LMFDB - Embedded newform 1134.2.d.b.1133.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(1133,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1134.1133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.d (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:	$9.05503558921$
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} - 8 x^{15} + 56 x^{14} - 252 x^{13} + 962 x^{12} - 2860 x^{11} + 7240 x^{10} - 15036 x^{9} + \cdots + 457 $ x^16 - 8x^15 + 56x^14 - 252x^13 + 962x^12 - 2860x^11 + 7240x^10 - 15036x^9 + 26533x^8 - 38796x^7 + 47500x^6 - 47396x^5 + 38144x^4 - 23676x^3 + 10748x^2 - 3160*x + 457
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1133.13
Root			$0.500000 + 0.221083i$ of defining polynomial
Character	$\chi$	$=$	1134.1133
Dual form			1134.2.d.b.1133.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +1.01976 q^{5} +(0.141281 + 2.64198i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +1.01976 q^{5} +(0.141281 + 2.64198i) q^{7} -1.00000i q^{8} +1.01976i q^{10} -5.07812i q^{11} -5.45173i q^{13} +(-2.64198 + 0.141281i) q^{14} +1.00000 q^{16} +6.19825 q^{17} -7.96453i q^{19} -1.01976 q^{20} +5.07812 q^{22} +0.835475i q^{23} -3.96008 q^{25} +5.45173 q^{26} +(-0.141281 - 2.64198i) q^{28} +8.91359i q^{29} -3.97359i q^{31} +1.00000i q^{32} +6.19825i q^{34} +(0.144073 + 2.69419i) q^{35} -2.64324 q^{37} +7.96453 q^{38} -1.01976i q^{40} +6.36603 q^{41} +5.67095 q^{43} +5.07812i q^{44} -0.835475 q^{46} -0.563843 q^{47} +(-6.96008 + 0.746520i) q^{49} -3.96008i q^{50} +5.45173i q^{52} -2.19615i q^{53} -5.17848i q^{55} +(2.64198 - 0.141281i) q^{56} -8.91359 q^{58} +7.21801 q^{59} +7.94963i q^{61} +3.97359 q^{62} -1.00000 q^{64} -5.55948i q^{65} +10.7091 q^{67} -6.19825 q^{68} +(-2.69419 + 0.144073i) q^{70} -6.20272i q^{71} -7.05024i q^{73} -2.64324i q^{74} +7.96453i q^{76} +(13.4163 - 0.717439i) q^{77} -4.74907 q^{79} +1.01976 q^{80} +6.36603i q^{82} +11.0089 q^{83} +6.32076 q^{85} +5.67095i q^{86} -5.07812 q^{88} +2.11919 q^{89} +(14.4033 - 0.770223i) q^{91} -0.835475i q^{92} -0.563843i q^{94} -8.12195i q^{95} +2.78605i q^{97} +(-0.746520 - 6.96008i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 8 q^{7}+O(q^{10}) $ 16 * q - 16 * q^4 + 8 * q^7	$ 16 q - 16 q^{4} + 8 q^{7} + 16 q^{16} + 16 q^{25} - 8 q^{28} + 16 q^{37} + 64 q^{43} - 32 q^{49} - 48 q^{58} - 16 q^{64} - 16 q^{67} - 24 q^{70} + 32 q^{79} - 48 q^{85} + 24 q^{91}+O(q^{100}) $ 16 * q - 16 * q^4 + 8 * q^7 + 16 * q^16 + 16 * q^25 - 8 * q^28 + 16 * q^37 + 64 * q^43 - 32 * q^49 - 48 * q^58 - 16 * q^64 - 16 * q^67 - 24 * q^70 + 32 * q^79 - 48 * q^85 + 24 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	1.01976			0.456053			0.228026	−	0.973655i	$-0.426773\pi$
$5$	1.01976			0.456053			0.228026	+	0.973655i	$0.426773\pi$
$6$		0			0
$7$	0.141281	+	2.64198i	0.0533990	+	0.998573i
$7$	0.141281	+	2.64198i	0.0533990	+	0.998573i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$			1.01976i			0.322478i
$11$		−	5.07812i		−	1.53111i	−0.643371	−	0.765555i	$-0.722465\pi$
$11$		−	5.07812i		−	1.53111i	0.643371	−	0.765555i	$-0.277535\pi$
$12$		0			0
$13$		−	5.45173i		−	1.51204i	−0.654550	−	0.756019i	$-0.727142\pi$
$13$		−	5.45173i		−	1.51204i	0.654550	−	0.756019i	$-0.272858\pi$
$14$	−2.64198	+	0.141281i	−0.706098	+	0.0377588i
$15$		0			0
$16$	1.00000			0.250000
$17$	6.19825			1.50330			0.751648	−	0.659564i	$-0.229259\pi$
$17$	6.19825			1.50330			0.751648	+	0.659564i	$0.229259\pi$
$18$		0			0
$19$		−	7.96453i		−	1.82719i	−0.406626	−	0.913595i	$-0.633295\pi$
$19$		−	7.96453i		−	1.82719i	0.406626	−	0.913595i	$-0.366705\pi$
$20$	−1.01976			−0.228026
$21$		0			0
$22$	5.07812			1.08266
$23$			0.835475i			0.174209i	0.996199	+	0.0871043i	$0.0277613\pi$
$23$			0.835475i			0.174209i	−0.996199	+	0.0871043i	$0.972239\pi$
$24$		0			0
$25$	−3.96008			−0.792016
$26$	5.45173			1.06917
$27$		0			0
$28$	−0.141281	−	2.64198i	−0.0266995	−	0.499287i
$29$			8.91359i			1.65521i	0.561309	+	0.827606i	$0.310298\pi$
$29$			8.91359i			1.65521i	−0.561309	+	0.827606i	$0.689702\pi$
$30$		0			0
$31$		−	3.97359i		−	0.713678i	−0.934166	−	0.356839i	$-0.883854\pi$
$31$		−	3.97359i		−	0.713678i	0.934166	−	0.356839i	$-0.116146\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$			6.19825i			1.06299i
$35$	0.144073	+	2.69419i	0.0243528	+	0.455402i
$36$		0			0
$37$	−2.64324			−0.434546			−0.217273	−	0.976111i	$-0.569716\pi$
$37$	−2.64324			−0.434546			−0.217273	+	0.976111i	$0.569716\pi$
$38$	7.96453			1.29202
$39$		0			0
$40$		−	1.01976i		−	0.161239i
$41$	6.36603			0.994206			0.497103	−	0.867691i	$-0.334397\pi$
$41$	6.36603			0.994206			0.497103	+	0.867691i	$0.334397\pi$
$42$		0			0
$43$	5.67095			0.864812			0.432406	−	0.901679i	$-0.357665\pi$
$43$	5.67095			0.864812			0.432406	+	0.901679i	$0.357665\pi$
$44$			5.07812i			0.765555i
$45$		0			0
$46$	−0.835475			−0.123184
$47$	−0.563843			−0.0822449			−0.0411224	−	0.999154i	$-0.513093\pi$
$47$	−0.563843			−0.0822449			−0.0411224	+	0.999154i	$0.513093\pi$
$48$		0			0
$49$	−6.96008	+	0.746520i	−0.994297	+	0.106646i
$50$		−	3.96008i		−	0.560040i
$51$		0			0
$52$			5.45173i			0.756019i
$53$		−	2.19615i		−	0.301665i	−0.988559	−	0.150832i	$-0.951805\pi$
$53$		−	2.19615i		−	0.301665i	0.988559	−	0.150832i	$-0.0481954\pi$
$54$		0			0
$55$		−	5.17848i		−	0.698267i
$56$	2.64198	−	0.141281i	0.353049	−	0.0188794i
$57$		0			0
$58$	−8.91359			−1.17041
$59$	7.21801			0.939705			0.469853	−	0.882745i	$-0.344307\pi$
$59$	7.21801			0.939705			0.469853	+	0.882745i	$0.344307\pi$
$60$		0			0
$61$			7.94963i			1.01785i	0.860812	+	0.508923i	$0.169956\pi$
$61$			7.94963i			1.01785i	−0.860812	+	0.508923i	$0.830044\pi$
$62$	3.97359			0.504647
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	5.55948i		−	0.689569i
$66$		0			0
$67$	10.7091			1.30833			0.654165	−	0.756352i	$-0.273020\pi$
$67$	10.7091			1.30833			0.654165	+	0.756352i	$0.273020\pi$
$68$	−6.19825			−0.751648
$69$		0			0
$70$	−2.69419	+	0.144073i	−0.322018	+	0.0172200i
