LMFDB - Embedded newform 840.2.bt.a.433.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(97,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.97"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bt (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.8
Character	$\chi$	$=$	840.433
Dual form			840.2.bt.a.97.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{3} +(-1.43773 + 1.71258i) q^{5} +(-2.23600 - 1.41433i) q^{7} -1.00000i q^{9} +0.566389 q^{11} +(5.03342 - 5.03342i) q^{13} +(0.194349 + 2.22761i) q^{15} +(-0.984515 - 0.984515i) q^{17} -7.61898 q^{19} +(-2.58117 + 0.581008i) q^{21} +(2.55065 + 2.55065i) q^{23} +(-0.865867 - 4.92446i) q^{25} +(-0.707107 - 0.707107i) q^{27} -7.85354i q^{29} -7.09067i q^{31} +(0.400498 - 0.400498i) q^{33} +(5.63691 - 1.79591i) q^{35} +(0.887993 - 0.887993i) q^{37} -7.11833i q^{39} -6.29837i q^{41} +(-2.74095 - 2.74095i) q^{43} +(1.71258 + 1.43773i) q^{45} +(-3.25393 - 3.25393i) q^{47} +(2.99936 + 6.32486i) q^{49} -1.39231 q^{51} +(7.27748 + 7.27748i) q^{53} +(-0.814314 + 0.969987i) q^{55} +(-5.38743 + 5.38743i) q^{57} -6.62029 q^{59} -5.46929i q^{61} +(-1.41433 + 2.23600i) q^{63} +(1.38344 + 15.8568i) q^{65} +(-2.53098 + 2.53098i) q^{67} +3.60716 q^{69} +8.01809 q^{71} +(-8.97309 + 8.97309i) q^{73} +(-4.09438 - 2.86986i) q^{75} +(-1.26644 - 0.801059i) q^{77} -1.85942i q^{79} -1.00000 q^{81} +(2.61775 - 2.61775i) q^{83} +(3.10153 - 0.270595i) q^{85} +(-5.55329 - 5.55329i) q^{87} +10.2289 q^{89} +(-18.3736 + 4.13581i) q^{91} +(-5.01386 - 5.01386i) q^{93} +(10.9540 - 13.0481i) q^{95} +(4.32885 + 4.32885i) q^{97} -0.566389i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{7} - 8 q^{11} + 16 q^{13} + 4 q^{15} + 20 q^{17} + 8 q^{19} + 24 q^{23} - 4 q^{25} + 4 q^{37} - 16 q^{43} - 4 q^{45} - 24 q^{47} + 36 q^{49} + 16 q^{53} + 28 q^{55} + 4 q^{57} + 8 q^{59} + 24 q^{65}+ \cdots - 28 q^{97}+O(q^{100}) $ 24 * q - 4 * q^7 - 8 * q^11 + 16 * q^13 + 4 * q^15 + 20 * q^17 + 8 * q^19 + 24 * q^23 - 4 * q^25 + 4 * q^37 - 16 * q^43 - 4 * q^45 - 24 * q^47 + 36 * q^49 + 16 * q^53 + 28 * q^55 + 4 * q^57 + 8 * q^59 + 24 * q^65 + 16 * q^67 - 8 * q^69 + 8 * q^71 - 28 * q^73 + 20 * q^77 - 24 * q^81 + 64 * q^83 - 20 * q^85 + 20 * q^87 + 16 * q^89 + 24 * q^91 - 12 * q^93 + 24 * q^95 - 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	−1.43773	+	1.71258i	−0.642972	+	0.765890i
$5$	−1.43773	+	1.71258i	−0.642972	+	0.765890i
$6$		0			0
$7$	−2.23600	−	1.41433i	−0.845127	−	0.534565i
$7$	−2.23600	−	1.41433i	−0.845127	−	0.534565i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	0.566389			0.170773			0.0853864	−	0.996348i	$-0.472788\pi$
$11$	0.566389			0.170773			0.0853864	+	0.996348i	$0.472788\pi$
$12$		0			0
$13$	5.03342	−	5.03342i	1.39602	−	1.39602i	0.584947	−	0.811071i	$-0.301115\pi$
$13$	5.03342	−	5.03342i	1.39602	−	1.39602i	0.811071	−	0.584947i	$-0.198885\pi$
$14$		0			0
$15$	0.194349	+	2.22761i	0.0501808	+	0.575165i
$16$		0			0
$17$	−0.984515	−	0.984515i	−0.238780	−	0.238780i	0.577565	−	0.816345i	$-0.304003\pi$
$17$	−0.984515	−	0.984515i	−0.238780	−	0.238780i	−0.816345	+	0.577565i	$0.804003\pi$
$18$		0			0
$19$	−7.61898			−1.74791			−0.873957	−	0.486004i	$-0.838454\pi$
$19$	−7.61898			−1.74791			−0.873957	+	0.486004i	$0.838454\pi$
$20$		0			0
$21$	−2.58117	+	0.581008i	−0.563257	+	0.126786i
$22$		0			0
$23$	2.55065	+	2.55065i	0.531847	+	0.531847i	0.921122	−	0.389275i	$-0.127274\pi$
$23$	2.55065	+	2.55065i	0.531847	+	0.531847i	−0.389275	+	0.921122i	$0.627274\pi$
$24$		0			0
$25$	−0.865867	−	4.92446i	−0.173173	−	0.984891i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	7.85354i		−	1.45837i	−0.684319	−	0.729183i	$-0.739900\pi$
$29$		−	7.85354i		−	1.45837i	0.684319	−	0.729183i	$-0.260100\pi$
$30$		0			0
$31$		−	7.09067i		−	1.27352i	−0.771061	−	0.636761i	$-0.780274\pi$
$31$		−	7.09067i		−	1.27352i	0.771061	−	0.636761i	$-0.219726\pi$
$32$		0			0
$33$	0.400498	−	0.400498i	0.0697177	−	0.0697177i
$34$		0			0
$35$	5.63691	−	1.79591i	0.952811	−	0.303563i
$36$		0			0
$37$	0.887993	−	0.887993i	0.145985	−	0.145985i	−0.630337	−	0.776322i	$-0.717083\pi$
$37$	0.887993	−	0.887993i	0.145985	−	0.145985i	0.776322	+	0.630337i	$0.217083\pi$
$38$		0			0
$39$		−	7.11833i		−	1.13984i
$40$		0			0
$41$		−	6.29837i		−	0.983640i	−0.870697	−	0.491820i	$-0.836332\pi$
$41$		−	6.29837i		−	0.983640i	0.870697	−	0.491820i	$-0.163668\pi$
$42$		0			0
$43$	−2.74095	−	2.74095i	−0.417992	−	0.417992i	0.466519	−	0.884511i	$-0.345508\pi$
$43$	−2.74095	−	2.74095i	−0.417992	−	0.417992i	−0.884511	+	0.466519i	$0.845508\pi$
$44$		0			0
$45$	1.71258	+	1.43773i	0.255297	+	0.214324i
$46$		0			0
$47$	−3.25393	−	3.25393i	−0.474634	−	0.474634i	0.428777	−	0.903411i	$-0.358945\pi$
$47$	−3.25393	−	3.25393i	−0.474634	−	0.474634i	−0.903411	+	0.428777i	$0.858945\pi$
$48$		0			0
$49$	2.99936	+	6.32486i	0.428480	+	0.903551i
$50$		0			0
$51$	−1.39231			−0.194963
$52$		0			0
$53$	7.27748	+	7.27748i	0.999639	+	0.999639i	1.00000		0.000361159i	$-0.000114960\pi$
$53$	7.27748	+	7.27748i	0.999639	+	0.999639i	−0.000361159		1.00000i	$0.500115\pi$
$54$		0			0
$55$	−0.814314	+	0.969987i	−0.109802	+	0.130793i
$56$		0			0
$57$	−5.38743	+	5.38743i	−0.713583	+	0.713583i
$58$		0			0
$59$	−6.62029			−0.861889			−0.430944	−	0.902378i	$-0.641819\pi$
$59$	−6.62029			−0.861889			−0.430944	+	0.902378i	$0.641819\pi$
$60$		0			0
$61$		−	5.46929i		−	0.700271i	−0.936699	−	0.350135i	$-0.886136\pi$
$61$		−	5.46929i		−	0.700271i	0.936699	−	0.350135i	$-0.113864\pi$
$62$		0			0
$63$	−1.41433	+	2.23600i	−0.178188	+	0.281709i
$64$		0			0
$65$	1.38344	+	15.8568i	0.171595	+	1.96680i
$66$		0			0
$67$	−2.53098	+	2.53098i	−0.309209	+	0.309209i	−0.844603	−	0.535394i	$-0.820163\pi$
$67$	−2.53098	+	2.53098i	−0.309209	+	0.309209i	0.535394	+	0.844603i	$0.320163\pi$
$68$		0			0
$69$	3.60716			0.434251
$70$		0			0
$71$	8.01809			0.951572			0.475786	−	0.879561i	$-0.342164\pi$
$71$	8.01809			0.951572			0.475786	+	0.879561i	$0.342164\pi$
$72$		0			0
$73$	−8.97309	+	8.97309i	−1.05022	+	1.05022i	−0.0515507	+	0.998670i	$0.516416\pi$
$73$	−8.97309	+	8.97309i	−1.05022	+	1.05022i	−0.998670	+	0.0515507i	$0.983584\pi$
$74$		0			0
$75$	−4.09438	−	2.86986i	−0.472778	−	0.331382i
$76$		0			0
$77$	−1.26644	−	0.801059i	−0.144325	−	0.0912892i
$78$		0			0
$79$		−	1.85942i		−	0.209201i	−0.994514	−	0.104601i	$-0.966644\pi$
