LMFDB - Embedded newform 160.4.n.f.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,4,Mod(63,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("160.63");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	160.n (of order $4$, degree $2$, 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:	$9.44030560092$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 48x^{6} + 628x^{4} + 1556x^{2} + 400 $ x^8 + 48x^6 + 628x^4 + 1556*x^2 + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.4
Root			$0.538834i$ of defining polynomial
Character	$\chi$	$=$	160.127
Dual form			160.4.n.f.63.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.17770 + 7.17770i) q^{3} +(8.50645 + 7.25537i) q^{5} +(7.22872 - 7.22872i) q^{7} +76.0387i q^{9} +O(q^{10})$	\(q+(7.17770 + 7.17770i) q^{3} +(8.50645 + 7.25537i) q^{5} +(7.22872 - 7.22872i) q^{7} +76.0387i q^{9} -22.5469i q^{11} +(44.0725 - 44.0725i) q^{13} +(8.97990 + 113.134i) q^{15} +(-37.0980 - 37.0980i) q^{17} -90.5796 q^{19} +103.771 q^{21} +(-77.6546 - 77.6546i) q^{23} +(19.7194 + 123.435i) q^{25} +(-351.985 + 351.985i) q^{27} -83.4978i q^{29} -33.6147i q^{31} +(161.835 - 161.835i) q^{33} +(113.938 - 9.04374i) q^{35} +(106.009 + 106.009i) q^{37} +632.678 q^{39} +215.984 q^{41} +(-116.709 - 116.709i) q^{43} +(-551.688 + 646.819i) q^{45} +(-96.1374 + 96.1374i) q^{47} +238.491i q^{49} -532.557i q^{51} +(-77.1541 + 77.1541i) q^{53} +(163.586 - 191.794i) q^{55} +(-650.153 - 650.153i) q^{57} +51.4970 q^{59} +77.1930 q^{61} +(549.662 + 549.662i) q^{63} +(694.662 - 55.1384i) q^{65} +(90.5523 - 90.5523i) q^{67} -1114.76i q^{69} -1151.60i q^{71} +(652.862 - 652.862i) q^{73} +(-744.438 + 1027.52i) q^{75} +(-162.985 - 162.985i) q^{77} -659.850 q^{79} -2999.84 q^{81} +(-443.591 - 443.591i) q^{83} +(-46.4127 - 584.732i) q^{85} +(599.322 - 599.322i) q^{87} +905.573i q^{89} -637.175i q^{91} +(241.276 - 241.276i) q^{93} +(-770.510 - 657.188i) q^{95} +(765.482 + 765.482i) q^{97} +1714.44 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} - 6 q^{5} + 70 q^{7}+O(q^{10}) $ 8 * q + 6 * q^3 - 6 * q^5 + 70 * q^7	$ 8 q + 6 q^{3} - 6 q^{5} + 70 q^{7} + 144 q^{13} - 134 q^{15} - 100 q^{17} + 176 q^{19} - 516 q^{21} - 198 q^{23} - 172 q^{25} - 288 q^{27} + 172 q^{33} + 170 q^{35} + 492 q^{37} + 756 q^{39} - 28 q^{41} + 654 q^{43} + 10 q^{45} - 690 q^{47} + 580 q^{53} - 2392 q^{55} - 248 q^{57} + 1808 q^{59} - 1068 q^{61} + 3106 q^{63} + 2200 q^{65} - 1878 q^{67} + 1952 q^{73} - 2178 q^{75} + 340 q^{77} - 1808 q^{79} - 7844 q^{81} - 506 q^{83} + 184 q^{85} + 784 q^{87} + 3708 q^{93} - 5800 q^{95} + 5576 q^{97} + 8412 q^{99}+O(q^{100}) $ 8 * q + 6 * q^3 - 6 * q^5 + 70 * q^7 + 144 * q^13 - 134 * q^15 - 100 * q^17 + 176 * q^19 - 516 * q^21 - 198 * q^23 - 172 * q^25 - 288 * q^27 + 172 * q^33 + 170 * q^35 + 492 * q^37 + 756 * q^39 - 28 * q^41 + 654 * q^43 + 10 * q^45 - 690 * q^47 + 580 * q^53 - 2392 * q^55 - 248 * q^57 + 1808 * q^59 - 1068 * q^61 + 3106 * q^63 + 2200 * q^65 - 1878 * q^67 + 1952 * q^73 - 2178 * q^75 + 340 * q^77 - 1808 * q^79 - 7844 * q^81 - 506 * q^83 + 184 * q^85 + 784 * q^87 + 3708 * q^93 - 5800 * q^95 + 5576 * q^97 + 8412 * q^99

Display 100 coefficients 10 coefficients

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
$3$	7.17770	+	7.17770i	1.38135	+	1.38135i	0.842230	+	0.539119i	$0.181243\pi$
$3$	7.17770	+	7.17770i	1.38135	+	1.38135i	0.539119	+	0.842230i	$0.318757\pi$
$4$		0			0
$5$	8.50645	+	7.25537i	0.760840	+	0.648940i
$5$	8.50645	+	7.25537i	0.760840	+	0.648940i
$6$		0			0
$7$	7.22872	−	7.22872i	0.390314	−	0.390314i	−0.484485	−	0.874799i	$-0.660993\pi$
$7$	7.22872	−	7.22872i	0.390314	−	0.390314i	0.874799	+	0.484485i	$0.160993\pi$
$8$		0			0
$9$			76.0387i			2.81625i
$10$		0			0
$11$		−	22.5469i		−	0.618013i	−0.951060	−	0.309007i	$-0.900003\pi$
$11$		−	22.5469i		−	0.618013i	0.951060	−	0.309007i	$-0.0999965\pi$
$12$		0			0
$13$	44.0725	−	44.0725i	0.940270	−	0.940270i	−0.0580442	−	0.998314i	$-0.518486\pi$
$13$	44.0725	−	44.0725i	0.940270	−	0.940270i	0.998314	+	0.0580442i	$0.0184864\pi$
$14$		0			0
$15$	8.97990	+	113.134i	0.154573	+	1.94740i
$16$		0			0
$17$	−37.0980	−	37.0980i	−0.529270	−	0.529270i	0.391085	−	0.920355i	$-0.372100\pi$
$17$	−37.0980	−	37.0980i	−0.529270	−	0.529270i	−0.920355	+	0.391085i	$0.872100\pi$
$18$		0			0
$19$	−90.5796			−1.09370			−0.546852	−	0.837229i	$-0.684174\pi$
$19$	−90.5796			−1.09370			−0.546852	+	0.837229i	$0.684174\pi$
$20$		0			0
$21$	103.771			1.07832
$22$		0			0
$23$	−77.6546	−	77.6546i	−0.704005	−	0.704005i	0.261263	−	0.965268i	$-0.415861\pi$
$23$	−77.6546	−	77.6546i	−0.704005	−	0.704005i	−0.965268	+	0.261263i	$0.915861\pi$
$24$		0			0
$25$	19.7194	+	123.435i	0.157755	+	0.987478i
$26$		0			0
$27$	−351.985	+	351.985i	−2.50887	+	2.50887i
$28$		0			0
$29$		−	83.4978i		−	0.534661i	−0.963605	−	0.267330i	$-0.913859\pi$
$29$		−	83.4978i		−	0.534661i	0.963605	−	0.267330i	$-0.0861415\pi$
$30$		0			0
$31$		−	33.6147i		−	0.194754i	−0.995248	−	0.0973770i	$-0.968955\pi$
$31$		−	33.6147i		−	0.194754i	0.995248	−	0.0973770i	$-0.0310453\pi$
$32$		0			0
$33$	161.835	−	161.835i	0.853692	−	0.853692i
$34$		0			0
$35$	113.938	−	9.04374i	0.550257	−	0.0436763i
$36$		0			0
$37$	106.009	+	106.009i	0.471021	+	0.471021i	0.902245	−	0.431224i	$-0.141918\pi$
$37$	106.009	+	106.009i	0.471021	+	0.471021i	−0.431224	+	0.902245i	$0.641918\pi$
$38$		0			0
$39$	632.678			2.59768
$40$		0			0
$41$	215.984			0.822710			0.411355	−	0.911475i	$-0.365056\pi$
$41$	215.984			0.822710			0.411355	+	0.911475i	$0.365056\pi$
$42$		0			0
$43$	−116.709	−	116.709i	−0.413905	−	0.413905i	0.469191	−	0.883097i	$-0.344545\pi$
$43$	−116.709	−	116.709i	−0.413905	−	0.413905i	−0.883097	+	0.469191i	$0.844545\pi$
$44$		0			0
$45$	−551.688	+	646.819i	−1.82757	+	2.14271i
$46$		0			0
$47$	−96.1374	+	96.1374i	−0.298363	+	0.298363i	−0.840373	−	0.542009i	$-0.817664\pi$
$47$	−96.1374	+	96.1374i	−0.298363	+	0.298363i	0.542009	+	0.840373i	$0.317664\pi$
$48$		0			0
$49$			238.491i			0.695310i
$50$		0			0
$51$		−	532.557i		−	1.46221i
$52$		0			0
$53$	−77.1541	+	77.1541i	−0.199961	+	0.199961i	−0.799983	−	0.600022i	$-0.795158\pi$
$53$	−77.1541	+	77.1541i	−0.199961	+	0.199961i	0.600022	+	0.799983i	$0.295158\pi$
$54$		0			0
$55$	163.586	−	191.794i	0.401053	−	0.470209i
$56$		0			0
$57$	−650.153	−	650.153i	−1.51079	−	1.51079i
$58$		0			0
$59$	51.4970			0.113633			0.0568164	−	0.998385i	$-0.481905\pi$
$59$	51.4970			0.113633			0.0568164	+	0.998385i	$0.481905\pi$
