LMFDB - Embedded newform 840.2.bt.a.433.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			433.6
Character	$\chi$	$=$	840.433
Dual form			840.2.bt.a.97.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{3} +(2.17640 + 0.513127i) q^{5} +(-2.56234 - 0.659108i) q^{7} -1.00000i q^{9} -1.57564 q^{11} +(3.14577 - 3.14577i) q^{13} +(-1.90178 + 1.17611i) q^{15} +(4.47060 + 4.47060i) q^{17} +6.38872 q^{19} +(2.27791 - 1.34579i) q^{21} +(1.38299 + 1.38299i) q^{23} +(4.47340 + 2.23353i) q^{25} +(0.707107 + 0.707107i) q^{27} -2.19669i q^{29} +1.53872i q^{31} +(1.11414 - 1.11414i) q^{33} +(-5.23846 - 2.74929i) q^{35} +(-8.06335 + 8.06335i) q^{37} +4.44879i q^{39} -4.79665i q^{41} +(0.0831671 + 0.0831671i) q^{43} +(0.513127 - 2.17640i) q^{45} +(3.14581 + 3.14581i) q^{47} +(6.13115 + 3.37772i) q^{49} -6.32238 q^{51} +(6.30175 + 6.30175i) q^{53} +(-3.42921 - 0.808502i) q^{55} +(-4.51751 + 4.51751i) q^{57} +7.59628 q^{59} -3.73588i q^{61} +(-0.659108 + 2.56234i) q^{63} +(8.46062 - 5.23226i) q^{65} +(-1.84357 + 1.84357i) q^{67} -1.95585 q^{69} +9.63918 q^{71} +(-2.46445 + 2.46445i) q^{73} +(-4.74252 + 1.58383i) q^{75} +(4.03732 + 1.03852i) q^{77} -15.8822i q^{79} -1.00000 q^{81} +(-2.70588 + 2.70588i) q^{83} +(7.43580 + 12.0238i) q^{85} +(1.55329 + 1.55329i) q^{87} +12.3852 q^{89} +(-10.1339 + 5.98712i) q^{91} +(-1.08804 - 1.08804i) q^{93} +(13.9044 + 3.27822i) q^{95} +(-8.82823 - 8.82823i) q^{97} +1.57564i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{7} - 8 q^{11} + 16 q^{13} + 4 q^{15} + 20 q^{17} + 8 q^{19} + 24 q^{23} - 4 q^{25} + 4 q^{37} - 16 q^{43} - 4 q^{45} - 24 q^{47} + 36 q^{49} + 16 q^{53} + 28 q^{55} + 4 q^{57} + 8 q^{59} + 24 q^{65}+ \cdots - 28 q^{97}+O(q^{100}) $ 24 * q - 4 * q^7 - 8 * q^11 + 16 * q^13 + 4 * q^15 + 20 * q^17 + 8 * q^19 + 24 * q^23 - 4 * q^25 + 4 * q^37 - 16 * q^43 - 4 * q^45 - 24 * q^47 + 36 * q^49 + 16 * q^53 + 28 * q^55 + 4 * q^57 + 8 * q^59 + 24 * q^65 + 16 * q^67 - 8 * q^69 + 8 * q^71 - 28 * q^73 + 20 * q^77 - 24 * q^81 + 64 * q^83 - 20 * q^85 + 20 * q^87 + 16 * q^89 + 24 * q^91 - 12 * q^93 + 24 * q^95 - 28 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	2.17640	+	0.513127i	0.973314	+	0.229477i
$5$	2.17640	+	0.513127i	0.973314	+	0.229477i
$6$		0			0
$7$	−2.56234	−	0.659108i	−0.968473	−	0.249119i
$7$	−2.56234	−	0.659108i	−0.968473	−	0.249119i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−1.57564			−0.475072			−0.237536	−	0.971379i	$-0.576340\pi$
$11$	−1.57564			−0.475072			−0.237536	+	0.971379i	$0.576340\pi$
$12$		0			0
$13$	3.14577	−	3.14577i	0.872479	−	0.872479i	−0.120263	−	0.992742i	$-0.538374\pi$
$13$	3.14577	−	3.14577i	0.872479	−	0.872479i	0.992742	+	0.120263i	$0.0383737\pi$
$14$		0			0
$15$	−1.90178	+	1.17611i	−0.491037	+	0.303670i
$16$		0			0
$17$	4.47060	+	4.47060i	1.08428	+	1.08428i	0.996105	+	0.0881736i	$0.0281030\pi$
$17$	4.47060	+	4.47060i	1.08428	+	1.08428i	0.0881736	+	0.996105i	$0.471897\pi$
$18$		0			0
$19$	6.38872			1.46567			0.732836	−	0.680405i	$-0.238196\pi$
$19$	6.38872			1.46567			0.732836	+	0.680405i	$0.238196\pi$
$20$		0			0
$21$	2.27791	−	1.34579i	0.497080	−	0.293675i
$22$		0			0
$23$	1.38299	+	1.38299i	0.288374	+	0.288374i	0.836437	−	0.548063i	$-0.184635\pi$
$23$	1.38299	+	1.38299i	0.288374	+	0.288374i	−0.548063	+	0.836437i	$0.684635\pi$
$24$		0			0
$25$	4.47340	+	2.23353i	0.894680	+	0.446707i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$		−	2.19669i		−	0.407915i	−0.978980	−	0.203958i	$-0.934620\pi$
$29$		−	2.19669i		−	0.407915i	0.978980	−	0.203958i	$-0.0653805\pi$
$30$		0			0
$31$			1.53872i			0.276362i	0.990407	+	0.138181i	$0.0441256\pi$
$31$			1.53872i			0.276362i	−0.990407	+	0.138181i	$0.955874\pi$
$32$		0			0
$33$	1.11414	−	1.11414i	0.193948	−	0.193948i
$34$		0			0
$35$	−5.23846	−	2.74929i	−0.885461	−	0.464714i
$36$		0			0
$37$	−8.06335	+	8.06335i	−1.32561	+	1.32561i	−0.416446	+	0.909161i	$0.636724\pi$
$37$	−8.06335	+	8.06335i	−1.32561	+	1.32561i	−0.909161	+	0.416446i	$0.863276\pi$
$38$		0			0
$39$			4.44879i			0.712376i
$40$		0			0
$41$		−	4.79665i		−	0.749111i	−0.927204	−	0.374556i	$-0.877795\pi$
$41$		−	4.79665i		−	0.749111i	0.927204	−	0.374556i	$-0.122205\pi$
$42$		0			0
$43$	0.0831671	+	0.0831671i	0.0126829	+	0.0126829i	0.713420	−	0.700737i	$-0.247145\pi$
$43$	0.0831671	+	0.0831671i	0.0126829	+	0.0126829i	−0.700737	+	0.713420i	$0.747145\pi$
$44$		0			0
$45$	0.513127	−	2.17640i	0.0764924	−	0.324438i
$46$		0			0
$47$	3.14581	+	3.14581i	0.458863	+	0.458863i	0.898282	−	0.439419i	$-0.144816\pi$
$47$	3.14581	+	3.14581i	0.458863	+	0.458863i	−0.439419	+	0.898282i	$0.644816\pi$
$48$		0			0
$49$	6.13115	+	3.37772i	0.875879	+	0.482531i
$50$		0			0
$51$	−6.32238			−0.885310
$52$		0			0
$53$	6.30175	+	6.30175i	0.865612	+	0.865612i	0.991983	−	0.126371i	$-0.0403330\pi$
$53$	6.30175	+	6.30175i	0.865612	+	0.865612i	−0.126371	+	0.991983i	$0.540333\pi$
$54$		0			0
$55$	−3.42921	−	0.808502i	−0.462395	−	0.109018i
$56$		0			0
$57$	−4.51751	+	4.51751i	−0.598358	+	0.598358i
$58$		0			0
$59$	7.59628			0.988952			0.494476	−	0.869191i	$-0.335360\pi$
$59$	7.59628			0.988952			0.494476	+	0.869191i	$0.335360\pi$
$60$		0			0
$61$		−	3.73588i		−	0.478331i	−0.970979	−	0.239165i	$-0.923126\pi$
$61$		−	3.73588i		−	0.478331i	0.970979	−	0.239165i	$-0.0768738\pi$
$62$		0			0
$63$	−0.659108	+	2.56234i	−0.0830398	+	0.322824i
$64$		0			0
$65$	8.46062	−	5.23226i	1.04941	−	0.648982i
$66$		0			0
$67$	−1.84357	+	1.84357i	−0.225228	+	0.225228i	−0.810696	−	0.585468i	$-0.800911\pi$
$67$	−1.84357	+	1.84357i	−0.225228	+	0.225228i	0.585468	+	0.810696i	$0.300911\pi$
$68$		0			0
$69$	−1.95585			−0.235457
$70$		0			0
$71$	9.63918			1.14396			0.571980	−	0.820268i	$-0.306176\pi$
$71$	9.63918			1.14396			0.571980	+	0.820268i	$0.306176\pi$
$72$		0			0
$73$	−2.46445	+	2.46445i	−0.288442	+	0.288442i	−0.836464	−	0.548022i	$-0.815381\pi$
$73$	−2.46445	+	2.46445i	−0.288442	+	0.288442i	0.548022	+	0.836464i	$0.315381\pi$
$74$		0			0
$75$	−4.74252	+	1.58383i	−0.547619	+	0.182884i
$76$		0			0
$77$	4.03732	+	1.03852i	0.460095	+	0.118350i
$78$		0			0
$79$		−	15.8822i		−	1.78689i	−0.449176	−	0.893443i	$-0.648282\pi$
$79$		−	15.8822i		−	1.78689i	0.449176	−	0.893443i	$-0.351718\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−2.70588	+	2.70588i	−0.297009	+	0.297009i	−0.839841	−	0.542832i	$-0.817352\pi$
