LMFDB - Embedded newform 3564.2.i.t.1189.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3564,2,Mod(1189,3564)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3564, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3564.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3564 = 2^{2} \cdot 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3564.i (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:	$28.4586832804$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 18x^{9} + 152x^{8} - 204x^{7} + 162x^{6} - 408x^{5} + 2800x^{4} - 4422x^{3} + 3528x^{2} - 252x + 9 $ x^12 - 18x^9 + 152x^8 - 204x^7 + 162x^6 - 408x^5 + 2800x^4 - 4422x^3 + 3528x^2 - 252*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1189.3
Root			$0.895540 - 0.895540i$ of defining polynomial
Character	$\chi$	$=$	3564.1189
Dual form			3564.2.i.t.2377.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.327790 - 0.567749i) q^{5} +(-1.34070 + 2.32217i) q^{7} +O(q^{10})$	$q+(-0.327790 - 0.567749i) q^{5} +(-1.34070 + 2.32217i) q^{7} +(0.500000 - 0.866025i) q^{11} +(-0.0382352 - 0.0662253i) q^{13} -1.89033 q^{17} -8.09100 q^{19} +(3.60227 + 6.23931i) q^{23} +(2.28511 - 3.95792i) q^{25} +(0.157517 - 0.272827i) q^{29} +(-3.86040 - 6.68641i) q^{31} +1.75788 q^{35} +6.04626 q^{37} +(4.59355 + 7.95626i) q^{41} +(4.72834 - 8.18972i) q^{43} +(6.37138 - 11.0356i) q^{47} +(-0.0949771 - 0.164505i) q^{49} -9.59217 q^{53} -0.655580 q^{55} +(-4.93926 - 8.55505i) q^{59} +(3.47879 - 6.02545i) q^{61} +(-0.0250662 + 0.0434160i) q^{65} +(-0.00872101 - 0.0151052i) q^{67} -8.54591 q^{71} +10.7308 q^{73} +(1.34070 + 2.32217i) q^{77} +(3.64577 - 6.31465i) q^{79} +(-5.29992 + 9.17973i) q^{83} +(0.619632 + 1.07323i) q^{85} +12.6870 q^{89} +0.205048 q^{91} +(2.65215 + 4.59366i) q^{95} +(-3.66397 + 6.34618i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{7}+O(q^{10}) $ 12 * q + 2 * q^7	$ 12 q + 2 q^{7} + 6 q^{11} + 6 q^{13} - 8 q^{17} + 4 q^{23} - 10 q^{25} - 4 q^{29} - 6 q^{31} - 28 q^{35} - 12 q^{37} + 22 q^{41} + 10 q^{43} + 20 q^{47} - 6 q^{49} - 8 q^{53} + 24 q^{59} + 10 q^{61} + 40 q^{65} + 6 q^{67} - 80 q^{71} - 16 q^{73} - 2 q^{77} + 14 q^{79} + 12 q^{83} - 6 q^{85} - 48 q^{89} + 20 q^{91} + 44 q^{95} - 20 q^{97}+O(q^{100}) $ 12 * q + 2 * q^7 + 6 * q^11 + 6 * q^13 - 8 * q^17 + 4 * q^23 - 10 * q^25 - 4 * q^29 - 6 * q^31 - 28 * q^35 - 12 * q^37 + 22 * q^41 + 10 * q^43 + 20 * q^47 - 6 * q^49 - 8 * q^53 + 24 * q^59 + 10 * q^61 + 40 * q^65 + 6 * q^67 - 80 * q^71 - 16 * q^73 - 2 * q^77 + 14 * q^79 + 12 * q^83 - 6 * q^85 - 48 * q^89 + 20 * q^91 + 44 * q^95 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3564\mathbb{Z}\right)^\times$.

$n$	$1541$	$1783$	$2917$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.327790	−	0.567749i	−0.146592	−	0.253905i	0.783374	−	0.621551i	$-0.213497\pi$
$5$	−0.327790	−	0.567749i	−0.146592	−	0.253905i	−0.929966	+	0.367646i	$0.880164\pi$
$6$		0			0
$7$	−1.34070	+	2.32217i	−0.506739	+	0.877697i	0.493231	+	0.869898i	$0.335816\pi$
$7$	−1.34070	+	2.32217i	−0.506739	+	0.877697i	−0.999970	+	0.00779870i	$0.997518\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	−0.0382352	−	0.0662253i	−0.0106045	−	0.0183676i	0.860674	−	0.509156i	$-0.170042\pi$
$13$	−0.0382352	−	0.0662253i	−0.0106045	−	0.0183676i	−0.871279	+	0.490788i	$0.836709\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.89033			−0.458472			−0.229236	−	0.973371i	$-0.573623\pi$
$17$	−1.89033			−0.458472			−0.229236	+	0.973371i	$0.573623\pi$
$18$		0			0
$19$	−8.09100			−1.85620			−0.928101	−	0.372329i	$-0.878559\pi$
$19$	−8.09100			−1.85620			−0.928101	+	0.372329i	$0.878559\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.60227	+	6.23931i	0.751125	+	1.30099i	0.947278	+	0.320413i	$0.103822\pi$
$23$	3.60227	+	6.23931i	0.751125	+	1.30099i	−0.196153	+	0.980573i	$0.562845\pi$
$24$		0			0
$25$	2.28511	−	3.95792i	0.457021	−	0.791584i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.157517	−	0.272827i	0.0292501	−	0.0506627i	−0.851030	−	0.525117i	$-0.824021\pi$
$29$	0.157517	−	0.272827i	0.0292501	−	0.0506627i	0.880280	+	0.474455i	$0.157355\pi$
$30$		0			0
$31$	−3.86040	−	6.68641i	−0.693349	−	1.20092i	−0.970734	−	0.240157i	$-0.922801\pi$
$31$	−3.86040	−	6.68641i	−0.693349	−	1.20092i	0.277385	−	0.960759i	$-0.410532\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.75788			0.297136
$36$		0			0
$37$	6.04626			0.993999			0.496999	−	0.867751i	$-0.334435\pi$
$37$	6.04626			0.993999			0.496999	+	0.867751i	$0.334435\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.59355	+	7.95626i	0.717392	+	1.24256i	0.962030	+	0.272944i	$0.0879975\pi$
$41$	4.59355	+	7.95626i	0.717392	+	1.24256i	−0.244638	+	0.969614i	$0.578669\pi$
$42$		0			0
$43$	4.72834	−	8.18972i	0.721064	−	1.24892i	−0.239509	−	0.970894i	$-0.576986\pi$
$43$	4.72834	−	8.18972i	0.721064	−	1.24892i	0.960574	−	0.278026i	$-0.0896802\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.37138	−	11.0356i	0.929362	−	1.60970i	0.144969	−	0.989436i	$-0.453692\pi$
$47$	6.37138	−	11.0356i	0.929362	−	1.60970i	0.784392	−	0.620265i	$-0.212975\pi$
$48$		0			0
$49$	−0.0949771	−	0.164505i	−0.0135682	−	0.0235007i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−9.59217			−1.31759			−0.658793	−	0.752324i	$-0.728933\pi$
$53$	−9.59217			−1.31759			−0.658793	+	0.752324i	$0.728933\pi$
$54$		0			0
$55$	−0.655580			−0.0883985
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.93926	−	8.55505i	−0.643037	−	1.11377i	−0.984751	−	0.173968i	$-0.944341\pi$
$59$	−4.93926	−	8.55505i	−0.643037	−	1.11377i	0.341714	−	0.939804i	$-0.388992\pi$
$60$		0			0
$61$	3.47879	−	6.02545i	0.445414	−	0.771480i	−0.552667	−	0.833402i	$-0.686390\pi$
$61$	3.47879	−	6.02545i	0.445414	−	0.771480i	0.998081	+	0.0619225i	$0.0197232\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.0250662	+	0.0434160i	−0.00310908	+	0.00538509i
$66$		0			0
