LMFDB - Embedded newform 1600.2.q.h.849.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(49,1600)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$12.7760643234$
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			849.1
Root			$1.38652 - 0.278517i$ of defining polynomial
Character	$\chi$	$=$	1600.849
Dual form			1600.2.q.h.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.32624 + 2.32624i) q^{3} -0.982011 q^{7} -7.82281i q^{9} +O(q^{10})$	$q+(-2.32624 + 2.32624i) q^{3} -0.982011 q^{7} -7.82281i q^{9} +(1.62645 - 1.62645i) q^{11} +(0.690562 - 0.690562i) q^{13} +2.19577i q^{17} +(1.92659 + 1.92659i) q^{19} +(2.28440 - 2.28440i) q^{21} -2.01442 q^{23} +(11.2190 + 11.2190i) q^{27} +(5.27182 + 5.27182i) q^{29} -0.435286 q^{31} +7.56703i q^{33} +(5.79805 + 5.79805i) q^{37} +3.21283i q^{39} -3.93139i q^{41} +(0.507592 + 0.507592i) q^{43} -9.21960i q^{47} -6.03565 q^{49} +(-5.10789 - 5.10789i) q^{51} +(6.29357 + 6.29357i) q^{53} -8.96345 q^{57} +(-5.67778 + 5.67778i) q^{59} +(-3.60301 - 3.60301i) q^{61} +7.68209i q^{63} +(-4.53563 + 4.53563i) q^{67} +(4.68603 - 4.68603i) q^{69} +10.3984i q^{71} -9.24439 q^{73} +(-1.59719 + 1.59719i) q^{77} +15.4493 q^{79} -28.7280 q^{81} +(-0.683244 + 0.683244i) q^{83} -24.5271 q^{87} +5.44401i q^{89} +(-0.678140 + 0.678140i) q^{91} +(1.01258 - 1.01258i) q^{93} -5.54540i q^{97} +(-12.7234 - 12.7234i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$577$	$901$	$1151$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−2.32624	+	2.32624i	−1.34306	+	1.34306i	−0.450058	+	0.893000i	$0.648597\pi$
$3$	−2.32624	+	2.32624i	−1.34306	+	1.34306i	−0.893000	+	0.450058i	$0.851403\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.982011			−0.371165			−0.185583	−	0.982629i	$-0.559417\pi$
$7$	−0.982011			−0.371165			−0.185583	+	0.982629i	$0.559417\pi$
$8$		0			0
$9$		−	7.82281i		−	2.60760i
$10$		0			0
$11$	1.62645	−	1.62645i	0.490393	−	0.490393i	−0.418037	−	0.908430i	$-0.637282\pi$
$11$	1.62645	−	1.62645i	0.490393	−	0.490393i	0.908430	+	0.418037i	$0.137282\pi$
$12$		0			0
$13$	0.690562	−	0.690562i	0.191528	−	0.191528i	−0.604828	−	0.796356i	$-0.706758\pi$
$13$	0.690562	−	0.690562i	0.191528	−	0.191528i	0.796356	+	0.604828i	$0.206758\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			2.19577i			0.532552i	0.963897	+	0.266276i	$0.0857933\pi$
$17$			2.19577i			0.532552i	−0.963897	+	0.266276i	$0.914207\pi$
$18$		0			0
$19$	1.92659	+	1.92659i	0.441991	+	0.441991i	0.892681	−	0.450690i	$-0.148822\pi$
$19$	1.92659	+	1.92659i	0.441991	+	0.441991i	−0.450690	+	0.892681i	$0.648822\pi$
$20$		0			0
$21$	2.28440	−	2.28440i	0.498496	−	0.498496i
$22$		0			0
$23$	−2.01442			−0.420035			−0.210018	−	0.977698i	$-0.567352\pi$
$23$	−2.01442			−0.420035			−0.210018	+	0.977698i	$0.567352\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	11.2190	+	11.2190i	2.15911	+	2.15911i
$28$		0			0
$29$	5.27182	+	5.27182i	0.978952	+	0.978952i	0.999783	−	0.0208314i	$-0.00663132\pi$
$29$	5.27182	+	5.27182i	0.978952	+	0.978952i	−0.0208314	+	0.999783i	$0.506631\pi$
$30$		0			0
$31$	−0.435286			−0.0781797			−0.0390898	−	0.999236i	$-0.512446\pi$
$31$	−0.435286			−0.0781797			−0.0390898	+	0.999236i	$0.512446\pi$
$32$		0			0
$33$			7.56703i			1.31725i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.79805	+	5.79805i	0.953194	+	0.953194i	0.998953	−	0.0457583i	$-0.0145704\pi$
$37$	5.79805	+	5.79805i	0.953194	+	0.953194i	−0.0457583	+	0.998953i	$0.514570\pi$
$38$		0			0
$39$			3.21283i			0.514465i
$40$		0			0
$41$		−	3.93139i		−	0.613980i	−0.951713	−	0.306990i	$-0.900678\pi$
$41$		−	3.93139i		−	0.613980i	0.951713	−	0.306990i	$-0.0993218\pi$
$42$		0			0
$43$	0.507592	+	0.507592i	0.0774071	+	0.0774071i	0.744750	−	0.667343i	$-0.232569\pi$
$43$	0.507592	+	0.507592i	0.0774071	+	0.0774071i	−0.667343	+	0.744750i	$0.732569\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	9.21960i		−	1.34482i	−0.740180	−	0.672409i	$-0.765260\pi$
$47$		−	9.21960i		−	1.34482i	0.740180	−	0.672409i	$-0.234740\pi$
$48$		0			0
$49$	−6.03565			−0.862236
$50$		0			0
$51$	−5.10789	−	5.10789i	−0.715248	−	0.715248i
$52$		0			0
$53$	6.29357	+	6.29357i	0.864488	+	0.864488i	0.991856	−	0.127367i	$-0.0406527\pi$
$53$	6.29357	+	6.29357i	0.864488	+	0.864488i	−0.127367	+	0.991856i	$0.540653\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−8.96345			−1.18724
$58$		0			0
$59$	−5.67778	+	5.67778i	−0.739183	+	0.739183i	−0.972420	−	0.233237i	$-0.925068\pi$
$59$	−5.67778	+	5.67778i	−0.739183	+	0.739183i	0.233237	+	0.972420i	$0.425068\pi$
$60$		0			0
$61$	−3.60301	−	3.60301i	−0.461318	−	0.461318i	0.437770	−	0.899087i	$-0.355769\pi$
$61$	−3.60301	−	3.60301i	−0.461318	−	0.461318i	−0.899087	+	0.437770i	$0.855769\pi$
$62$		0			0
$63$			7.68209i			0.967852i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.53563	+	4.53563i	−0.554116	+	0.554116i	−0.927626	−	0.373510i	$-0.878154\pi$
$67$	−4.53563	+	4.53563i	−0.554116	+	0.554116i	0.373510	+	0.927626i	$0.378154\pi$
$68$		0			0
$69$	4.68603	−	4.68603i	0.564132	−	0.564132i
$70$		0			0
$71$			10.3984i			1.23407i	0.786937	+	0.617033i	$0.211665\pi$
$71$			10.3984i			1.23407i	−0.786937	+	0.617033i	$0.788335\pi$
$72$		0			0
$73$	−9.24439			−1.08197			−0.540987	−	0.841031i	$-0.681949\pi$
$73$	−9.24439			−1.08197			−0.540987	+	0.841031i	$0.681949\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.59719	+	1.59719i	−0.182017	+	0.182017i
$78$		0			0
$79$	15.4493			1.73818			0.869091	−	0.494653i	$-0.164705\pi$
$79$	15.4493			1.73818			0.869091	+	0.494653i	$0.164705\pi$
$80$		0			0
$81$	−28.7280			−3.19200
$82$		0			0
$83$	−0.683244	+	0.683244i	−0.0749957	+	0.0749957i	−0.743610	−	0.668614i	$-0.766888\pi$
$83$	−0.683244	+	0.683244i	−0.0749957	+	0.0749957i	0.668614	+	0.743610i	$0.266888\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−24.5271			−2.62958
$88$		0			0
$89$			5.44401i			0.577064i	0.957470	+	0.288532i	$0.0931672\pi$
