LMFDB - Embedded newform 1050.3.p.c.901.3

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			901.3
Root			$1.85439 + 1.88713i$ of defining polynomial
Character	$\chi$	$=$	1050.901
Dual form			1050.3.p.c.451.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-3.97571 + 5.76140i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-3.97571 + 5.76140i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.64728 - 2.85317i) q^{11} +(3.00000 + 1.73205i) q^{12} -7.72850i q^{13} +(4.24500 + 8.94315i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-10.9280 + 6.30929i) q^{17} +(-2.12132 - 3.67423i) q^{18} +(1.54304 + 0.890872i) q^{19} +(0.974040 - 12.0852i) q^{21} -4.65921 q^{22} +(3.37819 - 5.85120i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-9.46544 - 5.46488i) q^{26} +5.19615i q^{27} +(13.9547 + 1.12472i) q^{28} +39.2933 q^{29} +(9.46751 - 5.46607i) q^{31} +(2.82843 + 4.89898i) q^{32} +(4.94184 + 2.85317i) q^{33} +17.8454i q^{34} -6.00000 q^{36} +(-17.1983 + 29.7883i) q^{37} +(2.18218 - 1.25988i) q^{38} +(6.69308 + 11.5928i) q^{39} -18.8536i q^{41} +(-14.1125 - 9.73845i) q^{42} +77.4197 q^{43} +(-3.29456 + 5.70635i) q^{44} +(-4.77748 - 8.27485i) q^{46} +(11.1602 + 6.44335i) q^{47} -6.92820i q^{48} +(-17.3875 - 45.8113i) q^{49} +(10.9280 - 18.9279i) q^{51} +(-13.3862 + 7.72850i) q^{52} +(25.8440 + 44.7631i) q^{53} +(6.36396 + 3.67423i) q^{54} +(11.2450 - 16.2957i) q^{56} -3.08607 q^{57} +(27.7846 - 48.1243i) q^{58} +(97.7973 - 56.4633i) q^{59} +(-22.7184 - 13.1165i) q^{61} -15.4604i q^{62} +(9.00500 + 18.9713i) q^{63} +8.00000 q^{64} +(6.98882 - 4.03500i) q^{66} +(9.95656 + 17.2453i) q^{67} +(21.8560 + 12.6186i) q^{68} +11.7024i q^{69} +87.4319 q^{71} +(-4.24264 + 7.34847i) q^{72} +(52.7540 - 30.4575i) q^{73} +(24.3220 + 42.1270i) q^{74} -3.56349i q^{76} +(22.9874 + 1.85274i) q^{77} +18.9309 q^{78} +(17.7888 - 30.8112i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-23.0909 - 13.3315i) q^{82} -46.6773i q^{83} +(-21.9062 + 10.3981i) q^{84} +(54.7440 - 94.8194i) q^{86} +(-58.9399 + 34.0290i) q^{87} +(4.65921 + 8.06999i) q^{88} +(-47.4706 - 27.4072i) q^{89} +(44.5270 + 30.7263i) q^{91} -13.5128 q^{92} +(-9.46751 + 16.3982i) q^{93} +(15.7829 - 9.11228i) q^{94} +(-8.48528 - 4.89898i) q^{96} +45.7447i q^{97} +(-68.4020 - 11.0982i) q^{98} -9.88368 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 $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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
$7$	−3.97571	+	5.76140i	−0.567958	+	0.823057i
$7$	−3.97571	+	5.76140i	−0.567958	+	0.823057i
$8$	−2.82843			−0.353553
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	−1.64728	−	2.85317i	−0.149753	−	0.259379i	0.781383	−	0.624051i	$-0.214514\pi$
$11$	−1.64728	−	2.85317i	−0.149753	−	0.259379i	−0.931136	+	0.364672i	$0.881181\pi$
$12$	3.00000	+	1.73205i	0.250000	+	0.144338i
$13$		−	7.72850i		−	0.594500i	−0.954800	−	0.297250i	$-0.903931\pi$
$13$		−	7.72850i		−	0.594500i	0.954800	−	0.297250i	$-0.0960695\pi$
$14$	4.24500	+	8.94315i	0.303214	+	0.638797i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−10.9280	+	6.30929i	−0.642824	+	0.371135i	−0.785702	−	0.618606i	$-0.787698\pi$
$17$	−10.9280	+	6.30929i	−0.642824	+	0.371135i	0.142877	+	0.989740i	$0.454365\pi$
$18$	−2.12132	−	3.67423i	−0.117851	−	0.204124i
$19$	1.54304	+	0.890872i	0.0812124	+	0.0468880i	0.540056	−	0.841629i	$-0.318403\pi$
$19$	1.54304	+	0.890872i	0.0812124	+	0.0468880i	−0.458844	+	0.888517i	$0.651736\pi$
$20$		0			0
$21$	0.974040	−	12.0852i	0.0463829	−	0.575484i
$22$	−4.65921			−0.211782
$23$	3.37819	−	5.85120i	0.146878	−	0.254400i	−0.783194	−	0.621777i	$-0.786411\pi$
$23$	3.37819	−	5.85120i	0.146878	−	0.254400i	0.930072	+	0.367377i	$0.119744\pi$
$24$	4.24264	−	2.44949i	0.176777	−	0.102062i
$25$		0			0
$26$	−9.46544	−	5.46488i	−0.364055	−	0.210188i
$27$			5.19615i			0.192450i
$28$	13.9547	+	1.12472i	0.498384	+	0.0401687i
$29$	39.2933			1.35494			0.677471	−	0.735550i	$-0.263076\pi$
$29$	39.2933			1.35494			0.677471	+	0.735550i	$0.263076\pi$
$30$		0			0
$31$	9.46751	−	5.46607i	0.305404	−	0.176325i	−0.339464	−	0.940619i	$-0.610246\pi$
$31$	9.46751	−	5.46607i	0.305404	−	0.176325i	0.644868	+	0.764294i	$0.276912\pi$
$32$	2.82843	+	4.89898i	0.0883883	+	0.153093i
$33$	4.94184	+	2.85317i	0.149753	+	0.0864598i
$34$			17.8454i			0.524864i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−17.1983	+	29.7883i	−0.464818	+	0.805089i	−0.999193	−	0.0401585i	$-0.987214\pi$
$37$	−17.1983	+	29.7883i	−0.464818	+	0.805089i	0.534375	+	0.845248i	$0.320547\pi$
$38$	2.18218	−	1.25988i	0.0574258	−	0.0331548i
$39$	6.69308	+	11.5928i	0.171617	+	0.297250i
$40$		0			0
$41$		−	18.8536i		−	0.459844i	−0.973209	−	0.229922i	$-0.926153\pi$
$41$		−	18.8536i		−	0.459844i	0.973209	−	0.229922i	$-0.0738472\pi$
$42$	−14.1125	−	9.73845i	−0.336012	−	0.231868i
$43$	77.4197			1.80046			0.900229	−	0.435416i	$-0.143399\pi$
$43$	77.4197			1.80046			0.900229	+	0.435416i	$0.143399\pi$
$44$	−3.29456	+	5.70635i	−0.0748764	+	0.129690i
$45$		0			0
$46$	−4.77748	−	8.27485i	−0.103858	−	0.179888i
$47$	11.1602	+	6.44335i	0.237451	+	0.137093i	0.614005	−	0.789302i	$-0.289558\pi$
$47$	11.1602	+	6.44335i	0.237451	+	0.137093i	−0.376553	+	0.926395i	$0.622891\pi$
$48$		−	6.92820i		−	0.144338i
$49$	−17.3875	−	45.8113i	−0.354847	−	0.934924i
$50$		0			0
$51$	10.9280	−	18.9279i	0.214275	−	0.371135i
$52$	−13.3862	+	7.72850i	−0.257426	+	0.148625i
$53$	25.8440	+	44.7631i	0.487622	+	0.844586i	0.999899	−	0.0142341i	$-0.00453101\pi$
$53$	25.8440	+	44.7631i	0.487622	+	0.844586i	−0.512276	+	0.858821i	$0.671198\pi$
$54$	6.36396	+	3.67423i	0.117851	+	0.0680414i
$55$		0			0
$56$	11.2450	−	16.2957i	0.200804	−	0.290995i
$57$	−3.08607			−0.0541416
$58$	27.7846	−	48.1243i	0.479044	−	0.829729i
$59$	97.7973	−	56.4633i	1.65758	−	0.957005i	0.683754	−	0.729713i	$-0.260346\pi$
$59$	97.7973	−	56.4633i	1.65758	−	0.957005i	0.973827	−	0.227292i	$-0.0729872\pi$
$60$		0			0
$61$	−22.7184	−	13.1165i	−0.372432	−	0.215024i	0.302088	−	0.953280i	$-0.402316\pi$
$61$	−22.7184	−	13.1165i	−0.372432	−	0.215024i	−0.674521	+	0.738256i	$0.735650\pi$
$62$		−	15.4604i		−	0.249361i
$63$	9.00500	+	18.9713i	0.142937	+	0.301132i
$64$	8.00000			0.125000
$65$		0			0
$66$	6.98882	−	4.03500i	0.105891	−	0.0611363i
$67$	9.95656	+	17.2453i	0.148605	+	0.257392i	0.930712	−	0.365752i	$-0.119188\pi$
$67$	9.95656	+	17.2453i	0.148605	+	0.257392i	−0.782107	+	0.623144i	$0.785855\pi$
$68$	21.8560	+	12.6186i	0.321412	+	0.185567i
$69$			11.7024i			0.169600i
$70$		0			0
$71$	87.4319			1.23144			0.615718	−	0.787967i	$-0.288866\pi$
$71$	87.4319			1.23144			0.615718	+	0.787967i	$0.288866\pi$
$72$	−4.24264	+	7.34847i	−0.0589256	+	0.102062i
$73$	52.7540	−	30.4575i	0.722657	−	0.417226i	−0.0930727	−	0.995659i	$-0.529669\pi$
$73$	52.7540	−	30.4575i	0.722657	−	0.417226i	0.815730	+	0.578433i	$0.196336\pi$
$74$	24.3220	+	42.1270i	0.328676	+	0.569284i
$75$		0			0
$76$		−	3.56349i		−	0.0468880i
$77$	22.9874	+	1.85274i	0.298537	+	0.0240615i
$78$	18.9309			0.242704
$79$	17.7888	−	30.8112i	0.225175	−	0.390015i	−0.731197	−	0.682167i	$-0.761038\pi$
$79$	17.7888	−	30.8112i	0.225175	−	0.390015i	0.956372	+	0.292152i	$0.0943712\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−23.0909	−	13.3315i	−0.281596	−	0.162580i
$83$		−	46.6773i		−	0.562377i	−0.959653	−	0.281188i	$-0.909271\pi$
$83$		−	46.6773i		−	0.562377i	0.959653	−	0.281188i	$-0.0907286\pi$
$84$	−21.9062	+	10.3981i	−0.260788	+	0.123787i
$85$		0			0
$86$	54.7440	−	94.8194i	0.636558	−	1.10255i
$87$	−58.9399	+	34.0290i	−0.677471	+	0.391138i