$67$	−0.00872101	−	0.0151052i	−0.00106544	−	0.00184540i	0.865492	−	0.500922i	$-0.167006\pi$
$67$	−0.00872101	−	0.0151052i	−0.00106544	−	0.00184540i	−0.866558	+	0.499077i	$0.833672\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.54591			−1.01421			−0.507106	−	0.861883i	$-0.669285\pi$
$71$	−8.54591			−1.01421			−0.507106	+	0.861883i	$0.669285\pi$
$72$		0			0
$73$	10.7308			1.25595			0.627974	−	0.778235i	$-0.283885\pi$
$73$	10.7308			1.25595			0.627974	+	0.778235i	$0.283885\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.34070	+	2.32217i	0.152787	+	0.264636i
$78$		0			0
$79$	3.64577	−	6.31465i	0.410181	−	0.710454i	−0.584729	−	0.811229i	$-0.698799\pi$
$79$	3.64577	−	6.31465i	0.410181	−	0.710454i	0.994909	+	0.100775i	$0.0321323\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−5.29992	+	9.17973i	−0.581741	+	1.00761i	0.413532	+	0.910490i	$0.364295\pi$
$83$	−5.29992	+	9.17973i	−0.581741	+	1.00761i	−0.995273	+	0.0971160i	$0.969038\pi$
$84$		0			0
$85$	0.619632	+	1.07323i	0.0672085	+	0.116409i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	12.6870			1.34482			0.672412	−	0.740177i	$-0.265258\pi$
$89$	12.6870			1.34482			0.672412	+	0.740177i	$0.265258\pi$
$90$		0			0
$91$	0.205048			0.0214949
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.65215	+	4.59366i	0.272105	+	0.471299i
$96$		0			0
$97$	−3.66397	+	6.34618i	−0.372019	+	0.644357i	−0.989876	−	0.141934i	$-0.954668\pi$
$97$	−3.66397	+	6.34618i	−0.372019	+	0.644357i	0.617857	+	0.786291i	$0.288001\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.66659	+	2.88661i	−0.165832	+	0.287229i	−0.936950	−	0.349463i	$-0.886364\pi$
$101$	−1.66659	+	2.88661i	−0.165832	+	0.287229i	0.771119	+	0.636691i	$0.219698\pi$
$102$		0			0
$103$	−5.25676	−	9.10497i	−0.517964	−	0.897139i	−0.999782	−	0.0208682i	$-0.993357\pi$
$103$	−5.25676	−	9.10497i	−0.517964	−	0.897139i	0.481819	−	0.876271i	$-0.339976\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.790123			−0.0763840			−0.0381920	−	0.999270i	$-0.512160\pi$
$107$	−0.790123			−0.0763840			−0.0381920	+	0.999270i	$0.512160\pi$
$108$		0			0
$109$	3.36800			0.322596			0.161298	−	0.986906i	$-0.448432\pi$
$109$	3.36800			0.322596			0.161298	+	0.986906i	$0.448432\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.38058	−	12.7835i	−0.694307	−	1.20257i	−0.970414	−	0.241448i	$-0.922378\pi$
$113$	−7.38058	−	12.7835i	−0.694307	−	1.20257i	0.276107	−	0.961127i	$-0.410956\pi$
$114$		0			0
$115$	2.36158	−	4.09037i	0.220218	−	0.381429i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.53437	−	4.38966i	0.232326	−	0.402400i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−6.27405			−0.561168
$126$		0			0
$127$	15.7248			1.39535			0.697676	−	0.716414i	$-0.254218\pi$
$127$	15.7248			1.39535			0.697676	+	0.716414i	$0.254218\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.80890	+	4.86516i	0.245415	+	0.425071i	0.962248	−	0.272173i	$-0.0877424\pi$
$131$	2.80890	+	4.86516i	0.245415	+	0.425071i	−0.716833	+	0.697245i	$0.754409\pi$
$132$		0			0
$133$	10.8476	−	18.7887i	0.940609	−	1.62918i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.45705	−	14.6480i	0.722535	−	1.25147i	−0.237446	−	0.971401i	$-0.576310\pi$
$137$	8.45705	−	14.6480i	0.722535	−	1.25147i	0.959981	−	0.280066i	$-0.0903563\pi$
$138$		0			0
$139$	−7.99333	−	13.8449i	−0.677986	−	1.17431i	−0.975587	−	0.219615i	$-0.929520\pi$
$139$	−7.99333	−	13.8449i	−0.677986	−	1.17431i	0.297601	−	0.954690i	$-0.403813\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.0764703			−0.00639477
$144$		0			0
$145$	−0.206530			−0.0171514
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6.86350	+	11.8879i	0.562280	+	0.973898i	0.997297	+	0.0734754i	$0.0234090\pi$
$149$	6.86350	+	11.8879i	0.562280	+	0.973898i	−0.435017	+	0.900422i	$0.643258\pi$
$150$		0			0
$151$	8.19101	−	14.1872i	0.666575	−	1.15454i	−0.312281	−	0.949990i	$-0.601093\pi$
$151$	8.19101	−	14.1872i	0.666575	−	1.15454i	0.978856	−	0.204552i	$-0.0655736\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.53081	+	4.38348i	−0.203279	+	0.352090i
$156$		0			0
$157$	−1.37650	−	2.38416i	−0.109856	−	0.190277i	0.805856	−	0.592112i	$-0.201706\pi$
$157$	−1.37650	−	2.38416i	−0.109856	−	0.190277i	−0.915712	+	0.401835i	$0.868372\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−19.3183			−1.52250
$162$		0			0
$163$	1.37101			0.107386			0.0536930	−	0.998557i	$-0.482901\pi$
$163$	1.37101			0.107386			0.0536930	+	0.998557i	$0.482901\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.8885	+	20.5915i	0.919961	+	1.59342i	0.799472	+	0.600704i	$0.205113\pi$
$167$	11.8885	+	20.5915i	0.919961	+	1.59342i	0.120489	+	0.992715i	$0.461554\pi$
$168$		0			0
$169$	6.49708	−	11.2533i	0.499775	−	0.865636i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.64014	−	11.5011i	0.504841	−	0.874410i	−0.495144	−	0.868811i	$-0.664885\pi$
$173$	6.64014	−	11.5011i	0.504841	−	0.874410i	0.999984	−	0.00559867i	$-0.00178212\pi$
$174$		0			0
$175$	6.12731	+	10.6128i	0.463181	+	0.802253i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−5.38531			−0.402517			−0.201258	−	0.979538i	$-0.564503\pi$
$179$	−5.38531			−0.402517			−0.201258	+	0.979538i	$0.564503\pi$
$180$		0			0
$181$	−1.34538			−0.100001			−0.0500005	−	0.998749i	$-0.515922\pi$
$181$	−1.34538			−0.100001			−0.0500005	+	0.998749i	$0.515922\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.98190	−	3.43276i	−0.145713	−	0.252382i
$186$		0			0
$187$	−0.945165	+	1.63707i	−0.0691173	+	0.119715i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.47635	−	16.4135i	0.685685	−	1.18764i	−0.287537	−	0.957770i	$-0.592836\pi$
$191$	9.47635	−	16.4135i	0.685685	−	1.18764i	0.973221	−	0.229871i	$-0.0738304\pi$
$192$		0			0
$193$	−5.65319	−	9.79160i	−0.406925	−	0.704815i	0.587618	−	0.809138i	$-0.300066\pi$
$193$	−5.65319	−	9.79160i	−0.406925	−	0.704815i	−0.994543	+	0.104323i	$0.966732\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.63595			0.615286			0.307643	−	0.951502i	$-0.400460\pi$