$89$			5.44401i			0.577064i	−0.957470	+	0.288532i	$0.906833\pi$
$90$		0			0
$91$	−0.678140	+	0.678140i	−0.0710884	+	0.0710884i
$92$		0			0
$93$	1.01258	−	1.01258i	0.105000	−	0.105000i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	5.54540i		−	0.563050i	−0.959554	−	0.281525i	$-0.909160\pi$
$97$		−	5.54540i		−	0.563050i	0.959554	−	0.281525i	$-0.0908402\pi$
$98$		0			0
$99$	−12.7234	−	12.7234i	−1.27875	−	1.27875i
$100$		0			0
$101$	−0.291294	+	0.291294i	−0.0289848	+	0.0289848i	−0.721451	−	0.692466i	$-0.756524\pi$
$101$	−0.291294	+	0.291294i	−0.0289848	+	0.0289848i	0.692466	+	0.721451i	$0.256524\pi$
$102$		0			0
$103$	−4.50219			−0.443614			−0.221807	−	0.975091i	$-0.571195\pi$
$103$	−4.50219			−0.443614			−0.221807	+	0.975091i	$0.571195\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.49890	−	6.49890i	−0.628272	−	0.628272i	0.319361	−	0.947633i	$-0.396532\pi$
$107$	−6.49890	−	6.49890i	−0.628272	−	0.628272i	−0.947633	+	0.319361i	$0.896532\pi$
$108$		0			0
$109$	2.51950	+	2.51950i	0.241324	+	0.241324i	0.817398	−	0.576074i	$-0.195416\pi$
$109$	2.51950	+	2.51950i	0.241324	+	0.241324i	−0.576074	+	0.817398i	$0.695416\pi$
$110$		0			0
$111$	−26.9754			−2.56039
$112$		0			0
$113$			5.38101i			0.506203i	0.967440	+	0.253102i	$0.0814507\pi$
$113$			5.38101i			0.506203i	−0.967440	+	0.253102i	$0.918549\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−5.40214	−	5.40214i	−0.499428	−	0.499428i
$118$		0			0
$119$		−	2.15627i		−	0.197665i
$120$		0			0
$121$			5.70933i			0.519030i
$122$		0			0
$123$	9.14536	+	9.14536i	0.824610	+	0.824610i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			4.86578i			0.431768i	0.976419	+	0.215884i	$0.0692634\pi$
$127$			4.86578i			0.431768i	−0.976419	+	0.215884i	$0.930737\pi$
$128$		0			0
$129$	−2.36157			−0.207924
$130$		0			0
$131$	−8.00581	−	8.00581i	−0.699471	−	0.699471i	0.264825	−	0.964296i	$-0.414686\pi$
$131$	−8.00581	−	8.00581i	−0.699471	−	0.699471i	−0.964296	+	0.264825i	$0.914686\pi$
$132$		0			0
$133$	−1.89194	−	1.89194i	−0.164052	−	0.164052i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.5567			1.15822			0.579112	−	0.815248i	$-0.303399\pi$
$137$	13.5567			1.15822			0.579112	+	0.815248i	$0.303399\pi$
$138$		0			0
$139$	8.22645	−	8.22645i	0.697758	−	0.697758i	−0.266168	−	0.963927i	$-0.585758\pi$
$139$	8.22645	−	8.22645i	0.697758	−	0.697758i	0.963927	+	0.266168i	$0.0857577\pi$
$140$		0			0
$141$	21.4470	+	21.4470i	1.80617	+	1.80617i
$142$		0			0
$143$		−	2.24633i		−	0.187847i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	14.0404	−	14.0404i	1.15803	−	1.15803i
$148$		0			0
$149$	−12.6363	+	12.6363i	−1.03521	+	1.03521i	−0.0358519	+	0.999357i	$0.511414\pi$
$149$	−12.6363	+	12.6363i	−1.03521	+	1.03521i	−0.999357	+	0.0358519i	$0.988586\pi$
$150$		0			0
$151$			15.1562i			1.23339i	0.787201	+	0.616696i	$0.211529\pi$
$151$			15.1562i			1.23339i	−0.787201	+	0.616696i	$0.788471\pi$
$152$		0			0
$153$	17.1771			1.38869
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.75816	+	1.75816i	−0.140316	+	0.140316i	−0.773776	−	0.633460i	$-0.781634\pi$
$157$	−1.75816	+	1.75816i	−0.140316	+	0.140316i	0.633460	+	0.773776i	$0.281634\pi$
$158$		0			0
$159$	−29.2807			−2.32211
$160$		0			0
$161$	1.97818			0.155903
$162$		0			0
$163$	−13.9102	+	13.9102i	−1.08953	+	1.08953i	−0.0939562	+	0.995576i	$0.529951\pi$
$163$	−13.9102	+	13.9102i	−1.08953	+	1.08953i	−0.995576	+	0.0939562i	$0.970049\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	18.8620			1.45958			0.729792	−	0.683669i	$-0.239617\pi$
$167$	18.8620			1.45958			0.729792	+	0.683669i	$0.239617\pi$
$168$		0			0
$169$			12.0462i			0.926634i
$170$		0			0
$171$	15.0714	−	15.0714i	1.15254	−	1.15254i
$172$		0			0
$173$	−16.0724	+	16.0724i	−1.22196	+	1.22196i	−0.255031	+	0.966933i	$0.582086\pi$
$173$	−16.0724	+	16.0724i	−1.22196	+	1.22196i	−0.966933	+	0.255031i	$0.917914\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	26.4158i		−	1.98553i
$178$		0			0
$179$	16.4341	+	16.4341i	1.22834	+	1.22834i	0.964591	+	0.263749i	$0.0849591\pi$
$179$	16.4341	+	16.4341i	1.22834	+	1.22834i	0.263749	+	0.964591i	$0.415041\pi$
$180$		0			0
$181$	−15.4539	+	15.4539i	−1.14868	+	1.14868i	−0.161870	+	0.986812i	$0.551753\pi$
$181$	−15.4539	+	15.4539i	−1.14868	+	1.14868i	−0.986812	+	0.161870i	$0.948247\pi$
$182$		0			0
$183$	16.7629			1.23915
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3.57130	+	3.57130i	0.261160	+	0.261160i
$188$		0			0
$189$	−11.0172	−	11.0172i	−0.801385	−	0.801385i
$190$		0			0
$191$	14.7872			1.06997			0.534983	−	0.844863i	$-0.320318\pi$
$191$	14.7872			1.06997			0.534983	+	0.844863i	$0.320318\pi$
$192$		0			0
$193$		−	11.2912i		−	0.812758i	−0.913705	−	0.406379i	$-0.866791\pi$
$193$		−	11.2912i		−	0.812758i	0.913705	−	0.406379i	$-0.133209\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	10.6152	+	10.6152i	0.756302	+	0.756302i	0.975647	−	0.219345i	$-0.0703920\pi$
$197$	10.6152	+	10.6152i	0.756302	+	0.756302i	−0.219345	+	0.975647i	$0.570392\pi$
$198$		0			0
$199$			4.68789i			0.332316i	0.986099	+	0.166158i	$0.0531361\pi$
$199$			4.68789i			0.332316i	−0.986099	+	0.166158i	$0.946864\pi$
$200$		0			0
$201$		−	21.1020i		−	1.48842i
$202$		0			0
$203$	−5.17698	−	5.17698i	−0.363353	−	0.363353i
$204$		0			0
$205$		0			0
$206$		0			0
$207$			15.7584i			1.09529i
$208$		0			0
$209$	6.26701			0.433498
$210$		0			0
$211$	2.63215	+	2.63215i	0.181205	+	0.181205i	0.791881	−	0.610676i	$-0.209102\pi$
$211$	2.63215	+	2.63215i	0.181205	+	0.181205i	−0.610676	+	0.791881i	$0.709102\pi$
$212$		0			0
$213$	−24.1893	−	24.1893i	−1.65742	−	1.65742i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.427456			0.0290176
$218$		0			0
$219$	21.5047	−	21.5047i	1.45315	−	1.45315i
$220$		0			0
$221$	1.51632	+	1.51632i	0.101998	+	0.101998i
$222$		0			0
$223$		−	3.45644i		−	0.231461i	−0.993281	−	0.115730i	$-0.963079\pi$