$88$	4.65921	+	8.06999i	0.0529456	+	0.0917044i
$89$	−47.4706	−	27.4072i	−0.533378	−	0.307946i	0.209013	−	0.977913i	$-0.432975\pi$
$89$	−47.4706	−	27.4072i	−0.533378	−	0.307946i	−0.742391	+	0.669967i	$0.766308\pi$
$90$		0			0
$91$	44.5270	+	30.7263i	0.489308	+	0.337651i
$92$	−13.5128			−0.146878
$93$	−9.46751	+	16.3982i	−0.101801	+	0.176325i
$94$	15.7829	−	9.11228i	0.167903	−	0.0969391i
$95$		0			0
$96$	−8.48528	−	4.89898i	−0.0883883	−	0.0510310i
$97$			45.7447i			0.471595i	0.971802	+	0.235798i	$0.0757703\pi$
$97$			45.7447i			0.471595i	−0.971802	+	0.235798i	$0.924230\pi$
$98$	−68.4020	−	11.0982i	−0.697979	−	0.113247i
$99$	−9.88368			−0.0998352
$100$		0			0
$101$	79.2589	−	45.7601i	0.784741	−	0.453071i	−0.0533667	−	0.998575i	$-0.516995\pi$
$101$	79.2589	−	45.7601i	0.784741	−	0.453071i	0.838108	+	0.545504i	$0.183662\pi$
$102$	−15.4545	−	26.7681i	−0.151515	−	0.262432i
$103$	−43.7414	−	25.2541i	−0.424674	−	0.245186i	0.272401	−	0.962184i	$-0.412182\pi$
$103$	−43.7414	−	25.2541i	−0.424674	−	0.245186i	−0.697075	+	0.716998i	$0.745516\pi$
$104$			21.8595i			0.210188i
$105$		0			0
$106$	73.0978			0.689602
$107$	−46.9747	+	81.3626i	−0.439016	+	0.760398i	−0.997614	−	0.0690404i	$-0.978006\pi$
$107$	−46.9747	+	81.3626i	−0.439016	+	0.760398i	0.558598	+	0.829439i	$0.311340\pi$
$108$	9.00000	−	5.19615i	0.0833333	−	0.0481125i
$109$	−60.3052	−	104.452i	−0.553258	−	0.958272i	−0.998037	−	0.0626310i	$-0.980051\pi$
$109$	−60.3052	−	104.452i	−0.553258	−	0.958272i	0.444778	−	0.895641i	$-0.353282\pi$
$110$		0			0
$111$		−	59.5766i		−	0.536726i
$112$	−12.0067	−	25.2951i	−0.107202	−	0.225849i
$113$	−10.7318			−0.0949713			−0.0474856	−	0.998872i	$-0.515121\pi$
$113$	−10.7318			−0.0949713			−0.0474856	+	0.998872i	$0.515121\pi$
$114$	−2.18218	+	3.77965i	−0.0191419	+	0.0331548i
$115$		0			0
$116$	−39.2933	−	68.0580i	−0.338735	−	0.586707i
$117$	−20.0792	−	11.5928i	−0.171617	−	0.0990834i
$118$		−	159.702i		−	1.35341i
$119$	7.09622	−	88.0446i	0.0596321	−	0.739870i
$120$		0			0
$121$	55.0729	−	95.3891i	0.455148	−	0.788340i
$122$	−32.1286	+	18.5495i	−0.263349	+	0.152045i
$123$	16.3277	+	28.2804i	0.132746	+	0.229922i
$124$	−18.9350	−	10.9321i	−0.152702	−	0.0881624i
$125$		0			0
$126$	29.6025	+	2.38590i	0.234940	+	0.0189357i
$127$	117.281			0.923476			0.461738	−	0.887016i	$-0.347226\pi$
$127$	117.281			0.923476			0.461738	+	0.887016i	$0.347226\pi$
$128$	5.65685	−	9.79796i	0.0441942	−	0.0765466i
$129$	−116.130	+	67.0475i	−0.900229	+	0.519748i
$130$		0			0
$131$	80.2758	+	46.3473i	0.612792	+	0.353796i	0.774058	−	0.633115i	$-0.218224\pi$
$131$	80.2758	+	46.3473i	0.612792	+	0.353796i	−0.161265	+	0.986911i	$0.551557\pi$
$132$		−	11.4127i		−	0.0864598i
$133$	−11.2673	+	5.34820i	−0.0847168	+	0.0402120i
$134$	28.1614			0.210160
$135$		0			0
$136$	30.9091	−	17.8454i	0.227273	−	0.131216i
$137$	13.7370	+	23.7932i	0.100270	+	0.173673i	0.911796	−	0.410644i	$-0.134696\pi$
$137$	13.7370	+	23.7932i	0.100270	+	0.173673i	−0.811526	+	0.584317i	$0.801363\pi$
$138$	14.3325	+	8.27485i	0.103858	+	0.0599626i
$139$		−	67.0127i		−	0.482106i	−0.970512	−	0.241053i	$-0.922507\pi$
$139$		−	67.0127i		−	0.482106i	0.970512	−	0.241053i	$-0.0774928\pi$
$140$		0			0
$141$	−22.3204			−0.158301
$142$	61.8237	−	107.082i	0.435378	−	0.754097i
$143$	−22.0507	+	12.7310i	−0.154201	+	0.0890280i
$144$	6.00000	+	10.3923i	0.0416667	+	0.0721688i
$145$		0			0
$146$		−	86.1469i		−	0.590047i
$147$	65.7550	+	53.6589i	0.447313	+	0.365027i
$148$	68.7931			0.464818
$149$	−25.5567	+	44.2656i	−0.171522	+	0.297084i	−0.938952	−	0.344048i	$-0.888202\pi$
$149$	−25.5567	+	44.2656i	−0.171522	+	0.297084i	0.767430	+	0.641132i	$0.221535\pi$
$150$		0			0
$151$	82.6090	+	143.083i	0.547079	+	0.947569i	0.998473	+	0.0552442i	$0.0175937\pi$
$151$	82.6090	+	143.083i	0.547079	+	0.947569i	−0.451394	+	0.892325i	$0.649073\pi$
$152$	−4.36436	−	2.51977i	−0.0287129	−	0.0165774i
$153$			37.8558i			0.247423i
$154$	18.5237	−	26.8436i	0.120284	−	0.174309i
$155$		0			0
$156$	13.3862	−	23.1855i	0.0858087	−	0.148625i
$157$	−165.248	+	95.4059i	−1.05253	+	0.607681i	−0.923358	−	0.383941i	$-0.874567\pi$
$157$	−165.248	+	95.4059i	−1.05253	+	0.607681i	−0.129176	+	0.991622i	$0.541233\pi$
$158$	−25.1572	−	43.5736i	−0.159223	−	0.275782i
$159$	−77.5319	−	44.7631i	−0.487622	−	0.281529i
$160$		0			0
$161$	20.2804	+	42.7258i	0.125965	+	0.265377i
$162$	−12.7279			−0.0785674
$163$	124.101	−	214.949i	0.761356	−	1.31871i	−0.180796	−	0.983521i	$-0.557867\pi$
$163$	124.101	−	214.949i	0.761356	−	1.31871i	0.942152	−	0.335186i	$-0.108799\pi$
$164$	−32.6554	+	18.8536i	−0.199118	+	0.114961i
$165$		0			0
$166$	−57.1678	−	33.0058i	−0.344384	−	0.198830i
$167$			29.2974i			0.175433i	0.996145	+	0.0877167i	$0.0279570\pi$
$167$			29.2974i			0.175433i	−0.996145	+	0.0877167i	$0.972043\pi$
$168$	−2.75500	+	34.1820i	−0.0163988	+	0.203464i
$169$	109.270			0.646570
$170$		0			0
$171$	4.62911	−	2.67262i	0.0270708	−	0.0156293i
$172$	−77.4197	−	134.095i	−0.450115	−	0.779622i
$173$	19.9982	+	11.5460i	0.115597	+	0.0667397i	0.556683	−	0.830725i	$-0.312074\pi$
$173$	19.9982	+	11.5460i	0.115597	+	0.0667397i	−0.441087	+	0.897464i	$0.645407\pi$
$174$			96.2485i			0.553152i
$175$		0			0
$176$	13.1782			0.0748764
$177$	−97.7973	+	169.390i	−0.552527	+	0.957005i
$178$	−67.1336	+	38.7596i	−0.377155	+	0.217751i
$179$	104.717	+	181.376i	0.585014	+	1.01327i	0.994874	+	0.101125i	$0.0322442\pi$
$179$	104.717	+	181.376i	0.585014	+	1.01327i	−0.409860	+	0.912148i	$0.634423\pi$
$180$		0			0
$181$			243.667i			1.34622i	0.739540	+	0.673112i	$0.235043\pi$
$181$			243.667i			1.34622i	−0.739540	+	0.673112i	$0.764957\pi$
$182$	69.1172	−	32.8075i	0.379765	−	0.180261i
$183$	45.4367			0.248288
$184$	−9.55497	+	16.5497i	−0.0519292	+	0.0899440i
$185$		0			0
$186$	13.3891	+	23.1906i	0.0719843	+	0.124681i
$187$	36.0030	+	20.7863i	0.192529	+	0.111157i
$188$		−	25.7734i		−	0.137093i
$189$	−29.9371	−	20.6584i	−0.158397	−	0.109304i
$190$		0			0
$191$	118.423	−	205.114i	0.620014	−	1.07390i	−0.369468	−	0.929243i	$-0.620460\pi$
$191$	118.423	−	205.114i	0.620014	−	1.07390i	0.989483	−	0.144653i	$-0.0462064\pi$
$192$	−12.0000	+	6.92820i	−0.0625000	+	0.0360844i
$193$	−66.4460	−	115.088i	−0.344280	−	0.596310i	0.640943	−	0.767589i	$-0.278544\pi$
$193$	−66.4460	−	115.088i	−0.344280	−	0.596310i	−0.985223	+	0.171278i	$0.945210\pi$
$194$	56.0256	+	32.3464i	0.288792	+	0.166734i
$195$		0			0
$196$	−61.9600	+	75.9273i	−0.316122	+	0.387384i
$197$	105.779			0.536950			0.268475	−	0.963287i	$-0.413480\pi$
$197$	105.779			0.536950			0.268475	+	0.963287i	$0.413480\pi$
$198$	−6.98882	+	12.1050i	−0.0352971	+	0.0611363i
$199$	174.541	−	100.771i	0.877091	−	0.506389i	0.00739279	−	0.999973i	$-0.497647\pi$
$199$	174.541	−	100.771i	0.877091	−	0.506389i	0.869698	+	0.493584i	$0.164313\pi$
$200$		0			0
$201$	−29.8697	−	17.2453i	−0.148605	−	0.0857973i
$202$		−	129.429i		−	0.640739i
$203$	−156.219	+	226.384i	−0.769550	+	1.11519i
$204$	−43.7121			−0.214275
$205$		0			0
$206$	−61.8597	+	35.7147i	−0.300290	+	0.173372i
$207$	−10.1346	−	17.5536i	−0.0489593	−	0.0848000i
$208$	26.7723	+	15.4570i	0.128713	+	0.0743125i
$209$		−	5.87006i		−	0.0280864i
$210$		0			0
$211$	29.6045			0.140306			0.0701528	−	0.997536i	$-0.477651\pi$
$211$	29.6045			0.140306			0.0701528	+	0.997536i	$0.477651\pi$
$212$	51.6880	−	89.5262i	0.243811	−	0.422293i
$213$	−131.148	+	75.7183i	−0.615718	+	0.355485i
$214$	66.4323	+	115.064i	0.310431	+	0.537683i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−6.14783	+	76.2777i	−0.0283310	+	0.351510i
$218$	−170.569			−0.782426
$219$	−52.7540	+	91.3726i	−0.240886	+	0.417226i
