LMFDB - Embedded newform 765.2.b.e.154.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [765,2,Mod(154,765)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(765, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("765.154"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.10855575463$
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} + 25x^{14} + 240x^{12} + 1160x^{10} + 3068x^{8} + 4457x^{6} + 3309x^{4} + 988x^{2} + 16 $ x^16 + 25x^14 + 240x^12 + 1160x^10 + 3068x^8 + 4457x^6 + 3309x^4 + 988*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			154.16
Root			$-0.130988i$ of defining polynomial
Character	$\chi$	$=$	765.154
Dual form			765.2.b.e.154.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.69353i q^{2} -5.25508 q^{4} +(1.80322 + 1.32226i) q^{5} -4.61905i q^{7} -8.76763i q^{8} +(-3.56155 + 4.85703i) q^{10} +1.48856 q^{11} -6.10761i q^{13} +12.4415 q^{14} +13.1057 q^{16} -1.00000i q^{17} -0.180969 q^{19} +(-9.47608 - 6.94860i) q^{20} +4.00947i q^{22} -6.74252i q^{23} +(1.50323 + 4.76868i) q^{25} +16.4510 q^{26} +24.2735i q^{28} -1.31185 q^{29} +3.02511 q^{31} +17.7652i q^{32} +2.69353 q^{34} +(6.10761 - 8.32919i) q^{35} -2.11789i q^{37} -0.487443i q^{38} +(11.5931 - 15.8100i) q^{40} -8.22550 q^{41} -2.32446i q^{43} -7.82248 q^{44} +18.1612 q^{46} +6.56155i q^{47} -14.3357 q^{49} +(-12.8446 + 4.04900i) q^{50} +32.0960i q^{52} -1.17450i q^{53} +(2.68420 + 1.96827i) q^{55} -40.4982 q^{56} -3.53351i q^{58} +3.42975 q^{59} -10.1482 q^{61} +8.14822i q^{62} -21.6397 q^{64} +(8.07588 - 11.0134i) q^{65} +12.6679i q^{67} +5.25508i q^{68} +(22.4349 + 16.4510i) q^{70} +7.21290 q^{71} -9.33079i q^{73} +5.70459 q^{74} +0.951004 q^{76} -6.87572i q^{77} +8.76117 q^{79} +(23.6325 + 17.3292i) q^{80} -22.1556i q^{82} +13.0203i q^{83} +(1.32226 - 1.80322i) q^{85} +6.26099 q^{86} -13.0511i q^{88} +8.43207 q^{89} -28.2114 q^{91} +35.4325i q^{92} -17.6737 q^{94} +(-0.326327 - 0.239288i) q^{95} +6.28431i q^{97} -38.6134i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 24 q^{10} + 32 q^{16} - 4 q^{19} + 6 q^{25} - 24 q^{31} + 8 q^{34} + 44 q^{40} + 80 q^{46} - 56 q^{49} + 26 q^{55} - 24 q^{61} - 108 q^{64} + 44 q^{70} + 12 q^{76} + 72 q^{79} + 2 q^{85}+ \cdots - 36 q^{94}+O(q^{100}) $ 16 * q - 16 * q^4 - 24 * q^10 + 32 * q^16 - 4 * q^19 + 6 * q^25 - 24 * q^31 + 8 * q^34 + 44 * q^40 + 80 * q^46 - 56 * q^49 + 26 * q^55 - 24 * q^61 - 108 * q^64 + 44 * q^70 + 12 * q^76 + 72 * q^79 + 2 * q^85 - 96 * q^91 - 36 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			2.69353i			1.90461i	0.305148	+	0.952305i	$0.401294\pi$
$2$			2.69353i			1.90461i	−0.305148	+	0.952305i	$0.598706\pi$
$3$		0			0
$3$		0			0
$4$	−5.25508			−2.62754
$5$	1.80322	+	1.32226i	0.806426	+	0.591335i
$5$	1.80322	+	1.32226i	0.806426	+	0.591335i
$6$		0			0
$7$		−	4.61905i		−	1.74584i	−0.487865	−	0.872919i	$-0.662224\pi$
$7$		−	4.61905i		−	1.74584i	0.487865	−	0.872919i	$-0.337776\pi$
$8$		−	8.76763i		−	3.09983i
$9$		0			0
$10$	−3.56155	+	4.85703i	−1.12626	+	1.53593i
$11$	1.48856			0.448817			0.224408	−	0.974495i	$-0.427955\pi$
$11$	1.48856			0.448817			0.224408	+	0.974495i	$0.427955\pi$
$12$		0			0
$13$		−	6.10761i		−	1.69395i	−0.531636	−	0.846973i	$-0.678422\pi$
$13$		−	6.10761i		−	1.69395i	0.531636	−	0.846973i	$-0.321578\pi$
$14$	12.4415			3.32514
$15$		0			0
$16$	13.1057			3.27642
$17$		−	1.00000i		−	0.242536i
$17$		−	1.00000i		−	0.242536i
$18$		0			0
$19$	−0.180969			−0.0415170			−0.0207585	−	0.999785i	$-0.506608\pi$
$19$	−0.180969			−0.0415170			−0.0207585	+	0.999785i	$0.506608\pi$
$20$	−9.47608	−	6.94860i	−2.11892	−	1.55375i
$21$		0			0
$22$			4.00947i			0.854821i
$23$		−	6.74252i		−	1.40591i	−0.711233	−	0.702956i	$-0.751863\pi$
$23$		−	6.74252i		−	1.40591i	0.711233	−	0.702956i	$-0.248137\pi$
$24$		0			0
$25$	1.50323	+	4.76868i	0.300647	+	0.953736i
$26$	16.4510			3.22631
$27$		0			0
$28$			24.2735i			4.58726i
$29$	−1.31185			−0.243605			−0.121803	−	0.992554i	$-0.538868\pi$
$29$	−1.31185			−0.243605			−0.121803	+	0.992554i	$0.538868\pi$
$30$		0			0
$31$	3.02511			0.543326			0.271663	−	0.962392i	$-0.412426\pi$
$31$	3.02511			0.543326			0.271663	+	0.962392i	$0.412426\pi$
$32$			17.7652i			3.14048i
$33$		0			0
$34$	2.69353			0.461936
$35$	6.10761	−	8.32919i	1.03237	−	1.40789i
$36$		0			0
$37$		−	2.11789i		−	0.348179i	−0.984730	−	0.174090i	$-0.944302\pi$
$37$		−	2.11789i		−	0.348179i	0.984730	−	0.174090i	$-0.0556982\pi$
$38$		−	0.487443i		−	0.0790738i
$39$		0			0
$40$	11.5931	−	15.8100i	1.83304	−	2.49978i
$41$	−8.22550			−1.28461			−0.642304	−	0.766450i	$-0.722021\pi$
$41$	−8.22550			−1.28461			−0.642304	+	0.766450i	$0.722021\pi$
$42$		0			0
$43$		−	2.32446i		−	0.354477i	−0.984168	−	0.177238i	$-0.943284\pi$
$43$		−	2.32446i		−	0.354477i	0.984168	−	0.177238i	$-0.0567164\pi$
$44$	−7.82248			−1.17928
$45$		0			0
$46$	18.1612			2.67772
$47$			6.56155i			0.957101i	0.878060	+	0.478550i	$0.158838\pi$
$47$			6.56155i			0.957101i	−0.878060	+	0.478550i	$0.841162\pi$
$48$		0			0
$49$	−14.3357			−2.04795
$50$	−12.8446	+	4.04900i	−1.81649	+	0.572615i
$51$		0			0
$52$			32.0960i			4.45091i
$53$		−	1.17450i		−	0.161330i	−0.996741	−	0.0806652i	$-0.974296\pi$
$53$		−	1.17450i		−	0.161330i	0.996741	−	0.0806652i	$-0.0257044\pi$
$54$		0			0
$55$	2.68420	+	1.96827i	0.361938	+	0.265401i
$56$	−40.4982			−5.41180
$57$		0			0
$58$		−	3.53351i		−	0.463973i
$59$	3.42975			0.446515			0.223257	−	0.974760i	$-0.428331\pi$
$59$	3.42975			0.446515			0.223257	+	0.974760i	$0.428331\pi$
$60$		0			0
$61$	−10.1482			−1.29935			−0.649673	−	0.760214i	$-0.725094\pi$
$61$	−10.1482			−1.29935			−0.649673	+	0.760214i	$0.725094\pi$
$62$			8.14822i			1.03482i
$63$		0			0
$64$	−21.6397			−2.70497
$65$	8.07588	−	11.0134i	1.00169	−	1.36604i
$66$		0			0
$67$			12.6679i			1.54762i	0.633415	+	0.773812i	$0.281653\pi$
$67$			12.6679i			1.54762i	−0.633415	+	0.773812i	$0.718347\pi$
$68$			5.25508i			0.637272i
$69$		0			0
$70$	22.4349	+	16.4510i	2.68148	+	1.96627i
