LMFDB - Embedded newform 138.2.e.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(13,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.e (of order $11$, degree $10$, 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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			49.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	138.49
Dual form			138.2.e.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.69894 - 1.96068i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-1.04019 + 0.668491i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.69894 - 1.96068i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-1.04019 + 0.668491i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-2.18251 - 1.40261i) q^{10} +(0.0886578 - 0.616629i) q^{11} +(-0.142315 + 0.989821i) q^{12} +(-1.11435 - 0.716152i) q^{13} +(0.809721 + 0.934468i) q^{14} +(-1.07773 - 2.35990i) q^{15} +(0.841254 - 0.540641i) q^{16} +(4.51691 + 1.32628i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(-3.63667 + 1.06782i) q^{19} +(-1.07773 + 2.35990i) q^{20} +(0.175969 + 1.22389i) q^{21} -0.622970 q^{22} +(3.35197 + 3.42992i) q^{23} +1.00000 q^{24} +(-0.246298 - 1.71304i) q^{25} +(-0.550273 + 1.20493i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(0.809721 - 0.934468i) q^{28} +(1.06699 + 0.313298i) q^{29} +(-2.18251 + 1.40261i) q^{30} +(3.92849 + 8.60219i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-0.524075 - 0.336803i) q^{33} +(0.669961 - 4.65968i) q^{34} +(-0.456526 + 3.17521i) q^{35} +(0.841254 + 0.540641i) q^{36} +(1.06560 + 1.22977i) q^{37} +(1.57450 + 3.44768i) q^{38} +(-1.11435 + 0.716152i) q^{39} +(2.48926 + 0.730913i) q^{40} +(7.75992 - 8.95543i) q^{41} +(1.18639 - 0.348356i) q^{42} +(-0.697393 + 1.52708i) q^{43} +(0.0886578 + 0.616629i) q^{44} -2.59435 q^{45} +(2.91797 - 3.80598i) q^{46} -6.94494 q^{47} +(-0.142315 - 0.989821i) q^{48} +(-2.27279 + 4.97671i) q^{49} +(-1.66055 + 0.487583i) q^{50} +(3.08282 - 3.55777i) q^{51} +(1.27098 + 0.373193i) q^{52} +(-9.46721 + 6.08421i) q^{53} +(0.415415 + 0.909632i) q^{54} +(-1.05839 - 1.22144i) q^{55} +(-1.04019 - 0.668491i) q^{56} +(-0.539401 + 3.75162i) q^{57} +(0.158260 - 1.10072i) q^{58} +(-8.19910 - 5.26924i) q^{59} +(1.69894 + 1.96068i) q^{60} +(-5.97099 - 13.0746i) q^{61} +(7.95555 - 5.11272i) q^{62} +(1.18639 + 0.348356i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-3.29736 + 0.968193i) q^{65} +(-0.258791 + 0.566673i) q^{66} +(0.871145 + 6.05895i) q^{67} -4.70760 q^{68} +(4.51242 - 1.62422i) q^{69} +3.20786 q^{70} +(-0.923986 - 6.42646i) q^{71} +(0.415415 - 0.909632i) q^{72} +(12.5598 - 3.68788i) q^{73} +(1.06560 - 1.22977i) q^{74} +(-1.66055 - 0.487583i) q^{75} +(3.18852 - 2.04913i) q^{76} +(0.319990 + 0.700679i) q^{77} +(0.867451 + 1.00109i) q^{78} +(-10.1643 - 6.53221i) q^{79} +(0.369215 - 2.56794i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-9.96863 - 6.40645i) q^{82} +(-4.83987 - 5.58551i) q^{83} +(-0.513652 - 1.12474i) q^{84} +(10.2744 - 6.60294i) q^{85} +(1.61078 + 0.472968i) q^{86} +(0.728231 - 0.840423i) q^{87} +(0.597735 - 0.175511i) q^{88} +(1.40618 - 3.07910i) q^{89} +(0.369215 + 2.56794i) q^{90} +1.63788 q^{91} +(-4.18251 - 2.34662i) q^{92} +9.45679 q^{93} +(0.988368 + 6.87425i) q^{94} +(-4.08482 + 8.94450i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(-7.49539 + 8.65015i) q^{97} +(5.24950 + 1.54139i) q^{98} +(-0.524075 + 0.336803i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{3} - q^{4} + 8 q^{5} - q^{6} + 8 q^{7} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 - q^3 - q^4 + 8 * q^5 - q^6 + 8 * q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} + 8 q^{5} - q^{6} + 8 q^{7} - q^{8} - q^{9} - 3 q^{10} + 7 q^{11} - q^{12} + 3 q^{13} - 3 q^{14} - 3 q^{15} - q^{16} + 4 q^{17} - q^{18} - 3 q^{20} - 3 q^{21} - 26 q^{22} - 12 q^{23} + 10 q^{24} - 15 q^{25} + 3 q^{26} - q^{27} - 3 q^{28} - 25 q^{29} - 3 q^{30} + 6 q^{31} - q^{32} - 4 q^{33} - 7 q^{34} + 2 q^{35} - q^{36} + 9 q^{37} + 11 q^{38} + 3 q^{39} - 3 q^{40} + 24 q^{41} + 8 q^{42} - 30 q^{43} + 7 q^{44} - 14 q^{45} + 21 q^{46} - 48 q^{47} - q^{48} + 9 q^{49} + 7 q^{50} + 15 q^{51} + 14 q^{52} + 15 q^{53} - q^{54} - 23 q^{55} + 8 q^{56} - 11 q^{57} - 3 q^{58} + 5 q^{59} + 8 q^{60} + 12 q^{61} + 28 q^{62} + 8 q^{63} - q^{64} - 13 q^{65} + 18 q^{66} + 18 q^{67} - 18 q^{68} - q^{69} + 2 q^{70} + 28 q^{71} - q^{72} + 19 q^{73} + 9 q^{74} + 7 q^{75} + 22 q^{76} - 12 q^{77} - 8 q^{78} - 52 q^{79} + 8 q^{80} - q^{81} - 20 q^{82} + 7 q^{83} - 3 q^{84} + 23 q^{85} + 14 q^{86} + 30 q^{87} - 4 q^{88} + 3 q^{89} + 8 q^{90} + 42 q^{91} - 23 q^{92} - 16 q^{93} + 29 q^{94} + 22 q^{95} - q^{96} + 51 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 + 8 * q^5 - q^6 + 8 * q^7 - q^8 - q^9 - 3 * q^10 + 7 * q^11 - q^12 + 3 * q^13 - 3 * q^14 - 3 * q^15 - q^16 + 4 * q^17 - q^18 - 3 * q^20 - 3 * q^21 - 26 * q^22 - 12 * q^23 + 10 * q^24 - 15 * q^25 + 3 * q^26 - q^27 - 3 * q^28 - 25 * q^29 - 3 * q^30 + 6 * q^31 - q^32 - 4 * q^33 - 7 * q^34 + 2 * q^35 - q^36 + 9 * q^37 + 11 * q^38 + 3 * q^39 - 3 * q^40 + 24 * q^41 + 8 * q^42 - 30 * q^43 + 7 * q^44 - 14 * q^45 + 21 * q^46 - 48 * q^47 - q^48 + 9 * q^49 + 7 * q^50 + 15 * q^51 + 14 * q^52 + 15 * q^53 - q^54 - 23 * q^55 + 8 * q^56 - 11 * q^57 - 3 * q^58 + 5 * q^59 + 8 * q^60 + 12 * q^61 + 28 * q^62 + 8 * q^63 - q^64 - 13 * q^65 + 18 * q^66 + 18 * q^67 - 18 * q^68 - q^69 + 2 * q^70 + 28 * q^71 - q^72 + 19 * q^73 + 9 * q^74 + 7 * q^75 + 22 * q^76 - 12 * q^77 - 8 * q^78 - 52 * q^79 + 8 * q^80 - q^81 - 20 * q^82 + 7 * q^83 - 3 * q^84 + 23 * q^85 + 14 * q^86 + 30 * q^87 - 4 * q^88 + 3 * q^89 + 8 * q^90 + 42 * q^91 - 23 * q^92 - 16 * q^93 + 29 * q^94 + 22 * q^95 - q^96 + 51 * q^97 - 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	1.69894	−	1.96068i	0.759788	−	0.876843i	−0.235690	−	0.971828i	$-0.575735\pi$
$5$	1.69894	−	1.96068i	0.759788	−	0.876843i	0.995479	+	0.0949856i	$0.0302805\pi$
$6$	−0.959493	−	0.281733i	−0.391711	−	0.115017i
$7$	−1.04019	+	0.668491i	−0.393156	+	0.252666i	−0.722251	−	0.691631i	$-0.756893\pi$
$7$	−1.04019	+	0.668491i	−0.393156	+	0.252666i	0.329096	+	0.944297i	$0.393256\pi$
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	−2.18251	−	1.40261i	−0.690169	−	0.443545i
$11$	0.0886578	−	0.616629i	0.0267313	−	0.185921i	−0.972081	−	0.234646i	$-0.924607\pi$
$11$	0.0886578	−	0.616629i	0.0267313	−	0.185921i	0.998812	+	0.0487255i	$0.0155160\pi$
$12$	−0.142315	+	0.989821i	−0.0410828	+	0.285737i
$13$	−1.11435	−	0.716152i	−0.309066	−	0.198625i	0.376908	−	0.926251i	$-0.376987\pi$
$13$	−1.11435	−	0.716152i	−0.309066	−	0.198625i	−0.685974	+	0.727626i	$0.740624\pi$
$14$	0.809721	+	0.934468i	0.216407	+	0.249747i
$15$	−1.07773	−	2.35990i	−0.278269	−	0.609325i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	4.51691	+	1.32628i	1.09551	+	0.321671i	0.779067	−	0.626940i	$-0.215693\pi$
$17$	4.51691	+	1.32628i	1.09551	+	0.321671i	0.316444	+	0.948611i	$0.397511\pi$
$18$	−0.654861	+	0.755750i	−0.154352	+	0.178132i
$19$	−3.63667	+	1.06782i	−0.834308	+	0.244975i	−0.670867	−	0.741578i	$-0.734078\pi$
$19$	−3.63667	+	1.06782i	−0.834308	+	0.244975i	−0.163442	+	0.986553i	$0.552260\pi$
