LMFDB - Embedded newform 2940.2.x.b.97.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2940,2,Mod(97,2940)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2940, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))

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

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

chi := DirichletCharacter("2940.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2940.x (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.4760181943$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.5
Character	$\chi$	$=$	2940.97
Dual form			2940.2.x.b.1273.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{3} +(-1.84810 + 1.25878i) q^{5} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{3} +(-1.84810 + 1.25878i) q^{5} +1.00000i q^{9} -2.10154 q^{11} +(1.55471 + 1.55471i) q^{13} +(2.19690 + 0.416708i) q^{15} +(-4.52598 + 4.52598i) q^{17} -1.31233 q^{19} +(-2.02899 + 2.02899i) q^{23} +(1.83093 - 4.65271i) q^{25} +(0.707107 - 0.707107i) q^{27} -5.67110i q^{29} -1.97666i q^{31} +(1.48601 + 1.48601i) q^{33} +(1.80603 + 1.80603i) q^{37} -2.19869i q^{39} +6.22289i q^{41} +(5.24957 - 5.24957i) q^{43} +(-1.25878 - 1.84810i) q^{45} +(3.56196 - 3.56196i) q^{47} +6.40071 q^{51} +(3.15993 - 3.15993i) q^{53} +(3.88385 - 2.64539i) q^{55} +(0.927958 + 0.927958i) q^{57} -8.98627 q^{59} +6.68806i q^{61} +(-4.83029 - 0.916212i) q^{65} +(3.33204 + 3.33204i) q^{67} +2.86943 q^{69} +2.70489 q^{71} +(-3.02145 - 3.02145i) q^{73} +(-4.58462 + 1.99530i) q^{75} -16.8538i q^{79} -1.00000 q^{81} +(5.76026 + 5.76026i) q^{83} +(2.66723 - 14.0617i) q^{85} +(-4.01007 + 4.01007i) q^{87} -9.22575 q^{89} +(-1.39771 + 1.39771i) q^{93} +(2.42531 - 1.65194i) q^{95} +(5.81278 - 5.81278i) q^{97} -2.10154i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{5}+O(q^{10}) $ 24 * q + 8 * q^5	$ 24 q + 8 q^{5} - 16 q^{13} - 32 q^{19} + 16 q^{23} - 16 q^{25} + 16 q^{37} - 16 q^{43} - 8 q^{45} + 16 q^{47} + 24 q^{53} + 16 q^{57} - 64 q^{59} - 32 q^{65} + 32 q^{67} + 32 q^{71} + 16 q^{73} - 24 q^{81} + 48 q^{85} + 40 q^{87} - 144 q^{89} + 16 q^{93} - 64 q^{95} - 16 q^{97}+O(q^{100}) $ 24 * q + 8 * q^5 - 16 * q^13 - 32 * q^19 + 16 * q^23 - 16 * q^25 + 16 * q^37 - 16 * q^43 - 8 * q^45 + 16 * q^47 + 24 * q^53 + 16 * q^57 - 64 * q^59 - 32 * q^65 + 32 * q^67 + 32 * q^71 + 16 * q^73 - 24 * q^81 + 48 * q^85 + 40 * q^87 - 144 * q^89 + 16 * q^93 - 64 * q^95 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times$.

$n$	$1081$	$1177$	$1471$	$1961$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	−1.84810	+	1.25878i	−0.826494	+	0.562945i
$5$	−1.84810	+	1.25878i	−0.826494	+	0.562945i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−2.10154			−0.633639			−0.316819	−	0.948486i	$-0.602615\pi$
$11$	−2.10154			−0.633639			−0.316819	+	0.948486i	$0.602615\pi$
$12$		0			0
$13$	1.55471	+	1.55471i	0.431199	+	0.431199i	0.889036	−	0.457837i	$-0.151376\pi$
$13$	1.55471	+	1.55471i	0.431199	+	0.431199i	−0.457837	+	0.889036i	$0.651376\pi$
$14$		0			0
$15$	2.19690	+	0.416708i	0.567236	+	0.107594i
$16$		0			0
$17$	−4.52598	+	4.52598i	−1.09771	+	1.09771i	−0.103035	+	0.994678i	$0.532855\pi$
$17$	−4.52598	+	4.52598i	−1.09771	+	1.09771i	−0.994678	+	0.103035i	$0.967145\pi$
$18$		0			0
$19$	−1.31233			−0.301069			−0.150535	−	0.988605i	$-0.548100\pi$
$19$	−1.31233			−0.301069			−0.150535	+	0.988605i	$0.548100\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.02899	+	2.02899i	−0.423075	+	0.423075i	−0.886261	−	0.463186i	$-0.846706\pi$
$23$	−2.02899	+	2.02899i	−0.423075	+	0.423075i	0.463186	+	0.886261i	$0.346706\pi$
$24$		0			0
$25$	1.83093	−	4.65271i	0.366186	−	0.930542i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$		−	5.67110i		−	1.05310i	−0.850145	−	0.526548i	$-0.823486\pi$
$29$		−	5.67110i		−	1.05310i	0.850145	−	0.526548i	$-0.176514\pi$
$30$		0			0
$31$		−	1.97666i		−	0.355019i	−0.984119	−	0.177509i	$-0.943196\pi$
$31$		−	1.97666i		−	0.355019i	0.984119	−	0.177509i	$-0.0568040\pi$
$32$		0			0
$33$	1.48601	+	1.48601i	0.258682	+	0.258682i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.80603	+	1.80603i	0.296910	+	0.296910i	0.839802	−	0.542893i	$-0.182671\pi$
$37$	1.80603	+	1.80603i	0.296910	+	0.296910i	−0.542893	+	0.839802i	$0.682671\pi$
$38$		0			0
$39$		−	2.19869i		−	0.352072i
$40$		0			0
$41$			6.22289i			0.971852i	0.874000	+	0.485926i	$0.161517\pi$
$41$			6.22289i			0.971852i	−0.874000	+	0.485926i	$0.838483\pi$
$42$		0			0
$43$	5.24957	−	5.24957i	0.800551	−	0.800551i	−0.182630	−	0.983182i	$-0.558461\pi$
$43$	5.24957	−	5.24957i	0.800551	−	0.800551i	0.983182	+	0.182630i	$0.0584612\pi$
$44$		0			0
$45$	−1.25878	−	1.84810i	−0.187648	−	0.275498i
$46$		0			0
$47$	3.56196	−	3.56196i	0.519565	−	0.519565i	−0.397875	−	0.917440i	$-0.630252\pi$
$47$	3.56196	−	3.56196i	0.519565	−	0.519565i	0.917440	+	0.397875i	$0.130252\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	6.40071			0.896279
$52$		0			0
$53$	3.15993	−	3.15993i	0.434050	−	0.434050i	−0.455954	−	0.890003i	$-0.650702\pi$
$53$	3.15993	−	3.15993i	0.434050	−	0.434050i	0.890003	+	0.455954i	$0.150702\pi$
$54$		0			0
$55$	3.88385	−	2.64539i	0.523699	−	0.356704i
$56$		0			0
$57$	0.927958	+	0.927958i	0.122911	+	0.122911i
$58$		0			0
$59$	−8.98627			−1.16991			−0.584957	−	0.811065i	$-0.698888\pi$
$59$	−8.98627			−1.16991			−0.584957	+	0.811065i	$0.698888\pi$
$60$		0			0
$61$			6.68806i			0.856318i	0.903703	+	0.428159i	$0.140838\pi$
$61$			6.68806i			0.856318i	−0.903703	+	0.428159i	$0.859162\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.83029	−	0.916212i	−0.599124	−	0.113642i
$66$		0			0
$67$	3.33204	+	3.33204i	0.407074	+	0.407074i	0.880717	−	0.473643i	$-0.157061\pi$
$67$	3.33204	+	3.33204i	0.407074	+	0.407074i	−0.473643	+	0.880717i	$0.657061\pi$
$68$		0			0
$69$	2.86943			0.345439
$70$		0			0
$71$	2.70489			0.321011			0.160506	−	0.987035i	$-0.448688\pi$
$71$	2.70489			0.321011			0.160506	+	0.987035i	$0.448688\pi$
$72$		0			0
$73$	−3.02145	−	3.02145i	−0.353634	−	0.353634i	0.507826	−	0.861460i	$-0.330449\pi$
