LMFDB - Embedded newform 840.2.bt.b.433.3

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 = [24,0,0,0,0,0,0] 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			433.3
Character	$\chi$	$=$	840.433
Dual form			840.2.bt.b.97.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.600524 + 2.15392i) q^{5} +(-0.367100 - 2.62016i) q^{7} -1.00000i q^{9} +4.78670 q^{11} +(0.368427 - 0.368427i) q^{13} +(-1.09842 - 1.94769i) q^{15} +(-1.10849 - 1.10849i) q^{17} +5.13150 q^{19} +(2.11231 + 1.59315i) q^{21} +(2.14942 + 2.14942i) q^{23} +(-4.27874 - 2.58696i) q^{25} +(0.707107 + 0.707107i) q^{27} +9.26310i q^{29} +8.98258i q^{31} +(-3.38471 + 3.38471i) q^{33} +(5.86407 + 0.782765i) q^{35} +(3.69797 - 3.69797i) q^{37} +0.521035i q^{39} -1.99873i q^{41} +(-1.62357 - 1.62357i) q^{43} +(2.15392 + 0.600524i) q^{45} +(7.81238 + 7.81238i) q^{47} +(-6.73047 + 1.92372i) q^{49} +1.56764 q^{51} +(0.588481 + 0.588481i) q^{53} +(-2.87453 + 10.3102i) q^{55} +(-3.62852 + 3.62852i) q^{57} +2.58034 q^{59} -1.56334i q^{61} +(-2.62016 + 0.367100i) q^{63} +(0.572313 + 1.01481i) q^{65} +(-6.06196 + 6.06196i) q^{67} -3.03974 q^{69} +7.74766 q^{71} +(-2.10421 + 2.10421i) q^{73} +(4.85479 - 1.19627i) q^{75} +(-1.75720 - 12.5419i) q^{77} -4.57977i q^{79} -1.00000 q^{81} +(6.55378 - 6.55378i) q^{83} +(3.05327 - 1.72192i) q^{85} +(-6.55000 - 6.55000i) q^{87} +8.77219 q^{89} +(-1.10059 - 0.830088i) q^{91} +(-6.35165 - 6.35165i) q^{93} +(-3.08159 + 11.0528i) q^{95} +(0.711808 + 0.711808i) q^{97} -4.78670i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 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} + 4 q^{63} + 24 q^{65}+ \cdots + 28 q^{97}+O(q^{100}) $ 24 * q - 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 + 4 * q^63 + 24 * q^65 + 16 * q^67 + 8 * q^69 + 8 * q^71 + 28 * q^73 + 28 * 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
$5$	−0.600524	+	2.15392i	−0.268562	+	0.963262i
$5$	−0.600524	+	2.15392i	−0.268562	+	0.963262i
$6$		0			0
$7$	−0.367100	−	2.62016i	−0.138751	−	0.990327i
$7$	−0.367100	−	2.62016i	−0.138751	−	0.990327i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	4.78670			1.44324			0.721622	−	0.692287i	$-0.243397\pi$
$11$	4.78670			1.44324			0.721622	+	0.692287i	$0.243397\pi$
$12$		0			0
$13$	0.368427	−	0.368427i	0.102183	−	0.102183i	−0.654167	−	0.756350i	$-0.726981\pi$
$13$	0.368427	−	0.368427i	0.102183	−	0.102183i	0.756350	+	0.654167i	$0.226981\pi$
$14$		0			0
$15$	−1.09842	−	1.94769i	−0.283610	−	0.502890i
$16$		0			0
$17$	−1.10849	−	1.10849i	−0.268848	−	0.268848i	0.559788	−	0.828636i	$-0.310883\pi$
$17$	−1.10849	−	1.10849i	−0.268848	−	0.268848i	−0.828636	+	0.559788i	$0.810883\pi$
$18$		0			0
$19$	5.13150			1.17725			0.588624	−	0.808407i	$-0.299670\pi$
$19$	5.13150			1.17725			0.588624	+	0.808407i	$0.299670\pi$
$20$		0			0
$21$	2.11231	+	1.59315i	0.460944	+	0.347655i
$22$		0			0
$23$	2.14942	+	2.14942i	0.448186	+	0.448186i	0.894751	−	0.446565i	$-0.147353\pi$
$23$	2.14942	+	2.14942i	0.448186	+	0.448186i	−0.446565	+	0.894751i	$0.647353\pi$
$24$		0			0
$25$	−4.27874	−	2.58696i	−0.855748	−	0.517392i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$			9.26310i			1.72011i	0.510198	+	0.860057i	$0.329572\pi$
$29$			9.26310i			1.72011i	−0.510198	+	0.860057i	$0.670428\pi$
$30$		0			0
$31$			8.98258i			1.61332i	0.591016	+	0.806660i	$0.298727\pi$
$31$			8.98258i			1.61332i	−0.591016	+	0.806660i	$0.701273\pi$
$32$		0			0
$33$	−3.38471	+	3.38471i	−0.589202	+	0.589202i
$34$		0			0
$35$	5.86407	+	0.782765i	0.991208	+	0.132311i
$36$		0			0
$37$	3.69797	−	3.69797i	0.607942	−	0.607942i	−0.334466	−	0.942408i	$-0.608556\pi$
$37$	3.69797	−	3.69797i	0.607942	−	0.607942i	0.942408	+	0.334466i	$0.108556\pi$
$38$		0			0
$39$			0.521035i			0.0834323i
$40$		0			0
$41$		−	1.99873i		−	0.312149i	−0.987745	−	0.156075i	$-0.950116\pi$
$41$		−	1.99873i		−	0.312149i	0.987745	−	0.156075i	$-0.0498841\pi$
$42$		0			0
$43$	−1.62357	−	1.62357i	−0.247592	−	0.247592i	0.572390	−	0.819982i	$-0.306016\pi$
$43$	−1.62357	−	1.62357i	−0.247592	−	0.247592i	−0.819982	+	0.572390i	$0.806016\pi$
$44$		0			0
$45$	2.15392	+	0.600524i	0.321087	+	0.0895208i
$46$		0			0
$47$	7.81238	+	7.81238i	1.13955	+	1.13955i	0.988530	+	0.151023i	$0.0482567\pi$
$47$	7.81238	+	7.81238i	1.13955	+	1.13955i	0.151023	+	0.988530i	$0.451743\pi$
$48$		0			0
$49$	−6.73047	+	1.92372i	−0.961496	+	0.274817i
$50$		0			0
$51$	1.56764			0.219513
$52$		0			0
$53$	0.588481	+	0.588481i	0.0808340	+	0.0808340i	0.746368	−	0.665534i	$-0.231796\pi$
$53$	0.588481	+	0.588481i	0.0808340	+	0.0808340i	−0.665534	+	0.746368i	$0.731796\pi$
$54$		0			0
$55$	−2.87453	+	10.3102i	−0.387601	+	1.39022i
$56$		0			0
$57$	−3.62852	+	3.62852i	−0.480609	+	0.480609i
$58$		0			0
$59$	2.58034			0.335932			0.167966	−	0.985793i	$-0.446280\pi$
$59$	2.58034			0.335932			0.167966	+	0.985793i	$0.446280\pi$
$60$		0			0
$61$		−	1.56334i		−	0.200165i	−0.994979	−	0.100083i	$-0.968089\pi$
$61$		−	1.56334i		−	0.200165i	0.994979	−	0.100083i	$-0.0319107\pi$
$62$		0			0
$63$	−2.62016	+	0.367100i	−0.330109	+	0.0462503i
$64$		0			0
$65$	0.572313	+	1.01481i	0.0709867	+	0.125872i
$66$		0			0
$67$	−6.06196	+	6.06196i	−0.740586	+	0.740586i	−0.972691	−	0.232105i	$-0.925439\pi$
$67$	−6.06196	+	6.06196i	−0.740586	+	0.740586i	0.232105	+	0.972691i	$0.425439\pi$
$68$		0			0
$69$	−3.03974			−0.365942
$70$		0			0
$71$	7.74766			0.919478			0.459739	−	0.888054i	$-0.347943\pi$
$71$	7.74766			0.919478			0.459739	+	0.888054i	$0.347943\pi$
$72$		0			0
$73$	−2.10421	+	2.10421i	−0.246279	+	0.246279i	−0.819441	−	0.573163i	$-0.805716\pi$
$73$	−2.10421	+	2.10421i	−0.246279	+	0.246279i	0.573163	+	0.819441i	$0.305716\pi$
$74$		0			0
$75$	4.85479	−	1.19627i	0.560582	−	0.138133i
$76$		0			0
$77$	−1.75720	−	12.5419i	−0.200251	−	1.42928i
$78$		0			0
$79$		−	4.57977i		−	0.515265i	−0.966243	−	0.257632i	$-0.917058\pi$
$79$		−	4.57977i		−	0.515265i	0.966243	−	0.257632i	$-0.0829423\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	6.55378	−	6.55378i	0.719371	−	0.719371i	−0.249105	−	0.968476i	$-0.580137\pi$
$83$	6.55378	−	6.55378i	0.719371	−	0.719371i	0.968476	+	0.249105i	$0.0801365\pi$
$84$		0			0
$85$	3.05327	−	1.72192i	0.331174	−	0.186769i
$86$		0			0
$87$	−6.55000	−	6.55000i	−0.702234	−	0.702234i