$197$	8.63595			0.615286			0.307643	+	0.951502i	$0.400460\pi$
$198$		0			0
$199$	−4.53905			−0.321765			−0.160882	−	0.986974i	$-0.551434\pi$
$199$	−4.53905			−0.321765			−0.160882	+	0.986974i	$0.551434\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.422367	+	0.731561i	0.0296443	+	0.0513455i
$204$		0			0
$205$	3.01144	−	5.21597i	0.210328	−	0.364299i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4.04550	+	7.00701i	−0.279833	+	0.484685i
$210$		0			0
$211$	−5.14551	−	8.91229i	−0.354232	−	0.613547i	0.632755	−	0.774352i	$-0.281924\pi$
$211$	−5.14551	−	8.91229i	−0.354232	−	0.613547i	−0.986986	+	0.160805i	$0.948591\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6.19961			−0.422810
$216$		0			0
$217$	20.7026			1.40539
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.0722771	+	0.125188i	0.00486188	+	0.00842103i
$222$		0			0
$223$	−0.794893	+	1.37679i	−0.0532300	+	0.0921970i	−0.891413	−	0.453193i	$-0.850285\pi$
$223$	−0.794893	+	1.37679i	−0.0532300	+	0.0921970i	0.838183	+	0.545390i	$0.183618\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.49868	−	2.59579i	0.0994709	−	0.172289i	−0.811995	−	0.583665i	$-0.801618\pi$
$227$	1.49868	−	2.59579i	0.0994709	−	0.172289i	0.911466	+	0.411376i	$0.134952\pi$
$228$		0			0
$229$	−12.3947	−	21.4682i	−0.819063	−	1.41866i	−0.906374	−	0.422477i	$-0.861161\pi$
$229$	−12.3947	−	21.4682i	−0.819063	−	1.41866i	0.0873108	−	0.996181i	$-0.472173\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.38173			−0.287056			−0.143528	−	0.989646i	$-0.545845\pi$
$233$	−4.38173			−0.287056			−0.143528	+	0.989646i	$0.545845\pi$
$234$		0			0
$235$	−8.35391			−0.544949
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−13.1993	−	22.8618i	−0.853791	−	1.47881i	−0.877762	−	0.479097i	$-0.840964\pi$
$239$	−13.1993	−	22.8618i	−0.853791	−	1.47881i	0.0239712	−	0.999713i	$-0.492369\pi$
$240$		0			0
$241$	−1.11938	+	1.93882i	−0.0721054	+	0.124890i	−0.899824	−	0.436253i	$-0.856305\pi$
$241$	−1.11938	+	1.93882i	−0.0721054	+	0.124890i	0.827718	+	0.561144i	$0.189638\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.0622651	+	0.107846i	−0.00397797	+	0.00689005i
$246$		0			0
$247$	0.309361	+	0.535828i	0.0196841	+	0.0340939i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−16.1652			−1.02034			−0.510170	−	0.860074i	$-0.670417\pi$
$251$	−16.1652			−1.02034			−0.510170	+	0.860074i	$0.670417\pi$
$252$		0			0
$253$	7.20454			0.452945
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.53120	+	11.3124i	0.407405	+	0.705646i	0.994598	−	0.103801i	$-0.0331005\pi$
$257$	6.53120	+	11.3124i	0.407405	+	0.705646i	−0.587193	+	0.809447i	$0.699767\pi$
$258$		0			0
$259$	−8.10625	+	14.0404i	−0.503698	+	0.872430i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	7.32204	−	12.6821i	0.451496	−	0.782015i	−0.546983	−	0.837144i	$-0.684224\pi$
$263$	7.32204	−	12.6821i	0.451496	−	0.782015i	0.998479	+	0.0551291i	$0.0175570\pi$
$264$		0			0
$265$	3.14422	+	5.44595i	0.193148	+	0.334542i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	19.8128			1.20801			0.604003	−	0.796982i	$-0.293572\pi$
$269$	19.8128			1.20801			0.604003	+	0.796982i	$0.293572\pi$
$270$		0			0
$271$	−18.0775			−1.09813			−0.549064	−	0.835780i	$-0.685016\pi$
$271$	−18.0775			−1.09813			−0.549064	+	0.835780i	$0.685016\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.28511	−	3.95792i	−0.137797	−	0.238672i
$276$		0			0
$277$	4.17048	−	7.22349i	0.250580	−	0.434017i	−0.713106	−	0.701057i	$-0.752712\pi$
$277$	4.17048	−	7.22349i	0.250580	−	0.434017i	0.963686	+	0.267039i	$0.0860454\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.61789	+	6.26637i	−0.215825	+	0.373820i	−0.953528	−	0.301306i	$-0.902578\pi$
$281$	−3.61789	+	6.26637i	−0.215825	+	0.373820i	0.737702	+	0.675126i	$0.235911\pi$
$282$		0			0
$283$	−6.49349	−	11.2471i	−0.385998	−	0.668568i	0.605909	−	0.795534i	$-0.292809\pi$
$283$	−6.49349	−	11.2471i	−0.385998	−	0.668568i	−0.991907	+	0.126966i	$0.959476\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−24.6344			−1.45412
$288$		0			0
$289$	−13.4267			−0.789803
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.0618433	+	0.107116i	0.00361293	+	0.00625777i	0.867826	−	0.496868i	$-0.165517\pi$
$293$	0.0618433	+	0.107116i	0.00361293	+	0.00625777i	−0.864213	+	0.503126i	$0.832183\pi$
$294$		0			0
$295$	−3.23808	+	5.60852i	−0.188528	+	0.326541i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.275467	−	0.477122i	0.0159307	−	0.0275927i
$300$		0			0
$301$	12.6786	+	21.9600i	0.730782	+	1.26575i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−4.56126			−0.261177
$306$		0			0
$307$	−27.9245			−1.59374			−0.796868	−	0.604153i	$-0.793512\pi$
$307$	−27.9245			−1.59374			−0.796868	+	0.604153i	$0.793512\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.54662	+	14.8032i	0.484634	+	0.839411i	0.999844	−	0.0176526i	$-0.00561930\pi$
$311$	8.54662	+	14.8032i	0.484634	+	0.839411i	−0.515210	+	0.857064i	$0.672286\pi$
$312$		0			0
$313$	8.83774	−	15.3074i	0.499539	−	0.865226i	−0.500461	−	0.865759i	$-0.666836\pi$
$313$	8.83774	−	15.3074i	0.499539	−	0.865226i	1.00000		0.000532695i	$0.000169562\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.4396	+	18.0819i	−0.586347	+	1.01558i	0.408359	+	0.912821i	$0.366101\pi$
$317$	−10.4396	+	18.0819i	−0.586347	+	1.01558i	−0.994706	+	0.102761i	$0.967232\pi$
$318$		0			0
$319$	−0.157517	−	0.272827i	−0.00881925	−	0.0152754i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	15.2947			0.851017
$324$		0			0
$325$	−0.349486			−0.0193860
$326$		0			0
$327$		0			0
$328$		0			0
$329$	17.0843	+	29.5908i	0.941887	+	1.63140i
$330$		0			0
$331$	−4.70342	+	8.14655i	−0.258523	+	0.447775i	−0.965846	−	0.259115i	$-0.916569\pi$
$331$	−4.70342	+	8.14655i	−0.258523	+	0.447775i	0.707323	+	0.706890i	$0.249902\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.00571733	+	0.00990270i	−0.000312371	+	0.000541042i
