LMFDB - Embedded newform 945.2.b.d.566.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(566,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("945.566");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.b (of order $2$, degree $1$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20x^{10} + 144x^{8} + 446x^{6} + 532x^{4} + 132x^{2} + 9 $ x^12 + 20x^10 + 144x^8 + 446x^6 + 532x^4 + 132*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			566.1
Root			$-2.76021i$ of defining polynomial
Character	$\chi$	$=$	945.566
Dual form			945.2.b.d.566.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76021i q^{2} -5.61875 q^{4} +1.00000 q^{5} +(-0.00652987 - 2.64574i) q^{7} +9.98851i q^{8} +O(q^{10})$	\(q-2.76021i q^{2} -5.61875 q^{4} +1.00000 q^{5} +(-0.00652987 - 2.64574i) q^{7} +9.98851i q^{8} -2.76021i q^{10} -4.51734i q^{11} -3.02369i q^{13} +(-7.30280 + 0.0180238i) q^{14} +16.3329 q^{16} -5.34602 q^{17} -2.84400i q^{19} -5.61875 q^{20} -12.4688 q^{22} +2.20030i q^{23} +1.00000 q^{25} -8.34602 q^{26} +(0.0366897 + 14.8658i) q^{28} +5.09860i q^{29} +7.68467i q^{31} -25.1051i q^{32} +14.7561i q^{34} +(-0.00652987 - 2.64574i) q^{35} +1.38116 q^{37} -7.85004 q^{38} +9.98851i q^{40} -9.70107 q^{41} +0.136811 q^{43} +25.3818i q^{44} +6.07329 q^{46} -0.149871 q^{47} +(-6.99991 + 0.0345527i) q^{49} -2.76021i q^{50} +16.9894i q^{52} -5.09355i q^{53} -4.51734i q^{55} +(26.4270 - 0.0652237i) q^{56} +14.0732 q^{58} +1.39422 q^{59} -7.68467i q^{61} +21.2113 q^{62} -36.6296 q^{64} -3.02369i q^{65} +12.5422 q^{67} +30.0380 q^{68} +(-7.30280 + 0.0180238i) q^{70} +10.8119i q^{71} -7.91866i q^{73} -3.81230i q^{74} +15.9798i q^{76} +(-11.9517 + 0.0294976i) q^{77} -1.95180 q^{79} +16.3329 q^{80} +26.7770i q^{82} -15.0052 q^{83} -5.34602 q^{85} -0.377628i q^{86} +45.1215 q^{88} -13.6538 q^{89} +(-7.99991 + 0.0197443i) q^{91} -12.3630i q^{92} +0.413676i q^{94} -2.84400i q^{95} -8.74331i q^{97} +(0.0953727 + 19.3212i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 16 q^{4} + 12 q^{5} - 2 q^{7}+O(q^{10}) $ 12 * q - 16 * q^4 + 12 * q^5 - 2 * q^7	$ 12 q - 16 q^{4} + 12 q^{5} - 2 q^{7} - 12 q^{14} + 32 q^{16} - 16 q^{20} - 4 q^{22} + 12 q^{25} - 36 q^{26} + 10 q^{28} - 2 q^{35} - 28 q^{37} - 4 q^{43} - 4 q^{46} + 12 q^{49} + 54 q^{56} - 4 q^{58} - 24 q^{59} + 48 q^{62} - 20 q^{64} + 24 q^{67} + 72 q^{68} - 12 q^{70} - 24 q^{77} + 32 q^{80} - 48 q^{83} + 64 q^{88} - 36 q^{89} - 60 q^{98}+O(q^{100}) $ 12 * q - 16 * q^4 + 12 * q^5 - 2 * q^7 - 12 * q^14 + 32 * q^16 - 16 * q^20 - 4 * q^22 + 12 * q^25 - 36 * q^26 + 10 * q^28 - 2 * q^35 - 28 * q^37 - 4 * q^43 - 4 * q^46 + 12 * q^49 + 54 * q^56 - 4 * q^58 - 24 * q^59 + 48 * q^62 - 20 * q^64 + 24 * q^67 + 72 * q^68 - 12 * q^70 - 24 * q^77 + 32 * q^80 - 48 * q^83 + 64 * q^88 - 36 * q^89 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	2.76021i		−	1.95176i	−0.218302	−	0.975881i	$-0.570052\pi$
$2$		−	2.76021i		−	1.95176i	0.218302	−	0.975881i	$-0.429948\pi$
$3$		0			0
$3$		0			0
$4$	−5.61875			−2.80938
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−0.00652987	−	2.64574i	−0.00246806	−	0.999997i
$7$	−0.00652987	−	2.64574i	−0.00246806	−	0.999997i
$8$			9.98851i			3.53147i
$9$		0			0
$10$		−	2.76021i		−	0.872855i
$11$		−	4.51734i		−	1.36203i	−0.732270	−	0.681014i	$-0.761539\pi$
$11$		−	4.51734i		−	1.36203i	0.732270	−	0.681014i	$-0.238461\pi$
$12$		0			0
$13$		−	3.02369i		−	0.838621i	−0.907843	−	0.419311i	$-0.862272\pi$
$13$		−	3.02369i		−	0.838621i	0.907843	−	0.419311i	$-0.137728\pi$
$14$	−7.30280	+	0.0180238i	−1.95176	+	0.00481706i
$15$		0			0
$16$	16.3329			4.08322
$17$	−5.34602			−1.29660			−0.648301	−	0.761385i	$-0.724520\pi$
$17$	−5.34602			−1.29660			−0.648301	+	0.761385i	$0.724520\pi$
$18$		0			0
$19$		−	2.84400i		−	0.652459i	−0.945291	−	0.326230i	$-0.894222\pi$
$19$		−	2.84400i		−	0.652459i	0.945291	−	0.326230i	$-0.105778\pi$
$20$	−5.61875			−1.25639
$21$		0			0
$22$	−12.4688			−2.65836
$23$			2.20030i			0.458795i	0.973333	+	0.229397i	$0.0736755\pi$
$23$			2.20030i			0.458795i	−0.973333	+	0.229397i	$0.926324\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−8.34602			−1.63679
$27$		0			0
$28$	0.0366897	+	14.8658i	0.00693370	+	2.80937i
$29$			5.09860i			0.946787i	0.880851	+	0.473393i	$0.156971\pi$
$29$			5.09860i			0.946787i	−0.880851	+	0.473393i	$0.843029\pi$
$30$		0			0
$31$			7.68467i			1.38021i	0.723710	+	0.690104i	$0.242435\pi$
$31$			7.68467i			1.38021i	−0.723710	+	0.690104i	$0.757565\pi$
$32$		−	25.1051i		−	4.43800i
$33$		0			0
$34$			14.7561i			2.53066i
$35$	−0.00652987	−	2.64574i	−0.00110375	−	0.447212i
$36$		0			0
$37$	1.38116			0.227062			0.113531	−	0.993534i	$-0.463784\pi$
$37$	1.38116			0.227062			0.113531	+	0.993534i	$0.463784\pi$
$38$	−7.85004			−1.27345
$39$		0			0
$40$			9.98851i			1.57932i
$41$	−9.70107			−1.51505			−0.757526	−	0.652805i	$-0.773592\pi$
$41$	−9.70107			−1.51505			−0.757526	+	0.652805i	$0.773592\pi$
$42$		0			0
$43$	0.136811			0.0208635			0.0104318	−	0.999946i	$-0.496679\pi$
$43$	0.136811			0.0208635			0.0104318	+	0.999946i	$0.496679\pi$
$44$			25.3818i			3.82645i
$45$		0			0
$46$	6.07329			0.895458
$47$	−0.149871			−0.0218609			−0.0109305	−	0.999940i	$-0.503479\pi$
$47$	−0.149871			−0.0218609			−0.0109305	+	0.999940i	$0.503479\pi$
$48$		0			0
$49$	−6.99991	+	0.0345527i	−0.999988	+	0.00493610i
$50$		−	2.76021i		−	0.390352i
$51$		0			0
$52$			16.9894i			2.35600i
$53$		−	5.09355i		−	0.699653i	−0.936815	−	0.349826i	$-0.886241\pi$
$53$		−	5.09355i		−	0.699653i	0.936815	−	0.349826i	$-0.113759\pi$
$54$		0			0
$55$		−	4.51734i		−	0.609118i
$56$	26.4270	−	0.0652237i	3.53146	−	0.00871588i
$57$		0			0
$58$	14.0732			1.84790
$59$	1.39422			0.181512			0.0907561	−	0.995873i	$-0.471072\pi$
$59$	1.39422			0.181512			0.0907561	+	0.995873i	$0.471072\pi$
$60$		0			0
$61$		−	7.68467i		−	0.983921i	−0.870617	−	0.491961i	$-0.836280\pi$
$61$		−	7.68467i		−	0.983921i	0.870617	−	0.491961i	$-0.163720\pi$
$62$	21.2113			2.69384
$63$		0			0