$88$		0			0
$89$	8.77219			0.929851			0.464925	−	0.885350i	$-0.346081\pi$
$89$	8.77219			0.929851			0.464925	+	0.885350i	$0.346081\pi$
$90$		0			0
$91$	−1.10059	−	0.830088i	−0.115373	−	0.0870169i
$92$		0			0
$93$	−6.35165	−	6.35165i	−0.658635	−	0.658635i
$94$		0			0
$95$	−3.08159	+	11.0528i	−0.316165	+	1.13400i
$96$		0			0
$97$	0.711808	+	0.711808i	0.0722731	+	0.0722731i	0.742319	−	0.670046i	$-0.233726\pi$
$97$	0.711808	+	0.711808i	0.0722731	+	0.0722731i	−0.670046	+	0.742319i	$0.733726\pi$
$98$		0			0
$99$		−	4.78670i		−	0.481082i
$100$		0			0
$101$		−	8.16606i		−	0.812554i	−0.913750	−	0.406277i	$-0.866827\pi$
$101$		−	8.16606i		−	0.812554i	0.913750	−	0.406277i	$-0.133173\pi$
$102$		0			0
$103$	1.23701	−	1.23701i	0.121886	−	0.121886i	−0.643533	−	0.765419i	$-0.722532\pi$
$103$	1.23701	−	1.23701i	0.121886	−	0.121886i	0.765419	+	0.643533i	$0.222532\pi$
$104$		0			0
$105$	−4.70002	+	3.59302i	−0.458675	+	0.350643i
$106$		0			0
$107$	12.0450	−	12.0450i	1.16444	−	1.16444i	0.180946	−	0.983493i	$-0.442084\pi$
$107$	12.0450	−	12.0450i	1.16444	−	1.16444i	0.983493	−	0.180946i	$-0.0579158\pi$
$108$		0			0
$109$			18.4026i			1.76265i	0.472512	+	0.881324i	$0.343347\pi$
$109$			18.4026i			1.76265i	−0.472512	+	0.881324i	$0.656653\pi$
$110$		0			0
$111$			5.22972i			0.496383i
$112$		0			0
$113$	−1.12534	−	1.12534i	−0.105864	−	0.105864i	0.652191	−	0.758055i	$-0.273850\pi$
$113$	−1.12534	−	1.12534i	−0.105864	−	0.105864i	−0.758055	+	0.652191i	$0.773850\pi$
$114$		0			0
$115$	−5.92046	+	3.33890i	−0.552086	+	0.311354i
$116$		0			0
$117$	−0.368427	−	0.368427i	−0.0340611	−	0.0340611i
$118$		0			0
$119$	−2.49749	+	3.31134i	−0.228945	+	0.303550i
$120$		0			0
$121$	11.9125			1.08296
$122$		0			0
$123$	1.41332	+	1.41332i	0.127434	+	0.127434i
$124$		0			0
$125$	8.14159	−	7.66254i	0.728206	−	0.685358i
$126$		0			0
$127$	14.0690	−	14.0690i	1.24842	−	1.24842i	0.292002	−	0.956418i	$-0.405678\pi$
$127$	14.0690	−	14.0690i	1.24842	−	1.24842i	0.956418	−	0.292002i	$-0.0943215\pi$
$128$		0			0
$129$	2.29607			0.202158
$130$		0			0
$131$		−	10.9757i		−	0.958951i	−0.877555	−	0.479476i	$-0.840827\pi$
$131$		−	10.9757i		−	0.958951i	0.877555	−	0.479476i	$-0.159173\pi$
$132$		0			0
$133$	−1.88378	−	13.4454i	−0.163344	−	1.16586i
$134$		0			0
$135$	−1.94769	+	1.09842i	−0.167630	+	0.0945367i
$136$		0			0
$137$	−14.4981	+	14.4981i	−1.23866	+	1.23866i	−0.278109	+	0.960549i	$0.589708\pi$
$137$	−14.4981	+	14.4981i	−1.23866	+	1.23866i	−0.960549	+	0.278109i	$0.910292\pi$
$138$		0			0
$139$	11.3904			0.966124			0.483062	−	0.875586i	$-0.339525\pi$
$139$	11.3904			0.966124			0.483062	+	0.875586i	$0.339525\pi$
$140$		0			0
$141$	−11.0484			−0.930441
$142$		0			0
$143$	1.76355	−	1.76355i	0.147476	−	0.147476i
$144$		0			0
$145$	−19.9520	−	5.56271i	−1.65692	−	0.461958i
$146$		0			0
$147$	3.39889	−	6.11944i	0.280336	−	0.504723i
$148$		0			0
$149$			10.9050i			0.893375i	0.894690	+	0.446688i	$0.147396\pi$
$149$			10.9050i			0.893375i	−0.894690	+	0.446688i	$0.852604\pi$
$150$		0			0
$151$	−18.0691			−1.47045			−0.735223	−	0.677826i	$-0.762922\pi$
$151$	−18.0691			−1.47045			−0.735223	+	0.677826i	$0.762922\pi$
$152$		0			0
$153$	−1.10849	+	1.10849i	−0.0896160	+	0.0896160i
$154$		0			0
$155$	−19.3478	−	5.39426i	−1.55405	−	0.433277i
$156$		0			0
$157$	−1.32204	−	1.32204i	−0.105511	−	0.105511i	0.652381	−	0.757891i	$-0.273770\pi$
$157$	−1.32204	−	1.32204i	−0.105511	−	0.105511i	−0.757891	+	0.652381i	$0.773770\pi$
$158$		0			0
$159$	−0.832237			−0.0660007
$160$		0			0
$161$	4.84278	−	6.42088i	0.381664	−	0.506037i
$162$		0			0
$163$	−11.8037	−	11.8037i	−0.924536	−	0.924536i	0.0728096	−	0.997346i	$-0.476803\pi$
$163$	−11.8037	−	11.8037i	−0.924536	−	0.924536i	−0.997346	+	0.0728096i	$0.976803\pi$
$164$		0			0
$165$	−5.25779	−	9.32299i	−0.409319	−	0.725794i
$166$		0			0
$167$	−14.8889	−	14.8889i	−1.15214	−	1.15214i	−0.986123	−	0.166017i	$-0.946909\pi$
$167$	−14.8889	−	14.8889i	−1.15214	−	1.15214i	−0.166017	−	0.986123i	$-0.553091\pi$
$168$		0			0
$169$			12.7285i			0.979117i
$170$		0			0
$171$		−	5.13150i		−	0.392416i
$172$		0			0
$173$	−14.6178	+	14.6178i	−1.11137	+	1.11137i	−0.118407	+	0.992965i	$0.537779\pi$
$173$	−14.6178	+	14.6178i	−1.11137	+	1.11137i	−0.992965	+	0.118407i	$0.962221\pi$
$174$		0			0
$175$	−5.20752	+	12.1607i	−0.393652	+	0.919260i
$176$		0			0
$177$	−1.82458	+	1.82458i	−0.137144	+	0.137144i
$178$		0			0
$179$			6.38689i			0.477379i	0.971096	+	0.238689i	$0.0767177\pi$
$179$			6.38689i			0.477379i	−0.971096	+	0.238689i	$0.923282\pi$
$180$		0			0
$181$		−	18.5609i		−	1.37962i	−0.723990	−	0.689811i	$-0.757694\pi$
$181$		−	18.5609i		−	1.37962i	0.723990	−	0.689811i	$-0.242306\pi$
$182$		0			0
$183$	1.10545	+	1.10545i	0.0817171	+	0.0817171i
$184$		0			0
$185$	5.74441	+	10.1858i	0.422337	+	0.748878i
$186$		0			0
$187$	−5.30600	−	5.30600i	−0.388013	−	0.388013i
$188$		0			0
$189$	1.59315	−	2.11231i	0.115885	−	0.153648i
$190$		0			0
$191$	19.6607			1.42260			0.711301	−	0.702888i	$-0.248106\pi$
$191$	19.6607			1.42260			0.711301	+	0.702888i	$0.248106\pi$
$192$		0			0
$193$	−15.4398	−	15.4398i	−1.11138	−	1.11138i	−0.992964	−	0.118419i	$-0.962217\pi$
$193$	−15.4398	−	15.4398i	−1.11138	−	1.11138i	−0.118419	−	0.992964i	$-0.537783\pi$
$194$		0			0
$195$	−1.12227	−	0.312894i	−0.0803672	−	0.0224068i
$196$		0			0
$197$	−2.12674	+	2.12674i	−0.151524	+	0.151524i	−0.778798	−	0.627274i	$-0.784170\pi$
$197$	−2.12674	+	2.12674i	−0.151524	+	0.151524i	0.627274	+	0.778798i	$0.284170\pi$
$198$		0			0
$199$	−3.94924			−0.279954			−0.139977	−	0.990155i	$-0.544703\pi$
$199$	−3.94924			−0.279954			−0.139977	+	0.990155i	$0.544703\pi$
$200$		0			0
$201$		−	8.57290i		−	0.604686i
$202$		0			0
$203$	24.2708	−	3.40048i	1.70348	−	0.238667i
$204$		0			0
$205$	4.30511	+	1.20029i	0.300682	+	0.0838316i
$206$		0			0
$207$	2.14942	−	2.14942i	0.149395	−	0.149395i
$208$		0			0
$209$	24.5630			1.69906
$210$		0			0
$211$	−18.1393			−1.24876			−0.624381	−	0.781120i	$-0.714649\pi$
$211$	−18.1393			−1.24876			−0.624381	+	0.781120i	$0.714649\pi$
$212$		0			0
$213$	−5.47843	+	5.47843i	−0.375376	+	0.375376i
$214$		0			0
$215$	4.47203	−	2.52204i	0.304990	−	0.172002i
$216$		0			0
$217$	23.5358	−	3.29751i	1.59771	−	0.223849i
