LMFDB - Embedded newform 1680.2.f.l.881.6

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			881.6
Root			$-1.34935 + 1.08593i$ of defining polynomial
Character	$\chi$	$=$	1680.881
Dual form			1680.2.f.l.881.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08593 + 1.34935i) q^{3} +1.00000 q^{5} +(-2.53123 - 0.769995i) q^{7} +(-0.641511 - 2.93061i) q^{9} +O(q^{10})$	\(q+(-1.08593 + 1.34935i) q^{3} +1.00000 q^{5} +(-2.53123 - 0.769995i) q^{7} +(-0.641511 - 2.93061i) q^{9} +1.53432i q^{11} -1.09114i q^{13} +(-1.08593 + 1.34935i) q^{15} +1.57385 q^{17} -4.32690i q^{19} +(3.78773 - 2.57936i) q^{21} +6.09548i q^{23} +1.00000 q^{25} +(4.65106 + 2.31681i) q^{27} +0.867889i q^{29} -4.03607i q^{31} +(-2.07034 - 1.66616i) q^{33} +(-2.53123 - 0.769995i) q^{35} +11.4253 q^{37} +(1.47233 + 1.18490i) q^{39} -2.70250 q^{41} +1.74571 q^{43} +(-0.641511 - 2.93061i) q^{45} +10.3471 q^{47} +(5.81421 + 3.89807i) q^{49} +(-1.70909 + 2.12368i) q^{51} +4.51290i q^{53} +1.53432i q^{55} +(5.83851 + 4.69871i) q^{57} +2.72120 q^{59} -10.7041i q^{61} +(-0.632746 + 7.91199i) q^{63} -1.09114i q^{65} -3.69294 q^{67} +(-8.22496 - 6.61927i) q^{69} +11.7996i q^{71} +2.71268i q^{73} +(-1.08593 + 1.34935i) q^{75} +(1.18142 - 3.88371i) q^{77} +7.04200 q^{79} +(-8.17693 + 3.76003i) q^{81} +6.68497 q^{83} +1.57385 q^{85} +(-1.17109 - 0.942467i) q^{87} -4.13646 q^{89} +(-0.840170 + 2.76191i) q^{91} +(5.44608 + 4.38289i) q^{93} -4.32690i q^{95} +16.9687i q^{97} +(4.49649 - 0.984283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 10 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} + 24 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 + 10 * 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 + 24 * 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
$3$	−1.08593	+	1.34935i	−0.626962	+	0.779050i
$3$	−1.08593	+	1.34935i	−0.626962	+	0.779050i
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−2.53123	−	0.769995i	−0.956714	−	0.291031i
$7$	−2.53123	−	0.769995i	−0.956714	−	0.291031i
$8$		0			0
$9$	−0.641511	−	2.93061i	−0.213837	−	0.976869i
$10$		0			0
$11$			1.53432i			0.462615i	0.972881	+	0.231307i	$0.0743003\pi$
$11$			1.53432i			0.462615i	−0.972881	+	0.231307i	$0.925700\pi$
$12$		0			0
$13$		−	1.09114i		−	0.302627i	−0.988486	−	0.151313i	$-0.951650\pi$
$13$		−	1.09114i		−	0.302627i	0.988486	−	0.151313i	$-0.0483503\pi$
$14$		0			0
$15$	−1.08593	+	1.34935i	−0.280386	+	0.348402i
$16$		0			0
$17$	1.57385			0.381714			0.190857	−	0.981618i	$-0.438873\pi$
$17$	1.57385			0.381714			0.190857	+	0.981618i	$0.438873\pi$
$18$		0			0
$19$		−	4.32690i		−	0.992658i	−0.868135	−	0.496329i	$-0.834681\pi$
$19$		−	4.32690i		−	0.992658i	0.868135	−	0.496329i	$-0.165319\pi$
$20$		0			0
$21$	3.78773	−	2.57936i	0.826551	−	0.562862i
$22$		0			0
$23$			6.09548i			1.27100i	0.772103	+	0.635498i	$0.219205\pi$
$23$			6.09548i			1.27100i	−0.772103	+	0.635498i	$0.780795\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	4.65106	+	2.31681i	0.895097	+	0.445871i
$28$		0			0
$29$			0.867889i			0.161163i	0.996748	+	0.0805814i	$0.0256777\pi$
$29$			0.867889i			0.161163i	−0.996748	+	0.0805814i	$0.974322\pi$
$30$		0			0
$31$		−	4.03607i		−	0.724899i	−0.932003	−	0.362450i	$-0.881940\pi$
$31$		−	4.03607i		−	0.724899i	0.932003	−	0.362450i	$-0.118060\pi$
$32$		0			0
$33$	−2.07034	−	1.66616i	−0.360400	−	0.290042i
$34$		0			0
$35$	−2.53123	−	0.769995i	−0.427855	−	0.130153i
$36$		0			0
$37$	11.4253			1.87831			0.939155	−	0.343493i	$-0.111610\pi$
$37$	11.4253			1.87831			0.939155	+	0.343493i	$0.111610\pi$
$38$		0			0
$39$	1.47233	+	1.18490i	0.235761	+	0.189736i
$40$		0			0
$41$	−2.70250			−0.422060			−0.211030	−	0.977480i	$-0.567682\pi$
$41$	−2.70250			−0.422060			−0.211030	+	0.977480i	$0.567682\pi$
$42$		0			0
$43$	1.74571			0.266218			0.133109	−	0.991101i	$-0.457504\pi$
$43$	1.74571			0.266218			0.133109	+	0.991101i	$0.457504\pi$
$44$		0			0
$45$	−0.641511	−	2.93061i	−0.0956308	−	0.436869i
$46$		0			0
$47$	10.3471			1.50928			0.754639	−	0.656140i	$-0.227812\pi$
$47$	10.3471			1.50928			0.754639	+	0.656140i	$0.227812\pi$
$48$		0			0
$49$	5.81421	+	3.89807i	0.830602	+	0.556867i
$50$		0			0
$51$	−1.70909	+	2.12368i	−0.239321	+	0.297375i
$52$		0			0
$53$			4.51290i			0.619895i	0.950754	+	0.309947i	$0.100311\pi$
$53$			4.51290i			0.619895i	−0.950754	+	0.309947i	$0.899689\pi$
$54$		0			0
$55$			1.53432i			0.206888i
$56$		0			0
$57$	5.83851	+	4.69871i	0.773330	+	0.622359i
$58$		0			0
$59$	2.72120			0.354270			0.177135	−	0.984187i	$-0.443317\pi$
$59$	2.72120			0.354270			0.177135	+	0.984187i	$0.443317\pi$
$60$		0			0
$61$		−	10.7041i		−	1.37052i	−0.728298	−	0.685261i	$-0.759688\pi$
$61$		−	10.7041i		−	1.37052i	0.728298	−	0.685261i	$-0.240312\pi$
$62$		0			0
$63$	−0.632746	+	7.91199i	−0.0797185	+	0.996817i
$64$		0			0
$65$		−	1.09114i		−	0.135339i
$66$		0			0
$67$	−3.69294			−0.451165			−0.225582	−	0.974224i	$-0.572428\pi$
$67$	−3.69294			−0.451165			−0.225582	+	0.974224i	$0.572428\pi$
$68$		0			0
$69$	−8.22496	−	6.61927i	−0.990169	−	0.796866i
$70$		0			0
$71$			11.7996i			1.40036i	0.713967	+	0.700179i	$0.246896\pi$
$71$			11.7996i			1.40036i	−0.713967	+	0.700179i	$0.753104\pi$
$72$		0			0
$73$			2.71268i			0.317495i	0.987319	+	0.158748i	$0.0507456\pi$
$73$			2.71268i			0.317495i	−0.987319	+	0.158748i	$0.949254\pi$
$74$		0			0
$75$	−1.08593	+	1.34935i	−0.125392	+	0.155810i
$76$		0			0
$77$	1.18142	−	3.88371i	0.134635	−	0.442590i
$78$		0			0
$79$	7.04200			0.792286			0.396143	−	0.918189i	$-0.370348\pi$
$79$	7.04200			0.792286			0.396143	+	0.918189i	$0.370348\pi$
$80$		0			0
$81$	−8.17693	+	3.76003i	−0.908548	+	0.417781i
$82$		0			0
$83$	6.68497			0.733771			0.366885	−	0.930266i	$-0.380424\pi$
$83$	6.68497			0.733771			0.366885	+	0.930266i	$0.380424\pi$