$71$		−	6.20272i		−	0.736127i	−0.929801	−	0.368064i	$-0.880021\pi$
$71$		−	6.20272i		−	0.736127i	0.929801	−	0.368064i	$-0.119979\pi$
$72$		0			0
$73$		−	7.05024i		−	0.825168i	−0.910920	−	0.412584i	$-0.864626\pi$
$73$		−	7.05024i		−	0.825168i	0.910920	−	0.412584i	$-0.135374\pi$
$74$		−	2.64324i		−	0.307270i
$75$		0			0
$76$			7.96453i			0.913595i
$77$	13.4163	−	0.717439i	1.52893	−	0.0817598i
$78$		0			0
$79$	−4.74907			−0.534312			−0.267156	−	0.963653i	$-0.586084\pi$
$79$	−4.74907			−0.534312			−0.267156	+	0.963653i	$0.586084\pi$
$80$	1.01976			0.114013
$81$		0			0
$82$			6.36603i			0.703010i
$83$	11.0089			1.20839			0.604193	−	0.796838i	$-0.293495\pi$
$83$	11.0089			1.20839			0.604193	+	0.796838i	$0.293495\pi$
$84$		0			0
$85$	6.32076			0.685582
$86$			5.67095i			0.611514i
$87$		0			0
$88$	−5.07812			−0.541329
$89$	2.11919			0.224634			0.112317	−	0.993672i	$-0.464173\pi$
$89$	2.11919			0.224634			0.112317	+	0.993672i	$0.464173\pi$
$90$		0			0
$91$	14.4033	−	0.770223i	1.50988	−	0.0807413i
$92$		−	0.835475i		−	0.0871043i
$93$		0			0
$94$		−	0.563843i		−	0.0581559i
$95$		−	8.12195i		−	0.833295i
$96$		0			0
$97$			2.78605i			0.282880i	0.989947	+	0.141440i	$0.0451733\pi$
$97$			2.78605i			0.282880i	−0.989947	+	0.141440i	$0.954827\pi$
$98$	−0.746520	−	6.96008i	−0.0754099	−	0.703074i
$99$		0			0
$100$	3.96008			0.396008
$101$	−12.0609			−1.20011			−0.600054	−	0.799959i	$-0.704854\pi$
$101$	−12.0609			−1.20011			−0.600054	+	0.799959i	$0.704854\pi$
$102$		0			0
$103$		−	14.4360i		−	1.42242i	−0.702978	−	0.711212i	$-0.748147\pi$
$103$		−	14.4360i		−	1.42242i	0.702978	−	0.711212i	$-0.251853\pi$
$104$	−5.45173			−0.534586
$105$		0			0
$106$	2.19615			0.213309
$107$			11.0039i			1.06379i	0.846811	+	0.531894i	$0.178520\pi$
$107$			11.0039i			1.06379i	−0.846811	+	0.531894i	$0.821480\pi$
$108$		0			0
$109$	−2.94130			−0.281726			−0.140863	−	0.990029i	$-0.544988\pi$
$109$	−2.94130			−0.281726			−0.140863	+	0.990029i	$0.544988\pi$
$110$	5.17848			0.493749
$111$		0			0
$112$	0.141281	+	2.64198i	0.0133498	+	0.249643i
$113$			6.93237i			0.652142i	0.945345	+	0.326071i	$0.105725\pi$
$113$			6.93237i			0.652142i	−0.945345	+	0.326071i	$0.894275\pi$
$114$		0			0
$115$			0.851988i			0.0794483i
$116$		−	8.91359i		−	0.827606i
$117$		0			0
$118$			7.21801i			0.664472i
$119$	0.875692	+	16.3756i	0.0802745	+	1.50115i
$120$		0			0
$121$	−14.7873			−1.34430
$122$	−7.94963			−0.719726
$123$		0			0
$124$			3.97359i			0.356839i
$125$	−9.13717			−0.817254
$126$		0			0
$127$	−13.3085			−1.18094			−0.590471	−	0.807059i	$-0.701058\pi$
$127$	−13.3085			−1.18094			−0.590471	+	0.807059i	$0.701058\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	5.55948			0.487599
$131$	12.0609			1.05377			0.526885	−	0.849937i	$-0.323360\pi$
$131$	12.0609			1.05377			0.526885	+	0.849937i	$0.323360\pi$
$132$		0			0
$133$	21.0421	−	1.12523i	1.82458	−	0.0975701i
$134$			10.7091i			0.925129i
$135$		0			0
$136$		−	6.19825i		−	0.531495i
$137$		−	13.3801i		−	1.14314i	−0.820554	−	0.571569i	$-0.806335\pi$
$137$		−	13.3801i		−	1.14314i	0.820554	−	0.571569i	$-0.193665\pi$
$138$		0			0
$139$			9.71592i			0.824093i	0.911163	+	0.412047i	$0.135186\pi$
$139$			9.71592i			0.824093i	−0.911163	+	0.412047i	$0.864814\pi$
$140$	−0.144073	−	2.69419i	−0.0121764	−	0.227701i
$141$		0			0
$142$	6.20272			0.520521
$143$	−27.6845			−2.31510
$144$		0			0
$145$			9.08977i			0.754864i
$146$	7.05024			0.583482
$147$		0			0
$148$	2.64324			0.217273
$149$			18.1357i			1.48574i	0.669437	+	0.742869i	$0.266535\pi$
$149$			18.1357i			1.48574i	−0.669437	+	0.742869i	$0.733465\pi$
$150$		0			0
$151$	−10.1750			−0.828030			−0.414015	−	0.910270i	$-0.635874\pi$
$151$	−10.1750			−0.828030			−0.414015	+	0.910270i	$0.635874\pi$
$152$	−7.96453			−0.646009
$153$		0			0
$154$	0.717439	+	13.4163i	0.0578129	+	1.08111i
$155$		−	4.05213i		−	0.325475i
$156$		0			0
$157$			9.53079i			0.760640i	0.924855	+	0.380320i	$0.124186\pi$
$157$			9.53079i			0.760640i	−0.924855	+	0.380320i	$0.875814\pi$
$158$		−	4.74907i		−	0.377815i
$159$		0			0
$160$			1.01976i			0.0806195i
$161$	−2.20731	+	0.118036i	−0.173960	+	0.00930257i
$162$		0			0
$163$	−7.33296			−0.574362			−0.287181	−	0.957876i	$-0.592718\pi$
$163$	−7.33296			−0.574362			−0.287181	+	0.957876i	$0.592718\pi$
$164$	−6.36603			−0.497103
$165$		0			0
$166$			11.0089i			0.854458i
$167$	−1.18754			−0.0918947			−0.0459474	−	0.998944i	$-0.514631\pi$
$167$	−1.18754			−0.0918947			−0.0459474	+	0.998944i	$0.514631\pi$
$168$		0			0
$169$	−16.7214			−1.28626
$170$			6.32076i			0.484780i
$171$		0			0
$172$	−5.67095			−0.432406
$173$	−3.59488			−0.273313			−0.136657	−	0.990618i	$-0.543636\pi$
$173$	−3.59488			−0.273313			−0.136657	+	0.990618i	$0.543636\pi$
$174$		0			0
$175$	−0.559482	−	10.4624i	−0.0422929	−	0.790886i
$176$		−	5.07812i		−	0.382777i
$177$		0			0
$178$			2.11919i			0.158840i
$179$		−	9.26770i		−	0.692700i	−0.938105	−	0.346350i	$-0.887421\pi$
$179$		−	9.26770i		−	0.692700i	0.938105	−	0.346350i	$-0.112579\pi$
$180$		0			0
$181$			5.81954i			0.432563i	0.976331	+	0.216281i	$0.0693928\pi$
$181$			5.81954i			0.432563i	−0.976331	+	0.216281i	$0.930607\pi$
$182$	0.770223	+	14.4033i	0.0570927	+	1.06765i
$183$		0			0
$184$	0.835475			0.0615921
$185$	−2.69548			−0.198176
$186$		0			0
$187$		−	31.4754i		−	2.30171i
$188$	0.563843			0.0411224
$189$		0			0
$190$	8.12195			0.589228
$191$		−	4.31684i		−	0.312356i	−0.987729	−	0.156178i	$-0.950083\pi$
$191$		−	4.31684i		−	0.312356i	0.987729	−	0.156178i	$-0.0499173\pi$
$192$		0			0
$193$	21.9861			1.58259			0.791296	−	0.611433i	$-0.209407\pi$
$193$	21.9861			1.58259			0.791296	+	0.611433i	$0.209407\pi$
$194$	−2.78605			−0.200027
$195$		0			0
$196$	6.96008	−	0.746520i	0.497149	−	0.0533228i
$197$		−	9.96399i		−	0.709905i	−0.934884	−	0.354953i	$-0.884497\pi$
$197$		−	9.96399i		−	0.709905i	0.934884	−	0.354953i	$-0.115503\pi$
$198$		0			0
$199$			11.6673i			0.827075i	0.910487	+	0.413538i	$0.135707\pi$
