LMFDB - Embedded newform 1950.2.y.n.199.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(49,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.y (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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 87 x^{10} - 380 x^{9} + 2556 x^{8} - 8010 x^{7} + 29687 x^{6} - 62556 x^{5} + \cdots + 14089 $ x^12 - 6x^11 + 87x^10 - 380x^9 + 2556x^8 - 8010x^7 + 29687x^6 - 62556x^5 + 115386x^4 - 135130x^3 + 113253x^2 - 54888*x + 14089
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			199.6
Root			$0.500000 - 4.41310i$ of defining polynomial
Character	$\chi$	$=$	1950.199
Dual form			1950.2.y.n.49.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(1.27354 + 2.20583i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(1.27354 + 2.20583i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.15713 - 0.668069i) q^{11} -1.00000i q^{12} +(-3.21677 + 1.62862i) q^{13} +2.54707 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.54870 - 1.47149i) q^{17} +1.00000 q^{18} +(6.05291 - 3.49465i) q^{19} +2.54707i q^{21} +(-1.15713 + 0.668069i) q^{22} +(3.70583 + 2.13956i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-0.197956 + 3.60011i) q^{26} +1.00000i q^{27} +(1.27354 - 2.20583i) q^{28} +(1.07721 - 1.86578i) q^{29} +8.74779i q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.668069 - 1.15713i) q^{33} -2.94298i q^{34} +(0.500000 - 0.866025i) q^{36} +(-2.62862 + 4.55291i) q^{37} -6.98929i q^{38} +(-3.60011 - 0.197956i) q^{39} +(2.54870 + 1.47149i) q^{41} +(2.20583 + 1.27354i) q^{42} +(4.70558 - 2.71677i) q^{43} +1.33614i q^{44} +(3.70583 - 2.13956i) q^{46} +11.6908 q^{47} +(-0.866025 + 0.500000i) q^{48} +(0.256215 - 0.443778i) q^{49} +2.94298 q^{51} +(3.01881 + 1.97149i) q^{52} +8.74779i q^{53} +(0.866025 + 0.500000i) q^{54} +(-1.27354 - 2.20583i) q^{56} +6.98929 q^{57} +(-1.07721 - 1.86578i) q^{58} +(8.25873 - 4.76818i) q^{59} +(3.62862 + 6.28496i) q^{61} +(7.57581 + 4.37390i) q^{62} +(-1.27354 + 2.20583i) q^{63} +1.00000 q^{64} -1.33614 q^{66} +(-3.04334 + 5.27123i) q^{67} +(-2.54870 - 1.47149i) q^{68} +(2.13956 + 3.70583i) q^{69} +(-11.3470 + 6.55122i) q^{71} +(-0.500000 - 0.866025i) q^{72} +2.59614 q^{73} +(2.62862 + 4.55291i) q^{74} +(-6.05291 - 3.49465i) q^{76} -3.40324i q^{77} +(-1.97149 + 3.01881i) q^{78} -13.9773 q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.54870 - 1.47149i) q^{82} +12.2440 q^{83} +(2.20583 - 1.27354i) q^{84} -5.43353i q^{86} +(1.86578 - 1.07721i) q^{87} +(1.15713 + 0.668069i) q^{88} +(-10.0591 - 5.80763i) q^{89} +(-7.68913 - 5.02153i) q^{91} -4.27912i q^{92} +(-4.37390 + 7.57581i) q^{93} +(5.84539 - 10.1245i) q^{94} +1.00000i q^{96} +(0.765663 + 1.32617i) q^{97} +(-0.256215 - 0.443778i) q^{98} -1.33614i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} - 4 q^{7} - 12 q^{8} + 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - 6 * q^4 - 4 * q^7 - 12 * q^8 + 6 * q^9	$ 12 q + 6 q^{2} - 6 q^{4} - 4 q^{7} - 12 q^{8} + 6 q^{9} - 12 q^{11} + 4 q^{13} - 8 q^{14} - 6 q^{16} + 12 q^{18} + 6 q^{19} - 12 q^{22} + 12 q^{23} - 4 q^{26} - 4 q^{28} + 6 q^{32} + 4 q^{33} + 6 q^{36} - 12 q^{37} - 6 q^{39} - 6 q^{42} + 12 q^{43} + 12 q^{46} + 16 q^{47} - 32 q^{49} - 8 q^{52} + 4 q^{56} + 24 q^{57} + 24 q^{61} + 4 q^{63} + 12 q^{64} + 8 q^{66} + 24 q^{67} - 4 q^{69} + 12 q^{71} - 6 q^{72} - 40 q^{73} + 12 q^{74} - 6 q^{76} - 6 q^{78} - 52 q^{79} - 6 q^{81} + 32 q^{83} - 6 q^{84} + 12 q^{88} - 24 q^{89} - 54 q^{91} - 8 q^{93} + 8 q^{94} + 24 q^{97} + 32 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 - 4 * q^7 - 12 * q^8 + 6 * q^9 - 12 * q^11 + 4 * q^13 - 8 * q^14 - 6 * q^16 + 12 * q^18 + 6 * q^19 - 12 * q^22 + 12 * q^23 - 4 * q^26 - 4 * q^28 + 6 * q^32 + 4 * q^33 + 6 * q^36 - 12 * q^37 - 6 * q^39 - 6 * q^42 + 12 * q^43 + 12 * q^46 + 16 * q^47 - 32 * q^49 - 8 * q^52 + 4 * q^56 + 24 * q^57 + 24 * q^61 + 4 * q^63 + 12 * q^64 + 8 * q^66 + 24 * q^67 - 4 * q^69 + 12 * q^71 - 6 * q^72 - 40 * q^73 + 12 * q^74 - 6 * q^76 - 6 * q^78 - 52 * q^79 - 6 * q^81 + 32 * q^83 - 6 * q^84 + 12 * q^88 - 24 * q^89 - 54 * q^91 - 8 * q^93 + 8 * q^94 + 24 * q^97 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	1.27354	+	2.20583i	0.481351	+	0.833725i	0.999771	−	0.0214016i	$-0.00681287\pi$
$7$	1.27354	+	2.20583i	0.481351	+	0.833725i	−0.518420	+	0.855126i	$0.673480\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−1.15713	−	0.668069i	−0.348888	−	0.201430i	0.315307	−	0.948990i	$-0.397892\pi$
$11$	−1.15713	−	0.668069i	−0.348888	−	0.201430i	−0.664195	+	0.747559i	$0.731226\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−3.21677	+	1.62862i	−0.892171	+	0.451698i
$13$	−3.21677	+	1.62862i	−0.892171	+	0.451698i
$14$	2.54707			0.680733
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.54870	−	1.47149i	0.618150	−	0.356889i	−0.157998	−	0.987439i	$-0.550504\pi$
$17$	2.54870	−	1.47149i	0.618150	−	0.356889i	0.776148	+	0.630550i	$0.217171\pi$
$18$	1.00000			0.235702
$19$	6.05291	−	3.49465i	1.38863	−	0.801727i	0.395471	−	0.918479i	$-0.370581\pi$
$19$	6.05291	−	3.49465i	1.38863	−	0.801727i	0.993161	+	0.116752i	$0.0372481\pi$
$20$		0			0
$21$			2.54707i			0.555816i
$22$	−1.15713	+	0.668069i	−0.246701	+	0.142433i
$23$	3.70583	+	2.13956i	0.772719	+	0.446129i	0.833844	−	0.552001i	$-0.186135\pi$
$23$	3.70583	+	2.13956i	0.772719	+	0.446129i	−0.0611250	+	0.998130i	$0.519469\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$		0			0
$26$	−0.197956	+	3.60011i	−0.0388224	+	0.706040i
$27$			1.00000i			0.192450i
$28$	1.27354	−	2.20583i	0.240676	−	0.416862i
$29$	1.07721	−	1.86578i	0.200032	−	0.346466i	−0.748506	−	0.663128i	$-0.769229\pi$
$29$	1.07721	−	1.86578i	0.200032	−	0.346466i	0.948539	+	0.316662i	$0.102562\pi$
$30$		0			0
$31$			8.74779i			1.57115i	0.618766	+	0.785575i	$0.287633\pi$
$31$			8.74779i			1.57115i	−0.618766	+	0.785575i	$0.712367\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.668069	−	1.15713i	−0.116296	−	0.201430i
$34$		−	2.94298i		−	0.504717i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−2.62862	+	4.55291i	−0.432143	+	0.748493i	−0.997058	−	0.0766560i	$-0.975576\pi$
$37$	−2.62862	+	4.55291i	−0.432143	+	0.748493i	0.564915	+	0.825149i	$0.308909\pi$
$38$		−	6.98929i		−	1.13381i
$39$	−3.60011	−	0.197956i	−0.576479	−	0.0316983i
$40$		0			0
$41$	2.54870	+	1.47149i	0.398040	+	0.229808i	0.685638	−	0.727943i	$-0.259523\pi$
$41$	2.54870	+	1.47149i	0.398040	+	0.229808i	−0.287598	+	0.957751i	$0.592857\pi$
$42$	2.20583	+	1.27354i	0.340367	+	0.196511i
$43$	4.70558	−	2.71677i	0.717594	−	0.414303i	−0.0962724	−	0.995355i	$-0.530692\pi$
$43$	4.70558	−	2.71677i	0.717594	−	0.414303i	0.813867	+	0.581052i	$0.197359\pi$
$44$			1.33614i			0.201430i
$45$		0			0
$46$	3.70583	−	2.13956i	0.546395	−	0.315461i
$47$	11.6908			1.70528			0.852638	−	0.522503i	$-0.175002\pi$
$47$	11.6908			1.70528			0.852638	+	0.522503i	$0.175002\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	0.256215	−	0.443778i	0.0366022	−	0.0633968i
$50$		0			0
$51$	2.94298			0.412100
$52$	3.01881	+	1.97149i	0.418634	+	0.273397i
$53$			8.74779i			1.20160i	0.799399	+	0.600801i	$0.205152\pi$
$53$			8.74779i			1.20160i	−0.799399	+	0.600801i	$0.794848\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$		0			0
$56$	−1.27354	−	2.20583i	−0.170183	−	0.294766i
$57$	6.98929			0.925755
$58$	−1.07721	−	1.86578i	−0.141444	−	0.244988i
$59$	8.25873	−	4.76818i	1.07520	−	0.620764i	0.145599	−	0.989344i	$-0.453489\pi$
$59$	8.25873	−	4.76818i	1.07520	−	0.620764i	0.929596	+	0.368579i	$0.120156\pi$
$60$		0			0
$61$	3.62862	+	6.28496i	0.464597	+	0.804706i	0.999183	−	0.0404079i	$-0.0128657\pi$
$61$	3.62862	+	6.28496i	0.464597	+	0.804706i	−0.534586	+	0.845114i	$0.679532\pi$
$62$	7.57581	+	4.37390i	0.962129	+	0.555486i
$63$	−1.27354	+	2.20583i	−0.160450	+	0.277908i
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.33614			−0.164467
