LMFDB - Embedded newform 840.2.bt.b.97.1

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			97.1
Character	$\chi$	$=$	840.97
Dual form			840.2.bt.b.433.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{3} +(-2.21371 + 0.315413i) q^{5} +(2.54973 + 0.706295i) q^{7} +1.00000i q^{9} -1.16955 q^{11} +(-1.47521 - 1.47521i) q^{13} +(1.78836 + 1.34230i) q^{15} +(-1.17748 + 1.17748i) q^{17} -2.09803 q^{19} +(-1.30351 - 2.30236i) q^{21} +(-5.33116 + 5.33116i) q^{23} +(4.80103 - 1.39647i) q^{25} +(0.707107 - 0.707107i) q^{27} +1.55395i q^{29} +2.66719i q^{31} +(0.826994 + 0.826994i) q^{33} +(-5.86715 - 0.759313i) q^{35} +(0.549430 + 0.549430i) q^{37} +2.08626i q^{39} +8.59246i q^{41} +(-5.86009 + 5.86009i) q^{43} +(-0.315413 - 2.21371i) q^{45} +(-8.22660 + 8.22660i) q^{47} +(6.00230 + 3.60173i) q^{49} +1.66520 q^{51} +(3.22603 - 3.22603i) q^{53} +(2.58904 - 0.368890i) q^{55} +(1.48353 + 1.48353i) q^{57} -3.54324 q^{59} +4.08335i q^{61} +(-0.706295 + 2.54973i) q^{63} +(3.73099 + 2.80039i) q^{65} +(3.06567 + 3.06567i) q^{67} +7.53940 q^{69} -1.65109 q^{71} +(-6.90630 - 6.90630i) q^{73} +(-4.38229 - 2.40739i) q^{75} +(-2.98203 - 0.826044i) q^{77} +12.6669i q^{79} -1.00000 q^{81} +(-3.91528 - 3.91528i) q^{83} +(2.23520 - 2.97798i) q^{85} +(1.09881 - 1.09881i) q^{87} +11.8136 q^{89} +(-2.71946 - 4.80333i) q^{91} +(1.88599 - 1.88599i) q^{93} +(4.64442 - 0.661744i) q^{95} +(-0.533694 + 0.533694i) q^{97} -1.16955i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

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

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
$5$	−2.21371	+	0.315413i	−0.990001	+	0.141057i
$5$	−2.21371	+	0.315413i	−0.990001	+	0.141057i
$6$		0			0
$7$	2.54973	+	0.706295i	0.963709	+	0.266954i
$7$	2.54973	+	0.706295i	0.963709	+	0.266954i
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−1.16955			−0.352631			−0.176316	−	0.984334i	$-0.556418\pi$
$11$	−1.16955			−0.352631			−0.176316	+	0.984334i	$0.556418\pi$
$12$		0			0
$13$	−1.47521	−	1.47521i	−0.409150	−	0.409150i	0.472292	−	0.881442i	$-0.343427\pi$
$13$	−1.47521	−	1.47521i	−0.409150	−	0.409150i	−0.881442	+	0.472292i	$0.843427\pi$
$14$		0			0
$15$	1.78836	+	1.34230i	0.461753	+	0.346580i
$16$		0			0
$17$	−1.17748	+	1.17748i	−0.285580	+	0.285580i	−0.835330	−	0.549750i	$-0.814723\pi$
$17$	−1.17748	+	1.17748i	−0.285580	+	0.285580i	0.549750	+	0.835330i	$0.314723\pi$
$18$		0			0
$19$	−2.09803			−0.481320			−0.240660	−	0.970609i	$-0.577364\pi$
$19$	−2.09803			−0.481320			−0.240660	+	0.970609i	$0.577364\pi$
$20$		0			0
$21$	−1.30351	−	2.30236i	−0.284449	−	0.502416i
$22$		0			0
$23$	−5.33116	+	5.33116i	−1.11162	+	1.11162i	−0.118693	+	0.992931i	$0.537870\pi$
$23$	−5.33116	+	5.33116i	−1.11162	+	1.11162i	−0.992931	+	0.118693i	$0.962130\pi$
$24$		0			0
$25$	4.80103	−	1.39647i	0.960206	−	0.279293i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$			1.55395i			0.288562i	0.989537	+	0.144281i	$0.0460869\pi$
$29$			1.55395i			0.288562i	−0.989537	+	0.144281i	$0.953913\pi$
$30$		0			0
$31$			2.66719i			0.479042i	0.970891	+	0.239521i	$0.0769904\pi$
$31$			2.66719i			0.479042i	−0.970891	+	0.239521i	$0.923010\pi$
$32$		0			0
$33$	0.826994	+	0.826994i	0.143961	+	0.143961i
$34$		0			0
$35$	−5.86715	−	0.759313i	−0.991729	−	0.128347i
$36$		0			0
$37$	0.549430	+	0.549430i	0.0903257	+	0.0903257i	0.750826	−	0.660500i	$-0.229656\pi$
$37$	0.549430	+	0.549430i	0.0903257	+	0.0903257i	−0.660500	+	0.750826i	$0.729656\pi$
$38$		0			0
$39$			2.08626i			0.334069i
$40$		0			0
$41$			8.59246i			1.34192i	0.741495	+	0.670959i	$0.234117\pi$
$41$			8.59246i			1.34192i	−0.741495	+	0.670959i	$0.765883\pi$
$42$		0			0
$43$	−5.86009	+	5.86009i	−0.893656	+	0.893656i	−0.994865	−	0.101209i	$-0.967729\pi$
$43$	−5.86009	+	5.86009i	−0.893656	+	0.893656i	0.101209	+	0.994865i	$0.467729\pi$
$44$		0			0
$45$	−0.315413	−	2.21371i	−0.0470190	−	0.330000i
$46$		0			0
$47$	−8.22660	+	8.22660i	−1.19997	+	1.19997i	−0.225800	+	0.974174i	$0.572500\pi$
$47$	−8.22660	+	8.22660i	−1.19997	+	1.19997i	−0.974174	+	0.225800i	$0.927500\pi$
$48$		0			0
$49$	6.00230	+	3.60173i	0.857471	+	0.514533i
$50$		0			0
$51$	1.66520			0.233175
$52$		0			0
$53$	3.22603	−	3.22603i	0.443129	−	0.443129i	−0.449933	−	0.893062i	$-0.648552\pi$
$53$	3.22603	−	3.22603i	0.443129	−	0.443129i	0.893062	+	0.449933i	$0.148552\pi$
$54$		0			0
$55$	2.58904	−	0.368890i	0.349105	−	0.0497411i
$56$		0			0
$57$	1.48353	+	1.48353i	0.196498	+	0.196498i
$58$		0			0
$59$	−3.54324			−0.461291			−0.230646	−	0.973038i	$-0.574084\pi$
$59$	−3.54324			−0.461291			−0.230646	+	0.973038i	$0.574084\pi$
$60$		0			0
$61$			4.08335i			0.522819i	0.965228	+	0.261409i	$0.0841873\pi$
$61$			4.08335i			0.522819i	−0.965228	+	0.261409i	$0.915813\pi$
$62$		0			0
$63$	−0.706295	+	2.54973i	−0.0889848	+	0.321236i
$64$		0			0
$65$	3.73099	+	2.80039i	0.462772	+	0.347345i
$66$		0			0
$67$	3.06567	+	3.06567i	0.374531	+	0.374531i	0.869124	−	0.494594i	$-0.164683\pi$
$67$	3.06567	+	3.06567i	0.374531	+	0.374531i	−0.494594	+	0.869124i	$0.664683\pi$
$68$		0			0
$69$	7.53940			0.907637
$70$		0			0
$71$	−1.65109			−0.195948			−0.0979739	−	0.995189i	$-0.531236\pi$
$71$	−1.65109			−0.195948			−0.0979739	+	0.995189i	$0.531236\pi$
$72$		0			0
$73$	−6.90630	−	6.90630i	−0.808321	−	0.808321i	0.176059	−	0.984380i	$-0.443665\pi$
$73$	−6.90630	−	6.90630i	−0.808321	−	0.808321i	−0.984380	+	0.176059i	$0.943665\pi$
$74$		0			0
$75$	−4.38229	−	2.40739i	−0.506023	−	0.277982i
$76$		0			0
$77$	−2.98203	−	0.826044i	−0.339834	−	0.0941364i
$78$		0			0
$79$			12.6669i			1.42513i	0.701605	+	0.712566i	$0.252467\pi$
$79$			12.6669i			1.42513i	−0.701605	+	0.712566i	$0.747533\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−3.91528	−	3.91528i	−0.429758	−	0.429758i	0.458788	−	0.888546i	$-0.348284\pi$
$83$	−3.91528	−	3.91528i	−0.429758	−	0.429758i	−0.888546	+	0.458788i	$0.848284\pi$
$84$		0			0
$85$	2.23520	−	2.97798i	0.242442	−	0.323008i
$86$		0			0
$87$	1.09881	−	1.09881i	0.117805	−	0.117805i
$88$		0			0
$89$	11.8136			1.25224			0.626120	−	0.779727i	$-0.284642\pi$
$89$	11.8136			1.25224			0.626120	+	0.779727i	$0.284642\pi$
$90$		0			0
$91$	−2.71946	−	4.80333i	−0.285077	−	0.503526i
