LMFDB - Embedded newform 1512.2.t.c.289.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(289,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))

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

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

chi := DirichletCharacter("1512.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.t (of order $3$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.9
Character	$\chi$	$=$	1512.289
Dual form			1512.2.t.c.361.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.66851 q^{5} +(-0.654882 - 2.56342i) q^{7} +O(q^{10})$	$q+2.66851 q^{5} +(-0.654882 - 2.56342i) q^{7} +3.98378 q^{11} +(1.00103 + 1.73384i) q^{13} +(3.57175 + 6.18646i) q^{17} +(-4.01956 + 6.96208i) q^{19} +0.887818 q^{23} +2.12092 q^{25} +(1.35035 - 2.33887i) q^{29} +(0.614943 - 1.06511i) q^{31} +(-1.74756 - 6.84051i) q^{35} +(5.26528 - 9.11973i) q^{37} +(1.43477 + 2.48509i) q^{41} +(3.40053 - 5.88989i) q^{43} +(-6.06845 - 10.5109i) q^{47} +(-6.14226 + 3.35748i) q^{49} +(2.38665 + 4.13380i) q^{53} +10.6307 q^{55} +(4.79029 - 8.29703i) q^{59} +(4.74981 + 8.22692i) q^{61} +(2.67126 + 4.62676i) q^{65} +(-5.49446 + 9.51668i) q^{67} +4.62888 q^{71} +(2.01004 + 3.48149i) q^{73} +(-2.60890 - 10.2121i) q^{77} +(0.514987 + 0.891984i) q^{79} +(5.26656 - 9.12195i) q^{83} +(9.53125 + 16.5086i) q^{85} +(-1.72788 + 2.99278i) q^{89} +(3.78900 - 3.70153i) q^{91} +(-10.7262 + 18.5784i) q^{95} +(-1.12061 + 1.94096i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q + 2 * q^5 - q^7	$ 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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
$5$	2.66851			1.19339			0.596696	−	0.802467i	$-0.296480\pi$
$5$	2.66851			1.19339			0.596696	+	0.802467i	$0.296480\pi$
$6$		0			0
$7$	−0.654882	−	2.56342i	−0.247522	−	0.968882i
$7$	−0.654882	−	2.56342i	−0.247522	−	0.968882i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.98378			1.20115			0.600577	−	0.799567i	$-0.294938\pi$
$11$	3.98378			1.20115			0.600577	+	0.799567i	$0.294938\pi$
$12$		0			0
$13$	1.00103	+	1.73384i	0.277636	+	0.480880i	0.970797	−	0.239903i	$-0.0771156\pi$
$13$	1.00103	+	1.73384i	0.277636	+	0.480880i	−0.693161	+	0.720783i	$0.743782\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.57175	+	6.18646i	0.866278	+	1.50044i	0.865773	+	0.500437i	$0.166827\pi$
$17$	3.57175	+	6.18646i	0.866278	+	1.50044i	0.000504947		1.00000i	$0.499839\pi$
$18$		0			0
$19$	−4.01956	+	6.96208i	−0.922150	+	1.59721i	−0.126068	+	0.992022i	$0.540236\pi$
$19$	−4.01956	+	6.96208i	−0.922150	+	1.59721i	−0.796082	+	0.605189i	$0.793097\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.887818			0.185123			0.0925614	−	0.995707i	$-0.470495\pi$
$23$	0.887818			0.185123			0.0925614	+	0.995707i	$0.470495\pi$
$24$		0			0
$25$	2.12092			0.424185
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.35035	−	2.33887i	0.250753	−	0.434317i	−0.712980	−	0.701184i	$-0.752655\pi$
$29$	1.35035	−	2.33887i	0.250753	−	0.434317i	0.963733	+	0.266867i	$0.0859885\pi$
$30$		0			0
$31$	0.614943	−	1.06511i	0.110447	−	0.191300i	−0.805504	−	0.592591i	$-0.798105\pi$
$31$	0.614943	−	1.06511i	0.110447	−	0.191300i	0.915951	+	0.401291i	$0.131438\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.74756	−	6.84051i	−0.295391	−	1.15626i
$36$		0			0
$37$	5.26528	−	9.11973i	0.865607	−	1.49928i	−0.000836477	−	1.00000i	$-0.500266\pi$
$37$	5.26528	−	9.11973i	0.865607	−	1.49928i	0.866443	−	0.499275i	$-0.166400\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.43477	+	2.48509i	0.224073	+	0.388105i	0.956041	−	0.293234i	$-0.0947313\pi$
$41$	1.43477	+	2.48509i	0.224073	+	0.388105i	−0.731968	+	0.681339i	$0.761398\pi$
$42$		0			0
$43$	3.40053	−	5.88989i	0.518576	−	0.898200i	−0.481191	−	0.876616i	$-0.659796\pi$
$43$	3.40053	−	5.88989i	0.518576	−	0.898200i	0.999767	−	0.0215840i	$-0.00687093\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.06845	−	10.5109i	−0.885175	−	1.53317i	−0.845513	−	0.533955i	$-0.820705\pi$
$47$	−6.06845	−	10.5109i	−0.885175	−	1.53317i	−0.0396620	−	0.999213i	$-0.512628\pi$
$48$		0			0
$49$	−6.14226	+	3.35748i	−0.877466	+	0.479639i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.38665	+	4.13380i	0.327832	+	0.567821i	0.982081	−	0.188457i	$-0.0603487\pi$
$53$	2.38665	+	4.13380i	0.327832	+	0.567821i	−0.654250	+	0.756279i	$0.727015\pi$
$54$		0			0
$55$	10.6307			1.43345
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.79029	−	8.29703i	0.623643	−	1.08018i	−0.365159	−	0.930945i	$-0.618985\pi$
$59$	4.79029	−	8.29703i	0.623643	−	1.08018i	0.988802	−	0.149236i	$-0.0476813\pi$
$60$		0			0
$61$	4.74981	+	8.22692i	0.608151	+	1.05335i	0.991545	+	0.129764i	$0.0414218\pi$
$61$	4.74981	+	8.22692i	0.608151	+	1.05335i	−0.383394	+	0.923585i	$0.625245\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.67126	+	4.62676i	0.331329	+	0.573879i
$66$		0			0
$67$	−5.49446	+	9.51668i	−0.671255	+	1.16265i	0.306294	+	0.951937i	$0.400911\pi$
$67$	−5.49446	+	9.51668i	−0.671255	+	1.16265i	−0.977549	+	0.210710i	$0.932422\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.62888			0.549347			0.274673	−	0.961538i	$-0.411430\pi$
$71$	4.62888			0.549347			0.274673	+	0.961538i	$0.411430\pi$
$72$		0			0
$73$	2.01004	+	3.48149i	0.235257	+	0.407478i	0.959347	−	0.282228i	$-0.0910733\pi$
$73$	2.01004	+	3.48149i	0.235257	+	0.407478i	−0.724090	+	0.689705i	$0.757740\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.60890	−	10.2121i	−0.297312	−	1.16378i
$78$		0			0
$79$	0.514987	+	0.891984i	0.0579406	+	0.100356i	0.893541	−	0.448982i	$-0.148213\pi$
$79$	0.514987	+	0.891984i	0.0579406	+	0.100356i	−0.835600	+	0.549338i	$0.814880\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.26656	−	9.12195i	0.578080	−	1.00126i	−0.417620	−	0.908622i	$-0.637135\pi$
