LMFDB - Embedded newform 680.2.h.b.509.37

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(509,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.509"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.h (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			509.37
Character	$\chi$	$=$	680.509
Dual form			680.2.h.b.509.40

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36282 - 0.377781i) q^{2} -0.944008i q^{3} +(1.71456 - 1.02970i) q^{4} +(-0.0976904 - 2.23393i) q^{5} +(-0.356628 - 1.28651i) q^{6} -2.88614 q^{7} +(1.94764 - 2.05102i) q^{8} +2.10885 q^{9} +(-0.977072 - 3.00755i) q^{10} +2.86893 q^{11} +(-0.972041 - 1.61856i) q^{12} -3.06569 q^{13} +(-3.93329 + 1.09033i) q^{14} +(-2.10885 + 0.0922205i) q^{15} +(1.87945 - 3.53096i) q^{16} +(1.50020 + 3.84050i) q^{17} +(2.87398 - 0.796683i) q^{18} -3.89224i q^{19} +(-2.46777 - 3.72963i) q^{20} +2.72453i q^{21} +(3.90984 - 1.08383i) q^{22} -5.12547 q^{23} +(-1.93618 - 1.83859i) q^{24} +(-4.98091 + 0.436468i) q^{25} +(-4.17799 + 1.15816i) q^{26} -4.82279i q^{27} +(-4.94846 + 2.97184i) q^{28} +2.76061 q^{29} +(-2.83915 + 0.922364i) q^{30} -3.49238i q^{31} +(1.22743 - 5.52208i) q^{32} -2.70829i q^{33} +(3.49537 + 4.66716i) q^{34} +(0.281948 + 6.44743i) q^{35} +(3.61576 - 2.17147i) q^{36} +7.07698i q^{37} +(-1.47041 - 5.30443i) q^{38} +2.89404i q^{39} +(-4.77211 - 4.15054i) q^{40} +4.23564i q^{41} +(1.02928 + 3.71305i) q^{42} +4.28164 q^{43} +(4.91896 - 2.95413i) q^{44} +(-0.206014 - 4.71103i) q^{45} +(-6.98510 + 1.93631i) q^{46} -0.586236i q^{47} +(-3.33325 - 1.77422i) q^{48} +1.32978 q^{49} +(-6.62320 + 2.47652i) q^{50} +(3.62546 - 1.41620i) q^{51} +(-5.25632 + 3.15673i) q^{52} +13.9162 q^{53} +(-1.82196 - 6.57260i) q^{54} +(-0.280267 - 6.40900i) q^{55} +(-5.62116 + 5.91952i) q^{56} -3.67430 q^{57} +(3.76221 - 1.04290i) q^{58} +7.50051i q^{59} +(-3.52080 + 2.32959i) q^{60} +12.3026 q^{61} +(-1.31935 - 4.75948i) q^{62} -6.08643 q^{63} +(-0.413374 - 7.98931i) q^{64} +(0.299489 + 6.84855i) q^{65} +(-1.02314 - 3.69092i) q^{66} -5.37694 q^{67} +(6.52673 + 5.04002i) q^{68} +4.83848i q^{69} +(2.81996 + 8.68018i) q^{70} +7.98364i q^{71} +(4.10729 - 4.32529i) q^{72} +13.4366 q^{73} +(2.67355 + 9.64466i) q^{74} +(0.412029 + 4.70202i) q^{75} +(-4.00782 - 6.67349i) q^{76} -8.28012 q^{77} +(1.09331 + 3.94405i) q^{78} +11.6592i q^{79} +(-8.07153 - 3.85363i) q^{80} +1.77380 q^{81} +(1.60015 + 5.77242i) q^{82} +2.53572 q^{83} +(2.80544 + 4.67138i) q^{84} +(8.43285 - 3.72652i) q^{85} +(5.83511 - 1.61752i) q^{86} -2.60603i q^{87} +(5.58765 - 5.88423i) q^{88} -10.2124 q^{89} +(-2.06050 - 6.34246i) q^{90} +8.84800 q^{91} +(-8.78794 + 5.27768i) q^{92} -3.29683 q^{93} +(-0.221469 - 0.798935i) q^{94} +(-8.69500 + 0.380235i) q^{95} +(-5.21289 - 1.15870i) q^{96} +5.19643 q^{97} +(1.81225 - 0.502365i) q^{98} +6.05014 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{4} - 56 q^{9} + 56 q^{15} - 4 q^{16} - 36 q^{26} - 28 q^{30} + 24 q^{34} + 88 q^{36} + 8 q^{49} - 16 q^{50} - 88 q^{55} - 88 q^{60} - 132 q^{64} + 208 q^{66} + 72 q^{70} - 20 q^{76} - 56 q^{81}+ \cdots - 36 q^{94}+O(q^{100}) $ 40 * q + 12 * q^4 - 56 * q^9 + 56 * q^15 - 4 * q^16 - 36 * q^26 - 28 * q^30 + 24 * q^34 + 88 * q^36 + 8 * q^49 - 16 * q^50 - 88 * q^55 - 88 * q^60 - 132 * q^64 + 208 * q^66 + 72 * q^70 - 20 * q^76 - 56 * q^81 + 144 * q^84 + 256 * q^86 - 96 * q^89 - 36 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	1.36282	−	0.377781i	0.963660	−	0.267132i
$2$	1.36282	−	0.377781i	0.963660	−	0.267132i
$3$		−	0.944008i		−	0.545023i	−0.962153	−	0.272512i	$-0.912146\pi$
$3$		−	0.944008i		−	0.545023i	0.962153	−	0.272512i	$-0.0878543\pi$
$4$	1.71456	−	1.02970i	0.857281	−	0.514848i
$5$	−0.0976904	−	2.23393i	−0.0436885	−	0.999045i
$5$	−0.0976904	−	2.23393i	−0.0436885	−	0.999045i
$6$	−0.356628	−	1.28651i	−0.145593	−	0.525217i
$7$	−2.88614			−1.09086			−0.545428	−	0.838157i	$-0.683633\pi$
$7$	−2.88614			−1.09086			−0.545428	+	0.838157i	$0.683633\pi$
$8$	1.94764	−	2.05102i	0.688596	−	0.725145i
$9$	2.10885			0.702950
$10$	−0.977072	−	3.00755i	−0.308977	−	0.951069i
$11$	2.86893			0.865015			0.432507	−	0.901630i	$-0.357629\pi$
$11$	2.86893			0.865015			0.432507	+	0.901630i	$0.357629\pi$
$12$	−0.972041	−	1.61856i	−0.280604	−	0.467238i
$13$	−3.06569			−0.850270			−0.425135	−	0.905130i	$-0.639773\pi$
$13$	−3.06569			−0.850270			−0.425135	+	0.905130i	$0.639773\pi$
$14$	−3.93329	+	1.09033i	−1.05122	+	0.291402i
$15$	−2.10885	+	0.0922205i	−0.544503	+	0.0238112i
$16$	1.87945	−	3.53096i	0.469863	−	0.882739i
$17$	1.50020	+	3.84050i	0.363852	+	0.931457i
$17$	1.50020	+	3.84050i	0.363852	+	0.931457i
$18$	2.87398	−	0.796683i	0.677405	−	0.187780i
$19$		−	3.89224i		−	0.892941i	−0.894798	−	0.446471i	$-0.852681\pi$
$19$		−	3.89224i		−	0.892941i	0.894798	−	0.446471i	$-0.147319\pi$
$20$	−2.46777	−	3.72963i	−0.551810	−	0.833970i
$21$			2.72453i			0.594542i
$22$	3.90984	−	1.08383i	0.833580	−	0.231073i
$23$	−5.12547			−1.06873			−0.534367	−	0.845252i	$-0.679450\pi$
$23$	−5.12547			−1.06873			−0.534367	+	0.845252i	$0.679450\pi$
$24$	−1.93618	−	1.83859i	−0.395221	−	0.375301i
$25$	−4.98091	+	0.436468i	−0.996183	+	0.0872936i
$26$	−4.17799	+	1.15816i	−0.819371	+	0.227134i
$27$		−	4.82279i		−	0.928147i
$28$	−4.94846	+	2.97184i	−0.935171	+	0.561625i
$29$	2.76061			0.512632			0.256316	−	0.966593i	$-0.417491\pi$
$29$	2.76061			0.512632			0.256316	+	0.966593i	$0.417491\pi$
$30$	−2.83915	+	0.922364i	−0.518355	+	0.168400i
$31$		−	3.49238i		−	0.627249i	−0.949547	−	0.313625i	$-0.898457\pi$
$31$		−	3.49238i		−	0.627249i	0.949547	−	0.313625i	$-0.101543\pi$
$32$	1.22743	−	5.52208i	0.216981	−	0.976176i
$33$		−	2.70829i		−	0.471453i
$34$	3.49537	+	4.66716i	0.599451	+	0.800412i
$35$	0.281948	+	6.44743i	0.0476579	+	1.08982i
$36$	3.61576	−	2.17147i	0.602626	−	0.361912i
$37$			7.07698i			1.16345i	0.813386	+	0.581724i	$0.197622\pi$
$37$			7.07698i			1.16345i	−0.813386	+	0.581724i	$0.802378\pi$
$38$	−1.47041	−	5.30443i	−0.238533	−	0.860492i
$39$			2.89404i			0.463417i
$40$	−4.77211	−	4.15054i	−0.754537	−	0.656258i
$41$			4.23564i			0.661496i	0.943719	+	0.330748i	$0.107301\pi$
$41$			4.23564i			0.661496i	−0.943719	+	0.330748i	$0.892699\pi$
$42$	1.02928	+	3.71305i	0.158821	+	0.572936i
$43$	4.28164			0.652944			0.326472	−	0.945207i	$-0.394140\pi$
$43$	4.28164			0.652944			0.326472	+	0.945207i	$0.394140\pi$
$44$	4.91896	−	2.95413i	0.741561	−	0.445351i
$45$	−0.206014	−	4.71103i	−0.0307108	−	0.702279i
$46$	−6.98510	+	1.93631i	−1.02990	+	0.285493i
$47$		−	0.586236i		−	0.0855113i	−0.999086	−	0.0427556i	$-0.986386\pi$
$47$		−	0.586236i		−	0.0855113i	0.999086	−	0.0427556i	$-0.0136137\pi$
$48$	−3.33325	−	1.77422i	−0.481113	−	0.256086i
$49$	1.32978			0.189968
$50$	−6.62320	+	2.47652i	−0.936663	+	0.350233i
$51$	3.62546	−	1.41620i	0.507665	−	0.198308i
$52$	−5.25632	+	3.15673i	−0.728920	+	0.437760i
$53$	13.9162			1.91154			0.955771	−	0.294112i	$-0.0950238\pi$
$53$	13.9162			1.91154			0.955771	+	0.294112i	$0.0950238\pi$
$54$	−1.82196	−	6.57260i	−0.247937	−	0.894418i
$55$	−0.280267	−	6.40900i	−0.0377912	−	0.864189i
$56$	−5.62116	+	5.91952i	−0.751159	+	0.791030i
$57$	−3.67430			−0.486673
$58$	3.76221	−	1.04290i	0.494003	−	0.136940i
$59$			7.50051i			0.976483i	0.872708	+	0.488242i	$0.162362\pi$
$59$			7.50051i			0.976483i	−0.872708	+	0.488242i	$0.837638\pi$
$60$	−3.52080	+	2.32959i	−0.454533	+	0.300749i
$61$	12.3026			1.57518			0.787590	−	0.616199i	$-0.211328\pi$
$61$	12.3026			1.57518			0.787590	+	0.616199i	$0.211328\pi$
$62$	−1.31935	−	4.75948i	−0.167558	−	0.604455i
$63$	−6.08643			−0.766818
$64$	−0.413374	−	7.98931i	−0.0516717	−	0.998664i
$65$	0.299489	+	6.84855i	0.0371470	+	0.849458i
$66$	−1.02314	−	3.69092i	−0.125940	−	0.454320i
$67$	−5.37694			−0.656897			−0.328449	−	0.944522i	$-0.606526\pi$
$67$	−5.37694			−0.656897			−0.328449	+	0.944522i	$0.606526\pi$
$68$	6.52673	+	5.04002i	0.791482	+	0.611192i
$69$			4.83848i			0.582485i
$70$	2.81996	+	8.68018i	0.337050	+	1.03748i
$71$			7.98364i			0.947484i	0.880664	+	0.473742i	$0.157097\pi$
$71$			7.98364i			0.947484i	−0.880664	+	0.473742i	$0.842903\pi$
