	$0.965794\pi$
$822$	283.494	+	163.676i	0.344884	+	0.199119i
$823$	−430.147	+	745.037i	−0.522657	+	0.905269i	0.476995	+	0.878906i	$0.341726\pi$
$823$	−430.147	+	745.037i	−0.522657	+	0.905269i	−0.999652	+	0.0263632i	$0.991607\pi$
$824$	427.398	−	246.758i	0.518686	−	0.299464i
$825$		0			0
$826$	298.456	−	18.8047i	0.361327	−	0.0227660i
$827$	703.661			0.850860			0.425430	−	0.904991i	$-0.360123\pi$
$827$	703.661			0.850860			0.425430	+	0.904991i	$0.360123\pi$
$828$	−35.7897	−	61.9896i	−0.0432243	−	0.0748667i
$829$	1282.06	+	740.196i	1.54651	+	0.892878i	0.998404	+	0.0564693i	$0.0179843\pi$
$829$	1282.06	+	740.196i	1.54651	+	0.892878i	0.548106	+	0.836409i	$0.315349\pi$
$830$		0			0
$831$	668.882	−	386.179i	0.804912	−	0.464716i
$832$			28.0347i			0.0336955i
$833$	−367.717	−	154.495i	−0.441437	−	0.185468i
$834$	−474.618			−0.569086
$835$		0			0
$836$	−170.134	−	98.2271i	−0.203510	−	0.117496i
$837$	−20.0422	+	34.7140i	−0.0239452	+	0.0414743i
$838$	−716.980	+	413.949i	−0.855585	+	0.493972i
$839$			1377.82i			1.64222i	0.570769	+	0.821111i	$0.306645\pi$
$839$			1377.82i			1.64222i	−0.570769	+	0.821111i	$0.693355\pi$
$840$		0			0
$841$	−768.346			−0.913610
$842$	283.032	+	490.225i	0.336142	+	0.582215i
$843$	−723.018	−	417.435i	−0.857672	−	0.495177i
$844$	−352.829	+	611.118i	−0.418044	+	0.724073i
$845$		0			0
$846$			79.3818i			0.0938319i
$847$	−526.687	+	350.000i	−0.621827	+	0.413223i
$848$	11.2716			0.0132920
$849$	187.506	+	324.770i	0.220855	+	0.382533i
$850$		0			0
$851$	−167.337	+	289.837i	−0.196636	+	0.340584i
$852$	−293.325	+	169.351i	−0.344278	+	0.198769i
$853$			383.511i			0.449602i	0.974405	+	0.224801i	$0.0721733\pi$
$853$			383.511i			0.449602i	−0.974405	+	0.224801i	$0.927827\pi$
$854$	208.397	−	419.909i	0.244024	−	0.491697i
$855$		0			0
$856$	−85.5265	−	148.136i	−0.0999141	−	0.173056i
$857$	−284.273	−	164.125i	−0.331708	−	0.191512i	0.324891	−	0.945751i	$-0.394672\pi$
$857$	−284.273	−	164.125i	−0.331708	−	0.191512i	−0.656599	+	0.754240i	$0.728006\pi$
$858$	23.7652	−	41.1625i	0.0276984	−	0.0479750i
$859$	−168.842	+	97.4811i	−0.196557	+	0.113482i	−0.595048	−	0.803690i	$-0.702867\pi$
$859$	−168.842	+	97.4811i	−0.196557	+	0.113482i	0.398492	+	0.917172i	$0.369534\pi$
$860$		0			0
$861$	−34.1242	−	16.9355i	−0.0396332	−	0.0196696i
$862$	−558.985			−0.648474
$863$	−267.881	−	463.984i	−0.310407	−	0.537641i	0.668043	−	0.744122i	$-0.267132\pi$
$863$	−267.881	−	463.984i	−0.310407	−	0.537641i	−0.978451	+	0.206481i	$0.933799\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$		0			0
$866$	−2.92986	+	1.69156i	−0.00338321	+	0.00195330i
$867$			385.801i			0.444984i
$868$	59.7741	+	89.9493i	0.0688641	+	0.103628i
$869$	−681.818			−0.784601
$870$		0			0
$871$	−19.9758	−	11.5331i	−0.0229344	−	0.0132412i
$872$	−142.569	+	246.936i	−0.163496	+	0.283184i
$873$	−169.385	+	97.7947i	−0.194027	+	0.112021i
$874$		−	299.291i		−	0.342438i
$875$		0			0
$876$	−211.869			−0.241859
$877$	603.606	+	1045.48i	0.688262	+	1.19210i	0.972400	+	0.233321i	$0.0749594\pi$
$877$	603.606	+	1045.48i	0.688262	+	1.19210i	−0.284138	+	0.958784i	$0.591707\pi$
$878$	−495.348	−	285.989i	−0.564177	−	0.325728i
$879$	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	$0.883711\pi$
$882$	80.5253	−	191.660i	0.0912985	−	0.217302i