$199$			11.6673i			0.827075i	−0.910487	+	0.413538i	$0.864293\pi$
$200$			3.96008i			0.280020i
$201$		0			0
$202$		−	12.0609i		−	0.848605i
$203$	−23.5495	+	1.25932i	−1.65285	+	0.0883867i
$204$		0			0
$205$	6.49185			0.453410
$206$	14.4360			1.00581
$207$		0			0
$208$		−	5.45173i		−	0.378009i
$209$	−40.4448			−2.79763
$210$		0			0
$211$	−1.60332			−0.110377			−0.0551885	−	0.998476i	$-0.517576\pi$
$211$	−1.60332			−0.110377			−0.0551885	+	0.998476i	$0.517576\pi$
$212$			2.19615i			0.150832i
$213$		0			0
$214$	−11.0039			−0.752212
$215$	5.78304			0.394400
$216$		0			0
$217$	10.4981	−	0.561391i	0.712660	−	0.0381097i
$218$		−	2.94130i		−	0.199210i
$219$		0			0
$220$			5.17848i			0.349133i
$221$		−	33.7912i		−	2.27304i
$222$		0			0
$223$		−	18.3042i		−	1.22574i	−0.790185	−	0.612868i	$-0.790016\pi$
$223$		−	18.3042i		−	1.22574i	0.790185	−	0.612868i	$-0.209984\pi$
$224$	−2.64198	+	0.141281i	−0.176524	+	0.00943970i
$225$		0			0
$226$	−6.93237			−0.461134
$227$	15.8519			1.05212			0.526062	−	0.850446i	$-0.323668\pi$
$227$	15.8519			1.05212			0.526062	+	0.850446i	$0.323668\pi$
$228$		0			0
$229$			21.7163i			1.43506i	0.696529	+	0.717528i	$0.254727\pi$
$229$			21.7163i			1.43506i	−0.696529	+	0.717528i	$0.745273\pi$
$230$	−0.851988			−0.0561785
$231$		0			0
$232$	8.91359			0.585206
$233$			17.0886i			1.11951i	0.828658	+	0.559756i	$0.189105\pi$
$233$			17.0886i			1.11951i	−0.828658	+	0.559756i	$0.810895\pi$
$234$		0			0
$235$	−0.574987			−0.0375080
$236$	−7.21801			−0.469853
$237$		0			0
$238$	−16.3756	+	0.875692i	−1.06147	+	0.0567627i
$239$		−	9.32969i		−	0.603488i	−0.953389	−	0.301744i	$-0.902431\pi$
$239$		−	9.32969i		−	0.603488i	0.953389	−	0.301744i	$-0.0975687\pi$
$240$		0			0
$241$		−	22.4030i		−	1.44310i	−0.692360	−	0.721552i	$-0.743429\pi$
$241$		−	22.4030i		−	1.44310i	0.692360	−	0.721552i	$-0.256571\pi$
$242$		−	14.7873i		−	0.950561i
$243$		0			0
$244$		−	7.94963i		−	0.508923i
$245$	−7.09764	+	0.761275i	−0.453452	+	0.0486360i
$246$		0			0
$247$	−43.4205			−2.76278
$248$	−3.97359			−0.252323
$249$		0			0
$250$		−	9.13717i		−	0.577886i
$251$	−5.13108			−0.323871			−0.161935	−	0.986801i	$-0.551774\pi$
$251$	−5.13108			−0.323871			−0.161935	+	0.986801i	$0.551774\pi$
$252$		0			0
$253$	4.24264			0.266733
$254$		−	13.3085i		−	0.835053i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−9.85364			−0.614653			−0.307327	−	0.951604i	$-0.599434\pi$
$257$	−9.85364			−0.614653			−0.307327	+	0.951604i	$0.599434\pi$
$258$		0			0
$259$	−0.373438	−	6.98337i	−0.0232043	−	0.433926i
$260$			5.55948i			0.344784i
$261$		0			0
$262$			12.0609i			0.745128i
$263$		−	11.4639i		−	0.706891i	−0.935455	−	0.353446i	$-0.885010\pi$
$263$		−	11.4639i		−	0.706891i	0.935455	−	0.353446i	$-0.114990\pi$
$264$		0			0
$265$		−	2.23956i		−	0.137575i
$266$	1.12523	+	21.0421i	0.0689925	+	1.29017i
$267$		0			0
$268$	−10.7091			−0.654165
$269$	20.8626			1.27201			0.636007	−	0.771684i	$-0.280585\pi$
$269$	20.8626			1.27201			0.636007	+	0.771684i	$0.280585\pi$
$270$		0			0
$271$		−	1.27566i		−	0.0774907i	−0.999249	−	0.0387453i	$-0.987664\pi$
$271$		−	1.27566i		−	0.0774907i	0.999249	−	0.0387453i	$-0.0123361\pi$
$272$	6.19825			0.375824
$273$		0			0
$274$	13.3801			0.808321
$275$			20.1097i			1.21266i
$276$		0			0
$277$	−7.94457			−0.477343			−0.238672	−	0.971100i	$-0.576712\pi$
$277$	−7.94457			−0.477343			−0.238672	+	0.971100i	$0.576712\pi$
$278$	−9.71592			−0.582722
$279$		0			0
$280$	2.69419	−	0.144073i	0.161009	−	0.00861000i
$281$			19.2304i			1.14719i	0.819139	+	0.573596i	$0.194452\pi$
$281$			19.2304i			1.14719i	−0.819139	+	0.573596i	$0.805548\pi$
$282$		0			0
$283$		−	5.36116i		−	0.318688i	−0.987223	−	0.159344i	$-0.949062\pi$
$283$		−	5.36116i		−	0.318688i	0.987223	−	0.159344i	$-0.0509379\pi$
$284$			6.20272i			0.368064i
$285$		0			0
$286$		−	27.6845i		−	1.63702i
$287$	0.899395	+	16.8189i	0.0530896	+	0.992788i
$288$		0			0
$289$	21.4183			1.25990
$290$	−9.08977			−0.533770
$291$		0			0
$292$			7.05024i			0.412584i
$293$	0.148630			0.00868304			0.00434152	−	0.999991i	$-0.498618\pi$
$293$	0.148630			0.00868304			0.00434152	+	0.999991i	$0.498618\pi$
$294$		0			0
$295$	7.36068			0.428555
$296$			2.64324i			0.153635i
$297$		0			0
$298$	−18.1357			−1.05057
$299$	4.55479			0.263410
$300$		0			0
$301$	0.801195	+	14.9825i	0.0461801	+	0.863578i
$302$		−	10.1750i		−	0.585506i
$303$		0			0
$304$		−	7.96453i		−	0.456797i
$305$			8.10676i			0.464192i
$306$		0			0
$307$		−	0.623699i		−	0.0355964i	−0.999842	−	0.0177982i	$-0.994334\pi$
$307$		−	0.623699i		−	0.0355964i	0.999842	−	0.0177982i	$-0.00566564\pi$
$308$	−13.4163	+	0.717439i	−0.764463	+	0.0408799i
$309$		0			0
$310$	4.05213			0.230145
$311$	−20.8303			−1.18118			−0.590589	−	0.806972i	$-0.701105\pi$
$311$	−20.8303			−1.18118			−0.590589	+	0.806972i	$0.701105\pi$
$312$		0			0
$313$			20.4042i			1.15331i	0.816987	+	0.576657i	$0.195643\pi$
$313$			20.4042i			1.15331i	−0.816987	+	0.576657i	$0.804357\pi$
$314$	−9.53079			−0.537854
$315$		0			0
$316$	4.74907			0.267156
$317$			10.0593i			0.564989i	0.959269	+	0.282494i	$0.0911619\pi$
$317$			10.0593i			0.564989i	−0.959269	+	0.282494i	$0.908838\pi$
$318$		0			0
$319$	45.2643			2.53431
$320$	−1.01976			−0.0570066
$321$		0			0
$322$	−0.118036	−	2.20731i	−0.00657791	−	0.123008i
$323$		−	49.3662i		−	2.74681i
$324$		0			0
$325$			21.5893i			1.19756i
$326$		−	7.33296i		−	0.406135i
$327$		0			0
$328$		−	6.36603i		−	0.351505i
$329$	−0.0796600	−	1.48966i	−0.00439180	−	0.0821275i
$330$		0			0
$331$	26.1229			1.43584			0.717922	−	0.696124i	$-0.245094\pi$
$331$	26.1229			1.43584			0.717922	+	0.696124i	$0.245094\pi$
$332$	−11.0089			−0.604193
$333$		0			0
$334$		−	1.18754i		−	0.0649794i
$335$	10.9208			0.596668
$336$		0			0
$337$	13.3950			0.729670			0.364835	−	0.931072i	$-0.381125\pi$
$337$	13.3950			0.729670			0.364835	+	0.931072i	$0.381125\pi$
$338$		−	16.7214i		−	0.909522i
$339$		0			0
$340$	−6.32076			−0.342791
$341$	−20.1784			−1.09272
