LMFDB - Embedded newform 2016.2.s.m.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2016,2,Mod(289,2016)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2016, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("2016.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2016 = 2^{5} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2016.s (of order $3$, degree $2$, 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:	$16.0978410475$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2016.289
Dual form			2016.2.s.m.865.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{5} +(0.500000 - 2.59808i) q^{7} +O(q^{10})$	$q+(1.50000 - 2.59808i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-2.50000 - 4.33013i) q^{11} +2.00000 q^{13} +(1.00000 + 1.73205i) q^{17} +(3.00000 - 5.19615i) q^{19} +(-1.00000 + 1.73205i) q^{23} +(-2.00000 - 3.46410i) q^{25} -1.00000 q^{29} +(0.500000 + 0.866025i) q^{31} +(-6.00000 - 5.19615i) q^{35} +(-5.00000 + 8.66025i) q^{37} -4.00000 q^{41} +4.00000 q^{43} +(4.00000 - 6.92820i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(2.50000 + 4.33013i) q^{53} -15.0000 q^{55} +(-6.50000 - 11.2583i) q^{59} +(4.00000 - 6.92820i) q^{61} +(3.00000 - 5.19615i) q^{65} +(7.00000 + 12.1244i) q^{67} -12.0000 q^{71} +(3.00000 + 5.19615i) q^{73} +(-12.5000 + 4.33013i) q^{77} +(-5.50000 + 9.52628i) q^{79} -7.00000 q^{83} +6.00000 q^{85} +(-3.00000 + 5.19615i) q^{89} +(1.00000 - 5.19615i) q^{91} +(-9.00000 - 15.5885i) q^{95} +19.0000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{5} + q^{7}+O(q^{10}) $ 2 * q + 3 * q^5 + q^7	$ 2 q + 3 q^{5} + q^{7} - 5 q^{11} + 4 q^{13} + 2 q^{17} + 6 q^{19} - 2 q^{23} - 4 q^{25} - 2 q^{29} + q^{31} - 12 q^{35} - 10 q^{37} - 8 q^{41} + 8 q^{43} + 8 q^{47} - 13 q^{49} + 5 q^{53} - 30 q^{55} - 13 q^{59} + 8 q^{61} + 6 q^{65} + 14 q^{67} - 24 q^{71} + 6 q^{73} - 25 q^{77} - 11 q^{79} - 14 q^{83} + 12 q^{85} - 6 q^{89} + 2 q^{91} - 18 q^{95} + 38 q^{97}+O(q^{100}) $ 2 * q + 3 * q^5 + q^7 - 5 * q^11 + 4 * q^13 + 2 * q^17 + 6 * q^19 - 2 * q^23 - 4 * q^25 - 2 * q^29 + q^31 - 12 * q^35 - 10 * q^37 - 8 * q^41 + 8 * q^43 + 8 * q^47 - 13 * q^49 + 5 * q^53 - 30 * q^55 - 13 * q^59 + 8 * q^61 + 6 * q^65 + 14 * q^67 - 24 * q^71 + 6 * q^73 - 25 * q^77 - 11 * q^79 - 14 * q^83 + 12 * q^85 - 6 * q^89 + 2 * q^91 - 18 * q^95 + 38 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$1765$	$1793$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		0			0
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	−0.284157	−	0.958778i	$-0.591714\pi$
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	0.972404	−	0.233301i	$-0.0749529\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	−0.951247	−	0.308431i	$-0.900196\pi$
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	0.742732	+	0.669588i	$0.233529\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$		0			0
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	0.907428	−	0.420208i	$-0.138043\pi$
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	−0.817625	+	0.575751i	$0.804710\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.00000	−	5.19615i	−1.01419	−	0.878310i
$36$		0			0
$37$	−5.00000	+	8.66025i	−0.821995	+	1.42374i	0.0821995	+	0.996616i	$0.473806\pi$
$37$	−5.00000	+	8.66025i	−0.821995	+	1.42374i	−0.904194	+	0.427121i	$0.859528\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.00000			−0.624695			−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000			−0.624695			−0.312348	+	0.949968i	$0.601115\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	−0.411606	−	0.911362i	$-0.635032\pi$
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	0.995066	−	0.0992202i	$-0.0316348\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.50000	+	4.33013i	0.343401	+	0.594789i	0.985062	−	0.172200i	$-0.0550875\pi$
$53$	2.50000	+	4.33013i	0.343401	+	0.594789i	−0.641661	+	0.766989i	$0.721754\pi$
$54$		0			0
$55$	−15.0000			−2.02260
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.50000	−	11.2583i	−0.846228	−	1.46571i	−0.884551	−	0.466444i	$-0.845535\pi$
$59$	−6.50000	−	11.2583i	−0.846228	−	1.46571i	0.0383226	−	0.999265i	$-0.487799\pi$
$60$		0			0
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	−0.487753	−	0.872982i	$-0.662183\pi$
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	0.999901	−	0.0140840i	$-0.00448323\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.00000	−	5.19615i	0.372104	−	0.644503i
$66$		0			0
$67$	7.00000	+	12.1244i	0.855186	+	1.48123i	0.876472	+	0.481452i	$0.159891\pi$
$67$	7.00000	+	12.1244i	0.855186	+	1.48123i	−0.0212861	+	0.999773i	$0.506776\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	0.986447	−	0.164083i	$-0.0524664\pi$
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	−0.635323	+	0.772246i	$0.719133\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−12.5000	+	4.33013i	−1.42451	+	0.493464i
$78$		0			0
$79$	−5.50000	+	9.52628i	−0.618798	+	1.07179i	0.370907	+	0.928670i	$0.379047\pi$
$79$	−5.50000	+	9.52628i	−0.618798	+	1.07179i	−0.989705	+	0.143120i	$0.954286\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.00000			−0.768350			−0.384175	−	0.923260i	$-0.625514\pi$
