LMFDB - Embedded newform 160.3.m.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,3,Mod(17,160)]

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([0, 2, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("160.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	160.m (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:	$4.35968422976$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} - 3x^{16} + 11x^{14} + x^{12} - 40x^{10} + 4x^{8} + 176x^{6} - 192x^{4} - 256x^{2} + 1024 $ x^20 - x^18 - 3x^16 + 11x^14 + x^12 - 40x^10 + 4x^8 + 176x^6 - 192x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{34} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.5
Root			$-0.541828 - 1.30630i$ of defining polynomial
Character	$\chi$	$=$	160.17
Dual form			160.3.m.a.113.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.130791 - 0.130791i) q^{3} +(-4.38731 - 2.39823i) q^{5} +(1.59713 + 1.59713i) q^{7} -8.96579i q^{9} -11.9427i q^{11} +(-9.59714 - 9.59714i) q^{13} +(0.260155 + 0.887490i) q^{15} +(0.857288 + 0.857288i) q^{17} -20.5611 q^{19} -0.417782i q^{21} +(22.1560 - 22.1560i) q^{23} +(13.4970 + 21.0435i) q^{25} +(-2.34977 + 2.34977i) q^{27} +27.3404 q^{29} -40.0267 q^{31} +(-1.56200 + 1.56200i) q^{33} +(-3.17684 - 10.8374i) q^{35} +(1.57131 - 1.57131i) q^{37} +2.51044i q^{39} -37.5504 q^{41} +(49.2602 + 49.2602i) q^{43} +(-21.5020 + 39.3357i) q^{45} +(34.0876 + 34.0876i) q^{47} -43.8983i q^{49} -0.224252i q^{51} +(28.8002 + 28.8002i) q^{53} +(-28.6412 + 52.3962i) q^{55} +(2.68921 + 2.68921i) q^{57} +92.7071 q^{59} -4.82618i q^{61} +(14.3196 - 14.3196i) q^{63} +(19.0895 + 65.1217i) q^{65} +(-54.6048 + 54.6048i) q^{67} -5.79564 q^{69} -59.2198 q^{71} +(34.1124 - 34.1124i) q^{73} +(0.987017 - 4.51761i) q^{75} +(19.0740 - 19.0740i) q^{77} -96.2455i q^{79} -80.0774 q^{81} +(-63.6959 - 63.6959i) q^{83} +(-1.70522 - 5.81716i) q^{85} +(-3.57588 - 3.57588i) q^{87} +3.68406i q^{89} -30.6558i q^{91} +(5.23514 + 5.23514i) q^{93} +(90.2080 + 49.3101i) q^{95} +(46.0410 + 46.0410i) q^{97} -107.075 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{7} + 4 q^{15} - 12 q^{17} + 4 q^{23} - 28 q^{25} + 136 q^{31} + 32 q^{33} - 8 q^{41} - 188 q^{47} - 96 q^{55} - 40 q^{57} - 228 q^{63} - 60 q^{65} - 248 q^{71} - 124 q^{73} + 132 q^{81} + 488 q^{87}+ \cdots + 100 q^{97}+O(q^{100}) $ 20 * q + 4 * q^7 + 4 * q^15 - 12 * q^17 + 4 * q^23 - 28 * q^25 + 136 * q^31 + 32 * q^33 - 8 * q^41 - 188 * q^47 - 96 * q^55 - 40 * q^57 - 228 * q^63 - 60 * q^65 - 248 * q^71 - 124 * q^73 + 132 * q^81 + 488 * q^87 + 488 * q^95 + 100 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.130791	−	0.130791i	−0.0435971	−	0.0435971i	0.684972	−	0.728569i	$-0.259814\pi$
$3$	−0.130791	−	0.130791i	−0.0435971	−	0.0435971i	−0.728569	+	0.684972i	$0.759814\pi$
$4$		0			0
$5$	−4.38731	−	2.39823i	−0.877463	−	0.479645i
$5$	−4.38731	−	2.39823i	−0.877463	−	0.479645i
$6$		0			0
$7$	1.59713	+	1.59713i	0.228162	+	0.228162i	0.811924	−	0.583763i	$-0.198420\pi$
$7$	1.59713	+	1.59713i	0.228162	+	0.228162i	−0.583763	+	0.811924i	$0.698420\pi$
$8$		0			0
$9$		−	8.96579i		−	0.996199i
$10$		0			0
$11$		−	11.9427i		−	1.08570i	−0.839831	−	0.542849i	$-0.817346\pi$
$11$		−	11.9427i		−	1.08570i	0.839831	−	0.542849i	$-0.182654\pi$
$12$		0			0
$13$	−9.59714	−	9.59714i	−0.738241	−	0.738241i	0.233996	−	0.972238i	$-0.424820\pi$
$13$	−9.59714	−	9.59714i	−0.738241	−	0.738241i	−0.972238	+	0.233996i	$0.924820\pi$
$14$		0			0
$15$	0.260155	+	0.887490i	0.0173437	+	0.0591660i
$16$		0			0
$17$	0.857288	+	0.857288i	0.0504287	+	0.0504287i	0.731871	−	0.681443i	$-0.238647\pi$
$17$	0.857288	+	0.857288i	0.0504287	+	0.0504287i	−0.681443	+	0.731871i	$0.738647\pi$
$18$		0			0
$19$	−20.5611			−1.08216			−0.541082	−	0.840970i	$-0.681985\pi$
$19$	−20.5611			−1.08216			−0.541082	+	0.840970i	$0.681985\pi$
$20$		0			0
$21$		−	0.417782i		−	0.0198944i
$22$		0			0
$23$	22.1560	−	22.1560i	0.963306	−	0.963306i	−0.0360441	−	0.999350i	$-0.511476\pi$
$23$	22.1560	−	22.1560i	0.963306	−	0.963306i	0.999350	+	0.0360441i	$0.0114757\pi$
$24$		0			0
$25$	13.4970	+	21.0435i	0.539881	+	0.841741i
$26$		0			0
$27$	−2.34977	+	2.34977i	−0.0870285	+	0.0870285i
$28$		0			0
$29$	27.3404			0.942771			0.471385	−	0.881927i	$-0.343754\pi$
$29$	27.3404			0.942771			0.471385	+	0.881927i	$0.343754\pi$
$30$		0			0
$31$	−40.0267			−1.29118			−0.645591	−	0.763683i	$-0.723389\pi$
$31$	−40.0267			−1.29118			−0.645591	+	0.763683i	$0.723389\pi$
$32$		0			0
$33$	−1.56200	+	1.56200i	−0.0473333	+	0.0473333i
$34$		0			0
$35$	−3.17684	−	10.8374i	−0.0907668	−	0.309640i
$36$		0			0
$37$	1.57131	−	1.57131i	0.0424677	−	0.0424677i	−0.685554	−	0.728022i	$-0.740440\pi$
$37$	1.57131	−	1.57131i	0.0424677	−	0.0424677i	0.728022	+	0.685554i	$0.240440\pi$
$38$		0			0
$39$			2.51044i			0.0643704i
$40$		0			0
$41$	−37.5504			−0.915864			−0.457932	−	0.888987i	$-0.651410\pi$
$41$	−37.5504			−0.915864			−0.457932	+	0.888987i	$0.651410\pi$
$42$		0			0
$43$	49.2602	+	49.2602i	1.14558	+	1.14558i	0.987411	+	0.158174i	$0.0505606\pi$
$43$	49.2602	+	49.2602i	1.14558	+	1.14558i	0.158174	+	0.987411i	$0.449439\pi$
$44$		0			0
$45$	−21.5020	+	39.3357i	−0.477822	+	0.874127i
$46$		0			0
$47$	34.0876	+	34.0876i	0.725268	+	0.725268i	0.969673	−	0.244405i	$-0.0785926\pi$
$47$	34.0876	+	34.0876i	0.725268	+	0.725268i	−0.244405	+	0.969673i	$0.578593\pi$
$48$		0			0
$49$		−	43.8983i		−	0.895884i
$50$		0			0
$51$		−	0.224252i		−	0.00439709i
$52$		0			0
$53$	28.8002	+	28.8002i	0.543401	+	0.543401i	0.924524	−	0.381124i	$-0.124463\pi$
$53$	28.8002	+	28.8002i	0.543401	+	0.543401i	−0.381124	+	0.924524i	$0.624463\pi$
$54$		0			0
$55$	−28.6412	+	52.3962i	−0.520749	+	0.952659i
$56$		0			0
$57$	2.68921	+	2.68921i	0.0471792	+	0.0471792i
$58$		0			0
$59$	92.7071			1.57131			0.785653	−	0.618667i	$-0.212327\pi$
$59$	92.7071			1.57131			0.785653	+	0.618667i	$0.212327\pi$
$60$		0			0
$61$		−	4.82618i		−	0.0791176i	−0.999217	−	0.0395588i	$-0.987405\pi$
$61$		−	4.82618i		−	0.0791176i	0.999217	−	0.0395588i	$-0.0125952\pi$
$62$		0			0
$63$	14.3196	−	14.3196i	0.227294	−	0.227294i
$64$		0			0
$65$	19.0895	+	65.1217i	0.293685	+	1.00187i
$66$		0			0
$67$	−54.6048	+	54.6048i	−0.814997	+	0.814997i	−0.985378	−	0.170381i	$-0.945500\pi$
$67$	−54.6048	+	54.6048i	−0.814997	+	0.814997i	0.170381	+	0.985378i	$0.445500\pi$
$68$		0			0
$69$	−5.79564			−0.0839947
$70$		0			0
$71$	−59.2198			−0.834082			−0.417041	−	0.908888i	$-0.636933\pi$