$84$		0			0
$85$	1.57385			0.170708
$86$		0			0
$87$	−1.17109	−	0.942467i	−0.125554	−	0.101043i
$88$		0			0
$89$	−4.13646			−0.438464			−0.219232	−	0.975673i	$-0.570355\pi$
$89$	−4.13646			−0.438464			−0.219232	+	0.975673i	$0.570355\pi$
$90$		0			0
$91$	−0.840170	+	2.76191i	−0.0880738	+	0.289527i
$92$		0			0
$93$	5.44608	+	4.38289i	0.564733	+	0.454484i
$94$		0			0
$95$		−	4.32690i		−	0.443930i
$96$		0			0
$97$			16.9687i			1.72291i	0.507831	+	0.861457i	$0.330447\pi$
$97$			16.9687i			1.72291i	−0.507831	+	0.861457i	$0.669553\pi$
$98$		0			0
$99$	4.49649	−	0.984283i	0.451914	−	0.0989242i
$100$		0			0
$101$	19.4582			1.93616			0.968082	−	0.250633i	$-0.0806388\pi$
$101$	19.4582			1.93616			0.968082	+	0.250633i	$0.0806388\pi$
$102$		0			0
$103$		−	13.0633i		−	1.28716i	−0.765377	−	0.643582i	$-0.777448\pi$
$103$		−	13.0633i		−	1.28716i	0.765377	−	0.643582i	$-0.222552\pi$
$104$		0			0
$105$	3.78773	−	2.57936i	0.369645	−	0.251720i
$106$		0			0
$107$			0.409687i			0.0396059i	0.999804	+	0.0198030i	$0.00630389\pi$
$107$			0.409687i			0.0396059i	−0.999804	+	0.0198030i	$0.993696\pi$
$108$		0			0
$109$	−13.3416			−1.27789			−0.638946	−	0.769251i	$-0.720629\pi$
$109$	−13.3416			−1.27789			−0.638946	+	0.769251i	$0.720629\pi$
$110$		0			0
$111$	−12.4071	+	15.4168i	−1.17763	+	1.46330i
$112$		0			0
$113$			9.57195i			0.900454i	0.892914	+	0.450227i	$0.148657\pi$
$113$			9.57195i			0.900454i	−0.892914	+	0.450227i	$0.851343\pi$
$114$		0			0
$115$			6.09548i			0.568407i
$116$		0			0
$117$	−3.19769	+	0.699976i	−0.295627	+	0.0647128i
$118$		0			0
$119$	−3.98377	−	1.21186i	−0.365191	−	0.111091i
$120$		0			0
$121$	8.64586			0.785987
$122$		0			0
$123$	2.93473	−	3.64663i	0.264615	−	0.328805i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.66734			0.769102			0.384551	−	0.923104i	$-0.374356\pi$
$127$	8.66734			0.769102			0.384551	+	0.923104i	$0.374356\pi$
$128$		0			0
$129$	−1.89572	+	2.35558i	−0.166909	+	0.207397i
$130$		0			0
$131$	−7.48846			−0.654270			−0.327135	−	0.944978i	$-0.606083\pi$
$131$	−7.48846			−0.654270			−0.327135	+	0.944978i	$0.606083\pi$
$132$		0			0
$133$	−3.33169	+	10.9524i	−0.288894	+	0.949689i
$134$		0			0
$135$	4.65106	+	2.31681i	0.400300	+	0.199399i
$136$		0			0
$137$			11.2768i			0.963445i	0.876324	+	0.481722i	$0.159989\pi$
$137$			11.2768i			0.963445i	−0.876324	+	0.481722i	$0.840011\pi$
$138$		0			0
$139$		−	5.95689i		−	0.505256i	−0.967563	−	0.252628i	$-0.918705\pi$
$139$		−	5.95689i		−	0.505256i	0.967563	−	0.252628i	$-0.0812950\pi$
$140$		0			0
$141$	−11.2362	+	13.9619i	−0.946260	+	1.17580i
$142$		0			0
$143$	1.67415			0.140000
$144$		0			0
$145$			0.867889i			0.0720742i
$146$		0			0
$147$	−11.5737	+	3.61240i	−0.954583	+	0.297946i
$148$		0			0
$149$		−	4.90815i		−	0.402091i	−0.979582	−	0.201046i	$-0.935566\pi$
$149$		−	4.90815i		−	0.402091i	0.979582	−	0.201046i	$-0.0644340\pi$
$150$		0			0
$151$	17.9251			1.45872			0.729362	−	0.684128i	$-0.239817\pi$
$151$	17.9251			1.45872			0.729362	+	0.684128i	$0.239817\pi$
$152$		0			0
$153$	−1.00964	−	4.61233i	−0.0816246	−	0.372885i
$154$		0			0
$155$		−	4.03607i		−	0.324185i
$156$		0			0
$157$			11.9270i			0.951877i	0.879478	+	0.475939i	$0.157892\pi$
$157$			11.9270i			0.951877i	−0.879478	+	0.475939i	$0.842108\pi$
$158$		0			0
$159$	−6.08950	−	4.90070i	−0.482929	−	0.388651i
$160$		0			0
$161$	4.69349	−	15.4290i	0.369899	−	1.21598i
$162$		0			0
$163$	−17.6018			−1.37868			−0.689340	−	0.724438i	$-0.742100\pi$
$163$	−17.6018			−1.37868			−0.689340	+	0.724438i	$0.742100\pi$
$164$		0			0
$165$	−2.07034	−	1.66616i	−0.161176	−	0.129711i
$166$		0			0
$167$	25.1048			1.94266			0.971332	−	0.237726i	$-0.0764019\pi$
$167$	25.1048			1.94266			0.971332	+	0.237726i	$0.0764019\pi$
$168$		0			0
$169$	11.8094			0.908417
$170$		0			0
$171$	−12.6804	+	2.77575i	−0.969697	+	0.212267i
$172$		0			0
$173$	10.4879			0.797381			0.398690	−	0.917086i	$-0.369465\pi$
$173$	10.4879			0.797381			0.398690	+	0.917086i	$0.369465\pi$
$174$		0			0
$175$	−2.53123	−	0.769995i	−0.191343	−	0.0582062i
$176$		0			0
$177$	−2.95504	+	3.67187i	−0.222114	+	0.275994i
$178$		0			0
$179$		−	21.6843i		−	1.62076i	−0.585906	−	0.810379i	$-0.699261\pi$
$179$		−	21.6843i		−	1.62076i	0.585906	−	0.810379i	$-0.300739\pi$
$180$		0			0
$181$			6.48943i			0.482356i	0.970481	+	0.241178i	$0.0775337\pi$
$181$			6.48943i			0.482356i	−0.970481	+	0.241178i	$0.922466\pi$
$182$		0			0
$183$	14.4436	+	11.6239i	1.06770	+	0.859265i
$184$		0			0
$185$	11.4253			0.840006
$186$		0			0
$187$			2.41479i			0.176587i
$188$		0			0
$189$	−9.98896	−	9.44567i	−0.726590	−	0.687071i
$190$		0			0
$191$			3.28120i			0.237420i	0.992929	+	0.118710i	$0.0378758\pi$
$191$			3.28120i			0.237420i	−0.992929	+	0.118710i	$0.962124\pi$
$192$		0			0
$193$	−10.2288			−0.736284			−0.368142	−	0.929770i	$-0.620006\pi$
$193$	−10.2288			−0.736284			−0.368142	+	0.929770i	$0.620006\pi$
$194$		0			0
$195$	1.47233	+	1.18490i	0.105436	+	0.0848523i
$196$		0			0
$197$			0.906822i			0.0646084i	0.999478	+	0.0323042i	$0.0102845\pi$
$197$			0.906822i			0.0646084i	−0.999478	+	0.0323042i	$0.989715\pi$
$198$		0			0
$199$		−	21.1896i		−	1.50209i	−0.660252	−	0.751044i	$-0.729550\pi$
$199$		−	21.1896i		−	1.50209i	0.660252	−	0.751044i	$-0.270450\pi$
$200$		0			0
$201$	4.01028	−	4.98308i	0.282863	−	0.351480i
$202$		0			0
$203$	0.668270	−	2.19682i	0.0469034	−	0.154187i
$204$		0			0
$205$	−2.70250			−0.188751
$206$		0			0
$207$	17.8635	−	3.91032i	1.24160	−	0.271786i
$208$		0			0
$209$	6.63884			0.459218
$210$		0			0
$211$	11.4616			0.789050			0.394525	−	0.918885i	$-0.370909\pi$
$211$	11.4616			0.789050			0.394525	+	0.918885i	$0.370909\pi$
$212$		0			0
$213$	−15.9219	−	12.8136i	−1.09095	−	0.877971i
$214$		0			0
$215$	1.74571			0.119056
$216$		0			0
