LMFDB - Embedded newform 1728.3.o.g.127.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,3,Mod(127,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1728.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1728.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$47.0845896815$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 $ x^16 - 3x^15 + 7x^14 - 30x^13 + 76x^12 - 144x^11 + 424x^10 - 912x^9 + 1552x^8 - 3648x^7 + 6784x^6 - 9216x^5 + 19456x^4 - 30720x^3 + 28672x^2 - 49152*x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.8
Root			$1.63139 + 1.15696i$ of defining polynomial
Character	$\chi$	$=$	1728.127
Dual form			1728.3.o.g.1279.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.07403 + 5.32438i) q^{5} +(0.511543 + 0.295340i) q^{7} +O(q^{10})$	$q+(3.07403 + 5.32438i) q^{5} +(0.511543 + 0.295340i) q^{7} +(15.1205 + 8.72982i) q^{11} +(0.892255 + 1.54543i) q^{13} +16.9171 q^{17} +19.5058i q^{19} +(6.86778 - 3.96511i) q^{23} +(-6.39933 + 11.0840i) q^{25} +(3.17517 - 5.49956i) q^{29} +(27.6558 - 15.9671i) q^{31} +3.63153i q^{35} -58.2834 q^{37} +(2.66948 + 4.62368i) q^{41} +(33.9324 + 19.5909i) q^{43} +(9.64117 + 5.56633i) q^{47} +(-24.3255 - 42.1331i) q^{49} +35.8770 q^{53} +107.343i q^{55} +(-20.8974 + 12.0651i) q^{59} +(37.9460 - 65.7244i) q^{61} +(-5.48564 + 9.50141i) q^{65} +(31.8200 - 18.3713i) q^{67} +87.8370i q^{71} -60.0423 q^{73} +(5.15652 + 8.93136i) q^{77} +(32.1841 + 18.5815i) q^{79} +(-66.0281 - 38.1214i) q^{83} +(52.0037 + 90.0730i) q^{85} +27.5873 q^{89} +1.05407i q^{91} +(-103.856 + 59.9614i) q^{95} +(13.0585 - 22.6180i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{5}+O(q^{10}) $ 16 * q + 6 * q^5	$ 16 q + 6 q^{5} + 46 q^{13} - 12 q^{17} - 30 q^{25} + 42 q^{29} - 56 q^{37} - 84 q^{41} + 58 q^{49} - 72 q^{53} + 34 q^{61} + 30 q^{65} + 116 q^{73} - 330 q^{77} + 140 q^{85} + 384 q^{89} - 148 q^{97}+O(q^{100}) $ 16 * q + 6 * q^5 + 46 * q^13 - 12 * q^17 - 30 * q^25 + 42 * q^29 - 56 * q^37 - 84 * q^41 + 58 * q^49 - 72 * q^53 + 34 * q^61 + 30 * q^65 + 116 * q^73 - 330 * q^77 + 140 * q^85 + 384 * q^89 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	3.07403	+	5.32438i	0.614806	+	1.06488i	0.990418	+	0.138099i	$0.0440991\pi$
$5$	3.07403	+	5.32438i	0.614806	+	1.06488i	−0.375612	+	0.926777i	$0.622568\pi$
$6$		0			0
$7$	0.511543	+	0.295340i	0.0730776	+	0.0421914i	0.536094	−	0.844159i	$-0.319899\pi$
$7$	0.511543	+	0.295340i	0.0730776	+	0.0421914i	−0.463016	+	0.886350i	$0.653233\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	15.1205	+	8.72982i	1.37459	+	0.793620i	0.991502	−	0.130092i	$-0.0415274\pi$
$11$	15.1205	+	8.72982i	1.37459	+	0.793620i	0.383088	+	0.923712i	$0.374861\pi$
$12$		0			0
$13$	0.892255	+	1.54543i	0.0686350	+	0.118879i	0.898301	−	0.439381i	$-0.144802\pi$
$13$	0.892255	+	1.54543i	0.0686350	+	0.118879i	−0.829666	+	0.558261i	$0.811469\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	16.9171			0.995123			0.497562	−	0.867429i	$-0.334229\pi$
$17$	16.9171			0.995123			0.497562	+	0.867429i	$0.334229\pi$
$18$		0			0
$19$			19.5058i			1.02662i	0.858203	+	0.513310i	$0.171581\pi$
$19$			19.5058i			1.02662i	−0.858203	+	0.513310i	$0.828419\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	6.86778	−	3.96511i	0.298599	−	0.172396i	−0.343214	−	0.939257i	$-0.611516\pi$
$23$	6.86778	−	3.96511i	0.298599	−	0.172396i	0.641813	+	0.766861i	$0.278182\pi$
$24$		0			0
$25$	−6.39933	+	11.0840i	−0.255973	+	0.443359i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.17517	−	5.49956i	0.109489	−	0.189640i	−0.806075	−	0.591814i	$-0.798412\pi$
$29$	3.17517	−	5.49956i	0.109489	−	0.189640i	0.915563	+	0.402174i	$0.131745\pi$
$30$		0			0
$31$	27.6558	−	15.9671i	0.892124	−	0.515068i	0.0174873	−	0.999847i	$-0.494433\pi$
$31$	27.6558	−	15.9671i	0.892124	−	0.515068i	0.874637	+	0.484779i	$0.161100\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			3.63153i			0.103758i
$36$		0			0
$37$	−58.2834			−1.57523			−0.787614	−	0.616169i	$-0.788684\pi$
$37$	−58.2834			−1.57523			−0.787614	+	0.616169i	$0.788684\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.66948	+	4.62368i	0.0651093	+	0.112773i	0.896742	−	0.442553i	$-0.145927\pi$
$41$	2.66948	+	4.62368i	0.0651093	+	0.112773i	−0.831633	+	0.555325i	$0.812594\pi$
$42$		0			0
$43$	33.9324	+	19.5909i	0.789126	+	0.455602i	0.839655	−	0.543121i	$-0.182757\pi$
$43$	33.9324	+	19.5909i	0.789126	+	0.455602i	−0.0505290	+	0.998723i	$0.516091\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	9.64117	+	5.56633i	0.205131	+	0.118433i	0.599047	−	0.800714i	$-0.295546\pi$
$47$	9.64117	+	5.56633i	0.205131	+	0.118433i	−0.393915	+	0.919147i	$0.628880\pi$
$48$		0			0
$49$	−24.3255	−	42.1331i	−0.496440	−	0.859859i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	35.8770			0.676925			0.338462	−	0.940980i	$-0.390093\pi$
$53$	35.8770			0.676925			0.338462	+	0.940980i	$0.390093\pi$
$54$		0			0
$55$			107.343i			1.95169i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−20.8974	+	12.0651i	−0.354194	+	0.204494i	−0.666531	−	0.745477i	$-0.732222\pi$
$59$	−20.8974	+	12.0651i	−0.354194	+	0.204494i	0.312337	+	0.949971i	$0.398888\pi$
$60$		0			0
$61$	37.9460	−	65.7244i	0.622066	−	1.07745i	−0.367034	−	0.930207i	$-0.619627\pi$
$61$	37.9460	−	65.7244i	0.622066	−	1.07745i	0.989100	−	0.147243i	$-0.0470398\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.48564	+	9.50141i	−0.0843944	+	0.146175i
$66$		0			0
$67$	31.8200	−	18.3713i	0.474925	−	0.274198i	−0.243374	−	0.969933i	$-0.578254\pi$
$67$	31.8200	−	18.3713i	0.474925	−	0.274198i	0.718299	+	0.695734i	$0.244921\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			87.8370i			1.23714i	0.785730	+	0.618570i	$0.212288\pi$
$71$			87.8370i			1.23714i	−0.785730	+	0.618570i	$0.787712\pi$
$72$		0			0
$73$	−60.0423			−0.822498			−0.411249	−	0.911523i	$-0.634907\pi$
$73$	−60.0423			−0.822498			−0.411249	+	0.911523i	$0.634907\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.15652	+	8.93136i	0.0669678	+	0.115992i