$67$	−3.04334	+	5.27123i	−0.371804	+	0.643983i	−0.989843	−	0.142164i	$-0.954594\pi$
$67$	−3.04334	+	5.27123i	−0.371804	+	0.643983i	0.618039	+	0.786147i	$0.287927\pi$
$68$	−2.54870	−	1.47149i	−0.309075	−	0.178445i
$69$	2.13956	+	3.70583i	0.257573	+	0.446129i
$70$		0			0
$71$	−11.3470	+	6.55122i	−1.34665	+	0.777486i	−0.987773	−	0.155900i	$-0.950172\pi$
$71$	−11.3470	+	6.55122i	−1.34665	+	0.777486i	−0.358873	+	0.933386i	$0.616839\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	2.59614			0.303855			0.151927	−	0.988392i	$-0.451452\pi$
$73$	2.59614			0.303855			0.151927	+	0.988392i	$0.451452\pi$
$74$	2.62862	+	4.55291i	0.305571	+	0.529265i
$75$		0			0
$76$	−6.05291	−	3.49465i	−0.694316	−	0.400863i
$77$		−	3.40324i		−	0.387835i
$78$	−1.97149	+	3.01881i	−0.223227	+	0.341813i
$79$	−13.9773			−1.57257			−0.786283	−	0.617867i	$-0.787997\pi$
$79$	−13.9773			−1.57257			−0.786283	+	0.617867i	$0.787997\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.54870	−	1.47149i	0.281457	−	0.162499i
$83$	12.2440			1.34395			0.671976	−	0.740573i	$-0.265446\pi$
$83$	12.2440			1.34395			0.671976	+	0.740573i	$0.265446\pi$
$84$	2.20583	−	1.27354i	0.240676	−	0.138954i
$85$		0			0
$86$		−	5.43353i		−	0.585913i
$87$	1.86578	−	1.07721i	0.200032	−	0.115489i
$88$	1.15713	+	0.668069i	0.123350	+	0.0712164i
$89$	−10.0591	−	5.80763i	−1.06626	−	0.615608i	−0.139105	−	0.990278i	$-0.544423\pi$
$89$	−10.0591	−	5.80763i	−1.06626	−	0.615608i	−0.927158	+	0.374670i	$0.877756\pi$
$90$		0			0
$91$	−7.68913	−	5.02153i	−0.806039	−	0.526399i
$92$		−	4.27912i		−	0.446129i
$93$	−4.37390	+	7.57581i	−0.453552	+	0.785575i
$94$	5.84539	−	10.1245i	0.602906	−	1.04426i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	0.765663	+	1.32617i	0.0777413	+	0.134652i	0.902275	−	0.431161i	$-0.141896\pi$
$97$	0.765663	+	1.32617i	0.0777413	+	0.134652i	−0.824534	+	0.565813i	$0.808563\pi$
$98$	−0.256215	−	0.443778i	−0.0258816	−	0.0448283i
$99$		−	1.33614i		−	0.134287i
$100$		0			0
$101$	0.258932	−	0.448484i	0.0257647	−	0.0446258i	−0.852856	−	0.522147i	$-0.825131\pi$
$101$	0.258932	−	0.448484i	0.0257647	−	0.0446258i	0.878620	+	0.477521i	$0.158465\pi$
$102$	1.47149	−	2.54870i	0.145699	−	0.252359i
$103$			2.42318i			0.238763i	0.992848	+	0.119382i	$0.0380912\pi$
$103$			2.42318i			0.238763i	−0.992848	+	0.119382i	$0.961909\pi$
$104$	3.21677	−	1.62862i	0.315430	−	0.159699i
$105$		0			0
$106$	7.57581	+	4.37390i	0.735828	+	0.424830i
$107$	5.30455	+	3.06258i	0.512810	+	0.296071i	0.733988	−	0.679163i	$-0.237657\pi$
$107$	5.30455	+	3.06258i	0.512810	+	0.296071i	−0.221178	+	0.975233i	$0.570990\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$			0.547569i			0.0524476i	0.999656	+	0.0262238i	$0.00834825\pi$
$109$			0.547569i			0.0524476i	−0.999656	+	0.0262238i	$0.991652\pi$
$110$		0			0
$111$	−4.55291	+	2.62862i	−0.432143	+	0.249498i
$112$	−2.54707			−0.240676
$113$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$113$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$114$	3.49465	−	6.05291i	0.327304	−	0.566907i
$115$		0			0
$116$	−2.15441			−0.200032
$117$	−3.01881	−	1.97149i	−0.279089	−	0.182264i
$118$		−	9.53636i		−	0.877894i
$119$	6.49171	+	3.74799i	0.595094	+	0.343578i
$120$		0			0
$121$	−4.60737	−	7.98019i	−0.418852	−	0.725472i
$122$	7.25724			0.657040
$123$	1.47149	+	2.54870i	0.132680	+	0.229808i
$124$	7.57581	−	4.37390i	0.680328	−	0.392788i
$125$		0			0
$126$	1.27354	+	2.20583i	0.113456	+	0.196511i
$127$	−6.16530	−	3.55954i	−0.547082	−	0.315858i	0.200862	−	0.979619i	$-0.435626\pi$
$127$	−6.16530	−	3.55954i	−0.547082	−	0.315858i	−0.747944	+	0.663762i	$0.768959\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	5.43353			0.478396
$130$		0			0
$131$	−9.42233			−0.823233			−0.411616	−	0.911357i	$-0.635036\pi$
$131$	−9.42233			−0.823233			−0.411616	+	0.911357i	$0.635036\pi$
$132$	−0.668069	+	1.15713i	−0.0581480	+	0.100715i
$133$	15.4172	+	8.90111i	1.33684	+	0.771824i
$134$	3.04334	+	5.27123i	0.262905	+	0.455365i
$135$		0			0
$136$	−2.54870	+	1.47149i	−0.218549	+	0.126179i
$137$	−9.27336	−	16.0619i	−0.792277	−	1.37226i	−0.924554	−	0.381050i	$-0.875562\pi$
$137$	−9.27336	−	16.0619i	−0.792277	−	1.37226i	0.132278	−	0.991213i	$-0.457771\pi$
$138$	4.27912			0.364263
$139$	−9.85885	−	17.0760i	−0.836216	−	1.44837i	−0.893036	−	0.449985i	$-0.851429\pi$
$139$	−9.85885	−	17.0760i	−0.836216	−	1.44837i	0.0568196	−	0.998384i	$-0.481904\pi$
$140$		0			0
$141$	10.1245	+	5.84539i	0.852638	+	0.492271i
$142$			13.1024i			1.09953i
$143$	4.81025	+	0.264497i	0.402253	+	0.0221183i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	1.29807	−	2.24832i	0.107429	−	0.186072i
$147$	0.443778	−	0.256215i	0.0366022	−	0.0211323i
$148$	5.25724			0.432143
$149$	6.84990	−	3.95479i	0.561165	−	0.323989i	−0.192448	−	0.981307i	$-0.561643\pi$
$149$	6.84990	−	3.95479i	0.561165	−	0.323989i	0.753613	+	0.657318i	$0.228309\pi$
$150$		0			0
$151$		−	17.1864i		−	1.39861i	−0.714823	−	0.699305i	$-0.753493\pi$
$151$		−	17.1864i		−	1.39861i	0.714823	−	0.699305i	$-0.246507\pi$
$152$	−6.05291	+	3.49465i	−0.490956	+	0.283453i
$153$	2.54870	+	1.47149i	0.206050	+	0.118963i
$154$	−2.94729	−	1.70162i	−0.237500	−	0.137120i
$155$		0			0
$156$	1.62862	+	3.21677i	0.130394	+	0.257548i
$157$			2.56103i			0.204393i	0.994764	+	0.102196i	$0.0325870\pi$
$157$			2.56103i			0.204393i	−0.994764	+	0.102196i	$0.967413\pi$
$158$	−6.98864	+	12.1047i	−0.555986	+	0.962996i
$159$	−4.37390	+	7.57581i	−0.346873	+	0.600801i
$160$		0			0
$161$			10.8992i			0.858979i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	8.80763	+	15.2553i	0.689867	+	1.19488i	0.971881	+	0.235474i	$0.0756643\pi$
$163$	8.80763	+	15.2553i	0.689867	+	1.19488i	−0.282014	+	0.959410i	$0.591002\pi$
$164$		−	2.94298i		−	0.229808i
$165$		0			0
$166$	6.12199	−	10.6036i	0.475159	−	0.822999i
$167$	2.13956	−	3.70583i	0.165564	−	0.286766i	−0.771291	−	0.636482i	$-0.780389\pi$
$167$	2.13956	−	3.70583i	0.165564	−	0.286766i	0.936855	+	0.349717i	$0.113722\pi$
$168$		−	2.54707i		−	0.196511i
$169$	7.69518	−	10.4778i	0.591937	−	0.805984i
$170$		0			0
$171$	6.05291	+	3.49465i	0.462877	+	0.267242i
$172$	−4.70558	−	2.71677i	−0.358797	−	0.207152i
$173$	7.31290	−	4.22210i	0.555989	−	0.321001i	−0.195545	−	0.980695i	$-0.562647\pi$
$173$	7.31290	−	4.22210i	0.555989	−	0.321001i	0.751534	+	0.659694i	$0.229314\pi$
$174$		−	2.15441i		−	0.163326i
$175$		0			0
$176$	1.15713	−	0.668069i	0.0872220	−	0.0503576i
$177$	9.53636			0.716797
$178$	−10.0591	+	5.80763i	−0.753962	+	0.435300i
$179$	−0.982856	+	1.70236i	−0.0734621	+	0.127240i	−0.900416	−	0.435029i	$-0.856738\pi$
$179$	−0.982856	+	1.70236i	−0.0734621	+	0.127240i	0.826954	+	0.562269i	$0.190071\pi$
$180$		0			0
$181$	−6.61526			−0.491708			−0.245854	−	0.969307i	$-0.579068\pi$
$181$	−6.61526			−0.491708			−0.245854	+	0.969307i	$0.579068\pi$
$182$	−8.19333	+	4.14821i	−0.607330	+	0.307486i
$183$			7.25724i			0.536471i
$184$	−3.70583	−	2.13956i	−0.273197	−	0.157731i
$185$		0			0
$186$	4.37390	+	7.57581i	0.320710	+	0.555486i
$187$	−3.93223			−0.287553
$188$	−5.84539	−	10.1245i	−0.426319	−	0.738406i
$189$	−2.20583	+	1.27354i	−0.160450	+	0.0926361i
$190$		0			0
$191$	−5.21624	−	9.03479i	−0.377434	−	0.653735i	0.613254	−	0.789886i	$-0.289860\pi$
$191$	−5.21624	−	9.03479i	−0.377434	−	0.653735i	−0.990688	+	0.136151i	$0.956527\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	0.407532	−	0.705866i	0.0293348	−	0.0508093i	−0.850985	−	0.525189i	$-0.823994\pi$
$193$	0.407532	−	0.705866i	0.0293348	−	0.0508093i	0.880320	+	0.474380i	$0.157328\pi$
$194$	1.53133			0.109943
$195$		0			0
$196$	−0.512430			−0.0366022
$197$	8.41742	−	14.5794i	0.599716	−	1.03874i	−0.393146	−	0.919476i	$-0.628613\pi$
$197$	8.41742	−	14.5794i	0.599716	−	1.03874i	0.992863	−	0.119263i	$-0.0380532\pi$
$198$	−1.15713	−	0.668069i	−0.0822337	−	0.0474776i
$199$	−3.36600	−	5.83009i	−0.238610	−	0.413284i	0.721706	−	0.692200i	$-0.243358\pi$