$92$		0			0
$93$	1.88599	−	1.88599i	0.195568	−	0.195568i
$94$		0			0
$95$	4.64442	−	0.661744i	0.476508	−	0.0678935i
$96$		0			0
$97$	−0.533694	+	0.533694i	−0.0541884	+	0.0541884i	−0.733682	−	0.679493i	$-0.762200\pi$
$97$	−0.533694	+	0.533694i	−0.0541884	+	0.0541884i	0.679493	+	0.733682i	$0.262200\pi$
$98$		0			0
$99$		−	1.16955i		−	0.117544i
$100$		0			0
$101$			2.20950i			0.219853i	0.993940	+	0.109927i	$0.0350616\pi$
$101$			2.20950i			0.219853i	−0.993940	+	0.109927i	$0.964938\pi$
$102$		0			0
$103$	−3.10352	−	3.10352i	−0.305799	−	0.305799i	0.537478	−	0.843278i	$-0.319377\pi$
$103$	−3.10352	−	3.10352i	−0.305799	−	0.305799i	−0.843278	+	0.537478i	$0.819377\pi$
$104$		0			0
$105$	3.61179	+	4.68562i	0.352474	+	0.457269i
$106$		0			0
$107$	−12.8183	−	12.8183i	−1.23919	−	1.23919i	−0.960331	−	0.278863i	$-0.910042\pi$
$107$	−12.8183	−	12.8183i	−1.23919	−	1.23919i	−0.278863	−	0.960331i	$-0.589958\pi$
$108$		0			0
$109$		−	10.5750i		−	1.01290i	−0.862269	−	0.506450i	$-0.830958\pi$
$109$		−	10.5750i		−	1.01290i	0.862269	−	0.506450i	$-0.169042\pi$
$110$		0			0
$111$		−	0.777011i		−	0.0737506i
$112$		0			0
$113$	13.4278	−	13.4278i	1.26318	−	1.26318i	0.313632	−	0.949545i	$-0.398454\pi$
$113$	13.4278	−	13.4278i	1.26318	−	1.26318i	0.949545	−	0.313632i	$-0.101546\pi$
$114$		0			0
$115$	10.1201	−	13.4832i	0.943707	−	1.25731i
$116$		0			0
$117$	1.47521	−	1.47521i	0.136383	−	0.136383i
$118$		0			0
$119$	−3.83390	+	2.17061i	−0.351453	+	0.198979i
$120$		0			0
$121$	−9.63216			−0.875651
$122$		0			0
$123$	6.07579	−	6.07579i	0.547836	−	0.547836i
$124$		0			0
$125$	−10.1876	+	4.60568i	−0.911209	+	0.411944i
$126$		0			0
$127$	−5.27244	−	5.27244i	−0.467854	−	0.467854i	0.433365	−	0.901219i	$-0.357326\pi$
$127$	−5.27244	−	5.27244i	−0.467854	−	0.467854i	−0.901219	+	0.433365i	$0.857326\pi$
$128$		0			0
$129$	8.28742			0.729667
$130$		0			0
$131$			8.06509i			0.704650i	0.935878	+	0.352325i	$0.114609\pi$
$131$			8.06509i			0.704650i	−0.935878	+	0.352325i	$0.885391\pi$
$132$		0			0
$133$	−5.34941	−	1.48182i	−0.463852	−	0.128490i
$134$		0			0
$135$	−1.34230	+	1.78836i	−0.115527	+	0.153918i
$136$		0			0
$137$	−10.8606	−	10.8606i	−0.927884	−	0.927884i	0.0696853	−	0.997569i	$-0.477801\pi$
$137$	−10.8606	−	10.8606i	−0.927884	−	0.927884i	−0.997569	+	0.0696853i	$0.977801\pi$
$138$		0			0
$139$	21.0607			1.78635			0.893175	−	0.449710i	$-0.148473\pi$
$139$	21.0607			1.78635			0.893175	+	0.449710i	$0.148473\pi$
$140$		0			0
$141$	11.6342			0.979774
$142$		0			0
$143$	1.72533	+	1.72533i	0.144279	+	0.144279i
$144$		0			0
$145$	−0.490137	−	3.44000i	−0.0407037	−	0.285677i
$146$		0			0
$147$	−1.69746	−	6.79107i	−0.140004	−	0.560118i
$148$		0			0
$149$			9.76883i			0.800294i	0.916451	+	0.400147i	$0.131041\pi$
$149$			9.76883i			0.800294i	−0.916451	+	0.400147i	$0.868959\pi$
$150$		0			0
$151$	18.6840			1.52049			0.760243	−	0.649639i	$-0.225080\pi$
$151$	18.6840			1.52049			0.760243	+	0.649639i	$0.225080\pi$
$152$		0			0
$153$	−1.17748	−	1.17748i	−0.0951933	−	0.0951933i
$154$		0			0
$155$	−0.841267	−	5.90440i	−0.0675722	−	0.474253i
$156$		0			0
$157$	−10.9680	+	10.9680i	−0.875342	+	0.875342i	−0.993048	−	0.117707i	$-0.962446\pi$
$157$	−10.9680	+	10.9680i	−0.875342	+	0.875342i	0.117707	+	0.993048i	$0.462446\pi$
$158$		0			0
$159$	−4.56229			−0.361813
$160$		0			0
$161$	−17.3584	+	9.82768i	−1.36803	+	0.774529i
$162$		0			0
$163$	−5.89745	+	5.89745i	−0.461924	+	0.461924i	−0.899286	−	0.437362i	$-0.855913\pi$
$163$	−5.89745	+	5.89745i	−0.461924	+	0.461924i	0.437362	+	0.899286i	$0.355913\pi$
$164$		0			0
$165$	−2.09157	−	1.56988i	−0.162828	−	0.122215i
$166$		0			0
$167$	−11.8929	+	11.8929i	−0.920301	+	0.920301i	−0.997050	−	0.0767495i	$-0.975546\pi$
$167$	−11.8929	+	11.8929i	−0.920301	+	0.920301i	0.0767495	+	0.997050i	$0.475546\pi$
$168$		0			0
$169$		−	8.64751i		−	0.665193i
$170$		0			0
$171$		−	2.09803i		−	0.160440i
$172$		0			0
$173$	4.79478	+	4.79478i	0.364540	+	0.364540i	0.865481	−	0.500941i	$-0.167013\pi$
$173$	4.79478	+	4.79478i	0.364540	+	0.364540i	−0.500941	+	0.865481i	$0.667013\pi$
$174$		0			0
$175$	13.2277	−	0.169675i	0.999918	−	0.0128262i
$176$		0			0
$177$	2.50545	+	2.50545i	0.188321	+	0.188321i
$178$		0			0
$179$		−	20.8432i		−	1.55790i	−0.627089	−	0.778948i	$-0.715754\pi$
$179$		−	20.8432i		−	1.55790i	0.627089	−	0.778948i	$-0.284246\pi$
$180$		0			0
$181$			6.01487i			0.447081i	0.974695	+	0.223541i	$0.0717616\pi$
$181$			6.01487i			0.447081i	−0.974695	+	0.223541i	$0.928238\pi$
$182$		0			0
$183$	2.88736	−	2.88736i	0.213440	−	0.213440i
$184$		0			0
$185$	−1.38958	−	1.04298i	−0.102164	−	0.0766815i
$186$		0			0
$187$	1.37711	−	1.37711i	0.100704	−	0.100704i
$188$		0			0
$189$	2.30236	−	1.30351i	0.167472	−	0.0948163i
$190$		0			0
$191$	3.91499			0.283279			0.141639	−	0.989918i	$-0.454763\pi$
$191$	3.91499			0.283279			0.141639	+	0.989918i	$0.454763\pi$
$192$		0			0
$193$	13.1766	−	13.1766i	0.948474	−	0.948474i	−0.0502617	−	0.998736i	$-0.516006\pi$
$193$	13.1766	−	13.1766i	0.948474	−	0.948474i	0.998736	+	0.0502617i	$0.0160055\pi$
$194$		0			0
$195$	−0.658034	−	4.61838i	−0.0471228	−	0.330729i
$196$		0			0
$197$	−3.59483	−	3.59483i	−0.256121	−	0.256121i	0.567353	−	0.823475i	$-0.307967\pi$
$197$	−3.59483	−	3.59483i	−0.256121	−	0.256121i	−0.823475	+	0.567353i	$0.807967\pi$
$198$		0			0
$199$	9.84894			0.698173			0.349086	−	0.937091i	$-0.386492\pi$
$199$	9.84894			0.698173			0.349086	+	0.937091i	$0.386492\pi$
$200$		0			0
$201$		−	4.33551i		−	0.305803i
$202$		0			0
$203$	−1.09755	+	3.96217i	−0.0770329	+	0.278090i
$204$		0			0
$205$	−2.71017	−	19.0212i	−0.189287	−	1.32850i
$206$		0			0
$207$	−5.33116	−	5.33116i	−0.370541	−	0.370541i
$208$		0			0
$209$	2.45374			0.169728
$210$		0			0
$211$	−24.1308			−1.66123			−0.830616	−	0.556845i	$-0.812012\pi$
$211$	−24.1308			−1.66123			−0.830616	+	0.556845i	$0.812012\pi$
$212$		0			0
$213$	1.16749	+	1.16749i	0.0799954	+	0.0799954i
$214$		0			0
$215$	11.1242	−	14.8209i	0.758664	−	1.01078i
$216$		0			0
$217$	−1.88383	+	6.80064i	−0.127882	+	0.461657i
$218$		0			0
$219$			9.76698i			0.659991i
$220$		0			0
$221$	3.47405			0.233690
$222$		0			0
$223$	−1.60954	−	1.60954i	−0.107783	−	0.107783i	0.651159	−	0.758942i	$-0.274283\pi$
