LMFDB - Embedded newform 1950.2.bc.e.751.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1950,2,Mod(751,1950)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1950.751"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1950, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.bc (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-4,4,0,0,0,0,-4,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.1
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1950.751
Dual form			1950.2.bc.e.901.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(0.417738 + 0.241181i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.00731 + 1.15892i) q^{11} -1.00000 q^{12} +(-3.08725 + 1.86250i) q^{13} -0.482362 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.39778 - 5.88512i) q^{17} -1.00000i q^{18} +(4.39778 + 2.53906i) q^{19} -0.482362i q^{21} +(1.15892 - 2.00731i) q^{22} +(-3.45327 - 5.98124i) q^{23} +(0.866025 - 0.500000i) q^{24} +(1.74238 - 3.15660i) q^{26} +1.00000 q^{27} +(0.417738 - 0.241181i) q^{28} +(4.20478 + 7.28290i) q^{29} +0.952516i q^{31} +(0.866025 + 0.500000i) q^{32} +(2.00731 + 1.15892i) q^{33} +6.79555i q^{34} +(0.500000 + 0.866025i) q^{36} +(-5.35948 + 3.09429i) q^{37} -5.07812 q^{38} +(3.15660 + 1.74238i) q^{39} +(7.55607 - 4.36250i) q^{41} +(0.241181 + 0.417738i) q^{42} +(-5.64747 + 9.78170i) q^{43} +2.31784i q^{44} +(5.98124 + 3.45327i) q^{46} +5.77729i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-3.38366 - 5.86068i) q^{49} -6.79555 q^{51} +(0.0693504 + 3.60488i) q^{52} +5.81017 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.241181 + 0.417738i) q^{56} -5.07812i q^{57} +(-7.28290 - 4.20478i) q^{58} +(10.2397 + 5.91189i) q^{59} +(-4.68764 + 8.11924i) q^{61} +(-0.476258 - 0.824903i) q^{62} +(-0.417738 + 0.241181i) q^{63} -1.00000 q^{64} -2.31784 q^{66} +(6.40300 - 3.69677i) q^{67} +(-3.39778 - 5.88512i) q^{68} +(-3.45327 + 5.98124i) q^{69} +(3.01876 + 1.74288i) q^{71} +(-0.866025 - 0.500000i) q^{72} -8.53465i q^{73} +(3.09429 - 5.35948i) q^{74} +(4.39778 - 2.53906i) q^{76} -1.11804 q^{77} +(-3.60488 + 0.0693504i) q^{78} +9.03820 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-4.36250 + 7.55607i) q^{82} -7.94887i q^{83} +(-0.417738 - 0.241181i) q^{84} -11.2949i q^{86} +(4.20478 - 7.28290i) q^{87} +(-1.15892 - 2.00731i) q^{88} +(7.80941 - 4.50877i) q^{89} +(-1.73886 + 0.0334520i) q^{91} -6.90654 q^{92} +(0.824903 - 0.476258i) q^{93} +(-2.88865 - 5.00328i) q^{94} -1.00000i q^{96} +(7.95189 + 4.59103i) q^{97} +(5.86068 + 3.38366i) q^{98} -2.31784i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} - 12 q^{11} - 8 q^{12} - 8 q^{14} - 4 q^{16} + 4 q^{17} + 12 q^{19} + 8 q^{22} + 4 q^{23} + 8 q^{27} + 4 q^{29} + 12 q^{33} + 4 q^{36} - 24 q^{37} + 4 q^{42} - 4 q^{43}+ \cdots + 12 q^{98}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9 - 12 * q^11 - 8 * q^12 - 8 * q^14 - 4 * q^16 + 4 * q^17 + 12 * q^19 + 8 * q^22 + 4 * q^23 + 8 * q^27 + 4 * q^29 + 12 * q^33 + 4 * q^36 - 24 * q^37 + 4 * q^42 - 4 * q^43 + 12 * q^46 - 4 * q^48 - 16 * q^49 - 8 * q^51 - 8 * q^53 - 4 * q^56 + 12 * q^58 - 12 * q^59 - 16 * q^61 + 4 * q^62 - 8 * q^64 - 16 * q^66 + 24 * q^67 - 4 * q^68 + 4 * q^69 + 60 * q^71 + 16 * q^74 + 12 * q^76 - 8 * q^77 - 8 * q^79 - 4 * q^81 - 20 * q^82 + 4 * q^87 - 8 * q^88 + 24 * q^89 + 8 * q^91 + 8 * q^92 - 24 * q^93 + 16 * q^94 + 12 * q^97 + 12 * q^98

Character values

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

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	0.417738	+	0.241181i	0.157890	+	0.0911578i	0.576863	−	0.816841i	$-0.304277\pi$
$7$	0.417738	+	0.241181i	0.157890	+	0.0911578i	−0.418973	+	0.907999i	$0.637610\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.00731	+	1.15892i	−0.605226	+	0.349427i	−0.771095	−	0.636721i	$-0.780290\pi$
$11$	−2.00731	+	1.15892i	−0.605226	+	0.349427i	0.165869	+	0.986148i	$0.446957\pi$
$12$	−1.00000			−0.288675
$13$	−3.08725	+	1.86250i	−0.856248	+	0.516565i
$13$	−3.08725	+	1.86250i	−0.856248	+	0.516565i
$14$	−0.482362			−0.128917
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.39778	−	5.88512i	0.824082	−	1.42735i	−0.0785367	−	0.996911i	$-0.525025\pi$
$17$	3.39778	−	5.88512i	0.824082	−	1.42735i	0.902619	−	0.430441i	$-0.141642\pi$
$18$		−	1.00000i		−	0.235702i
$19$	4.39778	+	2.53906i	1.00892	+	0.582500i	0.910875	−	0.412682i	$-0.135408\pi$
$19$	4.39778	+	2.53906i	1.00892	+	0.582500i	0.0980443	+	0.995182i	$0.468741\pi$
$20$		0			0
$21$		−	0.482362i		−	0.105260i
$22$	1.15892	−	2.00731i	0.247082	−	0.427959i
$23$	−3.45327	−	5.98124i	−0.720057	−	1.24718i	−0.960976	−	0.276630i	$-0.910782\pi$
$23$	−3.45327	−	5.98124i	−0.720057	−	1.24718i	0.240920	−	0.970545i	$-0.422551\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$		0			0
$26$	1.74238	−	3.15660i	0.341709	−	0.619060i
$27$	1.00000			0.192450
$28$	0.417738	−	0.241181i	0.0789450	−	0.0455789i
$29$	4.20478	+	7.28290i	0.780809	+	1.35240i	0.931471	+	0.363815i	$0.118526\pi$
$29$	4.20478	+	7.28290i	0.780809	+	1.35240i	−0.150662	+	0.988585i	$0.548141\pi$
$30$		0			0
$31$			0.952516i			0.171077i	0.996335	+	0.0855385i	$0.0272611\pi$
$31$			0.952516i			0.171077i	−0.996335	+	0.0855385i	$0.972739\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	2.00731	+	1.15892i	0.349427	+	0.201742i
$34$			6.79555i			1.16543i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−5.35948	+	3.09429i	−0.881092	+	0.508699i	−0.871018	−	0.491250i	$-0.836540\pi$
$37$	−5.35948	+	3.09429i	−0.881092	+	0.508699i	−0.0100739	+	0.999949i	$0.503207\pi$
$38$	−5.07812			−0.823779
$39$	3.15660	+	1.74238i	0.505460	+	0.279005i
$40$		0			0
$41$	7.55607	−	4.36250i	1.18006	−	0.681308i	0.224032	−	0.974582i	$-0.428078\pi$
$41$	7.55607	−	4.36250i	1.18006	−	0.681308i	0.956029	+	0.293274i	$0.0947447\pi$
$42$	0.241181	+	0.417738i	0.0372150	+	0.0644583i
$43$	−5.64747	+	9.78170i	−0.861231	+	1.49170i	0.00951136	+	0.999955i	$0.496972\pi$
$43$	−5.64747	+	9.78170i	−0.861231	+	1.49170i	−0.870742	+	0.491740i	$0.836361\pi$
$44$			2.31784i			0.349427i
$45$		0			0
$46$	5.98124	+	3.45327i	0.881886	+	0.509157i
$47$			5.77729i			0.842705i	0.906897	+	0.421353i	$0.138444\pi$
$47$			5.77729i			0.842705i	−0.906897	+	0.421353i	$0.861556\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−3.38366	−	5.86068i	−0.483380	−	0.837240i
$50$		0			0
$51$	−6.79555			−0.951568
$52$	0.0693504	+	3.60488i	0.00961716	+	0.499908i
$53$	5.81017			0.798088			0.399044	−	0.916932i	$-0.369342\pi$
$53$	5.81017			0.798088			0.399044	+	0.916932i	$0.369342\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$		0			0
$56$	−0.241181	+	0.417738i	−0.0322292	+	0.0558225i
$57$		−	5.07812i		−	0.672613i
$58$	−7.28290	−	4.20478i	−0.956292	−	0.552115i
$59$	10.2397	+	5.91189i	1.33309	+	0.769663i	0.985773	−	0.168083i	$-0.0537577\pi$
$59$	10.2397	+	5.91189i	1.33309	+	0.769663i	0.347322	+	0.937746i	$0.387091\pi$
$60$		0			0
$61$	−4.68764	+	8.11924i	−0.600191	+	1.03956i	0.392600	+	0.919709i	$0.371576\pi$
$61$	−4.68764	+	8.11924i	−0.600191	+	1.03956i	−0.992792	+	0.119853i	$0.961758\pi$
$62$	−0.476258	−	0.824903i	−0.0604848	−	0.104763i
$63$	−0.417738	+	0.241181i	−0.0526300	+	0.0303859i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−2.31784			−0.285306
$67$	6.40300	−	3.69677i	0.782251	−	0.451633i	−0.0549764	−	0.998488i	$-0.517508\pi$
$67$	6.40300	−	3.69677i	0.782251	−	0.451633i	0.837227	+	0.546855i	$0.184175\pi$
$68$	−3.39778	−	5.88512i	−0.412041	−	0.713676i
$69$	−3.45327	+	5.98124i	−0.415725	+	0.720057i
$70$		0			0
$71$	3.01876	+	1.74288i	0.358261	+	0.206842i	0.668318	−	0.743876i	$-0.267015\pi$
$71$	3.01876	+	1.74288i	0.358261	+	0.206842i	−0.310057	+	0.950718i	$0.600348\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$		−	8.53465i		−	0.998906i	−0.866341	−	0.499453i	$-0.833534\pi$