$83$	−7.00000			−0.768350			−0.384175	+	0.923260i	$0.625514\pi$
$84$		0			0
$85$	6.00000			0.650791
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$	1.00000	−	5.19615i	0.104828	−	0.544705i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−9.00000	−	15.5885i	−0.923381	−	1.59934i
$96$		0			0
$97$	19.0000			1.92916			0.964579	−	0.263795i	$-0.0849741\pi$
$97$	19.0000			1.92916			0.964579	+	0.263795i	$0.0849741\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$		0			0
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.50000	−	11.2583i	0.628379	−	1.08838i	−0.359498	−	0.933146i	$-0.617052\pi$
$107$	6.50000	−	11.2583i	0.628379	−	1.08838i	0.987877	−	0.155238i	$-0.0496145\pi$
$108$		0			0
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	0.520794	−	0.853682i	$-0.325636\pi$
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	−0.999708	+	0.0241802i	$0.992302\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$		0			0
$115$	3.00000	+	5.19615i	0.279751	+	0.484544i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	5.00000	−	1.73205i	0.458349	−	0.158777i
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.00000			0.268328
$126$		0			0
$127$	−7.00000			−0.621150			−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000			−0.621150			−0.310575	+	0.950549i	$0.600522\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	−0.992865	−	0.119241i	$-0.961954\pi$
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	0.599699	+	0.800226i	$0.295287\pi$
$132$		0			0
$133$	−12.0000	−	10.3923i	−1.04053	−	0.901127i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−11.0000	−	19.0526i	−0.939793	−	1.62777i	−0.765855	−	0.643013i	$-0.777684\pi$
$137$	−11.0000	−	19.0526i	−0.939793	−	1.62777i	−0.173939	−	0.984757i	$-0.555649\pi$
$138$		0			0
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5.00000	−	8.66025i	−0.418121	−	0.724207i
$144$		0			0
$145$	−1.50000	+	2.59808i	−0.124568	+	0.215758i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	−0.216394	−	0.976306i	$-0.569430\pi$
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	0.953703	−	0.300750i	$-0.0972370\pi$
$150$		0			0
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	0.550645	−	0.834740i	$-0.314382\pi$
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	−0.998228	+	0.0595022i	$0.981049\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.00000			0.240966
$156$		0			0
$157$	6.00000	+	10.3923i	0.478852	+	0.829396i	0.999706	−	0.0242497i	$-0.00771967\pi$
$157$	6.00000	+	10.3923i	0.478852	+	0.829396i	−0.520854	+	0.853646i	$0.674386\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	4.00000	+	3.46410i	0.315244	+	0.273009i
$162$		0			0
$163$	7.00000	−	12.1244i	0.548282	−	0.949653i	−0.450110	−	0.892973i	$-0.648615\pi$
$163$	7.00000	−	12.1244i	0.548282	−	0.949653i	0.998392	−	0.0566798i	$-0.0180514\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−22.0000			−1.70241			−0.851206	−	0.524832i	$-0.824128\pi$
$167$	−22.0000			−1.70241			−0.851206	+	0.524832i	$0.824128\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.00000	−	15.5885i	0.684257	−	1.18517i	−0.289412	−	0.957205i	$-0.593460\pi$
$173$	9.00000	−	15.5885i	0.684257	−	1.18517i	0.973670	−	0.227964i	$-0.0732068\pi$
$174$		0			0
$175$	−10.0000	+	3.46410i	−0.755929	+	0.261861i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	15.0000	+	25.9808i	1.10282	+	1.91014i
$186$		0			0
$187$	5.00000	−	8.66025i	0.365636	−	0.633300i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	−0.563081	−	0.826402i	$-0.690384\pi$
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	0.997225	+	0.0744412i	$0.0237173\pi$
$192$		0			0
$193$	−8.50000	−	14.7224i	−0.611843	−	1.05974i	−0.990930	−	0.134382i	$-0.957095\pi$
$193$	−8.50000	−	14.7224i	−0.611843	−	1.05974i	0.379086	−	0.925361i	$-0.376238\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	−0.996850	−	0.0793045i	$-0.974730\pi$
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	0.429745	−	0.902950i	$-0.358603\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.500000	+	2.59808i	−0.0350931	+	0.182349i
$204$		0			0
$205$	−6.00000	+	10.3923i	−0.419058	+	0.725830i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−30.0000			−2.07514
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.00000	−	10.3923i	0.409197	−	0.708749i
$216$		0			0
$217$	2.50000	−	0.866025i	0.169711	−	0.0587896i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.00000	+	3.46410i	0.134535	+	0.233021i
$222$		0			0
$223$	9.00000			0.602685			0.301342	−	0.953516i	$-0.402565\pi$
$223$	9.00000			0.602685			0.301342	+	0.953516i	$0.402565\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.500000	+	0.866025i	0.0331862	+	0.0574801i	0.882141	−	0.470985i	$-0.156101\pi$
$227$	0.500000	+	0.866025i	0.0331862	+	0.0574801i	−0.848955	+	0.528465i	$0.822768\pi$
$228$		0			0
$229$	4.00000	−	6.92820i	0.264327	−	0.457829i	−0.703060	−	0.711131i	$-0.748183\pi$
$229$	4.00000	−	6.92820i	0.264327	−	0.457829i	0.967387	+	0.253302i	$0.0815167\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$		0			0
