LMFDB - Embedded newform 1680.2.f.k.881.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1680,2,Mod(881,1680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1680, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1, 0, 1]))

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

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

chi := DirichletCharacter("1680.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.f (of order $2$, degree $1$, 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:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + x^{14} - 4 x^{13} + 10 x^{12} - 32 x^{11} + 71 x^{10} - 70 x^{9} + 74 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + x^14 - 4x^13 + 10x^12 - 32x^11 + 71x^10 - 70x^9 + 74x^8 - 210x^7 + 639x^6 - 864x^5 + 810x^4 - 972x^3 + 729x^2 - 4374x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	no (minimal twist has level 840)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			881.16
Root			$0.0964469 + 1.72936i$ of defining polynomial
Character	$\chi$	$=$	1680.881
Dual form			1680.2.f.k.881.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72936 + 0.0964469i) q^{3} -1.00000 q^{5} +(-0.208829 - 2.63750i) q^{7} +(2.98140 + 0.333584i) q^{9} +O(q^{10})$	\(q+(1.72936 + 0.0964469i) q^{3} -1.00000 q^{5} +(-0.208829 - 2.63750i) q^{7} +(2.98140 + 0.333584i) q^{9} -1.71212i q^{11} -3.11462i q^{13} +(-1.72936 - 0.0964469i) q^{15} -3.59399 q^{17} +1.04495i q^{19} +(-0.106762 - 4.58133i) q^{21} +0.587015i q^{23} +1.00000 q^{25} +(5.12374 + 0.864434i) q^{27} -4.47468i q^{29} -8.51183i q^{31} +(0.165129 - 2.96088i) q^{33} +(0.208829 + 2.63750i) q^{35} -7.99549 q^{37} +(0.300395 - 5.38630i) q^{39} -7.74927 q^{41} +5.05272 q^{43} +(-2.98140 - 0.333584i) q^{45} +9.90809 q^{47} +(-6.91278 + 1.10157i) q^{49} +(-6.21532 - 0.346630i) q^{51} +4.63566i q^{53} +1.71212i q^{55} +(-0.100783 + 1.80711i) q^{57} -2.11673 q^{59} -8.11222i q^{61} +(0.257225 - 7.93308i) q^{63} +3.11462i q^{65} +8.80626 q^{67} +(-0.0566158 + 1.01516i) q^{69} -2.57259i q^{71} -6.88336i q^{73} +(1.72936 + 0.0964469i) q^{75} +(-4.51572 + 0.357540i) q^{77} +7.01425 q^{79} +(8.77744 + 1.98909i) q^{81} -5.21838 q^{83} +3.59399 q^{85} +(0.431570 - 7.73836i) q^{87} +8.17632 q^{89} +(-8.21479 + 0.650421i) q^{91} +(0.820940 - 14.7200i) q^{93} -1.04495i q^{95} -13.5934i q^{97} +(0.571136 - 5.10451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{5} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 16 * q - 16 * q^5 - 2 * q^7 - 2 * q^9	$ 16 q - 16 q^{5} - 2 q^{7} - 2 q^{9} + 2 q^{21} + 16 q^{25} + 6 q^{27} - 6 q^{33} + 2 q^{35} + 12 q^{37} - 6 q^{39} - 32 q^{41} - 32 q^{43} + 2 q^{45} + 4 q^{47} - 4 q^{49} - 6 q^{51} - 24 q^{59} + 4 q^{63} - 8 q^{69} + 32 q^{77} + 4 q^{79} - 6 q^{81} + 20 q^{83} + 6 q^{87} + 24 q^{89} - 20 q^{91} - 32 q^{93} + 58 q^{99}+O(q^{100}) $ 16 * q - 16 * q^5 - 2 * q^7 - 2 * q^9 + 2 * q^21 + 16 * q^25 + 6 * q^27 - 6 * q^33 + 2 * q^35 + 12 * q^37 - 6 * q^39 - 32 * q^41 - 32 * q^43 + 2 * q^45 + 4 * q^47 - 4 * q^49 - 6 * q^51 - 24 * q^59 + 4 * q^63 - 8 * q^69 + 32 * q^77 + 4 * q^79 - 6 * q^81 + 20 * q^83 + 6 * q^87 + 24 * q^89 - 20 * q^91 - 32 * q^93 + 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$-1$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.72936	+	0.0964469i	0.998448	+	0.0556837i
$3$	1.72936	+	0.0964469i	0.998448	+	0.0556837i
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−0.208829	−	2.63750i	−0.0789298	−	0.996880i
$7$	−0.208829	−	2.63750i	−0.0789298	−	0.996880i
$8$		0			0
$9$	2.98140	+	0.333584i	0.993799	+	0.111195i
$10$		0			0
$11$		−	1.71212i		−	0.516224i	−0.966115	−	0.258112i	$-0.916900\pi$
$11$		−	1.71212i		−	0.516224i	0.966115	−	0.258112i	$-0.0831004\pi$
$12$		0			0
$13$		−	3.11462i		−	0.863839i	−0.901912	−	0.431920i	$-0.857836\pi$
$13$		−	3.11462i		−	0.863839i	0.901912	−	0.431920i	$-0.142164\pi$
$14$		0			0
$15$	−1.72936	−	0.0964469i	−0.446520	−	0.0249025i
$16$		0			0
$17$	−3.59399			−0.871671			−0.435836	−	0.900026i	$-0.643547\pi$
$17$	−3.59399			−0.871671			−0.435836	+	0.900026i	$0.643547\pi$
$18$		0			0
$19$			1.04495i			0.239729i	0.992790	+	0.119865i	$0.0382460\pi$
$19$			1.04495i			0.239729i	−0.992790	+	0.119865i	$0.961754\pi$
$20$		0			0
$21$	−0.106762	−	4.58133i	−0.0232974	−	0.999729i
$22$		0			0
$23$			0.587015i			0.122401i	0.998125	+	0.0612006i	$0.0194929\pi$
$23$			0.587015i			0.122401i	−0.998125	+	0.0612006i	$0.980507\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	5.12374	+	0.864434i	0.986065	+	0.166360i
$28$		0			0
$29$		−	4.47468i		−	0.830928i	−0.909610	−	0.415464i	$-0.863619\pi$
$29$		−	4.47468i		−	0.830928i	0.909610	−	0.415464i	$-0.136381\pi$
$30$		0			0
$31$		−	8.51183i		−	1.52877i	−0.644760	−	0.764385i	$-0.723043\pi$
$31$		−	8.51183i		−	1.52877i	0.644760	−	0.764385i	$-0.276957\pi$
$32$		0			0
$33$	0.165129	−	2.96088i	0.0287452	−	0.515423i
$34$		0			0
$35$	0.208829	+	2.63750i	0.0352985	+	0.445818i
$36$		0			0
$37$	−7.99549			−1.31445			−0.657225	−	0.753694i	$-0.728270\pi$
$37$	−7.99549			−1.31445			−0.657225	+	0.753694i	$0.728270\pi$
$38$		0			0
$39$	0.300395	−	5.38630i	0.0481017	−	0.862499i
$40$		0			0
$41$	−7.74927			−1.21023			−0.605116	−	0.796137i	$-0.706873\pi$
$41$	−7.74927			−1.21023			−0.605116	+	0.796137i	$0.706873\pi$
$42$		0			0
$43$	5.05272			0.770533			0.385266	−	0.922805i	$-0.374110\pi$
$43$	5.05272			0.770533			0.385266	+	0.922805i	$0.374110\pi$
$44$		0			0
$45$	−2.98140	−	0.333584i	−0.444440	−	0.0497277i
$46$		0			0
$47$	9.90809			1.44524			0.722622	−	0.691244i	$-0.242937\pi$
$47$	9.90809			1.44524			0.722622	+	0.691244i	$0.242937\pi$
$48$		0			0
$49$	−6.91278	+	1.10157i	−0.987540	+	0.157367i
$50$		0			0
$51$	−6.21532	−	0.346630i	−0.870319	−	0.0485378i
$52$		0			0
$53$			4.63566i			0.636757i	0.947964	+	0.318379i	$0.103138\pi$
$53$			4.63566i			0.636757i	−0.947964	+	0.318379i	$0.896862\pi$
$54$		0			0
$55$			1.71212i			0.230862i
$56$		0			0
$57$	−0.100783	+	1.80711i	−0.0133490	+	0.239357i
$58$		0			0