$220$		0			0
$221$	48.7614	+	84.4572i	0.220640	+	0.382159i
$222$	−72.9661	−	42.1270i	−0.328676	−	0.189761i
$223$		−	328.532i		−	1.47324i	−0.676307	−	0.736620i	$-0.736421\pi$
$223$		−	328.532i		−	1.47324i	0.676307	−	0.736620i	$-0.263579\pi$
$224$	−39.4700	−	3.18120i	−0.176205	−	0.0142018i
$225$		0			0
$226$	−7.58850	+	13.1437i	−0.0335774	+	0.0581578i
$227$	−315.628	+	182.228i	−1.39043	+	0.802766i	−0.993363	−	0.115023i	$-0.963306\pi$
$227$	−315.628	+	182.228i	−1.39043	+	0.802766i	−0.397069	+	0.917789i	$0.629972\pi$
$228$	3.08607	+	5.34523i	0.0135354	+	0.0234440i
$229$	−260.716	−	150.525i	−1.13850	−	0.657313i	−0.192441	−	0.981309i	$-0.561640\pi$
$229$	−260.716	−	150.525i	−1.13850	−	0.657313i	−0.946059	+	0.323996i	$0.894974\pi$
$230$		0			0
$231$	−36.0856	+	17.1285i	−0.156215	+	0.0741496i
$232$	−111.138			−0.479044
$233$	−141.013	+	244.241i	−0.605204	+	1.04824i	0.386815	+	0.922157i	$0.373575\pi$
$233$	−141.013	+	244.241i	−0.605204	+	1.04824i	−0.992019	+	0.126087i	$0.959758\pi$
$234$	−28.3963	+	16.3946i	−0.121352	+	0.0700625i
$235$		0			0
$236$	−195.595	−	112.927i	−0.828790	−	0.478502i
$237$			61.6224i			0.260010i
$238$	−102.814	−	70.9480i	−0.431993	−	0.298101i
$239$	83.0347			0.347425			0.173713	−	0.984796i	$-0.444424\pi$
$239$	83.0347			0.347425			0.173713	+	0.984796i	$0.444424\pi$
$240$		0			0
$241$	−287.369	+	165.912i	−1.19240	+	0.688433i	−0.958851	−	0.283911i	$-0.908368\pi$
$241$	−287.369	+	165.912i	−1.19240	+	0.688433i	−0.233551	+	0.972345i	$0.575035\pi$
$242$	−77.8849	−	134.901i	−0.321838	−	0.557440i
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$			52.4658i			0.215024i
$245$		0			0
$246$	46.1817			0.187731
$247$	6.88511	−	11.9254i	0.0278749	−	0.0482808i
$248$	−26.7782	+	15.4604i	−0.107977	+	0.0623403i
$249$	40.4237	+	70.0159i	0.162344	+	0.281188i
$250$		0			0
$251$			419.075i			1.66962i	0.550537	+	0.834811i	$0.314423\pi$
$251$			419.075i			1.66962i	−0.550537	+	0.834811i	$0.685577\pi$
$252$	23.8542	−	34.5684i	0.0946597	−	0.137176i
$253$	−22.2593			−0.0879815
$254$	82.9305	−	143.640i	0.326498	−	0.565511i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	289.215	+	166.979i	1.12535	+	0.649722i	0.942762	−	0.333467i	$-0.108219\pi$
$257$	289.215	+	166.979i	1.12535	+	0.649722i	0.182590	+	0.983189i	$0.441552\pi$
$258$			189.639i			0.735034i
$259$	−103.247	−	217.516i	−0.398637	−	0.839829i
$260$		0			0
$261$	58.9399	−	102.087i	0.225824	−	0.391138i
$262$	113.527	−	65.5449i	0.433310	−	0.250171i
$263$	102.188	+	176.995i	0.388549	+	0.672986i	0.992255	−	0.124221i	$-0.0396432\pi$
$263$	102.188	+	176.995i	0.388549	+	0.672986i	−0.603706	+	0.797207i	$0.706310\pi$
$264$	−13.9776	−	8.06999i	−0.0529456	−	0.0305681i
$265$		0			0
$266$	−1.41702	+	17.5814i	−0.00532715	+	0.0660953i
$267$	94.9412			0.355585
$268$	19.9131	−	34.4905i	0.0743027	−	0.128696i
$269$	−120.768	+	69.7257i	−0.448953	+	0.259203i	−0.707388	−	0.706825i	$-0.750127\pi$
$269$	−120.768	+	69.7257i	−0.448953	+	0.259203i	0.258435	+	0.966029i	$0.416793\pi$
$270$		0			0
$271$	−323.213	−	186.607i	−1.19267	−	0.688586i	−0.233756	−	0.972295i	$-0.575102\pi$
$271$	−323.213	−	186.607i	−1.19267	−	0.688586i	−0.958910	+	0.283709i	$0.908435\pi$
$272$		−	50.4743i		−	0.185567i
$273$	−93.4002	−	7.52787i	−0.342125	−	0.0275746i
$274$	38.8542			0.141804
$275$		0			0
$276$	20.2691	−	11.7024i	0.0734389	−	0.0424000i
$277$	−248.752	−	430.851i	−0.898022	−	1.55542i	−0.830019	−	0.557735i	$-0.811671\pi$
$277$	−248.752	−	430.851i	−0.898022	−	1.55542i	−0.0680029	−	0.997685i	$-0.521663\pi$
$278$	−82.0735	−	47.3852i	−0.295228	−	0.170450i
$279$		−	32.7964i		−	0.117550i
$280$		0			0
$281$	292.779			1.04192			0.520959	−	0.853582i	$-0.325574\pi$
$281$	292.779			1.04192			0.520959	+	0.853582i	$0.325574\pi$
$282$	−15.7829	+	27.3368i	−0.0559678	+	0.0969391i
$283$	239.686	−	138.383i	0.846949	−	0.488986i	−0.0126714	−	0.999920i	$-0.504034\pi$
$283$	239.686	−	138.383i	0.846949	−	0.488986i	0.859620	+	0.510934i	$0.170700\pi$
$284$	−87.4319	−	151.437i	−0.307859	−	0.533227i
$285$		0			0
$286$			36.0087i			0.125905i
$287$	108.623	+	74.9565i	0.378478	+	0.261172i
$288$	16.9706			0.0589256
$289$	−64.8857	+	112.385i	−0.224518	+	0.388876i
$290$		0			0
$291$	−39.6161	−	68.6171i	−0.136138	−	0.235798i
$292$	−105.508	−	60.9150i	−0.361329	−	0.208613i
$293$			375.299i			1.28088i	0.768006	+	0.640442i	$0.221249\pi$
$293$			375.299i			1.28088i	−0.768006	+	0.640442i	$0.778751\pi$
$294$	112.214	−	42.5905i	0.381681	−	0.144866i
$295$		0			0
$296$	48.6441	−	84.2540i	0.164338	−	0.284642i
$297$	14.8255	−	8.55952i	0.0499176	−	0.0288199i
$298$	36.1427	+	62.6009i	0.121284	+	0.210070i
$299$	−45.2210	−	26.1084i	−0.151241	−	0.0873189i
$300$		0			0
$301$	−307.798	+	446.046i	−1.02259	+	1.48188i
$302$	233.653			0.773687
$303$	−79.2589	+	137.280i	−0.261580	+	0.453071i
$304$	−6.17214	+	3.56349i	−0.0203031	+	0.0117220i
$305$		0			0
$306$	46.3636	+	26.7681i	0.151515	+	0.0874773i
$307$		−	107.784i		−	0.351088i	−0.984472	−	0.175544i	$-0.943832\pi$
$307$		−	107.784i		−	0.351088i	0.984472	−	0.175544i	$-0.0561684\pi$
$308$	−19.7783	−	41.6680i	−0.0642154	−	0.135286i
$309$	87.4828			0.283116
$310$		0			0
$311$	−499.771	+	288.543i	−1.60698	+	0.927791i	−0.616940	+	0.787010i	$0.711628\pi$
$311$	−499.771	+	288.543i	−1.60698	+	0.927791i	−0.990041	+	0.140780i	$0.955039\pi$
$312$	−18.9309	−	32.7893i	−0.0606759	−	0.105094i
$313$	−344.050	−	198.637i	−1.09920	−	0.634624i	−0.163190	−	0.986595i	$-0.552178\pi$
$313$	−344.050	−	198.637i	−1.09920	−	0.634624i	−0.936011	+	0.351971i	$0.885512\pi$
$314$			269.849i			0.859390i
$315$		0			0
$316$	−71.1554			−0.225175
$317$	40.1851	−	69.6026i	0.126767	−	0.219566i	−0.795655	−	0.605749i	$-0.792873\pi$
$317$	40.1851	−	69.6026i	0.126767	−	0.219566i	0.922422	+	0.386183i	$0.126207\pi$
$318$	−109.647	+	63.3046i	−0.344801	+	0.199071i
$319$	−64.7271	−	112.111i	−0.202906	−	0.351444i
$320$		0			0
$321$		−	162.725i		−	0.506932i
$322$	66.6686	+	5.37336i	0.207045	+	0.0166874i
$323$	−22.4831			−0.0696071
$324$	−9.00000	+	15.5885i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	−175.505	−	303.984i	−0.538360	−	0.932467i
$327$	180.915	+	104.452i	0.553258	+	0.319424i
$328$			53.3261i			0.162580i
$329$	−81.4925	+	38.6816i	−0.247698	+	0.117573i
$330$		0			0
$331$	−246.021	+	426.121i	−0.743266	+	1.28737i	0.207734	+	0.978185i	$0.433391\pi$
$331$	−246.021	+	426.121i	−0.743266	+	1.28737i	−0.951000	+	0.309189i	$0.899942\pi$
$332$	−80.8474	+	46.6773i	−0.243516	+	0.140594i
$333$	51.5948	+	89.3649i	0.154939	+	0.268363i
$334$	35.8818	+	20.7164i	0.107431	+	0.0620251i
$335$		0			0
$336$	39.9162	+	27.5445i	0.118798	+	0.0819777i
$337$	630.123			1.86980			0.934901	−	0.354910i	$-0.115488\pi$
$337$	630.123			1.86980			0.934901	+	0.354910i	$0.115488\pi$
$338$	77.2657	−	133.828i	0.228597	−	0.395941i
$339$	16.0976	−	9.29397i	0.0474856	−	0.0274159i
$340$		0			0
$341$	−31.1913	−	18.0083i	−0.0914701	−	0.0528103i
$342$		−	7.55930i		−	0.0221032i
$343$	333.065	+	81.9559i	0.971035	+	0.238938i
$344$	−218.976			−0.636558
$345$		0			0
$346$	28.2817	−	16.3285i	0.0817391	−	0.0471921i
$347$	−215.071	−	372.514i	−0.619802	−	1.07353i	−0.989522	−	0.144385i	$-0.953880\pi$
$347$	−215.071	−	372.514i	−0.619802	−	1.07353i	0.369720	−	0.929143i	$-0.379454\pi$
$348$	117.880	+	68.0580i	0.338735	+	0.195569i
$349$			95.1819i			0.272727i	0.990659	+	0.136364i	$0.0435416\pi$
$349$			95.1819i			0.272727i	−0.990659	+	0.136364i	$0.956458\pi$
$350$		0			0
$351$	40.1585			0.114412
$352$	9.31842	−	16.1400i	0.0264728	−	0.0458522i
$353$	−227.710	+	131.469i	−0.645071	+	0.372432i	−0.786565	−	0.617507i	$-0.788143\pi$
