LMFDB - Embedded newform 2100.2.x.d.1693.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1357,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, 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("2100.1357");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8x^{14} + 8x^{12} - 8x^{10} + 212x^{8} + 248x^{6} + 368x^{4} + 32x^{2} + 100 $ x^16 - 8x^14 + 8x^12 - 8x^10 + 212x^8 + 248x^6 + 368x^4 + 32*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1693.4
Root			$-2.36188 - 0.195512i$ of defining polynomial
Character	$\chi$	$=$	2100.1693
Dual form			2100.2.x.d.1357.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(1.57379 + 2.12678i) q^{7} -1.00000i q^{9} +O(q^{10})$	$q+(-0.707107 + 0.707107i) q^{3} +(1.57379 + 2.12678i) q^{7} -1.00000i q^{9} -2.40009 q^{11} +(0.697349 - 0.697349i) q^{13} +(3.50236 + 3.50236i) q^{17} -0.306326 q^{19} +(-2.61670 - 0.391024i) q^{21} +(2.63050 + 2.63050i) q^{23} +(0.707107 + 0.707107i) q^{27} +4.12741i q^{29} -9.14119i q^{31} +(1.69712 - 1.69712i) q^{33} +(-6.11361 + 6.11361i) q^{37} +0.986201i q^{39} +3.06840i q^{41} +(-3.56679 - 3.56679i) q^{43} +(-0.325841 - 0.325841i) q^{47} +(-2.04638 + 6.69420i) q^{49} -4.95308 q^{51} +(9.00299 + 9.00299i) q^{53} +(0.216605 - 0.216605i) q^{57} +13.0580 q^{59} +6.43890i q^{61} +(2.12678 - 1.57379i) q^{63} +(-9.48058 + 9.48058i) q^{67} -3.72008 q^{69} -9.39392 q^{71} +(3.69517 - 3.69517i) q^{73} +(-3.77724 - 5.10446i) q^{77} -12.2548i q^{79} -1.00000 q^{81} +(-2.89901 + 2.89901i) q^{83} +(-2.91852 - 2.91852i) q^{87} -1.75957 q^{89} +(2.58059 + 0.385628i) q^{91} +(6.46380 + 6.46380i) q^{93} +(-7.96812 - 7.96812i) q^{97} +2.40009i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 16 q^{11} + 8 q^{21} - 8 q^{23} - 16 q^{37} - 48 q^{43} - 16 q^{51} + 40 q^{53} + 8 q^{57} + 48 q^{67} - 32 q^{71} + 24 q^{77} - 16 q^{81} + 32 q^{91} + 8 q^{93}+O(q^{100}) $ 16 * q + 16 * q^11 + 8 * q^21 - 8 * q^23 - 16 * q^37 - 48 * q^43 - 16 * q^51 + 40 * q^53 + 8 * q^57 + 48 * q^67 - 32 * q^71 + 24 * q^77 - 16 * q^81 + 32 * q^91 + 8 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.57379	+	2.12678i	0.594836	+	0.803847i
$7$	1.57379	+	2.12678i	0.594836	+	0.803847i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−2.40009			−0.723655			−0.361827	−	0.932245i	$-0.617847\pi$
$11$	−2.40009			−0.723655			−0.361827	+	0.932245i	$0.617847\pi$
$12$		0			0
$13$	0.697349	−	0.697349i	0.193410	−	0.193410i	−0.603758	−	0.797168i	$-0.706331\pi$
$13$	0.697349	−	0.697349i	0.193410	−	0.193410i	0.797168	+	0.603758i	$0.206331\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.50236	+	3.50236i	0.849447	+	0.849447i	0.990064	−	0.140617i	$-0.0449087\pi$
$17$	3.50236	+	3.50236i	0.849447	+	0.849447i	−0.140617	+	0.990064i	$0.544909\pi$
$18$		0			0
$19$	−0.306326			−0.0702760			−0.0351380	−	0.999382i	$-0.511187\pi$
$19$	−0.306326			−0.0702760			−0.0351380	+	0.999382i	$0.511187\pi$
$20$		0			0
$21$	−2.61670	−	0.391024i	−0.571010	−	0.0853283i
$22$		0			0
$23$	2.63050	+	2.63050i	0.548496	+	0.548496i	0.926006	−	0.377509i	$-0.123219\pi$
$23$	2.63050	+	2.63050i	0.548496	+	0.548496i	−0.377509	+	0.926006i	$0.623219\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$			4.12741i			0.766441i	0.923657	+	0.383221i	$0.125185\pi$
$29$			4.12741i			0.766441i	−0.923657	+	0.383221i	$0.874815\pi$
$30$		0			0
$31$		−	9.14119i		−	1.64181i	−0.571068	−	0.820903i	$-0.693471\pi$
$31$		−	9.14119i		−	1.64181i	0.571068	−	0.820903i	$-0.306529\pi$
$32$		0			0
$33$	1.69712	−	1.69712i	0.295431	−	0.295431i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−6.11361	+	6.11361i	−1.00507	+	1.00507i	−0.00508461	+	0.999987i	$0.501618\pi$
$37$	−6.11361	+	6.11361i	−1.00507	+	1.00507i	−0.999987	+	0.00508461i	$0.998382\pi$
$38$		0			0
$39$			0.986201i			0.157919i
$40$		0			0
$41$			3.06840i			0.479204i	0.970871	+	0.239602i	$0.0770169\pi$
$41$			3.06840i			0.479204i	−0.970871	+	0.239602i	$0.922983\pi$
$42$		0			0
$43$	−3.56679	−	3.56679i	−0.543930	−	0.543930i	0.380748	−	0.924679i	$-0.375666\pi$
$43$	−3.56679	−	3.56679i	−0.543930	−	0.543930i	−0.924679	+	0.380748i	$0.875666\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.325841	−	0.325841i	−0.0475287	−	0.0475287i	0.682943	−	0.730472i	$-0.260700\pi$
$47$	−0.325841	−	0.325841i	−0.0475287	−	0.0475287i	−0.730472	+	0.682943i	$0.760700\pi$
$48$		0			0
$49$	−2.04638	+	6.69420i	−0.292340	+	0.956314i
$50$		0			0
$51$	−4.95308			−0.693570
$52$		0			0
$53$	9.00299	+	9.00299i	1.23666	+	1.23666i	0.961359	+	0.275296i	$0.0887759\pi$
$53$	9.00299	+	9.00299i	1.23666	+	1.23666i	0.275296	+	0.961359i	$0.411224\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.216605	−	0.216605i	0.0286900	−	0.0286900i
$58$		0			0
$59$	13.0580			1.70001			0.850003	−	0.526778i	$-0.176600\pi$
$59$	13.0580			1.70001			0.850003	+	0.526778i	$0.176600\pi$
$60$		0			0
$61$			6.43890i			0.824417i	0.911090	+	0.412208i	$0.135242\pi$
$61$			6.43890i			0.824417i	−0.911090	+	0.412208i	$0.864758\pi$
$62$		0			0
$63$	2.12678	−	1.57379i	0.267949	−	0.198279i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−9.48058	+	9.48058i	−1.15824	+	1.15824i	−0.173383	+	0.984854i	$0.555470\pi$
$67$	−9.48058	+	9.48058i	−1.15824	+	1.15824i	−0.984854	+	0.173383i	$0.944530\pi$
$68$		0			0
$69$	−3.72008			−0.447845
$70$		0			0
$71$	−9.39392			−1.11485			−0.557427	−	0.830226i	$-0.688211\pi$
$71$	−9.39392			−1.11485			−0.557427	+	0.830226i	$0.688211\pi$
$72$		0			0
$73$	3.69517	−	3.69517i	0.432487	−	0.432487i	−0.456986	−	0.889474i	$-0.651071\pi$
$73$	3.69517	−	3.69517i	0.432487	−	0.432487i	0.889474	+	0.456986i	$0.151071\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.77724	−	5.10446i	−0.430456	−	0.581708i
$78$		0			0
$79$		−	12.2548i		−	1.37878i	−0.724393	−	0.689388i	$-0.757880\pi$
$79$		−	12.2548i		−	1.37878i	0.724393	−	0.689388i	$-0.242120\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−2.89901	+	2.89901i	−0.318207	+	0.318207i	−0.848078	−	0.529871i	$-0.822240\pi$
