LMFDB - Embedded newform 160.6.o.a.47.3

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			47.3
Character	$\chi$	$=$	160.47
Dual form			160.6.o.a.143.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-17.2238 + 17.2238i) q^{3} +(-54.8737 - 10.6715i) q^{5} +(-14.7411 + 14.7411i) q^{7} -350.316i q^{9} +O(q^{10})$	\(q+(-17.2238 + 17.2238i) q^{3} +(-54.8737 - 10.6715i) q^{5} +(-14.7411 + 14.7411i) q^{7} -350.316i q^{9} -509.310 q^{11} +(-109.565 - 109.565i) q^{13} +(1128.93 - 761.328i) q^{15} +(-1321.86 - 1321.86i) q^{17} +688.865i q^{19} -507.795i q^{21} +(-696.700 - 696.700i) q^{23} +(2897.24 + 1171.17i) q^{25} +(1848.38 + 1848.38i) q^{27} +5972.48 q^{29} +9850.17i q^{31} +(8772.24 - 8772.24i) q^{33} +(966.209 - 651.590i) q^{35} +(-7498.27 + 7498.27i) q^{37} +3774.25 q^{39} +10808.4 q^{41} +(4687.08 - 4687.08i) q^{43} +(-3738.39 + 19223.1i) q^{45} +(-12465.9 + 12465.9i) q^{47} +16372.4i q^{49} +45534.8 q^{51} +(14235.3 + 14235.3i) q^{53} +(27947.7 + 5435.09i) q^{55} +(-11864.9 - 11864.9i) q^{57} -33254.7i q^{59} -36049.2i q^{61} +(5164.05 + 5164.05i) q^{63} +(4843.02 + 7181.47i) q^{65} +(-20208.6 - 20208.6i) q^{67} +23999.6 q^{69} -58102.6i q^{71} +(-2521.14 + 2521.14i) q^{73} +(-70073.2 + 29729.5i) q^{75} +(7507.80 - 7507.80i) q^{77} +12102.9 q^{79} +21454.5 q^{81} +(46356.9 - 46356.9i) q^{83} +(58429.1 + 86641.4i) q^{85} +(-102869. + 102869. i) q^{87} +8030.44i q^{89} +3230.23 q^{91} +(-169657. - 169657. i) q^{93} +(7351.21 - 37800.6i) q^{95} +(-73172.1 - 73172.1i) q^{97} +178419. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−17.2238	+	17.2238i	−1.10490	+	1.10490i	−0.111095	+	0.993810i	$0.535436\pi$
$3$	−17.2238	+	17.2238i	−1.10490	+	1.10490i	−0.993810	+	0.111095i	$0.964564\pi$
$4$		0			0
$5$	−54.8737	−	10.6715i	−0.981610	−	0.190897i
$5$	−54.8737	−	10.6715i	−0.981610	−	0.190897i
$6$		0			0
$7$	−14.7411	+	14.7411i	−0.113707	+	0.113707i	−0.761671	−	0.647964i	$-0.775621\pi$
$7$	−14.7411	+	14.7411i	−0.113707	+	0.113707i	0.647964	+	0.761671i	$0.275621\pi$
$8$		0			0
$9$		−	350.316i		−	1.44163i
$10$		0			0
$11$	−509.310			−1.26911			−0.634557	−	0.772876i	$-0.718817\pi$
$11$	−509.310			−1.26911			−0.634557	+	0.772876i	$0.718817\pi$
$12$		0			0
$13$	−109.565	−	109.565i	−0.179810	−	0.179810i	0.611463	−	0.791273i	$-0.290581\pi$
$13$	−109.565	−	109.565i	−0.179810	−	0.179810i	−0.791273	+	0.611463i	$0.790581\pi$
$14$		0			0
$15$	1128.93	−	761.328i	1.29551	−	0.873663i
$16$		0			0
$17$	−1321.86	−	1321.86i	−1.10934	−	1.10934i	−0.993238	−	0.116097i	$-0.962962\pi$
$17$	−1321.86	−	1321.86i	−1.10934	−	1.10934i	−0.116097	−	0.993238i	$-0.537038\pi$
$18$		0			0
$19$			688.865i			0.437774i	0.975750	+	0.218887i	$0.0702427\pi$
$19$			688.865i			0.437774i	−0.975750	+	0.218887i	$0.929757\pi$
$20$		0			0
$21$		−	507.795i		−	0.251270i
$22$		0			0
$23$	−696.700	−	696.700i	−0.274616	−	0.274616i	0.556339	−	0.830955i	$-0.312206\pi$
$23$	−696.700	−	696.700i	−0.274616	−	0.274616i	−0.830955	+	0.556339i	$0.812206\pi$
$24$		0			0
$25$	2897.24	+	1171.17i	0.927117	+	0.374773i
$26$		0			0
$27$	1848.38	+	1848.38i	0.487958	+	0.487958i
$28$		0			0
$29$	5972.48			1.31874			0.659371	−	0.751818i	$-0.270823\pi$
$29$	5972.48			1.31874			0.659371	+	0.751818i	$0.270823\pi$
$30$		0			0
$31$			9850.17i			1.84094i	0.390813	+	0.920470i	$0.372194\pi$
$31$			9850.17i			1.84094i	−0.390813	+	0.920470i	$0.627806\pi$
$32$		0			0
$33$	8772.24	−	8772.24i	1.40225	−	1.40225i
$34$		0			0
$35$	966.209	−	651.590i	0.133322	−	0.0899093i
$36$		0			0
$37$	−7498.27	+	7498.27i	−0.900444	+	0.900444i	−0.995474	−	0.0950301i	$-0.969705\pi$
$37$	−7498.27	+	7498.27i	−0.900444	+	0.900444i	0.0950301	+	0.995474i	$0.469705\pi$
$38$		0			0
$39$	3774.25			0.397346
$40$		0			0
$41$	10808.4			1.00416			0.502081	−	0.864821i	$-0.332568\pi$
$41$	10808.4			1.00416			0.502081	+	0.864821i	$0.332568\pi$
$42$		0			0
$43$	4687.08	−	4687.08i	0.386572	−	0.386572i	−0.486891	−	0.873463i	$-0.661869\pi$
$43$	4687.08	−	4687.08i	0.386572	−	0.386572i	0.873463	+	0.486891i	$0.161869\pi$
$44$		0			0
$45$	−3738.39	+	19223.1i	−0.275203	+	1.41512i
$46$		0			0
$47$	−12465.9	+	12465.9i	−0.823150	+	0.823150i	−0.986559	−	0.163408i	$-0.947751\pi$
$47$	−12465.9	+	12465.9i	−0.823150	+	0.823150i	0.163408	+	0.986559i	$0.447751\pi$
$48$		0			0
$49$			16372.4i			0.974142i
$50$		0			0
$51$	45534.8			2.45142
$52$		0			0
$53$	14235.3	+	14235.3i	0.696109	+	0.696109i	0.963569	−	0.267460i	$-0.0861842\pi$
$53$	14235.3	+	14235.3i	0.696109	+	0.696109i	−0.267460	+	0.963569i	$0.586184\pi$
$54$		0			0
$55$	27947.7	+	5435.09i	1.24578	+	0.242270i
$56$		0			0
$57$	−11864.9	−	11864.9i	−0.483699	−	0.483699i
$58$		0			0
$59$		−	33254.7i		−	1.24372i	−0.783127	−	0.621861i	$-0.786377\pi$
$59$		−	33254.7i		−	1.24372i	0.783127	−	0.621861i	$-0.213623\pi$
$60$		0			0
$61$		−	36049.2i		−	1.24043i	−0.784433	−	0.620213i	$-0.787046\pi$
$61$		−	36049.2i		−	1.24043i	0.784433	−	0.620213i	$-0.212954\pi$
$62$		0			0
$63$	5164.05	+	5164.05i	0.163923	+	0.163923i
$64$		0			0
$65$	4843.02	+	7181.47i	0.142178	+	0.210829i
$66$		0			0
$67$	−20208.6	−	20208.6i	−0.549984	−	0.549984i	0.376452	−	0.926436i	$-0.377144\pi$
$67$	−20208.6	−	20208.6i	−0.549984	−	0.549984i	−0.926436	+	0.376452i	$0.877144\pi$
$68$		0			0
$69$	23999.6			0.606850
$70$		0			0
$71$		−	58102.6i		−	1.36788i	−0.729536	−	0.683942i	$-0.760264\pi$
$71$		−	58102.6i		−	1.36788i	0.729536	−	0.683942i	$-0.239736\pi$
$72$		0			0
$73$	−2521.14	+	2521.14i	−0.0553719	+	0.0553719i	−0.734251	−	0.678879i	$-0.762466\pi$
$73$	−2521.14	+	2521.14i	−0.0553719	+	0.0553719i	0.678879	+	0.734251i	$0.262466\pi$
$74$		0			0
$75$	−70073.2	+	29729.5i	−1.43846	+	0.610287i
$76$		0			0
$77$	7507.80	−	7507.80i	0.144307	−	0.144307i
$78$		0			0
$79$	12102.9			0.218183			0.109091	−	0.994032i	$-0.465206\pi$
$79$	12102.9			0.218183			0.109091	+	0.994032i	$0.465206\pi$
$80$		0			0
$81$	21454.5			0.363334
$82$		0			0
$83$	46356.9	−	46356.9i	0.738617	−	0.738617i	−0.233693	−	0.972310i	$-0.575081\pi$
$83$	46356.9	−	46356.9i	0.738617	−	0.738617i	0.972310	+	0.233693i	$0.0750811\pi$
$84$		0			0
$85$	58429.1	+	86641.4i	0.877166	+	1.30070i
$86$		0			0
$87$	−102869.	+	102869.i	−1.45708	+	1.45708i
$88$		0			0
$89$			8030.44i			0.107464i	0.998555	+	0.0537322i	$0.0171117\pi$
