LMFDB - Embedded newform 2736.2.dc.e.449.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(449,2736)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2736, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))

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

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

chi := DirichletCharacter("2736.449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.dc (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:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} - 18 x^{18} + 232 x^{17} + 208 x^{16} - 3152 x^{15} - 2732 x^{14} + 24552 x^{13} + \cdots + 414864 $ x^20 - 8x^19 - 18x^18 + 232x^17 + 208x^16 - 3152x^15 - 2732x^14 + 24552x^13 + 30728x^12 - 110512x^11 - 211368x^10 + 231024x^9 + 827916x^8 + 179664x^7 - 1551960x^6 - 1894880x^5 + 305564x^4 + 2772832x^3 + 3072904x^2 + 1645728*x + 414864
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 1368)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.10
Root			$-1.64948 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2736.449
Dual form			2736.2.dc.e.1889.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.15998 - 1.82441i) q^{5} -1.21776 q^{7} +O(q^{10})$	$q+(3.15998 - 1.82441i) q^{5} -1.21776 q^{7} -3.18751i q^{11} +(3.24494 + 1.87347i) q^{13} +(-5.49639 + 3.17334i) q^{17} +(-1.51988 - 4.08534i) q^{19} +(-8.02130 - 4.63110i) q^{23} +(4.15696 - 7.20007i) q^{25} +(2.76663 - 4.79194i) q^{29} -7.28254i q^{31} +(-3.84810 + 2.22170i) q^{35} +7.63900i q^{37} +(-5.22131 - 9.04357i) q^{41} +(2.58113 + 4.47065i) q^{43} +(9.64157 + 5.56656i) q^{47} -5.51706 q^{49} +(6.30713 - 10.9243i) q^{53} +(-5.81533 - 10.0725i) q^{55} +(4.27618 + 7.40656i) q^{59} +(1.41554 - 2.45179i) q^{61} +13.6719 q^{65} +(-6.06428 - 3.50122i) q^{67} +(-1.96187 - 3.39806i) q^{71} +(-1.32730 - 2.29894i) q^{73} +3.88163i q^{77} +(-7.33078 + 4.23243i) q^{79} +0.122929i q^{83} +(-11.5790 + 20.0554i) q^{85} +(5.93303 - 10.2763i) q^{89} +(-3.95157 - 2.28144i) q^{91} +(-12.2561 - 10.1367i) q^{95} +(-7.33810 + 4.23665i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{7}+O(q^{10}) $ 20 * q + 4 * q^7	$ 20 q + 4 q^{7} + 6 q^{13} - 12 q^{17} - 4 q^{19} + 14 q^{25} - 12 q^{35} - 8 q^{41} + 2 q^{43} - 36 q^{47} + 32 q^{49} + 8 q^{53} - 12 q^{55} + 8 q^{59} - 2 q^{61} - 8 q^{65} - 30 q^{67} - 4 q^{71} - 22 q^{73} - 54 q^{79} - 4 q^{85} + 32 q^{89} - 18 q^{91} - 32 q^{95} + 12 q^{97}+O(q^{100}) $ 20 * q + 4 * q^7 + 6 * q^13 - 12 * q^17 - 4 * q^19 + 14 * q^25 - 12 * q^35 - 8 * q^41 + 2 * q^43 - 36 * q^47 + 32 * q^49 + 8 * q^53 - 12 * q^55 + 8 * q^59 - 2 * q^61 - 8 * q^65 - 30 * q^67 - 4 * q^71 - 22 * q^73 - 54 * q^79 - 4 * q^85 + 32 * q^89 - 18 * q^91 - 32 * q^95 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	3.15998	−	1.82441i	1.41318	−	0.815902i	0.417497	−	0.908678i	$-0.362907\pi$
$5$	3.15998	−	1.82441i	1.41318	−	0.815902i	0.995687	+	0.0927762i	$0.0295741\pi$
$6$		0			0
$7$	−1.21776			−0.460271			−0.230135	−	0.973159i	$-0.573917\pi$
$7$	−1.21776			−0.460271			−0.230135	+	0.973159i	$0.573917\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	3.18751i		−	0.961070i	−0.876975	−	0.480535i	$-0.840442\pi$
$11$		−	3.18751i		−	0.961070i	0.876975	−	0.480535i	$-0.159558\pi$
$12$		0			0
$13$	3.24494	+	1.87347i	0.899985	+	0.519607i	0.877195	−	0.480134i	$-0.159412\pi$
$13$	3.24494	+	1.87347i	0.899985	+	0.519607i	0.0227897	+	0.999740i	$0.492745\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.49639	+	3.17334i	−1.33307	+	0.769648i	−0.985769	−	0.168106i	$-0.946235\pi$
$17$	−5.49639	+	3.17334i	−1.33307	+	0.769648i	−0.347301	+	0.937754i	$0.612902\pi$
$18$		0			0
$19$	−1.51988	−	4.08534i	−0.348684	−	0.937240i
$19$	−1.51988	−	4.08534i	−0.348684	−	0.937240i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−8.02130	−	4.63110i	−1.67256	−	0.965651i	−0.966199	−	0.257796i	$-0.917004\pi$
$23$	−8.02130	−	4.63110i	−1.67256	−	0.965651i	−0.706357	−	0.707855i	$-0.749663\pi$
$24$		0			0
$25$	4.15696	−	7.20007i	0.831393	−	1.44001i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.76663	−	4.79194i	0.513750	−	0.889841i	−0.486123	−	0.873890i	$-0.661589\pi$
$29$	2.76663	−	4.79194i	0.513750	−	0.889841i	0.999873	−	0.0159505i	$-0.00507740\pi$
$30$		0			0
$31$		−	7.28254i		−	1.30798i	−0.756502	−	0.653991i	$-0.773093\pi$
$31$		−	7.28254i		−	1.30798i	0.756502	−	0.653991i	$-0.226907\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.84810	+	2.22170i	−0.650447	+	0.375536i
$36$		0			0
$37$			7.63900i			1.25584i	0.778277	+	0.627922i	$0.216094\pi$
$37$			7.63900i			1.25584i	−0.778277	+	0.627922i	$0.783906\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.22131	−	9.04357i	−0.815431	−	1.41237i	−0.909018	−	0.416757i	$-0.863167\pi$
$41$	−5.22131	−	9.04357i	−0.815431	−	1.41237i	0.0935867	−	0.995611i	$-0.470167\pi$
$42$		0			0
$43$	2.58113	+	4.47065i	0.393619	+	0.681768i	0.992924	−	0.118753i	$-0.0378895\pi$
$43$	2.58113	+	4.47065i	0.393619	+	0.681768i	−0.599305	+	0.800521i	$0.704556\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	9.64157	+	5.56656i	1.40637	+	0.811967i	0.995036	−	0.0995189i	$-0.0317304\pi$
$47$	9.64157	+	5.56656i	1.40637	+	0.811967i	0.411332	+	0.911486i	$0.365064\pi$
$48$		0			0
$49$	−5.51706			−0.788151
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.30713	−	10.9243i	0.866351	−	1.50056i	0.000651634	−	1.00000i	$-0.499793\pi$
$53$	6.30713	−	10.9243i	0.866351	−	1.50056i	0.865699	−	0.500564i	$-0.166874\pi$
$54$		0			0
$55$	−5.81533	−	10.0725i	−0.784139	−	1.35817i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.27618	+	7.40656i	0.556711	+	0.964253i	0.997768	+	0.0667733i	$0.0212704\pi$
$59$	4.27618	+	7.40656i	0.556711	+	0.964253i	−0.441057	+	0.897479i	$0.645396\pi$
$60$		0			0
$61$	1.41554	−	2.45179i	0.181242	−	0.313920i	−0.761062	−	0.648679i	$-0.775322\pi$
$61$	1.41554	−	2.45179i	0.181242	−	0.313920i	0.942304	+	0.334759i	$0.108655\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	13.6719			1.69579
