LMFDB - Embedded newform 160.3.p.e.97.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [160,3,Mod(33,160)] 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("160.33"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(160, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	160.p (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,4,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.35968422976$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.3534400.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 3x^{4} + 16x^{3} + x^{2} - 12x + 40 $ x^6 - 2x^5 - 3x^4 + 16x^3 + x^2 - 12x + 40
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.2
Root			$-1.81837 + 0.301352i$ of defining polynomial
Character	$\chi$	$=$	160.97
Dual form			160.3.p.e.33.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.602705 + 0.602705i) q^{3} +(-3.63675 - 3.43134i) q^{5} +(6.67079 + 6.67079i) q^{7} +8.27349i q^{9} +18.9308 q^{11} +(7.47890 - 7.47890i) q^{13} +(4.25997 - 0.123802i) q^{15} +(1.45185 + 1.45185i) q^{17} +24.9578i q^{19} -8.04103 q^{21} +(-3.74003 + 3.74003i) q^{23} +(1.45185 + 24.9578i) q^{25} +(-10.4108 - 10.4108i) q^{27} -29.8615i q^{29} +21.0692 q^{31} +(-11.4097 + 11.4097i) q^{33} +(-1.37025 - 47.1497i) q^{35} +(-18.8886 - 18.8886i) q^{37} +9.01514i q^{39} +40.9988 q^{41} +(-37.5064 + 37.5064i) q^{43} +(28.3891 - 30.0886i) q^{45} +(-48.9161 - 48.9161i) q^{47} +39.9988i q^{49} -1.75008 q^{51} +(-33.9308 + 33.9308i) q^{53} +(-68.8464 - 64.9578i) q^{55} +(-15.0422 - 15.0422i) q^{57} -20.6808i q^{59} -19.8228 q^{61} +(-55.1907 + 55.1907i) q^{63} +(-52.8615 + 1.53624i) q^{65} +(-35.9713 - 35.9713i) q^{67} -4.50827i q^{69} +120.900 q^{71} +(85.6808 - 85.6808i) q^{73} +(-15.9172 - 14.1672i) q^{75} +(126.283 + 126.283i) q^{77} +75.7230i q^{79} -61.9121 q^{81} +(21.5311 - 21.5311i) q^{83} +(-0.298225 - 10.2618i) q^{85} +(17.9977 + 17.9977i) q^{87} -43.7230i q^{89} +99.7804 q^{91} +(-12.6985 + 12.6985i) q^{93} +(85.6386 - 90.7652i) q^{95} +(-103.627 - 103.627i) q^{97} +156.623i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{5} - 8 q^{7} + 32 q^{11} - 14 q^{13} - 8 q^{15} - 14 q^{17} - 40 q^{21} - 56 q^{23} - 14 q^{25} - 48 q^{27} + 208 q^{31} + 72 q^{33} - 48 q^{35} + 86 q^{37} + 120 q^{41} - 176 q^{43} + 34 q^{45}+ \cdots - 250 q^{97}+O(q^{100}) $ 6 * q + 4 * q^5 - 8 * q^7 + 32 * q^11 - 14 * q^13 - 8 * q^15 - 14 * q^17 - 40 * q^21 - 56 * q^23 - 14 * q^25 - 48 * q^27 + 208 * q^31 + 72 * q^33 - 48 * q^35 + 86 * q^37 + 120 * q^41 - 176 * q^43 + 34 * q^45 - 104 * q^47 + 352 * q^51 - 122 * q^53 - 96 * q^55 - 208 * q^57 - 216 * q^61 - 216 * q^63 - 154 * q^65 - 80 * q^67 + 336 * q^71 + 70 * q^73 - 32 * q^75 + 264 * q^77 + 242 * q^81 - 208 * q^83 + 338 * q^85 - 144 * q^87 + 544 * q^91 - 72 * q^93 - 48 * q^95 - 250 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.602705	+	0.602705i	−0.200902	+	0.200902i	−0.800386	−	0.599485i	$-0.795372\pi$
$3$	−0.602705	+	0.602705i	−0.200902	+	0.200902i	0.599485	+	0.800386i	$0.295372\pi$
$4$		0			0
$5$	−3.63675	−	3.43134i	−0.727349	−	0.686267i
$5$	−3.63675	−	3.43134i	−0.727349	−	0.686267i
$6$		0			0
$7$	6.67079	+	6.67079i	0.952970	+	0.952970i	0.998943	−	0.0459729i	$-0.0146388\pi$
$7$	6.67079	+	6.67079i	0.952970	+	0.952970i	−0.0459729	+	0.998943i	$0.514639\pi$
$8$		0			0
$9$			8.27349i			0.919277i
$10$		0			0
$11$	18.9308			1.72098			0.860489	−	0.509469i	$-0.170158\pi$
$11$	18.9308			1.72098			0.860489	+	0.509469i	$0.170158\pi$
$12$		0			0
$13$	7.47890	−	7.47890i	0.575300	−	0.575300i	−0.358305	−	0.933605i	$-0.616645\pi$
$13$	7.47890	−	7.47890i	0.575300	−	0.575300i	0.933605	+	0.358305i	$0.116645\pi$
$14$		0			0
$15$	4.25997	−	0.123802i	0.283998	−	0.00825344i
$16$		0			0
$17$	1.45185	+	1.45185i	0.0854032	+	0.0854032i	0.748518	−	0.663115i	$-0.230766\pi$
$17$	1.45185	+	1.45185i	0.0854032	+	0.0854032i	−0.663115	+	0.748518i	$0.730766\pi$
$18$		0			0
$19$			24.9578i			1.31357i	0.754078	+	0.656784i	$0.228084\pi$
$19$			24.9578i			1.31357i	−0.754078	+	0.656784i	$0.771916\pi$
$20$		0			0
$21$	−8.04103			−0.382906
$22$		0			0
$23$	−3.74003	+	3.74003i	−0.162610	+	0.162610i	−0.783722	−	0.621112i	$-0.786681\pi$
$23$	−3.74003	+	3.74003i	−0.162610	+	0.162610i	0.621112	+	0.783722i	$0.286681\pi$
$24$		0			0
$25$	1.45185	+	24.9578i	0.0580742	+	0.998312i
$26$		0			0
$27$	−10.4108	−	10.4108i	−0.385586	−	0.385586i
$28$		0			0
$29$		−	29.8615i		−	1.02971i	−0.857278	−	0.514854i	$-0.827846\pi$
$29$		−	29.8615i		−	1.02971i	0.857278	−	0.514854i	$-0.172154\pi$
$30$		0			0
$31$	21.0692			0.679653			0.339826	−	0.940488i	$-0.389632\pi$
$31$	21.0692			0.679653			0.339826	+	0.940488i	$0.389632\pi$
$32$		0			0
$33$	−11.4097	+	11.4097i	−0.345747	+	0.345747i
$34$		0			0
$35$	−1.37025	−	47.1497i	−0.0391499	−	1.34713i
$36$		0			0
$37$	−18.8886	−	18.8886i	−0.510502	−	0.510502i	0.404178	−	0.914680i	$-0.367557\pi$
$37$	−18.8886	−	18.8886i	−0.510502	−	0.510502i	−0.914680	+	0.404178i	$0.867557\pi$
$38$		0			0
$39$			9.01514i			0.231158i
$40$		0			0
$41$	40.9988			0.999972			0.499986	−	0.866034i	$-0.333339\pi$
$41$	40.9988			0.999972			0.499986	+	0.866034i	$0.333339\pi$
$42$		0			0
$43$	−37.5064	+	37.5064i	−0.872242	+	0.872242i	−0.992716	−	0.120474i	$-0.961558\pi$
$43$	−37.5064	+	37.5064i	−0.872242	+	0.872242i	0.120474	+	0.992716i	$0.461558\pi$
$44$		0			0
$45$	28.3891	−	30.0886i	0.630870	−	0.668636i
$46$		0			0
$47$	−48.9161	−	48.9161i	−1.04077	−	1.04077i	−0.999133	−	0.0416346i	$-0.986743\pi$
$47$	−48.9161	−	48.9161i	−1.04077	−	1.04077i	−0.0416346	−	0.999133i	$-0.513257\pi$
$48$		0			0
$49$			39.9988i			0.816303i
$50$		0			0
$51$	−1.75008			−0.0343153
$52$		0			0
$53$	−33.9308	+	33.9308i	−0.640203	+	0.640203i	−0.950605	−	0.310402i	$-0.899536\pi$
$53$	−33.9308	+	33.9308i	−0.640203	+	0.640203i	0.310402	+	0.950605i	$0.399536\pi$
$54$		0			0
$55$	−68.8464	−	64.9578i	−1.25175	−	1.18105i
$56$		0			0
$57$	−15.0422	−	15.0422i	−0.263898	−	0.263898i
$58$		0			0
$59$		−	20.6808i		−	0.350523i	−0.984522	−	0.175261i	$-0.943923\pi$
$59$		−	20.6808i		−	0.350523i	0.984522	−	0.175261i	$-0.0560770\pi$
$60$		0			0
$61$	−19.8228			−0.324964			−0.162482	−	0.986712i	$-0.551950\pi$
$61$	−19.8228			−0.324964			−0.162482	+	0.986712i	$0.551950\pi$
$62$		0			0
$63$	−55.1907	+	55.1907i	−0.876043	+	0.876043i
$64$		0			0
$65$	−52.8615	+	1.53624i	−0.813254	+	0.0236345i
$66$		0			0
