LMFDB - Embedded newform 693.2.by.c.163.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(37,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 10, 6]))

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

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

chi := DirichletCharacter("693.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.by (of order $15$, degree $8$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			163.7
Character	$\chi$	$=$	693.163
Dual form			693.2.by.c.676.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.49404 + 1.65930i) q^{2} +(-0.312065 + 2.96910i) q^{4} +(1.00537 + 0.213698i) q^{5} +(2.49708 - 0.874397i) q^{7} +(-1.78011 + 1.29333i) q^{8} +O(q^{10})$	\(q+(1.49404 + 1.65930i) q^{2} +(-0.312065 + 2.96910i) q^{4} +(1.00537 + 0.213698i) q^{5} +(2.49708 - 0.874397i) q^{7} +(-1.78011 + 1.29333i) q^{8} +(1.14748 + 1.98749i) q^{10} +(0.216549 + 3.30955i) q^{11} +(1.56619 - 4.82025i) q^{13} +(5.18164 + 2.83703i) q^{14} +(1.03484 + 0.219963i) q^{16} +(-1.74191 + 1.93458i) q^{17} +(0.140718 + 1.33884i) q^{19} +(-0.948233 + 2.91836i) q^{20} +(-5.16801 + 5.30393i) q^{22} +(-0.946580 + 1.63952i) q^{23} +(-3.60262 - 1.60399i) q^{25} +(10.3382 - 4.60287i) q^{26} +(1.81692 + 7.68697i) q^{28} +(-3.25868 - 2.36757i) q^{29} +(-3.21210 + 0.682752i) q^{31} +(3.38146 + 5.85686i) q^{32} -5.81254 q^{34} +(2.69735 - 0.345471i) q^{35} +(-7.36469 + 3.27897i) q^{37} +(-2.01131 + 2.23379i) q^{38} +(-2.06605 + 0.919867i) q^{40} +(0.828434 - 0.601893i) q^{41} +9.19303 q^{43} +(-9.89396 - 0.389839i) q^{44} +(-4.13470 + 0.878858i) q^{46} +(-1.03382 - 9.83610i) q^{47} +(5.47086 - 4.36689i) q^{49} +(-2.72097 - 8.37428i) q^{50} +(13.8230 + 6.15442i) q^{52} +(-11.9272 + 2.53519i) q^{53} +(-0.489532 + 3.37360i) q^{55} +(-3.31421 + 4.78607i) q^{56} +(-0.940093 - 8.94438i) q^{58} +(0.645139 - 6.13808i) q^{59} +(3.41290 + 0.725434i) q^{61} +(-5.93191 - 4.30978i) q^{62} +(-4.01240 + 12.3489i) q^{64} +(2.60468 - 4.51144i) q^{65} +(-0.556014 - 0.963044i) q^{67} +(-5.20038 - 5.77561i) q^{68} +(4.60320 + 3.95958i) q^{70} +(2.29639 + 7.06755i) q^{71} +(-1.15674 + 11.0057i) q^{73} +(-16.4440 - 7.32133i) q^{74} -4.01908 q^{76} +(3.43460 + 8.07487i) q^{77} +(-9.35663 - 10.3916i) q^{79} +(0.993397 + 0.442289i) q^{80} +(2.23644 + 0.475370i) q^{82} +(-1.44739 - 4.45461i) q^{83} +(-2.16468 + 1.57273i) q^{85} +(13.7348 + 15.2540i) q^{86} +(-4.66581 - 5.61130i) q^{88} +(9.17730 - 15.8955i) q^{89} +(-0.303894 - 13.4060i) q^{91} +(-4.57252 - 3.32213i) q^{92} +(14.7765 - 16.4110i) q^{94} +(-0.144635 + 1.37611i) q^{95} +(-2.19712 + 6.76203i) q^{97} +(15.4197 + 2.55350i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{2} + 10 q^{4} + 4 q^{5} - q^{7} - 8 q^{8}+O(q^{10}) $ 64 * q - 4 * q^2 + 10 * q^4 + 4 * q^5 - q^7 - 8 * q^8	$ 64 q - 4 q^{2} + 10 q^{4} + 4 q^{5} - q^{7} - 8 q^{8} - 14 q^{10} - 11 q^{11} - 8 q^{13} - 6 q^{14} + 4 q^{17} - 2 q^{19} - 24 q^{20} - 14 q^{22} - 10 q^{25} - 4 q^{26} + 29 q^{28} + 58 q^{29} - 19 q^{31} + 64 q^{32} - 88 q^{34} - 17 q^{35} - 20 q^{37} - 29 q^{38} + 51 q^{40} + 68 q^{41} + 92 q^{43} + 21 q^{44} - 5 q^{46} + 26 q^{47} + 37 q^{49} + 10 q^{50} - 14 q^{52} + 3 q^{53} - 32 q^{55} - 24 q^{56} + 52 q^{58} - 7 q^{59} - 21 q^{61} - 92 q^{62} - 72 q^{64} + 66 q^{65} - 4 q^{67} + 17 q^{68} - q^{70} - 58 q^{71} - 3 q^{73} + 28 q^{74} + 168 q^{76} + 34 q^{77} + 9 q^{79} + 5 q^{80} - 42 q^{82} - 60 q^{83} + 110 q^{85} - 13 q^{86} + 92 q^{88} + 10 q^{89} + 10 q^{91} - 110 q^{92} - 46 q^{94} - 43 q^{95} + 64 q^{97} + 88 q^{98}+O(q^{100}) $ 64 * q - 4 * q^2 + 10 * q^4 + 4 * q^5 - q^7 - 8 * q^8 - 14 * q^10 - 11 * q^11 - 8 * q^13 - 6 * q^14 + 4 * q^17 - 2 * q^19 - 24 * q^20 - 14 * q^22 - 10 * q^25 - 4 * q^26 + 29 * q^28 + 58 * q^29 - 19 * q^31 + 64 * q^32 - 88 * q^34 - 17 * q^35 - 20 * q^37 - 29 * q^38 + 51 * q^40 + 68 * q^41 + 92 * q^43 + 21 * q^44 - 5 * q^46 + 26 * q^47 + 37 * q^49 + 10 * q^50 - 14 * q^52 + 3 * q^53 - 32 * q^55 - 24 * q^56 + 52 * q^58 - 7 * q^59 - 21 * q^61 - 92 * q^62 - 72 * q^64 + 66 * q^65 - 4 * q^67 + 17 * q^68 - q^70 - 58 * q^71 - 3 * q^73 + 28 * q^74 + 168 * q^76 + 34 * q^77 + 9 * q^79 + 5 * q^80 - 42 * q^82 - 60 * q^83 + 110 * q^85 - 13 * q^86 + 92 * q^88 + 10 * q^89 + 10 * q^91 - 110 * q^92 - 46 * q^94 - 43 * q^95 + 64 * q^97 + 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	1.49404	+	1.65930i	1.05645	+	1.17330i	0.984407	+	0.175903i	$0.0562846\pi$
$2$	1.49404	+	1.65930i	1.05645	+	1.17330i	0.0720411	+	0.997402i	$0.477049\pi$
$3$		0			0
$3$		0			0
$4$	−0.312065	+	2.96910i	−0.156033	+	1.48455i
$5$	1.00537	+	0.213698i	0.449615	+	0.0955687i	0.427154	−	0.904179i	$-0.359516\pi$
$5$	1.00537	+	0.213698i	0.449615	+	0.0955687i	0.0224617	+	0.999748i	$0.492850\pi$
$6$		0			0
$7$	2.49708	−	0.874397i	0.943809	−	0.330491i
$7$	2.49708	−	0.874397i	0.943809	−	0.330491i
$8$	−1.78011	+	1.29333i	−0.629365	+	0.457260i
$9$		0			0
$10$	1.14748	+	1.98749i	0.362864	+	0.628499i
$11$	0.216549	+	3.30955i	0.0652919	+	0.997866i
$11$	0.216549	+	3.30955i	0.0652919	+	0.997866i
$12$		0			0
$13$	1.56619	−	4.82025i	0.434384	−	1.33690i	−0.459333	−	0.888264i	$-0.651912\pi$
$13$	1.56619	−	4.82025i	0.434384	−	1.33690i	0.893717	−	0.448632i	$-0.148088\pi$
$14$	5.18164	+	2.83703i	1.38485	+	0.758229i
$15$		0			0
$16$	1.03484	+	0.219963i	0.258711	+	0.0549908i
$17$	−1.74191	+	1.93458i	−0.422474	+	0.469205i	−0.916380	−	0.400311i	$-0.868902\pi$
$17$	−1.74191	+	1.93458i	−0.422474	+	0.469205i	0.493905	+	0.869516i	$0.335569\pi$
$18$		0			0
$19$	0.140718	+	1.33884i	0.0322830	+	0.307152i	0.998734	+	0.0503013i	$0.0160182\pi$
$19$	0.140718	+	1.33884i	0.0322830	+	0.307152i	−0.966451	+	0.256851i	$0.917315\pi$
$20$	−0.948233	+	2.91836i	−0.212031	+	0.652565i
$21$		0			0
$22$	−5.16801	+	5.30393i	−1.10182	+	1.13080i
$23$	−0.946580	+	1.63952i	−0.197376	+	0.341864i	−0.947677	−	0.319232i	$-0.896575\pi$
$23$	−0.946580	+	1.63952i	−0.197376	+	0.341864i	0.750301	+	0.661096i	$0.229909\pi$
$24$		0			0
$25$	−3.60262	−	1.60399i	−0.720525	−	0.320798i
$26$	10.3382	−	4.60287i	2.02749	−	0.902697i
$27$		0			0
$28$	1.81692	+	7.68697i	0.343366	+	1.45270i
$29$	−3.25868	−	2.36757i	−0.605121	−	0.439646i	0.242572	−	0.970133i	$-0.422009\pi$
$29$	−3.25868	−	2.36757i	−0.605121	−	0.439646i	−0.847693	+	0.530487i	$0.822009\pi$
$30$		0			0
$31$	−3.21210	+	0.682752i	−0.576910	+	0.122626i	−0.487120	−	0.873335i	$-0.661953\pi$
$31$	−3.21210	+	0.682752i	−0.576910	+	0.122626i	−0.0897892	+	0.995961i	$0.528619\pi$
$32$	3.38146	+	5.85686i	0.597763	+	1.03536i
$33$		0			0
$34$	−5.81254			−0.996843
$35$	2.69735	−	0.345471i	0.455936	−	0.0583953i
$36$		0			0
$37$	−7.36469	+	3.27897i	−1.21075	+	0.539060i	−0.909986	−	0.414639i	$-0.863908\pi$
$37$	−7.36469	+	3.27897i	−1.21075	+	0.539060i	−0.300762	+	0.953699i	$0.597241\pi$
$38$	−2.01131	+	2.23379i	−0.326278	+	0.362368i
$39$		0			0
$40$	−2.06605	+	0.919867i	−0.326672	+	0.145444i
$41$	0.828434	−	0.601893i	0.129380	−	0.0939999i	−0.521213	−	0.853426i	$-0.674520\pi$
$41$	0.828434	−	0.601893i	0.129380	−	0.0939999i	0.650593	+	0.759427i	$0.274520\pi$
$42$		0			0
$43$	9.19303			1.40192			0.700962	−	0.713199i	$-0.252754\pi$
$43$	9.19303			1.40192			0.700962	+	0.713199i	$0.252754\pi$
$44$	−9.89396	−	0.389839i	−1.49157	−	0.0587705i
$45$		0			0
$46$	−4.13470	+	0.878858i	−0.609628	+	0.129581i
$47$	−1.03382	−	9.83610i	−0.150798	−	1.43474i	−0.764204	−	0.644975i	$-0.776868\pi$
$47$	−1.03382	−	9.83610i	−0.150798	−	1.43474i	0.613406	−	0.789768i	$-0.289799\pi$
$48$		0			0
$49$	5.47086	−	4.36689i	0.781551	−	0.623841i
$50$	−2.72097	−	8.37428i	−0.384803	−	1.18430i
$51$		0			0
$52$	13.8230	+	6.15442i	1.91691	+	0.853464i
$53$	−11.9272	+	2.53519i	−1.63832	+	0.348236i	−0.932784	−	0.360437i	$-0.882628\pi$
$53$	−11.9272	+	2.53519i	−1.63832	+	0.348236i	−0.705537	+	0.708673i	$0.749294\pi$
$54$		0			0
$55$	−0.489532	+	3.37360i	−0.0660085	+	0.454896i
$56$	−3.31421	+	4.78607i	−0.442880	+	0.639566i
$57$		0			0
$58$	−0.940093	−	8.94438i	−0.123440	−	1.17446i
$59$	0.645139	−	6.13808i	0.0839899	−	0.799110i	−0.868735	−	0.495277i	$-0.835067\pi$