$71$	7.21290			0.856013			0.428007	−	0.903776i	$-0.359216\pi$
$71$	7.21290			0.856013			0.428007	+	0.903776i	$0.359216\pi$
$72$		0			0
$73$		−	9.33079i		−	1.09209i	−0.837757	−	0.546043i	$-0.816134\pi$
$73$		−	9.33079i		−	1.09209i	0.837757	−	0.546043i	$-0.183866\pi$
$74$	5.70459			0.663145
$75$		0			0
$76$	0.951004			0.109088
$77$		−	6.87572i		−	0.783561i
$78$		0			0
$79$	8.76117			0.985708			0.492854	−	0.870112i	$-0.335954\pi$
$79$	8.76117			0.985708			0.492854	+	0.870112i	$0.335954\pi$
$80$	23.6325	+	17.3292i	2.64219	+	1.93746i
$81$		0			0
$82$		−	22.1556i		−	2.44668i
$83$			13.0203i			1.42916i	0.699551	+	0.714582i	$0.253383\pi$
$83$			13.0203i			1.42916i	−0.699551	+	0.714582i	$0.746617\pi$
$84$		0			0
$85$	1.32226	−	1.80322i	0.143420	−	0.195587i
$86$	6.26099			0.675140
$87$		0			0
$88$		−	13.0511i		−	1.39125i
$89$	8.43207			0.893798			0.446899	−	0.894584i	$-0.352528\pi$
$89$	8.43207			0.893798			0.446899	+	0.894584i	$0.352528\pi$
$90$		0			0
$91$	−28.2114			−2.95736
$92$			35.4325i			3.69409i
$93$		0			0
$94$	−17.6737			−1.82290
$95$	−0.326327	−	0.239288i	−0.0334804	−	0.0245505i
$96$		0			0
$97$			6.28431i			0.638075i	0.947742	+	0.319038i	$0.103360\pi$
$97$			6.28431i			0.638075i	−0.947742	+	0.319038i	$0.896640\pi$
$98$		−	38.6134i		−	3.90055i
$99$		0			0
$100$	−7.89961	−	25.0598i	−0.789961	−	2.50598i
$101$	4.23578			0.421476			0.210738	−	0.977543i	$-0.432413\pi$
$101$	4.23578			0.421476			0.210738	+	0.977543i	$0.432413\pi$
$102$		0			0
$103$		−	6.91365i		−	0.681222i	−0.940204	−	0.340611i	$-0.889366\pi$
$103$		−	6.91365i		−	0.681222i	0.940204	−	0.340611i	$-0.110634\pi$
$104$	−53.5493			−5.25094
$105$		0			0
$106$	3.16355			0.307271
$107$		−	0.116639i		−	0.0112760i	−0.999984	−	0.00563798i	$-0.998205\pi$
$107$		−	0.116639i		−	0.0112760i	0.999984	−	0.00563798i	$-0.00179464\pi$
$108$		0			0
$109$	6.95715			0.666374			0.333187	−	0.942861i	$-0.391876\pi$
$109$	6.95715			0.666374			0.333187	+	0.942861i	$0.391876\pi$
$110$	−5.30157	+	7.22996i	−0.505485	+	0.689350i
$111$		0			0
$112$		−	60.5359i		−	5.72010i
$113$		−	8.90847i		−	0.838039i	−0.907977	−	0.419019i	$-0.862374\pi$
$113$		−	8.90847i		−	0.838039i	0.907977	−	0.419019i	$-0.137626\pi$
$114$		0			0
$115$	8.91540	−	12.1583i	0.831365	−	1.13377i
$116$	6.89390			0.640083
$117$		0			0
$118$			9.23811i			0.850437i
$119$	−4.61905			−0.423428
$120$		0			0
$121$	−8.78420			−0.798563
$122$		−	27.3345i		−	2.47475i
$123$		0			0
$124$	−15.8972			−1.42761
$125$	−3.59479	+	10.5867i	−0.321528	+	0.946900i
$126$		0			0
$127$		−	10.3434i		−	0.917828i	−0.888481	−	0.458914i	$-0.848239\pi$
$127$		−	10.3434i		−	0.917828i	0.888481	−	0.458914i	$-0.151761\pi$
$128$		−	22.7567i		−	2.01143i
$129$		0			0
$130$	29.6648	+	21.7526i	2.60178	+	1.90783i
$131$	14.5397			1.27034			0.635169	−	0.772373i	$-0.280930\pi$
$131$	14.5397			1.27034			0.635169	+	0.772373i	$0.280930\pi$
$132$		0			0
$133$			0.835903i			0.0724820i
$134$	−34.1212			−2.94762
$135$		0			0
$136$	−8.76763			−0.751818
$137$			11.3907i			0.973172i	0.873633	+	0.486586i	$0.161758\pi$
$137$			11.3907i			0.973172i	−0.873633	+	0.486586i	$0.838242\pi$
$138$		0			0
$139$	5.48504			0.465235			0.232618	−	0.972568i	$-0.425271\pi$
$139$	5.48504			0.465235			0.232618	+	0.972568i	$0.425271\pi$
$140$	−32.0960	+	43.7705i	−2.71260	+	3.69928i
$141$		0			0
$142$			19.4281i			1.63037i
$143$		−	9.09153i		−	0.760272i
$144$		0			0
$145$	−2.36557	−	1.73462i	−0.196450	−	0.144052i
$146$	25.1327			2.08000
$147$		0			0
$148$			11.1297i			0.914854i
$149$	20.2342			1.65765			0.828823	−	0.559511i	$-0.189011\pi$
$149$	20.2342			1.65765			0.828823	+	0.559511i	$0.189011\pi$
$150$		0			0
$151$	7.23766			0.588993			0.294496	−	0.955653i	$-0.404848\pi$
$151$	7.23766			0.588993			0.294496	+	0.955653i	$0.404848\pi$
$152$			1.58667i			0.128696i
$153$		0			0
$154$	18.5199			1.49238
$155$	5.45496	+	4.00000i	0.438153	+	0.321288i
$156$		0			0
$157$		−	7.51215i		−	0.599534i	−0.954012	−	0.299767i	$-0.903091\pi$
$157$		−	7.51215i		−	0.599534i	0.954012	−	0.299767i	$-0.0969090\pi$
$158$			23.5984i			1.87739i
$159$		0			0
$160$	−23.4903	+	32.0347i	−1.85707	+	2.53257i
$161$	−31.1441			−2.45450
$162$		0			0
$163$			6.64426i			0.520419i	0.965552	+	0.260209i	$0.0837916\pi$
$163$			6.64426i			0.520419i	−0.965552	+	0.260209i	$0.916208\pi$
$164$	43.2257			3.37536
$165$		0			0
$166$	−35.0705			−2.72200
$167$		−	3.61461i		−	0.279707i	−0.990172	−	0.139854i	$-0.955337\pi$
$167$		−	3.61461i		−	0.279707i	0.990172	−	0.139854i	$-0.0446632\pi$
$168$		0			0
$169$	−24.3029			−1.86945
$170$	4.85703	+	3.56155i	0.372517	+	0.273159i
$171$		0			0
$172$			12.2152i			0.931402i
$173$			7.35067i			0.558861i	0.960166	+	0.279431i	$0.0901457\pi$
$173$			7.35067i			0.558861i	−0.960166	+	0.279431i	$0.909854\pi$
$174$		0			0
$175$	22.0268	−	6.94351i	1.66507	−	0.524880i
$176$	19.5086			1.47051
$177$		0			0
$178$			22.7120i			1.70234i
$179$	5.18768			0.387746			0.193873	−	0.981027i	$-0.437895\pi$
$179$	5.18768			0.387746			0.193873	+	0.981027i	$0.437895\pi$
$180$		0			0
$181$	0.693208			0.0515258			0.0257629	−	0.999668i	$-0.491799\pi$
$181$	0.693208			0.0515258			0.0257629	+	0.999668i	$0.491799\pi$
$182$		−	75.9881i		−	5.63261i
$183$		0			0
$184$	−59.1160			−4.35809
$185$	2.80041	−	3.81903i	0.205890	−	0.280781i
$186$		0			0
$187$		−	1.48856i		−	0.108854i
$188$		−	34.4815i		−	2.51482i
$189$		0			0
$190$	0.644529	−	0.878970i	0.0467591	−	0.0637672i
$191$	−3.42975			−0.248168			−0.124084	−	0.992272i	$-0.539599\pi$
$191$	−3.42975			−0.248168			−0.124084	+	0.992272i	$0.539599\pi$
$192$		0			0
$193$			5.33241i			0.383835i	0.981411	+	0.191918i	$0.0614706\pi$
$193$			5.33241i			0.383835i	−0.981411	+	0.191918i	$0.938529\pi$
$194$	−16.9270			−1.21528
$195$		0			0
$196$	75.3350			5.38107
$197$		−	14.0138i		−	0.998445i	−0.866474	−	0.499223i	$-0.833619\pi$
$197$		−	14.0138i		−	0.998445i	0.866474	−	0.499223i	$-0.166381\pi$
$198$		0			0
$199$	20.0932			1.42437			0.712184	−	0.701993i	$-0.247706\pi$
