LMFDB - Embedded newform 1600.2.s.d.207.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(207,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 1]))

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

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

chi := DirichletCharacter("1600.207");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.s (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			207.3
Root			$0.482716 + 1.32928i$ of defining polynomial
Character	$\chi$	$=$	1600.207
Dual form			1600.2.s.d.943.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.39319 q^{3} +(-2.13436 - 2.13436i) q^{7} -1.05903 q^{9} +(-2.17074 + 2.17074i) q^{11} +1.54663i q^{13} +(3.86386 + 3.86386i) q^{17} +(-0.0136865 + 0.0136865i) q^{19} +(2.97357 + 2.97357i) q^{21} +(-3.15240 + 3.15240i) q^{23} +5.65499 q^{27} +(3.33787 + 3.33787i) q^{29} -8.92639i q^{31} +(3.02424 - 3.02424i) q^{33} -7.24737i q^{37} -2.15475i q^{39} -10.3771i q^{41} +2.02975i q^{43} +(3.34313 - 3.34313i) q^{47} +2.11103i q^{49} +(-5.38308 - 5.38308i) q^{51} +7.30702 q^{53} +(0.0190679 - 0.0190679i) q^{57} +(3.52732 + 3.52732i) q^{59} +(1.41629 - 1.41629i) q^{61} +(2.26036 + 2.26036i) q^{63} +0.748197i q^{67} +(4.39187 - 4.39187i) q^{69} +0.269603 q^{71} +(-0.811870 - 0.811870i) q^{73} +9.26628 q^{77} +2.80567 q^{79} -4.70135 q^{81} +12.8279 q^{83} +(-4.65027 - 4.65027i) q^{87} -13.3732 q^{89} +(3.30108 - 3.30108i) q^{91} +12.4361i q^{93} +(-6.33466 - 6.33466i) q^{97} +(2.29888 - 2.29888i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{7} + 10 q^{9} + 2 q^{11} + 6 q^{17} + 2 q^{19} - 16 q^{21} - 2 q^{23} - 24 q^{27} + 14 q^{29} + 8 q^{33} + 38 q^{47} - 8 q^{51} - 12 q^{53} + 24 q^{57} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 32 q^{69}+ \cdots - 22 q^{99}+O(q^{100}) $ 18 * q + 2 * q^7 + 10 * q^9 + 2 * q^11 + 6 * q^17 + 2 * q^19 - 16 * q^21 - 2 * q^23 - 24 * q^27 + 14 * q^29 + 8 * q^33 + 38 * q^47 - 8 * q^51 - 12 * q^53 + 24 * q^57 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 32 * q^69 - 24 * q^71 + 14 * q^73 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 + 24 * q^87 + 12 * q^89 - 18 * q^97 - 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.39319			−0.804356			−0.402178	−	0.915561i	$-0.631747\pi$
$3$	−1.39319			−0.804356			−0.402178	+	0.915561i	$0.631747\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.13436	−	2.13436i	−0.806714	−	0.806714i	0.177421	−	0.984135i	$-0.443225\pi$
$7$	−2.13436	−	2.13436i	−0.806714	−	0.806714i	−0.984135	+	0.177421i	$0.943225\pi$
$8$		0			0
$9$	−1.05903			−0.353011
$10$		0			0
$11$	−2.17074	+	2.17074i	−0.654501	+	0.654501i	−0.954074	−	0.299572i	$-0.903156\pi$
$11$	−2.17074	+	2.17074i	−0.654501	+	0.654501i	0.299572	+	0.954074i	$0.403156\pi$
$12$		0			0
$13$			1.54663i			0.428958i	0.976729	+	0.214479i	$0.0688054\pi$
$13$			1.54663i			0.428958i	−0.976729	+	0.214479i	$0.931195\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.86386	+	3.86386i	0.937125	+	0.937125i	0.998137	−	0.0610123i	$-0.0194329\pi$
$17$	3.86386	+	3.86386i	0.937125	+	0.937125i	−0.0610123	+	0.998137i	$0.519433\pi$
$18$		0			0
$19$	−0.0136865	+	0.0136865i	−0.00313991	+	0.00313991i	−0.708675	−	0.705535i	$-0.750707\pi$
$19$	−0.0136865	+	0.0136865i	−0.00313991	+	0.00313991i	0.705535	+	0.708675i	$0.250707\pi$
$20$		0			0
$21$	2.97357	+	2.97357i	0.648886	+	0.648886i
$22$		0			0
$23$	−3.15240	+	3.15240i	−0.657320	+	0.657320i	−0.954745	−	0.297425i	$-0.903872\pi$
$23$	−3.15240	+	3.15240i	−0.657320	+	0.657320i	0.297425	+	0.954745i	$0.403872\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	5.65499			1.08830
$28$		0			0
$29$	3.33787	+	3.33787i	0.619826	+	0.619826i	0.945487	−	0.325660i	$-0.105587\pi$
$29$	3.33787	+	3.33787i	0.619826	+	0.619826i	−0.325660	+	0.945487i	$0.605587\pi$
$30$		0			0
$31$		−	8.92639i		−	1.60323i	−0.597843	−	0.801613i	$-0.703975\pi$
$31$		−	8.92639i		−	1.60323i	0.597843	−	0.801613i	$-0.296025\pi$
$32$		0			0
$33$	3.02424	−	3.02424i	0.526452	−	0.526452i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	7.24737i		−	1.19146i	−0.803184	−	0.595730i	$-0.796863\pi$
$37$		−	7.24737i		−	1.19146i	0.803184	−	0.595730i	$-0.203137\pi$
$38$		0			0
$39$		−	2.15475i		−	0.345035i
$40$		0			0
$41$		−	10.3771i		−	1.62063i	−0.585996	−	0.810314i	$-0.699296\pi$
$41$		−	10.3771i		−	1.62063i	0.585996	−	0.810314i	$-0.300704\pi$
$42$		0			0
$43$			2.02975i			0.309534i	0.987951	+	0.154767i	$0.0494627\pi$
$43$			2.02975i			0.309534i	−0.987951	+	0.154767i	$0.950537\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.34313	−	3.34313i	0.487646	−	0.487646i	−0.419917	−	0.907563i	$-0.637941\pi$
$47$	3.34313	−	3.34313i	0.487646	−	0.487646i	0.907563	+	0.419917i	$0.137941\pi$
$48$		0			0
$49$			2.11103i			0.301575i
$50$		0			0
$51$	−5.38308	−	5.38308i	−0.753782	−	0.753782i
$52$		0			0
$53$	7.30702			1.00370			0.501848	−	0.864956i	$-0.332654\pi$
$53$	7.30702			1.00370			0.501848	+	0.864956i	$0.332654\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.0190679	−	0.0190679i	0.00252560	−	0.00252560i
$58$		0			0
$59$	3.52732	+	3.52732i	0.459218	+	0.459218i	0.898399	−	0.439181i	$-0.144731\pi$
$59$	3.52732	+	3.52732i	0.459218	+	0.459218i	−0.439181	+	0.898399i	$0.644731\pi$
$60$		0			0
$61$	1.41629	−	1.41629i	0.181338	−	0.181338i	−0.610601	−	0.791939i	$-0.709072\pi$
$61$	1.41629	−	1.41629i	0.181338	−	0.181338i	0.791939	+	0.610601i	$0.209072\pi$
$62$		0			0
$63$	2.26036	+	2.26036i	0.284779	+	0.284779i
$64$		0			0
$65$		0			0
$66$		0			0
$67$			0.748197i			0.0914068i	0.998955	+	0.0457034i	$0.0145529\pi$
$67$			0.748197i			0.0914068i	−0.998955	+	0.0457034i	$0.985447\pi$
$68$		0			0
$69$	4.39187	−	4.39187i	0.528719	−	0.528719i
$70$		0			0
$71$	0.269603			0.0319960			0.0159980	−	0.999872i	$-0.494907\pi$
$71$	0.269603			0.0319960			0.0159980	+	0.999872i	$0.494907\pi$
$72$		0			0
$73$	−0.811870	−	0.811870i	−0.0950222	−	0.0950222i	0.657998	−	0.753020i	$-0.271404\pi$
$73$	−0.811870	−	0.811870i	−0.0950222	−	0.0950222i	−0.753020	+	0.657998i	$0.771404\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.26628			1.05599
