LMFDB - Embedded newform 1050.3.p.c.901.1

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			901.1
Root			$2.56149 + 0.662382i$ of defining polynomial
Character	$\chi$	$=$	1050.901
Dual form			1050.3.p.c.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-0.440173 + 6.98615i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(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} +(-3.76860 - 6.52741i) q^{11} +(3.00000 + 1.73205i) q^{12} +21.3906i q^{13} +(-8.24500 - 5.47905i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(18.1757 - 10.4937i) q^{17} +(2.12132 + 3.67423i) q^{18} +(20.8728 + 12.0509i) q^{19} +(-5.38992 - 10.8604i) q^{21} +10.6592 q^{22} +(2.79005 - 4.83250i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(-26.1981 - 15.1255i) q^{26} +5.19615i q^{27} +(12.5405 - 6.22374i) q^{28} -9.96625 q^{29} +(5.70073 - 3.29132i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(11.3058 + 6.52741i) q^{33} +29.6807i q^{34} -6.00000 q^{36} +(11.1983 - 19.3960i) q^{37} +(-29.5187 + 17.0426i) q^{38} +(-18.5248 - 32.0860i) q^{39} +51.0827i q^{41} +(17.1125 + 1.07820i) q^{42} -34.7656 q^{43} +(-7.53720 + 13.0548i) q^{44} +(3.94572 + 6.83419i) q^{46} +(67.2462 + 38.8246i) q^{47} -6.92820i q^{48} +(-48.6125 - 6.15023i) q^{49} +(-18.1757 + 31.4812i) q^{51} +(37.0497 - 21.3906i) q^{52} +(24.8989 + 43.1262i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(-1.24500 + 19.7598i) q^{56} -41.7457 q^{57} +(7.04720 - 12.2061i) q^{58} +(72.9362 - 42.1098i) q^{59} +(-72.4404 - 41.8235i) q^{61} +9.30925i q^{62} +(17.4903 + 11.6228i) q^{63} +8.00000 q^{64} +(-15.9888 + 9.23115i) q^{66} +(33.2911 + 57.6618i) q^{67} +(-36.3513 - 20.9874i) q^{68} +9.66501i q^{69} -68.1049 q^{71} +(4.24264 - 7.34847i) q^{72} +(-75.9128 + 43.8283i) q^{73} +(15.8368 + 27.4301i) q^{74} -48.2038i q^{76} +(47.2603 - 23.4548i) q^{77} +52.3962 q^{78} +(-49.3730 + 85.5165i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-62.5632 - 36.1209i) q^{82} +26.9448i q^{83} +(-13.4209 + 20.1960i) q^{84} +(24.5830 - 42.5790i) q^{86} +(14.9494 - 8.63103i) q^{87} +(-10.6592 - 18.4623i) q^{88} +(12.0453 + 6.95436i) q^{89} +(-149.438 - 9.41559i) q^{91} -11.1602 q^{92} +(-5.70073 + 9.87395i) q^{93} +(-95.1005 + 54.9063i) q^{94} +(8.48528 + 4.89898i) q^{96} +3.69132i q^{97} +(41.9067 - 55.1890i) q^{98} -22.6116 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 $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

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

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
$7$	−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
$11$	−3.76860	−	6.52741i	−0.342600	−	0.593401i	0.642315	−	0.766441i	$-0.277974\pi$
$11$	−3.76860	−	6.52741i	−0.342600	−	0.593401i	−0.984915	+	0.173040i	$0.944641\pi$
$12$	3.00000	+	1.73205i	0.250000	+	0.144338i
$13$			21.3906i			1.64543i	0.568451	+	0.822717i	$0.307543\pi$
$13$			21.3906i			1.64543i	−0.568451	+	0.822717i	$0.692457\pi$
$14$	−8.24500	−	5.47905i	−0.588928	−	0.391361i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	18.1757	−	10.4937i	1.06916	−	0.617278i	0.141205	−	0.989980i	$-0.454902\pi$
$17$	18.1757	−	10.4937i	1.06916	−	0.617278i	0.927951	+	0.372703i	$0.121569\pi$
$18$	2.12132	+	3.67423i	0.117851	+	0.204124i
$19$	20.8728	+	12.0509i	1.09857	+	0.634260i	0.935845	−	0.352411i	$-0.114638\pi$
$19$	20.8728	+	12.0509i	1.09857	+	0.634260i	0.162726	+	0.986671i	$0.447971\pi$
$20$		0			0
$21$	−5.38992	−	10.8604i	−0.256663	−	0.517163i
$22$	10.6592			0.484510
$23$	2.79005	−	4.83250i	0.121306	−	0.210109i	−0.798977	−	0.601362i	$-0.794625\pi$
$23$	2.79005	−	4.83250i	0.121306	−	0.210109i	0.920283	+	0.391253i	$0.127958\pi$
$24$	−4.24264	+	2.44949i	−0.176777	+	0.102062i
$25$		0			0
$26$	−26.1981	−	15.1255i	−1.00762	−	0.581749i
$27$			5.19615i			0.192450i
$28$	12.5405	−	6.22374i	0.447876	−	0.222277i
$29$	−9.96625			−0.343664			−0.171832	−	0.985126i	$-0.554969\pi$
$29$	−9.96625			−0.343664			−0.171832	+	0.985126i	$0.554969\pi$
$30$		0			0
$31$	5.70073	−	3.29132i	0.183894	−	0.106171i	−0.405227	−	0.914216i	$-0.632807\pi$
$31$	5.70073	−	3.29132i	0.183894	−	0.106171i	0.589121	+	0.808045i	$0.299474\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$	11.3058	+	6.52741i	0.342600	+	0.197800i
$34$			29.6807i			0.872962i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	11.1983	−	19.3960i	0.302656	−	0.524216i	−0.674080	−	0.738658i	$-0.735460\pi$
$37$	11.1983	−	19.3960i	0.302656	−	0.524216i	0.976737	+	0.214442i	$0.0687933\pi$
$38$	−29.5187	+	17.0426i	−0.776807	+	0.448490i
$39$	−18.5248	−	32.0860i	−0.474996	−	0.822717i
$40$		0			0
$41$			51.0827i			1.24592i	0.782254	+	0.622959i	$0.214070\pi$
$41$			51.0827i			1.24592i	−0.782254	+	0.622959i	$0.785930\pi$
$42$	17.1125	+	1.07820i	0.407440	+	0.0256714i
$43$	−34.7656			−0.808503			−0.404252	−	0.914648i	$-0.632468\pi$
$43$	−34.7656			−0.808503			−0.404252	+	0.914648i	$0.632468\pi$
$44$	−7.53720	+	13.0548i	−0.171300	+	0.296700i
$45$		0			0
$46$	3.94572	+	6.83419i	0.0857766	+	0.148569i
$47$	67.2462	+	38.8246i	1.43077	+	0.826056i	0.997179	−	0.0750536i	$-0.0239128\pi$
$47$	67.2462	+	38.8246i	1.43077	+	0.826056i	0.433591	+	0.901110i	$0.357246\pi$
$48$		−	6.92820i		−	0.144338i
$49$	−48.6125	−	6.15023i	−0.992092	−	0.125515i
$50$		0			0
$51$	−18.1757	+	31.4812i	−0.356385	+	0.617278i
$52$	37.0497	−	21.3906i	0.712494	−	0.411359i
$53$	24.8989	+	43.1262i	0.469791	+	0.813703i	0.999403	−	0.0345374i	$-0.0109958\pi$
$53$	24.8989	+	43.1262i	0.469791	+	0.813703i	−0.529612	+	0.848240i	$0.677662\pi$
$54$	−6.36396	−	3.67423i	−0.117851	−	0.0680414i
$55$		0			0
$56$	−1.24500	+	19.7598i	−0.0222321	+	0.352854i
$57$	−41.7457			−0.732381
$58$	7.04720	−	12.2061i	0.121504	−	0.210450i
$59$	72.9362	−	42.1098i	1.23621	−	0.713725i	0.267890	−	0.963449i	$-0.413673\pi$
$59$	72.9362	−	42.1098i	1.23621	−	0.713725i	0.968317	+	0.249725i	$0.0803401\pi$
$60$		0			0
$61$	−72.4404	−	41.8235i	−1.18755	−	0.685631i	−0.229799	−	0.973238i	$-0.573807\pi$
$61$	−72.4404	−	41.8235i	−1.18755	−	0.685631i	−0.957749	+	0.287607i	$0.907140\pi$
$62$			9.30925i			0.150149i
$63$	17.4903	+	11.6228i	0.277624	+	0.184489i
$64$	8.00000			0.125000
$65$		0			0
$66$	−15.9888	+	9.23115i	−0.242255	+	0.139866i
$67$	33.2911	+	57.6618i	0.496882	+	0.860625i	0.999994	−	0.00359682i	$-0.00114491\pi$
$67$	33.2911	+	57.6618i	0.496882	+	0.860625i	−0.503112	+	0.864221i	$0.667812\pi$
$68$	−36.3513	−	20.9874i	−0.534578	−	0.308639i
$69$			9.66501i			0.140073i
$70$		0			0
$71$	−68.1049			−0.959224			−0.479612	−	0.877481i	$-0.659223\pi$
$71$	−68.1049			−0.959224			−0.479612	+	0.877481i	$0.659223\pi$
$72$	4.24264	−	7.34847i	0.0589256	−	0.102062i
$73$	−75.9128	+	43.8283i	−1.03990	+	0.600387i	−0.919805	−	0.392375i	$-0.871654\pi$
$73$	−75.9128	+	43.8283i	−1.03990	+	0.600387i	−0.120096	+	0.992762i	$0.538320\pi$
$74$	15.8368	+	27.4301i	0.214010	+	0.370677i
$75$		0			0
$76$		−	48.2038i		−	0.634260i
$77$	47.2603	−	23.4548i	0.613770	−	0.304608i
$78$	52.3962			0.671746
$79$	−49.3730	+	85.5165i	−0.624974	+	1.08249i	0.363572	+	0.931566i	$0.381557\pi$
$79$	−49.3730	+	85.5165i	−0.624974	+	1.08249i	−0.988546	+	0.150921i	$0.951776\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−62.5632	−	36.1209i	−0.762966	−	0.440499i
$83$			26.9448i			0.324636i	0.986739	+	0.162318i	$0.0518970\pi$
$83$			26.9448i			0.324636i	−0.986739	+	0.162318i	$0.948103\pi$
$84$	−13.4209	+	20.1960i	−0.159772	+	0.240429i
$85$		0			0
$86$	24.5830	−	42.5790i	0.285849	−	0.495105i
$87$	14.9494	−	8.63103i	0.171832	−	0.0992072i
$88$	−10.6592	−	18.4623i	−0.121127	−	0.209799i