$89$			8030.44i			0.107464i	−0.998555	+	0.0537322i	$0.982888\pi$
$90$		0			0
$91$	3230.23			0.0408912
$92$		0			0
$93$	−169657.	−	169657.i	−2.03406	−	2.03406i
$94$		0			0
$95$	7351.21	−	37800.6i	0.0835698	−	0.429724i
$96$		0			0
$97$	−73172.1	−	73172.1i	−0.789616	−	0.789616i	0.191815	−	0.981431i	$-0.438563\pi$
$97$	−73172.1	−	73172.1i	−0.789616	−	0.789616i	−0.981431	+	0.191815i	$0.938563\pi$
$98$		0			0
$99$			178419.i			1.82959i
$100$		0			0
$101$			97263.1i			0.948735i	0.880327	+	0.474367i	$0.157323\pi$
$101$			97263.1i			0.948735i	−0.880327	+	0.474367i	$0.842677\pi$
$102$		0			0
$103$	75234.6	+	75234.6i	0.698755	+	0.698755i	0.964142	−	0.265387i	$-0.0854998\pi$
$103$	75234.6	+	75234.6i	0.698755	+	0.698755i	−0.265387	+	0.964142i	$0.585500\pi$
$104$		0			0
$105$	−5418.92	+	27864.6i	−0.0479667	+	0.246649i
$106$		0			0
$107$	−3052.73	−	3052.73i	−0.0257768	−	0.0257768i	0.694101	−	0.719878i	$-0.255802\pi$
$107$	−3052.73	−	3052.73i	−0.0257768	−	0.0257768i	−0.719878	+	0.694101i	$0.755802\pi$
$108$		0			0
$109$	51487.6			0.415084			0.207542	−	0.978226i	$-0.433454\pi$
$109$	51487.6			0.415084			0.207542	+	0.978226i	$0.433454\pi$
$110$		0			0
$111$		−	258297.i		−	1.98981i
$112$		0			0
$113$	20974.3	−	20974.3i	0.154522	−	0.154522i	−0.625612	−	0.780134i	$-0.715151\pi$
$113$	20974.3	−	20974.3i	0.154522	−	0.154522i	0.780134	+	0.625612i	$0.215151\pi$
$114$		0			0
$115$	30795.7	+	45665.3i	0.217143	+	0.321990i
$116$		0			0
$117$	−38382.4	+	38382.4i	−0.259220	+	0.259220i
$118$		0			0
$119$	38971.4			0.252277
$120$		0			0
$121$	98345.8			0.610650
$122$		0			0
$123$	−186162.	+	186162.i	−1.10950	+	1.10950i
$124$		0			0
$125$	−146484.	−	95184.0i	−0.838524	−	0.544865i
$126$		0			0
$127$	−71877.1	+	71877.1i	−0.395440	+	0.395440i	−0.876621	−	0.481181i	$-0.840208\pi$
$127$	−71877.1	+	71877.1i	−0.395440	+	0.395440i	0.481181	+	0.876621i	$0.340208\pi$
$128$		0			0
$129$			161458.i			0.854251i
$130$		0			0
$131$	−126943.			−0.646296			−0.323148	−	0.946348i	$-0.604741\pi$
$131$	−126943.			−0.646296			−0.323148	+	0.946348i	$0.604741\pi$
$132$		0			0
$133$	−10154.6	−	10154.6i	−0.0497778	−	0.0497778i
$134$		0			0
$135$	−81702.6	−	121153.i	−0.385835	−	0.572135i
$136$		0			0
$137$	−112379.	−	112379.i	−0.511546	−	0.511546i	0.403454	−	0.915000i	$-0.367809\pi$
$137$	−112379.	−	112379.i	−0.511546	−	0.511546i	−0.915000	+	0.403454i	$0.867809\pi$
$138$		0			0
$139$		−	1803.19i		−	0.00791597i	−0.999992	−	0.00395798i	$-0.998740\pi$
$139$		−	1803.19i		−	0.00791597i	0.999992	−	0.00395798i	$-0.00125987\pi$
$140$		0			0
$141$		−	429419.i		−	1.81901i
$142$		0			0
$143$	55802.7	+	55802.7i	0.228200	+	0.228200i
$144$		0			0
$145$	−327732.	−	63735.1i	−1.29449	−	0.251744i
$146$		0			0
$147$	−281994.	−	281994.i	−1.07633	−	1.07633i
$148$		0			0
$149$	492553.			1.81755			0.908777	−	0.417282i	$-0.137017\pi$
$149$	492553.			1.81755			0.908777	+	0.417282i	$0.137017\pi$
$150$		0			0
$151$		−	142766.i		−	0.509547i	−0.967001	−	0.254773i	$-0.917999\pi$
$151$		−	142766.i		−	0.509547i	0.967001	−	0.254773i	$-0.0820008\pi$
$152$		0			0
$153$	−463068.	+	463068.i	−1.59925	+	1.59925i
$154$		0			0
$155$	105116.	−	540515.i	0.351430	−	1.80708i
$156$		0			0
$157$	106174.	−	106174.i	0.343772	−	0.343772i	−0.514011	−	0.857784i	$-0.671841\pi$
$157$	106174.	−	106174.i	0.343772	−	0.343772i	0.857784	+	0.514011i	$0.171841\pi$
$158$		0			0
$159$	−490372.			−1.53827
$160$		0			0
$161$	20540.3			0.0624514
$162$		0			0
$163$	125925.	−	125925.i	0.371231	−	0.371231i	−0.496695	−	0.867925i	$-0.665453\pi$
$163$	125925.	−	125925.i	0.371231	−	0.371231i	0.867925	+	0.496695i	$0.165453\pi$
$164$		0			0
$165$	−574978.	+	387752.i	−1.64415	+	1.10878i
$166$		0			0
$167$	284753.	−	284753.i	0.790090	−	0.790090i	−0.191418	−	0.981509i	$-0.561309\pi$
$167$	284753.	−	284753.i	0.790090	−	0.790090i	0.981509	+	0.191418i	$0.0613087\pi$
$168$		0			0
$169$		−	347284.i		−	0.935337i
$170$		0			0
$171$	241320.			0.631108
$172$		0			0
$173$	186125.	+	186125.i	0.472813	+	0.472813i	0.902824	−	0.430010i	$-0.141490\pi$
$173$	186125.	+	186125.i	0.472813	+	0.472813i	−0.430010	+	0.902824i	$0.641490\pi$
$174$		0			0
$175$	−59972.9	+	25444.3i	−0.148033	+	0.0628051i
$176$		0			0
$177$	572772.	+	572772.i	1.37419	+	1.37419i
$178$		0			0
$179$			210311.i			0.490601i	0.969447	+	0.245300i	$0.0788866\pi$
$179$			210311.i			0.490601i	−0.969447	+	0.245300i	$0.921113\pi$
$180$		0			0
$181$			275853.i			0.625865i	0.949775	+	0.312933i	$0.101311\pi$
$181$			275853.i			0.625865i	−0.949775	+	0.312933i	$0.898689\pi$
$182$		0			0
$183$	620903.	+	620903.i	1.37055	+	1.37055i
$184$		0			0
$185$	491475.	−	331440.i	1.05578	−	0.711993i
$186$		0			0
$187$	673236.	+	673236.i	1.40787	+	1.40787i
$188$		0			0
$189$	−54494.5			−0.110968
$190$		0			0
$191$			338791.i			0.671968i	0.941868	+	0.335984i	$0.109069\pi$
$191$			338791.i			0.671968i	−0.941868	+	0.335984i	$0.890931\pi$
$192$		0			0
$193$	165073.	−	165073.i	0.318995	−	0.318995i	−0.529386	−	0.848381i	$-0.677578\pi$
$193$	165073.	−	165073.i	0.318995	−	0.318995i	0.848381	+	0.529386i	$0.177578\pi$
$194$		0			0
$195$	−207107.	−	40276.8i	−0.390039	−	0.0758523i
$196$		0			0
$197$	117816.	−	117816.i	0.216292	−	0.216292i	−0.590642	−	0.806934i	$-0.701125\pi$
$197$	117816.	−	117816.i	0.216292	−	0.216292i	0.806934	+	0.590642i	$0.201125\pi$
$198$		0			0
$199$	240189.			0.429952			0.214976	−	0.976619i	$-0.431033\pi$
$199$	240189.			0.429952			0.214976	+	0.976619i	$0.431033\pi$
$200$		0			0
$201$	696137.			1.21536
$202$		0			0
$203$	−88041.0	+	88041.0i	−0.149950	+	0.149950i
$204$		0			0
$205$	−593099.	−	115342.i	−0.985695	−	0.191692i
$206$		0			0
$207$	−244065.	+	244065.i	−0.395895	+	0.395895i
$208$		0			0
$209$		−	350846.i		−	0.555585i
$210$		0			0
$211$	896662.			1.38651			0.693254	−	0.720693i	$-0.256176\pi$
$211$	896662.			1.38651			0.693254	+	0.720693i	$0.256176\pi$
$212$		0			0
$213$	1.00075e6	+	1.00075e6i	1.51138	+	1.51138i
$214$		0			0
$215$	−307215.	+	207179.i	−0.453259	+	0.305668i
$216$		0			0
$217$	−145203.	−	145203.i	−0.209327	−	0.209327i
$218$		0			0
$219$		−	86846.9i		−	0.122361i
$220$		0			0
$221$			289660.i			0.398940i
$222$		0			0
$223$	39331.6	+	39331.6i	0.0529639	+	0.0529639i	0.733093	−	0.680129i	$-0.238076\pi$
$223$	39331.6	+	39331.6i	0.0529639	+	0.0529639i	−0.680129	+	0.733093i	$0.738076\pi$