$71$	−59.2198			−0.834082			−0.417041	+	0.908888i	$0.636933\pi$
$72$		0			0
$73$	34.1124	−	34.1124i	0.467293	−	0.467293i	−0.433743	−	0.901037i	$-0.642807\pi$
$73$	34.1124	−	34.1124i	0.467293	−	0.467293i	0.901037	+	0.433743i	$0.142807\pi$
$74$		0			0
$75$	0.987017	−	4.51761i	0.0131602	−	0.0602347i
$76$		0			0
$77$	19.0740	−	19.0740i	0.247715	−	0.247715i
$78$		0			0
$79$		−	96.2455i		−	1.21830i	−0.793056	−	0.609149i	$-0.791511\pi$
$79$		−	96.2455i		−	1.21830i	0.793056	−	0.609149i	$-0.208489\pi$
$80$		0			0
$81$	−80.0774			−0.988610
$82$		0			0
$83$	−63.6959	−	63.6959i	−0.767421	−	0.767421i	0.210231	−	0.977652i	$-0.432578\pi$
$83$	−63.6959	−	63.6959i	−0.767421	−	0.767421i	−0.977652	+	0.210231i	$0.932578\pi$
$84$		0			0
$85$	−1.70522	−	5.81716i	−0.0200614	−	0.0684372i
$86$		0			0
$87$	−3.57588	−	3.57588i	−0.0411021	−	0.0411021i
$88$		0			0
$89$			3.68406i			0.0413939i	0.999786	+	0.0206970i	$0.00658852\pi$
$89$			3.68406i			0.0413939i	−0.999786	+	0.0206970i	$0.993411\pi$
$90$		0			0
$91$		−	30.6558i		−	0.336877i
$92$		0			0
$93$	5.23514	+	5.23514i	0.0562918	+	0.0562918i
$94$		0			0
$95$	90.2080	+	49.3101i	0.949558	+	0.519054i
$96$		0			0
$97$	46.0410	+	46.0410i	0.474650	+	0.474650i	0.903416	−	0.428766i	$-0.141051\pi$
$97$	46.0410	+	46.0410i	0.474650	+	0.474650i	−0.428766	+	0.903416i	$0.641051\pi$
$98$		0			0
$99$	−107.075			−1.08157
$100$		0			0
$101$		−	108.173i		−	1.07102i	−0.844529	−	0.535510i	$-0.820120\pi$
$101$		−	108.173i		−	1.07102i	0.844529	−	0.535510i	$-0.179880\pi$
$102$		0			0
$103$	50.9112	−	50.9112i	0.494284	−	0.494284i	−0.415369	−	0.909653i	$-0.636348\pi$
$103$	50.9112	−	50.9112i	0.494284	−	0.494284i	0.909653	+	0.415369i	$0.136348\pi$
$104$		0			0
$105$	−1.00194	+	1.83294i	−0.00954225	+	0.0174566i
$106$		0			0
$107$	95.4147	−	95.4147i	0.891726	−	0.891726i	−0.102960	−	0.994686i	$-0.532831\pi$
$107$	95.4147	−	95.4147i	0.891726	−	0.891726i	0.994686	+	0.102960i	$0.0328312\pi$
$108$		0			0
$109$	−46.5432			−0.427002			−0.213501	−	0.976943i	$-0.568487\pi$
$109$	−46.5432			−0.427002			−0.213501	+	0.976943i	$0.568487\pi$
$110$		0			0
$111$	−0.411026			−0.00370294
$112$		0			0
$113$	88.0400	−	88.0400i	0.779115	−	0.779115i	−0.200565	−	0.979680i	$-0.564278\pi$
$113$	88.0400	−	88.0400i	0.779115	−	0.779115i	0.979680	+	0.200565i	$0.0642779\pi$
$114$		0			0
$115$	−150.341	+	44.0703i	−1.30731	+	0.383220i
$116$		0			0
$117$	−86.0459	+	86.0459i	−0.735435	+	0.735435i
$118$		0			0
$119$			2.73841i			0.0230118i
$120$		0			0
$121$	−21.6274			−0.178739
$122$		0			0
$123$	4.91127	+	4.91127i	0.0399290	+	0.0399290i
$124$		0			0
$125$	−8.74856	−	124.693i	−0.0699885	−	0.997548i
$126$		0			0
$127$	−44.3246	−	44.3246i	−0.349012	−	0.349012i	0.510729	−	0.859742i	$-0.329375\pi$
$127$	−44.3246	−	44.3246i	−0.349012	−	0.349012i	−0.859742	+	0.510729i	$0.829375\pi$
$128$		0			0
$129$		−	12.8856i		−	0.0998884i
$130$		0			0
$131$		−	82.8025i		−	0.632080i	−0.948746	−	0.316040i	$-0.897647\pi$
$131$		−	82.8025i		−	0.632080i	0.948746	−	0.316040i	$-0.102353\pi$
$132$		0			0
$133$	−32.8388	−	32.8388i	−0.246908	−	0.246908i
$134$		0			0
$135$	15.9444	−	4.67390i	0.118107	−	0.0346215i
$136$		0			0
$137$	25.0030	+	25.0030i	0.182503	+	0.182503i	0.792446	−	0.609942i	$-0.208807\pi$
$137$	25.0030	+	25.0030i	0.182503	+	0.182503i	−0.609942	+	0.792446i	$0.708807\pi$
$138$		0			0
$139$	104.684			0.753121			0.376561	−	0.926392i	$-0.377107\pi$
$139$	104.684			0.753121			0.376561	+	0.926392i	$0.377107\pi$
$140$		0			0
$141$		−	8.91673i		−	0.0632392i
$142$		0			0
$143$	−114.615	+	114.615i	−0.801507	+	0.801507i
$144$		0			0
$145$	−119.951	−	65.5683i	−0.827246	−	0.452195i
$146$		0			0
$147$	−5.74152	+	5.74152i	−0.0390580	+	0.0390580i
$148$		0			0
$149$	49.3481			0.331196			0.165598	−	0.986193i	$-0.447045\pi$
$149$	49.3481			0.331196			0.165598	+	0.986193i	$0.447045\pi$
$150$		0			0
$151$	22.1078			0.146409			0.0732047	−	0.997317i	$-0.476677\pi$
$151$	22.1078			0.146409			0.0732047	+	0.997317i	$0.476677\pi$
$152$		0			0
$153$	7.68626	−	7.68626i	0.0502370	−	0.0502370i
$154$		0			0
$155$	175.609	+	95.9930i	1.13296	+	0.619309i
$156$		0			0
$157$	−64.7264	+	64.7264i	−0.412270	+	0.412270i	−0.882529	−	0.470258i	$-0.844161\pi$
$157$	−64.7264	+	64.7264i	−0.412270	+	0.412270i	0.470258	+	0.882529i	$0.344161\pi$
$158$		0			0
$159$		−	7.53364i		−	0.0473814i
$160$		0			0
$161$	70.7723			0.439579
$162$		0			0
$163$	−25.7888	−	25.7888i	−0.158213	−	0.158213i	0.623561	−	0.781775i	$-0.285685\pi$
$163$	−25.7888	−	25.7888i	−0.158213	−	0.158213i	−0.781775	+	0.623561i	$0.785685\pi$
$164$		0			0
$165$	10.5990	−	3.10695i	0.0642363	−	0.0188300i
$166$		0			0
$167$	56.4754	+	56.4754i	0.338176	+	0.338176i	0.855681	−	0.517504i	$-0.173139\pi$
$167$	56.4754	+	56.4754i	0.338176	+	0.338176i	−0.517504	+	0.855681i	$0.673139\pi$
$168$		0			0
$169$			15.2101i			0.0900005i
$170$		0			0
$171$			184.346i			1.07805i
$172$		0			0
$173$	135.496	+	135.496i	0.783216	+	0.783216i	0.980372	−	0.197156i	$-0.0631706\pi$
$173$	135.496	+	135.496i	0.783216	+	0.783216i	−0.197156	+	0.980372i	$0.563171\pi$
$174$		0			0
$175$	−12.0528	+	55.1659i	−0.0688729	+	0.315233i
$176$		0			0
$177$	−12.1253	−	12.1253i	−0.0685044	−	0.0685044i
$178$		0			0
$179$	−15.5036			−0.0866121			−0.0433061	−	0.999062i	$-0.513789\pi$
$179$	−15.5036			−0.0866121			−0.0433061	+	0.999062i	$0.513789\pi$
$180$		0			0
$181$			263.672i			1.45675i	0.685179	+	0.728375i	$0.259724\pi$
$181$			263.672i			1.45675i	−0.685179	+	0.728375i	$0.740276\pi$
$182$		0			0
$183$	−0.631222	+	0.631222i	−0.00344930	+	0.00344930i
$184$		0			0
$185$	−10.6622	+	3.12546i	−0.0576333	+	0.0168944i
$186$		0			0
$187$	10.2383	−	10.2383i	0.0547503	−	0.0547503i
$188$		0			0
$189$	−7.50579			−0.0397132
$190$		0			0
$191$	120.714			0.632010			0.316005	−	0.948758i	$-0.397658\pi$
$191$	120.714			0.632010			0.316005	+	0.948758i	$0.397658\pi$
$192$		0			0
$193$	−182.404	+	182.404i	−0.945098	+	0.945098i	−0.998569	−	0.0534716i	$-0.982971\pi$
$193$	−182.404	+	182.404i	−0.945098	+	0.945098i	0.0534716	+	0.998569i	$0.482971\pi$
$194$		0			0
$195$	6.02061	−	11.0141i	0.0308749	−	0.0564826i
$196$		0			0
$197$	224.288	−	224.288i	1.13852	−	1.13852i	0.149799	−	0.988716i	$-0.452137\pi$
$197$	224.288	−	224.288i	1.13852	−	1.13852i	0.988716	−	0.149799i	$-0.0478626\pi$
$198$		0			0
$199$			87.9089i			0.441753i	0.975302	+	0.220877i	$0.0708918\pi$
$199$			87.9089i			0.441753i	−0.975302	+	0.220877i	$0.929108\pi$