$73$		−	8.53465i		−	0.998906i	0.866341	−	0.499453i	$-0.166466\pi$
$74$	3.09429	−	5.35948i	0.359704	−	0.623026i
$75$		0			0
$76$	4.39778	−	2.53906i	0.504460	−	0.291250i
$77$	−1.11804			−0.127412
$78$	−3.60488	+	0.0693504i	−0.408173	+	0.00785238i
$79$	9.03820			1.01688			0.508438	−	0.861098i	$-0.330223\pi$
$79$	9.03820			1.01688			0.508438	+	0.861098i	$0.330223\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.36250	+	7.55607i	−0.481758	+	0.834429i
$83$		−	7.94887i		−	0.872502i	−0.899825	−	0.436251i	$-0.856306\pi$
$83$		−	7.94887i		−	0.872502i	0.899825	−	0.436251i	$-0.143694\pi$
$84$	−0.417738	−	0.241181i	−0.0455789	−	0.0263150i
$85$		0			0
$86$		−	11.2949i		−	1.21796i
$87$	4.20478	−	7.28290i	0.450800	−	0.780809i
$88$	−1.15892	−	2.00731i	−0.123541	−	0.213980i
$89$	7.80941	−	4.50877i	0.827796	−	0.477928i	−0.0253015	−	0.999680i	$-0.508055\pi$
$89$	7.80941	−	4.50877i	0.827796	−	0.477928i	0.853097	+	0.521752i	$0.174721\pi$
$90$		0			0
$91$	−1.73886	+	0.0334520i	−0.182282	+	0.00350672i
$92$	−6.90654			−0.720057
$93$	0.824903	−	0.476258i	0.0855385	−	0.0493857i
$94$	−2.88865	−	5.00328i	−0.297941	−	0.516049i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	7.95189	+	4.59103i	0.807392	+	0.466148i	0.846050	−	0.533104i	$-0.178975\pi$
$97$	7.95189	+	4.59103i	0.807392	+	0.466148i	−0.0386571	+	0.999253i	$0.512308\pi$
$98$	5.86068	+	3.38366i	0.592018	+	0.341802i
$99$		−	2.31784i		−	0.232951i
$100$		0			0
$101$	−5.34108	−	9.25102i	−0.531457	−	0.920511i	−0.999326	−	0.0367132i	$-0.988311\pi$
$101$	−5.34108	−	9.25102i	−0.531457	−	0.920511i	0.467868	−	0.883798i	$-0.345022\pi$
$102$	5.88512	−	3.39778i	0.582714	−	0.336430i
$103$	9.17449			0.903990			0.451995	−	0.892021i	$-0.350713\pi$
$103$	9.17449			0.903990			0.451995	+	0.892021i	$0.350713\pi$
$104$	−1.86250	−	3.08725i	−0.182633	−	0.302729i
$105$		0			0
$106$	−5.03175	+	2.90508i	−0.488727	+	0.282167i
$107$	1.60867	+	2.78629i	0.155516	+	0.269361i	0.933247	−	0.359236i	$-0.116963\pi$
$107$	1.60867	+	2.78629i	0.155516	+	0.269361i	−0.777731	+	0.628597i	$0.783629\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$			17.0669i			1.63471i	0.576132	+	0.817356i	$0.304561\pi$
$109$			17.0669i			1.63471i	−0.576132	+	0.817356i	$0.695439\pi$
$110$		0			0
$111$	5.35948	+	3.09429i	0.508699	+	0.293697i
$112$		−	0.482362i		−	0.0455789i
$113$	0.828427	−	1.43488i	0.0779319	−	0.134982i	−0.824426	−	0.565970i	$-0.808502\pi$
$113$	0.828427	−	1.43488i	0.0779319	−	0.134982i	0.902357	+	0.430988i	$0.141835\pi$
$114$	2.53906	+	4.39778i	0.237805	+	0.411890i
$115$		0			0
$116$	8.40957			0.780809
$117$	−0.0693504	−	3.60488i	−0.00641144	−	0.333272i
$118$	−11.8238			−1.08847
$119$	2.83876	−	1.63896i	0.260229	−	0.150243i
$120$		0			0
$121$	−2.81382	+	4.87367i	−0.255801	+	0.443061i
$122$		−	9.37529i		−	0.848799i
$123$	−7.55607	−	4.36250i	−0.681308	−	0.393353i
$124$	0.824903	+	0.476258i	0.0740785	+	0.0427692i
$125$		0			0
$126$	0.241181	−	0.417738i	0.0214861	−	0.0372150i
$127$	9.45946	+	16.3843i	0.839391	+	1.45387i	0.890405	+	0.455170i	$0.150422\pi$
$127$	9.45946	+	16.3843i	0.839391	+	1.45387i	−0.0510134	+	0.998698i	$0.516245\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	11.2949			0.994463
$130$		0			0
$131$	−6.96812			−0.608808			−0.304404	−	0.952543i	$-0.598457\pi$
$131$	−6.96812			−0.608808			−0.304404	+	0.952543i	$0.598457\pi$
$132$	2.00731	−	1.15892i	0.174714	−	0.100871i
$133$	1.22474	+	2.12132i	0.106199	+	0.183942i
$134$	−3.69677	+	6.40300i	−0.319353	+	0.553135i
$135$		0			0
$136$	5.88512	+	3.39778i	0.504645	+	0.291357i
$137$	17.7616	+	10.2547i	1.51748	+	0.876116i	0.999789	+	0.0205465i	$0.00654060\pi$
$137$	17.7616	+	10.2547i	1.51748	+	0.876116i	0.517688	+	0.855569i	$0.326793\pi$
$138$		−	6.90654i		−	0.587924i
$139$	4.25467	−	7.36931i	0.360877	−	0.625057i	−0.627229	−	0.778835i	$-0.715811\pi$
$139$	4.25467	−	7.36931i	0.360877	−	0.625057i	0.988105	+	0.153778i	$0.0491442\pi$
$140$		0			0
$141$	5.00328	−	2.88865i	0.421353	−	0.243268i
$142$	−3.48576			−0.292519
$143$	4.03856	−	7.31648i	0.337721	−	0.611835i
$144$	1.00000			0.0833333
$145$		0			0
$146$	4.26733	+	7.39123i	0.353166	+	0.611702i
$147$	−3.38366	+	5.86068i	−0.279080	+	0.483380i
$148$			6.18859i			0.508699i
$149$	6.27439	+	3.62252i	0.514018	+	0.296769i	0.734484	−	0.678626i	$-0.237424\pi$
$149$	6.27439	+	3.62252i	0.514018	+	0.296769i	−0.220466	+	0.975395i	$0.570758\pi$
$150$		0			0
$151$			7.82743i			0.636987i	0.947925	+	0.318494i	$0.103177\pi$
$151$			7.82743i			0.636987i	−0.947925	+	0.318494i	$0.896823\pi$
$152$	−2.53906	+	4.39778i	−0.205945	+	0.356707i
$153$	3.39778	+	5.88512i	0.274694	+	0.475784i
$154$	0.968248	−	0.559018i	0.0780236	−	0.0450470i
$155$		0			0
$156$	3.08725	−	1.86250i	0.247178	−	0.149119i
$157$	4.42267			0.352967			0.176484	−	0.984304i	$-0.443528\pi$
$157$	4.42267			0.352967			0.176484	+	0.984304i	$0.443528\pi$
$158$	−7.82731	+	4.51910i	−0.622707	+	0.359520i
$159$	−2.90508	−	5.03175i	−0.230388	−	0.399044i
$160$		0			0
$161$		−	3.33145i		−	0.262555i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	9.72060	+	5.61219i	0.761376	+	0.439581i	0.829790	−	0.558076i	$-0.188460\pi$
$163$	9.72060	+	5.61219i	0.761376	+	0.439581i	−0.0684135	+	0.997657i	$0.521794\pi$
$164$		−	8.72500i		−	0.681308i
$165$		0			0
$166$	3.97443	+	6.88392i	0.308476	+	0.534296i
$167$	−13.0406	+	7.52898i	−1.00911	+	0.582610i	−0.910931	−	0.412558i	$-0.864635\pi$
$167$	−13.0406	+	7.52898i	−1.00911	+	0.582610i	−0.0981794	+	0.995169i	$0.531302\pi$
$168$	0.482362			0.0372150
$169$	6.06218	−	11.5000i	0.466321	−	0.884615i
$170$		0			0
$171$	−4.39778	+	2.53906i	−0.336306	+	0.194167i
$172$	5.64747	+	9.78170i	0.430615	+	0.745848i
$173$	7.37429	−	12.7727i	0.560657	−	0.971087i	−0.436782	−	0.899567i	$-0.643882\pi$
$173$	7.37429	−	12.7727i	0.560657	−	0.971087i	0.997439	−	0.0715193i	$-0.0227847\pi$
$174$			8.40957i			0.637528i
$175$		0			0
$176$	2.00731	+	1.15892i	0.151306	+	0.0873568i
$177$		−	11.8238i		−	0.888730i
$178$	−4.50877	+	7.80941i	−0.337946	+	0.585340i
$179$	4.30589	+	7.45802i	0.321837	+	0.557438i	0.980867	−	0.194678i	$-0.0623663\pi$
$179$	4.30589	+	7.45802i	0.321837	+	0.557438i	−0.659030	+	0.752117i	$0.729033\pi$
$180$		0			0
$181$	2.84493			0.211462			0.105731	−	0.994395i	$-0.466282\pi$
$181$	2.84493			0.211462			0.105731	+	0.994395i	$0.466282\pi$
$182$	1.48917	−	0.898400i	0.110385	−	0.0665938i
$183$	9.37529			0.693041
$184$	5.98124	−	3.45327i	0.440943	−	0.254579i
$185$		0			0
$186$	−0.476258	+	0.824903i	−0.0349209	+	0.0604848i
$187$			15.7510i			1.15183i
$188$	5.00328	+	2.88865i	0.364902	+	0.210676i
$189$	0.417738	+	0.241181i	0.0303859	+	0.0175433i
$190$		0			0
$191$	1.71794	−	2.97555i	0.124306	−	0.215304i	−0.797156	−	0.603774i	$-0.793663\pi$
$191$	1.71794	−	2.97555i	0.124306	−	0.215304i	0.921461	+	0.388470i	$0.126996\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−2.30090	+	1.32843i	−0.165623	+	0.0956223i	−0.580520	−	0.814246i	$-0.697151\pi$
$193$	−2.30090	+	1.32843i	−0.165623	+	0.0956223i	0.414898	+	0.909868i	$0.363817\pi$
$194$	−9.18206			−0.659233
$195$		0			0
$196$	−6.76733			−0.483380
$197$	18.2868	−	10.5579i	1.30288	−	0.752219i	0.321984	−	0.946745i	$-0.395650\pi$
$197$	18.2868	−	10.5579i	1.30288	−	0.752219i	0.980897	+	0.194526i	$0.0623168\pi$
$198$	1.15892	+	2.00731i	0.0823608	+	0.142653i
$199$	5.26941	−	9.12688i	0.373538	−	0.646988i	−0.616569	−	0.787301i	$-0.711478\pi$
$199$	5.26941	−	9.12688i	0.373538	−	0.646988i	0.990107	+	0.140314i	$0.0448110\pi$
$200$		0			0
$201$	−6.40300	−	3.69677i	−0.451633	−	0.260750i
$202$	9.25102	+	5.34108i	0.650900	+	0.375797i
$203$			4.05646i			0.284707i
$204$	−3.39778	+	5.88512i	−0.237892	+	0.412041i
$205$		0			0
$206$	−7.94534	+	4.58725i	−0.553578	+	0.319609i
