LMFDB - Embedded newform 187.2.d.a.67.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(67,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("187.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 21x^{14} + 172x^{12} + 700x^{10} + 1492x^{8} + 1620x^{6} + 840x^{4} + 196x^{2} + 16 $ x^16 + 21x^14 + 172x^12 + 700x^10 + 1492x^8 + 1620x^6 + 840x^4 + 196*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			67.3
Root			$1.77835i$ of defining polynomial
Character	$\chi$	$=$	187.67
Dual form			187.2.d.a.67.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.77835 q^{2} -2.30556i q^{3} +1.16253 q^{4} +0.346288i q^{5} +4.10009i q^{6} -3.32341i q^{7} +1.48932 q^{8} -2.31560 q^{9} +O(q^{10})$	\(q-1.77835 q^{2} -2.30556i q^{3} +1.16253 q^{4} +0.346288i q^{5} +4.10009i q^{6} -3.32341i q^{7} +1.48932 q^{8} -2.31560 q^{9} -0.615822i q^{10} -1.00000i q^{11} -2.68028i q^{12} -5.81993 q^{13} +5.91019i q^{14} +0.798387 q^{15} -4.97358 q^{16} +(1.66281 + 3.77294i) q^{17} +4.11794 q^{18} -6.95071 q^{19} +0.402570i q^{20} -7.66232 q^{21} +1.77835i q^{22} -6.57316i q^{23} -3.43371i q^{24} +4.88008 q^{25} +10.3499 q^{26} -1.57793i q^{27} -3.86356i q^{28} +3.17417i q^{29} -1.41981 q^{30} -0.00719883i q^{31} +5.86614 q^{32} -2.30556 q^{33} +(-2.95706 - 6.70960i) q^{34} +1.15086 q^{35} -2.69195 q^{36} -3.86226i q^{37} +12.3608 q^{38} +13.4182i q^{39} +0.515733i q^{40} -2.03452i q^{41} +13.6263 q^{42} +3.74820 q^{43} -1.16253i q^{44} -0.801864i q^{45} +11.6894i q^{46} +10.2713 q^{47} +11.4669i q^{48} -4.04506 q^{49} -8.67850 q^{50} +(8.69873 - 3.83371i) q^{51} -6.76583 q^{52} -0.260443 q^{53} +2.80611i q^{54} +0.346288 q^{55} -4.94961i q^{56} +16.0253i q^{57} -5.64478i q^{58} -5.10893 q^{59} +0.928148 q^{60} -0.751233i q^{61} +0.0128020i q^{62} +7.69568i q^{63} -0.484877 q^{64} -2.01537i q^{65} +4.10009 q^{66} +10.2953 q^{67} +(1.93306 + 4.38615i) q^{68} -15.1548 q^{69} -2.04663 q^{70} +0.826371i q^{71} -3.44866 q^{72} -14.6658i q^{73} +6.86845i q^{74} -11.2513i q^{75} -8.08039 q^{76} -3.32341 q^{77} -23.8622i q^{78} -13.5643i q^{79} -1.72229i q^{80} -10.5848 q^{81} +3.61808i q^{82} -0.881504 q^{83} -8.90766 q^{84} +(-1.30652 + 0.575812i) q^{85} -6.66561 q^{86} +7.31823 q^{87} -1.48932i q^{88} +5.85907 q^{89} +1.42599i q^{90} +19.3420i q^{91} -7.64149i q^{92} -0.0165973 q^{93} -18.2660 q^{94} -2.40695i q^{95} -13.5247i q^{96} +7.78977i q^{97} +7.19353 q^{98} +2.31560i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 10 * q^4 - 6 * q^8 - 20 * q^9	$ 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9} - 16 q^{13} + 4 q^{15} + 6 q^{16} + 4 q^{17} - 10 q^{18} + 20 q^{19} + 12 q^{21} + 4 q^{25} - 12 q^{26} + 28 q^{30} - 34 q^{32} + 4 q^{33} - 6 q^{34} + 12 q^{35} - 18 q^{36} + 8 q^{43} + 14 q^{47} - 42 q^{49} - 34 q^{50} - 18 q^{51} - 44 q^{52} + 26 q^{53} + 8 q^{55} - 30 q^{59} + 72 q^{60} - 10 q^{64} - 8 q^{66} + 10 q^{67} + 22 q^{68} + 4 q^{69} - 8 q^{70} - 46 q^{72} + 36 q^{76} - 10 q^{77} - 8 q^{81} - 8 q^{83} + 92 q^{84} - 2 q^{85} + 56 q^{86} + 8 q^{87} + 10 q^{89} - 20 q^{93} + 8 q^{94} + 38 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 + 10 * q^4 - 6 * q^8 - 20 * q^9 - 16 * q^13 + 4 * q^15 + 6 * q^16 + 4 * q^17 - 10 * q^18 + 20 * q^19 + 12 * q^21 + 4 * q^25 - 12 * q^26 + 28 * q^30 - 34 * q^32 + 4 * q^33 - 6 * q^34 + 12 * q^35 - 18 * q^36 + 8 * q^43 + 14 * q^47 - 42 * q^49 - 34 * q^50 - 18 * q^51 - 44 * q^52 + 26 * q^53 + 8 * q^55 - 30 * q^59 + 72 * q^60 - 10 * q^64 - 8 * q^66 + 10 * q^67 + 22 * q^68 + 4 * q^69 - 8 * q^70 - 46 * q^72 + 36 * q^76 - 10 * q^77 - 8 * q^81 - 8 * q^83 + 92 * q^84 - 2 * q^85 + 56 * q^86 + 8 * q^87 + 10 * q^89 - 20 * q^93 + 8 * q^94 + 38 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$-1$

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 $

$2$	−1.77835			−1.25748			−0.628742	−	0.777614i	$-0.716430\pi$
$2$	−1.77835			−1.25748			−0.628742	+	0.777614i	$0.716430\pi$
$3$		−	2.30556i		−	1.33111i	−0.746347	−	0.665557i	$-0.768194\pi$
$3$		−	2.30556i		−	1.33111i	0.746347	−	0.665557i	$-0.231806\pi$
$4$	1.16253			0.581264
$5$			0.346288i			0.154865i	0.996998	+	0.0774324i	$0.0246722\pi$
$5$			0.346288i			0.154865i	−0.996998	+	0.0774324i	$0.975328\pi$
$6$			4.10009i			1.67385i
$7$		−	3.32341i		−	1.25613i	−0.778160	−	0.628066i	$-0.783847\pi$
$7$		−	3.32341i		−	1.25613i	0.778160	−	0.628066i	$-0.216153\pi$
$8$	1.48932			0.526553
$9$	−2.31560			−0.771866
$10$		−	0.615822i		−	0.194740i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$		−	2.68028i		−	0.773729i
$13$	−5.81993			−1.61416			−0.807079	−	0.590444i	$-0.798953\pi$
$13$	−5.81993			−1.61416			−0.807079	+	0.590444i	$0.798953\pi$
$14$			5.91019i			1.57956i
$15$	0.798387			0.206143
$16$	−4.97358			−1.24340
$17$	1.66281	+	3.77294i	0.403291	+	0.915072i
$17$	1.66281	+	3.77294i	0.403291	+	0.915072i
$18$	4.11794			0.970608
$19$	−6.95071			−1.59460			−0.797301	−	0.603582i	$-0.793740\pi$
$19$	−6.95071			−1.59460			−0.797301	+	0.603582i	$0.793740\pi$
$20$			0.402570i			0.0900173i
$21$	−7.66232			−1.67205
$22$			1.77835i			0.379145i
$23$		−	6.57316i		−	1.37060i	−0.728261	−	0.685300i	$-0.759671\pi$
$23$		−	6.57316i		−	1.37060i	0.728261	−	0.685300i	$-0.240329\pi$
$24$		−	3.43371i		−	0.700903i
$25$	4.88008			0.976017
$26$	10.3499			2.02978
$27$		−	1.57793i		−	0.303673i
$28$		−	3.86356i		−	0.730144i
$29$			3.17417i			0.589428i	0.955585	+	0.294714i	$0.0952244\pi$
$29$			3.17417i			0.589428i	−0.955585	+	0.294714i	$0.904776\pi$
$30$	−1.41981			−0.259221
$31$		−	0.00719883i		−	0.00129295i	−1.00000		0.000646474i	$-0.999794\pi$
$31$		−	0.00719883i		−	0.00129295i	1.00000		0.000646474i	$-0.000205779\pi$
$32$	5.86614			1.03700
$33$	−2.30556			−0.401346
$34$	−2.95706	−	6.70960i	−0.507131	−	1.15069i
$35$	1.15086			0.194530
$36$	−2.69195			−0.448658
$37$		−	3.86226i		−	0.634951i	−0.948266	−	0.317476i	$-0.897165\pi$
$37$		−	3.86226i		−	0.634951i	0.948266	−	0.317476i	$-0.102835\pi$
$38$	12.3608			2.00518
$39$			13.4182i			2.14863i
$40$			0.515733i			0.0815446i
$41$		−	2.03452i		−	0.317738i	−0.987300	−	0.158869i	$-0.949215\pi$
$41$		−	2.03452i		−	0.317738i	0.987300	−	0.158869i	$-0.0507848\pi$
$42$	13.6263			2.10258
$43$	3.74820			0.571595			0.285797	−	0.958290i	$-0.407742\pi$
$43$	3.74820			0.571595			0.285797	+	0.958290i	$0.407742\pi$
$44$		−	1.16253i		−	0.175258i
$45$		−	0.801864i		−	0.119535i
$46$			11.6894i			1.72351i
$47$	10.2713			1.49822			0.749111	−	0.662445i	$-0.230481\pi$
$47$	10.2713			1.49822			0.749111	+	0.662445i	$0.230481\pi$
$48$			11.4669i			1.65510i
$49$	−4.04506			−0.577865
$50$	−8.67850			−1.22732
$51$	8.69873	−	3.83371i	1.21807	−	0.536826i
$52$	−6.76583			−0.938252
$53$	−0.260443			−0.0357746			−0.0178873	−	0.999840i	$-0.505694\pi$
$53$	−0.260443			−0.0357746			−0.0178873	+	0.999840i	$0.505694\pi$
