LMFDB - Embedded newform 1050.3.q.b.199.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1050.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			199.6
Root			$1.25838 - 0.337183i$ of defining polynomial
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.b.649.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.98615 - 0.440173i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.98615 - 0.440173i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-3.76860 + 6.52741i) q^{11} +(1.73205 + 3.00000i) q^{12} -21.3906 q^{13} +(8.24500 - 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-10.4937 + 18.1757i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(-20.8728 + 12.0509i) q^{19} +(-5.38992 + 10.8604i) q^{21} +10.6592i q^{22} +(4.83250 - 2.79005i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-26.1981 + 15.1255i) q^{26} +5.19615 q^{27} +(6.22374 - 12.5405i) q^{28} +9.96625 q^{29} +(5.70073 + 3.29132i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-6.52741 - 11.3058i) q^{33} +29.6807i q^{34} -6.00000 q^{36} +(-19.3960 + 11.1983i) q^{37} +(-17.0426 + 29.5187i) q^{38} +(18.5248 - 32.0860i) q^{39} -51.0827i q^{41} +(1.07820 + 17.1125i) q^{42} +34.7656i q^{43} +(7.53720 + 13.0548i) q^{44} +(3.94572 - 6.83419i) q^{46} +(38.8246 + 67.2462i) q^{47} +6.92820 q^{48} +(48.6125 - 6.15023i) q^{49} +(-18.1757 - 31.4812i) q^{51} +(-21.3906 + 37.0497i) q^{52} +(-43.1262 - 24.8989i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} -41.7457i q^{57} +(12.2061 - 7.04720i) q^{58} +(-72.9362 - 42.1098i) q^{59} +(-72.4404 + 41.8235i) q^{61} +9.30925 q^{62} +(-11.6228 - 17.4903i) q^{63} -8.00000 q^{64} +(-15.9888 - 9.23115i) q^{66} +(57.6618 + 33.2911i) q^{67} +(20.9874 + 36.3513i) q^{68} +9.66501i q^{69} -68.1049 q^{71} +(-7.34847 + 4.24264i) q^{72} +(-43.8283 + 75.9128i) q^{73} +(-15.8368 + 27.4301i) q^{74} +48.2038i q^{76} +(-23.4548 + 47.2603i) q^{77} -52.3962i q^{78} +(49.3730 + 85.5165i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-36.1209 - 62.5632i) q^{82} -26.9448 q^{83} +(13.4209 + 20.1960i) q^{84} +(24.5830 + 42.5790i) q^{86} +(-8.63103 + 14.9494i) q^{87} +(18.4623 + 10.6592i) q^{88} +(-12.0453 + 6.95436i) q^{89} +(-149.438 + 9.41559i) q^{91} -11.1602i q^{92} +(-9.87395 + 5.70073i) q^{93} +(95.1005 + 54.9063i) q^{94} +(8.48528 - 4.89898i) q^{96} +3.69132 q^{97} +(55.1890 - 41.9067i) q^{98} +22.6116 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) $ 16 * q + 16 * q^4 - 24 * q^9	$ 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 32 q^{14} - 32 q^{16} - 144 q^{19} - 144 q^{26} + 48 q^{29} + 192 q^{31} - 96 q^{36} + 24 q^{39} + 16 q^{44} + 64 q^{46} + 528 q^{49} + 48 q^{51} + 80 q^{56} - 624 q^{59} - 408 q^{61} - 128 q^{64} - 72 q^{66} - 128 q^{71} + 32 q^{74} + 288 q^{79} - 72 q^{81} + 352 q^{86} + 672 q^{89} - 592 q^{91} - 72 q^{94} + 48 q^{99}+O(q^{100}) $ 16 * q + 16 * q^4 - 24 * q^9 - 8 * q^11 + 32 * q^14 - 32 * q^16 - 144 * q^19 - 144 * q^26 + 48 * q^29 + 192 * q^31 - 96 * q^36 + 24 * q^39 + 16 * q^44 + 64 * q^46 + 528 * q^49 + 48 * q^51 + 80 * q^56 - 624 * q^59 - 408 * q^61 - 128 * q^64 - 72 * q^66 - 128 * q^71 + 32 * q^74 + 288 * q^79 - 72 * q^81 + 352 * q^86 + 672 * q^89 - 592 * q^91 - 72 * q^94 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	6.98615	−	0.440173i	0.998021	−	0.0628819i
$7$	6.98615	−	0.440173i	0.998021	−	0.0628819i
$8$		−	2.82843i		−	0.353553i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.76860	+	6.52741i	−0.342600	+	0.593401i	−0.984915	−	0.173040i	$-0.944641\pi$
$11$	−3.76860	+	6.52741i	−0.342600	+	0.593401i	0.642315	+	0.766441i	$0.277974\pi$
$12$	1.73205	+	3.00000i	0.144338	+	0.250000i
$13$	−21.3906			−1.64543			−0.822717	−	0.568451i	$-0.807543\pi$
$13$	−21.3906			−1.64543			−0.822717	+	0.568451i	$0.807543\pi$
$14$	8.24500	−	5.47905i	0.588928	−	0.391361i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−10.4937	+	18.1757i	−0.617278	+	1.06916i	0.372703	+	0.927951i	$0.378431\pi$
$17$	−10.4937	+	18.1757i	−0.617278	+	1.06916i	−0.989980	+	0.141205i	$0.954902\pi$
$18$	−3.67423	−	2.12132i	−0.204124	−	0.117851i
$19$	−20.8728	+	12.0509i	−1.09857	+	0.634260i	−0.935845	−	0.352411i	$-0.885362\pi$
$19$	−20.8728	+	12.0509i	−1.09857	+	0.634260i	−0.162726	+	0.986671i	$0.552029\pi$
$20$		0			0
$21$	−5.38992	+	10.8604i	−0.256663	+	0.517163i
$22$			10.6592i			0.484510i
$23$	4.83250	−	2.79005i	0.210109	−	0.121306i	−0.391253	−	0.920283i	$-0.627958\pi$
$23$	4.83250	−	2.79005i	0.210109	−	0.121306i	0.601362	+	0.798977i	$0.294625\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$		0			0
$26$	−26.1981	+	15.1255i	−1.00762	+	0.581749i
$27$	5.19615			0.192450
$28$	6.22374	−	12.5405i	0.222277	−	0.447876i
$29$	9.96625			0.343664			0.171832	−	0.985126i	$-0.445031\pi$
$29$	9.96625			0.343664			0.171832	+	0.985126i	$0.445031\pi$
$30$		0			0
$31$	5.70073	+	3.29132i	0.183894	+	0.106171i	0.589121	−	0.808045i	$-0.299474\pi$
$31$	5.70073	+	3.29132i	0.183894	+	0.106171i	−0.405227	+	0.914216i	$0.632807\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$	−6.52741	−	11.3058i	−0.197800	−	0.342600i
$34$			29.6807i			0.872962i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−19.3960	+	11.1983i	−0.524216	+	0.302656i	−0.738658	−	0.674080i	$-0.764540\pi$
$37$	−19.3960	+	11.1983i	−0.524216	+	0.302656i	0.214442	+	0.976737i	$0.431207\pi$
$38$	−17.0426	+	29.5187i	−0.448490	+	0.776807i
$39$	18.5248	−	32.0860i	0.474996	−	0.822717i
$40$		0			0
$41$		−	51.0827i		−	1.24592i	−0.782254	−	0.622959i	$-0.785930\pi$
$41$		−	51.0827i		−	1.24592i	0.782254	−	0.622959i	$-0.214070\pi$
$42$	1.07820	+	17.1125i	0.0256714	+	0.407440i
$43$			34.7656i			0.808503i	0.914648	+	0.404252i	$0.132468\pi$
$43$			34.7656i			0.808503i	−0.914648	+	0.404252i	$0.867532\pi$
$44$	7.53720	+	13.0548i	0.171300	+	0.296700i
$45$		0			0
$46$	3.94572	−	6.83419i	0.0857766	−	0.148569i
$47$	38.8246	+	67.2462i	0.826056	+	1.43077i	0.901110	+	0.433591i	$0.142754\pi$
$47$	38.8246	+	67.2462i	0.826056	+	1.43077i	−0.0750536	+	0.997179i	$0.523913\pi$
$48$	6.92820			0.144338
$49$	48.6125	−	6.15023i	0.992092	−	0.125515i
$50$		0			0
$51$	−18.1757	−	31.4812i	−0.356385	−	0.617278i
$52$	−21.3906	+	37.0497i	−0.411359	+	0.712494i
$53$	−43.1262	−	24.8989i	−0.813703	−	0.469791i	0.0345374	−	0.999403i	$-0.489004\pi$
$53$	−43.1262	−	24.8989i	−0.813703	−	0.469791i	−0.848240	+	0.529612i	$0.822338\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$		0			0
$56$	−1.24500	−	19.7598i	−0.0222321	−	0.352854i
$57$		−	41.7457i		−	0.732381i
$58$	12.2061	−	7.04720i	0.210450	−	0.121504i
$59$	−72.9362	−	42.1098i	−1.23621	−	0.713725i	−0.267890	−	0.963449i	$-0.586327\pi$
$59$	−72.9362	−	42.1098i	−1.23621	−	0.713725i	−0.968317	+	0.249725i	$0.919660\pi$
$60$		0			0
$61$	−72.4404	+	41.8235i	−1.18755	+	0.685631i	−0.957749	−	0.287607i	$-0.907140\pi$
$61$	−72.4404	+	41.8235i	−1.18755	+	0.685631i	−0.229799	+	0.973238i	$0.573807\pi$
$62$	9.30925			0.150149
$63$	−11.6228	−	17.4903i	−0.184489	−	0.277624i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−15.9888	−	9.23115i	−0.242255	−	0.139866i
$67$	57.6618	+	33.2911i	0.860625	+	0.496882i	0.864221	−	0.503112i	$-0.167812\pi$
$67$	57.6618	+	33.2911i	0.860625	+	0.496882i	−0.00359682	+	0.999994i	$0.501145\pi$
$68$	20.9874	+	36.3513i	0.308639	+	0.534578i
$69$			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	$0.659223\pi$
$72$	−7.34847	+	4.24264i	−0.102062	+	0.0589256i
$73$	−43.8283	+	75.9128i	−0.600387	+	1.03990i	0.392375	+	0.919805i	$0.371654\pi$
$73$	−43.8283	+	75.9128i	−0.600387	+	1.03990i	−0.992762	+	0.120096i	$0.961680\pi$