$199$	20.0932			1.42437			0.712184	+	0.701993i	$0.247706\pi$
$200$	41.8100	−	13.1798i	2.95642	−	0.931952i
$201$		0			0
$202$			11.4092i			0.802747i
$203$			6.05953i			0.425295i
$204$		0			0
$205$	−14.8324	−	10.8763i	−1.03594	−	0.759633i
$206$	18.6221			1.29746
$207$		0			0
$208$		−	80.0444i		−	5.55008i
$209$	−0.269382			−0.0186335
$210$		0			0
$211$	4.39923			0.302856			0.151428	−	0.988468i	$-0.451613\pi$
$211$	4.39923			0.302856			0.151428	+	0.988468i	$0.451613\pi$
$212$			6.17210i			0.423902i
$213$		0			0
$214$	0.314171			0.0214763
$215$	3.07355	−	4.19152i	0.209614	−	0.285859i
$216$		0			0
$217$		−	13.9732i		−	0.948560i
$218$			18.7393i			1.26918i
$219$		0			0
$220$	−14.1057	−	10.3434i	−0.951005	−	0.697351i
$221$	−6.10761			−0.410842
$222$		0			0
$223$			22.7045i			1.52040i	0.649687	+	0.760202i	$0.274900\pi$
$223$			22.7045i			1.52040i	−0.649687	+	0.760202i	$0.725100\pi$
$224$	82.0586			5.48277
$225$		0			0
$226$	23.9952			1.59614
$227$		−	20.6900i		−	1.37324i	−0.727016	−	0.686620i	$-0.759094\pi$
$227$		−	20.6900i		−	1.37324i	0.727016	−	0.686620i	$-0.240906\pi$
$228$		0			0
$229$	22.7050			1.50039			0.750193	−	0.661219i	$-0.229960\pi$
$229$	22.7050			1.50039			0.750193	+	0.661219i	$0.229960\pi$
$230$	32.7486	+	24.0138i	2.15938	+	1.58343i
$231$		0			0
$232$			11.5019i			0.755134i
$233$			12.0818i			0.791505i	0.918357	+	0.395753i	$0.129516\pi$
$233$			12.0818i			0.791505i	−0.918357	+	0.395753i	$0.870484\pi$
$234$		0			0
$235$	−8.67611	+	11.8319i	−0.565967	+	0.771831i
$236$	−18.0236			−1.17324
$237$		0			0
$238$		−	12.4415i		−	0.806465i
$239$	−24.1165			−1.55997			−0.779984	−	0.625799i	$-0.784773\pi$
$239$	−24.1165			−1.55997			−0.779984	+	0.625799i	$0.784773\pi$
$240$		0			0
$241$	−18.5733			−1.19641			−0.598206	−	0.801342i	$-0.704120\pi$
$241$	−18.5733			−1.19641			−0.598206	+	0.801342i	$0.704120\pi$
$242$		−	23.6605i		−	1.52095i
$243$		0			0
$244$	53.3297			3.41408
$245$	−25.8504	−	18.9555i	−1.65152	−	1.21102i
$246$		0			0
$247$			1.10529i			0.0703276i
$248$		−	26.5231i		−	1.68422i
$249$		0			0
$250$	−28.5155	−	9.68265i	−1.80348	−	0.612385i
$251$	12.6679			0.799588			0.399794	−	0.916605i	$-0.369082\pi$
$251$	12.6679			0.799588			0.399794	+	0.916605i	$0.369082\pi$
$252$		0			0
$253$		−	10.0366i		−	0.630997i
$254$	27.8602			1.74810
$255$		0			0
$256$	18.0162			1.12602
$257$			16.0502i			1.00119i	0.865683	+	0.500593i	$0.166885\pi$
$257$			16.0502i			1.00119i	−0.865683	+	0.500593i	$0.833115\pi$
$258$		0			0
$259$	−9.78265			−0.607864
$260$	−42.4394	+	57.8762i	−2.63198	+	3.58933i
$261$		0			0
$262$			39.1630i			2.41950i
$263$		−	0.481294i		−	0.0296779i	−0.999890	−	0.0148389i	$-0.995276\pi$
$263$		−	0.481294i		−	0.0296779i	0.999890	−	0.0148389i	$-0.00472355\pi$
$264$		0			0
$265$	1.55300	−	2.11789i	0.0954002	−	0.130101i
$266$	−2.25153			−0.138050
$267$		0			0
$268$		−	66.5706i		−	4.06644i
$269$	3.03782			0.185219			0.0926095	−	0.995703i	$-0.470479\pi$
$269$	3.03782			0.185219			0.0926095	+	0.995703i	$0.470479\pi$
$270$		0			0
$271$	−15.2527			−0.926534			−0.463267	−	0.886219i	$-0.653323\pi$
$271$	−15.2527			−0.926534			−0.463267	+	0.886219i	$0.653323\pi$
$272$		−	13.1057i		−	0.794649i
$273$		0			0
$274$	−30.6811			−1.85351
$275$	2.23765	+	7.09845i	0.134935	+	0.428053i
$276$		0			0
$277$		−	19.7582i		−	1.18716i	−0.804777	−	0.593578i	$-0.797715\pi$
$277$		−	19.7582i		−	1.18716i	0.804777	−	0.593578i	$-0.202285\pi$
$278$			14.7741i			0.886092i
$279$		0			0
$280$	−73.0273	−	53.5493i	−4.36421	−	3.20018i
$281$	−26.4557			−1.57821			−0.789106	−	0.614257i	$-0.789456\pi$
$281$	−26.4557			−1.57821			−0.789106	+	0.614257i	$0.789456\pi$
$282$		0			0
$283$		−	1.28854i		−	0.0765955i	−0.999266	−	0.0382977i	$-0.987806\pi$
$283$		−	1.28854i		−	0.0765955i	0.999266	−	0.0382977i	$-0.0121935\pi$
$284$	−37.9043			−2.24921
$285$		0			0
$286$	24.4883			1.44802
$287$			37.9940i			2.24272i
$288$		0			0
$289$	−1.00000			−0.0588235
$290$	4.67224	−	6.37172i	0.274363	−	0.374160i
$291$		0			0
$292$			49.0340i			2.86950i
$293$			6.86279i			0.400929i	0.979701	+	0.200464i	$0.0642451\pi$
$293$			6.86279i			0.400929i	−0.979701	+	0.200464i	$0.935755\pi$
$294$		0			0
$295$	6.18460	+	4.53503i	0.360081	+	0.264040i
$296$	−18.5689			−1.07929
$297$		0			0
$298$			54.5012i			3.15717i
$299$	−41.1807			−2.38154
$300$		0			0
$301$	−10.7368			−0.618859
$302$			19.4948i			1.12180i
$303$		0			0
$304$	−2.37172			−0.136027
$305$	−18.2995	−	13.4186i	−1.04783	−	0.768349i
$306$		0			0
$307$		−	19.0747i		−	1.08865i	−0.838874	−	0.544326i	$-0.816786\pi$
$307$		−	19.0747i		−	1.08865i	0.838874	−	0.544326i	$-0.183214\pi$
$308$			36.1325i			2.05884i
$309$		0			0
$310$	−10.7741	+	14.6931i	−0.611928	+	0.834510i
$311$	16.6884			0.946313			0.473156	−	0.880978i	$-0.343115\pi$
$311$	16.6884			0.946313			0.473156	+	0.880978i	$0.343115\pi$
$312$		0			0
$313$			19.5208i			1.10338i	0.834049	+	0.551690i	$0.186017\pi$
$313$			19.5208i			1.10338i	−0.834049	+	0.551690i	$0.813983\pi$
$314$	20.2342			1.14188
$315$		0			0
$316$	−46.0406			−2.58999
$317$			27.9952i			1.57237i	0.617993	+	0.786184i	$0.287946\pi$
$317$			27.9952i			1.57237i	−0.617993	+	0.786184i	$0.712054\pi$
$318$		0			0
$319$	−1.95277			−0.109334
$320$	−39.0213	−	28.6134i	−2.18136	−	1.59954i
$321$		0			0
$322$		−	83.8873i		−	4.67486i
$323$			0.180969i			0.0100694i
$324$		0			0
$325$	29.1252	−	9.18116i	1.61558	−	0.509279i
$326$	−17.8965			−0.991195
$327$		0			0
$328$			72.1182i			3.98206i
$329$	30.3082			1.67094
$330$		0			0
$331$	0.449715			0.0247185			0.0123593	−	0.999924i	$-0.496066\pi$
$331$	0.449715			0.0247185			0.0123593	+	0.999924i	$0.496066\pi$
$332$		−	68.4228i		−	3.75519i
$333$		0			0
$334$	9.73606			0.532733
$335$	−16.7503	+	22.8430i	−0.915164	+	1.24805i
$336$		0			0
$337$			13.9797i			0.761523i	0.924673	+	0.380762i	$0.124338\pi$
$337$			13.9797i			0.761523i	−0.924673	+	0.380762i	$0.875662\pi$
$338$		−	65.4605i		−	3.56058i
$339$		0			0
