LMFDB - Embedded newform 784.2.bg.c.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(65,784)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 0, 20]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("784.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bg (of order $21$, degree $12$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			81.2
Character	$\chi$	$=$	784.81
Dual form			784.2.bg.c.513.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.269714 + 0.0831957i) q^{3} +(-1.49036 + 1.38285i) q^{5} +(0.607511 + 2.57506i) q^{7} +(-2.41289 - 1.64508i) q^{9} +O(q^{10})$	\(q+(0.269714 + 0.0831957i) q^{3} +(-1.49036 + 1.38285i) q^{5} +(0.607511 + 2.57506i) q^{7} +(-2.41289 - 1.64508i) q^{9} +(-1.64705 + 1.12294i) q^{11} +(-3.26094 - 1.57038i) q^{13} +(-0.517018 + 0.248983i) q^{15} +(-0.409339 - 1.04298i) q^{17} +(-3.73687 - 6.47246i) q^{19} +(-0.0503796 + 0.745071i) q^{21} +(1.94485 - 4.95539i) q^{23} +(-0.0647567 + 0.864118i) q^{25} +(-1.04187 - 1.30647i) q^{27} +(1.28279 - 1.60857i) q^{29} +(-2.48025 + 4.29592i) q^{31} +(-0.537654 + 0.165844i) q^{33} +(-4.46634 - 2.99767i) q^{35} +(0.814555 + 0.122774i) q^{37} +(-0.748870 - 0.694850i) q^{39} +(-1.33292 - 5.83991i) q^{41} +(-0.518849 + 2.27323i) q^{43} +(5.87099 - 0.884909i) q^{45} +(0.407053 + 5.43174i) q^{47} +(-6.26186 + 3.12876i) q^{49} +(-0.0236330 - 0.315360i) q^{51} +(-13.4919 + 2.03358i) q^{53} +(0.901837 - 3.95120i) q^{55} +(-0.469406 - 2.05660i) q^{57} +(-7.41658 - 6.88158i) q^{59} +(8.84072 + 1.33252i) q^{61} +(2.77032 - 7.21275i) q^{63} +(7.03159 - 2.16896i) q^{65} +(-5.76466 + 9.98468i) q^{67} +(0.936820 - 1.17473i) q^{69} +(2.62321 + 3.28940i) q^{71} +(-0.880793 + 11.7534i) q^{73} +(-0.0893566 + 0.227677i) q^{75} +(-3.89223 - 3.55904i) q^{77} +(4.13300 + 7.15857i) q^{79} +(3.02844 + 7.71633i) q^{81} +(-8.17636 + 3.93753i) q^{83} +(2.05235 + 0.988358i) q^{85} +(0.479814 - 0.327131i) q^{87} +(-14.5109 - 9.89337i) q^{89} +(2.06278 - 9.35113i) q^{91} +(-1.02636 + 0.952322i) q^{93} +(14.5198 + 4.47875i) q^{95} +3.72740 q^{97} +5.82147 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 14 q^{3} - 14 q^{5} + 14 q^{7} + 6 q^{9}+O(q^{10}) $ 48 * q + 14 * q^3 - 14 * q^5 + 14 * q^7 + 6 * q^9	$ 48 q + 14 q^{3} - 14 q^{5} + 14 q^{7} + 6 q^{9} + 3 q^{11} - 14 q^{13} + 12 q^{15} - 7 q^{17} - 21 q^{19} - 14 q^{21} - 15 q^{23} - 4 q^{25} - 7 q^{27} + 12 q^{29} - 35 q^{31} - 14 q^{33} + 15 q^{37} + 7 q^{39} - 42 q^{41} + 30 q^{43} + 7 q^{45} - 21 q^{47} - 70 q^{49} + 52 q^{51} + 11 q^{53} + 7 q^{55} - 12 q^{57} + 28 q^{59} + 7 q^{61} - 35 q^{63} + 14 q^{65} - 11 q^{67} + 70 q^{69} - 19 q^{71} + 7 q^{73} - 112 q^{75} + 7 q^{77} - 15 q^{79} + 64 q^{81} - 26 q^{85} + 112 q^{87} - 14 q^{89} - 84 q^{91} - 80 q^{93} + 61 q^{95} + 16 q^{99}+O(q^{100}) $ 48 * q + 14 * q^3 - 14 * q^5 + 14 * q^7 + 6 * q^9 + 3 * q^11 - 14 * q^13 + 12 * q^15 - 7 * q^17 - 21 * q^19 - 14 * q^21 - 15 * q^23 - 4 * q^25 - 7 * q^27 + 12 * q^29 - 35 * q^31 - 14 * q^33 + 15 * q^37 + 7 * q^39 - 42 * q^41 + 30 * q^43 + 7 * q^45 - 21 * q^47 - 70 * q^49 + 52 * q^51 + 11 * q^53 + 7 * q^55 - 12 * q^57 + 28 * q^59 + 7 * q^61 - 35 * q^63 + 14 * q^65 - 11 * q^67 + 70 * q^69 - 19 * q^71 + 7 * q^73 - 112 * q^75 + 7 * q^77 - 15 * q^79 + 64 * q^81 - 26 * q^85 + 112 * q^87 - 14 * q^89 - 84 * q^91 - 80 * q^93 + 61 * q^95 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{21}\right)$

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
$3$	0.269714	+	0.0831957i	0.155719	+	0.0480330i	0.371635	−	0.928379i	$-0.378797\pi$
$3$	0.269714	+	0.0831957i	0.155719	+	0.0480330i	−0.215915	+	0.976412i	$0.569274\pi$
$4$		0			0
$5$	−1.49036	+	1.38285i	−0.666510	+	0.618431i	−0.939077	−	0.343706i	$-0.888318\pi$
$5$	−1.49036	+	1.38285i	−0.666510	+	0.618431i	0.272568	+	0.962137i	$0.412127\pi$
$6$		0			0
$7$	0.607511	+	2.57506i	0.229618	+	0.973281i
$7$	0.607511	+	2.57506i	0.229618	+	0.973281i
$8$		0			0
$9$	−2.41289	−	1.64508i	−0.804297	−	0.548361i
$10$		0			0
$11$	−1.64705	+	1.12294i	−0.496603	+	0.338578i	−0.785582	−	0.618757i	$-0.787637\pi$
$11$	−1.64705	+	1.12294i	−0.496603	+	0.338578i	0.288979	+	0.957335i	$0.406684\pi$
$12$		0			0
$13$	−3.26094	−	1.57038i	−0.904421	−	0.435546i	−0.0769375	−	0.997036i	$-0.524514\pi$
$13$	−3.26094	−	1.57038i	−0.904421	−	0.435546i	−0.827484	+	0.561490i	$0.810228\pi$
$14$		0			0
$15$	−0.517018	+	0.248983i	−0.133494	+	0.0642871i
$16$		0			0
$17$	−0.409339	−	1.04298i	−0.0992792	−	0.252959i	0.872602	−	0.488433i	$-0.162431\pi$
$17$	−0.409339	−	1.04298i	−0.0992792	−	0.252959i	−0.971881	+	0.235473i	$0.924336\pi$
$18$		0			0
$19$	−3.73687	−	6.47246i	−0.857298	−	1.48488i	−0.874497	−	0.485031i	$-0.838808\pi$
$19$	−3.73687	−	6.47246i	−0.857298	−	1.48488i	0.0171988	−	0.999852i	$-0.494525\pi$
$20$		0			0
$21$	−0.0503796	+	0.745071i	−0.0109937	+	0.162588i
$22$		0			0
$23$	1.94485	−	4.95539i	0.405529	−	1.03327i	−0.571583	−	0.820544i	$-0.693670\pi$
$23$	1.94485	−	4.95539i	0.405529	−	1.03327i	0.977112	−	0.212727i	$-0.0682344\pi$
$24$		0			0
$25$	−0.0647567	+	0.864118i	−0.0129513	+	0.172824i
$26$		0			0
$27$	−1.04187	−	1.30647i	−0.200509	−	0.251430i
$28$		0			0
$29$	1.28279	−	1.60857i	0.238209	−	0.298705i	−0.648329	−	0.761360i	$-0.724532\pi$
$29$	1.28279	−	1.60857i	0.238209	−	0.298705i	0.886538	+	0.462656i	$0.153103\pi$
$30$		0			0
$31$	−2.48025	+	4.29592i	−0.445466	+	0.771570i	−0.998085	−	0.0618646i	$-0.980295\pi$
$31$	−2.48025	+	4.29592i	−0.445466	+	0.771570i	0.552619	+	0.833434i	$0.313629\pi$
$32$		0			0
$33$	−0.537654	+	0.165844i	−0.0935936	+	0.0288698i
$34$		0			0
$35$	−4.46634	−	2.99767i	−0.754949	−	0.506699i
$36$		0			0
$37$	0.814555	+	0.122774i	0.133912	+	0.0201840i	0.215656	−	0.976469i	$-0.430811\pi$
$37$	0.814555	+	0.122774i	0.133912	+	0.0201840i	−0.0817442	+	0.996653i	$0.526049\pi$
$38$		0			0
$39$	−0.748870	−	0.694850i	−0.119915	−	0.111265i
$40$		0			0
$41$	−1.33292	−	5.83991i	−0.208167	−	0.912041i	−0.965785	−	0.259343i	$-0.916494\pi$
$41$	−1.33292	−	5.83991i	−0.208167	−	0.912041i	0.757618	−	0.652698i	$-0.226363\pi$
$42$		0			0
$43$	−0.518849	+	2.27323i	−0.0791238	+	0.346664i	−0.998958	−	0.0456439i	$-0.985466\pi$
$43$	−0.518849	+	2.27323i	−0.0791238	+	0.346664i	0.919834	+	0.392308i	$0.128323\pi$
$44$		0			0
$45$	5.87099	−	0.884909i	0.875195	−	0.131914i
$46$		0			0
$47$	0.407053	+	5.43174i	0.0593748	+	0.792301i	0.944827	+	0.327570i	$0.106230\pi$
$47$	0.407053	+	5.43174i	0.0593748	+	0.792301i	−0.885452	+	0.464731i	$0.846151\pi$
$48$		0			0
$49$	−6.26186	+	3.12876i	−0.894551	+	0.446965i
$50$		0			0
$51$	−0.0236330	−	0.315360i	−0.00330928	−	0.0441593i
$52$		0			0
$53$	−13.4919	+	2.03358i	−1.85326	+	0.279334i	−0.978655	−	0.205509i	$-0.934115\pi$
$53$	−13.4919	+	2.03358i	−1.85326	+	0.279334i	−0.874602	+	0.484842i	$0.838877\pi$
$54$		0			0
$55$	0.901837	−	3.95120i	0.121604	−	0.532780i
$56$		0			0
$57$	−0.469406	−	2.05660i	−0.0621743	−	0.272404i
$58$		0			0
$59$	−7.41658	−	6.88158i	−0.965556	−	0.895905i	0.0290552	−	0.999578i	$-0.490750\pi$
$59$	−7.41658	−	6.88158i	−0.965556	−	0.895905i	−0.994611	+	0.103673i	$0.966941\pi$
$60$		0			0
$61$	8.84072	+	1.33252i	1.13194	+	0.170612i	0.688184	−	0.725536i	$-0.258408\pi$
$61$	8.84072	+	1.33252i	1.13194	+	0.170612i	0.443754	+	0.896149i	$0.353646\pi$
$62$		0			0