$67$	−35.9713	−	35.9713i	−0.536886	−	0.536886i	0.385727	−	0.922613i	$-0.373951\pi$
$67$	−35.9713	−	35.9713i	−0.536886	−	0.536886i	−0.922613	+	0.385727i	$0.873951\pi$
$68$		0			0
$69$		−	4.50827i		−	0.0653373i
$70$		0			0
$71$	120.900			1.70282			0.851412	−	0.524498i	$-0.175747\pi$
$71$	120.900			1.70282			0.851412	+	0.524498i	$0.175747\pi$
$72$		0			0
$73$	85.6808	−	85.6808i	1.17371	−	1.17371i	0.192392	−	0.981318i	$-0.438376\pi$
$73$	85.6808	−	85.6808i	1.17371	−	1.17371i	0.981318	−	0.192392i	$-0.0616245\pi$
$74$		0			0
$75$	−15.9172	−	14.1672i	−0.212230	−	0.188895i
$76$		0			0
$77$	126.283	+	126.283i	1.64004	+	1.64004i
$78$		0			0
$79$			75.7230i			0.958519i	0.877673	+	0.479260i	$0.159095\pi$
$79$			75.7230i			0.958519i	−0.877673	+	0.479260i	$0.840905\pi$
$80$		0			0
$81$	−61.9121			−0.764347
$82$		0			0
$83$	21.5311	−	21.5311i	0.259411	−	0.259411i	−0.565403	−	0.824815i	$-0.691279\pi$
$83$	21.5311	−	21.5311i	0.259411	−	0.259411i	0.824815	+	0.565403i	$0.191279\pi$
$84$		0			0
$85$	−0.298225	−	10.2618i	−0.00350853	−	0.120727i
$86$		0			0
$87$	17.9977	+	17.9977i	0.206870	+	0.206870i
$88$		0			0
$89$		−	43.7230i		−	0.491270i	−0.969362	−	0.245635i	$-0.921004\pi$
$89$		−	43.7230i		−	0.491270i	0.969362	−	0.245635i	$-0.0789965\pi$
$90$		0			0
$91$	99.7804			1.09649
$92$		0			0
$93$	−12.6985	+	12.6985i	−0.136543	+	0.136543i
$94$		0			0
$95$	85.6386	−	90.7652i	0.901459	−	0.955423i
$96$		0			0
$97$	−103.627	−	103.627i	−1.06832	−	1.06832i	−0.997489	−	0.0708284i	$-0.977436\pi$
$97$	−103.627	−	103.627i	−1.06832	−	1.06832i	−0.0708284	−	0.997489i	$-0.522564\pi$
$98$		0			0
$99$			156.623i			1.58206i
$100$		0			0
$101$	−104.928			−1.03889			−0.519443	−	0.854505i	$-0.673861\pi$
$101$	−104.928			−1.03889			−0.519443	+	0.854505i	$0.673861\pi$
$102$		0			0
$103$	−58.4773	+	58.4773i	−0.567741	+	0.567741i	−0.931495	−	0.363754i	$-0.881495\pi$
$103$	−58.4773	+	58.4773i	−0.567741	+	0.567741i	0.363754	+	0.931495i	$0.381495\pi$
$104$		0			0
$105$	29.2432	+	27.5915i	0.278507	+	0.262776i
$106$		0			0
$107$	35.2285	+	35.2285i	0.329239	+	0.329239i	0.852297	−	0.523058i	$-0.175209\pi$
$107$	35.2285	+	35.2285i	0.329239	+	0.329239i	−0.523058	+	0.852297i	$0.675209\pi$
$108$		0			0
$109$			59.5976i			0.546767i	0.961905	+	0.273384i	$0.0881428\pi$
$109$			59.5976i			0.546767i	−0.961905	+	0.273384i	$0.911857\pi$
$110$		0			0
$111$	22.7685			0.205121
$112$		0			0
$113$	−7.17488	+	7.17488i	−0.0634945	+	0.0634945i	−0.738141	−	0.674646i	$-0.764296\pi$
$113$	−7.17488	+	7.17488i	−0.0634945	+	0.0634945i	0.674646	+	0.738141i	$0.264296\pi$
$114$		0			0
$115$	26.4349	−	0.768239i	0.229868	−	0.00668034i
$116$		0			0
$117$	61.8767	+	61.8767i	0.528860	+	0.528860i
$118$		0			0
$119$			19.3700i			0.162773i
$120$		0			0
$121$	237.374			1.96177
$122$		0			0
$123$	−24.7102	+	24.7102i	−0.200896	+	0.200896i
$124$		0			0
$125$	80.3586	−	95.7470i	0.642869	−	0.765976i
$126$		0			0
$127$	67.8468	+	67.8468i	0.534227	+	0.534227i	0.921827	−	0.387600i	$-0.126696\pi$
$127$	67.8468	+	67.8468i	0.534227	+	0.534227i	−0.387600	+	0.921827i	$0.626696\pi$
$128$		0			0
$129$		−	45.2106i		−	0.350470i
$130$		0			0
$131$	138.593			1.05796			0.528982	−	0.848633i	$-0.322574\pi$
$131$	138.593			1.05796			0.528982	+	0.848633i	$0.322574\pi$
$132$		0			0
$133$	−166.488	+	166.488i	−1.25179	+	1.25179i
$134$		0			0
$135$	2.13849	+	73.5845i	0.0158406	+	0.545071i
$136$		0			0
$137$	−132.862	−	132.862i	−0.969792	−	0.969792i	0.0297648	−	0.999557i	$-0.490524\pi$
$137$	−132.862	−	132.862i	−0.969792	−	0.969792i	−0.999557	+	0.0297648i	$0.990524\pi$
$138$		0			0
$139$		−	53.3430i		−	0.383762i	−0.981418	−	0.191881i	$-0.938541\pi$
$139$		−	53.3430i		−	0.383762i	0.981418	−	0.191881i	$-0.0614588\pi$
$140$		0			0
$141$	58.9639			0.418184
$142$		0			0
$143$	141.581	−	141.581i	0.990079	−	0.990079i
$144$		0			0
$145$	−102.465	+	108.599i	−0.706655	+	0.748957i
$146$		0			0
$147$	−24.1075	−	24.1075i	−0.163997	−	0.163997i
$148$		0			0
$149$		−	52.3157i		−	0.351112i	−0.984469	−	0.175556i	$-0.943828\pi$
$149$		−	52.3157i		−	0.351112i	0.984469	−	0.175556i	$-0.0561723\pi$
$150$		0			0
$151$	−54.6538			−0.361946			−0.180973	−	0.983488i	$-0.557925\pi$
$151$	−54.6538			−0.361946			−0.180973	+	0.983488i	$0.557925\pi$
$152$		0			0
$153$	−12.0119	+	12.0119i	−0.0785092	+	0.0785092i
$154$		0			0
$155$	−76.6235	−	72.2957i	−0.494345	−	0.466424i
$156$		0			0
$157$	52.6055	+	52.6055i	0.335067	+	0.335067i	0.854507	−	0.519440i	$-0.173859\pi$
$157$	52.6055	+	52.6055i	0.335067	+	0.335067i	−0.519440	+	0.854507i	$0.673859\pi$
$158$		0			0
$159$		−	40.9005i		−	0.257236i
$160$		0			0
$161$	−49.8979			−0.309925
$162$		0			0
$163$	−139.335	+	139.335i	−0.854818	+	0.854818i	−0.990722	−	0.135904i	$-0.956606\pi$
$163$	−139.335	+	139.335i	−0.854818	+	0.854818i	0.135904	+	0.990722i	$0.456606\pi$
$164$		0			0
$165$	80.6444	−	2.34366i	0.488754	−	0.0142040i
$166$		0			0
$167$	−137.651	−	137.651i	−0.824258	−	0.824258i	0.162458	−	0.986715i	$-0.448058\pi$
$167$	−137.651	−	137.651i	−0.824258	−	0.824258i	−0.986715	+	0.162458i	$0.948058\pi$
$168$		0			0
$169$			57.1320i			0.338059i
$170$		0			0
$171$	−206.488			−1.20753
$172$		0			0
$173$	166.581	−	166.581i	0.962898	−	0.962898i	−0.0364382	−	0.999336i	$-0.511601\pi$
$173$	166.581	−	166.581i	0.962898	−	0.962898i	0.999336	+	0.0364382i	$0.0116012\pi$
$174$		0			0
$175$	−156.803	+	176.173i	−0.896019	+	1.00670i
$176$		0			0
$177$	12.4644	+	12.4644i	0.0704206	+	0.0704206i
$178$		0			0
$179$		−	246.151i		−	1.37514i	−0.726116	−	0.687572i	$-0.758677\pi$
$179$		−	246.151i		−	1.37514i	0.726116	−	0.687572i	$-0.241323\pi$
$180$		0			0
$181$	−244.892			−1.35300			−0.676498	−	0.736445i	$-0.736503\pi$
$181$	−244.892			−1.35300			−0.676498	+	0.736445i	$0.736503\pi$
$182$		0			0
$183$	11.9473	−	11.9473i	0.0652858	−	0.0652858i
$184$		0			0
$185$	3.87990	+	133.506i	0.0209724	+	0.721654i
$186$		0			0
$187$	27.4847	+	27.4847i	0.146977	+	0.146977i
$188$		0			0
$189$		−	138.897i		−	0.734903i
$190$		0			0
$191$	−314.485			−1.64652			−0.823259	−	0.567666i	$-0.807847\pi$
$191$	−314.485			−1.64652			−0.823259	+	0.567666i	$0.807847\pi$
$192$		0			0
$193$	231.199	−	231.199i	1.19792	−	1.19792i	0.223133	−	0.974788i	$-0.428372\pi$
$193$	231.199	−	231.199i	1.19792	−	1.19792i	0.974788	−	0.223133i	$-0.0716283\pi$
$194$		0			0
$195$	30.9340	−	32.7858i	0.158636	−	0.168132i
$196$		0			0
$197$	−31.7923	−	31.7923i	−0.161382	−	0.161382i	0.621797	−	0.783179i	$-0.286403\pi$