$59$	0.645139	−	6.13808i	0.0839899	−	0.799110i	0.952725	−	0.303834i	$-0.0982667\pi$
$60$		0			0
$61$	3.41290	+	0.725434i	0.436977	+	0.0928823i	0.421147	−	0.906992i	$-0.361628\pi$
$61$	3.41290	+	0.725434i	0.436977	+	0.0928823i	0.0158300	+	0.999875i	$0.494961\pi$
$62$	−5.93191	−	4.30978i	−0.753353	−	0.547343i
$63$		0			0
$64$	−4.01240	+	12.3489i	−0.501550	+	1.54361i
$65$	2.60468	−	4.51144i	0.323071	−	0.559575i
$66$		0			0
$67$	−0.556014	−	0.963044i	−0.0679279	−	0.117655i	0.830061	−	0.557672i	$-0.188305\pi$
$67$	−0.556014	−	0.963044i	−0.0679279	−	0.117655i	−0.897989	+	0.440018i	$0.854972\pi$
$68$	−5.20038	−	5.77561i	−0.630639	−	0.700396i
$69$		0			0
$70$	4.60320	+	3.95958i	0.550188	+	0.473260i
$71$	2.29639	+	7.06755i	0.272531	+	0.838764i	0.989862	+	0.142032i	$0.0453635\pi$
$71$	2.29639	+	7.06755i	0.272531	+	0.838764i	−0.717331	+	0.696732i	$0.754636\pi$
$72$		0			0
$73$	−1.15674	+	11.0057i	−0.135386	+	1.28811i	0.690109	+	0.723706i	$0.257563\pi$
$73$	−1.15674	+	11.0057i	−0.135386	+	1.28811i	−0.825495	+	0.564409i	$0.809104\pi$
$74$	−16.4440	−	7.32133i	−1.91157	−	0.851088i
$75$		0			0
$76$	−4.01908			−0.461020
$77$	3.43460	+	8.07487i	0.391409	+	0.920217i
$78$		0			0
$79$	−9.35663	−	10.3916i	−1.05270	−	1.16915i	−0.985197	−	0.171426i	$-0.945162\pi$
$79$	−9.35663	−	10.3916i	−1.05270	−	1.16915i	−0.0675061	−	0.997719i	$-0.521504\pi$
$80$	0.993397	+	0.442289i	0.111065	+	0.0494494i
$81$		0			0
$82$	2.23644	+	0.475370i	0.246974	+	0.0524958i
$83$	−1.44739	−	4.45461i	−0.158872	−	0.488957i	0.839661	−	0.543111i	$-0.182754\pi$
$83$	−1.44739	−	4.45461i	−0.158872	−	0.488957i	−0.998533	+	0.0541542i	$0.982754\pi$
$84$		0			0
$85$	−2.16468	+	1.57273i	−0.234792	+	0.170587i
$86$	13.7348	+	15.2540i	1.48106	+	1.64488i
$87$		0			0
$88$	−4.66581	−	5.61130i	−0.497377	−	0.598166i
$89$	9.17730	−	15.8955i	0.972792	−	1.68492i	0.285754	−	0.958303i	$-0.407756\pi$
$89$	9.17730	−	15.8955i	0.972792	−	1.68492i	0.687038	−	0.726621i	$-0.258911\pi$
$90$		0			0
$91$	−0.303894	−	13.4060i	−0.0318568	−	1.40533i
$92$	−4.57252	−	3.32213i	−0.476718	−	0.346356i
$93$		0			0
$94$	14.7765	−	16.4110i	1.52408	−	1.69266i
$95$	−0.144635	+	1.37611i	−0.0148392	+	0.141185i
$96$		0			0
$97$	−2.19712	+	6.76203i	−0.223083	+	0.686580i	0.775397	+	0.631474i	$0.217550\pi$
$97$	−2.19712	+	6.76203i	−0.223083	+	0.686580i	−0.998481	+	0.0551061i	$0.982450\pi$
$98$	15.4197	+	2.55350i	1.55762	+	0.257942i
$99$		0			0
$100$	5.88667	−	10.1960i	0.588667	−	1.01960i
$101$	6.12292	−	1.30147i	0.609253	−	0.129501i	0.107055	−	0.994253i	$-0.465858\pi$
$101$	6.12292	−	1.30147i	0.609253	−	0.129501i	0.502199	+	0.864752i	$0.332525\pi$
$102$		0			0
$103$	9.63859	−	4.29138i	0.949719	−	0.422842i	0.127389	−	0.991853i	$-0.459340\pi$
$103$	9.63859	−	4.29138i	0.949719	−	0.422842i	0.822330	+	0.569011i	$0.192674\pi$
$104$	3.44616	+	10.6062i	0.337923	+	1.04002i
$105$		0			0
$106$	−22.0264	−	16.0031i	−2.13939	−	1.55436i
$107$	−0.669658	−	6.37137i	−0.0647383	−	0.615944i	−0.978005	−	0.208582i	$-0.933115\pi$
$107$	−0.669658	−	6.37137i	−0.0647383	−	0.615944i	0.913267	−	0.407362i	$-0.133551\pi$
$108$		0			0
$109$	0.0464491	+	0.0804522i	0.00444901	+	0.00770592i	0.868241	−	0.496142i	$-0.165250\pi$
$109$	0.0464491	+	0.0804522i	0.00444901	+	0.00770592i	−0.863792	+	0.503848i	$0.831917\pi$
$110$	−6.32921	+	4.22802i	−0.603466	+	0.403126i
$111$		0			0
$112$	2.77643	−	0.355599i	0.262348	−	0.0336010i
$113$	9.18338	−	6.67212i	0.863900	−	0.627660i	−0.0650432	−	0.997882i	$-0.520719\pi$
$113$	9.18338	−	6.67212i	0.863900	−	0.627660i	0.928943	+	0.370222i	$0.120719\pi$
$114$		0			0
$115$	−1.30203	+	1.44605i	−0.121415	+	0.134845i
$116$	8.04647	−	8.93651i	0.747096	−	0.829734i
$117$		0			0
$118$	11.1488	−	8.10009i	1.02633	−	0.745673i
$119$	−2.65809	+	6.35393i	−0.243667	+	0.582464i
$120$		0			0
$121$	−10.9062	+	1.43336i	−0.991474	+	0.130305i
$122$	3.89531	+	6.74687i	0.352664	+	0.610833i
$123$		0			0
$124$	−1.02478	−	9.75010i	−0.0920277	−	0.875585i
$125$	−7.43687	−	5.40320i	−0.665174	−	0.483277i
$126$		0			0
$127$	3.42572	+	10.5433i	0.303984	+	0.935566i	0.980054	+	0.198729i	$0.0636814\pi$
$127$	3.42572	+	10.5433i	0.303984	+	0.935566i	−0.676071	+	0.736837i	$0.736319\pi$
$128$	−14.1288	+	6.29055i	−1.24882	+	0.556012i
$129$		0			0
$130$	11.3774	−	2.41833i	0.997861	−	0.212102i
$131$	−2.66318	+	4.61277i	−0.232683	+	0.403019i	−0.958597	−	0.284767i	$-0.908084\pi$
$131$	−2.66318	+	4.61277i	−0.232683	+	0.403019i	0.725914	+	0.687786i	$0.241417\pi$
$132$		0			0
$133$	1.52207	+	3.22016i	0.131980	+	0.279224i
$134$	0.767274	−	2.36143i	0.0662824	−	0.203996i
$135$		0			0
$136$	0.598740	−	5.69663i	0.0513415	−	0.488482i
$137$	2.72980	−	3.03175i	0.233222	−	0.259020i	−0.615162	−	0.788401i	$-0.710909\pi$
$137$	2.72980	−	3.03175i	0.233222	−	0.259020i	0.848384	+	0.529381i	$0.177576\pi$
$138$		0			0
$139$	−15.9478	−	11.5867i	−1.35267	−	0.982774i	−0.998873	−	0.0474531i	$-0.984890\pi$
$139$	−15.9478	−	11.5867i	−1.35267	−	0.982774i	−0.353799	−	0.935321i	$-0.615110\pi$
$140$	0.183989	+	8.11652i	0.0155499	+	0.685971i
$141$		0			0
$142$	−8.29631	+	14.3696i	−0.696211	+	1.20587i
$143$	16.2920	+	4.13957i	1.36240	+	0.346168i
$144$		0			0
$145$	−2.77023	−	3.07666i	−0.230055	−	0.255502i
$146$	−19.9900	+	14.5236i	−1.65438	+	1.20198i
$147$		0			0
$148$	−7.43734	−	22.8898i	−0.611345	−	1.88153i
$149$	4.68041	+	0.994852i	0.383434	+	0.0815015i	0.395596	−	0.918425i	$-0.370538\pi$
$149$	4.68041	+	0.994852i	0.383434	+	0.0815015i	−0.0121618	+	0.999926i	$0.503871\pi$
$150$		0			0
$151$	−5.02084	−	2.23542i	−0.408590	−	0.181916i	0.192141	−	0.981367i	$-0.438457\pi$
$151$	−5.02084	−	2.23542i	−0.408590	−	0.181916i	−0.600731	+	0.799451i	$0.705124\pi$
$152$	−1.98206	−	2.20130i	−0.160766	−	0.178549i
$153$		0			0
$154$	−8.26722	+	17.7633i	−0.666192	+	1.43140i
$155$	−3.37525			−0.271107
$156$		0			0
$157$	18.9942	+	8.45676i	1.51590	+	0.674923i	0.985007	−	0.172516i	$-0.0551895\pi$
$157$	18.9942	+	8.45676i	1.51590	+	0.674923i	0.530894	+	0.847438i	$0.321856\pi$
$158$	3.26359	−	31.0510i	0.259637	−	2.47028i
$159$		0			0
$160$	2.14802	+	6.61092i	0.169816	+	0.522639i
$161$	−0.930094	+	4.92172i	−0.0733017	+	0.387886i
$162$		0			0
$163$	−4.89610	−	5.43767i	−0.383492	−	0.425911i	0.520233	−	0.854024i	$-0.325845\pi$
$163$	−4.89610	−	5.43767i	−0.383492	−	0.425911i	−0.903725	+	0.428113i	$0.859179\pi$
$164$	1.52856	+	2.64754i	0.119360	+	0.206738i
$165$		0			0
$166$	5.22908	−	9.05704i	0.405856	−	0.702963i
$167$	−1.84641	+	5.68265i	−0.142879	+	0.439737i	−0.996732	−	0.0807774i	$-0.974260\pi$
$167$	−1.84641	+	5.68265i	−0.142879	+	0.439737i	0.853853	+	0.520514i	$0.174260\pi$
$168$		0			0
$169$	−10.2646	−	7.45766i	−0.789584	−	0.573666i
$170$	−5.84376	−	1.24213i	−0.448196	−	0.0952670i
$171$		0			0
$172$	−2.86882	+	27.2950i	−0.218746	+	2.08123i
$173$	0.154714	+	1.47200i	0.0117627	+	0.111914i	0.998828	−	0.0484057i	$-0.0154140\pi$
$173$	0.154714	+	1.47200i	0.0117627	+	0.111914i	−0.987065	+	0.160320i	$0.948747\pi$
$174$		0			0
$175$	−10.3986	−	0.855178i	−0.786059	−	0.0646454i
$176$	−0.503884	+	3.47250i	−0.0379817	+	0.261750i
$177$		0			0
$178$	40.0868	−	8.52072i	3.00463	−	0.638655i
$179$	4.93541	+	2.19738i	0.368890	+	0.164240i	0.582805	−	0.812612i	$-0.301955\pi$
$179$	4.93541	+	2.19738i	0.368890	+	0.164240i	−0.213916	+	0.976852i	$0.568622\pi$
$180$		0			0
$181$	7.70985	+	23.7285i	0.573068	+	1.76372i	0.642664	+	0.766148i	$0.277829\pi$
$181$	7.70985	+	23.7285i	0.573068	+	1.76372i	−0.0695958	+	0.997575i	$0.522171\pi$
$182$	21.7907	−	20.5335i	1.61523	−	1.52204i
$183$		0			0
$184$	−0.435423	−	4.14278i	−0.0320998	−	0.305409i
$185$	−8.10496	+	1.72276i	−0.595888	+	0.126660i
$186$		0			0
$187$	−6.77980	−	5.34599i	−0.495788	−	0.390937i
$188$	29.5270			2.15348
$189$		0			0
$190$	−2.49947	+	1.81597i	−0.181330	+	0.131744i
$191$	−20.8770	+	9.29503i	−1.51061	+	0.672565i	−0.984101	−	0.177607i	$-0.943164\pi$
$191$	−20.8770	+	9.29503i	−1.51061	+	0.672565i	−0.526504	+	0.850172i	$0.676498\pi$
$192$		0			0
$193$	−4.91168	+	5.45497i	−0.353550	+	0.392657i	−0.893517	−	0.449029i	$-0.851770\pi$