$64$	−36.6296			−4.57871
$65$		−	3.02369i		−	0.375043i
$66$		0			0
$67$	12.5422			1.53227			0.766135	−	0.642679i	$-0.222177\pi$
$67$	12.5422			1.53227			0.766135	+	0.642679i	$0.222177\pi$
$68$	30.0380			3.64264
$69$		0			0
$70$	−7.30280	+	0.0180238i	−0.872852	+	0.00215426i
$71$			10.8119i			1.28314i	0.767066	+	0.641568i	$0.221716\pi$
$71$			10.8119i			1.28314i	−0.767066	+	0.641568i	$0.778284\pi$
$72$		0			0
$73$		−	7.91866i		−	0.926809i	−0.886147	−	0.463404i	$-0.846628\pi$
$73$		−	7.91866i		−	0.926809i	0.886147	−	0.463404i	$-0.153372\pi$
$74$		−	3.81230i		−	0.443170i
$75$		0			0
$76$			15.9798i			1.83300i
$77$	−11.9517	+	0.0294976i	−1.36202	+	0.00336157i
$78$		0			0
$79$	−1.95180			−0.219595			−0.109797	−	0.993954i	$-0.535020\pi$
$79$	−1.95180			−0.219595			−0.109797	+	0.993954i	$0.535020\pi$
$80$	16.3329			1.82607
$81$		0			0
$82$			26.7770i			2.95702i
$83$	−15.0052			−1.64704			−0.823519	−	0.567288i	$-0.807993\pi$
$83$	−15.0052			−1.64704			−0.823519	+	0.567288i	$0.807993\pi$
$84$		0			0
$85$	−5.34602			−0.579858
$86$		−	0.377628i		−	0.0407207i
$87$		0			0
$88$	45.1215			4.80997
$89$	−13.6538			−1.44730			−0.723650	−	0.690167i	$-0.757537\pi$
$89$	−13.6538			−1.44730			−0.723650	+	0.690167i	$0.757537\pi$
$90$		0			0
$91$	−7.99991	+	0.0197443i	−0.838619	+	0.00206977i
$92$		−	12.3630i		−	1.28893i
$93$		0			0
$94$			0.413676i			0.0426674i
$95$		−	2.84400i		−	0.291789i
$96$		0			0
$97$		−	8.74331i		−	0.887748i	−0.896089	−	0.443874i	$-0.853604\pi$
$97$		−	8.74331i		−	0.887748i	0.896089	−	0.443874i	$-0.146396\pi$
$98$	0.0953727	+	19.3212i	0.00963410	+	1.95174i
$99$		0			0
$100$	−5.61875			−0.561875
$101$	12.1159			1.20558			0.602790	−	0.797900i	$-0.294056\pi$
$101$	12.1159			1.20558			0.602790	+	0.797900i	$0.294056\pi$
$102$		0			0
$103$		−	8.74331i		−	0.861504i	−0.902470	−	0.430752i	$-0.858248\pi$
$103$		−	8.74331i		−	0.861504i	0.902470	−	0.430752i	$-0.141752\pi$
$104$	30.2022			2.96157
$105$		0			0
$106$	−14.0593			−1.36556
$107$		−	9.84893i		−	0.952132i	−0.879410	−	0.476066i	$-0.842062\pi$
$107$		−	9.84893i		−	0.952132i	0.879410	−	0.476066i	$-0.157938\pi$
$108$		0			0
$109$	9.93776			0.951865			0.475933	−	0.879482i	$-0.342111\pi$
$109$	9.93776			0.951865			0.475933	+	0.879482i	$0.342111\pi$
$110$	−12.4688			−1.18885
$111$		0			0
$112$	−0.106652	−	43.2126i	−0.0100776	−	4.08321i
$113$			1.07888i			0.101492i	0.998712	+	0.0507460i	$0.0161599\pi$
$113$			1.07888i			0.101492i	−0.998712	+	0.0507460i	$0.983840\pi$
$114$		0			0
$115$			2.20030i			0.205179i
$116$		−	28.6478i		−	2.65988i
$117$		0			0
$118$		−	3.84834i		−	0.354269i
$119$	0.0349088	+	14.1442i	0.00320009	+	1.29660i
$120$		0			0
$121$	−9.40634			−0.855122
$122$	−21.2113			−1.92038
$123$		0			0
$124$		−	43.1783i		−	3.87752i
$125$	1.00000			0.0894427
$126$		0			0
$127$	13.3140			1.18143			0.590713	−	0.806882i	$-0.298847\pi$
$127$	13.3140			1.18143			0.590713	+	0.806882i	$0.298847\pi$
$128$			50.8952i			4.49854i
$129$		0			0
$130$	−8.34602			−0.731995
$131$	−2.04726			−0.178870			−0.0894350	−	0.995993i	$-0.528506\pi$
$131$	−2.04726			−0.178870			−0.0894350	+	0.995993i	$0.528506\pi$
$132$		0			0
$133$	−7.52450	+	0.0185710i	−0.652457	+	0.00161031i
$134$		−	34.6190i		−	2.99063i
$135$		0			0
$136$		−	53.3988i		−	4.57891i
$137$			1.61579i			0.138046i	0.997615	+	0.0690231i	$0.0219882\pi$
$137$			1.61579i			0.138046i	−0.997615	+	0.0690231i	$0.978012\pi$
$138$		0			0
$139$		−	5.97828i		−	0.507071i	−0.967326	−	0.253536i	$-0.918407\pi$
$139$		−	5.97828i		−	0.507071i	0.967326	−	0.253536i	$-0.0815935\pi$
$140$	0.0366897	+	14.8658i	0.00310085	+	1.25639i
$141$		0			0
$142$	29.8431			2.50438
$143$	−13.6590			−1.14223
$144$		0			0
$145$			5.09860i			0.423416i
$146$	−21.8572			−1.80891
$147$		0			0
$148$	−7.76041			−0.637902
$149$		−	10.3540i		−	0.848236i	−0.905607	−	0.424118i	$-0.860584\pi$
$149$		−	10.3540i		−	0.848236i	0.905607	−	0.424118i	$-0.139416\pi$
$150$		0			0
$151$	−22.2735			−1.81259			−0.906294	−	0.422648i	$-0.861101\pi$
$151$	−22.2735			−1.81259			−0.906294	+	0.422648i	$0.861101\pi$
$152$	28.4074			2.30414
$153$		0			0
$154$	0.0814196	+	32.9892i	0.00656098	+	2.65835i
$155$			7.68467i			0.617248i
$156$		0			0
$157$		−	8.23819i		−	0.657479i	−0.944421	−	0.328740i	$-0.893376\pi$
$157$		−	8.23819i		−	0.657479i	0.944421	−	0.328740i	$-0.106624\pi$
$158$			5.38738i			0.428597i
$159$		0			0
$160$		−	25.1051i		−	1.98473i
$161$	5.82144	−	0.0143677i	0.458793	−	0.00113233i
$162$		0			0
$163$	23.8562			1.86856			0.934280	−	0.356541i	$-0.116044\pi$
$163$	23.8562			1.86856			0.934280	+	0.356541i	$0.116044\pi$
$164$	54.5079			4.25635
$165$		0			0
$166$			41.4176i			3.21463i
$167$	15.1551			1.17274			0.586369	−	0.810044i	$-0.300557\pi$
$167$	15.1551			1.17274			0.586369	+	0.810044i	$0.300557\pi$
$168$		0			0
$169$	3.85728			0.296714
$170$			14.7561i			1.13174i
$171$		0			0
$172$	−0.768709			−0.0586135
$173$	6.84472			0.520395			0.260197	−	0.965555i	$-0.416212\pi$
$173$	6.84472			0.520395			0.260197	+	0.965555i	$0.416212\pi$
$174$		0			0
$175$	−0.00652987	−	2.64574i	−0.000493612	−	0.199999i
$176$		−	73.7811i		−	5.56146i
$177$		0			0
$178$			37.6874i			2.82479i
$179$		−	5.17884i		−	0.387084i	−0.981092	−	0.193542i	$-0.938002\pi$
$179$		−	5.17884i		−	0.387084i	0.981092	−	0.193542i	$-0.0619977\pi$
$180$		0			0
$181$		−	0.484867i		−	0.0360399i	−0.999838	−	0.0180200i	$-0.994264\pi$
$181$		−	0.484867i		−	0.0360399i	0.999838	−	0.0180200i	$-0.00573624\pi$
$182$	0.0544984	+	22.0814i	0.00403969	+	1.63678i
$183$		0			0
$184$	−21.9778			−1.62022
$185$	1.38116			0.101545
$186$		0			0
$187$			24.1498i			1.76601i
$188$	0.842089			0.0614156
$189$		0			0
$190$	−7.85004			−0.569502
$191$			2.94790i			0.213302i	0.994296	+	0.106651i	$0.0340128\pi$
$191$			2.94790i			0.213302i	−0.994296	+	0.106651i	$0.965987\pi$
$192$		0			0
$193$	−15.0229			−1.08137			−0.540686	−	0.841225i	$-0.681835\pi$
$193$	−15.0229			−1.08137			−0.540686	+	0.841225i	$0.681835\pi$
$194$	−24.1334			−1.73267