$63$	2.77032	−	7.21275i	0.349028	−	0.908721i
$64$		0			0
$65$	7.03159	−	2.16896i	0.872161	−	0.269026i
$66$		0			0
$67$	−5.76466	+	9.98468i	−0.704265	+	1.21982i	0.262691	+	0.964880i	$0.415390\pi$
$67$	−5.76466	+	9.98468i	−0.704265	+	1.21982i	−0.966956	+	0.254943i	$0.917943\pi$
$68$		0			0
$69$	0.936820	−	1.17473i	0.112780	−	0.141421i
$70$		0			0
$71$	2.62321	+	3.28940i	0.311318	+	0.390380i	0.912733	−	0.408556i	$-0.133968\pi$
$71$	2.62321	+	3.28940i	0.311318	+	0.390380i	−0.601415	+	0.798937i	$0.705396\pi$
$72$		0			0
$73$	−0.880793	+	11.7534i	−0.103089	+	1.37563i	0.670486	+	0.741922i	$0.266086\pi$
$73$	−0.880793	+	11.7534i	−0.103089	+	1.37563i	−0.773575	+	0.633705i	$0.781533\pi$
$74$		0			0
$75$	−0.0893566	+	0.227677i	−0.0103180	+	0.0262899i
$76$		0			0
$77$	−3.89223	−	3.55904i	−0.443561	−	0.405591i
$78$		0			0
$79$	4.13300	+	7.15857i	0.464999	+	0.805402i	0.999201	−	0.0399547i	$-0.0127214\pi$
$79$	4.13300	+	7.15857i	0.464999	+	0.805402i	−0.534203	+	0.845357i	$0.679388\pi$
$80$		0			0
$81$	3.02844	+	7.71633i	0.336493	+	0.857370i
$82$		0			0
$83$	−8.17636	+	3.93753i	−0.897472	+	0.432200i	−0.824975	−	0.565169i	$-0.808811\pi$
$83$	−8.17636	+	3.93753i	−0.897472	+	0.432200i	−0.0724970	+	0.997369i	$0.523097\pi$
$84$		0			0
$85$	2.05235	+	0.988358i	0.222608	+	0.107202i
$86$		0			0
$87$	0.479814	−	0.327131i	0.0514414	−	0.0350722i
$88$		0			0
$89$	−14.5109	−	9.89337i	−1.53815	−	1.04870i	−0.974963	−	0.222369i	$-0.928621\pi$
$89$	−14.5109	−	9.89337i	−1.53815	−	1.04870i	−0.563191	−	0.826327i	$-0.690426\pi$
$90$		0			0
$91$	2.06278	−	9.35113i	0.216238	−	0.980265i
$92$		0			0
$93$	−1.02636	+	0.952322i	−0.106428	+	0.0987512i
$94$		0			0
$95$	14.5198	+	4.47875i	1.48969	+	0.459510i
$96$		0			0
$97$	3.72740			0.378460			0.189230	−	0.981933i	$-0.439401\pi$
$97$	3.72740			0.378460			0.189230	+	0.981933i	$0.439401\pi$
$98$		0			0
$99$	5.82147			0.585080
$100$		0			0
$101$	−3.43384	−	1.05920i	−0.341679	−	0.105394i	0.119167	−	0.992874i	$-0.461978\pi$
$101$	−3.43384	−	1.05920i	−0.341679	−	0.105394i	−0.460846	+	0.887480i	$0.652454\pi$
$102$		0			0
$103$	5.42624	−	5.03481i	0.534663	−	0.496095i	−0.365999	−	0.930615i	$-0.619273\pi$
$103$	5.42624	−	5.03481i	0.534663	−	0.496095i	0.900662	+	0.434521i	$0.143082\pi$
$104$		0			0
$105$	−0.955240	−	1.18009i	−0.0932219	−	0.115165i
$106$		0			0
$107$	3.64697	+	2.48646i	0.352566	+	0.240375i	0.726632	−	0.687027i	$-0.241084\pi$
$107$	3.64697	+	2.48646i	0.352566	+	0.240375i	−0.374066	+	0.927402i	$0.622037\pi$
$108$		0			0
$109$	3.55236	−	2.42196i	0.340255	−	0.231982i	−0.381122	−	0.924525i	$-0.624462\pi$
$109$	3.55236	−	2.42196i	0.340255	−	0.231982i	0.721376	+	0.692543i	$0.243510\pi$
$110$		0			0
$111$	0.209482	+	0.100881i	0.0198832	+	0.00957523i
$112$		0			0
$113$	11.2558	−	5.42048i	1.05885	−	0.509916i	0.178354	−	0.983966i	$-0.442923\pi$
$113$	11.2558	−	5.42048i	1.05885	−	0.509916i	0.880498	+	0.474050i	$0.157208\pi$
$114$		0			0
$115$	3.95406	+	10.0748i	0.368718	+	0.939477i
$116$		0			0
$117$	5.28488	+	9.15368i	0.488587	+	0.846258i
$118$		0			0
$119$	2.43705	−	1.68769i	0.223404	−	0.154710i
$120$		0			0
$121$	−2.56698	+	6.54055i	−0.233362	+	0.594596i
$122$		0			0
$123$	0.126348	−	1.68600i	0.0113924	−	0.152021i
$124$		0			0
$125$	−7.43649	−	9.32507i	−0.665140	−	0.834060i
$126$		0			0
$127$	3.46997	−	4.35120i	0.307910	−	0.386107i	−0.603667	−	0.797237i	$-0.706294\pi$
$127$	3.46997	−	4.35120i	0.307910	−	0.386107i	0.911577	+	0.411130i	$0.134866\pi$
$128$		0			0
$129$	−0.329063	+	0.569955i	−0.0289724	+	0.0501817i
$130$		0			0
$131$	−14.2825	+	4.40556i	−1.24787	+	0.384916i	−0.847183	−	0.531301i	$-0.821703\pi$
$131$	−14.2825	+	4.40556i	−1.24787	+	0.384916i	−0.400683	+	0.916217i	$0.631227\pi$
$132$		0			0
$133$	14.3968	−	13.5548i	1.24836	−	1.17535i
$134$		0			0
$135$	3.35942	+	0.506351i	0.289133	+	0.0435797i
$136$		0			0
$137$	−0.612467	−	0.568286i	−0.0523266	−	0.0485520i	0.653576	−	0.756861i	$-0.273268\pi$
$137$	−0.612467	−	0.568286i	−0.0523266	−	0.0485520i	−0.705903	+	0.708309i	$0.749458\pi$
$138$		0			0
$139$	−1.31718	−	5.77093i	−0.111721	−	0.489484i	−0.999569	−	0.0293465i	$-0.990657\pi$
$139$	−1.31718	−	5.77093i	−0.111721	−	0.489484i	0.887848	−	0.460137i	$-0.152200\pi$
$140$		0			0
$141$	−0.342110	+	1.49888i	−0.0288108	+	0.126229i
$142$		0			0
$143$	7.13436	−	1.07533i	0.596605	−	0.0899237i
$144$		0			0
$145$	0.312594	+	4.17127i	0.0259595	+	0.346405i
$146$		0			0
$147$	−1.94921	+	0.322909i	−0.160768	+	0.0266331i
$148$		0			0
$149$	0.681223	+	9.09029i	0.0558079	+	0.744705i	0.952982	+	0.303028i	$0.0979974\pi$
$149$	0.681223	+	9.09029i	0.0558079	+	0.744705i	−0.897174	+	0.441678i	$0.854384\pi$
$150$		0			0
$151$	−2.87758	+	0.433725i	−0.234174	+	0.0352960i	−0.265081	−	0.964226i	$-0.585399\pi$
$151$	−2.87758	+	0.433725i	−0.234174	+	0.0352960i	0.0309069	+	0.999522i	$0.490160\pi$
$152$		0			0
$153$	−0.728094	+	3.18999i	−0.0588629	+	0.257895i
$154$		0			0
$155$	−2.24416	−	9.83229i	−0.180255	−	0.789749i
$156$		0			0
$157$	3.88611	+	3.60578i	0.310145	+	0.287773i	0.819852	−	0.572576i	$-0.194056\pi$
$157$	3.88611	+	3.60578i	0.310145	+	0.287773i	−0.509707	+	0.860348i	$0.670246\pi$
$158$		0			0
$159$	−3.80814	−	0.573985i	−0.302005	−	0.0455199i
$160$		0			0
$161$	13.9420	+	1.99764i	1.09878	+	0.157436i
$162$		0			0
$163$	4.04529	−	1.24781i	0.316851	−	0.0977356i	−0.132250	−	0.991216i	$-0.542220\pi$
$163$	4.04529	−	1.24781i	0.316851	−	0.0977356i	0.449102	+	0.893481i	$0.351744\pi$
$164$		0			0
$165$	0.571961	−	0.990665i	0.0445271	−	0.0771232i
$166$		0			0
$167$	−5.46726	+	6.85572i	−0.423069	+	0.530512i	−0.946993	−	0.321253i	$-0.895896\pi$
$167$	−5.46726	+	6.85572i	−0.423069	+	0.530512i	0.523924	+	0.851765i	$0.324467\pi$
$168$		0			0
$169$	0.0622382	+	0.0780442i	0.00478755	+	0.00600340i
$170$		0			0
$171$	−1.63105	+	21.7648i	−0.124729	+	1.66440i
$172$		0			0
$173$	1.39588	−	3.55665i	0.106127	−	0.270407i	−0.867939	−	0.496670i	$-0.834556\pi$
$173$	1.39588	−	3.55665i	0.106127	−	0.270407i	0.974066	+	0.226264i	$0.0726511\pi$
$174$		0			0
$175$	−2.26450	+	0.358209i	−0.171180	+	0.0270781i
$176$		0			0
$177$	−1.42784	−	2.47308i	−0.107323	−	0.185888i
$178$		0			0
$179$	−2.23558	−	5.69617i	−0.167095	−	0.425752i	0.822659	−	0.568536i	$-0.192490\pi$
$179$	−2.23558	−	5.69617i	−0.167095	−	0.425752i	−0.989754	+	0.142784i	$0.954395\pi$
$180$		0			0
$181$	−20.2282	+	9.74138i	−1.50355	+	0.724071i	−0.990909	−	0.134533i	$-0.957047\pi$
$181$	−20.2282	+	9.74138i	−1.50355	+	0.724071i	−0.512639	+	0.858604i	$0.671332\pi$
$182$		0			0
$183$	2.27360	+	1.09491i	0.168069	+	0.0809380i
$184$		0			0
$185$	−1.38376	+	0.943431i	−0.101736	+	0.0693624i
$186$		0			0
$187$	1.84540	+	1.25817i	0.134949	+	0.0920066i
$188$		0			0
$189$	2.73128	−	3.47658i	0.198671	−	0.252884i
$190$		0			0
$191$	10.4264	−	9.67431i	0.754429	−	0.700008i	−0.205994	−	0.978553i	$-0.566043\pi$
$191$	10.4264	−	9.67431i	0.754429	−	0.700008i	0.960423	+	0.278545i	$0.0898522\pi$
$192$		0			0
$193$	6.27185	+	1.93461i	0.451457	+	0.139256i	0.512142	−	0.858901i	$-0.328852\pi$
$193$	6.27185	+	1.93461i	0.451457	+	0.139256i	−0.0606845	+	0.998157i	$0.519328\pi$
$194$		0			0
$195$	2.07696			0.148734
$196$		0			0
$197$	17.7880			1.26734			0.633670	−	0.773603i	$-0.281548\pi$
$197$	17.7880			1.26734			0.633670	+	0.773603i	$0.281548\pi$