$78$		0			0
$79$	2.80567			0.315662			0.157831	−	0.987466i	$-0.449550\pi$
$79$	2.80567			0.315662			0.157831	+	0.987466i	$0.449550\pi$
$80$		0			0
$81$	−4.70135			−0.522372
$82$		0			0
$83$	12.8279			1.40804			0.704022	−	0.710178i	$-0.251386\pi$
$83$	12.8279			1.40804			0.704022	+	0.710178i	$0.251386\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−4.65027	−	4.65027i	−0.498561	−	0.498561i
$88$		0			0
$89$	−13.3732			−1.41755			−0.708777	−	0.705432i	$-0.750753\pi$
$89$	−13.3732			−1.41755			−0.708777	+	0.705432i	$0.750753\pi$
$90$		0			0
$91$	3.30108	−	3.30108i	0.346047	−	0.346047i
$92$		0			0
$93$			12.4361i			1.28957i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.33466	−	6.33466i	−0.643187	−	0.643187i	0.308151	−	0.951338i	$-0.400290\pi$
$97$	−6.33466	−	6.33466i	−0.643187	−	0.643187i	−0.951338	+	0.308151i	$0.900290\pi$
$98$		0			0
$99$	2.29888	−	2.29888i	0.231046	−	0.231046i
$100$		0			0
$101$	−3.78129	−	3.78129i	−0.376252	−	0.376252i	0.493496	−	0.869748i	$-0.335719\pi$
$101$	−3.78129	−	3.78129i	−0.376252	−	0.376252i	−0.869748	+	0.493496i	$0.835719\pi$
$102$		0			0
$103$	10.7199	−	10.7199i	1.05626	−	1.05626i	0.0579430	−	0.998320i	$-0.481546\pi$
$103$	10.7199	−	10.7199i	1.05626	−	1.05626i	0.998320	−	0.0579430i	$-0.0184542\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	10.9109			1.05479			0.527397	−	0.849619i	$-0.323168\pi$
$107$	10.9109			1.05479			0.527397	+	0.849619i	$0.323168\pi$
$108$		0			0
$109$	9.12139	+	9.12139i	0.873670	+	0.873670i	0.992870	−	0.119200i	$-0.0380329\pi$
$109$	9.12139	+	9.12139i	0.873670	+	0.873670i	−0.119200	+	0.992870i	$0.538033\pi$
$110$		0			0
$111$			10.0969i			0.958359i
$112$		0			0
$113$	−4.88810	+	4.88810i	−0.459834	+	0.459834i	−0.898601	−	0.438767i	$-0.855415\pi$
$113$	−4.88810	+	4.88810i	−0.459834	+	0.459834i	0.438767	+	0.898601i	$0.355415\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		−	1.63793i		−	0.151427i
$118$		0			0
$119$		−	16.4938i		−	1.51198i
$120$		0			0
$121$			1.57582i			0.143256i
$122$		0			0
$123$			14.4572i			1.30356i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.38586	−	1.38586i	0.122975	−	0.122975i	−0.642941	−	0.765916i	$-0.722286\pi$
$127$	1.38586	−	1.38586i	0.122975	−	0.122975i	0.765916	+	0.642941i	$0.222286\pi$
$128$		0			0
$129$		−	2.82782i		−	0.248976i
$130$		0			0
$131$	3.52096	+	3.52096i	0.307627	+	0.307627i	0.843989	−	0.536361i	$-0.180202\pi$
$131$	3.52096	+	3.52096i	0.307627	+	0.307627i	−0.536361	+	0.843989i	$0.680202\pi$
$132$		0			0
$133$	0.0584241			0.00506601
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.62512	−	5.62512i	0.480587	−	0.480587i	−0.424732	−	0.905319i	$-0.639632\pi$
$137$	5.62512	−	5.62512i	0.480587	−	0.480587i	0.905319	+	0.424732i	$0.139632\pi$
$138$		0			0
$139$	12.1022	+	12.1022i	1.02650	+	1.02650i	0.999639	+	0.0268584i	$0.00855031\pi$
$139$	12.1022	+	12.1022i	1.02650	+	1.02650i	0.0268584	+	0.999639i	$0.491450\pi$
$140$		0			0
$141$	−4.65760	+	4.65760i	−0.392241	+	0.392241i
$142$		0			0
$143$	−3.35733	−	3.35733i	−0.280754	−	0.280754i
$144$		0			0
$145$		0			0
$146$		0			0
$147$		−	2.94105i		−	0.242574i
$148$		0			0
$149$	13.5590	−	13.5590i	1.11080	−	1.11080i	0.117757	−	0.993042i	$-0.462430\pi$
$149$	13.5590	−	13.5590i	1.11080	−	1.11080i	0.993042	−	0.117757i	$-0.0375702\pi$
$150$		0			0
$151$	20.7185			1.68605			0.843025	−	0.537874i	$-0.180772\pi$
$151$	20.7185			1.68605			0.843025	+	0.537874i	$0.180772\pi$
$152$		0			0
$153$	−4.09196	−	4.09196i	−0.330815	−	0.330815i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	5.72312			0.456755			0.228377	−	0.973573i	$-0.426658\pi$
$157$	5.72312			0.456755			0.228377	+	0.973573i	$0.426658\pi$
$158$		0			0
$159$	−10.1800			−0.807329
$160$		0			0
$161$	13.4567			1.06054
$162$		0			0
$163$	−17.9900			−1.40909			−0.704543	−	0.709662i	$-0.748848\pi$
$163$	−17.9900			−1.40909			−0.704543	+	0.709662i	$0.748848\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.39642	+	2.39642i	0.185441	+	0.185441i	0.793722	−	0.608281i	$-0.208141\pi$
$167$	2.39642	+	2.39642i	0.185441	+	0.185441i	−0.608281	+	0.793722i	$0.708141\pi$
$168$		0			0
$169$	10.6079			0.815995
$170$		0			0
$171$	0.0144945	−	0.0144945i	0.00110842	−	0.00110842i
$172$		0			0
$173$		−	9.45205i		−	0.718626i	−0.933217	−	0.359313i	$-0.883011\pi$
$173$		−	9.45205i		−	0.718626i	0.933217	−	0.359313i	$-0.116989\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.91421	−	4.91421i	−0.369375	−	0.369375i
$178$		0			0
$179$	−11.7991	+	11.7991i	−0.881905	+	0.881905i	−0.993728	−	0.111824i	$-0.964331\pi$
$179$	−11.7991	+	11.7991i	−0.881905	+	0.881905i	0.111824	+	0.993728i	$0.464331\pi$
$180$		0			0
$181$	2.54155	+	2.54155i	0.188912	+	0.188912i	0.795225	−	0.606314i	$-0.207352\pi$
$181$	2.54155	+	2.54155i	0.188912	+	0.188912i	−0.606314	+	0.795225i	$0.707352\pi$
$182$		0			0
$183$	−1.97316	+	1.97316i	−0.145860	+	0.145860i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−16.7748			−1.22670
$188$		0			0
$189$	−12.0698	−	12.0698i	−0.877949	−	0.877949i
$190$		0			0
$191$			5.46421i			0.395376i	0.980265	+	0.197688i	$0.0633433\pi$
$191$			5.46421i			0.395376i	−0.980265	+	0.197688i	$0.936657\pi$
$192$		0			0
$193$	−4.82485	+	4.82485i	−0.347300	+	0.347300i	−0.859103	−	0.511803i	$-0.828978\pi$
$193$	−4.82485	+	4.82485i	−0.347300	+	0.347300i	0.511803	+	0.859103i	$0.328978\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	2.94582i		−	0.209881i	−0.994478	−	0.104941i	$-0.966535\pi$
$197$		−	2.94582i		−	0.209881i	0.994478	−	0.104941i	$-0.0334653\pi$
$198$		0			0
$199$		−	2.14620i		−	0.152140i	−0.997102	−	0.0760700i	$-0.975763\pi$
$199$		−	2.14620i		−	0.152140i	0.997102	−	0.0760700i	$-0.0242372\pi$
$200$		0			0
$201$		−	1.04238i		−	0.0735236i
$202$		0			0
$203$		−	14.2485i		−	1.00005i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	3.33849	−	3.33849i	0.232041	−	0.232041i
$208$		0			0
$209$		−	0.0594197i		−	0.00411014i
$210$		0			0
