LMFDB - Embedded newform 2736.2.dc.f.1889.10

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			1889.10
Root			$-1.12095 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2736.1889
Dual form			2736.2.dc.f.449.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.57821 + 2.06588i) q^{5} +0.233685 q^{7} +O(q^{10})$	$q+(3.57821 + 2.06588i) q^{5} +0.233685 q^{7} -3.83309i q^{11} +(2.59762 - 1.49974i) q^{13} +(0.815683 + 0.470935i) q^{17} +(3.73462 - 2.24781i) q^{19} +(-1.80489 + 1.04205i) q^{23} +(6.03571 + 10.4542i) q^{25} +(-0.168517 - 0.291880i) q^{29} -0.259383i q^{31} +(0.836175 + 0.482766i) q^{35} -2.86497i q^{37} +(4.65716 - 8.06644i) q^{41} +(4.13427 - 7.16077i) q^{43} +(1.21822 - 0.703342i) q^{47} -6.94539 q^{49} +(0.843942 + 1.46175i) q^{53} +(7.91870 - 13.7156i) q^{55} +(1.25135 - 2.16740i) q^{59} +(-1.69679 - 2.93893i) q^{61} +12.3931 q^{65} +(5.78802 - 3.34172i) q^{67} +(-7.36634 + 12.7589i) q^{71} +(-1.26518 + 2.19135i) q^{73} -0.895738i q^{77} +(-9.48364 - 5.47538i) q^{79} +13.0654i q^{83} +(1.94579 + 3.37020i) q^{85} +(7.36865 + 12.7629i) q^{89} +(0.607026 - 0.350467i) q^{91} +(18.0069 - 0.327868i) q^{95} +(11.9493 + 6.89893i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

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

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
$5$	3.57821	+	2.06588i	1.60022	+	0.923889i	0.991442	+	0.130551i	$0.0416747\pi$
$5$	3.57821	+	2.06588i	1.60022	+	0.923889i	0.608781	+	0.793338i	$0.291659\pi$
$6$		0			0
$7$	0.233685			0.0883248			0.0441624	−	0.999024i	$-0.485938\pi$
$7$	0.233685			0.0883248			0.0441624	+	0.999024i	$0.485938\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	3.83309i		−	1.15572i	−0.816136	−	0.577860i	$-0.803888\pi$
$11$		−	3.83309i		−	1.15572i	0.816136	−	0.577860i	$-0.196112\pi$
$12$		0			0
$13$	2.59762	−	1.49974i	0.720450	−	0.415952i	−0.0944682	−	0.995528i	$-0.530115\pi$
$13$	2.59762	−	1.49974i	0.720450	−	0.415952i	0.814918	+	0.579576i	$0.196782\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.815683	+	0.470935i	0.197832	+	0.114218i	0.595644	−	0.803249i	$-0.296897\pi$
$17$	0.815683	+	0.470935i	0.197832	+	0.114218i	−0.397812	+	0.917467i	$0.630230\pi$
$18$		0			0
$19$	3.73462	−	2.24781i	0.856779	−	0.515683i
$19$	3.73462	−	2.24781i	0.856779	−	0.515683i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.80489	+	1.04205i	−0.376345	+	0.217283i	−0.676227	−	0.736693i	$-0.736386\pi$
$23$	−1.80489	+	1.04205i	−0.376345	+	0.217283i	0.299882	+	0.953976i	$0.403053\pi$
$24$		0			0
$25$	6.03571	+	10.4542i	1.20714	+	2.09083i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.168517	−	0.291880i	−0.0312928	−	0.0542007i	0.849955	−	0.526855i	$-0.176629\pi$
$29$	−0.168517	−	0.291880i	−0.0312928	−	0.0542007i	−0.881248	+	0.472655i	$0.843296\pi$
$30$		0			0
$31$		−	0.259383i		−	0.0465866i	−0.999729	−	0.0232933i	$-0.992585\pi$
$31$		−	0.259383i		−	0.0465866i	0.999729	−	0.0232933i	$-0.00741517\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.836175	+	0.482766i	0.141339	+	0.0816023i
$36$		0			0
$37$		−	2.86497i		−	0.470999i	−0.971875	−	0.235499i	$-0.924327\pi$
$37$		−	2.86497i		−	0.470999i	0.971875	−	0.235499i	$-0.0756725\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.65716	−	8.06644i	0.727327	−	1.25977i	−0.230682	−	0.973029i	$-0.574096\pi$
$41$	4.65716	−	8.06644i	0.727327	−	1.25977i	0.958009	−	0.286738i	$-0.0925708\pi$
$42$		0			0
$43$	4.13427	−	7.16077i	0.630470	−	1.09201i	−0.356985	−	0.934110i	$-0.616195\pi$
$43$	4.13427	−	7.16077i	0.630470	−	1.09201i	0.987456	−	0.157897i	$-0.0504713\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.21822	−	0.703342i	0.177696	−	0.102593i	−0.408514	−	0.912752i	$-0.633953\pi$
$47$	1.21822	−	0.703342i	0.177696	−	0.102593i	0.586210	+	0.810159i	$0.300619\pi$
$48$		0			0
$49$	−6.94539			−0.992199
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.843942	+	1.46175i	0.115924	+	0.200787i	0.918149	−	0.396236i	$-0.129684\pi$
$53$	0.843942	+	1.46175i	0.115924	+	0.200787i	−0.802224	+	0.597023i	$0.796350\pi$
$54$		0			0
$55$	7.91870	−	13.7156i	1.06776	−	1.84941i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.25135	−	2.16740i	0.162912	−	0.282172i	−0.773000	−	0.634406i	$-0.781245\pi$
$59$	1.25135	−	2.16740i	0.162912	−	0.282172i	0.935912	+	0.352234i	$0.114578\pi$
$60$		0			0
$61$	−1.69679	−	2.93893i	−0.217252	−	0.376292i	0.736715	−	0.676204i	$-0.236376\pi$
$61$	−1.69679	−	2.93893i	−0.217252	−	0.376292i	−0.953967	+	0.299912i	$0.903043\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	12.3931			1.53717
$66$		0			0
$67$	5.78802	−	3.34172i	0.707120	−	0.408256i	−0.102874	−	0.994694i	$-0.532804\pi$
$67$	5.78802	−	3.34172i	0.707120	−	0.408256i	0.809994	+	0.586439i	$0.199471\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.36634	+	12.7589i	−0.874224	+	1.51420i	−0.0166359	+	0.999862i	$0.505296\pi$
$71$	−7.36634	+	12.7589i	−0.874224	+	1.51420i	−0.857588	+	0.514338i	$0.828038\pi$
$72$		0			0
$73$	−1.26518	+	2.19135i	−0.148078	+	0.256478i	−0.930517	−	0.366249i	$-0.880642\pi$
$73$	−1.26518	+	2.19135i	−0.148078	+	0.256478i	0.782439	+	0.622727i	$0.213975\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	0.895738i		−	0.102079i
$78$		0			0
$79$	−9.48364	−	5.47538i	−1.06699	−	0.616028i	−0.139634	−	0.990203i	$-0.544593\pi$
$79$	−9.48364	−	5.47538i	−1.06699	−	0.616028i	−0.927358	+	0.374175i	$0.877926\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			13.0654i			1.43411i	0.697016	+	0.717056i	$0.254511\pi$
$83$			13.0654i			1.43411i	−0.697016	+	0.717056i	$0.745489\pi$
$84$		0			0
$85$	1.94579	+	3.37020i	0.211050	+	0.365550i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.36865	+	12.7629i	0.781076	+	1.35286i	0.931316	+	0.364213i	$0.118662\pi$