$193$	−4.91168	+	5.45497i	−0.353550	+	0.392657i	0.539967	+	0.841686i	$0.318437\pi$
$194$	−14.5028	+	6.45708i	−1.04124	+	0.463592i
$195$		0			0
$196$	11.2585	+	17.6063i	0.804176	+	1.25759i
$197$	−26.2782			−1.87224			−0.936121	−	0.351679i	$-0.885611\pi$
$197$	−26.2782			−1.87224			−0.936121	+	0.351679i	$0.885611\pi$
$198$		0			0
$199$	−6.06430	−	10.5037i	−0.429887	−	0.744586i	0.566976	−	0.823734i	$-0.308113\pi$
$199$	−6.06430	−	10.5037i	−0.429887	−	0.744586i	−0.996863	+	0.0791483i	$0.974780\pi$
$200$	8.48756	−	1.80409i	0.600161	−	0.127568i
$201$		0			0
$202$	11.3074	+	8.21534i	0.795589	+	0.578029i
$203$	−10.2074	−	3.06264i	−0.716418	−	0.214955i
$204$		0			0
$205$	0.961507	−	0.428090i	0.0671546	−	0.0298991i
$206$	21.5212	+	9.58184i	1.49945	+	0.667599i
$207$		0			0
$208$	2.68104	−	4.64370i	0.185897	−	0.321983i
$209$	−4.40050	+	0.755639i	−0.304389	+	0.0522686i
$210$		0			0
$211$	5.52303	−	16.9981i	0.380221	−	1.17020i	−0.559667	−	0.828718i	$-0.689071\pi$
$211$	5.52303	−	16.9981i	0.380221	−	1.17020i	0.939888	−	0.341483i	$-0.110929\pi$
$212$	−3.80520	−	36.2041i	−0.261342	−	2.48651i
$213$		0			0
$214$	9.57155	−	10.6303i	0.654297	−	0.726671i
$215$	9.24240	+	1.96453i	0.630326	+	0.133980i
$216$		0			0
$217$	−7.42388	+	4.51354i	−0.503966	+	0.306399i
$218$	−0.0640976	+	0.197272i	−0.00434124	+	0.0133610i
$219$		0			0
$220$	−9.86379	−	2.50625i	−0.665017	−	0.168972i
$221$	6.59700	+	11.4263i	0.443762	+	0.768619i
$222$		0			0
$223$	1.70719	−	1.24034i	0.114322	−	0.0830596i	−0.529155	−	0.848525i	$-0.677491\pi$
$223$	1.70719	−	1.24034i	0.114322	−	0.0830596i	0.643477	+	0.765465i	$0.277491\pi$
$224$	13.5650	+	11.6683i	0.906350	+	0.779623i
$225$		0			0
$226$	24.7914	+	5.26958i	1.64910	+	0.350528i
$227$	−1.18037	+	11.2305i	−0.0783440	+	0.745393i	0.882875	+	0.469608i	$0.155605\pi$
$227$	−1.18037	+	11.2305i	−0.0783440	+	0.745393i	−0.961219	+	0.275786i	$0.911062\pi$
$228$		0			0
$229$	18.6521	+	20.7153i	1.23257	+	1.36890i	0.905748	+	0.423817i	$0.139310\pi$
$229$	18.6521	+	20.7153i	1.23257	+	1.36890i	0.326819	+	0.945087i	$0.394023\pi$
$230$	−4.34472			−0.286482
$231$		0			0
$232$	8.86285			0.581875
$233$	4.59822	+	5.10684i	0.301240	+	0.334560i	0.874693	−	0.484678i	$-0.161063\pi$
$233$	4.59822	+	5.10684i	0.301240	+	0.334560i	−0.573453	+	0.819238i	$0.694397\pi$
$234$		0			0
$235$	1.06259	−	10.1099i	0.0693156	−	0.659494i
$236$	18.0233	+	3.83096i	1.17321	+	0.249375i
$237$		0			0
$238$	−14.5144	+	5.08247i	−0.940829	+	0.329448i
$239$	9.02995	−	6.56065i	0.584099	−	0.424373i	−0.256100	−	0.966650i	$-0.582438\pi$
$239$	9.02995	−	6.56065i	0.584099	−	0.424373i	0.840200	+	0.542277i	$0.182438\pi$
$240$		0			0
$241$	−8.25275	−	14.2942i	−0.531606	−	0.920769i	−0.999319	−	0.0368888i	$-0.988255\pi$
$241$	−8.25275	−	14.2942i	−0.531606	−	0.920769i	0.467713	−	0.883880i	$-0.345078\pi$
$242$	−18.6727	−	15.9552i	−1.20033	−	1.02564i
$243$		0			0
$244$	−3.21893	+	9.90686i	−0.206071	+	0.634222i
$245$	6.43344	−	3.22123i	0.411017	−	0.205797i
$246$		0			0
$247$	6.67395	+	1.41859i	0.424653	+	0.0902629i
$248$	4.83487	−	5.36967i	0.307015	−	0.340974i
$249$		0			0
$250$	−2.14545	−	20.4126i	−0.135690	−	1.29101i
$251$	7.05468	−	21.7121i	0.445288	−	1.37045i	−0.436880	−	0.899520i	$-0.643917\pi$
$251$	7.05468	−	21.7121i	0.445288	−	1.37045i	0.882168	−	0.470935i	$-0.156083\pi$
$252$		0			0
$253$	−5.63107	−	2.77771i	−0.354022	−	0.174633i
$254$	−12.3763	+	21.4365i	−0.776561	+	1.34504i
$255$		0			0
$256$	−7.82333	−	3.48317i	−0.488958	−	0.217698i
$257$	−6.82073	+	3.03679i	−0.425466	+	0.189430i	−0.608288	−	0.793716i	$-0.708143\pi$
$257$	−6.82073	+	3.03679i	−0.425466	+	0.189430i	0.182822	+	0.983146i	$0.441477\pi$
$258$		0			0
$259$	−15.5231	+	14.6275i	−0.964561	+	0.908911i
$260$	12.5821	+	9.14143i	0.780309	+	0.566927i
$261$		0			0
$262$	−11.6329	+	2.47265i	−0.718682	+	0.152761i
$263$	11.1744	+	19.3547i	0.689045	+	1.19346i	0.972147	+	0.234371i	$0.0753031\pi$
$263$	11.1744	+	19.3547i	0.689045	+	1.19346i	−0.283102	+	0.959090i	$0.591364\pi$
$264$		0			0
$265$	−12.5330			−0.769895
$266$	−3.06919	+	7.33664i	−0.188184	+	0.449838i
$267$		0			0
$268$	3.03289	−	1.35033i	0.185263	−	0.0824845i
$269$	0.771020	−	0.856304i	0.0470099	−	0.0522098i	−0.719181	−	0.694823i	$-0.755483\pi$
$269$	0.771020	−	0.856304i	0.0470099	−	0.0522098i	0.766191	+	0.642613i	$0.222150\pi$
$270$		0			0
$271$	−6.54462	+	2.91385i	−0.397558	+	0.177004i	−0.595770	−	0.803155i	$-0.703153\pi$
$271$	−6.54462	+	2.91385i	−0.397558	+	0.177004i	0.198213	+	0.980159i	$0.436486\pi$
$272$	−2.22814	+	1.61884i	−0.135101	+	0.0981564i
$273$		0			0
$274$	9.10902			0.550296
$275$	4.52834	−	12.2704i	0.273069	−	0.739933i
$276$		0			0
$277$	−9.88954	+	2.10209i	−0.594205	+	0.126302i	−0.495191	−	0.868784i	$-0.664902\pi$
$277$	−9.88954	+	2.10209i	−0.594205	+	0.126302i	−0.0990135	+	0.995086i	$0.531569\pi$
$278$	−4.60076	−	43.7733i	−0.275935	−	2.62535i
$279$		0			0
$280$	−4.35478	+	4.10354i	−0.260248	+	0.245233i
$281$	6.23152	+	19.1787i	0.371742	+	1.14410i	0.945651	+	0.325184i	$0.105426\pi$
$281$	6.23152	+	19.1787i	0.371742	+	1.14410i	−0.573909	+	0.818919i	$0.694574\pi$
$282$		0			0
$283$	−1.79246	−	0.798054i	−0.106551	−	0.0474394i	0.352769	−	0.935710i	$-0.385240\pi$
$283$	−1.79246	−	0.798054i	−0.106551	−	0.0474394i	−0.459320	+	0.888271i	$0.651907\pi$
$284$	−21.7009	+	4.61267i	−1.28771	+	0.273712i
$285$		0			0
$286$	17.4721	+	33.2181i	1.03315	+	1.96423i
$287$	1.54238	−	2.22736i	0.0910436	−	0.131477i
$288$		0			0
$289$	1.06861	+	10.1672i	0.0628595	+	0.598068i
$290$	0.966257	−	9.19332i	0.0567405	−	0.539850i
$291$		0			0
$292$	−32.3159	−	6.86897i	−1.89115	−	0.401976i
$293$	−22.6634	−	16.4659i	−1.32401	−	0.961949i	−0.999873	−	0.0159379i	$-0.994927\pi$
$293$	−22.6634	−	16.4659i	−1.32401	−	0.961949i	−0.324136	−	0.946011i	$-0.605073\pi$
$294$		0			0
$295$	1.96030	−	6.03318i	0.114133	−	0.351266i
$296$	8.86920	−	15.3619i	0.515512	−	0.892892i
$297$		0			0
$298$	5.34198	+	9.25258i	0.309453	+	0.535988i
$299$	6.42039	+	7.13056i	0.371300	+	0.412371i
$300$		0			0
$301$	22.9558	−	8.03836i	1.32315	−	0.463323i
$302$	−3.79211	−	11.6709i	−0.218211	−	0.671586i
$303$		0			0
$304$	−0.148875	+	1.41645i	−0.00853855	+	0.0812389i
$305$	3.27621	+	1.45866i	0.187595	+	0.0835227i
$306$		0			0
$307$	17.2450			0.984223			0.492111	−	0.870532i	$-0.336225\pi$
$307$	17.2450			0.984223			0.492111	+	0.870532i	$0.336225\pi$
$308$	−25.0469	+	7.67779i	−1.42718	+	0.437483i
$309$		0			0
$310$	−5.04277	−	5.60057i	−0.286410	−	0.318091i
$311$	−27.4253	−	12.2105i	−1.55515	−	0.692396i	−0.564075	−	0.825724i	$-0.690767\pi$
$311$	−27.4253	−	12.2105i	−1.55515	−	0.692396i	−0.991072	+	0.133328i	$0.957434\pi$
$312$		0			0
$313$	−26.7599	−	5.68800i	−1.51256	−	0.321505i	−0.624424	−	0.781085i	$-0.714666\pi$
$313$	−26.7599	−	5.68800i	−1.51256	−	0.321505i	−0.888136	+	0.459581i	$0.848000\pi$
$314$	14.3458	+	44.1519i	0.809581	+	2.49163i
$315$		0			0
$316$	33.7736	−	24.5379i	1.89991	−	1.38037i
$317$	17.1371	+	19.0327i	0.962516	+	1.06898i	0.997575	+	0.0695972i	$0.0221714\pi$
$317$	17.1371	+	19.0327i	0.962516	+	1.06898i	−0.0350591	+	0.999385i	$0.511162\pi$
$318$		0			0
$319$	7.12992	−	11.2974i	0.399199	−	0.632535i
$320$	−6.67289	+	11.5578i	−0.373026	+	0.646099i
$321$		0			0
$322$	−9.55623	+	5.80995i	−0.532548	+	0.323776i
$323$	−2.83522	−	2.05991i	−0.157756	−	0.114616i
$324$		0			0
$325$	−13.3740	+	14.8534i	−0.741858	+	0.823917i
$326$	1.70776	−	16.2482i	0.0945840	−	0.899907i
$327$		0			0
$328$	−0.696262	+	2.14287i	−0.0384446	+	0.118320i
$329$	−11.1822	−	23.6576i	−0.616494	−	1.30429i
$330$		0			0
$331$	6.59787	−	11.4279i	0.362652	−	0.628132i	−0.625744	−	0.780028i	$-0.715205\pi$
$331$	6.59787	−	11.4279i	0.362652	−	0.628132i	0.988396	+	0.151897i	$0.0485381\pi$
$332$	13.6779	−	2.90732i	0.750670	−	0.159560i
$333$		0			0
$334$	−12.1879	+	5.42638i	−0.666890	+	0.296918i
$335$	−0.353199	−	1.08704i	−0.0192973	−	0.0593911i
$336$		0			0
$337$	17.5919	+	12.7813i	0.958292	+	0.696240i	0.952754	−	0.303745i	$-0.0982369\pi$