$340$	−6.94860	+	9.47608i	−0.376841	+	0.513913i
$341$	4.50305			0.243854
$342$		0			0
$343$			33.8838i			1.82955i
$344$	−20.3800			−1.09882
$345$		0			0
$346$	−19.7992			−1.06441
$347$			18.8291i			1.01080i	0.862885	+	0.505400i	$0.168655\pi$
$347$			18.8291i			1.01080i	−0.862885	+	0.505400i	$0.831345\pi$
$348$		0			0
$349$	−1.04013			−0.0556769			−0.0278384	−	0.999612i	$-0.508862\pi$
$349$	−1.04013			−0.0556769			−0.0278384	+	0.999612i	$0.508862\pi$
$350$	18.7025	+	59.3297i	0.999692	+	3.17130i
$351$		0			0
$352$			26.4446i			1.40950i
$353$			21.1017i			1.12313i	0.827432	+	0.561566i	$0.189801\pi$
$353$			21.1017i			1.12313i	−0.827432	+	0.561566i	$0.810199\pi$
$354$		0			0
$355$	13.0065	+	9.53736i	0.690312	+	0.506190i
$356$	−44.3112			−2.34849
$357$		0			0
$358$			13.9732i			0.738504i
$359$	5.80836			0.306554			0.153277	−	0.988183i	$-0.451017\pi$
$359$	5.80836			0.306554			0.153277	+	0.988183i	$0.451017\pi$
$360$		0			0
$361$	−18.9673			−0.998276
$362$			1.86717i			0.0981365i
$363$		0			0
$364$	148.253			7.77057
$365$	12.3378	−	16.8255i	0.645788	−	0.880687i
$366$		0			0
$367$			15.6845i			0.818722i	0.912372	+	0.409361i	$0.134248\pi$
$367$			15.6845i			0.818722i	−0.912372	+	0.409361i	$0.865752\pi$
$368$		−	88.3654i		−	4.60636i
$369$		0			0
$370$	10.2867	+	7.54298i	0.534778	+	0.392141i
$371$	−5.42509			−0.281657
$372$		0			0
$373$		−	28.6662i		−	1.48428i	−0.670244	−	0.742140i	$-0.733811\pi$
$373$		−	28.6662i		−	1.48428i	0.670244	−	0.742140i	$-0.266189\pi$
$374$	4.00947			0.207325
$375$		0			0
$376$	57.5293			2.96685
$377$			8.01230i			0.412654i
$378$		0			0
$379$	−14.0803			−0.723254			−0.361627	−	0.932323i	$-0.617779\pi$
$379$	−14.0803			−0.723254			−0.361627	+	0.932323i	$0.617779\pi$
$380$	1.71487	+	1.25748i	0.0879711	+	0.0645073i
$381$		0			0
$382$		−	9.23811i		−	0.472663i
$383$		−	16.5445i		−	0.845382i	−0.906274	−	0.422691i	$-0.861086\pi$
$383$		−	16.5445i		−	0.845382i	0.906274	−	0.422691i	$-0.138914\pi$
$384$		0			0
$385$	9.09153	−	12.3985i	0.463347	−	0.631885i
$386$	−14.3630			−0.731056
$387$		0			0
$388$		−	33.0246i		−	1.67657i
$389$	−21.4533			−1.08773			−0.543863	−	0.839174i	$-0.683039\pi$
$389$	−21.4533			−1.08773			−0.543863	+	0.839174i	$0.683039\pi$
$390$		0			0
$391$	−6.74252			−0.340984
$392$			125.690i			6.34829i
$393$		0			0
$394$	37.7466			1.90165
$395$	15.7983	+	11.5846i	0.794901	+	0.582884i
$396$		0			0
$397$		−	32.8093i		−	1.64665i	−0.567568	−	0.823326i	$-0.692116\pi$
$397$		−	32.8093i		−	1.64665i	0.567568	−	0.823326i	$-0.307884\pi$
$398$			54.1215i			2.71287i
$399$		0			0
$400$	19.7009	+	62.4968i	0.985045	+	3.12484i
$401$	−0.246062			−0.0122878			−0.00614388	−	0.999981i	$-0.501956\pi$
$401$	−0.246062			−0.0122878			−0.00614388	+	0.999981i	$0.501956\pi$
$402$		0			0
$403$		−	18.4762i		−	0.920366i
$404$	−22.2594			−1.10744
$405$		0			0
$406$	−16.3215			−0.810022
$407$		−	3.15260i		−	0.156269i
$408$		0			0
$409$	3.77694			0.186757			0.0933787	−	0.995631i	$-0.470233\pi$
$409$	3.77694			0.186757			0.0933787	+	0.995631i	$0.470233\pi$
$410$	29.2956	−	39.9515i	1.44680	−	1.97306i
$411$		0			0
$412$			36.3318i			1.78994i
$413$		−	15.8422i		−	0.779543i
$414$		0			0
$415$	−17.2163	+	23.4785i	−0.845115	+	1.15252i
$416$	108.503			5.31980
$417$		0			0
$418$		−	0.725587i		−	0.0354896i
$419$	−18.4069			−0.899234			−0.449617	−	0.893222i	$-0.648439\pi$
$419$	−18.4069			−0.899234			−0.449617	+	0.893222i	$0.648439\pi$
$420$		0			0
$421$	−14.5252			−0.707914			−0.353957	−	0.935262i	$-0.615164\pi$
$421$	−14.5252			−0.707914			−0.353957	+	0.935262i	$0.615164\pi$
$422$			11.8494i			0.576822i
$423$		0			0
$424$	−10.2976			−0.500096
$425$	4.76868	−	1.50323i	0.231315	−	0.0729175i
$426$		0			0
$427$			46.8752i			2.26845i
$428$			0.612950i			0.0296280i
$429$		0			0
$430$	11.2900	+	8.27869i	0.544451	+	0.399234i
$431$	−37.0684			−1.78552			−0.892762	−	0.450529i	$-0.851235\pi$
$431$	−37.0684			−1.78552			−0.892762	+	0.450529i	$0.851235\pi$
$432$		0			0
$433$		−	16.7503i		−	0.804966i	−0.915428	−	0.402483i	$-0.868147\pi$
$433$		−	16.7503i		−	0.804966i	0.915428	−	0.402483i	$-0.131853\pi$
$434$	37.6371			1.80664
$435$		0			0
$436$	−36.5604			−1.75092
$437$			1.22018i			0.0583693i
$438$		0			0
$439$	17.4072			0.830802			0.415401	−	0.909638i	$-0.363641\pi$
$439$	17.4072			0.830802			0.415401	+	0.909638i	$0.363641\pi$
$440$	17.2570	−	23.5341i	0.822697	−	1.12194i
$441$		0			0
$442$		−	16.4510i		−	0.782494i
$443$		−	33.9402i		−	1.61255i	−0.591543	−	0.806273i	$-0.701481\pi$
$443$		−	33.9402i		−	1.61255i	0.591543	−	0.806273i	$-0.298519\pi$
$444$		0			0
$445$	15.2049	+	11.1494i	0.720782	+	0.528534i
$446$	−61.1551			−2.89578
$447$		0			0
$448$			99.9551i			4.72243i
$449$	18.1461			0.856369			0.428184	−	0.903691i	$-0.359153\pi$
$449$	18.1461			0.856369			0.428184	+	0.903691i	$0.359153\pi$
$450$		0			0
$451$	−12.2441			−0.576553
$452$			46.8147i			2.20198i
$453$		0			0
$454$	55.7289			2.61549
$455$	−50.8714	−	37.3029i	−2.38489	−	1.74879i
$456$		0			0
$457$		−	17.9694i		−	0.840574i	−0.907391	−	0.420287i	$-0.861929\pi$
$457$		−	17.9694i		−	0.840574i	0.907391	−	0.420287i	$-0.138071\pi$
$458$			61.1564i			2.85765i
$459$		0			0
$460$	−46.8511	+	63.8927i	−2.18444	+	2.97901i
$461$	−12.8532			−0.598634			−0.299317	−	0.954154i	$-0.596759\pi$
$461$	−12.8532			−0.598634			−0.299317	+	0.954154i	$0.596759\pi$
$462$		0			0
$463$			7.39826i			0.343826i	0.985112	+	0.171913i	$0.0549948\pi$
$463$			7.39826i			0.343826i	−0.985112	+	0.171913i	$0.945005\pi$
$464$	−17.1928			−0.798154
$465$		0			0
$466$	−32.5426			−1.50751
$467$			23.4159i			1.08356i	0.840521	+	0.541780i	$0.182249\pi$
$467$			23.4159i			1.08356i	−0.840521	+	0.541780i	$0.817751\pi$
$468$		0			0
$469$	58.5135			2.70190
$470$	−31.8697	−	23.3693i	−1.47004	−	1.07795i
$471$		0			0
$472$		−	30.0708i		−	1.38412i
$473$		−	3.46009i		−	0.159095i
$474$		0			0
$475$	−0.272038	−	0.862981i	−0.0124820	−	0.0395963i
$476$	24.2735			1.11257
$477$		0			0
$478$		−	64.9585i		−	2.97113i
