LMFDB - Embedded newform 160.4.o.a.47.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [160,4,Mod(47,160)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("160.47"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(160, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 4, names="a")

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

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$9.44030560092$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.1
Character	$\chi$	$=$	160.47
Dual form			160.4.o.a.143.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.15076 + 6.15076i) q^{3} +(-11.1441 + 0.899439i) q^{5} +(-16.5614 + 16.5614i) q^{7} -48.6638i q^{9} +11.0706 q^{11} +(-4.95962 - 4.95962i) q^{13} +(63.0125 - 74.0770i) q^{15} +(68.6010 + 68.6010i) q^{17} -29.4303i q^{19} -203.730i q^{21} +(-70.5372 - 70.5372i) q^{23} +(123.382 - 20.0469i) q^{25} +(133.249 + 133.249i) q^{27} +39.6115 q^{29} -167.596i q^{31} +(-68.0928 + 68.0928i) q^{33} +(169.666 - 199.458i) q^{35} +(38.3756 - 38.3756i) q^{37} +61.0109 q^{39} -305.291 q^{41} +(114.783 - 114.783i) q^{43} +(43.7701 + 542.314i) q^{45} +(-335.637 + 335.637i) q^{47} -205.559i q^{49} -843.897 q^{51} +(-455.381 - 455.381i) q^{53} +(-123.372 + 9.95735i) q^{55} +(181.019 + 181.019i) q^{57} -170.086i q^{59} +512.994i q^{61} +(805.939 + 805.939i) q^{63} +(59.7314 + 50.8096i) q^{65} +(476.312 + 476.312i) q^{67} +867.716 q^{69} -627.703i q^{71} +(-2.93764 + 2.93764i) q^{73} +(-635.590 + 882.197i) q^{75} +(-183.345 + 183.345i) q^{77} +132.081 q^{79} -325.240 q^{81} +(111.150 - 111.150i) q^{83} +(-826.199 - 702.794i) q^{85} +(-243.641 + 243.641i) q^{87} -836.950i q^{89} +164.276 q^{91} +(1030.84 + 1030.84i) q^{93} +(26.4708 + 327.975i) q^{95} +(-485.063 - 485.063i) q^{97} -538.738i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 8 q^{11} + 48 q^{17} + 40 q^{25} - 104 q^{27} - 112 q^{33} + 460 q^{35} - 8 q^{41} + 868 q^{43} - 1480 q^{51} + 104 q^{57} + 520 q^{65} + 1852 q^{67} - 744 q^{73} - 3300 q^{75} - 1240 q^{81}+ \cdots - 584 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 + 8 * q^11 + 48 * q^17 + 40 * q^25 - 104 * q^27 - 112 * q^33 + 460 * q^35 - 8 * q^41 + 868 * q^43 - 1480 * q^51 + 104 * q^57 + 520 * q^65 + 1852 * q^67 - 744 * q^73 - 3300 * q^75 - 1240 * q^81 - 2676 * q^83 + 1704 * q^91 - 584 * 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
$3$	−6.15076	+	6.15076i	−1.18371	+	1.18371i	−0.204940	+	0.978774i	$0.565700\pi$
$3$	−6.15076	+	6.15076i	−1.18371	+	1.18371i	−0.978774	+	0.204940i	$0.934300\pi$
$4$		0			0
$5$	−11.1441	+	0.899439i	−0.996759	+	0.0804483i
$5$	−11.1441	+	0.899439i	−0.996759	+	0.0804483i
$6$		0			0
$7$	−16.5614	+	16.5614i	−0.894231	+	0.894231i	−0.994918	−	0.100687i	$-0.967896\pi$
$7$	−16.5614	+	16.5614i	−0.894231	+	0.894231i	0.100687	+	0.994918i	$0.467896\pi$
$8$		0			0
$9$		−	48.6638i		−	1.80236i
$10$		0			0
$11$	11.0706			0.303447			0.151724	−	0.988423i	$-0.451518\pi$
$11$	11.0706			0.303447			0.151724	+	0.988423i	$0.451518\pi$
$12$		0			0
$13$	−4.95962	−	4.95962i	−0.105812	−	0.105812i	0.652219	−	0.758031i	$-0.273838\pi$
$13$	−4.95962	−	4.95962i	−0.105812	−	0.105812i	−0.758031	+	0.652219i	$0.773838\pi$
$14$		0			0
$15$	63.0125	−	74.0770i	1.08465	−	1.27511i
$16$		0			0
$17$	68.6010	+	68.6010i	0.978717	+	0.978717i	0.999778	−	0.0210615i	$-0.00670459\pi$
$17$	68.6010	+	68.6010i	0.978717	+	0.978717i	−0.0210615	+	0.999778i	$0.506705\pi$
$18$		0			0
$19$		−	29.4303i		−	0.355357i	−0.984089	−	0.177678i	$-0.943141\pi$
$19$		−	29.4303i		−	0.355357i	0.984089	−	0.177678i	$-0.0568587\pi$
$20$		0			0
$21$		−	203.730i		−	2.11703i
$22$		0			0
$23$	−70.5372	−	70.5372i	−0.639480	−	0.639480i	0.310947	−	0.950427i	$-0.399354\pi$
$23$	−70.5372	−	70.5372i	−0.639480	−	0.639480i	−0.950427	+	0.310947i	$0.899354\pi$
$24$		0			0
$25$	123.382	−	20.0469i	0.987056	−	0.160375i
$26$		0			0
$27$	133.249	+	133.249i	0.949767	+	0.949767i
$28$		0			0
$29$	39.6115			0.253644			0.126822	−	0.991925i	$-0.459522\pi$
$29$	39.6115			0.253644			0.126822	+	0.991925i	$0.459522\pi$
$30$		0			0
$31$		−	167.596i		−	0.971002i	−0.874236	−	0.485501i	$-0.838637\pi$
$31$		−	167.596i		−	0.971002i	0.874236	−	0.485501i	$-0.161363\pi$
$32$		0			0
$33$	−68.0928	+	68.0928i	−0.359195	+	0.359195i
$34$		0			0
$35$	169.666	−	199.458i	0.819393	−	0.963272i
$36$		0			0
$37$	38.3756	−	38.3756i	0.170511	−	0.170511i	−0.616693	−	0.787204i	$-0.711528\pi$
$37$	38.3756	−	38.3756i	0.170511	−	0.170511i	0.787204	+	0.616693i	$0.211528\pi$
$38$		0			0
$39$	61.0109			0.250501
$40$		0			0
$41$	−305.291			−1.16289			−0.581445	−	0.813586i	$-0.697512\pi$
$41$	−305.291			−1.16289			−0.581445	+	0.813586i	$0.697512\pi$
$42$		0			0
$43$	114.783	−	114.783i	0.407077	−	0.407077i	−0.473641	−	0.880718i	$-0.657061\pi$
$43$	114.783	−	114.783i	0.407077	−	0.407077i	0.880718	+	0.473641i	$0.157061\pi$
$44$		0			0
$45$	43.7701	+	542.314i	0.144997	+	1.79652i
$46$		0			0
$47$	−335.637	+	335.637i	−1.04165	+	1.04165i	−0.0425604	+	0.999094i	$0.513551\pi$
$47$	−335.637	+	335.637i	−1.04165	+	1.04165i	−0.999094	+	0.0425604i	$0.986449\pi$
$48$		0			0
$49$		−	205.559i		−	0.599297i
$50$		0			0
$51$	−843.897			−2.31704
$52$		0			0
$53$	−455.381	−	455.381i	−1.18022	−	1.18022i	−0.979688	−	0.200527i	$-0.935734\pi$
$53$	−455.381	−	455.381i	−1.18022	−	1.18022i	−0.200527	−	0.979688i	$-0.564266\pi$
$54$		0			0
$55$	−123.372	+	9.95735i	−0.302464	+	0.0244118i
$56$		0			0
$57$	181.019	+	181.019i	0.420641	+	0.420641i
$58$		0			0
$59$		−	170.086i		−	0.375311i	−0.982235	−	0.187655i	$-0.939911\pi$
$59$		−	170.086i		−	0.375311i	0.982235	−	0.187655i	$-0.0600888\pi$
$60$		0			0
$61$			512.994i			1.07676i	0.842703	+	0.538378i	$0.180963\pi$
$61$			512.994i			1.07676i	−0.842703	+	0.538378i	$0.819037\pi$
$62$		0			0
$63$	805.939	+	805.939i	1.61173	+	1.61173i
$64$		0			0
$65$	59.7314	+	50.8096i	0.113981	+	0.0969563i
$66$		0			0
$67$	476.312	+	476.312i	0.868519	+	0.868519i	0.992308	−	0.123790i	$-0.0395048\pi$
$67$	476.312	+	476.312i	0.868519	+	0.868519i	−0.123790	+	0.992308i	$0.539505\pi$
$68$		0			0
$69$	867.716			1.51392
$70$		0			0
$71$		−	627.703i		−	1.04922i	−0.851343	−	0.524610i	$-0.824211\pi$
$71$		−	627.703i		−	1.04922i	0.851343	−	0.524610i	$-0.175789\pi$
$72$		0			0
$73$	−2.93764	+	2.93764i	−0.00470992	+	0.00470992i	−0.709458	−	0.704748i	$-0.751060\pi$