$235$	−12.0000	−	20.7846i	−0.782794	−	1.35584i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	0.881680	−	0.471848i	$-0.156413\pi$
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	−0.849472	+	0.527633i	$0.823079\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−16.5000	+	12.9904i	−1.05415	+	0.829925i
$246$		0			0
$247$	6.00000	−	10.3923i	0.381771	−	0.661247i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	17.0000			1.07303			0.536515	−	0.843891i	$-0.319740\pi$
$251$	17.0000			1.07303			0.536515	+	0.843891i	$0.319740\pi$
$252$		0			0
$253$	10.0000			0.628695
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.00000	+	12.1244i	−0.436648	+	0.756297i	−0.997429	−	0.0716680i	$-0.977168\pi$
$257$	−7.00000	+	12.1244i	−0.436648	+	0.756297i	0.560781	+	0.827964i	$0.310501\pi$
$258$		0			0
$259$	20.0000	+	17.3205i	1.24274	+	1.07624i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	0.999970	−	0.00771799i	$-0.00245674\pi$
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	−0.506669	+	0.862141i	$0.669123\pi$
$264$		0			0
$265$	15.0000			0.921443
$266$		0			0
$267$		0			0
$268$		0			0
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	0.985389	+	0.170321i	$0.0544803\pi$
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	−0.345192	+	0.938532i	$0.612186\pi$
$270$		0			0
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	−0.983312	−	0.181928i	$-0.941766\pi$
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	0.649211	+	0.760609i	$0.275099\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−10.0000	+	17.3205i	−0.603023	+	1.04447i
$276$		0			0
$277$	14.0000	+	24.2487i	0.841178	+	1.45696i	0.888899	+	0.458103i	$0.151471\pi$
$277$	14.0000	+	24.2487i	0.841178	+	1.45696i	−0.0477206	+	0.998861i	$0.515196\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$		0			0
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.00000	+	10.3923i	−0.118056	+	0.613438i
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−25.0000			−1.46052			−0.730258	−	0.683172i	$-0.760600\pi$
$293$	−25.0000			−1.46052			−0.730258	+	0.683172i	$0.760600\pi$
$294$		0			0
$295$	−39.0000			−2.27067
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.00000	+	3.46410i	−0.115663	+	0.200334i
$300$		0			0
$301$	2.00000	−	10.3923i	0.115278	−	0.599002i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−12.0000	−	20.7846i	−0.687118	−	1.19012i
$306$		0			0
$307$	22.0000			1.25561			0.627803	−	0.778372i	$-0.283954\pi$
$307$	22.0000			1.25561			0.627803	+	0.778372i	$0.283954\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$		0			0
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	−0.879810	−	0.475325i	$-0.842331\pi$
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	0.851549	+	0.524276i	$0.175664\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.50000	−	11.2583i	0.365076	−	0.632331i	−0.623712	−	0.781654i	$-0.714376\pi$
$317$	6.50000	−	11.2583i	0.365076	−	0.632331i	0.988788	+	0.149323i	$0.0477095\pi$
$318$		0			0
$319$	2.50000	+	4.33013i	0.139973	+	0.242441i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	12.0000			0.667698
$324$		0			0
$325$	−4.00000	−	6.92820i	−0.221880	−	0.384308i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−16.0000	−	13.8564i	−0.882109	−	0.763928i
$330$		0			0
$331$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$331$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	42.0000			2.29471
$336$		0			0
$337$	−3.00000			−0.163420			−0.0817102	−	0.996656i	$-0.526038\pi$
$337$	−3.00000			−0.163420			−0.0817102	+	0.996656i	$0.526038\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.50000	−	4.33013i	0.135383	−	0.234490i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$		0			0
$349$	−22.0000			−1.17763			−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000			−1.17763			−0.588817	+	0.808267i	$0.700406\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	0.985719	+	0.168397i	$0.0538590\pi$
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	−0.347024	+	0.937856i	$0.612808\pi$
$354$		0			0
$355$	−18.0000	+	31.1769i	−0.955341	+	1.65470i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−13.0000	+	22.5167i	−0.686114	+	1.18838i	0.286972	+	0.957939i	$0.407351\pi$
$359$	−13.0000	+	22.5167i	−0.686114	+	1.18838i	−0.973085	+	0.230445i	$0.925982\pi$
$360$		0			0
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	18.0000			0.942163
$366$		0			0
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	0.999989	−	0.00473247i	$-0.00150640\pi$
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	−0.504093	+	0.863649i	$0.668173\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	12.5000	−	4.33013i	0.648968	−	0.224809i
$372$		0			0
$373$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$373$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.00000			−0.103005
$378$		0			0
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−19.0000	+	32.9090i	−0.970855	+	1.68157i	−0.277868	+	0.960619i	$0.589628\pi$
$383$	−19.0000	+	32.9090i	−0.970855	+	1.68157i	−0.692987	+	0.720950i	$0.743706\pi$
$384$		0			0
$385$	−7.50000	+	38.9711i	−0.382235	+	1.98615i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	0.998763	−	0.0497253i	$-0.0158346\pi$