$72$	4.10729	−	4.32529i	0.484048	−	0.509741i
$73$	13.4366			1.57263			0.786315	−	0.617825i	$-0.211986\pi$
$73$	13.4366			1.57263			0.786315	+	0.617825i	$0.211986\pi$
$74$	2.67355	+	9.64466i	0.310794	+	1.12117i
$75$	0.412029	+	4.70202i	0.0475770	+	0.542942i
$76$	−4.00782	−	6.67349i	−0.459729	−	0.765502i
$77$	−8.28012			−0.943607
$78$	1.09331	+	3.94405i	0.123793	+	0.446576i
$79$			11.6592i			1.31176i	0.754863	+	0.655882i	$0.227703\pi$
$79$			11.6592i			1.31176i	−0.754863	+	0.655882i	$0.772297\pi$
$80$	−8.07153	−	3.85363i	−0.902424	−	0.430849i
$81$	1.77380			0.197088
$82$	1.60015	+	5.77242i	0.176706	+	0.637457i
$83$	2.53572			0.278332			0.139166	−	0.990269i	$-0.455558\pi$
$83$	2.53572			0.278332			0.139166	+	0.990269i	$0.455558\pi$
$84$	2.80544	+	4.67138i	0.306099	+	0.509690i
$85$	8.43285	−	3.72652i	0.914671	−	0.404198i
$86$	5.83511	−	1.61752i	0.629216	−	0.174422i
$87$		−	2.60603i		−	0.279396i
$88$	5.58765	−	5.88423i	0.595645	−	0.627261i
$89$	−10.2124			−1.08251			−0.541257	−	0.840857i	$-0.682052\pi$
$89$	−10.2124			−1.08251			−0.541257	+	0.840857i	$0.682052\pi$
$90$	−2.06050	−	6.34246i	−0.217196	−	0.668554i
$91$	8.84800			0.927522
$92$	−8.78794	+	5.27768i	−0.916206	+	0.550236i
$93$	−3.29683			−0.341865
$94$	−0.221469	−	0.798935i	−0.0228428	−	0.0824038i
$95$	−8.69500	+	0.380235i	−0.892088	+	0.0390112i
$96$	−5.21289	−	1.15870i	−0.532038	−	0.118260i
$97$	5.19643			0.527618			0.263809	−	0.964575i	$-0.415021\pi$
$97$	5.19643			0.527618			0.263809	+	0.964575i	$0.415021\pi$
$98$	1.81225	−	0.502365i	0.183065	−	0.0507465i
$99$	6.05014			0.608062
$100$	−8.09066	+	5.87718i	−0.809066	+	0.587718i
$101$		−	13.3414i		−	1.32752i	−0.747946	−	0.663760i	$-0.768960\pi$
$101$		−	13.3414i		−	1.32752i	0.747946	−	0.663760i	$-0.231040\pi$
$102$	4.40584	−	3.29966i	0.436243	−	0.326715i
$103$		−	16.0191i		−	1.57841i	−0.614128	−	0.789207i	$-0.710492\pi$
$103$		−	16.0191i		−	1.57841i	0.614128	−	0.789207i	$-0.289508\pi$
$104$	−5.97087	+	6.28780i	−0.585492	+	0.616569i
$105$	6.08643	−	0.266161i	0.593974	−	0.0259746i
$106$	18.9653	−	5.25729i	1.84208	−	0.510633i
$107$		−	10.5592i		−	1.02079i	−0.859939	−	0.510397i	$-0.829498\pi$
$107$		−	10.5592i		−	1.02079i	0.859939	−	0.510397i	$-0.170502\pi$
$108$	−4.96601	−	8.26898i	−0.477855	−	0.795683i
$109$	−9.47164			−0.907218			−0.453609	−	0.891201i	$-0.649864\pi$
$109$	−9.47164			−0.907218			−0.453609	+	0.891201i	$0.649864\pi$
$110$	−2.80315	−	8.62844i	−0.267270	−	0.822689i
$111$	6.68072			0.634106
$112$	−5.42435	+	10.1908i	−0.512553	+	0.962942i
$113$	13.1039			1.23271			0.616356	−	0.787467i	$-0.288608\pi$
$113$	13.1039			1.23271			0.616356	+	0.787467i	$0.288608\pi$
$114$	−5.00742	+	1.38808i	−0.468988	+	0.130006i
$115$	0.500709	+	11.4500i	0.0466914	+	1.06771i
$116$	4.73323	−	2.84258i	0.439470	−	0.263927i
$117$	−6.46508			−0.597697
$118$	2.83355	+	10.2219i	0.260850	+	0.940998i
$119$	−4.32978	−	11.0842i	−0.396910	−	1.01609i
$120$	−3.91814	+	4.50491i	−0.357676	+	0.411240i
$121$	−2.76924			−0.251750
$122$	16.7662	−	4.64767i	1.51794	−	0.420780i
$123$	3.99848			0.360531
$124$	−3.59609	−	5.98790i	−0.322938	−	0.537729i
$125$	1.46163	+	11.0844i	0.130732	+	0.991418i
$126$	−8.29471	+	2.29934i	−0.738952	+	0.204841i
$127$			20.7857i			1.84443i	0.386676	+	0.922215i	$0.373623\pi$
$127$			20.7857i			1.84443i	−0.386676	+	0.922215i	$0.626377\pi$
$128$	−3.58157	−	10.7318i	−0.316569	−	0.948570i
$129$		−	4.04190i		−	0.355870i
$130$	2.99540	+	9.22020i	0.262714	+	0.808665i
$131$	−9.68301			−0.846008			−0.423004	−	0.906128i	$-0.639024\pi$
$131$	−9.68301			−0.846008			−0.423004	+	0.906128i	$0.639024\pi$
$132$	−2.78872	−	4.64354i	−0.242727	−	0.404168i
$133$			11.2335i			0.974071i
$134$	−7.32780	+	2.03130i	−0.633026	+	0.175478i
$135$	−10.7738	+	0.471141i	−0.927261	+	0.0405493i
$136$	10.7988	+	4.40297i	0.925988	+	0.377552i
$137$			17.9552i			1.53401i	0.641639	+	0.767007i	$0.278255\pi$
$137$			17.9552i			1.53401i	−0.641639	+	0.767007i	$0.721745\pi$
$138$	1.82789	+	6.59399i	0.155600	+	0.561317i
$139$	−8.02149			−0.680374			−0.340187	−	0.940358i	$-0.610490\pi$
$139$	−8.02149			−0.680374			−0.340187	+	0.940358i	$0.610490\pi$
$140$	7.12231	+	10.7642i	0.601945	+	0.909742i
$141$	−0.553411			−0.0466056
$142$	3.01607	+	10.8803i	0.253103	+	0.913052i
$143$	−8.79525			−0.735496
$144$	3.96348	−	7.44626i	0.330290	−	0.620522i
$145$	−0.269685	−	6.16701i	−0.0223961	−	0.512142i
$146$	18.3116	−	5.07608i	1.51548	−	0.420099i
$147$		−	1.25532i		−	0.103537i
$148$	7.28714	+	12.1339i	0.598999	+	0.997403i
$149$			2.32968i			0.190855i	0.995436	+	0.0954274i	$0.0304218\pi$
$149$			2.32968i			0.190855i	−0.995436	+	0.0954274i	$0.969578\pi$
$150$	2.33786	+	6.25236i	0.190885	+	0.510503i
$151$	19.0166			1.54755			0.773775	−	0.633461i	$-0.218366\pi$
$151$	19.0166			1.54755			0.773775	+	0.633461i	$0.218366\pi$
$152$	−7.98306	−	7.58069i	−0.647512	−	0.614875i
$153$	3.16369	+	8.09903i	0.255770	+	0.654768i
$154$	−11.2843	+	3.12807i	−0.909317	+	0.252067i
$155$	−7.80173	+	0.341172i	−0.626650	+	0.0274036i
$156$	2.97998	+	4.96201i	0.238589	+	0.397278i
$157$	−8.86354			−0.707388			−0.353694	−	0.935361i	$-0.615075\pi$
$157$	−8.86354			−0.707388			−0.353694	+	0.935361i	$0.615075\pi$
$158$	4.40463	+	15.8894i	0.350414	+	1.26410i
$159$		−	13.1370i		−	1.04183i
$160$	−12.4559	−	2.20254i	−0.984723	−	0.174126i
$161$	14.7928			1.16584
$162$	2.41737	−	0.670107i	0.189926	−	0.0526485i
$163$			15.7662i			1.23490i	0.786610	+	0.617450i	$0.211834\pi$
$163$			15.7662i			1.23490i	−0.786610	+	0.617450i	$0.788166\pi$
$164$	4.36142	+	7.26227i	0.340570	+	0.567088i
$165$	−6.05014	+	0.264574i	−0.471003	+	0.0205971i
$166$	3.45574	−	0.957949i	0.268217	−	0.0743512i
$167$	−11.9251			−0.922795			−0.461397	−	0.887194i	$-0.652652\pi$
$167$	−11.9251			−0.922795			−0.461397	+	0.887194i	$0.652652\pi$
$168$	5.58808	+	5.30642i	0.431129	+	0.409399i
$169$	−3.60154			−0.277042
$170$	10.0847	−	8.26436i	0.773458	−	0.633847i
$171$		−	8.20815i		−	0.627693i
$172$	7.34114	−	4.40879i	0.559757	−	0.336167i
$173$		−	1.90308i		−	0.144689i	−0.997380	−	0.0723443i	$-0.976952\pi$
$173$		−	1.90308i		−	0.144689i	0.997380	−	0.0723443i	$-0.0230480\pi$
$174$	−0.984510	−	3.55156i	−0.0746355	−	0.269243i
$175$	14.3756	−	1.25971i	1.08669	−	0.0952248i
$176$	5.39202	−	10.1301i	0.406438	−	0.763583i
$177$	7.08054			0.532206
$178$	−13.9177	+	3.85806i	−1.04318	+	0.289174i
$179$		−	13.9270i		−	1.04095i	−0.853875	−	0.520477i	$-0.825754\pi$
$179$		−	13.9270i		−	1.04095i	0.853875	−	0.520477i	$-0.174246\pi$
$180$	−5.20415	−	7.86522i	−0.387895	−	0.586239i
$181$	−8.52747			−0.633842			−0.316921	−	0.948452i	$-0.602649\pi$
$181$	−8.52747			−0.633842			−0.316921	+	0.948452i	$0.602649\pi$
$182$	12.0582	−	3.34261i	0.893816	−	0.247770i
$183$		−	11.6137i		−	0.858510i
$184$	−9.98259	+	10.5124i	−0.735926	+	0.774988i
$185$	15.8095	−	0.691353i	1.16234	−	0.0508293i
$186$	−4.49299	+	1.24548i	−0.329442	+	0.0913230i
$187$	4.30397	+	11.0181i	0.314737	+	0.805724i
$188$	−0.603645	−	1.00514i	−0.0440253	−	0.0733072i
$189$			13.9192i			1.01248i
$190$	−11.7061	+	3.80300i	−0.849249	+	0.275899i
$191$	−18.9784			−1.37323			−0.686616	−	0.727020i	$-0.740905\pi$
$191$	−18.9784			−1.37323			−0.686616	+	0.727020i	$0.740905\pi$
$192$	−7.54197	+	0.390228i	−0.544295	+	0.0281623i
$193$	10.4508			0.752267			0.376134	−	0.926565i	$-0.377253\pi$
$193$	10.4508			0.752267			0.376134	+	0.926565i	$0.377253\pi$
$194$	7.08181	−	1.96311i	0.508444	−	0.140943i
$195$	6.46508	−	0.282720i	0.462974	−	0.0202460i
$196$	2.27999	−	1.36927i	0.162856	−	0.0978048i
$197$			3.38131i			0.240908i	0.992719	+	0.120454i	$0.0384351\pi$
$197$			3.38131i			0.240908i	−0.992719	+	0.120454i	$0.961565\pi$
$198$	8.24526	−	2.28563i	0.585965	−	0.162433i
$199$		−	0.616510i		−	0.0437033i	−0.999761	−	0.0218516i	$-0.993044\pi$
$199$		−	0.616510i		−	0.0437033i	0.999761	−	0.0218516i	$-0.00695614\pi$
$200$	−8.80584	+	11.0660i	−0.622667	+	0.782487i
$201$			5.07587i			0.358024i
$202$	−5.04013	−	18.1820i	−0.354623	−	1.27928i
$203$	−7.96748			−0.559208
$204$	4.75782	−	6.16128i	0.333114	−	0.431376i
$205$	9.46214	−	0.413782i	0.660865	−	0.0288998i
$206$	−6.05173	−	21.8312i	−0.421644	−	1.52105i