$217$	−3.10775	+	10.2162i	−0.210968	+	0.693521i
$218$		0			0
$219$	−3.66036	−	2.94578i	−0.247345	−	0.199057i
$220$		0			0
$221$		−	1.71728i		−	0.115517i
$222$		0			0
$223$			4.71035i			0.315429i	0.987485	+	0.157714i	$0.0504125\pi$
$223$			4.71035i			0.315429i	−0.987485	+	0.157714i	$0.949587\pi$
$224$		0			0
$225$	−0.641511	−	2.93061i	−0.0427674	−	0.195374i
$226$		0			0
$227$	6.90224			0.458118			0.229059	−	0.973413i	$-0.426435\pi$
$227$	6.90224			0.458118			0.229059	+	0.973413i	$0.426435\pi$
$228$		0			0
$229$		−	11.8856i		−	0.785420i	−0.919662	−	0.392710i	$-0.871538\pi$
$229$		−	11.8856i		−	0.785420i	0.919662	−	0.392710i	$-0.128462\pi$
$230$		0			0
$231$	3.95756	+	5.81159i	0.260388	+	0.382375i
$232$		0			0
$233$			15.8951i			1.04132i	0.853763	+	0.520662i	$0.174315\pi$
$233$			15.8951i			1.04132i	−0.853763	+	0.520662i	$0.825685\pi$
$234$		0			0
$235$	10.3471			0.674970
$236$		0			0
$237$	−7.64712	+	9.50214i	−0.496734	+	0.617231i
$238$		0			0
$239$			0.613794i			0.0397031i	0.999803	+	0.0198515i	$0.00631935\pi$
$239$			0.613794i			0.0397031i	−0.999803	+	0.0198515i	$0.993681\pi$
$240$		0			0
$241$		−	15.4578i		−	0.995722i	−0.867257	−	0.497861i	$-0.834119\pi$
$241$		−	15.4578i		−	0.995722i	0.867257	−	0.497861i	$-0.165881\pi$
$242$		0			0
$243$	3.80596	−	15.1167i	0.244152	−	0.969737i
$244$		0			0
$245$	5.81421	+	3.89807i	0.371457	+	0.249038i
$246$		0			0
$247$	−4.72123			−0.300405
$248$		0			0
$249$	−7.25941	+	9.02039i	−0.460047	+	0.571644i
$250$		0			0
$251$	−13.6257			−0.860049			−0.430025	−	0.902817i	$-0.641495\pi$
$251$	−13.6257			−0.860049			−0.430025	+	0.902817i	$0.641495\pi$
$252$		0			0
$253$	−9.35242			−0.587982
$254$		0			0
$255$	−1.70909	+	2.12368i	−0.107027	+	0.132990i
$256$		0			0
$257$	−2.87557			−0.179373			−0.0896867	−	0.995970i	$-0.528587\pi$
$257$	−2.87557			−0.179373			−0.0896867	+	0.995970i	$0.528587\pi$
$258$		0			0
$259$	−28.9201	−	8.79744i	−1.79701	−	0.546646i
$260$		0			0
$261$	2.54344	−	0.556760i	0.157435	−	0.0344626i
$262$		0			0
$263$		−	29.5720i		−	1.82349i	−0.410756	−	0.911745i	$-0.634735\pi$
$263$		−	29.5720i		−	1.82349i	0.410756	−	0.911745i	$-0.365265\pi$
$264$		0			0
$265$			4.51290i			0.277225i
$266$		0			0
$267$	4.49190	−	5.58154i	0.274900	−	0.341585i
$268$		0			0
$269$	−15.5642			−0.948967			−0.474483	−	0.880264i	$-0.657365\pi$
$269$	−15.5642			−0.948967			−0.474483	+	0.880264i	$0.657365\pi$
$270$		0			0
$271$			10.7575i			0.653470i	0.945116	+	0.326735i	$0.105949\pi$
$271$			10.7575i			0.653470i	−0.945116	+	0.326735i	$0.894051\pi$
$272$		0			0
$273$	−2.81443	−	4.13293i	−0.170337	−	0.250136i
$274$		0			0
$275$			1.53432i			0.0925230i
$276$		0			0
$277$	−22.9044			−1.37619			−0.688095	−	0.725621i	$-0.741553\pi$
$277$	−22.9044			−1.37619			−0.688095	+	0.725621i	$0.741553\pi$
$278$		0			0
$279$	−11.8281	+	2.58918i	−0.708132	+	0.155010i
$280$		0			0
$281$			1.54489i			0.0921604i	0.998938	+	0.0460802i	$0.0146730\pi$
$281$			1.54489i			0.0921604i	−0.998938	+	0.0460802i	$0.985327\pi$
$282$		0			0
$283$			13.8395i			0.822672i	0.911484	+	0.411336i	$0.134938\pi$
$283$			13.8395i			0.822672i	−0.911484	+	0.411336i	$0.865062\pi$
$284$		0			0
$285$	5.83851	+	4.69871i	0.345844	+	0.278327i
$286$		0			0
$287$	6.84064	+	2.08091i	0.403790	+	0.122832i
$288$		0			0
$289$	−14.5230			−0.854294
$290$		0			0
$291$	−22.8968	−	18.4269i	−1.34224	−	1.08020i
$292$		0			0
$293$	11.9219			0.696483			0.348241	−	0.937405i	$-0.386779\pi$
$293$	11.9219			0.696483			0.348241	+	0.937405i	$0.386779\pi$
$294$		0			0
$295$	2.72120			0.158435
$296$		0			0
$297$	−3.55473	+	7.13622i	−0.206266	+	0.414086i
$298$		0			0
$299$	6.65100			0.384638
$300$		0			0
$301$	−4.41879	−	1.34419i	−0.254695	−	0.0774777i
$302$		0			0
$303$	−21.1303	+	26.2560i	−1.21390	+	1.50837i
$304$		0			0
$305$		−	10.7041i		−	0.612916i
$306$		0			0
$307$		−	25.2763i		−	1.44259i	−0.692626	−	0.721297i	$-0.743546\pi$
$307$		−	25.2763i		−	1.44259i	0.692626	−	0.721297i	$-0.256454\pi$
$308$		0			0
$309$	17.6270	+	14.1858i	1.00276	+	0.807003i
$310$		0			0
$311$	16.6410			0.943623			0.471811	−	0.881700i	$-0.343600\pi$
$311$	16.6410			0.943623			0.471811	+	0.881700i	$0.343600\pi$
$312$		0			0
$313$		−	31.6334i		−	1.78802i	−0.448042	−	0.894012i	$-0.647879\pi$
$313$		−	31.6334i		−	1.78802i	0.448042	−	0.894012i	$-0.352121\pi$
$314$		0			0
$315$	−0.632746	+	7.91199i	−0.0356512	+	0.445790i
$316$		0			0
$317$		−	29.1888i		−	1.63941i	−0.572787	−	0.819705i	$-0.694138\pi$
$317$		−	29.1888i		−	1.63941i	0.572787	−	0.819705i	$-0.305862\pi$
$318$		0			0
$319$	−1.33162			−0.0745564
$320$		0			0
$321$	−0.552812	−	0.444891i	−0.0308550	−	0.0248314i
$322$		0			0
$323$		−	6.80988i		−	0.378912i
$324$		0			0
$325$		−	1.09114i		−	0.0605254i
$326$		0			0
$327$	14.4880	−	18.0025i	0.801190	−	0.995542i
$328$		0			0
$329$	−26.1908	−	7.96721i	−1.44395	−	0.439247i
$330$		0			0
$331$	−8.58488			−0.471868			−0.235934	−	0.971769i	$-0.575815\pi$
$331$	−8.58488			−0.471868			−0.235934	+	0.971769i	$0.575815\pi$
$332$		0			0
$333$	−7.32946	−	33.4831i	−0.401652	−	1.83486i
$334$		0			0
$335$	−3.69294			−0.201767
$336$		0			0
$337$	−5.08040			−0.276747			−0.138373	−	0.990380i	$-0.544187\pi$
$337$	−5.08040			−0.276747			−0.138373	+	0.990380i	$0.544187\pi$
$338$		0			0
$339$	−12.9160	−	10.3945i	−0.701498	−	0.564550i
$340$		0			0
$341$	6.19262			0.335349
$342$		0			0
$343$	−11.7156	−	14.3438i	−0.632583	−	0.774493i
$344$		0			0
$345$	−8.22496	−	6.61927i	−0.442817	−	0.356369i
$346$		0			0
$347$		−	20.3423i		−	1.09203i	−0.837775	−	0.546016i	$-0.816144\pi$
$347$		−	20.3423i		−	1.09203i	0.837775	−	0.546016i	$-0.183856\pi$
$348$		0			0
$349$		−	13.1780i		−	0.705401i	−0.935736	−	0.352701i	$-0.885263\pi$
$349$		−	13.1780i		−	0.705401i	0.935736	−	0.352701i	$-0.114737\pi$
$350$		0			0