$83$	5.26656	−	9.12195i	0.578080	−	1.00126i	0.995699	−	0.0926419i	$-0.0295312\pi$
$84$		0			0
$85$	9.53125	+	16.5086i	1.03381	+	1.79061i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.72788	+	2.99278i	−0.183155	+	0.317234i	−0.942953	−	0.332925i	$-0.891964\pi$
$89$	−1.72788	+	2.99278i	−0.183155	+	0.317234i	0.759798	+	0.650159i	$0.225298\pi$
$90$		0			0
$91$	3.78900	−	3.70153i	0.397195	−	0.388025i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−10.7262	+	18.5784i	−1.10049	+	1.90610i
$96$		0			0
$97$	−1.12061	+	1.94096i	−0.113781	+	0.197075i	−0.917292	−	0.398216i	$-0.869630\pi$
$97$	−1.12061	+	1.94096i	−0.113781	+	0.197075i	0.803511	+	0.595290i	$0.202963\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.56830			0.454562			0.227281	−	0.973829i	$-0.427016\pi$
$101$	4.56830			0.454562			0.227281	+	0.973829i	$0.427016\pi$
$102$		0			0
$103$	−12.7502			−1.25631			−0.628156	−	0.778088i	$-0.716190\pi$
$103$	−12.7502			−1.25631			−0.628156	+	0.778088i	$0.716190\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.659761	−	1.14274i	0.0637815	−	0.110473i	−0.832371	−	0.554218i	$-0.813017\pi$
$107$	0.659761	−	1.14274i	0.0637815	−	0.110473i	0.896153	+	0.443746i	$0.146351\pi$
$108$		0			0
$109$	−6.31990	−	10.9464i	−0.605337	−	1.04847i	−0.991998	−	0.126252i	$-0.959705\pi$
$109$	−6.31990	−	10.9464i	−0.605337	−	1.04847i	0.386661	−	0.922222i	$-0.373628\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.503200	+	0.871568i	0.0473371	+	0.0819903i	0.888723	−	0.458444i	$-0.151593\pi$
$113$	0.503200	+	0.871568i	0.0473371	+	0.0819903i	−0.841386	+	0.540435i	$0.818260\pi$
$114$		0			0
$115$	2.36915			0.220924
$116$		0			0
$117$		0			0
$118$		0			0
$119$	13.5194	−	13.2073i	1.23932	−	1.21071i
$120$		0			0
$121$	4.87048			0.442771
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−7.68283			−0.687173
$126$		0			0
$127$	1.38400			0.122810			0.0614051	−	0.998113i	$-0.480442\pi$
$127$	1.38400			0.122810			0.0614051	+	0.998113i	$0.480442\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.329724			0.0288081			0.0144041	−	0.999896i	$-0.495415\pi$
$131$	0.329724			0.0288081			0.0144041	+	0.999896i	$0.495415\pi$
$132$		0			0
$133$	20.4791	+	5.74448i	1.77576	+	0.498110i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.94189			−0.763958			−0.381979	−	0.924171i	$-0.624757\pi$
$137$	−8.94189			−0.763958			−0.381979	+	0.924171i	$0.624757\pi$
$138$		0			0
$139$	3.92869	+	6.80470i	0.333227	+	0.577167i	0.983143	−	0.182840i	$-0.0585290\pi$
$139$	3.92869	+	6.80470i	0.333227	+	0.577167i	−0.649915	+	0.760007i	$0.725196\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.98789	+	6.90723i	0.333484	+	0.577611i
$144$		0			0
$145$	3.60341	−	6.24128i	0.299247	−	0.518310i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−16.3215			−1.33711			−0.668554	−	0.743663i	$-0.733087\pi$
$149$	−16.3215			−1.33711			−0.668554	+	0.743663i	$0.733087\pi$
$150$		0			0
$151$	−4.63354			−0.377072			−0.188536	−	0.982066i	$-0.560374\pi$
$151$	−4.63354			−0.377072			−0.188536	+	0.982066i	$0.560374\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.64098	−	2.84226i	0.131807	−	0.228296i
$156$		0			0
$157$	4.25926	−	7.37725i	0.339926	−	0.588769i	−0.644493	−	0.764611i	$-0.722931\pi$
$157$	4.25926	−	7.37725i	0.339926	−	0.588769i	0.984418	+	0.175842i	$0.0562647\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.581416	−	2.27585i	−0.0458220	−	0.179362i
$162$		0			0
$163$	1.22354	−	2.11923i	0.0958350	−	0.165991i	−0.814122	−	0.580694i	$-0.802781\pi$
$163$	1.22354	−	2.11923i	0.0958350	−	0.165991i	0.909957	+	0.414703i	$0.136115\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.0713948	+	0.123659i	0.00552470	+	0.00956906i	0.868775	−	0.495208i	$-0.164908\pi$
$167$	0.0713948	+	0.123659i	0.00552470	+	0.00956906i	−0.863250	+	0.504777i	$0.831575\pi$
$168$		0			0
$169$	4.49587	−	7.78708i	0.345836	−	0.599006i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	8.99834	+	15.5856i	0.684131	+	1.18495i	0.973709	+	0.227795i	$0.0731518\pi$
$173$	8.99834	+	15.5856i	0.684131	+	1.18495i	−0.289578	+	0.957154i	$0.593515\pi$
$174$		0			0
$175$	−1.38896	−	5.43682i	−0.104995	−	0.410985i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.02413	+	1.77384i	0.0765468	+	0.132583i	0.901758	−	0.432242i	$-0.142277\pi$
$179$	1.02413	+	1.77384i	0.0765468	+	0.132583i	−0.825211	+	0.564824i	$0.808944\pi$
$180$		0			0
$181$	1.81165			0.134659			0.0673294	−	0.997731i	$-0.478552\pi$
$181$	1.81165			0.134659			0.0673294	+	0.997731i	$0.478552\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	14.0504	−	24.3361i	1.03301	−	1.78922i
$186$		0			0
$187$	14.2291	+	24.6455i	1.04053	+	1.80226i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.40457	+	16.2892i	0.680491	+	1.17864i	0.974831	+	0.222944i	$0.0715667\pi$
$191$	9.40457	+	16.2892i	0.680491	+	1.17864i	−0.294341	+	0.955701i	$0.595100\pi$
$192$		0			0
$193$	−3.24357	+	5.61803i	−0.233477	+	0.404394i	−0.958829	−	0.283984i	$-0.908344\pi$
$193$	−3.24357	+	5.61803i	−0.233477	+	0.404394i	0.725352	+	0.688378i	$0.241677\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	10.8356			0.772007			0.386003	−	0.922497i	$-0.373855\pi$
$197$	10.8356			0.772007			0.386003	+	0.922497i	$0.373855\pi$
$198$		0			0
$199$	−9.43873	−	16.3484i	−0.669094	−	1.15890i	−0.978158	−	0.207863i	$-0.933349\pi$
$199$	−9.43873	−	16.3484i	−0.669094	−	1.15890i	0.309064	−	0.951041i	$-0.399984\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−6.87982	−	1.92982i	−0.482869	−	0.135447i
$204$		0			0
$205$	3.82868	+	6.63147i	0.267407	+	0.463162i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−16.0130	+	27.7354i	−1.10764	+	1.91850i
$210$		0			0
$211$	−11.9133	−	20.6344i	−0.820145	−	1.42053i	−0.905574	−	0.424188i	$-0.860560\pi$