$199$	−3.36600	−	5.83009i	−0.238610	−	0.413284i	−0.960316	+	0.278916i	$0.910025\pi$
$200$		0			0
$201$	−5.27123	+	3.04334i	−0.371804	+	0.214661i
$202$	−0.258932	−	0.448484i	−0.0182184	−	0.0315552i
$203$	5.48744			0.385143
$204$	−1.47149	−	2.54870i	−0.103025	−	0.178445i
$205$		0			0
$206$	2.09854	+	1.21159i	0.146212	+	0.0844155i
$207$			4.27912i			0.297420i
$208$	0.197956	−	3.60011i	0.0137258	−	0.249623i
$209$	−9.33867			−0.645969
$210$		0			0
$211$	6.00378	−	10.3989i	0.413317	−	0.715887i	−0.581933	−	0.813237i	$-0.697703\pi$
$211$	6.00378	−	10.3989i	0.413317	−	0.715887i	0.995250	+	0.0973501i	$0.0310367\pi$
$212$	7.57581	−	4.37390i	0.520309	−	0.300401i
$213$	−13.1024			−0.897764
$214$	5.30455	−	3.06258i	0.362611	−	0.209354i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−19.2961	+	11.1406i	−1.30991	+	0.756275i
$218$	0.474209	+	0.273784i	0.0321175	+	0.0185430i
$219$	2.24832	+	1.29807i	0.151927	+	0.0877154i
$220$		0			0
$221$	−5.80207	+	8.88431i	−0.390289	+	0.597623i
$222$			5.25724i			0.352843i
$223$	−0.253346	+	0.438808i	−0.0169653	+	0.0293848i	−0.874383	−	0.485236i	$-0.838734\pi$
$223$	−0.253346	+	0.438808i	−0.0169653	+	0.0293848i	0.857418	+	0.514620i	$0.172067\pi$
$224$	−1.27354	+	2.20583i	−0.0850917	+	0.147383i
$225$		0			0
$226$		0			0
$227$	−2.07973	−	3.60219i	−0.138036	−	0.239086i	0.788717	−	0.614756i	$-0.210746\pi$
$227$	−2.07973	−	3.60219i	−0.138036	−	0.239086i	−0.926753	+	0.375671i	$0.877412\pi$
$228$	−3.49465	−	6.05291i	−0.231439	−	0.400863i
$229$			22.3688i			1.47817i	0.673611	+	0.739086i	$0.264742\pi$
$229$			22.3688i			1.47817i	−0.673611	+	0.739086i	$0.735258\pi$
$230$		0			0
$231$	1.70162	−	2.94729i	0.111958	−	0.193918i
$232$	−1.07721	+	1.86578i	−0.0707221	+	0.122494i
$233$			8.82331i			0.578034i	0.957324	+	0.289017i	$0.0933285\pi$
$233$			8.82331i			0.578034i	−0.957324	+	0.289017i	$0.906672\pi$
$234$	−3.21677	+	1.62862i	−0.210287	+	0.106466i
$235$		0			0
$236$	−8.25873	−	4.76818i	−0.537598	−	0.310382i
$237$	−12.1047	−	6.98864i	−0.786283	−	0.453961i
$238$	6.49171	−	3.74799i	0.420795	−	0.242946i
$239$		−	25.6233i		−	1.65743i	−0.559669	−	0.828716i	$-0.689072\pi$
$239$		−	25.6233i		−	1.65743i	0.559669	−	0.828716i	$-0.310928\pi$
$240$		0			0
$241$	−11.9346	+	6.89042i	−0.768773	+	0.443851i	−0.832437	−	0.554120i	$-0.813055\pi$
$241$	−11.9346	+	6.89042i	−0.768773	+	0.443851i	0.0636639	+	0.997971i	$0.479721\pi$
$242$	−9.21473			−0.592345
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	3.62862	−	6.28496i	0.232299	−	0.402353i
$245$		0			0
$246$	2.94298			0.187638
$247$	−13.7793	+	21.0994i	−0.876758	+	1.34252i
$248$		−	8.74779i		−	0.555486i
$249$	10.6036	+	6.12199i	0.671976	+	0.387965i
$250$		0			0
$251$	10.5296	+	18.2378i	0.664621	+	1.15116i	0.979388	+	0.201988i	$0.0647402\pi$
$251$	10.5296	+	18.2378i	0.664621	+	1.15116i	−0.314767	+	0.949169i	$0.601926\pi$
$252$	2.54707			0.160450
$253$	−2.85875	−	4.95150i	−0.179728	−	0.311298i
$254$	−6.16530	+	3.55954i	−0.386845	+	0.223345i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.3734	+	7.14377i	0.771830	+	0.445616i	0.833527	−	0.552479i	$-0.186318\pi$
$257$	12.3734	+	7.14377i	0.771830	+	0.445616i	−0.0616973	+	0.998095i	$0.519651\pi$
$258$	2.71677	−	4.70558i	0.169139	−	0.292957i
$259$	−13.3906			−0.832050
$260$		0			0
$261$	2.15441			0.133355
$262$	−4.71117	+	8.15998i	−0.291057	+	0.504125i
$263$	−22.6272	−	13.0638i	−1.39526	−	0.805551i	−0.401365	−	0.915918i	$-0.631464\pi$
$263$	−22.6272	−	13.0638i	−1.39526	−	0.805551i	−0.993891	+	0.110367i	$0.964797\pi$
$264$	0.668069	+	1.15713i	0.0411168	+	0.0712164i
$265$		0			0
$266$	15.4172	−	8.90111i	0.945288	−	0.545762i
$267$	−5.80763	−	10.0591i	−0.355421	−	0.615608i
$268$	6.08669			0.371804
$269$	7.80743	+	13.5229i	0.476028	+	0.824504i	0.999623	−	0.0274633i	$-0.00874292\pi$
$269$	7.80743	+	13.5229i	0.476028	+	0.824504i	−0.523595	+	0.851967i	$0.675410\pi$
$270$		0			0
$271$	−22.6267	−	13.0635i	−1.37447	−	0.793553i	−0.382987	−	0.923754i	$-0.625105\pi$
$271$	−22.6267	−	13.0635i	−1.37447	−	0.793553i	−0.991488	+	0.130201i	$0.958438\pi$
$272$			2.94298i			0.178445i
$273$	−4.14821	−	8.19333i	−0.251061	−	0.495883i
$274$	−18.5467			−1.12045
$275$		0			0
$276$	2.13956	−	3.70583i	0.128786	−	0.223065i
$277$	−16.8252	+	9.71405i	−1.01093	+	0.583661i	−0.911464	−	0.411380i	$-0.865047\pi$
$277$	−16.8252	+	9.71405i	−1.01093	+	0.583661i	−0.0994662	+	0.995041i	$0.531714\pi$
$278$	−19.7177			−1.18259
$279$	−7.57581	+	4.37390i	−0.453552	+	0.261858i
$280$		0			0
$281$		−	10.6630i		−	0.636102i	−0.948074	−	0.318051i	$-0.896972\pi$
$281$		−	10.6630i		−	0.636102i	0.948074	−	0.318051i	$-0.103028\pi$
$282$	10.1245	−	5.84539i	0.602906	−	0.348088i
$283$	−1.26513	−	0.730424i	−0.0752042	−	0.0434192i	0.461926	−	0.886918i	$-0.347158\pi$
$283$	−1.26513	−	0.730424i	−0.0752042	−	0.0434192i	−0.537131	+	0.843499i	$0.680492\pi$
$284$	11.3470	+	6.55122i	0.673323	+	0.388743i
$285$		0			0
$286$	2.63419	−	4.03355i	0.155763	−	0.238509i
$287$			7.49599i			0.442474i
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−4.16943	+	7.22166i	−0.245260	+	0.424803i
$290$		0			0
$291$			1.53133i			0.0897680i
$292$	−1.29807	−	2.24832i	−0.0759637	−	0.131573i
$293$	8.86614	+	15.3566i	0.517965	+	0.897142i	0.999782	+	0.0208703i	$0.00664371\pi$
$293$	8.86614	+	15.3566i	0.517965	+	0.897142i	−0.481817	+	0.876272i	$0.660023\pi$
$294$		−	0.512430i		−	0.0298855i
$295$		0			0
$296$	2.62862	−	4.55291i	0.152786	−	0.264632i
$297$	0.668069	−	1.15713i	0.0387653	−	0.0671435i
$298$		−	7.90958i		−	0.458190i
$299$	−15.4053	−	0.847078i	−0.890913	−	0.0489878i
$300$		0			0
$301$	11.9854	+	6.91980i	0.690829	+	0.398851i
$302$	−14.8839	−	8.59321i	−0.856470	−	0.494483i
$303$	0.448484	−	0.258932i	0.0257647	−	0.0148753i
$304$			6.98929i			0.400863i
$305$		0			0
$306$	2.54870	−	1.47149i	0.145699	−	0.0841196i
$307$	−6.66890			−0.380614			−0.190307	−	0.981725i	$-0.560948\pi$
$307$	−6.66890			−0.380614			−0.190307	+	0.981725i	$0.560948\pi$
$308$	−2.94729	+	1.70162i	−0.167938	+	0.0969588i
$309$	−1.21159	+	2.09854i	−0.0689250	+	0.119382i
$310$		0			0
$311$	19.6233			1.11273			0.556367	−	0.830937i	$-0.312195\pi$
$311$	19.6233			1.11273			0.556367	+	0.830937i	$0.312195\pi$
$312$	3.60011	+	0.197956i	0.203816	+	0.0112071i
$313$		−	13.0538i		−	0.737846i	−0.929460	−	0.368923i	$-0.879727\pi$
$313$		−	13.0538i		−	0.737846i	0.929460	−	0.368923i	$-0.120273\pi$
$314$	2.21792	+	1.28052i	0.125164	+	0.0722637i
$315$		0			0
$316$	6.98864	+	12.1047i	0.393141	+	0.680941i
$317$	18.7916			1.05544			0.527719	−	0.849419i	$-0.323047\pi$
$317$	18.7916			1.05544			0.527719	+	0.849419i	$0.323047\pi$
$318$	4.37390	+	7.57581i	0.245276	+	0.424830i
$319$	−2.49294	+	1.43930i	−0.139578	+	0.0805852i
$320$		0			0
$321$	3.06258	+	5.30455i	0.170937	+	0.296071i
$322$	9.43901	+	5.44961i	0.526015	+	0.303695i
$323$	10.2847	−	17.8136i	0.572255	−	0.991175i
$324$	1.00000			0.0555556
$325$		0			0
$326$	17.6153			0.975619
$327$	−0.273784	+	0.474209i	−0.0151403	+	0.0262238i
$328$	−2.54870	−	1.47149i	−0.140728	−	0.0812495i
$329$	14.8886	+	25.7878i	0.820836	+	1.42173i
$330$		0			0
$331$	−20.4013	+	11.7787i	−1.12136	+	0.647417i	−0.941747	−	0.336321i	$-0.890817\pi$
$331$	−20.4013	+	11.7787i	−1.12136	+	0.647417i	−0.179611	+	0.983738i	$0.557484\pi$
$332$	−6.12199	−	10.6036i	−0.335988	−	0.581948i
$333$	−5.25724			−0.288095
$334$	−2.13956	−	3.70583i	−0.117072	−	0.202774i
$335$		0			0
$336$	−2.20583	−	1.27354i	−0.120338	−	0.0694771i
$337$		−	27.2137i		−	1.48242i	−0.671271	−	0.741212i	$-0.734251\pi$
$337$		−	27.2137i		−	1.48242i	0.671271	−	0.741212i	$-0.265749\pi$
$338$	−5.22644	−	11.9031i	−0.284281	−	0.647444i
$339$		0			0
$340$		0			0
$341$	5.84413	−	10.1223i	0.316478	−	0.548155i
$342$	6.05291	−	3.49465i	0.327304	−	0.188969i
$343$	19.1347			1.03318
$344$	−4.70558	+	2.71677i	−0.253708	+	0.146478i
$345$		0			0