$342$		0			0
$343$	−2.95561	−	18.2829i	−0.159588	−	0.987184i
$344$		−	5.67095i		−	0.305757i
$345$		0			0
$346$		−	3.59488i		−	0.193262i
$347$			15.7174i			0.843756i	0.906653	+	0.421878i	$0.138629\pi$
$347$			15.7174i			0.843756i	−0.906653	+	0.421878i	$0.861371\pi$
$348$		0			0
$349$		−	0.333758i		−	0.0178657i	−0.999960	−	0.00893284i	$-0.997157\pi$
$349$		−	0.333758i		−	0.0178657i	0.999960	−	0.00893284i	$-0.00284345\pi$
$350$	10.4624	−	0.559482i	0.559241	−	0.0299056i
$351$		0			0
$352$	5.07812			0.270664
$353$	−6.45414			−0.343519			−0.171760	−	0.985139i	$-0.554945\pi$
$353$	−6.45414			−0.343519			−0.171760	+	0.985139i	$0.554945\pi$
$354$		0			0
$355$		−	6.32532i		−	0.335713i
$356$	−2.11919			−0.112317
$357$		0			0
$358$	9.26770			0.489813
$359$		−	0.172817i		−	0.00912095i	−0.999990	−	0.00456047i	$-0.998548\pi$
$359$		−	0.172817i		−	0.00912095i	0.999990	−	0.00456047i	$-0.00145165\pi$
$360$		0			0
$361$	−44.4338			−2.33862
$362$	−5.81954			−0.305868
$363$		0			0
$364$	−14.4033	+	0.770223i	−0.754940	+	0.0403707i
$365$		−	7.18958i		−	0.376320i
$366$		0			0
$367$		−	13.3366i		−	0.696165i	−0.937464	−	0.348083i	$-0.886833\pi$
$367$		−	13.3366i		−	0.696165i	0.937464	−	0.348083i	$-0.113167\pi$
$368$			0.835475i			0.0435522i
$369$		0			0
$370$		−	2.69548i		−	0.140131i
$371$	5.80218	−	0.310274i	0.301234	−	0.0161086i
$372$		0			0
$373$	−17.3485			−0.898270			−0.449135	−	0.893464i	$-0.648268\pi$
$373$	−17.3485			−0.898270			−0.449135	+	0.893464i	$0.648268\pi$
$374$	31.4754			1.62756
$375$		0			0
$376$			0.563843i			0.0290780i
$377$	48.5945			2.50274
$378$		0			0
$379$	0.645891			0.0331772			0.0165886	−	0.999862i	$-0.494719\pi$
$379$	0.645891			0.0331772			0.0165886	+	0.999862i	$0.494719\pi$
$380$			8.12195i			0.416647i
$381$		0			0
$382$	4.31684			0.220869
$383$	−24.3455			−1.24400			−0.621999	−	0.783018i	$-0.713679\pi$
$383$	−24.3455			−1.24400			−0.621999	+	0.783018i	$0.713679\pi$
$384$		0			0
$385$	13.6814	−	0.731619i	0.697270	−	0.0372868i
$386$			21.9861i			1.11906i
$387$		0			0
$388$		−	2.78605i		−	0.141440i
$389$		−	34.7203i		−	1.76039i	−0.474614	−	0.880194i	$-0.657412\pi$
$389$		−	34.7203i		−	1.76039i	0.474614	−	0.880194i	$-0.342588\pi$
$390$		0			0
$391$			5.17848i			0.261887i
$392$	0.746520	+	6.96008i	0.0377049	+	0.351537i
$393$		0			0
$394$	9.96399			0.501979
$395$	−4.84293			−0.243674
$396$		0			0
$397$			9.89614i			0.496673i	0.968674	+	0.248337i	$0.0798839\pi$
$397$			9.89614i			0.496673i	−0.968674	+	0.248337i	$0.920116\pi$
$398$	−11.6673			−0.584830
$399$		0			0
$400$	−3.96008			−0.198004
$401$			13.3181i			0.665074i	0.943090	+	0.332537i	$0.107905\pi$
$401$			13.3181i			0.665074i	−0.943090	+	0.332537i	$0.892095\pi$
$402$		0			0
$403$	−21.6629			−1.07911
$404$	12.0609			0.600054
$405$		0			0
$406$	−1.25932	−	23.5495i	−0.0624988	−	1.16874i
$407$			13.4227i			0.665337i
$408$		0			0
$409$		−	7.80767i		−	0.386064i	−0.981192	−	0.193032i	$-0.938168\pi$
$409$		−	7.80767i		−	0.386064i	0.981192	−	0.193032i	$-0.0618322\pi$
$410$			6.49185i			0.320610i
$411$		0			0
$412$			14.4360i			0.711212i
$413$	1.01976	+	19.0698i	0.0501793	+	0.938365i
$414$		0			0
$415$	11.2265			0.551088
$416$	5.45173			0.267293
$417$		0			0
$418$		−	40.4448i		−	1.97822i
$419$	−30.5760			−1.49374			−0.746868	−	0.664972i	$-0.768444\pi$
$419$	−30.5760			−1.49374			−0.746868	+	0.664972i	$0.768444\pi$
$420$		0			0
$421$	−29.9686			−1.46058			−0.730289	−	0.683138i	$-0.760615\pi$
$421$	−29.9686			−1.46058			−0.730289	+	0.683138i	$0.760615\pi$
$422$		−	1.60332i		−	0.0780483i
$423$		0			0
$424$	−2.19615			−0.106655
$425$	−24.5456			−1.19063
$426$		0			0
$427$	−21.0027	+	1.12313i	−1.01639	+	0.0543520i
$428$		−	11.0039i		−	0.531894i
$429$		0			0
$430$			5.78304i			0.278883i
$431$			19.8981i			0.958457i	0.877690	+	0.479229i	$0.159083\pi$
$431$			19.8981i			0.958457i	−0.877690	+	0.479229i	$0.840917\pi$
$432$		0			0
$433$			26.6176i			1.27916i	0.768725	+	0.639580i	$0.220892\pi$
$433$			26.6176i			1.27916i	−0.768725	+	0.639580i	$0.779108\pi$
$434$	0.561391	+	10.4981i	0.0269476	+	0.503927i
$435$		0			0
$436$	2.94130			0.140863
$437$	6.65417			0.318312
$438$		0			0
$439$			29.1602i			1.39174i	0.718168	+	0.695870i	$0.244981\pi$
$439$			29.1602i			1.39174i	−0.718168	+	0.695870i	$0.755019\pi$
$440$	−5.17848			−0.246875
$441$		0			0
$442$	33.7912			1.60728
$443$			29.3107i			1.39260i	0.717753	+	0.696298i	$0.245171\pi$
$443$			29.3107i			1.39260i	−0.717753	+	0.696298i	$0.754829\pi$
$444$		0			0
$445$	2.16108			0.102445
$446$	18.3042			0.866727
$447$		0			0
$448$	−0.141281	−	2.64198i	−0.00667488	−	0.124822i
$449$		−	14.5485i		−	0.686588i	−0.939228	−	0.343294i	$-0.888457\pi$
$449$		−	14.5485i		−	0.686588i	0.939228	−	0.343294i	$-0.111543\pi$
$450$		0			0
$451$		−	32.3274i		−	1.52224i
$452$		−	6.93237i		−	0.326071i
$453$		0			0
$454$			15.8519i			0.743965i
$455$	14.6880	−	0.785447i	0.688585	−	0.0368223i
$456$		0			0
$457$	−5.21166			−0.243791			−0.121896	−	0.992543i	$-0.538897\pi$
$457$	−5.21166			−0.243791			−0.121896	+	0.992543i	$0.538897\pi$
$458$	−21.7163			−1.01474
$459$		0			0
$460$		−	0.851988i		−	0.0397242i
$461$	34.9906			1.62968			0.814838	−	0.579688i	$-0.196826\pi$
$461$	34.9906			1.62968			0.814838	+	0.579688i	$0.196826\pi$
$462$		0			0
$463$	−2.05213			−0.0953705			−0.0476852	−	0.998862i	$-0.515184\pi$
$463$	−2.05213			−0.0953705			−0.0476852	+	0.998862i	$0.515184\pi$
$464$			8.91359i			0.413803i
$465$		0			0
$466$	−17.0886			−0.791614
$467$	−20.4066			−0.944307			−0.472153	−	0.881516i	$-0.656523\pi$
$467$	−20.4066			−0.944307			−0.472153	+	0.881516i	$0.656523\pi$
$468$		0			0
$469$	1.51299	+	28.2933i	0.0698636	+	1.30646i
$470$		−	0.574987i		−	0.0265222i
$471$		0			0
$472$		−	7.21801i		−	0.332236i
$473$		−	28.7977i		−	1.32412i
$474$		0			0
$475$			31.5402i			1.44716i
$476$	−0.875692	−	16.3756i	−0.0401373	−	0.750576i
$477$		0			0
$478$	9.32969			0.426730
$479$	13.8722			0.633836			0.316918	−	0.948453i	$-0.397352\pi$
