LMFDB - Embedded newform 1360.2.bt.d.1041.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1360,2,Mod(81,1360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1360, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1360.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1360 = 2^{4} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1360.bt (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:	$10.8596546749$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 83x^{8} + 152x^{6} + 111x^{4} + 22x^{2} + 1 $ x^12 + 18x^10 + 83x^8 + 152x^6 + 111x^4 + 22*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1041.3
Root			$-1.19804i$ of defining polynomial
Character	$\chi$	$=$	1360.1041
Dual form			1360.2.bt.d.81.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.140032 + 0.140032i) q^{3} +(0.707107 - 0.707107i) q^{5} +(1.33807 + 1.33807i) q^{7} +2.96078i q^{9} +(-2.49536 - 2.49536i) q^{11} +1.27324 q^{13} +0.198035i q^{15} +(3.68381 + 1.85190i) q^{17} +4.69149i q^{19} -0.374744 q^{21} +(0.406537 + 0.406537i) q^{23} -1.00000i q^{25} +(-0.834700 - 0.834700i) q^{27} +(-3.81711 + 3.81711i) q^{29} +(4.39574 - 4.39574i) q^{31} +0.698861 q^{33} +1.89231 q^{35} +(-6.00080 + 6.00080i) q^{37} +(-0.178294 + 0.178294i) q^{39} +(4.28894 + 4.28894i) q^{41} +9.16040i q^{43} +(2.09359 + 2.09359i) q^{45} +10.7932 q^{47} -3.41915i q^{49} +(-0.775177 + 0.256526i) q^{51} -9.90174i q^{53} -3.52898 q^{55} +(-0.656958 - 0.656958i) q^{57} -3.15903i q^{59} +(3.63666 + 3.63666i) q^{61} +(-3.96173 + 3.96173i) q^{63} +(0.900316 - 0.900316i) q^{65} -0.281859 q^{67} -0.113856 q^{69} +(-8.30385 + 8.30385i) q^{71} +(-6.95405 + 6.95405i) q^{73} +(0.140032 + 0.140032i) q^{75} -6.67793i q^{77} +(11.9789 + 11.9789i) q^{79} -8.64858 q^{81} -8.51139i q^{83} +(3.91434 - 1.29536i) q^{85} -1.06903i q^{87} +16.7227 q^{89} +(1.70368 + 1.70368i) q^{91} +1.23109i q^{93} +(3.31738 + 3.31738i) q^{95} +(4.18100 - 4.18100i) q^{97} +(7.38823 - 7.38823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} + 4 q^{11} + 12 q^{17} - 16 q^{21} - 12 q^{23} + 4 q^{27} - 12 q^{29} - 16 q^{33} - 16 q^{35} + 12 q^{37} + 20 q^{39} - 24 q^{41} + 8 q^{45} + 48 q^{47} - 32 q^{51} + 40 q^{61} - 12 q^{63}+ \cdots + 4 q^{97}+O(q^{100}) $ 12 * q + 4 * q^3 + 4 * q^11 + 12 * q^17 - 16 * q^21 - 12 * q^23 + 4 * q^27 - 12 * q^29 - 16 * q^33 - 16 * q^35 + 12 * q^37 + 20 * q^39 - 24 * q^41 + 8 * q^45 + 48 * q^47 - 32 * q^51 + 40 * q^61 - 12 * q^63 + 4 * q^65 + 8 * q^67 - 28 * q^71 - 48 * q^73 - 4 * q^75 + 8 * q^79 + 28 * q^81 - 4 * q^85 + 24 * q^89 + 36 * q^91 + 8 * q^95 + 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1360\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.140032	+	0.140032i	−0.0808475	+	0.0808475i	−0.746374	−	0.665527i	$-0.768207\pi$
$3$	−0.140032	+	0.140032i	−0.0808475	+	0.0808475i	0.665527	+	0.746374i	$0.268207\pi$
$4$		0			0
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$	1.33807	+	1.33807i	0.505742	+	0.505742i	0.913217	−	0.407475i	$-0.133591\pi$
$7$	1.33807	+	1.33807i	0.505742	+	0.505742i	−0.407475	+	0.913217i	$0.633591\pi$
$8$		0			0
$9$			2.96078i			0.986927i
$10$		0			0
$11$	−2.49536	−	2.49536i	−0.752381	−	0.752381i	0.222542	−	0.974923i	$-0.428564\pi$
$11$	−2.49536	−	2.49536i	−0.752381	−	0.752381i	−0.974923	+	0.222542i	$0.928564\pi$
$12$		0			0
$13$	1.27324			0.353133			0.176566	−	0.984289i	$-0.443501\pi$
$13$	1.27324			0.353133			0.176566	+	0.984289i	$0.443501\pi$
$14$		0			0
$15$			0.198035i			0.0511324i
$16$		0			0
$17$	3.68381	+	1.85190i	0.893455	+	0.449152i
$17$	3.68381	+	1.85190i	0.893455	+	0.449152i
$18$		0			0
$19$			4.69149i			1.07630i	0.842849	+	0.538151i	$0.180877\pi$
$19$			4.69149i			1.07630i	−0.842849	+	0.538151i	$0.819123\pi$
$20$		0			0
$21$	−0.374744			−0.0817759
$22$		0			0
$23$	0.406537	+	0.406537i	0.0847687	+	0.0847687i	0.748220	−	0.663451i	$-0.230909\pi$
$23$	0.406537	+	0.406537i	0.0847687	+	0.0847687i	−0.663451	+	0.748220i	$0.730909\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$	−0.834700	−	0.834700i	−0.160638	−	0.160638i
$28$		0			0
$29$	−3.81711	+	3.81711i	−0.708819	+	0.708819i	−0.966287	−	0.257468i	$-0.917112\pi$
$29$	−3.81711	+	3.81711i	−0.708819	+	0.708819i	0.257468	+	0.966287i	$0.417112\pi$
$30$		0			0
$31$	4.39574	−	4.39574i	0.789499	−	0.789499i	−0.191913	−	0.981412i	$-0.561469\pi$
$31$	4.39574	−	4.39574i	0.789499	−	0.789499i	0.981412	+	0.191913i	$0.0614691\pi$
$32$		0			0
$33$	0.698861			0.121656
$34$		0			0
$35$	1.89231			0.319859
$36$		0			0
$37$	−6.00080	+	6.00080i	−0.986526	+	0.986526i	−0.999910	−	0.0133844i	$-0.995739\pi$
$37$	−6.00080	+	6.00080i	−0.986526	+	0.986526i	0.0133844	+	0.999910i	$0.495739\pi$
$38$		0			0
$39$	−0.178294	+	0.178294i	−0.0285499	+	0.0285499i
$40$		0			0
$41$	4.28894	+	4.28894i	0.669819	+	0.669819i	0.957674	−	0.287855i	$-0.0929421\pi$
$41$	4.28894	+	4.28894i	0.669819	+	0.669819i	−0.287855	+	0.957674i	$0.592942\pi$
$42$		0			0
$43$			9.16040i			1.39695i	0.715635	+	0.698474i	$0.246137\pi$
$43$			9.16040i			1.39695i	−0.715635	+	0.698474i	$0.753863\pi$
$44$		0			0
$45$	2.09359	+	2.09359i	0.312094	+	0.312094i
$46$		0			0
$47$	10.7932			1.57434			0.787172	−	0.616734i	$-0.211545\pi$
$47$	10.7932			1.57434			0.787172	+	0.616734i	$0.211545\pi$
$48$		0			0
$49$		−	3.41915i		−	0.488450i
$50$		0			0
$51$	−0.775177	+	0.256526i	−0.108546	+	0.0359208i
$52$		0			0
$53$		−	9.90174i		−	1.36011i	−0.733162	−	0.680054i	$-0.761956\pi$
$53$		−	9.90174i		−	1.36011i	0.733162	−	0.680054i	$-0.238044\pi$
$54$		0			0
$55$	−3.52898			−0.475847
$56$		0			0
$57$	−0.656958	−	0.656958i	−0.0870163	−	0.0870163i
$58$		0			0
$59$		−	3.15903i		−	0.411270i	−0.978629	−	0.205635i	$-0.934074\pi$
$59$		−	3.15903i		−	0.411270i	0.978629	−	0.205635i	$-0.0659260\pi$
$60$		0			0
$61$	3.63666	+	3.63666i	0.465627	+	0.465627i	0.900495	−	0.434867i	$-0.143205\pi$
$61$	3.63666	+	3.63666i	0.465627	+	0.465627i	−0.434867	+	0.900495i	$0.643205\pi$
$62$		0			0
$63$	−3.96173	+	3.96173i	−0.499130	+	0.499130i
$64$		0			0
$65$	0.900316	−	0.900316i	0.111670	−	0.111670i
$66$		0			0
$67$	−0.281859			−0.0344345			−0.0172173	−	0.999852i	$-0.505481\pi$
$67$	−0.281859			−0.0344345			−0.0172173	+	0.999852i	$0.505481\pi$
$68$		0			0
$69$	−0.113856			−0.0137067
$70$		0			0
$71$	−8.30385	+	8.30385i	−0.985486	+	0.985486i	−0.999896	−	0.0144101i	$-0.995413\pi$