$351$	2.52796	−	5.07495i	0.134932	−	0.270881i
$352$		0			0
$353$	−10.2645			−0.546325			−0.273163	−	0.961968i	$-0.588070\pi$
$353$	−10.2645			−0.546325			−0.273163	+	0.961968i	$0.588070\pi$
$354$		0			0
$355$			11.7996i			0.626259i
$356$		0			0
$357$	5.96132	−	4.05952i	0.315506	−	0.214853i
$358$		0			0
$359$			30.5613i			1.61297i	0.591258	+	0.806483i	$0.298632\pi$
$359$			30.5613i			1.61297i	−0.591258	+	0.806483i	$0.701368\pi$
$360$		0			0
$361$	0.277972			0.0146301
$362$		0			0
$363$	−9.38880	+	11.6663i	−0.492784	+	0.612323i
$364$		0			0
$365$			2.71268i			0.141988i
$366$		0			0
$367$			30.4092i			1.58735i	0.608345	+	0.793673i	$0.291834\pi$
$367$			30.4092i			1.58735i	−0.608345	+	0.793673i	$0.708166\pi$
$368$		0			0
$369$	1.73368	+	7.91997i	0.0902519	+	0.412297i
$370$		0			0
$371$	3.47491	−	11.4232i	0.180409	−	0.593062i
$372$		0			0
$373$	29.7881			1.54237			0.771184	−	0.636612i	$-0.219665\pi$
$373$	29.7881			1.54237			0.771184	+	0.636612i	$0.219665\pi$
$374$		0			0
$375$	−1.08593	+	1.34935i	−0.0560772	+	0.0696803i
$376$		0			0
$377$	0.946985			0.0487722
$378$		0			0
$379$	−26.8457			−1.37897			−0.689485	−	0.724300i	$-0.742163\pi$
$379$	−26.8457			−1.37897			−0.689485	+	0.724300i	$0.742163\pi$
$380$		0			0
$381$	−9.41213	+	11.6953i	−0.482198	+	0.599169i
$382$		0			0
$383$	−28.1644			−1.43913			−0.719566	−	0.694424i	$-0.755659\pi$
$383$	−28.1644			−1.43913			−0.719566	+	0.694424i	$0.755659\pi$
$384$		0			0
$385$	1.18142	−	3.88371i	0.0602107	−	0.197932i
$386$		0			0
$387$	−1.11989	−	5.11599i	−0.0569273	−	0.260060i
$388$		0			0
$389$		−	13.9816i		−	0.708893i	−0.935076	−	0.354447i	$-0.884669\pi$
$389$		−	13.9816i		−	0.708893i	0.935076	−	0.354447i	$-0.115331\pi$
$390$		0			0
$391$			9.59337i			0.485158i
$392$		0			0
$393$	8.13195	−	10.1046i	0.410203	−	0.509709i
$394$		0			0
$395$	7.04200			0.354321
$396$		0			0
$397$			15.6830i			0.787108i	0.919302	+	0.393554i	$0.128755\pi$
$397$			15.6830i			0.787108i	−0.919302	+	0.393554i	$0.871245\pi$
$398$		0			0
$399$	−11.1606	−	16.3891i	−0.558730	−	0.820482i
$400$		0			0
$401$		−	39.1483i		−	1.95497i	−0.210997	−	0.977487i	$-0.567671\pi$
$401$		−	39.1483i		−	1.95497i	0.210997	−	0.977487i	$-0.432329\pi$
$402$		0			0
$403$	−4.40390			−0.219374
$404$		0			0
$405$	−8.17693	+	3.76003i	−0.406315	+	0.186838i
$406$		0			0
$407$			17.5301i			0.868935i
$408$		0			0
$409$		−	12.4242i		−	0.614335i	−0.951655	−	0.307167i	$-0.900619\pi$
$409$		−	12.4242i		−	0.614335i	0.951655	−	0.307167i	$-0.0993812\pi$
$410$		0			0
$411$	−15.2164	−	12.2459i	−0.750571	−	0.604043i
$412$		0			0
$413$	−6.88798	−	2.09531i	−0.338935	−	0.103104i
$414$		0			0
$415$	6.68497			0.328152
$416$		0			0
$417$	8.03795	+	6.46876i	0.393620	+	0.316777i
$418$		0			0
$419$	−28.1376			−1.37461			−0.687305	−	0.726369i	$-0.741206\pi$
$419$	−28.1376			−1.37461			−0.687305	+	0.726369i	$0.741206\pi$
$420$		0			0
$421$	9.59168			0.467470			0.233735	−	0.972300i	$-0.424905\pi$
$421$	9.59168			0.467470			0.233735	+	0.972300i	$0.424905\pi$
$422$		0			0
$423$	−6.63777	−	30.3233i	−0.322739	−	1.47437i
$424$		0			0
$425$	1.57385			0.0763429
$426$		0			0
$427$	−8.24212	+	27.0945i	−0.398864	+	1.31120i
$428$		0			0
$429$	−1.81801	+	2.25902i	−0.0877745	+	0.109067i
$430$		0			0
$431$			20.1415i			0.970182i	0.874464	+	0.485091i	$0.161214\pi$
$431$			20.1415i			0.970182i	−0.874464	+	0.485091i	$0.838786\pi$
$432$		0			0
$433$			15.9297i			0.765531i	0.923846	+	0.382766i	$0.125028\pi$
$433$			15.9297i			0.765531i	−0.923846	+	0.382766i	$0.874972\pi$
$434$		0			0
$435$	−1.17109	−	0.942467i	−0.0561494	−	0.0451878i
$436$		0			0
$437$	26.3745			1.26166
$438$		0			0
$439$			28.3864i			1.35481i	0.735610	+	0.677405i	$0.236896\pi$
$439$			28.3864i			1.35481i	−0.735610	+	0.677405i	$0.763104\pi$
$440$		0			0
$441$	7.69382	−	19.5398i	0.366373	−	0.930468i
$442$		0			0
$443$		−	22.3721i		−	1.06293i	−0.847080	−	0.531465i	$-0.821642\pi$
$443$		−	22.3721i		−	1.06293i	0.847080	−	0.531465i	$-0.178358\pi$
$444$		0			0
$445$	−4.13646			−0.196087
$446$		0			0
$447$	6.62283	+	5.32991i	0.313249	+	0.252096i
$448$		0			0
$449$			17.4948i			0.825629i	0.910815	+	0.412814i	$0.135454\pi$
$449$			17.4948i			0.825629i	−0.910815	+	0.412814i	$0.864546\pi$
$450$		0			0
$451$		−	4.14650i		−	0.195251i
$452$		0			0
$453$	−19.4654	+	24.1873i	−0.914564	+	1.13642i
$454$		0			0
$455$	−0.840170	+	2.76191i	−0.0393878	+	0.129481i
$456$		0			0
$457$	−1.26772			−0.0593014			−0.0296507	−	0.999560i	$-0.509439\pi$
$457$	−1.26772			−0.0593014			−0.0296507	+	0.999560i	$0.509439\pi$
$458$		0			0
$459$	7.32007	+	3.64631i	0.341672	+	0.170195i
$460$		0			0
$461$	11.9339			0.555815			0.277908	−	0.960608i	$-0.410359\pi$
$461$	11.9339			0.555815			0.277908	+	0.960608i	$0.410359\pi$
$462$		0			0
$463$	24.3173			1.13012			0.565060	−	0.825050i	$-0.308853\pi$
$463$	24.3173			1.13012			0.565060	+	0.825050i	$0.308853\pi$
$464$		0			0
$465$	5.44608	+	4.38289i	0.252556	+	0.203252i
$466$		0			0
$467$	8.72666			0.403822			0.201911	−	0.979404i	$-0.435285\pi$
$467$	8.72666			0.403822			0.201911	+	0.979404i	$0.435285\pi$
$468$		0			0
$469$	9.34767	+	2.84355i	0.431635	+	0.131303i
$470$		0			0
$471$	−16.0937	−	12.9519i	−0.741560	−	0.596791i
$472$		0			0
$473$			2.67848i			0.123157i
$474$		0			0
$475$		−	4.32690i		−	0.198532i
$476$		0			0
$477$	13.2255	−	2.89508i	0.605556	−	0.132556i
$478$		0			0
$479$	31.8295			1.45433			0.727163	−	0.686464i	$-0.240838\pi$
$479$	31.8295			1.45433			0.727163	+	0.686464i	$0.240838\pi$
$480$		0			0
$481$		−	12.4666i		−	0.568427i
$482$		0			0
$483$	15.7224	+	23.0881i	0.715395	+	1.05054i
$484$		0			0
$485$			16.9687i			0.770510i
$486$		0			0
$487$	−17.0463			−0.772443			−0.386221	−	0.922406i	$-0.626220\pi$
$487$	−17.0463			−0.772443			−0.386221	+	0.922406i	$0.626220\pi$
$488$		0			0
