LMFDB - Embedded newform 1600.2.q.g.49.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1600,2,Mod(49,1600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1600.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1600, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.q (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$12.7760643234$
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} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			49.7
Root			$1.32070 - 0.505727i$ of defining polynomial
Character	$\chi$	$=$	1600.49
Dual form			1600.2.q.g.849.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.66366 + 1.66366i) q^{3} -2.89402 q^{7} +2.53555i q^{9} +(-1.84462 - 1.84462i) q^{11} +(-3.08011 - 3.08011i) q^{13} -7.29875i q^{17} +(-1.23593 + 1.23593i) q^{19} +(-4.81468 - 4.81468i) q^{21} -4.60490 q^{23} +(0.772683 - 0.772683i) q^{27} +(-4.24680 + 4.24680i) q^{29} -2.06299 q^{31} -6.13767i q^{33} +(-1.17899 + 1.17899i) q^{37} -10.2485i q^{39} +4.61484i q^{41} +(3.03019 - 3.03019i) q^{43} -11.7111i q^{47} +1.37537 q^{49} +(12.1427 - 12.1427i) q^{51} +(-2.73048 + 2.73048i) q^{53} -4.11235 q^{57} +(3.11306 + 3.11306i) q^{59} +(2.34962 - 2.34962i) q^{61} -7.33795i q^{63} +(8.24311 + 8.24311i) q^{67} +(-7.66101 - 7.66101i) q^{69} +3.25937i q^{71} -12.6877 q^{73} +(5.33839 + 5.33839i) q^{77} -0.113885 q^{79} +10.1776 q^{81} +(-9.76813 - 9.76813i) q^{83} -14.1305 q^{87} +3.74593i q^{89} +(8.91390 + 8.91390i) q^{91} +(-3.43212 - 3.43212i) q^{93} +13.9853i q^{97} +(4.67714 - 4.67714i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} + 8 q^{11} - 8 q^{19} - 24 q^{23} - 24 q^{27} + 16 q^{29} - 16 q^{37} + 8 q^{43} + 16 q^{49} + 32 q^{51} - 16 q^{53} - 8 q^{59} + 16 q^{61} + 40 q^{67} - 16 q^{69} - 16 q^{77} + 16 q^{79}+ \cdots - 8 q^{99}+O(q^{100}) $ 16 * q - 8 * q^7 + 8 * q^11 - 8 * q^19 - 24 * q^23 - 24 * q^27 + 16 * q^29 - 16 * q^37 + 8 * q^43 + 16 * q^49 + 32 * q^51 - 16 * q^53 - 8 * q^59 + 16 * q^61 + 40 * q^67 - 16 * q^69 - 16 * q^77 + 16 * q^79 - 16 * q^81 - 40 * q^83 - 32 * q^91 - 48 * q^93 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	1.66366	+	1.66366i	0.960517	+	0.960517i	0.999250	−	0.0387330i	$-0.0123322\pi$
$3$	1.66366	+	1.66366i	0.960517	+	0.960517i	−0.0387330	+	0.999250i	$0.512332\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.89402			−1.09384			−0.546919	−	0.837186i	$-0.684199\pi$
$7$	−2.89402			−1.09384			−0.546919	+	0.837186i	$0.684199\pi$
$8$		0			0
$9$			2.53555i			0.845184i
$10$		0			0
$11$	−1.84462	−	1.84462i	−0.556175	−	0.556175i	0.372041	−	0.928216i	$-0.378658\pi$
$11$	−1.84462	−	1.84462i	−0.556175	−	0.556175i	−0.928216	+	0.372041i	$0.878658\pi$
$12$		0			0
$13$	−3.08011	−	3.08011i	−0.854268	−	0.854268i	0.136388	−	0.990656i	$-0.456451\pi$
$13$	−3.08011	−	3.08011i	−0.854268	−	0.854268i	−0.990656	+	0.136388i	$0.956451\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	7.29875i		−	1.77021i	−0.465393	−	0.885104i	$-0.654087\pi$
$17$		−	7.29875i		−	1.77021i	0.465393	−	0.885104i	$-0.345913\pi$
$18$		0			0
$19$	−1.23593	+	1.23593i	−0.283542	+	0.283542i	−0.834520	−	0.550978i	$-0.814255\pi$
$19$	−1.23593	+	1.23593i	−0.283542	+	0.283542i	0.550978	+	0.834520i	$0.314255\pi$
$20$		0			0
$21$	−4.81468	−	4.81468i	−1.05065	−	1.05065i
$22$		0			0
$23$	−4.60490			−0.960189			−0.480094	−	0.877217i	$-0.659398\pi$
$23$	−4.60490			−0.960189			−0.480094	+	0.877217i	$0.659398\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.772683	−	0.772683i	0.148703	−	0.148703i
$28$		0			0
$29$	−4.24680	+	4.24680i	−0.788611	+	0.788611i	−0.981266	−	0.192656i	$-0.938290\pi$
$29$	−4.24680	+	4.24680i	−0.788611	+	0.788611i	0.192656	+	0.981266i	$0.438290\pi$
$30$		0			0
$31$	−2.06299			−0.370524			−0.185262	−	0.982689i	$-0.559313\pi$
$31$	−2.06299			−0.370524			−0.185262	+	0.982689i	$0.559313\pi$
$32$		0			0
$33$		−	6.13767i		−	1.06843i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.17899	+	1.17899i	−0.193825	+	0.193825i	−0.797346	−	0.603522i	$-0.793764\pi$
$37$	−1.17899	+	1.17899i	−0.193825	+	0.193825i	0.603522	+	0.797346i	$0.293764\pi$
$38$		0			0
$39$		−	10.2485i		−	1.64108i
$40$		0			0
$41$			4.61484i			0.720717i	0.932814	+	0.360359i	$0.117346\pi$
$41$			4.61484i			0.720717i	−0.932814	+	0.360359i	$0.882654\pi$
$42$		0			0
$43$	3.03019	−	3.03019i	0.462099	−	0.462099i	−0.437244	−	0.899343i	$-0.644045\pi$
$43$	3.03019	−	3.03019i	0.462099	−	0.462099i	0.899343	+	0.437244i	$0.144045\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	11.7111i		−	1.70823i	−0.520081	−	0.854117i	$-0.674098\pi$
$47$		−	11.7111i		−	1.70823i	0.520081	−	0.854117i	$-0.325902\pi$
$48$		0			0
$49$	1.37537			0.196481
$50$		0			0
$51$	12.1427	−	12.1427i	1.70031	−	1.70031i
$52$		0			0
$53$	−2.73048	+	2.73048i	−0.375061	+	0.375061i	−0.869316	−	0.494256i	$-0.835441\pi$
$53$	−2.73048	+	2.73048i	−0.375061	+	0.375061i	0.494256	+	0.869316i	$0.335441\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.11235			−0.544694
$58$		0			0
$59$	3.11306	+	3.11306i	0.405285	+	0.405285i	0.880091	−	0.474805i	$-0.157482\pi$
$59$	3.11306	+	3.11306i	0.405285	+	0.405285i	−0.474805	+	0.880091i	$0.657482\pi$
$60$		0			0
$61$	2.34962	−	2.34962i	0.300838	−	0.300838i	−0.540503	−	0.841342i	$-0.681766\pi$
$61$	2.34962	−	2.34962i	0.300838	−	0.300838i	0.841342	+	0.540503i	$0.181766\pi$
$62$		0			0
$63$		−	7.33795i		−	0.924495i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	8.24311	+	8.24311i	1.00706	+	1.00706i	0.999975	+	0.00708173i	$0.00225420\pi$
$67$	8.24311	+	8.24311i	1.00706	+	1.00706i	0.00708173	+	0.999975i	$0.497746\pi$
$68$		0			0
$69$	−7.66101	−	7.66101i	−0.922277	−	0.922277i
$70$		0			0
$71$			3.25937i			0.386816i	0.981118	+	0.193408i	$0.0619541\pi$
$71$			3.25937i			0.386816i	−0.981118	+	0.193408i	$0.938046\pi$
$72$		0			0
$73$	−12.6877			−1.48499			−0.742494	−	0.669853i	$-0.766357\pi$
$73$	−12.6877			−1.48499			−0.742494	+	0.669853i	$0.766357\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.33839	+	5.33839i	0.608365	+	0.608365i