$479$	13.8722			0.633836			0.316918	+	0.948453i	$0.397352\pi$
$480$		0			0
$481$			14.4102i			0.657049i
$482$	22.4030			1.02043
$483$		0			0
$484$	14.7873			0.672148
$485$			2.84112i			0.129008i
$486$		0			0
$487$	22.3646			1.01344			0.506718	−	0.862112i	$-0.330858\pi$
$487$	22.3646			1.01344			0.506718	+	0.862112i	$0.330858\pi$
$488$	7.94963			0.359863
$489$		0			0
$490$	−0.761275	−	7.09764i	−0.0343909	−	0.320639i
$491$			7.60770i			0.343330i	0.985155	+	0.171665i	$0.0549147\pi$
$491$			7.60770i			0.343330i	−0.985155	+	0.171665i	$0.945085\pi$
$492$		0			0
$493$			55.2487i			2.48827i
$494$		−	43.4205i		−	1.95358i
$495$		0			0
$496$		−	3.97359i		−	0.178419i
$497$	16.3874	−	0.876324i	0.735077	−	0.0393085i
$498$		0			0
$499$	−11.3208			−0.506787			−0.253393	−	0.967363i	$-0.581547\pi$
$499$	−11.3208			−0.506787			−0.253393	+	0.967363i	$0.581547\pi$
$500$	9.13717			0.408627
$501$		0			0
$502$		−	5.13108i		−	0.229011i
$503$	−21.2304			−0.946616			−0.473308	−	0.880897i	$-0.656940\pi$
$503$	−21.2304			−0.946616			−0.473308	+	0.880897i	$0.656940\pi$
$504$		0			0
$505$	−12.2993			−0.547313
$506$			4.24264i			0.188608i
$507$		0			0
$508$	13.3085			0.590471
$509$	30.3353			1.34459			0.672294	−	0.740284i	$-0.265309\pi$
$509$	30.3353			1.34459			0.672294	+	0.740284i	$0.265309\pi$
$510$		0			0
$511$	18.6266	−	0.996061i	0.823991	−	0.0440632i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$		−	9.85364i		−	0.434625i
$515$		−	14.7214i		−	0.648700i
$516$		0			0
$517$			2.86326i			0.125926i
$518$	6.98337	−	0.373438i	0.306832	−	0.0164079i
$519$		0			0
$520$	−5.55948			−0.243799
$521$	15.3479			0.672403			0.336201	−	0.941790i	$-0.390858\pi$
$521$	15.3479			0.672403			0.336201	+	0.941790i	$0.390858\pi$
$522$		0			0
$523$			9.95691i			0.435385i	0.976017	+	0.217693i	$0.0698530\pi$
$523$			9.95691i			0.435385i	−0.976017	+	0.217693i	$0.930147\pi$
$524$	−12.0609			−0.526885
$525$		0			0
$526$	11.4639			0.499848
$527$		−	24.6293i		−	1.07287i
$528$		0			0
$529$	22.3020			0.969651
$530$	2.23956			0.0972802
$531$		0			0
$532$	−21.0421	+	1.12523i	−0.912291	+	0.0487851i
$533$		−	34.7058i		−	1.50328i
$534$		0			0
$535$			11.2214i			0.485144i
$536$		−	10.7091i		−	0.462565i
$537$		0			0
$538$			20.8626i			0.899449i
$539$	3.79091	+	35.3441i	0.163286	+	1.52238i
$540$		0			0
$541$	−11.0521			−0.475168			−0.237584	−	0.971367i	$-0.576356\pi$
$541$	−11.0521			−0.475168			−0.237584	+	0.971367i	$0.576356\pi$
$542$	1.27566			0.0547942
$543$		0			0
$544$			6.19825i			0.265748i
$545$	−2.99944			−0.128482
$546$		0			0
$547$	−21.4305			−0.916302			−0.458151	−	0.888874i	$-0.651488\pi$
$547$	−21.4305			−0.916302			−0.458151	+	0.888874i	$0.651488\pi$
$548$			13.3801i			0.571569i
$549$		0			0
$550$	−20.1097			−0.857482
$551$	70.9926			3.02439
$552$		0			0
$553$	−0.670951	−	12.5469i	−0.0285317	−	0.533549i
$554$		−	7.94457i		−	0.337533i
$555$		0			0
$556$		−	9.71592i		−	0.412047i
$557$		−	27.0543i		−	1.14633i	−0.819441	−	0.573164i	$-0.805716\pi$
$557$		−	27.0543i		−	1.14633i	0.819441	−	0.573164i	$-0.194284\pi$
$558$		0			0
$559$		−	30.9165i		−	1.30763i
$560$	0.144073	+	2.69419i	0.00608819	+	0.113851i
$561$		0			0
$562$	−19.2304			−0.811187
$563$	9.97401			0.420354			0.210177	−	0.977663i	$-0.432596\pi$
$563$	9.97401			0.420354			0.210177	+	0.977663i	$0.432596\pi$
$564$		0			0
$565$			7.06938i			0.297411i
$566$	5.36116			0.225346
$567$		0			0
$568$	−6.20272			−0.260260
$569$			9.54635i			0.400204i	0.979775	+	0.200102i	$0.0641273\pi$
$569$			9.54635i			0.400204i	−0.979775	+	0.200102i	$0.935873\pi$
$570$		0			0
$571$	42.2616			1.76859			0.884296	−	0.466926i	$-0.154639\pi$
$571$	42.2616			1.76859			0.884296	+	0.466926i	$0.154639\pi$
$572$	27.6845			1.15755
$573$		0			0
$574$	−16.8189	+	0.899395i	−0.702007	+	0.0375400i
$575$		−	3.30855i		−	0.137976i
$576$		0			0
$577$		−	23.5258i		−	0.979392i	−0.871893	−	0.489696i	$-0.837108\pi$
$577$		−	23.5258i		−	0.979392i	0.871893	−	0.489696i	$-0.162892\pi$
$578$			21.4183i			0.890884i
$579$		0			0
$580$		−	9.08977i		−	0.377432i
$581$	1.55535	+	29.0853i	0.0645267	+	1.20666i
$582$		0			0
$583$	−11.1523			−0.461882
$584$	−7.05024			−0.291741
$585$		0			0
$586$			0.148630i			0.00613983i
$587$	16.1592			0.666960			0.333480	−	0.942757i	$-0.391777\pi$
$587$	16.1592			0.666960			0.333480	+	0.942757i	$0.391777\pi$
$588$		0			0
$589$	−31.6478			−1.30402
$590$			7.36068i			0.303034i
$591$		0			0
$592$	−2.64324			−0.108636
$593$	41.7403			1.71407			0.857034	−	0.515260i	$-0.172305\pi$
$593$	41.7403			1.71407			0.857034	+	0.515260i	$0.172305\pi$
$594$		0			0
$595$	0.893000	+	16.6993i	0.0366094	+	0.684604i
$596$		−	18.1357i		−	0.742869i
$597$		0			0
$598$			4.55479i			0.186259i
$599$		−	7.06261i		−	0.288570i	−0.989536	−	0.144285i	$-0.953912\pi$
$599$		−	7.06261i		−	0.288570i	0.989536	−	0.144285i	$-0.0460883\pi$
$600$		0			0
$601$			17.0369i			0.694952i	0.937689	+	0.347476i	$0.112961\pi$
$601$			17.0369i			0.694952i	−0.937689	+	0.347476i	$0.887039\pi$
$602$	−14.9825	+	0.801195i	−0.610642	+	0.0326543i
$603$		0			0
$604$	10.1750			0.414015
$605$	−15.0795			−0.613070
$606$		0			0
$607$			13.0060i			0.527895i	0.964537	+	0.263948i	$0.0850246\pi$
$607$			13.0060i			0.527895i	−0.964537	+	0.263948i	$0.914975\pi$
$608$	7.96453			0.323004
$609$		0			0
$610$	−8.10676			−0.328233
$611$			3.07392i			0.124357i
$612$		0			0
$613$	19.1434			0.773194			0.386597	−	0.922249i	$-0.373650\pi$
$613$	19.1434			0.773194			0.386597	+	0.922249i	$0.373650\pi$
$614$	0.623699			0.0251704
$615$		0			0
$616$	−0.717439	−	13.4163i	−0.0289064	−	0.540557i
$617$			23.4743i			0.945041i	0.881320	+	0.472521i	$0.156656\pi$
$617$			23.4743i			0.945041i	−0.881320	+	0.472521i	$0.843344\pi$
$618$		0			0
$619$			34.7025i			1.39481i	0.716677	+	0.697406i	$0.245662\pi$
$619$			34.7025i			1.39481i	−0.716677	+	0.697406i	$0.754338\pi$
$620$			4.05213i			0.162737i
$621$		0			0
$622$		−	20.8303i		−	0.835219i
$623$	0.299400	+	5.59885i	0.0119952	+	0.224313i