$89$	7.36865	+	12.7629i	0.781076	+	1.35286i	−0.150240	+	0.988650i	$0.548005\pi$
$90$		0			0
$91$	0.607026	−	0.350467i	0.0636336	−	0.0367389i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	18.0069	−	0.327868i	1.84747	−	0.0336386i
$96$		0			0
$97$	11.9493	+	6.89893i	1.21327	+	0.700480i	0.963470	−	0.267817i	$-0.0863024\pi$
$97$	11.9493	+	6.89893i	1.21327	+	0.700480i	0.249798	+	0.968298i	$0.419636\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−12.6669	+	7.31321i	−1.26040	+	0.727692i	−0.973152	−	0.230165i	$-0.926073\pi$
$101$	−12.6669	+	7.31321i	−1.26040	+	0.727692i	−0.287247	+	0.957856i	$0.592740\pi$
$102$		0			0
$103$			4.43124i			0.436623i	0.975879	+	0.218311i	$0.0700548\pi$
$103$			4.43124i			0.436623i	−0.975879	+	0.218311i	$0.929945\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−11.5455			−1.11614			−0.558072	−	0.829793i	$-0.688459\pi$
$107$	−11.5455			−1.11614			−0.558072	+	0.829793i	$0.688459\pi$
$108$		0			0
$109$	−14.3129	−	8.26354i	−1.37092	−	0.791503i	−0.379880	−	0.925036i	$-0.624035\pi$
$109$	−14.3129	−	8.26354i	−1.37092	−	0.791503i	−0.991044	+	0.133532i	$0.957368\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.29262			0.686032			0.343016	−	0.939330i	$-0.388551\pi$
$113$	7.29262			0.686032			0.343016	+	0.939330i	$0.388551\pi$
$114$		0			0
$115$	−8.61101			−0.802981
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.190613	+	0.110051i	0.0174735	+	0.0100883i
$120$		0			0
$121$	−3.69260			−0.335691
$122$		0			0
$123$		0			0
$124$		0			0
$125$			29.2174i			2.61328i
$126$		0			0
$127$	−7.31317	+	4.22226i	−0.648939	+	0.374665i	−0.788049	−	0.615612i	$-0.788909\pi$
$127$	−7.31317	+	4.22226i	−0.648939	+	0.374665i	0.139111	+	0.990277i	$0.455576\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	16.8762	+	9.74347i	1.47448	+	0.851291i	0.999587	−	0.0287522i	$-0.00915338\pi$
$131$	16.8762	+	9.74347i	1.47448	+	0.851291i	0.474893	+	0.880043i	$0.342487\pi$
$132$		0			0
$133$	0.872725	−	0.525281i	0.0756749	−	0.0455476i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.6567	−	7.88469i	1.16677	−	0.673635i	0.213853	−	0.976866i	$-0.431399\pi$
$137$	13.6567	−	7.88469i	1.16677	−	0.673635i	0.952917	+	0.303231i	$0.0980654\pi$
$138$		0			0
$139$	−0.0918598	−	0.159106i	−0.00779145	−	0.0134952i	0.862103	−	0.506732i	$-0.169147\pi$
$139$	−0.0918598	−	0.159106i	−0.00779145	−	0.0134952i	−0.869895	+	0.493237i	$0.835813\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5.74863	−	9.95692i	−0.480725	−	0.832639i
$144$		0			0
$145$		−	1.39254i		−	0.115644i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	12.6103	+	7.28056i	1.03308	+	0.596447i	0.917865	−	0.396894i	$-0.129912\pi$
$149$	12.6103	+	7.28056i	1.03308	+	0.596447i	0.115212	+	0.993341i	$0.463245\pi$
$150$		0			0
$151$		−	18.1826i		−	1.47968i	−0.672783	−	0.739840i	$-0.734901\pi$
$151$		−	18.1826i		−	1.47968i	0.672783	−	0.739840i	$-0.265099\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.535855	−	0.928128i	0.0430409	−	0.0745490i
$156$		0			0
$157$	6.07032	−	10.5141i	0.484464	−	0.839116i	−0.515377	−	0.856964i	$-0.672348\pi$
$157$	6.07032	−	10.5141i	0.484464	−	0.839116i	0.999841	+	0.0178475i	$0.00568135\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.421776	+	0.243512i	−0.0332406	+	0.0191915i
$162$		0			0
$163$	−20.0637			−1.57151			−0.785756	−	0.618537i	$-0.787726\pi$
$163$	−20.0637			−1.57151			−0.785756	+	0.618537i	$0.787726\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.79939	−	11.7769i	−0.526153	−	0.911323i	−0.999536	−	0.0304667i	$-0.990301\pi$
$167$	−6.79939	−	11.7769i	−0.526153	−	0.911323i	0.473383	−	0.880857i	$-0.343033\pi$
$168$		0			0
$169$	−2.00158	+	3.46684i	−0.153968	+	0.266680i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.61797	+	4.53447i	−0.199041	+	0.344749i	−0.948218	−	0.317621i	$-0.897116\pi$
$173$	−2.61797	+	4.53447i	−0.199041	+	0.344749i	0.749177	+	0.662370i	$0.230449\pi$
$174$		0			0
$175$	1.41046	+	2.44299i	0.106621	+	0.184672i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	5.50094			0.411160			0.205580	−	0.978640i	$-0.434092\pi$
$179$	5.50094			0.411160			0.205580	+	0.978640i	$0.434092\pi$
$180$		0			0
$181$	2.29549	−	1.32530i	0.170622	−	0.0985089i	−0.412257	−	0.911068i	$-0.635259\pi$
$181$	2.29549	−	1.32530i	0.170622	−	0.0985089i	0.582879	+	0.812559i	$0.301926\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	5.91869	−	10.2515i	0.435151	−	0.753703i
$186$		0			0
$187$	1.80514	−	3.12659i	0.132005	−	0.228639i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			21.9184i			1.58596i	0.609246	+	0.792981i	$0.291472\pi$
$191$			21.9184i			1.58596i	−0.609246	+	0.792981i	$0.708528\pi$
$192$		0			0
$193$	−23.0630	−	13.3154i	−1.66011	−	0.958464i	−0.972661	−	0.232228i	$-0.925398\pi$
$193$	−23.0630	−	13.3154i	−1.66011	−	0.958464i	−0.687446	−	0.726235i	$-0.741268\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			13.0508i			0.929834i	0.885354	+	0.464917i	$0.153916\pi$
$197$			13.0508i			0.929834i	−0.885354	+	0.464917i	$0.846084\pi$
$198$		0			0
$199$	10.2572	+	17.7660i	0.727112	+	1.25940i	0.958099	+	0.286438i	$0.0924713\pi$
$199$	10.2572	+	17.7660i	0.727112	+	1.25940i	−0.230987	+	0.972957i	$0.574195\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.0393799	−	0.0682080i	−0.00276393	−	0.00478726i
$204$		0			0
$205$	33.3286	−	19.2423i	2.32777	−	1.34394i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−8.61606	−	14.3151i	−0.595986	−	0.990198i
$210$		0			0
$211$	11.5524	+	6.66978i	0.795300	+	0.459166i	0.841825	−	0.539751i	$-0.181481\pi$