$73$	−3.02145	−	3.02145i	−0.353634	−	0.353634i	−0.861460	+	0.507826i	$0.830449\pi$
$74$		0			0
$75$	−4.58462	+	1.99530i	−0.529387	+	0.230397i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		−	16.8538i		−	1.89620i	−0.317969	−	0.948101i	$-0.603001\pi$
$79$		−	16.8538i		−	1.89620i	0.317969	−	0.948101i	$-0.396999\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	5.76026	+	5.76026i	0.632270	+	0.632270i	0.948637	−	0.316367i	$-0.102463\pi$
$83$	5.76026	+	5.76026i	0.632270	+	0.632270i	−0.316367	+	0.948637i	$0.602463\pi$
$84$		0			0
$85$	2.66723	−	14.0617i	0.289302	−	1.52521i
$86$		0			0
$87$	−4.01007	+	4.01007i	−0.429925	+	0.429925i
$88$		0			0
$89$	−9.22575			−0.977928			−0.488964	−	0.872304i	$-0.662625\pi$
$89$	−9.22575			−0.977928			−0.488964	+	0.872304i	$0.662625\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1.39771	+	1.39771i	−0.144936	+	0.144936i
$94$		0			0
$95$	2.42531	−	1.65194i	0.248832	−	0.169485i
$96$		0			0
$97$	5.81278	−	5.81278i	0.590198	−	0.590198i	−0.347487	−	0.937685i	$-0.612965\pi$
$97$	5.81278	−	5.81278i	0.590198	−	0.590198i	0.937685	+	0.347487i	$0.112965\pi$
$98$		0			0
$99$		−	2.10154i		−	0.211213i
$100$		0			0
$101$		−	5.34750i		−	0.532096i	−0.963960	−	0.266048i	$-0.914282\pi$
$101$		−	5.34750i		−	0.532096i	0.963960	−	0.266048i	$-0.0857180\pi$
$102$		0			0
$103$	−11.3050	−	11.3050i	−1.11392	−	1.11392i	−0.992616	−	0.121301i	$-0.961293\pi$
$103$	−11.3050	−	11.3050i	−1.11392	−	1.11392i	−0.121301	−	0.992616i	$-0.538707\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.44862	−	3.44862i	−0.333391	−	0.333391i	0.520482	−	0.853873i	$-0.325752\pi$
$107$	−3.44862	−	3.44862i	−0.333391	−	0.333391i	−0.853873	+	0.520482i	$0.825752\pi$
$108$		0			0
$109$			18.1751i			1.74086i	0.492296	+	0.870428i	$0.336158\pi$
$109$			18.1751i			1.74086i	−0.492296	+	0.870428i	$0.663842\pi$
$110$		0			0
$111$		−	2.55411i		−	0.242426i
$112$		0			0
$113$	12.3691	−	12.3691i	1.16359	−	1.16359i	0.179907	−	0.983684i	$-0.442420\pi$
$113$	12.3691	−	12.3691i	1.16359	−	1.16359i	0.983684	−	0.179907i	$-0.0575798\pi$
$114$		0			0
$115$	1.19572	−	6.30384i	0.111501	−	0.587836i
$116$		0			0
$117$	−1.55471	+	1.55471i	−0.143733	+	0.143733i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−6.58352			−0.598502
$122$		0			0
$123$	4.40025	−	4.40025i	0.396757	−	0.396757i
$124$		0			0
$125$	2.47301	+	10.9034i	0.221193	+	0.975230i
$126$		0			0
$127$	−11.6119	−	11.6119i	−1.03039	−	1.03039i	−0.999524	−	0.0308632i	$-0.990174\pi$
$127$	−11.6119	−	11.6119i	−1.03039	−	1.03039i	−0.0308632	−	0.999524i	$-0.509826\pi$
$128$		0			0
$129$	−7.42401			−0.653647
$130$		0			0
$131$		−	17.0831i		−	1.49256i	−0.665632	−	0.746280i	$-0.731838\pi$
$131$		−	17.0831i		−	1.49256i	0.665632	−	0.746280i	$-0.268162\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.416708	+	2.19690i	−0.0358645	+	0.189079i
$136$		0			0
$137$	−9.79400	−	9.79400i	−0.836758	−	0.836758i	0.151673	−	0.988431i	$-0.451534\pi$
$137$	−9.79400	−	9.79400i	−0.836758	−	0.836758i	−0.988431	+	0.151673i	$0.951534\pi$
$138$		0			0
$139$	17.8983			1.51811			0.759057	−	0.651024i	$-0.225660\pi$
$139$	17.8983			1.51811			0.759057	+	0.651024i	$0.225660\pi$
$140$		0			0
$141$	−5.03737			−0.424223
$142$		0			0
$143$	−3.26728	−	3.26728i	−0.273224	−	0.273224i
$144$		0			0
$145$	7.13868	+	10.4807i	0.592835	+	0.870379i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	1.16477i		−	0.0954213i	−0.998861	−	0.0477106i	$-0.984807\pi$
$149$		−	1.16477i		−	0.0954213i	0.998861	−	0.0477106i	$-0.0151925\pi$
$150$		0			0
$151$	6.24260			0.508016			0.254008	−	0.967202i	$-0.418251\pi$
$151$	6.24260			0.508016			0.254008	+	0.967202i	$0.418251\pi$
$152$		0			0
$153$	−4.52598	−	4.52598i	−0.365904	−	0.365904i
$154$		0			0
$155$	2.48819	+	3.65306i	0.199856	+	0.293421i
$156$		0			0
$157$	17.1539	−	17.1539i	1.36903	−	1.36903i	0.507195	−	0.861831i	$-0.330682\pi$
$157$	17.1539	−	17.1539i	1.36903	−	1.36903i	0.861831	−	0.507195i	$-0.169318\pi$
$158$		0			0
$159$	−4.46882			−0.354400
$160$		0			0
$161$		0			0
$162$		0			0
$163$	8.33923	−	8.33923i	0.653179	−	0.653179i	−0.300579	−	0.953757i	$-0.597180\pi$
$163$	8.33923	−	8.33923i	0.653179	−	0.653179i	0.953757	+	0.300579i	$0.0971797\pi$
$164$		0			0
$165$	−4.61687	−	0.875730i	−0.359423	−	0.0681755i
$166$		0			0
$167$	6.44069	−	6.44069i	0.498396	−	0.498396i	−0.412543	−	0.910938i	$-0.635359\pi$
$167$	6.44069	−	6.44069i	0.498396	−	0.498396i	0.910938	+	0.412543i	$0.135359\pi$
$168$		0			0
$169$		−	8.16576i		−	0.628136i
$170$		0			0
$171$		−	1.31233i		−	0.100356i
$172$		0			0
$173$	−7.07389	−	7.07389i	−0.537818	−	0.537818i	0.385069	−	0.922888i	$-0.374178\pi$
$173$	−7.07389	−	7.07389i	−0.537818	−	0.537818i	−0.922888	+	0.385069i	$0.874178\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	6.35426	+	6.35426i	0.477615	+	0.477615i
$178$		0			0
$179$			5.87174i			0.438874i	0.975627	+	0.219437i	$0.0704221\pi$
$179$			5.87174i			0.438874i	−0.975627	+	0.219437i	$0.929578\pi$
$180$		0			0
$181$			9.76971i			0.726176i	0.931755	+	0.363088i	$0.118278\pi$
$181$			9.76971i			0.726176i	−0.931755	+	0.363088i	$0.881722\pi$
$182$		0			0
$183$	4.72917	−	4.72917i	0.349591	−	0.349591i
$184$		0			0
$185$	−5.61112	−	1.06432i	−0.412538	−	0.0782504i
$186$		0			0
$187$	9.51155	−	9.51155i	0.695553	−	0.695553i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	14.1624			1.02475			0.512376	−	0.858761i	$-0.328765\pi$
$191$	14.1624			1.02475			0.512376	+	0.858761i	$0.328765\pi$
$192$		0			0
$193$	2.41151	−	2.41151i	0.173584	−	0.173584i	−0.614968	−	0.788552i	$-0.710831\pi$
$193$	2.41151	−	2.41151i	0.173584	−	0.173584i	0.788552	+	0.614968i	$0.210831\pi$
$194$		0			0
$195$	2.76767	+	4.06339i	0.198197	+	0.290986i
$196$		0			0
$197$	−10.8059	−	10.8059i	−0.769889	−	0.769889i	0.208198	−	0.978087i	$-0.433240\pi$
$197$	−10.8059	−	10.8059i	−0.769889	−	0.769889i	−0.978087	+	0.208198i	$0.933240\pi$
$198$		0			0
$199$	−10.4831			−0.743126			−0.371563	−	0.928408i	$-0.621178\pi$
