LMFDB - Embedded newform 731.2.d.d.560.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(560,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, 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("731.560");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			560.16
Character	$\chi$	$=$	731.560
Dual form			731.2.d.d.560.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.811392 q^{2} +2.87350i q^{3} -1.34164 q^{4} +2.95301i q^{5} -2.33154i q^{6} -2.64644i q^{7} +2.71138 q^{8} -5.25702 q^{9} +O(q^{10})$	\(q-0.811392 q^{2} +2.87350i q^{3} -1.34164 q^{4} +2.95301i q^{5} -2.33154i q^{6} -2.64644i q^{7} +2.71138 q^{8} -5.25702 q^{9} -2.39605i q^{10} +2.82870i q^{11} -3.85522i q^{12} -5.05713 q^{13} +2.14730i q^{14} -8.48549 q^{15} +0.483291 q^{16} +(0.416167 - 4.10205i) q^{17} +4.26551 q^{18} -4.73475 q^{19} -3.96189i q^{20} +7.60455 q^{21} -2.29518i q^{22} +1.01378i q^{23} +7.79117i q^{24} -3.72028 q^{25} +4.10331 q^{26} -6.48557i q^{27} +3.55057i q^{28} +7.27843i q^{29} +6.88506 q^{30} -6.31936i q^{31} -5.81490 q^{32} -8.12827 q^{33} +(-0.337675 + 3.32837i) q^{34} +7.81496 q^{35} +7.05305 q^{36} +3.34516i q^{37} +3.84174 q^{38} -14.5317i q^{39} +8.00675i q^{40} -8.08543i q^{41} -6.17027 q^{42} -1.00000 q^{43} -3.79510i q^{44} -15.5241i q^{45} -0.822572i q^{46} +10.9844 q^{47} +1.38874i q^{48} -0.00363116 q^{49} +3.01861 q^{50} +(11.7873 + 1.19586i) q^{51} +6.78486 q^{52} -2.52079 q^{53} +5.26234i q^{54} -8.35318 q^{55} -7.17550i q^{56} -13.6053i q^{57} -5.90566i q^{58} +5.42885 q^{59} +11.3845 q^{60} -9.03995i q^{61} +5.12748i q^{62} +13.9124i q^{63} +3.75159 q^{64} -14.9338i q^{65} +6.59521 q^{66} -10.3408 q^{67} +(-0.558348 + 5.50348i) q^{68} -2.91310 q^{69} -6.34100 q^{70} +15.0728i q^{71} -14.2538 q^{72} +8.01572i q^{73} -2.71424i q^{74} -10.6902i q^{75} +6.35235 q^{76} +7.48597 q^{77} +11.7909i q^{78} -7.91462i q^{79} +1.42716i q^{80} +2.86522 q^{81} +6.56046i q^{82} -13.6331 q^{83} -10.2026 q^{84} +(12.1134 + 1.22895i) q^{85} +0.811392 q^{86} -20.9146 q^{87} +7.66968i q^{88} -3.25108 q^{89} +12.5961i q^{90} +13.3834i q^{91} -1.36013i q^{92} +18.1587 q^{93} -8.91263 q^{94} -13.9818i q^{95} -16.7091i q^{96} +6.36302i q^{97} +0.00294629 q^{98} -14.8705i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9}+O(q^{10}) $ 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9	$ 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9} + 16 q^{13} - 8 q^{15} + 26 q^{16} + 14 q^{18} + 16 q^{19} + 20 q^{21} - 44 q^{25} - 26 q^{26} + 88 q^{30} - 42 q^{32} + 12 q^{33} - 42 q^{34} + 22 q^{35} + 34 q^{38} - 14 q^{42} - 34 q^{43} + 30 q^{47} - 62 q^{49} - 46 q^{50} - 10 q^{51} + 26 q^{52} - 46 q^{53} + 16 q^{55} - 20 q^{59} - 42 q^{60} + 102 q^{64} - 70 q^{66} - 32 q^{67} - 10 q^{68} + 74 q^{69} + 130 q^{70} + 22 q^{72} + 38 q^{76} - 78 q^{77} + 46 q^{81} - 60 q^{83} - 98 q^{84} - 38 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{89} + 14 q^{93} - 78 q^{94} + 78 q^{98}+O(q^{100}) $ 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9 + 16 * q^13 - 8 * q^15 + 26 * q^16 + 14 * q^18 + 16 * q^19 + 20 * q^21 - 44 * q^25 - 26 * q^26 + 88 * q^30 - 42 * q^32 + 12 * q^33 - 42 * q^34 + 22 * q^35 + 34 * q^38 - 14 * q^42 - 34 * q^43 + 30 * q^47 - 62 * q^49 - 46 * q^50 - 10 * q^51 + 26 * q^52 - 46 * q^53 + 16 * q^55 - 20 * q^59 - 42 * q^60 + 102 * q^64 - 70 * q^66 - 32 * q^67 - 10 * q^68 + 74 * q^69 + 130 * q^70 + 22 * q^72 + 38 * q^76 - 78 * q^77 + 46 * q^81 - 60 * q^83 - 98 * q^84 - 38 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^89 + 14 * q^93 - 78 * q^94 + 78 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$-1$	$1$

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 $

$2$	−0.811392			−0.573741			−0.286870	−	0.957969i	$-0.592615\pi$
$2$	−0.811392			−0.573741			−0.286870	+	0.957969i	$0.592615\pi$
$3$			2.87350i			1.65902i	0.558493	+	0.829509i	$0.311380\pi$
$3$			2.87350i			1.65902i	−0.558493	+	0.829509i	$0.688620\pi$
$4$	−1.34164			−0.670821
$5$			2.95301i			1.32063i	0.750990	+	0.660314i	$0.229577\pi$
$5$			2.95301i			1.32063i	−0.750990	+	0.660314i	$0.770423\pi$
$6$		−	2.33154i		−	0.951847i
$7$		−	2.64644i		−	1.00026i	−0.865951	−	0.500130i	$-0.833286\pi$
$7$		−	2.64644i		−	1.00026i	0.865951	−	0.500130i	$-0.166714\pi$
$8$	2.71138			0.958619
$9$	−5.25702			−1.75234
$10$		−	2.39605i		−	0.757698i
$11$			2.82870i			0.852884i	0.904515	+	0.426442i	$0.140233\pi$
$11$			2.82870i			0.852884i	−0.904515	+	0.426442i	$0.859767\pi$
$12$		−	3.85522i		−	1.11290i
$13$	−5.05713			−1.40259			−0.701297	−	0.712869i	$-0.747395\pi$
$13$	−5.05713			−1.40259			−0.701297	+	0.712869i	$0.747395\pi$
$14$			2.14730i			0.573890i
$15$	−8.48549			−2.19094
$16$	0.483291			0.120823
$17$	0.416167	−	4.10205i	0.100935	−	0.994893i
$17$	0.416167	−	4.10205i	0.100935	−	0.994893i
$18$	4.26551			1.00539
$19$	−4.73475			−1.08623			−0.543113	−	0.839659i	$-0.682755\pi$
$19$	−4.73475			−1.08623			−0.543113	+	0.839659i	$0.682755\pi$
$20$		−	3.96189i		−	0.885905i
$21$	7.60455			1.65945
$22$		−	2.29518i		−	0.489335i
$23$			1.01378i			0.211388i	0.994399	+	0.105694i	$0.0337063\pi$
$23$			1.01378i			0.211388i	−0.994399	+	0.105694i	$0.966294\pi$
$24$			7.79117i			1.59037i
$25$	−3.72028			−0.744056
$26$	4.10331			0.804726
$27$		−	6.48557i		−	1.24815i
$28$			3.55057i			0.670995i
$29$			7.27843i			1.35157i	0.737099	+	0.675785i	$0.236195\pi$
$29$			7.27843i			1.35157i	−0.737099	+	0.675785i	$0.763805\pi$
$30$	6.88506			1.25703
$31$		−	6.31936i		−	1.13499i	−0.823377	−	0.567495i	$-0.807912\pi$
$31$		−	6.31936i		−	1.13499i	0.823377	−	0.567495i	$-0.192088\pi$
$32$	−5.81490			−1.02794
$33$	−8.12827			−1.41495
$34$	−0.337675	+	3.32837i	−0.0579108	+	0.570811i
$35$	7.81496			1.32097
$36$	7.05305			1.17551
$37$			3.34516i			0.549941i	0.961453	+	0.274970i	$0.0886681\pi$
$37$			3.34516i			0.549941i	−0.961453	+	0.274970i	$0.911332\pi$
$38$	3.84174			0.623213
$39$		−	14.5317i		−	2.32693i
$40$			8.00675i			1.26598i
$41$		−	8.08543i		−	1.26273i	−0.775485	−	0.631366i	$-0.782495\pi$
$41$		−	8.08543i		−	1.26273i	0.775485	−	0.631366i	$-0.217505\pi$
$42$	−6.17027			−0.952093
$43$	−1.00000			−0.152499
$43$	−1.00000			−0.152499
$44$		−	3.79510i		−	0.572133i
$45$		−	15.5241i		−	2.31419i
$46$		−	0.822572i		−	0.121282i
$47$	10.9844			1.60224			0.801118	−	0.598507i	$-0.204239\pi$
$47$	10.9844			1.60224			0.801118	+	0.598507i	$0.204239\pi$
$48$			1.38874i			0.200447i
$49$	−0.00363116			−0.000518737
$50$	3.01861			0.426895
$51$	11.7873	+	1.19586i	1.65055	+	0.167454i
$52$	6.78486			0.940890
$53$	−2.52079			−0.346257			−0.173129	−	0.984899i	$-0.555388\pi$
$53$	−2.52079			−0.346257			−0.173129	+	0.984899i	$0.555388\pi$
$54$			5.26234i			0.716113i
$55$	−8.35318			−1.12634
