LMFDB - Embedded newform 310.2.b.b.249.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(249,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, 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("310.249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.b (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:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.2058981376.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 18x^{4} - 34x^{3} + 32x^{2} - 8x + 1 $ x^8 - 2x^7 + 2x^6 + 18x^4 - 34x^3 + 32x^2 - 8x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			249.2
Root			$1.52153 + 1.52153i$ of defining polynomial
Character	$\chi$	$=$	310.249
Dual form			310.2.b.b.249.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -0.287336i q^{3} -1.00000 q^{4} +(-0.437190 + 2.19291i) q^{5} -0.287336 q^{6} +1.04306i q^{7} +1.00000i q^{8} +2.91744 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -0.287336i q^{3} -1.00000 q^{4} +(-0.437190 + 2.19291i) q^{5} -0.287336 q^{6} +1.04306i q^{7} +1.00000i q^{8} +2.91744 q^{9} +(2.19291 + 0.437190i) q^{10} +3.63010 q^{11} +0.287336i q^{12} +1.41296i q^{13} +1.04306 q^{14} +(0.630102 + 0.125620i) q^{15} +1.00000 q^{16} -3.91744i q^{17} -2.91744i q^{18} +4.96050 q^{19} +(0.437190 - 2.19291i) q^{20} +0.299708 q^{21} -3.63010i q^{22} +8.00355i q^{23} +0.287336 q^{24} +(-4.61773 - 1.91744i) q^{25} +1.41296 q^{26} -1.70029i q^{27} -1.04306i q^{28} -6.59060 q^{29} +(0.125620 - 0.630102i) q^{30} +1.00000 q^{31} -1.00000i q^{32} -1.04306i q^{33} -3.91744 q^{34} +(-2.28734 - 0.456015i) q^{35} -2.91744 q^{36} -3.71266i q^{37} -4.96050i q^{38} +0.405993 q^{39} +(-2.19291 - 0.437190i) q^{40} +2.74335 q^{41} -0.299708i q^{42} +3.73639i q^{43} -3.63010 q^{44} +(-1.27547 + 6.39769i) q^{45} +8.00355 q^{46} -2.35753i q^{47} -0.287336i q^{48} +5.91203 q^{49} +(-1.91744 + 4.61773i) q^{50} -1.12562 q^{51} -1.41296i q^{52} +0.335803i q^{53} -1.70029 q^{54} +(-1.58704 + 7.96050i) q^{55} -1.04306 q^{56} -1.42533i q^{57} +6.59060i q^{58} -4.33736 q^{59} +(-0.630102 - 0.125620i) q^{60} -8.33936 q^{61} -1.00000i q^{62} +3.04306i q^{63} -1.00000 q^{64} +(-3.09849 - 0.617730i) q^{65} -1.04306 q^{66} -8.27496i q^{67} +3.91744i q^{68} +2.29971 q^{69} +(-0.456015 + 2.28734i) q^{70} -5.59756 q^{71} +2.91744i q^{72} -8.43785i q^{73} -3.71266 q^{74} +(-0.550949 + 1.32684i) q^{75} -4.96050 q^{76} +3.78641i q^{77} -0.405993i q^{78} +1.42533 q^{79} +(-0.437190 + 2.19291i) q^{80} +8.26376 q^{81} -2.74335i q^{82} +12.8939i q^{83} -0.299708 q^{84} +(8.59060 + 1.71266i) q^{85} +3.73639 q^{86} +1.89372i q^{87} +3.63010i q^{88} -16.4414 q^{89} +(6.39769 + 1.27547i) q^{90} -1.47380 q^{91} -8.00355i q^{92} -0.287336i q^{93} -2.35753 q^{94} +(-2.16868 + 10.8779i) q^{95} -0.287336 q^{96} -16.4141i q^{97} -5.91203i q^{98} +10.5906 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 2 q^{5} + 4 q^{6}+O(q^{10}) $ 8 * q - 8 * q^4 - 2 * q^5 + 4 * q^6	$ 8 q - 8 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{10} + 12 q^{11} - 12 q^{14} - 12 q^{15} + 8 q^{16} - 4 q^{19} + 2 q^{20} + 12 q^{21} - 4 q^{24} - 4 q^{25} + 8 q^{26} + 8 q^{29} + 4 q^{30} + 8 q^{31} - 8 q^{34} - 12 q^{35} + 8 q^{39} - 2 q^{40} - 8 q^{41} - 12 q^{44} - 18 q^{45} + 8 q^{50} - 12 q^{51} - 4 q^{54} - 16 q^{55} + 12 q^{56} + 12 q^{60} - 8 q^{64} + 12 q^{66} + 28 q^{69} + 20 q^{70} + 24 q^{71} - 36 q^{74} - 20 q^{75} + 4 q^{76} + 24 q^{79} - 2 q^{80} - 32 q^{81} - 12 q^{84} + 8 q^{85} + 8 q^{86} + 24 q^{89} + 6 q^{90} - 28 q^{91} - 20 q^{94} + 4 q^{96} + 24 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^10 + 12 * q^11 - 12 * q^14 - 12 * q^15 + 8 * q^16 - 4 * q^19 + 2 * q^20 + 12 * q^21 - 4 * q^24 - 4 * q^25 + 8 * q^26 + 8 * q^29 + 4 * q^30 + 8 * q^31 - 8 * q^34 - 12 * q^35 + 8 * q^39 - 2 * q^40 - 8 * q^41 - 12 * q^44 - 18 * q^45 + 8 * q^50 - 12 * q^51 - 4 * q^54 - 16 * q^55 + 12 * q^56 + 12 * q^60 - 8 * q^64 + 12 * q^66 + 28 * q^69 + 20 * q^70 + 24 * q^71 - 36 * q^74 - 20 * q^75 + 4 * q^76 + 24 * q^79 - 2 * q^80 - 32 * q^81 - 12 * q^84 + 8 * q^85 + 8 * q^86 + 24 * q^89 + 6 * q^90 - 28 * q^91 - 20 * q^94 + 4 * q^96 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$-1$	$1$

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
$3$		−	0.287336i		−	0.165893i	−0.996554	−	0.0829467i	$-0.973567\pi$
$3$		−	0.287336i		−	0.165893i	0.996554	−	0.0829467i	$-0.0264331\pi$
$4$	−1.00000			−0.500000
$5$	−0.437190	+	2.19291i	−0.195517	+	0.980700i
$5$	−0.437190	+	2.19291i	−0.195517	+	0.980700i
$6$	−0.287336			−0.117304
$7$			1.04306i			0.394239i	0.980379	+	0.197120i	$0.0631587\pi$
$7$			1.04306i			0.394239i	−0.980379	+	0.197120i	$0.936841\pi$
$8$			1.00000i			0.353553i
$9$	2.91744			0.972479
$10$	2.19291	+	0.437190i	0.693460	+	0.138252i
$11$	3.63010			1.09452			0.547259	−	0.836964i	$-0.315671\pi$
$11$	3.63010			1.09452			0.547259	+	0.836964i	$0.315671\pi$
$12$			0.287336i			0.0829467i
$13$			1.41296i			0.391884i	0.980616	+	0.195942i	$0.0627764\pi$
$13$			1.41296i			0.391884i	−0.980616	+	0.195942i	$0.937224\pi$
$14$	1.04306			0.278769
$15$	0.630102	+	0.125620i	0.162692	+	0.0324350i
$16$	1.00000			0.250000
$17$		−	3.91744i		−	0.950118i	−0.879954	−	0.475059i	$-0.842427\pi$
$17$		−	3.91744i		−	0.950118i	0.879954	−	0.475059i	$-0.157573\pi$
$18$		−	2.91744i		−	0.687647i
$19$	4.96050			1.13802			0.569008	−	0.822332i	$-0.307327\pi$
$19$	4.96050			1.13802			0.569008	+	0.822332i	$0.307327\pi$
$20$	0.437190	−	2.19291i	0.0977586	−	0.490350i
$21$	0.299708			0.0654017
$22$		−	3.63010i		−	0.773940i
$23$			8.00355i			1.66886i	0.551117	+	0.834428i	$0.314202\pi$
$23$			8.00355i			1.66886i	−0.551117	+	0.834428i	$0.685798\pi$
$24$	0.287336			0.0586522
$25$	−4.61773	−	1.91744i	−0.923546	−	0.383488i
$26$	1.41296			0.277103
$27$		−	1.70029i		−	0.327221i
$28$		−	1.04306i		−	0.197120i
$29$	−6.59060			−1.22384			−0.611922	−	0.790918i	$-0.709603\pi$
$29$	−6.59060			−1.22384			−0.611922	+	0.790918i	$0.709603\pi$
$30$	0.125620	−	0.630102i	0.0229350	−	0.115040i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$		−	1.00000i		−	0.176777i
$33$		−	1.04306i		−	0.181573i
$34$	−3.91744			−0.671835
$35$	−2.28734	−	0.456015i	−0.386630	−	0.0770805i
$36$	−2.91744			−0.486240
$37$		−	3.71266i		−	0.610358i	−0.952295	−	0.305179i	$-0.901284\pi$
$37$		−	3.71266i		−	0.610358i	0.952295	−	0.305179i	$-0.0987163\pi$
$38$		−	4.96050i		−	0.804699i
$39$	0.405993			0.0650109
$40$	−2.19291	−	0.437190i	−0.346730	−	0.0691258i
$41$	2.74335			0.428439			0.214220	−	0.976786i	$-0.431279\pi$
$41$	2.74335			0.428439			0.214220	+	0.976786i	$0.431279\pi$
$42$		−	0.299708i		−	0.0462460i
$43$			3.73639i			0.569794i	0.958558	+	0.284897i	$0.0919593\pi$
$43$			3.73639i			0.569794i	−0.958558	+	0.284897i	$0.908041\pi$
$44$	−3.63010			−0.547259
$45$	−1.27547	+	6.39769i	−0.190136	+	0.953711i
$46$	8.00355			1.18006
$47$		−	2.35753i		−	0.343880i	−0.985107	−	0.171940i	$-0.944996\pi$
$47$		−	2.35753i		−	0.343880i	0.985107	−	0.171940i	$-0.0550036\pi$
$48$		−	0.287336i		−	0.0414734i
$49$	5.91203			0.844576
$50$	−1.91744	+	4.61773i	−0.271167	+	0.653046i
$51$	−1.12562			−0.157618
$52$		−	1.41296i		−	0.195942i
$53$			0.335803i			0.0461261i	0.999734	+	0.0230631i	$0.00734185\pi$
