LMFDB - Embedded newform 693.2.by.c.676.7

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			676.7
Character	$\chi$	$=$	693.676
Dual form			693.2.by.c.163.7

$q$-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 $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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	0.0720411	−	0.997402i	$-0.477049\pi$
$2$	1.49404	−	1.65930i	1.05645	−	1.17330i	0.984407	−	0.175903i	$-0.0562846\pi$
$3$		0			0
$3$		0			0
$4$	−0.312065	−	2.96910i	−0.156033	−	1.48455i
$5$	1.00537	−	0.213698i	0.449615	−	0.0955687i	0.0224617	−	0.999748i	$-0.492850\pi$
$5$	1.00537	−	0.213698i	0.449615	−	0.0955687i	0.427154	+	0.904179i	$0.359516\pi$
$6$		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	0.893717	+	0.448632i	$0.148088\pi$
$13$	1.56619	+	4.82025i	0.434384	+	1.33690i	−0.459333	+	0.888264i	$0.651912\pi$
$14$	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	0.493905	−	0.869516i	$-0.335569\pi$
$17$	−1.74191	−	1.93458i	−0.422474	−	0.469205i	−0.916380	+	0.400311i	$0.868902\pi$
$18$		0			0
$19$	0.140718	−	1.33884i	0.0322830	−	0.307152i	−0.966451	−	0.256851i	$-0.917315\pi$
$19$	0.140718	−	1.33884i	0.0322830	−	0.307152i	0.998734	−	0.0503013i	$-0.0160182\pi$
$20$	−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	0.750301	−	0.661096i	$-0.229909\pi$
$23$	−0.946580	−	1.63952i	−0.197376	−	0.341864i	−0.947677	+	0.319232i	$0.896575\pi$
$24$		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	−0.847693	−	0.530487i	$-0.822009\pi$
$29$	−3.25868	+	2.36757i	−0.605121	+	0.439646i	0.242572	+	0.970133i	$0.422009\pi$
$30$		0			0
$31$	−3.21210	−	0.682752i	−0.576910	−	0.122626i	−0.0897892	−	0.995961i	$-0.528619\pi$
$31$	−3.21210	−	0.682752i	−0.576910	−	0.122626i	−0.487120	+	0.873335i	$0.661953\pi$
$32$	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	−0.300762	−	0.953699i	$-0.597241\pi$
$37$	−7.36469	−	3.27897i	−1.21075	−	0.539060i	−0.909986	+	0.414639i	$0.863908\pi$
$38$	−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	0.650593	−	0.759427i	$-0.274520\pi$
$41$	0.828434	+	0.601893i	0.129380	+	0.0939999i	−0.521213	+	0.853426i	$0.674520\pi$
$42$		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	0.613406	+	0.789768i	$0.289799\pi$
$47$	−1.03382	+	9.83610i	−0.150798	+	1.43474i	−0.764204	+	0.644975i	$0.776868\pi$
$48$		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	−0.705537	−	0.708673i	$-0.749294\pi$
$53$	−11.9272	−	2.53519i	−1.63832	−	0.348236i	−0.932784	+	0.360437i	$0.882628\pi$
$54$		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	0.952725	+	0.303834i	$0.0982667\pi$
$59$	0.645139	+	6.13808i	0.0839899	+	0.799110i	−0.868735	+	0.495277i	$0.835067\pi$
$60$		0			0
$61$	3.41290	−	0.725434i	0.436977	−	0.0928823i	0.0158300	−	0.999875i	$-0.494961\pi$
$61$	3.41290	−	0.725434i	0.436977	−	0.0928823i	0.421147	+	0.906992i	$0.361628\pi$
$62$	−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	−0.897989	−	0.440018i	$-0.854972\pi$
$67$	−0.556014	+	0.963044i	−0.0679279	+	0.117655i	0.830061	+	0.557672i	$0.188305\pi$
$68$	−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	−0.717331	−	0.696732i	$-0.754636\pi$
$71$	2.29639	−	7.06755i	0.272531	−	0.838764i	0.989862	−	0.142032i	$-0.0453635\pi$
$72$		0			0
$73$	−1.15674	−	11.0057i	−0.135386	−	1.28811i	−0.825495	−	0.564409i	$-0.809104\pi$
$73$	−1.15674	−	11.0057i	−0.135386	−	1.28811i	0.690109	−	0.723706i	$-0.257563\pi$
$74$	−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	−0.0675061	+	0.997719i	$0.521504\pi$
$79$	−9.35663	+	10.3916i	−1.05270	+	1.16915i	−0.985197	+	0.171426i	$0.945162\pi$
$80$	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	−0.998533	−	0.0541542i	$-0.982754\pi$