$71$	−8.30385	+	8.30385i	−0.985486	+	0.985486i	0.0144101	+	0.999896i	$0.495413\pi$
$72$		0			0
$73$	−6.95405	+	6.95405i	−0.813910	+	0.813910i	−0.985218	−	0.171308i	$-0.945201\pi$
$73$	−6.95405	+	6.95405i	−0.813910	+	0.813910i	0.171308	+	0.985218i	$0.445201\pi$
$74$		0			0
$75$	0.140032	+	0.140032i	0.0161695	+	0.0161695i
$76$		0			0
$77$		−	6.67793i		−	0.761021i
$78$		0			0
$79$	11.9789	+	11.9789i	1.34773	+	1.34773i	0.888126	+	0.459600i	$0.152007\pi$
$79$	11.9789	+	11.9789i	1.34773	+	1.34773i	0.459600	+	0.888126i	$0.347993\pi$
$80$		0			0
$81$	−8.64858			−0.960953
$82$		0			0
$83$		−	8.51139i		−	0.934246i	−0.884192	−	0.467123i	$-0.845291\pi$
$83$		−	8.51139i		−	0.934246i	0.884192	−	0.467123i	$-0.154709\pi$
$84$		0			0
$85$	3.91434	−	1.29536i	0.424570	−	0.140501i
$86$		0			0
$87$		−	1.06903i		−	0.114613i
$88$		0			0
$89$	16.7227			1.77260			0.886300	−	0.463112i	$-0.153267\pi$
$89$	16.7227			1.77260			0.886300	+	0.463112i	$0.153267\pi$
$90$		0			0
$91$	1.70368	+	1.70368i	0.178594	+	0.178594i
$92$		0			0
$93$			1.23109i			0.127658i
$94$		0			0
$95$	3.31738	+	3.31738i	0.340356	+	0.340356i
$96$		0			0
$97$	4.18100	−	4.18100i	0.424516	−	0.424516i	−0.462239	−	0.886755i	$-0.652954\pi$
$97$	4.18100	−	4.18100i	0.424516	−	0.424516i	0.886755	+	0.462239i	$0.152954\pi$
$98$		0			0
$99$	7.38823	−	7.38823i	0.742545	−	0.742545i
$100$		0			0
$101$	10.0971			1.00470			0.502348	−	0.864666i	$-0.332470\pi$
$101$	10.0971			1.00470			0.502348	+	0.864666i	$0.332470\pi$
$102$		0			0
$103$	1.07322			0.105747			0.0528736	−	0.998601i	$-0.483162\pi$
$103$	1.07322			0.105747			0.0528736	+	0.998601i	$0.483162\pi$
$104$		0			0
$105$	−0.264984	+	0.264984i	−0.0258598	+	0.0258598i
$106$		0			0
$107$	−4.48903	+	4.48903i	−0.433971	+	0.433971i	−0.889977	−	0.456006i	$-0.849280\pi$
$107$	−4.48903	+	4.48903i	−0.433971	+	0.433971i	0.456006	+	0.889977i	$0.349280\pi$
$108$		0			0
$109$	7.13161	+	7.13161i	0.683085	+	0.683085i	0.960694	−	0.277609i	$-0.0895421\pi$
$109$	7.13161	+	7.13161i	0.683085	+	0.683085i	−0.277609	+	0.960694i	$0.589542\pi$
$110$		0			0
$111$		−	1.68061i		−	0.159516i
$112$		0			0
$113$	−2.64734	−	2.64734i	−0.249041	−	0.249041i	0.571536	−	0.820577i	$-0.306348\pi$
$113$	−2.64734	−	2.64734i	−0.249041	−	0.249041i	−0.820577	+	0.571536i	$0.806348\pi$
$114$		0			0
$115$	0.574930			0.0536125
$116$		0			0
$117$			3.76978i			0.348516i
$118$		0			0
$119$	2.45122	+	7.40715i	0.224703	+	0.679013i
$120$		0			0
$121$			1.45368i			0.132153i
$122$		0			0
$123$	−1.20118			−0.108306
$124$		0			0
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$			12.8352i			1.13894i	0.822012	+	0.569470i	$0.192852\pi$
$127$			12.8352i			1.13894i	−0.822012	+	0.569470i	$0.807148\pi$
$128$		0			0
$129$	−1.28275	−	1.28275i	−0.112940	−	0.112940i
$130$		0			0
$131$	−4.96719	+	4.96719i	−0.433985	+	0.433985i	−0.889982	−	0.455996i	$-0.849283\pi$
$131$	−4.96719	+	4.96719i	−0.433985	+	0.433985i	0.455996	+	0.889982i	$0.349283\pi$
$132$		0			0
$133$	−6.27753	+	6.27753i	−0.544331	+	0.544331i
$134$		0			0
$135$	−1.18044			−0.101596
$136$		0			0
$137$	−15.1475			−1.29414			−0.647071	−	0.762430i	$-0.724006\pi$
$137$	−15.1475			−1.29414			−0.647071	+	0.762430i	$0.724006\pi$
$138$		0			0
$139$	8.79167	−	8.79167i	0.745700	−	0.745700i	−0.227969	−	0.973668i	$-0.573208\pi$
$139$	8.79167	−	8.79167i	0.745700	−	0.745700i	0.973668	+	0.227969i	$0.0732083\pi$
$140$		0			0
$141$	−1.51139	+	1.51139i	−0.127282	+	0.127282i
$142$		0			0
$143$	−3.17719	−	3.17719i	−0.265690	−	0.265690i
$144$		0			0
$145$			5.39821i			0.448297i
$146$		0			0
$147$	0.478791	+	0.478791i	0.0394900	+	0.0394900i
$148$		0			0
$149$	11.6094			0.951076			0.475538	−	0.879695i	$-0.342253\pi$
$149$	11.6094			0.951076			0.475538	+	0.879695i	$0.342253\pi$
$150$		0			0
$151$			1.31768i			0.107231i	0.998562	+	0.0536156i	$0.0170746\pi$
$151$			1.31768i			0.107231i	−0.998562	+	0.0536156i	$0.982925\pi$
$152$		0			0
$153$	−5.48307	+	10.9070i	−0.443280	+	0.881776i
$154$		0			0
$155$		−	6.21652i		−	0.499323i
$156$		0			0
$157$	−0.183886			−0.0146757			−0.00733783	−	0.999973i	$-0.502336\pi$
$157$	−0.183886			−0.0146757			−0.00733783	+	0.999973i	$0.502336\pi$
$158$		0			0
$159$	1.38656	+	1.38656i	0.109961	+	0.109961i
$160$		0			0
$161$			1.08795i			0.0857422i
$162$		0			0
$163$	−12.7635	−	12.7635i	−0.999718	−	0.999718i	0.000282311	−	1.00000i	$-0.499910\pi$
$163$	−12.7635	−	12.7635i	−0.999718	−	0.999718i	−1.00000		0.000282311i	$0.999910\pi$
$164$		0			0
$165$	0.494170	−	0.494170i	0.0384711	−	0.0384711i
$166$		0			0
$167$	5.35646	−	5.35646i	0.414495	−	0.414495i	−0.468806	−	0.883301i	$-0.655316\pi$
$167$	5.35646	−	5.35646i	0.414495	−	0.414495i	0.883301	+	0.468806i	$0.155316\pi$
$168$		0			0
$169$	−11.3789			−0.875297
$170$		0			0
$171$	−13.8905			−1.06223
$172$		0			0
$173$	−4.89485	+	4.89485i	−0.372149	+	0.372149i	−0.868259	−	0.496111i	$-0.834761\pi$
$173$	−4.89485	+	4.89485i	−0.372149	+	0.372149i	0.496111	+	0.868259i	$0.334761\pi$
$174$		0			0
$175$	1.33807	−	1.33807i	0.101148	−	0.101148i
$176$		0			0
$177$	0.442365	+	0.442365i	0.0332502	+	0.0332502i
$178$		0			0
$179$		−	10.2788i		−	0.768274i	−0.923276	−	0.384137i	$-0.874499\pi$
$179$		−	10.2788i		−	0.768274i	0.923276	−	0.384137i	$-0.125501\pi$
$180$		0			0
$181$	−14.1846	−	14.1846i	−1.05434	−	1.05434i	−0.998436	−	0.0558986i	$-0.982198\pi$
$181$	−14.1846	−	14.1846i	−1.05434	−	1.05434i	−0.0558986	−	0.998436i	$-0.517802\pi$
$182$		0			0
$183$	−1.01850			−0.0752896
$184$		0			0
$185$			8.48642i			0.623934i
$186$		0			0
$187$	−4.57128	−	13.8136i	−0.334285	−	1.01015i
$188$		0			0
$189$		−	2.23377i		−	0.162483i
$190$		0			0
$191$	−4.11140			−0.297491			−0.148745	−	0.988876i	$-0.547523\pi$
$191$	−4.11140			−0.297491			−0.148745	+	0.988876i	$0.547523\pi$
$192$		0			0
$193$	−10.1106	−	10.1106i	−0.727779	−	0.727779i	0.242398	−	0.970177i	$-0.422066\pi$
$193$	−10.1106	−	10.1106i	−0.727779	−	0.727779i	−0.970177	+	0.242398i	$0.922066\pi$
$194$		0			0
$195$			0.252146i			0.0180565i
$196$		0			0
$197$	3.78391	+	3.78391i	0.269593	+	0.269593i	0.828936	−	0.559343i	$-0.188947\pi$
$197$	3.78391	+	3.78391i	0.269593	+	0.269593i	−0.559343	+	0.828936i	$0.688947\pi$
$198$		0			0
$199$	−2.38613	+	2.38613i	−0.169148	+	0.169148i	−0.786605	−	0.617457i	$-0.788163\pi$
$199$	−2.38613	+	2.38613i	−0.169148	+	0.169148i	0.617457	+	0.786605i	$0.288163\pi$