$223$		−	3.45644i		−	0.231461i	0.993281	−	0.115730i	$-0.0369208\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.74550	−	4.74550i	0.314970	−	0.314970i	−0.531862	−	0.846831i	$-0.678507\pi$
$227$	4.74550	−	4.74550i	0.314970	−	0.314970i	0.846831	+	0.531862i	$0.178507\pi$
$228$		0			0
$229$	13.3576	−	13.3576i	0.882697	−	0.882697i	−0.111111	−	0.993808i	$-0.535441\pi$
$229$	13.3576	−	13.3576i	0.882697	−	0.882697i	0.993808	+	0.111111i	$0.0354410\pi$
$230$		0			0
$231$		−	7.43091i		−	0.488918i
$232$		0			0
$233$	−4.82691			−0.316222			−0.158111	−	0.987421i	$-0.550540\pi$
$233$	−4.82691			−0.316222			−0.158111	+	0.987421i	$0.550540\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−35.9388	+	35.9388i	−2.33448	+	2.33448i
$238$		0			0
$239$	−8.82497			−0.570840			−0.285420	−	0.958403i	$-0.592133\pi$
$239$	−8.82497			−0.570840			−0.285420	+	0.958403i	$0.592133\pi$
$240$		0			0
$241$	−3.74147			−0.241009			−0.120504	−	0.992713i	$-0.538451\pi$
$241$	−3.74147			−0.241009			−0.120504	+	0.992713i	$0.538451\pi$
$242$		0			0
$243$	33.1712	−	33.1712i	2.12793	−	2.12793i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.66087			0.169307
$248$		0			0
$249$		−	3.17878i		−	0.201447i
$250$		0			0
$251$	5.99322	−	5.99322i	0.378289	−	0.378289i	−0.492196	−	0.870484i	$-0.663806\pi$
$251$	5.99322	−	5.99322i	0.378289	−	0.378289i	0.870484	+	0.492196i	$0.163806\pi$
$252$		0			0
$253$	−3.27635	+	3.27635i	−0.205982	+	0.205982i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			14.7662i			0.921091i	0.887636	+	0.460545i	$0.152346\pi$
$257$			14.7662i			0.921091i	−0.887636	+	0.460545i	$0.847654\pi$
$258$		0			0
$259$	−5.69375	−	5.69375i	−0.353793	−	0.353793i
$260$		0			0
$261$	41.2404	−	41.2404i	2.55272	−	2.55272i
$262$		0			0
$263$	6.79486			0.418989			0.209494	−	0.977810i	$-0.432818\pi$
$263$	6.79486			0.418989			0.209494	+	0.977810i	$0.432818\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−12.6641	−	12.6641i	−0.775030	−	0.775030i
$268$		0			0
$269$	6.03990	+	6.03990i	0.368259	+	0.368259i	0.866842	−	0.498583i	$-0.166146\pi$
$269$	6.03990	+	6.03990i	0.368259	+	0.368259i	−0.498583	+	0.866842i	$0.666146\pi$
$270$		0			0
$271$	24.6221			1.49568			0.747842	−	0.663877i	$-0.231090\pi$
$271$	24.6221			1.49568			0.747842	+	0.663877i	$0.231090\pi$
$272$		0			0
$273$		−	3.15504i		−	0.190952i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−9.98018	−	9.98018i	−0.599651	−	0.599651i	0.340569	−	0.940220i	$-0.389380\pi$
$277$	−9.98018	−	9.98018i	−0.599651	−	0.599651i	−0.940220	+	0.340569i	$0.889380\pi$
$278$		0			0
$279$			3.40516i			0.203862i
$280$		0			0
$281$			14.4611i			0.862675i	0.902191	+	0.431337i	$0.141958\pi$
$281$			14.4611i			0.862675i	−0.902191	+	0.431337i	$0.858042\pi$
$282$		0			0
$283$	−20.0783	−	20.0783i	−1.19353	−	1.19353i	−0.976069	−	0.217462i	$-0.930222\pi$
$283$	−20.0783	−	20.0783i	−1.19353	−	1.19353i	−0.217462	−	0.976069i	$-0.569778\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			3.86067i			0.227888i
$288$		0			0
$289$	12.1786			0.716388
$290$		0			0
$291$	12.8999	+	12.8999i	0.756208	+	0.756208i
$292$		0			0
$293$	15.4038	+	15.4038i	0.899899	+	0.899899i	0.995427	−	0.0955279i	$-0.0304539\pi$
$293$	15.4038	+	15.4038i	0.899899	+	0.899899i	−0.0955279	+	0.995427i	$0.530454\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	36.4944			2.11762
$298$		0			0
$299$	−1.39108	+	1.39108i	−0.0804484	+	0.0804484i
$300$		0			0
$301$	−0.498461	−	0.498461i	−0.0287308	−	0.0287308i
$302$		0			0
$303$		−	1.35524i		−	0.0778566i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−9.12398	+	9.12398i	−0.520733	+	0.520733i	−0.917793	−	0.397060i	$-0.870031\pi$
$307$	−9.12398	+	9.12398i	−0.520733	+	0.520733i	0.397060	+	0.917793i	$0.370031\pi$
$308$		0			0
$309$	10.4732	−	10.4732i	0.595799	−	0.595799i
$310$		0			0
$311$		−	0.642911i		−	0.0364561i	−0.999834	−	0.0182281i	$-0.994198\pi$
$311$		−	0.642911i		−	0.0364561i	0.999834	−	0.0182281i	$-0.00580249\pi$
$312$		0			0
$313$	−21.3775			−1.20833			−0.604164	−	0.796860i	$-0.706493\pi$
$313$	−21.3775			−1.20833			−0.604164	+	0.796860i	$0.706493\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.66200	−	8.66200i	0.486507	−	0.486507i	−0.420695	−	0.907202i	$-0.638214\pi$
$317$	8.66200	−	8.66200i	0.486507	−	0.486507i	0.907202	+	0.420695i	$0.138214\pi$
$318$		0			0
$319$	17.1487			0.960141
$320$		0			0
$321$	30.2360			1.68761
$322$		0			0
$323$	−4.23035	+	4.23035i	−0.235383	+	0.235383i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−11.7219			−0.648224
$328$		0			0
$329$			9.05375i			0.499150i
$330$		0			0
$331$	8.43941	−	8.43941i	0.463872	−	0.463872i	−0.436050	−	0.899922i	$-0.643623\pi$
$331$	8.43941	−	8.43941i	0.463872	−	0.463872i	0.899922	+	0.436050i	$0.143623\pi$
$332$		0			0
$333$	45.3571	−	45.3571i	2.48555	−	2.48555i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	30.7047i		−	1.67259i	−0.548280	−	0.836295i	$-0.684717\pi$
$337$		−	30.7047i		−	1.67259i	0.548280	−	0.836295i	$-0.315283\pi$
$338$		0			0
$339$	−12.5175	−	12.5175i	−0.679860	−	0.679860i
$340$		0			0
$341$	−0.707970	+	0.707970i	−0.0383387	+	0.0383387i
$342$		0			0
$343$	12.8012			0.691197
$344$		0			0
$345$		0			0
$346$		0			0
$347$	13.6418	+	13.6418i	0.732329	+	0.732329i	0.971081	−	0.238752i	$-0.0767383\pi$
$347$	13.6418	+	13.6418i	0.732329	+	0.732329i	−0.238752	+	0.971081i	$0.576738\pi$
$348$		0			0
$349$	−9.97321	−	9.97321i	−0.533854	−	0.533854i	0.387863	−	0.921717i	$-0.373213\pi$
$349$	−9.97321	−	9.97321i	−0.533854	−	0.533854i	−0.921717	+	0.387863i	$0.873213\pi$
$350$		0			0
$351$	15.4949			0.827056
$352$		0			0
$353$		−	26.7843i		−	1.42559i	−0.701374	−	0.712793i	$-0.747430\pi$
$353$		−	26.7843i		−	1.42559i	0.701374	−	0.712793i	$-0.252570\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	5.01601	+	5.01601i	0.265475	+	0.265475i
$358$		0			0
$359$			19.1190i			1.00906i	0.863393	+	0.504532i	$0.168335\pi$