$78$		0			0
$79$	32.1841	+	18.5815i	0.407394	+	0.235209i	0.689669	−	0.724124i	$-0.257756\pi$
$79$	32.1841	+	18.5815i	0.407394	+	0.235209i	−0.282275	+	0.959333i	$0.591089\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−66.0281	−	38.1214i	−0.795520	−	0.459294i	0.0463824	−	0.998924i	$-0.485231\pi$
$83$	−66.0281	−	38.1214i	−0.795520	−	0.459294i	−0.841902	+	0.539630i	$0.818564\pi$
$84$		0			0
$85$	52.0037	+	90.0730i	0.611808	+	1.05968i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	27.5873			0.309969			0.154985	−	0.987917i	$-0.450467\pi$
$89$	27.5873			0.309969			0.154985	+	0.987917i	$0.450467\pi$
$90$		0			0
$91$			1.05407i			0.0115832i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−103.856	+	59.9614i	−1.09322	+	0.631172i
$96$		0			0
$97$	13.0585	−	22.6180i	0.134624	−	0.233176i	−0.790830	−	0.612036i	$-0.790351\pi$
$97$	13.0585	−	22.6180i	0.134624	−	0.233176i	0.925454	+	0.378861i	$0.123684\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−12.8831	+	22.3142i	−0.127556	+	0.220933i	−0.922729	−	0.385449i	$-0.874047\pi$
$101$	−12.8831	+	22.3142i	−0.127556	+	0.220933i	0.795173	+	0.606382i	$0.207380\pi$
$102$		0			0
$103$	−16.9947	+	9.81187i	−0.164997	+	0.0952609i	−0.580225	−	0.814457i	$-0.697035\pi$
$103$	−16.9947	+	9.81187i	−0.164997	+	0.0952609i	0.415228	+	0.909717i	$0.363702\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			183.200i			1.71215i	0.516850	+	0.856076i	$0.327105\pi$
$107$			183.200i			1.71215i	−0.516850	+	0.856076i	$0.672895\pi$
$108$		0			0
$109$	−100.841			−0.925147			−0.462573	−	0.886581i	$-0.653074\pi$
$109$	−100.841			−0.925147			−0.462573	+	0.886581i	$0.653074\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.12484	+	15.8047i	0.0807508	+	0.139865i	0.903573	−	0.428435i	$-0.140935\pi$
$113$	9.12484	+	15.8047i	0.0807508	+	0.139865i	−0.822822	+	0.568299i	$0.807602\pi$
$114$		0			0
$115$	42.2235	+	24.3778i	0.367161	+	0.211981i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	8.65383	+	4.99629i	0.0727212	+	0.0419856i
$120$		0			0
$121$	91.9194	+	159.209i	0.759664	+	1.31578i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	75.0146			0.600117
$126$		0			0
$127$		−	164.386i		−	1.29438i	−0.762331	−	0.647188i	$-0.775945\pi$
$127$		−	164.386i		−	1.29438i	0.762331	−	0.647188i	$-0.224055\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−123.421	+	71.2570i	−0.942143	+	0.543947i	−0.890631	−	0.454726i	$-0.849737\pi$
$131$	−123.421	+	71.2570i	−0.942143	+	0.543947i	−0.0515116	+	0.998672i	$0.516404\pi$
$132$		0			0
$133$	−5.76083	+	9.97805i	−0.0433145	+	0.0750229i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.08176	−	5.33777i	0.0224946	−	0.0389618i	−0.854559	−	0.519354i	$-0.826172\pi$
$137$	3.08176	−	5.33777i	0.0224946	−	0.0389618i	0.877054	+	0.480393i	$0.159506\pi$
$138$		0			0
$139$	−103.168	+	59.5642i	−0.742218	+	0.428519i	−0.822875	−	0.568222i	$-0.807631\pi$
$139$	−103.168	+	59.5642i	−0.742218	+	0.428519i	0.0806575	+	0.996742i	$0.474298\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			31.1569i			0.217880i
$144$		0			0
$145$	39.0423			0.269257
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−103.365	−	179.034i	−0.693726	−	1.20157i	−0.970608	−	0.240665i	$-0.922634\pi$
$149$	−103.365	−	179.034i	−0.693726	−	1.20157i	0.276882	−	0.960904i	$-0.410699\pi$
$150$		0			0
$151$	127.422	+	73.5670i	0.843853	+	0.487199i	0.858572	−	0.512693i	$-0.171352\pi$
$151$	127.422	+	73.5670i	0.843853	+	0.487199i	−0.0147190	+	0.999892i	$0.504685\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	170.030	+	98.1668i	1.09697	+	0.633334i
$156$		0			0
$157$	−31.4395	−	54.4548i	−0.200251	−	0.346846i	0.748358	−	0.663295i	$-0.230843\pi$
$157$	−31.4395	−	54.4548i	−0.200251	−	0.346846i	−0.948609	+	0.316449i	$0.897509\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	4.68422			0.0290946
$162$		0			0
$163$			143.325i			0.879292i	0.898171	+	0.439646i	$0.144896\pi$
$163$			143.325i			0.879292i	−0.898171	+	0.439646i	$0.855104\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−150.531	+	86.9089i	−0.901381	+	0.520413i	−0.877648	−	0.479306i	$-0.840889\pi$
$167$	−150.531	+	86.9089i	−0.901381	+	0.520413i	−0.0237332	+	0.999718i	$0.507555\pi$
$168$		0			0
$169$	82.9078	−	143.600i	0.490578	−	0.849707i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−125.806	+	217.902i	−0.727201	+	1.25955i	0.230861	+	0.972987i	$0.425846\pi$
$173$	−125.806	+	217.902i	−0.727201	+	1.25955i	−0.958062	+	0.286562i	$0.907488\pi$
$174$		0			0
$175$	−6.54707	+	3.77995i	−0.0374118	+	0.0215997i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			96.0059i			0.536346i	0.963371	+	0.268173i	$0.0864199\pi$
$179$			96.0059i			0.536346i	−0.963371	+	0.268173i	$0.913580\pi$
$180$		0			0
$181$	328.757			1.81634			0.908170	−	0.418603i	$-0.137480\pi$
$181$	328.757			1.81634			0.908170	+	0.418603i	$0.137480\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−179.165	−	310.323i	−0.968460	−	1.67742i
$186$		0			0
$187$	255.795	+	147.683i	1.36789	+	0.789749i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.351914	+	0.203178i	0.00184248	+	0.00106376i	0.500921	−	0.865493i	$-0.332995\pi$
$191$	0.351914	+	0.203178i	0.00184248	+	0.00106376i	−0.499078	+	0.866557i	$0.666328\pi$
$192$		0			0
$193$	−31.2230	−	54.0798i	−0.161777	−	0.280206i	0.773729	−	0.633517i	$-0.218389\pi$
$193$	−31.2230	−	54.0798i	−0.161777	−	0.280206i	−0.935506	+	0.353311i	$0.885056\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−207.861			−1.05513			−0.527566	−	0.849514i	$-0.676895\pi$
$197$	−207.861			−1.05513			−0.527566	+	0.849514i	$0.676895\pi$
$198$		0			0
$199$			299.128i			1.50316i	0.659643	+	0.751579i	$0.270707\pi$
$199$			299.128i			1.50316i	−0.659643	+	0.751579i	$0.729293\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.24848	−	1.87551i	0.0160024	−	0.00923896i
$204$		0			0
