LMFDB - Embedded newform 160.5.p.f.33.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [160,5,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, 5); 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, 5, names="a")

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

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,24,0,48] 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:	$16.5391940934$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 10 x^{10} + 68 x^{9} - 52 x^{8} - 784 x^{7} + 960 x^{6} + 3824 x^{5} - 13583 x^{4} + \cdots + 348466 $ x^12 - 4x^11 - 10x^10 + 68x^9 - 52x^8 - 784x^7 + 960x^6 + 3824x^5 - 13583x^4 - 8828x^3 + 191418x^2 + 478524*x + 348466
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{24}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			33.2
Root			$2.66185 - 2.69040i$ of defining polynomial
Character	$\chi$	$=$	160.33
Dual form			160.5.p.f.97.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.86997 - 5.86997i) q^{3} +(-23.6674 - 8.05314i) q^{5} +(9.78913 - 9.78913i) q^{7} -12.0869i q^{9} -49.7874 q^{11} +(-136.672 - 136.672i) q^{13} +(91.6554 + 186.199i) q^{15} +(19.1608 - 19.1608i) q^{17} +491.764i q^{19} -114.924 q^{21} +(454.416 + 454.416i) q^{23} +(495.294 + 381.194i) q^{25} +(-546.417 + 546.417i) q^{27} +342.763i q^{29} +160.245 q^{31} +(292.251 + 292.251i) q^{33} +(-310.517 + 152.850i) q^{35} +(741.212 - 741.212i) q^{37} +1604.53i q^{39} -291.713 q^{41} +(1589.69 + 1589.69i) q^{43} +(-97.3375 + 286.066i) q^{45} +(-1207.70 + 1207.70i) q^{47} +2209.35i q^{49} -224.947 q^{51} +(-3161.17 - 3161.17i) q^{53} +(1178.34 + 400.945i) q^{55} +(2886.64 - 2886.64i) q^{57} +3690.87i q^{59} -6470.44 q^{61} +(-118.320 - 118.320i) q^{63} +(2134.04 + 4335.33i) q^{65} +(4986.29 - 4986.29i) q^{67} -5334.82i q^{69} -6846.84 q^{71} +(2339.13 + 2339.13i) q^{73} +(-669.761 - 5144.96i) q^{75} +(-487.376 + 487.376i) q^{77} -8853.82i q^{79} +5435.87 q^{81} +(-4024.59 - 4024.59i) q^{83} +(-607.792 + 299.183i) q^{85} +(2012.01 - 2012.01i) q^{87} +9329.05i q^{89} -2675.81 q^{91} +(-940.632 - 940.632i) q^{93} +(3960.24 - 11638.8i) q^{95} +(2598.26 - 2598.26i) q^{97} +601.776i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 24 q^{5} + 48 q^{7} + 320 q^{11} + 260 q^{13} - 592 q^{15} - 60 q^{17} - 400 q^{21} - 176 q^{23} + 836 q^{25} + 2208 q^{27} - 480 q^{31} - 3120 q^{33} + 2208 q^{35} - 500 q^{37} + 2160 q^{41} + 3744 q^{43}+ \cdots + 36460 q^{97}+O(q^{100}) $ 12 * q + 24 * q^5 + 48 * q^7 + 320 * q^11 + 260 * q^13 - 592 * q^15 - 60 * q^17 - 400 * q^21 - 176 * q^23 + 836 * q^25 + 2208 * q^27 - 480 * q^31 - 3120 * q^33 + 2208 * q^35 - 500 * q^37 + 2160 * q^41 + 3744 * q^43 - 3116 * q^45 + 1264 * q^47 - 16960 * q^51 + 7020 * q^53 + 8256 * q^55 + 1760 * q^57 + 2928 * q^61 + 15504 * q^63 + 5196 * q^65 + 2400 * q^67 - 31200 * q^71 - 340 * q^73 + 1472 * q^75 - 6960 * q^77 - 27676 * q^81 + 25952 * q^83 - 7292 * q^85 + 27744 * q^87 - 66240 * q^91 - 2640 * q^93 - 3552 * q^95 + 36460 * q^97

Character values

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

$n$	$31$	$97$	$101$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−5.86997	−	5.86997i	−0.652219	−	0.652219i	0.301308	−	0.953527i	$-0.402577\pi$
$3$	−5.86997	−	5.86997i	−0.652219	−	0.652219i	−0.953527	+	0.301308i	$0.902577\pi$
$4$		0			0
$5$	−23.6674	−	8.05314i	−0.946697	−	0.322126i
$5$	−23.6674	−	8.05314i	−0.946697	−	0.322126i
$6$		0			0
$7$	9.78913	−	9.78913i	0.199778	−	0.199778i	−0.600127	−	0.799905i	$-0.704883\pi$
$7$	9.78913	−	9.78913i	0.199778	−	0.199778i	0.799905	+	0.600127i	$0.204883\pi$
$8$		0			0
$9$		−	12.0869i		−	0.149221i
$10$		0			0
$11$	−49.7874			−0.411466			−0.205733	−	0.978608i	$-0.565958\pi$
$11$	−49.7874			−0.411466			−0.205733	+	0.978608i	$0.565958\pi$
$12$		0			0
$13$	−136.672	−	136.672i	−0.808713	−	0.808713i	0.175726	−	0.984439i	$-0.443773\pi$
$13$	−136.672	−	136.672i	−0.808713	−	0.808713i	−0.984439	+	0.175726i	$0.943773\pi$
$14$		0			0
$15$	91.6554	+	186.199i	0.407357	+	0.827550i
$16$		0			0
$17$	19.1608	−	19.1608i	0.0663005	−	0.0663005i	−0.673179	−	0.739480i	$-0.735072\pi$
$17$	19.1608	−	19.1608i	0.0663005	−	0.0663005i	0.739480	+	0.673179i	$0.235072\pi$
$18$		0			0
$19$			491.764i			1.36223i	0.732178	+	0.681113i	$0.238504\pi$
$19$			491.764i			1.36223i	−0.732178	+	0.681113i	$0.761496\pi$
$20$		0			0
$21$	−114.924			−0.260598
$22$		0			0
$23$	454.416	+	454.416i	0.859010	+	0.859010i	0.991222	−	0.132211i	$-0.0422078\pi$
$23$	454.416	+	454.416i	0.859010	+	0.859010i	−0.132211	+	0.991222i	$0.542208\pi$
$24$		0			0
$25$	495.294	+	381.194i	0.792470	+	0.609911i
$26$		0			0
$27$	−546.417	+	546.417i	−0.749544	+	0.749544i
$28$		0			0
$29$			342.763i			0.407566i	0.979016	+	0.203783i	$0.0653238\pi$
$29$			342.763i			0.407566i	−0.979016	+	0.203783i	$0.934676\pi$
$30$		0			0
$31$	160.245			0.166748			0.0833740	−	0.996518i	$-0.473430\pi$
$31$	160.245			0.166748			0.0833740	+	0.996518i	$0.473430\pi$
$32$		0			0
$33$	292.251	+	292.251i	0.268366	+	0.268366i
$34$		0			0
$35$	−310.517	+	152.850i	−0.253483	+	0.124776i
$36$		0			0
$37$	741.212	−	741.212i	0.541426	−	0.541426i	−0.382521	−	0.923947i	$-0.624944\pi$
$37$	741.212	−	741.212i	0.541426	−	0.541426i	0.923947	+	0.382521i	$0.124944\pi$
$38$		0			0
$39$			1604.53i			1.05492i
$40$		0			0
$41$	−291.713			−0.173536			−0.0867678	−	0.996229i	$-0.527654\pi$
$41$	−291.713			−0.173536			−0.0867678	+	0.996229i	$0.527654\pi$
$42$		0			0
$43$	1589.69	+	1589.69i	0.859759	+	0.859759i	0.991309	−	0.131551i	$-0.0419956\pi$
$43$	1589.69	+	1589.69i	0.859759	+	0.859759i	−0.131551	+	0.991309i	$0.541996\pi$
$44$		0			0
$45$	−97.3375	+	286.066i	−0.0480679	+	0.141267i
$46$		0			0
$47$	−1207.70	+	1207.70i	−0.546718	+	0.546718i	−0.925490	−	0.378772i	$-0.876346\pi$
$47$	−1207.70	+	1207.70i	−0.546718	+	0.546718i	0.378772	+	0.925490i	$0.376346\pi$
$48$		0			0
$49$			2209.35i			0.920177i
$50$		0			0
$51$	−224.947			−0.0864848
$52$		0			0
$53$	−3161.17	−	3161.17i	−1.12537	−	1.12537i	−0.990920	−	0.134450i	$-0.957073\pi$
$53$	−3161.17	−	3161.17i	−1.12537	−	1.12537i	−0.134450	−	0.990920i	$-0.542927\pi$
$54$		0			0
$55$	1178.34	+	400.945i	0.389534	+	0.132544i
$56$		0			0
$57$	2886.64	−	2886.64i	0.888470	−	0.888470i
$58$		0			0
$59$			3690.87i			1.06029i	0.847907	+	0.530146i	$0.177863\pi$
$59$			3690.87i			1.06029i	−0.847907	+	0.530146i	$0.822137\pi$
$60$		0			0