$211$	−11.9133	−	20.6344i	−0.820145	−	1.42053i	0.0854297	−	0.996344i	$-0.472774\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	9.07433	−	15.7172i	0.618864	−	1.07190i
$216$		0			0
$217$	−3.13305	−	0.878836i	−0.212685	−	0.0596593i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−7.15088	+	12.3857i	−0.481020	+	0.833152i
$222$		0			0
$223$	6.53734	−	11.3230i	0.437773	−	0.758245i	−0.559745	−	0.828665i	$-0.689101\pi$
$223$	6.53734	−	11.3230i	0.437773	−	0.758245i	0.997517	+	0.0704203i	$0.0224341\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−23.1690			−1.53778			−0.768890	−	0.639381i	$-0.779191\pi$
$227$	−23.1690			−1.53778			−0.768890	+	0.639381i	$0.779191\pi$
$228$		0			0
$229$	−21.5588			−1.42465			−0.712323	−	0.701851i	$-0.752357\pi$
$229$	−21.5588			−1.42465			−0.712323	+	0.701851i	$0.752357\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.05558	−	13.9527i	0.527739	−	0.914070i	−0.471738	−	0.881739i	$-0.656373\pi$
$233$	8.05558	−	13.9527i	0.527739	−	0.914070i	0.999477	−	0.0323318i	$-0.0102933\pi$
$234$		0			0
$235$	−16.1937	−	28.0483i	−1.05636	−	1.82967i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.216059	−	0.374225i	−0.0139757	−	0.0242066i	0.858953	−	0.512054i	$-0.171115\pi$
$239$	−0.216059	−	0.374225i	−0.0139757	−	0.0242066i	−0.872929	+	0.487848i	$0.837782\pi$
$240$		0			0
$241$	3.05674			0.196902			0.0984509	−	0.995142i	$-0.468611\pi$
$241$	3.05674			0.196902			0.0984509	+	0.995142i	$0.468611\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−16.3907	+	8.95945i	−1.04716	+	0.572398i
$246$		0			0
$247$	−16.0948			−1.02409
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−11.9066			−0.751541			−0.375770	−	0.926713i	$-0.622622\pi$
$251$	−11.9066			−0.751541			−0.375770	+	0.926713i	$0.622622\pi$
$252$		0			0
$253$	3.53687			0.222361
$254$		0			0
$255$		0			0
$256$		0			0
$257$	31.9453			1.99269			0.996346	−	0.0854116i	$-0.0272205\pi$
$257$	31.9453			1.99269			0.996346	+	0.0854116i	$0.0272205\pi$
$258$		0			0
$259$	−26.8259	−	7.52479i	−1.66688	−	0.467567i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.70989			−0.413750			−0.206875	−	0.978367i	$-0.566329\pi$
$263$	−6.70989			−0.413750			−0.206875	+	0.978367i	$0.566329\pi$
$264$		0			0
$265$	6.36879	+	11.0311i	0.391232	+	0.677634i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−5.66510	−	9.81225i	−0.345408	−	0.598263i	0.640020	−	0.768358i	$-0.278926\pi$
$269$	−5.66510	−	9.81225i	−0.345408	−	0.598263i	−0.985428	+	0.170095i	$0.945593\pi$
$270$		0			0
$271$	−5.06846	+	8.77884i	−0.307887	+	0.533276i	−0.977900	−	0.209073i	$-0.932955\pi$
$271$	−5.06846	+	8.77884i	−0.307887	+	0.533276i	0.670013	+	0.742350i	$0.266289\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.44929			0.509512
$276$		0			0
$277$	−21.2865			−1.27898			−0.639492	−	0.768798i	$-0.720855\pi$
$277$	−21.2865			−1.27898			−0.639492	+	0.768798i	$0.720855\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.26945	−	10.8590i	0.374004	−	0.647794i	−0.616174	−	0.787610i	$-0.711318\pi$
$281$	6.26945	−	10.8590i	0.374004	−	0.647794i	0.990177	+	0.139817i	$0.0446513\pi$
$282$		0			0
$283$	−12.4749	+	21.6071i	−0.741554	+	1.28441i	0.210234	+	0.977651i	$0.432577\pi$
$283$	−12.4749	+	21.6071i	−0.741554	+	1.28441i	−0.951788	+	0.306758i	$0.900756\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.43072	−	5.30535i	0.320565	−	0.313165i
$288$		0			0
$289$	−17.0149	+	29.4706i	−1.00087	+	1.73357i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.42625	−	12.8626i	−0.433846	−	0.751443i	0.563355	−	0.826215i	$-0.309510\pi$
$293$	−7.42625	−	12.8626i	−0.433846	−	0.751443i	−0.997201	+	0.0747718i	$0.976177\pi$
$294$		0			0
$295$	12.7829	−	22.1407i	0.744250	−	1.28908i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.888734	+	1.53933i	0.0513968	+	0.0890219i
$300$		0			0
$301$	−17.3252	−	4.85981i	−0.998609	−	0.280115i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	12.6749	+	21.9536i	0.725763	+	1.25706i
$306$		0			0
$307$	−21.9045			−1.25016			−0.625079	−	0.780561i	$-0.714933\pi$
$307$	−21.9045			−1.25016			−0.625079	+	0.780561i	$0.714933\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−8.78359	+	15.2136i	−0.498072	+	0.862686i	−0.999998	−	0.00222515i	$-0.999292\pi$
$311$	−8.78359	+	15.2136i	−0.498072	+	0.862686i	0.501926	+	0.864911i	$0.332625\pi$
$312$		0			0
$313$	5.98820	+	10.3719i	0.338473	+	0.586252i	0.984146	−	0.177362i	$-0.0567563\pi$
$313$	5.98820	+	10.3719i	0.338473	+	0.586252i	−0.645673	+	0.763614i	$0.723423\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.866633	−	1.50105i	−0.0486750	−	0.0843075i	0.840661	−	0.541561i	$-0.182167\pi$
$317$	−0.866633	−	1.50105i	−0.0486750	−	0.0843075i	−0.889336	+	0.457254i	$0.848833\pi$
$318$		0			0
$319$	5.37948	−	9.31753i	0.301193	−	0.521681i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−57.4275			−3.19535
$324$		0			0
$325$	2.12311	+	3.67734i	0.117769	+	0.203982i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−22.9697	+	22.4394i	−1.26636	+	1.23712i
$330$		0			0
$331$	0.363127	+	0.628954i	0.0199593	+	0.0345705i	0.875833	−	0.482615i	$-0.160313\pi$
$331$	0.363127	+	0.628954i	0.0199593	+	0.0345705i	−0.855873	+	0.517186i	$0.826980\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−14.6620	+	25.3953i	−0.801070	+	1.38749i
$336$		0			0
$337$	−6.84810	−	11.8613i	−0.373040	−	0.646124i	0.616992	−	0.786970i	$-0.288351\pi$
$337$	−6.84810	−	11.8613i	−0.373040	−	0.646124i	−0.990032	+	0.140846i	$0.955018\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.44980	−	4.24317i	0.132664	−	0.229781i
$342$		0			0
$343$	12.6291	+	13.5465i	0.681906	+	0.731440i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.10709	+	3.64958i	−0.113114	+	0.195920i	−0.917024	−	0.398831i	$-0.869416\pi$
$347$	−2.10709	+	3.64958i	−0.113114	+	0.195920i	0.803910	+	0.594751i	$0.202749\pi$
$348$		0			0