$489$	19.1143	−	23.7511i	0.864381	−	1.07406i
$490$		0			0
$491$			22.2615i			1.00465i	0.864679	+	0.502324i	$0.167522\pi$
$491$			22.2615i			1.00465i	−0.864679	+	0.502324i	$0.832478\pi$
$492$		0			0
$493$			1.36593i			0.0615182i
$494$		0			0
$495$	4.49649	−	0.984283i	0.202102	−	0.0442402i
$496$		0			0
$497$	9.08566	−	29.8675i	0.407547	−	1.33974i
$498$		0			0
$499$	16.4554			0.736647			0.368323	−	0.929698i	$-0.379932\pi$
$499$	16.4554			0.736647			0.368323	+	0.929698i	$0.379932\pi$
$500$		0			0
$501$	−27.2620	+	33.8752i	−1.21798	+	1.51343i
$502$		0			0
$503$	−29.3172			−1.30719			−0.653596	−	0.756844i	$-0.726740\pi$
$503$	−29.3172			−1.30719			−0.653596	+	0.756844i	$0.726740\pi$
$504$		0			0
$505$	19.4582			0.865879
$506$		0			0
$507$	−12.8242	+	15.9351i	−0.569543	+	0.707702i
$508$		0			0
$509$	8.22719			0.364664			0.182332	−	0.983237i	$-0.441635\pi$
$509$	8.22719			0.364664			0.182332	+	0.983237i	$0.441635\pi$
$510$		0			0
$511$	2.08875	−	6.86641i	0.0924009	−	0.303752i
$512$		0			0
$513$	10.0246	−	20.1247i	0.442597	−	0.888526i
$514$		0			0
$515$		−	13.0633i		−	0.575637i
$516$		0			0
$517$			15.8757i			0.698215i
$518$		0			0
$519$	−11.3891	+	14.1519i	−0.499928	+	0.621199i
$520$		0			0
$521$	−25.3656			−1.11129			−0.555643	−	0.831421i	$-0.687528\pi$
$521$	−25.3656			−1.11129			−0.555643	+	0.831421i	$0.687528\pi$
$522$		0			0
$523$			20.6469i			0.902826i	0.892315	+	0.451413i	$0.149080\pi$
$523$			20.6469i			0.902826i	−0.892315	+	0.451413i	$0.850920\pi$
$524$		0			0
$525$	3.78773	−	2.57936i	0.165310	−	0.112572i
$526$		0			0
$527$		−	6.35216i		−	0.276705i
$528$		0			0
$529$	−14.1549			−0.615431
$530$		0			0
$531$	−1.74568	−	7.97478i	−0.0757561	−	0.346076i
$532$		0			0
$533$			2.94880i			0.127727i
$534$		0			0
$535$			0.409687i			0.0177123i
$536$		0			0
$537$	29.2597	+	23.5476i	1.26265	+	1.01615i
$538$		0			0
$539$	−5.98088	+	8.92087i	−0.257615	+	0.384249i
$540$		0			0
$541$	33.4184			1.43677			0.718385	−	0.695646i	$-0.244882\pi$
$541$	33.4184			1.43677			0.718385	+	0.695646i	$0.244882\pi$
$542$		0			0
$543$	−8.75654	−	7.04707i	−0.375779	−	0.302419i
$544$		0			0
$545$	−13.3416			−0.571491
$546$		0			0
$547$	10.9289			0.467286			0.233643	−	0.972322i	$-0.424935\pi$
$547$	10.9289			0.467286			0.233643	+	0.972322i	$0.424935\pi$
$548$		0			0
$549$	−31.3696	+	6.86680i	−1.33882	+	0.293068i
$550$		0			0
$551$	3.75526			0.159980
$552$		0			0
$553$	−17.8249	−	5.42231i	−0.757991	−	0.230580i
$554$		0			0
$555$	−12.4071	+	15.4168i	−0.526652	+	0.654406i
$556$		0			0
$557$		−	30.9445i		−	1.31116i	−0.755125	−	0.655580i	$-0.772424\pi$
$557$		−	30.9445i		−	1.31116i	0.755125	−	0.655580i	$-0.227576\pi$
$558$		0			0
$559$		−	1.90481i		−	0.0805648i
$560$		0			0
$561$	−3.25840	−	2.62229i	−0.137570	−	0.110713i
$562$		0			0
$563$	6.97402			0.293920			0.146960	−	0.989142i	$-0.453051\pi$
$563$	6.97402			0.293920			0.146960	+	0.989142i	$0.453051\pi$
$564$		0			0
$565$			9.57195i			0.402695i
$566$		0			0
$567$	23.5929	−	3.22130i	0.990807	−	0.135282i
$568$		0			0
$569$			10.7199i			0.449400i	0.974428	+	0.224700i	$0.0721401\pi$
$569$			10.7199i			0.449400i	−0.974428	+	0.224700i	$0.927860\pi$
$570$		0			0
$571$	−8.89387			−0.372197			−0.186099	−	0.982531i	$-0.559584\pi$
$571$	−8.89387			−0.372197			−0.186099	+	0.982531i	$0.559584\pi$
$572$		0			0
$573$	−4.42751	−	3.56316i	−0.184962	−	0.148853i
$574$		0			0
$575$			6.09548i			0.254199i
$576$		0			0
$577$		−	24.7135i		−	1.02884i	−0.857540	−	0.514418i	$-0.828008\pi$
$577$		−	24.7135i		−	1.02884i	0.857540	−	0.514418i	$-0.171992\pi$
$578$		0			0
$579$	11.1077	−	13.8023i	0.461622	−	0.573602i
$580$		0			0
$581$	−16.9212	−	5.14740i	−0.702009	−	0.213550i
$582$		0			0
$583$	−6.92424			−0.286773
$584$		0			0
$585$	−3.19769	+	0.699976i	−0.132208	+	0.0289404i
$586$		0			0
$587$	40.9528			1.69030			0.845151	−	0.534528i	$-0.179511\pi$
$587$	40.9528			1.69030			0.845151	+	0.534528i	$0.179511\pi$
$588$		0			0
$589$	−17.4636			−0.719577
$590$		0			0
$591$	−1.22362	−	0.984745i	−0.0503331	−	0.0405070i
$592$		0			0
$593$	−34.9172			−1.43388			−0.716938	−	0.697137i	$-0.754457\pi$
$593$	−34.9172			−1.43388			−0.716938	+	0.697137i	$0.754457\pi$
$594$		0			0
$595$	−3.98377	−	1.21186i	−0.163319	−	0.0496813i
$596$		0			0
$597$	28.5922	+	23.0104i	1.17020	+	0.941753i
$598$		0			0
$599$			16.5174i			0.674882i	0.941347	+	0.337441i	$0.109561\pi$
$599$			16.5174i			0.674882i	−0.941347	+	0.337441i	$0.890439\pi$
$600$		0			0
$601$		−	9.90367i		−	0.403979i	−0.979388	−	0.201990i	$-0.935259\pi$
$601$		−	9.90367i		−	0.403979i	0.979388	−	0.201990i	$-0.0647407\pi$
$602$		0			0
$603$	2.36906	+	10.8226i	0.0964756	+	0.440729i
$604$		0			0
$605$	8.64586			0.351504
$606$		0			0
$607$			46.2519i			1.87731i	0.344863	+	0.938653i	$0.387925\pi$
$607$			46.2519i			1.87731i	−0.344863	+	0.938653i	$0.612075\pi$
$608$		0			0
$609$	2.23860	+	3.28733i	0.0907125	+	0.133209i
$610$		0			0
$611$		−	11.2901i		−	0.456748i
$612$		0			0
$613$	1.96567			0.0793927			0.0396963	−	0.999212i	$-0.487361\pi$
$613$	1.96567			0.0793927			0.0396963	+	0.999212i	$0.487361\pi$
$614$		0			0
$615$	2.93473	−	3.64663i	0.118340	−	0.147046i
$616$		0			0
$617$			36.6378i			1.47498i	0.675356	+	0.737492i	$0.263990\pi$
$617$			36.6378i			1.47498i	−0.675356	+	0.737492i	$0.736010\pi$
$618$		0			0
$619$			22.1198i			0.889071i	0.895761	+	0.444536i	$0.146631\pi$
$619$			22.1198i			0.889071i	−0.895761	+	0.444536i	$0.853369\pi$
$620$		0			0
$621$	−14.1221	+	28.3505i	−0.566700	+	1.13767i
$622$		0			0
$623$	10.4703	+	3.18505i	0.419484	+	0.127606i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−7.20932	+	8.95815i	−0.287913	+	0.357754i
$628$		0			0
$629$	17.9817			0.716978
$630$		0			0
$631$	23.5970			0.939383			0.469692	−	0.882830i	$-0.344365\pi$