$79$		−	1.85942i		−	0.209201i	0.994514	−	0.104601i	$-0.0333565\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	2.61775	−	2.61775i	0.287336	−	0.287336i	−0.548690	−	0.836026i	$-0.684873\pi$
$83$	2.61775	−	2.61775i	0.287336	−	0.287336i	0.836026	+	0.548690i	$0.184873\pi$
$84$		0			0
$85$	3.10153	−	0.270595i	0.336408	−	0.0293502i
$86$		0			0
$87$	−5.55329	−	5.55329i	−0.595376	−	0.595376i
$88$		0			0
$89$	10.2289			1.08427			0.542133	−	0.840293i	$-0.317617\pi$
$89$	10.2289			1.08427			0.542133	+	0.840293i	$0.317617\pi$
$90$		0			0
$91$	−18.3736	+	4.13581i	−1.92608	+	0.433550i
$92$		0			0
$93$	−5.01386	−	5.01386i	−0.519913	−	0.519913i
$94$		0			0
$95$	10.9540	−	13.0481i	1.12386	−	1.33871i
$96$		0			0
$97$	4.32885	+	4.32885i	0.439528	+	0.439528i	0.891853	−	0.452325i	$-0.149405\pi$
$97$	4.32885	+	4.32885i	0.439528	+	0.439528i	−0.452325	+	0.891853i	$0.649405\pi$
$98$		0			0
$99$		−	0.566389i		−	0.0569242i
$100$		0			0
$101$			10.9284i			1.08741i	0.839275	+	0.543707i	$0.182980\pi$
$101$			10.9284i			1.08741i	−0.839275	+	0.543707i	$0.817020\pi$
$102$		0			0
$103$	6.13481	−	6.13481i	0.604481	−	0.604481i	−0.337018	−	0.941498i	$-0.609418\pi$
$103$	6.13481	−	6.13481i	0.604481	−	0.604481i	0.941498	+	0.337018i	$0.109418\pi$
$104$		0			0
$105$	2.71600	−	5.25579i	0.265054	−	0.512913i
$106$		0			0
$107$	−8.07798	+	8.07798i	−0.780927	+	0.780927i	−0.979987	−	0.199060i	$-0.936211\pi$
$107$	−8.07798	+	8.07798i	−0.780927	+	0.780927i	0.199060	+	0.979987i	$0.436211\pi$
$108$		0			0
$109$		−	10.4871i		−	1.00448i	−0.864729	−	0.502240i	$-0.832510\pi$
$109$		−	10.4871i		−	1.00448i	0.864729	−	0.502240i	$-0.167490\pi$
$110$		0			0
$111$		−	1.25581i		−	0.119196i
$112$		0			0
$113$	3.30769	+	3.30769i	0.311161	+	0.311161i	0.845359	−	0.534198i	$-0.179386\pi$
$113$	3.30769	+	3.30769i	0.311161	+	0.311161i	−0.534198	+	0.845359i	$0.679386\pi$
$114$		0			0
$115$	−8.03533	+	0.701049i	−0.749299	+	0.0653732i
$116$		0			0
$117$	−5.03342	−	5.03342i	−0.465340	−	0.465340i
$118$		0			0
$119$	0.808946	+	3.59380i	0.0741559	+	0.329443i
$120$		0			0
$121$	−10.6792			−0.970837
$122$		0			0
$123$	−4.45362	−	4.45362i	−0.401569	−	0.401569i
$124$		0			0
$125$	9.67841	+	5.59717i	0.865664	+	0.500626i
$126$		0			0
$127$	−1.85296	+	1.85296i	−0.164424	+	0.164424i	−0.784523	−	0.620099i	$-0.787092\pi$
$127$	−1.85296	+	1.85296i	−0.164424	+	0.164424i	0.620099	+	0.784523i	$0.287092\pi$
$128$		0			0
$129$	−3.87629			−0.341289
$130$		0			0
$131$			21.3166i			1.86244i	0.364461	+	0.931219i	$0.381253\pi$
$131$			21.3166i			1.86244i	−0.364461	+	0.931219i	$0.618747\pi$
$132$		0			0
$133$	17.0360	+	10.7757i	1.47721	+	0.934374i
$134$		0			0
$135$	2.22761	−	0.194349i	0.191722	−	0.0167269i
$136$		0			0
$137$	9.80531	−	9.80531i	0.837724	−	0.837724i	−0.150835	−	0.988559i	$-0.548196\pi$
$137$	9.80531	−	9.80531i	0.837724	−	0.837724i	0.988559	+	0.150835i	$0.0481962\pi$
$138$		0			0
$139$	0.596787			0.0506188			0.0253094	−	0.999680i	$-0.491943\pi$
$139$	0.596787			0.0506188			0.0253094	+	0.999680i	$0.491943\pi$
$140$		0			0
$141$	−4.60175			−0.387537
$142$		0			0
$143$	2.85087	−	2.85087i	0.238402	−	0.238402i
$144$		0			0
$145$	13.4498	+	11.2913i	1.11695	+	0.937689i
$146$		0			0
$147$	6.59322	+	2.35148i	0.543799	+	0.193947i
$148$		0			0
$149$			0.851348i			0.0697452i	0.999392	+	0.0348726i	$0.0111025\pi$
$149$			0.851348i			0.0697452i	−0.999392	+	0.0348726i	$0.988897\pi$
$150$		0			0
$151$	−9.10760			−0.741166			−0.370583	−	0.928799i	$-0.620842\pi$
$151$	−9.10760			−0.741166			−0.370583	+	0.928799i	$0.620842\pi$
$152$		0			0
$153$	−0.984515	+	0.984515i	−0.0795933	+	0.0795933i
$154$		0			0
$155$	12.1433	+	10.1945i	0.975377	+	0.818839i
$156$		0			0
$157$	12.6178	+	12.6178i	1.00701	+	1.00701i	0.999975	+	0.00703865i	$0.00224049\pi$
$157$	12.6178	+	12.6178i	1.00701	+	1.00701i	0.00703865	+	0.999975i	$0.497760\pi$
$158$		0			0
$159$	10.2919			0.816202
$160$		0			0
$161$	−2.09579	−	9.31069i	−0.165171	−	0.733785i
$162$		0			0
$163$	−0.137845	−	0.137845i	−0.0107968	−	0.0107968i	0.701688	−	0.712485i	$-0.252430\pi$
$163$	−0.137845	−	0.137845i	−0.0107968	−	0.0107968i	−0.712485	+	0.701688i	$0.752430\pi$
$164$		0			0
$165$	0.110077	+	1.26169i	0.00856951	+	0.0982226i
$166$		0			0
$167$	−10.4961	−	10.4961i	−0.812214	−	0.812214i	0.172752	−	0.984965i	$-0.444734\pi$
$167$	−10.4961	−	10.4961i	−0.812214	−	0.812214i	−0.984965	+	0.172752i	$0.944734\pi$
$168$		0			0
$169$		−	37.6706i		−	2.89774i
$170$		0			0
$171$			7.61898i			0.582638i
$172$		0			0
$173$	−11.0115	+	11.0115i	−0.837191	+	0.837191i	−0.988488	−	0.151297i	$-0.951655\pi$
$173$	−11.0115	+	11.0115i	−0.837191	+	0.837191i	0.151297	+	0.988488i	$0.451655\pi$
$174$		0			0
$175$	−5.02871	+	12.2357i	−0.380135	+	0.924931i
$176$		0			0
$177$	−4.68125	+	4.68125i	−0.351865	+	0.351865i
$178$		0			0
$179$		−	25.7774i		−	1.92669i	−0.268259	−	0.963347i	$-0.586448\pi$
$179$		−	25.7774i		−	1.92669i	0.268259	−	0.963347i	$-0.413552\pi$
$180$		0			0
$181$			10.3885i			0.772170i	0.922463	+	0.386085i	$0.126173\pi$
$181$			10.3885i			0.772170i	−0.922463	+	0.386085i	$0.873827\pi$
$182$		0			0
$183$	−3.86737	−	3.86737i	−0.285884	−	0.285884i
$184$		0			0
$185$	0.244066	+	2.79745i	0.0179441	+	0.205673i
$186$		0			0
$187$	−0.557618	−	0.557618i	−0.0407771	−	0.0407771i
$188$		0			0
$189$	0.581008	+	2.58117i	0.0422621	+	0.187752i
$190$		0			0
$191$	15.5937			1.12832			0.564161	−	0.825665i	$-0.309200\pi$
$191$	15.5937			1.12832			0.564161	+	0.825665i	$0.309200\pi$
$192$		0			0
$193$	2.02152	+	2.02152i	0.145512	+	0.145512i	0.776110	−	0.630598i	$-0.217190\pi$
$193$	2.02152	+	2.02152i	0.145512	+	0.145512i	−0.630598	+	0.776110i	$0.717190\pi$
$194$		0			0
$195$	12.1907	+	10.2342i	0.872995	+	0.732888i
$196$		0			0
$197$	−5.12206	+	5.12206i	−0.364932	+	0.364932i	−0.865625	−	0.500693i	$-0.833079\pi$
$197$	−5.12206	+	5.12206i	−0.364932	+	0.364932i	0.500693	+	0.865625i	$0.333079\pi$
$198$		0			0
$199$	22.9768			1.62878			0.814389	−	0.580319i	$-0.197072\pi$
$199$	22.9768			1.62878			0.814389	+	0.580319i	$0.197072\pi$
$200$		0			0
$201$			3.57935i			0.252468i
$202$		0			0
$203$	−11.1075	+	17.5605i	−0.779592	+	1.23251i
$204$		0			0
$205$	10.7865	+	9.05535i	0.753359	+	0.632453i
$206$		0			0
$207$	2.55065	−	2.55065i	0.177282	−	0.177282i
$208$		0			0
$209$	−4.31530			−0.298496
$210$		0			0