$218$		0			0
$219$		−	2.97580i		−	0.201086i
$220$		0			0
$221$	−0.816794			−0.0549435
$222$		0			0
$223$	−11.5740	+	11.5740i	−0.775055	+	0.775055i	−0.978985	−	0.203931i	$-0.934628\pi$
$223$	−11.5740	+	11.5740i	−0.775055	+	0.775055i	0.203931	+	0.978985i	$0.434628\pi$
$224$		0			0
$225$	−2.58696	+	4.27874i	−0.172464	+	0.285249i
$226$		0			0
$227$	−10.9495	−	10.9495i	−0.726742	−	0.726742i	0.243227	−	0.969969i	$-0.421794\pi$
$227$	−10.9495	−	10.9495i	−0.726742	−	0.726742i	−0.969969	+	0.243227i	$0.921794\pi$
$228$		0			0
$229$	12.3859			0.818484			0.409242	−	0.912426i	$-0.365793\pi$
$229$	12.3859			0.818484			0.409242	+	0.912426i	$0.365793\pi$
$230$		0			0
$231$	10.1110	+	7.62595i	0.665255	+	0.501751i
$232$		0			0
$233$	−4.46761	−	4.46761i	−0.292683	−	0.292683i	0.545456	−	0.838139i	$-0.316356\pi$
$233$	−4.46761	−	4.46761i	−0.292683	−	0.292683i	−0.838139	+	0.545456i	$0.816356\pi$
$234$		0			0
$235$	−21.5188	+	12.1357i	−1.40373	+	0.791647i
$236$		0			0
$237$	3.23839	+	3.23839i	0.210356	+	0.210356i
$238$		0			0
$239$			19.8745i			1.28557i	0.766046	+	0.642786i	$0.222222\pi$
$239$			19.8745i			1.28557i	−0.766046	+	0.642786i	$0.777778\pi$
$240$		0			0
$241$		−	25.8710i		−	1.66650i	−0.552897	−	0.833250i	$-0.686478\pi$
$241$		−	25.8710i		−	1.66650i	0.552897	−	0.833250i	$-0.313522\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	−0.101732	−	15.6521i	−0.00649939	−	0.999979i
$246$		0			0
$247$	1.89058	−	1.89058i	0.120295	−	0.120295i
$248$		0			0
$249$			9.26845i			0.587364i
$250$		0			0
$251$			0.651258i			0.0411070i	0.999789	+	0.0205535i	$0.00654285\pi$
$251$			0.651258i			0.0411070i	−0.999789	+	0.0205535i	$0.993457\pi$
$252$		0			0
$253$	10.2886	+	10.2886i	0.646842	+	0.646842i
$254$		0			0
$255$	−0.941405	+	3.37657i	−0.0589531	+	0.211449i
$256$		0			0
$257$	−8.31784	−	8.31784i	−0.518852	−	0.518852i	0.398372	−	0.917224i	$-0.369575\pi$
$257$	−8.31784	−	8.31784i	−0.518852	−	0.518852i	−0.917224	+	0.398372i	$0.869575\pi$
$258$		0			0
$259$	−11.0468	−	8.33174i	−0.686414	−	0.517709i
$260$		0			0
$261$	9.26310			0.573371
$262$		0			0
$263$	8.19445	+	8.19445i	0.505291	+	0.505291i	0.913077	−	0.407786i	$-0.133699\pi$
$263$	8.19445	+	8.19445i	0.505291	+	0.505291i	−0.407786	+	0.913077i	$0.633699\pi$
$264$		0			0
$265$	−1.62094	+	0.914143i	−0.0995734	+	0.0561554i
$266$		0			0
$267$	−6.20288	+	6.20288i	−0.379610	+	0.379610i
$268$		0			0
$269$	4.87565			0.297273			0.148637	−	0.988892i	$-0.452512\pi$
$269$	4.87565			0.297273			0.148637	+	0.988892i	$0.452512\pi$
$270$		0			0
$271$		−	19.5666i		−	1.18859i	−0.804248	−	0.594293i	$-0.797432\pi$
$271$		−	19.5666i		−	1.18859i	0.804248	−	0.594293i	$-0.202568\pi$
$272$		0			0
$273$	1.36519	−	0.191272i	0.0826253	−	0.0115763i
$274$		0			0
$275$	−20.4811	−	12.3830i	−1.23505	−	0.746724i
$276$		0			0
$277$	10.8235	−	10.8235i	0.650319	−	0.650319i	−0.302751	−	0.953070i	$-0.597905\pi$
$277$	10.8235	−	10.8235i	0.650319	−	0.650319i	0.953070	+	0.302751i	$0.0979051\pi$
$278$		0			0
$279$	8.98258			0.537773
$280$		0			0
$281$	−0.484103			−0.0288791			−0.0144396	−	0.999896i	$-0.504596\pi$
$281$	−0.484103			−0.0288791			−0.0144396	+	0.999896i	$0.504596\pi$
$282$		0			0
$283$	17.1672	−	17.1672i	1.02048	−	1.02048i	0.0206963	−	0.999786i	$-0.493412\pi$
$283$	17.1672	−	17.1672i	1.02048	−	1.02048i	0.999786	−	0.0206963i	$-0.00658831\pi$
$284$		0			0
$285$	−5.63653	−	9.99456i	−0.333879	−	0.592026i
$286$		0			0
$287$	−5.23700	+	0.733734i	−0.309130	+	0.0433110i
$288$		0			0
$289$		−	14.5425i		−	0.855442i
$290$		0			0
$291$	−1.00665			−0.0590107
$292$		0			0
$293$	−16.8967	+	16.8967i	−0.987117	+	0.987117i	−0.999918	−	0.0128009i	$-0.995925\pi$
$293$	−16.8967	+	16.8967i	−0.987117	+	0.987117i	0.0128009	+	0.999918i	$0.495925\pi$
$294$		0			0
$295$	−1.54956	+	5.55785i	−0.0902187	+	0.323590i
$296$		0			0
$297$	3.38471	+	3.38471i	0.196401	+	0.196401i
$298$		0			0
$299$	1.58381			0.0915942
$300$		0			0
$301$	−3.65800	+	4.85002i	−0.210843	+	0.279551i
$302$		0			0
$303$	5.77428	+	5.77428i	0.331724	+	0.331724i
$304$		0			0
$305$	3.36731	+	0.938823i	0.192812	+	0.0537568i
$306$		0			0
$307$	16.8244	+	16.8244i	0.960221	+	0.960221i	0.999239	−	0.0390173i	$-0.0124227\pi$
$307$	16.8244	+	16.8244i	0.960221	+	0.960221i	−0.0390173	+	0.999239i	$0.512423\pi$
$308$		0			0
$309$			1.74939i			0.0995194i
$310$		0			0
$311$			21.4211i			1.21468i	0.794442	+	0.607340i	$0.207763\pi$
$311$			21.4211i			1.21468i	−0.794442	+	0.607340i	$0.792237\pi$
$312$		0			0
$313$	8.97166	−	8.97166i	0.507108	−	0.507108i	−0.406530	−	0.913638i	$-0.633261\pi$
$313$	8.97166	−	8.97166i	0.507108	−	0.507108i	0.913638	+	0.406530i	$0.133261\pi$
$314$		0			0
$315$	0.782765	−	5.86407i	0.0441038	−	0.330403i
$316$		0			0
$317$	−3.50718	+	3.50718i	−0.196983	+	0.196983i	−0.798705	−	0.601722i	$-0.794481\pi$
$317$	−3.50718	+	3.50718i	−0.196983	+	0.196983i	0.601722	+	0.798705i	$0.294481\pi$
$318$		0			0
$319$			44.3397i			2.48255i
$320$		0			0
$321$			17.0343i			0.950760i
$322$		0			0
$323$	−5.68821	−	5.68821i	−0.316501	−	0.316501i
$324$		0			0
$325$	−2.52951	+	0.623298i	−0.140312	+	0.0345744i
$326$		0			0
$327$	−13.0126	−	13.0126i	−0.719598	−	0.719598i
$328$		0			0
$329$	17.6018	−	23.3376i	0.970417	−	1.28664i
$330$		0			0
$331$	12.6388			0.694692			0.347346	−	0.937737i	$-0.387083\pi$
$331$	12.6388			0.694692			0.347346	+	0.937737i	$0.387083\pi$
$332$		0			0
$333$	−3.69797	−	3.69797i	−0.202647	−	0.202647i
$334$		0			0
$335$	−9.41662	−	16.6973i	−0.514485	−	0.912272i
$336$		0			0
$337$	−12.0081	+	12.0081i	−0.654122	+	0.654122i	−0.953983	−	0.299861i	$-0.903060\pi$
$337$	−12.0081	+	12.0081i	−0.654122	+	0.654122i	0.299861	+	0.953983i	$0.403060\pi$
$338$		0			0
$339$	1.59148			0.0864372
$340$		0			0
$341$			42.9969i			2.32841i
$342$		0			0
$343$	7.51122	+	16.9287i	0.405568	+	0.914065i
$344$		0			0
$345$	1.82544	−	6.54736i	0.0982783	−	0.352498i
$346$		0			0
$347$	−9.70461	+	9.70461i	−0.520971	+	0.520971i	−0.917865	−	0.396894i	$-0.870088\pi$
$347$	−9.70461	+	9.70461i	−0.520971	+	0.520971i	0.396894	+	0.917865i	$0.370088\pi$
$348$		0			0
$349$	−8.05641			−0.431250			−0.215625	−	0.976476i	$-0.569179\pi$
$349$	−8.05641			−0.431250			−0.215625	+	0.976476i	$0.569179\pi$
$350$		0			0
$351$	0.521035			0.0278108
$352$		0			0