$207$	−10.8088			−0.751267
$208$	−5.76182	+	10.8248i	−0.399510	+	0.750566i
$209$		−	11.1666i		−	0.772407i
$210$	8.19416	−	2.66207i	0.565451	−	0.183700i
$211$	−7.06378			−0.486291			−0.243145	−	0.969990i	$-0.578179\pi$
$211$	−7.06378			−0.486291			−0.243145	+	0.969990i	$0.578179\pi$
$212$	23.8603	−	14.3295i	1.63873	−	0.984154i
$213$	7.53662			0.516401
$214$	−3.98906	−	14.3903i	−0.272686	−	0.983698i
$215$	−0.418275	−	9.56490i	−0.0285261	−	0.652321i
$216$	−9.89165	−	9.39308i	−0.673041	−	0.639118i
$217$			10.0795i			0.684239i
$218$	−12.9082	+	3.57821i	−0.874250	+	0.242347i
$219$		−	12.6842i		−	0.857120i
$220$	−7.07985	−	10.7000i	−0.477324	−	0.721396i
$221$	−4.59915	−	11.7738i	−0.309372	−	0.791989i
$222$	9.10463	−	2.52385i	0.611063	−	0.169390i
$223$			7.91167i			0.529804i	0.964275	+	0.264902i	$0.0853397\pi$
$223$			7.91167i			0.529804i	−0.964275	+	0.264902i	$0.914660\pi$
$224$	−3.54252	+	15.9375i	−0.236695	+	1.06487i
$225$	−10.5040	+	0.920445i	−0.700266	+	0.0613630i
$226$	17.8583	−	4.95041i	1.18792	−	0.329296i
$227$		−	16.8384i		−	1.11760i	−0.829302	−	0.558801i	$-0.811262\pi$
$227$		−	16.8384i		−	1.11760i	0.829302	−	0.558801i	$-0.188738\pi$
$228$	−6.29982	+	3.78342i	−0.417216	+	0.250563i
$229$			20.7187i			1.36913i	0.728953	+	0.684564i	$0.240007\pi$
$229$			20.7187i			1.36913i	−0.728953	+	0.684564i	$0.759993\pi$
$230$	5.00795	+	15.4151i	0.330215	+	1.01644i
$231$			7.81650i			0.514288i
$232$	5.37667	−	5.66206i	0.352996	−	0.371732i
$233$	−2.65309			−0.173809			−0.0869047	−	0.996217i	$-0.527698\pi$
$233$	−2.65309			−0.173809			−0.0869047	+	0.996217i	$0.527698\pi$
$234$	−8.81075	+	2.44239i	−0.575977	+	0.159664i
$235$	−1.30961	+	0.0572696i	−0.0854296	+	0.00373586i
$236$	7.72325	+	12.8601i	0.502741	+	0.837121i
$237$	11.0064			0.714942
$238$	−10.0881	−	13.4701i	−0.653915	−	0.873134i
$239$	6.79891			0.439785			0.219893	−	0.975524i	$-0.429429\pi$
$239$	6.79891			0.439785			0.219893	+	0.975524i	$0.429429\pi$
$240$	−3.63786	+	7.61958i	−0.234823	+	0.491842i
$241$			6.77933i			0.436695i	0.975871	+	0.218347i	$0.0700666\pi$
$241$			6.77933i			0.436695i	−0.975871	+	0.218347i	$0.929933\pi$
$242$	−3.77399	+	1.04617i	−0.242601	+	0.0672502i
$243$		−	16.1429i		−	1.03556i
$244$	21.0935	−	12.6679i	1.35037	−	0.810979i
$245$	−0.129907	−	2.97064i	−0.00829943	−	0.189787i
$246$	5.44921	−	1.51055i	0.347429	−	0.0963091i
$247$			11.9324i			0.759241i
$248$	−7.16294	−	6.80190i	−0.454847	−	0.431921i
$249$		−	2.39374i		−	0.151697i
$250$	6.17941	+	14.5539i	0.390820	+	0.920467i
$251$			2.78071i			0.175517i	0.996142	+	0.0877584i	$0.0279703\pi$
$251$			2.78071i			0.175517i	−0.996142	+	0.0877584i	$0.972030\pi$
$252$	−10.4356	+	6.26717i	−0.657379	+	0.394795i
$253$	−14.7046			−0.924471
$254$	7.85244	+	28.3272i	0.492706	+	1.77740i
$255$	−3.51787	−	7.96068i	−0.220297	−	0.498517i
$256$	−8.93532	−	13.2725i	−0.558457	−	0.829533i
$257$			5.39189i			0.336337i	0.985758	+	0.168168i	$0.0537852\pi$
$257$			5.39189i			0.336337i	−0.985758	+	0.168168i	$0.946215\pi$
$258$	−1.52695	−	5.50839i	−0.0950640	−	0.342937i
$259$		−	20.4251i		−	1.26916i
$260$	7.56541	+	11.4339i	0.469187	+	0.709099i
$261$	5.82170			0.360354
$262$	−13.1962	+	3.65806i	−0.815264	+	0.225995i
$263$		−	11.0291i		−	0.680081i	−0.940411	−	0.340040i	$-0.889559\pi$
$263$		−	11.0291i		−	0.680081i	0.940411	−	0.340040i	$-0.110441\pi$
$264$	−5.55476	−	5.27478i	−0.341872	−	0.324641i
$265$	−1.35948	−	31.0879i	−0.0835124	−	1.90972i
$266$	4.24382	+	15.3093i	0.260205	+	0.938673i
$267$			9.64061i			0.589996i
$268$	−9.21910	+	5.53661i	−0.563146	+	0.338202i
$269$	−21.6904			−1.32249			−0.661245	−	0.750170i	$-0.729971\pi$
$269$	−21.6904			−1.32249			−0.661245	+	0.750170i	$0.729971\pi$
$270$	−14.5048	+	4.71222i	−0.882732	+	0.286776i
$271$	6.24532			0.379376			0.189688	−	0.981844i	$-0.439252\pi$
$271$	6.24532			0.379376			0.189688	+	0.981844i	$0.439252\pi$
$272$	16.3802	+	1.92089i	0.993194	+	0.116471i
$273$		−	8.35258i		−	0.505521i
$274$	6.78313	+	24.4697i	0.409784	+	1.47827i
$275$	−14.2899	+	1.25220i	−0.861713	+	0.0755102i
$276$	4.98217	+	8.29588i	0.299891	+	0.499353i
$277$		−	15.4647i		−	0.929182i	−0.885525	−	0.464591i	$-0.846201\pi$
$277$		−	15.4647i		−	0.929182i	0.885525	−	0.464591i	$-0.153799\pi$
$278$	−10.9319	+	3.03037i	−0.655649	+	0.181749i
$279$		−	7.36490i		−	0.440925i
$280$	13.7730	+	11.9790i	0.823091	+	0.715883i
$281$	9.41962			0.561928			0.280964	−	0.959718i	$-0.409346\pi$
$281$	9.41962			0.561928			0.280964	+	0.959718i	$0.409346\pi$
$282$	−0.754200	+	0.209068i	−0.0449120	+	0.0124498i
$283$		−	14.8670i		−	0.883752i	−0.897076	−	0.441876i	$-0.854313\pi$
$283$		−	14.8670i		−	0.883752i	0.897076	−	0.441876i	$-0.145687\pi$
$284$	8.22072	+	13.6885i	0.487810	+	0.812260i
$285$	0.358944	+	8.20815i	0.0212620	+	0.486209i
$286$	−11.9864	+	3.32268i	−0.708768	+	0.196474i
$287$		−	12.2246i		−	0.721597i
$288$	2.58846	−	11.6452i	0.152527	−	0.686203i
$289$	−12.4988	+	11.5230i	−0.735224	+	0.677824i
$290$	−2.69731	−	8.30265i	−0.158392	−	0.487548i
$291$		−	4.90547i		−	0.287564i
$292$	23.0378	−	13.8356i	1.34819	−	0.809666i
$293$	−12.3249			−0.720029			−0.360014	−	0.932947i	$-0.617228\pi$
$293$	−12.3249			−0.720029			−0.360014	+	0.932947i	$0.617228\pi$
$294$	−0.474236	−	1.71078i	−0.0276580	−	0.0997746i
$295$	16.7556	−	0.732728i	0.975551	−	0.0426611i
$296$	14.5150	+	13.7834i	0.843669	+	0.801145i
$297$		−	13.8363i		−	0.802861i
$298$	0.880108	+	3.17494i	0.0509833	+	0.183919i
$299$	15.7131			0.908712
$300$	5.54810	+	7.63764i	0.320320	+	0.440960i
$301$	−12.3574			−0.712268
$302$	25.9162	−	7.18412i	1.49131	−	0.413399i
$303$	−12.5944			−0.723529
$304$	−13.7433	−	7.31528i	−0.788234	−	0.419560i
$305$	−1.20184	−	27.4831i	−0.0688173	−	1.57368i
$306$	7.37121	+	9.84234i	0.421384	+	0.562649i
$307$	−21.3733			−1.21984			−0.609919	−	0.792464i	$-0.708798\pi$
$307$	−21.3733			−1.21984			−0.609919	+	0.792464i	$0.708798\pi$
$308$	−14.1968	+	8.52601i	−0.808937	+	0.485814i
$309$	−15.1222			−0.860272
$310$	−10.5035	+	3.41230i	−0.596558	+	0.193806i
$311$		−	0.518584i		−	0.0294062i	−0.999892	−	0.0147031i	$-0.995320\pi$
$311$		−	0.518584i		−	0.0294062i	0.999892	−	0.0147031i	$-0.00468031\pi$
$312$	5.93573	+	5.63655i	0.336044	+	0.319107i
$313$	−23.0605			−1.30345			−0.651727	−	0.758454i	$-0.725955\pi$
$313$	−23.0605			−1.30345			−0.651727	+	0.758454i	$0.725955\pi$
$314$	−12.0794	+	3.34848i	−0.681681	+	0.188966i
$315$	0.594586	+	13.5967i	0.0335011	+	0.766085i
$316$	12.0055	+	19.9905i	0.675360	+	1.12455i
$317$		−	16.1043i		−	0.904509i	−0.891889	−	0.452254i	$-0.850620\pi$
$317$		−	16.1043i		−	0.904509i	0.891889	−	0.452254i	$-0.149380\pi$
$318$	−4.96292	−	17.9034i	−0.278307	−	1.00397i
$319$	7.91998			0.443434
$320$	−17.8072	+	1.70393i	−0.995453	+	0.0952525i
$321$	−9.96794			−0.556356
$322$	20.1599	−	5.58844i	1.12347	−	0.311432i
$323$	14.9481	−	5.83914i	0.831736	−	0.324898i
$324$	3.04128	−	1.82647i	0.168960	−	0.101471i
$325$	15.2699	−	1.33808i	0.847024	−	0.0742231i
$326$	5.95615	+	21.4864i	0.329881	+	1.19002i
$327$			8.94130i			0.494455i
$328$	8.68739	+	8.24952i	0.479681	+	0.455503i
$329$			1.69196i			0.0932806i
$330$	−8.14531	+	2.64620i	−0.448384	+	0.145668i
$331$			11.3323i			0.622880i	0.950266	+	0.311440i	$0.100811\pi$
$331$			11.3323i			0.622880i	−0.950266	+	0.311440i	$0.899189\pi$
$332$	4.34766	−	2.61103i	0.238609	−	0.143299i
$333$			14.9243i			0.817846i
$334$	−16.2518	+	4.50509i	−0.889260	+	0.246508i
$335$	0.525275	+	12.0117i	0.0286989	+	0.656270i
$336$	9.62021	+	5.12063i	0.524826	+	0.279353i
$337$	−33.1037			−1.80327			−0.901637	−	0.432494i	$-0.857634\pi$
$337$	−33.1037			−1.80327			−0.901637	+	0.432494i	$0.857634\pi$
$338$	−4.90826	+	1.36059i	−0.266974	+	0.0740066i
$339$		−	12.3702i		−	0.671857i
$340$	10.6215	−	15.0726i	0.576030	−	0.817428i
$341$		−	10.0194i		−	0.542580i
$342$	−3.10088	−	11.1862i	−0.167677	−	0.604882i
$343$	16.3650			0.883628
$344$	8.33911	−	8.78174i	0.449615	−	0.473479i
$345$	10.8088	−	0.472673i	0.581929	−	0.0254479i
$346$	−0.718948	−	2.59356i	−0.0386509	−	0.139431i
$347$			11.8594i			0.636644i	0.947983	+	0.318322i	$0.103119\pi$
$347$			11.8594i			0.636644i	−0.947983	+	0.318322i	$0.896881\pi$