$198$		0			0
$199$	15.0295	+	4.63598i	1.06541	+	0.328636i	0.777410	−	0.628994i	$-0.216533\pi$
$199$	15.0295	+	4.63598i	1.06541	+	0.328636i	0.288002	+	0.957630i	$0.407009\pi$
$200$		0			0
$201$	−2.38549	+	2.21341i	−0.168259	+	0.156122i
$202$		0			0
$203$	4.92148	+	2.32605i	0.345421	+	0.163256i
$204$		0			0
$205$	10.0623	+	6.86034i	0.702779	+	0.479147i
$206$		0			0
$207$	−12.8447	+	8.75740i	−0.892771	+	0.608681i
$208$		0			0
$209$	13.4230	+	6.46416i	0.928486	+	0.447135i
$210$		0			0
$211$	8.40082	−	4.04562i	0.578336	−	0.278512i	−0.121761	−	0.992559i	$-0.538854\pi$
$211$	8.40082	−	4.04562i	0.578336	−	0.278512i	0.700097	+	0.714047i	$0.253140\pi$
$212$		0			0
$213$	0.433852	+	1.10544i	0.0297270	+	0.0757432i
$214$		0			0
$215$	−2.37027	−	4.10542i	−0.161651	−	0.279988i
$216$		0			0
$217$	−12.5690	−	3.77697i	−0.853241	−	0.256397i
$218$		0			0
$219$	−1.21539	+	3.09677i	−0.0821285	+	0.209260i
$220$		0			0
$221$	−0.303049	+	4.04390i	−0.0203853	+	0.272022i
$222$		0			0
$223$	3.60573	+	4.52144i	0.241457	+	0.302778i	0.887763	−	0.460301i	$-0.152258\pi$
$223$	3.60573	+	4.52144i	0.241457	+	0.302778i	−0.646306	+	0.763079i	$0.723687\pi$
$224$		0			0
$225$	1.57780	−	1.97849i	0.105186	−	0.131900i
$226$		0			0
$227$	6.63933	−	11.4997i	0.440668	−	0.763259i	−0.557071	−	0.830465i	$-0.688075\pi$
$227$	6.63933	−	11.4997i	0.440668	−	0.763259i	0.997739	+	0.0672056i	$0.0214083\pi$
$228$		0			0
$229$	−20.4642	+	6.31236i	−1.35231	+	0.417132i	−0.884436	−	0.466662i	$-0.845456\pi$
$229$	−20.4642	+	6.31236i	−1.35231	+	0.417132i	−0.467875	+	0.883795i	$0.654980\pi$
$230$		0			0
$231$	−0.753690	−	1.28374i	−0.0495892	−	0.0844639i
$232$		0			0
$233$	23.6339	+	3.56224i	1.54831	+	0.233370i	0.866881	−	0.498514i	$-0.166121\pi$
$233$	23.6339	+	3.56224i	1.54831	+	0.233370i	0.681429	+	0.731885i	$0.261359\pi$
$234$		0			0
$235$	−8.11796	−	7.53237i	−0.529557	−	0.491357i
$236$		0			0
$237$	0.519165	+	2.27461i	0.0337234	+	0.147752i
$238$		0			0
$239$	2.60391	−	11.4085i	0.168433	−	0.737954i	−0.818192	−	0.574946i	$-0.805023\pi$
$239$	2.60391	−	11.4085i	0.168433	−	0.737954i	0.986625	−	0.163008i	$-0.0521197\pi$
$240$		0			0
$241$	12.7510	−	1.92191i	0.821366	−	0.123801i	0.275103	−	0.961415i	$-0.411288\pi$
$241$	12.7510	−	1.92191i	0.821366	−	0.123801i	0.546263	+	0.837614i	$0.316050\pi$
$242$		0			0
$243$	0.549475	+	7.33224i	0.0352489	+	0.470363i
$244$		0			0
$245$	5.00582	−	13.3222i	0.319810	−	0.851125i
$246$		0			0
$247$	2.02147	+	26.9746i	0.128623	+	1.71635i
$248$		0			0
$249$	−2.53286	+	0.381768i	−0.160514	+	0.0241935i
$250$		0			0
$251$	2.83406	−	12.4168i	0.178884	−	0.783744i	−0.803262	−	0.595626i	$-0.796904\pi$
$251$	2.83406	−	12.4168i	0.178884	−	0.783744i	0.982146	−	0.188118i	$-0.0602387\pi$
$252$		0			0
$253$	2.36134	+	10.3457i	0.148456	+	0.650429i
$254$		0			0
$255$	0.471319	+	0.437320i	0.0295151	+	0.0273860i
$256$		0			0
$257$	−15.8576	−	2.39015i	−0.989172	−	0.149094i	−0.365526	−	0.930801i	$-0.619111\pi$
$257$	−15.8576	−	2.39015i	−0.989172	−	0.149094i	−0.623645	+	0.781707i	$0.714349\pi$
$258$		0			0
$259$	0.178700	+	2.17211i	0.0111039	+	0.134969i
$260$		0			0
$261$	−5.74148	+	1.77101i	−0.355389	+	0.109623i
$262$		0			0
$263$	−3.50137	+	6.06455i	−0.215904	+	0.373956i	−0.953552	−	0.301229i	$-0.902603\pi$
$263$	−3.50137	+	6.06455i	−0.215904	+	0.373956i	0.737648	+	0.675185i	$0.235936\pi$
$264$		0			0
$265$	17.2957	−	21.6881i	1.06247	−	1.33229i
$266$		0			0
$267$	−3.09071	−	3.87562i	−0.189148	−	0.237184i
$268$		0			0
$269$	−1.42342	+	18.9942i	−0.0867874	+	1.15810i	0.768467	+	0.639890i	$0.221020\pi$
$269$	−1.42342	+	18.9942i	−0.0867874	+	1.15810i	−0.855254	+	0.518208i	$0.826599\pi$
$270$		0			0
$271$	−3.40664	+	8.67999i	−0.206939	+	0.527272i	−0.996230	−	0.0867470i	$-0.972353\pi$
$271$	−3.40664	+	8.67999i	−0.206939	+	0.527272i	0.789291	+	0.614019i	$0.210448\pi$
$272$		0			0
$273$	1.33433	−	2.35051i	0.0807575	−	0.142260i
$274$		0			0
$275$	−0.863693	−	1.49596i	−0.0520826	−	0.0902098i
$276$		0			0
$277$	−2.82229	−	7.19108i	−0.169575	−	0.432070i	0.820671	−	0.571401i	$-0.193600\pi$
$277$	−2.82229	−	7.19108i	−0.169575	−	0.432070i	−0.990246	+	0.139331i	$0.955505\pi$
$278$		0			0
$279$	13.0517	−	6.28537i	0.781386	−	0.376296i
$280$		0			0
$281$	−26.3988	−	12.7130i	−1.57482	−	0.758394i	−0.576544	−	0.817066i	$-0.695599\pi$
$281$	−26.3988	−	12.7130i	−1.57482	−	0.758394i	−0.998277	+	0.0586722i	$0.981313\pi$
$282$		0			0
$283$	3.34674	−	2.28177i	0.198943	−	0.135637i	−0.459751	−	0.888048i	$-0.652061\pi$
$283$	3.34674	−	2.28177i	0.198943	−	0.135637i	0.658694	+	0.752411i	$0.271109\pi$
$284$		0			0
$285$	3.54356	+	2.41596i	0.209903	+	0.143109i
$286$		0			0
$287$	14.2283	−	6.98016i	0.839873	−	0.412026i
$288$		0			0
$289$	11.5416	−	10.7091i	0.678920	−	0.629946i
$290$		0			0
$291$	1.00533	+	0.310103i	0.0589335	+	0.0181786i
$292$		0			0
$293$	−6.82335			−0.398624			−0.199312	−	0.979936i	$-0.563871\pi$
$293$	−6.82335			−0.398624			−0.199312	+	0.979936i	$0.563871\pi$
$294$		0			0
$295$	20.5696			1.19761
$296$		0			0
$297$	3.18309	+	0.981854i	0.184702	+	0.0569730i
$298$		0			0
$299$	−14.1239	+	13.1051i	−0.816807	+	0.757886i
$300$		0			0
$301$	−6.16890	+	0.0449441i	−0.355570	+	0.00259053i
$302$		0			0
$303$	−0.838032	−	0.571360i	−0.0481437	−	0.0328238i
$304$		0			0
$305$	−15.0185	+	10.2395i	−0.859959	+	0.586310i
$306$		0			0
$307$	−24.0748	−	11.5938i	−1.37402	−	0.661694i	−0.406306	−	0.913737i	$-0.633183\pi$
$307$	−24.0748	−	11.5938i	−1.37402	−	0.661694i	−0.967716	+	0.252043i	$0.918898\pi$
$308$		0			0
$309$	1.88240	−	0.906518i	0.107086	−	0.0515700i
$310$		0			0
$311$	1.49322	+	3.80465i	0.0846725	+	0.215742i	0.966939	−	0.255009i	$-0.0820784\pi$
$311$	1.49322	+	3.80465i	0.0846725	+	0.215742i	−0.882266	+	0.470751i	$0.843983\pi$
$312$		0			0
$313$	−13.7747	−	23.8585i	−0.778593	−	1.34856i	−0.932752	−	0.360517i	$-0.882600\pi$
$313$	−13.7747	−	23.8585i	−0.778593	−	1.34856i	0.154159	−	0.988046i	$-0.450733\pi$
$314$		0			0
$315$	5.84539	+	14.5805i	0.329350	+	0.821521i
$316$		0			0
$317$	2.31786	−	5.90580i	0.130184	−	0.331703i	−0.850888	−	0.525347i	$-0.823935\pi$
$317$	2.31786	−	5.90580i	0.130184	−	0.331703i	0.981072	+	0.193644i	$0.0620307\pi$
$318$		0			0
$319$	−0.306495	+	4.08989i	−0.0171604	+	0.228990i
$320$		0			0
$321$	0.776775	+	0.974045i	0.0433554	+	0.0543659i
$322$		0			0
$323$	−5.22098	+	6.54690i	−0.290503	+	0.364279i
$324$		0			0
$325$	1.56817	−	2.71614i	0.0869862	−	0.150664i
$326$		0			0
$327$	1.15962	−	0.357694i	0.0641270	−	0.0197806i
$328$		0			0
$329$	−13.7398	+	4.34803i	−0.757498	+	0.239715i
$330$		0			0
$331$	−5.92680	−	0.893321i	−0.325766	−	0.0491014i	−0.0158769	−	0.999874i	$-0.505054\pi$
$331$	−5.92680	−	0.893321i	−0.325766	−	0.0491014i	−0.309890	+	0.950773i	$0.600292\pi$
$332$		0			0
$333$	−1.76346	−	1.63625i	−0.0966369	−	0.0896660i
$334$		0			0
$335$	−5.21592	−	22.8525i	−0.284976	−	1.24856i
$336$		0			0
$337$	−1.51230	+	6.62581i	−0.0823801	+	0.360931i	−0.999270	−	0.0382101i	$-0.987834\pi$
$337$	−1.51230	+	6.62581i	−0.0823801	+	0.360931i	0.916890	+	0.399141i	$0.130692\pi$
$338$		0			0
$339$	3.48679	−	0.525549i	0.189376	−	0.0285439i
$340$		0			0
$341$	−0.738960	−	9.86074i	−0.0400169	−	0.533989i
$342$		0			0
$343$	−11.8609	−	14.2239i	−0.640428	−	0.768019i
$344$		0			0
$345$	0.228286	+	3.04626i	0.0122905	+	0.164005i