$60$		0			0
$61$	77.1930			0.162025			0.0810127	−	0.996713i	$-0.474185\pi$
$61$	77.1930			0.162025			0.0810127	+	0.996713i	$0.474185\pi$
$62$		0			0
$63$	549.662	+	549.662i	1.09922	+	1.09922i
$64$		0			0
$65$	694.662	−	55.1384i	1.32557	−	0.105217i
$66$		0			0
$67$	90.5523	−	90.5523i	0.165115	−	0.165115i	−0.619713	−	0.784828i	$-0.712751\pi$
$67$	90.5523	−	90.5523i	0.165115	−	0.165115i	0.784828	+	0.619713i	$0.212751\pi$
$68$		0			0
$69$		−	1114.76i		−	1.94495i
$70$		0			0
$71$		−	1151.60i		−	1.92493i	−0.271402	−	0.962466i	$-0.587487\pi$
$71$		−	1151.60i		−	1.92493i	0.271402	−	0.962466i	$-0.412513\pi$
$72$		0			0
$73$	652.862	−	652.862i	1.04674	−	1.04674i	0.0478835	−	0.998853i	$-0.484752\pi$
$73$	652.862	−	652.862i	1.04674	−	1.04674i	0.998853	−	0.0478835i	$-0.0152476\pi$
$74$		0			0
$75$	−744.438	+	1027.52i	−1.14614	+	1.58197i
$76$		0			0
$77$	−162.985	−	162.985i	−0.241219	−	0.241219i
$78$		0			0
$79$	−659.850			−0.939733			−0.469866	−	0.882738i	$-0.655698\pi$
$79$	−659.850			−0.939733			−0.469866	+	0.882738i	$0.655698\pi$
$80$		0			0
$81$	−2999.84			−4.11500
$82$		0			0
$83$	−443.591	−	443.591i	−0.586632	−	0.586632i	0.350086	−	0.936718i	$-0.386152\pi$
$83$	−443.591	−	443.591i	−0.586632	−	0.586632i	−0.936718	+	0.350086i	$0.886152\pi$
$84$		0			0
$85$	−46.4127	−	584.732i	−0.0592255	−	0.746154i
$86$		0			0
$87$	599.322	−	599.322i	0.738553	−	0.738553i
$88$		0			0
$89$			905.573i			1.07855i	0.842131	+	0.539273i	$0.181301\pi$
$89$			905.573i			1.07855i	−0.842131	+	0.539273i	$0.818699\pi$
$90$		0			0
$91$		−	637.175i		−	0.734001i
$92$		0			0
$93$	241.276	−	241.276i	0.269023	−	0.269023i
$94$		0			0
$95$	−770.510	−	657.188i	−0.832134	−	0.709748i
$96$		0			0
$97$	765.482	+	765.482i	0.801267	+	0.801267i	0.983294	−	0.182027i	$-0.0582658\pi$
$97$	765.482	+	765.482i	0.801267	+	0.801267i	−0.182027	+	0.983294i	$0.558266\pi$
$98$		0			0
$99$	1714.44			1.74048
$100$		0			0
$101$	−390.015			−0.384238			−0.192119	−	0.981372i	$-0.561536\pi$
$101$	−390.015			−0.384238			−0.192119	+	0.981372i	$0.561536\pi$
$102$		0			0
$103$	1313.47	+	1313.47i	1.25651	+	1.25651i	0.952749	+	0.303760i	$0.0982420\pi$
$103$	1313.47	+	1313.47i	1.25651	+	1.25651i	0.303760	+	0.952749i	$0.401758\pi$
$104$		0			0
$105$	882.724	+	752.898i	0.820429	+	0.699765i
$106$		0			0
$107$	109.469	−	109.469i	0.0989041	−	0.0989041i	−0.655923	−	0.754827i	$-0.727721\pi$
$107$	109.469	−	109.469i	0.0989041	−	0.0989041i	0.754827	+	0.655923i	$0.227721\pi$
$108$		0			0
$109$		−	1805.40i		−	1.58648i	−0.608910	−	0.793240i	$-0.708393\pi$
$109$		−	1805.40i		−	1.58648i	0.608910	−	0.793240i	$-0.291607\pi$
$110$		0			0
$111$			1521.80i			1.30129i
$112$		0			0
$113$	−830.023	+	830.023i	−0.690991	+	0.690991i	−0.962450	−	0.271459i	$-0.912494\pi$
$113$	−830.023	+	830.023i	−0.690991	+	0.690991i	0.271459	+	0.962450i	$0.412494\pi$
$114$		0			0
$115$	−97.1525	−	1223.98i	−0.0787784	−	0.992492i
$116$		0			0
$117$	3351.21	+	3351.21i	2.64803	+	2.64803i
$118$		0			0
$119$	−536.342			−0.413163
$120$		0			0
$121$	822.638			0.618060
$122$		0			0
$123$	1550.27	+	1550.27i	1.13645	+	1.13645i
$124$		0			0
$125$	−727.823	+	1193.06i	−0.520788	+	0.853686i
$126$		0			0
$127$	391.238	−	391.238i	0.273360	−	0.273360i	−0.557091	−	0.830451i	$-0.688083\pi$
$127$	391.238	−	391.238i	0.273360	−	0.273360i	0.830451	+	0.557091i	$0.188083\pi$
$128$		0			0
$129$		−	1675.40i		−	1.14349i
$130$		0			0
$131$			984.028i			0.656297i	0.944626	+	0.328149i	$0.106425\pi$
$131$			984.028i			0.656297i	−0.944626	+	0.328149i	$0.893575\pi$
$132$		0			0
$133$	−654.774	+	654.774i	−0.426888	+	0.426888i
$134$		0			0
$135$	−5547.92	+	440.363i	−3.53696	+	0.280744i
$136$		0			0
$137$	898.038	+	898.038i	0.560033	+	0.560033i	0.929317	−	0.369284i	$-0.120397\pi$
$137$	898.038	+	898.038i	0.560033	+	0.560033i	−0.369284	+	0.929317i	$0.620397\pi$
$138$		0			0
$139$	919.722			0.561222			0.280611	−	0.959822i	$-0.409463\pi$
$139$	919.722			0.561222			0.280611	+	0.959822i	$0.409463\pi$
$140$		0			0
$141$	−1380.09			−0.824287
$142$		0			0
$143$	−993.698	−	993.698i	−0.581099	−	0.581099i
$144$		0			0
$145$	605.807	−	710.270i	0.346962	−	0.406791i
$146$		0			0
$147$	−1711.82	+	1711.82i	−0.960465	+	0.960465i
$148$		0			0
$149$		−	14.7094i		−	0.00808751i	−0.999992	−	0.00404376i	$-0.998713\pi$
$149$		−	14.7094i		−	0.00808751i	0.999992	−	0.00404376i	$-0.00128717\pi$
$150$		0			0
$151$			1807.58i			0.974162i	0.873357	+	0.487081i	$0.161938\pi$
$151$			1807.58i			0.974162i	−0.873357	+	0.487081i	$0.838062\pi$
$152$		0			0
$153$	2820.88	−	2820.88i	1.49056	−	1.49056i
$154$		0			0
$155$	243.887	−	285.941i	0.126384	−	0.148177i
$156$		0			0
$157$	−1310.09	−	1310.09i	−0.665968	−	0.665968i	0.290813	−	0.956780i	$-0.406074\pi$
$157$	−1310.09	−	1310.09i	−0.665968	−	0.665968i	−0.956780	+	0.290813i	$0.906074\pi$
$158$		0			0
$159$	−1107.58			−0.552432
$160$		0			0
$161$	−1122.69			−0.549566
$162$		0			0
$163$	1651.12	+	1651.12i	0.793409	+	0.793409i	0.982047	−	0.188638i	$-0.0604072\pi$
$163$	1651.12	+	1651.12i	0.793409	+	0.793409i	−0.188638	+	0.982047i	$0.560407\pi$
$164$		0			0
$165$	2550.81	−	202.469i	1.20352	−	0.0955284i
$166$		0			0
$167$	−1351.83	+	1351.83i	−0.626393	+	0.626393i	−0.947159	−	0.320766i	$-0.896060\pi$
$167$	−1351.83	+	1351.83i	−0.626393	+	0.626393i	0.320766	+	0.947159i	$0.396060\pi$
$168$		0			0
$169$		−	1687.77i		−	0.768215i
$170$		0			0
$171$		−	6887.55i		−	3.08014i
$172$		0			0
$173$	−1023.63	+	1023.63i	−0.449855	+	0.449855i	−0.895306	−	0.445452i	$-0.853043\pi$
$173$	−1023.63	+	1023.63i	−0.449855	+	0.449855i	0.445452	+	0.895306i	$0.353043\pi$
$174$		0			0
$175$	1034.82	+	749.730i	0.447001	+	0.323853i
$176$		0			0
$177$	369.630	+	369.630i	0.156967	+	0.156967i
$178$		0			0
$179$	−3363.35			−1.40441			−0.702203	−	0.711977i	$-0.747800\pi$
$179$	−3363.35			−1.40441			−0.702203	+	0.711977i	$0.747800\pi$
$180$		0			0
$181$	−1060.52			−0.435514			−0.217757	−	0.976003i	$-0.569874\pi$
$181$	−1060.52			−0.435514			−0.217757	+	0.976003i	$0.569874\pi$
$182$		0			0
$183$	554.068	+	554.068i	0.223814	+	0.223814i
$184$		0			0
$185$	132.626	+	1670.89i	0.0527074	+	0.664035i
$186$		0			0
$187$	−836.445	+	836.445i	−0.327096	+	0.327096i
$188$		0			0
$189$			5088.80i			1.95850i
$190$		0			0
$191$		−	1129.90i		−	0.428045i	−0.976829	−	0.214023i	$-0.931343\pi$
$191$		−	1129.90i		−	0.428045i	0.976829	−	0.214023i	$-0.0686566\pi$
$192$		0			0
$193$	−2242.53	+	2242.53i	−0.836377	+	0.836377i	−0.988380	−	0.152003i	$-0.951428\pi$