$200$		0			0
$201$	0.0394692	−	0.0394692i	0.00278394	−	0.00278394i
$202$		0			0
$203$	−10.2151			−0.716959
$204$		0			0
$205$	6.06547			0.423631
$206$		0			0
$207$	−1.20367	+	1.20367i	−0.0836606	+	0.0836606i
$208$		0			0
$209$	11.7070	−	11.7070i	0.809788	−	0.809788i
$210$		0			0
$211$	1.66415	+	1.66415i	0.114565	+	0.114565i	0.762065	−	0.647500i	$-0.224186\pi$
$211$	1.66415	+	1.66415i	0.114565	+	0.114565i	−0.647500	+	0.762065i	$0.724186\pi$
$212$		0			0
$213$		−	2.32561i		−	0.159348i
$214$		0			0
$215$	6.47738	+	6.47738i	0.441754	+	0.441754i
$216$		0			0
$217$	11.7636			0.798565
$218$		0			0
$219$		−	1.94758i		−	0.131605i
$220$		0			0
$221$	4.69037	+	2.35791i	0.315508	+	0.158610i
$222$		0			0
$223$		−	3.45702i		−	0.231499i	−0.993278	−	0.115750i	$-0.963073\pi$
$223$		−	3.45702i		−	0.231499i	0.993278	−	0.115750i	$-0.0369270\pi$
$224$		0			0
$225$	2.96078			0.197385
$226$		0			0
$227$	−15.3558	−	15.3558i	−1.01920	−	1.01920i	−0.999812	−	0.0193889i	$-0.993828\pi$
$227$	−15.3558	−	15.3558i	−1.01920	−	1.01920i	−0.0193889	−	0.999812i	$-0.506172\pi$
$228$		0			0
$229$		−	8.59173i		−	0.567757i	−0.958860	−	0.283879i	$-0.908379\pi$
$229$		−	8.59173i		−	0.567757i	0.958860	−	0.283879i	$-0.0916213\pi$
$230$		0			0
$231$	0.935124	+	0.935124i	0.0615266	+	0.0615266i
$232$		0			0
$233$	6.29903	−	6.29903i	0.412663	−	0.412663i	−0.470002	−	0.882665i	$-0.655747\pi$
$233$	6.29903	−	6.29903i	0.412663	−	0.412663i	0.882665	+	0.470002i	$0.155747\pi$
$234$		0			0
$235$	7.63191	−	7.63191i	0.497851	−	0.497851i
$236$		0			0
$237$	−3.35484			−0.217921
$238$		0			0
$239$	12.3246			0.797212			0.398606	−	0.917122i	$-0.369494\pi$
$239$	12.3246			0.797212			0.398606	+	0.917122i	$0.369494\pi$
$240$		0			0
$241$	1.88979	−	1.88979i	0.121732	−	0.121732i	−0.643616	−	0.765348i	$-0.722567\pi$
$241$	1.88979	−	1.88979i	0.121732	−	0.121732i	0.765348	+	0.643616i	$0.222567\pi$
$242$		0			0
$243$	3.71518	−	3.71518i	0.238329	−	0.238329i
$244$		0			0
$245$	−2.41771	−	2.41771i	−0.154462	−	0.154462i
$246$		0			0
$247$			5.97338i			0.380077i
$248$		0			0
$249$	1.19187	+	1.19187i	0.0755315	+	0.0755315i
$250$		0			0
$251$	27.4415			1.73209			0.866046	−	0.499964i	$-0.166653\pi$
$251$	27.4415			1.73209			0.866046	+	0.499964i	$0.166653\pi$
$252$		0			0
$253$		−	2.02891i		−	0.127557i
$254$		0			0
$255$	−0.366741	+	0.729524i	−0.0229662	+	0.0456846i
$256$		0			0
$257$		−	22.8819i		−	1.42734i	−0.700484	−	0.713668i	$-0.747032\pi$
$257$		−	22.8819i		−	1.42734i	0.700484	−	0.713668i	$-0.252968\pi$
$258$		0			0
$259$	−16.0590			−0.997855
$260$		0			0
$261$	−11.3016	−	11.3016i	−0.699553	−	0.699553i
$262$		0			0
$263$		−	9.48703i		−	0.584995i	−0.956266	−	0.292498i	$-0.905514\pi$
$263$		−	9.48703i		−	0.584995i	0.956266	−	0.292498i	$-0.0944864\pi$
$264$		0			0
$265$	−7.00158	−	7.00158i	−0.430104	−	0.430104i
$266$		0			0
$267$	−2.34171	+	2.34171i	−0.143310	+	0.143310i
$268$		0			0
$269$	4.30494	−	4.30494i	0.262477	−	0.262477i	−0.563583	−	0.826060i	$-0.690577\pi$
$269$	4.30494	−	4.30494i	0.262477	−	0.262477i	0.826060	+	0.563583i	$0.190577\pi$
$270$		0			0
$271$	−23.6580			−1.43712			−0.718562	−	0.695463i	$-0.755199\pi$
$271$	−23.6580			−1.43712			−0.718562	+	0.695463i	$0.755199\pi$
$272$		0			0
$273$	−0.477139			−0.0288778
$274$		0			0
$275$	−2.49536	+	2.49536i	−0.150476	+	0.150476i
$276$		0			0
$277$	−5.82477	+	5.82477i	−0.349976	+	0.349976i	−0.860101	−	0.510124i	$-0.829599\pi$
$277$	−5.82477	+	5.82477i	−0.349976	+	0.349976i	0.510124	+	0.860101i	$0.329599\pi$
$278$		0			0
$279$	13.0148	+	13.0148i	0.779178	+	0.779178i
$280$		0			0
$281$		−	15.0835i		−	0.899808i	−0.893077	−	0.449904i	$-0.851458\pi$
$281$		−	15.0835i		−	0.899808i	0.893077	−	0.449904i	$-0.148542\pi$
$282$		0			0
$283$	−12.5516	−	12.5516i	−0.746115	−	0.746115i	0.227632	−	0.973747i	$-0.426902\pi$
$283$	−12.5516	−	12.5516i	−0.746115	−	0.746115i	−0.973747	+	0.227632i	$0.926902\pi$
$284$		0			0
$285$	−0.929079			−0.0550339
$286$		0			0
$287$			11.4778i			0.677511i
$288$		0			0
$289$	10.1409	+	13.6441i	0.596525	+	0.802594i
$290$		0			0
$291$			1.17095i			0.0686421i
$292$		0			0
$293$	10.9192			0.637907			0.318953	−	0.947770i	$-0.396669\pi$
$293$	10.9192			0.637907			0.318953	+	0.947770i	$0.396669\pi$
$294$		0			0
$295$	−2.23377	−	2.23377i	−0.130055	−	0.130055i
$296$		0			0
$297$			4.16576i			0.241722i
$298$		0			0
$299$	0.517618	+	0.517618i	0.0299346	+	0.0299346i
$300$		0			0
$301$	−12.2572	+	12.2572i	−0.706495	+	0.706495i
$302$		0			0
$303$	−1.41391	+	1.41391i	−0.0812272	+	0.0812272i
$304$		0			0
$305$	5.14302			0.294489
$306$		0			0
$307$	−6.82894			−0.389748			−0.194874	−	0.980828i	$-0.562430\pi$
$307$	−6.82894			−0.389748			−0.194874	+	0.980828i	$0.562430\pi$
$308$		0			0
$309$	−0.150285	+	0.150285i	−0.00854940	+	0.00854940i
$310$		0			0
$311$	−0.467408	+	0.467408i	−0.0265043	+	0.0265043i	−0.720235	−	0.693730i	$-0.755966\pi$
$311$	−0.467408	+	0.467408i	−0.0265043	+	0.0265043i	0.693730	+	0.720235i	$0.255966\pi$
$312$		0			0
$313$	−2.96511	−	2.96511i	−0.167598	−	0.167598i	0.618325	−	0.785923i	$-0.287812\pi$
$313$	−2.96511	−	2.96511i	−0.167598	−	0.167598i	−0.785923	+	0.618325i	$0.787812\pi$
$314$		0			0
$315$			5.60273i			0.315678i
$316$		0			0
$317$	−15.0370	−	15.0370i	−0.844564	−	0.844564i	0.144884	−	0.989449i	$-0.453719\pi$
$317$	−15.0370	−	15.0370i	−0.844564	−	0.844564i	−0.989449	+	0.144884i	$0.953719\pi$
$318$		0			0
$319$	19.0502			1.06660
$320$		0			0
$321$		−	1.25721i		−	0.0701709i
$322$		0			0
$323$	−8.68817	+	17.2826i	−0.483423	+	0.961627i
$324$		0			0
$325$		−	1.27324i		−	0.0706266i
$326$		0			0
$327$	−1.99731			−0.110451
$328$		0			0
$329$	14.4420	+	14.4420i	0.796211	+	0.796211i
$330$		0			0
$331$		−	27.7582i		−	1.52573i	−0.646559	−	0.762864i	$-0.723793\pi$
$331$		−	27.7582i		−	1.52573i	0.646559	−	0.762864i	$-0.276207\pi$
$332$		0			0
$333$	−17.7671	−	17.7671i	−0.973630	−	0.973630i
$334$		0			0
$335$	−0.199304	+	0.199304i	−0.0108891	+	0.0108891i
$336$		0			0
$337$	6.20814	−	6.20814i	0.338179	−	0.338179i	−0.517503	−	0.855682i	$-0.673138\pi$
$337$	6.20814	−	6.20814i	0.338179	−	0.338179i	0.855682	+	0.517503i	$0.173138\pi$
$338$		0			0
$339$	0.741426			0.0402687
$340$		0			0
$341$	−21.9380			−1.18801
$342$		0			0
$343$	13.9415	−	13.9415i	0.752772	−	0.752772i
$344$		0			0
$345$	−0.0805085	+	0.0805085i	−0.00433443	+	0.00433443i