$74$	−15.8368	+	27.4301i	−0.214010	+	0.370677i
$75$		0			0
$76$			48.2038i			0.634260i
$77$	−23.4548	+	47.2603i	−0.304608	+	0.613770i
$78$		−	52.3962i		−	0.671746i
$79$	49.3730	+	85.5165i	0.624974	+	1.08249i	0.988546	+	0.150921i	$0.0482238\pi$
$79$	49.3730	+	85.5165i	0.624974	+	1.08249i	−0.363572	+	0.931566i	$0.618443\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−36.1209	−	62.5632i	−0.440499	−	0.762966i
$83$	−26.9448			−0.324636			−0.162318	−	0.986739i	$-0.551897\pi$
$83$	−26.9448			−0.324636			−0.162318	+	0.986739i	$0.551897\pi$
$84$	13.4209	+	20.1960i	0.159772	+	0.240429i
$85$		0			0
$86$	24.5830	+	42.5790i	0.285849	+	0.495105i
$87$	−8.63103	+	14.9494i	−0.0992072	+	0.171832i
$88$	18.4623	+	10.6592i	0.209799	+	0.121127i
$89$	−12.0453	+	6.95436i	−0.135341	+	0.0781389i	−0.566142	−	0.824308i	$-0.691564\pi$
$89$	−12.0453	+	6.95436i	−0.135341	+	0.0781389i	0.430801	+	0.902447i	$0.358231\pi$
$90$		0			0
$91$	−149.438	+	9.41559i	−1.64218	+	0.103468i
$92$		−	11.1602i		−	0.121306i
$93$	−9.87395	+	5.70073i	−0.106171	+	0.0612981i
$94$	95.1005	+	54.9063i	1.01171	+	0.584110i
$95$		0			0
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$	3.69132			0.0380549			0.0190274	−	0.999819i	$-0.493943\pi$
$97$	3.69132			0.0380549			0.0190274	+	0.999819i	$0.493943\pi$
$98$	55.1890	−	41.9067i	0.563153	−	0.427619i
$99$	22.6116			0.228400
$100$		0			0
$101$	−158.170	−	91.3195i	−1.56604	−	0.904154i	−0.996624	−	0.0821041i	$-0.973836\pi$
$101$	−158.170	−	91.3195i	−1.56604	−	0.904154i	−0.569416	−	0.822049i	$-0.692831\pi$
$102$	−44.5211	−	25.7043i	−0.436481	−	0.252003i
$103$	45.5253	+	78.8521i	0.441993	+	0.765555i	0.997837	−	0.0657318i	$-0.0209382\pi$
$103$	45.5253	+	78.8521i	0.441993	+	0.765555i	−0.555844	+	0.831287i	$0.687605\pi$
$104$			60.5019i			0.581749i
$105$		0			0
$106$	−70.4249			−0.664385
$107$	44.6318	−	25.7682i	0.417120	−	0.240824i	−0.276724	−	0.960949i	$-0.589249\pi$
$107$	44.6318	−	25.7682i	0.417120	−	0.240824i	0.693844	+	0.720125i	$0.255916\pi$
$108$	5.19615	−	9.00000i	0.0481125	−	0.0833333i
$109$	19.1807	−	33.2219i	0.175970	−	0.304788i	−0.764527	−	0.644592i	$-0.777027\pi$
$109$	19.1807	−	33.2219i	0.175970	−	0.304788i	0.940496	+	0.339804i	$0.110361\pi$
$110$		0			0
$111$		−	38.7920i		−	0.349477i
$112$	−15.4971	−	23.3204i	−0.138367	−	0.208218i
$113$			198.558i			1.75715i	0.477608	+	0.878573i	$0.341504\pi$
$113$			198.558i			1.75715i	−0.477608	+	0.878573i	$0.658496\pi$
$114$	−29.5187	−	51.1278i	−0.258936	−	0.448490i
$115$		0			0
$116$	9.96625	−	17.2621i	0.0859160	−	0.148811i
$117$	32.0860	+	55.5745i	0.274239	+	0.474996i
$118$	−119.104			−1.00936
$119$	−65.3102	+	131.597i	−0.548825	+	1.10586i
$120$		0			0
$121$	32.0953	+	55.5907i	0.265250	+	0.459427i
$122$	−59.1474	+	102.446i	−0.484814	+	0.839723i
$123$	76.6240	+	44.2389i	0.622959	+	0.359666i
$124$	11.4015	−	6.58263i	0.0919472	−	0.0530857i
$125$		0			0
$126$	−26.6025	−	13.2026i	−0.211131	−	0.104782i
$127$		−	74.1132i		−	0.583569i	−0.956484	−	0.291784i	$-0.905751\pi$
$127$		−	74.1132i		−	0.583569i	0.956484	−	0.291784i	$-0.0942490\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$	−52.1485	−	30.1079i	−0.404252	−	0.233395i
$130$		0			0
$131$	17.3500	−	10.0170i	0.132443	−	0.0764657i	−0.432315	−	0.901723i	$-0.642303\pi$
$131$	17.3500	−	10.0170i	0.132443	−	0.0764657i	0.564757	+	0.825257i	$0.308970\pi$
$132$	−26.1096			−0.197800
$133$	−140.516	+	93.3773i	−1.05651	+	0.702085i
$134$	94.1614			0.702697
$135$		0			0
$136$	51.4085	+	29.6807i	0.378004	+	0.218241i
$137$	74.6259	+	43.0853i	0.544715	+	0.314491i	0.746988	−	0.664838i	$-0.231499\pi$
$137$	74.6259	+	43.0853i	0.544715	+	0.314491i	−0.202273	+	0.979329i	$0.564833\pi$
$138$	6.83419	+	11.8372i	0.0495231	+	0.0857766i
$139$		−	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
$142$	−83.4111	+	48.1574i	−0.587402	+	0.339137i
$143$	80.6128	−	139.625i	0.563726	−	0.976402i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$			123.965i			0.849076i
$147$	−32.8743	+	78.2450i	−0.223635	+	0.532279i
$148$			44.7931i			0.302656i
$149$	−109.963	−	190.462i	−0.738008	−	1.27827i	−0.953391	−	0.301738i	$-0.902433\pi$
$149$	−109.963	−	190.462i	−0.738008	−	1.27827i	0.215383	−	0.976530i	$-0.430900\pi$
$150$		0			0
$151$	130.461	−	225.965i	0.863980	−	1.49646i	−0.00407633	−	0.999992i	$-0.501298\pi$
$151$	130.461	−	225.965i	0.863980	−	1.49646i	0.868056	−	0.496466i	$-0.165369\pi$
$152$	34.0852	+	59.0373i	0.224245	+	0.388403i
$153$	62.9623			0.411518
$154$	4.69190	+	74.4668i	0.0304669	+	0.483551i
$155$		0			0
$156$	−37.0497	−	64.1719i	−0.237498	−	0.411359i
$157$	57.0954	−	98.8921i	0.363665	−	0.629886i	−0.624896	−	0.780708i	$-0.714859\pi$
$157$	57.0954	−	98.8921i	0.363665	−	0.629886i	0.988561	+	0.150822i	$0.0481920\pi$
$158$	120.939	+	69.8239i	0.765434	+	0.441923i
$159$	74.6968	−	43.1262i	0.469791	−	0.271234i
$160$		0			0
$161$	32.5325	−	21.6188i	0.202065	−	0.134278i
$162$			12.7279i			0.0785674i
$163$	−42.1894	+	24.3581i	−0.258831	+	0.149436i	−0.623801	−	0.781583i	$-0.714412\pi$
$163$	−42.1894	+	24.3581i	−0.258831	+	0.149436i	0.364970	+	0.931019i	$0.381079\pi$
$164$	−88.4777	−	51.0827i	−0.539498	−	0.311480i
$165$		0			0
$166$	−33.0005	+	19.0528i	−0.198798	+	0.114776i
$167$	−49.6127			−0.297082			−0.148541	−	0.988906i	$-0.547458\pi$
$167$	−49.6127			−0.297082			−0.148541	+	0.988906i	$0.547458\pi$
$168$	30.7179	+	15.2450i	0.182845	+	0.0907440i
$169$	288.560			1.70745
$170$		0			0
$171$	62.6185	+	36.1528i	0.366190	+	0.211420i
$172$	60.2159	+	34.7656i	0.350092	+	0.202126i
$173$	117.670	+	203.811i	0.680176	+	1.17810i	0.974927	+	0.222525i	$0.0714298\pi$
$173$	117.670	+	203.811i	0.680176	+	1.17810i	−0.294751	+	0.955574i	$0.595237\pi$
$174$			24.4122i			0.140300i
$175$		0			0
$176$	30.1488			0.171300
$177$	126.329	−	72.9362i	0.713725	−	0.412069i
$178$	−9.83495	+	17.0346i	−0.0552525	+	0.0957002i
$179$	−22.1049	+	38.2868i	−0.123491	+	0.213893i	−0.921142	−	0.389226i	$-0.872742\pi$
$179$	−22.1049	+	38.2868i	−0.123491	+	0.213893i	0.797651	+	0.603119i	$0.206076\pi$
$180$		0			0
$181$			117.049i			0.646679i	0.946283	+	0.323340i	$0.104806\pi$
$181$			117.049i			0.646679i	−0.946283	+	0.323340i	$0.895194\pi$
$182$	−176.366	+	117.200i	−0.969043	+	0.643958i
$183$		−	144.881i		−	0.791699i
$184$	−7.89145	−	13.6684i	−0.0428883	−	0.0742847i
$185$		0			0
$186$	−8.06204	+	13.9639i	−0.0433443	+	0.0750746i
$187$	−79.0933	−	136.994i	−0.422959	−	0.732586i
$188$	155.299			0.826056
$189$	36.3011	−	2.28721i	0.192069	−	0.0121016i
$190$		0			0
$191$	−117.156	−	202.920i	−0.613383	−	1.06241i	−0.990666	−	0.136313i	$-0.956475\pi$
$191$	−117.156	−	202.920i	−0.613383	−	1.06241i	0.377283	−	0.926098i	$-0.376858\pi$
$192$	6.92820	−	12.0000i	0.0360844	−	0.0625000i
$193$	−16.9438	−	9.78252i	−0.0877918	−	0.0506866i	0.455461	−	0.890256i	$-0.349474\pi$
$193$	−16.9438	−	9.78252i	−0.0877918	−	0.0506866i	−0.543253	+	0.839569i	$0.682808\pi$
$194$	4.52093	−	2.61016i	0.0233037	−	0.0134544i
$195$		0			0
$196$	37.9600	−	90.3495i	0.193673	−	0.460967i
$197$		−	179.443i		−	0.910877i	−0.890267	−	0.455438i	$-0.849483\pi$
$197$		−	179.443i		−	0.910877i	0.890267	−	0.455438i	$-0.150517\pi$
$198$	27.6934	−	15.9888i	0.139866	−	0.0807516i
$199$	221.630	+	127.958i	1.11372	+	0.643006i	0.939790	−	0.341753i	$-0.111021\pi$
$199$	221.630	+	127.958i	1.11372	+	0.643006i	0.173928	+	0.984758i	$0.444354\pi$
$200$		0			0
$201$	−99.8732	+	57.6618i	−0.496882	+	0.286875i
$202$	−258.291			−1.27867
$203$	69.6257	−	4.38688i	0.342984	−	0.0216102i
$204$	−72.7026			−0.356385
$205$		0			0
$206$	111.514	+	64.3825i	0.541329	+	0.312536i
$207$	−14.4975	−	8.37014i	−0.0700363	−	0.0404355i