$479$	−33.6761			−1.53870			−0.769349	−	0.638828i	$-0.779419\pi$
$479$	−33.6761			−1.53870			−0.769349	+	0.638828i	$0.779419\pi$
$480$		0			0
$481$	−12.9353			−0.589797
$482$		−	50.0277i		−	2.27870i
$483$		0			0
$484$	46.1616			2.09826
$485$	−8.30952	+	11.3320i	−0.377316	+	0.514561i
$486$		0			0
$487$			33.2554i			1.50695i	0.657479	+	0.753473i	$0.271623\pi$
$487$			33.2554i			1.50695i	−0.657479	+	0.753473i	$0.728377\pi$
$488$			88.9759i			4.02775i
$489$		0			0
$490$	51.0572	−	69.6287i	2.30653	−	3.14550i
$491$	35.2806			1.59219			0.796096	−	0.605170i	$-0.206895\pi$
$491$	35.2806			1.59219			0.796096	+	0.605170i	$0.206895\pi$
$492$		0			0
$493$			1.31185i			0.0590830i
$494$	−2.97711			−0.133947
$495$		0			0
$496$	39.6462			1.78017
$497$		−	33.3167i		−	1.49446i
$498$		0			0
$499$	13.7992			0.617738			0.308869	−	0.951105i	$-0.400050\pi$
$499$	13.7992			0.617738			0.308869	+	0.951105i	$0.400050\pi$
$500$	18.8909	−	55.6338i	0.844826	−	2.48802i
$501$		0			0
$502$			34.1212i			1.52290i
$503$		−	8.73772i		−	0.389596i	−0.980843	−	0.194798i	$-0.937595\pi$
$503$		−	8.73772i		−	0.389596i	0.980843	−	0.194798i	$-0.0624051\pi$
$504$		0			0
$505$	7.63806	+	5.60082i	0.339889	+	0.249233i
$506$	27.0339			1.20180
$507$		0			0
$508$			54.3553i			2.41163i
$509$	5.64032			0.250003			0.125001	−	0.992157i	$-0.460106\pi$
$509$	5.64032			0.250003			0.125001	+	0.992157i	$0.460106\pi$
$510$		0			0
$511$	−43.0994			−1.90661
$512$			3.01385i			0.133194i
$513$		0			0
$514$	−43.2317			−1.90687
$515$	9.14167	−	12.4669i	0.402830	−	0.549355i
$516$		0			0
$517$			9.76725i			0.429563i
$518$		−	26.3498i		−	1.15774i
$519$		0			0
$520$	−96.5614	−	70.8063i	−4.23450	−	3.10506i
$521$	24.8619			1.08922			0.544609	−	0.838690i	$-0.316678\pi$
$521$	24.8619			1.08922			0.544609	+	0.838690i	$0.316678\pi$
$522$		0			0
$523$			21.4533i			0.938089i	0.883175	+	0.469044i	$0.155402\pi$
$523$			21.4533i			0.938089i	−0.883175	+	0.469044i	$0.844598\pi$
$524$	−76.4072			−3.33786
$525$		0			0
$526$	1.29638			0.0565247
$527$		−	3.02511i		−	0.131776i
$528$		0			0
$529$	−22.4616			−0.976591
$530$	5.70459	+	4.18305i	0.247792	+	0.181700i
$531$		0			0
$532$		−	4.39274i		−	0.190449i
$533$			50.2382i			2.17606i
$534$		0			0
$535$	0.154228	−	0.210327i	0.00666787	−	0.00909323i
$536$	111.067			4.79737
$537$		0			0
$538$			8.18244i			0.352770i
$539$	−21.3394			−0.919155
$540$		0			0
$541$	−8.95779			−0.385125			−0.192563	−	0.981285i	$-0.561680\pi$
$541$	−8.95779			−0.385125			−0.192563	+	0.981285i	$0.561680\pi$
$542$		−	41.0835i		−	1.76469i
$543$		0			0
$544$	17.7652			0.761678
$545$	12.5453	+	9.19920i	0.537382	+	0.394050i
$546$		0			0
$547$		−	11.2335i		−	0.480308i	−0.970735	−	0.240154i	$-0.922802\pi$
$547$		−	11.2335i		−	0.480308i	0.970735	−	0.240154i	$-0.0771979\pi$
$548$		−	59.8589i		−	2.55705i
$549$		0			0
$550$	−19.1199	+	6.02716i	−0.815273	+	0.256999i
$551$	0.237404			0.0101138
$552$		0			0
$553$		−	40.4683i		−	1.72089i
$554$	53.2192			2.26107
$555$		0			0
$556$	−28.8243			−1.22242
$557$			38.6187i			1.63633i	0.574985	+	0.818164i	$0.305008\pi$
$557$			38.6187i			1.63633i	−0.574985	+	0.818164i	$0.694992\pi$
$558$		0			0
$559$	−14.1969			−0.600465
$560$	80.0444	−	109.160i	3.38249	−	4.61284i
$561$		0			0
$562$		−	71.2590i		−	3.00588i
$563$			19.3186i			0.814180i	0.913388	+	0.407090i	$0.133456\pi$
$563$			19.3186i			0.814180i	−0.913388	+	0.407090i	$0.866544\pi$
$564$		0			0
$565$	11.7794	−	16.0640i	0.495561	−	0.675816i
$566$	3.47070			0.145884
$567$		0			0
$568$		−	63.2400i		−	2.65349i
$569$	21.0402			0.882051			0.441025	−	0.897495i	$-0.354615\pi$
$569$	21.0402			0.882051			0.441025	+	0.897495i	$0.354615\pi$
$570$		0			0
$571$	15.9522			0.667580			0.333790	−	0.942647i	$-0.391672\pi$
$571$	15.9522			0.667580			0.333790	+	0.942647i	$0.391672\pi$
$572$			47.7767i			1.99764i
$573$		0			0
$574$	−102.338			−4.27150
$575$	32.1529	−	10.1356i	1.34087	−	0.422683i
$576$		0			0
$577$		−	10.0761i		−	0.419474i	−0.977758	−	0.209737i	$-0.932739\pi$
$577$		−	10.0761i		−	0.419474i	0.977758	−	0.209737i	$-0.0672608\pi$
$578$		−	2.69353i		−	0.112036i
$579$		0			0
$580$	12.4312	+	9.11556i	0.516179	+	0.378503i
$581$	60.1415			2.49509
$582$		0			0
$583$		−	1.74831i		−	0.0724078i
$584$	−81.8089			−3.38528
$585$		0			0
$586$	−18.4851			−0.763613
$587$			29.6248i			1.22275i	0.791342	+	0.611374i	$0.209383\pi$
$587$			29.6248i			1.22275i	−0.791342	+	0.611374i	$0.790617\pi$
$588$		0			0
$589$	−0.547450			−0.0225573
$590$	−12.2152	+	16.6584i	−0.502893	+	0.685814i
$591$		0			0
$592$		−	27.7564i		−	1.14078i
$593$		−	18.6199i		−	0.764628i	−0.924032	−	0.382314i	$-0.875127\pi$
$593$		−	18.6199i		−	0.764628i	0.924032	−	0.382314i	$-0.124873\pi$
$594$		0			0
$595$	−8.32919	−	6.10761i	−0.341463	−	0.250388i
$596$	−106.332			−4.35553
$597$		0			0
$598$		−	110.921i		−	4.53591i
$599$	44.2120			1.80645			0.903226	−	0.429165i	$-0.141192\pi$
$599$	44.2120			1.80645			0.903226	+	0.429165i	$0.141192\pi$
$600$		0			0
$601$	31.0357			1.26597			0.632986	−	0.774163i	$-0.281829\pi$
$601$	31.0357			1.26597			0.632986	+	0.774163i	$0.281829\pi$
$602$		−	28.9199i		−	1.17869i
$603$		0			0
$604$	−38.0345			−1.54760
$605$	−15.8399	−	11.6150i	−0.643983	−	0.472218i
$606$		0			0
$607$			35.1424i			1.42639i	0.700967	+	0.713194i	$0.252752\pi$
$607$			35.1424i			1.42639i	−0.700967	+	0.713194i	$0.747248\pi$
$608$		−	3.21495i		−	0.130383i
$609$		0			0
$610$	36.1434	−	49.2902i	1.46340	−	1.99570i
$611$	40.0754			1.62128
$612$		0			0
$613$		−	45.8296i		−	1.85104i	−0.378698	−	0.925520i	$-0.623628\pi$
$613$		−	45.8296i		−	1.85104i	0.378698	−	0.925520i	$-0.376372\pi$
$614$	51.3782			2.07346
$615$		0			0
$616$	−60.2838			−2.42891
$617$		−	19.3645i		−	0.779586i	−0.920902	−	0.389793i	$-0.872547\pi$
$617$		−	19.3645i		−	0.779586i	0.920902	−	0.389793i	$-0.127453\pi$
$618$		0			0
$619$	24.1232			0.969594			0.484797	−	0.874627i	$-0.338893\pi$
$619$	24.1232			0.969594			0.484797	+	0.874627i	$0.338893\pi$