$348$	−2.68342	−	4.46821i	−0.143846	−	0.239521i
$349$			0.0652143i			0.00349084i	0.999998	+	0.00174542i	$0.000555585\pi$
$349$			0.0652143i			0.00349084i	−0.999998	+	0.00174542i	$0.999444\pi$
$350$	19.1155	−	7.14758i	1.02176	−	0.382054i
$351$			14.7852i			0.789175i
$352$	3.52141	−	15.8425i	0.187692	−	0.844407i
$353$			18.2936i			0.973673i	0.873493	+	0.486836i	$0.161849\pi$
$353$			18.2936i			0.973673i	−0.873493	+	0.486836i	$0.838151\pi$
$354$	9.64951	−	2.67489i	0.512866	−	0.142169i
$355$	17.8349	−	0.779925i	0.946579	−	0.0413941i
$356$	−17.5098	+	10.5157i	−0.928020	+	0.557331i
$357$	−10.4636	+	4.08734i	−0.553790	+	0.216325i
$358$	−5.26137	−	18.9800i	−0.278072	−	1.00313i
$359$	8.34651			0.440512			0.220256	−	0.975442i	$-0.429311\pi$
$359$	8.34651			0.440512			0.220256	+	0.975442i	$0.429311\pi$
$360$	−10.0637	−	8.75286i	−0.530402	−	0.461316i
$361$	3.85047			0.202656
$362$	−11.6214	+	3.22152i	−0.610808	+	0.169319i
$363$			2.61419i			0.137209i
$364$	15.1705	−	9.11075i	0.795148	−	0.477533i
$365$	−1.31262	−	30.0164i	−0.0687059	−	1.57113i
$366$	−4.38744	−	15.8274i	−0.229335	−	0.827312i
$367$	−6.57511			−0.343218			−0.171609	−	0.985165i	$-0.554897\pi$
$367$	−6.57511			−0.343218			−0.171609	+	0.985165i	$0.554897\pi$
$368$	−9.63308	+	18.0978i	−0.502159	+	0.943414i
$369$			8.93233i			0.464999i
$370$	21.2843	−	6.91472i	1.10652	−	0.359479i
$371$	−40.1641			−2.08522
$372$	−5.65262	+	3.39473i	−0.293075	+	0.176009i
$373$	6.67146			0.345435			0.172718	−	0.984971i	$-0.444745\pi$
$373$	6.67146			0.345435			0.172718	+	0.984971i	$0.444745\pi$
$374$	10.0280	+	13.3898i	0.518534	+	0.692368i
$375$	10.4637	−	1.37979i	0.540346	−	0.0712519i
$376$	−1.20238	−	1.14178i	−0.0620081	−	0.0588827i
$377$	−8.46316			−0.435875
$378$	5.25842	+	18.9694i	0.270464	+	0.975682i
$379$	25.2216			1.29555			0.647774	−	0.761833i	$-0.275700\pi$
$379$	25.2216			1.29555			0.647774	+	0.761833i	$0.275700\pi$
$380$	−14.5166	+	9.60515i	−0.744686	+	0.492734i
$381$	19.6218			1.00526
$382$	−25.8642	+	7.16969i	−1.32333	+	0.366834i
$383$			12.0576i			0.616114i	0.951368	+	0.308057i	$0.0996788\pi$
$383$			12.0576i			0.616114i	−0.951368	+	0.308057i	$0.900321\pi$
$384$	−10.1309	+	3.38102i	−0.516992	+	0.172537i
$385$	0.808888	+	18.4972i	0.0412248	+	0.942706i
$386$	14.2426	−	3.94813i	0.724930	−	0.200954i
$387$	9.02934			0.458987
$388$	8.90961	−	5.35075i	0.452317	−	0.271643i
$389$			14.8108i			0.750936i	0.926835	+	0.375468i	$0.122518\pi$
$389$			14.8108i			0.750936i	−0.926835	+	0.375468i	$0.877482\pi$
$390$	8.70394	−	2.82768i	0.440741	−	0.143185i
$391$	−7.68923	−	19.6843i	−0.388861	−	0.995480i
$392$	2.58993	−	2.72740i	0.130811	−	0.137755i
$393$			9.14083i			0.461094i
$394$	1.27740	+	4.60812i	0.0643542	+	0.232154i
$395$	26.0459	−	1.13899i	1.31051	−	0.0573090i
$396$	10.3733	−	6.22981i	0.521280	−	0.313060i
$397$		−	27.5794i		−	1.38417i	−0.721816	−	0.692085i	$-0.756692\pi$
$397$		−	27.5794i		−	1.38417i	0.721816	−	0.692085i	$-0.243308\pi$
$398$	−0.232906	−	0.840193i	−0.0116745	−	0.0421151i
$399$	10.6045			0.530891
$400$	−7.82024	+	18.4077i	−0.391012	+	0.920386i
$401$		−	28.7380i		−	1.43511i	−0.696503	−	0.717553i	$-0.745262\pi$
$401$		−	28.7380i		−	1.43511i	0.696503	−	0.717553i	$-0.254738\pi$
$402$	1.91757	+	6.91750i	0.0956395	+	0.345014i
$403$			10.7065i			0.533331i
$404$	−13.7376	−	22.8747i	−0.683471	−	1.13806i
$405$	−0.173283	−	3.96254i	−0.00861050	−	0.196900i
$406$	−10.8583	+	3.00996i	−0.538886	+	0.149382i
$407$			20.3034i			1.00640i
$408$	4.15644	−	10.1941i	0.205774	−	0.504685i
$409$	−2.56137			−0.126652			−0.0633258	−	0.997993i	$-0.520171\pi$
$409$	−2.56137			−0.126652			−0.0633258	+	0.997993i	$0.520171\pi$
$410$	12.7389	−	4.13853i	0.629129	−	0.204387i
$411$	16.9498			0.836073
$412$	−16.4949	−	27.4658i	−0.812643	−	1.35314i
$413$		−	21.6475i		−	1.06520i
$414$	−14.7305	+	4.08338i	−0.723966	+	0.200687i
$415$	−0.247716	−	5.66464i	−0.0121599	−	0.278066i
$416$	−3.76292	+	16.9290i	−0.184492	+	0.830013i
$417$			7.57234i			0.370819i
$418$	−4.21851	−	15.2180i	−0.206334	−	0.744338i
$419$	−39.4186			−1.92572			−0.962861	−	0.269996i	$-0.912978\pi$
$419$	−39.4186			−1.92572			−0.962861	+	0.269996i	$0.912978\pi$
$420$	10.1615	−	6.72352i	0.495830	−	0.328074i
$421$		−	21.2325i		−	1.03481i	−0.855741	−	0.517405i	$-0.826898\pi$
$421$		−	21.2325i		−	1.03481i	0.855741	−	0.517405i	$-0.173102\pi$
$422$	−9.62667	+	2.66856i	−0.468619	+	0.129904i
$423$		−	1.23628i		−	0.0601101i
$424$	27.1039	−	28.5425i	1.31628	−	1.38615i
$425$	−9.14861	−	18.4744i	−0.443773	−	0.896139i
$426$	10.2711	−	2.84719i	0.497635	−	0.137947i
$427$	−35.5068			−1.71830
$428$	−10.8727	−	18.1044i	−0.525554	−	0.875108i
$429$			8.30278i			0.400862i
$430$	−4.18347	−	12.8772i	−0.201745	−	0.620995i
$431$		−	36.8583i		−	1.77540i	−0.460423	−	0.887700i	$-0.652302\pi$
$431$		−	36.8583i		−	1.77540i	0.460423	−	0.887700i	$-0.347698\pi$
$432$	−17.0291	−	9.06421i	−0.819312	−	0.436102i
$433$		−	22.3041i		−	1.07187i	−0.844260	−	0.535934i	$-0.819960\pi$
$433$		−	22.3041i		−	1.07187i	0.844260	−	0.535934i	$-0.180040\pi$
$434$	3.80783	+	13.7365i	0.182782	+	0.659374i
$435$	−5.82170	+	0.254584i	−0.279129	+	0.0122064i
$436$	−16.2397	+	9.75291i	−0.777742	+	0.467080i
$437$			19.9496i			0.954317i
$438$	−4.79186	−	17.2863i	−0.228964	−	0.825972i
$439$			37.0018i			1.76600i	0.469373	+	0.883000i	$0.344480\pi$
$439$			37.0018i			1.76600i	−0.469373	+	0.883000i	$0.655520\pi$
$440$	−13.6908	−	11.9076i	−0.652685	−	0.567673i
$441$	2.80430			0.133538
$442$	−10.7157	−	14.3081i	−0.509695	−	0.680566i
$443$	−22.5999			−1.07376			−0.536878	−	0.843660i	$-0.680396\pi$
$443$	−22.5999			−1.07376			−0.536878	+	0.843660i	$0.680396\pi$
$444$	11.4545	−	6.87911i	0.543607	−	0.326468i
$445$	0.997656	+	22.8139i	0.0472934	+	1.08148i
$446$	2.98888	+	10.7822i	0.141527	+	0.510551i
$447$	2.19923			0.104020
$448$	1.19305	+	23.0582i	0.0563664	+	1.08940i
$449$		−	17.0085i		−	0.802679i	−0.915929	−	0.401340i	$-0.868545\pi$
$449$		−	17.0085i		−	0.802679i	0.915929	−	0.401340i	$-0.131455\pi$
$450$	−13.9673	+	5.22261i	−0.658427	+	0.246196i
$451$			12.1518i			0.572204i
$452$	22.4675	−	13.4931i	1.05678	−	0.634660i
$453$		−	17.9518i		−	0.843450i
$454$	−6.36121	−	22.9477i	−0.298546	−	1.07699i
$455$	−0.864365	−	19.7658i	−0.0405220	−	0.926637i
$456$	−7.15623	+	7.53607i	−0.335121	+	0.352909i
$457$			26.3883i			1.23439i	0.786809	+	0.617196i	$0.211731\pi$
$457$			26.3883i			1.23439i	−0.786809	+	0.617196i	$0.788269\pi$
$458$	7.82711	+	28.2358i	0.365737	+	1.31937i
$459$	18.5219	−	7.23515i	0.864529	−	0.337708i
$460$	12.6485	+	19.1161i	0.589738	+	0.891292i
$461$		−	15.1560i		−	0.705885i	−0.935645	−	0.352942i	$-0.885181\pi$
$461$		−	15.1560i		−	0.705885i	0.935645	−	0.352942i	$-0.114819\pi$
$462$	2.95292	+	10.6525i	0.137382	+	0.495598i
$463$			17.0335i			0.791615i	0.918334	+	0.395807i	$0.129535\pi$
$463$			17.0335i			0.791615i	−0.918334	+	0.395807i	$0.870465\pi$
$464$	5.18843	−	9.74758i	0.240867	−	0.452520i
$465$	0.322069	+	7.36490i	0.0149356	+	0.341539i
$466$	−3.61568	+	1.00229i	−0.167493	+	0.0464300i
$467$	4.39784			0.203508			0.101754	−	0.994810i	$-0.467555\pi$
$467$	4.39784			0.203508			0.101754	+	0.994810i	$0.467555\pi$
$468$	−11.0848	+	6.65707i	−0.512395	+	0.307723i
$469$	15.5186			0.716581
$470$	−1.76313	+	0.572795i	−0.0813272	+	0.0264210i
$471$			8.36725i			0.385543i
$472$	15.3837	+	14.6083i	0.708093	+	0.672402i
$473$	12.2837			0.564806
$474$	14.9997	−	4.15801i	0.688961	−	0.190984i
$475$	1.69884	+	19.3869i	0.0779480	+	0.889532i
$476$	−18.8370	−	14.5462i	−0.863394	−	0.666723i
$477$	29.3472			1.34372
$478$	9.26570	−	2.56850i	0.423803	−	0.117480i
$479$		−	8.24757i		−	0.376841i	−0.982088	−	0.188420i	$-0.939663\pi$
$479$		−	8.24757i		−	0.376841i	0.982088	−	0.188420i	$-0.0603368\pi$
$480$	−2.07921	+	11.7584i	−0.0949026	+	0.536697i
$481$		−	21.6958i		−	0.989245i
$482$	2.56110	+	9.23901i	0.116655	+	0.420825i
$483$		−	13.9645i		−	0.635407i
$484$	−4.74804	+	2.85148i	−0.215820	+	0.129613i
$485$	−0.507642	−	11.6085i	−0.0230508	−	0.527114i
$486$	−6.09846	−	21.9998i	−0.276632	−	0.997932i
$487$	29.6417			1.34320			0.671598	−	0.740916i	$-0.265608\pi$