$54$			2.80611i			0.381864i
$55$	0.346288			0.0466935
$56$		−	4.94961i		−	0.661420i
$57$			16.0253i			2.12260i
$58$		−	5.64478i		−	0.741196i
$59$	−5.10893			−0.665126			−0.332563	−	0.943081i	$-0.607913\pi$
$59$	−5.10893			−0.665126			−0.332563	+	0.943081i	$0.607913\pi$
$60$	0.928148			0.119823
$61$		−	0.751233i		−	0.0961855i	−0.998843	−	0.0480928i	$-0.984686\pi$
$61$		−	0.751233i		−	0.0961855i	0.998843	−	0.0480928i	$-0.0153143\pi$
$62$			0.0128020i			0.00162586i
$63$			7.69568i			0.969564i
$64$	−0.484877			−0.0606097
$65$		−	2.01537i		−	0.249976i
$66$	4.10009			0.504686
$67$	10.2953			1.25778			0.628889	−	0.777495i	$-0.283510\pi$
$67$	10.2953			1.25778			0.628889	+	0.777495i	$0.283510\pi$
$68$	1.93306	+	4.38615i	0.234418	+	0.531898i
$69$	−15.1548			−1.82442
$70$	−2.04663			−0.244619
$71$			0.826371i			0.0980722i	0.998797	+	0.0490361i	$0.0156149\pi$
$71$			0.826371i			0.0980722i	−0.998797	+	0.0490361i	$0.984385\pi$
$72$	−3.44866			−0.406428
$73$		−	14.6658i		−	1.71650i	−0.513229	−	0.858252i	$-0.671551\pi$
$73$		−	14.6658i		−	1.71650i	0.513229	−	0.858252i	$-0.328449\pi$
$74$			6.86845i			0.798441i
$75$		−	11.2513i		−	1.29919i
$76$	−8.08039			−0.926885
$77$	−3.32341			−0.378738
$78$		−	23.8622i		−	2.70186i
$79$		−	13.5643i		−	1.52610i	−0.646339	−	0.763050i	$-0.723701\pi$
$79$		−	13.5643i		−	1.52610i	0.646339	−	0.763050i	$-0.276299\pi$
$80$		−	1.72229i		−	0.192558i
$81$	−10.5848			−1.17609
$82$			3.61808i			0.399550i
$83$	−0.881504			−0.0967576			−0.0483788	−	0.998829i	$-0.515405\pi$
$83$	−0.881504			−0.0967576			−0.0483788	+	0.998829i	$0.515405\pi$
$84$	−8.90766			−0.971905
$85$	−1.30652	+	0.575812i	−0.141712	+	0.0624555i
$86$	−6.66561			−0.718771
$87$	7.31823			0.784596
$88$		−	1.48932i		−	0.158762i
$89$	5.85907			0.621060			0.310530	−	0.950564i	$-0.399493\pi$
$89$	5.85907			0.621060			0.310530	+	0.950564i	$0.399493\pi$
$90$			1.42599i			0.150313i
$91$			19.3420i			2.02759i
$92$		−	7.64149i		−	0.796680i
$93$	−0.0165973			−0.00172106
$94$	−18.2660			−1.88399
$95$		−	2.40695i		−	0.246948i
$96$		−	13.5247i		−	1.38036i
$97$			7.78977i			0.790931i	0.918481	+	0.395466i	$0.129417\pi$
$97$			7.78977i			0.790931i	−0.918481	+	0.395466i	$0.870583\pi$
$98$	7.19353			0.726656
$99$			2.31560i			0.232726i
$100$	5.67324			0.567324
$101$	11.5217			1.14645			0.573226	−	0.819397i	$-0.305692\pi$
$101$	11.5217			1.14645			0.573226	+	0.819397i	$0.305692\pi$
$102$	−15.4694	+	6.81767i	−1.53170	+	0.675050i
$103$	−7.84717			−0.773204			−0.386602	−	0.922247i	$-0.626351\pi$
$103$	−7.84717			−0.773204			−0.386602	+	0.922247i	$0.626351\pi$
$104$	−8.66772			−0.849940
$105$		−	2.65337i		−	0.258942i
$106$	0.463159			0.0449859
$107$			18.5395i			1.79228i	0.443768	+	0.896142i	$0.353641\pi$
$107$			18.5395i			1.79228i	−0.443768	+	0.896142i	$0.646359\pi$
$108$		−	1.83439i		−	0.176514i
$109$		−	13.2726i		−	1.27128i	−0.771985	−	0.635640i	$-0.780736\pi$
$109$		−	13.2726i		−	1.27128i	0.771985	−	0.635640i	$-0.219264\pi$
$110$	−0.615822			−0.0587163
$111$	−8.90466			−0.845193
$112$			16.5293i			1.56187i
$113$		−	5.54616i		−	0.521739i	−0.965374	−	0.260869i	$-0.915991\pi$
$113$		−	5.54616i		−	0.521739i	0.965374	−	0.260869i	$-0.0840092\pi$
$114$		−	28.4985i		−	2.66913i
$115$	2.27621			0.212258
$116$			3.69006i			0.342613i
$117$	13.4766			1.24591
$118$	9.08547			0.836385
$119$	12.5390	−	5.52620i	1.14945	−	0.506586i
$120$	1.18905			0.108545
$121$	−1.00000			−0.0909091
$122$			1.33596i			0.120952i
$123$	−4.69070			−0.422946
$124$		−	0.00836885i		−	0.000751545i
$125$			3.42136i			0.306015i
$126$		−	13.6856i		−	1.21921i
$127$	−0.622523			−0.0552400			−0.0276200	−	0.999618i	$-0.508793\pi$
$127$	−0.622523			−0.0552400			−0.0276200	+	0.999618i	$0.508793\pi$
$128$	−10.8700			−0.960781
$129$		−	8.64168i		−	0.760858i
$130$			3.58404i			0.314341i
$131$			12.7714i			1.11584i	0.829893	+	0.557922i	$0.188401\pi$
$131$			12.7714i			1.11584i	−0.829893	+	0.557922i	$0.811599\pi$
$132$	−2.68028			−0.233288
$133$			23.1001i			2.00303i
$134$	−18.3087			−1.58163
$135$	0.546419			0.0470283
$136$	2.47645	+	5.61910i	0.212354	+	0.481834i
$137$	1.06166			0.0907033			0.0453517	−	0.998971i	$-0.485559\pi$
$137$	1.06166			0.0907033			0.0453517	+	0.998971i	$0.485559\pi$
$138$	26.9505			2.29418
$139$			2.79560i			0.237120i	0.992947	+	0.118560i	$0.0378277\pi$
$139$			2.79560i			0.237120i	−0.992947	+	0.118560i	$0.962172\pi$
$140$	1.33790			0.113074
$141$		−	23.6811i		−	1.99430i
$142$		−	1.46958i		−	0.123324i
$143$			5.81993i			0.486687i
$144$	11.5168			0.959735
$145$	−1.09918			−0.0912817
$146$			26.0809i			2.15847i
$147$			9.32611i			0.769205i
$148$		−	4.48998i		−	0.369074i
$149$	6.91091			0.566164			0.283082	−	0.959096i	$-0.408643\pi$
$149$	6.91091			0.566164			0.283082	+	0.959096i	$0.408643\pi$
$150$			20.0088i			1.63371i
$151$	18.0263			1.46696			0.733482	−	0.679709i	$-0.237894\pi$
$151$	18.0263			1.46696			0.733482	+	0.679709i	$0.237894\pi$
$152$	−10.3518			−0.839643
$153$	−3.85040	−	8.73660i	−0.311286	−	0.706312i
$154$	5.91019			0.476256
$155$	0.00249287			0.000200232
$156$			15.5990i			1.24892i
$157$	7.10270			0.566857			0.283429	−	0.958993i	$-0.408528\pi$
$157$	7.10270			0.566857			0.283429	+	0.958993i	$0.408528\pi$
$158$			24.1220i			1.91905i
$159$			0.600466i			0.0476201i
$160$			2.03137i			0.160594i
$161$	−21.8453			−1.72165
$162$	18.8235			1.47891
$163$		−	13.1303i		−	1.02845i	−0.857656	−	0.514224i	$-0.828080\pi$
$163$		−	13.1303i		−	1.02845i	0.857656	−	0.514224i	$-0.171920\pi$
$164$		−	2.36518i		−	0.184690i
$165$		−	0.798387i		−	0.0621544i
$166$	1.56762			0.121671
$167$		−	22.3589i		−	1.73018i	−0.501616	−	0.865090i	$-0.667261\pi$
$167$		−	22.3589i		−	1.73018i	0.501616	−	0.865090i	$-0.332739\pi$
$168$	−11.4116			−0.880426
$169$	20.8716			1.60550
$170$	2.32346	−	1.02399i	0.178201	−	0.0785368i
$171$	16.0950			1.23082
$172$	4.35739			0.332248
$173$			7.72726i			0.587492i	0.955883	+	0.293746i	$0.0949021\pi$
$173$			7.72726i			0.587492i	−0.955883	+	0.293746i	$0.905098\pi$
$174$	−13.0144			−0.986617
$175$		−	16.2185i		−	1.22601i
$176$			4.97358i			0.374898i
$177$			11.7789i			0.885359i
$178$	−10.4195			−0.780973
$179$	7.42340			0.554851			0.277426	−	0.960747i	$-0.410519\pi$
$179$	7.42340			0.554851			0.277426	+	0.960747i	$0.410519\pi$
$180$		−	0.932189i		−	0.0694813i
$181$			1.06213i			0.0789472i	0.999221	+	0.0394736i	$0.0125681\pi$
$181$			1.06213i			0.0789472i	−0.999221	+	0.0394736i	$0.987432\pi$
$182$		−	34.3969i		−	2.54966i
$183$	−1.73201			−0.128034
$184$		−	9.78953i		−	0.721694i
$185$	1.33745			0.0983316
$186$	0.0295158			0.00216421
$187$	3.77294	−	1.66281i	0.275905	−	0.121597i
$188$	11.9407			0.870863
$189$	−5.24411			−0.381453
$190$			4.28040i			0.310532i
$191$	−11.4170			−0.826104			−0.413052	−	0.910708i	$-0.635537\pi$