$346$		0			0
$347$	−3.72663	−	3.72663i	−0.200056	−	0.200056i	0.599968	−	0.800024i	$-0.295180\pi$
$347$	−3.72663	−	3.72663i	−0.200056	−	0.200056i	−0.800024	+	0.599968i	$0.795180\pi$
$348$		0			0
$349$		−	10.8634i		−	0.581504i	−0.956799	−	0.290752i	$-0.906095\pi$
$349$		−	10.8634i		−	0.581504i	0.956799	−	0.290752i	$-0.0939054\pi$
$350$		0			0
$351$	−1.06277	−	1.06277i	−0.0567266	−	0.0567266i
$352$		0			0
$353$	−27.2304			−1.44933			−0.724664	−	0.689102i	$-0.758005\pi$
$353$	−27.2304			−1.44933			−0.724664	+	0.689102i	$0.758005\pi$
$354$		0			0
$355$			11.7434i			0.623276i
$356$		0			0
$357$	−1.38049	−	0.693989i	−0.0730631	−	0.0367298i
$358$		0			0
$359$		−	13.0217i		−	0.687258i	−0.939105	−	0.343629i	$-0.888344\pi$
$359$		−	13.0217i		−	0.687258i	0.939105	−	0.343629i	$-0.111656\pi$
$360$		0			0
$361$	−3.01006			−0.158424
$362$		0			0
$363$	−0.203562	−	0.203562i	−0.0106842	−	0.0106842i
$364$		0			0
$365$			9.83451i			0.514762i
$366$		0			0
$367$	−11.8536	−	11.8536i	−0.618755	−	0.618755i	0.326457	−	0.945212i	$-0.394145\pi$
$367$	−11.8536	−	11.8536i	−0.618755	−	0.618755i	−0.945212	+	0.326457i	$0.894145\pi$
$368$		0			0
$369$	−12.6986	+	12.6986i	−0.661063	+	0.661063i
$370$		0			0
$371$	13.2492	−	13.2492i	0.687864	−	0.687864i
$372$		0			0
$373$	1.14057			0.0590567			0.0295283	−	0.999564i	$-0.490599\pi$
$373$	1.14057			0.0590567			0.0295283	+	0.999564i	$0.490599\pi$
$374$		0			0
$375$	0.198035			0.0102265
$376$		0			0
$377$	−4.86009	+	4.86009i	−0.250307	+	0.250307i
$378$		0			0
$379$	−6.20062	+	6.20062i	−0.318504	+	0.318504i	−0.848192	−	0.529688i	$-0.822309\pi$
$379$	−6.20062	+	6.20062i	−0.318504	+	0.318504i	0.529688	+	0.848192i	$0.322309\pi$
$380$		0			0
$381$	−1.79734	−	1.79734i	−0.0920805	−	0.0920805i
$382$		0			0
$383$			11.9977i			0.613053i	0.951862	+	0.306526i	$0.0991668\pi$
$383$			11.9977i			0.613053i	−0.951862	+	0.306526i	$0.900833\pi$
$384$		0			0
$385$	−4.72201	−	4.72201i	−0.240656	−	0.240656i
$386$		0			0
$387$	−27.1220			−1.37869
$388$		0			0
$389$		−	0.165600i		−	0.00839627i	−0.999991	−	0.00419813i	$-0.998664\pi$
$389$		−	0.165600i		−	0.00839627i	0.999991	−	0.00419813i	$-0.00133631\pi$
$390$		0			0
$391$	0.744739	+	2.25047i	0.0376631	+	0.113811i
$392$		0			0
$393$		−	1.39113i		−	0.0701733i
$394$		0			0
$395$	16.9407			0.852377
$396$		0			0
$397$	21.5282	+	21.5282i	1.08047	+	1.08047i	0.996465	+	0.0840060i	$0.0267715\pi$
$397$	21.5282	+	21.5282i	1.08047	+	1.08047i	0.0840060	+	0.996465i	$0.473228\pi$
$398$		0			0
$399$		−	1.75811i		−	0.0880155i
$400$		0			0
$401$	−26.0214	−	26.0214i	−1.29945	−	1.29945i	−0.928757	−	0.370690i	$-0.879121\pi$
$401$	−26.0214	−	26.0214i	−1.29945	−	1.29945i	−0.370690	−	0.928757i	$-0.620879\pi$
$402$		0			0
$403$	5.59683	−	5.59683i	0.278798	−	0.278798i
$404$		0			0
$405$	−6.11547	+	6.11547i	−0.303880	+	0.303880i
$406$		0			0
$407$	29.9484			1.48449
$408$		0			0
$409$	7.05575			0.348885			0.174442	−	0.984667i	$-0.444188\pi$
$409$	7.05575			0.348885			0.174442	+	0.984667i	$0.444188\pi$
$410$		0			0
$411$	2.12114	−	2.12114i	0.104628	−	0.104628i
$412$		0			0
$413$	4.22699	−	4.22699i	0.207997	−	0.207997i
$414$		0			0
$415$	−6.01846	−	6.01846i	−0.295435	−	0.295435i
$416$		0			0
$417$			2.46223i			0.120576i
$418$		0			0
$419$	−9.53560	−	9.53560i	−0.465844	−	0.465844i	0.434721	−	0.900565i	$-0.356847\pi$
$419$	−9.53560	−	9.53560i	−0.465844	−	0.465844i	−0.900565	+	0.434721i	$0.856847\pi$
$420$		0			0
$421$	11.9003			0.579984			0.289992	−	0.957029i	$-0.406347\pi$
$421$	11.9003			0.579984			0.289992	+	0.957029i	$0.406347\pi$
$422$		0			0
$423$			31.9562i			1.55376i
$424$		0			0
$425$	1.85190	−	3.68381i	0.0898304	−	0.178691i
$426$		0			0
$427$			9.73220i			0.470974i
$428$		0			0
$429$	0.889817			0.0429608
$430$		0			0
$431$	8.47563	+	8.47563i	0.408257	+	0.408257i	0.881130	−	0.472874i	$-0.156783\pi$
$431$	8.47563	+	8.47563i	0.408257	+	0.408257i	−0.472874	+	0.881130i	$0.656783\pi$
$432$		0			0
$433$		−	7.39430i		−	0.355347i	−0.984089	−	0.177674i	$-0.943143\pi$
$433$		−	7.39430i		−	0.355347i	0.984089	−	0.177674i	$-0.0568572\pi$
$434$		0			0
$435$	−0.755922	−	0.755922i	−0.0362437	−	0.0362437i
$436$		0			0
$437$	−1.90726	+	1.90726i	−0.0912367	+	0.0912367i
$438$		0			0
$439$	−22.3750	+	22.3750i	−1.06790	+	1.06790i	−0.0703785	+	0.997520i	$0.522421\pi$
$439$	−22.3750	+	22.3750i	−1.06790	+	1.06790i	−0.997520	+	0.0703785i	$0.977579\pi$
$440$		0			0
$441$	10.1234			0.482065
$442$		0			0
$443$	−35.6597			−1.69424			−0.847121	−	0.531401i	$-0.821666\pi$
$443$	−35.6597			−1.69424			−0.847121	+	0.531401i	$0.821666\pi$
$444$		0			0
$445$	11.8247	−	11.8247i	0.560545	−	0.560545i
$446$		0			0
$447$	−1.62568	+	1.62568i	−0.0768921	+	0.0768921i
$448$		0			0
$449$	−0.824876	−	0.824876i	−0.0389283	−	0.0389283i	0.687375	−	0.726303i	$-0.258763\pi$
$449$	−0.824876	−	0.824876i	−0.0389283	−	0.0389283i	−0.726303	+	0.687375i	$0.758763\pi$
$450$		0			0
$451$		−	21.4049i		−	1.00792i
$452$		0			0
$453$	−0.184517	−	0.184517i	−0.00866938	−	0.00866938i
$454$		0			0
$455$	2.40937			0.112953
$456$		0			0
$457$			37.6351i			1.76050i	0.474514	+	0.880248i	$0.342624\pi$
$457$			37.6351i			1.76050i	−0.474514	+	0.880248i	$0.657376\pi$
$458$		0			0
$459$	−1.52910	−	4.62066i	−0.0713721	−	0.215674i
$460$		0			0
$461$			22.0741i			1.02809i	0.857763	+	0.514046i	$0.171854\pi$
$461$			22.0741i			1.02809i	−0.857763	+	0.514046i	$0.828146\pi$
$462$		0			0
$463$	−11.0361			−0.512893			−0.256447	−	0.966558i	$-0.582552\pi$
$463$	−11.0361			−0.512893			−0.256447	+	0.966558i	$0.582552\pi$
$464$		0			0
$465$	0.870512	+	0.870512i	0.0403690	+	0.0403690i
$466$		0			0
$467$		−	22.0407i		−	1.01992i	−0.860198	−	0.509960i	$-0.829660\pi$
$467$		−	22.0407i		−	1.01992i	0.860198	−	0.509960i	$-0.170340\pi$
$468$		0			0
$469$	−0.377146	−	0.377146i	−0.0174150	−	0.0174150i
$470$		0			0
$471$	0.0257499	−	0.0257499i	0.00118649	−	0.00118649i
$472$		0			0
$473$	22.8585	−	22.8585i	1.05104	−	1.05104i
$474$		0			0
$475$	4.69149			0.215260
$476$		0			0
$477$	29.3169			1.34233
$478$		0			0
$479$	22.1659	−	22.1659i	1.01279	−	1.01279i	0.0128704	−	0.999917i	$-0.495903\pi$
$479$	22.1659	−	22.1659i	1.01279	−	1.01279i	0.999917	−	0.0128704i	$-0.00409688\pi$
$480$		0			0
$481$	−7.64045	+	7.64045i	−0.348375	+	0.348375i
$482$		0			0
$483$	−0.152347	−	0.152347i	−0.00693204	−	0.00693204i
$484$		0			0