$487$	29.6417			1.34320			0.671598	+	0.740916i	$0.265608\pi$
$488$	23.9610	−	25.2328i	1.08466	−	1.14224i
$489$	14.8834			0.673049
$490$	−1.29929	−	3.99937i	−0.0586959	−	0.180673i
$491$			34.2977i			1.54784i	0.633286	+	0.773918i	$0.281706\pi$
$491$			34.2977i			1.54784i	−0.633286	+	0.773918i	$0.718294\pi$
$492$	6.85564	−	4.11722i	0.309076	−	0.185618i
$493$	4.14146	+	10.6021i	0.186522	+	0.477494i
$494$	4.50784	+	16.2617i	0.202817	+	0.731650i
$495$	−0.591041	−	13.5156i	−0.0265653	−	0.607481i
$496$	−12.3314	−	6.56375i	−0.553698	−	0.294721i
$497$		−	23.0419i		−	1.03357i
$498$	−0.904311	−	3.26224i	−0.0405231	−	0.146185i
$499$	−2.30863			−0.103348			−0.0516741	−	0.998664i	$-0.516456\pi$
$499$	−2.30863			−0.103348			−0.0516741	+	0.998664i	$0.516456\pi$
$500$	13.9196	+	17.4998i	0.622504	+	0.782617i
$501$			11.2574i			0.502944i
$502$	1.05050	+	3.78961i	0.0468861	+	0.169139i
$503$	−0.640049			−0.0285384			−0.0142692	−	0.999898i	$-0.504542\pi$
$503$	−0.640049			−0.0285384			−0.0142692	+	0.999898i	$0.504542\pi$
$504$	−11.8542	+	12.4834i	−0.528027	+	0.556054i
$505$	−29.8038	+	1.30333i	−1.32625	+	0.0579974i
$506$	−20.0398	+	5.55512i	−0.890876	+	0.246955i
$507$			3.39988i			0.150994i
$508$	21.4029	+	35.6384i	0.949602	+	1.58120i
$509$			13.9844i			0.619850i	0.950761	+	0.309925i	$0.100304\pi$
$509$			13.9844i			0.619850i	−0.950761	+	0.309925i	$0.899696\pi$
$510$	−7.80162	−	9.52000i	−0.345461	−	0.421553i
$511$	−38.7797			−1.71551
$512$	−17.1914	−	14.7125i	−0.759758	−	0.650206i
$513$	−18.7715			−0.828780
$514$	2.03695	+	7.34818i	0.0898461	+	0.324114i
$515$	−35.7857	+	1.56492i	−1.57691	+	0.0689585i
$516$	−4.16193	−	6.93009i	−0.183219	−	0.305080i
$517$		−	1.68187i		−	0.0739685i
$518$	−7.71622	−	27.8358i	−0.339031	−	1.22303i
$519$	−1.79652			−0.0788586
$520$	14.6298	+	12.7243i	0.641560	+	0.557996i
$521$			22.6377i			0.991777i	0.868386	+	0.495888i	$0.165158\pi$
$521$			22.6377i			0.991777i	−0.868386	+	0.495888i	$0.834842\pi$
$522$	7.93394	−	2.19933i	0.347259	−	0.0962620i
$523$	28.4555			1.24427			0.622137	−	0.782908i	$-0.286265\pi$
$523$	28.4555			1.24427			0.622137	+	0.782908i	$0.286265\pi$
$524$	−16.6021	+	9.97055i	−0.725267	+	0.435566i
$525$	−1.18917	−	13.5707i	−0.0518997	−	0.592272i
$526$	−4.16657	−	15.0306i	−0.181671	−	0.655367i
$527$	13.4125	−	5.23926i	0.584256	−	0.228226i
$528$	−9.56286	−	5.09010i	−0.416170	−	0.221518i
$529$	3.27044			0.142193
$530$	−13.5972	−	41.8537i	−0.590623	−	1.81801i
$531$			15.8175i			0.686419i
$532$	11.5671	+	19.2606i	0.501498	+	0.835053i
$533$		−	12.9852i		−	0.562450i
$534$	3.64204	+	13.1384i	0.157606	+	0.568555i
$535$	−23.5885	+	1.03153i	−1.01982	+	0.0445969i
$536$	−10.4724	+	11.0282i	−0.452337	+	0.476346i
$537$	−13.1472			−0.567344
$538$	−29.5602	+	8.19423i	−1.27443	+	0.353279i
$539$	3.81504			0.164325
$540$	−17.9872	+	11.9015i	−0.774047	+	0.512161i
$541$	9.54279			0.410277			0.205138	−	0.978733i	$-0.434236\pi$
$541$	9.54279			0.410277			0.205138	+	0.978733i	$0.434236\pi$
$542$	8.51126	−	2.35936i	0.365590	−	0.101343i
$543$			8.04999i			0.345458i
$544$	23.0489	−	3.57029i	0.988215	−	0.153075i
$545$	0.925289	+	21.1590i	0.0396350	+	0.906352i
$546$	−3.15545	−	11.3831i	−0.135041	−	0.487150i
$547$			14.2853i			0.610794i	0.952225	+	0.305397i	$0.0987891\pi$
$547$			14.2853i			0.610794i	−0.952225	+	0.305397i	$0.901211\pi$
$548$	18.4884	+	30.7853i	0.789784	+	1.31508i
$549$	25.9442			1.10727
$550$	−19.0015	+	7.10497i	−0.810227	+	0.302957i
$551$		−	10.7449i		−	0.457750i
$552$	9.92383	+	9.42364i	0.422386	+	0.401097i
$553$		−	33.6501i		−	1.43095i
$554$	−5.84226	−	21.0756i	−0.248214	−	0.895416i
$555$	−0.652643	−	14.9243i	−0.0277031	−	0.633501i
$556$	−13.7533	+	8.25969i	−0.583272	+	0.350289i
$557$	−8.19911			−0.347407			−0.173704	−	0.984798i	$-0.555574\pi$
$557$	−8.19911			−0.347407			−0.173704	+	0.984798i	$0.555574\pi$
$558$	−2.78232	−	10.0370i	−0.117785	−	0.424902i
$559$	−13.1262			−0.555179
$560$	23.2955	+	11.1221i	0.984415	+	0.469994i
$561$	10.4012	−	4.06298i	0.439138	−	0.171539i
$562$	12.8373	−	3.55856i	0.541507	−	0.150109i
$563$	−35.9134			−1.51357			−0.756784	−	0.653665i	$-0.773230\pi$
$563$	−35.9134			−1.51357			−0.756784	+	0.653665i	$0.773230\pi$
$564$	−0.948858	+	0.569845i	−0.0399541	+	0.0239948i
$565$	−1.28013	−	29.2733i	−0.0538554	−	1.23154i
$566$	−5.61648	−	20.2611i	−0.236078	−	0.851637i
$567$	−5.11942			−0.214995
$568$	16.3746	+	15.5493i	0.687064	+	0.652433i
$569$	3.85286			0.161520			0.0807602	−	0.996734i	$-0.474265\pi$
$569$	3.85286			0.161520			0.0807602	+	0.996734i	$0.474265\pi$
$570$	3.59006	+	11.0506i	0.150371	+	0.462860i
$571$	7.18893			0.300848			0.150424	−	0.988622i	$-0.451936\pi$
$571$	7.18893			0.300848			0.150424	+	0.988622i	$0.451936\pi$
$572$	−15.0800	+	9.05643i	−0.630527	+	0.378669i
$573$			17.9158i			0.748443i
$574$	−4.61824	−	16.6600i	−0.192761	−	0.695375i
$575$	25.5295	−	2.23710i	1.06465	−	0.0932936i
$576$	−0.871743	−	16.8483i	−0.0363226	−	0.702011i
$577$			13.1871i			0.548984i	0.961589	+	0.274492i	$0.0885097\pi$
$577$			13.1871i			0.548984i	−0.961589	+	0.274492i	$0.911490\pi$
$578$	−12.6805	+	20.4256i	−0.527438	+	0.849594i
$579$		−	9.86566i		−	0.410003i
$580$	−6.81253	−	10.2960i	−0.282875	−	0.427519i
$581$	−7.31844			−0.303620
$582$	−1.85319	−	6.68528i	−0.0768174	−	0.277114i
$583$	39.9247			1.65351
$584$	26.1696	−	27.5587i	1.08291	−	1.14039i
$585$	0.631577	+	14.4426i	0.0261125	+	0.597126i
$586$	−16.7966	+	4.65612i	−0.693863	+	0.192342i
$587$	27.2958			1.12662			0.563310	−	0.826246i	$-0.309528\pi$
$587$	27.2958			1.12662			0.563310	+	0.826246i	$0.309528\pi$
$588$	−1.29260	−	2.15233i	−0.0533059	−	0.0887605i
$589$	−13.5932			−0.560097
$590$	22.5581	−	7.32854i	0.928704	−	0.301711i
$591$	3.19198			0.131301
$592$	24.9885	+	13.3008i	1.02702	+	0.546661i
$593$		−	29.1916i		−	1.19876i	−0.800466	−	0.599378i	$-0.795415\pi$
$593$		−	29.1916i		−	1.19876i	0.800466	−	0.599378i	$-0.204585\pi$
$594$	−5.22707	−	18.8563i	−0.214469	−	0.773685i
$595$	−24.3384	+	10.7553i	−0.997775	+	0.440922i
$596$	2.39886	+	3.99438i	0.0982612	+	0.163616i
$597$	−0.581990			−0.0238193
$598$	21.4142	−	5.93611i	0.875690	−	0.242746i
$599$	16.4164			0.670756			0.335378	−	0.942084i	$-0.391136\pi$
$599$	16.4164			0.670756			0.335378	+	0.942084i	$0.391136\pi$
$600$	10.4464	+	8.31278i	0.426474	+	0.339368i
$601$			24.1491i			0.985062i	0.870295	+	0.492531i	$0.163928\pi$
$601$			24.1491i			0.985062i	−0.870295	+	0.492531i	$0.836072\pi$
$602$	−16.8409	+	4.66839i	−0.686385	+	0.190269i
$603$	−11.3391			−0.461766
$604$	32.6052	−	19.5813i	1.32669	−	0.796753i
$605$	0.270529	+	6.18631i	0.0109986	+	0.251509i
$606$	−17.1639	+	4.75792i	−0.697236	+	0.193277i
$607$	13.0482			0.529609			0.264805	−	0.964302i	$-0.414693\pi$
$607$	13.0482			0.529609			0.264805	+	0.964302i	$0.414693\pi$
$608$	−21.4933	−	4.77745i	−0.871667	−	0.193751i
$609$			7.52136i			0.304781i
$610$	−12.0205	−	37.0005i	−0.486695	−	1.49811i
$611$			1.79722i			0.0727076i
$612$	13.7639	+	10.6286i	0.556372	+	0.429638i
$613$	−2.86925			−0.115888			−0.0579440	−	0.998320i	$-0.518454\pi$
$613$	−2.86925			−0.115888			−0.0579440	+	0.998320i	$0.518454\pi$
$614$	−29.1280	+	8.07442i	−1.17551	+	0.325857i
$615$	−0.390613	−	8.93233i	−0.0157510	−	0.360186i
$616$	−16.1267	+	16.9827i	−0.649764	+	0.684252i
$617$	5.43171			0.218672			0.109336	−	0.994005i	$-0.465127\pi$
$617$	5.43171			0.218672			0.109336	+	0.994005i	$0.465127\pi$
$618$	−20.6088	+	5.71288i	−0.829009	+	0.229806i
$619$	43.4998			1.74841			0.874203	−	0.485561i	$-0.161385\pi$
$619$	43.4998			1.74841			0.874203	+	0.485561i	$0.161385\pi$
$620$	−13.0253	+	8.61838i	−0.523107	+	0.346122i
$621$			24.7191i			0.991942i
$622$	−0.195911	−	0.706737i	−0.00785532	−	0.0283376i
$623$	29.4744			1.18087
$624$	10.2187	+	5.43920i	0.409076	+	0.217742i
$625$	24.6190	−	4.34802i	0.984760	−	0.173921i
$626$	−31.4273	+	8.71180i	−1.25609	+	0.348194i
$627$	−10.5413			−0.420980
$628$	−15.1971	+	9.12675i	−0.606430	+	0.364197i
$629$	−27.1791	+	10.6169i	−1.08370	+	0.423323i
$630$	5.94688	+	18.3052i	0.236929	+	0.729297i
$631$	−2.76768			−0.110180			−0.0550899	−	0.998481i	$-0.517545\pi$