$193$	−2242.53	+	2242.53i	−0.836377	+	0.836377i	0.152003	+	0.988380i	$0.451428\pi$
$194$		0			0
$195$	5381.84	+	4590.31i	1.97642	+	1.68574i
$196$		0			0
$197$	−2676.68	−	2676.68i	−0.968050	−	0.968050i	0.0314551	−	0.999505i	$-0.489986\pi$
$197$	−2676.68	−	2676.68i	−0.968050	−	0.968050i	−0.999505	+	0.0314551i	$0.989986\pi$
$198$		0			0
$199$	1895.72			0.675298			0.337649	−	0.941272i	$-0.390368\pi$
$199$	1895.72			0.675298			0.337649	+	0.941272i	$0.390368\pi$
$200$		0			0
$201$	1299.91			0.456164
$202$		0			0
$203$	−603.582	−	603.582i	−0.208686	−	0.208686i
$204$		0			0
$205$	1837.26	+	1567.05i	0.625950	+	0.533889i
$206$		0			0
$207$	5904.76	−	5904.76i	1.98265	−	1.98265i
$208$		0			0
$209$			2042.29i			0.675923i
$210$		0			0
$211$		−	142.506i		−	0.0464954i	−0.999730	−	0.0232477i	$-0.992599\pi$
$211$		−	142.506i		−	0.0464954i	0.999730	−	0.0232477i	$-0.00740064\pi$
$212$		0			0
$213$	8265.86	−	8265.86i	2.65900	−	2.65900i
$214$		0			0
$215$	−146.013	−	1839.54i	−0.0463161	−	0.583515i
$216$		0			0
$217$	−242.991	−	242.991i	−0.0760152	−	0.0760152i
$218$		0			0
$219$	9372.10			2.89182
$220$		0			0
$221$	−3270.00			−0.995313
$222$		0			0
$223$	817.872	+	817.872i	0.245600	+	0.245600i	0.819162	−	0.573562i	$-0.194439\pi$
$223$	817.872	+	817.872i	0.245600	+	0.245600i	−0.573562	+	0.819162i	$0.694439\pi$
$224$		0			0
$225$	−9385.82	+	1499.43i	−2.78098	+	0.444277i
$226$		0			0
$227$	−1645.11	+	1645.11i	−0.481013	+	0.481013i	−0.905455	−	0.424442i	$-0.860470\pi$
$227$	−1645.11	+	1645.11i	−0.481013	+	0.481013i	0.424442	+	0.905455i	$0.360470\pi$
$228$		0			0
$229$		−	1541.97i		−	0.444961i	−0.974937	−	0.222481i	$-0.928585\pi$
$229$		−	1541.97i		−	0.444961i	0.974937	−	0.222481i	$-0.0714154\pi$
$230$		0			0
$231$		−	2339.72i		−	0.666416i
$232$		0			0
$233$	−3898.79	+	3898.79i	−1.09621	+	1.09621i	−0.101365	+	0.994849i	$0.532321\pi$
$233$	−3898.79	+	3898.79i	−1.09621	+	1.09621i	−0.994849	+	0.101365i	$0.967679\pi$
$234$		0			0
$235$	−1515.30	+	120.276i	−0.420626	+	0.0333870i
$236$		0			0
$237$	−4736.20	−	4736.20i	−1.29810	−	1.29810i
$238$		0			0
$239$	−2825.46			−0.764703			−0.382351	−	0.924017i	$-0.624886\pi$
$239$	−2825.46			−0.764703			−0.382351	+	0.924017i	$0.624886\pi$
$240$		0			0
$241$	4910.23			1.31243			0.656215	−	0.754574i	$-0.272156\pi$
$241$	4910.23			1.31243			0.656215	+	0.754574i	$0.272156\pi$
$242$		0			0
$243$	−12028.3	−	12028.3i	−3.17538	−	3.17538i
$244$		0			0
$245$	−1730.34	+	2028.71i	−0.451214	+	0.529019i
$246$		0			0
$247$	−3992.07	+	3992.07i	−1.02838	+	1.02838i
$248$		0			0
$249$		−	6367.92i		−	1.62069i
$250$		0			0
$251$		−	3247.51i		−	0.816656i	−0.912835	−	0.408328i	$-0.866112\pi$
$251$		−	3247.51i		−	0.816656i	0.912835	−	0.408328i	$-0.133888\pi$
$252$		0			0
$253$	−1750.87	+	1750.87i	−0.435084	+	0.435084i
$254$		0			0
$255$	3863.89	−	4530.17i	0.948888	−	1.11251i
$256$		0			0
$257$	−4015.98	−	4015.98i	−0.974746	−	0.974746i	0.0249426	−	0.999689i	$-0.492060\pi$
$257$	−4015.98	−	4015.98i	−0.974746	−	0.974746i	−0.999689	+	0.0249426i	$0.992060\pi$
$258$		0			0
$259$	1532.62			0.367692
$260$		0			0
$261$	6349.07			1.50574
$262$		0			0
$263$	5220.50	+	5220.50i	1.22399	+	1.22399i	0.966200	+	0.257792i	$0.0829950\pi$
$263$	5220.50	+	5220.50i	1.22399	+	1.22399i	0.257792	+	0.966200i	$0.417005\pi$
$264$		0			0
$265$	−1216.09	+	96.5263i	−0.281901	+	0.0223757i
$266$		0			0
$267$	−6499.93	+	6499.93i	−1.48985	+	1.48985i
$268$		0			0
$269$			1195.10i			0.270880i	0.990786	+	0.135440i	$0.0432448\pi$
$269$			1195.10i			0.270880i	−0.990786	+	0.135440i	$0.956755\pi$
$270$		0			0
$271$			6076.07i			1.36197i	0.732295	+	0.680987i	$0.238449\pi$
$271$			6076.07i			1.36197i	−0.732295	+	0.680987i	$0.761551\pi$
$272$		0			0
$273$	4573.45	−	4573.45i	1.01391	−	1.01391i
$274$		0			0
$275$	2783.07	−	444.610i	0.610275	−	0.0974946i
$276$		0			0
$277$	−1891.18	−	1891.18i	−0.410216	−	0.410216i	0.471598	−	0.881814i	$-0.343677\pi$
$277$	−1891.18	−	1891.18i	−0.410216	−	0.410216i	−0.881814	+	0.471598i	$0.843677\pi$
$278$		0			0
$279$	2556.02			0.548475
$280$		0			0
$281$	4756.60			1.00980			0.504902	−	0.863176i	$-0.331528\pi$
$281$	4756.60			1.00980			0.504902	+	0.863176i	$0.331528\pi$
$282$		0			0
$283$	−1475.15	−	1475.15i	−0.309853	−	0.309853i	0.534999	−	0.844853i	$-0.320312\pi$
$283$	−1475.15	−	1475.15i	−0.309853	−	0.309853i	−0.844853	+	0.534999i	$0.820312\pi$
$284$		0			0
$285$	−813.396	−	10247.6i	−0.169058	−	2.12988i
$286$		0			0
$287$	1561.29	−	1561.29i	0.321115	−	0.321115i
$288$		0			0
$289$		−	2160.47i		−	0.439746i
$290$		0			0
$291$			10988.8i			2.21366i
$292$		0			0
$293$	−4216.60	+	4216.60i	−0.840739	+	0.840739i	−0.988955	−	0.148216i	$-0.952647\pi$
$293$	−4216.60	+	4216.60i	−0.840739	+	0.840739i	0.148216	+	0.988955i	$0.452647\pi$
$294$		0			0
$295$	438.057	+	373.630i	0.0864564	+	0.0737409i
$296$		0			0
$297$	7936.17	+	7936.17i	1.55052	+	1.55052i
$298$		0			0
$299$	−6844.87			−1.32391
$300$		0			0
$301$	−1687.31			−0.323106
$302$		0			0
$303$	−2799.41	−	2799.41i	−0.530766	−	0.530766i
$304$		0			0
$305$	656.639	+	560.064i	0.123275	+	0.105145i
$306$		0			0
$307$	1916.74	−	1916.74i	0.356332	−	0.356332i	−0.506127	−	0.862459i	$-0.668923\pi$
$307$	1916.74	−	1916.74i	0.356332	−	0.356332i	0.862459	+	0.506127i	$0.168923\pi$
$308$		0			0
$309$			18855.4i			3.47135i
$310$		0			0
$311$		−	8196.34i		−	1.49444i	−0.664575	−	0.747222i	$-0.731387\pi$
$311$		−	8196.34i		−	1.49444i	0.664575	−	0.747222i	$-0.268613\pi$
$312$		0			0
$313$	−2245.78	+	2245.78i	−0.405557	+	0.405557i	−0.880186	−	0.474629i	$-0.842582\pi$
$313$	−2245.78	+	2245.78i	−0.405557	+	0.405557i	0.474629	+	0.880186i	$0.342582\pi$
$314$		0			0
$315$	687.674	+	8663.68i	0.123003	+	1.54966i
$316$		0			0
$317$	6315.09	+	6315.09i	1.11890	+	1.11890i	0.991903	+	0.126996i	$0.0405335\pi$
$317$	6315.09	+	6315.09i	1.11890	+	1.11890i	0.126996	+	0.991903i	$0.459467\pi$
$318$		0			0
$319$	−1882.62			−0.330427
$320$		0			0
$321$	1571.47			0.273242
$322$		0			0
$323$	3360.32	+	3360.32i	0.578865	+	0.578865i
$324$		0			0
$325$	6309.16	+	4571.00i	1.07683	+	0.780164i
$326$		0			0
$327$	12958.6	−	12958.6i	2.19148	−	2.19148i
$328$		0			0
$329$			1389.90i			0.232911i
$330$		0			0
$331$		−	6647.92i		−	1.10394i	−0.833865	−	0.551968i	$-0.813877\pi$
$331$		−	6647.92i		−	1.10394i	0.833865	−	0.551968i	$-0.186123\pi$
$332$		0			0
$333$	−8060.78	+	8060.78i	−1.32651	+	1.32651i
$334$		0			0
$335$	1427.27	−	113.289i	0.232776	−	0.0184765i