$78$		0			0
$79$	−0.113885			−0.0128130			−0.00640652	−	0.999979i	$-0.502039\pi$
$79$	−0.113885			−0.0128130			−0.00640652	+	0.999979i	$0.502039\pi$
$80$		0			0
$81$	10.1776			1.13085
$82$		0			0
$83$	−9.76813	−	9.76813i	−1.07219	−	1.07219i	−0.997183	−	0.0750089i	$-0.976101\pi$
$83$	−9.76813	−	9.76813i	−1.07219	−	1.07219i	−0.0750089	−	0.997183i	$-0.523899\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−14.1305			−1.51495
$88$		0			0
$89$			3.74593i			0.397068i	0.980094	+	0.198534i	$0.0636180\pi$
$89$			3.74593i			0.397068i	−0.980094	+	0.198534i	$0.936382\pi$
$90$		0			0
$91$	8.91390	+	8.91390i	0.934430	+	0.934430i
$92$		0			0
$93$	−3.43212	−	3.43212i	−0.355894	−	0.355894i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			13.9853i			1.41999i	0.704206	+	0.709995i	$0.251303\pi$
$97$			13.9853i			1.41999i	−0.704206	+	0.709995i	$0.748697\pi$
$98$		0			0
$99$	4.67714	−	4.67714i	0.470071	−	0.470071i
$100$		0			0
$101$	3.52228	+	3.52228i	0.350480	+	0.350480i	0.860288	−	0.509808i	$-0.170284\pi$
$101$	3.52228	+	3.52228i	0.350480	+	0.350480i	−0.509808	+	0.860288i	$0.670284\pi$
$102$		0			0
$103$	0.150216			0.0148013			0.00740063	−	0.999973i	$-0.497644\pi$
$103$	0.150216			0.0148013			0.00740063	+	0.999973i	$0.497644\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.75062	−	2.75062i	0.265912	−	0.265912i	−0.561539	−	0.827451i	$-0.689790\pi$
$107$	2.75062	−	2.75062i	0.265912	−	0.265912i	0.827451	+	0.561539i	$0.189790\pi$
$108$		0			0
$109$	6.90778	−	6.90778i	0.661646	−	0.661646i	−0.294122	−	0.955768i	$-0.595027\pi$
$109$	6.90778	−	6.90778i	0.661646	−	0.661646i	0.955768	+	0.294122i	$0.0950273\pi$
$110$		0			0
$111$	−3.92288			−0.372344
$112$		0			0
$113$		−	3.49507i		−	0.328788i	−0.986395	−	0.164394i	$-0.947433\pi$
$113$		−	3.49507i		−	0.328788i	0.986395	−	0.164394i	$-0.0525669\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	7.80977	−	7.80977i	0.722014	−	0.722014i
$118$		0			0
$119$			21.1228i			1.93632i
$120$		0			0
$121$		−	4.19472i		−	0.381338i
$122$		0			0
$123$	−7.67755	+	7.67755i	−0.692261	+	0.692261i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			6.25357i			0.554915i	0.960738	+	0.277458i	$0.0894918\pi$
$127$			6.25357i			0.554915i	−0.960738	+	0.277458i	$0.910508\pi$
$128$		0			0
$129$	10.0824			0.887708
$130$		0			0
$131$	5.16490	−	5.16490i	0.451259	−	0.451259i	−0.444513	−	0.895772i	$-0.646623\pi$
$131$	5.16490	−	5.16490i	0.451259	−	0.451259i	0.895772	+	0.444513i	$0.146623\pi$
$132$		0			0
$133$	3.57681	−	3.57681i	0.310149	−	0.310149i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−18.9408			−1.61823			−0.809113	−	0.587654i	$-0.800052\pi$
$137$	−18.9408			−1.61823			−0.809113	+	0.587654i	$0.800052\pi$
$138$		0			0
$139$	2.79057	+	2.79057i	0.236693	+	0.236693i	0.815479	−	0.578786i	$-0.196473\pi$
$139$	2.79057	+	2.79057i	0.236693	+	0.236693i	−0.578786	+	0.815479i	$0.696473\pi$
$140$		0			0
$141$	19.4833	−	19.4833i	1.64079	−	1.64079i
$142$		0			0
$143$			11.3633i			0.950245i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.28815	+	2.28815i	0.188723	+	0.188723i
$148$		0			0
$149$	1.60372	+	1.60372i	0.131382	+	0.131382i	0.769740	−	0.638358i	$-0.220386\pi$
$149$	1.60372	+	1.60372i	0.131382	+	0.131382i	−0.638358	+	0.769740i	$0.720386\pi$
$150$		0			0
$151$		−	2.53754i		−	0.206502i	−0.994655	−	0.103251i	$-0.967076\pi$
$151$		−	2.53754i		−	0.206502i	0.994655	−	0.103251i	$-0.0329245\pi$
$152$		0			0
$153$	18.5064			1.49615
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−10.2405	−	10.2405i	−0.817278	−	0.817278i	0.168435	−	0.985713i	$-0.446129\pi$
$157$	−10.2405	−	10.2405i	−0.817278	−	0.817278i	−0.985713	+	0.168435i	$0.946129\pi$
$158$		0			0
$159$	−9.08521			−0.720504
$160$		0			0
$161$	13.3267			1.05029
$162$		0			0
$163$	−8.02607	−	8.02607i	−0.628650	−	0.628650i	0.319078	−	0.947728i	$-0.396627\pi$
$163$	−8.02607	−	8.02607i	−0.628650	−	0.628650i	−0.947728	+	0.319078i	$0.896627\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.82611			0.528221			0.264110	−	0.964492i	$-0.414922\pi$
$167$	6.82611			0.528221			0.264110	+	0.964492i	$0.414922\pi$
$168$		0			0
$169$			5.97411i			0.459547i
$170$		0			0
$171$	−3.13377	−	3.13377i	−0.239645	−	0.239645i
$172$		0			0
$173$	5.08901	+	5.08901i	0.386910	+	0.386910i	0.873584	−	0.486674i	$-0.161790\pi$
$173$	5.08901	+	5.08901i	0.386910	+	0.386910i	−0.486674	+	0.873584i	$0.661790\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			10.3582i			0.778567i
$178$		0			0
$179$	1.63797	−	1.63797i	0.122428	−	0.122428i	−0.643238	−	0.765666i	$-0.722410\pi$
$179$	1.63797	−	1.63797i	0.122428	−	0.122428i	0.765666	+	0.643238i	$0.222410\pi$
$180$		0			0
$181$	−16.7757	−	16.7757i	−1.24693	−	1.24693i	−0.957071	−	0.289855i	$-0.906393\pi$
$181$	−16.7757	−	16.7757i	−1.24693	−	1.24693i	−0.289855	−	0.957071i	$-0.593607\pi$
$182$		0			0
$183$	7.81797			0.577921
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−13.4635	+	13.4635i	−0.984546	+	0.984546i
$188$		0			0
$189$	−2.23616	+	2.23616i	−0.162657	+	0.162657i
$190$		0			0
$191$	−5.85815			−0.423881			−0.211940	−	0.977283i	$-0.567978\pi$
$191$	−5.85815			−0.423881			−0.211940	+	0.977283i	$0.567978\pi$
$192$		0			0
$193$		−	0.0241155i		−	0.00173587i	−1.00000		0.000867935i	$-0.999724\pi$
$193$		−	0.0241155i		−	0.00173587i	1.00000		0.000867935i	$-0.000276272\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	14.9086	−	14.9086i	1.06219	−	1.06219i	0.0642576	−	0.997933i	$-0.479532\pi$
$197$	14.9086	−	14.9086i	1.06219	−	1.06219i	0.997933	−	0.0642576i	$-0.0204679\pi$
$198$		0			0
$199$			13.6525i			0.967801i	0.875123	+	0.483900i	$0.160780\pi$
$199$			13.6525i			0.967801i	−0.875123	+	0.483900i	$0.839220\pi$
$200$		0			0
$201$			27.4275i			1.93459i
$202$		0			0
$203$	12.2903	−	12.2903i	0.862612	−	0.862612i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	11.6760i		−	0.811537i
$208$		0			0
$209$	4.55966			0.315398
$210$		0			0