$89$	12.0453	+	6.95436i	0.135341	+	0.0781389i	0.566142	−	0.824308i	$-0.308436\pi$
$89$	12.0453	+	6.95436i	0.135341	+	0.0781389i	−0.430801	+	0.902447i	$0.641769\pi$
$90$		0			0
$91$	−149.438	−	9.41559i	−1.64218	−	0.103468i
$92$	−11.1602			−0.121306
$93$	−5.70073	+	9.87395i	−0.0612981	+	0.106171i
$94$	−95.1005	+	54.9063i	−1.01171	+	0.584110i
$95$		0			0
$96$	8.48528	+	4.89898i	0.0883883	+	0.0510310i
$97$			3.69132i			0.0380549i	0.999819	+	0.0190274i	$0.00605698\pi$
$97$			3.69132i			0.0380549i	−0.999819	+	0.0190274i	$0.993943\pi$
$98$	41.9067	−	55.1890i	0.427619	−	0.563153i
$99$	−22.6116			−0.228400
$100$		0			0
$101$	−158.170	+	91.3195i	−1.56604	+	0.904154i	−0.569416	+	0.822049i	$0.692831\pi$
$101$	−158.170	+	91.3195i	−1.56604	+	0.904154i	−0.996624	+	0.0821041i	$0.973836\pi$
$102$	−25.7043	−	44.5211i	−0.252003	−	0.436481i
$103$	−78.8521	−	45.5253i	−0.765555	−	0.441993i	0.0657318	−	0.997837i	$-0.479062\pi$
$103$	−78.8521	−	45.5253i	−0.765555	−	0.441993i	−0.831287	+	0.555844i	$0.812395\pi$
$104$			60.5019i			0.581749i
$105$		0			0
$106$	−70.4249			−0.664385
$107$	−25.7682	+	44.6318i	−0.240824	+	0.417120i	−0.960949	−	0.276724i	$-0.910751\pi$
$107$	−25.7682	+	44.6318i	−0.240824	+	0.417120i	0.720125	+	0.693844i	$0.244084\pi$
$108$	9.00000	−	5.19615i	0.0833333	−	0.0481125i
$109$	−19.1807	−	33.2219i	−0.175970	−	0.304788i	0.764527	−	0.644592i	$-0.222973\pi$
$109$	−19.1807	−	33.2219i	−0.175970	−	0.304788i	−0.940496	+	0.339804i	$0.889639\pi$
$110$		0			0
$111$			38.7920i			0.349477i
$112$	−23.3204	−	15.4971i	−0.208218	−	0.138367i
$113$	−198.558			−1.75715			−0.878573	−	0.477608i	$-0.841504\pi$
$113$	−198.558			−1.75715			−0.878573	+	0.477608i	$0.841504\pi$
$114$	29.5187	−	51.1278i	0.258936	−	0.448490i
$115$		0			0
$116$	9.96625	+	17.2621i	0.0859160	+	0.148811i
$117$	55.5745	+	32.0860i	0.474996	+	0.274239i
$118$			119.104i			1.00936i
$119$	65.3102	+	131.597i	0.548825	+	1.10586i
$120$		0			0
$121$	32.0953	−	55.5907i	0.265250	−	0.459427i
$122$	102.446	−	59.1474i	0.839723	−	0.484814i
$123$	−44.2389	−	76.6240i	−0.359666	−	0.622959i
$124$	−11.4015	−	6.58263i	−0.0919472	−	0.0530857i
$125$		0			0
$126$	−26.6025	+	13.2026i	−0.211131	+	0.104782i
$127$	−74.1132			−0.583569			−0.291784	−	0.956484i	$-0.594249\pi$
$127$	−74.1132			−0.583569			−0.291784	+	0.956484i	$0.594249\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$	52.1485	−	30.1079i	0.404252	−	0.233395i
$130$		0			0
$131$	17.3500	+	10.0170i	0.132443	+	0.0764657i	0.564757	−	0.825257i	$-0.308970\pi$
$131$	17.3500	+	10.0170i	0.132443	+	0.0764657i	−0.432315	+	0.901723i	$0.642303\pi$
$132$		−	26.1096i		−	0.197800i
$133$	−93.3773	+	140.516i	−0.702085	+	1.05651i
$134$	−94.1614			−0.702697
$135$		0			0
$136$	51.4085	−	29.6807i	0.378004	−	0.218241i
$137$	43.0853	+	74.6259i	0.314491	+	0.544715i	0.979329	−	0.202273i	$-0.0648328\pi$
$137$	43.0853	+	74.6259i	0.314491	+	0.544715i	−0.664838	+	0.746988i	$0.731499\pi$
$138$	−11.8372	−	6.83419i	−0.0857766	−	0.0495231i
$139$		−	232.502i		−	1.67268i	−0.548213	−	0.836339i	$-0.684692\pi$
$139$		−	232.502i		−	1.67268i	0.548213	−	0.836339i	$-0.315308\pi$
$140$		0			0
$141$	−134.492			−0.953847
$142$	48.1574	−	83.4111i	0.339137	−	0.587402i
$143$	139.625	−	80.6128i	0.976402	−	0.563726i
$144$	6.00000	+	10.3923i	0.0416667	+	0.0721688i
$145$		0			0
$146$		−	123.965i		−	0.849076i
$147$	78.2450	−	32.8743i	0.532279	−	0.223635i
$148$	−44.7931			−0.302656
$149$	109.963	−	190.462i	0.738008	−	1.27827i	−0.215383	−	0.976530i	$-0.569100\pi$
$149$	109.963	−	190.462i	0.738008	−	1.27827i	0.953391	−	0.301738i	$-0.0975666\pi$
$150$		0			0
$151$	130.461	+	225.965i	0.863980	+	1.49646i	0.868056	+	0.496466i	$0.165369\pi$
$151$	130.461	+	225.965i	0.863980	+	1.49646i	−0.00407633	+	0.999992i	$0.501298\pi$
$152$	59.0373	+	34.0852i	0.388403	+	0.224245i
$153$		−	62.9623i		−	0.411518i
$154$	−4.69190	+	74.4668i	−0.0304669	+	0.483551i
$155$		0			0
$156$	−37.0497	+	64.1719i	−0.237498	+	0.411359i
$157$	−98.8921	+	57.0954i	−0.629886	+	0.363665i	−0.780708	−	0.624896i	$-0.785141\pi$
$157$	−98.8921	+	57.0954i	−0.629886	+	0.363665i	0.150822	+	0.988561i	$0.451808\pi$
$158$	−69.8239	−	120.939i	−0.441923	−	0.765434i
$159$	−74.6968	−	43.1262i	−0.469791	−	0.271234i
$160$		0			0
$161$	32.5325	+	21.6188i	0.202065	+	0.134278i
$162$	12.7279			0.0785674
$163$	−24.3581	+	42.1894i	−0.149436	+	0.258831i	−0.931019	−	0.364970i	$-0.881079\pi$
$163$	−24.3581	+	42.1894i	−0.149436	+	0.258831i	0.781583	+	0.623801i	$0.214412\pi$
$164$	88.4777	−	51.0827i	0.539498	−	0.311480i
$165$		0			0
$166$	−33.0005	−	19.0528i	−0.198798	−	0.114776i
$167$		−	49.6127i		−	0.297082i	−0.988906	−	0.148541i	$-0.952542\pi$
$167$		−	49.6127i		−	0.297082i	0.988906	−	0.148541i	$-0.0474577\pi$
$168$	−15.2450	−	30.7179i	−0.0907440	−	0.182845i
$169$	−288.560			−1.70745
$170$		0			0
$171$	62.6185	−	36.1528i	0.366190	−	0.211420i
$172$	34.7656	+	60.2159i	0.202126	+	0.350092i
$173$	−203.811	−	117.670i	−1.17810	−	0.680176i	−0.222525	−	0.974927i	$-0.571430\pi$
$173$	−203.811	−	117.670i	−1.17810	−	0.680176i	−0.955574	+	0.294751i	$0.904763\pi$
$174$			24.4122i			0.140300i
$175$		0			0
$176$	30.1488			0.171300
$177$	−72.9362	+	126.329i	−0.412069	+	0.713725i
$178$	−17.0346	+	9.83495i	−0.0957002	+	0.0552525i
$179$	22.1049	+	38.2868i	0.123491	+	0.213893i	0.921142	−	0.389226i	$-0.127258\pi$
$179$	22.1049	+	38.2868i	0.123491	+	0.213893i	−0.797651	+	0.603119i	$0.793924\pi$
$180$		0			0
$181$		−	117.049i		−	0.646679i	−0.946283	−	0.323340i	$-0.895194\pi$
$181$		−	117.049i		−	0.646679i	0.946283	−	0.323340i	$-0.104806\pi$
$182$	117.200	−	176.366i	0.643958	−	0.969043i
$183$	144.881			0.791699
$184$	7.89145	−	13.6684i	0.0428883	−	0.0742847i
$185$		0			0
$186$	−8.06204	−	13.9639i	−0.0433443	−	0.0750746i
$187$	−136.994	−	79.0933i	−0.732586	−	0.422959i
$188$		−	155.299i		−	0.826056i
$189$	−36.3011	−	2.28721i	−0.192069	−	0.0121016i
$190$		0			0
$191$	−117.156	+	202.920i	−0.613383	+	1.06241i	0.377283	+	0.926098i	$0.376858\pi$
$191$	−117.156	+	202.920i	−0.613383	+	1.06241i	−0.990666	+	0.136313i	$0.956475\pi$
$192$	−12.0000	+	6.92820i	−0.0625000	+	0.0360844i
$193$	9.78252	+	16.9438i	0.0506866	+	0.0877918i	0.890256	−	0.455461i	$-0.150526\pi$
$193$	9.78252	+	16.9438i	0.0506866	+	0.0877918i	−0.839569	+	0.543253i	$0.817192\pi$
$194$	−4.52093	−	2.61016i	−0.0233037	−	0.0134544i
$195$		0			0
$196$	37.9600	+	90.3495i	0.193673	+	0.460967i
$197$	−179.443			−0.910877			−0.455438	−	0.890267i	$-0.650517\pi$
$197$	−179.443			−0.910877			−0.455438	+	0.890267i	$0.650517\pi$
$198$	15.9888	−	27.6934i	0.0807516	−	0.139866i
$199$	−221.630	+	127.958i	−1.11372	+	0.643006i	−0.939790	−	0.341753i	$-0.888979\pi$
$199$	−221.630	+	127.958i	−1.11372	+	0.643006i	−0.173928	+	0.984758i	$0.555646\pi$
$200$		0			0
$201$	−99.8732	−	57.6618i	−0.496882	−	0.286875i
$202$		−	258.291i		−	1.27867i
$203$	4.38688	−	69.6257i	0.0216102	−	0.342984i
$204$	72.7026			0.356385
$205$		0			0
$206$	111.514	−	64.3825i	0.541329	−	0.312536i
$207$	−8.37014	−	14.4975i	−0.0404355	−	0.0700363i
$208$	−74.0994	−	42.7813i	−0.356247	−	0.205679i
$209$		−	181.661i		−	0.869190i
$210$		0			0
$211$	196.891			0.933132			0.466566	−	0.884486i	$-0.345491\pi$
$211$	196.891			0.933132			0.466566	+	0.884486i	$0.345491\pi$
$212$	49.7979	−	86.2525i	0.234896	−	0.406851i
$213$	102.157	−	58.9806i	0.479612	−	0.276904i
$214$	−36.4417	−	63.1189i	−0.170288	−	0.294948i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	20.4843	+	41.2749i	0.0943977	+	0.190207i
$218$	54.2512			0.248859
$219$	75.9128	−	131.485i	0.346634	−	0.600387i