$211$	11.5524	+	6.66978i	0.795300	+	0.459166i	−0.0465253	+	0.998917i	$0.514815\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	29.5866	−	17.0818i	2.01779	−	1.16497i
$216$		0			0
$217$		−	0.0606141i		−	0.00411476i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.82511			0.190038
$222$		0			0
$223$	22.5138	+	12.9983i	1.50763	+	0.870432i	0.999961	+	0.00888167i	$0.00282716\pi$
$223$	22.5138	+	12.9983i	1.50763	+	0.870432i	0.507672	+	0.861550i	$0.330506\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.03635			0.201530			0.100765	−	0.994910i	$-0.467871\pi$
$227$	3.03635			0.201530			0.100765	+	0.994910i	$0.467871\pi$
$228$		0			0
$229$	7.85030			0.518762			0.259381	−	0.965775i	$-0.416481\pi$
$229$	7.85030			0.518762			0.259381	+	0.965775i	$0.416481\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−18.3275	−	10.5814i	−1.20067	−	0.693210i	−0.239970	−	0.970780i	$-0.577137\pi$
$233$	−18.3275	−	10.5814i	−1.20067	−	0.693210i	−0.960705	+	0.277570i	$0.910471\pi$
$234$		0			0
$235$	5.81208			0.379138
$236$		0			0
$237$		0			0
$238$		0			0
$239$			21.3116i			1.37853i	0.724509	+	0.689266i	$0.242067\pi$
$239$			21.3116i			1.37853i	−0.724509	+	0.689266i	$0.757933\pi$
$240$		0			0
$241$	8.58273	−	4.95524i	0.552862	−	0.319195i	−0.197413	−	0.980320i	$-0.563254\pi$
$241$	8.58273	−	4.95524i	0.552862	−	0.319195i	0.750276	+	0.661125i	$0.229921\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−24.8520	−	14.3483i	−1.58774	−	0.916682i
$246$		0			0
$247$	6.32999	−	11.4399i	0.402767	−	0.727903i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−25.3157	+	14.6160i	−1.59791	+	0.922555i	−0.606024	+	0.795446i	$0.707237\pi$
$251$	−25.3157	+	14.6160i	−1.59791	+	0.922555i	−0.991889	+	0.127109i	$0.959430\pi$
$252$		0			0
$253$	3.99428	+	6.91830i	0.251118	+	0.434950i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.12480	−	15.8046i	−0.569189	−	0.985865i	−0.996646	−	0.0818292i	$-0.973924\pi$
$257$	−9.12480	−	15.8046i	−0.569189	−	0.985865i	0.427457	−	0.904036i	$-0.359410\pi$
$258$		0			0
$259$		−	0.669503i		−	0.0416009i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.80172	+	1.04023i	0.111099	+	0.0641430i	0.554520	−	0.832170i	$-0.312902\pi$
$263$	1.80172	+	1.04023i	0.111099	+	0.0641430i	−0.443421	+	0.896314i	$0.646235\pi$
$264$		0			0
$265$			6.97393i			0.428405i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.33955	+	7.51632i	−0.264587	+	0.458278i	−0.967455	−	0.253042i	$-0.918569\pi$
$269$	−4.33955	+	7.51632i	−0.264587	+	0.458278i	0.702868	+	0.711320i	$0.251902\pi$
$270$		0			0
$271$	−6.98572	+	12.0996i	−0.424352	+	0.734999i	−0.996360	−	0.0852489i	$-0.972831\pi$
$271$	−6.98572	+	12.0996i	−0.424352	+	0.734999i	0.572008	+	0.820248i	$0.306165\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	40.0718	−	23.1354i	2.41642	−	1.39512i
$276$		0			0
$277$	−0.649644			−0.0390333			−0.0195167	−	0.999810i	$-0.506213\pi$
$277$	−0.649644			−0.0390333			−0.0195167	+	0.999810i	$0.506213\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.22444	−	15.9772i	−0.550284	−	0.953120i	−0.998254	−	0.0590713i	$-0.981186\pi$
$281$	−9.22444	−	15.9772i	−0.550284	−	0.953120i	0.447970	−	0.894049i	$-0.352147\pi$
$282$		0			0
$283$	8.95163	−	15.5047i	0.532119	−	0.921657i	−0.467178	−	0.884163i	$-0.654729\pi$
$283$	8.95163	−	15.5047i	0.532119	−	0.921657i	0.999297	−	0.0374939i	$-0.0119375\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.08831	−	1.88501i	0.0642410	−	0.111269i
$288$		0			0
$289$	−8.05644	−	13.9542i	−0.473908	−	0.820833i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	24.2622			1.41741			0.708706	−	0.705504i	$-0.249279\pi$
$293$	24.2622			1.41741			0.708706	+	0.705504i	$0.249279\pi$
$294$		0			0
$295$	8.95518	−	5.17028i	0.521391	−	0.301025i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.12561	+	5.41371i	−0.180759	+	0.313083i
$300$		0			0
$301$	0.966119	−	1.67337i	0.0556862	−	0.0964513i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	14.0215i		−	0.802868i
$306$		0			0
$307$	21.4306	+	12.3730i	1.22311	+	0.706162i	0.965579	−	0.260109i	$-0.0837585\pi$
$307$	21.4306	+	12.3730i	1.22311	+	0.706162i	0.257529	+	0.966271i	$0.417092\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		−	17.1175i		−	0.970646i	−0.874335	−	0.485323i	$-0.838702\pi$
$311$		−	17.1175i		−	0.970646i	0.874335	−	0.485323i	$-0.161298\pi$
$312$		0			0
$313$	−6.59308	−	11.4196i	−0.372663	−	0.645471i	0.617311	−	0.786719i	$-0.288222\pi$
$313$	−6.59308	−	11.4196i	−0.372663	−	0.645471i	−0.989974	+	0.141248i	$0.954889\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.08220	−	1.87442i	−0.0607824	−	0.105278i	0.834033	−	0.551715i	$-0.186026\pi$
$317$	−1.08220	−	1.87442i	−0.0607824	−	0.105278i	−0.894815	+	0.446436i	$0.852693\pi$
$318$		0			0
$319$	−1.11880	+	0.645940i	−0.0626409	+	0.0361657i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.10483	−	0.0747404i	0.228399	−	0.00415867i
$324$		0			0
$325$	31.3570	+	18.1040i	1.73937	+	1.00423i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.284681	−	0.164361i	0.0156950	−	0.00906151i
$330$		0			0
$331$			31.4649i			1.72947i	0.502230	+	0.864734i	$0.332513\pi$
$331$			31.4649i			1.72947i	−0.502230	+	0.864734i	$0.667487\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	27.6143			1.50873
$336$		0			0
$337$	−20.4827	−	11.8257i	−1.11577	−	0.644188i	−0.175449	−	0.984488i	$-0.556138\pi$
$337$	−20.4827	−	11.8257i	−1.11577	−	0.644188i	−0.940317	+	0.340301i	$0.889471\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.994241			−0.0538412
$342$		0			0
$343$	−3.25884			−0.175961
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.8999	+	6.87040i	0.638819	+	0.368822i	0.784160	−	0.620559i	$-0.213094\pi$
$347$	11.8999	+	6.87040i	0.638819	+	0.368822i	−0.145340	+	0.989382i	$0.546428\pi$