$59$	−2.11673			−0.275575			−0.137788	−	0.990462i	$-0.543999\pi$
$59$	−2.11673			−0.275575			−0.137788	+	0.990462i	$0.543999\pi$
$60$		0			0
$61$		−	8.11222i		−	1.03866i	−0.854573	−	0.519332i	$-0.826181\pi$
$61$		−	8.11222i		−	1.03866i	0.854573	−	0.519332i	$-0.173819\pi$
$62$		0			0
$63$	0.257225	−	7.93308i	0.0324072	−	0.999475i
$64$		0			0
$65$			3.11462i			0.386321i
$66$		0			0
$67$	8.80626			1.07586			0.537928	−	0.842991i	$-0.319207\pi$
$67$	8.80626			1.07586			0.537928	+	0.842991i	$0.319207\pi$
$68$		0			0
$69$	−0.0566158	+	1.01516i	−0.00681574	+	0.122211i
$70$		0			0
$71$		−	2.57259i		−	0.305311i	−0.988279	−	0.152655i	$-0.951218\pi$
$71$		−	2.57259i		−	0.305311i	0.988279	−	0.152655i	$-0.0487825\pi$
$72$		0			0
$73$		−	6.88336i		−	0.805637i	−0.915280	−	0.402818i	$-0.868031\pi$
$73$		−	6.88336i		−	0.805637i	0.915280	−	0.402818i	$-0.131969\pi$
$74$		0			0
$75$	1.72936	+	0.0964469i	0.199690	+	0.0111367i
$76$		0			0
$77$	−4.51572	+	0.357540i	−0.514614	+	0.0407455i
$78$		0			0
$79$	7.01425			0.789164			0.394582	−	0.918861i	$-0.370889\pi$
$79$	7.01425			0.789164			0.394582	+	0.918861i	$0.370889\pi$
$80$		0			0
$81$	8.77744	+	1.98909i	0.975272	+	0.221010i
$82$		0			0
$83$	−5.21838			−0.572791			−0.286396	−	0.958111i	$-0.592457\pi$
$83$	−5.21838			−0.572791			−0.286396	+	0.958111i	$0.592457\pi$
$84$		0			0
$85$	3.59399			0.389823
$86$		0			0
$87$	0.431570	−	7.73836i	0.0462691	−	0.829639i
$88$		0			0
$89$	8.17632			0.866688			0.433344	−	0.901229i	$-0.357334\pi$
$89$	8.17632			0.866688			0.433344	+	0.901229i	$0.357334\pi$
$90$		0			0
$91$	−8.21479	+	0.650421i	−0.861144	+	0.0681827i
$92$		0			0
$93$	0.820940	−	14.7200i	0.0851275	−	1.52640i
$94$		0			0
$95$		−	1.04495i		−	0.107210i
$96$		0			0
$97$		−	13.5934i		−	1.38020i	−0.723715	−	0.690099i	$-0.757567\pi$
$97$		−	13.5934i		−	1.38020i	0.723715	−	0.690099i	$-0.242433\pi$
$98$		0			0
$99$	0.571136	−	5.10451i	0.0574013	−	0.513023i
$100$		0			0
$101$	4.28370			0.426245			0.213122	−	0.977026i	$-0.431637\pi$
$101$	4.28370			0.426245			0.213122	+	0.977026i	$0.431637\pi$
$102$		0			0
$103$		−	14.0227i		−	1.38170i	−0.722998	−	0.690850i	$-0.757236\pi$
$103$		−	14.0227i		−	1.38170i	0.722998	−	0.690850i	$-0.242764\pi$
$104$		0			0
$105$	0.106762	+	4.58133i	0.0104189	+	0.447092i
$106$		0			0
$107$			19.4771i			1.88292i	0.337118	+	0.941462i	$0.390548\pi$
$107$			19.4771i			1.88292i	−0.337118	+	0.941462i	$0.609452\pi$
$108$		0			0
$109$	−10.7331			−1.02804			−0.514021	−	0.857778i	$-0.671845\pi$
$109$	−10.7331			−1.02804			−0.514021	+	0.857778i	$0.671845\pi$
$110$		0			0
$111$	−13.8271	−	0.771140i	−1.31241	−	0.0731934i
$112$		0			0
$113$			8.81346i			0.829100i	0.910026	+	0.414550i	$0.136061\pi$
$113$			8.81346i			0.829100i	−0.910026	+	0.414550i	$0.863939\pi$
$114$		0			0
$115$		−	0.587015i		−	0.0547395i
$116$		0			0
$117$	1.03898	−	9.28590i	0.0960542	−	0.858482i
$118$		0			0
$119$	0.750529	+	9.47915i	0.0688009	+	0.868952i
$120$		0			0
$121$	8.06864			0.733513
$122$		0			0
$123$	−13.4013	−	0.747393i	−1.20835	−	0.0673902i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	17.2398			1.52978			0.764890	−	0.644160i	$-0.222793\pi$
$127$	17.2398			1.52978			0.764890	+	0.644160i	$0.222793\pi$
$128$		0			0
$129$	8.73799	+	0.487319i	0.769337	+	0.0429061i
$130$		0			0
$131$	6.92330			0.604891			0.302446	−	0.953167i	$-0.402197\pi$
$131$	6.92330			0.604891			0.302446	+	0.953167i	$0.402197\pi$
$132$		0			0
$133$	2.75606	−	0.218217i	0.238981	−	0.0189218i
$134$		0			0
$135$	−5.12374	−	0.864434i	−0.440982	−	0.0743986i
$136$		0			0
$137$			21.5200i			1.83858i	0.393584	+	0.919289i	$0.371235\pi$
$137$			21.5200i			1.83858i	−0.393584	+	0.919289i	$0.628765\pi$
$138$		0			0
$139$			5.37425i			0.455838i	0.973680	+	0.227919i	$0.0731921\pi$
$139$			5.37425i			0.455838i	−0.973680	+	0.227919i	$0.926808\pi$
$140$		0			0
$141$	17.1347	+	0.955605i	1.44300	+	0.0804764i
$142$		0			0
$143$	−5.33260			−0.445935
$144$		0			0
$145$			4.47468i			0.371602i
$146$		0			0
$147$	−12.0610	+	1.23830i	−0.994771	+	0.102133i
$148$		0			0
$149$		−	1.35482i		−	0.110992i	−0.998459	−	0.0554958i	$-0.982326\pi$
$149$		−	1.35482i		−	0.110992i	0.998459	−	0.0554958i	$-0.0176739\pi$
$150$		0			0
$151$	−14.4778			−1.17819			−0.589093	−	0.808065i	$-0.700515\pi$
$151$	−14.4778			−1.17819			−0.589093	+	0.808065i	$0.700515\pi$
$152$		0			0
$153$	−10.7151	−	1.19890i	−0.866266	−	0.0969251i
$154$		0			0
$155$			8.51183i			0.683687i
$156$		0			0
$157$			17.6973i			1.41239i	0.708015	+	0.706197i	$0.249591\pi$
$157$			17.6973i			1.41239i	−0.708015	+	0.706197i	$0.750409\pi$
$158$		0			0
$159$	−0.447095	+	8.01675i	−0.0354570	+	0.635769i
$160$		0			0
$161$	1.54825	−	0.122586i	0.122019	−	0.00966110i
$162$		0			0
$163$	14.1348			1.10713			0.553563	−	0.832807i	$-0.313268\pi$
$163$	14.1348			1.10713			0.553563	+	0.832807i	$0.313268\pi$
$164$		0			0
$165$	−0.165129	+	2.96088i	−0.0128553	+	0.230504i
$166$		0			0
$167$	−10.5005			−0.812554			−0.406277	−	0.913750i	$-0.633173\pi$
$167$	−10.5005			−0.812554			−0.406277	+	0.913750i	$0.633173\pi$
$168$		0			0
$169$	3.29917			0.253782
$170$		0			0
$171$	−0.348580	+	3.11542i	−0.0266566	+	0.238242i
$172$		0			0
$173$	19.6775			1.49605			0.748025	−	0.663671i	$-0.231002\pi$
$173$	19.6775			1.49605			0.748025	+	0.663671i	$0.231002\pi$
$174$		0			0
$175$	−0.208829	−	2.63750i	−0.0157860	−	0.199376i
$176$		0			0
$177$	−3.66060	−	0.204152i	−0.275148	−	0.0153450i
$178$		0			0
$179$		−	21.2730i		−	1.59002i	−0.606599	−	0.795008i	$-0.707466\pi$
$179$		−	21.2730i		−	1.59002i	0.606599	−	0.795008i	$-0.292534\pi$
$180$		0			0
$181$		−	9.52329i		−	0.707861i	−0.935272	−	0.353930i	$-0.884845\pi$
$181$		−	9.52329i		−	0.707861i	0.935272	−	0.353930i	$-0.115155\pi$
$182$		0			0
$183$	0.782399	−	14.0290i	0.0578366	−	1.03705i
$184$		0			0
$185$	7.99549			0.587840
$186$		0			0
$187$			6.15335i			0.449978i
$188$		0			0
$189$	1.20996	−	13.6944i	0.0880114	−	0.996119i
$190$		0			0
$191$			22.1742i			1.60447i	0.597007	+	0.802236i	$0.296356\pi$