$195$		0			0
$196$	39.3308	−	0.194143i	2.80934	−	0.0138674i
$197$		−	13.2631i		−	0.944956i	−0.881342	−	0.472478i	$-0.843360\pi$
$197$		−	13.2631i		−	0.944956i	0.881342	−	0.472478i	$-0.156640\pi$
$198$		0			0
$199$			1.20672i			0.0855419i	0.999085	+	0.0427709i	$0.0136186\pi$
$199$			1.20672i			0.0855419i	−0.999085	+	0.0427709i	$0.986381\pi$
$200$			9.98851i			0.706295i
$201$		0			0
$202$		−	33.4425i		−	2.35301i
$203$	13.4896	−	0.0332932i	0.946784	−	0.00233672i
$204$		0			0
$205$	−9.70107			−0.677552
$206$	−24.1334			−1.68145
$207$		0			0
$208$		−	49.3856i		−	3.42428i
$209$	−12.8473			−0.888668
$210$		0			0
$211$	−7.10660			−0.489239			−0.244619	−	0.969619i	$-0.578663\pi$
$211$	−7.10660			−0.489239			−0.244619	+	0.969619i	$0.578663\pi$
$212$			28.6194i			1.96559i
$213$		0			0
$214$	−27.1851			−1.85833
$215$	0.136811			0.00933046
$216$		0			0
$217$	20.3317	−	0.0501799i	1.38020	−	0.00340643i
$218$		−	27.4303i		−	1.85781i
$219$		0			0
$220$			25.3818i			1.71124i
$221$			16.1647i			1.08736i
$222$		0			0
$223$			12.8906i			0.863219i	0.902061	+	0.431610i	$0.142054\pi$
$223$			12.8906i			0.863219i	−0.902061	+	0.431610i	$0.857946\pi$
$224$	−66.4217	+	0.163933i	−4.43799	+	0.0109532i
$225$		0			0
$226$	2.97792			0.198088
$227$	−12.9946			−0.862481			−0.431241	−	0.902237i	$-0.641924\pi$
$227$	−12.9946			−0.862481			−0.431241	+	0.902237i	$0.641924\pi$
$228$		0			0
$229$		−	12.9679i		−	0.856945i	−0.903555	−	0.428472i	$-0.859052\pi$
$229$		−	12.9679i		−	0.856945i	0.903555	−	0.428472i	$-0.140948\pi$
$230$	6.07329			0.400461
$231$		0			0
$232$	−50.9275			−3.34355
$233$		−	13.5483i		−	0.887580i	−0.896131	−	0.443790i	$-0.853634\pi$
$233$		−	13.5483i		−	0.887580i	0.896131	−	0.443790i	$-0.146366\pi$
$234$		0			0
$235$	−0.149871			−0.00977651
$236$	−7.83379			−0.509936
$237$		0			0
$238$	39.0410	−	0.0963556i	2.53065	−	0.00624581i
$239$			9.39405i			0.607651i	0.952728	+	0.303825i	$0.0982640\pi$
$239$			9.39405i			0.607651i	−0.952728	+	0.303825i	$0.901736\pi$
$240$		0			0
$241$		−	25.8261i		−	1.66361i	−0.555070	−	0.831803i	$-0.687309\pi$
$241$		−	25.8261i		−	1.66361i	0.555070	−	0.831803i	$-0.312691\pi$
$242$			25.9635i			1.66900i
$243$		0			0
$244$			43.1783i			2.76421i
$245$	−6.99991	+	0.0345527i	−0.447208	+	0.00220749i
$246$		0			0
$247$	−8.59939			−0.547166
$248$	−76.7585			−4.87417
$249$		0			0
$250$		−	2.76021i		−	0.174571i
$251$	5.55660			0.350730			0.175365	−	0.984504i	$-0.443890\pi$
$251$	5.55660			0.350730			0.175365	+	0.984504i	$0.443890\pi$
$252$		0			0
$253$	9.93951			0.624892
$254$		−	36.7494i		−	2.30586i
$255$		0			0
$256$	67.2221			4.20138
$257$	−3.66380			−0.228542			−0.114271	−	0.993450i	$-0.536453\pi$
$257$	−3.66380			−0.228542			−0.114271	+	0.993450i	$0.536453\pi$
$258$		0			0
$259$	−0.00901880	−	3.65420i	−0.000560401	−	0.227061i
$260$			16.9894i			1.05364i
$261$		0			0
$262$			5.65087i			0.349112i
$263$		−	8.31962i		−	0.513010i	−0.966543	−	0.256505i	$-0.917429\pi$
$263$		−	8.31962i		−	0.513010i	0.966543	−	0.256505i	$-0.0825709\pi$
$264$		0			0
$265$		−	5.09355i		−	0.312894i
$266$	0.0512597	+	20.7692i	0.00314294	+	1.27344i
$267$		0			0
$268$	−70.4714			−4.30473
$269$	19.3244			1.17823			0.589115	−	0.808049i	$-0.299477\pi$
$269$	19.3244			1.17823			0.589115	+	0.808049i	$0.299477\pi$
$270$		0			0
$271$		−	13.3579i		−	0.811433i	−0.913999	−	0.405716i	$-0.867022\pi$
$271$		−	13.3579i		−	0.811433i	0.913999	−	0.405716i	$-0.132978\pi$
$272$	−87.3160			−5.29431
$273$		0			0
$274$	4.45991			0.269433
$275$		−	4.51734i		−	0.272406i
$276$		0			0
$277$	−13.0490			−0.784039			−0.392019	−	0.919957i	$-0.628223\pi$
$277$	−13.0490			−0.784039			−0.392019	+	0.919957i	$0.628223\pi$
$278$	−16.5013			−0.989682
$279$		0			0
$280$	26.4270	−	0.0652237i	1.57932	−	0.00389786i
$281$			19.1267i			1.14100i	0.821296	+	0.570502i	$0.193252\pi$
$281$			19.1267i			1.14100i	−0.821296	+	0.570502i	$0.806748\pi$
$282$		0			0
$283$			23.6837i			1.40785i	0.710274	+	0.703925i	$0.248571\pi$
$283$			23.6837i			1.40785i	−0.710274	+	0.703925i	$0.751429\pi$
$284$		−	60.7494i		−	3.60481i
$285$		0			0
$286$			37.7018i			2.22935i
$287$	0.0633467	+	25.6665i	0.00373924	+	1.51505i
$288$		0			0
$289$	11.5800			0.681175
$290$	14.0732			0.826407
$291$		0			0
$292$			44.4930i			2.60376i
$293$	14.1651			0.827534			0.413767	−	0.910383i	$-0.364213\pi$
$293$	14.1651			0.827534			0.413767	+	0.910383i	$0.364213\pi$
$294$		0			0
$295$	1.39422			0.0811747
$296$			13.7958i			0.801862i
$297$		0			0
$298$	−28.5793			−1.65556
$299$	6.65304			0.384755
$300$		0			0
$301$	−0.000893360	−	0.361968i	−5.14924e−5	−	0.0208635i
$302$			61.4794i			3.53774i
$303$		0			0
$304$		−	46.4508i		−	2.66413i
$305$		−	7.68467i		−	0.440023i
$306$		0			0
$307$		−	2.33725i		−	0.133394i	−0.997773	−	0.0666971i	$-0.978754\pi$
$307$		−	2.33725i		−	0.133394i	0.997773	−	0.0666971i	$-0.0212461\pi$
$308$	67.1537	−	0.165740i	3.82644	−	0.00944390i
$309$		0			0
$310$	21.2113			1.20472
$311$	−21.9607			−1.24527			−0.622637	−	0.782511i	$-0.713939\pi$
$311$	−21.9607			−1.24527			−0.622637	+	0.782511i	$0.713939\pi$
$312$		0			0
$313$		−	21.9210i		−	1.23905i	−0.784977	−	0.619525i	$-0.787325\pi$
$313$		−	21.9210i		−	1.23905i	0.784977	−	0.619525i	$-0.212675\pi$
$314$	−22.7391			−1.28324
$315$		0			0
$316$	10.9667			0.616925
$317$		−	2.00706i		−	0.112728i	−0.998410	−	0.0563640i	$-0.982049\pi$
$317$		−	2.00706i		−	0.112728i	0.998410	−	0.0563640i	$-0.0179507\pi$
$318$		0			0
$319$	23.0321			1.28955
$320$	−36.6296			−2.04766
$321$		0			0
$322$	−0.0396578	−	16.0684i	−0.00221004	−	0.895456i
$323$			15.2041i			0.845979i
$324$		0			0
$325$		−	3.02369i		−	0.167724i
$326$		−	65.8480i		−	3.64698i
$327$		0			0
$328$		−	96.8992i		−	5.35036i
$329$	0.000978638		0.396520i	5.39541e−5		0.0218609i
$330$		0			0
$331$	−16.9637			−0.932410			−0.466205	−	0.884677i	$-0.654379\pi$
$331$	−16.9637			−0.932410			−0.466205	+	0.884677i	$0.654379\pi$
$332$	84.3107			4.62715
$333$		0			0
$334$		−	41.8313i		−	2.28890i
$335$	12.5422			0.685252