$353$	−9.57556	+	9.57556i	−0.509656	+	0.509656i	−0.914421	−	0.404765i	$-0.867353\pi$
$353$	−9.57556	+	9.57556i	−0.509656	+	0.509656i	0.404765	+	0.914421i	$0.367353\pi$
$354$		0			0
$355$	−4.65266	+	16.6878i	−0.246937	+	0.885699i
$356$		0			0
$357$	−0.575481	−	4.10747i	−0.0304577	−	0.217390i
$358$		0			0
$359$		−	30.7707i		−	1.62402i	−0.583646	−	0.812008i	$-0.698375\pi$
$359$		−	30.7707i		−	1.62402i	0.583646	−	0.812008i	$-0.301625\pi$
$360$		0			0
$361$	7.33232			0.385912
$362$		0			0
$363$	−8.42341	+	8.42341i	−0.442115	+	0.442115i
$364$		0			0
$365$	−3.26866	−	5.79592i	−0.171090	−	0.303372i
$366$		0			0
$367$	7.66858	+	7.66858i	0.400296	+	0.400296i	0.878337	−	0.478041i	$-0.158653\pi$
$367$	7.66858	+	7.66858i	0.400296	+	0.400296i	−0.478041	+	0.878337i	$0.658653\pi$
$368$		0			0
$369$	−1.99873			−0.104050
$370$		0			0
$371$	1.32588	−	1.75794i	0.0688364	−	0.0912679i
$372$		0			0
$373$	2.47820	+	2.47820i	0.128316	+	0.128316i	0.768348	−	0.640032i	$-0.221079\pi$
$373$	2.47820	+	2.47820i	0.128316	+	0.128316i	−0.640032	+	0.768348i	$0.721079\pi$
$374$		0			0
$375$	−0.338746	+	11.1752i	−0.0174928	+	0.577085i
$376$		0			0
$377$	3.41278	+	3.41278i	0.175767	+	0.175767i
$378$		0			0
$379$		−	24.5502i		−	1.26106i	−0.776165	−	0.630530i	$-0.782838\pi$
$379$		−	24.5502i		−	1.26106i	0.776165	−	0.630530i	$-0.217162\pi$
$380$		0			0
$381$			19.8965i			1.01933i
$382$		0			0
$383$	−23.3694	+	23.3694i	−1.19412	+	1.19412i	−0.218219	+	0.975900i	$0.570025\pi$
$383$	−23.3694	+	23.3694i	−1.19412	+	1.19412i	−0.975900	+	0.218219i	$0.929975\pi$
$384$		0			0
$385$	28.0695	+	3.74686i	1.43056	+	0.190958i
$386$		0			0
$387$	−1.62357	+	1.62357i	−0.0825306	+	0.0825306i
$388$		0			0
$389$		−	22.9858i		−	1.16543i	−0.812678	−	0.582713i	$-0.801991\pi$
$389$		−	22.9858i		−	1.16543i	0.812678	−	0.582713i	$-0.198009\pi$
$390$		0			0
$391$		−	4.76522i		−	0.240988i
$392$		0			0
$393$	7.76099	+	7.76099i	0.391490	+	0.391490i
$394$		0			0
$395$	9.86446	+	2.75026i	0.496335	+	0.138381i
$396$		0			0
$397$	17.0798	+	17.0798i	0.857212	+	0.857212i	0.991009	−	0.133797i	$-0.0427169\pi$
$397$	17.0798	+	17.0798i	0.857212	+	0.857212i	−0.133797	+	0.991009i	$0.542717\pi$
$398$		0			0
$399$	10.8393	+	8.17527i	0.542645	+	0.409276i
$400$		0			0
$401$	23.0321			1.15017			0.575085	−	0.818094i	$-0.304969\pi$
$401$	23.0321			1.15017			0.575085	+	0.818094i	$0.304969\pi$
$402$		0			0
$403$	3.30943	+	3.30943i	0.164854	+	0.164854i
$404$		0			0
$405$	0.600524	−	2.15392i	0.0298403	−	0.107029i
$406$		0			0
$407$	17.7011	−	17.7011i	0.877409	−	0.877409i
$408$		0			0
$409$	−11.0331			−0.545550			−0.272775	−	0.962078i	$-0.587942\pi$
$409$	−11.0331			−0.545550			−0.272775	+	0.962078i	$0.587942\pi$
$410$		0			0
$411$		−	20.5034i		−	1.01136i
$412$		0			0
$413$	−0.947244	−	6.76091i	−0.0466108	−	0.332683i
$414$		0			0
$415$	10.1806	+	18.0520i	0.499747	+	0.886139i
$416$		0			0
$417$	−8.05426	+	8.05426i	−0.394419	+	0.394419i
$418$		0			0
$419$	−4.45079			−0.217435			−0.108718	−	0.994073i	$-0.534674\pi$
$419$	−4.45079			−0.217435			−0.108718	+	0.994073i	$0.534674\pi$
$420$		0			0
$421$	22.3309			1.08834			0.544170	−	0.838975i	$-0.316845\pi$
$421$	22.3309			1.08834			0.544170	+	0.838975i	$0.316845\pi$
$422$		0			0
$423$	7.81238	−	7.81238i	0.379851	−	0.379851i
$424$		0			0
$425$	1.87532	+	7.61055i	0.0909663	+	0.369166i
$426$		0			0
$427$	−4.09620	+	0.573902i	−0.198229	+	0.0277731i
$428$		0			0
$429$			2.49404i			0.120413i
$430$		0			0
$431$	−30.9684			−1.49170			−0.745848	−	0.666116i	$-0.767956\pi$
$431$	−30.9684			−1.49170			−0.745848	+	0.666116i	$0.767956\pi$
$432$		0			0
$433$	−20.1887	+	20.1887i	−0.970207	+	0.970207i	−0.999569	−	0.0293622i	$-0.990652\pi$
$433$	−20.1887	+	20.1887i	−0.970207	+	0.970207i	0.0293622	+	0.999569i	$0.490652\pi$
$434$		0			0
$435$	18.0416	−	10.1747i	0.865029	−	0.487842i
$436$		0			0
$437$	11.0298	+	11.0298i	0.527625	+	0.527625i
$438$		0			0
$439$	−33.1411			−1.58174			−0.790868	−	0.611986i	$-0.790371\pi$
$439$	−33.1411			−1.58174			−0.790868	+	0.611986i	$0.790371\pi$
$440$		0			0
$441$	1.92372	+	6.73047i	0.0916058	+	0.320499i
$442$		0			0
$443$	4.78296	+	4.78296i	0.227245	+	0.227245i	0.811541	−	0.584296i	$-0.198629\pi$
$443$	4.78296	+	4.78296i	0.227245	+	0.227245i	−0.584296	+	0.811541i	$0.698629\pi$
$444$		0			0
$445$	−5.26791	+	18.8946i	−0.249723	+	0.895690i
$446$		0			0
$447$	−7.71102	−	7.71102i	−0.364719	−	0.364719i
$448$		0			0
$449$			27.0892i			1.27842i	0.769034	+	0.639208i	$0.220738\pi$
$449$			27.0892i			1.27842i	−0.769034	+	0.639208i	$0.779262\pi$
$450$		0			0
$451$		−	9.56733i		−	0.450508i
$452$		0			0
$453$	12.7768	−	12.7768i	0.600307	−	0.600307i
$454$		0			0
$455$	2.44887	−	1.87209i	0.114805	−	0.0877649i
$456$		0			0
$457$	25.8202	−	25.8202i	1.20782	−	1.20782i	0.236086	−	0.971732i	$-0.424135\pi$
$457$	25.8202	−	25.8202i	1.20782	−	1.20782i	0.971732	−	0.236086i	$-0.0758647\pi$
$458$		0			0
$459$		−	1.56764i		−	0.0731711i
$460$		0			0
$461$		−	41.1231i		−	1.91529i	−0.287948	−	0.957646i	$-0.592973\pi$
$461$		−	41.1231i		−	1.91529i	0.287948	−	0.957646i	$-0.407027\pi$
$462$		0			0
$463$	−5.46544	−	5.46544i	−0.254000	−	0.254000i	0.568608	−	0.822609i	$-0.307482\pi$
$463$	−5.46544	−	5.46544i	−0.254000	−	0.254000i	−0.822609	+	0.568608i	$0.807482\pi$
$464$		0			0
$465$	17.4953	−	9.86662i	0.811323	−	0.457554i
$466$		0			0
$467$	11.2697	+	11.2697i	0.521500	+	0.521500i	0.918024	−	0.396525i	$-0.129784\pi$
$467$	11.2697	+	11.2697i	0.521500	+	0.521500i	−0.396525	+	0.918024i	$0.629784\pi$
$468$		0			0
$469$	18.1086	+	13.6579i	0.836179	+	0.630665i
$470$		0			0
$471$	1.86965			0.0861491
$472$		0			0
$473$	−7.77154	−	7.77154i	−0.357336	−	0.357336i
$474$		0			0
$475$	−21.9564	−	13.2750i	−1.00743	−	0.609099i
$476$		0			0
$477$	0.588481	−	0.588481i	0.0269447	−	0.0269447i
$478$		0			0
$479$	−16.3285			−0.746069			−0.373034	−	0.927818i	$-0.621683\pi$
$479$	−16.3285			−0.746069			−0.373034	+	0.927818i	$0.621683\pi$
$480$		0			0
$481$		−	2.72486i		−	0.124243i
$482$		0			0
$483$	1.11589	+	7.96461i	0.0507748	+	0.362402i
$484$		0			0
$485$	−1.96063	+	1.10572i	−0.0890278	+	0.0502081i
$486$		0			0
$487$	10.4003	−	10.4003i	0.471285	−	0.471285i	−0.431045	−	0.902330i	$-0.641855\pi$
