LMFDB - Embedded newform 494.2.d.b.77.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [494,2,Mod(77,494)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(494, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("494.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 494 = 2 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	494.d (of order $2$, degree $1$, 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:	$3.94460985985$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.153664.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 5x^{4} + 6x^{2} + 1 $ x^6 + 5x^4 + 6x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			77.6
Root			$1.80194i$ of defining polynomial
Character	$\chi$	$=$	494.77
Dual form			494.2.d.b.77.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +2.04892 q^{3} -1.00000 q^{4} +0.198062i q^{5} +2.04892i q^{6} +0.890084i q^{7} -1.00000i q^{8} +1.19806 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +2.04892 q^{3} -1.00000 q^{4} +0.198062i q^{5} +2.04892i q^{6} +0.890084i q^{7} -1.00000i q^{8} +1.19806 q^{9} -0.198062 q^{10} +4.13706i q^{11} -2.04892 q^{12} +(-0.109916 + 3.60388i) q^{13} -0.890084 q^{14} +0.405813i q^{15} +1.00000 q^{16} +2.66487 q^{17} +1.19806i q^{18} -1.00000i q^{19} -0.198062i q^{20} +1.82371i q^{21} -4.13706 q^{22} +8.45473 q^{23} -2.04892i q^{24} +4.96077 q^{25} +(-3.60388 - 0.109916i) q^{26} -3.69202 q^{27} -0.890084i q^{28} -4.13706 q^{29} -0.405813 q^{30} +1.08815i q^{31} +1.00000i q^{32} +8.47650i q^{33} +2.66487i q^{34} -0.176292 q^{35} -1.19806 q^{36} -10.7681i q^{37} +1.00000 q^{38} +(-0.225209 + 7.38404i) q^{39} +0.198062 q^{40} -6.66487i q^{41} -1.82371 q^{42} -6.19567 q^{43} -4.13706i q^{44} +0.237291i q^{45} +8.45473i q^{46} -7.38404i q^{47} +2.04892 q^{48} +6.20775 q^{49} +4.96077i q^{50} +5.46011 q^{51} +(0.109916 - 3.60388i) q^{52} -3.40581 q^{53} -3.69202i q^{54} -0.819396 q^{55} +0.890084 q^{56} -2.04892i q^{57} -4.13706i q^{58} -7.20775i q^{59} -0.405813i q^{60} -11.9215 q^{61} -1.08815 q^{62} +1.06638i q^{63} -1.00000 q^{64} +(-0.713792 - 0.0217703i) q^{65} -8.47650 q^{66} +3.87800i q^{67} -2.66487 q^{68} +17.3230 q^{69} -0.176292i q^{70} +6.07606i q^{71} -1.19806i q^{72} +5.16421i q^{73} +10.7681 q^{74} +10.1642 q^{75} +1.00000i q^{76} -3.68233 q^{77} +(-7.38404 - 0.225209i) q^{78} -15.6582 q^{79} +0.198062i q^{80} -11.1588 q^{81} +6.66487 q^{82} -13.1588i q^{83} -1.82371i q^{84} +0.527811i q^{85} -6.19567i q^{86} -8.47650 q^{87} +4.13706 q^{88} +4.53319i q^{89} -0.237291 q^{90} +(-3.20775 - 0.0978347i) q^{91} -8.45473 q^{92} +2.22952i q^{93} +7.38404 q^{94} +0.198062 q^{95} +2.04892i q^{96} +8.18060i q^{97} +6.20775i q^{98} +4.95646i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{3} - 6 q^{4} + 16 q^{9}+O(q^{10}) $ 6 * q - 6 * q^3 - 6 * q^4 + 16 * q^9	$ 6 q - 6 q^{3} - 6 q^{4} + 16 q^{9} - 10 q^{10} + 6 q^{12} - 2 q^{13} - 4 q^{14} + 6 q^{16} + 18 q^{17} - 14 q^{22} + 6 q^{23} + 4 q^{25} - 4 q^{26} - 12 q^{27} - 14 q^{29} + 24 q^{30} - 16 q^{35} - 16 q^{36} + 6 q^{38} + 2 q^{39} + 10 q^{40} + 4 q^{42} + 36 q^{43} - 6 q^{48} + 2 q^{49} - 18 q^{51} + 2 q^{52} + 6 q^{53} - 28 q^{55} + 4 q^{56} - 20 q^{61} - 14 q^{62} - 6 q^{64} + 12 q^{65} - 18 q^{68} + 64 q^{69} + 24 q^{74} + 38 q^{75} - 56 q^{77} - 24 q^{78} - 52 q^{79} - 50 q^{81} + 42 q^{82} + 14 q^{88} - 36 q^{90} + 16 q^{91} - 6 q^{92} + 24 q^{94} + 10 q^{95}+O(q^{100}) $ 6 * q - 6 * q^3 - 6 * q^4 + 16 * q^9 - 10 * q^10 + 6 * q^12 - 2 * q^13 - 4 * q^14 + 6 * q^16 + 18 * q^17 - 14 * q^22 + 6 * q^23 + 4 * q^25 - 4 * q^26 - 12 * q^27 - 14 * q^29 + 24 * q^30 - 16 * q^35 - 16 * q^36 + 6 * q^38 + 2 * q^39 + 10 * q^40 + 4 * q^42 + 36 * q^43 - 6 * q^48 + 2 * q^49 - 18 * q^51 + 2 * q^52 + 6 * q^53 - 28 * q^55 + 4 * q^56 - 20 * q^61 - 14 * q^62 - 6 * q^64 + 12 * q^65 - 18 * q^68 + 64 * q^69 + 24 * q^74 + 38 * q^75 - 56 * q^77 - 24 * q^78 - 52 * q^79 - 50 * q^81 + 42 * q^82 + 14 * q^88 - 36 * q^90 + 16 * q^91 - 6 * q^92 + 24 * q^94 + 10 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/494\mathbb{Z}\right)^\times$.

$n$	$287$	$457$
$\chi(n)$	$1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	2.04892			1.18294			0.591471	−	0.806326i	$-0.298547\pi$
$3$	2.04892			1.18294			0.591471	+	0.806326i	$0.298547\pi$
$4$	−1.00000			−0.500000
$5$			0.198062i			0.0885761i	0.999019	+	0.0442881i	$0.0141019\pi$
$5$			0.198062i			0.0885761i	−0.999019	+	0.0442881i	$0.985898\pi$
$6$			2.04892i			0.836467i
$7$			0.890084i			0.336420i	0.985751	+	0.168210i	$0.0537987\pi$
$7$			0.890084i			0.336420i	−0.985751	+	0.168210i	$0.946201\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.19806			0.399354
$10$	−0.198062			−0.0626328
$11$			4.13706i			1.24737i	0.781675	+	0.623686i	$0.214366\pi$
$11$			4.13706i			1.24737i	−0.781675	+	0.623686i	$0.785634\pi$
$12$	−2.04892			−0.591471
$13$	−0.109916	+	3.60388i	−0.0304853	+	0.999535i
$13$	−0.109916	+	3.60388i	−0.0304853	+	0.999535i
$14$	−0.890084			−0.237885
$15$			0.405813i			0.104781i
$16$	1.00000			0.250000
$17$	2.66487			0.646327			0.323163	−	0.946343i	$-0.395254\pi$
$17$	2.66487			0.646327			0.323163	+	0.946343i	$0.395254\pi$
$18$			1.19806i			0.282386i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$		−	0.198062i		−	0.0442881i
$21$			1.82371i			0.397966i
$22$	−4.13706			−0.882025
$23$	8.45473			1.76293			0.881467	−	0.472246i	$-0.156557\pi$
$23$	8.45473			1.76293			0.881467	+	0.472246i	$0.156557\pi$
$24$		−	2.04892i		−	0.418234i
$25$	4.96077			0.992154
$26$	−3.60388	−	0.109916i	−0.706778	−	0.0215564i
$27$	−3.69202			−0.710530
$28$		−	0.890084i		−	0.168210i
$29$	−4.13706			−0.768233			−0.384117	−	0.923285i	$-0.625494\pi$
$29$	−4.13706			−0.768233			−0.384117	+	0.923285i	$0.625494\pi$
$30$	−0.405813			−0.0740910
$31$			1.08815i			0.195437i	0.995214	+	0.0977184i	$0.0311544\pi$
$31$			1.08815i			0.195437i	−0.995214	+	0.0977184i	$0.968846\pi$
$32$			1.00000i			0.176777i
$33$			8.47650i			1.47557i
$34$			2.66487i			0.457022i
$35$	−0.176292			−0.0297988
$36$	−1.19806			−0.199677
$37$		−	10.7681i		−	1.77026i	−0.465342	−	0.885131i	$-0.654068\pi$
$37$		−	10.7681i		−	1.77026i	0.465342	−	0.885131i	$-0.345932\pi$
$38$	1.00000			0.162221
$39$	−0.225209	+	7.38404i	−0.0360624	+	1.18239i
$40$	0.198062			0.0313164
$41$		−	6.66487i		−	1.04088i	−0.853899	−	0.520439i	$-0.825768\pi$
$41$		−	6.66487i		−	1.04088i	0.853899	−	0.520439i	$-0.174232\pi$
$42$	−1.82371			−0.281404
$43$	−6.19567			−0.944831			−0.472415	−	0.881376i	$-0.656618\pi$
$43$	−6.19567			−0.944831			−0.472415	+	0.881376i	$0.656618\pi$
$44$		−	4.13706i		−	0.623686i
$45$			0.237291i			0.0353732i
$46$			8.45473i			1.24658i
$47$		−	7.38404i		−	1.07707i	−0.842602	−	0.538537i	$-0.818977\pi$
$47$		−	7.38404i		−	1.07707i	0.842602	−	0.538537i	$-0.181023\pi$
$48$	2.04892			0.295736
$49$	6.20775			0.886822
$50$			4.96077i			0.701559i
$51$	5.46011			0.764568