$73$	−2.93764	+	2.93764i	−0.00470992	+	0.00470992i	0.704748	+	0.709458i	$0.251060\pi$
$74$		0			0
$75$	−635.590	+	882.197i	−0.978555	+	1.35823i
$76$		0			0
$77$	−183.345	+	183.345i	−0.271352	+	0.271352i
$78$		0			0
$79$	132.081			0.188105			0.0940523	−	0.995567i	$-0.470018\pi$
$79$	132.081			0.188105			0.0940523	+	0.995567i	$0.470018\pi$
$80$		0			0
$81$	−325.240			−0.446145
$82$		0			0
$83$	111.150	−	111.150i	0.146991	−	0.146991i	−0.629781	−	0.776772i	$-0.716855\pi$
$83$	111.150	−	111.150i	0.146991	−	0.146991i	0.776772	+	0.629781i	$0.216855\pi$
$84$		0			0
$85$	−826.199	−	702.794i	−1.05428	−	0.896808i
$86$		0			0
$87$	−243.641	+	243.641i	−0.300242	+	0.300242i
$88$		0			0
$89$		−	836.950i		−	0.996815i	−0.866943	−	0.498407i	$-0.833918\pi$
$89$		−	836.950i		−	0.996815i	0.866943	−	0.498407i	$-0.166082\pi$
$90$		0			0
$91$	164.276			0.189240
$92$		0			0
$93$	1030.84	+	1030.84i	1.14939	+	1.14939i
$94$		0			0
$95$	26.4708	+	327.975i	0.0285878	+	0.354205i
$96$		0			0
$97$	−485.063	−	485.063i	−0.507739	−	0.507739i	0.406093	−	0.913832i	$-0.366891\pi$
$97$	−485.063	−	485.063i	−0.507739	−	0.507739i	−0.913832	+	0.406093i	$0.866891\pi$
$98$		0			0
$99$		−	538.738i		−	0.546922i
$100$		0			0
$101$		−	143.353i		−	0.141229i	−0.997504	−	0.0706146i	$-0.977504\pi$
$101$		−	143.353i		−	0.141229i	0.997504	−	0.0706146i	$-0.0224960\pi$
$102$		0			0
$103$	97.3092	+	97.3092i	0.0930889	+	0.0930889i	0.752118	−	0.659029i	$-0.229032\pi$
$103$	97.3092	+	97.3092i	0.0930889	+	0.0930889i	−0.659029	+	0.752118i	$0.729032\pi$
$104$		0			0
$105$	183.243	+	2270.39i	0.170311	+	2.11017i
$106$		0			0
$107$	−1354.74	−	1354.74i	−1.22400	−	1.22400i	−0.966197	−	0.257804i	$-0.917001\pi$
$107$	−1354.74	−	1354.74i	−1.22400	−	1.22400i	−0.257804	−	0.966197i	$-0.582999\pi$
$108$		0			0
$109$	−208.105			−0.182870			−0.0914350	−	0.995811i	$-0.529145\pi$
$109$	−208.105			−0.182870			−0.0914350	+	0.995811i	$0.529145\pi$
$110$		0			0
$111$			472.078i			0.403673i
$112$		0			0
$113$	821.764	−	821.764i	0.684115	−	0.684115i	−0.276810	−	0.960925i	$-0.589277\pi$
$113$	821.764	−	821.764i	0.684115	−	0.684115i	0.960925	+	0.276810i	$0.0892771\pi$
$114$		0			0
$115$	849.518	+	722.630i	0.688852	+	0.585962i
$116$		0			0
$117$	−241.354	+	241.354i	−0.190711	+	0.190711i
$118$		0			0
$119$	−2272.25			−1.75040
$120$		0			0
$121$	−1208.44			−0.907920
$122$		0			0
$123$	1877.77	−	1877.77i	1.37653	−	1.37653i
$124$		0			0
$125$	−1356.95	+	334.379i	−0.970955	+	0.239262i
$126$		0			0
$127$	1732.61	−	1732.61i	1.21059	−	1.21059i	0.239754	−	0.970834i	$-0.422933\pi$
$127$	1732.61	−	1732.61i	1.21059	−	1.21059i	0.970834	−	0.239754i	$-0.0770666\pi$
$128$		0			0
$129$			1412.01i			0.963726i
$130$		0			0
$131$	58.8534			0.0392523			0.0196261	−	0.999807i	$-0.493752\pi$
$131$	58.8534			0.0392523			0.0196261	+	0.999807i	$0.493752\pi$
$132$		0			0
$133$	487.407	+	487.407i	0.317771	+	0.317771i
$134$		0			0
$135$	−1604.79	−	1365.09i	−1.02310	−	0.870281i
$136$		0			0
$137$	105.459	+	105.459i	0.0657661	+	0.0657661i	0.739225	−	0.673459i	$-0.235192\pi$
$137$	105.459	+	105.459i	0.0657661	+	0.0657661i	−0.673459	+	0.739225i	$0.735192\pi$
$138$		0			0
$139$			918.385i			0.560406i	0.959941	+	0.280203i	$0.0904017\pi$
$139$			918.385i			0.560406i	−0.959941	+	0.280203i	$0.909598\pi$
$140$		0			0
$141$		−	4128.85i		−	2.46604i
$142$		0			0
$143$	−54.9061	−	54.9061i	−0.0321082	−	0.0321082i
$144$		0			0
$145$	−441.435	+	35.6281i	−0.252822	+	0.0204052i
$146$		0			0
$147$	1264.34	+	1264.34i	0.709396	+	0.709396i
$148$		0			0
$149$	414.329			0.227806			0.113903	−	0.993492i	$-0.463665\pi$
$149$	414.329			0.227806			0.113903	+	0.993492i	$0.463665\pi$
$150$		0			0
$151$		−	1749.49i		−	0.942860i	−0.881904	−	0.471430i	$-0.843738\pi$
$151$		−	1749.49i		−	0.942860i	0.881904	−	0.471430i	$-0.156262\pi$
$152$		0			0
$153$	3338.38	−	3338.38i	1.76400	−	1.76400i
$154$		0			0
$155$	150.742	+	1867.70i	0.0781154	+	0.967855i
$156$		0			0
$157$	1876.43	−	1876.43i	0.953859	−	0.953859i	−0.0451229	−	0.998981i	$-0.514368\pi$
$157$	1876.43	−	1876.43i	0.953859	−	0.953859i	0.998981	+	0.0451229i	$0.0143680\pi$
$158$		0			0
$159$	5601.88			2.79408
$160$		0			0
$161$	2336.39			1.14368
$162$		0			0
$163$	−842.965	+	842.965i	−0.405068	+	0.405068i	−0.880015	−	0.474947i	$-0.842467\pi$
$163$	−842.965	+	842.965i	−0.405068	+	0.405068i	0.474947	+	0.880015i	$0.342467\pi$
$164$		0			0
$165$	697.588	−	820.078i	0.329134	−	0.386927i
$166$		0			0
$167$	−274.097	+	274.097i	−0.127008	+	0.127008i	−0.767753	−	0.640746i	$-0.778625\pi$
$167$	−274.097	+	274.097i	−0.127008	+	0.127008i	0.640746	+	0.767753i	$0.278625\pi$
$168$		0			0
$169$		−	2147.80i		−	0.977608i
$170$		0			0
$171$	−1432.19			−0.640481
$172$		0			0
$173$	−763.567	−	763.567i	−0.335566	−	0.335566i	0.519130	−	0.854696i	$-0.326256\pi$
$173$	−763.567	−	763.567i	−0.335566	−	0.335566i	−0.854696	+	0.519130i	$0.826256\pi$
$174$		0			0
$175$	−1711.37	+	2375.38i	−0.739244	+	1.02607i
$176$		0			0
$177$	1046.16	+	1046.16i	0.444261	+	0.444261i
$178$		0			0
$179$		−	3353.66i		−	1.40036i	−0.713966	−	0.700180i	$-0.753103\pi$
$179$		−	3353.66i		−	1.40036i	0.713966	−	0.700180i	$-0.246897\pi$
$180$		0			0
$181$			3141.93i			1.29026i	0.764071	+	0.645132i	$0.223198\pi$
$181$			3141.93i			1.29026i	−0.764071	+	0.645132i	$0.776802\pi$
$182$		0			0
$183$	−3155.30	−	3155.30i	−1.27457	−	1.27457i
$184$		0			0
$185$	−393.145	+	462.178i	−0.156241	+	0.183676i
$186$		0			0
$187$	759.456	+	759.456i	0.296989	+	0.296989i
$188$		0			0
$189$	−4413.56			−1.69862
$190$		0			0
$191$			2646.53i			1.00260i	0.865275	+	0.501298i	$0.167144\pi$
$191$			2646.53i			1.00260i	−0.865275	+	0.501298i	$0.832856\pi$
$192$		0			0
$193$	−3524.97	+	3524.97i	−1.31468	+	1.31468i	−0.396754	+	0.917925i	$0.629863\pi$
$193$	−3524.97	+	3524.97i	−1.31468	+	1.31468i	−0.917925	+	0.396754i	$0.870137\pi$
$194$		0			0
$195$	−679.911	+	54.8755i	−0.249690	+	0.0201524i
$196$		0			0
$197$	−3725.92	+	3725.92i	−1.34752	+	1.34752i	−0.459164	+	0.888352i	$0.651851\pi$
$197$	−3725.92	+	3725.92i	−1.34752	+	1.34752i	−0.888352	+	0.459164i	$0.848149\pi$
$198$		0			0
$199$	2702.93			0.962841			0.481420	−	0.876490i	$-0.340121\pi$
$199$	2702.93			0.962841			0.481420	+	0.876490i	$0.340121\pi$
$200$		0			0
$201$	−5859.36			−2.05616