$191$	−11.4170			−0.826104			−0.413052	+	0.910708i	$0.635537\pi$
$192$			1.11791i			0.0806784i
$193$			12.6373i			0.909651i	0.890581	+	0.454825i	$0.150298\pi$
$193$			12.6373i			0.909651i	−0.890581	+	0.454825i	$0.849702\pi$
$194$		−	13.8529i		−	0.994583i
$195$	−4.64656			−0.332747
$196$	−4.70249			−0.335892
$197$		−	17.4081i		−	1.24028i	−0.784492	−	0.620139i	$-0.787076\pi$
$197$		−	17.4081i		−	1.24028i	0.784492	−	0.620139i	$-0.212924\pi$
$198$		−	4.11794i		−	0.292649i
$199$			13.7163i			0.972321i	0.873870	+	0.486160i	$0.161603\pi$
$199$			13.7163i			0.972321i	−0.873870	+	0.486160i	$0.838397\pi$
$200$	7.26800			0.513925
$201$		−	23.7365i		−	1.67425i
$202$	−20.4896			−1.44164
$203$	10.5491			0.740399
$204$	10.1125	−	4.45679i	0.708018	−	0.312038i
$205$	0.704529			0.0492064
$206$	13.9550			0.972292
$207$			15.2208i			1.05792i
$208$	28.9459			2.00704
$209$			6.95071i			0.480790i
$210$			4.71862i			0.325616i
$211$			15.7505i			1.08431i	0.840279	+	0.542154i	$0.182391\pi$
$211$			15.7505i			1.08431i	−0.840279	+	0.542154i	$0.817609\pi$
$212$	−0.302772			−0.0207945
$213$	1.90525			0.130545
$214$		−	32.9698i		−	2.25377i
$215$			1.29796i			0.0885199i
$216$		−	2.35004i		−	0.159900i
$217$	−0.0239247			−0.00162411
$218$			23.6033i			1.59861i
$219$	−33.8129			−2.28486
$220$	0.402570			0.0271413
$221$	−9.67744	−	21.9582i	−0.650975	−	1.47707i
$222$	15.8356			1.06282
$223$	−3.45944			−0.231662			−0.115831	−	0.993269i	$-0.536953\pi$
$223$	−3.45944			−0.231662			−0.115831	+	0.993269i	$0.536953\pi$
$224$		−	19.4956i		−	1.30260i
$225$	−11.3003			−0.753354
$226$			9.86301i			0.656078i
$227$			9.57321i			0.635396i	0.948192	+	0.317698i	$0.102910\pi$
$227$			9.57321i			0.635396i	−0.948192	+	0.317698i	$0.897090\pi$
$228$			18.6298i			1.23379i
$229$	−19.3434			−1.27825			−0.639123	−	0.769105i	$-0.720702\pi$
$229$	−19.3434			−1.27825			−0.639123	+	0.769105i	$0.720702\pi$
$230$	−4.04790			−0.266910
$231$			7.66232i			0.504143i
$232$			4.72734i			0.310365i
$233$		−	0.108501i		−	0.00710816i	−0.999994	−	0.00355408i	$-0.998869\pi$
$233$		−	0.108501i		−	0.00710816i	0.999994	−	0.00355408i	$-0.00113130\pi$
$234$	−23.9661			−1.56671
$235$			3.55683i			0.232022i
$236$	−5.93928			−0.386614
$237$	−31.2732			−2.03141
$238$	−22.2988	+	9.82752i	−1.44541	+	0.637024i
$239$	−24.0410			−1.55508			−0.777541	−	0.628832i	$-0.783533\pi$
$239$	−24.0410			−1.55508			−0.777541	+	0.628832i	$0.783533\pi$
$240$	−3.97085			−0.256317
$241$			29.0846i			1.87350i	0.349994	+	0.936752i	$0.386183\pi$
$241$			29.0846i			1.87350i	−0.349994	+	0.936752i	$0.613817\pi$
$242$	1.77835			0.114317
$243$			19.6701i			1.26184i
$244$		−	0.873330i		−	0.0559092i
$245$		−	1.40076i		−	0.0894910i
$246$	8.34170			0.531847
$247$	40.4526			2.57394
$248$		−	0.0107213i		−	0.000680806i
$249$			2.03236i			0.128795i
$250$		−	6.08437i		−	0.384809i
$251$	7.04753			0.444836			0.222418	−	0.974951i	$-0.428605\pi$
$251$	7.04753			0.444836			0.222418	+	0.974951i	$0.428605\pi$
$252$			8.94644i			0.563573i
$253$	−6.57316			−0.413251
$254$	1.10706			0.0694634
$255$	1.32757	+	3.01227i	0.0831355	+	0.188635i
$256$	20.3004			1.26878
$257$	−0.723821			−0.0451507			−0.0225754	−	0.999745i	$-0.507187\pi$
$257$	−0.723821			−0.0451507			−0.0225754	+	0.999745i	$0.507187\pi$
$258$			15.3679i			0.956766i
$259$	−12.8359			−0.797582
$260$		−	2.34293i		−	0.145302i
$261$		−	7.35009i		−	0.454959i
$262$		−	22.7121i		−	1.40316i
$263$	23.4134			1.44373			0.721867	−	0.692032i	$-0.243284\pi$
$263$	23.4134			1.44373			0.721867	+	0.692032i	$0.243284\pi$
$264$	−3.43371			−0.211330
$265$		−	0.0901883i		−	0.00554022i
$266$		−	41.0800i		−	2.51877i
$267$		−	13.5084i		−	0.826703i
$268$	11.9686			0.731101
$269$			6.24188i			0.380574i	0.981729	+	0.190287i	$0.0609418\pi$
$269$			6.24188i			0.380574i	−0.981729	+	0.190287i	$0.939058\pi$
$270$	−0.971724			−0.0591372
$271$	3.49019			0.212014			0.106007	−	0.994365i	$-0.466193\pi$
$271$	3.49019			0.212014			0.106007	+	0.994365i	$0.466193\pi$
$272$	−8.27013	−	18.7650i	−0.501450	−	1.13780i
$273$	44.5941			2.69896
$274$	−1.88799			−0.114058
$275$		−	4.88008i		−	0.294280i
$276$	−17.6179			−1.06047
$277$		−	11.1957i		−	0.672684i	−0.941740	−	0.336342i	$-0.890810\pi$
$277$		−	11.1957i		−	0.672684i	0.941740	−	0.336342i	$-0.109190\pi$
$278$		−	4.97155i		−	0.298174i
$279$			0.0166696i			0.000997982i
$280$	1.71399			0.102431
$281$	17.1663			1.02405			0.512027	−	0.858969i	$-0.328895\pi$
$281$	17.1663			1.02405			0.512027	+	0.858969i	$0.328895\pi$
$282$			42.1132i			2.50780i
$283$		−	10.3919i		−	0.617734i	−0.951105	−	0.308867i	$-0.900050\pi$
$283$		−	10.3919i		−	0.617734i	0.951105	−	0.308867i	$-0.0999498\pi$
$284$			0.960680i			0.0570059i
$285$	−5.54936			−0.328716
$286$		−	10.3499i		−	0.612000i
$287$	−6.76153			−0.399121
$288$	−13.5836			−0.800422
$289$	−11.4701	+	12.5474i	−0.674713	+	0.738080i
$290$	1.95472			0.114785
$291$	17.9598			1.05282
$292$		−	17.0494i		−	0.997742i
$293$	−7.98571			−0.466530			−0.233265	−	0.972413i	$-0.574941\pi$
$293$	−7.98571			−0.466530			−0.233265	+	0.972413i	$0.574941\pi$
$294$		−	16.5851i		−	0.967262i
$295$		−	1.76916i		−	0.103005i
$296$		−	5.75213i		−	0.334336i
$297$	−1.57793			−0.0915609
$298$	−12.2900			−0.711941
$299$			38.2553i			2.21236i
$300$		−	13.0800i		−	0.755173i
$301$		−	12.4568i		−	0.717998i
$302$	−32.0572			−1.84468
$303$		−	26.5639i		−	1.52606i
$304$	34.5699			1.98272
$305$	0.260143			0.0148957
$306$	6.84736	+	15.5367i	0.391437	+	0.888176i
$307$	13.8263			0.789109			0.394554	−	0.918873i	$-0.370899\pi$
$307$	13.8263			0.789109			0.394554	+	0.918873i	$0.370899\pi$
$308$	−3.86356			−0.220147
$309$			18.0921i			1.02922i
$310$	−0.00443320			−0.000251789
$311$			0.966201i			0.0547883i	0.999625	+	0.0273941i	$0.00872091\pi$
$311$			0.966201i			0.0547883i	−0.999625	+	0.0273941i	$0.991279\pi$
$312$			19.9839i			1.13137i
$313$			16.7101i			0.944514i	0.881461	+	0.472257i	$0.156560\pi$
$313$			16.7101i			0.944514i	−0.881461	+	0.472257i	$0.843440\pi$
$314$	−12.6311			−0.712814
$315$	−2.66492			−0.150151
$316$		−	15.7689i		−	0.887068i
$317$			6.87525i			0.386153i	0.981184	+	0.193076i	$0.0618465\pi$
$317$			6.87525i			0.386153i	−0.981184	+	0.193076i	$0.938153\pi$
$318$		−	1.06784i		−	0.0598814i
$319$	3.17417			0.177719
$320$		−	0.167907i		−	0.00938630i
$321$	42.7439			2.38573
$322$	38.8486			2.16495
$323$	−11.5577	−	26.2246i	−0.643088	−	1.45918i
$324$	−12.3051			−0.683618
$325$	−28.4017			−1.57544
$326$			23.3503i			1.29325i
$327$	−30.6007			−1.69222
$328$		−	3.03004i		−	0.167306i
$329$		−	34.1357i		−	1.88196i
$330$			1.41981i			0.0781581i
$331$	−35.3753			−1.94440			−0.972202	−	0.234144i	$-0.924771\pi$
$331$	−35.3753			−1.94440			−0.972202	+	0.234144i	$0.924771\pi$
$332$	−1.02477			−0.0562417
$333$			8.94343i			0.490097i
$334$			39.7619i			2.17567i