$346$		−	8.44421i		−	0.453963i
$347$	−5.52861	+	3.19194i	−0.296791	+	0.171353i	−0.641001	−	0.767540i	$-0.721480\pi$
$347$	−5.52861	+	3.19194i	−0.296791	+	0.171353i	0.344209	+	0.938893i	$0.388147\pi$
$348$	−1.86578	−	1.07721i	−0.100016	−	0.0577443i
$349$	−7.31585	−	4.22381i	−0.391608	−	0.226095i	0.291248	−	0.956647i	$-0.405929\pi$
$349$	−7.31585	−	4.22381i	−0.391608	−	0.226095i	−0.682857	+	0.730552i	$0.739263\pi$
$350$		0			0
$351$	−1.62862	−	3.21677i	−0.0869294	−	0.171698i
$352$		−	1.33614i		−	0.0712164i
$353$	−7.73075	+	13.3901i	−0.411466	+	0.712681i	−0.995050	−	0.0993721i	$-0.968317\pi$
$353$	−7.73075	+	13.3901i	−0.411466	+	0.712681i	0.583584	+	0.812053i	$0.301650\pi$
$354$	4.76818	−	8.25873i	0.253426	−	0.438947i
$355$		0			0
$356$			11.6153i			0.615608i
$357$	3.74799	+	6.49171i	0.198365	+	0.343578i
$358$	0.982856	+	1.70236i	0.0519456	+	0.0899724i
$359$			34.4839i			1.81999i	0.414617	+	0.909996i	$0.363916\pi$
$359$			34.4839i			1.81999i	−0.414617	+	0.909996i	$0.636084\pi$
$360$		0			0
$361$	14.9251	−	25.8511i	0.785532	−	1.36058i
$362$	−3.30763	+	5.72898i	−0.173845	+	0.301109i
$363$		−	9.21473i		−	0.483648i
$364$	−0.504208	+	9.16974i	−0.0264277	+	0.480625i
$365$		0			0
$366$	6.28496	+	3.62862i	0.328520	+	0.189671i
$367$	−31.9910	−	18.4700i	−1.66992	−	0.964128i	−0.967678	−	0.252188i	$-0.918850\pi$
$367$	−31.9910	−	18.4700i	−1.66992	−	0.964128i	−0.702240	−	0.711940i	$-0.747817\pi$
$368$	−3.70583	+	2.13956i	−0.193180	+	0.111532i
$369$			2.94298i			0.153206i
$370$		0			0
$371$	−19.2961	+	11.1406i	−1.00181	+	0.578393i
$372$	8.74779			0.453552
$373$	−10.5589	+	6.09620i	−0.546721	+	0.315649i	−0.747798	−	0.663926i	$-0.768889\pi$
$373$	−10.5589	+	6.09620i	−0.546721	+	0.315649i	0.201078	+	0.979575i	$0.435556\pi$
$374$	−1.96612	+	3.40541i	−0.101665	+	0.176090i
$375$		0			0
$376$	−11.6908			−0.602906
$377$	−0.426479	+	7.75613i	−0.0219648	+	0.399461i
$378$			2.54707i			0.131007i
$379$	1.24346	+	0.717912i	0.0638723	+	0.0368767i	0.531596	−	0.846998i	$-0.321592\pi$
$379$	1.24346	+	0.717912i	0.0638723	+	0.0368767i	−0.467724	+	0.883875i	$0.654926\pi$
$380$		0			0
$381$	−3.55954	−	6.16530i	−0.182361	−	0.315858i
$382$	−10.4325			−0.533772
$383$	−10.1097	−	17.5104i	−0.516579	−	0.894742i	−0.999815	−	0.0192512i	$-0.993872\pi$
$383$	−10.1097	−	17.5104i	−0.516579	−	0.894742i	0.483235	−	0.875491i	$-0.339462\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$		0			0
$386$	−0.407532	−	0.705866i	−0.0207428	−	0.0359276i
$387$	4.70558	+	2.71677i	0.239198	+	0.138101i
$388$	0.765663	−	1.32617i	0.0388707	−	0.0673260i
$389$	−2.15441			−0.109233			−0.0546165	−	0.998507i	$-0.517394\pi$
$389$	−2.15441			−0.109233			−0.0546165	+	0.998507i	$0.517394\pi$
$390$		0			0
$391$	12.5934			0.636875
$392$	−0.256215	+	0.443778i	−0.0129408	+	0.0224142i
$393$	−8.15998	−	4.71117i	−0.411616	−	0.237647i
$394$	−8.41742	−	14.5794i	−0.424063	−	0.734499i
$395$		0			0
$396$	−1.15713	+	0.668069i	−0.0581480	+	0.0335717i
$397$	−13.4286	−	23.2589i	−0.673960	−	1.16733i	−0.976772	−	0.214282i	$-0.931259\pi$
$397$	−13.4286	−	23.2589i	−0.673960	−	1.16733i	0.302812	−	0.953050i	$-0.402075\pi$
$398$	−6.73201			−0.337445
$399$	8.90111	+	15.4172i	0.445613	+	0.771824i
$400$		0			0
$401$	−17.8763	−	10.3209i	−0.892698	−	0.515399i	−0.0178737	−	0.999840i	$-0.505690\pi$
$401$	−17.8763	−	10.3209i	−0.892698	−	0.515399i	−0.874824	+	0.484441i	$0.839023\pi$
$402$			6.08669i			0.303576i
$403$	−14.2468	−	28.1396i	−0.709686	−	1.40173i
$404$	−0.517864			−0.0257647
$405$		0			0
$406$	2.74372	−	4.75226i	0.136169	−	0.235851i
$407$	6.08331	−	3.51220i	0.301539	−	0.174093i
$408$	−2.94298			−0.145699
$409$	3.62316	−	2.09183i	0.179154	−	0.103434i	−0.407741	−	0.913097i	$-0.633683\pi$
$409$	3.62316	−	2.09183i	0.179154	−	0.103434i	0.586895	+	0.809663i	$0.300350\pi$
$410$		0			0
$411$		−	18.5467i		−	0.914842i
$412$	2.09854	−	1.21159i	0.103387	−	0.0596908i
$413$	21.0356	+	12.1449i	1.03509	+	0.597611i
$414$	3.70583	+	2.13956i	0.182132	+	0.105154i
$415$		0			0
$416$	−3.01881	−	1.97149i	−0.148009	−	0.0966603i
$417$		−	19.7177i		−	0.965580i
$418$	−4.66933	+	8.08752i	−0.228385	+	0.395574i
$419$	14.4210	−	24.9779i	0.704511	−	1.22025i	−0.262357	−	0.964971i	$-0.584500\pi$
$419$	14.4210	−	24.9779i	0.704511	−	1.22025i	0.966868	−	0.255277i	$-0.0821668\pi$
$420$		0			0
$421$		−	11.3986i		−	0.555532i	−0.960649	−	0.277766i	$-0.910406\pi$
$421$		−	11.3986i		−	0.555532i	0.960649	−	0.277766i	$-0.0895939\pi$
$422$	−6.00378	−	10.3989i	−0.292260	−	0.506208i
$423$	5.84539	+	10.1245i	0.284213	+	0.492271i
$424$		−	8.74779i		−	0.424830i
$425$		0			0
$426$	−6.55122	+	11.3470i	−0.317407	+	0.549766i
$427$	−9.24236	+	16.0082i	−0.447269	+	0.774693i
$428$		−	6.12516i		−	0.296071i
$429$	4.03355	+	2.63419i	0.194742	+	0.127180i
$430$		0			0
$431$	26.5014	+	15.3006i	1.27653	+	0.737003i	0.976208	−	0.216836i	$-0.0695738\pi$
$431$	26.5014	+	15.3006i	1.27653	+	0.737003i	0.300318	+	0.953839i	$0.402907\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	−33.0332	+	19.0717i	−1.58747	+	0.916527i	−0.593750	+	0.804649i	$0.702353\pi$
$433$	−33.0332	+	19.0717i	−1.58747	+	0.916527i	−0.993722	+	0.111878i	$0.964313\pi$
$434$			22.2813i			1.06953i
$435$		0			0
$436$	0.474209	−	0.273784i	0.0227105	−	0.0131119i
$437$	29.9080			1.43070
$438$	2.24832	−	1.29807i	0.107429	−	0.0620241i
$439$	−7.39969	+	12.8166i	−0.353168	+	0.611705i	−0.986803	−	0.161928i	$-0.948229\pi$
$439$	−7.39969	+	12.8166i	−0.353168	+	0.611705i	0.633635	+	0.773632i	$0.281562\pi$
$440$		0			0
$441$	0.512430			0.0244014
$442$	4.79301	+	9.46689i	0.227980	+	0.450294i
$443$		−	2.07804i		−	0.0987309i	−0.998781	−	0.0493654i	$-0.984280\pi$
$443$		−	2.07804i		−	0.0987309i	0.998781	−	0.0493654i	$-0.0157199\pi$
$444$	4.55291	+	2.62862i	0.216071	+	0.124749i
$445$		0			0
$446$	0.253346	+	0.438808i	0.0119963	+	0.0207782i
$447$	7.90958			0.374110
$448$	1.27354	+	2.20583i	0.0601689	+	0.104216i
$449$	−8.50224	+	4.90877i	−0.401246	+	0.231659i	−0.687021	−	0.726637i	$-0.741082\pi$
$449$	−8.50224	+	4.90877i	−0.401246	+	0.231659i	0.285776	+	0.958297i	$0.407749\pi$
$450$		0			0
$451$	−1.96612	−	3.40541i	−0.0925808	−	0.160355i
$452$		0			0
$453$	8.59321	−	14.8839i	0.403744	−	0.699305i
$454$	−4.15945			−0.195213
$455$		0			0
$456$	−6.98929			−0.327304
$457$	16.0683	−	27.8311i	0.751642	−	1.30188i	−0.195385	−	0.980727i	$-0.562596\pi$
$457$	16.0683	−	27.8311i	0.751642	−	1.30188i	0.947027	−	0.321155i	$-0.104071\pi$
$458$	19.3719	+	11.1844i	0.905191	+	0.522613i
$459$	1.47149	+	2.54870i	0.0686833	+	0.118963i
$460$		0			0
$461$	17.8943	−	10.3313i	0.833423	−	0.481177i	−0.0216003	−	0.999767i	$-0.506876\pi$
$461$	17.8943	−	10.3313i	0.833423	−	0.481177i	0.855023	+	0.518590i	$0.173543\pi$
$462$	−1.70162	−	2.94729i	−0.0791665	−	0.137120i
$463$	−18.2175			−0.846639			−0.423319	−	0.905981i	$-0.639135\pi$
$463$	−18.2175			−0.846639			−0.423319	+	0.905981i	$0.639135\pi$
$464$	1.07721	+	1.86578i	0.0500081	+	0.0866165i
$465$		0			0
$466$	7.64121	+	4.41166i	0.353972	+	0.204366i
$467$		−	5.61909i		−	0.260021i	−0.991513	−	0.130010i	$-0.958499\pi$
$467$		−	5.61909i		−	0.260021i	0.991513	−	0.130010i	$-0.0415010\pi$
$468$	−0.197956	+	3.60011i	−0.00915052	+	0.166415i
$469$	−15.5032			−0.715873
$470$		0			0
$471$	−1.28052	+	2.21792i	−0.0590030	+	0.102196i
$472$	−8.25873	+	4.76818i	−0.380139	+	0.219473i
$473$	−7.25996			−0.333813
$474$	−12.1047	+	6.98864i	−0.555986	+	0.320999i
$475$		0			0
$476$		−	7.49599i		−	0.343578i
$477$	−7.57581	+	4.37390i	−0.346873	+	0.200267i
$478$	−22.1904	−	12.8116i	−1.01497	−	0.585991i
$479$	−23.1239	−	13.3506i	−1.05656	−	0.610003i	−0.132078	−	0.991239i	$-0.542165\pi$
$479$	−23.1239	−	13.3506i	−1.05656	−	0.610003i	−0.924478	+	0.381236i	$0.875498\pi$
$480$		0			0
$481$	1.04070	−	18.9267i	0.0474520	−	0.862982i
$482$			13.7808i			0.627700i
$483$	−5.44961	+	9.43901i	−0.247966	+	0.429490i