$205$	−16.4121	+	28.4266i	−0.0800592	+	0.138667i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−170.282	+	294.937i	−0.814746	+	1.41118i
$210$		0			0
$211$	141.744	−	81.8360i	0.671773	−	0.387848i	−0.124975	−	0.992160i	$-0.539885\pi$
$211$	141.744	−	81.8360i	0.671773	−	0.387848i	0.796748	+	0.604311i	$0.206552\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			240.892i			1.12043i
$216$		0			0
$217$	18.8629			0.0869257
$218$		0			0
$219$		0			0
$220$		0			0
$221$	15.0944	+	26.1442i	0.0683003	+	0.118300i
$222$		0			0
$223$	330.681	+	190.919i	1.48287	+	0.856138i	0.999811	−	0.0194478i	$-0.00619081\pi$
$223$	330.681	+	190.919i	1.48287	+	0.856138i	0.483063	+	0.875586i	$0.339524\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−51.5472	−	29.7608i	−0.227080	−	0.131105i	0.382144	−	0.924103i	$-0.375186\pi$
$227$	−51.5472	−	29.7608i	−0.227080	−	0.131105i	−0.609224	+	0.792998i	$0.708519\pi$
$228$		0			0
$229$	−64.4366	−	111.608i	−0.281383	−	0.487369i	0.690343	−	0.723482i	$-0.257460\pi$
$229$	−64.4366	−	111.608i	−0.281383	−	0.487369i	−0.971726	+	0.236113i	$0.924126\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−14.9939			−0.0643513			−0.0321757	−	0.999482i	$-0.510244\pi$
$233$	−14.9939			−0.0643513			−0.0321757	+	0.999482i	$0.510244\pi$
$234$		0			0
$235$			68.4443i			0.291252i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	315.244	−	182.006i	1.31901	−	0.761532i	0.335442	−	0.942061i	$-0.391114\pi$
$239$	315.244	−	182.006i	1.31901	−	0.761532i	0.983570	+	0.180529i	$0.0577811\pi$
$240$		0			0
$241$	−40.5235	+	70.1888i	−0.168147	+	0.291240i	−0.937769	−	0.347261i	$-0.887112\pi$
$241$	−40.5235	+	70.1888i	−0.168147	+	0.291240i	0.769621	+	0.638501i	$0.220445\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	149.555	−	259.037i	0.610428	−	1.05729i
$246$		0			0
$247$	−30.1448	+	17.4041i	−0.122044	+	0.0704620i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	281.883i		−	1.12304i	−0.827463	−	0.561520i	$-0.810217\pi$
$251$		−	281.883i		−	1.12304i	0.827463	−	0.561520i	$-0.189783\pi$
$252$		0			0
$253$	138.459			0.547268
$254$		0			0
$255$		0			0
$256$		0			0
$257$	37.6564	+	65.2227i	0.146523	+	0.253785i	0.929940	−	0.367711i	$-0.119858\pi$
$257$	37.6564	+	65.2227i	0.146523	+	0.253785i	−0.783417	+	0.621496i	$0.786525\pi$
$258$		0			0
$259$	−29.8145	−	17.2134i	−0.115114	−	0.0664610i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	105.914	+	61.1497i	0.402716	+	0.232508i	0.687655	−	0.726037i	$-0.258640\pi$
$263$	105.914	+	61.1497i	0.402716	+	0.232508i	−0.284939	+	0.958546i	$0.591973\pi$
$264$		0			0
$265$	110.287	+	191.023i	0.416178	+	0.720841i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	280.452			1.04257			0.521287	−	0.853382i	$-0.325452\pi$
$269$	280.452			1.04257			0.521287	+	0.853382i	$0.325452\pi$
$270$		0			0
$271$			81.4468i			0.300542i	0.988645	+	0.150271i	$0.0480146\pi$
$271$			81.4468i			0.300542i	−0.988645	+	0.150271i	$0.951985\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−193.522	+	111.730i	−0.703716	+	0.406291i
$276$		0			0
$277$	−224.861	+	389.471i	−0.811774	+	1.40603i	0.0998479	+	0.995003i	$0.468164\pi$
$277$	−224.861	+	389.471i	−0.811774	+	1.40603i	−0.911622	+	0.411031i	$0.865169\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	37.8649	−	65.5838i	0.134750	−	0.233394i	−0.790752	−	0.612137i	$-0.790310\pi$
$281$	37.8649	−	65.5838i	0.134750	−	0.233394i	0.925502	+	0.378743i	$0.123643\pi$
$282$		0			0
$283$	322.061	−	185.942i	1.13803	−	0.657039i	0.192084	−	0.981378i	$-0.438475\pi$
$283$	322.061	−	185.942i	1.13803	−	0.657039i	0.945941	+	0.324339i	$0.105142\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			3.15361i			0.0109882i
$288$		0			0
$289$	−2.81196			−0.00972996
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−66.3946	−	114.999i	−0.226603	−	0.392488i	0.730196	−	0.683237i	$-0.239429\pi$
$293$	−66.3946	−	114.999i	−0.226603	−	0.392488i	−0.956799	+	0.290750i	$0.906095\pi$
$294$		0			0
$295$	−128.479	−	74.1772i	−0.435521	−	0.251448i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	12.2556	+	7.07579i	0.0409887	+	0.0236648i
$300$		0			0
$301$	11.5719	+	20.0432i	0.0384450	+	0.0665886i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	466.589			1.52980
$306$		0			0
$307$			336.514i			1.09614i	0.836434	+	0.548068i	$0.184637\pi$
$307$			336.514i			1.09614i	−0.836434	+	0.548068i	$0.815363\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−304.206	+	175.634i	−0.978156	+	0.564738i	−0.901713	−	0.432336i	$-0.857690\pi$
$311$	−304.206	+	175.634i	−0.978156	+	0.564738i	−0.0764428	+	0.997074i	$0.524356\pi$
$312$		0			0
$313$	−95.4299	+	165.289i	−0.304888	+	0.528081i	−0.977236	−	0.212154i	$-0.931952\pi$
$313$	−95.4299	+	165.289i	−0.304888	+	0.528081i	0.672349	+	0.740235i	$0.265286\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−202.797	+	351.255i	−0.639738	+	1.10806i	0.345752	+	0.938326i	$0.387624\pi$
$317$	−202.797	+	351.255i	−0.639738	+	1.10806i	−0.985490	+	0.169733i	$0.945709\pi$
$318$		0			0
$319$	96.0203	−	55.4374i	0.301004	−	0.173785i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			329.981i			1.02161i
$324$		0			0
$325$	−22.8393			−0.0702749
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.28792	+	5.69484i	0.00999368	+	0.0173096i
$330$		0			0
$331$	−384.104	−	221.763i	−1.16044	−	0.669978i	−0.209027	−	0.977910i	$-0.567030\pi$
$331$	−384.104	−	221.763i	−1.16044	−	0.669978i	−0.951408	+	0.307932i	$0.900363\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	195.631	+	112.948i	0.583974	+	0.337158i
$336$		0			0
$337$	−254.239	−	440.356i	−0.754420	−	1.30669i	−0.945662	−	0.325150i	$-0.894585\pi$
$337$	−254.239	−	440.356i	−0.754420	−	1.30669i	0.191243	−	0.981543i	$-0.438748\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	557.560			1.63507
$342$		0			0
$343$		−	57.6805i		−	0.168165i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	492.773	−	284.503i	1.42010	−	0.819893i	0.423790	−	0.905761i	$-0.360700\pi$