$883$	−177.196			−0.200675			−0.100337	−	0.994953i	$-0.531992\pi$
$883$	−177.196			−0.200675			−0.100337	+	0.994953i	$0.531992\pi$
$884$	−28.5248	−	49.4065i	−0.0322679	−	0.0558897i
$885$		0			0
$886$	−206.483	+	357.639i	−0.233051	+	0.403655i
$887$	−1101.94	+	636.205i	−1.24232	+	0.717255i	−0.969566	−	0.244829i	$-0.921268\pi$
$887$	−1101.94	+	636.205i	−1.24232	+	0.717255i	−0.272755	+	0.962083i	$0.587935\pi$
$888$			137.433i			0.154767i
$889$	66.5072	+	1055.56i	0.0748112	+	1.18736i
$890$		0			0
$891$	24.9174	+	43.1582i	0.0279657	+	0.0484379i
$892$	106.940	+	61.7420i	0.119888	+	0.0692175i
$893$	−165.957	+	287.446i	−0.185842	+	0.321888i
$894$	−140.021	+	80.8410i	−0.156623	+	0.0904261i
$895$		0			0
$896$	−65.9600	+	43.8324i	−0.0736161	+	0.0489201i
$897$	72.4108			0.0807255
$898$	88.8693	+	153.926i	0.0989636	+	0.171410i
$899$	56.9447	+	32.8770i	0.0633423	+	0.0365707i
$900$		0			0
$901$	−19.8643	+	11.4687i	−0.0220470	+	0.0127288i
$902$		−	24.6048i		−	0.0272781i
$903$	−232.814	+	469.109i	−0.257823	+	0.519500i
$904$	−209.834			−0.232118
$905$		0			0
$906$	73.9958	+	42.7215i	0.0816731	+	0.0471540i
$907$	89.6364	−	155.255i	0.0988273	−	0.171174i	−0.812372	−	0.583139i	$-0.801824\pi$
$907$	89.6364	−	155.255i	0.0988273	−	0.171174i	0.911200	+	0.411965i	$0.135158\pi$
$908$	362.905	−	209.523i	0.399675	−	0.230752i
$909$		−	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	$0.377333\pi$
$912$	−61.4514	−	106.437i	−0.0673809	−	0.116707i
$913$	429.575	+	248.015i	0.470510	+	0.271649i
$914$	−60.8133	+	105.332i	−0.0665353	+	0.115243i
$915$		0			0
$916$		−	215.598i		−	0.235369i
$917$	−835.763	−	1257.67i	−0.911410	−	1.37151i
$918$	59.8156			0.0651586
$919$	−470.376	−	814.715i	−0.511835	−	0.886523i	−0.999906	−	0.0137197i	$-0.995633\pi$
$919$	−470.376	−	814.715i	−0.511835	−	0.886523i	0.488071	−	0.872804i	$-0.337701\pi$
$920$		0			0
$921$	18.2960	−	31.6896i	0.0198653	−	0.0344078i
$922$	160.991	−	92.9481i	0.174611	−	0.100811i
$923$		−	342.637i		−	0.371221i
$924$	134.004	−	8.44315i	0.145026	−	0.00913761i
$925$		0			0
$926$	−52.3169	−	90.6156i	−0.0564978	−	0.0978570i
$927$	−453.324	−	261.726i	−0.489022	−	0.282337i
$928$	−24.1088	+	41.7576i	−0.0259793	+	0.0449975i
$929$	5.55322	−	3.20616i	0.00597764	−	0.00345119i	−0.497008	−	0.867746i	$-0.665568\pi$
$929$	5.55322	−	3.20616i	0.00597764	−	0.00345119i	0.502986	+	0.864295i	$0.332235\pi$
$930$		0			0
$931$	692.275	−	525.665i	0.743582	−	0.564624i
$932$	−653.693			−0.701387
$933$	−75.0288	−	129.954i	−0.0804167	−	0.139286i
$934$	547.346	+	316.010i	0.586023	+	0.338341i
$935$		0			0
$936$	25.7515	−	14.8676i	0.0275123	−	0.0158842i
$937$			867.253i			0.925564i	0.886472	+	0.462782i	$0.153149\pi$
$937$			867.253i			0.925564i	−0.886472	+	0.462782i	$0.846851\pi$
$938$	−4.09739	−	65.0312i	−0.00436822	−	0.0693296i
$939$	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	$0.766041\pi$
$942$	−65.5246	+	113.492i	−0.0695590	+	0.120480i
$943$	32.4626	−	18.7423i	0.0344248	−	0.0198752i
$944$			120.833i			0.128002i
$945$		0			0
$946$	−338.246			−0.357553
$947$	−374.280	−	648.272i	−0.395227	−	0.684553i	0.597903	−	0.801568i	$-0.296001\pi$
$947$	−374.280	−	648.272i	−0.395227	−	0.684553i	−0.993130	+	0.117015i	$0.962667\pi$