$207$	6.90654			0.480038
$208$	3.15660	+	1.74238i	0.218871	+	0.120813i
$209$	−11.7702			−0.814165
$210$		0			0
$211$	5.74384	+	9.94863i	0.395422	+	0.684892i	0.993155	−	0.116804i	$-0.0372649\pi$
$211$	5.74384	+	9.94863i	0.395422	+	0.684892i	−0.597733	+	0.801696i	$0.703932\pi$
$212$	2.90508	−	5.03175i	0.199522	−	0.345582i
$213$		−	3.48576i		−	0.238840i
$214$	−2.78629	−	1.60867i	−0.190467	−	0.109966i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	−0.229729	+	0.397902i	−0.0155950	+	0.0270113i
$218$	−8.53345	−	14.7804i	−0.577958	−	1.00105i
$219$	−7.39123	+	4.26733i	−0.499453	+	0.288359i
$220$		0			0
$221$	0.471274	+	24.4972i	0.0317013	+	1.64786i
$222$	−6.18859			−0.415351
$223$	−4.52739	+	2.61389i	−0.303176	+	0.175039i	−0.643869	−	0.765136i	$-0.722672\pi$
$223$	−4.52739	+	2.61389i	−0.303176	+	0.175039i	0.340693	+	0.940175i	$0.389338\pi$
$224$	0.241181	+	0.417738i	0.0161146	+	0.0279113i
$225$		0			0
$226$			1.65685i			0.110212i
$227$	−9.41271	−	5.43443i	−0.624744	−	0.360696i	0.153970	−	0.988076i	$-0.450794\pi$
$227$	−9.41271	−	5.43443i	−0.624744	−	0.360696i	−0.778714	+	0.627380i	$0.784127\pi$
$228$	−4.39778	−	2.53906i	−0.291250	−	0.168153i
$229$		−	21.1932i		−	1.40048i	−0.713905	−	0.700242i	$-0.753075\pi$
$229$		−	21.1932i		−	1.40048i	0.713905	−	0.700242i	$-0.246925\pi$
$230$		0			0
$231$	0.559018	+	0.968248i	0.0367807	+	0.0637060i
$232$	−7.28290	+	4.20478i	−0.478146	+	0.276058i
$233$	−21.8423			−1.43094			−0.715469	−	0.698645i	$-0.753787\pi$
$233$	−21.8423			−1.43094			−0.715469	+	0.698645i	$0.753787\pi$
$234$	1.86250	+	3.08725i	0.121756	+	0.201820i
$235$		0			0
$236$	10.2397	−	5.91189i	0.666547	−	0.384831i
$237$	−4.51910	−	7.82731i	−0.293547	−	0.508438i
$238$	−1.63896	+	2.83876i	−0.106238	+	0.184009i
$239$			8.23027i			0.532372i	0.963922	+	0.266186i	$0.0857635\pi$
$239$			8.23027i			0.532372i	−0.963922	+	0.266186i	$0.914236\pi$
$240$		0			0
$241$	−2.68678	−	1.55121i	−0.173071	−	0.0999225i	0.410962	−	0.911652i	$-0.365193\pi$
$241$	−2.68678	−	1.55121i	−0.173071	−	0.0999225i	−0.584033	+	0.811730i	$0.698526\pi$
$242$		−	5.62763i		−	0.361758i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	4.68764	+	8.11924i	0.300096	+	0.519781i
$245$		0			0
$246$	8.72500			0.556286
$247$	−18.3060	+	0.352169i	−1.16478	+	0.0224080i
$248$	−0.952516			−0.0604848
$249$	−6.88392	+	3.97443i	−0.436251	+	0.251870i
$250$		0			0
$251$	7.81042	−	13.5281i	0.492990	−	0.853883i	−0.506978	−	0.861959i	$-0.669237\pi$
$251$	7.81042	−	13.5281i	0.492990	−	0.853883i	0.999967	+	0.00807605i	$0.00257072\pi$
$252$			0.482362i			0.0303859i
$253$	13.8635	+	8.00412i	0.871594	+	0.503215i
$254$	−16.3843	−	9.45946i	−1.02804	−	0.593539i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.76210	−	3.05205i	−0.109917	−	0.190382i	0.805819	−	0.592161i	$-0.201725\pi$
$257$	−1.76210	−	3.05205i	−0.109917	−	0.190382i	−0.915736	+	0.401780i	$0.868392\pi$
$258$	−9.78170	+	5.64747i	−0.608982	+	0.351596i
$259$	−2.98514			−0.185488
$260$		0			0
$261$	−8.40957			−0.520539
$262$	6.03457	−	3.48406i	0.372817	−	0.215246i
$263$	11.6415	+	20.1637i	0.717845	+	1.24334i	0.961852	+	0.273571i	$0.0882049\pi$
$263$	11.6415	+	20.1637i	0.717845	+	1.24334i	−0.244006	+	0.969774i	$0.578462\pi$
$264$	−1.15892	+	2.00731i	−0.0713265	+	0.123541i
$265$		0			0
$266$	−2.12132	−	1.22474i	−0.130066	−	0.0750939i
$267$	−7.80941	−	4.50877i	−0.477928	−	0.275932i
$268$		−	7.39355i		−	0.451633i
$269$	−4.90873	+	8.50217i	−0.299291	+	0.518387i	−0.975974	−	0.217888i	$-0.930083\pi$
$269$	−4.90873	+	8.50217i	−0.299291	+	0.518387i	0.676683	+	0.736274i	$0.263417\pi$
$270$		0			0
$271$	−18.8862	+	10.9040i	−1.14726	+	0.662369i	−0.948217	−	0.317623i	$-0.897115\pi$
$271$	−18.8862	+	10.9040i	−1.14726	+	0.662369i	−0.199039	+	0.979992i	$0.563782\pi$
$272$	−6.79555			−0.412041
$273$	0.898400	+	1.48917i	0.0543736	+	0.0901287i
$274$	−20.5093			−1.23901
$275$		0			0
$276$	3.45327	+	5.98124i	0.207863	+	0.360028i
$277$	6.73753	−	11.6697i	0.404819	−	0.701167i	−0.589481	−	0.807782i	$-0.700668\pi$
$277$	6.73753	−	11.6697i	0.404819	−	0.701167i	0.994300	+	0.106615i	$0.0340012\pi$
$278$			8.50935i			0.510357i
$279$	−0.824903	−	0.476258i	−0.0493857	−	0.0285128i
$280$		0			0
$281$		−	29.6167i		−	1.76678i	−0.468635	−	0.883392i	$-0.655254\pi$
$281$		−	29.6167i		−	1.76678i	0.468635	−	0.883392i	$-0.344746\pi$
$282$	−2.88865	+	5.00328i	−0.172016	+	0.297941i
$283$	6.09197	+	10.5516i	0.362130	+	0.627228i	0.988311	−	0.152450i	$-0.0487163\pi$
$283$	6.09197	+	10.5516i	0.362130	+	0.627228i	−0.626181	+	0.779678i	$0.715383\pi$
$284$	3.01876	−	1.74288i	0.179130	−	0.103421i
$285$		0			0
$286$	0.160743	+	8.35554i	0.00950492	+	0.494073i
$287$	4.20861			0.248426
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	−14.5898	−	25.2702i	−0.858223	−	1.48649i
$290$		0			0
$291$		−	9.18206i		−	0.538262i
$292$	−7.39123	−	4.26733i	−0.432539	−	0.249726i
$293$	13.0085	+	7.51047i	0.759965	+	0.438766i	0.829283	−	0.558829i	$-0.188749\pi$
$293$	13.0085	+	7.51047i	0.759965	+	0.438766i	−0.0693181	+	0.997595i	$0.522082\pi$
$294$		−	6.76733i		−	0.394679i
$295$		0			0
$296$	−3.09429	−	5.35948i	−0.179852	−	0.311513i
$297$	−2.00731	+	1.15892i	−0.116476	+	0.0672473i
$298$	−7.24504			−0.419694
$299$	21.8012	+	12.0338i	1.26079	+	0.695935i
$300$		0			0
$301$	−4.71832	+	2.72412i	−0.271959	+	0.157016i
$302$	−3.91372	−	6.77875i	−0.225209	−	0.390073i
$303$	−5.34108	+	9.25102i	−0.306837	+	0.531457i
$304$		−	5.07812i		−	0.291250i
$305$		0			0
$306$	−5.88512	−	3.39778i	−0.336430	−	0.194238i
$307$			27.9569i			1.59558i	0.602934	+	0.797791i	$0.293998\pi$
$307$			27.9569i			1.59558i	−0.602934	+	0.797791i	$0.706002\pi$
$308$	−0.559018	+	0.968248i	−0.0318530	+	0.0551710i
$309$	−4.58725	−	7.94534i	−0.260959	−	0.451995i
$310$		0			0
$311$	14.3067			0.811256			0.405628	−	0.914038i	$-0.367053\pi$
$311$	14.3067			0.811256			0.405628	+	0.914038i	$0.367053\pi$
$312$	−1.74238	+	3.15660i	−0.0986430	+	0.178707i
$313$	13.9895			0.790731			0.395366	−	0.918524i	$-0.370618\pi$
$313$	13.9895			0.790731			0.395366	+	0.918524i	$0.370618\pi$
$314$	−3.83014	+	2.21134i	−0.216148	+	0.124793i
$315$		0			0
$316$	4.51910	−	7.82731i	0.254219	−	0.440320i
$317$			7.29868i			0.409935i	0.978769	+	0.204967i	$0.0657089\pi$
$317$			7.29868i			0.409935i	−0.978769	+	0.204967i	$0.934291\pi$
$318$	5.03175	+	2.90508i	0.282167	+	0.162909i
$319$	−16.8806	−	9.74601i	−0.945131	−	0.545672i
$320$		0			0
$321$	1.60867	−	2.78629i	0.0897870	−	0.155516i
$322$	1.66573	+	2.88512i	0.0928273	+	0.160782i
$323$	29.8853	−	17.2543i	1.66286	−	0.960055i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−11.2244			−0.621661
$327$	14.7804	−	8.53345i	0.817356	−	0.471901i
$328$	4.36250	+	7.55607i	0.240879	+	0.417214i
$329$	−1.39337	+	2.41339i	−0.0768192	+	0.133055i
$330$		0			0
$331$	22.8279	+	13.1797i	1.25474	+	0.724423i	0.972046	−	0.234788i	$-0.0754397\pi$
$331$	22.8279	+	13.1797i	1.25474	+	0.724423i	0.282690	+	0.959211i	$0.408773\pi$
$332$	−6.88392	−	3.97443i	−0.377804	−	0.218125i
$333$		−	6.18859i		−	0.339133i
$334$	7.52898	−	13.0406i	0.411968	−	0.713549i
$335$		0			0
$336$	−0.417738	+	0.241181i	−0.0227895	+	0.0131575i
$337$	−24.4240			−1.33046			−0.665229	−	0.746639i	$-0.731666\pi$
$337$	−24.4240			−1.33046			−0.665229	+	0.746639i	$0.731666\pi$
$338$	0.500000	+	12.9904i	0.0271964	+	0.706584i
$339$	−1.65685			−0.0899880
$340$		0			0
$341$	−1.10389	−	1.91199i	−0.0597789	−	0.103540i
$342$	2.53906	−	4.39778i	0.137297	−	0.237805i
$343$		−	6.64083i		−	0.358571i
$344$	−9.78170	−	5.64747i	−0.527394	−	0.304491i
$345$		0			0
$346$			14.7486i			0.792889i
$347$	−6.70818	+	11.6189i	−0.360114	+	0.623736i	−0.987979	−	0.154586i	$-0.950596\pi$
$347$	−6.70818	+	11.6189i	−0.360114	+	0.623736i	0.627865	+	0.778322i	$0.283929\pi$