$620$	−28.6662	−	21.0203i	−1.15126	−	0.844196i
$621$		0			0
$622$			44.9506i			1.80236i
$623$		−	38.9482i		−	1.56043i
$624$		0			0
$625$	−20.4806	+	14.3369i	−0.819223	+	0.573475i
$626$	−52.5798			−2.10151
$627$		0			0
$628$			39.4769i			1.57530i
$629$	−2.11789			−0.0844458
$630$		0			0
$631$	42.5276			1.69300			0.846499	−	0.532390i	$-0.178706\pi$
$631$	42.5276			1.69300			0.846499	+	0.532390i	$0.178706\pi$
$632$		−	76.8147i		−	3.05553i
$633$		0			0
$634$	−75.4058			−2.99475
$635$	13.6767	−	18.6515i	0.542743	−	0.740160i
$636$		0			0
$637$			87.5566i			3.46912i
$638$		−	5.25984i		−	0.208239i
$639$		0			0
$640$	30.0904	−	41.0354i	1.18943	−	1.62207i
$641$	31.3506			1.23828			0.619138	−	0.785282i	$-0.287482\pi$
$641$	31.3506			1.23828			0.619138	+	0.785282i	$0.287482\pi$
$642$		0			0
$643$			20.3035i			0.800692i	0.916364	+	0.400346i	$0.131110\pi$
$643$			20.3035i			0.800692i	−0.916364	+	0.400346i	$0.868890\pi$
$644$	163.664			6.44928
$645$		0			0
$646$	−0.487443			−0.0191782
$647$			38.8373i			1.52685i	0.645896	+	0.763425i	$0.276484\pi$
$647$			38.8373i			1.52685i	−0.645896	+	0.763425i	$0.723516\pi$
$648$		0			0
$649$	5.10537			0.200403
$650$	24.7297	+	78.4495i	0.969978	+	3.07704i
$651$		0			0
$652$		−	34.9161i		−	1.36742i
$653$		−	34.5694i		−	1.35281i	−0.736532	−	0.676403i	$-0.763538\pi$
$653$		−	34.5694i		−	1.35281i	0.736532	−	0.676403i	$-0.236462\pi$
$654$		0			0
$655$	26.2183	+	19.2253i	1.02443	+	0.751195i
$656$	−107.801			−4.20892
$657$		0			0
$658$			81.6358i			3.18249i
$659$	−17.8777			−0.696417			−0.348208	−	0.937417i	$-0.613210\pi$
$659$	−17.8777			−0.696417			−0.348208	+	0.937417i	$0.613210\pi$
$660$		0			0
$661$	−10.7639			−0.418667			−0.209333	−	0.977844i	$-0.567129\pi$
$661$	−10.7639			−0.418667			−0.209333	+	0.977844i	$0.567129\pi$
$662$			1.21132i			0.0470792i
$663$		0			0
$664$	114.157			4.43016
$665$	−1.10529	+	1.50732i	−0.0428611	+	0.0584514i
$666$		0			0
$667$			8.84521i			0.342488i
$668$			18.9951i			0.734942i
$669$		0			0
$670$	−61.5281	−	45.1172i	−2.37704	−	1.74303i
$671$	−15.1062			−0.583168
$672$		0			0
$673$		−	7.18958i		−	0.277138i	−0.990353	−	0.138569i	$-0.955750\pi$
$673$		−	7.18958i		−	0.277138i	0.990353	−	0.138569i	$-0.0442502\pi$
$674$	−37.6547			−1.45040
$675$		0			0
$676$	127.714			4.91206
$677$			38.0770i			1.46342i	0.681617	+	0.731709i	$0.261277\pi$
$677$			38.0770i			1.46342i	−0.681617	+	0.731709i	$0.738723\pi$
$678$		0			0
$679$	29.0276			1.11398
$680$	−15.8100	−	11.5931i	−0.606286	−	0.444576i
$681$		0			0
$682$			12.1291i			0.464447i
$683$		−	7.36273i		−	0.281727i	−0.990029	−	0.140864i	$-0.955012\pi$
$683$		−	7.36273i		−	0.281727i	0.990029	−	0.140864i	$-0.0449879\pi$
$684$		0			0
$685$	−15.0615	+	20.5399i	−0.575470	+	0.784791i
$686$	−91.2668			−3.48458
$687$		0			0
$688$		−	30.4637i		−	1.16142i
$689$	−7.17340			−0.273285
$690$		0			0
$691$	40.5159			1.54130			0.770650	−	0.637259i	$-0.219932\pi$
$691$	40.5159			1.54130			0.770650	+	0.637259i	$0.219932\pi$
$692$		−	38.6283i		−	1.46843i
$693$		0			0
$694$	−50.7167			−1.92518
$695$	9.89076	+	7.25268i	0.375178	+	0.275110i
$696$		0			0
$697$			8.22550i			0.311563i
$698$		−	2.80161i		−	0.106043i
$699$		0			0
$700$	−115.752	+	36.4887i	−4.37503	+	1.37914i
$701$	−16.5969			−0.626855			−0.313428	−	0.949612i	$-0.601477\pi$
$701$	−16.5969			−0.626855			−0.313428	+	0.949612i	$0.601477\pi$
$702$		0			0
$703$			0.383272i			0.0144554i
$704$	−32.2120			−1.21403
$705$		0			0
$706$	−56.8381			−2.13913
$707$		−	19.5653i		−	0.735829i
$708$		0			0
$709$	−23.7142			−0.890604			−0.445302	−	0.895381i	$-0.646904\pi$
$709$	−23.7142			−0.890604			−0.445302	+	0.895381i	$0.646904\pi$
$710$	−25.6891	+	35.0332i	−0.964095	+	1.31477i
$711$		0			0
$712$		−	73.9293i		−	2.77062i
$713$		−	20.3969i		−	0.763870i
$714$		0			0
$715$	12.0214	−	16.3941i	0.449575	−	0.613103i
$716$	−27.2617			−1.01882
$717$		0			0
$718$			15.6450i			0.583865i
$719$	2.14873			0.0801339			0.0400670	−	0.999197i	$-0.487243\pi$
$719$	2.14873			0.0801339			0.0400670	+	0.999197i	$0.487243\pi$
$720$		0			0
$721$	−31.9345			−1.18930
$722$		−	51.0888i		−	1.90133i
$723$		0			0
$724$	−3.64286			−0.135386
$725$	−1.97202	−	6.25581i	−0.0732391	−	0.232335i
$726$		0			0
$727$		−	21.5131i		−	0.797875i	−0.916978	−	0.398938i	$-0.869379\pi$
$727$		−	21.5131i		−	0.797875i	0.916978	−	0.398938i	$-0.130621\pi$
$728$			247.347i			9.16729i
$729$		0			0
$730$	45.3199	+	33.2321i	1.67736	+	1.22997i
$731$	−2.32446			−0.0859733
$732$		0			0
$733$			37.4517i			1.38331i	0.722228	+	0.691655i	$0.243118\pi$
$733$			37.4517i			1.38331i	−0.722228	+	0.691655i	$0.756882\pi$
$734$	−42.2465			−1.55935
$735$		0			0
$736$	119.782			4.41524
$737$			18.8568i			0.694600i
$738$		0			0
$739$	29.9540			1.10188			0.550938	−	0.834546i	$-0.314270\pi$
$739$	29.9540			1.10188			0.550938	+	0.834546i	$0.314270\pi$
$740$	−14.7164	+	20.0693i	−0.540985	+	0.737762i
$741$		0			0
$742$		−	14.6126i		−	0.536446i
$743$		−	4.89399i		−	0.179543i	−0.995962	−	0.0897716i	$-0.971386\pi$
$743$		−	4.89399i		−	0.179543i	0.995962	−	0.0897716i	$-0.0286137\pi$
$744$		0			0
$745$	36.4867	+	26.7549i	1.33677	+	0.980224i
$746$	77.2132			2.82698
$747$		0			0
$748$			7.82248i			0.286018i
$749$	−0.538764			−0.0196860
$750$		0			0
$751$	17.7060			0.646102			0.323051	−	0.946382i	$-0.395291\pi$
$751$	17.7060			0.646102			0.323051	+	0.946382i	$0.395291\pi$
$752$			85.9937i			3.13587i
$753$		0			0
$754$	−21.5813			−0.785946
$755$	13.0511	+	9.57010i	0.474979	+	0.348292i
$756$		0			0
$757$		−	49.1135i		−	1.78506i	−0.450988	−	0.892530i	$-0.648928\pi$
$757$		−	49.1135i		−	1.78506i	0.450988	−	0.892530i	$-0.351072\pi$
$758$		−	37.9255i		−	1.37752i
$759$		0			0
$760$	−2.09799	+	2.86111i	−0.0761022	+	0.103784i
$761$	9.03057			0.327358			0.163679	−	0.986514i	$-0.447664\pi$
$761$	9.03057			0.327358			0.163679	+	0.986514i	$0.447664\pi$
$762$		0			0
$763$		−	32.1355i		−	1.16338i
$764$	18.0236			0.652070
$765$		0			0
$766$	44.5629			1.61012