$224$		0			0
$225$	410278.	−	1.01495e6i	0.540284	−	1.33656i
$226$		0			0
$227$	−372837.	−	372837.i	−0.480236	−	0.480236i	0.424971	−	0.905207i	$-0.360284\pi$
$227$	−372837.	−	372837.i	−0.480236	−	0.480236i	−0.905207	+	0.424971i	$0.860284\pi$
$228$		0			0
$229$	−349083.			−0.439886			−0.219943	−	0.975513i	$-0.570587\pi$
$229$	−349083.			−0.439886			−0.219943	+	0.975513i	$0.570587\pi$
$230$		0			0
$231$			258625.i			0.318890i
$232$		0			0
$233$	63835.2	−	63835.2i	0.0770319	−	0.0770319i	−0.667541	−	0.744573i	$-0.732653\pi$
$233$	63835.2	−	63835.2i	0.0770319	−	0.0770319i	0.744573	+	0.667541i	$0.232653\pi$
$234$		0			0
$235$	817079.	−	551020.i	0.965149	−	0.650875i
$236$		0			0
$237$	−208457.	+	208457.i	−0.241071	+	0.241071i
$238$		0			0
$239$	987818.			1.11862			0.559310	−	0.828959i	$-0.311066\pi$
$239$	987818.			1.11862			0.559310	+	0.828959i	$0.311066\pi$
$240$		0			0
$241$	−482388.			−0.535000			−0.267500	−	0.963558i	$-0.586198\pi$
$241$	−482388.			−0.535000			−0.267500	+	0.963558i	$0.586198\pi$
$242$		0			0
$243$	−818685.	+	818685.i	−0.889408	+	0.889408i
$244$		0			0
$245$	174718.	−	898414.i	0.185961	−	0.956227i
$246$		0			0
$247$	75475.7	−	75475.7i	0.0787163	−	0.0787163i
$248$		0			0
$249$			1.59688e6i			1.63220i
$250$		0			0
$251$	−777624.			−0.779086			−0.389543	−	0.921008i	$-0.627367\pi$
$251$	−777624.			−0.779086			−0.389543	+	0.921008i	$0.627367\pi$
$252$		0			0
$253$	354837.	+	354837.i	0.348519	+	0.348519i
$254$		0			0
$255$	−2.49866e6	−	485923.i	−2.40634	−	0.467969i
$256$		0			0
$257$	−683990.	−	683990.i	−0.645976	−	0.645976i	0.306042	−	0.952018i	$-0.400995\pi$
$257$	−683990.	−	683990.i	−0.645976	−	0.645976i	−0.952018	+	0.306042i	$0.900995\pi$
$258$		0			0
$259$		−	221066.i		−	0.204773i
$260$		0			0
$261$		−	2.09225e6i		−	1.90114i
$262$		0			0
$263$	491368.	+	491368.i	0.438044	+	0.438044i	0.891353	−	0.453309i	$-0.149757\pi$
$263$	491368.	+	491368.i	0.438044	+	0.438044i	−0.453309	+	0.891353i	$0.649757\pi$
$264$		0			0
$265$	−629232.	−	933056.i	−0.550423	−	0.816193i
$266$		0			0
$267$	−138314.	−	138314.i	−0.118738	−	0.118738i
$268$		0			0
$269$	800055.			0.674123			0.337062	−	0.941483i	$-0.390567\pi$
$269$	800055.			0.674123			0.337062	+	0.941483i	$0.390567\pi$
$270$		0			0
$271$		−	2.24545e6i		−	1.85729i	−0.370966	−	0.928646i	$-0.620973\pi$
$271$		−	2.24545e6i		−	1.85729i	0.370966	−	0.928646i	$-0.379027\pi$
$272$		0			0
$273$	−55636.7	+	55636.7i	−0.0451809	+	0.0451809i
$274$		0			0
$275$	−1.47559e6	−	596487.i	−1.17662	−	0.475630i
$276$		0			0
$277$	−417176.	+	417176.i	−0.326678	+	0.326678i	−0.851322	−	0.524644i	$-0.824199\pi$
$277$	−417176.	+	417176.i	−0.326678	+	0.326678i	0.524644	+	0.851322i	$0.324199\pi$
$278$		0			0
$279$	3.45067e6			2.65395
$280$		0			0
$281$	1.07676e6			0.813492			0.406746	−	0.913541i	$-0.366663\pi$
$281$	1.07676e6			0.813492			0.406746	+	0.913541i	$0.366663\pi$
$282$		0			0
$283$	−652652.	+	652652.i	−0.484413	+	0.484413i	−0.906538	−	0.422125i	$-0.861284\pi$
$283$	−652652.	+	652652.i	−0.484413	+	0.484413i	0.422125	+	0.906538i	$0.361284\pi$
$284$		0			0
$285$	524452.	+	777683.i	0.382467	+	0.567140i
$286$		0			0
$287$	−159329.	+	159329.i	−0.114180	+	0.114180i
$288$		0			0
$289$			2.07477e6i			1.46125i
$290$		0			0
$291$	2.52060e6			1.74490
$292$		0			0
$293$	−782068.	−	782068.i	−0.532201	−	0.532201i	0.389026	−	0.921227i	$-0.372812\pi$
$293$	−782068.	−	782068.i	−0.532201	−	0.532201i	−0.921227	+	0.389026i	$0.872812\pi$
$294$		0			0
$295$	−354877.	+	1.82481e6i	−0.237423	+	1.22085i
$296$		0			0
$297$	−941401.	−	941401.i	−0.619275	−	0.619275i
$298$		0			0
$299$			152668.i			0.0987577i
$300$		0			0
$301$			138186.i			0.0879116i
$302$		0			0
$303$	−1.67524e6	−	1.67524e6i	−1.04826	−	1.04826i
$304$		0			0
$305$	−384698.	+	1.97815e6i	−0.236794	+	1.21761i
$306$		0			0
$307$	403766.	+	403766.i	0.244503	+	0.244503i	0.818710	−	0.574207i	$-0.194690\pi$
$307$	403766.	+	403766.i	0.244503	+	0.244503i	−0.574207	+	0.818710i	$0.694690\pi$
$308$		0			0
$309$	−2.59165e6			−1.54411
$310$		0			0
$311$		−	1.05819e6i		−	0.620387i	−0.950673	−	0.310194i	$-0.899606\pi$
$311$		−	1.05819e6i		−	0.620387i	0.950673	−	0.310194i	$-0.100394\pi$
$312$		0			0
$313$	−1.88504e6	+	1.88504e6i	−1.08758	+	1.08758i	−0.0918012	+	0.995777i	$0.529262\pi$
$313$	−1.88504e6	+	1.88504e6i	−1.08758	+	1.08758i	−0.995777	+	0.0918012i	$0.970738\pi$
$314$		0			0
$315$	−228262.	−	338478.i	−0.129616	−	0.192201i
$316$		0			0
$317$	−1.20973e6	+	1.20973e6i	−0.676143	+	0.676143i	−0.959125	−	0.282982i	$-0.908676\pi$
$317$	−1.20973e6	+	1.20973e6i	−0.676143	+	0.676143i	0.282982	+	0.959125i	$0.408676\pi$
$318$		0			0
$319$	−3.04184e6			−1.67363
$320$		0			0
$321$	105159.			0.0569619
$322$		0			0
$323$	910583.	−	910583.i	0.485638	−	0.485638i
$324$		0			0
$325$	−189118.	−	445756.i	−0.0993170	−	0.234093i
$326$		0			0
$327$	−886810.	+	886810.i	−0.458629	+	0.458629i
$328$		0			0
$329$		−	367523.i		−	0.187195i
$330$		0			0
$331$	−487007.			−0.244324			−0.122162	−	0.992510i	$-0.538983\pi$
$331$	−487007.			−0.244324			−0.122162	+	0.992510i	$0.538983\pi$
$332$		0			0
$333$	2.62676e6	+	2.62676e6i	1.29811	+	1.29811i
$334$		0			0
$335$	893266.	+	1.32458e6i	0.434879	+	0.644860i
$336$		0			0
$337$	375270.	+	375270.i	0.179999	+	0.179999i	0.791355	−	0.611356i	$-0.209376\pi$
$337$	375270.	+	375270.i	0.179999	+	0.179999i	−0.611356	+	0.791355i	$0.709376\pi$
$338$		0			0
$339$			722511.i			0.341464i
$340$		0			0
$341$		−	5.01679e6i		−	2.33636i
$342$		0			0
$343$	−489102.	−	489102.i	−0.224473	−	0.224473i
$344$		0			0
$345$	−1.31695e6	−	256111.i	−0.595690	−	0.115846i
$346$		0			0
$347$	−2.79322e6	−	2.79322e6i	−1.24532	−	1.24532i	−0.957763	−	0.287559i	$-0.907156\pi$
$347$	−2.79322e6	−	2.79322e6i	−1.24532	−	1.24532i	−0.287559	−	0.957763i	$-0.592844\pi$
$348$		0			0
$349$	1.69016e6			0.742788			0.371394	−	0.928475i	$-0.378880\pi$
$349$	1.69016e6			0.742788			0.371394	+	0.928475i	$0.378880\pi$
$350$		0			0
$351$		−	405037.i		−	0.175480i
$352$		0			0
$353$	766651.	−	766651.i	0.327462	−	0.327462i	−0.524159	−	0.851621i	$-0.675620\pi$
$353$	766651.	−	766651.i	0.327462	−	0.327462i	0.851621	+	0.524159i	$0.175620\pi$
$354$		0			0
$355$	−620040.	+	3.18830e6i	−0.261125	+	1.34273i
$356$		0			0