$220$		0			0
$221$	224.467	+	388.789i	1.01569	+	1.75923i
$222$	−47.5103	−	27.4301i	−0.214010	−	0.123559i
$223$			431.015i			1.93280i	0.257039	+	0.966401i	$0.417253\pi$
$223$			431.015i			1.93280i	−0.257039	+	0.966401i	$0.582747\pi$
$224$	35.4700	−	17.6034i	0.158348	−	0.0785866i
$225$		0			0
$226$	140.401	−	243.182i	0.621245	−	1.07603i
$227$	151.637	−	87.5479i	0.668006	−	0.385673i	−0.127315	−	0.991862i	$-0.540636\pi$
$227$	151.637	−	87.5479i	0.668006	−	0.385673i	0.795321	+	0.606189i	$0.207302\pi$
$228$	41.7457	+	72.3057i	0.183095	+	0.317130i
$229$	29.0717	+	16.7846i	0.126951	+	0.0732951i	0.562131	−	0.827048i	$-0.309982\pi$
$229$	29.0717	+	16.7846i	0.126951	+	0.0732951i	−0.435180	+	0.900344i	$0.643315\pi$
$230$		0			0
$231$	−50.5779	+	76.1108i	−0.218952	+	0.329484i
$232$	−28.1888			−0.121504
$233$	77.4567	−	134.159i	0.332432	−	0.575790i	−0.650556	−	0.759458i	$-0.725464\pi$
$233$	77.4567	−	134.159i	0.332432	−	0.575790i	0.982988	+	0.183669i	$0.0587973\pi$
$234$	−78.5942	+	45.3764i	−0.335873	+	0.193916i
$235$		0			0
$236$	−145.872	−	84.2195i	−0.618104	−	0.356862i
$237$		−	171.033i		−	0.721658i
$238$	−207.354	−	13.0647i	−0.871235	−	0.0548935i
$239$	316.591			1.32465			0.662325	−	0.749217i	$-0.269570\pi$
$239$	316.591			1.32465			0.662325	+	0.749217i	$0.269570\pi$
$240$		0			0
$241$	202.219	−	116.751i	0.839084	−	0.484446i	−0.0178685	−	0.999840i	$-0.505688\pi$
$241$	202.219	−	116.751i	0.839084	−	0.484446i	0.856953	+	0.515395i	$0.172355\pi$
$242$	45.3896	+	78.6171i	0.187560	+	0.324864i
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$			167.294i			0.685631i
$245$		0			0
$246$	125.126			0.508644
$247$	−257.777	+	446.484i	−1.04363	+	1.80763i
$248$	16.1241	−	9.30925i	0.0650165	−	0.0375373i
$249$	−23.3349	−	40.4172i	−0.0937143	−	0.162318i
$250$		0			0
$251$			56.6879i			0.225848i	0.993604	+	0.112924i	$0.0360217\pi$
$251$			56.6879i			0.225848i	−0.993604	+	0.112924i	$0.963978\pi$
$252$	2.64104	−	41.9169i	0.0104803	−	0.166337i
$253$	−42.0583			−0.166238
$254$	52.4060	−	90.7698i	0.206323	−	0.357361i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	251.528	+	145.219i	0.978706	+	0.565056i	0.901879	−	0.431988i	$-0.142188\pi$
$257$	251.528	+	145.219i	0.978706	+	0.565056i	0.0768270	+	0.997044i	$0.475521\pi$
$258$			85.1581i			0.330070i
$259$	130.574	+	86.7704i	0.504147	+	0.335021i
$260$		0			0
$261$	−14.9494	+	25.8931i	−0.0572773	+	0.0992072i
$262$	−24.5366	+	14.1662i	−0.0936510	+	0.0540694i
$263$	222.298	+	385.031i	0.845238	+	1.46399i	0.885415	+	0.464802i	$0.153875\pi$
$263$	222.298	+	385.031i	0.845238	+	1.46399i	−0.0401768	+	0.999193i	$0.512792\pi$
$264$	31.9776	+	18.4623i	0.121127	+	0.0699329i
$265$		0			0
$266$	−106.069	−	213.723i	−0.398755	−	0.803471i
$267$	−24.0906			−0.0902270
$268$	66.5822	−	115.324i	0.248441	−	0.430312i
$269$	−144.956	+	83.6902i	−0.538869	+	0.311116i	−0.744620	−	0.667488i	$-0.767369\pi$
$269$	−144.956	+	83.6902i	−0.538869	+	0.311116i	0.205752	+	0.978604i	$0.434036\pi$
$270$		0			0
$271$	2.24099	+	1.29384i	0.00826933	+	0.00477430i	0.504129	−	0.863628i	$-0.331814\pi$
$271$	2.24099	+	1.29384i	0.00826933	+	0.00477430i	−0.495860	+	0.868403i	$0.665147\pi$
$272$			83.9498i			0.308639i
$273$	232.311	−	115.294i	0.850957	−	0.422322i
$274$	−121.864			−0.444758
$275$		0			0
$276$	16.7403	−	9.66501i	0.0606532	−	0.0350181i
$277$	254.556	+	440.903i	0.918973	+	1.59171i	0.800978	+	0.598694i	$0.204314\pi$
$277$	254.556	+	440.903i	0.918973	+	1.59171i	0.117996	+	0.993014i	$0.462353\pi$
$278$	284.756	+	164.404i	1.02430	+	0.591381i
$279$		−	19.7479i		−	0.0707810i
$280$		0			0
$281$	210.688			0.749779			0.374890	−	0.927069i	$-0.377681\pi$
$281$	210.688			0.749779			0.374890	+	0.927069i	$0.377681\pi$
$282$	95.1005	−	164.719i	0.337236	−	0.584110i
$283$	34.1964	−	19.7433i	0.120835	−	0.0697643i	−0.438364	−	0.898797i	$-0.644442\pi$
$283$	34.1964	−	19.7433i	0.120835	−	0.0697643i	0.559199	+	0.829033i	$0.311109\pi$
$284$	68.1049	+	117.961i	0.239806	+	0.415356i
$285$		0			0
$286$			228.007i			0.797229i
$287$	−356.871	−	22.4852i	−1.24345	−	0.0783457i
$288$	−16.9706			−0.0589256
$289$	75.7363	−	131.179i	0.262063	−	0.453907i
$290$		0			0
$291$	−3.19678	−	5.53698i	−0.0109855	−	0.0190274i
$292$	151.826	+	87.6565i	0.519951	+	0.300194i
$293$			89.6023i			0.305810i	0.988241	+	0.152905i	$0.0488628\pi$
$293$			89.6023i			0.305810i	−0.988241	+	0.152905i	$0.951137\pi$
$294$	−15.0649	+	119.076i	−0.0512412	+	0.405020i
$295$		0			0
$296$	31.6735	−	54.8602i	0.107005	−	0.185338i
$297$	33.9174	−	19.5822i	0.114200	−	0.0659334i
$298$	155.511	+	269.354i	0.521850	+	0.903871i
$299$	103.370	+	59.6809i	0.345720	+	0.199602i
$300$		0			0
$301$	15.3029	−	242.878i	0.0508402	−	0.806903i
$302$	−368.999			−1.22185
$303$	158.170	−	273.959i	0.522013	−	0.904154i
$304$	−83.4914	+	48.2038i	−0.274643	+	0.158565i
$305$		0			0
$306$	77.1128	+	44.5211i	0.252003	+	0.145494i
$307$			470.478i			1.53250i	0.642542	+	0.766251i	$0.277880\pi$
$307$			470.478i			1.53250i	−0.642542	+	0.766251i	$0.722120\pi$
$308$	−87.8852	−	58.4024i	−0.285341	−	0.189618i
$309$	157.704			0.510370
$310$		0			0
$311$	217.631	−	125.649i	0.699778	−	0.404017i	−0.107487	−	0.994207i	$-0.534280\pi$
$311$	217.631	−	125.649i	0.699778	−	0.404017i	0.807265	+	0.590189i	$0.200947\pi$
$312$	−52.3962	−	90.7528i	−0.167936	−	0.290874i
$313$	−336.417	−	194.231i	−1.07482	−	0.620545i	−0.145322	−	0.989384i	$-0.546422\pi$
$313$	−336.417	−	194.231i	−1.07482	−	0.620545i	−0.929493	+	0.368839i	$0.879755\pi$
$314$		−	161.490i		−	0.514300i
$315$		0			0
$316$	197.492			0.624974
$317$	−74.6898	+	129.366i	−0.235614	+	0.408096i	−0.959451	−	0.281875i	$-0.909044\pi$
$317$	−74.6898	+	129.366i	−0.235614	+	0.408096i	0.723837	+	0.689971i	$0.242377\pi$
$318$	105.637	−	60.9897i	0.332193	−	0.191792i
$319$	37.5588	+	65.0538i	0.117739	+	0.203930i
$320$		0			0
$321$		−	89.2636i		−	0.278080i
$322$	−49.4815	+	24.5572i	−0.153669	+	0.0762645i
$323$	505.837			1.56606
$324$	−9.00000	+	15.5885i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	−34.4475	−	59.6648i	−0.105667	−	0.183021i
$327$	57.5420	+	33.2219i	0.175970	+	0.101596i
$328$			144.484i			0.440499i
$329$	−300.835	+	452.702i	−0.914391	+	1.37600i
$330$		0			0
$331$	235.465	−	407.838i	0.711375	−	1.23214i	−0.252966	−	0.967475i	$-0.581406\pi$
$331$	235.465	−	407.838i	0.711375	−	1.23214i	0.964341	−	0.264663i	$-0.0852607\pi$
$332$	46.6697	−	26.9448i	0.140571	−	0.0811590i
$333$	−33.5948	−	58.1880i	−0.100885	−	0.174739i
$334$	60.7628	+	35.0814i	0.181925	+	0.105034i
$335$		0			0
$336$	48.4014	+	3.04961i	0.144052	+	0.00907622i
$337$	−532.478			−1.58005			−0.790027	−	0.613072i	$-0.789934\pi$
$337$	−532.478			−1.58005			−0.790027	+	0.613072i	$0.789934\pi$
$338$	204.042	−	353.412i	0.603676	−	1.04560i
$339$	297.836	−	171.956i	0.878573	−	0.507244i
$340$		0			0
$341$	−42.9675	−	24.8073i	−0.126004	−	0.0727487i
$342$			102.256i			0.298993i
$343$	64.3643	−	336.907i	0.187651	−	0.982236i
$344$	−98.3321			−0.285849
$345$		0			0
$346$	288.232	−	166.411i	0.833042	−	0.480957i
$347$	−224.812	−	389.385i	−0.647872	−	1.12215i	−0.983630	−	0.180199i	$-0.942326\pi$
$347$	−224.812	−	389.385i	−0.647872	−	1.12215i	0.335758	−	0.941948i	$-0.391008\pi$
$348$	−29.8988	−	17.2621i	−0.0859160	−	0.0496036i
$349$			330.676i			0.947495i	0.880661	+	0.473747i	$0.157099\pi$
$349$			330.676i			0.947495i	−0.880661	+	0.473747i	$0.842901\pi$
$350$		0			0
$351$	−111.149			−0.316664
$352$	−21.3184	+	36.9246i	−0.0605637	+	0.104899i
$353$	235.014	−	135.686i	0.665763	−	0.384379i	−0.128706	−	0.991683i	$-0.541082\pi$
