LMFDB - Embedded newform 320.2.l.a.81.8

Error: no document with id 261596595 found in table mf_hecke_traces.

Error: table True does not exist

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [320,2,Mod(81,320)] 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("320.81"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(320, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	320.l (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.55521286468$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.8
Root			$1.38652 + 0.278517i$ of defining polynomial
Character	$\chi$	$=$	320.81
Dual form			320.2.l.a.241.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.32624 + 2.32624i) q^{3} +(0.707107 - 0.707107i) q^{5} -0.982011i q^{7} +7.82281i q^{9} +(1.62645 - 1.62645i) q^{11} +(-0.690562 - 0.690562i) q^{13} +3.28980 q^{15} -2.19577 q^{17} +(-1.92659 - 1.92659i) q^{19} +(2.28440 - 2.28440i) q^{21} +2.01442i q^{23} -1.00000i q^{25} +(-11.2190 + 11.2190i) q^{27} +(-5.27182 - 5.27182i) q^{29} -0.435286 q^{31} +7.56703 q^{33} +(-0.694387 - 0.694387i) q^{35} +(-5.79805 + 5.79805i) q^{37} -3.21283i q^{39} -3.93139i q^{41} +(0.507592 - 0.507592i) q^{43} +(5.53157 + 5.53157i) q^{45} +9.21960 q^{47} +6.03565 q^{49} +(-5.10789 - 5.10789i) q^{51} +(6.29357 - 6.29357i) q^{53} -2.30015i q^{55} -8.96345i q^{57} +(5.67778 - 5.67778i) q^{59} +(-3.60301 - 3.60301i) q^{61} +7.68209 q^{63} -0.976603 q^{65} +(-4.53563 - 4.53563i) q^{67} +(-4.68603 + 4.68603i) q^{69} +10.3984i q^{71} +9.24439i q^{73} +(2.32624 - 2.32624i) q^{75} +(-1.59719 - 1.59719i) q^{77} -15.4493 q^{79} -28.7280 q^{81} +(0.683244 + 0.683244i) q^{83} +(-1.55264 + 1.55264i) q^{85} -24.5271i q^{87} -5.44401i q^{89} +(-0.678140 + 0.678140i) q^{91} +(-1.01258 - 1.01258i) q^{93} -2.72461 q^{95} +5.54540 q^{97} +(12.7234 + 12.7234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{11} + 8 q^{15} + 8 q^{19} - 24 q^{27} - 16 q^{29} - 16 q^{37} - 8 q^{43} + 40 q^{47} - 16 q^{49} + 32 q^{51} + 16 q^{53} + 8 q^{59} + 16 q^{61} - 40 q^{63} - 40 q^{67} + 16 q^{69} + 16 q^{77}+ \cdots + 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^11 + 8 * q^15 + 8 * q^19 - 24 * q^27 - 16 * q^29 - 16 * q^37 - 8 * q^43 + 40 * q^47 - 16 * q^49 + 32 * q^51 + 16 * q^53 + 8 * q^59 + 16 * q^61 - 40 * q^63 - 40 * q^67 + 16 * q^69 + 16 * q^77 - 16 * q^79 - 16 * q^81 - 40 * q^83 - 16 * q^85 - 32 * q^91 - 48 * q^93 - 32 * q^95 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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	0.893000	+	0.450058i	$0.148597\pi$
$3$	2.32624	+	2.32624i	1.34306	+	1.34306i	0.450058	+	0.893000i	$0.351403\pi$
$4$		0			0
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$		−	0.982011i		−	0.371165i	−0.982629	−	0.185583i	$-0.940583\pi$
$7$		−	0.982011i		−	0.371165i	0.982629	−	0.185583i	$-0.0594172\pi$
$8$		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	$-0.293242\pi$
$13$	−0.690562	−	0.690562i	−0.191528	−	0.191528i	−0.796356	+	0.604828i	$0.793242\pi$
$14$		0			0
$15$	3.28980			0.849424
$16$		0			0
$17$	−2.19577			−0.532552			−0.266276	−	0.963897i	$-0.585793\pi$
$17$	−2.19577			−0.532552			−0.266276	+	0.963897i	$0.585793\pi$
$18$		0			0
$19$	−1.92659	−	1.92659i	−0.441991	−	0.441991i	0.450690	−	0.892681i	$-0.351178\pi$
$19$	−1.92659	−	1.92659i	−0.441991	−	0.441991i	−0.892681	+	0.450690i	$0.851178\pi$
$20$		0			0
$21$	2.28440	−	2.28440i	0.498496	−	0.498496i
$22$		0			0
$23$			2.01442i			0.420035i	0.977698	+	0.210018i	$0.0673522\pi$
$23$			2.01442i			0.420035i	−0.977698	+	0.210018i	$0.932648\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$	−11.2190	+	11.2190i	−2.15911	+	2.15911i
$28$		0			0
$29$	−5.27182	−	5.27182i	−0.978952	−	0.978952i	0.0208314	−	0.999783i	$-0.493369\pi$
$29$	−5.27182	−	5.27182i	−0.978952	−	0.978952i	−0.999783	+	0.0208314i	$0.993369\pi$
$30$		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
$33$	7.56703			1.31725
$34$		0			0
$35$	−0.694387	−	0.694387i	−0.117373	−	0.117373i
$36$		0			0
$37$	−5.79805	+	5.79805i	−0.953194	+	0.953194i	−0.998953	−	0.0457583i	$-0.985430\pi$
$37$	−5.79805	+	5.79805i	−0.953194	+	0.953194i	0.0457583	+	0.998953i	$0.485430\pi$
$38$		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	−0.667343	−	0.744750i	$-0.732569\pi$
$43$	0.507592	−	0.507592i	0.0774071	−	0.0774071i	0.744750	+	0.667343i	$0.232569\pi$
$44$		0			0
$45$	5.53157	+	5.53157i	0.824597	+	0.824597i
$46$		0			0
$47$	9.21960			1.34482			0.672409	−	0.740180i	$-0.265260\pi$
$47$	9.21960			1.34482			0.672409	+	0.740180i	$0.265260\pi$
$48$		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	−0.127367	−	0.991856i	$-0.540653\pi$
$53$	6.29357	−	6.29357i	0.864488	−	0.864488i	0.991856	+	0.127367i	$0.0406527\pi$
$54$		0			0
$55$		−	2.30015i		−	0.310152i
$56$		0			0
$57$		−	8.96345i		−	1.18724i
$58$		0			0
$59$	5.67778	−	5.67778i	0.739183	−	0.739183i	−0.233237	−	0.972420i	$-0.574932\pi$
$59$	5.67778	−	5.67778i	0.739183	−	0.739183i	0.972420	+	0.233237i	$0.0749317\pi$
