LMFDB - Embedded newform 950.2.e.k.501.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(201,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("950.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			501.1
Root			$-1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	950.501
Dual form			950.2.e.k.201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.32288 - 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.32288 - 2.29129i) q^{6} +1.64575 q^{7} -1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.32288 - 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.32288 - 2.29129i) q^{6} +1.64575 q^{7} -1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +0.645751 q^{11} +2.64575 q^{12} +(1.00000 - 1.73205i) q^{13} +(0.822876 + 1.42526i) q^{14} +(-0.500000 - 0.866025i) q^{16} -4.00000 q^{18} +(4.32288 - 0.559237i) q^{19} +(-2.17712 - 3.77089i) q^{21} +(0.322876 + 0.559237i) q^{22} +(1.82288 - 3.15731i) q^{23} +(1.32288 + 2.29129i) q^{24} +2.00000 q^{26} +2.64575 q^{27} +(-0.822876 + 1.42526i) q^{28} +(1.82288 - 3.15731i) q^{29} -0.354249 q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.854249 - 1.47960i) q^{33} +(-2.00000 - 3.46410i) q^{36} -5.64575 q^{37} +(2.64575 + 3.46410i) q^{38} -5.29150 q^{39} +(-5.14575 - 8.91270i) q^{41} +(2.17712 - 3.77089i) q^{42} +(0.354249 + 0.613577i) q^{43} +(-0.322876 + 0.559237i) q^{44} +3.64575 q^{46} +(4.82288 - 8.35347i) q^{47} +(-1.32288 + 2.29129i) q^{48} -4.29150 q^{49} +(1.00000 + 1.73205i) q^{52} +(4.29150 - 7.43310i) q^{53} +(1.32288 + 2.29129i) q^{54} -1.64575 q^{56} +(-7.00000 - 9.16515i) q^{57} +3.64575 q^{58} +(-3.96863 - 6.87386i) q^{59} +(7.46863 - 12.9360i) q^{61} +(-0.177124 - 0.306788i) q^{62} +(-3.29150 + 5.70105i) q^{63} +1.00000 q^{64} +(0.854249 - 1.47960i) q^{66} +(-2.32288 + 4.02334i) q^{67} -9.64575 q^{69} +(6.64575 + 11.5108i) q^{71} +(2.00000 - 3.46410i) q^{72} +(6.14575 + 10.6448i) q^{73} +(-2.82288 - 4.88936i) q^{74} +(-1.67712 + 4.02334i) q^{76} +1.06275 q^{77} +(-2.64575 - 4.58258i) q^{78} +(2.00000 + 3.46410i) q^{79} +(2.50000 + 4.33013i) q^{81} +(5.14575 - 8.91270i) q^{82} +7.93725 q^{83} +4.35425 q^{84} +(-0.354249 + 0.613577i) q^{86} -9.64575 q^{87} -0.645751 q^{88} +(1.64575 - 2.85052i) q^{91} +(1.82288 + 3.15731i) q^{92} +(0.468627 + 0.811686i) q^{93} +9.64575 q^{94} -2.64575 q^{96} +(-7.14575 - 12.3768i) q^{97} +(-2.14575 - 3.71655i) q^{98} +(-1.29150 + 2.23695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^7 - 4 * q^8 - 8 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{7} - 4 q^{8} - 8 q^{9} - 8 q^{11} + 4 q^{13} - 2 q^{14} - 2 q^{16} - 16 q^{18} + 12 q^{19} - 14 q^{21} - 4 q^{22} + 2 q^{23} + 8 q^{26} + 2 q^{28} + 2 q^{29} - 12 q^{31} + 2 q^{32} - 14 q^{33} - 8 q^{36} - 12 q^{37} - 10 q^{41} + 14 q^{42} + 12 q^{43} + 4 q^{44} + 4 q^{46} + 14 q^{47} + 4 q^{49} + 4 q^{52} - 4 q^{53} + 4 q^{56} - 28 q^{57} + 4 q^{58} + 14 q^{61} - 6 q^{62} + 8 q^{63} + 4 q^{64} + 14 q^{66} - 4 q^{67} - 28 q^{69} + 16 q^{71} + 8 q^{72} + 14 q^{73} - 6 q^{74} - 12 q^{76} + 36 q^{77} + 8 q^{79} + 10 q^{81} + 10 q^{82} + 28 q^{84} - 12 q^{86} - 28 q^{87} + 8 q^{88} - 4 q^{91} + 2 q^{92} - 14 q^{93} + 28 q^{94} - 18 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^7 - 4 * q^8 - 8 * q^9 - 8 * q^11 + 4 * q^13 - 2 * q^14 - 2 * q^16 - 16 * q^18 + 12 * q^19 - 14 * q^21 - 4 * q^22 + 2 * q^23 + 8 * q^26 + 2 * q^28 + 2 * q^29 - 12 * q^31 + 2 * q^32 - 14 * q^33 - 8 * q^36 - 12 * q^37 - 10 * q^41 + 14 * q^42 + 12 * q^43 + 4 * q^44 + 4 * q^46 + 14 * q^47 + 4 * q^49 + 4 * q^52 - 4 * q^53 + 4 * q^56 - 28 * q^57 + 4 * q^58 + 14 * q^61 - 6 * q^62 + 8 * q^63 + 4 * q^64 + 14 * q^66 - 4 * q^67 - 28 * q^69 + 16 * q^71 + 8 * q^72 + 14 * q^73 - 6 * q^74 - 12 * q^76 + 36 * q^77 + 8 * q^79 + 10 * q^81 + 10 * q^82 + 28 * q^84 - 12 * q^86 - 28 * q^87 + 8 * q^88 - 4 * q^91 + 2 * q^92 - 14 * q^93 + 28 * q^94 - 18 * q^97 + 2 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.32288	−	2.29129i	−0.763763	−	1.32288i	−0.940898	−	0.338689i	$-0.890016\pi$
$3$	−1.32288	−	2.29129i	−0.763763	−	1.32288i	0.177136	−	0.984186i	$-0.443317\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.32288	−	2.29129i	0.540062	−	0.935414i
$7$	1.64575			0.622036			0.311018	−	0.950404i	$-0.399330\pi$
$7$	1.64575			0.622036			0.311018	+	0.950404i	$0.399330\pi$
$8$	−1.00000			−0.353553
$9$	−2.00000	+	3.46410i	−0.666667	+	1.15470i
$10$		0			0
$11$	0.645751			0.194701			0.0973507	−	0.995250i	$-0.468963\pi$
$11$	0.645751			0.194701			0.0973507	+	0.995250i	$0.468963\pi$
$12$	2.64575			0.763763
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$	0.822876	+	1.42526i	0.219923	+	0.380917i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	−4.00000			−0.942809
$19$	4.32288	−	0.559237i	0.991736	−	0.128298i
$19$	4.32288	−	0.559237i	0.991736	−	0.128298i
$20$		0			0
$21$	−2.17712	−	3.77089i	−0.475087	−	0.822876i
$22$	0.322876	+	0.559237i	0.0688373	+	0.119230i
$23$	1.82288	−	3.15731i	0.380096	−	0.658345i	−0.610980	−	0.791646i	$-0.709224\pi$
$23$	1.82288	−	3.15731i	0.380096	−	0.658345i	0.991076	+	0.133301i	$0.0425577\pi$
$24$	1.32288	+	2.29129i	0.270031	+	0.467707i
$25$		0			0
$26$	2.00000			0.392232
$27$	2.64575			0.509175
$28$	−0.822876	+	1.42526i	−0.155509	+	0.269349i
$29$	1.82288	−	3.15731i	0.338500	−	0.586298i	−0.645651	−	0.763632i	$-0.723414\pi$
$29$	1.82288	−	3.15731i	0.338500	−	0.586298i	0.984151	+	0.177334i	$0.0567473\pi$
$30$		0			0
$31$	−0.354249			−0.0636249			−0.0318125	−	0.999494i	$-0.510128\pi$
$31$	−0.354249			−0.0636249			−0.0318125	+	0.999494i	$0.510128\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−0.854249	−	1.47960i	−0.148706	−	0.257566i
$34$		0			0
$35$		0			0
$36$	−2.00000	−	3.46410i	−0.333333	−	0.577350i
$37$	−5.64575			−0.928156			−0.464078	−	0.885794i	$-0.653614\pi$
$37$	−5.64575			−0.928156			−0.464078	+	0.885794i	$0.653614\pi$
$38$	2.64575	+	3.46410i	0.429198	+	0.561951i
$39$	−5.29150			−0.847319
$40$		0			0
$41$	−5.14575	−	8.91270i	−0.803631	−	1.39193i	−0.917211	−	0.398401i	$-0.869565\pi$
$41$	−5.14575	−	8.91270i	−0.803631	−	1.39193i	0.113580	−	0.993529i	$-0.463768\pi$
$42$	2.17712	−	3.77089i	0.335938	−	0.581861i
$43$	0.354249	+	0.613577i	0.0540224	+	0.0935696i	0.891772	−	0.452485i	$-0.149462\pi$
$43$	0.354249	+	0.613577i	0.0540224	+	0.0935696i	−0.837750	+	0.546055i	$0.816129\pi$
$44$	−0.322876	+	0.559237i	−0.0486753	+	0.0843082i
$45$		0			0
$46$	3.64575			0.537537
$47$	4.82288	−	8.35347i	0.703489	−	1.21848i	−0.263745	−	0.964592i	$-0.584958\pi$
$47$	4.82288	−	8.35347i	0.703489	−	1.21848i	0.967234	−	0.253886i	$-0.0817088\pi$
$48$	−1.32288	+	2.29129i	−0.190941	+	0.330719i
$49$	−4.29150			−0.613072
$50$		0			0
$51$		0			0
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	4.29150	−	7.43310i	0.589483	−	1.02101i	−0.404817	−	0.914398i	$-0.632665\pi$
$53$	4.29150	−	7.43310i	0.589483	−	1.02101i	0.994300	−	0.106617i	$-0.0340019\pi$
$54$	1.32288	+	2.29129i	0.180021	+	0.311805i
$55$		0			0
$56$	−1.64575			−0.219923
$57$	−7.00000	−	9.16515i	−0.927173	−	1.21395i
$58$	3.64575			0.478711
$59$	−3.96863	−	6.87386i	−0.516671	−	0.894901i	−0.999813	−	0.0193585i	$-0.993838\pi$
$59$	−3.96863	−	6.87386i	−0.516671	−	0.894901i	0.483141	−	0.875542i	$-0.339496\pi$
$60$		0			0
$61$	7.46863	−	12.9360i	0.956260	−	1.65629i	0.224801	−	0.974405i	$-0.427827\pi$
$61$	7.46863	−	12.9360i	0.956260	−	1.65629i	0.731459	−	0.681886i	$-0.238840\pi$
$62$	−0.177124	−	0.306788i	−0.0224948	−	0.0389622i
$63$	−3.29150	+	5.70105i	−0.414690	+	0.718265i
$64$	1.00000			0.125000
$65$		0			0
$66$	0.854249	−	1.47960i	0.105151	−	0.182126i
$67$	−2.32288	+	4.02334i	−0.283784	+	0.491529i	−0.972314	−	0.233680i	$-0.924923\pi$
$67$	−2.32288	+	4.02334i	−0.283784	+	0.491529i	0.688529	+	0.725209i	$0.258257\pi$