$487$	10.4003	−	10.4003i	0.471285	−	0.471285i	0.902330	+	0.431045i	$0.141855\pi$
$488$		0			0
$489$	16.6929			0.754881
$490$		0			0
$491$	−8.45492			−0.381565			−0.190783	−	0.981632i	$-0.561103\pi$
$491$	−8.45492			−0.381565			−0.190783	+	0.981632i	$0.561103\pi$
$492$		0			0
$493$	10.2680	−	10.2680i	0.462449	−	0.462449i
$494$		0			0
$495$	10.3102	+	2.87453i	0.463408	+	0.129200i
$496$		0			0
$497$	−2.84417	−	20.3001i	−0.127578	−	0.910585i
$498$		0			0
$499$			0.399381i			0.0178788i	0.999960	+	0.00893938i	$0.00284553\pi$
$499$			0.399381i			0.0178788i	−0.999960	+	0.00893938i	$0.997154\pi$
$500$		0			0
$501$	21.0561			0.940718
$502$		0			0
$503$	−7.84578	+	7.84578i	−0.349826	+	0.349826i	−0.860045	−	0.510219i	$-0.829564\pi$
$503$	−7.84578	+	7.84578i	−0.349826	+	0.349826i	0.510219	+	0.860045i	$0.329564\pi$
$504$		0			0
$505$	17.5890	+	4.90392i	0.782702	+	0.218221i
$506$		0			0
$507$	−9.00042	−	9.00042i	−0.399723	−	0.399723i
$508$		0			0
$509$	6.99940			0.310243			0.155121	−	0.987895i	$-0.450423\pi$
$509$	6.99940			0.310243			0.155121	+	0.987895i	$0.450423\pi$
$510$		0			0
$511$	6.28581	+	4.74090i	0.278068	+	0.209725i
$512$		0			0
$513$	3.62852	+	3.62852i	0.160203	+	0.160203i
$514$		0			0
$515$	1.92156	+	3.40727i	0.0846741	+	0.150142i
$516$		0			0
$517$	37.3955	+	37.3955i	1.64465	+	1.64465i
$518$		0			0
$519$		−	20.6727i		−	0.907431i
$520$		0			0
$521$			37.1920i			1.62941i	0.579874	+	0.814706i	$0.303102\pi$
$521$			37.1920i			1.62941i	−0.579874	+	0.814706i	$0.696898\pi$
$522$		0			0
$523$	8.17019	−	8.17019i	0.357258	−	0.357258i	−0.505544	−	0.862801i	$-0.668708\pi$
$523$	8.17019	−	8.17019i	0.357258	−	0.357258i	0.862801	+	0.505544i	$0.168708\pi$
$524$		0			0
$525$	−4.91661	−	12.2812i	−0.214578	−	0.535994i
$526$		0			0
$527$	9.95709	−	9.95709i	0.433738	−	0.433738i
$528$		0			0
$529$		−	13.7600i		−	0.598259i
$530$		0			0
$531$		−	2.58034i		−	0.111977i
$532$		0			0
$533$	−0.736387	−	0.736387i	−0.0318965	−	0.0318965i
$534$		0			0
$535$	18.7107	+	33.1774i	0.808935	+	1.43438i
$536$		0			0
$537$	−4.51621	−	4.51621i	−0.194889	−	0.194889i
$538$		0			0
$539$	−32.2168	+	9.20828i	−1.38767	+	0.396629i
$540$		0			0
$541$	−18.2129			−0.783033			−0.391516	−	0.920171i	$-0.628049\pi$
$541$	−18.2129			−0.783033			−0.391516	+	0.920171i	$0.628049\pi$
$542$		0			0
$543$	13.1245	+	13.1245i	0.563228	+	0.563228i
$544$		0			0
$545$	−39.6377	−	11.0512i	−1.69789	−	0.473381i
$546$		0			0
$547$	13.6985	−	13.6985i	0.585704	−	0.585704i	−0.350761	−	0.936465i	$-0.614077\pi$
$547$	13.6985	−	13.6985i	0.585704	−	0.585704i	0.936465	+	0.350761i	$0.114077\pi$
$548$		0			0
$549$	−1.56334			−0.0667217
$550$		0			0
$551$			47.5336i			2.02500i
$552$		0			0
$553$	−11.9997	+	1.68123i	−0.510281	+	0.0714934i
$554$		0			0
$555$	−11.2644	−	3.14057i	−0.478147	−	0.133310i
$556$		0			0
$557$	−13.3482	+	13.3482i	−0.565581	+	0.565581i	−0.930887	−	0.365307i	$-0.880964\pi$
$557$	−13.3482	+	13.3482i	−0.565581	+	0.565581i	0.365307	+	0.930887i	$0.380964\pi$
$558$		0			0
$559$	−1.19633			−0.0505995
$560$		0			0
$561$	7.50382			0.316812
$562$		0			0
$563$	13.1421	−	13.1421i	0.553873	−	0.553873i	−0.373683	−	0.927556i	$-0.621905\pi$
$563$	13.1421	−	13.1421i	0.553873	−	0.553873i	0.927556	+	0.373683i	$0.121905\pi$
$564$		0			0
$565$	3.09970	−	1.74811i	0.130405	−	0.0735434i
$566$		0			0
$567$	0.367100	+	2.62016i	0.0154168	+	0.110036i
$568$		0			0
$569$			5.34566i			0.224102i	0.993702	+	0.112051i	$0.0357419\pi$
$569$			5.34566i			0.224102i	−0.993702	+	0.112051i	$0.964258\pi$
$570$		0			0
$571$	9.81737			0.410844			0.205422	−	0.978673i	$-0.434143\pi$
$571$	9.81737			0.410844			0.205422	+	0.978673i	$0.434143\pi$
$572$		0			0
$573$	−13.9022	+	13.9022i	−0.580775	+	0.580775i
$574$		0			0
$575$	−3.63635	−	14.7573i	−0.151646	−	0.615422i
$576$		0			0
$577$	−20.6021	−	20.6021i	−0.857678	−	0.857678i	0.133386	−	0.991064i	$-0.457415\pi$
$577$	−20.6021	−	20.6021i	−0.857678	−	0.857678i	−0.991064	+	0.133386i	$0.957415\pi$
$578$		0			0
$579$	21.8352			0.907440
$580$		0			0
$581$	−19.5779	−	14.7661i	−0.812226	−	0.612600i
$582$		0			0
$583$	2.81688	+	2.81688i	0.116663	+	0.116663i
$584$		0			0
$585$	1.01481	−	0.572313i	0.0419573	−	0.0236622i
$586$		0			0
$587$	9.64312	+	9.64312i	0.398014	+	0.398014i	0.877532	−	0.479518i	$-0.159188\pi$
$587$	9.64312	+	9.64312i	0.398014	+	0.398014i	−0.479518	+	0.877532i	$0.659188\pi$
$588$		0			0
$589$			46.0942i			1.89928i
$590$		0			0
$591$		−	3.00766i		−	0.123719i
$592$		0			0
$593$	9.48652	−	9.48652i	0.389565	−	0.389565i	−0.484967	−	0.874532i	$-0.661169\pi$
$593$	9.48652	−	9.48652i	0.389565	−	0.389565i	0.874532	+	0.484967i	$0.161169\pi$
$594$		0			0
$595$	−5.63256	−	7.36793i	−0.230913	−	0.302056i
$596$		0			0
$597$	2.79253	−	2.79253i	0.114291	−	0.114291i
$598$		0			0
$599$			6.91294i			0.282455i	0.989977	+	0.141227i	$0.0451049\pi$
$599$			6.91294i			0.282455i	−0.989977	+	0.141227i	$0.954895\pi$
$600$		0			0
$601$		−	6.24955i		−	0.254924i	−0.991843	−	0.127462i	$-0.959317\pi$
$601$		−	6.24955i		−	0.254924i	0.991843	−	0.127462i	$-0.0406831\pi$
$602$		0			0
$603$	6.06196	+	6.06196i	0.246862	+	0.246862i
$604$		0			0
$605$	−7.15375	+	25.6586i	−0.290841	+	1.04317i
$606$		0			0
$607$	−3.64513	−	3.64513i	−0.147951	−	0.147951i	0.629251	−	0.777202i	$-0.283362\pi$
$607$	−3.64513	−	3.64513i	−0.147951	−	0.147951i	−0.777202	+	0.629251i	$0.783362\pi$
$608$		0			0
$609$	−14.7575	+	19.5666i	−0.598006	+	0.792877i
$610$		0			0
$611$	5.75659			0.232887
$612$		0			0
$613$	−5.81420	−	5.81420i	−0.234833	−	0.234833i	0.579873	−	0.814707i	$-0.303102\pi$
$613$	−5.81420	−	5.81420i	−0.234833	−	0.234833i	−0.814707	+	0.579873i	$0.803102\pi$
$614$		0			0
$615$	−3.89290	+	2.19544i	−0.156977	+	0.0885287i
$616$		0			0
$617$	−10.6689	+	10.6689i	−0.429514	+	0.429514i	−0.888463	−	0.458949i	$-0.848226\pi$
$617$	−10.6689	+	10.6689i	−0.429514	+	0.429514i	0.458949	+	0.888463i	$0.348226\pi$
$618$		0			0
$619$	10.1962			0.409821			0.204911	−	0.978781i	$-0.434310\pi$
$619$	10.1962			0.409821			0.204911	+	0.978781i	$0.434310\pi$
$620$		0			0
$621$			3.03974i			0.121981i
$622$		0			0
$623$	−3.22027	−	22.9845i	−0.129018	−	0.920856i
$624$		0			0
$625$	11.6153	+	22.1379i	0.464611	+	0.885515i
$626$		0			0
$627$	−17.3686	+	17.3686i	−0.693637	+	0.693637i
$628$		0			0