$20$	−1.07773	+	2.35990i	−0.240988	+	0.527691i
$21$	0.175969	+	1.22389i	0.0383996	+	0.267075i
$22$	−0.622970			−0.132818
$23$	3.35197	+	3.42992i	0.698933	+	0.715187i
$23$	3.35197	+	3.42992i	0.698933	+	0.715187i
$24$	1.00000			0.204124
$25$	−0.246298	−	1.71304i	−0.0492597	−	0.342608i
$26$	−0.550273	+	1.20493i	−0.107917	+	0.236306i
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$	0.809721	−	0.934468i	0.153023	−	0.176598i
$29$	1.06699	+	0.313298i	0.198136	+	0.0581779i	0.379295	−	0.925276i	$-0.376167\pi$
$29$	1.06699	+	0.313298i	0.198136	+	0.0581779i	−0.181159	+	0.983454i	$0.557985\pi$
$30$	−2.18251	+	1.40261i	−0.398469	+	0.256081i
$31$	3.92849	+	8.60219i	0.705578	+	1.54500i	0.833075	+	0.553161i	$0.186578\pi$
$31$	3.92849	+	8.60219i	0.705578	+	1.54500i	−0.127497	+	0.991839i	$0.540694\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	−0.524075	−	0.336803i	−0.0912298	−	0.0586298i
$34$	0.669961	−	4.65968i	0.114897	−	0.799129i
$35$	−0.456526	+	3.17521i	−0.0771670	+	0.536708i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	1.06560	+	1.22977i	0.175183	+	0.202172i	0.836550	−	0.547890i	$-0.184569\pi$
$37$	1.06560	+	1.22977i	0.175183	+	0.202172i	−0.661367	+	0.750063i	$0.730023\pi$
$38$	1.57450	+	3.44768i	0.255418	+	0.559288i
$39$	−1.11435	+	0.716152i	−0.178439	+	0.114676i
$40$	2.48926	+	0.730913i	0.393587	+	0.115568i
$41$	7.75992	−	8.95543i	1.21190	−	1.39860i	0.319357	−	0.947635i	$-0.396533\pi$
$41$	7.75992	−	8.95543i	1.21190	−	1.39860i	0.892540	−	0.450969i	$-0.148921\pi$
$42$	1.18639	−	0.348356i	0.183064	−	0.0537526i
$43$	−0.697393	+	1.52708i	−0.106351	+	0.232877i	−0.955324	−	0.295559i	$-0.904494\pi$
$43$	−0.697393	+	1.52708i	−0.106351	+	0.232877i	0.848973	+	0.528436i	$0.177221\pi$
$44$	0.0886578	+	0.616629i	0.0133657	+	0.0929603i
$45$	−2.59435			−0.386743
$46$	2.91797	−	3.80598i	0.430231	−	0.561161i
$47$	−6.94494			−1.01302			−0.506512	−	0.862233i	$-0.669065\pi$
$47$	−6.94494			−1.01302			−0.506512	+	0.862233i	$0.669065\pi$
$48$	−0.142315	−	0.989821i	−0.0205414	−	0.142868i
$49$	−2.27279	+	4.97671i	−0.324684	+	0.710958i
$50$	−1.66055	+	0.487583i	−0.234838	+	0.0689546i
$51$	3.08282	−	3.55777i	0.431681	−	0.498187i
$52$	1.27098	+	0.373193i	0.176253	+	0.0517525i
$53$	−9.46721	+	6.08421i	−1.30042	+	0.835730i	−0.993258	−	0.115927i	$-0.963016\pi$
$53$	−9.46721	+	6.08421i	−1.30042	+	0.835730i	−0.307163	+	0.951657i	$0.599380\pi$
$54$	0.415415	+	0.909632i	0.0565308	+	0.123785i
$55$	−1.05839	−	1.22144i	−0.142713	−	0.164699i
$56$	−1.04019	−	0.668491i	−0.139002	−	0.0893309i
$57$	−0.539401	+	3.75162i	−0.0714454	+	0.496914i
$58$	0.158260	−	1.10072i	0.0207805	−	0.144532i
$59$	−8.19910	−	5.26924i	−1.06743	−	0.685997i	−0.115811	−	0.993271i	$-0.536947\pi$
$59$	−8.19910	−	5.26924i	−1.06743	−	0.685997i	−0.951621	+	0.307274i	$0.900583\pi$
$60$	1.69894	+	1.96068i	0.219332	+	0.253123i
$61$	−5.97099	−	13.0746i	−0.764507	−	1.67404i	−0.738386	−	0.674379i	$-0.764412\pi$
$61$	−5.97099	−	13.0746i	−0.764507	−	1.67404i	−0.0261214	−	0.999659i	$-0.508316\pi$
$62$	7.95555	−	5.11272i	1.01036	−	0.649317i
$63$	1.18639	+	0.348356i	0.149471	+	0.0438888i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	−3.29736	+	0.968193i	−0.408988	+	0.120090i
$66$	−0.258791	+	0.566673i	−0.0318550	+	0.0697526i
$67$	0.871145	+	6.05895i	0.106427	+	0.740218i	0.971236	+	0.238117i	$0.0765303\pi$
$67$	0.871145	+	6.05895i	0.106427	+	0.740218i	−0.864809	+	0.502101i	$0.832561\pi$
$68$	−4.70760			−0.570880
$69$	4.51242	−	1.62422i	0.543231	−	0.195533i
$70$	3.20786			0.383413
$71$	−0.923986	−	6.42646i	−0.109657	−	0.762681i	−0.968243	−	0.250011i	$-0.919566\pi$
$71$	−0.923986	−	6.42646i	−0.109657	−	0.762681i	0.858586	−	0.512669i	$-0.171343\pi$
$72$	0.415415	−	0.909632i	0.0489571	−	0.107201i
$73$	12.5598	−	3.68788i	1.47001	−	0.431634i	0.553907	−	0.832578i	$-0.313136\pi$
$73$	12.5598	−	3.68788i	1.47001	−	0.431634i	0.916102	+	0.400944i	$0.131318\pi$
$74$	1.06560	−	1.22977i	0.123873	−	0.142957i
$75$	−1.66055	−	0.487583i	−0.191744	−	0.0563012i
$76$	3.18852	−	2.04913i	0.365748	−	0.235052i
$77$	0.319990	+	0.700679i	0.0364662	+	0.0798498i
$78$	0.867451	+	1.00109i	0.0982195	+	0.113351i
$79$	−10.1643	−	6.53221i	−1.14357	−	0.734931i	−0.175225	−	0.984528i	$-0.556065\pi$
$79$	−10.1643	−	6.53221i	−1.14357	−	0.734931i	−0.968350	+	0.249598i	$0.919702\pi$
$80$	0.369215	−	2.56794i	0.0412795	−	0.287105i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−9.96863	−	6.40645i	−1.10085	−	0.707474i
$83$	−4.83987	−	5.58551i	−0.531245	−	0.613089i	0.425166	−	0.905116i	$-0.360216\pi$
$83$	−4.83987	−	5.58551i	−0.531245	−	0.613089i	−0.956410	+	0.292027i	$0.905670\pi$
$84$	−0.513652	−	1.12474i	−0.0560440	−	0.122719i
$85$	10.2744	−	6.60294i	1.11441	−	0.716189i
$86$	1.61078	+	0.472968i	0.173695	+	0.0510015i
$87$	0.728231	−	0.840423i	0.0780746	−	0.0901028i
$88$	0.597735	−	0.175511i	0.0637188	−	0.0187095i
$89$	1.40618	−	3.07910i	0.149055	−	0.326384i	−0.820346	−	0.571867i	$-0.806219\pi$
$89$	1.40618	−	3.07910i	0.149055	−	0.326384i	0.969401	+	0.245483i	$0.0789466\pi$
$90$	0.369215	+	2.56794i	0.0389186	+	0.270685i
$91$	1.63788			0.171697
$92$	−4.18251	−	2.34662i	−0.436057	−	0.244652i
$93$	9.45679			0.980623
$94$	0.988368	+	6.87425i	0.101942	+	0.709025i
$95$	−4.08482	+	8.94450i	−0.419093	+	0.917686i
$96$	−0.959493	+	0.281733i	−0.0979278	+	0.0287542i
$97$	−7.49539	+	8.65015i	−0.761042	+	0.878289i	−0.995590	−	0.0938155i	$-0.970094\pi$
$97$	−7.49539	+	8.65015i	−0.761042	+	0.878289i	0.234548	+	0.972105i	$0.424639\pi$
$98$	5.24950	+	1.54139i	0.530280	+	0.155704i
$99$	−0.524075	+	0.336803i	−0.0526716	+	0.0338500i
$100$	0.718941	+	1.57426i	0.0718941	+	0.157426i
$101$	1.16810	+	1.34806i	0.116230	+	0.134137i	0.810883	−	0.585208i	$-0.198987\pi$
$101$	1.16810	+	1.34806i	0.116230	+	0.134137i	−0.694653	+	0.719345i	$0.744442\pi$
$102$	−3.96028	−	2.54512i	−0.392127	−	0.252004i
$103$	−2.82502	+	19.6484i	−0.278357	+	1.93602i	0.0674723	+	0.997721i	$0.478507\pi$
$103$	−2.82502	+	19.6484i	−0.278357	+	1.93602i	−0.345830	+	0.938297i	$0.612403\pi$
$104$	0.188515	−	1.31115i	0.0184854	−	0.128569i
$105$	2.69862	+	1.73430i	0.263359	+	0.169250i
$106$	7.36960	+	8.50497i	0.715799	+	0.826076i
$107$	−1.81089	−	3.96529i	−0.175065	−	0.383339i	0.801677	−	0.597758i	$-0.203941\pi$
$107$	−1.81089	−	3.96529i	−0.175065	−	0.383339i	−0.976742	+	0.214419i	$0.931214\pi$
$108$	0.841254	−	0.540641i	0.0809497	−	0.0520232i
$109$	−6.20349	−	1.82151i	−0.594186	−	0.174469i	−0.0292063	−	0.999573i	$-0.509298\pi$
$109$	−6.20349	−	1.82151i	−0.594186	−	0.174469i	−0.564980	+	0.825105i	$0.691116\pi$
$110$	−1.05839	+	1.22144i	−0.100913	+	0.116460i
$111$	1.56130	−	0.458439i	0.148192	−	0.0435131i
$112$	−0.513652	+	1.12474i	−0.0485355	+	0.106278i
$113$	0.193894	+	1.34856i	0.0182400	+	0.126862i	0.996907	−	0.0785914i	$-0.0250422\pi$
$113$	0.193894	+	1.34856i	0.0182400	+	0.126862i	−0.978667	+	0.205453i	$0.934133\pi$
$114$	3.79020			0.354984
$115$	12.4198	−	0.744916i	1.15815	−	0.0694638i
$116$	−1.11204			−0.103250
$117$	0.188515	+	1.31115i	0.0174282	+	0.121216i
$118$	−4.04875	+	8.86554i	−0.372718	+	0.816139i
$119$	−5.58506	+	1.63992i	−0.511982	+	0.150331i