$208$	42.7813	+	74.0994i	0.205679	+	0.356247i
$209$		−	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	$0.345491\pi$
$212$	−86.2525	+	49.7979i	−0.406851	+	0.234896i
$213$	58.9806	−	102.157i	0.276904	−	0.479612i
$214$	36.4417	−	63.1189i	0.170288	−	0.294948i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	41.2749	+	20.4843i	0.190207	+	0.0943977i
$218$		−	54.2512i		−	0.248859i
$219$	−75.9128	−	131.485i	−0.346634	−	0.600387i
$220$		0			0
$221$	224.467	−	388.789i	1.01569	−	1.75923i
$222$	−27.4301	−	47.5103i	−0.123559	−	0.214010i
$223$	−431.015			−1.93280			−0.966401	−	0.257039i	$-0.917253\pi$
$223$	−431.015			−1.93280			−0.966401	+	0.257039i	$0.917253\pi$
$224$	−35.4700	−	17.6034i	−0.158348	−	0.0785866i
$225$		0			0
$226$	140.401	+	243.182i	0.621245	+	1.07603i
$227$	−87.5479	+	151.637i	−0.385673	+	0.668006i	−0.991862	−	0.127315i	$-0.959364\pi$
$227$	−87.5479	+	151.637i	−0.385673	+	0.668006i	0.606189	+	0.795321i	$0.292698\pi$
$228$	−72.3057	−	41.7457i	−0.317130	−	0.183095i
$229$	−29.0717	+	16.7846i	−0.126951	+	0.0732951i	−0.562131	−	0.827048i	$-0.690018\pi$
$229$	−29.0717	+	16.7846i	−0.126951	+	0.0732951i	0.435180	+	0.900344i	$0.356685\pi$
$230$		0			0
$231$	−50.5779	−	76.1108i	−0.218952	−	0.329484i
$232$		−	28.1888i		−	0.121504i
$233$	134.159	−	77.4567i	0.575790	−	0.332432i	−0.183669	−	0.982988i	$-0.558797\pi$
$233$	134.159	−	77.4567i	0.575790	−	0.332432i	0.759458	+	0.650556i	$0.225464\pi$
$234$	78.5942	+	45.3764i	0.335873	+	0.193916i
$235$		0			0
$236$	−145.872	+	84.2195i	−0.618104	+	0.356862i
$237$	−171.033			−0.721658
$238$	13.0647	+	207.354i	0.0548935	+	0.871235i
$239$	−316.591			−1.32465			−0.662325	−	0.749217i	$-0.730430\pi$
$239$	−316.591			−1.32465			−0.662325	+	0.749217i	$0.730430\pi$
$240$		0			0
$241$	202.219	+	116.751i	0.839084	+	0.484446i	0.856953	−	0.515395i	$-0.172355\pi$
$241$	202.219	+	116.751i	0.839084	+	0.484446i	−0.0178685	+	0.999840i	$0.505688\pi$
$242$	78.6171	+	45.3896i	0.324864	+	0.187560i
$243$	−7.79423	−	13.5000i	−0.0320750	−	0.0555556i
$244$			167.294i			0.685631i
$245$		0			0
$246$	125.126			0.508644
$247$	446.484	−	257.777i	1.80763	−	1.04363i
$248$	9.30925	−	16.1241i	0.0375373	−	0.0650165i
$249$	23.3349	−	40.4172i	0.0937143	−	0.162318i
$250$		0			0
$251$		−	56.6879i		−	0.225848i	−0.993604	−	0.112924i	$-0.963978\pi$
$251$		−	56.6879i		−	0.225848i	0.993604	−	0.112924i	$-0.0360217\pi$
$252$	−41.9169	+	2.64104i	−0.166337	+	0.0104803i
$253$			42.0583i			0.166238i
$254$	−52.4060	−	90.7698i	−0.206323	−	0.357361i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	145.219	+	251.528i	0.565056	+	0.978706i	0.997044	+	0.0768270i	$0.0244789\pi$
$257$	145.219	+	251.528i	0.565056	+	0.978706i	−0.431988	+	0.901879i	$0.642188\pi$
$258$	−85.1581			−0.330070
$259$	−130.574	+	86.7704i	−0.504147	+	0.335021i
$260$		0			0
$261$	−14.9494	−	25.8931i	−0.0572773	−	0.0992072i
$262$	14.1662	−	24.5366i	0.0540694	−	0.0936510i
$263$	−385.031	−	222.298i	−1.46399	−	0.845238i	−0.464802	−	0.885415i	$-0.653875\pi$
$263$	−385.031	−	222.298i	−1.46399	−	0.845238i	−0.999193	+	0.0401768i	$0.987208\pi$
$264$	−31.9776	+	18.4623i	−0.121127	+	0.0699329i
$265$		0			0
$266$	−106.069	+	213.723i	−0.398755	+	0.803471i
$267$		−	24.0906i		−	0.0902270i
$268$	115.324	−	66.5822i	0.430312	−	0.248441i
$269$	144.956	+	83.6902i	0.538869	+	0.311116i	0.744620	−	0.667488i	$-0.232631\pi$
$269$	144.956	+	83.6902i	0.538869	+	0.311116i	−0.205752	+	0.978604i	$0.565964\pi$
$270$		0			0
$271$	2.24099	−	1.29384i	0.00826933	−	0.00477430i	−0.495860	−	0.868403i	$-0.665147\pi$
$271$	2.24099	−	1.29384i	0.00826933	−	0.00477430i	0.504129	+	0.863628i	$0.331814\pi$
$272$	83.9498			0.308639
$273$	115.294	−	232.311i	0.422322	−	0.850957i
$274$	121.864			0.444758
$275$		0			0
$276$	16.7403	+	9.66501i	0.0606532	+	0.0350181i
$277$	440.903	+	254.556i	1.59171	+	0.918973i	0.993014	+	0.117996i	$0.0376468\pi$
$277$	440.903	+	254.556i	1.59171	+	0.918973i	0.598694	+	0.800978i	$0.295686\pi$
$278$	−164.404	−	284.756i	−0.591381	−	1.02430i
$279$		−	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	$0.377681\pi$
$282$	−164.719	+	95.1005i	−0.584110	+	0.337236i
$283$	19.7433	−	34.1964i	0.0697643	−	0.120835i	−0.829033	−	0.559199i	$-0.811109\pi$
$283$	19.7433	−	34.1964i	0.0697643	−	0.120835i	0.898797	+	0.438364i	$0.144442\pi$
$284$	−68.1049	+	117.961i	−0.239806	+	0.415356i
$285$		0			0
$286$		−	228.007i		−	0.797229i
$287$	−22.4852	−	356.871i	−0.0783457	−	1.24345i
$288$			16.9706i			0.0589256i
$289$	−75.7363	−	131.179i	−0.262063	−	0.453907i
$290$		0			0
$291$	−3.19678	+	5.53698i	−0.0109855	+	0.0190274i
$292$	87.6565	+	151.826i	0.300194	+	0.519951i
$293$	−89.6023			−0.305810			−0.152905	−	0.988241i	$-0.548863\pi$
$293$	−89.6023			−0.305810			−0.152905	+	0.988241i	$0.548863\pi$
$294$	15.0649	+	119.076i	0.0512412	+	0.405020i
$295$		0			0
$296$	31.6735	+	54.8602i	0.107005	+	0.185338i
$297$	−19.5822	+	33.9174i	−0.0659334	+	0.114200i
$298$	−269.354	−	155.511i	−0.903871	−	0.521850i
$299$	−103.370	+	59.6809i	−0.345720	+	0.199602i
$300$		0			0
$301$	15.3029	+	242.878i	0.0508402	+	0.806903i
$302$		−	368.999i		−	1.22185i
$303$	273.959	−	158.170i	0.904154	−	0.522013i
$304$	83.4914	+	48.2038i	0.274643	+	0.158565i
$305$		0			0
$306$	77.1128	−	44.5211i	0.252003	−	0.145494i
$307$	470.478			1.53250			0.766251	−	0.642542i	$-0.222120\pi$
$307$	470.478			1.53250			0.766251	+	0.642542i	$0.222120\pi$
$308$	58.4024	+	87.8852i	0.189618	+	0.285341i
$309$	−157.704			−0.510370
$310$		0			0
$311$	217.631	+	125.649i	0.699778	+	0.404017i	0.807265	−	0.590189i	$-0.200947\pi$
$311$	217.631	+	125.649i	0.699778	+	0.404017i	−0.107487	+	0.994207i	$0.534280\pi$
$312$	−90.7528	−	52.3962i	−0.290874	−	0.167936i
$313$	194.231	+	336.417i	0.620545	+	1.07482i	0.989384	+	0.145322i	$0.0464219\pi$
$313$	194.231	+	336.417i	0.620545	+	1.07482i	−0.368839	+	0.929493i	$0.620245\pi$
$314$		−	161.490i		−	0.514300i
$315$		0			0
$316$	197.492			0.624974
$317$	129.366	−	74.6898i	0.408096	−	0.235614i	−0.281875	−	0.959451i	$-0.590956\pi$
$317$	129.366	−	74.6898i	0.408096	−	0.235614i	0.689971	+	0.723837i	$0.257623\pi$
$318$	60.9897	−	105.637i	0.191792	−	0.332193i
$319$	−37.5588	+	65.0538i	−0.117739	+	0.203930i
$320$		0			0
$321$			89.2636i			0.278080i
$322$	24.5572	−	49.4815i	0.0762645	−	0.153669i
$323$		−	505.837i		−	1.56606i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	−34.4475	+	59.6648i	−0.105667	+	0.183021i
$327$	33.2219	+	57.5420i	0.101596	+	0.175970i
$328$	−144.484			−0.440499
$329$	300.835	+	452.702i	0.914391	+	1.37600i
$330$		0			0
$331$	235.465	+	407.838i	0.711375	+	1.23214i	0.964341	+	0.264663i	$0.0852607\pi$
$331$	235.465	+	407.838i	0.711375	+	1.23214i	−0.252966	+	0.967475i	$0.581406\pi$
$332$	−26.9448	+	46.6697i	−0.0811590	+	0.140571i
$333$	58.1880	+	33.5948i	0.174739	+	0.100885i
$334$	−60.7628	+	35.0814i	−0.181925	+	0.105034i
$335$		0			0
$336$	48.4014	−	3.04961i	0.144052	−	0.00907622i
$337$		−	532.478i		−	1.58005i	−0.613072	−	0.790027i	$-0.710066\pi$
$337$		−	532.478i		−	1.58005i	0.613072	−	0.790027i	$-0.289934\pi$
$338$	353.412	−	204.042i	1.04560	−	0.603676i
$339$	−297.836	−	171.956i	−0.878573	−	0.507244i
$340$		0			0
$341$	−42.9675	+	24.8073i	−0.126004	+	0.0727487i
$342$	102.256			0.298993
$343$	336.907	−	64.3643i	0.982236	−	0.187651i
$344$	98.3321			0.285849
$345$		0			0
$346$	288.232	+	166.411i	0.833042	+	0.480957i
$347$	−389.385	−	224.812i	−1.12215	−	0.647872i	−0.180199	−	0.983630i	$-0.557674\pi$
$347$	−389.385	−	224.812i	−1.12215	−	0.647872i	−0.941948	+	0.335758i	$0.891008\pi$
$348$	17.2621	+	29.8988i	0.0496036	+	0.0859160i