$83$	−1.44739	+	4.45461i	−0.158872	+	0.488957i	0.839661	+	0.543111i	$0.182754\pi$
$84$		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	0.687038	+	0.726621i	$0.258911\pi$
$89$	9.17730	+	15.8955i	0.972792	+	1.68492i	0.285754	+	0.958303i	$0.407756\pi$
$90$		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	−0.998481	−	0.0551061i	$-0.982450\pi$
$97$	−2.19712	−	6.76203i	−0.223083	−	0.686580i	0.775397	−	0.631474i	$-0.217550\pi$
$98$	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	0.502199	−	0.864752i	$-0.332525\pi$
$101$	6.12292	+	1.30147i	0.609253	+	0.129501i	0.107055	+	0.994253i	$0.465858\pi$
$102$		0			0
$103$	9.63859	+	4.29138i	0.949719	+	0.422842i	0.822330	−	0.569011i	$-0.192674\pi$
$103$	9.63859	+	4.29138i	0.949719	+	0.422842i	0.127389	+	0.991853i	$0.459340\pi$
$104$	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	0.913267	+	0.407362i	$0.133551\pi$
$107$	−0.669658	+	6.37137i	−0.0647383	+	0.615944i	−0.978005	+	0.208582i	$0.933115\pi$
$108$		0			0
$109$	0.0464491	−	0.0804522i	0.00444901	−	0.00770592i	−0.863792	−	0.503848i	$-0.831917\pi$
$109$	0.0464491	−	0.0804522i	0.00444901	−	0.00770592i	0.868241	+	0.496142i	$0.165250\pi$
$110$	−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	0.928943	−	0.370222i	$-0.120719\pi$
$113$	9.18338	+	6.67212i	0.863900	+	0.627660i	−0.0650432	+	0.997882i	$0.520719\pi$
$114$		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	−0.676071	−	0.736837i	$-0.736319\pi$
$127$	3.42572	−	10.5433i	0.303984	−	0.935566i	0.980054	−	0.198729i	$-0.0636814\pi$
$128$	−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	0.725914	−	0.687786i	$-0.241417\pi$
$131$	−2.66318	−	4.61277i	−0.232683	−	0.403019i	−0.958597	+	0.284767i	$0.908084\pi$
$132$		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	0.848384	−	0.529381i	$-0.177576\pi$
$137$	2.72980	+	3.03175i	0.233222	+	0.259020i	−0.615162	+	0.788401i	$0.710909\pi$
$138$		0			0
$139$	−15.9478	+	11.5867i	−1.35267	+	0.982774i	−0.353799	+	0.935321i	$0.615110\pi$
$139$	−15.9478	+	11.5867i	−1.35267	+	0.982774i	−0.998873	+	0.0474531i	$0.984890\pi$
$140$	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	−0.0121618	−	0.999926i	$-0.503871\pi$
$149$	4.68041	−	0.994852i	0.383434	−	0.0815015i	0.395596	+	0.918425i	$0.370538\pi$
$150$		0			0
$151$	−5.02084	+	2.23542i	−0.408590	+	0.181916i	−0.600731	−	0.799451i	$-0.705124\pi$
$151$	−5.02084	+	2.23542i	−0.408590	+	0.181916i	0.192141	+	0.981367i	$0.438457\pi$
$152$	−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	0.530894	−	0.847438i	$-0.321856\pi$
$157$	18.9942	−	8.45676i	1.51590	−	0.674923i	0.985007	+	0.172516i	$0.0551895\pi$
$158$	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	−0.903725	−	0.428113i	$-0.859179\pi$
$163$	−4.89610	+	5.43767i	−0.383492	+	0.425911i	0.520233	+	0.854024i	$0.325845\pi$
$164$	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	0.853853	−	0.520514i	$-0.174260\pi$
$167$	−1.84641	−	5.68265i	−0.142879	−	0.439737i	−0.996732	+	0.0807774i	$0.974260\pi$
$168$		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	−0.987065	−	0.160320i	$-0.948747\pi$
$173$	0.154714	−	1.47200i	0.0117627	−	0.111914i	0.998828	+	0.0484057i	$0.0154140\pi$
$174$		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	−0.213916	−	0.976852i	$-0.568622\pi$
$179$	4.93541	−	2.19738i	0.368890	−	0.164240i	0.582805	+	0.812612i	$0.301955\pi$
$180$		0			0
$181$	7.70985	−	23.7285i	0.573068	−	1.76372i	−0.0695958	−	0.997575i	$-0.522171\pi$
$181$	7.70985	−	23.7285i	0.573068	−	1.76372i	0.642664	−	0.766148i	$-0.277829\pi$