$359$			19.1190i			1.00906i	−0.863393	+	0.504532i	$0.831665\pi$
$360$		0			0
$361$		−	11.5765i		−	0.609288i
$362$		0			0
$363$	−13.2813	−	13.2813i	−0.697087	−	0.697087i
$364$		0			0
$365$		0			0
$366$		0			0
$367$			4.24385i			0.221527i	0.993847	+	0.110764i	$0.0353297\pi$
$367$			4.24385i			0.221527i	−0.993847	+	0.110764i	$0.964670\pi$
$368$		0			0
$369$	−30.7545			−1.60102
$370$		0			0
$371$	−6.18035	−	6.18035i	−0.320868	−	0.320868i
$372$		0			0
$373$	23.9514	+	23.9514i	1.24016	+	1.24016i	0.959935	+	0.280221i	$0.0904078\pi$
$373$	23.9514	+	23.9514i	1.24016	+	1.24016i	0.280221	+	0.959935i	$0.409592\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	7.28104			0.374992
$378$		0			0
$379$	−7.45685	+	7.45685i	−0.383033	+	0.383033i	−0.872194	−	0.489161i	$-0.837303\pi$
$379$	−7.45685	+	7.45685i	−0.383033	+	0.383033i	0.489161	+	0.872194i	$0.337303\pi$
$380$		0			0
$381$	−11.3190	−	11.3190i	−0.579890	−	0.579890i
$382$		0			0
$383$		−	5.19667i		−	0.265538i	−0.991147	−	0.132769i	$-0.957613\pi$
$383$		−	5.19667i		−	0.265538i	0.991147	−	0.132769i	$-0.0423868\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.97080	−	3.97080i	0.201847	−	0.201847i
$388$		0			0
$389$	−10.3846	+	10.3846i	−0.526522	+	0.526522i	−0.919534	−	0.393011i	$-0.871433\pi$
$389$	−10.3846	+	10.3846i	−0.526522	+	0.526522i	0.393011	+	0.919534i	$0.371433\pi$
$390$		0			0
$391$		−	4.42320i		−	0.223691i
$392$		0			0
$393$	37.2469			1.87886
$394$		0			0
$395$		0			0
$396$		0			0
$397$	9.93104	−	9.93104i	0.498425	−	0.498425i	−0.412523	−	0.910947i	$-0.635352\pi$
$397$	9.93104	−	9.93104i	0.498425	−	0.498425i	0.910947	+	0.412523i	$0.135352\pi$
$398$		0			0
$399$	8.80221			0.440662
$400$		0			0
$401$	9.51392			0.475102			0.237551	−	0.971375i	$-0.423655\pi$
$401$	9.51392			0.475102			0.237551	+	0.971375i	$0.423655\pi$
$402$		0			0
$403$	−0.300592	+	0.300592i	−0.0149736	+	0.0149736i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	18.8605			0.934879
$408$		0			0
$409$			4.81799i			0.238234i	0.992880	+	0.119117i	$0.0380064\pi$
$409$			4.81799i			0.238234i	−0.992880	+	0.119117i	$0.961994\pi$
$410$		0			0
$411$	−31.5361	+	31.5361i	−1.55556	+	1.55556i
$412$		0			0
$413$	5.57564	−	5.57564i	0.274359	−	0.274359i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			38.2734i			1.87426i
$418$		0			0
$419$	21.4380	+	21.4380i	1.04731	+	1.04731i	0.998824	+	0.0484914i	$0.0154413\pi$
$419$	21.4380	+	21.4380i	1.04731	+	1.04731i	0.0484914	+	0.998824i	$0.484559\pi$
$420$		0			0
$421$	−4.80145	+	4.80145i	−0.234008	+	0.234008i	−0.814363	−	0.580355i	$-0.802914\pi$
$421$	−4.80145	+	4.80145i	−0.234008	+	0.234008i	0.580355	+	0.814363i	$0.302914\pi$
$422$		0			0
$423$	−72.1232			−3.50675
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.53819	+	3.53819i	0.171225	+	0.171225i
$428$		0			0
$429$	5.22551	+	5.22551i	0.252290	+	0.252290i
$430$		0			0
$431$	−13.2369			−0.637597			−0.318799	−	0.947822i	$-0.603279\pi$
$431$	−13.2369			−0.637597			−0.318799	+	0.947822i	$0.603279\pi$
$432$		0			0
$433$		−	1.50709i		−	0.0724259i	−0.999344	−	0.0362129i	$-0.988471\pi$
$433$		−	1.50709i		−	0.0724259i	0.999344	−	0.0362129i	$-0.0115295\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.88097	−	3.88097i	−0.185652	−	0.185652i
$438$		0			0
$439$			10.3092i			0.492033i	0.969266	+	0.246016i	$0.0791217\pi$
$439$			10.3092i			0.492033i	−0.969266	+	0.246016i	$0.920878\pi$
$440$		0			0
$441$			47.2158i			2.24837i
$442$		0			0
$443$	14.2651	+	14.2651i	0.677755	+	0.677755i	0.959492	−	0.281736i	$-0.0909104\pi$
$443$	14.2651	+	14.2651i	0.677755	+	0.677755i	−0.281736	+	0.959492i	$0.590910\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	58.7904i		−	2.78069i
$448$		0			0
$449$	19.5711			0.923618			0.461809	−	0.886979i	$-0.347201\pi$
$449$	19.5711			0.923618			0.461809	+	0.886979i	$0.347201\pi$
$450$		0			0
$451$	−6.39420	−	6.39420i	−0.301091	−	0.301091i
$452$		0			0
$453$	−35.2569	−	35.2569i	−1.65652	−	1.65652i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−39.0185			−1.82521			−0.912604	−	0.408845i	$-0.865932\pi$
$457$	−39.0185			−1.82521			−0.912604	+	0.408845i	$0.865932\pi$
$458$		0			0
$459$	−24.6344	+	24.6344i	−1.14984	+	1.14984i
$460$		0			0
$461$	19.6941	+	19.6941i	0.917245	+	0.917245i	0.996828	−	0.0795833i	$-0.0253590\pi$
$461$	19.6941	+	19.6941i	0.917245	+	0.917245i	−0.0795833	+	0.996828i	$0.525359\pi$
$462$		0			0
$463$			14.9979i			0.697009i	0.937307	+	0.348505i	$0.113310\pi$
$463$			14.9979i			0.697009i	−0.937307	+	0.348505i	$0.886690\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.88870	+	4.88870i	−0.226222	+	0.226222i	−0.811112	−	0.584890i	$-0.801138\pi$
$467$	−4.88870	+	4.88870i	−0.226222	+	0.226222i	0.584890	+	0.811112i	$0.301138\pi$
$468$		0			0
$469$	4.45404	−	4.45404i	0.205669	−	0.205669i
$470$		0			0
$471$		−	8.17980i		−	0.376905i
$472$		0			0
$473$	1.65114			0.0759197
$474$		0			0
$475$		0			0
$476$		0			0
$477$	49.2334	−	49.2334i	2.25424	−	2.25424i
$478$		0			0
$479$	−27.3381			−1.24911			−0.624555	−	0.780981i	$-0.714720\pi$
$479$	−27.3381			−1.24911			−0.624555	+	0.780981i	$0.714720\pi$
$480$		0			0
$481$	8.00784			0.365126
$482$		0			0
$483$	−4.60173	+	4.60173i	−0.209386	+	0.209386i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−35.4769			−1.60761			−0.803806	−	0.594892i	$-0.797195\pi$
$487$	−35.4769			−1.60761			−0.803806	+	0.594892i	$0.797195\pi$
$488$		0			0
$489$		−	64.7171i		−	2.92661i
$490$		0			0
$491$	−3.55614	+	3.55614i	−0.160486	+	0.160486i	−0.782782	−	0.622296i	$-0.786200\pi$
$491$	−3.55614	+	3.55614i	−0.160486	+	0.160486i	0.622296	+	0.782782i	$0.286200\pi$
$492$		0			0
$493$	−11.5757	+	11.5757i	−0.521343	+	0.521343i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		−	10.2114i		−	0.458042i
$498$		0			0
$499$	−17.6521	−	17.6521i	−0.790218	−	0.790218i	0.191312	−	0.981529i	$-0.438726\pi$