$53$			0.335803i			0.0461261i	−0.999734	+	0.0230631i	$0.992658\pi$
$54$	−1.70029			−0.231380
$55$	−1.58704	+	7.96050i	−0.213997	+	1.07339i
$56$	−1.04306			−0.139385
$57$		−	1.42533i		−	0.188789i
$58$			6.59060i			0.865388i
$59$	−4.33736			−0.564676			−0.282338	−	0.959315i	$-0.591110\pi$
$59$	−4.33736			−0.564676			−0.282338	+	0.959315i	$0.591110\pi$
$60$	−0.630102	−	0.125620i	−0.0813459	−	0.0162175i
$61$	−8.33936			−1.06775			−0.533873	−	0.845565i	$-0.679264\pi$
$61$	−8.33936			−1.06775			−0.533873	+	0.845565i	$0.679264\pi$
$62$		−	1.00000i		−	0.127000i
$63$			3.04306i			0.383389i
$64$	−1.00000			−0.125000
$65$	−3.09849	−	0.617730i	−0.384320	−	0.0766200i
$66$	−1.04306			−0.128392
$67$		−	8.27496i		−	1.01095i	−0.862842	−	0.505474i	$-0.831318\pi$
$67$		−	8.27496i		−	1.01095i	0.862842	−	0.505474i	$-0.168682\pi$
$68$			3.91744i			0.475059i
$69$	2.29971			0.276852
$70$	−0.456015	+	2.28734i	−0.0545042	+	0.273389i
$71$	−5.59756			−0.664308			−0.332154	−	0.943225i	$-0.607775\pi$
$71$	−5.59756			−0.664308			−0.332154	+	0.943225i	$0.607775\pi$
$72$			2.91744i			0.343823i
$73$		−	8.43785i		−	0.987575i	−0.869583	−	0.493788i	$-0.835612\pi$
$73$		−	8.43785i		−	0.987575i	0.869583	−	0.493788i	$-0.164388\pi$
$74$	−3.71266			−0.431588
$75$	−0.550949	+	1.32684i	−0.0636181	+	0.153210i
$76$	−4.96050			−0.569008
$77$			3.78641i			0.431501i
$78$		−	0.405993i		−	0.0459696i
$79$	1.42533			0.160362			0.0801810	−	0.996780i	$-0.474450\pi$
$79$	1.42533			0.160362			0.0801810	+	0.996780i	$0.474450\pi$
$80$	−0.437190	+	2.19291i	−0.0488793	+	0.245175i
$81$	8.26376			0.918196
$82$		−	2.74335i		−	0.302952i
$83$			12.8939i			1.41529i	0.706571	+	0.707643i	$0.250241\pi$
$83$			12.8939i			1.41529i	−0.706571	+	0.707643i	$0.749759\pi$
$84$	−0.299708			−0.0327008
$85$	8.59060	+	1.71266i	0.931781	+	0.185765i
$86$	3.73639			0.402905
$87$			1.89372i			0.203028i
$88$			3.63010i			0.386970i
$89$	−16.4414			−1.74279			−0.871393	−	0.490586i	$-0.836783\pi$
$89$	−16.4414			−1.74279			−0.871393	+	0.490586i	$0.836783\pi$
$90$	6.39769	+	1.27547i	0.674375	+	0.134447i
$91$	−1.47380			−0.154496
$92$		−	8.00355i		−	0.834428i
$93$		−	0.287336i		−	0.0297953i
$94$	−2.35753			−0.243160
$95$	−2.16868	+	10.8779i	−0.222502	+	1.11605i
$96$	−0.287336			−0.0293261
$97$		−	16.4141i		−	1.66660i	−0.552820	−	0.833301i	$-0.686448\pi$
$97$		−	16.4141i		−	1.66660i	0.552820	−	0.833301i	$-0.313552\pi$
$98$		−	5.91203i		−	0.597205i
$99$	10.5906			1.06440
$100$	4.61773	+	1.91744i	0.461773	+	0.191744i
$101$	−13.4087			−1.33422			−0.667109	−	0.744961i	$-0.732468\pi$
$101$	−13.4087			−1.33422			−0.667109	+	0.744961i	$0.732468\pi$
$102$			1.12562i			0.111453i
$103$		−	17.7559i		−	1.74954i	−0.484540	−	0.874769i	$-0.661013\pi$
$103$		−	17.7559i		−	1.74954i	0.484540	−	0.874769i	$-0.338987\pi$
$104$	−1.41296			−0.138552
$105$	−0.131029	+	0.657234i	−0.0127872	+	0.0641394i
$106$	0.335803			0.0326161
$107$			12.5441i			1.21269i	0.795203	+	0.606344i	$0.207364\pi$
$107$			12.5441i			1.21269i	−0.795203	+	0.606344i	$0.792636\pi$
$108$			1.70029i			0.163611i
$109$	0.661810			0.0633899			0.0316949	−	0.999498i	$-0.489909\pi$
$109$	0.661810			0.0633899			0.0316949	+	0.999498i	$0.489909\pi$
$110$	7.96050	+	1.58704i	0.759004	+	0.151319i
$111$	−1.06678			−0.101254
$112$			1.04306i			0.0985598i
$113$		−	7.81471i		−	0.735146i	−0.929995	−	0.367573i	$-0.880189\pi$
$113$		−	7.81471i		−	0.735146i	0.929995	−	0.367573i	$-0.119811\pi$
$114$	−1.42533			−0.133494
$115$	−17.5511	−	3.49907i	−1.63665	−	0.326290i
$116$	6.59060			0.611922
$117$			4.12221i			0.381099i
$118$			4.33736i			0.399286i
$119$	4.08612			0.374574
$120$	−0.125620	+	0.630102i	−0.0114675	+	0.0575202i
$121$	2.17764			0.197968
$122$			8.33936i			0.755010i
$123$		−	0.788263i		−	0.0710753i
$124$	−1.00000			−0.0898027
$125$	6.22360	−	9.28799i	0.556656	−	0.830743i
$126$	3.04306			0.271097
$127$		−	10.4378i		−	0.926209i	−0.886304	−	0.463105i	$-0.846735\pi$
$127$		−	10.4378i		−	0.926209i	0.886304	−	0.463105i	$-0.153265\pi$
$128$			1.00000i			0.0883883i
$129$	1.07360			0.0945250
$130$	−0.617730	+	3.09849i	−0.0541785	+	0.271755i
$131$	−7.78641			−0.680302			−0.340151	−	0.940371i	$-0.610478\pi$
$131$	−7.78641			−0.680302			−0.340151	+	0.940371i	$0.610478\pi$
$132$			1.04306i			0.0907866i
$133$			5.17409i			0.448650i
$134$	−8.27496			−0.714848
$135$	3.72859	+	0.743350i	0.320906	+	0.0639774i
$136$	3.91744			0.335918
$137$		−	4.85421i		−	0.414723i	−0.978264	−	0.207362i	$-0.933512\pi$
$137$		−	4.85421i		−	0.414723i	0.978264	−	0.207362i	$-0.0664877\pi$
$138$		−	2.29971i		−	0.195764i
$139$	18.9527			1.60755			0.803774	−	0.594935i	$-0.202822\pi$
$139$	18.9527			1.60755			0.803774	+	0.594935i	$0.202822\pi$
$140$	2.28734	+	0.456015i	0.193315	+	0.0385403i
$141$	−0.677402			−0.0570475
$142$			5.59756i			0.469737i
$143$			5.12918i			0.428923i
$144$	2.91744			0.243120
$145$	2.88134	−	14.4526i	0.239283	−	1.20022i
$146$	−8.43785			−0.698321
$147$		−	1.69874i		−	0.140110i
$148$			3.71266i			0.305179i
$149$	23.5907			1.93263			0.966315	−	0.257364i	$-0.0828539\pi$
$149$	23.5907			1.93263			0.966315	+	0.257364i	$0.0828539\pi$
$150$	1.32684	+	0.550949i	0.108336	+	0.0449848i
$151$	3.97526			0.323502			0.161751	−	0.986832i	$-0.448286\pi$
$151$	3.97526			0.323502			0.161751	+	0.986832i	$0.448286\pi$
$152$			4.96050i			0.402349i
$153$		−	11.4289i		−	0.923970i
$154$	3.78641			0.305118
$155$	−0.437190	+	2.19291i	−0.0351159	+	0.176139i
$156$	−0.405993			−0.0325054
$157$		−	6.57467i		−	0.524716i	−0.964971	−	0.262358i	$-0.915500\pi$
$157$		−	6.57467i		−	0.524716i	0.964971	−	0.262358i	$-0.0845001\pi$
$158$		−	1.42533i		−	0.113393i
$159$	0.0964883			0.00765202
$160$	2.19291	+	0.437190i	0.173365	+	0.0345629i
$161$	−8.34818			−0.657928
$162$		−	8.26376i		−	0.649262i
$163$			18.1583i			1.42227i	0.703056	+	0.711134i	$0.251818\pi$
$163$			18.1583i			1.42227i	−0.703056	+	0.711134i	$0.748182\pi$
$164$	−2.74335			−0.214220
$165$	2.28734	+	0.456015i	0.178069	+	0.0355007i
$166$	12.8939			1.00076
$167$		−	5.75231i		−	0.445127i	−0.974918	−	0.222564i	$-0.928557\pi$
$167$		−	5.75231i		−	0.445127i	0.974918	−	0.222564i	$-0.0714425\pi$
$168$			0.299708i			0.0231230i
$169$	11.0036			0.846427
$170$	1.71266	−	8.59060i	0.131355	−	0.658869i
$171$	14.4719			1.10670
$172$		−	3.73639i		−	0.284897i
$173$		−	12.6608i		−	0.962582i	−0.876561	−	0.481291i	$-0.840168\pi$
$173$		−	12.6608i		−	0.962582i	0.876561	−	0.481291i	$-0.159832\pi$
$174$	1.89372			0.143562
$175$	2.00000	−	4.81656i	0.151186	−	0.364098i
$176$	3.63010			0.273629
$177$			1.24628i			0.0936760i
$178$			16.4414i			1.23234i
$179$	−13.3918			−1.00095			−0.500474	−	0.865752i	$-0.666841\pi$
$179$	−13.3918			−1.00095			−0.500474	+	0.865752i	$0.666841\pi$
$180$	1.27547	−	6.39769i	0.0950682	−	0.476855i
$181$	−9.18188			−0.682484			−0.341242	−	0.939975i	$-0.610848\pi$
$181$	−9.18188			−0.682484			−0.341242	+	0.939975i	$0.610848\pi$
$182$			1.47380i			0.109245i
$183$			2.39620i			0.177132i
$184$	−8.00355			−0.590030
$185$	8.14155	+	1.62314i	0.598578	+	0.119336i
$186$	−0.287336			−0.0210685
$187$		−	14.2207i		−	1.03992i
$188$			2.35753i			0.171940i
$189$	1.77350			0.129003
$190$	10.8779	+	2.16868i	0.789168	+	0.157332i
$191$	−5.34277			−0.386589			−0.193295	−	0.981141i	$-0.561917\pi$