$485$		−	5.91282i		−	0.268487i
$486$		0			0
$487$	1.89382	+	1.89382i	0.0858170	+	0.0858170i	0.748712	−	0.662895i	$-0.230673\pi$
$487$	1.89382	+	1.89382i	0.0858170	+	0.0858170i	−0.662895	+	0.748712i	$0.730673\pi$
$488$		0			0
$489$	3.57461			0.161649
$490$		0			0
$491$			19.7985i			0.893496i	0.894660	+	0.446748i	$0.147418\pi$
$491$			19.7985i			0.893496i	−0.894660	+	0.446748i	$0.852582\pi$
$492$		0			0
$493$	−21.1304	+	6.99260i	−0.951666	+	0.314931i
$494$		0			0
$495$		−	10.4485i		−	0.469627i
$496$		0			0
$497$	−22.2222			−0.996803
$498$		0			0
$499$	19.5941	+	19.5941i	0.877152	+	0.877152i	0.993239	−	0.116087i	$-0.0370351\pi$
$499$	19.5941	+	19.5941i	0.877152	+	0.877152i	−0.116087	+	0.993239i	$0.537035\pi$
$500$		0			0
$501$			1.50015i			0.0670218i
$502$		0			0
$503$	−2.90654	−	2.90654i	−0.129596	−	0.129596i	0.639333	−	0.768930i	$-0.279210\pi$
$503$	−2.90654	−	2.90654i	−0.129596	−	0.129596i	−0.768930	+	0.639333i	$0.779210\pi$
$504$		0			0
$505$	7.13971	−	7.13971i	0.317713	−	0.317713i
$506$		0			0
$507$	1.59340	−	1.59340i	0.0707656	−	0.0707656i
$508$		0			0
$509$	41.9347			1.85872			0.929362	−	0.369169i	$-0.120358\pi$
$509$	41.9347			1.85872			0.929362	+	0.369169i	$0.120358\pi$
$510$		0			0
$511$	−18.6100			−0.823256
$512$		0			0
$513$	3.91599	−	3.91599i	0.172895	−	0.172895i
$514$		0			0
$515$	0.758880	−	0.758880i	0.0334402	−	0.0334402i
$516$		0			0
$517$	−26.9328	−	26.9328i	−1.18451	−	1.18451i
$518$		0			0
$519$		−	1.37087i		−	0.0601746i
$520$		0			0
$521$	25.0405	+	25.0405i	1.09705	+	1.09705i	0.994754	+	0.102292i	$0.0326176\pi$
$521$	25.0405	+	25.0405i	1.09705	+	1.09705i	0.102292	+	0.994754i	$0.467382\pi$
$522$		0			0
$523$	−6.37043			−0.278560			−0.139280	−	0.990253i	$-0.544479\pi$
$523$	−6.37043			−0.278560			−0.139280	+	0.990253i	$0.544479\pi$
$524$		0			0
$525$			0.374744i			0.0163552i
$526$		0			0
$527$	24.3336	−	8.05261i	1.05999	−	0.350777i
$528$		0			0
$529$		−	22.6695i		−	0.985629i
$530$		0			0
$531$	9.35319			0.405894
$532$		0			0
$533$	5.46084	+	5.46084i	0.236535	+	0.236535i
$534$		0			0
$535$			6.34844i			0.274467i
$536$		0			0
$537$	1.43936	+	1.43936i	0.0621130	+	0.0621130i
$538$		0			0
$539$	−8.53203	+	8.53203i	−0.367501	+	0.367501i
$540$		0			0
$541$	−11.5578	+	11.5578i	−0.496908	+	0.496908i	−0.910474	−	0.413566i	$-0.864283\pi$
$541$	−11.5578	+	11.5578i	−0.496908	+	0.496908i	0.413566	+	0.910474i	$0.364283\pi$
$542$		0			0
$543$	3.97260			0.170481
$544$		0			0
$545$	10.0856			0.432021
$546$		0			0
$547$	0.909839	−	0.909839i	0.0389019	−	0.0389019i	−0.687388	−	0.726290i	$-0.741243\pi$
$547$	0.909839	−	0.909839i	0.0389019	−	0.0389019i	0.726290	+	0.687388i	$0.241243\pi$
$548$		0			0
$549$	−10.7674	+	10.7674i	−0.459540	+	0.459540i
$550$		0			0
$551$	−17.9079	−	17.9079i	−0.762903	−	0.762903i
$552$		0			0
$553$			32.0570i			1.36320i
$554$		0			0
$555$	−1.18837	−	1.18837i	−0.0504435	−	0.0504435i
$556$		0			0
$557$	35.2859			1.49511			0.747555	−	0.664200i	$-0.231227\pi$
$557$	35.2859			1.49511			0.747555	+	0.664200i	$0.231227\pi$
$558$		0			0
$559$			11.6634i			0.493308i
$560$		0			0
$561$	2.57447	+	1.29422i	0.108694	+	0.0546421i
$562$		0			0
$563$		−	0.931153i		−	0.0392434i	−0.999807	−	0.0196217i	$-0.993754\pi$
$563$		−	0.931153i		−	0.0392434i	0.999807	−	0.0196217i	$-0.00624618\pi$
$564$		0			0
$565$	−3.74391			−0.157507
$566$		0			0
$567$	−11.5724	−	11.5724i	−0.485994	−	0.485994i
$568$		0			0
$569$			17.5921i			0.737498i	0.929529	+	0.368749i	$0.120214\pi$
$569$			17.5921i			0.737498i	−0.929529	+	0.368749i	$0.879786\pi$
$570$		0			0
$571$	12.2000	+	12.2000i	0.510554	+	0.510554i	0.914696	−	0.404142i	$-0.132430\pi$
$571$	12.2000	+	12.2000i	0.510554	+	0.510554i	−0.404142	+	0.914696i	$0.632430\pi$
$572$		0			0
$573$	0.575728	−	0.575728i	0.0240514	−	0.0240514i
$574$		0			0
$575$	0.406537	−	0.406537i	0.0169537	−	0.0169537i
$576$		0			0
$577$	8.50534			0.354082			0.177041	−	0.984203i	$-0.443347\pi$
$577$	8.50534			0.354082			0.177041	+	0.984203i	$0.443347\pi$
$578$		0			0
$579$	2.83162			0.117678
$580$		0			0
$581$	11.3888	−	11.3888i	0.472487	−	0.472487i
$582$		0			0
$583$	−24.7084	+	24.7084i	−1.02332	+	1.02332i
$584$		0			0
$585$	2.66564	+	2.66564i	0.110211	+	0.110211i
$586$		0			0
$587$			1.55649i			0.0642433i	0.999484	+	0.0321217i	$0.0102264\pi$
$587$			1.55649i			0.0642433i	−0.999484	+	0.0321217i	$0.989774\pi$
$588$		0			0
$589$	20.6226	+	20.6226i	0.849739	+	0.849739i
$590$		0			0
$591$	−1.05974			−0.0435918
$592$		0			0
$593$			19.6862i			0.808415i	0.914667	+	0.404207i	$0.132453\pi$
$593$			19.6862i			0.808415i	−0.914667	+	0.404207i	$0.867547\pi$
$594$		0			0
$595$	6.97092	+	3.50437i	0.285780	+	0.143665i
$596$		0			0
$597$		−	0.668269i		−	0.0273504i
$598$		0			0
$599$	24.7552			1.01147			0.505735	−	0.862689i	$-0.331221\pi$
$599$	24.7552			1.01147			0.505735	+	0.862689i	$0.331221\pi$
$600$		0			0
$601$	−20.0336	−	20.0336i	−0.817186	−	0.817186i	0.168513	−	0.985699i	$-0.446103\pi$
$601$	−20.0336	−	20.0336i	−0.817186	−	0.817186i	−0.985699	+	0.168513i	$0.946103\pi$
$602$		0			0
$603$		−	0.834522i		−	0.0339844i
$604$		0			0
$605$	1.02791	+	1.02791i	0.0417904	+	0.0417904i
$606$		0			0
$607$	−32.9490	+	32.9490i	−1.33736	+	1.33736i	−0.438750	+	0.898609i	$0.644579\pi$
$607$	−32.9490	+	32.9490i	−1.33736	+	1.33736i	−0.898609	+	0.438750i	$0.855421\pi$
$608$		0			0
$609$	1.43044	−	1.43044i	0.0579644	−	0.0579644i
$610$		0			0
$611$	13.7423			0.555952
$612$		0			0
$613$	−42.0358			−1.69781			−0.848905	−	0.528546i	$-0.822737\pi$
$613$	−42.0358			−1.69781			−0.848905	+	0.528546i	$0.822737\pi$
$614$		0			0
$615$	−0.849360	+	0.849360i	−0.0342495	+	0.0342495i
$616$		0			0
$617$	12.8737	−	12.8737i	0.518275	−	0.518275i	−0.398774	−	0.917049i	$-0.630564\pi$
$617$	12.8737	−	12.8737i	0.518275	−	0.518275i	0.917049	+	0.398774i	$0.130564\pi$
$618$		0			0
$619$	9.74184	+	9.74184i	0.391558	+	0.391558i	0.875242	−	0.483685i	$-0.160702\pi$
$619$	9.74184	+	9.74184i	0.391558	+	0.391558i	−0.483685	+	0.875242i	$0.660702\pi$
$620$		0			0
$621$		−	0.678672i		−	0.0272342i
$622$		0			0
$623$	22.3761	+	22.3761i	0.896478	+	0.896478i
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$			3.27870i			0.130939i
$628$		0			0
$629$	−33.2187	+	10.9929i	−1.32452	+	0.438317i
$630$		0			0
$631$		−	20.2307i		−	0.805372i	−0.915338	−	0.402686i	$-0.868077\pi$
$631$		−	20.2307i		−	0.805372i	0.915338	−	0.402686i	$-0.131923\pi$