$197$	−31.7923	−	31.7923i	−0.161382	−	0.161382i	−0.783179	+	0.621797i	$0.786403\pi$
$198$		0			0
$199$		−	185.807i		−	0.933706i	−0.884335	−	0.466853i	$-0.845388\pi$
$199$		−	185.807i		−	0.933706i	0.884335	−	0.466853i	$-0.154612\pi$
$200$		0			0
$201$	43.3602			0.215722
$202$		0			0
$203$	199.200	−	199.200i	0.981280	−	0.981280i
$204$		0			0
$205$	−149.102	−	140.681i	−0.727329	−	0.686248i
$206$		0			0
$207$	−30.9431	−	30.9431i	−0.149484	−	0.149484i
$208$		0			0
$209$			472.470i			2.26062i
$210$		0			0
$211$	−208.238			−0.986912			−0.493456	−	0.869771i	$-0.664267\pi$
$211$	−208.238			−0.986912			−0.493456	+	0.869771i	$0.664267\pi$
$212$		0			0
$213$	−72.8673	+	72.8673i	−0.342100	+	0.342100i
$214$		0			0
$215$	265.098	−	7.70419i	1.23302	−	0.0358334i
$216$		0			0
$217$	140.548	+	140.548i	0.647689	+	0.647689i
$218$		0			0
$219$			103.281i			0.471601i
$220$		0			0
$221$	21.7166			0.0982649
$222$		0			0
$223$	17.2224	−	17.2224i	0.0772305	−	0.0772305i	−0.667436	−	0.744667i	$-0.732608\pi$
$223$	17.2224	−	17.2224i	0.0772305	−	0.0772305i	0.744667	+	0.667436i	$0.232608\pi$
$224$		0			0
$225$	−206.488	+	12.0119i	−0.917726	+	0.0533862i
$226$		0			0
$227$	22.8200	+	22.8200i	0.100529	+	0.100529i	0.755582	−	0.655054i	$-0.227354\pi$
$227$	22.8200	+	22.8200i	0.100529	+	0.100529i	−0.655054	+	0.755582i	$0.727354\pi$
$228$		0			0
$229$		−	295.440i		−	1.29013i	−0.764128	−	0.645065i	$-0.776830\pi$
$229$		−	295.440i		−	1.29013i	0.764128	−	0.645065i	$-0.223170\pi$
$230$		0			0
$231$	−152.223			−0.658973
$232$		0			0
$233$	−142.217	+	142.217i	−0.610374	+	0.610374i	−0.943043	−	0.332670i	$-0.892051\pi$
$233$	−142.217	+	142.217i	−0.610374	+	0.610374i	0.332670	+	0.943043i	$0.392051\pi$
$234$		0			0
$235$	10.0478	+	345.743i	0.0427568	+	1.47125i
$236$		0			0
$237$	−45.6386	−	45.6386i	−0.192568	−	0.192568i
$238$		0			0
$239$			19.8312i			0.0829758i	0.999139	+	0.0414879i	$0.0132098\pi$
$239$			19.8312i			0.0829758i	−0.999139	+	0.0414879i	$0.986790\pi$
$240$		0			0
$241$	177.318			0.735759			0.367879	−	0.929874i	$-0.380084\pi$
$241$	177.318			0.735759			0.367879	+	0.929874i	$0.380084\pi$
$242$		0			0
$243$	131.012	−	131.012i	0.539145	−	0.539145i
$244$		0			0
$245$	137.249	−	145.466i	0.560202	−	0.593737i
$246$		0			0
$247$	186.657	+	186.657i	0.755696	+	0.755696i
$248$		0			0
$249$			25.9539i			0.104232i
$250$		0			0
$251$	−193.563			−0.771166			−0.385583	−	0.922673i	$-0.626000\pi$
$251$	−193.563			−0.771166			−0.385583	+	0.922673i	$0.626000\pi$
$252$		0			0
$253$	−70.8016	+	70.8016i	−0.279848	+	0.279848i
$254$		0			0
$255$	6.36459	+	6.00511i	0.0249592	+	0.0235495i
$256$		0			0
$257$	−82.8979	−	82.8979i	−0.322560	−	0.322560i	0.527188	−	0.849748i	$-0.323246\pi$
$257$	−82.8979	−	82.8979i	−0.322560	−	0.322560i	−0.849748	+	0.527188i	$0.823246\pi$
$258$		0			0
$259$		−	252.003i		−	0.972985i
$260$		0			0
$261$	247.059			0.946586
$262$		0			0
$263$	62.7267	−	62.7267i	0.238505	−	0.238505i	−0.577726	−	0.816231i	$-0.696060\pi$
$263$	62.7267	−	62.7267i	0.238505	−	0.238505i	0.816231	+	0.577726i	$0.196060\pi$
$264$		0			0
$265$	239.825	−	6.96971i	0.905002	−	0.0263008i
$266$		0			0
$267$	26.3521	+	26.3521i	0.0986970	+	0.0986970i
$268$		0			0
$269$			182.699i			0.679177i	0.940574	+	0.339588i	$0.110288\pi$
$269$			182.699i			0.679177i	−0.940574	+	0.339588i	$0.889712\pi$
$270$		0			0
$271$	259.516			0.957622			0.478811	−	0.877918i	$-0.341068\pi$
$271$	259.516			0.957622			0.478811	+	0.877918i	$0.341068\pi$
$272$		0			0
$273$	−60.1381	+	60.1381i	−0.220286	+	0.220286i
$274$		0			0
$275$	27.4847	+	472.470i	0.0999444	+	1.71807i
$276$		0			0
$277$	−21.3166	−	21.3166i	−0.0769553	−	0.0769553i	0.667581	−	0.744537i	$-0.267330\pi$
$277$	−21.3166	−	21.3166i	−0.0769553	−	0.0769553i	−0.744537	+	0.667581i	$0.767330\pi$
$278$		0			0
$279$			174.316i			0.624789i
$280$		0			0
$281$	−95.2083			−0.338820			−0.169410	−	0.985546i	$-0.554186\pi$
$281$	−95.2083			−0.338820			−0.169410	+	0.985546i	$0.554186\pi$
$282$		0			0
$283$	187.360	−	187.360i	0.662050	−	0.662050i	−0.293813	−	0.955863i	$-0.594924\pi$
$283$	187.360	−	187.360i	0.662050	−	0.662050i	0.955863	+	0.293813i	$0.0949244\pi$
$284$		0			0
$285$	3.08981	+	106.319i	0.0108415	+	0.373051i
$286$		0			0
$287$	273.495	+	273.495i	0.952943	+	0.952943i
$288$		0			0
$289$		−	284.784i		−	0.985413i
$290$		0			0
$291$	124.913			0.429253
$292$		0			0
$293$	34.1359	−	34.1359i	0.116505	−	0.116505i	−0.646451	−	0.762956i	$-0.723747\pi$
$293$	34.1359	−	34.1359i	0.116505	−	0.116505i	0.762956	+	0.646451i	$0.223747\pi$
$294$		0			0
$295$	−70.9629	+	75.2110i	−0.240552	+	0.254952i
$296$		0			0
$297$	−197.085	−	197.085i	−0.663585	−	0.663585i
$298$		0			0
$299$			55.9427i			0.187099i
$300$		0			0
$301$	−500.395			−1.66244
$302$		0			0
$303$	63.2403	−	63.2403i	0.208714	−	0.208714i
$304$		0			0
$305$	72.0905	+	68.0187i	0.236362	+	0.223012i
$306$		0			0
$307$	361.766	+	361.766i	1.17839	+	1.17839i	0.980154	+	0.198238i	$0.0635218\pi$
$307$	361.766	+	361.766i	1.17839	+	1.17839i	0.198238	+	0.980154i	$0.436478\pi$
$308$		0			0
$309$		−	70.4891i		−	0.228120i
$310$		0			0
$311$	−119.100			−0.382957			−0.191478	−	0.981497i	$-0.561328\pi$
$311$	−119.100			−0.382957			−0.191478	+	0.981497i	$0.561328\pi$
$312$		0			0
$313$	−203.337	+	203.337i	−0.649640	+	0.649640i	−0.952906	−	0.303266i	$-0.901923\pi$
$313$	−203.337	+	203.337i	−0.649640	+	0.649640i	0.303266	+	0.952906i	$0.401923\pi$
$314$		0			0
$315$	390.093	−	11.3367i	1.23839	−	0.0359896i
$316$		0			0
$317$	139.533	+	139.533i	0.440167	+	0.440167i	0.892068	−	0.451901i	$-0.149254\pi$
$317$	139.533	+	139.533i	0.440167	+	0.440167i	−0.451901	+	0.892068i	$0.649254\pi$
$318$		0			0
$319$		−	565.301i		−	1.77210i
$320$		0			0
$321$	−42.4648			−0.132289
$322$		0			0
$323$	−36.2351	+	36.2351i	−0.112183	+	0.112183i
$324$		0			0
$325$	197.515	+	175.799i	0.607739	+	0.540919i
$326$		0			0
$327$	−35.9198	−	35.9198i	−0.109846	−	0.109846i
$328$		0			0
$329$		−	652.618i		−	1.98364i
$330$		0			0
$331$	−144.671			−0.437073			−0.218536	−	0.975829i	$-0.570128\pi$
$331$	−144.671			−0.437073			−0.218536	+	0.975829i	$0.570128\pi$
$332$		0			0
$333$	156.274	−	156.274i	0.469293	−	0.469293i
$334$		0			0
$335$	7.38887	+	254.248i	0.0220563	+	0.758950i
$336$		0			0
$337$	414.409	+	414.409i	1.22970	+	1.22970i	0.964077	+	0.265625i	$0.0855782\pi$
$337$	414.409	+	414.409i	1.22970	+	1.22970i	0.265625	+	0.964077i	$0.414422\pi$