$336$		0			0
$337$	31.9866			1.74242			0.871211	−	0.490910i	$-0.163335\pi$
$337$	31.9866			1.74242			0.871211	+	0.490910i	$0.163335\pi$
$338$		−	10.6469i		−	0.579115i
$339$		0			0
$340$	30.0380			1.62904
$341$	34.7143			1.87988
$342$		0			0
$343$	0.137126	+	18.5198i	0.00740411	+	0.999973i
$344$			1.36654i			0.0736790i
$345$		0			0
$346$		−	18.8929i		−	1.01569i
$347$		−	22.7703i		−	1.22238i	−0.791485	−	0.611188i	$-0.790692\pi$
$347$		−	22.7703i		−	1.22238i	0.791485	−	0.611188i	$-0.209308\pi$
$348$		0			0
$349$			13.1950i			0.706311i	0.935565	+	0.353156i	$0.114891\pi$
$349$			13.1950i			0.706311i	−0.935565	+	0.353156i	$0.885109\pi$
$350$	−7.30280	+	0.0180238i	−0.390351	+	0.000963413i
$351$		0			0
$352$	−113.408			−6.04469
$353$	15.1150			0.804490			0.402245	−	0.915532i	$-0.368230\pi$
$353$	15.1150			0.804490			0.402245	+	0.915532i	$0.368230\pi$
$354$		0			0
$355$			10.8119i			0.573836i
$356$	76.7174			4.06601
$357$		0			0
$358$	−14.2947			−0.755497
$359$		−	15.1690i		−	0.800587i	−0.916387	−	0.400294i	$-0.868908\pi$
$359$		−	15.1690i		−	0.800587i	0.916387	−	0.400294i	$-0.131092\pi$
$360$		0			0
$361$	10.9116			0.574297
$362$	−1.33834			−0.0703414
$363$		0			0
$364$	44.9495	−	0.110938i	2.35600	−	0.00581475i
$365$		−	7.91866i		−	0.414482i
$366$		0			0
$367$		−	24.9447i		−	1.30210i	−0.759033	−	0.651052i	$-0.774328\pi$
$367$		−	24.9447i		−	1.30210i	0.759033	−	0.651052i	$-0.225672\pi$
$368$			35.9373i			1.87336i
$369$		0			0
$370$		−	3.81230i		−	0.198192i
$371$	−13.4762	+	0.0332602i	−0.699650	+	0.00172678i
$372$		0			0
$373$	−13.0844			−0.677482			−0.338741	−	0.940880i	$-0.610001\pi$
$373$	−13.0844			−0.677482			−0.338741	+	0.940880i	$0.610001\pi$
$374$	66.6585			3.44683
$375$		0			0
$376$		−	1.49699i		−	0.0772013i
$377$	15.4166			0.793996
$378$		0			0
$379$	5.96711			0.306510			0.153255	−	0.988187i	$-0.451024\pi$
$379$	5.96711			0.306510			0.153255	+	0.988187i	$0.451024\pi$
$380$			15.9798i			0.819744i
$381$		0			0
$382$	8.13681			0.416315
$383$	11.5368			0.589501			0.294751	−	0.955574i	$-0.404763\pi$
$383$	11.5368			0.589501			0.294751	+	0.955574i	$0.404763\pi$
$384$		0			0
$385$	−11.9517	+	0.0294976i	−0.609116	+	0.00150334i
$386$			41.4663i			2.11058i
$387$		0			0
$388$			49.1265i			2.49402i
$389$			27.2788i			1.38309i	0.722334	+	0.691544i	$0.243069\pi$
$389$			27.2788i			1.38309i	−0.722334	+	0.691544i	$0.756931\pi$
$390$		0			0
$391$		−	11.7629i		−	0.594874i
$392$	−0.345130	−	69.9187i	−0.0174317	−	3.53143i
$393$		0			0
$394$	−36.6089			−1.84433
$395$	−1.95180			−0.0982058
$396$		0			0
$397$		−	18.4329i		−	0.925120i	−0.886588	−	0.462560i	$-0.846931\pi$
$397$		−	18.4329i		−	0.925120i	0.886588	−	0.462560i	$-0.153069\pi$
$398$	3.33079			0.166957
$399$		0			0
$400$	16.3329			0.816644
$401$		−	36.5709i		−	1.82626i	−0.407665	−	0.913131i	$-0.633657\pi$
$401$		−	36.5709i		−	1.82626i	0.407665	−	0.913131i	$-0.366343\pi$
$402$		0			0
$403$	23.2361			1.15747
$404$	−68.0764			−3.38693
$405$		0			0
$406$	−0.0918962	−	37.2341i	−0.00456073	−	1.84790i
$407$		−	6.23917i		−	0.309264i
$408$		0			0
$409$			11.7918i			0.583066i	0.956561	+	0.291533i	$0.0941653\pi$
$409$			11.7918i			0.583066i	−0.956561	+	0.291533i	$0.905835\pi$
$410$			26.7770i			1.32242i
$411$		0			0
$412$			49.1265i			2.42029i
$413$	−0.00910408	−	3.68875i	−0.000447983	−	0.181512i
$414$		0			0
$415$	−15.0052			−0.736578
$416$	−75.9102			−3.72180
$417$		0			0
$418$			35.4613i			1.73447i
$419$	12.0863			0.590453			0.295226	−	0.955427i	$-0.404605\pi$
$419$	12.0863			0.590453			0.295226	+	0.955427i	$0.404605\pi$
$420$		0			0
$421$	−18.9034			−0.921297			−0.460648	−	0.887583i	$-0.652383\pi$
$421$	−18.9034			−0.921297			−0.460648	+	0.887583i	$0.652383\pi$
$422$			19.6157i			0.954877i
$423$		0			0
$424$	50.8770			2.47080
$425$	−5.34602			−0.259320
$426$		0			0
$427$	−20.3317	+	0.0501799i	−0.983918	+	0.00242838i
$428$			55.3387i			2.67490i
$429$		0			0
$430$		−	0.377628i		−	0.0182108i
$431$		−	19.1769i		−	0.923721i	−0.886953	−	0.461860i	$-0.847182\pi$
$431$		−	19.1769i		−	0.923721i	0.886953	−	0.461860i	$-0.152818\pi$
$432$		0			0
$433$		−	6.40406i		−	0.307760i	−0.988090	−	0.153880i	$-0.950823\pi$
$433$		−	6.40406i		−	0.307760i	0.988090	−	0.153880i	$-0.0491769\pi$
$434$	−0.138507	−	56.1197i	−0.00664855	−	2.69383i
$435$		0			0
$436$	−55.8378			−2.67415
$437$	6.25767			0.299345
$438$		0			0
$439$			24.5503i			1.17172i	0.810412	+	0.585861i	$0.199244\pi$
$439$			24.5503i			1.17172i	−0.810412	+	0.585861i	$0.800756\pi$
$440$	45.1215			2.15108
$441$		0			0
$442$	44.6180			2.12226
$443$			2.17069i			0.103132i	0.998670	+	0.0515662i	$0.0164213\pi$
$443$			2.17069i			0.103132i	−0.998670	+	0.0515662i	$0.983579\pi$
$444$		0			0
$445$	−13.6538			−0.647252
$446$	35.5808			1.68480
$447$		0			0
$448$	0.239187	+	96.9126i	0.0113005	+	4.57869i
$449$			27.7220i			1.30828i	0.756374	+	0.654140i	$0.226969\pi$
$449$			27.7220i			1.30828i	−0.756374	+	0.654140i	$0.773031\pi$
$450$		0			0
$451$			43.8230i			2.06354i
$452$		−	6.06193i		−	0.285129i
$453$		0			0
$454$			35.8678i			1.68336i
$455$	−7.99991	+	0.0197443i	−0.375042	+	0.000925628i
$456$		0			0
$457$	19.3936			0.907194			0.453597	−	0.891207i	$-0.350141\pi$
$457$	19.3936			0.907194			0.453597	+	0.891207i	$0.350141\pi$
$458$	−35.7942			−1.67255
$459$		0			0
$460$		−	12.3630i		−	0.576426i
$461$	9.04615			0.421321			0.210661	−	0.977559i	$-0.432439\pi$
$461$	9.04615			0.421321			0.210661	+	0.977559i	$0.432439\pi$
$462$		0			0
$463$	−6.27290			−0.291526			−0.145763	−	0.989320i	$-0.546564\pi$
$463$	−6.27290			−0.291526			−0.145763	+	0.989320i	$0.546564\pi$
$464$			83.2749i			3.86594i
$465$		0			0
$466$	−37.3962			−1.73234
$467$	26.4591			1.22438			0.612190	−	0.790711i	$-0.290289\pi$
$467$	26.4591			1.22438			0.612190	+	0.790711i	$0.290289\pi$
$468$		0			0
$469$	−0.0818987	−	33.1834i	−0.00378173	−	1.53227i
$470$			0.413676i			0.0190814i
$471$		0			0
$472$			13.9262i			0.641005i
$473$		−	0.618023i		−	0.0284167i
$474$		0			0