$353$	−227.710	+	131.469i	−0.645071	+	0.372432i	0.141494	+	0.989939i	$0.454809\pi$
$354$	138.306	+	239.553i	0.390696	+	0.676704i
$355$		0			0
$356$			109.629i			0.307946i
$357$	65.6045	+	138.212i	0.183766	+	0.387150i
$358$	296.186			0.827334
$359$	−149.386	+	258.743i	−0.416116	+	0.720734i	−0.995545	−	0.0942890i	$-0.969942\pi$
$359$	−149.386	+	258.743i	−0.416116	+	0.720734i	0.579429	+	0.815023i	$0.303276\pi$
$360$		0			0
$361$	−178.913	−	309.886i	−0.495603	−	0.858410i
$362$	298.429	+	172.298i	0.824391	+	0.475962i
$363$			190.778i			0.525560i
$364$	8.69244	−	107.849i	0.0238803	−	0.296289i
$365$		0			0
$366$	32.1286	−	55.6484i	0.0877831	−	0.152045i
$367$	114.381	−	66.0380i	0.311665	−	0.179940i	−0.336006	−	0.941860i	$-0.609076\pi$
$367$	114.381	−	66.0380i	0.311665	−	0.179940i	0.647671	+	0.761920i	$0.275743\pi$
$368$	13.5128	+	23.4048i	0.0367195	+	0.0636000i
$369$	−48.9831	−	28.2804i	−0.132746	−	0.0766407i
$370$		0			0
$371$	−360.646	−	29.0674i	−0.972092	−	0.0783487i
$372$	37.8701			0.101801
$373$	5.34394	−	9.25597i	0.0143269	−	0.0248149i	−0.858773	−	0.512356i	$-0.828773\pi$
$373$	5.34394	−	9.25597i	0.0143269	−	0.0248149i	0.873100	+	0.487541i	$0.162106\pi$
$374$	50.9159	−	29.3963i	0.136139	−	0.0785998i
$375$		0			0
$376$	−31.5659	−	18.2246i	−0.0839517	−	0.0484696i
$377$		−	303.678i		−	0.805513i
$378$	−46.4700	+	22.0577i	−0.122936	+	0.0583536i
$379$	142.918			0.377092			0.188546	−	0.982064i	$-0.439622\pi$
$379$	142.918			0.377092			0.188546	+	0.982064i	$0.439622\pi$
$380$		0			0
$381$	−175.922	+	101.569i	−0.461738	+	0.266585i
$382$	−167.475	−	290.075i	−0.438416	−	0.759359i
$383$	534.349	+	308.507i	1.39517	+	0.805500i	0.993881	−	0.110452i	$-0.0352300\pi$
$383$	534.349	+	308.507i	1.39517	+	0.805500i	0.401286	+	0.915953i	$0.368563\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−187.938			−0.486885
$387$	116.130	−	201.142i	0.300076	−	0.519748i
$388$	79.2322	−	45.7447i	0.204207	−	0.117899i
$389$	346.969	+	600.968i	0.891951	+	1.54490i	0.837534	+	0.546386i	$0.183997\pi$
$389$	346.969	+	600.968i	0.891951	+	1.54490i	0.0544171	+	0.998518i	$0.482670\pi$
$390$		0			0
$391$			85.2560i			0.218046i
$392$	49.1793	+	129.574i	0.125457	+	0.330546i
$393$	−160.552			−0.408528
$394$	74.7972	−	129.553i	0.189841	−	0.328814i
$395$		0			0
$396$	9.88368	+	17.1190i	0.0249588	+	0.0432299i
$397$	484.587	+	279.776i	1.22062	+	0.704726i	0.965050	−	0.262065i	$-0.0844033\pi$
$397$	484.587	+	279.776i	1.22062	+	0.704726i	0.255571	+	0.966790i	$0.417737\pi$
$398$		−	285.024i		−	0.716142i
$399$	12.2693	−	17.7801i	0.0307502	−	0.0445616i
$400$		0			0
$401$	80.6033	−	139.609i	0.201006	−	0.348152i	−0.747847	−	0.663871i	$-0.768912\pi$
$401$	80.6033	−	139.609i	0.201006	−	0.348152i	0.948853	+	0.315719i	$0.102246\pi$
$402$	−42.2421	+	24.3885i	−0.105080	+	0.0606679i
$403$	−42.2445	−	73.1697i	−0.104825	−	0.181563i
$404$	−158.518	−	91.5203i	−0.392371	−	0.226535i
$405$		0			0
$406$	166.800	+	351.406i	0.410837	+	0.865532i
$407$	113.322			0.278431
$408$	−30.9091	+	53.5361i	−0.0757576	+	0.131216i
$409$	398.217	−	229.911i	0.973637	−	0.562129i	0.0732937	−	0.997310i	$-0.476649\pi$
$409$	398.217	−	229.911i	0.973637	−	0.562129i	0.900343	+	0.435181i	$0.143316\pi$
$410$		0			0
$411$	−41.2111	−	23.7932i	−0.100270	−	0.0578911i
$412$			101.016i			0.245186i
$413$	−63.5056	+	787.931i	−0.153767	+	1.90782i
$414$	−28.6649			−0.0692389
$415$		0			0
$416$	37.8618	−	21.8595i	0.0910139	−	0.0525469i
$417$	58.0347	+	100.519i	0.139172	+	0.241053i
$418$	−7.18933	−	4.15076i	−0.0171994	−	0.00993005i
$419$		−	93.5818i		−	0.223346i	−0.993745	−	0.111673i	$-0.964379\pi$
$419$		−	93.5818i		−	0.223346i	0.993745	−	0.111673i	$-0.0356208\pi$
$420$		0			0
$421$	162.957			0.387072			0.193536	−	0.981093i	$-0.438004\pi$
$421$	162.957			0.387072			0.193536	+	0.981093i	$0.438004\pi$
$422$	20.9335	−	36.2579i	0.0496055	−	0.0859193i
$423$	33.4806	−	19.3301i	0.0791504	−	0.0456975i
$424$	−73.0978	−	126.609i	−0.172400	−	0.298606i
$425$		0			0
$426$			214.164i			0.502731i
$427$	165.891	−	78.7425i	0.388503	−	0.184409i
$428$	187.899			0.439016
$429$	22.0507	−	38.1930i	0.0514003	−	0.0890280i
$430$		0			0
$431$	165.543	+	286.728i	0.384090	+	0.665263i	0.991642	−	0.129016i	$-0.0411820\pi$
$431$	165.543	+	286.728i	0.384090	+	0.665263i	−0.607553	+	0.794279i	$0.707849\pi$
$432$	−18.0000	−	10.3923i	−0.0416667	−	0.0240563i
$433$		−	88.4130i		−	0.204187i	−0.994775	−	0.102094i	$-0.967446\pi$
$433$		−	88.4130i		−	0.204187i	0.994775	−	0.102094i	$-0.0325541\pi$
$434$	89.0735	+	61.4660i	0.205238	+	0.141627i
$435$		0			0
$436$	−120.610	+	208.903i	−0.276629	+	0.479136i
$437$	10.4253	−	6.01907i	0.0238566	−	0.0137736i
$438$	74.6054	+	129.220i	0.170332	+	0.295024i
$439$	−60.4608	−	34.9070i	−0.137724	−	0.0795149i	0.429555	−	0.903041i	$-0.358670\pi$
$439$	−60.4608	−	34.9070i	−0.137724	−	0.0795149i	−0.567279	+	0.823526i	$0.692004\pi$
$440$		0			0
$441$	−145.102	−	23.5429i	−0.329031	−	0.0533852i
$442$	137.918			0.312032
$443$	330.217	−	571.953i	0.745411	−	1.29109i	−0.204592	−	0.978847i	$-0.565587\pi$
$443$	330.217	−	571.953i	0.745411	−	1.29109i	0.950003	−	0.312242i	$-0.101080\pi$
$444$	−103.190	+	59.5766i	−0.232409	+	0.134182i
$445$		0			0
$446$	−402.368	−	232.307i	−0.902171	−	0.520869i
$447$		−	88.5311i		−	0.198056i
$448$	−31.8057	+	46.0912i	−0.0709948	+	0.102882i
$449$	−560.274			−1.24783			−0.623913	−	0.781493i	$-0.714458\pi$
$449$	−560.274			−1.24783			−0.623913	+	0.781493i	$0.714458\pi$
$450$		0			0
$451$	−53.7926	+	31.0572i	−0.119274	+	0.0688629i
$452$	10.7318	+	18.5879i	0.0237428	+	0.0411238i
$453$	−247.827	−	143.083i	−0.547079	−	0.315856i
$454$			515.418i			1.13528i
$455$		0			0
$456$	8.72873			0.0191419
$457$	91.8900	−	159.158i	0.201072	−	0.348267i	−0.747802	−	0.663922i	$-0.768891\pi$
$457$	91.8900	−	159.158i	0.201072	−	0.348267i	0.948874	+	0.315655i	$0.102224\pi$
$458$	−368.709	+	212.874i	−0.805041	+	0.464790i
$459$	−32.7840	−	56.7836i	−0.0714249	−	0.123712i
$460$		0			0
$461$		−	28.4330i		−	0.0616767i	−0.999524	−	0.0308384i	$-0.990182\pi$
$461$		−	28.4330i		−	0.0616767i	0.999524	−	0.0308384i	$-0.00981771\pi$
$462$	−4.53826	+	56.3073i	−0.00982307	+	0.121877i
$463$	269.931			0.583005			0.291503	−	0.956570i	$-0.405845\pi$
$463$	269.931			0.583005			0.291503	+	0.956570i	$0.405845\pi$
$464$	−78.5866	+	136.116i	−0.169368	+	0.293353i
$465$		0			0
$466$	199.422	+	345.409i	0.427944	+	0.741221i
$467$	−289.539	−	167.166i	−0.619999	−	0.357956i	0.156870	−	0.987619i	$-0.449860\pi$
$467$	−289.539	−	167.166i	−0.619999	−	0.357956i	−0.776868	+	0.629663i	$0.783193\pi$
$468$			46.3710i			0.0990834i
$469$	−138.941	−	11.1984i	−0.296250	−	0.0238772i
$470$		0			0
$471$	165.248	−	286.218i	0.350845	−	0.607681i
$472$	−276.612	+	159.702i	−0.586043	+	0.338352i
$473$	−127.532	−	220.892i	−0.269624	−	0.467002i
$474$	75.4717	+	43.5736i	0.159223	+	0.0919274i
$475$		0			0
$476$	−159.594	+	75.7536i	−0.335281	+	0.159146i
$477$	155.064			0.325081
$478$	58.7144	−	101.696i	0.122833	−	0.212754i
$479$	114.560	−	66.1412i	0.239165	−	0.138082i	−0.375628	−	0.926771i	$-0.622573\pi$
$479$	114.560	−	66.1412i	0.239165	−	0.138082i	0.614793	+	0.788689i	$0.289240\pi$
$480$		0			0
$481$	230.219	+	132.917i	0.478626	+	0.276335i
$482$			469.271i			0.973592i
$483$	−67.4222	−	46.5253i	−0.139591	−	0.0963257i
$484$	−220.292			−0.455148
$485$		0			0
$486$	19.0919	−	11.0227i	0.0392837	−	0.0226805i
$487$	−258.635	−	447.970i	−0.531079	−	0.919856i	−0.999342	−	0.0362667i	$-0.988453\pi$
$487$	−258.635	−	447.970i	−0.531079	−	0.919856i	0.468263	−	0.883589i	$-0.344880\pi$
$488$	64.2573	+	37.0989i	0.131675	+	0.0760224i