$346$		0			0
$347$	−13.2639	+	1.99922i	−0.712045	+	0.107324i	−0.495069	−	0.868853i	$-0.664857\pi$
$347$	−13.2639	+	1.99922i	−0.712045	+	0.107324i	−0.216976	+	0.976177i	$0.569619\pi$
$348$		0			0
$349$	−1.84229	+	8.07162i	−0.0986157	+	0.432064i	−1.00000		0.000957302i	$-0.999695\pi$
$349$	−1.84229	+	8.07162i	−0.0986157	+	0.432064i	0.901384	+	0.433021i	$0.142552\pi$
$350$		0			0
$351$	1.34583	+	5.89645i	0.0718349	+	0.314729i
$352$		0			0
$353$	−2.87036	−	2.66330i	−0.152774	−	0.141753i	0.600083	−	0.799938i	$-0.295134\pi$
$353$	−2.87036	−	2.66330i	−0.152774	−	0.141753i	−0.752857	+	0.658185i	$0.771325\pi$
$354$		0			0
$355$	−8.45829	−	1.27488i	−0.448919	−	0.0676637i
$356$		0			0
$357$	0.797715	−	0.252441i	0.0422195	−	0.0133606i
$358$		0			0
$359$	−28.8513	+	8.89945i	−1.52271	+	0.469695i	−0.939478	−	0.342608i	$-0.888690\pi$
$359$	−28.8513	+	8.89945i	−1.52271	+	0.469695i	−0.583235	+	0.812303i	$0.698213\pi$
$360$		0			0
$361$	−18.4285	+	31.9190i	−0.969919	+	1.67995i
$362$		0			0
$363$	−1.23649	+	1.55052i	−0.0648991	+	0.0813809i
$364$		0			0
$365$	−14.9405	−	18.7348i	−0.782020	−	0.980623i
$366$		0			0
$367$	−1.44656	+	19.3031i	−0.0755100	+	1.00761i	0.822823	+	0.568297i	$0.192398\pi$
$367$	−1.44656	+	19.3031i	−0.0755100	+	1.00761i	−0.898333	+	0.439314i	$0.855221\pi$
$368$		0			0
$369$	−6.39094	+	16.2838i	−0.332699	+	0.847703i
$370$		0			0
$371$	−13.4331	−	33.5071i	−0.697411	−	1.73960i
$372$		0			0
$373$	−8.10061	−	14.0307i	−0.419434	−	0.726481i	0.576449	−	0.817133i	$-0.304438\pi$
$373$	−8.10061	−	14.0307i	−0.419434	−	0.726481i	−0.995883	+	0.0906525i	$0.971105\pi$
$374$		0			0
$375$	−1.22992	−	3.13378i	−0.0635128	−	0.161828i
$376$		0			0
$377$	−6.70919	+	3.23098i	−0.345541	+	0.166404i
$378$		0			0
$379$	−1.58848	−	0.764970i	−0.0815946	−	0.0392939i	0.392641	−	0.919692i	$-0.371561\pi$
$379$	−1.58848	−	0.764970i	−0.0815946	−	0.0392939i	−0.474236	+	0.880398i	$0.657276\pi$
$380$		0			0
$381$	1.29790	−	0.884893i	0.0664934	−	0.0453344i
$382$		0			0
$383$	−10.3539	−	7.05918i	−0.529060	−	0.360707i	0.269138	−	0.963102i	$-0.413261\pi$
$383$	−10.3539	−	7.05918i	−0.529060	−	0.360707i	−0.798199	+	0.602394i	$0.794214\pi$
$384$		0			0
$385$	10.7225	−	0.0781194i	0.546467	−	0.00398134i
$386$		0			0
$387$	4.99157	−	4.63150i	0.253736	−	0.235433i
$388$		0			0
$389$	16.8248	+	5.18977i	0.853053	+	0.263132i	0.690290	−	0.723533i	$-0.257483\pi$
$389$	16.8248	+	5.18977i	0.853053	+	0.263132i	0.162763	+	0.986665i	$0.447959\pi$
$390$		0			0
$391$	−5.96447			−0.301636
$392$		0			0
$393$	−4.21871			−0.212806
$394$		0			0
$395$	−16.0589	−	4.95352i	−0.808011	−	0.249239i
$396$		0			0
$397$	4.19877	−	3.89589i	0.210730	−	0.195529i	−0.567745	−	0.823204i	$-0.692184\pi$
$397$	4.19877	−	3.89589i	0.210730	−	0.195529i	0.778475	+	0.627676i	$0.215994\pi$
$398$		0			0
$399$	5.01070	−	2.45816i	0.250849	−	0.123062i
$400$		0			0
$401$	3.22300	+	2.19741i	0.160949	+	0.109733i	0.641116	−	0.767444i	$-0.278472\pi$
$401$	3.22300	+	2.19741i	0.160949	+	0.109733i	−0.480167	+	0.877177i	$0.659424\pi$
$402$		0			0
$403$	14.8342	−	10.1138i	0.738943	−	0.503803i
$404$		0			0
$405$	−15.1840	−	7.31224i	−0.754500	−	0.363348i
$406$		0			0
$407$	−1.47948	+	0.712479i	−0.0733350	+	0.0353163i
$408$		0			0
$409$	8.42068	+	21.4555i	0.416376	+	1.06091i	0.973135	+	0.230235i	$0.0739494\pi$
$409$	8.42068	+	21.4555i	0.416376	+	1.06091i	−0.556759	+	0.830674i	$0.687955\pi$
$410$		0			0
$411$	−0.117912	−	0.204229i	−0.00581616	−	0.0100739i
$412$		0			0
$413$	13.2148	−	23.2788i	0.650259	−	1.14547i
$414$		0			0
$415$	6.74071	−	17.1750i	0.330888	−	0.843090i
$416$		0			0
$417$	0.124856	−	1.66608i	0.00611420	−	0.0815884i
$418$		0			0
$419$	1.69685	+	2.12778i	0.0828965	+	0.103949i	0.821550	−	0.570136i	$-0.193110\pi$
$419$	1.69685	+	2.12778i	0.0828965	+	0.103949i	−0.738654	+	0.674085i	$0.764538\pi$
$420$		0			0
$421$	3.17877	−	3.98606i	0.154924	−	0.194269i	−0.698312	−	0.715793i	$-0.746065\pi$
$421$	3.17877	−	3.98606i	0.154924	−	0.194269i	0.853236	+	0.521525i	$0.174637\pi$
$422$		0			0
$423$	7.95349	−	13.7758i	0.386712	−	0.669805i
$424$		0			0
$425$	0.927763	−	0.286177i	0.0450031	−	0.0138816i
$426$		0			0
$427$	1.93951	+	23.5749i	0.0938595	+	1.14087i
$428$		0			0
$429$	2.01370	+	0.303516i	0.0972222	+	0.0146539i
$430$		0			0
$431$	10.7225	+	9.94903i	0.516485	+	0.479228i	0.894812	−	0.446444i	$-0.147310\pi$
$431$	10.7225	+	9.94903i	0.516485	+	0.479228i	−0.378326	+	0.925672i	$0.623500\pi$
$432$		0			0
$433$	−3.42780	−	15.0182i	−0.164729	−	0.721727i	−0.988048	−	0.154147i	$-0.950737\pi$
$433$	−3.42780	−	15.0182i	−0.164729	−	0.721727i	0.823319	−	0.567580i	$-0.192120\pi$
$434$		0			0
$435$	−0.262721	+	1.15106i	−0.0125965	+	0.0551889i
$436$		0			0
$437$	−39.3412	+	5.92974i	−1.88195	+	0.283658i
$438$		0			0
$439$	−0.321848	−	4.29476i	−0.0153609	−	0.204978i	−0.999604	−	0.0281544i	$-0.991037\pi$
$439$	−0.321848	−	4.29476i	−0.0153609	−	0.204978i	0.984243	−	0.176823i	$-0.0565821\pi$
$440$		0			0
$441$	20.2563	+	2.75192i	0.964584	+	0.131044i
$442$		0			0
$443$	0.174580	+	2.32961i	0.00829454	+	0.110683i	0.999814	−	0.0192735i	$-0.00613532\pi$
$443$	0.174580	+	2.32961i	0.00829454	+	0.110683i	−0.991520	+	0.129956i	$0.958516\pi$
$444$		0			0
$445$	35.3076	−	5.32176i	1.67374	−	0.252276i
$446$		0			0
$447$	−0.572537	+	2.50845i	−0.0270801	+	0.118646i
$448$		0			0
$449$	−3.93304	−	17.2318i	−0.185612	−	0.813219i	−0.978895	−	0.204365i	$-0.934487\pi$
$449$	−3.93304	−	17.2318i	−0.185612	−	0.813219i	0.793283	−	0.608853i	$-0.208370\pi$
$450$		0			0
$451$	8.75323	+	8.12181i	0.412174	+	0.382441i
$452$		0			0
$453$	−0.812205	−	0.122420i	−0.0381607	−	0.00575181i
$454$		0			0
$455$	9.85696	+	16.7891i	0.462102	+	0.787084i
$456$		0			0
$457$	1.20613	−	0.372040i	0.0564202	−	0.0174033i	−0.266417	−	0.963858i	$-0.585840\pi$
$457$	1.20613	−	0.372040i	0.0564202	−	0.0174033i	0.322837	+	0.946455i	$0.395364\pi$
$458$		0			0
$459$	−0.936137	+	1.62144i	−0.0436951	+	0.0756822i
$460$		0			0
$461$	−5.47928	+	6.87080i	−0.255195	+	0.320005i	−0.892882	−	0.450291i	$-0.851320\pi$
$461$	−5.47928	+	6.87080i	−0.255195	+	0.320005i	0.637686	+	0.770296i	$0.279892\pi$
$462$		0			0
$463$	−22.6266	−	28.3729i	−1.05155	−	1.31860i	−0.945994	−	0.324185i	$-0.894910\pi$
$463$	−22.6266	−	28.3729i	−1.05155	−	1.31860i	−0.105553	−	0.994414i	$-0.533661\pi$
$464$		0			0
$465$	0.212724	−	2.83861i	0.00986485	−	0.131637i
$466$		0			0
$467$	10.8812	−	27.7249i	0.503522	−	1.28295i	−0.422800	−	0.906223i	$-0.638953\pi$
$467$	10.8812	−	27.7249i	0.503522	−	1.28295i	0.926323	−	0.376731i	$-0.122952\pi$
$468$		0			0
$469$	−29.2132	−	8.77853i	−1.34894	−	0.405355i
$470$		0			0
$471$	0.748151	+	1.29584i	0.0344730	+	0.0597089i
$472$		0			0
$473$	−1.69812	−	4.32675i	−0.0780798	−	0.198944i
$474$		0			0
$475$	5.83495	−	2.80997i	0.267726	−	0.128930i
$476$		0			0
$477$	35.8999	+	17.2885i	1.64375	+	0.791586i
$478$		0			0
$479$	−30.8915	+	21.0614i	−1.41147	+	0.962322i	−0.412794	+	0.910824i	$0.635447\pi$
$479$	−30.8915	+	21.0614i	−1.41147	+	0.962322i	−0.998673	+	0.0514977i	$0.983601\pi$
$480$		0			0
$481$	−2.46341	−	1.67952i	−0.112322	−	0.0765797i
$482$		0			0
$483$	3.59414	+	1.69870i	0.163539	+	0.0772936i
$484$		0			0
$485$	−5.55517	+	5.15444i	−0.252247	+	0.234051i
$486$		0			0
