LMFDB - Embedded newform 1950.2.y.i.49.2

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:	$8$
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			49.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1950.49
Dual form			1950.2.y.i.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-0.241181 + 0.417738i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(-0.241181 + 0.417738i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.00731 + 1.15892i) q^{11} -1.00000i q^{12} +(1.86250 + 3.08725i) q^{13} +0.482362 q^{14} +(-0.500000 - 0.866025i) q^{16} +(5.88512 + 3.39778i) q^{17} -1.00000 q^{18} +(-4.39778 - 2.53906i) q^{19} -0.482362i q^{21} +(2.00731 + 1.15892i) q^{22} +(-5.98124 + 3.45327i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.74238 - 3.15660i) q^{26} +1.00000i q^{27} +(-0.241181 - 0.417738i) q^{28} +(-4.20478 - 7.28290i) q^{29} +0.952516i q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.15892 - 2.00731i) q^{33} -6.79555i q^{34} +(0.500000 + 0.866025i) q^{36} +(-3.09429 - 5.35948i) q^{37} +5.07812i q^{38} +(-3.15660 - 1.74238i) q^{39} +(7.55607 - 4.36250i) q^{41} +(-0.417738 + 0.241181i) q^{42} +(9.78170 + 5.64747i) q^{43} -2.31784i q^{44} +(5.98124 + 3.45327i) q^{46} -5.77729 q^{47} +(0.866025 + 0.500000i) q^{48} +(3.38366 + 5.86068i) q^{49} -6.79555 q^{51} +(-3.60488 + 0.0693504i) q^{52} -5.81017i q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.241181 + 0.417738i) q^{56} +5.07812 q^{57} +(-4.20478 + 7.28290i) q^{58} +(-10.2397 - 5.91189i) q^{59} +(-4.68764 + 8.11924i) q^{61} +(0.824903 - 0.476258i) q^{62} +(0.241181 + 0.417738i) q^{63} +1.00000 q^{64} -2.31784 q^{66} +(3.69677 + 6.40300i) q^{67} +(-5.88512 + 3.39778i) q^{68} +(3.45327 - 5.98124i) q^{69} +(3.01876 + 1.74288i) q^{71} +(0.500000 - 0.866025i) q^{72} -8.53465 q^{73} +(-3.09429 + 5.35948i) q^{74} +(4.39778 - 2.53906i) q^{76} -1.11804i q^{77} +(0.0693504 + 3.60488i) q^{78} -9.03820 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-7.55607 - 4.36250i) q^{82} -7.94887 q^{83} +(0.417738 + 0.241181i) q^{84} -11.2949i q^{86} +(7.28290 + 4.20478i) q^{87} +(-2.00731 + 1.15892i) q^{88} +(-7.80941 + 4.50877i) q^{89} +(-1.73886 + 0.0334520i) q^{91} -6.90654i q^{92} +(-0.476258 - 0.824903i) q^{93} +(2.88865 + 5.00328i) q^{94} -1.00000i q^{96} +(-4.59103 + 7.95189i) q^{97} +(3.38366 - 5.86068i) q^{98} +2.31784i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} - 4 q^{7} + 8 q^{8} + 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^7 + 8 * q^8 + 4 * q^9	$ 8 q - 4 q^{2} - 4 q^{4} - 4 q^{7} + 8 q^{8} + 4 q^{9} - 12 q^{11} + 8 q^{14} - 4 q^{16} - 8 q^{18} - 12 q^{19} + 12 q^{22} - 12 q^{23} - 4 q^{28} - 4 q^{29} - 4 q^{32} + 8 q^{33} + 4 q^{36} - 16 q^{37} + 24 q^{43} + 12 q^{46} + 32 q^{47} + 16 q^{49} - 8 q^{51} - 4 q^{56} - 4 q^{58} + 12 q^{59} - 16 q^{61} - 24 q^{62} + 4 q^{63} + 8 q^{64} - 16 q^{66} + 24 q^{67} - 4 q^{69} + 60 q^{71} + 4 q^{72} - 24 q^{73} - 16 q^{74} + 12 q^{76} + 8 q^{79} - 4 q^{81} - 8 q^{83} - 12 q^{87} - 12 q^{88} - 24 q^{89} + 8 q^{91} + 4 q^{93} - 16 q^{94} + 16 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^7 + 8 * q^8 + 4 * q^9 - 12 * q^11 + 8 * q^14 - 4 * q^16 - 8 * q^18 - 12 * q^19 + 12 * q^22 - 12 * q^23 - 4 * q^28 - 4 * q^29 - 4 * q^32 + 8 * q^33 + 4 * q^36 - 16 * q^37 + 24 * q^43 + 12 * q^46 + 32 * q^47 + 16 * q^49 - 8 * q^51 - 4 * q^56 - 4 * q^58 + 12 * q^59 - 16 * q^61 - 24 * q^62 + 4 * q^63 + 8 * q^64 - 16 * q^66 + 24 * q^67 - 4 * q^69 + 60 * q^71 + 4 * q^72 - 24 * q^73 - 16 * q^74 + 12 * q^76 + 8 * q^79 - 4 * q^81 - 8 * q^83 - 12 * q^87 - 12 * q^88 - 24 * q^89 + 8 * q^91 + 4 * q^93 - 16 * q^94 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	−	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
$7$	−0.241181	+	0.417738i	−0.0911578	+	0.157890i	−0.907999	−	0.418973i	$-0.862390\pi$
$7$	−0.241181	+	0.417738i	−0.0911578	+	0.157890i	0.816841	+	0.576863i	$0.195723\pi$
$8$	1.00000			0.353553
$9$	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	$0.446957\pi$
$12$		−	1.00000i		−	0.288675i
$13$	1.86250	+	3.08725i	0.516565	+	0.856248i
$13$	1.86250	+	3.08725i	0.516565	+	0.856248i
$14$	0.482362			0.128917
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	5.88512	+	3.39778i	1.42735	+	0.824082i	0.996911	−	0.0785367i	$-0.0250248\pi$
$17$	5.88512	+	3.39778i	1.42735	+	0.824082i	0.430441	+	0.902619i	$0.358358\pi$
$18$	−1.00000			−0.235702
$19$	−4.39778	−	2.53906i	−1.00892	−	0.582500i	−0.0980443	−	0.995182i	$-0.531259\pi$
$19$	−4.39778	−	2.53906i	−1.00892	−	0.582500i	−0.910875	+	0.412682i	$0.864592\pi$
$20$		0			0
$21$		−	0.482362i		−	0.105260i
$22$	2.00731	+	1.15892i	0.427959	+	0.247082i
$23$	−5.98124	+	3.45327i	−1.24718	+	0.720057i	−0.970545	−	0.240920i	$-0.922551\pi$
$23$	−5.98124	+	3.45327i	−1.24718	+	0.720057i	−0.276630	+	0.960976i	$0.589218\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$		0			0
$26$	1.74238	−	3.15660i	0.341709	−	0.619060i
$27$			1.00000i			0.192450i
$28$	−0.241181	−	0.417738i	−0.0455789	−	0.0789450i
$29$	−4.20478	−	7.28290i	−0.780809	−	1.35240i	−0.931471	−	0.363815i	$-0.881474\pi$
$29$	−4.20478	−	7.28290i	−0.780809	−	1.35240i	0.150662	−	0.988585i	$-0.451859\pi$
$30$		0			0
$31$			0.952516i			0.171077i	0.996335	+	0.0855385i	$0.0272611\pi$
$31$			0.952516i			0.171077i	−0.996335	+	0.0855385i	$0.972739\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.15892	−	2.00731i	0.201742	−	0.349427i
$34$		−	6.79555i		−	1.16543i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−3.09429	−	5.35948i	−0.508699	−	0.881092i	−0.999949	−	0.0100739i	$-0.996793\pi$
$37$	−3.09429	−	5.35948i	−0.508699	−	0.881092i	0.491250	−	0.871018i	$-0.336540\pi$
$38$			5.07812i			0.823779i
$39$	−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	$0.0947447\pi$
$42$	−0.417738	+	0.241181i	−0.0644583	+	0.0372150i
$43$	9.78170	+	5.64747i	1.49170	+	0.861231i	0.999955	−	0.00951136i	$-0.00302761\pi$
$43$	9.78170	+	5.64747i	1.49170	+	0.861231i	0.491740	+	0.870742i	$0.336361\pi$
$44$		−	2.31784i		−	0.349427i
$45$		0			0
$46$	5.98124	+	3.45327i	0.881886	+	0.509157i
$47$	−5.77729			−0.842705			−0.421353	−	0.906897i	$-0.638444\pi$
$47$	−5.77729			−0.842705			−0.421353	+	0.906897i	$0.638444\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	3.38366	+	5.86068i	0.483380	+	0.837240i
$50$		0			0
$51$	−6.79555			−0.951568
$52$	−3.60488	+	0.0693504i	−0.499908	+	0.00961716i
$53$		−	5.81017i		−	0.798088i	−0.916932	−	0.399044i	$-0.869342\pi$
$53$		−	5.81017i		−	0.798088i	0.916932	−	0.399044i	$-0.130658\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$		0			0
$56$	−0.241181	+	0.417738i	−0.0322292	+	0.0558225i
$57$	5.07812			0.672613
$58$	−4.20478	+	7.28290i	−0.552115	+	0.956292i
$59$	−10.2397	−	5.91189i	−1.33309	−	0.769663i	−0.347322	−	0.937746i	$-0.612909\pi$
$59$	−10.2397	−	5.91189i	−1.33309	−	0.769663i	−0.985773	+	0.168083i	$0.946242\pi$
$60$		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	$0.961758\pi$
$62$	0.824903	−	0.476258i	0.104763	−	0.0604848i
$63$	0.241181	+	0.417738i	0.0303859	+	0.0526300i
$64$	1.00000			0.125000
$65$		0			0
$66$	−2.31784			−0.285306
$67$	3.69677	+	6.40300i	0.451633	+	0.782251i	0.998488	−	0.0549764i	$-0.0175083\pi$
$67$	3.69677	+	6.40300i	0.451633	+	0.782251i	−0.546855	+	0.837227i	$0.684175\pi$