$349$			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
$352$	36.9246	−	21.3184i	0.104899	−	0.0605637i
$353$	135.686	−	235.014i	0.384379	−	0.665763i	−0.607304	−	0.794469i	$-0.707749\pi$
$353$	135.686	−	235.014i	0.384379	−	0.665763i	0.991683	+	0.128706i	$0.0410824\pi$
$354$	103.147	−	178.657i	0.291377	−	0.504680i
$355$		0			0
$356$			27.8174i			0.0781389i
$357$	−140.835	−	211.932i	−0.394496	−	0.593646i
$358$			62.5221i			0.174643i
$359$	−3.79200	−	6.56794i	−0.0105627	−	0.0182951i	0.860696	−	0.509120i	$-0.170029\pi$
$359$	−3.79200	−	6.56794i	−0.0105627	−	0.0182951i	−0.871258	+	0.490825i	$0.836696\pi$
$360$		0			0
$361$	109.950	−	190.440i	0.304572	−	0.527534i
$362$	82.7661	+	143.355i	0.228636	+	0.396009i
$363$	−111.181			−0.306285
$364$	−133.130	+	268.250i	−0.365741	+	0.736951i
$365$		0			0
$366$	−102.446	−	177.442i	−0.279908	−	0.484814i
$367$	−265.706	+	460.216i	−0.723995	+	1.25400i	0.235392	+	0.971901i	$0.424363\pi$
$367$	−265.706	+	460.216i	−0.723995	+	1.25400i	−0.959386	+	0.282095i	$0.908971\pi$
$368$	−19.3300	−	11.1602i	−0.0525272	−	0.0303266i
$369$	−132.717	+	76.6240i	−0.359666	+	0.207653i
$370$		0			0
$371$	−312.246	−	154.965i	−0.841634	−	0.417695i
$372$			22.8029i			0.0612981i
$373$	−497.937	+	287.484i	−1.33495	+	0.770734i	−0.986054	−	0.166427i	$-0.946777\pi$
$373$	−497.937	+	287.484i	−1.33495	+	0.770734i	−0.348897	+	0.937161i	$0.613444\pi$
$374$	−193.738	−	111.855i	−0.518016	−	0.299077i
$375$		0			0
$376$	190.201	−	109.813i	0.505854	−	0.292055i
$377$	−213.185			−0.565476
$378$	42.8423	−	28.4700i	0.113339	−	0.0753174i
$379$	−627.464			−1.65558			−0.827789	−	0.561040i	$-0.810402\pi$
$379$	−627.464			−1.65558			−0.827789	+	0.561040i	$0.810402\pi$
$380$		0			0
$381$	111.170	+	64.1839i	0.291784	+	0.168462i
$382$	−286.973	−	165.684i	−0.751238	−	0.433727i
$383$	−33.3056	−	57.6870i	−0.0869597	−	0.150619i	0.819265	−	0.573415i	$-0.194382\pi$
$383$	−33.3056	−	57.6870i	−0.0869597	−	0.150619i	−0.906225	+	0.422797i	$0.861048\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−27.6691			−0.0716817
$387$	90.3238	−	52.1485i	0.233395	−	0.134751i
$388$	3.69132	−	6.39356i	0.00951372	−	0.0164782i
$389$	274.525	−	475.491i	0.705719	−	1.22234i	−0.260713	−	0.965416i	$-0.583957\pi$
$389$	274.525	−	475.491i	0.705719	−	1.22234i	0.966431	−	0.256925i	$-0.0827092\pi$
$390$		0			0
$391$			117.112i			0.299519i
$392$	−17.3955	−	137.497i	−0.0443762	−	0.350757i
$393$			34.7000i			0.0882950i
$394$	−126.885	−	219.772i	−0.322044	−	0.557796i
$395$		0			0
$396$	22.6116	−	39.1644i	0.0571000	−	0.0989001i
$397$	−259.283	−	449.091i	−0.653106	−	1.13121i	−0.982365	−	0.186973i	$-0.940132\pi$
$397$	−259.283	−	449.091i	−0.653106	−	1.13121i	0.329259	−	0.944240i	$-0.393201\pi$
$398$	361.920			0.909347
$399$	−18.3753	−	291.642i	−0.0460535	−	0.730931i
$400$		0			0
$401$	238.149	+	412.486i	0.593888	+	1.02864i	0.993703	+	0.112048i	$0.0357411\pi$
$401$	238.149	+	412.486i	0.593888	+	1.02864i	−0.399815	+	0.916596i	$0.630926\pi$
$402$	−81.5462	+	141.242i	−0.202851	+	0.351349i
$403$	−121.942	−	70.4033i	−0.302586	−	0.174698i
$404$	−316.340	+	182.639i	−0.783020	+	0.452077i
$405$		0			0
$406$	82.1717	−	54.6056i	0.202393	−	0.134497i
$407$		−	168.807i		−	0.414760i
$408$	−89.0422	+	51.4085i	−0.218241	+	0.126001i
$409$	93.2552	+	53.8409i	0.228008	+	0.131640i	0.609653	−	0.792669i	$-0.291309\pi$
$409$	93.2552	+	53.8409i	0.228008	+	0.131640i	−0.381645	+	0.924309i	$0.624642\pi$
$410$		0			0
$411$	−129.256	+	74.6259i	−0.314491	+	0.181572i
$412$	182.101			0.441993
$413$	−528.079	−	262.080i	−1.27864	−	0.634577i
$414$	−23.6743			−0.0571844
$415$		0			0
$416$	104.792	+	60.5019i	0.251905	+	0.145437i
$417$	348.753	+	201.353i	0.836339	+	0.482861i
$418$	−128.454	−	222.488i	−0.307305	−	0.532268i
$419$		−	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	$0.591594\pi$
$422$	241.141	−	139.223i	0.571424	−	0.329912i
$423$	116.474	−	201.739i	0.275352	−	0.476924i
$424$	−70.4249	+	121.979i	−0.166096	+	0.287687i
$425$		0			0
$426$		−	166.822i		−	0.391601i
$427$	−487.670	+	324.071i	−1.14208	+	0.758950i
$428$		−	103.073i		−	0.240824i
$429$	139.625	+	241.838i	0.325467	+	0.563726i
$430$		0			0
$431$	95.8960	−	166.097i	0.222497	−	0.385375i	−0.733069	−	0.680154i	$-0.761913\pi$
$431$	95.8960	−	166.097i	0.222497	−	0.385375i	0.955565	+	0.294779i	$0.0952461\pi$
$432$	−10.3923	−	18.0000i	−0.0240563	−	0.0416667i
$433$	−122.083			−0.281946			−0.140973	−	0.990013i	$-0.545023\pi$
$433$	−122.083			−0.281946			−0.140973	+	0.990013i	$0.545023\pi$
$434$	65.0358	−	4.09768i	0.149852	−	0.00944166i
$435$		0			0
$436$	−38.3614	−	66.4438i	−0.0879848	−	0.152394i
$437$	−67.2454	+	116.472i	−0.153880	+	0.266527i
$438$	−185.948	−	107.357i	−0.424538	−	0.245107i
$439$	217.656	−	125.664i	0.495800	−	0.286250i	−0.231177	−	0.972912i	$-0.574258\pi$
$439$	217.656	−	125.664i	0.495800	−	0.286250i	0.726978	+	0.686661i	$0.240924\pi$
$440$		0			0
$441$	−88.8975	−	117.074i	−0.201582	−	0.265473i
$442$		−	634.890i		−	1.43640i
$443$	95.0802	−	54.8946i	0.214628	−	0.123916i	−0.388832	−	0.921309i	$-0.627121\pi$
$443$	95.0802	−	54.8946i	0.214628	−	0.123916i	0.603460	+	0.797393i	$0.293788\pi$
$444$	−67.1897	−	38.7920i	−0.151328	−	0.0873693i
$445$		0			0
$446$	−527.883	+	304.773i	−1.18359	+	0.683349i
$447$	380.924			0.852178
$448$	−55.8892	+	3.52139i	−0.124753	+	0.00786024i
$449$	−806.490			−1.79619			−0.898095	−	0.439801i	$-0.855049\pi$
$449$	−806.490			−1.79619			−0.898095	+	0.439801i	$0.855049\pi$
$450$		0			0
$451$	333.437	+	192.510i	0.739329	+	0.426852i
$452$	343.912	+	198.558i	0.760867	+	0.439287i
$453$	225.965	+	391.383i	0.498819	+	0.863980i
$454$			247.623i			0.545425i
$455$		0			0
$456$	−118.075			−0.258936
$457$	668.964	−	386.226i	1.46382	−	0.845135i	0.464631	−	0.885504i	$-0.346187\pi$
$457$	668.964	−	386.226i	1.46382	−	0.845135i	0.999185	+	0.0403698i	$0.0128536\pi$
$458$	−23.7370	+	41.1137i	−0.0518275	+	0.0897678i
$459$	−54.5270	+	94.4435i	−0.118795	+	0.205759i
$460$		0			0
$461$		−	793.611i		−	1.72150i	−0.509029	−	0.860749i	$-0.669995\pi$
$461$		−	793.611i		−	1.72150i	0.509029	−	0.860749i	$-0.330005\pi$
$462$	−115.764	−	57.4523i	−0.250570	−	0.124356i
$463$		−	274.227i		−	0.592284i	−0.955144	−	0.296142i	$-0.904300\pi$
$463$		−	274.227i		−	0.592284i	0.955144	−	0.296142i	$-0.0957001\pi$
$464$	−19.9325	−	34.5241i	−0.0429580	−	0.0744054i
$465$		0			0
$466$	109.540	−	189.730i	0.235065	−	0.407145i
$467$	−198.815	−	344.357i	−0.425727	−	0.737381i	0.570761	−	0.821116i	$-0.306648\pi$
$467$	−198.815	−	344.357i	−0.425727	−	0.737381i	−0.996488	+	0.0837354i	$0.973315\pi$
$468$	128.344			0.274239
$469$	417.488	+	207.195i	0.890166	+	0.441781i
$470$		0			0
$471$	98.8921	+	171.286i	0.209962	+	0.363665i
$472$	−119.104	+	206.295i	−0.252340	+	0.437065i
$473$	−226.930	−	131.018i	−0.479766	−	0.276993i
$474$	−209.472	+	120.939i	−0.441923	+	0.255145i
$475$		0			0
$476$	162.622	+	244.717i	0.341643	+	0.514112i
$477$			149.394i			0.313194i
$478$	−387.743	+	223.864i	−0.811179	+	0.468334i
$479$	165.573	+	95.5938i	0.345665	+	0.199570i	0.662774	−	0.748819i	$-0.269379\pi$
$479$	165.573	+	95.5938i	0.345665	+	0.199570i	−0.317110	+	0.948389i	$0.602712\pi$
$480$		0			0
$481$	414.893	−	239.538i	0.862563	−	0.498001i
$482$	330.223			0.685110
$483$	4.25428	+	67.5212i	0.00880803	+	0.139795i
$484$	128.381			0.265250
$485$		0			0
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	−164.561	−	95.0092i	−0.337907	−	0.195091i	0.321439	−	0.946930i	$-0.395833\pi$
$487$	−164.561	−	95.0092i	−0.337907	−	0.195091i	−0.659346	+	0.751840i	$0.729167\pi$
$488$	118.295	+	204.892i	0.242407	+	0.419862i