$336$		0			0
$337$	−1790.96	−	1790.96i	−0.289495	−	0.289495i	0.547385	−	0.836881i	$-0.315623\pi$
$337$	−1790.96	−	1790.96i	−0.289495	−	0.289495i	−0.836881	+	0.547385i	$0.815623\pi$
$338$		0			0
$339$	−11915.3			−1.90900
$340$		0			0
$341$	−757.906			−0.120361
$342$		0			0
$343$	4203.44	+	4203.44i	0.661703	+	0.661703i
$344$		0			0
$345$	8088.01	−	9482.68i	1.26216	−	1.47980i
$346$		0			0
$347$	−4191.29	+	4191.29i	−0.648416	+	0.648416i	−0.952610	−	0.304194i	$-0.901613\pi$
$347$	−4191.29	+	4191.29i	−0.648416	+	0.648416i	0.304194	+	0.952610i	$0.401613\pi$
$348$		0			0
$349$		−	7954.16i		−	1.21999i	−0.792405	−	0.609995i	$-0.791171\pi$
$349$		−	7954.16i		−	1.21999i	0.792405	−	0.609995i	$-0.208829\pi$
$350$		0			0
$351$			31025.7i			4.71803i
$352$		0			0
$353$	−334.701	+	334.701i	−0.0504655	+	0.0504655i	−0.731889	−	0.681424i	$-0.761361\pi$
$353$	−334.701	+	334.701i	−0.0504655	+	0.0504655i	0.681424	+	0.731889i	$0.261361\pi$
$354$		0			0
$355$	8355.30	−	9796.06i	1.24916	−	1.46457i
$356$		0			0
$357$	−3849.70	−	3849.70i	−0.570722	−	0.570722i
$358$		0			0
$359$	−7065.80			−1.03877			−0.519385	−	0.854540i	$-0.673839\pi$
$359$	−7065.80			−1.03877			−0.519385	+	0.854540i	$0.673839\pi$
$360$		0			0
$361$	1345.66			0.196188
$362$		0			0
$363$	5904.64	+	5904.64i	0.853756	+	0.853756i
$364$		0			0
$365$	10290.3	−	816.786i	1.47567	−	0.117130i
$366$		0			0
$367$	−731.992	+	731.992i	−0.104114	+	0.104114i	−0.757245	−	0.653131i	$-0.773455\pi$
$367$	−731.992	+	731.992i	−0.104114	+	0.104114i	0.653131	+	0.757245i	$0.273455\pi$
$368$		0			0
$369$			16423.2i			2.31695i
$370$		0			0
$371$			1115.45i			0.156095i
$372$		0			0
$373$	5878.63	−	5878.63i	0.816042	−	0.816042i	−0.169490	−	0.985532i	$-0.554212\pi$
$373$	5878.63	−	5878.63i	0.816042	−	0.816042i	0.985532	+	0.169490i	$0.0542119\pi$
$374$		0			0
$375$	−13787.5	+	3339.35i	−1.89863	+	0.459849i
$376$		0			0
$377$	−3679.96	−	3679.96i	−0.502725	−	0.502725i
$378$		0			0
$379$	−8020.17			−1.08699			−0.543494	−	0.839413i	$-0.682899\pi$
$379$	−8020.17			−1.08699			−0.543494	+	0.839413i	$0.682899\pi$
$380$		0			0
$381$	5616.38			0.755212
$382$		0			0
$383$	−8766.73	−	8766.73i	−1.16961	−	1.16961i	−0.982302	−	0.187304i	$-0.940025\pi$
$383$	−8766.73	−	8766.73i	−1.16961	−	1.16961i	−0.187304	−	0.982302i	$-0.559975\pi$
$384$		0			0
$385$	−203.908	−	2568.94i	−0.0269925	−	0.340066i
$386$		0			0
$387$	8874.39	−	8874.39i	1.16566	−	1.16566i
$388$		0			0
$389$		−	10159.9i		−	1.32423i	−0.749400	−	0.662117i	$-0.769658\pi$
$389$		−	10159.9i		−	1.32423i	0.749400	−	0.662117i	$-0.230342\pi$
$390$		0			0
$391$			5761.67i			0.745217i
$392$		0			0
$393$	−7063.06	+	7063.06i	−0.906575	+	0.906575i
$394$		0			0
$395$	−5612.98	−	4787.45i	−0.714986	−	0.609830i
$396$		0			0
$397$	7418.76	+	7418.76i	0.937876	+	0.937876i	0.998180	−	0.0603043i	$-0.0192071\pi$
$397$	7418.76	+	7418.76i	0.937876	+	0.937876i	−0.0603043	+	0.998180i	$0.519207\pi$
$398$		0			0
$399$	−9399.54			−1.17936
$400$		0			0
$401$	−6353.35			−0.791200			−0.395600	−	0.918423i	$-0.629463\pi$
$401$	−6353.35			−0.791200			−0.395600	+	0.918423i	$0.629463\pi$
$402$		0			0
$403$	−1481.48	−	1481.48i	−0.183121	−	0.183121i
$404$		0			0
$405$	−25518.0	−	21764.9i	−3.13086	−	2.67039i
$406$		0			0
$407$	2390.17	−	2390.17i	0.291097	−	0.291097i
$408$		0			0
$409$		−	5593.99i		−	0.676296i	−0.941093	−	0.338148i	$-0.890200\pi$
$409$		−	5593.99i		−	0.676296i	0.941093	−	0.338148i	$-0.109800\pi$
$410$		0			0
$411$			12891.7i			1.54720i
$412$		0			0
$413$	372.257	−	372.257i	0.0443525	−	0.0443525i
$414$		0			0
$415$	−554.969	−	6991.80i	−0.0656443	−	0.827021i
$416$		0			0
$417$	6601.49	+	6601.49i	0.775243	+	0.775243i
$418$		0			0
$419$	8919.36			1.03995			0.519975	−	0.854181i	$-0.325941\pi$
$419$	8919.36			1.03995			0.519975	+	0.854181i	$0.325941\pi$
$420$		0			0
$421$	11549.9			1.33707			0.668537	−	0.743679i	$-0.266921\pi$
$421$	11549.9			1.33707			0.668537	+	0.743679i	$0.266921\pi$
$422$		0			0
$423$	−7310.16	−	7310.16i	−0.840265	−	0.840265i
$424$		0			0
$425$	3847.64	−	5310.73i	0.439148	−	0.606138i
$426$		0			0
$427$	558.007	−	558.007i	0.0632409	−	0.0632409i
$428$		0			0
$429$		−	14264.9i		−	1.60540i
$430$		0			0
$431$		−	3682.87i		−	0.411595i	−0.978595	−	0.205798i	$-0.934021\pi$
$431$		−	3682.87i		−	0.411595i	0.978595	−	0.205798i	$-0.0659789\pi$
$432$		0			0
$433$	−4319.68	+	4319.68i	−0.479424	+	0.479424i	−0.904947	−	0.425524i	$-0.860090\pi$
$433$	−4319.68	+	4319.68i	−0.479424	+	0.479424i	0.425524	+	0.904947i	$0.360090\pi$
$434$		0			0
$435$	9446.41	−	749.802i	1.04120	−	0.0826443i
$436$		0			0
$437$	7033.92	+	7033.92i	0.769973	+	0.769973i
$438$		0			0
$439$	15576.7			1.69347			0.846737	−	0.532012i	$-0.178564\pi$
$439$	15576.7			1.69347			0.846737	+	0.532012i	$0.178564\pi$
$440$		0			0
$441$	−18134.6			−1.95816
$442$		0			0
$443$	2731.69	+	2731.69i	0.292972	+	0.292972i	0.838253	−	0.545281i	$-0.183577\pi$
$443$	2731.69	+	2731.69i	0.292972	+	0.292972i	−0.545281	+	0.838253i	$0.683577\pi$
$444$		0			0
$445$	−6570.26	+	7703.21i	−0.699911	+	0.820600i
$446$		0			0
$447$	105.579	−	105.579i	0.0111717	−	0.0111717i
$448$		0			0
$449$			87.7242i			0.00922041i	0.999989	+	0.00461020i	$0.00146748\pi$
$449$			87.7242i			0.00922041i	−0.999989	+	0.00461020i	$0.998533\pi$
$450$		0			0
$451$		−	4869.78i		−	0.508445i
$452$		0			0
$453$	−12974.2	+	12974.2i	−1.34566	+	1.34566i
$454$		0			0
$455$	4622.94	−	5420.10i	0.476323	−	0.558458i
$456$		0			0
$457$	−8129.42	−	8129.42i	−0.832119	−	0.832119i	0.155687	−	0.987806i	$-0.450241\pi$
$457$	−8129.42	−	8129.42i	−0.832119	−	0.832119i	−0.987806	+	0.155687i	$0.950241\pi$
$458$		0			0
$459$	26115.9			2.65574
$460$		0			0
$461$	8841.51			0.893254			0.446627	−	0.894720i	$-0.352625\pi$
$461$	8841.51			0.893254			0.446627	+	0.894720i	$0.352625\pi$
$462$		0			0
$463$	5557.83	+	5557.83i	0.557871	+	0.557871i	0.928701	−	0.370830i	$-0.120927\pi$
$463$	5557.83	+	5557.83i	0.557871	+	0.557871i	−0.370830	+	0.928701i	$0.620927\pi$
$464$		0			0
$465$	3802.95	−	301.856i	0.379263	−	0.0301038i
$466$		0			0
$467$	7220.22	−	7220.22i	0.715443	−	0.715443i	−0.252226	−	0.967668i	$-0.581163\pi$
$467$	7220.22	−	7220.22i	0.715443	−	0.715443i	0.967668	+	0.252226i	$0.0811626\pi$
$468$		0			0
$469$		−	1309.15i		−	0.128894i
$470$		0			0
$471$		−	18806.9i		−	1.83987i
$472$		0			0
$473$	−2631.42	+	2631.42i	−0.255799	+	0.255799i
$474$		0			0
$475$	−1786.17	−	11180.7i	−0.172537	−	1.08001i
$476$		0			0