$499$	−17.6521	−	17.6521i	−0.790218	−	0.790218i	−0.981529	+	0.191312i	$0.938726\pi$
$500$		0			0
$501$	−43.8776	+	43.8776i	−1.96031	+	1.96031i
$502$		0			0
$503$	31.8567			1.42042			0.710210	−	0.703990i	$-0.248600\pi$
$503$	31.8567			1.42042			0.710210	+	0.703990i	$0.248600\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−28.0225	−	28.0225i	−1.24452	−	1.24452i
$508$		0			0
$509$	5.61054	+	5.61054i	0.248683	+	0.248683i	0.820430	−	0.571747i	$-0.193734\pi$
$509$	5.61054	+	5.61054i	0.248683	+	0.248683i	−0.571747	+	0.820430i	$0.693734\pi$
$510$		0			0
$511$	9.07810			0.401591
$512$		0			0
$513$			43.2291i			1.90861i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−14.9952	−	14.9952i	−0.659489	−	0.659489i
$518$		0			0
$519$		−	74.7767i		−	3.28233i
$520$		0			0
$521$		−	33.1977i		−	1.45442i	−0.686417	−	0.727208i	$-0.740818\pi$
$521$		−	33.1977i		−	1.45442i	0.686417	−	0.727208i	$-0.259182\pi$
$522$		0			0
$523$	2.60707	+	2.60707i	0.113999	+	0.113999i	0.761805	−	0.647806i	$-0.224313\pi$
$523$	2.60707	+	2.60707i	0.113999	+	0.113999i	−0.647806	+	0.761805i	$0.724313\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	0.955787i		−	0.0416347i
$528$		0			0
$529$	−18.9421			−0.823570
$530$		0			0
$531$	44.4162	+	44.4162i	1.92750	+	1.92750i
$532$		0			0
$533$	−2.71487	−	2.71487i	−0.117594	−	0.117594i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−76.4593			−3.29946
$538$		0			0
$539$	−9.81668	+	9.81668i	−0.422834	+	0.422834i
$540$		0			0
$541$	−22.6839	−	22.6839i	−0.975257	−	0.975257i	0.0244439	−	0.999701i	$-0.492218\pi$
$541$	−22.6839	−	22.6839i	−0.975257	−	0.975257i	−0.999701	+	0.0244439i	$0.992218\pi$
$542$		0			0
$543$		−	71.8992i		−	3.08549i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	3.02284	−	3.02284i	0.129248	−	0.129248i	−0.639524	−	0.768771i	$-0.720868\pi$
$547$	3.02284	−	3.02284i	0.129248	−	0.129248i	0.768771	+	0.639524i	$0.220868\pi$
$548$		0			0
$549$	−28.1857	+	28.1857i	−1.20293	+	1.20293i
$550$		0			0
$551$			20.3133i			0.865375i
$552$		0			0
$553$	−15.1714			−0.645153
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.27495	−	9.27495i	0.392992	−	0.392992i	−0.482760	−	0.875753i	$-0.660366\pi$
$557$	9.27495	−	9.27495i	0.392992	−	0.392992i	0.875753	+	0.482760i	$0.160366\pi$
$558$		0			0
$559$	0.701048			0.0296512
$560$		0			0
$561$	−16.6154			−0.701504
$562$		0			0
$563$	−20.3025	+	20.3025i	−0.855649	+	0.855649i	−0.990822	−	0.135173i	$-0.956841\pi$
$563$	−20.3025	+	20.3025i	−0.855649	+	0.855649i	0.135173	+	0.990822i	$0.456841\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	28.2112			1.18476
$568$		0			0
$569$		−	14.3362i		−	0.601005i	−0.953781	−	0.300503i	$-0.902846\pi$
$569$		−	14.3362i		−	0.601005i	0.953781	−	0.300503i	$-0.0971544\pi$
$570$		0			0
$571$	−8.54368	+	8.54368i	−0.357542	+	0.357542i	−0.862906	−	0.505364i	$-0.831358\pi$
$571$	−8.54368	+	8.54368i	−0.357542	+	0.357542i	0.505364	+	0.862906i	$0.331358\pi$
$572$		0			0
$573$	−34.3987	+	34.3987i	−1.43703	+	1.43703i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			8.68179i			0.361428i	0.983536	+	0.180714i	$0.0578408\pi$
$577$			8.68179i			0.361428i	−0.983536	+	0.180714i	$0.942159\pi$
$578$		0			0
$579$	26.2661	+	26.2661i	1.09158	+	1.09158i
$580$		0			0
$581$	0.670953	−	0.670953i	0.0278358	−	0.0278358i
$582$		0			0
$583$	20.4723			0.847877
$584$		0			0
$585$		0			0
$586$		0			0
$587$	21.9042	+	21.9042i	0.904082	+	0.904082i	0.995786	−	0.0917043i	$-0.0292315\pi$
$587$	21.9042	+	21.9042i	0.904082	+	0.904082i	−0.0917043	+	0.995786i	$0.529231\pi$
$588$		0			0
$589$	−0.838619	−	0.838619i	−0.0345547	−	0.0345547i
$590$		0			0
$591$	−49.3871			−2.03151
$592$		0			0
$593$		−	17.5142i		−	0.719222i	−0.933102	−	0.359611i	$-0.882909\pi$
$593$		−	17.5142i		−	0.719222i	0.933102	−	0.359611i	$-0.117091\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−10.9052	−	10.9052i	−0.446319	−	0.446319i
$598$		0			0
$599$			19.0276i			0.777447i	0.921354	+	0.388724i	$0.127084\pi$
$599$			19.0276i			0.777447i	−0.921354	+	0.388724i	$0.872916\pi$
$600$		0			0
$601$		−	5.52545i		−	0.225388i	−0.993630	−	0.112694i	$-0.964052\pi$
$601$		−	5.52545i		−	0.225388i	0.993630	−	0.112694i	$-0.0359479\pi$
$602$		0			0
$603$	35.4814	+	35.4814i	1.44491	+	1.44491i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	12.1064i		−	0.491384i	−0.969348	−	0.245692i	$-0.920985\pi$
$607$		−	12.1064i		−	0.491384i	0.969348	−	0.245692i	$-0.0790151\pi$
$608$		0			0
$609$	24.0858			0.976007
$610$		0			0
$611$	−6.36671	−	6.36671i	−0.257570	−	0.257570i
$612$		0			0
$613$	17.8073	+	17.8073i	0.719230	+	0.719230i	0.968448	−	0.249218i	$-0.0801734\pi$
$613$	17.8073	+	17.8073i	0.719230	+	0.719230i	−0.249218	+	0.968448i	$0.580173\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.10944			0.0446642			0.0223321	−	0.999751i	$-0.492891\pi$
$617$	1.10944			0.0446642			0.0223321	+	0.999751i	$0.492891\pi$
$618$		0			0
$619$	−31.8702	+	31.8702i	−1.28097	+	1.28097i	−0.340859	+	0.940115i	$0.610718\pi$
$619$	−31.8702	+	31.8702i	−1.28097	+	1.28097i	−0.940115	+	0.340859i	$0.889282\pi$
$620$		0			0
$621$	−22.5998	−	22.5998i	−0.906901	−	0.906901i
$622$		0			0
$623$		−	5.34608i		−	0.214186i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−14.5786	+	14.5786i	−0.582213	+	0.582213i
$628$		0			0
$629$	−12.7312	+	12.7312i	−0.507626	+	0.507626i
$630$		0			0
$631$			6.80064i			0.270729i	0.990796	+	0.135365i	$0.0432206\pi$
$631$			6.80064i			0.270729i	−0.990796	+	0.135365i	$0.956779\pi$
$632$		0			0
$633$	−12.2460			−0.486736
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−4.16800	+	4.16800i	−0.165142	+	0.165142i
$638$		0			0
$639$	81.3449			3.21796
$640$		0			0
$641$	14.2566			0.563100			0.281550	−	0.959547i	$-0.409151\pi$
$641$	14.2566			0.563100			0.281550	+	0.959547i	$0.409151\pi$
$642$		0			0
$643$	14.4137	−	14.4137i	0.568422	−	0.568422i	−0.363264	−	0.931686i	$-0.618338\pi$