$211$	−5.54427	−	5.54427i	−0.381684	−	0.381684i	0.490025	−	0.871708i	$-0.336988\pi$
$211$	−5.54427	−	5.54427i	−0.381684	−	0.381684i	−0.871708	+	0.490025i	$0.836988\pi$
$212$		0			0
$213$	−0.375608			−0.0257362
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−19.0522	+	19.0522i	−1.29335	+	1.29335i
$218$		0			0
$219$	1.13109	+	1.13109i	0.0764317	+	0.0764317i
$220$		0			0
$221$	−5.97597	+	5.97597i	−0.401988	+	0.401988i
$222$		0			0
$223$	1.16163	+	1.16163i	0.0777882	+	0.0777882i	0.744930	−	0.667142i	$-0.232483\pi$
$223$	1.16163	+	1.16163i	0.0777882	+	0.0777882i	−0.667142	+	0.744930i	$0.732483\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			12.8161i			0.850632i	0.905045	+	0.425316i	$0.139837\pi$
$227$			12.8161i			0.850632i	−0.905045	+	0.425316i	$0.860163\pi$
$228$		0			0
$229$	0.976882	−	0.976882i	0.0645542	−	0.0645542i	−0.674093	−	0.738647i	$-0.735465\pi$
$229$	0.976882	−	0.976882i	0.0645542	−	0.0645542i	0.738647	+	0.674093i	$0.235465\pi$
$230$		0			0
$231$	−12.9097			−0.849393
$232$		0			0
$233$	0.303870	+	0.303870i	0.0199072	+	0.0199072i	0.716990	−	0.697083i	$-0.245519\pi$
$233$	0.303870	+	0.303870i	0.0199072	+	0.0199072i	−0.697083	+	0.716990i	$0.745519\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−3.90881			−0.253905
$238$		0			0
$239$	12.5096			0.809178			0.404589	−	0.914499i	$-0.367415\pi$
$239$	12.5096			0.809178			0.404589	+	0.914499i	$0.367415\pi$
$240$		0			0
$241$	−19.5775			−1.26110			−0.630548	−	0.776150i	$-0.717170\pi$
$241$	−19.5775			−1.26110			−0.630548	+	0.776150i	$0.717170\pi$
$242$		0			0
$243$	−10.4151			−0.668129
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.0211680	−	0.0211680i	−0.00134689	−	0.00134689i
$248$		0			0
$249$	−17.8716			−1.13257
$250$		0			0
$251$	−5.17763	+	5.17763i	−0.326809	+	0.326809i	−0.851372	−	0.524563i	$-0.824229\pi$
$251$	−5.17763	+	5.17763i	−0.326809	+	0.326809i	0.524563	+	0.851372i	$0.324229\pi$
$252$		0			0
$253$		−	13.6860i		−	0.860433i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.7989	+	14.7989i	0.923131	+	0.923131i	0.997249	−	0.0741183i	$-0.0236142\pi$
$257$	14.7989	+	14.7989i	0.923131	+	0.923131i	−0.0741183	+	0.997249i	$0.523614\pi$
$258$		0			0
$259$	−15.4685	+	15.4685i	−0.961168	+	0.961168i
$260$		0			0
$261$	−3.53491	−	3.53491i	−0.218805	−	0.218805i
$262$		0			0
$263$	11.7906	−	11.7906i	0.727038	−	0.727038i	−0.242991	−	0.970029i	$-0.578129\pi$
$263$	11.7906	−	11.7906i	0.727038	−	0.727038i	0.970029	+	0.242991i	$0.0781285\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	18.6313			1.14022
$268$		0			0
$269$	2.10121	+	2.10121i	0.128113	+	0.128113i	0.768256	−	0.640143i	$-0.221125\pi$
$269$	2.10121	+	2.10121i	0.128113	+	0.128113i	−0.640143	+	0.768256i	$0.721125\pi$
$270$		0			0
$271$		−	18.8596i		−	1.14564i	−0.819683	−	0.572818i	$-0.805850\pi$
$271$		−	18.8596i		−	1.14564i	0.819683	−	0.572818i	$-0.194150\pi$
$272$		0			0
$273$	−4.59901	+	4.59901i	−0.278345	+	0.278345i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		−	9.91909i		−	0.595980i	−0.954569	−	0.297990i	$-0.903684\pi$
$277$		−	9.91909i		−	0.595980i	0.954569	−	0.297990i	$-0.0963162\pi$
$278$		0			0
$279$			9.45334i			0.565956i
$280$		0			0
$281$		−	9.31434i		−	0.555647i	−0.960632	−	0.277823i	$-0.910387\pi$
$281$		−	9.31434i		−	0.555647i	0.960632	−	0.277823i	$-0.0896130\pi$
$282$		0			0
$283$			3.42364i			0.203514i	0.994809	+	0.101757i	$0.0324465\pi$
$283$			3.42364i			0.203514i	−0.994809	+	0.101757i	$0.967554\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−22.1485	+	22.1485i	−1.30738	+	1.30738i
$288$		0			0
$289$			12.8589i			0.756405i
$290$		0			0
$291$	8.82535	+	8.82535i	0.517351	+	0.517351i
$292$		0			0
$293$	−2.66471			−0.155674			−0.0778369	−	0.996966i	$-0.524801\pi$
$293$	−2.66471			−0.155674			−0.0778369	+	0.996966i	$0.524801\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−12.2755	+	12.2755i	−0.712296	+	0.712296i
$298$		0			0
$299$	−4.87559	−	4.87559i	−0.281963	−	0.281963i
$300$		0			0
$301$	4.33223	−	4.33223i	0.249706	−	0.249706i
$302$		0			0
$303$	5.26804	+	5.26804i	0.302641	+	0.302641i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			10.5554i			0.602430i	0.953556	+	0.301215i	$0.0973922\pi$
$307$			10.5554i			0.602430i	−0.953556	+	0.301215i	$0.902608\pi$
$308$		0			0
$309$	−14.9348	+	14.9348i	−0.849612	+	0.849612i
$310$		0			0
$311$	20.4762			1.16110			0.580550	−	0.814225i	$-0.302838\pi$
$311$	20.4762			1.16110			0.580550	+	0.814225i	$0.302838\pi$
$312$		0			0
$313$	2.82393	+	2.82393i	0.159618	+	0.159618i	0.782397	−	0.622780i	$-0.213997\pi$
$313$	2.82393	+	2.82393i	0.159618	+	0.159618i	−0.622780	+	0.782397i	$0.713997\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−20.2533			−1.13754			−0.568769	−	0.822497i	$-0.692580\pi$
$317$	−20.2533			−1.13754			−0.568769	+	0.822497i	$0.692580\pi$
$318$		0			0
$319$	−14.4913			−0.811354
$320$		0			0
$321$	−15.2009			−0.848430
$322$		0			0
$323$	−0.105766			−0.00588497
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−12.7078	−	12.7078i	−0.702742	−	0.702742i
$328$		0			0
$329$	−14.2709			−0.786781
$330$		0			0
$331$	−19.4930	+	19.4930i	−1.07143	+	1.07143i	−0.0741908	+	0.997244i	$0.523637\pi$
$331$	−19.4930	+	19.4930i	−1.07143	+	1.07143i	−0.997244	+	0.0741908i	$0.976363\pi$
$332$		0			0
$333$			7.67521i			0.420599i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	5.89449	+	5.89449i	0.321093	+	0.321093i	0.849186	−	0.528093i	$-0.177093\pi$
$337$	5.89449	+	5.89449i	0.321093	+	0.321093i	−0.528093	+	0.849186i	$0.677093\pi$
$338$		0			0
$339$	6.81003	−	6.81003i	0.369870	−	0.369870i
$340$		0			0
$341$	19.3768	+	19.3768i	1.04931	+	1.04931i
$342$		0			0
$343$	−10.4349	+	10.4349i	−0.563429	+	0.563429i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−11.4626			−0.615346			−0.307673	−	0.951492i	$-0.599550\pi$
$347$	−11.4626			−0.615346			−0.307673	+	0.951492i	$0.599550\pi$
$348$		0			0
$349$	0.317872	+	0.317872i	0.0170153	+	0.0170153i	0.715563	−	0.698548i	$-0.246170\pi$
$349$	0.317872	+	0.317872i	0.0170153	+	0.0170153i	−0.698548	+	0.715563i	$0.746170\pi$