$477$	−5866.70	−	5866.70i	−0.563140	−	0.563140i
$478$		0			0
$479$	−10319.8			−0.984391			−0.492196	−	0.870485i	$-0.663805\pi$
$479$	−10319.8			−0.984391			−0.492196	+	0.870485i	$0.663805\pi$
$480$		0			0
$481$	9344.15			0.885773
$482$		0			0
$483$	−8058.31	−	8058.31i	−0.759143	−	0.759143i
$484$		0			0
$485$	957.682	+	12065.4i	0.0896620	+	1.12961i
$486$		0			0
$487$	−11226.7	+	11226.7i	−1.04462	+	1.04462i	−0.0456667	+	0.998957i	$0.514541\pi$
$487$	−11226.7	+	11226.7i	−1.04462	+	1.04462i	−0.998957	+	0.0456667i	$0.985459\pi$
$488$		0			0
$489$			23702.5i			2.19195i
$490$		0			0
$491$			3492.04i			0.320965i	0.987039	+	0.160482i	$0.0513050\pi$
$491$			3492.04i			0.320965i	−0.987039	+	0.160482i	$0.948695\pi$
$492$		0			0
$493$	−3097.60	+	3097.60i	−0.282980	+	0.282980i
$494$		0			0
$495$	14583.8	+	12438.9i	1.32423	+	1.12947i
$496$		0			0
$497$	−8324.62	−	8324.62i	−0.751328	−	0.751328i
$498$		0			0
$499$	−798.452			−0.0716305			−0.0358152	−	0.999358i	$-0.511403\pi$
$499$	−798.452			−0.0716305			−0.0358152	+	0.999358i	$0.511403\pi$
$500$		0			0
$501$	−19406.0			−1.73053
$502$		0			0
$503$	5583.41	+	5583.41i	0.494934	+	0.494934i	0.909857	−	0.414923i	$-0.136191\pi$
$503$	5583.41	+	5583.41i	0.494934	+	0.494934i	−0.414923	+	0.909857i	$0.636191\pi$
$504$		0			0
$505$	−3317.65	−	2829.70i	−0.292343	−	0.249347i
$506$		0			0
$507$	12114.3	−	12114.3i	1.06117	−	1.06117i
$508$		0			0
$509$		−	873.608i		−	0.0760746i	−0.999276	−	0.0380373i	$-0.987889\pi$
$509$		−	873.608i		−	0.0760746i	0.999276	−	0.0380373i	$-0.0121106\pi$
$510$		0			0
$511$		−	9438.72i		−	0.817112i
$512$		0			0
$513$	31882.6	−	31882.6i	2.74396	−	2.74396i
$514$		0			0
$515$	1643.27	+	20702.7i	0.140604	+	1.77140i
$516$		0			0
$517$	2167.60	+	2167.60i	0.184392	+	0.184392i
$518$		0			0
$519$	−14694.6			−1.24281
$520$		0			0
$521$	16592.0			1.39522			0.697610	−	0.716477i	$-0.254247\pi$
$521$	16592.0			1.39522			0.697610	+	0.716477i	$0.254247\pi$
$522$		0			0
$523$	−9354.36	−	9354.36i	−0.782099	−	0.782099i	0.198086	−	0.980185i	$-0.436528\pi$
$523$	−9354.36	−	9354.36i	−0.782099	−	0.782099i	−0.980185	+	0.198086i	$0.936528\pi$
$524$		0			0
$525$	2046.30	+	12809.0i	0.170110	+	1.06482i
$526$		0			0
$527$	−1247.04	+	1247.04i	−0.103077	+	0.103077i
$528$		0			0
$529$		−	106.514i		−	0.00875432i
$530$		0			0
$531$			3915.76i			0.320018i
$532$		0			0
$533$	9518.97	−	9518.97i	0.773569	−	0.773569i
$534$		0			0
$535$	1725.43	−	136.955i	0.139433	−	0.0110674i
$536$		0			0
$537$	−24141.1	−	24141.1i	−1.93997	−	1.93997i
$538$		0			0
$539$	5377.24			0.429710
$540$		0			0
$541$	2745.15			0.218157			0.109079	−	0.994033i	$-0.465210\pi$
$541$	2745.15			0.218157			0.109079	+	0.994033i	$0.465210\pi$
$542$		0			0
$543$	−7612.11	−	7612.11i	−0.601596	−	0.601596i
$544$		0			0
$545$	13098.9	−	15357.6i	1.02953	−	1.20706i
$546$		0			0
$547$	−9521.32	+	9521.32i	−0.744246	+	0.744246i	−0.973392	−	0.229146i	$-0.926407\pi$
$547$	−9521.32	+	9521.32i	−0.744246	+	0.744246i	0.229146	+	0.973392i	$0.426407\pi$
$548$		0			0
$549$			5869.66i			0.456304i
$550$		0			0
$551$			7563.20i			0.584760i
$552$		0			0
$553$	−4769.87	+	4769.87i	−0.366791	+	0.366791i
$554$		0			0
$555$	−11041.2	+	12945.1i	−0.844457	+	0.990071i
$556$		0			0
$557$	−16453.3	−	16453.3i	−1.25161	−	1.25161i	−0.954998	−	0.296613i	$-0.904143\pi$
$557$	−16453.3	−	16453.3i	−1.25161	−	1.25161i	−0.296613	−	0.954998i	$-0.595857\pi$
$558$		0			0
$559$	−10287.3			−0.778365
$560$		0			0
$561$	−12007.5			−0.903667
$562$		0			0
$563$	11754.1	+	11754.1i	0.879883	+	0.879883i	0.993522	−	0.113639i	$-0.0362507\pi$
$563$	11754.1	+	11754.1i	0.879883	+	0.879883i	−0.113639	+	0.993522i	$0.536251\pi$
$564$		0			0
$565$	−13082.7	+	1038.43i	−0.974145	+	0.0773221i
$566$		0			0
$567$	−21685.0	+	21685.0i	−1.60614	+	1.60614i
$568$		0			0
$569$			502.235i			0.0370031i	0.999829	+	0.0185016i	$0.00588956\pi$
$569$			502.235i			0.0370031i	−0.999829	+	0.0185016i	$0.994110\pi$
$570$		0			0
$571$		−	25439.5i		−	1.86446i	−0.361860	−	0.932232i	$-0.617858\pi$
$571$		−	25439.5i		−	1.86446i	0.361860	−	0.932232i	$-0.382142\pi$
$572$		0			0
$573$	8110.08	−	8110.08i	0.591280	−	0.591280i
$574$		0			0
$575$	8053.98	−	11116.6i	0.584129	−	0.806250i
$576$		0			0
$577$	10345.3	+	10345.3i	0.746416	+	0.746416i	0.973804	−	0.227388i	$-0.0730187\pi$
$577$	10345.3	+	10345.3i	0.746416	+	0.746416i	−0.227388	+	0.973804i	$0.573019\pi$
$578$		0			0
$579$	−32192.4			−2.31066
$580$		0			0
$581$	−6413.19			−0.457941
$582$		0			0
$583$	1739.59	+	1739.59i	0.123578	+	0.123578i
$584$		0			0
$585$	4192.65	+	52821.2i	0.296316	+	3.73314i
$586$		0			0
$587$	−2803.68	+	2803.68i	−0.197139	+	0.197139i	−0.798772	−	0.601634i	$-0.794517\pi$
$587$	−2803.68	+	2803.68i	−0.197139	+	0.197139i	0.601634	+	0.798772i	$0.294517\pi$
$588$		0			0
$589$			3044.80i			0.213003i
$590$		0			0
$591$		−	38424.9i		−	2.67443i
$592$		0			0
$593$	2536.59	−	2536.59i	0.175658	−	0.175658i	−0.613802	−	0.789460i	$-0.710361\pi$
$593$	2536.59	−	2536.59i	0.175658	−	0.175658i	0.789460	+	0.613802i	$0.210361\pi$
$594$		0			0
$595$	−4562.37	−	3891.36i	−0.314351	−	0.268118i
$596$		0			0
$597$	13606.9	+	13606.9i	0.932821	+	0.932821i
$598$		0			0
$599$	13027.0			0.888598			0.444299	−	0.895879i	$-0.353453\pi$
$599$	13027.0			0.888598			0.444299	+	0.895879i	$0.353453\pi$
$600$		0			0
$601$	3763.05			0.255404			0.127702	−	0.991813i	$-0.459240\pi$
$601$	3763.05			0.255404			0.127702	+	0.991813i	$0.459240\pi$
$602$		0			0
$603$	6885.48	+	6885.48i	0.465006	+	0.465006i
$604$		0			0
$605$	6997.72	+	5968.54i	0.470245	+	0.401083i
$606$		0			0
$607$	−15669.2	+	15669.2i	−1.04777	+	1.04777i	−0.0489655	+	0.998800i	$0.515592\pi$
$607$	−15669.2	+	15669.2i	−1.04777	+	1.04777i	−0.998800	+	0.0489655i	$0.984408\pi$
$608$		0			0
$609$		−	8664.67i		−	0.576535i
$610$		0			0
$611$			8474.02i			0.561084i
$612$		0			0
$613$	−6355.42	+	6355.42i	−0.418749	+	0.418749i	−0.884772	−	0.466023i	$-0.845686\pi$
$613$	−6355.42	+	6355.42i	−0.418749	+	0.418749i	0.466023	+	0.884772i	$0.345686\pi$
$614$		0			0
$615$	1939.52	+	24435.1i	0.127169	+	1.60214i
$616$		0			0
$617$	−881.215	−	881.215i	−0.0574982	−	0.0574982i	0.677773	−	0.735271i	$-0.262945\pi$
$617$	−881.215	−	881.215i	−0.0574982	−	0.0574982i	−0.735271	+	0.677773i	$0.762945\pi$
$618$		0			0
$619$	5792.23			0.376106			0.188053	−	0.982159i	$-0.439782\pi$
$619$	5792.23			0.376106			0.188053	+	0.982159i	$0.439782\pi$
$620$		0			0
$621$	54666.5			3.53252
$622$		0			0