$353$	235.014	−	135.686i	0.665763	−	0.384379i	0.794469	+	0.607304i	$0.207749\pi$
$354$	−103.147	−	178.657i	−0.291377	−	0.504680i
$355$		0			0
$356$		−	27.8174i		−	0.0781389i
$357$	−211.932	−	140.835i	−0.593646	−	0.394496i
$358$	−62.5221			−0.174643
$359$	3.79200	−	6.56794i	0.0105627	−	0.0182951i	−0.860696	−	0.509120i	$-0.829971\pi$
$359$	3.79200	−	6.56794i	0.0105627	−	0.0182951i	0.871258	+	0.490825i	$0.163304\pi$
$360$		0			0
$361$	109.950	+	190.440i	0.304572	+	0.527534i
$362$	143.355	+	82.7661i	0.396009	+	0.228636i
$363$			111.181i			0.306285i
$364$	133.130	+	268.250i	0.365741	+	0.736951i
$365$		0			0
$366$	−102.446	+	177.442i	−0.279908	+	0.484814i
$367$	460.216	−	265.706i	1.25400	−	0.723995i	0.282095	−	0.959386i	$-0.408971\pi$
$367$	460.216	−	265.706i	1.25400	−	0.723995i	0.971901	+	0.235392i	$0.0756373\pi$
$368$	11.1602	+	19.3300i	0.0303266	+	0.0525272i
$369$	132.717	+	76.6240i	0.359666	+	0.207653i
$370$		0			0
$371$	−312.246	+	154.965i	−0.841634	+	0.417695i
$372$	22.8029			0.0612981
$373$	−287.484	+	497.937i	−0.770734	+	1.33495i	0.166427	+	0.986054i	$0.446777\pi$
$373$	−287.484	+	497.937i	−0.770734	+	1.33495i	−0.937161	+	0.348897i	$0.886556\pi$
$374$	193.738	−	111.855i	0.518016	−	0.299077i
$375$		0			0
$376$	190.201	+	109.813i	0.505854	+	0.292055i
$377$		−	213.185i		−	0.565476i
$378$	28.4700	−	42.8423i	0.0753174	−	0.113339i
$379$	627.464			1.65558			0.827789	−	0.561040i	$-0.189598\pi$
$379$	627.464			1.65558			0.827789	+	0.561040i	$0.189598\pi$
$380$		0			0
$381$	111.170	−	64.1839i	0.291784	−	0.168462i
$382$	−165.684	−	286.973i	−0.433727	−	0.751238i
$383$	57.6870	+	33.3056i	0.150619	+	0.0869597i	0.573415	−	0.819265i	$-0.305618\pi$
$383$	57.6870	+	33.3056i	0.150619	+	0.0869597i	−0.422797	+	0.906225i	$0.638952\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−27.6691			−0.0716817
$387$	−52.1485	+	90.3238i	−0.134751	+	0.233395i
$388$	6.39356	−	3.69132i	0.0164782	−	0.00951372i
$389$	−274.525	−	475.491i	−0.705719	−	1.22234i	−0.966431	−	0.256925i	$-0.917291\pi$
$389$	−274.525	−	475.491i	−0.705719	−	1.22234i	0.260713	−	0.965416i	$-0.416043\pi$
$390$		0			0
$391$		−	117.112i		−	0.299519i
$392$	−137.497	−	17.3955i	−0.350757	−	0.0443762i
$393$	−34.7000			−0.0882950
$394$	126.885	−	219.772i	0.322044	−	0.557796i
$395$		0			0
$396$	22.6116	+	39.1644i	0.0571000	+	0.0989001i
$397$	−449.091	−	259.283i	−1.13121	−	0.653106i	−0.186973	−	0.982365i	$-0.559868\pi$
$397$	−449.091	−	259.283i	−1.13121	−	0.653106i	−0.944240	+	0.329259i	$0.893201\pi$
$398$		−	361.920i		−	0.909347i
$399$	18.3753	−	291.642i	0.0460535	−	0.730931i
$400$		0			0
$401$	238.149	−	412.486i	0.593888	−	1.02864i	−0.399815	−	0.916596i	$-0.630926\pi$
$401$	238.149	−	412.486i	0.593888	−	1.02864i	0.993703	−	0.112048i	$-0.0357411\pi$
$402$	141.242	−	81.5462i	0.351349	−	0.202851i
$403$	70.4033	+	121.942i	0.174698	+	0.302586i
$404$	316.340	+	182.639i	0.783020	+	0.452077i
$405$		0			0
$406$	82.1717	+	54.6056i	0.202393	+	0.134497i
$407$	−168.807			−0.414760
$408$	−51.4085	+	89.0422i	−0.126001	+	0.218241i
$409$	−93.2552	+	53.8409i	−0.228008	+	0.131640i	−0.609653	−	0.792669i	$-0.708691\pi$
$409$	−93.2552	+	53.8409i	−0.228008	+	0.131640i	0.381645	+	0.924309i	$0.375358\pi$
$410$		0			0
$411$	−129.256	−	74.6259i	−0.314491	−	0.181572i
$412$			182.101i			0.441993i
$413$	262.080	+	528.079i	0.634577	+	1.27864i
$414$	23.6743			0.0571844
$415$		0			0
$416$	104.792	−	60.5019i	0.251905	−	0.145437i
$417$	201.353	+	348.753i	0.482861	+	0.836339i
$418$	222.488	+	128.454i	0.532268	+	0.307305i
$419$		−	323.811i		−	0.772818i	−0.922328	−	0.386409i	$-0.873715\pi$
$419$		−	323.811i		−	0.772818i	0.922328	−	0.386409i	$-0.126285\pi$
$420$		0			0
$421$	−238.957			−0.567595			−0.283797	−	0.958884i	$-0.591594\pi$
$421$	−238.957			−0.567595			−0.283797	+	0.958884i	$0.591594\pi$
$422$	−139.223	+	241.141i	−0.329912	+	0.571424i
$423$	201.739	−	116.474i	0.476924	−	0.275352i
$424$	70.4249	+	121.979i	0.166096	+	0.287687i
$425$		0			0
$426$			166.822i			0.391601i
$427$	324.071	−	487.670i	0.758950	−	1.14208i
$428$	103.073			0.240824
$429$	−139.625	+	241.838i	−0.325467	+	0.563726i
$430$		0			0
$431$	95.8960	+	166.097i	0.222497	+	0.385375i	0.955565	−	0.294779i	$-0.0952461\pi$
$431$	95.8960	+	166.097i	0.222497	+	0.385375i	−0.733069	+	0.680154i	$0.761913\pi$
$432$	−18.0000	−	10.3923i	−0.0416667	−	0.0240563i
$433$			122.083i			0.281946i	0.990013	+	0.140973i	$0.0450231\pi$
$433$			122.083i			0.281946i	−0.990013	+	0.140973i	$0.954977\pi$
$434$	−65.0358	−	4.09768i	−0.149852	−	0.00944166i
$435$		0			0
$436$	−38.3614	+	66.4438i	−0.0879848	+	0.152394i
$437$	116.472	−	67.2454i	0.266527	−	0.153880i
$438$	107.357	+	185.948i	0.245107	+	0.424538i
$439$	−217.656	−	125.664i	−0.495800	−	0.286250i	0.231177	−	0.972912i	$-0.425742\pi$
$439$	−217.656	−	125.664i	−0.495800	−	0.286250i	−0.726978	+	0.686661i	$0.759076\pi$
$440$		0			0
$441$	−88.8975	+	117.074i	−0.201582	+	0.265473i
$442$	−634.890			−1.43640
$443$	54.8946	−	95.0802i	0.123916	−	0.214628i	−0.797393	−	0.603460i	$-0.793788\pi$
$443$	54.8946	−	95.0802i	0.123916	−	0.214628i	0.921309	+	0.388832i	$0.127121\pi$
$444$	67.1897	−	38.7920i	0.151328	−	0.0873693i
$445$		0			0
$446$	−527.883	−	304.773i	−1.18359	−	0.683349i
$447$			380.924i			0.852178i
$448$	−3.52139	+	55.8892i	−0.00786024	+	0.124753i
$449$	806.490			1.79619			0.898095	−	0.439801i	$-0.144951\pi$
$449$	806.490			1.79619			0.898095	+	0.439801i	$0.144951\pi$
$450$		0			0
$451$	333.437	−	192.510i	0.739329	−	0.426852i
$452$	198.558	+	343.912i	0.439287	+	0.760867i
$453$	−391.383	−	225.965i	−0.863980	−	0.498819i
$454$			247.623i			0.545425i
$455$		0			0
$456$	−118.075			−0.258936
$457$	−386.226	+	668.964i	−0.845135	+	1.46382i	0.0403698	+	0.999185i	$0.487146\pi$
$457$	−386.226	+	668.964i	−0.845135	+	1.46382i	−0.885504	+	0.464631i	$0.846187\pi$
$458$	−41.1137	+	23.7370i	−0.0897678	+	0.0518275i
$459$	54.5270	+	94.4435i	0.118795	+	0.205759i
$460$		0			0
$461$			793.611i			1.72150i	0.509029	+	0.860749i	$0.330005\pi$
$461$			793.611i			1.72150i	−0.509029	+	0.860749i	$0.669995\pi$
$462$	−57.4523	−	115.764i	−0.124356	−	0.250570i
$463$	274.227			0.592284			0.296142	−	0.955144i	$-0.404300\pi$
$463$	274.227			0.592284			0.296142	+	0.955144i	$0.404300\pi$
$464$	19.9325	−	34.5241i	0.0429580	−	0.0744054i
$465$		0			0
$466$	109.540	+	189.730i	0.235065	+	0.407145i
$467$	−344.357	−	198.815i	−0.737381	−	0.425727i	0.0837354	−	0.996488i	$-0.473315\pi$
$467$	−344.357	−	198.815i	−0.737381	−	0.425727i	−0.821116	+	0.570761i	$0.806648\pi$
$468$		−	128.344i		−	0.274239i
$469$	−417.488	+	207.195i	−0.890166	+	0.441781i
$470$		0			0
$471$	98.8921	−	171.286i	0.209962	−	0.363665i
$472$	206.295	−	119.104i	0.437065	−	0.252340i
$473$	131.018	+	226.930i	0.276993	+	0.479766i
$474$	209.472	+	120.939i	0.441923	+	0.255145i
$475$		0			0
$476$	162.622	−	244.717i	0.341643	−	0.514112i
$477$	149.394			0.313194
$478$	−223.864	+	387.743i	−0.468334	+	0.811179i
$479$	−165.573	+	95.5938i	−0.345665	+	0.199570i	−0.662774	−	0.748819i	$-0.730621\pi$
$479$	−165.573	+	95.5938i	−0.345665	+	0.199570i	0.317110	+	0.948389i	$0.397288\pi$
$480$		0			0
$481$	414.893	+	239.538i	0.862563	+	0.498001i
$482$			330.223i			0.685110i
$483$	−67.5212	−	4.25428i	−0.139795	−	0.00880803i
$484$	−128.381			−0.265250
$485$		0			0
$486$	−19.0919	+	11.0227i	−0.0392837	+	0.0226805i
$487$	−95.0092	−	164.561i	−0.195091	−	0.337907i	0.751840	−	0.659346i	$-0.229167\pi$
$487$	−95.0092	−	164.561i	−0.195091	−	0.337907i	−0.946930	+	0.321439i	$0.895833\pi$
$488$	−204.892	−	118.295i	−0.419862	−	0.242407i