$200$		0			0
$201$	14.2837			0.0710631
$202$		0			0
$203$	43.6662	+	43.6662i	0.215104	+	0.215104i
$204$		0			0
$205$	164.745	+	90.0544i	0.803636	+	0.439290i
$206$		0			0
$207$	−198.646	−	198.646i	−0.959644	−	0.959644i
$208$		0			0
$209$			245.554i			1.17490i
$210$		0			0
$211$			119.117i			0.564534i	0.959336	+	0.282267i	$0.0910864\pi$
$211$			119.117i			0.564534i	−0.959336	+	0.282267i	$0.908914\pi$
$212$		0			0
$213$	7.74544	+	7.74544i	0.0363636	+	0.0363636i
$214$		0			0
$215$	−97.9828	−	334.257i	−0.455734	−	1.55468i
$216$		0			0
$217$	−63.9279	−	63.9279i	−0.294599	−	0.294599i
$218$		0			0
$219$	−8.92322			−0.0407453
$220$		0			0
$221$		−	16.4550i		−	0.0744571i
$222$		0			0
$223$	−111.993	+	111.993i	−0.502212	+	0.502212i	−0.912125	−	0.409913i	$-0.865559\pi$
$223$	−111.993	+	111.993i	−0.502212	+	0.502212i	0.409913	+	0.912125i	$0.365559\pi$
$224$		0			0
$225$	188.672	−	121.011i	0.838541	−	0.537829i
$226$		0			0
$227$	−85.8837	+	85.8837i	−0.378342	+	0.378342i	−0.870504	−	0.492162i	$-0.836207\pi$
$227$	−85.8837	+	85.8837i	−0.378342	+	0.378342i	0.492162	+	0.870504i	$0.336207\pi$
$228$		0			0
$229$	−26.5156			−0.115789			−0.0578943	−	0.998323i	$-0.518439\pi$
$229$	−26.5156			−0.115789			−0.0578943	+	0.998323i	$0.518439\pi$
$230$		0			0
$231$	−4.98944			−0.0215993
$232$		0			0
$233$	−71.6569	+	71.6569i	−0.307541	+	0.307541i	−0.843955	−	0.536414i	$-0.819778\pi$
$233$	−71.6569	+	71.6569i	−0.307541	+	0.307541i	0.536414	+	0.843955i	$0.319778\pi$
$234$		0			0
$235$	−67.8033	−	231.303i	−0.288524	−	0.984267i
$236$		0			0
$237$	−12.5881	+	12.5881i	−0.0531143	+	0.0531143i
$238$		0			0
$239$			114.913i			0.480809i	0.970673	+	0.240405i	$0.0772801\pi$
$239$			114.913i			0.480809i	−0.970673	+	0.240405i	$0.922720\pi$
$240$		0			0
$241$	219.080			0.909045			0.454522	−	0.890735i	$-0.349810\pi$
$241$	219.080			0.909045			0.454522	+	0.890735i	$0.349810\pi$
$242$		0			0
$243$	31.6214	+	31.6214i	0.130129	+	0.130129i
$244$		0			0
$245$	−105.278	+	192.596i	−0.429707	+	0.786105i
$246$		0			0
$247$	197.328	+	197.328i	0.798897	+	0.798897i
$248$		0			0
$249$			16.6618i			0.0669147i
$250$		0			0
$251$		−	95.0552i		−	0.378706i	−0.981909	−	0.189353i	$-0.939361\pi$
$251$		−	95.0552i		−	0.378706i	0.981909	−	0.189353i	$-0.0606390\pi$
$252$		0			0
$253$	−264.602	−	264.602i	−1.04586	−	1.04586i
$254$		0			0
$255$	−0.537806	+	0.983862i	−0.00210904	+	0.00385828i
$256$		0			0
$257$	−249.128	−	249.128i	−0.969369	−	0.969369i	0.0301755	−	0.999545i	$-0.490393\pi$
$257$	−249.128	−	249.128i	−0.969369	−	0.969369i	−0.999545	+	0.0301755i	$0.990393\pi$
$258$		0			0
$259$	5.01917			0.0193790
$260$		0			0
$261$		−	245.128i		−	0.939187i
$262$		0			0
$263$	85.6095	−	85.6095i	0.325511	−	0.325511i	−0.525365	−	0.850877i	$-0.676071\pi$
$263$	85.6095	−	85.6095i	0.325511	−	0.325511i	0.850877	+	0.525365i	$0.176071\pi$
$264$		0			0
$265$	−57.2862	−	195.425i	−0.216174	−	0.737453i
$266$		0			0
$267$	0.481843	−	0.481843i	0.00180465	−	0.00180465i
$268$		0			0
$269$	−192.119			−0.714196			−0.357098	−	0.934067i	$-0.616234\pi$
$269$	−192.119			−0.714196			−0.357098	+	0.934067i	$0.616234\pi$
$270$		0			0
$271$	485.780			1.79255			0.896274	−	0.443501i	$-0.146264\pi$
$271$	485.780			1.79255			0.896274	+	0.443501i	$0.146264\pi$
$272$		0			0
$273$	−4.00951	+	4.00951i	−0.0146869	+	0.0146869i
$274$		0			0
$275$	251.316	−	161.191i	0.913876	−	0.586148i
$276$		0			0
$277$	−88.8551	+	88.8551i	−0.320777	+	0.320777i	−0.849065	−	0.528288i	$-0.822834\pi$
$277$	−88.8551	+	88.8551i	−0.320777	+	0.320777i	0.528288	+	0.849065i	$0.322834\pi$
$278$		0			0
$279$			358.871i			1.28627i
$280$		0			0
$281$	390.006			1.38792			0.693961	−	0.720012i	$-0.255864\pi$
$281$	390.006			1.38792			0.693961	+	0.720012i	$0.255864\pi$
$282$		0			0
$283$	−121.062	−	121.062i	−0.427779	−	0.427779i	0.460092	−	0.887871i	$-0.347816\pi$
$283$	−121.062	−	121.062i	−0.427779	−	0.427779i	−0.887871	+	0.460092i	$0.847816\pi$
$284$		0			0
$285$	−5.34908	−	18.2478i	−0.0187687	−	0.0640272i
$286$		0			0
$287$	−59.9730	−	59.9730i	−0.208965	−	0.208965i
$288$		0			0
$289$		−	287.530i		−	0.994914i
$290$		0			0
$291$		−	12.0435i		−	0.0413867i
$292$		0			0
$293$	−244.956	−	244.956i	−0.836026	−	0.836026i	0.152307	−	0.988333i	$-0.451330\pi$
$293$	−244.956	−	244.956i	−0.836026	−	0.836026i	−0.988333	+	0.152307i	$0.951330\pi$
$294$		0			0
$295$	−406.735	−	222.332i	−1.37876	−	0.753669i
$296$		0			0
$297$	28.0625	+	28.0625i	0.0944866	+	0.0944866i
$298$		0			0
$299$	−425.269			−1.42230
$300$		0			0
$301$			157.350i			0.522757i
$302$		0			0
$303$	−14.1481	+	14.1481i	−0.0466934	+	0.0466934i
$304$		0			0
$305$	−11.5743	+	21.1739i	−0.0379484	+	0.0694228i
$306$		0			0
$307$	135.324	−	135.324i	0.440796	−	0.440796i	−0.451483	−	0.892280i	$-0.649105\pi$
$307$	135.324	−	135.324i	0.440796	−	0.440796i	0.892280	+	0.451483i	$0.149105\pi$
$308$		0			0
$309$	−13.3175			−0.0430987
$310$		0			0
$311$	−225.951			−0.726531			−0.363266	−	0.931686i	$-0.618338\pi$
$311$	−225.951			−0.726531			−0.363266	+	0.931686i	$0.618338\pi$
$312$		0			0
$313$	−230.622	+	230.622i	−0.736812	+	0.736812i	−0.971960	−	0.235148i	$-0.924443\pi$
$313$	−230.622	+	230.622i	−0.736812	+	0.736812i	0.235148	+	0.971960i	$0.424443\pi$
$314$		0			0
$315$	−97.1659	+	28.4828i	−0.308463	+	0.0904217i
$316$		0			0
$317$	221.563	−	221.563i	0.698938	−	0.698938i	−0.265243	−	0.964182i	$-0.585452\pi$
$317$	221.563	−	221.563i	0.698938	−	0.698938i	0.964182	+	0.265243i	$0.0854522\pi$
$318$		0			0
$319$		−	326.517i		−	1.02356i
$320$		0			0
$321$	−24.9588			−0.0777534
$322$		0			0
$323$	−17.6268	−	17.6268i	−0.0545721	−	0.0545721i
$324$		0			0
$325$	72.4248	−	331.490i	0.222846	−	1.01997i
$326$		0			0
$327$	6.08745	+	6.08745i	0.0186161	+	0.0186161i
$328$		0			0
$329$			108.885i			0.330957i
$330$		0			0
$331$		−	141.212i		−	0.426624i	−0.976984	−	0.213312i	$-0.931575\pi$
$331$		−	141.212i		−	0.426624i	0.976984	−	0.213312i	$-0.0684250\pi$
$332$		0			0
$333$	−14.0880	−	14.0880i	−0.0423063	−	0.0423063i
$334$		0			0
$335$	370.523	−	108.614i	1.10604	−	0.324220i
$336$		0			0
$337$	225.465	+	225.465i	0.669035	+	0.669035i	0.957493	−	0.288458i	$-0.0931424\pi$
$337$	225.465	+	225.465i	0.669035	+	0.669035i	−0.288458	+	0.957493i	$0.593142\pi$
$338$		0			0
$339$	−23.0297			−0.0679343
$340$		0			0
$341$			478.025i			1.40183i
$342$		0			0
$343$	148.371	−	148.371i	0.432568	−	0.432568i
$344$		0			0
$345$	25.4273	+	13.8992i	0.0737022	+	0.0402877i