$643$	14.4137	−	14.4137i	0.568422	−	0.568422i	0.931686	+	0.363264i	$0.118338\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	20.5723			0.808782			0.404391	−	0.914586i	$-0.367483\pi$
$647$	20.5723			0.808782			0.404391	+	0.914586i	$0.367483\pi$
$648$		0			0
$649$			18.4692i			0.724980i
$650$		0			0
$651$	−0.994365	+	0.994365i	−0.0389723	+	0.0389723i
$652$		0			0
$653$	9.79946	−	9.79946i	0.383482	−	0.383482i	−0.488873	−	0.872355i	$-0.662592\pi$
$653$	9.79946	−	9.79946i	0.383482	−	0.383482i	0.872355	+	0.488873i	$0.162592\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			72.3172i			2.82136i
$658$		0			0
$659$	−8.70669	−	8.70669i	−0.339165	−	0.339165i	0.516888	−	0.856053i	$-0.327090\pi$
$659$	−8.70669	−	8.70669i	−0.339165	−	0.339165i	−0.856053	+	0.516888i	$0.827090\pi$
$660$		0			0
$661$	19.7899	−	19.7899i	0.769737	−	0.769737i	−0.208323	−	0.978060i	$-0.566801\pi$
$661$	19.7899	−	19.7899i	0.769737	−	0.769737i	0.978060	+	0.208323i	$0.0668006\pi$
$662$		0			0
$663$	−7.05464			−0.273979
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−10.6196	−	10.6196i	−0.411194	−	0.411194i
$668$		0			0
$669$	8.04053	+	8.04053i	0.310865	+	0.310865i
$670$		0			0
$671$	−11.7202			−0.452454
$672$		0			0
$673$		−	14.0829i		−	0.542857i	−0.962459	−	0.271429i	$-0.912504\pi$
$673$		−	14.0829i		−	0.542857i	0.962459	−	0.271429i	$-0.0874961\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	29.8166	+	29.8166i	1.14594	+	1.14594i	0.987343	+	0.158601i	$0.0506984\pi$
$677$	29.8166	+	29.8166i	1.14594	+	1.14594i	0.158601	+	0.987343i	$0.449302\pi$
$678$		0			0
$679$			5.44564i			0.208984i
$680$		0			0
$681$			22.0784i			0.846045i
$682$		0			0
$683$	12.0646	+	12.0646i	0.461641	+	0.461641i	0.899193	−	0.437552i	$-0.144155\pi$
$683$	12.0646	+	12.0646i	0.461641	+	0.461641i	−0.437552	+	0.899193i	$0.644155\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			62.1462i			2.37102i
$688$		0			0
$689$	8.69221			0.331147
$690$		0			0
$691$	−2.58867	−	2.58867i	−0.0984776	−	0.0984776i	0.656152	−	0.754629i	$-0.272183\pi$
$691$	−2.58867	−	2.58867i	−0.0984776	−	0.0984776i	−0.754629	+	0.656152i	$0.772183\pi$
$692$		0			0
$693$	12.4945	+	12.4945i	0.474628	+	0.474628i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	8.63242			0.326976
$698$		0			0
$699$	11.2286	−	11.2286i	0.424704	−	0.424704i
$700$		0			0
$701$	−26.9943	−	26.9943i	−1.01956	−	1.01956i	−0.999805	−	0.0197572i	$-0.993711\pi$
$701$	−26.9943	−	26.9943i	−1.01956	−	1.01956i	−0.0197572	−	0.999805i	$-0.506289\pi$
$702$		0			0
$703$			22.3410i			0.842606i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.286054	−	0.286054i	0.0107582	−	0.0107582i
$708$		0			0
$709$	35.0639	−	35.0639i	1.31685	−	1.31685i	0.400598	−	0.916254i	$-0.368802\pi$
$709$	35.0639	−	35.0639i	1.31685	−	1.31685i	0.916254	−	0.400598i	$-0.131198\pi$
$710$		0			0
$711$		−	120.857i		−	4.53249i
$712$		0			0
$713$	0.876848			0.0328382
$714$		0			0
$715$		0			0
$716$		0			0
$717$	20.5290	−	20.5290i	0.766671	−	0.766671i
$718$		0			0
$719$	−0.436840			−0.0162914			−0.00814568	−	0.999967i	$-0.502593\pi$
$719$	−0.436840			−0.0162914			−0.00814568	+	0.999967i	$0.502593\pi$
$720$		0			0
$721$	4.42120			0.164654
$722$		0			0
$723$	8.70356	−	8.70356i	0.323689	−	0.323689i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	38.8072			1.43928			0.719640	−	0.694348i	$-0.244307\pi$
$727$	38.8072			1.43928			0.719640	+	0.694348i	$0.244307\pi$
$728$		0			0
$729$			68.1444i			2.52387i
$730$		0			0
$731$	−1.11455	+	1.11455i	−0.0412233	+	0.0412233i
$732$		0			0
$733$	24.3059	−	24.3059i	0.897758	−	0.897758i	−0.0974793	−	0.995238i	$-0.531078\pi$
$733$	24.3059	−	24.3059i	0.897758	−	0.897758i	0.995238	+	0.0974793i	$0.0310780\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			14.7539i			0.543469i
$738$		0			0
$739$	−27.0262	−	27.0262i	−0.994174	−	0.994174i	0.00580951	−	0.999983i	$-0.498151\pi$
$739$	−27.0262	−	27.0262i	−0.994174	−	0.994174i	−0.999983	+	0.00580951i	$0.998151\pi$
$740$		0			0
$741$	−6.18982	+	6.18982i	−0.227389	+	0.227389i
$742$		0			0
$743$	−12.1663			−0.446337			−0.223169	−	0.974780i	$-0.571640\pi$
$743$	−12.1663			−0.446337			−0.223169	+	0.974780i	$0.571640\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	5.34489	+	5.34489i	0.195559	+	0.195559i
$748$		0			0
$749$	6.38199	+	6.38199i	0.233193	+	0.233193i
$750$		0			0
$751$	40.8606			1.49102			0.745512	−	0.666492i	$-0.232205\pi$
$751$	40.8606			1.49102			0.745512	+	0.666492i	$0.232205\pi$
$752$		0			0
$753$			27.8834i			1.01613i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.00399171	+	0.00399171i	0.000145081	+	0.000145081i	0.707179	−	0.707034i	$-0.249967\pi$
$757$	0.00399171	+	0.00399171i	0.000145081	+	0.000145081i	−0.707034	+	0.707179i	$0.749967\pi$
$758$		0			0
$759$		−	15.2432i		−	0.553292i
$760$		0			0
$761$		−	0.751325i		−	0.0272355i	−0.999907	−	0.0136178i	$-0.995665\pi$
$761$		−	0.751325i		−	0.0272355i	0.999907	−	0.0136178i	$-0.00433480\pi$
$762$		0			0
$763$	−2.47418	−	2.47418i	−0.0895712	−	0.0895712i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			7.84172i			0.283148i
$768$		0			0
$769$	−35.4522			−1.27844			−0.639219	−	0.769025i	$-0.720742\pi$
$769$	−35.4522			−1.27844			−0.639219	+	0.769025i	$0.720742\pi$
$770$		0			0
$771$	−34.3498	−	34.3498i	−1.23708	−	1.23708i
$772$		0			0
$773$	−5.50186	−	5.50186i	−0.197888	−	0.197888i	0.601206	−	0.799094i	$-0.294687\pi$
$773$	−5.50186	−	5.50186i	−0.197888	−	0.197888i	−0.799094	+	0.601206i	$0.794687\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	26.4901			0.950327
$778$		0			0
$779$	7.57419	−	7.57419i	0.271373	−	0.271373i
$780$		0			0
$781$	16.9125	+	16.9125i	0.605177	+	0.605177i
$782$		0			0
$783$			118.289i			4.22732i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−28.6944	+	28.6944i	−1.02284	+	1.02284i	−0.0231107	+	0.999733i	$0.507357\pi$
$787$	−28.6944	+	28.6944i	−1.02284	+	1.02284i	−0.999733	+	0.0231107i	$0.992643\pi$