$489$		−	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	$0.569059\pi$
$492$	153.248	−	88.4777i	0.311480	−	0.179833i
$493$	−104.583	+	181.143i	−0.212136	+	0.367430i
$494$	364.552	−	631.423i	0.737960	−	1.27818i
$495$		0			0
$496$		−	26.3305i		−	0.0530857i
$497$	−475.791	+	29.9779i	−0.957325	+	0.0603178i
$498$		−	66.0010i		−	0.132532i
$499$	−126.864	−	219.734i	−0.254236	−	0.440349i	0.710452	−	0.703746i	$-0.248491\pi$
$499$	−126.864	−	219.734i	−0.254236	−	0.440349i	−0.964688	+	0.263396i	$0.915157\pi$
$500$		0			0
$501$	42.9658	−	74.4190i	0.0857601	−	0.148541i
$502$	−40.0844	−	69.4282i	−0.0798494	−	0.138303i
$503$	217.815			0.433033			0.216516	−	0.976279i	$-0.430531\pi$
$503$	217.815			0.433033			0.216516	+	0.976279i	$0.430531\pi$
$504$	−49.4700	+	32.8743i	−0.0981547	+	0.0652268i
$505$		0			0
$506$	29.7397	+	51.5107i	0.0587741	+	0.101800i
$507$	−249.900	+	432.839i	−0.492899	+	0.853727i
$508$	−128.368	−	74.1132i	−0.252693	−	0.145892i
$509$	24.6582	−	14.2364i	0.0484444	−	0.0279694i	−0.475582	−	0.879671i	$-0.657763\pi$
$509$	24.6582	−	14.2364i	0.0484444	−	0.0279694i	0.524027	+	0.851702i	$0.324429\pi$
$510$		0			0
$511$	−272.776	+	549.630i	−0.533808	+	1.07560i
$512$			22.6274i			0.0441942i
$513$	−108.458	+	62.6185i	−0.211420	+	0.122063i
$514$	355.714	+	205.371i	0.692050	+	0.399555i
$515$		0			0
$516$	−104.297	+	60.2159i	−0.202126	+	0.116697i
$517$	−585.258			−1.13203
$518$	−98.5640	+	198.601i	−0.190278	+	0.383400i
$519$	−407.622			−0.785399
$520$		0			0
$521$	671.401	+	387.634i	1.28868	+	0.744019i	0.978418	−	0.206633i	$-0.0662507\pi$
$521$	671.401	+	387.634i	1.28868	+	0.744019i	0.310260	+	0.950652i	$0.399584\pi$
$522$	−36.6184	−	21.1416i	−0.0701501	−	0.0405012i
$523$	−51.2334	−	88.7388i	−0.0979605	−	0.169673i	0.812880	−	0.582431i	$-0.197899\pi$
$523$	−51.2334	−	88.7388i	−0.0979605	−	0.169673i	−0.910840	+	0.412759i	$0.864565\pi$
$524$		−	40.0681i		−	0.0764657i
$525$		0			0
$526$	−628.752			−1.19535
$527$	−119.644	+	69.0763i	−0.227028	+	0.131075i
$528$	−26.1096	+	45.2232i	−0.0494501	+	0.0856500i
$529$	−248.931	+	431.162i	−0.470570	+	0.815050i
$530$		0			0
$531$			252.659i			0.475816i
$532$	21.2180	+	336.759i	0.0398835	+	0.633005i
$533$			1092.69i			2.05008i
$534$	−17.0346	−	29.5049i	−0.0319001	−	0.0552525i
$535$		0			0
$536$	94.1614	−	163.092i	0.175674	−	0.304277i
$537$	−38.2868	−	66.3147i	−0.0712976	−	0.123491i
$538$	236.712			0.439984
$539$	−143.056	+	340.491i	−0.265410	+	0.631709i
$540$		0			0
$541$	408.868	+	708.180i	0.755763	+	1.30902i	0.944994	+	0.327088i	$0.106067\pi$
$541$	408.868	+	708.180i	0.755763	+	1.30902i	−0.189231	+	0.981933i	$0.560599\pi$
$542$	1.82976	−	3.16924i	0.00337594	−	0.00584730i
$543$	−175.573	−	101.367i	−0.323340	−	0.186680i
$544$	102.817	−	59.3614i	0.189002	−	0.109120i
$545$		0			0
$546$	−23.0634	−	366.047i	−0.0422406	−	0.670416i
$547$			204.209i			0.373325i	0.982424	+	0.186662i	$0.0597670\pi$
$547$			204.209i			0.373325i	−0.982424	+	0.186662i	$0.940233\pi$
$548$	149.252	−	86.1706i	0.272357	−	0.157246i
$549$	217.321	+	125.471i	0.395849	+	0.228544i
$550$		0			0
$551$	−208.024	+	120.103i	−0.377539	+	0.217972i
$552$	27.3368			0.0495231
$553$	382.569	+	575.698i	0.691806	+	1.04105i
$554$	719.992			1.29962
$555$		0			0
$556$	−402.706	−	232.502i	−0.724291	−	0.418169i
$557$	464.253	+	268.036i	0.833487	+	0.481214i	0.855045	−	0.518553i	$-0.173529\pi$
$557$	464.253	+	268.036i	0.833487	+	0.481214i	−0.0215578	+	0.999768i	$0.506863\pi$
$558$	−13.9639	−	24.1861i	−0.0250249	−	0.0433443i
$559$		−	743.660i		−	1.33034i
$560$		0			0
$561$	273.987			0.488391
$562$	258.039	−	148.979i	0.459144	−	0.265087i
$563$	494.806	−	857.029i	0.878874	−	1.52225i	0.0262960	−	0.999654i	$-0.491629\pi$
$563$	494.806	−	857.029i	0.878874	−	1.52225i	0.852578	−	0.522600i	$-0.175038\pi$
$564$	−134.492	+	232.948i	−0.238462	+	0.413028i
$565$		0			0
$566$		−	55.8424i		−	0.0986616i
$567$	−28.0068	+	56.4324i	−0.0493948	+	0.0995281i
$568$			192.630i			0.339137i
$569$	248.330	+	430.120i	0.436432	+	0.755922i	0.997411	−	0.0719076i	$-0.0229087\pi$
$569$	248.330	+	430.120i	0.436432	+	0.755922i	−0.560979	+	0.827830i	$0.689575\pi$
$570$		0			0
$571$	71.0244	−	123.018i	0.124386	−	0.215443i	−0.797107	−	0.603838i	$-0.793637\pi$
$571$	71.0244	−	123.018i	0.124386	−	0.215443i	0.921493	+	0.388395i	$0.126971\pi$
$572$	−161.226	−	279.251i	−0.281863	−	0.488201i
$573$	405.841			0.708274
$574$	−279.884	−	421.176i	−0.487604	−	0.733757i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−189.689	+	328.551i	−0.328751	+	0.569413i	−0.982264	−	0.187502i	$-0.939961\pi$
$577$	−189.689	+	328.551i	−0.328751	+	0.569413i	0.653514	+	0.756915i	$0.273294\pi$
$578$	−185.515	−	107.107i	−0.320961	−	0.185307i
$579$	29.3476	−	16.9438i	0.0506866	−	0.0292639i
$580$		0			0
$581$	−188.240	+	11.8604i	−0.323993	+	0.0204137i
$582$			9.04185i			0.0155358i
$583$	325.051	−	187.668i	0.557549	−	0.321901i
$584$	214.714	+	123.965i	0.367661	+	0.212269i
$585$		0			0
$586$	−109.740	+	63.3584i	−0.187269	+	0.108120i
$587$	−234.204			−0.398984			−0.199492	−	0.979899i	$-0.563929\pi$
$587$	−234.204			−0.398984			−0.199492	+	0.979899i	$0.563929\pi$
$588$	102.650	+	135.185i	0.174575	+	0.229906i
$589$	−158.654			−0.269361
$590$		0			0
$591$	269.164	+	155.402i	0.455438	+	0.262948i
$592$	77.5840	+	44.7931i	0.131054	+	0.0756641i
$593$	−286.272	−	495.838i	−0.482753	−	0.836152i	0.517051	−	0.855954i	$-0.327030\pi$
$593$	−286.272	−	495.838i	−0.482753	−	0.836152i	−0.999804	+	0.0198023i	$0.993696\pi$
$594$			55.3869i			0.0932439i
$595$		0			0
$596$	−439.853			−0.738008
$597$	−383.874	+	221.630i	−0.643006	+	0.371239i
$598$	−84.4016	+	146.188i	−0.141140	+	0.244461i
$599$	46.7105	−	80.9049i	0.0779807	−	0.135067i	−0.824398	−	0.566011i	$-0.808486\pi$
$599$	46.7105	−	80.9049i	0.0779807	−	0.135067i	0.902379	+	0.430944i	$0.141819\pi$
$600$		0			0
$601$			167.140i			0.278103i	0.990285	+	0.139051i	$0.0444053\pi$
$601$			167.140i			0.278103i	−0.990285	+	0.139051i	$0.955595\pi$
$602$	190.483	+	286.643i	0.316417	+	0.476151i
$603$		−	199.746i		−	0.331255i
$604$	−260.922	−	451.930i	−0.431990	−	0.748229i
$605$		0			0
$606$	223.686	−	387.436i	0.369119	−	0.639333i
$607$	459.572	+	796.002i	0.757120	+	1.31137i	0.944314	+	0.329047i	$0.106727\pi$
$607$	459.572	+	796.002i	0.757120	+	1.31137i	−0.187194	+	0.982323i	$0.559939\pi$
$608$	136.341			0.224245
$609$	−53.7173	+	108.238i	−0.0882058	+	0.177730i
$610$		0			0
$611$	−830.484	−	1438.44i	−1.35922	−	2.35424i
$612$	62.9623	−	109.054i	0.102880	−	0.178193i
$613$	675.011	+	389.718i	1.10116	+	0.635755i	0.936525	−	0.350600i	$-0.114022\pi$
$613$	675.011	+	389.718i	1.10116	+	0.635755i	0.164635	+	0.986355i	$0.447356\pi$
$614$	576.215	−	332.678i	0.938462	−	0.541821i
$615$		0			0
$616$	133.672	+	66.3402i	0.217000	+	0.107695i
$617$		−	510.821i		−	0.827911i	−0.910297	−	0.413956i	$-0.864147\pi$
$617$		−	510.821i		−	0.827911i	0.910297	−	0.413956i	$-0.135853\pi$
$618$	−193.148	+	111.514i	−0.312536	+	0.180443i
$619$	808.792	+	466.956i	1.30661	+	0.754372i	0.981529	−	0.191314i	$-0.0612749\pi$
$619$	808.792	+	466.956i	1.30661	+	0.754372i	0.325082	+	0.945686i	$0.394608\pi$
$620$		0			0
$621$	25.1104	−	14.4975i	0.0404355	−	0.0233454i
$622$	355.390			0.571367
$623$	−81.0892	+	53.8862i	−0.130159	+	0.0864947i
$624$	−148.199			−0.237498
$625$		0			0
$626$	475.766	+	274.684i	0.760009	+	0.438792i
$627$	272.491	+	157.323i	0.434595	+	0.250914i
$628$	−114.191	−	197.784i	−0.181832	−	0.314943i
$629$		−	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	$0.661986\pi$
$632$	241.877	−	139.648i	0.382717	−	0.220962i