$631$	23.5970			0.939383			0.469692	+	0.882830i	$0.344365\pi$
$632$		0			0
$633$	−12.4465	+	15.4658i	−0.494704	+	0.614709i
$634$		0			0
$635$	8.66734			0.343953
$636$		0			0
$637$	4.25332	−	6.34410i	0.168523	−	0.251362i
$638$		0			0
$639$	34.5801	−	7.56959i	1.36797	−	0.299448i
$640$		0			0
$641$		−	5.22645i		−	0.206432i	−0.994659	−	0.103216i	$-0.967087\pi$
$641$		−	5.22645i		−	0.206432i	0.994659	−	0.103216i	$-0.0329133\pi$
$642$		0			0
$643$			2.94341i			0.116077i	0.998314	+	0.0580384i	$0.0184846\pi$
$643$			2.94341i			0.116077i	−0.998314	+	0.0580384i	$0.981515\pi$
$644$		0			0
$645$	−1.89572	+	2.35558i	−0.0746439	+	0.0927509i
$646$		0			0
$647$	−19.4203			−0.763492			−0.381746	−	0.924267i	$-0.624677\pi$
$647$	−19.4203			−0.763492			−0.381746	+	0.924267i	$0.624677\pi$
$648$		0			0
$649$			4.17520i			0.163891i
$650$		0			0
$651$	−10.4105	−	15.2875i	−0.408018	−	0.599166i
$652$		0			0
$653$			33.2213i			1.30005i	0.759913	+	0.650025i	$0.225242\pi$
$653$			33.2213i			1.30005i	−0.759913	+	0.650025i	$0.774758\pi$
$654$		0			0
$655$	−7.48846			−0.292599
$656$		0			0
$657$	7.94980	−	1.74021i	0.310151	−	0.0678922i
$658$		0			0
$659$			13.4515i			0.523995i	0.965069	+	0.261998i	$0.0843812\pi$
$659$			13.4515i			0.523995i	−0.965069	+	0.261998i	$0.915619\pi$
$660$		0			0
$661$		−	22.8185i		−	0.887536i	−0.896142	−	0.443768i	$-0.853641\pi$
$661$		−	22.8185i		−	0.887536i	0.896142	−	0.443768i	$-0.146359\pi$
$662$		0			0
$663$	2.31722	+	1.86485i	0.0899935	+	0.0724248i
$664$		0			0
$665$	−3.33169	+	10.9524i	−0.129197	+	0.424714i
$666$		0			0
$667$	−5.29020			−0.204837
$668$		0			0
$669$	−6.35593	−	5.11512i	−0.245735	−	0.197762i
$670$		0			0
$671$	16.4235			0.634024
$672$		0			0
$673$	−11.1495			−0.429783			−0.214892	−	0.976638i	$-0.568940\pi$
$673$	−11.1495			−0.429783			−0.214892	+	0.976638i	$0.568940\pi$
$674$		0			0
$675$	4.65106	+	2.31681i	0.179019	+	0.0891741i
$676$		0			0
$677$	−1.38580			−0.0532605			−0.0266302	−	0.999645i	$-0.508478\pi$
$677$	−1.38580			−0.0532605			−0.0266302	+	0.999645i	$0.508478\pi$
$678$		0			0
$679$	13.0658	−	42.9517i	0.501421	−	1.64833i
$680$		0			0
$681$	−7.49535	+	9.31357i	−0.287223	+	0.356897i
$682$		0			0
$683$		−	50.1211i		−	1.91783i	−0.283695	−	0.958914i	$-0.591560\pi$
$683$		−	50.1211i		−	1.91783i	0.283695	−	0.958914i	$-0.408440\pi$
$684$		0			0
$685$			11.2768i			0.430866i
$686$		0			0
$687$	16.0378	+	12.9069i	0.611882	+	0.492429i
$688$		0			0
$689$	4.92419			0.187597
$690$		0			0
$691$		−	14.9423i		−	0.568431i	−0.958760	−	0.284216i	$-0.908267\pi$
$691$		−	14.9423i		−	0.568431i	0.958760	−	0.284216i	$-0.0917332\pi$
$692$		0			0
$693$	−12.1395	−	0.970835i	−0.461143	−	0.0368790i
$694$		0			0
$695$		−	5.95689i		−	0.225958i
$696$		0			0
$697$	−4.25333			−0.161106
$698$		0			0
$699$	−21.4481	−	17.2610i	−0.811243	−	0.652871i
$700$		0			0
$701$			4.15524i			0.156941i	0.996916	+	0.0784706i	$0.0250037\pi$
$701$			4.15524i			0.156941i	−0.996916	+	0.0784706i	$0.974996\pi$
$702$		0			0
$703$		−	49.4362i		−	1.86452i
$704$		0			0
$705$	−11.2362	+	13.9619i	−0.423180	+	0.525835i
$706$		0			0
$707$	−49.2531	−	14.9827i	−1.85235	−	0.563484i
$708$		0			0
$709$	−25.6215			−0.962236			−0.481118	−	0.876656i	$-0.659769\pi$
$709$	−25.6215			−0.962236			−0.481118	+	0.876656i	$0.659769\pi$
$710$		0			0
$711$	−4.51752	−	20.6373i	−0.169420	−	0.773960i
$712$		0			0
$713$	24.6018			0.921344
$714$		0			0
$715$	1.67415			0.0626098
$716$		0			0
$717$	−0.828226	−	0.666538i	−0.0309307	−	0.0248923i
$718$		0			0
$719$	−26.9307			−1.00435			−0.502173	−	0.864767i	$-0.667466\pi$
$719$	−26.9307			−1.00435			−0.502173	+	0.864767i	$0.667466\pi$
$720$		0			0
$721$	−10.0587	+	33.0661i	−0.374604	+	1.23145i
$722$		0			0
$723$	20.8580	+	16.7861i	0.775717	+	0.624280i
$724$		0			0
$725$			0.867889i			0.0322326i
$726$		0			0
$727$			19.1560i			0.710457i	0.934779	+	0.355229i	$0.115597\pi$
$727$			19.1560i			0.710457i	−0.934779	+	0.355229i	$0.884403\pi$
$728$		0			0
$729$	16.2648	+	21.5513i	0.602399	+	0.798195i
$730$		0			0
$731$	2.74748			0.101619
$732$		0			0
$733$		−	48.7421i		−	1.80033i	−0.435550	−	0.900165i	$-0.643446\pi$
$733$		−	48.7421i		−	1.80033i	0.435550	−	0.900165i	$-0.356554\pi$
$734$		0			0
$735$	−11.5737	+	3.61240i	−0.426902	+	0.133245i
$736$		0			0
$737$		−	5.66615i		−	0.208715i
$738$		0			0
$739$	11.8269			0.435058			0.217529	−	0.976054i	$-0.430200\pi$
$739$	11.8269			0.435058			0.217529	+	0.976054i	$0.430200\pi$
$740$		0			0
$741$	5.12693	−	6.37062i	0.188343	−	0.234030i
$742$		0			0
$743$		−	5.29633i		−	0.194303i	−0.995270	−	0.0971517i	$-0.969027\pi$
$743$		−	5.29633i		−	0.194303i	0.995270	−	0.0971517i	$-0.0309732\pi$
$744$		0			0
$745$		−	4.90815i		−	0.179821i
$746$		0			0
$747$	−4.28848	−	19.5910i	−0.156907	−	0.716798i
$748$		0			0
$749$	0.315457	−	1.03701i	0.0115265	−	0.0378915i
$750$		0			0
$751$	37.4873			1.36793			0.683966	−	0.729514i	$-0.260254\pi$
$751$	37.4873			1.36793			0.683966	+	0.729514i	$0.260254\pi$
$752$		0			0
$753$	14.7966	−	18.3860i	0.539218	−	0.670021i
$754$		0			0
$755$	17.9251			0.652361
$756$		0			0
$757$	16.5354			0.600990			0.300495	−	0.953783i	$-0.402848\pi$
$757$	16.5354			0.600990			0.300495	+	0.953783i	$0.402848\pi$
$758$		0			0
$759$	10.1561	−	12.6197i	0.368642	−	0.458067i
$760$		0			0
$761$	−40.4921			−1.46784			−0.733918	−	0.679238i	$-0.762310\pi$
$761$	−40.4921			−1.46784			−0.733918	+	0.679238i	$0.762310\pi$
$762$		0			0
$763$	33.7706	+	10.2730i	1.22258	+	0.371906i
$764$		0			0
$765$	−1.00964	−	4.61233i	−0.0365037	−	0.166759i
$766$		0			0
$767$		−	2.96920i		−	0.107212i
$768$		0			0
$769$		−	40.8507i		−	1.47311i	−0.676376	−	0.736556i	$-0.736451\pi$
$769$		−	40.8507i		−	1.47311i	0.676376	−	0.736556i	$-0.263549\pi$
$770$		0			0
$771$	3.12267	−	3.88017i	0.112460	−	0.139741i
$772$		0			0