$357$	−671234.	+	671234.i	−0.278743	+	0.278743i
$358$		0			0
$359$	1.39596e6			0.571657			0.285829	−	0.958281i	$-0.407731\pi$
$359$	1.39596e6			0.571657			0.285829	+	0.958281i	$0.407731\pi$
$360$		0			0
$361$	2.00156e6			0.808354
$362$		0			0
$363$	−1.69389e6	+	1.69389e6i	−0.674710	+	0.674710i
$364$		0			0
$365$	165248.	−	111440.i	0.0649239	−	0.0437833i
$366$		0			0
$367$	85536.5	−	85536.5i	0.0331502	−	0.0331502i	−0.690337	−	0.723488i	$-0.742538\pi$
$367$	85536.5	−	85536.5i	0.0331502	−	0.0331502i	0.723488	+	0.690337i	$0.242538\pi$
$368$		0			0
$369$		−	3.78637e6i		−	1.44763i
$370$		0			0
$371$	−419689.			−0.158304
$372$		0			0
$373$	−2.12223e6	−	2.12223e6i	−0.789807	−	0.789807i	0.191656	−	0.981462i	$-0.438614\pi$
$373$	−2.12223e6	−	2.12223e6i	−0.789807	−	0.789807i	−0.981462	+	0.191656i	$0.938614\pi$
$374$		0			0
$375$	4.16243e6	−	883581.i	1.52851	−	0.324465i
$376$		0			0
$377$	−654376.	−	654376.i	−0.237123	−	0.237123i
$378$		0			0
$379$			3.51617e6i			1.25740i	0.777650	+	0.628698i	$0.216412\pi$
$379$			3.51617e6i			1.25740i	−0.777650	+	0.628698i	$0.783588\pi$
$380$		0			0
$381$		−	2.47599e6i		−	0.873848i
$382$		0			0
$383$	−3.23618e6	−	3.23618e6i	−1.12729	−	1.12729i	−0.990616	−	0.136674i	$-0.956359\pi$
$383$	−3.23618e6	−	3.23618e6i	−1.12729	−	1.12729i	−0.136674	−	0.990616i	$-0.543641\pi$
$384$		0			0
$385$	−492100.	+	331861.i	−0.169201	+	0.114105i
$386$		0			0
$387$	−1.64196e6	−	1.64196e6i	−0.557294	−	0.557294i
$388$		0			0
$389$	4.77783e6			1.60087			0.800436	−	0.599418i	$-0.204601\pi$
$389$	4.77783e6			1.60087			0.800436	+	0.599418i	$0.204601\pi$
$390$		0			0
$391$			1.84188e6i			0.609283i
$392$		0			0
$393$	2.18644e6	−	2.18644e6i	0.714096	−	0.714096i
$394$		0			0
$395$	−664129.	−	129156.i	−0.214171	−	0.0416505i
$396$		0			0
$397$	−2.85091e6	+	2.85091e6i	−0.907837	+	0.907837i	−0.996097	−	0.0882604i	$-0.971869\pi$
$397$	−2.85091e6	+	2.85091e6i	−0.907837	+	0.907837i	0.0882604	+	0.996097i	$0.471869\pi$
$398$		0			0
$399$	349802.			0.109999
$400$		0			0
$401$	−2.86873e6			−0.890899			−0.445450	−	0.895307i	$-0.646956\pi$
$401$	−2.86873e6			−0.890899			−0.445450	+	0.895307i	$0.646956\pi$
$402$		0			0
$403$	1.07924e6	−	1.07924e6i	0.331020	−	0.331020i
$404$		0			0
$405$	−1.17729e6	−	228951.i	−0.356653	−	0.0693595i
$406$		0			0
$407$	3.81895e6	−	3.81895e6i	1.14277	−	1.14277i
$408$		0			0
$409$			4.38344e6i			1.29571i	0.761765	+	0.647854i	$0.224333\pi$
$409$			4.38344e6i			1.29571i	−0.761765	+	0.647854i	$0.775667\pi$
$410$		0			0
$411$	3.87118e6			1.13042
$412$		0			0
$413$	490212.	+	490212.i	0.141419	+	0.141419i
$414$		0			0
$415$	−3.03847e6	+	2.04908e6i	−0.866034	+	0.584034i
$416$		0			0
$417$	31057.7	+	31057.7i	0.00874639	+	0.00874639i
$418$		0			0
$419$			1.83000e6i			0.509233i	0.967042	+	0.254617i	$0.0819493\pi$
$419$			1.83000e6i			0.509233i	−0.967042	+	0.254617i	$0.918051\pi$
$420$		0			0
$421$			5.81932e6i			1.60017i	0.599884	+	0.800087i	$0.295213\pi$
$421$			5.81932e6i			1.60017i	−0.599884	+	0.800087i	$0.704787\pi$
$422$		0			0
$423$	4.36700e6	+	4.36700e6i	1.18668	+	1.18668i
$424$		0			0
$425$	−2.28163e6	−	5.37786e6i	−0.612734	−	1.44423i
$426$		0			0
$427$	531406.	+	531406.i	0.141045	+	0.141045i
$428$		0			0
$429$	−1.92226e6			−0.504278
$430$		0			0
$431$		−	1.38778e6i		−	0.359855i	−0.983680	−	0.179927i	$-0.942414\pi$
$431$		−	1.38778e6i		−	0.359855i	0.983680	−	0.179927i	$-0.0575863\pi$
$432$		0			0
$433$	1.01509e6	−	1.01509e6i	0.260186	−	0.260186i	−0.564943	−	0.825130i	$-0.691102\pi$
$433$	1.01509e6	−	1.01509e6i	0.260186	−	0.260186i	0.825130	+	0.564943i	$0.191102\pi$
$434$		0			0
$435$	6.74253e6	−	4.54701e6i	1.70844	−	1.15213i
$436$		0			0
$437$	479933.	−	479933.i	0.120220	−	0.120220i
$438$		0			0
$439$	3.04621e6			0.754394			0.377197	−	0.926133i	$-0.376888\pi$
$439$	3.04621e6			0.754394			0.377197	+	0.926133i	$0.376888\pi$
$440$		0			0
$441$	5.73551e6			1.40435
$442$		0			0
$443$	4.41095e6	−	4.41095e6i	1.06788	−	1.06788i	0.0703580	−	0.997522i	$-0.477586\pi$
$443$	4.41095e6	−	4.41095e6i	1.06788	−	1.06788i	0.997522	−	0.0703580i	$-0.0224142\pi$
$444$		0			0
$445$	85696.6	−	440660.i	0.0205146	−	0.105488i
$446$		0			0
$447$	−8.48362e6	+	8.48362e6i	−2.00822	+	2.00822i
$448$		0			0
$449$		−	6.04065e6i		−	1.41406i	−0.707183	−	0.707030i	$-0.750035\pi$
$449$		−	6.04065e6i		−	1.41406i	0.707183	−	0.707030i	$-0.249965\pi$
$450$		0			0
$451$	−5.50485e6			−1.27440
$452$		0			0
$453$	2.45898e6	+	2.45898e6i	0.563000	+	0.563000i
$454$		0			0
$455$	−177255.	−	34471.3i	−0.0401392	−	0.00780601i
$456$		0			0
$457$	3.16526e6	+	3.16526e6i	0.708954	+	0.708954i	0.966315	−	0.257361i	$-0.0828529\pi$
$457$	3.16526e6	+	3.16526e6i	0.708954	+	0.708954i	−0.257361	+	0.966315i	$0.582853\pi$
$458$		0			0
$459$		−	4.88660e6i		−	1.08262i
$460$		0			0
$461$			5.81450e6i			1.27427i	0.770754	+	0.637133i	$0.219880\pi$
$461$			5.81450e6i			1.27427i	−0.770754	+	0.637133i	$0.780120\pi$
$462$		0			0
$463$	2.33240e6	+	2.33240e6i	0.505651	+	0.505651i	0.913188	−	0.407538i	$-0.133612\pi$
$463$	2.33240e6	+	2.33240e6i	0.505651	+	0.505651i	−0.407538	+	0.913188i	$0.633612\pi$
$464$		0			0
$465$	7.49921e6	+	1.11202e7i	1.60836	+	2.38495i
$466$		0			0
$467$	3.95924e6	+	3.95924e6i	0.840077	+	0.840077i	0.988869	−	0.148791i	$-0.0475382\pi$
$467$	3.95924e6	+	3.95924e6i	0.840077	+	0.840077i	−0.148791	+	0.988869i	$0.547538\pi$
$468$		0			0
$469$	595796.			0.125074
$470$		0			0
$471$			3.65745e6i			0.759672i
$472$		0			0
$473$	−2.38718e6	+	2.38718e6i	−0.490604	+	0.490604i
$474$		0			0
$475$	−806775.	+	1.99581e6i	−0.164066	+	0.405868i
$476$		0			0
$477$	4.98686e6	−	4.98686e6i	1.00353	−	1.00353i
$478$		0			0
$479$	−8.50896e6			−1.69448			−0.847242	−	0.531206i	$-0.821739\pi$
$479$	−8.50896e6			−1.69448			−0.847242	+	0.531206i	$0.821739\pi$
$480$		0			0
$481$	1.64310e6			0.323818
$482$		0			0
$483$	−353781.	+	353781.i	−0.0690028	+	0.0690028i
$484$		0			0
$485$	3.23437e6	+	4.79607e6i	0.624360	+	0.925831i
$486$		0			0
$487$	263623.	−	263623.i	0.0503687	−	0.0503687i	−0.681474	−	0.731843i	$-0.738661\pi$
$487$	263623.	−	263623.i	0.0503687	−	0.0503687i	0.731843	+	0.681474i	$0.238661\pi$
$488$		0			0
$489$			4.33781e6i			0.820349i
$490$		0			0
$491$	3.54302e6			0.663238			0.331619	−	0.943413i	$-0.392405\pi$
$491$	3.54302e6			0.663238			0.331619	+	0.943413i	$0.392405\pi$