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	−0.542445	+	0.840091i	$0.682501\pi$
$390$		0			0
$391$	−4.00000			−0.202289
$392$		0			0
$393$		0			0
$394$		0			0
$395$	16.5000	+	28.5788i	0.830205	+	1.43796i
$396$		0			0
$397$	−4.00000	+	6.92820i	−0.200754	+	0.347717i	−0.948772	−	0.315963i	$-0.897673\pi$
$397$	−4.00000	+	6.92820i	−0.200754	+	0.347717i	0.748017	+	0.663679i	$0.231006\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	16.0000	−	27.7128i	0.799002	−	1.38391i	−0.121265	−	0.992620i	$-0.538695\pi$
$401$	16.0000	−	27.7128i	0.799002	−	1.38391i	0.920267	−	0.391292i	$-0.127972\pi$
$402$		0			0
$403$	1.00000	+	1.73205i	0.0498135	+	0.0862796i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	50.0000			2.47841
$408$		0			0
$409$	−9.50000	−	16.4545i	−0.469745	−	0.813622i	0.529657	−	0.848212i	$-0.322321\pi$
$409$	−9.50000	−	16.4545i	−0.469745	−	0.813622i	−0.999402	+	0.0345902i	$0.988987\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−32.5000	+	11.2583i	−1.59922	+	0.553986i
$414$		0			0
$415$	−10.5000	+	18.1865i	−0.515425	+	0.892742i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	−12.0000			−0.584844			−0.292422	−	0.956289i	$-0.594461\pi$
$421$	−12.0000			−0.584844			−0.292422	+	0.956289i	$0.594461\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.00000	−	6.92820i	0.194029	−	0.336067i
$426$		0			0
$427$	−16.0000	−	13.8564i	−0.774294	−	0.670559i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	14.0000	+	24.2487i	0.674356	+	1.16802i	0.976657	+	0.214807i	$0.0689121\pi$
$431$	14.0000	+	24.2487i	0.674356	+	1.16802i	−0.302300	+	0.953213i	$0.597755\pi$
$432$		0			0
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.00000	+	10.3923i	0.287019	+	0.497131i
$438$		0			0
$439$	10.5000	−	18.1865i	0.501138	−	0.867996i	−0.498861	−	0.866682i	$-0.666248\pi$
$439$	10.5000	−	18.1865i	0.501138	−	0.867996i	0.999999	−	0.00131415i	$-0.000418308\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.50000	+	7.79423i	−0.213801	+	0.370315i	−0.952901	−	0.303281i	$-0.901918\pi$
$443$	−4.50000	+	7.79423i	−0.213801	+	0.370315i	0.739100	+	0.673596i	$0.235251\pi$
$444$		0			0
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$	10.0000	+	17.3205i	0.470882	+	0.815591i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−12.0000	−	10.3923i	−0.562569	−	0.487199i
$456$		0			0
$457$	14.5000	−	25.1147i	0.678281	−	1.17482i	−0.297217	−	0.954810i	$-0.596058\pi$
$457$	14.5000	−	25.1147i	0.678281	−	1.17482i	0.975498	−	0.220008i	$-0.0706083\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.00000			−0.0931493			−0.0465746	−	0.998915i	$-0.514831\pi$
$461$	−2.00000			−0.0931493			−0.0465746	+	0.998915i	$0.514831\pi$
$462$		0			0
$463$	36.0000			1.67306			0.836531	−	0.547920i	$-0.184580\pi$
$463$	36.0000			1.67306			0.836531	+	0.547920i	$0.184580\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	18.0000	−	31.1769i	0.832941	−	1.44270i	−0.0627555	−	0.998029i	$-0.519989\pi$
$467$	18.0000	−	31.1769i	0.832941	−	1.44270i	0.895696	−	0.444667i	$-0.146678\pi$
$468$		0			0
$469$	35.0000	−	12.1244i	1.61615	−	0.559851i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.0000	−	17.3205i	−0.459800	−	0.796398i
$474$		0			0
$475$	−24.0000			−1.10120
$476$		0			0
$477$		0			0
$478$		0			0
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$		0			0
$481$	−10.0000	+	17.3205i	−0.455961	+	0.789747i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	28.5000	−	49.3634i	1.29412	−	2.24148i
$486$		0			0
$487$	1.50000	+	2.59808i	0.0679715	+	0.117730i	0.898008	−	0.439979i	$-0.145014\pi$
$487$	1.50000	+	2.59808i	0.0679715	+	0.117730i	−0.830037	+	0.557709i	$0.811681\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−31.0000			−1.39901			−0.699505	−	0.714628i	$-0.746596\pi$
$491$	−31.0000			−1.39901			−0.699505	+	0.714628i	$0.746596\pi$
$492$		0			0
$493$	−1.00000	−	1.73205i	−0.0450377	−	0.0780076i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.00000	+	31.1769i	−0.269137	+	1.39848i
$498$		0			0
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	−0.955968	−	0.293471i	$-0.905190\pi$
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	0.732137	+	0.681157i	$0.238523\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	14.0000			0.624229			0.312115	−	0.950044i	$-0.398963\pi$
$503$	14.0000			0.624229			0.312115	+	0.950044i	$0.398963\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$		0			0
$507$		0			0
$508$		0			0
$509$	12.5000	−	21.6506i	0.554053	−	0.959648i	−0.443924	−	0.896065i	$-0.646414\pi$
$509$	12.5000	−	21.6506i	0.554053	−	0.959648i	0.997977	−	0.0635830i	$-0.0202528\pi$
$510$		0			0
$511$	15.0000	−	5.19615i	0.663561	−	0.229864i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	12.0000	+	20.7846i	0.528783	+	0.915879i
$516$		0			0
$517$	−40.0000			−1.75920
$518$		0			0
$519$		0			0
$520$		0			0
$521$	20.0000	+	34.6410i	0.876216	+	1.51765i	0.855462	+	0.517866i	$0.173273\pi$
$521$	20.0000	+	34.6410i	0.876216	+	1.51765i	0.0207541	+	0.999785i	$0.493393\pi$
$522$		0			0
$523$	13.0000	−	22.5167i	0.568450	−	0.984585i	−0.428269	−	0.903651i	$-0.640876\pi$