$61$	−6470.44			−1.73890			−0.869449	−	0.494022i	$-0.835526\pi$
$61$	−6470.44			−1.73890			−0.869449	+	0.494022i	$0.835526\pi$
$62$		0			0
$63$	−118.320	−	118.320i	−0.0298111	−	0.0298111i
$64$		0			0
$65$	2134.04	+	4335.33i	0.505099	+	1.02611i
$66$		0			0
$67$	4986.29	−	4986.29i	1.11078	−	1.11078i	0.117735	−	0.993045i	$-0.462437\pi$
$67$	4986.29	−	4986.29i	1.11078	−	1.11078i	0.993045	−	0.117735i	$-0.0375632\pi$
$68$		0			0
$69$		−	5334.82i		−	1.12053i
$70$		0			0
$71$	−6846.84			−1.35823			−0.679115	−	0.734032i	$-0.737636\pi$
$71$	−6846.84			−1.35823			−0.679115	+	0.734032i	$0.737636\pi$
$72$		0			0
$73$	2339.13	+	2339.13i	0.438943	+	0.438943i	0.891656	−	0.452713i	$-0.149544\pi$
$73$	2339.13	+	2339.13i	0.438943	+	0.438943i	−0.452713	+	0.891656i	$0.649544\pi$
$74$		0			0
$75$	−669.761	−	5144.96i	−0.119069	−	0.914659i
$76$		0			0
$77$	−487.376	+	487.376i	−0.0822020	+	0.0822020i
$78$		0			0
$79$		−	8853.82i		−	1.41865i	−0.704879	−	0.709327i	$-0.748999\pi$
$79$		−	8853.82i		−	1.41865i	0.704879	−	0.709327i	$-0.251001\pi$
$80$		0			0
$81$	5435.87			0.828512
$82$		0			0
$83$	−4024.59	−	4024.59i	−0.584206	−	0.584206i	0.351851	−	0.936056i	$-0.385553\pi$
$83$	−4024.59	−	4024.59i	−0.584206	−	0.584206i	−0.936056	+	0.351851i	$0.885553\pi$
$84$		0			0
$85$	−607.792	+	299.183i	−0.0841235	+	0.0414094i
$86$		0			0
$87$	2012.01	−	2012.01i	0.265822	−	0.265822i
$88$		0			0
$89$			9329.05i			1.17776i	0.808220	+	0.588881i	$0.200431\pi$
$89$			9329.05i			1.17776i	−0.808220	+	0.588881i	$0.799569\pi$
$90$		0			0
$91$	−2675.81			−0.323126
$92$		0			0
$93$	−940.632	−	940.632i	−0.108756	−	0.108756i
$94$		0			0
$95$	3960.24	−	11638.8i	0.438808	−	1.28962i
$96$		0			0
$97$	2598.26	−	2598.26i	0.276146	−	0.276146i	−0.555422	−	0.831568i	$-0.687443\pi$
$97$	2598.26	−	2598.26i	0.276146	−	0.276146i	0.831568	+	0.555422i	$0.187443\pi$
$98$		0			0
$99$			601.776i			0.0613994i
$100$		0			0
$101$	3327.69			0.326212			0.163106	−	0.986609i	$-0.447849\pi$
$101$	3327.69			0.326212			0.163106	+	0.986609i	$0.447849\pi$
$102$		0			0
$103$	8137.26	+	8137.26i	0.767014	+	0.767014i	0.977580	−	0.210565i	$-0.0675305\pi$
$103$	8137.26	+	8137.26i	0.767014	+	0.767014i	−0.210565	+	0.977580i	$0.567530\pi$
$104$		0			0
$105$	2719.95	+	925.498i	0.246708	+	0.0839454i
$106$		0			0
$107$	3124.52	−	3124.52i	0.272908	−	0.272908i	−0.557362	−	0.830270i	$-0.688186\pi$
$107$	3124.52	−	3124.52i	0.272908	−	0.272908i	0.830270	+	0.557362i	$0.188186\pi$
$108$		0			0
$109$			2631.32i			0.221473i	0.993850	+	0.110737i	$0.0353210\pi$
$109$			2631.32i			0.221473i	−0.993850	+	0.110737i	$0.964679\pi$
$110$		0			0
$111$	−8701.78			−0.706256
$112$		0			0
$113$	−2336.40	−	2336.40i	−0.182974	−	0.182974i	0.609676	−	0.792651i	$-0.291299\pi$
$113$	−2336.40	−	2336.40i	−0.182974	−	0.182974i	−0.792651	+	0.609676i	$0.791299\pi$
$114$		0			0
$115$	−7095.38	−	14414.3i	−0.536513	−	1.08993i
$116$		0			0
$117$	−1651.95	+	1651.95i	−0.120677	+	0.120677i
$118$		0			0
$119$		−	375.136i		−	0.0264908i
$120$		0			0
$121$	−12162.2			−0.830695
$122$		0			0
$123$	1712.35	+	1712.35i	0.113183	+	0.113183i
$124$		0			0
$125$	−8652.52	−	13010.6i	−0.553761	−	0.832676i
$126$		0			0
$127$	6166.99	−	6166.99i	0.382354	−	0.382354i	−0.489596	−	0.871950i	$-0.662856\pi$
$127$	6166.99	−	6166.99i	0.382354	−	0.382354i	0.871950	+	0.489596i	$0.162856\pi$
$128$		0			0
$129$		−	18662.9i		−	1.12150i
$130$		0			0
$131$	−20224.9			−1.17854			−0.589268	−	0.807938i	$-0.700584\pi$
$131$	−20224.9			−1.17854			−0.589268	+	0.807938i	$0.700584\pi$
$132$		0			0
$133$	4813.94	+	4813.94i	0.272143	+	0.272143i
$134$		0			0
$135$	17332.7	−	8531.91i	0.951038	−	0.468143i
$136$		0			0
$137$	−12087.7	+	12087.7i	−0.644026	+	0.644026i	−0.951543	−	0.307517i	$-0.900502\pi$
$137$	−12087.7	+	12087.7i	−0.644026	+	0.644026i	0.307517	+	0.951543i	$0.400502\pi$
$138$		0			0
$139$			26395.0i			1.36613i	0.730357	+	0.683066i	$0.239354\pi$
$139$			26395.0i			1.36613i	−0.730357	+	0.683066i	$0.760646\pi$
$140$		0			0
$141$	14178.3			0.713160
$142$		0			0
$143$	6804.57	+	6804.57i	0.332758	+	0.332758i
$144$		0			0
$145$	2760.32	−	8112.32i	0.131288	−	0.385842i
$146$		0			0
$147$	12968.8	−	12968.8i	0.600157	−	0.600157i
$148$		0			0
$149$		−	5424.74i		−	0.244347i	−0.992509	−	0.122173i	$-0.961014\pi$
$149$		−	5424.74i		−	0.244347i	0.992509	−	0.122173i	$-0.0389864\pi$
$150$		0			0
$151$	−35373.8			−1.55141			−0.775707	−	0.631093i	$-0.782607\pi$
$151$	−35373.8			−1.55141			−0.775707	+	0.631093i	$0.782607\pi$
$152$		0			0
$153$	−231.595	−	231.595i	−0.00989342	−	0.00989342i
$154$		0			0
$155$	−3792.58	−	1290.47i	−0.157860	−	0.0537138i
$156$		0			0
$157$	−25285.4	+	25285.4i	−1.02582	+	1.02582i	−0.0261610	+	0.999658i	$0.508328\pi$
$157$	−25285.4	+	25285.4i	−1.02582	+	1.02582i	−0.999658	+	0.0261610i	$0.991672\pi$
$158$		0			0
$159$			37111.9i			1.46798i
$160$		0			0
$161$	8896.68			0.343223
$162$		0			0
$163$	34060.2	+	34060.2i	1.28195	+	1.28195i	0.939554	+	0.342400i	$0.111240\pi$
$163$	34060.2	+	34060.2i	1.28195	+	1.28195i	0.342400	+	0.939554i	$0.388760\pi$
$164$		0			0
$165$	−4563.29	−	9270.36i	−0.167614	−	0.340509i
$166$		0			0
$167$	−15449.9	+	15449.9i	−0.553978	+	0.553978i	−0.927586	−	0.373609i	$-0.878120\pi$
$167$	−15449.9	+	15449.9i	−0.553978	+	0.553978i	0.373609	+	0.927586i	$0.378120\pi$
$168$		0			0
$169$			8797.71i			0.308032i
$170$		0			0
$171$	5943.89			0.203273
$172$		0			0
$173$	33327.6	+	33327.6i	1.11355	+	1.11355i	0.992666	+	0.120889i	$0.0385745\pi$
$173$	33327.6	+	33327.6i	1.11355	+	1.11355i	0.120889	+	0.992666i	$0.461426\pi$
$174$		0			0
$175$	8580.06	−	1116.94i	0.280165	−	0.0364714i
$176$		0			0
$177$	21665.3	−	21665.3i	0.691542	−	0.691542i
$178$		0			0
$179$			57241.9i			1.78652i	0.449539	+	0.893261i	$0.351588\pi$
$179$			57241.9i			1.78652i	−0.449539	+	0.893261i	$0.648412\pi$
$180$		0			0
$181$	59471.5			1.81531			0.907657	−	0.419712i	$-0.137869\pi$
$181$	59471.5			1.81531			0.907657	+	0.419712i	$0.137869\pi$
$182$		0			0
$183$	37981.3	+	37981.3i	1.13414	+	1.13414i
$184$		0			0
$185$	−23511.6	+	11573.5i	−0.686973	+	0.338159i
$186$		0			0
$187$	−953.969	+	953.969i	−0.0272804	+	0.0272804i
$188$		0			0
$189$			10697.9i			0.299485i
$190$		0			0
$191$	−45377.5			−1.24387			−0.621934	−	0.783070i	$-0.713653\pi$
$191$	−45377.5			−1.24387			−0.621934	+	0.783070i	$0.713653\pi$
$192$		0			0
$193$	−31631.1	−	31631.1i	−0.849181	−	0.849181i	0.140850	−	0.990031i	$-0.455016\pi$