$83$	−2.70588	+	2.70588i	−0.297009	+	0.297009i	0.542832	+	0.839841i	$0.317352\pi$
$84$		0			0
$85$	7.43580	+	12.0238i	0.806526	+	1.30416i
$86$		0			0
$87$	1.55329	+	1.55329i	0.166531	+	0.166531i
$88$		0			0
$89$	12.3852			1.31283			0.656415	−	0.754400i	$-0.272072\pi$
$89$	12.3852			1.31283			0.656415	+	0.754400i	$0.272072\pi$
$90$		0			0
$91$	−10.1339	+	5.98712i	−1.06232	+	0.627621i
$92$		0			0
$93$	−1.08804	−	1.08804i	−0.112824	−	0.112824i
$94$		0			0
$95$	13.9044	+	3.27822i	1.42656	+	0.336339i
$96$		0			0
$97$	−8.82823	−	8.82823i	−0.896371	−	0.896371i	0.0987420	−	0.995113i	$-0.468518\pi$
$97$	−8.82823	−	8.82823i	−0.896371	−	0.896371i	−0.995113	+	0.0987420i	$0.968518\pi$
$98$		0			0
$99$			1.57564i			0.158357i
$100$		0			0
$101$		−	6.46785i		−	0.643575i	−0.946812	−	0.321788i	$-0.895716\pi$
$101$		−	6.46785i		−	0.643575i	0.946812	−	0.321788i	$-0.104284\pi$
$102$		0			0
$103$	−10.3620	+	10.3620i	−1.02099	+	1.02099i	−0.0212195	+	0.999775i	$0.506755\pi$
$103$	−10.3620	+	10.3620i	−1.02099	+	1.02099i	−0.999775	+	0.0212195i	$0.993245\pi$
$104$		0			0
$105$	5.64819	−	1.76011i	0.551207	−	0.171769i
$106$		0			0
$107$	−0.548614	+	0.548614i	−0.0530365	+	0.0530365i	−0.733128	−	0.680091i	$-0.761940\pi$
$107$	−0.548614	+	0.548614i	−0.0530365	+	0.0530365i	0.680091	+	0.733128i	$0.261940\pi$
$108$		0			0
$109$			7.46934i			0.715433i	0.933830	+	0.357717i	$0.116445\pi$
$109$			7.46934i			0.715433i	−0.933830	+	0.357717i	$0.883555\pi$
$110$		0			0
$111$		−	11.4033i		−	1.08235i
$112$		0			0
$113$	−7.07940	−	7.07940i	−0.665974	−	0.665974i	0.290808	−	0.956782i	$-0.406076\pi$
$113$	−7.07940	−	7.07940i	−0.665974	−	0.665974i	−0.956782	+	0.290808i	$0.906076\pi$
$114$		0			0
$115$	2.30029	+	3.71959i	0.214503	+	0.346854i
$116$		0			0
$117$	−3.14577	−	3.14577i	−0.290826	−	0.290826i
$118$		0			0
$119$	−8.50857	−	14.4018i	−0.779979	−	1.32021i
$120$		0			0
$121$	−8.51737			−0.774306
$122$		0			0
$123$	3.39175	+	3.39175i	0.305823	+	0.305823i
$124$		0			0
$125$	8.58981	+	7.15648i	0.768296	+	0.640095i
$126$		0			0
$127$	5.55644	−	5.55644i	0.493055	−	0.493055i	−0.416213	−	0.909267i	$-0.636643\pi$
$127$	5.55644	−	5.55644i	0.493055	−	0.493055i	0.909267	+	0.416213i	$0.136643\pi$
$128$		0			0
$129$	−0.117616			−0.0103555
$130$		0			0
$131$			7.86455i			0.687129i	0.939129	+	0.343564i	$0.111634\pi$
$131$			7.86455i			0.687129i	−0.939129	+	0.343564i	$0.888366\pi$
$132$		0			0
$133$	−16.3701	−	4.21086i	−1.41946	−	0.365128i
$134$		0			0
$135$	1.17611	+	1.90178i	0.101223	+	0.163679i
$136$		0			0
$137$	7.47666	−	7.47666i	0.638774	−	0.638774i	−0.311479	−	0.950253i	$-0.600824\pi$
$137$	7.47666	−	7.47666i	0.638774	−	0.638774i	0.950253	+	0.311479i	$0.100824\pi$
$138$		0			0
$139$	3.84867			0.326440			0.163220	−	0.986590i	$-0.447812\pi$
$139$	3.84867			0.326440			0.163220	+	0.986590i	$0.447812\pi$
$140$		0			0
$141$	−4.44885			−0.374660
$142$		0			0
$143$	−4.95659	+	4.95659i	−0.414491	+	0.414491i
$144$		0			0
$145$	1.12718	−	4.78087i	0.0936073	−	0.397029i
$146$		0			0
$147$	−6.72379	+	1.94697i	−0.554568	+	0.160584i
$148$		0			0
$149$		−	18.6967i		−	1.53169i	−0.643023	−	0.765846i	$-0.722320\pi$
$149$		−	18.6967i		−	1.53169i	0.643023	−	0.765846i	$-0.277680\pi$
$150$		0			0
$151$	−18.8106			−1.53079			−0.765393	−	0.643563i	$-0.777455\pi$
$151$	−18.8106			−1.53079			−0.765393	+	0.643563i	$0.777455\pi$
$152$		0			0
$153$	4.47060	−	4.47060i	0.361426	−	0.361426i
$154$		0			0
$155$	−0.789558	+	3.34886i	−0.0634188	+	0.268987i
$156$		0			0
$157$	−13.5188	−	13.5188i	−1.07892	−	1.07892i	−0.996607	−	0.0823132i	$-0.973769\pi$
$157$	−13.5188	−	13.5188i	−1.07892	−	1.07892i	−0.0823132	−	0.996607i	$-0.526231\pi$
$158$		0			0
$159$	−8.91202			−0.706769
$160$		0			0
$161$	−2.63216	−	4.45524i	−0.207443	−	0.351122i
$162$		0			0
$163$	1.44506	+	1.44506i	0.113186	+	0.113186i	0.761431	−	0.648246i	$-0.224497\pi$
$163$	1.44506	+	1.44506i	0.113186	+	0.113186i	−0.648246	+	0.761431i	$0.724497\pi$
$164$		0			0
$165$	2.99652	−	1.85312i	0.233278	−	0.144265i
$166$		0			0
$167$	−14.7034	−	14.7034i	−1.13778	−	1.13778i	−0.988847	−	0.148936i	$-0.952415\pi$
$167$	−14.7034	−	14.7034i	−1.13778	−	1.13778i	−0.148936	−	0.988847i	$-0.547585\pi$
$168$		0			0
$169$		−	6.79173i		−	0.522441i
$170$		0			0
$171$		−	6.38872i		−	0.488558i
$172$		0			0
$173$	8.38457	−	8.38457i	0.637467	−	0.637467i	−0.312463	−	0.949930i	$-0.601154\pi$
$173$	8.38457	−	8.38457i	0.637467	−	0.637467i	0.949930	+	0.312463i	$0.101154\pi$
$174$		0			0
$175$	−9.99023	−	8.67153i	−0.755190	−	0.655506i
$176$		0			0
$177$	−5.37138	+	5.37138i	−0.403738	+	0.403738i
$178$		0			0
$179$		−	5.99327i		−	0.447958i	−0.974594	−	0.223979i	$-0.928095\pi$
$179$		−	5.99327i		−	0.447958i	0.974594	−	0.223979i	$-0.0719048\pi$
$180$		0			0
$181$			12.8079i			0.952002i	0.879445	+	0.476001i	$0.157914\pi$
$181$			12.8079i			0.952002i	−0.879445	+	0.476001i	$0.842086\pi$
$182$		0			0
$183$	2.64167	+	2.64167i	0.195278	+	0.195278i
$184$		0			0
$185$	−21.6866	+	13.4115i	−1.59443	+	0.986035i
$186$		0			0
$187$	−7.04404	−	7.04404i	−0.515111	−	0.515111i
$188$		0			0
$189$	−1.34579	−	2.27791i	−0.0978916	−	0.165693i
$190$		0			0
$191$	−20.9191			−1.51365			−0.756825	−	0.653617i	$-0.773251\pi$
$191$	−20.9191			−1.51365			−0.756825	+	0.653617i	$0.773251\pi$
$192$		0			0
$193$	17.2851	+	17.2851i	1.24421	+	1.24421i	0.958238	+	0.285970i	$0.0923159\pi$
$193$	17.2851	+	17.2851i	1.24421	+	1.24421i	0.285970	+	0.958238i	$0.407684\pi$
$194$		0			0
$195$	−2.28279	+	9.68233i	−0.163474	+	0.693366i
$196$		0			0
$197$	−9.86588	+	9.86588i	−0.702915	+	0.702915i	−0.965035	−	0.262120i	$-0.915578\pi$
$197$	−9.86588	+	9.86588i	−0.702915	+	0.702915i	0.262120	+	0.965035i	$0.415578\pi$
$198$		0			0
$199$	0.738250			0.0523332			0.0261666	−	0.999658i	$-0.491670\pi$
$199$	0.738250			0.0523332			0.0261666	+	0.999658i	$0.491670\pi$
$200$		0			0
$201$		−	2.60720i		−	0.183898i
$202$		0			0
$203$	−1.44786	+	5.62866i	−0.101620	+	0.395055i
$204$		0			0
$205$	2.46129	−	10.4394i	0.171904	−	0.729121i
$206$		0			0
$207$	1.38299	−	1.38299i	0.0961247	−	0.0961247i
$208$		0			0
$209$	−10.0663			−0.696301
$210$		0			0
$211$	15.0771			1.03795			0.518974	−	0.854790i	$-0.326314\pi$
$211$	15.0771			1.03795			0.518974	+	0.854790i	$0.326314\pi$