$60$		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
$63$	7.68209			0.967852
$64$		0			0
$65$	−0.976603			−0.121133
$66$		0			0
$67$	−4.53563	−	4.53563i	−0.554116	−	0.554116i	0.373510	−	0.927626i	$-0.378154\pi$
$67$	−4.53563	−	4.53563i	−0.554116	−	0.554116i	−0.927626	+	0.373510i	$0.878154\pi$
$68$		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
$73$			9.24439i			1.08197i	0.841031	+	0.540987i	$0.181949\pi$
$73$			9.24439i			1.08197i	−0.841031	+	0.540987i	$0.818051\pi$
$74$		0			0
$75$	2.32624	−	2.32624i	0.268611	−	0.268611i
$76$		0			0
$77$	−1.59719	−	1.59719i	−0.182017	−	0.182017i
$78$		0			0
$79$	−15.4493			−1.73818			−0.869091	−	0.494653i	$-0.835295\pi$
$79$	−15.4493			−1.73818			−0.869091	+	0.494653i	$0.835295\pi$
$80$		0			0
$81$	−28.7280			−3.19200
$82$		0			0
$83$	0.683244	+	0.683244i	0.0749957	+	0.0749957i	0.743610	−	0.668614i	$-0.233112\pi$
$83$	0.683244	+	0.683244i	0.0749957	+	0.0749957i	−0.668614	+	0.743610i	$0.733112\pi$
$84$		0			0
$85$	−1.55264	+	1.55264i	−0.168408	+	0.168408i
$86$		0			0
$87$		−	24.5271i		−	2.62958i
$88$		0			0
$89$		−	5.44401i		−	0.577064i	−0.957470	−	0.288532i	$-0.906833\pi$
$89$		−	5.44401i		−	0.577064i	0.957470	−	0.288532i	$-0.0931672\pi$
$90$		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
$95$	−2.72461			−0.279540
$96$		0			0
$97$	5.54540			0.563050			0.281525	−	0.959554i	$-0.409160\pi$
$97$	5.54540			0.563050			0.281525	+	0.959554i	$0.409160\pi$
$98$		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
$103$			4.50219i			0.443614i	0.975091	+	0.221807i	$0.0711955\pi$
$103$			4.50219i			0.443614i	−0.975091	+	0.221807i	$0.928805\pi$
$104$		0			0
$105$		−	3.23062i		−	0.315277i
$106$		0			0
$107$	6.49890	−	6.49890i	0.628272	−	0.628272i	−0.319361	−	0.947633i	$-0.603468\pi$
$107$	6.49890	−	6.49890i	0.628272	−	0.628272i	0.947633	+	0.319361i	$0.103468\pi$
$108$		0			0
$109$	−2.51950	−	2.51950i	−0.241324	−	0.241324i	0.576074	−	0.817398i	$-0.304584\pi$
$109$	−2.51950	−	2.51950i	−0.241324	−	0.241324i	−0.817398	+	0.576074i	$0.804584\pi$
$110$		0			0
$111$	−26.9754			−2.56039
$112$		0			0
$113$	5.38101			0.506203			0.253102	−	0.967440i	$-0.418549\pi$
$113$	5.38101			0.506203			0.253102	+	0.967440i	$0.418549\pi$
$114$		0			0
$115$	1.42441	+	1.42441i	0.132827	+	0.132827i
$116$		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
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	−4.86578			−0.431768			−0.215884	−	0.976419i	$-0.569263\pi$
$127$	−4.86578			−0.431768			−0.215884	+	0.976419i	$0.569263\pi$
$128$		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
$135$			15.8661i			1.36554i
$136$		0			0
$137$			13.5567i			1.15822i	0.815248	+	0.579112i	$0.196601\pi$
$137$			13.5567i			1.15822i	−0.815248	+	0.579112i	$0.803399\pi$
$138$		0			0
$139$	−8.22645	+	8.22645i	−0.697758	+	0.697758i	−0.963927	−	0.266168i	$-0.914242\pi$
$139$	−8.22645	+	8.22645i	−0.697758	+	0.697758i	0.266168	+	0.963927i	$0.414242\pi$
$140$		0			0
$141$	21.4470	+	21.4470i	1.80617	+	1.80617i
$142$		0			0
$143$	−2.24633			−0.187847
$144$		0			0
$145$	−7.45547			−0.619143
$146$		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	$-0.488586\pi$
$149$	12.6363	−	12.6363i	1.03521	−	1.03521i	0.999357	−	0.0358519i	$-0.0114144\pi$
$150$		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
$153$		−	17.1771i		−	1.38869i
$154$		0			0
$155$	−0.307794	+	0.307794i	−0.0247226	+	0.0247226i
$156$		0			0
$157$	−1.75816	−	1.75816i	−0.140316	−	0.140316i	0.633460	−	0.773776i	$-0.281634\pi$
$157$	−1.75816	−	1.75816i	−0.140316	−	0.140316i	−0.773776	+	0.633460i	$0.781634\pi$
$158$		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	0.995576	+	0.0939562i	$0.0299514\pi$
$163$	13.9102	+	13.9102i	1.08953	+	1.08953i	0.0939562	+	0.995576i	$0.470049\pi$
$164$		0			0
$165$	5.35070	−	5.35070i	0.416551	−	0.416551i
$166$		0			0
$167$			18.8620i			1.45958i	0.683669	+	0.729792i	$0.260383\pi$
$167$			18.8620i			1.45958i	−0.683669	+	0.729792i	$0.739617\pi$
$168$		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	0.966933	+	0.255031i	$0.0820856\pi$
$173$	16.0724	+	16.0724i	1.22196	+	1.22196i	0.255031	+	0.966933i	$0.417914\pi$
$174$		0			0
$175$	−0.982011			−0.0742331
$176$		0			0
$177$	26.4158			1.98553
$178$		0			0
$179$	−16.4341	−	16.4341i	−1.22834	−	1.22834i	−0.964591	−	0.263749i	$-0.915041\pi$
$179$	−16.4341	−	16.4341i	−1.22834	−	1.22834i	−0.263749	−	0.964591i	$-0.584959\pi$
$180$		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
$183$		−	16.7629i		−	1.23915i
$184$		0			0
$185$			8.19969i			0.602853i
$186$		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
$193$	−11.2912			−0.812758			−0.406379	−	0.913705i	$-0.633209\pi$
$193$	−11.2912			−0.812758			−0.406379	+	0.913705i	$0.633209\pi$
$194$		0			0
$195$	−2.27182	−	2.27182i	−0.162688	−	0.162688i
$196$		0			0
$197$	−10.6152	+	10.6152i	−0.756302	+	0.756302i	−0.975647	−	0.219345i	$-0.929608\pi$
$197$	−10.6152	+	10.6152i	−0.756302	+	0.756302i	0.219345	+	0.975647i	$0.429608\pi$