$348$	−4.20478	−	7.28290i	−0.225400	−	0.390404i
$349$	0.824457	−	0.476000i	0.0441322	−	0.0254797i	−0.477772	−	0.878484i	$-0.658555\pi$
$349$	0.824457	−	0.476000i	0.0441322	−	0.0254797i	0.521904	+	0.853004i	$0.325222\pi$
$350$		0			0
$351$	−3.08725	+	1.86250i	−0.164785	+	0.0994130i
$352$	−2.31784			−0.123541
$353$	12.5120	−	7.22380i	0.665946	−	0.384484i	−0.128593	−	0.991697i	$-0.541046\pi$
$353$	12.5120	−	7.22380i	0.665946	−	0.384484i	0.794539	+	0.607213i	$0.207713\pi$
$354$	5.91189	+	10.2397i	0.314213	+	0.544234i
$355$		0			0
$356$		−	9.01753i		−	0.477928i
$357$	−2.83876	−	1.63896i	−0.150243	−	0.0867429i
$358$	−7.45802	−	4.30589i	−0.394168	−	0.227573i
$359$			8.11291i			0.428183i	0.976814	+	0.214092i	$0.0686791\pi$
$359$			8.11291i			0.428183i	−0.976814	+	0.214092i	$0.931321\pi$
$360$		0			0
$361$	3.39363	+	5.87794i	0.178612	+	0.309365i
$362$	−2.46378	+	1.42246i	−0.129493	+	0.0747630i
$363$	5.62763			0.295374
$364$	−0.840459	+	1.52262i	−0.0440520	+	0.0798071i
$365$		0			0
$366$	−8.11924	+	4.68764i	−0.424399	+	0.245027i
$367$	11.9977	+	20.7806i	0.626274	+	1.08474i	0.988293	+	0.152568i	$0.0487543\pi$
$367$	11.9977	+	20.7806i	0.626274	+	1.08474i	−0.362019	+	0.932171i	$0.617912\pi$
$368$	−3.45327	+	5.98124i	−0.180014	+	0.311794i
$369$			8.72500i			0.454205i
$370$		0			0
$371$	2.42713	+	1.40130i	0.126010	+	0.0727520i
$372$		−	0.952516i		−	0.0493857i
$373$	−13.4288	+	23.2593i	−0.695316	+	1.20432i	0.274758	+	0.961513i	$0.411402\pi$
$373$	−13.4288	+	23.2593i	−0.695316	+	1.20432i	−0.970074	+	0.242809i	$0.921931\pi$
$374$	−7.87550	−	13.6408i	−0.407232	−	0.705347i
$375$		0			0
$376$	−5.77729			−0.297941
$377$	−26.5456	−	14.6527i	−1.36717	−	0.754652i
$378$	−0.482362			−0.0248100
$379$	−13.2638	+	7.65785i	−0.681315	+	0.393357i	−0.800350	−	0.599533i	$-0.795353\pi$
$379$	−13.2638	+	7.65785i	−0.681315	+	0.393357i	0.119035	+	0.992890i	$0.462020\pi$
$380$		0			0
$381$	9.45946	−	16.3843i	0.484623	−	0.839391i
$382$			3.43587i			0.175795i
$383$	−30.5185	−	17.6198i	−1.55942	−	0.900332i	−0.997312	−	0.0732675i	$-0.976657\pi$
$383$	−30.5185	−	17.6198i	−1.55942	−	0.900332i	−0.562108	−	0.827064i	$-0.690009\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$		0			0
$386$	1.32843	−	2.30090i	0.0676152	−	0.117113i
$387$	−5.64747	−	9.78170i	−0.287077	−	0.497232i
$388$	7.95189	−	4.59103i	0.403696	−	0.233074i
$389$	−18.0946			−0.917433			−0.458717	−	0.888583i	$-0.651691\pi$
$389$	−18.0946			−0.917433			−0.458717	+	0.888583i	$0.651691\pi$
$390$		0			0
$391$	−46.9338			−2.37354
$392$	5.86068	−	3.38366i	0.296009	−	0.170901i
$393$	3.48406	+	6.03457i	0.175748	+	0.304404i
$394$	−10.5579	+	18.2868i	−0.531899	+	0.921276i
$395$		0			0
$396$	−2.00731	−	1.15892i	−0.100871	−	0.0582379i
$397$	9.05105	+	5.22562i	0.454259	+	0.262267i	0.709627	−	0.704577i	$-0.248863\pi$
$397$	9.05105	+	5.22562i	0.454259	+	0.262267i	−0.255368	+	0.966844i	$0.582197\pi$
$398$			10.5388i			0.528263i
$399$	1.22474	−	2.12132i	0.0613139	−	0.106199i
$400$		0			0
$401$	−1.21317	+	0.700423i	−0.0605827	+	0.0349775i	−0.529985	−	0.848007i	$-0.677803\pi$
$401$	−1.21317	+	0.700423i	−0.0605827	+	0.0349775i	0.469403	+	0.882984i	$0.344469\pi$
$402$	7.39355			0.368757
$403$	−1.77406	−	2.94065i	−0.0883723	−	0.146484i
$404$	−10.6822			−0.531457
$405$		0			0
$406$	−2.02823	−	3.51299i	−0.100659	−	0.174347i
$407$	7.17207	−	12.4224i	0.355506	−	0.615755i
$408$		−	6.79555i		−	0.336430i
$409$	5.83817	+	3.37067i	0.288679	+	0.166669i	0.637346	−	0.770578i	$-0.280032\pi$
$409$	5.83817	+	3.37067i	0.288679	+	0.166669i	−0.348667	+	0.937247i	$0.613366\pi$
$410$		0			0
$411$		−	20.5093i		−	1.01165i
$412$	4.58725	−	7.94534i	0.225997	−	0.391439i
$413$	2.85167	+	4.93924i	0.140322	+	0.243044i
$414$	−5.98124	+	3.45327i	−0.293962	+	0.169719i
$415$		0			0
$416$	−3.60488	+	0.0693504i	−0.176744	+	0.00340018i
$417$	−8.50935			−0.416704
$418$	10.1933	−	5.88512i	0.498572	−	0.287851i
$419$	−18.2539	−	31.6166i	−0.891760	−	1.54457i	−0.837765	−	0.546032i	$-0.816138\pi$
$419$	−18.2539	−	31.6166i	−0.891760	−	1.54457i	−0.0539949	−	0.998541i	$-0.517195\pi$
$420$		0			0
$421$		−	40.8490i		−	1.99086i	−0.0955005	−	0.995429i	$-0.530445\pi$
$421$		−	40.8490i		−	1.99086i	0.0955005	−	0.995429i	$-0.469555\pi$
$422$	−9.94863	−	5.74384i	−0.484292	−	0.279606i
$423$	−5.00328	−	2.88865i	−0.243268	−	0.140451i
$424$			5.81017i			0.282167i
$425$		0			0
$426$	1.74288	+	3.01876i	0.0844429	+	0.146259i
$427$	−3.91641	+	2.26114i	−0.189528	+	0.109424i
$428$	3.21733			0.155516
$429$	−8.35554	+	0.160743i	−0.403409	+	0.00776074i
$430$		0			0
$431$	−15.9145	+	9.18824i	−0.766575	+	0.442582i	−0.831651	−	0.555298i	$-0.812604\pi$
$431$	−15.9145	+	9.18824i	−0.766575	+	0.442582i	0.0650767	+	0.997880i	$0.479271\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−0.699097	+	1.21087i	−0.0335964	+	0.0581907i	−0.882335	−	0.470622i	$-0.844029\pi$
$433$	−0.699097	+	1.21087i	−0.0335964	+	0.0581907i	0.848738	+	0.528813i	$0.177363\pi$
$434$		−	0.459457i		−	0.0220547i
$435$		0			0
$436$	14.7804	+	8.53345i	0.707851	+	0.408678i
$437$		−	35.0722i		−	1.67773i
$438$	4.26733	−	7.39123i	0.203901	−	0.353166i
$439$	−7.65685	−	13.2621i	−0.365442	−	0.632964i	0.623405	−	0.781899i	$-0.285749\pi$
$439$	−7.65685	−	13.2621i	−0.365442	−	0.632964i	−0.988847	+	0.148935i	$0.952415\pi$
$440$		0			0
$441$	6.76733			0.322254
$442$	−12.6567	−	20.9796i	−0.602019	−	0.997895i
$443$	−33.1769			−1.57628			−0.788141	−	0.615495i	$-0.788956\pi$
$443$	−33.1769			−1.57628			−0.788141	+	0.615495i	$0.788956\pi$
$444$	5.35948	−	3.09429i	0.254349	−	0.146849i
$445$		0			0
$446$	2.61389	−	4.52739i	0.123771	−	0.214378i
$447$		−	7.24504i		−	0.342679i
$448$	−0.417738	−	0.241181i	−0.0197362	−	0.0113947i
$449$	13.3408	+	7.70234i	0.629593	+	0.363496i	0.780595	−	0.625038i	$-0.214916\pi$
$449$	13.3408	+	7.70234i	0.629593	+	0.363496i	−0.151001	+	0.988534i	$0.548250\pi$
$450$		0			0
$451$	−10.1116	+	17.5137i	−0.476135	+	0.824690i
$452$	−0.828427	−	1.43488i	−0.0389659	−	0.0674910i
$453$	6.77875	−	3.91372i	0.318494	−	0.183882i
$454$	10.8689			0.510101
$455$		0			0
$456$	5.07812			0.237805
$457$	6.46224	−	3.73097i	0.302291	−	0.174528i	−0.341181	−	0.939998i	$-0.610827\pi$
$457$	6.46224	−	3.73097i	0.302291	−	0.174528i	0.643471	+	0.765470i	$0.277494\pi$
$458$	10.5966	+	18.3538i	0.495146	+	0.857618i
$459$	3.39778	−	5.88512i	0.158595	−	0.274694i
$460$		0			0
$461$	−3.97457	−	2.29472i	−0.185114	−	0.106876i	0.404579	−	0.914503i	$-0.367418\pi$
$461$	−3.97457	−	2.29472i	−0.185114	−	0.106876i	−0.589693	+	0.807627i	$0.700751\pi$
$462$	−0.968248	−	0.559018i	−0.0450470	−	0.0260079i
$463$		−	9.20888i		−	0.427973i	−0.976837	−	0.213986i	$-0.931355\pi$
$463$		−	9.20888i		−	0.427973i	0.976837	−	0.213986i	$-0.0686448\pi$
$464$	4.20478	−	7.28290i	0.195202	−	0.338100i
$465$		0			0
$466$	18.9160	−	10.9212i	0.876267	−	0.505913i
$467$	−0.219469			−0.0101558			−0.00507792	−	0.999987i	$-0.501616\pi$
$467$	−0.219469			−0.0101558			−0.00507792	+	0.999987i	$0.501616\pi$
$468$	−3.15660	−	1.74238i	−0.145914	−	0.0805417i
$469$	3.56637			0.164680
$470$		0			0
$471$	−2.21134	−	3.83014i	−0.101893	−	0.176484i
$472$	−5.91189	+	10.2397i	−0.272117	+	0.471320i
$473$		−	26.1798i		−	1.20375i
$474$	7.82731	+	4.51910i	0.359520	+	0.207569i
$475$		0			0
$476$		−	3.27792i		−	0.150243i
$477$	−2.90508	+	5.03175i	−0.133015	+	0.230388i
$478$	−4.11513	−	7.12762i	−0.188222	−	0.326010i
$479$	−5.49422	+	3.17209i	−0.251037	+	0.144936i	−0.620239	−	0.784413i	$-0.712964\pi$
$479$	−5.49422	+	3.17209i	−0.251037	+	0.144936i	0.369202	+	0.929349i	$0.379631\pi$
$480$		0			0
$481$	10.7829	−	19.5349i	0.491658	−	0.890714i
$482$	3.10243			0.141312
$483$	−2.88512	+	1.66573i	−0.131278	+	0.0757932i
