LMFDB - Embedded newform 160.6.o.a.47.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,6,Mod(47,160)]

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, 2, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("160.47");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	160.o (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$25.6614111701$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.20
Character	$\chi$	$=$	160.47
Dual form			160.6.o.a.143.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.52871 - 7.52871i) q^{3} +(-50.5551 + 23.8576i) q^{5} +(51.0903 - 51.0903i) q^{7} +129.637i q^{9} +O(q^{10})$	\(q+(7.52871 - 7.52871i) q^{3} +(-50.5551 + 23.8576i) q^{5} +(51.0903 - 51.0903i) q^{7} +129.637i q^{9} +209.146 q^{11} +(-528.819 - 528.819i) q^{13} +(-200.998 + 560.231i) q^{15} +(1178.43 + 1178.43i) q^{17} +386.096i q^{19} -769.289i q^{21} +(2784.05 + 2784.05i) q^{23} +(1986.63 - 2412.24i) q^{25} +(2805.48 + 2805.48i) q^{27} +162.172 q^{29} +764.769i q^{31} +(1574.60 - 1574.60i) q^{33} +(-1363.99 + 3801.77i) q^{35} +(-1723.18 + 1723.18i) q^{37} -7962.64 q^{39} +13822.2 q^{41} +(13834.7 - 13834.7i) q^{43} +(-3092.82 - 6553.81i) q^{45} +(8464.74 - 8464.74i) q^{47} +11586.6i q^{49} +17744.1 q^{51} +(3998.09 + 3998.09i) q^{53} +(-10573.4 + 4989.72i) q^{55} +(2906.81 + 2906.81i) q^{57} +1240.72i q^{59} +50507.3i q^{61} +(6623.20 + 6623.20i) q^{63} +(39350.8 + 14118.1i) q^{65} +(47228.8 + 47228.8i) q^{67} +41920.6 q^{69} -26226.6i q^{71} +(-13699.8 + 13699.8i) q^{73} +(-3204.29 - 33117.9i) q^{75} +(10685.4 - 10685.4i) q^{77} -41902.4 q^{79} +10741.4 q^{81} +(-20497.1 + 20497.1i) q^{83} +(-87689.8 - 31461.1i) q^{85} +(1220.95 - 1220.95i) q^{87} -64749.3i q^{89} -54035.1 q^{91} +(5757.73 + 5757.73i) q^{93} +(-9211.32 - 19519.1i) q^{95} +(-83188.7 - 83188.7i) q^{97} +27113.1i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{3}+O(q^{10}) $ 56 * q + 4 * q^3	$ 56 q + 4 q^{3} + 8 q^{11} - 408 q^{17} - 3120 q^{25} - 968 q^{27} - 976 q^{33} + 4780 q^{35} - 8 q^{41} - 1308 q^{43} - 20872 q^{51} + 968 q^{57} + 17680 q^{65} - 89252 q^{67} - 25184 q^{73} + 127740 q^{75} - 67792 q^{81} + 126444 q^{83} - 329432 q^{91} + 212576 q^{97}+O(q^{100}) $ 56 * q + 4 * q^3 + 8 * q^11 - 408 * q^17 - 3120 * q^25 - 968 * q^27 - 976 * q^33 + 4780 * q^35 - 8 * q^41 - 1308 * q^43 - 20872 * q^51 + 968 * q^57 + 17680 * q^65 - 89252 * q^67 - 25184 * q^73 + 127740 * q^75 - 67792 * q^81 + 126444 * q^83 - 329432 * q^91 + 212576 * q^97

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
$3$	7.52871	−	7.52871i	0.482967	−	0.482967i	−0.423111	−	0.906078i	$-0.639062\pi$
$3$	7.52871	−	7.52871i	0.482967	−	0.482967i	0.906078	+	0.423111i	$0.139062\pi$
$4$		0			0
$5$	−50.5551	+	23.8576i	−0.904357	+	0.426777i
$5$	−50.5551	+	23.8576i	−0.904357	+	0.426777i
$6$		0			0
$7$	51.0903	−	51.0903i	0.394088	−	0.394088i	−0.482053	−	0.876142i	$-0.660109\pi$
$7$	51.0903	−	51.0903i	0.394088	−	0.394088i	0.876142	+	0.482053i	$0.160109\pi$
$8$		0			0
$9$			129.637i			0.533486i
$10$		0			0
$11$	209.146			0.521157			0.260578	−	0.965453i	$-0.416087\pi$
$11$	209.146			0.521157			0.260578	+	0.965453i	$0.416087\pi$
$12$		0			0
$13$	−528.819	−	528.819i	−0.867857	−	0.867857i	0.124378	−	0.992235i	$-0.460307\pi$
$13$	−528.819	−	528.819i	−0.867857	−	0.867857i	−0.992235	+	0.124378i	$0.960307\pi$
$14$		0			0
$15$	−200.998	+	560.231i	−0.230655	+	0.642894i
$16$		0			0
$17$	1178.43	+	1178.43i	0.988963	+	0.988963i	0.999940	−	0.0109768i	$-0.00349409\pi$
$17$	1178.43	+	1178.43i	0.988963	+	0.988963i	−0.0109768	+	0.999940i	$0.503494\pi$
$18$		0			0
$19$			386.096i			0.245364i	0.992446	+	0.122682i	$0.0391496\pi$
$19$			386.096i			0.245364i	−0.992446	+	0.122682i	$0.960850\pi$
$20$		0			0
$21$		−	769.289i		−	0.380663i
$22$		0			0
$23$	2784.05	+	2784.05i	1.09738	+	1.09738i	0.994716	+	0.102666i	$0.0327372\pi$
$23$	2784.05	+	2784.05i	1.09738	+	1.09738i	0.102666	+	0.994716i	$0.467263\pi$
$24$		0			0
$25$	1986.63	−	2412.24i	0.635723	−	0.771918i
$26$		0			0
$27$	2805.48	+	2805.48i	0.740623	+	0.740623i
$28$		0			0
$29$	162.172			0.0358081			0.0179041	−	0.999840i	$-0.494301\pi$
$29$	162.172			0.0358081			0.0179041	+	0.999840i	$0.494301\pi$
$30$		0			0
$31$			764.769i			0.142931i	0.997443	+	0.0714655i	$0.0227676\pi$
$31$			764.769i			0.142931i	−0.997443	+	0.0714655i	$0.977232\pi$
$32$		0			0
$33$	1574.60	−	1574.60i	0.251702	−	0.251702i
$34$		0			0
$35$	−1363.99	+	3801.77i	−0.188209	+	0.524585i
$36$		0			0
$37$	−1723.18	+	1723.18i	−0.206932	+	0.206932i	−0.802962	−	0.596030i	$-0.796744\pi$
$37$	−1723.18	+	1723.18i	−0.206932	+	0.206932i	0.596030	+	0.802962i	$0.296744\pi$
$38$		0			0
$39$	−7962.64			−0.838293
$40$		0			0
$41$	13822.2			1.28415			0.642077	−	0.766640i	$-0.278073\pi$
$41$	13822.2			1.28415			0.642077	+	0.766640i	$0.278073\pi$
$42$		0			0
$43$	13834.7	−	13834.7i	1.14103	−	1.14103i	0.152768	−	0.988262i	$-0.451181\pi$
$43$	13834.7	−	13834.7i	1.14103	−	1.14103i	0.988262	−	0.152768i	$-0.0488187\pi$
$44$		0			0
$45$	−3092.82	−	6553.81i	−0.227680	−	0.482462i
$46$		0			0
$47$	8464.74	−	8464.74i	0.558945	−	0.558945i	−0.370062	−	0.929007i	$-0.620664\pi$
$47$	8464.74	−	8464.74i	0.558945	−	0.558945i	0.929007	+	0.370062i	$0.120664\pi$
$48$		0			0
$49$			11586.6i			0.689389i
$50$		0			0
$51$	17744.1			0.955273
$52$		0			0
$53$	3998.09	+	3998.09i	0.195507	+	0.195507i	0.798071	−	0.602564i	$-0.205854\pi$
$53$	3998.09	+	3998.09i	0.195507	+	0.195507i	−0.602564	+	0.798071i	$0.705854\pi$
$54$		0			0
$55$	−10573.4	+	4989.72i	−0.471312	+	0.222418i
$56$		0			0
$57$	2906.81	+	2906.81i	0.118503	+	0.118503i
$58$		0			0
$59$			1240.72i			0.0464027i	0.999731	+	0.0232013i	$0.00738588\pi$
$59$			1240.72i			0.0464027i	−0.999731	+	0.0232013i	$0.992614\pi$
$60$		0			0
$61$			50507.3i			1.73792i	0.494884	+	0.868959i	$0.335211\pi$
$61$			50507.3i			1.73792i	−0.494884	+	0.868959i	$0.664789\pi$
$62$		0			0
$63$	6623.20	+	6623.20i	0.210241	+	0.210241i
$64$		0			0
$65$	39350.8	+	14118.1i	1.15523	+	0.414471i
$66$		0			0
$67$	47228.8	+	47228.8i	1.28535	+	1.28535i	0.937583	+	0.347763i	$0.113058\pi$
$67$	47228.8	+	47228.8i	1.28535	+	1.28535i	0.347763	+	0.937583i	$0.386942\pi$
$68$		0			0
$69$	41920.6			1.06000
$70$		0			0
$71$		−	26226.6i		−	0.617443i	−0.951153	−	0.308721i	$-0.900099\pi$
$71$		−	26226.6i		−	0.617443i	0.951153	−	0.308721i	$-0.0999010\pi$
$72$		0			0
$73$	−13699.8	+	13699.8i	−0.300889	+	0.300889i	−0.841362	−	0.540473i	$-0.818245\pi$