$348$		0			0
$349$	−4.38511			−0.234730			−0.117365	−	0.993089i	$-0.537445\pi$
$349$	−4.38511			−0.234730			−0.117365	+	0.993089i	$0.537445\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			31.0301i			1.65157i	0.563988	+	0.825783i	$0.309266\pi$
$353$			31.0301i			1.65157i	−0.563988	+	0.825783i	$0.690734\pi$
$354$		0			0
$355$	−52.7166	+	30.4359i	−2.79791	+	1.61537i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−32.2953	−	18.6457i	−1.70448	−	0.984081i	−0.941100	−	0.338130i	$-0.890206\pi$
$359$	−32.2953	−	18.6457i	−1.70448	−	0.984081i	−0.763379	−	0.645951i	$-0.776461\pi$
$360$		0			0
$361$	8.89470	−	16.7894i	0.468142	−	0.883653i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−9.05412	+	5.22740i	−0.473914	+	0.273615i
$366$		0			0
$367$	9.17682	+	15.8947i	0.479026	+	0.829697i	0.999711	−	0.0240518i	$-0.00765667\pi$
$367$	9.17682	+	15.8947i	0.479026	+	0.829697i	−0.520685	+	0.853749i	$0.674323\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.197217	+	0.341590i	0.0102390	+	0.0177345i
$372$		0			0
$373$		−	9.90763i		−	0.512998i	−0.966545	−	0.256499i	$-0.917431\pi$
$373$		−	9.90763i		−	0.512998i	0.966545	−	0.256499i	$-0.0825690\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.875485	−	0.505462i	−0.0450898	−	0.0260326i
$378$		0			0
$379$		−	26.5428i		−	1.36341i	−0.731627	−	0.681705i	$-0.761239\pi$
$379$		−	26.5428i		−	1.36341i	0.731627	−	0.681705i	$-0.238761\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−13.9069	+	24.0874i	−0.710608	+	1.23081i	0.254021	+	0.967199i	$0.418247\pi$
$383$	−13.9069	+	24.0874i	−0.710608	+	1.23081i	−0.964629	+	0.263611i	$0.915087\pi$
$384$		0			0
$385$	1.85049	−	3.20514i	0.0943095	−	0.163349i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.28250	−	1.89515i	0.166430	−	0.0960881i	−0.414472	−	0.910062i	$-0.636034\pi$
$389$	3.28250	−	1.89515i	0.166430	−	0.0960881i	0.580901	+	0.813974i	$0.302700\pi$
$390$		0			0
$391$	−1.96295			−0.0992709
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−22.6229	−	39.1841i	−1.13828	−	1.97157i
$396$		0			0
$397$	−9.22524	+	15.9786i	−0.463002	+	0.801942i	−0.999109	−	0.0422076i	$-0.986561\pi$
$397$	−9.22524	+	15.9786i	−0.463002	+	0.801942i	0.536107	+	0.844150i	$0.319894\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.00465	−	1.74011i	0.0501701	−	0.0868971i	−0.839850	−	0.542819i	$-0.817357\pi$
$401$	1.00465	−	1.74011i	0.0501701	−	0.0868971i	0.890020	+	0.455922i	$0.150690\pi$
$402$		0			0
$403$	−0.389007	−	0.673780i	−0.0193778	−	0.0335634i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−10.9817			−0.544343
$408$		0			0
$409$	16.3465	−	9.43768i	0.808285	−	0.466663i	−0.0380751	−	0.999275i	$-0.512123\pi$
$409$	16.3465	−	9.43768i	0.808285	−	0.466663i	0.846360	+	0.532611i	$0.178789\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.292422	−	0.506491i	0.0143892	−	0.0249228i
$414$		0			0
$415$	−26.9915	+	46.7506i	−1.32496	+	2.29490i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			2.06748i			0.101003i	0.998724	+	0.0505015i	$0.0160820\pi$
$419$			2.06748i			0.101003i	−0.998724	+	0.0505015i	$0.983918\pi$
$420$		0			0
$421$	0.284368	+	0.164180i	0.0138592	+	0.00800164i	0.506914	−	0.861997i	$-0.330786\pi$
$421$	0.284368	+	0.164180i	0.0138592	+	0.00800164i	−0.493054	+	0.869998i	$0.664120\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$			11.3697i			0.551512i
$426$		0			0
$427$	−0.396516	−	0.686786i	−0.0191888	−	0.0332359i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.00313	−	1.73748i	−0.0483193	−	0.0836914i	0.840854	−	0.541262i	$-0.182053\pi$
$431$	−1.00313	−	1.73748i	−0.0483193	−	0.0836914i	−0.889173	+	0.457570i	$0.848720\pi$
$432$		0			0
$433$	16.5144	−	9.53457i	0.793629	−	0.458202i	−0.0476094	−	0.998866i	$-0.515160\pi$
$433$	16.5144	−	9.53457i	0.793629	−	0.458202i	0.841239	+	0.540664i	$0.181827\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.39822	+	7.94871i	−0.210396	+	0.380238i
$438$		0			0
$439$	−9.31280	−	5.37675i	−0.444476	−	0.256618i	0.261019	−	0.965334i	$-0.415942\pi$
$439$	−9.31280	−	5.37675i	−0.444476	−	0.256618i	−0.705494	+	0.708716i	$0.749275\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.31062	+	2.48874i	−0.204804	+	0.118244i	−0.598894	−	0.800828i	$-0.704393\pi$
$443$	−4.31062	+	2.48874i	−0.204804	+	0.118244i	0.394090	+	0.919072i	$0.371060\pi$
$444$		0			0
$445$			60.8910i			2.88651i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−20.3077			−0.958379			−0.479189	−	0.877711i	$-0.659069\pi$
$449$	−20.3077			−0.958379			−0.479189	+	0.877711i	$0.659069\pi$
$450$		0			0
$451$	−30.9194	−	17.8513i	−1.45594	−	0.840587i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.89609			0.135771
$456$		0			0
$457$	−41.6599			−1.94877			−0.974385	−	0.224887i	$-0.927799\pi$
$457$	−41.6599			−1.94877			−0.974385	+	0.224887i	$0.927799\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−18.5985	−	10.7378i	−0.866217	−	0.500110i	−0.000127444	−	1.00000i	$-0.500041\pi$
$461$	−18.5985	−	10.7378i	−0.866217	−	0.500110i	−0.866089	+	0.499890i	$0.833374\pi$
$462$		0			0
$463$	−22.3345			−1.03797			−0.518987	−	0.854782i	$-0.673691\pi$
$463$	−22.3345			−1.03797			−0.518987	+	0.854782i	$0.673691\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	23.9475i		−	1.10816i	−0.832464	−	0.554079i	$-0.813070\pi$
$467$		−	23.9475i		−	1.10816i	0.832464	−	0.554079i	$-0.186930\pi$
$468$		0			0
$469$	1.35258	−	0.780911i	0.0624562	−	0.0360591i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−27.4479	−	15.8470i	−1.26205	−	0.728648i
$474$		0			0
$475$	46.0400	+	25.4751i	2.11246	+	1.16888i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−17.7141	+	10.2272i	−0.809377	+	0.467294i	−0.846740	−	0.532008i	$-0.821438\pi$