$193$	−31631.1	−	31631.1i	−0.849181	−	0.849181i	−0.990031	+	0.140850i	$0.955016\pi$
$194$		0			0
$195$	12921.5	−	37975.0i	0.339815	−	0.998685i
$196$		0			0
$197$	−3453.09	+	3453.09i	−0.0889766	+	0.0889766i	−0.750194	−	0.661218i	$-0.770040\pi$
$197$	−3453.09	+	3453.09i	−0.0889766	+	0.0889766i	0.661218	+	0.750194i	$0.270040\pi$
$198$		0			0
$199$			10928.2i			0.275959i	0.990435	+	0.137979i	$0.0440608\pi$
$199$			10928.2i			0.275959i	−0.990435	+	0.137979i	$0.955939\pi$
$200$		0			0
$201$	−58538.7			−1.44894
$202$		0			0
$203$	3355.36	+	3355.36i	0.0814229	+	0.0814229i
$204$		0			0
$205$	6904.10	+	2349.21i	0.164286	+	0.0559002i
$206$		0			0
$207$	5492.48	−	5492.48i	0.128182	−	0.128182i
$208$		0			0
$209$		−	24483.7i		−	0.560510i
$210$		0			0
$211$	−27715.9			−0.622536			−0.311268	−	0.950322i	$-0.600754\pi$
$211$	−27715.9			−0.622536			−0.311268	+	0.950322i	$0.600754\pi$
$212$		0			0
$213$	40190.7	+	40190.7i	0.885863	+	0.885863i
$214$		0			0
$215$	−24821.9	−	50426.0i	−0.536981	−	1.09088i
$216$		0			0
$217$	1568.66	−	1568.66i	0.0333126	−	0.0333126i
$218$		0			0
$219$		−	27461.2i		−	0.572573i
$220$		0			0
$221$	−5237.51			−0.107236
$222$		0			0
$223$	9091.56	+	9091.56i	0.182822	+	0.182822i	0.792584	−	0.609762i	$-0.208735\pi$
$223$	9091.56	+	9091.56i	0.182822	+	0.182822i	−0.609762	+	0.792584i	$0.708735\pi$
$224$		0			0
$225$	4607.45	−	5986.56i	0.0910114	−	0.118253i
$226$		0			0
$227$	−8020.36	+	8020.36i	−0.155647	+	0.155647i	−0.780635	−	0.624987i	$-0.785104\pi$
$227$	−8020.36	+	8020.36i	−0.155647	+	0.155647i	0.624987	+	0.780635i	$0.285104\pi$
$228$		0			0
$229$		−	48238.0i		−	0.919853i	−0.887957	−	0.459927i	$-0.847876\pi$
$229$		−	48238.0i		−	0.919853i	0.887957	−	0.459927i	$-0.152124\pi$
$230$		0			0
$231$	5721.76			0.107227
$232$		0			0
$233$	−45097.1	−	45097.1i	−0.830685	−	0.830685i	0.156925	−	0.987610i	$-0.449842\pi$
$233$	−45097.1	−	45097.1i	−0.830685	−	0.830685i	−0.987610	+	0.156925i	$0.949842\pi$
$234$		0			0
$235$	38308.9	−	18857.4i	0.693688	−	0.341464i
$236$		0			0
$237$	−51971.7	+	51971.7i	−0.925274	+	0.925274i
$238$		0			0
$239$			6916.36i			0.121083i	0.998166	+	0.0605413i	$0.0192827\pi$
$239$			6916.36i			0.121083i	−0.998166	+	0.0605413i	$0.980717\pi$
$240$		0			0
$241$	−38121.8			−0.656355			−0.328177	−	0.944616i	$-0.606434\pi$
$241$	−38121.8			−0.656355			−0.328177	+	0.944616i	$0.606434\pi$
$242$		0			0
$243$	12351.4	+	12351.4i	0.209172	+	0.209172i
$244$		0			0
$245$	17792.2	−	52289.5i	0.296413	−	0.871129i
$246$		0			0
$247$	67210.5	−	67210.5i	1.10165	−	1.10165i
$248$		0			0
$249$			47248.5i			0.762060i
$250$		0			0
$251$	−124349.			−1.97375			−0.986877	−	0.161472i	$-0.948376\pi$
$251$	−124349.			−1.97375			−0.986877	+	0.161472i	$0.948376\pi$
$252$		0			0
$253$	−22624.2	−	22624.2i	−0.353454	−	0.353454i
$254$		0			0
$255$	5323.92	+	1811.53i	0.0818749	+	0.0278590i
$256$		0			0
$257$	84312.6	−	84312.6i	1.27652	−	1.27652i	0.333912	−	0.942604i	$-0.391631\pi$
$257$	84312.6	−	84312.6i	1.27652	−	1.27652i	0.942604	−	0.333912i	$-0.108369\pi$
$258$		0			0
$259$		−	14511.6i		−	0.216330i
$260$		0			0
$261$	4142.94			0.0608174
$262$		0			0
$263$	−54700.1	−	54700.1i	−0.790818	−	0.790818i	0.190809	−	0.981627i	$-0.438889\pi$
$263$	−54700.1	−	54700.1i	−0.790818	−	0.790818i	−0.981627	+	0.190809i	$0.938889\pi$
$264$		0			0
$265$	49359.3	+	100274.i	0.702874	+	1.42790i
$266$		0			0
$267$	54761.3	−	54761.3i	0.768159	−	0.768159i
$268$		0			0
$269$			73699.2i			1.01849i	0.860621	+	0.509246i	$0.170076\pi$
$269$			73699.2i			1.01849i	−0.860621	+	0.509246i	$0.829924\pi$
$270$		0			0
$271$	78168.3			1.06437			0.532185	−	0.846628i	$-0.321371\pi$
$271$	78168.3			1.06437			0.532185	+	0.846628i	$0.321371\pi$
$272$		0			0
$273$	15706.9	+	15706.9i	0.210749	+	0.210749i
$274$		0			0
$275$	−24659.4	−	18978.7i	−0.326075	−	0.250958i
$276$		0			0
$277$	65009.6	−	65009.6i	0.847263	−	0.847263i	−0.142528	−	0.989791i	$-0.545523\pi$
$277$	65009.6	−	65009.6i	0.847263	−	0.847263i	0.989791	+	0.142528i	$0.0455231\pi$
$278$		0			0
$279$		−	1936.86i		−	0.0248823i
$280$		0			0
$281$	−11459.2			−0.145125			−0.0725625	−	0.997364i	$-0.523118\pi$
$281$	−11459.2			−0.145125			−0.0725625	+	0.997364i	$0.523118\pi$
$282$		0			0
$283$	−28206.9	−	28206.9i	−0.352194	−	0.352194i	0.508731	−	0.860925i	$-0.330115\pi$
$283$	−28206.9	−	28206.9i	−0.352194	−	0.352194i	−0.860925	+	0.508731i	$0.830115\pi$
$284$		0			0
$285$	−91565.8	+	45072.8i	−1.12731	+	0.554913i
$286$		0			0
$287$	−2855.62	+	2855.62i	−0.0346686	+	0.0346686i
$288$		0			0
$289$			82786.7i			0.991208i
$290$		0			0
$291$	−30503.4			−0.360215
$292$		0			0
$293$	−22836.5	−	22836.5i	−0.266008	−	0.266008i	0.561481	−	0.827489i	$-0.310232\pi$
$293$	−22836.5	−	22836.5i	−0.266008	−	0.266008i	−0.827489	+	0.561481i	$0.810232\pi$
$294$		0			0
$295$	29723.1	−	87353.5i	0.341547	−	1.00377i
$296$		0			0
$297$	27204.7	−	27204.7i	0.308412	−	0.308412i
$298$		0			0
$299$		−	124212.i		−	1.38938i
$300$		0			0
$301$	31123.5			0.343522
$302$		0			0
$303$	−19533.5	−	19533.5i	−0.212762	−	0.212762i
$304$		0			0
$305$	153139.	+	52107.4i	1.64621	+	0.560144i
$306$		0			0
$307$	−8529.02	+	8529.02i	−0.0904946	+	0.0904946i	−0.750905	−	0.660410i	$-0.770382\pi$
$307$	−8529.02	+	8529.02i	−0.0904946	+	0.0904946i	0.660410	+	0.750905i	$0.270382\pi$
$308$		0			0
$309$		−	95530.9i		−	1.00052i
$310$		0			0
$311$	−105916.			−1.09507			−0.547533	−	0.836784i	$-0.684433\pi$
$311$	−105916.			−1.09507			−0.547533	+	0.836784i	$0.684433\pi$
$312$		0			0
$313$	−10898.7	−	10898.7i	−0.111246	−	0.111246i	0.649293	−	0.760539i	$-0.275065\pi$
$313$	−10898.7	−	10898.7i	−0.111246	−	0.111246i	−0.760539	+	0.649293i	$0.775065\pi$
$314$		0			0
$315$	1847.49	+	3753.18i	0.0186192	+	0.0378250i
$316$		0			0
$317$	−109920.	+	109920.i	−1.09385	+	1.09385i	−0.0987371	+	0.995114i	$0.531480\pi$
$317$	−109920.	+	109920.i	−1.09385	+	1.09385i	−0.995114	+	0.0987371i	$0.968520\pi$
$318$		0			0
$319$		−	17065.3i		−	0.167700i
$320$		0			0
$321$	−36681.7			−0.355991
$322$		0			0
$323$	9422.60	+	9422.60i	0.0903162	+	0.0903162i
$324$		0			0
$325$	−15594.3	−	119792.i	−0.147638	−	1.13412i
$326$		0			0
$327$	15445.8	−	15445.8i	0.144449	−	0.144449i
$328$		0			0
$329$			23644.7i			0.218445i
$330$		0			0
$331$	203372.			1.85624			0.928120	−	0.372281i	$-0.121424\pi$
$331$	203372.			1.85624			0.928120	+	0.372281i	$0.121424\pi$
$332$		0			0
$333$	−8958.95	−	8958.95i	−0.0807920	−	0.0807920i