$347$	492.773	−	284.503i	1.42010	−	0.819893i	0.996307	+	0.0858678i	$0.0273663\pi$
$348$		0			0
$349$	206.901	−	358.363i	0.592840	−	1.02683i	−0.401008	−	0.916074i	$-0.631340\pi$
$349$	206.901	−	358.363i	0.592840	−	1.02683i	0.993848	−	0.110754i	$-0.0353266\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−62.3070	+	107.919i	−0.176507	+	0.305719i	−0.940682	−	0.339290i	$-0.889813\pi$
$353$	−62.3070	+	107.919i	−0.176507	+	0.305719i	0.764175	+	0.645009i	$0.223147\pi$
$354$		0			0
$355$	−467.677	+	270.014i	−1.31740	+	0.760602i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	303.196i		−	0.844557i	−0.906466	−	0.422278i	$-0.861230\pi$
$359$		−	303.196i		−	0.844557i	0.906466	−	0.422278i	$-0.138770\pi$
$360$		0			0
$361$	−19.4752			−0.0539480
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−184.572	−	319.688i	−0.505677	−	0.875858i
$366$		0			0
$367$	−615.571	−	355.400i	−1.67730	−	0.968392i	−0.963369	−	0.268181i	$-0.913578\pi$
$367$	−615.571	−	355.400i	−1.67730	−	0.968392i	−0.713936	−	0.700211i	$-0.753089\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	18.3527	+	10.5959i	0.0494681	+	0.0285604i
$372$		0			0
$373$	−166.740	−	288.803i	−0.447025	−	0.774271i	0.551166	−	0.834396i	$-0.314183\pi$
$373$	−166.740	−	288.803i	−0.447025	−	0.774271i	−0.998191	+	0.0601254i	$0.980850\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	11.3323			0.0300590
$378$		0			0
$379$		−	662.686i		−	1.74851i	−0.485465	−	0.874256i	$-0.661350\pi$
$379$		−	662.686i		−	1.74851i	0.485465	−	0.874256i	$-0.338650\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	69.9008	−	40.3572i	0.182509	−	0.105371i	−0.405962	−	0.913890i	$-0.633064\pi$
$383$	69.9008	−	40.3572i	0.182509	−	0.105371i	0.588471	+	0.808518i	$0.299730\pi$
$384$		0			0
$385$	−31.7026	+	54.9106i	−0.0823445	+	0.142625i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−346.006	+	599.301i	−0.889476	+	1.54062i	−0.0489809	+	0.998800i	$0.515597\pi$
$389$	−346.006	+	599.301i	−0.889476	+	1.54062i	−0.840495	+	0.541819i	$0.817736\pi$
$390$		0			0
$391$	116.183	−	67.0782i	0.297143	−	0.171556i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			228.481i			0.578432i
$396$		0			0
$397$	−657.713			−1.65671			−0.828354	−	0.560206i	$-0.810722\pi$
$397$	−657.713			−1.65671			−0.828354	+	0.560206i	$0.810722\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−296.433	−	513.437i	−0.739235	−	1.28039i	−0.952840	−	0.303472i	$-0.901854\pi$
$401$	−296.433	−	513.437i	−0.739235	−	1.28039i	0.213606	−	0.976920i	$-0.431479\pi$
$402$		0			0
$403$	49.3521	+	28.4935i	0.122462	+	0.0707034i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−881.274	−	508.804i	−2.16529	−	1.25013i
$408$		0			0
$409$	−161.594	−	279.889i	−0.395095	−	0.684325i	0.598018	−	0.801483i	$-0.295955\pi$
$409$	−161.594	−	279.889i	−0.395095	−	0.684325i	−0.993113	+	0.117157i	$0.962622\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−14.2533			−0.0345115
$414$		0			0
$415$		−	468.745i		−	1.12951i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−222.744	+	128.601i	−0.531608	+	0.306924i	−0.741671	−	0.670764i	$-0.765967\pi$
$419$	−222.744	+	128.601i	−0.531608	+	0.306924i	0.210063	+	0.977688i	$0.432633\pi$
$420$		0			0
$421$	−41.9905	+	72.7297i	−0.0997400	+	0.172755i	−0.911577	−	0.411129i	$-0.865134\pi$
$421$	−41.9905	+	72.7297i	−0.0997400	+	0.172755i	0.811837	+	0.583884i	$0.198468\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−108.258	+	187.509i	−0.254725	+	0.441197i
$426$		0			0
$427$	38.8221	−	22.4139i	0.0909182	−	0.0524917i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	144.348i		−	0.334914i	−0.985879	−	0.167457i	$-0.946445\pi$
$431$		−	144.348i		−	0.334914i	0.985879	−	0.167457i	$-0.0535555\pi$
$432$		0			0
$433$	395.353			0.913057			0.456528	−	0.889709i	$-0.349093\pi$
$433$	395.353			0.913057			0.456528	+	0.889709i	$0.349093\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	77.3426	+	133.961i	0.176985	+	0.306548i
$438$		0			0
$439$	−194.776	−	112.454i	−0.443682	−	0.256160i	0.261476	−	0.965210i	$-0.415791\pi$
$439$	−194.776	−	112.454i	−0.443682	−	0.256160i	−0.705158	+	0.709050i	$0.749124\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−369.184	−	213.148i	−0.833373	−	0.481148i	0.0216335	−	0.999766i	$-0.493113\pi$
$443$	−369.184	−	213.148i	−0.833373	−	0.481148i	−0.855006	+	0.518618i	$0.826447\pi$
$444$		0			0
$445$	84.8041	+	146.885i	0.190571	+	0.330079i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	406.744			0.905888			0.452944	−	0.891539i	$-0.350374\pi$
$449$	406.744			0.905888			0.452944	+	0.891539i	$0.350374\pi$
$450$		0			0
$451$			93.2163i			0.206688i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−5.61228	+	3.24025i	−0.0123347	+	0.00712144i
$456$		0			0
$457$	−159.600	+	276.435i	−0.349234	+	0.604891i	−0.986114	−	0.166072i	$-0.946892\pi$
$457$	−159.600	+	276.435i	−0.349234	+	0.604891i	0.636879	+	0.770963i	$0.280225\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	293.888	−	509.029i	0.637501	−	1.10418i	−0.348478	−	0.937317i	$-0.613302\pi$
$461$	293.888	−	509.029i	0.637501	−	1.10418i	0.985979	−	0.166867i	$-0.0533652\pi$
$462$		0			0
$463$	230.088	−	132.841i	0.496950	−	0.286914i	−0.230503	−	0.973072i	$-0.574037\pi$
$463$	230.088	−	132.841i	0.496950	−	0.286914i	0.727453	+	0.686157i	$0.240704\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	794.598i		−	1.70149i	−0.525575	−	0.850747i	$-0.676150\pi$
$467$		−	794.598i		−	1.70149i	0.525575	−	0.850747i	$-0.323850\pi$
$468$		0			0
$469$	21.7031			0.0462752
$470$		0			0
$471$		0			0
$472$		0			0
$473$	342.050	+	592.447i	0.723149	+	1.25253i
$474$		0			0
$475$	−216.201	−	124.824i	−0.455161	−	0.262787i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	572.964	+	330.801i	1.19617	+	0.690607i	0.959698	−	0.281033i	$-0.0906769\pi$
$479$	572.964	+	330.801i	1.19617	+	0.690607i	0.236468	+	0.971639i	$0.424010\pi$
$480$		0			0
$481$	−52.0037	−	90.0730i	−0.108116	−	0.187262i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	160.569			0.331071