$211$	2.45103	−	2.45103i	0.168736	−	0.168736i	−0.617688	−	0.786424i	$-0.711930\pi$
$211$	2.45103	−	2.45103i	0.168736	−	0.168736i	0.786424	+	0.617688i	$0.211930\pi$
$212$		0			0
$213$	−5.42249	+	5.42249i	−0.371543	+	0.371543i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	5.97033			0.405293
$218$		0			0
$219$	−21.1081	−	21.1081i	−1.42636	−	1.42636i
$220$		0			0
$221$	−22.4809	+	22.4809i	−1.51223	+	1.51223i
$222$		0			0
$223$		−	13.9483i		−	0.934045i	−0.884245	−	0.467023i	$-0.845327\pi$
$223$		−	13.9483i		−	0.934045i	0.884245	−	0.467023i	$-0.154673\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.43883	+	4.43883i	0.294616	+	0.294616i	0.838901	−	0.544285i	$-0.183199\pi$
$227$	4.43883	+	4.43883i	0.294616	+	0.294616i	−0.544285	+	0.838901i	$0.683199\pi$
$228$		0			0
$229$	5.35068	+	5.35068i	0.353583	+	0.353583i	0.861441	−	0.507858i	$-0.169562\pi$
$229$	5.35068	+	5.35068i	0.353583	+	0.353583i	−0.507858	+	0.861441i	$0.669562\pi$
$230$		0			0
$231$			17.7626i			1.16869i
$232$		0			0
$233$	11.9370			0.782019			0.391010	−	0.920387i	$-0.372126\pi$
$233$	11.9370			0.782019			0.391010	+	0.920387i	$0.372126\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.189466	−	0.189466i	−0.0123071	−	0.0123071i
$238$		0			0
$239$	−16.7720			−1.08489			−0.542445	−	0.840091i	$-0.682501\pi$
$239$	−16.7720			−1.08489			−0.542445	+	0.840091i	$0.682501\pi$
$240$		0			0
$241$	−22.0294			−1.41904			−0.709519	−	0.704686i	$-0.751088\pi$
$241$	−22.0294			−1.41904			−0.709519	+	0.704686i	$0.751088\pi$
$242$		0			0
$243$	14.6141	+	14.6141i	0.937495	+	0.937495i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	7.61360			0.484442
$248$		0			0
$249$		−	32.5018i		−	2.05972i
$250$		0			0
$251$	−6.63925	−	6.63925i	−0.419066	−	0.419066i	0.465816	−	0.884882i	$-0.345761\pi$
$251$	−6.63925	−	6.63925i	−0.419066	−	0.419066i	−0.884882	+	0.465816i	$0.845761\pi$
$252$		0			0
$253$	8.49432	+	8.49432i	0.534033	+	0.534033i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			7.25821i			0.452755i	0.974040	+	0.226377i	$0.0726883\pi$
$257$			7.25821i			0.452755i	−0.974040	+	0.226377i	$0.927312\pi$
$258$		0			0
$259$	3.41202	−	3.41202i	0.212013	−	0.212013i
$260$		0			0
$261$	−10.7680	−	10.7680i	−0.666521	−	0.666521i
$262$		0			0
$263$	−9.27431			−0.571878			−0.285939	−	0.958248i	$-0.592306\pi$
$263$	−9.27431			−0.571878			−0.285939	+	0.958248i	$0.592306\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−6.23197	+	6.23197i	−0.381390	+	0.381390i
$268$		0			0
$269$	13.4195	−	13.4195i	0.818199	−	0.818199i	−0.167648	−	0.985847i	$-0.553617\pi$
$269$	13.4195	−	13.4195i	0.818199	−	0.818199i	0.985847	+	0.167648i	$0.0536173\pi$
$270$		0			0
$271$	−22.5999			−1.37285			−0.686423	−	0.727202i	$-0.740820\pi$
$271$	−22.5999			−1.37285			−0.686423	+	0.727202i	$0.740820\pi$
$272$		0			0
$273$			29.6595i			1.79507i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	16.2015	−	16.2015i	0.973451	−	0.973451i	−0.0262056	−	0.999657i	$-0.508342\pi$
$277$	16.2015	−	16.2015i	0.973451	−	0.973451i	0.999657	+	0.0262056i	$0.00834245\pi$
$278$		0			0
$279$		−	5.23082i		−	0.313161i
$280$		0			0
$281$		−	8.84793i		−	0.527824i	−0.964547	−	0.263912i	$-0.914987\pi$
$281$		−	8.84793i		−	0.527824i	0.964547	−	0.263912i	$-0.0850128\pi$
$282$		0			0
$283$	−20.3062	+	20.3062i	−1.20708	+	1.20708i	−0.235109	+	0.971969i	$0.575545\pi$
$283$	−20.3062	+	20.3062i	−1.20708	+	1.20708i	−0.971969	+	0.235109i	$0.924455\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	13.3555i		−	0.788348i
$288$		0			0
$289$	−36.2718			−2.13364
$290$		0			0
$291$	−23.2668	+	23.2668i	−1.36392	+	1.36392i
$292$		0			0
$293$	7.16936	−	7.16936i	0.418839	−	0.418839i	−0.465965	−	0.884803i	$-0.654293\pi$
$293$	7.16936	−	7.16936i	0.418839	−	0.418839i	0.884803	+	0.465965i	$0.154293\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.85062			−0.165410
$298$		0			0
$299$	14.1836	+	14.1836i	0.820258	+	0.820258i
$300$		0			0
$301$	−8.76943	+	8.76943i	−0.505461	+	0.505461i
$302$		0			0
$303$			11.7198i			0.673284i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−18.4308	−	18.4308i	−1.05190	−	1.05190i	−0.998577	−	0.0533241i	$-0.983018\pi$
$307$	−18.4308	−	18.4308i	−1.05190	−	1.05190i	−0.0533241	−	0.998577i	$-0.516982\pi$
$308$		0			0
$309$	0.249910	+	0.249910i	0.0142169	+	0.0142169i
$310$		0			0
$311$		−	7.08961i		−	0.402015i	−0.979590	−	0.201007i	$-0.935578\pi$
$311$		−	7.08961i		−	0.402015i	0.979590	−	0.201007i	$-0.0644215\pi$
$312$		0			0
$313$	−22.0477			−1.24621			−0.623104	−	0.782139i	$-0.714129\pi$
$313$	−22.0477			−1.24621			−0.623104	+	0.782139i	$0.714129\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.19670	+	6.19670i	0.348042	+	0.348042i	0.859380	−	0.511338i	$-0.170850\pi$
$317$	6.19670	+	6.19670i	0.348042	+	0.348042i	−0.511338	+	0.859380i	$0.670850\pi$
$318$		0			0
$319$	15.6675			0.877211
$320$		0			0
$321$	9.15220			0.510826
$322$		0			0
$323$	9.02076	+	9.02076i	0.501929	+	0.501929i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	22.9845			1.27104
$328$		0			0
$329$			33.8921i			1.86853i
$330$		0			0
$331$	18.6174	+	18.6174i	1.02330	+	1.02330i	0.999722	+	0.0235823i	$0.00750716\pi$
$331$	18.6174	+	18.6174i	1.02330	+	1.02330i	0.0235823	+	0.999722i	$0.492493\pi$
$332$		0			0
$333$	−2.98939	−	2.98939i	−0.163818	−	0.163818i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	14.2577i		−	0.776666i	−0.921519	−	0.388333i	$-0.873051\pi$
$337$		−	14.2577i		−	0.776666i	0.921519	−	0.388333i	$-0.126949\pi$
$338$		0			0
$339$	5.81462	−	5.81462i	0.315807	−	0.315807i
$340$		0			0
$341$	3.80544	+	3.80544i	0.206076	+	0.206076i
$342$		0			0
$343$	16.2778			0.878919
$344$		0			0
$345$		0			0
$346$		0			0
$347$	23.5395	−	23.5395i	1.26367	−	1.26367i	0.314363	−	0.949303i	$-0.398209\pi$
$347$	23.5395	−	23.5395i	1.26367	−	1.26367i	0.949303	−	0.314363i	$-0.101791\pi$
$348$		0			0
$349$	1.56682	−	1.56682i	0.0838701	−	0.0838701i	−0.663927	−	0.747797i	$-0.731112\pi$
$349$	1.56682	−	1.56682i	0.0838701	−	0.0838701i	0.747797	+	0.663927i	$0.231112\pi$