$191$			22.1742i			1.60447i	−0.597007	+	0.802236i	$0.703644\pi$
$192$		0			0
$193$	−13.1540			−0.946846			−0.473423	−	0.880835i	$-0.656982\pi$
$193$	−13.1540			−0.946846			−0.473423	+	0.880835i	$0.656982\pi$
$194$		0			0
$195$	−0.300395	+	5.38630i	−0.0215117	+	0.385721i
$196$		0			0
$197$			13.8493i			0.986721i	0.869825	+	0.493361i	$0.164232\pi$
$197$			13.8493i			0.986721i	−0.869825	+	0.493361i	$0.835768\pi$
$198$		0			0
$199$			1.51305i			0.107257i	0.998561	+	0.0536285i	$0.0170787\pi$
$199$			1.51305i			0.107257i	−0.998561	+	0.0536285i	$0.982921\pi$
$200$		0			0
$201$	15.2292	+	0.849336i	1.07419	+	0.0599076i
$202$		0			0
$203$	−11.8020	+	0.934443i	−0.828336	+	0.0655850i
$204$		0			0
$205$	7.74927			0.541232
$206$		0			0
$207$	−0.195819	+	1.75012i	−0.0136103	+	0.121642i
$208$		0			0
$209$	1.78909			0.123754
$210$		0			0
$211$	−3.10496			−0.213754			−0.106877	−	0.994272i	$-0.534085\pi$
$211$	−3.10496			−0.213754			−0.106877	+	0.994272i	$0.534085\pi$
$212$		0			0
$213$	0.248119	−	4.44895i	0.0170008	−	0.304837i
$214$		0			0
$215$	−5.05272			−0.344593
$216$		0			0
$217$	−22.4499	+	1.77751i	−1.52400	+	0.120666i
$218$		0			0
$219$	0.663879	−	11.9038i	0.0448608	−	0.804387i
$220$		0			0
$221$			11.1939i			0.752984i
$222$		0			0
$223$		−	6.39251i		−	0.428074i	−0.976826	−	0.214037i	$-0.931339\pi$
$223$		−	6.39251i		−	0.428074i	0.976826	−	0.214037i	$-0.0686614\pi$
$224$		0			0
$225$	2.98140	+	0.333584i	0.198760	+	0.0222389i
$226$		0			0
$227$	−13.2462			−0.879181			−0.439591	−	0.898198i	$-0.644876\pi$
$227$	−13.2462			−0.879181			−0.439591	+	0.898198i	$0.644876\pi$
$228$		0			0
$229$			15.4689i			1.02221i	0.859517	+	0.511107i	$0.170764\pi$
$229$			15.4689i			1.02221i	−0.859517	+	0.511107i	$0.829236\pi$
$230$		0			0
$231$	−7.84380	+	0.182790i	−0.516084	+	0.0120267i
$232$		0			0
$233$		−	28.5413i		−	1.86980i	−0.354907	−	0.934901i	$-0.615488\pi$
$233$		−	28.5413i		−	1.86980i	0.354907	−	0.934901i	$-0.384512\pi$
$234$		0			0
$235$	−9.90809			−0.646332
$236$		0			0
$237$	12.1302	+	0.676502i	0.787940	+	0.0439436i
$238$		0			0
$239$			4.61686i			0.298640i	0.988789	+	0.149320i	$0.0477084\pi$
$239$			4.61686i			0.298640i	−0.988789	+	0.149320i	$0.952292\pi$
$240$		0			0
$241$			10.3604i			0.667375i	0.942684	+	0.333687i	$0.108293\pi$
$241$			10.3604i			0.667375i	−0.942684	+	0.333687i	$0.891707\pi$
$242$		0			0
$243$	14.9875	+	4.28642i	0.961452	+	0.274974i
$244$		0			0
$245$	6.91278	−	1.10157i	0.441641	−	0.0703767i
$246$		0			0
$247$	3.25463			0.207087
$248$		0			0
$249$	−9.02447	−	0.503297i	−0.571903	−	0.0318951i
$250$		0			0
$251$	0.0748113			0.00472205			0.00236102	−	0.999997i	$-0.499248\pi$
$251$	0.0748113			0.00472205			0.00236102	+	0.999997i	$0.499248\pi$
$252$		0			0
$253$	1.00504			0.0631864
$254$		0			0
$255$	6.21532	+	0.346630i	0.389218	+	0.0217068i
$256$		0			0
$257$	7.49720			0.467663			0.233831	−	0.972277i	$-0.424874\pi$
$257$	7.49720			0.467663			0.233831	+	0.972277i	$0.424874\pi$
$258$		0			0
$259$	1.66969	+	21.0881i	0.103749	+	1.31035i
$260$		0			0
$261$	1.49268	−	13.3408i	0.0923947	−	0.825775i
$262$		0			0
$263$		−	20.0579i		−	1.23682i	−0.785855	−	0.618410i	$-0.787777\pi$
$263$		−	20.0579i		−	1.23682i	0.785855	−	0.618410i	$-0.212223\pi$
$264$		0			0
$265$		−	4.63566i		−	0.284766i
$266$		0			0
$267$	14.1398	+	0.788581i	0.865343	+	0.0482603i
$268$		0			0
$269$	−25.2069			−1.53689			−0.768447	−	0.639914i	$-0.778970\pi$
$269$	−25.2069			−1.53689			−0.768447	+	0.639914i	$0.778970\pi$
$270$		0			0
$271$		−	18.0716i		−	1.09777i	−0.835896	−	0.548887i	$-0.815052\pi$
$271$		−	18.0716i		−	1.09777i	0.835896	−	0.548887i	$-0.184948\pi$
$272$		0			0
$273$	−14.2691	+	0.332524i	−0.863605	+	0.0201252i
$274$		0			0
$275$		−	1.71212i		−	0.103245i
$276$		0			0
$277$	−13.7938			−0.828786			−0.414393	−	0.910098i	$-0.636006\pi$
$277$	−13.7938			−0.828786			−0.414393	+	0.910098i	$0.636006\pi$
$278$		0			0
$279$	2.83941	−	25.3771i	0.169991	−	1.51929i
$280$		0			0
$281$		−	0.315357i		−	0.0188126i	−0.999956	−	0.00940632i	$-0.997006\pi$
$281$		−	0.315357i		−	0.0188126i	0.999956	−	0.00940632i	$-0.00299417\pi$
$282$		0			0
$283$			20.6408i			1.22697i	0.789707	+	0.613484i	$0.210233\pi$
$283$			20.6408i			1.22697i	−0.789707	+	0.613484i	$0.789767\pi$
$284$		0			0
$285$	0.100783	−	1.80711i	0.00596985	−	0.107044i
$286$		0			0
$287$	1.61827	+	20.4387i	0.0955234	+	1.20646i
$288$		0			0
$289$	−4.08321			−0.240189
$290$		0			0
$291$	1.31104	−	23.5079i	0.0768544	−	1.37806i
$292$		0			0
$293$	3.75188			0.219187			0.109594	−	0.993976i	$-0.465045\pi$
$293$	3.75188			0.219187			0.109594	+	0.993976i	$0.465045\pi$
$294$		0			0
$295$	2.11673			0.123241
$296$		0			0
$297$	1.48002	−	8.77247i	0.0858792	−	0.509031i
$298$		0			0
$299$	1.82833			0.105735
$300$		0			0
$301$	−1.05515	−	13.3265i	−0.0608180	−	0.768129i
$302$		0			0
$303$	7.40808	+	0.413150i	0.425583	+	0.0237349i
$304$		0			0
$305$			8.11222i			0.464504i
$306$		0			0
$307$			29.9301i			1.70820i	0.520108	+	0.854101i	$0.325892\pi$
$307$			29.9301i			1.70820i	−0.520108	+	0.854101i	$0.674108\pi$
$308$		0			0
$309$	1.35245	−	24.2504i	0.0769381	−	1.37956i
$310$		0			0
$311$	21.0310			1.19256			0.596280	−	0.802777i	$-0.296645\pi$
$311$	21.0310			1.19256			0.596280	+	0.802777i	$0.296645\pi$
$312$		0			0
$313$			9.74984i			0.551094i	0.961288	+	0.275547i	$0.0888589\pi$
$313$			9.74984i			0.551094i	−0.961288	+	0.275547i	$0.911141\pi$
$314$		0			0
$315$	−0.257225	+	7.93308i	−0.0144930	+	0.446979i
$316$		0			0
$317$			16.2388i			0.912064i	0.889963	+	0.456032i	$0.150730\pi$
$317$			16.2388i			0.912064i	−0.889963	+	0.456032i	$0.849270\pi$
$318$		0			0
$319$	−7.66120			−0.428945
$320$		0			0
$321$	−1.87851	+	33.6830i	−0.104848	+	1.88000i
$322$		0			0
$323$		−	3.75556i		−	0.208965i
$324$		0			0
$325$		−	3.11462i		−	0.172768i
$326$		0			0
$327$	−18.5614	−	1.03517i	−1.02645	−	0.0572451i
$328$		0			0
$329$	−2.06909	−	26.1326i	−0.114073	−	1.44073i
$330$		0			0
$331$	−10.3877			−0.570957			−0.285479	−	0.958385i	$-0.592153\pi$
$331$	−10.3877			−0.570957			−0.285479	+	0.958385i	$0.592153\pi$