$633$	−170.512	+	295.336i	−0.269372	+	0.466566i
$634$	105.627	−	182.952i	0.166605	−	0.288568i
$635$		0			0
$636$		−	172.505i		−	0.271234i
$637$	−1039.85	+	131.557i	−1.63242	+	0.206526i
$638$			106.232i			0.166508i
$639$	102.157	+	176.942i	0.159871	+	0.276904i
$640$		0			0
$641$	94.1724	−	163.111i	0.146915	−	0.254464i	−0.783171	−	0.621807i	$-0.786399\pi$
$641$	94.1724	−	163.111i	0.146915	−	0.254464i	0.930086	+	0.367343i	$0.119732\pi$
$642$	63.1189	+	109.325i	0.0983161	+	0.170288i
$643$	−23.8831			−0.0371432			−0.0185716	−	0.999828i	$-0.505912\pi$
$643$	−23.8831			−0.0371432			−0.0185716	+	0.999828i	$0.505912\pi$
$644$	−4.91242	−	77.9667i	−0.00762798	−	0.121066i
$645$		0			0
$646$	−357.681	−	619.521i	−0.553685	−	0.959011i
$647$	−542.667	+	939.928i	−0.838744	+	1.45275i	0.0522010	+	0.998637i	$0.483376\pi$
$647$	−542.667	+	939.928i	−0.838744	+	1.45275i	−0.890945	+	0.454111i	$0.849957\pi$
$648$	22.0454	+	12.7279i	0.0340207	+	0.0196419i
$649$	549.735	−	317.390i	0.847049	−	0.489044i
$650$		0			0
$651$	−66.4715	+	44.1724i	−0.102107	+	0.0678531i
$652$			97.4323i			0.149436i
$653$	−550.536	+	317.852i	−0.843087	+	0.486756i	−0.858312	−	0.513128i	$-0.828487\pi$
$653$	−550.536	+	317.852i	−0.843087	+	0.486756i	0.0152254	+	0.999884i	$0.495153\pi$
$654$	81.3767	+	46.9829i	0.124429	+	0.0718393i
$655$		0			0
$656$	−176.955	+	102.165i	−0.269749	+	0.155740i
$657$	262.970			0.400258
$658$	688.555	+	341.723i	1.04644	+	0.519336i
$659$	888.955			1.34895			0.674473	−	0.738300i	$-0.264371\pi$
$659$	888.955			1.34895			0.674473	+	0.738300i	$0.264371\pi$
$660$		0			0
$661$	−656.362	−	378.951i	−0.992983	−	0.573299i	−0.0868187	−	0.996224i	$-0.527670\pi$
$661$	−656.362	−	378.951i	−0.992983	−	0.573299i	−0.906165	+	0.422925i	$0.861003\pi$
$662$	576.770	+	332.998i	0.871253	+	0.503018i
$663$	388.789	+	673.402i	0.586409	+	1.01569i
$664$			76.2114i			0.114776i
$665$		0			0
$666$	95.0206			0.142674
$667$	48.1620	−	27.8063i	0.0722068	−	0.0416886i
$668$	−49.6127	+	85.9316i	−0.0742704	+	0.128640i
$669$	373.270	−	646.522i	0.557952	−	0.966401i
$670$		0			0
$671$		−	630.464i		−	0.939589i
$672$	57.1230	−	37.9600i	0.0850045	−	0.0564881i
$673$			936.839i			1.39203i	0.718026	+	0.696017i	$0.245046\pi$
$673$			936.839i			1.39203i	−0.718026	+	0.696017i	$0.754954\pi$
$674$	−376.519	−	652.150i	−0.558634	−	0.967582i
$675$		0			0
$676$	288.560	−	499.800i	0.426863	−	0.739349i
$677$	−123.589	−	214.062i	−0.182554	−	0.316192i	0.760196	−	0.649694i	$-0.225103\pi$
$677$	−123.589	−	214.062i	−0.182554	−	0.316192i	−0.942749	+	0.333502i	$0.891770\pi$
$678$	−486.365			−0.717352
$679$	25.7881	−	1.62482i	0.0379795	−	0.00239296i
$680$		0			0
$681$	−151.637	−	262.644i	−0.222669	−	0.385673i
$682$	−35.0828	+	60.7652i	−0.0514411	+	0.0890986i
$683$	607.755	+	350.887i	0.889831	+	0.513744i	0.873887	−	0.486129i	$-0.161591\pi$
$683$	607.755	+	350.887i	0.889831	+	0.513744i	0.0159438	+	0.999873i	$0.494925\pi$
$684$	125.237	−	72.3057i	0.183095	−	0.105710i
$685$		0			0
$686$	367.112	−	317.059i	0.535149	−	0.462185i
$687$		−	58.1435i		−	0.0846339i
$688$	120.432	−	69.5313i	0.175046	−	0.101063i
$689$	922.498	+	532.604i	1.33889	+	0.773011i
$690$		0			0
$691$	−530.850	+	306.486i	−0.768234	+	0.443540i	−0.832244	−	0.554409i	$-0.812944\pi$
$691$	−530.850	+	306.486i	−0.768234	+	0.443540i	0.0640104	+	0.997949i	$0.479611\pi$
$692$	470.682			0.680176
$693$	157.968	−	9.95302i	0.227948	−	0.0143622i
$694$	−635.863			−0.916230
$695$		0			0
$696$	42.2832	+	24.4122i	0.0607518	+	0.0350750i
$697$	928.461	+	536.047i	1.33208	+	0.769078i
$698$	233.823	+	404.993i	0.334990	+	0.580220i
$699$			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	$0.463296\pi$
$702$	−136.129	+	78.5942i	−0.193916	+	0.111958i
$703$	269.900	−	467.480i	0.383926	−	0.664979i
$704$	30.1488	−	52.2193i	0.0428250	−	0.0741751i
$705$		0			0
$706$		−	383.777i		−	0.543593i
$707$	−1145.20	−	568.349i	−1.61980	−	0.803889i
$708$		−	291.745i		−	0.412069i
$709$	285.175	+	493.938i	0.402222	+	0.696669i	0.993994	−	0.109436i	$-0.0349046\pi$
$709$	285.175	+	493.938i	0.402222	+	0.696669i	−0.591772	+	0.806106i	$0.701571\pi$
$710$		0			0
$711$	148.119	−	256.549i	0.208325	−	0.360829i
$712$	19.6699	+	34.0693i	0.0276263	+	0.0478501i
$713$	36.7317			0.0515171
$714$	−322.345	−	159.977i	−0.451464	−	0.224057i
$715$		0			0
$716$	44.2098	+	76.5736i	0.0617455	+	0.106946i
$717$	274.176	−	474.887i	0.382393	−	0.662325i
$718$	−9.28847	−	5.36270i	−0.0129366	−	0.00746894i
$719$	−431.817	+	249.310i	−0.600580	+	0.346745i	−0.769270	−	0.638924i	$-0.779380\pi$
$719$	−431.817	+	249.310i	−0.600580	+	0.346745i	0.168690	+	0.985669i	$0.446046\pi$
$720$		0			0
$721$	352.755	+	530.834i	0.489258	+	0.736246i
$722$		−	310.987i		−	0.430730i
$723$	−350.254	+	202.219i	−0.484446	+	0.279695i
$724$	202.735	+	117.049i	0.280020	+	0.161670i
$725$		0			0
$726$	−136.169	+	78.6171i	−0.187560	+	0.108288i
$727$	−1058.79			−1.45638			−0.728190	−	0.685375i	$-0.759638\pi$
$727$	−1058.79			−1.45638			−0.728190	+	0.685375i	$0.759638\pi$
$728$	26.6313	+	422.675i	0.0365815	+	0.580597i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−631.888	−	364.821i	−0.864416	−	0.499071i
$732$	−250.941	−	144.881i	−0.342816	−	0.197925i
$733$	7.56721	+	13.1068i	0.0103236	+	0.0178810i	0.871141	−	0.491033i	$-0.163380\pi$
$733$	7.56721	+	13.1068i	0.0103236	+	0.0178810i	−0.860817	+	0.508914i	$0.830047\pi$
$734$			751.530i			1.02388i
$735$		0			0
$736$	−31.5658			−0.0428883
$737$	−434.609	+	250.922i	−0.589700	+	0.340463i
$738$	−108.363	+	187.690i	−0.146833	+	0.254322i
$739$	−81.3819	+	140.958i	−0.110124	+	0.190741i	−0.915820	−	0.401588i	$-0.868458\pi$
$739$	−81.3819	+	140.958i	−0.110124	+	0.190741i	0.805696	+	0.592329i	$0.201792\pi$
$740$		0			0
$741$			892.967i			1.20508i
$742$	−491.998	+	30.9991i	−0.663071	+	0.0417778i
$743$			338.071i			0.455009i	0.973777	+	0.227504i	$0.0730566\pi$
$743$			338.071i			0.455009i	−0.973777	+	0.227504i	$0.926943\pi$
$744$	16.1241	+	27.9277i	0.0216722	+	0.0375373i
$745$		0			0
$746$	−406.564	+	704.189i	−0.544991	+	0.943953i
$747$	40.4172	+	70.0046i	0.0541060	+	0.0937143i
$748$	−316.373			−0.422959
$749$	300.462	−	199.666i	0.401151	−	0.266577i
$750$		0			0
$751$	−239.087	−	414.111i	−0.318359	−	0.551413i	0.661787	−	0.749692i	$-0.269798\pi$
$751$	−239.087	−	414.111i	−0.318359	−	0.551413i	−0.980146	+	0.198279i	$0.936465\pi$
$752$	155.299	−	268.985i	0.206514	−	0.357693i
$753$	85.0319	+	49.0932i	0.112924	+	0.0651968i
$754$	−261.097	+	150.744i	−0.346282	+	0.199926i
$755$		0			0
$756$	32.3395	−	65.1625i	0.0427771	−	0.0861938i
$757$			397.788i			0.525479i	0.964867	+	0.262739i	$0.0846260\pi$
$757$			397.788i			0.525479i	−0.964867	+	0.262739i	$0.915374\pi$
$758$	−768.483	+	443.684i	−1.01383	+	0.585335i
$759$	−63.0874	−	36.4236i	−0.0831192	−	0.0479889i
$760$		0			0
$761$	−1264.02	+	729.785i	−1.66100	+	0.958981i	−0.688767	+	0.724983i	$0.741848\pi$
$761$	−1264.02	+	729.785i	−1.66100	+	0.958981i	−0.972237	+	0.233998i	$0.924819\pi$
$762$	181.540			0.238241
$763$	119.376	−	240.536i	0.156456	−	0.315250i
$764$	−468.625			−0.613383
$765$		0			0
$766$	−81.5817	−	47.1012i	−0.106503	−	0.0614898i
$767$	1560.15	+	900.755i	2.03410	+	1.17439i
$768$	−13.8564	−	24.0000i	−0.0180422	−	0.0312500i
$769$			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
$772$	−33.8876	+	19.5650i	−0.0438959	+	0.0253433i
$773$	−226.305	+	391.972i	−0.292762	+	0.507079i	−0.974462	−	0.224553i	$-0.927908\pi$
$773$	−226.305	+	391.972i	−0.292762	+	0.507079i	0.681700	+	0.731632i	$0.261241\pi$
$774$	73.7491	−	127.737i	0.0952830	−	0.165035i
$775$		0			0
$776$		−	10.4406i		−	0.0134544i