$73$	−13699.8	+	13699.8i	−0.300889	+	0.300889i	0.540473	+	0.841362i	$0.318245\pi$
$74$		0			0
$75$	−3204.29	−	33117.9i	−0.0657777	−	0.679844i
$76$		0			0
$77$	10685.4	−	10685.4i	0.205382	−	0.205382i
$78$		0			0
$79$	−41902.4			−0.755390			−0.377695	−	0.925930i	$-0.623283\pi$
$79$	−41902.4			−0.755390			−0.377695	+	0.925930i	$0.623283\pi$
$80$		0			0
$81$	10741.4			0.181907
$82$		0			0
$83$	−20497.1	+	20497.1i	−0.326586	+	0.326586i	−0.851287	−	0.524701i	$-0.824177\pi$
$83$	−20497.1	+	20497.1i	−0.326586	+	0.326586i	0.524701	+	0.851287i	$0.324177\pi$
$84$		0			0
$85$	−87689.8	−	31461.1i	−1.31644	−	0.472309i
$86$		0			0
$87$	1220.95	−	1220.95i	0.0172942	−	0.0172942i
$88$		0			0
$89$		−	64749.3i		−	0.866483i	−0.901278	−	0.433241i	$-0.857370\pi$
$89$		−	64749.3i		−	0.866483i	0.901278	−	0.433241i	$-0.142630\pi$
$90$		0			0
$91$	−54035.1			−0.684025
$92$		0			0
$93$	5757.73	+	5757.73i	0.0690309	+	0.0690309i
$94$		0			0
$95$	−9211.32	−	19519.1i	−0.104716	−	0.221897i
$96$		0			0
$97$	−83188.7	−	83188.7i	−0.897708	−	0.897708i	0.0975250	−	0.995233i	$-0.468907\pi$
$97$	−83188.7	−	83188.7i	−0.897708	−	0.897708i	−0.995233	+	0.0975250i	$0.968907\pi$
$98$		0			0
$99$			27113.1i			0.278030i
$100$		0			0
$101$		−	125685.i		−	1.22597i	−0.790096	−	0.612984i	$-0.789969\pi$
$101$		−	125685.i		−	1.22597i	0.790096	−	0.612984i	$-0.210031\pi$
$102$		0			0
$103$	125285.	+	125285.i	1.16361	+	1.16361i	0.983680	+	0.179926i	$0.0575858\pi$
$103$	125285.	+	125285.i	1.16361	+	1.16361i	0.179926	+	0.983680i	$0.442414\pi$
$104$		0			0
$105$	18353.4	+	38891.5i	0.162458	+	0.344256i
$106$		0			0
$107$	−103805.	−	103805.i	−0.876512	−	0.876512i	0.116660	−	0.993172i	$-0.462781\pi$
$107$	−103805.	−	103805.i	−0.876512	−	0.876512i	−0.993172	+	0.116660i	$0.962781\pi$
$108$		0			0
$109$	−39926.6			−0.321881			−0.160941	−	0.986964i	$-0.551453\pi$
$109$	−39926.6			−0.321881			−0.160941	+	0.986964i	$0.551453\pi$
$110$		0			0
$111$			25946.7i			0.199882i
$112$		0			0
$113$	−139038.	+	139038.i	−1.02432	+	1.02432i	−0.0246238	+	0.999697i	$0.507839\pi$
$113$	−139038.	+	139038.i	−1.02432	+	1.02432i	−0.999697	+	0.0246238i	$0.992161\pi$
$114$		0			0
$115$	−207169.	−	74327.3i	−1.46076	−	0.524087i
$116$		0			0
$117$	68554.5	−	68554.5i	0.462990	−	0.462990i
$118$		0			0
$119$	120412.			0.779478
$120$		0			0
$121$	−117309.			−0.728395
$122$		0			0
$123$	104063.	−	104063.i	0.620204	−	0.620204i
$124$		0			0
$125$	−42884.2	+	169347.i	−0.245483	+	0.969401i
$126$		0			0
$127$	16619.7	−	16619.7i	0.0914356	−	0.0914356i	−0.659910	−	0.751345i	$-0.729405\pi$
$127$	16619.7	−	16619.7i	0.0914356	−	0.0914356i	0.751345	+	0.659910i	$0.229405\pi$
$128$		0			0
$129$		−	208314.i		−	1.10216i
$130$		0			0
$131$	−155820.			−0.793314			−0.396657	−	0.917967i	$-0.629830\pi$
$131$	−155820.			−0.793314			−0.396657	+	0.917967i	$0.629830\pi$
$132$		0			0
$133$	19725.8	+	19725.8i	0.0966953	+	0.0966953i
$134$		0			0
$135$	−208763.	−	74899.3i	−0.985868	−	0.353707i
$136$		0			0
$137$	−41457.8	−	41457.8i	−0.188714	−	0.188714i	0.606426	−	0.795140i	$-0.292603\pi$
$137$	−41457.8	−	41457.8i	−0.188714	−	0.188714i	−0.795140	+	0.606426i	$0.792603\pi$
$138$		0			0
$139$			351852.i			1.54462i	0.635244	+	0.772312i	$0.280900\pi$
$139$			351852.i			1.54462i	−0.635244	+	0.772312i	$0.719100\pi$
$140$		0			0
$141$		−	127457.i		−	0.539904i
$142$		0			0
$143$	−110600.	−	110600.i	−0.452290	−	0.452290i
$144$		0			0
$145$	−8198.64	+	3869.04i	−0.0323833	+	0.0152821i
$146$		0			0
$147$	87231.8	+	87231.8i	0.332952	+	0.332952i
$148$		0			0
$149$	168103.			0.620312			0.310156	−	0.950686i	$-0.399619\pi$
$149$	168103.			0.620312			0.310156	+	0.950686i	$0.399619\pi$
$150$		0			0
$151$		−	327727.i		−	1.16969i	−0.811146	−	0.584844i	$-0.801156\pi$
$151$		−	327727.i		−	1.16969i	0.811146	−	0.584844i	$-0.198844\pi$
$152$		0			0
$153$	−152768.	+	152768.i	−0.527598	+	0.527598i
$154$		0			0
$155$	−18245.5	−	38663.0i	−0.0609997	−	0.129261i
$156$		0			0
$157$	−143534.	+	143534.i	−0.464735	+	0.464735i	−0.900204	−	0.435469i	$-0.856583\pi$
$157$	−143534.	+	143534.i	−0.464735	+	0.464735i	0.435469	+	0.900204i	$0.356583\pi$
$158$		0			0
$159$	60200.9			0.188847
$160$		0			0
$161$	284476.			0.864931
$162$		0			0
$163$	186517.	−	186517.i	0.549855	−	0.549855i	−0.376544	−	0.926399i	$-0.622887\pi$
$163$	186517.	−	186517.i	0.549855	−	0.549855i	0.926399	+	0.376544i	$0.122887\pi$
$164$		0			0
$165$	−42038.0	+	117170.i	−0.120208	+	0.335049i
$166$		0			0
$167$	−433646.	+	433646.i	−1.20322	+	1.20322i	−0.230036	+	0.973182i	$0.573884\pi$
$167$	−433646.	+	433646.i	−1.20322	+	1.20322i	−0.973182	+	0.230036i	$0.926116\pi$
$168$		0			0
$169$			188005.i			0.506353i
$170$		0			0
$171$	−50052.4			−0.130898
$172$		0			0
$173$	302751.	+	302751.i	0.769077	+	0.769077i	0.977944	−	0.208867i	$-0.0669777\pi$
$173$	302751.	+	302751.i	0.769077	+	0.769077i	−0.208867	+	0.977944i	$0.566978\pi$
$174$		0			0
$175$	−21744.5	−	224740.i	−0.0536729	−	0.554735i
$176$		0			0
$177$	9341.01	+	9341.01i	0.0224110	+	0.0224110i
$178$		0			0
$179$		−	262028.i		−	0.611245i	−0.952153	−	0.305623i	$-0.901135\pi$
$179$		−	262028.i		−	0.611245i	0.952153	−	0.305623i	$-0.0988646\pi$
$180$		0			0
$181$		−	323424.i		−	0.733798i	−0.930261	−	0.366899i	$-0.880419\pi$
$181$		−	323424.i		−	0.733798i	0.930261	−	0.366899i	$-0.119581\pi$
$182$		0			0
$183$	380255.	+	380255.i	0.839357	+	0.839357i
$184$		0			0
$185$	46004.7	−	128227.i	0.0988264	−	0.275454i
$186$		0			0
$187$	246463.	+	246463.i	0.515405	+	0.515405i
$188$		0			0
$189$	286666.			0.583742
$190$		0			0
$191$		−	672294.i		−	1.33345i	−0.745305	−	0.666724i	$-0.767696\pi$
$191$		−	672294.i		−	1.33345i	0.745305	−	0.666724i	$-0.232304\pi$
$192$		0			0
$193$	−25987.0	+	25987.0i	−0.0502185	+	0.0502185i	−0.731770	−	0.681552i	$-0.761306\pi$
$193$	−25987.0	+	25987.0i	−0.0502185	+	0.0502185i	0.681552	+	0.731770i	$0.261306\pi$
$194$		0			0
$195$	402552.	−	189969.i	0.758116	−	0.357764i
$196$		0			0
$197$	−223666.	+	223666.i	−0.410614	+	0.410614i	−0.881952	−	0.471338i	$-0.843771\pi$
$197$	−223666.	+	223666.i	−0.410614	+	0.410614i	0.471338	+	0.881952i	$0.343771\pi$
$198$		0			0
$199$	969198.			1.73492			0.867460	−	0.497506i	$-0.165751\pi$
$199$	969198.			1.73492			0.867460	+	0.497506i	$0.165751\pi$
$200$		0			0
$201$	711144.			1.24156
$202$		0			0
$203$	8285.44	−	8285.44i	0.0141116	−	0.0141116i
$204$		0			0
$205$	−698782.	+	329764.i	−1.16133	+	0.548048i
$206$		0			0
$207$	−360916.	+	360916.i	−0.585438	+	0.585438i
$208$		0			0
$209$			80750.6i			0.127873i
$210$		0			0