$332$		0			0
$333$	−23.8377	−	2.66716i	−1.30630	−	0.146160i
$334$		0			0
$335$	−8.80626			−0.481137
$336$		0			0
$337$	14.3020			0.779080			0.389540	−	0.921010i	$-0.372634\pi$
$337$	14.3020			0.779080			0.389540	+	0.921010i	$0.372634\pi$
$338$		0			0
$339$	−0.850031	+	15.2417i	−0.0461673	+	0.827814i
$340$		0			0
$341$	−14.5733			−0.789188
$342$		0			0
$343$	4.34898	+	18.0024i	0.234823	+	0.972038i
$344$		0			0
$345$	0.0566158	−	1.01516i	0.00304809	−	0.0546545i
$346$		0			0
$347$			3.55313i			0.190742i	0.995442	+	0.0953711i	$0.0304038\pi$
$347$			3.55313i			0.190742i	−0.995442	+	0.0953711i	$0.969596\pi$
$348$		0			0
$349$			33.8742i			1.81324i	0.421943	+	0.906622i	$0.361348\pi$
$349$			33.8742i			1.81324i	−0.421943	+	0.906622i	$0.638652\pi$
$350$		0			0
$351$	2.69238	−	15.9585i	0.143709	−	0.851802i
$352$		0			0
$353$	0.702991			0.0374165			0.0187082	−	0.999825i	$-0.494045\pi$
$353$	0.702991			0.0374165			0.0187082	+	0.999825i	$0.494045\pi$
$354$		0			0
$355$			2.57259i			0.136539i
$356$		0			0
$357$	0.383703	+	16.4653i	0.0203077	+	0.871435i
$358$		0			0
$359$		−	33.0033i		−	1.74185i	−0.491420	−	0.870923i	$-0.663522\pi$
$359$		−	33.0033i		−	1.74185i	0.491420	−	0.870923i	$-0.336478\pi$
$360$		0			0
$361$	17.9081			0.942530
$362$		0			0
$363$	13.9536	+	0.778195i	0.732375	+	0.0408447i
$364$		0			0
$365$			6.88336i			0.360292i
$366$		0			0
$367$		−	6.88379i		−	0.359331i	−0.983728	−	0.179666i	$-0.942498\pi$
$367$		−	6.88379i		−	0.359331i	0.983728	−	0.179666i	$-0.0575015\pi$
$368$		0			0
$369$	−23.1036	−	2.58503i	−1.20273	−	0.134571i
$370$		0			0
$371$	12.2265	−	0.968060i	0.634771	−	0.0502591i
$372$		0			0
$373$	27.1278			1.40462			0.702311	−	0.711870i	$-0.252152\pi$
$373$	27.1278			1.40462			0.702311	+	0.711870i	$0.252152\pi$
$374$		0			0
$375$	−1.72936	−	0.0964469i	−0.0893039	−	0.00498050i
$376$		0			0
$377$	−13.9369			−0.717788
$378$		0			0
$379$	25.2240			1.29567			0.647836	−	0.761780i	$-0.275674\pi$
$379$	25.2240			1.29567			0.647836	+	0.761780i	$0.275674\pi$
$380$		0			0
$381$	29.8138	+	1.66272i	1.52741	+	0.0851838i
$382$		0			0
$383$	10.8647			0.555163			0.277581	−	0.960702i	$-0.410467\pi$
$383$	10.8647			0.555163			0.277581	+	0.960702i	$0.410467\pi$
$384$		0			0
$385$	4.51572	−	0.357540i	0.230142	−	0.0182219i
$386$		0			0
$387$	15.0642	+	1.68550i	0.765754	+	0.0856790i
$388$		0			0
$389$			24.7623i			1.25550i	0.778415	+	0.627750i	$0.216024\pi$
$389$			24.7623i			1.25550i	−0.778415	+	0.627750i	$0.783976\pi$
$390$		0			0
$391$		−	2.10973i		−	0.106694i
$392$		0			0
$393$	11.9729	+	0.667731i	0.603953	+	0.0336826i
$394$		0			0
$395$	−7.01425			−0.352925
$396$		0			0
$397$			23.9258i			1.20080i	0.799699	+	0.600401i	$0.204992\pi$
$397$			23.9258i			1.20080i	−0.799699	+	0.600401i	$0.795008\pi$
$398$		0			0
$399$	4.78728	−	0.111562i	0.239664	−	0.00558507i
$400$		0			0
$401$		−	13.5963i		−	0.678966i	−0.940612	−	0.339483i	$-0.889748\pi$
$401$		−	13.5963i		−	0.678966i	0.940612	−	0.339483i	$-0.110252\pi$
$402$		0			0
$403$	−26.5111			−1.32061
$404$		0			0
$405$	−8.77744	−	1.98909i	−0.436155	−	0.0988386i
$406$		0			0
$407$			13.6892i			0.678551i
$408$		0			0
$409$		−	27.6024i		−	1.36485i	−0.730954	−	0.682426i	$-0.760925\pi$
$409$		−	27.6024i		−	1.36485i	0.730954	−	0.682426i	$-0.239075\pi$
$410$		0			0
$411$	−2.07554	+	37.2159i	−0.102379	+	1.83573i
$412$		0			0
$413$	0.442035	+	5.58288i	0.0217511	+	0.274715i
$414$		0			0
$415$	5.21838			0.256160
$416$		0			0
$417$	−0.518330	+	9.29403i	−0.0253827	+	0.455130i
$418$		0			0
$419$	29.2886			1.43084			0.715421	−	0.698694i	$-0.246235\pi$
$419$	29.2886			1.43084			0.715421	+	0.698694i	$0.246235\pi$
$420$		0			0
$421$	22.8900			1.11559			0.557794	−	0.829979i	$-0.311648\pi$
$421$	22.8900			1.11559			0.557794	+	0.829979i	$0.311648\pi$
$422$		0			0
$423$	29.5399	+	3.30518i	1.43628	+	0.160703i
$424$		0			0
$425$	−3.59399			−0.174334
$426$		0			0
$427$	−21.3960	+	1.69407i	−1.03542	+	0.0819816i
$428$		0			0
$429$	−9.22201	−	0.514313i	−0.445243	−	0.0248313i
$430$		0			0
$431$			14.1215i			0.680208i	0.940388	+	0.340104i	$0.110462\pi$
$431$			14.1215i			0.680208i	−0.940388	+	0.340104i	$0.889538\pi$
$432$		0			0
$433$			25.5976i			1.23014i	0.788471	+	0.615072i	$0.210873\pi$
$433$			25.5976i			1.23014i	−0.788471	+	0.615072i	$0.789127\pi$
$434$		0			0
$435$	−0.431570	+	7.73836i	−0.0206922	+	0.371026i
$436$		0			0
$437$	−0.613404			−0.0293431
$438$		0			0
$439$		−	19.5553i		−	0.933322i	−0.884436	−	0.466661i	$-0.845457\pi$
$439$		−	19.5553i		−	0.933322i	0.884436	−	0.466661i	$-0.154543\pi$
$440$		0			0
$441$	−20.9772	+	0.978227i	−0.998914	+	0.0465822i
$442$		0			0
$443$			35.7251i			1.69735i	0.528916	+	0.848674i	$0.322599\pi$
$443$			35.7251i			1.69735i	−0.528916	+	0.848674i	$0.677401\pi$
$444$		0			0
$445$	−8.17632			−0.387595
$446$		0			0
$447$	0.130669	−	2.34298i	0.00618042	−	0.110819i
$448$		0			0
$449$		−	20.1071i		−	0.948912i	−0.880279	−	0.474456i	$-0.842645\pi$
$449$		−	20.1071i		−	0.948912i	0.880279	−	0.474456i	$-0.157355\pi$
$450$		0			0
$451$			13.2677i			0.624751i
$452$		0			0
$453$	−25.0374	−	1.39634i	−1.17636	−	0.0656057i
$454$		0			0
$455$	8.21479	−	0.650421i	0.385115	−	0.0304922i
$456$		0			0
$457$	6.65005			0.311076			0.155538	−	0.987830i	$-0.450289\pi$
$457$	6.65005			0.311076			0.155538	+	0.987830i	$0.450289\pi$
$458$		0			0
$459$	−18.4147	−	3.10677i	−0.859525	−	0.145012i
$460$		0			0
$461$	−23.7531			−1.10629			−0.553146	−	0.833084i	$-0.686573\pi$
$461$	−23.7531			−1.10629			−0.553146	+	0.833084i	$0.686573\pi$
$462$		0			0
$463$	−9.26150			−0.430418			−0.215209	−	0.976568i	$-0.569043\pi$
$463$	−9.26150			−0.430418			−0.215209	+	0.976568i	$0.569043\pi$
$464$		0			0
$465$	−0.820940	+	14.7200i	−0.0380702	+	0.682626i
$466$		0			0
$467$	18.2641			0.845161			0.422580	−	0.906325i	$-0.361124\pi$
$467$	18.2641			0.845161			0.422580	+	0.906325i	$0.361124\pi$
$468$		0			0
$469$	−1.83900	−	23.2265i	−0.0849171	−	1.07250i
$470$		0			0
$471$	−1.70685	+	30.6050i	−0.0786473	+	1.41020i