$83$	−2.89901	+	2.89901i	−0.318207	+	0.318207i	0.529871	+	0.848078i	$0.322240\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.91852	−	2.91852i	−0.312898	−	0.312898i
$88$		0			0
$89$	−1.75957			−0.186514			−0.0932570	−	0.995642i	$-0.529728\pi$
$89$	−1.75957			−0.186514			−0.0932570	+	0.995642i	$0.529728\pi$
$90$		0			0
$91$	2.58059	+	0.385628i	0.270519	+	0.0404248i
$92$		0			0
$93$	6.46380	+	6.46380i	0.670265	+	0.670265i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−7.96812	−	7.96812i	−0.809040	−	0.809040i	0.175449	−	0.984489i	$-0.443862\pi$
$97$	−7.96812	−	7.96812i	−0.809040	−	0.809040i	−0.984489	+	0.175449i	$0.943862\pi$
$98$		0			0
$99$			2.40009i			0.241218i
$100$		0			0
$101$			13.0817i			1.30168i	0.759215	+	0.650840i	$0.225583\pi$
$101$			13.0817i			1.30168i	−0.759215	+	0.650840i	$0.774417\pi$
$102$		0			0
$103$	−2.52210	+	2.52210i	−0.248510	+	0.248510i	−0.820359	−	0.571849i	$-0.806226\pi$
$103$	−2.52210	+	2.52210i	−0.248510	+	0.248510i	0.571849	+	0.820359i	$0.306226\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−10.4245	+	10.4245i	−1.00778	+	1.00778i	−0.00780589	+	0.999970i	$0.502485\pi$
$107$	−10.4245	+	10.4245i	−1.00778	+	1.00778i	−0.999970	+	0.00780589i	$0.997515\pi$
$108$		0			0
$109$			9.90616i			0.948838i	0.880299	+	0.474419i	$0.157342\pi$
$109$			9.90616i			0.948838i	−0.880299	+	0.474419i	$0.842658\pi$
$110$		0			0
$111$		−	8.64595i		−	0.820638i
$112$		0			0
$113$	−3.12442	−	3.12442i	−0.293921	−	0.293921i	0.544706	−	0.838627i	$-0.316641\pi$
$113$	−3.12442	−	3.12442i	−0.293921	−	0.293921i	−0.838627	+	0.544706i	$0.816641\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.697349	−	0.697349i	−0.0644700	−	0.0644700i
$118$		0			0
$119$	−1.93677	+	12.9607i	−0.177544	+	1.18811i
$120$		0			0
$121$	−5.23956			−0.476324
$122$		0			0
$123$	−2.16969	−	2.16969i	−0.195634	−	0.195634i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−2.21196	+	2.21196i	−0.196280	+	0.196280i	−0.798403	−	0.602123i	$-0.794322\pi$
$127$	−2.21196	+	2.21196i	−0.196280	+	0.196280i	0.602123	+	0.798403i	$0.294322\pi$
$128$		0			0
$129$	5.04420			0.444117
$130$		0			0
$131$			9.61691i			0.840233i	0.907470	+	0.420117i	$0.138011\pi$
$131$			9.61691i			0.840233i	−0.907470	+	0.420117i	$0.861989\pi$
$132$		0			0
$133$	−0.482092	−	0.651488i	−0.0418027	−	0.0564911i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.90318	−	2.90318i	0.248035	−	0.248035i	−0.572129	−	0.820164i	$-0.693882\pi$
$137$	2.90318	−	2.90318i	0.248035	−	0.248035i	0.820164	+	0.572129i	$0.193882\pi$
$138$		0			0
$139$	7.39691			0.627398			0.313699	−	0.949523i	$-0.398432\pi$
$139$	7.39691			0.627398			0.313699	+	0.949523i	$0.398432\pi$
$140$		0			0
$141$	0.460808			0.0388070
$142$		0			0
$143$	−1.67370	+	1.67370i	−0.139962	+	0.139962i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−3.28651	−	6.18052i	−0.271066	−	0.509761i
$148$		0			0
$149$		−	12.5882i		−	1.03127i	−0.856809	−	0.515634i	$-0.827557\pi$
$149$		−	12.5882i		−	1.03127i	0.856809	−	0.515634i	$-0.172443\pi$
$150$		0			0
$151$	−1.90616			−0.155121			−0.0775607	−	0.996988i	$-0.524713\pi$
$151$	−1.90616			−0.155121			−0.0775607	+	0.996988i	$0.524713\pi$
$152$		0			0
$153$	3.50236	−	3.50236i	0.283149	−	0.283149i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	11.0128	+	11.0128i	0.878915	+	0.878915i	0.993422	−	0.114507i	$-0.0365288\pi$
$157$	11.0128	+	11.0128i	0.878915	+	0.878915i	−0.114507	+	0.993422i	$0.536529\pi$
$158$		0			0
$159$	−12.7321			−1.00973
$160$		0			0
$161$	−1.45464	+	9.73433i	−0.114642	+	0.767172i
$162$		0			0
$163$	9.69420	+	9.69420i	0.759308	+	0.759308i	0.976196	−	0.216888i	$-0.0695907\pi$
$163$	9.69420	+	9.69420i	0.759308	+	0.759308i	−0.216888	+	0.976196i	$0.569591\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	15.6702	+	15.6702i	1.21260	+	1.21260i	0.970170	+	0.242425i	$0.0779429\pi$
$167$	15.6702	+	15.6702i	1.21260	+	1.21260i	0.242425	+	0.970170i	$0.422057\pi$
$168$		0			0
$169$			12.0274i			0.925185i
$170$		0			0
$171$			0.306326i			0.0234253i
$172$		0			0
$173$	−11.3858	+	11.3858i	−0.865645	+	0.865645i	−0.991987	−	0.126342i	$-0.959676\pi$
$173$	−11.3858	+	11.3858i	−0.865645	+	0.865645i	0.126342	+	0.991987i	$0.459676\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−9.23339	+	9.23339i	−0.694024	+	0.694024i
$178$		0			0
$179$		−	10.7395i		−	0.802705i	−0.915924	−	0.401353i	$-0.868540\pi$
$179$		−	10.7395i		−	0.802705i	0.915924	−	0.401353i	$-0.131460\pi$
$180$		0			0
$181$			2.05717i			0.152908i	0.997073	+	0.0764542i	$0.0243599\pi$
$181$			2.05717i			0.152908i	−0.997073	+	0.0764542i	$0.975640\pi$
$182$		0			0
$183$	−4.55299	−	4.55299i	−0.336567	−	0.336567i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−8.40598	−	8.40598i	−0.614706	−	0.614706i
$188$		0			0
$189$	−0.391024	+	2.61670i	−0.0284428	+	0.190337i
$190$		0			0
$191$	1.54471			0.111771			0.0558857	−	0.998437i	$-0.482202\pi$
$191$	1.54471			0.111771			0.0558857	+	0.998437i	$0.482202\pi$
$192$		0			0
$193$	14.9414	+	14.9414i	1.07551	+	1.07551i	0.996906	+	0.0785987i	$0.0250446\pi$
$193$	14.9414	+	14.9414i	1.07551	+	1.07551i	0.0785987	+	0.996906i	$0.474955\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.9032	+	10.9032i	−0.776819	+	0.776819i	−0.979289	−	0.202469i	$-0.935103\pi$
$197$	−10.9032	+	10.9032i	−0.776819	+	0.776819i	0.202469	+	0.979289i	$0.435103\pi$
$198$		0			0
$199$	−14.0635			−0.996934			−0.498467	−	0.866909i	$-0.666103\pi$
$199$	−14.0635			−0.996934			−0.498467	+	0.866909i	$0.666103\pi$
$200$		0			0
$201$		−	13.4076i		−	0.945697i
$202$		0			0
$203$	−8.77809	+	6.49567i	−0.616101	+	0.455907i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.63050	−	2.63050i	0.182832	−	0.182832i
$208$		0			0
$209$	0.735210			0.0508555
$210$		0			0
$211$	−20.1334			−1.38604			−0.693020	−	0.720919i	$-0.743720\pi$
$211$	−20.1334			−1.38604			−0.693020	+	0.720919i	$0.743720\pi$