$223$	−1.60954	−	1.60954i	−0.107783	−	0.107783i	−0.758942	+	0.651159i	$0.774283\pi$
$224$		0			0
$225$	1.39647	+	4.80103i	0.0930977	+	0.320069i
$226$		0			0
$227$	−4.53928	+	4.53928i	−0.301282	+	0.301282i	−0.841515	−	0.540233i	$-0.818336\pi$
$227$	−4.53928	+	4.53928i	−0.301282	+	0.301282i	0.540233	+	0.841515i	$0.318336\pi$
$228$		0			0
$229$	15.1551			1.00148			0.500738	−	0.865599i	$-0.333062\pi$
$229$	15.1551			1.00148			0.500738	+	0.865599i	$0.333062\pi$
$230$		0			0
$231$	1.52451	+	2.69272i	0.100306	+	0.177168i
$232$		0			0
$233$	−8.24037	+	8.24037i	−0.539844	+	0.539844i	−0.923483	−	0.383639i	$-0.874671\pi$
$233$	−8.24037	+	8.24037i	−0.539844	+	0.539844i	0.383639	+	0.923483i	$0.374671\pi$
$234$		0			0
$235$	15.6165	−	20.8061i	1.01871	−	1.35724i
$236$		0			0
$237$	8.95682	−	8.95682i	0.581808	−	0.581808i
$238$		0			0
$239$			8.52067i			0.551156i	0.961279	+	0.275578i	$0.0888693\pi$
$239$			8.52067i			0.551156i	−0.961279	+	0.275578i	$0.911131\pi$
$240$		0			0
$241$		−	17.9877i		−	1.15869i	−0.815082	−	0.579346i	$-0.803308\pi$
$241$		−	17.9877i		−	1.15869i	0.815082	−	0.579346i	$-0.196692\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	−14.4234	−	6.07998i	−0.921476	−	0.388436i
$246$		0			0
$247$	3.09503	+	3.09503i	0.196932	+	0.196932i
$248$		0			0
$249$			5.53705i			0.350896i
$250$		0			0
$251$			9.19362i			0.580296i	0.956982	+	0.290148i	$0.0937045\pi$
$251$			9.19362i			0.580296i	−0.956982	+	0.290148i	$0.906295\pi$
$252$		0			0
$253$	6.23503	−	6.23503i	0.391993	−	0.391993i
$254$		0			0
$255$	−3.68628	+	0.525226i	−0.230844	+	0.0328910i
$256$		0			0
$257$	20.1040	−	20.1040i	1.25405	−	1.25405i	0.300167	−	0.953887i	$-0.402958\pi$
$257$	20.1040	−	20.1040i	1.25405	−	1.25405i	0.953887	−	0.300167i	$-0.0970423\pi$
$258$		0			0
$259$	1.01284	+	1.78896i	0.0629349	+	0.111161i
$260$		0			0
$261$	−1.55395			−0.0961873
$262$		0			0
$263$	15.8468	−	15.8468i	0.977154	−	0.977154i	−0.0225912	−	0.999745i	$-0.507192\pi$
$263$	15.8468	−	15.8468i	0.977154	−	0.977154i	0.999745	+	0.0225912i	$0.00719162\pi$
$264$		0			0
$265$	−6.12396	+	8.15902i	−0.376192	+	0.501205i
$266$		0			0
$267$	−8.35348	−	8.35348i	−0.511224	−	0.511224i
$268$		0			0
$269$	17.6809			1.07802			0.539012	−	0.842298i	$-0.318798\pi$
$269$	17.6809			1.07802			0.539012	+	0.842298i	$0.318798\pi$
$270$		0			0
$271$			4.30310i			0.261395i	0.991422	+	0.130697i	$0.0417217\pi$
$271$			4.30310i			0.261395i	−0.991422	+	0.130697i	$0.958278\pi$
$272$		0			0
$273$	−1.47352	+	5.31941i	−0.0891812	+	0.321946i
$274$		0			0
$275$	−5.61502	+	1.63323i	−0.338599	+	0.0984875i
$276$		0			0
$277$	7.12848	+	7.12848i	0.428309	+	0.428309i	0.888052	−	0.459743i	$-0.152059\pi$
$277$	7.12848	+	7.12848i	0.428309	+	0.428309i	−0.459743	+	0.888052i	$0.652059\pi$
$278$		0			0
$279$	−2.66719			−0.159681
$280$		0			0
$281$	0.0128067			0.000763985			0.000381992	−	1.00000i	$-0.499878\pi$
$281$	0.0128067			0.000763985			0.000381992		1.00000i	$0.499878\pi$
$282$		0			0
$283$	22.1980	+	22.1980i	1.31953	+	1.31953i	0.914146	+	0.405386i	$0.132863\pi$
$283$	22.1980	+	22.1980i	1.31953	+	1.31953i	0.405386	+	0.914146i	$0.367137\pi$
$284$		0			0
$285$	−3.75202	−	2.81618i	−0.222251	−	0.166816i
$286$		0			0
$287$	−6.06881	+	21.9085i	−0.358231	+	1.29322i
$288$		0			0
$289$			14.2271i			0.836888i
$290$		0			0
$291$	0.754757			0.0442446
$292$		0			0
$293$	−18.9408	−	18.9408i	−1.10653	−	1.10653i	−0.993603	−	0.112932i	$-0.963976\pi$
$293$	−18.9408	−	18.9408i	−1.10653	−	1.10653i	−0.112932	−	0.993603i	$-0.536024\pi$
$294$		0			0
$295$	7.84372	−	1.11758i	0.456679	−	0.0650683i
$296$		0			0
$297$	−0.826994	+	0.826994i	−0.0479870	+	0.0479870i
$298$		0			0
$299$	15.7292			0.909641
$300$		0			0
$301$	−19.0806	+	10.8027i	−1.09979	+	0.622659i
$302$		0			0
$303$	1.56235	−	1.56235i	0.0897547	−	0.0897547i
$304$		0			0
$305$	−1.28794	−	9.03935i	−0.0737472	−	0.517591i
$306$		0			0
$307$	2.64729	−	2.64729i	0.151089	−	0.151089i	−0.627515	−	0.778604i	$-0.715928\pi$
$307$	2.64729	−	2.64729i	0.151089	−	0.151089i	0.778604	+	0.627515i	$0.215928\pi$
$308$		0			0
$309$			4.38904i			0.249684i
$310$		0			0
$311$			2.01981i			0.114533i	0.998359	+	0.0572663i	$0.0182384\pi$
$311$			2.01981i			0.114533i	−0.998359	+	0.0572663i	$0.981762\pi$
$312$		0			0
$313$	−22.5469	−	22.5469i	−1.27442	−	1.27442i	−0.943742	−	0.330682i	$-0.892721\pi$
$313$	−22.5469	−	22.5469i	−1.27442	−	1.27442i	−0.330682	−	0.943742i	$-0.607279\pi$
$314$		0			0
$315$	0.759313	−	5.86715i	0.0427824	−	0.330576i
$316$		0			0
$317$	7.40527	+	7.40527i	0.415921	+	0.415921i	0.883795	−	0.467874i	$-0.154980\pi$
$317$	7.40527	+	7.40527i	0.415921	+	0.415921i	−0.467874	+	0.883795i	$0.654980\pi$
$318$		0			0
$319$		−	1.81742i		−	0.101756i
$320$		0			0
$321$			18.1278i			1.01180i
$322$		0			0
$323$	2.47038	−	2.47038i	0.137455	−	0.137455i
$324$		0			0
$325$	−9.14261	−	5.02245i	−0.507141	−	0.278595i
$326$		0			0
$327$	−7.47764	+	7.47764i	−0.413515	+	0.413515i
$328$		0			0
$329$	−26.7861	+	15.1653i	−1.47676	+	0.836087i
$330$		0			0
$331$	−19.1118			−1.05048			−0.525239	−	0.850955i	$-0.676024\pi$
$331$	−19.1118			−1.05048			−0.525239	+	0.850955i	$0.676024\pi$
$332$		0			0
$333$	−0.549430	+	0.549430i	−0.0301086	+	0.0301086i
$334$		0			0
$335$	−7.75345	−	5.81955i	−0.423616	−	0.317956i
$336$		0			0
$337$	21.3329	+	21.3329i	1.16208	+	1.16208i	0.984020	+	0.178056i	$0.0569808\pi$
$337$	21.3329	+	21.3329i	1.16208	+	1.16208i	0.178056	+	0.984020i	$0.443019\pi$
$338$		0			0
$339$	−18.9897			−1.03138
$340$		0			0
$341$		−	3.11941i		−	0.168925i
$342$		0			0
$343$	12.7604	+	13.4228i	0.688996	+	0.724765i
$344$		0			0
$345$	−16.6901	+	2.37802i	−0.898562	+	0.128028i
$346$		0			0
$347$	0.284538	+	0.284538i	0.0152748	+	0.0152748i	0.714703	−	0.699428i	$-0.246562\pi$
$347$	0.284538	+	0.284538i	0.0152748	+	0.0152748i	−0.699428	+	0.714703i	$0.746562\pi$
$348$		0			0
$349$	5.53962			0.296529			0.148265	−	0.988948i	$-0.452631\pi$
$349$	5.53962			0.296529			0.148265	+	0.988948i	$0.452631\pi$
$350$		0			0
$351$	−2.08626			−0.111356
$352$		0			0
$353$	10.5628	+	10.5628i	0.562203	+	0.562203i	0.929933	−	0.367730i	$-0.119865\pi$
$353$	10.5628	+	10.5628i	0.562203	+	0.562203i	−0.367730	+	0.929933i	$0.619865\pi$