$623$	6546.13	+	6546.13i	0.420971	+	0.420971i
$624$		0			0
$625$	−14847.3	+	4868.11i	−0.950227	+	0.311559i
$626$		0			0
$627$	−14658.9	+	14658.9i	−0.933686	+	0.933686i
$628$		0			0
$629$		−	7865.44i		−	0.498594i
$630$		0			0
$631$			25846.0i			1.63061i	0.579034	+	0.815304i	$0.303430\pi$
$631$			25846.0i			1.63061i	−0.579034	+	0.815304i	$0.696570\pi$
$632$		0			0
$633$	1022.87	−	1022.87i	0.0642263	−	0.0642263i
$634$		0			0
$635$	6166.62	−	489.472i	0.385378	−	0.0305891i
$636$		0			0
$637$	10510.9	+	10510.9i	0.653779	+	0.653779i
$638$		0			0
$639$	87566.4			5.42109
$640$		0			0
$641$	−3294.97			−0.203032			−0.101516	−	0.994834i	$-0.532369\pi$
$641$	−3294.97			−0.203032			−0.101516	+	0.994834i	$0.532369\pi$
$642$		0			0
$643$	−1353.51	−	1353.51i	−0.0830126	−	0.0830126i	0.664381	−	0.747394i	$-0.268695\pi$
$643$	−1353.51	−	1353.51i	−0.0830126	−	0.0830126i	−0.747394	+	0.664381i	$0.768695\pi$
$644$		0			0
$645$	12155.6	−	14251.7i	0.742059	−	0.870017i
$646$		0			0
$647$	3752.04	−	3752.04i	0.227988	−	0.227988i	−0.583864	−	0.811852i	$-0.698460\pi$
$647$	3752.04	−	3752.04i	0.227988	−	0.227988i	0.811852	+	0.583864i	$0.198460\pi$
$648$		0			0
$649$		−	1161.10i		−	0.0702266i
$650$		0			0
$651$		−	3488.23i		−	0.210007i
$652$		0			0
$653$	13931.0	−	13931.0i	0.834855	−	0.834855i	−0.153321	−	0.988176i	$-0.548997\pi$
$653$	13931.0	−	13931.0i	0.834855	−	0.834855i	0.988176	+	0.153321i	$0.0489970\pi$
$654$		0			0
$655$	−7139.48	+	8370.59i	−0.425897	+	0.499337i
$656$		0			0
$657$	49642.8	+	49642.8i	2.94787	+	2.94787i
$658$		0			0
$659$	16015.4			0.946696			0.473348	−	0.880876i	$-0.343045\pi$
$659$	16015.4			0.946696			0.473348	+	0.880876i	$0.343045\pi$
$660$		0			0
$661$	−28529.8			−1.67879			−0.839396	−	0.543521i	$-0.817091\pi$
$661$	−28529.8			−1.67879			−0.839396	+	0.543521i	$0.817091\pi$
$662$		0			0
$663$	−23471.1	−	23471.1i	−1.37487	−	1.37487i
$664$		0			0
$665$	−10320.4	+	819.178i	−0.601818	+	0.0477689i
$666$		0			0
$667$	−6483.99	+	6483.99i	−0.376404	+	0.376404i
$668$		0			0
$669$			11740.9i			0.678518i
$670$		0			0
$671$		−	1740.46i		−	0.100134i
$672$		0			0
$673$	−22680.4	+	22680.4i	−1.29906	+	1.29906i	−0.370040	+	0.929016i	$0.620656\pi$
$673$	−22680.4	+	22680.4i	−1.29906	+	1.29906i	−0.929016	+	0.370040i	$0.879344\pi$
$674$		0			0
$675$	−50388.1	−	36506.3i	−2.87324	−	2.08167i
$676$		0			0
$677$	−760.319	−	760.319i	−0.0431631	−	0.0431631i	0.685196	−	0.728359i	$-0.259717\pi$
$677$	−760.319	−	760.319i	−0.0431631	−	0.0431631i	−0.728359	+	0.685196i	$0.759717\pi$
$678$		0			0
$679$	11066.9			0.625492
$680$		0			0
$681$	−23616.2			−1.32889
$682$		0			0
$683$	12218.6	+	12218.6i	0.684525	+	0.684525i	0.961016	−	0.276491i	$-0.0891716\pi$
$683$	12218.6	+	12218.6i	0.684525	+	0.684525i	−0.276491	+	0.961016i	$0.589172\pi$
$684$		0			0
$685$	1123.52	+	14154.7i	0.0626679	+	0.789523i
$686$		0			0
$687$	11067.8	−	11067.8i	0.614647	−	0.614647i
$688$		0			0
$689$			6800.75i			0.376034i
$690$		0			0
$691$			32870.1i			1.80961i	0.425831	+	0.904803i	$0.359982\pi$
$691$			32870.1i			1.80961i	−0.425831	+	0.904803i	$0.640018\pi$
$692$		0			0
$693$	12393.2	−	12393.2i	0.679333	−	0.679333i
$694$		0			0
$695$	7823.57	+	6672.92i	0.427000	+	0.364199i
$696$		0			0
$697$	−8012.59	−	8012.59i	−0.435436	−	0.435436i
$698$		0			0
$699$	−55968.6			−3.02851
$700$		0			0
$701$	−27606.3			−1.48741			−0.743705	−	0.668508i	$-0.766933\pi$
$701$	−27606.3			−1.48741			−0.743705	+	0.668508i	$0.766933\pi$
$702$		0			0
$703$	−9602.24	−	9602.24i	−0.515157	−	0.515157i
$704$		0			0
$705$	−11739.7	−	10013.1i	−0.627151	−	0.534913i
$706$		0			0
$707$	−2819.31	+	2819.31i	−0.149973	+	0.149973i
$708$		0			0
$709$		−	14329.1i		−	0.759011i	−0.925189	−	0.379505i	$-0.876094\pi$
$709$		−	14329.1i		−	0.759011i	0.925189	−	0.379505i	$-0.123906\pi$
$710$		0			0
$711$		−	50174.1i		−	2.64652i
$712$		0			0
$713$	−2610.34	+	2610.34i	−0.137108	+	0.137108i
$714$		0			0
$715$	−1243.20	−	15662.5i	−0.0650252	−	0.819222i
$716$		0			0
$717$	−20280.3	−	20280.3i	−1.05632	−	1.05632i
$718$		0			0
$719$	−21403.9			−1.11019			−0.555097	−	0.831785i	$-0.687319\pi$
$719$	−21403.9			−1.11019			−0.555097	+	0.831785i	$0.687319\pi$
$720$		0			0
$721$	18989.5			0.980866
$722$		0			0
$723$	35244.1	+	35244.1i	1.81292	+	1.81292i
$724$		0			0
$725$	10306.5	−	1646.52i	0.527966	−	0.0843453i
$726$		0			0
$727$	14648.1	−	14648.1i	0.747272	−	0.747272i	−0.226694	−	0.973966i	$-0.572792\pi$
$727$	14648.1	−	14648.1i	0.747272	−	0.747272i	0.973966	+	0.226694i	$0.0727916\pi$
$728$		0			0
$729$		−	91675.9i		−	4.65762i
$730$		0			0
$731$			8659.33i			0.438135i
$732$		0			0
$733$	1257.52	−	1257.52i	0.0633663	−	0.0633663i	−0.674713	−	0.738080i	$-0.735733\pi$
$733$	1257.52	−	1257.52i	0.0633663	−	0.0633663i	0.738080	+	0.674713i	$0.235733\pi$
$734$		0			0
$735$	−26981.4	+	2141.63i	−1.35404	+	0.107476i
$736$		0			0
$737$	−2041.67	−	2041.67i	−0.102043	−	0.102043i
$738$		0			0
$739$	6789.76			0.337977			0.168989	−	0.985618i	$-0.445950\pi$
$739$	6789.76			0.337977			0.168989	+	0.985618i	$0.445950\pi$
$740$		0			0
$741$	−57307.7			−2.84109
$742$		0			0
$743$	25623.9	+	25623.9i	1.26521	+	1.26521i	0.948535	+	0.316672i	$0.102566\pi$
$743$	25623.9	+	25623.9i	1.26521	+	1.26521i	0.316672	+	0.948535i	$0.397434\pi$
$744$		0			0
$745$	106.722	−	125.125i	0.00524831	−	0.00615330i
$746$		0			0
$747$	33730.1	−	33730.1i	1.65210	−	1.65210i
$748$		0			0
$749$		−	1582.64i		−	0.0772074i
$750$		0			0
$751$			5410.53i			0.262894i	0.991323	+	0.131447i	$0.0419623\pi$
$751$			5410.53i			0.262894i	−0.991323	+	0.131447i	$0.958038\pi$
$752$		0			0
$753$	23309.6	−	23309.6i	1.12809	−	1.12809i
$754$		0			0
$755$	−13114.6	+	15376.1i	−0.632172	+	0.741181i
$756$		0			0
$757$	−668.042	−	668.042i	−0.0320745	−	0.0320745i	0.690888	−	0.722962i	$-0.257220\pi$
$757$	−668.042	−	668.042i	−0.0320745	−	0.0320745i	−0.722962	+	0.690888i	$0.757220\pi$
$758$		0			0
$759$	−25134.4			−1.20201
$760$		0			0
$761$	4190.15			0.199596			0.0997982	−	0.995008i	$-0.468180\pi$
$761$	4190.15			0.199596			0.0997982	+	0.995008i	$0.468180\pi$
$762$		0			0
$763$	−13050.8	−	13050.8i	−0.619225	−	0.619225i
$764$		0			0
$765$	44462.3	−	3529.16i	2.10135	−	0.166794i
$766$		0			0
$767$	2269.60	−	2269.60i	0.106846	−	0.106846i
$768$		0			0
$769$		−	1535.48i		−	0.0720035i	−0.999352	−	0.0360017i	$-0.988538\pi$
$769$		−	1535.48i		−	0.0720035i	0.999352	−	0.0360017i	$-0.0114622\pi$
$770$		0			0
$771$		−	57650.9i		−	2.69293i
$772$		0			0