$486$		0			0
$487$		−	57.1525i		−	0.117356i	−0.998277	−	0.0586781i	$-0.981311\pi$
$487$		−	57.1525i		−	0.117356i	0.998277	−	0.0586781i	$-0.0186886\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	48.6600	−	28.0939i	0.0991040	−	0.0572177i	−0.449629	−	0.893215i	$-0.648444\pi$
$491$	48.6600	−	28.0939i	0.0991040	−	0.0572177i	0.548733	+	0.835998i	$0.315110\pi$
$492$		0			0
$493$	53.7147	−	93.0366i	0.108955	−	0.188715i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−25.9417	+	44.9324i	−0.0521967	+	0.0904073i
$498$		0			0
$499$	−522.225	+	301.507i	−1.04654	+	0.604222i	−0.921679	−	0.387952i	$-0.873183\pi$
$499$	−522.225	+	301.507i	−1.04654	+	0.604222i	−0.124863	+	0.992174i	$0.539849\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	549.354i		−	1.09216i	−0.837734	−	0.546078i	$-0.816120\pi$
$503$		−	549.354i		−	1.09216i	0.837734	−	0.546078i	$-0.183880\pi$
$504$		0			0
$505$	−158.413			−0.313688
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−119.464	−	206.918i	−0.234704	−	0.406519i	0.724483	−	0.689293i	$-0.242079\pi$
$509$	−119.464	−	206.918i	−0.234704	−	0.406519i	−0.959187	+	0.282774i	$0.908745\pi$
$510$		0			0
$511$	−30.7143	−	17.7329i	−0.0601062	−	0.0347023i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−104.484	−	60.3240i	−0.202882	−	0.117134i
$516$		0			0
$517$	97.1862	+	168.331i	0.187981	+	0.325593i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	567.711			1.08966			0.544828	−	0.838548i	$-0.316595\pi$
$521$	567.711			1.08966			0.544828	+	0.838548i	$0.316595\pi$
$522$		0			0
$523$		−	941.999i		−	1.80114i	−0.434706	−	0.900572i	$-0.643148\pi$
$523$		−	941.999i		−	1.80114i	0.434706	−	0.900572i	$-0.356852\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	467.856	−	270.117i	0.887773	−	0.512556i
$528$		0			0
$529$	−233.056	+	403.664i	−0.440559	+	0.763071i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−4.76372	+	8.25100i	−0.00893755	+	0.0154803i
$534$		0			0
$535$	−975.428	+	563.163i	−1.82323	+	1.05264i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	849.430i		−	1.57594i
$540$		0			0
$541$	242.245			0.447772			0.223886	−	0.974615i	$-0.428126\pi$
$541$	242.245			0.447772			0.223886	+	0.974615i	$0.428126\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−309.988	−	536.915i	−0.568786	−	0.985166i
$546$		0			0
$547$	170.503	+	98.4402i	0.311706	+	0.179964i	0.647690	−	0.761904i	$-0.275735\pi$
$547$	170.503	+	98.4402i	0.311706	+	0.179964i	−0.335983	+	0.941868i	$0.609069\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	107.273	+	61.9342i	0.194688	+	0.112403i
$552$		0			0
$553$	10.9757	+	19.0105i	0.0198476	+	0.0343770i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	958.121			1.72015			0.860073	−	0.510171i	$-0.170418\pi$
$557$	958.121			1.72015			0.860073	+	0.510171i	$0.170418\pi$
$558$		0			0
$559$			69.9202i			0.125081i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	165.774	−	95.7097i	0.294448	−	0.169999i	−0.345498	−	0.938419i	$-0.612290\pi$
$563$	165.774	−	95.7097i	0.294448	−	0.169999i	0.639946	+	0.768420i	$0.278957\pi$
$564$		0			0
$565$	−56.1001	+	97.1682i	−0.0992922	+	0.171979i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−228.215	+	395.280i	−0.401081	+	0.694693i	−0.993857	−	0.110675i	$-0.964699\pi$
$569$	−228.215	+	395.280i	−0.401081	+	0.694693i	0.592775	+	0.805368i	$0.298032\pi$
$570$		0			0
$571$	842.764	−	486.570i	1.47594	−	0.852136i	0.476312	−	0.879276i	$-0.341973\pi$
$571$	842.764	−	486.570i	1.47594	−	0.852136i	0.999632	+	0.0271399i	$0.00863995\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			101.496i			0.176515i
$576$		0			0
$577$	138.527			0.240081			0.120040	−	0.992769i	$-0.461698\pi$
$577$	138.527			0.240081			0.120040	+	0.992769i	$0.461698\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−22.5175	−	39.0015i	−0.0387565	−	0.0671282i
$582$		0			0
$583$	542.478	+	313.200i	0.930494	+	0.537221i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	620.808	+	358.424i	1.05759	+	0.610602i	0.924766	−	0.380537i	$-0.124261\pi$
$587$	620.808	+	358.424i	1.05759	+	0.610602i	0.132829	+	0.991139i	$0.457594\pi$
$588$		0			0
$589$	311.451	+	539.449i	0.528779	+	0.915872i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−542.129			−0.914214			−0.457107	−	0.889412i	$-0.651114\pi$
$593$	−542.129			−0.914214			−0.457107	+	0.889412i	$0.651114\pi$
$594$		0			0
$595$			61.4350i			0.103252i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	245.527	−	141.755i	0.409895	−	0.236653i	−0.280850	−	0.959752i	$-0.590616\pi$
$599$	245.527	−	141.755i	0.409895	−	0.236653i	0.690744	+	0.723099i	$0.257283\pi$
$600$		0			0
$601$	377.424	−	653.717i	0.627993	−	1.08772i	−0.359961	−	0.932967i	$-0.617210\pi$
$601$	377.424	−	653.717i	0.627993	−	1.08772i	0.987954	−	0.154748i	$-0.0494567\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−565.126	+	978.827i	−0.934093	+	1.61790i
$606$		0			0
$607$	77.2227	−	44.5845i	0.127220	−	0.0734506i	−0.435039	−	0.900411i	$-0.643266\pi$
$607$	77.2227	−	44.5845i	0.127220	−	0.0734506i	0.562260	+	0.826961i	$0.309932\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			19.8664i			0.0325145i
$612$		0			0
$613$	316.779			0.516769			0.258385	−	0.966042i	$-0.416810\pi$
$613$	316.779			0.516769			0.258385	+	0.966042i	$0.416810\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−534.934	−	926.533i	−0.866992	−	1.50167i	−0.865056	−	0.501675i	$-0.832717\pi$
$617$	−534.934	−	926.533i	−0.866992	−	1.50167i	−0.00193565	−	0.999998i	$-0.500616\pi$
$618$		0			0
$619$	−578.542	−	334.021i	−0.934640	−	0.539615i	−0.0463638	−	0.998925i	$-0.514763\pi$
$619$	−578.542	−	334.021i	−0.934640	−	0.539615i	−0.888276	+	0.459310i	$0.848097\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	14.1121	+	8.14762i	0.0226518	+	0.0130780i
$624$		0			0
$625$	390.580	+	676.505i	0.624929	+	1.08241i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−985.986			−1.56755
$630$		0			0