$66$		0			0
$67$	−6.06428	−	3.50122i	−0.740870	−	0.427742i	0.0815154	−	0.996672i	$-0.474024\pi$
$67$	−6.06428	−	3.50122i	−0.740870	−	0.427742i	−0.822386	+	0.568930i	$0.807357\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.96187	−	3.39806i	−0.232831	−	0.403275i	0.725809	−	0.687896i	$-0.241466\pi$
$71$	−1.96187	−	3.39806i	−0.232831	−	0.403275i	−0.958640	+	0.284621i	$0.908132\pi$
$72$		0			0
$73$	−1.32730	−	2.29894i	−0.155348	−	0.269071i	0.777838	−	0.628465i	$-0.216317\pi$
$73$	−1.32730	−	2.29894i	−0.155348	−	0.269071i	−0.933186	+	0.359394i	$0.882983\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			3.88163i			0.442353i
$78$		0			0
$79$	−7.33078	+	4.23243i	−0.824777	+	0.476185i	−0.852061	−	0.523442i	$-0.824648\pi$
$79$	−7.33078	+	4.23243i	−0.824777	+	0.476185i	0.0272839	+	0.999628i	$0.491314\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			0.122929i			0.0134932i	0.999977	+	0.00674659i	$0.00214752\pi$
$83$			0.122929i			0.0134932i	−0.999977	+	0.00674659i	$0.997852\pi$
$84$		0			0
$85$	−11.5790	+	20.0554i	−1.25591	+	2.17531i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.93303	−	10.2763i	0.628900	−	1.08929i	−0.358873	−	0.933387i	$-0.616839\pi$
$89$	5.93303	−	10.2763i	0.628900	−	1.08929i	0.987773	−	0.155900i	$-0.0498279\pi$
$90$		0			0
$91$	−3.95157	−	2.28144i	−0.414237	−	0.239160i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−12.2561	−	10.1367i	−1.25745	−	1.04000i
$96$		0			0
$97$	−7.33810	+	4.23665i	−0.745071	+	0.430167i	−0.823910	−	0.566720i	$-0.808212\pi$
$97$	−7.33810	+	4.23665i	−0.745071	+	0.430167i	0.0788392	+	0.996887i	$0.474879\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.323298	−	0.186656i	−0.0321694	−	0.0185730i	0.483829	−	0.875163i	$-0.339246\pi$
$101$	−0.323298	−	0.186656i	−0.0321694	−	0.0185730i	−0.515998	+	0.856590i	$0.672579\pi$
$102$		0			0
$103$			12.7943i			1.26066i	0.776327	+	0.630331i	$0.217081\pi$
$103$			12.7943i			1.26066i	−0.776327	+	0.630331i	$0.782919\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.24983			0.410846			0.205423	−	0.978673i	$-0.434143\pi$
$107$	4.24983			0.410846			0.205423	+	0.978673i	$0.434143\pi$
$108$		0			0
$109$	4.08336	−	2.35753i	0.391115	−	0.225810i	−0.291528	−	0.956562i	$-0.594164\pi$
$109$	4.08336	−	2.35753i	0.391115	−	0.225810i	0.682643	+	0.730752i	$0.260830\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−13.1713			−1.23905			−0.619526	−	0.784976i	$-0.712675\pi$
$113$	−13.1713			−1.23905			−0.619526	+	0.784976i	$0.712675\pi$
$114$		0			0
$115$	−33.7962			−3.15151
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.69329	−	3.86437i	0.613573	−	0.354247i
$120$		0			0
$121$	0.839783			0.0763439
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	12.0919i		−	1.08154i
$126$		0			0
$127$	2.94642	+	1.70112i	0.261452	+	0.150950i	0.624997	−	0.780627i	$-0.285100\pi$
$127$	2.94642	+	1.70112i	0.261452	+	0.150950i	−0.363545	+	0.931577i	$0.618434\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.23254	−	5.33041i	0.806651	−	0.465720i	−0.0391405	−	0.999234i	$-0.512462\pi$
$131$	9.23254	−	5.33041i	0.806651	−	0.465720i	0.845792	+	0.533514i	$0.179129\pi$
$132$		0			0
$133$	1.85085	+	4.97497i	0.160489	+	0.431384i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.3226	+	7.69180i	1.13823	+	0.657155i	0.945991	−	0.324194i	$-0.105093\pi$
$137$	13.3226	+	7.69180i	1.13823	+	0.657155i	0.192235	+	0.981349i	$0.438426\pi$
$138$		0			0
$139$	8.64834	−	14.9794i	0.733542	−	1.27053i	−0.221818	−	0.975088i	$-0.571199\pi$
$139$	8.64834	−	14.9794i	0.733542	−	1.27053i	0.955360	−	0.295444i	$-0.0954677\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.97170	−	10.3433i	0.499378	−	0.864949i
$144$		0			0
$145$		−	20.1899i		−	1.67668i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.275774	+	0.159218i	−0.0225923	+	0.0130437i	−0.511254	−	0.859430i	$-0.670819\pi$
$149$	−0.275774	+	0.159218i	−0.0225923	+	0.0130437i	0.488661	+	0.872474i	$0.337485\pi$
$150$		0			0
$151$		−	3.30525i		−	0.268977i	−0.990915	−	0.134489i	$-0.957061\pi$
$151$		−	3.30525i		−	0.268977i	0.990915	−	0.134489i	$-0.0429392\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−13.2864	−	23.0126i	−1.06719	−	1.84842i
$156$		0			0
$157$	6.00347	+	10.3983i	0.479129	+	0.829876i	0.999714	−	0.0239343i	$-0.00761926\pi$
$157$	6.00347	+	10.3983i	0.479129	+	0.829876i	−0.520584	+	0.853810i	$0.674286\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	9.76804	+	5.63958i	0.769829	+	0.444461i
$162$		0			0
$163$	3.28630			0.257403			0.128701	−	0.991683i	$-0.458919\pi$
$163$	3.28630			0.257403			0.128701	+	0.991683i	$0.458919\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.50245	+	11.2626i	−0.503174	+	0.871524i	0.496819	+	0.867854i	$0.334501\pi$
$167$	−6.50245	+	11.2626i	−0.503174	+	0.871524i	−0.999993	+	0.00366929i	$0.998832\pi$
$168$		0			0
$169$	0.519766	+	0.900261i	0.0399820	+	0.0692508i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.77027	−	3.06620i	−0.134591	−	0.233119i	0.790850	−	0.612010i	$-0.209639\pi$
$173$	−1.77027	−	3.06620i	−0.134591	−	0.233119i	−0.925441	+	0.378891i	$0.876305\pi$
$174$		0			0
$175$	−5.06219	+	8.76797i	−0.382666	+	0.662797i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.31469			0.696212			0.348106	−	0.937455i	$-0.386825\pi$
$179$	9.31469			0.696212			0.348106	+	0.937455i	$0.386825\pi$
$180$		0			0
$181$	−6.07465	−	3.50720i	−0.451526	−	0.260688i	0.256949	−	0.966425i	$-0.417283\pi$
$181$	−6.07465	−	3.50720i	−0.451526	−	0.260688i	−0.708474	+	0.705737i	$0.750616\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	13.9367	+	24.1390i	1.02465	+	1.77474i
$186$		0			0
$187$	10.1151	+	17.5198i	0.739686	+	1.28117i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	7.84720i		−	0.567804i	−0.958853	−	0.283902i	$-0.908371\pi$
$191$		−	7.84720i		−	0.567804i	0.958853	−	0.283902i	$-0.0916290\pi$
$192$		0			0
$193$	13.5335	−	7.81358i	0.974164	−	0.562434i	0.0736605	−	0.997283i	$-0.476532\pi$