$182$	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	−0.526504	−	0.850172i	$-0.676498\pi$
$191$	−20.8770	−	9.29503i	−1.51061	−	0.672565i	−0.984101	+	0.177607i	$0.943164\pi$
$192$		0			0
$193$	−4.91168	−	5.45497i	−0.353550	−	0.392657i	0.539967	−	0.841686i	$-0.318437\pi$
$193$	−4.91168	−	5.45497i	−0.353550	−	0.392657i	−0.893517	+	0.449029i	$0.851770\pi$
$194$	−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	−0.996863	−	0.0791483i	$-0.974780\pi$
$199$	−6.06430	+	10.5037i	−0.429887	+	0.744586i	0.566976	+	0.823734i	$0.308113\pi$
$200$	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	0.939888	+	0.341483i	$0.110929\pi$
$211$	5.52303	+	16.9981i	0.380221	+	1.17020i	−0.559667	+	0.828718i	$0.689071\pi$
$212$	−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	0.643477	−	0.765465i	$-0.277491\pi$
$223$	1.70719	+	1.24034i	0.114322	+	0.0830596i	−0.529155	+	0.848525i	$0.677491\pi$
$224$	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	−0.961219	−	0.275786i	$-0.911062\pi$
$227$	−1.18037	−	11.2305i	−0.0783440	−	0.745393i	0.882875	−	0.469608i	$-0.155605\pi$
$228$		0			0
$229$	18.6521	−	20.7153i	1.23257	−	1.36890i	0.326819	−	0.945087i	$-0.394023\pi$
$229$	18.6521	−	20.7153i	1.23257	−	1.36890i	0.905748	−	0.423817i	$-0.139310\pi$
$230$	−4.34472			−0.286482
$231$		0			0
$232$	8.86285			0.581875
$233$	4.59822	−	5.10684i	0.301240	−	0.334560i	−0.573453	−	0.819238i	$-0.694397\pi$
$233$	4.59822	−	5.10684i	0.301240	−	0.334560i	0.874693	+	0.484678i	$0.161063\pi$
$234$		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	0.840200	−	0.542277i	$-0.182438\pi$
$239$	9.02995	+	6.56065i	0.584099	+	0.424373i	−0.256100	+	0.966650i	$0.582438\pi$
$240$		0			0
$241$	−8.25275	+	14.2942i	−0.531606	+	0.920769i	0.467713	+	0.883880i	$0.345078\pi$
$241$	−8.25275	+	14.2942i	−0.531606	+	0.920769i	−0.999319	+	0.0368888i	$0.988255\pi$
$242$	−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	0.882168	+	0.470935i	$0.156083\pi$
$251$	7.05468	+	21.7121i	0.445288	+	1.37045i	−0.436880	+	0.899520i	$0.643917\pi$
$252$		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	0.182822	−	0.983146i	$-0.441477\pi$
$257$	−6.82073	−	3.03679i	−0.425466	−	0.189430i	−0.608288	+	0.793716i	$0.708143\pi$
$258$		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	−0.283102	−	0.959090i	$-0.591364\pi$
$263$	11.1744	−	19.3547i	0.689045	−	1.19346i	0.972147	−	0.234371i	$-0.0753031\pi$
$264$		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	0.766191	−	0.642613i	$-0.222150\pi$
$269$	0.771020	+	0.856304i	0.0470099	+	0.0522098i	−0.719181	+	0.694823i	$0.755483\pi$
$270$		0			0
$271$	−6.54462	−	2.91385i	−0.397558	−	0.177004i	0.198213	−	0.980159i	$-0.436486\pi$
$271$	−6.54462	−	2.91385i	−0.397558	−	0.177004i	−0.595770	+	0.803155i	$0.703153\pi$
$272$	−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	−0.0990135	−	0.995086i	$-0.531569\pi$
$277$	−9.88954	−	2.10209i	−0.594205	−	0.126302i	−0.495191	+	0.868784i	$0.664902\pi$
$278$	−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	−0.573909	−	0.818919i	$-0.694574\pi$
$281$	6.23152	−	19.1787i	0.371742	−	1.14410i	0.945651	−	0.325184i	$-0.105426\pi$
$282$		0			0
$283$	−1.79246	+	0.798054i	−0.106551	+	0.0474394i	−0.459320	−	0.888271i	$-0.651907\pi$
$283$	−1.79246	+	0.798054i	−0.106551	+	0.0474394i	0.352769	+	0.935710i	$0.385240\pi$
$284$	−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	−0.324136	+	0.946011i	$0.605073\pi$
$293$	−22.6634	+	16.4659i	−1.32401	+	0.961949i	−0.999873	+	0.0159379i	$0.994927\pi$
$294$		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	−0.991072	−	0.133328i	$-0.957434\pi$
$311$	−27.4253	+	12.2105i	−1.55515	+	0.692396i	−0.564075	+	0.825724i	$0.690767\pi$