$523$	13.0000	−	22.5167i	0.568450	−	0.984585i	0.996719	−	0.0809336i	$-0.0257902\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.00000	+	1.73205i	−0.0435607	+	0.0754493i
$528$		0			0
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−8.00000			−0.346518
$534$		0			0
$535$	−19.5000	−	33.7750i	−0.843059	−	1.46022i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.00000	+	34.6410i	0.215365	+	1.49209i
$540$		0			0
$541$	12.0000	−	20.7846i	0.515920	−	0.893600i	−0.483909	−	0.875118i	$-0.660783\pi$
$541$	12.0000	−	20.7846i	0.515920	−	0.893600i	0.999829	−	0.0184818i	$-0.00588327\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−30.0000			−1.28506
$546$		0			0
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−3.00000	+	5.19615i	−0.127804	+	0.221364i
$552$		0			0
$553$	22.0000	+	19.0526i	0.935535	+	0.810197i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−16.5000	−	28.5788i	−0.699127	−	1.21092i	−0.968769	−	0.247964i	$-0.920239\pi$
$557$	−16.5000	−	28.5788i	−0.699127	−	1.21092i	0.269642	−	0.962961i	$-0.413095\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$		0			0
$562$		0			0
$563$	5.50000	+	9.52628i	0.231797	+	0.401485i	0.958337	−	0.285640i	$-0.0922060\pi$
$563$	5.50000	+	9.52628i	0.231797	+	0.401485i	−0.726540	+	0.687124i	$0.758873\pi$
$564$		0			0
$565$	18.0000	−	31.1769i	0.757266	−	1.31162i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	−0.922032	−	0.387113i	$-0.873472\pi$
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	0.796266	+	0.604947i	$0.206806\pi$
$570$		0			0
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	0.904835	−	0.425762i	$-0.139994\pi$
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	−0.821138	+	0.570730i	$0.806660\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	8.00000			0.333623
$576$		0			0
$577$	−3.50000	−	6.06218i	−0.145707	−	0.252372i	0.783930	−	0.620850i	$-0.213212\pi$
$577$	−3.50000	−	6.06218i	−0.145707	−	0.252372i	−0.929636	+	0.368478i	$0.879879\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.50000	+	18.1865i	−0.145204	+	0.754505i
$582$		0			0
$583$	12.5000	−	21.6506i	0.517697	−	0.896678i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	27.0000			1.11441			0.557205	−	0.830375i	$-0.311874\pi$
$587$	27.0000			1.11441			0.557205	+	0.830375i	$0.311874\pi$
$588$		0			0
$589$	6.00000			0.247226
$590$		0			0
$591$		0			0
$592$		0			0
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	−0.797831	−	0.602881i	$-0.794019\pi$
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	0.921026	+	0.389501i	$0.127353\pi$
$594$		0			0
$595$	3.00000	−	15.5885i	0.122988	−	0.639064i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	9.00000	+	15.5885i	0.367730	+	0.636927i	0.989210	−	0.146503i	$-0.0468017\pi$
$599$	9.00000	+	15.5885i	0.367730	+	0.636927i	−0.621480	+	0.783430i	$0.713468\pi$
$600$		0			0
$601$	23.0000			0.938190			0.469095	−	0.883148i	$-0.344580\pi$
$601$	23.0000			0.938190			0.469095	+	0.883148i	$0.344580\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	21.0000	+	36.3731i	0.853771	+	1.47878i
$606$		0			0
$607$	1.50000	−	2.59808i	0.0608831	−	0.105453i	−0.833977	−	0.551799i	$-0.813942\pi$
$607$	1.50000	−	2.59808i	0.0608831	−	0.105453i	0.894860	+	0.446346i	$0.147275\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	8.00000	−	13.8564i	0.323645	−	0.560570i
$612$		0			0
$613$	11.0000	+	19.0526i	0.444286	+	0.769526i	0.998002	−	0.0631797i	$-0.0201241\pi$
$613$	11.0000	+	19.0526i	0.444286	+	0.769526i	−0.553716	+	0.832705i	$0.686791\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−8.00000			−0.322068			−0.161034	−	0.986949i	$-0.551483\pi$
$617$	−8.00000			−0.322068			−0.161034	+	0.986949i	$0.551483\pi$
$618$		0			0
$619$	−16.0000	−	27.7128i	−0.643094	−	1.11387i	−0.984738	−	0.174042i	$-0.944317\pi$
$619$	−16.0000	−	27.7128i	−0.643094	−	1.11387i	0.341644	−	0.939829i	$-0.389016\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	12.0000	+	10.3923i	0.480770	+	0.416359i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−20.0000			−0.797452
$630$		0			0
$631$	29.0000			1.15447			0.577236	−	0.816577i	$-0.304131\pi$
$631$	29.0000			1.15447			0.577236	+	0.816577i	$0.304131\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−10.5000	+	18.1865i	−0.416680	+	0.721711i
$636$		0			0
$637$	−13.0000	−	5.19615i	−0.515079	−	0.205879i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	8.00000	+	13.8564i	0.315981	+	0.547295i	0.979646	−	0.200735i	$-0.0643331\pi$
$641$	8.00000	+	13.8564i	0.315981	+	0.547295i	−0.663665	+	0.748030i	$0.731000\pi$
$642$		0			0
$643$	−34.0000			−1.34083			−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000			−1.34083			−0.670415	+	0.741987i	$0.733884\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−24.0000	−	41.5692i	−0.943537	−	1.63425i	−0.758654	−	0.651494i	$-0.774142\pi$
$647$	−24.0000	−	41.5692i	−0.943537	−	1.63425i	−0.184884	−	0.982760i	$-0.559191\pi$
$648$		0			0
$649$	−32.5000	+	56.2917i	−1.27574	+	2.20964i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−12.5000	+	21.6506i	−0.489163	+	0.847255i	−0.999922	−	0.0124688i	$-0.996031\pi$
$653$	−12.5000	+	21.6506i	−0.489163	+	0.847255i	0.510759	+	0.859724i	$0.329364\pi$
$654$		0			0