$489$		−	84.3788i		−	0.172554i
$490$		0			0
$491$	−211.384			−0.430517			−0.215258	−	0.976557i	$-0.569059\pi$
$491$	−211.384			−0.430517			−0.215258	+	0.976557i	$0.569059\pi$
$492$	−88.4777	+	153.248i	−0.179833	+	0.311480i
$493$	−181.143	+	104.583i	−0.367430	+	0.212136i
$494$	−364.552	−	631.423i	−0.737960	−	1.27818i
$495$		0			0
$496$			26.3305i			0.0530857i
$497$	29.9779	−	475.791i	0.0603178	−	0.957325i
$498$	66.0010			0.132532
$499$	126.864	−	219.734i	0.254236	−	0.440349i	−0.710452	−	0.703746i	$-0.751509\pi$
$499$	126.864	−	219.734i	0.254236	−	0.440349i	0.964688	+	0.263396i	$0.0848427\pi$
$500$		0			0
$501$	42.9658	+	74.4190i	0.0857601	+	0.148541i
$502$	−69.4282	−	40.0844i	−0.138303	−	0.0798494i
$503$		−	217.815i		−	0.433033i	−0.976279	−	0.216516i	$-0.930531\pi$
$503$		−	217.815i		−	0.433033i	0.976279	−	0.216516i	$-0.0694695\pi$
$504$	49.4700	+	32.8743i	0.0981547	+	0.0652268i
$505$		0			0
$506$	29.7397	−	51.5107i	0.0587741	−	0.101800i
$507$	432.839	−	249.900i	0.853727	−	0.492899i
$508$	74.1132	+	128.368i	0.145892	+	0.252693i
$509$	−24.6582	−	14.2364i	−0.0484444	−	0.0279694i	0.475582	−	0.879671i	$-0.342237\pi$
$509$	−24.6582	−	14.2364i	−0.0484444	−	0.0279694i	−0.524027	+	0.851702i	$0.675571\pi$
$510$		0			0
$511$	−272.776	−	549.630i	−0.533808	−	1.07560i
$512$	22.6274			0.0441942
$513$	−62.6185	+	108.458i	−0.122063	+	0.211420i
$514$	−355.714	+	205.371i	−0.692050	+	0.399555i
$515$		0			0
$516$	−104.297	−	60.2159i	−0.202126	−	0.116697i
$517$		−	585.258i		−	1.13203i
$518$	−198.601	+	98.5640i	−0.383400	+	0.190278i
$519$	407.622			0.785399
$520$		0			0
$521$	671.401	−	387.634i	1.28868	−	0.744019i	0.310260	−	0.950652i	$-0.399584\pi$
$521$	671.401	−	387.634i	1.28868	−	0.744019i	0.978418	+	0.206633i	$0.0662507\pi$
$522$	−21.1416	−	36.6184i	−0.0405012	−	0.0701501i
$523$	88.7388	+	51.2334i	0.169673	+	0.0979605i	0.582431	−	0.812880i	$-0.302101\pi$
$523$	88.7388	+	51.2334i	0.169673	+	0.0979605i	−0.412759	+	0.910840i	$0.635435\pi$
$524$		−	40.0681i		−	0.0764657i
$525$		0			0
$526$	−628.752			−1.19535
$527$	69.0763	−	119.644i	0.131075	−	0.227028i
$528$	−45.2232	+	26.1096i	−0.0856500	+	0.0494501i
$529$	248.931	+	431.162i	0.470570	+	0.815050i
$530$		0			0
$531$		−	252.659i		−	0.475816i
$532$	336.759	+	21.2180i	0.633005	+	0.0398835i
$533$	−1092.69			−2.05008
$534$	17.0346	−	29.5049i	0.0319001	−	0.0552525i
$535$		0			0
$536$	94.1614	+	163.092i	0.175674	+	0.304277i
$537$	−66.3147	−	38.2868i	−0.123491	−	0.0712976i
$538$		−	236.712i		−	0.439984i
$539$	143.056	+	340.491i	0.265410	+	0.631709i
$540$		0			0
$541$	408.868	−	708.180i	0.755763	−	1.30902i	−0.189231	−	0.981933i	$-0.560599\pi$
$541$	408.868	−	708.180i	0.755763	−	1.30902i	0.944994	−	0.327088i	$-0.106067\pi$
$542$	−3.16924	+	1.82976i	−0.00584730	+	0.00337594i
$543$	101.367	+	175.573i	0.186680	+	0.323340i
$544$	−102.817	−	59.3614i	−0.189002	−	0.109120i
$545$		0			0
$546$	−23.0634	+	366.047i	−0.0422406	+	0.670416i
$547$	204.209			0.373325			0.186662	−	0.982424i	$-0.440233\pi$
$547$	204.209			0.373325			0.186662	+	0.982424i	$0.440233\pi$
$548$	86.1706	−	149.252i	0.157246	−	0.272357i
$549$	−217.321	+	125.471i	−0.395849	+	0.228544i
$550$		0			0
$551$	−208.024	−	120.103i	−0.377539	−	0.217972i
$552$			27.3368i			0.0495231i
$553$	−575.698	−	382.569i	−1.04105	−	0.691806i
$554$	−719.992			−1.29962
$555$		0			0
$556$	−402.706	+	232.502i	−0.724291	+	0.418169i
$557$	268.036	+	464.253i	0.481214	+	0.833487i	0.999768	−	0.0215578i	$-0.00686259\pi$
$557$	268.036	+	464.253i	0.481214	+	0.833487i	−0.518553	+	0.855045i	$0.673529\pi$
$558$	24.1861	+	13.9639i	0.0433443	+	0.0250249i
$559$		−	743.660i		−	1.33034i
$560$		0			0
$561$	273.987			0.488391
$562$	−148.979	+	258.039i	−0.265087	+	0.459144i
$563$	857.029	−	494.806i	1.52225	−	0.878874i	0.522600	−	0.852578i	$-0.324962\pi$
$563$	857.029	−	494.806i	1.52225	−	0.878874i	0.999654	−	0.0262960i	$-0.00837123\pi$
$564$	134.492	+	232.948i	0.238462	+	0.413028i
$565$		0			0
$566$			55.8424i			0.0986616i
$567$	56.4324	−	28.0068i	0.0995281	−	0.0493948i
$568$	−192.630			−0.339137
$569$	−248.330	+	430.120i	−0.436432	+	0.755922i	−0.997411	−	0.0719076i	$-0.977091\pi$
$569$	−248.330	+	430.120i	−0.436432	+	0.755922i	0.560979	+	0.827830i	$0.310425\pi$
$570$		0			0
$571$	71.0244	+	123.018i	0.124386	+	0.215443i	0.921493	−	0.388395i	$-0.126971\pi$
$571$	71.0244	+	123.018i	0.124386	+	0.215443i	−0.797107	+	0.603838i	$0.793637\pi$
$572$	−279.251	−	161.226i	−0.488201	−	0.281863i
$573$		−	405.841i		−	0.708274i
$574$	279.884	−	421.176i	0.487604	−	0.733757i
$575$		0			0
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	328.551	−	189.689i	0.569413	−	0.328751i	−0.187502	−	0.982264i	$-0.560039\pi$
$577$	328.551	−	189.689i	0.569413	−	0.328751i	0.756915	+	0.653514i	$0.226706\pi$
$578$	107.107	+	185.515i	0.185307	+	0.320961i
$579$	−29.3476	−	16.9438i	−0.0506866	−	0.0292639i
$580$		0			0
$581$	−188.240	−	11.8604i	−0.323993	−	0.0204137i
$582$	9.04185			0.0155358
$583$	187.668	−	325.051i	0.321901	−	0.557549i
$584$	−214.714	+	123.965i	−0.367661	+	0.212269i
$585$		0			0
$586$	−109.740	−	63.3584i	−0.187269	−	0.108120i
$587$		−	234.204i		−	0.398984i	−0.979899	−	0.199492i	$-0.936071\pi$
$587$		−	234.204i		−	0.398984i	0.979899	−	0.199492i	$-0.0639292\pi$
$588$	−135.185	−	102.650i	−0.229906	−	0.174575i
$589$	158.654			0.269361
$590$		0			0
$591$	269.164	−	155.402i	0.455438	−	0.262948i
$592$	44.7931	+	77.5840i	0.0756641	+	0.131054i
$593$	495.838	+	286.272i	0.836152	+	0.482753i	0.855954	−	0.517051i	$-0.172970\pi$
$593$	495.838	+	286.272i	0.836152	+	0.482753i	−0.0198023	+	0.999804i	$0.506304\pi$
$594$			55.3869i			0.0932439i
$595$		0			0
$596$	−439.853			−0.738008
$597$	221.630	−	383.874i	0.371239	−	0.643006i
$598$	−146.188	+	84.4016i	−0.244461	+	0.141140i
$599$	−46.7105	−	80.9049i	−0.0779807	−	0.135067i	0.824398	−	0.566011i	$-0.191514\pi$
$599$	−46.7105	−	80.9049i	−0.0779807	−	0.135067i	−0.902379	+	0.430944i	$0.858181\pi$
$600$		0			0
$601$		−	167.140i		−	0.278103i	−0.990285	−	0.139051i	$-0.955595\pi$
$601$		−	167.140i		−	0.278103i	0.990285	−	0.139051i	$-0.0444053\pi$
$602$	286.643	+	190.483i	0.476151	+	0.316417i
$603$	199.746			0.331255
$604$	260.922	−	451.930i	0.431990	−	0.748229i
$605$		0			0
$606$	223.686	+	387.436i	0.369119	+	0.639333i
$607$	796.002	+	459.572i	1.31137	+	0.757120i	0.982323	−	0.187194i	$-0.0599392\pi$
$607$	796.002	+	459.572i	1.31137	+	0.757120i	0.329047	+	0.944314i	$0.393273\pi$
$608$		−	136.341i		−	0.224245i
$609$	53.7173	+	108.238i	0.0882058	+	0.177730i
$610$		0			0
$611$	−830.484	+	1438.44i	−1.35922	+	2.35424i
$612$	−109.054	+	62.9623i	−0.178193	+	0.102880i
$613$	−389.718	−	675.011i	−0.635755	−	1.10116i	−0.986355	−	0.164635i	$-0.947356\pi$
$613$	−389.718	−	675.011i	−0.635755	−	1.10116i	0.350600	−	0.936525i	$-0.385978\pi$
$614$	−576.215	−	332.678i	−0.938462	−	0.541821i
$615$		0			0
$616$	133.672	−	66.3402i	0.217000	−	0.107695i
$617$	−510.821			−0.827911			−0.413956	−	0.910297i	$-0.635853\pi$
$617$	−510.821			−0.827911			−0.413956	+	0.910297i	$0.635853\pi$
$618$	−111.514	+	193.148i	−0.180443	+	0.312536i
$619$	−808.792	+	466.956i	−1.30661	+	0.754372i	−0.981529	−	0.191314i	$-0.938725\pi$
$619$	−808.792	+	466.956i	−1.30661	+	0.754372i	−0.325082	+	0.945686i	$0.605392\pi$
$620$		0			0
$621$	25.1104	+	14.4975i	0.0404355	+	0.0233454i
$622$			355.390i			0.571367i
$623$	−53.8862	+	81.0892i	−0.0864947	+	0.130159i
$624$	148.199			0.237498
$625$		0			0
$626$	475.766	−	274.684i	0.760009	−	0.438792i
$627$	157.323	+	272.491i	0.250914	+	0.434595i
$628$	197.784	+	114.191i	0.314943	+	0.181832i