$484$	2.81382	+	4.87367i	0.127901	+	0.221530i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	−32.2113	−	18.5972i	−1.45963	−	0.842720i	−0.460641	−	0.887586i	$-0.652381\pi$
$487$	−32.2113	−	18.5972i	−1.45963	−	0.842720i	−0.998993	+	0.0448662i	$0.985714\pi$
$488$	−8.11924	−	4.68764i	−0.367541	−	0.212200i
$489$		−	11.2244i		−	0.507584i
$490$		0			0
$491$	2.99901	+	5.19444i	0.135344	+	0.234422i	0.925729	−	0.378188i	$-0.123453\pi$
$491$	2.99901	+	5.19444i	0.135344	+	0.234422i	−0.790385	+	0.612610i	$0.790120\pi$
$492$	−7.55607	+	4.36250i	−0.340654	+	0.196677i
$493$	57.1477			2.57380
$494$	15.6774	−	9.45800i	0.705359	−	0.425535i
$495$		0			0
$496$	0.824903	−	0.476258i	0.0370392	−	0.0213846i
$497$	0.840699	+	1.45613i	0.0377105	+	0.0653165i
$498$	3.97443	−	6.88392i	0.178099	−	0.308476i
$499$		−	21.2908i		−	0.953107i	−0.879145	−	0.476554i	$-0.841886\pi$
$499$		−	21.2908i		−	0.953107i	0.879145	−	0.476554i	$-0.158114\pi$
$500$		0			0
$501$	13.0406	+	7.52898i	0.582610	+	0.336370i
$502$			15.6208i			0.697193i
$503$	−9.52194	+	16.4925i	−0.424562	+	0.735363i	−0.996379	−	0.0850178i	$-0.972905\pi$
$503$	−9.52194	+	16.4925i	−0.424562	+	0.735363i	0.571817	+	0.820381i	$0.306239\pi$
$504$	−0.241181	−	0.417738i	−0.0107431	−	0.0186075i
$505$		0			0
$506$	−16.0082			−0.711653
$507$	−12.9904	+	0.500000i	−0.576923	+	0.0222058i
$508$	18.9189			0.839391
$509$	−24.6679	+	14.2420i	−1.09339	+	0.631267i	−0.934476	−	0.356026i	$-0.884132\pi$
$509$	−24.6679	+	14.2420i	−1.09339	+	0.631267i	−0.158911	+	0.987293i	$0.550798\pi$
$510$		0			0
$511$	2.05840	−	3.56525i	0.0910581	−	0.157717i
$512$		−	1.00000i		−	0.0441942i
$513$	4.39778	+	2.53906i	0.194167	+	0.112102i
$514$	3.05205	+	1.76210i	0.134620	+	0.0777230i
$515$		0			0
$516$	5.64747	−	9.78170i	0.248616	−	0.430615i
$517$	−6.69541	−	11.5968i	−0.294464	−	0.510027i
$518$	2.58521	−	1.49257i	0.113587	−	0.0655797i
$519$	−14.7486			−0.647391
$520$		0			0
$521$	−27.6617			−1.21188			−0.605940	−	0.795511i	$-0.707203\pi$
$521$	−27.6617			−1.21188			−0.605940	+	0.795511i	$0.707203\pi$
$522$	7.28290	−	4.20478i	0.318764	−	0.184038i
$523$	8.44709	+	14.6308i	0.369365	+	0.639759i	0.989466	−	0.144762i	$-0.0462418\pi$
$523$	8.44709	+	14.6308i	0.369365	+	0.639759i	−0.620101	+	0.784522i	$0.712908\pi$
$524$	−3.48406	+	6.03457i	−0.152202	+	0.263622i
$525$		0			0
$526$	−20.1637	−	11.6415i	−0.879177	−	0.507593i
$527$	5.60567	+	3.23644i	0.244187	+	0.140981i
$528$		−	2.31784i		−	0.100871i
$529$	−12.3502	+	21.3911i	−0.536964	+	0.930049i
$530$		0			0
$531$	−10.2397	+	5.91189i	−0.444365	+	0.256554i
$532$	2.44949			0.106199
$533$	−15.2023	+	27.5413i	−0.658485	+	1.19295i
$534$	9.01753			0.390227
$535$		0			0
$536$	3.69677	+	6.40300i	0.159676	+	0.276568i
$537$	4.30589	−	7.45802i	0.185813	−	0.321837i
$538$		−	9.81746i		−	0.423261i
$539$	13.5841	+	7.84278i	0.585108	+	0.337813i
$540$		0			0
$541$		−	30.6639i		−	1.31834i	−0.751993	−	0.659171i	$-0.770907\pi$
$541$		−	30.6639i		−	1.31834i	0.751993	−	0.659171i	$-0.229093\pi$
$542$	10.9040	−	18.8862i	0.468365	−	0.811233i
$543$	−1.42246	−	2.46378i	−0.0610438	−	0.105731i
$544$	5.88512	−	3.39778i	0.252323	−	0.145679i
$545$		0			0
$546$	−1.52262	−	0.840459i	−0.0651622	−	0.0359683i
$547$	−40.6726			−1.73903			−0.869517	−	0.493903i	$-0.835570\pi$
$547$	−40.6726			−1.73903			−0.869517	+	0.493903i	$0.835570\pi$
$548$	17.7616	−	10.2547i	0.758739	−	0.438058i
$549$	−4.68764	−	8.11924i	−0.200064	−	0.346521i
$550$		0			0
$551$			42.7048i			1.81928i
$552$	−5.98124	−	3.45327i	−0.254579	−	0.146981i
$553$	3.77559	+	2.17984i	0.160555	+	0.0926963i
$554$			13.4751i			0.572501i
$555$		0			0
$556$	−4.25467	−	7.36931i	−0.180438	−	0.312528i
$557$	15.9822	−	9.22730i	0.677186	−	0.390973i	−0.121608	−	0.992578i	$-0.538805\pi$
$557$	15.9822	−	9.22730i	0.677186	−	0.390973i	0.798794	+	0.601605i	$0.205472\pi$
$558$	0.952516			0.0403232
$559$	−0.783308	−	40.7169i	−0.0331304	−	1.72214i
$560$		0			0
$561$	13.6408	−	7.87550i	0.575913	−	0.332504i
$562$	14.8083	+	25.6488i	0.624652	+	1.08193i
$563$	−4.71770	+	8.17129i	−0.198827	+	0.344379i	−0.948148	−	0.317828i	$-0.897047\pi$
$563$	−4.71770	+	8.17129i	−0.198827	+	0.344379i	0.749321	+	0.662207i	$0.230380\pi$
$564$		−	5.77729i		−	0.243268i
$565$		0			0
$566$	−10.5516	−	6.09197i	−0.443517	−	0.256065i
$567$		−	0.482362i		−	0.0202573i
$568$	−1.74288	+	3.01876i	−0.0731297	+	0.126664i
$569$	5.33503	+	9.24054i	0.223656	+	0.387384i	0.955915	−	0.293642i	$-0.0948674\pi$
$569$	5.33503	+	9.24054i	0.223656	+	0.387384i	−0.732259	+	0.681026i	$0.761534\pi$
$570$		0			0
$571$	0.532730			0.0222941			0.0111470	−	0.999938i	$-0.496452\pi$
$571$	0.532730			0.0222941			0.0111470	+	0.999938i	$0.496452\pi$
$572$	−4.31697	−	7.15573i	−0.180502	−	0.299196i
$573$	−3.43587			−0.143536
$574$	−3.64476	+	2.10430i	−0.152129	+	0.0878320i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	26.0683i		−	1.08524i	−0.839978	−	0.542620i	$-0.817432\pi$
$577$		−	26.0683i		−	1.08524i	0.839978	−	0.542620i	$-0.182568\pi$
$578$	25.2702	+	14.5898i	1.05110	+	0.606855i
$579$	2.30090	+	1.32843i	0.0956223	+	0.0552075i
$580$		0			0
$581$	1.91712	−	3.32054i	0.0795354	−	0.137759i
$582$	4.59103	+	7.95189i	0.190304	+	0.329617i
$583$	−11.6628	+	6.73351i	−0.483023	+	0.278874i
$584$	8.53465			0.353166
$585$		0			0
$586$	−15.0209			−0.620509
$587$	−12.7739	+	7.37501i	−0.527235	+	0.304399i	−0.739890	−	0.672728i	$-0.765122\pi$
$587$	−12.7739	+	7.37501i	−0.527235	+	0.304399i	0.212655	+	0.977127i	$0.431789\pi$
$588$	3.38366	+	5.86068i	0.139540	+	0.241690i
$589$	−2.41849	+	4.18895i	−0.0996523	+	0.172603i
$590$		0			0
$591$	−18.2868	−	10.5579i	−0.752219	−	0.434294i
$592$	5.35948	+	3.09429i	0.220273	+	0.127175i
$593$		−	23.4887i		−	0.964566i	−0.876015	−	0.482283i	$-0.839808\pi$
$593$		−	23.4887i		−	0.964566i	0.876015	−	0.482283i	$-0.160192\pi$
$594$	1.15892	−	2.00731i	0.0475510	−	0.0823608i
$595$		0			0
$596$	6.27439	−	3.62252i	0.257009	−	0.148384i
$597$	−10.5388			−0.431325
$598$	−24.8973	+	0.478971i	−1.01813	+	0.0195866i
$599$	3.72087			0.152031			0.0760154	−	0.997107i	$-0.475780\pi$
$599$	3.72087			0.152031			0.0760154	+	0.997107i	$0.475780\pi$
$600$		0			0
$601$	21.1757	+	36.6773i	0.863773	+	1.49610i	0.868261	+	0.496109i	$0.165238\pi$
$601$	21.1757	+	36.6773i	0.863773	+	1.49610i	−0.00448765	+	0.999990i	$0.501428\pi$
$602$	2.72412	−	4.71832i	0.111027	−	0.192304i
$603$			7.39355i			0.301089i
$604$	6.77875	+	3.91372i	0.275824	+	0.159247i
$605$		0			0
$606$		−	10.6822i		−	0.433933i
$607$	−9.50853	+	16.4692i	−0.385939	+	0.668466i	−0.991899	−	0.127029i	$-0.959456\pi$
$607$	−9.50853	+	16.4692i	−0.385939	+	0.668466i	0.605960	+	0.795495i	$0.292789\pi$
$608$	2.53906	+	4.39778i	0.102972	+	0.178353i
$609$	3.51299	−	2.02823i	0.142354	−	0.0821879i
$610$		0			0
$611$	−10.7602	−	17.8359i	−0.435312	−	0.721565i
$612$	6.79555			0.274694
$613$	−19.7672	+	11.4126i	−0.798390	+	0.460951i	−0.842908	−	0.538058i	$-0.819158\pi$
$613$	−19.7672	+	11.4126i	−0.798390	+	0.460951i	0.0445178	+	0.999009i	$0.485825\pi$
$614$	−13.9784	−	24.2114i	−0.564124	−	0.977091i
$615$		0			0
$616$		−	1.11804i		−	0.0450470i
$617$	15.0114	+	8.66682i	0.604335	+	0.348913i	0.770745	−	0.637144i	$-0.219884\pi$
$617$	15.0114	+	8.66682i	0.604335	+	0.348913i	−0.166410	+	0.986057i	$0.553217\pi$
$618$	7.94534	+	4.58725i	0.319609	+	0.184526i
$619$			0.972021i			0.0390688i	0.999809	+	0.0195344i	$0.00621839\pi$
$619$			0.972021i			0.0390688i	−0.999809	+	0.0195344i	$0.993782\pi$
$620$		0			0
$621$	−3.45327	−	5.98124i	−0.138575	−	0.240019i
$622$	−12.3899	+	7.15333i	−0.496791	+	0.286822i
$623$	4.34971			0.174268
$624$	−0.0693504	−	3.60488i	−0.00277624	−	0.144311i
$625$		0			0
$626$	−12.1152	+	6.99473i	−0.484222	+	0.279566i
$627$	5.88512	+	10.1933i	0.235029	+	0.407082i
$628$	2.21134	−	3.83014i	0.0882419	−	0.152839i
$629$			42.0549i			1.67684i
$630$		0			0