$629$	−8.19831			−0.326888
$630$		0			0
$631$	−44.6173			−1.77619			−0.888093	−	0.459664i	$-0.847970\pi$
$631$	−44.6173			−1.77619			−0.888093	+	0.459664i	$0.847970\pi$
$632$		0			0
$633$	12.8264	−	12.8264i	0.509805	−	0.509805i
$634$		0			0
$635$	21.8547	+	38.7522i	0.867277	+	1.53783i
$636$		0			0
$637$	−1.77094	+	3.18844i	−0.0701671	+	0.126331i
$638$		0			0
$639$		−	7.74766i		−	0.306493i
$640$		0			0
$641$	−38.0232			−1.50182			−0.750912	−	0.660402i	$-0.770386\pi$
$641$	−38.0232			−1.50182			−0.750912	+	0.660402i	$0.770386\pi$
$642$		0			0
$643$	8.15689	−	8.15689i	0.321676	−	0.321676i	−0.527734	−	0.849410i	$-0.676958\pi$
$643$	8.15689	−	8.15689i	0.321676	−	0.321676i	0.849410	+	0.527734i	$0.176958\pi$
$644$		0			0
$645$	−1.37885	+	4.94556i	−0.0542920	+	0.194731i
$646$		0			0
$647$	−11.4123	−	11.4123i	−0.448663	−	0.448663i	0.446247	−	0.894910i	$-0.352760\pi$
$647$	−11.4123	−	11.4123i	−0.448663	−	0.448663i	−0.894910	+	0.446247i	$0.852760\pi$
$648$		0			0
$649$	12.3513			0.484832
$650$		0			0
$651$	−14.3106	+	18.9740i	−0.560878	+	0.743650i
$652$		0			0
$653$	−32.4649	−	32.4649i	−1.27045	−	1.27045i	−0.945852	−	0.324597i	$-0.894771\pi$
$653$	−32.4649	−	32.4649i	−1.27045	−	1.27045i	−0.324597	−	0.945852i	$-0.605229\pi$
$654$		0			0
$655$	23.6408	+	6.59117i	0.923722	+	0.257538i
$656$		0			0
$657$	2.10421	+	2.10421i	0.0820929	+	0.0820929i
$658$		0			0
$659$		−	44.2780i		−	1.72483i	−0.506205	−	0.862413i	$-0.668952\pi$
$659$		−	44.2780i		−	1.72483i	0.506205	−	0.862413i	$-0.331048\pi$
$660$		0			0
$661$			9.13975i			0.355495i	0.984076	+	0.177748i	$0.0568811\pi$
$661$			9.13975i			0.355495i	−0.984076	+	0.177748i	$0.943119\pi$
$662$		0			0
$663$	0.577561	−	0.577561i	0.0224306	−	0.0224306i
$664$		0			0
$665$	30.0915	+	4.01676i	1.16690	+	0.155763i
$666$		0			0
$667$	−19.9103	+	19.9103i	−0.770930	+	0.770930i
$668$		0			0
$669$		−	16.3682i		−	0.632830i
$670$		0			0
$671$		−	7.48324i		−	0.288887i
$672$		0			0
$673$	−21.1984	−	21.1984i	−0.817139	−	0.817139i	0.168553	−	0.985693i	$-0.446091\pi$
$673$	−21.1984	−	21.1984i	−0.817139	−	0.817139i	−0.985693	+	0.168553i	$0.946091\pi$
$674$		0			0
$675$	−1.19627	−	4.85479i	−0.0460444	−	0.186861i
$676$		0			0
$677$	8.39277	+	8.39277i	0.322560	+	0.322560i	0.849748	−	0.527188i	$-0.176754\pi$
$677$	8.39277	+	8.39277i	0.322560	+	0.322560i	−0.527188	+	0.849748i	$0.676754\pi$
$678$		0			0
$679$	1.60374	−	2.12635i	0.0615461	−	0.0816020i
$680$		0			0
$681$	15.4849			0.593382
$682$		0			0
$683$	1.61458	+	1.61458i	0.0617801	+	0.0617801i	0.737322	−	0.675542i	$-0.236090\pi$
$683$	1.61458	+	1.61458i	0.0617801	+	0.0617801i	−0.675542	+	0.737322i	$0.736090\pi$
$684$		0			0
$685$	−22.5213	−	39.9343i	−0.860496	−	1.52581i
$686$		0			0
$687$	−8.75816	+	8.75816i	−0.334145	+	0.334145i
$688$		0			0
$689$	0.433624			0.0165198
$690$		0			0
$691$		−	42.7439i		−	1.62605i	−0.582226	−	0.813027i	$-0.697818\pi$
$691$		−	42.7439i		−	1.62605i	0.582226	−	0.813027i	$-0.302182\pi$
$692$		0			0
$693$	−12.5419	+	1.75720i	−0.476428	+	0.0667505i
$694$		0			0
$695$	−6.84023	+	24.5341i	−0.259465	+	0.930631i
$696$		0			0
$697$	−2.21557	+	2.21557i	−0.0839207	+	0.0839207i
$698$		0			0
$699$	6.31815			0.238975
$700$		0			0
$701$	5.34758			0.201975			0.100988	−	0.994888i	$-0.467800\pi$
$701$	5.34758			0.201975			0.100988	+	0.994888i	$0.467800\pi$
$702$		0			0
$703$	18.9761	−	18.9761i	0.715698	−	0.715698i
$704$		0			0
$705$	6.63482	−	23.7973i	0.249882	−	0.896259i
$706$		0			0
$707$	−21.3964	+	2.99776i	−0.804694	+	0.112742i
$708$		0			0
$709$			2.85514i			0.107227i	0.998562	+	0.0536136i	$0.0170739\pi$
$709$			2.85514i			0.107227i	−0.998562	+	0.0536136i	$0.982926\pi$
$710$		0			0
$711$	−4.57977			−0.171755
$712$		0			0
$713$	−19.3074	+	19.3074i	−0.723067	+	0.723067i
$714$		0			0
$715$	2.73949	+	4.85760i	0.102451	+	0.181664i
$716$		0			0
$717$	−14.0534	−	14.0534i	−0.524833	−	0.524833i
$718$		0			0
$719$	−32.1527			−1.19909			−0.599546	−	0.800340i	$-0.704652\pi$
$719$	−32.1527			−1.19909			−0.599546	+	0.800340i	$0.704652\pi$
$720$		0			0
$721$	−3.69526	−	2.78705i	−0.137619	−	0.103795i
$722$		0			0
$723$	18.2936	+	18.2936i	0.680346	+	0.680346i
$724$		0			0
$725$	23.9633	−	39.6344i	0.889974	−	1.47198i
$726$		0			0
$727$	4.41008	+	4.41008i	0.163561	+	0.163561i	0.784142	−	0.620581i	$-0.213103\pi$
$727$	4.41008	+	4.41008i	0.163561	+	0.163561i	−0.620581	+	0.784142i	$0.713103\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$			3.59941i			0.133129i
$732$		0			0
$733$	32.0676	−	32.0676i	1.18444	−	1.18444i	0.205862	−	0.978581i	$-0.434000\pi$
$733$	32.0676	−	32.0676i	1.18444	−	1.18444i	0.978581	−	0.205862i	$-0.0659998\pi$
$734$		0			0
$735$	11.1397	+	10.9958i	0.410893	+	0.405586i
$736$		0			0
$737$	−29.0168	+	29.0168i	−1.06885	+	1.06885i
$738$		0			0
$739$		−	8.17500i		−	0.300722i	−0.988631	−	0.150361i	$-0.951956\pi$
$739$		−	8.17500i		−	0.300722i	0.988631	−	0.150361i	$-0.0480437\pi$
$740$		0			0
$741$			2.67369i			0.0982205i
$742$		0			0
$743$	6.15599	+	6.15599i	0.225841	+	0.225841i	0.810953	−	0.585111i	$-0.198949\pi$
$743$	6.15599	+	6.15599i	0.225841	+	0.225841i	−0.585111	+	0.810953i	$0.698949\pi$
$744$		0			0
$745$	−23.4886	−	6.54874i	−0.860555	−	0.239927i
$746$		0			0
$747$	−6.55378	−	6.55378i	−0.239790	−	0.239790i
$748$		0			0
$749$	−35.9817	−	27.1382i	−1.31474	−	0.991609i
$750$		0			0
$751$	−35.1964			−1.28433			−0.642167	−	0.766565i	$-0.721964\pi$
$751$	−35.1964			−1.28433			−0.642167	+	0.766565i	$0.721964\pi$
$752$		0			0
$753$	−0.460509	−	0.460509i	−0.0167819	−	0.0167819i
$754$		0			0
$755$	10.8510	−	38.9195i	0.394907	−	1.41642i
$756$		0			0
$757$	−25.1623	+	25.1623i	−0.914539	+	0.914539i	−0.996625	−	0.0820858i	$-0.973842\pi$
$757$	−25.1623	+	25.1623i	−0.914539	+	0.914539i	0.0820858	+	0.996625i	$0.473842\pi$
$758$		0			0
$759$	−14.5503			−0.528144
$760$		0			0
$761$			7.64863i			0.277263i	0.990344	+	0.138631i	$0.0442703\pi$
$761$			7.64863i			0.277263i	−0.990344	+	0.138631i	$0.955730\pi$
$762$		0			0
$763$	48.2177	−	6.75559i	1.74560	−	0.244569i
$764$		0			0
$765$	−1.72192	−	3.05327i	−0.0622562	−	0.110391i
$766$		0			0
$767$	0.950668	−	0.950668i	0.0343266	−	0.0343266i
$768$		0			0
$769$	−2.07227			−0.0747281			−0.0373641	−	0.999302i	$-0.511896\pi$