$484$	−4.60737	+	7.98019i	−0.209426	+	0.362736i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	15.5146	+	26.8721i	0.703035	+	1.21769i	0.967396	+	0.253269i	$0.0815058\pi$
$487$	15.5146	+	26.8721i	0.703035	+	1.21769i	−0.264361	+	0.964424i	$0.585161\pi$
$488$	−3.62862	−	6.28496i	−0.164260	−	0.284507i
$489$			17.6153i			0.796590i
$490$		0			0
$491$	−7.27846	+	12.6067i	−0.328472	+	0.568931i	−0.982209	−	0.187791i	$-0.939867\pi$
$491$	−7.27846	+	12.6067i	−0.328472	+	0.568931i	0.653737	+	0.756722i	$0.273200\pi$
$492$	1.47149	−	2.54870i	0.0663400	−	0.114904i
$493$		−	6.34040i		−	0.285557i
$494$	11.3829	+	22.4829i	0.512142	+	1.01155i
$495$		0			0
$496$	−7.57581	−	4.37390i	−0.340164	−	0.196394i
$497$	−28.9017	−	16.6864i	−1.29642	−	0.748488i
$498$	10.6036	−	6.12199i	0.475159	−	0.274333i
$499$			26.5871i			1.19020i	0.803652	+	0.595100i	$0.202888\pi$
$499$			26.5871i			1.19020i	−0.803652	+	0.595100i	$0.797112\pi$
$500$		0			0
$501$	3.70583	−	2.13956i	0.165564	−	0.0955885i
$502$	21.0591			0.939916
$503$	11.8562	−	6.84516i	0.528640	−	0.305211i	−0.211822	−	0.977308i	$-0.567940\pi$
$503$	11.8562	−	6.84516i	0.528640	−	0.305211i	0.740463	+	0.672098i	$0.234606\pi$
$504$	1.27354	−	2.20583i	0.0567278	−	0.0982554i
$505$		0			0
$506$	−5.71750			−0.254174
$507$	11.9031	−	5.22644i	0.528636	−	0.232114i
$508$			7.11907i			0.315858i
$509$	−6.53323	−	3.77196i	−0.289581	−	0.167189i	0.348172	−	0.937431i	$-0.386802\pi$
$509$	−6.53323	−	3.77196i	−0.289581	−	0.167189i	−0.637753	+	0.770241i	$0.720136\pi$
$510$		0			0
$511$	3.30627	+	5.72663i	0.146261	+	0.253331i
$512$	−1.00000			−0.0441942
$513$	3.49465	+	6.05291i	0.154292	+	0.267242i
$514$	12.3734	−	7.14377i	0.545766	−	0.315098i
$515$		0			0
$516$	−2.71677	−	4.70558i	−0.119599	−	0.207152i
$517$	−13.5278	−	7.81025i	−0.594950	−	0.343494i
$518$	−6.69529	+	11.5966i	−0.294174	+	0.509524i
$519$	8.44421			0.370660
$520$		0			0
$521$	15.2218			0.666881			0.333440	−	0.942771i	$-0.391790\pi$
$521$	15.2218			0.666881			0.333440	+	0.942771i	$0.391790\pi$
$522$	1.07721	−	1.86578i	0.0471480	−	0.0816628i
$523$	21.6567	+	12.5035i	0.946980	+	0.546739i	0.892141	−	0.451756i	$-0.149202\pi$
$523$	21.6567	+	12.5035i	0.946980	+	0.546739i	0.0548385	+	0.998495i	$0.482536\pi$
$524$	4.71117	+	8.15998i	0.205808	+	0.356470i
$525$		0			0
$526$	−22.6272	+	13.0638i	−0.986595	+	0.569611i
$527$	12.8723	+	22.2955i	0.560726	+	0.971207i
$528$	1.33614			0.0581480
$529$	−2.34456	−	4.06090i	−0.101937	−	0.176561i
$530$		0			0
$531$	8.25873	+	4.76818i	0.358399	+	0.206921i
$532$		−	17.8022i		−	0.771824i
$533$	−10.5951	−	0.582581i	−0.458923	−	0.0252344i
$534$	−11.6153			−0.502641
$535$		0			0
$536$	3.04334	−	5.27123i	0.131452	−	0.227682i
$537$	−1.70236	+	0.982856i	−0.0734621	+	0.0424134i
$538$	15.6149			0.673205
$539$	−0.592949	+	0.342339i	−0.0255401	+	0.0147456i
$540$		0			0
$541$			32.2610i			1.38701i	0.720452	+	0.693504i	$0.243934\pi$
$541$			32.2610i			1.38701i	−0.720452	+	0.693504i	$0.756066\pi$
$542$	−22.6267	+	13.0635i	−0.971900	+	0.561127i
$543$	−5.72898	−	3.30763i	−0.245854	−	0.141944i
$544$	2.54870	+	1.47149i	0.109275	+	0.0630897i
$545$		0			0
$546$	−9.16974	−	0.504208i	−0.392429	−	0.0215781i
$547$			36.4353i			1.55786i	0.627110	+	0.778931i	$0.284238\pi$
$547$			36.4353i			1.55786i	−0.627110	+	0.778931i	$0.715762\pi$
$548$	−9.27336	+	16.0619i	−0.396138	+	0.686132i
$549$	−3.62862	+	6.28496i	−0.154866	+	0.268235i
$550$		0			0
$551$		−	15.0578i		−	0.641485i
$552$	−2.13956	−	3.70583i	−0.0910658	−	0.157731i
$553$	−17.8005	−	30.8315i	−0.756956	−	1.31109i
$554$			19.4281i			0.825421i
$555$		0			0
$556$	−9.85885	+	17.0760i	−0.418108	+	0.724185i
$557$	18.2648	−	31.6356i	0.773905	−	1.34044i	−0.161503	−	0.986872i	$-0.551634\pi$
$557$	18.2648	−	31.6356i	0.773905	−	1.34044i	0.935408	−	0.353570i	$-0.115032\pi$
$558$			8.74779i			0.370324i
$559$	−10.7122	+	16.4028i	−0.453076	+	0.693765i
$560$		0			0
$561$	−3.40541	−	1.96612i	−0.143777	−	0.0830095i
$562$	−9.23444	−	5.33151i	−0.389531	−	0.224896i
$563$	−38.9307	+	22.4766i	−1.64073	+	0.947277i	−0.660158	+	0.751127i	$0.729511\pi$
$563$	−38.9307	+	22.4766i	−1.64073	+	0.947277i	−0.980574	+	0.196150i	$0.937156\pi$
$564$		−	11.6908i		−	0.492271i
$565$		0			0
$566$	−1.26513	+	0.730424i	−0.0531774	+	0.0307020i
$567$	−2.54707			−0.106967
$568$	11.3470	−	6.55122i	0.476111	−	0.274883i
$569$	4.13745	−	7.16627i	0.173451	−	0.300426i	−0.766173	−	0.642634i	$-0.777842\pi$
$569$	4.13745	−	7.16627i	0.173451	−	0.300426i	0.939624	+	0.342209i	$0.111175\pi$
$570$		0			0
$571$	−22.2659			−0.931797			−0.465899	−	0.884838i	$-0.654269\pi$
$571$	−22.2659			−0.931797			−0.465899	+	0.884838i	$0.654269\pi$
$572$	−2.17606	−	4.29805i	−0.0909858	−	0.179710i
$573$		−	10.4325i		−	0.435823i
$574$	6.49171	+	3.74799i	0.270959	+	0.156438i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	35.3355			1.47104			0.735518	−	0.677505i	$-0.236939\pi$
$577$	35.3355			1.47104			0.735518	+	0.677505i	$0.236939\pi$
$578$	4.16943	+	7.22166i	0.173425	+	0.300381i
$579$	0.705866	−	0.407532i	0.0293348	−	0.0169364i
$580$		0			0
$581$	15.5931	+	27.0081i	0.646913	+	1.12049i
$582$	1.32617	+	0.765663i	0.0549714	+	0.0317378i
$583$	5.84413	−	10.1223i	0.242039	−	0.419224i
$584$	−2.59614			−0.107429
$585$		0			0
$586$	17.7323			0.732514
$587$	−2.02271	+	3.50343i	−0.0834861	+	0.144602i	−0.904745	−	0.425953i	$-0.859939\pi$
$587$	−2.02271	+	3.50343i	−0.0834861	+	0.144602i	0.821259	+	0.570556i	$0.193272\pi$
$588$	−0.443778	−	0.256215i	−0.0183011	−	0.0105661i
$589$	30.5705	+	52.9496i	1.25963	+	2.18175i
$590$		0			0
$591$	14.5794	−	8.41742i	0.599716	−	0.346246i
$592$	−2.62862	−	4.55291i	−0.108036	−	0.187123i
$593$	7.73381			0.317590			0.158795	−	0.987312i	$-0.449239\pi$
$593$	7.73381			0.317590			0.158795	+	0.987312i	$0.449239\pi$
$594$	−0.668069	−	1.15713i	−0.0274112	−	0.0474776i
$595$		0			0
$596$	−6.84990	−	3.95479i	−0.280583	−	0.161994i
$597$		−	6.73201i		−	0.275523i
$598$	−8.43625	+	12.9179i	−0.344984	+	0.528251i
$599$	−23.3807			−0.955310			−0.477655	−	0.878548i	$-0.658513\pi$
$599$	−23.3807			−0.955310			−0.477655	+	0.878548i	$0.658513\pi$
$600$		0			0
$601$	4.78494	−	8.28776i	0.195182	−	0.338065i	−0.751778	−	0.659416i	$-0.770804\pi$
$601$	4.78494	−	8.28776i	0.195182	−	0.338065i	0.946960	+	0.321351i	$0.104137\pi$
$602$	11.9854	−	6.91980i	0.488490	−	0.282030i
$603$	−6.08669			−0.247869
$604$	−14.8839	+	8.59321i	−0.605616	+	0.349653i
$605$		0			0
$606$		−	0.517864i		−	0.0210368i
$607$	−28.5604	+	16.4894i	−1.15923	+	0.669283i	−0.951120	−	0.308822i	$-0.900065\pi$
$607$	−28.5604	+	16.4894i	−1.15923	+	0.669283i	−0.208112	+	0.978105i	$0.566732\pi$
$608$	6.05291	+	3.49465i	0.245478	+	0.141727i
$609$	4.75226	+	2.74372i	0.192571	+	0.111181i
$610$		0			0
$611$	−37.6065	+	19.0399i	−1.52140	+	0.770270i
$612$		−	2.94298i		−	0.118963i
$613$	3.46687	−	6.00479i	0.140026	−	0.242531i	−0.787480	−	0.616340i	$-0.788615\pi$
$613$	3.46687	−	6.00479i	0.140026	−	0.242531i	0.927506	+	0.373808i	$0.121948\pi$
$614$	−3.33445	+	5.77544i	−0.134567	+	0.233078i
$615$		0			0
$616$			3.40324i			0.137120i
$617$	17.4915	+	30.2962i	0.704182	+	1.21968i	0.966986	+	0.254830i	$0.0820194\pi$
$617$	17.4915	+	30.2962i	0.704182	+	1.21968i	−0.262804	+	0.964849i	$0.584647\pi$
$618$	1.21159	+	2.09854i	0.0487373	+	0.0844155i
$619$		−	31.0002i		−	1.24600i	−0.782221	−	0.623001i	$-0.785913\pi$
$619$		−	31.0002i		−	1.24600i	0.782221	−	0.623001i	$-0.214087\pi$
$620$		0			0
$621$	−2.13956	+	3.70583i	−0.0858576	+	0.148710i
$622$	9.81164	−	16.9943i	0.393411	−	0.681408i
$623$		−	29.5849i		−	1.18529i
$624$	1.97149	−	3.01881i	0.0789228	−	0.120849i
$625$		0			0
$626$	−11.3050	−	6.52692i	−0.451837	−	0.260868i
$627$	−8.08752	−	4.66933i	−0.322985	−	0.186475i
$628$	2.21792	−	1.28052i	0.0885046	−	0.0510981i
$629$			15.4720i			0.616908i
$630$		0			0
$631$	12.5912	−	7.26955i	0.501249	−	0.289396i	−0.227980	−	0.973666i	$-0.573212\pi$