$336$		0			0
$337$	9.96379	+	17.2578i	0.542762	+	0.940092i	0.998744	+	0.0501026i	$0.0159548\pi$
$337$	9.96379	+	17.2578i	0.542762	+	0.940092i	−0.455982	+	0.889989i	$0.650712\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−7.72081			−0.418105
$342$		0			0
$343$	−18.2605			−0.985975
$344$		0			0
$345$		0			0
$346$		0			0
$347$	12.8991	+	22.3420i	0.692462	+	1.19938i	0.971029	+	0.238962i	$0.0768072\pi$
$347$	12.8991	+	22.3420i	0.692462	+	1.19938i	−0.278567	+	0.960417i	$0.589859\pi$
$348$		0			0
$349$	−8.70336	+	15.0747i	−0.465880	+	0.806929i	−0.999241	−	0.0389595i	$-0.987596\pi$
$349$	−8.70336	+	15.0747i	−0.465880	+	0.806929i	0.533360	+	0.845888i	$0.320929\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.34271	−	2.32564i	0.0714651	−	0.123781i	−0.828079	−	0.560612i	$-0.810566\pi$
$353$	1.34271	−	2.32564i	0.0714651	−	0.123781i	0.899544	+	0.436831i	$0.143899\pi$
$354$		0			0
$355$	2.80127	+	4.85193i	0.148676	+	0.257514i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.1629			0.536375			0.268187	−	0.963367i	$-0.413575\pi$
$359$	10.1629			0.536375			0.268187	+	0.963367i	$0.413575\pi$
$360$		0			0
$361$	46.4642			2.44549
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.51746	−	6.09242i	−0.184112	−	0.318892i
$366$		0			0
$367$	8.69055	−	15.0525i	0.453643	−	0.785732i	−0.544966	−	0.838458i	$-0.683458\pi$
$367$	8.69055	−	15.0525i	0.453643	−	0.785732i	0.998609	+	0.0527256i	$0.0167909\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	12.8603	−	22.2746i	0.667672	−	1.15644i
$372$		0			0
$373$	−16.2586	−	28.1608i	−0.841839	−	1.45811i	−0.888338	−	0.459190i	$-0.848140\pi$
$373$	−16.2586	−	28.1608i	−0.841839	−	1.45811i	0.0464985	−	0.998918i	$-0.485194\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.0240907			−0.00124074
$378$		0			0
$379$	12.1445			0.623822			0.311911	−	0.950111i	$-0.399031\pi$
$379$	12.1445			0.623822			0.311911	+	0.950111i	$0.399031\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.275480	−	0.477146i	−0.0140764	−	0.0243810i	0.858901	−	0.512141i	$-0.171147\pi$
$383$	−0.275480	−	0.477146i	−0.0140764	−	0.0243810i	−0.872978	+	0.487760i	$0.837814\pi$
$384$		0			0
$385$	0.878940	−	1.52237i	0.0447949	−	0.0775871i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.62448	+	16.6701i	−0.487981	+	0.845207i	−0.999904	−	0.0138236i	$-0.995600\pi$
$389$	−9.62448	+	16.6701i	−0.487981	+	0.845207i	0.511924	+	0.859031i	$0.328933\pi$
$390$		0			0
$391$	−6.80948	−	11.7944i	−0.344370	−	0.596466i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.78018			−0.240517
$396$		0			0
$397$	0.233984			0.0117433			0.00587166	−	0.999983i	$-0.498131\pi$
$397$	0.233984			0.0117433			0.00587166	+	0.999983i	$0.498131\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−18.4709	−	31.9925i	−0.922392	−	1.59763i	−0.795703	−	0.605686i	$-0.792899\pi$
$401$	−18.4709	−	31.9925i	−0.922392	−	1.59763i	−0.126688	−	0.991943i	$-0.540435\pi$
$402$		0			0
$403$	−0.295206	+	0.511312i	−0.0147053	+	0.0254703i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.02313	−	5.23621i	0.149851	−	0.259550i
$408$		0			0
$409$	10.2770	+	17.8003i	0.508165	+	0.880167i	0.999955	+	0.00945359i	$0.00300922\pi$
$409$	10.2770	+	17.8003i	0.508165	+	0.880167i	−0.491791	+	0.870713i	$0.663657\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	26.4883			1.30341
$414$		0			0
$415$	6.94904			0.341115
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.12444	+	10.6078i	0.299199	+	0.518227i	0.975953	−	0.217982i	$-0.0699474\pi$
$419$	6.12444	+	10.6078i	0.299199	+	0.518227i	−0.676754	+	0.736209i	$0.736614\pi$
$420$		0			0
$421$	16.6439	−	28.8281i	0.811173	−	1.40499i	−0.100870	−	0.994900i	$-0.532163\pi$
$421$	16.6439	−	28.8281i	0.811173	−	1.40499i	0.912043	−	0.410094i	$-0.134504\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.31961	+	7.48178i	−0.209532	+	0.362920i
$426$		0			0
$427$	9.32807	+	16.1567i	0.451417	+	0.781877i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	7.74063			0.372853			0.186427	−	0.982469i	$-0.440309\pi$
$431$	7.74063			0.372853			0.186427	+	0.982469i	$0.440309\pi$
$432$		0			0
$433$	1.29499			0.0622331			0.0311165	−	0.999516i	$-0.490094\pi$
$433$	1.29499			0.0622331			0.0311165	+	0.999516i	$0.490094\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−29.1459	−	50.4823i	−1.39424	−	2.41489i
$438$		0			0
$439$	3.45206	−	5.97914i	0.164758	−	0.285369i	−0.771812	−	0.635851i	$-0.780649\pi$
$439$	3.45206	−	5.97914i	0.164758	−	0.285369i	0.936569	+	0.350483i	$0.113982\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.20502	−	15.9436i	0.437344	−	0.757501i	−0.560140	−	0.828398i	$-0.689253\pi$
$443$	9.20502	−	15.9436i	0.437344	−	0.757501i	0.997484	+	0.0708965i	$0.0225860\pi$
$444$		0			0
$445$	−4.15869	−	7.20306i	−0.197141	−	0.341458i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	8.03355			0.379126			0.189563	−	0.981869i	$-0.439293\pi$
$449$	8.03355			0.379126			0.189563	+	0.981869i	$0.439293\pi$
$450$		0			0
$451$	9.18710			0.432603
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.0672128	−	0.116416i	−0.00315099	−	0.00545767i
$456$		0			0
$457$	11.6811	−	20.2323i	0.546421	−	0.946429i	−0.452095	−	0.891970i	$-0.649323\pi$
$457$	11.6811	−	20.2323i	0.546421	−	0.946429i	0.998516	−	0.0544589i	$-0.0173434\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−17.3133	+	29.9875i	−0.806359	+	1.39666i	0.109010	+	0.994041i	$0.465232\pi$
$461$	−17.3133	+	29.9875i	−0.806359	+	1.39666i	−0.915369	+	0.402615i	$0.868101\pi$
$462$		0			0
$463$	−3.35742	−	5.81522i	−0.156033	−	0.270256i	0.777402	−	0.629004i	$-0.216537\pi$
$463$	−3.35742	−	5.81522i	−0.156033	−	0.270256i	−0.933435	+	0.358748i	$0.883204\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.6105			−0.907468			−0.453734	−	0.891137i	$-0.649908\pi$
$467$	−19.6105			−0.907468			−0.453734	+	0.891137i	$0.649908\pi$
$468$		0			0
$469$	0.0467692			0.00215960