$68$	−5.88512	+	3.39778i	−0.713676	+	0.412041i
$69$	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	$0.600348\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−8.53465			−0.998906			−0.499453	−	0.866341i	$-0.666466\pi$
$73$	−8.53465			−0.998906			−0.499453	+	0.866341i	$0.666466\pi$
$74$	−3.09429	+	5.35948i	−0.359704	+	0.623026i
$75$		0			0
$76$	4.39778	−	2.53906i	0.504460	−	0.291250i
$77$		−	1.11804i		−	0.127412i
$78$	0.0693504	+	3.60488i	0.00785238	+	0.408173i
$79$	−9.03820			−1.01688			−0.508438	−	0.861098i	$-0.669777\pi$
$79$	−9.03820			−1.01688			−0.508438	+	0.861098i	$0.669777\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−7.55607	−	4.36250i	−0.834429	−	0.481758i
$83$	−7.94887			−0.872502			−0.436251	−	0.899825i	$-0.643694\pi$
$83$	−7.94887			−0.872502			−0.436251	+	0.899825i	$0.643694\pi$
$84$	0.417738	+	0.241181i	0.0455789	+	0.0263150i
$85$		0			0
$86$		−	11.2949i		−	1.21796i
$87$	7.28290	+	4.20478i	0.780809	+	0.450800i
$88$	−2.00731	+	1.15892i	−0.213980	+	0.123541i
$89$	−7.80941	+	4.50877i	−0.827796	+	0.477928i	−0.853097	−	0.521752i	$-0.825279\pi$
$89$	−7.80941	+	4.50877i	−0.827796	+	0.477928i	0.0253015	+	0.999680i	$0.491945\pi$
$90$		0			0
$91$	−1.73886	+	0.0334520i	−0.182282	+	0.00350672i
$92$		−	6.90654i		−	0.720057i
$93$	−0.476258	−	0.824903i	−0.0493857	−	0.0855385i
$94$	2.88865	+	5.00328i	0.297941	+	0.516049i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	−4.59103	+	7.95189i	−0.466148	+	0.807392i	−0.999253	−	0.0386571i	$-0.987692\pi$
$97$	−4.59103	+	7.95189i	−0.466148	+	0.807392i	0.533104	+	0.846050i	$0.321025\pi$
$98$	3.38366	−	5.86068i	0.341802	−	0.592018i
$99$			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	$-0.345022\pi$
$102$	3.39778	+	5.88512i	0.336430	+	0.582714i
$103$		−	9.17449i		−	0.903990i	−0.892021	−	0.451995i	$-0.850713\pi$
$103$		−	9.17449i		−	0.903990i	0.892021	−	0.451995i	$-0.149287\pi$
$104$	1.86250	+	3.08725i	0.182633	+	0.302729i
$105$		0			0
$106$	−5.03175	+	2.90508i	−0.488727	+	0.282167i
$107$	−2.78629	+	1.60867i	−0.269361	+	0.155516i	−0.628597	−	0.777731i	$-0.716371\pi$
$107$	−2.78629	+	1.60867i	−0.269361	+	0.155516i	0.359236	+	0.933247i	$0.383037\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$		−	17.0669i		−	1.63471i	−0.576132	−	0.817356i	$-0.695439\pi$
$109$		−	17.0669i		−	1.63471i	0.576132	−	0.817356i	$-0.304561\pi$
$110$		0			0
$111$	5.35948	+	3.09429i	0.508699	+	0.293697i
$112$	0.482362			0.0455789
$113$	−1.43488	−	0.828427i	−0.134982	−	0.0779319i	0.430988	−	0.902357i	$-0.358165\pi$
$113$	−1.43488	−	0.828427i	−0.134982	−	0.0779319i	−0.565970	+	0.824426i	$0.691498\pi$
$114$	−2.53906	−	4.39778i	−0.237805	−	0.411890i
$115$		0			0
$116$	8.40957			0.780809
$117$	3.60488	−	0.0693504i	0.333272	−	0.00641144i
$118$			11.8238i			1.08847i
$119$	−2.83876	+	1.63896i	−0.260229	+	0.150243i
$120$		0			0
$121$	−2.81382	+	4.87367i	−0.255801	+	0.443061i
$122$	9.37529			0.848799
$123$	−4.36250	+	7.55607i	−0.393353	+	0.681308i
$124$	−0.824903	−	0.476258i	−0.0740785	−	0.0427692i
$125$		0			0
$126$	0.241181	−	0.417738i	0.0214861	−	0.0372150i
$127$	−16.3843	+	9.45946i	−1.45387	+	0.839391i	−0.998698	−	0.0510134i	$-0.983755\pi$
$127$	−16.3843	+	9.45946i	−1.45387	+	0.839391i	−0.455170	+	0.890405i	$0.650422\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−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	$0.598457\pi$
$132$	1.15892	+	2.00731i	0.100871	+	0.174714i
$133$	2.12132	−	1.22474i	0.183942	−	0.106199i
$134$	3.69677	−	6.40300i	0.319353	−	0.553135i
$135$		0			0
$136$	5.88512	+	3.39778i	0.504645	+	0.291357i
$137$	−10.2547	+	17.7616i	−0.876116	+	1.51748i	−0.0205465	+	0.999789i	$0.506541\pi$
$137$	−10.2547	+	17.7616i	−0.876116	+	1.51748i	−0.855569	+	0.517688i	$0.826793\pi$
$138$	−6.90654			−0.587924
$139$	−4.25467	+	7.36931i	−0.360877	+	0.625057i	−0.988105	−	0.153778i	$-0.950856\pi$
$139$	−4.25467	+	7.36931i	−0.360877	+	0.625057i	0.627229	+	0.778835i	$0.284189\pi$
$140$		0			0
$141$	5.00328	−	2.88865i	0.421353	−	0.243268i
$142$		−	3.48576i		−	0.292519i
$143$	−7.31648	−	4.03856i	−0.611835	−	0.337721i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	4.26733	+	7.39123i	0.353166	+	0.611702i
$147$	−5.86068	−	3.38366i	−0.483380	−	0.279080i
$148$	6.18859			0.508699
$149$	−6.27439	−	3.62252i	−0.514018	−	0.296769i	0.220466	−	0.975395i	$-0.429242\pi$
$149$	−6.27439	−	3.62252i	−0.514018	−	0.296769i	−0.734484	+	0.678626i	$0.762576\pi$
$150$		0			0
$151$			7.82743i			0.636987i	0.947925	+	0.318494i	$0.103177\pi$
$151$			7.82743i			0.636987i	−0.947925	+	0.318494i	$0.896823\pi$
$152$	−4.39778	−	2.53906i	−0.356707	−	0.205945i
$153$	5.88512	−	3.39778i	0.475784	−	0.274694i
$154$	−0.968248	+	0.559018i	−0.0780236	+	0.0450470i
$155$		0			0
$156$	3.08725	−	1.86250i	0.247178	−	0.149119i
$157$			4.42267i			0.352967i	0.984304	+	0.176484i	$0.0564723\pi$
$157$			4.42267i			0.352967i	−0.984304	+	0.176484i	$0.943528\pi$
$158$	4.51910	+	7.82731i	0.359520	+	0.622707i
$159$	2.90508	+	5.03175i	0.230388	+	0.399044i
$160$		0			0
$161$		−	3.33145i		−	0.262555i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	5.61219	−	9.72060i	0.439581	−	0.761376i	−0.558076	−	0.829790i	$-0.688460\pi$
$163$	5.61219	−	9.72060i	0.439581	−	0.761376i	0.997657	+	0.0684135i	$0.0217937\pi$
$164$			8.72500i			0.681308i
$165$		0			0
$166$	3.97443	+	6.88392i	0.308476	+	0.534296i
$167$	−7.52898	−	13.0406i	−0.582610	−	1.00911i	−0.995169	−	0.0981794i	$-0.968698\pi$
$167$	−7.52898	−	13.0406i	−0.582610	−	1.00911i	0.412558	−	0.910931i	$-0.364635\pi$
$168$		−	0.482362i		−	0.0372150i
$169$	−6.06218	+	11.5000i	−0.466321	+	0.884615i
$170$		0			0
$171$	−4.39778	+	2.53906i	−0.336306	+	0.194167i
$172$	−9.78170	+	5.64747i	−0.745848	+	0.430615i
$173$	−12.7727	−	7.37429i	−0.971087	−	0.560657i	−0.0715193	−	0.997439i	$-0.522785\pi$
$173$	−12.7727	−	7.37429i	−0.971087	−	0.560657i	−0.899567	+	0.436782i	$0.856118\pi$
$174$		−	8.40957i		−	0.637528i
$175$		0			0
$176$	2.00731	+	1.15892i	0.151306	+	0.0873568i
$177$	11.8238			0.888730
$178$	7.80941	+	4.50877i	0.585340	+	0.337946i
$179$	−4.30589	−	7.45802i	−0.321837	−	0.557438i	0.659030	−	0.752117i	$-0.270967\pi$
$179$	−4.30589	−	7.45802i	−0.321837	−	0.557438i	−0.980867	+	0.194678i	$0.937634\pi$
$180$		0			0
$181$	2.84493			0.211462			0.105731	−	0.994395i	$-0.466282\pi$
$181$	2.84493			0.211462			0.105731	+	0.994395i	$0.466282\pi$
$182$	0.898400	+	1.48917i	0.0665938	+	0.110385i
$183$		−	9.37529i		−	0.693041i
$184$	−5.98124	+	3.45327i	−0.440943	+	0.254579i
$185$		0			0
$186$	−0.476258	+	0.824903i	−0.0349209	+	0.0604848i
$187$	−15.7510			−1.15183
$188$	2.88865	−	5.00328i	0.210676	−	0.364902i
$189$	−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	$0.126996\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	1.32843	+	2.30090i	0.0956223	+	0.165623i	0.909868	−	0.414898i	$-0.136183\pi$
$193$	1.32843	+	2.30090i	0.0956223	+	0.165623i	−0.814246	+	0.580520i	$0.802849\pi$
$194$	9.18206			0.659233
$195$		0			0
$196$	−6.76733			−0.483380
$197$	10.5579	+	18.2868i	0.752219	+	1.30288i	0.946745	+	0.321984i	$0.104350\pi$
$197$	10.5579	+	18.2868i	0.752219	+	1.30288i	−0.194526	+	0.980897i	$0.562317\pi$
$198$	2.00731	−	1.15892i	0.142653	−	0.0823608i