$349$	−10.8070	+	18.7183i	−0.578486	+	1.00197i	0.417167	+	0.908830i	$0.363023\pi$
$349$	−10.8070	+	18.7183i	−0.578486	+	1.00197i	−0.995653	+	0.0931372i	$0.970310\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4.85115			−0.258201			−0.129100	−	0.991632i	$-0.541209\pi$
$353$	−4.85115			−0.258201			−0.129100	+	0.991632i	$0.541209\pi$
$354$		0			0
$355$	12.3522			0.655586
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.90433	+	5.03045i	−0.153285	+	0.265497i	−0.932433	−	0.361343i	$-0.882318\pi$
$359$	−2.90433	+	5.03045i	−0.153285	+	0.265497i	0.779148	+	0.626839i	$0.215652\pi$
$360$		0			0
$361$	−22.8137	−	39.5145i	−1.20072	−	2.07971i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5.36381	+	9.29038i	0.280754	+	0.486281i
$366$		0			0
$367$	21.6890			1.13216			0.566078	−	0.824352i	$-0.308460\pi$
$367$	21.6890			1.13216			0.566078	+	0.824352i	$0.308460\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	9.03370	−	8.82515i	0.469006	−	0.458179i
$372$		0			0
$373$	24.7104			1.27946			0.639729	−	0.768601i	$-0.279047\pi$
$373$	24.7104			1.27946			0.639729	+	0.768601i	$0.279047\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	5.40696			0.278473
$378$		0			0
$379$	−27.9950			−1.43801			−0.719005	−	0.695005i	$-0.755402\pi$
$379$	−27.9950			−1.43801			−0.719005	+	0.695005i	$0.755402\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	20.6227			1.05377			0.526884	−	0.849937i	$-0.323360\pi$
$383$	20.6227			1.05377			0.526884	+	0.849937i	$0.323360\pi$
$384$		0			0
$385$	−6.96187	−	27.2511i	−0.354810	−	1.38884i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−17.4007			−0.882250			−0.441125	−	0.897446i	$-0.645420\pi$
$389$	−17.4007			−0.882250			−0.441125	+	0.897446i	$0.645420\pi$
$390$		0			0
$391$	3.17107	+	5.49245i	0.160368	+	0.277765i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.37425	+	2.38026i	0.0691458	+	0.119764i
$396$		0			0
$397$	9.74152	−	16.8728i	0.488913	−	0.846822i	−0.511006	−	0.859577i	$-0.670727\pi$
$397$	9.74152	−	16.8728i	0.488913	−	0.846822i	0.999919	+	0.0127553i	$0.00406024\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7.70529			−0.384784			−0.192392	−	0.981318i	$-0.561624\pi$
$401$	−7.70529			−0.384784			−0.192392	+	0.981318i	$0.561624\pi$
$402$		0			0
$403$	2.46231			0.122656
$404$		0			0
$405$		0			0
$406$		0			0
$407$	20.9757	−	36.3310i	1.03973	−	1.80086i
$408$		0			0
$409$	7.86755	−	13.6270i	0.389025	−	0.673811i	−0.603294	−	0.797519i	$-0.706145\pi$
$409$	7.86755	−	13.6270i	0.389025	−	0.673811i	0.992319	+	0.123708i	$0.0394786\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−24.4058	−	6.84596i	−1.20093	−	0.336868i
$414$		0			0
$415$	14.0538	−	24.3420i	0.689876	−	1.19490i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	17.3452	+	30.0428i	0.847369	+	1.46769i	0.883548	+	0.468341i	$0.155148\pi$
$419$	17.3452	+	30.0428i	0.847369	+	1.46769i	−0.0361784	+	0.999345i	$0.511518\pi$
$420$		0			0
$421$	−0.607053	+	1.05145i	−0.0295860	+	0.0512444i	−0.880439	−	0.474159i	$-0.842752\pi$
$421$	−0.607053	+	1.05145i	−0.0295860	+	0.0512444i	0.850853	+	0.525403i	$0.176086\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	7.57542	+	13.1210i	0.367462	+	0.636463i
$426$		0			0
$427$	17.9785	−	17.5634i	0.870040	−	0.849954i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.68495	−	2.91841i	−0.0811610	−	0.140575i	0.822588	−	0.568638i	$-0.192529\pi$
$431$	−1.68495	−	2.91841i	−0.0811610	−	0.140575i	−0.903749	+	0.428063i	$0.859196\pi$
$432$		0			0
$433$	−30.8651			−1.48328			−0.741640	−	0.670798i	$-0.765952\pi$
$433$	−30.8651			−1.48328			−0.741640	+	0.670798i	$0.765952\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.56864	+	6.18106i	−0.170711	+	0.295680i
$438$		0			0
$439$	16.5395	+	28.6472i	0.789385	+	1.36725i	0.926344	+	0.376678i	$0.122934\pi$
$439$	16.5395	+	28.6472i	0.789385	+	1.36725i	−0.136959	+	0.990577i	$0.543733\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.36682	+	2.36740i	0.0649397	+	0.112479i	0.896667	−	0.442705i	$-0.145981\pi$
$443$	1.36682	+	2.36740i	0.0649397	+	0.112479i	−0.831728	+	0.555184i	$0.812648\pi$
$444$		0			0
$445$	−4.61086	+	7.98625i	−0.218576	+	0.378584i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−22.7472			−1.07351			−0.536753	−	0.843740i	$-0.680349\pi$
$449$	−22.7472			−1.07351			−0.536753	+	0.843740i	$0.680349\pi$
$450$		0			0
$451$	5.71579	+	9.90003i	0.269146	+	0.466174i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	10.1110	−	9.87754i	0.474010	−	0.463066i
$456$		0			0
$457$	−1.68162	−	2.91265i	−0.0786628	−	0.136248i	0.824010	−	0.566575i	$-0.191732\pi$
$457$	−1.68162	−	2.91265i	−0.0786628	−	0.136248i	−0.902673	+	0.430327i	$0.858398\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	10.0040	−	17.3275i	0.465934	−	0.807021i	−0.533309	−	0.845920i	$-0.679052\pi$
$461$	10.0040	−	17.3275i	0.465934	−	0.807021i	0.999243	+	0.0388994i	$0.0123852\pi$
$462$		0			0
$463$	7.29434	+	12.6342i	0.338997	+	0.587160i	0.984244	−	0.176814i	$-0.0565791\pi$
$463$	7.29434	+	12.6342i	0.338997	+	0.587160i	−0.645247	+	0.763974i	$0.723246\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.26334	+	12.5805i	−0.336107	+	0.582155i	−0.983697	−	0.179834i	$-0.942444\pi$
$467$	−7.26334	+	12.5805i	−0.336107	+	0.582155i	0.647590	+	0.761989i	$0.275777\pi$
$468$		0			0
$469$	27.9935	+	7.85231i	1.29262	+	0.362586i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	13.5470	−	23.4640i	0.622889	−	1.07888i
$474$		0			0
$475$	−8.52518	+	14.7660i	−0.391162	+	0.677513i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	11.3243			0.517421			0.258710	−	0.965955i	$-0.416702\pi$
$479$	11.3243			0.517421			0.258710	+	0.965955i	$0.416702\pi$
$480$		0			0
$481$	21.0829			0.961296
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.99036	+	5.17946i	−0.135785	+	0.235187i