$193$	13.5335	−	7.81358i	0.974164	−	0.562434i	0.900503	+	0.434850i	$0.143199\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	27.2300i		−	1.94006i	−0.242988	−	0.970029i	$-0.578128\pi$
$197$		−	27.2300i		−	1.94006i	0.242988	−	0.970029i	$-0.421872\pi$
$198$		0			0
$199$	−6.76437	+	11.7162i	−0.479513	+	0.830542i	−0.999724	−	0.0234964i	$-0.992520\pi$
$199$	−6.76437	+	11.7162i	−0.479513	+	0.830542i	0.520210	+	0.854038i	$0.325854\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.36909	+	5.83544i	−0.236464	+	0.409568i
$204$		0			0
$205$	−32.9984	−	19.0516i	−2.30471	−	1.33062i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−13.0220	+	4.84462i	−0.900754	+	0.335110i
$210$		0			0
$211$	−0.280930	+	0.162195i	−0.0193400	+	0.0111660i	−0.509639	−	0.860388i	$-0.670221\pi$
$211$	−0.280930	+	0.162195i	−0.0193400	+	0.0111660i	0.490299	+	0.871554i	$0.336888\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	16.3126	+	9.41810i	1.11251	+	0.642309i
$216$		0			0
$217$			8.86840i			0.602026i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−23.7806			−1.59966
$222$		0			0
$223$	1.87840	−	1.08449i	0.125787	−	0.0726231i	−0.435786	−	0.900050i	$-0.643530\pi$
$223$	1.87840	−	1.08449i	0.125787	−	0.0726231i	0.561573	+	0.827427i	$0.310196\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	11.2658			0.747737			0.373868	−	0.927482i	$-0.378031\pi$
$227$	11.2658			0.747737			0.373868	+	0.927482i	$0.378031\pi$
$228$		0			0
$229$	−10.3778			−0.685783			−0.342892	−	0.939375i	$-0.611406\pi$
$229$	−10.3778			−0.685783			−0.342892	+	0.939375i	$0.611406\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.50305	+	2.59984i	−0.295005	+	0.170321i	−0.640197	−	0.768211i	$-0.721147\pi$
$233$	−4.50305	+	2.59984i	−0.295005	+	0.170321i	0.345192	+	0.938532i	$0.387814\pi$
$234$		0			0
$235$	40.6228			2.64994
$236$		0			0
$237$		0			0
$238$		0			0
$239$			23.8074i			1.53997i	0.638061	+	0.769986i	$0.279737\pi$
$239$			23.8074i			1.53997i	−0.638061	+	0.769986i	$0.720263\pi$
$240$		0			0
$241$	−3.86435	−	2.23108i	−0.248925	−	0.143717i	0.370347	−	0.928893i	$-0.379239\pi$
$241$	−3.86435	−	2.23108i	−0.248925	−	0.143717i	−0.619272	+	0.785177i	$0.712572\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−17.4338	+	10.0654i	−1.11380	+	0.643054i
$246$		0			0
$247$	2.72183	−	16.1041i	0.173186	−	1.02468i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.59681	−	1.49927i	−0.163909	−	0.0946330i	0.415802	−	0.909455i	$-0.363501\pi$
$251$	−2.59681	−	1.49927i	−0.163909	−	0.0946330i	−0.579711	+	0.814822i	$0.696834\pi$
$252$		0			0
$253$	−14.7617	+	25.5680i	−0.928059	+	1.60744i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.18435	−	7.24750i	0.261012	−	0.452087i	−0.705499	−	0.708711i	$-0.749277\pi$
$257$	4.18435	−	7.24750i	0.261012	−	0.452087i	0.966511	+	0.256624i	$0.0826103\pi$
$258$		0			0
$259$		−	9.30248i		−	0.578028i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	8.02503	−	4.63325i	0.494844	−	0.285699i	−0.231738	−	0.972778i	$-0.574441\pi$
$263$	8.02503	−	4.63325i	0.494844	−	0.285699i	0.726582	+	0.687080i	$0.241108\pi$
$264$		0			0
$265$		−	46.0272i		−	2.82743i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.917543	+	1.58923i	0.0559436	+	0.0968971i	0.892641	−	0.450768i	$-0.148850\pi$
$269$	0.917543	+	1.58923i	0.0559436	+	0.0968971i	−0.836697	+	0.547666i	$0.815517\pi$
$270$		0			0
$271$	−12.2080	−	21.1448i	−0.741582	−	1.28446i	−0.951775	−	0.306797i	$-0.900743\pi$
$271$	−12.2080	−	21.1448i	−0.741582	−	1.28446i	0.210193	−	0.977660i	$-0.432591\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−22.9503	−	13.2504i	−1.38395	−	0.799027i
$276$		0			0
$277$	−0.0584502			−0.00351193			−0.00175596	−	0.999998i	$-0.500559\pi$
$277$	−0.0584502			−0.00351193			−0.00175596	+	0.999998i	$0.500559\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	3.57303	−	6.18867i	0.213149	−	0.369185i	−0.739549	−	0.673102i	$-0.764961\pi$
$281$	3.57303	−	6.18867i	0.213149	−	0.369185i	0.952698	+	0.303917i	$0.0982947\pi$
$282$		0			0
$283$	2.99016	+	5.17910i	0.177746	+	0.307866i	0.941108	−	0.338105i	$-0.109786\pi$
$283$	2.99016	+	5.17910i	0.177746	+	0.307866i	−0.763362	+	0.645971i	$0.776453\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.35831	+	11.0129i	0.375319	+	0.650072i
$288$		0			0
$289$	11.6402	−	20.1614i	0.684716	−	1.18596i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−10.8725			−0.635179			−0.317589	−	0.948228i	$-0.602873\pi$
$293$	−10.8725			−0.635179			−0.317589	+	0.948228i	$0.602873\pi$
$294$		0			0
$295$	27.0253	+	15.6030i	1.57347	+	0.908444i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−17.3524	−	30.0553i	−1.00352	−	1.73814i
$300$		0			0
$301$	−3.14321	−	5.44419i	−0.181171	−	0.313798i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	10.3301i		−	0.591502i
$306$		0			0
$307$	7.38737	−	4.26510i	0.421619	−	0.243422i	−0.274150	−	0.961687i	$-0.588397\pi$
$307$	7.38737	−	4.26510i	0.421619	−	0.243422i	0.695770	+	0.718265i	$0.255063\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		−	32.8871i		−	1.86486i	−0.361353	−	0.932429i	$-0.617685\pi$
$311$		−	32.8871i		−	1.86486i	0.361353	−	0.932429i	$-0.382315\pi$
$312$		0			0
$313$	−13.1964	+	22.8568i	−0.745904	+	1.29194i	0.203867	+	0.978999i	$0.434649\pi$
$313$	−13.1964	+	22.8568i	−0.745904	+	1.29194i	−0.949771	+	0.312946i	$0.898684\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.0154	−	19.0792i	0.618684	−	1.07159i	−0.371042	−	0.928616i	$-0.620999\pi$
$317$	11.0154	−	19.0792i	0.618684	−	1.07159i	0.989726	−	0.142976i	$-0.0456672\pi$
$318$		0			0
$319$	−15.2744	−	8.81865i	−0.855200	−	0.493750i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	21.3180	+	17.6315i	1.18616	+	0.981043i
$324$		0			0
$325$	26.9782	−	15.5759i	1.49648	−	0.863994i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−11.7411	−	6.77875i	−0.647310	−	0.373725i
$330$		0			0
$331$			32.0104i			1.75945i	0.475481	+	0.879726i	$0.342274\pi$