$338$		0			0
$339$		−	8.64868i		−	0.0255123i
$340$		0			0
$341$	398.857			1.16967
$342$		0			0
$343$	60.0448	−	60.0448i	0.175058	−	0.175058i
$344$		0			0
$345$	−15.4694	+	16.3954i	−0.0448388	+	0.0475230i
$346$		0			0
$347$	−109.854	−	109.854i	−0.316583	−	0.316583i	0.530870	−	0.847453i	$-0.321865\pi$
$347$	−109.854	−	109.854i	−0.316583	−	0.316583i	−0.847453	+	0.530870i	$0.821865\pi$
$348$		0			0
$349$			466.068i			1.33544i	0.744414	+	0.667719i	$0.232729\pi$
$349$			466.068i			1.33544i	−0.744414	+	0.667719i	$0.767271\pi$
$350$		0			0
$351$	−155.723			−0.443655
$352$		0			0
$353$	275.940	−	275.940i	0.781699	−	0.781699i	−0.198418	−	0.980117i	$-0.563580\pi$
$353$	275.940	−	275.940i	0.781699	−	0.781699i	0.980117	+	0.198418i	$0.0635805\pi$
$354$		0			0
$355$	−439.684	−	414.850i	−1.23855	−	1.16859i
$356$		0			0
$357$	−11.6744	−	11.6744i	−0.0327014	−	0.0327014i
$358$		0			0
$359$			412.098i			1.14791i	0.818889	+	0.573953i	$0.194591\pi$
$359$			412.098i			1.14791i	−0.818889	+	0.573953i	$0.805409\pi$
$360$		0			0
$361$	−261.892			−0.725463
$362$		0			0
$363$	−143.066	+	143.066i	−0.394122	+	0.394122i
$364$		0			0
$365$	−605.599	+	17.5997i	−1.65918	+	0.0482183i
$366$		0			0
$367$	−203.209	−	203.209i	−0.553704	−	0.553704i	0.373804	−	0.927508i	$-0.378053\pi$
$367$	−203.209	−	203.209i	−0.553704	−	0.553704i	−0.927508	+	0.373804i	$0.878053\pi$
$368$		0			0
$369$			339.204i			0.919251i
$370$		0			0
$371$	−452.690			−1.22019
$372$		0			0
$373$	−181.027	+	181.027i	−0.485327	+	0.485327i	−0.906828	−	0.421501i	$-0.861503\pi$
$373$	−181.027	+	181.027i	−0.485327	+	0.485327i	0.421501	+	0.906828i	$0.361503\pi$
$374$		0			0
$375$	9.27467	+	106.140i	0.0247324	+	0.283039i
$376$		0			0
$377$	−223.331	−	223.331i	−0.592391	−	0.592391i
$378$		0			0
$379$		−	221.018i		−	0.583162i	−0.956546	−	0.291581i	$-0.905819\pi$
$379$		−	221.018i		−	0.583162i	0.956546	−	0.291581i	$-0.0941813\pi$
$380$		0			0
$381$	−81.7832			−0.214654
$382$		0			0
$383$	−159.322	+	159.322i	−0.415985	+	0.415985i	−0.883817	−	0.467832i	$-0.845035\pi$
$383$	−159.322	+	159.322i	−0.415985	+	0.415985i	0.467832	+	0.883817i	$0.345035\pi$
$384$		0			0
$385$	−25.9398	−	892.579i	−0.0673761	−	2.31839i
$386$		0			0
$387$	−310.309	−	310.309i	−0.801832	−	0.801832i
$388$		0			0
$389$			334.871i			0.860851i	0.902626	+	0.430426i	$0.141637\pi$
$389$			334.871i			0.860851i	−0.902626	+	0.430426i	$0.858363\pi$
$390$		0			0
$391$	−10.8600			−0.0277748
$392$		0			0
$393$	−83.5308	+	83.5308i	−0.212547	+	0.212547i
$394$		0			0
$395$	259.831	−	275.385i	0.657801	−	0.697178i
$396$		0			0
$397$	−0.785479	−	0.785479i	−0.00197854	−	0.00197854i	0.706117	−	0.708095i	$-0.250445\pi$
$397$	−0.785479	−	0.785479i	−0.00197854	−	0.00197854i	−0.708095	+	0.706117i	$0.750445\pi$
$398$		0			0
$399$		−	200.687i		−	0.502974i
$400$		0			0
$401$	−12.9629			−0.0323265			−0.0161632	−	0.999869i	$-0.505145\pi$
$401$	−12.9629			−0.0323265			−0.0161632	+	0.999869i	$0.505145\pi$
$402$		0			0
$403$	157.575	−	157.575i	0.391005	−	0.391005i
$404$		0			0
$405$	225.159	+	212.441i	0.555948	+	0.524547i
$406$		0			0
$407$	−357.575	−	357.575i	−0.878562	−	0.878562i
$408$		0			0
$409$			160.763i			0.393062i	0.980498	+	0.196531i	$0.0629677\pi$
$409$			160.763i			0.393062i	−0.980498	+	0.196531i	$0.937032\pi$
$410$		0			0
$411$	160.153			0.389666
$412$		0			0
$413$	137.957	−	137.957i	0.334038	−	0.334038i
$414$		0			0
$415$	−152.184	+	4.42271i	−0.366708	+	0.0106571i
$416$		0			0
$417$	32.1501	+	32.1501i	0.0770985	+	0.0770985i
$418$		0			0
$419$			615.188i			1.46823i	0.679026	+	0.734114i	$0.262402\pi$
$419$			615.188i			1.46823i	−0.679026	+	0.734114i	$0.737598\pi$
$420$		0			0
$421$	698.793			1.65984			0.829921	−	0.557881i	$-0.188386\pi$
$421$	698.793			1.65984			0.829921	+	0.557881i	$0.188386\pi$
$422$		0			0
$423$	404.707	−	404.707i	0.956754	−	0.956754i
$424$		0			0
$425$	−34.1272	+	38.3430i	−0.0802993	+	0.0902188i
$426$		0			0
$427$	−132.234	−	132.234i	−0.309681	−	0.309681i
$428$		0			0
$429$			170.664i			0.397817i
$430$		0			0
$431$	−217.377			−0.504355			−0.252178	−	0.967681i	$-0.581147\pi$
$431$	−217.377			−0.504355			−0.252178	+	0.967681i	$0.581147\pi$
$432$		0			0
$433$	335.157	−	335.157i	0.774035	−	0.774035i	−0.204774	−	0.978809i	$-0.565646\pi$
$433$	335.157	−	335.157i	0.774035	−	0.774035i	0.978809	+	0.204774i	$0.0656460\pi$
$434$		0			0
$435$	−3.69690	−	127.209i	−0.00849862	−	0.292435i
$436$		0			0
$437$	−93.3430	−	93.3430i	−0.213599	−	0.213599i
$438$		0			0
$439$		−	460.314i		−	1.04855i	−0.851548	−	0.524276i	$-0.824336\pi$
$439$		−	460.314i		−	1.04855i	0.851548	−	0.524276i	$-0.175664\pi$
$440$		0			0
$441$	−330.930			−0.750409
$442$		0			0
$443$	−596.819	+	596.819i	−1.34722	+	1.34722i	−0.458557	+	0.888665i	$0.651633\pi$
$443$	−596.819	+	596.819i	−1.34722	+	1.34722i	−0.888665	+	0.458557i	$0.848367\pi$
$444$		0			0
$445$	−150.028	+	159.010i	−0.337143	+	0.357325i
$446$		0			0
$447$	31.5309	+	31.5309i	0.0705390	+	0.0705390i
$448$		0			0
$449$		−	550.621i		−	1.22633i	−0.789956	−	0.613164i	$-0.789896\pi$
$449$		−	550.621i		−	1.22633i	0.789956	−	0.613164i	$-0.210104\pi$
$450$		0			0
$451$	776.139			1.72093
$452$		0			0
$453$	32.9401	−	32.9401i	0.0727155	−	0.0727155i
$454$		0			0
$455$	−362.876	−	342.380i	−0.797530	−	0.752484i
$456$		0			0
$457$	−37.3610	−	37.3610i	−0.0817527	−	0.0817527i	0.665048	−	0.746801i	$-0.268411\pi$
$457$	−37.3610	−	37.3610i	−0.0817527	−	0.0817527i	−0.746801	+	0.665048i	$0.768411\pi$
$458$		0			0
$459$		−	30.2300i		−	0.0658605i
$460$		0			0
$461$	−44.1096			−0.0956823			−0.0478412	−	0.998855i	$-0.515234\pi$
$461$	−44.1096			−0.0956823			−0.0478412	+	0.998855i	$0.515234\pi$
$462$		0			0
$463$	−456.480	+	456.480i	−0.985917	+	0.985917i	−0.999902	−	0.0139851i	$-0.995548\pi$
$463$	−456.480	+	456.480i	−0.985917	+	0.985917i	0.0139851	+	0.999902i	$0.495548\pi$
$464$		0			0
$465$	89.7543	−	2.60840i	0.193020	−	0.00560947i
$466$		0			0
$467$	−215.927	−	215.927i	−0.462369	−	0.462369i	0.437062	−	0.899431i	$-0.356019\pi$
$467$	−215.927	−	215.927i	−0.462369	−	0.462369i	−0.899431	+	0.437062i	$0.856019\pi$
$468$		0			0
$469$		−	479.914i		−	1.02327i
$470$		0			0
$471$	−63.4112			−0.134631
$472$		0			0
$473$	−710.025	+	710.025i	−1.50111	+	1.50111i
$474$		0			0
$475$	−622.892	+	36.2351i	−1.31135	+	0.0762844i
$476$		0			0
$477$	−280.726	−	280.726i	−0.588524	−	0.588524i
$478$		0			0