$773$	41.5333			1.49385			0.746924	−	0.664909i	$-0.231530\pi$
$773$	41.5333			1.49385			0.746924	+	0.664909i	$0.231530\pi$
$774$		0			0
$775$		−	4.03607i		−	0.144980i
$776$		0			0
$777$	43.2760	−	29.4700i	1.55252	−	1.05723i
$778$		0			0
$779$			11.6934i			0.418961i
$780$		0			0
$781$	−18.1044			−0.647826
$782$		0			0
$783$	−2.01073	+	4.03661i	−0.0718578	+	0.144257i
$784$		0			0
$785$			11.9270i			0.425692i
$786$		0			0
$787$			18.9154i			0.674263i	0.941458	+	0.337131i	$0.109457\pi$
$787$			18.9154i			0.674263i	−0.941458	+	0.337131i	$0.890543\pi$
$788$		0			0
$789$	39.9032	+	32.1132i	1.42059	+	1.14326i
$790$		0			0
$791$	7.37036	−	24.2288i	0.262060	−	0.861476i
$792$		0			0
$793$	−11.6797			−0.414757
$794$		0			0
$795$	−6.08950	−	4.90070i	−0.215972	−	0.173810i
$796$		0			0
$797$	−15.3516			−0.543780			−0.271890	−	0.962328i	$-0.587649\pi$
$797$	−15.3516			−0.543780			−0.271890	+	0.962328i	$0.587649\pi$
$798$		0			0
$799$	16.2848			0.576113
$800$		0			0
$801$	2.65358	+	12.1223i	0.0937597	+	0.428322i
$802$		0			0
$803$	−4.16212			−0.146878
$804$		0			0
$805$	4.69349	−	15.4290i	0.165424	−	0.543802i
$806$		0			0
$807$	16.9017	−	21.0016i	0.594966	−	0.739292i
$808$		0			0
$809$			41.6642i			1.46483i	0.680856	+	0.732417i	$0.261608\pi$
$809$			41.6642i			1.46483i	−0.680856	+	0.732417i	$0.738392\pi$
$810$		0			0
$811$		−	54.4198i		−	1.91094i	−0.295091	−	0.955469i	$-0.595350\pi$
$811$		−	54.4198i		−	1.91094i	0.295091	−	0.955469i	$-0.404650\pi$
$812$		0			0
$813$	−14.5156	−	11.6819i	−0.509086	−	0.409701i
$814$		0			0
$815$	−17.6018			−0.616565
$816$		0			0
$817$		−	7.55350i		−	0.264264i
$818$		0			0
$819$	8.63307	+	0.690413i	0.301664	+	0.0241250i
$820$		0			0
$821$			44.8506i			1.56530i	0.622463	+	0.782649i	$0.286132\pi$
$821$			44.8506i			1.56530i	−0.622463	+	0.782649i	$0.713868\pi$
$822$		0			0
$823$	11.2429			0.391904			0.195952	−	0.980614i	$-0.437220\pi$
$823$	11.2429			0.391904			0.195952	+	0.980614i	$0.437220\pi$
$824$		0			0
$825$	−2.07034	−	1.66616i	−0.0720800	−	0.0580084i
$826$		0			0
$827$			20.1971i			0.702322i	0.936315	+	0.351161i	$0.114213\pi$
$827$			20.1971i			0.702322i	−0.936315	+	0.351161i	$0.885787\pi$
$828$		0			0
$829$			38.1151i			1.32379i	0.749596	+	0.661895i	$0.230248\pi$
$829$			38.1151i			1.32379i	−0.749596	+	0.661895i	$0.769752\pi$
$830$		0			0
$831$	24.8725	−	30.9061i	0.862819	−	1.07212i
$832$		0			0
$833$	9.15070	+	6.13497i	0.317053	+	0.212564i
$834$		0			0
$835$	25.1048			0.868786
$836$		0			0
$837$	9.35081	−	18.7720i	0.323211	−	0.648855i
$838$		0			0
$839$	−26.9797			−0.931444			−0.465722	−	0.884931i	$-0.654205\pi$
$839$	−26.9797			−0.931444			−0.465722	+	0.884931i	$0.654205\pi$
$840$		0			0
$841$	28.2468			0.974027
$842$		0			0
$843$	−2.08460	−	1.67764i	−0.0717975	−	0.0577811i
$844$		0			0
$845$	11.8094			0.406256
$846$		0			0
$847$	−21.8846	−	6.65727i	−0.751965	−	0.228747i
$848$		0			0
$849$	−18.6744	−	15.0287i	−0.640902	−	0.515784i
$850$		0			0
$851$			69.6428i			2.38733i
$852$		0			0
$853$		−	17.5403i		−	0.600570i	−0.953850	−	0.300285i	$-0.902918\pi$
$853$		−	17.5403i		−	0.600570i	0.953850	−	0.300285i	$-0.0970817\pi$
$854$		0			0
$855$	−12.6804	+	2.77575i	−0.433662	+	0.0949287i
$856$		0			0
$857$	37.3123			1.27456			0.637282	−	0.770631i	$-0.280059\pi$
$857$	37.3123			1.27456			0.637282	+	0.770631i	$0.280059\pi$
$858$		0			0
$859$			49.6194i			1.69299i	0.532394	+	0.846497i	$0.321292\pi$
$859$			49.6194i			1.69299i	−0.532394	+	0.846497i	$0.678708\pi$
$860$		0			0
$861$	−10.2363	+	6.97072i	−0.348854	+	0.237561i
$862$		0			0
$863$			26.1184i			0.889080i	0.895759	+	0.444540i	$0.146633\pi$
$863$			26.1184i			0.889080i	−0.895759	+	0.444540i	$0.853367\pi$
$864$		0			0
$865$	10.4879			0.356600
$866$		0			0
$867$	15.7710	−	19.5967i	0.535610	−	0.665538i
$868$		0			0
$869$			10.8047i			0.366524i
$870$		0			0
$871$			4.02950i			0.136535i
$872$		0			0
$873$	49.7287	−	10.8856i	1.68306	−	0.368422i
$874$		0			0
$875$	−2.53123	−	0.769995i	−0.0855711	−	0.0260306i
$876$		0			0
$877$	−27.5345			−0.929773			−0.464887	−	0.885370i	$-0.653905\pi$
$877$	−27.5345			−0.929773			−0.464887	+	0.885370i	$0.653905\pi$
$878$		0			0
$879$	−12.9463	+	16.0868i	−0.436668	+	0.542595i
$880$		0			0
$881$	−35.4312			−1.19371			−0.596854	−	0.802350i	$-0.703583\pi$
$881$	−35.4312			−1.19371			−0.596854	+	0.802350i	$0.703583\pi$
$882$		0			0
$883$	12.2636			0.412703			0.206351	−	0.978478i	$-0.433841\pi$
$883$	12.2636			0.412703			0.206351	+	0.978478i	$0.433841\pi$
$884$		0			0
$885$	−2.95504	+	3.67187i	−0.0993325	+	0.123428i
$886$		0			0
$887$	−37.8263			−1.27008			−0.635041	−	0.772478i	$-0.719017\pi$
$887$	−37.8263			−1.27008			−0.635041	+	0.772478i	$0.719017\pi$
$888$		0			0
$889$	−21.9390	−	6.67381i	−0.735811	−	0.223833i
$890$		0			0
$891$	−5.76910	−	12.5460i	−0.193272	−	0.420308i
$892$		0			0
$893$		−	44.7708i		−	1.49820i
$894$		0			0
$895$		−	21.6843i		−	0.724825i
$896$		0			0
$897$	−7.22253	+	8.97456i	−0.241153	+	0.299652i
$898$		0			0
$899$	3.50286			0.116827
$900$		0			0
$901$			7.10263i			0.236623i
$902$		0			0
$903$	6.61228	−	4.50281i	0.220043	−	0.149844i
$904$		0			0
$905$			6.48943i			0.215716i
$906$		0			0
$907$	−9.93839			−0.329999			−0.164999	−	0.986294i	$-0.552762\pi$
$907$	−9.93839			−0.329999			−0.164999	+	0.986294i	$0.552762\pi$
$908$		0			0
$909$	−12.4827	−	57.0244i	−0.414023	−	1.89138i
$910$		0			0
$911$			5.48580i			0.181753i	0.995862	+	0.0908764i	$0.0289668\pi$
$911$			5.48580i			0.181753i	−0.995862	+	0.0908764i	$0.971033\pi$
$912$		0			0
$913$			10.2569i			0.339453i
$914$		0			0
$915$	14.4436	+	11.6239i	0.477492	+	0.384275i
$916$		0			0
$917$	18.9550	+	5.76608i	0.625949	+	0.190413i
$918$		0			0
$919$	−19.4292			−0.640911			−0.320456	−	0.947264i	$-0.603836\pi$