$632$		0			0
$633$	−0.466068			−0.0185245
$634$		0			0
$635$	9.07586	+	9.07586i	0.360165	+	0.360165i
$636$		0			0
$637$		−	4.35340i		−	0.172488i
$638$		0			0
$639$	−24.5859	−	24.5859i	−0.972603	−	0.972603i
$640$		0			0
$641$	−3.37688	+	3.37688i	−0.133379	+	0.133379i	−0.770644	−	0.637266i	$-0.780065\pi$
$641$	−3.37688	+	3.37688i	−0.133379	+	0.133379i	0.637266	+	0.770644i	$0.280065\pi$
$642$		0			0
$643$	6.97016	−	6.97016i	0.274876	−	0.274876i	−0.556183	−	0.831060i	$-0.687735\pi$
$643$	6.97016	−	6.97016i	0.274876	−	0.274876i	0.831060	+	0.556183i	$0.187735\pi$
$644$		0			0
$645$	−1.81408			−0.0714294
$646$		0			0
$647$	36.4555			1.43321			0.716607	−	0.697477i	$-0.245694\pi$
$647$	36.4555			1.43321			0.716607	+	0.697477i	$0.245694\pi$
$648$		0			0
$649$	−7.88292	+	7.88292i	−0.309432	+	0.309432i
$650$		0			0
$651$	−1.64728	+	1.64728i	−0.0645620	+	0.0645620i
$652$		0			0
$653$	12.7332	+	12.7332i	0.498288	+	0.498288i	0.910905	−	0.412617i	$-0.135385\pi$
$653$	12.7332	+	12.7332i	0.498288	+	0.498288i	−0.412617	+	0.910905i	$0.635385\pi$
$654$		0			0
$655$			7.02467i			0.274476i
$656$		0			0
$657$	−20.5894	−	20.5894i	−0.803270	−	0.803270i
$658$		0			0
$659$	0.175710			0.00684470			0.00342235	−	0.999994i	$-0.498911\pi$
$659$	0.175710			0.00684470			0.00342235	+	0.999994i	$0.498911\pi$
$660$		0			0
$661$			4.14751i			0.161319i	0.996742	+	0.0806597i	$0.0257027\pi$
$661$			4.14751i			0.161319i	−0.996742	+	0.0806597i	$0.974297\pi$
$662$		0			0
$663$	−0.986985	+	0.326619i	−0.0383313	+	0.0126848i
$664$		0			0
$665$			8.87776i			0.344265i
$666$		0			0
$667$	−3.10359			−0.120171
$668$		0			0
$669$	0.484093	+	0.484093i	0.0187161	+	0.0187161i
$670$		0			0
$671$		−	18.1496i		−	0.700658i
$672$		0			0
$673$	−6.18030	−	6.18030i	−0.238233	−	0.238233i	0.577885	−	0.816118i	$-0.303878\pi$
$673$	−6.18030	−	6.18030i	−0.238233	−	0.238233i	−0.816118	+	0.577885i	$0.803878\pi$
$674$		0			0
$675$	−0.834700	+	0.834700i	−0.0321276	+	0.0321276i
$676$		0			0
$677$	6.62704	−	6.62704i	0.254698	−	0.254698i	−0.568196	−	0.822893i	$-0.692358\pi$
$677$	6.62704	−	6.62704i	0.254698	−	0.254698i	0.822893	+	0.568196i	$0.192358\pi$
$678$		0			0
$679$	11.1889			0.429391
$680$		0			0
$681$	4.30061			0.164800
$682$		0			0
$683$	26.4889	−	26.4889i	1.01357	−	1.01357i	0.0136635	−	0.999907i	$-0.495651\pi$
$683$	26.4889	−	26.4889i	1.01357	−	1.01357i	0.999907	−	0.0136635i	$-0.00434937\pi$
$684$		0			0
$685$	−10.7109	+	10.7109i	−0.409244	+	0.409244i
$686$		0			0
$687$	1.20312	+	1.20312i	0.0459018	+	0.0459018i
$688$		0			0
$689$		−	12.6073i		−	0.480299i
$690$		0			0
$691$	31.5901	+	31.5901i	1.20175	+	1.20175i	0.973635	+	0.228110i	$0.0732547\pi$
$691$	31.5901	+	31.5901i	1.20175	+	1.20175i	0.228110	+	0.973635i	$0.426745\pi$
$692$		0			0
$693$	19.7719			0.751072
$694$		0			0
$695$		−	12.4333i		−	0.471622i
$696$		0			0
$697$	7.85695	+	23.7423i	0.297603	+	0.899304i
$698$		0			0
$699$			1.76413i			0.0667256i
$700$		0			0
$701$	−18.7355			−0.707630			−0.353815	−	0.935315i	$-0.615116\pi$
$701$	−18.7355			−0.707630			−0.353815	+	0.935315i	$0.615116\pi$
$702$		0			0
$703$	−28.1527	−	28.1527i	−1.06180	−	1.06180i
$704$		0			0
$705$			2.13742i			0.0805000i
$706$		0			0
$707$	13.5106	+	13.5106i	0.508117	+	0.508117i
$708$		0			0
$709$	4.05125	−	4.05125i	0.152148	−	0.152148i	−0.626929	−	0.779077i	$-0.715688\pi$
$709$	4.05125	−	4.05125i	0.152148	−	0.152148i	0.779077	+	0.626929i	$0.215688\pi$
$710$		0			0
$711$	−35.4668	+	35.4668i	−1.33011	+	1.33011i
$712$		0			0
$713$	3.57406			0.133850
$714$		0			0
$715$	−4.49323			−0.168037
$716$		0			0
$717$	−1.72584	+	1.72584i	−0.0644526	+	0.0644526i
$718$		0			0
$719$	20.7647	−	20.7647i	0.774393	−	0.774393i	−0.204478	−	0.978871i	$-0.565550\pi$
$719$	20.7647	−	20.7647i	0.774393	−	0.774393i	0.978871	+	0.204478i	$0.0655496\pi$
$720$		0			0
$721$	1.43604	+	1.43604i	0.0534808	+	0.0534808i
$722$		0			0
$723$			0.529263i			0.0196835i
$724$		0			0
$725$	3.81711	+	3.81711i	0.141764	+	0.141764i
$726$		0			0
$727$	48.1662			1.78639			0.893193	−	0.449674i	$-0.148460\pi$
$727$	48.1662			1.78639			0.893193	+	0.449674i	$0.148460\pi$
$728$		0			0
$729$		−	24.9052i		−	0.922416i
$730$		0			0
$731$	−16.9642	+	33.7452i	−0.627442	+	1.24811i
$732$		0			0
$733$			14.3419i			0.529731i	0.964285	+	0.264866i	$0.0853276\pi$
$733$			14.3419i			0.529731i	−0.964285	+	0.264866i	$0.914672\pi$
$734$		0			0
$735$	0.677112			0.0249757
$736$		0			0
$737$	0.703340	+	0.703340i	0.0259079	+	0.0259079i
$738$		0			0
$739$			9.73758i			0.358203i	0.983831	+	0.179101i	$0.0573190\pi$
$739$			9.73758i			0.358203i	−0.983831	+	0.179101i	$0.942681\pi$
$740$		0			0
$741$	−0.836465	−	0.836465i	−0.0307283	−	0.0307283i
$742$		0			0
$743$	16.9727	−	16.9727i	0.622667	−	0.622667i	−0.323545	−	0.946213i	$-0.604875\pi$
$743$	16.9727	−	16.9727i	0.622667	−	0.622667i	0.946213	+	0.323545i	$0.104875\pi$
$744$		0			0
$745$	8.20906	−	8.20906i	0.300757	−	0.300757i
$746$		0			0
$747$	25.2004			0.922033
$748$		0			0
$749$	−12.0132			−0.438954
$750$		0			0
$751$	−33.9092	+	33.9092i	−1.23736	+	1.23736i	−0.276289	+	0.961075i	$0.589105\pi$
$751$	−33.9092	+	33.9092i	−1.23736	+	1.23736i	−0.961075	+	0.276289i	$0.910895\pi$
$752$		0			0
$753$	−3.84269	+	3.84269i	−0.140035	+	0.140035i
$754$		0			0
$755$	0.931740	+	0.931740i	0.0339095	+	0.0339095i
$756$		0			0
$757$		−	18.5200i		−	0.673119i	−0.941662	−	0.336560i	$-0.890737\pi$
$757$		−	18.5200i		−	0.673119i	0.941662	−	0.336560i	$-0.109263\pi$
$758$		0			0
$759$	0.284113	+	0.284113i	0.0103126	+	0.0103126i
$760$		0			0
$761$	35.9145			1.30190			0.650950	−	0.759120i	$-0.274371\pi$
$761$	35.9145			1.30190			0.650950	+	0.759120i	$0.274371\pi$
$762$		0			0
$763$			19.0851i			0.690929i
$764$		0			0
$765$	3.83527	+	11.5895i	0.138664	+	0.419019i
$766$		0			0
$767$		−	4.02220i		−	0.145233i
$768$		0			0
$769$	17.7831			0.641276			0.320638	−	0.947202i	$-0.396103\pi$
$769$	17.7831			0.641276			0.320638	+	0.947202i	$0.396103\pi$
$770$		0			0
$771$	3.20420	+	3.20420i	0.115397	+	0.115397i
$772$		0			0
$773$		−	7.33018i		−	0.263648i	−0.991273	−	0.131824i	$-0.957917\pi$
$773$		−	7.33018i		−	0.263648i	0.991273	−	0.131824i	$-0.0420834\pi$
$774$		0			0
$775$	−4.39574	−	4.39574i	−0.157900	−	0.157900i
$776$		0			0
$777$	2.24877	−	2.24877i	0.0806741	−	0.0806741i
$778$		0			0