$479$			575.554i			1.20157i	0.799409	+	0.600787i	$0.205146\pi$
$479$			575.554i			1.20157i	−0.799409	+	0.600787i	$0.794854\pi$
$480$		0			0
$481$	−282.531			−0.587384
$482$		0			0
$483$	30.0737	−	30.0737i	0.0622644	−	0.0622644i
$484$		0			0
$485$	21.2860	+	732.442i	0.0438886	+	1.51019i
$486$		0			0
$487$	640.184	+	640.184i	1.31455	+	1.31455i	0.918027	+	0.396519i	$0.129782\pi$
$487$	640.184	+	640.184i	1.31455	+	1.31455i	0.396519	+	0.918027i	$0.370218\pi$
$488$		0			0
$489$		−	167.956i		−	0.343469i
$490$		0			0
$491$	366.437			0.746308			0.373154	−	0.927769i	$-0.378276\pi$
$491$	366.437			0.746308			0.373154	+	0.927769i	$0.378276\pi$
$492$		0			0
$493$	43.3546	−	43.3546i	0.0879403	−	0.0879403i
$494$		0			0
$495$	537.428	−	569.600i	1.08571	−	1.15071i
$496$		0			0
$497$	806.501	+	806.501i	1.62274	+	1.62274i
$498$		0			0
$499$		−	155.752i		−	0.312128i	−0.987747	−	0.156064i	$-0.950119\pi$
$499$		−	155.752i		−	0.312128i	0.987747	−	0.156064i	$-0.0498806\pi$
$500$		0			0
$501$	165.926			0.331189
$502$		0			0
$503$	−369.957	+	369.957i	−0.735501	+	0.735501i	−0.971704	−	0.236203i	$-0.924097\pi$
$503$	−369.957	+	369.957i	−0.735501	+	0.735501i	0.236203	+	0.971704i	$0.424097\pi$
$504$		0			0
$505$	381.595	+	360.042i	0.755633	+	0.712954i
$506$		0			0
$507$	−34.4337	−	34.4337i	−0.0679167	−	0.0679167i
$508$		0			0
$509$		−	26.6087i		−	0.0522764i	−0.999658	−	0.0261382i	$-0.991679\pi$
$509$		−	26.6087i		−	0.0522764i	0.999658	−	0.0261382i	$-0.00832099\pi$
$510$		0			0
$511$	1143.12			2.23702
$512$		0			0
$513$	259.831	−	259.831i	0.506494	−	0.506494i
$514$		0			0
$515$	413.322	−	12.0118i	0.802568	−	0.0233239i
$516$		0			0
$517$	−926.018	−	926.018i	−1.79114	−	1.79114i
$518$		0			0
$519$			200.799i			0.386895i
$520$		0			0
$521$	225.192			0.432229			0.216115	−	0.976368i	$-0.430661\pi$
$521$	225.192			0.432229			0.216115	+	0.976368i	$0.430661\pi$
$522$		0			0
$523$	149.824	−	149.824i	0.286470	−	0.286470i	−0.549212	−	0.835683i	$-0.685072\pi$
$523$	149.824	−	149.824i	0.286470	−	0.286470i	0.835683	+	0.549212i	$0.185072\pi$
$524$		0			0
$525$	−11.6744	−	200.687i	−0.0222370	−	0.382260i
$526$		0			0
$527$	30.5895	+	30.5895i	0.0580445	+	0.0580445i
$528$		0			0
$529$			501.024i			0.947116i
$530$		0			0
$531$	171.103			0.322227
$532$		0			0
$533$	306.626	−	306.626i	0.575284	−	0.575284i
$534$		0			0
$535$	−7.23629	−	248.998i	−0.0135258	−	0.465417i
$536$		0			0
$537$	148.356	+	148.356i	0.276269	+	0.276269i
$538$		0			0
$539$			757.208i			1.40484i
$540$		0			0
$541$	−88.9275			−0.164376			−0.0821881	−	0.996617i	$-0.526191\pi$
$541$	−88.9275			−0.164376			−0.0821881	+	0.996617i	$0.526191\pi$
$542$		0			0
$543$	147.598	−	147.598i	0.271819	−	0.271819i
$544$		0			0
$545$	204.499	−	216.741i	0.375228	−	0.397691i
$546$		0			0
$547$	500.839	+	500.839i	0.915611	+	0.915611i	0.996706	−	0.0810954i	$-0.0258418\pi$
$547$	500.839	+	500.839i	0.915611	+	0.915611i	−0.0810954	+	0.996706i	$0.525842\pi$
$548$		0			0
$549$		−	164.004i		−	0.298732i
$550$		0			0
$551$	745.278			1.35259
$552$		0			0
$553$	−505.132	+	505.132i	−0.913440	+	0.913440i
$554$		0			0
$555$	−82.8031	−	78.1263i	−0.149195	−	0.140768i
$556$		0			0
$557$	−154.004	−	154.004i	−0.276488	−	0.276488i	0.555218	−	0.831705i	$-0.312635\pi$
$557$	−154.004	−	154.004i	−0.276488	−	0.276488i	−0.831705	+	0.555218i	$0.812635\pi$
$558$		0			0
$559$			561.014i			1.00360i
$560$		0			0
$561$	−33.1303			−0.0590558
$562$		0			0
$563$	−37.9353	+	37.9353i	−0.0673806	+	0.0673806i	−0.739994	−	0.672613i	$-0.765172\pi$
$563$	−37.9353	+	37.9353i	−0.0673806	+	0.0673806i	0.672613	+	0.739994i	$0.265172\pi$
$564$		0			0
$565$	50.7127	−	1.47379i	0.0897570	−	0.00260848i
$566$		0			0
$567$	−413.003	−	413.003i	−0.728400	−	0.728400i
$568$		0			0
$569$		−	34.3477i		−	0.0603650i	−0.999544	−	0.0301825i	$-0.990391\pi$
$569$		−	34.3477i		−	0.0603650i	0.999544	−	0.0301825i	$-0.00960884\pi$
$570$		0			0
$571$	746.810			1.30790			0.653949	−	0.756539i	$-0.273111\pi$
$571$	746.810			1.30790			0.653949	+	0.756539i	$0.273111\pi$
$572$		0			0
$573$	189.542	−	189.542i	0.330788	−	0.330788i
$574$		0			0
$575$	−98.7730	−	87.9130i	−0.171779	−	0.152892i
$576$		0			0
$577$	159.680	+	159.680i	0.276741	+	0.276741i	0.831807	−	0.555065i	$-0.187307\pi$
$577$	159.680	+	159.680i	0.276741	+	0.276741i	−0.555065	+	0.831807i	$0.687307\pi$
$578$		0			0
$579$			278.689i			0.481328i
$580$		0			0
$581$	287.259			0.494422
$582$		0			0
$583$	−642.335	+	642.335i	−1.10178	+	1.10178i
$584$		0			0
$585$	−12.7101	−	437.349i	−0.0217266	−	0.747606i
$586$		0			0
$587$	142.577	+	142.577i	0.242892	+	0.242892i	0.818045	−	0.575154i	$-0.195058\pi$
$587$	142.577	+	142.577i	0.242892	+	0.242892i	−0.575154	+	0.818045i	$0.695058\pi$
$588$		0			0
$589$			525.842i			0.892771i
$590$		0			0
$591$	38.3227			0.0648439
$592$		0			0
$593$	−558.096	+	558.096i	−0.941139	+	0.941139i	−0.998361	−	0.0572222i	$-0.981776\pi$
$593$	−558.096	+	558.096i	−0.941139	+	0.941139i	0.0572222	+	0.998361i	$0.481776\pi$
$594$		0			0
$595$	66.4651	−	70.4439i	0.111706	−	0.118393i
$596$		0			0
$597$	111.987	+	111.987i	0.187583	+	0.187583i
$598$		0			0
$599$			490.457i			0.818792i	0.912357	+	0.409396i	$0.134261\pi$
$599$			490.457i			0.818792i	−0.912357	+	0.409396i	$0.865739\pi$
$600$		0			0
$601$	195.955			0.326049			0.163024	−	0.986622i	$-0.447875\pi$
$601$	195.955			0.326049			0.163024	+	0.986622i	$0.447875\pi$
$602$		0			0
$603$	297.609	−	297.609i	0.493547	−	0.493547i
$604$		0			0
$605$	−863.268	−	814.509i	−1.42689	−	1.34630i
$606$		0			0
$607$	−794.791	−	794.791i	−1.30938	−	1.30938i	−0.921866	−	0.387510i	$-0.873335\pi$
$607$	−794.791	−	794.791i	−1.30938	−	1.30938i	−0.387510	−	0.921866i	$-0.626665\pi$
$608$		0			0
$609$			240.117i			0.394282i
$610$		0			0
$611$	−731.677			−1.19751
$612$		0			0
$613$	375.064	−	375.064i	0.611850	−	0.611850i	−0.331578	−	0.943428i	$-0.607581\pi$
$613$	375.064	−	375.064i	0.611850	−	0.611850i	0.943428	+	0.331578i	$0.107581\pi$
$614$		0			0
$615$	174.654	−	5.07572i	0.283990	−	0.00825320i
$616$		0			0
$617$	−104.254	−	104.254i	−0.168969	−	0.168969i	0.617557	−	0.786526i	$-0.288122\pi$
$617$	−104.254	−	104.254i	−0.168969	−	0.168969i	−0.786526	+	0.617557i	$0.788122\pi$
$618$		0			0
$619$		−	814.175i		−	1.31531i	−0.753320	−	0.657654i	$-0.771549\pi$
$619$		−	814.175i		−	1.31531i	0.753320	−	0.657654i	$-0.228451\pi$
$620$		0			0
$621$	77.8736			0.125400
$622$		0			0