$212$		0			0
$213$	6.64251	−	6.64251i	0.455137	−	0.455137i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	19.4413	−	14.3863i	1.31976	−	0.976606i
$218$		0			0
$219$			5.22576i			0.353124i
$220$		0			0
$221$	4.88473			0.328583
$222$		0			0
$223$	7.62816	−	7.62816i	0.510819	−	0.510819i	−0.403958	−	0.914777i	$-0.632366\pi$
$223$	7.62816	−	7.62816i	0.510819	−	0.510819i	0.914777	+	0.403958i	$0.132366\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.71882	+	2.71882i	0.180454	+	0.180454i	0.791554	−	0.611099i	$-0.209272\pi$
$227$	2.71882	+	2.71882i	0.180454	+	0.180454i	−0.611099	+	0.791554i	$0.709272\pi$
$228$		0			0
$229$	−9.87998			−0.652887			−0.326444	−	0.945217i	$-0.605850\pi$
$229$	−9.87998			−0.652887			−0.326444	+	0.945217i	$0.605850\pi$
$230$		0			0
$231$	6.28031	+	0.938492i	0.413214	+	0.0617483i
$232$		0			0
$233$	2.10897	+	2.10897i	0.138163	+	0.138163i	0.772806	−	0.634643i	$-0.218853\pi$
$233$	2.10897	+	2.10897i	0.138163	+	0.138163i	−0.634643	+	0.772806i	$0.718853\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	8.66547	+	8.66547i	0.562883	+	0.562883i
$238$		0			0
$239$			3.32171i			0.214863i	0.994212	+	0.107432i	$0.0342627\pi$
$239$			3.32171i			0.214863i	−0.994212	+	0.107432i	$0.965737\pi$
$240$		0			0
$241$		−	29.3877i		−	1.89303i	−0.322666	−	0.946513i	$-0.604579\pi$
$241$		−	29.3877i		−	1.89303i	0.322666	−	0.946513i	$-0.395421\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.213616	+	0.213616i	−0.0135921	+	0.0135921i
$248$		0			0
$249$		−	4.09981i		−	0.259815i
$250$		0			0
$251$			3.74084i			0.236120i	0.993006	+	0.118060i	$0.0376675\pi$
$251$			3.74084i			0.236120i	−0.993006	+	0.118060i	$0.962333\pi$
$252$		0			0
$253$	−6.31343	−	6.31343i	−0.396922	−	0.396922i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.40308	+	5.40308i	0.337035	+	0.337035i	0.855250	−	0.518215i	$-0.173403\pi$
$257$	5.40308	+	5.40308i	0.337035	+	0.337035i	−0.518215	+	0.855250i	$0.673403\pi$
$258$		0			0
$259$	−22.6238	−	3.38077i	−1.40578	−	0.210071i
$260$		0			0
$261$	4.12741			0.255480
$262$		0			0
$263$	−18.7970	−	18.7970i	−1.15907	−	1.15907i	−0.984675	−	0.174398i	$-0.944202\pi$
$263$	−18.7970	−	18.7970i	−1.15907	−	1.15907i	−0.174398	−	0.984675i	$-0.555798\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.24420	−	1.24420i	0.0761440	−	0.0761440i
$268$		0			0
$269$	22.4710			1.37008			0.685040	−	0.728506i	$-0.259785\pi$
$269$	22.4710			1.37008			0.685040	+	0.728506i	$0.259785\pi$
$270$		0			0
$271$		−	2.69150i		−	0.163497i	−0.996653	−	0.0817484i	$-0.973950\pi$
$271$		−	2.69150i		−	0.163497i	0.996653	−	0.0817484i	$-0.0260504\pi$
$272$		0			0
$273$	−2.09743	+	1.55207i	−0.126942	+	0.0939357i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	11.3746	−	11.3746i	0.683434	−	0.683434i	−0.277339	−	0.960772i	$-0.589452\pi$
$277$	11.3746	−	11.3746i	0.683434	−	0.683434i	0.960772	+	0.277339i	$0.0894524\pi$
$278$		0			0
$279$	−9.14119			−0.547269
$280$		0			0
$281$	18.4728			1.10199			0.550996	−	0.834508i	$-0.314248\pi$
$281$	18.4728			1.10199			0.550996	+	0.834508i	$0.314248\pi$
$282$		0			0
$283$	18.5376	−	18.5376i	1.10195	−	1.10195i	0.107773	−	0.994176i	$-0.465628\pi$
$283$	18.5376	−	18.5376i	1.10195	−	1.10195i	0.994176	−	0.107773i	$-0.0343719\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.52581	+	4.82901i	−0.385207	+	0.285048i
$288$		0			0
$289$			7.53302i			0.443119i
$290$		0			0
$291$	11.2686			0.660578
$292$		0			0
$293$	−5.40308	+	5.40308i	−0.315652	+	0.315652i	−0.847094	−	0.531443i	$-0.821650\pi$
$293$	−5.40308	+	5.40308i	−0.315652	+	0.315652i	0.531443	+	0.847094i	$0.321650\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.69712	−	1.69712i	−0.0984769	−	0.0984769i
$298$		0			0
$299$	3.66875			0.212169
$300$		0			0
$301$	1.97240	−	13.1991i	0.113687	−	0.760786i
$302$		0			0
$303$	−9.25018	−	9.25018i	−0.531409	−	0.531409i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−18.9851	−	18.9851i	−1.08354	−	1.08354i	−0.996177	−	0.0873616i	$-0.972156\pi$
$307$	−18.9851	−	18.9851i	−1.08354	−	1.08354i	−0.0873616	−	0.996177i	$-0.527844\pi$
$308$		0			0
$309$		−	3.56679i		−	0.202908i
$310$		0			0
$311$		−	7.69244i		−	0.436198i	−0.975927	−	0.218099i	$-0.930014\pi$
$311$		−	7.69244i		−	0.436198i	0.975927	−	0.218099i	$-0.0699856\pi$
$312$		0			0
$313$	3.65913	−	3.65913i	0.206826	−	0.206826i	−0.596091	−	0.802917i	$-0.703280\pi$
$313$	3.65913	−	3.65913i	0.206826	−	0.206826i	0.802917	+	0.596091i	$0.203280\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	21.8032	−	21.8032i	1.22459	−	1.22459i	0.258605	−	0.965983i	$-0.416737\pi$
$317$	21.8032	−	21.8032i	1.22459	−	1.22459i	0.965983	−	0.258605i	$-0.0832628\pi$
$318$		0			0
$319$		−	9.90616i		−	0.554639i
$320$		0			0
$321$		−	14.7425i		−	0.822845i
$322$		0			0
$323$	−1.07286	−	1.07286i	−0.0596957	−	0.0596957i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−7.00472	−	7.00472i	−0.387362	−	0.387362i
$328$		0			0
$329$	0.180187	−	1.20580i	0.00993402	−	0.0664776i
$330$		0			0
$331$	−5.17222			−0.284291			−0.142145	−	0.989846i	$-0.545400\pi$
$331$	−5.17222			−0.284291			−0.142145	+	0.989846i	$0.545400\pi$
$332$		0			0
$333$	6.11361	+	6.11361i	0.335024	+	0.335024i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	8.41776	−	8.41776i	0.458545	−	0.458545i	−0.439633	−	0.898178i	$-0.644891\pi$
$337$	8.41776	−	8.41776i	0.458545	−	0.458545i	0.898178	+	0.439633i	$0.144891\pi$
$338$		0			0
$339$	4.41860			0.239985
$340$		0			0
$341$			21.9397i			1.18810i
$342$		0			0
$343$	−17.4577	+	6.18306i	−0.942625	+	0.333854i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.0753948	−	0.0753948i	0.00404740	−	0.00404740i	−0.705080	−	0.709128i	$-0.749089\pi$
$347$	0.0753948	−	0.0753948i	0.00404740	−	0.00404740i	0.709128	+	0.705080i	$0.249089\pi$
$348$		0			0
$349$	34.9899			1.87296			0.936482	−	0.350714i	$-0.114061\pi$
$349$	34.9899			1.87296			0.936482	+	0.350714i	$0.114061\pi$
$350$		0			0