$199$	−5.26941	+	9.12688i	−0.373538	+	0.646988i	−0.990107	−	0.140314i	$-0.955189\pi$
$199$	−5.26941	+	9.12688i	−0.373538	+	0.646988i	0.616569	+	0.787301i	$0.288522\pi$
$200$		0			0
$201$	−6.40300	−	3.69677i	−0.451633	−	0.260750i
$202$	−5.34108	+	9.25102i	−0.375797	+	0.650900i
$203$	4.05646			0.284707
$204$	3.39778	−	5.88512i	0.237892	−	0.412041i
$205$		0			0
$206$	−7.94534	+	4.58725i	−0.553578	+	0.319609i
$207$			6.90654i			0.480038i
$208$	1.74238	−	3.15660i	0.120813	−	0.218871i
$209$	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	$0.703932\pi$
$212$	5.03175	+	2.90508i	0.345582	+	0.199522i
$213$	−3.48576			−0.238840
$214$	2.78629	+	1.60867i	0.190467	+	0.109966i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	−0.397902	−	0.229729i	−0.0270113	−	0.0155950i
$218$	−14.7804	+	8.53345i	−1.00105	+	0.577958i
$219$	7.39123	−	4.26733i	0.499453	−	0.288359i
$220$		0			0
$221$	0.471274	+	24.4972i	0.0317013	+	1.64786i
$222$		−	6.18859i		−	0.415351i
$223$	2.61389	+	4.52739i	0.175039	+	0.303176i	0.940175	−	0.340693i	$-0.110662\pi$
$223$	2.61389	+	4.52739i	0.175039	+	0.303176i	−0.765136	+	0.643869i	$0.777328\pi$
$224$	−0.241181	−	0.417738i	−0.0161146	−	0.0279113i
$225$		0			0
$226$			1.65685i			0.110212i
$227$	5.43443	−	9.41271i	0.360696	−	0.624744i	−0.627380	−	0.778714i	$-0.715873\pi$
$227$	5.43443	−	9.41271i	0.360696	−	0.624744i	0.988076	+	0.153970i	$0.0492059\pi$
$228$	−2.53906	+	4.39778i	−0.168153	+	0.291250i
$229$			21.1932i			1.40048i	0.713905	+	0.700242i	$0.246925\pi$
$229$			21.1932i			1.40048i	−0.713905	+	0.700242i	$0.753075\pi$
$230$		0			0
$231$	0.559018	+	0.968248i	0.0367807	+	0.0637060i
$232$	−4.20478	−	7.28290i	−0.276058	−	0.478146i
$233$			21.8423i			1.43094i	0.698645	+	0.715469i	$0.253787\pi$
$233$			21.8423i			1.43094i	−0.698645	+	0.715469i	$0.746213\pi$
$234$	−1.86250	−	3.08725i	−0.121756	−	0.201820i
$235$		0			0
$236$	10.2397	−	5.91189i	0.666547	−	0.384831i
$237$	7.82731	−	4.51910i	0.508438	−	0.293547i
$238$	2.83876	+	1.63896i	0.184009	+	0.106238i
$239$		−	8.23027i		−	0.532372i	−0.963922	−	0.266186i	$-0.914236\pi$
$239$		−	8.23027i		−	0.532372i	0.963922	−	0.266186i	$-0.0857635\pi$
$240$		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	$0.698526\pi$
$242$	5.62763			0.361758
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−4.68764	−	8.11924i	−0.300096	−	0.519781i
$245$		0			0
$246$	8.72500			0.556286
$247$	−0.352169	−	18.3060i	−0.0224080	−	1.16478i
$248$			0.952516i			0.0604848i
$249$	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	$0.00257072\pi$
$252$	−0.482362			−0.0303859
$253$	8.00412	−	13.8635i	0.503215	−	0.871594i
$254$	16.3843	+	9.45946i	1.02804	+	0.593539i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.05205	−	1.76210i	0.190382	−	0.109917i	−0.401780	−	0.915736i	$-0.631608\pi$
$257$	3.05205	−	1.76210i	0.190382	−	0.109917i	0.592161	+	0.805819i	$0.298275\pi$
$258$	5.64747	+	9.78170i	0.351596	+	0.608982i
$259$	2.98514			0.185488
$260$		0			0
$261$	−8.40957			−0.520539
$262$	3.48406	+	6.03457i	0.215246	+	0.372817i
$263$	20.1637	−	11.6415i	1.24334	−	0.717845i	0.273571	−	0.961852i	$-0.411795\pi$
$263$	20.1637	−	11.6415i	1.24334	−	0.717845i	0.969774	+	0.244006i	$0.0784618\pi$
$264$	1.15892	−	2.00731i	0.0713265	−	0.123541i
$265$		0			0
$266$	−2.12132	−	1.22474i	−0.130066	−	0.0750939i
$267$	4.50877	−	7.80941i	0.275932	−	0.477928i
$268$	−7.39355			−0.451633
$269$	4.90873	−	8.50217i	0.299291	−	0.518387i	−0.676683	−	0.736274i	$-0.736583\pi$
$269$	4.90873	−	8.50217i	0.299291	−	0.518387i	0.975974	+	0.217888i	$0.0699166\pi$
$270$		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	$0.563782\pi$
$272$		−	6.79555i		−	0.412041i
$273$	1.48917	−	0.898400i	0.0901287	−	0.0543736i
$274$	20.5093			1.23901
$275$		0			0
$276$	3.45327	+	5.98124i	0.207863	+	0.360028i
$277$	11.6697	+	6.73753i	0.701167	+	0.404819i	0.807782	−	0.589481i	$-0.200668\pi$
$277$	11.6697	+	6.73753i	0.701167	+	0.404819i	−0.106615	+	0.994300i	$0.534001\pi$
$278$	8.50935			0.510357
$279$	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	$-0.344746\pi$
$282$	−5.00328	−	2.88865i	−0.297941	−	0.172016i
$283$	10.5516	−	6.09197i	0.627228	−	0.362130i	−0.152450	−	0.988311i	$-0.548716\pi$
$283$	10.5516	−	6.09197i	0.627228	−	0.362130i	0.779678	+	0.626181i	$0.215383\pi$
$284$	−3.01876	+	1.74288i	−0.179130	+	0.103421i
$285$		0			0
$286$	0.160743	+	8.35554i	0.00950492	+	0.494073i
$287$			4.20861i			0.248426i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	14.5898	+	25.2702i	0.858223	+	1.48649i
$290$		0			0
$291$		−	9.18206i		−	0.538262i
$292$	4.26733	−	7.39123i	0.249726	−	0.432539i
$293$	7.51047	−	13.0085i	0.438766	−	0.759965i	−0.558829	−	0.829283i	$-0.688749\pi$
$293$	7.51047	−	13.0085i	0.438766	−	0.759965i	0.997595	+	0.0693181i	$0.0220823\pi$
$294$			6.76733i			0.394679i
$295$		0			0
$296$	−3.09429	−	5.35948i	−0.179852	−	0.311513i
$297$	−1.15892	−	2.00731i	−0.0672473	−	0.116476i
$298$			7.24504i			0.419694i
$299$	−21.8012	−	12.0338i	−1.26079	−	0.695935i
$300$		0			0
$301$	−4.71832	+	2.72412i	−0.271959	+	0.157016i
$302$	6.77875	−	3.91372i	0.390073	−	0.225209i
$303$	9.25102	+	5.34108i	0.531457	+	0.306837i
$304$			5.07812i			0.291250i
$305$		0			0
$306$	−5.88512	−	3.39778i	−0.336430	−	0.194238i
$307$	−27.9569			−1.59558			−0.797791	−	0.602934i	$-0.793998\pi$
$307$	−27.9569			−1.59558			−0.797791	+	0.602934i	$0.793998\pi$
$308$	0.968248	+	0.559018i	0.0551710	+	0.0318530i
$309$	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	$0.367053\pi$
$312$	−3.15660	−	1.74238i	−0.178707	−	0.0986430i
$313$		−	13.9895i		−	0.790731i	−0.918524	−	0.395366i	$-0.870618\pi$
$313$		−	13.9895i		−	0.790731i	0.918524	−	0.395366i	$-0.129382\pi$
$314$	3.83014	−	2.21134i	0.216148	−	0.124793i
$315$		0			0
$316$	4.51910	−	7.82731i	0.254219	−	0.440320i
$317$	−7.29868			−0.409935			−0.204967	−	0.978769i	$-0.565709\pi$
$317$	−7.29868			−0.409935			−0.204967	+	0.978769i	$0.565709\pi$
$318$	2.90508	−	5.03175i	0.162909	−	0.282167i
$319$	16.8806	+	9.74601i	0.945131	+	0.545672i
$320$		0			0
$321$	1.60867	−	2.78629i	0.0897870	−	0.155516i
$322$	−2.88512	+	1.66573i	−0.160782	+	0.0928273i
$323$	−17.2543	−	29.8853i	−0.960055	−	1.66286i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−11.2244			−0.621661
$327$	8.53345	+	14.7804i	0.471901	+	0.817356i
$328$	7.55607	−	4.36250i	0.417214	−	0.240879i
$329$	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	$0.408773\pi$
$332$	3.97443	−	6.88392i	0.218125	−	0.377804i
$333$	−6.18859			−0.339133
$334$	−7.52898	+	13.0406i	−0.411968	+	0.713549i
$335$		0			0
$336$	−0.417738	+	0.241181i	−0.0227895	+	0.0131575i
$337$		−	24.4240i		−	1.33046i	−0.746639	−	0.665229i	$-0.768334\pi$
$337$		−	24.4240i		−	1.33046i	0.746639	−	0.665229i	$-0.231666\pi$
$338$	12.9904	−	0.500000i	0.706584	−	0.0271964i
$339$	1.65685			0.0899880
$340$		0			0
$341$	−1.10389	−	1.91199i	−0.0597789	−	0.103540i
$342$	4.39778	+	2.53906i	0.237805	+	0.137297i
$343$	−6.64083			−0.358571
$344$	9.78170	+	5.64747i	0.527394	+	0.304491i
$345$		0			0
$346$			14.7486i			0.792889i
$347$	−11.6189	−	6.70818i	−0.623736	−	0.360114i	0.154586	−	0.987979i	$-0.450596\pi$
$347$	−11.6189	−	6.70818i	−0.623736	−	0.360114i	−0.778322	+	0.627865i	$0.783929\pi$
$348$	−7.28290	+	4.20478i	−0.390404	+	0.225400i