$335$			3.56516i			0.194785i
$336$	38.1092			2.07903
$337$		−	28.2801i		−	1.54051i	−0.637734	−	0.770257i	$-0.720128\pi$
$337$		−	28.2801i		−	1.54051i	0.637734	−	0.770257i	$-0.279872\pi$
$338$	−37.1169			−2.01889
$339$	−12.7870			−0.694494
$340$	−1.51887	+	0.669397i	−0.0823723	+	0.0363032i
$341$	−0.00719883			−0.000389839
$342$	−28.6226			−1.54773
$343$		−	9.82049i		−	0.530256i
$344$	5.58226			0.300975
$345$		−	5.24793i		−	0.282539i
$346$		−	13.7418i		−	0.738762i
$347$		−	12.3440i		−	0.662662i	−0.943515	−	0.331331i	$-0.892502\pi$
$347$		−	12.3440i		−	0.662662i	0.943515	−	0.331331i	$-0.107498\pi$
$348$	8.50765			0.456058
$349$	−4.44435			−0.237900			−0.118950	−	0.992900i	$-0.537953\pi$
$349$	−4.44435			−0.237900			−0.118950	+	0.992900i	$0.537953\pi$
$350$			28.8422i			1.54168i
$351$			9.18344i			0.490176i
$352$		−	5.86614i		−	0.312666i
$353$	−10.5623			−0.562175			−0.281087	−	0.959682i	$-0.590695\pi$
$353$	−10.5623			−0.562175			−0.281087	+	0.959682i	$0.590695\pi$
$354$		−	20.9471i		−	1.11332i
$355$	−0.286163			−0.0151879
$356$	6.81134			0.361000
$357$	−12.7410	−	28.9094i	−0.674324	−	1.53005i
$358$	−13.2014			−0.697716
$359$	14.7033			0.776013			0.388006	−	0.921657i	$-0.373164\pi$
$359$	14.7033			0.776013			0.388006	+	0.921657i	$0.373164\pi$
$360$		−	1.19423i		−	0.0629414i
$361$	29.3123			1.54275
$362$		−	1.88883i		−	0.0992748i
$363$			2.30556i			0.121010i
$364$			22.4856i			1.17857i
$365$	5.07860			0.265826
$366$	3.08012			0.161001
$367$			1.29419i			0.0675560i	0.999429	+	0.0337780i	$0.0107539\pi$
$367$			1.29419i			0.0675560i	−0.999429	+	0.0337780i	$0.989246\pi$
$368$			32.6922i			1.70420i
$369$			4.71112i			0.245251i
$370$	−2.37846			−0.123650
$371$			0.865559i			0.0449376i
$372$	−0.0192949			−0.00100039
$373$	−27.6073			−1.42945			−0.714726	−	0.699404i	$-0.753449\pi$
$373$	−27.6073			−1.42945			−0.714726	+	0.699404i	$0.753449\pi$
$374$	−6.70960	+	2.95706i	−0.346945	+	0.152906i
$375$	7.88814			0.407342
$376$	15.2972			0.788894
$377$		−	18.4734i		−	0.951430i
$378$	9.32587			0.479671
$379$		−	8.62160i		−	0.442862i	−0.975176	−	0.221431i	$-0.928927\pi$
$379$		−	8.62160i		−	0.442862i	0.975176	−	0.221431i	$-0.0710727\pi$
$380$		−	2.79814i		−	0.143542i
$381$			1.43526i			0.0735307i
$382$	20.3034			1.03881
$383$	−36.8316			−1.88201			−0.941003	−	0.338398i	$-0.890115\pi$
$383$	−36.8316			−1.88201			−0.941003	+	0.338398i	$0.890115\pi$
$384$			25.0614i			1.27891i
$385$		−	1.15086i		−	0.0586531i
$386$		−	22.4735i		−	1.14387i
$387$	−8.67931			−0.441194
$388$			9.05583i			0.459740i
$389$	38.7346			1.96392			0.981961	−	0.189085i	$-0.0605522\pi$
$389$	38.7346			1.96392			0.981961	+	0.189085i	$0.0605522\pi$
$390$	8.26320			0.418424
$391$	24.8001	−	10.9299i	1.25420	−	0.552750i
$392$	−6.02438			−0.304277
$393$	29.4453			1.48532
$394$			30.9577i			1.55963i
$395$	4.69715			0.236339
$396$			2.69195i			0.135275i
$397$			5.43225i			0.272637i	0.990665	+	0.136318i	$0.0435270\pi$
$397$			5.43225i			0.272637i	−0.990665	+	0.136318i	$0.956473\pi$
$398$		−	24.3923i		−	1.22268i
$399$	53.2585			2.66626
$400$	−24.2715			−1.21358
$401$			25.9549i			1.29613i	0.761587	+	0.648063i	$0.224420\pi$
$401$			25.9549i			1.29613i	−0.761587	+	0.648063i	$0.775580\pi$
$402$			42.2118i			2.10534i
$403$			0.0418967i			0.00208702i
$404$	13.3943			0.666391
$405$		−	3.66539i		−	0.182135i
$406$	−18.7599			−0.931039
$407$	−3.86226			−0.191445
$408$	12.9552	−	5.70961i	0.641376	−	0.282668i
$409$	−23.2413			−1.14921			−0.574603	−	0.818432i	$-0.694844\pi$
$409$	−23.2413			−1.14921			−0.574603	+	0.818432i	$0.694844\pi$
$410$	−1.25290			−0.0618763
$411$		−	2.44771i		−	0.120736i
$412$	−9.12256			−0.449436
$413$			16.9791i			0.835486i
$414$		−	27.0679i		−	1.33031i
$415$		−	0.305254i		−	0.0149843i
$416$	−34.1405			−1.67388
$417$	6.44541			0.315633
$418$		−	12.3608i		−	0.604586i
$419$			22.5719i			1.10271i	0.834271	+	0.551354i	$0.185889\pi$
$419$			22.5719i			1.10271i	−0.834271	+	0.551354i	$0.814111\pi$
$420$		−	3.08462i		−	0.150514i
$421$	−18.4573			−0.899554			−0.449777	−	0.893141i	$-0.648496\pi$
$421$	−18.4573			−0.899554			−0.449777	+	0.893141i	$0.648496\pi$
$422$		−	28.0099i		−	1.36350i
$423$	−23.7842			−1.15643
$424$	−0.387882			−0.0188372
$425$	8.11466	+	18.4123i	0.393619	+	0.893126i
$426$	−3.38819			−0.164159
$427$	−2.49666			−0.120822
$428$			21.5527i			1.04179i
$429$	13.4182			0.647836
$430$		−	2.30822i		−	0.111312i
$431$		−	29.3541i		−	1.41394i	−0.707245	−	0.706969i	$-0.750062\pi$
$431$		−	29.3541i		−	1.41394i	0.707245	−	0.706969i	$-0.249938\pi$
$432$			7.84797i			0.377586i
$433$	17.7278			0.851943			0.425972	−	0.904737i	$-0.359932\pi$
$433$	17.7278			0.851943			0.425972	+	0.904737i	$0.359932\pi$
$434$	0.0425464			0.00204229
$435$			2.53422i			0.121506i
$436$		−	15.4297i		−	0.738950i
$437$			45.6881i			2.18556i
$438$	60.1311			2.87318
$439$			34.9773i			1.66938i	0.550723	+	0.834688i	$0.314352\pi$
$439$			34.9773i			1.66938i	−0.550723	+	0.834688i	$0.685648\pi$
$440$	0.515733			0.0245866
$441$	9.36672			0.446034
$442$	17.2099	+	39.0494i	0.818590	+	1.85739i
$443$	−25.3490			−1.20437			−0.602185	−	0.798357i	$-0.705703\pi$
$443$	−25.3490			−1.20437			−0.602185	+	0.798357i	$0.705703\pi$
$444$	−10.3519			−0.491280
$445$			2.02893i			0.0961804i
$446$	6.15210			0.291310
$447$		−	15.9335i		−	0.753629i
$448$			1.61145i			0.0761337i
$449$			30.3496i			1.43229i	0.697954	+	0.716143i	$0.254094\pi$
$449$			30.3496i			1.43229i	−0.697954	+	0.716143i	$0.745906\pi$
$450$	20.0959			0.947330
$451$	−2.03452			−0.0958017
$452$		−	6.44756i		−	0.303268i
$453$		−	41.5608i		−	1.95270i
$454$		−	17.0245i		−	0.799000i
$455$	−6.69791			−0.314003
$456$			23.8667i			1.11766i
$457$	17.5383			0.820408			0.410204	−	0.911994i	$-0.365458\pi$
$457$	17.5383			0.820408			0.410204	+	0.911994i	$0.365458\pi$
$458$	34.3993			1.60737
$459$	5.95344	−	2.62380i	0.277883	−	0.122469i
$460$	2.64616			0.123378
$461$	12.0286			0.560228			0.280114	−	0.959967i	$-0.409628\pi$
$461$	12.0286			0.560228			0.280114	+	0.959967i	$0.409628\pi$
$462$		−	13.6263i		−	0.633952i
$463$	6.84069			0.317914			0.158957	−	0.987286i	$-0.449187\pi$
$463$	6.84069			0.317914			0.158957	+	0.987286i	$0.449187\pi$
$464$		−	15.7870i		−	0.732893i
$465$		−	0.00574746i		−	0.000266532i
$466$			0.192953i			0.00893839i
$467$	3.22917			0.149428			0.0747141	−	0.997205i	$-0.476196\pi$
$467$	3.22917			0.149428			0.0747141	+	0.997205i	$0.476196\pi$
$468$	15.6669			0.724204
$469$		−	34.2157i		−	1.57993i
$470$		−	6.32528i		−	0.291764i
$471$		−	16.3757i		−	0.754552i
$472$	−7.60882			−0.350225
$473$		−	3.74820i		−	0.172342i
$474$	55.6147			2.55447
$475$	−33.9200			−1.55636
$476$	14.5770	−	6.42437i	0.668134	−	0.294460i
$477$	0.603081			0.0276132
$478$	42.7533			1.95549
$479$		−	28.1264i		−	1.28513i	−0.766233	−	0.642563i	$-0.777871\pi$