$769$	−2.07227			−0.0747281			−0.0373641	+	0.999302i	$0.511896\pi$
$770$		0			0
$771$	11.7632			0.423641
$772$		0			0
$773$	25.7947	−	25.7947i	0.927772	−	0.927772i	−0.0697902	−	0.997562i	$-0.522233\pi$
$773$	25.7947	−	25.7947i	0.927772	−	0.927772i	0.997562	+	0.0697902i	$0.0222330\pi$
$774$		0			0
$775$	23.2376	−	38.4342i	0.834719	−	1.38060i
$776$		0			0
$777$	13.7027	−	1.91983i	0.491581	−	0.0688735i
$778$		0			0
$779$		−	10.2565i		−	0.367477i
$780$		0			0
$781$	37.0857			1.32703
$782$		0			0
$783$	−6.55000	+	6.55000i	−0.234078	+	0.234078i
$784$		0			0
$785$	3.64150	−	2.05366i	0.129971	−	0.0732982i
$786$		0			0
$787$	31.0775	+	31.0775i	1.10779	+	1.10779i	0.993440	+	0.114354i	$0.0364798\pi$
$787$	31.0775	+	31.0775i	1.10779	+	1.10779i	0.114354	+	0.993440i	$0.463520\pi$
$788$		0			0
$789$	−11.5887			−0.412569
$790$		0			0
$791$	−2.53547	+	3.36170i	−0.0901509	+	0.119528i
$792$		0			0
$793$	−0.575977	−	0.575977i	−0.0204535	−	0.0204535i
$794$		0			0
$795$	0.499778	−	1.79257i	0.0177253	−	0.0635760i
$796$		0			0
$797$	−21.1554	−	21.1554i	−0.749364	−	0.749364i	0.224996	−	0.974360i	$-0.427763\pi$
$797$	−21.1554	−	21.1554i	−0.749364	−	0.749364i	−0.974360	+	0.224996i	$0.927763\pi$
$798$		0			0
$799$		−	17.3199i		−	0.612733i
$800$		0			0
$801$		−	8.77219i		−	0.309950i
$802$		0			0
$803$	−10.0722	+	10.0722i	−0.355440	+	0.355440i
$804$		0			0
$805$	10.9219	+	14.2869i	0.384945	+	0.503545i
$806$		0			0
$807$	−3.44760	+	3.44760i	−0.121361	+	0.121361i
$808$		0			0
$809$		−	38.1380i		−	1.34086i	−0.741972	−	0.670430i	$-0.766110\pi$
$809$		−	38.1380i		−	1.34086i	0.741972	−	0.670430i	$-0.233890\pi$
$810$		0			0
$811$			12.2397i			0.429794i	0.976637	+	0.214897i	$0.0689416\pi$
$811$			12.2397i			0.429794i	−0.976637	+	0.214897i	$0.931058\pi$
$812$		0			0
$813$	13.8357	+	13.8357i	0.485238	+	0.485238i
$814$		0			0
$815$	32.5126	−	18.3358i	1.13887	−	0.642275i
$816$		0			0
$817$	−8.33135	−	8.33135i	−0.291477	−	0.291477i
$818$		0			0
$819$	−0.830088	+	1.10059i	−0.0290056	+	0.0384576i
$820$		0			0
$821$	−7.07229			−0.246824			−0.123412	−	0.992355i	$-0.539384\pi$
$821$	−7.07229			−0.246824			−0.123412	+	0.992355i	$0.539384\pi$
$822$		0			0
$823$	−7.10521	−	7.10521i	−0.247672	−	0.247672i	0.572343	−	0.820015i	$-0.306035\pi$
$823$	−7.10521	−	7.10521i	−0.247672	−	0.247672i	−0.820015	+	0.572343i	$0.806035\pi$
$824$		0			0
$825$	23.2384	−	5.72619i	0.809057	−	0.199360i
$826$		0			0
$827$	2.18508	−	2.18508i	0.0759827	−	0.0759827i	−0.668094	−	0.744077i	$-0.732890\pi$
$827$	2.18508	−	2.18508i	0.0759827	−	0.0759827i	0.744077	+	0.668094i	$0.232890\pi$
$828$		0			0
$829$	−52.7377			−1.83166			−0.915828	−	0.401571i	$-0.868464\pi$
$829$	−52.7377			−1.83166			−0.915828	+	0.401571i	$0.868464\pi$
$830$		0			0
$831$			15.3067i			0.530983i
$832$		0			0
$833$	9.59308	+	5.32823i	0.332380	+	0.184612i
$834$		0			0
$835$	41.0107	−	23.1284i	1.41923	−	0.800391i
$836$		0			0
$837$	−6.35165	+	6.35165i	−0.219545	+	0.219545i
$838$		0			0
$839$	53.5395			1.84839			0.924194	−	0.381924i	$-0.124738\pi$
$839$	53.5395			1.84839			0.924194	+	0.381924i	$0.124738\pi$
$840$		0			0
$841$	−56.8050			−1.95879
$842$		0			0
$843$	0.342312	−	0.342312i	0.0117899	−	0.0117899i
$844$		0			0
$845$	−27.4162	−	7.64378i	−0.943147	−	0.262954i
$846$		0			0
$847$	−4.37308	−	31.2127i	−0.150261	−	1.07248i
$848$		0			0
$849$			24.2780i			0.833220i
$850$		0			0
$851$	15.8970			0.544942
$852$		0			0
$853$	−5.97907	+	5.97907i	−0.204720	+	0.204720i	−0.802019	−	0.597299i	$-0.796241\pi$
$853$	−5.97907	+	5.97907i	−0.204720	+	0.204720i	0.597299	+	0.802019i	$0.296241\pi$
$854$		0			0
$855$	11.0528	+	3.08159i	0.377999	+	0.105388i
$856$		0			0
$857$	−9.97564	−	9.97564i	−0.340761	−	0.340761i	0.515892	−	0.856654i	$-0.327461\pi$
$857$	−9.97564	−	9.97564i	−0.340761	−	0.340761i	−0.856654	+	0.515892i	$0.827461\pi$
$858$		0			0
$859$	−37.8454			−1.29127			−0.645634	−	0.763647i	$-0.723407\pi$
$859$	−37.8454			−1.29127			−0.645634	+	0.763647i	$0.723407\pi$
$860$		0			0
$861$	3.18429	−	4.22194i	0.108520	−	0.143883i
$862$		0			0
$863$	−21.4922	−	21.4922i	−0.731602	−	0.731602i	0.239335	−	0.970937i	$-0.423071\pi$
$863$	−21.4922	−	21.4922i	−0.731602	−	0.731602i	−0.970937	+	0.239335i	$0.923071\pi$
$864$		0			0
$865$	−22.7073	−	40.2640i	−0.772070	−	1.36902i
$866$		0			0
$867$	10.2831	+	10.2831i	0.349233	+	0.349233i
$868$		0			0
$869$		−	21.9220i		−	0.743653i
$870$		0			0
$871$			4.46678i			0.151351i
$872$		0			0
$873$	0.711808	−	0.711808i	0.0240910	−	0.0240910i
$874$		0			0
$875$	−23.0658	−	18.5194i	−0.779768	−	0.626069i
$876$		0			0
$877$	−36.6256	+	36.6256i	−1.23676	+	1.23676i	−0.275438	+	0.961319i	$0.588823\pi$
$877$	−36.6256	+	36.6256i	−1.23676	+	1.23676i	−0.961319	+	0.275438i	$0.911177\pi$
$878$		0			0
$879$		−	23.8956i		−	0.805978i
$880$		0			0
$881$		−	48.5757i		−	1.63656i	−0.574822	−	0.818279i	$-0.694929\pi$
$881$		−	48.5757i		−	1.63656i	0.574822	−	0.818279i	$-0.305071\pi$
$882$		0			0
$883$	24.1579	+	24.1579i	0.812977	+	0.812977i	0.985079	−	0.172102i	$-0.0550558\pi$
$883$	24.1579	+	24.1579i	0.812977	+	0.812977i	−0.172102	+	0.985079i	$0.555056\pi$
$884$		0			0
$885$	−2.83429	−	5.02570i	−0.0952736	−	0.168937i
$886$		0			0
$887$	31.8432	+	31.8432i	1.06919	+	1.06919i	0.997421	+	0.0717686i	$0.0228643\pi$
$887$	31.8432	+	31.8432i	1.06919	+	1.06919i	0.0717686	+	0.997421i	$0.477136\pi$
$888$		0			0
$889$	−42.0277	−	31.6982i	−1.40956	−	1.06313i
$890$		0			0
$891$	−4.78670			−0.160361
$892$		0			0
$893$	40.0893	+	40.0893i	1.34154	+	1.34154i
$894$		0			0
$895$	−13.7568	−	3.83548i	−0.459841	−	0.128206i
$896$		0			0
$897$	−1.11992	+	1.11992i	−0.0373932	+	0.0373932i
$898$		0			0
$899$	−83.2065			−2.77509
$900$		0			0
$901$		−	1.30465i		−	0.0434641i
$902$		0			0
$903$	−0.842888	−	6.01608i	−0.0280496	−	0.200202i
$904$		0			0
$905$	39.9787	+	11.1463i	1.32894	+	0.370515i
$906$		0			0
$907$	26.0574	−	26.0574i	0.865220	−	0.865220i	−0.126718	−	0.991939i	$-0.540444\pi$
$907$	26.0574	−	26.0574i	0.865220	−	0.865220i	0.991939	+	0.126718i	$0.0404444\pi$
$908$		0			0
$909$	−8.16606			−0.270851
$910$		0			0
$911$	−9.08581			−0.301026			−0.150513	−	0.988608i	$-0.548093\pi$
$911$	−9.08581			−0.301026			−0.150513	+	0.988608i	$0.548093\pi$
$912$		0			0
$913$	31.3710	−	31.3710i	1.03823	−	1.03823i