$211$	−3.50166			−0.241064			−0.120532	−	0.992709i	$-0.538460\pi$
$211$	−3.50166			−0.241064			−0.120532	+	0.992709i	$0.538460\pi$
$212$		0			0
$213$	5.66964	−	5.66964i	0.388477	−	0.388477i
$214$		0			0
$215$	8.63486	−	0.753355i	0.588892	−	0.0513784i
$216$		0			0
$217$	−10.0285	+	15.8547i	−0.680780	+	1.07629i
$218$		0			0
$219$			12.6899i			0.857502i
$220$		0			0
$221$	−9.91094			−0.666682
$222$		0			0
$223$	3.12336	−	3.12336i	0.209155	−	0.209155i	−0.594753	−	0.803908i	$-0.702750\pi$
$223$	3.12336	−	3.12336i	0.209155	−	0.209155i	0.803908	+	0.594753i	$0.202750\pi$
$224$		0			0
$225$	−4.92446	+	0.865867i	−0.328297	+	0.0577245i
$226$		0			0
$227$	8.58965	+	8.58965i	0.570115	+	0.570115i	0.932161	−	0.362045i	$-0.117921\pi$
$227$	8.58965	+	8.58965i	0.570115	+	0.570115i	−0.362045	+	0.932161i	$0.617921\pi$
$228$		0			0
$229$	−17.7361			−1.17204			−0.586018	−	0.810298i	$-0.699305\pi$
$229$	−17.7361			−1.17204			−0.586018	+	0.810298i	$0.699305\pi$
$230$		0			0
$231$	−1.46195	+	0.329077i	−0.0961889	+	0.0216517i
$232$		0			0
$233$	2.90534	+	2.90534i	0.190335	+	0.190335i	0.795841	−	0.605506i	$-0.207029\pi$
$233$	2.90534	+	2.90534i	0.190335	+	0.190335i	−0.605506	+	0.795841i	$0.707029\pi$
$234$		0			0
$235$	10.2509	−	0.894346i	0.668694	−	0.0583407i
$236$		0			0
$237$	−1.31481	−	1.31481i	−0.0854061	−	0.0854061i
$238$		0			0
$239$			22.2209i			1.43735i	0.695347	+	0.718674i	$0.255251\pi$
$239$			22.2209i			1.43735i	−0.695347	+	0.718674i	$0.744749\pi$
$240$		0			0
$241$		−	28.9186i		−	1.86281i	−0.363984	−	0.931405i	$-0.618584\pi$
$241$		−	28.9186i		−	1.86281i	0.363984	−	0.931405i	$-0.381416\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−15.1441	−	3.95679i	−0.967521	−	0.252790i
$246$		0			0
$247$	−38.3495	+	38.3495i	−2.44012	+	2.44012i
$248$		0			0
$249$		−	3.70206i		−	0.234609i
$250$		0			0
$251$			15.2202i			0.960693i	0.877079	+	0.480346i	$0.159489\pi$
$251$			15.2202i			0.960693i	−0.877079	+	0.480346i	$0.840511\pi$
$252$		0			0
$253$	1.44466	+	1.44466i	0.0908249	+	0.0908249i
$254$		0			0
$255$	2.00177	−	2.38445i	0.125356	−	0.149320i
$256$		0			0
$257$	14.5914	+	14.5914i	0.910186	+	0.910186i	0.996286	−	0.0861002i	$-0.0274405\pi$
$257$	14.5914	+	14.5914i	0.910186	+	0.910186i	−0.0861002	+	0.996286i	$0.527441\pi$
$258$		0			0
$259$	−3.24146	+	0.729637i	−0.201415	+	0.0453375i
$260$		0			0
$261$	−7.85354			−0.486122
$262$		0			0
$263$	−10.9688	−	10.9688i	−0.676363	−	0.676363i	0.282812	−	0.959175i	$-0.408733\pi$
$263$	−10.9688	−	10.9688i	−0.676363	−	0.676363i	−0.959175	+	0.282812i	$0.908733\pi$
$264$		0			0
$265$	−22.9263	+	2.00023i	−1.40835	+	0.122873i
$266$		0			0
$267$	7.23295	−	7.23295i	0.442650	−	0.442650i
$268$		0			0
$269$	18.8822			1.15127			0.575635	−	0.817707i	$-0.304755\pi$
$269$	18.8822			1.15127			0.575635	+	0.817707i	$0.304755\pi$
$270$		0			0
$271$		−	28.8900i		−	1.75494i	−0.479628	−	0.877472i	$-0.659228\pi$
$271$		−	28.8900i		−	1.75494i	0.479628	−	0.877472i	$-0.340772\pi$
$272$		0			0
$273$	−10.0676	+	15.9166i	−0.609321	+	0.963314i
$274$		0			0
$275$	−0.490418	−	2.78916i	−0.0295733	−	0.168193i
$276$		0			0
$277$	6.33752	−	6.33752i	0.380785	−	0.380785i	−0.490600	−	0.871385i	$-0.663222\pi$
$277$	6.33752	−	6.33752i	0.380785	−	0.380785i	0.871385	+	0.490600i	$0.163222\pi$
$278$		0			0
$279$	−7.09067			−0.424507
$280$		0			0
$281$	−21.3194			−1.27181			−0.635905	−	0.771768i	$-0.719373\pi$
$281$	−21.3194			−1.27181			−0.635905	+	0.771768i	$0.719373\pi$
$282$		0			0
$283$	−6.54910	+	6.54910i	−0.389304	+	0.389304i	−0.874439	−	0.485135i	$-0.838770\pi$
$283$	−6.54910	+	6.54910i	−0.389304	+	0.389304i	0.485135	+	0.874439i	$0.338770\pi$
$284$		0			0
$285$	−1.48074	−	16.9721i	−0.0877116	−	1.00534i
$286$		0			0
$287$	−8.90795	+	14.0831i	−0.525820	+	0.831301i
$288$		0			0
$289$		−	15.0615i		−	0.885968i
$290$		0			0
$291$	6.12192			0.358873
$292$		0			0
$293$	−3.25380	+	3.25380i	−0.190089	+	0.190089i	−0.795735	−	0.605645i	$-0.792915\pi$
$293$	−3.25380	+	3.25380i	−0.190089	+	0.190089i	0.605645	+	0.795735i	$0.292915\pi$
$294$		0			0
$295$	9.51819	−	11.3378i	0.554171	−	0.660112i
$296$		0			0
$297$	−0.400498	−	0.400498i	−0.0232392	−	0.0232392i
$298$		0			0
$299$	25.6769			1.48494
$300$		0			0
$301$	2.25216	+	10.0054i	0.129812	+	0.576700i
$302$		0			0
$303$	7.72753	+	7.72753i	0.443935	+	0.443935i
$304$		0			0
$305$	9.36660	+	7.86336i	0.536330	+	0.450255i
$306$		0			0
$307$	11.2615	+	11.2615i	0.642730	+	0.642730i	0.951226	−	0.308496i	$-0.0998256\pi$
$307$	11.2615	+	11.2615i	0.642730	+	0.642730i	−0.308496	+	0.951226i	$0.599826\pi$
$308$		0			0
$309$		−	8.67593i		−	0.493556i
$310$		0			0
$311$		−	9.21941i		−	0.522785i	−0.965233	−	0.261392i	$-0.915818\pi$
$311$		−	9.21941i		−	0.522785i	0.965233	−	0.261392i	$-0.0841816\pi$
$312$		0			0
$313$	8.95602	−	8.95602i	0.506224	−	0.506224i	−0.407141	−	0.913365i	$-0.633474\pi$
$313$	8.95602	−	8.95602i	0.506224	−	0.506224i	0.913365	+	0.407141i	$0.133474\pi$
$314$		0			0
$315$	−1.79591	−	5.63691i	−0.101188	−	0.317604i
$316$		0			0
$317$	−0.477985	+	0.477985i	−0.0268463	+	0.0268463i	−0.720403	−	0.693556i	$-0.756043\pi$
$317$	−0.477985	+	0.477985i	−0.0268463	+	0.0268463i	0.693556	+	0.720403i	$0.256043\pi$
$318$		0			0
$319$		−	4.44816i		−	0.249049i
$320$		0			0
$321$			11.4240i			0.637624i
$322$		0			0
$323$	7.50099	+	7.50099i	0.417366	+	0.417366i
$324$		0			0
$325$	−29.1451	−	20.4286i	−1.61668	−	1.13317i
$326$		0			0
$327$	−7.41548	−	7.41548i	−0.410077	−	0.410077i
$328$		0			0
$329$	2.67365	+	11.8779i	0.147403	+	0.654849i
$330$		0			0
$331$	17.9367			0.985892			0.492946	−	0.870060i	$-0.335920\pi$
$331$	17.9367			0.985892			0.492946	+	0.870060i	$0.335920\pi$
$332$		0			0
$333$	−0.887993	−	0.887993i	−0.0486617	−	0.0486617i
$334$		0			0
$335$	−0.695644	−	7.97338i	−0.0380071	−	0.435632i
$336$		0			0
$337$	16.3606	−	16.3606i	0.891217	−	0.891217i	−0.103421	−	0.994638i	$-0.532979\pi$
$337$	16.3606	−	16.3606i	0.891217	−	0.891217i	0.994638	+	0.103421i	$0.0329788\pi$
$338$		0			0
$339$	4.67778			0.254062
$340$		0			0
$341$		−	4.01608i		−	0.217483i
$342$		0			0
$343$	2.23886	−	18.3844i	0.120887	−	0.992666i
$344$		0			0
$345$	−5.18612	+	6.17756i	−0.279211	+	0.332588i
$346$		0			0
$347$	11.4656	−	11.4656i	0.615508	−	0.615508i	−0.328868	−	0.944376i	$-0.606667\pi$
$347$	11.4656	−	11.4656i	0.615508	−	0.615508i	0.944376	+	0.328868i	$0.106667\pi$