$486$		0			0
$487$	5.93684	+	10.2829i	0.269024	+	0.465963i	0.968610	−	0.248585i	$-0.0799657\pi$
$487$	5.93684	+	10.2829i	0.269024	+	0.465963i	−0.699586	+	0.714548i	$0.746632\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−11.9598	−	20.7150i	−0.539738	−	0.934853i	−0.998918	−	0.0465101i	$-0.985190\pi$
$491$	−11.9598	−	20.7150i	−0.539738	−	0.934853i	0.459180	−	0.888343i	$-0.348143\pi$
$492$		0			0
$493$	19.2924			0.868887
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.03137	−	11.8658i	−0.135975	−	0.532252i
$498$		0			0
$499$	−0.451968			−0.0202329			−0.0101164	−	0.999949i	$-0.503220\pi$
$499$	−0.451968			−0.0202329			−0.0101164	+	0.999949i	$0.503220\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	14.6077			0.651326			0.325663	−	0.945486i	$-0.394413\pi$
$503$	14.6077			0.651326			0.325663	+	0.945486i	$0.394413\pi$
$504$		0			0
$505$	12.1905			0.542471
$506$		0			0
$507$		0			0
$508$		0			0
$509$	0.493171			0.0218594			0.0109297	−	0.999940i	$-0.496521\pi$
$509$	0.493171			0.0218594			0.0109297	+	0.999940i	$0.496521\pi$
$510$		0			0
$511$	7.60819	−	7.43255i	0.336567	−	0.328797i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−34.0239			−1.49927
$516$		0			0
$517$	−24.1754	−	41.8730i	−1.06323	−	1.84157i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	6.06874	+	10.5114i	0.265876	+	0.460511i	0.967793	−	0.251748i	$-0.0810054\pi$
$521$	6.06874	+	10.5114i	0.265876	+	0.460511i	−0.701917	+	0.712259i	$0.747672\pi$
$522$		0			0
$523$	1.34058	−	2.32195i	0.0586193	−	0.101532i	−0.835227	−	0.549906i	$-0.814664\pi$
$523$	1.34058	−	2.32195i	0.0586193	−	0.101532i	0.893846	+	0.448374i	$0.147997\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.78571			0.382711
$528$		0			0
$529$	−22.2118			−0.965730
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.87249	+	4.97530i	−0.124421	+	0.215504i
$534$		0			0
$535$	1.76058	−	3.04941i	0.0761163	−	0.131837i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−24.4694	+	13.3754i	−1.05397	+	0.576121i
$540$		0			0
$541$	−13.5072	+	23.3951i	−0.580719	+	1.00583i	0.414676	+	0.909969i	$0.363895\pi$
$541$	−13.5072	+	23.3951i	−0.580719	+	1.00583i	−0.995394	+	0.0958650i	$0.969438\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−16.8647	−	29.2105i	−0.722404	−	1.25124i
$546$		0			0
$547$	−15.2496	+	26.4132i	−0.652028	+	1.12935i	0.330602	+	0.943770i	$0.392748\pi$
$547$	−15.2496	+	26.4132i	−0.652028	+	1.12935i	−0.982630	+	0.185575i	$0.940585\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	10.8556	+	18.8024i	0.462464	+	0.801011i
$552$		0			0
$553$	1.94928	−	1.90427i	0.0828916	−	0.0809779i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.39250	+	12.8042i	0.313230	+	0.542531i	0.979060	−	0.203573i	$-0.0652555\pi$
$557$	7.39250	+	12.8042i	0.313230	+	0.542531i	−0.665829	+	0.746104i	$0.731922\pi$
$558$		0			0
$559$	13.6162			0.575902
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.31411	−	2.27611i	0.0553831	−	0.0959264i	−0.837005	−	0.547196i	$-0.815695\pi$
$563$	1.31411	−	2.27611i	0.0553831	−	0.0959264i	0.892388	+	0.451269i	$0.149029\pi$
$564$		0			0
$565$	1.34279	+	2.32579i	0.0564917	+	0.0978465i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−16.0581	−	27.8134i	−0.673191	−	1.16600i	−0.976994	−	0.213266i	$-0.931590\pi$
$569$	−16.0581	−	27.8134i	−0.673191	−	1.16600i	0.303804	−	0.952735i	$-0.401743\pi$
$570$		0			0
$571$	−20.5907	+	35.6642i	−0.861696	+	1.49250i	0.00859553	+	0.999963i	$0.497264\pi$
$571$	−20.5907	+	35.6642i	−0.861696	+	1.49250i	−0.870291	+	0.492538i	$0.836069\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.88300			0.0785263
$576$		0			0
$577$	12.0735	+	20.9119i	0.502625	+	0.870573i	0.999995	+	0.00303429i	$0.000965847\pi$
$577$	12.0735	+	20.9119i	0.502625	+	0.870573i	−0.497370	+	0.867539i	$0.665701\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−26.8324	−	7.52661i	−1.11319	−	0.312257i
$582$		0			0
$583$	9.50789	+	16.4681i	0.393777	+	0.682041i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.98618	−	6.90426i	0.164527	−	0.284969i	−0.771960	−	0.635671i	$-0.780723\pi$
$587$	3.98618	−	6.90426i	0.164527	−	0.284969i	0.936487	+	0.350702i	$0.114057\pi$
$588$		0			0
$589$	4.94360	+	8.56257i	0.203698	+	0.352815i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	2.10338	−	3.64316i	0.0863753	−	0.149606i	−0.819601	−	0.572935i	$-0.805805\pi$
$593$	2.10338	−	3.64316i	0.0863753	−	0.149606i	0.905976	+	0.423328i	$0.139138\pi$
$594$		0			0
$595$	36.0767	−	35.2438i	1.47900	−	1.44485i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−18.6886	+	32.3696i	−0.763594	+	1.32258i	0.177392	+	0.984140i	$0.443234\pi$
$599$	−18.6886	+	32.3696i	−0.763594	+	1.32258i	−0.940987	+	0.338444i	$0.890099\pi$
$600$		0			0
$601$	6.81596	−	11.8056i	0.278029	−	0.481560i	−0.692866	−	0.721066i	$-0.743652\pi$
$601$	6.81596	−	11.8056i	0.278029	−	0.481560i	0.970895	+	0.239506i	$0.0769856\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	12.9969			0.528400
$606$		0			0
$607$	2.74228			0.111306			0.0556529	−	0.998450i	$-0.482276\pi$
$607$	2.74228			0.111306			0.0556529	+	0.998450i	$0.482276\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	12.1494	−	21.0434i	0.491513	−	0.851326i
$612$		0			0
$613$	0.798502	+	1.38305i	0.0322512	+	0.0558607i	0.881700	−	0.471810i	$-0.156399\pi$
$613$	0.798502	+	1.38305i	0.0322512	+	0.0558607i	−0.849449	+	0.527670i	$0.823066\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−12.6551	−	21.9192i	−0.509473	−	0.882433i	−0.999940	−	0.0109734i	$-0.996507\pi$
$617$	−12.6551	−	21.9192i	−0.509473	−	0.882433i	0.490467	−	0.871460i	$-0.336826\pi$
$618$		0			0
$619$	−27.1616			−1.09172			−0.545859	−	0.837877i	$-0.683796\pi$
$619$	−27.1616			−1.09172			−0.545859	+	0.837877i	$0.683796\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	8.80331	+	2.46937i	0.352697	+	0.0989333i