$212$		0			0
$213$	−6.81593	+	6.81593i	−0.467020	+	0.467020i
$214$		0			0
$215$	0.138329	+	0.223680i	0.00943398	+	0.0152548i
$216$		0			0
$217$	1.01418	−	3.94272i	0.0688472	−	0.267649i
$218$		0			0
$219$		−	3.48526i		−	0.235512i
$220$		0			0
$221$	28.1269			1.89202
$222$		0			0
$223$	12.9828	−	12.9828i	0.869395	−	0.869395i	−0.123010	−	0.992405i	$-0.539255\pi$
$223$	12.9828	−	12.9828i	0.869395	−	0.869395i	0.992405	+	0.123010i	$0.0392548\pi$
$224$		0			0
$225$	2.23353	−	4.47340i	0.148902	−	0.298227i
$226$		0			0
$227$	13.7182	+	13.7182i	0.910509	+	0.910509i	0.996312	−	0.0858031i	$-0.0273456\pi$
$227$	13.7182	+	13.7182i	0.910509	+	0.910509i	−0.0858031	+	0.996312i	$0.527346\pi$
$228$		0			0
$229$	−28.3626			−1.87425			−0.937126	−	0.348991i	$-0.886524\pi$
$229$	−28.3626			−1.87425			−0.937126	+	0.348991i	$0.886524\pi$
$230$		0			0
$231$	−3.58915	+	2.12047i	−0.236149	+	0.139517i
$232$		0			0
$233$	−14.4962	−	14.4962i	−0.949678	−	0.949678i	0.0491151	−	0.998793i	$-0.484360\pi$
$233$	−14.4962	−	14.4962i	−0.949678	−	0.949678i	−0.998793	+	0.0491151i	$0.984360\pi$
$234$		0			0
$235$	5.23233	+	8.46073i	0.341319	+	0.551917i
$236$		0			0
$237$	11.2304	+	11.2304i	0.729493	+	0.729493i
$238$		0			0
$239$		−	16.5223i		−	1.06874i	−0.845251	−	0.534369i	$-0.820549\pi$
$239$		−	16.5223i		−	1.06874i	0.845251	−	0.534369i	$-0.179451\pi$
$240$		0			0
$241$			3.66220i			0.235903i	0.993019	+	0.117951i	$0.0376327\pi$
$241$			3.66220i			0.235903i	−0.993019	+	0.117951i	$0.962367\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	11.6106	+	10.4973i	0.741775	+	0.670648i
$246$		0			0
$247$	20.0974	−	20.0974i	1.27877	−	1.27877i
$248$		0			0
$249$		−	3.82670i		−	0.242507i
$250$		0			0
$251$			18.0200i			1.13741i	0.822540	+	0.568707i	$0.192556\pi$
$251$			18.0200i			1.13741i	−0.822540	+	0.568707i	$0.807444\pi$
$252$		0			0
$253$	−2.17910	−	2.17910i	−0.136999	−	0.136999i
$254$		0			0
$255$	−13.7600	−	3.24418i	−0.861684	−	0.203159i
$256$		0			0
$257$	−8.98905	−	8.98905i	−0.560722	−	0.560722i	0.368791	−	0.929512i	$-0.379772\pi$
$257$	−8.98905	−	8.98905i	−0.560722	−	0.560722i	−0.929512	+	0.368791i	$0.879772\pi$
$258$		0			0
$259$	25.9756	−	15.3464i	1.61405	−	0.953579i
$260$		0			0
$261$	−2.19669			−0.135972
$262$		0			0
$263$	17.1828	+	17.1828i	1.05953	+	1.05953i	0.998112	+	0.0614227i	$0.0195638\pi$
$263$	17.1828	+	17.1828i	1.05953	+	1.05953i	0.0614227	+	0.998112i	$0.480436\pi$
$264$		0			0
$265$	10.4815	+	16.9487i	0.643874	+	1.04115i
$266$		0			0
$267$	−8.75767	+	8.75767i	−0.535960	+	0.535960i
$268$		0			0
$269$	9.41877			0.574273			0.287136	−	0.957890i	$-0.407297\pi$
$269$	9.41877			0.574273			0.287136	+	0.957890i	$0.407297\pi$
$270$		0			0
$271$		−	24.0250i		−	1.45942i	−0.683758	−	0.729709i	$-0.739656\pi$
$271$		−	24.0250i		−	1.45942i	0.683758	−	0.729709i	$-0.260344\pi$
$272$		0			0
$273$	2.93223	−	11.3993i	0.177467	−	0.689917i
$274$		0			0
$275$	−7.04846	−	3.51924i	−0.425038	−	0.212218i
$276$		0			0
$277$	−16.7055	+	16.7055i	−1.00374	+	1.00374i	−0.00374534	+	0.999993i	$0.501192\pi$
$277$	−16.7055	+	16.7055i	−1.00374	+	1.00374i	−0.999993	+	0.00374534i	$0.998808\pi$
$278$		0			0
$279$	1.53872			0.0921207
$280$		0			0
$281$	−7.42668			−0.443039			−0.221519	−	0.975156i	$-0.571102\pi$
$281$	−7.42668			−0.443039			−0.221519	+	0.975156i	$0.571102\pi$
$282$		0			0
$283$	−7.78227	+	7.78227i	−0.462608	+	0.462608i	−0.899509	−	0.436902i	$-0.856076\pi$
$283$	−7.78227	+	7.78227i	−0.462608	+	0.462608i	0.436902	+	0.899509i	$0.356076\pi$
$284$		0			0
$285$	−12.1499	+	7.51383i	−0.719700	+	0.445081i
$286$		0			0
$287$	−3.16151	+	12.2906i	−0.186618	+	0.725494i
$288$		0			0
$289$			22.9724i			1.35132i
$290$		0			0
$291$	12.4850			0.731884
$292$		0			0
$293$	−6.34563	+	6.34563i	−0.370716	+	0.370716i	−0.867738	−	0.497022i	$-0.834427\pi$
$293$	−6.34563	+	6.34563i	−0.370716	+	0.370716i	0.497022	+	0.867738i	$0.334427\pi$
$294$		0			0
$295$	16.5325	+	3.89786i	0.962561	+	0.226942i
$296$		0			0
$297$	−1.11414	−	1.11414i	−0.0646492	−	0.0646492i
$298$		0			0
$299$	8.70116			0.503201
$300$		0			0
$301$	−0.158286	−	0.267918i	−0.00912346	−	0.0154426i
$302$		0			0
$303$	4.57346	+	4.57346i	0.262739	+	0.262739i
$304$		0			0
$305$	1.91698	−	8.13076i	0.109766	−	0.465566i
$306$		0			0
$307$	−0.402617	−	0.402617i	−0.0229785	−	0.0229785i	0.695524	−	0.718503i	$-0.255172\pi$
$307$	−0.402617	−	0.402617i	−0.0229785	−	0.0229785i	−0.718503	+	0.695524i	$0.755172\pi$
$308$		0			0
$309$		−	14.6540i		−	0.833638i
$310$		0			0
$311$		−	22.7708i		−	1.29121i	−0.763671	−	0.645606i	$-0.776605\pi$
$311$		−	22.7708i		−	1.29121i	0.763671	−	0.645606i	$-0.223395\pi$
$312$		0			0
$313$	−18.6413	+	18.6413i	−1.05367	+	1.05367i	−0.0551906	+	0.998476i	$0.517577\pi$
$313$	−18.6413	+	18.6413i	−1.05367	+	1.05367i	−0.998476	+	0.0551906i	$0.982423\pi$
$314$		0			0
$315$	−2.74929	+	5.23846i	−0.154905	+	0.295154i
$316$		0			0
$317$	−2.01133	+	2.01133i	−0.112968	+	0.112968i	−0.761331	−	0.648363i	$-0.775454\pi$
$317$	−2.01133	+	2.01133i	−0.112968	+	0.112968i	0.648363	+	0.761331i	$0.275454\pi$
$318$		0			0
$319$			3.46119i			0.193789i
$320$		0			0
$321$		−	0.775857i		−	0.0433041i
$322$		0			0
$323$	28.5614	+	28.5614i	1.58920	+	1.58920i
$324$		0			0
$325$	21.0985	−	7.04610i	1.17033	−	0.390848i
$326$		0			0
$327$	−5.28162	−	5.28162i	−0.292074	−	0.292074i
$328$		0			0
$329$	−5.98720	−	10.1341i	−0.330085	−	0.558709i
$330$		0			0
$331$	−20.2906			−1.11527			−0.557637	−	0.830085i	$-0.688292\pi$
$331$	−20.2906			−1.11527			−0.557637	+	0.830085i	$0.688292\pi$
$332$		0			0
$333$	8.06335	+	8.06335i	0.441869	+	0.441869i
$334$		0			0
$335$	−4.95832	+	3.06635i	−0.270902	+	0.167533i
$336$		0			0
$337$	−12.3817	+	12.3817i	−0.674473	+	0.674473i	−0.958744	−	0.284271i	$-0.908249\pi$
$337$	−12.3817	+	12.3817i	−0.674473	+	0.674473i	0.284271	+	0.958744i	$0.408249\pi$
$338$		0			0
$339$	10.0118			0.543765
$340$		0			0
$341$		−	2.42446i		−	0.131292i
$342$		0			0
$343$	−13.4838	−	12.6959i	−0.728057	−	0.685517i
$344$		0			0
$345$	−4.25670	−	1.00360i	−0.229173	−	0.0540319i
$346$		0			0
$347$	−22.0988	+	22.0988i	−1.18633	+	1.18633i	−0.208252	+	0.978075i	$0.566777\pi$
$347$	−22.0988	+	22.0988i	−1.18633	+	1.18633i	−0.978075	+	0.208252i	$0.933223\pi$
$348$		0			0
$349$	2.92378			0.156506			0.0782530	−	0.996934i	$-0.475066\pi$