$348$		0			0
$349$	−4.37394			−0.234132			−0.117066	−	0.993124i	$-0.537349\pi$
$349$	−4.37394			−0.234132			−0.117066	+	0.993124i	$0.537349\pi$
$350$		0			0
$351$	−7.11833			−0.379948
$352$		0			0
$353$	−6.72792	+	6.72792i	−0.358091	+	0.358091i	−0.863109	−	0.505018i	$-0.831486\pi$
$353$	−6.72792	+	6.72792i	−0.358091	+	0.358091i	0.505018	+	0.863109i	$0.331486\pi$
$354$		0			0
$355$	−11.5278	+	13.7316i	−0.611834	+	0.728799i
$356$		0			0
$357$	3.11321	+	1.96919i	0.164768	+	0.104220i
$358$		0			0
$359$		−	17.4579i		−	0.921393i	−0.887558	−	0.460696i	$-0.847600\pi$
$359$		−	17.4579i		−	0.921393i	0.887558	−	0.460696i	$-0.152400\pi$
$360$		0			0
$361$	39.0488			2.05520
$362$		0			0
$363$	−7.55134	+	7.55134i	−0.396342	+	0.396342i
$364$		0			0
$365$	−2.46627	−	28.2680i	−0.129090	−	1.47962i
$366$		0			0
$367$	16.2987	+	16.2987i	0.850784	+	0.850784i	0.990230	−	0.139445i	$-0.0445320\pi$
$367$	16.2987	+	16.2987i	0.850784	+	0.850784i	−0.139445	+	0.990230i	$0.544532\pi$
$368$		0			0
$369$	−6.29837			−0.327880
$370$		0			0
$371$	−5.97969	−	26.5652i	−0.310450	−	1.37919i
$372$		0			0
$373$	11.2031	+	11.2031i	0.580073	+	0.580073i	0.934923	−	0.354850i	$-0.115468\pi$
$373$	11.2031	+	11.2031i	0.580073	+	0.580073i	−0.354850	+	0.934923i	$0.615468\pi$
$374$		0			0
$375$	10.8015	−	2.88588i	0.557785	−	0.149026i
$376$		0			0
$377$	−39.5302	−	39.5302i	−2.03591	−	2.03591i
$378$		0			0
$379$			24.5366i			1.26036i	0.776450	+	0.630179i	$0.217019\pi$
$379$			24.5366i			1.26036i	−0.776450	+	0.630179i	$0.782981\pi$
$380$		0			0
$381$			2.62048i			0.134251i
$382$		0			0
$383$	9.28703	−	9.28703i	0.474545	−	0.474545i	−0.428837	−	0.903382i	$-0.641077\pi$
$383$	9.28703	−	9.28703i	0.474545	−	0.474545i	0.903382	+	0.428837i	$0.141077\pi$
$384$		0			0
$385$	3.19268	−	1.01718i	0.162714	−	0.0518404i
$386$		0			0
$387$	−2.74095	+	2.74095i	−0.139331	+	0.139331i
$388$		0			0
$389$		−	25.4037i		−	1.28802i	−0.765018	−	0.644009i	$-0.777270\pi$
$389$		−	25.4037i		−	1.28802i	0.765018	−	0.644009i	$-0.222730\pi$
$390$		0			0
$391$		−	5.02230i		−	0.253989i
$392$		0			0
$393$	15.0731	+	15.0731i	0.760337	+	0.760337i
$394$		0			0
$395$	3.18441	+	2.67335i	0.160225	+	0.134511i
$396$		0			0
$397$	1.00474	+	1.00474i	0.0504265	+	0.0504265i	0.731870	−	0.681444i	$-0.238648\pi$
$397$	1.00474	+	1.00474i	0.0504265	+	0.0504265i	−0.681444	+	0.731870i	$0.738648\pi$
$398$		0			0
$399$	19.6659	−	4.42669i	0.984525	−	0.221612i
$400$		0			0
$401$	−18.3629			−0.916998			−0.458499	−	0.888695i	$-0.651613\pi$
$401$	−18.3629			−0.916998			−0.458499	+	0.888695i	$0.651613\pi$
$402$		0			0
$403$	−35.6903	−	35.6903i	−1.77786	−	1.77786i
$404$		0			0
$405$	1.43773	−	1.71258i	0.0714414	−	0.0850988i
$406$		0			0
$407$	0.502950	−	0.502950i	0.0249303	−	0.0249303i
$408$		0			0
$409$	−10.1369			−0.501237			−0.250619	−	0.968086i	$-0.580634\pi$
$409$	−10.1369			−0.501237			−0.250619	+	0.968086i	$0.580634\pi$
$410$		0			0
$411$		−	13.8668i		−	0.683999i
$412$		0			0
$413$	14.8030	+	9.36326i	0.728406	+	0.460736i
$414$		0			0
$415$	0.719493	+	8.24674i	0.0353185	+	0.404816i
$416$		0			0
$417$	0.421992	−	0.421992i	0.0206650	−	0.0206650i
$418$		0			0
$419$	−31.9057			−1.55869			−0.779347	−	0.626593i	$-0.784449\pi$
$419$	−31.9057			−1.55869			−0.779347	+	0.626593i	$0.784449\pi$
$420$		0			0
$421$	−8.98313			−0.437811			−0.218906	−	0.975746i	$-0.570249\pi$
$421$	−8.98313			−0.437811			−0.218906	+	0.975746i	$0.570249\pi$
$422$		0			0
$423$	−3.25393	+	3.25393i	−0.158211	+	0.158211i
$424$		0			0
$425$	−3.99574	+	5.70066i	−0.193822	+	0.276523i
$426$		0			0
$427$	−7.73536	+	12.2293i	−0.374340	+	0.591818i
$428$		0			0
$429$		−	4.03174i		−	0.194654i
$430$		0			0
$431$	−4.19551			−0.202091			−0.101045	−	0.994882i	$-0.532219\pi$
$431$	−4.19551			−0.202091			−0.101045	+	0.994882i	$0.532219\pi$
$432$		0			0
$433$	15.5040	−	15.5040i	0.745076	−	0.745076i	−0.228474	−	0.973550i	$-0.573374\pi$
$433$	15.5040	−	15.5040i	0.745076	−	0.745076i	0.973550	+	0.228474i	$0.0733737\pi$
$434$		0			0
$435$	17.4946	−	1.52633i	0.838802	−	0.0731820i
$436$		0			0
$437$	−19.4333	−	19.4333i	−0.929622	−	0.929622i
$438$		0			0
$439$	−19.5954			−0.935238			−0.467619	−	0.883930i	$-0.654888\pi$
$439$	−19.5954			−0.935238			−0.467619	+	0.883930i	$0.654888\pi$
$440$		0			0
$441$	6.32486	−	2.99936i	0.301184	−	0.142827i
$442$		0			0
$443$	−6.22602	−	6.22602i	−0.295807	−	0.295807i	0.543562	−	0.839369i	$-0.317075\pi$
$443$	−6.22602	−	6.22602i	−0.295807	−	0.295807i	−0.839369	+	0.543562i	$0.817075\pi$
$444$		0			0
$445$	−14.7065	+	17.5179i	−0.697153	+	0.830428i
$446$		0			0
$447$	0.601994	+	0.601994i	0.0284733	+	0.0284733i
$448$		0			0
$449$		−	14.4377i		−	0.681359i	−0.940179	−	0.340680i	$-0.889343\pi$
$449$		−	14.4377i		−	0.681359i	0.940179	−	0.340680i	$-0.110657\pi$
$450$		0			0
$451$		−	3.56733i		−	0.167979i
$452$		0			0
$453$	−6.44005	+	6.44005i	−0.302580	+	0.302580i
$454$		0			0
$455$	19.3334	−	37.4124i	0.906362	−	1.75392i
$456$		0			0
$457$	10.0166	−	10.0166i	0.468555	−	0.468555i	−0.432891	−	0.901446i	$-0.642507\pi$
$457$	10.0166	−	10.0166i	0.468555	−	0.468555i	0.901446	+	0.432891i	$0.142507\pi$
$458$		0			0
$459$			1.39231i			0.0649876i
$460$		0			0
$461$		−	27.1704i		−	1.26545i	−0.774375	−	0.632727i	$-0.781936\pi$
$461$		−	27.1704i		−	1.26545i	0.774375	−	0.632727i	$-0.218064\pi$
$462$		0			0
$463$	19.6279	+	19.6279i	0.912186	+	0.912186i	0.996444	−	0.0842578i	$-0.0268519\pi$
$463$	19.6279	+	19.6279i	0.912186	+	0.912186i	−0.0842578	+	0.996444i	$0.526852\pi$
$464$		0			0
$465$	15.7952	−	1.37807i	0.732485	−	0.0639063i
$466$		0			0
$467$	7.41841	+	7.41841i	0.343283	+	0.343283i	0.857600	−	0.514317i	$-0.171955\pi$
$467$	7.41841	+	7.41841i	0.343283	+	0.343283i	−0.514317	+	0.857600i	$0.671955\pi$
$468$		0			0
$469$	9.23891	−	2.07963i	0.426613	−	0.0960285i
$470$		0			0
$471$	17.8443			0.822223
$472$		0			0
$473$	−1.55245	−	1.55245i	−0.0713816	−	0.0713816i
$474$		0			0
$475$	6.59702	+	37.5193i	0.302692	+	1.72150i
$476$		0			0
$477$	7.27748	−	7.27748i	0.333213	−	0.333213i
$478$		0			0
$479$	−7.58693			−0.346656			−0.173328	−	0.984864i	$-0.555452\pi$
$479$	−7.58693			−0.346656			−0.173328	+	0.984864i	$0.555452\pi$
$480$		0			0
$481$		−	8.93928i		−	0.407596i
$482$		0			0
$483$	−8.06560	−	5.10170i	−0.366997	−	0.232136i
$484$		0			0