$199$	−10.4831			−0.743126			−0.371563	+	0.928408i	$0.621178\pi$
$200$		0			0
$201$		−	4.71222i		−	0.332375i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−7.83326	−	11.5005i	−0.547099	−	0.803230i
$206$		0			0
$207$	−2.02899	−	2.02899i	−0.141025	−	0.141025i
$208$		0			0
$209$	2.75792			0.190769
$210$		0			0
$211$	−8.31282			−0.572278			−0.286139	−	0.958188i	$-0.592372\pi$
$211$	−8.31282			−0.572278			−0.286139	+	0.958188i	$0.592372\pi$
$212$		0			0
$213$	−1.91264	−	1.91264i	−0.131052	−	0.131052i
$214$		0			0
$215$	−3.09365	+	16.3098i	−0.210985	+	1.11232i
$216$		0			0
$217$		0			0
$218$		0			0
$219$			4.27297i			0.288741i
$220$		0			0
$221$	−14.0732			−0.946664
$222$		0			0
$223$	0.335926	+	0.335926i	0.0224953	+	0.0224953i	0.718265	−	0.695770i	$-0.244937\pi$
$223$	0.335926	+	0.335926i	0.0224953	+	0.0224953i	−0.695770	+	0.718265i	$0.744937\pi$
$224$		0			0
$225$	4.65271	+	1.83093i	0.310181	+	0.122062i
$226$		0			0
$227$	−14.9082	+	14.9082i	−0.989492	+	0.989492i	−0.999945	−	0.0104537i	$-0.996672\pi$
$227$	−14.9082	+	14.9082i	−0.989492	+	0.989492i	0.0104537	+	0.999945i	$0.496672\pi$
$228$		0			0
$229$	−22.2226			−1.46851			−0.734256	−	0.678873i	$-0.762469\pi$
$229$	−22.2226			−1.46851			−0.734256	+	0.678873i	$0.762469\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.10634	−	7.10634i	0.465552	−	0.465552i	−0.434918	−	0.900470i	$-0.643223\pi$
$233$	7.10634	−	7.10634i	0.465552	−	0.465552i	0.900470	+	0.434918i	$0.143223\pi$
$234$		0			0
$235$	−2.09911	+	11.0666i	−0.136931	+	0.721903i
$236$		0			0
$237$	−11.9174	+	11.9174i	−0.774121	+	0.774121i
$238$		0			0
$239$			23.6494i			1.52975i	0.644177	+	0.764877i	$0.277200\pi$
$239$			23.6494i			1.52975i	−0.644177	+	0.764877i	$0.722800\pi$
$240$		0			0
$241$		−	9.32913i		−	0.600942i	−0.953791	−	0.300471i	$-0.902856\pi$
$241$		−	9.32913i		−	0.600942i	0.953791	−	0.300471i	$-0.0971438\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.04029	−	2.04029i	−0.129821	−	0.129821i
$248$		0			0
$249$		−	8.14624i		−	0.516247i
$250$		0			0
$251$		−	15.9392i		−	1.00608i	−0.864264	−	0.503038i	$-0.832215\pi$
$251$		−	15.9392i		−	1.00608i	0.864264	−	0.503038i	$-0.167785\pi$
$252$		0			0
$253$	4.26402	−	4.26402i	0.268076	−	0.268076i
$254$		0			0
$255$	−11.8291	+	8.05710i	−0.740769	+	0.504555i
$256$		0			0
$257$	−5.23976	+	5.23976i	−0.326847	+	0.326847i	−0.851386	−	0.524539i	$-0.824238\pi$
$257$	−5.23976	+	5.23976i	−0.326847	+	0.326847i	0.524539	+	0.851386i	$0.324238\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	5.67110			0.351032
$262$		0			0
$263$	17.7904	−	17.7904i	1.09701	−	1.09701i	0.102246	−	0.994759i	$-0.467397\pi$
$263$	17.7904	−	17.7904i	1.09701	−	1.09701i	0.994759	−	0.102246i	$-0.0326029\pi$
$264$		0			0
$265$	−1.86219	+	9.81752i	−0.114394	+	0.603086i
$266$		0			0
$267$	6.52359	+	6.52359i	0.399237	+	0.399237i
$268$		0			0
$269$	−24.0947			−1.46908			−0.734540	−	0.678566i	$-0.762602\pi$
$269$	−24.0947			−1.46908			−0.734540	+	0.678566i	$0.762602\pi$
$270$		0			0
$271$		−	28.8871i		−	1.75477i	−0.479790	−	0.877383i	$-0.659287\pi$
$271$		−	28.8871i		−	1.75477i	0.479790	−	0.877383i	$-0.340713\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.84778	+	9.77786i	−0.232030	+	0.589627i
$276$		0			0
$277$	5.49645	+	5.49645i	0.330250	+	0.330250i	0.852681	−	0.522431i	$-0.174975\pi$
$277$	5.49645	+	5.49645i	0.330250	+	0.330250i	−0.522431	+	0.852681i	$0.674975\pi$
$278$		0			0
$279$	1.97666			0.118340
$280$		0			0
$281$	−7.58120			−0.452257			−0.226128	−	0.974098i	$-0.572607\pi$
$281$	−7.58120			−0.452257			−0.226128	+	0.974098i	$0.572607\pi$
$282$		0			0
$283$	18.8099	+	18.8099i	1.11813	+	1.11813i	0.992015	+	0.126118i	$0.0402517\pi$
$283$	18.8099	+	18.8099i	1.11813	+	1.11813i	0.126118	+	0.992015i	$0.459748\pi$
$284$		0			0
$285$	−2.88305	−	0.546859i	−0.170777	−	0.0323931i
$286$		0			0
$287$		0			0
$288$		0			0
$289$		−	23.9691i		−	1.40995i
$290$		0			0
$291$	−8.22051			−0.481895
$292$		0			0
$293$	−3.05034	−	3.05034i	−0.178203	−	0.178203i	0.612369	−	0.790572i	$-0.290217\pi$
$293$	−3.05034	−	3.05034i	−0.178203	−	0.178203i	−0.790572	+	0.612369i	$0.790217\pi$
$294$		0			0
$295$	16.6075	−	11.3118i	0.966927	−	0.658597i
$296$		0			0
$297$	−1.48601	+	1.48601i	−0.0862273	+	0.0862273i
$298$		0			0
$299$	−6.30899			−0.364858
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−3.78126	+	3.78126i	−0.217227	+	0.217227i
$304$		0			0
$305$	−8.41882	−	12.3602i	−0.482060	−	0.707742i
$306$		0			0
$307$	8.84946	−	8.84946i	0.505065	−	0.505065i	−0.407942	−	0.913008i	$-0.633754\pi$
$307$	8.84946	−	8.84946i	0.505065	−	0.505065i	0.913008	+	0.407942i	$0.133754\pi$
$308$		0			0
$309$			15.9877i			0.909509i
$310$		0			0
$311$		−	8.05288i		−	0.456637i	−0.973586	−	0.228318i	$-0.926677\pi$
$311$		−	8.05288i		−	0.456637i	0.973586	−	0.228318i	$-0.0733227\pi$
$312$		0			0
$313$	14.2072	+	14.2072i	0.803039	+	0.803039i	0.983569	−	0.180530i	$-0.0577813\pi$
$313$	14.2072	+	14.2072i	0.803039	+	0.803039i	−0.180530	+	0.983569i	$0.557781\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	22.8288	+	22.8288i	1.28219	+	1.28219i	0.939419	+	0.342772i	$0.111366\pi$
$317$	22.8288	+	22.8288i	1.28219	+	1.28219i	0.342772	+	0.939419i	$0.388634\pi$
$318$		0			0
$319$			11.9181i			0.667283i
$320$		0			0
$321$			4.87709i			0.272212i
$322$		0			0
$323$	5.93959	−	5.93959i	0.330488	−	0.330488i
$324$		0			0
$325$	10.0802	−	4.38704i	0.559147	−	0.243349i
$326$		0			0
$327$	12.8517	−	12.8517i	0.710701	−	0.710701i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.474316			0.0260708			0.0130354	−	0.999915i	$-0.495851\pi$
$331$	0.474316			0.0260708			0.0130354	+	0.999915i	$0.495851\pi$
$332$		0			0
$333$	−1.80603	+	1.80603i	−0.0989699	+	0.0989699i
$334$		0			0
$335$	−10.3523	−	1.96362i	−0.565605	−	0.107284i
$336$		0			0
$337$	−6.53458	−	6.53458i	−0.355961	−	0.355961i	0.506361	−	0.862322i	$-0.330990\pi$
$337$	−6.53458	−	6.53458i	−0.355961	−	0.355961i	−0.862322	+	0.506361i	$0.830990\pi$
$338$		0			0
$339$	−17.4926			−0.950068
$340$		0			0