$472$		0			0
$473$		−	8.65087i		−	0.397767i
$474$		0			0
$475$			1.04495i			0.0479458i
$476$		0			0
$477$	−1.54638	+	13.8207i	−0.0708039	+	0.632808i
$478$		0			0
$479$	0.944391			0.0431503			0.0215752	−	0.999767i	$-0.493132\pi$
$479$	0.944391			0.0431503			0.0215752	+	0.999767i	$0.493132\pi$
$480$		0			0
$481$			24.9029i			1.13547i
$482$		0			0
$483$	2.68931	−	0.0626711i	0.122368	−	0.00285163i
$484$		0			0
$485$			13.5934i			0.617243i
$486$		0			0
$487$	−8.11446			−0.367701			−0.183851	−	0.982954i	$-0.558856\pi$
$487$	−8.11446			−0.367701			−0.183851	+	0.982954i	$0.558856\pi$
$488$		0			0
$489$	24.4443	+	1.36326i	1.10541	+	0.0616488i
$490$		0			0
$491$		−	18.9773i		−	0.856432i	−0.903676	−	0.428216i	$-0.859142\pi$
$491$		−	18.9773i		−	0.856432i	0.903676	−	0.428216i	$-0.140858\pi$
$492$		0			0
$493$			16.0820i			0.724296i
$494$		0			0
$495$	−0.571136	+	5.10451i	−0.0256706	+	0.229431i
$496$		0			0
$497$	−6.78521	+	0.537232i	−0.304358	+	0.0240981i
$498$		0			0
$499$	−20.1764			−0.903220			−0.451610	−	0.892215i	$-0.649150\pi$
$499$	−20.1764			−0.903220			−0.451610	+	0.892215i	$0.649150\pi$
$500$		0			0
$501$	−18.1592	−	1.01274i	−0.811293	−	0.0452460i
$502$		0			0
$503$	−33.6527			−1.50050			−0.750249	−	0.661155i	$-0.770066\pi$
$503$	−33.6527			−1.50050			−0.750249	+	0.661155i	$0.770066\pi$
$504$		0			0
$505$	−4.28370			−0.190622
$506$		0			0
$507$	5.70546	+	0.318194i	0.253388	+	0.0141315i
$508$		0			0
$509$	−14.4818			−0.641896			−0.320948	−	0.947097i	$-0.604001\pi$
$509$	−14.4818			−0.641896			−0.320948	+	0.947097i	$0.604001\pi$
$510$		0			0
$511$	−18.1548	+	1.43744i	−0.803123	+	0.0635888i
$512$		0			0
$513$	−0.903294	+	5.35408i	−0.0398814	+	0.236388i
$514$		0			0
$515$			14.0227i			0.617915i
$516$		0			0
$517$		−	16.9639i		−	0.746069i
$518$		0			0
$519$	34.0295	+	1.89783i	1.49373	+	0.0833055i
$520$		0			0
$521$	−31.7476			−1.39089			−0.695445	−	0.718580i	$-0.744793\pi$
$521$	−31.7476			−1.39089			−0.695445	+	0.718580i	$0.744793\pi$
$522$		0			0
$523$			3.24913i			0.142074i	0.997474	+	0.0710372i	$0.0226309\pi$
$523$			3.24913i			0.142074i	−0.997474	+	0.0710372i	$0.977369\pi$
$524$		0			0
$525$	−0.106762	−	4.58133i	−0.00465949	−	0.199946i
$526$		0			0
$527$			30.5915i			1.33259i
$528$		0			0
$529$	22.6554			0.985018
$530$		0			0
$531$	−6.31082	−	0.706107i	−0.273866	−	0.0306424i
$532$		0			0
$533$			24.1360i			1.04545i
$534$		0			0
$535$		−	19.4771i		−	0.842070i
$536$		0			0
$537$	2.05171	−	36.7887i	0.0885379	−	1.58755i
$538$		0			0
$539$	1.88602	+	11.8355i	0.0812367	+	0.509792i
$540$		0			0
$541$	−17.9697			−0.772578			−0.386289	−	0.922378i	$-0.626243\pi$
$541$	−17.9697			−0.772578			−0.386289	+	0.922378i	$0.626243\pi$
$542$		0			0
$543$	0.918492	−	16.4692i	0.0394163	−	0.706763i
$544$		0			0
$545$	10.7331			0.459754
$546$		0			0
$547$	−18.3387			−0.784107			−0.392054	−	0.919942i	$-0.628235\pi$
$547$	−18.3387			−0.784107			−0.392054	+	0.919942i	$0.628235\pi$
$548$		0			0
$549$	2.70610	−	24.1857i	0.115494	−	1.03222i
$550$		0			0
$551$	4.67584			0.199198
$552$		0			0
$553$	−1.46478	−	18.5001i	−0.0622886	−	0.786702i
$554$		0			0
$555$	13.8271	+	0.771140i	0.586928	+	0.0327331i
$556$		0			0
$557$			28.3017i			1.19918i	0.800306	+	0.599591i	$0.204670\pi$
$557$			28.3017i			1.19918i	−0.800306	+	0.599591i	$0.795330\pi$
$558$		0			0
$559$		−	15.7373i		−	0.665616i
$560$		0			0
$561$	−0.593472	+	10.6414i	−0.0250564	+	0.449280i
$562$		0			0
$563$	−17.8742			−0.753308			−0.376654	−	0.926354i	$-0.622925\pi$
$563$	−17.8742			−0.753308			−0.376654	+	0.926354i	$0.622925\pi$
$564$		0			0
$565$		−	8.81346i		−	0.370785i
$566$		0			0
$567$	3.41323	−	23.5659i	0.143342	−	0.989673i
$568$		0			0
$569$			2.42862i			0.101813i	0.998703	+	0.0509066i	$0.0162111\pi$
$569$			2.42862i			0.101813i	−0.998703	+	0.0509066i	$0.983789\pi$
$570$		0			0
$571$	23.8480			0.998008			0.499004	−	0.866600i	$-0.333699\pi$
$571$	23.8480			0.998008			0.499004	+	0.866600i	$0.333699\pi$
$572$		0			0
$573$	−2.13864	+	38.3473i	−0.0893429	+	1.60198i
$574$		0			0
$575$			0.587015i			0.0244802i
$576$		0			0
$577$			27.1298i			1.12943i	0.825287	+	0.564714i	$0.191013\pi$
$577$			27.1298i			1.12943i	−0.825287	+	0.564714i	$0.808987\pi$
$578$		0			0
$579$	−22.7481	−	1.26866i	−0.945377	−	0.0527239i
$580$		0			0
$581$	1.08975	+	13.7635i	0.0452103	+	0.571004i
$582$		0			0
$583$	7.93682			0.328709
$584$		0			0
$585$	−1.03898	+	9.28590i	−0.0429567	+	0.383925i
$586$		0			0
$587$	38.5360			1.59055			0.795275	−	0.606249i	$-0.207327\pi$
$587$	38.5360			1.59055			0.795275	+	0.606249i	$0.207327\pi$
$588$		0			0
$589$	8.89448			0.366490
$590$		0			0
$591$	−1.33572	+	23.9505i	−0.0549442	+	0.985190i
$592$		0			0
$593$	36.2739			1.48959			0.744796	−	0.667293i	$-0.232547\pi$
$593$	36.2739			1.48959			0.744796	+	0.667293i	$0.232547\pi$
$594$		0			0
$595$	−0.750529	−	9.47915i	−0.0307687	−	0.388607i
$596$		0			0
$597$	−0.145929	+	2.61661i	−0.00597246	+	0.107091i
$598$		0			0
$599$		−	13.4627i		−	0.550072i	−0.961434	−	0.275036i	$-0.911310\pi$
$599$		−	13.4627i		−	0.550072i	0.961434	−	0.275036i	$-0.0886898\pi$
$600$		0			0
$601$		−	15.0055i		−	0.612088i	−0.952017	−	0.306044i	$-0.900995\pi$
$601$		−	15.0055i		−	0.612088i	0.952017	−	0.306044i	$-0.0990054\pi$
$602$		0			0
$603$	26.2549	+	2.93762i	1.06918	+	0.119629i
$604$		0			0
$605$	−8.06864			−0.328037
$606$		0			0
$607$			9.84471i			0.399585i	0.979838	+	0.199792i	$0.0640267\pi$
$607$			9.84471i			0.399585i	−0.979838	+	0.199792i	$0.935973\pi$
$608$		0			0
$609$	−20.5000	+	0.477728i	−0.830703	+	0.0193585i
$610$		0			0
$611$		−	30.8599i		−	1.24846i
$612$		0			0
$613$	−35.8700			−1.44878			−0.724388	−	0.689392i	$-0.757878\pi$
$613$	−35.8700			−1.44878			−0.724388	+	0.689392i	$0.757878\pi$
$614$		0			0
$615$	13.4013	+	0.747393i	0.540393	+	0.0301378i
$616$		0			0
$617$		−	4.01170i		−	0.161505i	−0.996734	−	0.0807524i	$-0.974268\pi$
$617$		−	4.01170i		−	0.161505i	0.996734	−	0.0807524i	$-0.0257323\pi$
$618$		0			0
$619$			5.91495i			0.237742i	0.992910	+	0.118871i	$0.0379275\pi$