$485$	−13.6372	+	1.18979i	−0.619234	+	0.0540256i
$486$		0			0
$487$	23.2682	−	23.2682i	1.05438	−	1.05438i	0.0559496	−	0.998434i	$-0.482181\pi$
$487$	23.2682	−	23.2682i	1.05438	−	1.05438i	0.998434	−	0.0559496i	$-0.0178186\pi$
$488$		0			0
$489$	−0.194942			−0.00881557
$490$		0			0
$491$	−29.1533			−1.31567			−0.657835	−	0.753162i	$-0.728527\pi$
$491$	−29.1533			−1.31567			−0.657835	+	0.753162i	$0.728527\pi$
$492$		0			0
$493$	−7.73193	+	7.73193i	−0.348228	+	0.348228i
$494$		0			0
$495$	0.969987	+	0.814314i	0.0435977	+	0.0366007i
$496$		0			0
$497$	−17.9284	−	11.3402i	−0.804199	−	0.508677i
$498$		0			0
$499$			18.0636i			0.808637i	0.914618	+	0.404319i	$0.132491\pi$
$499$			18.0636i			0.808637i	−0.914618	+	0.404319i	$0.867509\pi$
$500$		0			0
$501$	−14.8437			−0.663170
$502$		0			0
$503$	22.9577	−	22.9577i	1.02363	−	1.02363i	0.0239171	−	0.999714i	$-0.492386\pi$
$503$	22.9577	−	22.9577i	1.02363	−	1.02363i	0.999714	−	0.0239171i	$-0.00761377\pi$
$504$		0			0
$505$	−18.7157	−	15.7120i	−0.832839	−	0.699177i
$506$		0			0
$507$	−26.6371	−	26.6371i	−1.18300	−	1.18300i
$508$		0			0
$509$	−17.2001			−0.762382			−0.381191	−	0.924496i	$-0.624486\pi$
$509$	−17.2001			−0.762382			−0.381191	+	0.924496i	$0.624486\pi$
$510$		0			0
$511$	32.7547	−	7.37292i	1.44898	−	0.326159i
$512$		0			0
$513$	5.38743	+	5.38743i	0.237861	+	0.237861i
$514$		0			0
$515$	1.68616	+	19.3266i	0.0743011	+	0.851630i
$516$		0			0
$517$	−1.84299	−	1.84299i	−0.0810545	−	0.0810545i
$518$		0			0
$519$			15.5727i			0.683564i
$520$		0			0
$521$			7.92609i			0.347248i	0.984812	+	0.173624i	$0.0555478\pi$
$521$			7.92609i			0.347248i	−0.984812	+	0.173624i	$0.944452\pi$
$522$		0			0
$523$	15.1308	−	15.1308i	0.661624	−	0.661624i	−0.294139	−	0.955763i	$-0.595033\pi$
$523$	15.1308	−	15.1308i	0.661624	−	0.661624i	0.955763	+	0.294139i	$0.0950327\pi$
$524$		0			0
$525$	5.09610	+	12.2078i	0.222412	+	0.532791i
$526$		0			0
$527$	−6.98087	+	6.98087i	−0.304091	+	0.304091i
$528$		0			0
$529$		−	9.98839i		−	0.434278i
$530$		0			0
$531$			6.62029i			0.287296i
$532$		0			0
$533$	−31.7023	−	31.7023i	−1.37318	−	1.37318i
$534$		0			0
$535$	−2.22024	−	25.4481i	−0.0959895	−	1.10022i
$536$		0			0
$537$	−18.2274	−	18.2274i	−0.786569	−	0.786569i
$538$		0			0
$539$	1.69880	+	3.58233i	0.0731727	+	0.154302i
$540$		0			0
$541$	5.37166			0.230946			0.115473	−	0.993311i	$-0.463162\pi$
$541$	5.37166			0.230946			0.115473	+	0.993311i	$0.463162\pi$
$542$		0			0
$543$	7.34576	+	7.34576i	0.315237	+	0.315237i
$544$		0			0
$545$	17.9600	+	15.0776i	0.769320	+	0.645852i
$546$		0			0
$547$	−8.12081	+	8.12081i	−0.347221	+	0.347221i	−0.859073	−	0.511853i	$-0.828959\pi$
$547$	−8.12081	+	8.12081i	−0.347221	+	0.347221i	0.511853	+	0.859073i	$0.328959\pi$
$548$		0			0
$549$	−5.46929			−0.233424
$550$		0			0
$551$			59.8360i			2.54910i
$552$		0			0
$553$	−2.62983	+	4.15766i	−0.111832	+	0.176802i
$554$		0			0
$555$	2.15068	+	1.80552i	0.0912913	+	0.0766400i
$556$		0			0
$557$	−21.4908	+	21.4908i	−0.910594	+	0.910594i	−0.996319	−	0.0857249i	$-0.972679\pi$
$557$	−21.4908	+	21.4908i	−0.910594	+	0.910594i	0.0857249	+	0.996319i	$0.472679\pi$
$558$		0			0
$559$	−27.5927			−1.16705
$560$		0			0
$561$	−0.788591			−0.0332943
$562$		0			0
$563$	−12.5985	+	12.5985i	−0.530962	+	0.530962i	−0.920859	−	0.389897i	$-0.872511\pi$
$563$	−12.5985	+	12.5985i	−0.530962	+	0.530962i	0.389897	+	0.920859i	$0.372511\pi$
$564$		0			0
$565$	−10.4203	+	0.909124i	−0.438383	+	0.0382471i
$566$		0			0
$567$	2.23600	+	1.41433i	0.0939030	+	0.0593961i
$568$		0			0
$569$			28.6425i			1.20075i	0.799717	+	0.600377i	$0.204983\pi$
$569$			28.6425i			1.20075i	−0.799717	+	0.600377i	$0.795017\pi$
$570$		0			0
$571$	14.2002			0.594260			0.297130	−	0.954837i	$-0.403971\pi$
$571$	14.2002			0.594260			0.297130	+	0.954837i	$0.403971\pi$
$572$		0			0
$573$	11.0264	−	11.0264i	0.460635	−	0.460635i
$574$		0			0
$575$	10.3520	−	14.7691i	0.431710	−	0.615913i
$576$		0			0
$577$	15.1116	+	15.1116i	0.629106	+	0.629106i	0.947843	−	0.318737i	$-0.103259\pi$
$577$	15.1116	+	15.1116i	0.629106	+	0.629106i	−0.318737	+	0.947843i	$0.603259\pi$
$578$		0			0
$579$	2.85886			0.118810
$580$		0			0
$581$	−9.55565	+	2.15093i	−0.396435	+	0.0892356i
$582$		0			0
$583$	4.12188	+	4.12188i	0.170711	+	0.170711i
$584$		0			0
$585$	15.8568	−	1.38344i	0.655599	−	0.0571983i
$586$		0			0
$587$	−2.55057	−	2.55057i	−0.105273	−	0.105273i	0.652508	−	0.757782i	$-0.273717\pi$
$587$	−2.55057	−	2.55057i	−0.105273	−	0.105273i	−0.757782	+	0.652508i	$0.773717\pi$
$588$		0			0
$589$			54.0236i			2.22601i
$590$		0			0
$591$			7.24369i			0.297966i
$592$		0			0
$593$	−22.3517	+	22.3517i	−0.917872	+	0.917872i	−0.996874	−	0.0790021i	$-0.974827\pi$
$593$	−22.3517	+	22.3517i	−0.917872	+	0.917872i	0.0790021	+	0.996874i	$0.474827\pi$
$594$		0			0
$595$	−7.31771	−	3.78152i	−0.299997	−	0.155027i
$596$		0			0
$597$	16.2470	−	16.2470i	0.664946	−	0.664946i
$598$		0			0
$599$			1.64390i			0.0671681i	0.999436	+	0.0335840i	$0.0106921\pi$
$599$			1.64390i			0.0671681i	−0.999436	+	0.0335840i	$0.989308\pi$
$600$		0			0
$601$			16.9911i			0.693081i	0.938035	+	0.346541i	$0.112644\pi$
$601$			16.9911i			0.693081i	−0.938035	+	0.346541i	$0.887356\pi$
$602$		0			0
$603$	2.53098	+	2.53098i	0.103070	+	0.103070i
$604$		0			0
$605$	15.3538	−	18.2890i	0.624221	−	0.743554i
$606$		0			0
$607$	−23.9674	−	23.9674i	−0.972808	−	0.972808i	0.0268319	−	0.999640i	$-0.491458\pi$
$607$	−23.9674	−	23.9674i	−0.972808	−	0.972808i	−0.999640	+	0.0268319i	$0.991458\pi$
$608$		0			0
$609$	4.56297	+	20.2713i	0.184901	+	0.821435i
$610$		0			0
$611$	−32.7567			−1.32520
$612$		0			0
$613$	28.8618	+	28.8618i	1.16572	+	1.16572i	0.983204	+	0.182512i	$0.0584228\pi$
$613$	28.8618	+	28.8618i	1.16572	+	1.16572i	0.182512	+	0.983204i	$0.441577\pi$
$614$		0			0
$615$	14.0303	−	1.22408i	0.565756	−	0.0493598i
$616$		0			0
$617$	28.8828	−	28.8828i	1.16278	−	1.16278i	0.178915	−	0.983865i	$-0.442741\pi$
$617$	28.8828	−	28.8828i	1.16278	−	1.16278i	0.983865	−	0.178915i	$-0.0572587\pi$
$618$		0			0
$619$	23.3279			0.937629			0.468814	−	0.883297i	$-0.344681\pi$
$619$	23.3279			0.937629			0.468814	+	0.883297i	$0.344681\pi$
$620$		0			0
$621$		−	3.60716i		−	0.144750i
$622$		0			0
$623$	−22.8719	−	14.4671i	−0.916342	−	0.579611i
$624$		0			0
$625$	−23.5005	+	8.52785i	−0.940022	+	0.341114i