$631$	−2.76768			−0.110180			−0.0550899	+	0.998481i	$0.517545\pi$
$632$	23.9133	+	22.7080i	0.951220	+	0.903276i
$633$			6.66826i			0.265040i
$634$	−6.08391	−	21.9473i	−0.241623	−	0.871639i
$635$	46.4338	−	2.03056i	1.84267	−	0.0805804i
$636$	−13.5271	−	22.5243i	−0.536386	−	0.893145i
$637$	−4.07669			−0.161524
$638$	10.7935	−	2.99202i	0.427319	−	0.118455i
$639$			16.8363i			0.666034i
$640$	−23.6243	+	9.04938i	−0.933834	+	0.357708i
$641$		−	33.2524i		−	1.31339i	−0.754155	−	0.656696i	$-0.771953\pi$
$641$		−	33.2524i		−	1.31339i	0.754155	−	0.656696i	$-0.228047\pi$
$642$	−13.5845	+	3.76570i	−0.536138	+	0.148620i
$643$			23.1775i			0.914030i	0.889459	+	0.457015i	$0.151081\pi$
$643$			23.1775i			0.914030i	−0.889459	+	0.457015i	$0.848919\pi$
$644$	25.3632	−	15.2321i	0.999450	−	0.600228i
$645$	−9.02934	+	0.394855i	−0.355530	+	0.0155474i
$646$	18.1657	−	13.6048i	0.714720	−	0.535274i
$647$			7.80320i			0.306776i	0.988166	+	0.153388i	$0.0490184\pi$
$647$			7.80320i			0.306776i	−0.988166	+	0.153388i	$0.950982\pi$
$648$	3.45472	−	3.63809i	0.135714	−	0.142918i
$649$			21.5184i			0.844673i
$650$	20.3047	−	7.59225i	0.796416	−	0.297793i
$651$	9.51510			0.372926
$652$	16.2343	+	27.0321i	0.635786	+	1.05866i
$653$			5.63478i			0.220506i	0.993904	+	0.110253i	$0.0351661\pi$
$653$			5.63478i			0.220506i	−0.993904	+	0.110253i	$0.964834\pi$
$654$	3.37785	+	12.1854i	0.132085	+	0.476487i
$655$	0.945937	+	21.6312i	0.0369608	+	0.845200i
$656$	14.9559	+	7.96069i	0.583929	+	0.310813i
$657$	28.3357			1.10548
$658$	0.639189	+	2.30583i	0.0249182	+	0.0898907i
$659$		−	27.2916i		−	1.06313i	−0.847017	−	0.531566i	$-0.821604\pi$
$659$		−	27.2916i		−	1.06313i	0.847017	−	0.531566i	$-0.178396\pi$
$660$	−10.1009	+	6.68343i	−0.393178	+	0.260152i
$661$			14.3284i			0.557311i	0.960391	+	0.278656i	$0.0898888\pi$
$661$			14.3284i			0.557311i	−0.960391	+	0.278656i	$0.910111\pi$
$662$	4.28113	+	15.4439i	0.166391	+	0.600244i
$663$	−11.1145	+	4.34163i	−0.431652	+	0.168615i
$664$	4.93869	−	5.20082i	0.191658	−	0.201831i
$665$	25.0950	−	1.09741i	0.973141	−	0.0425557i
$666$	5.63811	+	20.3391i	0.218472	+	0.788125i
$667$	−14.1494			−0.547867
$668$	−20.4464	+	12.2793i	−0.791095	+	0.475099i
$669$	7.46867			0.288756
$670$	5.25365	+	16.1714i	0.202966	+	0.624755i
$671$	35.2952			1.36255
$672$	15.0451	+	3.34417i	0.580378	+	0.129004i
$673$	−41.8173			−1.61194			−0.805969	−	0.591958i	$-0.798355\pi$
$673$	−41.8173			−1.61194			−0.805969	+	0.591958i	$0.798355\pi$
$674$	−45.1144	+	12.5060i	−1.73774	+	0.481711i
$675$	2.10499	+	24.0219i	0.0810212	+	0.924604i
$676$	−6.17507	+	3.70849i	−0.237503	+	0.142634i
$677$		−	2.49652i		−	0.0959492i	−0.998849	−	0.0479746i	$-0.984723\pi$
$677$		−	2.49652i		−	0.0959492i	0.998849	−	0.0479746i	$-0.0152766\pi$
$678$	−4.67323	−	16.8584i	−0.179474	−	0.647442i
$679$	−14.9976			−0.575555
$680$	8.78101	−	24.5539i	0.336736	−	0.941599i
$681$	−15.8955			−0.609118
$682$	−3.78513	−	13.6546i	−0.144940	−	0.522863i
$683$			45.0742i			1.72472i	0.506299	+	0.862358i	$0.331013\pi$
$683$			45.0742i			1.72472i	−0.506299	+	0.862358i	$0.668987\pi$
$684$	−8.45190	−	14.0734i	−0.323166	−	0.538109i
$685$	40.1107	−	1.75405i	1.53255	−	0.0670188i
$686$	22.3026	−	6.18240i	0.851517	−	0.236045i
$687$	19.5586			0.746206
$688$	8.04714	−	15.1183i	0.306794	−	0.576379i
$689$	−42.6629			−1.62533
$690$	14.5520	−	4.72755i	0.553983	−	0.179975i
$691$	−15.6346			−0.594769			−0.297385	−	0.954758i	$-0.596114\pi$
$691$	−15.6346			−0.594769			−0.297385	+	0.954758i	$0.596114\pi$
$692$	−1.95959	−	3.26295i	−0.0744926	−	0.124039i
$693$	−17.4615			−0.663309
$694$	4.48024	+	16.1622i	0.170068	+	0.613508i
$695$	0.783623	+	17.9195i	0.0297245	+	0.679724i
$696$	−5.34503	−	5.07562i	−0.202603	−	0.192391i
$697$	−16.2670	+	6.35431i	−0.616155	+	0.240687i
$698$	0.0246367	+	0.0888754i	0.000932514	+	0.00336398i
$699$			2.50453i			0.0947301i
$700$	23.3507	−	16.9623i	0.882575	−	0.641116i
$701$		−	9.79056i		−	0.369784i	−0.982759	−	0.184892i	$-0.940806\pi$
$701$		−	9.79056i		−	0.369784i	0.982759	−	0.184892i	$-0.0591936\pi$
$702$	5.58557	+	20.1496i	0.210814	+	0.760497i
$703$	27.5453			1.03889
$704$	−1.18594	−	22.9208i	−0.0446968	−	0.863859i
$705$	0.0540630	+	1.23628i	0.00203613	+	0.0465611i
$706$	6.91099	+	24.9310i	0.260099	+	0.938289i
$707$			38.5051i			1.44813i
$708$	12.1400	−	7.29080i	0.456250	−	0.274005i
$709$	43.9669			1.65121			0.825606	−	0.564247i	$-0.190833\pi$
$709$	43.9669			1.65121			0.825606	+	0.564247i	$0.190833\pi$
$710$	24.0112	−	7.80059i	0.901123	−	0.292751i
$711$			24.5875i			0.922105i
$712$	−19.8902	+	20.9459i	−0.745415	+	0.784981i
$713$			17.9001i			0.670363i
$714$	−12.7158	+	9.52325i	−0.475878	+	0.356399i
$715$	0.859212	+	19.6480i	0.0321327	+	0.734793i
$716$	−14.3406	−	23.8788i	−0.535933	−	0.892391i
$717$		−	6.41823i		−	0.239693i
$718$	11.3748	−	3.15315i	0.424504	−	0.117675i
$719$			46.3088i			1.72703i	0.504327	+	0.863513i	$0.331741\pi$
$719$			46.3088i			1.72703i	−0.504327	+	0.863513i	$0.668259\pi$
$720$	−17.0216	−	8.12673i	−0.634359	−	0.302865i
$721$			46.2334i			1.72182i
$722$	5.24750	−	1.45463i	0.195292	−	0.0541359i
$723$	6.39974			0.238009
$724$	−14.6209	+	8.78070i	−0.543381	+	0.326332i
$725$	−13.7503	+	1.20492i	−0.510675	+	0.0447494i
$726$	0.987591	+	3.56267i	0.0366529	+	0.132223i
$727$			47.1238i			1.74773i	0.486172	+	0.873863i	$0.338393\pi$
$727$			47.1238i			1.74773i	−0.486172	+	0.873863i	$0.661607\pi$
$728$	17.2327	−	18.1474i	0.638688	−	0.672589i
$729$	−9.91759			−0.367318
$730$	−13.1285	−	40.4111i	−0.485907	−	1.49568i
$731$	6.42331	+	16.4436i	0.237575	+	0.608189i
$732$	−11.9586	−	19.9124i	−0.442002	−	0.735985i
$733$	44.5039			1.64379			0.821895	−	0.569639i	$-0.192917\pi$
$733$	44.5039			1.64379			0.821895	+	0.569639i	$0.192917\pi$
$734$	−8.96069	+	2.48395i	−0.330745	+	0.0916843i
$735$	−2.80430	+	0.122633i	−0.103438	+	0.00452338i
$736$	−6.29115	+	28.3033i	−0.231895	+	1.04327i
$737$	−15.4260			−0.568226
$738$	3.37447	+	12.1732i	0.124216	+	0.448101i
$739$		−	39.7198i		−	1.46112i	−0.682851	−	0.730558i	$-0.739260\pi$
$739$		−	39.7198i		−	1.46112i	0.682851	−	0.730558i	$-0.260740\pi$
$740$	26.3945	−	17.4643i	0.970281	−	0.642002i
$741$	11.2643			0.413804
$742$	−54.7365	+	15.1733i	−2.00944	+	0.557028i
$743$	−41.5257			−1.52343			−0.761715	−	0.647913i	$-0.775642\pi$
$743$	−41.5257			−1.52343			−0.761715	+	0.647913i	$0.775642\pi$
$744$	−6.42105	+	6.76187i	−0.235407	+	0.247902i
$745$	5.20435	−	0.227587i	0.190672	−	0.00833815i
$746$	9.09201	−	2.52035i	0.332882	−	0.0922767i
$747$	5.34746			0.195653
$748$	18.7247	+	14.4595i	0.684644	+	0.528690i
$749$			30.4752i			1.11354i
$750$	13.7390	−	5.83341i	0.501676	−	0.213006i
$751$			13.9080i			0.507512i	0.967268	+	0.253756i	$0.0816660\pi$
$751$			13.9080i			0.507512i	−0.967268	+	0.253756i	$0.918334\pi$
$752$	−2.06997	−	1.10180i	−0.0754842	−	0.0401786i
$753$	2.62501			0.0956607
$754$	−11.5338	+	3.19722i	−0.420035	+	0.116436i
$755$	−1.85774	−	42.4818i	−0.0676101	−	1.54607i
$756$	14.3326	+	23.8654i	0.521271	+	0.867976i
$757$	−50.5775			−1.83827			−0.919136	−	0.393940i	$-0.871112\pi$
$757$	−50.5775			−1.83827			−0.919136	+	0.393940i	$0.871112\pi$
$758$	34.3725	−	9.52825i	1.24847	−	0.346082i
$759$			13.8813i			0.503858i
$760$	−16.1549	+	18.5742i	−0.586000	+	0.673757i
$761$	−49.2403			−1.78496			−0.892479	−	0.451089i	$-0.851036\pi$
$761$	−49.2403			−1.78496			−0.892479	+	0.451089i	$0.851036\pi$
$762$	26.7411	−	7.41276i	0.968726	−	0.268536i
$763$	27.3364			0.989645
$764$	−32.5397	+	19.5420i	−1.17725	+	0.707006i
$765$	17.7836	−	7.85868i	0.642968	−	0.284131i
$766$	4.55513	+	16.4323i	0.164583	+	0.593724i
$767$		−	22.9942i		−	0.830274i
$768$	−12.5294	+	8.43501i	−0.452115	+	0.304372i
$769$	29.6731			1.07004			0.535019	−	0.844840i	$-0.320304\pi$
$769$	29.6731			1.07004			0.535019	+	0.844840i	$0.320304\pi$
$770$	8.09027	+	24.9028i	0.291553	+	0.897436i
$771$	5.08998			0.183311
$772$	17.9186	−	10.7612i	0.644905	−	0.387303i
$773$	9.30255			0.334590			0.167295	−	0.985907i	$-0.446497\pi$
$773$	9.30255			0.334590			0.167295	+	0.985907i	$0.446497\pi$
$774$	12.3054	−	3.41111i	0.442307	−	0.122610i