$198$		0			0
$199$		−	4.68789i		−	0.332316i	−0.986099	−	0.166158i	$-0.946864\pi$
$199$		−	4.68789i		−	0.332316i	0.986099	−	0.166158i	$-0.0531361\pi$
$200$		0			0
$201$		−	21.1020i		−	1.48842i
$202$		0			0
$203$	−5.17698	+	5.17698i	−0.363353	+	0.363353i
$204$		0			0
$205$	−2.77991	−	2.77991i	−0.194157	−	0.194157i
$206$		0			0
$207$	−15.7584			−1.09529
$208$		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
$215$		−	0.717844i		−	0.0489565i
$216$		0			0
$217$			0.427456i			0.0290176i
$218$		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
$223$	−3.45644			−0.231461			−0.115730	−	0.993281i	$-0.536921\pi$
$223$	−3.45644			−0.231461			−0.115730	+	0.993281i	$0.536921\pi$
$224$		0			0
$225$	7.82281			0.521521
$226$		0			0
$227$	4.74550	+	4.74550i	0.314970	+	0.314970i	0.846831	−	0.531862i	$-0.178507\pi$
$227$	4.74550	+	4.74550i	0.314970	+	0.314970i	−0.531862	+	0.846831i	$0.678507\pi$
$228$		0			0
$229$	−13.3576	+	13.3576i	−0.882697	+	0.882697i	−0.993808	−	0.111111i	$-0.964559\pi$
$229$	−13.3576	+	13.3576i	−0.882697	+	0.882697i	0.111111	+	0.993808i	$0.464559\pi$
$230$		0			0
$231$		−	7.43091i		−	0.488918i
$232$		0			0
$233$			4.82691i			0.316222i	0.987421	+	0.158111i	$0.0505403\pi$
$233$			4.82691i			0.316222i	−0.987421	+	0.158111i	$0.949460\pi$
$234$		0			0
$235$	6.51924	−	6.51924i	0.425269	−	0.425269i
$236$		0			0
$237$	−35.9388	−	35.9388i	−2.33448	−	2.33448i
$238$		0			0
$239$	8.82497			0.570840			0.285420	−	0.958403i	$-0.407867\pi$
$239$	8.82497			0.570840			0.285420	+	0.958403i	$0.407867\pi$
$240$		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
$245$	4.26785	−	4.26785i	0.272663	−	0.272663i
$246$		0			0
$247$			2.66087i			0.169307i
$248$		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
$255$	−7.22365			−0.452362
$256$		0			0
$257$	−14.7662			−0.921091			−0.460545	−	0.887636i	$-0.652346\pi$
$257$	−14.7662			−0.921091			−0.460545	+	0.887636i	$0.652346\pi$
$258$		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
$263$		−	6.79486i		−	0.418989i	−0.977810	−	0.209494i	$-0.932818\pi$
$263$		−	6.79486i		−	0.418989i	0.977810	−	0.209494i	$-0.0671818\pi$
$264$		0			0
$265$		−	8.90045i		−	0.546750i
$266$		0			0
$267$	12.6641	−	12.6641i	0.775030	−	0.775030i
$268$		0			0
$269$	−6.03990	−	6.03990i	−0.368259	−	0.368259i	0.498583	−	0.866842i	$-0.333854\pi$
$269$	−6.03990	−	6.03990i	−0.368259	−	0.368259i	−0.866842	+	0.498583i	$0.833854\pi$
$270$		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
$273$	−3.15504			−0.190952
$274$		0			0
$275$	−1.62645	−	1.62645i	−0.0980785	−	0.0980785i
$276$		0			0
$277$	9.98018	−	9.98018i	0.599651	−	0.599651i	−0.340569	−	0.940220i	$-0.610620\pi$
$277$	9.98018	−	9.98018i	0.599651	−	0.599651i	0.940220	+	0.340569i	$0.110620\pi$
$278$		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	−0.217462	+	0.976069i	$0.569778\pi$
$283$	−20.0783	+	20.0783i	−1.19353	+	1.19353i	−0.976069	+	0.217462i	$0.930222\pi$
$284$		0			0
$285$	−6.33812	−	6.33812i	−0.375438	−	0.375438i
$286$		0			0
$287$	−3.86067			−0.227888
$288$		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	−0.0955279	−	0.995427i	$-0.530454\pi$
$293$	15.4038	−	15.4038i	0.899899	−	0.899899i	0.995427	+	0.0955279i	$0.0304539\pi$
$294$		0			0
$295$		−	8.02959i		−	0.467501i
$296$		0			0
$297$			36.4944i			2.11762i
$298$		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
$303$	−1.35524			−0.0778566
$304$		0			0
$305$	−5.09542			−0.291763
$306$		0			0
$307$	−9.12398	−	9.12398i	−0.520733	−	0.520733i	0.397060	−	0.917793i	$-0.370031\pi$
$307$	−9.12398	−	9.12398i	−0.520733	−	0.520733i	−0.917793	+	0.397060i	$0.870031\pi$
$308$		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
$313$			21.3775i			1.20833i	0.796860	+	0.604164i	$0.206493\pi$
$313$			21.3775i			1.20833i	−0.796860	+	0.604164i	$0.793507\pi$
$314$		0			0
$315$	5.43206	−	5.43206i	0.306062	−	0.306062i
$316$		0			0
$317$	8.66200	+	8.66200i	0.486507	+	0.486507i	0.907202	−	0.420695i	$-0.138214\pi$
$317$	8.66200	+	8.66200i	0.486507	+	0.486507i	−0.420695	+	0.907202i	$0.638214\pi$
$318$		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
$325$	−0.690562	+	0.690562i	−0.0383055	+	0.0383055i
$326$		0			0
$327$		−	11.7219i		−	0.648224i
$328$		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
$335$	−6.41435			−0.350454
$336$		0			0
$337$	30.7047			1.67259			0.836295	−	0.548280i	$-0.184717\pi$
$337$	30.7047			1.67259			0.836295	+	0.548280i	$0.184717\pi$
$338$		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
$343$		−	12.8012i		−	0.691197i
$344$		0			0
$345$			6.62705i			0.356788i
$346$		0			0
$347$	−13.6418	+	13.6418i	−0.732329	+	0.732329i	−0.971081	−	0.238752i	$-0.923262\pi$
$347$	−13.6418	+	13.6418i	−0.732329	+	0.732329i	0.238752	+	0.971081i	$0.423262\pi$
$348$		0			0
$349$	9.97321	+	9.97321i	0.533854	+	0.533854i	0.921717	−	0.387863i	$-0.126787\pi$
$349$	9.97321	+	9.97321i	0.533854	+	0.533854i	−0.387863	+	0.921717i	$0.626787\pi$