$479$		−	28.1264i		−	1.28513i	0.766233	−	0.642563i	$-0.222129\pi$
$480$	4.68345			0.213769
$481$			22.4781i			1.02491i
$482$		−	51.7226i		−	2.35590i
$483$			50.3656i			2.29172i
$484$	−1.16253			−0.0528422
$485$	−2.69751			−0.122487
$486$		−	34.9803i		−	1.58674i
$487$		−	39.4051i		−	1.78562i	−0.450436	−	0.892809i	$-0.648731\pi$
$487$		−	39.4051i		−	1.78562i	0.450436	−	0.892809i	$-0.351269\pi$
$488$		−	1.11882i		−	0.0506468i
$489$	−30.2727			−1.36898
$490$			2.49103i			0.112533i
$491$	7.05382			0.318334			0.159167	−	0.987252i	$-0.449119\pi$
$491$	7.05382			0.318334			0.159167	+	0.987252i	$0.449119\pi$
$492$	−5.45307			−0.245843
$493$	−11.9759	+	5.27804i	−0.539369	+	0.237711i
$494$	−71.9389			−3.23668
$495$	−0.801864			−0.0360411
$496$			0.0358040i			0.00160765i
$497$	2.74637			0.123192
$498$		−	3.61424i		−	0.161958i
$499$			20.8539i			0.933549i	0.884376	+	0.466774i	$0.154584\pi$
$499$			20.8539i			0.933549i	−0.884376	+	0.466774i	$0.845416\pi$
$500$			3.97742i			0.177876i
$501$	−51.5497			−2.30307
$502$	−12.5330			−0.559374
$503$			22.7539i			1.01454i	0.861786	+	0.507272i	$0.169346\pi$
$503$			22.7539i			1.01454i	−0.861786	+	0.507272i	$0.830654\pi$
$504$			11.4613i			0.510527i
$505$			3.98983i			0.177545i
$506$	11.6894			0.519656
$507$		−	48.1206i		−	2.13711i
$508$	−0.723701			−0.0321090
$509$	23.9979			1.06369			0.531844	−	0.846842i	$-0.321499\pi$
$509$	23.9979			1.06369			0.531844	+	0.846842i	$0.321499\pi$
$510$	−2.36088	−	5.35686i	−0.104541	−	0.237206i
$511$	−48.7405			−2.15615
$512$	−14.3612			−0.634683
$513$			10.9677i			0.484237i
$514$	1.28721			0.0567763
$515$		−	2.71738i		−	0.119742i
$516$		−	10.0462i		−	0.442259i
$517$		−	10.2713i		−	0.451731i
$518$	22.8267			1.00295
$519$	17.8156			0.782020
$520$		−	3.00153i		−	0.131626i
$521$			22.2917i			0.976618i	0.872671	+	0.488309i	$0.162386\pi$
$521$			22.2917i			0.976618i	−0.872671	+	0.488309i	$0.837614\pi$
$522$			13.0710i			0.572104i
$523$	41.3854			1.80966			0.904829	−	0.425774i	$-0.139998\pi$
$523$	41.3854			1.80966			0.904829	+	0.425774i	$0.139998\pi$
$524$			14.8471i			0.648600i
$525$	−37.3927			−1.63195
$526$	−41.6373			−1.81547
$527$	0.0271607	−	0.0119703i	0.00118314	−	0.000521434i
$528$	11.4669			0.499032
$529$	−20.2065			−0.878542
$530$			0.160386i			0.00696674i
$531$	11.8302			0.513388
$532$			26.8545i			1.16429i
$533$			11.8407i			0.512879i
$534$			24.0227i			1.03956i
$535$	−6.42002			−0.277562
$536$	15.3330			0.662287
$537$		−	17.1151i		−	0.738570i
$538$		−	11.1002i		−	0.478565i
$539$			4.04506i			0.174233i
$540$	0.635228			0.0273358
$541$			20.2628i			0.871168i	0.900148	+	0.435584i	$0.143458\pi$
$541$			20.2628i			0.871168i	−0.900148	+	0.435584i	$0.856542\pi$
$542$	−6.20678			−0.266604
$543$	2.44879			0.105088
$544$	9.75428	+	22.1326i	0.418211	+	0.948926i
$545$	4.59613			0.196877
$546$	−79.3039			−3.39390
$547$		−	14.0816i		−	0.602087i	−0.953610	−	0.301044i	$-0.902665\pi$
$547$		−	14.0816i		−	0.602087i	0.953610	−	0.301044i	$-0.0973350\pi$
$548$	1.23420			0.0527226
$549$			1.73955i			0.0742423i
$550$			8.67850i			0.370052i
$551$		−	22.0627i		−	0.939903i
$552$	−22.5703			−0.960657
$553$	−45.0797			−1.91698
$554$			19.9099i			0.845889i
$555$		−	3.08358i		−	0.130891i
$556$			3.24996i			0.137829i
$557$	−14.2866			−0.605342			−0.302671	−	0.953095i	$-0.597878\pi$
$557$	−14.2866			−0.605342			−0.302671	+	0.953095i	$0.597878\pi$
$558$		−	0.0296444i		−	0.00125495i
$559$	−21.8142			−0.922644
$560$	−5.72389			−0.241878
$561$	−3.83371	−	8.69873i	−0.161859	−	0.367261i
$562$	−30.5276			−1.28773
$563$	−21.6040			−0.910502			−0.455251	−	0.890363i	$-0.650450\pi$
$563$	−21.6040			−0.910502			−0.455251	+	0.890363i	$0.650450\pi$
$564$		−	27.5299i		−	1.15922i
$565$	1.92057			0.0807989
$566$			18.4804i			0.776790i
$567$			35.1776i			1.47732i
$568$			1.23073i			0.0516402i
$569$	20.5733			0.862476			0.431238	−	0.902238i	$-0.358077\pi$
$569$	20.5733			0.862476			0.431238	+	0.902238i	$0.358077\pi$
$570$	9.86870			0.413354
$571$		−	6.06238i		−	0.253703i	−0.991922	−	0.126851i	$-0.959513\pi$
$571$		−	6.06238i		−	0.253703i	0.991922	−	0.126851i	$-0.0404871\pi$
$572$			6.76583i			0.282894i
$573$			26.3225i			1.09964i
$574$	12.0244			0.501888
$575$		−	32.0776i		−	1.33773i
$576$	1.12278			0.0467825
$577$	6.25693			0.260479			0.130240	−	0.991483i	$-0.458425\pi$
$577$	6.25693			0.260479			0.130240	+	0.991483i	$0.458425\pi$
$578$	20.3979	−	22.3136i	0.848440	−	0.928123i
$579$	29.1360			1.21085
$580$	−1.27782			−0.0530588
$581$			2.92960i			0.121540i
$582$	−31.9387			−1.32390
$583$			0.260443i			0.0107864i
$584$		−	21.8420i		−	0.903830i
$585$			4.66679i			0.192948i
$586$	14.2014			0.586654
$587$	20.5988			0.850204			0.425102	−	0.905145i	$-0.360238\pi$
$587$	20.5988			0.850204			0.425102	+	0.905145i	$0.360238\pi$
$588$			10.8419i			0.447111i
$589$			0.0500370i			0.00206174i
$590$			3.14619i			0.129527i
$591$	−40.1355			−1.65095
$592$			19.2093i			0.789496i
$593$	19.6674			0.807644			0.403822	−	0.914838i	$-0.367682\pi$
$593$	19.6674			0.807644			0.403822	+	0.914838i	$0.367682\pi$
$594$	2.80611			0.115136
$595$	1.91366	+	4.34212i	0.0784523	+	0.178009i
$596$	8.03413			0.329091
$597$	31.6237			1.29427
$598$		−	68.0314i		−	2.78201i
$599$	0.696103			0.0284420			0.0142210	−	0.999899i	$-0.495473\pi$
$599$	0.696103			0.0284420			0.0142210	+	0.999899i	$0.495473\pi$
$600$		−	16.7568i		−	0.684093i
$601$		−	38.2559i		−	1.56049i	−0.625474	−	0.780245i	$-0.715094\pi$
$601$		−	38.2559i		−	1.56049i	0.625474	−	0.780245i	$-0.284906\pi$
$602$			22.1525i			0.902870i
$603$	−23.8399			−0.970835
$604$	20.9561			0.852693
$605$		−	0.346288i		−	0.0140786i
$606$			47.2400i			1.91899i
$607$			12.1063i			0.491378i	0.969349	+	0.245689i	$0.0790142\pi$
$607$			12.1063i			0.491378i	−0.969349	+	0.245689i	$0.920986\pi$
$608$	−40.7738			−1.65360
$609$		−	24.3215i		−	0.985556i
$610$	−0.462625			−0.0187312
$611$	−59.7782			−2.41837
$612$	−4.47620	−	10.1565i	−0.180940	−	0.410554i
$613$	3.06547			0.123813			0.0619066	−	0.998082i	$-0.480282\pi$
$613$	3.06547			0.123813			0.0619066	+	0.998082i	$0.480282\pi$
$614$	−24.5880			−0.992291
$615$		−	1.62433i		−	0.0654994i
$616$	−4.94961			−0.199426
$617$			27.8086i			1.11953i	0.828651	+	0.559766i	$0.189109\pi$
$617$			27.8086i			1.11953i	−0.828651	+	0.559766i	$0.810891\pi$
$618$		−	32.1741i		−	1.29423i
$619$		−	30.1278i		−	1.21094i	−0.795869	−	0.605469i	$-0.792985\pi$
$619$		−	30.1278i		−	1.21094i	0.795869	−	0.605469i	$-0.207015\pi$
$620$	0.00289803			0.000116388
$621$	−10.3720			−0.416214
$622$		−	1.71824i		−	0.0688953i
$623$		−	19.4721i		−	0.780133i
$624$		−	66.7364i		−	2.67160i
$625$	23.2156			0.928626
$626$		−	29.7165i		−	1.18771i
$627$	16.0253			0.639987
$628$	8.25709			0.329494
$629$	14.5721	−	6.42220i	0.581026	−	0.256070i
$630$	4.73916			0.188813