$56$		−	7.17550i		−	0.958867i
$57$		−	13.6053i		−	1.80207i
$58$		−	5.90566i		−	0.775451i
$59$	5.42885			0.706776			0.353388	−	0.935477i	$-0.385030\pi$
$59$	5.42885			0.706776			0.353388	+	0.935477i	$0.385030\pi$
$60$	11.3845			1.46973
$61$		−	9.03995i		−	1.15745i	−0.815524	−	0.578723i	$-0.803551\pi$
$61$		−	9.03995i		−	1.15745i	0.815524	−	0.578723i	$-0.196449\pi$
$62$			5.12748i			0.651191i
$63$			13.9124i			1.75280i
$64$	3.75159			0.468948
$65$		−	14.9338i		−	1.85230i
$66$	6.59521			0.811815
$67$	−10.3408			−1.26333			−0.631667	−	0.775240i	$-0.717629\pi$
$67$	−10.3408			−1.26333			−0.631667	+	0.775240i	$0.717629\pi$
$68$	−0.558348	+	5.50348i	−0.0677096	+	0.667395i
$69$	−2.91310			−0.350696
$70$	−6.34100			−0.757894
$71$			15.0728i			1.78881i	0.447258	+	0.894405i	$0.352400\pi$
$71$			15.0728i			1.78881i	−0.447258	+	0.894405i	$0.647600\pi$
$72$	−14.2538			−1.67983
$73$			8.01572i			0.938169i	0.883153	+	0.469084i	$0.155416\pi$
$73$			8.01572i			0.938169i	−0.883153	+	0.469084i	$0.844584\pi$
$74$		−	2.71424i		−	0.315524i
$75$		−	10.6902i		−	1.23440i
$76$	6.35235			0.728664
$77$	7.48597			0.853105
$78$			11.7909i			1.33505i
$79$		−	7.91462i		−	0.890464i	−0.895415	−	0.445232i	$-0.853121\pi$
$79$		−	7.91462i		−	0.890464i	0.895415	−	0.445232i	$-0.146879\pi$
$80$			1.42716i			0.159562i
$81$	2.86522			0.318358
$82$			6.56046i			0.724481i
$83$	−13.6331			−1.49643			−0.748213	−	0.663459i	$-0.769088\pi$
$83$	−13.6331			−1.49643			−0.748213	+	0.663459i	$0.769088\pi$
$84$	−10.2026			−1.11319
$85$	12.1134	+	1.22895i	1.31388	+	0.133298i
$86$	0.811392			0.0874947
$87$	−20.9146			−2.24228
$88$			7.66968i			0.817591i
$89$	−3.25108			−0.344613			−0.172307	−	0.985043i	$-0.555122\pi$
$89$	−3.25108			−0.344613			−0.172307	+	0.985043i	$0.555122\pi$
$90$			12.5961i			1.32775i
$91$			13.3834i			1.40296i
$92$		−	1.36013i		−	0.141803i
$93$	18.1587			1.88297
$94$	−8.91263			−0.919268
$95$		−	13.9818i		−	1.43450i
$96$		−	16.7091i		−	1.70537i
$97$			6.36302i			0.646067i	0.946388	+	0.323033i	$0.104703\pi$
$97$			6.36302i			0.646067i	−0.946388	+	0.323033i	$0.895297\pi$
$98$	0.00294629			0.000297621
$99$		−	14.8705i		−	1.49454i
$100$	4.99129			0.499129
$101$	−15.5227			−1.54457			−0.772284	−	0.635277i	$-0.780886\pi$
$101$	−15.5227			−1.54457			−0.772284	+	0.635277i	$0.780886\pi$
$102$	−9.56408	−	0.970310i	−0.946985	−	0.0960750i
$103$	0.748866			0.0737879			0.0368940	−	0.999319i	$-0.488254\pi$
$103$	0.748866			0.0737879			0.0368940	+	0.999319i	$0.488254\pi$
$104$	−13.7118			−1.34455
$105$			22.4563i			2.19151i
$106$	2.04535			0.198662
$107$		−	4.59662i		−	0.444372i	−0.975004	−	0.222186i	$-0.928681\pi$
$107$		−	4.59662i		−	0.444372i	0.975004	−	0.222186i	$-0.0713193\pi$
$108$			8.70131i			0.837284i
$109$			4.14221i			0.396752i	0.980126	+	0.198376i	$0.0635667\pi$
$109$			4.14221i			0.396752i	−0.980126	+	0.198376i	$0.936433\pi$
$110$	6.77770			0.646228
$111$	−9.61233			−0.912362
$112$		−	1.27900i		−	0.120854i
$113$		−	10.6611i		−	1.00291i	−0.865184	−	0.501455i	$-0.832798\pi$
$113$		−	10.6611i		−	1.00291i	0.865184	−	0.501455i	$-0.167202\pi$
$114$			11.0393i			1.03392i
$115$	−2.99370			−0.279164
$116$		−	9.76505i		−	0.906662i
$117$	26.5854			2.45782
$118$	−4.40492			−0.405506
$119$	−10.8558	−	1.10136i	−0.995151	−	0.100962i
$120$	−23.0074			−2.10028
$121$	2.99848			0.272589
$122$			7.33494i			0.664075i
$123$	23.2335			2.09490
$124$			8.47833i			0.761376i
$125$			3.77903i			0.338007i
$126$		−	11.2884i		−	1.00565i
$127$	−13.7566			−1.22070			−0.610349	−	0.792133i	$-0.708971\pi$
$127$	−13.7566			−1.22070			−0.610349	+	0.792133i	$0.708971\pi$
$128$	8.58580			0.758885
$129$		−	2.87350i		−	0.252998i
$130$			12.1171i			1.06274i
$131$			11.6344i			1.01650i	0.861209	+	0.508251i	$0.169708\pi$
$131$			11.6344i			1.01650i	−0.861209	+	0.508251i	$0.830292\pi$
$132$	10.9052			0.949179
$133$			12.5302i			1.08651i
$134$	8.39047			0.724826
$135$	19.1520			1.64834
$136$	1.12839	−	11.1222i	0.0967586	−	0.953723i
$137$	−7.20010			−0.615146			−0.307573	−	0.951524i	$-0.599517\pi$
$137$	−7.20010			−0.615146			−0.307573	+	0.951524i	$0.599517\pi$
$138$	2.36366			0.201208
$139$			5.99331i			0.508346i	0.967159	+	0.254173i	$0.0818033\pi$
$139$			5.99331i			0.508346i	−0.967159	+	0.254173i	$0.918197\pi$
$140$	−10.4849			−0.886135
$141$			31.5636i			2.65814i
$142$		−	12.2299i		−	1.02631i
$143$		−	14.3051i		−	1.19625i
$144$	−2.54067			−0.211723
$145$	−21.4933			−1.78492
$146$		−	6.50389i		−	0.538266i
$147$		−	0.0104342i		−	0.000860594i
$148$		−	4.48801i		−	0.368912i
$149$	−11.7203			−0.960165			−0.480082	−	0.877223i	$-0.659393\pi$
$149$	−11.7203			−0.960165			−0.480082	+	0.877223i	$0.659393\pi$
$150$			8.67398i			0.708227i
$151$	−12.8536			−1.04601			−0.523004	−	0.852330i	$-0.675189\pi$
$151$	−12.8536			−1.04601			−0.523004	+	0.852330i	$0.675189\pi$
$152$	−12.8377			−1.04128
$153$	−2.18780	+	21.5646i	−0.176873	+	1.74339i
$154$	−6.07406			−0.489461
$155$	18.6612			1.49890
$156$			19.4963i			1.56095i
$157$	6.38929			0.509921			0.254961	−	0.966951i	$-0.417937\pi$
$157$	6.38929			0.509921			0.254961	+	0.966951i	$0.417937\pi$
$158$			6.42186i			0.510896i
$159$		−	7.24351i		−	0.574447i
$160$		−	17.1715i		−	1.35752i
$161$	2.68290			0.211442
$162$	−2.32482			−0.182655
$163$			7.10377i			0.556410i	0.960522	+	0.278205i	$0.0897395\pi$
$163$			7.10377i			0.556410i	−0.960522	+	0.278205i	$0.910260\pi$
$164$			10.8478i			0.847068i
$165$		−	24.0029i		−	1.86862i
$166$	11.0618			0.858560
$167$		−	8.13690i		−	0.629652i	−0.949149	−	0.314826i	$-0.898054\pi$
$167$		−	8.13690i		−	0.629652i	0.949149	−	0.314826i	$-0.101946\pi$
$168$	20.6188			1.59078
$169$	12.5745			0.967271
$170$	−9.82872	−	0.997158i	−0.753828	−	0.0764785i
$171$	24.8907			1.90344
$172$	1.34164			0.102299
$173$		−	20.7473i		−	1.57739i	−0.614786	−	0.788694i	$-0.710758\pi$
$173$		−	20.7473i		−	1.57739i	0.614786	−	0.788694i	$-0.289242\pi$
$174$	16.9699			1.28649
$175$			9.84549i			0.744249i
$176$			1.36708i			0.103048i
$177$			15.5998i			1.17255i
$178$	2.63790			0.197719
$179$	−9.17997			−0.686143			−0.343072	−	0.939309i	$-0.611467\pi$
$179$	−9.17997			−0.686143			−0.343072	+	0.939309i	$0.611467\pi$
$180$			20.8277i			1.55241i
$181$			9.39803i			0.698550i	0.937020	+	0.349275i	$0.113572\pi$
$181$			9.39803i			0.698550i	−0.937020	+	0.349275i	$0.886428\pi$
$182$		−	10.8592i		−	0.804935i
$183$	25.9763			1.92023
$184$			2.74874i			0.202640i
$185$	−9.87830			−0.726267
$186$	−14.7338			−1.08034
$187$	11.6035	+	1.17721i	0.848528	+	0.0860862i
$188$	−14.7371			−1.07481
$189$	−17.1636			−1.24847
$190$			11.3447i			0.823032i
$191$	−21.4785			−1.55413			−0.777065	−	0.629420i	$-0.783292\pi$
$191$	−21.4785			−1.55413			−0.777065	+	0.629420i	$0.783292\pi$