$52$	0.109916	−	3.60388i	0.0152426	−	0.499768i
$53$	−3.40581			−0.467824			−0.233912	−	0.972258i	$-0.575153\pi$
$53$	−3.40581			−0.467824			−0.233912	+	0.972258i	$0.575153\pi$
$54$		−	3.69202i		−	0.502420i
$55$	−0.819396			−0.110487
$56$	0.890084			0.118942
$57$		−	2.04892i		−	0.271386i
$58$		−	4.13706i		−	0.543223i
$59$		−	7.20775i		−	0.938369i	−0.883100	−	0.469185i	$-0.844548\pi$
$59$		−	7.20775i		−	0.938369i	0.883100	−	0.469185i	$-0.155452\pi$
$60$		−	0.405813i		−	0.0523903i
$61$	−11.9215			−1.52640			−0.763199	−	0.646164i	$-0.776372\pi$
$61$	−11.9215			−1.52640			−0.763199	+	0.646164i	$0.776372\pi$
$62$	−1.08815			−0.138195
$63$			1.06638i			0.134351i
$64$	−1.00000			−0.125000
$65$	−0.713792	−	0.0217703i	−0.0885350	−	0.00270027i
$66$	−8.47650			−1.04339
$67$			3.87800i			0.473773i	0.971537	+	0.236887i	$0.0761270\pi$
$67$			3.87800i			0.473773i	−0.971537	+	0.236887i	$0.923873\pi$
$68$	−2.66487			−0.323163
$69$	17.3230			2.08545
$70$		−	0.176292i		−	0.0210709i
$71$			6.07606i			0.721096i	0.932741	+	0.360548i	$0.117410\pi$
$71$			6.07606i			0.721096i	−0.932741	+	0.360548i	$0.882590\pi$
$72$		−	1.19806i		−	0.141193i
$73$			5.16421i			0.604425i	0.953241	+	0.302213i	$0.0977252\pi$
$73$			5.16421i			0.604425i	−0.953241	+	0.302213i	$0.902275\pi$
$74$	10.7681			1.25176
$75$	10.1642			1.17366
$76$			1.00000i			0.114708i
$77$	−3.68233			−0.419641
$78$	−7.38404	−	0.225209i	−0.836078	−	0.0254999i
$79$	−15.6582			−1.76168			−0.880841	−	0.473412i	$-0.843022\pi$
$79$	−15.6582			−1.76168			−0.880841	+	0.473412i	$0.843022\pi$
$80$			0.198062i			0.0221440i
$81$	−11.1588			−1.23987
$82$	6.66487			0.736012
$83$		−	13.1588i		−	1.44437i	−0.691700	−	0.722185i	$-0.743138\pi$
$83$		−	13.1588i		−	1.44437i	0.691700	−	0.722185i	$-0.256862\pi$
$84$		−	1.82371i		−	0.198983i
$85$			0.527811i			0.0572491i
$86$		−	6.19567i		−	0.668096i
$87$	−8.47650			−0.908776
$88$	4.13706			0.441012
$89$			4.53319i			0.480517i	0.970709	+	0.240258i	$0.0772322\pi$
$89$			4.53319i			0.480517i	−0.970709	+	0.240258i	$0.922768\pi$
$90$	−0.237291			−0.0250127
$91$	−3.20775	−	0.0978347i	−0.336264	−	0.0102559i
$92$	−8.45473			−0.881467
$93$			2.22952i			0.231191i
$94$	7.38404			0.761606
$95$	0.198062			0.0203208
$96$			2.04892i			0.209117i
$97$			8.18060i			0.830614i	0.909681	+	0.415307i	$0.136326\pi$
$97$			8.18060i			0.830614i	−0.909681	+	0.415307i	$0.863674\pi$
$98$			6.20775i			0.627078i
$99$			4.95646i			0.498143i
$100$	−4.96077			−0.496077
$101$	−1.32975			−0.132315			−0.0661575	−	0.997809i	$-0.521074\pi$
$101$	−1.32975			−0.132315			−0.0661575	+	0.997809i	$0.521074\pi$
$102$			5.46011i			0.540631i
$103$	0.670251			0.0660418			0.0330209	−	0.999455i	$-0.489487\pi$
$103$	0.670251			0.0660418			0.0330209	+	0.999455i	$0.489487\pi$
$104$	3.60388	+	0.109916i	0.353389	+	0.0107782i
$105$	−0.361208			−0.0352503
$106$		−	3.40581i		−	0.330802i
$107$	13.1075			1.26715			0.633576	−	0.773680i	$-0.281586\pi$
$107$	13.1075			1.26715			0.633576	+	0.773680i	$0.281586\pi$
$108$	3.69202			0.355265
$109$		−	15.0858i		−	1.44495i	−0.691395	−	0.722477i	$-0.743004\pi$
$109$		−	15.0858i		−	1.44495i	0.691395	−	0.722477i	$-0.256996\pi$
$110$		−	0.819396i		−	0.0781264i
$111$		−	22.0629i		−	2.09412i
$112$			0.890084i			0.0841050i
$113$	19.5254			1.83680			0.918398	−	0.395657i	$-0.129483\pi$
$113$	19.5254			1.83680			0.918398	+	0.395657i	$0.129483\pi$
$114$	2.04892			0.191899
$115$			1.67456i			0.156154i
$116$	4.13706			0.384117
$117$	−0.131687	+	4.31767i	−0.0121744	+	0.399168i
$118$	7.20775			0.663527
$119$			2.37196i			0.217437i
$120$	0.405813			0.0370455
$121$	−6.11529			−0.555936
$122$		−	11.9215i		−	1.07933i
$123$		−	13.6558i		−	1.23130i
$124$		−	1.08815i		−	0.0977184i
$125$			1.97285i			0.176457i
$126$	−1.06638			−0.0950003
$127$	13.2078			1.17200			0.585999	−	0.810312i	$-0.300702\pi$
$127$	13.2078			1.17200			0.585999	+	0.810312i	$0.300702\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−12.6944			−1.11768
$130$	0.0217703	−	0.713792i	0.00190938	−	0.0626037i
$131$	14.9879			1.30950			0.654750	−	0.755845i	$-0.272774\pi$
$131$	14.9879			1.30950			0.654750	+	0.755845i	$0.272774\pi$
$132$		−	8.47650i		−	0.737785i
$133$	0.890084			0.0771800
$134$	−3.87800			−0.335008
$135$		−	0.731250i		−	0.0629360i
$136$		−	2.66487i		−	0.228511i
$137$		−	17.3056i		−	1.47852i	−0.673422	−	0.739258i	$-0.735176\pi$
$137$		−	17.3056i		−	1.47852i	0.673422	−	0.739258i	$-0.264824\pi$
$138$			17.3230i			1.47464i
$139$	14.4155			1.22271			0.611353	−	0.791358i	$-0.290625\pi$
$139$	14.4155			1.22271			0.611353	+	0.791358i	$0.290625\pi$
$140$	0.176292			0.0148994
$141$		−	15.1293i		−	1.27412i
$142$	−6.07606			−0.509892
$143$	−14.9095	−	0.454731i	−1.24679	−	0.0380265i
$144$	1.19806			0.0998385
$145$		−	0.819396i		−	0.0680471i
$146$	−5.16421			−0.427393
$147$	12.7192			1.04906
$148$			10.7681i			0.885131i
$149$			5.38942i			0.441518i	0.975328	+	0.220759i	$0.0708535\pi$
$149$			5.38942i			0.441518i	−0.975328	+	0.220759i	$0.929146\pi$
$150$			10.1642i			0.829904i
$151$			15.9366i			1.29690i	0.761256	+	0.648451i	$0.224583\pi$
$151$			15.9366i			1.29690i	−0.761256	+	0.648451i	$0.775417\pi$
$152$	−1.00000			−0.0811107
$153$	3.19269			0.258113
$154$		−	3.68233i		−	0.296731i
$155$	−0.215521			−0.0173110
$156$	0.225209	−	7.38404i	0.0180312	−	0.591197i
$157$	−10.5483			−0.841842			−0.420921	−	0.907097i	$-0.638293\pi$
$157$	−10.5483			−0.841842			−0.420921	+	0.907097i	$0.638293\pi$
$158$		−	15.6582i		−	1.24570i
$159$	−6.97823			−0.553410
$160$	−0.198062			−0.0156582
$161$			7.52542i			0.593086i
$162$		−	11.1588i		−	0.876721i
$163$			5.59850i			0.438508i	0.975668	+	0.219254i	$0.0703624\pi$
$163$			5.59850i			0.438508i	−0.975668	+	0.219254i	$0.929638\pi$
$164$			6.66487i			0.520439i
$165$	−1.67887			−0.130700
$166$	13.1588			1.02132
$167$		−	13.8485i		−	1.07163i	−0.844337	−	0.535813i	$-0.820005\pi$
$167$		−	13.8485i		−	1.07163i	0.844337	−	0.535813i	$-0.179995\pi$
$168$	1.82371			0.140702
$169$	−12.9758	−	0.792249i	−0.998141	−	0.0609422i
$170$	−0.527811			−0.0404813
$171$		−	1.19806i		−	0.0916181i
$172$	6.19567			0.472415
$173$	−15.4523			−1.17482			−0.587410	−	0.809290i	$-0.699852\pi$
$173$	−15.4523			−1.17482			−0.587410	+	0.809290i	$0.699852\pi$
$174$		−	8.47650i		−	0.642602i
$175$			4.41550i			0.333781i
$176$			4.13706i			0.311843i
$177$		−	14.7681i		−	1.11004i
$178$	−4.53319			−0.339777
$179$	12.7114			0.950095			0.475047	−	0.879960i	$-0.342431\pi$
$179$	12.7114			0.950095			0.475047	+	0.879960i	$0.342431\pi$
$180$		−	0.237291i		−	0.0176866i
$181$	−13.4765			−1.00170			−0.500850	−	0.865534i	$-0.666979\pi$
$181$	−13.4765			−1.00170			−0.500850	+	0.865534i	$0.666979\pi$
$182$	0.0978347	−	3.20775i	0.00725199	−	0.237774i
$183$	−24.4263			−1.80564
$184$		−	8.45473i		−	0.623291i
$185$	2.13275			0.156803
$186$	−2.22952			−0.163476
$187$			11.0248i			0.806210i
$188$			7.38404i			0.538537i