$623$	291.667	−	291.667i	0.468165	−	0.468165i
$624$		0			0
$625$	−620.784	+	72.4702i	−0.993255	+	0.115952i
$626$		0			0
$627$	−284.760	−	284.760i	−0.454163	−	0.454163i
$628$		0			0
$629$		−	54.8469i		−	0.0871969i
$630$		0			0
$631$	527.697			0.836287			0.418144	−	0.908381i	$-0.362681\pi$
$631$	527.697			0.836287			0.418144	+	0.908381i	$0.362681\pi$
$632$		0			0
$633$	125.506	−	125.506i	0.198272	−	0.198272i
$634$		0			0
$635$	−13.9364	−	479.547i	−0.0219471	−	0.755192i
$636$		0			0
$637$	299.147	+	299.147i	0.469619	+	0.469619i
$638$		0			0
$639$			1000.27i			1.56537i
$640$		0			0
$641$	−732.552			−1.14283			−0.571414	−	0.820662i	$-0.693605\pi$
$641$	−732.552			−1.14283			−0.571414	+	0.820662i	$0.693605\pi$
$642$		0			0
$643$	−823.427	+	823.427i	−1.28060	+	1.28060i	−0.340276	+	0.940326i	$0.610520\pi$
$643$	−823.427	+	823.427i	−1.28060	+	1.28060i	−0.940326	+	0.340276i	$0.889480\pi$
$644$		0			0
$645$	−155.133	+	164.420i	−0.240516	+	0.254914i
$646$		0			0
$647$	−15.7978	−	15.7978i	−0.0244170	−	0.0244170i	0.694793	−	0.719210i	$-0.255496\pi$
$647$	−15.7978	−	15.7978i	−0.0244170	−	0.0244170i	−0.719210	+	0.694793i	$0.755496\pi$
$648$		0			0
$649$		−	391.504i		−	0.603242i
$650$		0			0
$651$	−169.419			−0.260243
$652$		0			0
$653$	688.691	−	688.691i	1.05466	−	1.05466i	0.0562395	−	0.998417i	$-0.482089\pi$
$653$	688.691	−	688.691i	1.05466	−	1.05466i	0.998417	−	0.0562395i	$-0.0179110\pi$
$654$		0			0
$655$	−504.028	−	475.560i	−0.769509	−	0.726046i
$656$		0			0
$657$	708.880	+	708.880i	1.07896	+	1.07896i
$658$		0			0
$659$			107.478i			0.163092i	0.996670	+	0.0815461i	$0.0259858\pi$
$659$			107.478i			0.163092i	−0.996670	+	0.0815461i	$0.974014\pi$
$660$		0			0
$661$	90.5769			0.137030			0.0685151	−	0.997650i	$-0.478174\pi$
$661$	90.5769			0.137030			0.0685151	+	0.997650i	$0.478174\pi$
$662$		0			0
$663$	−13.0887	+	13.0887i	−0.0197416	+	0.0197416i
$664$		0			0
$665$	1176.75	−	34.1983i	1.76955	−	0.0514261i
$666$		0			0
$667$	111.683	+	111.683i	0.167441	+	0.167441i
$668$		0			0
$669$			20.7601i			0.0310315i
$670$		0			0
$671$	−375.261			−0.559256
$672$		0			0
$673$	475.529	−	475.529i	0.706582	−	0.706582i	−0.259233	−	0.965815i	$-0.583470\pi$
$673$	475.529	−	475.529i	0.706582	−	0.706582i	0.965815	+	0.259233i	$0.0834698\pi$
$674$		0			0
$675$	244.716	−	274.946i	0.362543	−	0.407328i
$676$		0			0
$677$	−180.515	−	180.515i	−0.266640	−	0.266640i	0.561105	−	0.827745i	$-0.310376\pi$
$677$	−180.515	−	180.515i	−0.266640	−	0.266640i	−0.827745	+	0.561105i	$0.810376\pi$
$678$		0			0
$679$		−	1382.54i		−	2.03615i
$680$		0			0
$681$	−27.5075			−0.0403928
$682$		0			0
$683$	−110.821	+	110.821i	−0.162257	+	0.162257i	−0.783566	−	0.621309i	$-0.786601\pi$
$683$	−110.821	+	110.821i	−0.162257	+	0.162257i	0.621309	+	0.783566i	$0.286601\pi$
$684$		0			0
$685$	27.2911	+	939.076i	0.0398410	+	1.37091i
$686$		0			0
$687$	178.063	+	178.063i	0.259189	+	0.259189i
$688$		0			0
$689$			507.530i			0.736618i
$690$		0			0
$691$	151.424			0.219138			0.109569	−	0.993979i	$-0.465053\pi$
$691$	151.424			0.219138			0.109569	+	0.993979i	$0.465053\pi$
$692$		0			0
$693$	−1044.80	+	1044.80i	−1.50765	+	1.50765i
$694$		0			0
$695$	−183.038	+	193.995i	−0.263364	+	0.279129i
$696$		0			0
$697$	59.5243	+	59.5243i	0.0854008	+	0.0854008i
$698$		0			0
$699$		−	171.430i		−	0.245250i
$700$		0			0
$701$	−749.571			−1.06929			−0.534644	−	0.845078i	$-0.679554\pi$
$701$	−749.571			−1.06929			−0.534644	+	0.845078i	$0.679554\pi$
$702$		0			0
$703$	471.417	−	471.417i	0.670579	−	0.670579i
$704$		0			0
$705$	−214.437	−	202.325i	−0.304166	−	0.286986i
$706$		0			0
$707$	−699.949	−	699.949i	−0.990027	−	0.990027i
$708$		0			0
$709$		−	693.295i		−	0.977849i	−0.872326	−	0.488924i	$-0.837389\pi$
$709$		−	693.295i		−	0.977849i	0.872326	−	0.488924i	$-0.162611\pi$
$710$		0			0
$711$	−626.494			−0.881145
$712$		0			0
$713$	−78.7996	+	78.7996i	−0.110518	+	0.110518i
$714$		0			0
$715$	−1000.71	+	29.0822i	−1.39959	+	0.0406744i
$716$		0			0
$717$	−11.9524	−	11.9524i	−0.0166700	−	0.0166700i
$718$		0			0
$719$		−	551.737i		−	0.767368i	−0.923465	−	0.383684i	$-0.874655\pi$
$719$		−	551.737i		−	0.767368i	0.923465	−	0.383684i	$-0.125345\pi$
$720$		0			0
$721$	−780.179			−1.08208
$722$		0			0
$723$	−106.870	+	106.870i	−0.147815	+	0.147815i
$724$		0			0
$725$	745.278	−	43.3546i	1.02797	−	0.0597994i
$726$		0			0
$727$	135.393	+	135.393i	0.186235	+	0.186235i	0.794066	−	0.607831i	$-0.207960\pi$
$727$	135.393	+	135.393i	0.186235	+	0.186235i	−0.607831	+	0.794066i	$0.707960\pi$
$728$		0			0
$729$		−	399.286i		−	0.547717i
$730$		0			0
$731$	−108.908			−0.148985
$732$		0			0
$733$	175.077	−	175.077i	0.238850	−	0.238850i	−0.577524	−	0.816374i	$-0.695981\pi$
$733$	175.077	−	175.077i	0.238850	−	0.238850i	0.816374	+	0.577524i	$0.195981\pi$
$734$		0			0
$735$	4.95192	+	170.394i	0.00673730	+	0.231828i
$736$		0			0
$737$	−680.965	−	680.965i	−0.923968	−	0.923968i
$738$		0			0
$739$		−	843.090i		−	1.14085i	−0.821349	−	0.570426i	$-0.806778\pi$
$739$		−	843.090i		−	1.14085i	0.821349	−	0.570426i	$-0.193222\pi$
$740$		0			0
$741$	−224.998			−0.303641
$742$		0			0
$743$	−258.146	+	258.146i	−0.347438	+	0.347438i	−0.859154	−	0.511717i	$-0.829010\pi$
$743$	−258.146	+	258.146i	−0.347438	+	0.347438i	0.511717	+	0.859154i	$0.329010\pi$
$744$		0			0
$745$	−179.513	+	190.259i	−0.240957	+	0.255381i
$746$		0			0
$747$	178.138	+	178.138i	0.238471	+	0.238471i
$748$		0			0
$749$			470.004i			0.627509i
$750$		0			0
$751$	−1085.72			−1.44569			−0.722847	−	0.691008i	$-0.757167\pi$
$751$	−1085.72			−1.44569			−0.722847	+	0.691008i	$0.757167\pi$
$752$		0			0
$753$	116.661	−	116.661i	0.154928	−	0.154928i
$754$		0			0
$755$	198.762	+	187.536i	0.263261	+	0.248391i
$756$		0			0
$757$	−66.2802	−	66.2802i	−0.0875564	−	0.0875564i	0.661972	−	0.749528i	$-0.269720\pi$
$757$	−66.2802	−	66.2802i	−0.0875564	−	0.0875564i	−0.749528	+	0.661972i	$0.769720\pi$
$758$		0			0
$759$		−	85.3450i		−	0.112444i
$760$		0			0
$761$	843.565			1.10850			0.554248	−	0.832352i	$-0.313006\pi$
$761$	843.565			1.10850			0.554248	+	0.832352i	$0.313006\pi$
$762$		0			0
$763$	−397.563	+	397.563i	−0.521052	+	0.521052i
$764$		0			0
$765$	84.9012	−	2.46736i	0.110982	−	0.00322531i
$766$		0			0
$767$	−154.670	−	154.670i	−0.201656	−	0.201656i
$768$		0			0
$769$		−	510.795i		−	0.664233i	−0.943238	−	0.332117i	$-0.892237\pi$
$769$		−	510.795i		−	0.664233i	0.943238	−	0.332117i	$-0.107763\pi$