$350$		0			0
$351$			8.74618i			0.466837i
$352$		0			0
$353$	18.4551	−	18.4551i	0.982266	−	0.982266i	−0.0175800	−	0.999845i	$-0.505596\pi$
$353$	18.4551	−	18.4551i	0.982266	−	0.982266i	0.999845	+	0.0175800i	$0.00559616\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			22.9789i			1.21617i
$358$		0			0
$359$		−	15.5802i		−	0.822292i	−0.911569	−	0.411146i	$-0.865129\pi$
$359$		−	15.5802i		−	0.822292i	0.911569	−	0.411146i	$-0.134871\pi$
$360$		0			0
$361$			18.9996i			0.999980i
$362$		0			0
$363$		−	2.19541i		−	0.115229i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−5.37489	+	5.37489i	−0.280567	+	0.280567i	−0.833335	−	0.552768i	$-0.813572\pi$
$367$	−5.37489	+	5.37489i	−0.280567	+	0.280567i	0.552768	+	0.833335i	$0.313572\pi$
$368$		0			0
$369$			10.9897i			0.572100i
$370$		0			0
$371$	−15.5958	−	15.5958i	−0.809696	−	0.809696i
$372$		0			0
$373$	−3.24424			−0.167980			−0.0839902	−	0.996467i	$-0.526766\pi$
$373$	−3.24424			−0.167980			−0.0839902	+	0.996467i	$0.526766\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.16245	+	5.16245i	−0.265880	+	0.265880i
$378$		0			0
$379$	−25.7690	−	25.7690i	−1.32367	−	1.32367i	−0.910785	−	0.412882i	$-0.864522\pi$
$379$	−25.7690	−	25.7690i	−1.32367	−	1.32367i	−0.412882	−	0.910785i	$-0.635478\pi$
$380$		0			0
$381$	−1.93076	+	1.93076i	−0.0989160	+	0.0989160i
$382$		0			0
$383$	−0.418091	−	0.418091i	−0.0213634	−	0.0213634i	0.696344	−	0.717708i	$-0.254809\pi$
$383$	−0.418091	−	0.418091i	−0.0213634	−	0.0213634i	−0.717708	+	0.696344i	$0.754809\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	2.14957i		−	0.109269i
$388$		0			0
$389$	−13.3626	+	13.3626i	−0.677508	+	0.677508i	−0.959436	−	0.281927i	$-0.909026\pi$
$389$	−13.3626	+	13.3626i	−0.677508	+	0.677508i	0.281927	+	0.959436i	$0.409026\pi$
$390$		0			0
$391$	−24.3609			−1.23198
$392$		0			0
$393$	−4.90535	−	4.90535i	−0.247442	−	0.247442i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	13.8391			0.694564			0.347282	−	0.937761i	$-0.387105\pi$
$397$	13.8391			0.694564			0.347282	+	0.937761i	$0.387105\pi$
$398$		0			0
$399$	−0.0813957			−0.00407488
$400$		0			0
$401$	20.3112			1.01430			0.507148	−	0.861859i	$-0.330700\pi$
$401$	20.3112			1.01430			0.507148	+	0.861859i	$0.330700\pi$
$402$		0			0
$403$	13.8058			0.687718
$404$		0			0
$405$		0			0
$406$		0			0
$407$	15.7321	+	15.7321i	0.779813	+	0.779813i
$408$		0			0
$409$	18.2875			0.904259			0.452130	−	0.891952i	$-0.350664\pi$
$409$	18.2875			0.904259			0.452130	+	0.891952i	$0.350664\pi$
$410$		0			0
$411$	−7.83684	+	7.83684i	−0.386563	+	0.386563i
$412$		0			0
$413$		−	15.0572i		−	0.740915i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−16.8607	−	16.8607i	−0.825670	−	0.825670i
$418$		0			0
$419$	17.3188	−	17.3188i	0.846079	−	0.846079i	−0.143563	−	0.989641i	$-0.545856\pi$
$419$	17.3188	−	17.3188i	0.846079	−	0.846079i	0.989641	+	0.143563i	$0.0458558\pi$
$420$		0			0
$421$	11.5457	+	11.5457i	0.562703	+	0.562703i	0.930074	−	0.367372i	$-0.119742\pi$
$421$	11.5457	+	11.5457i	0.562703	+	0.562703i	−0.367372	+	0.930074i	$0.619742\pi$
$422$		0			0
$423$	−3.54048	+	3.54048i	−0.172144	+	0.172144i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−6.04577			−0.292576
$428$		0			0
$429$	4.67738	+	4.67738i	0.225826	+	0.225826i
$430$		0			0
$431$			15.9479i			0.768185i	0.923295	+	0.384093i	$0.125486\pi$
$431$			15.9479i			0.768185i	−0.923295	+	0.384093i	$0.874514\pi$
$432$		0			0
$433$	−3.52109	+	3.52109i	−0.169213	+	0.169213i	−0.786633	−	0.617420i	$-0.788178\pi$
$433$	−3.52109	+	3.52109i	−0.169213	+	0.169213i	0.617420	+	0.786633i	$0.288178\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	0.0862907i		−	0.00412784i
$438$		0			0
$439$			6.45840i			0.308242i	0.988052	+	0.154121i	$0.0492546\pi$
$439$			6.45840i			0.308242i	−0.988052	+	0.154121i	$0.950745\pi$
$440$		0			0
$441$		−	2.23565i		−	0.106459i
$442$		0			0
$443$		−	27.0992i		−	1.28752i	−0.765226	−	0.643761i	$-0.777373\pi$
$443$		−	27.0992i		−	1.28752i	0.765226	−	0.643761i	$-0.222627\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−18.8903	+	18.8903i	−0.893478	+	0.893478i
$448$		0			0
$449$		−	41.0879i		−	1.93906i	−0.244976	−	0.969529i	$-0.578780\pi$
$449$		−	41.0879i		−	1.93906i	0.244976	−	0.969529i	$-0.421220\pi$
$450$		0			0
$451$	22.5259	+	22.5259i	1.06070	+	1.06070i
$452$		0			0
$453$	−28.8648			−1.35619
$454$		0			0
$455$		0			0
$456$		0			0
$457$	18.2449	−	18.2449i	0.853462	−	0.853462i	−0.137096	−	0.990558i	$-0.543777\pi$
$457$	18.2449	−	18.2449i	0.853462	−	0.853462i	0.990558	+	0.137096i	$0.0437769\pi$
$458$		0			0
$459$	21.8501	+	21.8501i	1.01988	+	1.01988i
$460$		0			0
$461$	6.68802	−	6.68802i	0.311492	−	0.311492i	−0.533995	−	0.845488i	$-0.679310\pi$
$461$	6.68802	−	6.68802i	0.311492	−	0.311492i	0.845488	+	0.533995i	$0.179310\pi$
$462$		0			0
$463$	−28.6926	−	28.6926i	−1.33346	−	1.33346i	−0.902254	−	0.431205i	$-0.858089\pi$
$463$	−28.6926	−	28.6926i	−1.33346	−	1.33346i	−0.431205	−	0.902254i	$-0.641911\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	32.4161i		−	1.50004i	−0.661417	−	0.750018i	$-0.730045\pi$
$467$		−	32.4161i		−	1.50004i	0.661417	−	0.750018i	$-0.269955\pi$
$468$		0			0
$469$	1.59693	−	1.59693i	0.0737392	−	0.0737392i
$470$		0			0
$471$	−7.97337			−0.367394
$472$		0			0
$473$	−4.40605	−	4.40605i	−0.202591	−	0.202591i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−7.73837			−0.354316
$478$		0			0
$479$	7.33117			0.334970			0.167485	−	0.985875i	$-0.446435\pi$
$479$	7.33117			0.334970			0.167485	+	0.985875i	$0.446435\pi$
$480$		0			0
$481$	11.2090			0.511087
$482$		0			0
$483$	−18.7477			−0.853051
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−11.7773	−	11.7773i	−0.533681	−	0.533681i	0.387985	−	0.921666i	$-0.373171\pi$
$487$	−11.7773	−	11.7773i	−0.533681	−	0.533681i	−0.921666	+	0.387985i	$0.873171\pi$
$488$		0			0
$489$	25.0634			1.13341
$490$		0			0
$491$	27.3556	−	27.3556i	1.23454	−	1.23454i	0.272343	−	0.962200i	$-0.412202\pi$
$491$	27.3556	−	27.3556i	1.23454	−	1.23454i	0.962200	−	0.272343i	$-0.0877985\pi$