$189$		−	3.28621i		−	0.239036i
$190$			0.198062i			0.0143689i
$191$	18.5157			1.33975			0.669876	−	0.742473i	$-0.266347\pi$
$191$	18.5157			1.33975			0.669876	+	0.742473i	$0.266347\pi$
$192$	−2.04892			−0.147868
$193$			3.55496i			0.255891i	0.991781	+	0.127946i	$0.0408383\pi$
$193$			3.55496i			0.255891i	−0.991781	+	0.127946i	$0.959162\pi$
$194$	−8.18060			−0.587333
$195$	−1.46250	−	0.0446055i	−0.104732	−	0.00319426i
$196$	−6.20775			−0.443411
$197$		−	2.19567i		−	0.156435i	−0.996936	−	0.0782175i	$-0.975077\pi$
$197$		−	2.19567i		−	0.156435i	0.996936	−	0.0782175i	$-0.0249229\pi$
$198$	−4.95646			−0.352240
$199$	15.2228			1.07912			0.539558	−	0.841948i	$-0.318591\pi$
$199$	15.2228			1.07912			0.539558	+	0.841948i	$0.318591\pi$
$200$		−	4.96077i		−	0.350780i
$201$			7.94571i			0.560447i
$202$		−	1.32975i		−	0.0935608i
$203$		−	3.68233i		−	0.258449i
$204$	−5.46011			−0.382284
$205$	1.32006			0.0921970
$206$			0.670251i			0.0466986i
$207$	10.1293			0.704035
$208$	−0.109916	+	3.60388i	−0.00762132	+	0.249884i
$209$	4.13706			0.286167
$210$		−	0.361208i		−	0.0249257i
$211$	−17.2905			−1.19033			−0.595164	−	0.803604i	$-0.702913\pi$
$211$	−17.2905			−1.19033			−0.595164	+	0.803604i	$0.702913\pi$
$212$	3.40581			0.233912
$213$			12.4494i			0.853016i
$214$			13.1075i			0.896012i
$215$		−	1.22713i		−	0.0836895i
$216$			3.69202i			0.251210i
$217$	−0.968541			−0.0657489
$218$	15.0858			1.02174
$219$			10.5810i			0.715000i
$220$	0.819396			0.0552437
$221$	−0.292913	+	9.60388i	−0.0197035	+	0.646027i
$222$	22.0629			1.48077
$223$			19.8726i			1.33077i	0.746501	+	0.665385i	$0.231732\pi$
$223$			19.8726i			1.33077i	−0.746501	+	0.665385i	$0.768268\pi$
$224$	−0.890084			−0.0594712
$225$	5.94331			0.396221
$226$			19.5254i			1.29881i
$227$		−	4.76809i		−	0.316469i	−0.987402	−	0.158234i	$-0.949420\pi$
$227$		−	4.76809i		−	0.316469i	0.987402	−	0.158234i	$-0.0505802\pi$
$228$			2.04892i			0.135693i
$229$			23.8931i			1.57890i	0.613816	+	0.789449i	$0.289634\pi$
$229$			23.8931i			1.57890i	−0.613816	+	0.789449i	$0.710366\pi$
$230$	−1.67456			−0.110417
$231$	−7.54480			−0.496411
$232$			4.13706i			0.271612i
$233$	−11.7778			−0.771588			−0.385794	−	0.922585i	$-0.626072\pi$
$233$	−11.7778			−0.771588			−0.385794	+	0.922585i	$0.626072\pi$
$234$	−4.31767	−	0.131687i	−0.282255	−	0.00860862i
$235$	1.46250			0.0954030
$236$			7.20775i			0.469185i
$237$	−32.0823			−2.08397
$238$	−2.37196			−0.153751
$239$		−	12.2983i		−	0.795510i	−0.917492	−	0.397755i	$-0.869789\pi$
$239$		−	12.2983i		−	0.795510i	0.917492	−	0.397755i	$-0.130211\pi$
$240$			0.405813i			0.0261951i
$241$		−	0.613564i		−	0.0395231i	−0.999805	−	0.0197616i	$-0.993709\pi$
$241$		−	0.613564i		−	0.0395231i	0.999805	−	0.0197616i	$-0.00629071\pi$
$242$		−	6.11529i		−	0.393106i
$243$	−11.7875			−0.756166
$244$	11.9215			0.763199
$245$			1.22952i			0.0785512i
$246$	13.6558			0.870661
$247$	3.60388	+	0.109916i	0.229309	+	0.00699380i
$248$	1.08815			0.0690973
$249$		−	26.9614i		−	1.70861i
$250$	−1.97285			−0.124774
$251$	21.1836			1.33710			0.668548	−	0.743669i	$-0.266916\pi$
$251$	21.1836			1.33710			0.668548	+	0.743669i	$0.266916\pi$
$252$		−	1.06638i		−	0.0671754i
$253$			34.9778i			2.19903i
$254$			13.2078i			0.828728i
$255$			1.08144i			0.0677225i
$256$	1.00000			0.0625000
$257$	−15.1535			−0.945247			−0.472623	−	0.881265i	$-0.656693\pi$
$257$	−15.1535			−0.945247			−0.472623	+	0.881265i	$0.656693\pi$
$258$		−	12.6944i		−	0.790320i
$259$	9.58450			0.595552
$260$	0.713792	+	0.0217703i	0.0442675	+	0.00135013i
$261$	−4.95646			−0.306797
$262$			14.9879i			0.925957i
$263$	−9.45712			−0.583151			−0.291576	−	0.956548i	$-0.594179\pi$
$263$	−9.45712			−0.583151			−0.291576	+	0.956548i	$0.594179\pi$
$264$	8.47650			0.521693
$265$		−	0.674563i		−	0.0414381i
$266$			0.890084i			0.0545745i
$267$			9.28813i			0.568424i
$268$		−	3.87800i		−	0.236887i
$269$	−13.4034			−0.817221			−0.408610	−	0.912709i	$-0.633987\pi$
$269$	−13.4034			−0.817221			−0.408610	+	0.912709i	$0.633987\pi$
$270$	0.731250			0.0445025
$271$			24.7138i			1.50126i	0.660725	+	0.750628i	$0.270249\pi$
$271$			24.7138i			1.50126i	−0.660725	+	0.750628i	$0.729751\pi$
$272$	2.66487			0.161582
$273$	−6.57242	−	0.200455i	−0.397781	−	0.0121321i
$274$	17.3056			1.04547
$275$			20.5230i			1.23758i
$276$	−17.3230			−1.04272
$277$	−8.78746			−0.527987			−0.263994	−	0.964524i	$-0.585040\pi$
$277$	−8.78746			−0.527987			−0.263994	+	0.964524i	$0.585040\pi$
$278$			14.4155i			0.864584i
$279$			1.30367i			0.0780485i
$280$			0.176292i			0.0105355i
$281$			17.7168i			1.05689i	0.848966	+	0.528447i	$0.177226\pi$
$281$			17.7168i			1.05689i	−0.848966	+	0.528447i	$0.822774\pi$
$282$	15.1293			0.900936
$283$	9.96508			0.592363			0.296181	−	0.955132i	$-0.404287\pi$
$283$	9.96508			0.592363			0.296181	+	0.955132i	$0.404287\pi$
$284$		−	6.07606i		−	0.360548i
$285$	0.405813			0.0240383
$286$	0.454731	−	14.9095i	0.0268888	−	0.881615i
$287$	5.93230			0.350172
$288$			1.19806i			0.0705965i
$289$	−9.89844			−0.582261
$290$	0.819396			0.0481166
$291$			16.7614i			0.982570i
$292$		−	5.16421i		−	0.302213i
$293$		−	11.1099i		−	0.649048i	−0.945877	−	0.324524i	$-0.894796\pi$
$293$		−	11.1099i		−	0.649048i	0.945877	−	0.324524i	$-0.105204\pi$
$294$			12.7192i			0.741797i
$295$	1.42758			0.0831171
$296$	−10.7681			−0.625882
$297$		−	15.2741i		−	0.886295i
$298$	−5.38942			−0.312201
$299$	−0.929312	+	30.4698i	−0.0537435	+	1.76211i
$300$	−10.1642			−0.586831
$301$		−	5.51466i		−	0.317860i
$302$	−15.9366			−0.917049
$303$	−2.72455			−0.156521
$304$		−	1.00000i		−	0.0573539i
$305$		−	2.36121i		−	0.135202i
$306$			3.19269i			0.182514i
$307$		−	9.83446i		−	0.561282i	−0.959813	−	0.280641i	$-0.909453\pi$
$307$		−	9.83446i		−	0.561282i	0.959813	−	0.280641i	$-0.0905471\pi$
$308$	3.68233			0.209820
$309$	1.37329			0.0781237
$310$		−	0.215521i		−	0.0122408i
$311$	−11.8726			−0.673235			−0.336617	−	0.941642i	$-0.609283\pi$
$311$	−11.8726			−0.673235			−0.336617	+	0.941642i	$0.609283\pi$
$312$	7.38404	+	0.225209i	0.418039	+	0.0127500i
$313$	−8.81402			−0.498198			−0.249099	−	0.968478i	$-0.580134\pi$
$313$	−8.81402			−0.498198			−0.249099	+	0.968478i	$0.580134\pi$
$314$		−	10.5483i		−	0.595272i
$315$	−0.211209			−0.0119003
$316$	15.6582			0.880841
$317$		−	12.7138i		−	0.714078i	−0.934090	−	0.357039i	$-0.883786\pi$
$317$		−	12.7138i		−	0.714078i	0.934090	−	0.357039i	$-0.116214\pi$
$318$		−	6.97823i		−	0.391320i
$319$		−	17.1153i		−	0.958272i
$320$		−	0.198062i		−	0.0110720i
$321$	26.8562			1.49897
$322$	−7.52542			−0.419375
$323$		−	2.66487i		−	0.148278i
$324$	11.1588			0.619935
$325$	−0.545269	+	17.8780i	−0.0302461	+	0.991693i
$326$	−5.59850			−0.310072
$327$		−	30.9095i		−	1.70930i
$328$	−6.66487			−0.368006
$329$	6.57242			0.362349
$330$		−	1.67887i		−	0.0924190i
$331$		−	18.1715i		−	0.998796i	−0.866373	−	0.499398i	$-0.833554\pi$