$349$	2.92378			0.156506			0.0782530	+	0.996934i	$0.475066\pi$
$350$		0			0
$351$	4.44879			0.237459
$352$		0			0
$353$	12.4408	−	12.4408i	0.662159	−	0.662159i	−0.293730	−	0.955888i	$-0.594897\pi$
$353$	12.4408	−	12.4408i	0.662159	−	0.662159i	0.955888	+	0.293730i	$0.0948966\pi$
$354$		0			0
$355$	20.9787	+	4.94612i	1.11343	+	0.262513i
$356$		0			0
$357$	16.2001	+	4.16713i	0.857398	+	0.220548i
$358$		0			0
$359$			3.05847i			0.161420i	0.996738	+	0.0807098i	$0.0257187\pi$
$359$			3.05847i			0.161420i	−0.996738	+	0.0807098i	$0.974281\pi$
$360$		0			0
$361$	21.8157			1.14820
$362$		0			0
$363$	6.02269	−	6.02269i	0.316109	−	0.316109i
$364$		0			0
$365$	−6.62819	+	4.09904i	−0.346935	+	0.214554i
$366$		0			0
$367$	−7.33035	−	7.33035i	−0.382641	−	0.382641i	0.489412	−	0.872053i	$-0.337212\pi$
$367$	−7.33035	−	7.33035i	−0.382641	−	0.382641i	−0.872053	+	0.489412i	$0.837212\pi$
$368$		0			0
$369$	−4.79665			−0.249704
$370$		0			0
$371$	−11.9937	−	20.3007i	−0.622681	−	1.05396i
$372$		0			0
$373$	−14.1652	−	14.1652i	−0.733448	−	0.733448i	0.237853	−	0.971301i	$-0.423556\pi$
$373$	−14.1652	−	14.1652i	−0.733448	−	0.733448i	−0.971301	+	0.237853i	$0.923556\pi$
$374$		0			0
$375$	−11.1343	+	1.01352i	−0.574973	+	0.0523378i
$376$		0			0
$377$	−6.91028	−	6.91028i	−0.355898	−	0.355898i
$378$		0			0
$379$		−	14.5199i		−	0.745837i	−0.927864	−	0.372918i	$-0.878357\pi$
$379$		−	14.5199i		−	0.745837i	0.927864	−	0.372918i	$-0.121643\pi$
$380$		0			0
$381$			7.85800i			0.402577i
$382$		0			0
$383$	21.3732	−	21.3732i	1.09212	−	1.09212i	0.0968177	−	0.995302i	$-0.469134\pi$
$383$	21.3732	−	21.3732i	1.09212	−	1.09212i	0.995302	−	0.0968177i	$-0.0308664\pi$
$384$		0			0
$385$	8.25391	+	4.33188i	0.420658	+	0.220773i
$386$		0			0
$387$	0.0831671	−	0.0831671i	0.00422762	−	0.00422762i
$388$		0			0
$389$			19.3181i			0.979467i	0.871872	+	0.489733i	$0.162906\pi$
$389$			19.3181i			0.979467i	−0.871872	+	0.489733i	$0.837094\pi$
$390$		0			0
$391$			12.3656i			0.625356i
$392$		0			0
$393$	−5.56107	−	5.56107i	−0.280519	−	0.280519i
$394$		0			0
$395$	8.14958	−	34.5660i	0.410050	−	1.73920i
$396$		0			0
$397$	−10.1855	−	10.1855i	−0.511194	−	0.511194i	0.403698	−	0.914892i	$-0.367725\pi$
$397$	−10.1855	−	10.1855i	−0.511194	−	0.511194i	−0.914892	+	0.403698i	$0.867725\pi$
$398$		0			0
$399$	14.5529	−	8.59785i	0.728557	−	0.430431i
$400$		0			0
$401$	−15.8944			−0.793729			−0.396865	−	0.917877i	$-0.629902\pi$
$401$	−15.8944			−0.793729			−0.396865	+	0.917877i	$0.629902\pi$
$402$		0			0
$403$	4.84045	+	4.84045i	0.241120	+	0.241120i
$404$		0			0
$405$	−2.17640	−	0.513127i	−0.108146	−	0.0254975i
$406$		0			0
$407$	12.7049	−	12.7049i	0.629759	−	0.629759i
$408$		0			0
$409$	7.40100			0.365956			0.182978	−	0.983117i	$-0.441426\pi$
$409$	7.40100			0.365956			0.182978	+	0.983117i	$0.441426\pi$
$410$		0			0
$411$			10.5736i			0.521557i
$412$		0			0
$413$	−19.4642	−	5.00677i	−0.957773	−	0.246367i
$414$		0			0
$415$	−7.27754	+	4.50061i	−0.357240	+	0.220926i
$416$		0			0
$417$	−2.72142	+	2.72142i	−0.133269	+	0.133269i
$418$		0			0
$419$	−10.7730			−0.526297			−0.263148	−	0.964755i	$-0.584761\pi$
$419$	−10.7730			−0.526297			−0.263148	+	0.964755i	$0.584761\pi$
$420$		0			0
$421$	−35.0048			−1.70603			−0.853015	−	0.521887i	$-0.825228\pi$
$421$	−35.0048			−1.70603			−0.853015	+	0.521887i	$0.825228\pi$
$422$		0			0
$423$	3.14581	−	3.14581i	0.152954	−	0.152954i
$424$		0			0
$425$	10.0135	+	29.9840i	0.485728	+	1.45444i
$426$		0			0
$427$	−2.46235	+	9.57259i	−0.119161	+	0.463250i
$428$		0			0
$429$		−	7.00968i		−	0.338430i
$430$		0			0
$431$	−12.4338			−0.598916			−0.299458	−	0.954109i	$-0.596806\pi$
$431$	−12.4338			−0.598916			−0.299458	+	0.954109i	$0.596806\pi$
$432$		0			0
$433$	13.4030	−	13.4030i	0.644109	−	0.644109i	−0.307454	−	0.951563i	$-0.599477\pi$
$433$	13.4030	−	13.4030i	0.644109	−	0.644109i	0.951563	+	0.307454i	$0.0994769\pi$
$434$		0			0
$435$	2.58355	+	4.17762i	0.123872	+	0.200302i
$436$		0			0
$437$	8.83556	+	8.83556i	0.422662	+	0.422662i
$438$		0			0
$439$	26.8299			1.28052			0.640261	−	0.768158i	$-0.278826\pi$
$439$	26.8299			1.28052			0.640261	+	0.768158i	$0.278826\pi$
$440$		0			0
$441$	3.37772	−	6.13115i	0.160844	−	0.291960i
$442$		0			0
$443$	14.6362	+	14.6362i	0.695386	+	0.695386i	0.963412	−	0.268025i	$-0.0863711\pi$
$443$	14.6362	+	14.6362i	0.695386	+	0.695386i	−0.268025	+	0.963412i	$0.586371\pi$
$444$		0			0
$445$	26.9551	+	6.35518i	1.27780	+	0.301265i
$446$		0			0
$447$	13.2206	+	13.2206i	0.625311	+	0.625311i
$448$		0			0
$449$			36.6213i			1.72827i	0.503263	+	0.864134i	$0.332133\pi$
$449$			36.6213i			1.72827i	−0.503263	+	0.864134i	$0.667867\pi$
$450$		0			0
$451$			7.55779i			0.355882i
$452$		0			0
$453$	13.3011	−	13.3011i	0.624941	−	0.624941i
$454$		0			0
$455$	−25.1276	+	7.83036i	−1.17800	+	0.367093i
$456$		0			0
$457$	19.6901	−	19.6901i	0.921062	−	0.921062i	−0.0760426	−	0.997105i	$-0.524229\pi$
$457$	19.6901	−	19.6901i	0.921062	−	0.921062i	0.997105	+	0.0760426i	$0.0242285\pi$
$458$		0			0
$459$			6.32238i			0.295103i
$460$		0			0
$461$			1.66338i			0.0774715i	0.999249	+	0.0387358i	$0.0123331\pi$
$461$			1.66338i			0.0774715i	−0.999249	+	0.0387358i	$0.987667\pi$
$462$		0			0
$463$	20.2415	+	20.2415i	0.940701	+	0.940701i	0.998338	−	0.0576369i	$-0.0183566\pi$
$463$	20.2415	+	20.2415i	0.940701	+	0.940701i	−0.0576369	+	0.998338i	$0.518357\pi$
$464$		0			0
$465$	−1.80970	−	2.92630i	−0.0839229	−	0.135704i
$466$		0			0
$467$	30.2737	+	30.2737i	1.40090	+	1.40090i	0.797256	+	0.603642i	$0.206284\pi$
$467$	30.2737	+	30.2737i	1.40090	+	1.40090i	0.603642	+	0.797256i	$0.293716\pi$
$468$		0			0
$469$	5.93895	−	3.50873i	0.274235	−	0.162018i
$470$		0			0
$471$	19.1185			0.880934
$472$		0			0
$473$	−0.131041	−	0.131041i	−0.00602528	−	0.00602528i
$474$		0			0
$475$	28.5793	+	14.2694i	1.31131	+	0.654726i
$476$		0			0
$477$	6.30175	−	6.30175i	0.288537	−	0.288537i
$478$		0			0
$479$	−12.7446			−0.582315			−0.291158	−	0.956675i	$-0.594040\pi$
$479$	−12.7446			−0.582315			−0.291158	+	0.956675i	$0.594040\pi$
$480$		0			0
$481$			50.7309i			2.31313i
$482$		0			0
$483$	5.01155	+	1.28912i	0.228033	+	0.0586568i
$484$		0			0
$485$	−14.6837	−	23.7437i	−0.666754	−	1.07815i
$486$		0			0
$487$	30.3740	−	30.3740i	1.37638	−	1.37638i	0.525723	−	0.850656i	$-0.323795\pi$