$68$		0			0
$69$	−9.64575			−1.16121
$70$		0			0
$71$	6.64575	+	11.5108i	0.788706	+	1.36608i	0.926760	+	0.375654i	$0.122582\pi$
$71$	6.64575	+	11.5108i	0.788706	+	1.36608i	−0.138055	+	0.990425i	$0.544085\pi$
$72$	2.00000	−	3.46410i	0.235702	−	0.408248i
$73$	6.14575	+	10.6448i	0.719306	+	1.24587i	0.961275	+	0.275590i	$0.0888733\pi$
$73$	6.14575	+	10.6448i	0.719306	+	1.24587i	−0.241969	+	0.970284i	$0.577793\pi$
$74$	−2.82288	−	4.88936i	−0.328153	−	0.568377i
$75$		0			0
$76$	−1.67712	+	4.02334i	−0.192379	+	0.461509i
$77$	1.06275			0.121111
$78$	−2.64575	−	4.58258i	−0.299572	−	0.518875i
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$		0			0
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	5.14575	−	8.91270i	0.568253	−	0.984243i
$83$	7.93725			0.871227			0.435613	−	0.900134i	$-0.356531\pi$
$83$	7.93725			0.871227			0.435613	+	0.900134i	$0.356531\pi$
$84$	4.35425			0.475087
$85$		0			0
$86$	−0.354249	+	0.613577i	−0.0381996	+	0.0661637i
$87$	−9.64575			−1.03413
$88$	−0.645751			−0.0688373
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$	1.64575	−	2.85052i	0.172522	−	0.298816i
$92$	1.82288	+	3.15731i	0.190048	+	0.329173i
$93$	0.468627	+	0.811686i	0.0485944	+	0.0841679i
$94$	9.64575			0.994883
$95$		0			0
$96$	−2.64575			−0.270031
$97$	−7.14575	−	12.3768i	−0.725541	−	1.25667i	−0.958751	−	0.284248i	$-0.908256\pi$
$97$	−7.14575	−	12.3768i	−0.725541	−	1.25667i	0.233210	−	0.972426i	$-0.425077\pi$
$98$	−2.14575	−	3.71655i	−0.216754	−	0.375428i
$99$	−1.29150	+	2.23695i	−0.129801	+	0.224822i
$100$		0			0
$101$	4.17712	−	7.23499i	0.415639	−	0.719909i	−0.579856	−	0.814719i	$-0.696891\pi$
$101$	4.17712	−	7.23499i	0.415639	−	0.719909i	0.995495	+	0.0948105i	$0.0302245\pi$
$102$		0			0
$103$	2.70850			0.266876			0.133438	−	0.991057i	$-0.457398\pi$
$103$	2.70850			0.266876			0.133438	+	0.991057i	$0.457398\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$		0			0
$106$	8.58301			0.833655
$107$	−4.70850			−0.455188			−0.227594	−	0.973756i	$-0.573086\pi$
$107$	−4.70850			−0.455188			−0.227594	+	0.973756i	$0.573086\pi$
$108$	−1.32288	+	2.29129i	−0.127294	+	0.220479i
$109$	3.29150	+	5.70105i	0.315269	+	0.546062i	0.979495	−	0.201470i	$-0.0645720\pi$
$109$	3.29150	+	5.70105i	0.315269	+	0.546062i	−0.664226	+	0.747532i	$0.731239\pi$
$110$		0			0
$111$	7.46863	+	12.9360i	0.708891	+	1.22783i
$112$	−0.822876	−	1.42526i	−0.0777544	−	0.134675i
$113$	−5.58301			−0.525205			−0.262602	−	0.964904i	$-0.584581\pi$
$113$	−5.58301			−0.525205			−0.262602	+	0.964904i	$0.584581\pi$
$114$	4.43725	−	10.6448i	0.415587	−	0.996973i
$115$		0			0
$116$	1.82288	+	3.15731i	0.169250	+	0.293149i
$117$	4.00000	+	6.92820i	0.369800	+	0.640513i
$118$	3.96863	−	6.87386i	0.365342	−	0.632790i
$119$		0			0
$120$		0			0
$121$	−10.5830			−0.962091
$122$	14.9373			1.35236
$123$	−13.6144	+	23.5808i	−1.22757	+	2.12621i
$124$	0.177124	−	0.306788i	0.0159062	−	0.0275504i
$125$		0			0
$126$	−6.58301			−0.586461
$127$	−1.35425	+	2.34563i	−0.120170	+	0.208141i	−0.919835	−	0.392306i	$-0.871677\pi$
$127$	−1.35425	+	2.34563i	−0.120170	+	0.208141i	0.799665	+	0.600447i	$0.205011\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	0.937254	−	1.62337i	0.0825206	−	0.142930i
$130$		0			0
$131$	6.96863	+	12.0700i	0.608852	+	1.05456i	0.991430	+	0.130639i	$0.0417029\pi$
$131$	6.96863	+	12.0700i	0.608852	+	1.05456i	−0.382578	+	0.923923i	$0.624964\pi$
$132$	1.70850			0.148706
$133$	7.11438	−	0.920365i	0.616895	−	0.0798058i
$134$	−4.64575			−0.401332
$135$		0			0
$136$		0			0
$137$	−2.79150	+	4.83502i	−0.238494	+	0.413084i	−0.960282	−	0.279030i	$-0.909987\pi$
$137$	−2.79150	+	4.83502i	−0.238494	+	0.413084i	0.721788	+	0.692114i	$0.243320\pi$
$138$	−4.82288	−	8.35347i	−0.410550	−	0.711094i
$139$	−6.67712	+	11.5651i	−0.566346	+	0.980941i	0.430577	+	0.902554i	$0.358310\pi$
$139$	−6.67712	+	11.5651i	−0.566346	+	0.980941i	−0.996923	+	0.0783866i	$0.975023\pi$
$140$		0			0
$141$	−25.5203			−2.14919
$142$	−6.64575	+	11.5108i	−0.557699	+	0.965963i
$143$	0.645751	−	1.11847i	0.0540004	−	0.0935315i
$144$	4.00000			0.333333
$145$		0			0
$146$	−6.14575	+	10.6448i	−0.508626	+	0.880966i
$147$	5.67712	+	9.83307i	0.468241	+	0.811018i
$148$	2.82288	−	4.88936i	0.232039	−	0.401903i
$149$	2.46863	+	4.27579i	0.202238	+	0.350286i	0.949249	−	0.314525i	$-0.101845\pi$
$149$	2.46863	+	4.27579i	0.202238	+	0.350286i	−0.747011	+	0.664811i	$0.768512\pi$
$150$		0			0
$151$	−2.93725			−0.239030			−0.119515	−	0.992832i	$-0.538134\pi$
$151$	−2.93725			−0.239030			−0.119515	+	0.992832i	$0.538134\pi$
$152$	−4.32288	+	0.559237i	−0.350632	+	0.0453601i
$153$		0			0
$154$	0.531373	+	0.920365i	0.0428193	+	0.0741651i
$155$		0			0
$156$	2.64575	−	4.58258i	0.211830	−	0.366900i
$157$	5.29150	+	9.16515i	0.422308	+	0.731459i	0.996165	−	0.0874969i	$-0.0278868\pi$
$157$	5.29150	+	9.16515i	0.422308	+	0.731459i	−0.573857	+	0.818956i	$0.694553\pi$
$158$	−2.00000	+	3.46410i	−0.159111	+	0.275589i
$159$	−22.7085			−1.80090
$160$		0			0
$161$	3.00000	−	5.19615i	0.236433	−	0.409514i
$162$	−2.50000	+	4.33013i	−0.196419	+	0.340207i
$163$	11.9373			0.934998			0.467499	−	0.883994i	$-0.345155\pi$
$163$	11.9373			0.934998			0.467499	+	0.883994i	$0.345155\pi$
$164$	10.2915			0.803631
$165$		0			0
$166$	3.96863	+	6.87386i	0.308025	+	0.533515i
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$	2.17712	+	3.77089i	0.167969	+	0.290930i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$	−6.70850	+	16.0934i	−0.513012	+	1.23069i
$172$	−0.708497			−0.0540224
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$	−4.82288	−	8.35347i	−0.365621	−	0.633275i
$175$		0			0
$176$	−0.322876	−	0.559237i	−0.0243377	−	0.0421541i
$177$	−10.5000	+	18.1865i	−0.789228	+	1.36698i
$178$		0			0
$179$	19.9373			1.49018			0.745090	−	0.666964i	$-0.232406\pi$
$179$	19.9373			1.49018			0.745090	+	0.666964i	$0.232406\pi$
$180$		0			0
$181$	2.11438	−	3.66221i	0.157160	−	0.272210i	−0.776683	−	0.629892i	$-0.783099\pi$
$181$	2.11438	−	3.66221i	0.157160	−	0.272210i	0.933844	+	0.357682i	$0.116433\pi$
$182$	3.29150			0.243982
$183$	−39.5203			−2.92142
$184$	−1.82288	+	3.15731i	−0.134384	+	0.232760i
$185$		0			0
$186$	−0.468627	+	0.811686i	−0.0343614	+	0.0595157i
$187$		0			0
$188$	4.82288	+	8.35347i	0.351744	+	0.609239i
$189$	4.35425			0.316725
$190$		0			0
$191$	−14.5830			−1.05519			−0.527595	−	0.849496i	$-0.676906\pi$
$191$	−14.5830			−1.05519			−0.527595	+	0.849496i	$0.676906\pi$
$192$	−1.32288	−	2.29129i	−0.0954703	−	0.165359i
$193$	−3.29150	−	5.70105i	−0.236928	−	0.410371i	0.722904	−	0.690949i	$-0.242807\pi$
$193$	−3.29150	−	5.70105i	−0.236928	−	0.410371i	−0.959831	+	0.280578i	$0.909474\pi$
$194$	7.14575	−	12.3768i	0.513035	−	0.888603i
$195$		0			0
$196$	2.14575	−	3.71655i	0.153268	−	0.265468i
$197$	2.35425			0.167733			0.0838666	−	0.996477i	$-0.473273\pi$
$197$	2.35425			0.167733			0.0838666	+	0.996477i	$0.473273\pi$
$198$	−2.58301			−0.183566
$199$	−5.93725	+	10.2836i	−0.420881	+	0.728987i	−0.996026	−	0.0890645i	$-0.971612\pi$
$199$	−5.93725	+	10.2836i	−0.420881	+	0.728987i	0.575145	+	0.818051i	$0.304946\pi$
$200$		0			0
$201$	12.2915			0.866976
$202$	8.35425			0.587803
$203$	3.00000	−	5.19615i	0.210559	−	0.364698i
$204$		0			0
$205$		0			0
$206$	1.35425	+	2.34563i	0.0943550	+	0.163428i
$207$	7.29150	+	12.6293i	0.506794	+	0.877794i
$208$	−2.00000			−0.138675
$209$	2.79150	−	0.361128i	0.193092	−	0.0249797i
$210$		0			0
$211$	1.35425	+	2.34563i	0.0932303	+	0.161480i	0.908869	−	0.417082i	$-0.136947\pi$
$211$	1.35425	+	2.34563i	0.0932303	+	0.161480i	−0.815638	+	0.578562i	$0.803614\pi$
$212$	4.29150	+	7.43310i	0.294742	+	0.510507i
$213$	17.5830	−	30.4547i	1.20477	−	2.08672i
$214$	−2.35425	−	4.07768i	−0.160933	−	0.278744i
$215$		0			0