$334$		0			0
$335$	−158168.	+	77857.3i	−1.40938	+	0.693761i
$336$		0			0
$337$	65706.7	−	65706.7i	0.578562	−	0.578562i	−0.355945	−	0.934507i	$-0.615841\pi$
$337$	65706.7	−	65706.7i	0.578562	−	0.578562i	0.934507	+	0.355945i	$0.115841\pi$
$338$		0			0
$339$			27429.2i			0.238679i
$340$		0			0
$341$	−7978.18			−0.0686112
$342$		0			0
$343$	45131.3	+	45131.3i	0.383610	+	0.383610i
$344$		0			0
$345$	−42962.1	+	126261.i	−0.360950	+	1.06080i
$346$		0			0
$347$	−163409.	+	163409.i	−1.35712	+	1.35712i	−0.479669	+	0.877450i	$0.659243\pi$
$347$	−163409.	+	163409.i	−1.35712	+	1.35712i	−0.877450	+	0.479669i	$0.840757\pi$
$348$		0			0
$349$		−	88734.9i		−	0.728523i	−0.931297	−	0.364262i	$-0.881321\pi$
$349$		−	88734.9i		−	0.728523i	0.931297	−	0.364262i	$-0.118679\pi$
$350$		0			0
$351$	149360.			1.21233
$352$		0			0
$353$	−55238.6	−	55238.6i	−0.443296	−	0.443296i	0.449822	−	0.893118i	$-0.351487\pi$
$353$	−55238.6	−	55238.6i	−0.443296	−	0.443296i	−0.893118	+	0.449822i	$0.851487\pi$
$354$		0			0
$355$	162047.	+	55138.5i	1.28583	+	0.437521i
$356$		0			0
$357$	−2202.04	+	2202.04i	−0.0172778	+	0.0172778i
$358$		0			0
$359$			185465.i			1.43904i	0.694472	+	0.719520i	$0.255638\pi$
$359$			185465.i			1.43904i	−0.694472	+	0.719520i	$0.744362\pi$
$360$		0			0
$361$	−111510.			−0.855660
$362$		0			0
$363$	71391.8	+	71391.8i	0.541795	+	0.541795i
$364$		0			0
$365$	−36523.8	−	74198.4i	−0.274151	−	0.556940i
$366$		0			0
$367$	−46321.2	+	46321.2i	−0.343913	+	0.343913i	−0.857836	−	0.513923i	$-0.828192\pi$
$367$	−46321.2	+	46321.2i	−0.343913	+	0.343913i	0.513923	+	0.857836i	$0.328192\pi$
$368$		0			0
$369$			3525.91i			0.0258951i
$370$		0			0
$371$	−61890.2			−0.449649
$372$		0			0
$373$	13254.6	+	13254.6i	0.0952685	+	0.0952685i	0.753135	−	0.657866i	$-0.228541\pi$
$373$	13254.6	+	13254.6i	0.0952685	+	0.0952685i	−0.657866	+	0.753135i	$0.728541\pi$
$374$		0			0
$375$	−25581.6	+	127162.i	−0.181913	+	0.904260i
$376$		0			0
$377$	46846.3	−	46846.3i	0.329604	−	0.329604i
$378$		0			0
$379$		−	22044.3i		−	0.153468i	−0.997052	−	0.0767339i	$-0.975551\pi$
$379$		−	22044.3i		−	0.153468i	0.997052	−	0.0767339i	$-0.0244492\pi$
$380$		0			0
$381$	−72400.1			−0.498757
$382$		0			0
$383$	−85971.7	−	85971.7i	−0.586082	−	0.586082i	0.350486	−	0.936568i	$-0.386016\pi$
$383$	−85971.7	−	85971.7i	−0.586082	−	0.586082i	−0.936568	+	0.350486i	$0.886016\pi$
$384$		0			0
$385$	15459.8	−	7610.02i	0.104300	−	0.0513410i
$386$		0			0
$387$	19214.5	−	19214.5i	0.128294	−	0.128294i
$388$		0			0
$389$		−	87723.7i		−	0.579719i	−0.957069	−	0.289860i	$-0.906391\pi$
$389$		−	87723.7i		−	0.579719i	0.957069	−	0.289860i	$-0.0936086\pi$
$390$		0			0
$391$	17414.0			0.113906
$392$		0			0
$393$	118719.	+	118719.i	0.768663	+	0.768663i
$394$		0			0
$395$	−71301.1	+	209547.i	−0.456985	+	1.34304i
$396$		0			0
$397$	−109959.	+	109959.i	−0.697672	+	0.697672i	−0.963908	−	0.266236i	$-0.914220\pi$
$397$	−109959.	+	109959.i	−0.697672	+	0.697672i	0.266236	+	0.963908i	$0.414220\pi$
$398$		0			0
$399$		−	56515.4i		−	0.354994i
$400$		0			0
$401$	185829.			1.15565			0.577823	−	0.816162i	$-0.303903\pi$
$401$	185829.			1.15565			0.577823	+	0.816162i	$0.303903\pi$
$402$		0			0
$403$	−21901.0	−	21901.0i	−0.134851	−	0.134851i
$404$		0			0
$405$	−128653.	−	43775.8i	−0.784350	−	0.266885i
$406$		0			0
$407$	−36903.0	+	36903.0i	−0.222778	+	0.222778i
$408$		0			0
$409$			292244.i			1.74702i	0.486804	+	0.873511i	$0.338163\pi$
$409$			292244.i			1.74702i	−0.486804	+	0.873511i	$0.661837\pi$
$410$		0			0
$411$	141909.			0.840091
$412$		0			0
$413$	36130.5	+	36130.5i	0.211823	+	0.211823i
$414$		0			0
$415$	62841.1	+	127662.i	0.364878	+	0.741253i
$416$		0			0
$417$	154938.	−	154938.i	0.891017	−	0.891017i
$418$		0			0
$419$		−	16893.3i		−	0.0962250i	−0.998842	−	0.0481125i	$-0.984679\pi$
$419$		−	16893.3i		−	0.0962250i	0.998842	−	0.0481125i	$-0.0153206\pi$
$420$		0			0
$421$	189191.			1.06742			0.533711	−	0.845667i	$-0.320797\pi$
$421$	189191.			1.06742			0.533711	+	0.845667i	$0.320797\pi$
$422$		0			0
$423$	14597.3	+	14597.3i	0.0815818	+	0.0815818i
$424$		0			0
$425$	16794.2	−	2186.24i	0.0929785	−	0.0121038i
$426$		0			0
$427$	−63340.0	+	63340.0i	−0.347394	+	0.347394i
$428$		0			0
$429$		−	79885.3i		−	0.434062i
$430$		0			0
$431$	142307.			0.766078			0.383039	−	0.923732i	$-0.374877\pi$
$431$	142307.			0.766078			0.383039	+	0.923732i	$0.374877\pi$
$432$		0			0
$433$	−26214.7	−	26214.7i	−0.139820	−	0.139820i	0.633732	−	0.773552i	$-0.281522\pi$
$433$	−26214.7	−	26214.7i	−0.139820	−	0.139820i	−0.773552	+	0.633732i	$0.781522\pi$
$434$		0			0
$435$	−63822.1	+	31416.1i	−0.337282	+	0.166025i
$436$		0			0
$437$	−223465.	+	223465.i	−1.17017	+	1.17017i
$438$		0			0
$439$			992.994i			0.00515250i	0.999997	+	0.00257625i	$0.000820046\pi$
$439$			992.994i			0.00515250i	−0.999997	+	0.00257625i	$0.999180\pi$
$440$		0			0
$441$	26704.1			0.137310
$442$		0			0
$443$	−178707.	−	178707.i	−0.910616	−	0.910616i	0.0857046	−	0.996321i	$-0.472686\pi$
$443$	−178707.	−	178707.i	−0.910616	−	0.910616i	−0.996321	+	0.0857046i	$0.972686\pi$
$444$		0			0
$445$	75128.2	−	220795.i	0.379387	−	1.11498i
$446$		0			0
$447$	−31843.1	+	31843.1i	−0.159368	+	0.159368i
$448$		0			0
$449$		−	113623.i		−	0.563602i	−0.959473	−	0.281801i	$-0.909068\pi$
$449$		−	113623.i		−	0.563602i	0.959473	−	0.281801i	$-0.0909318\pi$
$450$		0			0
$451$	14523.7			0.0714040
$452$		0			0
$453$	207643.	+	207643.i	1.01186	+	1.01186i
$454$		0			0
$455$	63329.5	+	21548.7i	0.305903	+	0.104087i
$456$		0			0
$457$	−183745.	+	183745.i	−0.879800	+	0.879800i	−0.993514	−	0.113713i	$-0.963725\pi$
$457$	−183745.	+	183745.i	−0.879800	+	0.879800i	0.113713	+	0.993514i	$0.463725\pi$
$458$		0			0
$459$			20939.6i			0.0993902i
$460$		0			0
$461$	153365.			0.721648			0.360824	−	0.932634i	$-0.382495\pi$
$461$	153365.			0.721648			0.360824	+	0.932634i	$0.382495\pi$
$462$		0			0
$463$	−26760.0	−	26760.0i	−0.124831	−	0.124831i	0.641931	−	0.766762i	$-0.278134\pi$
$463$	−26760.0	−	26760.0i	−0.124831	−	0.124831i	−0.766762	+	0.641931i	$0.778134\pi$
$464$		0			0
$465$	14687.3	+	29837.4i	0.0679260	+	0.137992i
$466$		0			0
$467$	−16906.2	+	16906.2i	−0.0775197	+	0.0775197i	−0.744804	−	0.667284i	$-0.767457\pi$
$467$	−16906.2	+	16906.2i	−0.0775197	+	0.0775197i	0.667284	+	0.744804i	$0.267457\pi$
$468$		0			0
$469$		−	97622.9i		−	0.443819i
$470$		0			0
$471$	296849.			1.33812