$487$	30.3740	−	30.3740i	1.37638	−	1.37638i	0.850656	−	0.525723i	$-0.176205\pi$
$488$		0			0
$489$	−2.04362			−0.0924157
$490$		0			0
$491$	8.63580			0.389728			0.194864	−	0.980830i	$-0.437573\pi$
$491$	8.63580			0.389728			0.194864	+	0.980830i	$0.437573\pi$
$492$		0			0
$493$	9.82051	−	9.82051i	0.442294	−	0.442294i
$494$		0			0
$495$	−0.808502	+	3.42921i	−0.0363395	+	0.154132i
$496$		0			0
$497$	−24.6988	−	6.35326i	−1.10789	−	0.284983i
$498$		0			0
$499$			19.7882i			0.885844i	0.896560	+	0.442922i	$0.146058\pi$
$499$			19.7882i			0.885844i	−0.896560	+	0.442922i	$0.853942\pi$
$500$		0			0
$501$	20.7937			0.928996
$502$		0			0
$503$	13.9595	−	13.9595i	0.622425	−	0.622425i	−0.323726	−	0.946151i	$-0.604935\pi$
$503$	13.9595	−	13.9595i	0.622425	−	0.622425i	0.946151	+	0.323726i	$0.104935\pi$
$504$		0			0
$505$	3.31883	−	14.0766i	0.147686	−	0.626401i
$506$		0			0
$507$	4.80248	+	4.80248i	0.213286	+	0.213286i
$508$		0			0
$509$	34.1604			1.51413			0.757067	−	0.653337i	$-0.226632\pi$
$509$	34.1604			1.51413			0.757067	+	0.653337i	$0.226632\pi$
$510$		0			0
$511$	7.93909	−	4.69041i	0.351205	−	0.207492i
$512$		0			0
$513$	4.51751	+	4.51751i	0.199453	+	0.199453i
$514$		0			0
$515$	−27.8687	+	17.2347i	−1.22804	+	0.759453i
$516$		0			0
$517$	−4.95665	−	4.95665i	−0.217993	−	0.217993i
$518$		0			0
$519$			11.8576i			0.520490i
$520$		0			0
$521$		−	1.42192i		−	0.0622956i	−0.999515	−	0.0311478i	$-0.990084\pi$
$521$		−	1.42192i		−	0.0622956i	0.999515	−	0.0311478i	$-0.00991626\pi$
$522$		0			0
$523$	−12.7406	+	12.7406i	−0.557108	+	0.557108i	−0.928483	−	0.371375i	$-0.878886\pi$
$523$	−12.7406	+	12.7406i	−0.557108	+	0.557108i	0.371375	+	0.928483i	$0.378886\pi$
$524$		0			0
$525$	13.1959	−	0.932461i	0.575914	−	0.0406959i
$526$		0			0
$527$	−6.87899	+	6.87899i	−0.299653	+	0.299653i
$528$		0			0
$529$		−	19.1747i		−	0.833681i
$530$		0			0
$531$		−	7.59628i		−	0.329651i
$532$		0			0
$533$	−15.0892	−	15.0892i	−0.653584	−	0.653584i
$534$		0			0
$535$	−1.47551	+	0.912492i	−0.0637918	+	0.0394505i
$536$		0			0
$537$	4.23788	+	4.23788i	0.182878	+	0.182878i
$538$		0			0
$539$	−9.66047	−	5.32206i	−0.416106	−	0.229237i
$540$		0			0
$541$	−25.3194			−1.08857			−0.544283	−	0.838902i	$-0.683198\pi$
$541$	−25.3194			−1.08857			−0.544283	+	0.838902i	$0.683198\pi$
$542$		0			0
$543$	−9.05654	−	9.05654i	−0.388653	−	0.388653i
$544$		0			0
$545$	−3.83272	+	16.2562i	−0.164176	+	0.696341i
$546$		0			0
$547$	5.29763	−	5.29763i	0.226510	−	0.226510i	−0.584723	−	0.811233i	$-0.698797\pi$
$547$	5.29763	−	5.29763i	0.226510	−	0.226510i	0.811233	+	0.584723i	$0.198797\pi$
$548$		0			0
$549$	−3.73588			−0.159444
$550$		0			0
$551$		−	14.0340i		−	0.597870i
$552$		0			0
$553$	−10.4681	+	40.6956i	−0.445148	+	1.73055i
$554$		0			0
$555$	5.85134	−	24.8181i	0.248375	−	1.05347i
$556$		0			0
$557$	−12.7776	+	12.7776i	−0.541405	+	0.541405i	−0.923941	−	0.382536i	$-0.875051\pi$
$557$	−12.7776	+	12.7776i	−0.541405	+	0.541405i	0.382536	+	0.923941i	$0.375051\pi$
$558$		0			0
$559$	0.523249			0.0221311
$560$		0			0
$561$	9.96177			0.420586
$562$		0			0
$563$	−11.5060	+	11.5060i	−0.484920	+	0.484920i	−0.906699	−	0.421779i	$-0.861406\pi$
$563$	−11.5060	+	11.5060i	−0.484920	+	0.484920i	0.421779	+	0.906699i	$0.361406\pi$
$564$		0			0
$565$	−11.7749	−	19.0402i	−0.495376	−	0.801028i
$566$		0			0
$567$	2.56234	+	0.659108i	0.107608	+	0.0276799i
$568$		0			0
$569$			38.1182i			1.59800i	0.601331	+	0.799000i	$0.294637\pi$
$569$			38.1182i			1.59800i	−0.601331	+	0.799000i	$0.705363\pi$
$570$		0			0
$571$	7.46420			0.312367			0.156184	−	0.987728i	$-0.450081\pi$
$571$	7.46420			0.312367			0.156184	+	0.987728i	$0.450081\pi$
$572$		0			0
$573$	14.7920	−	14.7920i	0.617945	−	0.617945i
$574$		0			0
$575$	3.09772	+	9.27565i	0.129184	+	0.386821i
$576$		0			0
$577$	2.77309	+	2.77309i	0.115445	+	0.115445i	0.762469	−	0.647024i	$-0.223987\pi$
$577$	2.77309	+	2.77309i	0.115445	+	0.115445i	−0.647024	+	0.762469i	$0.723987\pi$
$578$		0			0
$579$	−24.4448			−1.01589
$580$		0			0
$581$	8.71686	−	5.14992i	0.361636	−	0.213655i
$582$		0			0
$583$	−9.92927	−	9.92927i	−0.411228	−	0.411228i
$584$		0			0
$585$	−5.23226	−	8.46062i	−0.216327	−	0.349804i
$586$		0			0
$587$	−14.9272	−	14.9272i	−0.616113	−	0.616113i	0.328419	−	0.944532i	$-0.393484\pi$
$587$	−14.9272	−	14.9272i	−0.616113	−	0.616113i	−0.944532	+	0.328419i	$0.893484\pi$
$588$		0			0
$589$			9.83044i			0.405056i
$590$		0			0
$591$		−	13.9525i		−	0.573927i
$592$		0			0
$593$	29.6826	−	29.6826i	1.21892	−	1.21892i	0.250909	−	0.968011i	$-0.419271\pi$
$593$	29.6826	−	29.6826i	1.21892	−	1.21892i	0.968011	−	0.250909i	$-0.0807294\pi$
$594$		0			0
$595$	−11.1281	−	35.7100i	−0.456207	−	1.46397i
$596$		0			0
$597$	−0.522022	+	0.522022i	−0.0213649	+	0.0213649i
$598$		0			0
$599$			25.5447i			1.04373i	0.853029	+	0.521863i	$0.174763\pi$
$599$			25.5447i			1.04373i	−0.853029	+	0.521863i	$0.825237\pi$
$600$		0			0
$601$			4.95154i			0.201978i	0.994888	+	0.100989i	$0.0322006\pi$
$601$			4.95154i			0.201978i	−0.994888	+	0.100989i	$0.967799\pi$
$602$		0			0
$603$	1.84357	+	1.84357i	0.0750759	+	0.0750759i
$604$		0			0
$605$	−18.5372	−	4.37049i	−0.753643	−	0.177686i
$606$		0			0
$607$	−10.9597	−	10.9597i	−0.444841	−	0.444841i	0.448794	−	0.893635i	$-0.351854\pi$
$607$	−10.9597	−	10.9597i	−0.444841	−	0.444841i	−0.893635	+	0.448794i	$0.851854\pi$
$608$		0			0
$609$	−2.95628	−	5.00385i	−0.119794	−	0.202766i
$610$		0			0
$611$	19.7920			0.800698
$612$		0			0
$613$	−11.2154	−	11.2154i	−0.452985	−	0.452985i	0.443359	−	0.896344i	$-0.353787\pi$
$613$	−11.2154	−	11.2154i	−0.452985	−	0.452985i	−0.896344	+	0.443359i	$0.853787\pi$
$614$		0			0
$615$	5.64139	+	9.12218i	0.227483	+	0.367842i
$616$		0			0
$617$	−19.2309	+	19.2309i	−0.774209	+	0.774209i	−0.978839	−	0.204630i	$-0.934401\pi$
$617$	−19.2309	+	19.2309i	−0.774209	+	0.774209i	0.204630	+	0.978839i	$0.434401\pi$
$618$		0			0
$619$	9.96280			0.400439			0.200219	−	0.979751i	$-0.435835\pi$
$619$	9.96280			0.400439			0.200219	+	0.979751i	$0.435835\pi$
$620$		0			0
$621$			1.95585i			0.0784855i
$622$		0			0
$623$	−31.7351	−	8.16319i	−1.27144	−	0.327051i
$624$		0			0
$625$	15.0226	+	19.9830i	0.600906	+	0.799320i
$626$		0			0
$627$	7.11795	−	7.11795i	0.284264	−	0.284264i
$628$		0			0