$337$	17.5919	+	12.7813i	0.958292	+	0.696240i	0.00553877	+	0.999985i	$0.498237\pi$
$338$	−2.96122	−	28.1742i	−0.161069	−	1.53247i
$339$		0			0
$340$	−3.99408	−	6.91794i	−0.216609	−	0.375178i
$341$	−2.95518	−	10.4827i	−0.160032	−	0.567672i
$342$		0			0
$343$	9.84280	−	15.6882i	0.531461	−	0.847083i
$344$	−16.3646	+	11.8896i	−0.882321	+	0.641044i
$345$		0			0
$346$	−2.21135	+	2.45596i	−0.118883	+	0.132033i
$347$	−9.18671	+	10.2029i	−0.493168	+	0.547719i	−0.937428	−	0.348179i	$-0.886800\pi$
$347$	−9.18671	+	10.2029i	−0.493168	+	0.547719i	0.444260	+	0.895898i	$0.353467\pi$
$348$		0			0
$349$	−18.6455	+	13.5467i	−0.998070	+	0.725140i	−0.961673	−	0.274197i	$-0.911588\pi$
$349$	−18.6455	+	13.5467i	−0.998070	+	0.725140i	−0.0363964	+	0.999337i	$0.511588\pi$
$350$	−14.1169	−	18.5321i	−0.754582	−	0.990581i
$351$		0			0
$352$	−18.6513	+	12.4594i	−0.994117	+	0.664088i
$353$	−2.13324	−	3.69489i	−0.113541	−	0.196659i	0.803655	−	0.595096i	$-0.202886\pi$
$353$	−2.13324	−	3.69489i	−0.113541	−	0.196659i	−0.917196	+	0.398437i	$0.869553\pi$
$354$		0			0
$355$	0.798397	+	7.59624i	0.0423745	+	0.403167i
$356$	44.3316	+	32.2088i	2.34957	+	1.70706i
$357$		0			0
$358$	3.72758	+	11.4723i	0.197009	+	0.606331i
$359$	−14.3328	+	6.38140i	−0.756459	+	0.336797i	−0.748468	−	0.663171i	$-0.769210\pi$
$359$	−14.3328	+	6.38140i	−0.756459	+	0.336797i	−0.00799080	+	0.999968i	$0.502544\pi$
$360$		0			0
$361$	16.8121	−	3.57352i	0.884847	−	0.188080i
$362$	−27.8539	+	48.2444i	−1.46397	+	2.53567i
$363$		0			0
$364$	39.8987	+	3.28126i	2.09126	+	0.171985i
$365$	−3.51484	+	10.8176i	−0.183975	+	0.566218i
$366$		0			0
$367$	1.40004	−	13.3205i	0.0730814	−	0.695323i	−0.895235	−	0.445595i	$-0.852992\pi$
$367$	1.40004	−	13.3205i	0.0730814	−	0.695323i	0.968316	−	0.249728i	$-0.0803411\pi$
$368$	−1.34020	+	1.48844i	−0.0698627	+	0.0775903i
$369$		0			0
$370$	−14.9677	−	10.8747i	−0.778136	−	0.565349i
$371$	−27.5663	+	16.7597i	−1.43117	+	0.870118i
$372$		0			0
$373$	−12.3967	+	21.4717i	−0.641877	+	1.11176i	0.343137	+	0.939286i	$0.388511\pi$
$373$	−12.3967	+	21.4717i	−0.641877	+	1.11176i	−0.985013	+	0.172478i	$0.944823\pi$
$374$	−1.25870	−	19.2369i	−0.0650858	−	0.994716i
$375$		0			0
$376$	14.5616	+	16.1723i	0.750958	+	0.834023i
$377$	−16.5160	+	11.9996i	−0.850616	+	0.618009i
$378$		0			0
$379$	3.42758	+	10.5490i	0.176063	+	0.541865i	0.999680	−	0.0252801i	$-0.00804775\pi$
$379$	3.42758	+	10.5490i	0.176063	+	0.541865i	−0.823618	+	0.567145i	$0.808048\pi$
$380$	−4.04066	−	0.858869i	−0.207282	−	0.0440591i
$381$		0			0
$382$	−46.6144	−	20.7541i	−2.38500	−	1.06187i
$383$	1.82252	+	2.02412i	0.0931266	+	0.103428i	0.787907	−	0.615795i	$-0.211165\pi$
$383$	1.82252	+	2.02412i	0.0931266	+	0.103428i	−0.694780	+	0.719222i	$0.744498\pi$
$384$		0			0
$385$	1.72746	+	8.85220i	0.0880396	+	0.451150i
$386$	−16.3897			−0.834214
$387$		0			0
$388$	−19.3915	−	8.63365i	−0.984455	−	0.438307i
$389$	−2.29204	+	21.8073i	−0.116211	+	1.10567i	0.768602	+	0.639727i	$0.220953\pi$
$389$	−2.29204	+	21.8073i	−0.116211	+	1.10567i	−0.884813	+	0.465946i	$0.845714\pi$
$390$		0			0
$391$	−1.52294	−	4.68713i	−0.0770185	−	0.237039i
$392$	−4.09093	+	14.8492i	−0.206623	+	0.749996i
$393$		0			0
$394$	−39.2607	−	43.6035i	−1.97793	−	2.19671i
$395$	−7.18622	−	12.4469i	−0.361578	−	0.626271i
$396$		0			0
$397$	−6.46252	+	11.1934i	−0.324344	+	0.561781i	−0.981379	−	0.192079i	$-0.938477\pi$
$397$	−6.46252	+	11.1934i	−0.324344	+	0.561781i	0.657035	+	0.753860i	$0.271810\pi$
$398$	8.36846	−	25.7555i	0.419473	−	1.29101i
$399$		0			0
$400$	−3.37534	−	2.45233i	−0.168767	−	0.122616i
$401$	10.7671	+	2.28863i	0.537685	+	0.114289i	0.468747	−	0.883332i	$-0.344706\pi$
$401$	10.7671	+	2.28863i	0.537685	+	0.114289i	0.0689382	+	0.997621i	$0.478039\pi$
$402$		0			0
$403$	−1.73973	+	16.5524i	−0.0866621	+	0.824535i
$404$	1.95344	+	18.5857i	0.0971871	+	0.924674i
$405$		0			0
$406$	−10.1684	−	21.5129i	−0.504651	−	1.06767i
$407$	−12.4467	−	23.6637i	−0.616962	−	1.17297i
$408$		0			0
$409$	−10.8632	+	2.30904i	−0.537149	+	0.114175i	−0.468495	−	0.883466i	$-0.655204\pi$
$409$	−10.8632	+	2.30904i	−0.537149	+	0.114175i	−0.0686538	+	0.997641i	$0.521870\pi$
$410$	2.14687	+	0.955846i	0.106026	+	0.0472059i
$411$		0			0
$412$	9.73367	+	29.9571i	0.479543	+	1.47588i
$413$	−3.75616	−	15.8914i	−0.184828	−	0.781966i
$414$		0			0
$415$	−0.503222	−	4.78784i	−0.0247022	−	0.235026i
$416$	33.5275	−	7.12649i	1.64382	−	0.349405i
$417$		0			0
$418$	−7.82837	−	6.17280i	−0.382898	−	0.301922i
$419$	35.9681			1.75716			0.878578	−	0.477599i	$-0.158493\pi$
$419$	35.9681			1.75716			0.878578	+	0.477599i	$0.158493\pi$
$420$		0			0
$421$	16.1469	−	11.7314i	0.786953	−	0.571755i	−0.120105	−	0.992761i	$-0.538323\pi$
$421$	16.1469	−	11.7314i	0.786953	−	0.571755i	0.907058	+	0.421006i	$0.138323\pi$
$422$	36.4567	−	16.2316i	1.77469	−	0.790141i
$423$		0			0
$424$	17.9528	−	19.9386i	0.871867	−	0.968306i
$425$	9.37848	−	4.17557i	0.454923	−	0.202545i
$426$		0			0
$427$	9.15662	−	1.17276i	0.443120	−	0.0567538i
$428$	19.1262			0.924501
$429$		0			0
$430$	10.5488	+	18.2710i	0.508708	+	0.881108i
$431$	14.1620	−	3.01022i	0.682157	−	0.144997i	0.146217	−	0.989253i	$-0.453290\pi$
$431$	14.1620	−	3.01022i	0.682157	−	0.144997i	0.535941	+	0.844256i	$0.319957\pi$
$432$		0			0
$433$	−23.6623	−	17.1917i	−1.13714	−	0.826179i	−0.150420	−	0.988622i	$-0.548063\pi$
$433$	−23.6623	−	17.1917i	−1.13714	−	0.826179i	−0.986718	+	0.162443i	$0.948063\pi$
$434$	−18.5809	−	5.57505i	−0.891913	−	0.267611i
$435$		0			0
$436$	−0.253366	+	0.112806i	−0.0121340	+	0.00540241i
$437$	−2.32827	−	1.03661i	−0.111376	−	0.0495879i
$438$		0			0
$439$	−9.92126	+	17.1841i	−0.473516	+	0.820154i	−0.999540	−	0.0303159i	$-0.990349\pi$
$439$	−9.92126	+	17.1841i	−0.473516	+	0.820154i	0.526025	+	0.850469i	$0.323682\pi$
$440$	−3.49174	−	6.63851i	−0.166462	−	0.316479i
$441$		0			0
$442$	−9.10356	+	28.0179i	−0.433012	+	1.33268i
$443$	−0.891676	−	8.48373i	−0.0423648	−	0.403074i	−0.995070	−	0.0991773i	$-0.968379\pi$
$443$	−0.891676	−	8.48373i	−0.0423648	−	0.403074i	0.952705	−	0.303897i	$-0.0982878\pi$
$444$		0			0
$445$	12.6234	−	14.0197i	0.598408	−	0.664600i
$446$	4.60872	+	0.979614i	0.218229	+	0.0463860i
$447$		0			0
$448$	0.778541	+	34.3447i	0.0367826	+	1.62263i
$449$	3.28407	−	10.1073i	0.154985	−	0.476994i	−0.843175	−	0.537640i	$-0.819316\pi$
$449$	3.28407	−	10.1073i	0.154985	−	0.476994i	0.998159	+	0.0606458i	$0.0193160\pi$
$450$		0			0
$451$	2.17139	+	2.61140i	0.102247	+	0.122966i
$452$	16.9444	+	29.3485i	0.796997	+	1.38044i
$453$		0			0
$454$	−20.3983	+	14.8202i	−0.957340	+	0.695548i
$455$	2.55932	−	13.5430i	0.119983	−	0.634905i
$456$		0			0
$457$	−4.92526	−	1.04690i	−0.230394	−	0.0489718i	0.0912677	−	0.995826i	$-0.470908\pi$
$457$	−4.92526	−	1.04690i	−0.230394	−	0.0489718i	−0.321662	+	0.946855i	$0.604241\pi$
$458$	−6.50585	+	61.8991i	−0.303999	+	2.89235i
$459$		0			0
$460$	−3.88714	−	4.31711i	−0.181239	−	0.201286i
$461$	−15.3843			−0.716519			−0.358260	−	0.933622i	$-0.616630\pi$
$461$	−15.3843			−0.716519			−0.358260	+	0.933622i	$0.616630\pi$
$462$		0			0
$463$	31.6955			1.47302			0.736508	−	0.676429i	$-0.236473\pi$
$463$	31.6955			1.47302			0.736508	+	0.676429i	$0.236473\pi$
$464$	−2.85145	−	3.16685i	−0.132375	−	0.147017i
$465$		0			0
$466$	−1.60386	+	15.2597i	−0.0742973	+	0.706892i
$467$	17.6587	+	3.75348i	0.817149	+	0.173690i	0.597480	−	0.801884i	$-0.296169\pi$
$467$	17.6587	+	3.75348i	0.817149	+	0.173690i	0.219669	+	0.975574i	$0.429502\pi$
$468$		0			0
$469$	−2.23050	−	1.91863i	−0.102995	−	0.0885939i
$470$	18.3629	−	13.3414i	0.847016	−	0.615393i
$471$		0			0
$472$	6.79013	+	11.7609i	0.312541	+	0.541337i
$473$	1.99074	+	30.4248i	0.0915342	+	1.39893i
$474$		0			0
$475$	1.64054	−	5.04906i	0.0752731	−	0.231667i
$476$	−18.0360	−	9.87499i	−0.826677	−	0.452619i
$477$		0			0
$478$	24.3773	+	5.18155i	1.11499	+	0.236998i
$479$	−4.32294	+	4.80111i	−0.197520	+	0.219368i	−0.833766	−	0.552118i	$-0.813820\pi$
$479$	−4.32294	+	4.80111i	−0.197520	+	0.219368i	0.636246	+	0.771486i	$0.280486\pi$
$480$		0			0