$472$		0			0
$473$	−79146.8	−	79146.8i	−0.353762	−	0.353762i
$474$		0			0
$475$	−187457.	+	243567.i	−0.830836	+	1.07952i
$476$		0			0
$477$	−38208.7	+	38208.7i	−0.167929	+	0.167929i
$478$		0			0
$479$		−	306921.i		−	1.33769i	−0.743402	−	0.668845i	$-0.766789\pi$
$479$		−	306921.i		−	1.33769i	0.743402	−	0.668845i	$-0.233211\pi$
$480$		0			0
$481$	−202606.			−0.875715
$482$		0			0
$483$	−52223.3	−	52223.3i	−0.223857	−	0.223857i
$484$		0			0
$485$	−82418.2	+	40569.9i	−0.350380	+	0.172473i
$486$		0			0
$487$	−108919.	+	108919.i	−0.459246	+	0.459246i	−0.898408	−	0.439162i	$-0.855276\pi$
$487$	−108919.	+	108919.i	−0.459246	+	0.459246i	0.439162	+	0.898408i	$0.355276\pi$
$488$		0			0
$489$		−	399865.i		−	1.67223i
$490$		0			0
$491$	326694.			1.35512			0.677561	−	0.735466i	$-0.263037\pi$
$491$	326694.			1.35512			0.677561	+	0.735466i	$0.263037\pi$
$492$		0			0
$493$	6567.63	+	6567.63i	0.0270218	+	0.0270218i
$494$		0			0
$495$	4846.18	−	14242.5i	0.0197783	−	0.0581266i
$496$		0			0
$497$	−67024.6	+	67024.6i	−0.271345	+	0.271345i
$498$		0			0
$499$		−	326410.i		−	1.31088i	−0.755249	−	0.655438i	$-0.772484\pi$
$499$		−	326410.i		−	1.31088i	0.755249	−	0.655438i	$-0.227516\pi$
$500$		0			0
$501$	181381.			0.722630
$502$		0			0
$503$	−85489.2	−	85489.2i	−0.337890	−	0.337890i	0.517683	−	0.855573i	$-0.326795\pi$
$503$	−85489.2	−	85489.2i	−0.337890	−	0.337890i	−0.855573	+	0.517683i	$0.826795\pi$
$504$		0			0
$505$	−78757.9	−	26798.4i	−0.308824	−	0.105081i
$506$		0			0
$507$	51642.3	−	51642.3i	0.200904	−	0.200904i
$508$		0			0
$509$			305248.i			1.17819i	0.808062	+	0.589097i	$0.200517\pi$
$509$			305248.i			1.17819i	−0.808062	+	0.589097i	$0.799483\pi$
$510$		0			0
$511$	45796.0			0.175382
$512$		0			0
$513$	−268708.	−	268708.i	−1.02105	−	1.02105i
$514$		0			0
$515$	−127057.	−	258118.i	−0.479055	−	0.973205i
$516$		0			0
$517$	60128.3	−	60128.3i	0.224956	−	0.224956i
$518$		0			0
$519$		−	391264.i		−	1.45256i
$520$		0			0
$521$	−402585.			−1.48314			−0.741570	−	0.670876i	$-0.765918\pi$
$521$	−402585.			−1.48314			−0.741570	+	0.670876i	$0.765918\pi$
$522$		0			0
$523$	−221582.	−	221582.i	−0.810085	−	0.810085i	0.174562	−	0.984646i	$-0.444149\pi$
$523$	−221582.	−	221582.i	−0.810085	−	0.810085i	−0.984646	+	0.174562i	$0.944149\pi$
$524$		0			0
$525$	−56921.1	−	43808.3i	−0.206516	−	0.158942i
$526$		0			0
$527$	3070.42	−	3070.42i	0.0110555	−	0.0110555i
$528$		0			0
$529$			133147.i			0.475797i
$530$		0			0
$531$	44611.2			0.158218
$532$		0			0
$533$	39869.2	+	39869.2i	0.140340	+	0.140340i
$534$		0			0
$535$	−99111.6	+	48787.2i	−0.346272	+	0.170450i
$536$		0			0
$537$	336008.	−	336008.i	1.16520	−	1.16520i
$538$		0			0
$539$		−	109998.i		−	0.378622i
$540$		0			0
$541$	368732.			1.25984			0.629921	−	0.776660i	$-0.283087\pi$
$541$	368732.			1.25984			0.629921	+	0.776660i	$0.283087\pi$
$542$		0			0
$543$	−349096.	−	349096.i	−1.18398	−	1.18398i
$544$		0			0
$545$	21190.4	−	62276.7i	0.0713422	−	0.209668i
$546$		0			0
$547$	156455.	−	156455.i	0.522894	−	0.522894i	−0.395550	−	0.918444i	$-0.629446\pi$
$547$	156455.	−	156455.i	0.522894	−	0.522894i	0.918444	+	0.395550i	$0.129446\pi$
$548$		0			0
$549$			78207.6i			0.259480i
$550$		0			0
$551$	−168558.			−0.555197
$552$		0			0
$553$	−86671.3	−	86671.3i	−0.283416	−	0.283416i
$554$		0			0
$555$	205949.	+	70076.7i	0.668610	+	0.227503i
$556$		0			0
$557$	−8510.31	+	8510.31i	−0.0274306	+	0.0274306i	−0.720689	−	0.693258i	$-0.756174\pi$
$557$	−8510.31	+	8510.31i	−0.0274306	+	0.0274306i	0.693258	+	0.720689i	$0.256174\pi$
$558$		0			0
$559$		−	434535.i		−	1.39060i
$560$		0			0
$561$	11199.5			0.0355856
$562$		0			0
$563$	−94453.3	−	94453.3i	−0.297989	−	0.297989i	0.542237	−	0.840226i	$-0.317578\pi$
$563$	−94453.3	−	94453.3i	−0.297989	−	0.297989i	−0.840226	+	0.542237i	$0.817578\pi$
$564$		0			0
$565$	36481.2	+	74111.9i	0.114281	+	0.232162i
$566$		0			0
$567$	53212.4	−	53212.4i	0.165519	−	0.165519i
$568$		0			0
$569$			45472.2i			0.140450i	0.997531	+	0.0702250i	$0.0223717\pi$
$569$			45472.2i			0.140450i	−0.997531	+	0.0702250i	$0.977628\pi$
$570$		0			0
$571$	118436.			0.363253			0.181627	−	0.983368i	$-0.441864\pi$
$571$	118436.			0.363253			0.181627	+	0.983368i	$0.441864\pi$
$572$		0			0
$573$	266365.	+	266365.i	0.811274	+	0.811274i
$574$		0			0
$575$	51848.7	+	398290.i	0.156820	+	1.20466i
$576$		0			0
$577$	−382393.	+	382393.i	−1.14857	+	1.14857i	−0.161737	+	0.986834i	$0.551710\pi$
$577$	−382393.	+	382393.i	−1.14857	+	1.14857i	−0.986834	+	0.161737i	$0.948290\pi$
$578$		0			0
$579$			371348.i			1.10770i
$580$		0			0
$581$	−78794.5			−0.233423
$582$		0			0
$583$	157386.	+	157386.i	0.463052	+	0.463052i
$584$		0			0
$585$	52400.6	−	25793.9i	0.153118	−	0.0753713i
$586$		0			0
$587$	127125.	−	127125.i	0.368938	−	0.368938i	−0.498152	−	0.867090i	$-0.665988\pi$
$587$	127125.	−	127125.i	0.368938	−	0.368938i	0.867090	+	0.498152i	$0.165988\pi$
$588$		0			0
$589$			78802.5i			0.227148i
$590$		0			0
$591$	40539.1			0.116064
$592$		0			0
$593$	82595.6	+	82595.6i	0.234881	+	0.234881i	0.814726	−	0.579846i	$-0.196887\pi$
$593$	82595.6	+	82595.6i	0.234881	+	0.234881i	−0.579846	+	0.814726i	$0.696887\pi$
$594$		0			0
$595$	−3021.02	+	8878.50i	−0.00853336	+	0.0250787i
$596$		0			0
$597$	64148.5	−	64148.5i	0.179986	−	0.179986i
$598$		0			0
$599$			284407.i			0.792658i	0.918109	+	0.396329i	$0.129716\pi$
$599$			284407.i			0.792658i	−0.918109	+	0.396329i	$0.870284\pi$
$600$		0			0
$601$	77011.4			0.213209			0.106605	−	0.994301i	$-0.466002\pi$
$601$	77011.4			0.213209			0.106605	+	0.994301i	$0.466002\pi$
$602$		0			0
$603$	−60268.8	−	60268.8i	−0.165752	−	0.165752i
$604$		0			0
$605$	287848.	+	97944.0i	0.786417	+	0.267588i
$606$		0			0
$607$	−218416.	+	218416.i	−0.592797	+	0.592797i	−0.938386	−	0.345589i	$-0.887679\pi$
$607$	−218416.	+	218416.i	−0.592797	+	0.592797i	0.345589	+	0.938386i	$0.387679\pi$
$608$		0			0
$609$		−	39391.7i		−	0.106211i
$610$		0			0
$611$	330119.			0.884276
$612$		0			0
$613$	51582.1	+	51582.1i	0.137271	+	0.137271i	0.772403	−	0.635132i	$-0.219054\pi$
$613$	51582.1	+	51582.1i	0.137271	+	0.137271i	−0.635132	+	0.772403i	$0.719054\pi$
$614$		0			0
$615$	−26737.1	−	54316.6i	−0.0706909	−	0.143609i
$616$		0			0
$617$	443595.	−	443595.i	1.16524	−	1.16524i	0.181932	−	0.983311i	$-0.441765\pi$
$617$	443595.	−	443595.i	1.16524	−	1.16524i	0.983311	−	0.181932i	$-0.0582351\pi$
$618$		0			0