$631$	12.5912	−	7.26955i	0.501249	−	0.289396i	0.729229	+	0.684269i	$0.239879\pi$
$632$	13.9773			0.555986
$633$	10.3989	−	6.00378i	0.413317	−	0.238629i
$634$	9.39578	−	16.2740i	0.373154	−	0.646322i
$635$		0			0
$636$	8.74779			0.346873
$637$	−0.101439	+	1.84481i	−0.00401915	+	0.0730939i
$638$			2.87859i			0.113965i
$639$	−11.3470	−	6.55122i	−0.448882	−	0.259162i
$640$		0			0
$641$	20.5538	+	35.6002i	0.811825	+	1.40612i	0.911585	+	0.411111i	$0.134859\pi$
$641$	20.5538	+	35.6002i	0.811825	+	1.40612i	−0.0997605	+	0.995011i	$0.531808\pi$
$642$	6.12516			0.241741
$643$	−12.1347	−	21.0180i	−0.478547	−	0.828868i	0.521150	−	0.853465i	$-0.325503\pi$
$643$	−12.1347	−	21.0180i	−0.478547	−	0.828868i	−0.999697	+	0.0245971i	$0.992170\pi$
$644$	9.43901	−	5.44961i	0.371949	−	0.214745i
$645$		0			0
$646$	−10.2847	−	17.8136i	−0.404646	−	0.700867i
$647$	−34.9290	−	20.1663i	−1.37320	−	0.792818i	−0.381872	−	0.924215i	$-0.624720\pi$
$647$	−34.9290	−	20.1663i	−1.37320	−	0.792818i	−0.991330	+	0.131397i	$0.958054\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−12.7419			−0.500164
$650$		0			0
$651$	−22.2813			−0.873271
$652$	8.80763	−	15.2553i	0.344933	−	0.597442i
$653$	−34.0173	−	19.6399i	−1.33120	−	0.768568i	−0.345716	−	0.938339i	$-0.612364\pi$
$653$	−34.0173	−	19.6399i	−1.33120	−	0.768568i	−0.985483	+	0.169771i	$0.945697\pi$
$654$	0.273784	+	0.474209i	0.0107058	+	0.0185430i
$655$		0			0
$656$	−2.54870	+	1.47149i	−0.0995099	+	0.0574521i
$657$	1.29807	+	2.24832i	0.0506425	+	0.0877154i
$658$	29.7772			1.16084
$659$	−10.5336	−	18.2448i	−0.410333	−	0.710717i	0.584593	−	0.811326i	$-0.301254\pi$
$659$	−10.5336	−	18.2448i	−0.410333	−	0.710717i	−0.994926	+	0.100609i	$0.967921\pi$
$660$		0			0
$661$	−20.3964	−	11.7759i	−0.793330	−	0.458029i	0.0478037	−	0.998857i	$-0.484778\pi$
$661$	−20.3964	−	11.7759i	−0.793330	−	0.458029i	−0.841133	+	0.540828i	$0.818111\pi$
$662$			23.5574i			0.915585i
$663$	−9.46689	+	4.79301i	−0.367664	+	0.186145i
$664$	−12.2440			−0.475159
$665$		0			0
$666$	−2.62862	+	4.55291i	−0.101857	+	0.176422i
$667$	7.98388	−	4.60950i	0.309137	−	0.178480i
$668$	−4.27912			−0.165564
$669$	−0.438808	+	0.253346i	−0.0169653	+	0.00979492i
$670$		0			0
$671$		−	9.69668i		−	0.374336i
$672$	−2.20583	+	1.27354i	−0.0850917	+	0.0491277i
$673$	11.7603	+	6.78980i	0.453325	+	0.261728i	0.709234	−	0.704974i	$-0.249041\pi$
$673$	11.7603	+	6.78980i	0.453325	+	0.261728i	−0.255908	+	0.966701i	$0.582374\pi$
$674$	−23.5677	−	13.6068i	−0.907795	−	0.524116i
$675$		0			0
$676$	−12.9216	−	1.42533i	−0.496986	−	0.0548203i
$677$			18.1429i			0.697288i	0.937255	+	0.348644i	$0.113358\pi$
$677$			18.1429i			0.697288i	−0.937255	+	0.348644i	$0.886642\pi$
$678$		0			0
$679$	−1.95020	+	3.37784i	−0.0748418	+	0.129630i
$680$		0			0
$681$		−	4.15945i		−	0.159391i
$682$	−5.84413	−	10.1223i	−0.223783	−	0.387604i
$683$	9.66980	+	16.7486i	0.370005	+	0.640867i	0.989566	−	0.144082i	$-0.0460228\pi$
$683$	9.66980	+	16.7486i	0.370005	+	0.640867i	−0.619561	+	0.784948i	$0.712689\pi$
$684$		−	6.98929i		−	0.267242i
$685$		0			0
$686$	9.56735	−	16.5711i	0.365283	−	0.632689i
$687$	−11.1844	+	19.3719i	−0.426711	+	0.739086i
$688$			5.43353i			0.207152i
$689$	−14.2468	−	28.1396i	−0.542762	−	1.07203i
$690$		0			0
$691$	16.8778	+	9.74437i	0.642060	+	0.370693i	0.785408	−	0.618979i	$-0.212453\pi$
$691$	16.8778	+	9.74437i	0.642060	+	0.370693i	−0.143348	+	0.989672i	$0.545787\pi$
$692$	−7.31290	−	4.22210i	−0.277995	−	0.160500i
$693$	2.94729	−	1.70162i	0.111958	−	0.0646392i
$694$			6.38389i			0.242329i
$695$		0			0
$696$	−1.86578	+	1.07721i	−0.0707221	+	0.0408314i
$697$	8.66115			0.328064
$698$	−7.31585	+	4.22381i	−0.276909	+	0.159873i
$699$	−4.41166	+	7.64121i	−0.166864	+	0.289017i
$700$		0			0
$701$	10.6682			0.402931			0.201466	−	0.979496i	$-0.435430\pi$
$701$	10.6682			0.402931			0.201466	+	0.979496i	$0.435430\pi$
$702$	−3.60011	−	0.197956i	−0.135878	−	0.00747137i
$703$			36.7444i			1.38584i
$704$	−1.15713	−	0.668069i	−0.0436110	−	0.0251788i
$705$		0			0
$706$	7.73075	+	13.3901i	0.290951	+	0.503941i
$707$	1.31904			0.0496075
$708$	−4.76818	−	8.25873i	−0.179199	−	0.310382i
$709$	35.9403	−	20.7502i	1.34977	−	0.779289i	0.361551	−	0.932352i	$-0.382247\pi$
$709$	35.9403	−	20.7502i	1.34977	−	0.779289i	0.988216	+	0.153063i	$0.0489138\pi$
$710$		0			0
$711$	−6.98864	−	12.1047i	−0.262094	−	0.453961i
$712$	10.0591	+	5.80763i	0.376981	+	0.217650i
$713$	−18.7164	+	32.4178i	−0.700936	+	1.21406i
$714$	7.49599			0.280530
$715$		0			0
$716$	1.96571			0.0734621
$717$	12.8116	−	22.1904i	0.478459	−	0.828716i
$718$	29.8640	+	17.2420i	1.11451	+	0.643464i
$719$	−20.4278	−	35.3820i	−0.761828	−	1.31953i	−0.941907	−	0.335873i	$-0.890969\pi$
$719$	−20.4278	−	35.3820i	−0.761828	−	1.31953i	0.180079	−	0.983652i	$-0.442365\pi$
$720$		0			0
$721$	−5.34512	+	3.08601i	−0.199063	+	0.114929i
$722$	−14.9251	−	25.8511i	−0.555455	−	0.962077i
$723$	−13.7808			−0.512515
$724$	3.30763	+	5.72898i	0.122927	+	0.212916i
$725$		0			0
$726$	−7.98019	−	4.60737i	−0.296173	−	0.170995i
$727$		−	6.84248i		−	0.253773i	−0.991917	−	0.126887i	$-0.959502\pi$
$727$		−	6.84248i		−	0.253773i	0.991917	−	0.126887i	$-0.0404985\pi$
$728$	7.68913	+	5.02153i	0.284978	+	0.186110i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	7.99540	−	13.8484i	0.295721	−	0.512203i
$732$	6.28496	−	3.62862i	0.232299	−	0.134118i
$733$	25.2614			0.933051			0.466525	−	0.884508i	$-0.345506\pi$
$733$	25.2614			0.933051			0.466525	+	0.884508i	$0.345506\pi$
$734$	−31.9910	+	18.4700i	−1.18081	+	0.681741i
$735$		0			0
$736$			4.27912i			0.157731i
$737$	7.04309	−	4.06633i	0.259436	−	0.149785i
$738$	2.54870	+	1.47149i	0.0938189	+	0.0541663i
$739$	−3.67362	−	2.12096i	−0.135136	−	0.0780209i	0.430908	−	0.902396i	$-0.358193\pi$
$739$	−3.67362	−	2.12096i	−0.135136	−	0.0780209i	−0.566044	+	0.824375i	$0.691527\pi$
$740$		0			0
$741$	−22.4829	+	11.3829i	−0.825931	+	0.418162i
$742$			22.2813i			0.817971i
$743$	3.04879	−	5.28067i	0.111849	−	0.193729i	−0.804667	−	0.593727i	$-0.797656\pi$
$743$	3.04879	−	5.28067i	0.111849	−	0.193729i	0.916516	+	0.399998i	$0.130989\pi$
$744$	4.37390	−	7.57581i	0.160355	−	0.277743i
$745$		0			0
$746$			12.1924i			0.446395i
$747$	6.12199	+	10.6036i	0.223992	+	0.387965i
$748$	1.96612	+	3.40541i	0.0718883	+	0.124514i
$749$			15.6012i			0.570056i
$750$		0			0
$751$	17.3192	−	29.9977i	0.631986	−	1.09463i	−0.355160	−	0.934806i	$-0.615574\pi$
$751$	17.3192	−	29.9977i	0.631986	−	1.09463i	0.987145	−	0.159825i	$-0.0510931\pi$
$752$	−5.84539	+	10.1245i	−0.213159	+	0.369203i
$753$			21.0591i			0.767438i
$754$	6.50377	+	4.24741i	0.236853	+	0.154681i
$755$		0			0
$756$	2.20583	+	1.27354i	0.0802252	+	0.0463180i
$757$	−2.28724	−	1.32054i	−0.0831310	−	0.0479957i	0.457858	−	0.889025i	$-0.348617\pi$
$757$	−2.28724	−	1.32054i	−0.0831310	−	0.0479957i	−0.540989	+	0.841029i	$0.681950\pi$
$758$	1.24346	−	0.717912i	0.0451645	−	0.0260757i
$759$		−	5.71750i		−	0.207532i
$760$		0			0
$761$	47.6508	−	27.5112i	1.72734	−	0.997281i	0.826826	−	0.562458i	$-0.190144\pi$
$761$	47.6508	−	27.5112i	1.72734	−	0.997281i	0.900516	−	0.434823i	$-0.143189\pi$
$762$	−7.11907			−0.257897
$763$	−1.20784	+	0.697348i	−0.0437268	+	0.0252457i
$764$	−5.21624	+	9.03479i	−0.188717	+	0.326867i
$765$		0			0
$766$	−20.2193			−0.730554
$767$	−18.8009	+	28.7885i	−0.678860	+	1.03949i
$768$		−	1.00000i		−	0.0360844i
$769$	27.7928	+	16.0462i	1.00223	+	0.578639i	0.908908	−	0.416997i	$-0.136917\pi$
$769$	27.7928	+	16.0462i	1.00223	+	0.578639i	0.0933243	+	0.995636i	$0.470251\pi$
$770$		0			0
$771$	7.14377	+	12.3734i	0.257277	+	0.445616i
$772$	−0.815063			−0.0293348
$773$	26.8465	+	46.4995i	0.965601	+	1.67247i	0.707993	+	0.706220i	$0.249601\pi$
$773$	26.8465	+	46.4995i	0.965601	+	1.67247i	0.257608	+	0.966250i	$0.417066\pi$
$774$	4.70558	−	2.71677i	0.169139	−	0.0976522i
$775$		0			0
$776$	−0.765663	−	1.32617i	−0.0274857	−	0.0476067i
$777$	−11.5966	−	6.69529i	−0.416025	−	0.240192i