$626$		0			0
$627$	−3.05138	+	3.05138i	−0.121860	+	0.121860i
$628$		0			0
$629$	−1.74848			−0.0697166
$630$		0			0
$631$	14.4398			0.574840			0.287420	−	0.957805i	$-0.407202\pi$
$631$	14.4398			0.574840			0.287420	+	0.957805i	$0.407202\pi$
$632$		0			0
$633$	−2.47605	+	2.47605i	−0.0984141	+	0.0984141i
$634$		0			0
$635$	−0.509289	−	5.83740i	−0.0202105	−	0.231650i
$636$		0			0
$637$	46.9327	+	16.7386i	1.85954	+	0.663208i
$638$		0			0
$639$		−	8.01809i		−	0.317191i
$640$		0			0
$641$	33.5748			1.32612			0.663062	−	0.748564i	$-0.269256\pi$
$641$	33.5748			1.32612			0.663062	+	0.748564i	$0.269256\pi$
$642$		0			0
$643$	14.6432	−	14.6432i	0.577473	−	0.577473i	−0.356733	−	0.934206i	$-0.616109\pi$
$643$	14.6432	−	14.6432i	0.577473	−	0.577473i	0.934206	+	0.356733i	$0.116109\pi$
$644$		0			0
$645$	5.57306	−	6.63847i	0.219439	−	0.261389i
$646$		0			0
$647$	8.05411	+	8.05411i	0.316640	+	0.316640i	0.847475	−	0.530835i	$-0.178122\pi$
$647$	8.05411	+	8.05411i	0.316640	+	0.316640i	−0.530835	+	0.847475i	$0.678122\pi$
$648$		0			0
$649$	−3.74966			−0.147187
$650$		0			0
$651$	4.11974	+	18.3022i	0.161465	+	0.717320i
$652$		0			0
$653$	−9.98708	−	9.98708i	−0.390825	−	0.390825i	0.484157	−	0.874981i	$-0.339126\pi$
$653$	−9.98708	−	9.98708i	−0.390825	−	0.390825i	−0.874981	+	0.484157i	$0.839126\pi$
$654$		0			0
$655$	−36.5064	−	30.6475i	−1.42642	−	1.19750i
$656$		0			0
$657$	8.97309	+	8.97309i	0.350074	+	0.350074i
$658$		0			0
$659$			1.39462i			0.0543266i	0.999631	+	0.0271633i	$0.00864741\pi$
$659$			1.39462i			0.0543266i	−0.999631	+	0.0271633i	$0.991353\pi$
$660$		0			0
$661$		−	21.6158i		−	0.840756i	−0.907349	−	0.420378i	$-0.861897\pi$
$661$		−	21.6158i		−	0.840756i	0.907349	−	0.420378i	$-0.138103\pi$
$662$		0			0
$663$	−7.00810	+	7.00810i	−0.272172	+	0.272172i
$664$		0			0
$665$	−42.9475	+	13.6830i	−1.66543	+	0.530603i
$666$		0			0
$667$	20.0316	−	20.0316i	0.775628	−	0.775628i
$668$		0			0
$669$		−	4.41709i		−	0.170775i
$670$		0			0
$671$		−	3.09774i		−	0.119587i
$672$		0			0
$673$	5.24015	+	5.24015i	0.201993	+	0.201993i	0.800853	−	0.598861i	$-0.204380\pi$
$673$	5.24015	+	5.24015i	0.201993	+	0.201993i	−0.598861	+	0.800853i	$0.704380\pi$
$674$		0			0
$675$	−2.86986	+	4.09438i	−0.110461	+	0.157593i
$676$		0			0
$677$	6.97956	+	6.97956i	0.268246	+	0.268246i	0.828393	−	0.560147i	$-0.189255\pi$
$677$	6.97956	+	6.97956i	0.268246	+	0.268246i	−0.560147	+	0.828393i	$0.689255\pi$
$678$		0			0
$679$	−3.55689	−	15.8017i	−0.136501	−	0.606414i
$680$		0			0
$681$	12.1476			0.465497
$682$		0			0
$683$	−35.7411	−	35.7411i	−1.36759	−	1.36759i	−0.863857	−	0.503737i	$-0.831958\pi$
$683$	−35.7411	−	35.7411i	−1.36759	−	1.36759i	−0.503737	−	0.863857i	$-0.668042\pi$
$684$		0			0
$685$	2.69500	+	30.8898i	0.102971	+	1.18024i
$686$		0			0
$687$	−12.5413	+	12.5413i	−0.478482	+	0.478482i
$688$		0			0
$689$	73.2612			2.79103
$690$		0			0
$691$			17.4404i			0.663466i	0.943373	+	0.331733i	$0.107633\pi$
$691$			17.4404i			0.663466i	−0.943373	+	0.331733i	$0.892367\pi$
$692$		0			0
$693$	−0.801059	+	1.26644i	−0.0304297	+	0.0481082i
$694$		0			0
$695$	−0.858018	+	1.02205i	−0.0325465	+	0.0387684i
$696$		0			0
$697$	−6.20083	+	6.20083i	−0.234873	+	0.234873i
$698$		0			0
$699$	4.10877			0.155408
$700$		0			0
$701$	4.54698			0.171737			0.0858686	−	0.996306i	$-0.472633\pi$
$701$	4.54698			0.171737			0.0858686	+	0.996306i	$0.472633\pi$
$702$		0			0
$703$	−6.76560	+	6.76560i	−0.255169	+	0.255169i
$704$		0			0
$705$	6.61607	−	7.88086i	0.249175	−	0.296810i
$706$		0			0
$707$	15.4563	−	24.4358i	0.581294	−	0.919003i
$708$		0			0
$709$		−	26.2362i		−	0.985320i	−0.870222	−	0.492660i	$-0.836025\pi$
$709$		−	26.2362i		−	0.985320i	0.870222	−	0.492660i	$-0.163975\pi$
$710$		0			0
$711$	−1.85942			−0.0697338
$712$		0			0
$713$	18.0858	−	18.0858i	0.677318	−	0.677318i
$714$		0			0
$715$	0.783566	+	8.98113i	0.0293037	+	0.335875i
$716$		0			0
$717$	15.7125	+	15.7125i	0.586795	+	0.586795i
$718$		0			0
$719$	−8.49807			−0.316924			−0.158462	−	0.987365i	$-0.550654\pi$
$719$	−8.49807			−0.316924			−0.158462	+	0.987365i	$0.550654\pi$
$720$		0			0
$721$	−22.3940	+	5.04079i	−0.833998	+	0.187729i
$722$		0			0
$723$	−20.4485	−	20.4485i	−0.760489	−	0.760489i
$724$		0			0
$725$	−38.6744	+	6.80013i	−1.43633	+	0.252550i
$726$		0			0
$727$	5.00053	+	5.00053i	0.185459	+	0.185459i	0.793730	−	0.608271i	$-0.208136\pi$
$727$	5.00053	+	5.00053i	0.185459	+	0.185459i	−0.608271	+	0.793730i	$0.708136\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$			5.39702i			0.199616i
$732$		0			0
$733$	16.5721	−	16.5721i	0.612105	−	0.612105i	−0.331389	−	0.943494i	$-0.607517\pi$
$733$	16.5721	−	16.5721i	0.612105	−	0.612105i	0.943494	+	0.331389i	$0.107517\pi$
$734$		0			0
$735$	−13.5064	+	7.91062i	−0.498190	+	0.291788i
$736$		0			0
$737$	−1.43352	+	1.43352i	−0.0528044	+	0.0528044i
$738$		0			0
$739$			15.1772i			0.558304i	0.960247	+	0.279152i	$0.0900534\pi$
$739$			15.1772i			0.558304i	−0.960247	+	0.279152i	$0.909947\pi$
$740$		0			0
$741$			54.2344i			1.99235i
$742$		0			0
$743$	21.9303	+	21.9303i	0.804545	+	0.804545i	0.983802	−	0.179257i	$-0.0573694\pi$
$743$	21.9303	+	21.9303i	0.804545	+	0.804545i	−0.179257	+	0.983802i	$0.557369\pi$
$744$		0			0
$745$	−1.45800	−	1.22401i	−0.0534171	−	0.0448442i
$746$		0			0
$747$	−2.61775	−	2.61775i	−0.0957786	−	0.0957786i
$748$		0			0
$749$	29.4872	−	6.63743i	1.07744	−	0.242526i
$750$		0			0
$751$	13.6852			0.499380			0.249690	−	0.968326i	$-0.419671\pi$
$751$	13.6852			0.499380			0.249690	+	0.968326i	$0.419671\pi$
$752$		0			0
$753$	10.7623	+	10.7623i	0.392201	+	0.392201i
$754$		0			0
$755$	13.0943	−	15.5975i	0.476549	−	0.567651i
$756$		0			0
$757$	−6.30930	+	6.30930i	−0.229315	+	0.229315i	−0.812407	−	0.583091i	$-0.801843\pi$
$757$	−6.30930	+	6.30930i	−0.229315	+	0.229315i	0.583091	+	0.812407i	$0.301843\pi$
$758$		0			0
$759$	2.04306			0.0741582
$760$		0			0
$761$			7.62961i			0.276573i	0.990392	+	0.138287i	$0.0441595\pi$
$761$			7.62961i			0.276573i	−0.990392	+	0.138287i	$0.955841\pi$
$762$		0			0
$763$	−14.8321	+	23.4491i	−0.536960	+	0.848913i
$764$		0			0
$765$	−0.270595	−	3.10153i	−0.00978339	−	0.112136i
$766$		0			0
$767$	−33.3227	+	33.3227i	−1.20321	+	1.20321i
$768$		0			0
$769$	−6.15472			−0.221945			−0.110973	−	0.993823i	$-0.535397\pi$
$769$	−6.15472			−0.221945			−0.110973	+	0.993823i	$0.535397\pi$