$349$	−0.824457	+	0.476000i	−0.0441322	+	0.0254797i	−0.521904	−	0.853004i	$-0.674778\pi$
$349$	−0.824457	+	0.476000i	−0.0441322	+	0.0254797i	0.477772	+	0.878484i	$0.341445\pi$
$350$		0			0
$351$	−3.08725	+	1.86250i	−0.164785	+	0.0994130i
$352$		−	2.31784i		−	0.123541i
$353$	−7.22380	−	12.5120i	−0.384484	−	0.665946i	0.607213	−	0.794539i	$-0.292287\pi$
$353$	−7.22380	−	12.5120i	−0.384484	−	0.665946i	−0.991697	+	0.128593i	$0.958954\pi$
$354$	−5.91189	−	10.2397i	−0.314213	−	0.544234i
$355$		0			0
$356$		−	9.01753i		−	0.477928i
$357$	1.63896	−	2.83876i	0.0867429	−	0.150243i
$358$	−4.30589	+	7.45802i	−0.227573	+	0.394168i
$359$		−	8.11291i		−	0.428183i	−0.976814	−	0.214092i	$-0.931321\pi$
$359$		−	8.11291i		−	0.428183i	0.976814	−	0.214092i	$-0.0686791\pi$
$360$		0			0
$361$	3.39363	+	5.87794i	0.178612	+	0.309365i
$362$	−1.42246	−	2.46378i	−0.0747630	−	0.129493i
$363$		−	5.62763i		−	0.295374i
$364$	0.840459	−	1.52262i	0.0440520	−	0.0798071i
$365$		0			0
$366$	−8.11924	+	4.68764i	−0.424399	+	0.245027i
$367$	−20.7806	+	11.9977i	−1.08474	+	0.626274i	−0.932171	−	0.362019i	$-0.882088\pi$
$367$	−20.7806	+	11.9977i	−1.08474	+	0.626274i	−0.152568	+	0.988293i	$0.548754\pi$
$368$	5.98124	+	3.45327i	0.311794	+	0.180014i
$369$		−	8.72500i		−	0.454205i
$370$		0			0
$371$	2.42713	+	1.40130i	0.126010	+	0.0727520i
$372$	0.952516			0.0493857
$373$	23.2593	+	13.4288i	1.20432	+	0.695316i	0.961513	−	0.274758i	$-0.0885977\pi$
$373$	23.2593	+	13.4288i	1.20432	+	0.695316i	0.242809	+	0.970074i	$0.421931\pi$
$374$	7.87550	+	13.6408i	0.407232	+	0.705347i
$375$		0			0
$376$	−5.77729			−0.297941
$377$	14.6527	−	26.5456i	0.754652	−	1.36717i
$378$			0.482362i			0.0248100i
$379$	13.2638	−	7.65785i	0.681315	−	0.393357i	−0.119035	−	0.992890i	$-0.537980\pi$
$379$	13.2638	−	7.65785i	0.681315	−	0.393357i	0.800350	+	0.599533i	$0.204647\pi$
$380$		0			0
$381$	9.45946	−	16.3843i	0.484623	−	0.839391i
$382$	−3.43587			−0.175795
$383$	−17.6198	+	30.5185i	−0.900332	+	1.55942i	−0.0732675	+	0.997312i	$0.523343\pi$
$383$	−17.6198	+	30.5185i	−0.900332	+	1.55942i	−0.827064	+	0.562108i	$0.809991\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		0			0
$386$	1.32843	−	2.30090i	0.0676152	−	0.117113i
$387$	9.78170	−	5.64747i	0.497232	−	0.287077i
$388$	−4.59103	−	7.95189i	−0.233074	−	0.403696i
$389$	18.0946			0.917433			0.458717	−	0.888583i	$-0.348309\pi$
$389$	18.0946			0.917433			0.458717	+	0.888583i	$0.348309\pi$
$390$		0			0
$391$	−46.9338			−2.37354
$392$	3.38366	+	5.86068i	0.170901	+	0.296009i
$393$	6.03457	−	3.48406i	0.304404	−	0.175748i
$394$	10.5579	−	18.2868i	0.531899	−	0.921276i
$395$		0			0
$396$	−2.00731	−	1.15892i	−0.100871	−	0.0582379i
$397$	−5.22562	+	9.05105i	−0.262267	+	0.454259i	−0.966844	−	0.255368i	$-0.917803\pi$
$397$	−5.22562	+	9.05105i	−0.262267	+	0.454259i	0.704577	+	0.709627i	$0.251137\pi$
$398$	10.5388			0.528263
$399$	−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	$0.344469\pi$
$402$			7.39355i			0.368757i
$403$	−2.94065	+	1.77406i	−0.146484	+	0.0883723i
$404$	10.6822			0.531457
$405$		0			0
$406$	−2.02823	−	3.51299i	−0.100659	−	0.174347i
$407$	12.4224	+	7.17207i	0.615755	+	0.355506i
$408$	−6.79555			−0.336430
$409$	−5.83817	−	3.37067i	−0.288679	−	0.166669i	0.348667	−	0.937247i	$-0.386634\pi$
$409$	−5.83817	−	3.37067i	−0.288679	−	0.166669i	−0.637346	+	0.770578i	$0.719968\pi$
$410$		0			0
$411$		−	20.5093i		−	1.01165i
$412$	7.94534	+	4.58725i	0.391439	+	0.225997i
$413$	4.93924	−	2.85167i	0.243044	−	0.140322i
$414$	5.98124	−	3.45327i	0.293962	−	0.169719i
$415$		0			0
$416$	−3.60488	+	0.0693504i	−0.176744	+	0.00340018i
$417$		−	8.50935i		−	0.416704i
$418$	−5.88512	−	10.1933i	−0.287851	−	0.498572i
$419$	18.2539	+	31.6166i	0.891760	+	1.54457i	0.837765	+	0.546032i	$0.183862\pi$
$419$	18.2539	+	31.6166i	0.891760	+	1.54457i	0.0539949	+	0.998541i	$0.482805\pi$
$420$		0			0
$421$		−	40.8490i		−	1.99086i	−0.0955005	−	0.995429i	$-0.530445\pi$
$421$		−	40.8490i		−	1.99086i	0.0955005	−	0.995429i	$-0.469555\pi$
$422$	5.74384	−	9.94863i	0.279606	−	0.484292i
$423$	−2.88865	+	5.00328i	−0.140451	+	0.243268i
$424$		−	5.81017i		−	0.282167i
$425$		0			0
$426$	1.74288	+	3.01876i	0.0844429	+	0.146259i
$427$	−2.26114	−	3.91641i	−0.109424	−	0.189528i
$428$		−	3.21733i		−	0.155516i
$429$	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	$0.479271\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	1.21087	+	0.699097i	0.0581907	+	0.0335964i	0.528813	−	0.848738i	$-0.322637\pi$
$433$	1.21087	+	0.699097i	0.0581907	+	0.0335964i	−0.470622	+	0.882335i	$0.655971\pi$
$434$			0.459457i			0.0220547i
$435$		0			0
$436$	14.7804	+	8.53345i	0.707851	+	0.408678i
$437$	35.0722			1.67773
$438$	−7.39123	−	4.26733i	−0.353166	−	0.203901i
$439$	7.65685	+	13.2621i	0.365442	+	0.632964i	0.988847	−	0.148935i	$-0.0475846\pi$
$439$	7.65685	+	13.2621i	0.365442	+	0.632964i	−0.623405	+	0.781899i	$0.714251\pi$
$440$		0			0
$441$	6.76733			0.322254
$442$	20.9796	−	12.6567i	0.997895	−	0.602019i
$443$			33.1769i			1.57628i	0.615495	+	0.788141i	$0.288956\pi$
$443$			33.1769i			1.57628i	−0.615495	+	0.788141i	$0.711044\pi$
$444$	−5.35948	+	3.09429i	−0.254349	+	0.146849i
$445$		0			0
$446$	2.61389	−	4.52739i	0.123771	−	0.214378i
$447$	7.24504			0.342679
$448$	−0.241181	+	0.417738i	−0.0113947	+	0.0197362i
$449$	−13.3408	−	7.70234i	−0.629593	−	0.363496i	0.151001	−	0.988534i	$-0.451750\pi$
$449$	−13.3408	−	7.70234i	−0.629593	−	0.363496i	−0.780595	+	0.625038i	$0.785084\pi$
$450$		0			0
$451$	−10.1116	+	17.5137i	−0.476135	+	0.824690i
$452$	1.43488	−	0.828427i	0.0674910	−	0.0389659i
$453$	−3.91372	−	6.77875i	−0.183882	−	0.318494i
$454$	−10.8689			−0.510101
$455$		0			0
$456$	5.07812			0.237805
$457$	3.73097	+	6.46224i	0.174528	+	0.302291i	0.939998	−	0.341181i	$-0.110827\pi$
$457$	3.73097	+	6.46224i	0.174528	+	0.302291i	−0.765470	+	0.643471i	$0.777494\pi$
$458$	18.3538	−	10.5966i	0.857618	−	0.495146i
$459$	−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	$0.700751\pi$
$462$	0.559018	−	0.968248i	0.0260079	−	0.0450470i
$463$	−9.20888			−0.427973			−0.213986	−	0.976837i	$-0.568645\pi$
$463$	−9.20888			−0.427973			−0.213986	+	0.976837i	$0.568645\pi$
$464$	−4.20478	+	7.28290i	−0.195202	+	0.338100i
$465$		0			0
$466$	18.9160	−	10.9212i	0.876267	−	0.505913i
$467$		−	0.219469i		−	0.0101558i	−0.999987	−	0.00507792i	$-0.998384\pi$
$467$		−	0.219469i		−	0.0101558i	0.999987	−	0.00507792i	$-0.00161636\pi$
$468$	−1.74238	+	3.15660i	−0.0805417	+	0.145914i
$469$	−3.56637			−0.164680
$470$		0			0
$471$	−2.21134	−	3.83014i	−0.101893	−	0.176484i
$472$	−10.2397	−	5.91189i	−0.471320	−	0.272117i
$473$	−26.1798			−1.20375
$474$	−7.82731	−	4.51910i	−0.359520	−	0.207569i
$475$		0			0
$476$		−	3.27792i		−	0.150243i
$477$	−5.03175	−	2.90508i	−0.230388	−	0.133015i
$478$	−7.12762	+	4.11513i	−0.326010	+	0.188222i
$479$	5.49422	−	3.17209i	0.251037	−	0.144936i	−0.369202	−	0.929349i	$-0.620369\pi$
$479$	5.49422	−	3.17209i	0.251037	−	0.144936i	0.620239	+	0.784413i	$0.287036\pi$
$480$		0			0
$481$	10.7829	−	19.5349i	0.491658	−	0.890714i
$482$			3.10243i			0.141312i
$483$	1.66573	+	2.88512i	0.0757932	+	0.131278i
$484$	−2.81382	−	4.87367i	−0.127901	−	0.221530i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	18.5972	−	32.2113i	0.842720	−	1.45963i	−0.0448662	−	0.998993i	$-0.514286\pi$