$770$		0			0
$771$	99.9260			0.129606
$772$		0			0
$773$	−738.046	+	738.046i	−0.954782	+	0.954782i	−0.999021	−	0.0442392i	$-0.985914\pi$
$773$	−738.046	+	738.046i	−0.954782	+	0.954782i	0.0442392	+	0.999021i	$0.485914\pi$
$774$		0			0
$775$	30.5895	+	525.842i	0.0394703	+	0.678506i
$776$		0			0
$777$	151.884	+	151.884i	0.195474	+	0.195474i
$778$		0			0
$779$			1023.24i			1.31353i
$780$		0			0
$781$	2288.74			2.93052
$782$		0			0
$783$	−310.883	+	310.883i	−0.397041	+	0.397041i
$784$		0			0
$785$	−10.8057	−	371.820i	−0.0137652	−	0.473656i
$786$		0			0
$787$	37.7557	+	37.7557i	0.0479742	+	0.0479742i	0.730687	−	0.682713i	$-0.239200\pi$
$787$	37.7557	+	37.7557i	0.0479742	+	0.0479742i	−0.682713	+	0.730687i	$0.739200\pi$
$788$		0			0
$789$			75.6114i			0.0958320i
$790$		0			0
$791$	−95.7243			−0.121017
$792$		0			0
$793$	−148.253	+	148.253i	−0.186952	+	0.186952i
$794$		0			0
$795$	−140.343	+	148.745i	−0.176532	+	0.187100i
$796$		0			0
$797$	548.908	+	548.908i	0.688717	+	0.688717i	0.961948	−	0.273231i	$-0.0880924\pi$
$797$	548.908	+	548.908i	0.688717	+	0.688717i	−0.273231	+	0.961948i	$0.588092\pi$
$798$		0			0
$799$		−	142.038i		−	0.177770i
$800$		0			0
$801$	361.742			0.451613
$802$		0			0
$803$	1622.00	−	1622.00i	2.01993	−	2.01993i
$804$		0			0
$805$	181.466	+	171.217i	0.225424	+	0.212691i
$806$		0			0
$807$	−110.113	−	110.113i	−0.136448	−	0.136448i
$808$		0			0
$809$		−	1107.00i		−	1.36836i	−0.729314	−	0.684179i	$-0.760161\pi$
$809$		−	1107.00i		−	1.36836i	0.729314	−	0.684179i	$-0.239839\pi$
$810$		0			0
$811$	515.451			0.635575			0.317787	−	0.948162i	$-0.397060\pi$
$811$	515.451			0.635575			0.317787	+	0.948162i	$0.397060\pi$
$812$		0			0
$813$	−156.411	+	156.411i	−0.192388	+	0.192388i
$814$		0			0
$815$	984.834	−	28.6208i	1.20838	−	0.0351176i
$816$		0			0
$817$	−936.078	−	936.078i	−1.14575	−	1.14575i
$818$		0			0
$819$			825.532i			1.00798i
$820$		0			0
$821$	−1033.03			−1.25826			−0.629132	−	0.777299i	$-0.716589\pi$
$821$	−1033.03			−1.25826			−0.629132	+	0.777299i	$0.716589\pi$
$822$		0			0
$823$	914.257	−	914.257i	1.11088	−	1.11088i	0.117852	−	0.993031i	$-0.462399\pi$
$823$	914.257	−	914.257i	1.11088	−	1.11088i	0.993031	−	0.117852i	$-0.0376009\pi$
$824$		0			0
$825$	−301.325	−	268.195i	−0.365243	−	0.325085i
$826$		0			0
$827$	−78.1826	−	78.1826i	−0.0945376	−	0.0945376i	0.658256	−	0.752794i	$-0.271294\pi$
$827$	−78.1826	−	78.1826i	−0.0945376	−	0.0945376i	−0.752794	+	0.658256i	$0.771294\pi$
$828$		0			0
$829$			585.489i			0.706260i	0.935574	+	0.353130i	$0.114883\pi$
$829$			585.489i			0.706260i	−0.935574	+	0.353130i	$0.885117\pi$
$830$		0			0
$831$	25.6952			0.0309209
$832$		0			0
$833$	−58.0725	+	58.0725i	−0.0697149	+	0.0697149i
$834$		0			0
$835$	28.2749	+	972.929i	0.0338621	+	1.16518i
$836$		0			0
$837$	−219.348	−	219.348i	−0.262065	−	0.262065i
$838$		0			0
$839$		−	562.781i		−	0.670776i	−0.942080	−	0.335388i	$-0.891133\pi$
$839$		−	562.781i		−	0.670776i	0.942080	−	0.335388i	$-0.108867\pi$
$840$		0			0
$841$	−50.7101			−0.0602974
$842$		0			0
$843$	57.3825	−	57.3825i	0.0680694	−	0.0680694i
$844$		0			0
$845$	196.039	−	207.775i	0.231999	−	0.245887i
$846$		0			0
$847$	1583.47	+	1583.47i	1.86950	+	1.86950i
$848$		0			0
$849$			225.846i			0.266014i
$850$		0			0
$851$	141.288			0.166025
$852$		0			0
$853$	−802.876	+	802.876i	−0.941238	+	0.941238i	−0.998367	−	0.0571289i	$-0.981805\pi$
$853$	−802.876	+	802.876i	−0.941238	+	0.941238i	0.0571289	+	0.998367i	$0.481805\pi$
$854$		0			0
$855$	750.945	+	708.531i	0.878299	+	0.828691i
$856$		0			0
$857$	−326.199	−	326.199i	−0.380629	−	0.380629i	0.490700	−	0.871329i	$-0.336741\pi$
$857$	−326.199	−	326.199i	−0.380629	−	0.380629i	−0.871329	+	0.490700i	$0.836741\pi$
$858$		0			0
$859$		−	316.369i		−	0.368299i	−0.982898	−	0.184150i	$-0.941047\pi$
$859$		−	316.369i		−	0.368299i	0.982898	−	0.184150i	$-0.0589531\pi$
$860$		0			0
$861$	−329.673			−0.382896
$862$		0			0
$863$	−58.4008	+	58.4008i	−0.0676718	+	0.0676718i	−0.740133	−	0.672461i	$-0.765237\pi$
$863$	−58.4008	+	58.4008i	−0.0676718	+	0.0676718i	0.672461	+	0.740133i	$0.265237\pi$
$864$		0			0
$865$	−1177.41	+	34.2174i	−1.36117	+	0.0395577i
$866$		0			0
$867$	171.641	+	171.641i	0.197971	+	0.197971i
$868$		0			0
$869$			1433.49i			1.64959i
$870$		0			0
$871$	−538.052			−0.617741
$872$		0			0
$873$	857.355	−	857.355i	0.982079	−	0.982079i
$874$		0			0
$875$	1174.76	−	102.653i	1.34259	−	0.117317i
$876$		0			0
$877$	385.728	+	385.728i	0.439826	+	0.439826i	0.891953	−	0.452127i	$-0.149335\pi$
$877$	385.728	+	385.728i	0.439826	+	0.439826i	−0.452127	+	0.891953i	$0.649335\pi$
$878$		0			0
$879$			41.1478i			0.0468120i
$880$		0			0
$881$	571.152			0.648299			0.324150	−	0.946006i	$-0.394922\pi$
$881$	571.152			0.648299			0.324150	+	0.946006i	$0.394922\pi$
$882$		0			0
$883$	−421.346	+	421.346i	−0.477176	+	0.477176i	−0.904227	−	0.427052i	$-0.859552\pi$
$883$	−421.346	+	421.346i	−0.477176	+	0.477176i	0.427052	+	0.904227i	$0.359552\pi$
$884$		0			0
$885$	−2.56032	−	88.0997i	−0.00289302	−	0.0995477i
$886$		0			0
$887$	630.048	+	630.048i	0.710313	+	0.710313i	0.966601	−	0.256287i	$-0.0824993\pi$
$887$	630.048	+	630.048i	0.710313	+	0.710313i	−0.256287	+	0.966601i	$0.582499\pi$
$888$		0			0
$889$			905.184i			1.01820i
$890$		0			0
$891$	−1172.04			−1.31542
$892$		0			0
$893$	1220.84	−	1220.84i	1.36712	−	1.36712i
$894$		0			0
$895$	−844.626	+	895.188i	−0.943716	+	1.00021i
$896$		0			0
$897$	−33.7169	−	33.7169i	−0.0375885	−	0.0375885i
$898$		0			0
$899$		−	629.160i		−	0.699844i
$900$		0			0
$901$	−98.5250			−0.109351
$902$		0			0
$903$	301.590	−	301.590i	0.333987	−	0.333987i
$904$		0			0
$905$	890.611	+	840.307i	0.984100	+	0.928516i
$906$		0			0
$907$	442.774	+	442.774i	0.488174	+	0.488174i	0.907730	−	0.419556i	$-0.137814\pi$
$907$	442.774	+	442.774i	0.488174	+	0.488174i	−0.419556	+	0.907730i	$0.637814\pi$
$908$		0			0
$909$		−	868.117i		−	0.955024i
$910$		0			0
$911$	66.1784			0.0726437			0.0363218	−	0.999340i	$-0.488436\pi$
$911$	66.1784			0.0726437			0.0363218	+	0.999340i	$0.488436\pi$
$912$		0			0
$913$	407.601	−	407.601i	0.446441	−	0.446441i
$914$		0			0
$915$	−84.4445	+	2.45409i	−0.0922891	+	0.00268207i
$916$		0			0
$917$	924.526	+	924.526i	1.00821	+	1.00821i
$918$		0			0
$919$			1418.58i			1.54361i	0.635858	+	0.771806i	$0.280647\pi$
$919$			1418.58i			1.54361i	−0.635858	+	0.771806i	$0.719353\pi$
$920$		0			0