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.72834	−	8.18972i	−0.217409	−	0.376564i
$474$		0			0
$475$	−18.4888	+	32.0235i	−0.848324	+	1.46934i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−11.0616	+	19.1593i	−0.505418	+	0.875409i	0.494562	+	0.869142i	$0.335328\pi$
$479$	−11.0616	+	19.1593i	−0.505418	+	0.875409i	−0.999980	+	0.00626736i	$0.998005\pi$
$480$		0			0
$481$	−0.231180	−	0.400415i	−0.0105409	−	0.0182574i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.80405			0.218141
$486$		0			0
$487$	15.8788			0.719538			0.359769	−	0.933041i	$-0.382856\pi$
$487$	15.8788			0.719538			0.359769	+	0.933041i	$0.382856\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.84911	+	11.8630i	0.309096	+	0.535370i	0.978165	−	0.207830i	$-0.0666402\pi$
$491$	6.84911	+	11.8630i	0.309096	+	0.535370i	−0.669069	+	0.743200i	$0.733307\pi$
$492$		0			0
$493$	−0.297759	+	0.515733i	−0.0134104	+	0.0232274i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	11.4575	−	19.8450i	0.513941	−	0.890172i
$498$		0			0
$499$	10.0608	+	17.4259i	0.450385	+	0.780090i	0.998410	−	0.0563721i	$-0.0179533\pi$
$499$	10.0608	+	17.4259i	0.450385	+	0.780090i	−0.548025	+	0.836462i	$0.684620\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−26.2246			−1.16930			−0.584649	−	0.811286i	$-0.698768\pi$
$503$	−26.2246			−1.16930			−0.584649	+	0.811286i	$0.698768\pi$
$504$		0			0
$505$	2.18516			0.0972386
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5.92359	−	10.2600i	−0.262558	−	0.454765i	0.704363	−	0.709840i	$-0.251233\pi$
$509$	−5.92359	−	10.2600i	−0.262558	−	0.454765i	−0.966921	+	0.255076i	$0.917900\pi$
$510$		0			0
$511$	−14.3869	+	24.9188i	−0.636437	+	1.10234i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.44623	+	5.96904i	−0.151859	+	0.263027i
$516$		0			0
$517$	−6.37138	−	11.0356i	−0.280213	−	0.485343i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	37.0475			1.62308			0.811540	−	0.584296i	$-0.198629\pi$
$521$	37.0475			1.62308			0.811540	+	0.584296i	$0.198629\pi$
$522$		0			0
$523$	−33.5131			−1.46543			−0.732713	−	0.680538i	$-0.761746\pi$
$523$	−33.5131			−1.46543			−0.732713	+	0.680538i	$0.761746\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7.29744	+	12.6395i	0.317881	+	0.550587i
$528$		0			0
$529$	−14.4527	+	25.0328i	−0.628378	+	1.08838i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.351270	−	0.608418i	0.0152152	−	0.0263535i
$534$		0			0
$535$	0.258994	+	0.448592i	0.0111973	+	0.0193943i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.189954			−0.00818191
$540$		0			0
$541$	−17.1591			−0.737729			−0.368864	−	0.929483i	$-0.620253\pi$
$541$	−17.1591			−0.737729			−0.368864	+	0.929483i	$0.620253\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.10400	−	1.91218i	−0.0472901	−	0.0819088i
$546$		0			0
$547$	−17.9677	+	31.1210i	−0.768243	+	1.33064i	0.170271	+	0.985397i	$0.445536\pi$
$547$	−17.9677	+	31.1210i	−0.768243	+	1.33064i	−0.938515	+	0.345239i	$0.887798\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.27447	+	2.20744i	−0.0542941	+	0.0940402i
$552$		0			0
$553$	9.77579	+	16.9322i	0.415709	+	0.720029i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	36.2470			1.53584			0.767918	−	0.640548i	$-0.221293\pi$
$557$	36.2470			1.53584			0.767918	+	0.640548i	$0.221293\pi$
$558$		0			0
$559$	−0.723155			−0.0305862
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.27920	+	3.94770i	0.0960570	+	0.166376i	0.910049	−	0.414500i	$-0.136044\pi$
$563$	2.27920	+	3.94770i	0.0960570	+	0.166376i	−0.813992	+	0.580876i	$0.802710\pi$
$564$		0			0
$565$	−4.83856	+	8.38064i	−0.203560	+	0.352576i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.97290	+	12.0774i	−0.292319	+	0.506312i	−0.974358	−	0.225005i	$-0.927760\pi$
$569$	−6.97290	+	12.0774i	−0.292319	+	0.506312i	0.682039	+	0.731316i	$0.261094\pi$
$570$		0			0
$571$	20.2682	+	35.1056i	0.848199	+	1.46912i	0.882813	+	0.469724i	$0.155647\pi$
$571$	20.2682	+	35.1056i	0.848199	+	1.46912i	−0.0346139	+	0.999401i	$0.511020\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	32.9263			1.37312
$576$		0			0
$577$	7.66190			0.318969			0.159485	−	0.987200i	$-0.449017\pi$
$577$	7.66190			0.318969			0.159485	+	0.987200i	$0.449017\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−14.2112	−	24.6146i	−0.589582	−	1.02119i
$582$		0			0
$583$	−4.79609	+	8.30706i	−0.198634	+	0.344043i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.16417	+	5.48051i	−0.130599	+	0.226205i	−0.923908	−	0.382615i	$-0.875024\pi$
$587$	−3.16417	+	5.48051i	−0.130599	+	0.226205i	0.793308	+	0.608820i	$0.208357\pi$
$588$		0			0
$589$	31.2345	+	54.0998i	1.28700	+	2.22914i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	17.2688			0.709146			0.354573	−	0.935028i	$-0.384626\pi$
$593$	17.2688			0.709146			0.354573	+	0.935028i	$0.384626\pi$
$594$		0			0
$595$	−3.32297			−0.136229
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−4.37729	−	7.58168i	−0.178851	−	0.309779i	0.762636	−	0.646828i	$-0.223905\pi$
$599$	−4.37729	−	7.58168i	−0.178851	−	0.309779i	−0.941487	+	0.337048i	$0.890571\pi$
$600$		0			0
$601$	−3.74538	+	6.48718i	−0.152777	+	0.264618i	−0.932247	−	0.361821i	$-0.882155\pi$
$601$	−3.74538	+	6.48718i	−0.152777	+	0.264618i	0.779470	+	0.626439i	$0.215488\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.327790	+	0.567749i	−0.0133266	+	0.0230823i
$606$		0			0
$607$	1.07780	+	1.86680i	0.0437466	+	0.0757713i	0.887070	−	0.461636i	$-0.152737\pi$
$607$	1.07780	+	1.86680i	0.0437466	+	0.0757713i	−0.843323	+	0.537407i	$0.819404\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.974444			−0.0394218
$612$		0			0
$613$	8.92069			0.360303			0.180152	−	0.983639i	$-0.442341\pi$
$613$	8.92069			0.360303			0.180152	+	0.983639i	$0.442341\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.98886	+	5.17685i	0.120327	+	0.208412i	0.919897	−	0.392161i	$-0.128272\pi$