$631$	9.25355			0.368378			0.184189	−	0.982891i	$-0.441034\pi$
$631$	9.25355			0.368378			0.184189	+	0.982891i	$0.441034\pi$
$632$		−	20.2015i		−	0.803573i
$633$	36.3136			1.44334
$634$		−	12.2266i		−	0.485581i
$635$		−	0.215572i		−	0.00855473i
$636$			0.698059i			0.0276798i
$637$	23.5419			0.932766
$638$	−5.64478			−0.223479
$639$		−	1.91354i		−	0.0756986i
$640$		−	3.76415i		−	0.148791i
$641$			32.7053i			1.29178i	0.763430	+	0.645891i	$0.223514\pi$
$641$			32.7053i			1.29178i	−0.763430	+	0.645891i	$0.776486\pi$
$642$	−76.0137			−3.00002
$643$		−	37.2584i		−	1.46933i	−0.678430	−	0.734665i	$-0.737339\pi$
$643$		−	37.2584i		−	1.46933i	0.678430	−	0.734665i	$-0.262661\pi$
$644$	−25.3958			−1.00073
$645$	2.99251			0.117830
$646$	20.5537	+	46.6365i	0.808673	+	1.83489i
$647$	−0.829047			−0.0325932			−0.0162966	−	0.999867i	$-0.505188\pi$
$647$	−0.829047			−0.0325932			−0.0162966	+	0.999867i	$0.505188\pi$
$648$	−15.7641			−0.619274
$649$			5.10893i			0.200543i
$650$	50.5082			1.98110
$651$			0.0551597i			0.00216188i
$652$		−	15.2644i		−	0.597799i
$653$			21.4375i			0.838914i	0.907775	+	0.419457i	$0.137780\pi$
$653$			21.4375i			0.838914i	−0.907775	+	0.419457i	$0.862220\pi$
$654$	54.4187			2.12794
$655$	−4.42259			−0.172805
$656$			10.1188i			0.395074i
$657$			33.9601i			1.32491i
$658$			60.7053i			2.36654i
$659$	12.2335			0.476549			0.238275	−	0.971198i	$-0.423418\pi$
$659$	12.2335			0.476549			0.238275	+	0.971198i	$0.423418\pi$
$660$		−	0.928148i		−	0.0361281i
$661$	16.7885			0.652998			0.326499	−	0.945198i	$-0.394131\pi$
$661$	16.7885			0.652998			0.326499	+	0.945198i	$0.394131\pi$
$662$	62.9097			2.44506
$663$	−50.6260	+	22.3119i	−1.96615	+	0.866522i
$664$	−1.31284			−0.0509480
$665$	−7.99928			−0.310199
$666$		−	15.9045i		−	0.616289i
$667$	20.8643			0.807870
$668$		−	25.9928i		−	1.00569i
$669$			7.97595i			0.308368i
$670$		−	6.34010i		−	0.244939i
$671$	−0.751233			−0.0290010
$672$	−44.9482			−1.73391
$673$			16.2101i			0.624853i	0.949942	+	0.312427i	$0.101142\pi$
$673$			16.2101i			0.624853i	−0.949942	+	0.312427i	$0.898858\pi$
$674$			50.2919i			1.93717i
$675$		−	7.70044i		−	0.296390i
$676$	24.2638			0.933222
$677$			3.99791i			0.153652i	0.997045	+	0.0768261i	$0.0244786\pi$
$677$			3.99791i			0.153652i	−0.997045	+	0.0768261i	$0.975521\pi$
$678$	22.7397			0.873314
$679$	25.8886			0.993513
$680$	−1.94583	+	0.857566i	−0.0746191	+	0.0328862i
$681$	22.0716			0.845785
$682$	0.0128020			0.000490215
$683$		−	39.8098i		−	1.52328i	−0.648000	−	0.761640i	$-0.724394\pi$
$683$		−	39.8098i		−	1.52328i	0.648000	−	0.761640i	$-0.275606\pi$
$684$	18.7109			0.715430
$685$			0.367639i			0.0140467i
$686$			17.4643i			0.666789i
$687$			44.5972i			1.70149i
$688$	−18.6420			−0.710719
$689$	1.51576			0.0577458
$690$			9.33266i			0.355288i
$691$		−	39.3447i		−	1.49674i	−0.663279	−	0.748372i	$-0.730836\pi$
$691$		−	39.3447i		−	1.49674i	0.663279	−	0.748372i	$-0.269164\pi$
$692$			8.98316i			0.341488i
$693$	7.69568			0.292335
$694$			21.9520i			0.833286i
$695$	−0.968082			−0.0367215
$696$	10.8992			0.413132
$697$	7.67611	−	3.38302i	0.290753	−	0.128141i
$698$	7.90360			0.299156
$699$	−0.250156			−0.00946178
$700$		−	18.8545i		−	0.712633i
$701$	11.3232			0.427671			0.213835	−	0.976870i	$-0.431404\pi$
$701$	11.3232			0.427671			0.213835	+	0.976870i	$0.431404\pi$
$702$		−	16.3314i		−	0.616388i
$703$			26.8454i			1.01249i
$704$			0.484877i			0.0182745i
$705$	8.20047			0.308848
$706$	18.7835			0.706925
$707$		−	38.2913i		−	1.44009i
$708$			13.6934i			0.514628i
$709$		−	13.3817i		−	0.502560i	−0.967915	−	0.251280i	$-0.919149\pi$
$709$		−	13.3817i		−	0.502560i	0.967915	−	0.251280i	$-0.0808514\pi$
$710$	0.508897			0.0190986
$711$			31.4094i			1.17794i
$712$	8.72602			0.327021
$713$	−0.0473191			−0.00177211
$714$	22.6579	+	51.4111i	0.847951	+	1.92401i
$715$	−2.01537			−0.0753706
$716$	8.62992			0.322515
$717$			55.4279i			2.06999i
$718$	−26.1477			−0.975823
$719$		−	21.4994i		−	0.801794i	−0.916123	−	0.400897i	$-0.868699\pi$
$719$		−	21.4994i		−	0.801794i	0.916123	−	0.400897i	$-0.131301\pi$
$720$			3.98814i			0.148629i
$721$			26.0794i			0.971246i
$722$	−52.1276			−1.93999
$723$	67.0562			2.49385
$724$			1.23475i			0.0458892i
$725$			15.4902i			0.575292i
$726$		−	4.10009i		−	0.152169i
$727$	−16.2252			−0.601761			−0.300880	−	0.953662i	$-0.597281\pi$
$727$	−16.2252			−0.601761			−0.300880	+	0.953662i	$0.597281\pi$
$728$			28.8064i			1.06764i
$729$	13.5961			0.503559
$730$	−9.03152			−0.334272
$731$	6.23254	+	14.1417i	0.230519	+	0.523050i
$732$	−2.01351			−0.0744215
$733$	−30.0698			−1.11065			−0.555327	−	0.831632i	$-0.687407\pi$
$733$	−30.0698			−1.11065			−0.555327	+	0.831632i	$0.687407\pi$
$734$		−	2.30152i		−	0.0849505i
$735$	−3.22952			−0.119123
$736$		−	38.5591i		−	1.42131i
$737$		−	10.2953i		−	0.379234i
$738$		−	8.37802i		−	0.308399i
$739$	26.3485			0.969247			0.484623	−	0.874723i	$-0.338957\pi$
$739$	26.3485			0.969247			0.484623	+	0.874723i	$0.338957\pi$
$740$	1.55483			0.0571566
$741$		−	93.2658i		−	3.42621i
$742$		−	1.53927i		−	0.0565082i
$743$			1.19251i			0.0437489i	0.999761	+	0.0218744i	$0.00696340\pi$
$743$			1.19251i			0.0437489i	−0.999761	+	0.0218744i	$0.993037\pi$
$744$	−0.0247187			−0.000906231
$745$			2.39317i			0.0876788i
$746$	49.0955			1.79751
$747$	2.04121			0.0746839
$748$	4.38615	−	1.93306i	0.160373	−	0.0706798i
$749$	61.6144			2.25134
$750$	−14.0279			−0.512225
$751$			34.2207i			1.24873i	0.781132	+	0.624366i	$0.214642\pi$
$751$			34.2207i			1.24873i	−0.781132	+	0.624366i	$0.785358\pi$
$752$	−51.0851			−1.86288
$753$		−	16.2485i		−	0.592128i
$754$			32.8522i			1.19641i
$755$			6.24231i			0.227181i
$756$	−6.09643			−0.221725
$757$	14.9850			0.544640			0.272320	−	0.962207i	$-0.412209\pi$
$757$	14.9850			0.544640			0.272320	+	0.962207i	$0.412209\pi$
$758$			15.3322i			0.556891i
$759$			15.1548i			0.550085i
$760$		−	3.58471i		−	0.130031i
$761$	36.5672			1.32556			0.662779	−	0.748815i	$-0.269377\pi$
$761$	36.5672			1.32556			0.662779	+	0.748815i	$0.269377\pi$
$762$		−	2.55240i		−	0.0924637i
$763$	−44.1102			−1.59690
$764$	−13.2726			−0.480184
$765$	3.02538	−	1.33335i	0.109383	−	0.0482073i
$766$	65.4995			2.36659
$767$	29.7336			1.07362
$768$		−	46.8038i		−	1.68889i
$769$	0.398031			0.0143534			0.00717669	−	0.999974i	$-0.497716\pi$
$769$	0.398031			0.0143534			0.00717669	+	0.999974i	$0.497716\pi$
$770$			2.04663i			0.0737553i
$771$			1.66881i			0.0601008i
$772$			14.6912i			0.528748i
$773$	40.2919			1.44920			0.724600	−	0.689170i	$-0.242025\pi$
$773$	40.2919			1.44920			0.724600	+	0.689170i	$0.242025\pi$
$774$	15.4349			0.554794
$775$		−	0.0351309i		−	0.00126194i
$776$			11.6014i			0.416467i
$777$			29.5938i			1.06167i
$778$	−68.8836			−2.46960
$779$			14.1413i			0.506666i