$354$		0			0
$355$	3.65503	−	0.520774i	0.193989	−	0.0276398i
$356$		0			0
$357$	4.24583	+	1.17612i	0.224713	+	0.0622471i
$358$		0			0
$359$		−	3.33136i		−	0.175823i	−0.996128	−	0.0879113i	$-0.971981\pi$
$359$		−	3.33136i		−	0.175823i	0.996128	−	0.0879113i	$-0.0280192\pi$
$360$		0			0
$361$	−14.5983			−0.768331
$362$		0			0
$363$	6.81097	+	6.81097i	0.357483	+	0.357483i
$364$		0			0
$365$	17.4669	+	13.1102i	0.914258	+	0.686220i
$366$		0			0
$367$	−22.3369	+	22.3369i	−1.16598	+	1.16598i	−0.182831	+	0.983144i	$0.558526\pi$
$367$	−22.3369	+	22.3369i	−1.16598	+	1.16598i	−0.983144	+	0.182831i	$0.941474\pi$
$368$		0			0
$369$	−8.59246			−0.447306
$370$		0			0
$371$	10.5040	−	5.94699i	0.545343	−	0.308752i
$372$		0			0
$373$	−20.9830	+	20.9830i	−1.08646	+	1.08646i	−0.0905682	+	0.995890i	$0.528868\pi$
$373$	−20.9830	+	20.9830i	−1.08646	+	1.08646i	−0.995890	+	0.0905682i	$0.971132\pi$
$374$		0			0
$375$	10.4604	+	3.94704i	0.540175	+	0.203824i
$376$		0			0
$377$	2.29241	−	2.29241i	0.118065	−	0.118065i
$378$		0			0
$379$		−	14.9942i		−	0.770202i	−0.922875	−	0.385101i	$-0.874167\pi$
$379$		−	14.9942i		−	0.770202i	0.922875	−	0.385101i	$-0.125833\pi$
$380$		0			0
$381$			7.45636i			0.382001i
$382$		0			0
$383$	14.1677	+	14.1677i	0.723937	+	0.723937i	0.969405	−	0.245468i	$-0.0789416\pi$
$383$	14.1677	+	14.1677i	0.723937	+	0.723937i	−0.245468	+	0.969405i	$0.578942\pi$
$384$		0			0
$385$	6.86190	+	0.888051i	0.349715	+	0.0452593i
$386$		0			0
$387$	−5.86009	−	5.86009i	−0.297885	−	0.297885i
$388$		0			0
$389$			33.0008i			1.67321i	0.547808	+	0.836604i	$0.315463\pi$
$389$			33.0008i			1.67321i	−0.547808	+	0.836604i	$0.684537\pi$
$390$		0			0
$391$		−	12.5546i		−	0.634915i
$392$		0			0
$393$	5.70288	−	5.70288i	0.287672	−	0.287672i
$394$		0			0
$395$	−3.99529	−	28.0408i	−0.201025	−	1.41088i
$396$		0			0
$397$	−24.2791	+	24.2791i	−1.21853	+	1.21853i	−0.250385	+	0.968146i	$0.580557\pi$
$397$	−24.2791	+	24.2791i	−1.21853	+	1.21853i	−0.968146	+	0.250385i	$0.919443\pi$
$398$		0			0
$399$	2.73479	+	4.83041i	0.136911	+	0.241823i
$400$		0			0
$401$	7.14242			0.356676			0.178338	−	0.983969i	$-0.442928\pi$
$401$	7.14242			0.356676			0.178338	+	0.983969i	$0.442928\pi$
$402$		0			0
$403$	3.93467	−	3.93467i	0.196000	−	0.196000i
$404$		0			0
$405$	2.21371	−	0.315413i	0.110000	−	0.0156730i
$406$		0			0
$407$	−0.642583	−	0.642583i	−0.0318517	−	0.0318517i
$408$		0			0
$409$	−12.5120			−0.618679			−0.309340	−	0.950952i	$-0.600108\pi$
$409$	−12.5120			−0.618679			−0.309340	+	0.950952i	$0.600108\pi$
$410$		0			0
$411$			15.3592i			0.757614i
$412$		0			0
$413$	−9.03433	−	2.50257i	−0.444551	−	0.123144i
$414$		0			0
$415$	9.90224	+	7.43237i	0.486082	+	0.364841i
$416$		0			0
$417$	−14.8922	−	14.8922i	−0.729274	−	0.729274i
$418$		0			0
$419$	−1.88070			−0.0918783			−0.0459392	−	0.998944i	$-0.514628\pi$
$419$	−1.88070			−0.0918783			−0.0459392	+	0.998944i	$0.514628\pi$
$420$		0			0
$421$	−1.76836			−0.0861848			−0.0430924	−	0.999071i	$-0.513721\pi$
$421$	−1.76836			−0.0861848			−0.0430924	+	0.999071i	$0.513721\pi$
$422$		0			0
$423$	−8.22660	−	8.22660i	−0.399991	−	0.399991i
$424$		0			0
$425$	−4.00879	+	7.29740i	−0.194455	+	0.353976i
$426$		0			0
$427$	−2.88405	+	10.4114i	−0.139569	+	0.503845i
$428$		0			0
$429$		−	2.43998i		−	0.117803i
$430$		0			0
$431$	36.9420			1.77943			0.889717	−	0.456513i	$-0.150902\pi$
$431$	36.9420			1.77943			0.889717	+	0.456513i	$0.150902\pi$
$432$		0			0
$433$	−24.2328	−	24.2328i	−1.16456	−	1.16456i	−0.983467	−	0.181089i	$-0.942038\pi$
$433$	−24.2328	−	24.2328i	−1.16456	−	1.16456i	−0.181089	−	0.983467i	$-0.557962\pi$
$434$		0			0
$435$	−2.08587	+	2.77903i	−0.100010	+	0.133244i
$436$		0			0
$437$	11.1849	−	11.1849i	0.535047	−	0.535047i
$438$		0			0
$439$	−21.3785			−1.02034			−0.510170	−	0.860073i	$-0.670418\pi$
$439$	−21.3785			−1.02034			−0.510170	+	0.860073i	$0.670418\pi$
$440$		0			0
$441$	−3.60173	+	6.00230i	−0.171511	+	0.285824i
$442$		0			0
$443$	−14.7576	+	14.7576i	−0.701157	+	0.701157i	−0.964659	−	0.263502i	$-0.915122\pi$
$443$	−14.7576	+	14.7576i	−0.701157	+	0.701157i	0.263502	+	0.964659i	$0.415122\pi$
$444$		0			0
$445$	−26.1519	+	3.72616i	−1.23972	+	0.176637i
$446$		0			0
$447$	6.90761	−	6.90761i	0.326719	−	0.326719i
$448$		0			0
$449$			12.3378i			0.582258i	0.956684	+	0.291129i	$0.0940308\pi$
$449$			12.3378i			0.582258i	−0.956684	+	0.291129i	$0.905969\pi$
$450$		0			0
$451$		−	10.0493i		−	0.473202i
$452$		0			0
$453$	−13.2116	−	13.2116i	−0.620736	−	0.620736i
$454$		0			0
$455$	7.53513	+	9.77542i	0.353252	+	0.458279i
$456$		0			0
$457$	8.21102	+	8.21102i	0.384095	+	0.384095i	0.872575	−	0.488480i	$-0.162448\pi$
$457$	8.21102	+	8.21102i	0.384095	+	0.384095i	−0.488480	+	0.872575i	$0.662448\pi$
$458$		0			0
$459$			1.66520i			0.0777250i
$460$		0			0
$461$		−	12.1207i		−	0.564518i	−0.959338	−	0.282259i	$-0.908916\pi$
$461$		−	12.1207i		−	0.564518i	0.959338	−	0.282259i	$-0.0910837\pi$
$462$		0			0
$463$	−10.1259	+	10.1259i	−0.470590	+	0.470590i	−0.902105	−	0.431516i	$-0.857979\pi$
$463$	−10.1259	+	10.1259i	−0.470590	+	0.470590i	0.431516	+	0.902105i	$0.357979\pi$
$464$		0			0
$465$	−3.58017	+	4.76991i	−0.166027	+	0.221199i
$466$		0			0
$467$	29.1547	−	29.1547i	1.34912	−	1.34912i	0.462496	−	0.886621i	$-0.346954\pi$
$467$	29.1547	−	29.1547i	1.34912	−	1.34912i	0.886621	−	0.462496i	$-0.153046\pi$
$468$		0			0
$469$	5.65137	+	9.98190i	0.260956	+	0.460921i
$470$		0			0
$471$	15.5111			0.714714
$472$		0			0
$473$	6.85364	−	6.85364i	0.315131	−	0.315131i
$474$		0			0
$475$	−10.0727	+	2.92982i	−0.462166	+	0.134429i
$476$		0			0
$477$	3.22603	+	3.22603i	0.147710	+	0.147710i
$478$		0			0
$479$	−7.98164			−0.364691			−0.182345	−	0.983235i	$-0.558369\pi$
$479$	−7.98164			−0.364691			−0.182345	+	0.983235i	$0.558369\pi$
$480$		0			0
$481$		−	1.62105i		−	0.0739134i
$482$		0			0
$483$	19.2235	+	5.32504i	0.874698	+	0.242298i
$484$		0			0
$485$	1.01311	−	1.34978i	0.0460029	−	0.0612902i
$486$		0			0
$487$	20.2029	+	20.2029i	0.915480	+	0.915480i	0.996696	−	0.0812164i	$-0.0258805\pi$
$487$	20.2029	+	20.2029i	0.915480	+	0.915480i	−0.0812164	+	0.996696i	$0.525881\pi$
$488$		0			0
$489$	8.34026			0.377160
$490$		0			0