$631$		−	150.631i		−	0.238718i	−0.992851	−	0.119359i	$-0.961916\pi$
$631$		−	150.631i		−	0.238718i	0.992851	−	0.119359i	$-0.0380839\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	875.252	−	505.327i	1.37835	−	0.795790i
$636$		0			0
$637$	43.4092	−	75.1869i	0.0681463	−	0.118033i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−351.521	+	608.852i	−0.548395	+	0.949847i	0.449990	+	0.893034i	$0.351427\pi$
$641$	−351.521	+	608.852i	−0.548395	+	0.949847i	−0.998385	+	0.0568139i	$0.981906\pi$
$642$		0			0
$643$	−742.057	+	428.427i	−1.15405	+	0.666293i	−0.949872	−	0.312639i	$-0.898787\pi$
$643$	−742.057	+	428.427i	−1.15405	+	0.666293i	−0.204182	+	0.978933i	$0.565454\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			156.257i			0.241510i	0.992682	+	0.120755i	$0.0385316\pi$
$647$			156.257i			0.241510i	−0.992682	+	0.120755i	$0.961468\pi$
$648$		0			0
$649$	−421.306			−0.649162
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−441.773	−	765.173i	−0.676528	−	1.17178i	−0.976020	−	0.217682i	$-0.930151\pi$
$653$	−441.773	−	765.173i	−0.676528	−	1.17178i	0.299492	−	0.954099i	$-0.403183\pi$
$654$		0			0
$655$	−758.798	−	438.092i	−1.15847	−	0.668843i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−379.533	−	219.123i	−0.575922	−	0.332509i	0.183589	−	0.983003i	$-0.441228\pi$
$659$	−379.533	−	219.123i	−0.575922	−	0.332509i	−0.759511	+	0.650494i	$0.774562\pi$
$660$		0			0
$661$	−233.924	−	405.168i	−0.353894	−	0.612963i	0.633034	−	0.774124i	$-0.281809\pi$
$661$	−233.924	−	405.168i	−0.353894	−	0.612963i	−0.986928	+	0.161161i	$0.948476\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−70.8359			−0.106520
$666$		0			0
$667$		−	50.3597i		−	0.0755018i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1147.52	−	662.524i	1.71017	−	0.987368i
$672$		0			0
$673$	273.302	−	473.372i	0.406094	−	0.703376i	−0.588354	−	0.808604i	$-0.700224\pi$
$673$	273.302	−	473.372i	0.406094	−	0.703376i	0.994448	+	0.105227i	$0.0335571\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	227.606	−	394.225i	0.336198	−	0.582312i	−0.647516	−	0.762052i	$-0.724192\pi$
$677$	227.606	−	394.225i	0.336198	−	0.582312i	0.983714	+	0.179740i	$0.0575255\pi$
$678$		0			0
$679$	13.3600	−	7.71341i	0.0196760	−	0.0113600i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	123.214i		−	0.180400i	−0.995924	−	0.0902002i	$-0.971249\pi$
$683$		−	123.214i		−	0.180400i	0.995924	−	0.0902002i	$-0.0287507\pi$
$684$		0			0
$685$	37.8937			0.0553193
$686$		0			0
$687$		0			0
$688$		0			0
$689$	32.0115	+	55.4455i	0.0464607	+	0.0804724i
$690$		0			0
$691$	163.326	+	94.2965i	0.236362	+	0.136464i	0.613504	−	0.789692i	$-0.289760\pi$
$691$	163.326	+	94.2965i	0.236362	+	0.136464i	−0.377141	+	0.926156i	$0.623093\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−634.285	−	366.204i	−0.912640	−	0.526913i
$696$		0			0
$697$	45.1599	+	78.2192i	0.0647918	+	0.112223i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−810.064			−1.15558			−0.577792	−	0.816184i	$-0.696085\pi$
$701$	−810.064			−1.15558			−0.577792	+	0.816184i	$0.696085\pi$
$702$		0			0
$703$		−	1136.86i		−	1.61716i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−13.1806	+	7.60980i	−0.0186429	+	0.0107635i
$708$		0			0
$709$	651.819	−	1128.98i	0.919349	−	1.59236i	0.118944	−	0.992901i	$-0.462049\pi$
$709$	651.819	−	1128.98i	0.919349	−	1.59236i	0.800406	−	0.599459i	$-0.204618\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	126.623	−	219.317i	0.177592	−	0.307598i
$714$		0			0
$715$	−165.891	+	95.7772i	−0.232015	+	0.133954i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	788.981i		−	1.09733i	−0.836042	−	0.548666i	$-0.815136\pi$
$719$		−	788.981i		−	1.09733i	0.836042	−	0.548666i	$-0.184864\pi$
$720$		0			0
$721$	−11.5913			−0.0160768
$722$		0			0
$723$		0			0
$724$		0			0
$725$	40.6380	+	70.3870i	0.0560524	+	0.0970856i
$726$		0			0
$727$	−232.676	−	134.335i	−0.320049	−	0.184780i	0.331365	−	0.943502i	$-0.392491\pi$
$727$	−232.676	−	134.335i	−0.320049	−	0.184780i	−0.651414	+	0.758722i	$0.725824\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	574.038	+	331.421i	0.785277	+	0.453380i
$732$		0			0
$733$	36.8343	+	63.7989i	0.0502514	+	0.0870380i	0.890057	−	0.455849i	$-0.150664\pi$
$733$	36.8343	+	63.7989i	0.0502514	+	0.0870380i	−0.839806	+	0.542887i	$0.817331\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	641.512			0.870437
$738$		0			0
$739$			448.249i			0.606562i	0.952901	+	0.303281i	$0.0980820\pi$
$739$			448.249i			0.606562i	−0.952901	+	0.303281i	$0.901918\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−656.602	+	379.089i	−0.883718	+	0.510215i	−0.871882	−	0.489715i	$-0.837101\pi$
$743$	−656.602	+	379.089i	−0.883718	+	0.510215i	−0.0118352	+	0.999930i	$0.503767\pi$
$744$		0			0
$745$	635.496	−	1100.71i	0.853015	−	1.47746i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−54.1063	+	93.7149i	−0.0722381	+	0.125120i
$750$		0			0
$751$	1141.58	−	659.091i	1.52008	−	0.877618i	0.520358	−	0.853948i	$-0.325798\pi$
$751$	1141.58	−	659.091i	1.52008	−	0.877618i	0.999720	−	0.0236697i	$-0.00753501\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			904.589i			1.19813i
$756$		0			0
$757$	−587.874			−0.776583			−0.388292	−	0.921537i	$-0.626935\pi$
$757$	−587.874			−0.776583			−0.388292	+	0.921537i	$0.626935\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	188.496	+	326.485i	0.247695	+	0.429021i	0.962886	−	0.269908i	$-0.0869934\pi$
$761$	188.496	+	326.485i	0.247695	+	0.429021i	−0.715191	+	0.698929i	$0.753660\pi$
$762$		0			0
$763$	−51.5845	−	29.7823i	−0.0676075	−	0.0390332i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−37.2917	−	21.5304i	−0.0486202	−	0.0280709i
$768$		0			0
$769$	643.939	+	1115.34i	0.837372	+	1.45037i	0.892084	+	0.451869i	$0.149243\pi$
$769$	643.939	+	1115.34i	0.837372	+	1.45037i	−0.0547122	+	0.998502i	$0.517424\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	778.578			1.00722			0.503608	−	0.863932i	$-0.332006\pi$