$191$	−5.34277			−0.386589			−0.193295	+	0.981141i	$0.561917\pi$
$192$			0.287336i			0.0207367i
$193$			6.50248i			0.468059i	0.972230	+	0.234029i	$0.0751912\pi$
$193$			6.50248i			0.468059i	−0.972230	+	0.234029i	$0.924809\pi$
$194$	−16.4141			−1.17847
$195$	−0.177496	+	0.890307i	−0.0127108	+	0.0637562i
$196$	−5.91203			−0.422288
$197$		−	11.5794i		−	0.824998i	−0.910958	−	0.412499i	$-0.864656\pi$
$197$		−	11.5794i		−	0.824998i	0.910958	−	0.412499i	$-0.135344\pi$
$198$		−	10.5906i		−	0.752641i
$199$	−3.70842			−0.262883			−0.131442	−	0.991324i	$-0.541961\pi$
$199$	−3.70842			−0.262883			−0.131442	+	0.991324i	$0.541961\pi$
$200$	1.91744	−	4.61773i	0.135583	−	0.326523i
$201$	−2.37769			−0.167710
$202$			13.4087i			0.943434i
$203$		−	6.87438i		−	0.482487i
$204$	1.12562			0.0788092
$205$	−1.19936	+	6.01593i	−0.0837673	+	0.420171i
$206$	−17.7559			−1.23711
$207$			23.3499i			1.62293i
$208$			1.41296i			0.0979709i
$209$	18.0071			1.24558
$210$	0.657234	+	0.131029i	0.0453534	+	0.00904188i
$211$	23.7501			1.63502			0.817511	−	0.575913i	$-0.195353\pi$
$211$	23.7501			1.63502			0.817511	+	0.575913i	$0.195353\pi$
$212$		−	0.335803i		−	0.0230631i
$213$			1.60838i			0.110204i
$214$	12.5441			0.857499
$215$	−8.19357	−	1.63351i	−0.558797	−	0.111404i
$216$	1.70029			0.115690
$217$			1.04306i			0.0708074i
$218$		−	0.661810i		−	0.0448234i
$219$	−2.42450			−0.163832
$220$	1.58704	−	7.96050i	0.106998	−	0.536697i
$221$	5.53517			0.372336
$222$			1.06678i			0.0715977i
$223$		−	5.72757i		−	0.383546i	−0.981439	−	0.191773i	$-0.938576\pi$
$223$		−	5.72757i		−	0.383546i	0.981439	−	0.191773i	$-0.0614238\pi$
$224$	1.04306			0.0696923
$225$	−13.4719	−	5.59401i	−0.898129	−	0.372934i
$226$	−7.81471			−0.519827
$227$			24.7716i			1.64415i	0.569378	+	0.822076i	$0.307184\pi$
$227$			24.7716i			1.64415i	−0.569378	+	0.822076i	$0.692816\pi$
$228$			1.42533i			0.0943947i
$229$	−4.26717			−0.281982			−0.140991	−	0.990011i	$-0.545029\pi$
$229$	−4.26717			−0.281982			−0.140991	+	0.990011i	$0.545029\pi$
$230$	−3.49907	+	17.5511i	−0.230722	+	1.15728i
$231$	1.08797			0.0715832
$232$		−	6.59060i		−	0.432694i
$233$			2.10628i			0.137987i	0.997617	+	0.0689937i	$0.0219788\pi$
$233$			2.10628i			0.137987i	−0.997617	+	0.0689937i	$0.978021\pi$
$234$	4.12221			0.269477
$235$	5.16985	+	1.03069i	0.337244	+	0.0672346i
$236$	4.33736			0.282338
$237$		−	0.409548i		−	0.0266030i
$238$		−	4.08612i		−	0.264864i
$239$	−16.9686			−1.09761			−0.548805	−	0.835951i	$-0.684917\pi$
$239$	−16.9686			−1.09761			−0.548805	+	0.835951i	$0.684917\pi$
$240$	0.630102	+	0.125620i	0.0406729	+	0.00810876i
$241$	−27.3921			−1.76448			−0.882240	−	0.470800i	$-0.843966\pi$
$241$	−27.3921			−1.76448			−0.882240	+	0.470800i	$0.843966\pi$
$242$		−	2.17764i		−	0.139984i
$243$		−	7.47535i		−	0.479544i
$244$	8.33936			0.533873
$245$	−2.58468	+	12.9646i	−0.165129	+	0.828276i
$246$	−0.788263			−0.0502578
$247$			7.00896i			0.445970i
$248$			1.00000i			0.0635001i
$249$	3.70487			0.234786
$250$	−9.28799	−	6.22360i	−0.587424	−	0.393615i
$251$	14.1010			0.890049			0.445024	−	0.895518i	$-0.353195\pi$
$251$	14.1010			0.890049			0.445024	+	0.895518i	$0.353195\pi$
$252$		−	3.04306i		−	0.191695i
$253$			29.0537i			1.82659i
$254$	−10.4378			−0.654929
$255$	0.492110	−	2.46839i	0.0308171	−	0.154576i
$256$	1.00000			0.0625000
$257$			16.6469i			1.03840i	0.854652	+	0.519201i	$0.173771\pi$
$257$			16.6469i			1.03840i	−0.854652	+	0.519201i	$0.826229\pi$
$258$		−	1.07360i		−	0.0668393i
$259$	3.87253			0.240627
$260$	3.09849	+	0.617730i	0.192160	+	0.0383100i
$261$	−19.2277			−1.19016
$262$			7.78641i			0.481046i
$263$		−	4.72942i		−	0.291629i	−0.989312	−	0.145814i	$-0.953420\pi$
$263$		−	4.72942i		−	0.291629i	0.989312	−	0.145814i	$-0.0465802\pi$
$264$	1.04306			0.0641958
$265$	−0.736387	−	0.146810i	−0.0452359	−	0.00901845i
$266$	5.17409			0.317244
$267$			4.72420i			0.289117i
$268$			8.27496i			0.505474i
$269$	−3.44228			−0.209879			−0.104940	−	0.994479i	$-0.533465\pi$
$269$	−3.44228			−0.209879			−0.104940	+	0.994479i	$0.533465\pi$
$270$	0.743350	−	3.72859i	0.0452389	−	0.226915i
$271$	6.27599			0.381239			0.190619	−	0.981664i	$-0.438950\pi$
$271$	6.27599			0.381239			0.190619	+	0.981664i	$0.438950\pi$
$272$		−	3.91744i		−	0.237530i
$273$			0.423474i			0.0256298i
$274$	−4.85421			−0.293254
$275$	−16.7628	−	6.96050i	−1.01084	−	0.419734i
$276$	−2.29971			−0.138426
$277$			17.1796i			1.03222i	0.856521	+	0.516112i	$0.172621\pi$
$277$			17.1796i			1.03222i	−0.856521	+	0.516112i	$0.827379\pi$
$278$		−	18.9527i		−	1.13671i
$279$	2.91744			0.174662
$280$	0.456015	−	2.28734i	0.0272521	−	0.136694i
$281$	−19.7559			−1.17854			−0.589268	−	0.807938i	$-0.700584\pi$
$281$	−19.7559			−1.17854			−0.589268	+	0.807938i	$0.700584\pi$
$282$			0.677402i			0.0403387i
$283$		−	13.3782i		−	0.795250i	−0.917548	−	0.397625i	$-0.869835\pi$
$283$		−	13.3782i		−	0.795250i	0.917548	−	0.397625i	$-0.130165\pi$
$284$	5.59756			0.332154
$285$	3.12562	+	0.623139i	0.185146	+	0.0369116i
$286$	5.12918			0.303294
$287$			2.86147i			0.168908i
$288$		−	2.91744i		−	0.171912i
$289$	1.65368			0.0972752
$290$	−14.4526	−	2.88134i	−0.848686	−	0.169198i
$291$	−4.71637			−0.276478
$292$			8.43785i			0.493788i
$293$		−	4.40142i		−	0.257133i	−0.991701	−	0.128567i	$-0.958962\pi$
$293$		−	4.40142i		−	0.257133i	0.991701	−	0.128567i	$-0.0410377\pi$
$294$	−1.69874			−0.0990724
$295$	1.89625	−	9.51145i	0.110404	−	0.553778i
$296$	3.71266			0.215794
$297$		−	6.17223i		−	0.358149i
$298$		−	23.5907i		−	1.36658i
$299$	−11.3087			−0.653997
$300$	0.550949	−	1.32684i	0.0318090	−	0.0766051i
$301$	−3.89727			−0.224635
$302$		−	3.97526i		−	0.228750i
$303$			3.85280i			0.221338i
$304$	4.96050			0.284504
$305$	3.64588	−	18.2875i	0.208763	−	1.04714i
$306$	−11.4289			−0.653346
$307$			5.18699i			0.296037i	0.988985	+	0.148019i	$0.0472896\pi$
$307$			5.18699i			0.296037i	−0.988985	+	0.148019i	$0.952710\pi$
$308$		−	3.78641i		−	0.215751i
$309$	−5.10190			−0.290237
$310$	2.19291	+	0.437190i	0.124549	+	0.0248307i
$311$	24.8330			1.40815			0.704076	−	0.710125i	$-0.251362\pi$
$311$	24.8330			1.40815			0.704076	+	0.710125i	$0.251362\pi$
$312$			0.405993i			0.0229848i
$313$			15.4221i			0.871707i	0.900018	+	0.435853i	$0.143553\pi$
$313$			15.4221i			0.871707i	−0.900018	+	0.435853i	$0.856447\pi$
$314$	−6.57467			−0.371030
$315$	−6.67316	−	1.33039i	−0.375990	−	0.0749592i
$316$	−1.42533			−0.0801810
$317$			17.0547i			0.957890i	0.877845	+	0.478945i	$0.158981\pi$
$317$			17.0547i			0.957890i	−0.877845	+	0.478945i	$0.841019\pi$
$318$		−	0.0964883i		−	0.00541080i
$319$	−23.9245			−1.33952
$320$	0.437190	−	2.19291i	0.0244397	−	0.122588i
$321$	3.60438			0.201177
$322$			8.34818i			0.465226i
$323$		−	19.4324i		−	1.08125i
$324$	−8.26376			−0.459098
$325$	2.70926	−	6.52465i	0.150282	−	0.361922i
$326$	18.1583			1.00570
$327$		−	0.190162i		−	0.0105160i
$328$			2.74335i			0.151476i
$329$	2.45904			0.135571
$330$	0.456015	−	2.28734i	0.0251028	−	0.125914i
$331$	−29.1181			−1.60048			−0.800238	−	0.599682i	$-0.795294\pi$
$331$	−29.1181			−1.60048			−0.800238	+	0.599682i	$0.795294\pi$
$332$		−	12.8939i		−	0.707643i
$333$		−	10.8315i		−	0.593561i
$334$	−5.75231			−0.314753
$335$	18.1463	+	3.61773i	0.991437	+	0.197658i