$350$		0			0
$351$	15.4949			0.827056
$352$		0			0
$353$	−26.7843			−1.42559			−0.712793	−	0.701374i	$-0.752570\pi$
$353$	−26.7843			−1.42559			−0.712793	+	0.701374i	$0.752570\pi$
$354$		0			0
$355$	7.35280	+	7.35280i	0.390246	+	0.390246i
$356$		0			0
$357$	−5.01601	+	5.01601i	−0.265475	+	0.265475i
$358$		0			0
$359$		−	19.1190i		−	1.00906i	−0.863393	−	0.504532i	$-0.831665\pi$
$359$		−	19.1190i		−	1.00906i	0.863393	−	0.504532i	$-0.168335\pi$
$360$		0			0
$361$		−	11.5765i		−	0.609288i
$362$		0			0
$363$	−13.2813	+	13.2813i	−0.697087	+	0.697087i
$364$		0			0
$365$	6.53677	+	6.53677i	0.342150	+	0.342150i
$366$		0			0
$367$	−4.24385			−0.221527			−0.110764	−	0.993847i	$-0.535330\pi$
$367$	−4.24385			−0.221527			−0.110764	+	0.993847i	$0.535330\pi$
$368$		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	0.280221	−	0.959935i	$-0.409592\pi$
$373$	23.9514	−	23.9514i	1.24016	−	1.24016i	0.959935	−	0.280221i	$-0.0904078\pi$
$374$		0			0
$375$		−	3.28980i		−	0.169885i
$376$		0			0
$377$			7.28104i			0.374992i
$378$		0			0
$379$	7.45685	−	7.45685i	0.383033	−	0.383033i	−0.489161	−	0.872194i	$-0.662697\pi$
$379$	7.45685	−	7.45685i	0.383033	−	0.383033i	0.872194	+	0.489161i	$0.162697\pi$
$380$		0			0
$381$	−11.3190	−	11.3190i	−0.579890	−	0.579890i
$382$		0			0
$383$	−5.19667			−0.265538			−0.132769	−	0.991147i	$-0.542387\pi$
$383$	−5.19667			−0.265538			−0.132769	+	0.991147i	$0.542387\pi$
$384$		0			0
$385$	−2.25877			−0.115117
$386$		0			0
$387$	3.97080	+	3.97080i	0.201847	+	0.201847i
$388$		0			0
$389$	10.3846	−	10.3846i	0.526522	−	0.526522i	−0.393011	−	0.919534i	$-0.628567\pi$
$389$	10.3846	−	10.3846i	0.526522	−	0.526522i	0.919534	+	0.393011i	$0.128567\pi$
$390$		0			0
$391$		−	4.42320i		−	0.223691i
$392$		0			0
$393$		−	37.2469i		−	1.87886i
$394$		0			0
$395$	−10.9243	+	10.9243i	−0.549661	+	0.549661i
$396$		0			0
$397$	9.93104	+	9.93104i	0.498425	+	0.498425i	0.910947	−	0.412523i	$-0.135352\pi$
$397$	9.93104	+	9.93104i	0.498425	+	0.498425i	−0.412523	+	0.910947i	$0.635352\pi$
$398$		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
$405$	−20.3138	+	20.3138i	−1.00940	+	1.00940i
$406$		0			0
$407$			18.8605i			0.934879i
$408$		0			0
$409$		−	4.81799i		−	0.238234i	−0.992880	−	0.119117i	$-0.961994\pi$
$409$		−	4.81799i		−	0.238234i	0.992880	−	0.119117i	$-0.0380064\pi$
$410$		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
$415$	0.966253			0.0474315
$416$		0			0
$417$	−38.2734			−1.87426
$418$		0			0
$419$	−21.4380	−	21.4380i	−1.04731	−	1.04731i	−0.998824	−	0.0484914i	$-0.984559\pi$
$419$	−21.4380	−	21.4380i	−1.04731	−	1.04731i	−0.0484914	−	0.998824i	$-0.515441\pi$
$420$		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
$423$			72.1232i			3.50675i
$424$		0			0
$425$			2.19577i			0.106510i
$426$		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
$433$	−1.50709			−0.0724259			−0.0362129	−	0.999344i	$-0.511529\pi$
$433$	−1.50709			−0.0724259			−0.0362129	+	0.999344i	$0.511529\pi$
$434$		0			0
$435$	−17.3432	−	17.3432i	−0.831545	−	0.831545i
$436$		0			0
$437$	3.88097	−	3.88097i	0.185652	−	0.185652i
$438$		0			0
$439$		−	10.3092i		−	0.492033i	−0.969266	−	0.246016i	$-0.920878\pi$
$439$		−	10.3092i		−	0.492033i	0.969266	−	0.246016i	$-0.0791217\pi$
$440$		0			0
$441$			47.2158i			2.24837i
$442$		0			0
$443$	14.2651	−	14.2651i	0.677755	−	0.677755i	−0.281736	−	0.959492i	$-0.590910\pi$
$443$	14.2651	−	14.2651i	0.677755	−	0.677755i	0.959492	+	0.281736i	$0.0909104\pi$
$444$		0			0
$445$	−3.84950	−	3.84950i	−0.182484	−	0.182484i
$446$		0			0
$447$	58.7904			2.78069
$448$		0			0
$449$	−19.5711			−0.923618			−0.461809	−	0.886979i	$-0.652799\pi$
$449$	−19.5711			−0.923618			−0.461809	+	0.886979i	$0.652799\pi$
$450$		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
$455$			0.959035i			0.0449602i
$456$		0			0
$457$		−	39.0185i		−	1.82521i	−0.408845	−	0.912604i	$-0.634068\pi$
$457$		−	39.0185i		−	1.82521i	0.408845	−	0.912604i	$-0.365932\pi$
$458$		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
$463$	14.9979			0.697009			0.348505	−	0.937307i	$-0.386690\pi$
$463$	14.9979			0.697009			0.348505	+	0.937307i	$0.386690\pi$
$464$		0			0
$465$	−1.43201			−0.0664077
$466$		0			0
$467$	−4.88870	−	4.88870i	−0.226222	−	0.226222i	0.584890	−	0.811112i	$-0.301138\pi$
$467$	−4.88870	−	4.88870i	−0.226222	−	0.226222i	−0.811112	+	0.584890i	$0.801138\pi$
$468$		0			0
$469$	−4.45404	+	4.45404i	−0.205669	+	0.205669i
$470$		0			0
$471$		−	8.17980i		−	0.376905i
$472$		0			0
$473$		−	1.65114i		−	0.0759197i
$474$		0			0
$475$	−1.92659	+	1.92659i	−0.0883982	+	0.0883982i
$476$		0			0
$477$	49.2334	+	49.2334i	2.25424	+	2.25424i
$478$		0			0
$479$	27.3381			1.24911			0.624555	−	0.780981i	$-0.285280\pi$
$479$	27.3381			1.24911			0.624555	+	0.780981i	$0.285280\pi$
$480$		0			0
$481$	8.00784			0.365126
$482$		0			0
$483$	4.60173	+	4.60173i	0.209386	+	0.209386i
$484$		0			0
$485$	3.92119	−	3.92119i	0.178052	−	0.178052i
$486$		0			0