$619$		−	83558.0i		−	0.218076i	−0.994038	−	0.109038i	$-0.965223\pi$
$619$		−	83558.0i		−	0.218076i	0.994038	−	0.109038i	$-0.0347769\pi$
$620$		0			0
$621$	−496602.			−1.28773
$622$		0			0
$623$	91323.4	+	91323.4i	0.235291	+	0.235291i
$624$		0			0
$625$	100007.	+	377606.i	0.256018	+	0.966672i
$626$		0			0
$627$	−143718.	+	143718.i	−0.365575	+	0.365575i
$628$		0			0
$629$		−	28404.5i		−	0.0717935i
$630$		0			0
$631$	−353413.			−0.887614			−0.443807	−	0.896122i	$-0.646372\pi$
$631$	−353413.			−0.887614			−0.443807	+	0.896122i	$0.646372\pi$
$632$		0			0
$633$	162692.	+	162692.i	0.406030	+	0.406030i
$634$		0			0
$635$	−195620.	+	96293.1i	−0.485139	+	0.238807i
$636$		0			0
$637$	301957.	−	301957.i	0.744159	−	0.744159i
$638$		0			0
$639$			82757.0i			0.202676i
$640$		0			0
$641$	−158849.			−0.386605			−0.193302	−	0.981139i	$-0.561920\pi$
$641$	−158849.			−0.386605			−0.193302	+	0.981139i	$0.561920\pi$
$642$		0			0
$643$	340018.	+	340018.i	0.822395	+	0.822395i	0.986451	−	0.164056i	$-0.0524579\pi$
$643$	340018.	+	340018.i	0.822395	+	0.822395i	−0.164056	+	0.986451i	$0.552458\pi$
$644$		0			0
$645$	−150295.	+	441703.i	−0.361265	+	1.06172i
$646$		0			0
$647$	−18322.4	+	18322.4i	−0.0437696	+	0.0437696i	−0.728653	−	0.684883i	$-0.759853\pi$
$647$	−18322.4	+	18322.4i	−0.0437696	+	0.0437696i	0.684883	+	0.728653i	$0.259853\pi$
$648$		0			0
$649$		−	183759.i		−	0.436274i
$650$		0			0
$651$	−18415.9			−0.0434542
$652$		0			0
$653$	−471423.	−	471423.i	−1.10557	−	1.10557i	−0.993726	−	0.111840i	$-0.964326\pi$
$653$	−471423.	−	471423.i	−1.10557	−	1.10557i	−0.111840	−	0.993726i	$-0.535674\pi$
$654$		0			0
$655$	478670.	+	162874.i	1.11572	+	0.379637i
$656$		0			0
$657$	28272.8	−	28272.8i	0.0654994	−	0.0654994i
$658$		0			0
$659$			293208.i			0.675158i	0.941297	+	0.337579i	$0.109608\pi$
$659$			293208.i			0.675158i	−0.941297	+	0.337579i	$0.890392\pi$
$660$		0			0
$661$	−372067.			−0.851567			−0.425783	−	0.904825i	$-0.640001\pi$
$661$	−372067.			−0.851567			−0.425783	+	0.904825i	$0.640001\pi$
$662$		0			0
$663$	30744.1	+	30744.1i	0.0699414	+	0.0699414i
$664$		0			0
$665$	−75166.2	−	152701.i	−0.169973	−	0.345301i
$666$		0			0
$667$	−155757.	+	155757.i	−0.350104	+	0.350104i
$668$		0			0
$669$		−	106734.i		−	0.238480i
$670$		0			0
$671$	322147.			0.715499
$672$		0			0
$673$	−523473.	−	523473.i	−1.15575	−	1.15575i	−0.985380	−	0.170370i	$-0.945504\pi$
$673$	−523473.	−	523473.i	−1.15575	−	1.15575i	−0.170370	−	0.985380i	$-0.554496\pi$
$674$		0			0
$675$	−478928.	+	62346.0i	−1.05115	+	0.136836i
$676$		0			0
$677$	−41663.3	+	41663.3i	−0.0909025	+	0.0909025i	−0.751096	−	0.660193i	$-0.770474\pi$
$677$	−41663.3	+	41663.3i	−0.0909025	+	0.0909025i	0.660193	+	0.751096i	$0.270474\pi$
$678$		0			0
$679$		−	50869.4i		−	0.110336i
$680$		0			0
$681$	94158.5			0.203032
$682$		0			0
$683$	43709.0	+	43709.0i	0.0936978	+	0.0936978i	0.752402	−	0.658704i	$-0.228895\pi$
$683$	43709.0	+	43709.0i	0.0936978	+	0.0936978i	−0.658704	+	0.752402i	$0.728895\pi$
$684$		0			0
$685$	383429.	−	188741.i	0.817154	−	0.402240i
$686$		0			0
$687$	−283156.	+	283156.i	−0.599946	+	0.599946i
$688$		0			0
$689$			864089.i			1.82020i
$690$		0			0
$691$	−376222.			−0.787932			−0.393966	−	0.919125i	$-0.628897\pi$
$691$	−376222.			−0.787932			−0.393966	+	0.919125i	$0.628897\pi$
$692$		0			0
$693$	5890.86	+	5890.86i	0.0122663	+	0.0122663i
$694$		0			0
$695$	212563.	−	624702.i	0.440066	−	1.29331i
$696$		0			0
$697$	−5589.47	+	5589.47i	−0.0115055	+	0.0115055i
$698$		0			0
$699$			529437.i			1.08358i
$700$		0			0
$701$	368085.			0.749052			0.374526	−	0.927216i	$-0.377805\pi$
$701$	368085.			0.749052			0.374526	+	0.927216i	$0.377805\pi$
$702$		0			0
$703$	364501.	+	364501.i	0.737544	+	0.737544i
$704$		0			0
$705$	−335565.	−	114180.i	−0.675146	−	0.229727i
$706$		0			0
$707$	32575.2	−	32575.2i	0.0651701	−	0.0651701i
$708$		0			0
$709$		−	98291.9i		−	0.195535i	−0.995209	−	0.0977676i	$-0.968830\pi$
$709$		−	98291.9i		−	0.195535i	0.995209	−	0.0977676i	$-0.0311702\pi$
$710$		0			0
$711$	−107015.			−0.211693
$712$		0			0
$713$	72817.8	+	72817.8i	0.143238	+	0.143238i
$714$		0			0
$715$	−106248.	−	215845.i	−0.207831	−	0.422211i
$716$		0			0
$717$	40598.8	−	40598.8i	0.0789724	−	0.0789724i
$718$		0			0
$719$			794535.i			1.53693i	0.639889	+	0.768467i	$0.278980\pi$
$719$			794535.i			1.53693i	−0.639889	+	0.768467i	$0.721020\pi$
$720$		0			0
$721$	159313.			0.306466
$722$		0			0
$723$	223774.	+	223774.i	0.428087	+	0.428087i
$724$		0			0
$725$	−130659.	+	169769.i	−0.248579	+	0.322984i
$726$		0			0
$727$	128220.	−	128220.i	0.242598	−	0.242598i	−0.575326	−	0.817924i	$-0.695125\pi$
$727$	128220.	−	128220.i	0.242598	−	0.242598i	0.817924	+	0.575326i	$0.195125\pi$
$728$		0			0
$729$		−	585310.i		−	1.10136i
$730$		0			0
$731$	60919.7			0.114005
$732$		0			0
$733$	−395711.	−	395711.i	−0.736496	−	0.736496i	0.235402	−	0.971898i	$-0.424359\pi$
$733$	−395711.	−	395711.i	−0.736496	−	0.736496i	−0.971898	+	0.235402i	$0.924359\pi$
$734$		0			0
$735$	−411377.	+	202498.i	−0.761493	+	0.374841i
$736$		0			0
$737$	−248255.	+	248255.i	−0.457049	+	0.457049i
$738$		0			0
$739$			60404.7i			0.110607i	0.998470	+	0.0553034i	$0.0176126\pi$
$739$			60404.7i			0.110607i	−0.998470	+	0.0553034i	$0.982387\pi$
$740$		0			0
$741$	−789048.			−1.43703
$742$		0			0
$743$	507349.	+	507349.i	0.919028	+	0.919028i	0.996959	−	0.0779307i	$-0.0248313\pi$
$743$	507349.	+	507349.i	0.919028	+	0.919028i	−0.0779307	+	0.996959i	$0.524831\pi$
$744$		0			0
$745$	−43686.2	+	128390.i	−0.0787103	+	0.231322i
$746$		0			0
$747$	−48644.8	+	48644.8i	−0.0871757	+	0.0871757i
$748$		0			0
$749$		−	61172.7i		−	0.109042i
$750$		0			0
$751$	−232337.			−0.411944			−0.205972	−	0.978558i	$-0.566036\pi$
$751$	−232337.			−0.411944			−0.205972	+	0.978558i	$0.566036\pi$
$752$		0			0
$753$	729922.	+	729922.i	1.28732	+	1.28732i
$754$		0			0
$755$	837206.	+	284870.i	1.46872	+	0.499750i
$756$		0			0
$757$	230972.	−	230972.i	0.403059	−	0.403059i	−0.476251	−	0.879309i	$-0.658005\pi$
$757$	230972.	−	230972.i	0.403059	−	0.403059i	0.879309	+	0.476251i	$0.158005\pi$
$758$		0			0
$759$			265607.i			0.461059i
$760$		0			0
$761$	772369.			1.33369			0.666846	−	0.745196i	$-0.267644\pi$
$761$	772369.			1.33369			0.666846	+	0.745196i	$0.267644\pi$
$762$		0			0
$763$	25758.4	+	25758.4i	0.0442455	+	0.0442455i
$764$		0			0
$765$	3616.19	+	7346.32i	0.00617914	+	0.0125530i
$766$		0			0