$312$		0			0
$313$	−26.7599	+	5.68800i	−1.51256	+	0.321505i	−0.888136	−	0.459581i	$-0.848000\pi$
$313$	−26.7599	+	5.68800i	−1.51256	+	0.321505i	−0.624424	+	0.781085i	$0.714666\pi$
$314$	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	−0.0350591	−	0.999385i	$-0.511162\pi$
$317$	17.1371	−	19.0327i	0.962516	−	1.06898i	0.997575	−	0.0695972i	$-0.0221714\pi$
$318$		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	0.988396	−	0.151897i	$-0.0485381\pi$
$331$	6.59787	+	11.4279i	0.362652	+	0.628132i	−0.625744	+	0.780028i	$0.715205\pi$
$332$	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	0.00553877	−	0.999985i	$-0.498237\pi$
$337$	17.5919	−	12.7813i	0.958292	−	0.696240i	0.952754	+	0.303745i	$0.0982369\pi$
$338$	−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	0.444260	−	0.895898i	$-0.353467\pi$
$347$	−9.18671	−	10.2029i	−0.493168	−	0.547719i	−0.937428	+	0.348179i	$0.886800\pi$
$348$		0			0
$349$	−18.6455	−	13.5467i	−0.998070	−	0.725140i	−0.0363964	−	0.999337i	$-0.511588\pi$
$349$	−18.6455	−	13.5467i	−0.998070	−	0.725140i	−0.961673	+	0.274197i	$0.911588\pi$
$350$	−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	−0.917196	−	0.398437i	$-0.869553\pi$
$353$	−2.13324	+	3.69489i	−0.113541	+	0.196659i	0.803655	+	0.595096i	$0.202886\pi$
$354$		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	−0.00799080	−	0.999968i	$-0.502544\pi$
$359$	−14.3328	−	6.38140i	−0.756459	−	0.336797i	−0.748468	+	0.663171i	$0.769210\pi$
$360$		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	0.968316	+	0.249728i	$0.0803411\pi$
$367$	1.40004	+	13.3205i	0.0730814	+	0.695323i	−0.895235	+	0.445595i	$0.852992\pi$
$368$	−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	−0.985013	−	0.172478i	$-0.944823\pi$
$373$	−12.3967	−	21.4717i	−0.641877	−	1.11176i	0.343137	−	0.939286i	$-0.388511\pi$
$374$	−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	−0.823618	−	0.567145i	$-0.808048\pi$
$379$	3.42758	−	10.5490i	0.176063	−	0.541865i	0.999680	+	0.0252801i	$0.00804775\pi$
$380$	−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	−0.694780	−	0.719222i	$-0.744498\pi$
$383$	1.82252	−	2.02412i	0.0931266	−	0.103428i	0.787907	+	0.615795i	$0.211165\pi$
$384$		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	−0.884813	−	0.465946i	$-0.845714\pi$
$389$	−2.29204	−	21.8073i	−0.116211	−	1.10567i	0.768602	−	0.639727i	$-0.220953\pi$
$390$		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	0.657035	−	0.753860i	$-0.271810\pi$
$397$	−6.46252	−	11.1934i	−0.324344	−	0.561781i	−0.981379	+	0.192079i	$0.938477\pi$
$398$	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	0.0689382	−	0.997621i	$-0.478039\pi$
$401$	10.7671	−	2.28863i	0.537685	−	0.114289i	0.468747	+	0.883332i	$0.344706\pi$
$402$		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	−0.0686538	−	0.997641i	$-0.521870\pi$
$409$	−10.8632	−	2.30904i	−0.537149	−	0.114175i	−0.468495	+	0.883466i	$0.655204\pi$
$410$	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	0.907058	−	0.421006i	$-0.138323\pi$
$421$	16.1469	+	11.7314i	0.786953	+	0.571755i	−0.120105	+	0.992761i	$0.538323\pi$
$422$	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	0.535941	−	0.844256i	$-0.319957\pi$
$431$	14.1620	+	3.01022i	0.682157	+	0.144997i	0.146217	+	0.989253i	$0.453290\pi$
$432$		0			0
$433$	−23.6623	+	17.1917i	−1.13714	+	0.826179i	−0.986718	−	0.162443i	$-0.948063\pi$
$433$	−23.6623	+	17.1917i	−1.13714	+	0.826179i	−0.150420	+	0.988622i	$0.548063\pi$
$434$	−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	0.526025	−	0.850469i	$-0.323682\pi$