$629$		−	470.047i		−	0.747292i
$630$		0			0
$631$	−614.861			−0.974423			−0.487212	−	0.873284i	$-0.661986\pi$
$631$	−614.861			−0.974423			−0.487212	+	0.873284i	$0.661986\pi$
$632$	−139.648	+	241.877i	−0.220962	+	0.382717i
$633$	−295.336	+	170.512i	−0.466566	+	0.269372i
$634$	−105.627	−	182.952i	−0.166605	−	0.288568i
$635$		0			0
$636$			172.505i			0.271234i
$637$	131.557	−	1039.85i	0.206526	−	1.63242i
$638$	−106.232			−0.166508
$639$	−102.157	+	176.942i	−0.159871	+	0.276904i
$640$		0			0
$641$	94.1724	+	163.111i	0.146915	+	0.254464i	0.930086	−	0.367343i	$-0.119732\pi$
$641$	94.1724	+	163.111i	0.146915	+	0.254464i	−0.783171	+	0.621807i	$0.786399\pi$
$642$	109.325	+	63.1189i	0.170288	+	0.0983161i
$643$			23.8831i			0.0371432i	0.999828	+	0.0185716i	$0.00591187\pi$
$643$			23.8831i			0.0371432i	−0.999828	+	0.0185716i	$0.994088\pi$
$644$	4.91242	−	77.9667i	0.00762798	−	0.121066i
$645$		0			0
$646$	−357.681	+	619.521i	−0.553685	+	0.959011i
$647$	939.928	−	542.667i	1.45275	−	0.838744i	0.454111	−	0.890945i	$-0.349957\pi$
$647$	939.928	−	542.667i	1.45275	−	0.838744i	0.998637	+	0.0522010i	$0.0166237\pi$
$648$	−12.7279	−	22.0454i	−0.0196419	−	0.0340207i
$649$	−549.735	−	317.390i	−0.847049	−	0.489044i
$650$		0			0
$651$	−66.4715	−	44.1724i	−0.102107	−	0.0678531i
$652$	97.4323			0.149436
$653$	−317.852	+	550.536i	−0.486756	+	0.843087i	−0.999884	−	0.0152254i	$-0.995153\pi$
$653$	−317.852	+	550.536i	−0.486756	+	0.843087i	0.513128	+	0.858312i	$0.328487\pi$
$654$	−81.3767	+	46.9829i	−0.124429	+	0.0718393i
$655$		0			0
$656$	−176.955	−	102.165i	−0.269749	−	0.155740i
$657$			262.970i			0.400258i
$658$	−341.723	−	688.555i	−0.519336	−	1.04644i
$659$	−888.955			−1.34895			−0.674473	−	0.738300i	$-0.735629\pi$
$659$	−888.955			−1.34895			−0.674473	+	0.738300i	$0.735629\pi$
$660$		0			0
$661$	−656.362	+	378.951i	−0.992983	+	0.573299i	−0.906165	−	0.422925i	$-0.861003\pi$
$661$	−656.362	+	378.951i	−0.992983	+	0.573299i	−0.0868187	+	0.996224i	$0.527670\pi$
$662$	332.998	+	576.770i	0.503018	+	0.871253i
$663$	−673.402	−	388.789i	−1.01569	−	0.586409i
$664$			76.2114i			0.114776i
$665$		0			0
$666$	95.0206			0.142674
$667$	−27.8063	+	48.1620i	−0.0416886	+	0.0722068i
$668$	−85.9316	+	49.6127i	−0.128640	+	0.0742704i
$669$	−373.270	−	646.522i	−0.557952	−	0.966401i
$670$		0			0
$671$			630.464i			0.939589i
$672$	−37.9600	+	57.1230i	−0.0564881	+	0.0850045i
$673$	−936.839			−1.39203			−0.696017	−	0.718026i	$-0.745046\pi$
$673$	−936.839			−1.39203			−0.696017	+	0.718026i	$0.745046\pi$
$674$	376.519	−	652.150i	0.558634	−	0.967582i
$675$		0			0
$676$	288.560	+	499.800i	0.426863	+	0.739349i
$677$	−214.062	−	123.589i	−0.316192	−	0.182554i	0.333502	−	0.942749i	$-0.391770\pi$
$677$	−214.062	−	123.589i	−0.316192	−	0.182554i	−0.649694	+	0.760196i	$0.725103\pi$
$678$			486.365i			0.717352i
$679$	−25.7881	−	1.62482i	−0.0379795	−	0.00239296i
$680$		0			0
$681$	−151.637	+	262.644i	−0.222669	+	0.385673i
$682$	60.7652	−	35.0828i	0.0890986	−	0.0514411i
$683$	−350.887	−	607.755i	−0.513744	−	0.889831i	−0.999873	−	0.0159438i	$-0.994925\pi$
$683$	−350.887	−	607.755i	−0.513744	−	0.889831i	0.486129	−	0.873887i	$-0.338409\pi$
$684$	−125.237	−	72.3057i	−0.183095	−	0.105710i
$685$		0			0
$686$	367.112	+	317.059i	0.535149	+	0.462185i
$687$	−58.1435			−0.0846339
$688$	69.5313	−	120.432i	0.101063	−	0.175046i
$689$	−922.498	+	532.604i	−1.33889	+	0.773011i
$690$		0			0
$691$	−530.850	−	306.486i	−0.768234	−	0.443540i	0.0640104	−	0.997949i	$-0.479611\pi$
$691$	−530.850	−	306.486i	−0.768234	−	0.443540i	−0.832244	+	0.554409i	$0.812944\pi$
$692$			470.682i			0.680176i
$693$	9.95302	−	157.968i	0.0143622	−	0.227948i
$694$	635.863			0.916230
$695$		0			0
$696$	42.2832	−	24.4122i	0.0607518	−	0.0350750i
$697$	536.047	+	928.461i	0.769078	+	1.33208i
$698$	−404.993	−	233.823i	−0.580220	−	0.334990i
$699$			268.318i			0.383860i
$700$		0			0
$701$	161.307			0.230110			0.115055	−	0.993359i	$-0.463296\pi$
$701$	161.307			0.230110			0.115055	+	0.993359i	$0.463296\pi$
$702$	78.5942	−	136.129i	0.111958	−	0.193916i
$703$	467.480	−	269.900i	0.664979	−	0.383926i
$704$	−30.1488	−	52.2193i	−0.0428250	−	0.0741751i
$705$		0			0
$706$			383.777i			0.543593i
$707$	−568.349	−	1145.20i	−0.803889	−	1.61980i
$708$	291.745			0.412069
$709$	−285.175	+	493.938i	−0.402222	+	0.696669i	−0.993994	−	0.109436i	$-0.965095\pi$
$709$	−285.175	+	493.938i	−0.402222	+	0.696669i	0.591772	+	0.806106i	$0.298429\pi$
$710$		0			0
$711$	148.119	+	256.549i	0.208325	+	0.360829i
$712$	34.0693	+	19.6699i	0.0478501	+	0.0276263i
$713$		−	36.7317i		−	0.0515171i
$714$	322.345	−	159.977i	0.451464	−	0.224057i
$715$		0			0
$716$	44.2098	−	76.5736i	0.0617455	−	0.106946i
$717$	−474.887	+	274.176i	−0.662325	+	0.382393i
$718$	5.36270	+	9.28847i	0.00746894	+	0.0129366i
$719$	431.817	+	249.310i	0.600580	+	0.346745i	0.769270	−	0.638924i	$-0.220620\pi$
$719$	431.817	+	249.310i	0.600580	+	0.346745i	−0.168690	+	0.985669i	$0.553954\pi$
$720$		0			0
$721$	352.755	−	530.834i	0.489258	−	0.736246i
$722$	−310.987			−0.430730
$723$	−202.219	+	350.254i	−0.279695	+	0.484446i
$724$	−202.735	+	117.049i	−0.280020	+	0.161670i
$725$		0			0
$726$	−136.169	−	78.6171i	−0.187560	−	0.108288i
$727$		−	1058.79i		−	1.45638i	−0.685375	−	0.728190i	$-0.740362\pi$
$727$		−	1058.79i		−	1.45638i	0.685375	−	0.728190i	$-0.259638\pi$
$728$	−422.675	−	26.6313i	−0.580597	−	0.0365815i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−631.888	+	364.821i	−0.864416	+	0.499071i
$732$	−144.881	−	250.941i	−0.197925	−	0.342816i
$733$	−13.1068	−	7.56721i	−0.0178810	−	0.0103236i	0.491033	−	0.871141i	$-0.336620\pi$
$733$	−13.1068	−	7.56721i	−0.0178810	−	0.0103236i	−0.508914	+	0.860817i	$0.669953\pi$
$734$			751.530i			1.02388i
$735$		0			0
$736$	−31.5658			−0.0428883
$737$	250.922	−	434.609i	0.340463	−	0.589700i
$738$	−187.690	+	108.363i	−0.254322	+	0.146833i
$739$	81.3819	+	140.958i	0.110124	+	0.190741i	0.915820	−	0.401588i	$-0.131542\pi$
$739$	81.3819	+	140.958i	0.110124	+	0.190741i	−0.805696	+	0.592329i	$0.798208\pi$
$740$		0			0
$741$		−	892.967i		−	1.20508i
$742$	30.9991	−	491.998i	0.0417778	−	0.663071i
$743$	−338.071			−0.455009			−0.227504	−	0.973777i	$-0.573057\pi$
$743$	−338.071			−0.455009			−0.227504	+	0.973777i	$0.573057\pi$
$744$	−16.1241	+	27.9277i	−0.0216722	+	0.0375373i
$745$		0			0
$746$	−406.564	−	704.189i	−0.544991	−	0.943953i
$747$	70.0046	+	40.4172i	0.0937143	+	0.0541060i
$748$			316.373i			0.422959i
$749$	−300.462	−	199.666i	−0.401151	−	0.266577i
$750$		0			0
$751$	−239.087	+	414.111i	−0.318359	+	0.551413i	−0.980146	−	0.198279i	$-0.936465\pi$
$751$	−239.087	+	414.111i	−0.318359	+	0.551413i	0.661787	+	0.749692i	$0.269798\pi$
$752$	−268.985	+	155.299i	−0.357693	+	0.206514i
$753$	−49.0932	−	85.0319i	−0.0651968	−	0.112924i
$754$	261.097	+	150.744i	0.346282	+	0.199926i
$755$		0			0
$756$	32.3395	+	65.1625i	0.0427771	+	0.0861938i
$757$	397.788			0.525479			0.262739	−	0.964867i	$-0.415374\pi$
$757$	397.788			0.525479			0.262739	+	0.964867i	$0.415374\pi$
$758$	−443.684	+	768.483i	−0.585335	+	1.01383i
$759$	63.0874	−	36.4236i	0.0831192	−	0.0479889i
$760$		0			0
$761$	−1264.02	−	729.785i	−1.66100	−	0.958981i	−0.972237	−	0.233998i	$-0.924819\pi$
$761$	−1264.02	−	729.785i	−1.66100	−	0.958981i	−0.688767	−	0.724983i	$-0.741848\pi$
$762$			181.540i			0.238241i
$763$	240.536	−	119.376i	0.315250	−	0.156456i
$764$	468.625			0.613383
$765$		0			0
$766$	−81.5817	+	47.1012i	−0.106503	+	0.0614898i
$767$	900.755	+	1560.15i	1.17439	+	2.03410i
$768$	24.0000	+	13.8564i	0.0312500	+	0.0180422i