$336$	0.299708			0.0163504
$337$			32.7257i			1.78268i	0.453332	+	0.891342i	$0.350235\pi$
$337$			32.7257i			1.78268i	−0.453332	+	0.891342i	$0.649765\pi$
$338$		−	11.0036i		−	0.598514i
$339$	−2.24545			−0.121956
$340$	−8.59060	−	1.71266i	−0.465891	−	0.0928823i
$341$	3.63010			0.196581
$342$		−	14.4719i		−	0.782553i
$343$			13.4680i			0.727204i
$344$	−3.73639			−0.201452
$345$	−1.00541	+	5.04306i	−0.0541294	+	0.271509i
$346$	−12.6608			−0.680648
$347$			11.9323i			0.640562i	0.947323	+	0.320281i	$0.103777\pi$
$347$			11.9323i			0.640562i	−0.947323	+	0.320281i	$0.896223\pi$
$348$		−	1.89372i		−	0.101514i
$349$	−18.3940			−0.984606			−0.492303	−	0.870424i	$-0.663845\pi$
$349$	−18.3940			−0.984606			−0.492303	+	0.870424i	$0.663845\pi$
$350$	−4.81656	−	2.00000i	−0.257456	−	0.106904i
$351$	2.40244			0.128233
$352$		−	3.63010i		−	0.193485i
$353$		−	31.8384i		−	1.69459i	−0.531124	−	0.847294i	$-0.678230\pi$
$353$		−	31.8384i		−	1.69459i	0.531124	−	0.847294i	$-0.321770\pi$
$354$	1.24628			0.0662389
$355$	2.44720	−	12.2750i	0.129884	−	0.651487i
$356$	16.4414			0.871393
$357$		−	1.17409i		−	0.0621393i
$358$			13.3918i			0.707777i
$359$	0.523964			0.0276538			0.0138269	−	0.999904i	$-0.495599\pi$
$359$	0.523964			0.0276538			0.0138269	+	0.999904i	$0.495599\pi$
$360$	−6.39769	−	1.27547i	−0.337188	−	0.0672234i
$361$	5.60653			0.295080
$362$			9.18188i			0.482589i
$363$		−	0.625715i		−	0.0328415i
$364$	1.47380			0.0772479
$365$	18.5035	+	3.68894i	0.968515	+	0.193088i
$366$	2.39620			0.125251
$367$		−	13.3885i		−	0.698876i	−0.936959	−	0.349438i	$-0.886372\pi$
$367$		−	13.3885i		−	0.698876i	0.936959	−	0.349438i	$-0.113628\pi$
$368$			8.00355i			0.417214i
$369$	8.00355			0.416648
$370$	1.62314	−	8.14155i	0.0843830	−	0.423259i
$371$	−0.350262			−0.0181847
$372$			0.287336i			0.0148977i
$373$			19.4087i			1.00495i	0.864593	+	0.502473i	$0.167576\pi$
$373$			19.4087i			1.00495i	−0.864593	+	0.502473i	$0.832424\pi$
$374$	−14.2207			−0.735335
$375$	−2.66877	−	1.78826i	−0.137815	−	0.0923455i
$376$	2.35753			0.121580
$377$		−	9.31223i		−	0.479604i
$378$		−	1.77350i		−	0.0912192i
$379$	17.9054			0.919739			0.459869	−	0.887987i	$-0.347896\pi$
$379$	17.9054			0.919739			0.459869	+	0.887987i	$0.347896\pi$
$380$	2.16868	−	10.8779i	0.111251	−	0.558026i
$381$	−2.99917			−0.153652
$382$			5.34277i			0.273360i
$383$			1.89269i			0.0967121i	0.998830	+	0.0483561i	$0.0153982\pi$
$383$			1.89269i			0.0967121i	−0.998830	+	0.0483561i	$0.984602\pi$
$384$	0.287336			0.0146630
$385$	−8.30326	−	1.65538i	−0.423173	−	0.0843660i
$386$	6.50248			0.330968
$387$			10.9007i			0.554113i
$388$			16.4141i			0.833301i
$389$	32.4089			1.64319			0.821597	−	0.570068i	$-0.193083\pi$
$389$	32.4089			1.64319			0.821597	+	0.570068i	$0.193083\pi$
$390$	0.890307	+	0.177496i	0.0450824	+	0.00898786i
$391$	31.3534			1.58561
$392$			5.91203i			0.298603i
$393$			2.23731i			0.112858i
$394$	−11.5794			−0.583361
$395$	−0.623139	+	3.12562i	−0.0313535	+	0.157267i
$396$	−10.5906			−0.532198
$397$			23.8559i			1.19729i	0.801013	+	0.598647i	$0.204295\pi$
$397$			23.8559i			1.19729i	−0.801013	+	0.598647i	$0.795705\pi$
$398$			3.70842i			0.185886i
$399$	1.48670			0.0744281
$400$	−4.61773	−	1.91744i	−0.230887	−	0.0958719i
$401$	−34.0319			−1.69947			−0.849735	−	0.527210i	$-0.823238\pi$
$401$	−34.0319			−1.69947			−0.849735	+	0.527210i	$0.823238\pi$
$402$			2.37769i			0.118589i
$403$			1.41296i			0.0703844i
$404$	13.4087			0.667109
$405$	−3.61283	+	18.1217i	−0.179523	+	0.900475i
$406$	−6.87438			−0.341170
$407$		−	13.4774i		−	0.668047i
$408$		−	1.12562i		−	0.0557265i
$409$	−3.84880			−0.190311			−0.0951555	−	0.995462i	$-0.530335\pi$
$409$	−3.84880			−0.190311			−0.0951555	+	0.995462i	$0.530335\pi$
$410$	6.01593	+	1.19936i	0.297105	+	0.0592324i
$411$	−1.39479			−0.0687999
$412$			17.7559i			0.874769i
$413$		−	4.52412i		−	0.222617i
$414$	23.3499			1.14758
$415$	−28.2751	−	5.63707i	−1.38797	−	0.276713i
$416$	1.41296			0.0692759
$417$		−	5.44579i		−	0.266681i
$418$		−	18.0071i		−	0.880757i
$419$	−17.6993			−0.864666			−0.432333	−	0.901714i	$-0.642309\pi$
$419$	−17.6993			−0.864666			−0.432333	+	0.901714i	$0.642309\pi$
$420$	0.131029	−	0.657234i	0.00639358	−	0.0320697i
$421$	29.8667			1.45562			0.727808	−	0.685781i	$-0.240539\pi$
$421$	29.8667			1.45562			0.727808	+	0.685781i	$0.240539\pi$
$422$		−	23.7501i		−	1.15614i
$423$		−	6.87793i		−	0.334417i
$424$	−0.335803			−0.0163080
$425$	−7.51145	+	18.0897i	−0.364359	+	0.877478i
$426$	1.60838			0.0779263
$427$		−	8.69844i		−	0.420947i
$428$		−	12.5441i		−	0.606344i
$429$	1.47380			0.0711555
$430$	−1.63351	+	8.19357i	−0.0787749	+	0.395129i
$431$	31.5469			1.51956			0.759779	−	0.650181i	$-0.225307\pi$
$431$	31.5469			1.51956			0.759779	+	0.650181i	$0.225307\pi$
$432$		−	1.70029i		−	0.0818053i
$433$		−	21.4112i		−	1.02896i	−0.857503	−	0.514479i	$-0.827985\pi$
$433$		−	21.4112i		−	1.02896i	0.857503	−	0.514479i	$-0.172015\pi$
$434$	1.04306			0.0500684
$435$	−4.15275	−	0.827913i	−0.199109	−	0.0396954i
$436$	−0.661810			−0.0316949
$437$			39.7016i			1.89919i
$438$			2.42450i			0.115847i
$439$	13.8245			0.659808			0.329904	−	0.944015i	$-0.392984\pi$
$439$	13.8245			0.659808			0.329904	+	0.944015i	$0.392984\pi$
$440$	−7.96050	−	1.58704i	−0.379502	−	0.0756593i
$441$	17.2480			0.821332
$442$		−	5.53517i		−	0.263281i
$443$			1.00896i			0.0479373i	0.999713	+	0.0239687i	$0.00763019\pi$
$443$			1.00896i			0.0479373i	−0.999713	+	0.0239687i	$0.992370\pi$
$444$	1.06678			0.0506272
$445$	7.18801	−	36.0546i	0.340745	−	1.70915i
$446$	−5.72757			−0.271208
$447$		−	6.77847i		−	0.320610i
$448$		−	1.04306i		−	0.0492799i
$449$	20.1675			0.951761			0.475881	−	0.879510i	$-0.342129\pi$
$449$	20.1675			0.951761			0.475881	+	0.879510i	$0.342129\pi$
$450$	−5.59401	+	13.4719i	−0.263704	+	0.635073i
$451$	9.95864			0.468934
$452$			7.81471i			0.367573i
$453$		−	1.14223i		−	0.0536668i
$454$	24.7716			1.16259
$455$	0.644329	−	3.23191i	0.0302066	−	0.151514i
$456$	1.42533			0.0667471
$457$		−	32.9630i		−	1.54195i	−0.636868	−	0.770973i	$-0.719770\pi$
$457$		−	32.9630i		−	1.54195i	0.636868	−	0.770973i	$-0.280230\pi$
$458$			4.26717i			0.199392i
$459$	−6.66079			−0.310899
$460$	17.5511	+	3.49907i	0.818324	+	0.163145i
$461$	12.0644			0.561895			0.280947	−	0.959723i	$-0.409351\pi$
$461$	12.0644			0.561895			0.280947	+	0.959723i	$0.409351\pi$
$462$		−	1.08797i		−	0.0506170i
$463$			3.88558i			0.180578i	0.995916	+	0.0902892i	$0.0287791\pi$
$463$			3.88558i			0.180578i	−0.995916	+	0.0902892i	$0.971221\pi$
$464$	−6.59060			−0.305961
$465$	0.630102	+	0.125620i	0.0292203	+	0.00582550i
$466$	2.10628			0.0975718
$467$			2.89231i			0.133840i	0.997758	+	0.0669200i	$0.0213172\pi$
$467$			2.89231i			0.133840i	−0.997758	+	0.0669200i	$0.978683\pi$
$468$		−	4.12221i		−	0.190549i
$469$	8.63127			0.398555
$470$	1.03069	−	5.16985i	0.0475420	−	0.238467i
$471$	−1.88914			−0.0870469
$472$		−	4.33736i		−	0.199643i
$473$			13.5635i			0.623649i
$474$	−0.409548			−0.0188112
$475$	−22.9062	−	9.51145i	−1.05101	−	0.436415i
$476$	−4.08612			−0.187287
$477$			0.979685i			0.0448567i
$478$			16.9686i			0.776127i
$479$	−31.7786			−1.45200			−0.726000	−	0.687695i	$-0.758623\pi$