$439$	−9.92126	−	17.1841i	−0.473516	−	0.820154i	−0.999540	+	0.0303159i	$0.990349\pi$
$440$	−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	0.952705	+	0.303897i	$0.0982878\pi$
$443$	−0.891676	+	8.48373i	−0.0423648	+	0.403074i	−0.995070	+	0.0991773i	$0.968379\pi$
$444$		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	0.998159	−	0.0606458i	$-0.0193160\pi$
$449$	3.28407	+	10.1073i	0.154985	+	0.476994i	−0.843175	+	0.537640i	$0.819316\pi$
$450$		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	−0.321662	−	0.946855i	$-0.604241\pi$
$457$	−4.92526	+	1.04690i	−0.230394	+	0.0489718i	0.0912677	+	0.995826i	$0.470908\pi$
$458$	−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	0.219669	−	0.975574i	$-0.429502\pi$
$467$	17.6587	−	3.75348i	0.817149	−	0.173690i	0.597480	+	0.801884i	$0.296169\pi$
$468$		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	0.636246	−	0.771486i	$-0.280486\pi$
$479$	−4.32294	−	4.80111i	−0.197520	−	0.219368i	−0.833766	+	0.552118i	$0.813820\pi$
$480$		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	−0.314056	−	0.949404i	$-0.601688\pi$
$487$	4.00193	−	1.78177i	0.181345	−	0.0807398i	0.495401	+	0.868665i	$0.335021\pi$
$488$	−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	0.518510	−	0.855071i	$-0.326487\pi$
$491$	33.0596	−	24.0192i	1.49196	−	1.08397i	0.973450	−	0.228901i	$-0.0735132\pi$
$492$		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	0.950980	−	0.309252i	$-0.100079\pi$
$499$	30.3241	+	13.5011i	1.35749	+	0.604394i	0.406511	+	0.913646i	$0.366745\pi$
$500$	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	0.139939	−	0.990160i	$-0.455309\pi$
$503$	−17.0117	−	12.3597i	−0.758516	−	0.551094i	−0.898455	+	0.439066i	$0.855309\pi$
$504$		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	−0.648834	−	0.760930i	$-0.724743\pi$
$509$	3.24941	−	30.9161i	0.144028	−	1.37033i	0.792862	−	0.609401i	$-0.208590\pi$
$510$		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	0.830187	+	0.557486i	$0.188234\pi$
$521$	3.05973	+	29.1114i	0.134049	+	1.27539i	−0.696137	+	0.717909i	$0.745099\pi$
$522$		0			0
$523$	9.16995	−	1.94913i	0.400974	−	0.0852296i	−0.00301064	−	0.999995i	$-0.500958\pi$
$523$	9.16995	−	1.94913i	0.400974	−	0.0852296i	0.403984	+	0.914766i	$0.367625\pi$
$524$	−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	0.164859	−	0.986317i	$-0.447283\pi$
$541$	26.2492	−	29.1527i	1.12854	−	1.25337i	0.963681	−	0.267055i	$-0.0860504\pi$
$542$	−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	0.671268	−	0.741215i	$-0.265750\pi$
$547$	4.06399	+	2.95266i	0.173764	+	0.126247i	−0.497504	+	0.867462i	$0.665750\pi$
$548$	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	−0.995082	−	0.0990533i	$-0.968419\pi$
$557$	−0.999243	−	9.50716i	−0.0423393	−	0.402831i	0.952743	−	0.303778i	$-0.0982481\pi$
$558$		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	0.698065	−	0.716034i	$-0.254045\pi$
$563$	24.7845	+	5.26811i	1.04454	+	0.222024i	0.346477	+	0.938059i	$0.387378\pi$
$564$		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	0.619928	+	0.784659i	$0.287162\pi$
$569$	−3.56834	+	33.9505i	−0.149593	+	1.42328i	−0.769521	+	0.638622i	$0.779505\pi$
$570$		0			0
$571$	22.6152	−	39.1707i	0.946416	−	1.63924i	0.193525	−	0.981095i	$-0.438008\pi$
$571$	22.6152	−	39.1707i	0.946416	−	1.63924i	0.752891	−	0.658145i	$-0.228659\pi$
$572$	−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	0.730244	−	0.683186i	$-0.239406\pi$
$577$	−0.613256	−	0.681090i	−0.0255302	−	0.0283541i	−0.755775	+	0.654832i	$0.772739\pi$
$578$	−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	−0.588442	−	0.808540i	$-0.700258\pi$