$919$	−19.4292			−0.640911			−0.320456	+	0.947264i	$0.603836\pi$
$920$		0			0
$921$	34.1066	+	27.4483i	1.12385	+	0.904452i
$922$		0			0
$923$	12.8750			0.423786
$924$		0			0
$925$	11.4253			0.375662
$926$		0			0
$927$	−38.2834	+	8.38024i	−1.25739	+	0.275243i
$928$		0			0
$929$	11.3268			0.371622			0.185811	−	0.982586i	$-0.440509\pi$
$929$	11.3268			0.371622			0.185811	+	0.982586i	$0.440509\pi$
$930$		0			0
$931$	16.8665	−	25.1575i	0.552778	−	0.824504i
$932$		0			0
$933$	−18.0709	+	22.4545i	−0.591616	+	0.735129i
$934$		0			0
$935$			2.41479i			0.0789720i
$936$		0			0
$937$			49.6626i			1.62241i	0.584764	+	0.811203i	$0.301187\pi$
$937$			49.6626i			1.62241i	−0.584764	+	0.811203i	$0.698813\pi$
$938$		0			0
$939$	42.6846	+	34.3517i	1.39296	+	1.12102i
$940$		0			0
$941$	−20.4749			−0.667464			−0.333732	−	0.942668i	$-0.608308\pi$
$941$	−20.4749			−0.667464			−0.333732	+	0.942668i	$0.608308\pi$
$942$		0			0
$943$		−	16.4730i		−	0.536436i
$944$		0			0
$945$	−9.98896	−	9.44567i	−0.324941	−	0.307268i
$946$		0			0
$947$			47.1306i			1.53154i	0.643115	+	0.765770i	$0.277642\pi$
$947$			47.1306i			1.53154i	−0.643115	+	0.765770i	$0.722358\pi$
$948$		0			0
$949$	2.95990			0.0960826
$950$		0			0
$951$	39.3861	+	31.6971i	1.27718	+	1.02785i
$952$		0			0
$953$			28.3599i			0.918669i	0.888263	+	0.459334i	$0.151912\pi$
$953$			28.3599i			0.918669i	−0.888263	+	0.459334i	$0.848088\pi$
$954$		0			0
$955$			3.28120i			0.106177i
$956$		0			0
$957$	1.44605	−	1.79683i	0.0467440	−	0.0580831i
$958$		0			0
$959$	8.68311	−	28.5442i	0.280392	−	0.921741i
$960$		0			0
$961$	14.7102			0.474521
$962$		0			0
$963$	1.20063	−	0.262818i	0.0386898	−	0.00846920i
$964$		0			0
$965$	−10.2288			−0.329276
$966$		0			0
$967$	−21.0726			−0.677650			−0.338825	−	0.940849i	$-0.610029\pi$
$967$	−21.0726			−0.677650			−0.338825	+	0.940849i	$0.610029\pi$
$968$		0			0
$969$	9.18894	+	7.39506i	0.295191	+	0.237563i
$970$		0			0
$971$	−10.0620			−0.322905			−0.161452	−	0.986880i	$-0.551618\pi$
$971$	−10.0620			−0.322905			−0.161452	+	0.986880i	$0.551618\pi$
$972$		0			0
$973$	−4.58678	+	15.0782i	−0.147045	+	0.483386i
$974$		0			0
$975$	1.47233	+	1.18490i	0.0471523	+	0.0379471i
$976$		0			0
$977$			46.0967i			1.47476i	0.675476	+	0.737382i	$0.263938\pi$
$977$			46.0967i			1.47476i	−0.675476	+	0.737382i	$0.736062\pi$
$978$		0			0
$979$		−	6.34665i		−	0.202840i
$980$		0			0
$981$	8.55877	+	39.0990i	0.273261	+	1.24833i
$982$		0			0
$983$	−7.74364			−0.246984			−0.123492	−	0.992346i	$-0.539409\pi$
$983$	−7.74364			−0.246984			−0.123492	+	0.992346i	$0.539409\pi$
$984$		0			0
$985$			0.906822i			0.0288937i
$986$		0			0
$987$	39.1920	−	26.6888i	1.24749	−	0.849515i
$988$		0			0
$989$			10.6409i			0.338362i
$990$		0			0
$991$	−34.4156			−1.09325			−0.546624	−	0.837378i	$-0.684087\pi$
$991$	−34.4156			−1.09325			−0.546624	+	0.837378i	$0.684087\pi$
$992$		0			0
$993$	9.32259	−	11.5840i	0.295843	−	0.367609i
$994$		0			0
$995$		−	21.1896i		−	0.671754i
$996$		0			0
$997$		−	52.5355i		−	1.66382i	−0.554913	−	0.831908i	$-0.687249\pi$
$997$		−	52.5355i		−	1.66382i	0.554913	−	0.831908i	$-0.312751\pi$
$998$		0			0
$999$	53.1399	+	26.4703i	1.68127	+	0.837483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.f.l.881.6		16
3.2	odd	2		1680.2.f.k.881.12		16
4.3	odd	2		840.2.f.b.41.11	yes	16
7.6	odd	2		1680.2.f.k.881.11		16
12.11	even	2		840.2.f.a.41.5	✓	16
21.20	even	2	inner	1680.2.f.l.881.5		16
28.27	even	2		840.2.f.a.41.6	yes	16
84.83	odd	2		840.2.f.b.41.12	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.f.a.41.5	✓	16	12.11	even	2
840.2.f.a.41.6	yes	16	28.27	even	2
840.2.f.b.41.11	yes	16	4.3	odd	2
840.2.f.b.41.12	yes	16	84.83	odd	2
1680.2.f.k.881.11		16	7.6	odd	2
1680.2.f.k.881.12		16	3.2	odd	2
1680.2.f.l.881.5		16	21.20	even	2	inner
1680.2.f.l.881.6		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.08593 + 1.34935i) q^{3} +1.00000 q^{5} +(-2.53123 - 0.769995i) q^{7} +(-0.641511 - 2.93061i) q^{9} +O(q^{10})\)	\(q+(-1.08593 + 1.34935i) q^{3} +1.00000 q^{5} +(-2.53123 - 0.769995i) q^{7} +(-0.641511 - 2.93061i) q^{9} +1.53432i q^{11} -1.09114i q^{13} +(-1.08593 + 1.34935i) q^{15} +1.57385 q^{17} -4.32690i q^{19} +(3.78773 - 2.57936i) q^{21} +6.09548i q^{23} +1.00000 q^{25} +(4.65106 + 2.31681i) q^{27} +0.867889i q^{29} -4.03607i q^{31} +(-2.07034 - 1.66616i) q^{33} +(-2.53123 - 0.769995i) q^{35} +11.4253 q^{37} +(1.47233 + 1.18490i) q^{39} -2.70250 q^{41} +1.74571 q^{43} +(-0.641511 - 2.93061i) q^{45} +10.3471 q^{47} +(5.81421 + 3.89807i) q^{49} +(-1.70909 + 2.12368i) q^{51} +4.51290i q^{53} +1.53432i q^{55} +(5.83851 + 4.69871i) q^{57} +2.72120 q^{59} -10.7041i q^{61} +(-0.632746 + 7.91199i) q^{63} -1.09114i q^{65} -3.69294 q^{67} +(-8.22496 - 6.61927i) q^{69} +11.7996i q^{71} +2.71268i q^{73} +(-1.08593 + 1.34935i) q^{75} +(1.18142 - 3.88371i) q^{77} +7.04200 q^{79} +(-8.17693 + 3.76003i) q^{81} +6.68497 q^{83} +1.57385 q^{85} +(-1.17109 - 0.942467i) q^{87} -4.13646 q^{89} +(-0.840170 + 2.76191i) q^{91} +(5.44608 + 4.38289i) q^{93} -4.32690i q^{95} +16.9687i q^{97} +(4.49649 - 0.984283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{5} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 16 * q + 16 * q^5 - 2 * q^7 - 2 * q^9	\( 16 q + 16 q^{5} - 2 q^{7} - 2 q^{9} + 10 q^{21} + 16 q^{25} - 6 q^{27} + 6 q^{33} - 2 q^{35} + 12 q^{37} - 6 q^{39} + 32 q^{41} - 32 q^{43} - 2 q^{45} - 4 q^{47} - 4 q^{49} - 6 q^{51} + 24 q^{59} + 24 q^{63} + 8 q^{69} - 32 q^{77} + 4 q^{79} - 6 q^{81} - 20 q^{83} - 6 q^{87} - 24 q^{89} - 20 q^{91} - 32 q^{93} + 58 q^{99}+O(q^{100}) \) 16 * q + 16 * q^5 - 2 * q^7 - 2 * q^9 + 10 * 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 + 24 * 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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