$475$		−	2.84400i		−	0.130492i
$476$	−0.196144	−	79.4728i	−0.00899025	−	3.64263i
$477$		0			0
$478$	25.9296			1.18599
$479$	29.5972			1.35233			0.676166	−	0.736749i	$-0.263640\pi$
$479$	29.5972			1.35233			0.676166	+	0.736749i	$0.263640\pi$
$480$		0			0
$481$		−	4.17621i		−	0.190419i
$482$	−71.2855			−3.24696
$483$		0			0
$484$	52.8519			2.40236
$485$		−	8.74331i		−	0.397013i
$486$		0			0
$487$	16.0570			0.727614			0.363807	−	0.931474i	$-0.381477\pi$
$487$	16.0570			0.727614			0.363807	+	0.931474i	$0.381477\pi$
$488$	76.7585			3.47469
$489$		0			0
$490$	0.0953727	+	19.3212i	0.00430850	+	0.872844i
$491$		−	18.5879i		−	0.838861i	−0.907787	−	0.419430i	$-0.862230\pi$
$491$		−	18.5879i		−	0.838861i	0.907787	−	0.419430i	$-0.137770\pi$
$492$		0			0
$493$		−	27.2573i		−	1.22760i
$494$			23.7361i			1.06794i
$495$		0			0
$496$			125.513i			5.63569i
$497$	28.6055	−	0.0706003i	1.28313	−	0.00316686i
$498$		0			0
$499$	3.17866			0.142297			0.0711483	−	0.997466i	$-0.477334\pi$
$499$	3.17866			0.142297			0.0711483	+	0.997466i	$0.477334\pi$
$500$	−5.61875			−0.251278
$501$		0			0
$502$		−	15.3374i		−	0.684541i
$503$	−22.2166			−0.990590			−0.495295	−	0.868725i	$-0.664940\pi$
$503$	−22.2166			−0.990590			−0.495295	+	0.868725i	$0.664940\pi$
$504$		0			0
$505$	12.1159			0.539152
$506$		−	27.4351i		−	1.21964i
$507$		0			0
$508$	−74.8081			−3.31907
$509$	−12.5975			−0.558376			−0.279188	−	0.960237i	$-0.590065\pi$
$509$	−12.5975			−0.558376			−0.279188	+	0.960237i	$0.590065\pi$
$510$		0			0
$511$	−20.9507	+	0.0517078i	−0.926806	+	0.00228742i
$512$		−	83.7566i		−	3.70156i
$513$		0			0
$514$			10.1129i			0.446059i
$515$		−	8.74331i		−	0.385276i
$516$		0			0
$517$			0.677018i			0.0297752i
$518$	−10.0864	+	0.0248938i	−0.443169	+	0.00109377i
$519$		0			0
$520$	30.2022			1.32445
$521$	−1.06675			−0.0467352			−0.0233676	−	0.999727i	$-0.507439\pi$
$521$	−1.06675			−0.0467352			−0.0233676	+	0.999727i	$0.507439\pi$
$522$		0			0
$523$			8.73578i			0.381989i	0.981591	+	0.190995i	$0.0611713\pi$
$523$			8.73578i			0.381989i	−0.981591	+	0.190995i	$0.938829\pi$
$524$	11.5030			0.502513
$525$		0			0
$526$	−22.9639			−1.00127
$527$		−	41.0824i		−	1.78958i
$528$		0			0
$529$	18.1587			0.789507
$530$	−14.0593			−0.610695
$531$		0			0
$532$	42.2783	−	0.104346i	1.83300	−	0.00452396i
$533$			29.3330i			1.27056i
$534$		0			0
$535$		−	9.84893i		−	0.425806i
$536$			125.278i			5.41117i
$537$		0			0
$538$		−	53.3394i		−	2.29962i
$539$	0.156086	+	31.6210i	0.00672311	+	1.36201i
$540$		0			0
$541$	−42.0360			−1.80727			−0.903634	−	0.428305i	$-0.859111\pi$
$541$	−42.0360			−1.80727			−0.903634	+	0.428305i	$0.859111\pi$
$542$	−36.8705			−1.58372
$543$		0			0
$544$			134.213i			5.75432i
$545$	9.93776			0.425687
$546$		0			0
$547$	19.2870			0.824653			0.412327	−	0.911036i	$-0.364716\pi$
$547$	19.2870			0.824653			0.412327	+	0.911036i	$0.364716\pi$
$548$		−	9.07871i		−	0.387823i
$549$		0			0
$550$	−12.4688			−0.531671
$551$	14.5004			0.617740
$552$		0			0
$553$	0.0127450	+	5.16397i	0.000541973	+	0.219594i
$554$			36.0180i			1.53026i
$555$		0			0
$556$			33.5905i			1.42455i
$557$		−	16.9867i		−	0.719752i	−0.933000	−	0.359876i	$-0.882819\pi$
$557$		−	16.9867i		−	0.719752i	0.933000	−	0.359876i	$-0.117181\pi$
$558$		0			0
$559$		−	0.413676i		−	0.0174966i
$560$	−0.106652	−	43.2126i	−0.00450685	−	1.82607i
$561$		0			0
$562$	52.7938			2.22697
$563$	31.2647			1.31765			0.658825	−	0.752296i	$-0.271054\pi$
$563$	31.2647			1.31765			0.658825	+	0.752296i	$0.271054\pi$
$564$		0			0
$565$			1.07888i			0.0453886i
$566$	65.3720			2.74779
$567$		0			0
$568$	−107.995			−4.53136
$569$			14.0702i			0.589853i	0.955520	+	0.294927i	$0.0952952\pi$
$569$			14.0702i			0.589853i	−0.955520	+	0.294927i	$0.904705\pi$
$570$		0			0
$571$	−41.4913			−1.73636			−0.868178	−	0.496253i	$-0.834709\pi$
$571$	−41.4913			−1.73636			−0.868178	+	0.496253i	$0.834709\pi$
$572$	76.7468			3.20894
$573$		0			0
$574$	70.8450	−	0.174850i	2.95701	−	0.00729810i
$575$			2.20030i			0.0917590i
$576$		0			0
$577$		−	6.15328i		−	0.256164i	−0.991764	−	0.128082i	$-0.959118\pi$
$577$		−	6.15328i		−	0.256164i	0.991764	−	0.128082i	$-0.0408821\pi$
$578$		−	31.9631i		−	1.32949i
$579$		0			0
$580$		−	28.6478i		−	1.18953i
$581$	0.0979822	+	39.7000i	0.00406499	+	1.64703i
$582$		0			0
$583$	−23.0093			−0.952947
$584$	79.0956			3.27300
$585$		0			0
$586$		−	39.0986i		−	1.61515i
$587$	9.77084			0.403286			0.201643	−	0.979459i	$-0.435372\pi$
$587$	9.77084			0.403286			0.201643	+	0.979459i	$0.435372\pi$
$588$		0			0
$589$	21.8552			0.900529
$590$		−	3.84834i		−	0.158434i
$591$		0			0
$592$	22.5583			0.927142
$593$	−6.87536			−0.282337			−0.141169	−	0.989986i	$-0.545086\pi$
$593$	−6.87536			−0.282337			−0.141169	+	0.989986i	$0.545086\pi$
$594$		0			0
$595$	0.0349088	+	14.1442i	0.00143112	+	0.579856i
$596$			58.1768i			2.38301i
$597$		0			0
$598$		−	18.3638i		−	0.750951i
$599$		−	4.94739i		−	0.202145i	−0.994879	−	0.101072i	$-0.967773\pi$
$599$		−	4.94739i		−	0.202145i	0.994879	−	0.101072i	$-0.0322274\pi$
$600$		0			0
$601$			27.3774i			1.11675i	0.829589	+	0.558374i	$0.188575\pi$
$601$			27.3774i			1.11675i	−0.829589	+	0.558374i	$0.811425\pi$
$602$	−0.999107	+	0.00246586i	−0.0407205	+	0.000100501i
$603$		0			0
$604$	125.149			5.09224
$605$	−9.40634			−0.382422
$606$		0			0
$607$			27.3630i			1.11063i	0.831639	+	0.555316i	$0.187403\pi$
$607$			27.3630i			1.11063i	−0.831639	+	0.555316i	$0.812597\pi$
$608$	−71.3991			−2.89561
$609$		0			0
$610$	−21.2113			−0.858820
$611$			0.453164i			0.0183331i
$612$		0			0
$613$	17.0373			0.688129			0.344064	−	0.938946i	$-0.388196\pi$
$613$	17.0373			0.688129			0.344064	+	0.938946i	$0.388196\pi$
$614$	−6.45131			−0.260354
$615$		0			0
$616$	−0.294637	−	119.380i	−0.0118713	−	4.80995i
$617$			26.5717i			1.06974i	0.844935	+	0.534869i	$0.179639\pi$
$617$			26.5717i			1.06974i	−0.844935	+	0.534869i	$0.820361\pi$
$618$		0			0
$619$			12.3597i			0.496776i	0.968661	+	0.248388i	$0.0799009\pi$