$351$	0.986201			0.0526395
$352$		0			0
$353$	−7.53299	+	7.53299i	−0.400941	+	0.400941i	−0.878564	−	0.477624i	$-0.841498\pi$
$353$	−7.53299	+	7.53299i	−0.400941	+	0.400941i	0.477624	+	0.878564i	$0.341498\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−7.79510	−	10.5341i	−0.412561	−	0.557524i
$358$		0			0
$359$		−	22.1572i		−	1.16941i	−0.811245	−	0.584707i	$-0.801210\pi$
$359$		−	22.1572i		−	1.16941i	0.811245	−	0.584707i	$-0.198790\pi$
$360$		0			0
$361$	−18.9062			−0.995061
$362$		0			0
$363$	3.70493	−	3.70493i	0.194458	−	0.194458i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	21.8093	+	21.8093i	1.13844	+	1.13844i	0.988730	+	0.149707i	$0.0478331\pi$
$367$	21.8093	+	21.8093i	1.13844	+	1.13844i	0.149707	+	0.988730i	$0.452167\pi$
$368$		0			0
$369$	3.06840			0.159735
$370$		0			0
$371$	−4.97857	+	33.3162i	−0.258474	+	1.72969i
$372$		0			0
$373$	−6.90616	−	6.90616i	−0.357588	−	0.357588i	0.505335	−	0.862923i	$-0.331369\pi$
$373$	−6.90616	−	6.90616i	−0.357588	−	0.357588i	−0.862923	+	0.505335i	$0.831369\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.87825	+	2.87825i	0.148237	+	0.148237i
$378$		0			0
$379$		−	33.2546i		−	1.70818i	−0.520129	−	0.854088i	$-0.674116\pi$
$379$		−	33.2546i		−	1.70818i	0.520129	−	0.854088i	$-0.325884\pi$
$380$		0			0
$381$		−	3.12819i		−	0.160262i
$382$		0			0
$383$	5.14086	−	5.14086i	0.262686	−	0.262686i	−0.563459	−	0.826144i	$-0.690530\pi$
$383$	5.14086	−	5.14086i	0.262686	−	0.262686i	0.826144	+	0.563459i	$0.190530\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.56679	+	3.56679i	−0.181310	+	0.181310i
$388$		0			0
$389$			29.2670i			1.48389i	0.670458	+	0.741947i	$0.266097\pi$
$389$			29.2670i			1.48389i	−0.670458	+	0.741947i	$0.733903\pi$
$390$		0			0
$391$			18.4259i			0.931836i
$392$		0			0
$393$	−6.80018	−	6.80018i	−0.343024	−	0.343024i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−22.3632	−	22.3632i	−1.12238	−	1.12238i	−0.991383	−	0.130992i	$-0.958184\pi$
$397$	−22.3632	−	22.3632i	−1.12238	−	1.12238i	−0.130992	−	0.991383i	$-0.541816\pi$
$398$		0			0
$399$	0.801562	+	0.119781i	0.0401283	+	0.00599653i
$400$		0			0
$401$	25.8675			1.29176			0.645881	−	0.763438i	$-0.276490\pi$
$401$	25.8675			1.29176			0.645881	+	0.763438i	$0.276490\pi$
$402$		0			0
$403$	−6.37460	−	6.37460i	−0.317542	−	0.317542i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	14.6732	−	14.6732i	0.727325	−	0.727325i
$408$		0			0
$409$	36.4392			1.80180			0.900902	−	0.434023i	$-0.142906\pi$
$409$	36.4392			1.80180			0.900902	+	0.434023i	$0.142906\pi$
$410$		0			0
$411$			4.10571i			0.202520i
$412$		0			0
$413$	20.5505	+	27.7715i	1.01122	+	1.36654i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−5.23040	+	5.23040i	−0.256134	+	0.256134i
$418$		0			0
$419$	22.9097			1.11921			0.559607	−	0.828758i	$-0.310952\pi$
$419$	22.9097			1.11921			0.559607	+	0.828758i	$0.310952\pi$
$420$		0			0
$421$	29.3098			1.42847			0.714237	−	0.699904i	$-0.246774\pi$
$421$	29.3098			1.42847			0.714237	+	0.699904i	$0.246774\pi$
$422$		0			0
$423$	−0.325841	+	0.325841i	−0.0158429	+	0.0158429i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−13.6941	+	10.1335i	−0.662705	+	0.490393i
$428$		0			0
$429$		−	2.36697i		−	0.114279i
$430$		0			0
$431$	40.5947			1.95538			0.977688	−	0.210063i	$-0.0673669\pi$
$431$	40.5947			1.95538			0.977688	+	0.210063i	$0.0673669\pi$
$432$		0			0
$433$	1.09377	−	1.09377i	0.0525632	−	0.0525632i	−0.680337	−	0.732900i	$-0.738166\pi$
$433$	1.09377	−	1.09377i	0.0525632	−	0.0525632i	0.732900	+	0.680337i	$0.238166\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.805789	−	0.805789i	−0.0385461	−	0.0385461i
$438$		0			0
$439$	−18.2283			−0.869991			−0.434995	−	0.900433i	$-0.643250\pi$
$439$	−18.2283			−0.869991			−0.434995	+	0.900433i	$0.643250\pi$
$440$		0			0
$441$	6.69420	+	2.04638i	0.318771	+	0.0974467i
$442$		0			0
$443$	−22.3914	−	22.3914i	−1.06385	−	1.06385i	−0.997818	−	0.0660294i	$-0.978967\pi$
$443$	−22.3914	−	22.3914i	−1.06385	−	1.06385i	−0.0660294	−	0.997818i	$-0.521033\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	8.90122	+	8.90122i	0.421013	+	0.421013i
$448$		0			0
$449$		−	26.1223i		−	1.23279i	−0.787437	−	0.616395i	$-0.788593\pi$
$449$		−	26.1223i		−	1.23279i	0.787437	−	0.616395i	$-0.211407\pi$
$450$		0			0
$451$		−	7.36444i		−	0.346778i
$452$		0			0
$453$	1.34786	−	1.34786i	0.0633281	−	0.0633281i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	11.3546	−	11.3546i	0.531147	−	0.531147i	−0.389766	−	0.920914i	$-0.627444\pi$
$457$	11.3546	−	11.3546i	0.531147	−	0.531147i	0.920914	+	0.389766i	$0.127444\pi$
$458$		0			0
$459$			4.95308i			0.231190i
$460$		0			0
$461$		−	10.9957i		−	0.512120i	−0.966661	−	0.256060i	$-0.917576\pi$
$461$		−	10.9957i		−	0.512120i	0.966661	−	0.256060i	$-0.0824244\pi$
$462$		0			0
$463$	−7.01215	−	7.01215i	−0.325882	−	0.325882i	0.525136	−	0.851018i	$-0.324014\pi$
$463$	−7.01215	−	7.01215i	−0.325882	−	0.325882i	−0.851018	+	0.525136i	$0.824014\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.80297	−	3.80297i	−0.175980	−	0.175980i	0.613621	−	0.789601i	$-0.289712\pi$
$467$	−3.80297	−	3.80297i	−0.175980	−	0.175980i	−0.789601	+	0.613621i	$0.789712\pi$
$468$		0			0
$469$	−35.0835	−	5.24268i	−1.62001	−	0.242084i
$470$		0			0
$471$	−15.5744			−0.717631
$472$		0			0
$473$	8.56062	+	8.56062i	0.393618	+	0.393618i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	9.00299	−	9.00299i	0.412219	−	0.412219i
$478$		0			0
$479$	33.5693			1.53382			0.766910	−	0.641755i	$-0.221793\pi$
$479$	33.5693			1.53382			0.766910	+	0.641755i	$0.221793\pi$
$480$		0			0
$481$			8.52665i			0.388782i
$482$		0			0
$483$	−5.85462	−	7.91179i	−0.266395	−	0.359999i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	8.90000	−	8.90000i	0.403297	−	0.403297i	−0.476096	−	0.879393i	$-0.657949\pi$
$487$	8.90000	−	8.90000i	0.403297	−	0.403297i	0.879393	+	0.476096i	$0.157949\pi$
$488$		0			0