$489$			429.898i			0.879138i
$490$		0			0
$491$	484.805			0.987383			0.493692	−	0.869637i	$-0.335647\pi$
$491$	484.805			0.987383			0.493692	+	0.869637i	$0.335647\pi$
$492$	32.6554	−	56.5609i	0.0663728	−	0.114961i
$493$	−429.398	+	247.913i	−0.870989	+	0.502866i
$494$	−9.73701	−	16.8650i	−0.0197105	−	0.0341397i
$495$		0			0
$496$			43.7286i			0.0881624i
$497$	−347.604	+	503.730i	−0.699404	+	1.01354i
$498$	114.336			0.229589
$499$	64.6450	−	111.968i	0.129549	−	0.224385i	−0.793953	−	0.607979i	$-0.791980\pi$
$499$	64.6450	−	111.968i	0.129549	−	0.224385i	0.923502	+	0.383594i	$0.125314\pi$
$500$		0			0
$501$	−25.3723	−	43.9461i	−0.0506432	−	0.0877167i
$502$	513.260	+	296.331i	1.02243	+	0.590300i
$503$		−	160.905i		−	0.319890i	−0.987126	−	0.159945i	$-0.948868\pi$
$503$		−	160.905i		−	0.319890i	0.987126	−	0.159945i	$-0.0511317\pi$
$504$	−25.4700	−	53.6589i	−0.0505357	−	0.106466i
$505$		0			0
$506$	−15.7397	+	27.2620i	−0.0311061	+	0.0538774i
$507$	−163.905	+	94.6308i	−0.323285	+	0.186649i
$508$	−117.281	−	203.137i	−0.230869	−	0.399877i
$509$	−320.453	−	185.014i	−0.629575	−	0.363485i	0.151013	−	0.988532i	$-0.451747\pi$
$509$	−320.453	−	185.014i	−0.629575	−	0.363485i	−0.780587	+	0.625047i	$0.785080\pi$
$510$		0			0
$511$	−34.2563	+	425.027i	−0.0670378	+	0.831755i
$512$	−22.6274			−0.0441942
$513$	−4.62911	+	8.01785i	−0.00902360	+	0.0156293i
$514$	409.012	−	236.143i	0.795744	−	0.459423i
$515$		0			0
$516$	232.259	+	134.095i	0.450115	+	0.259874i
$517$		−	42.4560i		−	0.0821200i
$518$	−339.408	−	27.3556i	−0.655228	−	0.0528101i
$519$	−39.9964			−0.0770644
$520$		0			0
$521$	65.1395	−	37.6083i	0.125028	−	0.0721849i	−0.436182	−	0.899859i	$-0.643670\pi$
$521$	65.1395	−	37.6083i	0.125028	−	0.0721849i	0.561210	+	0.827674i	$0.310336\pi$
$522$	−83.3537	−	144.373i	−0.159681	−	0.276576i
$523$	−810.701	−	468.058i	−1.55010	−	0.894949i	−0.998133	−	0.0610819i	$-0.980545\pi$
$523$	−810.701	−	468.058i	−1.55010	−	0.894949i	−0.551965	−	0.833867i	$-0.686122\pi$
$524$		−	185.389i		−	0.353796i
$525$		0			0
$526$	289.032			0.549491
$527$	−68.9741	+	119.467i	−0.130881	+	0.226692i
$528$	−19.7674	+	11.4127i	−0.0374382	+	0.0216149i
$529$	241.676	+	418.594i	0.456854	+	0.791294i
$530$		0			0
$531$		−	338.780i		−	0.638003i
$532$	20.5307	+	14.1674i	0.0385915	+	0.0266304i
$533$	−145.710			−0.273377
$534$	67.1336	−	116.279i	0.125718	−	0.217751i
$535$		0			0
$536$	−28.1614	−	48.7770i	−0.0525399	−	0.0910018i
$537$	−314.152	−	181.376i	−0.585014	−	0.337758i
$538$			197.214i			0.366569i
$539$	−102.065	+	125.074i	−0.189361	+	0.232047i
$540$		0			0
$541$	304.692	−	527.742i	0.563201	−	0.975493i	−0.434013	−	0.900906i	$-0.642903\pi$
$541$	304.692	−	527.742i	0.563201	−	0.975493i	0.997215	−	0.0745867i	$-0.0237638\pi$
$542$	−457.092	+	263.902i	−0.843343	+	0.486904i
$543$	−211.021	−	365.500i	−0.388622	−	0.673112i
$544$	−61.8182	−	35.6907i	−0.113636	−	0.0656080i
$545$		0			0
$546$	−75.2637	+	109.068i	−0.137846	+	0.199759i
$547$	491.361			0.898283			0.449141	−	0.893461i	$-0.351730\pi$
$547$	491.361			0.898283			0.449141	+	0.893461i	$0.351730\pi$
$548$	27.4741	−	47.5865i	0.0501351	−	0.0868366i
$549$	−68.1551	+	39.3494i	−0.124144	+	0.0716746i
$550$		0			0
$551$	60.6310	+	35.0053i	0.110038	+	0.0635305i
$552$		−	33.0994i		−	0.0599626i
$553$	106.792	+	224.985i	0.193115	+	0.406844i
$554$	−703.577			−1.27000
$555$		0			0
$556$	−116.069	+	67.0127i	−0.208758	+	0.120527i
$557$	−526.110	−	911.250i	−0.944543	−	1.63600i	−0.756665	−	0.653803i	$-0.773172\pi$
$557$	−526.110	−	911.250i	−0.944543	−	1.63600i	−0.187878	−	0.982192i	$-0.560161\pi$
$558$	−40.1673	−	23.1906i	−0.0719843	−	0.0415602i
$559$		−	598.339i		−	1.07037i
$560$		0			0
$561$	−72.0060			−0.128353
$562$	207.026	−	358.580i	0.368374	−	0.638042i
$563$	670.769	−	387.269i	1.19142	−	0.687866i	0.232791	−	0.972527i	$-0.425214\pi$
$563$	670.769	−	387.269i	1.19142	−	0.687866i	0.958628	+	0.284661i	$0.0918810\pi$
$564$	22.3204	+	38.6601i	0.0395752	+	0.0685463i
$565$		0			0
$566$		−	391.406i		−	0.691531i
$567$	62.7964	+	5.06126i	0.110752	+	0.00892639i
$568$	−247.295			−0.435378
$569$	−156.525	+	271.109i	−0.275088	+	0.476466i	−0.970157	−	0.242477i	$-0.922040\pi$
$569$	−156.525	+	271.109i	−0.275088	+	0.476466i	0.695070	+	0.718942i	$0.255374\pi$
$570$		0			0
$571$	−324.711	−	562.416i	−0.568670	−	0.984966i	−0.996698	−	0.0812002i	$-0.974125\pi$
$571$	−324.711	−	562.416i	−0.568670	−	0.984966i	0.428027	−	0.903766i	$-0.359209\pi$
$572$	44.1015	+	25.4620i	0.0771005	+	0.0445140i
$573$			410.228i			0.715931i
$574$	168.611	−	80.0336i	0.293747	−	0.139431i
$575$		0			0
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	−891.822	+	514.893i	−1.54562	+	0.892363i	−0.547150	+	0.837035i	$0.684287\pi$
$577$	−891.822	+	514.893i	−1.54562	+	0.892363i	−0.998468	+	0.0553284i	$0.982379\pi$
$578$	91.7622	+	158.937i	0.158758	+	0.274977i
$579$	199.338	+	115.088i	0.344280	+	0.198770i
$580$		0			0
$581$	268.927	+	185.575i	0.462868	+	0.319406i
$582$	−112.051			−0.192528
$583$	85.1445	−	147.475i	0.146046	−	0.252958i
$584$	−149.211	+	86.1469i	−0.255498	+	0.147512i
$585$		0			0
$586$	459.646	+	265.376i	0.784378	+	0.452861i
$587$		−	791.817i		−	1.34892i	−0.738311	−	0.674461i	$-0.764376\pi$
$587$		−	791.817i		−	1.34892i	0.738311	−	0.674461i	$-0.235624\pi$
$588$	27.1850	−	167.550i	0.0462329	−	0.284949i
$589$	19.4783			0.0330701
$590$		0			0
$591$	−158.669	+	91.6075i	−0.268475	+	0.155004i
$592$	−68.7931	−	119.153i	−0.116205	−	0.201272i
$593$	73.1807	+	42.2509i	0.123408	+	0.0712494i	0.560433	−	0.828200i	$-0.310635\pi$
$593$	73.1807	+	42.2509i	0.123408	+	0.0712494i	−0.437025	+	0.899449i	$0.643968\pi$
$594$		−	24.2100i		−	0.0407575i
$595$		0			0
$596$	102.227			0.171522
$597$	−174.541	+	302.314i	−0.292364	+	0.506389i
$598$	−63.9522	+	36.9228i	−0.106943	+	0.0617438i
$599$	233.463	+	404.369i	0.389754	+	0.675074i	0.992416	−	0.122922i	$-0.0392266\pi$
$599$	233.463	+	404.369i	0.389754	+	0.675074i	−0.602662	+	0.797997i	$0.705893\pi$
$600$		0			0
$601$		−	1095.93i		−	1.82351i	−0.410733	−	0.911756i	$-0.634727\pi$
$601$		−	1095.93i		−	1.82351i	0.410733	−	0.911756i	$-0.365273\pi$
$602$	328.647	+	692.377i	0.545925	+	1.15013i
$603$	59.7394			0.0990702
$604$	165.218	−	286.166i	0.273540	−	0.473785i
$605$		0			0
$606$	112.089	+	194.144i	0.184965	+	0.320369i
$607$	310.815	+	179.449i	0.512051	+	0.295633i	0.733676	−	0.679499i	$-0.237803\pi$
$607$	310.815	+	179.449i	0.512051	+	0.295633i	−0.221625	+	0.975132i	$0.571136\pi$
$608$			10.0791i			0.0165774i
$609$	38.2733	−	474.866i	0.0628461	−	0.779747i
$610$		0			0
$611$	49.7975	−	86.2517i	0.0815016	−	0.141165i
$612$	65.5681	−	37.8558i	0.107137	−	0.0618558i
$613$	−231.029	−	400.154i	−0.376883	−	0.652780i	0.613724	−	0.789520i	$-0.289671\pi$
$613$	−231.029	−	400.154i	−0.376883	−	0.652780i	−0.990607	+	0.136741i	$0.956337\pi$
$614$	−132.008	−	76.2148i	−0.214996	−	0.124128i
$615$		0			0
$616$	−65.0181	−	5.24033i	−0.105549	−	0.00850703i
$617$	−219.440			−0.355656			−0.177828	−	0.984062i	$-0.556907\pi$
$617$	−219.440			−0.355656			−0.177828	+	0.984062i	$0.556907\pi$
$618$	61.8597	−	107.144i	0.100097	−	0.173372i
$619$	832.792	−	480.813i	1.34538	−	0.776757i	0.357791	−	0.933802i	$-0.383530\pi$
$619$	832.792	−	480.813i	1.34538	−	0.776757i	0.987592	+	0.157044i	$0.0501966\pi$
$620$		0			0
$621$	30.4037	+	17.5536i	0.0489593	+	0.0282667i
$622$			816.123i			1.31209i
$623$	346.633	−	164.534i	0.556393	−	0.264100i
$624$	−53.5446			−0.0858087
$625$		0			0
$626$	−486.560	+	280.915i	−0.777252	+	0.448747i
$627$	5.08362	+	8.80509i	0.00810785	+	0.0140432i
$628$	330.496	+	190.812i	0.526267	+	0.303840i