$619$			5.91495i			0.237742i	−0.992910	+	0.118871i	$0.962073\pi$
$620$		0			0
$621$	−0.507436	+	3.00772i	−0.0203627	+	0.120695i
$622$		0			0
$623$	−1.70745	−	21.5650i	−0.0684075	−	0.863984i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	3.09399	+	0.172552i	0.123562	+	0.00689107i
$628$		0			0
$629$	28.7357			1.14577
$630$		0			0
$631$	44.3710			1.76638			0.883191	−	0.469014i	$-0.155391\pi$
$631$	44.3710			1.76638			0.883191	+	0.469014i	$0.155391\pi$
$632$		0			0
$633$	−5.36960	−	0.299464i	−0.213423	−	0.0119026i
$634$		0			0
$635$	−17.2398			−0.684139
$636$		0			0
$637$	3.43097	+	21.5307i	0.135940	+	0.853076i
$638$		0			0
$639$	0.858175	−	7.66992i	0.0339489	−	0.303417i
$640$		0			0
$641$		−	32.2004i		−	1.27184i	−0.771756	−	0.635919i	$-0.780621\pi$
$641$		−	32.2004i		−	1.27184i	0.771756	−	0.635919i	$-0.219379\pi$
$642$		0			0
$643$		−	10.9089i		−	0.430204i	−0.976592	−	0.215102i	$-0.930992\pi$
$643$		−	10.9089i		−	0.430204i	0.976592	−	0.215102i	$-0.0690084\pi$
$644$		0			0
$645$	−8.73799	−	0.487319i	−0.344058	−	0.0191882i
$646$		0			0
$647$	5.60683			0.220427			0.110214	−	0.993908i	$-0.464847\pi$
$647$	5.60683			0.220427			0.110214	+	0.993908i	$0.464847\pi$
$648$		0			0
$649$			3.62410i			0.142259i
$650$		0			0
$651$	−38.9955	+	0.908743i	−1.52835	+	0.0356164i
$652$		0			0
$653$		−	21.1436i		−	0.827414i	−0.910410	−	0.413707i	$-0.864234\pi$
$653$		−	21.1436i		−	0.827414i	0.910410	−	0.413707i	$-0.135766\pi$
$654$		0			0
$655$	−6.92330			−0.270516
$656$		0			0
$657$	2.29618	−	20.5220i	0.0895824	−	0.800641i
$658$		0			0
$659$		−	5.88542i		−	0.229264i	−0.993408	−	0.114632i	$-0.963431\pi$
$659$		−	5.88542i		−	0.229264i	0.993408	−	0.114632i	$-0.0365688\pi$
$660$		0			0
$661$		−	49.9175i		−	1.94157i	−0.239956	−	0.970784i	$-0.577133\pi$
$661$		−	49.9175i		−	1.94157i	0.239956	−	0.970784i	$-0.422867\pi$
$662$		0			0
$663$	−1.07962	+	19.3583i	−0.0419289	+	0.751816i
$664$		0			0
$665$	−2.75606	+	0.218217i	−0.106876	+	0.00846207i
$666$		0			0
$667$	2.62671			0.101707
$668$		0			0
$669$	0.616538	−	11.0550i	0.0238367	−	0.427410i
$670$		0			0
$671$	−13.8891			−0.536183
$672$		0			0
$673$	33.1364			1.27732			0.638658	−	0.769491i	$-0.279490\pi$
$673$	33.1364			1.27732			0.638658	+	0.769491i	$0.279490\pi$
$674$		0			0
$675$	5.12374	+	0.864434i	0.197213	+	0.0332721i
$676$		0			0
$677$	−6.16011			−0.236752			−0.118376	−	0.992969i	$-0.537769\pi$
$677$	−6.16011			−0.236752			−0.118376	+	0.992969i	$0.537769\pi$
$678$		0			0
$679$	−35.8525	+	2.83869i	−1.37589	+	0.108939i
$680$		0			0
$681$	−22.9075	−	1.27756i	−0.877817	−	0.0489560i
$682$		0			0
$683$			28.6145i			1.09490i	0.836837	+	0.547451i	$0.184402\pi$
$683$			28.6145i			1.09490i	−0.836837	+	0.547451i	$0.815598\pi$
$684$		0			0
$685$		−	21.5200i		−	0.822237i
$686$		0			0
$687$	−1.49193	+	26.7513i	−0.0569206	+	1.02063i
$688$		0			0
$689$	14.4383			0.550056
$690$		0			0
$691$		−	32.4683i		−	1.23515i	−0.786511	−	0.617576i	$-0.788115\pi$
$691$		−	32.4683i		−	1.23515i	0.786511	−	0.617576i	$-0.211885\pi$
$692$		0			0
$693$	−13.5824	−	0.440400i	−0.515953	−	0.0167294i
$694$		0			0
$695$		−	5.37425i		−	0.203857i
$696$		0			0
$697$	27.8508			1.05492
$698$		0			0
$699$	2.75272	−	49.3583i	0.104117	−	1.86690i
$700$		0			0
$701$		−	2.46493i		−	0.0930990i	−0.998916	−	0.0465495i	$-0.985177\pi$
$701$		−	2.46493i		−	0.0930990i	0.998916	−	0.0465495i	$-0.0148225\pi$
$702$		0			0
$703$		−	8.35492i		−	0.315112i
$704$		0			0
$705$	−17.1347	−	0.955605i	−0.645330	−	0.0359902i
$706$		0			0
$707$	−0.894561	−	11.2983i	−0.0336434	−	0.424915i
$708$		0			0
$709$	26.7646			1.00517			0.502584	−	0.864529i	$-0.332383\pi$
$709$	26.7646			1.00517			0.502584	+	0.864529i	$0.332383\pi$
$710$		0			0
$711$	20.9122	+	2.33984i	0.784270	+	0.0877507i
$712$		0			0
$713$	4.99657			0.187123
$714$		0			0
$715$	5.33260			0.199428
$716$		0			0
$717$	−0.445281	+	7.98422i	−0.0166293	+	0.298176i
$718$		0			0
$719$	−29.2186			−1.08967			−0.544835	−	0.838543i	$-0.683408\pi$
$719$	−29.2186			−1.08967			−0.544835	+	0.838543i	$0.683408\pi$
$720$		0			0
$721$	−36.9849	+	2.92835i	−1.37739	+	0.109057i
$722$		0			0
$723$	−0.999233	+	17.9170i	−0.0371619	+	0.666339i
$724$		0			0
$725$		−	4.47468i		−	0.166186i
$726$		0			0
$727$			49.9735i			1.85341i	0.375784	+	0.926707i	$0.377373\pi$
$727$			49.9735i			1.85341i	−0.375784	+	0.926707i	$0.622627\pi$
$728$		0			0
$729$	25.5055	+	8.85827i	0.944648	+	0.328084i
$730$		0			0
$731$	−18.1594			−0.671651
$732$		0			0
$733$			8.25200i			0.304795i	0.988319	+	0.152397i	$0.0486993\pi$
$733$			8.25200i			0.304795i	−0.988319	+	0.152397i	$0.951301\pi$
$734$		0			0
$735$	12.0610	−	1.23830i	0.444875	−	0.0456753i
$736$		0			0
$737$		−	15.0774i		−	0.555382i
$738$		0			0
$739$	9.17080			0.337353			0.168677	−	0.985671i	$-0.446051\pi$
$739$	9.17080			0.337353			0.168677	+	0.985671i	$0.446051\pi$
$740$		0			0
$741$	5.62844	+	0.313899i	0.206766	+	0.0115314i
$742$		0			0
$743$		−	45.3646i		−	1.66427i	−0.554575	−	0.832133i	$-0.687119\pi$
$743$		−	45.3646i		−	1.66427i	0.554575	−	0.832133i	$-0.312881\pi$
$744$		0			0
$745$			1.35482i			0.0496369i
$746$		0			0
$747$	−15.5581	−	1.74077i	−0.569239	−	0.0636913i
$748$		0			0
$749$	51.3709	−	4.06738i	1.87705	−	0.148619i
$750$		0			0
$751$	6.19247			0.225966			0.112983	−	0.993597i	$-0.463959\pi$
$751$	6.19247			0.225966			0.112983	+	0.993597i	$0.463959\pi$
$752$		0			0
$753$	0.129376	+	0.00721532i	0.00471472	+	0.000262941i
$754$		0			0
$755$	14.4778			0.526901
$756$		0			0
$757$	37.0168			1.34540			0.672700	−	0.739916i	$-0.265135\pi$
$757$	37.0168			1.34540			0.672700	+	0.739916i	$0.265135\pi$
$758$		0			0
$759$	1.73808	+	0.0969332i	0.0630884	+	0.00351845i
$760$		0			0
$761$	12.5683			0.455600			0.227800	−	0.973708i	$-0.426847\pi$
$761$	12.5683			0.455600			0.227800	+	0.973708i	$0.426847\pi$
$762$		0			0
$763$	2.24137	+	28.3085i	0.0811432	+	1.02483i
$764$		0			0
$765$	10.7151	+	1.19890i	0.387406	+	0.0433462i
$766$		0			0
$767$			6.59281i			0.238053i
$768$		0			0