$773$	9434.90	−	9434.90i	0.439004	−	0.439004i	−0.452673	−	0.891677i	$-0.649529\pi$
$773$	9434.90	−	9434.90i	0.439004	−	0.439004i	0.891677	+	0.452673i	$0.149529\pi$
$774$		0			0
$775$	4149.22	−	662.860i	0.192315	−	0.0307234i
$776$		0			0
$777$	11000.7	+	11000.7i	0.507911	+	0.507911i
$778$		0			0
$779$	−19563.8			−0.899801
$780$		0			0
$781$	−25965.1			−1.18963
$782$		0			0
$783$	29390.0	+	29390.0i	1.34139	+	1.34139i
$784$		0			0
$785$	−1639.04	−	20649.5i	−0.0745220	−	0.938867i
$786$		0			0
$787$	24576.8	−	24576.8i	1.11317	−	1.11317i	0.120456	−	0.992719i	$-0.461564\pi$
$787$	24576.8	−	24576.8i	1.11317	−	1.11317i	0.992719	−	0.120456i	$-0.0384357\pi$
$788$		0			0
$789$			74942.4i			3.38152i
$790$		0			0
$791$			12000.0i			0.539407i
$792$		0			0
$793$	3402.09	−	3402.09i	0.152348	−	0.152348i
$794$		0			0
$795$	−9421.55	−	8035.88i	−0.420312	−	0.358495i
$796$		0			0
$797$	−9506.15	−	9506.15i	−0.422491	−	0.422491i	0.463570	−	0.886060i	$-0.346568\pi$
$797$	−9506.15	−	9506.15i	−0.422491	−	0.422491i	−0.886060	+	0.463570i	$0.846568\pi$
$798$		0			0
$799$	7133.01			0.315829
$800$		0			0
$801$	−68858.6			−3.03745
$802$		0			0
$803$	−14720.0	−	14720.0i	−0.646897	−	0.646897i
$804$		0			0
$805$	−9550.08	−	8145.51i	−0.418132	−	0.356635i
$806$		0			0
$807$	−8578.09	+	8578.09i	−0.374180	+	0.374180i
$808$		0			0
$809$			5959.85i			0.259008i	0.991579	+	0.129504i	$0.0413385\pi$
$809$			5959.85i			0.259008i	−0.991579	+	0.129504i	$0.958662\pi$
$810$		0			0
$811$			36609.0i			1.58510i	0.609806	+	0.792551i	$0.291247\pi$
$811$			36609.0i			1.58510i	−0.609806	+	0.792551i	$0.708753\pi$
$812$		0			0
$813$	−43612.2	+	43612.2i	−1.88136	+	1.88136i
$814$		0			0
$815$	2065.69	+	26024.6i	0.0887828	+	1.11853i
$816$		0			0
$817$	10571.4	+	10571.4i	0.452690	+	0.452690i
$818$		0			0
$819$	48450.0			2.06713
$820$		0			0
$821$	−11503.8			−0.489020			−0.244510	−	0.969647i	$-0.578627\pi$
$821$	−11503.8			−0.489020			−0.244510	+	0.969647i	$0.578627\pi$
$822$		0			0
$823$	−21146.1	−	21146.1i	−0.895636	−	0.895636i	0.0994105	−	0.995047i	$-0.468304\pi$
$823$	−21146.1	−	21146.1i	−0.895636	−	0.895636i	−0.995047	+	0.0994105i	$0.968304\pi$
$824$		0			0
$825$	23167.3	+	16784.8i	0.977676	+	0.708328i
$826$		0			0
$827$	20316.9	−	20316.9i	0.854277	−	0.854277i	−0.136379	−	0.990657i	$-0.543547\pi$
$827$	20316.9	−	20316.9i	0.854277	−	0.854277i	0.990657	+	0.136379i	$0.0435466\pi$
$828$		0			0
$829$		−	37098.2i		−	1.55425i	−0.629346	−	0.777125i	$-0.716677\pi$
$829$		−	37098.2i		−	1.55425i	0.629346	−	0.777125i	$-0.283323\pi$
$830$		0			0
$831$		−	27148.6i		−	1.13330i
$832$		0			0
$833$	8847.55	−	8847.55i	0.368007	−	0.368007i
$834$		0			0
$835$	−21307.3	+	1691.25i	−0.883076	+	0.0700936i
$836$		0			0
$837$	11831.9	+	11831.9i	0.488613	+	0.488613i
$838$		0			0
$839$	17615.5			0.724856			0.362428	−	0.932012i	$-0.381948\pi$
$839$	17615.5			0.724856			0.362428	+	0.932012i	$0.381948\pi$
$840$		0			0
$841$	17417.1			0.714138
$842$		0			0
$843$	34141.5	+	34141.5i	1.39489	+	1.39489i
$844$		0			0
$845$	12245.4	−	14356.9i	0.498525	−	0.584488i
$846$		0			0
$847$	5946.62	−	5946.62i	0.241238	−	0.241238i
$848$		0			0
$849$		−	21176.3i		−	0.856031i
$850$		0			0
$851$		−	16464.2i		−	0.663202i
$852$		0			0
$853$	2287.26	−	2287.26i	0.0918103	−	0.0918103i	−0.659710	−	0.751520i	$-0.729321\pi$
$853$	2287.26	−	2287.26i	0.0918103	−	0.0918103i	0.751520	+	0.659710i	$0.229321\pi$
$854$		0			0
$855$	49971.7	−	58588.6i	1.99883	−	2.34349i
$856$		0			0
$857$	21776.2	+	21776.2i	0.867982	+	0.867982i	0.992249	−	0.124267i	$-0.0396580\pi$
$857$	21776.2	+	21776.2i	0.867982	+	0.867982i	−0.124267	+	0.992249i	$0.539658\pi$
$858$		0			0
$859$	35564.2			1.41261			0.706307	−	0.707905i	$-0.250360\pi$
$859$	35564.2			1.41261			0.706307	+	0.707905i	$0.250360\pi$
$860$		0			0
$861$	22413.0			0.887144
$862$		0			0
$863$	10921.2	+	10921.2i	0.430780	+	0.430780i	0.888894	−	0.458114i	$-0.151475\pi$
$863$	10921.2	+	10921.2i	0.430780	+	0.430780i	−0.458114	+	0.888894i	$0.651475\pi$
$864$		0			0
$865$	−16134.2	+	1280.64i	−0.634196	+	0.0503389i
$866$		0			0
$867$	15507.2	−	15507.2i	0.607443	−	0.607443i
$868$		0			0
$869$			14877.6i			0.580767i
$870$		0			0
$871$		−	7981.73i		−	0.310506i
$872$		0			0
$873$	−58206.2	+	58206.2i	−2.25657	+	2.25657i
$874$		0			0
$875$	3363.09	+	13885.5i	0.129935	+	0.536477i
$876$		0			0
$877$	15479.9	+	15479.9i	0.596032	+	0.596032i	0.939254	−	0.343222i	$-0.111518\pi$
$877$	15479.9	+	15479.9i	0.596032	+	0.596032i	−0.343222	+	0.939254i	$0.611518\pi$
$878$		0			0
$879$	−60531.0			−2.32271
$880$		0			0
$881$	49828.5			1.90552			0.952761	−	0.303721i	$-0.0982291\pi$
$881$	49828.5			1.90552			0.952761	+	0.303721i	$0.0982291\pi$
$882$		0			0
$883$	13568.9	+	13568.9i	0.517133	+	0.517133i	0.916703	−	0.399570i	$-0.130841\pi$
$883$	13568.9	+	13568.9i	0.517133	+	0.517133i	−0.399570	+	0.916703i	$0.630841\pi$
$884$		0			0
$885$	462.438	+	5826.04i	0.0175646	+	0.221288i
$886$		0			0
$887$	−20078.1	+	20078.1i	−0.760040	+	0.760040i	−0.976329	−	0.216289i	$-0.930605\pi$
$887$	−20078.1	+	20078.1i	−0.760040	+	0.760040i	0.216289	+	0.976329i	$0.430605\pi$
$888$		0			0
$889$		−	5656.30i		−	0.213393i
$890$		0			0
$891$			67637.0i			2.54313i
$892$		0			0
$893$	8708.08	−	8708.08i	0.326321	−	0.326321i
$894$		0			0
$895$	−28610.2	−	24402.3i	−1.06853	−	0.911374i
$896$		0			0
$897$	−49130.4	−	49130.4i	−1.82878	−	1.82878i
$898$		0			0
$899$	−2806.75			−0.104127
$900$		0			0
$901$	5724.53			0.211667
$902$		0			0
$903$	−12111.0	−	12111.0i	−0.446322	−	0.446322i
$904$		0			0
$905$	−9021.28	−	7694.47i	−0.331356	−	0.282622i
$906$		0			0
$907$	−30930.5	+	30930.5i	−1.13234	+	1.13234i	−0.142550	+	0.989788i	$0.545530\pi$
$907$	−30930.5	+	30930.5i	−1.13234	+	1.13234i	−0.989788	+	0.142550i	$0.954470\pi$
$908$		0			0
$909$		−	29656.3i		−	1.08211i
$910$		0			0
$911$		−	47660.7i		−	1.73334i	−0.498884	−	0.866669i	$-0.666257\pi$
$911$		−	47660.7i		−	1.73334i	0.498884	−	0.866669i	$-0.333743\pi$
$912$		0			0
$913$	−10001.6	+	10001.6i	−0.362546	+	0.362546i
$914$		0			0
$915$	693.186	+	8733.12i	0.0250448	+	0.315528i
$916$		0			0
$917$	7113.26	+	7113.26i	0.256162	+	0.256162i
$918$		0			0
$919$	36298.6			1.30292			0.651458	−	0.758685i	$-0.274158\pi$
$919$	36298.6			1.30292			0.651458	+	0.758685i	$0.274158\pi$
$920$		0			0
$921$	27515.5			0.984439
$922$		0			0
$923$	−50754.0	−	50754.0i	−1.80996	−	1.80996i
$924$		0			0
$925$	−10994.8	+	15175.6i	−0.390817	+	0.539428i
$926$		0			0