$211$	495120.			0.765604			0.382802	−	0.923830i	$-0.374959\pi$
$211$	495120.			0.765604			0.382802	+	0.923830i	$0.374959\pi$
$212$		0			0
$213$	−197453.	−	197453.i	−0.298204	−	0.298204i
$214$		0			0
$215$	−369351.	+	1.02947e6i	−0.544933	+	1.51886i
$216$		0			0
$217$	39072.3	+	39072.3i	0.0563274	+	0.0563274i
$218$		0			0
$219$			206283.i			0.290639i
$220$		0			0
$221$		−	1.24635e6i		−	1.71656i
$222$		0			0
$223$	−5174.56	−	5174.56i	−0.00696804	−	0.00696804i	0.703614	−	0.710582i	$-0.251568\pi$
$223$	−5174.56	−	5174.56i	−0.00696804	−	0.00696804i	−0.710582	+	0.703614i	$0.751568\pi$
$224$		0			0
$225$	312716.	+	257541.i	0.411807	+	0.339149i
$226$		0			0
$227$	−96110.1	−	96110.1i	−0.123795	−	0.123795i	0.642495	−	0.766290i	$-0.277899\pi$
$227$	−96110.1	−	96110.1i	−0.123795	−	0.123795i	−0.766290	+	0.642495i	$0.777899\pi$
$228$		0			0
$229$	521668.			0.657363			0.328682	−	0.944441i	$-0.393396\pi$
$229$	521668.			0.657363			0.328682	+	0.944441i	$0.393396\pi$
$230$		0			0
$231$		−	160894.i		−	0.198385i
$232$		0			0
$233$	884493.	−	884493.i	1.06734	−	1.06734i	0.0697820	−	0.997562i	$-0.477770\pi$
$233$	884493.	−	884493.i	1.06734	−	1.06734i	0.997562	−	0.0697820i	$-0.0222304\pi$
$234$		0			0
$235$	−225988.	+	629884.i	−0.266941	+	0.744031i
$236$		0			0
$237$	−315471.	+	315471.i	−0.364829	+	0.364829i
$238$		0			0
$239$	−258110.			−0.292287			−0.146144	−	0.989263i	$-0.546686\pi$
$239$	−258110.			−0.292287			−0.146144	+	0.989263i	$0.546686\pi$
$240$		0			0
$241$	297510.			0.329958			0.164979	−	0.986297i	$-0.447244\pi$
$241$	297510.			0.329958			0.164979	+	0.986297i	$0.447244\pi$
$242$		0			0
$243$	−600862.	+	600862.i	−0.652768	+	0.652768i
$244$		0			0
$245$	−276427.	−	585759.i	−0.294215	−	0.623453i
$246$		0			0
$247$	204175.	−	204175.i	0.212941	−	0.212941i
$248$		0			0
$249$			308634.i			0.315460i
$250$		0			0
$251$	1.73836e6			1.74162			0.870812	−	0.491617i	$-0.163594\pi$
$251$	1.73836e6			1.74162			0.870812	+	0.491617i	$0.163594\pi$
$252$		0			0
$253$	582274.	+	582274.i	0.571908	+	0.571908i
$254$		0			0
$255$	−897052.	+	423330.i	−0.863908	+	0.407689i
$256$		0			0
$257$	217479.	+	217479.i	0.205392	+	0.205392i	0.802306	−	0.596913i	$-0.203606\pi$
$257$	217479.	+	217479.i	0.205392	+	0.205392i	−0.596913	+	0.802306i	$0.703606\pi$
$258$		0			0
$259$			176076.i			0.163099i
$260$		0			0
$261$			21023.5i			0.0191031i
$262$		0			0
$263$	1.05381e6	+	1.05381e6i	0.939446	+	0.939446i	0.998268	−	0.0588228i	$-0.0187347\pi$
$263$	1.05381e6	+	1.05381e6i	0.939446	+	0.939446i	−0.0588228	+	0.998268i	$0.518735\pi$
$264$		0			0
$265$	−297508.	−	106739.i	−0.260246	−	0.0933703i
$266$		0			0
$267$	−487479.	−	487479.i	−0.418483	−	0.418483i
$268$		0			0
$269$	584734.			0.492695			0.246347	−	0.969182i	$-0.420770\pi$
$269$	584734.			0.492695			0.246347	+	0.969182i	$0.420770\pi$
$270$		0			0
$271$		−	2.15271e6i		−	1.78059i	−0.455389	−	0.890293i	$-0.650500\pi$
$271$		−	2.15271e6i		−	1.78059i	0.455389	−	0.890293i	$-0.349500\pi$
$272$		0			0
$273$	−406814.	+	406814.i	−0.330362	+	0.330362i
$274$		0			0
$275$	415497.	−	504512.i	0.331311	−	0.402290i
$276$		0			0
$277$	−1.45027e6	+	1.45027e6i	−1.13566	+	1.13566i	−0.146441	+	0.989219i	$0.546782\pi$
$277$	−1.45027e6	+	1.45027e6i	−1.13566	+	1.13566i	−0.989219	+	0.146441i	$0.953218\pi$
$278$		0			0
$279$	−99142.5			−0.0762516
$280$		0			0
$281$	−2.60522e6			−1.96825			−0.984123	−	0.177487i	$-0.943203\pi$
$281$	−2.60522e6			−1.96825			−0.984123	+	0.177487i	$0.943203\pi$
$282$		0			0
$283$	−873350.	+	873350.i	−0.648220	+	0.648220i	−0.952563	−	0.304343i	$-0.901563\pi$
$283$	−873350.	+	873350.i	−0.648220	+	0.648220i	0.304343	+	0.952563i	$0.401563\pi$
$284$		0			0
$285$	−216303.	−	77604.5i	−0.157743	−	0.0565946i
$286$		0			0
$287$	706181.	−	706181.i	0.506071	−	0.506071i
$288$		0			0
$289$			1.35752e6i			0.956096i
$290$		0			0
$291$	−1.25261e6			−0.867127
$292$		0			0
$293$	1.34847e6	+	1.34847e6i	0.917640	+	0.917640i	0.996857	−	0.0792171i	$-0.0252420\pi$
$293$	1.34847e6	+	1.34847e6i	0.917640	+	0.917640i	−0.0792171	+	0.996857i	$0.525242\pi$
$294$		0			0
$295$	−29600.5	−	62724.6i	−0.0198036	−	0.0419646i
$296$		0			0
$297$	586755.	+	586755.i	0.385981	+	0.385981i
$298$		0			0
$299$		−	2.94452e6i		−	1.90474i
$300$		0			0
$301$		−	1.41363e6i		−	0.899334i
$302$		0			0
$303$	−946244.	−	946244.i	−0.592102	−	0.592102i
$304$		0			0
$305$	−1.20498e6	−	2.55340e6i	−0.741704	−	1.57170i
$306$		0			0
$307$	−740904.	−	740904.i	−0.448659	−	0.448659i	0.446250	−	0.894908i	$-0.352759\pi$
$307$	−740904.	−	740904.i	−0.448659	−	0.448659i	−0.894908	+	0.446250i	$0.852759\pi$
$308$		0			0
$309$	1.88647e6			1.12397
$310$		0			0
$311$			984867.i			0.577400i	0.957420	+	0.288700i	$0.0932230\pi$
$311$			984867.i			0.577400i	−0.957420	+	0.288700i	$0.906777\pi$
$312$		0			0
$313$	−84112.7	+	84112.7i	−0.0485289	+	0.0485289i	−0.730955	−	0.682426i	$-0.760925\pi$
$313$	−84112.7	+	84112.7i	−0.0485289	+	0.0485289i	0.682426	+	0.730955i	$0.260925\pi$
$314$		0			0
$315$	−492850.	−	176823.i	−0.279858	−	0.100407i
$316$		0			0
$317$	965201.	−	965201.i	0.539473	−	0.539473i	−0.383901	−	0.923374i	$-0.625420\pi$
$317$	965201.	−	965201.i	0.539473	−	0.539473i	0.923374	+	0.383901i	$0.125420\pi$
$318$		0			0
$319$	33917.7			0.0186617
$320$		0			0
$321$	−1.56303e6			−0.846653
$322$		0			0
$323$	−454986.	+	454986.i	−0.242656	+	0.242656i
$324$		0			0
$325$	−2.32621e6	+	225070.i	−1.22163	+	0.118198i
$326$		0			0
$327$	−300595.	+	300595.i	−0.155458	+	0.155458i
$328$		0			0
$329$		−	864933.i		−	0.440548i
$330$		0			0
$331$	−1.22036e6			−0.612235			−0.306117	−	0.951994i	$-0.599030\pi$
$331$	−1.22036e6			−0.612235			−0.306117	+	0.951994i	$0.599030\pi$
$332$		0			0
$333$	−223388.	−	223388.i	−0.110395	−	0.110395i
$334$		0			0
$335$	−3.51442e6	−	1.26089e6i	−1.71097	−	0.613855i
$336$		0			0
$337$	−1.36373e6	−	1.36373e6i	−0.654114	−	0.654114i	0.299867	−	0.953981i	$-0.403058\pi$
$337$	−1.36373e6	−	1.36373e6i	−0.654114	−	0.654114i	−0.953981	+	0.299867i	$0.903058\pi$
$338$		0			0
$339$			2.09355e6i			0.989426i
$340$		0			0
$341$			159949.i			0.0744895i
$342$		0			0
$343$	1.45064e6	+	1.45064e6i	0.665769	+	0.665769i
$344$		0			0
$345$	−2.11930e6	+	1.00012e6i	−0.958617	+	0.452383i
$346$		0			0
$347$	−1.57060e6	−	1.57060e6i	−0.700231	−	0.700231i	0.264229	−	0.964460i	$-0.414883\pi$
$347$	−1.57060e6	−	1.57060e6i	−0.700231	−	0.700231i	−0.964460	+	0.264229i	$0.914883\pi$
$348$		0			0
$349$	−1.88122e6			−0.826751			−0.413376	−	0.910561i	$-0.635650\pi$