$350$		0			0
$351$	−4.75989			−0.254064
$352$		0			0
$353$			9.44678i			0.502801i	0.967883	+	0.251401i	$0.0808912\pi$
$353$			9.44678i			0.502801i	−0.967883	+	0.251401i	$0.919109\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−35.1412	+	35.1412i	−1.85987	+	1.85987i
$358$		0			0
$359$		−	18.0452i		−	0.952392i	−0.879339	−	0.476196i	$-0.842015\pi$
$359$		−	18.0452i		−	0.952392i	0.879339	−	0.476196i	$-0.157985\pi$
$360$		0			0
$361$			15.9449i			0.839208i
$362$		0			0
$363$	6.97860	−	6.97860i	0.366282	−	0.366282i
$364$		0			0
$365$		0			0
$366$		0			0
$367$			29.1329i			1.52073i	0.649498	+	0.760363i	$0.274979\pi$
$367$			29.1329i			1.52073i	−0.649498	+	0.760363i	$0.725021\pi$
$368$		0			0
$369$	−11.7012			−0.609139
$370$		0			0
$371$	7.90208	−	7.90208i	0.410255	−	0.410255i
$372$		0			0
$373$	−3.35598	+	3.35598i	−0.173766	+	0.173766i	−0.788632	−	0.614866i	$-0.789210\pi$
$373$	−3.35598	+	3.35598i	−0.173766	+	0.173766i	0.614866	+	0.788632i	$0.289210\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	26.1612			1.34737
$378$		0			0
$379$	11.6507	+	11.6507i	0.598457	+	0.598457i	0.939902	−	0.341445i	$-0.110916\pi$
$379$	11.6507	+	11.6507i	0.598457	+	0.598457i	−0.341445	+	0.939902i	$0.610916\pi$
$380$		0			0
$381$	−10.4038	+	10.4038i	−0.533005	+	0.533005i
$382$		0			0
$383$			21.8044i			1.11415i	0.830461	+	0.557077i	$0.188077\pi$
$383$			21.8044i			1.11415i	−0.830461	+	0.557077i	$0.811923\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	7.68320	+	7.68320i	0.390559	+	0.390559i
$388$		0			0
$389$	11.8899	+	11.8899i	0.602842	+	0.602842i	0.941066	−	0.338224i	$-0.109826\pi$
$389$	11.8899	+	11.8899i	0.602842	+	0.602842i	−0.338224	+	0.941066i	$0.609826\pi$
$390$		0			0
$391$			33.6101i			1.69973i
$392$		0			0
$393$	17.1853			0.866884
$394$		0			0
$395$		0			0
$396$		0			0
$397$	9.23905	+	9.23905i	0.463694	+	0.463694i	0.899864	−	0.436170i	$-0.143665\pi$
$397$	9.23905	+	9.23905i	0.463694	+	0.463694i	−0.436170	+	0.899864i	$0.643665\pi$
$398$		0			0
$399$	11.9012			0.595807
$400$		0			0
$401$	−14.4744			−0.722818			−0.361409	−	0.932407i	$-0.617704\pi$
$401$	−14.4744			−0.722818			−0.361409	+	0.932407i	$0.617704\pi$
$402$		0			0
$403$	6.35422	+	6.35422i	0.316526	+	0.316526i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.34958			0.215601
$408$		0			0
$409$			9.54117i			0.471781i	0.971780	+	0.235890i	$0.0758006\pi$
$409$			9.54117i			0.471781i	−0.971780	+	0.235890i	$0.924199\pi$
$410$		0			0
$411$	−31.5112	−	31.5112i	−1.55433	−	1.55433i
$412$		0			0
$413$	−9.00925	−	9.00925i	−0.443316	−	0.443316i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			9.28514i			0.454695i
$418$		0			0
$419$	0.837667	−	0.837667i	0.0409227	−	0.0409227i	−0.686349	−	0.727272i	$-0.740788\pi$
$419$	0.837667	−	0.837667i	0.0409227	−	0.0409227i	0.727272	+	0.686349i	$0.240788\pi$
$420$		0			0
$421$	17.9679	+	17.9679i	0.875702	+	0.875702i	0.993087	−	0.117385i	$-0.0374511\pi$
$421$	17.9679	+	17.9679i	0.875702	+	0.875702i	−0.117385	+	0.993087i	$0.537451\pi$
$422$		0			0
$423$	29.6940			1.44377
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−6.79986	+	6.79986i	−0.329068	+	0.329068i
$428$		0			0
$429$	−18.9047	+	18.9047i	−0.912726	+	0.912726i
$430$		0			0
$431$	3.85473			0.185676			0.0928380	−	0.995681i	$-0.470406\pi$
$431$	3.85473			0.185676			0.0928380	+	0.995681i	$0.470406\pi$
$432$		0			0
$433$		−	25.5651i		−	1.22858i	−0.789081	−	0.614289i	$-0.789443\pi$
$433$		−	25.5651i		−	1.22858i	0.789081	−	0.614289i	$-0.210557\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.69135	−	5.69135i	0.272254	−	0.272254i
$438$		0			0
$439$		−	30.1311i		−	1.43808i	−0.694970	−	0.719039i	$-0.744582\pi$
$439$		−	30.1311i		−	1.43808i	0.694970	−	0.719039i	$-0.255418\pi$
$440$		0			0
$441$			3.48732i			0.166063i
$442$		0			0
$443$	20.1625	−	20.1625i	0.957948	−	0.957948i	−0.0412027	−	0.999151i	$-0.513119\pi$
$443$	20.1625	−	20.1625i	0.957948	−	0.957948i	0.999151	+	0.0412027i	$0.0131189\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			5.33610i			0.252389i
$448$		0			0
$449$	36.5827			1.72644			0.863221	−	0.504826i	$-0.168443\pi$
$449$	36.5827			1.72644			0.863221	+	0.504826i	$0.168443\pi$
$450$		0			0
$451$	8.51265	−	8.51265i	0.400845	−	0.400845i
$452$		0			0
$453$	4.22161	−	4.22161i	0.198349	−	0.198349i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−16.7340			−0.782785			−0.391392	−	0.920224i	$-0.628006\pi$
$457$	−16.7340			−0.782785			−0.391392	+	0.920224i	$0.628006\pi$
$458$		0			0
$459$	−5.63962	−	5.63962i	−0.263235	−	0.263235i
$460$		0			0
$461$	11.8377	−	11.8377i	0.551335	−	0.551335i	−0.375491	−	0.926826i	$-0.622526\pi$
$461$	11.8377	−	11.8377i	0.551335	−	0.551335i	0.926826	+	0.375491i	$0.122526\pi$
$462$		0			0
$463$			32.2711i			1.49976i	0.661572	+	0.749882i	$0.269890\pi$
$463$			32.2711i			1.49976i	−0.661572	+	0.749882i	$0.730110\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.22565	+	1.22565i	0.0567163	+	0.0567163i	0.734896	−	0.678180i	$-0.237231\pi$
$467$	1.22565	+	1.22565i	0.0567163	+	0.0567163i	−0.678180	+	0.734896i	$0.737231\pi$
$468$		0			0
$469$	−23.8558	−	23.8558i	−1.10156	−	1.10156i
$470$		0			0
$471$		−	34.0734i		−	1.57002i
$472$		0			0
$473$	−11.1791			−0.514016
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−6.92328	−	6.92328i	−0.316995	−	0.316995i
$478$		0			0
$479$	28.8399			1.31773			0.658865	−	0.752261i	$-0.271037\pi$
$479$	28.8399			1.31773			0.658865	+	0.752261i	$0.271037\pi$
$480$		0			0
$481$	7.26282			0.331156
$482$		0			0
$483$	22.1711	+	22.1711i	1.00882	+	1.00882i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−32.1668			−1.45762			−0.728808	−	0.684718i	$-0.759925\pi$
$487$	−32.1668			−1.45762			−0.728808	+	0.684718i	$0.759925\pi$
$488$		0			0
$489$		−	26.7054i		−	1.20766i
$490$		0			0
$491$	5.43607	+	5.43607i	0.245326	+	0.245326i	0.819049	−	0.573723i	$-0.194501\pi$
$491$	5.43607	+	5.43607i	0.245326	+	0.245326i	−0.573723	+	0.819049i	$0.694501\pi$
$492$		0			0