$779$	−20.1215	+	20.1215i	−0.720927	+	0.720927i
$780$		0			0
$781$	41.4423			1.48292
$782$		0			0
$783$	6.37228			0.227727
$784$		0			0
$785$	−0.130027	+	0.130027i	−0.00464085	+	0.00464085i
$786$		0			0
$787$	−27.4321	+	27.4321i	−0.977850	+	0.977850i	−0.999760	−	0.0219095i	$-0.993025\pi$
$787$	−27.4321	+	27.4321i	−0.977850	+	0.977850i	0.0219095	+	0.999760i	$0.493025\pi$
$788$		0			0
$789$	1.32849	+	1.32849i	0.0472954	+	0.0472954i
$790$		0			0
$791$		−	7.08465i		−	0.251901i
$792$		0			0
$793$	4.63034	+	4.63034i	0.164428	+	0.164428i
$794$		0			0
$795$	1.96089			0.0695457
$796$		0			0
$797$			36.6386i			1.29780i	0.760872	+	0.648902i	$0.224772\pi$
$797$			36.6386i			1.29780i	−0.760872	+	0.648902i	$0.775228\pi$
$798$		0			0
$799$	39.7599	+	19.9878i	1.40661	+	0.707119i
$800$		0			0
$801$			49.5122i			1.74943i
$802$		0			0
$803$	34.7058			1.22474
$804$		0			0
$805$	0.769294	+	0.769294i	0.0271141	+	0.0271141i
$806$		0			0
$807$			1.20566i			0.0424412i
$808$		0			0
$809$	−11.0838	−	11.0838i	−0.389685	−	0.389685i	0.484890	−	0.874575i	$-0.338860\pi$
$809$	−11.0838	−	11.0838i	−0.389685	−	0.389685i	−0.874575	+	0.484890i	$0.838860\pi$
$810$		0			0
$811$	−5.58363	+	5.58363i	−0.196068	+	0.196068i	−0.798312	−	0.602244i	$-0.794273\pi$
$811$	−5.58363	+	5.58363i	−0.196068	+	0.196068i	0.602244	+	0.798312i	$0.294273\pi$
$812$		0			0
$813$	3.31288	−	3.31288i	0.116188	−	0.116188i
$814$		0			0
$815$	−18.0504			−0.632277
$816$		0			0
$817$	−42.9759			−1.50354
$818$		0			0
$819$	−5.04422	+	5.04422i	−0.176259	+	0.176259i
$820$		0			0
$821$	16.6878	−	16.6878i	0.582408	−	0.582408i	−0.353157	−	0.935564i	$-0.614892\pi$
$821$	16.6878	−	16.6878i	0.582408	−	0.582408i	0.935564	+	0.353157i	$0.114892\pi$
$822$		0			0
$823$	10.0348	+	10.0348i	0.349792	+	0.349792i	0.860032	−	0.510240i	$-0.170444\pi$
$823$	10.0348	+	10.0348i	0.349792	+	0.349792i	−0.510240	+	0.860032i	$0.670444\pi$
$824$		0			0
$825$		−	0.698861i		−	0.0243312i
$826$		0			0
$827$	−26.8417	−	26.8417i	−0.933377	−	0.933377i	0.0645378	−	0.997915i	$-0.479443\pi$
$827$	−26.8417	−	26.8417i	−0.933377	−	0.933377i	−0.997915	+	0.0645378i	$0.979443\pi$
$828$		0			0
$829$	4.91163			0.170588			0.0852939	−	0.996356i	$-0.472817\pi$
$829$	4.91163			0.170588			0.0852939	+	0.996356i	$0.472817\pi$
$830$		0			0
$831$		−	1.63131i		−	0.0565894i
$832$		0			0
$833$	6.33193	−	12.5955i	0.219388	−	0.436409i
$834$		0			0
$835$		−	7.57518i		−	0.262150i
$836$		0			0
$837$	−7.33826			−0.253647
$838$		0			0
$839$	−7.80546	−	7.80546i	−0.269474	−	0.269474i	0.559414	−	0.828888i	$-0.311026\pi$
$839$	−7.80546	−	7.80546i	−0.269474	−	0.269474i	−0.828888	+	0.559414i	$0.811026\pi$
$840$		0			0
$841$		−	0.140644i		−	0.00484980i
$842$		0			0
$843$	2.11218	+	2.11218i	0.0727472	+	0.0727472i
$844$		0			0
$845$	−8.04607	+	8.04607i	−0.276793	+	0.276793i
$846$		0			0
$847$	−1.94513	+	1.94513i	−0.0668353	+	0.0668353i
$848$		0			0
$849$	3.51525			0.120643
$850$		0			0
$851$	−4.87909			−0.167253
$852$		0			0
$853$	28.8483	−	28.8483i	0.987746	−	0.987746i	−0.0121803	−	0.999926i	$-0.503877\pi$
$853$	28.8483	−	28.8483i	0.987746	−	0.987746i	0.999926	+	0.0121803i	$0.00387721\pi$
$854$		0			0
$855$	−9.82205	+	9.82205i	−0.335907	+	0.335907i
$856$		0			0
$857$	−2.91939	−	2.91939i	−0.0997244	−	0.0997244i	0.655484	−	0.755209i	$-0.272465\pi$
$857$	−2.91939	−	2.91939i	−0.0997244	−	0.0997244i	−0.755209	+	0.655484i	$0.772465\pi$
$858$		0			0
$859$		−	8.53800i		−	0.291313i	−0.989335	−	0.145656i	$-0.953471\pi$
$859$		−	8.53800i		−	0.291313i	0.989335	−	0.145656i	$-0.0465294\pi$
$860$		0			0
$861$	−1.60725	−	1.60725i	−0.0547751	−	0.0547751i
$862$		0			0
$863$	−3.08921			−0.105158			−0.0525790	−	0.998617i	$-0.516744\pi$
$863$	−3.08921			−0.105158			−0.0525790	+	0.998617i	$0.516744\pi$
$864$		0			0
$865$			6.92236i			0.235367i
$866$		0			0
$867$	−3.33067	−	0.490556i	−0.113115	−	0.0166602i
$868$		0			0
$869$		−	59.7832i		−	2.02801i
$870$		0			0
$871$	−0.358873			−0.0121600
$872$		0			0
$873$	12.3790	+	12.3790i	0.418966	+	0.418966i
$874$		0			0
$875$		−	1.89231i		−	0.0639718i
$876$		0			0
$877$	−21.7154	−	21.7154i	−0.733278	−	0.733278i	0.237990	−	0.971268i	$-0.423512\pi$
$877$	−21.7154	−	21.7154i	−0.733278	−	0.733278i	−0.971268	+	0.237990i	$0.923512\pi$
$878$		0			0
$879$	−1.52904	+	1.52904i	−0.0515731	+	0.0515731i
$880$		0			0
$881$	−6.18749	+	6.18749i	−0.208462	+	0.208462i	−0.803613	−	0.595152i	$-0.797092\pi$
$881$	−6.18749	+	6.18749i	−0.208462	+	0.208462i	0.595152	+	0.803613i	$0.297092\pi$
$882$		0			0
$883$	29.5875			0.995698			0.497849	−	0.867264i	$-0.334123\pi$
$883$	29.5875			0.995698			0.497849	+	0.867264i	$0.334123\pi$
$884$		0			0
$885$	0.625598			0.0210293
$886$		0			0
$887$	−5.92290	+	5.92290i	−0.198872	+	0.198872i	−0.799516	−	0.600645i	$-0.794911\pi$
$887$	−5.92290	+	5.92290i	−0.198872	+	0.198872i	0.600645	+	0.799516i	$0.294911\pi$
$888$		0			0
$889$	−17.1744	+	17.1744i	−0.576010	+	0.576010i
$890$		0			0
$891$	21.5813	+	21.5813i	0.723002	+	0.723002i
$892$		0			0
$893$			50.6360i			1.69447i
$894$		0			0
$895$	−7.26821	−	7.26821i	−0.242950	−	0.242950i
$896$		0			0
$897$	−0.144966			−0.00484028
$898$		0			0
$899$			33.5581i			1.11922i
$900$		0			0
$901$	18.3370	−	36.4761i	0.610895	−	1.21520i
$902$		0			0
$903$		−	3.43281i		−	0.114237i
$904$		0			0
$905$	−20.0601			−0.666820
$906$		0			0
$907$	−14.2310	−	14.2310i	−0.472534	−	0.472534i	0.430200	−	0.902734i	$-0.358443\pi$
$907$	−14.2310	−	14.2310i	−0.472534	−	0.472534i	−0.902734	+	0.430200i	$0.858443\pi$
$908$		0			0
$909$			29.8952i			0.991562i
$910$		0			0
$911$	−5.67260	−	5.67260i	−0.187942	−	0.187942i	0.606864	−	0.794806i	$-0.292427\pi$
$911$	−5.67260	−	5.67260i	−0.187942	−	0.187942i	−0.794806	+	0.606864i	$0.792427\pi$
$912$		0			0
$913$	−21.2390	+	21.2390i	−0.702909	+	0.702909i
$914$		0			0
$915$	−0.720187	+	0.720187i	−0.0238087	+	0.0238087i
$916$		0			0
$917$	−13.2929			−0.438969
$918$		0			0
$919$	−30.7678			−1.01494			−0.507468	−	0.861671i	$-0.669418\pi$
$919$	−30.7678			−1.01494			−0.507468	+	0.861671i	$0.669418\pi$
$920$		0			0
$921$	0.956270	−	0.956270i	0.0315102	−	0.0315102i
$922$		0			0
$923$	−10.5728	+	10.5728i	−0.348008	+	0.348008i
$924$		0			0
$925$	6.00080	+	6.00080i	0.197305	+	0.197305i
$926$		0			0
$927$			3.17756i			0.104365i
$928$		0			0
$929$	25.5343	+	25.5343i	0.837755	+	0.837755i	0.988563	−	0.150808i	$-0.0481876\pi$