$624$		0			0
$625$	10.4826			0.419305
$626$	−20.4042			−0.815516
$627$		0			0
$628$		−	9.53079i		−	0.380320i
$629$	−16.3834			−0.653251
$630$		0			0
$631$	−15.5503			−0.619046			−0.309523	−	0.950892i	$-0.600169\pi$
$631$	−15.5503			−0.619046			−0.309523	+	0.950892i	$0.600169\pi$
$632$			4.74907i			0.188908i
$633$		0			0
$634$	−10.0593			−0.399507
$635$	−13.5716			−0.538572
$636$		0			0
$637$	4.06982	+	37.9445i	0.161252	+	1.50341i
$638$			45.2643i			1.79203i
$639$		0			0
$640$		−	1.01976i		−	0.0403097i
$641$			50.1944i			1.98256i	0.131770	+	0.991280i	$0.457934\pi$
$641$			50.1944i			1.98256i	−0.131770	+	0.991280i	$0.542066\pi$
$642$		0			0
$643$		−	49.4142i		−	1.94871i	−0.225023	−	0.974353i	$-0.572246\pi$
$643$		−	49.4142i		−	1.94871i	0.225023	−	0.974353i	$-0.427754\pi$
$644$	2.20731	−	0.118036i	0.0869800	−	0.00465129i
$645$		0			0
$646$	49.3662			1.94229
$647$	32.9511			1.29544			0.647721	−	0.761878i	$-0.275722\pi$
$647$	32.9511			1.29544			0.647721	+	0.761878i	$0.275722\pi$
$648$		0			0
$649$		−	36.6539i		−	1.43879i
$650$	−21.5893			−0.846801
$651$		0			0
$652$	7.33296			0.287181
$653$			25.3395i			0.991613i	0.868433	+	0.495806i	$0.165127\pi$
$653$			25.3395i			0.991613i	−0.868433	+	0.495806i	$0.834873\pi$
$654$		0			0
$655$	12.2993			0.480575
$656$	6.36603			0.248552
$657$		0			0
$658$	1.48966	−	0.0796600i	0.0580729	−	0.00310547i
$659$		−	15.1268i		−	0.589256i	−0.955612	−	0.294628i	$-0.904804\pi$
$659$		−	15.1268i		−	0.589256i	0.955612	−	0.294628i	$-0.0951958\pi$
$660$		0			0
$661$			35.3585i			1.37528i	0.726050	+	0.687642i	$0.241354\pi$
$661$			35.3585i			1.37528i	−0.726050	+	0.687642i	$0.758646\pi$
$662$			26.1229i			1.01529i
$663$		0			0
$664$		−	11.0089i		−	0.427229i
$665$	21.4580	−	1.14747i	0.832106	−	0.0444971i
$666$		0			0
$667$	−7.44709			−0.288352
$668$	1.18754			0.0459474
$669$		0			0
$670$			10.9208i			0.421908i
$671$	40.3692			1.55843
$672$		0			0
$673$	−12.5512			−0.483813			−0.241906	−	0.970300i	$-0.577773\pi$
$673$	−12.5512			−0.483813			−0.241906	+	0.970300i	$0.577773\pi$
$674$			13.3950i			0.515954i
$675$		0			0
$676$	16.7214			0.643129
$677$	−5.40677			−0.207799			−0.103900	−	0.994588i	$-0.533132\pi$
$677$	−5.40677			−0.207799			−0.103900	+	0.994588i	$0.533132\pi$
$678$		0			0
$679$	−7.36068	+	0.393615i	−0.282477	+	0.0151055i
$680$		−	6.32076i		−	0.242390i
$681$		0			0
$682$		−	20.1784i		−	0.772669i
$683$		−	3.51472i		−	0.134487i	−0.997737	−	0.0672435i	$-0.978580\pi$
$683$		−	3.51472i		−	0.134487i	0.997737	−	0.0672435i	$-0.0214204\pi$
$684$		0			0
$685$		−	13.6446i		−	0.521332i
$686$	18.2829	−	2.95561i	0.698044	−	0.112846i
$687$		0			0
$688$	5.67095			0.216203
$689$	−11.9728			−0.456128
$690$		0			0
$691$		−	12.7668i		−	0.485670i	−0.970068	−	0.242835i	$-0.921923\pi$
$691$		−	12.7668i		−	0.485670i	0.970068	−	0.242835i	$-0.0780774\pi$
$692$	3.59488			0.136657
$693$		0			0
$694$	−15.7174			−0.596626
$695$			9.90795i			0.375830i
$696$		0			0
$697$	39.4582			1.49459
$698$	0.333758			0.0126329
$699$		0			0
$700$	0.559482	+	10.4624i	0.0211464	+	0.395443i
$701$		−	14.4414i		−	0.545446i	−0.962093	−	0.272723i	$-0.912076\pi$
$701$		−	14.4414i		−	0.545446i	0.962093	−	0.272723i	$-0.0879242\pi$
$702$		0			0
$703$			21.0522i			0.793997i
$704$			5.07812i			0.191389i
$705$		0			0
$706$		−	6.45414i		−	0.242905i
$707$	−1.70398	−	31.8647i	−0.0640846	−	1.19840i
$708$		0			0
$709$	17.9297			0.673365			0.336682	−	0.941618i	$-0.390695\pi$
$709$	17.9297			0.673365			0.336682	+	0.941618i	$0.390695\pi$
$710$	6.32532			0.237385
$711$		0			0
$712$		−	2.11919i		−	0.0794200i
$713$	3.31984			0.124329
$714$		0			0
$715$	−28.2317			−1.05581
$716$			9.26770i			0.346350i
$717$		0			0
$718$	0.172817			0.00644948
$719$	36.9013			1.37619			0.688094	−	0.725622i	$-0.258448\pi$
$719$	36.9013			1.37619			0.688094	+	0.725622i	$0.258448\pi$
$720$		0			0
$721$	38.1396	−	2.03953i	1.42039	−	0.0759561i
$722$		−	44.4338i		−	1.65365i
$723$		0			0
$724$		−	5.81954i		−	0.216281i
$725$		−	35.2985i		−	1.31095i
$726$		0			0
$727$		−	19.0100i		−	0.705040i	−0.935804	−	0.352520i	$-0.885325\pi$
$727$		−	19.0100i		−	0.705040i	0.935804	−	0.352520i	$-0.114675\pi$
$728$	−0.770223	−	14.4033i	−0.0285464	−	0.533823i
$729$		0			0
$730$	7.18958			0.266098
$731$	35.1500			1.30007
$732$		0			0
$733$		−	29.2058i		−	1.07874i	−0.842068	−	0.539371i	$-0.818662\pi$
$733$		−	29.2058i		−	1.07874i	0.842068	−	0.539371i	$-0.181338\pi$
$734$	13.3366			0.492263
$735$		0			0
$736$	−0.835475			−0.0307960
$737$		−	54.3823i		−	2.00320i
$738$		0			0
$739$	−3.10127			−0.114082			−0.0570410	−	0.998372i	$-0.518167\pi$
$739$	−3.10127			−0.114082			−0.0570410	+	0.998372i	$0.518167\pi$
$740$	2.69548			0.0990879
$741$		0			0
$742$	0.310274	+	5.80218i	0.0113905	+	0.213005i
$743$			41.8237i			1.53436i	0.641430	+	0.767182i	$0.278342\pi$
$743$			41.8237i			1.53436i	−0.641430	+	0.767182i	$0.721658\pi$
$744$		0			0
$745$			18.4942i			0.677574i
$746$		−	17.3485i		−	0.635173i
$747$		0			0
$748$			31.4754i			1.15086i
$749$	−29.0721	+	1.55464i	−1.06227	+	0.0568053i
$750$		0			0
$751$	9.61553			0.350876			0.175438	−	0.984491i	$-0.443866\pi$
$751$	9.61553			0.350876			0.175438	+	0.984491i	$0.443866\pi$
$752$	−0.563843			−0.0205612
$753$		0			0
$754$			48.5945i			1.76971i
$755$	−10.3761			−0.377626
$756$		0			0
$757$	−30.1331			−1.09521			−0.547603	−	0.836738i	$-0.684459\pi$
$757$	−30.1331			−1.09521			−0.547603	+	0.836738i	$0.684459\pi$
$758$			0.645891i			0.0234598i
$759$		0			0
$760$	−8.12195			−0.294614
$761$	−4.64689			−0.168450			−0.0842249	−	0.996447i	$-0.526841\pi$
$761$	−4.64689			−0.168450			−0.0842249	+	0.996447i	$0.526841\pi$
$762$		0			0
$763$	−0.415549	−	7.77086i	−0.0150439	−	0.281324i
$764$			4.31684i			0.156178i
$765$		0			0
$766$		−	24.3455i		−	0.879640i
$767$		−	39.3507i		−	1.42087i
$768$		0			0
$769$			46.3656i			1.67199i	0.548740	+	0.835993i	$0.315108\pi$
$769$			46.3656i			1.67199i	−0.548740	+	0.835993i	$0.684892\pi$