$491$	−12.8079			−0.578013			−0.289006	−	0.957327i	$-0.593325\pi$
$491$	−12.8079			−0.578013			−0.289006	+	0.957327i	$0.593325\pi$
$492$		0			0
$493$	−1.82974	−	1.82974i	−0.0824075	−	0.0824075i
$494$		0			0
$495$	0.368890	+	2.58904i	0.0165804	+	0.116368i
$496$		0			0
$497$	−4.20983	−	1.16615i	−0.188837	−	0.0523091i
$498$		0			0
$499$			1.54064i			0.0689687i	0.999405	+	0.0344844i	$0.0109789\pi$
$499$			1.54064i			0.0689687i	−0.999405	+	0.0344844i	$0.989021\pi$
$500$		0			0
$501$	16.8191			0.751423
$502$		0			0
$503$	−23.3462	−	23.3462i	−1.04096	−	1.04096i	−0.999125	−	0.0418326i	$-0.986680\pi$
$503$	−23.3462	−	23.3462i	−1.04096	−	1.04096i	−0.0418326	−	0.999125i	$-0.513320\pi$
$504$		0			0
$505$	−0.696904	−	4.89119i	−0.0310118	−	0.217655i
$506$		0			0
$507$	−6.11471	+	6.11471i	−0.271564	+	0.271564i
$508$		0			0
$509$	16.4830			0.730595			0.365297	−	0.930891i	$-0.380967\pi$
$509$	16.4830			0.730595			0.365297	+	0.930891i	$0.380967\pi$
$510$		0			0
$511$	−12.7313	−	22.4871i	−0.563202	−	0.994771i
$512$		0			0
$513$	−1.48353	+	1.48353i	−0.0654994	+	0.0654994i
$514$		0			0
$515$	7.84919	+	5.89141i	0.345877	+	0.259607i
$516$		0			0
$517$	9.62139	−	9.62139i	0.423148	−	0.423148i
$518$		0			0
$519$		−	6.78084i		−	0.297646i
$520$		0			0
$521$			9.53921i			0.417920i	0.977924	+	0.208960i	$0.0670079\pi$
$521$			9.53921i			0.417920i	−0.977924	+	0.208960i	$0.932992\pi$
$522$		0			0
$523$	−15.0269	−	15.0269i	−0.657081	−	0.657081i	0.297607	−	0.954688i	$-0.403811\pi$
$523$	−15.0269	−	15.0269i	−0.657081	−	0.657081i	−0.954688	+	0.297607i	$0.903811\pi$
$524$		0			0
$525$	−9.47335	−	9.23340i	−0.413451	−	0.402978i
$526$		0			0
$527$	−3.14056	−	3.14056i	−0.136805	−	0.136805i
$528$		0			0
$529$		−	33.8426i		−	1.47142i
$530$		0			0
$531$		−	3.54324i		−	0.153764i
$532$		0			0
$533$	12.6757	−	12.6757i	0.549045	−	0.549045i
$534$		0			0
$535$	32.4191	+	24.3330i	1.40160	+	1.05201i
$536$		0			0
$537$	−14.7384	+	14.7384i	−0.636008	+	0.636008i
$538$		0			0
$539$	−7.01996	−	4.21238i	−0.302371	−	0.181440i
$540$		0			0
$541$	9.59097			0.412348			0.206174	−	0.978515i	$-0.433899\pi$
$541$	9.59097			0.412348			0.206174	+	0.978515i	$0.433899\pi$
$542$		0			0
$543$	4.25315	−	4.25315i	0.182520	−	0.182520i
$544$		0			0
$545$	3.33549	+	23.4100i	0.142876	+	1.00277i
$546$		0			0
$547$	7.34333	+	7.34333i	0.313978	+	0.313978i	0.846449	−	0.532470i	$-0.178736\pi$
$547$	7.34333	+	7.34333i	0.313978	+	0.313978i	−0.532470	+	0.846449i	$0.678736\pi$
$548$		0			0
$549$	−4.08335			−0.174273
$550$		0			0
$551$		−	3.26023i		−	0.138891i
$552$		0			0
$553$	−8.94653	+	32.2971i	−0.380445	+	1.37341i
$554$		0			0
$555$	0.245079	+	1.72008i	0.0104030	+	0.0730132i
$556$		0			0
$557$	−4.35752	−	4.35752i	−0.184634	−	0.184634i	0.608738	−	0.793372i	$-0.291676\pi$
$557$	−4.35752	−	4.35752i	−0.184634	−	0.184634i	−0.793372	+	0.608738i	$0.791676\pi$
$558$		0			0
$559$	17.2897			0.731278
$560$		0			0
$561$	−1.94753			−0.0822248
$562$		0			0
$563$	9.52617	+	9.52617i	0.401480	+	0.401480i	0.878754	−	0.477274i	$-0.158375\pi$
$563$	9.52617	+	9.52617i	0.401480	+	0.401480i	−0.477274	+	0.878754i	$0.658375\pi$
$564$		0			0
$565$	−25.4899	+	33.9604i	−1.07237	+	1.42873i
$566$		0			0
$567$	−2.54973	−	0.706295i	−0.107079	−	0.0296616i
$568$		0			0
$569$			45.4914i			1.90710i	0.301234	+	0.953550i	$0.402602\pi$
$569$			45.4914i			1.90710i	−0.301234	+	0.953550i	$0.597398\pi$
$570$		0			0
$571$	−1.58586			−0.0663662			−0.0331831	−	0.999449i	$-0.510564\pi$
$571$	−1.58586			−0.0663662			−0.0331831	+	0.999449i	$0.510564\pi$
$572$		0			0
$573$	−2.76832	−	2.76832i	−0.115648	−	0.115648i
$574$		0			0
$575$	−18.1503	+	33.0398i	−0.756919	+	1.37786i
$576$		0			0
$577$	−0.0900964	+	0.0900964i	−0.00375076	+	0.00375076i	−0.708980	−	0.705229i	$-0.750844\pi$
$577$	−0.0900964	+	0.0900964i	−0.00375076	+	0.00375076i	0.705229	+	0.708980i	$0.250844\pi$
$578$		0			0
$579$	−18.6346			−0.774426
$580$		0			0
$581$	−7.21759	−	12.7483i	−0.299436	−	0.528888i
$582$		0			0
$583$	−3.77299	+	3.77299i	−0.156261	+	0.156261i
$584$		0			0
$585$	−2.80039	+	3.73099i	−0.115782	+	0.154257i
$586$		0			0
$587$	19.4877	−	19.4877i	0.804343	−	0.804343i	−0.179428	−	0.983771i	$-0.557425\pi$
$587$	19.4877	−	19.4877i	0.804343	−	0.804343i	0.983771	+	0.179428i	$0.0574248\pi$
$588$		0			0
$589$		−	5.59584i		−	0.230573i
$590$		0			0
$591$			5.08386i			0.209122i
$592$		0			0
$593$	3.32187	+	3.32187i	0.136413	+	0.136413i	0.772016	−	0.635603i	$-0.219248\pi$
$593$	3.32187	+	3.32187i	0.136413	+	0.136413i	−0.635603	+	0.772016i	$0.719248\pi$
$594$		0			0
$595$	7.80250	−	6.01436i	0.319871	−	0.246565i
$596$		0			0
$597$	−6.96425	−	6.96425i	−0.285028	−	0.285028i
$598$		0			0
$599$		−	9.57594i		−	0.391262i	−0.980678	−	0.195631i	$-0.937324\pi$
$599$		−	9.57594i		−	0.391262i	0.980678	−	0.195631i	$-0.0626755\pi$
$600$		0			0
$601$		−	1.74051i		−	0.0709968i	−0.999370	−	0.0354984i	$-0.988698\pi$
$601$		−	1.74051i		−	0.0709968i	0.999370	−	0.0354984i	$-0.0113019\pi$
$602$		0			0
$603$	−3.06567	+	3.06567i	−0.124844	+	0.124844i
$604$		0			0
$605$	21.3228	−	3.03811i	0.866896	−	0.123517i
$606$		0			0
$607$	−17.3146	+	17.3146i	−0.702780	+	0.702780i	−0.965006	−	0.262227i	$-0.915543\pi$
$607$	−17.3146	+	17.3146i	−0.702780	+	0.702780i	0.262227	+	0.965006i	$0.415543\pi$
$608$		0			0
$609$	3.57776	−	2.02559i	0.144978	−	0.0820812i
$610$		0			0
$611$	24.2719			0.981938
$612$		0			0
$613$	−29.7369	+	29.7369i	−1.20106	+	1.20106i	−0.227220	+	0.973843i	$0.572964\pi$
$613$	−29.7369	+	29.7369i	−1.20106	+	1.20106i	−0.973843	+	0.227220i	$0.927036\pi$
$614$		0			0
$615$	−11.5337	+	15.3664i	−0.465082	+	0.619634i
$616$		0			0
$617$	−11.9800	−	11.9800i	−0.482299	−	0.482299i	0.423566	−	0.905865i	$-0.360778\pi$
$617$	−11.9800	−	11.9800i	−0.482299	−	0.482299i	−0.905865	+	0.423566i	$0.860778\pi$
$618$		0			0
$619$	−49.2792			−1.98070			−0.990350	−	0.138591i	$-0.955743\pi$
$619$	−49.2792			−1.98070			−0.990350	+	0.138591i	$0.955743\pi$
$620$		0			0
$621$			7.53940i			0.302546i
$622$		0			0
$623$	30.1215	+	8.34388i	1.20679	+	0.334291i
$624$		0			0
$625$	21.0998	−	13.4089i	0.843991	−	0.536358i
$626$		0			0
$627$	−1.73505	−	1.73505i	−0.0692913	−	0.0692913i
$628$		0			0
$629$	−1.29388			−0.0515904