$487$		−	35.4769i		−	1.60761i	−0.594892	−	0.803806i	$-0.702805\pi$
$487$		−	35.4769i		−	1.60761i	0.594892	−	0.803806i	$-0.297195\pi$
$488$		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
$495$	17.9936			0.808753
$496$		0			0
$497$	10.2114			0.458042
$498$		0			0
$499$	17.6521	+	17.6521i	0.790218	+	0.790218i	0.981529	−	0.191312i	$-0.0612742\pi$
$499$	17.6521	+	17.6521i	0.790218	+	0.790218i	−0.191312	+	0.981529i	$0.561274\pi$
$500$		0			0
$501$	−43.8776	+	43.8776i	−1.96031	+	1.96031i
$502$		0			0
$503$		−	31.8567i		−	1.42042i	−0.703990	−	0.710210i	$-0.748600\pi$
$503$		−	31.8567i		−	1.42042i	0.703990	−	0.710210i	$-0.251400\pi$
$504$		0			0
$505$			0.411952i			0.0183316i
$506$		0			0
$507$	28.0225	−	28.0225i	1.24452	−	1.24452i
$508$		0			0
$509$	−5.61054	−	5.61054i	−0.248683	−	0.248683i	0.571747	−	0.820430i	$-0.306266\pi$
$509$	−5.61054	−	5.61054i	−0.248683	−	0.248683i	−0.820430	+	0.571747i	$0.806266\pi$
$510$		0			0
$511$	9.07810			0.401591
$512$		0			0
$513$	43.2291			1.90861
$514$		0			0
$515$	3.18353	+	3.18353i	0.140283	+	0.140283i
$516$		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	−0.647806	−	0.761805i	$-0.724313\pi$
$523$	2.60707	−	2.60707i	0.113999	−	0.113999i	0.761805	+	0.647806i	$0.224313\pi$
$524$		0			0
$525$	−2.28440	−	2.28440i	−0.0996992	−	0.0996992i
$526$		0			0
$527$	0.955787			0.0416347
$528$		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
$535$		−	9.19083i		−	0.397354i
$536$		0			0
$537$		−	76.4593i		−	3.29946i
$538$		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
$543$	−71.8992			−3.08549
$544$		0			0
$545$	−3.56311			−0.152627
$546$		0			0
$547$	3.02284	+	3.02284i	0.129248	+	0.129248i	0.768771	−	0.639524i	$-0.220868\pi$
$547$	3.02284	+	3.02284i	0.129248	+	0.129248i	−0.639524	+	0.768771i	$0.720868\pi$
$548$		0			0
$549$	28.1857	−	28.1857i	1.20293	−	1.20293i
$550$		0			0
$551$			20.3133i			0.865375i
$552$		0			0
$553$			15.1714i			0.645153i
$554$		0			0
$555$	−19.0745	+	19.0745i	−0.809666	+	0.809666i
$556$		0			0
$557$	9.27495	+	9.27495i	0.392992	+	0.392992i	0.875753	−	0.482760i	$-0.160366\pi$
$557$	9.27495	+	9.27495i	0.392992	+	0.392992i	−0.482760	+	0.875753i	$0.660366\pi$
$558$		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	$-0.0431589\pi$
$563$	20.3025	+	20.3025i	0.855649	+	0.855649i	−0.135173	+	0.990822i	$0.543159\pi$
$564$		0			0
$565$	3.80495	−	3.80495i	0.160076	−	0.160076i
$566$		0			0
$567$			28.2112i			1.18476i
$568$		0			0
$569$			14.3362i			0.601005i	0.953781	+	0.300503i	$0.0971544\pi$
$569$			14.3362i			0.601005i	−0.953781	+	0.300503i	$0.902846\pi$
$570$		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
$575$	2.01442			0.0840071
$576$		0			0
$577$	−8.68179			−0.361428			−0.180714	−	0.983536i	$-0.557841\pi$
$577$	−8.68179			−0.361428			−0.180714	+	0.983536i	$0.557841\pi$
$578$		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
$583$		−	20.4723i		−	0.847877i
$584$		0			0
$585$		−	7.63978i		−	0.315866i
$586$		0			0
$587$	−21.9042	+	21.9042i	−0.904082	+	0.904082i	−0.995786	−	0.0917043i	$-0.970769\pi$
$587$	−21.9042	+	21.9042i	−0.904082	+	0.904082i	0.0917043	+	0.995786i	$0.470769\pi$
$588$		0			0
$589$	0.838619	+	0.838619i	0.0345547	+	0.0345547i
$590$		0			0
$591$	−49.3871			−2.03151
$592$		0			0
$593$	−17.5142			−0.719222			−0.359611	−	0.933102i	$-0.617091\pi$
$593$	−17.5142			−0.719222			−0.359611	+	0.933102i	$0.617091\pi$
$594$		0			0
$595$	1.52471	+	1.52471i	0.0625071	+	0.0625071i
$596$		0			0
$597$	10.9052	−	10.9052i	0.446319	−	0.446319i
$598$		0			0
$599$		−	19.0276i		−	0.777447i	−0.921354	−	0.388724i	$-0.872916\pi$
$599$		−	19.0276i		−	0.777447i	0.921354	−	0.388724i	$-0.127084\pi$
$600$		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
$605$	4.03711	+	4.03711i	0.164132	+	0.164132i
$606$		0			0
$607$	12.1064			0.491384			0.245692	−	0.969348i	$-0.420985\pi$
$607$	12.1064			0.491384			0.245692	+	0.969348i	$0.420985\pi$
$608$		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	−0.249218	−	0.968448i	$-0.580173\pi$
$613$	17.8073	−	17.8073i	0.719230	−	0.719230i	0.968448	+	0.249218i	$0.0801734\pi$
$614$		0			0
$615$		−	12.9335i		−	0.521529i
$616$		0			0
$617$			1.10944i			0.0446642i	0.999751	+	0.0223321i	$0.00710912\pi$
$617$			1.10944i			0.0446642i	−0.999751	+	0.0223321i	$0.992891\pi$
$618$		0			0
$619$	31.8702	−	31.8702i	1.28097	−	1.28097i	0.340859	−	0.940115i	$-0.389282\pi$
$619$	31.8702	−	31.8702i	1.28097	−	1.28097i	0.940115	−	0.340859i	$-0.110718\pi$
$620$		0			0
$621$	−22.5998	−	22.5998i	−0.906901	−	0.906901i
$622$		0			0
$623$	−5.34608			−0.214186
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		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
$633$			12.2460i			0.486736i
$634$		0			0
$635$	−3.44063	+	3.44063i	−0.136537	+	0.136537i
$636$		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	$-0.381662\pi$
$643$	−14.4137	−	14.4137i	−0.568422	−	0.568422i	−0.931686	+	0.363264i	$0.881662\pi$
$644$		0			0
$645$	1.66988	−	1.66988i	0.0657514	−	0.0657514i