$770$	0.731619	+	13.6814i	0.0263657	+	0.493045i
$771$		0			0
$772$	−21.9861			−0.791296
$773$	−48.4069			−1.74108			−0.870538	−	0.492102i	$-0.836229\pi$
$773$	−48.4069			−1.74108			−0.870538	+	0.492102i	$0.836229\pi$
$774$		0			0
$775$			15.7357i			0.565244i
$776$	2.78605			0.100013
$777$		0			0
$778$	34.7203			1.24478
$779$		−	50.7024i		−	1.81660i
$780$		0			0
$781$	−31.4981			−1.12709
$782$	−5.17848			−0.185182
$783$		0			0
$784$	−6.96008	+	0.746520i	−0.248574	+	0.0266614i
$785$			9.71916i			0.346892i
$786$		0			0
$787$		−	31.1997i		−	1.11215i	−0.831132	−	0.556075i	$-0.812307\pi$
$787$		−	31.1997i		−	1.11215i	0.831132	−	0.556075i	$-0.187693\pi$
$788$			9.96399i			0.354953i
$789$		0			0
$790$		−	4.84293i		−	0.172304i
$791$	−18.3152	+	0.979409i	−0.651212	+	0.0348238i
$792$		0			0
$793$	43.3392			1.53902
$794$	−9.89614			−0.351201
$795$		0			0
$796$		−	11.6673i		−	0.413538i
$797$	3.59488			0.127337			0.0636685	−	0.997971i	$-0.479720\pi$
$797$	3.59488			0.127337			0.0636685	+	0.997971i	$0.479720\pi$
$798$		0			0
$799$	−3.49484			−0.123638
$800$		−	3.96008i		−	0.140010i
$801$		0			0
$802$	−13.3181			−0.470279
$803$	−35.8019			−1.26342
$804$		0			0
$805$	−2.25093	+	0.120369i	−0.0793350	+	0.00424246i
$806$		−	21.6629i		−	0.763045i
$807$		0			0
$808$			12.0609i			0.424303i
$809$			47.0398i			1.65383i	0.562327	+	0.826915i	$0.309906\pi$
$809$			47.0398i			1.65383i	−0.562327	+	0.826915i	$0.690094\pi$
$810$		0			0
$811$			7.29343i			0.256107i	0.991767	+	0.128053i	$0.0408729\pi$
$811$			7.29343i			0.256107i	−0.991767	+	0.128053i	$0.959127\pi$
$812$	23.5495	−	1.25932i	0.826425	−	0.0441934i
$813$		0			0
$814$	−13.4227			−0.470464
$815$	−7.47790			−0.261939
$816$		0			0
$817$		−	45.1665i		−	1.58018i
$818$	7.80767			0.272989
$819$		0			0
$820$	−6.49185			−0.226705
$821$			2.74077i			0.0956537i	0.998856	+	0.0478268i	$0.0152296\pi$
$821$			2.74077i			0.0956537i	−0.998856	+	0.0478268i	$0.984770\pi$
$822$		0			0
$823$	−11.8348			−0.412536			−0.206268	−	0.978496i	$-0.566132\pi$
$823$	−11.8348			−0.412536			−0.206268	+	0.978496i	$0.566132\pi$
$824$	−14.4360			−0.502903
$825$		0			0
$826$	−19.0698	+	1.01976i	−0.663524	+	0.0354822i
$827$			38.9241i			1.35352i	0.736202	+	0.676761i	$0.236617\pi$
$827$			38.9241i			1.35352i	−0.736202	+	0.676761i	$0.763383\pi$
$828$		0			0
$829$			33.3214i			1.15730i	0.815576	+	0.578650i	$0.196420\pi$
$829$			33.3214i			1.15730i	−0.815576	+	0.578650i	$0.803580\pi$
$830$			11.2265i			0.389678i
$831$		0			0
$832$			5.45173i			0.189005i
$833$	−43.1403	+	4.62712i	−1.49472	+	0.160320i
$834$		0			0
$835$	−1.21101			−0.0419088
$836$	40.4448			1.39881
$837$		0			0
$838$		−	30.5760i		−	1.05623i
$839$	−24.8404			−0.857586			−0.428793	−	0.903403i	$-0.641061\pi$
$839$	−24.8404			−0.857586			−0.428793	+	0.903403i	$0.641061\pi$
$840$		0			0
$841$	−50.4521			−1.73973
$842$		−	29.9686i		−	1.03278i
$843$		0			0
$844$	1.60332			0.0551885
$845$	−17.0518			−0.586601
$846$		0			0
$847$	−2.08915	−	39.0676i	−0.0717841	−	1.34238i
$848$		−	2.19615i		−	0.0754162i
$849$		0			0
$850$		−	24.5456i		−	0.841906i
$851$		−	2.20836i		−	0.0757016i
$852$		0			0
$853$			2.43959i			0.0835299i	0.999127	+	0.0417650i	$0.0132981\pi$
$853$			2.43959i			0.0835299i	−0.999127	+	0.0417650i	$0.986702\pi$
$854$	−1.12313	−	21.0027i	−0.0384327	−	0.718699i
$855$		0			0
$856$	11.0039			0.376106
$857$	−11.8287			−0.404059			−0.202030	−	0.979379i	$-0.564754\pi$
$857$	−11.8287			−0.404059			−0.202030	+	0.979379i	$0.564754\pi$
$858$		0			0
$859$		−	35.3135i		−	1.20488i	−0.798164	−	0.602440i	$-0.794195\pi$
$859$		−	35.3135i		−	1.20488i	0.798164	−	0.602440i	$-0.205805\pi$
$860$	−5.78304			−0.197200
$861$		0			0
$862$	−19.8981			−0.677732
$863$		−	15.5568i		−	0.529561i	−0.964309	−	0.264780i	$-0.914701\pi$
$863$		−	15.5568i		−	0.529561i	0.964309	−	0.264780i	$-0.0852994\pi$
$864$		0			0
$865$	−3.66593			−0.124645
$866$	−26.6176			−0.904503
$867$		0			0
$868$	−10.4981	+	0.561391i	−0.356330	+	0.0190549i
$869$			24.1163i			0.818090i
$870$		0			0
$871$		−	58.3834i		−	1.97824i
$872$			2.94130i			0.0996051i
$873$		0			0
$874$			6.65417i			0.225081i
$875$	−1.29090	−	24.1402i	−0.0436405	−	0.816088i
$876$		0			0
$877$	38.5957			1.30328			0.651642	−	0.758527i	$-0.274081\pi$
$877$	38.5957			1.30328			0.651642	+	0.758527i	$0.274081\pi$
$878$	−29.1602			−0.984109
$879$		0			0
$880$		−	5.17848i		−	0.174567i
$881$	38.9816			1.31332			0.656662	−	0.754185i	$-0.271968\pi$
$881$	38.9816			1.31332			0.656662	+	0.754185i	$0.271968\pi$
$882$		0			0
$883$	1.32421			0.0445631			0.0222815	−	0.999752i	$-0.492907\pi$
$883$	1.32421			0.0445631			0.0222815	+	0.999752i	$0.492907\pi$
$884$			33.7912i			1.13652i
$885$		0			0
$886$	−29.3107			−0.984714
$887$	−32.2584			−1.08313			−0.541566	−	0.840658i	$-0.682168\pi$
$887$	−32.2584			−1.08313			−0.541566	+	0.840658i	$0.682168\pi$
$888$		0			0
$889$	−1.88024	−	35.1609i	−0.0630612	−	1.17926i
$890$			2.16108i			0.0724394i
$891$		0			0
$892$			18.3042i			0.612868i
$893$			4.49074i			0.150277i
$894$		0			0
$895$		−	9.45088i		−	0.315908i
$896$	2.64198	−	0.141281i	0.0882622	−	0.00471985i
$897$		0			0
$898$	14.5485			0.485491
$899$	35.4190			1.18129
$900$		0			0
$901$		−	13.6123i		−	0.453491i
$902$	32.3274			1.07639
$903$		0			0
$904$	6.93237			0.230567
$905$			5.93456i			0.197271i
$906$		0			0
$907$	53.3164			1.77034			0.885171	−	0.465266i	$-0.154041\pi$
$907$	53.3164			1.77034			0.885171	+	0.465266i	$0.154041\pi$
$908$	−15.8519			−0.526062
$909$		0			0
$910$	0.785447	+	14.6880i	0.0260373	+	0.486903i
$911$			5.24548i			0.173790i	0.996217	+	0.0868952i	$0.0276945\pi$
$911$			5.24548i			0.173790i	−0.996217	+	0.0868952i	$0.972305\pi$
$912$		0			0
$913$		−	55.9046i		−	1.85017i
$914$		−	5.21166i		−	0.172386i
$915$		0			0
$916$		−	21.7163i		−	0.717528i
$917$	1.70398	+	31.8647i	0.0562703	+	1.05227i
$918$		0			0
$919$	−12.6393			−0.416933			−0.208466	−	0.978030i	$-0.566847\pi$
$919$	−12.6393			−0.416933			−0.208466	+	0.978030i	$0.566847\pi$