$216$	−2.64575			−0.180021
$217$	−0.583005			−0.0395770
$218$	−3.29150	+	5.70105i	−0.222929	+	0.386124i
$219$	16.2601	−	28.1634i	1.09876	−	1.90310i
$220$		0			0
$221$		0			0
$222$	−7.46863	+	12.9360i	−0.501261	+	0.868210i
$223$	14.4059	+	24.9517i	0.964689	+	1.67089i	0.710448	+	0.703750i	$0.248492\pi$
$223$	14.4059	+	24.9517i	0.964689	+	1.67089i	0.254241	+	0.967141i	$0.418174\pi$
$224$	0.822876	−	1.42526i	0.0549807	−	0.0952294i
$225$		0			0
$226$	−2.79150	−	4.83502i	−0.185688	−	0.321621i
$227$	12.6458			0.839328			0.419664	−	0.907680i	$-0.362148\pi$
$227$	12.6458			0.839328			0.419664	+	0.907680i	$0.362148\pi$
$228$	11.4373	−	1.47960i	0.757451	−	0.0979890i
$229$	20.0000			1.32164			0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000			1.32164			0.660819	+	0.750546i	$0.270209\pi$
$230$		0			0
$231$	−1.40588	−	2.43506i	−0.0925002	−	0.160215i
$232$	−1.82288	+	3.15731i	−0.119678	+	0.207288i
$233$	−6.43725	−	11.1497i	−0.421719	−	0.730438i	0.574389	−	0.818582i	$-0.305240\pi$
$233$	−6.43725	−	11.1497i	−0.421719	−	0.730438i	−0.996108	+	0.0881444i	$0.971906\pi$
$234$	−4.00000	+	6.92820i	−0.261488	+	0.452911i
$235$		0			0
$236$	7.93725			0.516671
$237$	5.29150	−	9.16515i	0.343720	−	0.595341i
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	−6.79150	+	11.7632i	−0.437479	+	0.757736i	−0.997494	−	0.0707462i	$-0.977462\pi$
$241$	−6.79150	+	11.7632i	−0.437479	+	0.757736i	0.560015	+	0.828482i	$0.310795\pi$
$242$	−5.29150	−	9.16515i	−0.340151	−	0.589158i
$243$	10.5830	−	18.3303i	0.678900	−	1.17589i
$244$	7.46863	+	12.9360i	0.478130	+	0.828145i
$245$		0			0
$246$	−27.2288			−1.73604
$247$	3.35425	−	8.04668i	0.213426	−	0.511998i
$248$	0.354249			0.0224948
$249$	−10.5000	−	18.1865i	−0.665410	−	1.15252i
$250$		0			0
$251$	−1.38562	+	2.39997i	−0.0874597	+	0.151485i	−0.906437	−	0.422342i	$-0.861208\pi$
$251$	−1.38562	+	2.39997i	−0.0874597	+	0.151485i	0.818977	+	0.573826i	$0.194542\pi$
$252$	−3.29150	−	5.70105i	−0.207345	−	0.359132i
$253$	1.17712	−	2.03884i	0.0740052	−	0.128181i
$254$	−2.70850			−0.169946
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.854249	−	1.47960i	0.0532866	−	0.0922950i	−0.838152	−	0.545437i	$-0.816364\pi$
$257$	0.854249	−	1.47960i	0.0532866	−	0.0922950i	0.891438	+	0.453142i	$0.149697\pi$
$258$	1.87451			0.116702
$259$	−9.29150			−0.577346
$260$		0			0
$261$	7.29150	+	12.6293i	0.451333	+	0.781731i
$262$	−6.96863	+	12.0700i	−0.430523	+	0.745688i
$263$	2.46863	+	4.27579i	0.152222	+	0.263656i	0.932044	−	0.362345i	$-0.118024\pi$
$263$	2.46863	+	4.27579i	0.152222	+	0.263656i	−0.779822	+	0.626001i	$0.784690\pi$
$264$	0.854249	+	1.47960i	0.0525754	+	0.0910632i
$265$		0			0
$266$	4.35425	+	5.70105i	0.266976	+	0.349554i
$267$		0			0
$268$	−2.32288	−	4.02334i	−0.141892	−	0.245765i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	−8.82288	−	15.2817i	−0.535952	−	0.928295i	−0.999117	−	0.0420233i	$-0.986620\pi$
$271$	−8.82288	−	15.2817i	−0.535952	−	0.928295i	0.463165	−	0.886272i	$-0.346714\pi$
$272$		0			0
$273$	−8.70850			−0.527062
$274$	−5.58301			−0.337282
$275$		0			0
$276$	4.82288	−	8.35347i	0.290303	−	0.502820i
$277$	−9.52026			−0.572017			−0.286008	−	0.958227i	$-0.592329\pi$
$277$	−9.52026			−0.572017			−0.286008	+	0.958227i	$0.592329\pi$
$278$	−13.3542			−0.800935
$279$	0.708497	−	1.22715i	0.0424166	−	0.0734678i
$280$		0			0
$281$	13.7288	−	23.7789i	0.818989	−	1.41853i	−0.0874389	−	0.996170i	$-0.527868\pi$
$281$	13.7288	−	23.7789i	0.818989	−	1.41853i	0.906428	−	0.422361i	$-0.138798\pi$
$282$	−12.7601	−	22.1012i	−0.759855	−	1.31611i
$283$	12.6771	+	21.9574i	0.753577	+	1.30523i	0.946079	+	0.323937i	$0.105007\pi$
$283$	12.6771	+	21.9574i	0.753577	+	1.30523i	−0.192502	+	0.981297i	$0.561660\pi$
$284$	−13.2915			−0.788706
$285$		0			0
$286$	1.29150			0.0763682
$287$	−8.46863	−	14.6681i	−0.499887	−	0.865830i
$288$	2.00000	+	3.46410i	0.117851	+	0.204124i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$	−18.9059	+	32.7459i	−1.10828	+	1.91960i
$292$	−12.2915			−0.719306
$293$	−13.0627			−0.763134			−0.381567	−	0.924341i	$-0.624615\pi$
$293$	−13.0627			−0.763134			−0.381567	+	0.924341i	$0.624615\pi$
$294$	−5.67712	+	9.83307i	−0.331097	+	0.573476i
$295$		0			0
$296$	5.64575			0.328153
$297$	1.70850			0.0991371
$298$	−2.46863	+	4.27579i	−0.143004	+	0.247690i
$299$	−3.64575	−	6.31463i	−0.210839	−	0.365184i
$300$		0			0
$301$	0.583005	+	1.00979i	0.0336039	+	0.0582036i
$302$	−1.46863	−	2.54374i	−0.0845100	−	0.146376i
$303$	−22.1033			−1.26980
$304$	−2.64575	−	3.46410i	−0.151744	−	0.198680i
$305$		0			0
$306$		0			0
$307$	−2.32288	−	4.02334i	−0.132574	−	0.229624i	0.792094	−	0.610399i	$-0.208991\pi$
$307$	−2.32288	−	4.02334i	−0.132574	−	0.229624i	−0.924668	+	0.380775i	$0.875657\pi$
$308$	−0.531373	+	0.920365i	−0.0302778	+	0.0524427i
$309$	−3.58301	−	6.20595i	−0.203830	−	0.353044i
$310$		0			0
$311$	8.35425			0.473726			0.236863	−	0.971543i	$-0.423881\pi$
$311$	8.35425			0.473726			0.236863	+	0.971543i	$0.423881\pi$
$312$	5.29150			0.299572
$313$	−11.4373	+	19.8099i	−0.646472	+	1.11972i	0.337488	+	0.941330i	$0.390423\pi$
$313$	−11.4373	+	19.8099i	−0.646472	+	1.11972i	−0.983959	+	0.178392i	$0.942910\pi$
$314$	−5.29150	+	9.16515i	−0.298617	+	0.517219i
$315$		0			0
$316$	−4.00000			−0.225018
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$	−11.3542	−	19.6661i	−0.636715	−	1.10282i
$319$	1.17712	−	2.03884i	0.0659063	−	0.114153i
$320$		0			0
$321$	6.22876	+	10.7885i	0.347655	+	0.602157i
$322$	6.00000			0.334367
$323$		0			0
$324$	−5.00000			−0.277778
$325$		0			0
$326$	5.96863	+	10.3380i	0.330572	+	0.572567i
$327$	8.70850	−	15.0836i	0.481581	−	0.834123i
$328$	5.14575	+	8.91270i	0.284127	+	0.492122i
$329$	7.93725	−	13.7477i	0.437595	−	0.757937i
$330$		0			0
$331$	−27.8118			−1.52867			−0.764336	−	0.644818i	$-0.776933\pi$
$331$	−27.8118			−1.52867			−0.764336	+	0.644818i	$0.776933\pi$
$332$	−3.96863	+	6.87386i	−0.217807	+	0.377252i
$333$	11.2915	−	19.5575i	0.618771	−	1.07174i
$334$	−12.0000			−0.656611
$335$		0			0
$336$	−2.17712	+	3.77089i	−0.118772	+	0.205719i
$337$	−10.1458	−	17.5730i	−0.552674	−	0.957260i	−0.998080	−	0.0619313i	$-0.980274\pi$
$337$	−10.1458	−	17.5730i	−0.552674	−	0.957260i	0.445406	−	0.895329i	$-0.353059\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$	7.38562	+	12.7923i	0.401132	+	0.694781i
$340$		0			0
$341$	−0.228757			−0.0123879
$342$	−17.2915	+	2.23695i	−0.935017	+	0.120960i
$343$	−18.5830			−1.00339
$344$	−0.354249	−	0.613577i	−0.0190998	−	0.0330818i
$345$		0			0
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	1.61438	+	2.79619i	0.0866644	+	0.150107i	0.906099	−	0.423065i	$-0.139046\pi$
$347$	1.61438	+	2.79619i	0.0866644	+	0.150107i	−0.819435	+	0.573172i	$0.805713\pi$
$348$	4.82288	−	8.35347i	0.258533	−	0.447793i
$349$	−21.1660			−1.13299			−0.566495	−	0.824065i	$-0.691701\pi$
$349$	−21.1660			−1.13299			−0.566495	+	0.824065i	$0.691701\pi$
$350$		0			0
$351$	2.64575	−	4.58258i	0.141220	−	0.244600i
$352$	0.322876	−	0.559237i	0.0172093	−	0.0298074i
$353$	18.8745			1.00459			0.502294	−	0.864697i	$-0.332489\pi$
$353$	18.8745			1.00459			0.502294	+	0.864697i	$0.332489\pi$
$354$	−21.0000			−1.11614
$355$		0			0
$356$		0			0
$357$		0			0
$358$	9.96863	+	17.2662i	0.526858	+	0.912545i
$359$	−5.46863	−	9.47194i	−0.288623	−	0.499910i	0.684858	−	0.728676i	$-0.259864\pi$
$359$	−5.46863	−	9.47194i	−0.288623	−	0.499910i	−0.973481	+	0.228766i	$0.926531\pi$
$360$		0			0
$361$	18.3745	−	4.83502i	0.967079	−	0.254475i
$362$	4.22876			0.222259
$363$	14.0000	+	24.2487i	0.734809	+	1.27273i
$364$	1.64575	+	2.85052i	0.0862608	+	0.149408i
$365$		0			0
$366$	−19.7601	−	34.2255i	−1.03288	−	1.78900i
$367$	−5.11438	+	8.85836i	−0.266968	+	0.462403i	−0.968077	−	0.250651i	$-0.919355\pi$