$479$	−31.7786			−1.45200			−0.726000	+	0.687695i	$0.758623\pi$
$480$	0.125620	−	0.630102i	0.00573376	−	0.0287601i
$481$	5.24583			0.239189
$482$			27.3921i			1.24768i
$483$			2.39873i			0.109146i
$484$	−2.17764			−0.0989838
$485$	35.9947	+	7.17609i	1.63444	+	0.325849i
$486$	−7.47535			−0.339089
$487$			15.4360i			0.699472i	0.936848	+	0.349736i	$0.113729\pi$
$487$			15.4360i			0.699472i	−0.936848	+	0.349736i	$0.886271\pi$
$488$		−	8.33936i		−	0.377505i
$489$	5.21753			0.235945
$490$	12.9646	+	2.58468i	0.585679	+	0.116764i
$491$	38.8018			1.75110			0.875550	−	0.483127i	$-0.160499\pi$
$491$	38.8018			1.75110			0.875550	+	0.483127i	$0.160499\pi$
$492$			0.788263i			0.0355376i
$493$			25.8183i			1.16280i
$494$	7.00896			0.315348
$495$	−4.63010	+	23.2243i	−0.208108	+	1.04385i
$496$	1.00000			0.0449013
$497$		−	5.83858i		−	0.261896i
$498$		−	3.70487i		−	0.166019i
$499$	−20.2275			−0.905506			−0.452753	−	0.891636i	$-0.649558\pi$
$499$	−20.2275			−0.905506			−0.452753	+	0.891636i	$0.649558\pi$
$500$	−6.22360	+	9.28799i	−0.278328	+	0.415372i
$501$	−1.65285			−0.0738437
$502$		−	14.1010i		−	0.629359i
$503$		−	9.40058i		−	0.419151i	−0.977792	−	0.209576i	$-0.932792\pi$
$503$		−	9.40058i		−	0.419151i	0.977792	−	0.209576i	$-0.0672083\pi$
$504$	−3.04306			−0.135549
$505$	5.86215	−	29.4041i	0.260862	−	1.30847i
$506$	29.0537			1.29160
$507$		−	3.16172i		−	0.140417i
$508$			10.4378i			0.463105i
$509$	−6.62514			−0.293654			−0.146827	−	0.989162i	$-0.546906\pi$
$509$	−6.62514			−0.293654			−0.146827	+	0.989162i	$0.546906\pi$
$510$	−2.46839	−	0.492110i	−0.109302	−	0.0217910i
$511$	8.80117			0.389341
$512$		−	1.00000i		−	0.0441942i
$513$		−	8.43429i		−	0.372383i
$514$	16.6469			0.734262
$515$	38.9371	+	7.76269i	1.71577	+	0.342065i
$516$	−1.07360			−0.0472625
$517$		−	8.55806i		−	0.376383i
$518$		−	3.87253i		−	0.170149i
$519$	−3.63790			−0.159686
$520$	0.617730	−	3.09849i	0.0270893	−	0.135878i
$521$	1.40974			0.0617617			0.0308808	−	0.999523i	$-0.490169\pi$
$521$	1.40974			0.0617617			0.0308808	+	0.999523i	$0.490169\pi$
$522$			19.2277i			0.841572i
$523$		−	27.2502i		−	1.19157i	−0.803145	−	0.595783i	$-0.796842\pi$
$523$		−	27.2502i		−	1.19157i	0.803145	−	0.595783i	$-0.203158\pi$
$524$	7.78641			0.340151
$525$	−1.38397	−	0.574672i	−0.0604014	−	0.0250807i
$526$	−4.72942			−0.206213
$527$		−	3.91744i		−	0.170646i
$528$		−	1.04306i		−	0.0453933i
$529$	−41.0569			−1.78508
$530$	−0.146810	+	0.736387i	−0.00637701	+	0.0319866i
$531$	−12.6540			−0.549136
$532$		−	5.17409i		−	0.224325i
$533$			3.87623i			0.167898i
$534$	4.72420			0.204436
$535$	−27.5082	−	5.48417i	−1.18928	−	0.237101i
$536$	8.27496			0.357424
$537$			3.84793i			0.166051i
$538$			3.44228i			0.148407i
$539$	21.4613			0.924402
$540$	−3.72859	−	0.743350i	−0.160453	−	0.0319887i
$541$	25.3561			1.09014			0.545072	−	0.838389i	$-0.316502\pi$
$541$	25.3561			1.09014			0.545072	+	0.838389i	$0.316502\pi$
$542$		−	6.27599i		−	0.269577i
$543$			2.63828i			0.113220i
$544$	−3.91744			−0.167959
$545$	−0.289337	+	1.45129i	−0.0123938	+	0.0621665i
$546$	0.423474			0.0181230
$547$		−	12.7645i		−	0.545772i	−0.962046	−	0.272886i	$-0.912022\pi$
$547$		−	12.7645i		−	0.545772i	0.962046	−	0.272886i	$-0.0879782\pi$
$548$			4.85421i			0.207362i
$549$	−24.3296			−1.03836
$550$	−6.96050	+	16.7628i	−0.296797	+	0.714770i
$551$	−32.6926			−1.39275
$552$			2.29971i			0.0978821i
$553$			1.48670i			0.0632209i
$554$	17.1796			0.729893
$555$	0.466386	−	2.33936i	0.0197970	−	0.0993002i
$556$	−18.9527			−0.803774
$557$			26.7179i			1.13207i	0.824380	+	0.566037i	$0.191524\pi$
$557$			26.7179i			1.13207i	−0.824380	+	0.566037i	$0.808476\pi$
$558$		−	2.91744i		−	0.123505i
$559$	−5.27935			−0.223293
$560$	−2.28734	−	0.456015i	−0.0966576	−	0.0192701i
$561$	−4.08612			−0.172516
$562$			19.7559i			0.833351i
$563$			20.3472i			0.857530i	0.903416	+	0.428765i	$0.141051\pi$
$563$			20.3472i			0.857530i	−0.903416	+	0.428765i	$0.858949\pi$
$564$	0.677402			0.0285237
$565$	17.1370	+	3.41651i	0.720958	+	0.143734i
$566$	−13.3782			−0.562327
$567$			8.61958i			0.361989i
$568$		−	5.59756i		−	0.234868i
$569$	−5.56093			−0.233126			−0.116563	−	0.993183i	$-0.537188\pi$
$569$	−5.56093			−0.233126			−0.116563	+	0.993183i	$0.537188\pi$
$570$	0.623139	−	3.12562i	0.0261004	−	0.130918i
$571$	−29.9491			−1.25333			−0.626664	−	0.779289i	$-0.715580\pi$
$571$	−29.9491			−1.25333			−0.626664	+	0.779289i	$0.715580\pi$
$572$		−	5.12918i		−	0.214462i
$573$			1.53517i			0.0641326i
$574$	2.86147			0.119436
$575$	15.3463	−	36.9583i	0.639986	−	1.54127i
$576$	−2.91744			−0.121560
$577$			17.5635i			0.731177i	0.930777	+	0.365588i	$0.119132\pi$
$577$			17.5635i			0.731177i	−0.930777	+	0.365588i	$0.880868\pi$
$578$		−	1.65368i		−	0.0687840i
$579$	1.86840			0.0776479
$580$	−2.88134	+	14.4526i	−0.119641	+	0.600112i
$581$	−13.4491			−0.557961
$582$			4.71637i			0.195500i
$583$			1.21900i			0.0504858i
$584$	8.43785			0.349161
$585$	−9.03965	−	1.80219i	−0.373744	−	0.0745114i
$586$	−4.40142			−0.181821
$587$		−	43.0427i		−	1.77656i	−0.459301	−	0.888280i	$-0.651900\pi$
$587$		−	43.0427i		−	1.77656i	0.459301	−	0.888280i	$-0.348100\pi$
$588$			1.69874i			0.0700548i
$589$	4.96050			0.204394
$590$	−9.51145	−	1.89625i	−0.391580	−	0.0780673i
$591$	−3.32717			−0.136862
$592$		−	3.71266i		−	0.152590i
$593$		−	3.47735i		−	0.142798i	−0.997448	−	0.0713988i	$-0.977254\pi$
$593$		−	3.47735i		−	0.142798i	0.997448	−	0.0713988i	$-0.0227463\pi$
$594$	−6.17223			−0.253250
$595$	−1.78641	+	8.96050i	−0.0732356	+	0.367345i
$596$	−23.5907			−0.966315
$597$			1.06556i			0.0436106i
$598$			11.3087i			0.462446i
$599$	26.6172			1.08755			0.543774	−	0.839231i	$-0.316995\pi$
$599$	26.6172			1.08755			0.543774	+	0.839231i	$0.316995\pi$
$600$	−1.32684	−	0.550949i	−0.0541680	−	0.0224924i
$601$	0.984220			0.0401472			0.0200736	−	0.999799i	$-0.493610\pi$
$601$	0.984220			0.0401472			0.0200736	+	0.999799i	$0.493610\pi$
$602$			3.89727i			0.158841i
$603$		−	24.1417i		−	0.983126i
$604$	−3.97526			−0.161751
$605$	−0.952043	+	4.77538i	−0.0387061	+	0.194147i
$606$	3.85280			0.156509
$607$		−	41.8986i		−	1.70061i	−0.526289	−	0.850306i	$-0.676417\pi$
$607$		−	41.8986i		−	1.70061i	0.526289	−	0.850306i	$-0.323583\pi$
$608$		−	4.96050i		−	0.201175i
$609$	−1.97526			−0.0800414
$610$	−18.2875	−	3.64588i	−0.740439	−	0.147617i
$611$	3.33108			0.134761
$612$			11.4289i			0.461985i
$613$		−	0.656548i		−	0.0265177i	−0.999912	−	0.0132589i	$-0.995779\pi$
$613$		−	0.656548i		−	0.0265177i	0.999912	−	0.0132589i	$-0.00422055\pi$
$614$	5.18699			0.209330
$615$	1.72859	+	0.344621i	0.0697035	+	0.0138964i
$616$	−3.78641			−0.152559
$617$		−	27.6518i		−	1.11322i	−0.830774	−	0.556610i	$-0.812102\pi$
$617$		−	27.6518i		−	1.11322i	0.830774	−	0.556610i	$-0.187898\pi$
$618$			5.10190i			0.205228i
$619$	−31.3090			−1.25842			−0.629208	−	0.777237i	$-0.716620\pi$
$619$	−31.3090			−1.25842			−0.629208	+	0.777237i	$0.716620\pi$
$620$	0.437190	−	2.19291i	0.0175580	−	0.0880695i
$621$	13.6084			0.546085
$622$		−	24.8330i		−	0.995713i
$623$		−	17.1493i		−	0.687074i
$624$	0.405993			0.0162527
$625$	17.6469	+	17.7084i	0.705874	+	0.708337i
$626$	15.4221			0.616390
$627$		−	5.17409i		−	0.206633i
$628$			6.57467i			0.262358i
$629$	−14.5441			−0.579913