$914$		0			0
$915$	−3.04489	+	1.71720i	−0.100661	+	0.0567688i
$916$		0			0
$917$	−28.7581	+	4.02918i	−0.949676	+	0.133055i
$918$		0			0
$919$		−	37.7755i		−	1.24610i	−0.782183	−	0.623049i	$-0.785894\pi$
$919$		−	37.7755i		−	1.24610i	0.782183	−	0.623049i	$-0.214106\pi$
$920$		0			0
$921$	−23.7933			−0.784017
$922$		0			0
$923$	2.85445	−	2.85445i	0.0939553	−	0.0939553i
$924$		0			0
$925$	−25.3891	+	6.25615i	−0.834790	+	0.205701i
$926$		0			0
$927$	−1.23701	−	1.23701i	−0.0406286	−	0.0406286i
$928$		0			0
$929$	20.3341			0.667140			0.333570	−	0.942725i	$-0.391747\pi$
$929$	20.3341			0.667140			0.333570	+	0.942725i	$0.391747\pi$
$930$		0			0
$931$	−34.5375	+	9.87158i	−1.13192	+	0.323528i
$932$		0			0
$933$	−15.1470	−	15.1470i	−0.495891	−	0.495891i
$934$		0			0
$935$	14.6151	−	8.24232i	0.477964	−	0.269553i
$936$		0			0
$937$	19.7285	+	19.7285i	0.644502	+	0.644502i	0.951659	−	0.307157i	$-0.0993777\pi$
$937$	19.7285	+	19.7285i	0.644502	+	0.644502i	−0.307157	+	0.951659i	$0.599378\pi$
$938$		0			0
$939$			12.6878i			0.414052i
$940$		0			0
$941$		−	10.4805i		−	0.341656i	−0.985301	−	0.170828i	$-0.945356\pi$
$941$		−	10.4805i		−	0.341656i	0.985301	−	0.170828i	$-0.0546442\pi$
$942$		0			0
$943$	4.29612	−	4.29612i	0.139901	−	0.139901i
$944$		0			0
$945$	3.59302	+	4.70002i	0.116881	+	0.152892i
$946$		0			0
$947$	−27.0886	+	27.0886i	−0.880262	+	0.880262i	−0.993561	−	0.113299i	$-0.963858\pi$
$947$	−27.0886	+	27.0886i	−0.880262	+	0.880262i	0.113299	+	0.993561i	$0.463858\pi$
$948$		0			0
$949$			1.55049i			0.0503311i
$950$		0			0
$951$		−	4.95990i		−	0.160836i
$952$		0			0
$953$	29.8729	+	29.8729i	0.967679	+	0.967679i	0.999494	−	0.0318151i	$-0.0101288\pi$
$953$	29.8729	+	29.8729i	0.967679	+	0.967679i	−0.0318151	+	0.999494i	$0.510129\pi$
$954$		0			0
$955$	−11.8068	+	42.3477i	−0.382057	+	1.37034i
$956$		0			0
$957$	−31.3529	−	31.3529i	−1.01349	−	1.01349i
$958$		0			0
$959$	43.3097	+	32.6651i	1.39854	+	1.05481i
$960$		0			0
$961$	−49.6868			−1.60280
$962$		0			0
$963$	−12.0450	−	12.0450i	−0.388146	−	0.388146i
$964$		0			0
$965$	42.5281	−	23.9842i	1.36903	−	0.772077i
$966$		0			0
$967$	−7.87697	+	7.87697i	−0.253306	+	0.253306i	−0.822325	−	0.569019i	$-0.807323\pi$
$967$	−7.87697	+	7.87697i	−0.253306	+	0.253306i	0.569019	+	0.822325i	$0.307323\pi$
$968$		0			0
$969$	8.04434			0.258422
$970$		0			0
$971$			44.6424i			1.43264i	0.697770	+	0.716322i	$0.254176\pi$
$971$			44.6424i			1.43264i	−0.697770	+	0.716322i	$0.745824\pi$
$972$		0			0
$973$	−4.18143	−	29.8448i	−0.134051	−	0.956779i
$974$		0			0
$975$	1.34790	−	2.22937i	0.0431672	−	0.0713971i
$976$		0			0
$977$	−12.6826	+	12.6826i	−0.405754	+	0.405754i	−0.880255	−	0.474501i	$-0.842628\pi$
$977$	−12.6826	+	12.6826i	−0.405754	+	0.405754i	0.474501	+	0.880255i	$0.342628\pi$
$978$		0			0
$979$	41.9899			1.34200
$980$		0			0
$981$	18.4026			0.587550
$982$		0			0
$983$	−15.3018	+	15.3018i	−0.488051	+	0.488051i	−0.907691	−	0.419640i	$-0.862156\pi$
$983$	−15.3018	+	15.3018i	−0.488051	+	0.488051i	0.419640	+	0.907691i	$0.362156\pi$
$984$		0			0
$985$	−3.30367	−	5.85798i	−0.105264	−	0.186651i
$986$		0			0
$987$	4.05586	+	28.9485i	0.129099	+	0.921441i
$988$		0			0
$989$		−	6.97947i		−	0.221934i
$990$		0			0
$991$	38.4563			1.22160			0.610802	−	0.791784i	$-0.290847\pi$
$991$	38.4563			1.22160			0.610802	+	0.791784i	$0.290847\pi$
$992$		0			0
$993$	−8.93699	+	8.93699i	−0.283607	+	0.283607i
$994$		0			0
$995$	2.37161	−	8.50634i	0.0751851	−	0.269669i
$996$		0			0
$997$	−10.4066	−	10.4066i	−0.329581	−	0.329581i	0.522846	−	0.852427i	$-0.324870\pi$
$997$	−10.4066	−	10.4066i	−0.329581	−	0.329581i	−0.852427	+	0.522846i	$0.824870\pi$
$998$		0			0
$999$	5.22972			0.165461

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bt.b.433.3	yes	24
4.3	odd	2		1680.2.cz.e.433.8		24
5.2	odd	4		840.2.bt.a.97.10	✓	24
7.6	odd	2		840.2.bt.a.433.10	yes	24
20.7	even	4		1680.2.cz.f.97.5		24
28.27	even	2		1680.2.cz.f.433.5		24
35.27	even	4	inner	840.2.bt.b.97.3	yes	24
140.27	odd	4		1680.2.cz.e.97.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bt.a.97.10	✓	24	5.2	odd	4
840.2.bt.a.433.10	yes	24	7.6	odd	2
840.2.bt.b.97.3	yes	24	35.27	even	4	inner
840.2.bt.b.433.3	yes	24	1.1	even	1	trivial
1680.2.cz.e.97.8		24	140.27	odd	4
1680.2.cz.e.433.8		24	4.3	odd	2
1680.2.cz.f.97.5		24	20.7	even	4
1680.2.cz.f.433.5		24	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.600524 + 2.15392i) q^{5} +(-0.367100 - 2.62016i) q^{7} -1.00000i q^{9} +4.78670 q^{11} +(0.368427 - 0.368427i) q^{13} +(-1.09842 - 1.94769i) q^{15} +(-1.10849 - 1.10849i) q^{17} +5.13150 q^{19} +(2.11231 + 1.59315i) q^{21} +(2.14942 + 2.14942i) q^{23} +(-4.27874 - 2.58696i) q^{25} +(0.707107 + 0.707107i) q^{27} +9.26310i q^{29} +8.98258i q^{31} +(-3.38471 + 3.38471i) q^{33} +(5.86407 + 0.782765i) q^{35} +(3.69797 - 3.69797i) q^{37} +0.521035i q^{39} -1.99873i q^{41} +(-1.62357 - 1.62357i) q^{43} +(2.15392 + 0.600524i) q^{45} +(7.81238 + 7.81238i) q^{47} +(-6.73047 + 1.92372i) q^{49} +1.56764 q^{51} +(0.588481 + 0.588481i) q^{53} +(-2.87453 + 10.3102i) q^{55} +(-3.62852 + 3.62852i) q^{57} +2.58034 q^{59} -1.56334i q^{61} +(-2.62016 + 0.367100i) q^{63} +(0.572313 + 1.01481i) q^{65} +(-6.06196 + 6.06196i) q^{67} -3.03974 q^{69} +7.74766 q^{71} +(-2.10421 + 2.10421i) q^{73} +(4.85479 - 1.19627i) q^{75} +(-1.75720 - 12.5419i) q^{77} -4.57977i q^{79} -1.00000 q^{81} +(6.55378 - 6.55378i) q^{83} +(3.05327 - 1.72192i) q^{85} +(-6.55000 - 6.55000i) q^{87} +8.77219 q^{89} +(-1.10059 - 0.830088i) q^{91} +(-6.35165 - 6.35165i) q^{93} +(-3.08159 + 11.0528i) q^{95} +(0.711808 + 0.711808i) q^{97} -4.78670i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{11} - 16 q^{13} + 4 q^{15} - 20 q^{17} - 8 q^{19} + 24 q^{23} - 4 q^{25} + 4 q^{37} - 16 q^{43} + 4 q^{45} + 24 q^{47} - 36 q^{49} + 16 q^{53} - 28 q^{55} + 4 q^{57} - 8 q^{59} + 4 q^{63} + 24 q^{65}+ \cdots + 28 q^{97}+O(q^{100}) \) 24 * q - 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 + 4 * q^63 + 24 * q^65 + 16 * q^67 + 8 * q^69 + 8 * q^71 + 28 * q^73 + 28 * 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

Modular forms

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Database

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