$767$	504441.	−	504441.i	0.857471	−	0.857471i
$768$		0			0
$769$			451596.i			0.763656i	0.924233	+	0.381828i	$0.124705\pi$
$769$			451596.i			0.763656i	−0.924233	+	0.381828i	$0.875295\pi$
$770$		0			0
$771$	−989825.			−1.66514
$772$		0			0
$773$	−133837.	−	133837.i	−0.223983	−	0.223983i	0.586190	−	0.810174i	$-0.300627\pi$
$773$	−133837.	−	133837.i	−0.223983	−	0.223983i	−0.810174	+	0.586190i	$0.800627\pi$
$774$		0			0
$775$	79368.2	+	61084.4i	0.132143	+	0.101701i
$776$		0			0
$777$	−85182.9	+	85182.9i	−0.141095	+	0.141095i
$778$		0			0
$779$		−	143454.i		−	0.236395i
$780$		0			0
$781$	340886.			0.558866
$782$		0			0
$783$	−187292.	−	187292.i	−0.305489	−	0.305489i
$784$		0			0
$785$	802067.	−	394813.i	1.30158	−	0.640697i
$786$		0			0
$787$	−126454.	+	126454.i	−0.204166	+	0.204166i	−0.801782	−	0.597616i	$-0.796115\pi$
$787$	−126454.	+	126454.i	−0.204166	+	0.204166i	0.597616	+	0.801782i	$0.296115\pi$
$788$		0			0
$789$			642176.i			1.03157i
$790$		0			0
$791$	−45742.7			−0.0731086
$792$		0			0
$793$	884331.	+	884331.i	1.40627	+	1.40627i
$794$		0			0
$795$	298867.	−	878343.i	0.472873	−	1.38973i
$796$		0			0
$797$	120100.	−	120100.i	0.189072	−	0.189072i	−0.606223	−	0.795295i	$-0.707316\pi$
$797$	120100.	−	120100.i	0.189072	−	0.189072i	0.795295	+	0.606223i	$0.207316\pi$
$798$		0			0
$799$			46281.1i			0.0724953i
$800$		0			0
$801$	112759.			0.175747
$802$		0			0
$803$	−116459.	−	116459.i	−0.180610	−	0.180610i
$804$		0			0
$805$	−210562.	−	71646.3i	−0.324928	−	0.110561i
$806$		0			0
$807$	432612.	−	432612.i	0.664280	−	0.664280i
$808$		0			0
$809$		−	752935.i		−	1.15043i	−0.818002	−	0.575215i	$-0.804918\pi$
$809$		−	752935.i		−	1.15043i	0.818002	−	0.575215i	$-0.195082\pi$
$810$		0			0
$811$	−703128.			−1.06904			−0.534518	−	0.845157i	$-0.679507\pi$
$811$	−703128.			−1.06904			−0.534518	+	0.845157i	$0.679507\pi$
$812$		0			0
$813$	−458846.	−	458846.i	−0.694202	−	0.694202i
$814$		0			0
$815$	−531826.	−	1.08041e6i	−0.800672	−	1.62657i
$816$		0			0
$817$	−781754.	+	781754.i	−1.17119	+	1.17119i
$818$		0			0
$819$			32342.2i			0.0482172i
$820$		0			0
$821$	−981569.			−1.45624			−0.728122	−	0.685447i	$-0.759607\pi$
$821$	−981569.			−1.45624			−0.728122	+	0.685447i	$0.759607\pi$
$822$		0			0
$823$	−612290.	−	612290.i	−0.903977	−	0.903977i	0.0918005	−	0.995777i	$-0.470738\pi$
$823$	−612290.	−	612290.i	−0.903977	−	0.903977i	−0.995777	+	0.0918005i	$0.970738\pi$
$824$		0			0
$825$	33345.7	+	256154.i	0.0489928	+	0.376352i
$826$		0			0
$827$	733789.	−	733789.i	1.07290	−	1.07290i	0.0757773	−	0.997125i	$-0.475856\pi$
$827$	733789.	−	733789.i	1.07290	−	1.07290i	0.997125	−	0.0757773i	$-0.0241438\pi$
$828$		0			0
$829$		−	716433.i		−	1.04248i	−0.853411	−	0.521239i	$-0.825470\pi$
$829$		−	716433.i		−	1.04248i	0.853411	−	0.521239i	$-0.174530\pi$
$830$		0			0
$831$	−763209.			−1.10520
$832$		0			0
$833$	42332.9	+	42332.9i	0.0610082	+	0.0610082i
$834$		0			0
$835$	490079.	−	241239.i	0.702900	−	0.345999i
$836$		0			0
$837$	−87560.5	+	87560.5i	−0.124985	+	0.124985i
$838$		0			0
$839$		−	451894.i		−	0.641967i	−0.947085	−	0.320983i	$-0.895987\pi$
$839$		−	451894.i		−	0.641967i	0.947085	−	0.320983i	$-0.104013\pi$
$840$		0			0
$841$	589794.			0.833890
$842$		0			0
$843$	67265.2	+	67265.2i	0.0946532	+	0.0946532i
$844$		0			0
$845$	70849.2	−	208219.i	0.0992251	−	0.291613i
$846$		0			0
$847$	−119058.	+	119058.i	−0.165955	+	0.165955i
$848$		0			0
$849$			331147.i			0.459415i
$850$		0			0
$851$	673637.			0.930180
$852$		0			0
$853$	119583.	+	119583.i	0.164351	+	0.164351i	0.784491	−	0.620140i	$-0.212924\pi$
$853$	119583.	+	119583.i	0.164351	+	0.164351i	−0.620140	+	0.784491i	$0.712924\pi$
$854$		0			0
$855$	−140677.	−	47867.0i	−0.192438	−	0.0654793i
$856$		0			0
$857$	−43402.1	+	43402.1i	−0.0590947	+	0.0590947i	−0.736037	−	0.676942i	$-0.763305\pi$
$857$	−43402.1	+	43402.1i	−0.0590947	+	0.0590947i	0.676942	+	0.736037i	$0.263305\pi$
$858$		0			0
$859$		−	979955.i		−	1.32807i	−0.747703	−	0.664033i	$-0.768843\pi$
$859$		−	979955.i		−	1.32807i	0.747703	−	0.664033i	$-0.231157\pi$
$860$		0			0
$861$	33524.8			0.0452231
$862$		0			0
$863$	584170.	+	584170.i	0.784365	+	0.784365i	0.980564	−	0.196199i	$-0.0628600\pi$
$863$	584170.	+	584170.i	0.784365	+	0.784365i	−0.196199	+	0.980564i	$0.562860\pi$
$864$		0			0
$865$	−520386.	−	1.05717e6i	−0.695494	−	1.41290i
$866$		0			0
$867$	485956.	−	485956.i	0.646485	−	0.646485i
$868$		0			0
$869$			440809.i			0.583729i
$870$		0			0
$871$	−1.36298e6			−1.79660
$872$		0			0
$873$	−31404.9	−	31404.9i	−0.0412067	−	0.0412067i
$874$		0			0
$875$	−212063.	−	42661.4i	−0.276980	−	0.0557210i
$876$		0			0
$877$	513510.	−	513510.i	0.667651	−	0.667651i	−0.289521	−	0.957172i	$-0.593496\pi$
$877$	513510.	−	513510.i	0.667651	−	0.667651i	0.957172	+	0.289521i	$0.0934959\pi$
$878$		0			0
$879$			268100.i			0.346991i
$880$		0			0
$881$	855655.			1.10242			0.551210	−	0.834367i	$-0.314166\pi$
$881$	855655.			1.10242			0.551210	+	0.834367i	$0.314166\pi$
$882$		0			0
$883$	198666.	+	198666.i	0.254802	+	0.254802i	0.822936	−	0.568134i	$-0.192335\pi$
$883$	198666.	+	198666.i	0.254802	+	0.254802i	−0.568134	+	0.822936i	$0.692335\pi$
$884$		0			0
$885$	−687236.	+	338289.i	−0.877444	+	0.431917i
$886$		0			0
$887$	383776.	−	383776.i	0.487787	−	0.487787i	−0.419820	−	0.907607i	$-0.637907\pi$
$887$	383776.	−	383776.i	0.487787	−	0.487787i	0.907607	+	0.419820i	$0.137907\pi$
$888$		0			0
$889$		−	120739.i		−	0.152772i
$890$		0			0
$891$	−270638.			−0.340905
$892$		0			0
$893$	−593903.	−	593903.i	−0.744754	−	0.744754i
$894$		0			0
$895$	460977.	−	1.35477e6i	0.575484	−	1.69129i
$896$		0			0
$897$	−729123.	+	729123.i	−0.906183	+	0.906183i
$898$		0			0
$899$			54926.0i			0.0679608i
$900$		0			0
$901$	−121141.			−0.149225
$902$		0			0
$903$	−182694.	−	182694.i	−0.224052	−	0.224052i
$904$		0			0
$905$	−1.40754e6	−	478933.i	−1.71855	−	0.584759i
$906$		0			0
$907$	−871665.	+	871665.i	−1.05958	+	1.05958i	−0.0614745	+	0.998109i	$0.519580\pi$
$907$	−871665.	+	871665.i	−1.05958	+	1.05958i	−0.998109	+	0.0614745i	$0.980420\pi$
$908$		0			0
$909$		−	40221.5i		−	0.0486777i
$910$		0			0
$911$	533857.			0.643263			0.321631	−	0.946865i	$-0.395769\pi$
$911$	533857.			0.643263			0.321631	+	0.946865i	$0.395769\pi$
$912$		0			0
$913$	200374.	+	200374.i	0.240381	+	0.240381i
$914$		0			0
$915$	−593051.	−	1.20479e6i	−0.708353	−	1.43903i
$916$		0			0
$917$	−197984.	+	197984.i	−0.235446	+	0.235446i