$331$			32.0104i			1.75945i	−0.475481	+	0.879726i	$0.657726\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−25.5507			−1.39598
$336$		0			0
$337$	13.3867	−	7.72881i	0.729220	−	0.421015i	−0.0889168	−	0.996039i	$-0.528341\pi$
$337$	13.3867	−	7.72881i	0.729220	−	0.421015i	0.818137	+	0.575024i	$0.195007\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−23.2132			−1.25706
$342$		0			0
$343$	15.2428			0.823034
$344$		0			0
$345$		0			0
$346$		0			0
$347$	15.3943	−	8.88789i	0.826408	−	0.477127i	−0.0262134	−	0.999656i	$-0.508345\pi$
$347$	15.3943	−	8.88789i	0.826408	−	0.477127i	0.852621	+	0.522530i	$0.175012\pi$
$348$		0			0
$349$	5.42515			0.290402			0.145201	−	0.989402i	$-0.453617\pi$
$349$	5.42515			0.290402			0.145201	+	0.989402i	$0.453617\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			28.3678i			1.50987i	0.655801	+	0.754933i	$0.272331\pi$
$353$			28.3678i			1.50987i	−0.655801	+	0.754933i	$0.727669\pi$
$354$		0			0
$355$	−12.3989	−	7.15851i	−0.658066	−	0.379935i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	30.8981	−	17.8390i	1.63074	−	0.941509i	0.646876	−	0.762595i	$-0.276075\pi$
$359$	30.8981	−	17.8390i	1.63074	−	0.941509i	0.983865	−	0.178914i	$-0.0572584\pi$
$360$		0			0
$361$	−14.3799	+	12.4184i	−0.756839	+	0.653601i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−8.38845	−	4.84307i	−0.439071	−	0.253498i
$366$		0			0
$367$	−15.5092	+	26.8627i	−0.809574	+	1.40222i	0.103585	+	0.994621i	$0.466969\pi$
$367$	−15.5092	+	26.8627i	−0.809574	+	1.40222i	−0.913159	+	0.407603i	$0.866365\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.68058	+	13.3032i	−0.398756	+	0.690666i
$372$		0			0
$373$		−	5.93811i		−	0.307464i	−0.988113	−	0.153732i	$-0.950871\pi$
$373$		−	5.93811i		−	0.307464i	0.988113	−	0.153732i	$-0.0491292\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	17.9551	−	10.3664i	0.924734	−	0.533896i
$378$		0			0
$379$			17.4981i			0.898818i	0.893326	+	0.449409i	$0.148365\pi$
$379$			17.4981i			0.898818i	−0.893326	+	0.449409i	$0.851635\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−13.4026	−	23.2140i	−0.684842	−	1.18618i	−0.973486	−	0.228745i	$-0.926538\pi$
$383$	−13.4026	−	23.2140i	−0.684842	−	1.18618i	0.288645	−	0.957436i	$-0.406795\pi$
$384$		0			0
$385$	7.08169	+	12.2658i	0.360916	+	0.625126i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.61994	+	3.82202i	0.335644	+	0.193784i	0.658344	−	0.752717i	$-0.271257\pi$
$389$	6.61994	+	3.82202i	0.335644	+	0.193784i	−0.322700	+	0.946501i	$0.604591\pi$
$390$		0			0
$391$	58.7842			2.97285
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−15.4434	+	26.7487i	−0.777041	+	1.34587i
$396$		0			0
$397$	−7.84564	−	13.5890i	−0.393761	−	0.682015i	0.599181	−	0.800614i	$-0.295493\pi$
$397$	−7.84564	−	13.5890i	−0.393761	−	0.682015i	−0.992942	+	0.118599i	$0.962160\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	18.1399	+	31.4193i	0.905866	+	1.56901i	0.819751	+	0.572720i	$0.194112\pi$
$401$	18.1399	+	31.4193i	0.905866	+	1.56901i	0.0861143	+	0.996285i	$0.472555\pi$
$402$		0			0
$403$	13.6436	−	23.6314i	0.679637	−	1.17716i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	24.3494			1.20695
$408$		0			0
$409$	11.8367	+	6.83389i	0.585285	+	0.337914i	0.763231	−	0.646126i	$-0.223612\pi$
$409$	11.8367	+	6.83389i	0.585285	+	0.337914i	−0.177946	+	0.984040i	$0.556945\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−5.20737	−	9.01943i	−0.256238	−	0.443817i
$414$		0			0
$415$	0.224273	+	0.388452i	0.0110091	+	0.0190683i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	1.71472i		−	0.0837694i	−0.999122	−	0.0418847i	$-0.986664\pi$
$419$		−	1.71472i		−	0.0837694i	0.999122	−	0.0418847i	$-0.0133362\pi$
$420$		0			0
$421$	−12.8145	+	7.39846i	−0.624541	+	0.360579i	−0.778635	−	0.627477i	$-0.784088\pi$
$421$	−12.8145	+	7.39846i	−0.624541	+	0.360579i	0.154094	+	0.988056i	$0.450754\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$			52.7658i			2.55952i
$426$		0			0
$427$	−1.72379	+	2.98570i	−0.0834202	+	0.144488i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−15.9868	+	27.6899i	−0.770057	+	1.33378i	0.167474	+	0.985876i	$0.446439\pi$
$431$	−15.9868	+	27.6899i	−0.770057	+	1.33378i	−0.937531	+	0.347901i	$0.886894\pi$
$432$		0			0
$433$	−6.20491	−	3.58241i	−0.298189	−	0.172159i	0.343440	−	0.939175i	$-0.388408\pi$
$433$	−6.20491	−	3.58241i	−0.298189	−	0.172159i	−0.641629	+	0.767015i	$0.721741\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.72821	+	39.8084i	−0.321854	+	1.90429i
$438$		0			0
$439$	11.6933	−	6.75115i	0.558092	−	0.322215i	−0.194287	−	0.980945i	$-0.562239\pi$
$439$	11.6933	−	6.75115i	0.558092	−	0.322215i	0.752379	+	0.658730i	$0.228906\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.117063	+	0.0675862i	0.00556182	+	0.00321112i	0.502778	−	0.864415i	$-0.332311\pi$
$443$	0.117063	+	0.0675862i	0.00556182	+	0.00321112i	−0.497217	+	0.867626i	$0.665645\pi$
$444$		0			0
$445$		−	43.2972i		−	2.05248i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	3.88647			0.183414			0.0917069	−	0.995786i	$-0.470768\pi$
$449$	3.88647			0.183414			0.0917069	+	0.995786i	$0.470768\pi$
$450$		0			0
$451$	−28.8265	+	16.6430i	−1.35739	+	0.783687i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−16.6491			−0.780524
$456$		0			0
$457$	26.5032			1.23977			0.619885	−	0.784693i	$-0.287179\pi$
$457$	26.5032			1.23977			0.619885	+	0.784693i	$0.287179\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.59519	+	3.80774i	−0.307169	+	0.177344i	−0.645659	−	0.763626i	$-0.723417\pi$
$461$	−6.59519	+	3.80774i	−0.307169	+	0.177344i	0.338490	+	0.940970i	$0.390084\pi$
$462$		0			0
$463$	−20.8758			−0.970181			−0.485091	−	0.874464i	$-0.661213\pi$
$463$	−20.8758			−0.970181			−0.485091	+	0.874464i	$0.661213\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	7.09778i		−	0.328446i	−0.986423	−	0.164223i	$-0.947488\pi$
$467$		−	7.09778i		−	0.328446i	0.986423	−	0.164223i	$-0.0525117\pi$
$468$		0			0