$487$	18.5972	−	32.2113i	0.842720	−	1.45963i	0.887586	−	0.460641i	$-0.152381\pi$
$488$	−4.68764	+	8.11924i	−0.212200	+	0.367541i
$489$			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	$0.790120\pi$
$492$	−4.36250	−	7.55607i	−0.196677	−	0.340654i
$493$		−	57.1477i		−	2.57380i
$494$	−15.6774	+	9.45800i	−0.705359	+	0.425535i
$495$		0			0
$496$	0.824903	−	0.476258i	0.0370392	−	0.0213846i
$497$	−1.45613	+	0.840699i	−0.0653165	+	0.0377105i
$498$	−6.88392	−	3.97443i	−0.308476	−	0.178099i
$499$			21.2908i			0.953107i	0.879145	+	0.476554i	$0.158114\pi$
$499$			21.2908i			0.953107i	−0.879145	+	0.476554i	$0.841886\pi$
$500$		0			0
$501$	13.0406	+	7.52898i	0.582610	+	0.336370i
$502$	−15.6208			−0.697193
$503$	16.4925	+	9.52194i	0.735363	+	0.424562i	0.820381	−	0.571817i	$-0.193761\pi$
$503$	16.4925	+	9.52194i	0.735363	+	0.424562i	−0.0850178	+	0.996379i	$0.527095\pi$
$504$	0.241181	+	0.417738i	0.0107431	+	0.0186075i
$505$		0			0
$506$	−16.0082			−0.711653
$507$	−0.500000	−	12.9904i	−0.0222058	−	0.576923i
$508$		−	18.9189i		−	0.839391i
$509$	24.6679	−	14.2420i	1.09339	−	0.631267i	0.158911	−	0.987293i	$-0.449202\pi$
$509$	24.6679	−	14.2420i	1.09339	−	0.631267i	0.934476	+	0.356026i	$0.115868\pi$
$510$		0			0
$511$	2.05840	−	3.56525i	0.0910581	−	0.157717i
$512$	1.00000			0.0441942
$513$	2.53906	−	4.39778i	0.112102	−	0.194167i
$514$	−3.05205	−	1.76210i	−0.134620	−	0.0777230i
$515$		0			0
$516$	5.64747	−	9.78170i	0.248616	−	0.430615i
$517$	11.5968	−	6.69541i	0.510027	−	0.294464i
$518$	−1.49257	−	2.58521i	−0.0655797	−	0.113587i
$519$	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	$0.707203\pi$
$522$	4.20478	+	7.28290i	0.184038	+	0.318764i
$523$	14.6308	−	8.44709i	0.639759	−	0.369365i	−0.144762	−	0.989466i	$-0.546242\pi$
$523$	14.6308	−	8.44709i	0.639759	−	0.369365i	0.784522	+	0.620101i	$0.212908\pi$
$524$	3.48406	−	6.03457i	0.152202	−	0.263622i
$525$		0			0
$526$	−20.1637	−	11.6415i	−0.879177	−	0.507593i
$527$	−3.23644	+	5.60567i	−0.140981	+	0.244187i
$528$	−2.31784			−0.100871
$529$	12.3502	−	21.3911i	0.536964	−	0.930049i
$530$		0			0
$531$	−10.2397	+	5.91189i	−0.444365	+	0.256554i
$532$			2.44949i			0.106199i
$533$	27.5413	+	15.2023i	1.19295	+	0.658485i
$534$	−9.01753			−0.390227
$535$		0			0
$536$	3.69677	+	6.40300i	0.159676	+	0.276568i
$537$	7.45802	+	4.30589i	0.321837	+	0.185813i
$538$	−9.81746			−0.423261
$539$	−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	$-0.229093\pi$
$542$	18.8862	+	10.9040i	0.811233	+	0.468365i
$543$	−2.46378	+	1.42246i	−0.105731	+	0.0610438i
$544$	−5.88512	+	3.39778i	−0.252323	+	0.145679i
$545$		0			0
$546$	−1.52262	−	0.840459i	−0.0651622	−	0.0359683i
$547$		−	40.6726i		−	1.73903i	−0.493903	−	0.869517i	$-0.664430\pi$
$547$		−	40.6726i		−	1.73903i	0.493903	−	0.869517i	$-0.335570\pi$
$548$	−10.2547	−	17.7616i	−0.438058	−	0.758739i
$549$	4.68764	+	8.11924i	0.200064	+	0.346521i
$550$		0			0
$551$			42.7048i			1.81928i
$552$	3.45327	−	5.98124i	0.146981	−	0.254579i
$553$	2.17984	−	3.77559i	0.0926963	−	0.160555i
$554$		−	13.4751i		−	0.572501i
$555$		0			0
$556$	−4.25467	−	7.36931i	−0.180438	−	0.312528i
$557$	9.22730	+	15.9822i	0.390973	+	0.677186i	0.992578	−	0.121608i	$-0.0388052\pi$
$557$	9.22730	+	15.9822i	0.390973	+	0.677186i	−0.601605	+	0.798794i	$0.705472\pi$
$558$		−	0.952516i		−	0.0403232i
$559$	0.783308	+	40.7169i	0.0331304	+	1.72214i
$560$		0			0
$561$	13.6408	−	7.87550i	0.575913	−	0.332504i
$562$	−25.6488	+	14.8083i	−1.08193	+	0.624652i
$563$	8.17129	+	4.71770i	0.344379	+	0.198827i	0.662207	−	0.749321i	$-0.269620\pi$
$563$	8.17129	+	4.71770i	0.344379	+	0.198827i	−0.317828	+	0.948148i	$0.602953\pi$
$564$			5.77729i			0.243268i
$565$		0			0
$566$	−10.5516	−	6.09197i	−0.443517	−	0.256065i
$567$	0.482362			0.0202573
$568$	3.01876	+	1.74288i	0.126664	+	0.0731297i
$569$	−5.33503	−	9.24054i	−0.223656	−	0.387384i	0.732259	−	0.681026i	$-0.238466\pi$
$569$	−5.33503	−	9.24054i	−0.223656	−	0.387384i	−0.955915	+	0.293642i	$0.905133\pi$
$570$		0			0
$571$	0.532730			0.0222941			0.0111470	−	0.999938i	$-0.496452\pi$
$571$	0.532730			0.0222941			0.0111470	+	0.999938i	$0.496452\pi$
$572$	7.15573	−	4.31697i	0.299196	−	0.180502i
$573$			3.43587i			0.143536i
$574$	3.64476	−	2.10430i	0.152129	−	0.0878320i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	26.0683			1.08524			0.542620	−	0.839978i	$-0.317432\pi$
$577$	26.0683			1.08524			0.542620	+	0.839978i	$0.317432\pi$
$578$	14.5898	−	25.2702i	0.606855	−	1.05110i
$579$	−2.30090	−	1.32843i	−0.0956223	−	0.0552075i
$580$		0			0
$581$	1.91712	−	3.32054i	0.0795354	−	0.137759i
$582$	−7.95189	+	4.59103i	−0.329617	+	0.190304i
$583$	6.73351	+	11.6628i	0.278874	+	0.483023i
$584$	−8.53465			−0.353166
$585$		0			0
$586$	−15.0209			−0.620509
$587$	−7.37501	−	12.7739i	−0.304399	−	0.527235i	0.672728	−	0.739890i	$-0.265122\pi$
$587$	−7.37501	−	12.7739i	−0.304399	−	0.527235i	−0.977127	+	0.212655i	$0.931789\pi$
$588$	5.86068	−	3.38366i	0.241690	−	0.139540i
$589$	2.41849	−	4.18895i	0.0996523	−	0.172603i
$590$		0			0
$591$	−18.2868	−	10.5579i	−0.752219	−	0.434294i
$592$	−3.09429	+	5.35948i	−0.127175	+	0.220273i
$593$	−23.4887			−0.964566			−0.482283	−	0.876015i	$-0.660192\pi$
$593$	−23.4887			−0.964566			−0.482283	+	0.876015i	$0.660192\pi$
$594$	−1.15892	+	2.00731i	−0.0475510	+	0.0823608i
$595$		0			0
$596$	6.27439	−	3.62252i	0.257009	−	0.148384i
$597$		−	10.5388i		−	0.431325i
$598$	0.478971	+	24.8973i	0.0195866	+	1.01813i
$599$	−3.72087			−0.152031			−0.0760154	−	0.997107i	$-0.524220\pi$
$599$	−3.72087			−0.152031			−0.0760154	+	0.997107i	$0.524220\pi$
$600$		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	$0.501428\pi$
$602$	4.71832	+	2.72412i	0.192304	+	0.111027i
$603$	7.39355			0.301089
$604$	−6.77875	−	3.91372i	−0.275824	−	0.159247i
$605$		0			0
$606$		−	10.6822i		−	0.433933i
$607$	−16.4692	−	9.50853i	−0.668466	−	0.385939i	0.127029	−	0.991899i	$-0.459456\pi$
$607$	−16.4692	−	9.50853i	−0.668466	−	0.385939i	−0.795495	+	0.605960i	$0.792789\pi$
$608$	4.39778	−	2.53906i	0.178353	−	0.102972i
$609$	−3.51299	+	2.02823i	−0.142354	+	0.0821879i
$610$		0			0
$611$	−10.7602	−	17.8359i	−0.435312	−	0.721565i
$612$			6.79555i			0.274694i
$613$	11.4126	+	19.7672i	0.460951	+	0.798390i	0.999009	−	0.0445178i	$-0.0141751\pi$
$613$	11.4126	+	19.7672i	0.460951	+	0.798390i	−0.538058	+	0.842908i	$0.680842\pi$
$614$	13.9784	+	24.2114i	0.564124	+	0.977091i
$615$		0			0
$616$		−	1.11804i		−	0.0450470i
$617$	−8.66682	+	15.0114i	−0.348913	+	0.604335i	−0.986057	−	0.166410i	$-0.946783\pi$
$617$	−8.66682	+	15.0114i	−0.348913	+	0.604335i	0.637144	+	0.770745i	$0.280116\pi$
$618$	4.58725	−	7.94534i	0.184526	−	0.319609i
$619$		−	0.972021i		−	0.0390688i	−0.999809	−	0.0195344i	$-0.993782\pi$
$619$		−	0.972021i		−	0.0390688i	0.999809	−	0.0195344i	$-0.00621839\pi$
$620$		0			0
$621$	−3.45327	−	5.98124i	−0.138575	−	0.240019i
$622$	−7.15333	−	12.3899i	−0.286822	−	0.496791i
$623$		−	4.34971i		−	0.174268i
$624$	0.0693504	+	3.60488i	0.00277624	+	0.144311i
$625$		0			0
$626$	−12.1152	+	6.99473i	−0.484222	+	0.279566i
$627$	−10.1933	+	5.88512i	−0.407082	+	0.235029i
$628$	−3.83014	−	2.21134i	−0.152839	−	0.0882419i
$629$		−	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	$0.633393\pi$