$920$	0.851988			0.0280892
$921$		0			0
$922$			34.9906i			1.15236i
$923$	−33.8156			−1.11305
$924$		0			0
$925$	10.4674			0.344167
$926$		−	2.05213i		−	0.0674371i
$927$		0			0
$928$	−8.91359			−0.292603
$929$	−50.7221			−1.66414			−0.832070	−	0.554671i	$-0.812844\pi$
$929$	−50.7221			−1.66414			−0.832070	+	0.554671i	$0.812844\pi$
$930$		0			0
$931$	5.94568	+	55.4338i	0.194862	+	1.81677i
$932$		−	17.0886i		−	0.559756i
$933$		0			0
$934$		−	20.4066i		−	0.667726i
$935$		−	32.0975i		−	1.04970i
$936$		0			0
$937$		−	7.88667i		−	0.257646i	−0.991668	−	0.128823i	$-0.958880\pi$
$937$		−	7.88667i		−	0.257646i	0.991668	−	0.128823i	$-0.0411199\pi$
$938$	−28.2933	+	1.51299i	−0.923809	+	0.0494010i
$939$		0			0
$940$	0.574987			0.0187540
$941$	50.4702			1.64528			0.822641	−	0.568561i	$-0.192500\pi$
$941$	50.4702			1.64528			0.822641	+	0.568561i	$0.192500\pi$
$942$		0			0
$943$			5.31866i			0.173199i
$944$	7.21801			0.234926
$945$		0			0
$946$	28.7977			0.936295
$947$			41.1489i			1.33716i	0.743641	+	0.668579i	$0.233097\pi$
$947$			41.1489i			1.33716i	−0.743641	+	0.668579i	$0.766903\pi$
$948$		0			0
$949$	−38.4360			−1.24768
$950$	−31.5402			−1.02330
$951$		0			0
$952$	16.3756	−	0.875692i	0.530737	−	0.0283813i
$953$			2.06918i			0.0670273i	0.999438	+	0.0335136i	$0.0106697\pi$
$953$			2.06918i			0.0670273i	−0.999438	+	0.0335136i	$0.989330\pi$
$954$		0			0
$955$		−	4.40216i		−	0.142451i
$956$			9.32969i			0.301744i
$957$		0			0
$958$			13.8722i			0.448190i
$959$	35.3499	−	1.89035i	1.14151	−	0.0610425i
$960$		0			0
$961$	15.2106			0.490664
$962$	−14.4102			−0.464604
$963$		0			0
$964$			22.4030i			0.721552i
$965$	22.4206			0.721745
$966$		0			0
$967$	36.6936			1.17999			0.589994	−	0.807408i	$-0.299130\pi$
$967$	36.6936			1.17999			0.589994	+	0.807408i	$0.299130\pi$
$968$			14.7873i			0.475281i
$969$		0			0
$970$	−2.84112			−0.0912227
$971$	−31.2280			−1.00215			−0.501077	−	0.865403i	$-0.667063\pi$
$971$	−31.2280			−1.00215			−0.501077	+	0.865403i	$0.667063\pi$
$972$		0			0
$973$	−25.6692	+	1.37267i	−0.822918	+	0.0440058i
$974$			22.3646i			0.716608i
$975$		0			0
$976$			7.94963i			0.254462i
$977$		−	16.0686i		−	0.514079i	−0.966401	−	0.257039i	$-0.917253\pi$
$977$		−	16.0686i		−	0.514079i	0.966401	−	0.257039i	$-0.0827470\pi$
$978$		0			0
$979$		−	10.7615i		−	0.343939i
$980$	7.09764	−	0.761275i	0.226726	−	0.0243180i
$981$		0			0
$982$	−7.60770			−0.242771
$983$	−27.1207			−0.865015			−0.432508	−	0.901630i	$-0.642371\pi$
$983$	−27.1207			−0.865015			−0.432508	+	0.901630i	$0.642371\pi$
$984$		0			0
$985$		−	10.1609i		−	0.323754i
$986$	−55.2487			−1.75948
$987$		0			0
$988$	43.4205			1.38139
$989$			4.73794i			0.150658i
$990$		0			0
$991$	14.3814			0.456839			0.228419	−	0.973563i	$-0.426644\pi$
$991$	14.3814			0.456839			0.228419	+	0.973563i	$0.426644\pi$
$992$	3.97359			0.126162
$993$		0			0
$994$	0.876324	+	16.3874i	0.0277953	+	0.519778i
$995$			11.8979i			0.377190i
$996$		0			0
$997$		−	34.3585i		−	1.08814i	−0.839038	−	0.544072i	$-0.816882\pi$
$997$		−	34.3585i		−	1.08814i	0.839038	−	0.544072i	$-0.183118\pi$
$998$		−	11.3208i		−	0.358352i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.d.b.1133.13	yes	16
3.2	odd	2	inner	1134.2.d.b.1133.4	✓	16
7.6	odd	2	inner	1134.2.d.b.1133.12	yes	16
9.2	odd	6		1134.2.m.i.377.3		16
9.4	even	3		1134.2.m.i.755.2		16
9.5	odd	6		1134.2.m.h.755.7		16
9.7	even	3		1134.2.m.h.377.6		16
21.20	even	2	inner	1134.2.d.b.1133.5	yes	16
63.13	odd	6		1134.2.m.i.755.3		16
63.20	even	6		1134.2.m.i.377.2		16
63.34	odd	6		1134.2.m.h.377.7		16
63.41	even	6		1134.2.m.h.755.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.d.b.1133.4	✓	16	3.2	odd	2	inner
1134.2.d.b.1133.5	yes	16	21.20	even	2	inner
1134.2.d.b.1133.12	yes	16	7.6	odd	2	inner
1134.2.d.b.1133.13	yes	16	1.1	even	1	trivial
1134.2.m.h.377.6		16	9.7	even	3
1134.2.m.h.377.7		16	63.34	odd	6
1134.2.m.h.755.6		16	63.41	even	6
1134.2.m.h.755.7		16	9.5	odd	6
1134.2.m.i.377.2		16	63.20	even	6
1134.2.m.i.377.3		16	9.2	odd	6
1134.2.m.i.755.2		16	9.4	even	3
1134.2.m.i.755.3		16	63.13	odd	6

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +1.01976 q^{5} +(0.141281 + 2.64198i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +1.01976 q^{5} +(0.141281 + 2.64198i) q^{7} -1.00000i q^{8} +1.01976i q^{10} -5.07812i q^{11} -5.45173i q^{13} +(-2.64198 + 0.141281i) q^{14} +1.00000 q^{16} +6.19825 q^{17} -7.96453i q^{19} -1.01976 q^{20} +5.07812 q^{22} +0.835475i q^{23} -3.96008 q^{25} +5.45173 q^{26} +(-0.141281 - 2.64198i) q^{28} +8.91359i q^{29} -3.97359i q^{31} +1.00000i q^{32} +6.19825i q^{34} +(0.144073 + 2.69419i) q^{35} -2.64324 q^{37} +7.96453 q^{38} -1.01976i q^{40} +6.36603 q^{41} +5.67095 q^{43} +5.07812i q^{44} -0.835475 q^{46} -0.563843 q^{47} +(-6.96008 + 0.746520i) q^{49} -3.96008i q^{50} +5.45173i q^{52} -2.19615i q^{53} -5.17848i q^{55} +(2.64198 - 0.141281i) q^{56} -8.91359 q^{58} +7.21801 q^{59} +7.94963i q^{61} +3.97359 q^{62} -1.00000 q^{64} -5.55948i q^{65} +10.7091 q^{67} -6.19825 q^{68} +(-2.69419 + 0.144073i) q^{70} -6.20272i q^{71} -7.05024i q^{73} -2.64324i q^{74} +7.96453i q^{76} +(13.4163 - 0.717439i) q^{77} -4.74907 q^{79} +1.01976 q^{80} +6.36603i q^{82} +11.0089 q^{83} +6.32076 q^{85} +5.67095i q^{86} -5.07812 q^{88} +2.11919 q^{89} +(14.4033 - 0.770223i) q^{91} -0.835475i q^{92} -0.563843i q^{94} -8.12195i q^{95} +2.78605i q^{97} +(-0.746520 - 6.96008i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 8 q^{7}+O(q^{10}) \) 16 * q - 16 * q^4 + 8 * q^7	\( 16 q - 16 q^{4} + 8 q^{7} + 16 q^{16} + 16 q^{25} - 8 q^{28} + 16 q^{37} + 64 q^{43} - 32 q^{49} - 48 q^{58} - 16 q^{64} - 16 q^{67} - 24 q^{70} + 32 q^{79} - 48 q^{85} + 24 q^{91}+O(q^{100}) \) 16 * q - 16 * q^4 + 8 * q^7 + 16 * q^16 + 16 * q^25 - 8 * q^28 + 16 * q^37 + 64 * q^43 - 32 * q^49 - 48 * q^58 - 16 * q^64 - 16 * q^67 - 24 * q^70 + 32 * q^79 - 48 * q^85 + 24 * q^91

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