$629$	−72.0959			−2.87465
$630$		0			0
$631$	−4.16519			−0.165814			−0.0829068	−	0.996557i	$-0.526420\pi$
$631$	−4.16519			−0.165814			−0.0829068	+	0.996557i	$0.526420\pi$
$632$		0			0
$633$	−10.6611	+	10.6611i	−0.423741	+	0.423741i
$634$		0			0
$635$	14.9442	−	9.24186i	0.593042	−	0.366752i
$636$		0			0
$637$	29.9127	−	8.66168i	1.18518	−	0.343188i
$638$		0			0
$639$		−	9.63918i		−	0.381320i
$640$		0			0
$641$	2.48428			0.0981232			0.0490616	−	0.998796i	$-0.484377\pi$
$641$	2.48428			0.0981232			0.0490616	+	0.998796i	$0.484377\pi$
$642$		0			0
$643$	−21.8995	+	21.8995i	−0.863634	+	0.863634i	−0.991758	−	0.128124i	$-0.959104\pi$
$643$	−21.8995	+	21.8995i	−0.863634	+	0.863634i	0.128124	+	0.991758i	$0.459104\pi$
$644$		0			0
$645$	−0.255979	−	0.0603520i	−0.0100792	−	0.00237636i
$646$		0			0
$647$	11.7234	+	11.7234i	0.460893	+	0.460893i	0.898948	−	0.438055i	$-0.144332\pi$
$647$	11.7234	+	11.7234i	0.460893	+	0.460893i	−0.438055	+	0.898948i	$0.644332\pi$
$648$		0			0
$649$	−11.9690			−0.469824
$650$		0			0
$651$	2.07079	+	3.50506i	0.0811605	+	0.137374i
$652$		0			0
$653$	12.6601	+	12.6601i	0.495427	+	0.495427i	0.910011	−	0.414584i	$-0.136073\pi$
$653$	12.6601	+	12.6601i	0.495427	+	0.495427i	−0.414584	+	0.910011i	$0.636073\pi$
$654$		0			0
$655$	−4.03551	+	17.1164i	−0.157680	+	0.668792i
$656$		0			0
$657$	2.46445	+	2.46445i	0.0961473	+	0.0961473i
$658$		0			0
$659$		−	9.80154i		−	0.381814i	−0.981608	−	0.190907i	$-0.938857\pi$
$659$		−	9.80154i		−	0.381814i	0.981608	−	0.190907i	$-0.0611429\pi$
$660$		0			0
$661$			1.78672i			0.0694952i	0.999396	+	0.0347476i	$0.0110627\pi$
$661$			1.78672i			0.0694952i	−0.999396	+	0.0347476i	$0.988937\pi$
$662$		0			0
$663$	−19.8887	+	19.8887i	−0.772415	+	0.772415i
$664$		0			0
$665$	−33.4670	−	17.5644i	−1.29780	−	0.681119i
$666$		0			0
$667$	3.03801	−	3.03801i	0.117632	−	0.117632i
$668$		0			0
$669$			18.3605i			0.709858i
$670$		0			0
$671$			5.88639i			0.227242i
$672$		0			0
$673$	−21.8778	−	21.8778i	−0.843327	−	0.843327i	0.145963	−	0.989290i	$-0.453372\pi$
$673$	−21.8778	−	21.8778i	−0.843327	−	0.843327i	−0.989290	+	0.145963i	$0.953372\pi$
$674$		0			0
$675$	1.58383	+	4.74252i	0.0609615	+	0.182540i
$676$		0			0
$677$	5.68498	+	5.68498i	0.218492	+	0.218492i	0.807863	−	0.589371i	$-0.200624\pi$
$677$	5.68498	+	5.68498i	0.218492	+	0.218492i	−0.589371	+	0.807863i	$0.700624\pi$
$678$		0			0
$679$	16.8022	+	28.4397i	0.644807	+	1.09141i
$680$		0			0
$681$	−19.4005			−0.743427
$682$		0			0
$683$	−24.8622	−	24.8622i	−0.951326	−	0.951326i	0.0475435	−	0.998869i	$-0.484861\pi$
$683$	−24.8622	−	24.8622i	−0.951326	−	0.951326i	−0.998869	+	0.0475435i	$0.984861\pi$
$684$		0			0
$685$	20.1086	−	12.4357i	0.768312	−	0.475144i
$686$		0			0
$687$	20.0554	−	20.0554i	0.765160	−	0.765160i
$688$		0			0
$689$	39.6477			1.51046
$690$		0			0
$691$		−	9.17144i		−	0.348898i	−0.984666	−	0.174449i	$-0.944186\pi$
$691$		−	9.17144i		−	0.348898i	0.984666	−	0.174449i	$-0.0558144\pi$
$692$		0			0
$693$	1.03852	−	4.03732i	0.0394499	−	0.153365i
$694$		0			0
$695$	8.37623	+	1.97486i	0.317729	+	0.0749106i
$696$		0			0
$697$	21.4439	−	21.4439i	0.812246	−	0.812246i
$698$		0			0
$699$	20.5007			0.775409
$700$		0			0
$701$	15.0578			0.568725			0.284362	−	0.958717i	$-0.408218\pi$
$701$	15.0578			0.568725			0.284362	+	0.958717i	$0.408218\pi$
$702$		0			0
$703$	−51.5145	+	51.5145i	−1.94291	+	1.94291i
$704$		0			0
$705$	−9.68245	−	2.28282i	−0.364662	−	0.0859761i
$706$		0			0
$707$	−4.26302	+	16.5728i	−0.160327	+	0.623285i
$708$		0			0
$709$			1.68713i			0.0633616i	0.999498	+	0.0316808i	$0.0100860\pi$
$709$			1.68713i			0.0633616i	−0.999498	+	0.0316808i	$0.989914\pi$
$710$		0			0
$711$	−15.8822			−0.595629
$712$		0			0
$713$	−2.12804	+	2.12804i	−0.0796957	+	0.0796957i
$714$		0			0
$715$	−13.3309	+	8.24415i	−0.498546	+	0.308314i
$716$		0			0
$717$	11.6830	+	11.6830i	0.436310	+	0.436310i
$718$		0			0
$719$	−39.5132			−1.47359			−0.736797	−	0.676114i	$-0.763663\pi$
$719$	−39.5132			−1.47359			−0.736797	+	0.676114i	$0.763663\pi$
$720$		0			0
$721$	33.3805	−	19.7212i	1.24315	−	0.734456i
$722$		0			0
$723$	−2.58956	−	2.58956i	−0.0963069	−	0.0963069i
$724$		0			0
$725$	4.90638	−	9.82668i	0.182219	−	0.364954i
$726$		0			0
$727$	−21.9077	−	21.9077i	−0.812510	−	0.812510i	0.172499	−	0.985010i	$-0.444816\pi$
$727$	−21.9077	−	21.9077i	−0.812510	−	0.812510i	−0.985010	+	0.172499i	$0.944816\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$			0.743613i			0.0275035i
$732$		0			0
$733$	25.9013	−	25.9013i	0.956686	−	0.956686i	−0.0424140	−	0.999100i	$-0.513505\pi$
$733$	25.9013	−	25.9013i	0.956686	−	0.956686i	0.999100	+	0.0424140i	$0.0135048\pi$
$734$		0			0
$735$	−15.6327	+	0.787231i	−0.576620	+	0.0290375i
$736$		0			0
$737$	2.90479	−	2.90479i	0.106999	−	0.106999i
$738$		0			0
$739$		−	12.1682i		−	0.447614i	−0.974633	−	0.223807i	$-0.928151\pi$
$739$		−	12.1682i		−	0.447614i	0.974633	−	0.223807i	$-0.0718485\pi$
$740$		0			0
$741$			28.4221i			1.04411i
$742$		0			0
$743$	−23.6178	−	23.6178i	−0.866454	−	0.866454i	0.125624	−	0.992078i	$-0.459907\pi$
$743$	−23.6178	−	23.6178i	−0.866454	−	0.866454i	−0.992078	+	0.125624i	$0.959907\pi$
$744$		0			0
$745$	9.59378	−	40.6914i	0.351489	−	1.49082i
$746$		0			0
$747$	2.70588	+	2.70588i	0.0990031	+	0.0990031i
$748$		0			0
$749$	1.76733	−	1.04414i	0.0645768	−	0.0381520i
$750$		0			0
$751$	22.7684			0.830831			0.415415	−	0.909632i	$-0.363636\pi$
$751$	22.7684			0.830831			0.415415	+	0.909632i	$0.363636\pi$
$752$		0			0
$753$	−12.7421	−	12.7421i	−0.464347	−	0.464347i
$754$		0			0
$755$	−40.9393	−	9.65223i	−1.48994	−	0.351281i
$756$		0			0
$757$	4.52538	−	4.52538i	0.164478	−	0.164478i	−0.620069	−	0.784547i	$-0.712896\pi$
$757$	4.52538	−	4.52538i	0.164478	−	0.164478i	0.784547	+	0.620069i	$0.212896\pi$
$758$		0			0
$759$	3.08171			0.111859
$760$		0			0
$761$			8.58211i			0.311101i	0.987828	+	0.155551i	$0.0497152\pi$
$761$			8.58211i			0.311101i	−0.987828	+	0.155551i	$0.950285\pi$
$762$		0			0
$763$	4.92310	−	19.1390i	0.178228	−	0.692878i
$764$		0			0
$765$	12.0238	−	7.43580i	0.434720	−	0.268842i
$766$		0			0
$767$	23.8962	−	23.8962i	0.862840	−	0.862840i
$768$		0			0
$769$	−3.31019			−0.119368			−0.0596842	−	0.998217i	$-0.519009\pi$
$769$	−3.31019			−0.119368			−0.0596842	+	0.998217i	$0.519009\pi$