$489$	−13.7097			−0.619973
$490$		0			0
$491$	−21.4491			−0.967985			−0.483993	−	0.875072i	$-0.660814\pi$
$491$	−21.4491			−0.967985			−0.483993	+	0.875072i	$0.660814\pi$
$492$		0			0
$493$	−14.4557	+	14.4557i	−0.651051	+	0.651051i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−14.7840	−	19.9788i	−0.663155	−	0.896172i
$498$		0			0
$499$			27.0826i			1.21238i	0.795318	+	0.606192i	$0.207304\pi$
$499$			27.0826i			1.21238i	−0.795318	+	0.606192i	$0.792696\pi$
$500$		0			0
$501$	−22.1610			−0.990080
$502$		0			0
$503$	−6.35303	+	6.35303i	−0.283268	+	0.283268i	−0.834411	−	0.551143i	$-0.814192\pi$
$503$	−6.35303	+	6.35303i	−0.283268	+	0.283268i	0.551143	+	0.834411i	$0.314192\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−8.50466	−	8.50466i	−0.377705	−	0.377705i
$508$		0			0
$509$	−28.8456			−1.27856			−0.639279	−	0.768975i	$-0.720767\pi$
$509$	−28.8456			−1.27856			−0.639279	+	0.768975i	$0.720767\pi$
$510$		0			0
$511$	13.6742	+	2.04340i	0.604912	+	0.0903945i
$512$		0			0
$513$	−0.216605	−	0.216605i	−0.00956335	−	0.00956335i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.782047	+	0.782047i	0.0343944	+	0.0343944i
$518$		0			0
$519$		−	16.1019i		−	0.706796i
$520$		0			0
$521$		−	2.35064i		−	0.102983i	−0.998673	−	0.0514917i	$-0.983602\pi$
$521$		−	2.35064i		−	0.102983i	0.998673	−	0.0514917i	$-0.0163976\pi$
$522$		0			0
$523$	−5.70011	+	5.70011i	−0.249248	+	0.249248i	−0.820662	−	0.571414i	$-0.806395\pi$
$523$	−5.70011	+	5.70011i	−0.249248	+	0.249248i	0.571414	+	0.820662i	$0.306395\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	32.0157	−	32.0157i	1.39463	−	1.39463i
$528$		0			0
$529$		−	9.16099i		−	0.398304i
$530$		0			0
$531$		−	13.0580i		−	0.566668i
$532$		0			0
$533$	2.13975	+	2.13975i	0.0926828	+	0.0926828i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	7.59395	+	7.59395i	0.327703	+	0.327703i
$538$		0			0
$539$	4.91150	−	16.0667i	0.211553	−	0.692042i
$540$		0			0
$541$	26.3730			1.13386			0.566931	−	0.823765i	$-0.308131\pi$
$541$	26.3730			1.13386			0.566931	+	0.823765i	$0.308131\pi$
$542$		0			0
$543$	−1.45464	−	1.45464i	−0.0624246	−	0.0624246i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	2.45318	−	2.45318i	0.104890	−	0.104890i	−0.652714	−	0.757604i	$-0.726370\pi$
$547$	2.45318	−	2.45318i	0.104890	−	0.104890i	0.757604	+	0.652714i	$0.226370\pi$
$548$		0			0
$549$	6.43890			0.274806
$550$		0			0
$551$		−	1.26433i		−	0.0538624i
$552$		0			0
$553$	26.0633	−	19.2865i	1.10832	−	0.820145i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	20.2516	−	20.2516i	0.858090	−	0.858090i	−0.133023	−	0.991113i	$-0.542468\pi$
$557$	20.2516	−	20.2516i	0.858090	−	0.858090i	0.991113	+	0.133023i	$0.0424685\pi$
$558$		0			0
$559$	−4.97460			−0.210403
$560$		0			0
$561$	11.8879			0.501905
$562$		0			0
$563$	13.0580	−	13.0580i	0.550329	−	0.550329i	−0.376207	−	0.926536i	$-0.622772\pi$
$563$	13.0580	−	13.0580i	0.550329	−	0.550329i	0.926536	+	0.376207i	$0.122772\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.57379	−	2.12678i	−0.0660929	−	0.0893163i
$568$		0			0
$569$			41.7104i			1.74859i	0.485395	+	0.874295i	$0.338676\pi$
$569$			41.7104i			1.74859i	−0.485395	+	0.874295i	$0.661324\pi$
$570$		0			0
$571$	23.5728			0.986490			0.493245	−	0.869891i	$-0.335811\pi$
$571$	23.5728			0.986490			0.493245	+	0.869891i	$0.335811\pi$
$572$		0			0
$573$	−1.09228	+	1.09228i	−0.0456305	+	0.0456305i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	20.3191	+	20.3191i	0.845897	+	0.845897i	0.989618	−	0.143721i	$-0.0459069\pi$
$577$	20.3191	+	20.3191i	0.845897	+	0.845897i	−0.143721	+	0.989618i	$0.545907\pi$
$578$		0			0
$579$	−21.1303			−0.878146
$580$		0			0
$581$	−10.7280	−	1.60312i	−0.445071	−	0.0665088i
$582$		0			0
$583$	−21.6080	−	21.6080i	−0.894912	−	0.894912i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	21.5042	+	21.5042i	0.887575	+	0.887575i	0.994290	−	0.106715i	$-0.0340331\pi$
$587$	21.5042	+	21.5042i	0.887575	+	0.887575i	−0.106715	+	0.994290i	$0.534033\pi$
$588$		0			0
$589$			2.80018i			0.115380i
$590$		0			0
$591$		−	15.4194i		−	0.634270i
$592$		0			0
$593$	−24.2636	+	24.2636i	−0.996386	+	0.996386i	−0.999993	−	0.00360761i	$-0.998852\pi$
$593$	−24.2636	+	24.2636i	−0.996386	+	0.996386i	0.00360761	+	0.999993i	$0.498852\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	9.94438	−	9.94438i	0.406996	−	0.406996i
$598$		0			0
$599$		−	20.5458i		−	0.839479i	−0.907645	−	0.419740i	$-0.862121\pi$
$599$		−	20.5458i		−	0.839479i	0.907645	−	0.419740i	$-0.137879\pi$
$600$		0			0
$601$		−	10.2578i		−	0.418424i	−0.977870	−	0.209212i	$-0.932910\pi$
$601$		−	10.2578i		−	0.418424i	0.977870	−	0.209212i	$-0.0670899\pi$
$602$		0			0
$603$	9.48058	+	9.48058i	0.386079	+	0.386079i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−3.82671	−	3.82671i	−0.155321	−	0.155321i	0.625169	−	0.780490i	$-0.285030\pi$
$607$	−3.82671	−	3.82671i	−0.155321	−	0.155321i	−0.780490	+	0.625169i	$0.785030\pi$
$608$		0			0
$609$	1.61392	−	10.8002i	0.0653991	−	0.437645i
$610$		0			0
$611$	−0.454449			−0.0183851
$612$		0			0
$613$	−17.7615	−	17.7615i	−0.717382	−	0.717382i	0.250686	−	0.968068i	$-0.419344\pi$
$613$	−17.7615	−	17.7615i	−0.717382	−	0.717382i	−0.968068	+	0.250686i	$0.919344\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−26.4852	+	26.4852i	−1.06626	+	1.06626i	−0.0686116	+	0.997643i	$0.521857\pi$
$617$	−26.4852	+	26.4852i	−1.06626	+	1.06626i	−0.997643	+	0.0686116i	$0.978143\pi$
$618$		0			0
$619$	1.71847			0.0690712			0.0345356	−	0.999403i	$-0.489005\pi$
$619$	1.71847			0.0690712			0.0345356	+	0.999403i	$0.489005\pi$
$620$		0			0
$621$			3.72008i			0.149282i
$622$		0			0
$623$	−2.76919	−	3.74221i	−0.110945	−	0.149929i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.519872	+	0.519872i	−0.0207617	+	0.0207617i
$628$		0			0
$629$	−42.8241			−1.70751
$630$		0			0
$631$	22.5960			0.899531			0.449765	−	0.893147i	$-0.351508\pi$