$630$	−1.33039	+	6.67316i	−0.0530042	+	0.265865i
$631$	6.66283			0.265243			0.132622	−	0.991167i	$-0.457661\pi$
$631$	6.66283			0.265243			0.132622	+	0.991167i	$0.457661\pi$
$632$			1.42533i			0.0566965i
$633$		−	6.82425i		−	0.271239i
$634$	17.0547			0.677330
$635$	22.8893	+	4.56332i	0.908334	+	0.181090i
$636$	−0.0964883			−0.00382601
$637$			8.35344i			0.330975i
$638$			23.9245i			0.947182i
$639$	−16.3305			−0.646026
$640$	−2.19291	−	0.437190i	−0.0866825	−	0.0172814i
$641$	−29.2673			−1.15599			−0.577995	−	0.816041i	$-0.696165\pi$
$641$	−29.2673			−1.15599			−0.577995	+	0.816041i	$0.696165\pi$
$642$		−	3.60438i		−	0.142253i
$643$		−	1.49328i		−	0.0588891i	−0.999566	−	0.0294446i	$-0.990626\pi$
$643$		−	1.49328i		−	0.0588891i	0.999566	−	0.0294446i	$-0.00937385\pi$
$644$	8.34818			0.328964
$645$	−0.469366	+	2.35431i	−0.0184813	+	0.0927007i
$646$	−19.4324			−0.764559
$647$		−	19.3817i		−	0.761974i	−0.924580	−	0.380987i	$-0.875584\pi$
$647$		−	19.3817i		−	0.761974i	0.924580	−	0.380987i	$-0.124416\pi$
$648$			8.26376i			0.324631i
$649$	−15.7451			−0.618047
$650$	−6.52465	−	2.70926i	−0.255918	−	0.106266i
$651$	0.299708			0.0117465
$652$		−	18.1583i		−	0.711134i
$653$			7.04661i			0.275755i	0.990449	+	0.137878i	$0.0440281\pi$
$653$			7.04661i			0.275755i	−0.990449	+	0.137878i	$0.955972\pi$
$654$	−0.190162			−0.00743591
$655$	3.40414	−	17.0749i	0.133011	−	0.667172i
$656$	2.74335			0.107110
$657$		−	24.6169i		−	0.960397i
$658$		−	2.45904i		−	0.0958632i
$659$	−12.9449			−0.504262			−0.252131	−	0.967693i	$-0.581131\pi$
$659$	−12.9449			−0.504262			−0.252131	+	0.967693i	$0.581131\pi$
$660$	−2.28734	−	0.456015i	−0.0890344	−	0.0177503i
$661$	−38.3247			−1.49066			−0.745330	−	0.666696i	$-0.767708\pi$
$661$	−38.3247			−1.49066			−0.745330	+	0.666696i	$0.767708\pi$
$662$			29.1181i			1.13171i
$663$		−	1.59045i		−	0.0617680i
$664$	−12.8939			−0.500379
$665$	−11.3463	−	2.26206i	−0.439991	−	0.0877189i
$666$	−10.8315			−0.419711
$667$		−	52.7482i		−	2.04242i
$668$			5.75231i			0.222564i
$669$	−1.64574			−0.0636278
$670$	3.61773	−	18.1463i	0.139765	−	0.701052i
$671$	−30.2727			−1.16867
$672$		−	0.299708i		−	0.0115615i
$673$			43.3678i			1.67171i	0.548953	+	0.835853i	$0.315026\pi$
$673$			43.3678i			1.67171i	−0.548953	+	0.835853i	$0.684974\pi$
$674$	32.7257			1.26055
$675$	−3.26020	+	7.85149i	−0.125485	+	0.302204i
$676$	−11.0036			−0.423214
$677$			16.1738i			0.621609i	0.950474	+	0.310805i	$0.100598\pi$
$677$			16.1738i			0.621609i	−0.950474	+	0.310805i	$0.899402\pi$
$678$			2.24545i			0.0862358i
$679$	17.1209			0.657039
$680$	−1.71266	+	8.59060i	−0.0656777	+	0.329434i
$681$	7.11778			0.272754
$682$		−	3.63010i		−	0.139004i
$683$		−	10.4156i		−	0.398543i	−0.979944	−	0.199272i	$-0.936142\pi$
$683$		−	10.4156i		−	0.398543i	0.979944	−	0.199272i	$-0.0638576\pi$
$684$	−14.4719			−0.553349
$685$	10.6449	+	2.12221i	0.406719	+	0.0810856i
$686$	13.4680			0.514211
$687$			1.22611i			0.0467790i
$688$			3.73639i			0.142448i
$689$	−0.474475			−0.0180761
$690$	5.04306	+	1.00541i	0.191986	+	0.0382753i
$691$	1.66946			0.0635092			0.0317546	−	0.999496i	$-0.489890\pi$
$691$	1.66946			0.0635092			0.0317546	+	0.999496i	$0.489890\pi$
$692$			12.6608i			0.481291i
$693$			11.0466i			0.419626i
$694$	11.9323			0.452946
$695$	−8.28593	+	41.5616i	−0.314303	+	1.57652i
$696$	−1.89372			−0.0717811
$697$		−	10.7469i		−	0.407068i
$698$			18.3940i			0.696222i
$699$	0.605211			0.0228912
$700$	−2.00000	+	4.81656i	−0.0755929	+	0.182049i
$701$	−18.6903			−0.705923			−0.352962	−	0.935638i	$-0.614825\pi$
$701$	−18.6903			−0.705923			−0.352962	+	0.935638i	$0.614825\pi$
$702$		−	2.40244i		−	0.0906742i
$703$		−	18.4167i		−	0.694597i
$704$	−3.63010			−0.136815
$705$	0.296153	−	1.48548i	0.0111538	−	0.0559465i
$706$	−31.8384			−1.19826
$707$		−	13.9861i		−	0.526000i
$708$		−	1.24628i		−	0.0468380i
$709$	−35.3999			−1.32947			−0.664736	−	0.747079i	$-0.731456\pi$
$709$	−35.3999			−1.32947			−0.664736	+	0.747079i	$0.731456\pi$
$710$	−12.2750	−	2.44720i	−0.460671	−	0.0918417i
$711$	4.15831			0.155949
$712$		−	16.4414i		−	0.616168i
$713$			8.00355i			0.299735i
$714$	−1.17409			−0.0439391
$715$	−11.2478	−	2.24242i	−0.420645	−	0.0838619i
$716$	13.3918			0.500474
$717$			4.87569i			0.182086i
$718$		−	0.523964i		−	0.0195542i
$719$	−23.1585			−0.863666			−0.431833	−	0.901954i	$-0.642133\pi$
$719$	−23.1585			−0.863666			−0.431833	+	0.901954i	$0.642133\pi$
$720$	−1.27547	+	6.39769i	−0.0475341	+	0.238428i
$721$	18.5204			0.689736
$722$		−	5.60653i		−	0.208653i
$723$			7.87073i			0.292716i
$724$	9.18188			0.341242
$725$	30.4336	+	12.6371i	1.13028	+	0.469329i
$726$	−0.625715			−0.0232225
$727$			31.4165i			1.16517i	0.812769	+	0.582586i	$0.197959\pi$
$727$			31.4165i			1.16517i	−0.812769	+	0.582586i	$0.802041\pi$
$728$		−	1.47380i		−	0.0546225i
$729$	22.6433			0.838642
$730$	3.68894	−	18.5035i	0.136534	−	0.684844i
$731$	14.6371			0.541371
$732$		−	2.39620i		−	0.0885660i
$733$			45.9057i			1.69557i	0.530344	+	0.847783i	$0.322063\pi$
$733$			45.9057i			1.69557i	−0.530344	+	0.847783i	$0.677937\pi$
$734$	−13.3885			−0.494180
$735$	3.72518	+	0.742671i	0.137405	+	0.0273938i
$736$	8.00355			0.295015
$737$		−	30.0390i		−	1.10650i
$738$		−	8.00355i		−	0.294615i
$739$	12.1858			0.448263			0.224131	−	0.974559i	$-0.428046\pi$
$739$	12.1858			0.448263			0.224131	+	0.974559i	$0.428046\pi$
$740$	−8.14155	−	1.62314i	−0.299289	−	0.0596678i
$741$	2.01393			0.0739834
$742$			0.350262i			0.0128585i
$743$			46.4185i			1.70293i	0.524410	+	0.851466i	$0.324286\pi$
$743$			46.4185i			1.70293i	−0.524410	+	0.851466i	$0.675714\pi$
$744$	0.287336			0.0105342
$745$	−10.3136	+	51.7324i	−0.377862	+	1.89533i
$746$	19.4087			0.710604
$747$			37.6170i			1.37634i
$748$			14.2207i			0.519960i
$749$	−13.0843			−0.478089
$750$	−1.78826	+	2.66877i	−0.0652981	+	0.0974498i
$751$	3.42207			0.124873			0.0624365	−	0.998049i	$-0.480113\pi$
$751$	3.42207			0.124873			0.0624365	+	0.998049i	$0.480113\pi$
$752$		−	2.35753i		−	0.0859701i
$753$		−	4.05173i		−	0.147653i
$754$	−9.31223			−0.339131
$755$	−1.73794	+	8.71739i	−0.0632502	+	0.317258i
$756$	−1.77350			−0.0645017
$757$		−	41.9392i		−	1.52430i	−0.647398	−	0.762152i	$-0.724143\pi$
$757$		−	41.9392i		−	1.52430i	0.647398	−	0.762152i	$-0.275857\pi$
$758$		−	17.9054i		−	0.650353i
$759$	8.34818			0.303020
$760$	−10.8779	−	2.16868i	−0.394584	−	0.0786662i
$761$	−41.7311			−1.51275			−0.756376	−	0.654137i	$-0.773032\pi$
$761$	−41.7311			−1.51275			−0.756376	+	0.654137i	$0.773032\pi$
$762$			2.99917i			0.108648i
$763$			0.690306i			0.0249908i
$764$	5.34277			0.193295
$765$	25.0625	+	4.99659i	0.906138	+	0.180652i
$766$	1.89269			0.0683858
$767$		−	6.12850i		−	0.221287i
$768$		−	0.287336i		−	0.0103683i
$769$	46.6399			1.68188			0.840939	−	0.541130i	$-0.182003\pi$
$769$	46.6399			1.68188			0.840939	+	0.541130i	$0.182003\pi$
$770$	−1.65538	+	8.30326i	−0.0596557	+	0.299229i
$771$	4.78324			0.172264
$772$		−	6.50248i		−	0.234029i
$773$			42.7704i			1.53834i	0.639042	+	0.769172i	$0.279331\pi$
$773$			42.7704i			1.53834i	−0.639042	+	0.769172i	$0.720669\pi$
$774$	10.9007			0.391817
$775$	−4.61773	−	1.91744i	−0.165874	−	0.0688764i
$776$	16.4141			0.589233
$777$		−	1.11272i		−	0.0399184i
$778$		−	32.4089i		−	1.16191i