$120$	1.69894	−	1.96068i	0.155091	−	0.178985i
$121$	10.1821	+	2.98972i	0.925641	+	0.271793i
$122$	−12.0918	+	7.77093i	−1.09474	+	0.703547i
$123$	−4.92256	−	10.7789i	−0.443852	−	0.971900i
$124$	−6.19288	−	7.14696i	−0.556137	−	0.641816i
$125$	7.13536	+	4.58562i	0.638206	+	0.410150i
$126$	0.175969	−	1.22389i	0.0156766	−	0.109033i
$127$	−0.491724	+	3.42002i	−0.0436335	+	0.303478i	0.956305	+	0.292371i	$0.0944444\pi$
$127$	−0.491724	+	3.42002i	−0.0436335	+	0.303478i	−0.999938	+	0.0111061i	$0.996465\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	1.09937	+	1.26874i	0.0967942	+	0.111706i
$130$	1.42760	+	3.12601i	0.125209	+	0.274169i
$131$	15.9396	−	10.2437i	1.39265	−	0.895000i	0.392948	−	0.919561i	$-0.371455\pi$
$131$	15.9396	−	10.2437i	1.39265	−	0.895000i	0.999698	+	0.0245608i	$0.00781872\pi$
$132$	0.597735	+	0.175511i	0.0520262	+	0.0152763i
$133$	3.06900	−	3.54182i	0.266116	−	0.307115i
$134$	5.87330	−	1.72456i	0.507376	−	0.148979i
$135$	−1.07773	+	2.35990i	−0.0927564	+	0.203108i
$136$	0.669961	+	4.65968i	0.0574487	+	0.399564i
$137$	−11.3960			−0.973629			−0.486815	−	0.873505i	$-0.661841\pi$
$137$	−11.3960			−0.973629			−0.486815	+	0.873505i	$0.661841\pi$
$138$	−2.24987	−	4.23534i	−0.191522	−	0.360536i
$139$	5.30267			0.449766			0.224883	−	0.974386i	$-0.427800\pi$
$139$	5.30267			0.449766			0.224883	+	0.974386i	$0.427800\pi$
$140$	−0.456526	−	3.17521i	−0.0385835	−	0.268354i
$141$	−2.88503	+	6.31734i	−0.242964	+	0.532016i
$142$	−6.22955	+	1.82916i	−0.522772	+	0.153500i
$143$	−0.540396	+	0.623650i	−0.0451902	+	0.0521522i
$144$	−0.959493	−	0.281733i	−0.0799577	−	0.0234777i
$145$	2.42703	−	1.55976i	0.201554	−	0.129531i
$146$	−5.43779	−	11.9071i	−0.450034	−	0.985438i
$147$	3.58282	+	4.13480i	0.295506	+	0.341032i
$148$	−1.36890	−	0.879739i	−0.112523	−	0.0723141i
$149$	−1.96659	+	13.6779i	−0.161109	+	1.12054i	0.735439	+	0.677591i	$0.236976\pi$
$149$	−1.96659	+	13.6779i	−0.161109	+	1.12054i	−0.896548	+	0.442947i	$0.853933\pi$
$150$	−0.246298	+	1.71304i	−0.0201102	+	0.139869i
$151$	−4.57223	−	2.93840i	−0.372083	−	0.239123i	0.341213	−	0.939986i	$-0.389162\pi$
$151$	−4.57223	−	2.93840i	−0.372083	−	0.239123i	−0.713296	+	0.700863i	$0.752799\pi$
$152$	−2.48205	−	2.86444i	−0.201321	−	0.232337i
$153$	−1.95561	−	4.28218i	−0.158101	−	0.346194i
$154$	0.648008	−	0.416450i	0.0522180	−	0.0335585i
$155$	23.5404	+	6.91209i	1.89081	+	0.555192i
$156$	0.867451	−	1.00109i	0.0694517	−	0.0801515i
$157$	−5.06808	+	1.48812i	−0.404477	+	0.118765i	−0.477642	−	0.878555i	$-0.658508\pi$
$157$	−5.06808	+	1.48812i	−0.404477	+	0.118765i	0.0731647	+	0.997320i	$0.476690\pi$
$158$	−5.01919	+	10.9905i	−0.399305	+	0.874356i
$159$	1.60157	+	11.1391i	0.127013	+	0.883392i
$160$	−2.59435			−0.205101
$161$	−5.77956	−	1.32701i	−0.455493	−	0.104583i
$162$	1.00000			0.0785674
$163$	−1.29373	−	8.99811i	−0.101333	−	0.704786i	−0.975634	−	0.219403i	$-0.929589\pi$
$163$	−1.29373	−	8.99811i	−0.101333	−	0.704786i	0.874301	−	0.485383i	$-0.161320\pi$
$164$	−4.92256	+	10.7789i	−0.384387	+	0.841690i
$165$	−1.55073	+	0.455337i	−0.120725	+	0.0354479i
$166$	−4.83987	+	5.58551i	−0.375647	+	0.433519i
$167$	−2.76133	−	0.810798i	−0.213678	−	0.0627415i	0.173142	−	0.984897i	$-0.444608\pi$
$167$	−2.76133	−	0.810798i	−0.213678	−	0.0627415i	−0.386819	+	0.922155i	$0.626426\pi$
$168$	−1.04019	+	0.668491i	−0.0802526	+	0.0515752i
$169$	−4.67148	−	10.2291i	−0.359345	−	0.786856i
$170$	−7.99792	−	9.23009i	−0.613413	−	0.707916i
$171$	3.18852	+	2.04913i	0.243832	+	0.156701i
$172$	0.238916	−	1.66170i	0.0182172	−	0.126703i
$173$	−1.94440	+	13.5236i	−0.147830	+	1.02818i	0.771932	+	0.635705i	$0.219291\pi$
$173$	−1.94440	+	13.5236i	−0.147830	+	1.02818i	−0.919762	+	0.392477i	$0.871618\pi$
$174$	−0.935507	−	0.601214i	−0.0709206	−	0.0455779i
$175$	1.40135	+	1.61725i	0.105932	+	0.122252i
$176$	−0.258791	−	0.566673i	−0.0195071	−	0.0427146i
$177$	−8.19910	+	5.26924i	−0.616282	+	0.396060i
$178$	−3.24788	−	0.953664i	−0.243439	−	0.0714801i
$179$	13.3589	−	15.4169i	0.998488	−	1.15232i	0.0101646	−	0.999948i	$-0.496764\pi$
$179$	13.3589	−	15.4169i	0.998488	−	1.15232i	0.988324	−	0.152369i	$-0.0486901\pi$
$180$	2.48926	−	0.730913i	0.185539	−	0.0544791i
$181$	3.96163	−	8.67476i	0.294466	−	0.644790i	−0.703350	−	0.710843i	$-0.748313\pi$
$181$	3.96163	−	8.67476i	0.294466	−	0.644790i	0.997816	+	0.0660534i	$0.0210408\pi$
$182$	−0.233095	−	1.62121i	−0.0172782	−	0.120172i
$183$	−14.3736			−1.06252
$184$	−1.72750	+	4.47389i	−0.127353	+	0.329820i
$185$	4.22157			0.310376
$186$	−1.34584	−	9.36053i	−0.0986818	−	0.686347i
$187$	1.21828	−	2.66767i	0.0890897	−	0.195079i
$188$	6.66362	−	1.95662i	0.485995	−	0.142701i
$189$	0.809721	−	0.934468i	0.0588986	−	0.0679726i
$190$	9.43479	+	2.77030i	0.684471	+	0.200979i
$191$	1.34015	−	0.861261i	0.0969697	−	0.0623186i	−0.491257	−	0.871014i	$-0.663463\pi$
$191$	1.34015	−	0.861261i	0.0969697	−	0.0623186i	0.588227	+	0.808696i	$0.299826\pi$
$192$	0.415415	+	0.909632i	0.0299800	+	0.0656470i
$193$	−11.5112	−	13.2847i	−0.828597	−	0.956252i	0.170982	−	0.985274i	$-0.445306\pi$
$193$	−11.5112	−	13.2847i	−0.828597	−	0.956252i	−0.999579	+	0.0290223i	$0.990761\pi$
$194$	9.62880	+	6.18806i	0.691308	+	0.444277i
$195$	−0.489075	+	3.40159i	−0.0350234	+	0.243593i
$196$	0.778622	−	5.41543i	0.0556158	−	0.386817i
$197$	1.02768	+	0.660450i	0.0732191	+	0.0470551i	0.576738	−	0.816929i	$-0.304325\pi$
$197$	1.02768	+	0.660450i	0.0732191	+	0.0470551i	−0.503519	+	0.863984i	$0.667962\pi$
$198$	0.407958	+	0.470809i	0.0289923	+	0.0334589i
$199$	−0.0416361	−	0.0911703i	−0.00295150	−	0.00646289i	0.908151	−	0.418644i	$-0.137494\pi$
$199$	−0.0416361	−	0.0911703i	−0.00295150	−	0.00646289i	−0.911102	+	0.412181i	$0.864767\pi$
$200$	1.45592	−	0.935664i	0.102949	−	0.0661615i
$201$	5.87330	+	1.72456i	0.414271	+	0.121641i
$202$	1.16810	−	1.34806i	0.0821873	−	0.0948491i
$203$	−1.31932	+	0.387386i	−0.0925978	+	0.0271892i
$204$	−1.95561	+	4.28218i	−0.136920	+	0.299813i
$205$	−4.37510	−	30.4295i	−0.305570	−	2.12529i
$206$	19.8505			1.38305
$207$	0.397086	−	4.77936i	0.0275994	−	0.332189i
$208$	−1.32463			−0.0918469
$209$	0.336030	+	2.33714i	0.0232437	+	0.161664i
$210$	1.33259	−	2.91797i	0.0919577	−	0.201359i
$211$	16.0208	−	4.70412i	1.10291	−	0.323845i	0.320905	−	0.947111i	$-0.396013\pi$
$211$	16.0208	−	4.70412i	1.10291	−	0.323845i	0.782010	+	0.623266i	$0.214195\pi$
$212$	7.36960	−	8.50497i	0.506146	−	0.584124i
$213$	−6.22955	−	1.82916i	−0.426842	−	0.125332i
$214$	−3.66721	+	2.35677i	−0.250685	+	0.161106i
$215$	1.80928	+	3.96177i	0.123392	+	0.270191i
$216$	−0.654861	−	0.755750i	−0.0445576	−	0.0514222i
$217$	−9.83687	−	6.32178i	−0.667771	−	0.429150i
$218$	−0.920120	+	6.39957i	−0.0623184	+	0.433434i
$219$	1.86290	−	12.9568i	0.125883	−	0.875537i
$220$	1.35964	+	0.873785i	0.0916666	+	0.0589106i
$221$	−4.08361	−	4.71274i	−0.274694	−	0.317013i
$222$	−0.675969	−	1.48017i	−0.0453681	−	0.0993423i
$223$	15.3177	−	9.84407i	1.02575	−	0.659207i	0.0843248	−	0.996438i	$-0.473127\pi$
$223$	15.3177	−	9.84407i	1.02575	−	0.659207i	0.941422	+	0.337231i	$0.109490\pi$
$224$	1.18639	+	0.348356i	0.0792692	+	0.0232755i
$225$	−1.13334	+	1.30794i	−0.0755560	+	0.0871963i
$226$	1.30724	−	0.383840i	0.0869563	−	0.0255327i