$632$	−9.03820			−0.359520
$633$	−9.94863	−	5.74384i	−0.395422	−	0.228297i
$634$	3.64934	+	6.32085i	0.144934	+	0.251033i
$635$		0			0
$636$	−5.81017			−0.230388
$637$	−11.7913	+	21.3617i	−0.467187	+	0.846382i
$638$		−	19.4920i		−	0.771696i
$639$	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	$0.942248\pi$
$642$	−3.21733			−0.126978
$643$	−5.82478	+	10.0888i	−0.229707	+	0.397864i	−0.957721	−	0.287698i	$-0.907110\pi$
$643$	−5.82478	+	10.0888i	−0.229707	+	0.397864i	0.728014	+	0.685562i	$0.240443\pi$
$644$	2.88512	+	1.66573i	0.113690	+	0.0656388i
$645$		0			0
$646$	−17.2543	+	29.8853i	−0.678862	+	1.17582i
$647$	−19.2123	+	11.0922i	−0.755314	+	0.436081i	−0.827611	−	0.561303i	$-0.810300\pi$
$647$	−19.2123	+	11.0922i	−0.755314	+	0.436081i	0.0722970	+	0.997383i	$0.476967\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	27.4056			1.07576
$650$		0			0
$651$	0.459457			0.0180076
$652$	5.61219	+	9.72060i	0.219790	+	0.380688i
$653$	−28.8844	+	16.6764i	−1.13033	+	0.652598i	−0.944019	−	0.329892i	$-0.892988\pi$
$653$	−28.8844	+	16.6764i	−1.13033	+	0.652598i	−0.186314	+	0.982490i	$0.559654\pi$
$654$	8.53345	−	14.7804i	0.333684	−	0.577958i
$655$		0			0
$656$	−7.55607	−	4.36250i	−0.295015	−	0.170327i
$657$	−4.26733	+	7.39123i	−0.166484	+	0.288359i
$658$	−2.78675			−0.108639
$659$	−12.2280	+	21.1796i	−0.476337	+	0.825039i	−0.999632	−	0.0271118i	$-0.991369\pi$
$659$	−12.2280	+	21.1796i	−0.476337	+	0.825039i	0.523296	+	0.852151i	$0.324702\pi$
$660$		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	$0.108773\pi$
$662$		−	26.3594i		−	1.02449i
$663$	−12.6567	−	20.9796i	−0.491547	−	0.814778i
$664$	−7.94887			−0.308476
$665$		0			0
$666$	3.09429	+	5.35948i	0.119901	+	0.207675i
$667$	50.2997	+	29.0405i	1.94761	+	1.12445i
$668$	15.0580			0.582610
$669$	−4.52739	−	2.61389i	−0.175039	−	0.101059i
$670$		0			0
$671$		−	21.7304i		−	0.838893i
$672$	0.417738	+	0.241181i	0.0161146	+	0.00930376i
$673$	−29.4265	+	16.9894i	−1.13431	+	0.654893i	−0.945015	−	0.327028i	$-0.893953\pi$
$673$	−29.4265	+	16.9894i	−1.13431	+	0.654893i	−0.189293	+	0.981921i	$0.560620\pi$
$674$	−21.1518	+	12.2120i	−0.814736	+	0.470388i
$675$		0			0
$676$	−6.92820	−	11.0000i	−0.266469	−	0.423077i
$677$		−	10.3145i		−	0.396417i	−0.980160	−	0.198208i	$-0.936488\pi$
$677$		−	10.3145i		−	0.396417i	0.980160	−	0.198208i	$-0.0635123\pi$
$678$	−0.828427	−	1.43488i	−0.0318156	−	0.0551062i
$679$	−2.21454	−	3.83569i	−0.0849861	−	0.147200i
$680$		0			0
$681$			10.8689i			0.416496i
$682$	−1.10389	+	1.91199i	−0.0422701	+	0.0732139i
$683$	24.5191	−	42.4682i	0.938196	−	1.62500i	0.169362	−	0.985554i	$-0.445829\pi$
$683$	24.5191	−	42.4682i	0.938196	−	1.62500i	0.768834	−	0.639448i	$-0.220837\pi$
$684$		−	5.07812i		−	0.194167i
$685$		0			0
$686$	3.32042	+	5.75113i	0.126774	+	0.219579i
$687$	−10.5966	−	18.3538i	−0.404285	−	0.700242i
$688$		−	11.2949i		−	0.430615i
$689$	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	$0.106818\pi$
$692$	12.7727	−	7.37429i	0.485543	−	0.280329i
$693$	−0.968248	−	0.559018i	−0.0367807	−	0.0212353i
$694$			13.4164i			0.509278i
$695$		0			0
$696$	7.28290	+	4.20478i	0.276058	+	0.159382i
$697$	59.2912			2.24582
$698$	0.824457	+	0.476000i	0.0312061	+	0.0180169i
$699$	−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	$0.706781\pi$
$702$	3.15660	+	1.74238i	0.119138	+	0.0657620i
$703$			31.4264i			1.18527i
$704$	−2.00731	+	1.15892i	−0.0756532	+	0.0436784i
$705$		0			0
$706$	−7.22380	+	12.5120i	−0.271871	+	0.470895i
$707$	5.15267			0.193786
$708$	−5.91189	+	10.2397i	−0.222182	+	0.384831i
$709$	−27.0809	−	15.6352i	−1.01704	−	0.587190i	−0.103797	−	0.994598i	$-0.533099\pi$
$709$	−27.0809	−	15.6352i	−1.01704	−	0.587190i	−0.913246	+	0.407408i	$0.866433\pi$
$710$		0			0
$711$	−4.51910	+	7.82731i	−0.169479	+	0.293547i
$712$	−7.80941	+	4.50877i	−0.292670	+	0.168973i
$713$	−3.28930	−	5.69723i	−0.123185	−	0.213363i
$714$	−3.27792			−0.122673
$715$		0			0
$716$	8.61177			0.321837
$717$	4.11513	+	7.12762i	0.153683	+	0.266186i
$718$	−7.02599	+	4.05646i	−0.262208	+	0.151386i
$719$	10.6716	−	18.4838i	0.397984	−	0.689328i	−0.595494	−	0.803360i	$-0.703043\pi$
$719$	10.6716	−	18.4838i	0.397984	−	0.689328i	0.993477	+	0.114032i	$0.0363768\pi$
$720$		0			0
$721$	3.83253	+	2.21271i	0.142731	+	0.0824057i
$722$	3.39363	−	5.87794i	0.126298	−	0.218754i
$723$	3.10243			0.115381
$724$	−1.42246	+	2.46378i	−0.0528655	+	0.0915656i
$725$		0			0
$726$	−4.87367	+	2.81382i	−0.180879	+	0.104430i
$727$		−	8.80283i		−	0.326479i	−0.986586	−	0.163240i	$-0.947806\pi$
$727$		−	8.80283i		−	0.326479i	0.986586	−	0.163240i	$-0.0521943\pi$
$728$	−1.73886	+	0.0334520i	−0.0644464	+	0.00123981i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	38.3777	+	66.4721i	1.41945	+	2.45856i
$732$	8.11924	+	4.68764i	0.300096	+	0.173260i
$733$	−7.86883			−0.290642			−0.145321	−	0.989385i	$-0.546421\pi$
$733$	−7.86883			−0.290642			−0.145321	+	0.989385i	$0.546421\pi$
$734$	20.7806	+	11.9977i	0.767026	+	0.442843i
$735$		0			0
$736$		−	6.90654i		−	0.254579i
$737$	−14.8411	−	8.56852i	−0.546680	−	0.315626i
$738$	−7.55607	+	4.36250i	−0.278143	+	0.160586i
$739$	−15.6988	+	9.06368i	−0.577488	+	0.333413i	−0.760134	−	0.649766i	$-0.774867\pi$
$739$	−15.6988	+	9.06368i	−0.577488	+	0.333413i	0.182646	+	0.983179i	$0.441534\pi$
$740$		0			0
$741$	9.45800	+	15.6774i	0.347448	+	0.575923i
$742$		−	2.80260i		−	0.102887i
$743$	0.687322	+	1.19048i	0.0252154	+	0.0436744i	0.878358	−	0.478004i	$-0.158640\pi$
$743$	0.687322	+	1.19048i	0.0252154	+	0.0436744i	−0.853142	+	0.521678i	$0.825306\pi$
$744$	−0.476258	−	0.824903i	−0.0174605	−	0.0302424i
$745$		0			0
$746$		−	26.8576i		−	0.983325i
$747$	−3.97443	+	6.88392i	−0.145417	+	0.251870i
$748$	7.87550	−	13.6408i	0.287957	−	0.498756i
$749$		−	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	$-0.410724\pi$
$752$	2.88865	+	5.00328i	0.105338	+	0.182451i
$753$			15.6208i			0.569255i
$754$	−30.3155	+	0.583207i	−1.10403	+	0.0212391i
$755$		0			0
$756$	0.417738	−	0.241181i	0.0151930	−	0.00877167i
$757$	−32.0033	+	18.4771i	−1.16318	+	0.671562i	−0.952064	−	0.305899i	$-0.901043\pi$
$757$	−32.0033	+	18.4771i	−1.16318	+	0.671562i	−0.211115	+	0.977461i	$0.567710\pi$
$758$	−13.2638	−	7.65785i	−0.481762	−	0.278146i
$759$			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	$0.483544\pi$
$762$	−18.9189			−0.685360
$763$	7.12949	+	4.11621i	0.258105	+	0.149017i
$764$	1.71794	+	2.97555i	0.0621528	+	0.107652i
$765$		0			0
$766$	35.2397			1.27326
$767$	−0.819984	−	42.6234i	−0.0296079	−	1.53904i
$768$		−	1.00000i		−	0.0360844i
$769$	39.3038	−	22.6921i	1.41733	−	0.818297i	0.421268	−	0.906936i	$-0.361585\pi$
$769$	39.3038	−	22.6921i	1.41733	−	0.818297i	0.996064	+	0.0886391i	$0.0282518\pi$
$770$		0			0
$771$	−1.76210	+	3.05205i	−0.0634606	+	0.109917i
$772$	−2.65685			−0.0956223
$773$	−12.7671	+	22.1132i	−0.459200	+	0.795358i	−0.998919	−	0.0464877i	$-0.985197\pi$
$773$	−12.7671	+	22.1132i	−0.459200	+	0.795358i	0.539719	+	0.841845i	$0.318531\pi$
$774$	−9.78170	−	5.64747i	−0.351596	−	0.202994i
$775$		0			0
$776$	−4.59103	+	7.95189i	−0.164808	+	0.285456i
$777$	−2.58521	+	1.49257i	−0.0927438	+	0.0535456i
$778$	−9.04731	−	15.6704i	−0.324362	−	0.561811i
$779$	−44.3066			−1.58745
$780$		0			0