$619$			12.3597i			0.496776i	−0.968661	+	0.248388i	$0.920099\pi$
$620$		−	43.1783i		−	1.73408i
$621$		0			0
$622$			60.6160i			2.43048i
$623$	0.0891575	+	36.1245i	0.00357202	+	1.44730i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−60.5066			−2.41833
$627$		0			0
$628$			46.2884i			1.84711i
$629$	−7.38372			−0.294408
$630$		0			0
$631$	−19.9336			−0.793544			−0.396772	−	0.917917i	$-0.629870\pi$
$631$	−19.9336			−0.793544			−0.396772	+	0.917917i	$0.629870\pi$
$632$		−	19.4956i		−	0.775493i
$633$		0			0
$634$	−5.53992			−0.220018
$635$	13.3140			0.528350
$636$		0			0
$637$	0.104477	+	21.1656i	0.00413952	+	0.838611i
$638$		−	63.5734i		−	2.51690i
$639$		0			0
$640$			50.8952i			2.01181i
$641$			43.0178i			1.69910i	0.527508	+	0.849550i	$0.323126\pi$
$641$			43.0178i			1.69910i	−0.527508	+	0.849550i	$0.676874\pi$
$642$		0			0
$643$			1.86574i			0.0735776i	0.999323	+	0.0367888i	$0.0117129\pi$
$643$			1.86574i			0.0735776i	−0.999323	+	0.0367888i	$0.988287\pi$
$644$	−32.7092	+	0.0807285i	−1.28892	+	0.00318115i
$645$		0			0
$646$	41.9665			1.65115
$647$	−5.39933			−0.212269			−0.106135	−	0.994352i	$-0.533847\pi$
$647$	−5.39933			−0.212269			−0.106135	+	0.994352i	$0.533847\pi$
$648$		0			0
$649$		−	6.29817i		−	0.247225i
$650$	−8.34602			−0.327358
$651$		0			0
$652$	−134.042			−5.24949
$653$		−	44.6372i		−	1.74679i	−0.487015	−	0.873394i	$-0.661914\pi$
$653$		−	44.6372i		−	1.74679i	0.487015	−	0.873394i	$-0.338086\pi$
$654$		0			0
$655$	−2.04726			−0.0799931
$656$	−158.446			−6.18629
$657$		0			0
$658$	1.09448	−	0.00270125i	0.0426672	−	0.000105306i
$659$		−	5.56767i		−	0.216886i	−0.994103	−	0.108443i	$-0.965414\pi$
$659$		−	5.56767i		−	0.216886i	0.994103	−	0.108443i	$-0.0345864\pi$
$660$		0			0
$661$		−	21.3765i		−	0.831451i	−0.909490	−	0.415725i	$-0.863528\pi$
$661$		−	21.3765i		−	0.831451i	0.909490	−	0.415725i	$-0.136472\pi$
$662$			46.8234i			1.81984i
$663$		0			0
$664$		−	149.880i		−	5.81647i
$665$	−7.52450	+	0.0185710i	−0.291788	+	0.000720151i
$666$		0			0
$667$	−11.2185			−0.434381
$668$	−85.1528			−3.29466
$669$		0			0
$670$		−	34.6190i		−	1.33745i
$671$	−34.7143			−1.34013
$672$		0			0
$673$	18.7549			0.722949			0.361475	−	0.932382i	$-0.382273\pi$
$673$	18.7549			0.722949			0.361475	+	0.932382i	$0.382273\pi$
$674$		−	88.2897i		−	3.40079i
$675$		0			0
$676$	−21.6731			−0.833581
$677$	−29.7801			−1.14454			−0.572270	−	0.820065i	$-0.693937\pi$
$677$	−29.7801			−1.14454			−0.572270	+	0.820065i	$0.693937\pi$
$678$		0			0
$679$	−23.1325	+	0.0570926i	−0.887746	+	0.00219101i
$680$		−	53.3988i		−	2.04775i
$681$		0			0
$682$		−	95.8186i		−	3.66908i
$683$			23.6059i			0.903256i	0.892206	+	0.451628i	$0.149157\pi$
$683$			23.6059i			0.903256i	−0.892206	+	0.451628i	$0.850843\pi$
$684$		0			0
$685$			1.61579i			0.0617361i
$686$	51.1184	−	0.378497i	1.95171	−	0.0144511i
$687$		0			0
$688$	2.23452			0.0851904
$689$	−15.4013			−0.586744
$690$		0			0
$691$			41.6388i			1.58401i	0.610513	+	0.792006i	$0.290963\pi$
$691$			41.6388i			1.58401i	−0.610513	+	0.792006i	$0.709037\pi$
$692$	−38.4588			−1.46198
$693$		0			0
$694$	−62.8509			−2.38579
$695$		−	5.97828i		−	0.226769i
$696$		0			0
$697$	51.8621			1.96442
$698$	36.4209			1.37855
$699$		0			0
$700$	0.0366897	+	14.8658i	0.00138674	+	0.561874i
$701$		−	14.4990i		−	0.547620i	−0.961784	−	0.273810i	$-0.911716\pi$
$701$		−	14.4990i		−	0.547620i	0.961784	−	0.273810i	$-0.0882839\pi$
$702$		0			0
$703$		−	3.92803i		−	0.148148i
$704$			165.468i			6.23633i
$705$		0			0
$706$		−	41.7205i		−	1.57017i
$707$	−0.0791154	−	32.0556i	−0.00297544	−	1.20558i
$708$		0			0
$709$	−11.8195			−0.443889			−0.221945	−	0.975059i	$-0.571240\pi$
$709$	−11.8195			−0.443889			−0.221945	+	0.975059i	$0.571240\pi$
$710$	29.8431			1.11999
$711$		0			0
$712$		−	136.381i		−	5.11110i
$713$	−16.9086			−0.633232
$714$		0			0
$715$	−13.6590			−0.510819
$716$			29.0986i			1.08747i
$717$		0			0
$718$	−41.8695			−1.56256
$719$	22.1050			0.824377			0.412189	−	0.911099i	$-0.364764\pi$
$719$	22.1050			0.824377			0.412189	+	0.911099i	$0.364764\pi$
$720$		0			0
$721$	−23.1325	+	0.0570926i	−0.861501	+	0.00212624i
$722$		−	30.1184i		−	1.12089i
$723$		0			0
$724$			2.72435i			0.101250i
$725$			5.09860i			0.189357i
$726$		0			0
$727$			53.0226i			1.96650i	0.182268	+	0.983249i	$0.441656\pi$
$727$			53.0226i			1.96650i	−0.182268	+	0.983249i	$0.558344\pi$
$728$	−0.197216	−	79.9073i	−0.00730932	−	2.96156i
$729$		0			0
$730$	−21.8572			−0.808969
$731$	−0.731397			−0.0270517
$732$		0			0
$733$		−	12.5229i		−	0.462544i	−0.972889	−	0.231272i	$-0.925711\pi$
$733$		−	12.5229i		−	0.462544i	0.972889	−	0.231272i	$-0.0742887\pi$
$734$	−68.8527			−2.54140
$735$		0			0
$736$	55.2389			2.03613
$737$		−	56.6572i		−	2.08700i
$738$		0			0
$739$	4.12468			0.151729			0.0758644	−	0.997118i	$-0.475828\pi$
$739$	4.12468			0.151729			0.0758644	+	0.997118i	$0.475828\pi$
$740$	−7.76041			−0.285278
$741$		0			0
$742$	0.0918051	+	37.1972i	0.00337027	+	1.36555i
$743$			20.7072i			0.759673i	0.925054	+	0.379836i	$0.124020\pi$
$743$			20.7072i			0.759673i	−0.925054	+	0.379836i	$0.875980\pi$
$744$		0			0
$745$		−	10.3540i		−	0.379343i
$746$			36.1155i			1.32228i
$747$		0			0
$748$		−	135.692i		−	4.96138i
$749$	−26.0577	+	0.0643122i	−0.952129	+	0.00234992i
$750$		0			0
$751$	39.1585			1.42891			0.714457	−	0.699679i	$-0.246674\pi$
$751$	39.1585			1.42891			0.714457	+	0.699679i	$0.246674\pi$
$752$	−2.44783			−0.0892631
$753$		0			0
$754$		−	42.5531i		−	1.54969i
$755$	−22.2735			−0.810614
$756$		0			0
$757$	2.72898			0.0991865			0.0495932	−	0.998769i	$-0.484208\pi$
$757$	2.72898			0.0991865			0.0495932	+	0.998769i	$0.484208\pi$
$758$		−	16.4705i		−	0.598234i
$759$		0			0
$760$	28.4074			1.03044
$761$	−44.5652			−1.61549			−0.807743	−	0.589535i	$-0.799311\pi$
$761$	−44.5652			−1.61549			−0.807743	+	0.589535i	$0.799311\pi$
$762$		0			0
$763$	−0.0648923	−	26.2928i	−0.00234926	−	0.951862i
$764$		−	16.5635i		−	0.599247i
$765$		0			0
$766$		−	31.8439i		−	1.15057i