$367$	−5.11438	+	8.85836i	−0.266968	+	0.462403i	0.701109	+	0.713054i	$0.252689\pi$
$368$	−3.64575			−0.190048
$369$	41.1660			2.14302
$370$		0			0
$371$	7.06275	−	12.2330i	0.366680	−	0.635108i
$372$	−0.937254			−0.0485944
$373$	4.00000			0.207112			0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000			0.207112			0.103556	+	0.994624i	$0.466978\pi$
$374$		0			0
$375$		0			0
$376$	−4.82288	+	8.35347i	−0.248721	+	0.430797i
$377$	−3.64575	−	6.31463i	−0.187766	−	0.325220i
$378$	2.17712	+	3.77089i	0.111979	+	0.193954i
$379$	21.2915			1.09367			0.546836	−	0.837240i	$-0.315832\pi$
$379$	21.2915			1.09367			0.546836	+	0.837240i	$0.315832\pi$
$380$		0			0
$381$	7.16601			0.367126
$382$	−7.29150	−	12.6293i	−0.373066	−	0.646169i
$383$	−15.7601	−	27.2973i	−0.805305	−	1.39483i	−0.916085	−	0.400984i	$-0.868668\pi$
$383$	−15.7601	−	27.2973i	−0.805305	−	1.39483i	0.110780	−	0.993845i	$-0.464665\pi$
$384$	1.32288	−	2.29129i	0.0675077	−	0.116927i
$385$		0			0
$386$	3.29150	−	5.70105i	0.167533	−	0.290176i
$387$	−2.83399			−0.144060
$388$	14.2915			0.725541
$389$	−6.00000	+	10.3923i	−0.304212	+	0.526911i	−0.977086	−	0.212847i	$-0.931726\pi$
$389$	−6.00000	+	10.3923i	−0.304212	+	0.526911i	0.672874	+	0.739758i	$0.265060\pi$
$390$		0			0
$391$		0			0
$392$	4.29150			0.216754
$393$	18.4373	−	31.9343i	0.930036	−	1.61087i
$394$	1.17712	+	2.03884i	0.0593027	+	0.102715i
$395$		0			0
$396$	−1.29150	−	2.23695i	−0.0649004	−	0.112411i
$397$	18.4686	+	31.9886i	0.926914	+	1.60546i	0.788454	+	0.615094i	$0.210882\pi$
$397$	18.4686	+	31.9886i	0.926914	+	1.60546i	0.138460	+	0.990368i	$0.455785\pi$
$398$	−11.8745			−0.595215
$399$	−11.5203	−	15.0836i	−0.576734	−	0.755122i
$400$		0			0
$401$	−3.20850	−	5.55728i	−0.160225	−	0.277517i	0.774724	−	0.632299i	$-0.217889\pi$
$401$	−3.20850	−	5.55728i	−0.160225	−	0.277517i	−0.934949	+	0.354782i	$0.884555\pi$
$402$	6.14575	+	10.6448i	0.306522	+	0.530912i
$403$	−0.354249	+	0.613577i	−0.0176464	+	0.0305644i
$404$	4.17712	+	7.23499i	0.207820	+	0.359954i
$405$		0			0
$406$	6.00000			0.297775
$407$	−3.64575			−0.180713
$408$		0			0
$409$	−6.79150	+	11.7632i	−0.335818	+	0.581654i	−0.983642	−	0.180136i	$-0.942346\pi$
$409$	−6.79150	+	11.7632i	−0.335818	+	0.581654i	0.647823	+	0.761790i	$0.275679\pi$
$410$		0			0
$411$	14.7712			0.728612
$412$	−1.35425	+	2.34563i	−0.0667190	+	0.115561i
$413$	−6.53137	−	11.3127i	−0.321388	−	0.556660i
$414$	−7.29150	+	12.6293i	−0.358358	+	0.620694i
$415$		0			0
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	35.3320			1.73022
$418$	1.70850	+	2.23695i	0.0835653	+	0.109413i
$419$	31.7490			1.55104			0.775520	−	0.631322i	$-0.217488\pi$
$419$	31.7490			1.55104			0.775520	+	0.631322i	$0.217488\pi$
$420$		0			0
$421$	−11.4059	−	19.7556i	−0.555889	−	0.962827i	−0.997834	−	0.0657853i	$-0.979045\pi$
$421$	−11.4059	−	19.7556i	−0.555889	−	0.962827i	0.441945	−	0.897042i	$-0.354289\pi$
$422$	−1.35425	+	2.34563i	−0.0659238	+	0.114183i
$423$	19.2915	+	33.4139i	0.937985	+	1.62464i
$424$	−4.29150	+	7.43310i	−0.208414	+	0.360983i
$425$		0			0
$426$	35.1660			1.70380
$427$	12.2915	−	21.2895i	0.594828	−	1.03027i
$428$	2.35425	−	4.07768i	0.113797	−	0.197102i
$429$	−3.41699			−0.164974
$430$		0			0
$431$	1.93725	−	3.35542i	0.0933142	−	0.161625i	−0.815590	−	0.578631i	$-0.803587\pi$
$431$	1.93725	−	3.35542i	0.0933142	−	0.161625i	0.908904	+	0.417006i	$0.136921\pi$
$432$	−1.32288	−	2.29129i	−0.0636469	−	0.110240i
$433$	−6.93725	+	12.0157i	−0.333383	+	0.577437i	−0.983173	−	0.182677i	$-0.941524\pi$
$433$	−6.93725	+	12.0157i	−0.333383	+	0.577437i	0.649790	+	0.760114i	$0.274857\pi$
$434$	−0.291503	−	0.504897i	−0.0139926	−	0.0242358i
$435$		0			0
$436$	−6.58301			−0.315269
$437$	6.11438	−	14.6681i	0.292490	−	0.701670i
$438$	32.5203			1.55388
$439$	18.4059	+	31.8799i	0.878465	+	1.52155i	0.853025	+	0.521869i	$0.174765\pi$
$439$	18.4059	+	31.8799i	0.878465	+	1.52155i	0.0254393	+	0.999676i	$0.491902\pi$
$440$		0			0
$441$	8.58301	−	14.8662i	0.408715	−	0.707914i
$442$		0			0
$443$	2.67712	−	4.63692i	0.127194	−	0.220306i	−0.795394	−	0.606092i	$-0.792736\pi$
$443$	2.67712	−	4.63692i	0.127194	−	0.220306i	0.922588	+	0.385786i	$0.126070\pi$
$444$	−14.9373			−0.708891
$445$		0			0
$446$	−14.4059	+	24.9517i	−0.682138	+	1.18150i
$447$	6.53137	−	11.3127i	0.308923	−	0.535071i
$448$	1.64575			0.0777544
$449$	−13.7085			−0.646944			−0.323472	−	0.946238i	$-0.604850\pi$
$449$	−13.7085			−0.646944			−0.323472	+	0.946238i	$0.604850\pi$
$450$		0			0
$451$	−3.32288	−	5.75539i	−0.156468	−	0.271011i
$452$	2.79150	−	4.83502i	0.131301	−	0.227420i
$453$	3.88562	+	6.73009i	0.182562	+	0.316207i
$454$	6.32288	+	10.9515i	0.296747	+	0.513981i
$455$		0			0
$456$	7.00000	+	9.16515i	0.327805	+	0.429198i
$457$	−1.12549			−0.0526483			−0.0263242	−	0.999653i	$-0.508380\pi$
$457$	−1.12549			−0.0526483			−0.0263242	+	0.999653i	$0.508380\pi$
$458$	10.0000	+	17.3205i	0.467269	+	0.809334i
$459$		0			0
$460$		0			0
$461$	11.5830	+	20.0624i	0.539474	+	0.934397i	0.998932	+	0.0461975i	$0.0147103\pi$
$461$	11.5830	+	20.0624i	0.539474	+	0.934397i	−0.459458	+	0.888200i	$0.651956\pi$
$462$	1.40588	−	2.43506i	0.0654075	−	0.113289i
$463$	−14.4575			−0.671898			−0.335949	−	0.941880i	$-0.609057\pi$
$463$	−14.4575			−0.671898			−0.335949	+	0.941880i	$0.609057\pi$
$464$	−3.64575			−0.169250
$465$		0			0
$466$	6.43725	−	11.1497i	0.298200	−	0.516498i
$467$	24.6458			1.14047			0.570235	−	0.821482i	$-0.306852\pi$
$467$	24.6458			1.14047			0.570235	+	0.821482i	$0.306852\pi$
$468$	−8.00000			−0.369800
$469$	−3.82288	+	6.62141i	−0.176524	+	0.305749i
$470$		0			0
$471$	14.0000	−	24.2487i	0.645086	−	1.11732i
$472$	3.96863	+	6.87386i	0.182671	+	0.316395i
$473$	0.228757	+	0.396218i	0.0105182	+	0.0182181i
$474$	10.5830			0.486094
$475$		0			0
$476$		0			0
$477$	17.1660	+	29.7324i	0.785978	+	1.36135i
$478$	−6.00000	−	10.3923i	−0.274434	−	0.475333i
$479$	7.29150	−	12.6293i	0.333157	−	0.577045i	−0.649972	−	0.759958i	$-0.725219\pi$
$479$	7.29150	−	12.6293i	0.333157	−	0.577045i	0.983129	+	0.182913i	$0.0585527\pi$
$480$		0			0
$481$	−5.64575	+	9.77873i	−0.257424	+	0.445872i
$482$	−13.5830			−0.618689
$483$	−15.8745			−0.722315
$484$	5.29150	−	9.16515i	0.240523	−	0.416598i
$485$		0			0
$486$	21.1660			0.960110
$487$	22.2288			1.00728			0.503641	−	0.863913i	$-0.331994\pi$
$487$	22.2288			1.00728			0.503641	+	0.863913i	$0.331994\pi$
$488$	−7.46863	+	12.9360i	−0.338089	+	0.585587i
$489$	−15.7915	−	27.3517i	−0.714116	−	1.23689i
$490$		0			0
$491$	−14.3542	−	24.8623i	−0.647798	−	1.12202i	−0.983648	−	0.180104i	$-0.942357\pi$
$491$	−14.3542	−	24.8623i	−0.647798	−	1.12202i	0.335849	−	0.941916i	$-0.390977\pi$
$492$	−13.6144	−	23.5808i	−0.613784	−	1.06310i
$493$		0			0
$494$	8.64575	−	1.11847i	0.388991	−	0.0503225i
$495$		0			0
$496$	0.177124	+	0.306788i	0.00795312	+	0.0137752i
$497$	10.9373	+	18.9439i	0.490603	+	0.849749i
$498$	10.5000	−	18.1865i	0.470516	−	0.814958i
$499$	15.6144	+	27.0449i	0.698996	+	1.21070i	0.968815	+	0.247785i	$0.0797026\pi$
$499$	15.6144	+	27.0449i	0.698996	+	1.21070i	−0.269819	+	0.962911i	$0.586964\pi$
$500$		0			0
$501$	31.7490			1.41844
$502$	−2.77124			−0.123687
$503$	−12.5314	+	21.7050i	−0.558746	+	0.967777i	0.438855	+	0.898558i	$0.355384\pi$
$503$	−12.5314	+	21.7050i	−0.558746	+	0.967777i	−0.997601	+	0.0692192i	$0.977949\pi$
$504$	3.29150	−	5.70105i	0.146615	−	0.253945i
$505$		0			0
$506$	2.35425			0.104659
$507$	11.9059	−	20.6216i	0.528759	−	0.915837i
$508$	−1.35425	−	2.34563i	−0.0600851	−	0.104070i
$509$	−15.8745	+	27.4955i	−0.703625	+	1.21871i	0.263560	+	0.964643i	$0.415103\pi$
$509$	−15.8745	+	27.4955i	−0.703625	+	1.21871i	−0.967185	+	0.254072i	$0.918230\pi$
$510$		0			0
$511$	10.1144	+	17.5186i	0.447434	+	0.774978i
$512$	−1.00000			−0.0441942
$513$	11.4373	−	1.47960i	0.504967	−	0.0653260i