$479$	−17.7141	+	10.2272i	−0.809377	+	0.467294i	0.0373622	+	0.999302i	$0.488104\pi$
$480$		0			0
$481$	−4.29670	−	7.44211i	−0.195913	−	0.339331i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	28.5047	+	49.3716i	1.29433	+	2.24185i
$486$		0			0
$487$		−	25.7852i		−	1.16844i	−0.811596	−	0.584220i	$-0.801401\pi$
$487$		−	25.7852i		−	1.16844i	0.811596	−	0.584220i	$-0.198599\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.77306	+	1.02367i	0.0800169	+	0.0461978i	0.539475	−	0.842002i	$-0.318623\pi$
$491$	1.77306	+	1.02367i	0.0800169	+	0.0461978i	−0.459458	+	0.888200i	$0.651956\pi$
$492$		0			0
$493$		−	0.317442i		−	0.0142969i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.72141	+	2.98156i	−0.0772156	+	0.133741i
$498$		0			0
$499$	−4.14368	+	7.17707i	−0.185497	+	0.321290i	−0.943744	−	0.330678i	$-0.892723\pi$
$499$	−4.14368	+	7.17707i	−0.185497	+	0.321290i	0.758247	+	0.651967i	$0.226056\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	17.8059	−	10.2803i	0.793927	−	0.458374i	−0.0474160	−	0.998875i	$-0.515099\pi$
$503$	17.8059	−	10.2803i	0.793927	−	0.458374i	0.841343	+	0.540501i	$0.181765\pi$
$504$		0			0
$505$	−60.4328			−2.68923
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.595348	−	1.03117i	−0.0263884	−	0.0457060i	0.852530	−	0.522679i	$-0.175067\pi$
$509$	−0.595348	−	1.03117i	−0.0263884	−	0.0457060i	−0.878918	+	0.476973i	$0.841734\pi$
$510$		0			0
$511$	−0.295653	+	0.512086i	−0.0130789	+	0.0226534i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−9.15440	+	15.8559i	−0.403391	+	0.698694i
$516$		0			0
$517$	−2.69598	−	4.66957i	−0.118569	−	0.205367i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	10.5060			0.460276			0.230138	−	0.973158i	$-0.426082\pi$
$521$	10.5060			0.460276			0.230138	+	0.973158i	$0.426082\pi$
$522$		0			0
$523$	22.8222	−	13.1764i	0.997946	−	0.576164i	0.0903058	−	0.995914i	$-0.471216\pi$
$523$	22.8222	−	13.1764i	0.997946	−	0.576164i	0.907640	+	0.419750i	$0.137882\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.122153	−	0.211575i	0.00532105	−	0.00921634i
$528$		0			0
$529$	−9.32825	+	16.1570i	−0.405576	+	0.702479i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	27.9381i		−	1.21013i
$534$		0			0
$535$	−41.3121	−	23.8516i	−1.78608	−	1.03119i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			26.6223i			1.14670i
$540$		0			0
$541$	2.53096	+	4.38375i	0.108814	+	0.188472i	0.915290	−	0.402795i	$-0.131961\pi$
$541$	2.53096	+	4.38375i	0.108814	+	0.188472i	−0.806476	+	0.591267i	$0.798628\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−34.1429	−	59.1373i	−1.46252	−	2.53316i
$546$		0			0
$547$	0.727431	−	0.419983i	0.0311027	−	0.0179572i	−0.484368	−	0.874864i	$-0.660950\pi$
$547$	0.727431	−	0.419983i	0.0311027	−	0.0179572i	0.515471	+	0.856907i	$0.327617\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.28544	−	0.711264i	−0.0547614	−	0.0303009i
$552$		0			0
$553$	−2.21619	−	1.27952i	−0.0942419	−	0.0544106i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	17.6406	−	10.1848i	0.747455	−	0.431543i	−0.0773186	−	0.997006i	$-0.524636\pi$
$557$	17.6406	−	10.1848i	0.747455	−	0.431543i	0.824774	+	0.565463i	$0.191303\pi$
$558$		0			0
$559$		−	24.8013i		−	1.04898i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−33.7731			−1.42337			−0.711683	−	0.702501i	$-0.752067\pi$
$563$	−33.7731			−1.42337			−0.711683	+	0.702501i	$0.752067\pi$
$564$		0			0
$565$	26.0945	+	15.0657i	1.09780	+	0.633818i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	0.869144			0.0364364			0.0182182	−	0.999834i	$-0.494201\pi$
$569$	0.869144			0.0364364			0.0182182	+	0.999834i	$0.494201\pi$
$570$		0			0
$571$	−32.1179			−1.34409			−0.672045	−	0.740510i	$-0.734584\pi$
$571$	−32.1179			−1.34409			−0.672045	+	0.740510i	$0.734584\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−21.7876	−	12.5791i	−0.908604	−	0.524583i
$576$		0			0
$577$	−23.1682			−0.964506			−0.482253	−	0.876032i	$-0.660181\pi$
$577$	−23.1682			−0.964506			−0.482253	+	0.876032i	$0.660181\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$			3.05319i			0.126668i
$582$		0			0
$583$	5.60303	−	3.23491i	0.232054	−	0.133976i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.8667	−	8.58330i	−0.613615	−	0.354271i	0.160764	−	0.986993i	$-0.448604\pi$
$587$	−14.8667	−	8.58330i	−0.613615	−	0.354271i	−0.774379	+	0.632722i	$0.781937\pi$
$588$		0			0
$589$	−0.583045	−	0.968697i	−0.0240239	−	0.0399145i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.95632	+	2.28418i	−0.162467	+	0.0938002i	−0.579029	−	0.815307i	$-0.696568\pi$
$593$	−3.95632	+	2.28418i	−0.162467	+	0.0938002i	0.416562	+	0.909107i	$0.363235\pi$
$594$		0			0
$595$	0.454703	+	0.787568i	0.0186410	+	0.0322871i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	8.75085	+	15.1569i	0.357550	+	0.619295i	0.987551	−	0.157300i	$-0.0502788\pi$
$599$	8.75085	+	15.1569i	0.357550	+	0.619295i	−0.630001	+	0.776594i	$0.716946\pi$
$600$		0			0
$601$		−	32.0381i		−	1.30686i	−0.756986	−	0.653431i	$-0.773329\pi$
$601$		−	32.0381i		−	1.30686i	0.756986	−	0.653431i	$-0.226671\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−13.2129	−	7.62846i	−0.537180	−	0.310141i
$606$		0			0
$607$		−	19.8572i		−	0.805980i	−0.915204	−	0.402990i	$-0.867971\pi$
$607$		−	19.8572i		−	0.805980i	0.915204	−	0.402990i	$-0.132029\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.10966	−	3.65403i	0.0853475	−	0.147826i
$612$		0			0
$613$	−13.4676	+	23.3265i	−0.543950	+	0.942148i	0.454723	+	0.890633i	$0.349738\pi$
$613$	−13.4676	+	23.3265i	−0.543950	+	0.942148i	−0.998672	+	0.0515153i	$0.983595\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.150016	+	0.0866119i	−0.00603943	+	0.00348686i	−0.503017	−	0.864277i	$-0.667777\pi$