$646$		0			0
$647$			20.5723i			0.808782i	0.914586	+	0.404391i	$0.132517\pi$
$647$			20.5723i			0.808782i	−0.914586	+	0.404391i	$0.867483\pi$
$648$		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	$-0.337408\pi$
$653$	−9.79946	−	9.79946i	−0.383482	−	0.383482i	−0.872355	+	0.488873i	$0.837408\pi$
$654$		0			0
$655$	−11.3219			−0.442384
$656$		0			0
$657$	−72.3172			−2.82136
$658$		0			0
$659$	8.70669	+	8.70669i	0.339165	+	0.339165i	0.856053	−	0.516888i	$-0.172910\pi$
$659$	8.70669	+	8.70669i	0.339165	+	0.339165i	−0.516888	+	0.856053i	$0.672910\pi$
$660$		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
$663$			7.05464i			0.273979i
$664$		0			0
$665$			2.67560i			0.103755i
$666$		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
$673$	−14.0829			−0.542857			−0.271429	−	0.962459i	$-0.587496\pi$
$673$	−14.0829			−0.542857			−0.271429	+	0.962459i	$0.587496\pi$
$674$		0			0
$675$	11.2190	+	11.2190i	0.431821	+	0.431821i
$676$		0			0
$677$	−29.8166	+	29.8166i	−1.14594	+	1.14594i	−0.158601	+	0.987343i	$0.550698\pi$
$677$	−29.8166	+	29.8166i	−1.14594	+	1.14594i	−0.987343	+	0.158601i	$0.949302\pi$
$678$		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	−0.437552	−	0.899193i	$-0.644155\pi$
$683$	12.0646	−	12.0646i	0.461641	−	0.461641i	0.899193	+	0.437552i	$0.144155\pi$
$684$		0			0
$685$	9.58601	+	9.58601i	0.366263	+	0.366263i
$686$		0			0
$687$	−62.1462			−2.37102
$688$		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
$695$			11.6340i			0.441301i
$696$		0			0
$697$			8.63242i			0.326976i
$698$		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
$703$	22.3410			0.842606
$704$		0			0
$705$	30.3307			1.14232
$706$		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	$0.631198\pi$
$709$	−35.0639	+	35.0639i	−1.31685	+	1.31685i	−0.916254	+	0.400598i	$0.868802\pi$
$710$		0			0
$711$		−	120.857i		−	4.53249i
$712$		0			0
$713$		−	0.876848i		−	0.0328382i
$714$		0			0
$715$	−1.58839	+	1.58839i	−0.0594026	+	0.0594026i
$716$		0			0
$717$	20.5290	+	20.5290i	0.766671	+	0.766671i
$718$		0			0
$719$	0.436840			0.0162914			0.00814568	−	0.999967i	$-0.497407\pi$
$719$	0.436840			0.0162914			0.00814568	+	0.999967i	$0.497407\pi$
$720$		0			0
$721$	4.42120			0.164654
$722$		0			0
$723$	−8.70356	−	8.70356i	−0.323689	−	0.323689i
$724$		0			0
$725$	−5.27182	+	5.27182i	−0.195790	+	0.195790i
$726$		0			0
$727$			38.8072i			1.43928i	0.694348	+	0.719640i	$0.255693\pi$
$727$			38.8072i			1.43928i	−0.694348	+	0.719640i	$0.744307\pi$
$728$		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	$-0.468922\pi$
$733$	−24.3059	−	24.3059i	−0.897758	−	0.897758i	−0.995238	+	0.0974793i	$0.968922\pi$
$734$		0			0
$735$	19.8561			0.732404
$736$		0			0
$737$	−14.7539			−0.543469
$738$		0			0
$739$	27.0262	+	27.0262i	0.994174	+	0.994174i	0.999983	−	0.00580951i	$-0.00184923\pi$
$739$	27.0262	+	27.0262i	0.994174	+	0.994174i	−0.00580951	+	0.999983i	$0.501849\pi$
$740$		0			0
$741$	−6.18982	+	6.18982i	−0.227389	+	0.227389i
$742$		0			0
$743$			12.1663i			0.446337i	0.974780	+	0.223169i	$0.0716401\pi$
$743$			12.1663i			0.446337i	−0.974780	+	0.223169i	$0.928360\pi$
$744$		0			0
$745$		−	17.8705i		−	0.654724i
$746$		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
$753$	27.8834			1.01613
$754$		0			0
$755$	10.7170	+	10.7170i	0.390033	+	0.390033i
$756$		0			0
$757$	−0.00399171	+	0.00399171i	−0.000145081	+	0.000145081i	−0.707179	−	0.707034i	$-0.750033\pi$
$757$	−0.00399171	+	0.00399171i	−0.000145081	+	0.000145081i	0.707034	+	0.707179i	$0.250033\pi$
$758$		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
$765$	−12.1460	−	12.1460i	−0.439141	−	0.439141i
$766$		0			0
$767$	−7.84172			−0.283148
$768$		0			0
$769$	35.4522			1.27844			0.639219	−	0.769025i	$-0.279258\pi$
$769$	35.4522			1.27844			0.639219	+	0.769025i	$0.279258\pi$
$770$		0			0
$771$	−34.3498	−	34.3498i	−1.23708	−	1.23708i
$772$		0			0
$773$	−5.50186	+	5.50186i	−0.197888	+	0.197888i	−0.799094	−	0.601206i	$-0.794687\pi$
$773$	−5.50186	+	5.50186i	−0.197888	+	0.197888i	0.601206	+	0.799094i	$0.294687\pi$
$774$		0			0
$775$			0.435286i			0.0156359i
$776$		0			0
$777$			26.4901i			0.950327i
$778$		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
$783$	118.289			4.22732
$784$		0			0
$785$	−2.48641			−0.0887438
$786$		0			0
$787$	−28.6944	−	28.6944i	−1.02284	−	1.02284i	−0.999733	−	0.0231107i	$-0.992643\pi$
$787$	−28.6944	−	28.6944i	−1.02284	−	1.02284i	−0.0231107	−	0.999733i	$-0.507357\pi$
$788$		0			0
$789$	15.8065	−	15.8065i	0.562726	−	0.562726i
$790$		0			0
$791$		−	5.28422i		−	0.187885i
$792$		0			0
$793$			4.97620i			0.176710i
$794$		0			0
$795$	20.7046	−	20.7046i	0.734317	−	0.734317i
$796$		0			0
$797$	−6.29277	−	6.29277i	−0.222901	−	0.222901i	0.586818	−	0.809719i	$-0.300381\pi$
$797$	−6.29277	−	6.29277i	−0.222901	−	0.222901i	−0.809719	+	0.586818i	$0.800381\pi$
$798$		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
$805$	1.39879	−	1.39879i	0.0493007	−	0.0493007i