$587$	−0.0318255	+	0.0231226i	−0.00131358	+	0.000954370i	0.587128	+	0.809494i	$0.300258\pi$
$588$		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	0.942760	−	0.333471i	$-0.108220\pi$
$593$	4.44625	+	7.70113i	0.182586	+	0.316248i	−0.760175	+	0.649719i	$0.774887\pi$
$594$		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	0.980471	−	0.196665i	$-0.0630112\pi$
$599$	16.7013	+	18.5486i	0.682396	+	0.757877i	−0.298075	+	0.954542i	$0.596345\pi$
$600$		0			0
$601$	−22.5755	+	16.4021i	−0.920874	+	0.669054i	−0.943741	−	0.330685i	$-0.892720\pi$
$601$	−22.5755	+	16.4021i	−0.920874	+	0.669054i	0.0228677	+	0.999738i	$0.492720\pi$
$602$	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	−0.618505	−	0.785781i	$-0.712261\pi$
$607$	5.60803	−	6.22835i	0.227623	−	0.252801i	0.846128	+	0.532980i	$0.178928\pi$
$608$	−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	−0.742618	−	0.669716i	$-0.766416\pi$
$613$	−18.3669	+	8.17745i	−0.741830	+	0.330284i	0.000787513		1.00000i	$0.499749\pi$
$614$	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	−0.0642870	−	0.997931i	$-0.520477\pi$
$619$	15.7813	−	7.02629i	0.634304	−	0.282410i	0.698591	+	0.715521i	$0.253811\pi$
$620$	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	−0.997591	−	0.0693729i	$-0.977900\pi$
$631$	−31.1456	+	22.6286i	−1.23989	+	0.900830i	−0.242295	+	0.970203i	$0.577900\pi$
$632$	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	−0.0429611	−	0.999077i	$-0.513679\pi$
$641$	16.9821	−	7.56090i	0.670751	−	0.298638i	0.713712	+	0.700439i	$0.247012\pi$
$642$		0			0
$643$	−2.98936	+	9.20029i	−0.117889	+	0.362824i	−0.992539	−	0.121931i	$-0.961091\pi$
$643$	−2.98936	+	9.20029i	−0.117889	+	0.362824i	0.874650	+	0.484755i	$0.161091\pi$
$644$	−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	−0.222090	−	0.975026i	$-0.571288\pi$
$647$	−20.8973	−	4.44186i	−0.821557	−	0.174627i	−0.599468	+	0.800399i	$0.704621\pi$
$648$		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	−0.254913	−	0.966964i	$-0.582047\pi$
$653$	−29.2356	−	13.0165i	−1.14408	−	0.509376i	−0.889164	+	0.457588i	$0.848713\pi$
$654$		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	0.480248	+	0.877133i	$0.340547\pi$
$661$	−13.3562	+	23.1336i	−0.519495	+	0.899792i	−0.999743	+	0.0226592i	$0.992787\pi$
$662$	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	0.960359	−	0.278764i	$-0.0899249\pi$
$673$	0.507396	+	1.56161i	0.0195587	+	0.0601954i	−0.940801	+	0.338960i	$0.889925\pi$
$674$	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	−0.198619	−	0.980077i	$-0.563646\pi$
$677$	0.483086	−	0.102683i	0.0185665	−	0.00394643i	0.217186	+	0.976130i	$0.430312\pi$
$678$		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	−0.999831	−	0.0183779i	$-0.994150\pi$
$683$	−12.6490	+	21.9087i	−0.484000	+	0.838312i	0.515831	+	0.856690i	$0.327483\pi$
$684$		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	−0.762431	−	0.647069i	$-0.775994\pi$
$691$	−1.03073	+	1.14475i	−0.0392110	+	0.0435482i	0.723220	+	0.690617i	$0.242661\pi$
$692$	−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	0.463515	−	0.886089i	$-0.346588\pi$
$701$	−6.24771	−	4.53922i	−0.235973	−	0.171444i	−0.699487	+	0.714645i	$0.746588\pi$
$702$		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	−0.561991	−	0.827143i	$-0.689965\pi$
$709$	−19.6765	+	4.18237i	−0.738967	+	0.157072i	−0.176975	+	0.984215i	$0.556631\pi$
$710$	−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	0.730062	−	0.683381i	$-0.239491\pi$
$719$	19.0573	+	8.48487i	0.710718	+	0.316432i	−0.0193438	+	0.999813i	$0.506158\pi$
$720$		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	0.999681	+	0.0252675i	$0.00804374\pi$