$492$		0			0
$493$			25.7941i			1.16171i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.575432	−	0.575432i	−0.0258117	−	0.0258117i
$498$		0			0
$499$	12.1629	−	12.1629i	0.544488	−	0.544488i	−0.380353	−	0.924841i	$-0.624198\pi$
$499$	12.1629	−	12.1629i	0.544488	−	0.544488i	0.924841	+	0.380353i	$0.124198\pi$
$500$		0			0
$501$	−3.33866	−	3.33866i	−0.149160	−	0.149160i
$502$		0			0
$503$	−13.2748	+	13.2748i	−0.591892	+	0.591892i	−0.938142	−	0.346250i	$-0.887455\pi$
$503$	−13.2748	+	13.2748i	−0.591892	+	0.591892i	0.346250	+	0.938142i	$0.387455\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−14.7788			−0.656350
$508$		0			0
$509$	−9.29995	−	9.29995i	−0.412213	−	0.412213i	0.470296	−	0.882509i	$-0.344147\pi$
$509$	−9.29995	−	9.29995i	−0.412213	−	0.412213i	−0.882509	+	0.470296i	$0.844147\pi$
$510$		0			0
$511$			3.46565i			0.153312i
$512$		0			0
$513$	−0.0773972	+	0.0773972i	−0.00341717	+	0.00341717i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			14.5141i			0.638329i
$518$		0			0
$519$			13.1685i			0.578031i
$520$		0			0
$521$			33.5279i			1.46888i	0.678671	+	0.734442i	$0.262556\pi$
$521$			33.5279i			1.46888i	−0.678671	+	0.734442i	$0.737444\pi$
$522$		0			0
$523$			25.9463i			1.13455i	0.823528	+	0.567276i	$0.192003\pi$
$523$			25.9463i			1.13455i	−0.823528	+	0.567276i	$0.807997\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	34.4903	−	34.4903i	1.50242	−	1.50242i
$528$		0			0
$529$			3.12481i			0.135861i
$530$		0			0
$531$	−3.73554	−	3.73554i	−0.162109	−	0.162109i
$532$		0			0
$533$	16.0495			0.695182
$534$		0			0
$535$		0			0
$536$		0			0
$537$	16.4383	−	16.4383i	0.709365	−	0.709365i
$538$		0			0
$539$	−4.58248	−	4.58248i	−0.197381	−	0.197381i
$540$		0			0
$541$	4.47122	−	4.47122i	0.192233	−	0.192233i	−0.604428	−	0.796660i	$-0.706598\pi$
$541$	4.47122	−	4.47122i	0.192233	−	0.192233i	0.796660	+	0.604428i	$0.206598\pi$
$542$		0			0
$543$	−3.54085	−	3.54085i	−0.151952	−	0.151952i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			15.5964i			0.666853i	0.942776	+	0.333426i	$0.108205\pi$
$547$			15.5964i			0.666853i	−0.942776	+	0.333426i	$0.891795\pi$
$548$		0			0
$549$	−1.49990	+	1.49990i	−0.0640142	+	0.0640142i
$550$		0			0
$551$	−0.0913677			−0.00389239
$552$		0			0
$553$	−5.98831	−	5.98831i	−0.254649	−	0.254649i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−15.5348			−0.658231			−0.329116	−	0.944290i	$-0.606751\pi$
$557$	−15.5348			−0.658231			−0.329116	+	0.944290i	$0.606751\pi$
$558$		0			0
$559$	−3.13928			−0.132777
$560$		0			0
$561$	23.3705			0.986703
$562$		0			0
$563$	24.3087			1.02449			0.512245	−	0.858839i	$-0.328814\pi$
$563$	24.3087			1.02449			0.512245	+	0.858839i	$0.328814\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	10.0344	+	10.0344i	0.421405	+	0.421405i
$568$		0			0
$569$	−0.187259			−0.00785029			−0.00392515	−	0.999992i	$-0.501249\pi$
$569$	−0.187259			−0.00785029			−0.00392515	+	0.999992i	$0.501249\pi$
$570$		0			0
$571$	9.07187	−	9.07187i	0.379646	−	0.379646i	−0.491328	−	0.870974i	$-0.663489\pi$
$571$	9.07187	−	9.07187i	0.379646	−	0.379646i	0.870974	+	0.491328i	$0.163489\pi$
$572$		0			0
$573$		−	7.61266i		−	0.318023i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	1.53648	+	1.53648i	0.0639645	+	0.0639645i	0.738365	−	0.674401i	$-0.235598\pi$
$577$	1.53648	+	1.53648i	0.0639645	+	0.0639645i	−0.674401	+	0.738365i	$0.735598\pi$
$578$		0			0
$579$	6.72191	−	6.72191i	0.279353	−	0.279353i
$580$		0			0
$581$	−27.3794	−	27.3794i	−1.13589	−	1.13589i
$582$		0			0
$583$	−15.8616	+	15.8616i	−0.656920	+	0.656920i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.06150			−0.126362			−0.0631808	−	0.998002i	$-0.520124\pi$
$587$	−3.06150			−0.126362			−0.0631808	+	0.998002i	$0.520124\pi$
$588$		0			0
$589$	0.122171	+	0.122171i	0.00503398	+	0.00503398i
$590$		0			0
$591$			4.10408i			0.168819i
$592$		0			0
$593$	20.8213	−	20.8213i	0.855029	−	0.855029i	−0.135718	−	0.990747i	$-0.543334\pi$
$593$	20.8213	−	20.8213i	0.855029	−	0.855029i	0.990747	+	0.135718i	$0.0433342\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			2.99005i			0.122375i
$598$		0			0
$599$			27.8866i			1.13942i	0.821847	+	0.569709i	$0.192944\pi$
$599$			27.8866i			1.13942i	−0.821847	+	0.569709i	$0.807056\pi$
$600$		0			0
$601$			4.70260i			0.191823i	0.995390	+	0.0959115i	$0.0305766\pi$
$601$			4.70260i			0.191823i	−0.995390	+	0.0959115i	$0.969423\pi$
$602$		0			0
$603$		−	0.792365i		−	0.0322676i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	28.8294	−	28.8294i	1.17015	−	1.17015i	0.187975	−	0.982174i	$-0.439807\pi$
$607$	28.8294	−	28.8294i	1.17015	−	1.17015i	0.982174	−	0.187975i	$-0.0601925\pi$
$608$		0			0
$609$			19.8507i			0.804393i
$610$		0			0
$611$	5.17059	+	5.17059i	0.209180	+	0.209180i
$612$		0			0
$613$	38.7980			1.56704			0.783518	−	0.621369i	$-0.213423\pi$
$613$	38.7980			1.56704			0.783518	+	0.621369i	$0.213423\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−7.06723	+	7.06723i	−0.284516	+	0.284516i	−0.834907	−	0.550391i	$-0.814479\pi$
$617$	−7.06723	+	7.06723i	−0.284516	+	0.284516i	0.550391	+	0.834907i	$0.314479\pi$
$618$		0			0
$619$	−28.1001	−	28.1001i	−1.12944	−	1.12944i	−0.990268	−	0.139172i	$-0.955556\pi$
$619$	−28.1001	−	28.1001i	−1.12944	−	1.12944i	−0.139172	−	0.990268i	$-0.544444\pi$
$620$		0			0
$621$	−17.8268	+	17.8268i	−0.715363	+	0.715363i
$622$		0			0
$623$	28.5432	+	28.5432i	1.14356	+	1.14356i
$624$		0			0
$625$		0			0
$626$		0			0
$627$			0.0827827i			0.00330602i
$628$		0			0
$629$	28.0029	−	28.0029i	1.11655	−	1.11655i
$630$		0			0
$631$	−38.2613			−1.52316			−0.761580	−	0.648071i	$-0.775576\pi$
$631$	−38.2613			−1.52316			−0.761580	+	0.648071i	$0.775576\pi$
$632$		0			0
$633$	7.72420	+	7.72420i	0.307010	+	0.307010i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−3.26498			−0.129363
$638$		0			0
$639$	−0.285519			−0.0112950
$640$		0			0
$641$	7.15922			0.282772			0.141386	−	0.989955i	$-0.454844\pi$
$641$	7.15922			0.282772			0.141386	+	0.989955i	$0.454844\pi$