$514$	1.70850			0.0753586
$515$		0			0
$516$	0.937254	+	1.62337i	0.0412603	+	0.0714649i
$517$	3.11438	−	5.39426i	0.136970	−	0.237239i
$518$	−4.64575	−	8.04668i	−0.204123	−	0.353551i
$519$	−7.93725	+	13.7477i	−0.348407	+	0.603458i
$520$		0			0
$521$	−22.2915			−0.976608			−0.488304	−	0.872673i	$-0.662384\pi$
$521$	−22.2915			−0.976608			−0.488304	+	0.872673i	$0.662384\pi$
$522$	−7.29150	+	12.6293i	−0.319140	+	0.552767i
$523$	14.9373	−	25.8721i	0.653161	−	1.13131i	−0.329191	−	0.944263i	$-0.606776\pi$
$523$	14.9373	−	25.8721i	0.653161	−	1.13131i	0.982352	−	0.187044i	$-0.0598906\pi$
$524$	−13.9373			−0.608852
$525$		0			0
$526$	−2.46863	+	4.27579i	−0.107637	+	0.186433i
$527$		0			0
$528$	−0.854249	+	1.47960i	−0.0371764	+	0.0643914i
$529$	4.85425	+	8.40781i	0.211054	+	0.365557i
$530$		0			0
$531$	31.7490			1.37779
$532$	−2.76013	+	6.62141i	−0.119667	+	0.287075i
$533$	−20.5830			−0.891549
$534$		0			0
$535$		0			0
$536$	2.32288	−	4.02334i	0.100333	−	0.173782i
$537$	−26.3745	−	45.6820i	−1.13814	−	1.97132i
$538$		0			0
$539$	−2.77124			−0.119366
$540$		0			0
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	−0.939110	−	0.343617i	$-0.888348\pi$
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	0.767136	+	0.641484i	$0.221681\pi$
$542$	8.82288	−	15.2817i	0.378975	−	0.656404i
$543$	−11.1882			−0.480133
$544$		0			0
$545$		0			0
$546$	−4.35425	−	7.54178i	−0.186345	−	0.322758i
$547$	0.354249	−	0.613577i	0.0151466	−	0.0262346i	−0.858353	−	0.513060i	$-0.828512\pi$
$547$	0.354249	−	0.613577i	0.0151466	−	0.0262346i	0.873499	+	0.486825i	$0.161845\pi$
$548$	−2.79150	−	4.83502i	−0.119247	−	0.206542i
$549$	29.8745	+	51.7442i	1.27501	+	2.20839i
$550$		0			0
$551$	6.11438	−	14.6681i	0.260481	−	0.624882i
$552$	9.64575			0.410550
$553$	3.29150	+	5.70105i	0.139969	+	0.242433i
$554$	−4.76013	−	8.24479i	−0.202239	−	0.350287i
$555$		0			0
$556$	−6.67712	−	11.5651i	−0.283173	−	0.490470i
$557$	−13.2915	+	23.0216i	−0.563179	+	0.975455i	0.434037	+	0.900895i	$0.357089\pi$
$557$	−13.2915	+	23.0216i	−0.563179	+	0.975455i	−0.997217	+	0.0745599i	$0.976245\pi$
$558$	1.41699			0.0599862
$559$	1.41699			0.0599325
$560$		0			0
$561$		0			0
$562$	27.4575			1.15823
$563$	−25.9373			−1.09312			−0.546562	−	0.837418i	$-0.684064\pi$
$563$	−25.9373			−1.09312			−0.546562	+	0.837418i	$0.684064\pi$
$564$	12.7601	−	22.1012i	0.537298	−	0.930628i
$565$		0			0
$566$	−12.6771	+	21.9574i	−0.532859	+	0.922939i
$567$	4.11438	+	7.12631i	0.172788	+	0.299277i
$568$	−6.64575	−	11.5108i	−0.278850	−	0.482982i
$569$	−14.5830			−0.611351			−0.305676	−	0.952136i	$-0.598882\pi$
$569$	−14.5830			−0.611351			−0.305676	+	0.952136i	$0.598882\pi$
$570$		0			0
$571$	−39.8118			−1.66607			−0.833035	−	0.553220i	$-0.813399\pi$
$571$	−39.8118			−1.66607			−0.833035	+	0.553220i	$0.813399\pi$
$572$	0.645751	+	1.11847i	0.0270002	+	0.0467658i
$573$	19.2915	+	33.4139i	0.805914	+	1.39588i
$574$	8.46863	−	14.6681i	0.353474	−	0.612234i
$575$		0			0
$576$	−2.00000	+	3.46410i	−0.0833333	+	0.144338i
$577$	−11.0000			−0.457936			−0.228968	−	0.973434i	$-0.573535\pi$
$577$	−11.0000			−0.457936			−0.228968	+	0.973434i	$0.573535\pi$
$578$	17.0000			0.707107
$579$	−8.70850	+	15.0836i	−0.361913	+	0.626851i
$580$		0			0
$581$	13.0627			0.541934
$582$	−37.8118			−1.56735
$583$	2.77124	−	4.79993i	0.114773	−	0.198793i
$584$	−6.14575	−	10.6448i	−0.254313	−	0.440483i
$585$		0			0
$586$	−6.53137	−	11.3127i	−0.269809	−	0.467322i
$587$	−22.9373	−	39.7285i	−0.946722	−	1.63977i	−0.752267	−	0.658859i	$-0.771039\pi$
$587$	−22.9373	−	39.7285i	−0.946722	−	1.63977i	−0.194455	−	0.980911i	$-0.562294\pi$
$588$	−11.3542			−0.468241
$589$	−1.53137	+	0.198109i	−0.0630991	+	0.00816294i
$590$		0			0
$591$	−3.11438	−	5.39426i	−0.128108	−	0.221890i
$592$	2.82288	+	4.88936i	0.116019	+	0.200952i
$593$	20.1458	−	34.8935i	0.827287	−	1.43290i	−0.0728721	−	0.997341i	$-0.523216\pi$
$593$	20.1458	−	34.8935i	0.827287	−	1.43290i	0.900159	−	0.435562i	$-0.143450\pi$
$594$	0.854249	+	1.47960i	0.0350502	+	0.0607088i
$595$		0			0
$596$	−4.93725			−0.202238
$597$	31.4170			1.28581
$598$	3.64575	−	6.31463i	0.149086	−	0.258224i
$599$	0.531373	−	0.920365i	0.0217113	−	0.0376051i	−0.854966	−	0.518685i	$-0.826422\pi$
$599$	0.531373	−	0.920365i	0.0217113	−	0.0376051i	0.876677	+	0.481080i	$0.159755\pi$
$600$		0			0
$601$	31.5830			1.28830			0.644149	−	0.764900i	$-0.277212\pi$
$601$	31.5830			1.28830			0.644149	+	0.764900i	$0.277212\pi$
$602$	−0.583005	+	1.00979i	−0.0237615	+	0.0411562i
$603$	−9.29150	−	16.0934i	−0.378379	−	0.655372i
$604$	1.46863	−	2.54374i	0.0597576	−	0.103503i
$605$		0			0
$606$	−11.0516	−	19.1420i	−0.448942	−	0.777590i
$607$	8.93725			0.362752			0.181376	−	0.983414i	$-0.441945\pi$
$607$	8.93725			0.362752			0.181376	+	0.983414i	$0.441945\pi$
$608$	1.67712	−	4.02334i	0.0680164	−	0.163168i
$609$	−15.8745			−0.643268
$610$		0			0
$611$	−9.64575	−	16.7069i	−0.390225	−	0.675890i
$612$		0			0
$613$	14.2915	+	24.7536i	0.577228	+	0.999789i	0.995796	+	0.0916030i	$0.0291991\pi$
$613$	14.2915	+	24.7536i	0.577228	+	0.999789i	−0.418567	+	0.908186i	$0.637468\pi$
$614$	2.32288	−	4.02334i	0.0937436	−	0.162369i
$615$		0			0
$616$	−1.06275			−0.0428193
$617$	0.437254	−	0.757346i	0.0176032	−	0.0304896i	−0.857090	−	0.515167i	$-0.827730\pi$
$617$	0.437254	−	0.757346i	0.0176032	−	0.0304896i	0.874693	+	0.484678i	$0.161063\pi$
$618$	3.58301	−	6.20595i	0.144130	−	0.249640i
$619$	44.4575			1.78690			0.893449	−	0.449164i	$-0.148278\pi$
$619$	44.4575			1.78690			0.893449	+	0.449164i	$0.148278\pi$
$620$		0			0
$621$	4.82288	−	8.35347i	0.193535	−	0.335213i
$622$	4.17712	+	7.23499i	0.167487	+	0.290097i
$623$		0			0
$624$	2.64575	+	4.58258i	0.105915	+	0.183450i
$625$		0			0
$626$	−22.8745			−0.914249
$627$	−4.52026	−	5.91841i	−0.180522	−	0.236358i
$628$	−10.5830			−0.422308
$629$		0			0
$630$		0			0
$631$	−11.4059	+	19.7556i	−0.454061	+	0.786457i	−0.998634	−	0.0522570i	$-0.983359\pi$
$631$	−11.4059	+	19.7556i	−0.454061	+	0.786457i	0.544573	+	0.838714i	$0.316692\pi$
$632$	−2.00000	−	3.46410i	−0.0795557	−	0.137795i
$633$	3.58301	−	6.20595i	0.142412	−	0.246664i
$634$	−6.00000			−0.238290
$635$		0			0
$636$	11.3542	−	19.6661i	0.450225	−	0.779813i
$637$	−4.29150	+	7.43310i	−0.170036	+	0.294510i
$638$	2.35425			0.0932056
$639$	−53.1660			−2.10321
$640$		0			0
$641$	9.43725	+	16.3458i	0.372749	+	0.645620i	0.989987	−	0.141156i	$-0.0450819\pi$
$641$	9.43725	+	16.3458i	0.372749	+	0.645620i	−0.617238	+	0.786776i	$0.711749\pi$
$642$	−6.22876	+	10.7885i	−0.245829	+	0.425789i
$643$	15.2601	+	26.4313i	0.601801	+	1.04235i	0.992548	+	0.121852i	$0.0388832\pi$
$643$	15.2601	+	26.4313i	0.601801	+	1.04235i	−0.390748	+	0.920498i	$0.627783\pi$
$644$	3.00000	+	5.19615i	0.118217	+	0.204757i
$645$		0			0
$646$		0			0
$647$	−30.4575			−1.19741			−0.598704	−	0.800970i	$-0.704317\pi$
$647$	−30.4575			−1.19741			−0.598704	+	0.800970i	$0.704317\pi$
$648$	−2.50000	−	4.33013i	−0.0982093	−	0.170103i
$649$	−2.56275	−	4.43881i	−0.100597	−	0.174238i
$650$		0			0
$651$	0.771243	+	1.33583i	0.0302274	+	0.0523554i
$652$	−5.96863	+	10.3380i	−0.233749	+	0.404866i
$653$	−24.0000			−0.939193			−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000			−0.939193			−0.469596	+	0.882881i	$0.655601\pi$
$654$	17.4170			0.681058
$655$		0			0
$656$	−5.14575	+	8.91270i	−0.200908	+	0.347983i
$657$	−49.1660			−1.91815
$658$	15.8745			0.618853
$659$	−1.29150	+	2.23695i	−0.0503098	+	0.0871391i	−0.890084	−	0.455797i	$-0.849354\pi$
$659$	−1.29150	+	2.23695i	−0.0503098	+	0.0871391i	0.839774	+	0.542936i	$0.182688\pi$
$660$		0			0
$661$	5.11438	−	8.85836i	0.198926	−	0.344550i	−0.749254	−	0.662282i	$-0.769588\pi$
$661$	5.11438	−	8.85836i	0.198926	−	0.344550i	0.948181	+	0.317732i	$0.102921\pi$