$630$		0			0
$631$	−4.70534			−0.187317			−0.0936583	−	0.995604i	$-0.529856\pi$
$631$	−4.70534			−0.187317			−0.0936583	+	0.995604i	$0.529856\pi$
$632$		0			0
$633$	17.0630	+	17.0630i	0.678195	+	0.678195i
$634$		0			0
$635$	13.3347	+	10.0087i	0.529170	+	0.397182i
$636$		0			0
$637$	−3.54134	−	14.1680i	−0.140313	−	0.561355i
$638$		0			0
$639$		−	1.65109i		−	0.0653160i
$640$		0			0
$641$	4.12279			0.162840			0.0814201	−	0.996680i	$-0.474054\pi$
$641$	4.12279			0.162840			0.0814201	+	0.996680i	$0.474054\pi$
$642$		0			0
$643$	22.0559	+	22.0559i	0.869798	+	0.869798i	0.992450	−	0.122651i	$-0.0391397\pi$
$643$	22.0559	+	22.0559i	0.869798	+	0.869798i	−0.122651	+	0.992450i	$0.539140\pi$
$644$		0			0
$645$	−18.3460	+	2.61396i	−0.722371	+	0.102925i
$646$		0			0
$647$	3.13686	−	3.13686i	0.123323	−	0.123323i	−0.642752	−	0.766075i	$-0.722207\pi$
$647$	3.13686	−	3.13686i	0.123323	−	0.123323i	0.766075	+	0.642752i	$0.222207\pi$
$648$		0			0
$649$	4.14399			0.162666
$650$		0			0
$651$	6.14084	−	3.47671i	0.240679	−	0.136263i
$652$		0			0
$653$	24.2492	−	24.2492i	0.948945	−	0.948945i	−0.0498138	−	0.998759i	$-0.515863\pi$
$653$	24.2492	−	24.2492i	0.948945	−	0.948945i	0.998759	+	0.0498138i	$0.0158628\pi$
$654$		0			0
$655$	−2.54383	−	17.8538i	−0.0993958	−	0.697605i
$656$		0			0
$657$	6.90630	−	6.90630i	0.269440	−	0.269440i
$658$		0			0
$659$		−	29.8530i		−	1.16291i	−0.813579	−	0.581454i	$-0.802484\pi$
$659$		−	29.8530i		−	1.16291i	0.813579	−	0.581454i	$-0.197516\pi$
$660$		0			0
$661$			19.9011i			0.774063i	0.922066	+	0.387032i	$0.126500\pi$
$661$			19.9011i			0.774063i	−0.922066	+	0.387032i	$0.873500\pi$
$662$		0			0
$663$	−2.45652	−	2.45652i	−0.0954035	−	0.0954035i
$664$		0			0
$665$	12.3094	+	1.59306i	0.477339	+	0.0617761i
$666$		0			0
$667$	−8.28438	−	8.28438i	−0.320772	−	0.320772i
$668$		0			0
$669$			2.27624i			0.0880044i
$670$		0			0
$671$		−	4.77566i		−	0.184362i
$672$		0			0
$673$	28.0668	−	28.0668i	1.08190	−	1.08190i	0.0855648	−	0.996333i	$-0.472731\pi$
$673$	28.0668	−	28.0668i	1.08190	−	1.08190i	0.996333	−	0.0855648i	$-0.0272695\pi$
$674$		0			0
$675$	2.40739	−	4.38229i	0.0926605	−	0.168674i
$676$		0			0
$677$	16.1832	−	16.1832i	0.621970	−	0.621970i	−0.324065	−	0.946035i	$-0.605050\pi$
$677$	16.1832	−	16.1832i	0.621970	−	0.621970i	0.946035	+	0.324065i	$0.105050\pi$
$678$		0			0
$679$	−1.73772	+	0.983832i	−0.0666877	+	0.0377560i
$680$		0			0
$681$	6.41951			0.245996
$682$		0			0
$683$	−22.7744	+	22.7744i	−0.871438	+	0.871438i	−0.992629	−	0.121192i	$-0.961328\pi$
$683$	−22.7744	+	22.7744i	−0.871438	+	0.871438i	0.121192	+	0.992629i	$0.461328\pi$
$684$		0			0
$685$	27.4678	+	20.6167i	1.04949	+	0.787722i
$686$		0			0
$687$	−10.7163	−	10.7163i	−0.408851	−	0.408851i
$688$		0			0
$689$	−9.51814			−0.362612
$690$		0			0
$691$		−	19.1625i		−	0.728977i	−0.931208	−	0.364489i	$-0.881244\pi$
$691$		−	19.1625i		−	0.728977i	0.931208	−	0.364489i	$-0.118756\pi$
$692$		0			0
$693$	0.826044	−	2.98203i	0.0313788	−	0.113278i
$694$		0			0
$695$	−46.6224	+	6.64283i	−1.76849	+	0.251977i
$696$		0			0
$697$	−10.1174	−	10.1174i	−0.383225	−	0.383225i
$698$		0			0
$699$	11.6536			0.440781
$700$		0			0
$701$	24.1293			0.911350			0.455675	−	0.890146i	$-0.349398\pi$
$701$	24.1293			0.911350			0.455675	+	0.890146i	$0.349398\pi$
$702$		0			0
$703$	−1.15272	−	1.15272i	−0.0434756	−	0.0434756i
$704$		0			0
$705$	−25.7547	+	3.66957i	−0.969978	+	0.138204i
$706$		0			0
$707$	−1.56056	+	5.63363i	−0.0586908	+	0.211875i
$708$		0			0
$709$		−	39.3631i		−	1.47831i	−0.673534	−	0.739157i	$-0.735224\pi$
$709$		−	39.3631i		−	1.47831i	0.673534	−	0.739157i	$-0.264776\pi$
$710$		0			0
$711$	−12.6669			−0.475044
$712$		0			0
$713$	−14.2192	−	14.2192i	−0.532515	−	0.532515i
$714$		0			0
$715$	−4.36356	−	3.27518i	−0.163188	−	0.122485i
$716$		0			0
$717$	6.02502	−	6.02502i	0.225009	−	0.225009i
$718$		0			0
$719$	40.3865			1.50616			0.753081	−	0.657928i	$-0.228567\pi$
$719$	40.3865			1.50616			0.753081	+	0.657928i	$0.228567\pi$
$720$		0			0
$721$	−5.72116	−	10.1052i	−0.213067	−	0.376336i
$722$		0			0
$723$	−12.7193	+	12.7193i	−0.473034	+	0.473034i
$724$		0			0
$725$	2.17004	+	7.46058i	0.0805934	+	0.277079i
$726$		0			0
$727$	−0.406979	+	0.406979i	−0.0150940	+	0.0150940i	−0.714614	−	0.699519i	$-0.753397\pi$
$727$	−0.406979	+	0.406979i	−0.0150940	+	0.0150940i	0.699519	+	0.714614i	$0.253397\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$		−	13.8002i		−	0.510420i
$732$		0			0
$733$	25.6665	+	25.6665i	0.948015	+	0.948015i	0.998714	−	0.0506988i	$-0.0161448\pi$
$733$	25.6665	+	25.6665i	0.948015	+	0.948015i	−0.0506988	+	0.998714i	$0.516145\pi$
$734$		0			0
$735$	5.89967	+	14.4981i	0.217613	+	0.534769i
$736$		0			0
$737$	−3.58544	−	3.58544i	−0.132071	−	0.132071i
$738$		0			0
$739$		−	34.8421i		−	1.28169i	−0.767672	−	0.640843i	$-0.778585\pi$
$739$		−	34.8421i		−	1.28169i	0.767672	−	0.640843i	$-0.221415\pi$
$740$		0			0
$741$		−	4.37703i		−	0.160794i
$742$		0			0
$743$	−17.2110	+	17.2110i	−0.631409	+	0.631409i	−0.948421	−	0.317012i	$-0.897320\pi$
$743$	−17.2110	+	17.2110i	−0.631409	+	0.631409i	0.317012	+	0.948421i	$0.397320\pi$
$744$		0			0
$745$	−3.08122	−	21.6254i	−0.112887	−	0.792292i
$746$		0			0
$747$	3.91528	−	3.91528i	0.143253	−	0.143253i
$748$		0			0
$749$	−23.6298	−	41.7368i	−0.863414	−	1.52503i
$750$		0			0
$751$	−8.12809			−0.296598			−0.148299	−	0.988943i	$-0.547380\pi$
$751$	−8.12809			−0.296598			−0.148299	+	0.988943i	$0.547380\pi$
$752$		0			0
$753$	6.50087	−	6.50087i	0.236905	−	0.236905i
$754$		0			0
$755$	−41.3611	+	5.89318i	−1.50528	+	0.214475i
$756$		0			0
$757$	29.3910	+	29.3910i	1.06824	+	1.06824i	0.997495	+	0.0707411i	$0.0225364\pi$
$757$	29.3910	+	29.3910i	1.06824	+	1.06824i	0.0707411	+	0.997495i	$0.477464\pi$
$758$		0			0
$759$	−8.81767			−0.320061
$760$		0			0
$761$		−	33.1696i		−	1.20240i	−0.799100	−	0.601198i	$-0.794690\pi$
$761$		−	33.1696i		−	1.20240i	0.799100	−	0.601198i	$-0.205310\pi$
$762$		0			0
$763$	7.46905	−	26.9634i	0.270398	−	0.976141i
$764$		0			0
$765$	2.97798	+	2.23520i	0.107669	+	0.0808139i
$766$		0			0
$767$	5.22703	+	5.22703i	0.188737	+	0.188737i
$768$		0			0
$769$	42.5161			1.53317			0.766584	−	0.642144i	$-0.221955\pi$