$349$	−1.88122e6			−0.826751			−0.413376	+	0.910561i	$0.635650\pi$
$350$		0			0
$351$		−	2.96718e6i		−	1.28551i
$352$		0			0
$353$	1.85407e6	−	1.85407e6i	0.791936	−	0.791936i	−0.189873	−	0.981809i	$-0.560808\pi$
$353$	1.85407e6	−	1.85407e6i	0.791936	−	0.791936i	0.981809	+	0.189873i	$0.0608077\pi$
$354$		0			0
$355$	625703.	+	1.32589e6i	0.263510	+	0.558388i
$356$		0			0
$357$	906550.	−	906550.i	0.376462	−	0.376462i
$358$		0			0
$359$	4.03875e6			1.65390			0.826952	−	0.562272i	$-0.190073\pi$
$359$	4.03875e6			1.65390			0.826952	+	0.562272i	$0.190073\pi$
$360$		0			0
$361$	2.32703e6			0.939796
$362$		0			0
$363$	−883184.	+	883184.i	−0.351791	+	0.351791i
$364$		0			0
$365$	365750.	−	1.01944e6i	0.143699	−	0.400524i
$366$		0			0
$367$	−699570.	+	699570.i	−0.271123	+	0.271123i	−0.829552	−	0.558429i	$-0.811404\pi$
$367$	−699570.	+	699570.i	−0.271123	+	0.271123i	0.558429	+	0.829552i	$0.311404\pi$
$368$		0			0
$369$			1.79187e6i			0.685078i
$370$		0			0
$371$	408528.			0.154094
$372$		0			0
$373$	1.43587e6	+	1.43587e6i	0.534373	+	0.534373i	0.921871	−	0.387498i	$-0.126661\pi$
$373$	1.43587e6	+	1.43587e6i	0.534373	+	0.534373i	−0.387498	+	0.921871i	$0.626661\pi$
$374$		0			0
$375$	952105.	+	1.59783e6i	0.349628	+	0.586749i
$376$		0			0
$377$	−85759.8	−	85759.8i	−0.0310764	−	0.0310764i
$378$		0			0
$379$			196527.i			0.0702789i	0.999382	+	0.0351395i	$0.0111875\pi$
$379$			196527.i			0.0702789i	−0.999382	+	0.0351395i	$0.988812\pi$
$380$		0			0
$381$		−	250251.i		−	0.0883207i
$382$		0			0
$383$	14751.8	+	14751.8i	0.00513865	+	0.00513865i	0.709671	−	0.704533i	$-0.248843\pi$
$383$	14751.8	+	14751.8i	0.00513865	+	0.00513865i	−0.704533	+	0.709671i	$0.748843\pi$
$384$		0			0
$385$	−285273.	+	795126.i	−0.0980863	+	0.273391i
$386$		0			0
$387$	1.79348e6	+	1.79348e6i	0.608723	+	0.608723i
$388$		0			0
$389$	−3.21899e6			−1.07856			−0.539282	−	0.842125i	$-0.681304\pi$
$389$	−3.21899e6			−1.07856			−0.539282	+	0.842125i	$0.681304\pi$
$390$		0			0
$391$			6.56160e6i			2.17054i
$392$		0			0
$393$	−1.17312e6	+	1.17312e6i	−0.383145	+	0.383145i
$394$		0			0
$395$	2.11838e6	−	999690.i	0.683143	−	0.322383i
$396$		0			0
$397$	1.36965e6	−	1.36965e6i	0.436147	−	0.436147i	−0.454566	−	0.890713i	$-0.650206\pi$
$397$	1.36965e6	−	1.36965e6i	0.436147	−	0.436147i	0.890713	+	0.454566i	$0.150206\pi$
$398$		0			0
$399$	297020.			0.0934013
$400$		0			0
$401$	4.21327e6			1.30845			0.654227	−	0.756298i	$-0.272994\pi$
$401$	4.21327e6			1.30845			0.654227	+	0.756298i	$0.272994\pi$
$402$		0			0
$403$	404424.	−	404424.i	0.124044	−	0.124044i
$404$		0			0
$405$	−543034.	+	256264.i	−0.164509	+	0.0776338i
$406$		0			0
$407$	−360397.	+	360397.i	−0.107844	+	0.107844i
$408$		0			0
$409$		−	87415.5i		−	0.0258393i	−0.999917	−	0.0129196i	$-0.995887\pi$
$409$		−	87415.5i		−	0.0258393i	0.999917	−	0.0129196i	$-0.00411256\pi$
$410$		0			0
$411$	−624248.			−0.182286
$412$		0			0
$413$	63388.7	+	63388.7i	0.0182868	+	0.0182868i
$414$		0			0
$415$	547222.	−	1.52524e6i	0.155971	−	0.434729i
$416$		0			0
$417$	2.64899e6	+	2.64899e6i	0.746002	+	0.746002i
$418$		0			0
$419$		−	3.03985e6i		−	0.845897i	−0.906154	−	0.422948i	$-0.860995\pi$
$419$		−	3.03985e6i		−	0.845897i	0.906154	−	0.422948i	$-0.139005\pi$
$420$		0			0
$421$		−	2.59517e6i		−	0.713608i	−0.934179	−	0.356804i	$-0.883866\pi$
$421$		−	2.59517e6i		−	0.713608i	0.934179	−	0.356804i	$-0.116134\pi$
$422$		0			0
$423$	1.09734e6	+	1.09734e6i	0.298189	+	0.298189i
$424$		0			0
$425$	5.18375e6	−	501549.i	1.39210	−	0.134692i
$426$		0			0
$427$	2.58043e6	+	2.58043e6i	0.684894	+	0.684894i
$428$		0			0
$429$	−1.66536e6			−0.436882
$430$		0			0
$431$		−	3.24379e6i		−	0.841122i	−0.907264	−	0.420561i	$-0.861833\pi$
$431$		−	3.24379e6i		−	0.841122i	0.907264	−	0.420561i	$-0.138167\pi$
$432$		0			0
$433$	−2.83919e6	+	2.83919e6i	−0.727738	+	0.727738i	−0.970169	−	0.242431i	$-0.922055\pi$
$433$	−2.83919e6	+	2.83919e6i	−0.727738	+	0.727738i	0.242431	+	0.970169i	$0.422055\pi$
$434$		0			0
$435$	−32596.3	+	90854.0i	−0.00825934	+	0.0230208i
$436$		0			0
$437$	−1.07491e6	+	1.07491e6i	−0.269258	+	0.269258i
$438$		0			0
$439$	−4.72246e6			−1.16952			−0.584759	−	0.811207i	$-0.698811\pi$
$439$	−4.72246e6			−1.16952			−0.584759	+	0.811207i	$0.698811\pi$
$440$		0			0
$441$	−1.50205e6			−0.367779
$442$		0			0
$443$	3.54476e6	−	3.54476e6i	0.858178	−	0.858178i	−0.132945	−	0.991123i	$-0.542444\pi$
$443$	3.54476e6	−	3.54476e6i	0.858178	−	0.858178i	0.991123	+	0.132945i	$0.0424435\pi$
$444$		0			0
$445$	1.54476e6	+	3.27341e6i	0.369795	+	0.783610i
$446$		0			0
$447$	1.26560e6	−	1.26560e6i	0.299590	−	0.299590i
$448$		0			0
$449$		−	5.55787e6i		−	1.30105i	−0.759487	−	0.650523i	$-0.774550\pi$
$449$		−	5.55787e6i		−	1.30105i	0.759487	−	0.650523i	$-0.225450\pi$
$450$		0			0
$451$	2.89086e6			0.669246
$452$		0			0
$453$	−2.46736e6	−	2.46736e6i	−0.564921	−	0.564921i
$454$		0			0
$455$	2.73175e6	−	1.28914e6i	0.618603	−	0.291926i
$456$		0			0
$457$	827241.	+	827241.i	0.185286	+	0.185286i	0.793654	−	0.608369i	$-0.208176\pi$
$457$	827241.	+	827241.i	0.185286	+	0.185286i	−0.608369	+	0.793654i	$0.708176\pi$
$458$		0			0
$459$			6.61209e6i			1.46490i
$460$		0			0
$461$			5.22863e6i			1.14587i	0.819600	+	0.572936i	$0.194196\pi$
$461$			5.22863e6i			1.14587i	−0.819600	+	0.572936i	$0.805804\pi$
$462$		0			0
$463$	−5.71441e6	−	5.71441e6i	−1.23885	−	1.23885i	−0.960471	−	0.278380i	$-0.910203\pi$
$463$	−5.71441e6	−	5.71441e6i	−1.23885	−	1.23885i	−0.278380	−	0.960471i	$-0.589797\pi$
$464$		0			0
$465$	−428448.	−	153717.i	−0.0918894	−	0.0329678i
$466$		0			0
$467$	−1.68851e6	−	1.68851e6i	−0.358271	−	0.358271i	0.504904	−	0.863175i	$-0.331528\pi$
$467$	−1.68851e6	−	1.68851e6i	−0.358271	−	0.358271i	−0.863175	+	0.504904i	$0.831528\pi$
$468$		0			0
$469$	4.82587e6			1.01308
$470$		0			0
$471$			2.16125e6i			0.448904i
$472$		0			0
$473$	2.89347e6	−	2.89347e6i	0.594656	−	0.594656i
$474$		0			0
$475$	931358.	+	767032.i	0.189401	+	0.155984i
$476$		0			0
$477$	−518301.	+	518301.i	−0.104300	+	0.104300i
$478$		0			0
$479$	−2.52841e6			−0.503510			−0.251755	−	0.967791i	$-0.581008\pi$
$479$	−2.52841e6			−0.503510			−0.251755	+	0.967791i	$0.581008\pi$
$480$		0			0
$481$	1.82250e6			0.359174
$482$		0			0
$483$	2.14174e6	−	2.14174e6i	0.417733	−	0.417733i
$484$		0			0
$485$	6.19029e6	+	2.22093e6i	1.19497	+	0.428727i
$486$		0			0
$487$	−618270.	+	618270.i	−0.118129	+	0.118129i	−0.763700	−	0.645571i	$-0.776619\pi$
$487$	−618270.	+	618270.i	−0.118129	+	0.118129i	0.645571	+	0.763700i	$0.276619\pi$