$331$		−	18.1715i		−	0.998796i	0.866373	−	0.499398i	$-0.166446\pi$
$332$			13.1588i			0.722185i
$333$		−	12.9008i		−	0.706962i
$334$	13.8485			0.757754
$335$	−0.768086			−0.0419650
$336$			1.82371i			0.0994914i
$337$	−13.9323			−0.758941			−0.379470	−	0.925204i	$-0.623894\pi$
$337$	−13.9323			−0.758941			−0.379470	+	0.925204i	$0.623894\pi$
$338$	0.792249	−	12.9758i	0.0430927	−	0.705792i
$339$	40.0060			2.17283
$340$		−	0.527811i		−	0.0286246i
$341$	−4.50173			−0.243782
$342$	1.19806			0.0647838
$343$			11.7560i			0.634765i
$344$			6.19567i			0.334048i
$345$			3.43104i			0.184721i
$346$		−	15.4523i		−	0.830723i
$347$	−8.02416			−0.430760			−0.215380	−	0.976530i	$-0.569099\pi$
$347$	−8.02416			−0.430760			−0.215380	+	0.976530i	$0.569099\pi$
$348$	8.47650			0.454388
$349$		−	10.7192i		−	0.573784i	−0.957963	−	0.286892i	$-0.907378\pi$
$349$		−	10.7192i		−	0.573784i	0.957963	−	0.286892i	$-0.0926221\pi$
$350$	−4.41550			−0.236019
$351$	0.405813	−	13.3056i	0.0216607	−	0.710200i
$352$	−4.13706			−0.220506
$353$			36.1172i			1.92233i	0.275983	+	0.961163i	$0.410997\pi$
$353$			36.1172i			1.92233i	−0.275983	+	0.961163i	$0.589003\pi$
$354$	14.7681			0.784915
$355$	−1.20344			−0.0638719
$356$		−	4.53319i		−	0.240258i
$357$			4.85995i			0.257216i
$358$			12.7114i			0.671818i
$359$		−	32.3129i		−	1.70541i	−0.522394	−	0.852704i	$-0.674961\pi$
$359$		−	32.3129i		−	1.70541i	0.522394	−	0.852704i	$-0.325039\pi$
$360$	0.237291			0.0125063
$361$	−1.00000			−0.0526316
$362$		−	13.4765i		−	0.708309i
$363$	−12.5297			−0.657640
$364$	3.20775	+	0.0978347i	0.168132	+	0.00512793i
$365$	−1.02284			−0.0535376
$366$		−	24.4263i		−	1.27678i
$367$	5.24027			0.273540			0.136770	−	0.990603i	$-0.456328\pi$
$367$	5.24027			0.273540			0.136770	+	0.990603i	$0.456328\pi$
$368$	8.45473			0.440733
$369$		−	7.98493i		−	0.415679i
$370$			2.13275i			0.110876i
$371$		−	3.03146i		−	0.157386i
$372$		−	2.22952i		−	0.115595i
$373$	−14.6213			−0.757064			−0.378532	−	0.925588i	$-0.623571\pi$
$373$	−14.6213			−0.757064			−0.378532	+	0.925588i	$0.623571\pi$
$374$	−11.0248			−0.570076
$375$			4.04221i			0.208739i
$376$	−7.38404			−0.380803
$377$	0.454731	−	14.9095i	0.0234198	−	0.767876i
$378$	3.28621			0.169024
$379$		−	14.8116i		−	0.760822i	−0.924818	−	0.380411i	$-0.875783\pi$
$379$		−	14.8116i		−	0.760822i	0.924818	−	0.380411i	$-0.124217\pi$
$380$	−0.198062			−0.0101604
$381$	27.0616			1.38641
$382$			18.5157i			0.947347i
$383$			12.2524i			0.626066i	0.949742	+	0.313033i	$0.101345\pi$
$383$			12.2524i			0.626066i	−0.949742	+	0.313033i	$0.898655\pi$
$384$		−	2.04892i		−	0.104558i
$385$		−	0.729331i		−	0.0371702i
$386$	−3.55496			−0.180943
$387$	−7.42280			−0.377322
$388$		−	8.18060i		−	0.415307i
$389$	−33.6969			−1.70850			−0.854251	−	0.519861i	$-0.825984\pi$
$389$	−33.6969			−1.70850			−0.854251	+	0.519861i	$0.825984\pi$
$390$	0.0446055	−	1.46250i	0.00225869	−	0.0740566i
$391$	22.5308			1.13943
$392$		−	6.20775i		−	0.313539i
$393$	30.7090			1.54906
$394$	2.19567			0.110616
$395$		−	3.10129i		−	0.156043i
$396$		−	4.95646i		−	0.249071i
$397$			0.198062i			0.00994046i	0.999988	+	0.00497023i	$0.00158208\pi$
$397$			0.198062i			0.00994046i	−0.999988	+	0.00497023i	$0.998418\pi$
$398$			15.2228i			0.763051i
$399$	1.82371			0.0912996
$400$	4.96077			0.248039
$401$		−	7.22952i		−	0.361025i	−0.983573	−	0.180513i	$-0.942224\pi$
$401$		−	7.22952i		−	0.361025i	0.983573	−	0.180513i	$-0.0577756\pi$
$402$	−7.94571			−0.396296
$403$	−3.92154	−	0.119605i	−0.195346	−	0.00595795i
$404$	1.32975			0.0661575
$405$		−	2.21014i		−	0.109823i
$406$	3.68233			0.182751
$407$	44.5483			2.20817
$408$		−	5.46011i		−	0.270316i
$409$			10.5483i			0.521578i	0.965396	+	0.260789i	$0.0839826\pi$
$409$			10.5483i			0.521578i	−0.965396	+	0.260789i	$0.916017\pi$
$410$			1.32006i			0.0651931i
$411$		−	35.4577i		−	1.74900i
$412$	−0.670251			−0.0330209
$413$	6.41550			0.315686
$414$			10.1293i			0.497828i
$415$	2.60627			0.127937
$416$	−3.60388	−	0.109916i	−0.176695	−	0.00538909i
$417$	29.5362			1.44639
$418$			4.13706i			0.202350i
$419$	−9.92154			−0.484699			−0.242350	−	0.970189i	$-0.577918\pi$
$419$	−9.92154			−0.484699			−0.242350	+	0.970189i	$0.577918\pi$
$420$	0.361208			0.0176251
$421$		−	25.4577i		−	1.24073i	−0.784312	−	0.620367i	$-0.786984\pi$
$421$		−	25.4577i		−	1.24073i	0.784312	−	0.620367i	$-0.213016\pi$
$422$		−	17.2905i		−	0.841689i
$423$		−	8.84654i		−	0.430134i
$424$			3.40581i			0.165401i
$425$	13.2198			0.641256
$426$	−12.4494			−0.603173
$427$		−	10.6112i		−	0.513511i
$428$	−13.1075			−0.633576
$429$	−30.5483	−	0.931705i	−1.47488	−	0.0449832i
$430$	1.22713			0.0591774
$431$		−	1.26145i		−	0.0607621i	−0.999538	−	0.0303811i	$-0.990328\pi$
$431$		−	1.26145i		−	0.0607621i	0.999538	−	0.0303811i	$-0.00967208\pi$
$432$	−3.69202			−0.177632
$433$	5.78017			0.277777			0.138889	−	0.990308i	$-0.455647\pi$
$433$	5.78017			0.277777			0.138889	+	0.990308i	$0.455647\pi$
$434$		−	0.968541i		−	0.0464915i
$435$		−	1.67887i		−	0.0804959i
$436$			15.0858i			0.722477i
$437$		−	8.45473i		−	0.404445i
$438$	−10.5810			−0.505582
$439$	−15.6668			−0.747735			−0.373868	−	0.927482i	$-0.621969\pi$
$439$	−15.6668			−0.747735			−0.373868	+	0.927482i	$0.621969\pi$
$440$			0.819396i			0.0390632i
$441$	7.43727			0.354156
$442$	−9.60388	−	0.292913i	−0.456810	−	0.0139325i
$443$	4.89008			0.232335			0.116167	−	0.993230i	$-0.462939\pi$
$443$	4.89008			0.232335			0.116167	+	0.993230i	$0.462939\pi$
$444$			22.0629i			1.04706i
$445$	−0.897853			−0.0425623
$446$	−19.8726			−0.940996
$447$			11.0425i			0.522291i
$448$		−	0.890084i		−	0.0420525i
$449$		−	0.347207i		−	0.0163857i	−0.999966	−	0.00819286i	$-0.997392\pi$
$449$		−	0.347207i		−	0.0163857i	0.999966	−	0.00819286i	$-0.00260790\pi$
$450$			5.94331i			0.280170i
$451$	27.5730			1.29836
$452$	−19.5254			−0.918398
$453$			32.6528i			1.53416i
$454$	4.76809			0.223777
$455$	0.0193774	−	0.635334i	0.000908425	−	0.0297849i
$456$	−2.04892			−0.0959493
$457$			31.7754i			1.48639i	0.669075	+	0.743195i	$0.266690\pi$
$457$			31.7754i			1.48639i	−0.669075	+	0.743195i	$0.733310\pi$
$458$	−23.8931			−1.11645
$459$	−9.83877			−0.459235
$460$		−	1.67456i		−	0.0780769i
$461$		−	28.2543i		−	1.31593i	−0.753047	−	0.657966i	$-0.771417\pi$
$461$		−	28.2543i		−	1.31593i	0.753047	−	0.657966i	$-0.228583\pi$
$462$		−	7.54480i		−	0.351016i
$463$			2.42029i			0.112480i	0.998417	+	0.0562402i	$0.0179112\pi$
$463$			2.42029i			0.112480i	−0.998417	+	0.0562402i	$0.982089\pi$
$464$	−4.13706			−0.192058
$465$	−0.441584			−0.0204780
$466$		−	11.7778i		−	0.545595i
$467$	10.5724			0.489233			0.244617	−	0.969620i	$-0.421338\pi$
$467$	10.5724			0.489233			0.244617	+	0.969620i	$0.421338\pi$
$468$	0.131687	−	4.31767i	0.00608721	−	0.199584i
$469$	−3.45175			−0.159387
$470$			1.46250i			0.0674601i
$471$	−21.6125			−0.995851
$472$	−7.20775			−0.331764
$473$		−	25.6319i		−	1.17855i