$733$	45.6839	+	20.3398i	1.68738	+	0.751268i	0.687694	+	0.726000i	$0.258623\pi$
$734$	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	0.137743	−	0.990468i	$-0.456015\pi$
$739$	−3.78631	−	0.804805i	−0.139282	−	0.0296052i	−0.277025	+	0.960863i	$0.589348\pi$
$740$	−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	−0.884485	−	0.466568i	$-0.845490\pi$
$743$	2.87081	−	8.83546i	0.105320	−	0.324141i	0.989805	+	0.142426i	$0.0454904\pi$
$744$		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	−0.872407	−	0.488780i	$-0.837442\pi$
$751$	2.26247	−	21.5260i	0.0825589	−	0.785495i	0.954966	−	0.296715i	$-0.0958912\pi$
$752$	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	0.990949	−	0.134239i	$-0.0428591\pi$
$757$	3.03614	+	9.34428i	0.110350	+	0.339624i	−0.880599	+	0.473863i	$0.842859\pi$
$758$	−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	−0.189896	−	0.981804i	$-0.560815\pi$
$761$	22.2450	−	24.7055i	0.806379	−	0.895575i	0.996275	+	0.0862293i	$0.0274818\pi$
$762$		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	0.139620	−	0.990205i	$-0.455412\pi$
$773$	26.9385	−	11.9938i	0.968910	−	0.431387i	0.829290	+	0.558818i	$0.188745\pi$
$774$		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	0.375697	−	0.926743i	$-0.377403\pi$
$787$	−16.4180	−	18.2341i	−0.585240	−	0.649975i	−0.960937	+	0.276768i	$0.910737\pi$
$788$	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	−0.805345	−	0.592806i	$-0.798020\pi$
$797$	5.49479	−	16.9112i	0.194635	−	0.599026i	0.999981	−	0.00622010i	$-0.00197993\pi$
$798$		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	0.871535	−	0.490333i	$-0.163125\pi$
$809$	8.32774	+	9.24889i	0.292788	+	0.325174i	−0.578747	+	0.815507i	$0.696458\pi$
$810$		0			0
$811$	22.4462	+	16.3081i	0.788191	+	0.572654i	0.907426	−	0.420212i	$-0.138044\pi$
$811$	22.4462	+	16.3081i	0.788191	+	0.572654i	−0.119235	+	0.992866i	$0.538044\pi$
$812$	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	0.856480	−	0.516181i	$-0.172647\pi$
$821$	29.9706	+	13.3438i	1.04598	+	0.465700i	0.189500	+	0.981881i	$0.439313\pi$
$822$		0			0
$823$	0.642109	+	0.136484i	0.0223825	+	0.00475755i	0.219089	−	0.975705i	$-0.429691\pi$
$823$	0.642109	+	0.136484i	0.0223825	+	0.00475755i	−0.196707	+	0.980462i	$0.563025\pi$
$824$	−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	−0.998725	−	0.0504794i	$-0.983925\pi$
$827$	−6.33848	−	19.5078i	−0.220411	−	0.678354i	0.778315	−	0.627875i	$-0.216075\pi$
$828$		0			0
$829$	0.879970	+	8.37236i	0.0305626	+	0.290784i	0.999118	+	0.0419866i	$0.0133687\pi$
$829$	0.879970	+	8.37236i	0.0305626	+	0.290784i	−0.968556	+	0.248797i	$0.919965\pi$
$830$	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	0.981129	−	0.193356i	$-0.0619373\pi$
$839$	31.8742	+	23.1580i	1.10042	+	0.799503i	0.119293	+	0.992859i	$0.461937\pi$
$840$		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	−0.700428	−	0.713723i	$-0.747007\pi$
$853$	8.34555	−	25.6850i	0.285746	−	0.879436i	0.986174	−	0.165713i	$-0.0529925\pi$
$854$	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	−0.961239	−	0.275716i	$-0.911085\pi$
$857$	−7.07983	+	12.2626i	−0.241842	+	0.418883i	0.719397	+	0.694599i	$0.244418\pi$
$858$		0			0
$859$	−8.62094	−	14.9319i	−0.294143	−	0.509470i	0.680642	−	0.732616i	$-0.261701\pi$
$859$	−8.62094	−	14.9319i	−0.294143	−	0.509470i	−0.974785	+	0.223146i	$0.928367\pi$
$860$	−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	0.162607	−	0.986691i	$-0.448010\pi$
$863$	20.9304	−	4.44889i	0.712479	−	0.151442i	0.549872	+	0.835249i	$0.314677\pi$
$864$		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	0.927367	+	0.374152i	$0.122066\pi$