$493$	30.9963	+	30.9963i	1.39600	+	1.39600i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		−	9.43268i		−	0.423114i
$498$		0			0
$499$	−17.1282	+	17.1282i	−0.766762	+	0.766762i	−0.977535	−	0.210773i	$-0.932402\pi$
$499$	−17.1282	+	17.1282i	−0.766762	+	0.766762i	0.210773	+	0.977535i	$0.432402\pi$
$500$		0			0
$501$	11.3564	+	11.3564i	0.507365	+	0.507365i
$502$		0			0
$503$	−23.5180			−1.04862			−0.524308	−	0.851529i	$-0.675676\pi$
$503$	−23.5180			−1.04862			−0.524308	+	0.851529i	$0.675676\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−9.93890	+	9.93890i	−0.441402	+	0.441402i
$508$		0			0
$509$	−20.3147	+	20.3147i	−0.900434	+	0.900434i	−0.995474	−	0.0950391i	$-0.969702\pi$
$509$	−20.3147	+	20.3147i	−0.900434	+	0.900434i	0.0950391	+	0.995474i	$0.469702\pi$
$510$		0			0
$511$	36.7186			1.62434
$512$		0			0
$513$			1.90997i			0.0843271i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−21.6025	+	21.6025i	−0.950077	+	0.950077i
$518$		0			0
$519$			16.9328i			0.743268i
$520$		0			0
$521$		−	35.5082i		−	1.55564i	−0.628487	−	0.777820i	$-0.716325\pi$
$521$		−	35.5082i		−	1.55564i	0.628487	−	0.777820i	$-0.283675\pi$
$522$		0			0
$523$	0.677766	−	0.677766i	0.0296366	−	0.0296366i	−0.692133	−	0.721770i	$-0.743329\pi$
$523$	0.677766	−	0.677766i	0.0296366	−	0.0296366i	0.721770	+	0.692133i	$0.243329\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			15.0572i			0.655904i
$528$		0			0
$529$	−1.79485			−0.0780371
$530$		0			0
$531$	−7.89332	+	7.89332i	−0.342541	+	0.342541i
$532$		0			0
$533$	14.2142	−	14.2142i	0.615686	−	0.615686i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	5.45007			0.235188
$538$		0			0
$539$	−2.53704	−	2.53704i	−0.109278	−	0.109278i
$540$		0			0
$541$	5.37099	−	5.37099i	0.230917	−	0.230917i	−0.582158	−	0.813075i	$-0.697792\pi$
$541$	5.37099	−	5.37099i	0.230917	−	0.230917i	0.813075	+	0.582158i	$0.197792\pi$
$542$		0			0
$543$		−	55.8181i		−	2.39539i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	8.86782	+	8.86782i	0.379161	+	0.379161i	0.870799	−	0.491639i	$-0.163602\pi$
$547$	8.86782	+	8.86782i	0.379161	+	0.379161i	−0.491639	+	0.870799i	$0.663602\pi$
$548$		0			0
$549$	5.95760	+	5.95760i	0.254264	+	0.254264i
$550$		0			0
$551$		−	10.4975i		−	0.447209i
$552$		0			0
$553$	0.329585			0.0140154
$554$		0			0
$555$		0			0
$556$		0			0
$557$	22.8089	+	22.8089i	0.966446	+	0.966446i	0.999455	−	0.0330091i	$-0.0105090\pi$
$557$	22.8089	+	22.8089i	0.966446	+	0.966446i	−0.0330091	+	0.999455i	$0.510509\pi$
$558$		0			0
$559$	−18.6666			−0.789513
$560$		0			0
$561$	−44.7973			−1.89135
$562$		0			0
$563$	−20.9711	−	20.9711i	−0.883826	−	0.883826i	0.110095	−	0.993921i	$-0.464884\pi$
$563$	−20.9711	−	20.9711i	−0.883826	−	0.883826i	−0.993921	+	0.110095i	$0.964884\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−29.4543			−1.23696
$568$		0			0
$569$			8.05295i			0.337597i	0.985651	+	0.168799i	$0.0539888\pi$
$569$			8.05295i			0.337597i	−0.985651	+	0.168799i	$0.946011\pi$
$570$		0			0
$571$	22.5040	+	22.5040i	0.941762	+	0.941762i	0.998395	−	0.0566333i	$-0.0180366\pi$
$571$	22.5040	+	22.5040i	0.941762	+	0.941762i	−0.0566333	+	0.998395i	$0.518037\pi$
$572$		0			0
$573$	−9.74599	−	9.74599i	−0.407144	−	0.407144i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	15.9819i		−	0.665334i	−0.943044	−	0.332667i	$-0.892051\pi$
$577$		−	15.9819i		−	0.665334i	0.943044	−	0.332667i	$-0.107949\pi$
$578$		0			0
$579$	0.0401200	−	0.0401200i	0.00166733	−	0.00166733i
$580$		0			0
$581$	28.2692	+	28.2692i	1.17280	+	1.17280i
$582$		0			0
$583$	10.0734			0.417199
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.25752	−	5.25752i	0.217001	−	0.217001i	−0.590232	−	0.807233i	$-0.700964\pi$
$587$	5.25752	−	5.25752i	0.217001	−	0.217001i	0.807233	+	0.590232i	$0.200964\pi$
$588$		0			0
$589$	2.54971	−	2.54971i	0.105059	−	0.105059i
$590$		0			0
$591$	49.6057			2.04050
$592$		0			0
$593$			3.96571i			0.162852i	0.996679	+	0.0814260i	$0.0259474\pi$
$593$			3.96571i			0.162852i	−0.996679	+	0.0814260i	$0.974053\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−22.7132	+	22.7132i	−0.929589	+	0.929589i
$598$		0			0
$599$			8.31600i			0.339783i	0.985463	+	0.169891i	$0.0543417\pi$
$599$			8.31600i			0.339783i	−0.985463	+	0.169891i	$0.945658\pi$
$600$		0			0
$601$		−	46.0550i		−	1.87862i	−0.343068	−	0.939310i	$-0.611466\pi$
$601$		−	46.0550i		−	1.87862i	0.343068	−	0.939310i	$-0.388534\pi$
$602$		0			0
$603$	−20.9009	+	20.9009i	−0.851149	+	0.851149i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	5.05760i		−	0.205282i	−0.994718	−	0.102641i	$-0.967271\pi$
$607$		−	5.05760i		−	0.205282i	0.994718	−	0.102641i	$-0.0327292\pi$
$608$		0			0
$609$	40.8940			1.65711
$610$		0			0
$611$	−36.0713	+	36.0713i	−1.45929	+	1.45929i
$612$		0			0
$613$	−31.2000	+	31.2000i	−1.26016	+	1.26016i	−0.309141	+	0.951016i	$0.600042\pi$
$613$	−31.2000	+	31.2000i	−1.26016	+	1.26016i	−0.951016	+	0.309141i	$0.899958\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	30.7412			1.23759			0.618796	−	0.785551i	$-0.287621\pi$
$617$	30.7412			1.23759			0.618796	+	0.785551i	$0.287621\pi$
$618$		0			0
$619$	−16.8766	−	16.8766i	−0.678329	−	0.678329i	0.281293	−	0.959622i	$-0.409237\pi$
$619$	−16.8766	−	16.8766i	−0.678329	−	0.678329i	−0.959622	+	0.281293i	$0.909237\pi$
$620$		0			0
$621$	−3.55813	+	3.55813i	−0.142783	+	0.142783i
$622$		0			0
$623$		−	10.8408i		−	0.434328i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	7.58574	+	7.58574i	0.302945	+	0.302945i
$628$		0			0
$629$	8.60515	+	8.60515i	0.343110	+	0.343110i
$630$		0			0
$631$		−	30.7318i		−	1.22342i	−0.791084	−	0.611708i	$-0.790483\pi$
$631$		−	30.7318i		−	1.22342i	0.791084	−	0.611708i	$-0.209517\pi$
$632$		0			0
$633$	8.15539			0.324147
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−4.23628	−	4.23628i	−0.167848	−	0.167848i
$638$		0			0
$639$	−8.26430			−0.326931
$640$		0			0
$641$	22.1658			0.875496			0.437748	−	0.899098i	$-0.355776\pi$