$474$		−	32.0823i		−	1.47359i
$475$		−	4.96077i		−	0.227616i
$476$		−	2.37196i		−	0.108719i
$477$	−4.08038			−0.186828
$478$	12.2983			0.562511
$479$			29.0616i			1.32786i	0.747796	+	0.663929i	$0.231112\pi$
$479$			29.0616i			1.32786i	−0.747796	+	0.663929i	$0.768888\pi$
$480$	−0.405813			−0.0185228
$481$	38.8068	+	1.18359i	1.76944	+	0.0539670i
$482$	0.613564			0.0279471
$483$			15.4190i			0.701587i
$484$	6.11529			0.277968
$485$	−1.62027			−0.0735726
$486$		−	11.7875i		−	0.534690i
$487$			11.9366i			0.540899i	0.962734	+	0.270450i	$0.0871724\pi$
$487$			11.9366i			0.540899i	−0.962734	+	0.270450i	$0.912828\pi$
$488$			11.9215i			0.539663i
$489$			11.4709i			0.518730i
$490$	−1.22952			−0.0555441
$491$	29.3163			1.32303			0.661514	−	0.749933i	$-0.269914\pi$
$491$	29.3163			1.32303			0.661514	+	0.749933i	$0.269914\pi$
$492$			13.6558i			0.615650i
$493$	−11.0248			−0.496530
$494$	−0.109916	+	3.60388i	−0.00494537	+	0.162146i
$495$	−0.981688			−0.0441236
$496$			1.08815i			0.0488592i
$497$	−5.40821			−0.242591
$498$	26.9614			1.20817
$499$			1.30499i			0.0584196i	0.999573	+	0.0292098i	$0.00929909\pi$
$499$			1.30499i			0.0584196i	−0.999573	+	0.0292098i	$0.990701\pi$
$500$		−	1.97285i		−	0.0882287i
$501$		−	28.3744i		−	1.26767i
$502$			21.1836i			0.945470i
$503$	−6.13275			−0.273446			−0.136723	−	0.990609i	$-0.543657\pi$
$503$	−6.13275			−0.273446			−0.136723	+	0.990609i	$0.543657\pi$
$504$	1.06638			0.0475002
$505$		−	0.263373i		−	0.0117199i
$506$	−34.9778			−1.55495
$507$	−26.5864	−	1.62325i	−1.18074	−	0.0720912i
$508$	−13.2078			−0.585999
$509$		−	22.6219i		−	1.00270i	−0.865245	−	0.501350i	$-0.832837\pi$
$509$		−	22.6219i		−	1.00270i	0.865245	−	0.501350i	$-0.167163\pi$
$510$	−1.08144			−0.0478870
$511$	−4.59658			−0.203341
$512$			1.00000i			0.0441942i
$513$			3.69202i			0.163007i
$514$		−	15.1535i		−	0.668390i
$515$			0.132751i			0.00584973i
$516$	12.6944			0.558840
$517$	30.5483			1.34351
$518$			9.58450i			0.421119i
$519$	−31.6606			−1.38974
$520$	−0.0217703	+	0.713792i	−0.000954689	+	0.0313018i
$521$	−11.0858			−0.485676			−0.242838	−	0.970067i	$-0.578078\pi$
$521$	−11.0858			−0.485676			−0.242838	+	0.970067i	$0.578078\pi$
$522$		−	4.95646i		−	0.216938i
$523$	−35.0834			−1.53409			−0.767044	−	0.641594i	$-0.778273\pi$
$523$	−35.0834			−1.53409			−0.767044	+	0.641594i	$0.778273\pi$
$524$	−14.9879			−0.654750
$525$			9.04700i			0.394843i
$526$		−	9.45712i		−	0.412350i
$527$			2.89977i			0.126316i
$528$			8.47650i			0.368892i
$529$	48.4825			2.10793
$530$	0.674563			0.0293011
$531$		−	8.63533i		−	0.374742i
$532$	−0.890084			−0.0385900
$533$	24.0194	+	0.732578i	1.04039	+	0.0317315i
$534$	−9.28813			−0.401937
$535$			2.59611i			0.112239i
$536$	3.87800			0.167504
$537$	26.0446			1.12391
$538$		−	13.4034i		−	0.577862i
$539$			25.6819i			1.10620i
$540$			0.731250i			0.0314680i
$541$		−	17.8261i		−	0.766404i	−0.923665	−	0.383202i	$-0.874821\pi$
$541$		−	17.8261i		−	0.766404i	0.923665	−	0.383202i	$-0.125179\pi$
$542$	−24.7138			−1.06155
$543$	−27.6122			−1.18495
$544$			2.66487i			0.114256i
$545$	2.98792			0.127988
$546$	0.200455	−	6.57242i	0.00857869	−	0.281273i
$547$	−13.1075			−0.560437			−0.280219	−	0.959936i	$-0.590407\pi$
$547$	−13.1075			−0.560437			−0.280219	+	0.959936i	$0.590407\pi$
$548$			17.3056i			0.739258i
$549$	−14.2828			−0.609573
$550$	−20.5230			−0.875105
$551$			4.13706i			0.176245i
$552$		−	17.3230i		−	0.737318i
$553$		−	13.9371i		−	0.592665i
$554$		−	8.78746i		−	0.373344i
$555$	4.36983			0.185489
$556$	−14.4155			−0.611353
$557$			35.4534i			1.50221i	0.660183	+	0.751104i	$0.270479\pi$
$557$			35.4534i			1.50221i	−0.660183	+	0.751104i	$0.729521\pi$
$558$	−1.30367			−0.0551886
$559$	0.681005	−	22.3284i	0.0288034	−	0.944392i
$560$	−0.176292			−0.00744970
$561$			22.5888i			0.953700i
$562$	−17.7168			−0.747337
$563$	−3.14914			−0.132721			−0.0663603	−	0.997796i	$-0.521139\pi$
$563$	−3.14914			−0.132721			−0.0663603	+	0.997796i	$0.521139\pi$
$564$			15.1293i			0.637058i
$565$			3.86725i			0.162696i
$566$			9.96508i			0.418864i
$567$		−	9.93230i		−	0.417117i
$568$	6.07606			0.254946
$569$	−20.3827			−0.854488			−0.427244	−	0.904136i	$-0.640515\pi$
$569$	−20.3827			−0.854488			−0.427244	+	0.904136i	$0.640515\pi$
$570$			0.405813i			0.0169976i
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$	14.9095	+	0.454731i	0.623396	+	0.0190132i
$573$	37.9372			1.58485
$574$			5.93230i			0.247609i
$575$	41.9420			1.74910
$576$	−1.19806			−0.0499193
$577$		−	30.6219i		−	1.27481i	−0.770530	−	0.637404i	$-0.780008\pi$
$577$		−	30.6219i		−	1.27481i	0.770530	−	0.637404i	$-0.219992\pi$
$578$		−	9.89844i		−	0.411721i
$579$			7.28382i			0.302705i
$580$			0.819396i			0.0340236i
$581$	11.7125			0.485915
$582$	−16.7614			−0.694782
$583$		−	14.0901i		−	0.583551i
$584$	5.16421			0.213697
$585$	−0.855167	−	0.0260821i	−0.0353568	−	0.00107836i
$586$	11.1099			0.458946
$587$			3.40342i			0.140474i	0.997530	+	0.0702371i	$0.0223756\pi$
$587$			3.40342i			0.140474i	−0.997530	+	0.0702371i	$0.977624\pi$
$588$	−12.7192			−0.524530
$589$	1.08815			0.0448363
$590$			1.42758i			0.0587727i
$591$		−	4.49875i		−	0.185054i
$592$		−	10.7681i		−	0.442566i
$593$			4.31767i			0.177305i	0.996063	+	0.0886527i	$0.0282561\pi$
$593$			4.31767i			0.177305i	−0.996063	+	0.0886527i	$0.971744\pi$
$594$	15.2741			0.626705
$595$	−0.469796			−0.0192598
$596$		−	5.38942i		−	0.220759i
$597$	31.1903			1.27653
$598$	−30.4698	−	0.929312i	−1.24600	−	0.0380024i
$599$	−13.0616			−0.533682			−0.266841	−	0.963741i	$-0.585980\pi$
$599$	−13.0616			−0.533682			−0.266841	+	0.963741i	$0.585980\pi$
$600$		−	10.1642i		−	0.414952i
$601$	−42.7284			−1.74293			−0.871464	−	0.490460i	$-0.836829\pi$
$601$	−42.7284			−1.74293			−0.871464	+	0.490460i	$0.836829\pi$
$602$	5.51466			0.224761
$603$			4.64609i			0.189203i
$604$		−	15.9366i		−	0.648451i
$605$		−	1.21121i		−	0.0492426i
$606$		−	2.72455i		−	0.110677i
$607$	−43.9168			−1.78253			−0.891263	−	0.453487i	$-0.850180\pi$
$607$	−43.9168			−1.78253			−0.891263	+	0.453487i	$0.850180\pi$
$608$	1.00000			0.0405554
$609$		−	7.54480i		−	0.305731i
$610$	2.36121			0.0956025
$611$	26.6112	+	0.811626i	1.07657	+	0.0328349i
$612$	−3.19269			−0.129057
$613$		−	1.42519i		−	0.0575629i	−0.999586	−	0.0287815i	$-0.990837\pi$
$613$		−	1.42519i		−	0.0575629i	0.999586	−	0.0287815i	$-0.00916269\pi$
$614$	9.83446			0.396887
$615$	2.70469			0.109064
$616$			3.68233i			0.148365i
$617$			12.4832i			0.502555i	0.967915	+	0.251277i	$0.0808507\pi$
$617$			12.4832i			0.502555i	−0.967915	+	0.251277i	$0.919149\pi$
$618$			1.37329i			0.0552418i
$619$		−	36.1148i		−	1.45158i	−0.687918	−	0.725789i	$-0.741475\pi$
$619$		−	36.1148i		−	1.45158i	0.687918	−	0.725789i	$-0.258525\pi$
$620$	0.215521			0.00865552
$621$	−31.2150			−1.25262
$622$		−	11.8726i		−	0.476049i
$623$	−4.03492			−0.161656
$624$	−0.225209	+	7.38404i	−0.00901559	+	0.295598i