$341$			4.15404i			0.224954i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−5.30299	+	3.61199i	−0.285503	+	0.194463i
$346$		0			0
$347$	1.49686	+	1.49686i	0.0803556	+	0.0803556i	0.746142	−	0.665787i	$-0.231904\pi$
$347$	1.49686	+	1.49686i	0.0803556	+	0.0803556i	−0.665787	+	0.746142i	$0.731904\pi$
$348$		0			0
$349$	−13.5315			−0.724327			−0.362163	−	0.932115i	$-0.617962\pi$
$349$	−13.5315			−0.724327			−0.362163	+	0.932115i	$0.617962\pi$
$350$		0			0
$351$	2.19869			0.117357
$352$		0			0
$353$	−11.1370	−	11.1370i	−0.592765	−	0.592765i	0.345612	−	0.938377i	$-0.387671\pi$
$353$	−11.1370	−	11.1370i	−0.592765	−	0.592765i	−0.938377	+	0.345612i	$0.887671\pi$
$354$		0			0
$355$	−4.99890	+	3.40487i	−0.265314	+	0.180712i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			19.0410i			1.00495i	0.864592	+	0.502474i	$0.167577\pi$
$359$			19.0410i			1.00495i	−0.864592	+	0.502474i	$0.832423\pi$
$360$		0			0
$361$	−17.2778			−0.909357
$362$		0			0
$363$	4.65525	+	4.65525i	0.244337	+	0.244337i
$364$		0			0
$365$	9.38728	+	1.78058i	0.491353	+	0.0932000i
$366$		0			0
$367$	7.87571	−	7.87571i	0.411109	−	0.411109i	−0.471016	−	0.882125i	$-0.656113\pi$
$367$	7.87571	−	7.87571i	0.411109	−	0.411109i	0.882125	+	0.471016i	$0.156113\pi$
$368$		0			0
$369$	−6.22289			−0.323951
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−15.4612	+	15.4612i	−0.800551	+	0.800551i	−0.983182	−	0.182630i	$-0.941539\pi$
$373$	−15.4612	+	15.4612i	−0.800551	+	0.800551i	0.182630	+	0.983182i	$0.441539\pi$
$374$		0			0
$375$	5.96119	−	9.45855i	0.307834	−	0.488438i
$376$		0			0
$377$	8.81691	−	8.81691i	0.454094	−	0.454094i
$378$		0			0
$379$			10.5686i			0.542874i	0.962456	+	0.271437i	$0.0874988\pi$
$379$			10.5686i			0.542874i	−0.962456	+	0.271437i	$0.912501\pi$
$380$		0			0
$381$			16.4217i			0.841307i
$382$		0			0
$383$	11.5078	+	11.5078i	0.588021	+	0.588021i	0.937095	−	0.349074i	$-0.113504\pi$
$383$	11.5078	+	11.5078i	0.588021	+	0.588021i	−0.349074	+	0.937095i	$0.613504\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	5.24957	+	5.24957i	0.266850	+	0.266850i
$388$		0			0
$389$			11.3185i			0.573872i	0.957950	+	0.286936i	$0.0926367\pi$
$389$			11.3185i			0.573872i	−0.957950	+	0.286936i	$0.907363\pi$
$390$		0			0
$391$		−	18.3664i		−	0.928828i
$392$		0			0
$393$	−12.0796	+	12.0796i	−0.609335	+	0.609335i
$394$		0			0
$395$	21.2153	+	31.1475i	1.06746	+	1.56720i
$396$		0			0
$397$	14.3925	−	14.3925i	0.722340	−	0.722340i	−0.246741	−	0.969081i	$-0.579360\pi$
$397$	14.3925	−	14.3925i	0.722340	−	0.722340i	0.969081	+	0.246741i	$0.0793598\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	15.4925			0.773660			0.386830	−	0.922151i	$-0.373570\pi$
$401$	15.4925			0.773660			0.386830	+	0.922151i	$0.373570\pi$
$402$		0			0
$403$	3.07313	−	3.07313i	0.153084	−	0.153084i
$404$		0			0
$405$	1.84810	−	1.25878i	0.0918327	−	0.0625494i
$406$		0			0
$407$	−3.79545	−	3.79545i	−0.188133	−	0.188133i
$408$		0			0
$409$	33.8332			1.67294			0.836472	−	0.548010i	$-0.184614\pi$
$409$	33.8332			1.67294			0.836472	+	0.548010i	$0.184614\pi$
$410$		0			0
$411$			13.8508i			0.683210i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−17.8964	−	3.39460i	−0.878501	−	0.166635i
$416$		0			0
$417$	−12.6560	−	12.6560i	−0.619768	−	0.619768i
$418$		0			0
$419$	−24.1285			−1.17875			−0.589376	−	0.807859i	$-0.700626\pi$
$419$	−24.1285			−1.17875			−0.589376	+	0.807859i	$0.700626\pi$
$420$		0			0
$421$	−30.8395			−1.50303			−0.751514	−	0.659718i	$-0.770676\pi$
$421$	−30.8395			−1.50303			−0.751514	+	0.659718i	$0.770676\pi$
$422$		0			0
$423$	3.56196	+	3.56196i	0.173188	+	0.173188i
$424$		0			0
$425$	12.7713	+	29.3449i	0.619500	+	1.42343i
$426$		0			0
$427$		0			0
$428$		0			0
$429$			4.62064i			0.223087i
$430$		0			0
$431$	1.79008			0.0862249			0.0431125	−	0.999070i	$-0.486273\pi$
$431$	1.79008			0.0862249			0.0431125	+	0.999070i	$0.486273\pi$
$432$		0			0
$433$	4.15829	+	4.15829i	0.199835	+	0.199835i	0.799929	−	0.600094i	$-0.204870\pi$
$433$	4.15829	+	4.15829i	0.199835	+	0.199835i	−0.600094	+	0.799929i	$0.704870\pi$
$434$		0			0
$435$	2.36319	−	12.4588i	0.113306	−	0.597355i
$436$		0			0
$437$	2.66271	−	2.66271i	0.127375	−	0.127375i
$438$		0			0
$439$	−0.636630			−0.0303847			−0.0151923	−	0.999885i	$-0.504836\pi$
$439$	−0.636630			−0.0303847			−0.0151923	+	0.999885i	$0.504836\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.08148	+	4.08148i	−0.193917	+	0.193917i	−0.797386	−	0.603469i	$-0.793785\pi$
$443$	−4.08148	+	4.08148i	−0.193917	+	0.193917i	0.603469	+	0.797386i	$0.293785\pi$
$444$		0			0
$445$	17.0501	−	11.6132i	0.808252	−	0.550519i
$446$		0			0
$447$	−0.823613	+	0.823613i	−0.0389556	+	0.0389556i
$448$		0			0
$449$			41.1244i			1.94078i	0.241543	+	0.970390i	$0.422346\pi$
$449$			41.1244i			1.94078i	−0.241543	+	0.970390i	$0.577654\pi$
$450$		0			0
$451$		−	13.0777i		−	0.615803i
$452$		0			0
$453$	−4.41419	−	4.41419i	−0.207397	−	0.207397i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−14.5296	−	14.5296i	−0.679665	−	0.679665i	0.280259	−	0.959924i	$-0.409580\pi$
$457$	−14.5296	−	14.5296i	−0.679665	−	0.679665i	−0.959924	+	0.280259i	$0.909580\pi$
$458$		0			0
$459$			6.40071i			0.298760i
$460$		0			0
$461$			31.3250i			1.45895i	0.684008	+	0.729475i	$0.260235\pi$
$461$			31.3250i			1.45895i	−0.684008	+	0.729475i	$0.739765\pi$
$462$		0			0
$463$	−3.48579	+	3.48579i	−0.161998	+	0.161998i	−0.783451	−	0.621453i	$-0.786543\pi$
$463$	−3.48579	+	3.48579i	−0.161998	+	0.161998i	0.621453	+	0.783451i	$0.286543\pi$
$464$		0			0
$465$	0.823691	−	4.34252i	0.0381978	−	0.201380i
$466$		0			0
$467$	17.4798	−	17.4798i	0.808868	−	0.808868i	−0.175595	−	0.984463i	$-0.556185\pi$
$467$	17.4798	−	17.4798i	0.808868	−	0.808868i	0.984463	+	0.175595i	$0.0561848\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−24.2592			−1.11781
$472$		0			0
$473$	−11.0322	+	11.0322i	−0.507260	+	0.507260i
$474$		0			0
$475$	−2.40279	+	6.10589i	−0.110247	+	0.280157i
$476$		0			0
$477$	3.15993	+	3.15993i	0.144683	+	0.144683i
$478$		0			0