$346$		0			0
$347$	−346.013	+	346.013i	−0.997155	+	0.997155i	−0.999996	−	0.00284067i	$-0.999096\pi$
$347$	−346.013	+	346.013i	−0.997155	+	0.997155i	0.00284067	+	0.999996i	$0.499096\pi$
$348$		0			0
$349$	428.411			1.22754			0.613769	−	0.789486i	$-0.289653\pi$
$349$	428.411			1.22754			0.613769	+	0.789486i	$0.289653\pi$
$350$		0			0
$351$	45.1021			0.128496
$352$		0			0
$353$	25.9724	−	25.9724i	0.0735762	−	0.0735762i	−0.669361	−	0.742937i	$-0.733432\pi$
$353$	25.9724	−	25.9724i	0.0735762	−	0.0735762i	0.742937	+	0.669361i	$0.233432\pi$
$354$		0			0
$355$	259.816	+	142.022i	0.731876	+	0.400063i
$356$		0			0
$357$	0.358160	−	0.358160i	0.00100325	−	0.00100325i
$358$		0			0
$359$			288.043i			0.802348i	0.916002	+	0.401174i	$0.131398\pi$
$359$			288.043i			0.802348i	−0.916002	+	0.401174i	$0.868602\pi$
$360$		0			0
$361$	61.7587			0.171077
$362$		0			0
$363$	2.82868	+	2.82868i	0.00779249	+	0.00779249i
$364$		0			0
$365$	−231.471	+	67.8526i	−0.634168	+	0.185898i
$366$		0			0
$367$	−160.854	−	160.854i	−0.438295	−	0.438295i	0.453143	−	0.891438i	$-0.350303\pi$
$367$	−160.854	−	160.854i	−0.438295	−	0.438295i	−0.891438	+	0.453143i	$0.850303\pi$
$368$		0			0
$369$			336.669i			0.912382i
$370$		0			0
$371$			91.9956i			0.247966i
$372$		0			0
$373$	360.121	+	360.121i	0.965471	+	0.965471i	0.999423	−	0.0339529i	$-0.0108096\pi$
$373$	360.121	+	360.121i	0.965471	+	0.965471i	−0.0339529	+	0.999423i	$0.510810\pi$
$374$		0			0
$375$	−15.1646	+	17.4531i	−0.0404389	+	0.0465415i
$376$		0			0
$377$	−262.389	−	262.389i	−0.695992	−	0.695992i
$378$		0			0
$379$	−64.1572			−0.169280			−0.0846402	−	0.996412i	$-0.526974\pi$
$379$	−64.1572			−0.169280			−0.0846402	+	0.996412i	$0.526974\pi$
$380$		0			0
$381$			11.5945i			0.0304319i
$382$		0			0
$383$	−376.877	+	376.877i	−0.984014	+	0.984014i	−0.999874	−	0.0158604i	$-0.994951\pi$
$383$	−376.877	+	376.877i	−0.984014	+	0.984014i	0.0158604	+	0.999874i	$0.494951\pi$
$384$		0			0
$385$	−129.428	+	37.9399i	−0.336175	+	0.0985452i
$386$		0			0
$387$	441.656	−	441.656i	1.14123	−	1.14123i
$388$		0			0
$389$	−10.3794			−0.0266823			−0.0133411	−	0.999911i	$-0.504247\pi$
$389$	−10.3794			−0.0266823			−0.0133411	+	0.999911i	$0.504247\pi$
$390$		0			0
$391$	37.9882			0.0971566
$392$		0			0
$393$	−10.8298	+	10.8298i	−0.0275569	+	0.0275569i
$394$		0			0
$395$	−230.818	+	422.259i	−0.584350	+	1.06901i
$396$		0			0
$397$	−184.458	+	184.458i	−0.464630	+	0.464630i	−0.900169	−	0.435540i	$-0.856558\pi$
$397$	−184.458	+	184.458i	−0.464630	+	0.464630i	0.435540	+	0.900169i	$0.356558\pi$
$398$		0			0
$399$			8.59006i			0.0215290i
$400$		0			0
$401$	−262.943			−0.655719			−0.327859	−	0.944727i	$-0.606327\pi$
$401$	−262.943			−0.655719			−0.327859	+	0.944727i	$0.606327\pi$
$402$		0			0
$403$	384.141	+	384.141i	0.953204	+	0.953204i
$404$		0			0
$405$	351.325	+	192.044i	0.867468	+	0.474182i
$406$		0			0
$407$	−18.7656	−	18.7656i	−0.0461071	−	0.0461071i
$408$		0			0
$409$		−	245.618i		−	0.600532i	−0.953855	−	0.300266i	$-0.902925\pi$
$409$		−	245.618i		−	0.600532i	0.953855	−	0.300266i	$-0.0970755\pi$
$410$		0			0
$411$		−	6.54034i		−	0.0159132i
$412$		0			0
$413$	148.065	+	148.065i	0.358512	+	0.358512i
$414$		0			0
$415$	126.697	+	432.211i	0.305293	+	1.04147i
$416$		0			0
$417$	−13.6917	−	13.6917i	−0.0328339	−	0.0328339i
$418$		0			0
$419$	673.011			1.60623			0.803116	−	0.595823i	$-0.203174\pi$
$419$	673.011			1.60623			0.803116	+	0.595823i	$0.203174\pi$
$420$		0			0
$421$		−	701.227i		−	1.66562i	−0.553557	−	0.832811i	$-0.686730\pi$
$421$		−	701.227i		−	1.66562i	0.553557	−	0.832811i	$-0.313270\pi$
$422$		0			0
$423$	305.622	−	305.622i	0.722511	−	0.722511i
$424$		0			0
$425$	−6.46952	+	29.6112i	−0.0152224	+	0.0696734i
$426$		0			0
$427$	7.70804	−	7.70804i	0.0180516	−	0.0180516i
$428$		0			0
$429$	29.9814			0.0698868
$430$		0			0
$431$	−405.559			−0.940973			−0.470486	−	0.882407i	$-0.655922\pi$
$431$	−405.559			−0.940973			−0.470486	+	0.882407i	$0.655922\pi$
$432$		0			0
$433$	145.764	−	145.764i	0.336638	−	0.336638i	−0.518462	−	0.855100i	$-0.673495\pi$
$433$	145.764	−	145.764i	0.336638	−	0.336638i	0.855100	+	0.518462i	$0.173495\pi$
$434$		0			0
$435$	7.11274	+	24.2643i	0.0163511	+	0.0557800i
$436$		0			0
$437$	−455.553	+	455.553i	−1.04245	+	1.04245i
$438$		0			0
$439$		−	62.3888i		−	0.142116i	−0.997472	−	0.0710579i	$-0.977362\pi$
$439$		−	62.3888i		−	0.142116i	0.997472	−	0.0710579i	$-0.0226375\pi$
$440$		0			0
$441$	−393.583			−0.892479
$442$		0			0
$443$	−169.632	−	169.632i	−0.382918	−	0.382918i	0.489235	−	0.872152i	$-0.337276\pi$
$443$	−169.632	−	169.632i	−0.382918	−	0.382918i	−0.872152	+	0.489235i	$0.837276\pi$
$444$		0			0
$445$	8.83520	−	16.1631i	0.0198544	−	0.0363216i
$446$		0			0
$447$	−6.45431	−	6.45431i	−0.0144392	−	0.0144392i
$448$		0			0
$449$			17.0056i			0.0378743i	0.999821	+	0.0189371i	$0.00602824\pi$
$449$			17.0056i			0.0378743i	−0.999821	+	0.0189371i	$0.993972\pi$
$450$		0			0
$451$			448.452i			0.994351i
$452$		0			0
$453$	−2.89151	−	2.89151i	−0.00638303	−	0.00638303i
$454$		0			0
$455$	−73.5195	+	134.497i	−0.161581	+	0.295597i
$456$		0			0
$457$	559.163	+	559.163i	1.22355	+	1.22355i	0.966360	+	0.257191i	$0.0827971\pi$
$457$	559.163	+	559.163i	1.22355	+	1.22355i	0.257191	+	0.966360i	$0.417203\pi$
$458$		0			0
$459$	−4.02886			−0.00877747
$460$		0			0
$461$			327.625i			0.710683i	0.934737	+	0.355341i	$0.115635\pi$
$461$			327.625i			0.710683i	−0.934737	+	0.355341i	$0.884365\pi$
$462$		0			0
$463$	−605.934	+	605.934i	−1.30871	+	1.30871i	−0.386367	+	0.922345i	$0.626270\pi$
$463$	−605.934	+	605.934i	−1.30871	+	1.30871i	−0.922345	+	0.386367i	$0.873730\pi$
$464$		0			0
$465$	−10.4132	−	35.5232i	−0.0223939	−	0.0763941i
$466$		0			0
$467$	−83.9231	+	83.9231i	−0.179707	+	0.179707i	−0.791228	−	0.611521i	$-0.790558\pi$
$467$	−83.9231	+	83.9231i	−0.179707	+	0.179707i	0.611521	+	0.791228i	$0.290558\pi$
$468$		0			0
$469$	−174.422			−0.371903
$470$		0			0
$471$	16.9313			0.0359476
$472$		0			0
$473$	588.298	−	588.298i	1.24376	−	1.24376i
$474$		0			0
$475$	−277.514	−	432.678i	−0.584239	−	0.910901i
$476$		0			0
$477$	258.217	−	258.217i	0.541335	−	0.541335i
$478$		0			0
$479$		−	831.992i		−	1.73694i	−0.495746	−	0.868468i	$-0.665105\pi$
$479$		−	831.992i		−	1.73694i	0.495746	−	0.868468i	$-0.334895\pi$
$480$		0			0
$481$	−30.1601			−0.0627028
$482$		0			0
$483$	−9.25640	−	9.25640i	−0.0191644	−	0.0191644i
$484$		0			0
$485$	−91.5797	−	312.413i	−0.188824	−	0.644151i