$769$	42.5161			1.53317			0.766584	+	0.642144i	$0.221955\pi$
$770$		0			0
$771$	−28.4314			−1.02393
$772$		0			0
$773$	11.4240	+	11.4240i	0.410894	+	0.410894i	0.882050	−	0.471156i	$-0.156163\pi$
$773$	11.4240	+	11.4240i	0.410894	+	0.410894i	−0.471156	+	0.882050i	$0.656163\pi$
$774$		0			0
$775$	3.72464	+	12.8053i	0.133793	+	0.459979i
$776$		0			0
$777$	0.548799	−	1.98117i	0.0196880	−	0.0710741i
$778$		0			0
$779$		−	18.0272i		−	0.645892i
$780$		0			0
$781$	1.93102			0.0690973
$782$		0			0
$783$	1.09881	+	1.09881i	0.0392683	+	0.0392683i
$784$		0			0
$785$	20.8205	−	27.7394i	0.743117	−	0.990063i
$786$		0			0
$787$	15.4459	−	15.4459i	0.550586	−	0.550586i	−0.376024	−	0.926610i	$-0.622709\pi$
$787$	15.4459	−	15.4459i	0.550586	−	0.550586i	0.926610	+	0.376024i	$0.122709\pi$
$788$		0			0
$789$	−22.4107			−0.797843
$790$		0			0
$791$	43.7212	−	24.7533i	1.55455	−	0.880125i
$792$		0			0
$793$	6.02379	−	6.02379i	0.213911	−	0.213911i
$794$		0			0
$795$	10.0996	−	1.43901i	0.358196	−	0.0510363i
$796$		0			0
$797$	25.0499	−	25.0499i	0.887314	−	0.887314i	−0.106951	−	0.994264i	$-0.534109\pi$
$797$	25.0499	−	25.0499i	0.887314	−	0.887314i	0.994264	+	0.106951i	$0.0341087\pi$
$798$		0			0
$799$		−	19.3733i		−	0.685377i
$800$		0			0
$801$			11.8136i			0.417413i
$802$		0			0
$803$	8.07723	+	8.07723i	0.285039	+	0.285039i
$804$		0			0
$805$	35.3267	−	27.2307i	1.24510	−	0.959756i
$806$		0			0
$807$	−12.5023	−	12.5023i	−0.440102	−	0.440102i
$808$		0			0
$809$			1.93007i			0.0678577i	0.999424	+	0.0339288i	$0.0108020\pi$
$809$			1.93007i			0.0678577i	−0.999424	+	0.0339288i	$0.989198\pi$
$810$		0			0
$811$			16.6713i			0.585410i	0.956203	+	0.292705i	$0.0945554\pi$
$811$			16.6713i			0.585410i	−0.956203	+	0.292705i	$0.905445\pi$
$812$		0			0
$813$	3.04275	−	3.04275i	0.106714	−	0.106714i
$814$		0			0
$815$	11.1951	−	14.9154i	0.392148	−	0.522463i
$816$		0			0
$817$	12.2946	−	12.2946i	0.430134	−	0.430134i
$818$		0			0
$819$	4.80333	−	2.71946i	0.167842	−	0.0950257i
$820$		0			0
$821$	−8.32072			−0.290395			−0.145198	−	0.989403i	$-0.546382\pi$
$821$	−8.32072			−0.290395			−0.145198	+	0.989403i	$0.546382\pi$
$822$		0			0
$823$	−27.4683	+	27.4683i	−0.957486	+	0.957486i	−0.999132	−	0.0416468i	$-0.986740\pi$
$823$	−27.4683	+	27.4683i	−0.957486	+	0.957486i	0.0416468	+	0.999132i	$0.486740\pi$
$824$		0			0
$825$	5.12529	+	2.81555i	0.178440	+	0.0980250i
$826$		0			0
$827$	3.01076	+	3.01076i	0.104695	+	0.104695i	0.757514	−	0.652819i	$-0.226414\pi$
$827$	3.01076	+	3.01076i	0.104695	+	0.104695i	−0.652819	+	0.757514i	$0.726414\pi$
$828$		0			0
$829$	−17.6623			−0.613438			−0.306719	−	0.951800i	$-0.599231\pi$
$829$	−17.6623			−0.613438			−0.306719	+	0.951800i	$0.599231\pi$
$830$		0			0
$831$		−	10.0812i		−	0.349713i
$832$		0			0
$833$	−11.3085	+	2.82661i	−0.391817	+	0.0979363i
$834$		0			0
$835$	22.5763	−	30.0786i	0.781284	−	1.04091i
$836$		0			0
$837$	1.88599	+	1.88599i	0.0651894	+	0.0651894i
$838$		0			0
$839$	−23.0587			−0.796075			−0.398038	−	0.917369i	$-0.630309\pi$
$839$	−23.0587			−0.796075			−0.398038	+	0.917369i	$0.630309\pi$
$840$		0			0
$841$	26.5852			0.916732
$842$		0			0
$843$	−0.00905572	−	0.00905572i	−0.000311895	−	0.000311895i
$844$		0			0
$845$	2.72754	+	19.1431i	0.0938301	+	0.658542i
$846$		0			0
$847$	−24.5595	−	6.80315i	−0.843873	−	0.233759i
$848$		0			0
$849$		−	31.3927i		−	1.07739i
$850$		0			0
$851$	−5.85820			−0.200816
$852$		0			0
$853$	−29.7111	−	29.7111i	−1.01729	−	1.01729i	−0.999848	−	0.0174392i	$-0.994449\pi$
$853$	−29.7111	−	29.7111i	−1.01729	−	1.01729i	−0.0174392	−	0.999848i	$-0.505551\pi$
$854$		0			0
$855$	0.661744	+	4.64442i	0.0226312	+	0.158836i
$856$		0			0
$857$	14.7575	−	14.7575i	0.504107	−	0.504107i	−0.408604	−	0.912712i	$-0.633984\pi$
$857$	14.7575	−	14.7575i	0.504107	−	0.504107i	0.912712	+	0.408604i	$0.133984\pi$
$858$		0			0
$859$	−32.9265			−1.12344			−0.561720	−	0.827328i	$-0.689860\pi$
$859$	−32.9265			−1.12344			−0.561720	+	0.827328i	$0.689860\pi$
$860$		0			0
$861$	19.7830	−	11.2004i	0.674201	−	0.381707i
$862$		0			0
$863$	20.2394	−	20.2394i	0.688959	−	0.688959i	−0.273043	−	0.962002i	$-0.588030\pi$
$863$	20.2394	−	20.2394i	0.688959	−	0.688959i	0.962002	+	0.273043i	$0.0880301\pi$
$864$		0			0
$865$	−12.1266	−	9.10192i	−0.412316	−	0.309475i
$866$		0			0
$867$	10.0601	−	10.0601i	0.341658	−	0.341658i
$868$		0			0
$869$		−	14.8145i		−	0.502546i
$870$		0			0
$871$		−	9.04500i		−	0.306478i
$872$		0			0
$873$	−0.533694	−	0.533694i	−0.0180628	−	0.0180628i
$874$		0			0
$875$	−29.2287	+	4.54779i	−0.988111	+	0.153743i
$876$		0			0
$877$	2.09834	+	2.09834i	0.0708560	+	0.0708560i	0.741647	−	0.670791i	$-0.234045\pi$
$877$	2.09834	+	2.09834i	0.0708560	+	0.0708560i	−0.670791	+	0.741647i	$0.734045\pi$
$878$		0			0
$879$			26.7864i			0.903481i
$880$		0			0
$881$			37.2576i			1.25524i	0.778519	+	0.627621i	$0.215971\pi$
$881$			37.2576i			1.25524i	−0.778519	+	0.627621i	$0.784029\pi$
$882$		0			0
$883$	−25.0295	+	25.0295i	−0.842309	+	0.842309i	−0.989159	−	0.146850i	$-0.953087\pi$
$883$	−25.0295	+	25.0295i	−0.842309	+	0.842309i	0.146850	+	0.989159i	$0.453087\pi$
$884$		0			0
$885$	−6.33660	−	4.75609i	−0.213002	−	0.159874i
$886$		0			0
$887$	20.4997	−	20.4997i	0.688313	−	0.688313i	−0.273546	−	0.961859i	$-0.588197\pi$
$887$	20.4997	−	20.4997i	0.688313	−	0.688313i	0.961859	+	0.273546i	$0.0881965\pi$
$888$		0			0
$889$	−9.71943	−	17.1672i	−0.325979	−	0.575770i
$890$		0			0
$891$	1.16955			0.0391812
$892$		0			0
$893$	17.2596	−	17.2596i	0.577571	−	0.577571i
$894$		0			0
$895$	6.57422	+	46.1408i	0.219752	+	1.54232i
$896$		0			0
$897$	−11.1222	−	11.1222i	−0.371359	−	0.371359i
$898$		0			0
$899$	−4.14470			−0.138233
$900$		0			0
$901$			7.59714i			0.253098i
$902$		0			0
$903$	21.1307	+	5.85336i	0.703187	+	0.194788i
$904$		0			0
$905$	−1.89717	−	13.3152i	−0.0630639	−	0.442611i
$906$		0			0
$907$	19.6072	+	19.6072i	0.651045	+	0.651045i	0.953245	−	0.302199i	$-0.0977208\pi$
$907$	19.6072	+	19.6072i	0.651045	+	0.651045i	−0.302199	+	0.953245i	$0.597721\pi$
$908$		0			0
$909$	−2.20950			−0.0732844
$910$		0			0
$911$	−22.6134			−0.749217			−0.374608	−	0.927183i	$-0.622223\pi$
$911$	−22.6134			−0.749217			−0.374608	+	0.927183i	$0.622223\pi$