$769$			3.34523i			0.120632i	0.998179	+	0.0603161i	$0.0192109\pi$
$769$			3.34523i			0.120632i	−0.998179	+	0.0603161i	$0.980789\pi$
$770$		0			0
$771$	12.9654	+	0.723082i	0.466937	+	0.0260412i
$772$		0			0
$773$	32.9333			1.18453			0.592265	−	0.805743i	$-0.298234\pi$
$773$	32.9333			1.18453			0.592265	+	0.805743i	$0.298234\pi$
$774$		0			0
$775$		−	8.51183i		−	0.305754i
$776$		0			0
$777$	0.853617	+	36.6300i	0.0306233	+	1.31409i
$778$		0			0
$779$		−	8.09763i		−	0.290128i
$780$		0			0
$781$	−4.40459			−0.157609
$782$		0			0
$783$	3.86807	−	22.9271i	0.138233	−	0.819349i
$784$		0			0
$785$		−	17.6973i		−	0.631642i
$786$		0			0
$787$		−	28.4703i		−	1.01486i	−0.861694	−	0.507429i	$-0.830596\pi$
$787$		−	28.4703i		−	1.01486i	0.861694	−	0.507429i	$-0.169404\pi$
$788$		0			0
$789$	1.93452	−	34.6873i	0.0688707	−	1.23490i
$790$		0			0
$791$	23.2455	−	1.84050i	0.826514	−	0.0654408i
$792$		0			0
$793$	−25.2665			−0.897238
$794$		0			0
$795$	0.447095	−	8.01675i	0.0158568	−	0.284325i
$796$		0			0
$797$	3.80494			0.134778			0.0673890	−	0.997727i	$-0.478533\pi$
$797$	3.80494			0.134778			0.0673890	+	0.997727i	$0.478533\pi$
$798$		0			0
$799$	−35.6096			−1.25978
$800$		0			0
$801$	24.3768	+	2.72748i	0.861313	+	0.0963709i
$802$		0			0
$803$	−11.7852			−0.415889
$804$		0			0
$805$	−1.54825	+	0.122586i	−0.0545687	+	0.00432058i
$806$		0			0
$807$	−43.5919	−	2.43113i	−1.53451	−	0.0855799i
$808$		0			0
$809$		−	41.4444i		−	1.45711i	−0.684989	−	0.728553i	$-0.740193\pi$
$809$		−	41.4444i		−	1.45711i	0.684989	−	0.728553i	$-0.259807\pi$
$810$		0			0
$811$		−	14.7455i		−	0.517784i	−0.965906	−	0.258892i	$-0.916643\pi$
$811$		−	14.7455i		−	0.517784i	0.965906	−	0.258892i	$-0.0833574\pi$
$812$		0			0
$813$	1.74295	−	31.2524i	0.0611281	−	1.09607i
$814$		0			0
$815$	−14.1348			−0.495122
$816$		0			0
$817$			5.27986i			0.184719i
$818$		0			0
$819$	−24.7085	−	0.801156i	−0.863385	−	0.0279946i
$820$		0			0
$821$			16.8830i			0.589222i	0.955617	+	0.294611i	$0.0951901\pi$
$821$			16.8830i			0.589222i	−0.955617	+	0.294611i	$0.904810\pi$
$822$		0			0
$823$	−51.4749			−1.79430			−0.897151	−	0.441725i	$-0.854367\pi$
$823$	−51.4749			−1.79430			−0.897151	+	0.441725i	$0.854367\pi$
$824$		0			0
$825$	0.165129	−	2.96088i	0.00574905	−	0.103085i
$826$		0			0
$827$		−	19.1522i		−	0.665988i	−0.942929	−	0.332994i	$-0.891941\pi$
$827$		−	19.1522i		−	0.665988i	0.942929	−	0.332994i	$-0.108059\pi$
$828$		0			0
$829$			1.62424i			0.0564121i	0.999602	+	0.0282060i	$0.00897946\pi$
$829$			1.62424i			0.0564121i	−0.999602	+	0.0282060i	$0.991021\pi$
$830$		0			0
$831$	−23.8544	−	1.33036i	−0.827500	−	0.0461499i
$832$		0			0
$833$	24.8445	−	3.95904i	0.860811	−	0.137172i
$834$		0			0
$835$	10.5005			0.363385
$836$		0			0
$837$	7.35791	−	43.6124i	0.254327	−	1.50747i
$838$		0			0
$839$	−31.8128			−1.09830			−0.549150	−	0.835724i	$-0.685048\pi$
$839$	−31.8128			−1.09830			−0.549150	+	0.835724i	$0.685048\pi$
$840$		0			0
$841$	8.97719			0.309558
$842$		0			0
$843$	0.0304152	−	0.545367i	0.00104756	−	0.0187835i
$844$		0			0
$845$	−3.29917			−0.113495
$846$		0			0
$847$	−1.68496	−	21.2810i	−0.0578960	−	0.731224i
$848$		0			0
$849$	−1.99074	+	35.6954i	−0.0683221	+	1.22506i
$850$		0			0
$851$		−	4.69347i		−	0.160890i
$852$		0			0
$853$		−	43.0272i		−	1.47322i	−0.676316	−	0.736612i	$-0.736425\pi$
$853$		−	43.0272i		−	1.47322i	0.676316	−	0.736612i	$-0.263575\pi$
$854$		0			0
$855$	0.348580	−	3.11542i	0.0119212	−	0.106545i
$856$		0			0
$857$	−13.7323			−0.469086			−0.234543	−	0.972106i	$-0.575359\pi$
$857$	−13.7323			−0.469086			−0.234543	+	0.972106i	$0.575359\pi$
$858$		0			0
$859$		−	24.6976i		−	0.842673i	−0.906904	−	0.421336i	$-0.861561\pi$
$859$		−	24.6976i		−	0.842673i	0.906904	−	0.421336i	$-0.138439\pi$
$860$		0			0
$861$	0.827330	+	35.5020i	0.0281953	+	1.20990i
$862$		0			0
$863$		−	49.4217i		−	1.68233i	−0.540775	−	0.841167i	$-0.681869\pi$
$863$		−	49.4217i		−	1.68233i	0.540775	−	0.841167i	$-0.318131\pi$
$864$		0			0
$865$	−19.6775			−0.669054
$866$		0			0
$867$	−7.06136	−	0.393813i	−0.239816	−	0.0133746i
$868$		0			0
$869$		−	12.0092i		−	0.407386i
$870$		0			0
$871$		−	27.4281i		−	0.929366i
$872$		0			0
$873$	4.53452	−	40.5272i	0.153470	−	1.37164i
$874$		0			0
$875$	0.208829	+	2.63750i	0.00705970	+	0.0891637i
$876$		0			0
$877$	46.8346			1.58149			0.790746	−	0.612144i	$-0.209693\pi$
$877$	46.8346			1.58149			0.790746	+	0.612144i	$0.209693\pi$
$878$		0			0
$879$	6.48837	+	0.361857i	0.218847	+	0.0122051i
$880$		0			0
$881$	25.2322			0.850096			0.425048	−	0.905171i	$-0.360257\pi$
$881$	25.2322			0.850096			0.425048	+	0.905171i	$0.360257\pi$
$882$		0			0
$883$	0.140777			0.00473751			0.00236876	−	0.999997i	$-0.499246\pi$
$883$	0.140777			0.00473751			0.00236876	+	0.999997i	$0.499246\pi$
$884$		0			0
$885$	3.66060	+	0.204152i	0.123050	+	0.00686251i
$886$		0			0
$887$	0.336941			0.0113134			0.00565669	−	0.999984i	$-0.498199\pi$
$887$	0.336941			0.0113134			0.00565669	+	0.999984i	$0.498199\pi$
$888$		0			0
$889$	−3.60016	−	45.4698i	−0.120745	−	1.52501i
$890$		0			0
$891$	3.40556	−	15.0281i	0.114091	−	0.503459i
$892$		0			0
$893$			10.3535i			0.346467i
$894$		0			0
$895$			21.2730i			0.711077i
$896$		0			0
$897$	3.16184	+	0.176337i	0.105571	+	0.00588771i
$898$		0			0
$899$	−38.0878			−1.27030
$900$		0			0
$901$		−	16.6605i		−	0.555043i
$902$		0			0
$903$	−0.539440	−	23.1482i	−0.0179514	−	0.770323i
$904$		0			0
$905$			9.52329i			0.316565i
$906$		0			0
$907$	−41.5312			−1.37902			−0.689511	−	0.724275i	$-0.742175\pi$
$907$	−41.5312			−1.37902			−0.689511	+	0.724275i	$0.742175\pi$
$908$		0			0
$909$	12.7714	+	1.42897i	0.423601	+	0.0473961i
$910$		0			0
$911$			45.7168i			1.51467i	0.653029	+	0.757333i	$0.273498\pi$
$911$			45.7168i			1.51467i	−0.653029	+	0.757333i	$0.726502\pi$
$912$		0			0
$913$			8.93450i			0.295689i
$914$		0			0
$915$	−0.782399	+	14.0290i	−0.0258653	+	0.463784i
$916$		0			0
$917$	−1.44578	−	18.2602i	−0.0477440	−	0.603004i
$918$		0			0
$919$	11.6957			0.385806			0.192903	−	0.981218i	$-0.438210\pi$