$488$		0			0
$489$		−	2.80846e6i		−	0.531124i
$490$		0			0
$491$	3.42336e6			0.640839			0.320420	−	0.947276i	$-0.396176\pi$
$491$	3.42336e6			0.640839			0.320420	+	0.947276i	$0.396176\pi$
$492$		0			0
$493$	191108.	+	191108.i	0.0354129	+	0.0354129i
$494$		0			0
$495$	−646853.	−	1.37071e6i	−0.118657	−	0.251438i
$496$		0			0
$497$	−1.33993e6	−	1.33993e6i	−0.243327	−	0.243327i
$498$		0			0
$499$			116929.i			0.0210218i	0.999945	+	0.0105109i	$0.00334578\pi$
$499$			116929.i			0.0210218i	−0.999945	+	0.0105109i	$0.996654\pi$
$500$		0			0
$501$			6.52959e6i			1.16223i
$502$		0			0
$503$	2.68560e6	+	2.68560e6i	0.473284	+	0.473284i	0.902976	−	0.429692i	$-0.141378\pi$
$503$	2.68560e6	+	2.68560e6i	0.473284	+	0.473284i	−0.429692	+	0.902976i	$0.641378\pi$
$504$		0			0
$505$	2.99853e6	+	6.35400e6i	0.523215	+	1.10871i
$506$		0			0
$507$	1.41544e6	+	1.41544e6i	0.244552	+	0.244552i
$508$		0			0
$509$	4.09184e6			0.700043			0.350021	−	0.936742i	$-0.386174\pi$
$509$	4.09184e6			0.700043			0.350021	+	0.936742i	$0.386174\pi$
$510$		0			0
$511$			1.39985e6i			0.237154i
$512$		0			0
$513$	−1.08318e6	+	1.08318e6i	−0.181723	+	0.181723i
$514$		0			0
$515$	−9.32279e6	−	3.34480e6i	−1.54892	−	0.555715i
$516$		0			0
$517$	1.77037e6	−	1.77037e6i	0.291298	−	0.291298i
$518$		0			0
$519$	4.55864e6			0.742877
$520$		0			0
$521$	−5.55983e6			−0.897360			−0.448680	−	0.893692i	$-0.648106\pi$
$521$	−5.55983e6			−0.897360			−0.448680	+	0.893692i	$0.648106\pi$
$522$		0			0
$523$	−1.22502e6	+	1.22502e6i	−0.195835	+	0.195835i	−0.798212	−	0.602377i	$-0.794220\pi$
$523$	−1.22502e6	+	1.22502e6i	−0.195835	+	0.195835i	0.602377	+	0.798212i	$0.294220\pi$
$524$		0			0
$525$	−1.85571e6	−	1.52829e6i	−0.293841	−	0.241996i
$526$		0			0
$527$	−901224.	+	901224.i	−0.141353	+	0.141353i
$528$		0			0
$529$			9.06554e6i			1.40849i
$530$		0			0
$531$	−160843.			−0.0247552
$532$		0			0
$533$	−7.30944e6	−	7.30944e6i	−1.11446	−	1.11446i
$534$		0			0
$535$	7.72439e6	+	2.77133e6i	1.16676	+	0.418604i
$536$		0			0
$537$	−1.97273e6	−	1.97273e6i	−0.295211	−	0.295211i
$538$		0			0
$539$			2.42328e6i			0.359280i
$540$		0			0
$541$		−	3.09831e6i		−	0.455126i	−0.973763	−	0.227563i	$-0.926924\pi$
$541$		−	3.09831e6i		−	0.455126i	0.973763	−	0.227563i	$-0.0730758\pi$
$542$		0			0
$543$	−2.43497e6	−	2.43497e6i	−0.354400	−	0.354400i
$544$		0			0
$545$	2.01849e6	−	952550.i	0.291095	−	0.137372i
$546$		0			0
$547$	3.00330e6	+	3.00330e6i	0.429171	+	0.429171i	0.888346	−	0.459175i	$-0.151855\pi$
$547$	3.00330e6	+	3.00330e6i	0.429171	+	0.429171i	−0.459175	+	0.888346i	$0.651855\pi$
$548$		0			0
$549$	−6.54761e6			−0.927155
$550$		0			0
$551$			62614.1i			0.00878605i
$552$		0			0
$553$	−2.14081e6	+	2.14081e6i	−0.297691	+	0.297691i
$554$		0			0
$555$	−619025.	−	1.31174e6i	−0.0853052	−	0.180765i
$556$		0			0
$557$	−7.17930e6	+	7.17930e6i	−0.980492	+	0.980492i	−0.999813	−	0.0193214i	$-0.993849\pi$
$557$	−7.17930e6	+	7.17930e6i	−0.980492	+	0.980492i	0.0193214	+	0.999813i	$0.493849\pi$
$558$		0			0
$559$	−1.46320e7			−1.98050
$560$		0			0
$561$	3.71110e6			0.497847
$562$		0			0
$563$	6.92226e6	−	6.92226e6i	0.920400	−	0.920400i	−0.0766573	−	0.997057i	$-0.524425\pi$
$563$	6.92226e6	−	6.92226e6i	0.920400	−	0.920400i	0.997057	+	0.0766573i	$0.0244247\pi$
$564$		0			0
$565$	3.71196e6	−	1.03462e7i	0.489195	−	1.36351i
$566$		0			0
$567$	548784.	−	548784.i	0.0716875	−	0.0716875i
$568$		0			0
$569$		−	9.05668e6i		−	1.17270i	−0.810057	−	0.586352i	$-0.800564\pi$
$569$		−	9.05668e6i		−	1.17270i	0.810057	−	0.586352i	$-0.199436\pi$
$570$		0			0
$571$	−1.49702e7			−1.92149			−0.960745	−	0.277435i	$-0.910516\pi$
$571$	−1.49702e7			−1.92149			−0.960745	+	0.277435i	$0.910516\pi$
$572$		0			0
$573$	−5.06151e6	−	5.06151e6i	−0.644011	−	0.644011i
$574$		0			0
$575$	1.22467e7	−	1.18492e6i	1.54472	−	0.149458i
$576$		0			0
$577$	−7.13017e6	−	7.13017e6i	−0.891580	−	0.891580i	0.103092	−	0.994672i	$-0.467126\pi$
$577$	−7.13017e6	−	7.13017e6i	−0.891580	−	0.891580i	−0.994672	+	0.103092i	$0.967126\pi$
$578$		0			0
$579$			391298.i			0.0485077i
$580$		0			0
$581$			2.09441e6i			0.257407i
$582$		0			0
$583$	836186.	+	836186.i	0.101890	+	0.101890i
$584$		0			0
$585$	−1.83023e6	+	5.10132e6i	−0.221114	+	0.616301i
$586$		0			0
$587$	−1.85509e6	−	1.85509e6i	−0.222213	−	0.222213i	0.587217	−	0.809430i	$-0.300224\pi$
$587$	−1.85509e6	−	1.85509e6i	−0.222213	−	0.222213i	−0.809430	+	0.587217i	$0.800224\pi$
$588$		0			0
$589$	−295275.			−0.0350702
$590$		0			0
$591$			3.36783e6i			0.396626i
$592$		0			0
$593$	−4.16864e6	+	4.16864e6i	−0.486808	+	0.486808i	−0.907298	−	0.420489i	$-0.861858\pi$
$593$	−4.16864e6	+	4.16864e6i	−0.486808	+	0.486808i	0.420489	+	0.907298i	$0.361858\pi$
$594$		0			0
$595$	−6.08746e6	+	2.87275e6i	−0.704926	+	0.332663i
$596$		0			0
$597$	7.29681e6	−	7.29681e6i	0.837910	−	0.837910i
$598$		0			0
$599$	−199615.			−0.0227314			−0.0113657	−	0.999935i	$-0.503618\pi$
$599$	−199615.			−0.0227314			−0.0113657	+	0.999935i	$0.503618\pi$
$600$		0			0
$601$	−4.47068e6			−0.504880			−0.252440	−	0.967613i	$-0.581233\pi$
$601$	−4.47068e6			−0.504880			−0.252440	+	0.967613i	$0.581233\pi$
$602$		0			0
$603$	−6.12260e6	+	6.12260e6i	−0.685713	+	0.685713i
$604$		0			0
$605$	5.93056e6	−	2.79870e6i	0.658729	−	0.310863i
$606$		0			0
$607$	4.55140e6	−	4.55140e6i	0.501387	−	0.501387i	−0.410481	−	0.911869i	$-0.634639\pi$
$607$	4.55140e6	−	4.55140e6i	0.501387	−	0.501387i	0.911869	+	0.410481i	$0.134639\pi$
$608$		0			0
$609$		−	124757.i		−	0.0136309i
$610$		0			0
$611$	−8.95263e6			−0.970169
$612$		0			0
$613$	−256784.	−	256784.i	−0.0276005	−	0.0276005i	0.693172	−	0.720772i	$-0.256213\pi$
$613$	−256784.	−	256784.i	−0.0276005	−	0.0276005i	−0.720772	+	0.693172i	$0.756213\pi$
$614$		0			0
$615$	−2.77823e6	+	7.74363e6i	−0.296197	+	0.825575i
$616$		0			0
$617$	−3.63901e6	−	3.63901e6i	−0.384831	−	0.384831i	0.488008	−	0.872839i	$-0.337724\pi$
$617$	−3.63901e6	−	3.63901e6i	−0.384831	−	0.384831i	−0.872839	+	0.488008i	$0.837724\pi$
$618$		0			0
$619$		−	1.22111e7i		−	1.28094i	−0.767983	−	0.640470i	$-0.778739\pi$
$619$		−	1.22111e7i		−	1.28094i	0.767983	−	0.640470i	$-0.221261\pi$
$620$		0			0
$621$			1.56212e7i			1.62549i
$622$		0			0
$623$	−3.30806e6	−	3.30806e6i	−0.341471	−	0.341471i
$624$		0			0
$625$	−1.87220e6	−	9.58448e6i	−0.191714	−	0.981451i
$626$		0			0
$627$	607948.	+	607948.i	0.0617586	+	0.0617586i
$628$		0			0
$629$	−4.06129e6			−0.409296
$630$		0			0
$631$			5.51289e6i			0.551196i	0.961273	+	0.275598i	$0.0888759\pi$