$788$		0			0
$789$	−15.8065	+	15.8065i	−0.562726	+	0.562726i
$790$		0			0
$791$		−	5.28422i		−	0.187885i
$792$		0			0
$793$	−4.97620			−0.176710
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.29277	+	6.29277i	−0.222901	+	0.222901i	−0.809719	−	0.586818i	$-0.800381\pi$
$797$	−6.29277	+	6.29277i	−0.222901	+	0.222901i	0.586818	+	0.809719i	$0.300381\pi$
$798$		0			0
$799$	20.2441			0.716185
$800$		0			0
$801$	42.5875			1.50476
$802$		0			0
$803$	−15.0355	+	15.0355i	−0.530592	+	0.530592i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−28.1005			−0.989186
$808$		0			0
$809$			27.0850i			0.952257i	0.879376	+	0.476128i	$0.157960\pi$
$809$			27.0850i			0.952257i	−0.879376	+	0.476128i	$0.842040\pi$
$810$		0			0
$811$	14.6690	−	14.6690i	0.515098	−	0.515098i	−0.400986	−	0.916084i	$-0.631332\pi$
$811$	14.6690	−	14.6690i	0.515098	−	0.515098i	0.916084	+	0.400986i	$0.131332\pi$
$812$		0			0
$813$	−57.2769	+	57.2769i	−2.00879	+	2.00879i
$814$		0			0
$815$		0			0
$816$		0			0
$817$			1.95585i			0.0684264i
$818$		0			0
$819$	5.30496	+	5.30496i	0.185370	+	0.185370i
$820$		0			0
$821$	−15.4717	+	15.4717i	−0.539965	+	0.539965i	−0.923519	−	0.383553i	$-0.874700\pi$
$821$	−15.4717	+	15.4717i	−0.539965	+	0.539965i	0.383553	+	0.923519i	$0.374700\pi$
$822$		0			0
$823$	−7.64319			−0.266425			−0.133212	−	0.991088i	$-0.542529\pi$
$823$	−7.64319			−0.266425			−0.133212	+	0.991088i	$0.542529\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.781185	−	0.781185i	−0.0271645	−	0.0271645i	0.693394	−	0.720559i	$-0.256115\pi$
$827$	−0.781185	−	0.781185i	−0.0271645	−	0.0271645i	−0.720559	+	0.693394i	$0.756115\pi$
$828$		0			0
$829$	−28.9122	−	28.9122i	−1.00416	−	1.00416i	−0.999991	−	0.00417165i	$-0.998672\pi$
$829$	−28.9122	−	28.9122i	−1.00416	−	1.00416i	−0.00417165	−	0.999991i	$-0.501328\pi$
$830$		0			0
$831$	46.4326			1.61073
$832$		0			0
$833$		−	13.2529i		−	0.459186i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−4.88349	−	4.88349i	−0.168798	−	0.168798i
$838$		0			0
$839$		−	35.9665i		−	1.24170i	−0.783928	−	0.620851i	$-0.786787\pi$
$839$		−	35.9665i		−	1.24170i	0.783928	−	0.620851i	$-0.213213\pi$
$840$		0			0
$841$			26.5841i			0.916692i
$842$		0			0
$843$	−33.6400	−	33.6400i	−1.15862	−	1.15862i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		−	5.60663i		−	0.192646i
$848$		0			0
$849$	93.4140			3.20596
$850$		0			0
$851$	−11.6797	−	11.6797i	−0.400375	−	0.400375i
$852$		0			0
$853$	8.53167	+	8.53167i	0.292119	+	0.292119i	0.837917	−	0.545798i	$-0.183773\pi$
$853$	8.53167	+	8.53167i	0.292119	+	0.292119i	−0.545798	+	0.837917i	$0.683773\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	20.6681			0.706010			0.353005	−	0.935621i	$-0.385160\pi$
$857$	20.6681			0.706010			0.353005	+	0.935621i	$0.385160\pi$
$858$		0			0
$859$	26.6003	−	26.6003i	0.907590	−	0.907590i	−0.0884877	−	0.996077i	$-0.528203\pi$
$859$	26.6003	−	26.6003i	0.907590	−	0.907590i	0.996077	+	0.0884877i	$0.0282034\pi$
$860$		0			0
$861$	−8.98085	−	8.98085i	−0.306066	−	0.306066i
$862$		0			0
$863$		−	24.2911i		−	0.826880i	−0.910531	−	0.413440i	$-0.864327\pi$
$863$		−	24.2911i		−	0.826880i	0.910531	−	0.413440i	$-0.135673\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−28.3304	+	28.3304i	−0.962150	+	0.962150i
$868$		0			0
$869$	25.1275	−	25.1275i	0.852391	−	0.852391i
$870$		0			0
$871$			6.26428i			0.212257i
$872$		0			0
$873$	−43.3806			−1.46821
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−17.5305	+	17.5305i	−0.591963	+	0.591963i	−0.938161	−	0.346198i	$-0.887472\pi$
$877$	−17.5305	+	17.5305i	−0.591963	+	0.591963i	0.346198	+	0.938161i	$0.387472\pi$
$878$		0			0
$879$	−71.6659			−2.41723
$880$		0			0
$881$	35.1334			1.18367			0.591837	−	0.806058i	$-0.298403\pi$
$881$	35.1334			1.18367			0.591837	+	0.806058i	$0.298403\pi$
$882$		0			0
$883$	18.0965	−	18.0965i	0.608997	−	0.608997i	−0.333687	−	0.942684i	$-0.608293\pi$
$883$	18.0965	−	18.0965i	0.608997	−	0.608997i	0.942684	+	0.333687i	$0.108293\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.6666			0.492455			0.246228	−	0.969212i	$-0.420809\pi$
$887$	14.6666			0.492455			0.246228	+	0.969212i	$0.420809\pi$
$888$		0			0
$889$		−	4.77825i		−	0.160257i
$890$		0			0
$891$	−46.7246	+	46.7246i	−1.56533	+	1.56533i
$892$		0			0
$893$	17.7624	−	17.7624i	0.594397	−	0.594397i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	6.47199i		−	0.216094i
$898$		0			0
$899$	−2.29475	−	2.29475i	−0.0765341	−	0.0765341i
$900$		0			0
$901$	−13.8192	+	13.8192i	−0.460385	+	0.460385i
$902$		0			0
$903$	2.31908			0.0771743
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−25.4429	−	25.4429i	−0.844817	−	0.844817i	0.144664	−	0.989481i	$-0.453790\pi$
$907$	−25.4429	−	25.4429i	−0.844817	−	0.844817i	−0.989481	+	0.144664i	$0.953790\pi$
$908$		0			0
$909$	2.27874	+	2.27874i	0.0755810	+	0.0755810i
$910$		0			0
$911$	−14.6852			−0.486542			−0.243271	−	0.969958i	$-0.578220\pi$
$911$	−14.6852			−0.486542			−0.243271	+	0.969958i	$0.578220\pi$
$912$		0			0
$913$			2.22252i			0.0735547i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.86179	+	7.86179i	0.259619	+	0.259619i
$918$		0			0
$919$		−	46.2157i		−	1.52451i	−0.647274	−	0.762257i	$-0.724091\pi$
$919$		−	46.2157i		−	1.52451i	0.647274	−	0.762257i	$-0.275909\pi$
$920$		0			0
$921$		−	42.4492i		−	1.39875i
$922$		0			0
$923$	7.18076	+	7.18076i	0.236358	+	0.236358i
$924$		0			0
$925$		0			0
$926$		0			0
$927$			35.2198i			1.15677i
$928$		0			0
$929$	−52.0543			−1.70785			−0.853923	−	0.520400i	$-0.825783\pi$
$929$	−52.0543			−1.70785			−0.853923	+	0.520400i	$0.825783\pi$
$930$		0			0
$931$	−11.6283	−	11.6283i	−0.381101	−	0.381101i
$932$		0			0
$933$	1.49557	+	1.49557i	0.0489627	+	0.0489627i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	33.7454			1.10241			0.551207	−	0.834368i	$-0.314167\pi$
$937$	33.7454			1.10241			0.551207	+	0.834368i	$0.314167\pi$
$938$		0			0