$192$			10.7802i			0.777994i
$193$		−	23.5642i		−	1.69619i	−0.529848	−	0.848093i	$-0.677751\pi$
$193$		−	23.5642i		−	1.69619i	0.529848	−	0.848093i	$-0.322249\pi$
$194$		−	5.16290i		−	0.370675i
$195$	42.9122			3.07301
$196$	0.00487172			0.000347980
$197$		−	4.23569i		−	0.301781i	−0.988551	−	0.150890i	$-0.951786\pi$
$197$		−	4.23569i		−	0.301781i	0.988551	−	0.150890i	$-0.0482140\pi$
$198$			12.0658i			0.857481i
$199$			19.0140i			1.34786i	0.738794	+	0.673932i	$0.235396\pi$
$199$			19.0140i			1.34786i	−0.738794	+	0.673932i	$0.764604\pi$
$200$	−10.0871			−0.713266
$201$		−	29.7144i		−	2.09589i
$202$	12.5950			0.886182
$203$	19.2619			1.35192
$204$	−15.8143	−	1.60441i	−1.10722	−	0.112331i
$205$	23.8764			1.66760
$206$	−0.607624			−0.0423352
$207$		−	5.32946i		−	0.370423i
$208$	−2.44406			−0.169465
$209$		−	13.3932i		−	0.926425i
$210$		−	18.2209i		−	1.25736i
$211$		−	7.20238i		−	0.495832i	−0.968782	−	0.247916i	$-0.920254\pi$
$211$		−	7.20238i		−	0.495832i	0.968782	−	0.247916i	$-0.0797457\pi$
$212$	3.38200			0.232277
$213$	−43.3117			−2.96767
$214$			3.72966i			0.254955i
$215$		−	2.95301i		−	0.201394i
$216$		−	17.5848i		−	1.19650i
$217$	−16.7238			−1.13529
$218$		−	3.36096i		−	0.227633i
$219$	−23.0332			−1.55644
$220$	11.2070			0.755574
$221$	−2.10461	+	20.7446i	−0.141571	+	1.39543i
$222$	7.79937			0.523459
$223$	3.75247			0.251284			0.125642	−	0.992076i	$-0.459901\pi$
$223$	3.75247			0.251284			0.125642	+	0.992076i	$0.459901\pi$
$224$			15.3888i			1.02821i
$225$	19.5576			1.30384
$226$			8.65032i			0.575410i
$227$			19.4473i			1.29076i	0.763860	+	0.645382i	$0.223302\pi$
$227$			19.4473i			1.29076i	−0.763860	+	0.645382i	$0.776698\pi$
$228$			18.2535i			1.20887i
$229$	18.6195			1.23041			0.615205	−	0.788367i	$-0.289073\pi$
$229$	18.6195			1.23041			0.615205	+	0.788367i	$0.289073\pi$
$230$	2.42907			0.160168
$231$			21.5110i			1.41532i
$232$			19.7346i			1.29564i
$233$			24.5243i			1.60664i	0.595549	+	0.803319i	$0.296934\pi$
$233$			24.5243i			1.60664i	−0.595549	+	0.803319i	$0.703066\pi$
$234$	−21.5712			−1.41015
$235$			32.4370i			2.11596i
$236$	−7.28357			−0.474120
$237$	22.7427			1.47730
$238$	8.80832	+	0.893636i	0.570959	+	0.0579258i
$239$	−14.8293			−0.959228			−0.479614	−	0.877480i	$-0.659223\pi$
$239$	−14.8293			−0.959228			−0.479614	+	0.877480i	$0.659223\pi$
$240$	−4.10096			−0.264716
$241$			12.9752i			0.835809i	0.908491	+	0.417904i	$0.137235\pi$
$241$			12.9752i			0.835809i	−0.908491	+	0.417904i	$0.862765\pi$
$242$	−2.43294			−0.156395
$243$		−	11.2235i		−	0.719985i
$244$			12.1284i			0.776440i
$245$		−	0.0107229i		−	0.000685058i
$246$	−18.8515			−1.20193
$247$	23.9442			1.52354
$248$		−	17.1342i		−	1.08802i
$249$		−	39.1747i		−	2.48260i
$250$		−	3.06627i		−	0.193928i
$251$	−15.6528			−0.987995			−0.493997	−	0.869463i	$-0.664465\pi$
$251$	−15.6528			−0.987995			−0.493997	+	0.869463i	$0.664465\pi$
$252$		−	18.6654i		−	1.17581i
$253$	−2.86767			−0.180289
$254$	11.1620			0.700364
$255$	−3.53138	+	34.8079i	−0.221144	+	2.17976i
$256$	−14.4696			−0.904351
$257$	16.8497			1.05106			0.525528	−	0.850776i	$-0.323868\pi$
$257$	16.8497			1.05106			0.525528	+	0.850776i	$0.323868\pi$
$258$			2.33154i			0.145155i
$259$	8.85276			0.550084
$260$			20.0358i			1.24257i
$261$		−	38.2629i		−	2.36841i
$262$		−	9.44007i		−	0.583209i
$263$	6.88999			0.424855			0.212427	−	0.977177i	$-0.431863\pi$
$263$	6.88999			0.424855			0.212427	+	0.977177i	$0.431863\pi$
$264$	−22.0389			−1.35640
$265$		−	7.44393i		−	0.457277i
$266$		−	10.1669i		−	0.623374i
$267$		−	9.34198i		−	0.571720i
$268$	13.8737			0.847471
$269$		−	9.16692i		−	0.558917i	−0.960158	−	0.279459i	$-0.909845\pi$
$269$		−	9.16692i		−	0.558917i	0.960158	−	0.279459i	$-0.0901549\pi$
$270$	−15.5397			−0.945719
$271$	−15.6587			−0.951196			−0.475598	−	0.879663i	$-0.657768\pi$
$271$	−15.6587			−0.951196			−0.475598	+	0.879663i	$0.657768\pi$
$272$	0.201130	−	1.98248i	0.0121953	−	0.120206i
$273$	−38.4572			−2.32753
$274$	5.84211			0.352935
$275$		−	10.5235i		−	0.634594i
$276$	3.90834			0.235254
$277$		−	13.3038i		−	0.799350i	−0.916657	−	0.399675i	$-0.869123\pi$
$277$		−	13.3038i		−	0.799350i	0.916657	−	0.399675i	$-0.130877\pi$
$278$		−	4.86293i		−	0.291659i
$279$			33.2210i			1.98889i
$280$	21.1894			1.26631
$281$	26.2005			1.56299			0.781495	−	0.623912i	$-0.214457\pi$
$281$	26.2005			1.56299			0.781495	+	0.623912i	$0.214457\pi$
$282$		−	25.6105i		−	1.52508i
$283$			16.6179i			0.987830i	0.869510	+	0.493915i	$0.164435\pi$
$283$			16.6179i			0.987830i	−0.869510	+	0.493915i	$0.835565\pi$
$284$		−	20.2223i		−	1.19997i
$285$	40.1767			2.37986
$286$			11.6070i			0.686338i
$287$	−21.3976			−1.26306
$288$	30.5691			1.80130
$289$	−16.6536	−	3.41428i	−0.979624	−	0.200840i
$290$	17.4395			1.02408
$291$	−18.2842			−1.07184
$292$		−	10.7542i		−	0.629344i
$293$	4.02429			0.235101			0.117551	−	0.993067i	$-0.462496\pi$
$293$	4.02429			0.235101			0.117551	+	0.993067i	$0.462496\pi$
$294$			0.00846619i			0.000493758i
$295$			16.0314i			0.933387i
$296$			9.07001i			0.527184i
$297$	18.3457			1.06453
$298$	9.50977			0.550886
$299$		−	5.12681i		−	0.296491i
$300$			14.3425i			0.828063i
$301$			2.64644i			0.152538i
$302$	10.4293			0.600138
$303$		−	44.6046i		−	2.56247i
$304$	−2.28826			−0.131241
$305$	26.6951			1.52856
$306$	1.77517	−	17.4973i	0.101479	−	1.00026i
$307$	−14.3692			−0.820093			−0.410047	−	0.912065i	$-0.634488\pi$
$307$	−14.3692			−0.820093			−0.410047	+	0.912065i	$0.634488\pi$
$308$	−10.0435			−0.572281
$309$			2.15187i			0.122416i
$310$	−15.1415			−0.859980
$311$			20.1861i			1.14465i	0.820028	+	0.572324i	$0.193958\pi$
$311$			20.1861i			1.14465i	−0.820028	+	0.572324i	$0.806042\pi$
$312$		−	39.4009i		−	2.23064i
$313$			0.844513i			0.0477347i	0.999715	+	0.0238673i	$0.00759793\pi$
$313$			0.844513i			0.0477347i	−0.999715	+	0.0238673i	$0.992402\pi$
$314$	−5.18422			−0.292563
$315$	−41.0834			−2.31479
$316$			10.6186i			0.597342i
$317$		−	28.8393i		−	1.61977i	−0.586586	−	0.809887i	$-0.699528\pi$
$317$		−	28.8393i		−	1.61977i	0.586586	−	0.809887i	$-0.300472\pi$
$318$			5.87732i			0.329584i
$319$	−20.5885			−1.15273
$320$			11.0785i			0.619306i
$321$	13.2084			0.737222
$322$	−2.17689			−0.121313
$323$	−1.97045	+	19.4222i	−0.109639	+	1.08068i
$324$	−3.84411			−0.213562
$325$	18.8139			1.04361
$326$		−	5.76394i		−	0.319235i
$327$	−11.9027			−0.658219
$328$		−	21.9227i		−	1.21048i
$329$		−	29.0695i		−	1.60265i
$330$			19.4757i			1.07210i
$331$	3.89379			0.214022			0.107011	−	0.994258i	$-0.465872\pi$
$331$	3.89379			0.214022			0.107011	+	0.994258i	$0.465872\pi$
$332$	18.2907			1.00383
$333$		−	17.5856i		−	0.963684i
$334$			6.60221i			0.361257i
$335$		−	30.5366i		−	1.66839i