$919$	11.6957			0.385806			0.192903	+	0.981218i	$0.438210\pi$
$920$		0			0
$921$	−2.88667	+	51.7600i	−0.0951189	+	1.70555i
$922$		0			0
$923$	−8.01264			−0.263739
$924$		0			0
$925$	−7.99549			−0.262890
$926$		0			0
$927$	4.67775	−	41.8073i	0.153637	−	1.37313i
$928$		0			0
$929$	−56.6691			−1.85925			−0.929627	−	0.368501i	$-0.879871\pi$
$929$	−56.6691			−1.85925			−0.929627	+	0.368501i	$0.879871\pi$
$930$		0			0
$931$	−1.15109	−	7.22354i	−0.0377255	−	0.236742i
$932$		0			0
$933$	36.3703	+	2.02838i	1.19071	+	0.0664061i
$934$		0			0
$935$		−	6.15335i		−	0.201236i
$936$		0			0
$937$		−	56.2225i		−	1.83671i	−0.395760	−	0.918354i	$-0.629519\pi$
$937$		−	56.2225i		−	1.83671i	0.395760	−	0.918354i	$-0.370481\pi$
$938$		0			0
$939$	−0.940342	+	16.8610i	−0.0306869	+	0.550239i
$940$		0			0
$941$	−26.1463			−0.852345			−0.426172	−	0.904642i	$-0.640138\pi$
$941$	−26.1463			−0.852345			−0.426172	+	0.904642i	$0.640138\pi$
$942$		0			0
$943$		−	4.54894i		−	0.148134i
$944$		0			0
$945$	−1.20996	+	13.6944i	−0.0393599	+	0.445478i
$946$		0			0
$947$		−	29.7126i		−	0.965530i	−0.875750	−	0.482765i	$-0.839632\pi$
$947$		−	29.7126i		−	0.965530i	0.875750	−	0.482765i	$-0.160368\pi$
$948$		0			0
$949$	−21.4390			−0.695940
$950$		0			0
$951$	−1.56619	+	28.0828i	−0.0507870	+	0.910648i
$952$		0			0
$953$		−	29.6858i		−	0.961618i	−0.876825	−	0.480809i	$-0.840343\pi$
$953$		−	29.6858i		−	0.961618i	0.876825	−	0.480809i	$-0.159657\pi$
$954$		0			0
$955$		−	22.1742i		−	0.717542i
$956$		0			0
$957$	−13.2490	−	0.738900i	−0.428280	−	0.0238852i
$958$		0			0
$959$	56.7589	−	4.49399i	1.83284	−	0.145119i
$960$		0			0
$961$	−41.4513			−1.33714
$962$		0			0
$963$	−6.49725	+	58.0690i	−0.209371	+	1.87125i
$964$		0			0
$965$	13.1540			0.423443
$966$		0			0
$967$	48.0668			1.54572			0.772862	−	0.634574i	$-0.218824\pi$
$967$	48.0668			1.54572			0.772862	+	0.634574i	$0.218824\pi$
$968$		0			0
$969$	0.362212	−	6.49473i	0.0116359	−	0.208641i
$970$		0			0
$971$	26.6857			0.856385			0.428192	−	0.903688i	$-0.359151\pi$
$971$	26.6857			0.856385			0.428192	+	0.903688i	$0.359151\pi$
$972$		0			0
$973$	14.1746	−	1.12230i	0.454416	−	0.0359792i
$974$		0			0
$975$	0.300395	−	5.38630i	0.00962034	−	0.172500i
$976$		0			0
$977$		−	32.3351i		−	1.03449i	−0.855837	−	0.517246i	$-0.826957\pi$
$977$		−	32.3351i		−	1.03449i	0.855837	−	0.517246i	$-0.173043\pi$
$978$		0			0
$979$		−	13.9988i		−	0.447405i
$980$		0			0
$981$	−31.9995	−	3.58038i	−1.02167	−	0.114313i
$982$		0			0
$983$	−17.7145			−0.565005			−0.282502	−	0.959267i	$-0.591165\pi$
$983$	−17.7145			−0.565005			−0.282502	+	0.959267i	$0.591165\pi$
$984$		0			0
$985$		−	13.8493i		−	0.441275i
$986$		0			0
$987$	−1.05781	−	45.3922i	−0.0336705	−	1.44485i
$988$		0			0
$989$			2.96602i			0.0943141i
$990$		0			0
$991$	52.5895			1.67056			0.835280	−	0.549825i	$-0.185305\pi$
$991$	52.5895			1.67056			0.835280	+	0.549825i	$0.185305\pi$
$992$		0			0
$993$	−17.9640	−	1.00186i	−0.570072	−	0.0317930i
$994$		0			0
$995$		−	1.51305i		−	0.0479668i
$996$		0			0
$997$			38.0605i			1.20539i	0.797972	+	0.602695i	$0.205906\pi$
$997$			38.0605i			1.20539i	−0.797972	+	0.602695i	$0.794094\pi$
$998$		0			0
$999$	−40.9668	−	6.91157i	−1.29613	−	0.218672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.f.k.881.16		16
3.2	odd	2		1680.2.f.l.881.2		16
4.3	odd	2		840.2.f.a.41.1	✓	16
7.6	odd	2		1680.2.f.l.881.1		16
12.11	even	2		840.2.f.b.41.15	yes	16
21.20	even	2	inner	1680.2.f.k.881.15		16
28.27	even	2		840.2.f.b.41.16	yes	16
84.83	odd	2		840.2.f.a.41.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.f.a.41.1	✓	16	4.3	odd	2
840.2.f.a.41.2	yes	16	84.83	odd	2
840.2.f.b.41.15	yes	16	12.11	even	2
840.2.f.b.41.16	yes	16	28.27	even	2
1680.2.f.k.881.15		16	21.20	even	2	inner
1680.2.f.k.881.16		16	1.1	even	1	trivial
1680.2.f.l.881.1		16	7.6	odd	2
1680.2.f.l.881.2		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.72936 + 0.0964469i) q^{3} -1.00000 q^{5} +(-0.208829 - 2.63750i) q^{7} +(2.98140 + 0.333584i) q^{9} +O(q^{10})\)	\(q+(1.72936 + 0.0964469i) q^{3} -1.00000 q^{5} +(-0.208829 - 2.63750i) q^{7} +(2.98140 + 0.333584i) q^{9} -1.71212i q^{11} -3.11462i q^{13} +(-1.72936 - 0.0964469i) q^{15} -3.59399 q^{17} +1.04495i q^{19} +(-0.106762 - 4.58133i) q^{21} +0.587015i q^{23} +1.00000 q^{25} +(5.12374 + 0.864434i) q^{27} -4.47468i q^{29} -8.51183i q^{31} +(0.165129 - 2.96088i) q^{33} +(0.208829 + 2.63750i) q^{35} -7.99549 q^{37} +(0.300395 - 5.38630i) q^{39} -7.74927 q^{41} +5.05272 q^{43} +(-2.98140 - 0.333584i) q^{45} +9.90809 q^{47} +(-6.91278 + 1.10157i) q^{49} +(-6.21532 - 0.346630i) q^{51} +4.63566i q^{53} +1.71212i q^{55} +(-0.100783 + 1.80711i) q^{57} -2.11673 q^{59} -8.11222i q^{61} +(0.257225 - 7.93308i) q^{63} +3.11462i q^{65} +8.80626 q^{67} +(-0.0566158 + 1.01516i) q^{69} -2.57259i q^{71} -6.88336i q^{73} +(1.72936 + 0.0964469i) q^{75} +(-4.51572 + 0.357540i) q^{77} +7.01425 q^{79} +(8.77744 + 1.98909i) q^{81} -5.21838 q^{83} +3.59399 q^{85} +(0.431570 - 7.73836i) q^{87} +8.17632 q^{89} +(-8.21479 + 0.650421i) q^{91} +(0.820940 - 14.7200i) q^{93} -1.04495i q^{95} -13.5934i q^{97} +(0.571136 - 5.10451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{5} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 16 * q - 16 * q^5 - 2 * q^7 - 2 * q^9	\( 16 q - 16 q^{5} - 2 q^{7} - 2 q^{9} + 2 q^{21} + 16 q^{25} + 6 q^{27} - 6 q^{33} + 2 q^{35} + 12 q^{37} - 6 q^{39} - 32 q^{41} - 32 q^{43} + 2 q^{45} + 4 q^{47} - 4 q^{49} - 6 q^{51} - 24 q^{59} + 4 q^{63} - 8 q^{69} + 32 q^{77} + 4 q^{79} - 6 q^{81} + 20 q^{83} + 6 q^{87} + 24 q^{89} - 20 q^{91} - 32 q^{93} + 58 q^{99}+O(q^{100}) \) 16 * q - 16 * q^5 - 2 * q^7 - 2 * q^9 + 2 * q^21 + 16 * q^25 + 6 * q^27 - 6 * q^33 + 2 * q^35 + 12 * q^37 - 6 * q^39 - 32 * q^41 - 32 * q^43 + 2 * q^45 + 4 * q^47 - 4 * q^49 - 6 * q^51 - 24 * q^59 + 4 * q^63 - 8 * q^69 + 32 * q^77 + 4 * q^79 - 6 * q^81 + 20 * q^83 + 6 * q^87 + 24 * q^89 - 20 * q^91 - 32 * q^93 + 58 * q^99

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