$641$	22.1658			0.875496			0.437748	+	0.899098i	$0.355776\pi$
$642$		0			0
$643$	−0.975773	−	0.975773i	−0.0384807	−	0.0384807i	0.687605	−	0.726085i	$-0.258662\pi$
$643$	−0.975773	−	0.975773i	−0.0384807	−	0.0384807i	−0.726085	+	0.687605i	$0.758662\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	23.2610			0.914484			0.457242	−	0.889342i	$-0.348837\pi$
$647$	23.2610			0.914484			0.457242	+	0.889342i	$0.348837\pi$
$648$		0			0
$649$		−	11.4848i		−	0.450819i
$650$		0			0
$651$	9.93263	+	9.93263i	0.389290	+	0.389290i
$652$		0			0
$653$	−23.9372	−	23.9372i	−0.936735	−	0.936735i	0.0613792	−	0.998115i	$-0.480450\pi$
$653$	−23.9372	−	23.9372i	−0.936735	−	0.936735i	−0.998115	+	0.0613792i	$0.980450\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	32.1704i		−	1.25509i
$658$		0			0
$659$	−14.1064	+	14.1064i	−0.549508	+	0.549508i	−0.926299	−	0.376790i	$-0.877028\pi$
$659$	−14.1064	+	14.1064i	−0.549508	+	0.549508i	0.376790	+	0.926299i	$0.377028\pi$
$660$		0			0
$661$	−3.04121	−	3.04121i	−0.118289	−	0.118289i	0.645484	−	0.763774i	$-0.276656\pi$
$661$	−3.04121	−	3.04121i	−0.118289	−	0.118289i	−0.763774	+	0.645484i	$0.776656\pi$
$662$		0			0
$663$	−74.8014			−2.90505
$664$		0			0
$665$		0			0
$666$		0			0
$667$	19.5561	−	19.5561i	0.757215	−	0.757215i
$668$		0			0
$669$	23.2052	−	23.2052i	0.897166	−	0.897166i
$670$		0			0
$671$	−8.66835			−0.334638
$672$		0			0
$673$		−	25.3628i		−	0.977662i	−0.872378	−	0.488831i	$-0.837423\pi$
$673$		−	25.3628i		−	0.977662i	0.872378	−	0.488831i	$-0.162577\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9.36526	−	9.36526i	0.359936	−	0.359936i	−0.503853	−	0.863789i	$-0.668085\pi$
$677$	9.36526	−	9.36526i	0.359936	−	0.359936i	0.863789	+	0.503853i	$0.168085\pi$
$678$		0			0
$679$		−	40.4737i		−	1.55324i
$680$		0			0
$681$			14.7695i			0.565967i
$682$		0			0
$683$	4.20530	−	4.20530i	0.160911	−	0.160911i	−0.622059	−	0.782970i	$-0.713704\pi$
$683$	4.20530	−	4.20530i	0.160911	−	0.160911i	0.782970	+	0.622059i	$0.213704\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			17.8035i			0.679245i
$688$		0			0
$689$	16.8204			0.640804
$690$		0			0
$691$	−5.79295	+	5.79295i	−0.220374	+	0.220374i	−0.808656	−	0.588282i	$-0.799805\pi$
$691$	−5.79295	+	5.79295i	−0.220374	+	0.220374i	0.588282	+	0.808656i	$0.299805\pi$
$692$		0			0
$693$	−13.5358	+	13.5358i	−0.514181	+	0.514181i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	33.6826			1.27582
$698$		0			0
$699$	19.8592	+	19.8592i	0.751142	+	0.751142i
$700$		0			0
$701$	−0.258991	+	0.258991i	−0.00978196	+	0.00978196i	−0.711981	−	0.702199i	$-0.752202\pi$
$701$	−0.258991	+	0.258991i	−0.00978196	+	0.00978196i	0.702199	+	0.711981i	$0.252202\pi$
$702$		0			0
$703$		−	2.91430i		−	0.109915i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−10.1936	−	10.1936i	−0.383368	−	0.383368i
$708$		0			0
$709$	0.751674	+	0.751674i	0.0282297	+	0.0282297i	0.721081	−	0.692851i	$-0.243646\pi$
$709$	0.751674	+	0.751674i	0.0282297	+	0.0282297i	−0.692851	+	0.721081i	$0.743646\pi$
$710$		0			0
$711$		−	0.288761i		−	0.0108294i
$712$		0			0
$713$	9.49986			0.355773
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−27.9029	−	27.9029i	−1.04205	−	1.04205i
$718$		0			0
$719$	39.6557			1.47891			0.739455	−	0.673206i	$-0.235083\pi$
$719$	39.6557			1.47891			0.739455	+	0.673206i	$0.235083\pi$
$720$		0			0
$721$	−0.434730			−0.0161902
$722$		0			0
$723$	−36.6495	−	36.6495i	−1.36301	−	1.36301i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−22.2952			−0.826881			−0.413441	−	0.910531i	$-0.635673\pi$
$727$	−22.2952			−0.826881			−0.413441	+	0.910531i	$0.635673\pi$
$728$		0			0
$729$			18.0930i			0.670112i
$730$		0			0
$731$	−22.1166	−	22.1166i	−0.818011	−	0.818011i
$732$		0			0
$733$	28.2309	+	28.2309i	1.04273	+	1.04273i	0.999045	+	0.0436851i	$0.0139098\pi$
$733$	28.2309	+	28.2309i	1.04273	+	1.04273i	0.0436851	+	0.999045i	$0.486090\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	30.4109i		−	1.12020i
$738$		0			0
$739$	−5.45140	+	5.45140i	−0.200533	+	0.200533i	−0.800228	−	0.599695i	$-0.795288\pi$
$739$	−5.45140	+	5.45140i	−0.200533	+	0.200533i	0.599695	+	0.800228i	$0.295288\pi$
$740$		0			0
$741$	12.6665	+	12.6665i	0.465314	+	0.465314i
$742$		0			0
$743$	52.5667			1.92849			0.964243	−	0.265020i	$-0.0853786\pi$
$743$	52.5667			1.92849			0.964243	+	0.265020i	$0.0853786\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	24.7676	−	24.7676i	0.906200	−	0.906200i
$748$		0			0
$749$	−7.96035	+	7.96035i	−0.290865	+	0.290865i
$750$		0			0
$751$	−31.0189			−1.13190			−0.565948	−	0.824441i	$-0.691490\pi$
$751$	−31.0189			−1.13190			−0.565948	+	0.824441i	$0.691490\pi$
$752$		0			0
$753$		−	22.0910i		−	0.805040i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−2.47389	+	2.47389i	−0.0899152	+	0.0899152i	−0.750634	−	0.660719i	$-0.770252\pi$
$757$	−2.47389	+	2.47389i	−0.0899152	+	0.0899152i	0.660719	+	0.750634i	$0.270252\pi$
$758$		0			0
$759$			28.2634i			1.02590i
$760$		0			0
$761$		−	2.48375i		−	0.0900358i	−0.998986	−	0.0450179i	$-0.985666\pi$
$761$		−	2.48375i		−	0.0900358i	0.998986	−	0.0450179i	$-0.0143345\pi$
$762$		0			0
$763$	−19.9913	+	19.9913i	−0.723733	+	0.723733i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	19.1771i		−	0.692444i
$768$		0			0
$769$	−43.4690			−1.56753			−0.783767	−	0.621055i	$-0.786704\pi$
$769$	−43.4690			−1.56753			−0.783767	+	0.621055i	$0.786704\pi$
$770$		0			0
$771$	−12.0752	+	12.0752i	−0.434879	+	0.434879i
$772$		0			0
$773$	−0.297026	+	0.297026i	−0.0106833	+	0.0106833i	−0.712428	−	0.701745i	$-0.752405\pi$
$773$	−0.297026	+	0.297026i	−0.0106833	+	0.0106833i	0.701745	+	0.712428i	$0.252405\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	11.3529			0.407283
$778$		0			0
$779$	−5.70363	−	5.70363i	−0.204354	−	0.204354i
$780$		0			0
$781$	6.01231	−	6.01231i	0.215137	−	0.215137i
$782$		0			0
$783$			6.56286i			0.234537i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−23.6931	−	23.6931i	−0.844567	−	0.844567i	0.144882	−	0.989449i	$-0.453720\pi$