$631$	4.53981	+	2.62106i	0.180727	+	0.104343i	0.587634	−	0.809127i	$-0.300059\pi$
$631$	4.53981	+	2.62106i	0.180727	+	0.104343i	−0.406907	+	0.913470i	$0.633393\pi$
$632$			9.03820i			0.359520i
$633$	5.74384	−	9.94863i	0.228297	−	0.395422i
$634$	−3.64934	−	6.32085i	−0.144934	−	0.251033i
$635$		0			0
$636$	−5.81017			−0.230388
$637$	21.3617	+	11.7913i	0.846382	+	0.467187i
$638$	19.4920			0.771696
$639$	−3.01876	+	1.74288i	−0.119420	+	0.0689473i
$640$		0			0
$641$	−16.4075	+	28.4186i	−0.648057	+	1.12247i	0.335529	+	0.942030i	$0.391085\pi$
$641$	−16.4075	+	28.4186i	−0.648057	+	1.12247i	−0.983586	+	0.180439i	$0.942248\pi$
$642$			3.21733i			0.126978i
$643$	−10.0888	−	5.82478i	−0.397864	−	0.229707i	0.287698	−	0.957721i	$-0.407110\pi$
$643$	−10.0888	−	5.82478i	−0.397864	−	0.229707i	−0.685562	+	0.728014i	$0.740443\pi$
$644$	−2.88512	−	1.66573i	−0.113690	−	0.0656388i
$645$		0			0
$646$	−17.2543	+	29.8853i	−0.678862	+	1.17582i
$647$	11.0922	+	19.2123i	0.436081	+	0.755314i	0.997383	−	0.0722970i	$-0.0230329\pi$
$647$	11.0922	+	19.2123i	0.436081	+	0.755314i	−0.561303	+	0.827611i	$0.689700\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−27.4056			−1.07576
$650$		0			0
$651$	0.459457			0.0180076
$652$	9.72060	−	5.61219i	0.380688	−	0.219790i
$653$	−16.6764	−	28.8844i	−0.652598	−	1.13033i	−0.982490	−	0.186314i	$-0.940346\pi$
$653$	−16.6764	−	28.8844i	−0.652598	−	1.13033i	0.329892	−	0.944019i	$-0.392988\pi$
$654$	−8.53345	+	14.7804i	−0.333684	+	0.577958i
$655$		0			0
$656$	−7.55607	−	4.36250i	−0.295015	−	0.170327i
$657$	7.39123	+	4.26733i	0.288359	+	0.166484i
$658$		−	2.78675i		−	0.108639i
$659$	12.2280	−	21.1796i	0.476337	−	0.825039i	−0.523296	−	0.852151i	$-0.675298\pi$
$659$	12.2280	−	21.1796i	0.476337	−	0.825039i	0.999632	+	0.0271118i	$0.00863100\pi$
$660$		0			0
$661$	28.8737	−	16.6702i	1.12306	−	0.648396i	0.180876	−	0.983506i	$-0.442107\pi$
$661$	28.8737	−	16.6702i	1.12306	−	0.648396i	0.942179	+	0.335109i	$0.108773\pi$
$662$	−26.3594			−1.02449
$663$	20.9796	−	12.6567i	0.814778	−	0.491547i
$664$	7.94887			0.308476
$665$		0			0
$666$	3.09429	+	5.35948i	0.119901	+	0.207675i
$667$	29.0405	−	50.2997i	1.12445	−	1.94761i
$668$			15.0580i			0.582610i
$669$	4.52739	+	2.61389i	0.175039	+	0.101059i
$670$		0			0
$671$		−	21.7304i		−	0.838893i
$672$	0.241181	−	0.417738i	0.00930376	−	0.0161146i
$673$	−16.9894	−	29.4265i	−0.654893	−	1.13431i	−0.981921	−	0.189293i	$-0.939380\pi$
$673$	−16.9894	−	29.4265i	−0.654893	−	1.13431i	0.327028	−	0.945015i	$-0.393953\pi$
$674$	21.1518	−	12.2120i	0.814736	−	0.470388i
$675$		0			0
$676$	−6.92820	−	11.0000i	−0.266469	−	0.423077i
$677$	−10.3145			−0.396417			−0.198208	−	0.980160i	$-0.563512\pi$
$677$	−10.3145			−0.396417			−0.198208	+	0.980160i	$0.563512\pi$
$678$	1.43488	−	0.828427i	0.0551062	−	0.0318156i
$679$	2.21454	+	3.83569i	0.0849861	+	0.147200i
$680$		0			0
$681$			10.8689i			0.416496i
$682$	1.91199	+	1.10389i	0.0732139	+	0.0422701i
$683$	42.4682	+	24.5191i	1.62500	+	0.938196i	0.985554	+	0.169362i	$0.0541706\pi$
$683$	42.4682	+	24.5191i	1.62500	+	0.938196i	0.639448	+	0.768834i	$0.279163\pi$
$684$			5.07812i			0.194167i
$685$		0			0
$686$	3.32042	+	5.75113i	0.126774	+	0.219579i
$687$	−18.3538	+	10.5966i	−0.700242	+	0.404285i
$688$	11.2949			0.430615
$689$	−17.9374	+	10.8214i	−0.683361	+	0.412264i
$690$		0			0
$691$	29.7340	−	17.1669i	1.13113	−	0.653061i	0.186914	−	0.982376i	$-0.440151\pi$
$691$	29.7340	−	17.1669i	1.13113	−	0.653061i	0.944220	+	0.329315i	$0.106818\pi$
$692$	−7.37429	−	12.7727i	−0.280329	−	0.485543i
$693$	0.559018	−	0.968248i	0.0212353	−	0.0367807i
$694$		−	13.4164i		−	0.509278i
$695$		0			0
$696$	7.28290	+	4.20478i	0.276058	+	0.159382i
$697$		−	59.2912i		−	2.24582i
$698$	−0.476000	+	0.824457i	−0.0180169	+	0.0312061i
$699$	10.9212	+	18.9160i	0.413076	+	0.715469i
$700$		0			0
$701$	−32.0303			−1.20977			−0.604885	−	0.796313i	$-0.706781\pi$
$701$	−32.0303			−1.20977			−0.604885	+	0.796313i	$0.706781\pi$
$702$	1.74238	−	3.15660i	0.0657620	−	0.119138i
$703$	−31.4264			−1.18527
$704$	2.00731	−	1.15892i	0.0756532	−	0.0436784i
$705$		0			0
$706$	−7.22380	+	12.5120i	−0.271871	+	0.470895i
$707$		−	5.15267i		−	0.193786i
$708$	−10.2397	−	5.91189i	−0.384831	−	0.222182i
$709$	27.0809	+	15.6352i	1.01704	+	0.587190i	0.913246	−	0.407408i	$-0.133567\pi$
$709$	27.0809	+	15.6352i	1.01704	+	0.587190i	0.103797	+	0.994598i	$0.466901\pi$
$710$		0			0
$711$	−4.51910	+	7.82731i	−0.169479	+	0.293547i
$712$	4.50877	+	7.80941i	0.168973	+	0.292670i
$713$	5.69723	−	3.28930i	0.213363	−	0.123185i
$714$	3.27792			0.122673
$715$		0			0
$716$	8.61177			0.321837
$717$	7.12762	−	4.11513i	0.266186	−	0.153683i
$718$	−4.05646	−	7.02599i	−0.151386	−	0.262208i
$719$	−10.6716	+	18.4838i	−0.397984	+	0.689328i	−0.993477	−	0.114032i	$-0.963623\pi$
$719$	−10.6716	+	18.4838i	−0.397984	+	0.689328i	0.595494	+	0.803360i	$0.296957\pi$
$720$		0			0
$721$	3.83253	+	2.21271i	0.142731	+	0.0824057i
$722$	−5.87794	−	3.39363i	−0.218754	−	0.126298i
$723$			3.10243i			0.115381i
$724$	1.42246	−	2.46378i	0.0528655	−	0.0915656i
$725$		0			0
$726$	−4.87367	+	2.81382i	−0.180879	+	0.104430i
$727$	−8.80283			−0.326479			−0.163240	−	0.986586i	$-0.552194\pi$
$727$	−8.80283			−0.326479			−0.163240	+	0.986586i	$0.552194\pi$
$728$	−0.0334520	−	1.73886i	−0.00123981	−	0.0644464i
$729$	1.00000			0.0370370
$730$		0			0
$731$	38.3777	+	66.4721i	1.41945	+	2.45856i
$732$	4.68764	−	8.11924i	0.173260	−	0.300096i
$733$		−	7.86883i		−	0.290642i	−0.989385	−	0.145321i	$-0.953579\pi$
$733$		−	7.86883i		−	0.290642i	0.989385	−	0.145321i	$-0.0464215\pi$
$734$	−20.7806	−	11.9977i	−0.767026	−	0.442843i
$735$		0			0
$736$		−	6.90654i		−	0.254579i
$737$	−8.56852	+	14.8411i	−0.315626	+	0.546680i
$738$	−4.36250	−	7.55607i	−0.160586	−	0.278143i
$739$	15.6988	−	9.06368i	0.577488	−	0.333413i	−0.182646	−	0.983179i	$-0.558466\pi$
$739$	15.6988	−	9.06368i	0.577488	−	0.333413i	0.760134	+	0.649766i	$0.225133\pi$
$740$		0			0
$741$	9.45800	+	15.6774i	0.347448	+	0.575923i
$742$	−2.80260			−0.102887
$743$	−1.19048	+	0.687322i	−0.0436744	+	0.0252154i	−0.521678	−	0.853142i	$-0.674694\pi$
$743$	−1.19048	+	0.687322i	−0.0436744	+	0.0252154i	0.478004	+	0.878358i	$0.341360\pi$
$744$	0.476258	+	0.824903i	0.0174605	+	0.0302424i
$745$		0			0
$746$		−	26.8576i		−	0.983325i
$747$	6.88392	+	3.97443i	0.251870	+	0.145417i
$748$	13.6408	+	7.87550i	0.498756	+	0.287957i
$749$			1.55192i			0.0567059i
$750$		0			0
$751$	−19.0127	−	32.9310i	−0.693784	−	1.20167i	−0.970589	−	0.240743i	$-0.922609\pi$
$751$	−19.0127	−	32.9310i	−0.693784	−	1.20167i	0.276805	−	0.960926i	$-0.410724\pi$
$752$	5.00328	−	2.88865i	0.182451	−	0.105338i
$753$	−15.6208			−0.569255
$754$	30.3155	−	0.583207i	1.10403	−	0.0212391i
$755$		0			0
$756$	0.417738	−	0.241181i	0.0151930	−	0.00877167i
$757$	18.4771	+	32.0033i	0.671562	+	1.16318i	0.977461	+	0.211115i	$0.0677096\pi$
$757$	18.4771	+	32.0033i	0.671562	+	1.16318i	−0.305899	+	0.952064i	$0.598957\pi$
$758$	7.65785	−	13.2638i	0.278146	−	0.481762i
$759$		−	16.0082i		−	0.581062i
$760$		0			0
$761$	25.9967	+	15.0092i	0.942380	+	0.544084i	0.890706	−	0.454580i	$-0.150211\pi$
$761$	25.9967	+	15.0092i	0.942380	+	0.544084i	0.0516746	+	0.998664i	$0.483544\pi$
$762$			18.9189i			0.685360i
$763$	−4.11621	+	7.12949i	−0.149017	+	0.258105i
$764$	−1.71794	−	2.97555i	−0.0621528	−	0.107652i
$765$		0			0
$766$	35.2397			1.27326
$767$	−42.6234	+	0.819984i	−1.53904	+	0.0296079i
$768$	1.00000			0.0360844
$769$	−39.3038	+	22.6921i	−1.41733	+	0.818297i	−0.996064	−	0.0886391i	$-0.971748\pi$
$769$	−39.3038	+	22.6921i	−1.41733	+	0.818297i	−0.421268	+	0.906936i	$0.638415\pi$
$770$		0			0
$771$	−1.76210	+	3.05205i	−0.0634606	+	0.109917i
$772$			2.65685i			0.0956223i