$617$	−0.150016	+	0.0866119i	−0.00603943	+	0.00348686i	0.496977	+	0.867764i	$0.334443\pi$
$618$		0			0
$619$	27.1200			1.09005			0.545023	−	0.838421i	$-0.316521\pi$
$619$	27.1200			1.09005			0.545023	+	0.838421i	$0.316521\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.72195	+	2.98250i	0.0689883	+	0.119491i
$624$		0			0
$625$	−30.1811	+	52.2752i	−1.20724	+	2.09101i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.34922	−	2.33691i	0.0537967	−	0.0931787i
$630$		0			0
$631$	−8.35471	−	14.4708i	−0.332596	−	0.576073i	0.650424	−	0.759571i	$-0.274591\pi$
$631$	−8.35471	−	14.4708i	−0.332596	−	0.576073i	−0.983020	+	0.183498i	$0.941258\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−34.8907			−1.38460
$636$		0			0
$637$	−18.0415	+	10.4163i	−0.714830	+	0.412707i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	8.93605	−	15.4777i	0.352953	−	0.611332i	−0.633813	−	0.773487i	$-0.718511\pi$
$641$	8.93605	−	15.4777i	0.352953	−	0.611332i	0.986765	+	0.162155i	$0.0518443\pi$
$642$		0			0
$643$	−2.78310	+	4.82047i	−0.109755	+	0.190101i	−0.915671	−	0.401929i	$-0.868340\pi$
$643$	−2.78310	+	4.82047i	−0.109755	+	0.190101i	0.805916	+	0.592030i	$0.201673\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	9.75898i		−	0.383665i	−0.981428	−	0.191833i	$-0.938557\pi$
$647$		−	9.75898i		−	0.383665i	0.981428	−	0.191833i	$-0.0614430\pi$
$648$		0			0
$649$	−8.30786	−	4.79654i	−0.326112	−	0.188281i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			43.9489i			1.71985i	0.510418	+	0.859927i	$0.329491\pi$
$653$			43.9489i			1.71985i	−0.510418	+	0.859927i	$0.670509\pi$
$654$		0			0
$655$	40.2577	+	69.7283i	1.57300	+	2.72451i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	17.9921	+	31.1633i	0.700874	+	1.21395i	0.968160	+	0.250332i	$0.0805398\pi$
$659$	17.9921	+	31.1633i	0.700874	+	1.21395i	−0.267286	+	0.963617i	$0.586127\pi$
$660$		0			0
$661$	2.92434	−	1.68837i	0.113744	−	0.0656699i	−0.442049	−	0.896991i	$-0.645748\pi$
$661$	2.92434	−	1.68837i	0.113744	−	0.0656699i	0.555793	+	0.831321i	$0.312415\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	4.20796	−	0.0766181i	0.163178	−	0.00297112i
$666$		0			0
$667$	0.608307	+	0.351206i	0.0235538	+	0.0135988i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−11.2652	+	6.50397i	−0.434888	+	0.251083i
$672$		0			0
$673$			41.0041i			1.58059i	0.612726	+	0.790295i	$0.290073\pi$
$673$			41.0041i			1.58059i	−0.612726	+	0.790295i	$0.709927\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.6109			−0.446243			−0.223121	−	0.974791i	$-0.571625\pi$
$677$	−11.6109			−0.446243			−0.223121	+	0.974791i	$0.571625\pi$
$678$		0			0
$679$	2.79238	+	1.61218i	0.107162	+	0.0618698i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−21.9653			−0.840479			−0.420239	−	0.907413i	$-0.638054\pi$
$683$	−21.9653			−0.840479			−0.420239	+	0.907413i	$0.638054\pi$
$684$		0			0
$685$	65.1553			2.48946
$686$		0			0
$687$		0			0
$688$		0			0
$689$	4.38448	+	2.53138i	0.167036	+	0.0964380i
$690$		0			0
$691$	7.51825			0.286008			0.143004	−	0.989722i	$-0.454324\pi$
$691$	7.51825			0.286008			0.143004	+	0.989722i	$0.454324\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	0.759085i		−	0.0287937i
$696$		0			0
$697$	7.59754	−	4.38644i	0.287777	−	0.166148i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	17.0043	+	9.81746i	0.642245	+	0.370800i	0.785479	−	0.618888i	$-0.212417\pi$
$701$	17.0043	+	9.81746i	0.642245	+	0.370800i	−0.143234	+	0.989689i	$0.545750\pi$
$702$		0			0
$703$	−6.43992	−	10.6996i	−0.242886	−	0.403542i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.96006	+	1.70899i	−0.111324	+	0.0642732i
$708$		0			0
$709$	−3.77875	−	6.54499i	−0.141914	−	0.245802i	0.786303	−	0.617841i	$-0.211992\pi$
$709$	−3.77875	−	6.54499i	−0.141914	−	0.245802i	−0.928217	+	0.372038i	$0.878659\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.270291	+	0.468158i	0.0101225	+	0.0175327i
$714$		0			0
$715$		−	47.5039i		−	1.77654i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−22.8645	−	13.2008i	−0.852703	−	0.492308i	0.00885906	−	0.999961i	$-0.497180\pi$
$719$	−22.8645	−	13.2008i	−0.852703	−	0.492308i	−0.861562	+	0.507653i	$0.830513\pi$
$720$		0			0
$721$			1.03552i			0.0385646i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.03424	−	3.52340i	0.0755497	−	0.130856i
$726$		0			0
$727$	14.5343	−	25.1742i	0.539047	−	0.933658i	−0.459908	−	0.887966i	$-0.652118\pi$
$727$	14.5343	−	25.1742i	0.539047	−	0.933658i	0.998956	−	0.0456911i	$-0.0145490\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	6.74451	−	3.89394i	0.249455	−	0.144023i
$732$		0			0
$733$	−17.3485			−0.640780			−0.320390	−	0.947286i	$-0.603814\pi$
$733$	−17.3485			−0.640780			−0.320390	+	0.947286i	$0.603814\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.8091	−	22.1860i	−0.471830	−	0.817233i
$738$		0			0
$739$	−12.3049	+	21.3127i	−0.452642	+	0.783999i	−0.998549	−	0.0538464i	$-0.982852\pi$
$739$	−12.3049	+	21.3127i	−0.452642	+	0.783999i	0.545907	+	0.837846i	$0.316185\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−9.18118	+	15.9023i	−0.336825	+	0.583398i	−0.983834	−	0.179085i	$-0.942686\pi$
$743$	−9.18118	+	15.9023i	−0.336825	+	0.583398i	0.647009	+	0.762483i	$0.276020\pi$
$744$		0			0
$745$	30.0815	+	52.1027i	1.10210	+	1.90890i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.69801			−0.0985832
$750$		0			0
$751$	−29.0160	+	16.7524i	−1.05881	+	0.611303i	−0.925102	−	0.379718i	$-0.876021\pi$
$751$	−29.0160	+	16.7524i	−1.05881	+	0.611303i	−0.133705	+	0.991021i	$0.542688\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	37.5631	−	65.0612i	1.36706	−	2.36782i