$202$		0			0
$203$	−656.021	+	656.021i	−0.226816	+	0.226816i
$204$		0			0
$205$	3402.20	−	274.591i	1.15912	−	0.0935525i
$206$		0			0
$207$	−3432.61	+	3432.61i	−1.15257	+	1.15257i
$208$		0			0
$209$		−	325.812i		−	0.107832i
$210$		0			0
$211$	−1795.92			−0.585952			−0.292976	−	0.956120i	$-0.594646\pi$
$211$	−1795.92			−0.585952			−0.292976	+	0.956120i	$0.594646\pi$
$212$		0			0
$213$	3860.85	+	3860.85i	1.24198	+	1.24198i
$214$		0			0
$215$	−1175.92	+	1382.40i	−0.373009	+	0.438506i
$216$		0			0
$217$	2775.61	+	2775.61i	0.868300	+	0.868300i
$218$		0			0
$219$		−	36.1374i		−	0.0111504i
$220$		0			0
$221$		−	680.469i		−	0.207119i
$222$		0			0
$223$	3586.69	+	3586.69i	1.07705	+	1.07705i	0.996772	+	0.0802797i	$0.0255814\pi$
$223$	3586.69	+	3586.69i	1.07705	+	1.07705i	0.0802797	+	0.996772i	$0.474419\pi$
$224$		0			0
$225$	−975.556	−	6004.23i	−0.289054	−	1.77903i
$226$		0			0
$227$	−2116.05	−	2116.05i	−0.618710	−	0.618710i	0.326491	−	0.945200i	$-0.394134\pi$
$227$	−2116.05	−	2116.05i	−0.618710	−	0.618710i	−0.945200	+	0.326491i	$0.894134\pi$
$228$		0			0
$229$	1547.09			0.446440			0.223220	−	0.974768i	$-0.428343\pi$
$229$	1547.09			0.446440			0.223220	+	0.974768i	$0.428343\pi$
$230$		0			0
$231$		−	2255.42i		−	0.642406i
$232$		0			0
$233$	−1819.85	+	1819.85i	−0.511684	+	0.511684i	−0.915042	−	0.403358i	$-0.867843\pi$
$233$	−1819.85	+	1819.85i	−0.511684	+	0.511684i	0.403358	+	0.915042i	$0.367843\pi$
$234$		0			0
$235$	3438.49	−	4042.26i	0.954479	−	1.12208i
$236$		0			0
$237$	−812.398	+	812.398i	−0.222662	+	0.222662i
$238$		0			0
$239$	−3314.62			−0.897091			−0.448546	−	0.893760i	$-0.648058\pi$
$239$	−3314.62			−0.897091			−0.448546	+	0.893760i	$0.648058\pi$
$240$		0			0
$241$	1482.29			0.396193			0.198096	−	0.980183i	$-0.436524\pi$
$241$	1482.29			0.396193			0.198096	+	0.980183i	$0.436524\pi$
$242$		0			0
$243$	−1597.24	+	1597.24i	−0.421658	+	0.421658i
$244$		0			0
$245$	184.888	+	2290.77i	0.0482124	+	0.597354i
$246$		0			0
$247$	−145.963	+	145.963i	−0.0376009	+	0.0376009i
$248$		0			0
$249$			1367.31i			0.347991i
$250$		0			0
$251$	−1272.42			−0.319978			−0.159989	−	0.987119i	$-0.551146\pi$
$251$	−1272.42			−0.319978			−0.159989	+	0.987119i	$0.551146\pi$
$252$		0			0
$253$	−780.892	−	780.892i	−0.194048	−	0.194048i
$254$		0			0
$255$	9404.47	−	759.034i	2.30953	−	0.186402i
$256$		0			0
$257$	−3124.86	−	3124.86i	−0.758457	−	0.758457i	0.217584	−	0.976042i	$-0.430182\pi$
$257$	−3124.86	−	3124.86i	−0.758457	−	0.758457i	−0.976042	+	0.217584i	$0.930182\pi$
$258$		0			0
$259$			1271.11i			0.304952i
$260$		0			0
$261$		−	1927.64i		−	0.457158i
$262$		0			0
$263$	−2331.55	−	2331.55i	−0.546653	−	0.546653i	0.378818	−	0.925471i	$-0.376331\pi$
$263$	−2331.55	−	2331.55i	−0.546653	−	0.546653i	−0.925471	+	0.378818i	$0.876331\pi$
$264$		0			0
$265$	5484.40	+	4665.23i	1.27134	+	1.08144i
$266$		0			0
$267$	5147.88	+	5147.88i	1.17994	+	1.17994i
$268$		0			0
$269$	5963.79			1.35174			0.675871	−	0.737020i	$-0.263768\pi$
$269$	5963.79			1.35174			0.675871	+	0.737020i	$0.263768\pi$
$270$		0			0
$271$		−	207.168i		−	0.0464374i	−0.999730	−	0.0232187i	$-0.992609\pi$
$271$		−	207.168i		−	0.0464374i	0.999730	−	0.0232187i	$-0.00739141\pi$
$272$		0			0
$273$	−1010.42	+	1010.42i	−0.224006	+	0.224006i
$274$		0			0
$275$	1365.92	−	221.932i	0.299519	−	0.0486654i
$276$		0			0
$277$	1139.43	−	1139.43i	0.247154	−	0.247154i	−0.572647	−	0.819802i	$-0.694084\pi$
$277$	1139.43	−	1139.43i	0.247154	−	0.247154i	0.819802	+	0.572647i	$0.194084\pi$
$278$		0			0
$279$	−8155.83			−1.75010
$280$		0			0
$281$	−4385.55			−0.931032			−0.465516	−	0.885039i	$-0.654131\pi$
$281$	−4385.55			−0.931032			−0.465516	+	0.885039i	$0.654131\pi$
$282$		0			0
$283$	−3933.88	+	3933.88i	−0.826307	+	0.826307i	−0.987004	−	0.160697i	$-0.948626\pi$
$283$	−3933.88	+	3933.88i	−0.826307	+	0.826307i	0.160697	+	0.987004i	$0.448626\pi$
$284$		0			0
$285$	−2180.11	−	1854.48i	−0.453118	−	0.385438i
$286$		0			0
$287$	5056.05	−	5056.05i	1.03989	−	1.03989i
$288$		0			0
$289$			4499.19i			0.915773i
$290$		0			0
$291$	5967.02			1.20204
$292$		0			0
$293$	−6361.20	−	6361.20i	−1.26835	−	1.26835i	−0.946943	−	0.321403i	$-0.895846\pi$
$293$	−6361.20	−	6361.20i	−1.26835	−	1.26835i	−0.321403	−	0.946943i	$-0.604154\pi$
$294$		0			0
$295$	152.982	+	1895.46i	0.0301931	+	0.374094i
$296$		0			0
$297$	1475.15	+	1475.15i	0.288204	+	0.288204i
$298$		0			0
$299$			699.675i			0.135329i
$300$		0			0
$301$			3801.95i			0.728042i
$302$		0			0
$303$	881.730	+	881.730i	0.167175	+	0.167175i
$304$		0			0
$305$	−461.407	−	5716.86i	−0.0866232	−	1.07327i
$306$		0			0
$307$	−5521.61	−	5521.61i	−1.02650	−	1.02650i	−0.999639	−	0.0268586i	$-0.991450\pi$
$307$	−5521.61	−	5521.61i	−1.02650	−	1.02650i	−0.0268586	−	0.999639i	$-0.508550\pi$
$308$		0			0
$309$	−1197.05			−0.220381
$310$		0			0
$311$			6319.98i			1.15233i	0.817335	+	0.576163i	$0.195451\pi$
$311$			6319.98i			1.15233i	−0.817335	+	0.576163i	$0.804549\pi$
$312$		0			0
$313$	5524.29	−	5524.29i	0.997608	−	0.997608i	−0.00238920	−	0.999997i	$-0.500761\pi$
$313$	5524.29	−	5524.29i	0.997608	−	0.997608i	0.999997	+	0.00238920i	$0.000760506\pi$
$314$		0			0
$315$	−9706.36	−	8256.57i	−1.73616	−	1.47684i
$316$		0			0
$317$	−4123.56	+	4123.56i	−0.730606	+	0.730606i	−0.970740	−	0.240134i	$-0.922809\pi$
$317$	−4123.56	+	4123.56i	−0.730606	+	0.730606i	0.240134	+	0.970740i	$0.422809\pi$
$318$		0			0
$319$	438.524			0.0769675
$320$		0			0
$321$	16665.4			2.89774
$322$		0			0
$323$	2018.95	−	2018.95i	0.347794	−	0.347794i
$324$		0			0
$325$	−711.352	−	512.503i	−0.121411	−	0.0874724i
$326$		0			0
$327$	1280.00	−	1280.00i	0.216466	−	0.216466i
$328$		0			0
$329$		−	11117.2i		−	1.86296i
$330$		0			0
$331$	1756.83			0.291734			0.145867	−	0.989304i	$-0.453403\pi$
$331$	1756.83			0.291734			0.145867	+	0.989304i	$0.453403\pi$
$332$		0			0
$333$	−1867.50	−	1867.50i	−0.307322	−	0.307322i
$334$		0			0
$335$	−5736.48	−	4879.66i	−0.935575	−	0.795833i
$336$		0			0
$337$	−5055.88	−	5055.88i	−0.817245	−	0.817245i	0.168463	−	0.985708i	$-0.446120\pi$
$337$	−5055.88	−	5055.88i	−0.817245	−	0.817245i	−0.985708	+	0.168463i	$0.946120\pi$
$338$		0			0
$339$			10108.9i			1.61959i
$340$		0			0
$341$		−	1855.39i		−	0.294648i
$342$		0			0
$343$	−2276.22	−	2276.22i	−0.358321	−	0.358321i
$344$		0			0