$777$	−17.0752	−	271.007i	−0.0219758	−	0.348786i
$778$		−	776.473i		−	0.998037i
$779$	615.594	+	1066.24i	0.790236	+	1.36873i
$780$		0			0
$781$	256.660	−	444.548i	0.328630	−	0.569204i
$782$	82.8106	+	143.432i	0.105896	+	0.183417i
$783$	51.7862			0.0661381
$784$	−118.530	−	156.098i	−0.151186	−	0.199105i
$785$		0			0
$786$	24.5366	+	42.4986i	0.0312170	+	0.0540694i
$787$	−65.0535	+	112.676i	−0.0826601	+	0.143171i	−0.904392	−	0.426703i	$-0.859675\pi$
$787$	−65.0535	+	112.676i	−0.0826601	+	0.143171i	0.821732	+	0.569875i	$0.193008\pi$
$788$	−310.804	−	179.443i	−0.394421	−	0.227719i
$789$	666.893	−	385.031i	0.845238	−	0.487998i
$790$		0			0
$791$	87.3997	+	1387.15i	0.110493	+	1.75367i
$792$		−	63.9553i		−	0.0807516i
$793$	1549.55	−	894.632i	1.95403	−	1.12816i
$794$	−635.111	−	366.681i	−0.799888	−	0.461815i
$795$		0			0
$796$	443.260	−	255.916i	0.556859	−	0.321503i
$797$	−1170.92			−1.46915			−0.734577	−	0.678525i	$-0.762619\pi$
$797$	−1170.92			−1.46915			−0.734577	+	0.678525i	$0.762619\pi$
$798$	−228.727	−	344.193i	−0.286625	−	0.431320i
$799$	−1629.66			−2.03962
$800$		0			0
$801$	36.1359	+	20.8631i	0.0451135	+	0.0260463i
$802$	583.344	+	336.794i	0.727361	+	0.419942i
$803$	−330.342	−	572.170i	−0.411385	−	0.712540i
$804$			230.647i			0.286875i
$805$		0			0
$806$	−199.131			−0.247060
$807$	−251.071	+	144.956i	−0.311116	+	0.179623i
$808$	−258.291	+	447.372i	−0.319667	+	0.553679i
$809$	−102.442	+	177.435i	−0.126628	+	0.219327i	−0.922368	−	0.386312i	$-0.873749\pi$
$809$	−102.442	+	177.435i	−0.126628	+	0.219327i	0.795740	+	0.605639i	$0.207082\pi$
$810$		0			0
$811$		−	541.011i		−	0.667092i	−0.942734	−	0.333546i	$-0.891755\pi$
$811$		−	541.011i		−	0.667092i	0.942734	−	0.333546i	$-0.108245\pi$
$812$	62.0274	−	124.982i	0.0763884	−	0.153919i
$813$			4.48198i			0.00551289i
$814$	−119.365	−	206.746i	−0.146640	−	0.253988i
$815$		0			0
$816$	−72.7026	+	125.925i	−0.0890964	+	0.154319i
$817$	−418.959	−	725.658i	−0.512801	−	0.888198i
$818$	152.285			0.186168
$819$	248.620	+	374.128i	0.303565	+	0.456811i
$820$		0			0
$821$	212.913	+	368.777i	0.259334	+	0.449180i	0.966064	−	0.258304i	$-0.0831636\pi$
$821$	212.913	+	368.777i	0.259334	+	0.449180i	−0.706730	+	0.707484i	$0.749830\pi$
$822$	−105.537	+	182.795i	−0.128391	+	0.222379i
$823$	−667.700	−	385.497i	−0.811301	−	0.468405i	0.0361067	−	0.999348i	$-0.488504\pi$
$823$	−667.700	−	385.497i	−0.811301	−	0.468405i	−0.847407	+	0.530943i	$0.821838\pi$
$824$	223.028	−	128.765i	0.270665	−	0.156268i
$825$		0			0
$826$	−832.081	+	52.4266i	−1.00736	+	0.0634704i
$827$			448.579i			0.542417i	0.962521	+	0.271209i	$0.0874234\pi$
$827$			448.579i			0.542417i	−0.962521	+	0.271209i	$0.912577\pi$
$828$	−28.9950	+	16.7403i	−0.0350181	+	0.0202177i
$829$	737.022	+	425.520i	0.889050	+	0.513293i	0.873632	−	0.486588i	$-0.161759\pi$
$829$	737.022	+	425.520i	0.889050	+	0.513293i	0.0154183	+	0.999881i	$0.495092\pi$
$830$		0			0
$831$	−763.667	+	440.903i	−0.918973	+	0.530569i
$832$	171.125			0.205679
$833$	−398.341	+	948.103i	−0.478201	+	1.13818i
$834$	569.512			0.682868
$835$		0			0
$836$	−314.646	−	181.661i	−0.376370	−	0.217298i
$837$	29.6218	+	17.1022i	0.0353905	+	0.0204327i
$838$	−228.969	−	396.585i	−0.273232	−	0.473252i
$839$			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
$842$	−292.662	+	168.968i	−0.347579	+	0.200675i
$843$	−182.461	+	316.032i	−0.216443	+	0.374890i
$844$	196.891	−	341.025i	0.233283	−	0.404058i
$845$		0			0
$846$		−	329.438i		−	0.389407i
$847$	248.692	+	374.237i	0.293615	+	0.441839i
$848$			199.192i			0.234896i
$849$	34.1964	+	59.2299i	0.0402784	+	0.0697643i
$850$		0			0
$851$	−62.4875	+	108.231i	−0.0734283	+	0.127182i
$852$	−117.961	−	204.315i	−0.138452	−	0.239806i
$853$	−176.785			−0.207251			−0.103626	−	0.994616i	$-0.533044\pi$
$853$	−176.785			−0.207251			−0.103626	+	0.994616i	$0.533044\pi$
$854$	−368.118	+	741.740i	−0.431052	+	0.868547i
$855$		0			0
$856$	−72.8835	−	126.238i	−0.0851442	−	0.147474i
$857$	−623.618	+	1080.14i	−0.727676	+	1.26037i	0.230187	+	0.973146i	$0.426066\pi$
$857$	−623.618	+	1080.14i	−0.727676	+	1.26037i	−0.957863	+	0.287225i	$0.907267\pi$
$858$	342.011	+	197.460i	0.398614	+	0.230140i
$859$	−1319.99	+	762.098i	−1.53666	+	0.887192i	−0.537630	+	0.843181i	$0.680680\pi$
$859$	−1319.99	+	762.098i	−1.53666	+	0.887192i	−0.999031	+	0.0440111i	$0.985986\pi$
$860$		0			0
$861$	554.779	+	275.331i	0.644343	+	0.319781i
$862$		−	271.235i		−	0.314658i
$863$	−1243.69	+	718.043i	−1.44112	+	0.832032i	−0.997925	−	0.0643926i	$-0.979489\pi$
$863$	−1243.69	+	718.043i	−1.44112	+	0.832032i	−0.443197	+	0.896424i	$0.646156\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$		0			0
$866$	−149.520	+	86.3255i	−0.172656	+	0.0996830i
$867$	262.358			0.302605
$868$	76.7547	−	51.0058i	0.0884271	−	0.0587625i
$869$	−744.268			−0.856465
$870$		0			0
$871$	−1233.42	−	712.118i	−1.41610	−	0.817586i
$872$	−93.9658	−	54.2512i	−0.107759	−	0.0622146i
$873$	−5.53698	−	9.59033i	−0.00634248	−	0.0109855i
$874$			190.199i			0.217619i
$875$		0			0
$876$	−303.651			−0.346634
$877$	1031.65	−	595.626i	1.17634	−	0.679163i	0.221179	−	0.975233i	$-0.429010\pi$
$877$	1031.65	−	595.626i	1.17634	−	0.679163i	0.955166	+	0.296070i	$0.0956763\pi$
$878$	177.716	−	307.813i	0.202410	−	0.350584i
$879$	77.5978	−	134.403i	0.0882797	−	0.152905i
$880$		0			0
$881$		−	81.6610i		−	0.0926912i	−0.998925	−	0.0463456i	$-0.985242\pi$
$881$		−	81.6610i		−	0.0926912i	0.998925	−	0.0463456i	$-0.0147576\pi$
$882$	−191.660	−	80.5253i	−0.217302	−	0.0912985i
$883$			506.404i			0.573504i	0.958005	+	0.286752i	$0.0925755\pi$
$883$			506.404i			0.573504i	−0.958005	+	0.286752i	$0.907424\pi$
$884$	−448.935	−	777.578i	−0.507845	−	0.879613i
$885$		0			0
$886$	77.6327	−	134.464i	0.0876215	−	0.151765i
$887$	10.3172	+	17.8700i	0.0116316	+	0.0201466i	0.871783	−	0.489893i	$-0.162964\pi$
$887$	10.3172	+	17.8700i	0.0116316	+	0.0201466i	−0.860151	+	0.510039i	$0.829631\pi$
$888$	−109.720			−0.123559
$889$	−32.6227	−	517.766i	−0.0366959	−	0.582414i
$890$		0			0
$891$	−33.9174	−	58.7467i	−0.0380667	−	0.0659334i
$892$	−431.015	+	746.540i	−0.483200	+	0.836928i
$893$	−1620.76	−	935.747i	−1.81496	−	1.04787i
$894$	466.534	−	269.354i	0.521850	−	0.301290i
$895$		0			0
$896$	−65.9600	+	43.8324i	−0.0736161	+	0.0489201i
$897$		−	206.741i		−	0.230480i
$898$	−987.744	+	570.274i	−1.09994	+	0.635049i
$899$	56.8149	+	32.8021i	0.0631979	+	0.0364873i
$900$		0			0
$901$	905.109	−	522.565i	1.00456	−	0.579983i
$902$	544.501			0.603659
$903$	−377.570	−	187.384i	−0.418128	−	0.207513i
$904$	561.606			0.621245
$905$		0			0
$906$	553.499	+	319.563i	0.610926	+	0.352718i
$907$	222.402	+	128.404i	0.245206	+	0.141570i	0.617567	−	0.786518i	$-0.288118\pi$
$907$	222.402	+	128.404i	0.245206	+	0.141570i	−0.372361	+	0.928088i	$0.621452\pi$
$908$	175.096	+	303.275i	0.192837	+	0.334003i
$909$			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	$0.272461\pi$
$912$	−144.611	+	83.4914i	−0.158565	+	0.0915476i
$913$	101.544	−	175.880i	0.111220	−	0.192639i
$914$	546.207	−	946.058i	0.597600	−	1.03507i
$915$		0			0
$916$			67.1383i			0.0732951i
$917$	116.800	−	77.6173i	0.127372	−	0.0846427i
$918$			154.226i			0.168002i
$919$	−446.876	−	774.012i	−0.486263	−	0.842232i	0.513612	−	0.858022i	$-0.328307\pi$
$919$	−446.876	−	774.012i	−0.486263	−	0.842232i	−0.999875	+	0.0157900i	$0.994974\pi$
$920$		0			0
$921$	−407.446	+	705.717i	−0.442395	+	0.766251i
$922$	−561.168	−	971.971i	−0.608642	−	1.05420i
$923$	1456.81			1.57834
$924$	−182.406	+	11.4928i	−0.197409	+	0.0124381i
$925$		0			0
$926$	−193.908	−	335.859i	−0.209404	−	0.362698i