$642$		0			0
$643$	8.74864			0.345013			0.172506	−	0.985008i	$-0.444813\pi$
$643$	8.74864			0.345013			0.172506	+	0.985008i	$0.444813\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.84125	+	8.84125i	0.347585	+	0.347585i	0.859209	−	0.511624i	$-0.170956\pi$
$647$	8.84125	+	8.84125i	0.347585	+	0.347585i	−0.511624	+	0.859209i	$0.670956\pi$
$648$		0			0
$649$	−15.3137			−0.601117
$650$		0			0
$651$	26.5432	−	26.5432i	1.04031	−	1.04031i
$652$		0			0
$653$		−	20.7854i		−	0.813396i	−0.913563	−	0.406698i	$-0.866680\pi$
$653$		−	20.7854i		−	0.813396i	0.913563	−	0.406698i	$-0.133320\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	0.859797	+	0.859797i	0.0335439	+	0.0335439i
$658$		0			0
$659$	13.3330	−	13.3330i	0.519382	−	0.519382i	−0.398003	−	0.917384i	$-0.630297\pi$
$659$	13.3330	−	13.3330i	0.519382	−	0.519382i	0.917384	+	0.398003i	$0.130297\pi$
$660$		0			0
$661$	−30.5831	−	30.5831i	−1.18954	−	1.18954i	−0.977194	−	0.212350i	$-0.931888\pi$
$661$	−30.5831	−	30.5831i	−1.18954	−	1.18954i	−0.212350	−	0.977194i	$-0.568112\pi$
$662$		0			0
$663$	8.32564	−	8.32564i	0.323341	−	0.323341i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−21.0446			−0.814848
$668$		0			0
$669$	−1.61836	−	1.61836i	−0.0625695	−	0.0625695i
$670$		0			0
$671$			6.14880i			0.237372i
$672$		0			0
$673$	−29.9888	+	29.9888i	−1.15598	+	1.15598i	−0.170652	+	0.985331i	$0.554587\pi$
$673$	−29.9888	+	29.9888i	−1.15598	+	1.15598i	−0.985331	+	0.170652i	$0.945413\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			33.4274i			1.28472i	0.766403	+	0.642360i	$0.222044\pi$
$677$			33.4274i			1.28472i	−0.766403	+	0.642360i	$0.777956\pi$
$678$		0			0
$679$			27.0409i			1.03774i
$680$		0			0
$681$		−	17.8551i		−	0.684211i
$682$		0			0
$683$			4.07583i			0.155957i	0.996955	+	0.0779787i	$0.0248466\pi$
$683$			4.07583i			0.155957i	−0.996955	+	0.0779787i	$0.975153\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−1.36098	+	1.36098i	−0.0519246	+	0.0519246i
$688$		0			0
$689$			11.3013i			0.430544i
$690$		0			0
$691$	8.69768	+	8.69768i	0.330875	+	0.330875i	0.852919	−	0.522044i	$-0.174830\pi$
$691$	8.69768	+	8.69768i	0.330875	+	0.330875i	−0.522044	+	0.852919i	$0.674830\pi$
$692$		0			0
$693$	−9.81330			−0.372776
$694$		0			0
$695$		0			0
$696$		0			0
$697$	40.0956	−	40.0956i	1.51873	−	1.51873i
$698$		0			0
$699$	−0.423347	−	0.423347i	−0.0160125	−	0.0160125i
$700$		0			0
$701$	11.8325	−	11.8325i	0.446908	−	0.446908i	−0.447418	−	0.894325i	$-0.647656\pi$
$701$	11.8325	−	11.8325i	0.446908	−	0.446908i	0.894325	+	0.447418i	$0.147656\pi$
$702$		0			0
$703$	0.0991914	+	0.0991914i	0.00374108	+	0.00374108i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			16.1413i			0.607056i
$708$		0			0
$709$	−32.3901	+	32.3901i	−1.21643	+	1.21643i	−0.247563	+	0.968872i	$0.579630\pi$
$709$	−32.3901	+	32.3901i	−1.21643	+	1.21643i	−0.968872	+	0.247563i	$0.920370\pi$
$710$		0			0
$711$	−2.97129			−0.111432
$712$		0			0
$713$	28.1395	+	28.1395i	1.05383	+	1.05383i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−17.4282			−0.650868
$718$		0			0
$719$	−4.16893			−0.155475			−0.0777374	−	0.996974i	$-0.524770\pi$
$719$	−4.16893			−0.155475			−0.0777374	+	0.996974i	$0.524770\pi$
$720$		0			0
$721$	−45.7603			−1.70420
$722$		0			0
$723$	27.2751			1.01437
$724$		0			0
$725$		0			0
$726$		0			0
$727$	28.6014	+	28.6014i	1.06077	+	1.06077i	0.998030	+	0.0627368i	$0.0199829\pi$
$727$	28.6014	+	28.6014i	1.06077	+	1.06077i	0.0627368	+	0.998030i	$0.480017\pi$
$728$		0			0
$729$	28.6142			1.05979
$730$		0			0
$731$	−7.84269	+	7.84269i	−0.290072	+	0.290072i
$732$		0			0
$733$			18.7069i			0.690956i	0.938427	+	0.345478i	$0.112283\pi$
$733$			18.7069i			0.690956i	−0.938427	+	0.345478i	$0.887717\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.62414	−	1.62414i	−0.0598259	−	0.0598259i
$738$		0			0
$739$	−34.6914	+	34.6914i	−1.27614	+	1.27614i	−0.333337	+	0.942808i	$0.608175\pi$
$739$	−34.6914	+	34.6914i	−1.27614	+	1.27614i	−0.942808	+	0.333337i	$0.891825\pi$
$740$		0			0
$741$	0.0294910	+	0.0294910i	0.00108338	+	0.00108338i
$742$		0			0
$743$	24.7660	−	24.7660i	0.908577	−	0.908577i	−0.0875803	−	0.996157i	$-0.527913\pi$
$743$	24.7660	−	24.7660i	0.908577	−	0.908577i	0.996157	+	0.0875803i	$0.0279134\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−13.5852			−0.497055
$748$		0			0
$749$	−23.2878	−	23.2878i	−0.850917	−	0.850917i
$750$		0			0
$751$		−	45.2370i		−	1.65072i	−0.564606	−	0.825361i	$-0.690972\pi$
$751$		−	45.2370i		−	1.65072i	0.564606	−	0.825361i	$-0.309028\pi$
$752$		0			0
$753$	7.21340	−	7.21340i	0.262871	−	0.262871i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	6.44058i		−	0.234087i	−0.993127	−	0.117044i	$-0.962658\pi$
$757$		−	6.44058i		−	0.234087i	0.993127	−	0.117044i	$-0.0373417\pi$
$758$		0			0
$759$			19.0672i			0.692095i
$760$		0			0
$761$		−	9.50571i		−	0.344582i	−0.985046	−	0.172291i	$-0.944883\pi$
$761$		−	9.50571i		−	0.344582i	0.985046	−	0.172291i	$-0.0551169\pi$
$762$		0			0
$763$		−	38.9367i		−	1.40960i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.45546	+	5.45546i	−0.196985	+	0.196985i
$768$		0			0
$769$		−	46.8513i		−	1.68950i	−0.535159	−	0.844751i	$-0.679748\pi$
$769$		−	46.8513i		−	1.68950i	0.535159	−	0.844751i	$-0.320252\pi$
$770$		0			0
$771$	−20.6176	−	20.6176i	−0.742526	−	0.742526i
$772$		0			0
$773$	−10.9964			−0.395513			−0.197756	−	0.980251i	$-0.563365\pi$
$773$	−10.9964			−0.395513			−0.197756	+	0.980251i	$0.563365\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	21.5506	−	21.5506i	0.773122	−	0.773122i
$778$		0			0
$779$	0.142026	+	0.142026i	0.00508862	+	0.00508862i
$780$		0			0
$781$	−0.585238	+	0.585238i	−0.0209414	+	0.0209414i
$782$		0			0
$783$	18.8756	+	18.8756i	0.674559	+	0.674559i
$784$		0			0
$785$		0			0
$786$		0			0
$787$		−	25.5190i		−	0.909653i	−0.890580	−	0.454826i	$-0.849701\pi$
$787$		−	25.5190i		−	0.909653i	0.890580	−	0.454826i	$-0.150299\pi$
$788$		0			0
$789$	−16.4265	+	16.4265i	−0.584797	+	0.584797i