$469$	7.38486	+	4.26365i	0.341001	+	0.196877i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	14.2503	−	8.22739i	0.655227	−	0.378296i
$474$		0			0
$475$	−35.7328	−	6.03936i	−1.63953	−	0.277105i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.93757	+	2.85071i	0.225603	+	0.130252i	0.608542	−	0.793522i	$-0.291755\pi$
$479$	4.93757	+	2.85071i	0.225603	+	0.130252i	−0.382939	+	0.923774i	$0.625088\pi$
$480$		0			0
$481$	−14.3114	+	24.7881i	−0.652544	+	1.13024i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−15.4588	+	26.7754i	−0.701948	+	1.21581i
$486$		0			0
$487$			6.21984i			0.281848i	0.990020	+	0.140924i	$0.0450073\pi$
$487$			6.21984i			0.281848i	−0.990020	+	0.140924i	$0.954993\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	10.7109	−	6.18391i	0.483374	−	0.279076i	−0.238447	−	0.971155i	$-0.576638\pi$
$491$	10.7109	−	6.18391i	0.483374	−	0.279076i	0.721822	+	0.692079i	$0.243305\pi$
$492$		0			0
$493$			35.1178i			1.58163i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.38909	+	4.13802i	0.107165	+	0.185616i
$498$		0			0
$499$	12.1843	+	21.1039i	0.545445	+	0.944738i	0.998579	+	0.0532957i	$0.0169726\pi$
$499$	12.1843	+	21.1039i	0.545445	+	0.944738i	−0.453134	+	0.891442i	$0.649694\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	21.7331	+	12.5476i	0.969033	+	0.559471i	0.898941	−	0.438069i	$-0.144338\pi$
$503$	21.7331	+	12.5476i	0.969033	+	0.559471i	0.0700916	+	0.997541i	$0.477671\pi$
$504$		0			0
$505$	−1.36215			−0.0606150
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−12.9977	+	22.5127i	−0.576113	+	0.997858i	0.419806	+	0.907614i	$0.362098\pi$
$509$	−12.9977	+	22.5127i	−0.576113	+	0.997858i	−0.995920	+	0.0902440i	$0.971235\pi$
$510$		0			0
$511$	1.61633	+	2.79957i	0.0715023	+	0.123846i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	23.3421	+	40.4297i	1.02858	+	1.78155i
$516$		0			0
$517$	17.7435	−	30.7326i	0.780357	−	1.35162i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	32.7031			1.43275			0.716375	−	0.697716i	$-0.245800\pi$
$521$	32.7031			1.43275			0.716375	+	0.697716i	$0.245800\pi$
$522$		0			0
$523$	−6.80593	−	3.92941i	−0.297603	−	0.171821i	0.343763	−	0.939057i	$-0.388298\pi$
$523$	−6.80593	−	3.92941i	−0.297603	−	0.171821i	−0.641365	+	0.767236i	$0.721632\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	23.1100	+	40.0277i	1.00669	+	1.74363i
$528$		0			0
$529$	31.3942	+	54.3763i	1.36496	+	2.36419i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	39.1278i		−	1.69481i
$534$		0			0
$535$	13.4293	−	7.75344i	0.580601	−	0.335210i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			17.5857i			0.757468i
$540$		0			0
$541$	−16.0058	+	27.7229i	−0.688143	+	1.19190i	0.284295	+	0.958737i	$0.408241\pi$
$541$	−16.0058	+	27.7229i	−0.688143	+	1.19190i	−0.972438	+	0.233162i	$0.925093\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	8.60221	−	14.8995i	0.368478	−	0.638223i
$546$		0			0
$547$	−23.7990	−	13.7404i	−1.01757	−	0.587496i	−0.104173	−	0.994559i	$-0.533220\pi$
$547$	−23.7990	−	13.7404i	−1.01757	−	0.587496i	−0.913400	+	0.407063i	$0.866553\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−23.7816	−	4.01944i	−1.01313	−	0.171234i
$552$		0			0
$553$	8.92715	−	5.15409i	0.379621	−	0.219174i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.25425	−	2.45619i	−0.180258	−	0.104072i	0.407156	−	0.913359i	$-0.366521\pi$
$557$	−4.25425	−	2.45619i	−0.180258	−	0.104072i	−0.587414	+	0.809287i	$0.699854\pi$
$558$		0			0
$559$			19.3427i			0.818108i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−22.3288			−0.941048			−0.470524	−	0.882387i	$-0.655935\pi$
$563$	−22.3288			−0.941048			−0.470524	+	0.882387i	$0.655935\pi$
$564$		0			0
$565$	−41.6210	+	24.0299i	−1.75101	+	1.01095i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.09656			−0.213659			−0.106830	−	0.994277i	$-0.534070\pi$
$569$	−5.09656			−0.213659			−0.106830	+	0.994277i	$0.534070\pi$
$570$		0			0
$571$	24.7635			1.03632			0.518160	−	0.855284i	$-0.326617\pi$
$571$	24.7635			1.03632			0.518160	+	0.855284i	$0.326617\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−66.6885	+	38.5026i	−2.78110	+	1.60567i
$576$		0			0
$577$	21.1718			0.881394			0.440697	−	0.897656i	$-0.354731\pi$
$577$	21.1718			0.881394			0.440697	+	0.897656i	$0.354731\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		−	0.149698i		−	0.00621051i
$582$		0			0
$583$	−34.8212	−	20.1040i	−1.44215	−	0.832624i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.51950	−	2.03198i	0.145265	−	0.0838689i	−0.425606	−	0.904909i	$-0.639939\pi$
$587$	3.51950	−	2.03198i	0.145265	−	0.0838689i	0.570871	+	0.821040i	$0.306606\pi$
$588$		0			0
$589$	−29.7516	+	11.0686i	−1.22589	+	0.456073i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−9.86438	−	5.69520i	−0.405081	−	0.233874i	0.283593	−	0.958945i	$-0.408474\pi$
$593$	−9.86438	−	5.69520i	−0.405081	−	0.233874i	−0.688674	+	0.725071i	$0.741807\pi$
$594$		0			0
$595$	14.1004	−	24.4226i	0.578061	−	1.00123i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−4.30181	+	7.45095i	−0.175767	+	0.304438i	−0.940427	−	0.339997i	$-0.889574\pi$
$599$	−4.30181	+	7.45095i	−0.175767	+	0.304438i	0.764659	+	0.644435i	$0.222907\pi$
$600$		0			0
$601$			11.9931i			0.489208i	0.969623	+	0.244604i	$0.0786580\pi$
$601$			11.9931i			0.489208i	−0.969623	+	0.244604i	$0.921342\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.65369	−	1.53211i	0.107888	−	0.0622892i
$606$		0			0
$607$			29.6979i			1.20540i	0.797968	+	0.602699i	$0.205908\pi$
$607$			29.6979i			1.20540i	−0.797968	+	0.602699i	$0.794092\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	20.8576	+	36.1264i	0.843806	+	1.46152i
$612$		0			0
$613$	−7.25385	−	12.5640i	−0.292980	−	0.507457i	0.681533	−	0.731788i	$-0.261314\pi$
$613$	−7.25385	−	12.5640i	−0.292980	−	0.507457i	−0.974513	+	0.224331i	$0.927980\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	23.9288	+	13.8153i	0.963335	+	0.556182i	0.897198	−	0.441629i	$-0.145599\pi$
$617$	23.9288	+	13.8153i	0.963335	+	0.556182i	0.0661375	+	0.997811i	$0.478932\pi$