$486$		0			0
$487$	373.676	+	373.676i	0.767301	+	0.767301i	0.977631	−	0.210329i	$-0.0674537\pi$
$487$	373.676	+	373.676i	0.767301	+	0.767301i	−0.210329	+	0.977631i	$0.567454\pi$
$488$		0			0
$489$			6.74590i			0.0137953i
$490$		0			0
$491$			42.8051i			0.0871795i	0.999050	+	0.0435898i	$0.0138794\pi$
$491$			42.8051i			0.0871795i	−0.999050	+	0.0435898i	$0.986121\pi$
$492$		0			0
$493$	23.4386	+	23.4386i	0.0475427	+	0.0475427i
$494$		0			0
$495$	469.773	+	256.791i	0.949037	+	0.518770i
$496$		0			0
$497$	−94.5819	−	94.5819i	−0.190306	−	0.190306i
$498$		0			0
$499$	485.100			0.972143			0.486072	−	0.873919i	$-0.338429\pi$
$499$	485.100			0.972143			0.486072	+	0.873919i	$0.338429\pi$
$500$		0			0
$501$		−	14.7730i		−	0.0294870i
$502$		0			0
$503$	666.926	−	666.926i	1.32590	−	1.32590i	0.416980	−	0.908916i	$-0.363088\pi$
$503$	666.926	−	666.926i	1.32590	−	1.32590i	0.908916	−	0.416980i	$-0.136912\pi$
$504$		0			0
$505$	−259.423	+	474.589i	−0.513709	+	0.939780i
$506$		0			0
$507$	1.98935	−	1.98935i	0.00392376	−	0.00392376i
$508$		0			0
$509$	−779.971			−1.53236			−0.766180	−	0.642626i	$-0.777845\pi$
$509$	−779.971			−1.53236			−0.766180	+	0.642626i	$0.777845\pi$
$510$		0			0
$511$	108.964			0.213237
$512$		0			0
$513$	48.3138	−	48.3138i	0.0941790	−	0.0941790i
$514$		0			0
$515$	−345.460	+	101.267i	−0.670796	+	0.196635i
$516$		0			0
$517$	407.097	−	407.097i	0.787422	−	0.787422i
$518$		0			0
$519$		−	35.4435i		−	0.0682919i
$520$		0			0
$521$	−736.972			−1.41453			−0.707267	−	0.706947i	$-0.750072\pi$
$521$	−736.972			−1.41453			−0.707267	+	0.706947i	$0.750072\pi$
$522$		0			0
$523$	−671.690	−	671.690i	−1.28430	−	1.28430i	−0.938195	−	0.346108i	$-0.887503\pi$
$523$	−671.690	−	671.690i	−1.28430	−	1.28430i	−0.346108	−	0.938195i	$-0.612497\pi$
$524$		0			0
$525$	8.79161	−	5.63882i	0.0167459	−	0.0107406i
$526$		0			0
$527$	−34.3144	−	34.3144i	−0.0651127	−	0.0651127i
$528$		0			0
$529$		−	452.780i		−	0.855917i
$530$		0			0
$531$		−	831.192i		−	1.56533i
$532$		0			0
$533$	360.377	+	360.377i	0.676129	+	0.676129i
$534$		0			0
$535$	−647.440	+	189.788i	−1.21017	+	0.354744i
$536$		0			0
$537$	2.02773	+	2.02773i	0.00377604	+	0.00377604i
$538$		0			0
$539$	−524.263			−0.972659
$540$		0			0
$541$		−	1039.61i		−	1.92164i	−0.277168	−	0.960822i	$-0.589396\pi$
$541$		−	1039.61i		−	1.92164i	0.277168	−	0.960822i	$-0.410604\pi$
$542$		0			0
$543$	34.4860	−	34.4860i	0.0635101	−	0.0635101i
$544$		0			0
$545$	204.200	+	111.621i	0.374678	+	0.204809i
$546$		0			0
$547$	−238.506	+	238.506i	−0.436026	+	0.436026i	−0.890672	−	0.454646i	$-0.849766\pi$
$547$	−238.506	+	238.506i	−0.436026	+	0.436026i	0.454646	+	0.890672i	$0.349766\pi$
$548$		0			0
$549$	−43.2705			−0.0788169
$550$		0			0
$551$	−562.148			−1.02023
$552$		0			0
$553$	153.717	−	153.717i	0.277969	−	0.277969i
$554$		0			0
$555$	1.80330	+	0.985734i	0.00324919	+	0.00177610i
$556$		0			0
$557$	−263.387	+	263.387i	−0.472867	+	0.472867i	−0.902841	−	0.429974i	$-0.858523\pi$
$557$	−263.387	+	263.387i	−0.472867	+	0.472867i	0.429974	+	0.902841i	$0.358523\pi$
$558$		0			0
$559$		−	945.513i		−	1.69144i
$560$		0			0
$561$	−2.67816			−0.00477391
$562$		0			0
$563$	−160.698	−	160.698i	−0.285431	−	0.285431i	0.549839	−	0.835270i	$-0.314689\pi$
$563$	−160.698	−	160.698i	−0.285431	−	0.285431i	−0.835270	+	0.549839i	$0.814689\pi$
$564$		0			0
$565$	−597.399	+	175.119i	−1.05734	+	0.309946i
$566$		0			0
$567$	−127.894	−	127.894i	−0.225563	−	0.225563i
$568$		0			0
$569$			407.195i			0.715633i	0.933792	+	0.357817i	$0.116479\pi$
$569$			407.195i			0.715633i	−0.933792	+	0.357817i	$0.883521\pi$
$570$		0			0
$571$			131.146i			0.229678i	0.993384	+	0.114839i	$0.0366351\pi$
$571$			131.146i			0.229678i	−0.993384	+	0.114839i	$0.963365\pi$
$572$		0			0
$573$	−15.7883	−	15.7883i	−0.0275538	−	0.0275538i
$574$		0			0
$575$	765.282	+	167.201i	1.33093	+	0.290784i
$576$		0			0
$577$	417.933	+	417.933i	0.724321	+	0.724321i	0.969482	−	0.245162i	$-0.0788410\pi$
$577$	417.933	+	417.933i	0.724321	+	0.724321i	−0.245162	+	0.969482i	$0.578841\pi$
$578$		0			0
$579$	47.7137			0.0824071
$580$		0			0
$581$		−	203.462i		−	0.350192i
$582$		0			0
$583$	343.952	−	343.952i	0.589969	−	0.589969i
$584$		0			0
$585$	583.868	−	171.153i	0.998064	−	0.292569i
$586$		0			0
$587$	−212.882	+	212.882i	−0.362660	+	0.362660i	−0.864791	−	0.502131i	$-0.832549\pi$
$587$	−212.882	+	212.882i	−0.362660	+	0.362660i	0.502131	+	0.864791i	$0.332549\pi$
$588$		0			0
$589$	822.992			1.39727
$590$		0			0
$591$	−58.6697			−0.0992720
$592$		0			0
$593$	97.2530	−	97.2530i	0.164002	−	0.164002i	−0.620335	−	0.784337i	$-0.713003\pi$
$593$	97.2530	−	97.2530i	0.164002	−	0.164002i	0.784337	+	0.620335i	$0.213003\pi$
$594$		0			0
$595$	6.56731	−	12.0142i	0.0110375	−	0.0201920i
$596$		0			0
$597$	11.4977	−	11.4977i	0.0192592	−	0.0192592i
$598$		0			0
$599$			712.479i			1.18945i	0.803930	+	0.594723i	$0.202738\pi$
$599$			712.479i			1.18945i	−0.803930	+	0.594723i	$0.797262\pi$
$600$		0			0
$601$	217.550			0.361980			0.180990	−	0.983485i	$-0.442070\pi$
$601$	217.550			0.361980			0.180990	+	0.983485i	$0.442070\pi$
$602$		0			0
$603$	489.575	+	489.575i	0.811899	+	0.811899i
$604$		0			0
$605$	94.8861	+	51.8674i	0.156837	+	0.0857312i
$606$		0			0
$607$	−12.6560	−	12.6560i	−0.0208501	−	0.0208501i	0.696605	−	0.717455i	$-0.254693\pi$
$607$	−12.6560	−	12.6560i	−0.0208501	−	0.0208501i	−0.717455	+	0.696605i	$0.754693\pi$
$608$		0			0
$609$		−	11.4223i		−	0.0187558i
$610$		0			0
$611$		−	654.287i		−	1.07085i
$612$		0			0
$613$	−523.841	−	523.841i	−0.854552	−	0.854552i	0.136138	−	0.990690i	$-0.456531\pi$
$613$	−523.841	−	523.841i	−0.854552	−	0.854552i	−0.990690	+	0.136138i	$0.956531\pi$
$614$		0			0
$615$	−9.76895	−	33.3256i	−0.0158845	−	0.0541880i
$616$		0			0
$617$	−331.035	−	331.035i	−0.536523	−	0.536523i	0.385983	−	0.922506i	$-0.373862\pi$
$617$	−331.035	−	331.035i	−0.536523	−	0.536523i	−0.922506	+	0.385983i	$0.873862\pi$
$618$		0			0
$619$	277.907			0.448961			0.224481	−	0.974479i	$-0.427931\pi$
$619$	277.907			0.448961			0.224481	+	0.974479i	$0.427931\pi$
$620$		0			0
$621$			104.123i			0.167670i
$622$		0			0
$623$	−5.88393	+	5.88393i	−0.00944451	+	0.00944451i
$624$		0			0
$625$	−260.660	+	568.050i	−0.417057	+	0.908881i
$626$		0			0
$627$	32.1164	−	32.1164i	0.0512223	−	0.0512223i
$628$		0			0
$629$	2.69412			0.00428318
$630$		0			0
$631$	−425.237			−0.673910			−0.336955	−	0.941521i	$-0.609397\pi$