$806$		0			0
$807$		−	28.1005i		−	0.989186i
$808$		0			0
$809$		−	27.0850i		−	0.952257i	−0.879376	−	0.476128i	$-0.842040\pi$
$809$		−	27.0850i		−	0.952257i	0.879376	−	0.476128i	$-0.157960\pi$
$810$		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
$815$	19.6720			0.689081
$816$		0			0
$817$	−1.95585			−0.0684264
$818$		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
$823$			7.64319i			0.266425i	0.991088	+	0.133212i	$0.0425292\pi$
$823$			7.64319i			0.266425i	−0.991088	+	0.133212i	$0.957471\pi$
$824$		0			0
$825$		−	7.56703i		−	0.263450i
$826$		0			0
$827$	0.781185	−	0.781185i	0.0271645	−	0.0271645i	−0.693394	−	0.720559i	$-0.743885\pi$
$827$	0.781185	−	0.781185i	0.0271645	−	0.0271645i	0.720559	+	0.693394i	$0.243885\pi$
$828$		0			0
$829$	28.9122	+	28.9122i	1.00416	+	1.00416i	0.999991	+	0.00417165i	$0.00132788\pi$
$829$	28.9122	+	28.9122i	1.00416	+	1.00416i	0.00417165	+	0.999991i	$0.498672\pi$
$830$		0			0
$831$	46.4326			1.61073
$832$		0			0
$833$	−13.2529			−0.459186
$834$		0			0
$835$	13.3374	+	13.3374i	0.461561	+	0.461561i
$836$		0			0
$837$	4.88349	−	4.88349i	0.168798	−	0.168798i
$838$		0			0
$839$			35.9665i			1.24170i	0.783928	+	0.620851i	$0.213213\pi$
$839$			35.9665i			1.24170i	−0.783928	+	0.620851i	$0.786787\pi$
$840$		0			0
$841$			26.5841i			0.916692i
$842$		0			0
$843$	−33.6400	+	33.6400i	−1.15862	+	1.15862i
$844$		0			0
$845$	−8.51798	−	8.51798i	−0.293028	−	0.293028i
$846$		0			0
$847$	5.60663			0.192646
$848$		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	−0.545798	−	0.837917i	$-0.683773\pi$
$853$	8.53167	−	8.53167i	0.292119	−	0.292119i	0.837917	+	0.545798i	$0.183773\pi$
$854$		0			0
$855$		−	21.3142i		−	0.728929i
$856$		0			0
$857$			20.6681i			0.706010i	0.935621	+	0.353005i	$0.114840\pi$
$857$			20.6681i			0.706010i	−0.935621	+	0.353005i	$0.885160\pi$
$858$		0			0
$859$	−26.6003	+	26.6003i	−0.907590	+	0.907590i	−0.996077	−	0.0884877i	$-0.971797\pi$
$859$	−26.6003	+	26.6003i	−0.907590	+	0.907590i	0.0884877	+	0.996077i	$0.471797\pi$
$860$		0			0
$861$	−8.98085	−	8.98085i	−0.306066	−	0.306066i
$862$		0			0
$863$	−24.2911			−0.826880			−0.413440	−	0.910531i	$-0.635673\pi$
$863$	−24.2911			−0.826880			−0.413440	+	0.910531i	$0.635673\pi$
$864$		0			0
$865$	22.7298			0.772838
$866$		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
$873$			43.3806i			1.46821i
$874$		0			0
$875$	−0.694387	+	0.694387i	−0.0234746	+	0.0234746i
$876$		0			0
$877$	−17.5305	−	17.5305i	−0.591963	−	0.591963i	0.346198	−	0.938161i	$-0.387472\pi$
$877$	−17.5305	−	17.5305i	−0.591963	−	0.591963i	−0.938161	+	0.346198i	$0.887472\pi$
$878$		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	$-0.391707\pi$
$883$	−18.0965	−	18.0965i	−0.608997	−	0.608997i	−0.942684	+	0.333687i	$0.891707\pi$
$884$		0			0
$885$	18.6788	−	18.6788i	0.627880	−	0.627880i
$886$		0			0
$887$			14.6666i			0.492455i	0.969212	+	0.246228i	$0.0791911\pi$
$887$			14.6666i			0.492455i	−0.969212	+	0.246228i	$0.920809\pi$
$888$		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
$895$	−23.2413			−0.776871
$896$		0			0
$897$	6.47199			0.216094
$898$		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
$903$		−	2.31908i		−	0.0771743i
$904$		0			0
$905$			21.8552i			0.726490i
$906$		0			0
$907$	25.4429	−	25.4429i	0.844817	−	0.844817i	−0.144664	−	0.989481i	$-0.546210\pi$
$907$	25.4429	−	25.4429i	0.844817	−	0.844817i	0.989481	+	0.144664i	$0.0462100\pi$
$908$		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
$913$	2.22252			0.0735547
$914$		0			0
$915$	−11.8532	−	11.8532i	−0.391854	−	0.391854i
$916$		0			0
$917$	−7.86179	+	7.86179i	−0.259619	+	0.259619i
$918$		0			0
$919$			46.2157i			1.52451i	0.647274	+	0.762257i	$0.275909\pi$
$919$			46.2157i			1.52451i	−0.647274	+	0.762257i	$0.724091\pi$
$920$		0			0
$921$		−	42.4492i		−	1.39875i
$922$		0			0
$923$	7.18076	−	7.18076i	0.236358	−	0.236358i
$924$		0			0
$925$	5.79805	+	5.79805i	0.190639	+	0.190639i
$926$		0			0
$927$	−35.2198			−1.15677
$928$		0			0
$929$	52.0543			1.70785			0.853923	−	0.520400i	$-0.174217\pi$
$929$	52.0543			1.70785			0.853923	+	0.520400i	$0.174217\pi$
$930$		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
$935$			5.05059i			0.165172i
$936$		0			0
$937$			33.7454i			1.10241i	0.834368	+	0.551207i	$0.185833\pi$
$937$			33.7454i			1.10241i	−0.834368	+	0.551207i	$0.814167\pi$
$938$		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
$943$	7.91946			0.257893
$944$		0			0
$945$	15.5807			0.506840
$946$		0			0
$947$	37.7582	+	37.7582i	1.22698	+	1.22698i	0.965102	+	0.261876i	$0.0843410\pi$
$947$	37.7582	+	37.7582i	1.22698	+	1.22698i	0.261876	+	0.965102i	$0.415659\pi$
$948$		0			0
$949$	6.38383	−	6.38383i	0.207228	−	0.207228i
$950$		0			0
$951$			40.2998i			1.30681i
$952$		0			0
$953$		−	48.6441i		−	1.57574i	−0.615844	−	0.787868i	$-0.711185\pi$
$953$		−	48.6441i		−	1.57574i	0.615844	−	0.787868i	$-0.288815\pi$
$954$		0			0
$955$	10.4562	−	10.4562i	0.338353	−	0.338353i