$336$	3.67521			0.200499
$337$		−	5.82629i		−	0.317378i	−0.987329	−	0.158689i	$-0.949273\pi$
$337$		−	5.82629i		−	0.317378i	0.987329	−	0.158689i	$-0.0507268\pi$
$338$	−10.2029			−0.554963
$339$	30.6346			1.66385
$340$	−16.2519	−	1.64881i	−0.881381	−	0.0894192i
$341$	17.8756			0.968016
$342$	−20.1961			−1.09208
$343$		−	18.5155i		−	0.999740i
$344$	−2.71138			−0.146188
$345$		−	8.60241i		−	0.463138i
$346$			16.8342i			0.905012i
$347$		−	6.63415i		−	0.356140i	−0.984018	−	0.178070i	$-0.943015\pi$
$347$		−	6.63415i		−	0.356140i	0.984018	−	0.178070i	$-0.0569853\pi$
$348$	28.0599			1.50417
$349$	−11.1677			−0.597794			−0.298897	−	0.954285i	$-0.596619\pi$
$349$	−11.1677			−0.597794			−0.298897	+	0.954285i	$0.596619\pi$
$350$		−	7.98855i		−	0.427006i
$351$			32.7983i			1.75065i
$352$		−	16.4486i		−	0.876713i
$353$	14.9471			0.795555			0.397778	−	0.917482i	$-0.369782\pi$
$353$	14.9471			0.795555			0.397778	+	0.917482i	$0.369782\pi$
$354$		−	12.6576i		−	0.672742i
$355$	−44.5101			−2.36235
$356$	4.36178			0.231174
$357$	3.16476	−	31.1942i	0.167497	−	1.65097i
$358$	7.44855			0.393668
$359$	−6.25411			−0.330079			−0.165040	−	0.986287i	$-0.552775\pi$
$359$	−6.25411			−0.330079			−0.165040	+	0.986287i	$0.552775\pi$
$360$		−	42.0917i		−	2.21842i
$361$	3.41788			0.179888
$362$		−	7.62549i		−	0.400787i
$363$			8.61613i			0.452230i
$364$		−	17.9557i		−	0.941134i
$365$	−23.6705			−1.23897
$366$	−21.0770			−1.10171
$367$			31.5056i			1.64458i	0.569071	+	0.822288i	$0.307303\pi$
$367$			31.5056i			1.64458i	−0.569071	+	0.822288i	$0.692697\pi$
$368$			0.489950i			0.0255404i
$369$			42.5053i			2.21274i
$370$	8.01517			0.416689
$371$			6.67112i			0.346347i
$372$	−24.3625			−1.26314
$373$	−16.4886			−0.853745			−0.426873	−	0.904312i	$-0.640385\pi$
$373$	−16.4886			−0.853745			−0.426873	+	0.904312i	$0.640385\pi$
$374$	−9.41495	−	0.955180i	−0.486835	−	0.0493912i
$375$	−10.8591			−0.560759
$376$	29.7828			1.53593
$377$		−	36.8079i		−	1.89570i
$378$	13.9264			0.716299
$379$			23.8252i			1.22382i	0.790929	+	0.611908i	$0.209598\pi$
$379$			23.8252i			1.22382i	−0.790929	+	0.611908i	$0.790402\pi$
$380$			18.7586i			0.962293i
$381$		−	39.5295i		−	2.02516i
$382$	17.4275			0.891668
$383$	16.4664			0.841395			0.420697	−	0.907201i	$-0.361785\pi$
$383$	16.4664			0.841395			0.420697	+	0.907201i	$0.361785\pi$
$384$			24.6713i			1.25900i
$385$			22.1062i			1.12663i
$386$			19.1198i			0.973171i
$387$	5.25702			0.267230
$388$		−	8.53690i		−	0.433395i
$389$	−32.0334			−1.62416			−0.812080	−	0.583547i	$-0.801665\pi$
$389$	−32.0334			−1.62416			−0.812080	+	0.583547i	$0.801665\pi$
$390$	−34.8186			−1.76311
$391$	4.15857	+	0.421902i	0.210308	+	0.0213365i
$392$	−0.00984546			−0.000497271
$393$	−33.4315			−1.68640
$394$			3.43681i			0.173144i
$395$	23.3720			1.17597
$396$			19.9509i			1.00257i
$397$		−	12.5648i		−	0.630607i	−0.948991	−	0.315304i	$-0.897894\pi$
$397$		−	12.5648i		−	0.630607i	0.948991	−	0.315304i	$-0.102106\pi$
$398$		−	15.4278i		−	0.773324i
$399$	−36.0056			−1.80254
$400$	−1.79798			−0.0898988
$401$			2.15455i			0.107593i	0.998552	+	0.0537966i	$0.0171323\pi$
$401$			2.15455i			0.107593i	−0.998552	+	0.0537966i	$0.982868\pi$
$402$			24.1100i			1.20250i
$403$			31.9578i			1.59193i
$404$	20.8259			1.03613
$405$			8.46104i			0.420433i
$406$	−15.6290			−0.775652
$407$	−9.46244			−0.469036
$408$	31.9598	+	3.24243i	1.58224	+	0.160524i
$409$	−4.28867			−0.212061			−0.106031	−	0.994363i	$-0.533814\pi$
$409$	−4.28867			−0.212061			−0.106031	+	0.994363i	$0.533814\pi$
$410$	−19.3731			−0.956769
$411$		−	20.6895i		−	1.02054i
$412$	−1.00471			−0.0494985
$413$		−	14.3671i		−	0.706959i
$414$			4.32428i			0.212527i
$415$		−	40.2587i		−	1.97622i
$416$	29.4067			1.44178
$417$	−17.2218			−0.843355
$418$			10.8671i			0.531528i
$419$		−	0.480550i		−	0.0234764i	−0.999931	−	0.0117382i	$-0.996264\pi$
$419$		−	0.480550i		−	0.0234764i	0.999931	−	0.0117382i	$-0.00373647\pi$
$420$		−	30.1284i		−	1.47011i
$421$	−12.2963			−0.599287			−0.299644	−	0.954051i	$-0.596868\pi$
$421$	−12.2963			−0.599287			−0.299644	+	0.954051i	$0.596868\pi$
$422$			5.84395i			0.284479i
$423$	−57.7451			−2.80766
$424$	−6.83483			−0.331929
$425$	−1.54826	+	15.2608i	−0.0751016	+	0.740256i
$426$	35.1428			1.70267
$427$	−23.9237			−1.15775
$428$			6.16703i			0.298094i
$429$	41.1057			1.98460
$430$			2.39605i			0.115548i
$431$			41.3320i			1.99089i	0.0953148	+	0.995447i	$0.469614\pi$
$431$			41.3320i			1.99089i	−0.0953148	+	0.995447i	$0.530386\pi$
$432$		−	3.13441i		−	0.150805i
$433$	−21.2170			−1.01962			−0.509812	−	0.860286i	$-0.670285\pi$
$433$	−21.2170			−1.01962			−0.509812	+	0.860286i	$0.670285\pi$
$434$	13.5696			0.651360
$435$		−	61.7610i		−	2.96121i
$436$		−	5.55737i		−	0.266150i
$437$		−	4.79999i		−	0.229615i
$438$	18.6890			0.892993
$439$			27.0749i			1.29221i	0.763247	+	0.646106i	$0.223604\pi$
$439$			27.0749i			1.29221i	−0.763247	+	0.646106i	$0.776396\pi$
$440$	−22.6487			−1.07973
$441$	0.0190891			0.000909004
$442$	1.70766	−	16.8320i	0.0812253	−	0.800616i
$443$	5.12831			0.243653			0.121827	−	0.992551i	$-0.461125\pi$
$443$	5.12831			0.243653			0.121827	+	0.992551i	$0.461125\pi$
$444$	12.8963			0.612032
$445$		−	9.60047i		−	0.455106i
$446$	−3.04473			−0.144172
$447$		−	33.6783i		−	1.59293i
$448$		−	9.92834i		−	0.469070i
$449$		−	9.09341i		−	0.429144i	−0.976708	−	0.214572i	$-0.931164\pi$
$449$		−	9.09341i		−	0.429144i	0.976708	−	0.214572i	$-0.0688357\pi$
$450$	−15.8689			−0.748066
$451$	22.8712			1.07696
$452$			14.3034i			0.672773i
$453$		−	36.9348i		−	1.73535i
$454$		−	15.7794i		−	0.740564i
$455$	−39.5213			−1.85278
$456$		−	36.8892i		−	1.72750i
$457$	34.1337			1.59671			0.798353	−	0.602190i	$-0.205705\pi$
$457$	34.1337			1.59671			0.798353	+	0.602190i	$0.205705\pi$
$458$	−15.1077			−0.705937
$459$	−26.6041	−	2.69908i	−1.24177	−	0.125982i
$460$	4.01648			0.187269
$461$	−24.4220			−1.13745			−0.568723	−	0.822529i	$-0.692562\pi$
$461$	−24.4220			−1.13745			−0.568723	+	0.822529i	$0.692562\pi$
$462$		−	17.4538i		−	0.812025i
$463$	−42.5389			−1.97695			−0.988475	−	0.151386i	$-0.951626\pi$
$463$	−42.5389			−1.97695			−0.988475	+	0.151386i	$0.951626\pi$
$464$			3.51760i			0.163300i
$465$			53.6229i			2.48670i
$466$		−	19.8988i		−	0.921794i
$467$	22.8276			1.05634			0.528168	−	0.849140i	$-0.322879\pi$
$467$	22.8276			1.05634			0.528168	+	0.849140i	$0.322879\pi$
$468$	−35.6682			−1.64876
$469$			27.3664i			1.26366i
$470$		−	26.3191i		−	1.21401i
$471$			18.3597i			0.845969i
$472$	14.7197			0.677528
$473$		−	2.82870i		−	0.130064i
$474$	−18.4532			−0.847585
$475$	17.6146			0.808213
$476$	14.5646	+	1.47763i	0.667569	+	0.0677272i
$477$	13.2519			0.606761
$478$	12.0324			0.550348