$479$	21.3122			0.973778			0.486889	−	0.873464i	$-0.338132\pi$
$479$	21.3122			0.973778			0.486889	+	0.873464i	$0.338132\pi$
$480$		0			0
$481$			5.61570i			0.256054i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.42555	+	18.0596i	−0.155546	+	0.820044i
$486$		0			0
$487$	27.6627	+	27.6627i	1.25352	+	1.25352i	0.954132	+	0.299386i	$0.0967818\pi$
$487$	27.6627	+	27.6627i	1.25352	+	1.25352i	0.299386	+	0.954132i	$0.403218\pi$
$488$		0			0
$489$	−11.7934			−0.533318
$490$		0			0
$491$	32.0866			1.44805			0.724025	−	0.689774i	$-0.242290\pi$
$491$	32.0866			1.44805			0.724025	+	0.689774i	$0.242290\pi$
$492$		0			0
$493$	25.6673	+	25.6673i	1.15600	+	1.15600i
$494$		0			0
$495$	2.64539	+	3.88385i	0.118901	+	0.174566i
$496$		0			0
$497$		0			0
$498$		0			0
$499$		−	35.7177i		−	1.59894i	−0.600703	−	0.799472i	$-0.705112\pi$
$499$		−	35.7177i		−	1.59894i	0.600703	−	0.799472i	$-0.294888\pi$
$500$		0			0
$501$	−9.10851			−0.406938
$502$		0			0
$503$	−3.34130	−	3.34130i	−0.148981	−	0.148981i	0.628682	−	0.777663i	$-0.283595\pi$
$503$	−3.34130	−	3.34130i	−0.148981	−	0.148981i	−0.777663	+	0.628682i	$0.783595\pi$
$504$		0			0
$505$	6.73135	+	9.88271i	0.299541	+	0.439775i
$506$		0			0
$507$	−5.77407	+	5.77407i	−0.256435	+	0.256435i
$508$		0			0
$509$	−22.2345			−0.985528			−0.492764	−	0.870163i	$-0.664013\pi$
$509$	−22.2345			−0.985528			−0.492764	+	0.870163i	$0.664013\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−0.927958	+	0.927958i	−0.0409703	+	0.0409703i
$514$		0			0
$515$	35.1233	+	6.66221i	1.54772	+	0.293572i
$516$		0			0
$517$	−7.48560	+	7.48560i	−0.329216	+	0.329216i
$518$		0			0
$519$			10.0040i			0.439127i
$520$		0			0
$521$		−	25.4884i		−	1.11667i	−0.829616	−	0.558335i	$-0.811441\pi$
$521$		−	25.4884i		−	1.11667i	0.829616	−	0.558335i	$-0.188559\pi$
$522$		0			0
$523$	29.3250	+	29.3250i	1.28229	+	1.28229i	0.939359	+	0.342935i	$0.111421\pi$
$523$	29.3250	+	29.3250i	1.28229	+	1.28229i	0.342935	+	0.939359i	$0.388579\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.94634	+	8.94634i	0.389709	+	0.389709i
$528$		0			0
$529$			14.7664i			0.642016i
$530$		0			0
$531$		−	8.98627i		−	0.389971i
$532$		0			0
$533$	−9.67477	+	9.67477i	−0.419061	+	0.419061i
$534$		0			0
$535$	10.7145	+	2.03232i	0.463226	+	0.0878649i
$536$		0			0
$537$	4.15195	−	4.15195i	0.179170	−	0.179170i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−10.0729			−0.433066			−0.216533	−	0.976275i	$-0.569475\pi$
$541$	−10.0729			−0.433066			−0.216533	+	0.976275i	$0.569475\pi$
$542$		0			0
$543$	6.90822	−	6.90822i	0.296460	−	0.296460i
$544$		0			0
$545$	−22.8785	−	33.5893i	−0.980006	−	1.43881i
$546$		0			0
$547$	−4.77871	−	4.77871i	−0.204323	−	0.204323i	0.597526	−	0.801849i	$-0.296150\pi$
$547$	−4.77871	−	4.77871i	−0.204323	−	0.204323i	−0.801849	+	0.597526i	$0.796150\pi$
$548$		0			0
$549$	−6.68806			−0.285439
$550$		0			0
$551$			7.44236i			0.317055i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	3.21507	+	4.72025i	0.136472	+	0.200363i
$556$		0			0
$557$	−14.7390	−	14.7390i	−0.624512	−	0.624512i	0.322170	−	0.946682i	$-0.395588\pi$
$557$	−14.7390	−	14.7390i	−0.624512	−	0.624512i	−0.946682	+	0.322170i	$0.895588\pi$
$558$		0			0
$559$	16.3231			0.690393
$560$		0			0
$561$	−13.4514			−0.567917
$562$		0			0
$563$	5.66088	+	5.66088i	0.238578	+	0.238578i	0.816261	−	0.577683i	$-0.196043\pi$
$563$	5.66088	+	5.66088i	0.238578	+	0.238578i	−0.577683	+	0.816261i	$0.696043\pi$
$564$		0			0
$565$	−7.28931	+	38.4294i	−0.306664	+	1.61674i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	44.6920i		−	1.87359i	−0.349883	−	0.936793i	$-0.613779\pi$
$569$		−	44.6920i		−	1.87359i	0.349883	−	0.936793i	$-0.386221\pi$
$570$		0			0
$571$	−0.218434			−0.00914120			−0.00457060	−	0.999990i	$-0.501455\pi$
$571$	−0.218434			−0.00914120			−0.00457060	+	0.999990i	$0.501455\pi$
$572$		0			0
$573$	−10.0143	−	10.0143i	−0.418353	−	0.418353i
$574$		0			0
$575$	5.72537	+	13.1553i	0.238764	+	0.548612i
$576$		0			0
$577$	23.5518	−	23.5518i	0.980473	−	0.980473i	−0.0193398	−	0.999813i	$-0.506156\pi$
$577$	23.5518	−	23.5518i	0.980473	−	0.980473i	0.999813	+	0.0193398i	$0.00615643\pi$
$578$		0			0
$579$	−3.41039			−0.141731
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−6.64072	+	6.64072i	−0.275031	+	0.275031i
$584$		0			0
$585$	0.916212	−	4.83029i	0.0378807	−	0.199708i
$586$		0			0
$587$	−3.96609	+	3.96609i	−0.163698	+	0.163698i	−0.784203	−	0.620505i	$-0.786928\pi$
$587$	−3.96609	+	3.96609i	−0.163698	+	0.163698i	0.620505	+	0.784203i	$0.286928\pi$
$588$		0			0
$589$			2.59403i			0.106885i
$590$		0			0
$591$			15.2819i			0.628612i
$592$		0			0
$593$	0.0780570	+	0.0780570i	0.00320542	+	0.00320542i	0.708708	−	0.705502i	$-0.249279\pi$
$593$	0.0780570	+	0.0780570i	0.00320542	+	0.00320542i	−0.705502	+	0.708708i	$0.749279\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	7.41266	+	7.41266i	0.303380	+	0.303380i
$598$		0			0
$599$			0.968565i			0.0395745i	0.999804	+	0.0197873i	$0.00629889\pi$
$599$			0.968565i			0.0395745i	−0.999804	+	0.0197873i	$0.993701\pi$
$600$		0			0
$601$		−	21.5615i		−	0.879512i	−0.898117	−	0.439756i	$-0.855065\pi$
$601$		−	21.5615i		−	0.879512i	0.898117	−	0.439756i	$-0.144935\pi$
$602$		0			0
$603$	−3.33204	+	3.33204i	−0.135691	+	0.135691i
$604$		0			0
$605$	12.1670	−	8.28723i	0.494659	−	0.336924i
$606$		0			0
$607$	24.9987	−	24.9987i	1.01466	−	1.01466i	0.0147733	−	0.999891i	$-0.495297\pi$
$607$	24.9987	−	24.9987i	1.01466	−	1.01466i	0.999891	−	0.0147733i	$-0.00470266\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	11.0756			0.448071
$612$		0			0
$613$	−15.6620	+	15.6620i	−0.632580	+	0.632580i	−0.948714	−	0.316134i	$-0.897615\pi$
$613$	−15.6620	+	15.6620i	−0.632580	+	0.632580i	0.316134	+	0.948714i	$0.397615\pi$
$614$		0			0
$615$	−2.59313	+	13.6710i	−0.104565	+	0.551269i
$616$		0			0
$617$	−21.0041	−	21.0041i	−0.845595	−	0.845595i	0.143985	−	0.989580i	$-0.454008\pi$
$617$	−21.0041	−	21.0041i	−0.845595	−	0.845595i	−0.989580	+	0.143985i	$0.954008\pi$
$618$		0			0