$629$		−	434.036i		−	0.690041i
$630$		0			0
$631$	584.721			0.926658			0.463329	−	0.886186i	$-0.346655\pi$
$631$	584.721			0.926658			0.463329	+	0.886186i	$0.346655\pi$
$632$	−50.3144	+	87.1472i	−0.0796115	+	0.137891i
$633$	−44.4067	+	25.6382i	−0.0701528	+	0.0405027i
$634$	−56.8303	−	98.4329i	−0.0896376	−	0.155257i
$635$		0			0
$636$			179.052i			0.281529i
$637$	−354.053	+	134.379i	−0.555813	+	0.210957i
$638$	−183.076			−0.286953
$639$	131.148	−	227.155i	0.205239	−	0.355485i
$640$		0			0
$641$	−269.518	−	466.819i	−0.420465	−	0.728268i	0.575520	−	0.817788i	$-0.304800\pi$
$641$	−269.518	−	466.819i	−0.420465	−	0.728268i	−0.995985	+	0.0895205i	$0.971467\pi$
$642$	−199.297	−	115.064i	−0.310431	−	0.179228i
$643$			150.959i			0.234773i	0.993086	+	0.117386i	$0.0374516\pi$
$643$			150.959i			0.234773i	−0.993086	+	0.117386i	$0.962548\pi$
$644$	53.7228	−	77.8525i	0.0834205	−	0.120889i
$645$		0			0
$646$	−15.8979	+	27.5360i	−0.0246098	+	0.0426255i
$647$	−391.111	+	225.808i	−0.604499	+	0.349008i	−0.770809	−	0.637066i	$-0.780148\pi$
$647$	−391.111	+	225.808i	−0.604499	+	0.349008i	0.166310	+	0.986073i	$0.446815\pi$
$648$	12.7279	+	22.0454i	0.0196419	+	0.0340207i
$649$	−322.199	−	186.022i	−0.496454	−	0.286628i
$650$		0			0
$651$	−56.8366	−	119.741i	−0.0873067	−	0.183933i
$652$	−496.404			−0.761356
$653$	215.848	−	373.860i	0.330548	−	0.572526i	−0.652071	−	0.758158i	$-0.726100\pi$
$653$	215.848	−	373.860i	0.330548	−	0.572526i	0.982619	+	0.185631i	$0.0594330\pi$
$654$	255.853	−	147.717i	0.391213	−	0.225867i
$655$		0			0
$656$	65.3108	+	37.7072i	0.0995592	+	0.0574805i
$657$		−	182.745i		−	0.278151i
$658$	−10.2488	+	127.160i	−0.0155757	+	0.193252i
$659$	−195.185			−0.296184			−0.148092	−	0.988974i	$-0.547313\pi$
$659$	−195.185			−0.296184			−0.148092	+	0.988974i	$0.547313\pi$
$660$		0			0
$661$	596.305	−	344.277i	0.902126	−	0.520843i	0.0242368	−	0.999706i	$-0.492284\pi$
$661$	596.305	−	344.277i	0.902126	−	0.520843i	0.877889	+	0.478863i	$0.158951\pi$
$662$	347.926	+	602.626i	0.525569	+	0.910311i
$663$	−146.284	−	84.4572i	−0.220640	−	0.127386i
$664$			132.023i			0.198830i
$665$		0			0
$666$	145.932			0.219118
$667$	132.740	−	229.913i	0.199011	−	0.344697i
$668$	50.7445	−	29.2974i	0.0759649	−	0.0438583i
$669$	284.517	+	492.799i	0.425288	+	0.736620i
$670$		0			0
$671$			86.4259i			0.128802i
$672$	61.9600	−	29.4102i	0.0922024	−	0.0437652i
$673$	−200.020			−0.297206			−0.148603	−	0.988897i	$-0.547478\pi$
$673$	−200.020			−0.297206			−0.148603	+	0.988897i	$0.547478\pi$
$674$	445.564	−	771.740i	0.661075	−	1.14501i
$675$		0			0
$676$	−109.270	−	189.262i	−0.161642	−	0.279973i
$677$	−735.787	−	424.807i	−1.08683	−	0.627484i	−0.154103	−	0.988055i	$-0.549249\pi$
$677$	−735.787	−	424.807i	−1.08683	−	0.627484i	−0.932732	+	0.360571i	$0.882582\pi$
$678$		−	26.2873i		−	0.0387719i
$679$	−263.554	−	181.868i	−0.388150	−	0.267846i
$680$		0			0
$681$	315.628	−	546.684i	0.463477	−	0.802766i
$682$	−44.1111	+	25.4676i	−0.0646791	+	0.0373425i
$683$	−224.005	−	387.988i	−0.327972	−	0.568064i	0.654137	−	0.756376i	$-0.273032\pi$
$683$	−224.005	−	387.988i	−0.327972	−	0.568064i	−0.982109	+	0.188311i	$0.939699\pi$
$684$	−9.25821	−	5.34523i	−0.0135354	−	0.00781467i
$685$		0			0
$686$	335.888	−	349.968i	0.489632	−	0.510157i
$687$	521.433			0.759000
$688$	−154.839	+	268.190i	−0.225057	+	0.389811i
$689$	345.952	−	199.735i	0.502107	−	0.289891i
$690$		0			0
$691$	−337.930	−	195.104i	−0.489044	−	0.282350i	0.235134	−	0.971963i	$-0.424447\pi$
$691$	−337.930	−	195.104i	−0.489044	−	0.282350i	−0.724178	+	0.689613i	$0.757781\pi$
$692$		−	46.1839i		−	0.0667397i
$693$	39.2946	−	56.9439i	0.0567022	−	0.0821701i
$694$	−608.313			−0.876532
$695$		0			0
$696$	166.707	−	96.2485i	0.239522	−	0.138288i
$697$	118.953	+	206.033i	0.170664	+	0.295599i
$698$	116.574	+	67.3038i	0.167011	+	0.0964237i
$699$		−	488.482i		−	0.698830i
$700$		0			0
$701$	989.018			1.41087			0.705434	−	0.708776i	$-0.250752\pi$
$701$	989.018			1.41087			0.705434	+	0.708776i	$0.250752\pi$
$702$	28.3963	−	49.1839i	0.0404506	−	0.0700625i
$703$	−53.0751	+	30.6429i	−0.0754980	+	0.0435888i
$704$	−13.1782	−	22.8254i	−0.0187191	−	0.0324224i
$705$		0			0
$706$			371.849i			0.526699i
$707$	−51.4676	+	638.571i	−0.0727971	+	0.903212i
$708$	391.189			0.552527
$709$	−554.927	+	961.161i	−0.782689	+	1.35566i	0.147680	+	0.989035i	$0.452819\pi$
$709$	−554.927	+	961.161i	−0.782689	+	1.35566i	−0.930370	+	0.366623i	$0.880514\pi$
$710$		0			0
$711$	−53.3665	−	92.4335i	−0.0750584	−	0.130005i
$712$	134.267	+	77.5192i	0.188578	+	0.108875i
$713$		−	73.8617i		−	0.103593i
$714$	215.664	+	17.3821i	0.302051	+	0.0243447i
$715$		0			0
$716$	209.435	−	362.752i	0.292507	−	0.506637i
$717$	−124.552	+	71.9101i	−0.173713	+	0.100293i
$718$	211.263	+	365.918i	0.294238	+	0.509636i
$719$	936.393	+	540.627i	1.30235	+	0.751915i	0.980807	−	0.194979i	$-0.0624638\pi$
$719$	936.393	+	540.627i	1.30235	+	0.751915i	0.321547	+	0.946894i	$0.395797\pi$
$720$		0			0
$721$	319.402	−	151.609i	0.442999	−	0.210276i
$722$	−506.042			−0.700889
$723$	287.369	−	497.737i	0.397467	−	0.688433i
$724$	422.043	−	243.667i	0.582932	−	0.336556i
$725$		0			0
$726$	233.655	+	134.901i	0.321838	+	0.185813i
$727$		−	491.493i		−	0.676056i	−0.941136	−	0.338028i	$-0.890240\pi$
$727$		−	491.493i		−	0.676056i	0.941136	−	0.338028i	$-0.109760\pi$
$728$	−125.941	−	86.9070i	−0.172996	−	0.119378i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−846.044	+	488.464i	−1.15738	+	0.668213i
$732$	−45.4367	−	78.6988i	−0.0620721	−	0.107512i
$733$	40.4999	+	23.3826i	0.0552522	+	0.0318999i	0.527372	−	0.849635i	$-0.323178\pi$
$733$	40.4999	+	23.3826i	0.0552522	+	0.0318999i	−0.472119	+	0.881535i	$0.656511\pi$
$734$		−	186.784i		−	0.254474i
$735$		0			0
$736$	38.2199			0.0519292
$737$	32.8025	−	56.8156i	0.0445081	−	0.0770903i
$738$	−69.2726	+	39.9946i	−0.0938653	+	0.0541932i
$739$	368.856	+	638.878i	0.499129	+	0.864517i	0.999999	−	0.00100544i	$-0.000320040\pi$
$739$	368.856	+	638.878i	0.499129	+	0.864517i	−0.500870	+	0.865522i	$0.666987\pi$
$740$		0			0
$741$			23.8507i			0.0321872i
$742$	−290.615	+	421.146i	−0.391665	+	0.567582i
$743$	258.593			0.348039			0.174020	−	0.984742i	$-0.444324\pi$
$743$	258.593			0.348039			0.174020	+	0.984742i	$0.444324\pi$
$744$	26.7782	−	46.3812i	0.0359922	−	0.0623403i
$745$		0			0
$746$	−7.55747	−	13.0899i	−0.0101307	−	0.0175468i
$747$	−121.271	−	70.0159i	−0.162344	−	0.0937295i
$748$		−	83.1454i		−	0.111157i
$749$	−282.005	−	594.114i	−0.376509	−	0.793210i
$750$		0			0
$751$	−175.310	+	303.645i	−0.233435	+	0.404321i	−0.958817	−	0.284025i	$-0.908330\pi$
$751$	−175.310	+	303.645i	−0.233435	+	0.404321i	0.725382	+	0.688347i	$0.241663\pi$
$752$	−44.6409	+	25.7734i	−0.0593628	+	0.0342731i
$753$	−362.930	−	628.613i	−0.481978	−	0.834811i
$754$	−371.928	−	214.733i	−0.493274	−	0.284792i
$755$		0			0
$756$	−5.84424	+	72.5110i	−0.00773048	+	0.0959140i
$757$	−907.187			−1.19840			−0.599199	−	0.800600i	$-0.704514\pi$
$757$	−907.187			−1.19840			−0.599199	+	0.800600i	$0.704514\pi$
$758$	101.058	−	175.038i	0.133322	−	0.230921i
$759$	33.3890	−	19.2771i	0.0439907	−	0.0253981i
$760$		0			0
$761$	1067.66	+	616.416i	1.40297	+	0.810007i	0.994697	−	0.102851i	$-0.0327965\pi$
$761$	1067.66	+	616.416i	1.40297	+	0.810007i	0.408277	+	0.912858i	$0.366130\pi$
$762$			287.280i			0.377008i
$763$	841.543	+	67.8267i	1.10294	+	0.0888948i
$764$	−473.691			−0.620014
$765$		0			0
$766$	755.684	−	436.294i	0.986532	−	0.569575i
$767$	−436.376	−	755.826i	−0.568939	−	0.985432i
$768$	24.0000	+	13.8564i	0.0312500	+	0.0180422i