$479$		−	32.5511i		−	1.48730i	−0.668571	−	0.743649i	$-0.733094\pi$
$479$		−	32.5511i		−	1.48730i	0.668571	−	0.743649i	$-0.266906\pi$
$480$	49.3423			2.25216
$481$		−	16.9169i		−	0.771344i
$482$		−	10.5280i		−	0.479538i
$483$			7.70933i			0.350787i
$484$	−4.02288			−0.182858
$485$	−18.7901			−0.853213
$486$			9.10663i			0.413085i
$487$			29.7807i			1.34949i	0.738049	+	0.674747i	$0.235747\pi$
$487$			29.7807i			1.34949i	−0.738049	+	0.674747i	$0.764253\pi$
$488$		−	24.5108i		−	1.10955i
$489$	−20.4127			−0.923095
$490$			0.00870044i			0.000393046i
$491$	17.4910			0.789360			0.394680	−	0.918819i	$-0.370855\pi$
$491$	17.4910			0.789360			0.394680	+	0.918819i	$0.370855\pi$
$492$	−31.1711			−1.40530
$493$	29.8565	+	3.02904i	1.34467	+	0.136421i
$494$	−19.4282			−0.874115
$495$	43.9128			1.97374
$496$		−	3.05409i		−	0.137133i
$497$	39.8892			1.78927
$498$			31.7861i			1.42437i
$499$			3.63330i			0.162649i	0.996688	+	0.0813244i	$0.0259150\pi$
$499$			3.63330i			0.162649i	−0.996688	+	0.0813244i	$0.974085\pi$
$500$		−	5.07011i		−	0.226742i
$501$	23.3814			1.04460
$502$	12.7005			0.566853
$503$			32.0275i			1.42803i	0.700128	+	0.714017i	$0.253126\pi$
$503$			32.0275i			1.42803i	−0.700128	+	0.714017i	$0.746874\pi$
$504$			37.7218i			1.68026i
$505$		−	45.8388i		−	2.03980i
$506$	2.32681			0.103439
$507$			36.1330i			1.60472i
$508$	18.4564			0.818870
$509$	34.5037			1.52935			0.764676	−	0.644415i	$-0.222899\pi$
$509$	34.5037			1.52935			0.764676	+	0.644415i	$0.222899\pi$
$510$	2.86534	−	28.2429i	0.126879	−	1.25061i
$511$	21.2131			0.938412
$512$	−5.43106			−0.240021
$513$			30.7075i			1.35577i
$514$	−13.6717			−0.603034
$515$			2.21141i			0.0974463i
$516$			3.85522i			0.169716i
$517$			31.0715i			1.36652i
$518$	−7.18306			−0.315605
$519$	59.6174			2.61692
$520$		−	40.4911i		−	1.77565i
$521$			37.7144i			1.65230i	0.563452	+	0.826149i	$0.309473\pi$
$521$			37.7144i			1.65230i	−0.563452	+	0.826149i	$0.690527\pi$
$522$			31.0462i			1.35885i
$523$	39.5615			1.72990			0.864951	−	0.501856i	$-0.167349\pi$
$523$	39.5615			1.72990			0.864951	+	0.501856i	$0.167349\pi$
$524$		−	15.6092i		−	0.681892i
$525$	−28.2910			−1.23472
$526$	−5.59048			−0.243757
$527$	−25.9223	−	2.62991i	−1.12919	−	0.114561i
$528$	−3.92832			−0.170958
$529$	21.9723			0.955315
$530$			6.03995i			0.262359i
$531$	−28.5396			−1.23851
$532$		−	16.8111i		−	0.728853i
$533$			40.8891i			1.77110i
$534$			7.58001i			0.328019i
$535$	13.5739			0.586850
$536$	−28.0379			−1.21105
$537$		−	26.3787i		−	1.13832i
$538$			7.43797i			0.320674i
$539$		−	0.0102714i		−	0.000442423i
$540$	−25.6951			−1.10574
$541$		−	0.204984i		−	0.00881296i	−0.999990	−	0.00440648i	$-0.998597\pi$
$541$		−	0.204984i		−	0.00881296i	0.999990	−	0.00440648i	$-0.00140263\pi$
$542$	12.7053			0.545740
$543$	−27.0053			−1.15891
$544$	−2.41997	+	23.8530i	−0.103755	+	1.02269i
$545$	−12.2320			−0.523962
$546$	31.2038			1.33540
$547$			33.6145i			1.43725i	0.695396	+	0.718627i	$0.255229\pi$
$547$			33.6145i			1.43725i	−0.695396	+	0.718627i	$0.744771\pi$
$548$	9.65997			0.412653
$549$			47.5232i			2.02824i
$550$			8.53872i			0.364092i
$551$		−	34.4615i		−	1.46811i
$552$	−7.89852			−0.336183
$553$	−20.9455			−0.890695
$554$			10.7946i			0.458620i
$555$		−	28.3853i		−	1.20489i
$556$		−	8.04088i		−	0.341009i
$557$	11.1607			0.472892			0.236446	−	0.971645i	$-0.424017\pi$
$557$	11.1607			0.472892			0.236446	+	0.971645i	$0.424017\pi$
$558$		−	26.9553i		−	1.14111i
$559$	5.05713			0.213894
$560$	3.77690			0.159603
$561$	−3.38272	+	33.3426i	−0.142819	+	1.40772i
$562$	−21.2589			−0.896751
$563$	44.0893			1.85814			0.929071	−	0.369901i	$-0.120608\pi$
$563$	44.0893			1.85814			0.929071	+	0.369901i	$0.120608\pi$
$564$		−	42.3471i		−	1.78314i
$565$	31.4823			1.32447
$566$		−	13.4836i		−	0.566759i
$567$		−	7.58264i		−	0.318441i
$568$			40.8681i			1.71479i
$569$	31.9053			1.33754			0.668769	−	0.743470i	$-0.266822\pi$
$569$	31.9053			1.33754			0.668769	+	0.743470i	$0.266822\pi$
$570$	−32.5991			−1.36542
$571$			15.4207i			0.645337i	0.946512	+	0.322669i	$0.104580\pi$
$571$			15.4207i			0.645337i	−0.946512	+	0.322669i	$0.895420\pi$
$572$			19.1923i			0.802470i
$573$		−	61.7186i		−	2.57833i
$574$	17.3618			0.724669
$575$		−	3.77154i		−	0.157284i
$576$	−19.7222			−0.821757
$577$	−32.4784			−1.35209			−0.676047	−	0.736859i	$-0.736308\pi$
$577$	−32.4784			−1.35209			−0.676047	+	0.736859i	$0.736308\pi$
$578$	13.5126	+	2.77032i	0.562050	+	0.115230i
$579$	67.7117			2.81400
$580$	28.8363			1.19736
$581$			36.0791i			1.49681i
$582$	14.8356			0.614956
$583$		−	7.13056i		−	0.295317i
$584$			21.7337i			0.899346i
$585$			78.5071i			3.24587i
$586$	−3.26527			−0.134887
$587$	26.7802			1.10534			0.552669	−	0.833401i	$-0.313609\pi$
$587$	26.7802			1.10534			0.552669	+	0.833401i	$0.313609\pi$
$588$			0.0139989i			0.000577305i
$589$			29.9206i			1.23286i
$590$		−	13.0078i		−	0.535522i
$591$	12.1713			0.500660
$592$			1.61668i			0.0664453i
$593$	40.5721			1.66609			0.833047	−	0.553202i	$-0.186594\pi$
$593$	40.5721			1.66609			0.833047	+	0.553202i	$0.186594\pi$
$594$	−14.8856			−0.610762
$595$	3.25233	−	32.0574i	0.133333	−	1.31422i
$596$	15.7245			0.644099
$597$	−54.6367			−2.23613
$598$			4.15985i			0.170109i
$599$	−29.8496			−1.21962			−0.609811	−	0.792547i	$-0.708755\pi$
$599$	−29.8496			−1.21962			−0.609811	+	0.792547i	$0.708755\pi$
$600$		−	28.9853i		−	1.18332i
$601$		−	9.23728i		−	0.376797i	−0.982093	−	0.188398i	$-0.939670\pi$
$601$		−	9.23728i		−	0.376797i	0.982093	−	0.188398i	$-0.0603296\pi$
$602$		−	2.14730i		−	0.0875174i
$603$	54.3620			2.21379
$604$	17.2449			0.701684
$605$			8.85453i			0.359988i
$606$			36.1918i			1.47019i
$607$			3.67484i			0.149157i	0.997215	+	0.0745786i	$0.0237612\pi$
$607$			3.67484i			0.149157i	−0.997215	+	0.0745786i	$0.976239\pi$
$608$	27.5321			1.11658
$609$			55.3491i			2.24286i
$610$	−21.6602			−0.876995
$611$	−55.5494			−2.24729
$612$	2.93525	−	28.9319i	0.118650	−	1.16950i
$613$	27.0949			1.09435			0.547176	−	0.837018i	$-0.315703\pi$
$613$	27.0949			1.09435			0.547176	+	0.837018i	$0.315703\pi$
$614$	11.6591			0.470521
$615$			68.6089i			2.76658i
$616$	20.2973			0.817803
$617$		−	0.539648i		−	0.0217254i	−0.999941	−	0.0108627i	$-0.996542\pi$
$617$		−	0.539648i		−	0.0217254i	0.999941	−	0.0108627i	$-0.00345778\pi$
$618$		−	1.74601i		−	0.0702348i
$619$			16.5975i			0.667110i	0.942731	+	0.333555i	$0.108248\pi$
$619$			16.5975i			0.667110i	−0.942731	+	0.333555i	$0.891752\pi$
$620$	−25.0366			−1.00549
$621$	6.57493			0.263843
$622$		−	16.3788i		−	0.656731i
$623$			8.60377i			0.344703i
$624$		−	7.02302i		−	0.281146i
$625$	−29.7609			−1.19044
$626$		−	0.685231i		−	0.0273873i
$627$	38.4853			1.53696
$628$	−8.57215			−0.342066