$227$	6.64052	−	14.5407i	0.440747	−	0.965101i	−0.550714	−	0.834694i	$-0.685644\pi$
$227$	6.64052	−	14.5407i	0.440747	−	0.965101i	0.991461	−	0.130407i	$-0.0416283\pi$
$228$	−0.539401	−	3.75162i	−0.0357227	−	0.248457i
$229$	−17.7317			−1.17174			−0.585872	−	0.810404i	$-0.699248\pi$
$229$	−17.7317			−1.17174			−0.585872	+	0.810404i	$0.699248\pi$
$230$	−2.50485	−	12.1873i	−0.165165	−	0.803608i
$231$	0.770289			0.0506813
$232$	0.158260	+	1.10072i	0.0103903	+	0.0722658i
$233$	−3.88183	+	8.50002i	−0.254307	+	0.556855i	−0.993126	−	0.117049i	$-0.962657\pi$
$233$	−3.88183	+	8.50002i	−0.254307	+	0.556855i	0.738819	+	0.673904i	$0.235384\pi$
$234$	1.27098	−	0.373193i	0.0830864	−	0.0243964i
$235$	−11.7990	+	13.6168i	−0.769684	+	0.888263i
$236$	9.35150	+	2.74585i	0.608731	+	0.178739i
$237$	−10.1643	+	6.53221i	−0.660243	+	0.424312i
$238$	2.41807	+	5.29483i	0.156740	+	0.343213i
$239$	3.28022	+	3.78558i	0.212180	+	0.244869i	0.851856	−	0.523776i	$-0.175477\pi$
$239$	3.28022	+	3.78558i	0.212180	+	0.244869i	−0.639676	+	0.768644i	$0.720932\pi$
$240$	−2.18251	−	1.40261i	−0.140880	−	0.0905382i
$241$	−2.07440	+	14.4278i	−0.133624	+	0.929375i	0.807151	+	0.590345i	$0.201008\pi$
$241$	−2.07440	+	14.4278i	−0.133624	+	0.929375i	−0.940775	+	0.339031i	$0.889901\pi$
$242$	1.51023	−	10.5039i	0.0970814	−	0.675216i
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$	9.41268	+	10.8628i	0.602585	+	0.695420i
$245$	5.89640	+	12.9113i	0.376707	+	0.824874i
$246$	−9.96863	+	6.40645i	−0.635577	+	0.408460i
$247$	4.81725	+	1.41447i	0.306515	+	0.0900008i
$248$	−6.19288	+	7.14696i	−0.393248	+	0.453833i
$249$	−7.09131	+	2.08220i	−0.449394	+	0.131954i
$250$	3.52348	−	7.71534i	0.222844	−	0.487961i
$251$	2.66634	+	18.5448i	0.168298	+	1.17054i	0.882401	+	0.470499i	$0.155926\pi$
$251$	2.66634	+	18.5448i	0.168298	+	1.17054i	−0.714103	+	0.700041i	$0.753165\pi$
$252$	−1.23648			−0.0778908
$253$	2.41216	−	1.76283i	0.151651	−	0.110828i
$254$	3.45519			0.216798
$255$	−1.73811	−	12.0889i	−0.108845	−	0.757033i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	1.67895	−	0.492983i	0.104730	−	0.0307514i	−0.228948	−	0.973439i	$-0.573529\pi$
$257$	1.67895	−	0.492983i	0.104730	−	0.0307514i	0.333678	+	0.942687i	$0.391710\pi$
$258$	1.09937	−	1.26874i	0.0684438	−	0.0789884i
$259$	−1.93052	−	0.566850i	−0.119956	−	0.0352224i
$260$	2.89102	−	1.85795i	0.179294	−	0.115225i
$261$	−0.461958	−	1.01155i	−0.0285945	−	0.0626132i
$262$	−12.4079	−	14.3195i	−0.766563	−	0.884661i
$263$	−14.0110	−	9.00435i	−0.863958	−	0.555232i	0.0319412	−	0.999490i	$-0.489831\pi$
$263$	−14.0110	−	9.00435i	−0.863958	−	0.555232i	−0.895899	+	0.444258i	$0.853467\pi$
$264$	0.0886578	−	0.616629i	0.00545651	−	0.0379509i
$265$	−4.15503	+	28.8989i	−0.255241	+	1.77524i
$266$	−3.94253	−	2.53371i	−0.241732	−	0.155352i
$267$	−2.21670	−	2.55821i	−0.135660	−	0.156560i
$268$	−2.54286	−	5.56809i	−0.155330	−	0.340125i
$269$	−22.4639	+	14.4367i	−1.36965	+	0.880219i	−0.998824	−	0.0484848i	$-0.984561\pi$
$269$	−22.4639	+	14.4367i	−1.36965	+	0.880219i	−0.370823	+	0.928703i	$0.620924\pi$
$270$	2.48926	+	0.730913i	0.151492	+	0.0444820i
$271$	−17.6209	+	20.3356i	−1.07039	+	1.23530i	−0.0996919	+	0.995018i	$0.531786\pi$
$271$	−17.6209	+	20.3356i	−1.07039	+	1.23530i	−0.970703	+	0.240283i	$0.922760\pi$
$272$	4.51691	−	1.32628i	0.273878	−	0.0804178i
$273$	0.680401	−	1.48987i	0.0411798	−	0.0901711i
$274$	1.62183	+	11.2800i	0.0979781	+	0.681452i
$275$	−1.07815			−0.0650147
$276$	−3.87204	+	2.82972i	−0.233069	+	0.170329i
$277$	−2.13714			−0.128408			−0.0642042	−	0.997937i	$-0.520451\pi$
$277$	−2.13714			−0.128408			−0.0642042	+	0.997937i	$0.520451\pi$
$278$	−0.754648	−	5.24869i	−0.0452608	−	0.314796i
$279$	3.92849	−	8.60219i	0.235193	−	0.515000i
$280$	−3.07792	+	0.903759i	−0.183941	+	0.0540099i
$281$	18.1958	−	20.9990i	1.08547	−	1.25270i	0.119833	−	0.992794i	$-0.461764\pi$
$281$	18.1958	−	20.9990i	1.08547	−	1.25270i	0.965635	−	0.259902i	$-0.0836904\pi$
$282$	6.66362	+	1.95662i	0.396813	+	0.116515i
$283$	19.7538	−	12.6950i	1.17424	−	0.754638i	0.199921	−	0.979812i	$-0.435931\pi$
$283$	19.7538	−	12.6950i	1.17424	−	0.754638i	0.974319	+	0.225174i	$0.0722950\pi$
$284$	2.69710	+	5.90583i	0.160043	+	0.350446i
$285$	6.43931	+	7.43136i	0.381432	+	0.440196i
$286$	0.694209	+	0.446141i	0.0410494	+	0.0263809i
$287$	−2.08519	+	14.5028i	−0.123085	+	0.856074i
$288$	−0.142315	+	0.989821i	−0.00838598	+	0.0583258i
$289$	4.34212	+	2.79051i	0.255419	+	0.164148i
$290$	−1.88929	−	2.18035i	−0.110943	−	0.128035i
$291$	4.75475	+	10.4114i	0.278728	+	0.610330i
$292$	−11.0120	+	7.07699i	−0.644429	+	0.414150i
$293$	18.2115	+	5.34738i	1.06393	+	0.312398i	0.766432	−	0.642325i	$-0.222030\pi$
$293$	18.2115	+	5.34738i	1.06393	+	0.312398i	0.297496	+	0.954723i	$0.403848\pi$
$294$	3.58282	−	4.13480i	0.208954	−	0.241146i
$295$	−24.2611	+	7.12369i	−1.41253	+	0.414757i
$296$	−0.675969	+	1.48017i	−0.0392899	+	0.0860329i
$297$	0.0886578	+	0.616629i	0.00514445	+	0.0357804i
$298$	13.8186			0.800488
$299$	−1.27894	−	6.22266i	−0.0739628	−	0.359865i
$300$	1.73066			0.0999196
$301$	−0.295415	−	2.05465i	−0.0170274	−	0.118428i
$302$	−2.25779	+	4.94387i	−0.129921	+	0.284488i
$303$	1.71148	−	0.502537i	0.0983222	−	0.0288700i
$304$	−2.48205	+	2.86444i	−0.142355	+	0.164287i
$305$	−35.7796	−	10.5058i	−2.04873	−	0.601562i
$306$	−3.96028	+	2.54512i	−0.226394	+	0.145495i
$307$	6.19445	+	13.5640i	0.353536	+	0.774136i	0.999938	+	0.0111390i	$0.00354572\pi$
$307$	6.19445	+	13.5640i	0.353536	+	0.774136i	−0.646402	+	0.762997i	$0.723727\pi$
$308$	−0.504432	−	0.582145i	−0.0287427	−	0.0331708i
$309$	16.6993	+	10.7320i	0.949990	+	0.610521i
$310$	3.49158	−	24.2845i	0.198309	−	1.37927i
$311$	0.752614	−	5.23455i	0.0426769	−	0.296824i	−0.957293	−	0.289118i	$-0.906638\pi$
$311$	0.752614	−	5.23455i	0.0426769	−	0.296824i	0.999970	−	0.00770598i	$-0.00245292\pi$
$312$	−1.11435	−	0.716152i	−0.0630879	−	0.0405441i
$313$	5.80888	+	6.70380i	0.328337	+	0.378921i	0.895785	−	0.444488i	$-0.146614\pi$
$313$	5.80888	+	6.70380i	0.328337	+	0.378921i	−0.567448	+	0.823410i	$0.692069\pi$
$314$	2.19424	+	4.80472i	0.123828	+	0.271146i
$315$	2.69862	−	1.73430i	0.152050	−	0.0977168i
$316$	11.5929	+	3.40399i	0.652153	+	0.191489i
$317$	−1.99059	+	2.29726i	−0.111802	+	0.129027i	−0.808892	−	0.587957i	$-0.799932\pi$
$317$	−1.99059	+	2.29726i	−0.111802	+	0.129027i	0.697090	+	0.716984i	$0.254478\pi$
$318$	10.7978	−	3.17053i	0.605513	−	0.177795i
$319$	0.287786	−	0.630163i	0.0161129	−	0.0352823i
$320$	0.369215	+	2.56794i	0.0206397	+	0.143552i
$321$	−4.35922			−0.243308
$322$	−0.490989	+	5.90958i	−0.0273617	+	0.329328i
$323$	−17.8427			−0.992795
$324$	−0.142315	−	0.989821i	−0.00790638	−	0.0549901i
$325$	−0.952335	+	2.08532i	−0.0528260	+	0.115673i
$326$	−8.72240	+	2.56113i	−0.483089	+	0.141848i
$327$	−4.23392	+	4.88621i	−0.234137	+	0.270208i
$328$	11.3697	+	3.33846i	0.627789	+	0.184335i
$329$	7.22407	−	4.64263i	0.398276	−	0.255957i
$330$	0.671395	+	1.47015i	0.0369591	+	0.0809290i
$331$	−1.07480	−	1.24038i	−0.0590762	−	0.0681776i	0.725442	−	0.688283i	$-0.241635\pi$
$331$	−1.07480	−	1.24038i	−0.0590762	−	0.0681776i	−0.784518	+	0.620105i	$0.787090\pi$