$487$	−31.9034	−	9.84090i	−1.44568	−	0.445934i	−0.530055	−	0.847963i	$-0.677829\pi$
$487$	−31.9034	−	9.84090i	−1.44568	−	0.445934i	−0.915627	+	0.402029i	$0.868305\pi$
$488$		0			0
$489$	1.19488			0.0540344
$490$		0			0
$491$	1.56442			0.0706015			0.0353007	−	0.999377i	$-0.488761\pi$
$491$	1.56442			0.0706015			0.0353007	+	0.999377i	$0.488761\pi$
$492$		0			0
$493$	−2.20280	−	0.679475i	−0.0992093	−	0.0306020i
$494$		0			0
$495$	−8.67609	+	8.05024i	−0.389961	+	0.361831i
$496$		0			0
$497$	−6.87677	+	8.75327i	−0.308465	+	0.392638i
$498$		0			0
$499$	26.8259	+	18.2896i	1.20089	+	0.818753i	0.987408	−	0.158193i	$-0.0505670\pi$
$499$	26.8259	+	18.2896i	1.20089	+	0.818753i	0.213483	+	0.976947i	$0.431519\pi$
$500$		0			0
$501$	−2.04496	+	1.39423i	−0.0913621	+	0.0622896i
$502$		0			0
$503$	−23.6844	−	11.4058i	−1.05604	−	0.508561i	−0.176455	−	0.984309i	$-0.556463\pi$
$503$	−23.6844	−	11.4058i	−1.05604	−	0.508561i	−0.879582	+	0.475748i	$0.842177\pi$
$504$		0			0
$505$	6.58237	−	3.16990i	0.292912	−	0.141059i
$506$		0			0
$507$	0.0102936	+	0.0262275i	0.000457153	+	0.00116481i
$508$		0			0
$509$	9.44590	+	16.3608i	0.418682	+	0.725179i	0.995807	−	0.0914771i	$-0.0291588\pi$
$509$	9.44590	+	16.3608i	0.418682	+	0.725179i	−0.577125	+	0.816656i	$0.695826\pi$
$510$		0			0
$511$	−30.8007	+	4.87221i	−1.36254	+	0.215534i
$512$		0			0
$513$	−4.56270	+	11.6256i	−0.201448	+	0.513282i
$514$		0			0
$515$	−1.12465	+	15.0074i	−0.0495579	+	0.661304i
$516$		0			0
$517$	−6.76994	−	8.48924i	−0.297742	−	0.373356i
$518$		0			0
$519$	0.672386	−	0.843145i	0.0295145	−	0.0370100i
$520$		0			0
$521$	7.75661	−	13.4348i	0.339823	−	0.588591i	−0.644576	−	0.764540i	$-0.722966\pi$
$521$	7.75661	−	13.4348i	0.339823	−	0.588591i	0.984399	+	0.175949i	$0.0562994\pi$
$522$		0			0
$523$	34.6951	−	10.7020i	1.51711	−	0.467967i	0.579301	−	0.815113i	$-0.303325\pi$
$523$	34.6951	−	10.7020i	1.51711	−	0.467967i	0.937811	+	0.347146i	$0.112849\pi$
$524$		0			0
$525$	−0.640567	−	0.0917822i	−0.0279566	−	0.00400570i
$526$		0			0
$527$	5.49581	+	0.828360i	0.239401	+	0.0360839i
$528$		0			0
$529$	−3.91331	−	3.63102i	−0.170144	−	0.157870i
$530$		0			0
$531$	6.57464	+	28.8054i	0.285315	+	1.25005i
$532$		0			0
$533$	−4.82433	+	21.1368i	−0.208965	+	0.915536i
$534$		0			0
$535$	−8.87372	+	1.33750i	−0.383644	+	0.0578251i
$536$		0			0
$537$	−0.129071	−	1.72233i	−0.00556981	−	0.0743239i
$538$		0			0
$539$	6.80018	−	12.1849i	0.292904	−	0.524840i
$540$		0			0
$541$	1.71802	+	22.9253i	0.0738633	+	0.985637i	0.903849	+	0.427852i	$0.140730\pi$
$541$	1.71802	+	22.9253i	0.0738633	+	0.985637i	−0.829985	+	0.557785i	$0.811651\pi$
$542$		0			0
$543$	−6.26626	+	0.944486i	−0.268911	+	0.0405318i
$544$		0			0
$545$	−1.94509	+	8.52199i	−0.0833184	+	0.365042i
$546$		0			0
$547$	0.402078	+	1.76162i	0.0171916	+	0.0753213i	0.982796	−	0.184694i	$-0.0591295\pi$
$547$	0.402078	+	1.76162i	0.0171916	+	0.0753213i	−0.965604	+	0.260016i	$0.916272\pi$
$548$		0			0
$549$	−19.1396	−	17.7589i	−0.816858	−	0.757933i
$550$		0			0
$551$	−15.2051	−	2.29180i	−0.647758	−	0.0976338i
$552$		0			0
$553$	−15.9229	+	14.9916i	−0.677110	+	0.637509i
$554$		0			0
$555$	−0.451708	+	0.139334i	−0.0191739	+	0.00591438i
$556$		0			0
$557$	−0.0865296	+	0.149874i	−0.00366638	+	0.00635035i	−0.867853	−	0.496821i	$-0.834500\pi$
$557$	−0.0865296	+	0.149874i	−0.00366638	+	0.00635035i	0.864186	+	0.503172i	$0.167834\pi$
$558$		0			0
$559$	5.26178	−	6.59806i	0.222549	−	0.279068i
$560$		0			0
$561$	0.393055	+	0.492875i	0.0165948	+	0.0208092i
$562$		0			0
$563$	0.508314	−	6.78298i	0.0214229	−	0.285869i	−0.976195	−	0.216893i	$-0.930408\pi$
$563$	0.508314	−	6.78298i	0.0214229	−	0.285869i	0.997618	−	0.0689759i	$-0.0219732\pi$
$564$		0			0
$565$	−9.27940	+	23.6435i	−0.390387	+	0.994691i
$566$		0			0
$567$	−18.0302	+	12.4862i	−0.757197	+	0.524370i
$568$		0			0
$569$	−15.8713	−	27.4899i	−0.665358	−	1.15243i	−0.979188	−	0.202955i	$-0.934945\pi$
$569$	−15.8713	−	27.4899i	−0.665358	−	1.15243i	0.313830	−	0.949479i	$-0.398388\pi$
$570$		0			0
$571$	13.0140	+	33.1590i	0.544617	+	1.38766i	0.892892	+	0.450270i	$0.148672\pi$
$571$	13.0140	+	33.1590i	0.544617	+	1.38766i	−0.348275	+	0.937392i	$0.613232\pi$
$572$		0			0
$573$	3.61701	−	1.74186i	0.151103	−	0.0727672i
$574$		0			0
$575$	4.15610	+	2.00147i	0.173322	+	0.0834672i
$576$		0			0
$577$	−0.103690	+	0.0706949i	−0.00431669	+	0.00294307i	−0.565476	−	0.824764i	$-0.691308\pi$
$577$	−0.103690	+	0.0706949i	−0.00431669	+	0.00294307i	0.561160	+	0.827707i	$0.310355\pi$
$578$		0			0
$579$	1.53065	+	1.04358i	0.0636117	+	0.0433697i
$580$		0			0
$581$	−15.1066	−	18.6625i	−0.626728	−	0.774252i
$582$		0			0
$583$	19.9382	−	18.5000i	0.825757	−	0.766190i
$584$		0			0
$585$	−20.5346	−	6.33408i	−0.849000	−	0.261882i
$586$		0			0
$587$	21.6190			0.892311			0.446155	−	0.894956i	$-0.352793\pi$
$587$	21.6190			0.892311			0.446155	+	0.894956i	$0.352793\pi$
$588$		0			0
$589$	37.0735			1.52759
$590$		0			0
$591$	4.79766	+	1.47988i	0.197349	+	0.0608742i
$592$		0			0
$593$	30.7265	−	28.5101i	1.26179	−	1.17077i	0.284540	−	0.958664i	$-0.408159\pi$
$593$	30.7265	−	28.5101i	1.26179	−	1.17077i	0.977247	−	0.212103i	$-0.0680313\pi$
$594$		0			0
$595$	−1.29826	+	5.88535i	−0.0532233	+	0.241276i
$596$		0			0
$597$	3.66796	+	2.50078i	0.150120	+	0.102350i
$598$		0			0
$599$	7.57891	−	5.16722i	0.309666	−	0.211127i	−0.398508	−	0.917165i	$-0.630472\pi$
$599$	7.57891	−	5.16722i	0.309666	−	0.211127i	0.708174	+	0.706038i	$0.249519\pi$
$600$		0			0
$601$	−17.0184	−	8.19563i	−0.694195	−	0.334307i	0.0532960	−	0.998579i	$-0.483027\pi$
$601$	−17.0184	−	8.19563i	−0.694195	−	0.334307i	−0.747491	+	0.664272i	$0.768742\pi$
$602$		0			0
$603$	30.3351	−	14.6086i	1.23534	−	0.594909i
$604$		0			0
$605$	−5.21890	−	13.2975i	−0.212178	−	0.540622i
$606$		0			0
$607$	10.8325	+	18.7625i	0.439678	+	0.761545i	0.997664	−	0.0683051i	$-0.0217591\pi$
$607$	10.8325	+	18.7625i	0.439678	+	0.761545i	−0.557986	+	0.829850i	$0.688426\pi$
$608$		0			0
$609$	1.13387	+	1.03681i	0.0459469	+	0.0420138i
$610$		0			0
$611$	7.20255	−	18.3518i	0.291384	−	0.742435i
$612$		0			0
$613$	1.85572	−	24.7628i	0.0749517	−	1.00016i	−0.825273	−	0.564735i	$-0.808979\pi$
$613$	1.85572	−	24.7628i	0.0749517	−	1.00016i	0.900224	−	0.435426i	$-0.143402\pi$
$614$		0			0
$615$	2.14318	+	2.68746i	0.0864214	+	0.108369i
$616$		0			0
$617$	−18.7007	+	23.4499i	−0.752862	+	0.944059i	−0.999687	−	0.0250006i	$-0.992041\pi$
$617$	−18.7007	+	23.4499i	−0.752862	+	0.944059i	0.246825	+	0.969060i	$0.420613\pi$
$618$		0			0
$619$	10.7544	−	18.6272i	0.432256	−	0.748690i	−0.564811	−	0.825220i	$-0.691051\pi$
$619$	10.7544	−	18.6272i	0.432256	−	0.748690i	0.997067	+	0.0765305i	$0.0243843\pi$
$620$		0			0
$621$	−8.50035	+	2.62201i	−0.341107	+	0.105218i
$622$		0			0
$623$	16.6605	−	43.3768i	0.667488	−	1.73785i
$624$		0			0
$625$	19.6940	+	2.96839i	0.787758	+	0.118735i
$626$		0			0
$627$	3.08257	+	2.86021i	0.123106	+	0.114226i
$628$		0			0
$629$	−0.205378	−	0.899818i	−0.00818894	−	0.0358781i
$630$		0			0
$631$	−8.96758	+	39.2895i	−0.356994	+	1.56409i	0.403644	+	0.914916i	$0.367743\pi$
$631$	−8.96758	+	39.2895i	−0.356994	+	1.56409i	−0.760638	+	0.649176i	$0.775114\pi$
$632$		0			0
$633$	2.60239	−	0.392248i	0.103436	−	0.0155904i
$634$		0			0
$635$	0.845568	+	11.2833i	0.0335553	+	0.447765i