$492$		0			0
$493$	−7.89477e6	−	7.89477e6i	−1.46293	−	1.46293i
$494$		0			0
$495$	1.90400e6	−	9.79053e6i	0.349264	−	1.79595i
$496$		0			0
$497$	856497.	+	856497.i	0.155537	+	0.155537i
$498$		0			0
$499$		−	5.63099e6i		−	1.01236i	−0.862429	−	0.506178i	$-0.831058\pi$
$499$		−	5.63099e6i		−	1.01236i	0.862429	−	0.506178i	$-0.168942\pi$
$500$		0			0
$501$			9.80903e6i			1.74595i
$502$		0			0
$503$	7.50633e6	+	7.50633e6i	1.32284	+	1.32284i	0.911466	+	0.411376i	$0.134952\pi$
$503$	7.50633e6	+	7.50633e6i	1.32284	+	1.32284i	0.411376	+	0.911466i	$0.365048\pi$
$504$		0			0
$505$	1.03794e6	−	5.33718e6i	0.181111	−	0.931287i
$506$		0			0
$507$	5.98154e6	+	5.98154e6i	1.03346	+	1.03346i
$508$		0			0
$509$	−720493.			−0.123264			−0.0616318	−	0.998099i	$-0.519630\pi$
$509$	−720493.			−0.123264			−0.0616318	+	0.998099i	$0.519630\pi$
$510$		0			0
$511$		−	74328.8i		−	0.0125923i
$512$		0			0
$513$	−1.27329e6	+	1.27329e6i	−0.213616	+	0.213616i
$514$		0			0
$515$	−3.32554e6	−	4.93126e6i	−0.552514	−	0.819295i
$516$		0			0
$517$	6.34901e6	−	6.34901e6i	1.04467	−	1.04467i
$518$		0			0
$519$	−6.41155e6			−1.04483
$520$		0			0
$521$	−8.81132e6			−1.42215			−0.711077	−	0.703114i	$-0.751792\pi$
$521$	−8.81132e6			−1.42215			−0.711077	+	0.703114i	$0.751792\pi$
$522$		0			0
$523$	1.65743e6	−	1.65743e6i	0.264961	−	0.264961i	−0.562105	−	0.827066i	$-0.690008\pi$
$523$	1.65743e6	−	1.65743e6i	0.264961	−	0.264961i	0.827066	+	0.562105i	$0.190008\pi$
$524$		0			0
$525$	594712.	−	1.47120e6i	0.0941692	−	0.232956i
$526$		0			0
$527$	1.30205e7	−	1.30205e7i	2.04222	−	2.04222i
$528$		0			0
$529$		−	5.46556e6i		−	0.849172i
$530$		0			0
$531$	−1.16497e7			−1.79299
$532$		0			0
$533$	−1.18423e6	−	1.18423e6i	−0.180559	−	0.180559i
$534$		0			0
$535$	134938.	+	200092.i	0.0203821	+	0.0302235i
$536$		0			0
$537$	−3.62234e6	−	3.62234e6i	−0.542067	−	0.542067i
$538$		0			0
$539$		−	8.33863e6i		−	1.23630i
$540$		0			0
$541$		−	272627.i		−	0.0400475i	−0.999800	−	0.0200238i	$-0.993626\pi$
$541$		−	272627.i		−	0.0400475i	0.999800	−	0.0200238i	$-0.00637419\pi$
$542$		0			0
$543$	−4.75122e6	−	4.75122e6i	−0.691522	−	0.691522i
$544$		0			0
$545$	−2.82531e6	−	549448.i	−0.407451	−	0.0792384i
$546$		0			0
$547$	2.52658e6	+	2.52658e6i	0.361047	+	0.361047i	0.864198	−	0.503151i	$-0.167826\pi$
$547$	2.52658e6	+	2.52658e6i	0.361047	+	0.361047i	−0.503151	+	0.864198i	$0.667826\pi$
$548$		0			0
$549$	−1.26286e7			−1.78823
$550$		0			0
$551$			4.11423e6i			0.577311i
$552$		0			0
$553$	−178410.	+	178410.i	−0.0248088	+	0.0248088i
$554$		0			0
$555$	−2.75641e6	+	1.41737e7i	−0.379849	+	1.95322i
$556$		0			0
$557$	9.90042e6	−	9.90042e6i	1.35212	−	1.35212i	0.468836	−	0.883285i	$-0.344673\pi$
$557$	9.90042e6	−	9.90042e6i	1.35212	−	1.35212i	0.883285	−	0.468836i	$-0.155327\pi$
$558$		0			0
$559$	−1.02708e6			−0.139019
$560$		0			0
$561$	−2.31913e7			−3.11113
$562$		0			0
$563$	−7.61172e6	+	7.61172e6i	−1.01207	+	1.01207i	−0.0121466	+	0.999926i	$0.503866\pi$
$563$	−7.61172e6	+	7.61172e6i	−1.01207	+	1.01207i	−0.999926	+	0.0121466i	$0.996134\pi$
$564$		0			0
$565$	−1.37476e6	+	927109.i	−0.181178	+	0.122183i
$566$		0			0
$567$	−316264.	+	316264.i	−0.0413135	+	0.0413135i
$568$		0			0
$569$		−	4.28630e6i		−	0.555011i	−0.960724	−	0.277505i	$-0.910492\pi$
$569$		−	4.28630e6i		−	0.555011i	0.960724	−	0.277505i	$-0.0895077\pi$
$570$		0			0
$571$	−7.75507e6			−0.995396			−0.497698	−	0.867351i	$-0.665821\pi$
$571$	−7.75507e6			−0.995396			−0.497698	+	0.867351i	$0.665821\pi$
$572$		0			0
$573$	−5.83526e6	−	5.83526e6i	−0.742461	−	0.742461i
$574$		0			0
$575$	−1.20256e6	−	2.83446e6i	−0.151683	−	0.357520i
$576$		0			0
$577$	7.36203e6	+	7.36203e6i	0.920572	+	0.920572i	0.997070	−	0.0764975i	$-0.0243737\pi$
$577$	7.36203e6	+	7.36203e6i	0.920572	+	0.920572i	−0.0764975	+	0.997070i	$0.524374\pi$
$578$		0			0
$579$			5.68637e6i			0.704918i
$580$		0			0
$581$			1.36671e6i			0.167971i
$582$		0			0
$583$	−7.25019e6	−	7.25019e6i	−0.883442	−	0.883442i
$584$		0			0
$585$	2.51578e6	−	1.69659e6i	0.303937	−	0.204968i
$586$		0			0
$587$	−6.07649e6	−	6.07649e6i	−0.727876	−	0.727876i	0.242321	−	0.970196i	$-0.422091\pi$
$587$	−6.07649e6	−	6.07649e6i	−0.727876	−	0.727876i	−0.970196	+	0.242321i	$0.922091\pi$
$588$		0			0
$589$	−6.78544e6			−0.805916
$590$		0			0
$591$			4.05848e6i			0.477964i
$592$		0			0
$593$	1.10736e7	−	1.10736e7i	1.29316	−	1.29316i	0.360341	−	0.932821i	$-0.382660\pi$
$593$	1.10736e7	−	1.10736e7i	1.29316	−	1.29316i	0.932821	−	0.360341i	$-0.117340\pi$
$594$		0			0
$595$	−2.13850e6	−	415882.i	−0.247638	−	0.0481590i
$596$		0			0
$597$	−4.13695e6	+	4.13695e6i	−0.475056	+	0.475056i
$598$		0			0
$599$	5.28835e6			0.602217			0.301108	−	0.953590i	$-0.402643\pi$
$599$	5.28835e6			0.602217			0.301108	+	0.953590i	$0.402643\pi$
$600$		0			0
$601$	1.35758e7			1.53313			0.766565	−	0.642167i	$-0.221964\pi$
$601$	1.35758e7			1.53313			0.766565	+	0.642167i	$0.221964\pi$
$602$		0			0
$603$	−7.07940e6	+	7.07940e6i	−0.792873	+	0.792873i
$604$		0			0
$605$	−5.39660e6	−	1.04949e6i	−0.599420	−	0.116571i
$606$		0			0
$607$	−7.46791e6	+	7.46791e6i	−0.822674	+	0.822674i	−0.986491	−	0.163817i	$-0.947619\pi$
$607$	−7.46791e6	+	7.46791e6i	−0.822674	+	0.822674i	0.163817	+	0.986491i	$0.447619\pi$
$608$		0			0
$609$		−	3.03280e6i		−	0.331360i
$610$		0			0
$611$	2.73166e6			0.296022
$612$		0			0
$613$	5.63189e6	+	5.63189e6i	0.605345	+	0.605345i	0.941726	−	0.336381i	$-0.109203\pi$
$613$	5.63189e6	+	5.63189e6i	0.605345	+	0.605345i	−0.336381	+	0.941726i	$0.609203\pi$
$614$		0			0
$615$	1.22020e7	−	8.22877e6i	1.30090	−	0.877298i
$616$		0			0
$617$	−402006.	−	402006.i	−0.0425128	−	0.0425128i	0.685531	−	0.728044i	$-0.259570\pi$
$617$	−402006.	−	402006.i	−0.0425128	−	0.0425128i	−0.728044	+	0.685531i	$0.759570\pi$
$618$		0			0
$619$			5.67335e6i			0.595131i	0.954701	+	0.297566i	$0.0961747\pi$
$619$			5.67335e6i			0.595131i	−0.954701	+	0.297566i	$0.903825\pi$
$620$		0			0
$621$		−	2.57554e6i		−	0.268003i
$622$		0			0
$623$	−118378.	−	118378.i	−0.0122194	−	0.0122194i
$624$		0			0
$625$	7.02237e6	+	6.78629e6i	0.719090	+	0.694917i
$626$		0			0
$627$	6.04289e6	+	6.04289e6i	0.613869	+	0.613869i
$628$		0			0
$629$	1.98233e7			1.99779
$630$		0			0