$332$	6.21744	+	3.99571i	0.341226	+	0.219293i
$333$	0.231577	−	1.61065i	0.0126903	−	0.0882632i
$334$	−0.409568	+	2.84861i	−0.0224106	+	0.155869i
$335$	13.3597	+	8.58574i	0.729917	+	0.469089i
$336$	0.809721	+	0.934468i	0.0441739	+	0.0509794i
$337$	7.46526	+	16.3466i	0.406659	+	0.890458i	0.996551	+	0.0829766i	$0.0264427\pi$
$337$	7.46526	+	16.3466i	0.406659	+	0.890458i	−0.589893	+	0.807481i	$0.700830\pi$
$338$	−9.46018	+	6.07969i	−0.514566	+	0.330692i
$339$	1.30724	+	0.383840i	0.0709995	+	0.0208473i
$340$	−7.99792	+	9.23009i	−0.433748	+	0.500572i
$341$	5.65265	−	1.65977i	0.306108	−	0.0898815i
$342$	1.57450	−	3.44768i	0.0851394	−	0.186429i
$343$	−2.19453	−	15.2633i	−0.118494	−	0.824142i
$344$	−1.67879			−0.0905140
$345$	4.48175	−	11.6069i	0.241289	−	0.624892i
$346$	13.6627			0.734511
$347$	−0.0317652	−	0.220932i	−0.00170524	−	0.0118602i	0.988951	−	0.148242i	$-0.0473616\pi$
$347$	−0.0317652	−	0.220932i	−0.00170524	−	0.0118602i	−0.990656	+	0.136382i	$0.956452\pi$
$348$	−0.461958	+	1.01155i	−0.0247635	+	0.0542246i
$349$	19.4199	−	5.70221i	1.03953	−	0.305232i	0.282947	−	0.959136i	$-0.408688\pi$
$349$	19.4199	−	5.70221i	1.03953	−	0.305232i	0.756578	+	0.653903i	$0.226870\pi$
$350$	1.40135	−	1.61725i	0.0749054	−	0.0864454i
$351$	1.27098	+	0.373193i	0.0678398	+	0.0199196i
$352$	−0.524075	+	0.336803i	−0.0279333	+	0.0179516i
$353$	7.89861	+	17.2956i	0.420401	+	0.920549i	0.994788	+	0.101966i	$0.0325131\pi$
$353$	7.89861	+	17.2956i	0.420401	+	0.920549i	−0.574387	+	0.818584i	$0.694760\pi$
$354$	6.38246	+	7.36575i	0.339224	+	0.391485i
$355$	−14.1700	−	9.10652i	−0.752067	−	0.483324i
$356$	−0.481735	+	3.35054i	−0.0255319	+	0.177578i
$357$	−0.828393	+	5.76160i	−0.0438432	+	0.304936i
$358$	−17.1612	−	11.0288i	−0.906997	−	0.582892i
$359$	−3.36334	−	3.88150i	−0.177510	−	0.204858i	0.660021	−	0.751247i	$-0.270547\pi$
$359$	−3.36334	−	3.88150i	−0.177510	−	0.204858i	−0.837531	+	0.546389i	$0.816002\pi$
$360$	−1.07773	−	2.35990i	−0.0568015	−	0.124378i
$361$	−3.89872	+	2.50556i	−0.205196	+	0.131871i
$362$	−9.15026	−	2.68676i	−0.480927	−	0.141213i
$363$	6.94932	−	8.01995i	0.364745	−	0.420938i
$364$	−1.57154	+	0.461445i	−0.0823709	+	0.0241863i
$365$	14.1075	−	30.8912i	0.738422	−	1.61692i
$366$	2.04557	+	14.2273i	0.106924	+	0.743671i
$367$	24.7772			1.29336			0.646679	−	0.762762i	$-0.276157\pi$
$367$	24.7772			1.29336			0.646679	+	0.762762i	$0.276157\pi$
$368$	4.67421	+	1.07322i	0.243660	+	0.0559454i
$369$	−11.8497			−0.616872
$370$	−0.600791	−	4.17860i	−0.0312337	−	0.217235i
$371$	5.78048	−	12.6575i	0.300108	−	0.657144i
$372$	−9.07372	+	2.66428i	−0.470450	+	0.138137i
$373$	−24.3045	+	28.0489i	−1.25844	+	1.45231i	−0.419808	+	0.907613i	$0.637903\pi$
$373$	−24.3045	+	28.0489i	−1.25844	+	1.45231i	−0.838630	+	0.544702i	$0.816643\pi$
$374$	−2.81390	−	0.826235i	−0.145503	−	0.0427236i
$375$	7.13536	−	4.58562i	0.368469	−	0.236800i
$376$	−2.88503	−	6.31734i	−0.148784	−	0.325792i
$377$	−0.964640	−	1.11325i	−0.0496815	−	0.0573355i
$378$	−1.04019	−	0.668491i	−0.0535017	−	0.0343835i
$379$	4.43761	−	30.8642i	0.227945	−	1.58539i	−0.478802	−	0.877923i	$-0.658929\pi$
$379$	4.43761	−	30.8642i	0.227945	−	1.58539i	0.706747	−	0.707467i	$-0.250162\pi$
$380$	1.39940	−	9.73301i	0.0717875	−	0.499293i
$381$	2.90669	+	1.86802i	0.148914	+	0.0957013i
$382$	−1.04322	−	1.20394i	−0.0533756	−	0.0615988i
$383$	−4.80062	−	10.5119i	−0.245300	−	0.537132i	0.746431	−	0.665462i	$-0.231766\pi$
$383$	−4.80062	−	10.5119i	−0.245300	−	0.537132i	−0.991732	+	0.128330i	$0.959038\pi$
$384$	0.841254	−	0.540641i	0.0429300	−	0.0275895i
$385$	1.91745	+	0.563014i	0.0977223	+	0.0286939i
$386$	−11.5112	+	13.2847i	−0.585907	+	0.676172i
$387$	1.61078	−	0.472968i	0.0818807	−	0.0240423i
$388$	4.75475	−	10.4114i	0.241386	−	0.528561i
$389$	−3.38765	−	23.5616i	−0.171761	−	1.19462i	−0.875163	−	0.483829i	$-0.839246\pi$
$389$	−3.38765	−	23.5616i	−0.171761	−	1.19462i	0.703402	−	0.710792i	$-0.251663\pi$
$390$	3.43657			0.174017
$391$	10.5915	+	19.9383i	0.535634	+	1.00832i
$392$	−5.47112			−0.276333
$393$	−2.69650	−	18.7545i	−0.136020	−	0.946042i
$394$	0.507473	−	1.11121i	0.0255661	−	0.0559820i
$395$	−30.0761	+	8.83114i	−1.51329	+	0.444343i
$396$	0.407958	−	0.470809i	0.0205007	−	0.0236590i
$397$	21.2291	+	6.23343i	1.06546	+	0.312847i	0.767047	−	0.641591i	$-0.221725\pi$
$397$	21.2291	+	6.23343i	1.06546	+	0.312847i	0.298411	+	0.954437i	$0.403543\pi$
$398$	−0.0843169	+	0.0541872i	−0.00422642	+	0.00271616i
$399$	−1.94684	−	4.26299i	−0.0974640	−	0.213416i
$400$	−1.13334	−	1.30794i	−0.0566670	−	0.0653972i
$401$	−8.99099	−	5.77816i	−0.448989	−	0.288548i	0.296541	−	0.955020i	$-0.404167\pi$
$401$	−8.99099	−	5.77816i	−0.448989	−	0.288548i	−0.745530	+	0.666473i	$0.767803\pi$
$402$	0.871145	−	6.05895i	0.0434488	−	0.302193i
$403$	1.78275	−	12.3993i	0.0888050	−	0.617652i
$404$	−1.50058	−	0.964362i	−0.0746565	−	0.0479788i
$405$	1.69894	+	1.96068i	0.0844209	+	0.0974270i
$406$	0.571201	+	1.25076i	0.0283482	+	0.0620740i
$407$	0.852783	−	0.548050i	0.0422709	−	0.0271658i
$408$	4.51691	+	1.32628i	0.223620	+	0.0656608i
$409$	10.3992	−	12.0014i	0.514209	−	0.593429i	−0.437962	−	0.898993i	$-0.644300\pi$
$409$	10.3992	−	12.0014i	0.514209	−	0.593429i	0.952171	+	0.305564i	$0.0988451\pi$
$410$	−29.4971	+	8.66113i	−1.45676	+	0.427743i
$411$	−4.73409	+	10.3662i	−0.233515	+	0.511327i
$412$	−2.82502	−	19.6484i	−0.139179	−	0.968009i
$413$	12.0511			0.592995
$414$	−4.78723	+	0.287130i	−0.235279	+	0.0141117i
$415$	−19.1740			−0.941216
$416$	0.188515	+	1.31115i	0.00924272	+	0.0642845i
$417$	2.20281	−	4.82348i	0.107872	−	0.236207i
$418$	2.26553	−	0.665220i	0.110811	−	0.0325370i
$419$	3.03210	−	3.49923i	0.148128	−	0.170948i	−0.676837	−	0.736133i	$-0.736650\pi$
$419$	3.03210	−	3.49923i	0.148128	−	0.170948i	0.824964	+	0.565185i	$0.191195\pi$
$420$	−3.07792	−	0.903759i	−0.150187	−	0.0440989i
$421$	−8.84060	+	5.68151i	−0.430865	+	0.276900i	−0.738045	−	0.674751i	$-0.764251\pi$
$421$	−8.84060	+	5.68151i	−0.430865	+	0.276900i	0.307180	+	0.951651i	$0.400614\pi$
$422$	−6.93623	−	15.1882i	−0.337650	−	0.739351i
$423$	4.54797	+	5.24864i	0.221130	+	0.255197i
$424$	−9.46721	−	6.08421i	−0.459768	−	0.295475i
$425$	1.15947	−	8.06432i	0.0562427	−	0.391177i
$426$	−0.923986	+	6.42646i	−0.0447672	+	0.311363i
$427$	14.9513	+	9.60859i	0.723542	+	0.464992i
$428$	2.85468	+	3.29448i	0.137986	+	0.159245i
$429$	0.342803	+	0.750635i	0.0165507	+	0.0362410i
$430$	3.66396	−	2.35468i	0.176692	−	0.113553i
$431$	−13.0764	−	3.83957i	−0.629867	−	0.184946i	−0.0488095	−	0.998808i	$-0.515543\pi$
$431$	−13.0764	−	3.83957i	−0.629867	−	0.184946i	−0.581058	+	0.813862i	$0.697361\pi$
$432$	−0.654861	+	0.755750i	−0.0315070	+	0.0363610i
$433$	8.26166	−	2.42584i	0.397030	−	0.116579i	−0.0771217	−	0.997022i	$-0.524573\pi$
$433$	8.26166	−	2.42584i	0.397030	−	0.116579i	0.474152	+	0.880443i	$0.342755\pi$
$434$	−4.85750	+	10.6364i	−0.233167	+	0.510565i
$435$	−0.410581	−	2.85566i	−0.0196859	−	0.136918i
$436$	6.46538			0.309636
$437$	−15.8525	−	8.89416i	−0.758329	−	0.425465i
$438$	−13.0900			−0.625465
$439$	5.27024	+	36.6553i	0.251535	+	1.74946i	0.589007	+	0.808128i	$0.299519\pi$
$439$	5.27024	+	36.6553i	0.251535	+	1.74946i	−0.337472	+	0.941336i	$0.609572\pi$