$636$		0			0
$637$	25.3329	−	0.369150i	1.00373	−	0.0146262i
$638$		0			0
$639$	−0.918188	−	12.2524i	−0.0363229	−	0.484696i
$640$		0			0
$641$	−15.7961	+	2.38088i	−0.623908	+	0.0940389i	−0.453385	−	0.891315i	$-0.649784\pi$
$641$	−15.7961	+	2.38088i	−0.623908	+	0.0940389i	−0.170523	+	0.985354i	$0.554546\pi$
$642$		0			0
$643$	−5.04636	+	22.1096i	−0.199009	+	0.871916i	0.772519	+	0.634992i	$0.218996\pi$
$643$	−5.04636	+	22.1096i	−0.199009	+	0.871916i	−0.971528	+	0.236924i	$0.923861\pi$
$644$		0			0
$645$	−0.297740	−	1.30448i	−0.0117235	−	0.0513640i
$646$		0			0
$647$	−26.0305	−	24.1528i	−1.02336	−	0.949543i	−0.0246228	−	0.999697i	$-0.507838\pi$
$647$	−26.0305	−	24.1528i	−1.02336	−	0.949543i	−0.998742	+	0.0501534i	$0.984029\pi$
$648$		0			0
$649$	19.9430	+	3.00593i	0.782832	+	0.117993i
$650$		0			0
$651$	−3.07581	−	2.06439i	−0.120551	−	0.0809098i
$652$		0			0
$653$	10.1546	−	3.13229i	0.397382	−	0.122576i	−0.0896221	−	0.995976i	$-0.528566\pi$
$653$	10.1546	−	3.13229i	0.397382	−	0.122576i	0.487004	+	0.873400i	$0.338090\pi$
$654$		0			0
$655$	15.1938	−	26.3165i	0.593671	−	1.02827i
$656$		0			0
$657$	21.4605	−	26.9106i	0.837254	−	1.04988i
$658$		0			0
$659$	18.0931	+	22.6881i	0.704808	+	0.883802i	0.997372	−	0.0724441i	$-0.0230799\pi$
$659$	18.0931	+	22.6881i	0.704808	+	0.883802i	−0.292564	+	0.956246i	$0.594508\pi$
$660$		0			0
$661$	0.606333	−	8.09095i	0.0235836	−	0.314701i	−0.972919	−	0.231145i	$-0.925753\pi$
$661$	0.606333	−	8.09095i	0.0235836	−	0.314701i	0.996503	−	0.0835568i	$-0.0266280\pi$
$662$		0			0
$663$	−0.418172	+	1.06548i	−0.0162404	+	0.0413800i
$664$		0			0
$665$	−2.71213	+	40.1101i	−0.105172	+	1.55540i
$666$		0			0
$667$	−5.47628	−	9.48519i	−0.212042	−	0.367268i
$668$		0			0
$669$	0.596350	+	1.51947i	0.0230562	+	0.0587463i
$670$		0			0
$671$	−16.0574	+	7.73284i	−0.619889	+	0.298523i
$672$		0			0
$673$	−12.9761	−	6.24897i	−0.500193	−	0.240880i	0.166736	−	0.986002i	$-0.446677\pi$
$673$	−12.9761	−	6.24897i	−0.500193	−	0.240880i	−0.666929	+	0.745121i	$0.732392\pi$
$674$		0			0
$675$	1.19641	−	0.815699i	0.0460498	−	0.0313963i
$676$		0			0
$677$	17.9144	+	12.2139i	0.688508	+	0.469417i	0.856349	−	0.516397i	$-0.172727\pi$
$677$	17.9144	+	12.2139i	0.688508	+	0.469417i	−0.167841	+	0.985814i	$0.553680\pi$
$678$		0			0
$679$	2.26444	+	9.59827i	0.0869011	+	0.368348i
$680$		0			0
$681$	2.74744	−	2.54925i	0.105282	−	0.0976875i
$682$		0			0
$683$	4.64443	+	1.43262i	0.177714	+	0.0548176i	0.382335	−	0.924024i	$-0.375120\pi$
$683$	4.64443	+	1.43262i	0.177714	+	0.0548176i	−0.204621	+	0.978841i	$0.565596\pi$
$684$		0			0
$685$	1.69865			0.0649022
$686$		0			0
$687$	−6.04463			−0.230617
$688$		0			0
$689$	47.1898	+	14.5561i	1.79779	+	0.554544i
$690$		0			0
$691$	−23.9530	+	22.2251i	−0.911215	+	0.845484i	−0.988453	−	0.151529i	$-0.951580\pi$
$691$	−23.9530	+	22.2251i	−0.911215	+	0.845484i	0.0772383	+	0.997013i	$0.475390\pi$
$692$		0			0
$693$	3.53661	+	14.9906i	0.134345	+	0.569447i
$694$		0			0
$695$	9.94341	+	6.77930i	0.377175	+	0.257154i
$696$		0			0
$697$	−5.54528	+	3.78071i	−0.210042	+	0.143204i
$698$		0			0
$699$	6.07803	+	2.92702i	0.229892	+	0.110710i
$700$		0			0
$701$	17.6281	−	8.48923i	0.665803	−	0.320634i	−0.0702781	−	0.997527i	$-0.522389\pi$
$701$	17.6281	−	8.48923i	0.665803	−	0.320634i	0.736081	+	0.676894i	$0.236674\pi$
$702$		0			0
$703$	−2.24924	−	5.73096i	−0.0848316	−	0.216147i
$704$		0			0
$705$	−1.56286	−	2.70696i	−0.0588609	−	0.101950i
$706$		0			0
$707$	0.641403	−	9.48580i	0.0241224	−	0.356750i
$708$		0			0
$709$	−12.3708	+	31.5204i	−0.464597	+	1.18377i	0.486170	+	0.873864i	$0.338394\pi$
$709$	−12.3708	+	31.5204i	−0.464597	+	1.18377i	−0.950766	+	0.309908i	$0.899702\pi$
$710$		0			0
$711$	1.80395	−	24.0720i	0.0676532	−	0.902770i
$712$		0			0
$713$	16.4643	+	20.6455i	0.616591	+	0.773181i
$714$		0			0
$715$	−9.14575	+	11.4684i	−0.342031	+	0.428894i
$716$		0			0
$717$	1.65145	−	2.86039i	0.0616745	−	0.106823i
$718$		0			0
$719$	12.9175	−	3.98453i	0.481742	−	0.148598i	−0.0443663	−	0.999015i	$-0.514127\pi$
$719$	12.9175	−	3.98453i	0.481742	−	0.148598i	0.526108	+	0.850418i	$0.323651\pi$
$720$		0			0
$721$	16.2614	+	10.9142i	0.605608	+	0.406465i
$722$		0			0
$723$	3.59902	+	0.542465i	0.133849	+	0.0201745i
$724$		0			0
$725$	1.30693	+	1.21265i	0.0485381	+	0.0450368i
$726$		0			0
$727$	−4.10803	−	17.9985i	−0.152358	−	0.667526i	−0.992196	−	0.124688i	$-0.960207\pi$
$727$	−4.10803	−	17.9985i	−0.152358	−	0.667526i	0.839837	−	0.542838i	$-0.182650\pi$
$728$		0			0
$729$	5.07185	−	22.2212i	0.187846	−	0.823008i
$730$		0			0
$731$	2.58331	−	0.389371i	0.0955472	−	0.0144014i
$732$		0			0
$733$	1.06286	+	14.1828i	0.0392575	+	0.523855i	0.981819	+	0.189821i	$0.0607908\pi$
$733$	1.06286	+	14.1828i	0.0392575	+	0.523855i	−0.942561	+	0.334033i	$0.891590\pi$
$734$		0			0
$735$	2.45849	−	3.17672i	0.0906827	−	0.117175i
$736$		0			0
$737$	−1.71751	−	22.9186i	−0.0632653	−	0.844217i
$738$		0			0
$739$	22.1816	−	3.34334i	0.815964	−	0.122987i	0.272217	−	0.962236i	$-0.412243\pi$
$739$	22.1816	−	3.34334i	0.815964	−	0.122987i	0.543747	+	0.839249i	$0.317005\pi$
$740$		0			0
$741$	−1.69895	+	7.44360i	−0.0624126	+	0.273447i
$742$		0			0
$743$	1.99719	+	8.75028i	0.0732700	+	0.321017i	0.998259	−	0.0589761i	$-0.0187836\pi$
$743$	1.99719	+	8.75028i	0.0732700	+	0.321017i	−0.924989	+	0.379993i	$0.875926\pi$
$744$		0			0
$745$	−13.5858	−	12.6058i	−0.497745	−	0.461840i
$746$		0			0
$747$	26.2062	+	3.94996i	0.958836	+	0.144521i
$748$		0			0
$749$	−4.18721	+	10.9017i	−0.152997	+	0.398340i
$750$		0			0
$751$	−21.4956	+	6.63051i	−0.784386	+	0.241951i	−0.660978	−	0.750405i	$-0.729858\pi$
$751$	−21.4956	+	6.63051i	−0.784386	+	0.241951i	−0.123407	+	0.992356i	$0.539382\pi$
$752$		0			0
$753$	1.79741	−	3.11321i	0.0655013	−	0.113452i
$754$		0			0
$755$	3.68885	−	4.62567i	0.134251	−	0.168345i
$756$		0			0
$757$	1.47107	+	1.84466i	0.0534669	+	0.0670454i	0.807846	−	0.589394i	$-0.200633\pi$
$757$	1.47107	+	1.84466i	0.0534669	+	0.0670454i	−0.754379	+	0.656439i	$0.772062\pi$
$758$		0			0
$759$	−0.223832	+	2.98683i	−0.00812459	+	0.108415i
$760$		0			0
$761$	5.12400	−	13.0557i	0.185745	−	0.473270i	−0.807422	−	0.589975i	$-0.799138\pi$
$761$	5.12400	−	13.0557i	0.185745	−	0.473270i	0.993167	+	0.116704i	$0.0372330\pi$
$762$		0			0
$763$	8.39479	+	7.67617i	0.303912	+	0.277896i
$764$		0			0
$765$	−3.32616	−	5.76108i	−0.120258	−	0.208292i
$766$		0			0
$767$	13.3783	+	34.0873i	0.483061	+	1.23082i
$768$		0			0
$769$	17.5379	−	8.44581i	0.632433	−	0.304564i	−0.0900657	−	0.995936i	$-0.528708\pi$
$769$	17.5379	−	8.44581i	0.632433	−	0.304564i	0.722499	+	0.691372i	$0.242993\pi$
$770$		0			0
$771$	−4.07817	−	1.96394i	−0.146872	−	0.0707297i
$772$		0			0
$773$	7.04361	−	4.80225i	0.253341	−	0.172725i	−0.429990	−	0.902834i	$-0.641483\pi$
$773$	7.04361	−	4.80225i	0.253341	−	0.172725i	0.683331	+	0.730109i	$0.260531\pi$
$774$		0			0
$775$	−3.55157	−	2.42142i	−0.127576	−	0.0869799i
$776$		0			0
$777$	−0.132513	+	0.600716i	−0.00475386	+	0.0215506i
$778$		0			0
$779$	−32.8176	+	30.4503i	−1.17581	+	1.09099i
$780$		0			0
$781$	−8.01434	−	2.47210i	−0.286776	−	0.0884585i
$782$		0			0
$783$	−3.43806			−0.122866
$784$		0			0
$785$	−10.7780			−0.384682
$786$		0			0
$787$	7.77607	+	2.39860i	0.277187	+	0.0855009i	0.430232	−	0.902718i	$-0.358432\pi$