$939$	49.7293	−	49.7293i	1.62285	−	1.62285i
$940$		0			0
$941$	−14.5814	−	14.5814i	−0.475341	−	0.475341i	0.428297	−	0.903638i	$-0.359114\pi$
$941$	−14.5814	−	14.5814i	−0.475341	−	0.475341i	−0.903638	+	0.428297i	$0.859114\pi$
$942$		0			0
$943$			7.91946i			0.257893i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	37.7582	−	37.7582i	1.22698	−	1.22698i	0.261876	−	0.965102i	$-0.415659\pi$
$947$	37.7582	−	37.7582i	1.22698	−	1.22698i	0.965102	−	0.261876i	$-0.0843410\pi$
$948$		0			0
$949$	−6.38383	+	6.38383i	−0.207228	+	0.207228i
$950$		0			0
$951$			40.2998i			1.30681i
$952$		0			0
$953$	48.6441			1.57574			0.787868	−	0.615844i	$-0.211185\pi$
$953$	48.6441			1.57574			0.787868	+	0.615844i	$0.211185\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−39.8920	+	39.8920i	−1.28952	+	1.28952i
$958$		0			0
$959$	−13.3128			−0.429893
$960$		0			0
$961$	−30.8105			−0.993888
$962$		0			0
$963$	−50.8397	+	50.8397i	−1.63829	+	1.63829i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−12.4521			−0.400433			−0.200216	−	0.979752i	$-0.564165\pi$
$967$	−12.4521			−0.400433			−0.200216	+	0.979752i	$0.564165\pi$
$968$		0			0
$969$		−	19.6817i		−	0.632266i
$970$		0			0
$971$	−14.1931	+	14.1931i	−0.455478	+	0.455478i	−0.897168	−	0.441690i	$-0.854379\pi$
$971$	−14.1931	+	14.1931i	−0.455478	+	0.455478i	0.441690	+	0.897168i	$0.354379\pi$
$972$		0			0
$973$	−8.07846	+	8.07846i	−0.258984	+	0.258984i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	18.3144i		−	0.585929i	−0.956123	−	0.292965i	$-0.905358\pi$
$977$		−	18.3144i		−	0.585929i	0.956123	−	0.292965i	$-0.0946419\pi$
$978$		0			0
$979$	8.85441	+	8.85441i	0.282988	+	0.282988i
$980$		0			0
$981$	19.7096	−	19.7096i	0.629278	−	0.629278i
$982$		0			0
$983$	27.0583			0.863027			0.431513	−	0.902107i	$-0.357980\pi$
$983$	27.0583			0.863027			0.431513	+	0.902107i	$0.357980\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−21.0612	−	21.0612i	−0.670386	−	0.670386i
$988$		0			0
$989$	−1.02250	−	1.02250i	−0.0325137	−	0.0325137i
$990$		0			0
$991$	−25.7759			−0.818799			−0.409400	−	0.912355i	$-0.634262\pi$
$991$	−25.7759			−0.818799			−0.409400	+	0.912355i	$0.634262\pi$
$992$		0			0
$993$			39.2642i			1.24601i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−11.1158	−	11.1158i	−0.352041	−	0.352041i	0.508828	−	0.860868i	$-0.330079\pi$
$997$	−11.1158	−	11.1158i	−0.352041	−	0.352041i	−0.860868	+	0.508828i	$0.830079\pi$
$998$		0			0
$999$			130.097i			4.11609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.q.h.849.1		16
4.3	odd	2		400.2.q.g.349.6		16
5.2	odd	4		320.2.l.a.81.8		16
5.3	odd	4		1600.2.l.i.401.1		16
5.4	even	2		1600.2.q.g.849.8		16
15.2	even	4		2880.2.t.c.721.2		16
16.5	even	4		1600.2.q.g.49.8		16
16.11	odd	4		400.2.q.h.149.3		16
20.3	even	4		400.2.l.h.301.1		16
20.7	even	4		80.2.l.a.61.8	yes	16
20.19	odd	2		400.2.q.h.349.3		16
40.27	even	4		640.2.l.b.161.8		16
40.37	odd	4		640.2.l.a.161.1		16
60.47	odd	4		720.2.t.c.541.1		16
80.27	even	4		80.2.l.a.21.8	✓	16
80.37	odd	4		320.2.l.a.241.8		16
80.43	even	4		400.2.l.h.101.1		16
80.53	odd	4		1600.2.l.i.1201.1		16
80.59	odd	4		400.2.q.g.149.6		16
80.67	even	4		640.2.l.b.481.8		16
80.69	even	4	inner	1600.2.q.h.49.1		16
80.77	odd	4		640.2.l.a.481.1		16
160.27	even	8		5120.2.a.v.1.8		8
160.37	odd	8		5120.2.a.t.1.1		8
160.107	even	8		5120.2.a.s.1.1		8
160.117	odd	8		5120.2.a.u.1.8		8
240.107	odd	4		720.2.t.c.181.1		16
240.197	even	4		2880.2.t.c.2161.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.8	✓	16	80.27	even	4
80.2.l.a.61.8	yes	16	20.7	even	4
320.2.l.a.81.8		16	5.2	odd	4
320.2.l.a.241.8		16	80.37	odd	4
400.2.l.h.101.1		16	80.43	even	4
400.2.l.h.301.1		16	20.3	even	4
400.2.q.g.149.6		16	80.59	odd	4
400.2.q.g.349.6		16	4.3	odd	2
400.2.q.h.149.3		16	16.11	odd	4
400.2.q.h.349.3		16	20.19	odd	2
640.2.l.a.161.1		16	40.37	odd	4
640.2.l.a.481.1		16	80.77	odd	4
640.2.l.b.161.8		16	40.27	even	4
640.2.l.b.481.8		16	80.67	even	4
720.2.t.c.181.1		16	240.107	odd	4
720.2.t.c.541.1		16	60.47	odd	4
1600.2.l.i.401.1		16	5.3	odd	4
1600.2.l.i.1201.1		16	80.53	odd	4
1600.2.q.g.49.8		16	16.5	even	4
1600.2.q.g.849.8		16	5.4	even	2
1600.2.q.h.49.1		16	80.69	even	4	inner
1600.2.q.h.849.1		16	1.1	even	1	trivial
2880.2.t.c.721.2		16	15.2	even	4
2880.2.t.c.2161.3		16	240.197	even	4
5120.2.a.s.1.1		8	160.107	even	8
5120.2.a.t.1.1		8	160.37	odd	8
5120.2.a.u.1.8		8	160.117	odd	8
5120.2.a.v.1.8		8	160.27	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.32624 + 2.32624i) q^{3} -0.982011 q^{7} -7.82281i q^{9} +O(q^{10})\)	\(q+(-2.32624 + 2.32624i) q^{3} -0.982011 q^{7} -7.82281i q^{9} +(1.62645 - 1.62645i) q^{11} +(0.690562 - 0.690562i) q^{13} +2.19577i q^{17} +(1.92659 + 1.92659i) q^{19} +(2.28440 - 2.28440i) q^{21} -2.01442 q^{23} +(11.2190 + 11.2190i) q^{27} +(5.27182 + 5.27182i) q^{29} -0.435286 q^{31} +7.56703i q^{33} +(5.79805 + 5.79805i) q^{37} +3.21283i q^{39} -3.93139i q^{41} +(0.507592 + 0.507592i) q^{43} -9.21960i q^{47} -6.03565 q^{49} +(-5.10789 - 5.10789i) q^{51} +(6.29357 + 6.29357i) q^{53} -8.96345 q^{57} +(-5.67778 + 5.67778i) q^{59} +(-3.60301 - 3.60301i) q^{61} +7.68209i q^{63} +(-4.53563 + 4.53563i) q^{67} +(4.68603 - 4.68603i) q^{69} +10.3984i q^{71} -9.24439 q^{73} +(-1.59719 + 1.59719i) q^{77} +15.4493 q^{79} -28.7280 q^{81} +(-0.683244 + 0.683244i) q^{83} -24.5271 q^{87} +5.44401i q^{89} +(-0.678140 + 0.678140i) q^{91} +(1.01258 - 1.01258i) q^{93} -5.54540i q^{97} +(-12.7234 - 12.7234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} + 8 q^{11} - 8 q^{19} + 24 q^{23} + 24 q^{27} + 16 q^{29} + 16 q^{37} - 8 q^{43} + 16 q^{49} + 32 q^{51} + 16 q^{53} - 8 q^{59} + 16 q^{61} - 40 q^{67} - 16 q^{69} + 16 q^{77} + 16 q^{79} - 16 q^{81} + 40 q^{83} - 32 q^{91} + 48 q^{93} - 8 q^{99}+O(q^{100}) \) 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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