$775$	1.52431	+	17.3952i	0.0547548	+	0.624855i
$776$	10.1208	−	10.6580i	0.363315	−	0.382600i
$777$	−19.2815			−0.691719
$778$	5.59523	+	20.1844i	0.200599	+	0.723647i
$779$	16.4861			0.590677
$780$	10.7937	−	7.14181i	0.386475	−	0.255718i
$781$			22.9045i			0.819588i
$782$	−17.9154	−	23.9214i	−0.640654	−	0.855427i
$783$		−	13.3138i		−	0.475797i
$784$	2.49926	−	4.69539i	0.0892591	−	0.167693i
$785$	0.865883	+	19.8006i	0.0309047	+	0.706712i
$786$	3.45323	+	12.4573i	0.123173	+	0.444338i
$787$		−	22.3169i		−	0.795511i	−0.917492	−	0.397755i	$-0.869789\pi$
$787$		−	22.3169i		−	0.795511i	0.917492	−	0.397755i	$-0.130211\pi$
$788$	3.48172	+	5.79747i	0.124031	+	0.206526i
$789$	−10.4115			−0.370660
$790$	35.0656	−	11.3919i	1.24758	−	0.405306i
$791$	−37.8197			−1.34471
$792$	11.7835	−	12.4090i	0.418709	−	0.440933i
$793$	−37.7158			−1.33933
$794$	−10.4190	−	37.5858i	−0.369756	−	1.33387i
$795$	−29.3472	+	1.28336i	−1.04084	+	0.0455162i
$796$	−0.634818	−	1.05705i	−0.0225005	−	0.0374660i
$797$	8.09672			0.286801			0.143400	−	0.989665i	$-0.454196\pi$
$797$	8.09672			0.286801			0.143400	+	0.989665i	$0.454196\pi$
$798$	14.4521	−	4.00619i	0.511598	−	0.141818i
$799$	2.25144	−	0.879471i	0.0796501	−	0.0311134i
$800$	−3.70350	+	28.0408i	−0.130939	+	0.991390i
$801$	−21.5365			−0.760954
$802$	−10.8567	−	39.1647i	−0.383362	−	1.38296i
$803$	38.5486			1.36035
$804$	5.22660	+	8.70290i	0.184328	+	0.306927i
$805$	−1.44512	−	33.0461i	−0.0509336	−	1.16472i
$806$	4.04473	+	14.5911i	0.142470	+	0.513950i
$807$			20.4759i			0.720787i
$808$	−27.3635	−	25.9843i	−0.962645	−	0.914125i
$809$		−	30.7913i		−	1.08256i	−0.840842	−	0.541281i	$-0.817939\pi$
$809$		−	30.7913i		−	1.08256i	0.840842	−	0.541281i	$-0.182061\pi$
$810$	−1.73313	−	5.33477i	−0.0608959	−	0.187445i
$811$	11.4867			0.403351			0.201676	−	0.979452i	$-0.435361\pi$
$811$	11.4867			0.403351			0.201676	+	0.979452i	$0.435361\pi$
$812$	−13.6607	+	8.20408i	−0.479398	+	0.287907i
$813$		−	5.89563i		−	0.206769i
$814$	7.67022	+	27.6698i	0.268841	+	0.969827i
$815$	35.2205	−	1.54020i	1.23372	−	0.0539509i
$816$	1.81333	−	15.4630i	0.0634793	−	0.541314i
$817$		−	16.6652i		−	0.583041i
$818$	−3.49069	+	0.967638i	−0.122049	+	0.0338327i
$819$	18.6591			0.652002
$820$	15.7974	−	10.4526i	0.551668	−	0.365020i
$821$	−0.485038			−0.0169280			−0.00846398	−	0.999964i	$-0.502694\pi$
$821$	−0.485038			−0.0169280			−0.00846398	+	0.999964i	$0.502694\pi$
$822$	23.0996	−	6.40332i	0.805690	−	0.223341i
$823$	46.5510			1.62267			0.811333	−	0.584585i	$-0.198743\pi$
$823$	46.5510			1.62267			0.811333	+	0.584585i	$0.198743\pi$
$824$	−32.8556	−	31.1996i	−1.14458	−	1.08689i
$825$	1.18208	+	13.4898i	0.0411548	+	0.469653i
$826$	−8.17801	−	29.5017i	−0.284549	−	1.02649i
$827$		−	36.8656i		−	1.28194i	−0.767565	−	0.640972i	$-0.778532\pi$
$827$		−	36.8656i		−	1.28194i	0.767565	−	0.640972i	$-0.221468\pi$
$828$	−18.5324	+	11.1298i	−0.644047	+	0.386788i
$829$			44.6114i			1.54942i	0.632318	+	0.774709i	$0.282104\pi$
$829$			44.6114i			1.54942i	−0.632318	+	0.774709i	$0.717896\pi$
$830$	−2.47759	−	7.62631i	−0.0859982	−	0.264713i
$831$	−14.5988			−0.506426
$832$	1.26728	+	24.4928i	0.0439349	+	0.849134i
$833$	1.99493	+	5.10701i	0.0691203	+	0.176947i
$834$	2.86069	+	10.3198i	0.0990575	+	0.357344i
$835$	1.16497	+	26.6400i	0.0403155	+	0.921914i
$836$	−11.4982	−	19.1458i	−0.397672	−	0.662170i
$837$	−16.8430			−0.582179
$838$	−53.7205	+	14.8916i	−1.85574	+	0.514421i
$839$		−	38.0112i		−	1.31229i	−0.754633	−	0.656147i	$-0.772185\pi$
$839$		−	38.0112i		−	1.31229i	0.754633	−	0.656147i	$-0.227815\pi$
$840$	11.3083	−	13.0018i	0.390173	−	0.448604i
$841$	−21.3791			−0.737209
$842$	−8.02124	−	28.9361i	−0.276430	−	0.997204i
$843$		−	8.89220i		−	0.306264i
$844$	−12.1113	+	7.27355i	−0.416888	+	0.250366i
$845$	0.351836	+	8.04560i	0.0121035	+	0.276777i
$846$	−0.467044	−	1.68483i	−0.0160573	−	0.0579257i
$847$	7.99242			0.274623
$848$	26.1549	−	49.1376i	0.898163	−	1.68739i
$849$	−14.0346			−0.481665
$850$	−19.4472	−	21.7211i	−0.667033	−	0.745028i
$851$		−	36.2728i		−	1.24342i
$852$	12.9220	−	7.76043i	0.442701	−	0.265868i
$853$			18.0880i			0.619321i	0.950847	+	0.309660i	$0.100215\pi$
$853$			18.0880i			0.619321i	−0.950847	+	0.309660i	$0.899785\pi$
$854$	−48.3895	+	13.4138i	−1.65585	+	0.459011i
$855$	−18.3365	+	0.801858i	−0.627093	+	0.0274230i
$856$	−21.6571	−	20.5655i	−0.740224	−	0.702914i
$857$	25.9872			0.887707			0.443853	−	0.896099i	$-0.353611\pi$
$857$	25.9872			0.887707			0.443853	+	0.896099i	$0.353611\pi$
$858$	3.13663	+	11.3152i	0.107083	+	0.386295i
$859$		−	17.9911i		−	0.613848i	−0.951734	−	0.306924i	$-0.900700\pi$
$859$		−	17.9911i		−	0.613848i	0.951734	−	0.306924i	$-0.0992998\pi$
$860$	−10.5661	−	15.9689i	−0.360301	−	0.544536i
$861$	−11.5401			−0.393287
$862$	−13.9244	−	50.2312i	−0.474265	−	1.71088i
$863$			0.213466i			0.00726648i	0.999993	+	0.00363324i	$0.00115650\pi$
$863$			0.213466i			0.00726648i	−0.999993	+	0.00363324i	$0.998844\pi$
$864$	−26.6319	−	5.91963i	−0.906035	−	0.201390i
$865$	−4.25135	+	0.185913i	−0.144550	+	0.00632122i
$866$	−8.42607	−	30.3965i	−0.286329	−	1.03292i
$867$	10.8778	+	11.7990i	0.369430	+	0.400714i
$868$	10.3788	+	17.2819i	0.352279	+	0.586585i
$869$			33.4495i			1.13470i
$870$	−7.83776	+	2.54628i	−0.265725	+	0.0863270i
$871$	16.4840			0.558540
$872$	−18.4474	+	19.4265i	−0.624707	+	0.657865i
$873$	10.9585			0.370889
$874$	7.53656	+	27.1877i	0.254928	+	0.919637i
$875$	−4.21845	−	31.9910i	−0.142610	−	1.08149i
$876$	−13.0609	−	21.7479i	−0.441287	−	0.734793i
$877$			17.2333i			0.581928i	0.956734	+	0.290964i	$0.0939760\pi$
$877$			17.2333i			0.581928i	−0.956734	+	0.290964i	$0.906024\pi$
$878$	13.9786	+	50.4268i	0.471754	+	1.70182i
$879$			11.6348i			0.392432i
$880$	−23.1566	−	11.0558i	−0.780610	−	0.372691i
$881$		−	26.9750i		−	0.908812i	−0.890795	−	0.454406i	$-0.849852\pi$
$881$		−	26.9750i		−	0.908812i	0.890795	−	0.454406i	$-0.150148\pi$
$882$	3.82176	−	1.05941i	0.128685	−	0.0356723i
$883$	−22.7907			−0.766969			−0.383484	−	0.923547i	$-0.625276\pi$
$883$	−22.7907			−0.766969			−0.383484	+	0.923547i	$0.625276\pi$
$884$	−20.0089	−	15.4511i	−0.672973	−	0.519678i
$885$	−0.691701	−	15.8175i	−0.0232513	−	0.531698i
$886$	−30.7997	+	8.53783i	−1.03474	+	0.286834i
$887$	−51.7486			−1.73755			−0.868774	−	0.495209i	$-0.835091\pi$
$887$	−51.7486			−1.73755			−0.868774	+	0.495209i	$0.835091\pi$
$888$	13.0117	−	13.7023i	0.436643	−	0.459819i
$889$		−	59.9903i		−	2.01201i
$890$	9.97828	+	30.7143i	0.334473	+	1.02955i
$891$	5.08890			0.170484
$892$	8.14661	+	13.5651i	0.272769	+	0.454191i
$893$	−2.28177			−0.0763565
$894$	2.99716	−	0.830829i	0.100240	−	0.0277871i
$895$	−31.1120	+	1.36054i	−1.03996	+	0.0454777i
$896$	10.3369	+	30.9735i	0.345331	+	1.03475i
$897$		−	14.8333i		−	0.495269i
$898$	−6.42548	−	23.1795i	−0.214421	−	0.773510i
$899$		−	9.64107i		−	0.321548i
$900$	−17.0620	+	12.3941i	−0.568733	+	0.413136i
$901$	20.8771	+	53.4452i	0.695518	+	1.78052i
$902$	4.59070	+	16.5607i	0.152854	+	0.551410i
$903$			11.6655i			0.388203i
$904$	25.5218	−	26.8764i	0.848841	−	0.893896i
$905$	0.833052	+	19.0498i	0.0276916	+	0.633236i
$906$	−6.78186	−	24.4651i	−0.225312	−	0.812799i
$907$		−	14.4689i		−	0.480433i	−0.970719	−	0.240216i	$-0.922782\pi$
$907$		−	14.4689i		−	0.480433i	0.970719	−	0.240216i	$-0.0772184\pi$
$908$	−17.3384	−	28.8704i	−0.575395	−	0.958099i
$909$		−	28.1350i		−	0.933180i
$910$	−8.64513	−	26.6108i	−0.286583	−	0.882138i
$911$		−	12.4799i		−	0.413478i	−0.978396	−	0.206739i	$-0.933715\pi$
$911$		−	12.4799i		−	0.413478i	0.978396	−	0.206739i	$-0.0662852\pi$
$912$	−6.90568	+	12.9738i	−0.228670	+	0.429606i
$913$	7.27481			0.240761
$914$	9.96900	+	35.9625i	0.329745	+	1.18953i
$915$	−25.9442	+	1.13455i	−0.857690	+	0.0375070i
$916$	21.3339	+	35.5234i	0.704892	+	1.17373i
$917$	27.9465			0.922874
$918$	22.5088	−	16.8574i	0.742899	−	0.556379i
$919$	25.5411			0.842524			0.421262	−	0.906939i	$-0.361587\pi$
$919$	25.5411			0.842524			0.421262	+	0.906939i	$0.361587\pi$
$920$	24.4593	+	21.2735i	0.806399	+	0.701365i
$921$			20.1765i			0.664839i
$922$	−5.72565	−	20.6549i	−0.188564	−	0.680233i
$923$		−	24.4754i		−	0.805617i