$918$		0			0
$919$			801208.i			0.948668i	0.880345	+	0.474334i	$0.157311\pi$
$919$			801208.i			0.948668i	−0.880345	+	0.474334i	$0.842689\pi$
$920$		0			0
$921$	100130.			0.118045
$922$		0			0
$923$	935774.	+	935774.i	1.09842	+	1.09842i
$924$		0			0
$925$	649663.	−	84572.0i	0.759285	−	0.0988423i
$926$		0			0
$927$	98354.2	−	98354.2i	0.114455	−	0.114455i
$928$		0			0
$929$		−	1.50011e6i		−	1.73817i	−0.494666	−	0.869083i	$-0.664710\pi$
$929$		−	1.50011e6i		−	1.73817i	0.494666	−	0.869083i	$-0.335290\pi$
$930$		0			0
$931$	−1.08648e6			−1.25349
$932$		0			0
$933$	621724.	+	621724.i	0.714223	+	0.714223i
$934$		0			0
$935$	30260.4	−	14895.5i	0.0346140	−	0.0170386i
$936$		0			0
$937$	−108595.	+	108595.i	−0.123688	+	0.123688i	−0.766241	−	0.642553i	$-0.777875\pi$
$937$	−108595.	+	108595.i	−0.123688	+	0.123688i	0.642553	+	0.766241i	$0.277875\pi$
$938$		0			0
$939$			127950.i			0.145114i
$940$		0			0
$941$	690224.			0.779490			0.389745	−	0.920923i	$-0.372563\pi$
$941$	690224.			0.779490			0.389745	+	0.920923i	$0.372563\pi$
$942$		0			0
$943$	−132559.	−	132559.i	−0.149069	−	0.149069i
$944$		0			0
$945$	86151.7	−	253192.i	0.0964718	−	0.283522i
$946$		0			0
$947$	498365.	−	498365.i	0.555709	−	0.555709i	−0.372374	−	0.928083i	$-0.621456\pi$
$947$	498365.	−	498365.i	0.555709	−	0.555709i	0.928083	+	0.372374i	$0.121456\pi$
$948$		0			0
$949$		−	639388.i		−	0.709957i
$950$		0			0
$951$	1.29045e6			1.42686
$952$		0			0
$953$	512766.	+	512766.i	0.564590	+	0.564590i	0.930608	−	0.366018i	$-0.119279\pi$
$953$	512766.	+	512766.i	0.564590	+	0.564590i	−0.366018	+	0.930608i	$0.619279\pi$
$954$		0			0
$955$	1.07397e6	+	365432.i	1.17757	+	0.400682i
$956$		0			0
$957$	−100173.	+	100173.i	−0.109377	+	0.109377i
$958$		0			0
$959$			236657.i			0.257325i
$960$		0			0
$961$	−897843.			−0.972195
$962$		0			0
$963$	−37765.8	−	37765.8i	−0.0407236	−	0.0407236i
$964$		0			0
$965$	493897.	+	1.00336e6i	0.530374	+	1.07746i
$966$		0			0
$967$	−396636.	+	396636.i	−0.424169	+	0.424169i	−0.886636	−	0.462467i	$-0.846964\pi$
$967$	−396636.	+	396636.i	−0.424169	+	0.424169i	0.462467	+	0.886636i	$0.346964\pi$
$968$		0			0
$969$		−	110621.i		−	0.117812i
$970$		0			0
$971$	−850885.			−0.902469			−0.451235	−	0.892405i	$-0.649016\pi$
$971$	−850885.			−0.902469			−0.451235	+	0.892405i	$0.649016\pi$
$972$		0			0
$973$	258384.	+	258384.i	0.272923	+	0.272923i
$974$		0			0
$975$	−611636.	+	794712.i	−0.643404	+	0.835989i
$976$		0			0
$977$	−322165.	+	322165.i	−0.337512	+	0.337512i	−0.855430	−	0.517918i	$-0.826707\pi$
$977$	−322165.	+	322165.i	−0.337512	+	0.337512i	0.517918	+	0.855430i	$0.326707\pi$
$978$		0			0
$979$		−	464470.i		−	0.484610i
$980$		0			0
$981$	31804.5			0.0330484
$982$		0			0
$983$	36685.2	+	36685.2i	0.0379650	+	0.0379650i	0.725834	−	0.687869i	$-0.241454\pi$
$983$	36685.2	+	36685.2i	0.0379650	+	0.0379650i	−0.687869	+	0.725834i	$0.741454\pi$
$984$		0			0
$985$	109534.	−	53917.5i	0.112895	−	0.0555722i
$986$		0			0
$987$	138794.	−	138794.i	0.142474	−	0.142474i
$988$		0			0
$989$			1.44477e6i			1.47708i
$990$		0			0
$991$	−1.13688e6			−1.15762			−0.578810	−	0.815462i	$-0.696483\pi$
$991$	−1.13688e6			−1.15762			−0.578810	+	0.815462i	$0.696483\pi$
$992$		0			0
$993$	−1.19378e6	−	1.19378e6i	−1.21067	−	1.21067i
$994$		0			0
$995$	88006.7	−	258643.i	0.0888934	−	0.261249i
$996$		0			0
$997$	893711.	−	893711.i	0.899097	−	0.899097i	−0.0962593	−	0.995356i	$-0.530688\pi$
$997$	893711.	−	893711.i	0.899097	−	0.899097i	0.995356	+	0.0962593i	$0.0306878\pi$
$998$		0			0
$999$			810022.i			0.811644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.5.p.f.33.2	yes	12
4.3	odd	2		160.5.p.e.33.5	✓	12
5.2	odd	4	inner	160.5.p.f.97.2	yes	12
8.3	odd	2		320.5.p.r.193.2		12
8.5	even	2		320.5.p.s.193.5		12
20.7	even	4		160.5.p.e.97.5	yes	12
40.27	even	4		320.5.p.r.257.2		12
40.37	odd	4		320.5.p.s.257.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.5.p.e.33.5	✓	12	4.3	odd	2
160.5.p.e.97.5	yes	12	20.7	even	4
160.5.p.f.33.2	yes	12	1.1	even	1	trivial
160.5.p.f.97.2	yes	12	5.2	odd	4	inner
320.5.p.r.193.2		12	8.3	odd	2
320.5.p.r.257.2		12	40.27	even	4
320.5.p.s.193.5		12	8.5	even	2
320.5.p.s.257.5		12	40.37	odd	4

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	160.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.86997 - 5.86997i) q^{3} +(-23.6674 - 8.05314i) q^{5} +(9.78913 - 9.78913i) q^{7} -12.0869i q^{9} -49.7874 q^{11} +(-136.672 - 136.672i) q^{13} +(91.6554 + 186.199i) q^{15} +(19.1608 - 19.1608i) q^{17} +491.764i q^{19} -114.924 q^{21} +(454.416 + 454.416i) q^{23} +(495.294 + 381.194i) q^{25} +(-546.417 + 546.417i) q^{27} +342.763i q^{29} +160.245 q^{31} +(292.251 + 292.251i) q^{33} +(-310.517 + 152.850i) q^{35} +(741.212 - 741.212i) q^{37} +1604.53i q^{39} -291.713 q^{41} +(1589.69 + 1589.69i) q^{43} +(-97.3375 + 286.066i) q^{45} +(-1207.70 + 1207.70i) q^{47} +2209.35i q^{49} -224.947 q^{51} +(-3161.17 - 3161.17i) q^{53} +(1178.34 + 400.945i) q^{55} +(2886.64 - 2886.64i) q^{57} +3690.87i q^{59} -6470.44 q^{61} +(-118.320 - 118.320i) q^{63} +(2134.04 + 4335.33i) q^{65} +(4986.29 - 4986.29i) q^{67} -5334.82i q^{69} -6846.84 q^{71} +(2339.13 + 2339.13i) q^{73} +(-669.761 - 5144.96i) q^{75} +(-487.376 + 487.376i) q^{77} -8853.82i q^{79} +5435.87 q^{81} +(-4024.59 - 4024.59i) q^{83} +(-607.792 + 299.183i) q^{85} +(2012.01 - 2012.01i) q^{87} +9329.05i q^{89} -2675.81 q^{91} +(-940.632 - 940.632i) q^{93} +(3960.24 - 11638.8i) q^{95} +(2598.26 - 2598.26i) q^{97} +601.776i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 24 q^{5} + 48 q^{7} + 320 q^{11} + 260 q^{13} - 592 q^{15} - 60 q^{17} - 400 q^{21} - 176 q^{23} + 836 q^{25} + 2208 q^{27} - 480 q^{31} - 3120 q^{33} + 2208 q^{35} - 500 q^{37} + 2160 q^{41} + 3744 q^{43}+ \cdots + 36460 q^{97}+O(q^{100}) \) 12 * q + 24 * q^5 + 48 * q^7 + 320 * q^11 + 260 * q^13 - 592 * q^15 - 60 * q^17 - 400 * q^21 - 176 * q^23 + 836 * q^25 + 2208 * q^27 - 480 * q^31 - 3120 * q^33 + 2208 * q^35 - 500 * q^37 + 2160 * q^41 + 3744 * q^43 - 3116 * q^45 + 1264 * q^47 - 16960 * q^51 + 7020 * q^53 + 8256 * q^55 + 1760 * q^57 + 2928 * q^61 + 15504 * q^63 + 5196 * q^65 + 2400 * q^67 - 31200 * q^71 - 340 * q^73 + 1472 * q^75 - 6960 * q^77 - 27676 * q^81 + 25952 * q^83 - 7292 * q^85 + 27744 * q^87 - 66240 * q^91 - 2640 * q^93 - 3552 * q^95 + 36460 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more