$773$	−22.1132	−	12.7671i	−0.795358	−	0.459200i	0.0464877	−	0.998919i	$-0.485197\pi$
$773$	−22.1132	−	12.7671i	−0.795358	−	0.459200i	−0.841845	+	0.539719i	$0.818531\pi$
$774$	9.78170	+	5.64747i	0.351596	+	0.202994i
$775$		0			0
$776$	−4.59103	+	7.95189i	−0.164808	+	0.285456i
$777$	1.49257	+	2.58521i	0.0535456	+	0.0927438i
$778$	15.6704	−	9.04731i	0.561811	−	0.324362i
$779$	44.3066			1.58745
$780$		0			0
$781$	−8.07943			−0.289105
$782$	40.6459	−	23.4669i	1.45349	−	0.839175i
$783$	4.20478	+	7.28290i	0.150267	+	0.260270i
$784$	−3.38366	+	5.86068i	−0.120845	+	0.209310i
$785$		0			0
$786$	−6.03457	−	3.48406i	−0.215246	−	0.124272i
$787$	27.2796	+	15.7499i	0.972413	+	0.561423i	0.899971	−	0.435949i	$-0.143587\pi$
$787$	27.2796	+	15.7499i	0.972413	+	0.561423i	0.0724422	+	0.997373i	$0.476921\pi$
$788$		−	21.1158i		−	0.752219i
$789$	11.6415	−	20.1637i	0.414448	−	0.717845i
$790$		0			0
$791$	0.692130	−	0.399602i	0.0246093	−	0.0142082i
$792$	2.31784			0.0823608
$793$	−0.650180	−	33.7968i	−0.0230886	−	1.20016i
$794$	−10.4512			−0.370901
$795$		0			0
$796$	−5.26941	−	9.12688i	−0.186769	−	0.323494i
$797$	21.6986	−	37.5831i	0.768605	−	1.33126i	−0.169715	−	0.985493i	$-0.554285\pi$
$797$	21.6986	−	37.5831i	0.768605	−	1.33126i	0.938320	−	0.345769i	$-0.112382\pi$
$798$			2.44949i			0.0867110i
$799$	34.0001	+	19.6300i	1.20284	+	0.694458i
$800$		0			0
$801$			9.01753i			0.318619i
$802$	0.700423	−	1.21317i	0.0247328	−	0.0428385i
$803$	9.89097	+	17.1317i	0.349045	+	0.604563i
$804$	−6.40300	+	3.69677i	−0.225816	+	0.130375i
$805$		0			0
$806$	3.00671	+	1.65965i	0.105907	+	0.0584586i
$807$	9.81746			0.345591
$808$	9.25102	−	5.34108i	0.325450	−	0.187899i
$809$	−16.3279	−	28.2807i	−0.574057	−	0.994296i	−0.996143	−	0.0877407i	$-0.972035\pi$
$809$	−16.3279	−	28.2807i	−0.574057	−	0.994296i	0.422086	−	0.906556i	$-0.361298\pi$
$810$		0			0
$811$			30.1669i			1.05930i	0.848216	+	0.529651i	$0.177677\pi$
$811$			30.1669i			1.05930i	−0.848216	+	0.529651i	$0.822323\pi$
$812$	3.51299	+	2.02823i	0.123282	+	0.0711768i
$813$	18.8862	+	10.9040i	0.662369	+	0.382419i
$814$			14.3441i			0.502762i
$815$		0			0
$816$	3.39778	+	5.88512i	0.118946	+	0.206021i
$817$	−49.6726	+	28.6785i	−1.73782	+	1.00333i
$818$	−6.74134			−0.235705
$819$	0.840459	−	1.52262i	0.0293680	−	0.0532047i
$820$		0			0
$821$	6.92648	−	3.99900i	0.241736	−	0.139566i	−0.374238	−	0.927332i	$-0.622096\pi$
$821$	6.92648	−	3.99900i	0.241736	−	0.139566i	0.615974	+	0.787766i	$0.288763\pi$
$822$	10.2547	+	17.7616i	0.357673	+	0.619507i
$823$	−20.5022	+	35.5109i	−0.714663	+	1.23783i	0.248426	+	0.968651i	$0.420087\pi$
$823$	−20.5022	+	35.5109i	−0.714663	+	1.23783i	−0.963089	+	0.269182i	$0.913247\pi$
$824$			9.17449i			0.319609i
$825$		0			0
$826$	−4.93924	−	2.85167i	−0.171858	−	0.0992223i
$827$			32.0321i			1.11386i	0.830558	+	0.556932i	$0.188022\pi$
$827$			32.0321i			1.11386i	−0.830558	+	0.556932i	$0.811978\pi$
$828$	3.45327	−	5.98124i	0.120009	−	0.207863i
$829$	−9.75006	−	16.8876i	−0.338634	−	0.586531i	0.645542	−	0.763725i	$-0.276631\pi$
$829$	−9.75006	−	16.8876i	−0.338634	−	0.586531i	−0.984176	+	0.177194i	$0.943298\pi$
$830$		0			0
$831$	−13.4751			−0.467445
$832$	3.08725	−	1.86250i	0.107031	−	0.0645706i
$833$	−45.9877			−1.59338
$834$	7.36931	−	4.25467i	0.255178	−	0.147327i
$835$		0			0
$836$	−5.88512	+	10.1933i	−0.203541	+	0.352544i
$837$			0.952516i			0.0329238i
$838$	31.6166	+	18.2539i	1.09218	+	0.630569i
$839$	−7.55900	−	4.36419i	−0.260966	−	0.150669i	0.363809	−	0.931473i	$-0.381476\pi$
$839$	−7.55900	−	4.36419i	−0.260966	−	0.150669i	−0.624775	+	0.780805i	$0.714809\pi$
$840$		0			0
$841$	−20.8604	+	36.1313i	−0.719325	+	1.24591i
$842$	20.4245	+	35.3763i	0.703875	+	1.21915i
$843$	−25.6488	+	14.8083i	−0.883392	+	0.510026i
$844$	11.4877			0.395422
$845$		0			0
$846$	5.77729			0.198627
$847$	−2.35087	+	1.35728i	−0.0807770	+	0.0466366i
$848$	−2.90508	−	5.03175i	−0.0997610	−	0.172791i
$849$	6.09197	−	10.5516i	0.209076	−	0.362130i
$850$		0			0
$851$	37.0154	+	21.3709i	1.26887	+	0.732584i
$852$	−3.01876	−	1.74288i	−0.103421	−	0.0597101i
$853$			25.1210i			0.860125i	0.902799	+	0.430063i	$0.141509\pi$
$853$			25.1210i			0.860125i	−0.902799	+	0.430063i	$0.858491\pi$
$854$	2.26114	−	3.91641i	0.0773747	−	0.134017i
$855$		0			0
$856$	−2.78629	+	1.60867i	−0.0952335	+	0.0549831i
$857$	48.1300			1.64409			0.822045	−	0.569423i	$-0.192833\pi$
$857$	48.1300			1.64409			0.822045	+	0.569423i	$0.192833\pi$
$858$	7.15573	−	4.31697i	0.244293	−	0.147379i
$859$	−47.1707			−1.60944			−0.804721	−	0.593653i	$-0.797685\pi$
$859$	−47.1707			−1.60944			−0.804721	+	0.593653i	$0.797685\pi$
$860$		0			0
$861$	−2.10430	−	3.64476i	−0.0717145	−	0.124213i
$862$	9.18824	−	15.9145i	0.312953	−	0.542050i
$863$			26.6095i			0.905799i	0.891562	+	0.452900i	$0.149610\pi$
$863$			26.6095i			0.905799i	−0.891562	+	0.452900i	$0.850390\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$		0			0
$866$		−	1.39819i		−	0.0475125i
$867$	−14.5898	+	25.2702i	−0.495495	+	0.858223i
$868$	0.229729	+	0.397902i	0.00779750	+	0.0135057i
$869$	−18.1424	+	10.4745i	−0.615440	+	0.355324i
$870$		0			0
$871$	−12.8824	+	23.3385i	−0.436503	+	0.790793i
$872$	−17.0669			−0.577958
$873$	−7.95189	+	4.59103i	−0.269131	+	0.155383i
$874$	17.5361	+	30.3734i	0.593168	+	1.02740i
$875$		0			0
$876$			8.53465i			0.288359i
$877$	−5.80548	−	3.35180i	−0.196037	−	0.113182i	0.398769	−	0.917052i	$-0.369438\pi$
$877$	−5.80548	−	3.35180i	−0.196037	−	0.113182i	−0.594806	+	0.803870i	$0.702771\pi$
$878$	13.2621	+	7.65685i	0.447573	+	0.258406i
$879$		−	15.0209i		−	0.506643i
$880$		0			0
$881$	−5.09215	−	8.81986i	−0.171559	−	0.297149i	0.767406	−	0.641161i	$-0.221547\pi$
$881$	−5.09215	−	8.81986i	−0.171559	−	0.297149i	−0.938965	+	0.344013i	$0.888214\pi$
$882$	−5.86068	+	3.38366i	−0.197339	+	0.113934i
$883$	−45.3554			−1.52633			−0.763165	−	0.646204i	$-0.776356\pi$
$883$	−45.3554			−1.52633			−0.763165	+	0.646204i	$0.776356\pi$
$884$	21.4508	+	11.8405i	0.721469	+	0.398238i
$885$		0			0
$886$	28.7320	−	16.5884i	0.965272	−	0.557300i
$887$	17.1908	+	29.7753i	0.577210	+	0.999757i	0.995798	+	0.0915805i	$0.0291919\pi$
$887$	17.1908	+	29.7753i	0.577210	+	0.999757i	−0.418588	+	0.908176i	$0.637475\pi$
$888$	−3.09429	+	5.35948i	−0.103838	+	0.179852i
$889$			9.12576i			0.306068i
$890$		0			0
$891$	2.00731	+	1.15892i	0.0672473	+	0.0388252i
$892$			5.22778i			0.175039i
$893$	−14.6689	+	25.4073i	−0.490876	+	0.850221i
$894$	3.62252	+	6.27439i	0.121155	+	0.209847i
$895$		0			0
$896$	0.482362			0.0161146
$897$	−0.478971	−	24.8973i	−0.0159924	−	0.831296i
$898$	−15.4047			−0.514061
$899$	−6.93708	+	4.00512i	−0.231365	+	0.133578i
$900$		0			0
$901$	19.7417	−	34.1935i	0.657690	−	1.13915i
$902$		−	20.2231i		−	0.673357i
$903$	4.71832	+	2.72412i	0.157016	+	0.0906531i
$904$	1.43488	+	0.828427i	0.0477233	+	0.0275531i
$905$		0			0
$906$	−3.91372	+	6.77875i	−0.130024	+	0.225209i
$907$	16.9804	+	29.4110i	0.563826	+	0.976575i	0.997158	+	0.0753408i	$0.0240045\pi$
$907$	16.9804	+	29.4110i	0.563826	+	0.976575i	−0.433332	+	0.901234i	$0.642662\pi$
$908$	−9.41271	+	5.43443i	−0.312372	+	0.180348i
$909$	10.6822			0.354305
$910$		0			0
$911$	35.0487			1.16121			0.580607	−	0.814184i	$-0.302815\pi$
$911$	35.0487			1.16121			0.580607	+	0.814184i	$0.302815\pi$
$912$	−4.39778	+	2.53906i	−0.145625	+	0.0840766i
$913$	9.21209	+	15.9558i	0.304876	+	0.528060i
$914$	−3.73097	+	6.46224i	−0.123410	+	0.213752i
$915$		0			0
$916$	−18.3538	−	10.5966i	−0.606428	−	0.350121i
$917$	−2.91085	−	1.68058i	−0.0961247	−	0.0554976i
$918$			6.79555i			0.224287i
$919$	8.74038	−	15.1388i	0.288319	−	0.499383i	−0.685090	−	0.728459i	$-0.740237\pi$
$919$	8.74038	−	15.1388i	0.288319	−	0.499383i	0.973409	+	0.229076i	$0.0735704\pi$
$920$		0			0
$921$	24.2114	−	13.9784i	0.797791	−	0.460605i