$631$	22.5960			0.899531			0.449765	+	0.893147i	$0.351508\pi$
$632$		0			0
$633$	14.2365	−	14.2365i	0.565848	−	0.565848i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	3.24116	+	6.09524i	0.128419	+	0.241502i
$638$		0			0
$639$			9.39392i			0.371618i
$640$		0			0
$641$	−16.9828			−0.670780			−0.335390	−	0.942079i	$-0.608868\pi$
$641$	−16.9828			−0.670780			−0.335390	+	0.942079i	$0.608868\pi$
$642$		0			0
$643$	−16.3153	+	16.3153i	−0.643413	+	0.643413i	−0.951393	−	0.307980i	$-0.900347\pi$
$643$	−16.3153	+	16.3153i	−0.643413	+	0.643413i	0.307980	+	0.951393i	$0.400347\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	20.1017	+	20.1017i	0.790281	+	0.790281i	0.981540	−	0.191259i	$-0.0612570\pi$
$647$	20.1017	+	20.1017i	0.790281	+	0.790281i	−0.191259	+	0.981540i	$0.561257\pi$
$648$		0			0
$649$	−31.3404			−1.23022
$650$		0			0
$651$	−3.57442	+	23.9197i	−0.140093	+	0.937488i
$652$		0			0
$653$	−15.0968	−	15.0968i	−0.590784	−	0.590784i	0.347059	−	0.937843i	$-0.387180\pi$
$653$	−15.0968	−	15.0968i	−0.590784	−	0.590784i	−0.937843	+	0.347059i	$0.887180\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−3.69517	−	3.69517i	−0.144162	−	0.144162i
$658$		0			0
$659$			9.68446i			0.377253i	0.982049	+	0.188627i	$0.0604036\pi$
$659$			9.68446i			0.377253i	−0.982049	+	0.188627i	$0.939596\pi$
$660$		0			0
$661$		−	31.4292i		−	1.22245i	−0.791455	−	0.611227i	$-0.790676\pi$
$661$		−	31.4292i		−	1.22245i	0.791455	−	0.611227i	$-0.209324\pi$
$662$		0			0
$663$	−3.45403	+	3.45403i	−0.134143	+	0.134143i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−10.8571	+	10.8571i	−0.420390	+	0.420390i
$668$		0			0
$669$			10.7878i			0.417082i
$670$		0			0
$671$		−	15.4540i		−	0.596593i
$672$		0			0
$673$	13.2472	+	13.2472i	0.510642	+	0.510642i	0.914723	−	0.404081i	$-0.132409\pi$
$673$	13.2472	+	13.2472i	0.510642	+	0.510642i	−0.404081	+	0.914723i	$0.632409\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−17.0979	−	17.0979i	−0.657127	−	0.657127i	0.297573	−	0.954699i	$-0.403823\pi$
$677$	−17.0979	−	17.0979i	−0.657127	−	0.657127i	−0.954699	+	0.297573i	$0.903823\pi$
$678$		0			0
$679$	4.40630	−	29.4866i	0.169098	−	1.13159i
$680$		0			0
$681$	−3.84499			−0.147340
$682$		0			0
$683$	−2.78505	−	2.78505i	−0.106567	−	0.106567i	0.651813	−	0.758380i	$-0.274009\pi$
$683$	−2.78505	−	2.78505i	−0.106567	−	0.106567i	−0.758380	+	0.651813i	$0.774009\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	6.98620	−	6.98620i	0.266540	−	0.266540i
$688$		0			0
$689$	12.5565			0.478363
$690$		0			0
$691$		−	13.5727i		−	0.516331i	−0.966101	−	0.258166i	$-0.916882\pi$
$691$		−	13.5727i		−	0.516331i	0.966101	−	0.258166i	$-0.0831180\pi$
$692$		0			0
$693$	−5.10446	+	3.77724i	−0.193903	+	0.143485i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−10.7466	+	10.7466i	−0.407058	+	0.407058i
$698$		0			0
$699$	−2.98253			−0.112810
$700$		0			0
$701$	−20.5513			−0.776213			−0.388107	−	0.921614i	$-0.626871\pi$
$701$	−20.5513			−0.776213			−0.388107	+	0.921614i	$0.626871\pi$
$702$		0			0
$703$	1.87276	−	1.87276i	0.0706324	−	0.0706324i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−27.8220	+	20.5879i	−1.04635	+	0.774287i
$708$		0			0
$709$			0.976812i			0.0366850i	0.999832	+	0.0183425i	$0.00583892\pi$
$709$			0.976812i			0.0366850i	−0.999832	+	0.0183425i	$0.994161\pi$
$710$		0			0
$711$	−12.2548			−0.459592
$712$		0			0
$713$	24.0459	−	24.0459i	0.900524	−	0.900524i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−2.34880	−	2.34880i	−0.0877176	−	0.0877176i
$718$		0			0
$719$	−30.0286			−1.11988			−0.559938	−	0.828534i	$-0.689175\pi$
$719$	−30.0286			−1.11988			−0.559938	+	0.828534i	$0.689175\pi$
$720$		0			0
$721$	−9.33321	−	1.39470i	−0.347587	−	0.0519413i
$722$		0			0
$723$	20.7802	+	20.7802i	0.772825	+	0.772825i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−18.4518	−	18.4518i	−0.684338	−	0.684338i	0.276636	−	0.960975i	$-0.410780\pi$
$727$	−18.4518	−	18.4518i	−0.684338	−	0.684338i	−0.960975	+	0.276636i	$0.910780\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	24.9843i		−	0.924080i
$732$		0			0
$733$	3.66693	−	3.66693i	0.135441	−	0.135441i	−0.636136	−	0.771577i	$-0.719468\pi$
$733$	3.66693	−	3.66693i	0.135441	−	0.135441i	0.771577	+	0.636136i	$0.219468\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	22.7543	−	22.7543i	0.838164	−	0.838164i
$738$		0			0
$739$			28.2515i			1.03925i	0.854395	+	0.519624i	$0.173928\pi$
$739$			28.2515i			1.03925i	−0.854395	+	0.519624i	$0.826072\pi$
$740$		0			0
$741$		−	0.302099i		−	0.0110979i
$742$		0			0
$743$	38.3914	+	38.3914i	1.40844	+	1.40844i	0.768032	+	0.640412i	$0.221236\pi$
$743$	38.3914	+	38.3914i	1.40844	+	1.40844i	0.640412	+	0.768032i	$0.278764\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.89901	+	2.89901i	0.106069	+	0.106069i
$748$		0			0
$749$	−38.5766	−	5.76466i	−1.40956	−	0.210636i
$750$		0			0
$751$	−27.8938			−1.01786			−0.508930	−	0.860808i	$-0.669959\pi$
$751$	−27.8938			−1.01786			−0.508930	+	0.860808i	$0.669959\pi$
$752$		0			0
$753$	−2.64517	−	2.64517i	−0.0963955	−	0.0963955i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−17.7786	+	17.7786i	−0.646173	+	0.646173i	−0.952066	−	0.305893i	$-0.901045\pi$
$757$	−17.7786	+	17.7786i	−0.646173	+	0.646173i	0.305893	+	0.952066i	$0.401045\pi$
$758$		0			0
$759$	8.92854			0.324085
$760$		0			0
$761$			44.4107i			1.60989i	0.593353	+	0.804943i	$0.297804\pi$
$761$			44.4107i			1.60989i	−0.593353	+	0.804943i	$0.702196\pi$
$762$		0			0
$763$	−21.0682	+	15.5902i	−0.762721	+	0.564403i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	9.10598	−	9.10598i	0.328798	−	0.328798i
$768$		0			0
$769$	12.1042			0.436489			0.218244	−	0.975894i	$-0.429967\pi$
$769$	12.1042			0.436489			0.218244	+	0.975894i	$0.429967\pi$
$770$		0			0
$771$	−7.64112			−0.275188
$772$		0			0
$773$	28.8991	−	28.8991i	1.03943	−	1.03943i	0.0402368	−	0.999190i	$-0.487189\pi$