$618$		0			0
$619$	38.6886			1.55503			0.777514	−	0.628866i	$-0.216481\pi$
$619$	38.6886			1.55503			0.777514	+	0.628866i	$0.216481\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−7.22502	+	12.5141i	−0.289464	+	0.501367i
$624$		0			0
$625$	−1.27587	−	2.20987i	−0.0510347	−	0.0883946i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−24.2411	−	41.9869i	−0.966557	−	1.67413i
$630$		0			0
$631$	0.862978	−	1.49472i	0.0343546	−	0.0595039i	−0.848337	−	0.529457i	$-0.822396\pi$
$631$	0.862978	−	1.49472i	0.0343546	−	0.0595039i	0.882691	+	0.469953i	$0.155729\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	12.4141			0.492640
$636$		0			0
$637$	−17.9025	−	10.3360i	−0.709324	−	0.409528i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.548109	−	0.949352i	−0.0216490	−	0.0374972i	0.854998	−	0.518631i	$-0.173558\pi$
$641$	−0.548109	−	0.949352i	−0.0216490	−	0.0374972i	−0.876647	+	0.481134i	$0.840225\pi$
$642$		0			0
$643$	0.765255	+	1.32546i	0.0301787	+	0.0522710i	0.880720	−	0.473637i	$-0.157059\pi$
$643$	0.765255	+	1.32546i	0.0301787	+	0.0522710i	−0.850542	+	0.525908i	$0.823726\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			18.7014i			0.735228i	0.929978	+	0.367614i	$0.119825\pi$
$647$			18.7014i			0.735228i	−0.929978	+	0.367614i	$0.880175\pi$
$648$		0			0
$649$	23.6085	−	13.6304i	0.926715	−	0.535039i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			8.55387i			0.334739i	0.985894	+	0.167369i	$0.0535273\pi$
$653$			8.55387i			0.334739i	−0.985894	+	0.167369i	$0.946473\pi$
$654$		0			0
$655$	19.4497	−	33.6879i	0.759964	−	1.31630i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.38724	+	2.40277i	−0.0540392	+	0.0935986i	−0.891780	−	0.452470i	$-0.850543\pi$
$659$	−1.38724	+	2.40277i	−0.0540392	+	0.0935986i	0.837740	+	0.546069i	$0.183876\pi$
$660$		0			0
$661$	25.2961	+	14.6047i	0.983904	+	0.568057i	0.903447	−	0.428701i	$-0.141028\pi$
$661$	25.2961	+	14.6047i	0.983904	+	0.568057i	0.0804576	+	0.996758i	$0.474362\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	14.9250	+	12.3441i	0.578768	+	0.478682i
$666$		0			0
$667$	−44.3839	+	25.6251i	−1.71855	+	0.992206i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−7.81511	−	4.51205i	−0.301699	−	0.174186i
$672$		0			0
$673$		−	22.8009i		−	0.878910i	−0.898265	−	0.439455i	$-0.855172\pi$
$673$		−	22.8009i		−	0.878910i	0.898265	−	0.439455i	$-0.144828\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−6.06640			−0.233151			−0.116575	−	0.993182i	$-0.537192\pi$
$677$	−6.06640			−0.233151			−0.116575	+	0.993182i	$0.537192\pi$
$678$		0			0
$679$	8.93606	−	5.15924i	0.342934	−	0.197993i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−16.3971			−0.627417			−0.313708	−	0.949519i	$-0.601571\pi$
$683$	−16.3971			−0.627417			−0.313708	+	0.949519i	$0.601571\pi$
$684$		0			0
$685$	56.1321			2.14470
$686$		0			0
$687$		0			0
$688$		0			0
$689$	40.9325	−	23.6324i	1.55941	−	0.900323i
$690$		0			0
$691$	26.3737			1.00330			0.501651	−	0.865070i	$-0.332726\pi$
$691$	26.3737			1.00330			0.501651	+	0.865070i	$0.332726\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	63.1125i		−	2.39400i
$696$		0			0
$697$	57.3966	+	33.1380i	2.17405	+	1.25519i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	4.17135	−	2.40833i	0.157550	−	0.0909615i	−0.419152	−	0.907916i	$-0.637673\pi$
$701$	4.17135	−	2.40833i	0.157550	−	0.0909615i	0.576702	+	0.816954i	$0.304339\pi$
$702$		0			0
$703$	31.2079	−	11.6103i	1.17703	−	0.437892i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.393700	+	0.227303i	0.0148066	+	0.00854860i
$708$		0			0
$709$	−8.96198	+	15.5226i	−0.336574	+	0.582963i	−0.983786	−	0.179347i	$-0.942602\pi$
$709$	−8.96198	+	15.5226i	−0.336574	+	0.582963i	0.647212	+	0.762310i	$0.275935\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−33.7262	+	58.4154i	−1.26306	+	2.18768i
$714$		0			0
$715$		−	43.5794i		−	1.62978i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	4.08555	−	2.35879i	0.152365	−	0.0879681i	−0.421879	−	0.906652i	$-0.638629\pi$
$719$	4.08555	−	2.35879i	0.152365	−	0.0879681i	0.574244	+	0.818684i	$0.305296\pi$
$720$		0			0
$721$		−	15.5804i		−	0.580246i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−23.0015	−	39.8398i	−0.854256	−	1.47961i
$726$		0			0
$727$	−13.9072	−	24.0880i	−0.515791	−	0.893376i	−0.999832	−	0.0183307i	$-0.994165\pi$
$727$	−13.9072	−	24.0880i	−0.515791	−	0.893376i	0.484041	−	0.875045i	$-0.339168\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−28.3738	−	16.3816i	−1.04944	−	0.605896i
$732$		0			0
$733$	53.6310			1.98090			0.990452	−	0.137855i	$-0.0440209\pi$
$733$	53.6310			1.98090			0.990452	+	0.137855i	$0.0440209\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−11.1602	+	19.3300i	−0.411090	+	0.712028i
$738$		0			0
$739$	9.67660	+	16.7604i	0.355960	+	0.616540i	0.987282	−	0.158981i	$-0.0508208\pi$
$739$	9.67660	+	16.7604i	0.355960	+	0.616540i	−0.631322	+	0.775521i	$0.717487\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	3.42880	+	5.93885i	0.125790	+	0.217875i	0.922042	−	0.387091i	$-0.126520\pi$
$743$	3.42880	+	5.93885i	0.125790	+	0.217875i	−0.796251	+	0.604966i	$0.793187\pi$
$744$		0			0
$745$	−0.580960	+	1.00625i	−0.0212847	+	0.0368662i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−5.17528			−0.189101
$750$		0			0
$751$	16.2351	+	9.37336i	0.592428	+	0.342039i	0.766057	−	0.642772i	$-0.222216\pi$
$751$	16.2351	+	9.37336i	0.592428	+	0.342039i	−0.173629	+	0.984811i	$0.555549\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−6.03013	−	10.4445i	−0.219459	−	0.380114i
$756$		0			0
$757$	−1.11675	−	1.93427i	−0.0405889	−	0.0703021i	0.845017	−	0.534739i	$-0.179590\pi$
$757$	−1.11675	−	1.93427i	−0.0405889	−	0.0703021i	−0.885606	+	0.464437i	$0.846257\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		−	8.25936i		−	0.299402i	−0.988731	−	0.149701i	$-0.952169\pi$
$761$		−	8.25936i		−	0.299402i	0.988731	−	0.149701i	$-0.0478311\pi$
$762$		0			0