$790$		0			0
$791$	20.8660			0.741909
$792$		0			0
$793$	2.19048	+	2.19048i	0.0777864	+	0.0777864i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	13.3808			0.473972			0.236986	−	0.971513i	$-0.423840\pi$
$797$	13.3808			0.473972			0.236986	+	0.971513i	$0.423840\pi$
$798$		0			0
$799$	25.8348			0.913969
$800$		0			0
$801$	14.1626			0.500412
$802$		0			0
$803$	3.52471			0.124384
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.92738	−	2.92738i	−0.103049	−	0.103049i
$808$		0			0
$809$	52.7958			1.85620			0.928102	−	0.372327i	$-0.121440\pi$
$809$	52.7958			1.85620			0.928102	+	0.372327i	$0.121440\pi$
$810$		0			0
$811$	−1.57411	+	1.57411i	−0.0552745	+	0.0552745i	−0.734204	−	0.678929i	$-0.762444\pi$
$811$	−1.57411	+	1.57411i	−0.0552745	+	0.0552745i	0.678929	+	0.734204i	$0.262444\pi$
$812$		0			0
$813$			26.2749i			0.921500i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−0.0277803	−	0.0277803i	−0.000971909	−	0.000971909i
$818$		0			0
$819$	−3.49595	+	3.49595i	−0.122158	+	0.122158i
$820$		0			0
$821$	−25.7715	−	25.7715i	−0.899431	−	0.899431i	0.0959548	−	0.995386i	$-0.469410\pi$
$821$	−25.7715	−	25.7715i	−0.899431	−	0.899431i	−0.995386	+	0.0959548i	$0.969410\pi$
$822$		0			0
$823$	−17.5565	+	17.5565i	−0.611982	+	0.611982i	−0.943462	−	0.331480i	$-0.892452\pi$
$823$	−17.5565	+	17.5565i	−0.611982	+	0.611982i	0.331480	+	0.943462i	$0.392452\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	14.8548			0.516551			0.258276	−	0.966071i	$-0.416846\pi$
$827$	14.8548			0.516551			0.258276	+	0.966071i	$0.416846\pi$
$828$		0			0
$829$	9.71444	+	9.71444i	0.337397	+	0.337397i	0.855387	−	0.517990i	$-0.173320\pi$
$829$	9.71444	+	9.71444i	0.337397	+	0.337397i	−0.517990	+	0.855387i	$0.673320\pi$
$830$		0			0
$831$			13.8191i			0.479380i
$832$		0			0
$833$	−8.15672	+	8.15672i	−0.282614	+	0.282614i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	50.4786i		−	1.74480i
$838$		0			0
$839$			4.54484i			0.156905i	0.996918	+	0.0784527i	$0.0249979\pi$
$839$			4.54484i			0.156905i	−0.996918	+	0.0784527i	$0.975002\pi$
$840$		0			0
$841$		−	6.71729i		−	0.231631i
$842$		0			0
$843$			12.9766i			0.446938i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	3.36337	−	3.36337i	0.115567	−	0.115567i
$848$		0			0
$849$		−	4.76977i		−	0.163698i
$850$		0			0
$851$	22.8466	+	22.8466i	0.783171	+	0.783171i
$852$		0			0
$853$	−37.3745			−1.27968			−0.639839	−	0.768509i	$-0.720999\pi$
$853$	−37.3745			−1.27968			−0.639839	+	0.768509i	$0.720999\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−16.4541	+	16.4541i	−0.562062	+	0.562062i	−0.929893	−	0.367831i	$-0.880101\pi$
$857$	−16.4541	+	16.4541i	−0.562062	+	0.562062i	0.367831	+	0.929893i	$0.380101\pi$
$858$		0			0
$859$	15.7662	+	15.7662i	0.537935	+	0.537935i	0.922922	−	0.384987i	$-0.125794\pi$
$859$	15.7662	+	15.7662i	0.537935	+	0.537935i	−0.384987	+	0.922922i	$0.625794\pi$
$860$		0			0
$861$	30.8570	−	30.8570i	1.05160	−	1.05160i
$862$		0			0
$863$	−22.6395	−	22.6395i	−0.770659	−	0.770659i	0.207563	−	0.978222i	$-0.433447\pi$
$863$	−22.6395	−	22.6395i	−0.770659	−	0.770659i	−0.978222	+	0.207563i	$0.933447\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	17.9148i		−	0.608419i
$868$		0			0
$869$	−6.09036	+	6.09036i	−0.206601	+	0.206601i
$870$		0			0
$871$	−1.15719			−0.0392097
$872$		0			0
$873$	6.70861	+	6.70861i	0.227052	+	0.227052i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	30.0542			1.01486			0.507429	−	0.861694i	$-0.330596\pi$
$877$	30.0542			1.01486			0.507429	+	0.861694i	$0.330596\pi$
$878$		0			0
$879$	3.71243			0.125217
$880$		0			0
$881$	−3.86747			−0.130298			−0.0651492	−	0.997876i	$-0.520752\pi$
$881$	−3.86747			−0.130298			−0.0651492	+	0.997876i	$0.520752\pi$
$882$		0			0
$883$	−0.485919			−0.0163525			−0.00817624	−	0.999967i	$-0.502603\pi$
$883$	−0.485919			−0.0163525			−0.00817624	+	0.999967i	$0.502603\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.9762	+	12.9762i	0.435699	+	0.435699i	0.890561	−	0.454863i	$-0.150312\pi$
$887$	12.9762	+	12.9762i	0.435699	+	0.435699i	−0.454863	+	0.890561i	$0.650312\pi$
$888$		0			0
$889$	−5.91587			−0.198412
$890$		0			0
$891$	10.2054	−	10.2054i	0.341893	−	0.341893i
$892$		0			0
$893$			0.0915117i			0.00306232i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	6.79261	+	6.79261i	0.226799	+	0.226799i
$898$		0			0
$899$	29.7951	−	29.7951i	0.993722	−	0.993722i
$900$		0			0
$901$	28.2333	+	28.2333i	0.940588	+	0.940588i
$902$		0			0
$903$	−6.03560	+	6.03560i	−0.200852	+	0.200852i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	54.3645			1.80514			0.902571	−	0.430540i	$-0.141677\pi$
$907$	54.3645			1.80514			0.902571	+	0.430540i	$0.141677\pi$
$908$		0			0
$909$	4.00451	+	4.00451i	0.132821	+	0.132821i
$910$		0			0
$911$		−	40.0402i		−	1.32659i	−0.748358	−	0.663295i	$-0.769157\pi$
$911$		−	40.0402i		−	1.32659i	0.748358	−	0.663295i	$-0.230843\pi$
$912$		0			0
$913$	−27.8460	+	27.8460i	−0.921567	+	0.921567i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	15.0300i		−	0.496335i
$918$		0			0
$919$		−	8.81475i		−	0.290772i	−0.989375	−	0.145386i	$-0.953558\pi$
$919$		−	8.81475i		−	0.290772i	0.989375	−	0.145386i	$-0.0464423\pi$
$920$		0			0
$921$		−	14.7057i		−	0.484568i
$922$		0			0
$923$			0.416977i			0.0137250i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−11.3527	+	11.3527i	−0.372872	+	0.372872i
$928$		0			0
$929$			47.9673i			1.57376i	0.617109	+	0.786878i	$0.288304\pi$
$929$			47.9673i			1.57376i	−0.617109	+	0.786878i	$0.711696\pi$
$930$		0			0
$931$	−0.0288926	−	0.0288926i	−0.000946918	−	0.000946918i
$932$		0			0
$933$	−28.5272			−0.933938
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−13.8299	+	13.8299i	−0.451803	+	0.451803i	−0.895953	−	0.444150i	$-0.853506\pi$
$937$	−13.8299	+	13.8299i	−0.451803	+	0.451803i	0.444150	+	0.895953i	$0.353506\pi$
$938$		0			0
$939$	−3.93426	−	3.93426i	−0.128390	−	0.128390i
$940$		0			0
$941$	−5.19108	+	5.19108i	−0.169224	+	0.169224i	−0.786638	−	0.617414i	$-0.788180\pi$