$929$	25.5343	+	25.5343i	0.837755	+	0.837755i	−0.150808	+	0.988563i	$0.548188\pi$
$930$		0			0
$931$	16.0409			0.525720
$932$		0			0
$933$		−	0.130904i		−	0.00428561i
$934$		0			0
$935$	−13.0001	−	6.53532i	−0.425148	−	0.213728i
$936$		0			0
$937$			36.7492i			1.20054i	0.799796	+	0.600272i	$0.204941\pi$
$937$			36.7492i			1.20054i	−0.799796	+	0.600272i	$0.795059\pi$
$938$		0			0
$939$	0.830420			0.0270997
$940$		0			0
$941$	−8.24873	−	8.24873i	−0.268901	−	0.268901i	0.559756	−	0.828657i	$-0.310895\pi$
$941$	−8.24873	−	8.24873i	−0.268901	−	0.268901i	−0.828657	+	0.559756i	$0.810895\pi$
$942$		0			0
$943$			3.48722i			0.113559i
$944$		0			0
$945$	−1.57951	−	1.57951i	−0.0513816	−	0.0513816i
$946$		0			0
$947$	−32.9727	+	32.9727i	−1.07147	+	1.07147i	−0.0742285	+	0.997241i	$0.523649\pi$
$947$	−32.9727	+	32.9727i	−1.07147	+	1.07147i	−0.997241	+	0.0742285i	$0.976351\pi$
$948$		0			0
$949$	−8.85416	+	8.85416i	−0.287418	+	0.287418i
$950$		0			0
$951$	4.21133			0.136562
$952$		0			0
$953$	15.8298			0.512778			0.256389	−	0.966574i	$-0.417467\pi$
$953$	15.8298			0.512778			0.256389	+	0.966574i	$0.417467\pi$
$954$		0			0
$955$	−2.90720	+	2.90720i	−0.0940748	+	0.0940748i
$956$		0			0
$957$	−2.66763	+	2.66763i	−0.0862322	+	0.0862322i
$958$		0			0
$959$	−20.2684	−	20.2684i	−0.654502	−	0.654502i
$960$		0			0
$961$		−	7.64513i		−	0.246617i
$962$		0			0
$963$	−13.2910	−	13.2910i	−0.428297	−	0.428297i
$964$		0			0
$965$	−14.2986			−0.460288
$966$		0			0
$967$		−	18.4139i		−	0.592152i	−0.955164	−	0.296076i	$-0.904322\pi$
$967$		−	18.4139i		−	0.592152i	0.955164	−	0.296076i	$-0.0956781\pi$
$968$		0			0
$969$	−1.20349	−	3.63673i	−0.0386616	−	0.116829i
$970$		0			0
$971$		−	16.3118i		−	0.523470i	−0.965140	−	0.261735i	$-0.915705\pi$
$971$		−	16.3118i		−	0.523470i	0.965140	−	0.261735i	$-0.0842947\pi$
$972$		0			0
$973$	23.5277			0.754263
$974$		0			0
$975$	0.178294	+	0.178294i	0.00570998	+	0.00570998i
$976$		0			0
$977$		−	52.7849i		−	1.68874i	−0.535762	−	0.844369i	$-0.679976\pi$
$977$		−	52.7849i		−	1.68874i	0.535762	−	0.844369i	$-0.320024\pi$
$978$		0			0
$979$	−41.7291	−	41.7291i	−1.33367	−	1.33367i
$980$		0			0
$981$	−21.1151	+	21.1151i	−0.674155	+	0.674155i
$982$		0			0
$983$	23.5672	−	23.5672i	0.751677	−	0.751677i	−0.223115	−	0.974792i	$-0.571622\pi$
$983$	23.5672	−	23.5672i	0.751677	−	0.751677i	0.974792	+	0.223115i	$0.0716225\pi$
$984$		0			0
$985$	5.35126			0.170505
$986$		0			0
$987$	−4.04467			−0.128743
$988$		0			0
$989$	−3.72404	+	3.72404i	−0.118418	+	0.118418i
$990$		0			0
$991$	27.9267	−	27.9267i	0.887122	−	0.887122i	−0.107124	−	0.994246i	$-0.534164\pi$
$991$	27.9267	−	27.9267i	0.887122	−	0.887122i	0.994246	+	0.107124i	$0.0341642\pi$
$992$		0			0
$993$	3.88703	+	3.88703i	0.123351	+	0.123351i
$994$		0			0
$995$			3.37450i			0.106979i
$996$		0			0
$997$	18.8643	+	18.8643i	0.597437	+	0.597437i	0.939630	−	0.342193i	$-0.111170\pi$
$997$	18.8643	+	18.8643i	0.597437	+	0.597437i	−0.342193	+	0.939630i	$0.611170\pi$
$998$		0			0
$999$	10.0177			0.316947

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1360.2.bt.d.1041.3		12
4.3	odd	2		85.2.e.a.21.1	✓	12
12.11	even	2		765.2.k.b.361.6		12
17.13	even	4	inner	1360.2.bt.d.81.3		12
20.3	even	4		425.2.j.c.174.1		12
20.7	even	4		425.2.j.b.174.6		12
20.19	odd	2		425.2.e.f.276.6		12
68.15	odd	8		1445.2.d.g.866.12		12
68.19	odd	8		1445.2.d.g.866.11		12
68.43	odd	8		1445.2.a.n.1.1		6
68.47	odd	4		85.2.e.a.81.6	yes	12
68.59	odd	8		1445.2.a.o.1.1		6
204.47	even	4		765.2.k.b.676.1		12
340.47	even	4		425.2.j.c.149.1		12
340.59	odd	8		7225.2.a.z.1.6		6
340.179	odd	8		7225.2.a.bb.1.6		6
340.183	even	4		425.2.j.b.149.6		12
340.319	odd	4		425.2.e.f.251.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.1	✓	12	4.3	odd	2
85.2.e.a.81.6	yes	12	68.47	odd	4
425.2.e.f.251.1		12	340.319	odd	4
425.2.e.f.276.6		12	20.19	odd	2
425.2.j.b.149.6		12	340.183	even	4
425.2.j.b.174.6		12	20.7	even	4
425.2.j.c.149.1		12	340.47	even	4
425.2.j.c.174.1		12	20.3	even	4
765.2.k.b.361.6		12	12.11	even	2
765.2.k.b.676.1		12	204.47	even	4
1360.2.bt.d.81.3		12	17.13	even	4	inner
1360.2.bt.d.1041.3		12	1.1	even	1	trivial
1445.2.a.n.1.1		6	68.43	odd	8
1445.2.a.o.1.1		6	68.59	odd	8
1445.2.d.g.866.11		12	68.19	odd	8
1445.2.d.g.866.12		12	68.15	odd	8
7225.2.a.z.1.6		6	340.59	odd	8
7225.2.a.bb.1.6		6	340.179	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1360.bt (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.140032 + 0.140032i) q^{3} +(0.707107 - 0.707107i) q^{5} +(1.33807 + 1.33807i) q^{7} +2.96078i q^{9} +(-2.49536 - 2.49536i) q^{11} +1.27324 q^{13} +0.198035i q^{15} +(3.68381 + 1.85190i) q^{17} +4.69149i q^{19} -0.374744 q^{21} +(0.406537 + 0.406537i) q^{23} -1.00000i q^{25} +(-0.834700 - 0.834700i) q^{27} +(-3.81711 + 3.81711i) q^{29} +(4.39574 - 4.39574i) q^{31} +0.698861 q^{33} +1.89231 q^{35} +(-6.00080 + 6.00080i) q^{37} +(-0.178294 + 0.178294i) q^{39} +(4.28894 + 4.28894i) q^{41} +9.16040i q^{43} +(2.09359 + 2.09359i) q^{45} +10.7932 q^{47} -3.41915i q^{49} +(-0.775177 + 0.256526i) q^{51} -9.90174i q^{53} -3.52898 q^{55} +(-0.656958 - 0.656958i) q^{57} -3.15903i q^{59} +(3.63666 + 3.63666i) q^{61} +(-3.96173 + 3.96173i) q^{63} +(0.900316 - 0.900316i) q^{65} -0.281859 q^{67} -0.113856 q^{69} +(-8.30385 + 8.30385i) q^{71} +(-6.95405 + 6.95405i) q^{73} +(0.140032 + 0.140032i) q^{75} -6.67793i q^{77} +(11.9789 + 11.9789i) q^{79} -8.64858 q^{81} -8.51139i q^{83} +(3.91434 - 1.29536i) q^{85} -1.06903i q^{87} +16.7227 q^{89} +(1.70368 + 1.70368i) q^{91} +1.23109i q^{93} +(3.31738 + 3.31738i) q^{95} +(4.18100 - 4.18100i) q^{97} +(7.38823 - 7.38823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 4 q^{11} + 12 q^{17} - 16 q^{21} - 12 q^{23} + 4 q^{27} - 12 q^{29} - 16 q^{33} - 16 q^{35} + 12 q^{37} + 20 q^{39} - 24 q^{41} + 8 q^{45} + 48 q^{47} - 32 q^{51} + 40 q^{61} - 12 q^{63}+ \cdots + 4 q^{97}+O(q^{100}) \) 12 * q + 4 * q^3 + 4 * q^11 + 12 * q^17 - 16 * q^21 - 12 * q^23 + 4 * q^27 - 12 * q^29 - 16 * q^33 - 16 * q^35 + 12 * q^37 + 20 * q^39 - 24 * q^41 + 8 * q^45 + 48 * q^47 - 32 * q^51 + 40 * q^61 - 12 * q^63 + 4 * q^65 + 8 * q^67 - 28 * q^71 - 48 * q^73 - 4 * q^75 + 8 * q^79 + 28 * q^81 - 4 * q^85 + 24 * q^89 + 36 * q^91 + 8 * q^95 + 4 * q^97

Introduction

L-functions

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