$756$		0			0
$757$	−19.7316	+	34.1762i	−0.717158	+	1.24215i	0.244964	+	0.969532i	$0.421224\pi$
$757$	−19.7316	+	34.1762i	−0.717158	+	1.24215i	−0.962121	+	0.272621i	$0.912109\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		−	26.1398i		−	0.947568i	−0.880641	−	0.473784i	$-0.842888\pi$
$761$		−	26.1398i		−	0.947568i	0.880641	−	0.473784i	$-0.157112\pi$
$762$		0			0
$763$	−3.34471	−	1.93107i	−0.121087	−	0.0699094i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	7.50679i		−	0.271054i
$768$		0			0
$769$	3.84002	+	6.65111i	0.138475	+	0.239845i	0.926919	−	0.375260i	$-0.122447\pi$
$769$	3.84002	+	6.65111i	0.138475	+	0.239845i	−0.788445	+	0.615106i	$0.789113\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	11.3907	+	19.7293i	0.409695	+	0.709612i	0.994855	−	0.101305i	$-0.0323018\pi$
$773$	11.3907	+	19.7293i	0.409695	+	0.709612i	−0.585161	+	0.810917i	$0.698969\pi$
$774$		0			0
$775$	2.71164	−	1.56556i	0.0974048	−	0.0562367i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.739122	−	40.5935i	−0.0264818	−	1.45441i
$780$		0			0
$781$	48.9059	+	28.2359i	1.74999	+	1.01036i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	43.4417	−	25.0811i	1.55050	−	0.895182i
$786$		0			0
$787$		−	3.39157i		−	0.120896i	−0.998171	−	0.0604482i	$-0.980747\pi$
$787$		−	3.39157i		−	0.120896i	0.998171	−	0.0604482i	$-0.0192530\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.70418			0.0605936
$792$		0			0
$793$	−8.81525	−	5.08949i	−0.313039	−	0.180733i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	36.6623			1.29865			0.649323	−	0.760513i	$-0.275052\pi$
$797$	36.6623			1.29865			0.649323	+	0.760513i	$0.275052\pi$
$798$		0			0
$799$	1.32491			0.0468721
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.39964	+	4.84954i	0.296417	+	0.171136i
$804$		0			0
$805$	−2.01227			−0.0709232
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	8.21490i		−	0.288820i	−0.989518	−	0.144410i	$-0.953872\pi$
$809$		−	8.21490i		−	0.288820i	0.989518	−	0.144410i	$-0.0461285\pi$
$810$		0			0
$811$	−12.9615	+	7.48335i	−0.455141	+	0.262776i	−0.709999	−	0.704203i	$-0.751305\pi$
$811$	−12.9615	+	7.48335i	−0.455141	+	0.262776i	0.254858	+	0.966979i	$0.417971\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−71.7921	−	41.4492i	−2.51477	−	1.45190i
$816$		0			0
$817$	−0.656135	−	36.0358i	−0.0229553	−	1.26073i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−18.8453	+	10.8804i	−0.657706	+	0.379727i	−0.791402	−	0.611295i	$-0.790649\pi$
$821$	−18.8453	+	10.8804i	−0.657706	+	0.379727i	0.133696	+	0.991022i	$0.457315\pi$
$822$		0			0
$823$	15.6978	+	27.1894i	0.547191	+	0.947763i	0.998465	+	0.0553775i	$0.0176362\pi$
$823$	15.6978	+	27.1894i	0.547191	+	0.947763i	−0.451274	+	0.892385i	$0.649030\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−23.4296	−	40.5812i	−0.814726	−	1.41115i	−0.909525	−	0.415650i	$-0.863554\pi$
$827$	−23.4296	−	40.5812i	−0.814726	−	1.41115i	0.0947989	−	0.995496i	$-0.469779\pi$
$828$		0			0
$829$			24.0526i			0.835382i	0.908589	+	0.417691i	$0.137160\pi$
$829$			24.0526i			0.835382i	−0.908589	+	0.417691i	$0.862840\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−5.66524	−	3.27083i	−0.196289	−	0.113327i
$834$		0			0
$835$		−	56.1869i		−	1.94443i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	16.5964	−	28.7459i	0.572973	−	0.992418i	−0.423286	−	0.905996i	$-0.639123\pi$
$839$	16.5964	−	28.7459i	0.572973	−	0.992418i	0.996259	−	0.0864219i	$-0.0275433\pi$
$840$		0			0
$841$	14.4432	−	25.0164i	0.498042	−	0.862633i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−14.3241	+	8.27004i	−0.492765	+	0.284498i
$846$		0			0
$847$	−0.862906			−0.0296498
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2.98545	+	5.17095i	0.102340	+	0.177258i
$852$		0			0
$853$	17.8373	−	30.8950i	0.610736	−	1.05783i	−0.380381	−	0.924830i	$-0.624207\pi$
$853$	17.8373	−	30.8950i	0.610736	−	1.05783i	0.991117	−	0.132996i	$-0.0424596\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	13.6539	−	23.6492i	0.466407	−	0.807840i	−0.532857	−	0.846205i	$-0.678882\pi$
$857$	13.6539	−	23.6492i	0.466407	−	0.807840i	0.999264	+	0.0383650i	$0.0122149\pi$
$858$		0			0
$859$	−6.37803	−	11.0471i	−0.217615	−	0.376921i	0.736463	−	0.676478i	$-0.236495\pi$
$859$	−6.37803	−	11.0471i	−0.217615	−	0.376921i	−0.954078	+	0.299557i	$0.903161\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	6.71164			0.228467			0.114233	−	0.993454i	$-0.463559\pi$
$863$	6.71164			0.228467			0.114233	+	0.993454i	$0.463559\pi$
$864$		0			0
$865$	−18.7353	+	10.8168i	−0.637020	+	0.367784i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−20.9876	+	36.3517i	−0.711957	+	1.23315i
$870$		0			0
$871$	10.0234	−	17.3610i	0.339630	−	0.588256i
$872$		0			0
$873$		0			0
$874$		0			0
$875$			6.82768i			0.230818i
$876$		0			0
$877$	−31.6460	−	18.2708i	−1.06861	−	0.616962i	−0.140808	−	0.990037i	$-0.544970\pi$
$877$	−31.6460	−	18.2708i	−1.06861	−	0.616962i	−0.927801	+	0.373075i	$0.878303\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			13.2795i			0.447399i	0.974658	+	0.223699i	$0.0718133\pi$
$881$			13.2795i			0.447399i	−0.974658	+	0.223699i	$0.928187\pi$
$882$		0			0
$883$	5.61377	+	9.72333i	0.188918	+	0.327216i	0.944890	−	0.327388i	$-0.106169\pi$
$883$	5.61377	+	9.72333i	0.188918	+	0.327216i	−0.755972	+	0.654605i	$0.772835\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−0.558226	−	0.966876i	−0.0187434	−	0.0324645i	0.856502	−	0.516144i	$-0.172633\pi$
$887$	−0.558226	−	0.966876i	−0.0187434	−	0.0324645i	−0.875245	+	0.483680i	$0.839300\pi$
$888$		0			0
$889$	−1.70898	+	0.986680i	−0.0573174	+	0.0330922i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	2.96862	−	5.36505i	0.0993410	−	0.179535i