$769$			2.10093i			0.00273203i	0.999999	+	0.00136602i	$0.000434817\pi$
$769$			2.10093i			0.00273203i	−0.999999	+	0.00136602i	$0.999565\pi$
$770$		0			0
$771$	−503.055			−0.652471
$772$	19.5650	−	33.8876i	0.0253433	−	0.0438959i
$773$	−391.972	+	226.305i	−0.507079	+	0.292762i	−0.731632	−	0.681700i	$-0.761241\pi$
$773$	−391.972	+	226.305i	−0.507079	+	0.292762i	0.224553	+	0.974462i	$0.427908\pi$
$774$	−73.7491	−	127.737i	−0.0952830	−	0.165035i
$775$		0			0
$776$			10.4406i			0.0134544i
$777$	−271.007	−	17.0752i	−0.348786	−	0.0219758i
$778$	776.473			0.998037
$779$	−615.594	+	1066.24i	−0.790236	+	1.36873i
$780$		0			0
$781$	256.660	+	444.548i	0.328630	+	0.569204i
$782$	143.432	+	82.8106i	0.183417	+	0.105896i
$783$		−	51.7862i		−	0.0661381i
$784$	118.530	−	156.098i	0.151186	−	0.199105i
$785$		0			0
$786$	24.5366	−	42.4986i	0.0312170	−	0.0540694i
$787$	112.676	−	65.0535i	0.143171	−	0.0826601i	−0.426703	−	0.904392i	$-0.640325\pi$
$787$	112.676	−	65.0535i	0.143171	−	0.0826601i	0.569875	+	0.821732i	$0.306992\pi$
$788$	179.443	+	310.804i	0.227719	+	0.394421i
$789$	−666.893	−	385.031i	−0.845238	−	0.487998i
$790$		0			0
$791$	87.3997	−	1387.15i	0.110493	−	1.75367i
$792$	−63.9553			−0.0807516
$793$	894.632	−	1549.55i	1.12816	−	1.95403i
$794$	635.111	−	366.681i	0.799888	−	0.461815i
$795$		0			0
$796$	443.260	+	255.916i	0.556859	+	0.321503i
$797$		−	1170.92i		−	1.46915i	−0.678525	−	0.734577i	$-0.737381\pi$
$797$		−	1170.92i		−	1.46915i	0.678525	−	0.734577i	$-0.262619\pi$
$798$	344.193	+	228.727i	0.431320	+	0.286625i
$799$	1629.66			2.03962
$800$		0			0
$801$	36.1359	−	20.8631i	0.0451135	−	0.0260463i
$802$	336.794	+	583.344i	0.419942	+	0.727361i
$803$	572.170	+	330.342i	0.712540	+	0.411385i
$804$			230.647i			0.286875i
$805$		0			0
$806$	−199.131			−0.247060
$807$	144.956	−	251.071i	0.179623	−	0.311116i
$808$	−447.372	+	258.291i	−0.553679	+	0.319667i
$809$	102.442	+	177.435i	0.126628	+	0.219327i	0.922368	−	0.386312i	$-0.126251\pi$
$809$	102.442	+	177.435i	0.126628	+	0.219327i	−0.795740	+	0.605639i	$0.792918\pi$
$810$		0			0
$811$			541.011i			0.667092i	0.942734	+	0.333546i	$0.108245\pi$
$811$			541.011i			0.667092i	−0.942734	+	0.333546i	$0.891755\pi$
$812$	−124.982	+	62.0274i	−0.153919	+	0.0763884i
$813$	−4.48198			−0.00551289
$814$	119.365	−	206.746i	0.146640	−	0.253988i
$815$		0			0
$816$	−72.7026	−	125.925i	−0.0890964	−	0.154319i
$817$	−725.658	−	418.959i	−0.888198	−	0.512801i
$818$		−	152.285i		−	0.186168i
$819$	−248.620	+	374.128i	−0.303565	+	0.456811i
$820$		0			0
$821$	212.913	−	368.777i	0.259334	−	0.449180i	−0.706730	−	0.707484i	$-0.749830\pi$
$821$	212.913	−	368.777i	0.259334	−	0.449180i	0.966064	+	0.258304i	$0.0831636\pi$
$822$	182.795	−	105.537i	0.222379	−	0.128391i
$823$	385.497	+	667.700i	0.468405	+	0.811301i	0.999348	−	0.0361067i	$-0.0114956\pi$
$823$	385.497	+	667.700i	0.468405	+	0.811301i	−0.530943	+	0.847407i	$0.678162\pi$
$824$	−223.028	−	128.765i	−0.270665	−	0.156268i
$825$		0			0
$826$	−832.081	−	52.4266i	−1.00736	−	0.0634704i
$827$	448.579			0.542417			0.271209	−	0.962521i	$-0.412577\pi$
$827$	448.579			0.542417			0.271209	+	0.962521i	$0.412577\pi$
$828$	−16.7403	+	28.9950i	−0.0202177	+	0.0350181i
$829$	−737.022	+	425.520i	−0.889050	+	0.513293i	−0.873632	−	0.486588i	$-0.838241\pi$
$829$	−737.022	+	425.520i	−0.889050	+	0.513293i	−0.0154183	+	0.999881i	$0.504908\pi$
$830$		0			0
$831$	−763.667	−	440.903i	−0.918973	−	0.530569i
$832$			171.125i			0.205679i
$833$	−948.103	+	398.341i	−1.13818	+	0.478201i
$834$	−569.512			−0.682868
$835$		0			0
$836$	−314.646	+	181.661i	−0.376370	+	0.217298i
$837$	17.1022	+	29.6218i	0.0204327	+	0.0353905i
$838$	396.585	+	228.969i	0.473252	+	0.273232i
$839$			77.0829i			0.0918747i	0.998944	+	0.0459373i	$0.0146275\pi$
$839$			77.0829i			0.0918747i	−0.998944	+	0.0459373i	$0.985373\pi$
$840$		0			0
$841$	−741.674			−0.881895
$842$	168.968	−	292.662i	0.200675	−	0.347579i
$843$	−316.032	+	182.461i	−0.374890	+	0.216443i
$844$	−196.891	−	341.025i	−0.233283	−	0.404058i
$845$		0			0
$846$			329.438i			0.389407i
$847$	374.237	+	248.692i	0.441839	+	0.293615i
$848$	−199.192			−0.234896
$849$	−34.1964	+	59.2299i	−0.0402784	+	0.0697643i
$850$		0			0
$851$	−62.4875	−	108.231i	−0.0734283	−	0.127182i
$852$	−204.315	−	117.961i	−0.239806	−	0.138452i
$853$			176.785i			0.207251i	0.994616	+	0.103626i	$0.0330443\pi$
$853$			176.785i			0.207251i	−0.994616	+	0.103626i	$0.966956\pi$
$854$	368.118	+	741.740i	0.431052	+	0.868547i
$855$		0			0
$856$	−72.8835	+	126.238i	−0.0851442	+	0.147474i
$857$	1080.14	−	623.618i	1.26037	−	0.727676i	0.287225	−	0.957863i	$-0.407267\pi$
$857$	1080.14	−	623.618i	1.26037	−	0.727676i	0.973146	+	0.230187i	$0.0739339\pi$
$858$	−197.460	−	342.011i	−0.230140	−	0.398614i
$859$	1319.99	+	762.098i	1.53666	+	0.887192i	0.999031	+	0.0440111i	$0.0140137\pi$
$859$	1319.99	+	762.098i	1.53666	+	0.887192i	0.537630	+	0.843181i	$0.319320\pi$
$860$		0			0
$861$	554.779	−	275.331i	0.644343	−	0.319781i
$862$	−271.235			−0.314658
$863$	−718.043	+	1243.69i	−0.832032	+	1.44112i	0.0643926	+	0.997925i	$0.479489\pi$
$863$	−718.043	+	1243.69i	−0.832032	+	1.44112i	−0.896424	+	0.443197i	$0.853844\pi$
$864$	25.4558	−	14.6969i	0.0294628	−	0.0170103i
$865$		0			0
$866$	−149.520	−	86.3255i	−0.172656	−	0.0996830i
$867$			262.358i			0.302605i
$868$	51.0058	−	76.7547i	0.0587625	−	0.0884271i
$869$	744.268			0.856465
$870$		0			0
$871$	−1233.42	+	712.118i	−1.41610	+	0.817586i
$872$	−54.2512	−	93.9658i	−0.0622146	−	0.107759i
$873$	9.59033	+	5.53698i	0.0109855	+	0.00634248i
$874$			190.199i			0.217619i
$875$		0			0
$876$	−303.651			−0.346634
$877$	−595.626	+	1031.65i	−0.679163	+	1.17634i	0.296070	+	0.955166i	$0.404324\pi$
$877$	−595.626	+	1031.65i	−0.679163	+	1.17634i	−0.975233	+	0.221179i	$0.929010\pi$
$878$	307.813	−	177.716i	0.350584	−	0.202410i
$879$	−77.5978	−	134.403i	−0.0882797	−	0.152905i
$880$		0			0
$881$			81.6610i			0.0926912i	0.998925	+	0.0463456i	$0.0147576\pi$
$881$			81.6610i			0.0926912i	−0.998925	+	0.0463456i	$0.985242\pi$
$882$	−80.5253	−	191.660i	−0.0912985	−	0.217302i
$883$	−506.404			−0.573504			−0.286752	−	0.958005i	$-0.592576\pi$
$883$	−506.404			−0.573504			−0.286752	+	0.958005i	$0.592576\pi$
$884$	448.935	−	777.578i	0.507845	−	0.879613i
$885$		0			0
$886$	77.6327	+	134.464i	0.0876215	+	0.151765i
$887$	17.8700	+	10.3172i	0.0201466	+	0.0116316i	0.510039	−	0.860151i	$-0.329631\pi$
$887$	17.8700	+	10.3172i	0.0201466	+	0.0116316i	−0.489893	+	0.871783i	$0.662964\pi$
$888$			109.720i			0.123559i
$889$	32.6227	−	517.766i	0.0366959	−	0.582414i
$890$		0			0
$891$	−33.9174	+	58.7467i	−0.0380667	+	0.0659334i
$892$	746.540	−	431.015i	0.836928	−	0.483200i
$893$	935.747	+	1620.76i	1.04787	+	1.81496i
$894$	−466.534	−	269.354i	−0.521850	−	0.301290i
$895$		0			0
$896$	−65.9600	−	43.8324i	−0.0736161	−	0.0489201i
$897$	−206.741			−0.230480
$898$	−570.274	+	987.744i	−0.635049	+	1.09994i
$899$	−56.8149	+	32.8021i	−0.0631979	+	0.0364873i
$900$		0			0
$901$	905.109	+	522.565i	1.00456	+	0.579983i
$902$			544.501i			0.603659i
$903$	187.384	+	377.570i	0.207513	+	0.418128i
$904$	−561.606			−0.621245
$905$		0			0
$906$	553.499	−	319.563i	0.610926	−	0.352718i
$907$	128.404	+	222.402i	0.141570	+	0.245206i	0.928088	−	0.372361i	$-0.121452\pi$
$907$	128.404	+	222.402i	0.141570	+	0.245206i	−0.786518	+	0.617567i	$0.788118\pi$
$908$	−303.275	−	175.096i	−0.334003	−	0.192837i
$909$			547.917i			0.602769i
$910$		0			0
$911$	1194.31			1.31098			0.655492	−	0.755202i	$-0.272461\pi$
$911$	1194.31			1.31098			0.655492	+	0.755202i	$0.272461\pi$