$631$			5.51289e6i			0.551196i	−0.961273	+	0.275598i	$0.911124\pi$
$632$		0			0
$633$	3.72761e6	−	3.72761e6i	0.369761	−	0.369761i
$634$		0			0
$635$	−443706.	+	1.23672e6i	−0.0436678	+	0.121713i
$636$		0			0
$637$	6.12719e6	−	6.12719e6i	0.598291	−	0.598291i
$638$		0			0
$639$	3.39994e6			0.329397
$640$		0			0
$641$	−5.49557e6			−0.528285			−0.264142	−	0.964484i	$-0.585089\pi$
$641$	−5.49557e6			−0.528285			−0.264142	+	0.964484i	$0.585089\pi$
$642$		0			0
$643$	−3.73494e6	+	3.73494e6i	−0.356252	+	0.356252i	−0.862429	−	0.506178i	$-0.831058\pi$
$643$	−3.73494e6	+	3.73494e6i	−0.356252	+	0.356252i	0.506178	+	0.862429i	$0.331058\pi$
$644$		0			0
$645$	4.96987e6	+	1.05313e7i	0.470377	+	0.996746i
$646$		0			0
$647$	1.39016e6	−	1.39016e6i	0.130558	−	0.130558i	−0.638808	−	0.769366i	$-0.720572\pi$
$647$	1.39016e6	−	1.39016e6i	0.130558	−	0.130558i	0.769366	+	0.638808i	$0.220572\pi$
$648$		0			0
$649$			259492.i			0.0241831i
$650$		0			0
$651$	588329.			0.0544086
$652$		0			0
$653$	−4.89294e6	−	4.89294e6i	−0.449042	−	0.449042i	0.445994	−	0.895036i	$-0.352850\pi$
$653$	−4.89294e6	−	4.89294e6i	−0.449042	−	0.449042i	−0.895036	+	0.445994i	$0.852850\pi$
$654$		0			0
$655$	7.87750e6	−	3.71749e6i	0.717439	−	0.338568i
$656$		0			0
$657$	−1.77600e6	−	1.77600e6i	−0.160520	−	0.160520i
$658$		0			0
$659$			5.27341e6i			0.473019i	0.971629	+	0.236509i	$0.0760034\pi$
$659$			5.27341e6i			0.473019i	−0.971629	+	0.236509i	$0.923997\pi$
$660$		0			0
$661$			1.94657e6i			0.173287i	0.996239	+	0.0866434i	$0.0276141\pi$
$661$			1.94657e6i			0.173287i	−0.996239	+	0.0866434i	$0.972386\pi$
$662$		0			0
$663$	−9.38339e6	−	9.38339e6i	−0.829041	−	0.829041i
$664$		0			0
$665$	−1.46785e6	−	526630.i	−0.128714	−	0.0461797i
$666$		0			0
$667$	451496.	+	451496.i	0.0392952	+	0.0392952i
$668$		0			0
$669$	−77915.5			−0.00673067
$670$		0			0
$671$			1.05634e7i			0.905728i
$672$		0			0
$673$	−3.79903e6	+	3.79903e6i	−0.323322	+	0.323322i	−0.850040	−	0.526718i	$-0.823422\pi$
$673$	−3.79903e6	+	3.79903e6i	−0.323322	+	0.323322i	0.526718	+	0.850040i	$0.323422\pi$
$674$		0			0
$675$	1.23409e7	−	1.19404e6i	1.04253	−	0.100869i
$676$		0			0
$677$	5.44238e6	−	5.44238e6i	0.456370	−	0.456370i	−0.441092	−	0.897462i	$-0.645409\pi$
$677$	5.44238e6	−	5.44238e6i	0.456370	−	0.456370i	0.897462	+	0.441092i	$0.145409\pi$
$678$		0			0
$679$	−8.50028e6			−0.707553
$680$		0			0
$681$	−1.44717e6			−0.119578
$682$		0			0
$683$	4.04342e6	−	4.04342e6i	0.331663	−	0.331663i	−0.521555	−	0.853218i	$-0.674648\pi$
$683$	4.04342e6	−	4.04342e6i	0.331663	−	0.331663i	0.853218	+	0.521555i	$0.174648\pi$
$684$		0			0
$685$	3.08499e6	+	1.10682e6i	0.251204	+	0.0901262i
$686$		0			0
$687$	3.92749e6	−	3.92749e6i	0.317485	−	0.317485i
$688$		0			0
$689$		−	4.22853e6i		−	0.339345i
$690$		0			0
$691$	1.81841e6			0.144876			0.0724382	−	0.997373i	$-0.476922\pi$
$691$	1.81841e6			0.144876			0.0724382	+	0.997373i	$0.476922\pi$
$692$		0			0
$693$	1.38522e6	+	1.38522e6i	0.109568	+	0.109568i
$694$		0			0
$695$	−8.39432e6	−	1.77879e7i	−0.659210	−	1.39689i
$696$		0			0
$697$	1.62884e7	+	1.62884e7i	1.26998	+	1.26998i
$698$		0			0
$699$		−	1.33182e7i		−	1.03098i
$700$		0			0
$701$			8.48609e6i			0.652248i	0.945327	+	0.326124i	$0.105743\pi$
$701$			8.48609e6i			0.652248i	−0.945327	+	0.326124i	$0.894257\pi$
$702$		0			0
$703$	−665315.	−	665315.i	−0.0507737	−	0.0507737i
$704$		0			0
$705$	3.04082e6	+	6.44361e6i	0.230419	+	0.488266i
$706$		0			0
$707$	−6.42127e6	−	6.42127e6i	−0.483140	−	0.483140i
$708$		0			0
$709$	−1.68500e7			−1.25888			−0.629440	−	0.777049i	$-0.716716\pi$
$709$	−1.68500e7			−1.25888			−0.629440	+	0.777049i	$0.716716\pi$
$710$		0			0
$711$		−	5.43211e6i		−	0.402990i
$712$		0			0
$713$	−2.12916e6	+	2.12916e6i	−0.156850	+	0.156850i
$714$		0			0
$715$	8.23007e6	+	2.95276e6i	0.602058	+	0.216004i
$716$		0			0
$717$	−1.94324e6	+	1.94324e6i	−0.141165	+	0.141165i
$718$		0			0
$719$	−5.25706e6			−0.379245			−0.189623	−	0.981857i	$-0.560726\pi$
$719$	−5.25706e6			−0.379245			−0.189623	+	0.981857i	$0.560726\pi$
$720$		0			0
$721$	1.28017e7			0.917128
$722$		0			0
$723$	2.23987e6	−	2.23987e6i	0.159359	−	0.159359i
$724$		0			0
$725$	322177.	−	391199.i	0.0227640	−	0.0276409i
$726$		0			0
$727$	351685.	−	351685.i	0.0246784	−	0.0246784i	−0.694660	−	0.719338i	$-0.744445\pi$
$727$	351685.	−	351685.i	0.0246784	−	0.0246784i	0.719338	+	0.694660i	$0.244445\pi$
$728$		0			0
$729$			1.16576e7i			0.812438i
$730$		0			0
$731$	3.26062e7			2.25687
$732$		0			0
$733$	1.15656e7	+	1.15656e7i	0.795076	+	0.795076i	0.982314	−	0.187239i	$-0.0599538\pi$
$733$	1.15656e7	+	1.15656e7i	0.795076	+	0.795076i	−0.187239	+	0.982314i	$0.559954\pi$
$734$		0			0
$735$	−6.49115e6	−	2.32887e6i	−0.443204	−	0.159011i
$736$		0			0
$737$	9.87773e6	+	9.87773e6i	0.669867	+	0.669867i
$738$		0			0
$739$			1.72691e7i			1.16321i	0.813470	+	0.581606i	$0.197576\pi$
$739$			1.72691e7i			1.16321i	−0.813470	+	0.581606i	$0.802424\pi$
$740$		0			0
$741$		−	3.07435e6i		−	0.205687i
$742$		0			0
$743$	6.71067e6	+	6.71067e6i	0.445958	+	0.445958i	0.894008	−	0.448050i	$-0.147881\pi$
$743$	6.71067e6	+	6.71067e6i	0.445958	+	0.445958i	−0.448050	+	0.894008i	$0.647881\pi$
$744$		0			0
$745$	−8.49847e6	+	4.01053e6i	−0.560984	+	0.264735i
$746$		0			0
$747$	−2.65718e6	−	2.65718e6i	−0.174229	−	0.174229i
$748$		0			0
$749$	−1.06068e7			−0.690847
$750$		0			0
$751$			1.91770e7i			1.24074i	0.784310	+	0.620369i	$0.213017\pi$
$751$			1.91770e7i			1.24074i	−0.784310	+	0.620369i	$0.786983\pi$
$752$		0			0
$753$	1.30876e7	−	1.30876e7i	0.841147	−	0.841147i
$754$		0			0
$755$	7.81877e6	+	1.65683e7i	0.499196	+	1.05782i
$756$		0			0
$757$	−9.28826e6	+	9.28826e6i	−0.589107	+	0.589107i	−0.937390	−	0.348282i	$-0.886765\pi$
$757$	−9.28826e6	+	9.28826e6i	−0.589107	+	0.589107i	0.348282	+	0.937390i	$0.386765\pi$
$758$		0			0
$759$	8.76755e6			0.552425
$760$		0			0
$761$	−1.51980e6			−0.0951315			−0.0475657	−	0.998868i	$-0.515146\pi$
$761$	−1.51980e6			−0.0951315			−0.0475657	+	0.998868i	$0.515146\pi$
$762$		0			0
$763$	−2.03986e6	+	2.03986e6i	−0.126850	+	0.126850i
$764$		0			0
$765$	4.07852e6	−	1.13678e7i	0.251970	−	0.702303i
$766$		0			0
$767$	656115.	−	656115.i	0.0402709	−	0.0402709i
$768$		0			0
$769$			3.15675e6i			0.192497i	0.995357	+	0.0962485i	$0.0306843\pi$
$769$			3.15675e6i			0.192497i	−0.995357	+	0.0962485i	$0.969316\pi$
$770$		0			0
$771$	3.27467e6			0.198395
$772$		0			0
$773$	1.10811e7	+	1.10811e7i	0.667012	+	0.667012i	0.957023	−	0.290011i	$-0.0936590\pi$