$625$	24.4131			0.976524
$626$		−	8.81402i		−	0.352279i
$627$	8.47650			0.338519
$628$	10.5483			0.420921
$629$		−	28.6956i		−	1.14417i
$630$		−	0.211209i		−	0.00841476i
$631$			2.85517i			0.113662i	0.998384	+	0.0568312i	$0.0180997\pi$
$631$			2.85517i			0.113662i	−0.998384	+	0.0568312i	$0.981900\pi$
$632$			15.6582i			0.622849i
$633$	−35.4268			−1.40809
$634$	12.7138			0.504929
$635$			2.61596i			0.103811i
$636$	6.97823			0.276705
$637$	−0.682333	+	22.3720i	−0.0270350	+	0.886409i
$638$	17.1153			0.677601
$639$			7.27950i			0.287973i
$640$	0.198062			0.00782910
$641$	19.0508			0.752463			0.376231	−	0.926526i	$-0.377220\pi$
$641$	19.0508			0.752463			0.376231	+	0.926526i	$0.377220\pi$
$642$			26.8562i			1.05993i
$643$		−	50.0877i		−	1.97526i	−0.156787	−	0.987632i	$-0.550114\pi$
$643$		−	50.0877i		−	1.97526i	0.156787	−	0.987632i	$-0.449886\pi$
$644$		−	7.52542i		−	0.296543i
$645$		−	2.51428i		−	0.0989999i
$646$	2.66487			0.104848
$647$	−4.00836			−0.157585			−0.0787925	−	0.996891i	$-0.525106\pi$
$647$	−4.00836			−0.157585			−0.0787925	+	0.996891i	$0.525106\pi$
$648$			11.1588i			0.438360i
$649$	29.8189			1.17050
$650$	−17.8780	−	0.545269i	−0.701233	−	0.0213872i
$651$	−1.98446			−0.0777771
$652$		−	5.59850i		−	0.219254i
$653$	14.8116			0.579624			0.289812	−	0.957084i	$-0.406407\pi$
$653$	14.8116			0.579624			0.289812	+	0.957084i	$0.406407\pi$
$654$	30.9095			1.20866
$655$			2.96854i			0.115990i
$656$		−	6.66487i		−	0.260220i
$657$			6.18705i			0.241380i
$658$			6.57242i			0.256219i
$659$	13.0019			0.506483			0.253241	−	0.967403i	$-0.418503\pi$
$659$	13.0019			0.506483			0.253241	+	0.967403i	$0.418503\pi$
$660$	1.67887			0.0653501
$661$		−	2.18705i		−	0.0850662i	−0.999095	−	0.0425331i	$-0.986457\pi$
$661$		−	2.18705i		−	0.0850662i	0.999095	−	0.0425331i	$-0.0135428\pi$
$662$	18.1715			0.706256
$663$	−0.600155	+	19.6775i	−0.0233081	+	0.764213i
$664$	−13.1588			−0.510662
$665$			0.176292i			0.00683631i
$666$	12.9008			0.499897
$667$	−34.9778			−1.35434
$668$			13.8485i			0.535813i
$669$			40.7174i			1.57422i
$670$		−	0.768086i		−	0.0296737i
$671$		−	49.3202i		−	1.90398i
$672$	−1.82371			−0.0703511
$673$	40.6762			1.56795			0.783977	−	0.620790i	$-0.213188\pi$
$673$	40.6762			1.56795			0.783977	+	0.620790i	$0.213188\pi$
$674$		−	13.9323i		−	0.536652i
$675$	−18.3153			−0.704955
$676$	12.9758	+	0.792249i	0.499071	+	0.0304711i
$677$	−1.47757			−0.0567875			−0.0283937	−	0.999597i	$-0.509039\pi$
$677$	−1.47757			−0.0567875			−0.0283937	+	0.999597i	$0.509039\pi$
$678$			40.0060i			1.53642i
$679$	−7.28142			−0.279435
$680$	0.527811			0.0202406
$681$		−	9.76941i		−	0.374365i
$682$		−	4.50173i		−	0.172380i
$683$			48.2210i			1.84513i	0.385847	+	0.922563i	$0.373909\pi$
$683$			48.2210i			1.84513i	−0.385847	+	0.922563i	$0.626091\pi$
$684$			1.19806i			0.0458091i
$685$	3.42758			0.130961
$686$	−11.7560			−0.448846
$687$			48.9549i			1.86775i
$688$	−6.19567			−0.236208
$689$	0.374354	−	12.2741i	0.0142618	−	0.467607i
$690$	−3.43104			−0.130618
$691$			9.73019i			0.370154i	0.982724	+	0.185077i	$0.0592534\pi$
$691$			9.73019i			0.370154i	−0.982724	+	0.185077i	$0.940747\pi$
$692$	15.4523			0.587410
$693$	−4.41166			−0.167585
$694$		−	8.02416i		−	0.304593i
$695$			2.85517i			0.108303i
$696$			8.47650i			0.321301i
$697$		−	17.7611i		−	0.672748i
$698$	10.7192			0.405727
$699$	−24.1317			−0.912744
$700$		−	4.41550i		−	0.166890i
$701$	−33.2030			−1.25406			−0.627029	−	0.778996i	$-0.715729\pi$
$701$	−33.2030			−1.25406			−0.627029	+	0.778996i	$0.715729\pi$
$702$	13.3056	+	0.405813i	0.502187	+	0.0153164i
$703$	−10.7681			−0.406126
$704$		−	4.13706i		−	0.155921i
$705$	2.99654			0.112856
$706$	−36.1172			−1.35929
$707$		−	1.18359i		−	0.0445134i
$708$			14.7681i			0.555019i
$709$		−	12.1715i		−	0.457111i	−0.973531	−	0.228555i	$-0.926600\pi$
$709$		−	12.1715i		−	0.457111i	0.973531	−	0.228555i	$-0.0734002\pi$
$710$		−	1.20344i		−	0.0451643i
$711$	−18.7595			−0.703535
$712$	4.53319			0.169888
$713$			9.19998i			0.344542i
$714$	−4.85995			−0.181879
$715$	0.0900650	−	2.95300i	0.00336824	−	0.110436i
$716$	−12.7114			−0.475047
$717$		−	25.1982i		−	0.941043i
$718$	32.3129			1.20591
$719$	8.43967			0.314746			0.157373	−	0.987539i	$-0.449697\pi$
$719$	8.43967			0.314746			0.157373	+	0.987539i	$0.449697\pi$
$720$			0.237291i			0.00884331i
$721$			0.596580i			0.0222178i
$722$		−	1.00000i		−	0.0372161i
$723$		−	1.25714i		−	0.0467536i
$724$	13.4765			0.500850
$725$	−20.5230			−0.762206
$726$		−	12.5297i		−	0.465022i
$727$	−16.8498			−0.624924			−0.312462	−	0.949930i	$-0.601154\pi$
$727$	−16.8498			−0.624924			−0.312462	+	0.949930i	$0.601154\pi$
$728$	−0.0978347	+	3.20775i	−0.00362599	+	0.118887i
$729$	9.32496			0.345369
$730$		−	1.02284i		−	0.0378568i
$731$	−16.5107			−0.610670
$732$	24.4263			0.902820
$733$			50.3086i			1.85819i	0.369842	+	0.929095i	$0.379412\pi$
$733$			50.3086i			1.85819i	−0.369842	+	0.929095i	$0.620588\pi$
$734$			5.24027i			0.193422i
$735$			2.51919i			0.0929216i
$736$			8.45473i			0.311646i
$737$	−16.0435			−0.590971
$738$	7.98493			0.293930
$739$			9.67324i			0.355836i	0.984045	+	0.177918i	$0.0569361\pi$
$739$			9.67324i			0.355836i	−0.984045	+	0.177918i	$0.943064\pi$
$740$	−2.13275			−0.0784015
$741$	7.38404	+	0.225209i	0.271260	+	0.00827327i
$742$	3.03146			0.111288
$743$			41.6364i			1.52749i	0.645517	+	0.763746i	$0.276642\pi$
$743$			41.6364i			1.52749i	−0.645517	+	0.763746i	$0.723358\pi$
$744$	2.22952			0.0817382
$745$	−1.06744			−0.0391080
$746$		−	14.6213i		−	0.535325i
$747$		−	15.7651i		−	0.576815i
$748$		−	11.0248i		−	0.403105i
$749$			11.6668i			0.426295i
$750$	−4.04221			−0.147601
$751$	43.1680			1.57522			0.787612	−	0.616171i	$-0.211317\pi$
$751$	43.1680			1.57522			0.787612	+	0.616171i	$0.211317\pi$
$752$		−	7.38404i		−	0.269268i
$753$	43.4034			1.58171
$754$	14.9095	+	0.454731i	0.542971	+	0.0165603i
$755$	−3.15644			−0.114875
$756$			3.28621i			0.119518i
$757$	23.1535			0.841527			0.420763	−	0.907170i	$-0.361762\pi$
$757$	23.1535			0.841527			0.420763	+	0.907170i	$0.361762\pi$
$758$	14.8116			0.537982
$759$			71.6665i			2.60133i
$760$		−	0.198062i		−	0.00718447i
$761$			22.2258i			0.805685i	0.915269	+	0.402842i	$0.131978\pi$
$761$			22.2258i			0.805685i	−0.915269	+	0.402842i	$0.868022\pi$
$762$			27.0616i			0.980338i
$763$	13.4276			0.486111
$764$	−18.5157			−0.669876
$765$			0.632351i			0.0228627i
$766$	−12.2524			−0.442696
$767$	25.9758	+	0.792249i	0.937933	+	0.0286065i
$768$	2.04892			0.0739339
$769$		−	14.8552i		−	0.535691i	−0.963462	−	0.267846i	$-0.913688\pi$
$769$		−	14.8552i		−	0.535691i	0.963462	−	0.267846i	$-0.0863117\pi$
$770$	0.729331			0.0262833
$771$	−31.0482			−1.11817
$772$		−	3.55496i		−	0.127946i
$773$			0.537500i			0.0193325i	0.999953	+	0.00966626i	$0.00307691\pi$
$773$			0.537500i			0.0193325i	−0.999953	+	0.00966626i	$0.996923\pi$
$774$		−	7.42280i		−	0.266807i