$619$	30.1530			1.21195			0.605976	−	0.795483i	$-0.292783\pi$
$619$	30.1530			1.21195			0.605976	+	0.795483i	$0.292783\pi$
$620$		0			0
$621$			2.86943i			0.115146i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−18.2954	−	17.0376i	−0.731816	−	0.681503i
$626$		0			0
$627$	−1.95014	−	1.95014i	−0.0778812	−	0.0778812i
$628$		0			0
$629$	−16.3481			−0.651843
$630$		0			0
$631$	−43.9829			−1.75093			−0.875465	−	0.483282i	$-0.839445\pi$
$631$	−43.9829			−1.75093			−0.875465	+	0.483282i	$0.839445\pi$
$632$		0			0
$633$	5.87805	+	5.87805i	0.233632	+	0.233632i
$634$		0			0
$635$	36.0767	+	6.84304i	1.43166	+	0.271558i
$636$		0			0
$637$		0			0
$638$		0			0
$639$			2.70489i			0.107004i
$640$		0			0
$641$	−1.25341			−0.0495068			−0.0247534	−	0.999694i	$-0.507880\pi$
$641$	−1.25341			−0.0495068			−0.0247534	+	0.999694i	$0.507880\pi$
$642$		0			0
$643$	−22.5269	−	22.5269i	−0.888375	−	0.888375i	0.105992	−	0.994367i	$-0.466198\pi$
$643$	−22.5269	−	22.5269i	−0.888375	−	0.888375i	−0.994367	+	0.105992i	$0.966198\pi$
$644$		0			0
$645$	13.7203	−	9.34522i	0.540236	−	0.367967i
$646$		0			0
$647$	−7.29477	+	7.29477i	−0.286787	+	0.286787i	−0.835808	−	0.549021i	$-0.815001\pi$
$647$	−7.29477	+	7.29477i	−0.286787	+	0.286787i	0.549021	+	0.835808i	$0.315001\pi$
$648$		0			0
$649$	18.8850			0.741302
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−32.9950	+	32.9950i	−1.29120	+	1.29120i	−0.357148	+	0.934048i	$0.616251\pi$
$653$	−32.9950	+	32.9950i	−1.29120	+	1.29120i	−0.934048	+	0.357148i	$0.883749\pi$
$654$		0			0
$655$	21.5040	+	31.5713i	0.840230	+	1.23359i
$656$		0			0
$657$	3.02145	−	3.02145i	0.117878	−	0.117878i
$658$		0			0
$659$			42.1172i			1.64065i	0.571894	+	0.820327i	$0.306209\pi$
$659$			42.1172i			1.64065i	−0.571894	+	0.820327i	$0.693791\pi$
$660$		0			0
$661$			9.68765i			0.376806i	0.982092	+	0.188403i	$0.0603311\pi$
$661$			9.68765i			0.376806i	−0.982092	+	0.188403i	$0.939669\pi$
$662$		0			0
$663$	9.95124	+	9.95124i	0.386474	+	0.386474i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	11.5066	+	11.5066i	0.445538	+	0.445538i
$668$		0			0
$669$		−	0.475071i		−	0.0183673i
$670$		0			0
$671$		−	14.0552i		−	0.542596i
$672$		0			0
$673$	10.8746	−	10.8746i	0.419184	−	0.419184i	−0.465739	−	0.884922i	$-0.654211\pi$
$673$	10.8746	−	10.8746i	0.419184	−	0.419184i	0.884922	+	0.465739i	$0.154211\pi$
$674$		0			0
$675$	−1.99530	−	4.58462i	−0.0767991	−	0.176462i
$676$		0			0
$677$	−4.23913	+	4.23913i	−0.162923	+	0.162923i	−0.783860	−	0.620937i	$-0.786752\pi$
$677$	−4.23913	+	4.23913i	−0.162923	+	0.162923i	0.620937	+	0.783860i	$0.286752\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	21.0834			0.807917
$682$		0			0
$683$	13.3588	−	13.3588i	0.511162	−	0.511162i	−0.403720	−	0.914882i	$-0.632283\pi$
$683$	13.3588	−	13.3588i	0.511162	−	0.511162i	0.914882	+	0.403720i	$0.132283\pi$
$684$		0			0
$685$	30.4288	+	5.77175i	1.16262	+	0.220527i
$686$		0			0
$687$	15.7138	+	15.7138i	0.599518	+	0.599518i
$688$		0			0
$689$	9.82554			0.374323
$690$		0			0
$691$		−	41.6550i		−	1.58463i	−0.610111	−	0.792316i	$-0.708875\pi$
$691$		−	41.6550i		−	1.58463i	0.610111	−	0.792316i	$-0.291125\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−33.0778	+	22.5301i	−1.25471	+	0.854615i
$696$		0			0
$697$	−28.1647	−	28.1647i	−1.06681	−	1.06681i
$698$		0			0
$699$	−10.0499			−0.380121
$700$		0			0
$701$	−28.5549			−1.07850			−0.539252	−	0.842144i	$-0.681293\pi$
$701$	−28.5549			−1.07850			−0.539252	+	0.842144i	$0.681293\pi$
$702$		0			0
$703$	−2.37011	−	2.37011i	−0.0893904	−	0.0893904i
$704$		0			0
$705$	9.30954	−	6.34095i	0.350618	−	0.238814i
$706$		0			0
$707$		0			0
$708$		0			0
$709$			19.4664i			0.731077i	0.930796	+	0.365539i	$0.119115\pi$
$709$			19.4664i			0.731077i	−0.930796	+	0.365539i	$0.880885\pi$
$710$		0			0
$711$	16.8538			0.632068
$712$		0			0
$713$	4.01064	+	4.01064i	0.150199	+	0.150199i
$714$		0			0
$715$	10.1511	+	1.92546i	0.379628	+	0.0720081i
$716$		0			0
$717$	16.7227	−	16.7227i	0.624519	−	0.624519i
$718$		0			0
$719$	−1.68425			−0.0628118			−0.0314059	−	0.999507i	$-0.509998\pi$
$719$	−1.68425			−0.0628118			−0.0314059	+	0.999507i	$0.509998\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−6.59669	+	6.59669i	−0.245333	+	0.245333i
$724$		0			0
$725$	−26.3860	−	10.3834i	−0.979950	−	0.385629i
$726$		0			0
$727$	−25.3252	+	25.3252i	−0.939260	+	0.939260i	−0.998258	−	0.0589986i	$-0.981209\pi$
$727$	−25.3252	+	25.3252i	−0.939260	+	0.939260i	0.0589986	+	0.998258i	$0.481209\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			47.5189i			1.75755i
$732$		0			0
$733$	15.9891	+	15.9891i	0.590569	+	0.590569i	0.937785	−	0.347216i	$-0.112873\pi$
$733$	15.9891	+	15.9891i	0.590569	+	0.590569i	−0.347216	+	0.937785i	$0.612873\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.00243	−	7.00243i	−0.257938	−	0.257938i
$738$		0			0
$739$			40.2512i			1.48067i	0.672241	+	0.740333i	$0.265332\pi$
$739$			40.2512i			1.48067i	−0.672241	+	0.740333i	$0.734668\pi$
$740$		0			0
$741$			2.88541i			0.105998i
$742$		0			0
$743$	4.54797	−	4.54797i	0.166849	−	0.166849i	−0.618744	−	0.785593i	$-0.712358\pi$
$743$	4.54797	−	4.54797i	0.166849	−	0.166849i	0.785593	+	0.618744i	$0.212358\pi$
$744$		0			0
$745$	1.46619	+	2.15260i	0.0537169	+	0.0788652i
$746$		0			0
$747$	−5.76026	+	5.76026i	−0.210757	+	0.210757i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	43.1634			1.57506			0.787528	−	0.616279i	$-0.211361\pi$
$751$	43.1634			1.57506			0.787528	+	0.616279i	$0.211361\pi$
$752$		0			0
$753$	−11.2708	+	11.2708i	−0.410729	+	0.410729i
$754$		0			0
$755$	−11.5369	+	7.85808i	−0.419872	+	0.285985i
$756$		0			0
$757$	26.6680	+	26.6680i	0.969266	+	0.969266i	0.999542	−	0.0302758i	$-0.00963857\pi$
$757$	26.6680	+	26.6680i	0.969266	+	0.969266i	−0.0302758	+	0.999542i	$0.509639\pi$
$758$		0			0
$759$	−6.03023			−0.218883
$760$		0			0
$761$		−	43.7959i		−	1.58760i	−0.608180	−	0.793799i	$-0.708100\pi$
$761$		−	43.7959i		−	1.58760i	0.608180	−	0.793799i	$-0.291900\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	14.0617	+	2.66723i	0.508402	+	0.0964339i