$631$	−425.237			−0.673910			−0.336955	+	0.941521i	$0.609397\pi$
$632$		0			0
$633$	15.5794	−	15.5794i	0.0246121	−	0.0246121i
$634$		0			0
$635$	88.1655	+	300.766i	0.138843	+	0.473647i
$636$		0			0
$637$	−421.298	+	421.298i	−0.661379	+	0.661379i
$638$		0			0
$639$			530.952i			0.830911i
$640$		0			0
$641$	−474.056			−0.739558			−0.369779	−	0.929120i	$-0.620567\pi$
$641$	−474.056			−0.739558			−0.369779	+	0.929120i	$0.620567\pi$
$642$		0			0
$643$	490.408	+	490.408i	0.762687	+	0.762687i	0.976807	−	0.214121i	$-0.0686885\pi$
$643$	490.408	+	490.408i	0.762687	+	0.762687i	−0.214121	+	0.976807i	$0.568689\pi$
$644$		0			0
$645$	−30.9026	+	56.5332i	−0.0479110	+	0.0876483i
$646$		0			0
$647$	319.187	+	319.187i	0.493334	+	0.493334i	0.909355	−	0.416021i	$-0.136576\pi$
$647$	319.187	+	319.187i	0.493334	+	0.493334i	−0.416021	+	0.909355i	$0.636576\pi$
$648$		0			0
$649$		−	1107.17i		−	1.70596i
$650$		0			0
$651$			16.7224i			0.0256873i
$652$		0			0
$653$	95.6351	+	95.6351i	0.146455	+	0.146455i	0.776532	−	0.630077i	$-0.216977\pi$
$653$	95.6351	+	95.6351i	0.146455	+	0.146455i	−0.630077	+	0.776532i	$0.716977\pi$
$654$		0			0
$655$	−198.579	+	363.280i	−0.303174	+	0.554626i
$656$		0			0
$657$	−305.845	−	305.845i	−0.465517	−	0.465517i
$658$		0			0
$659$	−295.703			−0.448715			−0.224358	−	0.974507i	$-0.572028\pi$
$659$	−295.703			−0.448715			−0.224358	+	0.974507i	$0.572028\pi$
$660$		0			0
$661$			1223.87i			1.85154i	0.378088	+	0.925770i	$0.376582\pi$
$661$			1223.87i			1.85154i	−0.378088	+	0.925770i	$0.623418\pi$
$662$		0			0
$663$	−2.15217	+	2.15217i	−0.00324611	+	0.00324611i
$664$		0			0
$665$	65.3192	+	222.829i	0.0982244	+	0.335081i
$666$		0			0
$667$	605.754	−	605.754i	0.908177	−	0.908177i
$668$		0			0
$669$	29.2955			0.0437900
$670$		0			0
$671$	−57.6374			−0.0858978
$672$		0			0
$673$	−95.3663	+	95.3663i	−0.141703	+	0.141703i	−0.774400	−	0.632697i	$-0.781948\pi$
$673$	−95.3663	+	95.3663i	−0.141703	+	0.141703i	0.632697	+	0.774400i	$0.281948\pi$
$674$		0			0
$675$	−81.1623	−	17.7325i	−0.120241	−	0.0262704i
$676$		0			0
$677$	208.006	−	208.006i	0.307247	−	0.307247i	−0.536594	−	0.843841i	$-0.680289\pi$
$677$	208.006	−	208.006i	0.307247	−	0.307247i	0.843841	+	0.536594i	$0.180289\pi$
$678$		0			0
$679$			147.067i			0.216594i
$680$		0			0
$681$	22.4657			0.0329892
$682$		0			0
$683$	704.881	+	704.881i	1.03204	+	1.03204i	0.999470	+	0.0325668i	$0.0103682\pi$
$683$	704.881	+	704.881i	1.03204	+	1.03204i	0.0325668	+	0.999470i	$0.489632\pi$
$684$		0			0
$685$	−49.7331	−	169.658i	−0.0726030	−	0.247677i
$686$		0			0
$687$	3.46801	+	3.46801i	0.00504805	+	0.00504805i
$688$		0			0
$689$		−	552.800i		−	0.802321i
$690$		0			0
$691$			814.437i			1.17864i	0.807901	+	0.589318i	$0.200603\pi$
$691$			814.437i			1.17864i	−0.807901	+	0.589318i	$0.799397\pi$
$692$		0			0
$693$	−171.014	−	171.014i	−0.246773	−	0.246773i
$694$		0			0
$695$	−459.281	−	251.056i	−0.660836	−	0.361231i
$696$		0			0
$697$	−32.1915	−	32.1915i	−0.0461858	−	0.0461858i
$698$		0			0
$699$	18.7442			0.0268158
$700$		0			0
$701$			39.4607i			0.0562920i	0.999604	+	0.0281460i	$0.00896033\pi$
$701$			39.4607i			0.0562920i	−0.999604	+	0.0281460i	$0.991040\pi$
$702$		0			0
$703$	−32.3078	+	32.3078i	−0.0459570	+	0.0459570i
$704$		0			0
$705$	−21.3843	+	39.1205i	−0.0303324	+	0.0554900i
$706$		0			0
$707$	172.767	−	172.767i	0.244366	−	0.244366i
$708$		0			0
$709$	1177.86			1.66130			0.830648	−	0.556798i	$-0.187970\pi$
$709$	1177.86			1.66130			0.830648	+	0.556798i	$0.187970\pi$
$710$		0			0
$711$	−862.917			−1.21367
$712$		0			0
$713$	−886.832	+	886.832i	−1.24380	+	1.24380i
$714$		0			0
$715$	777.728	−	227.980i	1.08773	−	0.318853i
$716$		0			0
$717$	15.0297	−	15.0297i	0.0209619	−	0.0209619i
$718$		0			0
$719$		−	242.835i		−	0.337740i	−0.985638	−	0.168870i	$-0.945988\pi$
$719$		−	242.835i		−	0.337740i	0.985638	−	0.168870i	$-0.0540119\pi$
$720$		0			0
$721$	162.624			0.225553
$722$		0			0
$723$	−28.6537	−	28.6537i	−0.0396317	−	0.0396317i
$724$		0			0
$725$	369.014	+	575.338i	0.508984	+	0.793569i
$726$		0			0
$727$	619.622	+	619.622i	0.852300	+	0.852300i	0.990416	−	0.138116i	$-0.0441048\pi$
$727$	619.622	+	619.622i	0.852300	+	0.852300i	−0.138116	+	0.990416i	$0.544105\pi$
$728$		0			0
$729$			712.425i			0.977264i
$730$		0			0
$731$			84.4603i			0.115541i
$732$		0			0
$733$	281.127	+	281.127i	0.383529	+	0.383529i	0.872372	−	0.488843i	$-0.162581\pi$
$733$	281.127	+	281.127i	0.383529	+	0.383529i	−0.488843	+	0.872372i	$0.662581\pi$
$734$		0			0
$735$	38.9593	−	11.4204i	0.0530059	−	0.0155379i
$736$		0			0
$737$	652.127	+	652.127i	0.884841	+	0.884841i
$738$		0			0
$739$	−1109.74			−1.50168			−0.750839	−	0.660485i	$-0.770351\pi$
$739$	−1109.74			−1.50168			−0.750839	+	0.660485i	$0.770351\pi$
$740$		0			0
$741$		−	51.6175i		−	0.0696592i
$742$		0			0
$743$	339.850	−	339.850i	0.457403	−	0.457403i	−0.440399	−	0.897802i	$-0.645163\pi$
$743$	339.850	−	339.850i	0.457403	−	0.457403i	0.897802	+	0.440399i	$0.145163\pi$
$744$		0			0
$745$	−216.506	−	118.348i	−0.290612	−	0.158856i
$746$		0			0
$747$	−571.084	+	571.084i	−0.764504	+	0.764504i
$748$		0			0
$749$	304.780			0.406916
$750$		0			0
$751$	980.557			1.30567			0.652834	−	0.757501i	$-0.273580\pi$
$751$	980.557			1.30567			0.652834	+	0.757501i	$0.273580\pi$
$752$		0			0
$753$	−12.4324	+	12.4324i	−0.0165105	+	0.0165105i
$754$		0			0
$755$	−96.9939	−	53.0195i	−0.128469	−	0.0702245i
$756$		0			0
$757$	−101.564	+	101.564i	−0.134166	+	0.134166i	−0.771001	−	0.636834i	$-0.780243\pi$
$757$	−101.564	+	101.564i	−0.134166	+	0.134166i	0.636834	+	0.771001i	$0.280243\pi$
$758$		0			0
$759$			69.2154i			0.0911929i
$760$		0			0
$761$	767.675			1.00877			0.504386	−	0.863478i	$-0.331719\pi$
$761$	767.675			1.00877			0.504386	+	0.863478i	$0.331719\pi$
$762$		0			0
$763$	−74.3357	−	74.3357i	−0.0974256	−	0.0974256i
$764$		0			0
$765$	−52.1554	+	15.2886i	−0.0681770	+	0.0199852i
$766$		0			0
$767$	−889.722	−	889.722i	−1.16000	−	1.16000i
$768$		0			0
$769$			331.840i			0.431522i	0.976446	+	0.215761i	$0.0692232\pi$
$769$			331.840i			0.431522i	−0.976446	+	0.215761i	$0.930777\pi$
$770$		0			0
$771$			65.1675i			0.0845234i
$772$		0			0
$773$	−180.328	−	180.328i	−0.233283	−	0.233283i	0.580779	−	0.814061i	$-0.302748\pi$
$773$	−180.328	−	180.328i	−0.233283	−	0.233283i	−0.814061	+	0.580779i	$0.802748\pi$
$774$		0			0
$775$	−540.241	−	842.302i	−0.697085	−	1.08684i
$776$		0			0