$481$	4.27093	+	40.6351i	0.194737	+	1.85280i
$482$	11.3884	−	35.0500i	0.518728	−	1.59648i
$483$		0			0
$484$	−0.852333	−	32.8290i	−0.0387424	−	1.49223i
$485$	−3.65395	+	6.32883i	−0.165917	+	0.287377i
$486$		0			0
$487$	4.00193	+	1.78177i	0.181345	+	0.0807398i	0.495401	−	0.868665i	$-0.335021\pi$
$487$	4.00193	+	1.78177i	0.181345	+	0.0807398i	−0.314056	+	0.949404i	$0.601688\pi$
$488$	−7.01357	+	3.12264i	−0.317489	+	0.141355i
$489$		0			0
$490$	14.9568	+	5.86237i	0.675681	+	0.264835i
$491$	33.0596	+	24.0192i	1.49196	+	1.08397i	0.973450	+	0.228901i	$0.0735132\pi$
$491$	33.0596	+	24.0192i	1.49196	+	1.08397i	0.518510	+	0.855071i	$0.326487\pi$
$492$		0			0
$493$	10.2566	−	2.18010i	0.461932	−	0.0981867i
$494$	7.61730	+	13.1936i	0.342719	+	0.593606i
$495$		0			0
$496$	−3.47420			−0.155996
$497$	11.9141	+	15.6403i	0.534421	+	0.701564i
$498$		0			0
$499$	30.3241	−	13.5011i	1.35749	−	0.604394i	0.406511	−	0.913646i	$-0.366745\pi$
$499$	30.3241	−	13.5011i	1.35749	−	0.604394i	0.950980	+	0.309252i	$0.100079\pi$
$500$	18.3634	−	20.3947i	0.821238	−	0.912077i
$501$		0			0
$502$	46.5669	−	20.7329i	2.07838	−	0.925356i
$503$	−17.0117	+	12.3597i	−0.758516	+	0.551094i	−0.898455	−	0.439066i	$-0.855309\pi$
$503$	−17.0117	+	12.3597i	−0.758516	+	0.551094i	0.139939	+	0.990160i	$0.455309\pi$
$504$		0			0
$505$	6.43392			0.286306
$506$	−3.80399	−	13.4937i	−0.169108	−	0.599867i
$507$		0			0
$508$	−32.3732	+	6.88113i	−1.43633	+	0.305301i
$509$	3.24941	+	30.9161i	0.144028	+	1.37033i	0.792862	+	0.609401i	$0.208590\pi$
$509$	3.24941	+	30.9161i	0.144028	+	1.37033i	−0.648834	+	0.760930i	$0.724743\pi$
$510$		0			0
$511$	6.73484	+	28.4935i	0.297932	+	1.26048i
$512$	3.64970	+	11.2326i	0.161296	+	0.496417i
$513$		0			0
$514$	−15.2294	−	6.78058i	−0.671741	−	0.299078i
$515$	10.6074	−	2.25468i	0.467419	−	0.0993529i
$516$		0			0
$517$	32.3292	−	5.55146i	1.42184	−	0.244153i
$518$	−47.4638	−	3.90341i	−2.08544	−	0.171506i
$519$		0			0
$520$	1.19814	+	11.3996i	0.0525421	+	0.499905i
$521$	3.05973	−	29.1114i	0.134049	−	1.27539i	−0.696137	−	0.717909i	$-0.745099\pi$
$521$	3.05973	−	29.1114i	0.134049	−	1.27539i	0.830187	−	0.557486i	$-0.188234\pi$
$522$		0			0
$523$	9.16995	+	1.94913i	0.400974	+	0.0852296i	0.403984	−	0.914766i	$-0.367625\pi$
$523$	9.16995	+	1.94913i	0.400974	+	0.0852296i	−0.00301064	+	0.999995i	$0.500958\pi$
$524$	−12.8647	−	9.34674i	−0.561996	−	0.408314i
$525$		0			0
$526$	−15.4202	+	47.4585i	−0.672353	+	2.06929i
$527$	4.27433	−	7.40335i	0.186193	−	0.322495i
$528$		0			0
$529$	9.70797	+	16.8147i	0.422086	+	0.731074i
$530$	−18.7248	−	20.7960i	−0.813354	−	0.903321i
$531$		0			0
$532$	−10.0360	+	3.51427i	−0.435115	+	0.152363i
$533$	−1.60378	−	4.93594i	−0.0694676	−	0.213799i
$534$		0			0
$535$	0.688296	−	6.54870i	0.0297576	−	0.283125i
$536$	2.23530	+	0.995219i	0.0965502	+	0.0429869i
$537$		0			0
$538$	2.57281			0.110922
$539$	15.6371	+	17.1604i	0.673539	+	0.739152i
$540$		0			0
$541$	26.2492	+	29.1527i	1.12854	+	1.25337i	0.963681	+	0.267055i	$0.0860504\pi$
$541$	26.2492	+	29.1527i	1.12854	+	1.25337i	0.164859	+	0.986317i	$0.447283\pi$
$542$	−14.6129	−	6.50609i	−0.627679	−	0.279461i
$543$		0			0
$544$	−17.2208	−	3.66038i	−0.738334	−	0.156938i
$545$	0.0295061	+	0.0908103i	0.00126390	+	0.00388989i
$546$		0			0
$547$	4.06399	−	2.95266i	0.173764	−	0.126247i	−0.497504	−	0.867462i	$-0.665750\pi$
$547$	4.06399	−	2.95266i	0.173764	−	0.126247i	0.671268	+	0.741215i	$0.265750\pi$
$548$	8.14969	+	9.05115i	0.348137	+	0.386646i
$549$		0			0
$550$	27.1259	−	10.8186i	1.15665	−	0.461307i
$551$	2.71125	−	4.69602i	0.115503	−	0.200057i
$552$		0			0
$553$	−32.4507	−	17.7673i	−1.37994	−	0.755541i
$554$	−18.2634	−	13.2691i	−0.775938	−	0.563752i
$555$		0			0
$556$	39.3790	−	43.7348i	1.67004	−	1.85477i
$557$	−0.999243	+	9.50716i	−0.0423393	+	0.402831i	0.952743	+	0.303778i	$0.0982481\pi$
$557$	−0.999243	+	9.50716i	−0.0423393	+	0.402831i	−0.995082	+	0.0990533i	$0.968419\pi$
$558$		0			0
$559$	14.3981	−	44.3126i	0.608973	−	1.87423i
$560$	2.86733	+	0.235809i	0.121167	+	0.00996474i
$561$		0			0
$562$	−22.5130	+	38.9937i	−0.949656	+	1.64485i
$563$	24.7845	−	5.26811i	1.04454	−	0.222024i	0.346477	−	0.938059i	$-0.387378\pi$
$563$	24.7845	−	5.26811i	1.04454	−	0.222024i	0.698065	+	0.716034i	$0.254045\pi$
$564$		0			0
$565$	10.6585	−	4.74548i	0.448407	−	0.199644i
$566$	−1.35380	−	4.16656i	−0.0569044	−	0.175134i
$567$		0			0
$568$	−13.2285	−	9.61106i	−0.555055	−	0.403271i
$569$	−3.56834	−	33.9505i	−0.149593	−	1.42328i	−0.769521	−	0.638622i	$-0.779505\pi$
$569$	−3.56834	−	33.9505i	−0.149593	−	1.42328i	0.619928	−	0.784659i	$-0.287162\pi$
$570$		0			0
$571$	22.6152	+	39.1707i	0.946416	+	1.63924i	0.752891	+	0.658145i	$0.228659\pi$
$571$	22.6152	+	39.1707i	0.946416	+	1.63924i	0.193525	+	0.981095i	$0.438008\pi$
$572$	−17.3750	+	47.0808i	−0.726484	+	1.96855i
$573$		0			0
$574$	6.00024	−	0.768498i	0.250445	−	0.0320765i
$575$	6.03995	−	4.38828i	0.251884	−	0.183004i
$576$		0			0
$577$	−0.613256	+	0.681090i	−0.0255302	+	0.0283541i	−0.755775	−	0.654832i	$-0.772739\pi$
$577$	−0.613256	+	0.681090i	−0.0255302	+	0.0283541i	0.730244	+	0.683186i	$0.239406\pi$
$578$	−15.2738	+	16.9633i	−0.635308	+	0.705581i
$579$		0			0
$580$	9.99940	−	7.26499i	0.415202	−	0.301662i
$581$	−7.50935	−	9.85794i	−0.311540	−	0.408976i
$582$		0			0
$583$	−10.9732	−	38.9245i	−0.454462	−	1.61209i
$584$	−12.1748	−	21.0874i	−0.503796	−	0.872601i
$585$		0			0
$586$	−6.53814	−	62.2062i	−0.270088	−	2.56972i
$587$	−0.0318255	−	0.0231226i	−0.00131358	−	0.000954370i	0.587128	−	0.809494i	$-0.300258\pi$
$587$	−0.0318255	−	0.0231226i	−0.00131358	−	0.000954370i	−0.588442	+	0.808540i	$0.700258\pi$
$588$		0			0
$589$	−1.36610	−	4.20442i	−0.0562891	−	0.173240i
$590$	12.9397	−	5.76111i	0.532717	−	0.237181i
$591$		0			0
$592$	−8.34257	+	1.77327i	−0.342877	+	0.0728808i
$593$	4.44625	−	7.70113i	0.182586	−	0.316248i	−0.760175	−	0.649719i	$-0.774887\pi$
$593$	4.44625	−	7.70113i	0.182586	−	0.316248i	0.942760	+	0.333471i	$0.108220\pi$
$594$		0			0
$595$	−4.03019	+	5.82003i	−0.165222	+	0.238598i
$596$	−4.41441	+	13.5862i	−0.180821	+	0.556511i
$597$		0			0
$598$	−2.23943	+	21.3067i	−0.0915770	+	0.871297i
$599$	16.7013	−	18.5486i	0.682396	−	0.757877i	−0.298075	−	0.954542i	$-0.596345\pi$
$599$	16.7013	−	18.5486i	0.682396	−	0.757877i	0.980471	+	0.196665i	$0.0630112\pi$
$600$		0			0
$601$	−22.5755	−	16.4021i	−0.920874	−	0.669054i	0.0228677	−	0.999738i	$-0.492720\pi$
$601$	−22.5755	−	16.4021i	−0.920874	−	0.669054i	−0.943741	+	0.330685i	$0.892720\pi$
$602$	47.6350	+	26.0809i	1.94146	+	1.06298i
$603$		0			0
$604$	8.20402	−	14.2098i	0.333817	−	0.578188i
$605$	−11.2711	−	0.889582i	−0.458235	−	0.0361667i
$606$		0			0
$607$	5.60803	+	6.22835i	0.227623	+	0.252801i	0.846128	−	0.532980i	$-0.178928\pi$
$607$	5.60803	+	6.22835i	0.227623	+	0.252801i	−0.618505	+	0.785781i	$0.712261\pi$
$608$	−7.36559	+	5.35141i	−0.298714	+	0.217028i
$609$		0			0
$610$	2.47443	+	7.61552i	0.100187	+	0.308343i
$611$	−49.0316	−	10.4220i	−1.98361	−	0.421628i
$612$		0			0
$613$	−18.3669	−	8.17745i	−0.741830	−	0.330284i	0.000787513	−	1.00000i	$-0.499749\pi$
$613$	−18.3669	−	8.17745i	−0.741830	−	0.330284i	−0.742618	+	0.669716i	$0.766416\pi$
$614$	25.7648	+	28.6147i	1.03978	+	1.15479i
$615$		0			0
$616$	−16.5574	−	9.93211i	−0.667118	−	0.400176i
$617$	22.3648			0.900374			0.450187	−	0.892934i	$-0.351357\pi$
$617$	22.3648			0.900374			0.450187	+	0.892934i	$0.351357\pi$
$618$		0			0
$619$	15.7813	+	7.02629i	0.634304	+	0.282410i	0.698591	−	0.715521i	$-0.253811\pi$
$619$	15.7813	+	7.02629i	0.634304	+	0.282410i	−0.0642870	+	0.997931i	$0.520477\pi$
$620$	1.05330	−	10.0215i	0.0423015	−	0.402472i
$621$		0			0
$622$	−20.7136	−	63.7500i	−0.830541	−	2.55614i
$623$	9.01746	−	47.7171i	0.361277	−	1.91175i
$624$		0			0
$625$	6.87164	+	7.63173i	0.274866	+	0.305269i
$626$	−30.5424	−	52.9010i	−1.22072	−	2.11435i
$627$		0			0
$628$	−31.0364	+	53.7566i	−1.23849	+	2.14512i
$629$	6.48516	−	19.9593i	0.258580	−	0.795828i
$630$		0			0
$631$	−31.1456	−	22.6286i	−1.23989	−	0.900830i	−0.242295	−	0.970203i	$-0.577900\pi$