$766$		0			0
$767$	−13.9710	−	13.9710i	−0.504465	−	0.504465i
$768$		0			0
$769$	−50.3914			−1.81716			−0.908580	−	0.417710i	$-0.862833\pi$
$769$	−50.3914			−1.81716			−0.908580	+	0.417710i	$0.862833\pi$
$770$		0			0
$771$	7.41014			0.266870
$772$		0			0
$773$	17.6426	+	17.6426i	0.634560	+	0.634560i	0.949208	−	0.314648i	$-0.101887\pi$
$773$	17.6426	+	17.6426i	0.634560	+	0.634560i	−0.314648	+	0.949208i	$0.601887\pi$
$774$		0			0
$775$	−9.19683	−	3.61913i	−0.330360	−	0.130003i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	8.16648i		−	0.292595i
$780$		0			0
$781$	−5.68443			−0.203405
$782$		0			0
$783$	−4.01007	−	4.01007i	−0.143308	−	0.143308i
$784$		0			0
$785$	−10.1090	+	53.2950i	−0.360806	+	1.90218i
$786$		0			0
$787$	15.7837	−	15.7837i	0.562629	−	0.562629i	−0.367424	−	0.930053i	$-0.619760\pi$
$787$	15.7837	−	15.7837i	0.562629	−	0.562629i	0.930053	+	0.367424i	$0.119760\pi$
$788$		0			0
$789$	−25.1595			−0.895701
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−10.3980	+	10.3980i	−0.369243	+	0.369243i
$794$		0			0
$795$	8.25881	−	5.62527i	0.292910	−	0.199508i
$796$		0			0
$797$	18.4313	−	18.4313i	0.652871	−	0.652871i	−0.300812	−	0.953683i	$-0.597258\pi$
$797$	18.4313	−	18.4313i	0.652871	−	0.652871i	0.953683	+	0.300812i	$0.0972577\pi$
$798$		0			0
$799$			32.2427i			1.14067i
$800$		0			0
$801$		−	9.22575i		−	0.325976i
$802$		0			0
$803$	6.34970	+	6.34970i	0.224076	+	0.224076i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	17.0375	+	17.0375i	0.599749	+	0.599749i
$808$		0			0
$809$			4.27178i			0.150188i	0.997176	+	0.0750940i	$0.0239257\pi$
$809$			4.27178i			0.150188i	−0.997176	+	0.0750940i	$0.976074\pi$
$810$		0			0
$811$		−	36.1795i		−	1.27044i	−0.772333	−	0.635218i	$-0.780910\pi$
$811$		−	36.1795i		−	1.27044i	0.772333	−	0.635218i	$-0.219090\pi$
$812$		0			0
$813$	−20.4263	+	20.4263i	−0.716381	+	0.716381i
$814$		0			0
$815$	−4.91443	+	25.9090i	−0.172145	+	0.907552i
$816$		0			0
$817$	−6.88917	+	6.88917i	−0.241021	+	0.241021i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	16.0155			0.558944			0.279472	−	0.960154i	$-0.409841\pi$
$821$	16.0155			0.558944			0.279472	+	0.960154i	$0.409841\pi$
$822$		0			0
$823$	15.0678	−	15.0678i	0.525231	−	0.525231i	−0.393915	−	0.919147i	$-0.628880\pi$
$823$	15.0678	−	15.0678i	0.525231	−	0.525231i	0.919147	+	0.393915i	$0.128880\pi$
$824$		0			0
$825$	9.63478	−	4.19320i	0.335440	−	0.145989i
$826$		0			0
$827$	−29.3374	−	29.3374i	−1.02016	−	1.02016i	−0.999793	−	0.0203673i	$-0.993516\pi$
$827$	−29.3374	−	29.3374i	−1.02016	−	1.02016i	−0.0203673	−	0.999793i	$-0.506484\pi$
$828$		0			0
$829$	−4.95180			−0.171983			−0.0859915	−	0.996296i	$-0.527406\pi$
$829$	−4.95180			−0.171983			−0.0859915	+	0.996296i	$0.527406\pi$
$830$		0			0
$831$		−	7.77316i		−	0.269648i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−3.79559	+	20.0105i	−0.131352	+	0.692490i
$836$		0			0
$837$	−1.39771	−	1.39771i	−0.0483120	−	0.0483120i
$838$		0			0
$839$	5.32702			0.183909			0.0919546	−	0.995763i	$-0.470689\pi$
$839$	5.32702			0.183909			0.0919546	+	0.995763i	$0.470689\pi$
$840$		0			0
$841$	−3.16137			−0.109013
$842$		0			0
$843$	5.36072	+	5.36072i	0.184633	+	0.184633i
$844$		0			0
$845$	10.2789	+	15.0911i	0.353606	+	0.519151i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		−	26.6012i		−	0.912952i
$850$		0			0
$851$	−7.32885			−0.251230
$852$		0			0
$853$	10.7238	+	10.7238i	0.367174	+	0.367174i	0.866446	−	0.499271i	$-0.166399\pi$
$853$	10.7238	+	10.7238i	0.367174	+	0.367174i	−0.499271	+	0.866446i	$0.666399\pi$
$854$		0			0
$855$	1.65194	+	2.42531i	0.0564951	+	0.0829440i
$856$		0			0
$857$	−21.8284	+	21.8284i	−0.745644	+	0.745644i	−0.973658	−	0.228013i	$-0.926777\pi$
$857$	−21.8284	+	21.8284i	−0.745644	+	0.745644i	0.228013	+	0.973658i	$0.426777\pi$
$858$		0			0
$859$	−51.5280			−1.75811			−0.879056	−	0.476719i	$-0.841826\pi$
$859$	−51.5280			−1.75811			−0.879056	+	0.476719i	$0.841826\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	10.6823	−	10.6823i	0.363631	−	0.363631i	−0.501517	−	0.865148i	$-0.667225\pi$
$863$	10.6823	−	10.6823i	0.363631	−	0.363631i	0.865148	+	0.501517i	$0.167225\pi$
$864$		0			0
$865$	21.9777	+	4.16875i	0.747266	+	0.141742i
$866$		0			0
$867$	−16.9487	+	16.9487i	−0.575608	+	0.575608i
$868$		0			0
$869$			35.4190i			1.20151i
$870$		0			0
$871$			10.3607i			0.351059i
$872$		0			0
$873$	5.81278	+	5.81278i	0.196733	+	0.196733i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.58194	+	1.58194i	0.0534185	+	0.0534185i	0.733311	−	0.679893i	$-0.237974\pi$
$877$	1.58194	+	1.58194i	0.0534185	+	0.0534185i	−0.679893	+	0.733311i	$0.737974\pi$
$878$		0			0
$879$			4.31383i			0.145502i
$880$		0			0
$881$			42.4090i			1.42880i	0.699740	+	0.714398i	$0.253299\pi$
$881$			42.4090i			1.42880i	−0.699740	+	0.714398i	$0.746701\pi$
$882$		0			0
$883$	−31.0895	+	31.0895i	−1.04624	+	1.04624i	−0.0473662	+	0.998878i	$0.515083\pi$
$883$	−31.0895	+	31.0895i	−1.04624	+	1.04624i	−0.998878	+	0.0473662i	$0.984917\pi$
$884$		0			0
$885$	−19.7419	−	3.74466i	−0.663617	−	0.125875i
$886$		0			0
$887$	−11.8589	+	11.8589i	−0.398183	+	0.398183i	−0.877592	−	0.479409i	$-0.840851\pi$
$887$	−11.8589	+	11.8589i	−0.398183	+	0.398183i	0.479409	+	0.877592i	$0.340851\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2.10154			0.0704043
$892$		0			0
$893$	−4.67446	+	4.67446i	−0.156425	+	0.156425i
$894$		0			0
$895$	−7.39124	−	10.8515i	−0.247062	−	0.362727i
$896$		0			0
$897$	4.46113	+	4.46113i	0.148953	+	0.148953i
$898$		0			0
$899$	−11.2098			−0.373869
$900$		0			0
$901$			28.6036i			0.952924i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−12.2979	−	18.0554i	−0.408797	−	0.600181i
$906$		0			0
$907$	−22.5578	−	22.5578i	−0.749019	−	0.749019i	0.225276	−	0.974295i	$-0.427672\pi$
$907$	−22.5578	−	22.5578i	−0.749019	−	0.749019i	−0.974295	+	0.225276i	$0.927672\pi$
$908$		0			0
$909$	5.34750			0.177365
$910$		0			0