$787$	−23.6931	−	23.6931i	−0.844567	−	0.844567i	−0.989449	+	0.144882i	$0.953720\pi$
$788$		0			0
$789$	−15.4293	−	15.4293i	−0.549299	−	0.549299i
$790$		0			0
$791$			10.1148i			0.359641i
$792$		0			0
$793$	−14.4742			−0.513993
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−38.2292	−	38.2292i	−1.35415	−	1.35415i	−0.880963	−	0.473186i	$-0.843104\pi$
$797$	−38.2292	−	38.2292i	−1.35415	−	1.35415i	−0.473186	−	0.880963i	$-0.656896\pi$
$798$		0			0
$799$	−85.4762			−3.02393
$800$		0			0
$801$	−9.49801			−0.335596
$802$		0			0
$803$	23.4041	+	23.4041i	0.825913	+	0.825913i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	44.6509			1.57179
$808$		0			0
$809$		−	53.8310i		−	1.89260i	−0.323296	−	0.946298i	$-0.604791\pi$
$809$		−	53.8310i		−	1.89260i	0.323296	−	0.946298i	$-0.395209\pi$
$810$		0			0
$811$	−27.0549	−	27.0549i	−0.950025	−	0.950025i	0.0487847	−	0.998809i	$-0.484465\pi$
$811$	−27.0549	−	27.0549i	−0.950025	−	0.950025i	−0.998809	+	0.0487847i	$0.984465\pi$
$812$		0			0
$813$	−37.5986	−	37.5986i	−1.31864	−	1.31864i
$814$		0			0
$815$		0			0
$816$		0			0
$817$			7.49020i			0.262049i
$818$		0			0
$819$	−22.6017	+	22.6017i	−0.789766	+	0.789766i
$820$		0			0
$821$	−24.2170	−	24.2170i	−0.845180	−	0.845180i	0.144347	−	0.989527i	$-0.453892\pi$
$821$	−24.2170	−	24.2170i	−0.845180	−	0.845180i	−0.989527	+	0.144347i	$0.953892\pi$
$822$		0			0
$823$	−41.3013			−1.43967			−0.719836	−	0.694144i	$-0.755783\pi$
$823$	−41.3013			−1.43967			−0.719836	+	0.694144i	$0.755783\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−15.7264	+	15.7264i	−0.546862	+	0.546862i	−0.925532	−	0.378670i	$-0.876382\pi$
$827$	−15.7264	+	15.7264i	−0.546862	+	0.546862i	0.378670	+	0.925532i	$0.376382\pi$
$828$		0			0
$829$	20.7323	−	20.7323i	0.720061	−	0.720061i	−0.248556	−	0.968618i	$-0.579956\pi$
$829$	20.7323	−	20.7323i	0.720061	−	0.720061i	0.968618	+	0.248556i	$0.0799560\pi$
$830$		0			0
$831$	53.9075			1.87003
$832$		0			0
$833$		−	10.0385i		−	0.347813i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.59404	+	1.59404i	−0.0550980	+	0.0550980i
$838$		0			0
$839$			43.6919i			1.50841i	0.656638	+	0.754206i	$0.271978\pi$
$839$			43.6919i			1.50841i	−0.656638	+	0.754206i	$0.728022\pi$
$840$		0			0
$841$		−	7.07060i		−	0.243814i
$842$		0			0
$843$	14.7200	−	14.7200i	0.506983	−	0.506983i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			12.1396i			0.417122i
$848$		0			0
$849$	−67.5654			−2.31884
$850$		0			0
$851$	5.42913	−	5.42913i	0.186108	−	0.186108i
$852$		0			0
$853$	35.0610	−	35.0610i	1.20046	−	1.20046i	0.226439	−	0.974025i	$-0.427292\pi$
$853$	35.0610	−	35.0610i	1.20046	−	1.20046i	0.974025	−	0.226439i	$-0.0727084\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−45.3397			−1.54878			−0.774388	−	0.632711i	$-0.781942\pi$
$857$	−45.3397			−1.54878			−0.774388	+	0.632711i	$0.781942\pi$
$858$		0			0
$859$	32.1229	+	32.1229i	1.09602	+	1.09602i	0.994871	+	0.101147i	$0.0322514\pi$
$859$	32.1229	+	32.1229i	1.09602	+	1.09602i	0.101147	+	0.994871i	$0.467749\pi$
$860$		0			0
$861$	22.2190	−	22.2190i	0.757221	−	0.757221i
$862$		0			0
$863$		−	36.9142i		−	1.25657i	−0.777981	−	0.628287i	$-0.783756\pi$
$863$		−	36.9142i		−	1.25657i	0.777981	−	0.628287i	$-0.216244\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−60.3441	−	60.3441i	−2.04939	−	2.04939i
$868$		0			0
$869$	0.210075	+	0.210075i	0.00712630	+	0.00712630i
$870$		0			0
$871$		−	50.7793i		−	1.72059i
$872$		0			0
$873$	−35.4604			−1.20015
$874$		0			0
$875$		0			0
$876$		0			0
$877$	15.7178	+	15.7178i	0.530753	+	0.530753i	0.920796	−	0.390044i	$-0.127540\pi$
$877$	15.7178	+	15.7178i	0.530753	+	0.530753i	−0.390044	+	0.920796i	$0.627540\pi$
$878$		0			0
$879$	23.8548			0.804603
$880$		0			0
$881$	1.16748			0.0393335			0.0196667	−	0.999807i	$-0.493739\pi$
$881$	1.16748			0.0393335			0.0196667	+	0.999807i	$0.493739\pi$
$882$		0			0
$883$	−32.2410	−	32.2410i	−1.08500	−	1.08500i	−0.996035	−	0.0889621i	$-0.971645\pi$
$883$	−32.2410	−	32.2410i	−1.08500	−	1.08500i	−0.0889621	−	0.996035i	$-0.528355\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	42.7282			1.43467			0.717336	−	0.696728i	$-0.245361\pi$
$887$	42.7282			1.43467			0.717336	+	0.696728i	$0.245361\pi$
$888$		0			0
$889$		−	18.0980i		−	0.606987i
$890$		0			0
$891$	−18.7739	−	18.7739i	−0.628949	−	0.628949i
$892$		0			0
$893$	14.4741	+	14.4741i	0.484356	+	0.484356i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			47.1935i			1.57574i
$898$		0			0
$899$	8.76109	−	8.76109i	0.292199	−	0.292199i
$900$		0			0
$901$	19.9291	+	19.9291i	0.663935	+	0.663935i
$902$		0			0
$903$	−29.1788			−0.971008
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−1.23335	+	1.23335i	−0.0409528	+	0.0409528i	−0.727287	−	0.686334i	$-0.759219\pi$
$907$	−1.23335	+	1.23335i	−0.0409528	+	0.0409528i	0.686334	+	0.727287i	$0.259219\pi$
$908$		0			0
$909$	−8.93093	+	8.93093i	−0.296220	+	0.296220i
$910$		0			0
$911$	−23.9284			−0.792785			−0.396392	−	0.918081i	$-0.629738\pi$
$911$	−23.9284			−0.792785			−0.396392	+	0.918081i	$0.629738\pi$
$912$		0			0
$913$			36.0371i			1.19265i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−14.9473	+	14.9473i	−0.493605	+	0.493605i
$918$		0			0
$919$		−	45.3844i		−	1.49709i	−0.663082	−	0.748546i	$-0.730752\pi$
$919$		−	45.3844i		−	1.49709i	0.663082	−	0.748546i	$-0.269248\pi$
$920$		0			0
$921$		−	61.3253i		−	2.02074i
$922$		0			0
$923$	10.0392	−	10.0392i	0.330444	−	0.330444i
$924$		0			0
$925$		0			0
$926$		0			0
$927$			0.380882i			0.0125098i
$928$		0			0
$929$	6.51036			0.213598			0.106799	−	0.994281i	$-0.465940\pi$
$929$	6.51036			0.213598			0.106799	+	0.994281i	$0.465940\pi$
$930$		0			0
$931$	−1.69986	+	1.69986i	−0.0557107	+	0.0557107i
$932$		0			0
$933$	11.7947	−	11.7947i	0.386142	−	0.386142i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−40.2986			−1.31650			−0.658248	−	0.752801i	$-0.728702\pi$
$937$	−40.2986			−1.31650			−0.658248	+	0.752801i	$0.728702\pi$