$631$	−31.1456	−	22.6286i	−1.23989	−	0.900830i	−0.997591	+	0.0693729i	$0.977900\pi$
$632$	30.0956	+	6.39701i	1.19714	+	0.254459i
$633$		0			0
$634$	−5.97742	+	56.8714i	−0.237394	+	2.25865i
$635$	1.19104	+	11.3320i	0.0472650	+	0.449696i
$636$		0			0
$637$	−12.4810	−	33.2103i	−0.494517	−	1.31584i
$638$	29.3983	−	5.04818i	1.16389	−	0.199859i
$639$		0			0
$640$	−15.5490	+	3.30504i	−0.614627	+	0.130643i
$641$	16.9821	+	7.56090i	0.670751	+	0.298638i	0.713712	−	0.700439i	$-0.247012\pi$
$641$	16.9821	+	7.56090i	0.670751	+	0.298638i	−0.0429611	+	0.999077i	$0.513679\pi$
$642$		0			0
$643$	−2.98936	−	9.20029i	−0.117889	−	0.362824i	0.874650	−	0.484755i	$-0.161091\pi$
$643$	−2.98936	−	9.20029i	−0.117889	−	0.362824i	−0.992539	+	0.121931i	$0.961091\pi$
$644$	−14.3228	−	4.29744i	−0.564399	−	0.169343i
$645$		0			0
$646$	−0.817931	−	7.78209i	−0.0321811	−	0.306182i
$647$	−20.8973	+	4.44186i	−0.821557	+	0.174627i	−0.599468	−	0.800399i	$-0.704621\pi$
$647$	−20.8973	+	4.44186i	−0.821557	+	0.174627i	−0.222090	+	0.975026i	$0.571288\pi$
$648$		0			0
$649$	20.4540	+	0.805923i	0.802889	+	0.0316352i
$650$	−44.6277			−1.75044
$651$		0			0
$652$	17.6729	−	12.8401i	0.692124	−	0.502858i
$653$	−29.2356	+	13.0165i	−1.14408	+	0.509376i	−0.889164	−	0.457588i	$-0.848713\pi$
$653$	−29.2356	+	13.0165i	−1.14408	+	0.509376i	−0.254913	+	0.966964i	$0.582047\pi$
$654$		0			0
$655$	−3.66322	+	4.06842i	−0.143134	+	0.158966i
$656$	0.989695	−	0.440641i	0.0386411	−	0.0172041i
$657$		0			0
$658$	22.5485	−	53.9001i	0.879031	−	2.10125i
$659$	33.3651			1.29972			0.649860	−	0.760054i	$-0.274827\pi$
$659$	33.3651			1.29972			0.649860	+	0.760054i	$0.274827\pi$
$660$		0			0
$661$	−13.3562	−	23.1336i	−0.519495	−	0.899792i	−0.999743	−	0.0226592i	$-0.992787\pi$
$661$	−13.3562	−	23.1336i	−0.519495	−	0.899792i	0.480248	−	0.877133i	$-0.340547\pi$
$662$	28.8198	−	6.12584i	1.12011	−	0.238087i
$663$		0			0
$664$	8.33778	+	6.05775i	0.323569	+	0.235086i
$665$	0.842099	+	3.56272i	0.0326552	+	0.138156i
$666$		0			0
$667$	6.96628	−	3.10159i	0.269736	−	0.120094i
$668$	−16.2962	−	7.25552i	−0.630518	−	0.280725i
$669$		0			0
$670$	1.27603	−	2.21014i	0.0492972	−	0.0853853i
$671$	−1.66180	+	11.4522i	−0.0641531	+	0.442109i
$672$		0			0
$673$	0.507396	−	1.56161i	0.0195587	−	0.0601954i	−0.940801	−	0.338960i	$-0.889925\pi$
$673$	0.507396	−	1.56161i	0.0195587	−	0.0601954i	0.960359	+	0.278764i	$0.0899249\pi$
$674$	5.07507	+	48.2861i	0.195485	+	1.85991i
$675$		0			0
$676$	25.3458	−	28.1493i	0.974838	−	1.08267i
$677$	0.483086	+	0.102683i	0.0185665	+	0.00394643i	0.217186	−	0.976130i	$-0.430312\pi$
$677$	0.483086	+	0.102683i	0.0185665	+	0.00394643i	−0.198619	+	0.980077i	$0.563646\pi$
$678$		0			0
$679$	0.426315	+	18.8065i	0.0163604	+	0.721728i
$680$	1.81931	−	5.59927i	0.0697675	−	0.214722i
$681$		0			0
$682$	12.9789	−	20.5652i	0.496987	−	0.787482i
$683$	−12.6490	−	21.9087i	−0.484000	−	0.838312i	0.515831	−	0.856690i	$-0.327483\pi$
$683$	−12.6490	−	21.9087i	−0.484000	−	0.838312i	−0.999831	+	0.0183779i	$0.994150\pi$
$684$		0			0
$685$	3.39234	−	2.46468i	0.129614	−	0.0941704i
$686$	40.7370	−	7.10664i	1.55535	−	0.271333i
$687$		0			0
$688$	9.51335	+	2.02213i	0.362693	+	0.0770928i
$689$	−6.45996	+	61.4624i	−0.246105	+	2.34153i
$690$		0			0
$691$	−1.03073	−	1.14475i	−0.0392110	−	0.0435482i	0.723220	−	0.690617i	$-0.242661\pi$
$691$	−1.03073	−	1.14475i	−0.0392110	−	0.0435482i	−0.762431	+	0.647069i	$0.775994\pi$
$692$	−4.41881			−0.167978
$693$		0			0
$694$	−30.6550			−1.16365
$695$	−13.5574	−	15.0570i	−0.514260	−	0.571144i
$696$		0			0
$697$	−0.278643	+	2.65111i	−0.0105544	+	0.100418i
$698$	−50.3353	−	10.6991i	−1.90522	−	0.404967i
$699$		0			0
$700$	5.78414	−	30.6076i	0.218620	−	1.15686i
$701$	−6.24771	+	4.53922i	−0.235973	+	0.171444i	−0.699487	−	0.714645i	$-0.746588\pi$
$701$	−6.24771	+	4.53922i	−0.235973	+	0.171444i	0.463515	+	0.886089i	$0.346588\pi$
$702$		0			0
$703$	−5.42638	−	9.39877i	−0.204660	−	0.354481i
$704$	−41.7382	−	10.6051i	−1.57307	−	0.399694i
$705$		0			0
$706$	2.94378	−	9.06002i	0.110791	−	0.340979i
$707$	14.1514	−	8.60374i	0.532220	−	0.323577i
$708$		0			0
$709$	−19.6765	−	4.18237i	−0.738967	−	0.157072i	−0.176975	−	0.984215i	$-0.556631\pi$
$709$	−19.6765	−	4.18237i	−0.738967	−	0.157072i	−0.561991	+	0.827143i	$0.689965\pi$
$710$	−11.4116	+	12.6739i	−0.428271	+	0.475643i
$711$		0			0
$712$	4.22152	+	40.1651i	0.158208	+	1.50525i
$713$	1.92112	−	5.91259i	0.0719464	−	0.221428i
$714$		0			0
$715$	15.4949	+	7.64337i	0.579475	+	0.285846i
$716$	−8.06442	+	13.9680i	−0.301382	+	0.522008i
$717$		0			0
$718$	−32.0026	−	14.2485i	−1.19433	−	0.531748i
$719$	19.0573	−	8.48487i	0.710718	−	0.316432i	−0.0193438	−	0.999813i	$-0.506158\pi$
$719$	19.0573	−	8.48487i	0.710718	−	0.316432i	0.730062	+	0.683381i	$0.239491\pi$
$720$		0			0
$721$	20.3160	−	19.1439i	0.756608	−	0.712956i
$722$	31.0476	+	22.5574i	1.15547	+	0.839499i
$723$		0			0
$724$	−72.8582	+	15.4865i	−2.70775	+	0.575551i
$725$	7.94223	+	13.7563i	0.294967	+	0.510898i
$726$		0			0
$727$	−41.6247			−1.54378			−0.771888	−	0.635758i	$-0.780687\pi$
$727$	−41.6247			−1.54378			−0.771888	+	0.635758i	$0.780687\pi$
$728$	17.8794	+	23.4712i	0.662653	+	0.869901i
$729$		0			0
$730$	−23.2010	+	10.3297i	−0.858706	+	0.382321i
$731$	−16.0134	+	17.7847i	−0.592276	+	0.657790i
$732$		0			0
$733$	45.6839	−	20.3398i	1.68738	−	0.751268i	0.687694	−	0.726000i	$-0.258623\pi$
$733$	45.6839	−	20.3398i	1.68738	−	0.751268i	0.999681	−	0.0252675i	$-0.00804374\pi$
$734$	24.1944	−	17.5783i	0.893032	−	0.648826i
$735$		0			0
$736$	−12.8033			−0.471935
$737$	3.06684	−	2.04870i	0.112968	−	0.0754648i
$738$		0			0
$739$	−3.78631	+	0.804805i	−0.139282	+	0.0296052i	−0.277025	−	0.960863i	$-0.589348\pi$
$739$	−3.78631	+	0.804805i	−0.139282	+	0.0296052i	0.137743	+	0.990468i	$0.456015\pi$
$740$	−2.58578	−	24.6021i	−0.0950552	−	0.904389i
$741$		0			0
$742$	−68.9947	−	20.7013i	−2.53288	−	0.759967i
$743$	2.87081	+	8.83546i	0.105320	+	0.324141i	0.989805	−	0.142426i	$-0.0454904\pi$
$743$	2.87081	+	8.83546i	0.105320	+	0.324141i	−0.884485	+	0.466568i	$0.845490\pi$
$744$		0			0
$745$	4.49295	+	2.00039i	0.164609	+	0.0732887i
$746$	−54.1493	+	11.5098i	−1.98255	+	0.421403i
$747$		0			0
$748$	17.9885	−	18.4616i	0.657726	−	0.675024i
$749$	−7.24330	−	15.3243i	−0.264665	−	0.559938i
$750$		0			0
$751$	2.26247	+	21.5260i	0.0825589	+	0.785495i	0.954966	+	0.296715i	$0.0958912\pi$
$751$	2.26247	+	21.5260i	0.0825589	+	0.785495i	−0.872407	+	0.488780i	$0.837442\pi$
$752$	1.09374	−	10.4062i	0.0398846	−	0.379477i
$753$		0			0
$754$	−44.5865	−	9.47715i	−1.62374	−	0.345138i
$755$	−4.57010	−	3.32037i	−0.166323	−	0.120841i
$756$		0			0
$757$	3.03614	−	9.34428i	0.110350	−	0.339624i	−0.880599	−	0.473863i	$-0.842859\pi$
$757$	3.03614	−	9.34428i	0.110350	−	0.339624i	0.990949	+	0.134239i	$0.0428591\pi$
$758$	−12.3830	+	21.4480i	−0.449772	+	0.779028i
$759$		0			0
$760$	−1.52229	−	2.63668i	−0.0552193	−	0.0956426i
$761$	22.2450	+	24.7055i	0.806379	+	0.895575i	0.996275	−	0.0862293i	$-0.0274818\pi$
$761$	22.2450	+	24.7055i	0.806379	+	0.895575i	−0.189896	+	0.981804i	$0.560815\pi$
$762$		0			0
$763$	0.186334	+	0.160281i	0.00674576	+	0.00580256i
$764$	−21.0829	−	64.8866i	−0.762753	−	2.34751i
$765$		0			0
$766$	−0.635696	+	6.04824i	−0.0229686	+	0.218532i
$767$	−28.5767	−	12.7232i	−1.03184	−	0.459406i
$768$		0			0
$769$	2.47573			0.0892770			0.0446385	−	0.999003i	$-0.485786\pi$
$769$	2.47573			0.0892770			0.0446385	+	0.999003i	$0.485786\pi$
$770$	−12.1076	+	16.0920i	−0.436327	+	0.579914i
$771$		0			0
$772$	−14.6636	−	16.2856i	−0.527754	−	0.586130i
$773$	26.9385	+	11.9938i	0.968910	+	0.431387i	0.829290	−	0.558818i	$-0.188745\pi$
$773$	26.9385	+	11.9938i	0.968910	+	0.431387i	0.139620	+	0.990205i	$0.455412\pi$
$774$		0			0
$775$	12.6671	+	2.69248i	0.455016	+	0.0967166i
$776$	−4.83440	−	14.8788i	−0.173545	−	0.534116i
$777$		0			0
$778$	−39.6093	+	28.7779i	−1.42006	+	1.03174i
$779$	0.922417	+	1.02445i	0.0330490	+	0.0367046i
$780$		0			0
$781$	−22.8931	+	9.13047i	−0.819180	+	0.326714i