$773$	1.10811e7	+	1.10811e7i	0.667012	+	0.667012i	−0.290011	+	0.957023i	$0.593659\pi$
$774$		0			0
$775$	1.84481e6	+	1.51932e6i	0.110331	+	0.0908644i
$776$		0			0
$777$	1.32563e6	+	1.32563e6i	0.0787713	+	0.0787713i
$778$		0			0
$779$			5.33670e6i			0.315086i
$780$		0			0
$781$		−	5.48520e6i		−	0.321784i
$782$		0			0
$783$	454971.	+	454971.i	0.0265203	+	0.0265203i
$784$		0			0
$785$	3.83200e6	−	1.06807e7i	0.221948	−	0.618625i
$786$		0			0
$787$	8.62335e6	+	8.62335e6i	0.496294	+	0.496294i	0.910282	−	0.413988i	$-0.135865\pi$
$787$	8.62335e6	+	8.62335e6i	0.496294	+	0.496294i	−0.413988	+	0.910282i	$0.635865\pi$
$788$		0			0
$789$	1.58676e7			0.907442
$790$		0			0
$791$			1.42069e7i			0.807346i
$792$		0			0
$793$	2.67092e7	−	2.67092e7i	1.50827	−	1.50827i
$794$		0			0
$795$	−3.04346e6	+	1.43625e6i	−0.170785	+	0.0805956i
$796$		0			0
$797$	1.59570e7	−	1.59570e7i	0.889825	−	0.889825i	−0.104681	−	0.994506i	$-0.533382\pi$
$797$	1.59570e7	−	1.59570e7i	0.889825	−	0.889825i	0.994506	+	0.104681i	$0.0333822\pi$
$798$		0			0
$799$	1.99501e7			1.10555
$800$		0			0
$801$	8.39391e6			0.462256
$802$		0			0
$803$	−2.86526e6	+	2.86526e6i	−0.156810	+	0.156810i
$804$		0			0
$805$	−1.43817e7	+	6.78691e6i	−0.782206	+	0.369133i
$806$		0			0
$807$	4.40230e6	−	4.40230e6i	0.237955	−	0.237955i
$808$		0			0
$809$		−	8.86014e6i		−	0.475959i	−0.971270	−	0.237979i	$-0.923515\pi$
$809$		−	8.86014e6i		−	0.475959i	0.971270	−	0.237979i	$-0.0764851\pi$
$810$		0			0
$811$	−7.70669e6			−0.411449			−0.205724	−	0.978610i	$-0.565955\pi$
$811$	−7.70669e6			−0.411449			−0.205724	+	0.978610i	$0.565955\pi$
$812$		0			0
$813$	−1.62071e7	−	1.62071e7i	−0.859964	−	0.859964i
$814$		0			0
$815$	−4.97953e6	+	1.38792e7i	−0.262600	+	0.731931i
$816$		0			0
$817$	5.34151e6	+	5.34151e6i	0.279968	+	0.279968i
$818$		0			0
$819$		−	7.00494e6i		−	0.364918i
$820$		0			0
$821$		−	7.43845e6i		−	0.385145i	−0.981283	−	0.192573i	$-0.938317\pi$
$821$		−	7.43845e6i		−	0.385145i	0.981283	−	0.192573i	$-0.0616831\pi$
$822$		0			0
$823$	−1.58115e7	−	1.58115e7i	−0.813719	−	0.813719i	0.171471	−	0.985189i	$-0.445148\pi$
$823$	−1.58115e7	−	1.58115e7i	−0.813719	−	0.813719i	−0.985189	+	0.171471i	$0.945148\pi$
$824$		0			0
$825$	−670165.	−	6.92648e6i	−0.0342805	−	0.354305i
$826$		0			0
$827$	−6.62472e6	−	6.62472e6i	−0.336824	−	0.336824i	0.518346	−	0.855171i	$-0.326548\pi$
$827$	−6.62472e6	−	6.62472e6i	−0.336824	−	0.336824i	−0.855171	+	0.518346i	$0.826548\pi$
$828$		0			0
$829$	−9.68299e6			−0.489354			−0.244677	−	0.969605i	$-0.578682\pi$
$829$	−9.68299e6			−0.489354			−0.244677	+	0.969605i	$0.578682\pi$
$830$		0			0
$831$			2.18373e7i			1.09697i
$832$		0			0
$833$	−1.36539e7	+	1.36539e7i	−0.681780	+	0.681780i
$834$		0			0
$835$	1.15773e7	−	3.22688e7i	0.574632	−	1.60164i
$836$		0			0
$837$	−2.14554e6	+	2.14554e6i	−0.105858	+	0.105858i
$838$		0			0
$839$	−1.12154e7			−0.550061			−0.275031	−	0.961435i	$-0.588688\pi$
$839$	−1.12154e7			−0.550061			−0.275031	+	0.961435i	$0.588688\pi$
$840$		0			0
$841$	−2.04848e7			−0.998718
$842$		0			0
$843$	−1.96140e7	+	1.96140e7i	−0.950598	+	0.950598i
$844$		0			0
$845$	−4.48535e6	−	9.50463e6i	−0.216100	−	0.457924i
$846$		0			0
$847$	−5.99335e6	+	5.99335e6i	−0.287052	+	0.287052i
$848$		0			0
$849$			1.31504e7i			0.626138i
$850$		0			0
$851$	−9.59486e6			−0.454166
$852$		0			0
$853$	5.42137e6	+	5.42137e6i	0.255115	+	0.255115i	0.823064	−	0.567949i	$-0.192263\pi$
$853$	5.42137e6	+	5.42137e6i	0.255115	+	0.255115i	−0.567949	+	0.823064i	$0.692263\pi$
$854$		0			0
$855$	2.53040e6	−	1.19413e6i	0.118379	−	0.0558645i
$856$		0			0
$857$	1.56889e7	+	1.56889e7i	0.729692	+	0.729692i	0.970558	−	0.240866i	$-0.0774316\pi$
$857$	1.56889e7	+	1.56889e7i	0.729692	+	0.729692i	−0.240866	+	0.970558i	$0.577432\pi$
$858$		0			0
$859$		−	2.32917e7i		−	1.07701i	−0.842624	−	0.538503i	$-0.818990\pi$
$859$		−	2.32917e7i		−	1.07701i	0.842624	−	0.538503i	$-0.181010\pi$
$860$		0			0
$861$		−	1.06333e7i		−	0.488831i
$862$		0			0
$863$	1.82269e7	+	1.82269e7i	0.833080	+	0.833080i	0.987937	−	0.154857i	$-0.0494917\pi$
$863$	1.82269e7	+	1.82269e7i	0.833080	+	0.833080i	−0.154857	+	0.987937i	$0.549492\pi$
$864$		0			0
$865$	−2.25285e7	−	8.08269e6i	−1.02374	−	0.367295i
$866$		0			0
$867$	1.02204e7	+	1.02204e7i	0.461763	+	0.461763i
$868$		0			0
$869$	−8.76374e6			−0.393677
$870$		0			0
$871$		−	4.99509e7i		−	2.23099i
$872$		0			0
$873$	1.07843e7	−	1.07843e7i	0.478915	−	0.478915i
$874$		0			0
$875$	6.46105e6	+	1.08430e7i	0.285288	+	0.478772i
$876$		0			0
$877$	−9.59239e6	+	9.59239e6i	−0.421141	+	0.421141i	−0.885597	−	0.464455i	$-0.846250\pi$
$877$	−9.59239e6	+	9.59239e6i	−0.421141	+	0.421141i	0.464455	+	0.885597i	$0.346250\pi$
$878$		0			0
$879$	2.03045e7			0.886380
$880$		0			0
$881$	−6.57569e6			−0.285431			−0.142716	−	0.989764i	$-0.545583\pi$
$881$	−6.57569e6			−0.285431			−0.142716	+	0.989764i	$0.545583\pi$
$882$		0			0
$883$	4.41888e6	−	4.41888e6i	0.190726	−	0.190726i	−0.605284	−	0.796010i	$-0.706940\pi$
$883$	4.41888e6	−	4.41888e6i	0.190726	−	0.190726i	0.796010	+	0.605284i	$0.206940\pi$
$884$		0			0
$885$	−695089.	−	249382.i	−0.0298320	−	0.0107030i
$886$		0			0
$887$	301239.	−	301239.i	0.0128559	−	0.0128559i	−0.700650	−	0.713505i	$-0.747106\pi$
$887$	301239.	−	301239.i	0.0128559	−	0.0128559i	0.713505	+	0.700650i	$0.247106\pi$
$888$		0			0
$889$		−	1.69822e6i		−	0.0720674i
$890$		0			0
$891$	2.24653e6			0.0948022
$892$		0			0
$893$	3.26821e6	+	3.26821e6i	0.137145	+	0.137145i
$894$		0			0
$895$	6.25135e6	+	1.32469e7i	0.260865	+	0.552784i
$896$		0			0
$897$	−2.21684e7	−	2.21684e7i	−0.919927	−	0.919927i
$898$		0			0
$899$			124024.i			0.00511809i
$900$		0			0
$901$			9.42291e6i			0.386699i
$902$		0			0
$903$	−1.06428e7	−	1.06428e7i	−0.434348	−	0.434348i
$904$		0			0
$905$	7.71612e6	+	1.63508e7i	0.313168	+	0.663615i
$906$		0			0
$907$	−8.72829e6	−	8.72829e6i	−0.352298	−	0.352298i	0.508666	−	0.860964i	$-0.330139\pi$
$907$	−8.72829e6	−	8.72829e6i	−0.352298	−	0.352298i	−0.860964	+	0.508666i	$0.830139\pi$
$908$		0			0
$909$	1.62934e7			0.654036
$910$		0			0
$911$		−	3.87384e7i		−	1.54649i	−0.634110	−	0.773243i	$-0.718633\pi$
$911$		−	3.87384e7i		−	1.54649i	0.634110	−	0.773243i	$-0.281367\pi$
$912$		0			0
$913$	−4.28689e6	+	4.28689e6i	−0.170202	+	0.170202i
$914$		0			0
$915$	−2.82958e7	−	1.01519e7i	−1.11730	−	0.400860i
$916$		0			0
$917$	−7.96090e6	+	7.96090e6i	−0.312636	+	0.312636i
$918$		0			0
$919$	−2.08867e7			−0.815794			−0.407897	−	0.913028i	$-0.633738\pi$