$787$	7.77607	+	2.39860i	0.277187	+	0.0855009i	−0.153045	+	0.988219i	$0.548908\pi$
$788$		0			0
$789$	−1.44891	+	1.34439i	−0.0515826	+	0.0478616i
$790$		0			0
$791$	20.7961	+	25.6912i	0.739423	+	0.913475i
$792$		0			0
$793$	−26.7364	−	18.2286i	−0.949439	−	0.647317i
$794$		0			0
$795$	6.46924	−	4.41065i	0.229440	−	0.156430i
$796$		0			0
$797$	20.7141	+	9.97537i	0.733730	+	0.353346i	0.763150	−	0.646221i	$-0.223652\pi$
$797$	20.7141	+	9.97537i	0.733730	+	0.353346i	−0.0294198	+	0.999567i	$0.509366\pi$
$798$		0			0
$799$	5.49856	−	2.64797i	0.194525	−	0.0936784i
$800$		0			0
$801$	18.7379	+	47.7433i	0.662070	+	1.68693i
$802$		0			0
$803$	−11.7476	−	20.3474i	−0.414563	−	0.718045i
$804$		0			0
$805$	−23.5410	+	16.3025i	−0.829711	+	0.574586i
$806$		0			0
$807$	−1.96415	+	5.00458i	−0.0691414	+	0.176169i
$808$		0			0
$809$	−1.29728	+	17.3110i	−0.0456099	+	0.608622i	0.926832	+	0.375476i	$0.122521\pi$
$809$	−1.29728	+	17.3110i	−0.0456099	+	0.608622i	−0.972442	+	0.233146i	$0.925098\pi$
$810$		0			0
$811$	8.15099	+	10.2210i	0.286220	+	0.358909i	0.904068	−	0.427389i	$-0.140567\pi$
$811$	8.15099	+	10.2210i	0.286220	+	0.358909i	−0.617848	+	0.786298i	$0.711995\pi$
$812$		0			0
$813$	−1.64096	+	2.05769i	−0.0575508	+	0.0721665i
$814$		0			0
$815$	−4.30340	+	7.45372i	−0.150742	+	0.261092i
$816$		0			0
$817$	16.6522	−	5.13654i	0.582588	−	0.179705i
$818$		0			0
$819$	−20.3606	+	19.1698i	−0.711458	+	0.669849i
$820$		0			0
$821$	−10.1999	−	1.53739i	−0.355979	−	0.0536551i	−0.0313814	−	0.999507i	$-0.509991\pi$
$821$	−10.1999	−	1.53739i	−0.355979	−	0.0536551i	−0.324597	+	0.945852i	$0.605229\pi$
$822$		0			0
$823$	11.4821	+	10.6538i	0.400240	+	0.371368i	0.854457	−	0.519523i	$-0.173890\pi$
$823$	11.4821	+	10.6538i	0.400240	+	0.371368i	−0.454217	+	0.890891i	$0.650081\pi$
$824$		0			0
$825$	−0.108492	−	0.475336i	−0.00377722	−	0.0165491i
$826$		0			0
$827$	−1.48144	+	6.49060i	−0.0515146	+	0.225700i	−0.994132	−	0.108175i	$-0.965499\pi$
$827$	−1.48144	+	6.49060i	−0.0515146	+	0.225700i	0.942617	+	0.333875i	$0.108356\pi$
$828$		0			0
$829$	17.1579	−	2.58614i	0.595919	−	0.0898204i	0.155845	−	0.987782i	$-0.450190\pi$
$829$	17.1579	−	2.58614i	0.595919	−	0.0898204i	0.440075	+	0.897961i	$0.354952\pi$
$830$		0			0
$831$	−0.162944	−	2.17434i	−0.00565246	−	0.0754269i
$832$		0			0
$833$	5.82644	+	5.25026i	0.201874	+	0.181911i
$834$		0			0
$835$	−1.33227	−	17.7779i	−0.0461051	−	0.615230i
$836$		0			0
$837$	8.19658	−	1.23544i	0.283315	−	0.0427029i
$838$		0			0
$839$	−6.97366	+	30.5536i	−0.240758	+	1.05483i	0.699572	+	0.714562i	$0.253374\pi$
$839$	−6.97366	+	30.5536i	−0.240758	+	1.05483i	−0.940329	+	0.340265i	$0.889483\pi$
$840$		0			0
$841$	5.51116	+	24.1460i	0.190040	+	0.832620i
$842$		0			0
$843$	−6.06246	−	5.62514i	−0.208802	−	0.193740i
$844$		0			0
$845$	−0.200681	−	0.0302478i	−0.00690364	−	0.00104056i
$846$		0			0
$847$	−18.4018	−	2.63666i	−0.632293	−	0.0905967i
$848$		0			0
$849$	1.09249	−	0.336990i	0.0374943	−	0.0115655i
$850$		0			0
$851$	2.19258	−	3.79766i	0.0751607	−	0.130182i
$852$		0			0
$853$	3.71287	−	4.65580i	0.127126	−	0.159411i	−0.714195	−	0.699947i	$-0.753207\pi$
$853$	3.71287	−	4.65580i	0.127126	−	0.159411i	0.841321	+	0.540536i	$0.181778\pi$
$854$		0			0
$855$	−27.6667	−	34.6929i	−0.946181	−	1.18647i
$856$		0			0
$857$	−2.57175	+	34.3177i	−0.0878495	+	1.17227i	0.762835	+	0.646593i	$0.223807\pi$
$857$	−2.57175	+	34.3177i	−0.0878495	+	1.17227i	−0.850685	+	0.525677i	$0.823812\pi$
$858$		0			0
$859$	3.78291	−	9.63870i	0.129071	−	0.328868i	−0.851700	−	0.524030i	$-0.824428\pi$
$859$	3.78291	−	9.63870i	0.129071	−	0.328868i	0.980771	+	0.195162i	$0.0625232\pi$
$860$		0			0
$861$	4.41830	−	0.698909i	0.150575	−	0.0238188i
$862$		0			0
$863$	6.04299	+	10.4668i	0.205706	+	0.356293i	0.950357	−	0.311160i	$-0.100718\pi$
$863$	6.04299	+	10.4668i	0.205706	+	0.356293i	−0.744652	+	0.667453i	$0.767384\pi$
$864$		0			0
$865$	2.83795	+	7.23098i	0.0964933	+	0.245861i
$866$		0			0
$867$	4.00389	−	1.92817i	0.135979	−	0.0654841i
$868$		0			0
$869$	−14.8459	−	7.14939i	−0.503611	−	0.242527i
$870$		0			0
$871$	34.4780	−	23.5067i	1.16824	−	0.796494i
$872$		0			0
$873$	−8.99381	−	6.13187i	−0.304394	−	0.207532i
$874$		0			0
$875$	19.4948	−	24.8145i	0.659046	−	0.838883i
$876$		0			0
$877$	−40.1349	+	37.2398i	−1.35526	+	1.25750i	−0.418188	+	0.908360i	$0.637335\pi$
$877$	−40.1349	+	37.2398i	−1.35526	+	1.25750i	−0.937072	+	0.349137i	$0.886475\pi$
$878$		0			0
$879$	−1.84035	−	0.567673i	−0.0620735	−	0.0191471i
$880$		0			0
$881$	14.9335			0.503124			0.251562	−	0.967841i	$-0.419056\pi$
$881$	14.9335			0.503124			0.251562	+	0.967841i	$0.419056\pi$
$882$		0			0
$883$	10.8928			0.366570			0.183285	−	0.983060i	$-0.441327\pi$
$883$	10.8928			0.366570			0.183285	+	0.983060i	$0.441327\pi$
$884$		0			0
$885$	5.54790	+	1.71130i	0.186491	+	0.0575247i
$886$		0			0
$887$	40.2092	−	37.3087i	1.35009	−	1.25270i	0.409872	−	0.912143i	$-0.365574\pi$
$887$	40.2092	−	37.3087i	1.35009	−	1.25270i	0.940222	−	0.340561i	$-0.110617\pi$
$888$		0			0
$889$	13.3127	+	6.29197i	0.446492	+	0.211026i
$890$		0			0
$891$	−13.6529	−	9.30841i	−0.457390	−	0.311844i
$892$		0			0
$893$	33.6356	−	22.9324i	1.12557	−	0.767403i
$894$		0			0
$895$	11.2088	+	5.39787i	0.374669	+	0.180431i
$896$		0			0
$897$	−4.89970	+	2.35957i	−0.163596	+	0.0787837i
$898$		0			0
$899$	3.72865	+	9.50045i	0.124357	+	0.316858i
$900$		0			0
$901$	7.64374	+	13.2393i	0.254650	+	0.441066i
$902$		0			0
$903$	−1.66758	−	0.501104i	−0.0554935	−	0.0166757i
$904$		0			0
$905$	16.6764	−	42.4908i	0.554342	−	1.41244i
$906$		0			0
$907$	1.95619	−	26.1035i	0.0649541	−	0.866753i	−0.865632	−	0.500680i	$-0.833083\pi$
$907$	1.95619	−	26.1035i	0.0649541	−	0.866753i	0.930586	−	0.366072i	$-0.119298\pi$
$908$		0			0
$909$	6.54301	+	8.20467i	0.217018	+	0.272132i
$910$		0			0
$911$	−27.8205	+	34.8858i	−0.921734	+	1.15582i	0.0657087	+	0.997839i	$0.479069\pi$
$911$	−27.8205	+	34.8858i	−0.921734	+	1.15582i	−0.987443	+	0.157979i	$0.949502\pi$
$912$		0			0
$913$	9.04525	−	15.6668i	0.299354	−	0.518496i
$914$		0			0
$915$	−4.90259	+	1.51225i	−0.162074	+	0.0499934i
$916$		0			0
$917$	−20.0214	−	34.1018i	−0.661164	−	1.12614i
$918$		0			0
$919$	−32.3241	−	4.87207i	−1.06627	−	0.160715i	−0.407613	−	0.913155i	$-0.633639\pi$
$919$	−32.3241	−	4.87207i	−1.06627	−	0.160715i	−0.658661	+	0.752440i	$0.728877\pi$
$920$		0			0
$921$	−5.52875	−	5.12993i	−0.182179	−	0.169037i
$922$		0			0
$923$	−3.38850	−	14.8460i	−0.111534	−	0.488661i
$924$		0			0
$925$	−0.158839	+	0.695921i	−0.00522261	+	0.0228817i
$926$		0			0
$927$	−21.3756	+	3.22185i	−0.702067	+	0.105820i
$928$		0			0
$929$	−2.18613	−	29.1719i	−0.0717247	−	0.957100i	−0.910737	−	0.412987i	$-0.864485\pi$
$929$	−2.18613	−	29.1719i	−0.0717247	−	0.957100i	0.839012	−	0.544113i	$-0.183134\pi$
$930$		0			0
$931$	43.6505	+	28.8378i	1.43059	+	0.945122i
$932$		0			0
$933$	0.0862102	+	1.15040i	0.00282240	+	0.0376622i
$934$		0			0
$935$	−4.49017	+	0.676785i	−0.146844	+	0.0221332i
$936$		0			0
$937$	−5.73292	+	25.1176i	−0.187286	+	0.820555i	0.790753	+	0.612135i	$0.209689\pi$
$937$	−5.73292	+	25.1176i	−0.187286	+	0.820555i	−0.978039	+	0.208420i	$0.933168\pi$
$938$		0			0
$939$	−1.73031	−	7.58097i	−0.0564664	−	0.247396i
$940$		0			0