$922$	4.58943			0.151145
$923$	−12.5658	+	0.241739i	−0.413607	+	0.00795693i
$924$	1.11804			0.0367807
$925$		0			0
$926$	4.60444	+	7.97512i	0.151311	+	0.262079i
$927$	−4.58725	+	7.94534i	−0.150665	+	0.260959i
$928$			8.40957i			0.276058i
$929$	6.74907	+	3.89658i	0.221430	+	0.127842i	0.606612	−	0.794998i	$-0.292528\pi$
$929$	6.74907	+	3.89658i	0.221430	+	0.127842i	−0.385182	+	0.922840i	$0.625861\pi$
$930$		0			0
$931$		−	34.3653i		−	1.12628i
$932$	−10.9212	+	18.9160i	−0.357734	+	0.619614i
$933$	−7.15333	−	12.3899i	−0.234190	−	0.405628i
$934$	0.190066	−	0.109735i	0.00621915	−	0.00359063i
$935$		0			0
$936$	3.60488	−	0.0693504i	0.117829	−	0.00226679i
$937$	39.5690			1.29266			0.646331	−	0.763057i	$-0.276303\pi$
$937$	39.5690			1.29266			0.646331	+	0.763057i	$0.276303\pi$
$938$	−3.08856	+	1.78318i	−0.100845	+	0.0582230i
$939$	−6.99473	−	12.1152i	−0.228265	−	0.395366i
$940$		0			0
$941$		−	23.6107i		−	0.769687i	−0.922982	−	0.384844i	$-0.874255\pi$
$941$		−	23.6107i		−	0.769687i	0.922982	−	0.384844i	$-0.125745\pi$
$942$	3.83014	+	2.21134i	0.124793	+	0.0720492i
$943$	−52.1864	−	30.1298i	−1.69942	−	0.981161i
$944$		−	11.8238i		−	0.384831i
$945$		0			0
$946$	13.0899	+	22.6724i	0.425590	+	0.737143i
$947$	−16.6283	+	9.60036i	−0.540348	+	0.311970i	−0.745220	−	0.666819i	$-0.767655\pi$
$947$	−16.6283	+	9.60036i	−0.540348	+	0.311970i	0.204872	+	0.978789i	$0.434322\pi$
$948$	−9.03820			−0.293547
$949$	15.8958	+	26.3486i	0.516000	+	0.855311i
$950$		0			0
$951$	6.32085	−	3.64934i	0.204967	−	0.118338i
$952$	1.63896	+	2.83876i	0.0531189	+	0.0920047i
$953$	−0.303161	+	0.525090i	−0.00982035	+	0.0170093i	−0.870894	−	0.491471i	$-0.836459\pi$
$953$	−0.303161	+	0.525090i	−0.00982035	+	0.0170093i	0.861073	+	0.508481i	$0.169793\pi$
$954$		−	5.81017i		−	0.188111i
$955$		0			0
$956$	7.12762	+	4.11513i	0.230524	+	0.133093i
$957$			19.4920i			0.630087i
$958$	3.17209	−	5.49422i	0.102486	−	0.177510i
$959$	4.94646	+	8.56753i	0.159730	+	0.276660i
$960$		0			0
$961$	30.0927			0.970733
$962$	0.429181	+	22.3091i	0.0138373	+	0.719276i
$963$	−3.21733			−0.103677
$964$	−2.68678	+	1.55121i	−0.0865354	+	0.0499613i
$965$		0			0
$966$	1.66573	−	2.88512i	0.0535939	−	0.0928273i
$967$		−	1.49478i		−	0.0480690i	−0.999711	−	0.0240345i	$-0.992349\pi$
$967$		−	1.49478i		−	0.0480690i	0.999711	−	0.0240345i	$-0.00765115\pi$
$968$	−4.87367	−	2.81382i	−0.156646	−	0.0904394i
$969$	−29.8853	−	17.2543i	−0.960055	−	0.554288i
$970$		0			0
$971$	−1.72859	+	2.99401i	−0.0554731	+	0.0960823i	−0.892428	−	0.451189i	$-0.851000\pi$
$971$	−1.72859	+	2.99401i	−0.0554731	+	0.0960823i	0.836955	+	0.547271i	$0.184333\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	3.55467	−	2.05229i	0.113958	−	0.0657935i
$974$	37.1944			1.19179
$975$		0			0
$976$	9.37529			0.300096
$977$	41.2109	−	23.7932i	1.31845	−	0.761210i	0.334975	−	0.942227i	$-0.391272\pi$
$977$	41.2109	−	23.7932i	1.31845	−	0.761210i	0.983480	+	0.181017i	$0.0579388\pi$
$978$	5.61219	+	9.72060i	0.179458	+	0.310830i
$979$	−10.4506	+	18.1009i	−0.334002	+	0.578509i
$980$		0			0
$981$	−14.7804	−	8.53345i	−0.471901	−	0.272452i
$982$	−5.19444	−	2.99901i	−0.165761	−	0.0957024i
$983$		−	27.8101i		−	0.887003i	−0.896274	−	0.443502i	$-0.853736\pi$
$983$		−	27.8101i		−	0.887003i	0.896274	−	0.443502i	$-0.146264\pi$
$984$	4.36250	−	7.55607i	0.139071	−	0.240879i
$985$		0			0
$986$	−49.4914	+	28.5738i	−1.57613	+	0.909977i
$987$	2.78675			0.0887031
$988$	−8.84802	+	16.0296i	−0.281493	+	0.509968i
$989$	78.0089			2.48054
$990$		0			0
$991$	−24.0369	−	41.6331i	−0.763557	−	1.32252i	−0.941006	−	0.338390i	$-0.890118\pi$
$991$	−24.0369	−	41.6331i	−0.763557	−	1.32252i	0.177449	−	0.984130i	$-0.443216\pi$
$992$	−0.476258	+	0.824903i	−0.0151212	+	0.0261907i
$993$		−	26.3594i		−	0.836491i
$994$	−1.45613	−	0.840699i	−0.0461858	−	0.0266654i
$995$		0			0
$996$			7.94887i			0.251870i
$997$	8.40884	−	14.5645i	0.266311	−	0.461264i	−0.701596	−	0.712575i	$-0.747529\pi$
$997$	8.40884	−	14.5645i	0.266311	−	0.461264i	0.967906	+	0.251312i	$0.0808620\pi$
$998$	10.6454	+	18.4384i	0.336974	+	0.583657i
$999$	−5.35948	+	3.09429i	−0.169566	+	0.0978991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.e.751.1	✓	8
5.2	odd	4		1950.2.y.i.49.2		8
5.3	odd	4		1950.2.y.l.49.3		8
5.4	even	2		1950.2.bc.f.751.4	yes	8
13.4	even	6	inner	1950.2.bc.e.901.1	yes	8
65.4	even	6		1950.2.bc.f.901.4	yes	8
65.17	odd	12		1950.2.y.l.199.3		8
65.43	odd	12		1950.2.y.i.199.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.y.i.49.2		8	5.2	odd	4
1950.2.y.i.199.2		8	65.43	odd	12
1950.2.y.l.49.3		8	5.3	odd	4
1950.2.y.l.199.3		8	65.17	odd	12
1950.2.bc.e.751.1	✓	8	1.1	even	1	trivial
1950.2.bc.e.901.1	yes	8	13.4	even	6	inner
1950.2.bc.f.751.4	yes	8	5.4	even	2
1950.2.bc.f.901.4	yes	8	65.4	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(0.417738 + 0.241181i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.00731 + 1.15892i) q^{11} -1.00000 q^{12} +(-3.08725 + 1.86250i) q^{13} -0.482362 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.39778 - 5.88512i) q^{17} -1.00000i q^{18} +(4.39778 + 2.53906i) q^{19} -0.482362i q^{21} +(1.15892 - 2.00731i) q^{22} +(-3.45327 - 5.98124i) q^{23} +(0.866025 - 0.500000i) q^{24} +(1.74238 - 3.15660i) q^{26} +1.00000 q^{27} +(0.417738 - 0.241181i) q^{28} +(4.20478 + 7.28290i) q^{29} +0.952516i q^{31} +(0.866025 + 0.500000i) q^{32} +(2.00731 + 1.15892i) q^{33} +6.79555i q^{34} +(0.500000 + 0.866025i) q^{36} +(-5.35948 + 3.09429i) q^{37} -5.07812 q^{38} +(3.15660 + 1.74238i) q^{39} +(7.55607 - 4.36250i) q^{41} +(0.241181 + 0.417738i) q^{42} +(-5.64747 + 9.78170i) q^{43} +2.31784i q^{44} +(5.98124 + 3.45327i) q^{46} +5.77729i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-3.38366 - 5.86068i) q^{49} -6.79555 q^{51} +(0.0693504 + 3.60488i) q^{52} +5.81017 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.241181 + 0.417738i) q^{56} -5.07812i q^{57} +(-7.28290 - 4.20478i) q^{58} +(10.2397 + 5.91189i) q^{59} +(-4.68764 + 8.11924i) q^{61} +(-0.476258 - 0.824903i) q^{62} +(-0.417738 + 0.241181i) q^{63} -1.00000 q^{64} -2.31784 q^{66} +(6.40300 - 3.69677i) q^{67} +(-3.39778 - 5.88512i) q^{68} +(-3.45327 + 5.98124i) q^{69} +(3.01876 + 1.74288i) q^{71} +(-0.866025 - 0.500000i) q^{72} -8.53465i q^{73} +(3.09429 - 5.35948i) q^{74} +(4.39778 - 2.53906i) q^{76} -1.11804 q^{77} +(-3.60488 + 0.0693504i) q^{78} +9.03820 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-4.36250 + 7.55607i) q^{82} -7.94887i q^{83} +(-0.417738 - 0.241181i) q^{84} -11.2949i q^{86} +(4.20478 - 7.28290i) q^{87} +(-1.15892 - 2.00731i) q^{88} +(7.80941 - 4.50877i) q^{89} +(-1.73886 + 0.0334520i) q^{91} -6.90654 q^{92} +(0.824903 - 0.476258i) q^{93} +(-2.88865 - 5.00328i) q^{94} -1.00000i q^{96} +(7.95189 + 4.59103i) q^{97} +(5.86068 + 3.38366i) q^{98} -2.31784i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} - 12 q^{11} - 8 q^{12} - 8 q^{14} - 4 q^{16} + 4 q^{17} + 12 q^{19} + 8 q^{22} + 4 q^{23} + 8 q^{27} + 4 q^{29} + 12 q^{33} + 4 q^{36} - 24 q^{37} + 4 q^{42} - 4 q^{43}+ \cdots + 12 q^{98}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9 - 12 * q^11 - 8 * q^12 - 8 * q^14 - 4 * q^16 + 4 * q^17 + 12 * q^19 + 8 * q^22 + 4 * q^23 + 8 * q^27 + 4 * q^29 + 12 * q^33 + 4 * q^36 - 24 * q^37 + 4 * q^42 - 4 * q^43 + 12 * q^46 - 4 * q^48 - 16 * q^49 - 8 * q^51 - 8 * q^53 - 4 * q^56 + 12 * q^58 - 12 * q^59 - 16 * q^61 + 4 * q^62 - 8 * q^64 - 16 * q^66 + 24 * q^67 - 4 * q^68 + 4 * q^69 + 60 * q^71 + 16 * q^74 + 12 * q^76 - 8 * q^77 - 8 * q^79 - 4 * q^81 - 20 * q^82 + 4 * q^87 - 8 * q^88 + 24 * q^89 + 8 * q^91 + 8 * q^92 - 24 * q^93 + 16 * q^94 + 12 * q^97 + 12 * q^98

Introduction

L-functions

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