$624$		0			0
$625$	−31.1063			−1.24425
$626$		0			0
$627$		0			0
$628$		0			0
$629$	75.2252			2.99942
$630$		0			0
$631$	−29.6597			−1.18073			−0.590366	−	0.807136i	$-0.701017\pi$
$631$	−29.6597			−1.18073			−0.590366	+	0.807136i	$0.701017\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	3.69321			0.146561
$636$		0			0
$637$	−11.9699	−	7.28874i	−0.474265	−	0.288791i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−42.1975			−1.66670			−0.833350	−	0.552746i	$-0.813580\pi$
$641$	−42.1975			−1.66670			−0.833350	+	0.552746i	$0.813580\pi$
$642$		0			0
$643$	10.1099	+	17.5109i	0.398696	+	0.690562i	0.993565	−	0.113260i	$-0.0361294\pi$
$643$	10.1099	+	17.5109i	0.398696	+	0.690562i	−0.594869	+	0.803823i	$0.702796\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.08988	+	1.88772i	0.0428475	+	0.0742141i	0.886654	−	0.462434i	$-0.153024\pi$
$647$	1.08988	+	1.88772i	0.0428475	+	0.0742141i	−0.843806	+	0.536648i	$0.819690\pi$
$648$		0			0
$649$	19.0834	−	33.0535i	0.749091	−	1.29746i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	34.1069			1.33471			0.667354	−	0.744741i	$-0.267427\pi$
$653$	34.1069			1.33471			0.667354	+	0.744741i	$0.267427\pi$
$654$		0			0
$655$	0.879871			0.0343794
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.994211	−	1.72202i	0.0387290	−	0.0670805i	−0.846011	−	0.533165i	$-0.821002\pi$
$659$	0.994211	−	1.72202i	0.0387290	−	0.0670805i	0.884740	+	0.466085i	$0.154336\pi$
$660$		0			0
$661$	4.24205	−	7.34744i	0.164997	−	0.285782i	−0.771658	−	0.636038i	$-0.780572\pi$
$661$	4.24205	−	7.34744i	0.164997	−	0.285782i	0.936654	+	0.350256i	$0.113905\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	54.6486	+	15.3292i	2.11918	+	0.594440i
$666$		0			0
$667$	1.19886	−	2.07649i	0.0464201	−	0.0804020i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	18.9222	+	32.7742i	0.730483	+	1.26523i
$672$		0			0
$673$	22.4056	−	38.8077i	0.863674	−	1.49593i	−0.00468438	−	0.999989i	$-0.501491\pi$
$673$	22.4056	−	38.8077i	0.863674	−	1.49593i	0.868358	−	0.495938i	$-0.165176\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4.02684	+	6.97469i	0.154764	+	0.268059i	0.932973	−	0.359946i	$-0.117205\pi$
$677$	4.02684	+	6.97469i	0.154764	+	0.268059i	−0.778209	+	0.628005i	$0.783872\pi$
$678$		0			0
$679$	5.70937	+	1.60151i	0.219105	+	0.0614602i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−20.8446	−	36.1039i	−0.797597	−	1.38148i	−0.921177	−	0.389144i	$-0.872771\pi$
$683$	−20.8446	−	36.1039i	−0.797597	−	1.38148i	0.123580	−	0.992335i	$-0.460562\pi$
$684$		0			0
$685$	−23.8615			−0.911701
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4.77823	+	8.27614i	−0.182036	+	0.315296i
$690$		0			0
$691$	−5.66345	−	9.80938i	−0.215448	−	0.373166i	0.737963	−	0.674841i	$-0.235788\pi$
$691$	−5.66345	−	9.80938i	−0.215448	−	0.373166i	−0.953411	+	0.301674i	$0.902454\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	10.4837	+	18.1584i	0.397671	+	0.688786i
$696$		0			0
$697$	−10.2493	+	17.7522i	−0.388218	+	0.672414i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	22.6560			0.855705			0.427853	−	0.903849i	$-0.359270\pi$
$701$	22.6560			0.855705			0.427853	+	0.903849i	$0.359270\pi$
$702$		0			0
$703$	42.3282	+	73.3146i	1.59644	+	2.76511i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.99169	−	11.7105i	−0.112514	−	0.440418i
$708$		0			0
$709$	−22.6074	−	39.1571i	−0.849037	−	1.47058i	−0.882069	−	0.471121i	$-0.843850\pi$
$709$	−22.6074	−	39.1571i	−0.849037	−	1.47058i	0.0330317	−	0.999454i	$-0.489484\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.545958	−	0.945626i	0.0204463	−	0.0354140i
$714$		0			0
$715$	10.6417	+	18.4320i	0.397977	+	0.689317i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−11.3171	+	19.6018i	−0.422057	+	0.731024i	−0.996141	−	0.0877727i	$-0.972025\pi$
$719$	−11.3171	+	19.6018i	−0.422057	+	0.731024i	0.574084	+	0.818797i	$0.305358\pi$
$720$		0			0
$721$	8.34986	+	32.6841i	0.310965	+	1.21722i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.86398	−	4.96056i	0.106366	−	0.184231i
$726$		0			0
$727$	1.04956	−	1.81789i	0.0389259	−	0.0674217i	−0.845906	−	0.533332i	$-0.820940\pi$
$727$	1.04956	−	1.81789i	0.0389259	−	0.0674217i	0.884832	+	0.465910i	$0.154273\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	48.5834			1.79692
$732$		0			0
$733$	−31.2906			−1.15574			−0.577872	−	0.816127i	$-0.696117\pi$
$733$	−31.2906			−1.15574			−0.577872	+	0.816127i	$0.696117\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−21.8887	+	37.9123i	−0.806280	+	1.39652i
$738$		0			0
$739$	21.1229	+	36.5859i	0.777017	+	1.34583i	0.933654	+	0.358177i	$0.116601\pi$
$739$	21.1229	+	36.5859i	0.777017	+	1.34583i	−0.156637	+	0.987656i	$0.550065\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−6.48482	−	11.2320i	−0.237905	−	0.412064i	0.722208	−	0.691676i	$-0.243127\pi$
$743$	−6.48482	−	11.2320i	−0.237905	−	0.412064i	−0.960113	+	0.279612i	$0.909794\pi$
$744$		0			0
$745$	−43.5540			−1.59570
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.36139	−	0.942886i	−0.122822	−	0.0344523i
$750$		0			0
$751$	32.7298			1.19433			0.597164	−	0.802119i	$-0.296294\pi$
$751$	32.7298			1.19433			0.597164	+	0.802119i	$0.296294\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−12.3646			−0.449995
$756$		0			0
$757$	31.6305			1.14963			0.574815	−	0.818283i	$-0.305074\pi$
$757$	31.6305			1.14963			0.574815	+	0.818283i	$0.305074\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	38.2936			1.38814			0.694070	−	0.719907i	$-0.255816\pi$
$761$	38.2936			1.38814			0.694070	+	0.719907i	$0.255816\pi$
$762$		0			0
$763$	−23.9214	+	23.3692i	−0.866014	+	0.846020i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	19.1809			0.692583
$768$		0			0