$767$		−	20.9476i		−	0.756372i
$768$		0			0
$769$	46.2896			1.66924			0.834622	−	0.550823i	$-0.185686\pi$
$769$	46.2896			1.66924			0.834622	+	0.550823i	$0.185686\pi$
$770$	33.3956	+	24.4883i	1.20349	+	0.882495i
$771$		0			0
$772$		−	28.0222i		−	1.00854i
$773$			0.350175i			0.0125949i	0.999980	+	0.00629746i	$0.00200456\pi$
$773$			0.350175i			0.0125949i	−0.999980	+	0.00629746i	$0.997995\pi$
$774$		0			0
$775$	4.54745	+	14.4258i	0.163349	+	0.518190i
$776$	55.0986			1.97792
$777$		0			0
$778$		−	57.7851i		−	2.07170i
$779$	1.48856			0.0533331
$780$		0			0
$781$	10.7368			0.384193
$782$		−	18.1612i		−	0.649441i
$783$		0			0
$784$	−187.879			−6.70995
$785$	9.93304	−	13.5461i	0.354526	−	0.483480i
$786$		0			0
$787$		−	18.6914i		−	0.666278i	−0.942878	−	0.333139i	$-0.891892\pi$
$787$		−	18.6914i		−	0.666278i	0.942878	−	0.333139i	$-0.108108\pi$
$788$			73.6439i			2.62345i
$789$		0			0
$790$	−31.2034	+	42.5533i	−1.11017	+	1.51398i
$791$	−41.1487			−1.46308
$792$		0			0
$793$			61.9814i			2.20102i
$794$	88.3727			3.13623
$795$		0			0
$796$	−105.591			−3.74258
$797$		−	32.4669i		−	1.15004i	−0.818141	−	0.575018i	$-0.804995\pi$
$797$		−	32.4669i		−	1.15004i	0.818141	−	0.575018i	$-0.195005\pi$
$798$		0			0
$799$	6.56155			0.232131
$800$	−84.7167	+	26.7053i	−2.99519	+	0.944174i
$801$		0			0
$802$		−	0.662775i		−	0.0234034i
$803$		−	13.8894i		−	0.490147i
$804$		0			0
$805$	−56.1597	−	41.1807i	−1.97937	−	1.45143i
$806$	49.7661			1.75294
$807$		0			0
$808$		−	37.1378i		−	1.30650i
$809$	7.30347			0.256776			0.128388	−	0.991724i	$-0.459020\pi$
$809$	7.30347			0.256776			0.128388	+	0.991724i	$0.459020\pi$
$810$		0			0
$811$	−3.42434			−0.120245			−0.0601225	−	0.998191i	$-0.519149\pi$
$811$	−3.42434			−0.120245			−0.0601225	+	0.998191i	$0.519149\pi$
$812$		−	31.8433i		−	1.11748i
$813$		0			0
$814$	8.49161			0.297631
$815$	−8.78547	+	11.9811i	−0.307742	+	0.419679i
$816$		0			0
$817$			0.420654i			0.0147168i
$818$			10.1733i			0.355700i
$819$		0			0
$820$	77.9455	+	57.1557i	2.72198	+	1.99597i
$821$	40.2521			1.40481			0.702404	−	0.711778i	$-0.252110\pi$
$821$	40.2521			1.40481			0.702404	+	0.711778i	$0.252110\pi$
$822$		0			0
$823$			9.80674i			0.341841i	0.985285	+	0.170921i	$0.0546742\pi$
$823$			9.80674i			0.341841i	−0.985285	+	0.170921i	$0.945326\pi$
$824$	−60.6163			−2.11167
$825$		0			0
$826$	42.6713			1.48472
$827$			4.78549i			0.166408i	0.996533	+	0.0832038i	$0.0265153\pi$
$827$			4.78549i			0.166408i	−0.996533	+	0.0832038i	$0.973485\pi$
$828$		0			0
$829$	−38.5349			−1.33837			−0.669185	−	0.743096i	$-0.733357\pi$
$829$	−38.5349			−1.33837			−0.669185	+	0.743096i	$0.733357\pi$
$830$	−63.2400	−	46.3725i	−2.19509	−	1.60961i
$831$		0			0
$832$			132.167i			4.58207i
$833$			14.3357i			0.496701i
$834$		0			0
$835$	4.77948	−	6.51796i	0.165401	−	0.225563i
$836$	1.41562			0.0489604
$837$		0			0
$838$		−	49.5793i		−	1.71269i
$839$	−3.20700			−0.110718			−0.0553590	−	0.998467i	$-0.517630\pi$
$839$	−3.20700			−0.110718			−0.0553590	+	0.998467i	$0.517630\pi$
$840$		0			0
$841$	−27.2790			−0.940656
$842$		−	39.1239i		−	1.34830i
$843$		0			0
$844$	−23.1183			−0.795765
$845$	−43.8236	−	32.1349i	−1.50758	−	1.10547i
$846$		0			0
$847$			40.5747i			1.39416i
$848$		−	15.3927i		−	0.528586i
$849$		0			0
$850$	4.04900	+	12.8446i	0.138879	+	0.440565i
$851$	−14.2799			−0.489509
$852$		0			0
$853$			18.4995i			0.633412i	0.948524	+	0.316706i	$0.102577\pi$
$853$			18.4995i			0.633412i	−0.948524	+	0.316706i	$0.897423\pi$
$854$	−126.259			−4.32051
$855$		0			0
$856$	−1.02265			−0.0349535
$857$		−	7.84698i		−	0.268048i	−0.990978	−	0.134024i	$-0.957210\pi$
$857$		−	7.84698i		−	0.268048i	0.990978	−	0.134024i	$-0.0427899\pi$
$858$		0			0
$859$	−28.9487			−0.987718			−0.493859	−	0.869542i	$-0.664414\pi$
$859$	−28.9487			−0.987718			−0.493859	+	0.869542i	$0.664414\pi$
$860$	−16.1518	+	22.0268i	−0.550770	+	0.751107i
$861$		0			0
$862$		−	99.8447i		−	3.40073i
$863$		−	34.1900i		−	1.16384i	−0.813245	−	0.581921i	$-0.802301\pi$
$863$		−	34.1900i		−	1.16384i	0.813245	−	0.581921i	$-0.197699\pi$
$864$		0			0
$865$	−9.71953	+	13.2549i	−0.330474	+	0.450680i
$866$	45.1172			1.53315
$867$		0			0
$868$			73.4300i			2.49238i
$869$	13.0415			0.442403
$870$		0			0
$871$	77.3703			2.62159
$872$		−	60.9978i		−	2.06565i
$873$		0			0
$874$	−3.28660			−0.111171
$875$	48.9004	+	16.6045i	1.65313	+	0.561335i
$876$		0			0
$877$			2.93107i			0.0989753i	0.998775	+	0.0494877i	$0.0157588\pi$
$877$			2.93107i			0.0989753i	−0.998775	+	0.0494877i	$0.984241\pi$
$878$			46.8869i			1.58235i
$879$		0			0
$880$	35.1783	+	25.7955i	1.18586	+	0.869566i
$881$	−56.2657			−1.89564			−0.947820	−	0.318807i	$-0.896718\pi$
$881$	−56.2657			−1.89564			−0.947820	+	0.318807i	$0.896718\pi$
$882$		0			0
$883$		−	0.966565i		−	0.0325275i	−0.999868	−	0.0162638i	$-0.994823\pi$
$883$		−	0.966565i		−	0.0325275i	0.999868	−	0.0162638i	$-0.00517714\pi$
$884$	32.0960			1.07950
$885$		0			0
$886$	91.4187			3.07127
$887$		−	41.0673i		−	1.37890i	−0.724331	−	0.689452i	$-0.757851\pi$
$887$		−	41.0673i		−	1.37890i	0.724331	−	0.689452i	$-0.242149\pi$
$888$		0			0
$889$	−47.7767			−1.60238
$890$	−30.0313	+	40.9548i	−1.00665	+	1.37281i
$891$		0			0
$892$		−	119.314i		−	3.99492i
$893$		−	1.18743i		−	0.0397360i
$894$		0			0
$895$	9.35456	+	6.85949i	0.312688	+	0.229288i
$896$	−105.114			−3.51162
$897$		0			0
$898$			48.8771i			1.63105i
$899$	−3.96851			−0.132357
$900$		0			0
$901$	−1.17450			−0.0391283
$902$		−	32.9799i		−	1.09811i
$903$		0			0
$904$	−78.1062			−2.59778
$905$	1.25001	+	0.916605i	0.0415517	+	0.0304690i
$906$		0			0
$907$		−	43.2302i		−	1.43543i	−0.696334	−	0.717717i	$-0.745187\pi$
$907$		−	43.2302i		−	1.43543i	0.696334	−	0.717717i	$-0.254813\pi$
$908$			108.727i			3.60824i
$909$		0			0
$910$	100.476	−	137.023i	3.33076	−	4.54228i
$911$	44.9471			1.48916			0.744581	−	0.667532i	$-0.232649\pi$
$911$	44.9471			1.48916			0.744581	+	0.667532i	$0.232649\pi$
$912$		0			0