$631$			782842.i			0.0782710i	0.999234	+	0.0391355i	$0.0124604\pi$
$631$			782842.i			0.0782710i	−0.999234	+	0.0391355i	$0.987540\pi$
$632$		0			0
$633$	−1.54439e7	+	1.54439e7i	−1.53196	+	1.53196i
$634$		0			0
$635$	4.71119e6	−	3.17712e6i	0.463657	−	0.312680i
$636$		0			0
$637$	1.79385e6	−	1.79385e6i	0.175161	−	0.175161i
$638$		0			0
$639$	−2.03543e7			−1.97198
$640$		0			0
$641$	−1.77905e7			−1.71018			−0.855090	−	0.518479i	$-0.826498\pi$
$641$	−1.77905e7			−1.71018			−0.855090	+	0.518479i	$0.826498\pi$
$642$		0			0
$643$	1.25143e7	−	1.25143e7i	1.19366	−	1.19366i	0.217625	−	0.976032i	$-0.430169\pi$
$643$	1.25143e7	−	1.25143e7i	1.19366	−	1.19366i	0.976032	−	0.217625i	$-0.0698310\pi$
$644$		0			0
$645$	1.72300e6	−	8.85980e6i	0.163074	−	0.838542i
$646$		0			0
$647$	−1.29041e6	+	1.29041e6i	−0.121190	+	0.121190i	−0.765101	−	0.643911i	$-0.777311\pi$
$647$	−1.29041e6	+	1.29041e6i	−0.121190	+	0.121190i	0.643911	+	0.765101i	$0.277311\pi$
$648$		0			0
$649$			1.69370e7i			1.57843i
$650$		0			0
$651$	5.00187e6			0.462573
$652$		0			0
$653$	−4.78461e6	−	4.78461e6i	−0.439100	−	0.439100i	0.452609	−	0.891709i	$-0.350493\pi$
$653$	−4.78461e6	−	4.78461e6i	−0.439100	−	0.439100i	−0.891709	+	0.452609i	$0.850493\pi$
$654$		0			0
$655$	6.96585e6	+	1.35467e6i	0.634411	+	0.123376i
$656$		0			0
$657$	883194.	+	883194.i	0.0798257	+	0.0798257i
$658$		0			0
$659$		−	4.07985e6i		−	0.365957i	−0.983117	−	0.182979i	$-0.941426\pi$
$659$		−	4.07985e6i		−	0.365957i	0.983117	−	0.182979i	$-0.0585739\pi$
$660$		0			0
$661$			4.24912e6i			0.378265i	0.981952	+	0.189132i	$0.0605675\pi$
$661$			4.24912e6i			0.378265i	−0.981952	+	0.189132i	$0.939432\pi$
$662$		0			0
$663$	−4.98903e6	−	4.98903e6i	−0.440790	−	0.440790i
$664$		0			0
$665$	448858.	+	665588.i	0.0393600	+	0.0583648i
$666$		0			0
$667$	−4.16103e6	−	4.16103e6i	−0.362148	−	0.362148i
$668$		0			0
$669$	−1.35488e6			−0.117040
$670$		0			0
$671$			1.83602e7i			1.57424i
$672$		0			0
$673$	7.08151e6	−	7.08151e6i	0.602682	−	0.602682i	−0.338341	−	0.941023i	$-0.609866\pi$
$673$	7.08151e6	−	7.08151e6i	0.602682	−	0.602682i	0.941023	+	0.338341i	$0.109866\pi$
$674$		0			0
$675$	3.19045e6	+	7.51997e6i	0.269521	+	0.635268i
$676$		0			0
$677$	−1.17428e7	+	1.17428e7i	−0.984691	+	0.984691i	−0.999885	−	0.0151933i	$-0.995164\pi$
$677$	−1.17428e7	+	1.17428e7i	−0.984691	+	0.984691i	0.0151933	+	0.999885i	$0.495164\pi$
$678$		0			0
$679$	2.15728e6			0.179569
$680$		0			0
$681$	1.28433e7			1.06123
$682$		0			0
$683$	9.30853e6	−	9.30853e6i	0.763536	−	0.763536i	−0.213424	−	0.976960i	$-0.568462\pi$
$683$	9.30853e6	−	9.30853e6i	0.763536	−	0.763536i	0.976960	+	0.213424i	$0.0684615\pi$
$684$		0			0
$685$	4.96741e6	+	7.36591e6i	0.404486	+	0.599791i
$686$		0			0
$687$	6.01252e6	−	6.01252e6i	0.486032	−	0.486032i
$688$		0			0
$689$		−	3.11939e6i		−	0.250335i
$690$		0			0
$691$	−9.51389e6			−0.757989			−0.378995	−	0.925399i	$-0.623730\pi$
$691$	−9.51389e6			−0.757989			−0.378995	+	0.925399i	$0.623730\pi$
$692$		0			0
$693$	−2.63010e6	−	2.63010e6i	−0.208037	−	0.208037i
$694$		0			0
$695$	−19242.7	+	98947.5i	−0.00151113	+	0.00777039i
$696$		0			0
$697$	−1.42872e7	−	1.42872e7i	−1.11395	−	1.11395i
$698$		0			0
$699$			2.19896e6i			0.170226i
$700$		0			0
$701$		−	1.03313e7i		−	0.794069i	−0.917804	−	0.397034i	$-0.870039\pi$
$701$		−	1.03313e7i		−	0.794069i	0.917804	−	0.397034i	$-0.129961\pi$
$702$		0			0
$703$	−5.16530e6	−	5.16530e6i	−0.394191	−	0.394191i
$704$		0			0
$705$	−4.58254e6	+	2.35638e7i	−0.347243	+	1.78555i
$706$		0			0
$707$	−1.43377e6	−	1.43377e6i	−0.107877	−	0.107877i
$708$		0			0
$709$	−6.08555e6			−0.454657			−0.227329	−	0.973818i	$-0.572999\pi$
$709$	−6.08555e6			−0.454657			−0.227329	+	0.973818i	$0.572999\pi$
$710$		0			0
$711$		−	4.23983e6i		−	0.314539i
$712$		0			0
$713$	6.86262e6	−	6.86262e6i	0.505552	−	0.505552i
$714$		0			0
$715$	−2.46660e6	−	3.65760e6i	−0.180440	−	0.267566i
$716$		0			0
$717$	−1.70139e7	+	1.70139e7i	−1.23597	+	1.23597i
$718$		0			0
$719$	1.95226e7			1.40836			0.704182	−	0.710019i	$-0.251314\pi$
$719$	1.95226e7			1.40836			0.704182	+	0.710019i	$0.251314\pi$
$720$		0			0
$721$	−2.21809e6			−0.158906
$722$		0			0
$723$	8.30854e6	−	8.30854e6i	0.591125	−	0.591125i
$724$		0			0
$725$	1.73037e7	+	6.99476e6i	1.22263	+	0.494229i
$726$		0			0
$727$	6.97825e6	−	6.97825e6i	0.489678	−	0.489678i	−0.418527	−	0.908204i	$-0.637453\pi$
$727$	6.97825e6	−	6.97825e6i	0.489678	−	0.489678i	0.908204	+	0.418527i	$0.137453\pi$
$728$		0			0
$729$		−	2.29882e7i		−	1.60209i
$730$		0			0
$731$	−1.23913e7			−0.857677
$732$		0			0
$733$	5.90984e6	+	5.90984e6i	0.406271	+	0.406271i	0.880436	−	0.474165i	$-0.157250\pi$
$733$	5.90984e6	+	5.90984e6i	0.406271	+	0.406271i	−0.474165	+	0.880436i	$0.657250\pi$
$734$		0			0
$735$	1.24648e7	+	1.84834e7i	0.851071	+	1.26201i
$736$		0			0
$737$	1.02925e7	+	1.02925e7i	0.697992	+	0.697992i
$738$		0			0
$739$		−	1.16561e7i		−	0.785128i	−0.919725	−	0.392564i	$-0.871588\pi$
$739$		−	1.16561e7i		−	0.785128i	0.919725	−	0.392564i	$-0.128412\pi$
$740$		0			0
$741$			2.59995e6i			0.173948i
$742$		0			0
$743$	−1.06995e7	−	1.06995e7i	−0.711038	−	0.711038i	0.255714	−	0.966752i	$-0.417689\pi$
$743$	−1.06995e7	−	1.06995e7i	−0.711038	−	0.711038i	−0.966752	+	0.255714i	$0.917689\pi$
$744$		0			0
$745$	−2.70282e7	−	5.25627e6i	−1.78413	−	0.346966i
$746$		0			0
$747$	−1.62396e7	−	1.62396e7i	−1.06481	−	1.06481i
$748$		0			0
$749$	90001.4			0.00586199
$750$		0			0
$751$		−	1.31404e7i		−	0.850176i	−0.905152	−	0.425088i	$-0.860243\pi$
$751$		−	1.31404e7i		−	0.850176i	0.905152	−	0.425088i	$-0.139757\pi$
$752$		0			0
$753$	1.33936e7	−	1.33936e7i	0.860816	−	0.860816i
$754$		0			0
$755$	−1.52353e6	+	7.83412e6i	−0.0972710	+	0.500176i
$756$		0			0
$757$	2.09821e7	−	2.09821e7i	1.33079	−	1.33079i	0.426121	−	0.904666i	$-0.359880\pi$
$757$	2.09821e7	−	2.09821e7i	1.33079	−	1.33079i	0.904666	−	0.426121i	$-0.140120\pi$
$758$		0			0
$759$	−1.22232e7			−0.770162
$760$		0			0
$761$	2.53115e7			1.58437			0.792184	−	0.610282i	$-0.208944\pi$
$761$	2.53115e7			1.58437			0.792184	+	0.610282i	$0.208944\pi$
$762$		0			0
$763$	−758985.	+	758985.i	−0.0471978	+	0.0471978i
$764$		0			0
$765$	3.03519e7	−	2.04686e7i	1.87513	−	1.26455i
$766$		0			0
$767$	−3.64356e6	+	3.64356e6i	−0.223634	+	0.223634i
$768$		0			0