$770$		0			0
$771$	20.6354			0.743164
$772$		0			0
$773$	−8.65805	+	8.65805i	−0.311408	+	0.311408i	−0.845455	−	0.534047i	$-0.820671\pi$
$773$	−8.65805	+	8.65805i	−0.311408	+	0.311408i	0.534047	+	0.845455i	$0.320671\pi$
$774$		0			0
$775$	−34.9177	+	6.13958i	−1.25428	+	0.220540i
$776$		0			0
$777$	−1.77613	+	2.80799i	−0.0637183	+	0.100736i
$778$		0			0
$779$			47.9871i			1.71932i
$780$		0			0
$781$	4.54136			0.162502
$782$		0			0
$783$	−5.55329	+	5.55329i	−0.198459	+	0.198459i
$784$		0			0
$785$	−39.7501	+	3.46803i	−1.41874	+	0.123779i
$786$		0			0
$787$	23.1970	+	23.1970i	0.826884	+	0.826884i	0.987085	−	0.160200i	$-0.0512140\pi$
$787$	23.1970	+	23.1970i	0.826884	+	0.826884i	−0.160200	+	0.987085i	$0.551214\pi$
$788$		0			0
$789$	−15.5122			−0.552248
$790$		0			0
$791$	−2.71783	−	12.0741i	−0.0966349	−	0.429307i
$792$		0			0
$793$	−27.5292	−	27.5292i	−0.977591	−	0.977591i
$794$		0			0
$795$	−14.7970	+	17.6257i	−0.524795	+	0.625120i
$796$		0			0
$797$	−0.125809	−	0.125809i	−0.00445637	−	0.00445637i	0.704875	−	0.709331i	$-0.251003\pi$
$797$	−0.125809	−	0.125809i	−0.00445637	−	0.00445637i	−0.709331	+	0.704875i	$0.751003\pi$
$798$		0			0
$799$			6.40707i			0.226666i
$800$		0			0
$801$		−	10.2289i		−	0.361422i
$802$		0			0
$803$	−5.08226	+	5.08226i	−0.179349	+	0.179349i
$804$		0			0
$805$	18.9585	+	9.79704i	0.668199	+	0.345300i
$806$		0			0
$807$	13.3518	−	13.3518i	0.470004	−	0.470004i
$808$		0			0
$809$			19.4348i			0.683292i	0.939829	+	0.341646i	$0.110984\pi$
$809$			19.4348i			0.683292i	−0.939829	+	0.341646i	$0.889016\pi$
$810$		0			0
$811$		−	35.3797i		−	1.24235i	−0.783672	−	0.621175i	$-0.786656\pi$
$811$		−	35.3797i		−	1.24235i	0.783672	−	0.621175i	$-0.213344\pi$
$812$		0			0
$813$	−20.4283	−	20.4283i	−0.716453	−	0.716453i
$814$		0			0
$815$	0.434254	−	0.0378868i	0.0152112	−	0.00132712i
$816$		0			0
$817$	20.8833	+	20.8833i	0.730613	+	0.730613i
$818$		0			0
$819$	4.13581	+	18.3736i	0.144517	+	0.642025i
$820$		0			0
$821$	51.0482			1.78159			0.890797	−	0.454402i	$-0.150147\pi$
$821$	51.0482			1.78159			0.890797	+	0.454402i	$0.150147\pi$
$822$		0			0
$823$	16.3286	+	16.3286i	0.569178	+	0.569178i	0.931898	−	0.362720i	$-0.118152\pi$
$823$	16.3286	+	16.3286i	0.569178	+	0.569178i	−0.362720	+	0.931898i	$0.618152\pi$
$824$		0			0
$825$	−2.31901	−	1.62545i	−0.0807376	−	0.0565911i
$826$		0			0
$827$	6.41901	−	6.41901i	0.223211	−	0.223211i	−0.586638	−	0.809849i	$-0.699549\pi$
$827$	6.41901	−	6.41901i	0.223211	−	0.223211i	0.809849	+	0.586638i	$0.199549\pi$
$828$		0			0
$829$	−54.3081			−1.88620			−0.943100	−	0.332509i	$-0.892105\pi$
$829$	−54.3081			−1.88620			−0.943100	+	0.332509i	$0.892105\pi$
$830$		0			0
$831$		−	8.96261i		−	0.310909i
$832$		0			0
$833$	3.27400	−	9.17983i	0.113437	−	0.318062i
$834$		0			0
$835$	33.0660	−	2.88487i	1.14430	−	0.0998351i
$836$		0			0
$837$	−5.01386	+	5.01386i	−0.173304	+	0.173304i
$838$		0			0
$839$	−34.7651			−1.20022			−0.600112	−	0.799916i	$-0.704877\pi$
$839$	−34.7651			−1.20022			−0.600112	+	0.799916i	$0.704877\pi$
$840$		0			0
$841$	−32.6781			−1.12683
$842$		0			0
$843$	−15.0751	+	15.0751i	−0.519214	+	0.519214i
$844$		0			0
$845$	64.5139	+	54.1601i	2.21935	+	1.86316i
$846$		0			0
$847$	23.8787	+	15.1039i	0.820481	+	0.518976i
$848$		0			0
$849$			9.26183i			0.317865i
$850$		0			0
$851$	4.52992			0.155284
$852$		0			0
$853$	23.2485	−	23.2485i	0.796013	−	0.796013i	−0.186451	−	0.982464i	$-0.559699\pi$
$853$	23.2485	−	23.2485i	0.796013	−	0.796013i	0.982464	+	0.186451i	$0.0596987\pi$
$854$		0			0
$855$	−13.0481	−	10.9540i	−0.446236	−	0.374620i
$856$		0			0
$857$	17.6594	+	17.6594i	0.603234	+	0.603234i	0.941169	−	0.337936i	$-0.109729\pi$
$857$	17.6594	+	17.6594i	0.603234	+	0.603234i	−0.337936	+	0.941169i	$0.609729\pi$
$858$		0			0
$859$	−28.4270			−0.969916			−0.484958	−	0.874538i	$-0.661165\pi$
$859$	−28.4270			−0.969916			−0.484958	+	0.874538i	$0.661165\pi$
$860$		0			0
$861$	3.65940	+	16.2571i	0.124712	+	0.554042i
$862$		0			0
$863$	−20.7557	−	20.7557i	−0.706533	−	0.706533i	0.259271	−	0.965805i	$-0.416518\pi$
$863$	−20.7557	−	20.7557i	−0.706533	−	0.706533i	−0.965805	+	0.259271i	$0.916518\pi$
$864$		0			0
$865$	−3.02653	−	34.6897i	−0.102905	−	1.17949i
$866$		0			0
$867$	−10.6501	−	10.6501i	−0.361695	−	0.361695i
$868$		0			0
$869$		−	1.05316i		−	0.0357259i
$870$		0			0
$871$			25.4790i			0.863322i
$872$		0			0
$873$	4.32885	−	4.32885i	0.146509	−	0.146509i
$874$		0			0
$875$	−13.7247	−	26.2037i	−0.463979	−	0.885846i
$876$		0			0
$877$	−19.2652	+	19.2652i	−0.650538	+	0.650538i	−0.953123	−	0.302584i	$-0.902151\pi$
$877$	−19.2652	+	19.2652i	−0.650538	+	0.650538i	0.302584	+	0.953123i	$0.402151\pi$
$878$		0			0
$879$			4.60157i			0.155207i
$880$		0			0
$881$			48.3786i			1.62992i	0.579520	+	0.814958i	$0.303240\pi$
$881$			48.3786i			1.62992i	−0.579520	+	0.814958i	$0.696760\pi$
$882$		0			0
$883$	−5.45177	−	5.45177i	−0.183467	−	0.183467i	0.609398	−	0.792865i	$-0.291411\pi$
$883$	−5.45177	−	5.45177i	−0.183467	−	0.183467i	−0.792865	+	0.609398i	$0.791411\pi$
$884$		0			0
$885$	−1.28665	−	14.7474i	−0.0432502	−	0.495729i
$886$		0			0
$887$	34.6612	+	34.6612i	1.16381	+	1.16381i	0.983635	+	0.180173i	$0.0576659\pi$
$887$	34.6612	+	34.6612i	1.16381	+	1.16381i	0.180173	+	0.983635i	$0.442334\pi$
$888$		0			0
$889$	6.76391	−	1.52252i	0.226854	−	0.0510638i
$890$		0			0
$891$	−0.566389			−0.0189747
$892$		0			0
$893$	24.7916	+	24.7916i	0.829619	+	0.829619i
$894$		0			0
$895$	44.1459	+	37.0609i	1.47563	+	1.23881i
$896$		0			0
$897$	18.1563	−	18.1563i	0.606223	−	0.606223i
$898$		0			0
$899$	−55.6869			−1.85726
$900$		0			0
$901$		−	14.3296i		−	0.477387i
$902$		0			0
$903$	8.66738	+	5.48235i	0.288432	+	0.182441i
$904$		0			0
$905$	−17.7911	−	14.9358i	−0.591397	−	0.496484i
$906$		0			0
$907$	24.8856	−	24.8856i	0.826313	−	0.826313i	−0.160692	−	0.987005i	$-0.551373\pi$
$907$	24.8856	−	24.8856i	0.826313	−	0.826313i	0.987005	+	0.160692i	$0.0513726\pi$
$908$		0			0
$909$	10.9284			0.362471
$910$		0			0
$911$	30.5002			1.01052			0.505258	−	0.862968i	$-0.331397\pi$
$911$	30.5002			1.01052			0.505258	+	0.862968i	$0.331397\pi$
$912$		0			0
$913$	1.48267	−	1.48267i	0.0490691	−	0.0490691i
$914$		0			0
$915$	12.1834	−	1.06295i	0.402771	−	0.0351401i
$916$		0			0
$917$	30.1486	−	47.6638i	0.995594	−	1.57400i