$629$	13.7220	+	1.39215i	0.547132	+	0.0555085i
$630$	33.3348			1.32809
$631$	−24.4718			−0.974206			−0.487103	−	0.873344i	$-0.661946\pi$
$631$	−24.4718			−0.974206			−0.487103	+	0.873344i	$0.661946\pi$
$632$		−	21.4596i		−	0.853616i
$633$	20.6961			0.822594
$634$			23.4000i			0.929331i
$635$		−	40.6233i		−	1.61209i
$636$			9.71820i			0.385352i
$637$	0.0183632			0.000727578
$638$	16.7053			0.661370
$639$		−	79.2379i		−	3.13460i
$640$			25.3540i			1.00220i
$641$			20.3908i			0.805389i	0.915334	+	0.402695i	$0.131926\pi$
$641$			20.3908i			0.805389i	−0.915334	+	0.402695i	$0.868074\pi$
$642$	−10.7172			−0.422974
$643$			7.37863i			0.290985i	0.989359	+	0.145492i	$0.0464766\pi$
$643$			7.37863i			0.290985i	−0.989359	+	0.145492i	$0.953523\pi$
$644$	−3.59950			−0.141840
$645$	8.48549			0.334116
$646$	1.59881	−	15.7590i	0.0629042	−	0.620030i
$647$	−2.14794			−0.0844441			−0.0422221	−	0.999108i	$-0.513444\pi$
$647$	−2.14794			−0.0844441			−0.0422221	+	0.999108i	$0.513444\pi$
$648$	7.76872			0.305184
$649$			15.3566i			0.602798i
$650$	−15.2655			−0.598761
$651$		−	48.0559i		−	1.88346i
$652$		−	9.53072i		−	0.373252i
$653$			2.63286i			0.103032i	0.998672	+	0.0515159i	$0.0164053\pi$
$653$			2.63286i			0.103032i	−0.998672	+	0.0515159i	$0.983595\pi$
$654$	9.65773			0.377647
$655$	−34.3565			−1.34242
$656$		−	3.90761i		−	0.152567i
$657$		−	42.1388i		−	1.64399i
$658$			23.5867i			0.919506i
$659$	33.5084			1.30530			0.652651	−	0.757659i	$-0.273657\pi$
$659$	33.5084			1.30530			0.652651	+	0.757659i	$0.273657\pi$
$660$			32.2033i			1.25351i
$661$	4.07617			0.158544			0.0792722	−	0.996853i	$-0.474740\pi$
$661$	4.07617			0.158544			0.0792722	+	0.996853i	$0.474740\pi$
$662$	−3.15939			−0.122793
$663$	−59.6096	−	6.04761i	−2.31505	−	0.234870i
$664$	−36.9645			−1.43450
$665$	−37.0019			−1.43487
$666$			14.2688i			0.552905i
$667$	−7.37872			−0.285705
$668$			10.9168i			0.422384i
$669$			10.7827i			0.416885i
$670$			24.7772i			0.957225i
$671$	25.5713			0.987168
$672$	−44.2197			−1.70581
$673$		−	19.1818i		−	0.739405i	−0.929150	−	0.369702i	$-0.879460\pi$
$673$		−	19.1818i		−	0.739405i	0.929150	−	0.369702i	$-0.120540\pi$
$674$			4.72741i			0.182093i
$675$			24.1281i			0.928692i
$676$	−16.8705			−0.648866
$677$		−	16.4066i		−	0.630558i	−0.948999	−	0.315279i	$-0.897902\pi$
$677$		−	16.4066i		−	0.630558i	0.948999	−	0.315279i	$-0.102098\pi$
$678$	−24.8567			−0.954616
$679$	16.8393			0.646234
$680$	32.8441	+	3.33215i	1.25951	+	0.127782i
$681$	−55.8820			−2.14140
$682$	−14.5041			−0.555390
$683$		−	0.963630i		−	0.0368723i	−0.999830	−	0.0184361i	$-0.994131\pi$
$683$		−	0.963630i		−	0.0368723i	0.999830	−	0.0184361i	$-0.00586874\pi$
$684$	−33.3944			−1.27687
$685$		−	21.2620i		−	0.812379i
$686$			15.0233i			0.573592i
$687$			53.5032i			2.04127i
$688$	−0.483291			−0.0184253
$689$	12.7480			0.485659
$690$			6.97993i			0.265721i
$691$		−	25.9271i		−	0.986315i	−0.869940	−	0.493158i	$-0.835843\pi$
$691$		−	25.9271i		−	0.986315i	0.869940	−	0.493158i	$-0.164157\pi$
$692$			27.8355i			1.05815i
$693$	−39.3539			−1.49493
$694$			5.38290i			0.204332i
$695$	−17.6983			−0.671336
$696$	−56.7074			−2.14949
$697$	−33.1668	−	3.36489i	−1.25628	−	0.127454i
$698$	9.06139			0.342979
$699$	−70.4705			−2.66544
$700$		−	13.2091i		−	0.499258i
$701$	−50.7368			−1.91630			−0.958151	−	0.286265i	$-0.907586\pi$
$701$	−50.7368			−1.91630			−0.958151	+	0.286265i	$0.907586\pi$
$702$		−	26.6123i		−	1.00442i
$703$		−	15.8385i		−	0.597361i
$704$			10.6121i			0.399959i
$705$	−93.2078			−3.51041
$706$	−12.1280			−0.456443
$707$			41.0799i			1.54497i
$708$		−	20.9294i		−	0.786574i
$709$		−	19.4276i		−	0.729617i	−0.931083	−	0.364809i	$-0.881134\pi$
$709$		−	19.4276i		−	0.729617i	0.931083	−	0.364809i	$-0.118866\pi$
$710$	36.1151			1.35538
$711$			41.6073i			1.56040i
$712$	−8.81491			−0.330353
$713$	6.40644			0.239923
$714$	−2.56787	+	25.3108i	−0.0960999	+	0.947231i
$715$	42.2431			1.57980
$716$	12.3162			0.460279
$717$		−	42.6120i		−	1.59138i
$718$	5.07453			0.189380
$719$			19.0100i			0.708953i	0.935065	+	0.354476i	$0.115341\pi$
$719$			19.0100i			0.708953i	−0.935065	+	0.354476i	$0.884659\pi$
$720$		−	7.50263i		−	0.279606i
$721$		−	1.98183i		−	0.0738071i
$722$	−2.77324			−0.103209
$723$	−37.2844			−1.38662
$724$		−	12.6088i		−	0.468603i
$725$		−	27.0778i		−	1.00564i
$726$		−	6.99106i		−	0.259463i
$727$	−7.21893			−0.267735			−0.133868	−	0.990999i	$-0.542740\pi$
$727$	−7.21893			−0.267735			−0.133868	+	0.990999i	$0.542740\pi$
$728$			36.2874i			1.34490i
$729$	40.8463			1.51283
$730$	19.2061			0.710848
$731$	−0.416167	+	4.10205i	−0.0153925	+	0.151720i
$732$	−34.8510			−1.28813
$733$	44.3246			1.63717			0.818584	−	0.574387i	$-0.194759\pi$
$733$	44.3246			1.63717			0.818584	+	0.574387i	$0.194759\pi$
$734$		−	25.5634i		−	0.943561i
$735$	0.0308122			0.00113652
$736$		−	5.89503i		−	0.217294i
$737$		−	29.2511i		−	1.07748i
$738$		−	34.4885i		−	1.26954i
$739$	−30.2502			−1.11277			−0.556386	−	0.830924i	$-0.687812\pi$
$739$	−30.2502			−1.11277			−0.556386	+	0.830924i	$0.687812\pi$
$740$	13.2531			0.487195
$741$			68.8039i			2.52757i
$742$		−	5.41289i		−	0.198714i
$743$			4.91760i			0.180409i	0.995923	+	0.0902046i	$0.0287521\pi$
$743$			4.91760i			0.180409i	−0.995923	+	0.0902046i	$0.971248\pi$
$744$	49.2352			1.80505
$745$		−	34.6102i		−	1.26802i
$746$	13.3787			0.489829
$747$	71.6694			2.62225
$748$	−15.5677	−	1.57940i	−0.569211	−	0.0577485i
$749$	−12.1647			−0.444488
$750$	8.81095			0.321730
$751$		−	38.7527i		−	1.41411i	−0.707161	−	0.707053i	$-0.750024\pi$
$751$		−	38.7527i		−	1.41411i	0.707161	−	0.707053i	$-0.249976\pi$
$752$	5.30864			0.193586
$753$		−	44.9783i		−	1.63910i
$754$			29.8657i			1.08764i
$755$		−	37.9567i		−	1.38139i
$756$	23.0275			0.837501
$757$	3.21162			0.116728			0.0583642	−	0.998295i	$-0.481412\pi$
$757$	3.21162			0.116728			0.0583642	+	0.998295i	$0.481412\pi$
$758$		−	19.3316i		−	0.702154i
$759$		−	8.24027i		−	0.299103i
$760$		−	37.9100i		−	1.37514i
$761$	4.81035			0.174375			0.0871876	−	0.996192i	$-0.472212\pi$
$761$	4.81035			0.174375			0.0871876	+	0.996192i	$0.472212\pi$
$762$			32.0740i			1.16192i
$763$	10.9621			0.396855
$764$	28.8165			1.04254
$765$	−63.6804	−	6.46060i	−2.30237	−	0.233584i
$766$	−13.3607			−0.482742
$767$	−27.4544			−0.991319
$768$		−	41.5785i		−	1.50034i
$769$	33.7097			1.21560			0.607801	−	0.794089i	$-0.292052\pi$
$769$	33.7097			1.21560			0.607801	+	0.794089i	$0.292052\pi$
$770$		−	17.9368i		−	0.646396i
$771$			48.4177i			1.74372i
$772$			31.6147i			1.13784i
$773$	−20.8783			−0.750942			−0.375471	−	0.926834i	$-0.622519\pi$
$773$	−20.8783			−0.750942			−0.375471	+	0.926834i	$0.622519\pi$
$774$	−4.26551			−0.153321
$775$			23.5098i			0.844497i