$617$	2.98886	+	5.17685i	0.120327	+	0.208412i	−0.799570	+	0.600573i	$0.794939\pi$
$618$		0			0
$619$	−10.2962	+	17.8335i	−0.413837	+	0.716787i	−0.995306	−	0.0967818i	$-0.969145\pi$
$619$	−10.2962	+	17.8335i	−0.413837	+	0.716787i	0.581468	+	0.813569i	$0.302478\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−17.0096	+	29.4614i	−0.681474	+	1.18035i
$624$		0			0
$625$	−9.36896	−	16.2275i	−0.374759	−	0.649101i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−11.4294			−0.455721
$630$		0			0
$631$	−6.65003			−0.264733			−0.132367	−	0.991201i	$-0.542258\pi$
$631$	−6.65003			−0.264733			−0.132367	+	0.991201i	$0.542258\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−5.15444	−	8.92775i	−0.204548	−	0.354287i
$636$		0			0
$637$	−0.00726293	+	0.0125798i	−0.000287768	+	0.000498429i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−13.5675	+	23.4995i	−0.535882	+	0.928176i	0.463238	+	0.886234i	$0.346688\pi$
$641$	−13.5675	+	23.4995i	−0.535882	+	0.928176i	−0.999120	+	0.0419414i	$0.986646\pi$
$642$		0			0
$643$	−6.09514	−	10.5571i	−0.240369	−	0.416331i	0.720450	−	0.693506i	$-0.243935\pi$
$643$	−6.09514	−	10.5571i	−0.240369	−	0.416331i	−0.960819	+	0.277175i	$0.910602\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−41.9132			−1.64778			−0.823889	−	0.566750i	$-0.808200\pi$
$647$	−41.9132			−1.64778			−0.823889	+	0.566750i	$0.808200\pi$
$648$		0			0
$649$	−9.87852			−0.387766
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.38264	−	5.85890i	−0.132373	−	0.229276i	0.792218	−	0.610238i	$-0.208926\pi$
$653$	−3.38264	−	5.85890i	−0.132373	−	0.229276i	−0.924591	+	0.380962i	$0.875593\pi$
$654$		0			0
$655$	1.84146	−	3.18951i	0.0719519	−	0.124624i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	5.73604	−	9.93511i	0.223444	−	0.387017i	−0.732407	−	0.680867i	$-0.761603\pi$
$659$	5.73604	−	9.93511i	0.223444	−	0.387017i	0.955852	+	0.293850i	$0.0949366\pi$
$660$		0			0
$661$	2.98019	+	5.16185i	0.115916	+	0.200773i	0.918146	−	0.396243i	$-0.129686\pi$
$661$	2.98019	+	5.16185i	0.115916	+	0.200773i	−0.802229	+	0.597016i	$0.796353\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−14.2230			−0.551544
$666$		0			0
$667$	2.26967			0.0878820
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.47879	−	6.02545i	−0.134297	−	0.232610i
$672$		0			0
$673$	12.8530	−	22.2620i	0.495445	−	0.858136i	−0.504541	−	0.863388i	$-0.668338\pi$
$673$	12.8530	−	22.2620i	0.495445	−	0.858136i	0.999986	+	0.00525181i	$0.00167171\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−4.70226	+	8.14456i	−0.180723	+	0.313021i	−0.942127	−	0.335257i	$-0.891177\pi$
$677$	−4.70226	+	8.14456i	−0.180723	+	0.313021i	0.761404	+	0.648277i	$0.224510\pi$
$678$		0			0
$679$	−9.82459	−	17.0167i	−0.377033	−	0.653041i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	47.0022			1.79849			0.899244	−	0.437447i	$-0.144117\pi$
$683$	47.0022			1.79849			0.899244	+	0.437447i	$0.144117\pi$
$684$		0			0
$685$	−11.0886			−0.423672
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.366758	+	0.635244i	0.0139724	+	0.0242009i
$690$		0			0
$691$	−25.3217	+	43.8585i	−0.963282	+	1.66845i	−0.249122	+	0.968472i	$0.580142\pi$
$691$	−25.3217	+	43.8585i	−0.963282	+	1.66845i	−0.714160	+	0.699982i	$0.753191\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−5.24027	+	9.07642i	−0.198775	+	0.344288i
$696$		0			0
$697$	−8.68332	−	15.0400i	−0.328904	−	0.569679i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−25.5825			−0.966239			−0.483119	−	0.875554i	$-0.660496\pi$
$701$	−25.5825			−0.966239			−0.483119	+	0.875554i	$0.660496\pi$
$702$		0			0
$703$	−48.9203			−1.84506
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.46880	−	7.74020i	−0.168067	−	0.291100i
$708$		0			0
$709$	−15.3466	+	26.5812i	−0.576355	+	0.998276i	0.419538	+	0.907738i	$0.362192\pi$
$709$	−15.3466	+	26.5812i	−0.576355	+	0.998276i	−0.995893	+	0.0905384i	$0.971141\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	27.8124	−	48.1725i	1.04158	−	1.80408i
$714$		0			0
$715$	0.0250662	+	0.0434160i	0.000937424	+	0.00162367i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−27.9959			−1.04407			−0.522036	−	0.852923i	$-0.674827\pi$
$719$	−27.9959			−1.04407			−0.522036	+	0.852923i	$0.674827\pi$
$720$		0			0
$721$	28.1910			1.04989
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.719885	−	1.24688i	−0.0267359	−	0.0463079i
$726$		0			0
$727$	12.0006	−	20.7857i	0.445078	−	0.770898i	−0.552979	−	0.833195i	$-0.686509\pi$
$727$	12.0006	−	20.7857i	0.445078	−	0.770898i	0.998058	+	0.0622966i	$0.0198425\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−8.93811	+	15.4813i	−0.330588	+	0.572595i
$732$		0			0
$733$	−15.6477	−	27.1026i	−0.577960	−	1.00106i	−0.995713	−	0.0924958i	$-0.970516\pi$
$733$	−15.6477	−	27.1026i	−0.577960	−	1.00106i	0.417753	−	0.908561i	$-0.362818\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.0174420			−0.000642485
$738$		0			0
$739$	13.9643			0.513685			0.256842	−	0.966453i	$-0.417318\pi$
$739$	13.9643			0.513685			0.256842	+	0.966453i	$0.417318\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.31613	+	9.20781i	0.195030	+	0.337802i	0.946910	−	0.321498i	$-0.104186\pi$
$743$	5.31613	+	9.20781i	0.195030	+	0.337802i	−0.751880	+	0.659299i	$0.770853\pi$
$744$		0			0
$745$	4.49958	−	7.79350i	0.164852	−	0.285532i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.05932	−	1.83480i	0.0387067	−	0.0670421i
$750$		0			0
$751$	−7.25712	−	12.5697i	−0.264816	−	0.458675i	0.702699	−	0.711487i	$-0.251978\pi$
$751$	−7.25712	−	12.5697i	−0.264816	−	0.458675i	−0.967515	+	0.252812i	$0.918645\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−10.7397			−0.390859
$756$		0			0
$757$	−29.3607			−1.06713			−0.533567	−	0.845758i	$-0.679149\pi$
$757$	−29.3607			−1.06713			−0.533567	+	0.845758i	$0.679149\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13.0963	+	22.6834i	0.474740	+	0.822274i	0.999582	−	0.0289262i	$-0.00920877\pi$