$779$	13.6084			0.487571
$780$	0.177496	−	0.890307i	0.00635538	−	0.0318781i
$781$	−20.3197			−0.727097
$782$		−	31.3534i		−	1.12120i
$783$			11.2059i			0.400468i
$784$	5.91203			0.211144
$785$	14.4177	+	2.87438i	0.514589	+	0.102591i
$786$	2.23731			0.0798024
$787$			39.7991i			1.41868i	0.704865	+	0.709342i	$0.251008\pi$
$787$			39.7991i			1.41868i	−0.704865	+	0.709342i	$0.748992\pi$
$788$			11.5794i			0.412499i
$789$	−1.35893			−0.0483793
$790$	3.12562	+	0.623139i	0.111205	+	0.0221703i
$791$	8.15120			0.289823
$792$			10.5906i			0.376321i
$793$		−	11.7831i		−	0.418432i
$794$	23.8559			0.846615
$795$	−0.0421837	+	0.211590i	−0.00149610	+	0.00750434i
$796$	3.70842			0.131442
$797$		−	44.2450i		−	1.56724i	−0.621242	−	0.783618i	$-0.713372\pi$
$797$		−	44.2450i		−	1.56724i	0.621242	−	0.783618i	$-0.286628\pi$
$798$		−	1.48670i		−	0.0526286i
$799$	−9.23546			−0.326727
$800$	−1.91744	+	4.61773i	−0.0677917	+	0.163261i
$801$	−47.9668			−1.69482
$802$			34.0319i			1.20171i
$803$		−	30.6302i		−	1.08092i
$804$	2.37769			0.0838548
$805$	3.64974	−	18.3068i	0.128636	−	0.645231i
$806$	1.41296			0.0497693
$807$			0.989090i			0.0348176i
$808$		−	13.4087i		−	0.471717i
$809$	−15.6063			−0.548690			−0.274345	−	0.961631i	$-0.588461\pi$
$809$	−15.6063			−0.548690			−0.274345	+	0.961631i	$0.588461\pi$
$810$	18.1217	+	3.61283i	0.636732	+	0.126942i
$811$	−38.7113			−1.35934			−0.679670	−	0.733518i	$-0.737877\pi$
$811$	−38.7113			−1.35934			−0.679670	+	0.733518i	$0.737877\pi$
$812$			6.87438i			0.241243i
$813$		−	1.80332i		−	0.0632450i
$814$	−13.4774			−0.472381
$815$	−39.8196	−	7.93863i	−1.39482	−	0.278078i
$816$	−1.12562			−0.0394046
$817$			18.5343i			0.648434i
$818$			3.84880i			0.134570i
$819$	−4.29971			−0.150244
$820$	1.19936	−	6.01593i	0.0418836	−	0.210085i
$821$	30.1271			1.05144			0.525721	−	0.850657i	$-0.323796\pi$
$821$	30.1271			1.05144			0.525721	+	0.850657i	$0.323796\pi$
$822$			1.39479i			0.0486488i
$823$		−	12.4674i		−	0.434585i	−0.976107	−	0.217293i	$-0.930277\pi$
$823$		−	12.4674i		−	0.434585i	0.976107	−	0.217293i	$-0.0697226\pi$
$824$	17.7559			0.618555
$825$	−2.00000	+	4.81656i	−0.0696311	+	0.167691i
$826$	−4.52412			−0.157414
$827$			41.0898i			1.42883i	0.699721	+	0.714416i	$0.253308\pi$
$827$			41.0898i			1.42883i	−0.699721	+	0.714416i	$0.746692\pi$
$828$		−	23.3499i		−	0.811464i
$829$	−4.17292			−0.144931			−0.0724657	−	0.997371i	$-0.523087\pi$
$829$	−4.17292			−0.144931			−0.0724657	+	0.997371i	$0.523087\pi$
$830$	−5.63707	+	28.2751i	−0.195665	+	0.981443i
$831$	4.93633			0.171239
$832$		−	1.41296i		−	0.0489854i
$833$		−	23.1600i		−	0.802447i
$834$	−5.44579			−0.188572
$835$	12.6143	+	2.51485i	0.436537	+	0.0870301i
$836$	−18.0071			−0.622789
$837$		−	1.70029i		−	0.0587707i
$838$			17.6993i			0.611411i
$839$	49.1097			1.69546			0.847728	−	0.530431i	$-0.177970\pi$
$839$	49.1097			1.69546			0.847728	+	0.530431i	$0.177970\pi$
$840$	−0.657234	−	0.131029i	−0.0226767	−	0.00452094i
$841$	14.4360			0.497793
$842$		−	29.8667i		−	1.02928i
$843$			5.67657i			0.195511i
$844$	−23.7501			−0.817511
$845$	−4.81064	+	24.1298i	−0.165491	+	0.830091i
$846$	−6.87793			−0.236468
$847$			2.27141i			0.0780465i
$848$			0.335803i			0.0115315i
$849$	−3.84403			−0.131927
$850$	18.0897	+	7.51145i	0.620471	+	0.257640i
$851$	29.7145			1.01860
$852$		−	1.60838i		−	0.0551022i
$853$		−	55.2897i		−	1.89308i	−0.322583	−	0.946541i	$-0.604551\pi$
$853$		−	55.2897i		−	1.89308i	0.322583	−	0.946541i	$-0.395449\pi$
$854$	−8.69844			−0.297654
$855$	−6.32699	+	31.7357i	−0.216378	+	1.08534i
$856$	−12.5441			−0.428750
$857$		−	17.8536i		−	0.609867i	−0.952374	−	0.304933i	$-0.901366\pi$
$857$		−	17.8536i		−	0.609867i	0.952374	−	0.304933i	$-0.0986342\pi$
$858$		−	1.47380i		−	0.0503146i
$859$	4.28407			0.146171			0.0730854	−	0.997326i	$-0.476715\pi$
$859$	4.28407			0.146171			0.0730854	+	0.997326i	$0.476715\pi$
$860$	8.19357	+	1.63351i	0.279398	+	0.0557022i
$861$	0.822204			0.0280206
$862$		−	31.5469i		−	1.07449i
$863$		−	41.0128i		−	1.39609i	−0.716053	−	0.698046i	$-0.754053\pi$
$863$		−	41.0128i		−	1.39609i	0.716053	−	0.698046i	$-0.245947\pi$
$864$	−1.70029			−0.0578451
$865$	27.7640	+	5.53517i	0.944004	+	0.188201i
$866$	−21.4112			−0.727584
$867$		−	0.475161i		−	0.0161373i
$868$		−	1.04306i		−	0.0354037i
$869$	5.17409			0.175519
$870$	−0.827913	+	4.15275i	−0.0280689	+	0.140791i
$871$	11.6922			0.396174
$872$			0.661810i			0.0224117i
$873$		−	47.8872i		−	1.62074i
$874$	39.7016			1.34293
$875$	9.68792	+	6.49158i	0.327511	+	0.219455i
$876$	2.42450			0.0819161
$877$			24.8507i			0.839147i	0.907721	+	0.419574i	$0.137820\pi$
$877$			24.8507i			0.839147i	−0.907721	+	0.419574i	$0.862180\pi$
$878$		−	13.8245i		−	0.466554i
$879$	−1.26468			−0.0426568
$880$	−1.58704	+	7.96050i	−0.0534992	+	0.268348i
$881$	7.15479			0.241051			0.120525	−	0.992710i	$-0.461542\pi$
$881$	7.15479			0.241051			0.120525	+	0.992710i	$0.461542\pi$
$882$		−	17.2480i		−	0.580770i
$883$			50.4721i			1.69852i	0.527973	+	0.849261i	$0.322952\pi$
$883$			50.4721i			1.69852i	−0.527973	+	0.849261i	$0.677048\pi$
$884$	−5.53517			−0.186168
$885$	−2.73298	−	0.544860i	−0.0918681	−	0.0183153i
$886$	1.00896			0.0338968
$887$			11.0817i			0.372088i	0.982541	+	0.186044i	$0.0595667\pi$
$887$			11.0817i			0.372088i	−0.982541	+	0.186044i	$0.940433\pi$
$888$		−	1.06678i		−	0.0357988i
$889$	10.8873			0.365148
$890$	−36.0546	−	7.18801i	−1.20855	−	0.240943i
$891$	29.9983			1.00498
$892$			5.72757i			0.191773i
$893$		−	11.6945i		−	0.391341i
$894$	−6.77847			−0.226706
$895$	5.85474	−	29.3670i	0.195703	−	0.981630i
$896$	−1.04306			−0.0348461
$897$			3.24939i			0.108494i
$898$		−	20.1675i		−	0.672997i
$899$	−6.59060			−0.219809
$900$	13.4719	+	5.59401i	0.449065	+	0.186467i
$901$	1.31549			0.0438253
$902$		−	9.95864i		−	0.331587i
$903$			1.11983i			0.0372655i
$904$	7.81471			0.259913
$905$	4.01423	−	20.1351i	0.133437	−	0.669312i
$906$	−1.14223			−0.0379482
$907$		−	42.9086i		−	1.42476i	−0.701796	−	0.712378i	$-0.747618\pi$
$907$		−	42.9086i		−	1.42476i	0.701796	−	0.712378i	$-0.252382\pi$
$908$		−	24.7716i		−	0.822076i
$909$	−39.1191			−1.29750
$910$	−3.23191	−	0.644329i	−0.107137	−	0.0213593i
$911$	42.4980			1.40802			0.704011	−	0.710189i	$-0.251391\pi$
$911$	42.4980			1.40802			0.704011	+	0.710189i	$0.251391\pi$
$912$		−	1.42533i		−	0.0471973i
$913$			46.8060i			1.54905i
$914$	−32.9630			−1.09032
$915$	−5.25465	−	1.04759i	−0.173713	−	0.0346323i
$916$	4.26717			0.140991
$917$		−	8.12168i		−	0.268201i
$918$			6.66079i			0.219839i
$919$	10.7964			0.356140			0.178070	−	0.984018i	$-0.443015\pi$
$919$	10.7964			0.356140			0.178070	+	0.984018i	$0.443015\pi$
$920$	3.49907	−	17.5511i	0.115361	−	0.578642i
$921$	1.49041			0.0491106
$922$		−	12.0644i		−	0.397320i
$923$		−	7.90911i		−	0.260332i
$924$	−1.08797			−0.0357916
$925$	−7.11880	+	17.1441i	−0.234065	+	0.563694i
$926$	3.88558			0.127688
$927$		−	51.8017i		−	1.70139i
$928$			6.59060i			0.216347i
$929$	54.8984			1.80116			0.900579	−	0.434692i	$-0.143143\pi$
$929$	54.8984			1.80116			0.900579	+	0.434692i	$0.143143\pi$
$930$	0.125620	−	0.630102i	0.00411925	−	0.0206619i
$931$	29.3266			0.961140
$932$		−	2.10628i		−	0.0689937i
$933$		−	7.13542i		−	0.233603i