$769$			685.828i			0.891844i	0.895072	+	0.445922i	$0.147124\pi$
$769$			685.828i			0.891844i	−0.895072	+	0.445922i	$0.852876\pi$
$770$		0			0
$771$	−578.431			−0.750235
$772$	−132.892	+	230.176i	−0.172140	+	0.298155i
$773$	−334.420	+	193.077i	−0.432625	+	0.249776i	−0.700465	−	0.713687i	$-0.747024\pi$
$773$	−334.420	+	193.077i	−0.432625	+	0.249776i	0.267839	+	0.963464i	$0.413690\pi$
$774$	−164.232	−	284.458i	−0.212186	−	0.367517i
$775$		0			0
$776$		−	129.386i		−	0.166734i
$777$	343.245	+	236.859i	0.441756	+	0.304838i
$778$	981.376			1.26141
$779$	16.7962	−	29.0918i	0.0215612	−	0.0373451i
$780$		0			0
$781$	−144.025	−	249.458i	−0.184411	−	0.319409i
$782$	104.417	+	60.2851i	0.133525	+	0.0770909i
$783$			204.174i			0.260759i
$784$	193.470	+	31.3905i	0.246773	+	0.0400389i
$785$		0			0
$786$	−113.527	+	196.635i	−0.144437	+	0.250171i
$787$	−1064.42	+	614.543i	−1.35250	+	0.780867i	−0.988599	−	0.150570i	$-0.951889\pi$
$787$	−1064.42	+	614.543i	−1.35250	+	0.780867i	−0.363902	+	0.931437i	$0.618556\pi$
$788$	−105.779	−	183.215i	−0.134238	−	0.232506i
$789$	−306.565	−	176.995i	−0.388549	−	0.224329i
$790$		0			0
$791$	42.6663	−	61.8300i	0.0539397	−	0.0781668i
$792$	27.9553			0.0352971
$793$	−101.371	+	175.579i	−0.127832	+	0.221411i
$794$	685.309	−	395.663i	0.863109	−	0.498316i
$795$		0			0
$796$	−349.082	−	201.543i	−0.438545	−	0.253194i
$797$		−	821.718i		−	1.03101i	−0.856886	−	0.515507i	$-0.827604\pi$
$797$		−	821.718i		−	1.03101i	0.856886	−	0.515507i	$-0.172396\pi$
$798$	−13.1004	−	27.5992i	−0.0164165	−	0.0345855i
$799$	−162.612			−0.203519
$800$		0			0
$801$	−142.412	+	82.2215i	−0.177793	+	0.102649i
$802$	−113.990	−	197.437i	−0.142132	−	0.246181i
$803$	−173.801	−	100.344i	−0.216440	−	0.124962i
$804$			68.9811i			0.0857973i
$805$		0			0
$806$	−119.486			−0.148245
$807$	120.768	−	209.177i	0.149651	−	0.259203i
$808$	−224.178	+	129.429i	−0.277448	+	0.160185i
$809$	216.809	+	375.524i	0.267996	+	0.464184i	0.968344	−	0.249618i	$-0.0803051\pi$
$809$	216.809	+	375.524i	0.267996	+	0.464184i	−0.700348	+	0.713802i	$0.746972\pi$
$810$		0			0
$811$		−	1618.04i		−	1.99512i	−0.0698416	−	0.997558i	$-0.522249\pi$
$811$		−	1618.04i		−	1.99512i	0.0698416	−	0.997558i	$-0.477751\pi$
$812$	548.328	+	44.1941i	0.675281	+	0.0544263i
$813$	646.425			0.795111
$814$	80.1304	−	138.790i	0.0984403	−	0.170504i
$815$		0			0
$816$	43.7121	+	75.7115i	0.0535687	+	0.0927837i
$817$	119.461	+	68.9711i	0.146220	+	0.0844199i
$818$		−	650.286i		−	0.794971i
$819$	146.620	−	69.5952i	0.179023	−	0.0849758i
$820$		0			0
$821$	429.043	−	743.125i	0.522586	−	0.905146i	−0.477068	−	0.878866i	$-0.658301\pi$
$821$	429.043	−	743.125i	0.522586	−	0.905146i	0.999655	−	0.0262799i	$-0.00836612\pi$
$822$	−58.2813	+	33.6487i	−0.0709018	+	0.0409352i
$823$	−392.287	−	679.461i	−0.476655	−	0.825591i	0.522987	−	0.852341i	$-0.324818\pi$
$823$	−392.287	−	679.461i	−0.476655	−	0.825591i	−0.999642	+	0.0267498i	$0.991484\pi$
$824$	123.719	+	71.4294i	0.150145	+	0.0866862i
$825$		0			0
$826$	920.109	+	634.929i	1.11393	+	0.768680i
$827$	773.795			0.935665			0.467833	−	0.883817i	$-0.345035\pi$
$827$	773.795			0.935665			0.467833	+	0.883817i	$0.345035\pi$
$828$	−20.2691	+	35.1072i	−0.0244796	+	0.0424000i
$829$	−573.640	+	331.191i	−0.691966	+	0.399507i	−0.804348	−	0.594158i	$-0.797485\pi$
$829$	−573.640	+	331.191i	−0.691966	+	0.399507i	0.112382	+	0.993665i	$0.464152\pi$
$830$		0			0
$831$	746.256	+	430.851i	0.898022	+	0.518473i
$832$		−	61.8280i		−	0.0743125i
$833$	479.048	+	390.924i	0.575087	+	0.469296i
$834$	164.147			0.196819
$835$		0			0
$836$	−10.1672	+	5.87006i	−0.0121618	+	0.00702161i
$837$	28.4025	+	49.1946i	0.0339337	+	0.0587750i
$838$	−114.614	−	66.1723i	−0.136771	−	0.0789646i
$839$		−	359.133i		−	0.428049i	−0.976828	−	0.214024i	$-0.931343\pi$
$839$		−	359.133i		−	0.428049i	0.976828	−	0.214024i	$-0.0686572\pi$
$840$		0			0
$841$	702.963			0.835866
$842$	115.228	−	199.581i	0.136851	−	0.237032i
$843$	−439.169	+	253.554i	−0.520959	+	0.300776i
$844$	−29.6045	−	51.2764i	−0.0350764	−	0.0607541i
$845$		0			0
$846$		−	54.6737i		−	0.0646261i
$847$	330.621	+	696.537i	0.390344	+	0.822357i
$848$	−206.752			−0.243811
$849$	−239.686	+	415.149i	−0.282316	+	0.488986i
$850$		0			0
$851$	116.198	+	201.261i	0.136543	+	0.236500i
$852$	262.296	+	151.437i	0.307859	+	0.177742i
$853$			1089.78i			1.27758i	0.769379	+	0.638792i	$0.220566\pi$
$853$			1089.78i			1.27758i	−0.769379	+	0.638792i	$0.779434\pi$
$854$	20.8631	−	258.853i	0.0244298	−	0.303107i
$855$		0			0
$856$	132.865	−	230.128i	0.155216	−	0.268841i
$857$	56.2155	−	32.4560i	0.0655956	−	0.0378717i	−0.466843	−	0.884340i	$-0.654609\pi$
$857$	56.2155	−	32.4560i	0.0655956	−	0.0378717i	0.532439	+	0.846468i	$0.321276\pi$
$858$	−31.1845	−	54.0131i	−0.0363455	−	0.0629523i
$859$	250.689	+	144.735i	0.291838	+	0.168493i	0.638770	−	0.769397i	$-0.279443\pi$
$859$	250.689	+	144.735i	0.291838	+	0.168493i	−0.346933	+	0.937890i	$0.612777\pi$
$860$		0			0
$861$	−227.849	−	18.3642i	−0.264633	−	0.0213289i
$862$	468.225			0.543185
$863$	469.234	−	812.738i	0.543725	−	0.941759i	−0.454961	−	0.890511i	$-0.650347\pi$
$863$	469.234	−	812.738i	0.543725	−	0.941759i	0.998686	−	0.0512476i	$-0.0163198\pi$
$864$	−25.4558	+	14.6969i	−0.0294628	+	0.0170103i
$865$		0			0
$866$	−108.283	−	62.5174i	−0.125038	−	0.0721910i
$867$		−	224.771i		−	0.259251i
$868$	138.265	−	65.6293i	0.159291	−	0.0756098i
$869$	−117.213			−0.134882
$870$		0			0
$871$	133.280	−	76.9493i	0.153020	−	0.0883459i
$872$	170.569	+	295.434i	0.195606	+	0.338800i
$873$	118.848	+	68.6171i	0.136138	+	0.0785992i
$874$		−	17.0245i		−	0.0194788i
$875$		0			0
$876$	211.016			0.240886
$877$	110.543	−	191.465i	0.126046	−	0.218318i	−0.796095	−	0.605171i	$-0.793105\pi$
$877$	110.543	−	191.465i	0.126046	−	0.218318i	0.922141	+	0.386853i	$0.126438\pi$
$878$	−85.5044	+	49.3660i	−0.0973855	+	0.0562255i
$879$	−325.019	−	562.949i	−0.369759	−	0.640442i
$880$		0			0
$881$		−	154.796i		−	0.175704i	−0.996134	−	0.0878522i	$-0.972000\pi$
$881$		−	154.796i		−	0.175704i	0.996134	−	0.0878522i	$-0.0280003\pi$
$882$	−131.437	+	161.066i	−0.149022	+	0.182615i
$883$	1267.40			1.43534			0.717668	−	0.696385i	$-0.245209\pi$
$883$	1267.40			1.43534			0.717668	+	0.696385i	$0.245209\pi$
$884$	97.5227	−	168.914i	0.110320	−	0.191080i
$885$		0			0
$886$	−466.997	−	808.863i	−0.527085	−	0.912938i
$887$	1434.83	+	828.399i	1.61762	+	0.933934i	0.987533	+	0.157410i	$0.0503143\pi$
$887$	1434.83	+	828.399i	1.61762	+	0.933934i	0.630087	+	0.776524i	$0.283019\pi$
$888$			168.508i			0.189761i
$889$	−466.277	+	675.706i	−0.524496	+	0.760074i
$890$		0			0
$891$	−14.8255	+	25.6786i	−0.0166392	+	0.0288199i
$892$	−569.035	+	328.532i	−0.637931	+	0.368310i
$893$	11.4804	+	19.8846i	0.0128560	+	0.0222672i
$894$	−108.428	−	62.6009i	−0.121284	−	0.0700234i
$895$		0			0
$896$	33.9600	+	71.5452i	0.0379018	+	0.0798496i
$897$	90.4420			0.100827
$898$	−396.174	+	686.193i	−0.441173	+	0.764135i
$899$	372.010	−	214.780i	0.413804	−	0.238910i
$900$		0			0
$901$	−564.847	−	326.114i	−0.626911	−	0.361947i
$902$			87.8430i			0.0973869i
$903$	75.4099	−	935.630i	0.0835105	−	1.03614i
$904$	30.3540			0.0335774
$905$		0			0
$906$	−350.480	+	202.350i	−0.386844	+	0.223344i
$907$	−368.230	−	637.793i	−0.405987	−	0.703190i	0.588449	−	0.808534i	$-0.299739\pi$
$907$	−368.230	−	637.793i	−0.405987	−	0.703190i	−0.994436	+	0.105345i	$0.966405\pi$
$908$	631.256	+	364.456i	0.695216	+	0.401383i
$909$		−	274.561i		−	0.302047i
$910$		0			0
$911$	197.935			0.217273			0.108636	−	0.994082i	$-0.465352\pi$
$911$	197.935			0.217273			0.108636	+	0.994082i	$0.465352\pi$