$345$	−9669.91	+	780.457i	−1.50902	+	0.121792i
$346$		0			0
$347$	3049.33	+	3049.33i	0.471748	+	0.471748i	0.902480	−	0.430732i	$-0.141745\pi$
$347$	3049.33	+	3049.33i	0.471748	+	0.471748i	−0.430732	+	0.902480i	$0.641745\pi$
$348$		0			0
$349$	1009.65			0.154858			0.0774292	−	0.996998i	$-0.475329\pi$
$349$	1009.65			0.154858			0.0774292	+	0.996998i	$0.475329\pi$
$350$		0			0
$351$		−	1321.72i		−	0.200993i
$352$		0			0
$353$	−8243.95	+	8243.95i	−1.24301	+	1.24301i	−0.284259	+	0.958748i	$0.591747\pi$
$353$	−8243.95	+	8243.95i	−1.24301	+	1.24301i	−0.958748	+	0.284259i	$0.908253\pi$
$354$		0			0
$355$	564.581	+	6995.19i	0.0844080	+	1.04582i
$356$		0			0
$357$	13976.1	−	13976.1i	2.07197	−	2.07197i
$358$		0			0
$359$	1663.12			0.244502			0.122251	−	0.992499i	$-0.460989\pi$
$359$	1663.12			0.244502			0.122251	+	0.992499i	$0.460989\pi$
$360$		0			0
$361$	5992.86			0.873721
$362$		0			0
$363$	7432.83	−	7432.83i	1.07472	−	1.07472i
$364$		0			0
$365$	30.0951	−	35.3795i	0.00431575	−	0.00507356i
$366$		0			0
$367$	−2941.96	+	2941.96i	−0.418445	+	0.418445i	−0.884667	−	0.466223i	$-0.845615\pi$
$367$	−2941.96	+	2941.96i	−0.418445	+	0.418445i	0.466223	+	0.884667i	$0.345615\pi$
$368$		0			0
$369$			14856.6i			2.09595i
$370$		0			0
$371$	15083.5			2.11077
$372$		0			0
$373$	−6831.30	−	6831.30i	−0.948288	−	0.948288i	0.0504396	−	0.998727i	$-0.483938\pi$
$373$	−6831.30	−	6831.30i	−0.948288	−	0.948288i	−0.998727	+	0.0504396i	$0.983938\pi$
$374$		0			0
$375$	6289.60	−	10403.0i	0.866116	−	1.43255i
$376$		0			0
$377$	−196.458	−	196.458i	−0.0268385	−	0.0268385i
$378$		0			0
$379$		−	1604.62i		−	0.217477i	−0.994070	−	0.108739i	$-0.965319\pi$
$379$		−	1604.62i		−	0.217477i	0.994070	−	0.108739i	$-0.0346812\pi$
$380$		0			0
$381$			21313.8i			2.86598i
$382$		0			0
$383$	−1085.46	−	1085.46i	−0.144815	−	0.144815i	0.630982	−	0.775797i	$-0.282652\pi$
$383$	−1085.46	−	1085.46i	−0.144815	−	0.144815i	−0.775797	+	0.630982i	$0.782652\pi$
$384$		0			0
$385$	1878.31	−	2208.12i	0.248643	−	0.292302i
$386$		0			0
$387$	−5585.80	−	5585.80i	−0.733700	−	0.733700i
$388$		0			0
$389$	−9833.10			−1.28164			−0.640820	−	0.767691i	$-0.721406\pi$
$389$	−9833.10			−1.28164			−0.640820	+	0.767691i	$0.721406\pi$
$390$		0			0
$391$		−	9677.85i		−	1.25174i
$392$		0			0
$393$	−361.993	+	361.993i	−0.0464635	+	0.0464635i
$394$		0			0
$395$	−1471.92	+	118.799i	−0.187495	+	0.0151327i
$396$		0			0
$397$	9888.55	−	9888.55i	1.25011	−	1.25011i	0.294435	−	0.955672i	$-0.404869\pi$
$397$	9888.55	−	9888.55i	1.25011	−	1.25011i	0.955672	−	0.294435i	$-0.0951314\pi$
$398$		0			0
$399$	−5995.85			−0.752300
$400$		0			0
$401$	8106.73			1.00955			0.504777	−	0.863250i	$-0.331575\pi$
$401$	8106.73			1.00955			0.504777	+	0.863250i	$0.331575\pi$
$402$		0			0
$403$	−831.210	+	831.210i	−0.102743	+	0.102743i
$404$		0			0
$405$	3624.51	−	292.533i	0.444699	−	0.0358916i
$406$		0			0
$407$	424.842	−	424.842i	0.0517411	−	0.0517411i
$408$		0			0
$409$			8464.46i			1.02333i	0.859186	+	0.511663i	$0.170970\pi$
$409$			8464.46i			1.02333i	−0.859186	+	0.511663i	$0.829030\pi$
$410$		0			0
$411$	−1297.30			−0.155697
$412$		0			0
$413$	2816.86	+	2816.86i	0.335614	+	0.335614i
$414$		0			0
$415$	−1138.69	+	1338.64i	−0.134690	+	0.158340i
$416$		0			0
$417$	−5648.77	−	5648.77i	−0.663360	−	0.663360i
$418$		0			0
$419$		−	2455.99i		−	0.286355i	−0.989697	−	0.143178i	$-0.954268\pi$
$419$		−	2455.99i		−	0.286355i	0.989697	−	0.143178i	$-0.0457320\pi$
$420$		0			0
$421$		−	2783.22i		−	0.322199i	−0.986938	−	0.161100i	$-0.948496\pi$
$421$		−	2783.22i		−	0.322199i	0.986938	−	0.161100i	$-0.0515040\pi$
$422$		0			0
$423$	16333.4	+	16333.4i	1.87744	+	1.87744i
$424$		0			0
$425$	9839.36	+	7088.89i	1.12301	+	0.809087i
$426$		0			0
$427$	−8495.89	−	8495.89i	−0.962869	−	0.962869i
$428$		0			0
$429$	675.429			0.0760140
$430$		0			0
$431$			8674.68i			0.969477i	0.874659	+	0.484738i	$0.161085\pi$
$431$			8674.68i			0.969477i	−0.874659	+	0.484738i	$0.838915\pi$
$432$		0			0
$433$	−2596.19	+	2596.19i	−0.288141	+	0.288141i	−0.836345	−	0.548204i	$-0.815312\pi$
$433$	−2596.19	+	2596.19i	−0.288141	+	0.288141i	0.548204	+	0.836345i	$0.315312\pi$
$434$		0			0
$435$	2496.02	−	2934.30i	0.275115	−	0.323423i
$436$		0			0
$437$	−2075.93	+	2075.93i	−0.227243	+	0.227243i
$438$		0			0
$439$	−337.310			−0.0366718			−0.0183359	−	0.999832i	$-0.505837\pi$
$439$	−337.310			−0.0366718			−0.0183359	+	0.999832i	$0.505837\pi$
$440$		0			0
$441$	−10003.3			−1.08015
$442$		0			0
$443$	−3963.04	+	3963.04i	−0.425033	+	0.425033i	−0.886932	−	0.461899i	$-0.847168\pi$
$443$	−3963.04	+	3963.04i	−0.425033	+	0.425033i	0.461899	+	0.886932i	$0.347168\pi$
$444$		0			0
$445$	752.785	+	9327.05i	0.0801920	+	0.993584i
$446$		0			0
$447$	−2548.44	+	2548.44i	−0.269658	+	0.269658i
$448$		0			0
$449$		−	5050.61i		−	0.530853i	−0.964131	−	0.265426i	$-0.914487\pi$
$449$		−	5050.61i		−	0.530853i	0.964131	−	0.265426i	$-0.0855127\pi$
$450$		0			0
$451$	−3379.77			−0.352876
$452$		0			0
$453$	10760.7	+	10760.7i	1.11608	+	1.11608i
$454$		0			0
$455$	−1830.71	+	147.756i	−0.188627	+	0.0152240i
$456$		0			0
$457$	−11219.5	−	11219.5i	−1.14842	−	1.14842i	−0.986864	−	0.161551i	$-0.948350\pi$
$457$	−11219.5	−	11219.5i	−1.14842	−	1.14842i	−0.161551	−	0.986864i	$-0.551650\pi$
$458$		0			0
$459$			18282.0i			1.85911i
$460$		0			0
$461$		−	7285.56i		−	0.736057i	−0.929814	−	0.368029i	$-0.880033\pi$
$461$		−	7285.56i		−	0.736057i	0.929814	−	0.368029i	$-0.119967\pi$
$462$		0			0
$463$	−8950.11	−	8950.11i	−0.898373	−	0.898373i	0.0969191	−	0.995292i	$-0.469101\pi$
$463$	−8950.11	−	8950.11i	−0.898373	−	0.898373i	−0.995292	+	0.0969191i	$0.969101\pi$
$464$		0			0
$465$	−12415.0	−	10560.6i	−1.23813	−	1.05320i
$466$		0			0
$467$	−3141.84	−	3141.84i	−0.311322	−	0.311322i	0.534100	−	0.845421i	$-0.320651\pi$
$467$	−3141.84	−	3141.84i	−0.311322	−	0.311322i	−0.845421	+	0.534100i	$0.820651\pi$
$468$		0			0
$469$	−15776.8			−1.55331
$470$		0			0
$471$			23083.0i			2.25819i
$472$		0			0
$473$	1270.73	−	1270.73i	0.123526	−	0.123526i
$474$		0			0
$475$	−589.986	−	3631.17i	−0.0569904	−	0.350757i
$476$		0			0
$477$	−22160.6	+	22160.6i	−2.12717	+	2.12717i
$478$		0			0
$479$	1511.49			0.144179			0.0720894	−	0.997398i	$-0.477033\pi$
$479$	1511.49			0.144179			0.0720894	+	0.997398i	$0.477033\pi$
$480$		0			0