$894$		0			0
$895$	19.6835	+	11.3643i	0.657947	+	0.379866i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.0757087	+	0.0437105i	−0.00252503	+	0.00145783i
$900$		0			0
$901$			1.58977i			0.0529628i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	10.9516			0.364045
$906$		0			0
$907$	11.0506	+	6.38005i	0.366928	+	0.211846i	0.672116	−	0.740446i	$-0.265386\pi$
$907$	11.0506	+	6.38005i	0.366928	+	0.211846i	−0.305187	+	0.952292i	$0.598719\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−6.48491			−0.214855			−0.107427	−	0.994213i	$-0.534261\pi$
$911$	−6.48491			−0.214855			−0.107427	+	0.994213i	$0.534261\pi$
$912$		0			0
$913$	50.0808			1.65743
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.94372	+	2.27691i	0.130233	+	0.0751901i
$918$		0			0
$919$	40.6473			1.34083			0.670415	−	0.741986i	$-0.266116\pi$
$919$	40.6473			1.34083			0.670415	+	0.741986i	$0.266116\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			44.1903i			1.45454i
$924$		0			0
$925$	29.9509	−	17.2922i	0.984779	−	0.568562i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	49.2972	+	28.4618i	1.61739	+	0.933801i	0.987592	+	0.157042i	$0.0501958\pi$
$929$	49.2972	+	28.4618i	1.61739	+	0.933801i	0.629798	+	0.776759i	$0.283138\pi$
$930$		0			0
$931$	−25.9384	+	15.6119i	−0.850095	+	0.511660i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	12.9183	−	7.45839i	0.422474	−	0.243915i
$936$		0			0
$937$	8.59145	+	14.8808i	0.280670	+	0.486135i	0.971550	−	0.236835i	$-0.0761099\pi$
$937$	8.59145	+	14.8808i	0.280670	+	0.486135i	−0.690880	+	0.722970i	$0.742777\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−8.88309	−	15.3860i	−0.289580	−	0.501568i	0.684129	−	0.729361i	$-0.260182\pi$
$941$	−8.88309	−	15.3860i	−0.289580	−	0.501568i	−0.973710	+	0.227793i	$0.926849\pi$
$942$		0			0
$943$			19.4120i			0.632143i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−29.8998	−	17.2627i	−0.971613	−	0.560961i	−0.0718852	−	0.997413i	$-0.522902\pi$
$947$	−29.8998	−	17.2627i	−0.971613	−	0.560961i	−0.899728	+	0.436452i	$0.856235\pi$
$948$		0			0
$949$			7.58972i			0.246373i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	8.98197	−	15.5572i	0.290954	−	0.503948i	−0.683081	−	0.730342i	$-0.739361\pi$
$953$	8.98197	−	15.5572i	0.290954	−	0.503948i	0.974036	+	0.226395i	$0.0726939\pi$
$954$		0			0
$955$	−45.2808	+	78.4287i	−1.46525	+	2.53789i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	3.19137	−	1.84254i	0.103055	−	0.0594987i
$960$		0			0
$961$	30.9327			0.997830
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−55.0160	−	95.2905i	−1.77103	−	3.06751i
$966$		0			0
$967$	15.6693	−	27.1401i	0.503892	−	0.872766i	−0.496098	−	0.868266i	$-0.665234\pi$
$967$	15.6693	−	27.1401i	0.503892	−	0.872766i	0.999990	−	0.00449971i	$-0.00143231\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−13.0509	+	22.6048i	−0.418823	+	0.725422i	−0.995821	−	0.0913228i	$-0.970890\pi$
$971$	−13.0509	+	22.6048i	−0.418823	+	0.725422i	0.576999	+	0.816745i	$0.304224\pi$
$972$		0			0
$973$	−0.0214663	−	0.0371807i	−0.000688178	−	0.00119196i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−52.2886			−1.67286			−0.836430	−	0.548074i	$-0.815361\pi$
$977$	−52.2886			−1.67286			−0.836430	+	0.548074i	$0.815361\pi$
$978$		0			0
$979$	48.9213	−	28.2447i	1.56353	−	0.902705i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	12.9644	−	22.4550i	0.413500	−	0.716204i	−0.581769	−	0.813354i	$-0.697639\pi$
$983$	12.9644	−	22.4550i	0.413500	−	0.716204i	0.995270	+	0.0971501i	$0.0309727\pi$
$984$		0			0
$985$	−26.9614	+	46.6986i	−0.859063	+	1.48794i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			17.2325i			0.547962i
$990$		0			0
$991$	−34.6841	−	20.0249i	−1.10178	−	0.636111i	−0.165089	−	0.986279i	$-0.552791\pi$
$991$	−34.6841	−	20.0249i	−1.10178	−	0.636111i	−0.936687	+	0.350168i	$0.886125\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			84.7604i			2.68708i
$996$		0			0
$997$	−9.68699	−	16.7784i	−0.306790	−	0.531376i	0.670868	−	0.741576i	$-0.265922\pi$
$997$	−9.68699	−	16.7784i	−0.306790	−	0.531376i	−0.977658	+	0.210201i	$0.932588\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1368.2.cu.a.449.1	✓	20	76.31	even	6
1368.2.cu.a.521.1	yes	20	12.11	even	2
1368.2.cu.b.449.10	yes	20	228.107	odd	6
1368.2.cu.b.521.10	yes	20	4.3	odd	2
2736.2.dc.e.449.1		20	19.12	odd	6
2736.2.dc.e.1889.1		20	3.2	odd	2
2736.2.dc.f.449.10		20	57.50	even	6	inner
2736.2.dc.f.1889.10		20	1.1	even	1	trivial

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

\(f(q)\)	\(=\)	\(q+(3.57821 + 2.06588i) q^{5} +0.233685 q^{7} +O(q^{10})\)	\(q+(3.57821 + 2.06588i) q^{5} +0.233685 q^{7} -3.83309i q^{11} +(2.59762 - 1.49974i) q^{13} +(0.815683 + 0.470935i) q^{17} +(3.73462 - 2.24781i) q^{19} +(-1.80489 + 1.04205i) q^{23} +(6.03571 + 10.4542i) q^{25} +(-0.168517 - 0.291880i) q^{29} -0.259383i q^{31} +(0.836175 + 0.482766i) q^{35} -2.86497i q^{37} +(4.65716 - 8.06644i) q^{41} +(4.13427 - 7.16077i) q^{43} +(1.21822 - 0.703342i) q^{47} -6.94539 q^{49} +(0.843942 + 1.46175i) q^{53} +(7.91870 - 13.7156i) q^{55} +(1.25135 - 2.16740i) q^{59} +(-1.69679 - 2.93893i) q^{61} +12.3931 q^{65} +(5.78802 - 3.34172i) q^{67} +(-7.36634 + 12.7589i) q^{71} +(-1.26518 + 2.19135i) q^{73} -0.895738i q^{77} +(-9.48364 - 5.47538i) q^{79} +13.0654i q^{83} +(1.94579 + 3.37020i) q^{85} +(7.36865 + 12.7629i) q^{89} +(0.607026 - 0.350467i) q^{91} +(18.0069 - 0.327868i) q^{95} +(11.9493 + 6.89893i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{7}+O(q^{10}) \) 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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