$763$	−4.97256	+	2.87091i	−0.180019	+	0.103934i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			32.0452i			1.15708i
$768$		0			0
$769$	−4.94428	+	8.56374i	−0.178295	+	0.308816i	−0.941297	−	0.337580i	$-0.890392\pi$
$769$	−4.94428	+	8.56374i	−0.178295	+	0.308816i	0.763001	+	0.646397i	$0.223725\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−9.74847	+	16.8848i	−0.350628	+	0.607306i	−0.986360	−	0.164605i	$-0.947365\pi$
$773$	−9.74847	+	16.8848i	−0.350628	+	0.607306i	0.635732	+	0.771910i	$0.280699\pi$
$774$		0			0
$775$	−52.4348	−	30.2733i	−1.88351	−	1.08745i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−29.0103	+	35.0759i	−1.03940	+	1.25672i
$780$		0			0
$781$	−10.8313	+	6.25347i	−0.387576	+	0.223767i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	37.9416	+	21.9056i	1.35419	+	0.781845i
$786$		0			0
$787$		−	50.5191i		−	1.80081i	−0.435051	−	0.900406i	$-0.643270\pi$
$787$		−	50.5191i		−	1.80081i	0.435051	−	0.900406i	$-0.356730\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	16.0395			0.570299
$792$		0			0
$793$	9.18670	−	5.30395i	0.326229	−	0.188349i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−19.5240			−0.691575			−0.345788	−	0.938313i	$-0.612388\pi$
$797$	−19.5240			−0.691575			−0.345788	+	0.938313i	$0.612388\pi$
$798$		0			0
$799$	−70.6584			−2.49971
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−7.32791	+	4.23077i	−0.258596	+	0.149301i
$804$		0			0
$805$	41.1557			1.45055
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	18.9059i		−	0.664695i	−0.943157	−	0.332347i	$-0.892159\pi$
$809$		−	18.9059i		−	0.664695i	0.943157	−	0.332347i	$-0.107841\pi$
$810$		0			0
$811$	26.5087	+	15.3048i	0.930845	+	0.537424i	0.887079	−	0.461618i	$-0.152731\pi$
$811$	26.5087	+	15.3048i	0.930845	+	0.537424i	0.0437663	+	0.999042i	$0.486064\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	10.3846	−	5.99557i	0.363758	−	0.210015i
$816$		0			0
$817$	14.3411	−	17.3396i	0.501732	−	0.606637i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	13.8924	+	8.02077i	0.484848	+	0.279927i	0.722435	−	0.691439i	$-0.243023\pi$
$821$	13.8924	+	8.02077i	0.484848	+	0.279927i	−0.237587	+	0.971366i	$0.576356\pi$
$822$		0			0
$823$	−19.1196	+	33.1162i	−0.666469	+	1.15436i	0.312416	+	0.949945i	$0.398862\pi$
$823$	−19.1196	+	33.1162i	−0.666469	+	1.15436i	−0.978885	+	0.204412i	$0.934472\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.9295	+	22.3945i	−0.449601	+	0.778732i	−0.998360	−	0.0572487i	$-0.981767\pi$
$827$	−12.9295	+	22.3945i	−0.449601	+	0.778732i	0.548759	+	0.835981i	$0.315101\pi$
$828$		0			0
$829$		−	3.12362i		−	0.108488i	−0.998528	−	0.0542438i	$-0.982725\pi$
$829$		−	3.12362i		−	0.108488i	0.998528	−	0.0542438i	$-0.0172748\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	30.3239	−	17.5075i	1.05066	−	0.606599i
$834$		0			0
$835$			47.4526i			1.64216i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−23.3375	−	40.4217i	−0.805700	−	1.39551i	−0.915817	−	0.401595i	$-0.868456\pi$
$839$	−23.3375	−	40.4217i	−0.805700	−	1.39551i	0.110117	−	0.993919i	$-0.464877\pi$
$840$		0			0
$841$	−0.808459	−	1.40029i	−0.0278779	−	0.0482860i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	3.28489	+	1.89653i	0.113004	+	0.0652428i
$846$		0			0
$847$	−1.02266			−0.0351389
$848$		0			0
$849$		0			0
$850$		0			0
$851$	35.3770	−	61.2747i	1.21271	−	2.10047i
$852$		0			0
$853$	−26.0093	−	45.0495i	−0.890543	−	1.54247i	−0.839226	−	0.543783i	$-0.816992\pi$
$853$	−26.0093	−	45.0495i	−0.890543	−	1.54247i	−0.0513166	−	0.998682i	$-0.516342\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12.0105	+	20.8028i	0.410271	+	0.710611i	0.994919	−	0.100676i	$-0.0321007\pi$
$857$	12.0105	+	20.8028i	0.410271	+	0.710611i	−0.584648	+	0.811287i	$0.698767\pi$
$858$		0			0
$859$	−6.21978	+	10.7730i	−0.212216	+	0.367569i	−0.952408	−	0.304827i	$-0.901401\pi$
$859$	−6.21978	+	10.7730i	−0.212216	+	0.367569i	0.740192	+	0.672396i	$0.234735\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.18195			0.312557			0.156279	−	0.987713i	$-0.450050\pi$
$863$	9.18195			0.312557			0.156279	+	0.987713i	$0.450050\pi$
$864$		0			0
$865$	−11.1880	−	6.45941i	−0.380404	−	0.219627i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	13.4909	+	23.3669i	0.457648	+	0.792669i
$870$		0			0
$871$	−13.1188	−	22.7225i	−0.444515	−	0.769922i
$872$		0			0
$873$		0			0
$874$		0			0
$875$			14.7251i			0.497799i
$876$		0			0
$877$	−17.0870	+	9.86520i	−0.576988	+	0.333124i	−0.759935	−	0.649999i	$-0.774769\pi$
$877$	−17.0870	+	9.86520i	−0.576988	+	0.333124i	0.182947	+	0.983123i	$0.441436\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			8.97139i			0.302254i	0.988514	+	0.151127i	$0.0482902\pi$
$881$			8.97139i			0.302254i	−0.988514	+	0.151127i	$0.951710\pi$
$882$		0			0
$883$	23.2783	−	40.3191i	0.783376	−	1.35685i	−0.146588	−	0.989198i	$-0.546829\pi$
$883$	23.2783	−	40.3191i	0.783376	−	1.35685i	0.929964	−	0.367650i	$-0.119837\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.19188	+	12.4567i	−0.241480	+	0.418255i	−0.961136	−	0.276075i	$-0.910966\pi$
$887$	−7.19188	+	12.4567i	−0.241480	+	0.418255i	0.719656	+	0.694330i	$0.244299\pi$
$888$		0			0
$889$	−3.58804	−	2.07155i	−0.120339	−	0.0694777i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	8.08728	−	47.8496i	0.270630	−	1.60122i
$894$		0			0
$895$	29.4342	−	16.9938i	0.983876	−	0.568041i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−34.8975	−	20.1481i	−1.16390	−	0.671976i
$900$		0			0
$901$			80.0587i			2.66714i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−25.5943			−0.850785
$906$		0			0
$907$	39.9887	−	23.0875i	1.32780	−	0.766608i	0.342844	−	0.939393i	$-0.388610\pi$
$907$	39.9887	−	23.0875i	1.32780	−	0.766608i	0.984960	+	0.172785i	$0.0552766\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−10.7270			−0.355401			−0.177701	−	0.984085i	$-0.556866\pi$
$911$	−10.7270			−0.355401			−0.177701	+	0.984085i	$0.556866\pi$
$912$		0			0
$913$	0.391836			0.0129679