$481$	−380.656			−0.0360841
$482$		0			0
$483$	−14370.6	+	14370.6i	−1.35380	+	1.35380i
$484$		0			0
$485$	5841.88	+	4969.31i	0.546941	+	0.465247i
$486$		0			0
$487$	−4174.17	+	4174.17i	−0.388397	+	0.388397i	−0.874115	−	0.485718i	$-0.838558\pi$
$487$	−4174.17	+	4174.17i	−0.388397	+	0.388397i	0.485718	+	0.874115i	$0.338558\pi$
$488$		0			0
$489$		−	10369.8i		−	0.958970i
$490$		0			0
$491$	−7841.60			−0.720746			−0.360373	−	0.932808i	$-0.617351\pi$
$491$	−7841.60			−0.720746			−0.360373	+	0.932808i	$0.617351\pi$
$492$		0			0
$493$	2717.39	+	2717.39i	0.248245	+	0.248245i
$494$		0			0
$495$	484.562	+	6003.76i	0.0439989	+	0.545149i
$496$		0			0
$497$	10395.6	+	10395.6i	0.938245	+	0.938245i
$498$		0			0
$499$		−	11318.0i		−	1.01535i	−0.861548	−	0.507677i	$-0.830504\pi$
$499$		−	11318.0i		−	1.01535i	0.861548	−	0.507677i	$-0.169496\pi$
$500$		0			0
$501$		−	3371.82i		−	0.300682i
$502$		0			0
$503$	−2339.87	−	2339.87i	−0.207415	−	0.207415i	0.595753	−	0.803168i	$-0.296854\pi$
$503$	−2339.87	−	2339.87i	−0.207415	−	0.207415i	−0.803168	+	0.595753i	$0.796854\pi$
$504$		0			0
$505$	128.937	+	1597.54i	0.0113616	+	0.140771i
$506$		0			0
$507$	13210.6	+	13210.6i	1.15721	+	1.15721i
$508$		0			0
$509$	12201.2			1.06249			0.531245	−	0.847218i	$-0.321724\pi$
$509$	12201.2			1.06249			0.531245	+	0.847218i	$0.321724\pi$
$510$		0			0
$511$		−	97.3026i		−	0.00842351i
$512$		0			0
$513$	3921.55	−	3921.55i	0.337506	−	0.337506i
$514$		0			0
$515$	−1171.95	−	996.900i	−0.100276	−	0.0852984i
$516$		0			0
$517$	−3715.72	+	3715.72i	−0.316087	+	0.316087i
$518$		0			0
$519$	9393.04			0.794429
$520$		0			0
$521$	−1704.22			−0.143307			−0.0716536	−	0.997430i	$-0.522828\pi$
$521$	−1704.22			−0.143307			−0.0716536	+	0.997430i	$0.522828\pi$
$522$		0			0
$523$	7612.08	−	7612.08i	0.636430	−	0.636430i	−0.313243	−	0.949673i	$-0.601415\pi$
$523$	7612.08	−	7612.08i	0.636430	−	0.636430i	0.949673	+	0.313243i	$0.101415\pi$
$524$		0			0
$525$	−4084.16	−	25136.7i	−0.339518	−	2.08963i
$526$		0			0
$527$	11497.2	−	11497.2i	0.950336	−	0.950336i
$528$		0			0
$529$		−	2215.99i		−	0.182132i
$530$		0			0
$531$	−8277.03			−0.676445
$532$		0			0
$533$	1514.13	+	1514.13i	0.123047	+	0.123047i
$534$		0			0
$535$	16315.9	+	13878.9i	1.31850	+	1.12157i
$536$		0			0
$537$	20627.6	+	20627.6i	1.65763	+	1.65763i
$538$		0			0
$539$		−	2275.66i		−	0.181855i
$540$		0			0
$541$		−	10667.2i		−	0.847723i	−0.905727	−	0.423861i	$-0.860674\pi$
$541$		−	10667.2i		−	0.847723i	0.905727	−	0.423861i	$-0.139326\pi$
$542$		0			0
$543$	−19325.3	−	19325.3i	−1.52731	−	1.52731i
$544$		0			0
$545$	2319.14	−	187.178i	0.182277	−	0.0147116i
$546$		0			0
$547$	11723.3	+	11723.3i	0.916366	+	0.916366i	0.996763	−	0.0803966i	$-0.0256187\pi$
$547$	11723.3	+	11723.3i	0.916366	+	0.916366i	−0.0803966	+	0.996763i	$0.525619\pi$
$548$		0			0
$549$	24964.2			1.94070
$550$		0			0
$551$		−	1165.78i		−	0.0901341i
$552$		0			0
$553$	−2187.44	+	2187.44i	−0.168209	+	0.168209i
$554$		0			0
$555$	−424.606	−	5260.89i	−0.0324748	−	0.402364i
$556$		0			0
$557$	13466.7	−	13466.7i	1.02442	−	1.02442i	0.0247247	−	0.999694i	$-0.492129\pi$
$557$	13466.7	−	13466.7i	1.02442	−	1.02442i	0.999694	−	0.0247247i	$-0.00787092\pi$
$558$		0			0
$559$	−1138.56			−0.0861469
$560$		0			0
$561$	−9342.47			−0.703100
$562$		0			0
$563$	−13321.7	+	13321.7i	−0.997236	+	0.997236i	−0.999996	−	0.00276031i	$-0.999121\pi$
$563$	−13321.7	+	13321.7i	−0.997236	+	0.997236i	0.00276031	+	0.999996i	$0.499121\pi$
$564$		0			0
$565$	−8418.69	+	9896.94i	−0.626862	+	0.736934i
$566$		0			0
$567$	5386.42	−	5386.42i	0.398957	−	0.398957i
$568$		0			0
$569$			8946.03i			0.659117i	0.944135	+	0.329558i	$0.106900\pi$
$569$			8946.03i			0.659117i	−0.944135	+	0.329558i	$0.893100\pi$
$570$		0			0
$571$	15237.7			1.11678			0.558388	−	0.829580i	$-0.311420\pi$
$571$	15237.7			1.11678			0.558388	+	0.829580i	$0.311420\pi$
$572$		0			0
$573$	−16278.2	−	16278.2i	−1.18679	−	1.18679i
$574$		0			0
$575$	−10117.1	−	7288.98i	−0.733759	−	0.528646i
$576$		0			0
$577$	1665.78	+	1665.78i	0.120186	+	0.120186i	0.764642	−	0.644456i	$-0.222916\pi$
$577$	1665.78	+	1665.78i	0.120186	+	0.120186i	−0.644456	+	0.764642i	$0.722916\pi$
$578$		0			0
$579$		−	43362.5i		−	3.11241i
$580$		0			0
$581$			3681.59i			0.262888i
$582$		0			0
$583$	−5041.36	−	5041.36i	−0.358133	−	0.358133i
$584$		0			0
$585$	2472.59	−	2906.75i	0.174750	−	0.205435i
$586$		0			0
$587$	−2011.28	−	2011.28i	−0.141421	−	0.141421i	0.632852	−	0.774273i	$-0.281884\pi$
$587$	−2011.28	−	2011.28i	−0.141421	−	0.141421i	−0.774273	+	0.632852i	$0.781884\pi$
$588$		0			0
$589$	−4932.39			−0.345052
$590$		0			0
$591$		−	45834.5i		−	3.19015i
$592$		0			0
$593$	−2415.44	+	2415.44i	−0.167269	+	0.167269i	−0.785778	−	0.618509i	$-0.787737\pi$
$593$	−2415.44	+	2415.44i	−0.167269	+	0.167269i	0.618509	+	0.785778i	$0.287737\pi$
$594$		0			0
$595$	25322.2	−	2043.75i	1.74472	−	0.140816i
$596$		0			0
$597$	−16625.1	+	16625.1i	−1.13973	+	1.13973i
$598$		0			0
$599$	20522.7			1.39989			0.699944	−	0.714198i	$-0.253208\pi$
$599$	20522.7			1.39989			0.699944	+	0.714198i	$0.253208\pi$
$600$		0			0
$601$	−20598.5			−1.39806			−0.699028	−	0.715095i	$-0.746384\pi$
$601$	−20598.5			−1.39806			−0.699028	+	0.715095i	$0.746384\pi$
$602$		0			0
$603$	23179.1	−	23179.1i	1.56538	−	1.56538i
$604$		0			0
$605$	13467.0	−	1086.92i	0.904977	−	0.0730406i
$606$		0			0
$607$	−12526.9	+	12526.9i	−0.837643	+	0.837643i	−0.988548	−	0.150905i	$-0.951781\pi$
$607$	−12526.9	+	12526.9i	−0.837643	+	0.837643i	0.150905	+	0.988548i	$0.451781\pi$
$608$		0			0
$609$		−	8070.06i		−	0.536971i
$610$		0			0
$611$	3329.27			0.220438
$612$		0			0
$613$	7326.67	+	7326.67i	0.482743	+	0.482743i	0.906007	−	0.423264i	$-0.139116\pi$
$613$	7326.67	+	7326.67i	0.482743	+	0.482743i	−0.423264	+	0.906007i	$0.639116\pi$
$614$		0			0
$615$	−19237.2	+	22615.1i	−1.26133	+	1.48281i
$616$		0			0
$617$	6314.93	+	6314.93i	0.412042	+	0.412042i	0.882449	−	0.470408i	$-0.155893\pi$
$617$	6314.93	+	6314.93i	0.412042	+	0.412042i	−0.470408	+	0.882449i	$0.655893\pi$
$618$		0			0
$619$			28929.2i			1.87845i	0.343300	+	0.939226i	$0.388455\pi$
$619$			28929.2i			1.87845i	−0.343300	+	0.939226i	$0.611545\pi$
$620$		0			0
$621$		−	18798.0i		−	1.21471i
$622$		0			0
$623$	13861.0	+	13861.0i	0.891382	+	0.891382i
$624$		0			0