$918$		0			0
$919$		−	14.2577i		−	0.470317i	−0.971957	−	0.235158i	$-0.924439\pi$
$919$		−	14.2577i		−	0.470317i	0.971957	−	0.235158i	$-0.0755608\pi$
$920$		0			0
$921$	15.9262			0.524787
$922$		0			0
$923$	40.3584	−	40.3584i	1.32841	−	1.32841i
$924$		0			0
$925$	−5.14177	−	3.60400i	−0.169060	−	0.118499i
$926$		0			0
$927$	−6.13481	−	6.13481i	−0.201494	−	0.201494i
$928$		0			0
$929$	44.9793			1.47572			0.737861	−	0.674953i	$-0.235836\pi$
$929$	44.9793			1.47572			0.737861	+	0.674953i	$0.235836\pi$
$930$		0			0
$931$	−22.8521	−	48.1890i	−0.748946	−	1.57933i
$932$		0			0
$933$	−6.51911	−	6.51911i	−0.213426	−	0.213426i
$934$		0			0
$935$	1.75667	−	0.153262i	0.0574493	−	0.00501221i
$936$		0			0
$937$	6.27637	+	6.27637i	0.205040	+	0.205040i	0.802155	−	0.597115i	$-0.203687\pi$
$937$	6.27637	+	6.27637i	0.205040	+	0.205040i	−0.597115	+	0.802155i	$0.703687\pi$
$938$		0			0
$939$		−	12.6657i		−	0.413330i
$940$		0			0
$941$			17.1580i			0.559334i	0.960097	+	0.279667i	$0.0902241\pi$
$941$			17.1580i			0.559334i	−0.960097	+	0.279667i	$0.909776\pi$
$942$		0			0
$943$	16.0649	−	16.0649i	0.523146	−	0.523146i
$944$		0			0
$945$	−5.25579	−	2.71600i	−0.170971	−	0.0883514i
$946$		0			0
$947$	29.8882	−	29.8882i	0.971235	−	0.971235i	−0.0283627	−	0.999598i	$-0.509029\pi$
$947$	29.8882	−	29.8882i	0.971235	−	0.971235i	0.999598	+	0.0283627i	$0.00902935\pi$
$948$		0			0
$949$			90.3306i			2.93226i
$950$		0			0
$951$			0.675973i			0.0219199i
$952$		0			0
$953$	17.5878	+	17.5878i	0.569726	+	0.569726i	0.932052	−	0.362325i	$-0.118017\pi$
$953$	17.5878	+	17.5878i	0.569726	+	0.569726i	−0.362325	+	0.932052i	$0.618017\pi$
$954$		0			0
$955$	−22.4195	+	26.7055i	−0.725479	+	0.864169i
$956$		0			0
$957$	−3.14532	−	3.14532i	−0.101674	−	0.101674i
$958$		0			0
$959$	−35.7925	+	8.05673i	−1.15580	+	0.260165i
$960$		0			0
$961$	−19.2776			−0.621857
$962$		0			0
$963$	8.07798	+	8.07798i	0.260309	+	0.260309i
$964$		0			0
$965$	−6.36841	+	0.555617i	−0.205006	+	0.0178859i
$966$		0			0
$967$	−23.9895	+	23.9895i	−0.771450	+	0.771450i	−0.978360	−	0.206910i	$-0.933659\pi$
$967$	−23.9895	+	23.9895i	−0.771450	+	0.771450i	0.206910	+	0.978360i	$0.433659\pi$
$968$		0			0
$969$	10.6080			0.340778
$970$		0			0
$971$			18.8172i			0.603872i	0.953328	+	0.301936i	$0.0976329\pi$
$971$			18.8172i			0.603872i	−0.953328	+	0.301936i	$0.902367\pi$
$972$		0			0
$973$	−1.33441	−	0.844052i	−0.0427793	−	0.0270591i
$974$		0			0
$975$	−35.0539	+	6.16353i	−1.12262	+	0.197391i
$976$		0			0
$977$	−6.84647	+	6.84647i	−0.219038	+	0.219038i	−0.808093	−	0.589055i	$-0.799500\pi$
$977$	−6.84647	+	6.84647i	−0.219038	+	0.219038i	0.589055	+	0.808093i	$0.299500\pi$
$978$		0			0
$979$	5.79356			0.185163
$980$		0			0
$981$	−10.4871			−0.334826
$982$		0			0
$983$	−31.3553	+	31.3553i	−1.00008	+	1.00008i	−7.76361e−5		1.00000i	$0.500025\pi$
$983$	−31.3553	+	31.3553i	−1.00008	+	1.00008i	−1.00000		7.76361e-5i	$0.999975\pi$
$984$		0			0
$985$	−1.40781	−	16.1361i	−0.0448564	−	0.514139i
$986$		0			0
$987$	10.2895	+	6.50837i	0.327518	+	0.207164i
$988$		0			0
$989$		−	13.9824i		−	0.444615i
$990$		0			0
$991$	18.2867			0.580896			0.290448	−	0.956891i	$-0.406196\pi$
$991$	18.2867			0.580896			0.290448	+	0.956891i	$0.406196\pi$
$992$		0			0
$993$	12.6832	−	12.6832i	0.402489	−	0.402489i
$994$		0			0
$995$	−33.0344	+	39.3496i	−1.04726	+	1.24746i
$996$		0			0
$997$	−13.1117	−	13.1117i	−0.415251	−	0.415251i	0.468312	−	0.883563i	$-0.344862\pi$
$997$	−13.1117	−	13.1117i	−0.415251	−	0.415251i	−0.883563	+	0.468312i	$0.844862\pi$
$998$		0			0
$999$	−1.25581			−0.0397321

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bt.a.433.8	yes	24
4.3	odd	2		1680.2.cz.f.433.4		24
5.2	odd	4		840.2.bt.b.97.5	yes	24
7.6	odd	2		840.2.bt.b.433.5	yes	24
20.7	even	4		1680.2.cz.e.97.9		24
28.27	even	2		1680.2.cz.e.433.9		24
35.27	even	4	inner	840.2.bt.a.97.8	✓	24
140.27	odd	4		1680.2.cz.f.97.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bt.a.97.8	✓	24	35.27	even	4	inner
840.2.bt.a.433.8	yes	24	1.1	even	1	trivial
840.2.bt.b.97.5	yes	24	5.2	odd	4
840.2.bt.b.433.5	yes	24	7.6	odd	2
1680.2.cz.e.97.9		24	20.7	even	4
1680.2.cz.e.433.9		24	28.27	even	2
1680.2.cz.f.97.4		24	140.27	odd	4
1680.2.cz.f.433.4		24	4.3	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bt (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-1.43773 + 1.71258i) q^{5} +(-2.23600 - 1.41433i) q^{7} -1.00000i q^{9} +0.566389 q^{11} +(5.03342 - 5.03342i) q^{13} +(0.194349 + 2.22761i) q^{15} +(-0.984515 - 0.984515i) q^{17} -7.61898 q^{19} +(-2.58117 + 0.581008i) q^{21} +(2.55065 + 2.55065i) q^{23} +(-0.865867 - 4.92446i) q^{25} +(-0.707107 - 0.707107i) q^{27} -7.85354i q^{29} -7.09067i q^{31} +(0.400498 - 0.400498i) q^{33} +(5.63691 - 1.79591i) q^{35} +(0.887993 - 0.887993i) q^{37} -7.11833i q^{39} -6.29837i q^{41} +(-2.74095 - 2.74095i) q^{43} +(1.71258 + 1.43773i) q^{45} +(-3.25393 - 3.25393i) q^{47} +(2.99936 + 6.32486i) q^{49} -1.39231 q^{51} +(7.27748 + 7.27748i) q^{53} +(-0.814314 + 0.969987i) q^{55} +(-5.38743 + 5.38743i) q^{57} -6.62029 q^{59} -5.46929i q^{61} +(-1.41433 + 2.23600i) q^{63} +(1.38344 + 15.8568i) q^{65} +(-2.53098 + 2.53098i) q^{67} +3.60716 q^{69} +8.01809 q^{71} +(-8.97309 + 8.97309i) q^{73} +(-4.09438 - 2.86986i) q^{75} +(-1.26644 - 0.801059i) q^{77} -1.85942i q^{79} -1.00000 q^{81} +(2.61775 - 2.61775i) q^{83} +(3.10153 - 0.270595i) q^{85} +(-5.55329 - 5.55329i) q^{87} +10.2289 q^{89} +(-18.3736 + 4.13581i) q^{91} +(-5.01386 - 5.01386i) q^{93} +(10.9540 - 13.0481i) q^{95} +(4.32885 + 4.32885i) q^{97} -0.566389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7} - 8 q^{11} + 16 q^{13} + 4 q^{15} + 20 q^{17} + 8 q^{19} + 24 q^{23} - 4 q^{25} + 4 q^{37} - 16 q^{43} - 4 q^{45} - 24 q^{47} + 36 q^{49} + 16 q^{53} + 28 q^{55} + 4 q^{57} + 8 q^{59} + 24 q^{65}+ \cdots - 28 q^{97}+O(q^{100}) \) 24 * q - 4 * q^7 - 8 * q^11 + 16 * q^13 + 4 * q^15 + 20 * q^17 + 8 * q^19 + 24 * q^23 - 4 * q^25 + 4 * q^37 - 16 * q^43 - 4 * q^45 - 24 * q^47 + 36 * q^49 + 16 * q^53 + 28 * q^55 + 4 * q^57 + 8 * q^59 + 24 * q^65 + 16 * q^67 - 8 * q^69 + 8 * q^71 - 28 * q^73 + 20 * q^77 - 24 * q^81 + 64 * q^83 - 20 * q^85 + 20 * q^87 + 16 * q^89 + 24 * q^91 - 12 * q^93 + 24 * q^95 - 28 * q^97

Introduction

L-functions

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