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−11.2430	+	6.49117i	−0.371278	+	0.214357i
$918$		0			0
$919$	45.0778			1.48698			0.743490	−	0.668747i	$-0.233169\pi$
$919$	45.0778			1.48698			0.743490	+	0.668747i	$0.233169\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	14.7020i		−	0.483922i
$924$		0			0
$925$	55.0013	+	31.7550i	1.80843	+	1.04410i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	4.78458	−	2.76238i	0.156977	−	0.0906306i	−0.419454	−	0.907777i	$-0.637778\pi$
$929$	4.78458	−	2.76238i	0.156977	−	0.0906306i	0.576431	+	0.817146i	$0.304445\pi$
$930$		0			0
$931$	8.38525	+	22.5390i	0.274815	+	0.738687i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	63.9266	+	36.9081i	2.09062	+	1.20702i
$936$		0			0
$937$	21.7193	−	37.6189i	0.709539	−	1.22896i	−0.255490	−	0.966812i	$-0.582237\pi$
$937$	21.7193	−	37.6189i	0.709539	−	1.22896i	0.965028	−	0.262145i	$-0.0844300\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−7.49724	+	12.9856i	−0.244403	+	0.423319i	−0.961964	−	0.273178i	$-0.911925\pi$
$941$	−7.49724	+	12.9856i	−0.244403	+	0.423319i	0.717561	+	0.696496i	$0.245259\pi$
$942$		0			0
$943$			96.7216i			3.14969i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	11.9471	−	6.89767i	0.388229	−	0.224144i	−0.293163	−	0.956062i	$-0.594708\pi$
$947$	11.9471	−	6.89767i	0.388229	−	0.224144i	0.681393	+	0.731918i	$0.261375\pi$
$948$		0			0
$949$		−	9.94659i		−	0.322880i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−16.4066	−	28.4170i	−0.531461	−	0.920517i	−0.999326	−	0.0367172i	$-0.988310\pi$
$953$	−16.4066	−	28.4170i	−0.531461	−	0.920517i	0.467865	−	0.883800i	$-0.345023\pi$
$954$		0			0
$955$	−14.3165	−	24.7970i	−0.463272	−	0.802411i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−16.2238	−	9.36679i	−0.523892	−	0.302469i
$960$		0			0
$961$	−22.0354			−0.710819
$962$		0			0
$963$		0			0
$964$		0			0
$965$	28.5104	−	49.3814i	0.917781	−	1.58964i
$966$		0			0
$967$	−20.3017	−	35.1635i	−0.652858	−	1.13078i	−0.982426	−	0.186651i	$-0.940237\pi$
$967$	−20.3017	−	35.1635i	−0.652858	−	1.13078i	0.329569	−	0.944132i	$-0.393097\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−6.73999	−	11.6740i	−0.216297	−	0.374637i	0.737376	−	0.675482i	$-0.236064\pi$
$971$	−6.73999	−	11.6740i	−0.216297	−	0.374637i	−0.953673	+	0.300846i	$0.902731\pi$
$972$		0			0
$973$	−10.5316	+	18.2413i	−0.337628	+	0.584789i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−31.4927			−1.00754			−0.503770	−	0.863838i	$-0.668054\pi$
$977$	−31.4927			−1.00754			−0.503770	+	0.863838i	$0.668054\pi$
$978$		0			0
$979$	−32.7558	−	18.9116i	−1.04688	−	0.604417i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−11.1677	−	19.3430i	−0.356195	−	0.616947i	0.631127	−	0.775679i	$-0.282593\pi$
$983$	−11.1677	−	19.3430i	−0.356195	−	0.616947i	−0.987322	+	0.158732i	$0.949259\pi$
$984$		0			0
$985$	−49.6788	−	86.0462i	−1.58290	−	2.74166i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	47.8139i		−	1.52040i
$990$		0			0
$991$	45.4902	−	26.2638i	1.44504	−	0.834296i	0.446864	−	0.894602i	$-0.352541\pi$
$991$	45.4902	−	26.2638i	1.44504	−	0.834296i	0.998180	+	0.0603055i	$0.0192075\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			49.3640i			1.56494i
$996$		0			0
$997$	−1.12647	+	1.95111i	−0.0356758	+	0.0617923i	−0.883312	−	0.468786i	$-0.844692\pi$
$997$	−1.12647	+	1.95111i	−0.0356758	+	0.0617923i	0.847636	+	0.530578i	$0.178025\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.dc.e.449.10		20
3.2	odd	2		2736.2.dc.f.449.1		20
4.3	odd	2		1368.2.cu.a.449.10	✓	20
12.11	even	2		1368.2.cu.b.449.1	yes	20
19.8	odd	6		2736.2.dc.f.1889.1		20
57.8	even	6	inner	2736.2.dc.e.1889.10		20
76.27	even	6		1368.2.cu.b.521.1	yes	20
228.179	odd	6		1368.2.cu.a.521.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1368.2.cu.a.449.10	✓	20	4.3	odd	2
1368.2.cu.a.521.10	yes	20	228.179	odd	6
1368.2.cu.b.449.1	yes	20	12.11	even	2
1368.2.cu.b.521.1	yes	20	76.27	even	6
2736.2.dc.e.449.10		20	1.1	even	1	trivial
2736.2.dc.e.1889.10		20	57.8	even	6	inner
2736.2.dc.f.449.1		20	3.2	odd	2
2736.2.dc.f.1889.1		20	19.8	odd	6

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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:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.dc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.15998 - 1.82441i) q^{5} -1.21776 q^{7} +O(q^{10})\)	\(q+(3.15998 - 1.82441i) q^{5} -1.21776 q^{7} -3.18751i q^{11} +(3.24494 + 1.87347i) q^{13} +(-5.49639 + 3.17334i) q^{17} +(-1.51988 - 4.08534i) q^{19} +(-8.02130 - 4.63110i) q^{23} +(4.15696 - 7.20007i) q^{25} +(2.76663 - 4.79194i) q^{29} -7.28254i q^{31} +(-3.84810 + 2.22170i) q^{35} +7.63900i q^{37} +(-5.22131 - 9.04357i) q^{41} +(2.58113 + 4.47065i) q^{43} +(9.64157 + 5.56656i) q^{47} -5.51706 q^{49} +(6.30713 - 10.9243i) q^{53} +(-5.81533 - 10.0725i) q^{55} +(4.27618 + 7.40656i) q^{59} +(1.41554 - 2.45179i) q^{61} +13.6719 q^{65} +(-6.06428 - 3.50122i) q^{67} +(-1.96187 - 3.39806i) q^{71} +(-1.32730 - 2.29894i) q^{73} +3.88163i q^{77} +(-7.33078 + 4.23243i) q^{79} +0.122929i q^{83} +(-11.5790 + 20.0554i) q^{85} +(5.93303 - 10.2763i) q^{89} +(-3.95157 - 2.28144i) q^{91} +(-12.2561 - 10.1367i) q^{95} +(-7.33810 + 4.23665i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{7}+O(q^{10}) \) 20 * q + 4 * q^7	\( 20 q + 4 q^{7} + 6 q^{13} - 12 q^{17} - 4 q^{19} + 14 q^{25} - 12 q^{35} - 8 q^{41} + 2 q^{43} - 36 q^{47} + 32 q^{49} + 8 q^{53} - 12 q^{55} + 8 q^{59} - 2 q^{61} - 8 q^{65} - 30 q^{67} - 4 q^{71} - 22 q^{73} - 54 q^{79} - 4 q^{85} + 32 q^{89} - 18 q^{91} - 32 q^{95} + 12 q^{97}+O(q^{100}) \) 20 * q + 4 * q^7 + 6 * q^13 - 12 * q^17 - 4 * q^19 + 14 * q^25 - 12 * q^35 - 8 * q^41 + 2 * q^43 - 36 * q^47 + 32 * q^49 + 8 * q^53 - 12 * q^55 + 8 * q^59 - 2 * q^61 - 8 * q^65 - 30 * q^67 - 4 * q^71 - 22 * q^73 - 54 * q^79 - 4 * q^85 + 32 * q^89 - 18 * q^91 - 32 * q^95 + 12 * q^97

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