$761$	13.0963	+	22.6834i	0.474740	+	0.822274i	−0.524842	+	0.851200i	$0.675875\pi$
$762$		0			0
$763$	−4.51549	+	7.82107i	−0.163472	+	0.283142i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.377707	+	0.654207i	−0.0136382	+	0.0236221i
$768$		0			0
$769$	27.6800	+	47.9431i	0.998165	+	1.72887i	0.551518	+	0.834163i	$0.314049\pi$
$769$	27.6800	+	47.9431i	0.998165	+	1.72887i	0.446647	+	0.894710i	$0.352618\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−6.11318			−0.219876			−0.109938	−	0.993938i	$-0.535065\pi$
$773$	−6.11318			−0.219876			−0.109938	+	0.993938i	$0.535065\pi$
$774$		0			0
$775$	−35.2857			−1.26750
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−37.1664	−	64.3741i	−1.33162	−	2.30644i
$780$		0			0
$781$	−4.27296	+	7.40098i	−0.152898	+	0.264828i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.902404	+	1.56301i	−0.0322082	+	0.0557862i
$786$		0			0
$787$	3.91902	+	6.78793i	0.139698	+	0.241964i	0.927382	−	0.374115i	$-0.122054\pi$
$787$	3.91902	+	6.78793i	0.139698	+	0.241964i	−0.787684	+	0.616079i	$0.788720\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	39.5807			1.40733
$792$		0			0
$793$	−0.532049			−0.0188936
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.28735	−	5.69385i	−0.116444	−	0.201687i	0.801912	−	0.597442i	$-0.203816\pi$
$797$	−3.28735	−	5.69385i	−0.116444	−	0.201687i	−0.918356	+	0.395755i	$0.870483\pi$
$798$		0			0
$799$	−12.0440	+	20.8608i	−0.426087	+	0.738004i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	5.36541	−	9.29316i	0.189341	−	0.327949i
$804$		0			0
$805$	6.33236	+	10.9680i	0.223186	+	0.386570i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−6.37648			−0.224185			−0.112093	−	0.993698i	$-0.535755\pi$
$809$	−6.37648			−0.224185			−0.112093	+	0.993698i	$0.535755\pi$
$810$		0			0
$811$	6.22728			0.218669			0.109335	−	0.994005i	$-0.465128\pi$
$811$	6.22728			0.218669			0.109335	+	0.994005i	$0.465128\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.449405	−	0.778392i	−0.0157420	−	0.0272659i
$816$		0			0
$817$	−38.2569	+	66.2630i	−1.33844	+	2.31825i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	24.9564	−	43.2258i	0.870985	−	1.50859i	0.0100064	−	0.999950i	$-0.496815\pi$
$821$	24.9564	−	43.2258i	0.870985	−	1.50859i	0.860979	−	0.508641i	$-0.169852\pi$
$822$		0			0
$823$	−6.88625	−	11.9273i	−0.240040	−	0.415761i	0.720686	−	0.693262i	$-0.243827\pi$
$823$	−6.88625	−	11.9273i	−0.240040	−	0.415761i	−0.960725	+	0.277501i	$0.910494\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	49.6189			1.72542			0.862710	−	0.505699i	$-0.168765\pi$
$827$	49.6189			1.72542			0.862710	+	0.505699i	$0.168765\pi$
$828$		0			0
$829$	12.5002			0.434150			0.217075	−	0.976155i	$-0.430348\pi$
$829$	12.5002			0.434150			0.217075	+	0.976155i	$0.430348\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.179538	+	0.310969i	0.00622063	+	0.0107744i
$834$		0			0
$835$	7.79387	−	13.4994i	0.269718	−	0.467166i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	0.624035	−	1.08086i	0.0215441	−	0.0373154i	−0.855052	−	0.518542i	$-0.826475\pi$
$839$	0.624035	−	1.08086i	0.0215441	−	0.0373154i	0.876596	+	0.481226i	$0.159808\pi$
$840$		0			0
$841$	14.4504	+	25.0288i	0.498289	+	0.863062i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−8.51871			−0.293053
$846$		0			0
$847$	2.68141			0.0921343
$848$		0			0
$849$		0			0
$850$		0			0
$851$	21.7803	+	37.7245i	0.746618	+	1.29318i
$852$		0			0
$853$	−7.09160	+	12.2830i	−0.242812	+	0.420562i	−0.961514	−	0.274756i	$-0.911403\pi$
$853$	−7.09160	+	12.2830i	−0.242812	+	0.420562i	0.718702	+	0.695318i	$0.244736\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−22.5568	+	39.0695i	−0.770525	+	1.33459i	0.166751	+	0.985999i	$0.446672\pi$
$857$	−22.5568	+	39.0695i	−0.770525	+	1.33459i	−0.937276	+	0.348589i	$0.886661\pi$
$858$		0			0
$859$	23.4487	+	40.6144i	0.800060	+	1.38575i	0.919576	+	0.392913i	$0.128533\pi$
$859$	23.4487	+	40.6144i	0.800060	+	1.38575i	−0.119515	+	0.992832i	$0.538134\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−24.9643			−0.849795			−0.424898	−	0.905241i	$-0.639690\pi$
$863$	−24.9643			−0.849795			−0.424898	+	0.905241i	$0.639690\pi$
$864$		0			0
$865$	−8.70630			−0.296023
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−3.64577	−	6.31465i	−0.123674	−	0.214210i
$870$		0			0
$871$	−0.000666899		0.00115510i	−2.25970e−5		3.91392e-5i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	8.41164	−	14.5694i	0.284365	−	0.492535i
$876$		0			0
$877$	2.97695	+	5.15624i	0.100525	+	0.174114i	0.911901	−	0.410410i	$-0.134615\pi$
$877$	2.97695	+	5.15624i	0.100525	+	0.174114i	−0.811376	+	0.584524i	$0.801281\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	52.6172			1.77272			0.886359	−	0.462999i	$-0.153227\pi$
$881$	52.6172			1.77272			0.886359	+	0.462999i	$0.153227\pi$
$882$		0			0
$883$	−36.0798			−1.21418			−0.607091	−	0.794632i	$-0.707664\pi$
$883$	−36.0798			−1.21418			−0.607091	+	0.794632i	$0.707664\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−18.3946	−	31.8604i	−0.617630	−	1.06977i	−0.989917	−	0.141649i	$-0.954760\pi$
$887$	−18.3946	−	31.8604i	−0.617630	−	1.06977i	0.372287	−	0.928118i	$-0.378574\pi$
$888$		0			0
$889$	−21.0823	+	36.5157i	−0.707079	+	1.22470i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−51.5508	+	89.2886i	−1.72508	+	2.98793i
$894$		0			0
$895$	1.76525	+	3.05750i	0.0590058	+	0.102201i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.43231			−0.0811222
$900$		0			0
$901$	18.1324			0.604077
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.441001	+	0.763836i	0.0146594	+	0.0253908i
$906$		0			0
$907$	−1.98039	+	3.43014i	−0.0657578	+	0.113896i	−0.897030	−	0.441970i	$-0.854280\pi$
$907$	−1.98039	+	3.43014i	−0.0657578	+	0.113896i	0.831272	+	0.555866i	$0.187613\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	19.2887	−	33.4090i	0.639064	−	1.10689i	−0.346575	−	0.938022i	$-0.612655\pi$