$941$	−44.7390	−	41.5117i	−1.45845	−	1.35324i	−0.798640	−	0.601809i	$-0.794447\pi$
$941$	−44.7390	−	41.5117i	−1.45845	−	1.35324i	−0.659809	−	0.751434i	$-0.729363\pi$
$942$		0			0
$943$	−31.5314	−	4.75259i	−1.02680	−	0.154766i
$944$		0			0
$945$	0.737002	+	8.95832i	0.0239747	+	0.291414i
$946$		0			0
$947$	50.4968	−	15.5762i	1.64092	−	0.506158i	0.669361	−	0.742937i	$-0.266568\pi$
$947$	50.4968	−	15.5762i	1.64092	−	0.506158i	0.971563	+	0.236779i	$0.0760918\pi$
$948$		0			0
$949$	21.3295	−	36.9438i	0.692385	−	1.19925i
$950$		0			0
$951$	1.11650	−	1.40004i	0.0362048	−	0.0453994i
$952$		0			0
$953$	−33.3284	−	41.7925i	−1.07961	−	1.35379i	−0.931052	−	0.364887i	$-0.881107\pi$
$953$	−33.3284	−	41.7925i	−1.07961	−	1.35379i	−0.148560	−	0.988903i	$-0.547464\pi$
$954$		0			0
$955$	−2.16099	+	28.8364i	−0.0699280	+	0.933125i
$956$		0			0
$957$	−0.422927	+	1.07760i	−0.0136713	+	0.0348339i
$958$		0			0
$959$	1.09129	−	1.92238i	0.0352396	−	0.0620768i
$960$		0			0
$961$	3.19672	+	5.53689i	0.103120	+	0.178609i
$962$		0			0
$963$	−4.70931	−	11.9991i	−0.151755	−	0.386667i
$964$		0			0
$965$	−12.0226	+	5.78978i	−0.387021	+	0.186380i
$966$		0			0
$967$	−31.0375	−	14.9469i	−0.998100	−	0.480659i	−0.137807	−	0.990459i	$-0.544005\pi$
$967$	−31.0375	−	14.9469i	−0.998100	−	0.480659i	−0.860293	+	0.509800i	$0.829720\pi$
$968$		0			0
$969$	−1.95284	+	1.33143i	−0.0627344	+	0.0427716i
$970$		0			0
$971$	24.0376	+	16.3886i	0.771404	+	0.525934i	0.883876	−	0.467721i	$-0.154925\pi$
$971$	24.0376	+	16.3886i	0.771404	+	0.525934i	−0.112473	+	0.993655i	$0.535877\pi$
$972$		0			0
$973$	14.0603	−	6.89771i	0.450752	−	0.221130i
$974$		0			0
$975$	0.648927	−	0.602116i	0.0207823	−	0.0192831i
$976$		0			0
$977$	−4.82826	−	1.48932i	−0.154470	−	0.0476476i	0.216556	−	0.976270i	$-0.430518\pi$
$977$	−4.82826	−	1.48932i	−0.154470	−	0.0476476i	−0.371026	+	0.928623i	$0.620994\pi$
$978$		0			0
$979$	35.0098			1.11892
$980$		0			0
$981$	−12.5558			−0.400875
$982$		0			0
$983$	35.7982	+	11.0423i	1.14179	+	0.352194i	0.807262	−	0.590193i	$-0.200948\pi$
$983$	35.7982	+	11.0423i	1.14179	+	0.352194i	0.334523	+	0.942387i	$0.391425\pi$
$984$		0			0
$985$	−26.5105	+	24.5982i	−0.844695	+	0.783762i
$986$		0			0
$987$	−4.06754	+	0.0296344i	−0.129471	+	0.000943275i
$988$		0			0
$989$	10.2557	+	6.99219i	0.326111	+	0.222339i
$990$		0			0
$991$	−11.6974	+	7.97515i	−0.371580	+	0.253339i	−0.734684	−	0.678410i	$-0.762669\pi$
$991$	−11.6974	+	7.97515i	−0.371580	+	0.253339i	0.363104	+	0.931749i	$0.381717\pi$
$992$		0			0
$993$	−1.52422	−	0.734025i	−0.0483696	−	0.0232936i
$994$		0			0
$995$	−28.8102	+	13.8743i	−0.913346	+	0.439844i
$996$		0			0
$997$	−13.6960	−	34.8969i	−0.433757	−	1.10519i	−0.965986	−	0.258594i	$-0.916741\pi$
$997$	−13.6960	−	34.8969i	−0.433757	−	1.10519i	0.532229	−	0.846600i	$-0.321355\pi$
$998$		0			0
$999$	−0.688262	−	1.19210i	−0.0217756	−	0.0377165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bg.c.81.2		48
4.3	odd	2		49.2.g.a.32.3	yes	48
12.11	even	2		441.2.bb.d.424.2		48
28.3	even	6		343.2.e.c.197.3		48
28.11	odd	6		343.2.e.d.197.3		48
28.19	even	6		343.2.g.h.30.3		48
28.23	odd	6		343.2.g.i.30.3		48
28.27	even	2		343.2.g.g.116.3		48
49.23	even	21	inner	784.2.bg.c.513.2		48
196.11	odd	42		2401.2.a.h.1.16		24
196.23	odd	42		49.2.g.a.23.3	✓	48
196.27	even	14		343.2.g.h.263.3		48
196.71	odd	14		343.2.g.i.263.3		48
196.75	even	42		343.2.g.g.275.3		48
196.87	even	42		2401.2.a.i.1.16		24
196.143	even	42		343.2.e.c.148.3		48
196.151	odd	42		343.2.e.d.148.3		48
588.23	even	42		441.2.bb.d.415.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.23.3	✓	48	196.23	odd	42
49.2.g.a.32.3	yes	48	4.3	odd	2
343.2.e.c.148.3		48	196.143	even	42
343.2.e.c.197.3		48	28.3	even	6
343.2.e.d.148.3		48	196.151	odd	42
343.2.e.d.197.3		48	28.11	odd	6
343.2.g.g.116.3		48	28.27	even	2
343.2.g.g.275.3		48	196.75	even	42
343.2.g.h.30.3		48	28.19	even	6
343.2.g.h.263.3		48	196.27	even	14
343.2.g.i.30.3		48	28.23	odd	6
343.2.g.i.263.3		48	196.71	odd	14
441.2.bb.d.415.2		48	588.23	even	42
441.2.bb.d.424.2		48	12.11	even	2
784.2.bg.c.81.2		48	1.1	even	1	trivial
784.2.bg.c.513.2		48	49.23	even	21	inner
2401.2.a.h.1.16		24	196.11	odd	42
2401.2.a.i.1.16		24	196.87	even	42

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bg (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.269714 + 0.0831957i) q^{3} +(-1.49036 + 1.38285i) q^{5} +(0.607511 + 2.57506i) q^{7} +(-2.41289 - 1.64508i) q^{9} +O(q^{10})\)	\(q+(0.269714 + 0.0831957i) q^{3} +(-1.49036 + 1.38285i) q^{5} +(0.607511 + 2.57506i) q^{7} +(-2.41289 - 1.64508i) q^{9} +(-1.64705 + 1.12294i) q^{11} +(-3.26094 - 1.57038i) q^{13} +(-0.517018 + 0.248983i) q^{15} +(-0.409339 - 1.04298i) q^{17} +(-3.73687 - 6.47246i) q^{19} +(-0.0503796 + 0.745071i) q^{21} +(1.94485 - 4.95539i) q^{23} +(-0.0647567 + 0.864118i) q^{25} +(-1.04187 - 1.30647i) q^{27} +(1.28279 - 1.60857i) q^{29} +(-2.48025 + 4.29592i) q^{31} +(-0.537654 + 0.165844i) q^{33} +(-4.46634 - 2.99767i) q^{35} +(0.814555 + 0.122774i) q^{37} +(-0.748870 - 0.694850i) q^{39} +(-1.33292 - 5.83991i) q^{41} +(-0.518849 + 2.27323i) q^{43} +(5.87099 - 0.884909i) q^{45} +(0.407053 + 5.43174i) q^{47} +(-6.26186 + 3.12876i) q^{49} +(-0.0236330 - 0.315360i) q^{51} +(-13.4919 + 2.03358i) q^{53} +(0.901837 - 3.95120i) q^{55} +(-0.469406 - 2.05660i) q^{57} +(-7.41658 - 6.88158i) q^{59} +(8.84072 + 1.33252i) q^{61} +(2.77032 - 7.21275i) q^{63} +(7.03159 - 2.16896i) q^{65} +(-5.76466 + 9.98468i) q^{67} +(0.936820 - 1.17473i) q^{69} +(2.62321 + 3.28940i) q^{71} +(-0.880793 + 11.7534i) q^{73} +(-0.0893566 + 0.227677i) q^{75} +(-3.89223 - 3.55904i) q^{77} +(4.13300 + 7.15857i) q^{79} +(3.02844 + 7.71633i) q^{81} +(-8.17636 + 3.93753i) q^{83} +(2.05235 + 0.988358i) q^{85} +(0.479814 - 0.327131i) q^{87} +(-14.5109 - 9.89337i) q^{89} +(2.06278 - 9.35113i) q^{91} +(-1.02636 + 0.952322i) q^{93} +(14.5198 + 4.47875i) q^{95} +3.72740 q^{97} +5.82147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 14 q^{3} - 14 q^{5} + 14 q^{7} + 6 q^{9}+O(q^{10}) \) 48 * q + 14 * q^3 - 14 * q^5 + 14 * q^7 + 6 * q^9	\( 48 q + 14 q^{3} - 14 q^{5} + 14 q^{7} + 6 q^{9} + 3 q^{11} - 14 q^{13} + 12 q^{15} - 7 q^{17} - 21 q^{19} - 14 q^{21} - 15 q^{23} - 4 q^{25} - 7 q^{27} + 12 q^{29} - 35 q^{31} - 14 q^{33} + 15 q^{37} + 7 q^{39} - 42 q^{41} + 30 q^{43} + 7 q^{45} - 21 q^{47} - 70 q^{49} + 52 q^{51} + 11 q^{53} + 7 q^{55} - 12 q^{57} + 28 q^{59} + 7 q^{61} - 35 q^{63} + 14 q^{65} - 11 q^{67} + 70 q^{69} - 19 q^{71} + 7 q^{73} - 112 q^{75} + 7 q^{77} - 15 q^{79} + 64 q^{81} - 26 q^{85} + 112 q^{87} - 14 q^{89} - 84 q^{91} - 80 q^{93} + 61 q^{95} + 16 q^{99}+O(q^{100}) \) 48 * q + 14 * q^3 - 14 * q^5 + 14 * q^7 + 6 * q^9 + 3 * q^11 - 14 * q^13 + 12 * q^15 - 7 * q^17 - 21 * q^19 - 14 * q^21 - 15 * q^23 - 4 * q^25 - 7 * q^27 + 12 * q^29 - 35 * q^31 - 14 * q^33 + 15 * q^37 + 7 * q^39 - 42 * q^41 + 30 * q^43 + 7 * q^45 - 21 * q^47 - 70 * q^49 + 52 * q^51 + 11 * q^53 + 7 * q^55 - 12 * q^57 + 28 * q^59 + 7 * q^61 - 35 * q^63 + 14 * q^65 - 11 * q^67 + 70 * q^69 - 19 * q^71 + 7 * q^73 - 112 * q^75 + 7 * q^77 - 15 * q^79 + 64 * q^81 - 26 * q^85 + 112 * q^87 - 14 * q^89 - 84 * q^91 - 80 * q^93 + 61 * q^95 + 16 * q^99

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