$662$	−13.9059	−	24.0857i	−0.540467	−	0.936117i
$663$		0			0
$664$	−7.93725			−0.308025
$665$		0			0
$666$	22.5830			0.875074
$667$	−6.64575	−	11.5108i	−0.257325	−	0.445699i
$668$	−6.00000	−	10.3923i	−0.232147	−	0.402090i
$669$	38.1144	−	66.0160i	1.47359	−	2.55233i
$670$		0			0
$671$	4.82288	−	8.35347i	0.186185	−	0.322482i
$672$	−4.35425			−0.167969
$673$	−17.8745			−0.689012			−0.344506	−	0.938784i	$-0.611954\pi$
$673$	−17.8745			−0.689012			−0.344506	+	0.938784i	$0.611954\pi$
$674$	10.1458	−	17.5730i	0.390800	−	0.676885i
$675$		0			0
$676$	−9.00000			−0.346154
$677$	32.5830			1.25227			0.626133	−	0.779716i	$-0.284637\pi$
$677$	32.5830			1.25227			0.626133	+	0.779716i	$0.284637\pi$
$678$	−7.38562	+	12.7923i	−0.283643	+	0.491284i
$679$	−11.7601	−	20.3691i	−0.451312	−	0.781696i
$680$		0			0
$681$	−16.7288	−	28.9751i	−0.641047	−	1.11033i
$682$	−0.114378	−	0.198109i	−0.00437977	−	0.00758599i
$683$	26.5830			1.01717			0.508585	−	0.861012i	$-0.330169\pi$
$683$	26.5830			1.01717			0.508585	+	0.861012i	$0.330169\pi$
$684$	−10.5830	−	13.8564i	−0.404651	−	0.529813i
$685$		0			0
$686$	−9.29150	−	16.0934i	−0.354751	−	0.614447i
$687$	−26.4575	−	45.8258i	−1.00942	−	1.74836i
$688$	0.354249	−	0.613577i	0.0135056	−	0.0233924i
$689$	−8.58301	−	14.8662i	−0.326986	−	0.566357i
$690$		0			0
$691$	−18.5830			−0.706931			−0.353465	−	0.935448i	$-0.614997\pi$
$691$	−18.5830			−0.706931			−0.353465	+	0.935448i	$0.614997\pi$
$692$	6.00000			0.228086
$693$	−2.12549	+	3.68146i	−0.0807408	+	0.139847i
$694$	−1.61438	+	2.79619i	−0.0612810	+	0.106142i
$695$		0			0
$696$	9.64575			0.365621
$697$		0			0
$698$	−10.5830	−	18.3303i	−0.400573	−	0.693812i
$699$	−17.0314	+	29.4992i	−0.644186	+	1.11576i
$700$		0			0
$701$	−7.82288	−	13.5496i	−0.295466	−	0.511762i	0.679627	−	0.733558i	$-0.262142\pi$
$701$	−7.82288	−	13.5496i	−0.295466	−	0.511762i	−0.975093	+	0.221796i	$0.928808\pi$
$702$	5.29150			0.199715
$703$	−24.4059	+	3.15731i	−0.920485	+	0.119080i
$704$	0.645751			0.0243377
$705$		0			0
$706$	9.43725	+	16.3458i	0.355176	+	0.615182i
$707$	6.87451	−	11.9070i	0.258542	−	0.447809i
$708$	−10.5000	−	18.1865i	−0.394614	−	0.683492i
$709$	0.822876	−	1.42526i	0.0309037	−	0.0535269i	−0.850160	−	0.526525i	$-0.823495\pi$
$709$	0.822876	−	1.42526i	0.0309037	−	0.0535269i	0.881064	+	0.472998i	$0.156828\pi$
$710$		0			0
$711$	−16.0000			−0.600047
$712$		0			0
$713$	−0.645751	+	1.11847i	−0.0241836	+	0.0418872i
$714$		0			0
$715$		0			0
$716$	−9.96863	+	17.2662i	−0.372545	+	0.645267i
$717$	15.8745	+	27.4955i	0.592844	+	1.02684i
$718$	5.46863	−	9.47194i	0.204087	−	0.353490i
$719$	−6.64575	−	11.5108i	−0.247845	−	0.429280i	0.715083	−	0.699040i	$-0.246389\pi$
$719$	−6.64575	−	11.5108i	−0.247845	−	0.429280i	−0.962928	+	0.269760i	$0.913056\pi$
$720$		0			0
$721$	4.45751			0.166006
$722$	13.3745	+	13.4953i	0.497748	+	0.502242i
$723$	35.9373			1.33652
$724$	2.11438	+	3.66221i	0.0785802	+	0.136105i
$725$		0			0
$726$	−14.0000	+	24.2487i	−0.519589	+	0.899954i
$727$	11.2915	+	19.5575i	0.418779	+	0.725346i	0.995817	−	0.0913712i	$-0.0291250\pi$
$727$	11.2915	+	19.5575i	0.418779	+	0.725346i	−0.577038	+	0.816717i	$0.695792\pi$
$728$	−1.64575	+	2.85052i	−0.0609956	+	0.105647i
$729$	−41.0000			−1.51852
$730$		0			0
$731$		0			0
$732$	19.7601	−	34.2255i	0.730355	−	1.26501i
$733$	−42.1033			−1.55512			−0.777560	−	0.628809i	$-0.783543\pi$
$733$	−42.1033			−1.55512			−0.777560	+	0.628809i	$0.783543\pi$
$734$	−10.2288			−0.377550
$735$		0			0
$736$	−1.82288	−	3.15731i	−0.0671921	−	0.116380i
$737$	−1.50000	+	2.59808i	−0.0552532	+	0.0957014i
$738$	20.5830	+	35.6508i	0.757671	+	1.31232i
$739$	−6.90588	−	11.9613i	−0.254037	−	0.440005i	0.710597	−	0.703600i	$-0.248425\pi$
$739$	−6.90588	−	11.9613i	−0.254037	−	0.440005i	−0.964633	+	0.263595i	$0.915092\pi$
$740$		0			0
$741$	−22.8745	+	2.95920i	−0.840316	+	0.108709i
$742$	14.1255			0.518563
$743$	−5.23987	−	9.07572i	−0.192232	−	0.332956i	0.753757	−	0.657153i	$-0.228239\pi$
$743$	−5.23987	−	9.07572i	−0.192232	−	0.332956i	−0.945990	+	0.324197i	$0.894906\pi$
$744$	−0.468627	−	0.811686i	−0.0171807	−	0.0297578i
$745$		0			0
$746$	2.00000	+	3.46410i	0.0732252	+	0.126830i
$747$	−15.8745	+	27.4955i	−0.580818	+	1.00601i
$748$		0			0
$749$	−7.74902			−0.283143
$750$		0			0
$751$	−11.9373	+	20.6759i	−0.435597	+	0.754475i	−0.997344	−	0.0728333i	$-0.976796\pi$
$751$	−11.9373	+	20.6759i	−0.435597	+	0.754475i	0.561748	+	0.827309i	$0.310129\pi$
$752$	−9.64575			−0.351744
$753$	7.33202			0.267194
$754$	3.64575	−	6.31463i	0.132770	−	0.229965i
$755$		0			0
$756$	−2.17712	+	3.77089i	−0.0791812	+	0.137146i
$757$	8.29150	+	14.3613i	0.301360	+	0.521970i	0.976444	−	0.215770i	$-0.0692261\pi$
$757$	8.29150	+	14.3613i	0.301360	+	0.521970i	−0.675084	+	0.737740i	$0.735893\pi$
$758$	10.6458	+	18.4390i	0.386671	+	0.669734i
$759$	−6.22876			−0.226090
$760$		0			0
$761$	11.1255			0.403299			0.201649	−	0.979458i	$-0.435370\pi$
$761$	11.1255			0.403299			0.201649	+	0.979458i	$0.435370\pi$
$762$	3.58301	+	6.20595i	0.129799	+	0.224818i
$763$	5.41699	+	9.38251i	0.196108	+	0.339670i
$764$	7.29150	−	12.6293i	0.263797	−	0.456910i
$765$		0			0
$766$	15.7601	−	27.2973i	0.569437	−	0.986293i
$767$	−15.8745			−0.573195
$768$	2.64575			0.0954703
$769$	−12.3542	+	21.3982i	−0.445506	+	0.771638i	−0.998087	−	0.0618204i	$-0.980309\pi$
$769$	−12.3542	+	21.3982i	−0.445506	+	0.771638i	0.552582	+	0.833459i	$0.313643\pi$
$770$		0			0
$771$	−4.52026			−0.162793
$772$	6.58301			0.236928
$773$	5.46863	−	9.47194i	0.196693	−	0.340682i	−0.750761	−	0.660574i	$-0.770313\pi$
$773$	5.46863	−	9.47194i	0.196693	−	0.340682i	0.947454	+	0.319892i	$0.103646\pi$
$774$	−1.41699	−	2.45431i	−0.0509328	−	0.0882182i
$775$		0			0
$776$	7.14575	+	12.3768i	0.256518	+	0.444301i
$777$	12.2915	+	21.2895i	0.440955	+	0.763757i
$778$	−12.0000			−0.430221
$779$	−27.2288	−	35.6508i	−0.975571	−	1.27732i
$780$		0			0
$781$	4.29150	+	7.43310i	0.153562	+	0.265977i
$782$		0			0
$783$	4.82288	−	8.35347i	0.172356	−	0.298529i
$784$	2.14575	+	3.71655i	0.0766340	+	0.132734i
$785$		0			0
$786$	36.8745			1.31527
$787$	5.47974			0.195332			0.0976658	−	0.995219i	$-0.468862\pi$
$787$	5.47974			0.195332			0.0976658	+	0.995219i	$0.468862\pi$
$788$	−1.17712	+	2.03884i	−0.0419333	+	0.0726306i
$789$	6.53137	−	11.3127i	0.232523	−	0.402742i
$790$		0			0
$791$	−9.18824			−0.326696
$792$	1.29150	−	2.23695i	0.0458915	−	0.0794865i
$793$	−14.9373	−	25.8721i	−0.530437	−	0.918745i
$794$	−18.4686	+	31.9886i	−0.655427	+	1.13523i
$795$		0			0
$796$	−5.93725	−	10.2836i	−0.210440	−	0.364493i
$797$	−2.81176			−0.0995977			−0.0497989	−	0.998759i	$-0.515858\pi$
$797$	−2.81176			−0.0995977			−0.0497989	+	0.998759i	$0.515858\pi$
$798$	7.30262	−	17.5186i	0.258510	−	0.620152i
$799$		0			0
$800$		0			0
$801$		0			0
$802$	3.20850	−	5.55728i	0.113296	−	0.196234i
$803$	3.96863	+	6.87386i	0.140050	+	0.242573i
$804$	−6.14575	+	10.6448i	−0.216744	+	0.375412i
$805$		0			0
$806$	−0.708497			−0.0249558
$807$		0			0
$808$	−4.17712	+	7.23499i	−0.146951	+	0.254526i
$809$	−9.00000			−0.316423			−0.158212	−	0.987405i	$-0.550573\pi$
$809$	−9.00000			−0.316423			−0.158212	+	0.987405i	$0.550573\pi$
$810$		0			0
$811$	10.3542	−	17.9341i	0.363587	−	0.629751i	−0.624961	−	0.780656i	$-0.714885\pi$
$811$	10.3542	−	17.9341i	0.363587	−	0.629751i	0.988548	+	0.150905i	$0.0482187\pi$
$812$	3.00000	+	5.19615i	0.105279	+	0.182349i
$813$	−23.3431	+	40.4315i	−0.818679	+	1.41799i
$814$	−1.82288	−	3.15731i	−0.0638918	−	0.110664i
$815$		0			0
$816$		0			0
$817$	1.87451	+	2.45431i	0.0655807	+	0.0858653i
$818$	−13.5830			−0.474919
$819$	6.58301	+	11.4021i	0.230029	+	0.398422i
$820$		0			0
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	−0.808915	−	0.587925i	$-0.799945\pi$