$655$	13.5000	+	23.3827i	0.527489	+	0.913637i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$661$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−45.0000	+	15.5885i	−1.74503	+	0.604494i
$666$		0			0
$667$	1.00000	−	1.73205i	0.0387202	−	0.0670653i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−40.0000			−1.54418
$672$		0			0
$673$	−39.0000			−1.50334			−0.751670	−	0.659540i	$-0.770751\pi$
$673$	−39.0000			−1.50334			−0.751670	+	0.659540i	$0.770751\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−4.50000	+	7.79423i	−0.172949	+	0.299557i	−0.939450	−	0.342687i	$-0.888663\pi$
$677$	−4.50000	+	7.79423i	−0.172949	+	0.299557i	0.766501	+	0.642244i	$0.221996\pi$
$678$		0			0
$679$	9.50000	−	49.3634i	0.364577	−	1.89440i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.50000	−	2.59808i	−0.0573959	−	0.0994126i	0.835900	−	0.548882i	$-0.184946\pi$
$683$	−1.50000	−	2.59808i	−0.0573959	−	0.0994126i	−0.893296	+	0.449469i	$0.851613\pi$
$684$		0			0
$685$	−66.0000			−2.52173
$686$		0			0
$687$		0			0
$688$		0			0
$689$	5.00000	+	8.66025i	0.190485	+	0.329929i
$690$		0			0
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	−0.466691	−	0.884420i	$-0.654554\pi$
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	0.999276	−	0.0380440i	$-0.0121127\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	21.0000	−	36.3731i	0.796575	−	1.37971i
$696$		0			0
$697$	−4.00000	−	6.92820i	−0.151511	−	0.262424i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	15.0000			0.566542			0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000			0.566542			0.283271	+	0.959040i	$0.408580\pi$
$702$		0			0
$703$	30.0000	+	51.9615i	1.13147	+	1.95977i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	15.0000	−	5.19615i	0.564133	−	0.195421i
$708$		0			0
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	−0.756730	−	0.653727i	$-0.773204\pi$
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	0.944509	+	0.328484i	$0.106538\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−2.00000			−0.0749006
$714$		0			0
$715$	−30.0000			−1.12194
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−15.0000	+	25.9808i	−0.559406	+	0.968919i	0.438141	+	0.898906i	$0.355637\pi$
$719$	−15.0000	+	25.9808i	−0.559406	+	0.968919i	−0.997546	+	0.0700124i	$0.977696\pi$
$720$		0			0
$721$	16.0000	+	13.8564i	0.595871	+	0.516040i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.00000	+	3.46410i	0.0742781	+	0.128654i
$726$		0			0
$727$	−17.0000			−0.630495			−0.315248	−	0.949009i	$-0.602088\pi$
$727$	−17.0000			−0.630495			−0.315248	+	0.949009i	$0.602088\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$		0			0
$733$	2.00000	−	3.46410i	0.0738717	−	0.127950i	−0.826723	−	0.562609i	$-0.809798\pi$
$733$	2.00000	−	3.46410i	0.0738717	−	0.127950i	0.900595	+	0.434659i	$0.143131\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	35.0000	−	60.6218i	1.28924	−	2.23303i
$738$		0			0
$739$	25.0000	+	43.3013i	0.919640	+	1.59286i	0.799962	+	0.600050i	$0.204853\pi$
$739$	25.0000	+	43.3013i	0.919640	+	1.59286i	0.119677	+	0.992813i	$0.461814\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−26.0000			−0.953847			−0.476924	−	0.878945i	$-0.658248\pi$
$743$	−26.0000			−0.953847			−0.476924	+	0.878945i	$0.658248\pi$
$744$		0			0
$745$	−27.0000	−	46.7654i	−0.989203	−	1.71335i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−26.0000	−	22.5167i	−0.950019	−	0.822741i
$750$		0			0
$751$	7.50000	−	12.9904i	0.273679	−	0.474026i	−0.696122	−	0.717923i	$-0.745093\pi$
$751$	7.50000	−	12.9904i	0.273679	−	0.474026i	0.969801	+	0.243898i	$0.0784261\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−33.0000			−1.20099
$756$		0			0
$757$	−8.00000			−0.290765			−0.145382	−	0.989376i	$-0.546441\pi$
$757$	−8.00000			−0.290765			−0.145382	+	0.989376i	$0.546441\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	−0.454935	−	0.890525i	$-0.650337\pi$
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	0.998684	−	0.0512772i	$-0.0163292\pi$
$762$		0			0
$763$	−25.0000	+	8.66025i	−0.905061	+	0.313522i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−13.0000	−	22.5167i	−0.469403	−	0.813029i
$768$		0			0
$769$	21.0000			0.757279			0.378640	−	0.925544i	$-0.376392\pi$
$769$	21.0000			0.757279			0.378640	+	0.925544i	$0.376392\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	15.0000	+	25.9808i	0.539513	+	0.934463i	0.998930	+	0.0462427i	$0.0147248\pi$
$773$	15.0000	+	25.9808i	0.539513	+	0.934463i	−0.459418	+	0.888220i	$0.651942\pi$
$774$		0			0
$775$	2.00000	−	3.46410i	0.0718421	−	0.124434i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−12.0000	+	20.7846i	−0.429945	+	0.744686i
$780$		0			0
$781$	30.0000	+	51.9615i	1.07348	+	1.85933i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	36.0000			1.28490
$786$		0			0
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	0.899468	−	0.436987i	$-0.143954\pi$
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	−0.828176	+	0.560469i	$0.810621\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	6.00000	−	31.1769i	0.213335	−	1.10852i
$792$		0			0