$913$			19.3815i			0.641433i
$914$	48.4011			1.60097
$915$		0			0
$916$	−119.316			−3.94232
$917$		−	67.1596i		−	2.21780i
$918$		0			0
$919$	−1.36957			−0.0451781			−0.0225890	−	0.999745i	$-0.507191\pi$
$919$	−1.36957			−0.0451781			−0.0225890	+	0.999745i	$0.507191\pi$
$920$	−106.599	−	78.1669i	−3.51448	−	2.57709i
$921$		0			0
$922$		−	34.6205i		−	1.14016i
$923$		−	44.0536i		−	1.45004i
$924$		0			0
$925$	10.0995	−	3.18368i	0.332071	−	0.104679i
$926$	−19.9274			−0.654855
$927$		0			0
$928$		−	23.3054i		−	0.765038i
$929$	2.67132			0.0876431			0.0438215	−	0.999039i	$-0.486047\pi$
$929$	2.67132			0.0876431			0.0438215	+	0.999039i	$0.486047\pi$
$930$		0			0
$931$	2.59430			0.0850248
$932$		−	63.4908i		−	2.07971i
$933$		0			0
$934$	−63.0714			−2.06376
$935$	1.96827	−	2.68420i	0.0643692	−	0.0877828i
$936$		0			0
$937$		−	26.6015i		−	0.869034i	−0.900664	−	0.434517i	$-0.856919\pi$
$937$		−	26.6015i		−	0.869034i	0.900664	−	0.434517i	$-0.143081\pi$
$938$			157.608i			5.14607i
$939$		0			0
$940$	45.5936	−	62.1778i	1.48710	−	2.02802i
$941$	24.8072			0.808690			0.404345	−	0.914606i	$-0.367499\pi$
$941$	24.8072			0.808690			0.404345	+	0.914606i	$0.367499\pi$
$942$		0			0
$943$			55.4606i			1.80605i
$944$	44.9492			1.46297
$945$		0			0
$946$	9.31984			0.303014
$947$			39.6057i			1.28701i	0.765441	+	0.643506i	$0.222521\pi$
$947$			39.6057i			1.28701i	−0.765441	+	0.643506i	$0.777479\pi$
$948$		0			0
$949$	−56.9888			−1.84994
$950$	2.32446	−	0.732741i	0.0754155	−	0.0237733i
$951$		0			0
$952$			40.4982i			1.31255i
$953$			43.2247i			1.40019i	0.714052	+	0.700093i	$0.246858\pi$
$953$			43.2247i			1.40019i	−0.714052	+	0.700093i	$0.753142\pi$
$954$		0			0
$955$	−6.18460	−	4.53503i	−0.200129	−	0.146750i
$956$	126.734			4.09888
$957$		0			0
$958$		−	90.7073i		−	2.93062i
$959$	52.6142			1.69900
$960$		0			0
$961$	−21.8487			−0.704796
$962$		−	34.8414i		−	1.12333i
$963$		0			0
$964$	97.6042			3.14362
$965$	−7.05086	+	9.61553i	−0.226975	+	0.309535i
$966$		0			0
$967$			0.630476i			0.0202748i	0.999949	+	0.0101374i	$0.00322688\pi$
$967$			0.630476i			0.0202748i	−0.999949	+	0.0101374i	$0.996773\pi$
$968$			77.0166i			2.47541i
$969$		0			0
$970$	−30.5231	−	22.3819i	−0.980037	−	0.718640i
$971$	−62.1272			−1.99376			−0.996879	−	0.0789458i	$-0.974845\pi$
$971$	−62.1272			−1.99376			−0.996879	+	0.0789458i	$0.974845\pi$
$972$		0			0
$973$		−	25.3357i		−	0.812225i
$974$	−89.5743			−2.87015
$975$		0			0
$976$	−132.999			−4.25721
$977$			43.0462i			1.37717i	0.725156	+	0.688585i	$0.241768\pi$
$977$			43.0462i			1.37717i	−0.725156	+	0.688585i	$0.758232\pi$
$978$		0			0
$979$	12.5516			0.401151
$980$	135.846	+	99.6128i	4.33944	+	3.18201i
$981$		0			0
$982$			95.0292i			3.03250i
$983$			26.5628i			0.847222i	0.905844	+	0.423611i	$0.139238\pi$
$983$			26.5628i			0.847222i	−0.905844	+	0.423611i	$0.860762\pi$
$984$		0			0
$985$	18.5300	−	25.2701i	0.590415	−	0.805172i
$986$	−3.53351			−0.112530
$987$		0			0
$988$		−	5.80836i		−	0.184789i
$989$	−15.6727			−0.498364
$990$		0			0
$991$	−35.8067			−1.13744			−0.568719	−	0.822532i	$-0.692561\pi$
$991$	−35.8067			−1.13744			−0.568719	+	0.822532i	$0.692561\pi$
$992$			53.7418i			1.70631i
$993$		0			0
$994$	89.7395			2.84636
$995$	36.2325	+	26.5685i	1.14865	+	0.842279i
$996$		0			0
$997$			2.94417i			0.0932428i	0.998913	+	0.0466214i	$0.0148454\pi$
$997$			2.94417i			0.0932428i	−0.998913	+	0.0466214i	$0.985155\pi$
$998$			37.1685i			1.17655i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.b.e.154.16	yes	16
3.2	odd	2	inner	765.2.b.e.154.1	✓	16
5.2	odd	4		3825.2.a.bs.1.2		8
5.3	odd	4		3825.2.a.bt.1.7		8
5.4	even	2	inner	765.2.b.e.154.2	yes	16
15.2	even	4		3825.2.a.bt.1.8		8
15.8	even	4		3825.2.a.bs.1.1		8
15.14	odd	2	inner	765.2.b.e.154.15	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
765.2.b.e.154.1	✓	16	3.2	odd	2	inner
765.2.b.e.154.2	yes	16	5.4	even	2	inner
765.2.b.e.154.15	yes	16	15.14	odd	2	inner
765.2.b.e.154.16	yes	16	1.1	even	1	trivial
3825.2.a.bs.1.1		8	15.8	even	4
3825.2.a.bs.1.2		8	5.2	odd	4
3825.2.a.bt.1.7		8	5.3	odd	4
3825.2.a.bt.1.8		8	15.2	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.69353i q^{2} -5.25508 q^{4} +(1.80322 + 1.32226i) q^{5} -4.61905i q^{7} -8.76763i q^{8} +(-3.56155 + 4.85703i) q^{10} +1.48856 q^{11} -6.10761i q^{13} +12.4415 q^{14} +13.1057 q^{16} -1.00000i q^{17} -0.180969 q^{19} +(-9.47608 - 6.94860i) q^{20} +4.00947i q^{22} -6.74252i q^{23} +(1.50323 + 4.76868i) q^{25} +16.4510 q^{26} +24.2735i q^{28} -1.31185 q^{29} +3.02511 q^{31} +17.7652i q^{32} +2.69353 q^{34} +(6.10761 - 8.32919i) q^{35} -2.11789i q^{37} -0.487443i q^{38} +(11.5931 - 15.8100i) q^{40} -8.22550 q^{41} -2.32446i q^{43} -7.82248 q^{44} +18.1612 q^{46} +6.56155i q^{47} -14.3357 q^{49} +(-12.8446 + 4.04900i) q^{50} +32.0960i q^{52} -1.17450i q^{53} +(2.68420 + 1.96827i) q^{55} -40.4982 q^{56} -3.53351i q^{58} +3.42975 q^{59} -10.1482 q^{61} +8.14822i q^{62} -21.6397 q^{64} +(8.07588 - 11.0134i) q^{65} +12.6679i q^{67} +5.25508i q^{68} +(22.4349 + 16.4510i) q^{70} +7.21290 q^{71} -9.33079i q^{73} +5.70459 q^{74} +0.951004 q^{76} -6.87572i q^{77} +8.76117 q^{79} +(23.6325 + 17.3292i) q^{80} -22.1556i q^{82} +13.0203i q^{83} +(1.32226 - 1.80322i) q^{85} +6.26099 q^{86} -13.0511i q^{88} +8.43207 q^{89} -28.2114 q^{91} +35.4325i q^{92} -17.6737 q^{94} +(-0.326327 - 0.239288i) q^{95} +6.28431i q^{97} -38.6134i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 24 q^{10} + 32 q^{16} - 4 q^{19} + 6 q^{25} - 24 q^{31} + 8 q^{34} + 44 q^{40} + 80 q^{46} - 56 q^{49} + 26 q^{55} - 24 q^{61} - 108 q^{64} + 44 q^{70} + 12 q^{76} + 72 q^{79} + 2 q^{85}+ \cdots - 36 q^{94}+O(q^{100}) \) 16 * q - 16 * q^4 - 24 * q^10 + 32 * q^16 - 4 * q^19 + 6 * q^25 - 24 * q^31 + 8 * q^34 + 44 * q^40 + 80 * q^46 - 56 * q^49 + 26 * q^55 - 24 * q^61 - 108 * q^64 + 44 * q^70 + 12 * q^76 + 72 * q^79 + 2 * q^85 - 96 * q^91 - 36 * q^94

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