$773$	28.8991	−	28.8991i	1.03943	−	1.03943i	0.999190	−	0.0402368i	$-0.0128112\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	18.3880	−	13.6069i	0.659667	−	0.488145i
$778$		0			0
$779$		−	0.939931i		−	0.0336765i
$780$		0			0
$781$	22.5463			0.806769
$782$		0			0
$783$	−2.91852	+	2.91852i	−0.104299	+	0.104299i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	14.7200	+	14.7200i	0.524711	+	0.524711i	0.918990	−	0.394280i	$-0.129006\pi$
$787$	14.7200	+	14.7200i	0.524711	+	0.524711i	−0.394280	+	0.918990i	$0.629006\pi$
$788$		0			0
$789$	26.5830			0.946379
$790$		0			0
$791$	1.72778	−	11.5621i	0.0614327	−	0.411102i
$792$		0			0
$793$	4.49016	+	4.49016i	0.159450	+	0.159450i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−12.4784	−	12.4784i	−0.442007	−	0.442007i	0.450679	−	0.892686i	$-0.351182\pi$
$797$	−12.4784	−	12.4784i	−0.442007	−	0.442007i	−0.892686	+	0.450679i	$0.851182\pi$
$798$		0			0
$799$		−	2.28242i		−	0.0807462i
$800$		0			0
$801$			1.75957i			0.0621713i
$802$		0			0
$803$	−8.86875	+	8.86875i	−0.312971	+	0.312971i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−15.8894	+	15.8894i	−0.559333	+	0.559333i
$808$		0			0
$809$		−	21.3149i		−	0.749392i	−0.927148	−	0.374696i	$-0.877747\pi$
$809$		−	21.3149i		−	0.749392i	0.927148	−	0.374696i	$-0.122253\pi$
$810$		0			0
$811$			40.4684i			1.42104i	0.703678	+	0.710519i	$0.251540\pi$
$811$			40.4684i			1.42104i	−0.703678	+	0.710519i	$0.748460\pi$
$812$		0			0
$813$	1.90318	+	1.90318i	0.0667473	+	0.0667473i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	1.09260	+	1.09260i	0.0382252	+	0.0382252i
$818$		0			0
$819$	0.385628	−	2.58059i	0.0134749	−	0.0901731i
$820$		0			0
$821$	24.0722			0.840126			0.420063	−	0.907495i	$-0.362008\pi$
$821$	24.0722			0.840126			0.420063	+	0.907495i	$0.362008\pi$
$822$		0			0
$823$	−19.3332	−	19.3332i	−0.673913	−	0.673913i	0.284703	−	0.958616i	$-0.408105\pi$
$823$	−19.3332	−	19.3332i	−0.673913	−	0.673913i	−0.958616	+	0.284703i	$0.908105\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−29.1309	+	29.1309i	−1.01298	+	1.01298i	−0.0130645	+	0.999915i	$0.504159\pi$
$827$	−29.1309	+	29.1309i	−1.01298	+	1.01298i	−0.999915	+	0.0130645i	$0.995841\pi$
$828$		0			0
$829$	16.6708			0.579001			0.289500	−	0.957178i	$-0.406511\pi$
$829$	16.6708			0.579001			0.289500	+	0.957178i	$0.406511\pi$
$830$		0			0
$831$			16.0861i			0.558021i
$832$		0			0
$833$	−30.6126	+	16.2783i	−1.06067	+	0.564011i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	6.46380	−	6.46380i	0.223422	−	0.223422i
$838$		0			0
$839$	34.5881			1.19411			0.597057	−	0.802198i	$-0.296336\pi$
$839$	34.5881			1.19411			0.597057	+	0.802198i	$0.296336\pi$
$840$		0			0
$841$	11.9645			0.412568
$842$		0			0
$843$	−13.0622	+	13.0622i	−0.449887	+	0.449887i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−8.24596	−	11.1434i	−0.283335	−	0.382891i
$848$		0			0
$849$			26.2162i			0.899737i
$850$		0			0
$851$	−32.1637			−1.10256
$852$		0			0
$853$	19.0158	−	19.0158i	0.651088	−	0.651088i	−0.302167	−	0.953255i	$-0.597710\pi$
$853$	19.0158	−	19.0158i	0.651088	−	0.651088i	0.953255	+	0.302167i	$0.0977101\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.52545	+	3.52545i	0.120427	+	0.120427i	0.764752	−	0.644325i	$-0.222861\pi$
$857$	3.52545	+	3.52545i	0.120427	+	0.120427i	−0.644325	+	0.764752i	$0.722861\pi$
$858$		0			0
$859$	22.2575			0.759415			0.379707	−	0.925107i	$-0.376025\pi$
$859$	22.2575			0.759415			0.379707	+	0.925107i	$0.376025\pi$
$860$		0			0
$861$	1.19982	−	8.02907i	0.0408897	−	0.273630i
$862$		0			0
$863$	−16.2156	−	16.2156i	−0.551985	−	0.551985i	0.375028	−	0.927013i	$-0.377633\pi$
$863$	−16.2156	−	16.2156i	−0.551985	−	0.551985i	−0.927013	+	0.375028i	$0.877633\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−5.32665	−	5.32665i	−0.180903	−	0.180903i
$868$		0			0
$869$			29.4127i			0.997757i
$870$		0			0
$871$			13.2226i			0.448029i
$872$		0			0
$873$	−7.96812	+	7.96812i	−0.269680	+	0.269680i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−21.7768	+	21.7768i	−0.735350	+	0.735350i	−0.971674	−	0.236324i	$-0.924057\pi$
$877$	−21.7768	+	21.7768i	−0.735350	+	0.735350i	0.236324	+	0.971674i	$0.424057\pi$
$878$		0			0
$879$		−	7.64112i		−	0.257728i
$880$		0			0
$881$			9.67968i			0.326117i	0.986616	+	0.163058i	$0.0521359\pi$
$881$			9.67968i			0.326117i	−0.986616	+	0.163058i	$0.947864\pi$
$882$		0			0
$883$	12.7140	+	12.7140i	0.427859	+	0.427859i	0.887899	−	0.460039i	$-0.152165\pi$
$883$	12.7140	+	12.7140i	0.427859	+	0.427859i	−0.460039	+	0.887899i	$0.652165\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−17.6352	−	17.6352i	−0.592132	−	0.592132i	0.346075	−	0.938207i	$-0.387514\pi$
$887$	−17.6352	−	17.6352i	−0.592132	−	0.592132i	−0.938207	+	0.346075i	$0.887514\pi$
$888$		0			0
$889$	−8.18552	−	1.22320i	−0.274534	−	0.0410247i
$890$		0			0
$891$	2.40009			0.0804061
$892$		0			0
$893$	0.0998134	+	0.0998134i	0.00334013	+	0.00334013i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−2.59420	+	2.59420i	−0.0866177	+	0.0866177i
$898$		0			0
$899$	37.7294			1.25835
$900$		0			0
$901$			63.0634i			2.10095i
$902$		0			0
$903$	7.93851	+	10.7279i	0.264177	+	0.357002i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−3.91380	+	3.91380i	−0.129955	+	0.129955i	−0.769093	−	0.639137i	$-0.779292\pi$
$907$	−3.91380	+	3.91380i	−0.129955	+	0.129955i	0.639137	+	0.769093i	$0.279292\pi$
$908$		0			0
$909$	13.0817			0.433894
$910$		0			0
$911$	−25.2908			−0.837922			−0.418961	−	0.908004i	$-0.637606\pi$
$911$	−25.2908			−0.837922			−0.418961	+	0.908004i	$0.637606\pi$
$912$		0			0
$913$	6.95788	−	6.95788i	0.230272	−	0.230272i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−20.4530	+	15.1350i	−0.675419	+	0.499801i
$918$		0			0
$919$			35.4513i			1.16943i	0.811238	+	0.584716i	$0.198794\pi$
$919$			35.4513i			1.16943i	−0.811238	+	0.584716i	$0.801206\pi$
$920$		0			0
$921$	26.8490			0.884705
$922$		0			0