$934$	2.89231			0.0946392
$935$	31.1848	+	6.21715i	1.01985	+	0.203322i
$936$	−4.12221			−0.134739
$937$			20.5554i			0.671515i	0.941949	+	0.335757i	$0.108992\pi$
$937$			20.5554i			0.671515i	−0.941949	+	0.335757i	$0.891008\pi$
$938$		−	8.63127i		−	0.281821i
$939$	4.43131			0.144610
$940$	−5.16985	−	1.03069i	−0.168622	−	0.0336173i
$941$	21.0602			0.686543			0.343272	−	0.939236i	$-0.388465\pi$
$941$	21.0602			0.686543			0.343272	+	0.939236i	$0.388465\pi$
$942$			1.88914i			0.0615515i
$943$			21.9566i			0.715004i
$944$	−4.33736			−0.141169
$945$	−0.775358	+	3.88914i	−0.0252224	+	0.126514i
$946$	13.5635			0.440986
$947$			40.3666i			1.31174i	0.754874	+	0.655870i	$0.227698\pi$
$947$			40.3666i			1.31174i	−0.754874	+	0.655870i	$0.772302\pi$
$948$			0.409548i			0.0133015i
$949$	11.9223			0.387014
$950$	−9.51145	+	22.9062i	−0.308592	+	0.743176i
$951$	4.90044			0.158908
$952$			4.08612i			0.132432i
$953$		−	10.8386i		−	0.351097i	−0.984471	−	0.175549i	$-0.943830\pi$
$953$		−	10.8386i		−	0.351097i	0.984471	−	0.175549i	$-0.0561699\pi$
$954$	0.979685			0.0317185
$955$	2.33580	−	11.7162i	0.0755848	−	0.379128i
$956$	16.9686			0.548805
$957$			6.87438i			0.222217i
$958$			31.7786i			1.02672i
$959$	5.06323			0.163500
$960$	−0.630102	−	0.125620i	−0.0203365	−	0.00405438i
$961$	1.00000			0.0322581
$962$		−	5.24583i		−	0.169132i
$963$			36.5967i			1.17931i
$964$	27.3921			0.882240
$965$	−14.2594	−	2.84282i	−0.459025	−	0.0915136i
$966$	2.39873			0.0771779
$967$			9.32347i			0.299822i	0.988699	+	0.149911i	$0.0478988\pi$
$967$			9.32347i			0.299822i	−0.988699	+	0.149911i	$0.952101\pi$
$968$			2.17764i			0.0699921i
$969$	−5.58364			−0.179372
$970$	7.17609	−	35.9947i	0.230410	−	1.15572i
$971$	15.5067			0.497633			0.248816	−	0.968551i	$-0.419958\pi$
$971$	15.5067			0.497633			0.248816	+	0.968551i	$0.419958\pi$
$972$			7.47535i			0.239772i
$973$			19.7688i			0.633758i
$974$	15.4360			0.494601
$975$	−1.87477	−	0.778466i	−0.0600406	−	0.0249309i
$976$	−8.33936			−0.266936
$977$		−	60.3329i		−	1.93022i	−0.261845	−	0.965110i	$-0.584331\pi$
$977$		−	60.3329i		−	1.93022i	0.261845	−	0.965110i	$-0.415669\pi$
$978$		−	5.21753i		−	0.166838i
$979$	−59.6840			−1.90751
$980$	2.58468	−	12.9646i	0.0825645	−	0.414138i
$981$	1.93079			0.0616454
$982$		−	38.8018i		−	1.23822i
$983$			12.3796i			0.394847i	0.980318	+	0.197424i	$0.0632575\pi$
$983$			12.3796i			0.394847i	−0.980318	+	0.197424i	$0.936743\pi$
$984$	0.788263			0.0251289
$985$	25.3926	+	5.06239i	0.809075	+	0.161301i
$986$	25.8183			0.822221
$987$		−	0.706569i		−	0.0224904i
$988$		−	7.00896i		−	0.222985i
$989$	−29.9044			−0.950904
$990$	23.2243	+	4.63010i	0.738115	+	0.147154i
$991$	22.9368			0.728611			0.364305	−	0.931280i	$-0.381306\pi$
$991$	22.9368			0.728611			0.364305	+	0.931280i	$0.381306\pi$
$992$		−	1.00000i		−	0.0317500i
$993$			8.36668i			0.265509i
$994$	−5.83858			−0.185189
$995$	1.62129	−	8.13225i	0.0513982	−	0.257810i
$996$	−3.70487			−0.117393
$997$			10.3882i			0.328996i	0.986377	+	0.164498i	$0.0526005\pi$
$997$			10.3882i			0.328996i	−0.986377	+	0.164498i	$0.947400\pi$
$998$			20.2275i			0.640290i
$999$	−6.31261			−0.199722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.b.b.249.2	✓	8
3.2	odd	2		2790.2.d.l.559.7		8
4.3	odd	2		2480.2.d.e.1489.5		8
5.2	odd	4		1550.2.a.q.1.2		4
5.3	odd	4		1550.2.a.n.1.3		4
5.4	even	2	inner	310.2.b.b.249.7	yes	8
15.14	odd	2		2790.2.d.l.559.3		8
20.19	odd	2		2480.2.d.e.1489.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.b.b.249.2	✓	8	1.1	even	1	trivial
310.2.b.b.249.7	yes	8	5.4	even	2	inner
1550.2.a.n.1.3		4	5.3	odd	4
1550.2.a.q.1.2		4	5.2	odd	4
2480.2.d.e.1489.4		8	20.19	odd	2
2480.2.d.e.1489.5		8	4.3	odd	2
2790.2.d.l.559.3		8	15.14	odd	2
2790.2.d.l.559.7		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -0.287336i q^{3} -1.00000 q^{4} +(-0.437190 + 2.19291i) q^{5} -0.287336 q^{6} +1.04306i q^{7} +1.00000i q^{8} +2.91744 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -0.287336i q^{3} -1.00000 q^{4} +(-0.437190 + 2.19291i) q^{5} -0.287336 q^{6} +1.04306i q^{7} +1.00000i q^{8} +2.91744 q^{9} +(2.19291 + 0.437190i) q^{10} +3.63010 q^{11} +0.287336i q^{12} +1.41296i q^{13} +1.04306 q^{14} +(0.630102 + 0.125620i) q^{15} +1.00000 q^{16} -3.91744i q^{17} -2.91744i q^{18} +4.96050 q^{19} +(0.437190 - 2.19291i) q^{20} +0.299708 q^{21} -3.63010i q^{22} +8.00355i q^{23} +0.287336 q^{24} +(-4.61773 - 1.91744i) q^{25} +1.41296 q^{26} -1.70029i q^{27} -1.04306i q^{28} -6.59060 q^{29} +(0.125620 - 0.630102i) q^{30} +1.00000 q^{31} -1.00000i q^{32} -1.04306i q^{33} -3.91744 q^{34} +(-2.28734 - 0.456015i) q^{35} -2.91744 q^{36} -3.71266i q^{37} -4.96050i q^{38} +0.405993 q^{39} +(-2.19291 - 0.437190i) q^{40} +2.74335 q^{41} -0.299708i q^{42} +3.73639i q^{43} -3.63010 q^{44} +(-1.27547 + 6.39769i) q^{45} +8.00355 q^{46} -2.35753i q^{47} -0.287336i q^{48} +5.91203 q^{49} +(-1.91744 + 4.61773i) q^{50} -1.12562 q^{51} -1.41296i q^{52} +0.335803i q^{53} -1.70029 q^{54} +(-1.58704 + 7.96050i) q^{55} -1.04306 q^{56} -1.42533i q^{57} +6.59060i q^{58} -4.33736 q^{59} +(-0.630102 - 0.125620i) q^{60} -8.33936 q^{61} -1.00000i q^{62} +3.04306i q^{63} -1.00000 q^{64} +(-3.09849 - 0.617730i) q^{65} -1.04306 q^{66} -8.27496i q^{67} +3.91744i q^{68} +2.29971 q^{69} +(-0.456015 + 2.28734i) q^{70} -5.59756 q^{71} +2.91744i q^{72} -8.43785i q^{73} -3.71266 q^{74} +(-0.550949 + 1.32684i) q^{75} -4.96050 q^{76} +3.78641i q^{77} -0.405993i q^{78} +1.42533 q^{79} +(-0.437190 + 2.19291i) q^{80} +8.26376 q^{81} -2.74335i q^{82} +12.8939i q^{83} -0.299708 q^{84} +(8.59060 + 1.71266i) q^{85} +3.73639 q^{86} +1.89372i q^{87} +3.63010i q^{88} -16.4414 q^{89} +(6.39769 + 1.27547i) q^{90} -1.47380 q^{91} -8.00355i q^{92} -0.287336i q^{93} -2.35753 q^{94} +(-2.16868 + 10.8779i) q^{95} -0.287336 q^{96} -16.4141i q^{97} -5.91203i q^{98} +10.5906 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 2 q^{5} + 4 q^{6}+O(q^{10}) \) 8 * q - 8 * q^4 - 2 * q^5 + 4 * q^6	\( 8 q - 8 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{10} + 12 q^{11} - 12 q^{14} - 12 q^{15} + 8 q^{16} - 4 q^{19} + 2 q^{20} + 12 q^{21} - 4 q^{24} - 4 q^{25} + 8 q^{26} + 8 q^{29} + 4 q^{30} + 8 q^{31} - 8 q^{34} - 12 q^{35} + 8 q^{39} - 2 q^{40} - 8 q^{41} - 12 q^{44} - 18 q^{45} + 8 q^{50} - 12 q^{51} - 4 q^{54} - 16 q^{55} + 12 q^{56} + 12 q^{60} - 8 q^{64} + 12 q^{66} + 28 q^{69} + 20 q^{70} + 24 q^{71} - 36 q^{74} - 20 q^{75} + 4 q^{76} + 24 q^{79} - 2 q^{80} - 32 q^{81} - 12 q^{84} + 8 q^{85} + 8 q^{86} + 24 q^{89} + 6 q^{90} - 28 q^{91} - 20 q^{94} + 4 q^{96} + 24 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^10 + 12 * q^11 - 12 * q^14 - 12 * q^15 + 8 * q^16 - 4 * q^19 + 2 * q^20 + 12 * q^21 - 4 * q^24 - 4 * q^25 + 8 * q^26 + 8 * q^29 + 4 * q^30 + 8 * q^31 - 8 * q^34 - 12 * q^35 + 8 * q^39 - 2 * q^40 - 8 * q^41 - 12 * q^44 - 18 * q^45 + 8 * q^50 - 12 * q^51 - 4 * q^54 - 16 * q^55 + 12 * q^56 + 12 * q^60 - 8 * q^64 + 12 * q^66 + 28 * q^69 + 20 * q^70 + 24 * q^71 - 36 * q^74 - 20 * q^75 + 4 * q^76 + 24 * q^79 - 2 * q^80 - 32 * q^81 - 12 * q^84 + 8 * q^85 + 8 * q^86 + 24 * q^89 + 6 * q^90 - 28 * q^91 - 20 * q^94 + 4 * q^96 + 24 * q^99

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