$769$	11.0674	+	19.1693i	0.399100	+	0.691262i	0.993615	−	0.112823i	$-0.0359892\pi$
$769$	11.0674	+	19.1693i	0.399100	+	0.691262i	−0.594515	+	0.804085i	$0.702656\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−25.8165	−	44.7155i	−0.928555	−	1.60830i	−0.785742	−	0.618555i	$-0.787719\pi$
$773$	−25.8165	−	44.7155i	−0.928555	−	1.60830i	−0.142813	−	0.989750i	$-0.545615\pi$
$774$		0			0
$775$	1.30425	−	2.25902i	0.0468500	−	0.0811466i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−23.0685			−0.826515
$780$		0			0
$781$	18.4404			0.659850
$782$		0			0
$783$		0			0
$784$		0			0
$785$	11.3659	−	19.6862i	0.405665	−	0.702632i
$786$		0			0
$787$	16.1523	−	27.9766i	0.575767	−	0.997257i	−0.420191	−	0.907436i	$-0.638037\pi$
$787$	16.1523	−	27.9766i	0.575767	−	0.997257i	0.995958	−	0.0898216i	$-0.0286297\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.90466	−	1.86069i	0.0677219	−	0.0661585i
$792$		0			0
$793$	−9.50943	+	16.4708i	−0.337690	+	0.584896i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	11.6877	+	20.2438i	0.414001	+	0.717071i	0.995323	−	0.0966026i	$-0.0307976\pi$
$797$	11.6877	+	20.2438i	0.414001	+	0.717071i	−0.581322	+	0.813674i	$0.697464\pi$
$798$		0			0
$799$	43.3501	−	75.0845i	1.53361	−	2.65630i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.00755	+	13.8695i	0.282580	+	0.489444i
$804$		0			0
$805$	−1.55151	−	6.07312i	−0.0546836	−	0.214049i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−15.2503	−	26.4143i	−0.536171	−	0.928676i	−0.999106	−	0.0422832i	$-0.986537\pi$
$809$	−15.2503	−	26.4143i	−0.536171	−	0.928676i	0.462935	−	0.886392i	$-0.346797\pi$
$810$		0			0
$811$	−51.6454			−1.81352			−0.906758	−	0.421652i	$-0.861450\pi$
$811$	−51.6454			−1.81352			−0.906758	+	0.421652i	$0.861450\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.26502	−	5.65518i	0.114369	−	0.198092i
$816$		0			0
$817$	27.3373	+	47.3495i	0.956409	+	1.65655i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−13.3787	−	23.1727i	−0.466921	−	0.808731i	0.532365	−	0.846515i	$-0.321304\pi$
$821$	−13.3787	−	23.1727i	−0.466921	−	0.808731i	−0.999286	+	0.0377837i	$0.987970\pi$
$822$		0			0
$823$	20.2449	−	35.0652i	0.705693	−	1.22230i	−0.260747	−	0.965407i	$-0.583969\pi$
$823$	20.2449	−	35.0652i	0.705693	−	1.22230i	0.966441	−	0.256890i	$-0.0826977\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	27.9452			0.971749			0.485875	−	0.874029i	$-0.338501\pi$
$827$	27.9452			0.971749			0.485875	+	0.874029i	$0.338501\pi$
$828$		0			0
$829$	−20.0226	−	34.6802i	−0.695415	−	1.20449i	−0.970040	−	0.242943i	$-0.921887\pi$
$829$	−20.0226	−	34.6802i	−0.695415	−	1.20449i	0.274625	−	0.961551i	$-0.411446\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−42.7095	−	26.0068i	−1.47980	−	0.901081i
$834$		0			0
$835$	0.190518	+	0.329986i	0.00659313	+	0.0114196i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	16.6312	−	28.8061i	0.574174	−	0.994499i	−0.421957	−	0.906616i	$-0.638657\pi$
$839$	16.6312	−	28.8061i	0.574174	−	0.994499i	0.996131	−	0.0878827i	$-0.0280101\pi$
$840$		0			0
$841$	10.8531	+	18.7982i	0.374246	+	0.648213i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	11.9973	−	20.7799i	0.412718	−	0.714849i
$846$		0			0
$847$	−3.18959	−	12.4851i	−0.109596	−	0.428993i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	4.67461	−	8.09666i	0.160244	−	0.277550i
$852$		0			0
$853$	−4.38730	+	7.59902i	−0.150218	+	0.260186i	−0.931308	−	0.364234i	$-0.881331\pi$
$853$	−4.38730	+	7.59902i	−0.150218	+	0.260186i	0.781089	+	0.624419i	$0.214664\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.35440			0.0462653			0.0231327	−	0.999732i	$-0.492636\pi$
$857$	1.35440			0.0462653			0.0231327	+	0.999732i	$0.492636\pi$
$858$		0			0
$859$	−18.0387			−0.615472			−0.307736	−	0.951472i	$-0.599571\pi$
$859$	−18.0387			−0.615472			−0.307736	+	0.951472i	$0.599571\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	6.37624	−	11.0440i	0.217050	−	0.375941i	−0.736855	−	0.676051i	$-0.763690\pi$
$863$	6.37624	−	11.0440i	0.217050	−	0.375941i	0.953905	+	0.300110i	$0.0970233\pi$
$864$		0			0
$865$	24.0121	+	41.5902i	0.816437	+	1.41411i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.05159	+	3.55347i	0.0695956	+	0.120543i
$870$		0			0
$871$	−22.0005			−0.745459
$872$		0			0
$873$		0			0
$874$		0			0
$875$	5.03135	+	19.6943i	0.170091	+	0.665790i
$876$		0			0
$877$	−17.5807			−0.593657			−0.296829	−	0.954931i	$-0.595929\pi$
$877$	−17.5807			−0.593657			−0.296829	+	0.954931i	$0.595929\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	25.8682			0.871523			0.435762	−	0.900062i	$-0.356479\pi$
$881$	25.8682			0.871523			0.435762	+	0.900062i	$0.356479\pi$
$882$		0			0
$883$	40.5923			1.36604			0.683020	−	0.730400i	$-0.260666\pi$
$883$	40.5923			1.36604			0.683020	+	0.730400i	$0.260666\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.93571			0.0985715			0.0492858	−	0.998785i	$-0.484305\pi$
$887$	2.93571			0.0985715			0.0492858	+	0.998785i	$0.484305\pi$
$888$		0			0
$889$	−0.906357	−	3.54778i	−0.0303982	−	0.118989i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	97.5700			3.26506
$894$		0			0
$895$	2.73289	+	4.73350i	0.0913504	+	0.158223i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−1.66077	−	2.87654i	−0.0553899	−	0.0959381i
$900$		0			0
$901$	−17.0491	+	29.5299i	−0.567987	+	0.983782i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.83439			0.160701
$906$		0			0
$907$	−34.2790			−1.13822			−0.569108	−	0.822263i	$-0.692711\pi$
$907$	−34.2790			−1.13822			−0.569108	+	0.822263i	$0.692711\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	4.98338	−	8.63146i	0.165107	−	0.285973i	−0.771586	−	0.636124i	$-0.780536\pi$
$911$	4.98338	−	8.63146i	0.165107	−	0.285973i	0.936693	+	0.350151i	$0.113870\pi$
$912$		0			0