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	0.913616	+	0.406578i	$0.133278\pi$
$822$	7.38562	+	12.7923i	0.257603	+	0.446182i
$823$	−0.0627461	+	0.108679i	−0.00218719	+	0.00378832i	−0.867117	−	0.498105i	$-0.834030\pi$
$823$	−0.0627461	+	0.108679i	−0.00218719	+	0.00378832i	0.864930	+	0.501893i	$0.167363\pi$
$824$	−2.70850			−0.0943550
$825$		0			0
$826$	6.53137	−	11.3127i	0.227256	−	0.393618i
$827$	−23.6771	+	41.0100i	−0.823334	+	1.42606i	0.0798514	+	0.996807i	$0.474555\pi$
$827$	−23.6771	+	41.0100i	−0.823334	+	1.42606i	−0.903186	+	0.429250i	$0.858778\pi$
$828$	−14.5830			−0.506794
$829$	25.1660			0.874052			0.437026	−	0.899449i	$-0.356032\pi$
$829$	25.1660			0.874052			0.437026	+	0.899449i	$0.356032\pi$
$830$		0			0
$831$	12.5941	+	21.8137i	0.436885	+	0.756707i
$832$	1.00000	−	1.73205i	0.0346688	−	0.0600481i
$833$		0			0
$834$	17.6660	+	30.5984i	0.611724	+	1.05954i
$835$		0			0
$836$	−1.08301	+	2.59808i	−0.0374565	+	0.0898563i
$837$	−0.937254			−0.0323962
$838$	15.8745	+	27.4955i	0.548376	+	0.949815i
$839$	2.23987	+	3.87957i	0.0773289	+	0.133938i	0.902097	−	0.431534i	$-0.142028\pi$
$839$	2.23987	+	3.87957i	0.0773289	+	0.133938i	−0.824768	+	0.565472i	$0.808694\pi$
$840$		0			0
$841$	7.85425	+	13.6040i	0.270836	+	0.469102i
$842$	11.4059	−	19.7556i	0.393073	−	0.680822i
$843$	−72.6458			−2.50205
$844$	−2.70850			−0.0932303
$845$		0			0
$846$	−19.2915	+	33.4139i	−0.663256	+	1.14879i
$847$	−17.4170			−0.598455
$848$	−8.58301			−0.294742
$849$	33.5405	−	58.0939i	1.15111	−	1.99378i
$850$		0			0
$851$	−10.2915	+	17.8254i	−0.352788	+	0.611047i
$852$	17.5830	+	30.4547i	0.602384	+	1.04336i
$853$	−6.29150	−	10.8972i	−0.215417	−	0.373113i	0.737985	−	0.674818i	$-0.235778\pi$
$853$	−6.29150	−	10.8972i	−0.215417	−	0.373113i	−0.953401	+	0.301705i	$0.902444\pi$
$854$	24.5830			0.841213
$855$		0			0
$856$	4.70850			0.160933
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	0.987739	−	0.156112i	$-0.0498959\pi$
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	−0.629066	+	0.777352i	$0.716563\pi$
$858$	−1.70850	−	2.95920i	−0.0583271	−	0.101026i
$859$	6.61438	−	11.4564i	0.225680	−	0.390889i	−0.730843	−	0.682545i	$-0.760873\pi$
$859$	6.61438	−	11.4564i	0.225680	−	0.390889i	0.956523	+	0.291656i	$0.0942064\pi$
$860$		0			0
$861$	−22.4059	+	38.8081i	−0.763590	+	1.32258i
$862$	3.87451			0.131966
$863$	46.9373			1.59776			0.798881	−	0.601489i	$-0.205425\pi$
$863$	46.9373			1.59776			0.798881	+	0.601489i	$0.205425\pi$
$864$	1.32288	−	2.29129i	0.0450051	−	0.0779512i
$865$		0			0
$866$	−13.8745			−0.471475
$867$	−44.9778			−1.52753
$868$	0.291503	−	0.504897i	0.00989424	−	0.0171373i
$869$	1.29150	+	2.23695i	0.0438112	+	0.0758833i
$870$		0			0
$871$	4.64575	+	8.04668i	0.157415	+	0.272651i
$872$	−3.29150	−	5.70105i	−0.111464	−	0.193062i
$873$	57.1660			1.93478
$874$	15.7601	−	2.03884i	0.533094	−	0.0689648i
$875$		0			0
$876$	16.2601	+	28.1634i	0.549379	+	0.951552i
$877$	−18.1771	−	31.4837i	−0.613798	−	1.06313i	−0.990594	−	0.136833i	$-0.956308\pi$
$877$	−18.1771	−	31.4837i	−0.613798	−	1.06313i	0.376796	−	0.926296i	$-0.377026\pi$
$878$	−18.4059	+	31.8799i	−0.621168	+	1.07590i
$879$	17.2804	+	29.9305i	0.582853	+	1.00953i
$880$		0			0
$881$	−5.12549			−0.172682			−0.0863411	−	0.996266i	$-0.527517\pi$
$881$	−5.12549			−0.172682			−0.0863411	+	0.996266i	$0.527517\pi$
$882$	17.1660			0.578010
$883$	20.1974	−	34.9829i	0.679696	−	1.17727i	−0.295376	−	0.955381i	$-0.595445\pi$
$883$	20.1974	−	34.9829i	0.679696	−	1.17727i	0.975072	−	0.221887i	$-0.0712217\pi$
$884$		0			0
$885$		0			0
$886$	5.35425			0.179880
$887$	−19.2915	+	33.4139i	−0.647745	+	1.12193i	0.335915	+	0.941892i	$0.390955\pi$
$887$	−19.2915	+	33.4139i	−0.647745	+	1.12193i	−0.983660	+	0.180035i	$0.942379\pi$
$888$	−7.46863	−	12.9360i	−0.250631	−	0.434105i
$889$	−2.22876	+	3.86032i	−0.0747501	+	0.129471i
$890$		0			0
$891$	1.61438	+	2.79619i	0.0540837	+	0.0936757i
$892$	−28.8118			−0.964689
$893$	16.1771	−	38.8081i	0.541347	−	1.29866i
$894$	13.0627			0.436884
$895$		0			0
$896$	0.822876	+	1.42526i	0.0274903	+	0.0476147i
$897$	−9.64575	+	16.7069i	−0.322062	+	0.557828i
$898$	−6.85425	−	11.8719i	−0.228729	−	0.396171i
$899$	−0.645751	+	1.11847i	−0.0215370	+	0.0373032i
$900$		0			0
$901$		0			0
$902$	3.32288	−	5.75539i	0.110640	−	0.191634i
$903$	1.54249	−	2.67167i	0.0513307	−	0.0889075i
$904$	5.58301			0.185688
$905$		0			0
$906$	−3.88562	+	6.73009i	−0.129091	+	0.223592i
$907$	12.0314	+	20.8389i	0.399495	+	0.691946i	0.993664	−	0.112395i	$-0.0358521\pi$
$907$	12.0314	+	20.8389i	0.399495	+	0.691946i	−0.594168	+	0.804341i	$0.702519\pi$
$908$	−6.32288	+	10.9515i	−0.209832	+	0.363440i
$909$	16.7085	+	28.9400i	0.554186	+	0.959878i
$910$		0			0
$911$	1.06275			0.0352103			0.0176052	−	0.999845i	$-0.494396\pi$
$911$	1.06275			0.0352103			0.0176052	+	0.999845i	$0.494396\pi$
$912$	−4.43725	+	10.6448i	−0.146932	+	0.352483i
$913$	5.12549			0.169629
$914$	−0.562746	−	0.974705i	−0.0186140	−	0.0322404i
$915$		0			0
$916$	−10.0000	+	17.3205i	−0.330409	+	0.572286i
$917$	11.4686	+	19.8642i	0.378727	+	0.655975i
$918$		0			0
$919$	11.8745			0.391704			0.195852	−	0.980633i	$-0.437253\pi$
$919$	11.8745			0.391704			0.195852	+	0.980633i	$0.437253\pi$
$920$		0			0
$921$	−6.14575	+	10.6448i	−0.202509	+	0.350757i
$922$	−11.5830	+	20.0624i	−0.381466	+	0.660718i
$923$	26.5830			0.874990
$924$	2.81176			0.0925002
$925$		0			0
$926$	−7.22876	−	12.5206i	−0.237552	−	0.411452i
$927$	−5.41699	+	9.38251i	−0.177917	+	0.308162i
$928$	−1.82288	−	3.15731i	−0.0598388	−	0.103644i
$929$	−5.79150	−	10.0312i	−0.190013	−	0.329112i	0.755241	−	0.655447i	$-0.227520\pi$
$929$	−5.79150	−	10.0312i	−0.190013	−	0.329112i	−0.945254	+	0.326335i	$0.894186\pi$
$930$		0			0
$931$	−18.5516	+	2.39997i	−0.608005	+	0.0786557i
$932$	12.8745			0.421719
$933$	−11.0516	−	19.1420i	−0.361814	−	0.626681i
$934$	12.3229	+	21.3438i	0.403217	+	0.698392i
$935$		0			0
$936$	−4.00000	−	6.92820i	−0.130744	−	0.226455i
$937$	19.4373	−	33.6663i	0.634987	−	1.09983i	−0.351530	−	0.936176i	$-0.614339\pi$
$937$	19.4373	−	33.6663i	0.634987	−	1.09983i	0.986518	−	0.163654i	$-0.0523281\pi$
$938$	−7.64575			−0.249643
$939$	60.5203			1.97500
$940$		0			0
$941$	−29.5830	+	51.2393i	−0.964378	+	1.67035i	−0.253103	+	0.967439i	$0.581451\pi$
$941$	−29.5830	+	51.2393i	−0.964378	+	1.67035i	−0.711276	+	0.702913i	$0.751882\pi$
$942$	28.0000			0.912289
$943$	−37.5203			−1.22183
$944$	−3.96863	+	6.87386i	−0.129168	+	0.223725i
$945$		0			0
$946$	−0.228757	+	0.396218i	−0.00743752	+	0.0128822i
$947$	27.8745	+	48.2801i	0.905800	+	1.56889i	0.819840	+	0.572593i	$0.194062\pi$
$947$	27.8745	+	48.2801i	0.905800	+	1.56889i	0.0859598	+	0.996299i	$0.472604\pi$
$948$	5.29150	+	9.16515i	0.171860	+	0.297670i
$949$	24.5830			0.797998
$950$		0			0
$951$	15.8745			0.514766
$952$		0			0
$953$	19.7288	+	34.1712i	0.639077	+	1.10691i	0.985636	+	0.168886i	$0.0540169\pi$
$953$	19.7288	+	34.1712i	0.639077	+	1.10691i	−0.346559	+	0.938028i	$0.612650\pi$
$954$	−17.1660	+	29.7324i	−0.555770	+	0.962622i
$955$		0			0
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$	−6.22876			−0.201347
$958$	14.5830			0.471156
$959$	−4.59412	+	7.95725i	−0.148352	+	0.256953i
$960$		0			0
$961$	−30.8745			−0.995952
$962$	−11.2915			−0.364053
$963$	9.41699	−	16.3107i	0.303458	−	0.525605i
$964$	−6.79150	−	11.7632i	−0.218740	−	0.378868i
$965$		0			0
$966$	−7.93725	−	13.7477i	−0.255377	−	0.442326i
$967$	−1.35425	−	2.34563i	−0.0435497	−	0.0754303i	0.843429	−	0.537241i	$-0.180533\pi$
$967$	−1.35425	−	2.34563i	−0.0435497	−	0.0754303i	−0.886979	+	0.461810i	$0.847200\pi$
$968$	10.5830			0.340151
$969$		0			0
$970$		0			0
$971$	−7.19738	−	12.4662i	−0.230975	−	0.400060i	0.727120	−	0.686510i	$-0.240858\pi$