$775$			5.39804i			0.193903i
$776$	8.18060			0.293667
$777$	19.6378			0.704504
$778$		−	33.6969i		−	1.20809i
$779$	−6.66487			−0.238794
$780$	1.46250	+	0.0446055i	0.0523659	+	0.00159713i
$781$	−25.1371			−0.899475
$782$			22.5308i			0.805700i
$783$	15.2741			0.545853
$784$	6.20775			0.221705
$785$		−	2.08921i		−	0.0745671i
$786$			30.7090i			1.09535i
$787$			36.1124i			1.28727i	0.765333	+	0.643634i	$0.222574\pi$
$787$			36.1124i			1.28727i	−0.765333	+	0.643634i	$0.777426\pi$
$788$			2.19567i			0.0782175i
$789$	−19.3769			−0.689835
$790$	3.10129			0.110339
$791$			17.3793i			0.617935i
$792$	4.95646			0.176120
$793$	1.31037	−	42.9638i	0.0465327	−	1.52569i
$794$	−0.198062			−0.00702897
$795$		−	1.38212i		−	0.0490189i
$796$	−15.2228			−0.539558
$797$	−20.4413			−0.724069			−0.362034	−	0.932165i	$-0.617918\pi$
$797$	−20.4413			−0.724069			−0.362034	+	0.932165i	$0.617918\pi$
$798$			1.82371i			0.0645586i
$799$		−	19.6775i		−	0.696142i
$800$			4.96077i			0.175390i
$801$			5.43104i			0.191896i
$802$	7.22952			0.255283
$803$	−21.3647			−0.753943
$804$		−	7.94571i		−	0.280223i
$805$	−1.49050			−0.0525333
$806$	0.119605	−	3.92154i	0.00421290	−	0.138130i
$807$	−27.4625			−0.966726
$808$			1.32975i			0.0467804i
$809$	35.5271			1.24907			0.624533	−	0.780999i	$-0.285289\pi$
$809$	35.5271			1.24907			0.624533	+	0.780999i	$0.285289\pi$
$810$	2.21014			0.0776565
$811$			12.9250i			0.453858i	0.973911	+	0.226929i	$0.0728686\pi$
$811$			12.9250i			0.453858i	−0.973911	+	0.226929i	$0.927131\pi$
$812$			3.68233i			0.129225i
$813$			50.6365i			1.77590i
$814$			44.5483i			1.56142i
$815$	−1.10885			−0.0388414
$816$	5.46011			0.191142
$817$			6.19567i			0.216759i
$818$	−10.5483			−0.368811
$819$	−3.84309	−	0.117212i	−0.134288	−	0.00409572i
$820$	−1.32006			−0.0460985
$821$			41.4905i			1.44803i	0.689785	+	0.724014i	$0.257705\pi$
$821$			41.4905i			1.44803i	−0.689785	+	0.724014i	$0.742295\pi$
$822$	35.4577			1.23673
$823$	−2.29185			−0.0798888			−0.0399444	−	0.999202i	$-0.512718\pi$
$823$	−2.29185			−0.0798888			−0.0399444	+	0.999202i	$0.512718\pi$
$824$		−	0.670251i		−	0.0233493i
$825$			42.0500i			1.46399i
$826$			6.41550i			0.223224i
$827$			28.0194i			0.974329i	0.873310	+	0.487165i	$0.161969\pi$
$827$			28.0194i			0.974329i	−0.873310	+	0.487165i	$0.838031\pi$
$828$	−10.1293			−0.352017
$829$	20.1497			0.699829			0.349915	−	0.936782i	$-0.386211\pi$
$829$	20.1497			0.699829			0.349915	+	0.936782i	$0.386211\pi$
$830$			2.60627i			0.0904649i
$831$	−18.0048			−0.624579
$832$	0.109916	−	3.60388i	0.00381066	−	0.124942i
$833$	16.5429			0.573177
$834$			29.5362i			1.02275i
$835$	2.74286			0.0949205
$836$	−4.13706			−0.143083
$837$		−	4.01746i		−	0.138864i
$838$		−	9.92154i		−	0.342734i
$839$		−	46.7348i		−	1.61347i	−0.590917	−	0.806733i	$-0.701234\pi$
$839$		−	46.7348i		−	1.61347i	0.590917	−	0.806733i	$-0.298766\pi$
$840$			0.361208i			0.0124629i
$841$	−11.8847			−0.409817
$842$	25.4577			0.877331
$843$			36.3002i			1.25025i
$844$	17.2905			0.595164
$845$	0.156915	−	2.57002i	0.00539803	−	0.0884115i
$846$	8.84654			0.304150
$847$		−	5.44312i		−	0.187028i
$848$	−3.40581			−0.116956
$849$	20.4176			0.700731
$850$			13.2198i			0.453437i
$851$		−	91.0413i		−	3.12085i
$852$		−	12.4494i		−	0.426508i
$853$		−	9.02608i		−	0.309047i	−0.987989	−	0.154524i	$-0.950616\pi$
$853$		−	9.02608i		−	0.309047i	0.987989	−	0.154524i	$-0.0493843\pi$
$854$	10.6112			0.363107
$855$	0.237291			0.00811518
$856$		−	13.1075i		−	0.448006i
$857$	14.0194			0.478893			0.239446	−	0.970910i	$-0.423034\pi$
$857$	14.0194			0.478893			0.239446	+	0.970910i	$0.423034\pi$
$858$	0.931705	−	30.5483i	0.0318079	−	1.04290i
$859$	−32.1500			−1.09694			−0.548472	−	0.836169i	$-0.684790\pi$
$859$	−32.1500			−1.09694			−0.548472	+	0.836169i	$0.684790\pi$
$860$			1.22713i			0.0418447i
$861$	12.1548			0.414234
$862$	1.26145			0.0429653
$863$			31.5357i			1.07349i	0.843745	+	0.536744i	$0.180346\pi$
$863$			31.5357i			1.07349i	−0.843745	+	0.536744i	$0.819654\pi$
$864$		−	3.69202i		−	0.125605i
$865$		−	3.06052i		−	0.104061i
$866$			5.78017i			0.196418i
$867$	−20.2811			−0.688782
$868$	0.968541			0.0328744
$869$		−	64.7788i		−	2.19747i
$870$	1.67887			0.0569192
$871$	−13.9758	−	0.426256i	−0.473553	−	0.0144431i
$872$	−15.0858			−0.510868
$873$			9.80087i			0.331709i
$874$	8.45473			0.285986
$875$	−1.75600			−0.0593638
$876$		−	10.5810i		−	0.357500i
$877$			39.3551i			1.32893i	0.747321	+	0.664464i	$0.231340\pi$
$877$			39.3551i			1.32893i	−0.747321	+	0.664464i	$0.768660\pi$
$878$		−	15.6668i		−	0.528729i
$879$		−	22.7633i		−	0.767787i
$880$	−0.819396			−0.0276218
$881$	39.9734			1.34674			0.673370	−	0.739306i	$-0.264846\pi$
$881$	39.9734			1.34674			0.673370	+	0.739306i	$0.264846\pi$
$882$			7.43727i			0.250426i
$883$	−30.1366			−1.01418			−0.507088	−	0.861894i	$-0.669278\pi$
$883$	−30.1366			−1.01418			−0.507088	+	0.861894i	$0.669278\pi$
$884$	0.292913	−	9.60388i	0.00985173	−	0.323013i
$885$	2.92500			0.0983228
$886$			4.89008i			0.164286i
$887$	−34.0823			−1.14437			−0.572186	−	0.820124i	$-0.693904\pi$
$887$	−34.0823			−1.14437			−0.572186	+	0.820124i	$0.693904\pi$
$888$	−22.0629			−0.740383
$889$			11.7560i			0.394284i
$890$		−	0.897853i		−	0.0300961i
$891$		−	46.1648i		−	1.54658i
$892$		−	19.8726i		−	0.665385i
$893$	−7.38404			−0.247098
$894$	−11.0425			−0.369316
$895$			2.51765i			0.0841557i
$896$	0.890084			0.0297356
$897$	−1.90408	+	62.4301i	−0.0635755	+	2.08448i
$898$	0.347207			0.0115865
$899$		−	4.50173i		−	0.150141i
$900$	−5.94331			−0.198110
$901$	−9.07606			−0.302368
$902$			27.5730i			0.918081i
$903$		−	11.2991i		−	0.376010i
$904$		−	19.5254i		−	0.649406i
$905$		−	2.66919i		−	0.0887268i
$906$	−32.6528			−1.08482
$907$	−35.2403			−1.17013			−0.585067	−	0.810985i	$-0.698932\pi$
$907$	−35.2403			−1.17013			−0.585067	+	0.810985i	$0.698932\pi$
$908$			4.76809i			0.158234i
$909$	−1.59312			−0.0528405
$910$	0.635334	+	0.0193774i	0.0210611	+	0.000642353i
$911$	23.8237			0.789315			0.394657	−	0.918828i	$-0.370863\pi$
$911$	23.8237			0.789315			0.394657	+	0.918828i	$0.370863\pi$
$912$		−	2.04892i		−	0.0678464i
$913$	54.4389			1.80167
$914$	−31.7754			−1.05104
$915$		−	4.83792i		−	0.159937i
$916$		−	23.8931i		−	0.789449i
$917$			13.3405i			0.440542i
$918$		−	9.83877i		−	0.324728i
$919$	−19.1675			−0.632276			−0.316138	−	0.948713i	$-0.602386\pi$
$919$	−19.1675			−0.632276			−0.316138	+	0.948713i	$0.602386\pi$
$920$	1.67456			0.0552087
$921$		−	20.1500i		−	0.663965i
$922$	28.2543			0.930505
$923$	−21.8974	−	0.667858i	−0.720761	−	0.0219828i
$924$	7.54480			0.248206
$925$		−	53.4180i		−	1.75637i
$926$	−2.42029			−0.0795356
$927$	0.803003			0.0263741
$928$		−	4.13706i		−	0.135806i
$929$			59.9120i			1.96565i	0.184545	+	0.982824i	$0.440919\pi$
$929$			59.9120i			1.96565i	−0.184545	+	0.982824i	$0.559081\pi$
$930$		−	0.441584i		−	0.0144801i
$931$		−	6.20775i		−	0.203451i