$781$	−8.07943			−0.289105
$782$	23.4669	+	40.6459i	0.839175	+	1.45349i
$783$	7.28290	−	4.20478i	0.260270	−	0.150267i
$784$	3.38366	−	5.86068i	0.120845	−	0.209310i
$785$		0			0
$786$	−6.03457	−	3.48406i	−0.215246	−	0.124272i
$787$	−15.7499	+	27.2796i	−0.561423	+	0.972413i	0.435949	+	0.899971i	$0.356413\pi$
$787$	−15.7499	+	27.2796i	−0.561423	+	0.972413i	−0.997373	+	0.0724422i	$0.976921\pi$
$788$	−21.1158			−0.752219
$789$	−11.6415	+	20.1637i	−0.414448	+	0.717845i
$790$		0			0
$791$	0.692130	−	0.399602i	0.0246093	−	0.0142082i
$792$			2.31784i			0.0823608i
$793$	−33.7968	+	0.650180i	−1.20016	+	0.0230886i
$794$	10.4512			0.370901
$795$		0			0
$796$	−5.26941	−	9.12688i	−0.186769	−	0.323494i
$797$	37.5831	+	21.6986i	1.33126	+	0.768605i	0.985493	−	0.169715i	$-0.0542847\pi$
$797$	37.5831	+	21.6986i	1.33126	+	0.768605i	0.345769	+	0.938320i	$0.387618\pi$
$798$	2.44949			0.0867110
$799$	−34.0001	−	19.6300i	−1.20284	−	0.694458i
$800$		0			0
$801$			9.01753i			0.318619i
$802$	1.21317	+	0.700423i	0.0428385	+	0.0247328i
$803$	17.1317	−	9.89097i	0.604563	−	0.349045i
$804$	6.40300	−	3.69677i	0.225816	−	0.130375i
$805$		0			0
$806$	3.00671	+	1.65965i	0.105907	+	0.0584586i
$807$			9.81746i			0.345591i
$808$	−5.34108	−	9.25102i	−0.187899	−	0.325450i
$809$	16.3279	+	28.2807i	0.574057	+	0.994296i	0.996143	+	0.0877407i	$0.0279647\pi$
$809$	16.3279	+	28.2807i	0.574057	+	0.994296i	−0.422086	+	0.906556i	$0.638702\pi$
$810$		0			0
$811$			30.1669i			1.05930i	0.848216	+	0.529651i	$0.177677\pi$
$811$			30.1669i			1.05930i	−0.848216	+	0.529651i	$0.822323\pi$
$812$	−2.02823	+	3.51299i	−0.0711768	+	0.123282i
$813$	10.9040	−	18.8862i	0.382419	−	0.662369i
$814$		−	14.3441i		−	0.502762i
$815$		0			0
$816$	3.39778	+	5.88512i	0.118946	+	0.206021i
$817$	−28.6785	−	49.6726i	−1.00333	−	1.73782i
$818$			6.74134i			0.235705i
$819$	−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	$0.288763\pi$
$822$	−17.7616	+	10.2547i	−0.619507	+	0.357673i
$823$	35.5109	+	20.5022i	1.23783	+	0.714663i	0.968651	−	0.248426i	$-0.0799132\pi$
$823$	35.5109	+	20.5022i	1.23783	+	0.714663i	0.269182	+	0.963089i	$0.413247\pi$
$824$		−	9.17449i		−	0.319609i
$825$		0			0
$826$	−4.93924	−	2.85167i	−0.171858	−	0.0992223i
$827$	−32.0321			−1.11386			−0.556932	−	0.830558i	$-0.688022\pi$
$827$	−32.0321			−1.11386			−0.556932	+	0.830558i	$0.688022\pi$
$828$	−5.98124	−	3.45327i	−0.207863	−	0.120009i
$829$	9.75006	+	16.8876i	0.338634	+	0.586531i	0.984176	−	0.177194i	$-0.0567019\pi$
$829$	9.75006	+	16.8876i	0.338634	+	0.586531i	−0.645542	+	0.763725i	$0.723369\pi$
$830$		0			0
$831$	−13.4751			−0.467445
$832$	1.86250	+	3.08725i	0.0645706	+	0.107031i
$833$			45.9877i			1.59338i
$834$	−7.36931	+	4.25467i	−0.255178	+	0.147327i
$835$		0			0
$836$	−5.88512	+	10.1933i	−0.203541	+	0.352544i
$837$	−0.952516			−0.0329238
$838$	18.2539	−	31.6166i	0.630569	−	1.09218i
$839$	7.55900	+	4.36419i	0.260966	+	0.150669i	0.624775	−	0.780805i	$-0.285191\pi$
$839$	7.55900	+	4.36419i	0.260966	+	0.150669i	−0.363809	+	0.931473i	$0.618524\pi$
$840$		0			0
$841$	−20.8604	+	36.1313i	−0.719325	+	1.24591i
$842$	−35.3763	+	20.4245i	−1.21915	+	0.703875i
$843$	14.8083	+	25.6488i	0.510026	+	0.883392i
$844$	−11.4877			−0.395422
$845$		0			0
$846$	5.77729			0.198627
$847$	−1.35728	−	2.35087i	−0.0466366	−	0.0807770i
$848$	−5.03175	+	2.90508i	−0.172791	+	0.0997610i
$849$	−6.09197	+	10.5516i	−0.209076	+	0.362130i
$850$		0			0
$851$	37.0154	+	21.3709i	1.26887	+	0.732584i
$852$	1.74288	−	3.01876i	0.0597101	−	0.103421i
$853$	25.1210			0.860125			0.430063	−	0.902799i	$-0.358491\pi$
$853$	25.1210			0.860125			0.430063	+	0.902799i	$0.358491\pi$
$854$	−2.26114	+	3.91641i	−0.0773747	+	0.134017i
$855$		0			0
$856$	−2.78629	+	1.60867i	−0.0952335	+	0.0549831i
$857$			48.1300i			1.64409i	0.569423	+	0.822045i	$0.307167\pi$
$857$			48.1300i			1.64409i	−0.569423	+	0.822045i	$0.692833\pi$
$858$	−4.31697	−	7.15573i	−0.147379	−	0.244293i
$859$	47.1707			1.60944			0.804721	−	0.593653i	$-0.202315\pi$
$859$	47.1707			1.60944			0.804721	+	0.593653i	$0.202315\pi$
$860$		0			0
$861$	−2.10430	−	3.64476i	−0.0717145	−	0.124213i
$862$	15.9145	+	9.18824i	0.542050	+	0.312953i
$863$	26.6095			0.905799			0.452900	−	0.891562i	$-0.350390\pi$
$863$	26.6095			0.905799			0.452900	+	0.891562i	$0.350390\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		0			0
$866$		−	1.39819i		−	0.0475125i
$867$	−25.2702	−	14.5898i	−0.858223	−	0.495495i
$868$	0.397902	−	0.229729i	0.0135057	−	0.00779750i
$869$	18.1424	−	10.4745i	0.615440	−	0.355324i
$870$		0			0
$871$	−12.8824	+	23.3385i	−0.436503	+	0.790793i
$872$		−	17.0669i		−	0.577958i
$873$	4.59103	+	7.95189i	0.155383	+	0.269131i
$874$	−17.5361	−	30.3734i	−0.593168	−	1.02740i
$875$		0			0
$876$			8.53465i			0.288359i
$877$	3.35180	−	5.80548i	0.113182	−	0.196037i	−0.803870	−	0.594806i	$-0.797229\pi$
$877$	3.35180	−	5.80548i	0.113182	−	0.196037i	0.917052	+	0.398769i	$0.130562\pi$
$878$	7.65685	−	13.2621i	0.258406	−	0.447573i
$879$			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	$0.888214\pi$
$882$	−3.38366	−	5.86068i	−0.113934	−	0.197339i
$883$			45.3554i			1.52633i	0.646204	+	0.763165i	$0.276356\pi$
$883$			45.3554i			1.52633i	−0.646204	+	0.763165i	$0.723644\pi$
$884$	−21.4508	−	11.8405i	−0.721469	−	0.398238i
$885$		0			0
$886$	28.7320	−	16.5884i	0.965272	−	0.557300i
$887$	−29.7753	+	17.1908i	−0.999757	+	0.577210i	−0.908176	−	0.418588i	$-0.862525\pi$
$887$	−29.7753	+	17.1908i	−0.999757	+	0.577210i	−0.0915805	+	0.995798i	$0.529192\pi$
$888$	5.35948	+	3.09429i	0.179852	+	0.103838i
$889$		−	9.12576i		−	0.306068i
$890$		0			0
$891$	2.00731	+	1.15892i	0.0672473	+	0.0388252i
$892$	−5.22778			−0.175039
$893$	25.4073	+	14.6689i	0.850221	+	0.490876i
$894$	−3.62252	−	6.27439i	−0.121155	−	0.209847i
$895$		0			0
$896$	0.482362			0.0161146
$897$	24.8973	−	0.478971i	0.831296	−	0.0159924i
$898$			15.4047i			0.514061i
$899$	6.93708	−	4.00512i	0.231365	−	0.133578i
$900$		0			0
$901$	19.7417	−	34.1935i	0.657690	−	1.13915i
$902$	20.2231			0.673357
$903$	2.72412	−	4.71832i	0.0906531	−	0.157016i
$904$	−1.43488	−	0.828427i	−0.0477233	−	0.0275531i
$905$		0			0
$906$	−3.91372	+	6.77875i	−0.130024	+	0.225209i
$907$	−29.4110	+	16.9804i	−0.976575	+	0.563826i	−0.901234	−	0.433332i	$-0.857338\pi$
$907$	−29.4110	+	16.9804i	−0.976575	+	0.563826i	−0.0753408	+	0.997158i	$0.524004\pi$
$908$	5.43443	+	9.41271i	0.180348	+	0.312372i
$909$	−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	$0.302815\pi$
$912$	−2.53906	−	4.39778i	−0.0840766	−	0.145625i
$913$	15.9558	−	9.21209i	0.528060	−	0.304876i
$914$	3.73097	−	6.46224i	0.123410	−	0.213752i
$915$		0			0
$916$	−18.3538	−	10.5966i	−0.606428	−	0.350121i
$917$	1.68058	−	2.91085i	0.0554976	−	0.0961247i
$918$	6.79555			0.224287
$919$	−8.74038	+	15.1388i	−0.288319	+	0.499383i	−0.973409	−	0.229076i	$-0.926430\pi$
$919$	−8.74038	+	15.1388i	−0.288319	+	0.499383i	0.685090	+	0.728459i	$0.259763\pi$
$920$		0			0
$921$	24.2114	−	13.9784i	0.797791	−	0.460605i
$922$			4.58943i			0.151145i
$923$	0.241739	+	12.5658i	0.00795693	+	0.413607i
$924$	−1.11804			−0.0367807
$925$		0			0
$926$	4.60444	+	7.97512i	0.151311	+	0.262079i
$927$	−7.94534	−	4.58725i	−0.260959	−	0.150665i
$928$	8.40957			0.276058