$911$	8.14365			0.269811			0.134906	−	0.990858i	$-0.456927\pi$
$911$	8.14365			0.269811			0.134906	+	0.990858i	$0.456927\pi$
$912$		0			0
$913$	−12.1054	−	12.1054i	−0.400631	−	0.400631i
$914$		0			0
$915$	−2.78697	+	14.6930i	−0.0921344	+	0.485735i
$916$		0			0
$917$		0			0
$918$		0			0
$919$			2.42689i			0.0800557i	0.999199	+	0.0400278i	$0.0127447\pi$
$919$			2.42689i			0.0800557i	−0.999199	+	0.0400278i	$0.987255\pi$
$920$		0			0
$921$	−12.5150			−0.412384
$922$		0			0
$923$	4.20531	+	4.20531i	0.138420	+	0.138420i
$924$		0			0
$925$	11.7096	−	5.09622i	0.385011	−	0.167563i
$926$		0			0
$927$	11.3050	−	11.3050i	0.371306	−	0.371306i
$928$		0			0
$929$	5.55257			0.182174			0.0910869	−	0.995843i	$-0.470966\pi$
$929$	5.55257			0.182174			0.0910869	+	0.995843i	$0.470966\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−5.69425	+	5.69425i	−0.186421	+	0.186421i
$934$		0			0
$935$	−5.60529	+	29.5512i	−0.183313	+	0.966429i
$936$		0			0
$937$	−3.03763	+	3.03763i	−0.0992351	+	0.0992351i	−0.754981	−	0.655746i	$-0.772354\pi$
$937$	−3.03763	+	3.03763i	−0.0992351	+	0.0992351i	0.655746	+	0.754981i	$0.272354\pi$
$938$		0			0
$939$		−	20.0920i		−	0.655679i
$940$		0			0
$941$		−	23.3230i		−	0.760307i	−0.924924	−	0.380153i	$-0.875871\pi$
$941$		−	23.3230i		−	0.760307i	0.924924	−	0.380153i	$-0.124129\pi$
$942$		0			0
$943$	−12.6262	−	12.6262i	−0.411166	−	0.411166i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.0492	+	14.0492i	0.456539	+	0.456539i	0.897517	−	0.440979i	$-0.145369\pi$
$947$	14.0492	+	14.0492i	0.456539	+	0.456539i	−0.440979	+	0.897517i	$0.645369\pi$
$948$		0			0
$949$		−	9.39494i		−	0.304973i
$950$		0			0
$951$		−	32.2847i		−	1.04690i
$952$		0			0
$953$	18.3048	−	18.3048i	0.592950	−	0.592950i	−0.345477	−	0.938427i	$-0.612283\pi$
$953$	18.3048	−	18.3048i	0.592950	−	0.592950i	0.938427	+	0.345477i	$0.112283\pi$
$954$		0			0
$955$	−26.1734	+	17.8273i	−0.846952	+	0.576879i
$956$		0			0
$957$	8.42734	−	8.42734i	0.272417	−	0.272417i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	27.0928			0.873962
$962$		0			0
$963$	3.44862	−	3.44862i	0.111130	−	0.111130i
$964$		0			0
$965$	−1.42114	+	7.49228i	−0.0457481	+	0.241185i
$966$		0			0
$967$	−15.8785	−	15.8785i	−0.510619	−	0.510619i	0.404097	−	0.914716i	$-0.367586\pi$
$967$	−15.8785	−	15.8785i	−0.510619	−	0.510619i	−0.914716	+	0.404097i	$0.867586\pi$
$968$		0			0
$969$	−8.39985			−0.269842
$970$		0			0
$971$		−	45.4507i		−	1.45858i	−0.684204	−	0.729290i	$-0.739850\pi$
$971$		−	45.4507i		−	1.45858i	0.684204	−	0.729290i	$-0.260150\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−10.2299	−	4.02565i	−0.327618	−	0.128924i
$976$		0			0
$977$	−29.2700	−	29.2700i	−0.936431	−	0.936431i	0.0616656	−	0.998097i	$-0.480359\pi$
$977$	−29.2700	−	29.2700i	−0.936431	−	0.936431i	−0.998097	+	0.0616656i	$0.980359\pi$
$978$		0			0
$979$	19.3883			0.619653
$980$		0			0
$981$	−18.1751			−0.580285
$982$		0			0
$983$	−29.8386	−	29.8386i	−0.951704	−	0.951704i	0.0471826	−	0.998886i	$-0.484976\pi$
$983$	−29.8386	−	29.8386i	−0.951704	−	0.951704i	−0.998886	+	0.0471826i	$0.984976\pi$
$984$		0			0
$985$	33.5727	+	6.36808i	1.06971	+	0.202904i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			21.3027i			0.677386i
$990$		0			0
$991$	−17.2407			−0.547669			−0.273834	−	0.961777i	$-0.588292\pi$
$991$	−17.2407			−0.547669			−0.273834	+	0.961777i	$0.588292\pi$
$992$		0			0
$993$	−0.335392	−	0.335392i	−0.0106433	−	0.0106433i
$994$		0			0
$995$	19.3738	−	13.1959i	0.614189	−	0.418339i
$996$		0			0
$997$	23.9088	−	23.9088i	0.757200	−	0.757200i	−0.218612	−	0.975812i	$-0.570153\pi$
$997$	23.9088	−	23.9088i	0.757200	−	0.757200i	0.975812	+	0.218612i	$0.0701529\pi$
$998$		0			0
$999$	2.55411			0.0808086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.x.b.97.5	yes	24
5.3	odd	4		2940.2.x.a.1273.8	yes	24
7.6	odd	2		2940.2.x.a.97.8	✓	24
35.13	even	4	inner	2940.2.x.b.1273.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2940.2.x.a.97.8	✓	24	7.6	odd	2
2940.2.x.a.1273.8	yes	24	5.3	odd	4
2940.2.x.b.97.5	yes	24	1.1	even	1	trivial
2940.2.x.b.1273.5	yes	24	35.13	even	4	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:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-1.84810 + 1.25878i) q^{5} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-1.84810 + 1.25878i) q^{5} +1.00000i q^{9} -2.10154 q^{11} +(1.55471 + 1.55471i) q^{13} +(2.19690 + 0.416708i) q^{15} +(-4.52598 + 4.52598i) q^{17} -1.31233 q^{19} +(-2.02899 + 2.02899i) q^{23} +(1.83093 - 4.65271i) q^{25} +(0.707107 - 0.707107i) q^{27} -5.67110i q^{29} -1.97666i q^{31} +(1.48601 + 1.48601i) q^{33} +(1.80603 + 1.80603i) q^{37} -2.19869i q^{39} +6.22289i q^{41} +(5.24957 - 5.24957i) q^{43} +(-1.25878 - 1.84810i) q^{45} +(3.56196 - 3.56196i) q^{47} +6.40071 q^{51} +(3.15993 - 3.15993i) q^{53} +(3.88385 - 2.64539i) q^{55} +(0.927958 + 0.927958i) q^{57} -8.98627 q^{59} +6.68806i q^{61} +(-4.83029 - 0.916212i) q^{65} +(3.33204 + 3.33204i) q^{67} +2.86943 q^{69} +2.70489 q^{71} +(-3.02145 - 3.02145i) q^{73} +(-4.58462 + 1.99530i) q^{75} -16.8538i q^{79} -1.00000 q^{81} +(5.76026 + 5.76026i) q^{83} +(2.66723 - 14.0617i) q^{85} +(-4.01007 + 4.01007i) q^{87} -9.22575 q^{89} +(-1.39771 + 1.39771i) q^{93} +(2.42531 - 1.65194i) q^{95} +(5.81278 - 5.81278i) q^{97} -2.10154i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{5}+O(q^{10}) \) 24 * q + 8 * q^5	\( 24 q + 8 q^{5} - 16 q^{13} - 32 q^{19} + 16 q^{23} - 16 q^{25} + 16 q^{37} - 16 q^{43} - 8 q^{45} + 16 q^{47} + 24 q^{53} + 16 q^{57} - 64 q^{59} - 32 q^{65} + 32 q^{67} + 32 q^{71} + 16 q^{73} - 24 q^{81} + 48 q^{85} + 40 q^{87} - 144 q^{89} + 16 q^{93} - 64 q^{95} - 16 q^{97}+O(q^{100}) \) 24 * q + 8 * q^5 - 16 * q^13 - 32 * q^19 + 16 * q^23 - 16 * q^25 + 16 * q^37 - 16 * q^43 - 8 * q^45 + 16 * q^47 + 24 * q^53 + 16 * q^57 - 64 * q^59 - 32 * q^65 + 32 * q^67 + 32 * q^71 + 16 * q^73 - 24 * q^81 + 48 * q^85 + 40 * q^87 - 144 * q^89 + 16 * q^93 - 64 * q^95 - 16 * q^97

Introduction

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