$877$	−1.70357	+	16.2083i	−0.0575253	+	0.547317i	−0.984893	+	0.173165i	$0.944601\pi$
$878$	−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	0.685757	−	0.727831i	$-0.259471\pi$
$883$	6.10529	+	4.43575i	0.205459	+	0.149275i	−0.480298	+	0.877106i	$0.659471\pi$
$884$	−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	0.209043	−	0.977907i	$-0.432965\pi$
$887$	−11.2521	−	5.00974i	−0.377807	−	0.168210i	−0.586849	+	0.809696i	$0.699632\pi$
$888$		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	0.759776	−	0.650185i	$-0.225309\pi$
$907$	1.01594	+	1.12831i	0.0337337	+	0.0374650i	−0.726042	+	0.687651i	$0.758642\pi$
$908$	−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	0.998317	−	0.0579998i	$-0.0184723\pi$
$911$	4.72572	+	14.5443i	0.156570	+	0.481873i	−0.841747	+	0.539873i	$0.818472\pi$
$912$		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	0.105023	−	0.994470i	$-0.466508\pi$
$919$	18.3544	−	3.90134i	0.605454	−	0.128693i	0.500431	+	0.865776i	$0.333175\pi$
$920$	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	0.387258	−	0.921971i	$-0.373422\pi$
$929$	34.0162	−	7.23037i	1.11604	−	0.237221i	0.728778	+	0.684750i	$0.240089\pi$
$930$		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	0.911759	−	0.410725i	$-0.134725\pi$
$937$	−2.05971	−	6.33914i	−0.0672878	−	0.207091i	−0.979047	+	0.203635i	$0.934725\pi$
$938$	−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	0.988840	+	0.148979i	$0.0475987\pi$
$941$	31.7077	+	35.2150i	1.03364	+	1.14798i	0.0448011	+	0.998996i	$0.485735\pi$
$942$		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	0.680350	−	0.732888i	$-0.261828\pi$
$947$	−9.06351	−	15.6985i	−0.294524	−	0.510131i	−0.974874	+	0.222756i	$0.928495\pi$
$948$		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	−0.986560	−	0.163398i	$-0.947755\pi$
$953$	−35.0699	+	25.4797i	−1.13602	+	0.825370i	−0.149464	+	0.988767i	$0.547755\pi$
$954$		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	0.363453	+	0.931613i	$0.381598\pi$
$971$	−5.78816	+	55.0707i	−0.185751	+	1.76730i	−0.549204	+	0.835689i	$0.685069\pi$
$972$		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	−0.0154182	−	0.999881i	$-0.504908\pi$
$977$	−13.6340	−	2.89801i	−0.436192	−	0.0927154i	−0.420774	+	0.907166i	$0.638241\pi$
$978$		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	−0.999045	−	0.0436848i	$-0.986090\pi$
$983$	−0.969245	−	9.22175i	−0.0309141	−	0.294128i	0.968131	−	0.250443i	$-0.0805764\pi$
$984$		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	−0.985277	−	0.170968i	$-0.945311\pi$
$991$	−10.8473	+	18.7881i	−0.344576	+	0.596823i	0.640701	+	0.767791i	$0.278644\pi$
$992$	−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	0.998714	+	0.0506909i	$0.0161423\pi$
$997$	1.02189	+	9.72262i	0.0323635	+	0.307918i	−0.966351	+	0.257228i	$0.917191\pi$
$998$	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.676.7		64
3.2	odd	2		231.2.y.b.214.2	yes	64
7.2	even	3	inner	693.2.by.c.478.2		64
11.9	even	5	inner	693.2.by.c.361.2		64
21.2	odd	6		231.2.y.b.16.7	✓	64
33.20	odd	10		231.2.y.b.130.7	yes	64
77.9	even	15	inner	693.2.by.c.163.7		64
231.86	odd	30		231.2.y.b.163.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.b.16.7	✓	64	21.2	odd	6
231.2.y.b.130.7	yes	64	33.20	odd	10
231.2.y.b.163.2	yes	64	231.86	odd	30
231.2.y.b.214.2	yes	64	3.2	odd	2
693.2.by.c.163.7		64	77.9	even	15	inner
693.2.by.c.361.2		64	11.9	even	5	inner
693.2.by.c.478.2		64	7.2	even	3	inner
693.2.by.c.676.7		64	1.1	even	1	trivial

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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