$929$	−6.74907	−	3.89658i	−0.221430	−	0.127842i	0.385182	−	0.922840i	$-0.374139\pi$
$929$	−6.74907	−	3.89658i	−0.221430	−	0.127842i	−0.606612	+	0.794998i	$0.707472\pi$
$930$		0			0
$931$		−	34.3653i		−	1.12628i
$932$	−18.9160	−	10.9212i	−0.619614	−	0.357734i
$933$	−12.3899	+	7.15333i	−0.405628	+	0.234190i
$934$	−0.190066	+	0.109735i	−0.00621915	+	0.00359063i
$935$		0			0
$936$	3.60488	−	0.0693504i	0.117829	−	0.00226679i
$937$			39.5690i			1.29266i	0.763057	+	0.646331i	$0.223697\pi$
$937$			39.5690i			1.29266i	−0.763057	+	0.646331i	$0.776303\pi$
$938$	1.78318	+	3.08856i	0.0582230	+	0.100845i
$939$	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	$-0.125745\pi$
$942$	−2.21134	+	3.83014i	−0.0720492	+	0.124793i
$943$	−30.1298	+	52.1864i	−0.981161	+	1.69942i
$944$			11.8238i			0.384831i
$945$		0			0
$946$	13.0899	+	22.6724i	0.425590	+	0.737143i
$947$	−9.60036	−	16.6283i	−0.311970	−	0.540348i	0.666819	−	0.745220i	$-0.267655\pi$
$947$	−9.60036	−	16.6283i	−0.311970	−	0.540348i	−0.978789	+	0.204872i	$0.934322\pi$
$948$			9.03820i			0.293547i
$949$	−15.8958	−	26.3486i	−0.516000	−	0.855311i
$950$		0			0
$951$	6.32085	−	3.64934i	0.204967	−	0.118338i
$952$	−2.83876	+	1.63896i	−0.0920047	+	0.0531189i
$953$	0.525090	+	0.303161i	0.0170093	+	0.00982035i	0.508481	−	0.861073i	$-0.330207\pi$
$953$	0.525090	+	0.303161i	0.0170093	+	0.00982035i	−0.491471	+	0.870894i	$0.663541\pi$
$954$			5.81017i			0.188111i
$955$		0			0
$956$	7.12762	+	4.11513i	0.230524	+	0.133093i
$957$	−19.4920			−0.630087
$958$	−5.49422	−	3.17209i	−0.177510	−	0.102486i
$959$	−4.94646	−	8.56753i	−0.159730	−	0.276660i
$960$		0			0
$961$	30.0927			0.970733
$962$	−22.3091	+	0.429181i	−0.719276	+	0.0138373i
$963$			3.21733i			0.103677i
$964$	2.68678	−	1.55121i	0.0865354	−	0.0499613i
$965$		0			0
$966$	1.66573	−	2.88512i	0.0535939	−	0.0928273i
$967$	1.49478			0.0480690			0.0240345	−	0.999711i	$-0.492349\pi$
$967$	1.49478			0.0480690			0.0240345	+	0.999711i	$0.492349\pi$
$968$	−2.81382	+	4.87367i	−0.0904394	+	0.156646i
$969$	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	$0.184333\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	−2.05229	−	3.55467i	−0.0657935	−	0.113958i
$974$	−37.1944			−1.19179
$975$		0			0
$976$	9.37529			0.300096
$977$	23.7932	+	41.2109i	0.761210	+	1.31845i	0.942227	+	0.334975i	$0.108728\pi$
$977$	23.7932	+	41.2109i	0.761210	+	1.31845i	−0.181017	+	0.983480i	$0.557939\pi$
$978$	9.72060	−	5.61219i	0.310830	−	0.179458i
$979$	10.4506	−	18.1009i	0.334002	−	0.578509i
$980$		0			0
$981$	−14.7804	−	8.53345i	−0.471901	−	0.272452i
$982$	2.99901	−	5.19444i	0.0957024	−	0.165761i
$983$	−27.8101			−0.887003			−0.443502	−	0.896274i	$-0.646264\pi$
$983$	−27.8101			−0.887003			−0.443502	+	0.896274i	$0.646264\pi$
$984$	−4.36250	+	7.55607i	−0.139071	+	0.240879i
$985$		0			0
$986$	−49.4914	+	28.5738i	−1.57613	+	0.909977i
$987$			2.78675i			0.0887031i
$988$	16.0296	+	8.84802i	0.509968	+	0.281493i
$989$	−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	$-0.443216\pi$
$992$	−0.824903	−	0.476258i	−0.0261907	−	0.0151212i
$993$	−26.3594			−0.836491
$994$	1.45613	+	0.840699i	0.0461858	+	0.0266654i
$995$		0			0
$996$			7.94887i			0.251870i
$997$	14.5645	+	8.40884i	0.461264	+	0.266311i	0.712575	−	0.701596i	$-0.247529\pi$
$997$	14.5645	+	8.40884i	0.461264	+	0.266311i	−0.251312	+	0.967906i	$0.580862\pi$
$998$	18.4384	−	10.6454i	0.583657	−	0.336974i
$999$	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.y.i.49.2		8
5.2	odd	4		1950.2.bc.f.751.4	yes	8
5.3	odd	4		1950.2.bc.e.751.1	✓	8
5.4	even	2		1950.2.y.l.49.3		8
13.4	even	6		1950.2.y.l.199.3		8
65.4	even	6	inner	1950.2.y.i.199.2		8
65.17	odd	12		1950.2.bc.f.901.4	yes	8
65.43	odd	12		1950.2.bc.e.901.1	yes	8

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

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-0.241181 + 0.417738i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-0.241181 + 0.417738i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.00731 + 1.15892i) q^{11} -1.00000i q^{12} +(1.86250 + 3.08725i) q^{13} +0.482362 q^{14} +(-0.500000 - 0.866025i) q^{16} +(5.88512 + 3.39778i) q^{17} -1.00000 q^{18} +(-4.39778 - 2.53906i) q^{19} -0.482362i q^{21} +(2.00731 + 1.15892i) q^{22} +(-5.98124 + 3.45327i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.74238 - 3.15660i) q^{26} +1.00000i q^{27} +(-0.241181 - 0.417738i) q^{28} +(-4.20478 - 7.28290i) q^{29} +0.952516i q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.15892 - 2.00731i) q^{33} -6.79555i q^{34} +(0.500000 + 0.866025i) q^{36} +(-3.09429 - 5.35948i) q^{37} +5.07812i q^{38} +(-3.15660 - 1.74238i) q^{39} +(7.55607 - 4.36250i) q^{41} +(-0.417738 + 0.241181i) q^{42} +(9.78170 + 5.64747i) q^{43} -2.31784i q^{44} +(5.98124 + 3.45327i) q^{46} -5.77729 q^{47} +(0.866025 + 0.500000i) q^{48} +(3.38366 + 5.86068i) q^{49} -6.79555 q^{51} +(-3.60488 + 0.0693504i) q^{52} -5.81017i q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.241181 + 0.417738i) q^{56} +5.07812 q^{57} +(-4.20478 + 7.28290i) q^{58} +(-10.2397 - 5.91189i) q^{59} +(-4.68764 + 8.11924i) q^{61} +(0.824903 - 0.476258i) q^{62} +(0.241181 + 0.417738i) q^{63} +1.00000 q^{64} -2.31784 q^{66} +(3.69677 + 6.40300i) q^{67} +(-5.88512 + 3.39778i) q^{68} +(3.45327 - 5.98124i) q^{69} +(3.01876 + 1.74288i) q^{71} +(0.500000 - 0.866025i) q^{72} -8.53465 q^{73} +(-3.09429 + 5.35948i) q^{74} +(4.39778 - 2.53906i) q^{76} -1.11804i q^{77} +(0.0693504 + 3.60488i) q^{78} -9.03820 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-7.55607 - 4.36250i) q^{82} -7.94887 q^{83} +(0.417738 + 0.241181i) q^{84} -11.2949i q^{86} +(7.28290 + 4.20478i) q^{87} +(-2.00731 + 1.15892i) q^{88} +(-7.80941 + 4.50877i) q^{89} +(-1.73886 + 0.0334520i) q^{91} -6.90654i q^{92} +(-0.476258 - 0.824903i) q^{93} +(2.88865 + 5.00328i) q^{94} -1.00000i q^{96} +(-4.59103 + 7.95189i) q^{97} +(3.38366 - 5.86068i) q^{98} +2.31784i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} - 4 q^{7} + 8 q^{8} + 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^7 + 8 * q^8 + 4 * q^9	\( 8 q - 4 q^{2} - 4 q^{4} - 4 q^{7} + 8 q^{8} + 4 q^{9} - 12 q^{11} + 8 q^{14} - 4 q^{16} - 8 q^{18} - 12 q^{19} + 12 q^{22} - 12 q^{23} - 4 q^{28} - 4 q^{29} - 4 q^{32} + 8 q^{33} + 4 q^{36} - 16 q^{37} + 24 q^{43} + 12 q^{46} + 32 q^{47} + 16 q^{49} - 8 q^{51} - 4 q^{56} - 4 q^{58} + 12 q^{59} - 16 q^{61} - 24 q^{62} + 4 q^{63} + 8 q^{64} - 16 q^{66} + 24 q^{67} - 4 q^{69} + 60 q^{71} + 4 q^{72} - 24 q^{73} - 16 q^{74} + 12 q^{76} + 8 q^{79} - 4 q^{81} - 8 q^{83} - 12 q^{87} - 12 q^{88} - 24 q^{89} + 8 q^{91} + 4 q^{93} - 16 q^{94} + 16 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^7 + 8 * q^8 + 4 * q^9 - 12 * q^11 + 8 * q^14 - 4 * q^16 - 8 * q^18 - 12 * q^19 + 12 * q^22 - 12 * q^23 - 4 * q^28 - 4 * q^29 - 4 * q^32 + 8 * q^33 + 4 * q^36 - 16 * q^37 + 24 * q^43 + 12 * q^46 + 32 * q^47 + 16 * q^49 - 8 * q^51 - 4 * q^56 - 4 * q^58 + 12 * q^59 - 16 * q^61 - 24 * q^62 + 4 * q^63 + 8 * q^64 - 16 * q^66 + 24 * q^67 - 4 * q^69 + 60 * q^71 + 4 * q^72 - 24 * q^73 - 16 * q^74 + 12 * q^76 + 8 * q^79 - 4 * q^81 - 8 * q^83 - 12 * q^87 - 12 * q^88 - 24 * q^89 + 8 * q^91 + 4 * q^93 - 16 * q^94 + 16 * q^98

Introduction

L-functions

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