$912$		0			0
$913$	4.57910	+	4.57910i	0.151546	+	0.151546i
$914$		0			0
$915$	−5.48107	+	7.30249i	−0.181199	+	0.241413i
$916$		0			0
$917$	−5.69633	+	20.5638i	−0.188109	+	0.679078i
$918$		0			0
$919$			10.6164i			0.350204i	0.984550	+	0.175102i	$0.0560255\pi$
$919$			10.6164i			0.350204i	−0.984550	+	0.175102i	$0.943975\pi$
$920$		0			0
$921$	−3.74383			−0.123364
$922$		0			0
$923$	2.43570	+	2.43570i	0.0801720	+	0.0801720i
$924$		0			0
$925$	3.40509	+	1.87057i	0.111959	+	0.0615039i
$926$		0			0
$927$	3.10352	−	3.10352i	0.101933	−	0.101933i
$928$		0			0
$929$	15.3896			0.504917			0.252458	−	0.967608i	$-0.418761\pi$
$929$	15.3896			0.504917			0.252458	+	0.967608i	$0.418761\pi$
$930$		0			0
$931$	−12.5930	−	7.55652i	−0.412718	−	0.247655i
$932$		0			0
$933$	1.42822	−	1.42822i	0.0467578	−	0.0467578i
$934$		0			0
$935$	−2.61417	+	3.48289i	−0.0854925	+	0.113903i
$936$		0			0
$937$	32.6586	−	32.6586i	1.06691	−	1.06691i	0.0693155	−	0.997595i	$-0.477918\pi$
$937$	32.6586	−	32.6586i	1.06691	−	1.06691i	0.997595	−	0.0693155i	$-0.0220815\pi$
$938$		0			0
$939$			31.8861i			1.04056i
$940$		0			0
$941$		−	35.7168i		−	1.16433i	−0.813069	−	0.582167i	$-0.802205\pi$
$941$		−	35.7168i		−	1.16433i	0.813069	−	0.582167i	$-0.197795\pi$
$942$		0			0
$943$	−45.8078	−	45.8078i	−1.49171	−	1.49171i
$944$		0			0
$945$	−4.68562	+	3.61179i	−0.152423	+	0.117491i
$946$		0			0
$947$	28.1597	+	28.1597i	0.915067	+	0.915067i	0.996665	−	0.0815980i	$-0.0260023\pi$
$947$	28.1597	+	28.1597i	0.915067	+	0.915067i	−0.0815980	+	0.996665i	$0.526002\pi$
$948$		0			0
$949$			20.3765i			0.661448i
$950$		0			0
$951$		−	10.4726i		−	0.339598i
$952$		0			0
$953$	−28.0790	+	28.0790i	−0.909569	+	0.909569i	−0.996237	−	0.0866684i	$-0.972378\pi$
$953$	−28.0790	+	28.0790i	−0.909569	+	0.909569i	0.0866684	+	0.996237i	$0.472378\pi$
$954$		0			0
$955$	−8.66666	+	1.23484i	−0.280446	+	0.0399584i
$956$		0			0
$957$	−1.28511	+	1.28511i	−0.0415417	+	0.0415417i
$958$		0			0
$959$	−20.0209	−	35.3624i	−0.646508	−	1.14191i
$960$		0			0
$961$	23.8861			0.770518
$962$		0			0
$963$	12.8183	−	12.8183i	0.413065	−	0.413065i
$964$		0			0
$965$	−25.0132	+	33.3253i	−0.805202	+	1.07278i
$966$		0			0
$967$	−3.67710	−	3.67710i	−0.118248	−	0.118248i	0.645507	−	0.763755i	$-0.276646\pi$
$967$	−3.67710	−	3.67710i	−0.118248	−	0.118248i	−0.763755	+	0.645507i	$0.776646\pi$
$968$		0			0
$969$	−3.49364			−0.112232
$970$		0			0
$971$			50.0511i			1.60622i	0.595834	+	0.803108i	$0.296822\pi$
$971$			50.0511i			1.60622i	−0.595834	+	0.803108i	$0.703178\pi$
$972$		0			0
$973$	53.6993	+	14.8751i	1.72152	+	0.476874i
$974$		0			0
$975$	2.91339	+	10.0162i	0.0933032	+	0.320775i
$976$		0			0
$977$	−22.4734	−	22.4734i	−0.718986	−	0.718986i	0.249411	−	0.968398i	$-0.419763\pi$
$977$	−22.4734	−	22.4734i	−0.718986	−	0.718986i	−0.968398	+	0.249411i	$0.919763\pi$
$978$		0			0
$979$	−13.8165			−0.441579
$980$		0			0
$981$	10.5750			0.337633
$982$		0			0
$983$	22.7861	+	22.7861i	0.726763	+	0.726763i	0.969974	−	0.243210i	$-0.0782005\pi$
$983$	22.7861	+	22.7861i	0.726763	+	0.726763i	−0.243210	+	0.969974i	$0.578201\pi$
$984$		0			0
$985$	9.09178	+	6.82406i	0.289688	+	0.217433i
$986$		0			0
$987$	29.6641	+	8.21716i	0.944218	+	0.261555i
$988$		0			0
$989$		−	62.4822i		−	1.98682i
$990$		0			0
$991$	−34.5490			−1.09749			−0.548743	−	0.835991i	$-0.684893\pi$
$991$	−34.5490			−1.09749			−0.548743	+	0.835991i	$0.684893\pi$
$992$		0			0
$993$	13.5141	+	13.5141i	0.428856	+	0.428856i
$994$		0			0
$995$	−21.8027	+	3.10648i	−0.691192	+	0.0984821i
$996$		0			0
$997$	−19.9762	+	19.9762i	−0.632653	+	0.632653i	−0.948733	−	0.316079i	$-0.897633\pi$
$997$	−19.9762	+	19.9762i	−0.632653	+	0.632653i	0.316079	+	0.948733i	$0.397633\pi$
$998$		0			0
$999$	0.777011			0.0245835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bt.b.97.1	yes	24
4.3	odd	2		1680.2.cz.e.97.10		24
5.3	odd	4		840.2.bt.a.433.12	yes	24
7.6	odd	2		840.2.bt.a.97.12	✓	24
20.3	even	4		1680.2.cz.f.433.3		24
28.27	even	2		1680.2.cz.f.97.3		24
35.13	even	4	inner	840.2.bt.b.433.1	yes	24
140.83	odd	4		1680.2.cz.e.433.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bt.a.97.12	✓	24	7.6	odd	2
840.2.bt.a.433.12	yes	24	5.3	odd	4
840.2.bt.b.97.1	yes	24	1.1	even	1	trivial
840.2.bt.b.433.1	yes	24	35.13	even	4	inner
1680.2.cz.e.97.10		24	4.3	odd	2
1680.2.cz.e.433.10		24	140.83	odd	4
1680.2.cz.f.97.3		24	28.27	even	2
1680.2.cz.f.433.3		24	20.3	even	4

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-2.21371 + 0.315413i) q^{5} +(2.54973 + 0.706295i) q^{7} +1.00000i q^{9} -1.16955 q^{11} +(-1.47521 - 1.47521i) q^{13} +(1.78836 + 1.34230i) q^{15} +(-1.17748 + 1.17748i) q^{17} -2.09803 q^{19} +(-1.30351 - 2.30236i) q^{21} +(-5.33116 + 5.33116i) q^{23} +(4.80103 - 1.39647i) q^{25} +(0.707107 - 0.707107i) q^{27} +1.55395i q^{29} +2.66719i q^{31} +(0.826994 + 0.826994i) q^{33} +(-5.86715 - 0.759313i) q^{35} +(0.549430 + 0.549430i) q^{37} +2.08626i q^{39} +8.59246i q^{41} +(-5.86009 + 5.86009i) q^{43} +(-0.315413 - 2.21371i) q^{45} +(-8.22660 + 8.22660i) q^{47} +(6.00230 + 3.60173i) q^{49} +1.66520 q^{51} +(3.22603 - 3.22603i) q^{53} +(2.58904 - 0.368890i) q^{55} +(1.48353 + 1.48353i) q^{57} -3.54324 q^{59} +4.08335i q^{61} +(-0.706295 + 2.54973i) q^{63} +(3.73099 + 2.80039i) q^{65} +(3.06567 + 3.06567i) q^{67} +7.53940 q^{69} -1.65109 q^{71} +(-6.90630 - 6.90630i) q^{73} +(-4.38229 - 2.40739i) q^{75} +(-2.98203 - 0.826044i) q^{77} +12.6669i q^{79} -1.00000 q^{81} +(-3.91528 - 3.91528i) q^{83} +(2.23520 - 2.97798i) q^{85} +(1.09881 - 1.09881i) q^{87} +11.8136 q^{89} +(-2.71946 - 4.80333i) q^{91} +(1.88599 - 1.88599i) q^{93} +(4.64442 - 0.661744i) q^{95} +(-0.533694 + 0.533694i) q^{97} -1.16955i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{11} - 16 q^{13} + 4 q^{15} - 20 q^{17} - 8 q^{19} + 24 q^{23} - 4 q^{25} + 4 q^{37} - 16 q^{43} + 4 q^{45} + 24 q^{47} - 36 q^{49} + 16 q^{53} - 28 q^{55} + 4 q^{57} - 8 q^{59} + 4 q^{63} + 24 q^{65}+ \cdots + 28 q^{97}+O(q^{100}) \) 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

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Database

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