$938$		0			0
$939$	−36.6799	−	36.6799i	−1.19700	−	1.19700i
$940$		0			0
$941$	1.10649	−	1.10649i	0.0360705	−	0.0360705i	−0.688841	−	0.724912i	$-0.741880\pi$
$941$	1.10649	−	1.10649i	0.0360705	−	0.0360705i	0.724912	+	0.688841i	$0.241880\pi$
$942$		0			0
$943$		−	21.2509i		−	0.692025i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.83833	−	8.83833i	−0.287207	−	0.287207i	0.548768	−	0.835975i	$-0.315097\pi$
$947$	−8.83833	−	8.83833i	−0.287207	−	0.287207i	−0.835975	+	0.548768i	$0.815097\pi$
$948$		0			0
$949$	39.0796	+	39.0796i	1.26858	+	1.26858i
$950$		0			0
$951$			20.6185i			0.668600i
$952$		0			0
$953$	−14.9610			−0.484636			−0.242318	−	0.970197i	$-0.577908\pi$
$953$	−14.9610			−0.484636			−0.242318	+	0.970197i	$0.577908\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	26.0654	+	26.0654i	0.842576	+	0.842576i
$958$		0			0
$959$	54.8152			1.77008
$960$		0			0
$961$	−26.7441			−0.862712
$962$		0			0
$963$	6.97433	+	6.97433i	0.224745	+	0.224745i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	3.95287			0.127116			0.0635578	−	0.997978i	$-0.479755\pi$
$967$	3.95287			0.127116			0.0635578	+	0.997978i	$0.479755\pi$
$968$		0			0
$969$			30.0150i			0.964221i
$970$		0			0
$971$	29.0538	+	29.0538i	0.932380	+	0.932380i	0.997854	−	0.0654740i	$-0.0208560\pi$
$971$	29.0538	+	29.0538i	0.932380	+	0.932380i	−0.0654740	+	0.997854i	$0.520856\pi$
$972$		0			0
$973$	−8.07597	−	8.07597i	−0.258904	−	0.258904i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	25.8962i		−	0.828494i	−0.910164	−	0.414247i	$-0.864045\pi$
$977$		−	25.8962i		−	0.828494i	0.910164	−	0.414247i	$-0.135955\pi$
$978$		0			0
$979$	6.90984	−	6.90984i	0.220839	−	0.220839i
$980$		0			0
$981$	17.5151	+	17.5151i	0.559213	+	0.559213i
$982$		0			0
$983$	22.0151			0.702173			0.351087	−	0.936343i	$-0.385812\pi$
$983$	22.0151			0.702173			0.351087	+	0.936343i	$0.385812\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−56.3850	+	56.3850i	−1.79476	+	1.79476i
$988$		0			0
$989$	−13.9537	+	13.9537i	−0.443702	+	0.443702i
$990$		0			0
$991$	54.3207			1.72556			0.862778	−	0.505583i	$-0.168723\pi$
$991$	54.3207			1.72556			0.862778	+	0.505583i	$0.168723\pi$
$992$		0			0
$993$			61.9461i			1.96580i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	8.14405	−	8.14405i	0.257925	−	0.257925i	−0.566285	−	0.824210i	$-0.691620\pi$
$997$	8.14405	−	8.14405i	0.257925	−	0.257925i	0.824210	+	0.566285i	$0.191620\pi$
$998$		0			0
$999$			1.82197i			0.0576446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.q.g.49.7		16
4.3	odd	2		400.2.q.h.149.7		16
5.2	odd	4		320.2.l.a.241.7		16
5.3	odd	4		1600.2.l.i.1201.2		16
5.4	even	2		1600.2.q.h.49.2		16
15.2	even	4		2880.2.t.c.2161.6		16
16.3	odd	4		400.2.q.g.349.2		16
16.13	even	4		1600.2.q.h.849.2		16
20.3	even	4		400.2.l.h.101.5		16
20.7	even	4		80.2.l.a.21.4	✓	16
20.19	odd	2		400.2.q.g.149.2		16
40.27	even	4		640.2.l.b.481.7		16
40.37	odd	4		640.2.l.a.481.2		16
60.47	odd	4		720.2.t.c.181.5		16
80.3	even	4		400.2.l.h.301.5		16
80.13	odd	4		1600.2.l.i.401.2		16
80.19	odd	4		400.2.q.h.349.7		16
80.27	even	4		640.2.l.b.161.7		16
80.29	even	4	inner	1600.2.q.g.849.7		16
80.37	odd	4		640.2.l.a.161.2		16
80.67	even	4		80.2.l.a.61.4	yes	16
80.77	odd	4		320.2.l.a.81.7		16
160.67	even	8		5120.2.a.v.1.1		8
160.77	odd	8		5120.2.a.u.1.1		8
160.147	even	8		5120.2.a.s.1.8		8
160.157	odd	8		5120.2.a.t.1.8		8
240.77	even	4		2880.2.t.c.721.7		16
240.227	odd	4		720.2.t.c.541.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.4	✓	16	20.7	even	4
80.2.l.a.61.4	yes	16	80.67	even	4
320.2.l.a.81.7		16	80.77	odd	4
320.2.l.a.241.7		16	5.2	odd	4
400.2.l.h.101.5		16	20.3	even	4
400.2.l.h.301.5		16	80.3	even	4
400.2.q.g.149.2		16	20.19	odd	2
400.2.q.g.349.2		16	16.3	odd	4
400.2.q.h.149.7		16	4.3	odd	2
400.2.q.h.349.7		16	80.19	odd	4
640.2.l.a.161.2		16	80.37	odd	4
640.2.l.a.481.2		16	40.37	odd	4
640.2.l.b.161.7		16	80.27	even	4
640.2.l.b.481.7		16	40.27	even	4
720.2.t.c.181.5		16	60.47	odd	4
720.2.t.c.541.5		16	240.227	odd	4
1600.2.l.i.401.2		16	80.13	odd	4
1600.2.l.i.1201.2		16	5.3	odd	4
1600.2.q.g.49.7		16	1.1	even	1	trivial
1600.2.q.g.849.7		16	80.29	even	4	inner
1600.2.q.h.49.2		16	5.4	even	2
1600.2.q.h.849.2		16	16.13	even	4
2880.2.t.c.721.7		16	240.77	even	4
2880.2.t.c.2161.6		16	15.2	even	4
5120.2.a.s.1.8		8	160.147	even	8
5120.2.a.t.1.8		8	160.157	odd	8
5120.2.a.u.1.1		8	160.77	odd	8
5120.2.a.v.1.1		8	160.67	even	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.66366 + 1.66366i) q^{3} -2.89402 q^{7} +2.53555i q^{9} +(-1.84462 - 1.84462i) q^{11} +(-3.08011 - 3.08011i) q^{13} -7.29875i q^{17} +(-1.23593 + 1.23593i) q^{19} +(-4.81468 - 4.81468i) q^{21} -4.60490 q^{23} +(0.772683 - 0.772683i) q^{27} +(-4.24680 + 4.24680i) q^{29} -2.06299 q^{31} -6.13767i q^{33} +(-1.17899 + 1.17899i) q^{37} -10.2485i q^{39} +4.61484i q^{41} +(3.03019 - 3.03019i) q^{43} -11.7111i q^{47} +1.37537 q^{49} +(12.1427 - 12.1427i) q^{51} +(-2.73048 + 2.73048i) q^{53} -4.11235 q^{57} +(3.11306 + 3.11306i) q^{59} +(2.34962 - 2.34962i) q^{61} -7.33795i q^{63} +(8.24311 + 8.24311i) q^{67} +(-7.66101 - 7.66101i) q^{69} +3.25937i q^{71} -12.6877 q^{73} +(5.33839 + 5.33839i) q^{77} -0.113885 q^{79} +10.1776 q^{81} +(-9.76813 - 9.76813i) q^{83} -14.1305 q^{87} +3.74593i q^{89} +(8.91390 + 8.91390i) q^{91} +(-3.43212 - 3.43212i) q^{93} +13.9853i q^{97} +(4.67714 - 4.67714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} + 8 q^{11} - 8 q^{19} - 24 q^{23} - 24 q^{27} + 16 q^{29} - 16 q^{37} + 8 q^{43} + 16 q^{49} + 32 q^{51} - 16 q^{53} - 8 q^{59} + 16 q^{61} + 40 q^{67} - 16 q^{69} - 16 q^{77} + 16 q^{79}+ \cdots - 8 q^{99}+O(q^{100}) \) 16 * q - 8 * q^7 + 8 * q^11 - 8 * q^19 - 24 * q^23 - 24 * q^27 + 16 * q^29 - 16 * q^37 + 8 * q^43 + 16 * q^49 + 32 * q^51 - 16 * q^53 - 8 * q^59 + 16 * q^61 + 40 * q^67 - 16 * q^69 - 16 * q^77 + 16 * q^79 - 16 * q^81 - 40 * q^83 - 32 * q^91 - 48 * q^93 - 8 * q^99

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