$777$	−0.656463	−	0.656463i	−0.000844869	−	0.000844869i
$778$		0			0
$779$	772.078			0.991114
$780$		0			0
$781$			707.243i			0.905561i
$782$		0			0
$783$	−64.2435	+	64.2435i	−0.0820479	+	0.0820479i
$784$		0			0
$785$	439.204	−	128.747i	0.559495	−	0.164008i
$786$		0			0
$787$	−945.029	+	945.029i	−1.20080	+	1.20080i	−0.226876	+	0.973924i	$0.572851\pi$
$787$	−945.029	+	945.029i	−1.20080	+	1.20080i	−0.973924	+	0.226876i	$0.927149\pi$
$788$		0			0
$789$	−22.3940			−0.0283827
$790$		0			0
$791$	281.223			0.355529
$792$		0			0
$793$	−46.3175	+	46.3175i	−0.0584079	+	0.0584079i
$794$		0			0
$795$	−18.0674	+	33.0524i	−0.0227263	+	0.0415754i
$796$		0			0
$797$	680.774	−	680.774i	0.854171	−	0.854171i	−0.136473	−	0.990644i	$-0.543577\pi$
$797$	680.774	−	680.774i	0.854171	−	0.854171i	0.990644	+	0.136473i	$0.0435766\pi$
$798$		0			0
$799$			58.4458i			0.0731487i
$800$		0			0
$801$	33.0305			0.0412366
$802$		0			0
$803$	−407.393	−	407.393i	−0.507339	−	0.507339i
$804$		0			0
$805$	−310.500	−	169.728i	−0.385714	−	0.210842i
$806$		0			0
$807$	25.1275	+	25.1275i	0.0311369	+	0.0311369i
$808$		0			0
$809$			427.952i			0.528989i	0.964387	+	0.264495i	$0.0852051\pi$
$809$			427.952i			0.528989i	−0.964387	+	0.264495i	$0.914795\pi$
$810$		0			0
$811$		−	1222.46i		−	1.50735i	−0.657245	−	0.753677i	$-0.728278\pi$
$811$		−	1222.46i		−	1.50735i	0.657245	−	0.753677i	$-0.271722\pi$
$812$		0			0
$813$	−63.5359	−	63.5359i	−0.0781499	−	0.0781499i
$814$		0			0
$815$	51.2962	+	174.991i	0.0629401	+	0.214713i
$816$		0			0
$817$	−1012.84	−	1012.84i	−1.23971	−	1.23971i
$818$		0			0
$819$	−274.853			−0.335596
$820$		0			0
$821$		−	1019.26i		−	1.24148i	−0.784015	−	0.620742i	$-0.786831\pi$
$821$		−	1019.26i		−	1.24148i	0.784015	−	0.620742i	$-0.213169\pi$
$822$		0			0
$823$	158.477	−	158.477i	0.192560	−	0.192560i	−0.604241	−	0.796801i	$-0.706524\pi$
$823$	158.477	−	158.477i	0.192560	−	0.192560i	0.796801	+	0.604241i	$0.206524\pi$
$824$		0			0
$825$	−53.9523	−	11.7876i	−0.0653967	−	0.0142880i
$826$		0			0
$827$	573.534	−	573.534i	0.693511	−	0.693511i	−0.269492	−	0.963003i	$-0.586856\pi$
$827$	573.534	−	573.534i	0.693511	−	0.693511i	0.963003	+	0.269492i	$0.0868557\pi$
$828$		0			0
$829$	−1133.71			−1.36756			−0.683782	−	0.729686i	$-0.739666\pi$
$829$	−1133.71			−1.36756			−0.683782	+	0.729686i	$0.739666\pi$
$830$		0			0
$831$	23.2430			0.0279699
$832$		0			0
$833$	37.6335	−	37.6335i	0.0451783	−	0.0451783i
$834$		0			0
$835$	−112.335	−	383.216i	−0.134532	−	0.458941i
$836$		0			0
$837$	94.0534	−	94.0534i	0.112370	−	0.112370i
$838$		0			0
$839$			1109.49i			1.32240i	0.750212	+	0.661198i	$0.229952\pi$
$839$			1109.49i			1.32240i	−0.750212	+	0.661198i	$0.770048\pi$
$840$		0			0
$841$	−93.5052			−0.111183
$842$		0			0
$843$	−51.0094	−	51.0094i	−0.0605094	−	0.0605094i
$844$		0			0
$845$	36.4772	−	66.7314i	0.0431683	−	0.0789721i
$846$		0			0
$847$	−34.5418	−	34.5418i	−0.0407814	−	0.0407814i
$848$		0			0
$849$			31.6676i			0.0372999i
$850$		0			0
$851$		−	69.6278i		−	0.0818188i
$852$		0			0
$853$	−1.51055	−	1.51055i	−0.00177087	−	0.00177087i	0.706221	−	0.707992i	$-0.250399\pi$
$853$	−1.51055	−	1.51055i	−0.00177087	−	0.00177087i	−0.707992	+	0.706221i	$0.750399\pi$
$854$		0			0
$855$	442.104	−	808.785i	0.517081	−	0.945948i
$856$		0			0
$857$	−396.892	−	396.892i	−0.463118	−	0.463118i	0.436558	−	0.899676i	$-0.356197\pi$
$857$	−396.892	−	396.892i	−0.463118	−	0.463118i	−0.899676	+	0.436558i	$0.856197\pi$
$858$		0			0
$859$	941.956			1.09657			0.548286	−	0.836291i	$-0.315280\pi$
$859$	941.956			1.09657			0.548286	+	0.836291i	$0.315280\pi$
$860$		0			0
$861$			15.6879i			0.0182206i
$862$		0			0
$863$	−833.800	+	833.800i	−0.966164	+	0.966164i	−0.999446	−	0.0332818i	$-0.989404\pi$
$863$	−833.800	+	833.800i	−0.966164	+	0.966164i	0.0332818	+	0.999446i	$0.489404\pi$
$864$		0			0
$865$	−269.514	−	919.416i	−0.311577	−	1.06291i
$866$		0			0
$867$	−37.6064	+	37.6064i	−0.0433754	+	0.0433754i
$868$		0			0
$869$	−1149.43			−1.32270
$870$		0			0
$871$	1048.10			1.20333
$872$		0			0
$873$	412.794	−	412.794i	0.472846	−	0.472846i
$874$		0			0
$875$	185.179	−	213.125i	0.211634	−	0.243571i
$876$		0			0
$877$	−33.6015	+	33.6015i	−0.0383142	+	0.0383142i	−0.726004	−	0.687690i	$-0.758625\pi$
$877$	−33.6015	+	33.6015i	−0.0383142	+	0.0383142i	0.687690	+	0.726004i	$0.258625\pi$
$878$		0			0
$879$			64.0762i			0.0728967i
$880$		0			0
$881$	1084.55			1.23104			0.615521	−	0.788121i	$-0.288946\pi$
$881$	1084.55			1.23104			0.615521	+	0.788121i	$0.288946\pi$
$882$		0			0
$883$	−1165.53	−	1165.53i	−1.31997	−	1.31997i	−0.913796	−	0.406174i	$-0.866863\pi$
$883$	−1165.53	−	1165.53i	−1.31997	−	1.31997i	−0.406174	−	0.913796i	$-0.633137\pi$
$884$		0			0
$885$	24.1182	+	82.2765i	0.0272523	+	0.0929679i
$886$		0			0
$887$	381.705	+	381.705i	0.430333	+	0.430333i	0.888742	−	0.458409i	$-0.151580\pi$
$887$	381.705	+	381.705i	0.430333	+	0.430333i	−0.458409	+	0.888742i	$0.651580\pi$
$888$		0			0
$889$		−	141.584i		−	0.159263i
$890$		0			0
$891$			956.338i			1.07333i
$892$		0			0
$893$	−700.879	−	700.879i	−0.784859	−	0.784859i
$894$		0			0
$895$	68.0190	+	37.1811i	0.0759989	+	0.0415431i
$896$		0			0
$897$	55.6215	+	55.6215i	0.0620084	+	0.0620084i
$898$		0			0
$899$	−1094.34			−1.21729
$900$		0			0
$901$			49.3802i			0.0548060i
$902$		0			0
$903$	20.5800	−	20.5800i	0.0227907	−	0.0227907i
$904$		0			0
$905$	632.344	−	1156.81i	0.698723	−	1.27824i
$906$		0			0
$907$	457.511	−	457.511i	0.504422	−	0.504422i	−0.408387	−	0.912809i	$-0.633908\pi$
$907$	457.511	−	457.511i	0.504422	−	0.504422i	0.912809	+	0.408387i	$0.133908\pi$
$908$		0			0
$909$	−969.856			−1.06695
$910$		0			0
$911$	620.530			0.681152			0.340576	−	0.940217i	$-0.389378\pi$
$911$	620.530			0.681152			0.340576	+	0.940217i	$0.389378\pi$
$912$		0			0
$913$	−760.699	+	760.699i	−0.833187	+	0.833187i
$914$		0			0
$915$	4.28318	−	1.25556i	0.00468107	−	0.00137219i
$916$		0			0
$917$	132.247	−	132.247i	0.144216	−	0.144216i
$918$		0			0
$919$		−	981.064i		−	1.06753i	−0.845631	−	0.533767i	$-0.820776\pi$
$919$		−	981.064i		−	1.06753i	0.845631	−	0.533767i	$-0.179224\pi$
$920$		0			0
$921$	−35.3985			−0.0384349
$922$		0			0
$923$	568.341	+	568.341i	0.615754	+	0.615754i
$924$		0			0
$925$	54.2738	+	11.8579i	0.0586743	+	0.0128193i
$926$		0			0
$927$	−456.459	−	456.459i	−0.492405	−	0.492405i
$928$		0			0
$929$			776.484i			0.835827i	0.908487	+	0.417914i	$0.137239\pi$
$929$			776.484i			0.835827i	−0.908487	+	0.417914i	$0.862761\pi$