$773$	778.578			1.00722			0.503608	+	0.863932i	$0.332006\pi$
$774$		0			0
$775$			408.715i			0.527375i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−90.1884	+	52.0703i	−0.115775	+	0.0668425i
$780$		0			0
$781$	−766.801	+	1328.14i	−0.981819	+	1.70056i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	193.292	−	334.791i	0.246232	−	0.426486i
$786$		0			0
$787$	390.283	−	225.330i	0.495913	−	0.286315i	−0.231111	−	0.972927i	$-0.574236\pi$
$787$	390.283	−	225.330i	0.495913	−	0.286315i	0.727024	+	0.686612i	$0.240903\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			10.7797i			0.0136280i
$792$		0			0
$793$	135.430			0.170782
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−182.891	−	316.776i	−0.229474	−	0.397461i	0.728178	−	0.685388i	$-0.240367\pi$
$797$	−182.891	−	316.776i	−0.229474	−	0.397461i	−0.957652	+	0.287927i	$0.907034\pi$
$798$		0			0
$799$	163.101	+	94.1662i	0.204131	+	0.117855i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−907.869	−	524.158i	−1.13060	−	0.652750i
$804$		0			0
$805$	14.3994	+	24.9406i	0.0178875	+	0.0309821i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1167.70			−1.44339			−0.721695	−	0.692212i	$-0.756636\pi$
$809$	−1167.70			−1.44339			−0.721695	+	0.692212i	$0.756636\pi$
$810$		0			0
$811$			810.121i			0.998916i	0.866338	+	0.499458i	$0.166467\pi$
$811$			810.121i			0.998916i	−0.866338	+	0.499458i	$0.833533\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−763.114	+	440.584i	−0.936336	+	0.540594i
$816$		0			0
$817$	−382.135	+	661.878i	−0.467730	+	0.810132i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−280.513	+	485.862i	−0.341672	+	0.591793i	−0.984743	−	0.174013i	$-0.944327\pi$
$821$	−280.513	+	485.862i	−0.341672	+	0.591793i	0.643071	+	0.765806i	$0.277660\pi$
$822$		0			0
$823$	−1016.04	+	586.612i	−1.23456	+	0.712773i	−0.967977	−	0.251039i	$-0.919228\pi$
$823$	−1016.04	+	586.612i	−1.23456	+	0.712773i	−0.266583	+	0.963812i	$0.585895\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	267.739i		−	0.323747i	−0.986811	−	0.161874i	$-0.948246\pi$
$827$		−	267.739i		−	0.323747i	0.986811	−	0.161874i	$-0.0517537\pi$
$828$		0			0
$829$	432.474			0.521682			0.260841	−	0.965382i	$-0.416000\pi$
$829$	432.474			0.521682			0.260841	+	0.965382i	$0.416000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−411.518	−	712.769i	−0.494019	−	0.855665i
$834$		0			0
$835$	−925.472	−	534.321i	−1.10835	−	0.639906i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	459.103	+	265.063i	0.547202	+	0.315927i	0.747993	−	0.663707i	$-0.231018\pi$
$839$	459.103	+	265.063i	0.547202	+	0.315927i	−0.200790	+	0.979634i	$0.564351\pi$
$840$		0			0
$841$	400.337	+	693.403i	0.476024	+	0.824499i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1019.44			1.20644
$846$		0			0
$847$			108.590i			0.128205i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−400.278	+	231.100i	−0.470361	+	0.271563i
$852$		0			0
$853$	−88.3868	+	153.090i	−0.103619	+	0.179473i	−0.913173	−	0.407572i	$-0.866376\pi$
$853$	−88.3868	+	153.090i	−0.103619	+	0.179473i	0.809554	+	0.587045i	$0.199709\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	194.859	−	337.505i	0.227373	−	0.393821i	−0.729656	−	0.683815i	$-0.760320\pi$
$857$	194.859	−	337.505i	0.227373	−	0.393821i	0.957029	+	0.289993i	$0.0936531\pi$
$858$		0			0
$859$	503.279	−	290.568i	0.585889	−	0.338263i	−0.177581	−	0.984106i	$-0.556827\pi$
$859$	503.279	−	290.568i	0.585889	−	0.338263i	0.763470	+	0.645843i	$0.223494\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	827.326i		−	0.958663i	−0.877634	−	0.479331i	$-0.840879\pi$
$863$		−	827.326i		−	0.958663i	0.877634	−	0.479331i	$-0.159121\pi$
$864$		0			0
$865$	−1546.92			−1.78835
$866$		0			0
$867$		0			0
$868$		0			0
$869$	324.426	+	561.923i	0.373333	+	0.646632i
$870$		0			0
$871$	56.7831	+	32.7837i	0.0651930	+	0.0376392i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	38.3732	+	22.1548i	0.0438551	+	0.0253198i
$876$		0			0
$877$	279.815	+	484.653i	0.319059	+	0.552626i	0.980292	−	0.197554i	$-0.0632999\pi$
$877$	279.815	+	484.653i	0.319059	+	0.552626i	−0.661233	+	0.750181i	$0.729967\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	957.127			1.08641			0.543205	−	0.839600i	$-0.317211\pi$
$881$	957.127			1.08641			0.543205	+	0.839600i	$0.317211\pi$
$882$		0			0
$883$		−	625.252i		−	0.708100i	−0.935227	−	0.354050i	$-0.884804\pi$
$883$		−	625.252i		−	0.708100i	0.935227	−	0.354050i	$-0.115196\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−921.187	+	531.847i	−1.03854	+	0.599602i	−0.919420	−	0.393277i	$-0.871341\pi$
$887$	−921.187	+	531.847i	−1.03854	+	0.599602i	−0.119122	+	0.992880i	$0.538008\pi$
$888$		0			0
$889$	48.5496	−	84.0904i	0.0546115	−	0.0945899i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−108.576	+	188.059i	−0.121585	+	0.210592i
$894$		0			0
$895$	−511.172	+	295.125i	−0.571142	+	0.329749i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	202.793i		−	0.225577i
$900$		0			0
$901$	606.935			0.673624
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1010.61	+	1750.43i	1.11670	+	1.93418i
$906$		0			0
$907$	−207.207	−	119.631i	−0.228453	−	0.131898i	0.381405	−	0.924408i	$-0.375440\pi$
$907$	−207.207	−	119.631i	−0.228453	−	0.131898i	−0.609858	+	0.792510i	$0.708774\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−175.804	−	101.501i	−0.192980	−	0.111417i	0.400397	−	0.916342i	$-0.368872\pi$
$911$	−175.804	−	101.501i	−0.192980	−	0.111417i	−0.593377	+	0.804925i	$0.702206\pi$
$912$		0			0
$913$	−665.585	−	1152.83i	−0.729009	−	1.26268i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−84.1801			−0.0917994
$918$		0			0
$919$			878.708i			0.956156i	0.878317	+	0.478078i	$0.158666\pi$
$919$			878.708i			0.956156i	−0.878317	+	0.478078i	$0.841334\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−135.746	+	78.3730i	−0.147070	+	0.0849111i
$924$		0			0