$948$	−369.402	−	213.274i	−0.389665	−	0.224973i
$949$	107.165	−	185.615i	0.112924	−	0.195590i
$950$		0			0
$951$			536.677i			0.564329i
$952$	71.6447	−	144.361i	0.0752571	−	0.151639i
$953$	21.6304			0.0226972			0.0113486	−	0.999936i	$-0.496388\pi$
$953$	21.6304			0.0226972			0.0113486	+	0.999936i	$0.496388\pi$
$954$	−5.97767	−	10.3536i	−0.00626590	−	0.0108529i
$955$		0			0
$956$	9.20117	−	15.9369i	0.00962466	−	0.0166704i
$957$	70.7965	−	40.8744i	0.0739776	−	0.0427110i
$958$			839.062i			0.875847i
$959$	−837.962	−	415.872i	−0.873787	−	0.433652i
$960$		0			0
$961$	−450.745	−	780.714i	−0.469038	−	0.812397i
$962$	−120.403	−	69.5147i	−0.125159	−	0.0722606i
$963$	−90.7146	+	157.122i	−0.0941999	+	0.163159i
$964$	−556.311	+	321.186i	−0.577086	+	0.333181i
$965$		0			0
$966$	113.215	+	170.368i	0.117200	+	0.176365i
$967$	452.988			0.468447			0.234224	−	0.972183i	$-0.424745\pi$
$967$	452.988			0.468447			0.234224	+	0.972183i	$0.424745\pi$
$968$	−127.759	−	221.285i	−0.131983	−	0.228601i
$969$	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	$0.0967791\pi$
$972$			31.1769i			0.0320750i
$973$	1353.65	−	85.2889i	1.39121	−	0.0876556i
$974$	−1159.01			−1.18995
$975$		0			0
$976$	164.038	+	94.7075i	0.168072	+	0.0970364i
$977$	−588.653	+	1019.58i	−0.602511	+	1.04358i	0.389929	+	0.920845i	$0.372500\pi$
$977$	−588.653	+	1019.58i	−0.602511	+	1.04358i	−0.992440	+	0.122734i	$0.960834\pi$
$978$	−436.957	+	252.278i	−0.446787	+	0.257952i
$979$			654.025i			0.668054i
$980$		0			0
$981$	302.434			0.308292
$982$	392.249	+	679.395i	0.399439	+	0.691848i
$983$	−695.029	−	401.275i	−0.707049	−	0.408215i	0.102918	−	0.994690i	$-0.467182\pi$
$983$	−695.029	−	401.275i	−0.707049	−	0.408215i	−0.809967	+	0.586475i	$0.800515\pi$
$984$	7.69646	−	13.3307i	0.00782161	−	0.0135474i
$985$		0			0
$986$		−	98.1212i		−	0.0995144i
$987$	−14.2649	−	226.404i	−0.0144528	−	0.229386i
$988$	124.330			0.125840
$989$	−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	$0.137140\pi$
$992$	−37.7918	+	21.8191i	−0.0380966	+	0.0219951i
$993$		−	721.554i		−	0.726640i
$994$	806.155	−	535.715i	0.811021	−	0.538948i
$995$		0			0
$996$	155.160	+	268.745i	0.155783	+	0.269824i
$997$	−808.088	−	466.550i	−0.810519	−	0.467953i	0.0366170	−	0.999329i	$-0.488342\pi$
$997$	−808.088	−	466.550i	−0.810519	−	0.467953i	−0.847136	+	0.531376i	$0.821675\pi$
$998$	448.862	−	777.453i	0.449762	−	0.779011i
$999$	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.p.c.451.4	✓	8
5.2	odd	4		1050.3.q.b.199.1		16
5.3	odd	4		1050.3.q.b.199.8		16
5.4	even	2		1050.3.p.d.451.1	yes	8
7.5	odd	6	inner	1050.3.p.c.901.4	yes	8
35.12	even	12		1050.3.q.b.649.8		16
35.19	odd	6		1050.3.p.d.901.1	yes	8
35.33	even	12		1050.3.q.b.649.1		16

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

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.