$793$	8.00000	−	13.8564i	0.284088	−	0.492055i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−19.0000			−0.673015			−0.336507	−	0.941681i	$-0.609246\pi$
$797$	−19.0000			−0.673015			−0.336507	+	0.941681i	$0.609246\pi$
$798$		0			0
$799$	16.0000			0.566039
$800$		0			0
$801$		0			0
$802$		0			0
$803$	15.0000	−	25.9808i	0.529339	−	0.916841i
$804$		0			0
$805$	15.0000	−	5.19615i	0.528681	−	0.183140i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−2.00000	−	3.46410i	−0.0703163	−	0.121791i	0.828724	−	0.559658i	$-0.189068\pi$
$809$	−2.00000	−	3.46410i	−0.0703163	−	0.121791i	−0.899040	+	0.437867i	$0.855734\pi$
$810$		0			0
$811$	−38.0000			−1.33436			−0.667180	−	0.744896i	$-0.732499\pi$
$811$	−38.0000			−1.33436			−0.667180	+	0.744896i	$0.732499\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−21.0000	−	36.3731i	−0.735598	−	1.27409i
$816$		0			0
$817$	12.0000	−	20.7846i	0.419827	−	0.727161i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	20.5000	−	35.5070i	0.715455	−	1.23920i	−0.247329	−	0.968932i	$-0.579553\pi$
$821$	20.5000	−	35.5070i	0.715455	−	1.23920i	0.962784	−	0.270273i	$-0.0871139\pi$
$822$		0			0
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	−0.997686	−	0.0679910i	$-0.978341\pi$
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	0.439961	−	0.898017i	$-0.354992\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	9.00000			0.312961			0.156480	−	0.987681i	$-0.449985\pi$
$827$	9.00000			0.312961			0.156480	+	0.987681i	$0.449985\pi$
$828$		0			0
$829$	21.0000	+	36.3731i	0.729360	+	1.26329i	0.957154	+	0.289579i	$0.0935154\pi$
$829$	21.0000	+	36.3731i	0.729360	+	1.26329i	−0.227794	+	0.973709i	$0.573151\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.00000	−	13.8564i	−0.0692959	−	0.480096i
$834$		0			0
$835$	−33.0000	+	57.1577i	−1.14201	+	1.97802i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−10.0000			−0.345238			−0.172619	−	0.984989i	$-0.555223\pi$
$839$	−10.0000			−0.345238			−0.172619	+	0.984989i	$0.555223\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−13.5000	+	23.3827i	−0.464414	+	0.804389i
$846$		0			0
$847$	28.0000	+	24.2487i	0.962091	+	0.833196i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−10.0000	−	17.3205i	−0.342796	−	0.593739i
$852$		0			0
$853$	6.00000			0.205436			0.102718	−	0.994711i	$-0.467246\pi$
$853$	6.00000			0.205436			0.102718	+	0.994711i	$0.467246\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$857$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$858$		0			0
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	0.291858	+	0.956462i	$0.405727\pi$
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	−0.974249	+	0.225475i	$0.927607\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3.00000	−	5.19615i	0.102121	−	0.176879i	−0.810437	−	0.585826i	$-0.800770\pi$
$863$	3.00000	−	5.19615i	0.102121	−	0.176879i	0.912558	+	0.408946i	$0.134104\pi$
$864$		0			0
$865$	−27.0000	−	46.7654i	−0.918028	−	1.59007i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	55.0000			1.86575
$870$		0			0
$871$	14.0000	+	24.2487i	0.474372	+	0.821636i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.50000	−	7.79423i	0.0507093	−	0.263493i
$876$		0			0
$877$	4.00000	−	6.92820i	0.135070	−	0.233949i	−0.790554	−	0.612392i	$-0.790207\pi$
$877$	4.00000	−	6.92820i	0.135070	−	0.233949i	0.925624	+	0.378444i	$0.123541\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−26.0000			−0.875962			−0.437981	−	0.898984i	$-0.644306\pi$
$881$	−26.0000			−0.875962			−0.437981	+	0.898984i	$0.644306\pi$
$882$		0			0
$883$	−16.0000			−0.538443			−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000			−0.538443			−0.269221	+	0.963078i	$0.586766\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	19.0000	−	32.9090i	0.637958	−	1.10497i	−0.347923	−	0.937523i	$-0.613113\pi$
$887$	19.0000	−	32.9090i	0.637958	−	1.10497i	0.985880	−	0.167452i	$-0.0535538\pi$
$888$		0			0
$889$	−3.50000	+	18.1865i	−0.117386	+	0.609957i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−24.0000	−	41.5692i	−0.803129	−	1.39106i
$894$		0			0
$895$	36.0000			1.20335
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.500000	−	0.866025i	−0.0166759	−	0.0288836i
$900$		0			0
$901$	−5.00000	+	8.66025i	−0.166574	+	0.288515i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−19.0000	−	32.9090i	−0.630885	−	1.09272i	−0.987371	−	0.158424i	$-0.949359\pi$
$907$	−19.0000	−	32.9090i	−0.630885	−	1.09272i	0.356487	−	0.934300i	$-0.383975\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−20.0000			−0.662630			−0.331315	−	0.943520i	$-0.607492\pi$
$911$	−20.0000			−0.662630			−0.331315	+	0.943520i	$0.607492\pi$
$912$		0			0
$913$	17.5000	+	30.3109i	0.579165	+	1.00314i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	18.0000	+	15.5885i	0.594412	+	0.514776i
$918$		0			0
$919$	−22.0000	+	38.1051i	−0.725713	+	1.25697i	0.232967	+	0.972485i	$0.425157\pi$
$919$	−22.0000	+	38.1051i	−0.725713	+	1.25697i	−0.958680	+	0.284487i	$0.908177\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−24.0000			−0.789970
$924$		0			0
$925$	40.0000			1.31519
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$929$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$930$		0			0