$625$	14821.2	−	4946.85i	0.948560	−	0.316598i
$626$		0			0
$627$	2003.99	+	2003.99i	0.127642	+	0.127642i
$628$		0			0
$629$	5265.21			0.333764
$630$		0			0
$631$		−	8708.83i		−	0.549434i	−0.961525	−	0.274717i	$-0.911416\pi$
$631$		−	8708.83i		−	0.549434i	0.961525	−	0.274717i	$-0.0885842\pi$
$632$		0			0
$633$	11046.3	−	11046.3i	0.693601	−	0.693601i
$634$		0			0
$635$	−17750.0	+	20866.8i	−1.10927	+	1.30405i
$636$		0			0
$637$	−1019.49	+	1019.49i	−0.0634125	+	0.0634125i
$638$		0			0
$639$	−30546.4			−1.89107
$640$		0			0
$641$	−14575.4			−0.898118			−0.449059	−	0.893502i	$-0.648241\pi$
$641$	−14575.4			−0.898118			−0.449059	+	0.893502i	$0.648241\pi$
$642$		0			0
$643$	−3421.95	+	3421.95i	−0.209873	+	0.209873i	−0.804214	−	0.594340i	$-0.797413\pi$
$643$	−3421.95	+	3421.95i	−0.209873	+	0.209873i	0.594340	+	0.804214i	$0.297413\pi$
$644$		0			0
$645$	−1270.02	−	15735.6i	−0.0775301	−	0.960603i
$646$		0			0
$647$	4080.27	−	4080.27i	0.247932	−	0.247932i	−0.572189	−	0.820122i	$-0.693906\pi$
$647$	4080.27	−	4080.27i	0.247932	−	0.247932i	0.820122	+	0.572189i	$0.193906\pi$
$648$		0			0
$649$		−	1882.96i		−	0.113887i
$650$		0			0
$651$	−34144.3			−2.05564
$652$		0			0
$653$	2251.86	+	2251.86i	0.134950	+	0.134950i	0.771355	−	0.636405i	$-0.219579\pi$
$653$	2251.86	+	2251.86i	0.134950	+	0.134950i	−0.636405	+	0.771355i	$0.719579\pi$
$654$		0			0
$655$	−655.868	+	52.9350i	−0.0391250	+	0.00315778i
$656$		0			0
$657$	142.956	+	142.956i	0.00848898	+	0.00848898i
$658$		0			0
$659$		−	1844.63i		−	0.109039i	−0.998513	−	0.0545195i	$-0.982637\pi$
$659$		−	1844.63i		−	0.109039i	0.998513	−	0.0545195i	$-0.0173627\pi$
$660$		0			0
$661$			11209.4i			0.659597i	0.944051	+	0.329798i	$0.106981\pi$
$661$			11209.4i			0.659597i	−0.944051	+	0.329798i	$0.893019\pi$
$662$		0			0
$663$	4185.40	+	4185.40i	0.245170	+	0.245170i
$664$		0			0
$665$	−5870.11	−	4993.32i	−0.342305	−	0.291177i
$666$		0			0
$667$	−2794.09	−	2794.09i	−0.162200	−	0.162200i
$668$		0			0
$669$	−44121.8			−2.54984
$670$		0			0
$671$			5679.17i			0.326739i
$672$		0			0
$673$	16141.4	−	16141.4i	0.924522	−	0.924522i	−0.0728227	−	0.997345i	$-0.523201\pi$
$673$	16141.4	−	16141.4i	0.924522	−	0.924522i	0.997345	+	0.0728227i	$0.0232007\pi$
$674$		0			0
$675$	19111.7	+	13769.3i	1.08979	+	0.785154i
$676$		0			0
$677$	−1696.37	+	1696.37i	−0.0963026	+	0.0963026i	−0.753617	−	0.657314i	$-0.771692\pi$
$677$	−1696.37	+	1696.37i	−0.0963026	+	0.0963026i	0.657314	+	0.753617i	$0.271692\pi$
$678$		0			0
$679$	16066.6			0.908072
$680$		0			0
$681$	26030.6			1.46475
$682$		0			0
$683$	14046.1	−	14046.1i	0.786911	−	0.786911i	−0.194075	−	0.980987i	$-0.562171\pi$
$683$	14046.1	−	14046.1i	0.786911	−	0.786911i	0.980987	+	0.194075i	$0.0621706\pi$
$684$		0			0
$685$	−1270.10	−	1080.39i	−0.0708437	−	0.0602621i
$686$		0			0
$687$	−9515.80	+	9515.80i	−0.528458	+	0.528458i
$688$		0			0
$689$			4517.03i			0.249761i
$690$		0			0
$691$	−29252.6			−1.61045			−0.805225	−	0.592969i	$-0.797956\pi$
$691$	−29252.6			−1.61045			−0.805225	+	0.592969i	$0.797956\pi$
$692$		0			0
$693$	8922.25	+	8922.25i	0.489074	+	0.489074i
$694$		0			0
$695$	−826.031	−	10234.6i	−0.0450837	−	0.558589i
$696$		0			0
$697$	−20943.3	−	20943.3i	−1.13814	−	1.13814i
$698$		0			0
$699$		−	22386.9i		−	1.21137i
$700$		0			0
$701$		−	14092.5i		−	0.759294i	−0.925132	−	0.379647i	$-0.876046\pi$
$701$		−	14092.5i		−	0.759294i	0.925132	−	0.379647i	$-0.123954\pi$
$702$		0			0
$703$	−1129.41	−	1129.41i	−0.0605923	−	0.0605923i
$704$		0			0
$705$	3713.65	+	46012.4i	0.198389	+	2.45805i
$706$		0			0
$707$	2374.12	+	2374.12i	0.126291	+	0.126291i
$708$		0			0
$709$	−10464.5			−0.554303			−0.277151	−	0.960826i	$-0.589390\pi$
$709$	−10464.5			−0.554303			−0.277151	+	0.960826i	$0.589390\pi$
$710$		0			0
$711$		−	6427.55i		−	0.339032i
$712$		0			0
$713$	−11821.7	+	11821.7i	−0.620936	+	0.620936i
$714$		0			0
$715$	661.264	+	562.494i	0.0345872	+	0.0294211i
$716$		0			0
$717$	20387.4	−	20387.4i	1.06190	−	1.06190i
$718$		0			0
$719$	27447.1			1.42365			0.711826	−	0.702356i	$-0.247869\pi$
$719$	27447.1			1.42365			0.711826	+	0.702356i	$0.247869\pi$
$720$		0			0
$721$	−3223.15			−0.166486
$722$		0			0
$723$	−9117.19	+	9117.19i	−0.468979	+	0.468979i
$724$		0			0
$725$	4887.35	−	794.087i	0.250361	−	0.0406781i
$726$		0			0
$727$	14500.4	−	14500.4i	0.739740	−	0.739740i	−0.232787	−	0.972528i	$-0.574785\pi$
$727$	14500.4	−	14500.4i	0.739740	−	0.739740i	0.972528	+	0.232787i	$0.0747846\pi$
$728$		0			0
$729$		−	28430.0i		−	1.44439i
$730$		0			0
$731$	15748.5			0.796826
$732$		0			0
$733$	22844.9	+	22844.9i	1.15115	+	1.15115i	0.986322	+	0.164831i	$0.0527078\pi$
$733$	22844.9	+	22844.9i	1.15115	+	1.15115i	0.164831	+	0.986322i	$0.447292\pi$
$734$		0			0
$735$	−15227.2	−	12952.8i	−0.764167	−	0.650027i
$736$		0			0
$737$	5273.07	+	5273.07i	0.263550	+	0.263550i
$738$		0			0
$739$			16174.1i			0.805109i	0.915396	+	0.402554i	$0.131878\pi$
$739$			16174.1i			0.805109i	−0.915396	+	0.402554i	$0.868122\pi$
$740$		0			0
$741$		−	1795.57i		−	0.0890174i
$742$		0			0
$743$	25013.9	+	25013.9i	1.23509	+	1.23509i	0.961984	+	0.273106i	$0.0880510\pi$
$743$	25013.9	+	25013.9i	1.23509	+	1.23509i	0.273106	+	0.961984i	$0.411949\pi$
$744$		0			0
$745$	−4617.32	+	372.663i	−0.227068	+	0.0183266i
$746$		0			0
$747$	−5408.96	−	5408.96i	−0.264931	−	0.264931i
$748$		0			0
$749$	44872.9			2.18908
$750$		0			0
$751$			23266.8i			1.13052i	0.824914	+	0.565258i	$0.191223\pi$
$751$			23266.8i			1.13052i	−0.824914	+	0.565258i	$0.808777\pi$
$752$		0			0
$753$	7826.36	−	7826.36i	0.378763	−	0.378763i
$754$		0			0
$755$	1573.56	+	19496.5i	0.0758514	+	0.939804i
$756$		0			0
$757$	−1070.85	+	1070.85i	−0.0514146	+	0.0514146i	−0.732347	−	0.680932i	$-0.761575\pi$
$757$	−1070.85	+	1070.85i	−0.0514146	+	0.0514146i	0.680932	+	0.732347i	$0.261575\pi$
$758$		0			0
$759$	9606.16			0.459396
$760$		0			0
$761$	18964.3			0.903358			0.451679	−	0.892181i	$-0.350825\pi$
$761$	18964.3			0.903358			0.451679	+	0.892181i	$0.350825\pi$
$762$		0			0
$763$	3446.50	−	3446.50i	0.163528	−	0.163528i
$764$		0			0
$765$	−34200.6	+	40205.9i	−1.61637	+	1.90019i
$766$		0			0
$767$	−843.562	+	843.562i	−0.0397122	+	0.0397122i
$768$		0			0
$769$			2675.93i			0.125483i	0.998030	+	0.0627416i	$0.0199844\pi$
$769$			2675.93i			0.125483i	−0.998030	+	0.0627416i	$0.980016\pi$