$911$	19.2887	−	33.4090i	0.639064	−	1.10689i	0.985639	−	0.168869i	$-0.0540114\pi$
$912$		0			0
$913$	5.29992	+	9.17973i	0.175402	+	0.303805i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.0636			−0.497445
$918$		0			0
$919$	−33.8155			−1.11547			−0.557735	−	0.830019i	$-0.688329\pi$
$919$	−33.8155			−1.11547			−0.557735	+	0.830019i	$0.688329\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.326754	+	0.565955i	0.0107553	+	0.0186286i
$924$		0			0
$925$	13.8164	−	23.9306i	0.454279	−	0.786834i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	6.57999	−	11.3969i	0.215883	−	0.373920i	−0.737663	−	0.675169i	$-0.764070\pi$
$929$	6.57999	−	11.3969i	0.215883	−	0.373920i	0.953545	+	0.301250i	$0.0974038\pi$
$930$		0			0
$931$	0.768459	+	1.33101i	0.0251852	+	0.0436221i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.23926			0.0405282
$936$		0			0
$937$	−5.64514			−0.184419			−0.0922094	−	0.995740i	$-0.529393\pi$
$937$	−5.64514			−0.184419			−0.0922094	+	0.995740i	$0.529393\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.0093	−	22.5328i	−0.424091	−	0.734547i	0.572244	−	0.820083i	$-0.306073\pi$
$941$	−13.0093	−	22.5328i	−0.424091	−	0.734547i	−0.996335	+	0.0855363i	$0.972740\pi$
$942$		0			0
$943$	−33.0944	+	57.3212i	−1.07770	+	1.86663i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−23.6630	+	40.9856i	−0.768945	+	1.33185i	0.169190	+	0.985583i	$0.445885\pi$
$947$	−23.6630	+	40.9856i	−0.768945	+	1.33185i	−0.938135	+	0.346269i	$0.887448\pi$
$948$		0			0
$949$	−0.410295	−	0.710651i	−0.0133187	−	0.0230687i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−22.6378			−0.733310			−0.366655	−	0.930357i	$-0.619497\pi$
$953$	−22.6378			−0.733310			−0.366655	+	0.930357i	$0.619497\pi$
$954$		0			0
$955$	−12.4250			−0.402064
$956$		0			0
$957$		0			0
$958$		0			0
$959$	22.6768	+	39.2774i	0.732272	+	1.26833i
$960$		0			0
$961$	−14.3054	+	24.7777i	−0.461465	+	0.799282i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−3.70612	+	6.41918i	−0.119304	+	0.206641i
$966$		0			0
$967$	6.48891	+	11.2391i	0.208669	+	0.361426i	0.951296	−	0.308280i	$-0.0997534\pi$
$967$	6.48891	+	11.2391i	0.208669	+	0.361426i	−0.742626	+	0.669706i	$0.766420\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−31.5139			−1.01133			−0.505664	−	0.862730i	$-0.668752\pi$
$971$	−31.5139			−1.01133			−0.505664	+	0.862730i	$0.668752\pi$
$972$		0			0
$973$	42.8668			1.37425
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−21.3664	−	37.0077i	−0.683571	−	1.18398i	−0.973884	−	0.227048i	$-0.927093\pi$
$977$	−21.3664	−	37.0077i	−0.683571	−	1.18398i	0.290313	−	0.956932i	$-0.406241\pi$
$978$		0			0
$979$	6.34352	−	10.9873i	0.202740	−	0.351156i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−12.7208	+	22.0330i	−0.405730	+	0.702745i	−0.994406	−	0.105624i	$-0.966316\pi$
$983$	−12.7208	+	22.0330i	−0.405730	+	0.702745i	0.588676	+	0.808369i	$0.299649\pi$
$984$		0			0
$985$	−2.83078	−	4.90305i	−0.0901962	−	0.156224i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	68.1310			2.16644
$990$		0			0
$991$	−37.1895			−1.18136			−0.590682	−	0.806904i	$-0.701141\pi$
$991$	−37.1895			−1.18136			−0.590682	+	0.806904i	$0.701141\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.48786	+	2.57704i	0.0471682	+	0.0816977i
$996$		0			0
$997$	1.71106	−	2.96364i	0.0541898	−	0.0938596i	−0.837658	−	0.546195i	$-0.816076\pi$
$997$	1.71106	−	2.96364i	0.0541898	−	0.0938596i	0.891848	+	0.452336i	$0.149409\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3564.2.i.t.1189.3		12
3.2	odd	2		3564.2.i.s.1189.4		12
9.2	odd	6		3564.2.a.p.1.3	yes	6
9.4	even	3	inner	3564.2.i.t.2377.3		12
9.5	odd	6		3564.2.i.s.2377.4		12
9.7	even	3		3564.2.a.o.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3564.2.a.o.1.4	✓	6	9.7	even	3
3564.2.a.p.1.3	yes	6	9.2	odd	6
3564.2.i.s.1189.4		12	3.2	odd	2
3564.2.i.s.2377.4		12	9.5	odd	6
3564.2.i.t.1189.3		12	1.1	even	1	trivial
3564.2.i.t.2377.3		12	9.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3564 = 2^{2} \cdot 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3564.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.327790 - 0.567749i) q^{5} +(-1.34070 + 2.32217i) q^{7} +O(q^{10})\)	\(q+(-0.327790 - 0.567749i) q^{5} +(-1.34070 + 2.32217i) q^{7} +(0.500000 - 0.866025i) q^{11} +(-0.0382352 - 0.0662253i) q^{13} -1.89033 q^{17} -8.09100 q^{19} +(3.60227 + 6.23931i) q^{23} +(2.28511 - 3.95792i) q^{25} +(0.157517 - 0.272827i) q^{29} +(-3.86040 - 6.68641i) q^{31} +1.75788 q^{35} +6.04626 q^{37} +(4.59355 + 7.95626i) q^{41} +(4.72834 - 8.18972i) q^{43} +(6.37138 - 11.0356i) q^{47} +(-0.0949771 - 0.164505i) q^{49} -9.59217 q^{53} -0.655580 q^{55} +(-4.93926 - 8.55505i) q^{59} +(3.47879 - 6.02545i) q^{61} +(-0.0250662 + 0.0434160i) q^{65} +(-0.00872101 - 0.0151052i) q^{67} -8.54591 q^{71} +10.7308 q^{73} +(1.34070 + 2.32217i) q^{77} +(3.64577 - 6.31465i) q^{79} +(-5.29992 + 9.17973i) q^{83} +(0.619632 + 1.07323i) q^{85} +12.6870 q^{89} +0.205048 q^{91} +(2.65215 + 4.59366i) q^{95} +(-3.66397 + 6.34618i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{7}+O(q^{10}) \) 12 * q + 2 * q^7	\( 12 q + 2 q^{7} + 6 q^{11} + 6 q^{13} - 8 q^{17} + 4 q^{23} - 10 q^{25} - 4 q^{29} - 6 q^{31} - 28 q^{35} - 12 q^{37} + 22 q^{41} + 10 q^{43} + 20 q^{47} - 6 q^{49} - 8 q^{53} + 24 q^{59} + 10 q^{61} + 40 q^{65} + 6 q^{67} - 80 q^{71} - 16 q^{73} - 2 q^{77} + 14 q^{79} + 12 q^{83} - 6 q^{85} - 48 q^{89} + 20 q^{91} + 44 q^{95} - 20 q^{97}+O(q^{100}) \) 12 * q + 2 * q^7 + 6 * q^11 + 6 * q^13 - 8 * q^17 + 4 * q^23 - 10 * q^25 - 4 * q^29 - 6 * q^31 - 28 * q^35 - 12 * q^37 + 22 * q^41 + 10 * q^43 + 20 * q^47 - 6 * q^49 - 8 * q^53 + 24 * q^59 + 10 * q^61 + 40 * q^65 + 6 * q^67 - 80 * q^71 - 16 * q^73 - 2 * q^77 + 14 * q^79 + 12 * q^83 - 6 * q^85 - 48 * q^89 + 20 * q^91 + 44 * q^95 - 20 * q^97

Introduction

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