$912$	6.17214	−	10.6905i	0.00676770	−	0.0117220i
$913$	−133.178	+	76.8905i	−0.145869	+	0.0842175i
$914$	−129.952	−	225.084i	−0.142180	−	0.246262i
$915$		0			0
$916$			602.099i			0.657313i
$917$	−586.178	+	278.238i	−0.639235	+	0.303422i
$918$	−92.7273			−0.101010
$919$	−821.091	+	1422.17i	−0.893462	+	1.54752i	−0.0577645	+	0.998330i	$0.518397\pi$
$919$	−821.091	+	1422.17i	−0.893462	+	1.54752i	−0.835697	+	0.549191i	$0.814936\pi$
$920$		0			0
$921$	93.3436	+	161.676i	0.101350	+	0.175544i
$922$	−34.8231	−	20.1051i	−0.0377691	−	0.0218060i
$923$		−	675.718i		−	0.732089i
$924$	65.7531	+	45.3735i	0.0711614	+	0.0491055i
$925$		0			0
$926$	190.870	−	330.597i	0.206123	−	0.357016i
$927$	−131.224	+	75.7623i	−0.141558	+	0.0817285i
$928$	111.138	+	192.497i	0.119761	+	0.207432i
$929$	1317.18	+	760.473i	1.41784	+	0.818593i	0.996109	−	0.0881263i	$-0.0280879\pi$
$929$	1317.18	+	760.473i	1.41784	+	0.818593i	0.421735	+	0.906719i	$0.361421\pi$
$930$		0			0
$931$	13.9825	−	86.1785i	0.0150188	−	0.0925655i
$932$	564.050			0.605204
$933$	499.771	−	865.629i	0.535660	−	0.927791i
$934$	−409.471	+	236.408i	−0.438405	+	0.253113i
$935$		0			0
$936$	56.7927	+	32.7893i	0.0606759	+	0.0350313i
$937$			682.636i			0.728534i	0.931295	+	0.364267i	$0.118680\pi$
$937$			682.636i			0.728534i	−0.931295	+	0.364267i	$0.881320\pi$
$938$	−111.961	+	162.249i	−0.119362	+	0.172974i
$939$	688.100			0.732800
$940$		0			0
$941$	−248.545	+	143.497i	−0.264129	+	0.152495i	−0.626216	−	0.779649i	$-0.715397\pi$
$941$	−248.545	+	143.497i	−0.264129	+	0.152495i	0.362088	+	0.932144i	$0.382064\pi$
$942$	−233.696	−	404.773i	−0.248085	−	0.429695i
$943$	−110.316	−	63.6911i	−0.116984	−	0.0675410i
$944$			451.706i			0.478502i
$945$		0			0
$946$	−360.715			−0.381305
$947$	240.057	−	415.790i	0.253492	−	0.439061i	−0.710993	−	0.703199i	$-0.751754\pi$
$947$	240.057	−	415.790i	0.253492	−	0.439061i	0.964485	+	0.264139i	$0.0850876\pi$
$948$	106.733	−	61.6224i	0.112588	−	0.0650025i
$949$	−235.391	−	407.709i	−0.248041	−	0.429620i
$950$		0			0
$951$			139.205i			0.146378i
$952$	−20.0711	+	249.028i	−0.0210831	+	0.261584i
$953$	−1147.30			−1.20388			−0.601941	−	0.798540i	$-0.705606\pi$
$953$	−1147.30			−1.20388			−0.601941	+	0.798540i	$0.705606\pi$
$954$	109.647	−	189.914i	0.114934	−	0.199071i
$955$		0			0
$956$	−83.0347	−	143.820i	−0.0868563	−	0.150440i
$957$	194.181	+	112.111i	0.202906	+	0.117148i
$958$		−	187.076i		−	0.195277i
$959$	−191.697	−	15.4504i	−0.199892	−	0.0161109i
$960$		0			0
$961$	−420.744	+	728.750i	−0.437819	+	0.758325i
$962$	325.579	−	187.973i	0.338439	−	0.195398i
$963$	140.924	+	244.088i	0.146339	+	0.253466i
$964$	574.737	+	331.825i	0.596201	+	0.344217i
$965$		0			0
$966$	−104.656	+	49.6767i	−0.108340	+	0.0514251i
$967$	1400.07			1.44785			0.723923	−	0.689881i	$-0.242337\pi$
$967$	1400.07			1.44785			0.723923	+	0.689881i	$0.242337\pi$
$968$	−155.770	+	269.801i	−0.160919	+	0.278720i
$969$	33.7246	−	19.4709i	0.0348035	−	0.0200938i
$970$		0			0
$971$	226.263	+	130.633i	0.233020	+	0.134534i	0.611965	−	0.790885i	$-0.290379\pi$
$971$	226.263	+	130.633i	0.233020	+	0.134534i	−0.378944	+	0.925419i	$0.623713\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	386.087	+	266.423i	0.396801	+	0.273816i
$974$	−731.532			−0.751059
$975$		0			0
$976$	90.8735	−	52.4658i	0.0931081	−	0.0537560i
$977$	389.723	+	675.019i	0.398897	+	0.690910i	0.993590	−	0.113043i	$-0.0360597\pi$
$977$	389.723	+	675.019i	0.398897	+	0.690910i	−0.594693	+	0.803953i	$0.702726\pi$
$978$	526.516	+	303.984i	0.538360	+	0.310822i
$979$			180.589i			0.184463i
$980$		0			0
$981$	−361.831			−0.368839
$982$	342.809	−	593.763i	0.349093	−	0.604646i
$983$	1332.15	−	769.118i	1.35519	−	0.782419i	0.366219	−	0.930529i	$-0.380652\pi$
$983$	1332.15	−	769.118i	1.35519	−	0.782419i	0.988971	+	0.148110i	$0.0473189\pi$
$984$	−46.1817	−	79.9891i	−0.0469327	−	0.0812898i
$985$		0			0
$986$			701.204i			0.711160i
$987$	88.7395	−	128.597i	0.0899083	−	0.130291i
$988$	−27.5404			−0.0278749
$989$	261.539	−	452.998i	0.264448	−	0.458037i
$990$		0			0
$991$	−482.270	−	835.316i	−0.486650	−	0.842902i	0.513233	−	0.858250i	$-0.328448\pi$
$991$	−482.270	−	835.316i	−0.486650	−	0.842902i	−0.999882	+	0.0153476i	$0.995115\pi$
$992$	53.5563	+	30.9208i	0.0539883	+	0.0311701i
$993$		−	852.242i		−	0.858250i
$994$	371.148	+	781.917i	0.373389	+	0.786637i
$995$		0			0
$996$	80.8474	−	140.032i	0.0811721	−	0.140594i
$997$	−361.770	+	208.868i	−0.362858	+	0.209496i	−0.670334	−	0.742060i	$-0.733849\pi$
$997$	−361.770	+	208.868i	−0.362858	+	0.209496i	0.307476	+	0.951556i	$0.400516\pi$
$998$	−91.4218	−	158.347i	−0.0916050	−	0.158664i
$999$	−154.785	−	89.3649i	−0.154939	−	0.0894543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.c.901.3	yes	8
5.2	odd	4		1050.3.q.b.649.7		16
5.3	odd	4		1050.3.q.b.649.2		16
5.4	even	2		1050.3.p.d.901.2	yes	8
7.3	odd	6	inner	1050.3.p.c.451.3	✓	8
35.3	even	12		1050.3.q.b.199.7		16
35.17	even	12		1050.3.q.b.199.2		16
35.24	odd	6		1050.3.p.d.451.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.c.451.3	✓	8	7.3	odd	6	inner
1050.3.p.c.901.3	yes	8	1.1	even	1	trivial
1050.3.p.d.451.2	yes	8	35.24	odd	6
1050.3.p.d.901.2	yes	8	5.4	even	2
1050.3.q.b.199.2		16	35.17	even	12
1050.3.q.b.199.7		16	35.3	even	12
1050.3.q.b.649.2		16	5.3	odd	4
1050.3.q.b.649.7		16	5.2	odd	4

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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-3.97571 + 5.76140i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-3.97571 + 5.76140i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.64728 - 2.85317i) q^{11} +(3.00000 + 1.73205i) q^{12} -7.72850i q^{13} +(4.24500 + 8.94315i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-10.9280 + 6.30929i) q^{17} +(-2.12132 - 3.67423i) q^{18} +(1.54304 + 0.890872i) q^{19} +(0.974040 - 12.0852i) q^{21} -4.65921 q^{22} +(3.37819 - 5.85120i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-9.46544 - 5.46488i) q^{26} +5.19615i q^{27} +(13.9547 + 1.12472i) q^{28} +39.2933 q^{29} +(9.46751 - 5.46607i) q^{31} +(2.82843 + 4.89898i) q^{32} +(4.94184 + 2.85317i) q^{33} +17.8454i q^{34} -6.00000 q^{36} +(-17.1983 + 29.7883i) q^{37} +(2.18218 - 1.25988i) q^{38} +(6.69308 + 11.5928i) q^{39} -18.8536i q^{41} +(-14.1125 - 9.73845i) q^{42} +77.4197 q^{43} +(-3.29456 + 5.70635i) q^{44} +(-4.77748 - 8.27485i) q^{46} +(11.1602 + 6.44335i) q^{47} -6.92820i q^{48} +(-17.3875 - 45.8113i) q^{49} +(10.9280 - 18.9279i) q^{51} +(-13.3862 + 7.72850i) q^{52} +(25.8440 + 44.7631i) q^{53} +(6.36396 + 3.67423i) q^{54} +(11.2450 - 16.2957i) q^{56} -3.08607 q^{57} +(27.7846 - 48.1243i) q^{58} +(97.7973 - 56.4633i) q^{59} +(-22.7184 - 13.1165i) q^{61} -15.4604i q^{62} +(9.00500 + 18.9713i) q^{63} +8.00000 q^{64} +(6.98882 - 4.03500i) q^{66} +(9.95656 + 17.2453i) q^{67} +(21.8560 + 12.6186i) q^{68} +11.7024i q^{69} +87.4319 q^{71} +(-4.24264 + 7.34847i) q^{72} +(52.7540 - 30.4575i) q^{73} +(24.3220 + 42.1270i) q^{74} -3.56349i q^{76} +(22.9874 + 1.85274i) q^{77} +18.9309 q^{78} +(17.7888 - 30.8112i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-23.0909 - 13.3315i) q^{82} -46.6773i q^{83} +(-21.9062 + 10.3981i) q^{84} +(54.7440 - 94.8194i) q^{86} +(-58.9399 + 34.0290i) q^{87} +(4.65921 + 8.06999i) q^{88} +(-47.4706 - 27.4072i) q^{89} +(44.5270 + 30.7263i) q^{91} -13.5128 q^{92} +(-9.46751 + 16.3982i) q^{93} +(15.7829 - 9.11228i) q^{94} +(-8.48528 - 4.89898i) q^{96} +45.7447i q^{97} +(-68.4020 - 11.0982i) q^{98} -9.88368 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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