$778$	−1.07721	+	1.86578i	−0.0386197	+	0.0668913i
$779$	20.5694			0.736974
$780$		0			0
$781$	17.5067			0.626438
$782$	6.29669	−	10.9062i	0.225169	−	0.390005i
$783$	1.86578	+	1.07721i	0.0666774	+	0.0384962i
$784$	0.256215	+	0.443778i	0.00915054	+	0.0158492i
$785$		0			0
$786$	−8.15998	+	4.71117i	−0.291057	+	0.168042i
$787$	8.44876	+	14.6337i	0.301166	+	0.521635i	0.976400	−	0.215969i	$-0.0692909\pi$
$787$	8.44876	+	14.6337i	0.301166	+	0.521635i	−0.675234	+	0.737603i	$0.735958\pi$
$788$	−16.8348			−0.599716
$789$	−13.0638	−	22.6272i	−0.465085	−	0.805551i
$790$		0			0
$791$		0			0
$792$			1.33614i			0.0474776i
$793$	−21.9082	−	14.3076i	−0.777985	−	0.508078i
$794$	−26.8571			−0.953123
$795$		0			0
$796$	−3.36600	+	5.83009i	−0.119305	+	0.206642i
$797$	13.1928	−	7.61687i	0.467313	−	0.269803i	−0.247801	−	0.968811i	$-0.579708\pi$
$797$	13.1928	−	7.61687i	0.467313	−	0.269803i	0.715114	+	0.699008i	$0.246375\pi$
$798$	17.8022			0.630192
$799$	29.7963	−	17.2029i	1.05412	−	0.608594i
$800$		0			0
$801$		−	11.6153i		−	0.410405i
$802$	−17.8763	+	10.3209i	−0.631233	+	0.364442i
$803$	−3.00407	−	1.73440i	−0.106011	−	0.0612057i
$804$	5.27123	+	3.04334i	0.185902	+	0.107330i
$805$		0			0
$806$	−31.4930	−	1.73168i	−1.10930	−	0.0609958i
$807$			15.6149i			0.549669i
$808$	−0.258932	+	0.448484i	−0.00910920	+	0.0157776i
$809$	27.9518	−	48.4139i	0.982733	−	1.70214i	0.331127	−	0.943586i	$-0.392571\pi$
$809$	27.9518	−	48.4139i	0.982733	−	1.70214i	0.651606	−	0.758557i	$-0.274095\pi$
$810$		0			0
$811$			0.263496i			0.00925261i	0.999989	+	0.00462630i	$0.00147260\pi$
$811$			0.263496i			0.00925261i	−0.999989	+	0.00462630i	$0.998527\pi$
$812$	−2.74372	−	4.75226i	−0.0962857	−	0.166772i
$813$	−13.0635	−	22.6267i	−0.458158	−	0.793553i
$814$		−	7.02441i		−	0.246205i
$815$		0			0
$816$	−1.47149	+	2.54870i	−0.0515125	+	0.0892223i
$817$	18.9883	−	32.8887i	0.664316	−	1.15063i
$818$		−	4.18366i		−	0.146278i
$819$	0.504208	−	9.16974i	0.0176185	−	0.320417i
$820$		0			0
$821$	34.0125	+	19.6371i	1.18705	+	0.685341i	0.957634	−	0.287989i	$-0.0929866\pi$
$821$	34.0125	+	19.6371i	1.18705	+	0.685341i	0.229411	+	0.973330i	$0.426320\pi$
$822$	−16.0619	−	9.27336i	−0.560224	−	0.323446i
$823$	−19.3855	+	11.1922i	−0.675737	+	0.390137i	−0.798247	−	0.602330i	$-0.794239\pi$
$823$	−19.3855	+	11.1922i	−0.675737	+	0.390137i	0.122510	+	0.992467i	$0.460906\pi$
$824$		−	2.42318i		−	0.0844155i
$825$		0			0
$826$	21.0356	−	12.1449i	0.731921	−	0.422575i
$827$	−10.0484			−0.349417			−0.174709	−	0.984620i	$-0.555898\pi$
$827$	−10.0484			−0.349417			−0.174709	+	0.984620i	$0.555898\pi$
$828$	3.70583	−	2.13956i	0.128786	−	0.0743549i
$829$	15.2722	−	26.4522i	0.530425	−	0.918723i	−0.468945	−	0.883228i	$-0.655366\pi$
$829$	15.2722	−	26.4522i	0.530425	−	0.918723i	0.999370	−	0.0354958i	$-0.0113010\pi$
$830$		0			0
$831$	−19.4281			−0.673953
$832$	−3.21677	+	1.62862i	−0.111521	+	0.0564623i
$833$		−	1.50807i		−	0.0522517i
$834$	−17.0760	−	9.85885i	−0.591294	−	0.341384i
$835$		0			0
$836$	4.66933	+	8.08752i	0.161492	+	0.279713i
$837$	−8.74779			−0.302368
$838$	−14.4210	−	24.9779i	−0.498164	−	0.862846i
$839$	28.8867	−	16.6777i	0.997279	−	0.575780i	0.0898372	−	0.995956i	$-0.471365\pi$
$839$	28.8867	−	16.6777i	0.997279	−	0.575780i	0.907442	+	0.420177i	$0.138032\pi$
$840$		0			0
$841$	12.1793	+	21.0951i	0.419974	+	0.727417i
$842$	−9.87144	−	5.69928i	−0.340192	−	0.196410i
$843$	5.33151	−	9.23444i	0.183627	−	0.318051i
$844$	−12.0076			−0.413317
$845$		0			0
$846$	11.6908			0.401937
$847$	11.7353	−	20.3261i	0.403229	−	0.698414i
$848$	−7.57581	−	4.37390i	−0.260154	−	0.150200i
$849$	−0.730424	−	1.26513i	−0.0250681	−	0.0434192i
$850$		0			0
$851$	−19.4824	+	11.2482i	−0.667849	+	0.385583i
$852$	6.55122	+	11.3470i	0.224441	+	0.388743i
$853$	−10.4152			−0.356609			−0.178305	−	0.983975i	$-0.557061\pi$
$853$	−10.4152			−0.356609			−0.178305	+	0.983975i	$0.557061\pi$
$854$	9.24236	+	16.0082i	0.316267	+	0.547790i
$855$		0			0
$856$	−5.30455	−	3.06258i	−0.181306	−	0.104677i
$857$			46.7684i			1.59758i	0.601611	+	0.798789i	$0.294526\pi$
$857$			46.7684i			1.59758i	−0.601611	+	0.798789i	$0.705474\pi$
$858$	4.29805	−	2.17606i	0.146733	−	0.0742896i
$859$	9.19564			0.313751			0.156876	−	0.987618i	$-0.449858\pi$
$859$	9.19564			0.313751			0.156876	+	0.987618i	$0.449858\pi$
$860$		0			0
$861$	−3.74799	+	6.49171i	−0.127731	+	0.221237i
$862$	26.5014	−	15.3006i	0.902640	−	0.521140i
$863$	25.7961			0.878108			0.439054	−	0.898461i	$-0.355314\pi$
$863$	25.7961			0.878108			0.439054	+	0.898461i	$0.355314\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$		0			0
$866$			38.1434i			1.29617i
$867$	−7.22166	+	4.16943i	−0.245260	+	0.141601i
$868$	19.2961	+	11.1406i	0.654953	+	0.378137i
$869$	16.1735	+	9.33779i	0.548649	+	0.316763i
$870$		0			0
$871$	1.20490	−	21.9128i	0.0408264	−	0.742486i
$872$		−	0.547569i		−	0.0185430i
$873$	−0.765663	+	1.32617i	−0.0259138	+	0.0448840i
$874$	14.9540	−	25.9011i	0.505827	−	0.876118i
$875$		0			0
$876$		−	2.59614i		−	0.0877154i
$877$	2.41271	+	4.17893i	0.0814713	+	0.141112i	0.903882	−	0.427782i	$-0.140705\pi$
$877$	2.41271	+	4.17893i	0.0814713	+	0.141112i	−0.822411	+	0.568894i	$0.807371\pi$
$878$	7.39969	+	12.8166i	0.249727	+	0.432541i
$879$			17.7323i			0.598095i
$880$		0			0
$881$	−2.98574	+	5.17145i	−0.100592	+	0.174231i	−0.911929	−	0.410349i	$-0.865407\pi$
$881$	−2.98574	+	5.17145i	−0.100592	+	0.174231i	0.811337	+	0.584579i	$0.198740\pi$
$882$	0.256215	−	0.443778i	0.00862721	−	0.0149428i
$883$		−	36.7779i		−	1.23767i	−0.785520	−	0.618837i	$-0.787604\pi$
$883$		−	36.7779i		−	1.23767i	0.785520	−	0.618837i	$-0.212396\pi$
$884$	10.5951	+	0.582581i	0.356351	+	0.0195943i
$885$		0			0
$886$	−1.79964	−	1.03902i	−0.0604601	−	0.0349066i
$887$	−42.8974	−	24.7668i	−1.44035	−	0.831588i	−0.442480	−	0.896779i	$-0.645901\pi$
$887$	−42.8974	−	24.7668i	−1.44035	−	0.831588i	−0.997873	+	0.0651906i	$0.979234\pi$
$888$	4.55291	−	2.62862i	0.152786	−	0.0882108i
$889$		−	18.1328i		−	0.608154i
$890$		0			0
$891$	1.15713	−	0.668069i	0.0387653	−	0.0223812i
$892$	0.506692			0.0169653
$893$	70.7632	−	40.8551i	2.36800	−	1.36717i
$894$	3.95479	−	6.84990i	0.132268	−	0.229095i
$895$		0			0
$896$	2.54707			0.0850917
$897$	−12.9179	−	8.43625i	−0.431315	−	0.281678i
$898$			9.81754i			0.327616i
$899$	16.3214	+	9.42318i	0.544350	+	0.314281i
$900$		0			0
$901$	12.8723	+	22.2955i	0.428839	+	0.742770i
$902$	−3.93223			−0.130929
$903$	6.91980	+	11.9854i	0.230276	+	0.398851i
$904$		0			0
$905$		0			0
$906$	−8.59321	−	14.8839i	−0.285490	−	0.494483i
$907$	26.3728	+	15.2263i	0.875694	+	0.505582i	0.869236	−	0.494397i	$-0.164611\pi$
$907$	26.3728	+	15.2263i	0.875694	+	0.505582i	0.00645802	+	0.999979i	$0.497944\pi$
$908$	−2.07973	+	3.60219i	−0.0690181	+	0.119543i
$909$	0.517864			0.0171765
$910$		0			0
$911$	14.0258			0.464696			0.232348	−	0.972633i	$-0.425359\pi$
$911$	14.0258			0.464696			0.232348	+	0.972633i	$0.425359\pi$
$912$	−3.49465	+	6.05291i	−0.115719	+	0.200432i
$913$	−14.1679	−	8.17983i	−0.468888	−	0.270713i
$914$	−16.0683	−	27.8311i	−0.531491	−	0.920570i
$915$		0			0
$916$	19.3719	−	11.1844i	0.640067	−	0.369543i
$917$	−11.9997	−	20.7840i	−0.396264	−	0.686349i
$918$	2.94298			0.0971329
$919$	−2.17806	−	3.77251i	−0.0718476	−	0.124444i	0.827863	−	0.560930i	$-0.189556\pi$
$919$	−2.17806	−	3.77251i	−0.0718476	−	0.124444i	−0.899711	+	0.436486i	$0.856223\pi$
$920$		0			0
$921$	−5.77544	−	3.33445i	−0.190307	−	0.109874i
$922$		−	20.6626i		−	0.680487i
$923$	25.8313	−	39.5538i	0.850249	−	1.30193i
$924$	−3.40324			−0.111958
$925$		0			0
$926$	−9.10874	+	15.7768i	−0.299332	+	0.518458i
$927$	−2.09854	+	1.21159i	−0.0689250	+	0.0397939i
$928$	2.15441			0.0707221
$929$	31.7664	−	18.3403i	1.04222	−	0.601727i	0.121759	−	0.992560i	$-0.461146\pi$
$929$	31.7664	−	18.3403i	1.04222	−	0.601727i	0.920462	+	0.390833i	$0.127813\pi$