$925$	372.975	−	646.011i	0.403216	−	0.698391i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−300.259	+	520.064i	−0.323207	+	0.559810i	−0.981148	−	0.193259i	$-0.938094\pi$
$929$	−300.259	+	520.064i	−0.323207	+	0.559810i	0.657941	+	0.753069i	$0.271428\pi$
$930$		0			0
$931$	821.838	−	474.489i	0.882748	−	0.509655i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			1815.93i			1.94217i
$936$		0			0
$937$	−184.325			−0.196718			−0.0983589	−	0.995151i	$-0.531359\pi$
$937$	−184.325			−0.196718			−0.0983589	+	0.995151i	$0.531359\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−377.587	−	653.999i	−0.401261	−	0.695005i	0.592617	−	0.805484i	$-0.298095\pi$
$941$	−377.587	−	653.999i	−0.401261	−	0.695005i	−0.993878	+	0.110479i	$0.964761\pi$
$942$		0			0
$943$	36.6668	+	21.1696i	0.0388831	+	0.0224492i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−769.965	−	444.539i	−0.813057	−	0.469419i	0.0349595	−	0.999389i	$-0.488870\pi$
$947$	−769.965	−	444.539i	−0.813057	−	0.469419i	−0.848016	+	0.529970i	$0.822203\pi$
$948$		0			0
$949$	−53.5731	−	92.7913i	−0.0564521	−	0.0977779i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−15.5920			−0.0163610			−0.00818050	−	0.999967i	$-0.502604\pi$
$953$	−15.5920			−0.0163610			−0.00818050	+	0.999967i	$0.502604\pi$
$954$		0			0
$955$			2.49830i			0.00261602i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	3.15291	−	1.82033i	0.00328770	−	0.00189816i
$960$		0			0
$961$	29.3970	−	50.9172i	0.0305900	−	0.0529835i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	191.961	−	332.486i	0.198923	−	0.344545i
$966$		0			0
$967$	847.921	−	489.548i	0.876858	−	0.506254i	0.00723669	−	0.999974i	$-0.497696\pi$
$967$	847.921	−	489.548i	0.876858	−	0.506254i	0.869621	+	0.493720i	$0.164363\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			67.3838i			0.0693963i	0.999398	+	0.0346982i	$0.0110470\pi$
$971$			67.3838i			0.0693963i	−0.999398	+	0.0346982i	$0.988953\pi$
$972$		0			0
$973$	−70.3667			−0.0723193
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−353.710	−	612.644i	−0.362037	−	0.627067i	0.626259	−	0.779615i	$-0.284585\pi$
$977$	−353.710	−	612.644i	−0.362037	−	0.627067i	−0.988296	+	0.152549i	$0.951252\pi$
$978$		0			0
$979$	417.133	+	240.832i	0.426081	+	0.245998i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	338.829	+	195.623i	0.344689	+	0.199006i	0.662343	−	0.749200i	$-0.269562\pi$
$983$	338.829	+	195.623i	0.344689	+	0.199006i	−0.317655	+	0.948206i	$0.602895\pi$
$984$		0			0
$985$	−638.971	−	1106.73i	−0.648701	−	1.12358i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	310.720			0.314176
$990$		0			0
$991$			104.988i			0.105941i	0.998596	+	0.0529706i	$0.0168690\pi$
$991$			104.988i			0.105941i	−0.998596	+	0.0529706i	$0.983131\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1592.67	+	919.530i	−1.60068	+	0.924151i
$996$		0			0
$997$	39.0028	−	67.5547i	0.0391201	−	0.0677580i	−0.845802	−	0.533496i	$-0.820878\pi$
$997$	39.0028	−	67.5547i	0.0391201	−	0.0677580i	0.884923	+	0.465738i	$0.154211\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.3.o.g.127.8		16
3.2	odd	2		576.3.o.g.511.7		16
4.3	odd	2	inner	1728.3.o.g.127.7		16
8.3	odd	2		108.3.f.c.19.6		16
8.5	even	2		108.3.f.c.19.5		16
9.4	even	3	inner	1728.3.o.g.1279.7		16
9.5	odd	6		576.3.o.g.319.2		16
12.11	even	2		576.3.o.g.511.2		16
24.5	odd	2		36.3.f.c.7.4	yes	16
24.11	even	2		36.3.f.c.7.3	✓	16
36.23	even	6		576.3.o.g.319.7		16
36.31	odd	6	inner	1728.3.o.g.1279.8		16
72.5	odd	6		36.3.f.c.31.3	yes	16
72.11	even	6		324.3.d.i.163.8		8
72.13	even	6		108.3.f.c.91.6		16
72.29	odd	6		324.3.d.i.163.7		8
72.43	odd	6		324.3.d.g.163.1		8
72.59	even	6		36.3.f.c.31.4	yes	16
72.61	even	6		324.3.d.g.163.2		8
72.67	odd	6		108.3.f.c.91.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.3	✓	16	24.11	even	2
36.3.f.c.7.4	yes	16	24.5	odd	2
36.3.f.c.31.3	yes	16	72.5	odd	6
36.3.f.c.31.4	yes	16	72.59	even	6
108.3.f.c.19.5		16	8.5	even	2
108.3.f.c.19.6		16	8.3	odd	2
108.3.f.c.91.5		16	72.67	odd	6
108.3.f.c.91.6		16	72.13	even	6
324.3.d.g.163.1		8	72.43	odd	6
324.3.d.g.163.2		8	72.61	even	6
324.3.d.i.163.7		8	72.29	odd	6
324.3.d.i.163.8		8	72.11	even	6
576.3.o.g.319.2		16	9.5	odd	6
576.3.o.g.319.7		16	36.23	even	6
576.3.o.g.511.2		16	12.11	even	2
576.3.o.g.511.7		16	3.2	odd	2
1728.3.o.g.127.7		16	4.3	odd	2	inner
1728.3.o.g.127.8		16	1.1	even	1	trivial
1728.3.o.g.1279.7		16	9.4	even	3	inner
1728.3.o.g.1279.8		16	36.31	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1728.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.07403 + 5.32438i) q^{5} +(0.511543 + 0.295340i) q^{7} +O(q^{10})\)	\(q+(3.07403 + 5.32438i) q^{5} +(0.511543 + 0.295340i) q^{7} +(15.1205 + 8.72982i) q^{11} +(0.892255 + 1.54543i) q^{13} +16.9171 q^{17} +19.5058i q^{19} +(6.86778 - 3.96511i) q^{23} +(-6.39933 + 11.0840i) q^{25} +(3.17517 - 5.49956i) q^{29} +(27.6558 - 15.9671i) q^{31} +3.63153i q^{35} -58.2834 q^{37} +(2.66948 + 4.62368i) q^{41} +(33.9324 + 19.5909i) q^{43} +(9.64117 + 5.56633i) q^{47} +(-24.3255 - 42.1331i) q^{49} +35.8770 q^{53} +107.343i q^{55} +(-20.8974 + 12.0651i) q^{59} +(37.9460 - 65.7244i) q^{61} +(-5.48564 + 9.50141i) q^{65} +(31.8200 - 18.3713i) q^{67} +87.8370i q^{71} -60.0423 q^{73} +(5.15652 + 8.93136i) q^{77} +(32.1841 + 18.5815i) q^{79} +(-66.0281 - 38.1214i) q^{83} +(52.0037 + 90.0730i) q^{85} +27.5873 q^{89} +1.05407i q^{91} +(-103.856 + 59.9614i) q^{95} +(13.0585 - 22.6180i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5}+O(q^{10}) \) 16 * q + 6 * q^5	\( 16 q + 6 q^{5} + 46 q^{13} - 12 q^{17} - 30 q^{25} + 42 q^{29} - 56 q^{37} - 84 q^{41} + 58 q^{49} - 72 q^{53} + 34 q^{61} + 30 q^{65} + 116 q^{73} - 330 q^{77} + 140 q^{85} + 384 q^{89} - 148 q^{97}+O(q^{100}) \) 16 * q + 6 * q^5 + 46 * q^13 - 12 * q^17 - 30 * q^25 + 42 * q^29 - 56 * q^37 - 84 * q^41 + 58 * q^49 - 72 * q^53 + 34 * q^61 + 30 * q^65 + 116 * q^73 - 330 * q^77 + 140 * q^85 + 384 * q^89 - 148 * q^97

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