$780$	−5.40175			−0.193414
$781$	0.826371			0.0295699
$782$	−44.1033	+	19.4372i	−1.57713	+	0.695074i
$783$	5.00862			0.178993
$784$	20.1184			0.718516
$785$			2.45958i			0.0877863i
$786$	−52.3640			−1.86776
$787$		−	4.32673i		−	0.154231i	−0.997022	−	0.0771156i	$-0.975429\pi$
$787$		−	4.32673i		−	0.154231i	0.997022	−	0.0771156i	$-0.0245710\pi$
$788$		−	20.2374i		−	0.720929i
$789$		−	53.9810i		−	1.92177i
$790$	−8.35317			−0.297193
$791$	−18.4322			−0.655372
$792$			3.44866i			0.122543i
$793$			4.37212i			0.155259i
$794$		−	9.66045i		−	0.342836i
$795$	−0.207934			−0.00737467
$796$			15.9456i			0.565175i
$797$	−39.5613			−1.40133			−0.700667	−	0.713489i	$-0.747114\pi$
$797$	−39.5613			−1.40133			−0.700667	+	0.713489i	$0.747114\pi$
$798$	−94.7123			−3.35278
$799$	17.0792	+	38.7529i	0.604219	+	1.37098i
$800$	28.6273			1.01213
$801$	−13.5672			−0.479375
$802$		−	46.1569i		−	1.62986i
$803$	−14.6658			−0.517545
$804$		−	27.5944i		−	0.973179i
$805$		−	7.56478i		−	0.266623i
$806$		−	0.0745069i		−	0.00262440i
$807$	14.3910			0.506587
$808$	17.1595			0.603668
$809$		−	7.54254i		−	0.265182i	−0.991171	−	0.132591i	$-0.957670\pi$
$809$		−	7.54254i		−	0.265182i	0.991171	−	0.132591i	$-0.0423296\pi$
$810$			6.51835i			0.229031i
$811$			35.6699i			1.25254i	0.779607	+	0.626269i	$0.215419\pi$
$811$			35.6699i			1.25254i	−0.779607	+	0.626269i	$0.784581\pi$
$812$	12.2636			0.430367
$813$		−	8.04684i		−	0.282215i
$814$	6.86845			0.240739
$815$	4.54688			0.159270
$816$	−43.2639	+	19.0673i	−1.51454	+	0.667488i
$817$	−26.0526			−0.911466
$818$	41.3311			1.44511
$819$		−	44.7883i		−	1.56503i
$820$	0.819035			0.0286019
$821$			44.2588i			1.54464i	0.635231	+	0.772322i	$0.280905\pi$
$821$			44.2588i			1.54464i	−0.635231	+	0.772322i	$0.719095\pi$
$822$			4.35288i			0.151824i
$823$			27.2097i			0.948471i	0.880398	+	0.474235i	$0.157275\pi$
$823$			27.2097i			0.948471i	−0.880398	+	0.474235i	$0.842725\pi$
$824$	−11.6869			−0.407133
$825$	−11.2513			−0.391721
$826$		−	30.1948i		−	1.05061i
$827$			19.3246i			0.671983i	0.941865	+	0.335991i	$0.109071\pi$
$827$			19.3246i			0.671983i	−0.941865	+	0.335991i	$0.890929\pi$
$828$			17.6946i			0.614930i
$829$	−15.1716			−0.526932			−0.263466	−	0.964669i	$-0.584866\pi$
$829$	−15.1716			−0.526932			−0.263466	+	0.964669i	$0.584866\pi$
$830$			0.542849i			0.0188426i
$831$	−25.8123			−0.895420
$832$	2.82195			0.0978335
$833$	−6.72616	−	15.2618i	−0.233048	−	0.528788i
$834$	−11.4622			−0.396903
$835$	7.74261			0.267944
$836$			8.08039i			0.279466i
$837$	−0.0113593			−0.000392633
$838$		−	40.1407i		−	1.38664i
$839$		−	22.7804i		−	0.786467i	−0.919439	−	0.393234i	$-0.871356\pi$
$839$		−	22.7804i		−	0.786467i	0.919439	−	0.393234i	$-0.128644\pi$
$840$		−	3.95171i		−	0.136347i
$841$	18.9247			0.652575
$842$	32.8235			1.13117
$843$		−	39.5778i		−	1.36313i
$844$			18.3104i			0.630269i
$845$			7.22757i			0.248636i
$846$	42.2966			1.45419
$847$			3.32341i			0.114194i
$848$	1.29533			0.0444820
$849$	−23.9591			−0.822274
$850$	−14.4307	−	32.7434i	−0.494969	−	1.12309i
$851$	−25.3872			−0.870264
$852$	2.21490			0.0758813
$853$		−	45.8353i		−	1.56937i	−0.619895	−	0.784685i	$-0.712825\pi$
$853$		−	45.8353i		−	1.56937i	0.619895	−	0.784685i	$-0.287175\pi$
$854$	4.43993			0.151931
$855$			5.57352i			0.190610i
$856$			27.6112i			0.943733i
$857$		−	31.2582i		−	1.06776i	−0.845561	−	0.533879i	$-0.820734\pi$
$857$		−	31.2582i		−	1.06776i	0.845561	−	0.533879i	$-0.179266\pi$
$858$	−23.8622			−0.814643
$859$	−5.81247			−0.198319			−0.0991594	−	0.995072i	$-0.531615\pi$
$859$	−5.81247			−0.198319			−0.0991594	+	0.995072i	$0.531615\pi$
$860$			1.50891i			0.0514534i
$861$			15.5891i			0.531275i
$862$			52.2019i			1.77800i
$863$	27.7222			0.943675			0.471838	−	0.881686i	$-0.343591\pi$
$863$	27.7222			0.943675			0.471838	+	0.881686i	$0.343591\pi$
$864$		−	9.25636i		−	0.314908i
$865$	−2.67586			−0.0909819
$866$	−31.5262			−1.07130
$867$	28.9287	+	26.4450i	0.982469	+	0.898120i
$868$	−0.0278131			−0.000944038
$869$	−13.5643			−0.460137
$870$		−	4.50672i		−	0.152792i
$871$	−59.9182			−2.03025
$872$		−	19.7671i		−	0.669397i
$873$		−	18.0380i		−	0.610493i
$874$		−	81.2495i		−	2.74830i
$875$	11.3706			0.384395
$876$	−39.3084			−1.32811
$877$		−	15.6661i		−	0.529005i	−0.964385	−	0.264502i	$-0.914792\pi$
$877$		−	15.6661i		−	0.529005i	0.964385	−	0.264502i	$-0.0852077\pi$
$878$		−	62.2019i		−	2.09921i
$879$			18.4115i			0.621005i
$880$	−1.72229			−0.0580585
$881$			7.72022i			0.260101i	0.991507	+	0.130050i	$0.0415139\pi$
$881$			7.72022i			0.260101i	−0.991507	+	0.130050i	$0.958486\pi$
$882$	−16.6573			−0.560881
$883$	24.7648			0.833401			0.416701	−	0.909044i	$-0.363186\pi$
$883$	24.7648			0.833401			0.416701	+	0.909044i	$0.363186\pi$
$884$	−11.2503	−	25.5271i	−0.378388	−	0.858568i
$885$	−4.07891			−0.137111
$886$	45.0795			1.51447
$887$			19.1823i			0.644078i	0.946726	+	0.322039i	$0.104368\pi$
$887$			19.1823i			0.644078i	−0.946726	+	0.322039i	$0.895632\pi$
$888$	−13.2619			−0.445039
$889$			2.06890i			0.0693887i
$890$		−	3.60814i		−	0.120945i
$891$			10.5848i			0.354604i
$892$	−4.02170			−0.134657
$893$	−71.3927			−2.38907
$894$			28.3353i			0.947675i
$895$			2.57064i			0.0859269i
$896$			36.1255i			1.20687i
$897$	88.1999			2.94491
$898$		−	53.9722i		−	1.80108i
$899$	0.0228503			0.000762100
$900$	−13.1369			−0.437898
$901$	−0.433067	−	0.982635i	−0.0144276	−	0.0327363i
$902$	3.61808			0.120469
$903$	−28.7199			−0.955737
$904$		−	8.25999i		−	0.274723i
$905$	−0.367802			−0.0122261
$906$			73.9096i			2.45548i
$907$		−	16.8943i		−	0.560965i	−0.959859	−	0.280483i	$-0.909505\pi$
$907$		−	16.8943i		−	0.560965i	0.959859	−	0.280483i	$-0.0904945\pi$
$908$			11.1291i			0.369333i
$909$	−26.6796			−0.884907
$910$	11.9112			0.394853
$911$			13.3934i			0.443742i	0.975076	+	0.221871i	$0.0712163\pi$
$911$			13.3934i			0.443742i	−0.975076	+	0.221871i	$0.928784\pi$
$912$		−	79.7030i		−	2.63923i
$913$			0.881504i			0.0291735i
$914$	−31.1893			−1.03165
$915$		−	0.599775i		−	0.0198279i
$916$	−22.4872			−0.742998
$917$	42.4447			1.40165
$918$	−10.5873	+	4.66604i	−0.349433	+	0.154002i
$919$	21.8339			0.720234			0.360117	−	0.932907i	$-0.382737\pi$
$919$	21.8339			0.720234			0.360117	+	0.932907i	$0.382737\pi$
$920$	3.39000			0.111765
$921$		−	31.8773i		−	1.05039i
$922$	−21.3911			−0.704478
$923$		−	4.80942i		−	0.158304i
$924$			8.90766i			0.293040i
$925$		−	18.8481i		−	0.619723i
$926$	−12.1651			−0.399772
$927$	18.1709			0.596810
$928$			18.6201i			0.611235i
$929$		−	32.8378i		−	1.07737i	−0.842506	−	0.538687i	$-0.818921\pi$
$929$		−	32.8378i		−	1.07737i	0.842506	−	0.538687i	$-0.181079\pi$
$930$			0.0102210i			0.000335159i
$931$	28.1160			0.921465
$932$		−	0.126136i		−	0.00413172i
$933$	2.22763			0.0729294
$934$	−5.74259			−0.187903