$770$		0			0
$771$	38440.6			1.79559
$772$		0			0
$773$	−17717.3	−	17717.3i	−0.824384	−	0.824384i	0.162349	−	0.986733i	$-0.448093\pi$
$773$	−17717.3	−	17717.3i	−0.824384	−	0.824384i	−0.986733	+	0.162349i	$0.948093\pi$
$774$		0			0
$775$	−3359.77	−	20678.3i	−0.155724	−	0.958433i
$776$		0			0
$777$	−7818.27	−	7818.27i	−0.360977	−	0.360977i
$778$		0			0
$779$			8984.82i			0.413241i
$780$		0			0
$781$		−	6949.07i		−	0.318383i
$782$		0			0
$783$	5278.18	+	5278.18i	0.240903	+	0.240903i
$784$		0			0
$785$	−19223.4	+	22598.9i	−0.874031	+	1.02750i
$786$		0			0
$787$	−17445.8	−	17445.8i	−0.790185	−	0.790185i	0.191339	−	0.981524i	$-0.438717\pi$
$787$	−17445.8	−	17445.8i	−0.790185	−	0.790185i	−0.981524	+	0.191339i	$0.938717\pi$
$788$		0			0
$789$	28681.7			1.29416
$790$		0			0
$791$			27219.1i			1.22351i
$792$		0			0
$793$	2544.25	−	2544.25i	0.113933	−	0.113933i
$794$		0			0
$795$	−62428.0	+	5038.55i	−2.78502	+	0.224779i
$796$		0			0
$797$	−20145.7	+	20145.7i	−0.895353	+	0.895353i	−0.995021	−	0.0996680i	$-0.968222\pi$
$797$	−20145.7	+	20145.7i	−0.895353	+	0.895353i	0.0996680	+	0.995021i	$0.468222\pi$
$798$		0			0
$799$	−46050.1			−2.03897
$800$		0			0
$801$	−40729.1			−1.79662
$802$		0			0
$803$	−32.5215	+	32.5215i	−0.00142921	+	0.00142921i
$804$		0			0
$805$	−26037.0	+	2101.44i	−1.13998	+	0.0920074i
$806$		0			0
$807$	−36681.9	+	36681.9i	−1.60008	+	1.60008i
$808$		0			0
$809$			25649.3i			1.11469i	0.830282	+	0.557344i	$0.188180\pi$
$809$			25649.3i			1.11469i	−0.830282	+	0.557344i	$0.811820\pi$
$810$		0			0
$811$	−27578.5			−1.19410			−0.597048	−	0.802205i	$-0.703660\pi$
$811$	−27578.5			−1.19410			−0.597048	+	0.802205i	$0.703660\pi$
$812$		0			0
$813$	1274.24	+	1274.24i	0.0549687	+	0.0549687i
$814$		0			0
$815$	8635.89	−	10152.3i	0.371168	−	0.436342i
$816$		0			0
$817$	−3378.12	−	3378.12i	−0.144658	−	0.144658i
$818$		0			0
$819$		−	7994.30i		−	0.341079i
$820$		0			0
$821$			22360.3i			0.950526i	0.879844	+	0.475263i	$0.157647\pi$
$821$			22360.3i			0.950526i	−0.879844	+	0.475263i	$0.842353\pi$
$822$		0			0
$823$	9906.84	+	9906.84i	0.419600	+	0.419600i	0.885066	−	0.465466i	$-0.154113\pi$
$823$	9906.84	+	9906.84i	0.419600	+	0.419600i	−0.465466	+	0.885066i	$0.654113\pi$
$824$		0			0
$825$	−7036.38	+	9766.48i	−0.296940	+	0.412152i
$826$		0			0
$827$	25335.7	+	25335.7i	1.06531	+	1.06531i	0.997713	+	0.0675922i	$0.0215317\pi$
$827$	25335.7	+	25335.7i	1.06531	+	1.06531i	0.0675922	+	0.997713i	$0.478468\pi$
$828$		0			0
$829$	−10159.2			−0.425625			−0.212813	−	0.977093i	$-0.568262\pi$
$829$	−10159.2			−0.425625			−0.212813	+	0.977093i	$0.568262\pi$
$830$		0			0
$831$			14016.7i			0.585120i
$832$		0			0
$833$	14101.5	−	14101.5i	0.586542	−	0.586542i
$834$		0			0
$835$	2808.04	−	3301.10i	0.116379	−	0.136814i
$836$		0			0
$837$	22331.9	−	22331.9i	0.922226	−	0.922226i
$838$		0			0
$839$	−39775.3			−1.63671			−0.818353	−	0.574716i	$-0.805112\pi$
$839$	−39775.3			−1.63671			−0.818353	+	0.574716i	$0.805112\pi$
$840$		0			0
$841$	−22819.9			−0.935665
$842$		0			0
$843$	26974.5	−	26974.5i	1.10208	−	1.10208i
$844$		0			0
$845$	1931.82	+	23935.4i	0.0786469	+	0.974439i
$846$		0			0
$847$	20013.5	−	20013.5i	0.811890	−	0.811890i
$848$		0			0
$849$		−	48392.7i		−	1.95622i
$850$		0			0
$851$	−5413.82			−0.218077
$852$		0			0
$853$	3720.58	+	3720.58i	0.149344	+	0.149344i	0.777825	−	0.628481i	$-0.216323\pi$
$853$	3720.58	+	3720.58i	0.149344	+	0.149344i	−0.628481	+	0.777825i	$0.716323\pi$
$854$		0			0
$855$	15960.5	−	1288.17i	0.638406	−	0.0515256i
$856$		0			0
$857$	2905.23	+	2905.23i	0.115800	+	0.115800i	0.762632	−	0.646832i	$-0.223907\pi$
$857$	2905.23	+	2905.23i	0.115800	+	0.115800i	−0.646832	+	0.762632i	$0.723907\pi$
$858$		0			0
$859$		−	1978.23i		−	0.0785756i	−0.999228	−	0.0392878i	$-0.987491\pi$
$859$		−	1978.23i		−	0.0785756i	0.999228	−	0.0392878i	$-0.0125089\pi$
$860$		0			0
$861$			62197.1i			2.46187i
$862$		0			0
$863$	−10391.5	−	10391.5i	−0.409886	−	0.409886i	0.471813	−	0.881699i	$-0.343600\pi$
$863$	−10391.5	−	10391.5i	−0.409886	−	0.409886i	−0.881699	+	0.471813i	$0.843600\pi$
$864$		0			0
$865$	9196.05	+	7822.49i	0.361474	+	0.307483i
$866$		0			0
$867$	−27673.5	−	27673.5i	−1.08401	−	1.08401i
$868$		0			0
$869$	1462.22			0.0570798
$870$		0			0
$871$		−	4724.65i		−	0.183799i
$872$		0			0
$873$	−23605.0	+	23605.0i	−0.915130	+	0.915130i
$874$		0			0
$875$	16935.2	−	28010.8i	0.654302	−	1.08221i
$876$		0			0
$877$	18807.7	−	18807.7i	0.724163	−	0.724163i	−0.245287	−	0.969450i	$-0.578882\pi$
$877$	18807.7	−	18807.7i	0.724163	−	0.724163i	0.969450	+	0.245287i	$0.0788823\pi$
$878$		0			0
$879$	78252.4			3.00272
$880$		0			0
$881$	−2797.46			−0.106979			−0.0534896	−	0.998568i	$-0.517034\pi$
$881$	−2797.46			−0.106979			−0.0534896	+	0.998568i	$0.517034\pi$
$882$		0			0
$883$	24319.6	−	24319.6i	0.926861	−	0.926861i	−0.0706407	−	0.997502i	$-0.522504\pi$
$883$	24319.6	−	24319.6i	0.926861	−	0.926861i	0.997502	+	0.0706407i	$0.0225044\pi$
$884$		0			0
$885$	−12599.5	−	10717.6i	−0.478561	−	0.407081i
$886$		0			0
$887$	−8358.09	+	8358.09i	−0.316389	+	0.316389i	−0.847379	−	0.530989i	$-0.821820\pi$
$887$	−8358.09	+	8358.09i	−0.316389	+	0.316389i	0.530989	+	0.847379i	$0.321820\pi$
$888$		0			0
$889$			57389.0i			2.16509i
$890$		0			0
$891$	−3600.61			−0.135382
$892$		0			0
$893$	9877.92	+	9877.92i	0.370159	+	0.370159i
$894$		0			0
$895$	3016.41	+	37373.5i	0.112657	+	1.39582i
$896$		0			0
$897$	−4303.54	−	4303.54i	−0.160191	−	0.160191i
$898$		0			0
$899$		−	6638.71i		−	0.246289i
$900$		0			0
$901$		−	62479.2i		−	2.31019i
$902$		0			0
$903$	−23384.9	−	23384.9i	−0.861794	−	0.861794i
$904$		0			0
$905$	−2825.98	−	35014.0i	−0.103800	−	1.28608i
$906$		0			0
$907$	8805.22	+	8805.22i	0.322351	+	0.322351i	0.849669	−	0.527317i	$-0.176802\pi$
$907$	8805.22	+	8805.22i	0.322351	+	0.322351i	−0.527317	+	0.849669i	$0.676802\pi$
$908$		0			0
$909$	−6976.09			−0.254546
$910$		0			0
$911$		−	50985.2i		−	1.85424i	−0.374762	−	0.927121i	$-0.622276\pi$
$911$		−	50985.2i		−	1.85424i	0.374762	−	0.927121i	$-0.377724\pi$
$912$		0			0
$913$	1230.50	−	1230.50i	0.0446041	−	0.0446041i
$914$		0			0
$915$	38001.0	+	32325.0i	1.37298	+	1.16790i
$916$		0			0
$917$	−974.694	+	974.694i	−0.0351006	+	0.0351006i
$918$		0			0