$440$	0.671395	−	1.47015i	0.0320075	−	0.0700866i
$441$	5.24950	−	1.54139i	0.249976	−	0.0733996i
$442$	−4.08361	+	4.71274i	−0.194238	+	0.224162i
$443$	−13.8173	−	4.05713i	−0.656481	−	0.192760i	−0.0635066	−	0.997981i	$-0.520228\pi$
$443$	−13.8173	−	4.05713i	−0.656481	−	0.192760i	−0.592975	+	0.805221i	$0.702047\pi$
$444$	−1.36890	+	0.879739i	−0.0649651	+	0.0417505i
$445$	−3.64812	−	7.98827i	−0.172938	−	0.378680i
$446$	−11.9238	−	13.7608i	−0.564608	−	0.651593i
$447$	11.6249	+	7.47088i	0.549839	+	0.353360i
$448$	0.175969	−	1.22389i	0.00831377	−	0.0578235i
$449$	−2.10099	+	14.6127i	−0.0991516	+	0.689615i	0.878247	+	0.478208i	$0.158714\pi$
$449$	−2.10099	+	14.6127i	−0.0991516	+	0.689615i	−0.977398	+	0.211407i	$0.932196\pi$
$450$	1.45592	+	0.935664i	0.0686328	+	0.0441076i
$451$	−4.83420	−	5.57896i	−0.227633	−	0.262703i
$452$	−0.565973	−	1.23931i	−0.0266211	−	0.0582921i
$453$	−4.57223	+	2.93840i	−0.214822	+	0.138058i
$454$	−15.3378	−	4.50357i	−0.719836	−	0.211363i
$455$	2.78266	−	3.21136i	0.130453	−	0.150551i
$456$	−3.63667	+	1.06782i	−0.170302	+	0.0500053i
$457$	2.75189	−	6.02580i	0.128728	−	0.281875i	−0.834283	−	0.551336i	$-0.814118\pi$
$457$	2.75189	−	6.02580i	0.128728	−	0.281875i	0.963011	+	0.269461i	$0.0868455\pi$
$458$	2.52348	+	17.5512i	0.117915	+	0.820114i
$459$	−4.70760			−0.219732
$460$	−11.7068	+	4.21379i	−0.545832	+	0.196469i
$461$	7.35627			0.342616			0.171308	−	0.985218i	$-0.445201\pi$
$461$	7.35627			0.342616			0.171308	+	0.985218i	$0.445201\pi$
$462$	−0.109624	−	0.762448i	−0.00510015	−	0.0354723i
$463$	14.3882	−	31.5059i	0.668678	−	1.46420i	−0.205530	−	0.978651i	$-0.565892\pi$
$463$	14.3882	−	31.5059i	0.668678	−	1.46420i	0.874209	−	0.485551i	$-0.161381\pi$
$464$	1.06699	−	0.313298i	0.0495340	−	0.0145445i
$465$	16.0665	−	18.5417i	0.745066	−	0.859852i
$466$	8.96595	+	2.63264i	0.415340	+	0.121955i
$467$	−11.8642	+	7.62464i	−0.549008	+	0.352826i	−0.785553	−	0.618794i	$-0.787621\pi$
$467$	−11.8642	+	7.62464i	−0.549008	+	0.352826i	0.236545	+	0.971621i	$0.423985\pi$
$468$	−0.550273	−	1.20493i	−0.0254364	−	0.0556979i
$469$	−4.95651	−	5.72012i	−0.228870	−	0.264131i
$470$	15.1574	+	9.74106i	0.699158	+	0.449322i
$471$	−0.751713	+	5.22828i	−0.0346371	+	0.240906i
$472$	1.38704	−	9.64709i	0.0638438	−	0.444043i
$473$	0.879810	+	0.565420i	0.0404537	+	0.0259980i
$474$	7.91225	+	9.13122i	0.363422	+	0.419411i
$475$	2.72493	+	5.96676i	0.125028	+	0.273774i
$476$	4.89681	−	3.14699i	0.224445	−	0.144242i
$477$	10.7978	+	3.17053i	0.494399	+	0.145169i
$478$	3.28022	−	3.78558i	0.150034	−	0.173148i
$479$	16.3570	−	4.80286i	0.747372	−	0.219448i	0.114198	−	0.993458i	$-0.463570\pi$
$479$	16.3570	−	4.80286i	0.747372	−	0.219448i	0.633174	+	0.774010i	$0.281752\pi$
$480$	−1.07773	+	2.35990i	−0.0491915	+	0.107714i
$481$	−0.306755	−	2.13353i	−0.0139868	−	0.0972804i
$482$	14.5761			0.663925
$483$	−3.60801	+	4.70601i	−0.164170	+	0.214131i
$484$	−10.6119			−0.482359
$485$	4.22595	+	29.3921i	0.191891	+	1.33463i
$486$	0.415415	−	0.909632i	0.0188436	−	0.0412617i
$487$	11.8285	−	3.47316i	0.536000	−	0.157384i	−0.00251946	−	0.999997i	$-0.500802\pi$
$487$	11.8285	−	3.47316i	0.536000	−	0.157384i	0.538520	+	0.842613i	$0.318984\pi$
$488$	9.41268	−	10.8628i	0.426092	−	0.491736i
$489$	−8.72240	−	2.56113i	−0.394441	−	0.115818i
$490$	11.9408	−	7.67386i	0.539428	−	0.346670i
$491$	−2.69768	−	5.90709i	−0.121744	−	0.266583i	0.838941	−	0.544223i	$-0.183175\pi$
$491$	−2.69768	−	5.90709i	−0.121744	−	0.266583i	−0.960685	+	0.277639i	$0.910448\pi$
$492$	7.75992	+	8.95543i	0.349844	+	0.403742i
$493$	4.40399	+	2.83027i	0.198346	+	0.127469i
$494$	0.714509	−	4.96952i	0.0321473	−	0.223589i
$495$	−0.230010	+	1.59975i	−0.0103382	+	0.0719035i
$496$	7.95555	+	5.11272i	0.357215	+	0.229568i
$497$	5.25715	+	6.06708i	0.235816	+	0.272146i
$498$	3.07020	+	6.72280i	0.137579	+	0.301256i
$499$	−11.4414	+	7.35297i	−0.512189	+	0.329164i	−0.771076	−	0.636744i	$-0.780281\pi$
$499$	−11.4414	+	7.35297i	−0.512189	+	0.329164i	0.258886	+	0.965908i	$0.416645\pi$
$500$	−8.13825	−	2.38961i	−0.363954	−	0.106866i
$501$	−1.88462	+	2.17497i	−0.0841988	+	0.0971706i
$502$	17.9766	−	5.27841i	0.802336	−	0.235587i
$503$	1.25141	−	2.74021i	0.0557977	−	0.122180i	−0.879679	−	0.475567i	$-0.842243\pi$
$503$	1.25141	−	2.74021i	0.0557977	−	0.122180i	0.935477	+	0.353387i	$0.114970\pi$
$504$	0.175969	+	1.22389i	0.00783830	+	0.0545165i
$505$	4.62764			0.205927
$506$	−2.08817	−	2.13673i	−0.0928306	−	0.0949894i
$507$	−11.2453			−0.499423
$508$	−0.491724	−	3.42002i	−0.0218167	−	0.151739i
$509$	17.8751	−	39.1410i	0.792300	−	1.73490i	0.122354	−	0.992486i	$-0.460956\pi$
$509$	17.8751	−	39.1410i	0.792300	−	1.73490i	0.669946	−	0.742410i	$-0.266317\pi$
$510$	−11.7184	+	3.44085i	−0.518901	+	0.152363i
$511$	−10.5993	+	12.2322i	−0.468884	+	0.541121i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	3.18852	−	2.04913i	0.140776	−	0.0904715i
$514$	−0.726904	−	1.59170i	−0.0320623	−	0.0702068i
$515$	33.7248	+	38.9205i	1.48609	+	1.71504i
$516$	−1.41228	−	0.907620i	−0.0621723	−	0.0399557i
$517$	−0.615723	+	4.28245i	−0.0270795	+	0.188342i
$518$	−0.286340	+	1.99154i	−0.0125810	+	0.0875031i
$519$	11.4938	+	7.38661i	0.504521	+	0.324236i
$520$	−2.25047	−	2.59718i	−0.0986898	−	0.113894i
$521$	−6.29609	−	13.7865i	−0.275837	−	0.603998i	0.720118	−	0.693851i	$-0.244088\pi$
$521$	−6.29609	−	13.7865i	−0.275837	−	0.603998i	−0.995955	+	0.0898530i	$0.971360\pi$
$522$	−0.935507	+	0.601214i	−0.0409460	+	0.0263144i
$523$	−15.0544	−	4.42038i	−0.658284	−	0.193290i	−0.0645043	−	0.997917i	$-0.520547\pi$
$523$	−15.0544	−	4.42038i	−0.658284	−	0.193290i	−0.593779	+	0.804628i	$0.702365\pi$
$524$	−12.4079	+	14.3195i	−0.542042	+	0.625550i
$525$	2.05324	−	0.602886i	0.0896107	−	0.0263121i
$526$	−6.91872	+	15.1499i	−0.301670	+	0.660566i
$527$	6.33568	+	44.0656i	0.275987	+	1.91953i
$528$	−0.622970			−0.0271113
$529$	−0.528643	+	22.9939i	−0.0229845	+	0.999736i
$530$	29.1960			1.26819
$531$	1.38704	+	9.64709i	0.0601925	+	0.418648i
$532$	−1.94684	+	4.26299i	−0.0844063	+	0.184824i
$533$	−15.0607	+	4.42223i	−0.652353	+	0.191548i
$534$	−2.21670	+	2.55821i	−0.0959261	+	0.110705i
$535$	−10.8512	−	3.18621i	−0.469140	−	0.137752i
$536$	−5.14953	+	3.30940i	−0.222426	+	0.142944i
$537$	−8.47428	−	18.5561i	−0.365692	−	0.800754i
$538$	17.4867	+	20.1807i	0.753903	+	0.870051i
$539$	2.86728	+	1.84269i	0.123502	+	0.0793702i
$540$	0.369215	−	2.56794i	0.0158885	−	0.110507i
$541$	3.09092	−	21.4978i	0.132889	−	0.924265i	−0.808873	−	0.587984i	$-0.799922\pi$
$541$	3.09092	−	21.4978i	0.132889	−	0.924265i	0.941762	−	0.336281i	$-0.109169\pi$
$542$	22.6364	+	14.5475i	0.972315	+	0.624869i
$543$	−6.24512	−	7.20725i	−0.268004	−	0.309293i
$544$	−1.95561	−	4.28218i	−0.0838460	−	0.183597i
$545$	−14.1107	+	9.06842i	−0.604438	+	0.388449i
$546$	−1.57154	−	0.461445i	−0.0672556	−	0.0197480i
$547$	−7.99651	+	9.22846i	−0.341906	+	0.394581i	−0.900497	−	0.434863i	$-0.856797\pi$
$547$	−7.99651	+	9.22846i	−0.341906	+	0.394581i	0.558591	+	0.829443i	$0.311342\pi$
$548$	10.9344	−	3.21064i	0.467095	−	0.137152i
$549$	−5.97099	+	13.0746i	−0.254836	+	0.558012i
$550$	0.153436	+	1.06717i	0.00654255	+	0.0455044i