$932$	11.7778			0.385794
$933$	−24.3260			−0.796398
$934$			10.5724i			0.345940i
$935$	−2.18359			−0.0714110
$936$	4.31767	+	0.131687i	0.141127	+	0.00430431i
$937$	−45.9057			−1.49968			−0.749838	−	0.661622i	$-0.769868\pi$
$937$	−45.9057			−1.49968			−0.749838	+	0.661622i	$0.769868\pi$
$938$		−	3.45175i		−	0.112704i
$939$	−18.0592			−0.589340
$940$	−1.46250			−0.0477015
$941$		−	16.8009i		−	0.547693i	−0.961773	−	0.273846i	$-0.911704\pi$
$941$		−	16.8009i		−	0.547693i	0.961773	−	0.273846i	$-0.0882960\pi$
$942$		−	21.6125i		−	0.704173i
$943$		−	56.3497i		−	1.83500i
$944$		−	7.20775i		−	0.234592i
$945$	0.650874			0.0211729
$946$	25.6319			0.833364
$947$		−	8.02774i		−	0.260866i	−0.991457	−	0.130433i	$-0.958363\pi$
$947$		−	8.02774i		−	0.260866i	0.991457	−	0.130433i	$-0.0416368\pi$
$948$	32.0823			1.04198
$949$	−18.6112	−	0.567631i	−0.604144	−	0.0184261i
$950$	4.96077			0.160949
$951$		−	26.0495i		−	0.844713i
$952$	2.37196			0.0768757
$953$	−23.1353			−0.749425			−0.374712	−	0.927141i	$-0.622259\pi$
$953$	−23.1353			−0.749425			−0.374712	+	0.927141i	$0.622259\pi$
$954$		−	4.08038i		−	0.132107i
$955$			3.66727i			0.118670i
$956$			12.2983i			0.397755i
$957$		−	35.0678i		−	1.13358i
$958$	−29.0616			−0.938937
$959$	15.4034			0.497402
$960$		−	0.405813i		−	0.0130976i
$961$	29.8159			0.961804
$962$	−1.18359	+	38.8068i	−0.0381604	+	1.25118i
$963$	15.7036			0.506042
$964$			0.613564i			0.0197616i
$965$	−0.704103			−0.0226659
$966$	−15.4190			−0.496097
$967$			3.93495i			0.126540i	0.997996	+	0.0632698i	$0.0201529\pi$
$967$			3.93495i			0.126540i	−0.997996	+	0.0632698i	$0.979847\pi$
$968$			6.11529i			0.196553i
$969$		−	5.46011i		−	0.175404i
$970$		−	1.62027i		−	0.0520237i
$971$	−9.46011			−0.303589			−0.151795	−	0.988412i	$-0.548505\pi$
$971$	−9.46011			−0.303589			−0.151795	+	0.988412i	$0.548505\pi$
$972$	11.7875			0.378083
$973$			12.8310i			0.411343i
$974$	−11.9366			−0.382474
$975$	−1.11721	+	36.6305i	−0.0357794	+	1.17312i
$976$	−11.9215			−0.381599
$977$		−	33.8340i		−	1.08245i	−0.840879	−	0.541223i	$-0.817962\pi$
$977$		−	33.8340i		−	1.08245i	0.840879	−	0.541223i	$-0.182038\pi$
$978$	−11.4709			−0.366798
$979$	−18.7541			−0.599383
$980$		−	1.22952i		−	0.0392756i
$981$		−	18.0737i		−	0.577048i
$982$			29.3163i			0.935522i
$983$		−	13.7614i		−	0.438920i	−0.975622	−	0.219460i	$-0.929570\pi$
$983$		−	13.7614i		−	0.438920i	0.975622	−	0.219460i	$-0.0704295\pi$
$984$	−13.6558			−0.435330
$985$	0.434879			0.0138564
$986$		−	11.0248i		−	0.351100i
$987$	13.4663			0.428638
$988$	−3.60388	−	0.109916i	−0.114655	−	0.00349690i
$989$	−52.3827			−1.66567
$990$		−	0.981688i		−	0.0312001i
$991$	24.7525			0.786291			0.393145	−	0.919476i	$-0.371387\pi$
$991$	24.7525			0.786291			0.393145	+	0.919476i	$0.371387\pi$
$992$	−1.08815			−0.0345487
$993$		−	37.2319i		−	1.18152i
$994$		−	5.40821i		−	0.171538i
$995$			3.01507i			0.0955840i
$996$			26.9614i			0.854303i
$997$	58.4951			1.85256			0.926280	−	0.376836i	$-0.122988\pi$
$997$	58.4951			1.85256			0.926280	+	0.376836i	$0.122988\pi$
$998$	−1.30499			−0.0413089
$999$			39.7560i			1.25782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	494.2.d.b.77.6	yes	6
13.5	odd	4		6422.2.a.t.1.3		3
13.8	odd	4		6422.2.a.k.1.3		3
13.12	even	2	inner	494.2.d.b.77.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.d.b.77.3	✓	6	13.12	even	2	inner
494.2.d.b.77.6	yes	6	1.1	even	1	trivial
6422.2.a.k.1.3		3	13.8	odd	4
6422.2.a.t.1.3		3	13.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 494 = 2 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	494.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +2.04892 q^{3} -1.00000 q^{4} +0.198062i q^{5} +2.04892i q^{6} +0.890084i q^{7} -1.00000i q^{8} +1.19806 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +2.04892 q^{3} -1.00000 q^{4} +0.198062i q^{5} +2.04892i q^{6} +0.890084i q^{7} -1.00000i q^{8} +1.19806 q^{9} -0.198062 q^{10} +4.13706i q^{11} -2.04892 q^{12} +(-0.109916 + 3.60388i) q^{13} -0.890084 q^{14} +0.405813i q^{15} +1.00000 q^{16} +2.66487 q^{17} +1.19806i q^{18} -1.00000i q^{19} -0.198062i q^{20} +1.82371i q^{21} -4.13706 q^{22} +8.45473 q^{23} -2.04892i q^{24} +4.96077 q^{25} +(-3.60388 - 0.109916i) q^{26} -3.69202 q^{27} -0.890084i q^{28} -4.13706 q^{29} -0.405813 q^{30} +1.08815i q^{31} +1.00000i q^{32} +8.47650i q^{33} +2.66487i q^{34} -0.176292 q^{35} -1.19806 q^{36} -10.7681i q^{37} +1.00000 q^{38} +(-0.225209 + 7.38404i) q^{39} +0.198062 q^{40} -6.66487i q^{41} -1.82371 q^{42} -6.19567 q^{43} -4.13706i q^{44} +0.237291i q^{45} +8.45473i q^{46} -7.38404i q^{47} +2.04892 q^{48} +6.20775 q^{49} +4.96077i q^{50} +5.46011 q^{51} +(0.109916 - 3.60388i) q^{52} -3.40581 q^{53} -3.69202i q^{54} -0.819396 q^{55} +0.890084 q^{56} -2.04892i q^{57} -4.13706i q^{58} -7.20775i q^{59} -0.405813i q^{60} -11.9215 q^{61} -1.08815 q^{62} +1.06638i q^{63} -1.00000 q^{64} +(-0.713792 - 0.0217703i) q^{65} -8.47650 q^{66} +3.87800i q^{67} -2.66487 q^{68} +17.3230 q^{69} -0.176292i q^{70} +6.07606i q^{71} -1.19806i q^{72} +5.16421i q^{73} +10.7681 q^{74} +10.1642 q^{75} +1.00000i q^{76} -3.68233 q^{77} +(-7.38404 - 0.225209i) q^{78} -15.6582 q^{79} +0.198062i q^{80} -11.1588 q^{81} +6.66487 q^{82} -13.1588i q^{83} -1.82371i q^{84} +0.527811i q^{85} -6.19567i q^{86} -8.47650 q^{87} +4.13706 q^{88} +4.53319i q^{89} -0.237291 q^{90} +(-3.20775 - 0.0978347i) q^{91} -8.45473 q^{92} +2.22952i q^{93} +7.38404 q^{94} +0.198062 q^{95} +2.04892i q^{96} +8.18060i q^{97} +6.20775i q^{98} +4.95646i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{3} - 6 q^{4} + 16 q^{9}+O(q^{10}) \) 6 * q - 6 * q^3 - 6 * q^4 + 16 * q^9	\( 6 q - 6 q^{3} - 6 q^{4} + 16 q^{9} - 10 q^{10} + 6 q^{12} - 2 q^{13} - 4 q^{14} + 6 q^{16} + 18 q^{17} - 14 q^{22} + 6 q^{23} + 4 q^{25} - 4 q^{26} - 12 q^{27} - 14 q^{29} + 24 q^{30} - 16 q^{35} - 16 q^{36} + 6 q^{38} + 2 q^{39} + 10 q^{40} + 4 q^{42} + 36 q^{43} - 6 q^{48} + 2 q^{49} - 18 q^{51} + 2 q^{52} + 6 q^{53} - 28 q^{55} + 4 q^{56} - 20 q^{61} - 14 q^{62} - 6 q^{64} + 12 q^{65} - 18 q^{68} + 64 q^{69} + 24 q^{74} + 38 q^{75} - 56 q^{77} - 24 q^{78} - 52 q^{79} - 50 q^{81} + 42 q^{82} + 14 q^{88} - 36 q^{90} + 16 q^{91} - 6 q^{92} + 24 q^{94} + 10 q^{95}+O(q^{100}) \) 6 * q - 6 * q^3 - 6 * q^4 + 16 * q^9 - 10 * q^10 + 6 * q^12 - 2 * q^13 - 4 * q^14 + 6 * q^16 + 18 * q^17 - 14 * q^22 + 6 * q^23 + 4 * q^25 - 4 * q^26 - 12 * q^27 - 14 * q^29 + 24 * q^30 - 16 * q^35 - 16 * q^36 + 6 * q^38 + 2 * q^39 + 10 * q^40 + 4 * q^42 + 36 * q^43 - 6 * q^48 + 2 * q^49 - 18 * q^51 + 2 * q^52 + 6 * q^53 - 28 * q^55 + 4 * q^56 - 20 * q^61 - 14 * q^62 - 6 * q^64 + 12 * q^65 - 18 * q^68 + 64 * q^69 + 24 * q^74 + 38 * q^75 - 56 * q^77 - 24 * q^78 - 52 * q^79 - 50 * q^81 + 42 * q^82 + 14 * q^88 - 36 * q^90 + 16 * q^91 - 6 * q^92 + 24 * q^94 + 10 * q^95

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