$776$			17.2526i			0.619331i
$777$			25.4384i			0.912599i
$778$	25.9917			0.931847
$779$			38.2825i			1.37161i
$780$	−57.5728			−2.06144
$781$	−42.6363			−1.52565
$782$	−3.37423	−	0.342328i	−0.120662	−	0.0122416i
$783$	47.2047			1.68696
$784$	−0.00175491			−6.26752e−5
$785$			18.8677i			0.673416i
$786$	27.1261			0.967555
$787$		−	37.6284i		−	1.34131i	−0.741771	−	0.670653i	$-0.766014\pi$
$787$		−	37.6284i		−	1.34131i	0.741771	−	0.670653i	$-0.233986\pi$
$788$			5.68279i			0.202441i
$789$			19.7984i			0.704842i
$790$	−18.9638			−0.674703
$791$	−28.2139			−1.00317
$792$		−	40.3197i		−	1.43270i
$793$			45.7162i			1.62343i
$794$			10.1949i			0.361805i
$795$	21.3902			0.758631
$796$		−	25.5099i		−	0.904176i
$797$	8.90471			0.315421			0.157711	−	0.987485i	$-0.449589\pi$
$797$	8.90471			0.315421			0.157711	+	0.987485i	$0.449589\pi$
$798$	29.2147			1.03419
$799$	4.57134	−	45.0584i	0.161722	−	1.59405i
$800$	21.6331			0.764845
$801$	17.0910			0.603880
$802$		−	1.74819i		−	0.0617306i
$803$	−22.6740			−0.800149
$804$			39.8661i			1.40597i
$805$			7.92264i			0.279236i
$806$		−	25.9303i		−	0.913357i
$807$	26.3412			0.927253
$808$	−42.0880			−1.48065
$809$			11.9619i			0.420557i	0.977642	+	0.210278i	$0.0674371\pi$
$809$			11.9619i			0.420557i	−0.977642	+	0.210278i	$0.932563\pi$
$810$		−	6.86522i		−	0.241219i
$811$			27.8695i			0.978630i	0.872107	+	0.489315i	$0.162753\pi$
$811$			27.8695i			0.978630i	−0.872107	+	0.489315i	$0.837247\pi$
$812$	−25.8426			−0.906897
$813$		−	44.9952i		−	1.57805i
$814$	7.67775			0.269105
$815$	−20.9775			−0.734811
$816$	5.69667	+	0.577947i	0.199423	+	0.0202322i
$817$	4.73475			0.165648
$818$	3.47979			0.121668
$819$		−	70.3567i		−	2.45846i
$820$	−32.0336			−1.11866
$821$			17.6357i			0.615490i	0.951469	+	0.307745i	$0.0995744\pi$
$821$			17.6357i			0.615490i	−0.951469	+	0.307745i	$0.900426\pi$
$822$			16.7873i			0.585525i
$823$		−	2.67619i		−	0.0932861i	−0.998912	−	0.0466431i	$-0.985148\pi$
$823$		−	2.67619i		−	0.0932861i	0.998912	−	0.0466431i	$-0.0148523\pi$
$824$	2.03046			0.0707345
$825$	30.2394			1.05280
$826$			11.6574i			0.405611i
$827$			2.79159i			0.0970733i	0.998821	+	0.0485366i	$0.0154558\pi$
$827$			2.79159i			0.0970733i	−0.998821	+	0.0485366i	$0.984544\pi$
$828$			7.15023i			0.248488i
$829$	34.2102			1.18817			0.594085	−	0.804403i	$-0.297514\pi$
$829$	34.2102			1.18817			0.594085	+	0.804403i	$0.297514\pi$
$830$			32.6656i			1.13384i
$831$	38.2286			1.32614
$832$	−18.9722			−0.657744
$833$	−0.00151117	+	0.0148952i	−5.23589e−5	+	0.000516088i
$834$	13.9736			0.483867
$835$	24.0284			0.831535
$836$			17.9689i			0.621466i
$837$	−40.9846			−1.41664
$838$			0.389914i			0.0134694i
$839$			7.18732i			0.248134i	0.992274	+	0.124067i	$0.0395937\pi$
$839$			7.18732i			0.248134i	−0.992274	+	0.124067i	$0.960406\pi$
$840$			60.8877i			2.10082i
$841$	−23.9755			−0.826741
$842$	9.97716			0.343836
$843$			75.2872i			2.59303i
$844$			9.66302i			0.332615i
$845$			37.1327i			1.27740i
$846$	46.8539			1.61087
$847$		−	7.93528i		−	0.272659i
$848$	−1.21828			−0.0418357
$849$	−47.7515			−1.63883
$850$	1.25625	−	12.3825i	0.0430889	−	0.424715i
$851$	−3.39125			−0.116251
$852$	58.1088			1.99077
$853$			44.2671i			1.51568i	0.652443	+	0.757838i	$0.273744\pi$
$853$			44.2671i			1.51568i	−0.652443	+	0.757838i	$0.726256\pi$
$854$	19.4115			0.664247
$855$			73.5025i			2.51373i
$856$		−	12.4632i		−	0.425984i
$857$		−	38.8003i		−	1.32539i	−0.748889	−	0.662696i	$-0.769412\pi$
$857$		−	38.8003i		−	1.32539i	0.748889	−	0.662696i	$-0.230588\pi$
$858$	−33.3528			−1.13865
$859$	−28.3924			−0.968738			−0.484369	−	0.874864i	$-0.660951\pi$
$859$	−28.3924			−0.968738			−0.484369	+	0.874864i	$0.660951\pi$
$860$			3.96189i			0.135099i
$861$		−	61.4860i		−	2.09544i
$862$		−	33.5365i		−	1.14226i
$863$	41.8502			1.42460			0.712299	−	0.701876i	$-0.247654\pi$
$863$	41.8502			1.42460			0.712299	+	0.701876i	$0.247654\pi$
$864$			37.7129i			1.28302i
$865$	61.2670			2.08314
$866$	17.2153			0.585000
$867$	9.81094	−	47.8542i	0.333197	−	1.62521i
$868$	22.4374			0.761574
$869$	22.3881			0.759463
$870$			50.1124i			1.69897i
$871$	52.2949			1.77194
$872$			11.2311i			0.380334i
$873$		−	33.4505i		−	1.13213i
$874$			3.89468i			0.131739i
$875$	10.0010			0.338094
$876$	30.9023			1.04409
$877$			34.8584i			1.17709i	0.808466	+	0.588543i	$0.200298\pi$
$877$			34.8584i			1.17709i	−0.808466	+	0.588543i	$0.799702\pi$
$878$		−	21.9683i		−	0.741395i
$879$			11.5638i			0.390037i
$880$	−4.03701			−0.136088
$881$			25.0924i			0.845383i	0.906274	+	0.422691i	$0.138915\pi$
$881$			25.0924i			0.845383i	−0.906274	+	0.422691i	$0.861085\pi$
$882$	−0.0154887			−0.000521533
$883$	−11.0515			−0.371912			−0.185956	−	0.982558i	$-0.559538\pi$
$883$	−11.0515			−0.371912			−0.185956	+	0.982558i	$0.559538\pi$
$884$	2.82364	−	27.8318i	0.0949692	−	0.936085i
$885$	−46.0664			−1.54851
$886$	−4.16107			−0.139794
$887$			44.7582i			1.50283i	0.659829	+	0.751416i	$0.270629\pi$
$887$			44.7582i			1.50283i	−0.659829	+	0.751416i	$0.729371\pi$
$888$	−26.0627			−0.874607
$889$			36.4059i			1.22101i
$890$			7.78975i			0.261113i
$891$			8.10485i			0.271523i
$892$	−5.03448			−0.168567
$893$	−52.0083			−1.74039
$894$			27.3263i			0.913930i
$895$		−	27.1086i		−	0.906139i
$896$		−	22.7218i		−	0.759081i
$897$	14.7319			0.491884
$898$			7.37832i			0.246218i
$899$	45.9950			1.53402
$900$	−26.2393			−0.874644
$901$	−1.04907	+	10.3404i	−0.0349496	+	0.344489i
$902$	−18.5575			−0.617898
$903$	−7.60455			−0.253064
$904$		−	28.9063i		−	0.961408i
$905$	−27.7525			−0.922525
$906$			29.9686i			0.995639i
$907$		−	34.7918i		−	1.15524i	−0.816305	−	0.577621i	$-0.803981\pi$
$907$		−	34.7918i		−	1.15524i	0.816305	−	0.577621i	$-0.196019\pi$
$908$		−	26.0914i		−	0.865872i
$909$	81.6033			2.70661
$910$	32.0672			1.06302
$911$		−	5.20324i		−	0.172391i	−0.996278	−	0.0861956i	$-0.972529\pi$
$911$		−	5.20324i		−	0.172391i	0.996278	−	0.0861956i	$-0.0274710\pi$
$912$		−	6.57533i		−	0.217731i
$913$		−	38.5639i		−	1.27628i
$914$	−27.6958			−0.916096
$915$			76.7084i			2.53590i
$916$	−24.9807			−0.825386
$917$	30.7897			1.01677
$918$	21.5864	+	2.19001i	0.712456	+	0.0722812i
$919$	−15.4915			−0.511018			−0.255509	−	0.966807i	$-0.582243\pi$
$919$	−15.4915			−0.511018			−0.255509	+	0.966807i	$0.582243\pi$
$920$	−8.11707			−0.267612
$921$		−	41.2899i		−	1.36055i
$922$	19.8158			0.652599
$923$		−	76.2249i		−	2.50897i
$924$		−	28.8600i		−	0.949425i
$925$		−	12.4449i		−	0.409187i
$926$	34.5157			1.13426
$927$	−3.93680			−0.129302
$928$		−	42.3234i		−	1.38933i
$929$		−	12.9299i		−	0.424216i	−0.977246	−	0.212108i	$-0.931967\pi$
$929$		−	12.9299i		−	0.424216i	0.977246	−	0.212108i	$-0.0680329\pi$
$930$		−	43.5092i		−	1.42672i