$551$	−4.21485			−0.179559
$552$	3.35197	+	3.42992i	0.142669	+	0.145987i
$553$	14.9396			0.635295
$554$	0.304147	+	2.11539i	0.0129220	+	0.0898742i
$555$	1.75370	−	3.84007i	0.0744405	−	0.163002i
$556$	−5.08787	+	1.49393i	−0.215774	+	0.0633569i
$557$	−10.6515	+	12.2924i	−0.451317	+	0.520848i	−0.935121	−	0.354329i	$-0.884709\pi$
$557$	−10.6515	+	12.2924i	−0.451317	+	0.520848i	0.483804	+	0.875176i	$0.339255\pi$
$558$	−9.07372	−	2.66428i	−0.384121	−	0.112788i
$559$	1.87076	−	1.20226i	0.0791247	−	0.0508504i
$560$	1.33259	+	2.91797i	0.0563123	+	0.123307i
$561$	−1.92050	−	2.21638i	−0.0810838	−	0.0935756i
$562$	−23.3748	−	15.0221i	−0.986007	−	0.633668i
$563$	−4.50622	+	31.3414i	−0.189914	+	1.32088i	0.642310	+	0.766445i	$0.277976\pi$
$563$	−4.50622	+	31.3414i	−0.189914	+	1.32088i	−0.832224	+	0.554439i	$0.812933\pi$
$564$	0.988368	−	6.87425i	0.0416178	−	0.289458i
$565$	2.97351	+	1.91096i	0.125096	+	0.0803946i
$566$	−15.3770	−	17.7460i	−0.646344	−	0.745921i
$567$	−0.513652	−	1.12474i	−0.0215714	−	0.0472347i
$568$	5.46188	−	3.51014i	0.229175	−	0.147282i
$569$	−35.3667	−	10.3846i	−1.48265	−	0.435345i	−0.562461	−	0.826824i	$-0.690145\pi$
$569$	−35.3667	−	10.3846i	−1.48265	−	0.435345i	−0.920187	+	0.391479i	$0.871964\pi$
$570$	6.43931	−	7.43136i	0.269713	−	0.311265i
$571$	−29.6036	+	8.69239i	−1.23887	+	0.363765i	−0.834591	−	0.550870i	$-0.814296\pi$
$571$	−29.6036	+	8.69239i	−1.23887	+	0.363765i	−0.404280	+	0.914635i	$0.632478\pi$
$572$	0.342803	−	0.750635i	0.0143333	−	0.0313856i
$573$	−0.226713	−	1.57682i	−0.00947106	−	0.0658727i
$574$	14.6519			0.611560
$575$	5.05001	−	6.58684i	0.210600	−	0.274690i
$576$	1.00000			0.0416667
$577$	6.50139	+	45.2182i	0.270657	+	1.88246i	0.441652	+	0.897186i	$0.354392\pi$
$577$	6.50139	+	45.2182i	0.270657	+	1.88246i	−0.170996	+	0.985272i	$0.554698\pi$
$578$	2.14416	−	4.69505i	0.0891853	−	0.195288i
$579$	−16.8661	+	4.95234i	−0.700931	+	0.205812i
$580$	−1.88929	+	2.18035i	−0.0784484	+	0.0905342i
$581$	8.76825	+	2.57459i	0.363769	+	0.106812i
$582$	9.62880	−	6.18806i	0.399127	−	0.256503i
$583$	2.91235	+	6.37716i	0.120617	+	0.264115i
$584$	8.57213	+	9.89277i	0.354717	+	0.409366i
$585$	2.89102	+	1.85795i	0.119529	+	0.0768167i
$586$	2.70119	−	18.7872i	0.111585	−	0.776091i
$587$	4.32880	−	30.1075i	0.178669	−	1.24267i	−0.681179	−	0.732117i	$-0.738532\pi$
$587$	4.32880	−	30.1075i	0.178669	−	1.24267i	0.859848	−	0.510551i	$-0.170558\pi$
$588$	−4.60260	−	2.95791i	−0.189808	−	0.121982i
$589$	−23.4722	−	27.0884i	−0.967156	−	1.11616i
$590$	10.5039	+	23.0003i	0.432438	+	0.946908i
$591$	1.02768	−	0.660450i	0.0422731	−	0.0271673i
$592$	1.56130	+	0.458439i	0.0641691	+	0.0188417i
$593$	18.2190	−	21.0258i	0.748163	−	0.863426i	−0.246226	−	0.969213i	$-0.579190\pi$
$593$	18.2190	−	21.0258i	0.748163	−	0.863426i	0.994389	+	0.105786i	$0.0337359\pi$
$594$	0.597735	−	0.175511i	0.0245254	−	0.00720130i
$595$	−6.27332	+	13.7366i	−0.257181	+	0.563147i
$596$	−1.96659	−	13.6779i	−0.0805545	−	0.560269i
$597$	−0.100228			−0.00410205
$598$	−5.97731	+	2.15149i	−0.244430	+	0.0879812i
$599$	−11.1914			−0.457270			−0.228635	−	0.973512i	$-0.573426\pi$
$599$	−11.1914			−0.457270			−0.228635	+	0.973512i	$0.573426\pi$
$600$	−0.246298	−	1.71304i	−0.0100551	−	0.0699347i
$601$	−17.0438	+	37.3206i	−0.695229	+	1.52234i	0.150432	+	0.988620i	$0.451934\pi$
$601$	−17.0438	+	37.3206i	−0.695229	+	1.52234i	−0.845661	+	0.533720i	$0.820794\pi$
$602$	−1.99170	+	0.584816i	−0.0811756	+	0.0238353i
$603$	4.00857	−	4.62614i	0.163242	−	0.188391i
$604$	5.21487	+	1.53122i	0.212190	+	0.0623046i
$605$	23.1606	−	14.8844i	0.941611	−	0.605137i
$606$	−0.740992	−	1.62255i	−0.0301007	−	0.0659114i
$607$	−24.0132	−	27.7127i	−0.974667	−	1.12483i	−0.992159	−	0.124979i	$-0.960114\pi$
$607$	−24.0132	−	27.7127i	−0.974667	−	1.12483i	0.0174926	−	0.999847i	$-0.494432\pi$
$608$	3.18852	+	2.04913i	0.129311	+	0.0831034i
$609$	−0.195685	+	1.36102i	−0.00792955	+	0.0551512i
$610$	−5.30693	+	36.9105i	−0.214871	+	1.49446i
$611$	7.73912	+	4.97363i	0.313091	+	0.201212i
$612$	3.08282	+	3.55777i	0.124616	+	0.143814i
$613$	−0.0971676	−	0.212767i	−0.00392456	−	0.00859360i	0.907660	−	0.419707i	$-0.137867\pi$
$613$	−0.0971676	−	0.212767i	−0.00392456	−	0.00859360i	−0.911584	+	0.411114i	$0.865140\pi$
$614$	12.5443	−	8.06176i	0.506248	−	0.325346i
$615$	−29.4971	−	8.66113i	−1.18944	−	0.349250i
$616$	−0.504432	+	0.582145i	−0.0203241	+	0.0234553i
$617$	41.8810	−	12.2974i	1.68606	−	0.495073i	0.708500	−	0.705711i	$-0.249372\pi$
$617$	41.8810	−	12.2974i	1.68606	−	0.495073i	0.977564	+	0.210637i	$0.0675539\pi$
$618$	8.24619	−	18.0566i	0.331710	−	0.726345i
$619$	0.169206	+	1.17685i	0.00680096	+	0.0473017i	0.992939	−	0.118623i	$-0.0378481\pi$
$619$	0.169206	+	1.17685i	0.00680096	+	0.0473017i	−0.986138	+	0.165925i	$0.946939\pi$
$620$	−24.5342			−0.985318
$621$	−4.18251	−	2.34662i	−0.167838	−	0.0941667i
$622$	−5.28838			−0.212045
$623$	0.595655	+	4.14287i	0.0238644	+	0.165981i
$624$	−0.550273	+	1.20493i	−0.0220286	+	0.0482358i
$625$	29.4162	−	8.63739i	1.17665	−	0.345496i
$626$	5.80888	−	6.70380i	0.232169	−	0.267938i
$627$	2.26553	+	0.665220i	0.0904766	+	0.0265663i
$628$	4.44354	−	2.85569i	0.177316	−	0.113954i
$629$	3.18219	+	6.96803i	0.126882	+	0.277834i
$630$	−2.10070	−	2.42434i	−0.0836940	−	0.0965880i
$631$	14.0184	+	9.00907i	0.558063	+	0.358646i	0.789067	−	0.614307i	$-0.210565\pi$
$631$	14.0184	+	9.00907i	0.558063	+	0.358646i	−0.231003	+	0.972953i	$0.574201\pi$
$632$	1.71950	−	11.9594i	0.0683979	−	0.475718i
$633$	2.37625	−	16.5272i	0.0944473	−	0.656896i
$634$	2.55717	+	1.64339i	0.101558	+	0.0652674i
$635$	5.87015	+	6.77452i	0.232950	+	0.268838i
$636$	−4.67495	−	10.2367i	−0.185374	−	0.405912i
$637$	6.09676	−	3.91815i	0.241563	−	0.155243i
$638$	−0.664705	−	0.195175i	−0.0263159	−	0.00772705i
$639$	−4.25171	+	4.90674i	−0.168195	+	0.194108i
$640$	2.48926	−	0.730913i	0.0983967	−	0.0288919i
$641$	−12.3967	+	27.1451i	−0.489641	+	1.07217i	0.490057	+	0.871690i	$0.336976\pi$
$641$	−12.3967	+	27.1451i	−0.489641	+	1.07217i	−0.979699	+	0.200475i	$0.935751\pi$
$642$	0.620382	+	4.31485i	0.0244845	+	0.170294i
$643$	−36.9937			−1.45889			−0.729445	−	0.684040i	$-0.760221\pi$
$643$	−36.9937			−1.45889			−0.729445	+	0.684040i	$0.760221\pi$
$644$	5.91931	−	0.355030i	0.233253	−	0.0139902i
$645$	4.35536			0.171492
$646$	2.53928	+	17.6611i	0.0999068	+	0.694867i
$647$	12.8336	−	28.1016i	0.504540	−	1.10479i	−0.470427	−	0.882439i	$-0.655900\pi$
$647$	12.8336	−	28.1016i	0.504540	−	1.10479i	0.974967	−	0.222349i	$-0.0713725\pi$
$648$	−0.959493	+	0.281733i	−0.0376924	+	0.0110675i
$649$	−3.97608	+	4.58864i	−0.156075	+	0.180120i
$650$	2.19963	+	0.645869i	0.0862765	+	0.0253331i
$651$	−9.83687	+	6.32178i	−0.385538	+	0.247770i
$652$	3.77639	+	8.26913i	0.147895	+	0.323844i
$653$	16.9793	+	19.5952i	0.664452	+	0.766819i	0.983498	−	0.180921i	$-0.0579077\pi$
$653$	16.9793	+	19.5952i	0.664452	+	0.766819i	−0.319045	+	0.947739i	$0.603362\pi$
$654$	5.43902	+	3.49545i	0.212683	+	0.136683i
$655$	6.99566	−	48.6559i	0.273343	−	1.90114i
$656$	1.68639	−	11.7291i	0.0658426	−	0.457945i
$657$	−11.0120	−	7.07699i	−0.429620	−	0.276100i
$658$	−5.62347	−	6.48983i	−0.219226	−	0.253000i