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(0.440173 + 6.98615i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(0.440173 + 6.98615i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(2.76860 - 4.79536i) q^{11} +(3.00000 - 1.73205i) q^{12} +3.50434i q^{13} +(-8.24500 + 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(7.04933 + 4.06994i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-15.3628 + 8.86974i) q^{19} +(5.38992 - 10.8604i) q^{21} +7.83078 q^{22} +(5.96495 + 10.3316i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-4.29192 + 2.47794i) q^{26} -5.19615i q^{27} +(-12.5405 - 6.22374i) q^{28} -8.52374 q^{29} +(-6.68072 - 3.85711i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-8.30580 + 4.79536i) q^{33} +11.5115i q^{34} -6.00000 q^{36} +(14.0267 + 24.2950i) q^{37} +(-21.7263 - 12.5437i) q^{38} +(3.03484 - 5.25650i) q^{39} -3.14207i q^{41} +(17.1125 - 1.07820i) q^{42} -43.1943 q^{43} +(5.53720 + 9.59071i) q^{44} +(-8.43572 + 14.6111i) q^{46} +(16.2037 - 9.35524i) q^{47} +6.92820i q^{48} +(-48.6125 + 6.15023i) q^{49} +(-7.04933 - 12.2098i) q^{51} +(-6.06969 - 3.50434i) q^{52} +(-1.40895 + 2.44037i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} +30.7257 q^{57} +(-6.02720 - 10.4394i) q^{58} +(-26.1612 - 15.1042i) q^{59} +(-41.0095 + 23.6769i) q^{61} -10.9096i q^{62} +(-17.4903 + 11.6228i) q^{63} +8.00000 q^{64} +(-11.7462 - 6.78166i) q^{66} +(-3.29108 + 5.70032i) q^{67} +(-14.0987 + 8.13987i) q^{68} -20.6632i q^{69} -97.7751 q^{71} +(-4.24264 - 7.34847i) q^{72} +(-52.9672 - 30.5806i) q^{73} +(-19.8368 + 34.3583i) q^{74} -35.4790i q^{76} +(34.7197 + 17.2311i) q^{77} +8.58383 q^{78} +(-61.5670 - 106.637i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(3.84823 - 2.22178i) q^{82} +89.5815i q^{83} +(13.4209 + 20.1960i) q^{84} +(-30.5430 - 52.9020i) q^{86} +(12.7856 + 7.38178i) q^{87} +(-7.83078 + 13.5633i) q^{88} +(-102.290 + 59.0573i) q^{89} +(-24.4818 + 1.54251i) q^{91} -23.8598 q^{92} +(6.68072 + 11.5713i) q^{93} +(22.9156 + 13.2303i) q^{94} +(-8.48528 + 4.89898i) q^{96} +65.1965i q^{97} +(-41.9067 - 55.1890i) q^{98} +16.6116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9}+O(q^{10}) \) 8 * q - 12 * q^3 - 8 * q^4 + 12 * q^9	\( 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} + 24 q^{12} - 16 q^{14} - 16 q^{16} - 24 q^{17} + 72 q^{19} + 24 q^{22} + 60 q^{23} - 72 q^{26} - 24 q^{29} + 96 q^{31} + 12 q^{33} - 48 q^{36} - 24 q^{37} - 180 q^{38} - 12 q^{39} + 12 q^{42} - 112 q^{43} - 8 q^{44} + 32 q^{46} + 84 q^{47} - 264 q^{49} + 24 q^{51} + 24 q^{52} + 44 q^{53} + 40 q^{56} - 144 q^{57} + 104 q^{58} + 312 q^{59} - 204 q^{61} + 64 q^{64} - 36 q^{66} + 120 q^{67} + 48 q^{68} - 64 q^{71} + 84 q^{73} - 16 q^{74} + 228 q^{77} + 144 q^{78} - 144 q^{79} - 36 q^{81} - 60 q^{82} + 176 q^{86} + 36 q^{87} - 24 q^{88} - 336 q^{89} - 296 q^{91} - 240 q^{92} - 96 q^{93} + 36 q^{94} - 24 q^{99}+O(q^{100}) \) 8 * q - 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 + 24 * q^12 - 16 * q^14 - 16 * q^16 - 24 * q^17 + 72 * q^19 + 24 * q^22 + 60 * q^23 - 72 * q^26 - 24 * q^29 + 96 * q^31 + 12 * q^33 - 48 * q^36 - 24 * q^37 - 180 * q^38 - 12 * q^39 + 12 * q^42 - 112 * q^43 - 8 * q^44 + 32 * q^46 + 84 * q^47 - 264 * q^49 + 24 * q^51 + 24 * q^52 + 44 * q^53 + 40 * q^56 - 144 * q^57 + 104 * q^58 + 312 * q^59 - 204 * q^61 + 64 * q^64 - 36 * q^66 + 120 * q^67 + 48 * q^68 - 64 * q^71 + 84 * q^73 - 16 * q^74 + 228 * q^77 + 144 * q^78 - 144 * q^79 - 36 * q^81 - 60 * q^82 + 176 * q^86 + 36 * q^87 - 24 * q^88 - 336 * q^89 - 296 * q^91 - 240 * q^92 - 96 * q^93 + 36 * q^94 - 24 * q^99

Introduction

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