$913$	20.9808	−	36.3398i	0.694363	−	1.20267i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.215930	−	0.845222i	−0.00713065	−	0.0279117i
$918$		0			0
$919$	13.9444	−	24.1524i	0.459983	−	0.796714i	−0.538976	−	0.842321i	$-0.681189\pi$
$919$	13.9444	−	24.1524i	0.459983	−	0.796714i	0.998959	+	0.0456069i	$0.0145222\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	4.63365	+	8.02573i	0.152519	+	0.264170i
$924$		0			0
$925$	11.1673	−	19.3423i	0.367177	−	0.635970i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−9.15294	−	15.8534i	−0.300298	−	0.520132i	0.675905	−	0.736989i	$-0.263753\pi$
$929$	−9.15294	−	15.8534i	−0.300298	−	0.520132i	−0.976203	+	0.216857i	$0.930420\pi$
$930$		0			0
$931$	1.31415	−	56.2585i	0.0430697	−	1.84380i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	37.9704	+	65.7666i	1.24176	+	2.15080i
$936$		0			0
$937$	46.2063			1.50950			0.754748	−	0.656015i	$-0.227759\pi$
$937$	46.2063			1.50950			0.754748	+	0.656015i	$0.227759\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	18.2251	−	31.5668i	0.594120	−	1.02905i	−0.399550	−	0.916711i	$-0.630834\pi$
$941$	18.2251	−	31.5668i	0.594120	−	1.02905i	0.993670	−	0.112335i	$-0.0358331\pi$
$942$		0			0
$943$	1.27381	+	2.20630i	0.0414810	+	0.0718472i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	23.7202	+	41.0846i	0.770803	+	1.33507i	0.937124	+	0.348998i	$0.113478\pi$
$947$	23.7202	+	41.0846i	0.770803	+	1.33507i	−0.166321	+	0.986072i	$0.553189\pi$
$948$		0			0
$949$	−4.02423	+	6.97017i	−0.130632	+	0.226261i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	6.68090			0.216415			0.108208	−	0.994128i	$-0.465489\pi$
$953$	6.68090			0.216415			0.108208	+	0.994128i	$0.465489\pi$
$954$		0			0
$955$	25.0961	+	43.4678i	0.812092	+	1.40659i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	5.85588	+	22.9218i	0.189096	+	0.740185i
$960$		0			0
$961$	14.7437	+	25.5368i	0.475603	+	0.823768i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−8.65548	+	14.9917i	−0.278630	+	0.482601i
$966$		0			0
$967$	7.60180	+	13.1667i	0.244457	+	0.423413i	0.961979	−	0.273124i	$-0.0880568\pi$
$967$	7.60180	+	13.1667i	0.244457	+	0.423413i	−0.717522	+	0.696536i	$0.754724\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.363057	+	0.628834i	−0.0116511	+	0.0201802i	−0.871792	−	0.489876i	$-0.837042\pi$
$971$	−0.363057	+	0.628834i	−0.0116511	+	0.0201802i	0.860141	+	0.510056i	$0.170375\pi$
$972$		0			0
$973$	14.8705	−	14.5272i	0.476726	−	0.465720i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−21.5203	+	37.2742i	−0.688494	+	1.19251i	0.283831	+	0.958874i	$0.408395\pi$
$977$	−21.5203	+	37.2742i	−0.688494	+	1.19251i	−0.972325	+	0.233633i	$0.924939\pi$
$978$		0			0
$979$	−6.88350	+	11.9226i	−0.219997	+	0.381047i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−43.0382			−1.37271			−0.686353	−	0.727269i	$-0.740789\pi$
$983$	−43.0382			−1.37271			−0.686353	+	0.727269i	$0.740789\pi$
$984$		0			0
$985$	28.9149			0.921307
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.01905	−	5.22915i	0.0960002	−	0.166277i
$990$		0			0
$991$	−11.2758	−	19.5302i	−0.358187	−	0.620398i	0.629471	−	0.777024i	$-0.283272\pi$
$991$	−11.2758	−	19.5302i	−0.358187	−	0.620398i	−0.987658	+	0.156626i	$0.949938\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−25.1873	−	43.6257i	−0.798491	−	1.38303i
$996$		0			0
$997$	−28.3341			−0.897350			−0.448675	−	0.893695i	$-0.648104\pi$
$997$	−28.3341			−0.897350			−0.448675	+	0.893695i	$0.648104\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.t.c.289.9		22
3.2	odd	2		504.2.t.c.457.8	yes	22
4.3	odd	2		3024.2.t.k.289.9		22
7.4	even	3		1512.2.q.d.1369.3		22
9.4	even	3		1512.2.q.d.793.3		22
9.5	odd	6		504.2.q.c.121.9	yes	22
12.11	even	2		1008.2.t.l.961.4		22
21.11	odd	6		504.2.q.c.25.9	✓	22
28.11	odd	6		3024.2.q.l.2881.3		22
36.23	even	6		1008.2.q.l.625.3		22
36.31	odd	6		3024.2.q.l.2305.3		22
63.4	even	3	inner	1512.2.t.c.361.9		22
63.32	odd	6		504.2.t.c.193.8	yes	22
84.11	even	6		1008.2.q.l.529.3		22
252.67	odd	6		3024.2.t.k.1873.9		22
252.95	even	6		1008.2.t.l.193.4		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.9	✓	22	21.11	odd	6
504.2.q.c.121.9	yes	22	9.5	odd	6
504.2.t.c.193.8	yes	22	63.32	odd	6
504.2.t.c.457.8	yes	22	3.2	odd	2
1008.2.q.l.529.3		22	84.11	even	6
1008.2.q.l.625.3		22	36.23	even	6
1008.2.t.l.193.4		22	252.95	even	6
1008.2.t.l.961.4		22	12.11	even	2
1512.2.q.d.793.3		22	9.4	even	3
1512.2.q.d.1369.3		22	7.4	even	3
1512.2.t.c.289.9		22	1.1	even	1	trivial
1512.2.t.c.361.9		22	63.4	even	3	inner
3024.2.q.l.2305.3		22	36.31	odd	6
3024.2.q.l.2881.3		22	28.11	odd	6
3024.2.t.k.289.9		22	4.3	odd	2
3024.2.t.k.1873.9		22	252.67	odd	6

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.66851 q^{5} +(-0.654882 - 2.56342i) q^{7} +O(q^{10})\)	\(q+2.66851 q^{5} +(-0.654882 - 2.56342i) q^{7} +3.98378 q^{11} +(1.00103 + 1.73384i) q^{13} +(3.57175 + 6.18646i) q^{17} +(-4.01956 + 6.96208i) q^{19} +0.887818 q^{23} +2.12092 q^{25} +(1.35035 - 2.33887i) q^{29} +(0.614943 - 1.06511i) q^{31} +(-1.74756 - 6.84051i) q^{35} +(5.26528 - 9.11973i) q^{37} +(1.43477 + 2.48509i) q^{41} +(3.40053 - 5.88989i) q^{43} +(-6.06845 - 10.5109i) q^{47} +(-6.14226 + 3.35748i) q^{49} +(2.38665 + 4.13380i) q^{53} +10.6307 q^{55} +(4.79029 - 8.29703i) q^{59} +(4.74981 + 8.22692i) q^{61} +(2.67126 + 4.62676i) q^{65} +(-5.49446 + 9.51668i) q^{67} +4.62888 q^{71} +(2.01004 + 3.48149i) q^{73} +(-2.60890 - 10.2121i) q^{77} +(0.514987 + 0.891984i) q^{79} +(5.26656 - 9.12195i) q^{83} +(9.53125 + 16.5086i) q^{85} +(-1.72788 + 2.99278i) q^{89} +(3.78900 - 3.70153i) q^{91} +(-10.7262 + 18.5784i) q^{95} +(-1.12061 + 1.94096i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q + 2 * q^5 - q^7	\( 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

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