$770$		0			0
$771$	12.7124			0.457827
$772$		0			0
$773$	−29.8638	+	29.8638i	−1.07413	+	1.07413i	−0.0771032	+	0.997023i	$0.524567\pi$
$773$	−29.8638	+	29.8638i	−1.07413	+	1.07413i	−0.997023	+	0.0771032i	$0.975433\pi$
$774$		0			0
$775$	−3.43678	+	6.88331i	−0.123453	+	0.247256i
$776$		0			0
$777$	−7.51601	+	29.2191i	−0.269635	+	1.04823i
$778$		0			0
$779$		−	30.6445i		−	1.09795i
$780$		0			0
$781$	−15.1878			−0.543464
$782$		0			0
$783$	1.55329	−	1.55329i	0.0555102	−	0.0555102i
$784$		0			0
$785$	−22.4854	−	36.3592i	−0.802540	−	1.29772i
$786$		0			0
$787$	−14.0546	−	14.0546i	−0.500993	−	0.500993i	0.410754	−	0.911746i	$-0.365266\pi$
$787$	−14.0546	−	14.0546i	−0.500993	−	0.500993i	−0.911746	+	0.410754i	$0.865266\pi$
$788$		0			0
$789$	−24.3001			−0.865106
$790$		0			0
$791$	13.4737	+	22.8059i	0.479070	+	0.810885i
$792$		0			0
$793$	−11.7522	−	11.7522i	−0.417334	−	0.417334i
$794$		0			0
$795$	−19.3961	−	4.57300i	−0.687908	−	0.162187i
$796$		0			0
$797$	−17.5571	−	17.5571i	−0.621903	−	0.621903i	0.324115	−	0.946018i	$-0.394934\pi$
$797$	−17.5571	−	17.5571i	−0.621903	−	0.621903i	−0.946018	+	0.324115i	$0.894934\pi$
$798$		0			0
$799$			28.1273i			0.995072i
$800$		0			0
$801$		−	12.3852i		−	0.437610i
$802$		0			0
$803$	3.88308	−	3.88308i	0.137031	−	0.137031i
$804$		0			0
$805$	−3.44251	−	11.0470i	−0.121333	−	0.389356i
$806$		0			0
$807$	−6.66008	+	6.66008i	−0.234446	+	0.234446i
$808$		0			0
$809$		−	9.58716i		−	0.337067i	−0.985696	−	0.168533i	$-0.946097\pi$
$809$		−	9.58716i		−	0.337067i	0.985696	−	0.168533i	$-0.0539031\pi$
$810$		0			0
$811$			37.8740i			1.32994i	0.746872	+	0.664968i	$0.231555\pi$
$811$			37.8740i			1.32994i	−0.746872	+	0.664968i	$0.768445\pi$
$812$		0			0
$813$	16.9883	+	16.9883i	0.595805	+	0.595805i
$814$		0			0
$815$	2.40352	+	3.88652i	0.0841917	+	0.136139i
$816$		0			0
$817$	0.531332	+	0.531332i	0.0185889	+	0.0185889i
$818$		0			0
$819$	5.98712	+	10.1339i	0.209207	+	0.354108i
$820$		0			0
$821$	19.5838			0.683480			0.341740	−	0.939795i	$-0.388984\pi$
$821$	19.5838			0.683480			0.341740	+	0.939795i	$0.388984\pi$
$822$		0			0
$823$	−5.74170	−	5.74170i	−0.200143	−	0.200143i	0.599918	−	0.800061i	$-0.295200\pi$
$823$	−5.74170	−	5.74170i	−0.200143	−	0.200143i	−0.800061	+	0.599918i	$0.795200\pi$
$824$		0			0
$825$	7.47249	−	2.49553i	0.260159	−	0.0868833i
$826$		0			0
$827$	17.2222	−	17.2222i	0.598876	−	0.598876i	−0.341138	−	0.940013i	$-0.610812\pi$
$827$	17.2222	−	17.2222i	0.598876	−	0.598876i	0.940013	+	0.341138i	$0.110812\pi$
$828$		0			0
$829$	16.8042			0.583632			0.291816	−	0.956474i	$-0.405740\pi$
$829$	16.8042			0.583632			0.291816	+	0.956474i	$0.405740\pi$
$830$		0			0
$831$		−	23.6252i		−	0.819549i
$832$		0			0
$833$	12.3095	+	42.5103i	0.426499	+	1.47289i
$834$		0			0
$835$	−24.4557	−	39.5451i	−0.846325	−	1.36852i
$836$		0			0
$837$	−1.08804	+	1.08804i	−0.0376081	+	0.0376081i
$838$		0			0
$839$	−48.1783			−1.66330			−0.831650	−	0.555300i	$-0.812603\pi$
$839$	−48.1783			−1.66330			−0.831650	+	0.555300i	$0.812603\pi$
$840$		0			0
$841$	24.1746			0.833605
$842$		0			0
$843$	5.25146	−	5.25146i	0.180870	−	0.180870i
$844$		0			0
$845$	3.48502	−	14.7815i	0.119888	−	0.508499i
$846$		0			0
$847$	21.8244	+	5.61387i	0.749894	+	0.192895i
$848$		0			0
$849$		−	11.0058i		−	0.377718i
$850$		0			0
$851$	−22.3031			−0.764541
$852$		0			0
$853$	26.8575	−	26.8575i	0.919584	−	0.919584i	−0.0774147	−	0.996999i	$-0.524667\pi$
$853$	26.8575	−	26.8575i	0.919584	−	0.919584i	0.996999	+	0.0774147i	$0.0246665\pi$
$854$		0			0
$855$	3.27822	−	13.9044i	0.112113	−	0.475520i
$856$		0			0
$857$	−4.95401	−	4.95401i	−0.169226	−	0.169226i	0.617413	−	0.786639i	$-0.288181\pi$
$857$	−4.95401	−	4.95401i	−0.169226	−	0.169226i	−0.786639	+	0.617413i	$0.788181\pi$
$858$		0			0
$859$	−44.9211			−1.53269			−0.766343	−	0.642431i	$-0.777926\pi$
$859$	−44.9211			−1.53269			−0.766343	+	0.642431i	$0.777926\pi$
$860$		0			0
$861$	−6.45527	−	10.9263i	−0.219995	−	0.372368i
$862$		0			0
$863$	9.77825	+	9.77825i	0.332856	+	0.332856i	0.853670	−	0.520814i	$-0.174372\pi$
$863$	9.77825	+	9.77825i	0.332856	+	0.332856i	−0.520814	+	0.853670i	$0.674372\pi$
$864$		0			0
$865$	22.5505	−	13.9458i	0.766740	−	0.474172i
$866$		0			0
$867$	−16.2440	−	16.2440i	−0.551674	−	0.551674i
$868$		0			0
$869$			25.0246i			0.848901i
$870$		0			0
$871$			11.5989i			0.393013i
$872$		0			0
$873$	−8.82823	+	8.82823i	−0.298790	+	0.298790i
$874$		0			0
$875$	−17.2931	−	23.9989i	−0.584613	−	0.811312i
$876$		0			0
$877$	11.5983	−	11.5983i	0.391646	−	0.391646i	−0.483628	−	0.875274i	$-0.660681\pi$
$877$	11.5983	−	11.5983i	0.391646	−	0.391646i	0.875274	+	0.483628i	$0.160681\pi$
$878$		0			0
$879$		−	8.97408i		−	0.302688i
$880$		0			0
$881$		−	49.8810i		−	1.68053i	−0.542173	−	0.840267i	$-0.682398\pi$
$881$		−	49.8810i		−	1.68053i	0.542173	−	0.840267i	$-0.317602\pi$
$882$		0			0
$883$	−27.4128	−	27.4128i	−0.922514	−	0.922514i	0.0746926	−	0.997207i	$-0.476202\pi$
$883$	−27.4128	−	27.4128i	−0.922514	−	0.922514i	−0.997207	+	0.0746926i	$0.976202\pi$
$884$		0			0
$885$	−14.4465	+	8.93406i	−0.485613	+	0.300315i
$886$		0			0
$887$	31.8818	+	31.8818i	1.07049	+	1.07049i	0.997320	+	0.0731658i	$0.0233102\pi$
$887$	31.8818	+	31.8818i	1.07049	+	1.07049i	0.0731658	+	0.997320i	$0.476690\pi$
$888$		0			0
$889$	−17.8998	+	10.5752i	−0.600340	+	0.354680i
$890$		0			0
$891$	1.57564			0.0527858
$892$		0			0
$893$	20.0977	+	20.0977i	0.672544	+	0.672544i
$894$		0			0
$895$	3.07531	−	13.0437i	0.102796	−	0.436004i
$896$		0			0
$897$	−6.15265	+	6.15265i	−0.205431	+	0.205431i
$898$		0			0
$899$	3.38009			0.112732
$900$		0			0
$901$			56.3452i			1.87713i
$902$		0			0
$903$	0.301372	+	0.0775217i	0.0100290	+	0.00257976i
$904$		0			0
$905$	−6.57207	+	27.8750i	−0.218463	+	0.926597i
$906$		0			0
$907$	−18.9575	+	18.9575i	−0.629474	+	0.629474i	−0.947936	−	0.318461i	$-0.896834\pi$
$907$	−18.9575	+	18.9575i	−0.629474	+	0.629474i	0.318461	+	0.947936i	$0.396834\pi$
$908$		0			0
$909$	−6.46785			−0.214525
$910$		0			0
$911$	−6.42192			−0.212768			−0.106384	−	0.994325i	$-0.533927\pi$
$911$	−6.42192			−0.212768			−0.106384	+	0.994325i	$0.533927\pi$
$912$		0			0
$913$	4.26349	−	4.26349i	0.141101	−	0.141101i
$914$		0			0
$915$	4.39380	+	7.10482i	0.145255	+	0.234878i
$916$		0			0