$767$		−	4.21570i		−	0.152220i
$768$		0			0
$769$		−	51.7495i		−	1.86614i	−0.359700	−	0.933068i	$-0.617121\pi$
$769$		−	51.7495i		−	1.86614i	0.359700	−	0.933068i	$-0.382879\pi$
$770$	0.0814196	+	32.9892i	0.00293416	+	1.18885i
$771$		0			0
$772$	84.4099			3.03798
$773$	−26.2593			−0.944481			−0.472240	−	0.881470i	$-0.656555\pi$
$773$	−26.2593			−0.944481			−0.472240	+	0.881470i	$0.656555\pi$
$774$		0			0
$775$			7.68467i			0.276042i
$776$	87.3327			3.13506
$777$		0			0
$778$	75.2951			2.69946
$779$			27.5899i			0.988510i
$780$		0			0
$781$	48.8410			1.74767
$782$	−32.4680			−1.16105
$783$		0			0
$784$	−114.329	+	0.564345i	−4.08317	+	0.0201552i
$785$		−	8.23819i		−	0.294034i
$786$		0			0
$787$		−	0.251532i		−	0.00896615i	−0.999990	−	0.00448307i	$-0.998573\pi$
$787$		−	0.251532i		−	0.00896615i	0.999990	−	0.00448307i	$-0.00142701\pi$
$788$			74.5220i			2.65474i
$789$		0			0
$790$			5.38738i			0.191674i
$791$	2.85443	−	0.00704491i	0.101492	−	0.000250488i
$792$		0			0
$793$	−23.2361			−0.825138
$794$	−50.8786			−1.80561
$795$		0			0
$796$		−	6.78024i		−	0.240319i
$797$	−22.7590			−0.806164			−0.403082	−	0.915164i	$-0.632061\pi$
$797$	−22.7590			−0.806164			−0.403082	+	0.915164i	$0.632061\pi$
$798$		0			0
$799$	0.801214			0.0283449
$800$		−	25.1051i		−	0.887600i
$801$		0			0
$802$	−100.943			−3.56443
$803$	−35.7713			−1.26234
$804$		0			0
$805$	5.82144	−	0.0143677i	0.205179	−	0.000506394i
$806$		−	64.1365i		−	2.25911i
$807$		0			0
$808$			121.020i			4.25747i
$809$		−	9.60638i		−	0.337742i	−0.985638	−	0.168871i	$-0.945988\pi$
$809$		−	9.60638i		−	0.337742i	0.985638	−	0.168871i	$-0.0540122\pi$
$810$		0			0
$811$			42.8476i			1.50458i	0.658831	+	0.752291i	$0.271051\pi$
$811$			42.8476i			1.50458i	−0.658831	+	0.752291i	$0.728949\pi$
$812$	−75.7947	+	0.187066i	−2.65987	+	0.00656474i
$813$		0			0
$814$	−17.2214			−0.603611
$815$	23.8562			0.835645
$816$		0			0
$817$		−	0.389092i		−	0.0136126i
$818$	32.5478			1.13801
$819$		0			0
$820$	54.5079			1.90350
$821$		−	26.1708i		−	0.913367i	−0.889629	−	0.456683i	$-0.849037\pi$
$821$		−	26.1708i		−	0.913367i	0.889629	−	0.456683i	$-0.150963\pi$
$822$		0			0
$823$	42.3117			1.47489			0.737447	−	0.675405i	$-0.236031\pi$
$823$	42.3117			1.47489			0.737447	+	0.675405i	$0.236031\pi$
$824$	87.3327			3.04238
$825$		0			0
$826$	−10.1817	+	0.0251292i	−0.354268	+	0.000874356i
$827$		−	29.6738i		−	1.03186i	−0.856631	−	0.515930i	$-0.827446\pi$
$827$		−	29.6738i		−	1.03186i	0.856631	−	0.515930i	$-0.172554\pi$
$828$		0			0
$829$			50.1412i			1.74147i	0.491749	+	0.870737i	$0.336358\pi$
$829$			50.1412i			1.74147i	−0.491749	+	0.870737i	$0.663642\pi$
$830$			41.4176i			1.43763i
$831$		0			0
$832$			110.757i			3.83980i
$833$	37.4217	−	0.184720i	1.29659	−	0.00640015i
$834$		0			0
$835$	15.1551			0.524464
$836$	72.1859			2.49660
$837$		0			0
$838$		−	33.3606i		−	1.15242i
$839$	39.4599			1.36231			0.681153	−	0.732141i	$-0.261479\pi$
$839$	39.4599			1.36231			0.681153	+	0.732141i	$0.261479\pi$
$840$		0			0
$841$	3.00425			0.103595
$842$			52.1774i			1.79815i
$843$		0			0
$844$	39.9302			1.37446
$845$	3.85728			0.132695
$846$		0			0
$847$	0.0614222	+	24.8868i	0.00211049	+	0.855120i
$848$		−	83.1923i		−	2.85684i
$849$		0			0
$850$			14.7561i			0.506131i
$851$			3.03897i			0.104175i
$852$		0			0
$853$			26.4657i			0.906167i	0.891468	+	0.453084i	$0.149676\pi$
$853$			26.4657i			0.906167i	−0.891468	+	0.453084i	$0.850324\pi$
$854$	0.138507	+	56.1197i	0.00473961	+	1.92038i
$855$		0			0
$856$	98.3761			3.36243
$857$	32.9495			1.12553			0.562767	−	0.826615i	$-0.309737\pi$
$857$	32.9495			1.12553			0.562767	+	0.826615i	$0.309737\pi$
$858$		0			0
$859$			41.8954i			1.42945i	0.699404	+	0.714727i	$0.253449\pi$
$859$			41.8954i			1.42945i	−0.699404	+	0.714727i	$0.746551\pi$
$860$	−0.768709			−0.0262128
$861$		0			0
$862$	−52.9324			−1.80288
$863$			23.3773i			0.795774i	0.917434	+	0.397887i	$0.130256\pi$
$863$			23.3773i			0.795774i	−0.917434	+	0.397887i	$0.869744\pi$
$864$		0			0
$865$	6.84472			0.232728
$866$	−17.6766			−0.600674
$867$		0			0
$868$	−114.239	+	0.281948i	−3.87751	+	0.00956995i
$869$			8.81695i			0.299095i
$870$		0			0
$871$		−	37.9237i		−	1.28500i
$872$			99.2635i			3.36149i
$873$		0			0
$874$		−	17.2725i		−	0.584250i
$875$	−0.00652987	−	2.64574i	−0.000220750	−	0.0894424i
$876$		0			0
$877$	−16.3697			−0.552767			−0.276384	−	0.961047i	$-0.589136\pi$
$877$	−16.3697			−0.552767			−0.276384	+	0.961047i	$0.589136\pi$
$878$	67.7640			2.28692
$879$		0			0
$880$		−	73.7811i		−	2.48716i
$881$	−40.1272			−1.35192			−0.675960	−	0.736938i	$-0.736271\pi$
$881$	−40.1272			−1.35192			−0.675960	+	0.736938i	$0.736271\pi$
$882$		0			0
$883$	−39.4930			−1.32905			−0.664523	−	0.747268i	$-0.731365\pi$
$883$	−39.4930			−1.32905			−0.664523	+	0.747268i	$0.731365\pi$
$884$		−	90.8256i		−	3.05480i
$885$		0			0
$886$	5.99155			0.201290
$887$	−51.6224			−1.73331			−0.866656	−	0.498907i	$-0.833735\pi$
$887$	−51.6224			−1.73331			−0.866656	+	0.498907i	$0.833735\pi$
$888$		0			0
$889$	−0.0869386	−	35.2254i	−0.00291583	−	1.18142i
$890$			37.6874i			1.26328i
$891$		0			0
$892$		−	72.4292i		−	2.42511i
$893$			0.426234i			0.0142634i
$894$		0			0
$895$		−	5.17884i		−	0.173109i
$896$	134.656	−	0.332339i	4.49853	−	0.0111027i
$897$		0			0
$898$	76.5184			2.55345
$899$	−39.1811			−1.30676
$900$		0			0
$901$			27.2302i			0.907170i
$902$	120.961			4.02755
$903$		0			0
$904$	−10.7764			−0.358416
$905$		−	0.484867i		−	0.0161175i
$906$		0			0
$907$	27.5288			0.914079			0.457040	−	0.889446i	$-0.348910\pi$
$907$	27.5288			0.914079			0.457040	+	0.889446i	$0.348910\pi$
$908$	73.0134			2.42304
$909$		0			0
$910$	0.0544984	+	22.0814i	0.00180661	+	0.731992i
$911$			7.81123i			0.258798i	0.991593	+	0.129399i	$0.0413047\pi$
$911$			7.81123i			0.258798i	−0.991593	+	0.129399i	$0.958695\pi$
$912$		0			0
$913$			67.7837i			2.24331i
$914$		−	53.5304i		−	1.77063i
$915$		0			0
$916$			72.8636i			2.40748i
$917$	0.0133683	+	5.41652i	0.000441461	+	0.178869i