$923$	−6.55085	+	6.55085i	−0.215624	+	0.215624i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	2.52210	+	2.52210i	0.0828367	+	0.0828367i
$928$		0			0
$929$	25.9756			0.852233			0.426117	−	0.904668i	$-0.359881\pi$
$929$	25.9756			0.852233			0.426117	+	0.904668i	$0.359881\pi$
$930$		0			0
$931$	0.626859	−	2.05061i	0.0205445	−	0.0672059i
$932$		0			0
$933$	5.43938	+	5.43938i	0.178077	+	0.178077i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−4.53485	−	4.53485i	−0.148147	−	0.148147i	0.629143	−	0.777290i	$-0.283406\pi$
$937$	−4.53485	−	4.53485i	−0.148147	−	0.148147i	−0.777290	+	0.629143i	$0.783406\pi$
$938$		0			0
$939$			5.17479i			0.168873i
$940$		0			0
$941$			9.84843i			0.321050i	0.987032	+	0.160525i	$0.0513187\pi$
$941$			9.84843i			0.321050i	−0.987032	+	0.160525i	$0.948681\pi$
$942$		0			0
$943$	−8.07142	+	8.07142i	−0.262841	+	0.262841i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.0694	−	10.0694i	0.327212	−	0.327212i	−0.524313	−	0.851525i	$-0.675678\pi$
$947$	10.0694	−	10.0694i	0.327212	−	0.327212i	0.851525	+	0.524313i	$0.175678\pi$
$948$		0			0
$949$		−	5.15365i		−	0.167295i
$950$		0			0
$951$			30.8343i			0.999872i
$952$		0			0
$953$	10.5086	+	10.5086i	0.340407	+	0.340407i	0.856520	−	0.516113i	$-0.172622\pi$
$953$	10.5086	+	10.5086i	0.340407	+	0.340407i	−0.516113	+	0.856520i	$0.672622\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	7.00472	+	7.00472i	0.226430	+	0.226430i
$958$		0			0
$959$	10.7434	+	1.60543i	0.346922	+	0.0518420i
$960$		0			0
$961$	−52.5613			−1.69553
$962$		0			0
$963$	10.4245	+	10.4245i	0.335925	+	0.335925i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	33.6925	−	33.6925i	1.08348	−	1.08348i	0.0872970	−	0.996182i	$-0.472177\pi$
$967$	33.6925	−	33.6925i	1.08348	−	1.08348i	0.996182	−	0.0872970i	$-0.0278229\pi$
$968$		0			0
$969$	1.51726			0.0487413
$970$		0			0
$971$		−	46.3619i		−	1.48782i	−0.668278	−	0.743911i	$-0.732968\pi$
$971$		−	46.3619i		−	1.48782i	0.668278	−	0.743911i	$-0.267032\pi$
$972$		0			0
$973$	11.6412	+	15.7316i	0.373199	+	0.504332i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−29.2362	+	29.2362i	−0.935349	+	0.935349i	−0.998033	−	0.0626847i	$-0.980034\pi$
$977$	−29.2362	+	29.2362i	−0.935349	+	0.935349i	0.0626847	+	0.998033i	$0.480034\pi$
$978$		0			0
$979$	4.22313			0.134972
$980$		0			0
$981$	9.90616			0.316279
$982$		0			0
$983$	−2.72180	+	2.72180i	−0.0868120	+	0.0868120i	−0.749179	−	0.662367i	$-0.769552\pi$
$983$	−2.72180	+	2.72180i	−0.0868120	+	0.0868120i	0.662367	+	0.749179i	$0.269552\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	0.725215	+	0.980037i	0.0230838	+	0.0311949i
$988$		0			0
$989$		−	18.7648i		−	0.596687i
$990$		0			0
$991$	1.53413			0.0487332			0.0243666	−	0.999703i	$-0.492243\pi$
$991$	1.53413			0.0487332			0.0243666	+	0.999703i	$0.492243\pi$
$992$		0			0
$993$	3.65731	−	3.65731i	0.116061	−	0.116061i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	6.64616	+	6.64616i	0.210486	+	0.210486i	0.804474	−	0.593988i	$-0.202447\pi$
$997$	6.64616	+	6.64616i	0.210486	+	0.210486i	−0.593988	+	0.804474i	$0.702447\pi$
$998$		0			0
$999$	−8.64595			−0.273546

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.x.d.1693.4		16
5.2	odd	4	inner	2100.2.x.d.1357.5		16
5.3	odd	4		420.2.x.a.97.4	yes	16
5.4	even	2		420.2.x.a.13.5	yes	16
7.6	odd	2	inner	2100.2.x.d.1693.5		16
15.8	even	4		1260.2.ba.b.937.2		16
15.14	odd	2		1260.2.ba.b.433.7		16
20.3	even	4		1680.2.cz.c.97.8		16
20.19	odd	2		1680.2.cz.c.433.1		16
35.13	even	4		420.2.x.a.97.5	yes	16
35.27	even	4	inner	2100.2.x.d.1357.4		16
35.34	odd	2		420.2.x.a.13.4	✓	16
105.83	odd	4		1260.2.ba.b.937.7		16
105.104	even	2		1260.2.ba.b.433.2		16
140.83	odd	4		1680.2.cz.c.97.1		16
140.139	even	2		1680.2.cz.c.433.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.x.a.13.4	✓	16	35.34	odd	2
420.2.x.a.13.5	yes	16	5.4	even	2
420.2.x.a.97.4	yes	16	5.3	odd	4
420.2.x.a.97.5	yes	16	35.13	even	4
1260.2.ba.b.433.2		16	105.104	even	2
1260.2.ba.b.433.7		16	15.14	odd	2
1260.2.ba.b.937.2		16	15.8	even	4
1260.2.ba.b.937.7		16	105.83	odd	4
1680.2.cz.c.97.1		16	140.83	odd	4
1680.2.cz.c.97.8		16	20.3	even	4
1680.2.cz.c.433.1		16	20.19	odd	2
1680.2.cz.c.433.8		16	140.139	even	2
2100.2.x.d.1357.4		16	35.27	even	4	inner
2100.2.x.d.1357.5		16	5.2	odd	4	inner
2100.2.x.d.1693.4		16	1.1	even	1	trivial
2100.2.x.d.1693.5		16	7.6	odd	2	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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(1.57379 + 2.12678i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(1.57379 + 2.12678i) q^{7} -1.00000i q^{9} -2.40009 q^{11} +(0.697349 - 0.697349i) q^{13} +(3.50236 + 3.50236i) q^{17} -0.306326 q^{19} +(-2.61670 - 0.391024i) q^{21} +(2.63050 + 2.63050i) q^{23} +(0.707107 + 0.707107i) q^{27} +4.12741i q^{29} -9.14119i q^{31} +(1.69712 - 1.69712i) q^{33} +(-6.11361 + 6.11361i) q^{37} +0.986201i q^{39} +3.06840i q^{41} +(-3.56679 - 3.56679i) q^{43} +(-0.325841 - 0.325841i) q^{47} +(-2.04638 + 6.69420i) q^{49} -4.95308 q^{51} +(9.00299 + 9.00299i) q^{53} +(0.216605 - 0.216605i) q^{57} +13.0580 q^{59} +6.43890i q^{61} +(2.12678 - 1.57379i) q^{63} +(-9.48058 + 9.48058i) q^{67} -3.72008 q^{69} -9.39392 q^{71} +(3.69517 - 3.69517i) q^{73} +(-3.77724 - 5.10446i) q^{77} -12.2548i q^{79} -1.00000 q^{81} +(-2.89901 + 2.89901i) q^{83} +(-2.91852 - 2.91852i) q^{87} -1.75957 q^{89} +(2.58059 + 0.385628i) q^{91} +(6.46380 + 6.46380i) q^{93} +(-7.96812 - 7.96812i) q^{97} +2.40009i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 16 q^{11} + 8 q^{21} - 8 q^{23} - 16 q^{37} - 48 q^{43} - 16 q^{51} + 40 q^{53} + 8 q^{57} + 48 q^{67} - 32 q^{71} + 24 q^{77} - 16 q^{81} + 32 q^{91} + 8 q^{93}+O(q^{100}) \) 16 * q + 16 * q^11 + 8 * q^21 - 8 * q^23 - 16 * q^37 - 48 * q^43 - 16 * q^51 + 40 * q^53 + 8 * q^57 + 48 * q^67 - 32 * q^71 + 24 * q^77 - 16 * q^81 + 32 * q^91 + 8 * q^93

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