$917$	5.18359	−	20.1516i	0.171177	−	0.665465i
$918$		0			0
$919$			21.6980i			0.715750i	0.933769	+	0.357875i	$0.116499\pi$
$919$			21.6980i			0.715750i	−0.933769	+	0.357875i	$0.883501\pi$
$920$		0			0
$921$	0.569386			0.0187619
$922$		0			0
$923$	30.3226	−	30.3226i	0.998082	−	0.998082i
$924$		0			0
$925$	−54.0804	+	18.0608i	−1.77815	+	0.593836i
$926$		0			0
$927$	10.3620	+	10.3620i	0.340331	+	0.340331i
$928$		0			0
$929$	36.5821			1.20022			0.600110	−	0.799917i	$-0.295123\pi$
$929$	36.5821			1.20022			0.600110	+	0.799917i	$0.295123\pi$
$930$		0			0
$931$	39.1702	+	21.5793i	1.28375	+	0.707232i
$932$		0			0
$933$	16.1014	+	16.1014i	0.527135	+	0.527135i
$934$		0			0
$935$	−11.7161	−	18.9451i	−0.383158	−	0.619571i
$936$		0			0
$937$	−11.8683	−	11.8683i	−0.387722	−	0.387722i	0.486152	−	0.873874i	$-0.338400\pi$
$937$	−11.8683	−	11.8683i	−0.387722	−	0.387722i	−0.873874	+	0.486152i	$0.838400\pi$
$938$		0			0
$939$		−	26.3627i		−	0.860315i
$940$		0			0
$941$		−	11.1295i		−	0.362810i	−0.983408	−	0.181405i	$-0.941936\pi$
$941$		−	11.1295i		−	0.362810i	0.983408	−	0.181405i	$-0.0580644\pi$
$942$		0			0
$943$	6.63374	−	6.63374i	0.216024	−	0.216024i
$944$		0			0
$945$	−1.76011	−	5.64819i	−0.0572564	−	0.183736i
$946$		0			0
$947$	−36.4604	+	36.4604i	−1.18480	+	1.18480i	−0.206318	+	0.978485i	$0.566148\pi$
$947$	−36.4604	+	36.4604i	−1.18480	+	1.18480i	−0.978485	+	0.206318i	$0.933852\pi$
$948$		0			0
$949$			15.5052i			0.503319i
$950$		0			0
$951$		−	2.84446i		−	0.0922378i
$952$		0			0
$953$	−27.7997	−	27.7997i	−0.900521	−	0.900521i	0.0949600	−	0.995481i	$-0.469728\pi$
$953$	−27.7997	−	27.7997i	−0.900521	−	0.900521i	−0.995481	+	0.0949600i	$0.969728\pi$
$954$		0			0
$955$	−45.5282	−	10.7341i	−1.47326	−	0.347349i
$956$		0			0
$957$	−2.44743	−	2.44743i	−0.0791141	−	0.0791141i
$958$		0			0
$959$	−24.0857	+	14.2298i	−0.777766	+	0.459504i
$960$		0			0
$961$	28.6323			0.923624
$962$		0			0
$963$	0.548614	+	0.548614i	0.0176788	+	0.0176788i
$964$		0			0
$965$	28.7498	+	46.4887i	0.925488	+	1.49652i
$966$		0			0
$967$	5.99769	−	5.99769i	0.192873	−	0.192873i	−0.604064	−	0.796936i	$-0.706453\pi$
$967$	5.99769	−	5.99769i	0.192873	−	0.192873i	0.796936	+	0.604064i	$0.206453\pi$
$968$		0			0
$969$	−40.3919			−1.29757
$970$		0			0
$971$		−	16.2214i		−	0.520568i	−0.965532	−	0.260284i	$-0.916184\pi$
$971$		−	16.2214i		−	0.520568i	0.965532	−	0.260284i	$-0.0838162\pi$
$972$		0			0
$973$	−9.86160	−	2.53669i	−0.316148	−	0.0813226i
$974$		0			0
$975$	−9.93653	+	19.9012i	−0.318224	+	0.637349i
$976$		0			0
$977$	21.4886	−	21.4886i	0.687481	−	0.687481i	−0.274193	−	0.961675i	$-0.588411\pi$
$977$	21.4886	−	21.4886i	0.687481	−	0.687481i	0.961675	+	0.274193i	$0.0884109\pi$
$978$		0			0
$979$	−19.5146			−0.623689
$980$		0			0
$981$	7.46934			0.238478
$982$		0			0
$983$	21.9507	−	21.9507i	0.700118	−	0.700118i	−0.264318	−	0.964436i	$-0.585147\pi$
$983$	21.9507	−	21.9507i	0.700118	−	0.700118i	0.964436	+	0.264318i	$0.0851469\pi$
$984$		0			0
$985$	−26.5345	+	16.4096i	−0.845460	+	0.522854i
$986$		0			0
$987$	11.3994	+	2.93227i	0.362848	+	0.0933352i
$988$		0			0
$989$			0.230039i			0.00731483i
$990$		0			0
$991$	−60.2806			−1.91488			−0.957439	−	0.288636i	$-0.906798\pi$
$991$	−60.2806			−1.91488			−0.957439	+	0.288636i	$0.906798\pi$
$992$		0			0
$993$	14.3476	−	14.3476i	0.455309	−	0.455309i
$994$		0			0
$995$	1.60673	+	0.378816i	0.0509366	+	0.0120093i
$996$		0			0
$997$	17.4365	+	17.4365i	0.552221	+	0.552221i	0.927081	−	0.374861i	$-0.122309\pi$
$997$	17.4365	+	17.4365i	0.552221	+	0.552221i	−0.374861	+	0.927081i	$0.622309\pi$
$998$		0			0
$999$	−11.4033			−0.360784

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bt.a.433.6	yes	24
4.3	odd	2		1680.2.cz.f.433.10		24
5.2	odd	4		840.2.bt.b.97.7	yes	24
7.6	odd	2		840.2.bt.b.433.7	yes	24
20.7	even	4		1680.2.cz.e.97.3		24
28.27	even	2		1680.2.cz.e.433.3		24
35.27	even	4	inner	840.2.bt.a.97.6	✓	24
140.27	odd	4		1680.2.cz.f.97.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bt.a.97.6	✓	24	35.27	even	4	inner
840.2.bt.a.433.6	yes	24	1.1	even	1	trivial
840.2.bt.b.97.7	yes	24	5.2	odd	4
840.2.bt.b.433.7	yes	24	7.6	odd	2
1680.2.cz.e.97.3		24	20.7	even	4
1680.2.cz.e.433.3		24	28.27	even	2
1680.2.cz.f.97.10		24	140.27	odd	4
1680.2.cz.f.433.10		24	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(2.17640 + 0.513127i) q^{5} +(-2.56234 - 0.659108i) q^{7} -1.00000i q^{9} -1.57564 q^{11} +(3.14577 - 3.14577i) q^{13} +(-1.90178 + 1.17611i) q^{15} +(4.47060 + 4.47060i) q^{17} +6.38872 q^{19} +(2.27791 - 1.34579i) q^{21} +(1.38299 + 1.38299i) q^{23} +(4.47340 + 2.23353i) q^{25} +(0.707107 + 0.707107i) q^{27} -2.19669i q^{29} +1.53872i q^{31} +(1.11414 - 1.11414i) q^{33} +(-5.23846 - 2.74929i) q^{35} +(-8.06335 + 8.06335i) q^{37} +4.44879i q^{39} -4.79665i q^{41} +(0.0831671 + 0.0831671i) q^{43} +(0.513127 - 2.17640i) q^{45} +(3.14581 + 3.14581i) q^{47} +(6.13115 + 3.37772i) q^{49} -6.32238 q^{51} +(6.30175 + 6.30175i) q^{53} +(-3.42921 - 0.808502i) q^{55} +(-4.51751 + 4.51751i) q^{57} +7.59628 q^{59} -3.73588i q^{61} +(-0.659108 + 2.56234i) q^{63} +(8.46062 - 5.23226i) q^{65} +(-1.84357 + 1.84357i) q^{67} -1.95585 q^{69} +9.63918 q^{71} +(-2.46445 + 2.46445i) q^{73} +(-4.74252 + 1.58383i) q^{75} +(4.03732 + 1.03852i) q^{77} -15.8822i q^{79} -1.00000 q^{81} +(-2.70588 + 2.70588i) q^{83} +(7.43580 + 12.0238i) q^{85} +(1.55329 + 1.55329i) q^{87} +12.3852 q^{89} +(-10.1339 + 5.98712i) q^{91} +(-1.08804 - 1.08804i) q^{93} +(13.9044 + 3.27822i) q^{95} +(-8.82823 - 8.82823i) q^{97} +1.57564i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7} - 8 q^{11} + 16 q^{13} + 4 q^{15} + 20 q^{17} + 8 q^{19} + 24 q^{23} - 4 q^{25} + 4 q^{37} - 16 q^{43} - 4 q^{45} - 24 q^{47} + 36 q^{49} + 16 q^{53} + 28 q^{55} + 4 q^{57} + 8 q^{59} + 24 q^{65}+ \cdots - 28 q^{97}+O(q^{100}) \) 24 * q - 4 * q^7 - 8 * q^11 + 16 * q^13 + 4 * q^15 + 20 * q^17 + 8 * q^19 + 24 * q^23 - 4 * q^25 + 4 * q^37 - 16 * q^43 - 4 * q^45 - 24 * q^47 + 36 * q^49 + 16 * q^53 + 28 * q^55 + 4 * q^57 + 8 * q^59 + 24 * q^65 + 16 * q^67 - 8 * q^69 + 8 * q^71 - 28 * q^73 + 20 * q^77 - 24 * q^81 + 64 * q^83 - 20 * q^85 + 20 * q^87 + 16 * q^89 + 24 * q^91 - 12 * q^93 + 24 * q^95 - 28 * q^97

Introduction

L-functions

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