$782$	5.50204	−	9.52981i	0.196752	−	0.340785i
$783$		0			0
$784$	6.62204	−	3.31566i	0.236502	−	0.118417i
$785$	17.2890	+	12.5612i	0.617071	+	0.448328i
$786$		0			0
$787$	−16.4180	+	18.2341i	−0.585240	+	0.649975i	−0.960937	−	0.276768i	$-0.910737\pi$
$787$	−16.4180	+	18.2341i	−0.585240	+	0.649975i	0.375697	+	0.926743i	$0.377403\pi$
$788$	8.20050	−	78.0225i	0.292131	−	2.77944i
$789$		0			0
$790$	9.91665	−	30.5203i	0.352819	−	1.08586i
$791$	17.0976	−	24.6908i	0.607921	−	0.877903i
$792$		0			0
$793$	8.84203	−	15.3148i	0.313990	−	0.543846i
$794$	−28.2285	+	6.00016i	−1.00179	+	0.212938i
$795$		0			0
$796$	33.0790	−	14.7277i	1.17245	−	0.522009i
$797$	5.49479	+	16.9112i	0.194635	+	0.599026i	0.999981	+	0.00622010i	$0.00197993\pi$
$797$	5.49479	+	16.9112i	0.194635	+	0.599026i	−0.805345	+	0.592806i	$0.798020\pi$
$798$		0			0
$799$	20.8296	+	15.1336i	0.736897	+	0.535387i
$800$	−2.78777	−	26.5239i	−0.0985626	−	0.937761i
$801$		0			0
$802$	12.2891	+	21.2853i	0.433942	+	0.751609i
$803$	−36.6742	−	1.44503i	−1.29421	−	0.0509940i
$804$		0			0
$805$	−1.98685	+	4.74939i	−0.0700273	+	0.167394i
$806$	−30.0647	+	21.8433i	−1.05898	+	0.769397i
$807$		0			0
$808$	−9.21626	+	10.2357i	−0.324227	+	0.360091i
$809$	8.32774	−	9.24889i	0.292788	−	0.325174i	−0.578747	−	0.815507i	$-0.696458\pi$
$809$	8.32774	−	9.24889i	0.292788	−	0.325174i	0.871535	+	0.490333i	$0.163125\pi$
$810$		0			0
$811$	22.4462	−	16.3081i	0.788191	−	0.572654i	−0.119235	−	0.992866i	$-0.538044\pi$
$811$	22.4462	−	16.3081i	0.788191	−	0.572654i	0.907426	+	0.420212i	$0.138044\pi$
$812$	12.2786	−	29.3510i	0.430896	−	1.03002i
$813$		0			0
$814$	20.6694	−	56.0076i	0.724461	−	1.96306i
$815$	−3.76038	−	6.51317i	−0.131720	−	0.228146i
$816$		0			0
$817$	1.29363	+	12.3080i	0.0452582	+	0.430603i
$818$	−20.0614	−	14.5755i	−0.701432	−	0.509620i
$819$		0			0
$820$	0.970991	+	2.98840i	0.0339085	+	0.104360i
$821$	29.9706	−	13.3438i	1.04598	−	0.465700i	0.189500	−	0.981881i	$-0.439313\pi$
$821$	29.9706	−	13.3438i	1.04598	−	0.465700i	0.856480	+	0.516181i	$0.172647\pi$
$822$		0			0
$823$	0.642109	−	0.136484i	0.0223825	−	0.00475755i	−0.196707	−	0.980462i	$-0.563025\pi$
$823$	0.642109	−	0.136484i	0.0223825	−	0.00475755i	0.219089	+	0.975705i	$0.429691\pi$
$824$	−11.6076	+	20.1050i	−0.404371	+	0.700390i
$825$		0			0
$826$	20.7568	−	29.9751i	0.722222	−	1.04297i
$827$	−6.33848	+	19.5078i	−0.220411	+	0.678354i	0.778315	+	0.627875i	$0.216075\pi$
$827$	−6.33848	+	19.5078i	−0.220411	+	0.678354i	−0.998725	+	0.0504794i	$0.983925\pi$
$828$		0			0
$829$	0.879970	−	8.37236i	0.0305626	−	0.290784i	−0.968556	−	0.248797i	$-0.919965\pi$
$829$	0.879970	−	8.37236i	0.0305626	−	0.290784i	0.999118	−	0.0419866i	$-0.0133687\pi$
$830$	7.19264	−	7.98824i	0.249660	−	0.277276i
$831$		0			0
$832$	53.2405	+	38.6815i	1.84578	+	1.34104i
$833$	−1.08162	+	18.1905i	−0.0374759	+	0.630265i
$834$		0			0
$835$	−3.07069	+	5.31860i	−0.106266	+	0.184058i
$836$	−0.870326	−	13.3013i	−0.0301009	−	0.460036i
$837$		0			0
$838$	53.7379	+	59.6820i	1.85634	+	2.06168i
$839$	31.8742	−	23.1580i	1.10042	−	0.799503i	0.119293	−	0.992859i	$-0.461937\pi$
$839$	31.8742	−	23.1580i	1.10042	−	0.799503i	0.981129	+	0.193356i	$0.0619373\pi$
$840$		0			0
$841$	−3.94789	−	12.1504i	−0.136134	−	0.418978i
$842$	43.5902	+	9.26539i	1.50222	+	0.319306i
$843$		0			0
$844$	48.7457	+	21.7030i	1.67789	+	0.747047i
$845$	−8.72603	−	9.69124i	−0.300185	−	0.333389i
$846$		0			0
$847$	−25.9804	+	13.1156i	−0.892697	+	0.450657i
$848$	−12.9004			−0.443002
$849$		0			0
$850$	20.9404	+	9.32327i	0.718250	+	0.319786i
$851$	1.59531	−	15.1784i	0.0546867	−	0.520309i
$852$		0			0
$853$	8.34555	+	25.6850i	0.285746	+	0.879436i	0.986174	+	0.165713i	$0.0529925\pi$
$853$	8.34555	+	25.6850i	0.285746	+	0.879436i	−0.700428	+	0.713723i	$0.747007\pi$
$854$	15.6263	+	13.4415i	0.534723	+	0.459957i
$855$		0			0
$856$	9.43234	+	10.4757i	0.322391	+	0.358051i
$857$	−7.07983	−	12.2626i	−0.241842	−	0.418883i	0.719397	−	0.694599i	$-0.244418\pi$
$857$	−7.07983	−	12.2626i	−0.241842	−	0.418883i	−0.961239	+	0.275716i	$0.911085\pi$
$858$		0			0
$859$	−8.62094	+	14.9319i	−0.294143	+	0.509470i	−0.974785	−	0.223146i	$-0.928367\pi$
$859$	−8.62094	+	14.9319i	−0.294143	+	0.509470i	0.680642	+	0.732616i	$0.261701\pi$
$860$	−8.71713	+	26.8286i	−0.297252	+	0.914846i
$861$		0			0
$862$	26.1534	+	19.0016i	0.890790	+	0.647197i
$863$	20.9304	+	4.44889i	0.712479	+	0.151442i	0.549872	−	0.835249i	$-0.314677\pi$
$863$	20.9304	+	4.44889i	0.712479	+	0.151442i	0.162607	+	0.986691i	$0.448010\pi$
$864$		0			0
$865$	−0.159020	+	1.51297i	−0.00540684	+	0.0514426i
$866$	−6.82632	−	64.9481i	−0.231968	−	2.20703i
$867$		0			0
$868$	−11.0844	−	23.4508i	−0.376230	−	0.795971i
$869$	32.3653	−	33.2165i	1.09792	−	1.12679i
$870$		0			0
$871$	−5.51293	+	1.17181i	−0.186799	+	0.0397053i
$872$	−0.186736	−	0.0831400i	−0.00632366	−	0.00281548i
$873$		0			0
$874$	−1.75848	−	5.41205i	−0.0594815	−	0.183065i
$875$	−23.2950	−	6.98947i	−0.787516	−	0.236287i
$876$		0			0
$877$	−1.70357	−	16.2083i	−0.0575253	−	0.547317i	−0.984893	−	0.173165i	$-0.944601\pi$
$877$	−1.70357	−	16.2083i	−0.0575253	−	0.547317i	0.927367	−	0.374152i	$-0.122066\pi$
$878$	−43.3365	+	9.21145i	−1.46254	+	0.310871i
$879$		0			0
$880$	−1.24866	+	3.38347i	−0.0420922	+	0.114057i
$881$	−36.6728			−1.23554			−0.617769	−	0.786359i	$-0.711964\pi$
$881$	−36.6728			−1.23554			−0.617769	+	0.786359i	$0.711964\pi$
$882$		0			0
$883$	6.10529	−	4.43575i	0.205459	−	0.149275i	−0.480298	−	0.877106i	$-0.659471\pi$
$883$	6.10529	−	4.43575i	0.205459	−	0.149275i	0.685757	+	0.727831i	$0.259471\pi$
$884$	−35.9847	+	16.0214i	−1.21030	+	0.538858i
$885$		0			0
$886$	12.7449	−	14.1546i	0.428173	−	0.475534i
$887$	−11.2521	+	5.00974i	−0.377807	+	0.168210i	−0.586849	−	0.809696i	$-0.699632\pi$
$887$	−11.2521	+	5.00974i	−0.377807	+	0.168210i	0.209043	+	0.977907i	$0.432965\pi$
$888$		0			0
$889$	17.7733	+	23.3320i	0.596099	+	0.782532i
$890$	42.1230			1.41197
$891$		0			0
$892$	3.14995	+	5.45588i	0.105468	+	0.182676i
$893$	13.0235	−	2.76824i	0.435816	−	0.0926355i
$894$		0			0
$895$	4.49234	+	3.26387i	0.150162	+	0.109099i
$896$	−29.7804	+	28.0622i	−0.994893	+	0.937494i
$897$		0			0
$898$	21.6777	−	9.65152i	0.723393	−	0.322075i
$899$	12.0836	+	5.37999i	0.403012	+	0.179433i
$900$		0			0
$901$	15.8714	−	27.4901i	0.528754	−	0.915829i
$902$	−1.08896	+	7.50455i	−0.0362585	+	0.249874i
$903$		0			0
$904$	−7.71822	+	23.7542i	−0.256704	+	0.790054i
$905$	2.68052	+	25.5035i	0.0891036	+	0.847765i
$906$		0			0
$907$	1.01594	−	1.12831i	0.0337337	−	0.0374650i	−0.726042	−	0.687651i	$-0.758642\pi$
$907$	1.01594	−	1.12831i	0.0337337	−	0.0374650i	0.759776	+	0.650185i	$0.225309\pi$
$908$	−32.9761	−	7.00928i	−1.09435	−	0.232611i
$909$		0			0
$910$	26.2956	−	15.9871i	0.871692	−	0.529968i
$911$	4.72572	−	14.5443i	0.156570	−	0.481873i	−0.841747	−	0.539873i	$-0.818472\pi$
$911$	4.72572	−	14.5443i	0.156570	−	0.481873i	0.998317	+	0.0579998i	$0.0184723\pi$
$912$		0			0
$913$	14.4293	−	5.75485i	0.477540	−	0.190458i
$914$	−5.62144	−	9.73662i	−0.185941	−	0.322059i
$915$		0			0
$916$	−67.3264	+	48.9155i	−2.22453	+	1.61621i
$917$	−2.61680	+	13.8471i	−0.0864143	+	0.457273i
$918$		0			0
$919$	18.3544	+	3.90134i	0.605454	+	0.128693i	0.500431	−	0.865776i	$-0.333175\pi$
$919$	18.3544	+	3.90134i	0.605454	+	0.128693i	0.105023	+	0.994470i	$0.466508\pi$
$920$	0.447542	−	4.25807i	0.0147550	−	0.140385i
$921$		0			0
$922$	−22.9849	−	25.5273i	−0.756966	−	0.840696i
$923$	37.6639			1.23972
$924$		0			0
$925$	31.7917			1.04530
$926$	47.3545	+	52.5925i	1.55617	+	1.72830i
$927$		0			0
$928$	2.84742	−	27.0914i	0.0934713	−	0.889320i
$929$	34.0162	+	7.23037i	1.11604	+	0.237221i	0.728778	−	0.684750i	$-0.240089\pi$
$929$	34.0162	+	7.23037i	1.11604	+	0.237221i	0.387258	+	0.921971i	$0.373422\pi$
$930$		0			0
$931$	6.61643	+	6.71013i	0.216845	+	0.219916i
$932$	−16.5977	+	12.0589i	−0.543675	+	0.395003i
$933$		0			0
$934$	20.1548	+	34.9091i	0.659484	+	1.14226i
$935$	−5.67378	−	6.82353i	−0.185553	−	0.223153i
$936$		0			0