$769$		−	6.63393e6i		−	0.404534i	−0.979330	−	0.202267i	$-0.935169\pi$
$769$		−	6.63393e6i		−	0.404534i	0.979330	−	0.202267i	$-0.0648308\pi$
$770$		0			0
$771$	2.35617e7			1.42748
$772$		0			0
$773$	−1.93715e7	−	1.93715e7i	−1.16604	−	1.16604i	−0.983129	−	0.182915i	$-0.941447\pi$
$773$	−1.93715e7	−	1.93715e7i	−1.16604	−	1.16604i	−0.182915	−	0.983129i	$-0.558553\pi$
$774$		0			0
$775$	−1.15362e7	+	2.85383e7i	−0.689935	+	1.70677i
$776$		0			0
$777$	3.80759e6	+	3.80759e6i	0.226255	+	0.226255i
$778$		0			0
$779$			7.44556e6i			0.439596i
$780$		0			0
$781$			2.95922e7i			1.73600i
$782$		0			0
$783$	1.10394e7	+	1.10394e7i	0.643491	+	0.643491i
$784$		0			0
$785$	−6.95922e6	+	4.69315e6i	−0.403076	+	0.271825i
$786$		0			0
$787$	1.81394e7	+	1.81394e7i	1.04396	+	1.04396i	0.998988	+	0.0449752i	$0.0143209\pi$
$787$	1.81394e7	+	1.81394e7i	1.04396	+	1.04396i	0.0449752	+	0.998988i	$0.485679\pi$
$788$		0			0
$789$	−1.69264e7			−0.967994
$790$		0			0
$791$			618369.i			0.0351404i
$792$		0			0
$793$	−3.94974e6	+	3.94974e6i	−0.223041	+	0.223041i
$794$		0			0
$795$	2.69085e7	+	5.23299e6i	1.50998	+	0.293651i
$796$		0			0
$797$	−1.06991e7	+	1.06991e7i	−0.596624	+	0.596624i	−0.939413	−	0.342789i	$-0.888628\pi$
$797$	−1.06991e7	+	1.06991e7i	−0.596624	+	0.596624i	0.342789	+	0.939413i	$0.388628\pi$
$798$		0			0
$799$	3.29563e7			1.82630
$800$		0			0
$801$	2.81319e6			0.154924
$802$		0			0
$803$	1.28404e6	−	1.28404e6i	0.0702732	−	0.0702732i
$804$		0			0
$805$	−1.12712e6	−	219195.i	−0.0613029	−	0.0119218i
$806$		0			0
$807$	−1.37800e7	+	1.37800e7i	−0.744842	+	0.744842i
$808$		0			0
$809$			2.83714e7i			1.52409i	0.647526	+	0.762043i	$0.275804\pi$
$809$			2.83714e7i			1.52409i	−0.647526	+	0.762043i	$0.724196\pi$
$810$		0			0
$811$	1.34252e7			0.716752			0.358376	−	0.933577i	$-0.383331\pi$
$811$	1.34252e7			0.716752			0.358376	+	0.933577i	$0.383331\pi$
$812$		0			0
$813$	3.86751e7	+	3.86751e7i	2.05213	+	2.05213i
$814$		0			0
$815$	−8.25379e6	+	5.56617e6i	−0.435271	+	0.293537i
$816$		0			0
$817$	3.22876e6	+	3.22876e6i	0.169231	+	0.169231i
$818$		0			0
$819$		−	1.13160e6i		−	0.0589500i
$820$		0			0
$821$		−	1.77101e7i		−	0.916987i	−0.888698	−	0.458494i	$-0.848389\pi$
$821$		−	1.77101e7i		−	0.916987i	0.888698	−	0.458494i	$-0.151611\pi$
$822$		0			0
$823$	564216.	+	564216.i	0.0290366	+	0.0290366i	0.721476	−	0.692439i	$-0.243464\pi$
$823$	564216.	+	564216.i	0.0290366	+	0.0290366i	−0.692439	+	0.721476i	$0.743464\pi$
$824$		0			0
$825$	3.56890e7	−	1.51415e7i	1.82557	−	0.774524i
$826$		0			0
$827$	444181.	+	444181.i	0.0225838	+	0.0225838i	0.718309	−	0.695725i	$-0.244917\pi$
$827$	444181.	+	444181.i	0.0225838	+	0.0225838i	−0.695725	+	0.718309i	$0.744917\pi$
$828$		0			0
$829$	−4.84536e6			−0.244872			−0.122436	−	0.992476i	$-0.539071\pi$
$829$	−4.84536e6			−0.244872			−0.122436	+	0.992476i	$0.539071\pi$
$830$		0			0
$831$		−	1.43707e7i		−	0.721897i
$832$		0			0
$833$	2.16420e7	−	2.16420e7i	1.08065	−	1.08065i
$834$		0			0
$835$	−1.86642e7	+	1.25867e7i	−0.926386	+	0.624735i
$836$		0			0
$837$	−1.82069e7	+	1.82069e7i	−0.898302	+	0.898302i
$838$		0			0
$839$	−7.31295e6			−0.358664			−0.179332	−	0.983789i	$-0.557394\pi$
$839$	−7.31295e6			−0.358664			−0.179332	+	0.983789i	$0.557394\pi$
$840$		0			0
$841$	1.51593e7			0.739078
$842$		0			0
$843$	−1.85459e7	+	1.85459e7i	−0.898831	+	0.898831i
$844$		0			0
$845$	−3.70603e6	+	1.90567e7i	−0.178553	+	0.918136i
$846$		0			0
$847$	−1.44973e6	+	1.44973e6i	−0.0694349	+	0.0694349i
$848$		0			0
$849$		−	2.24822e7i		−	1.07046i
$850$		0			0
$851$	1.04481e7			0.494553
$852$		0			0
$853$	−3.80964e6	−	3.80964e6i	−0.179272	−	0.179272i	0.611767	−	0.791038i	$-0.290459\pi$
$853$	−3.80964e6	−	3.80964e6i	−0.179272	−	0.179272i	−0.791038	+	0.611767i	$0.790459\pi$
$854$		0			0
$855$	−1.32421e7	−	2.57524e6i	−0.619502	−	0.120477i
$856$		0			0
$857$	−9.23229e6	−	9.23229e6i	−0.429395	−	0.429395i	0.459027	−	0.888422i	$-0.348198\pi$
$857$	−9.23229e6	−	9.23229e6i	−0.429395	−	0.429395i	−0.888422	+	0.459027i	$0.848198\pi$
$858$		0			0
$859$			272935.i			0.0126205i	0.999980	+	0.00631024i	$0.00200863\pi$
$859$			272935.i			0.0126205i	−0.999980	+	0.00631024i	$0.997991\pi$
$860$		0			0
$861$		−	5.48848e6i		−	0.252316i
$862$		0			0
$863$	−3.16913e6	−	3.16913e6i	−0.144848	−	0.144848i	0.630964	−	0.775812i	$-0.282660\pi$
$863$	−3.16913e6	−	3.16913e6i	−0.144848	−	0.144848i	−0.775812	+	0.630964i	$0.782660\pi$
$864$		0			0
$865$	−8.22714e6	−	1.21996e7i	−0.373860	−	0.554377i
$866$		0			0
$867$	−3.57353e7	−	3.57353e7i	−1.61454	−	1.61454i
$868$		0			0
$869$	−6.16412e6			−0.276899
$870$		0			0
$871$			4.42833e6i			0.197785i
$872$		0			0
$873$	−2.56333e7	+	2.56333e7i	−1.13833	+	1.13833i
$874$		0			0
$875$	3.56246e6	−	756222.i	0.157300	−	0.0333910i
$876$		0			0
$877$	−8.13844e6	+	8.13844e6i	−0.357308	+	0.357308i	−0.862820	−	0.505512i	$-0.831304\pi$
$877$	−8.13844e6	+	8.13844e6i	−0.357308	+	0.357308i	0.505512	+	0.862820i	$0.331304\pi$
$878$		0			0
$879$	2.69403e7			1.17606
$880$		0			0
$881$	−1.39725e7			−0.606504			−0.303252	−	0.952910i	$-0.598072\pi$
$881$	−1.39725e7			−0.606504			−0.303252	+	0.952910i	$0.598072\pi$
$882$		0			0
$883$	4.80471e6	−	4.80471e6i	0.207379	−	0.207379i	−0.595773	−	0.803153i	$-0.703154\pi$
$883$	4.80471e6	−	4.80471e6i	0.207379	−	0.207379i	0.803153	+	0.595773i	$0.203154\pi$
$884$		0			0
$885$	−2.53178e7	−	3.75424e7i	−1.08659	−	1.61125i
$886$		0			0
$887$	962500.	−	962500.i	0.0410763	−	0.0410763i	−0.686270	−	0.727347i	$-0.740753\pi$
$887$	962500.	−	962500.i	0.0410763	−	0.0410763i	0.727347	+	0.686270i	$0.240753\pi$
$888$		0			0
$889$		−	2.11910e6i		−	0.0899283i
$890$		0			0
$891$	−1.09270e7			−0.461113
$892$		0			0
$893$	−8.58733e6	−	8.58733e6i	−0.360354	−	0.360354i
$894$		0			0
$895$	2.24432e6	−	1.15405e7i	0.0936543	−	0.481579i
$896$		0			0
$897$	−2.62952e6	−	2.62952e6i	−0.109118	−	0.109118i
$898$		0			0
$899$			5.88299e7i			2.42772i
$900$		0			0
$901$		−	3.76342e7i		−	1.54444i
$902$		0			0
$903$	−2.38007e6	−	2.38007e6i	−0.0971340	−	0.0971340i
$904$		0			0
$905$	2.94375e6	−	1.51371e7i	0.119476	−	0.614356i
$906$		0			0
$907$	3.07745e7	+	3.07745e7i	1.24215	+	1.24215i	0.959109	+	0.283038i	$0.0913423\pi$
$907$	3.07745e7	+	3.07745e7i	1.24215	+	1.24215i	0.283038	+	0.959109i	$0.408658\pi$
$908$		0			0