$956$		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
$965$	−7.98408	+	7.98408i	−0.257017	+	0.257017i
$966$		0			0
$967$		−	12.4521i		−	0.400433i	−0.979752	−	0.200216i	$-0.935835\pi$
$967$		−	12.4521i		−	0.400433i	0.979752	−	0.200216i	$-0.0641645\pi$
$968$		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
$975$	−3.21283			−0.102893
$976$		0			0
$977$	18.3144			0.585929			0.292965	−	0.956123i	$-0.405358\pi$
$977$	18.3144			0.585929			0.292965	+	0.956123i	$0.405358\pi$
$978$		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
$983$		−	27.0583i		−	0.863027i	−0.902107	−	0.431513i	$-0.857980\pi$
$983$		−	27.0583i		−	0.863027i	0.902107	−	0.431513i	$-0.142020\pi$
$984$		0			0
$985$			15.0122i			0.478328i
$986$		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
$993$	39.2642			1.24601
$994$		0			0
$995$	−3.31484	−	3.31484i	−0.105087	−	0.105087i
$996$		0			0
$997$	11.1158	−	11.1158i	0.352041	−	0.352041i	−0.508828	−	0.860868i	$-0.669921\pi$
$997$	11.1158	−	11.1158i	0.352041	−	0.352041i	0.860868	+	0.508828i	$0.169921\pi$
$998$		0			0
$999$		−	130.097i		−	4.11609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.2.l.a.81.8		16
3.2	odd	2		2880.2.t.c.721.2		16
4.3	odd	2		80.2.l.a.61.8	yes	16
5.2	odd	4		1600.2.q.g.849.8		16
5.3	odd	4		1600.2.q.h.849.1		16
5.4	even	2		1600.2.l.i.401.1		16
8.3	odd	2		640.2.l.b.161.8		16
8.5	even	2		640.2.l.a.161.1		16
12.11	even	2		720.2.t.c.541.1		16
16.3	odd	4		640.2.l.b.481.8		16
16.5	even	4	inner	320.2.l.a.241.8		16
16.11	odd	4		80.2.l.a.21.8	✓	16
16.13	even	4		640.2.l.a.481.1		16
20.3	even	4		400.2.q.g.349.6		16
20.7	even	4		400.2.q.h.349.3		16
20.19	odd	2		400.2.l.h.301.1		16
32.5	even	8		5120.2.a.t.1.1		8
32.11	odd	8		5120.2.a.s.1.1		8
32.21	even	8		5120.2.a.u.1.8		8
32.27	odd	8		5120.2.a.v.1.8		8
48.5	odd	4		2880.2.t.c.2161.3		16
48.11	even	4		720.2.t.c.181.1		16
80.27	even	4		400.2.q.g.149.6		16
80.37	odd	4		1600.2.q.h.49.1		16
80.43	even	4		400.2.q.h.149.3		16
80.53	odd	4		1600.2.q.g.49.8		16
80.59	odd	4		400.2.l.h.101.1		16
80.69	even	4		1600.2.l.i.1201.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.8	✓	16	16.11	odd	4
80.2.l.a.61.8	yes	16	4.3	odd	2
320.2.l.a.81.8		16	1.1	even	1	trivial
320.2.l.a.241.8		16	16.5	even	4	inner
400.2.l.h.101.1		16	80.59	odd	4
400.2.l.h.301.1		16	20.19	odd	2
400.2.q.g.149.6		16	80.27	even	4
400.2.q.g.349.6		16	20.3	even	4
400.2.q.h.149.3		16	80.43	even	4
400.2.q.h.349.3		16	20.7	even	4
640.2.l.a.161.1		16	8.5	even	2
640.2.l.a.481.1		16	16.13	even	4
640.2.l.b.161.8		16	8.3	odd	2
640.2.l.b.481.8		16	16.3	odd	4
720.2.t.c.181.1		16	48.11	even	4
720.2.t.c.541.1		16	12.11	even	2
1600.2.l.i.401.1		16	5.4	even	2
1600.2.l.i.1201.1		16	80.69	even	4
1600.2.q.g.49.8		16	80.53	odd	4
1600.2.q.g.849.8		16	5.2	odd	4
1600.2.q.h.49.1		16	80.37	odd	4
1600.2.q.h.849.1		16	5.3	odd	4
2880.2.t.c.721.2		16	3.2	odd	2
2880.2.t.c.2161.3		16	48.5	odd	4
5120.2.a.s.1.1		8	32.11	odd	8
5120.2.a.t.1.1		8	32.5	even	8
5120.2.a.u.1.8		8	32.21	even	8
5120.2.a.v.1.8		8	32.27	odd	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	320.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.32624 + 2.32624i) q^{3} +(0.707107 - 0.707107i) q^{5} -0.982011i q^{7} +7.82281i q^{9} +(1.62645 - 1.62645i) q^{11} +(-0.690562 - 0.690562i) q^{13} +3.28980 q^{15} -2.19577 q^{17} +(-1.92659 - 1.92659i) q^{19} +(2.28440 - 2.28440i) q^{21} +2.01442i q^{23} -1.00000i q^{25} +(-11.2190 + 11.2190i) q^{27} +(-5.27182 - 5.27182i) q^{29} -0.435286 q^{31} +7.56703 q^{33} +(-0.694387 - 0.694387i) q^{35} +(-5.79805 + 5.79805i) q^{37} -3.21283i q^{39} -3.93139i q^{41} +(0.507592 - 0.507592i) q^{43} +(5.53157 + 5.53157i) q^{45} +9.21960 q^{47} +6.03565 q^{49} +(-5.10789 - 5.10789i) q^{51} +(6.29357 - 6.29357i) q^{53} -2.30015i q^{55} -8.96345i q^{57} +(5.67778 - 5.67778i) q^{59} +(-3.60301 - 3.60301i) q^{61} +7.68209 q^{63} -0.976603 q^{65} +(-4.53563 - 4.53563i) q^{67} +(-4.68603 + 4.68603i) q^{69} +10.3984i q^{71} +9.24439i q^{73} +(2.32624 - 2.32624i) q^{75} +(-1.59719 - 1.59719i) q^{77} -15.4493 q^{79} -28.7280 q^{81} +(0.683244 + 0.683244i) q^{83} +(-1.55264 + 1.55264i) q^{85} -24.5271i q^{87} -5.44401i q^{89} +(-0.678140 + 0.678140i) q^{91} +(-1.01258 - 1.01258i) q^{93} -2.72461 q^{95} +5.54540 q^{97} +(12.7234 + 12.7234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{11} + 8 q^{15} + 8 q^{19} - 24 q^{27} - 16 q^{29} - 16 q^{37} - 8 q^{43} + 40 q^{47} - 16 q^{49} + 32 q^{51} + 16 q^{53} + 8 q^{59} + 16 q^{61} - 40 q^{63} - 40 q^{67} + 16 q^{69} + 16 q^{77}+ \cdots + 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^11 + 8 * q^15 + 8 * q^19 - 24 * q^27 - 16 * q^29 - 16 * q^37 - 8 * q^43 + 40 * q^47 - 16 * q^49 + 32 * q^51 + 16 * q^53 + 8 * q^59 + 16 * q^61 - 40 * q^63 - 40 * q^67 + 16 * q^69 + 16 * q^77 - 16 * q^79 - 16 * q^81 - 40 * q^83 - 16 * q^85 - 32 * q^91 - 48 * q^93 - 32 * q^95 + 8 * q^99

Introduction

L-functions

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