$937$	−2.05971	+	6.33914i	−0.0672878	+	0.207091i	−0.979047	−	0.203635i	$-0.934725\pi$
$937$	−2.05971	+	6.33914i	−0.0672878	+	0.207091i	0.911759	+	0.410725i	$0.134725\pi$
$938$	−0.148877	−	6.56758i	−0.00486100	−	0.214439i
$939$		0			0
$940$	29.6856	+	6.30987i	0.968237	+	0.205805i
$941$	31.7077	−	35.2150i	1.03364	−	1.14798i	0.0448011	−	0.998996i	$-0.485735\pi$
$941$	31.7077	−	35.2150i	1.03364	−	1.14798i	0.988840	−	0.148979i	$-0.0475987\pi$
$942$		0			0
$943$	0.202639	+	1.92798i	0.00659882	+	0.0627836i
$944$	2.01777	−	6.21006i	0.0656728	−	0.202120i
$945$		0			0
$946$	−47.5097	+	48.7592i	−1.54467	+	1.58530i
$947$	−9.06351	+	15.6985i	−0.294524	+	0.510131i	−0.974874	−	0.222756i	$-0.928495\pi$
$947$	−9.06351	+	15.6985i	−0.294524	+	0.510131i	0.680350	+	0.732888i	$0.261828\pi$
$948$		0			0
$949$	51.2383	+	22.8128i	1.66327	+	0.740534i
$950$	10.8290	−	4.82137i	0.351338	−	0.156426i
$951$		0			0
$952$	−3.48601	−	14.7485i	−0.112982	−	0.478002i
$953$	−35.0699	−	25.4797i	−1.13602	−	0.825370i	−0.149464	−	0.988767i	$-0.547755\pi$
$953$	−35.0699	−	25.4797i	−1.13602	−	0.825370i	−0.986560	+	0.163398i	$0.947755\pi$
$954$		0			0
$955$	−22.9754	+	4.88358i	−0.743468	+	0.158029i
$956$	16.6613	+	28.8582i	0.538865	+	0.933341i
$957$		0			0
$958$	−14.4252			−0.466056
$959$	4.16558	−	9.95745i	0.134514	−	0.321543i
$960$		0			0
$961$	−18.4685	+	8.22270i	−0.595758	+	0.265249i
$962$	−61.0451	+	67.7974i	−1.96817	+	2.18588i
$963$		0			0
$964$	45.0163	−	20.0425i	1.44988	−	0.645527i
$965$	−6.10377	+	4.43465i	−0.196487	+	0.142756i
$966$		0			0
$967$	−48.3991			−1.55641			−0.778205	−	0.628011i	$-0.783869\pi$
$967$	−48.3991			−1.55641			−0.778205	+	0.628011i	$0.783869\pi$
$968$	17.5605	−	16.6568i	0.564415	−	0.535371i
$969$		0			0
$970$	−15.9606	+	3.39253i	−0.512464	+	0.108928i
$971$	−5.78816	−	55.0707i	−0.185751	−	1.76730i	−0.549204	−	0.835689i	$-0.685069\pi$
$971$	−5.78816	−	55.0707i	−0.185751	−	1.76730i	0.363453	−	0.931613i	$-0.381598\pi$
$972$		0			0
$973$	−49.9544	−	14.9884i	−1.60146	−	0.480505i
$974$	3.02255	+	9.30246i	0.0968488	+	0.298070i
$975$		0			0
$976$	3.37225	+	1.50142i	0.107943	+	0.0480594i
$977$	−13.6340	+	2.89801i	−0.436192	+	0.0927154i	−0.420774	−	0.907166i	$-0.638241\pi$
$977$	−13.6340	+	2.89801i	−0.436192	+	0.0927154i	−0.0154182	+	0.999881i	$0.504908\pi$
$978$		0			0
$979$	54.5944	+	26.9305i	1.74484	+	0.860704i
$980$	7.55650	+	20.1068i	0.241384	+	0.642287i
$981$		0			0
$982$	9.53734	+	90.7417i	0.304349	+	2.89568i
$983$	−0.969245	+	9.22175i	−0.0309141	+	0.294128i	0.968131	+	0.250443i	$0.0805764\pi$
$983$	−0.969245	+	9.22175i	−0.0309141	+	0.294128i	−0.999045	+	0.0436848i	$0.986090\pi$
$984$		0			0
$985$	−26.4193	−	5.61559i	−0.841789	−	0.178928i
$986$	18.9412	+	13.7616i	0.603211	+	0.438258i
$987$		0			0
$988$	−6.29465	+	19.3729i	−0.200260	+	0.616336i
$989$	−8.70193	+	15.0722i	−0.276705	+	0.479268i
$990$		0			0
$991$	−10.8473	−	18.7881i	−0.344576	−	0.596823i	0.640701	−	0.767791i	$-0.278644\pi$
$991$	−10.8473	−	18.7881i	−0.344576	−	0.596823i	−0.985277	+	0.170968i	$0.945311\pi$
$992$	−14.8603	−	16.5041i	−0.471817	−	0.524005i
$993$		0			0
$994$	−8.15182	+	43.1365i	−0.258560	+	1.36821i
$995$	−3.85226	−	11.8560i	−0.122125	−	0.375861i
$996$		0			0
$997$	1.02189	−	9.72262i	0.0323635	−	0.307918i	−0.966351	−	0.257228i	$-0.917191\pi$
$997$	1.02189	−	9.72262i	0.0323635	−	0.307918i	0.998714	−	0.0506909i	$-0.0161423\pi$
$998$	67.7080	+	30.1455i	2.14326	+	0.954240i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.by.c.163.7		64
3.2	odd	2		231.2.y.b.163.2	yes	64
7.4	even	3	inner	693.2.by.c.361.2		64
11.5	even	5	inner	693.2.by.c.478.2		64
21.11	odd	6		231.2.y.b.130.7	yes	64
33.5	odd	10		231.2.y.b.16.7	✓	64
77.60	even	15	inner	693.2.by.c.676.7		64
231.137	odd	30		231.2.y.b.214.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.b.16.7	✓	64	33.5	odd	10
231.2.y.b.130.7	yes	64	21.11	odd	6
231.2.y.b.163.2	yes	64	3.2	odd	2
231.2.y.b.214.2	yes	64	231.137	odd	30
693.2.by.c.163.7		64	1.1	even	1	trivial
693.2.by.c.361.2		64	7.4	even	3	inner
693.2.by.c.478.2		64	11.5	even	5	inner
693.2.by.c.676.7		64	77.60	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.by (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.49404 + 1.65930i) q^{2} +(-0.312065 + 2.96910i) q^{4} +(1.00537 + 0.213698i) q^{5} +(2.49708 - 0.874397i) q^{7} +(-1.78011 + 1.29333i) q^{8} +O(q^{10})\)	\(q+(1.49404 + 1.65930i) q^{2} +(-0.312065 + 2.96910i) q^{4} +(1.00537 + 0.213698i) q^{5} +(2.49708 - 0.874397i) q^{7} +(-1.78011 + 1.29333i) q^{8} +(1.14748 + 1.98749i) q^{10} +(0.216549 + 3.30955i) q^{11} +(1.56619 - 4.82025i) q^{13} +(5.18164 + 2.83703i) q^{14} +(1.03484 + 0.219963i) q^{16} +(-1.74191 + 1.93458i) q^{17} +(0.140718 + 1.33884i) q^{19} +(-0.948233 + 2.91836i) q^{20} +(-5.16801 + 5.30393i) q^{22} +(-0.946580 + 1.63952i) q^{23} +(-3.60262 - 1.60399i) q^{25} +(10.3382 - 4.60287i) q^{26} +(1.81692 + 7.68697i) q^{28} +(-3.25868 - 2.36757i) q^{29} +(-3.21210 + 0.682752i) q^{31} +(3.38146 + 5.85686i) q^{32} -5.81254 q^{34} +(2.69735 - 0.345471i) q^{35} +(-7.36469 + 3.27897i) q^{37} +(-2.01131 + 2.23379i) q^{38} +(-2.06605 + 0.919867i) q^{40} +(0.828434 - 0.601893i) q^{41} +9.19303 q^{43} +(-9.89396 - 0.389839i) q^{44} +(-4.13470 + 0.878858i) q^{46} +(-1.03382 - 9.83610i) q^{47} +(5.47086 - 4.36689i) q^{49} +(-2.72097 - 8.37428i) q^{50} +(13.8230 + 6.15442i) q^{52} +(-11.9272 + 2.53519i) q^{53} +(-0.489532 + 3.37360i) q^{55} +(-3.31421 + 4.78607i) q^{56} +(-0.940093 - 8.94438i) q^{58} +(0.645139 - 6.13808i) q^{59} +(3.41290 + 0.725434i) q^{61} +(-5.93191 - 4.30978i) q^{62} +(-4.01240 + 12.3489i) q^{64} +(2.60468 - 4.51144i) q^{65} +(-0.556014 - 0.963044i) q^{67} +(-5.20038 - 5.77561i) q^{68} +(4.60320 + 3.95958i) q^{70} +(2.29639 + 7.06755i) q^{71} +(-1.15674 + 11.0057i) q^{73} +(-16.4440 - 7.32133i) q^{74} -4.01908 q^{76} +(3.43460 + 8.07487i) q^{77} +(-9.35663 - 10.3916i) q^{79} +(0.993397 + 0.442289i) q^{80} +(2.23644 + 0.475370i) q^{82} +(-1.44739 - 4.45461i) q^{83} +(-2.16468 + 1.57273i) q^{85} +(13.7348 + 15.2540i) q^{86} +(-4.66581 - 5.61130i) q^{88} +(9.17730 - 15.8955i) q^{89} +(-0.303894 - 13.4060i) q^{91} +(-4.57252 - 3.32213i) q^{92} +(14.7765 - 16.4110i) q^{94} +(-0.144635 + 1.37611i) q^{95} +(-2.19712 + 6.76203i) q^{97} +(15.4197 + 2.55350i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{2} + 10 q^{4} + 4 q^{5} - q^{7} - 8 q^{8}+O(q^{10}) \) 64 * q - 4 * q^2 + 10 * q^4 + 4 * q^5 - q^7 - 8 * q^8	\( 64 q - 4 q^{2} + 10 q^{4} + 4 q^{5} - q^{7} - 8 q^{8} - 14 q^{10} - 11 q^{11} - 8 q^{13} - 6 q^{14} + 4 q^{17} - 2 q^{19} - 24 q^{20} - 14 q^{22} - 10 q^{25} - 4 q^{26} + 29 q^{28} + 58 q^{29} - 19 q^{31} + 64 q^{32} - 88 q^{34} - 17 q^{35} - 20 q^{37} - 29 q^{38} + 51 q^{40} + 68 q^{41} + 92 q^{43} + 21 q^{44} - 5 q^{46} + 26 q^{47} + 37 q^{49} + 10 q^{50} - 14 q^{52} + 3 q^{53} - 32 q^{55} - 24 q^{56} + 52 q^{58} - 7 q^{59} - 21 q^{61} - 92 q^{62} - 72 q^{64} + 66 q^{65} - 4 q^{67} + 17 q^{68} - q^{70} - 58 q^{71} - 3 q^{73} + 28 q^{74} + 168 q^{76} + 34 q^{77} + 9 q^{79} + 5 q^{80} - 42 q^{82} - 60 q^{83} + 110 q^{85} - 13 q^{86} + 92 q^{88} + 10 q^{89} + 10 q^{91} - 110 q^{92} - 46 q^{94} - 43 q^{95} + 64 q^{97} + 88 q^{98}+O(q^{100}) \) 64 * q - 4 * q^2 + 10 * q^4 + 4 * q^5 - q^7 - 8 * q^8 - 14 * q^10 - 11 * q^11 - 8 * q^13 - 6 * q^14 + 4 * q^17 - 2 * q^19 - 24 * q^20 - 14 * q^22 - 10 * q^25 - 4 * q^26 + 29 * q^28 + 58 * q^29 - 19 * q^31 + 64 * q^32 - 88 * q^34 - 17 * q^35 - 20 * q^37 - 29 * q^38 + 51 * q^40 + 68 * q^41 + 92 * q^43 + 21 * q^44 - 5 * q^46 + 26 * q^47 + 37 * q^49 + 10 * q^50 - 14 * q^52 + 3 * q^53 - 32 * q^55 - 24 * q^56 + 52 * q^58 - 7 * q^59 - 21 * q^61 - 92 * q^62 - 72 * q^64 + 66 * q^65 - 4 * q^67 + 17 * q^68 - q^70 - 58 * q^71 - 3 * q^73 + 28 * q^74 + 168 * q^76 + 34 * q^77 + 9 * q^79 + 5 * q^80 - 42 * q^82 - 60 * q^83 + 110 * q^85 - 13 * q^86 + 92 * q^88 + 10 * q^89 + 10 * q^91 - 110 * q^92 - 46 * q^94 - 43 * q^95 + 64 * q^97 + 88 * q^98

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