$971$	−7.19738	−	12.4662i	−0.230975	−	0.400060i	−0.958095	+	0.286450i	$0.907525\pi$
$972$	10.5830	+	18.3303i	0.339450	+	0.587945i
$973$	−10.9889	+	19.0333i	−0.352288	+	0.610180i
$974$	11.1144	+	19.2507i	0.356128	+	0.616831i
$975$		0			0
$976$	−14.9373			−0.478130
$977$	−45.4575			−1.45431			−0.727157	−	0.686471i	$-0.759159\pi$
$977$	−45.4575			−1.45431			−0.727157	+	0.686471i	$0.759159\pi$
$978$	15.7915	−	27.3517i	0.504957	−	0.874610i
$979$		0			0
$980$		0			0
$981$	−26.3320			−0.840717
$982$	14.3542	−	24.8623i	0.458062	−	0.793387i
$983$	−15.8745	−	27.4955i	−0.506318	−	0.876969i	−0.999973	−	0.00731102i	$-0.997673\pi$
$983$	−15.8745	−	27.4955i	−0.506318	−	0.876969i	0.493655	−	0.869658i	$-0.335661\pi$
$984$	13.6144	−	23.5808i	0.434011	−	0.751728i
$985$		0			0
$986$		0			0
$987$	−42.0000			−1.33687
$988$	5.29150	+	6.92820i	0.168345	+	0.220416i
$989$	2.58301			0.0821348
$990$		0			0
$991$	22.5830	+	39.1149i	0.717373	+	1.24253i	0.962037	+	0.272918i	$0.0879889\pi$
$991$	22.5830	+	39.1149i	0.717373	+	1.24253i	−0.244664	+	0.969608i	$0.578678\pi$
$992$	−0.177124	+	0.306788i	−0.00562370	+	0.00974054i
$993$	36.7915	+	63.7248i	1.16754	+	2.02224i
$994$	−10.9373	+	18.9439i	−0.346909	+	0.600863i
$995$		0			0
$996$	21.0000			0.665410
$997$	−5.11438	+	8.85836i	−0.161974	+	0.280547i	−0.935577	−	0.353124i	$-0.885119\pi$
$997$	−5.11438	+	8.85836i	−0.161974	+	0.280547i	0.773603	+	0.633671i	$0.218453\pi$
$998$	−15.6144	+	27.0449i	−0.494265	+	0.856091i
$999$	−14.9373			−0.472594

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.e.k.501.1		4
5.2	odd	4		950.2.j.g.349.1		8
5.3	odd	4		950.2.j.g.349.4		8
5.4	even	2		38.2.c.b.7.2	✓	4
15.14	odd	2		342.2.g.f.235.2		4
19.11	even	3	inner	950.2.e.k.201.1		4
20.19	odd	2		304.2.i.e.273.1		4
40.19	odd	2		1216.2.i.k.577.2		4
40.29	even	2		1216.2.i.l.577.1		4
60.59	even	2		2736.2.s.v.577.2		4
95.4	even	18		722.2.e.n.245.1		12
95.9	even	18		722.2.e.n.415.2		12
95.14	odd	18		722.2.e.o.99.2		12
95.24	even	18		722.2.e.n.99.1		12
95.29	odd	18		722.2.e.o.415.1		12
95.34	odd	18		722.2.e.o.245.2		12
95.44	even	18		722.2.e.n.423.1		12
95.49	even	6		38.2.c.b.11.2	yes	4
95.54	even	18		722.2.e.n.595.2		12
95.59	odd	18		722.2.e.o.389.2		12
95.64	even	6		722.2.a.j.1.1		2
95.68	odd	12		950.2.j.g.49.1		8
95.69	odd	6		722.2.a.g.1.2		2
95.74	even	18		722.2.e.n.389.1		12
95.79	odd	18		722.2.e.o.595.1		12
95.84	odd	6		722.2.c.j.429.1		4
95.87	odd	12		950.2.j.g.49.4		8
95.89	odd	18		722.2.e.o.423.2		12
95.94	odd	2		722.2.c.j.653.1		4
285.164	even	6		6498.2.a.bg.1.1		2
285.239	odd	6		342.2.g.f.163.2		4
285.254	odd	6		6498.2.a.ba.1.1		2
380.159	odd	6		5776.2.a.ba.1.2		2
380.239	odd	6		304.2.i.e.49.1		4
380.259	even	6		5776.2.a.z.1.1		2
760.429	even	6		1216.2.i.l.961.1		4
760.619	odd	6		1216.2.i.k.961.2		4
1140.239	even	6		2736.2.s.v.1873.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.b.7.2	✓	4	5.4	even	2
38.2.c.b.11.2	yes	4	95.49	even	6
304.2.i.e.49.1		4	380.239	odd	6
304.2.i.e.273.1		4	20.19	odd	2
342.2.g.f.163.2		4	285.239	odd	6
342.2.g.f.235.2		4	15.14	odd	2
722.2.a.g.1.2		2	95.69	odd	6
722.2.a.j.1.1		2	95.64	even	6
722.2.c.j.429.1		4	95.84	odd	6
722.2.c.j.653.1		4	95.94	odd	2
722.2.e.n.99.1		12	95.24	even	18
722.2.e.n.245.1		12	95.4	even	18
722.2.e.n.389.1		12	95.74	even	18
722.2.e.n.415.2		12	95.9	even	18
722.2.e.n.423.1		12	95.44	even	18
722.2.e.n.595.2		12	95.54	even	18
722.2.e.o.99.2		12	95.14	odd	18
722.2.e.o.245.2		12	95.34	odd	18
722.2.e.o.389.2		12	95.59	odd	18
722.2.e.o.415.1		12	95.29	odd	18
722.2.e.o.423.2		12	95.89	odd	18
722.2.e.o.595.1		12	95.79	odd	18
950.2.e.k.201.1		4	19.11	even	3	inner
950.2.e.k.501.1		4	1.1	even	1	trivial
950.2.j.g.49.1		8	95.68	odd	12
950.2.j.g.49.4		8	95.87	odd	12
950.2.j.g.349.1		8	5.2	odd	4
950.2.j.g.349.4		8	5.3	odd	4
1216.2.i.k.577.2		4	40.19	odd	2
1216.2.i.k.961.2		4	760.619	odd	6
1216.2.i.l.577.1		4	40.29	even	2
1216.2.i.l.961.1		4	760.429	even	6
2736.2.s.v.577.2		4	60.59	even	2
2736.2.s.v.1873.2		4	1140.239	even	6
5776.2.a.z.1.1		2	380.259	even	6
5776.2.a.ba.1.2		2	380.159	odd	6
6498.2.a.ba.1.1		2	285.254	odd	6
6498.2.a.bg.1.1		2	285.164	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.32288 - 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.32288 - 2.29129i) q^{6} +1.64575 q^{7} -1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.32288 - 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.32288 - 2.29129i) q^{6} +1.64575 q^{7} -1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +0.645751 q^{11} +2.64575 q^{12} +(1.00000 - 1.73205i) q^{13} +(0.822876 + 1.42526i) q^{14} +(-0.500000 - 0.866025i) q^{16} -4.00000 q^{18} +(4.32288 - 0.559237i) q^{19} +(-2.17712 - 3.77089i) q^{21} +(0.322876 + 0.559237i) q^{22} +(1.82288 - 3.15731i) q^{23} +(1.32288 + 2.29129i) q^{24} +2.00000 q^{26} +2.64575 q^{27} +(-0.822876 + 1.42526i) q^{28} +(1.82288 - 3.15731i) q^{29} -0.354249 q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.854249 - 1.47960i) q^{33} +(-2.00000 - 3.46410i) q^{36} -5.64575 q^{37} +(2.64575 + 3.46410i) q^{38} -5.29150 q^{39} +(-5.14575 - 8.91270i) q^{41} +(2.17712 - 3.77089i) q^{42} +(0.354249 + 0.613577i) q^{43} +(-0.322876 + 0.559237i) q^{44} +3.64575 q^{46} +(4.82288 - 8.35347i) q^{47} +(-1.32288 + 2.29129i) q^{48} -4.29150 q^{49} +(1.00000 + 1.73205i) q^{52} +(4.29150 - 7.43310i) q^{53} +(1.32288 + 2.29129i) q^{54} -1.64575 q^{56} +(-7.00000 - 9.16515i) q^{57} +3.64575 q^{58} +(-3.96863 - 6.87386i) q^{59} +(7.46863 - 12.9360i) q^{61} +(-0.177124 - 0.306788i) q^{62} +(-3.29150 + 5.70105i) q^{63} +1.00000 q^{64} +(0.854249 - 1.47960i) q^{66} +(-2.32288 + 4.02334i) q^{67} -9.64575 q^{69} +(6.64575 + 11.5108i) q^{71} +(2.00000 - 3.46410i) q^{72} +(6.14575 + 10.6448i) q^{73} +(-2.82288 - 4.88936i) q^{74} +(-1.67712 + 4.02334i) q^{76} +1.06275 q^{77} +(-2.64575 - 4.58258i) q^{78} +(2.00000 + 3.46410i) q^{79} +(2.50000 + 4.33013i) q^{81} +(5.14575 - 8.91270i) q^{82} +7.93725 q^{83} +4.35425 q^{84} +(-0.354249 + 0.613577i) q^{86} -9.64575 q^{87} -0.645751 q^{88} +(1.64575 - 2.85052i) q^{91} +(1.82288 + 3.15731i) q^{92} +(0.468627 + 0.811686i) q^{93} +9.64575 q^{94} -2.64575 q^{96} +(-7.14575 - 12.3768i) q^{97} +(-2.14575 - 3.71655i) q^{98} +(-1.29150 + 2.23695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^7 - 4 * q^8 - 8 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{7} - 4 q^{8} - 8 q^{9} - 8 q^{11} + 4 q^{13} - 2 q^{14} - 2 q^{16} - 16 q^{18} + 12 q^{19} - 14 q^{21} - 4 q^{22} + 2 q^{23} + 8 q^{26} + 2 q^{28} + 2 q^{29} - 12 q^{31} + 2 q^{32} - 14 q^{33} - 8 q^{36} - 12 q^{37} - 10 q^{41} + 14 q^{42} + 12 q^{43} + 4 q^{44} + 4 q^{46} + 14 q^{47} + 4 q^{49} + 4 q^{52} - 4 q^{53} + 4 q^{56} - 28 q^{57} + 4 q^{58} + 14 q^{61} - 6 q^{62} + 8 q^{63} + 4 q^{64} + 14 q^{66} - 4 q^{67} - 28 q^{69} + 16 q^{71} + 8 q^{72} + 14 q^{73} - 6 q^{74} - 12 q^{76} + 36 q^{77} + 8 q^{79} + 10 q^{81} + 10 q^{82} + 28 q^{84} - 12 q^{86} - 28 q^{87} + 8 q^{88} - 4 q^{91} + 2 q^{92} - 14 q^{93} + 28 q^{94} - 18 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^7 - 4 * q^8 - 8 * q^9 - 8 * q^11 + 4 * q^13 - 2 * q^14 - 2 * q^16 - 16 * q^18 + 12 * q^19 - 14 * q^21 - 4 * q^22 + 2 * q^23 + 8 * q^26 + 2 * q^28 + 2 * q^29 - 12 * q^31 + 2 * q^32 - 14 * q^33 - 8 * q^36 - 12 * q^37 - 10 * q^41 + 14 * q^42 + 12 * q^43 + 4 * q^44 + 4 * q^46 + 14 * q^47 + 4 * q^49 + 4 * q^52 - 4 * q^53 + 4 * q^56 - 28 * q^57 + 4 * q^58 + 14 * q^61 - 6 * q^62 + 8 * q^63 + 4 * q^64 + 14 * q^66 - 4 * q^67 - 28 * q^69 + 16 * q^71 + 8 * q^72 + 14 * q^73 - 6 * q^74 - 12 * q^76 + 36 * q^77 + 8 * q^79 + 10 * q^81 + 10 * q^82 + 28 * q^84 - 12 * q^86 - 28 * q^87 + 8 * q^88 - 4 * q^91 + 2 * q^92 - 14 * q^93 + 28 * q^94 - 18 * q^97 + 2 * q^98 + 16 * q^99

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