$930$		0			0
$931$			902.598i			0.969493i
$932$		0			0
$933$	29.5525	+	29.5525i	0.0316747	+	0.0316747i
$934$		0			0
$935$	−69.4724	+	20.3649i	−0.0743021	+	0.0217806i
$936$		0			0
$937$	759.800	+	759.800i	0.810885	+	0.810885i	0.984767	−	0.173881i	$-0.0556309\pi$
$937$	759.800	+	759.800i	0.810885	+	0.810885i	−0.173881	+	0.984767i	$0.555631\pi$
$938$		0			0
$939$	60.3267			0.0642457
$940$		0			0
$941$		−	759.500i		−	0.807120i	−0.914953	−	0.403560i	$-0.867773\pi$
$941$		−	759.500i		−	0.807120i	0.914953	−	0.403560i	$-0.132227\pi$
$942$		0			0
$943$	−831.969	+	831.969i	−0.882257	+	0.882257i
$944$		0			0
$945$	32.9302	+	18.0006i	0.0348468	+	0.0190482i
$946$		0			0
$947$	822.618	−	822.618i	0.868657	−	0.868657i	−0.123667	−	0.992324i	$-0.539465\pi$
$947$	822.618	−	822.618i	0.868657	−	0.868657i	0.992324	+	0.123667i	$0.0394653\pi$
$948$		0			0
$949$	−654.763			−0.689951
$950$		0			0
$951$	−57.9572			−0.0609434
$952$		0			0
$953$	659.139	−	659.139i	0.691647	−	0.691647i	−0.270947	−	0.962594i	$-0.587337\pi$
$953$	659.139	−	659.139i	0.691647	−	0.691647i	0.962594	+	0.270947i	$0.0873369\pi$
$954$		0			0
$955$	−529.610	−	289.499i	−0.554565	−	0.303140i
$956$		0			0
$957$	−42.7056	+	42.7056i	−0.0446244	+	0.0446244i
$958$		0			0
$959$			79.8661i			0.0832806i
$960$		0			0
$961$	641.133			0.667152
$962$		0			0
$963$	−855.468	−	855.468i	−0.888336	−	0.888336i
$964$		0			0
$965$	1237.71	−	362.817i	1.28260	−	0.375976i
$966$		0			0
$967$	−332.005	−	332.005i	−0.343335	−	0.343335i	0.514284	−	0.857620i	$-0.328058\pi$
$967$	−332.005	−	332.005i	−0.343335	−	0.343335i	−0.857620	+	0.514284i	$0.828058\pi$
$968$		0			0
$969$			4.61086i			0.00475837i
$970$		0			0
$971$			960.961i			0.989661i	0.868989	+	0.494831i	$0.164770\pi$
$971$			960.961i			0.989661i	−0.868989	+	0.494831i	$0.835230\pi$
$972$		0			0
$973$	167.194	+	167.194i	0.171834	+	0.171834i
$974$		0			0
$975$	−52.8286	+	33.8835i	−0.0541832	+	0.0347524i
$976$		0			0
$977$	69.4628	+	69.4628i	0.0710980	+	0.0710980i	0.741762	−	0.670664i	$-0.233991\pi$
$977$	69.4628	+	69.4628i	0.0710980	+	0.0710980i	−0.670664	+	0.741762i	$0.733991\pi$
$978$		0			0
$979$	43.9975			0.0449413
$980$		0			0
$981$			417.297i			0.425379i
$982$		0			0
$983$	−234.943	+	234.943i	−0.239006	+	0.239006i	−0.816438	−	0.577433i	$-0.804055\pi$
$983$	−234.943	+	234.943i	−0.239006	+	0.239006i	0.577433	+	0.816438i	$0.304055\pi$
$984$		0			0
$985$	−1521.91	+	446.128i	−1.54509	+	0.452921i
$986$		0			0
$987$	14.2412	−	14.2412i	0.0144288	−	0.0144288i
$988$		0			0
$989$	2182.82			2.20710
$990$		0			0
$991$	919.592			0.927944			0.463972	−	0.885850i	$-0.346424\pi$
$991$	919.592			0.927944			0.463972	+	0.885850i	$0.346424\pi$
$992$		0			0
$993$	−18.4694	+	18.4694i	−0.0185996	+	0.0185996i
$994$		0			0
$995$	210.825	−	385.684i	0.211885	−	0.387622i
$996$		0			0
$997$	−835.935	+	835.935i	−0.838450	+	0.838450i	−0.988655	−	0.150205i	$-0.952007\pi$
$997$	−835.935	+	835.935i	−0.838450	+	0.838450i	0.150205	+	0.988655i	$0.452007\pi$
$998$		0			0
$999$			7.38441i			0.00739180i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.3.m.a.17.5		20
4.3	odd	2		40.3.i.a.37.9	yes	20
5.2	odd	4		800.3.m.b.593.5		20
5.3	odd	4	inner	160.3.m.a.113.6		20
5.4	even	2		800.3.m.b.657.6		20
8.3	odd	2		40.3.i.a.37.7	yes	20
8.5	even	2	inner	160.3.m.a.17.6		20
12.11	even	2		360.3.u.b.37.2		20
20.3	even	4		40.3.i.a.13.7	✓	20
20.7	even	4		200.3.i.b.93.4		20
20.19	odd	2		200.3.i.b.157.2		20
24.11	even	2		360.3.u.b.37.4		20
40.3	even	4		40.3.i.a.13.9	yes	20
40.13	odd	4	inner	160.3.m.a.113.5		20
40.19	odd	2		200.3.i.b.157.4		20
40.27	even	4		200.3.i.b.93.2		20
40.29	even	2		800.3.m.b.657.5		20
40.37	odd	4		800.3.m.b.593.6		20
60.23	odd	4		360.3.u.b.253.4		20
120.83	odd	4		360.3.u.b.253.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.i.a.13.7	✓	20	20.3	even	4
40.3.i.a.13.9	yes	20	40.3	even	4
40.3.i.a.37.7	yes	20	8.3	odd	2
40.3.i.a.37.9	yes	20	4.3	odd	2
160.3.m.a.17.5		20	1.1	even	1	trivial
160.3.m.a.17.6		20	8.5	even	2	inner
160.3.m.a.113.5		20	40.13	odd	4	inner
160.3.m.a.113.6		20	5.3	odd	4	inner
200.3.i.b.93.2		20	40.27	even	4
200.3.i.b.93.4		20	20.7	even	4
200.3.i.b.157.2		20	20.19	odd	2
200.3.i.b.157.4		20	40.19	odd	2
360.3.u.b.37.2		20	12.11	even	2
360.3.u.b.37.4		20	24.11	even	2
360.3.u.b.253.2		20	120.83	odd	4
360.3.u.b.253.4		20	60.23	odd	4
800.3.m.b.593.5		20	5.2	odd	4
800.3.m.b.593.6		20	40.37	odd	4
800.3.m.b.657.5		20	40.29	even	2
800.3.m.b.657.6		20	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	160.m (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.130791 - 0.130791i) q^{3} +(-4.38731 - 2.39823i) q^{5} +(1.59713 + 1.59713i) q^{7} -8.96579i q^{9} -11.9427i q^{11} +(-9.59714 - 9.59714i) q^{13} +(0.260155 + 0.887490i) q^{15} +(0.857288 + 0.857288i) q^{17} -20.5611 q^{19} -0.417782i q^{21} +(22.1560 - 22.1560i) q^{23} +(13.4970 + 21.0435i) q^{25} +(-2.34977 + 2.34977i) q^{27} +27.3404 q^{29} -40.0267 q^{31} +(-1.56200 + 1.56200i) q^{33} +(-3.17684 - 10.8374i) q^{35} +(1.57131 - 1.57131i) q^{37} +2.51044i q^{39} -37.5504 q^{41} +(49.2602 + 49.2602i) q^{43} +(-21.5020 + 39.3357i) q^{45} +(34.0876 + 34.0876i) q^{47} -43.8983i q^{49} -0.224252i q^{51} +(28.8002 + 28.8002i) q^{53} +(-28.6412 + 52.3962i) q^{55} +(2.68921 + 2.68921i) q^{57} +92.7071 q^{59} -4.82618i q^{61} +(14.3196 - 14.3196i) q^{63} +(19.0895 + 65.1217i) q^{65} +(-54.6048 + 54.6048i) q^{67} -5.79564 q^{69} -59.2198 q^{71} +(34.1124 - 34.1124i) q^{73} +(0.987017 - 4.51761i) q^{75} +(19.0740 - 19.0740i) q^{77} -96.2455i q^{79} -80.0774 q^{81} +(-63.6959 - 63.6959i) q^{83} +(-1.70522 - 5.81716i) q^{85} +(-3.57588 - 3.57588i) q^{87} +3.68406i q^{89} -30.6558i q^{91} +(5.23514 + 5.23514i) q^{93} +(90.2080 + 49.3101i) q^{95} +(46.0410 + 46.0410i) q^{97} -107.075 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{7} + 4 q^{15} - 12 q^{17} + 4 q^{23} - 28 q^{25} + 136 q^{31} + 32 q^{33} - 8 q^{41} - 188 q^{47} - 96 q^{55} - 40 q^{57} - 228 q^{63} - 60 q^{65} - 248 q^{71} - 124 q^{73} + 132 q^{81} + 488 q^{87}+ \cdots + 100 q^{97}+O(q^{100}) \) 20 * q + 4 * q^7 + 4 * q^15 - 12 * q^17 + 4 * q^23 - 28 * q^25 + 136 * q^31 + 32 * q^33 - 8 * q^41 - 188 * q^47 - 96 * q^55 - 40 * q^57 - 228 * q^63 - 60 * q^65 - 248 * q^71 - 124 * q^73 + 132 * q^81 + 488 * q^87 + 488 * q^95 + 100 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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