$918$		0			0
$919$	37.9402			1.25153			0.625766	−	0.780011i	$-0.284787\pi$
$919$	37.9402			1.25153			0.625766	+	0.780011i	$0.284787\pi$
$920$	−21.9778			−0.724585
$921$		0			0
$922$		−	24.9693i		−	0.822319i
$923$	32.6919			1.07607
$924$		0			0
$925$	1.38116			0.0454123
$926$			17.3145i			0.568990i
$927$		0			0
$928$	128.001			4.20184
$929$	−6.48353			−0.212718			−0.106359	−	0.994328i	$-0.533919\pi$
$929$	−6.48353			−0.212718			−0.106359	+	0.994328i	$0.533919\pi$
$930$		0			0
$931$	0.0982680	+	19.9078i	0.00322060	+	0.652451i
$932$			76.1246i			2.49355i
$933$		0			0
$934$		−	73.0325i		−	2.38970i
$935$			24.1498i			0.789783i
$936$		0			0
$937$		−	50.3253i		−	1.64406i	−0.569448	−	0.822028i	$-0.692843\pi$
$937$		−	50.3253i		−	1.64406i	0.569448	−	0.822028i	$-0.307157\pi$
$938$	−91.5931	+	0.226058i	−2.99062	+	0.00738104i
$939$		0			0
$940$	0.842089			0.0274659
$941$	1.29863			0.0423342			0.0211671	−	0.999776i	$-0.493262\pi$
$941$	1.29863			0.0423342			0.0211671	+	0.999776i	$0.493262\pi$
$942$		0			0
$943$		−	21.3453i		−	0.695098i
$944$	22.7717			0.741154
$945$		0			0
$946$	−1.70587			−0.0554627
$947$		−	19.9246i		−	0.647463i	−0.946149	−	0.323731i	$-0.895063\pi$
$947$		−	19.9246i		−	0.647463i	0.946149	−	0.323731i	$-0.104937\pi$
$948$		0			0
$949$	−23.9436			−0.777242
$950$	−7.85004			−0.254689
$951$		0			0
$952$	−141.280	+	0.348687i	−4.57890	+	0.0113010i
$953$			13.2440i			0.429014i	0.976722	+	0.214507i	$0.0688145\pi$
$953$			13.2440i			0.429014i	−0.976722	+	0.214507i	$0.931186\pi$
$954$		0			0
$955$			2.94790i			0.0953917i
$956$		−	52.7829i		−	1.70712i
$957$		0			0
$958$		−	81.6945i		−	2.63943i
$959$	4.27496	−	0.0105509i	0.138046	−	0.000340706i
$960$		0			0
$961$	−28.0542			−0.904974
$962$	−11.5272			−0.371652
$963$		0			0
$964$			145.111i			4.67370i
$965$	−15.0229			−0.483604
$966$		0			0
$967$	−11.5833			−0.372493			−0.186246	−	0.982503i	$-0.559632\pi$
$967$	−11.5833			−0.372493			−0.186246	+	0.982503i	$0.559632\pi$
$968$		−	93.9554i		−	3.01984i
$969$		0			0
$970$	−24.1334			−0.774875
$971$	3.53283			0.113374			0.0566869	−	0.998392i	$-0.481946\pi$
$971$	3.53283			0.113374			0.0566869	+	0.998392i	$0.481946\pi$
$972$		0			0
$973$	−15.8170	+	0.0390374i	−0.507070	+	0.00125148i
$974$		−	44.3208i		−	1.42013i
$975$		0			0
$976$		−	125.513i		−	4.01757i
$977$		−	42.3072i		−	1.35353i	−0.736200	−	0.676764i	$-0.763382\pi$
$977$		−	42.3072i		−	1.35353i	0.736200	−	0.676764i	$-0.236618\pi$
$978$		0			0
$979$			61.6789i			1.97126i
$980$	39.3308	−	0.194143i	1.25638	−	0.00620167i
$981$		0			0
$982$	−51.3065			−1.63726
$983$	−49.7688			−1.58738			−0.793689	−	0.608324i	$-0.791842\pi$
$983$	−49.7688			−1.58738			−0.793689	+	0.608324i	$0.791842\pi$
$984$		0			0
$985$		−	13.2631i		−	0.422597i
$986$	−75.2357			−2.39599
$987$		0			0
$988$	48.3179			1.53720
$989$			0.301026i			0.00957208i
$990$		0			0
$991$	35.2815			1.12075			0.560377	−	0.828237i	$-0.310656\pi$
$991$	35.2815			1.12075			0.560377	+	0.828237i	$0.310656\pi$
$992$	192.925			6.12536
$993$		0			0
$994$	−0.194872	−	78.9572i	−0.00618095	−	2.50437i
$995$			1.20672i			0.0382555i
$996$		0			0
$997$		−	28.2489i		−	0.894652i	−0.894371	−	0.447326i	$-0.852376\pi$
$997$		−	28.2489i		−	0.894652i	0.894371	−	0.447326i	$-0.147624\pi$
$998$		−	8.77378i		−	0.277729i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.b.d.566.1	yes	12
3.2	odd	2		945.2.b.c.566.12	yes	12
7.6	odd	2		945.2.b.c.566.1	✓	12
21.20	even	2	inner	945.2.b.d.566.12	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.b.c.566.1	✓	12	7.6	odd	2
945.2.b.c.566.12	yes	12	3.2	odd	2
945.2.b.d.566.1	yes	12	1.1	even	1	trivial
945.2.b.d.566.12	yes	12	21.20	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.76021i q^{2} -5.61875 q^{4} +1.00000 q^{5} +(-0.00652987 - 2.64574i) q^{7} +9.98851i q^{8} +O(q^{10})\)	\(q-2.76021i q^{2} -5.61875 q^{4} +1.00000 q^{5} +(-0.00652987 - 2.64574i) q^{7} +9.98851i q^{8} -2.76021i q^{10} -4.51734i q^{11} -3.02369i q^{13} +(-7.30280 + 0.0180238i) q^{14} +16.3329 q^{16} -5.34602 q^{17} -2.84400i q^{19} -5.61875 q^{20} -12.4688 q^{22} +2.20030i q^{23} +1.00000 q^{25} -8.34602 q^{26} +(0.0366897 + 14.8658i) q^{28} +5.09860i q^{29} +7.68467i q^{31} -25.1051i q^{32} +14.7561i q^{34} +(-0.00652987 - 2.64574i) q^{35} +1.38116 q^{37} -7.85004 q^{38} +9.98851i q^{40} -9.70107 q^{41} +0.136811 q^{43} +25.3818i q^{44} +6.07329 q^{46} -0.149871 q^{47} +(-6.99991 + 0.0345527i) q^{49} -2.76021i q^{50} +16.9894i q^{52} -5.09355i q^{53} -4.51734i q^{55} +(26.4270 - 0.0652237i) q^{56} +14.0732 q^{58} +1.39422 q^{59} -7.68467i q^{61} +21.2113 q^{62} -36.6296 q^{64} -3.02369i q^{65} +12.5422 q^{67} +30.0380 q^{68} +(-7.30280 + 0.0180238i) q^{70} +10.8119i q^{71} -7.91866i q^{73} -3.81230i q^{74} +15.9798i q^{76} +(-11.9517 + 0.0294976i) q^{77} -1.95180 q^{79} +16.3329 q^{80} +26.7770i q^{82} -15.0052 q^{83} -5.34602 q^{85} -0.377628i q^{86} +45.1215 q^{88} -13.6538 q^{89} +(-7.99991 + 0.0197443i) q^{91} -12.3630i q^{92} +0.413676i q^{94} -2.84400i q^{95} -8.74331i q^{97} +(0.0953727 + 19.3212i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 16 q^{4} + 12 q^{5} - 2 q^{7}+O(q^{10}) \) 12 * q - 16 * q^4 + 12 * q^5 - 2 * q^7	\( 12 q - 16 q^{4} + 12 q^{5} - 2 q^{7} - 12 q^{14} + 32 q^{16} - 16 q^{20} - 4 q^{22} + 12 q^{25} - 36 q^{26} + 10 q^{28} - 2 q^{35} - 28 q^{37} - 4 q^{43} - 4 q^{46} + 12 q^{49} + 54 q^{56} - 4 q^{58} - 24 q^{59} + 48 q^{62} - 20 q^{64} + 24 q^{67} + 72 q^{68} - 12 q^{70} - 24 q^{77} + 32 q^{80} - 48 q^{83} + 64 q^{88} - 36 q^{89} - 60 q^{98}+O(q^{100}) \) 12 * q - 16 * q^4 + 12 * q^5 - 2 * q^7 - 12 * q^14 + 32 * q^16 - 16 * q^20 - 4 * q^22 + 12 * q^25 - 36 * q^26 + 10 * q^28 - 2 * q^35 - 28 * q^37 - 4 * q^43 - 4 * q^46 + 12 * q^49 + 54 * q^56 - 4 * q^58 - 24 * q^59 + 48 * q^62 - 20 * q^64 + 24 * q^67 + 72 * q^68 - 12 * q^70 - 24 * q^77 + 32 * q^80 - 48 * q^83 + 64 * q^88 - 36 * q^89 - 60 * q^98

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