$931$	0.0171926			0.000563466
$932$		−	32.9028i		−	1.07777i
$933$	−58.0048			−1.89899
$934$	−18.5222			−0.606064
$935$	−3.47632	+	34.2651i	−0.113688	+	1.12059i
$936$	72.0833			2.35612
$937$	5.08058			0.165975			0.0829877	−	0.996551i	$-0.473554\pi$
$937$	5.08058			0.165975			0.0829877	+	0.996551i	$0.473554\pi$
$938$		−	22.2048i		−	0.725014i
$939$	−2.42671			−0.0791927
$940$		−	43.5188i		−	1.41943i
$941$		−	23.9977i		−	0.782303i	−0.920326	−	0.391151i	$-0.872077\pi$
$941$		−	23.9977i		−	0.782303i	0.920326	−	0.391151i	$-0.127923\pi$
$942$		−	14.8969i		−	0.485367i
$943$	8.19684			0.266926
$944$	2.62371			0.0853945
$945$		−	50.6844i		−	1.64877i
$946$			2.29518i			0.0746228i
$947$		−	11.4902i		−	0.373380i	−0.982419	−	0.186690i	$-0.940224\pi$
$947$		−	11.4902i		−	0.373380i	0.982419	−	0.186690i	$-0.0597760\pi$
$948$	−30.5126			−0.991002
$949$		−	40.5365i		−	1.31587i
$950$	−14.2924			−0.463705
$951$	82.8697			2.68723
$952$	−29.4343	−	2.98621i	−0.953970	−	0.0967836i
$953$	7.01283			0.227168			0.113584	−	0.993528i	$-0.463767\pi$
$953$	7.01283			0.227168			0.113584	+	0.993528i	$0.463767\pi$
$954$	−10.7525			−0.348124
$955$		−	63.4263i		−	2.05243i
$956$	19.8956			0.643470
$957$		−	59.1610i		−	1.91240i
$958$			26.4117i			0.853323i
$959$			19.0546i			0.615306i
$960$	−31.8341			−1.02744
$961$	−8.93433			−0.288204
$962$			13.7262i			0.442552i
$963$			24.1646i			0.778692i
$964$		−	17.4081i		−	0.560678i
$965$	69.5852			2.24003
$966$		−	6.25529i		−	0.201261i
$967$	−44.2967			−1.42448			−0.712242	−	0.701934i	$-0.752320\pi$
$967$	−44.2967			−1.42448			−0.712242	+	0.701934i	$0.752320\pi$
$968$	8.13001			0.261309
$969$	−55.8097	−	5.66209i	−1.79287	−	0.181893i
$970$	15.2461			0.489523
$971$	−26.3049			−0.844164			−0.422082	−	0.906558i	$-0.638701\pi$
$971$	−26.3049			−0.844164			−0.422082	+	0.906558i	$0.638701\pi$
$972$			15.0579i			0.482982i
$973$	15.8609			0.508478
$974$		−	24.1639i		−	0.774260i
$975$			54.0619i			1.73137i
$976$		−	4.36892i		−	0.139846i
$977$	−2.34588			−0.0750512			−0.0375256	−	0.999296i	$-0.511948\pi$
$977$	−2.34588			−0.0750512			−0.0375256	+	0.999296i	$0.511948\pi$
$978$	16.5627			0.529617
$979$		−	9.19631i		−	0.293915i
$980$			0.0143862i			0.000459552i
$981$		−	21.7757i		−	0.695245i
$982$	−14.1921			−0.452888
$983$			33.3857i			1.06484i	0.846480	+	0.532420i	$0.178717\pi$
$983$			33.3857i			1.06484i	−0.846480	+	0.532420i	$0.821283\pi$
$984$	62.9950			2.00821
$985$	12.5081			0.398540
$986$	−24.2253	−	2.45774i	−0.771491	−	0.0782705i
$987$	83.5312			2.65883
$988$	−32.1246			−1.02202
$989$		−	1.01378i		−	0.0322363i
$990$	−35.6305			−1.13241
$991$		−	15.2450i		−	0.484273i	−0.970242	−	0.242137i	$-0.922152\pi$
$991$		−	15.2450i		−	0.484273i	0.970242	−	0.242137i	$-0.0778482\pi$
$992$			36.7465i			1.16670i
$993$			11.1888i			0.355067i
$994$	−32.3658			−1.02658
$995$	−56.1484			−1.78003
$996$			52.5585i			1.66538i
$997$		−	36.2302i		−	1.14742i	−0.819058	−	0.573711i	$-0.805503\pi$
$997$		−	36.2302i		−	1.14742i	0.819058	−	0.573711i	$-0.194497\pi$
$998$		−	2.94803i		−	0.0933183i
$999$	21.6953			0.686407

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.d.d.560.16	yes	34
17.16	even	2	inner	731.2.d.d.560.15	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.d.d.560.15	✓	34	17.16	even	2	inner
731.2.d.d.560.16	yes	34	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.811392 q^{2} +2.87350i q^{3} -1.34164 q^{4} +2.95301i q^{5} -2.33154i q^{6} -2.64644i q^{7} +2.71138 q^{8} -5.25702 q^{9} +O(q^{10})\)	\(q-0.811392 q^{2} +2.87350i q^{3} -1.34164 q^{4} +2.95301i q^{5} -2.33154i q^{6} -2.64644i q^{7} +2.71138 q^{8} -5.25702 q^{9} -2.39605i q^{10} +2.82870i q^{11} -3.85522i q^{12} -5.05713 q^{13} +2.14730i q^{14} -8.48549 q^{15} +0.483291 q^{16} +(0.416167 - 4.10205i) q^{17} +4.26551 q^{18} -4.73475 q^{19} -3.96189i q^{20} +7.60455 q^{21} -2.29518i q^{22} +1.01378i q^{23} +7.79117i q^{24} -3.72028 q^{25} +4.10331 q^{26} -6.48557i q^{27} +3.55057i q^{28} +7.27843i q^{29} +6.88506 q^{30} -6.31936i q^{31} -5.81490 q^{32} -8.12827 q^{33} +(-0.337675 + 3.32837i) q^{34} +7.81496 q^{35} +7.05305 q^{36} +3.34516i q^{37} +3.84174 q^{38} -14.5317i q^{39} +8.00675i q^{40} -8.08543i q^{41} -6.17027 q^{42} -1.00000 q^{43} -3.79510i q^{44} -15.5241i q^{45} -0.822572i q^{46} +10.9844 q^{47} +1.38874i q^{48} -0.00363116 q^{49} +3.01861 q^{50} +(11.7873 + 1.19586i) q^{51} +6.78486 q^{52} -2.52079 q^{53} +5.26234i q^{54} -8.35318 q^{55} -7.17550i q^{56} -13.6053i q^{57} -5.90566i q^{58} +5.42885 q^{59} +11.3845 q^{60} -9.03995i q^{61} +5.12748i q^{62} +13.9124i q^{63} +3.75159 q^{64} -14.9338i q^{65} +6.59521 q^{66} -10.3408 q^{67} +(-0.558348 + 5.50348i) q^{68} -2.91310 q^{69} -6.34100 q^{70} +15.0728i q^{71} -14.2538 q^{72} +8.01572i q^{73} -2.71424i q^{74} -10.6902i q^{75} +6.35235 q^{76} +7.48597 q^{77} +11.7909i q^{78} -7.91462i q^{79} +1.42716i q^{80} +2.86522 q^{81} +6.56046i q^{82} -13.6331 q^{83} -10.2026 q^{84} +(12.1134 + 1.22895i) q^{85} +0.811392 q^{86} -20.9146 q^{87} +7.66968i q^{88} -3.25108 q^{89} +12.5961i q^{90} +13.3834i q^{91} -1.36013i q^{92} +18.1587 q^{93} -8.91263 q^{94} -13.9818i q^{95} -16.7091i q^{96} +6.36302i q^{97} +0.00294629 q^{98} -14.8705i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9}+O(q^{10}) \) 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9	\( 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9} + 16 q^{13} - 8 q^{15} + 26 q^{16} + 14 q^{18} + 16 q^{19} + 20 q^{21} - 44 q^{25} - 26 q^{26} + 88 q^{30} - 42 q^{32} + 12 q^{33} - 42 q^{34} + 22 q^{35} + 34 q^{38} - 14 q^{42} - 34 q^{43} + 30 q^{47} - 62 q^{49} - 46 q^{50} - 10 q^{51} + 26 q^{52} - 46 q^{53} + 16 q^{55} - 20 q^{59} - 42 q^{60} + 102 q^{64} - 70 q^{66} - 32 q^{67} - 10 q^{68} + 74 q^{69} + 130 q^{70} + 22 q^{72} + 38 q^{76} - 78 q^{77} + 46 q^{81} - 60 q^{83} - 98 q^{84} - 38 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{89} + 14 q^{93} - 78 q^{94} + 78 q^{98}+O(q^{100}) \) 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9 + 16 * q^13 - 8 * q^15 + 26 * q^16 + 14 * q^18 + 16 * q^19 + 20 * q^21 - 44 * q^25 - 26 * q^26 + 88 * q^30 - 42 * q^32 + 12 * q^33 - 42 * q^34 + 22 * q^35 + 34 * q^38 - 14 * q^42 - 34 * q^43 + 30 * q^47 - 62 * q^49 - 46 * q^50 - 10 * q^51 + 26 * q^52 - 46 * q^53 + 16 * q^55 - 20 * q^59 - 42 * q^60 + 102 * q^64 - 70 * q^66 - 32 * q^67 - 10 * q^68 + 74 * q^69 + 130 * q^70 + 22 * q^72 + 38 * q^76 - 78 * q^77 + 46 * q^81 - 60 * q^83 - 98 * q^84 - 38 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^89 + 14 * q^93 - 78 * q^94 + 78 * q^98

Introduction

L-functions

Modular forms

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Database

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