$921$	−436.077			−0.473482
$922$		0			0
$923$	904.203	−	904.203i	0.979635	−	0.979635i
$924$		0			0
$925$	443.994	−	498.841i	0.479993	−	0.539287i
$926$		0			0
$927$	−483.811	−	483.811i	−0.521911	−	0.521911i
$928$		0			0
$929$			594.537i			0.639975i	0.947422	+	0.319987i	$0.103679\pi$
$929$			594.537i			0.639975i	−0.947422	+	0.319987i	$0.896321\pi$
$930$		0			0
$931$	−998.283			−1.07227
$932$		0			0
$933$	71.7819	−	71.7819i	0.0769366	−	0.0769366i
$934$		0			0
$935$	−5.64563	−	194.264i	−0.00603810	−	0.207769i
$936$		0			0
$937$	183.026	+	183.026i	0.195332	+	0.195332i	0.797996	−	0.602663i	$-0.205894\pi$
$937$	183.026	+	183.026i	0.195332	+	0.195332i	−0.602663	+	0.797996i	$0.705894\pi$
$938$		0			0
$939$		−	245.105i		−	0.261027i
$940$		0			0
$941$	−1438.39			−1.52857			−0.764286	−	0.644877i	$-0.776908\pi$
$941$	−1438.39			−1.52857			−0.764286	+	0.644877i	$0.776908\pi$
$942$		0			0
$943$	−153.337	+	153.337i	−0.162605	+	0.162605i
$944$		0			0
$945$	−476.602	+	505.132i	−0.504340	+	0.534532i
$946$		0			0
$947$	917.916	+	917.916i	0.969289	+	0.969289i	0.999542	−	0.0302535i	$-0.00963145\pi$
$947$	917.916	+	917.916i	0.969289	+	0.969289i	−0.0302535	+	0.999542i	$0.509631\pi$
$948$		0			0
$949$		−	1281.60i		−	1.35047i
$950$		0			0
$951$	−168.194			−0.176861
$952$		0			0
$953$	304.518	−	304.518i	0.319537	−	0.319537i	−0.529052	−	0.848589i	$-0.677453\pi$
$953$	304.518	−	304.518i	0.319537	−	0.319537i	0.848589	+	0.529052i	$0.177453\pi$
$954$		0			0
$955$	1143.70	+	1079.10i	1.19759	+	1.12995i
$956$		0			0
$957$	340.710	+	340.710i	0.356019	+	0.356019i
$958$		0			0
$959$		−	1772.58i		−	1.84837i
$960$		0			0
$961$	−517.087			−0.538072
$962$		0			0
$963$	−291.463	+	291.463i	−0.302661	+	0.302661i
$964$		0			0
$965$	−1634.13	+	47.4905i	−1.69340	+	0.0492129i
$966$		0			0
$967$	−196.607	−	196.607i	−0.203317	−	0.203317i	0.598103	−	0.801419i	$-0.295921\pi$
$967$	−196.607	−	196.607i	−0.203317	−	0.203317i	−0.801419	+	0.598103i	$0.795921\pi$
$968$		0			0
$969$		−	43.6781i		−	0.0450755i
$970$		0			0
$971$	−508.204			−0.523382			−0.261691	−	0.965152i	$-0.584280\pi$
$971$	−508.204			−0.523382			−0.261691	+	0.965152i	$0.584280\pi$
$972$		0			0
$973$	355.840	−	355.840i	0.365714	−	0.365714i
$974$		0			0
$975$	−224.998	+	13.0887i	−0.230767	+	0.0134243i
$976$		0			0
$977$	−312.722	−	312.722i	−0.320084	−	0.320084i	0.528716	−	0.848799i	$-0.322674\pi$
$977$	−312.722	−	312.722i	−0.320084	−	0.320084i	−0.848799	+	0.528716i	$0.822674\pi$
$978$		0			0
$979$		−	827.710i		−	0.845465i
$980$		0			0
$981$	−493.080			−0.502630
$982$		0			0
$983$	978.034	−	978.034i	0.994948	−	0.994948i	−0.00503914	−	0.999987i	$-0.501604\pi$
$983$	978.034	−	978.034i	0.994948	−	0.994948i	0.999987	+	0.00503914i	$0.00160401\pi$
$984$		0			0
$985$	6.53045	+	224.710i	0.00662989	+	0.228132i
$986$		0			0
$987$	393.336	+	393.336i	0.398517	+	0.398517i
$988$		0			0
$989$		−	280.550i		−	0.283671i
$990$		0			0
$991$	1032.30			1.04168			0.520838	−	0.853656i	$-0.325620\pi$
$991$	1032.30			1.04168			0.520838	+	0.853656i	$0.325620\pi$
$992$		0			0
$993$	87.1940	−	87.1940i	0.0878087	−	0.0878087i
$994$		0			0
$995$	−637.568	+	675.735i	−0.640772	+	0.679130i
$996$		0			0
$997$	−430.764	−	430.764i	−0.432060	−	0.432060i	0.457268	−	0.889329i	$-0.348828\pi$
$997$	−430.764	−	430.764i	−0.432060	−	0.432060i	−0.889329	+	0.457268i	$0.848828\pi$
$998$		0			0
$999$			393.291i			0.393685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.3.p.e.97.2	yes	6
4.3	odd	2		160.3.p.f.97.2	yes	6
5.2	odd	4		800.3.p.j.193.2		6
5.3	odd	4	inner	160.3.p.e.33.2	✓	6
5.4	even	2		800.3.p.j.257.2		6
8.3	odd	2		320.3.p.n.257.2		6
8.5	even	2		320.3.p.m.257.2		6
20.3	even	4		160.3.p.f.33.2	yes	6
20.7	even	4		800.3.p.i.193.2		6
20.19	odd	2		800.3.p.i.257.2		6
40.3	even	4		320.3.p.n.193.2		6
40.13	odd	4		320.3.p.m.193.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.3.p.e.33.2	✓	6	5.3	odd	4	inner
160.3.p.e.97.2	yes	6	1.1	even	1	trivial
160.3.p.f.33.2	yes	6	20.3	even	4
160.3.p.f.97.2	yes	6	4.3	odd	2
320.3.p.m.193.2		6	40.13	odd	4
320.3.p.m.257.2		6	8.5	even	2
320.3.p.n.193.2		6	40.3	even	4
320.3.p.n.257.2		6	8.3	odd	2
800.3.p.i.193.2		6	20.7	even	4
800.3.p.i.257.2		6	20.19	odd	2
800.3.p.j.193.2		6	5.2	odd	4
800.3.p.j.257.2		6	5.4	even	2

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	160.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.602705 + 0.602705i) q^{3} +(-3.63675 - 3.43134i) q^{5} +(6.67079 + 6.67079i) q^{7} +8.27349i q^{9} +18.9308 q^{11} +(7.47890 - 7.47890i) q^{13} +(4.25997 - 0.123802i) q^{15} +(1.45185 + 1.45185i) q^{17} +24.9578i q^{19} -8.04103 q^{21} +(-3.74003 + 3.74003i) q^{23} +(1.45185 + 24.9578i) q^{25} +(-10.4108 - 10.4108i) q^{27} -29.8615i q^{29} +21.0692 q^{31} +(-11.4097 + 11.4097i) q^{33} +(-1.37025 - 47.1497i) q^{35} +(-18.8886 - 18.8886i) q^{37} +9.01514i q^{39} +40.9988 q^{41} +(-37.5064 + 37.5064i) q^{43} +(28.3891 - 30.0886i) q^{45} +(-48.9161 - 48.9161i) q^{47} +39.9988i q^{49} -1.75008 q^{51} +(-33.9308 + 33.9308i) q^{53} +(-68.8464 - 64.9578i) q^{55} +(-15.0422 - 15.0422i) q^{57} -20.6808i q^{59} -19.8228 q^{61} +(-55.1907 + 55.1907i) q^{63} +(-52.8615 + 1.53624i) q^{65} +(-35.9713 - 35.9713i) q^{67} -4.50827i q^{69} +120.900 q^{71} +(85.6808 - 85.6808i) q^{73} +(-15.9172 - 14.1672i) q^{75} +(126.283 + 126.283i) q^{77} +75.7230i q^{79} -61.9121 q^{81} +(21.5311 - 21.5311i) q^{83} +(-0.298225 - 10.2618i) q^{85} +(17.9977 + 17.9977i) q^{87} -43.7230i q^{89} +99.7804 q^{91} +(-12.6985 + 12.6985i) q^{93} +(85.6386 - 90.7652i) q^{95} +(-103.627 - 103.627i) q^{97} +156.623i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{5} - 8 q^{7} + 32 q^{11} - 14 q^{13} - 8 q^{15} - 14 q^{17} - 40 q^{21} - 56 q^{23} - 14 q^{25} - 48 q^{27} + 208 q^{31} + 72 q^{33} - 48 q^{35} + 86 q^{37} + 120 q^{41} - 176 q^{43} + 34 q^{45}+ \cdots - 250 q^{97}+O(q^{100}) \) 6 * q + 4 * q^5 - 8 * q^7 + 32 * q^11 - 14 * q^13 - 8 * q^15 - 14 * q^17 - 40 * q^21 - 56 * q^23 - 14 * q^25 - 48 * q^27 + 208 * q^31 + 72 * q^33 - 48 * q^35 + 86 * q^37 + 120 * q^41 - 176 * q^43 + 34 * q^45 - 104 * q^47 + 352 * q^51 - 122 * q^53 - 96 * q^55 - 208 * q^57 - 216 * q^61 - 216 * q^63 - 154 * q^65 - 80 * q^67 + 336 * q^71 + 70 * q^73 - 32 * q^75 + 264 * q^77 + 242 * q^81 - 208 * q^83 + 338 * q^85 - 144 * q^87 + 544 * q^91 - 72 * q^93 - 48 * q^95 - 250 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more