$912$	83.4914	−	144.611i	0.0915476	−	0.158565i
$913$	175.880	−	101.544i	0.192639	−	0.111220i
$914$	−546.207	−	946.058i	−0.597600	−	1.03507i
$915$		0			0
$916$		−	67.1383i		−	0.0732951i
$917$	−77.6173	+	116.800i	−0.0846427	+	0.127372i
$918$	−154.226			−0.168002
$919$	446.876	−	774.012i	0.486263	−	0.842232i	−0.513612	−	0.858022i	$-0.671693\pi$
$919$	446.876	−	774.012i	0.486263	−	0.842232i	0.999875	+	0.0157900i	$0.00502633\pi$
$920$		0			0
$921$	−407.446	−	705.717i	−0.442395	−	0.766251i
$922$	−971.971	−	561.168i	−1.05420	−	0.608642i
$923$		−	1456.81i		−	1.57834i
$924$	182.406	+	11.4928i	0.197409	+	0.0124381i
$925$		0			0
$926$	−193.908	+	335.859i	−0.209404	+	0.362698i
$927$	−236.556	+	136.576i	−0.255185	+	0.147331i
$928$	28.1888	+	48.8245i	0.0303759	+	0.0526126i
$929$	295.237	+	170.455i	0.317801	+	0.183482i	0.650412	−	0.759582i	$-0.274596\pi$
$929$	295.237	+	170.455i	0.317801	+	0.183482i	−0.332611	+	0.943064i	$0.607930\pi$
$930$		0			0
$931$	−940.565	−	714.199i	−1.01027	−	0.767131i
$932$	−309.827			−0.332432
$933$	−217.631	+	376.948i	−0.233259	+	0.404017i
$934$	486.994	−	281.166i	0.521407	−	0.301034i
$935$		0			0
$936$	157.188	+	90.7528i	0.167936	+	0.0969581i
$937$			217.347i			0.231961i	0.993251	+	0.115981i	$0.0370010\pi$
$937$			217.347i			0.231961i	−0.993251	+	0.115981i	$0.962999\pi$
$938$	41.4473	−	657.825i	0.0441869	−	0.701306i
$939$	672.834			0.716544
$940$		0			0
$941$	1226.68	−	708.226i	1.30360	−	0.752631i	0.322577	−	0.946543i	$-0.395451\pi$
$941$	1226.68	−	708.226i	1.30360	−	0.752631i	0.981019	+	0.193912i	$0.0621177\pi$
$942$	139.855	+	242.235i	0.148466	+	0.257150i
$943$	246.857	+	142.523i	0.261779	+	0.151138i
$944$			336.878i			0.356862i
$945$		0			0
$946$	−370.574			−0.391728
$947$	−692.365	+	1199.21i	−0.731114	+	1.26633i	0.225294	+	0.974291i	$0.427666\pi$
$947$	−692.365	+	1199.21i	−0.731114	+	1.26633i	−0.956408	+	0.292035i	$0.905667\pi$
$948$	−296.238	+	171.033i	−0.312487	+	0.180415i
$949$	−937.515	−	1623.82i	−0.987897	−	1.71109i
$950$		0			0
$951$		−	258.733i		−	0.272064i
$952$	184.725	+	372.212i	0.194039	+	0.390979i
$953$	−1365.38			−1.43272			−0.716359	−	0.697732i	$-0.754193\pi$
$953$	−1365.38			−1.43272			−0.716359	+	0.697732i	$0.754193\pi$
$954$	−105.637	+	182.969i	−0.110731	+	0.191792i
$955$		0			0
$956$	−316.591	−	548.352i	−0.331162	−	0.573590i
$957$	−112.676	−	65.0538i	−0.117739	−	0.0679768i
$958$		−	270.380i		−	0.282234i
$959$	−540.313	+	268.152i	−0.563413	+	0.279616i
$960$		0			0
$961$	−458.834	+	794.725i	−0.477455	+	0.826977i
$962$	−586.747	+	338.758i	−0.609924	+	0.352140i
$963$	77.3046	+	133.895i	0.0802748	+	0.139040i
$964$	−404.439	−	233.503i	−0.419542	−	0.242223i
$965$		0			0
$966$	52.9551	−	79.6880i	0.0548189	−	0.0824927i
$967$	1718.05			1.77668			0.888341	−	0.459185i	$-0.151858\pi$
$967$	1718.05			1.77668			0.888341	+	0.459185i	$0.151858\pi$
$968$	90.7792	−	157.234i	0.0937802	−	0.162432i
$969$	−758.755	+	438.068i	−0.783029	+	0.452082i
$970$		0			0
$971$	387.463	+	223.702i	0.399035	+	0.230383i	0.686068	−	0.727538i	$-0.259335\pi$
$971$	387.463	+	223.702i	0.399035	+	0.230383i	−0.287033	+	0.957921i	$0.592669\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	1624.29	+	102.341i	1.66937	+	0.105181i
$974$	268.727			0.275900
$975$		0			0
$976$	289.762	−	167.294i	0.296887	−	0.171408i
$977$	−910.447	−	1576.94i	−0.931880	−	1.61406i	−0.780105	−	0.625648i	$-0.784835\pi$
$977$	−910.447	−	1576.94i	−0.931880	−	1.61406i	−0.151775	−	0.988415i	$-0.548499\pi$
$978$	103.343	+	59.6648i	0.105667	+	0.0610070i
$979$		−	104.833i		−	0.107082i
$980$		0			0
$981$	−115.084			−0.117313
$982$	149.471	−	258.891i	0.152211	−	0.263637i
$983$	1438.65	−	830.607i	1.46353	−	0.844972i	0.464362	−	0.885646i	$-0.346284\pi$
$983$	1438.65	−	830.607i	1.46353	−	0.844972i	0.999172	+	0.0406735i	$0.0129503\pi$
$984$	−125.126	−	216.725i	−0.127161	−	0.220249i
$985$		0			0
$986$		−	295.806i		−	0.300006i
$987$	59.2000	−	939.584i	0.0599797	−	0.951960i
$988$	1031.11			1.04363
$989$	−96.9978	+	168.005i	−0.0980767	+	0.169874i
$990$		0			0
$991$	−275.795	−	477.690i	−0.278299	−	0.482029i	0.692663	−	0.721261i	$-0.256437\pi$
$991$	−275.795	−	477.690i	−0.278299	−	0.482029i	−0.970962	+	0.239233i	$0.923104\pi$
$992$	−32.2482	−	18.6185i	−0.0325082	−	0.0187686i
$993$			815.676i			0.821426i
$994$	561.525	+	373.150i	0.564914	+	0.375403i
$995$		0			0
$996$	−46.6697	+	80.8344i	−0.0468572	+	0.0811590i
$997$	1562.86	−	902.319i	1.56757	−	0.905034i	0.571113	−	0.820871i	$-0.306512\pi$
$997$	1562.86	−	902.319i	1.56757	−	0.905034i	0.996452	−	0.0841629i	$-0.0268216\pi$
$998$	179.412	+	310.751i	0.179772	+	0.311374i
$999$	100.785	+	58.1880i	0.100885	+	0.0582462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.c.901.1	yes	8
5.2	odd	4		1050.3.q.b.649.3		16
5.3	odd	4		1050.3.q.b.649.6		16
5.4	even	2		1050.3.p.d.901.4	yes	8
7.3	odd	6	inner	1050.3.p.c.451.1	✓	8
35.3	even	12		1050.3.q.b.199.3		16
35.17	even	12		1050.3.q.b.199.6		16
35.24	odd	6		1050.3.p.d.451.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.c.451.1	✓	8	7.3	odd	6	inner
1050.3.p.c.901.1	yes	8	1.1	even	1	trivial
1050.3.p.d.451.4	yes	8	35.24	odd	6
1050.3.p.d.901.4	yes	8	5.4	even	2
1050.3.q.b.199.3		16	35.3	even	12
1050.3.q.b.199.6		16	35.17	even	12
1050.3.q.b.649.3		16	5.2	odd	4
1050.3.q.b.649.6		16	5.3	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-0.440173 + 6.98615i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(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} +(-3.76860 - 6.52741i) q^{11} +(3.00000 + 1.73205i) q^{12} +21.3906i q^{13} +(-8.24500 - 5.47905i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(18.1757 - 10.4937i) q^{17} +(2.12132 + 3.67423i) q^{18} +(20.8728 + 12.0509i) q^{19} +(-5.38992 - 10.8604i) q^{21} +10.6592 q^{22} +(2.79005 - 4.83250i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(-26.1981 - 15.1255i) q^{26} +5.19615i q^{27} +(12.5405 - 6.22374i) q^{28} -9.96625 q^{29} +(5.70073 - 3.29132i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(11.3058 + 6.52741i) q^{33} +29.6807i q^{34} -6.00000 q^{36} +(11.1983 - 19.3960i) q^{37} +(-29.5187 + 17.0426i) q^{38} +(-18.5248 - 32.0860i) q^{39} +51.0827i q^{41} +(17.1125 + 1.07820i) q^{42} -34.7656 q^{43} +(-7.53720 + 13.0548i) q^{44} +(3.94572 + 6.83419i) q^{46} +(67.2462 + 38.8246i) q^{47} -6.92820i q^{48} +(-48.6125 - 6.15023i) q^{49} +(-18.1757 + 31.4812i) q^{51} +(37.0497 - 21.3906i) q^{52} +(24.8989 + 43.1262i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(-1.24500 + 19.7598i) q^{56} -41.7457 q^{57} +(7.04720 - 12.2061i) q^{58} +(72.9362 - 42.1098i) q^{59} +(-72.4404 - 41.8235i) q^{61} +9.30925i q^{62} +(17.4903 + 11.6228i) q^{63} +8.00000 q^{64} +(-15.9888 + 9.23115i) q^{66} +(33.2911 + 57.6618i) q^{67} +(-36.3513 - 20.9874i) q^{68} +9.66501i q^{69} -68.1049 q^{71} +(4.24264 - 7.34847i) q^{72} +(-75.9128 + 43.8283i) q^{73} +(15.8368 + 27.4301i) q^{74} -48.2038i q^{76} +(47.2603 - 23.4548i) q^{77} +52.3962 q^{78} +(-49.3730 + 85.5165i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-62.5632 - 36.1209i) q^{82} +26.9448i q^{83} +(-13.4209 + 20.1960i) q^{84} +(24.5830 - 42.5790i) q^{86} +(14.9494 - 8.63103i) q^{87} +(-10.6592 - 18.4623i) q^{88} +(12.0453 + 6.95436i) q^{89} +(-149.438 - 9.41559i) q^{91} -11.1602 q^{92} +(-5.70073 + 9.87395i) q^{93} +(-95.1005 + 54.9063i) q^{94} +(8.48528 + 4.89898i) q^{96} +3.69132i q^{97} +(41.9067 - 55.1890i) q^{98} -22.6116 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

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