$935$	0.575812	+	1.30652i	0.0188311	+	0.0427279i
$936$	20.0709			0.656039
$937$	14.5017			0.473750			0.236875	−	0.971540i	$-0.423877\pi$
$937$	14.5017			0.473750			0.236875	+	0.971540i	$0.423877\pi$
$938$			60.8474i			1.98674i
$939$	38.5262			1.25726
$940$			4.13491i			0.134866i
$941$		−	52.6510i		−	1.71637i	−0.513339	−	0.858186i	$-0.671592\pi$
$941$		−	52.6510i		−	1.71637i	0.513339	−	0.858186i	$-0.328408\pi$
$942$			29.1217i			0.948837i
$943$	−13.3732			−0.435492
$944$	25.4097			0.827016
$945$		−	1.81597i		−	0.0590737i
$946$			6.66561i			0.216718i
$947$		−	9.64153i		−	0.313308i	−0.987654	−	0.156654i	$-0.949929\pi$
$947$		−	9.64153i		−	0.313308i	0.987654	−	0.156654i	$-0.0500707\pi$
$948$	−36.3560			−1.18079
$949$			85.3539i			2.77071i
$950$	60.3217			1.95709
$951$	15.8513			0.514013
$952$	18.6746	−	8.23027i	0.605247	−	0.266745i
$953$	15.9320			0.516088			0.258044	−	0.966133i	$-0.416922\pi$
$953$	15.9320			0.516088			0.258044	+	0.966133i	$0.416922\pi$
$954$	−1.07249			−0.0347231
$955$		−	3.95356i		−	0.127934i
$956$	−27.9483			−0.903914
$957$		−	7.31823i		−	0.236565i
$958$			50.0185i			1.61602i
$959$		−	3.52832i		−	0.113935i
$960$	−0.387120			−0.0124942
$961$	30.9999			0.999998
$962$		−	39.9739i		−	1.28881i
$963$		−	42.9301i		−	1.38340i
$964$			33.8117i			1.08900i
$965$	−4.37614			−0.140873
$966$		−	89.5677i		−	2.88179i
$967$	−49.7323			−1.59928			−0.799642	−	0.600477i	$-0.794977\pi$
$967$	−49.7323			−1.59928			−0.799642	+	0.600477i	$0.794977\pi$
$968$	−1.48932			−0.0478685
$969$	−60.4623	+	26.6470i	−1.94233	+	0.856024i
$970$	4.79711			0.154026
$971$	−44.1383			−1.41647			−0.708233	−	0.705979i	$-0.750507\pi$
$971$	−44.1383			−1.41647			−0.708233	+	0.705979i	$0.750507\pi$
$972$			22.8670i			0.733460i
$973$	9.29092			0.297853
$974$			70.0761i			2.24538i
$975$			65.4818i			2.09710i
$976$			3.73632i			0.119597i
$977$	−9.01649			−0.288463			−0.144232	−	0.989544i	$-0.546071\pi$
$977$	−9.01649			−0.288463			−0.144232	+	0.989544i	$0.546071\pi$
$978$	53.8355			1.72147
$979$		−	5.85907i		−	0.187257i
$980$		−	1.62842i		−	0.0520179i
$981$			30.7339i			0.981258i
$982$	−12.5442			−0.400300
$983$			2.69659i			0.0860077i	0.999075	+	0.0430039i	$0.0136928\pi$
$983$			2.69659i			0.0860077i	−0.999075	+	0.0430039i	$0.986307\pi$
$984$	−6.98594			−0.222704
$985$	6.02823			0.192075
$986$	21.2974	−	9.38620i	0.678248	−	0.298918i
$987$	−78.7019			−2.50511
$988$	47.0273			1.49614
$989$		−	24.6375i		−	0.783427i
$990$	1.42599			0.0453211
$991$			17.3936i			0.552526i	0.961082	+	0.276263i	$0.0890961\pi$
$991$			17.3936i			0.552526i	−0.961082	+	0.276263i	$0.910904\pi$
$992$		−	0.0422293i		−	0.00134078i
$993$			81.5599i			2.58822i
$994$	−4.88401			−0.154911
$995$	−4.74978			−0.150578
$996$			2.36267i			0.0748642i
$997$			13.2814i			0.420627i	0.977634	+	0.210313i	$0.0674484\pi$
$997$			13.2814i			0.420627i	−0.977634	+	0.210313i	$0.932552\pi$
$998$		−	37.0855i		−	1.17392i
$999$	−6.09438			−0.192818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.d.a.67.3	✓	16
3.2	odd	2		1683.2.g.b.1189.13		16
4.3	odd	2		2992.2.b.g.1937.13		16
17.4	even	4		3179.2.a.bc.1.7		8
17.13	even	4		3179.2.a.bb.1.7		8
17.16	even	2	inner	187.2.d.a.67.4	yes	16
51.50	odd	2		1683.2.g.b.1189.14		16
68.67	odd	2		2992.2.b.g.1937.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.d.a.67.3	✓	16	1.1	even	1	trivial
187.2.d.a.67.4	yes	16	17.16	even	2	inner
1683.2.g.b.1189.13		16	3.2	odd	2
1683.2.g.b.1189.14		16	51.50	odd	2
2992.2.b.g.1937.4		16	68.67	odd	2
2992.2.b.g.1937.13		16	4.3	odd	2
3179.2.a.bb.1.7		8	17.13	even	4
3179.2.a.bc.1.7		8	17.4	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.77835 q^{2} -2.30556i q^{3} +1.16253 q^{4} +0.346288i q^{5} +4.10009i q^{6} -3.32341i q^{7} +1.48932 q^{8} -2.31560 q^{9} +O(q^{10})\)	\(q-1.77835 q^{2} -2.30556i q^{3} +1.16253 q^{4} +0.346288i q^{5} +4.10009i q^{6} -3.32341i q^{7} +1.48932 q^{8} -2.31560 q^{9} -0.615822i q^{10} -1.00000i q^{11} -2.68028i q^{12} -5.81993 q^{13} +5.91019i q^{14} +0.798387 q^{15} -4.97358 q^{16} +(1.66281 + 3.77294i) q^{17} +4.11794 q^{18} -6.95071 q^{19} +0.402570i q^{20} -7.66232 q^{21} +1.77835i q^{22} -6.57316i q^{23} -3.43371i q^{24} +4.88008 q^{25} +10.3499 q^{26} -1.57793i q^{27} -3.86356i q^{28} +3.17417i q^{29} -1.41981 q^{30} -0.00719883i q^{31} +5.86614 q^{32} -2.30556 q^{33} +(-2.95706 - 6.70960i) q^{34} +1.15086 q^{35} -2.69195 q^{36} -3.86226i q^{37} +12.3608 q^{38} +13.4182i q^{39} +0.515733i q^{40} -2.03452i q^{41} +13.6263 q^{42} +3.74820 q^{43} -1.16253i q^{44} -0.801864i q^{45} +11.6894i q^{46} +10.2713 q^{47} +11.4669i q^{48} -4.04506 q^{49} -8.67850 q^{50} +(8.69873 - 3.83371i) q^{51} -6.76583 q^{52} -0.260443 q^{53} +2.80611i q^{54} +0.346288 q^{55} -4.94961i q^{56} +16.0253i q^{57} -5.64478i q^{58} -5.10893 q^{59} +0.928148 q^{60} -0.751233i q^{61} +0.0128020i q^{62} +7.69568i q^{63} -0.484877 q^{64} -2.01537i q^{65} +4.10009 q^{66} +10.2953 q^{67} +(1.93306 + 4.38615i) q^{68} -15.1548 q^{69} -2.04663 q^{70} +0.826371i q^{71} -3.44866 q^{72} -14.6658i q^{73} +6.86845i q^{74} -11.2513i q^{75} -8.08039 q^{76} -3.32341 q^{77} -23.8622i q^{78} -13.5643i q^{79} -1.72229i q^{80} -10.5848 q^{81} +3.61808i q^{82} -0.881504 q^{83} -8.90766 q^{84} +(-1.30652 + 0.575812i) q^{85} -6.66561 q^{86} +7.31823 q^{87} -1.48932i q^{88} +5.85907 q^{89} +1.42599i q^{90} +19.3420i q^{91} -7.64149i q^{92} -0.0165973 q^{93} -18.2660 q^{94} -2.40695i q^{95} -13.5247i q^{96} +7.78977i q^{97} +7.19353 q^{98} +2.31560i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 10 * q^4 - 6 * q^8 - 20 * q^9	\( 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9} - 16 q^{13} + 4 q^{15} + 6 q^{16} + 4 q^{17} - 10 q^{18} + 20 q^{19} + 12 q^{21} + 4 q^{25} - 12 q^{26} + 28 q^{30} - 34 q^{32} + 4 q^{33} - 6 q^{34} + 12 q^{35} - 18 q^{36} + 8 q^{43} + 14 q^{47} - 42 q^{49} - 34 q^{50} - 18 q^{51} - 44 q^{52} + 26 q^{53} + 8 q^{55} - 30 q^{59} + 72 q^{60} - 10 q^{64} - 8 q^{66} + 10 q^{67} + 22 q^{68} + 4 q^{69} - 8 q^{70} - 46 q^{72} + 36 q^{76} - 10 q^{77} - 8 q^{81} - 8 q^{83} + 92 q^{84} - 2 q^{85} + 56 q^{86} + 8 q^{87} + 10 q^{89} - 20 q^{93} + 8 q^{94} + 38 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 + 10 * q^4 - 6 * q^8 - 20 * q^9 - 16 * q^13 + 4 * q^15 + 6 * q^16 + 4 * q^17 - 10 * q^18 + 20 * q^19 + 12 * q^21 + 4 * q^25 - 12 * q^26 + 28 * q^30 - 34 * q^32 + 4 * q^33 - 6 * q^34 + 12 * q^35 - 18 * q^36 + 8 * q^43 + 14 * q^47 - 42 * q^49 - 34 * q^50 - 18 * q^51 - 44 * q^52 + 26 * q^53 + 8 * q^55 - 30 * q^59 + 72 * q^60 - 10 * q^64 - 8 * q^66 + 10 * q^67 + 22 * q^68 + 4 * q^69 - 8 * q^70 - 46 * q^72 + 36 * q^76 - 10 * q^77 - 8 * q^81 - 8 * q^83 + 92 * q^84 - 2 * q^85 + 56 * q^86 + 8 * q^87 + 10 * q^89 - 20 * q^93 + 8 * q^94 + 38 * q^98

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