$941$	−5.19108	+	5.19108i	−0.169224	+	0.169224i	0.617414	+	0.786638i	$0.288180\pi$
$942$		0			0
$943$	32.7127	+	32.7127i	1.06527	+	1.06527i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	24.1342i		−	0.784255i	−0.919911	−	0.392128i	$-0.871739\pi$
$947$		−	24.1342i		−	0.784255i	0.919911	−	0.392128i	$-0.128261\pi$
$948$		0			0
$949$	1.25566	−	1.25566i	0.0407606	−	0.0407606i
$950$		0			0
$951$	28.2166			0.914986
$952$		0			0
$953$	−22.8500	−	22.8500i	−0.740183	−	0.740183i	0.232430	−	0.972613i	$-0.425332\pi$
$953$	−22.8500	−	22.8500i	−0.740183	−	0.740183i	−0.972613	+	0.232430i	$0.925332\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	20.1890			0.652618
$958$		0			0
$959$	−24.0121			−0.775392
$960$		0			0
$961$	−48.6804			−1.57034
$962$		0			0
$963$	−11.5550			−0.372354
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−21.4211	−	21.4211i	−0.688855	−	0.688855i	0.273124	−	0.961979i	$-0.411943\pi$
$967$	−21.4211	−	21.4211i	−0.688855	−	0.688855i	−0.961979	+	0.273124i	$0.911943\pi$
$968$		0			0
$969$	0.147351			0.00473361
$970$		0			0
$971$	11.7978	−	11.7978i	0.378609	−	0.378609i	−0.491991	−	0.870600i	$-0.663731\pi$
$971$	11.7978	−	11.7978i	0.378609	−	0.378609i	0.870600	+	0.491991i	$0.163731\pi$
$972$		0			0
$973$		−	51.6611i		−	1.65618i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.15703	−	2.15703i	−0.0690096	−	0.0690096i	0.671760	−	0.740769i	$-0.265539\pi$
$977$	−2.15703	−	2.15703i	−0.0690096	−	0.0690096i	−0.740769	+	0.671760i	$0.765539\pi$
$978$		0			0
$979$	29.0296	−	29.0296i	0.927791	−	0.927791i
$980$		0			0
$981$	−9.65985	−	9.65985i	−0.308415	−	0.308415i
$982$		0			0
$983$	19.9712	−	19.9712i	0.636983	−	0.636983i	−0.312827	−	0.949810i	$-0.601276\pi$
$983$	19.9712	−	19.9712i	0.636983	−	0.636983i	0.949810	+	0.312827i	$0.101276\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	19.8820			0.632852
$988$		0			0
$989$	−6.39858	−	6.39858i	−0.203463	−	0.203463i
$990$		0			0
$991$			19.2270i			0.610767i	0.952230	+	0.305383i	$0.0987846\pi$
$991$			19.2270i			0.610767i	−0.952230	+	0.305383i	$0.901215\pi$
$992$		0			0
$993$	27.1574	−	27.1574i	0.861815	−	0.861815i
$994$		0			0
$995$		0			0
$996$		0			0
$997$			2.01694i			0.0638771i	0.999490	+	0.0319385i	$0.0101681\pi$
$997$			2.01694i			0.0638771i	−0.999490	+	0.0319385i	$0.989832\pi$
$998$		0			0
$999$		−	40.9838i		−	1.29667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.s.d.207.3		18
4.3	odd	2		400.2.s.d.107.2		18
5.2	odd	4		320.2.j.b.143.7		18
5.3	odd	4		1600.2.j.d.143.3		18
5.4	even	2		320.2.s.b.207.7		18
16.3	odd	4		1600.2.j.d.1007.7		18
16.13	even	4		400.2.j.d.307.2		18
20.3	even	4		400.2.j.d.43.2		18
20.7	even	4		80.2.j.b.43.8	✓	18
20.19	odd	2		80.2.s.b.27.8	yes	18
40.19	odd	2		640.2.s.d.287.7		18
40.27	even	4		640.2.j.d.543.7		18
40.29	even	2		640.2.s.c.287.3		18
40.37	odd	4		640.2.j.c.543.3		18
60.47	odd	4		720.2.bd.g.523.2		18
60.59	even	2		720.2.z.g.667.2		18
80.3	even	4	inner	1600.2.s.d.943.3		18
80.13	odd	4		400.2.s.d.243.2		18
80.19	odd	4		320.2.j.b.47.3		18
80.27	even	4		640.2.s.c.223.3		18
80.29	even	4		80.2.j.b.67.8	yes	18
80.37	odd	4		640.2.s.d.223.7		18
80.59	odd	4		640.2.j.c.607.7		18
80.67	even	4		320.2.s.b.303.7		18
80.69	even	4		640.2.j.d.607.3		18
80.77	odd	4		80.2.s.b.3.8	yes	18
240.29	odd	4		720.2.bd.g.307.2		18
240.77	even	4		720.2.z.g.163.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.8	✓	18	20.7	even	4
80.2.j.b.67.8	yes	18	80.29	even	4
80.2.s.b.3.8	yes	18	80.77	odd	4
80.2.s.b.27.8	yes	18	20.19	odd	2
320.2.j.b.47.3		18	80.19	odd	4
320.2.j.b.143.7		18	5.2	odd	4
320.2.s.b.207.7		18	5.4	even	2
320.2.s.b.303.7		18	80.67	even	4
400.2.j.d.43.2		18	20.3	even	4
400.2.j.d.307.2		18	16.13	even	4
400.2.s.d.107.2		18	4.3	odd	2
400.2.s.d.243.2		18	80.13	odd	4
640.2.j.c.543.3		18	40.37	odd	4
640.2.j.c.607.7		18	80.59	odd	4
640.2.j.d.543.7		18	40.27	even	4
640.2.j.d.607.3		18	80.69	even	4
640.2.s.c.223.3		18	80.27	even	4
640.2.s.c.287.3		18	40.29	even	2
640.2.s.d.223.7		18	80.37	odd	4
640.2.s.d.287.7		18	40.19	odd	2
720.2.z.g.163.2		18	240.77	even	4
720.2.z.g.667.2		18	60.59	even	2
720.2.bd.g.307.2		18	240.29	odd	4
720.2.bd.g.523.2		18	60.47	odd	4
1600.2.j.d.143.3		18	5.3	odd	4
1600.2.j.d.1007.7		18	16.3	odd	4
1600.2.s.d.207.3		18	1.1	even	1	trivial
1600.2.s.d.943.3		18	80.3	even	4	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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.39319 q^{3} +(-2.13436 - 2.13436i) q^{7} -1.05903 q^{9} +(-2.17074 + 2.17074i) q^{11} +1.54663i q^{13} +(3.86386 + 3.86386i) q^{17} +(-0.0136865 + 0.0136865i) q^{19} +(2.97357 + 2.97357i) q^{21} +(-3.15240 + 3.15240i) q^{23} +5.65499 q^{27} +(3.33787 + 3.33787i) q^{29} -8.92639i q^{31} +(3.02424 - 3.02424i) q^{33} -7.24737i q^{37} -2.15475i q^{39} -10.3771i q^{41} +2.02975i q^{43} +(3.34313 - 3.34313i) q^{47} +2.11103i q^{49} +(-5.38308 - 5.38308i) q^{51} +7.30702 q^{53} +(0.0190679 - 0.0190679i) q^{57} +(3.52732 + 3.52732i) q^{59} +(1.41629 - 1.41629i) q^{61} +(2.26036 + 2.26036i) q^{63} +0.748197i q^{67} +(4.39187 - 4.39187i) q^{69} +0.269603 q^{71} +(-0.811870 - 0.811870i) q^{73} +9.26628 q^{77} +2.80567 q^{79} -4.70135 q^{81} +12.8279 q^{83} +(-4.65027 - 4.65027i) q^{87} -13.3732 q^{89} +(3.30108 - 3.30108i) q^{91} +12.4361i q^{93} +(-6.33466 - 6.33466i) q^{97} +(2.29888 - 2.29888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{7} + 10 q^{9} + 2 q^{11} + 6 q^{17} + 2 q^{19} - 16 q^{21} - 2 q^{23} - 24 q^{27} + 14 q^{29} + 8 q^{33} + 38 q^{47} - 8 q^{51} - 12 q^{53} + 24 q^{57} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 32 q^{69}+ \cdots - 22 q^{99}+O(q^{100}) \) 18 * q + 2 * q^7 + 10 * q^9 + 2 * q^11 + 6 * q^17 + 2 * q^19 - 16 * q^21 - 2 * q^23 - 24 * q^27 + 14 * q^29 + 8 * q^33 + 38 * q^47 - 8 * q^51 - 12 * q^53 + 24 * q^57 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 32 * q^69 - 24 * q^71 + 14 * q^73 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 + 24 * q^87 + 12 * q^89 - 18 * q^97 - 22 * q^99

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