$930$		0			0
$931$		−	3.58153i		−	0.117380i
$932$	7.64121	−	4.41166i	0.250296	−	0.144509i
$933$	16.9943	+	9.81164i	0.556367	+	0.321219i
$934$	−4.86628	−	2.80955i	−0.159229	−	0.0919312i
$935$		0			0
$936$	3.01881	+	1.97149i	0.0986729	+	0.0644402i
$937$			37.1292i			1.21296i	0.795100	+	0.606478i	$0.207418\pi$
$937$			37.1292i			1.21296i	−0.795100	+	0.606478i	$0.792582\pi$
$938$	−7.75161	+	13.4262i	−0.253099	+	0.438381i
$939$	6.52692	−	11.3050i	0.212998	−	0.368923i
$940$		0			0
$941$		−	4.28642i		−	0.139733i	−0.997556	−	0.0698666i	$-0.977743\pi$
$941$		−	4.28642i		−	0.139733i	0.997556	−	0.0698666i	$-0.0222574\pi$
$942$	1.28052	+	2.21792i	0.0417215	+	0.0722637i
$943$	6.29669	+	10.9062i	0.205048	+	0.355154i
$944$			9.53636i			0.310382i
$945$		0			0
$946$	−3.62998	+	6.28731i	−0.118021	+	0.204418i
$947$	−20.6314	+	35.7346i	−0.670429	+	1.16122i	0.307353	+	0.951596i	$0.400557\pi$
$947$	−20.6314	+	35.7346i	−0.670429	+	1.16122i	−0.977782	+	0.209622i	$0.932777\pi$
$948$			13.9773i			0.453961i
$949$	−8.35117	+	4.22813i	−0.271091	+	0.137251i
$950$		0			0
$951$	16.2740	+	9.39578i	0.527719	+	0.304679i
$952$	−6.49171	−	3.74799i	−0.210398	−	0.121473i
$953$	−6.13723	+	3.54333i	−0.198804	+	0.114780i	−0.596098	−	0.802912i	$-0.703283\pi$
$953$	−6.13723	+	3.54333i	−0.198804	+	0.114780i	0.397293	+	0.917692i	$0.369950\pi$
$954$			8.74779i			0.283220i
$955$		0			0
$956$	−22.1904	+	12.8116i	−0.717689	+	0.414358i
$957$	−2.87859			−0.0930517
$958$	−23.1239	+	13.3506i	−0.747098	+	0.431337i
$959$	23.6199	−	40.9109i	0.762726	−	1.32108i
$960$		0			0
$961$	−45.5239			−1.46851
$962$	−15.8706	−	10.3646i	−0.511689	−	0.334168i
$963$			6.12516i			0.197381i
$964$	11.9346	+	6.89042i	0.384386	+	0.221926i
$965$		0			0
$966$	5.44961	+	9.43901i	0.175338	+	0.303695i
$967$	29.4591			0.947340			0.473670	−	0.880702i	$-0.342929\pi$
$967$	29.4591			0.947340			0.473670	+	0.880702i	$0.342929\pi$
$968$	4.60737	+	7.98019i	0.148086	+	0.256493i
$969$	17.8136	−	10.2847i	0.572255	−	0.330392i
$970$		0			0
$971$	−25.6123	−	44.3618i	−0.821938	−	1.42364i	−0.904237	−	0.427031i	$-0.859559\pi$
$971$	−25.6123	−	44.3618i	−0.821938	−	1.42364i	0.0822983	−	0.996608i	$-0.473774\pi$
$972$	0.866025	+	0.500000i	0.0277778	+	0.0160375i
$973$	25.1112	−	43.4938i	0.805028	−	1.39435i
$974$	31.0293			0.994242
$975$		0			0
$976$	−7.25724			−0.232299
$977$	1.75058	−	3.03210i	0.0560061	−	0.0970054i	−0.836663	−	0.547718i	$-0.815497\pi$
$977$	1.75058	−	3.03210i	0.0560061	−	0.0970054i	0.892669	+	0.450713i	$0.148830\pi$
$978$	15.2553	+	8.80763i	0.487810	+	0.281637i
$979$	7.75980	+	13.4404i	0.248004	+	0.429556i
$980$		0			0
$981$	−0.474209	+	0.273784i	−0.0151403	+	0.00874126i
$982$	7.27846	+	12.6067i	0.232265	+	0.402295i
$983$	0.473855			0.0151136			0.00755682	−	0.999971i	$-0.497595\pi$
$983$	0.473855			0.0151136			0.00755682	+	0.999971i	$0.497595\pi$
$984$	−1.47149	−	2.54870i	−0.0469094	−	0.0812495i
$985$		0			0
$986$	−5.49095	−	3.17020i	−0.174867	−	0.100960i
$987$			29.7772i			0.947820i
$988$	25.1622	+	1.38357i	0.800518	+	0.0440173i
$989$	23.2508			0.739331
$990$		0			0
$991$	4.50506	−	7.80299i	0.143108	−	0.247870i	−0.785558	−	0.618789i	$-0.787624\pi$
$991$	4.50506	−	7.80299i	0.143108	−	0.247870i	0.928665	+	0.370918i	$0.120957\pi$
$992$	−7.57581	+	4.37390i	−0.240532	+	0.138871i
$993$	−23.5574			−0.747572
$994$	−28.9017	+	16.6864i	−0.916707	+	0.529261i
$995$		0			0
$996$		−	12.2440i		−	0.387965i
$997$	−27.9096	+	16.1136i	−0.883906	+	0.510324i	−0.871944	−	0.489605i	$-0.837141\pi$
$997$	−27.9096	+	16.1136i	−0.883906	+	0.510324i	−0.0119620	+	0.999928i	$0.503808\pi$
$998$	23.0251	+	13.2935i	0.728846	+	0.420799i
$999$	−4.55291	−	2.62862i	−0.144048	−	0.0831659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.y.n.199.6		12
5.2	odd	4		1950.2.bc.k.901.4	yes	12
5.3	odd	4		1950.2.bc.h.901.3	yes	12
5.4	even	2		1950.2.y.m.199.1		12
13.10	even	6		1950.2.y.m.49.1		12
65.23	odd	12		1950.2.bc.h.751.3	✓	12
65.49	even	6	inner	1950.2.y.n.49.6		12
65.62	odd	12		1950.2.bc.k.751.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.y.m.49.1		12	13.10	even	6
1950.2.y.m.199.1		12	5.4	even	2
1950.2.y.n.49.6		12	65.49	even	6	inner
1950.2.y.n.199.6		12	1.1	even	1	trivial
1950.2.bc.h.751.3	✓	12	65.23	odd	12
1950.2.bc.h.901.3	yes	12	5.3	odd	4
1950.2.bc.k.751.4	yes	12	65.62	odd	12
1950.2.bc.k.901.4	yes	12	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(1.27354 + 2.20583i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(1.27354 + 2.20583i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.15713 - 0.668069i) q^{11} -1.00000i q^{12} +(-3.21677 + 1.62862i) q^{13} +2.54707 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.54870 - 1.47149i) q^{17} +1.00000 q^{18} +(6.05291 - 3.49465i) q^{19} +2.54707i q^{21} +(-1.15713 + 0.668069i) q^{22} +(3.70583 + 2.13956i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-0.197956 + 3.60011i) q^{26} +1.00000i q^{27} +(1.27354 - 2.20583i) q^{28} +(1.07721 - 1.86578i) q^{29} +8.74779i q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.668069 - 1.15713i) q^{33} -2.94298i q^{34} +(0.500000 - 0.866025i) q^{36} +(-2.62862 + 4.55291i) q^{37} -6.98929i q^{38} +(-3.60011 - 0.197956i) q^{39} +(2.54870 + 1.47149i) q^{41} +(2.20583 + 1.27354i) q^{42} +(4.70558 - 2.71677i) q^{43} +1.33614i q^{44} +(3.70583 - 2.13956i) q^{46} +11.6908 q^{47} +(-0.866025 + 0.500000i) q^{48} +(0.256215 - 0.443778i) q^{49} +2.94298 q^{51} +(3.01881 + 1.97149i) q^{52} +8.74779i q^{53} +(0.866025 + 0.500000i) q^{54} +(-1.27354 - 2.20583i) q^{56} +6.98929 q^{57} +(-1.07721 - 1.86578i) q^{58} +(8.25873 - 4.76818i) q^{59} +(3.62862 + 6.28496i) q^{61} +(7.57581 + 4.37390i) q^{62} +(-1.27354 + 2.20583i) q^{63} +1.00000 q^{64} -1.33614 q^{66} +(-3.04334 + 5.27123i) q^{67} +(-2.54870 - 1.47149i) q^{68} +(2.13956 + 3.70583i) q^{69} +(-11.3470 + 6.55122i) q^{71} +(-0.500000 - 0.866025i) q^{72} +2.59614 q^{73} +(2.62862 + 4.55291i) q^{74} +(-6.05291 - 3.49465i) q^{76} -3.40324i q^{77} +(-1.97149 + 3.01881i) q^{78} -13.9773 q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.54870 - 1.47149i) q^{82} +12.2440 q^{83} +(2.20583 - 1.27354i) q^{84} -5.43353i q^{86} +(1.86578 - 1.07721i) q^{87} +(1.15713 + 0.668069i) q^{88} +(-10.0591 - 5.80763i) q^{89} +(-7.68913 - 5.02153i) q^{91} -4.27912i q^{92} +(-4.37390 + 7.57581i) q^{93} +(5.84539 - 10.1245i) q^{94} +1.00000i q^{96} +(0.765663 + 1.32617i) q^{97} +(-0.256215 - 0.443778i) q^{98} -1.33614i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} - 4 q^{7} - 12 q^{8} + 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - 6 * q^4 - 4 * q^7 - 12 * q^8 + 6 * q^9	\( 12 q + 6 q^{2} - 6 q^{4} - 4 q^{7} - 12 q^{8} + 6 q^{9} - 12 q^{11} + 4 q^{13} - 8 q^{14} - 6 q^{16} + 12 q^{18} + 6 q^{19} - 12 q^{22} + 12 q^{23} - 4 q^{26} - 4 q^{28} + 6 q^{32} + 4 q^{33} + 6 q^{36} - 12 q^{37} - 6 q^{39} - 6 q^{42} + 12 q^{43} + 12 q^{46} + 16 q^{47} - 32 q^{49} - 8 q^{52} + 4 q^{56} + 24 q^{57} + 24 q^{61} + 4 q^{63} + 12 q^{64} + 8 q^{66} + 24 q^{67} - 4 q^{69} + 12 q^{71} - 6 q^{72} - 40 q^{73} + 12 q^{74} - 6 q^{76} - 6 q^{78} - 52 q^{79} - 6 q^{81} + 32 q^{83} - 6 q^{84} + 12 q^{88} - 24 q^{89} - 54 q^{91} - 8 q^{93} + 8 q^{94} + 24 q^{97} + 32 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 - 4 * q^7 - 12 * q^8 + 6 * q^9 - 12 * q^11 + 4 * q^13 - 8 * q^14 - 6 * q^16 + 12 * q^18 + 6 * q^19 - 12 * q^22 + 12 * q^23 - 4 * q^26 - 4 * q^28 + 6 * q^32 + 4 * q^33 + 6 * q^36 - 12 * q^37 - 6 * q^39 - 6 * q^42 + 12 * q^43 + 12 * q^46 + 16 * q^47 - 32 * q^49 - 8 * q^52 + 4 * q^56 + 24 * q^57 + 24 * q^61 + 4 * q^63 + 12 * q^64 + 8 * q^66 + 24 * q^67 - 4 * q^69 + 12 * q^71 - 6 * q^72 - 40 * q^73 + 12 * q^74 - 6 * q^76 - 6 * q^78 - 52 * q^79 - 6 * q^81 + 32 * q^83 - 6 * q^84 + 12 * q^88 - 24 * q^89 - 54 * q^91 - 8 * q^93 + 8 * q^94 + 24 * q^97 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more