$909$	3.40728e7			1.36772
$910$		0			0
$911$			3.26334e7i			1.30277i	0.758749	+	0.651383i	$0.225811\pi$
$911$			3.26334e7i			1.30277i	−0.758749	+	0.651383i	$0.774189\pi$
$912$		0			0
$913$	−2.36101e7	+	2.36101e7i	−0.937390	+	0.937390i
$914$		0			0
$915$	−2.74453e7	−	4.06972e7i	−1.08371	−	1.60698i
$916$		0			0
$917$	1.87129e6	−	1.87129e6i	0.0734881	−	0.0734881i
$918$		0			0
$919$	−1.37192e7			−0.535845			−0.267923	−	0.963440i	$-0.586337\pi$
$919$	−1.37192e7			−0.535845			−0.267923	+	0.963440i	$0.586337\pi$
$920$		0			0
$921$	−1.39087e7			−0.540305
$922$		0			0
$923$	−6.36602e6	+	6.36602e6i	−0.245960	+	0.245960i
$924$		0			0
$925$	−3.05060e7	+	1.29426e7i	−1.17228	+	0.497355i
$926$		0			0
$927$	2.63559e7	−	2.63559e7i	1.00735	−	1.00735i
$928$		0			0
$929$			5.06594e7i			1.92584i	0.269782	+	0.962922i	$0.413048\pi$
$929$			5.06594e7i			1.92584i	−0.269782	+	0.962922i	$0.586952\pi$
$930$		0			0
$931$	−1.12784e7			−0.426454
$932$		0			0
$933$	1.82260e7	+	1.82260e7i	0.685469	+	0.685469i
$934$		0			0
$935$	−2.97585e7	−	4.41274e7i	−1.11322	−	1.65074i
$936$		0			0
$937$	−7.26923e6	−	7.26923e6i	−0.270483	−	0.270483i	0.558812	−	0.829294i	$-0.311257\pi$
$937$	−7.26923e6	−	7.26923e6i	−0.270483	−	0.270483i	−0.829294	+	0.558812i	$0.811257\pi$
$938$		0			0
$939$		−	6.49351e7i		−	2.40334i
$940$		0			0
$941$		−	795711.i		−	0.0292942i	−0.999893	−	0.0146471i	$-0.995338\pi$
$941$		−	795711.i		−	0.0292942i	0.999893	−	0.0146471i	$-0.00466248\pi$
$942$		0			0
$943$	−7.53025e6	−	7.53025e6i	−0.275759	−	0.275759i
$944$		0			0
$945$	2.99031e6	+	581537.i	0.108927	+	0.0211835i
$946$		0			0
$947$	−4.02780e6	−	4.02780e6i	−0.145946	−	0.145946i	0.630358	−	0.776304i	$-0.282908\pi$
$947$	−4.02780e6	−	4.02780e6i	−0.145946	−	0.145946i	−0.776304	+	0.630358i	$0.782908\pi$
$948$		0			0
$949$	552458.			0.0199129
$950$		0			0
$951$		−	4.16720e7i		−	1.49415i
$952$		0			0
$953$	−2.67453e7	+	2.67453e7i	−0.953929	+	0.953929i	−0.998984	−	0.0450557i	$-0.985653\pi$
$953$	−2.67453e7	+	2.67453e7i	−0.953929	+	0.953929i	0.0450557	+	0.998984i	$0.485653\pi$
$954$		0			0
$955$	3.61540e6	−	1.85907e7i	0.128277	−	0.659610i
$956$		0			0
$957$	5.23920e7	−	5.23920e7i	1.84920	−	1.84920i
$958$		0			0
$959$	3.31319e6			0.116332
$960$		0			0
$961$	−6.83967e7			−2.38906
$962$		0			0
$963$	−1.06942e6	+	1.06942e6i	−0.0371606	+	0.0371606i
$964$		0			0
$965$	−1.08198e7	+	7.29660e6i	−0.374024	+	0.252233i
$966$		0			0
$967$	6.46334e6	−	6.46334e6i	0.222275	−	0.222275i	−0.587181	−	0.809456i	$-0.699762\pi$
$967$	6.46334e6	−	6.46334e6i	0.222275	−	0.222275i	0.809456	+	0.587181i	$0.199762\pi$
$968$		0			0
$969$			3.13673e7i			1.07317i
$970$		0			0
$971$	−8.63113e6			−0.293778			−0.146889	−	0.989153i	$-0.546926\pi$
$971$	−8.63113e6			−0.293778			−0.146889	+	0.989153i	$0.546926\pi$
$972$		0			0
$973$	26581.0	+	26581.0i	0.000900097	+	0.000900097i
$974$		0			0
$975$	1.09349e7	+	4.42027e6i	0.368386	+	0.148915i
$976$		0			0
$977$	7.17562e6	+	7.17562e6i	0.240504	+	0.240504i	0.817059	−	0.576554i	$-0.195603\pi$
$977$	7.17562e6	+	7.17562e6i	0.240504	+	0.240504i	−0.576554	+	0.817059i	$0.695603\pi$
$978$		0			0
$979$		−	4.08998e6i		−	0.136384i
$980$		0			0
$981$		−	1.80369e7i		−	0.598398i
$982$		0			0
$983$	−3.06048e7	−	3.06048e7i	−1.01020	−	1.01020i	−0.999947	−	0.0102486i	$-0.996738\pi$
$983$	−3.06048e7	−	3.06048e7i	−1.01020	−	1.01020i	−0.0102486	−	0.999947i	$-0.503262\pi$
$984$		0			0
$985$	−7.72229e6	+	5.20774e6i	−0.253604	+	0.171025i
$986$		0			0
$987$	6.33013e6	+	6.33013e6i	0.206833	+	0.206833i
$988$		0			0
$989$	−6.53097e6			−0.212318
$990$		0			0
$991$		−	873414.i		−	0.0282511i	−0.999900	−	0.0141256i	$-0.995504\pi$
$991$		−	873414.i		−	0.0282511i	0.999900	−	0.0141256i	$-0.00449646\pi$
$992$		0			0
$993$	8.38810e6	−	8.38810e6i	0.269954	−	0.269954i
$994$		0			0
$995$	−1.31800e7	−	2.56317e6i	−0.422045	−	0.0820766i
$996$		0			0
$997$	2.43412e7	−	2.43412e7i	0.775539	−	0.775539i	−0.203530	−	0.979069i	$-0.565241\pi$
$997$	2.43412e7	−	2.43412e7i	0.775539	−	0.775539i	0.979069	+	0.203530i	$0.0652413\pi$
$998$		0			0
$999$	−2.77194e7			−0.878758

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.o.a.47.3		56
4.3	odd	2		40.6.k.a.27.16	yes	56
5.3	odd	4	inner	160.6.o.a.143.4		56
8.3	odd	2	inner	160.6.o.a.47.4		56
8.5	even	2		40.6.k.a.27.2	yes	56
20.3	even	4		40.6.k.a.3.2	✓	56
40.3	even	4	inner	160.6.o.a.143.3		56
40.13	odd	4		40.6.k.a.3.16	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.2	✓	56	20.3	even	4
40.6.k.a.3.16	yes	56	40.13	odd	4
40.6.k.a.27.2	yes	56	8.5	even	2
40.6.k.a.27.16	yes	56	4.3	odd	2
160.6.o.a.47.3		56	1.1	even	1	trivial
160.6.o.a.47.4		56	8.3	odd	2	inner
160.6.o.a.143.3		56	40.3	even	4	inner
160.6.o.a.143.4		56	5.3	odd	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)

\(f(q)\)	\(=\)	\(q+(-17.2238 + 17.2238i) q^{3} +(-54.8737 - 10.6715i) q^{5} +(-14.7411 + 14.7411i) q^{7} -350.316i q^{9} +O(q^{10})\)	\(q+(-17.2238 + 17.2238i) q^{3} +(-54.8737 - 10.6715i) q^{5} +(-14.7411 + 14.7411i) q^{7} -350.316i q^{9} -509.310 q^{11} +(-109.565 - 109.565i) q^{13} +(1128.93 - 761.328i) q^{15} +(-1321.86 - 1321.86i) q^{17} +688.865i q^{19} -507.795i q^{21} +(-696.700 - 696.700i) q^{23} +(2897.24 + 1171.17i) q^{25} +(1848.38 + 1848.38i) q^{27} +5972.48 q^{29} +9850.17i q^{31} +(8772.24 - 8772.24i) q^{33} +(966.209 - 651.590i) q^{35} +(-7498.27 + 7498.27i) q^{37} +3774.25 q^{39} +10808.4 q^{41} +(4687.08 - 4687.08i) q^{43} +(-3738.39 + 19223.1i) q^{45} +(-12465.9 + 12465.9i) q^{47} +16372.4i q^{49} +45534.8 q^{51} +(14235.3 + 14235.3i) q^{53} +(27947.7 + 5435.09i) q^{55} +(-11864.9 - 11864.9i) q^{57} -33254.7i q^{59} -36049.2i q^{61} +(5164.05 + 5164.05i) q^{63} +(4843.02 + 7181.47i) q^{65} +(-20208.6 - 20208.6i) q^{67} +23999.6 q^{69} -58102.6i q^{71} +(-2521.14 + 2521.14i) q^{73} +(-70073.2 + 29729.5i) q^{75} +(7507.80 - 7507.80i) q^{77} +12102.9 q^{79} +21454.5 q^{81} +(46356.9 - 46356.9i) q^{83} +(58429.1 + 86641.4i) q^{85} +(-102869. + 102869. i) q^{87} +8030.44i q^{89} +3230.23 q^{91} +(-169657. - 169657. i) q^{93} +(7351.21 - 37800.6i) q^{95} +(-73172.1 - 73172.1i) q^{97} +178419. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3}+O(q^{10}) \) 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

Related objects

Downloads

Learn more