$927$	−99874.8	+	99874.8i	−3.53864	+	3.53864i
$928$		0			0
$929$			27670.1i			0.977210i	0.872505	+	0.488605i	$0.162494\pi$
$929$			27670.1i			0.977210i	−0.872505	+	0.488605i	$0.837506\pi$
$930$		0			0
$931$		−	21602.4i		−	0.760463i
$932$		0			0
$933$	58830.9	−	58830.9i	2.06435	−	2.06435i
$934$		0			0
$935$	−13183.9	+	1046.46i	−0.461133	+	0.0366021i
$936$		0			0
$937$	27182.3	+	27182.3i	0.947712	+	0.947712i	0.998699	−	0.0509874i	$-0.0162368\pi$
$937$	27182.3	+	27182.3i	0.947712	+	0.947712i	−0.0509874	+	0.998699i	$0.516237\pi$
$938$		0			0
$939$	−32239.1			−1.12043
$940$		0			0
$941$	−36516.6			−1.26504			−0.632522	−	0.774543i	$-0.717980\pi$
$941$	−36516.6			−1.26504			−0.632522	+	0.774543i	$0.717980\pi$
$942$		0			0
$943$	−16772.2	−	16772.2i	−0.579192	−	0.579192i
$944$		0			0
$945$	−36921.1	+	43287.6i	−1.27095	+	1.49010i
$946$		0			0
$947$	23765.4	−	23765.4i	0.815493	−	0.815493i	−0.169958	−	0.985451i	$-0.554363\pi$
$947$	23765.4	−	23765.4i	0.815493	−	0.815493i	0.985451	+	0.169958i	$0.0543632\pi$
$948$		0			0
$949$		−	57546.5i		−	1.96843i
$950$		0			0
$951$			90655.7i			3.09118i
$952$		0			0
$953$	8821.26	−	8821.26i	0.299841	−	0.299841i	−0.541110	−	0.840952i	$-0.681996\pi$
$953$	8821.26	−	8821.26i	0.299841	−	0.299841i	0.840952	+	0.541110i	$0.181996\pi$
$954$		0			0
$955$	8197.83	−	9611.43i	0.277776	−	0.325674i
$956$		0			0
$957$	−13512.9	−	13512.9i	−0.456435	−	0.456435i
$958$		0			0
$959$	12983.3			0.437178
$960$		0			0
$961$	28661.1			0.962071
$962$		0			0
$963$	8323.86	+	8323.86i	0.278539	+	0.278539i
$964$		0			0
$965$	−35346.3	+	2805.59i	−1.17911	+	0.0935909i
$966$		0			0
$967$	4285.68	−	4285.68i	0.142521	−	0.142521i	−0.632246	−	0.774768i	$-0.717867\pi$
$967$	4285.68	−	4285.68i	0.142521	−	0.142521i	0.774768	+	0.632246i	$0.217867\pi$
$968$		0			0
$969$			48238.8i			1.59923i
$970$		0			0
$971$			14160.5i			0.468004i	0.972236	+	0.234002i	$0.0751823\pi$
$971$			14160.5i			0.468004i	−0.972236	+	0.234002i	$0.924818\pi$
$972$		0			0
$973$	6648.41	−	6648.41i	0.219053	−	0.219053i
$974$		0			0
$975$	12476.0	+	78094.5i	0.409797	+	2.56515i
$976$		0			0
$977$	6133.35	+	6133.35i	0.200843	+	0.200843i	0.800361	−	0.599518i	$-0.204641\pi$
$977$	6133.35	+	6133.35i	0.200843	+	0.200843i	−0.599518	+	0.800361i	$0.704641\pi$
$978$		0			0
$979$	20417.9			0.666555
$980$		0			0
$981$	137280.			4.46792
$982$		0			0
$983$	−20489.0	−	20489.0i	−0.664799	−	0.664799i	0.291708	−	0.956507i	$-0.405776\pi$
$983$	−20489.0	−	20489.0i	−0.664799	−	0.664799i	−0.956507	+	0.291708i	$0.905776\pi$
$984$		0			0
$985$	−3348.76	−	42189.4i	−0.108325	−	1.36474i
$986$		0			0
$987$	−9976.28	+	9976.28i	−0.321731	+	0.321731i
$988$		0			0
$989$			18126.0i			0.582783i
$990$		0			0
$991$			34441.4i			1.10400i	0.833843	+	0.552002i	$0.186136\pi$
$991$			34441.4i			1.10400i	−0.833843	+	0.552002i	$0.813864\pi$
$992$		0			0
$993$	47716.8	−	47716.8i	1.52492	−	1.52492i
$994$		0			0
$995$	16125.9	+	13754.2i	0.513793	+	0.438227i
$996$		0			0
$997$	−6922.84	−	6922.84i	−0.219908	−	0.219908i	0.588551	−	0.808460i	$-0.299698\pi$
$997$	−6922.84	−	6922.84i	−0.219908	−	0.219908i	−0.808460	+	0.588551i	$0.799698\pi$
$998$		0			0
$999$	−74627.1			−2.36346

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.4.n.f.127.4	yes	8
4.3	odd	2		160.4.n.c.127.1	yes	8
5.3	odd	4		160.4.n.c.63.1	✓	8
8.3	odd	2		320.4.n.i.127.4		8
8.5	even	2		320.4.n.f.127.1		8
20.3	even	4	inner	160.4.n.f.63.4	yes	8
40.3	even	4		320.4.n.f.63.1		8
40.13	odd	4		320.4.n.i.63.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.4.n.c.63.1	✓	8	5.3	odd	4
160.4.n.c.127.1	yes	8	4.3	odd	2
160.4.n.f.63.4	yes	8	20.3	even	4	inner
160.4.n.f.127.4	yes	8	1.1	even	1	trivial
320.4.n.f.63.1		8	40.3	even	4
320.4.n.f.127.1		8	8.5	even	2
320.4.n.i.63.4		8	40.13	odd	4
320.4.n.i.127.4		8	8.3	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(7.17770 + 7.17770i) q^{3} +(8.50645 + 7.25537i) q^{5} +(7.22872 - 7.22872i) q^{7} +76.0387i q^{9} +O(q^{10})\)	\(q+(7.17770 + 7.17770i) q^{3} +(8.50645 + 7.25537i) q^{5} +(7.22872 - 7.22872i) q^{7} +76.0387i q^{9} -22.5469i q^{11} +(44.0725 - 44.0725i) q^{13} +(8.97990 + 113.134i) q^{15} +(-37.0980 - 37.0980i) q^{17} -90.5796 q^{19} +103.771 q^{21} +(-77.6546 - 77.6546i) q^{23} +(19.7194 + 123.435i) q^{25} +(-351.985 + 351.985i) q^{27} -83.4978i q^{29} -33.6147i q^{31} +(161.835 - 161.835i) q^{33} +(113.938 - 9.04374i) q^{35} +(106.009 + 106.009i) q^{37} +632.678 q^{39} +215.984 q^{41} +(-116.709 - 116.709i) q^{43} +(-551.688 + 646.819i) q^{45} +(-96.1374 + 96.1374i) q^{47} +238.491i q^{49} -532.557i q^{51} +(-77.1541 + 77.1541i) q^{53} +(163.586 - 191.794i) q^{55} +(-650.153 - 650.153i) q^{57} +51.4970 q^{59} +77.1930 q^{61} +(549.662 + 549.662i) q^{63} +(694.662 - 55.1384i) q^{65} +(90.5523 - 90.5523i) q^{67} -1114.76i q^{69} -1151.60i q^{71} +(652.862 - 652.862i) q^{73} +(-744.438 + 1027.52i) q^{75} +(-162.985 - 162.985i) q^{77} -659.850 q^{79} -2999.84 q^{81} +(-443.591 - 443.591i) q^{83} +(-46.4127 - 584.732i) q^{85} +(599.322 - 599.322i) q^{87} +905.573i q^{89} -637.175i q^{91} +(241.276 - 241.276i) q^{93} +(-770.510 - 657.188i) q^{95} +(765.482 + 765.482i) q^{97} +1714.44 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} - 6 q^{5} + 70 q^{7}+O(q^{10}) \) 8 * q + 6 * q^3 - 6 * q^5 + 70 * q^7	\( 8 q + 6 q^{3} - 6 q^{5} + 70 q^{7} + 144 q^{13} - 134 q^{15} - 100 q^{17} + 176 q^{19} - 516 q^{21} - 198 q^{23} - 172 q^{25} - 288 q^{27} + 172 q^{33} + 170 q^{35} + 492 q^{37} + 756 q^{39} - 28 q^{41} + 654 q^{43} + 10 q^{45} - 690 q^{47} + 580 q^{53} - 2392 q^{55} - 248 q^{57} + 1808 q^{59} - 1068 q^{61} + 3106 q^{63} + 2200 q^{65} - 1878 q^{67} + 1952 q^{73} - 2178 q^{75} + 340 q^{77} - 1808 q^{79} - 7844 q^{81} - 506 q^{83} + 184 q^{85} + 784 q^{87} + 3708 q^{93} - 5800 q^{95} + 5576 q^{97} + 8412 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 - 6 * q^5 + 70 * q^7 + 144 * q^13 - 134 * q^15 - 100 * q^17 + 176 * q^19 - 516 * q^21 - 198 * q^23 - 172 * q^25 - 288 * q^27 + 172 * q^33 + 170 * q^35 + 492 * q^37 + 756 * q^39 - 28 * q^41 + 654 * q^43 + 10 * q^45 - 690 * q^47 + 580 * q^53 - 2392 * q^55 - 248 * q^57 + 1808 * q^59 - 1068 * q^61 + 3106 * q^63 + 2200 * q^65 - 1878 * q^67 + 1952 * q^73 - 2178 * q^75 + 340 * q^77 - 1808 * q^79 - 7844 * q^81 - 506 * q^83 + 184 * q^85 + 784 * q^87 + 3708 * q^93 - 5800 * q^95 + 5576 * q^97 + 8412 * q^99

Introduction

L-functions

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