$931$	−33.0000	+	25.9808i	−1.08153	+	0.851485i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−15.0000	−	25.9808i	−0.490552	−	0.849662i
$936$		0			0
$937$	35.0000			1.14340			0.571700	−	0.820463i	$-0.306284\pi$
$937$	35.0000			1.14340			0.571700	+	0.820463i	$0.306284\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	15.5000	+	26.8468i	0.505286	+	0.875180i	0.999981	+	0.00611403i	$0.00194617\pi$
$941$	15.5000	+	26.8468i	0.505286	+	0.875180i	−0.494696	+	0.869066i	$0.664720\pi$
$942$		0			0
$943$	4.00000	−	6.92820i	0.130258	−	0.225613i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.0000	−	24.2487i	0.454939	−	0.787977i	−0.543746	−	0.839250i	$-0.682994\pi$
$947$	14.0000	−	24.2487i	0.454939	−	0.787977i	0.998685	+	0.0512727i	$0.0163278\pi$
$948$		0			0
$949$	6.00000	+	10.3923i	0.194768	+	0.337348i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−4.00000			−0.129573			−0.0647864	−	0.997899i	$-0.520637\pi$
$953$	−4.00000			−0.129573			−0.0647864	+	0.997899i	$0.520637\pi$
$954$		0			0
$955$	−18.0000	−	31.1769i	−0.582466	−	1.00886i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−55.0000	+	19.0526i	−1.77604	+	0.615239i
$960$		0			0
$961$	15.0000	−	25.9808i	0.483871	−	0.838089i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−51.0000			−1.64175
$966$		0			0
$967$	19.0000			0.610999			0.305499	−	0.952192i	$-0.401177\pi$
$967$	19.0000			0.610999			0.305499	+	0.952192i	$0.401177\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	0.720224	+	0.693742i	$0.244039\pi$
$972$		0			0
$973$	7.00000	−	36.3731i	0.224410	−	1.16607i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	26.0000	+	45.0333i	0.831814	+	1.44074i	0.896599	+	0.442844i	$0.146031\pi$
$977$	26.0000	+	45.0333i	0.831814	+	1.44074i	−0.0647848	+	0.997899i	$0.520636\pi$
$978$		0			0
$979$	30.0000			0.958804
$980$		0			0
$981$		0			0
$982$		0			0
$983$	6.00000	+	10.3923i	0.191370	+	0.331463i	0.945705	−	0.325027i	$-0.105374\pi$
$983$	6.00000	+	10.3923i	0.191370	+	0.331463i	−0.754334	+	0.656490i	$0.772040\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.00000	+	6.92820i	−0.127193	+	0.220304i
$990$		0			0
$991$	18.5000	+	32.0429i	0.587672	+	1.01788i	0.994537	+	0.104389i	$0.0332887\pi$
$991$	18.5000	+	32.0429i	0.587672	+	1.01788i	−0.406865	+	0.913488i	$0.633378\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−48.0000			−1.52170
$996$		0			0
$997$	−19.0000	−	32.9090i	−0.601736	−	1.04224i	−0.992558	−	0.121771i	$-0.961143\pi$
$997$	−19.0000	−	32.9090i	−0.601736	−	1.04224i	0.390822	−	0.920466i	$-0.372191\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2016.2.s.m.289.1	yes	2
3.2	odd	2		2016.2.s.d.289.1	yes	2
4.3	odd	2		2016.2.s.l.289.1	yes	2
7.4	even	3	inner	2016.2.s.m.865.1	yes	2
12.11	even	2		2016.2.s.c.289.1	✓	2
21.11	odd	6		2016.2.s.d.865.1	yes	2
28.11	odd	6		2016.2.s.l.865.1	yes	2
84.11	even	6		2016.2.s.c.865.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2016.2.s.c.289.1	✓	2	12.11	even	2
2016.2.s.c.865.1	yes	2	84.11	even	6
2016.2.s.d.289.1	yes	2	3.2	odd	2
2016.2.s.d.865.1	yes	2	21.11	odd	6
2016.2.s.l.289.1	yes	2	4.3	odd	2
2016.2.s.l.865.1	yes	2	28.11	odd	6
2016.2.s.m.289.1	yes	2	1.1	even	1	trivial
2016.2.s.m.865.1	yes	2	7.4	even	3	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:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2016.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{5} +(0.500000 - 2.59808i) q^{7} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-2.50000 - 4.33013i) q^{11} +2.00000 q^{13} +(1.00000 + 1.73205i) q^{17} +(3.00000 - 5.19615i) q^{19} +(-1.00000 + 1.73205i) q^{23} +(-2.00000 - 3.46410i) q^{25} -1.00000 q^{29} +(0.500000 + 0.866025i) q^{31} +(-6.00000 - 5.19615i) q^{35} +(-5.00000 + 8.66025i) q^{37} -4.00000 q^{41} +4.00000 q^{43} +(4.00000 - 6.92820i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(2.50000 + 4.33013i) q^{53} -15.0000 q^{55} +(-6.50000 - 11.2583i) q^{59} +(4.00000 - 6.92820i) q^{61} +(3.00000 - 5.19615i) q^{65} +(7.00000 + 12.1244i) q^{67} -12.0000 q^{71} +(3.00000 + 5.19615i) q^{73} +(-12.5000 + 4.33013i) q^{77} +(-5.50000 + 9.52628i) q^{79} -7.00000 q^{83} +6.00000 q^{85} +(-3.00000 + 5.19615i) q^{89} +(1.00000 - 5.19615i) q^{91} +(-9.00000 - 15.5885i) q^{95} +19.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{5} + q^{7}+O(q^{10}) \) 2 * q + 3 * q^5 + q^7	\( 2 q + 3 q^{5} + q^{7} - 5 q^{11} + 4 q^{13} + 2 q^{17} + 6 q^{19} - 2 q^{23} - 4 q^{25} - 2 q^{29} + q^{31} - 12 q^{35} - 10 q^{37} - 8 q^{41} + 8 q^{43} + 8 q^{47} - 13 q^{49} + 5 q^{53} - 30 q^{55} - 13 q^{59} + 8 q^{61} + 6 q^{65} + 14 q^{67} - 24 q^{71} + 6 q^{73} - 25 q^{77} - 11 q^{79} - 14 q^{83} + 12 q^{85} - 6 q^{89} + 2 q^{91} - 18 q^{95} + 38 q^{97}+O(q^{100}) \) 2 * q + 3 * q^5 + q^7 - 5 * q^11 + 4 * q^13 + 2 * q^17 + 6 * q^19 - 2 * q^23 - 4 * q^25 - 2 * q^29 + q^31 - 12 * q^35 - 10 * q^37 - 8 * q^41 + 8 * q^43 + 8 * q^47 - 13 * q^49 + 5 * q^53 - 30 * q^55 - 13 * q^59 + 8 * q^61 + 6 * q^65 + 14 * q^67 - 24 * q^71 + 6 * q^73 - 25 * q^77 - 11 * q^79 - 14 * q^83 + 12 * q^85 - 6 * q^89 + 2 * q^91 - 18 * q^95 + 38 * q^97

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