$919$	−2.08867e7			−0.815794			−0.407897	+	0.913028i	$0.633738\pi$
$920$		0			0
$921$	−1.11561e7			−0.433375
$922$		0			0
$923$	−1.38691e7	+	1.38691e7i	−0.535852	+	0.535852i
$924$		0			0
$925$	733403.	+	7.58007e6i	0.0281831	+	0.291285i
$926$		0			0
$927$	−1.62416e7	+	1.62416e7i	−0.620767	+	0.620767i
$928$		0			0
$929$			2.74270e7i			1.04265i	0.853358	+	0.521326i	$0.174562\pi$
$929$			2.74270e7i			1.04265i	−0.853358	+	0.521326i	$0.825438\pi$
$930$		0			0
$931$	−4.47353e6			−0.169151
$932$		0			0
$933$	7.41478e6	+	7.41478e6i	0.278865	+	0.278865i
$934$		0			0
$935$	−1.83400e7	−	6.57996e6i	−0.686073	−	0.246147i
$936$		0			0
$937$	−3.37108e7	−	3.37108e7i	−1.25435	−	1.25435i	−0.953749	−	0.300603i	$-0.902812\pi$
$937$	−3.37108e7	−	3.37108e7i	−1.25435	−	1.25435i	−0.300603	−	0.953749i	$-0.597188\pi$
$938$		0			0
$939$			1.26652e6i			0.0468757i
$940$		0			0
$941$		−	1.48625e7i		−	0.547165i	−0.961849	−	0.273582i	$-0.911791\pi$
$941$		−	1.48625e7i		−	0.547165i	0.961849	−	0.273582i	$-0.0882086\pi$
$942$		0			0
$943$	3.84817e7	+	3.84817e7i	1.40921	+	1.40921i
$944$		0			0
$945$	−1.44924e7	+	6.83914e6i	−0.527911	+	0.249128i
$946$		0			0
$947$	−2.08076e7	−	2.08076e7i	−0.753957	−	0.753957i	0.221258	−	0.975215i	$-0.428984\pi$
$947$	−2.08076e7	−	2.08076e7i	−0.753957	−	0.753957i	−0.975215	+	0.221258i	$0.928984\pi$
$948$		0			0
$949$	1.44894e7			0.522258
$950$		0			0
$951$		−	1.45334e7i		−	0.521095i
$952$		0			0
$953$	−2.11871e7	+	2.11871e7i	−0.755681	+	0.755681i	−0.975533	−	0.219852i	$-0.929443\pi$
$953$	−2.11871e7	+	2.11871e7i	−0.755681	+	0.755681i	0.219852	+	0.975533i	$0.429443\pi$
$954$		0			0
$955$	1.60393e7	+	3.39879e7i	0.569085	+	1.20591i
$956$		0			0
$957$	255357.	−	255357.i	0.00901297	−	0.00901297i
$958$		0			0
$959$	−4.23619e6			−0.148740
$960$		0			0
$961$	2.80443e7			0.979571
$962$		0			0
$963$	1.34569e7	−	1.34569e7i	0.467607	−	0.467607i
$964$		0			0
$965$	693789.	−	1.93376e6i	0.0239833	−	0.0668475i
$966$		0			0
$967$	1.10939e7	−	1.10939e7i	0.381521	−	0.381521i	−0.490129	−	0.871650i	$-0.663050\pi$
$967$	1.10939e7	−	1.10939e7i	0.381521	−	0.381521i	0.871650	+	0.490129i	$0.163050\pi$
$968$		0			0
$969$			6.85092e6i			0.234390i
$970$		0			0
$971$	5.51613e6			0.187753			0.0938765	−	0.995584i	$-0.470074\pi$
$971$	5.51613e6			0.187753			0.0938765	+	0.995584i	$0.470074\pi$
$972$		0			0
$973$	1.79762e7	+	1.79762e7i	0.608718	+	0.608718i
$974$		0			0
$975$	−1.58189e7	+	1.92078e7i	−0.532922	+	0.647093i
$976$		0			0
$977$	7.17940e6	+	7.17940e6i	0.240631	+	0.240631i	0.817111	−	0.576480i	$-0.195574\pi$
$977$	7.17940e6	+	7.17940e6i	0.240631	+	0.240631i	−0.576480	+	0.817111i	$0.695574\pi$
$978$		0			0
$979$		−	1.35421e7i		−	0.451574i
$980$		0			0
$981$		−	5.17596e6i		−	0.171719i
$982$		0			0
$983$	−2.42340e7	−	2.42340e7i	−0.799911	−	0.799911i	0.183170	−	0.983081i	$-0.441364\pi$
$983$	−2.42340e7	−	2.42340e7i	−0.799911	−	0.799911i	−0.983081	+	0.183170i	$0.941364\pi$
$984$		0			0
$985$	5.97132e6	−	1.66436e7i	0.196101	−	0.546582i
$986$		0			0
$987$	−6.51183e6	−	6.51183e6i	−0.212770	−	0.212770i
$988$		0			0
$989$	7.70328e7			2.50429
$990$		0			0
$991$		−	3.29661e7i		−	1.06631i	−0.846017	−	0.533156i	$-0.821006\pi$
$991$		−	3.29661e7i		−	1.06631i	0.846017	−	0.533156i	$-0.178994\pi$
$992$		0			0
$993$	−9.18774e6	+	9.18774e6i	−0.295689	+	0.295689i
$994$		0			0
$995$	−4.89979e7	+	2.31227e7i	−1.56899	+	0.740425i
$996$		0			0
$997$	−1.80740e7	+	1.80740e7i	−0.575859	+	0.575859i	−0.933760	−	0.357901i	$-0.883493\pi$
$997$	−1.80740e7	+	1.80740e7i	−0.575859	+	0.575859i	0.357901	+	0.933760i	$0.383493\pi$
$998$		0			0
$999$	−9.66870e6			−0.306517

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.o.a.47.20		56
4.3	odd	2		40.6.k.a.27.20	yes	56
5.3	odd	4	inner	160.6.o.a.143.19		56
8.3	odd	2	inner	160.6.o.a.47.19		56
8.5	even	2		40.6.k.a.27.5	yes	56
20.3	even	4		40.6.k.a.3.5	✓	56
40.3	even	4	inner	160.6.o.a.143.20		56
40.13	odd	4		40.6.k.a.3.20	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.5	✓	56	20.3	even	4
40.6.k.a.3.20	yes	56	40.13	odd	4
40.6.k.a.27.5	yes	56	8.5	even	2
40.6.k.a.27.20	yes	56	4.3	odd	2
160.6.o.a.47.19		56	8.3	odd	2	inner
160.6.o.a.47.20		56	1.1	even	1	trivial
160.6.o.a.143.19		56	5.3	odd	4	inner
160.6.o.a.143.20		56	40.3	even	4	inner

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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	160.o (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(7.52871 - 7.52871i) q^{3} +(-50.5551 + 23.8576i) q^{5} +(51.0903 - 51.0903i) q^{7} +129.637i q^{9} +O(q^{10})\)	\(q+(7.52871 - 7.52871i) q^{3} +(-50.5551 + 23.8576i) q^{5} +(51.0903 - 51.0903i) q^{7} +129.637i q^{9} +209.146 q^{11} +(-528.819 - 528.819i) q^{13} +(-200.998 + 560.231i) q^{15} +(1178.43 + 1178.43i) q^{17} +386.096i q^{19} -769.289i q^{21} +(2784.05 + 2784.05i) q^{23} +(1986.63 - 2412.24i) q^{25} +(2805.48 + 2805.48i) q^{27} +162.172 q^{29} +764.769i q^{31} +(1574.60 - 1574.60i) q^{33} +(-1363.99 + 3801.77i) q^{35} +(-1723.18 + 1723.18i) q^{37} -7962.64 q^{39} +13822.2 q^{41} +(13834.7 - 13834.7i) q^{43} +(-3092.82 - 6553.81i) q^{45} +(8464.74 - 8464.74i) q^{47} +11586.6i q^{49} +17744.1 q^{51} +(3998.09 + 3998.09i) q^{53} +(-10573.4 + 4989.72i) q^{55} +(2906.81 + 2906.81i) q^{57} +1240.72i q^{59} +50507.3i q^{61} +(6623.20 + 6623.20i) q^{63} +(39350.8 + 14118.1i) q^{65} +(47228.8 + 47228.8i) q^{67} +41920.6 q^{69} -26226.6i q^{71} +(-13699.8 + 13699.8i) q^{73} +(-3204.29 - 33117.9i) q^{75} +(10685.4 - 10685.4i) q^{77} -41902.4 q^{79} +10741.4 q^{81} +(-20497.1 + 20497.1i) q^{83} +(-87689.8 - 31461.1i) q^{85} +(1220.95 - 1220.95i) q^{87} -64749.3i q^{89} -54035.1 q^{91} +(5757.73 + 5757.73i) q^{93} +(-9211.32 - 19519.1i) q^{95} +(-83188.7 - 83188.7i) q^{97} +27113.1i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3}+O(q^{10}) \) 56 * q + 4 * q^3	\( 56 q + 4 q^{3} + 8 q^{11} - 408 q^{17} - 3120 q^{25} - 968 q^{27} - 976 q^{33} + 4780 q^{35} - 8 q^{41} - 1308 q^{43} - 20872 q^{51} + 968 q^{57} + 17680 q^{65} - 89252 q^{67} - 25184 q^{73} + 127740 q^{75} - 67792 q^{81} + 126444 q^{83} - 329432 q^{91} + 212576 q^{97}+O(q^{100}) \) 56 * q + 4 * q^3 + 8 * q^11 - 408 * q^17 - 3120 * q^25 - 968 * q^27 - 976 * q^33 + 4780 * q^35 - 8 * q^41 - 1308 * q^43 - 20872 * q^51 + 968 * q^57 + 17680 * q^65 - 89252 * q^67 - 25184 * q^73 + 127740 * q^75 - 67792 * q^81 + 126444 * q^83 - 329432 * q^91 + 212576 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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