$927$	136.576	−	236.556i	0.147331	−	0.255185i
$928$	−48.8245	−	28.1888i	−0.0526126	−	0.0303759i
$929$	−295.237	+	170.455i	−0.317801	+	0.183482i	−0.650412	−	0.759582i	$-0.725404\pi$
$929$	−295.237	+	170.455i	−0.317801	+	0.183482i	0.332611	+	0.943064i	$0.392070\pi$
$930$		0			0
$931$	−940.565	+	714.199i	−1.01027	+	0.767131i
$932$		−	309.827i		−	0.332432i
$933$	−376.948	+	217.631i	−0.404017	+	0.233259i
$934$	−486.994	−	281.166i	−0.521407	−	0.301034i
$935$		0			0
$936$	157.188	−	90.7528i	0.167936	−	0.0969581i
$937$	217.347			0.231961			0.115981	−	0.993251i	$-0.462999\pi$
$937$	217.347			0.231961			0.115981	+	0.993251i	$0.462999\pi$
$938$	657.825	−	41.4473i	0.701306	−	0.0441869i
$939$	−672.834			−0.716544
$940$		0			0
$941$	1226.68	+	708.226i	1.30360	+	0.752631i	0.981019	−	0.193912i	$-0.0621177\pi$
$941$	1226.68	+	708.226i	1.30360	+	0.752631i	0.322577	+	0.946543i	$0.395451\pi$
$942$	242.235	+	139.855i	0.257150	+	0.148466i
$943$	−142.523	−	246.857i	−0.151138	−	0.261779i
$944$			336.878i			0.356862i
$945$		0			0
$946$	−370.574			−0.391728
$947$	1199.21	−	692.365i	1.26633	−	0.731114i	0.292035	−	0.956408i	$-0.405667\pi$
$947$	1199.21	−	692.365i	1.26633	−	0.731114i	0.974291	+	0.225294i	$0.0723341\pi$
$948$	−171.033	+	296.238i	−0.180415	+	0.312487i
$949$	937.515	−	1623.82i	0.987897	−	1.71109i
$950$		0			0
$951$			258.733i			0.272064i
$952$	372.212	+	184.725i	0.390979	+	0.194039i
$953$			1365.38i			1.43272i	0.697732	+	0.716359i	$0.254193\pi$
$953$			1365.38i			1.43272i	−0.697732	+	0.716359i	$0.745807\pi$
$954$	105.637	+	182.969i	0.110731	+	0.191792i
$955$		0			0
$956$	−316.591	+	548.352i	−0.331162	+	0.573590i
$957$	−65.0538	−	112.676i	−0.0679768	−	0.117739i
$958$	270.380			0.282234
$959$	540.313	+	268.152i	0.563413	+	0.279616i
$960$		0			0
$961$	−458.834	−	794.725i	−0.477455	−	0.826977i
$962$	338.758	−	586.747i	0.352140	−	0.609924i
$963$	−133.895	−	77.3046i	−0.139040	−	0.0802748i
$964$	404.439	−	233.503i	0.419542	−	0.242223i
$965$		0			0
$966$	52.9551	+	79.6880i	0.0548189	+	0.0824927i
$967$			1718.05i			1.77668i	0.459185	+	0.888341i	$0.348142\pi$
$967$			1718.05i			1.77668i	−0.459185	+	0.888341i	$0.651858\pi$
$968$	157.234	−	90.7792i	0.162432	−	0.0937802i
$969$	758.755	+	438.068i	0.783029	+	0.452082i
$970$		0			0
$971$	387.463	−	223.702i	0.399035	−	0.230383i	−0.287033	−	0.957921i	$-0.592669\pi$
$971$	387.463	−	223.702i	0.399035	−	0.230383i	0.686068	+	0.727538i	$0.259335\pi$
$972$	−31.1769			−0.0320750
$973$	−102.341	−	1624.29i	−0.105181	−	1.66937i
$974$	−268.727			−0.275900
$975$		0			0
$976$	289.762	+	167.294i	0.296887	+	0.171408i
$977$	−1576.94	−	910.447i	−1.61406	−	0.931880i	−0.988415	−	0.151775i	$-0.951501\pi$
$977$	−1576.94	−	910.447i	−1.61406	−	0.931880i	−0.625648	−	0.780105i	$-0.715165\pi$
$978$	−59.6648	−	103.343i	−0.0610070	−	0.105667i
$979$		−	104.833i		−	0.107082i
$980$		0			0
$981$	−115.084			−0.117313
$982$	−258.891	+	149.471i	−0.263637	+	0.152211i
$983$	830.607	−	1438.65i	0.844972	−	1.46353i	−0.0406735	−	0.999172i	$-0.512950\pi$
$983$	830.607	−	1438.65i	0.844972	−	1.46353i	0.885646	−	0.464362i	$-0.153716\pi$
$984$	125.126	−	216.725i	0.127161	−	0.220249i
$985$		0			0
$986$			295.806i			0.300006i
$987$	−939.584	+	59.2000i	−0.951960	+	0.0599797i
$988$		−	1031.11i		−	1.04363i
$989$	96.9978	+	168.005i	0.0980767	+	0.169874i
$990$		0			0
$991$	−275.795	+	477.690i	−0.278299	+	0.482029i	−0.970962	−	0.239233i	$-0.923104\pi$
$991$	−275.795	+	477.690i	−0.278299	+	0.482029i	0.692663	+	0.721261i	$0.256437\pi$
$992$	−18.6185	−	32.2482i	−0.0187686	−	0.0325082i
$993$	−815.676			−0.821426
$994$	−561.525	+	373.150i	−0.564914	+	0.375403i
$995$		0			0
$996$	−46.6697	−	80.8344i	−0.0468572	−	0.0811590i
$997$	−902.319	+	1562.86i	−0.905034	+	1.56757i	−0.0841629	+	0.996452i	$0.526822\pi$
$997$	−902.319	+	1562.86i	−0.905034	+	1.56757i	−0.820871	+	0.571113i	$0.806512\pi$
$998$	−310.751	−	179.412i	−0.311374	−	0.179772i
$999$	−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.q.b.199.6		16
5.2	odd	4		1050.3.p.d.451.4	yes	8
5.3	odd	4		1050.3.p.c.451.1	✓	8
5.4	even	2	inner	1050.3.q.b.199.3		16
7.5	odd	6	inner	1050.3.q.b.649.3		16
35.12	even	12		1050.3.p.d.901.4	yes	8
35.19	odd	6	inner	1050.3.q.b.649.6		16
35.33	even	12		1050.3.p.c.901.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.c.451.1	✓	8	5.3	odd	4
1050.3.p.c.901.1	yes	8	35.33	even	12
1050.3.p.d.451.4	yes	8	5.2	odd	4
1050.3.p.d.901.4	yes	8	35.12	even	12
1050.3.q.b.199.3		16	5.4	even	2	inner
1050.3.q.b.199.6		16	1.1	even	1	trivial
1050.3.q.b.649.3		16	7.5	odd	6	inner
1050.3.q.b.649.6		16	35.19	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.98615 - 0.440173i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.98615 - 0.440173i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-3.76860 + 6.52741i) q^{11} +(1.73205 + 3.00000i) q^{12} -21.3906 q^{13} +(8.24500 - 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-10.4937 + 18.1757i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(-20.8728 + 12.0509i) q^{19} +(-5.38992 + 10.8604i) q^{21} +10.6592i q^{22} +(4.83250 - 2.79005i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-26.1981 + 15.1255i) q^{26} +5.19615 q^{27} +(6.22374 - 12.5405i) q^{28} +9.96625 q^{29} +(5.70073 + 3.29132i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-6.52741 - 11.3058i) q^{33} +29.6807i q^{34} -6.00000 q^{36} +(-19.3960 + 11.1983i) q^{37} +(-17.0426 + 29.5187i) q^{38} +(18.5248 - 32.0860i) q^{39} -51.0827i q^{41} +(1.07820 + 17.1125i) q^{42} +34.7656i q^{43} +(7.53720 + 13.0548i) q^{44} +(3.94572 - 6.83419i) q^{46} +(38.8246 + 67.2462i) q^{47} +6.92820 q^{48} +(48.6125 - 6.15023i) q^{49} +(-18.1757 - 31.4812i) q^{51} +(-21.3906 + 37.0497i) q^{52} +(-43.1262 - 24.8989i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} -41.7457i q^{57} +(12.2061 - 7.04720i) q^{58} +(-72.9362 - 42.1098i) q^{59} +(-72.4404 + 41.8235i) q^{61} +9.30925 q^{62} +(-11.6228 - 17.4903i) q^{63} -8.00000 q^{64} +(-15.9888 - 9.23115i) q^{66} +(57.6618 + 33.2911i) q^{67} +(20.9874 + 36.3513i) q^{68} +9.66501i q^{69} -68.1049 q^{71} +(-7.34847 + 4.24264i) q^{72} +(-43.8283 + 75.9128i) q^{73} +(-15.8368 + 27.4301i) q^{74} +48.2038i q^{76} +(-23.4548 + 47.2603i) q^{77} -52.3962i q^{78} +(49.3730 + 85.5165i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-36.1209 - 62.5632i) q^{82} -26.9448 q^{83} +(13.4209 + 20.1960i) q^{84} +(24.5830 + 42.5790i) q^{86} +(-8.63103 + 14.9494i) q^{87} +(18.4623 + 10.6592i) q^{88} +(-12.0453 + 6.95436i) q^{89} +(-149.438 + 9.41559i) q^{91} -11.1602i q^{92} +(-9.87395 + 5.70073i) q^{93} +(95.1005 + 54.9063i) q^{94} +(8.48528 - 4.89898i) q^{96} +3.69132 q^{97} +(55.1890 - 41.9067i) q^{98} +22.6116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) 16 * q + 16 * q^4 - 24 * q^9	\( 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 32 q^{14} - 32 q^{16} - 144 q^{19} - 144 q^{26} + 48 q^{29} + 192 q^{31} - 96 q^{36} + 24 q^{39} + 16 q^{44} + 64 q^{46} + 528 q^{49} + 48 q^{51} + 80 q^{56} - 624 q^{59} - 408 q^{61} - 128 q^{64} - 72 q^{66} - 128 q^{71} + 32 q^{74} + 288 q^{79} - 72 q^{81} + 352 q^{86} + 672 q^{89} - 592 q^{91} - 72 q^{94} + 48 q^{99}+O(q^{100}) \) 16 * q + 16 * q^4 - 24 * q^9 - 8 * q^11 + 32 * q^14 - 32 * q^16 - 144 * q^19 - 144 * q^26 + 48 * q^29 + 192 * q^31 - 96 * q^36 + 24 * q^39 + 16 * q^44 + 64 * q^46 + 528 * q^49 + 48 * q^51 + 80 * q^56 - 624 * q^59 - 408 * q^61 - 128 * q^64 - 72 * q^66 - 128 * q^71 + 32 * q^74 + 288 * q^79 - 72 * q^81 + 352 * q^86 + 672 * q^89 - 592 * q^91 - 72 * q^94 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more