$924$	8.04861	+	13.4019i	0.264780	+	0.440889i
$925$	−3.08887	−	35.2498i	−0.101562	−	1.15901i
$926$	6.43494	+	23.2136i	0.211465	+	0.762848i
$927$		−	33.7820i		−	1.10955i
$928$	3.38845	−	15.2443i	0.111231	−	0.500419i
$929$			50.9512i			1.67165i	0.548993	+	0.835827i	$0.315012\pi$
$929$			50.9512i			1.67165i	−0.548993	+	0.835827i	$0.684988\pi$
$930$	3.22124	+	9.91537i	0.105629	+	0.325138i
$931$		−	5.17582i		−	0.169631i
$932$	−4.54888	+	2.73187i	−0.149004	+	0.0894854i
$933$	−0.489547			−0.0160270
$934$	5.99347	−	1.66142i	0.196112	−	0.0543634i
$935$	24.1933	−	10.6911i	0.791204	−	0.349637i
$936$	−12.5917	+	13.2600i	−0.411572	+	0.433417i
$937$		−	44.2126i		−	1.44436i	−0.691703	−	0.722182i	$-0.743139\pi$
$937$		−	44.2126i		−	1.44436i	0.691703	−	0.722182i	$-0.256861\pi$
$938$	21.1490	−	5.86262i	0.690540	−	0.191421i
$939$			21.7692i			0.710412i
$940$	−2.18644	+	1.44669i	−0.0713138	+	0.0471860i
$941$	−10.6780			−0.348092			−0.174046	−	0.984738i	$-0.555684\pi$
$941$	−10.6780			−0.348092			−0.174046	+	0.984738i	$0.555684\pi$
$942$	3.16099	+	11.4031i	0.102991	+	0.371532i
$943$		−	21.7097i		−	0.706964i
$944$	26.4840	+	14.0969i	0.861980	+	0.458814i
$945$	31.0946	−	1.35978i	1.01151	−	0.0442335i
$946$	16.7405	−	4.64056i	0.544281	−	0.150878i
$947$			10.5198i			0.341848i	0.985284	+	0.170924i	$0.0546753\pi$
$947$			10.5198i			0.341848i	−0.985284	+	0.170924i	$0.945325\pi$
$948$	18.8712	−	11.3332i	0.612907	−	0.368086i
$949$	−41.1923			−1.33716
$950$	9.63922	+	25.7791i	0.312738	+	0.836384i
$951$	−15.2026			−0.492978
$952$	−31.1668	−	12.7076i	−1.01012	−	0.411855i
$953$		−	5.19626i		−	0.168323i	−0.996452	−	0.0841616i	$-0.973179\pi$
$953$		−	5.19626i		−	0.168323i	0.996452	−	0.0841616i	$-0.0268212\pi$
$954$	39.9951	−	11.0868i	1.29489	−	0.358950i
$955$	1.85401	+	42.3966i	0.0599944	+	1.37192i
$956$	11.6572	−	7.00081i	0.377020	−	0.226423i
$957$		−	7.47652i		−	0.241682i
$958$	−3.11577	−	11.2400i	−0.100666	−	0.363147i
$959$		−	51.8211i		−	1.67339i
$960$	1.60852	+	16.8101i	0.0519148	+	0.542545i
$961$	18.8033			0.606558
$962$	−8.19627	−	29.5675i	−0.264258	−	0.953295i
$963$		−	22.2677i		−	0.717567i
$964$	6.98065	+	11.6236i	0.224831	+	0.374370i
$965$	−1.02095	−	23.3465i	−0.0328654	−	0.751549i
$966$	−5.27553	−	19.0311i	−0.169737	−	0.612317i
$967$		−	10.2630i		−	0.330036i	−0.986291	−	0.165018i	$-0.947232\pi$
$967$		−	10.2630i		−	0.330036i	0.986291	−	0.165018i	$-0.0527682\pi$
$968$	−5.39350	+	5.67978i	−0.173354	+	0.182555i
$969$	−5.51219	−	14.1111i	−0.177077	−	0.453315i
$970$	−5.07729	−	15.6285i	−0.163022	−	0.501801i
$971$			3.83731i			0.123145i	0.998103	+	0.0615726i	$0.0196116\pi$
$971$			3.83731i			0.123145i	−0.998103	+	0.0615726i	$0.980388\pi$
$972$	−16.6222	−	27.6779i	−0.533158	−	0.887770i
$973$	23.1511			0.742190
$974$	40.3964	−	11.1981i	1.29438	−	0.358810i
$975$	−1.26315	−	14.4149i	−0.0404533	−	0.461647i
$976$	23.1221	−	43.4398i	0.740119	−	1.39047i
$977$			35.7392i			1.14340i	0.820463	+	0.571700i	$0.193716\pi$
$977$			35.7392i			1.14340i	−0.820463	+	0.571700i	$0.806284\pi$
$978$	20.2834	−	5.62266i	0.648591	−	0.179793i
$979$	−29.2987			−0.936391
$980$	−3.28159	−	4.95958i	−0.104826	−	0.158428i
$981$	−19.9743			−0.637729
$982$	12.9570	+	46.7417i	0.413476	+	1.49159i
$983$	−7.72185			−0.246289			−0.123144	−	0.992389i	$-0.539298\pi$
$983$	−7.72185			−0.246289			−0.123144	+	0.992389i	$0.539298\pi$
$984$	7.78761	−	8.20096i	0.248260	−	0.261437i
$985$	7.55362	−	0.330322i	0.240678	−	0.0105249i
$986$	9.64934	+	12.8842i	0.307297	+	0.410316i
$987$	1.59722			0.0508401
$988$	12.2867	+	20.4589i	0.390894	+	0.650883i
$989$	−21.9454			−0.697824
$990$	−5.91142	−	18.1961i	−0.187877	−	0.578309i
$991$			37.2508i			1.18331i	0.806192	+	0.591655i	$0.201525\pi$
$991$			37.2508i			1.18331i	−0.806192	+	0.591655i	$0.798475\pi$
$992$	−19.2852	−	4.28664i	−0.612306	−	0.136101i
$993$	10.6978			0.339484
$994$	−8.70478	−	31.4020i	−0.276099	−	0.996009i
$995$	−1.37724	+	0.0602272i	−0.0436615	+	0.00190933i
$996$	−2.46483	−	4.10422i	−0.0781010	−	0.130047i
$997$			6.30628i			0.199722i	0.995001	+	0.0998610i	$0.0318398\pi$
$997$			6.30628i			0.199722i	−0.995001	+	0.0998610i	$0.968160\pi$
$998$	−3.14624	+	0.872155i	−0.0995926	+	0.0276076i
$999$	34.1308			1.07985

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.h.b.509.37	yes	40
5.4	even	2	inner	680.2.h.b.509.4	yes	40
8.5	even	2	inner	680.2.h.b.509.2	yes	40
17.16	even	2	inner	680.2.h.b.509.38	yes	40
40.29	even	2	inner	680.2.h.b.509.39	yes	40
85.84	even	2	inner	680.2.h.b.509.3	yes	40
136.101	even	2	inner	680.2.h.b.509.1	✓	40
680.509	even	2	inner	680.2.h.b.509.40	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.h.b.509.1	✓	40	136.101	even	2	inner
680.2.h.b.509.2	yes	40	8.5	even	2	inner
680.2.h.b.509.3	yes	40	85.84	even	2	inner
680.2.h.b.509.4	yes	40	5.4	even	2	inner
680.2.h.b.509.37	yes	40	1.1	even	1	trivial
680.2.h.b.509.38	yes	40	17.16	even	2	inner
680.2.h.b.509.39	yes	40	40.29	even	2	inner
680.2.h.b.509.40	yes	40	680.509	even	2	inner

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36282 - 0.377781i) q^{2} -0.944008i q^{3} +(1.71456 - 1.02970i) q^{4} +(-0.0976904 - 2.23393i) q^{5} +(-0.356628 - 1.28651i) q^{6} -2.88614 q^{7} +(1.94764 - 2.05102i) q^{8} +2.10885 q^{9} +(-0.977072 - 3.00755i) q^{10} +2.86893 q^{11} +(-0.972041 - 1.61856i) q^{12} -3.06569 q^{13} +(-3.93329 + 1.09033i) q^{14} +(-2.10885 + 0.0922205i) q^{15} +(1.87945 - 3.53096i) q^{16} +(1.50020 + 3.84050i) q^{17} +(2.87398 - 0.796683i) q^{18} -3.89224i q^{19} +(-2.46777 - 3.72963i) q^{20} +2.72453i q^{21} +(3.90984 - 1.08383i) q^{22} -5.12547 q^{23} +(-1.93618 - 1.83859i) q^{24} +(-4.98091 + 0.436468i) q^{25} +(-4.17799 + 1.15816i) q^{26} -4.82279i q^{27} +(-4.94846 + 2.97184i) q^{28} +2.76061 q^{29} +(-2.83915 + 0.922364i) q^{30} -3.49238i q^{31} +(1.22743 - 5.52208i) q^{32} -2.70829i q^{33} +(3.49537 + 4.66716i) q^{34} +(0.281948 + 6.44743i) q^{35} +(3.61576 - 2.17147i) q^{36} +7.07698i q^{37} +(-1.47041 - 5.30443i) q^{38} +2.89404i q^{39} +(-4.77211 - 4.15054i) q^{40} +4.23564i q^{41} +(1.02928 + 3.71305i) q^{42} +4.28164 q^{43} +(4.91896 - 2.95413i) q^{44} +(-0.206014 - 4.71103i) q^{45} +(-6.98510 + 1.93631i) q^{46} -0.586236i q^{47} +(-3.33325 - 1.77422i) q^{48} +1.32978 q^{49} +(-6.62320 + 2.47652i) q^{50} +(3.62546 - 1.41620i) q^{51} +(-5.25632 + 3.15673i) q^{52} +13.9162 q^{53} +(-1.82196 - 6.57260i) q^{54} +(-0.280267 - 6.40900i) q^{55} +(-5.62116 + 5.91952i) q^{56} -3.67430 q^{57} +(3.76221 - 1.04290i) q^{58} +7.50051i q^{59} +(-3.52080 + 2.32959i) q^{60} +12.3026 q^{61} +(-1.31935 - 4.75948i) q^{62} -6.08643 q^{63} +(-0.413374 - 7.98931i) q^{64} +(0.299489 + 6.84855i) q^{65} +(-1.02314 - 3.69092i) q^{66} -5.37694 q^{67} +(6.52673 + 5.04002i) q^{68} +4.83848i q^{69} +(2.81996 + 8.68018i) q^{70} +7.98364i q^{71} +(4.10729 - 4.32529i) q^{72} +13.4366 q^{73} +(2.67355 + 9.64466i) q^{74} +(0.412029 + 4.70202i) q^{75} +(-4.00782 - 6.67349i) q^{76} -8.28012 q^{77} +(1.09331 + 3.94405i) q^{78} +11.6592i q^{79} +(-8.07153 - 3.85363i) q^{80} +1.77380 q^{81} +(1.60015 + 5.77242i) q^{82} +2.53572 q^{83} +(2.80544 + 4.67138i) q^{84} +(8.43285 - 3.72652i) q^{85} +(5.83511 - 1.61752i) q^{86} -2.60603i q^{87} +(5.58765 - 5.88423i) q^{88} -10.2124 q^{89} +(-2.06050 - 6.34246i) q^{90} +8.84800 q^{91} +(-8.78794 + 5.27768i) q^{92} -3.29683 q^{93} +(-0.221469 - 0.798935i) q^{94} +(-8.69500 + 0.380235i) q^{95} +(-5.21289 - 1.15870i) q^{96} +5.19643 q^{97} +(1.81225 - 0.502365i) q^{98} +6.05014 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{4} - 56 q^{9} + 56 q^{15} - 4 q^{16} - 36 q^{26} - 28 q^{30} + 24 q^{34} + 88 q^{36} + 8 q^{49} - 16 q^{50} - 88 q^{55} - 88 q^{60} - 132 q^{64} + 208 q^{66} + 72 q^{70} - 20 q^{76} - 56 q^{81}+ \cdots - 36 q^{94}+O(q^{100}) \) 40 * q + 12 * q^4 - 56 * q^9 + 56 * q^15 - 4 * q^16 - 36 * q^26 - 28 * q^30 + 24 * q^34 + 88 * q^36 + 8 * q^49 - 16 * q^50 - 88 * q^55 - 88 * q^60 - 132 * q^64 + 208 * q^66 + 72 * q^70 - 20 * q^76 - 56 * q^81 + 144 * q^84 + 256 * q^86 - 96 * q^89 - 36 * q^94

Introduction

L-functions

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