$919$	−42995.3			−1.54329			−0.771645	−	0.636054i	$-0.780566\pi$
$919$	−42995.3			−1.54329			−0.771645	+	0.636054i	$0.780566\pi$
$920$		0			0
$921$	67924.2			2.43016
$922$		0			0
$923$	−3113.17	+	3113.17i	−0.111020	+	0.111020i
$924$		0			0
$925$	3965.55	−	5504.17i	0.140958	−	0.195650i
$926$		0			0
$927$	4735.43	−	4735.43i	0.167780	−	0.167780i
$928$		0			0
$929$		−	42375.8i		−	1.49656i	−0.663383	−	0.748280i	$-0.730880\pi$
$929$		−	42375.8i		−	1.49656i	0.663383	−	0.748280i	$-0.269120\pi$
$930$		0			0
$931$	−6049.66			−0.212964
$932$		0			0
$933$	−38872.7	−	38872.7i	−1.36403	−	1.36403i
$934$		0			0
$935$	−9146.54	−	7780.37i	−0.319919	−	0.272134i
$936$		0			0
$937$	8563.59	+	8563.59i	0.298570	+	0.298570i	0.840454	−	0.541884i	$-0.182289\pi$
$937$	8563.59	+	8563.59i	0.298570	+	0.298570i	−0.541884	+	0.840454i	$0.682289\pi$
$938$		0			0
$939$			67957.2i			2.36177i
$940$		0			0
$941$		−	33594.2i		−	1.16380i	−0.813259	−	0.581902i	$-0.802309\pi$
$941$		−	33594.2i		−	1.16380i	0.813259	−	0.581902i	$-0.197691\pi$
$942$		0			0
$943$	21534.4	+	21534.4i	0.743645	+	0.743645i
$944$		0			0
$945$	49185.2	−	3969.73i	1.69312	−	0.136651i
$946$		0			0
$947$	−11378.3	−	11378.3i	−0.390437	−	0.390437i	0.484406	−	0.874843i	$-0.339036\pi$
$947$	−11378.3	−	11378.3i	−0.390437	−	0.390437i	−0.874843	+	0.484406i	$0.839036\pi$
$948$		0			0
$949$	29.1391			0.000996728
$950$		0			0
$951$		−	50726.0i		−	1.72966i
$952$		0			0
$953$	956.027	−	956.027i	0.0324961	−	0.0324961i	−0.690672	−	0.723168i	$-0.742685\pi$
$953$	956.027	−	956.027i	0.0324961	−	0.0324961i	0.723168	+	0.690672i	$0.242685\pi$
$954$		0			0
$955$	−2380.39	−	29493.2i	−0.0806571	−	0.999347i
$956$		0			0
$957$	−2697.26	+	2697.26i	−0.0911076	+	0.0911076i
$958$		0			0
$959$	−3493.09			−0.117620
$960$		0			0
$961$	1702.72			0.0571554
$962$		0			0
$963$	−65927.0	+	65927.0i	−2.20609	+	2.20609i
$964$		0			0
$965$	36112.1	−	42453.1i	1.20465	−	1.41618i
$966$		0			0
$967$	29318.1	−	29318.1i	0.974981	−	0.974981i	−0.0247134	−	0.999695i	$-0.507867\pi$
$967$	29318.1	−	29318.1i	0.974981	−	0.974981i	0.999695	+	0.0247134i	$0.00786732\pi$
$968$		0			0
$969$			24836.2i			0.823377i
$970$		0			0
$971$	−3662.16			−0.121034			−0.0605171	−	0.998167i	$-0.519275\pi$
$971$	−3662.16			−0.121034			−0.0605171	+	0.998167i	$0.519275\pi$
$972$		0			0
$973$	−15209.7	−	15209.7i	−0.501132	−	0.501132i
$974$		0			0
$975$	7527.64	−	1223.08i	0.247259	−	0.0401742i
$976$		0			0
$977$	25024.4	+	25024.4i	0.819449	+	0.819449i	0.986028	−	0.166579i	$-0.0532721\pi$
$977$	25024.4	+	25024.4i	0.819449	+	0.819449i	−0.166579	+	0.986028i	$0.553272\pi$
$978$		0			0
$979$		−	9265.56i		−	0.302481i
$980$		0			0
$981$			10127.2i			0.329598i
$982$		0			0
$983$	6252.93	+	6252.93i	0.202886	+	0.202886i	0.801236	−	0.598349i	$-0.204176\pi$
$983$	6252.93	+	6252.93i	0.202886	+	0.202886i	−0.598349	+	0.801236i	$0.704176\pi$
$984$		0			0
$985$	38170.8	−	44873.2i	1.23474	−	1.45155i
$986$		0			0
$987$	68379.5	+	68379.5i	2.20521	+	2.20521i
$988$		0			0
$989$	−16193.0			−0.520635
$990$		0			0
$991$		−	4516.98i		−	0.144790i	−0.997376	−	0.0723948i	$-0.976936\pi$
$991$		−	4516.98i		−	0.144790i	0.997376	−	0.0723948i	$-0.0230642\pi$
$992$		0			0
$993$	−10805.8	+	10805.8i	−0.345330	+	0.345330i
$994$		0			0
$995$	−30121.7	+	2431.12i	−0.959720	+	0.0774589i
$996$		0			0
$997$	−10276.7	+	10276.7i	−0.326447	+	0.326447i	−0.851234	−	0.524787i	$-0.824145\pi$
$997$	−10276.7	+	10276.7i	−0.326447	+	0.326447i	0.524787	+	0.851234i	$0.324145\pi$
$998$		0			0
$999$	10227.0			0.323891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.4.o.a.47.1		32
4.3	odd	2		40.4.k.a.27.1	yes	32
5.3	odd	4	inner	160.4.o.a.143.2		32
8.3	odd	2	inner	160.4.o.a.47.2		32
8.5	even	2		40.4.k.a.27.8	yes	32
20.3	even	4		40.4.k.a.3.8	yes	32
20.7	even	4		200.4.k.j.43.9		32
20.19	odd	2		200.4.k.j.107.16		32
40.3	even	4	inner	160.4.o.a.143.1		32
40.13	odd	4		40.4.k.a.3.1	✓	32
40.29	even	2		200.4.k.j.107.9		32
40.37	odd	4		200.4.k.j.43.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.k.a.3.1	✓	32	40.13	odd	4
40.4.k.a.3.8	yes	32	20.3	even	4
40.4.k.a.27.1	yes	32	4.3	odd	2
40.4.k.a.27.8	yes	32	8.5	even	2
160.4.o.a.47.1		32	1.1	even	1	trivial
160.4.o.a.47.2		32	8.3	odd	2	inner
160.4.o.a.143.1		32	40.3	even	4	inner
160.4.o.a.143.2		32	5.3	odd	4	inner
200.4.k.j.43.9		32	20.7	even	4
200.4.k.j.43.16		32	40.37	odd	4
200.4.k.j.107.9		32	40.29	even	2
200.4.k.j.107.16		32	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-6.15076 + 6.15076i) q^{3} +(-11.1441 + 0.899439i) q^{5} +(-16.5614 + 16.5614i) q^{7} -48.6638i q^{9} +11.0706 q^{11} +(-4.95962 - 4.95962i) q^{13} +(63.0125 - 74.0770i) q^{15} +(68.6010 + 68.6010i) q^{17} -29.4303i q^{19} -203.730i q^{21} +(-70.5372 - 70.5372i) q^{23} +(123.382 - 20.0469i) q^{25} +(133.249 + 133.249i) q^{27} +39.6115 q^{29} -167.596i q^{31} +(-68.0928 + 68.0928i) q^{33} +(169.666 - 199.458i) q^{35} +(38.3756 - 38.3756i) q^{37} +61.0109 q^{39} -305.291 q^{41} +(114.783 - 114.783i) q^{43} +(43.7701 + 542.314i) q^{45} +(-335.637 + 335.637i) q^{47} -205.559i q^{49} -843.897 q^{51} +(-455.381 - 455.381i) q^{53} +(-123.372 + 9.95735i) q^{55} +(181.019 + 181.019i) q^{57} -170.086i q^{59} +512.994i q^{61} +(805.939 + 805.939i) q^{63} +(59.7314 + 50.8096i) q^{65} +(476.312 + 476.312i) q^{67} +867.716 q^{69} -627.703i q^{71} +(-2.93764 + 2.93764i) q^{73} +(-635.590 + 882.197i) q^{75} +(-183.345 + 183.345i) q^{77} +132.081 q^{79} -325.240 q^{81} +(111.150 - 111.150i) q^{83} +(-826.199 - 702.794i) q^{85} +(-243.641 + 243.641i) q^{87} -836.950i q^{89} +164.276 q^{91} +(1030.84 + 1030.84i) q^{93} +(26.4708 + 327.975i) q^{95} +(-485.063 - 485.063i) q^{97} -538.738i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 8 q^{11} + 48 q^{17} + 40 q^{25} - 104 q^{27} - 112 q^{33} + 460 q^{35} - 8 q^{41} + 868 q^{43} - 1480 q^{51} + 104 q^{57} + 520 q^{65} + 1852 q^{67} - 744 q^{73} - 3300 q^{75} - 1240 q^{81}+ \cdots - 584 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 + 8 * q^11 + 48 * q^17 + 40 * q^25 - 104 * q^27 - 112 * q^33 + 460 * q^35 - 8 * q^41 + 868 * q^43 - 1480 * q^51 + 104 * q^57 + 520 * q^65 + 1852 * q^67 - 744 * q^73 - 3300 * q^75 - 1240 * q^81 - 2676 * q^83 + 1704 * q^91 - 584 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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