$659$	−8.46149	−	18.5281i	−0.329613	−	0.721752i	0.670178	−	0.742200i	$-0.266218\pi$
$659$	−8.46149	−	18.5281i	−0.329613	−	0.721752i	−0.999791	+	0.0204488i	$0.993490\pi$
$660$	1.35964	−	0.873785i	0.0529237	−	0.0340120i
$661$	−40.3726	−	11.8545i	−1.57031	−	0.461085i	−0.623220	−	0.782047i	$-0.714176\pi$
$661$	−40.3726	−	11.8545i	−1.57031	−	0.461085i	−0.947092	+	0.320962i	$0.895994\pi$
$662$	−1.07480	+	1.24038i	−0.0417732	+	0.0482088i
$663$	−5.98325	+	1.75684i	−0.232370	+	0.0682301i
$664$	3.07020	−	6.72280i	0.119147	−	0.260895i
$665$	−1.73032	−	12.0347i	−0.0670991	−	0.466684i
$666$	−1.62721			−0.0630533
$667$	2.50194	+	4.70986i	0.0968756	+	0.182367i
$668$	2.87790			0.111349
$669$	−2.59129	−	18.0228i	−0.100185	−	0.696802i
$670$	6.59707	−	14.4456i	0.254867	−	0.558081i
$671$	−8.59158	+	2.52272i	−0.331674	+	0.0973883i
$672$	0.809721	−	0.934468i	0.0312357	−	0.0360479i
$673$	−19.5196	−	5.73148i	−0.752426	−	0.220932i	−0.117040	−	0.993127i	$-0.537341\pi$
$673$	−19.5196	−	5.73148i	−0.752426	−	0.220932i	−0.635386	+	0.772195i	$0.719159\pi$
$674$	15.1178	−	9.71564i	0.582317	−	0.374233i
$675$	0.718941	+	1.57426i	0.0276721	+	0.0605934i
$676$	7.36413	+	8.49866i	0.283236	+	0.326872i
$677$	9.29082	+	5.97085i	0.357075	+	0.229478i	0.706863	−	0.707351i	$-0.250110\pi$
$677$	9.29082	+	5.97085i	0.357075	+	0.229478i	−0.349788	+	0.936829i	$0.613746\pi$
$678$	0.193894	−	1.34856i	0.00744644	−	0.0517911i
$679$	2.01411	−	14.0084i	0.0772943	−	0.537594i
$680$	10.2744	+	6.60294i	0.394004	+	0.253211i
$681$	−10.4681	−	12.0809i	−0.401139	−	0.462940i
$682$	−2.44733	−	5.35891i	−0.0937131	−	0.205203i
$683$	−9.04131	+	5.81050i	−0.345956	+	0.222332i	−0.702066	−	0.712111i	$-0.747739\pi$
$683$	−9.04131	+	5.81050i	−0.345956	+	0.222332i	0.356110	+	0.934444i	$0.384103\pi$
$684$	−3.63667	−	1.06782i	−0.139051	−	0.0408292i
$685$	−19.3612	+	22.3440i	−0.739752	+	0.853720i
$686$	−14.7956	+	4.34439i	−0.564900	+	0.165870i
$687$	−7.36601	+	16.1293i	−0.281031	+	0.615372i
$688$	0.238916	+	1.66170i	0.00910859	+	0.0633516i
$689$	14.9070			0.567913
$690$	−12.1265	−	2.78431i	−0.461649	−	0.105997i
$691$	−21.3444			−0.811980			−0.405990	−	0.913878i	$-0.633073\pi$
$691$	−21.3444			−0.811980			−0.405990	+	0.913878i	$0.633073\pi$
$692$	−1.94440	−	13.5236i	−0.0739151	−	0.514091i
$693$	0.319990	−	0.700679i	0.0121554	−	0.0266166i
$694$	−0.214162	+	0.0628837i	−0.00812948	+	0.00238703i
$695$	9.00891	−	10.3968i	0.341727	−	0.394374i
$696$	1.06699	+	0.313298i	0.0404443	+	0.0118755i
$697$	46.9283	−	30.1590i	1.77754	−	1.14235i
$698$	−8.40791	−	18.4108i	−0.318244	−	0.696857i
$699$	6.11932	+	7.06208i	0.231454	+	0.267112i
$700$	−1.80022	−	1.15693i	−0.0680418	−	0.0437278i
$701$	4.68799	−	32.6057i	0.177063	−	1.23150i	−0.686452	−	0.727175i	$-0.740833\pi$
$701$	4.68799	−	32.6057i	0.177063	−	1.23150i	0.863515	−	0.504324i	$-0.168258\pi$
$702$	0.188515	−	1.31115i	0.00711505	−	0.0494862i
$703$	−5.18840	−	3.33438i	−0.195684	−	0.125759i
$704$	0.407958	+	0.470809i	0.0153755	+	0.0177443i
$705$	7.48479	+	16.3894i	0.281893	+	0.617261i
$706$	15.9954	−	10.2796i	0.601996	−	0.386879i
$707$	−2.11621	−	0.621377i	−0.0795884	−	0.0233693i
$708$	6.38246	−	7.36575i	0.239868	−	0.276822i
$709$	39.8126	−	11.6900i	1.49519	−	0.439028i	0.570998	−	0.820951i	$-0.306556\pi$
$709$	39.8126	−	11.6900i	1.49519	−	0.439028i	0.924194	+	0.381923i	$0.124738\pi$
$710$	−6.99723	+	15.3218i	−0.262601	+	0.575017i
$711$	1.71950	+	11.9594i	0.0644862	+	0.448511i
$712$	3.38500			0.126858
$713$	−16.3366	+	42.3087i	−0.611812	+	1.58447i
$714$	5.82085			0.217840
$715$	0.304679	+	2.11909i	0.0113943	+	0.0792493i
$716$	−8.47428	+	18.5561i	−0.316699	+	0.693473i
$717$	4.80613	−	1.41121i	0.179488	−	0.0527025i
$718$	−3.36334	+	3.88150i	−0.125519	+	0.144856i
$719$	26.8918	+	7.89614i	1.00289	+	0.294476i	0.741643	−	0.670795i	$-0.234047\pi$
$719$	26.8918	+	7.89614i	1.00289	+	0.294476i	0.261251	+	0.965271i	$0.415865\pi$
$720$	−2.18251	+	1.40261i	−0.0813372	+	0.0522723i
$721$	−10.1962	−	22.3267i	−0.379728	−	0.831488i
$722$	3.03490	+	3.50246i	0.112947	+	0.130348i
$723$	12.2622	+	7.88046i	0.456037	+	0.293077i
$724$	−1.35719	+	9.43949i	−0.0504397	+	0.350816i
$725$	0.273893	−	1.90497i	0.0101721	−	0.0707488i
$726$	−8.92731	−	5.73723i	−0.331323	−	0.212929i
$727$	−6.50261	−	7.50441i	−0.241168	−	0.278323i	0.622242	−	0.782825i	$-0.286222\pi$
$727$	−6.50261	−	7.50441i	−0.241168	−	0.278323i	−0.863411	+	0.504501i	$0.831676\pi$
$728$	0.680401	+	1.48987i	0.0252173	+	0.0552183i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	−32.5845	−	9.56766i	−1.20600	−	0.354115i
$731$	−5.17540	+	5.97273i	−0.191419	+	0.220909i
$732$	13.7913	−	4.04950i	0.509742	−	0.149674i
$733$	7.39687	−	16.1969i	0.273209	−	0.598245i	−0.722439	−	0.691435i	$-0.756979\pi$
$733$	7.39687	−	16.1969i	0.273209	−	0.598245i	0.995648	+	0.0931894i	$0.0297062\pi$
$734$	−3.52616	−	24.5250i	−0.130153	−	0.905234i
$735$	14.1940			0.523554
$736$	0.397086	−	4.77936i	0.0146368	−	0.176170i
$737$	3.81336			0.140467
$738$	1.68639	+	11.7291i	0.0620770	+	0.431755i
$739$	9.04059	−	19.7961i	0.332564	−	0.728213i	−0.667299	−	0.744790i	$-0.732550\pi$
$739$	9.04059	−	19.7961i	0.332564	−	0.728213i	0.999863	+	0.0165773i	$0.00527697\pi$
$740$	−4.05056	+	1.18935i	−0.148902	+	0.0437215i
$741$	3.28781	−	3.79433i	0.120781	−	0.139388i
$742$	−13.3513	−	3.92030i	−0.490142	−	0.143919i
$743$	−13.9637	+	8.97393i	−0.512279	+	0.329222i	−0.771111	−	0.636701i	$-0.780299\pi$
$743$	−13.9637	+	8.97393i	−0.512279	+	0.329222i	0.258832	+	0.965922i	$0.416662\pi$
$744$	3.92849	+	8.60219i	0.144025	+	0.315372i
$745$	23.4769	+	27.0938i	0.860126	+	0.992639i
$746$	31.2222	+	20.0653i	1.14313	+	0.734644i
$747$	−1.05180	+	7.31546i	−0.0384835	+	0.267659i
$748$	−0.417365	+	2.90284i	−0.0152604	+	0.106138i
$749$	4.53443	+	2.91410i	0.165684	+	0.106479i
$750$	−5.55441	−	6.41013i	−0.202818	−	0.234065i
$751$	−1.69926	−	3.72086i	−0.0620068	−	0.135776i	0.876092	−	0.482144i	$-0.160142\pi$
$751$	−1.69926	−	3.72086i	−0.0620068	−	0.135776i	−0.938099	+	0.346368i	$0.887415\pi$
$752$	−5.84246	+	3.75472i	−0.213052	+	0.136921i
$753$	17.9766	+	5.27841i	0.655104	+	0.192356i
$754$	−0.964640	+	1.11325i	−0.0351301	+	0.0405423i
$755$	−13.5292	+	3.97253i	−0.492378	+	0.144575i
$756$	−0.513652	+	1.12474i	−0.0186813	+	0.0409064i
$757$	−1.41901	−	9.86945i	−0.0515749	−	0.358711i	−0.999224	−	0.0393966i	$-0.987456\pi$
$757$	−1.41901	−	9.86945i	−0.0515749	−	0.358711i	0.947649	−	0.319315i	$-0.103453\pi$
$758$	−31.1816			−1.13257
$759$	−0.601478	−	2.92649i	−0.0218323	−	0.106225i
$760$	−9.83310			−0.356684
$761$	−6.54762	−	45.5397i	−0.237351	−	1.65081i	−0.664983	−	0.746859i	$-0.731561\pi$
$761$	−6.54762	−	45.5397i	−0.237351	−	1.65081i	0.427632	−	0.903953i	$-0.359348\pi$
$762$	1.43534	−	3.14295i	0.0519968	−	0.113857i
$763$	7.67048	−	2.25226i	0.277690	−	0.0815372i
$764$	−1.04322	+	1.20394i	−0.0377423	+	0.0435569i
$765$	−11.7184	−	3.44085i	−0.423681	−	0.124404i
$766$	−9.72169	+	6.24775i	−0.351259	+	0.225740i
$767$	5.36312	+	11.7436i	0.193651	+	0.424037i
$768$	−0.654861	−	0.755750i	−0.0236303	−	0.0272708i
$769$	23.0960	+	14.8429i	0.832863	+	0.535249i	0.886187	−	0.463329i	$-0.153345\pi$
$769$	23.0960	+	14.8429i	0.832863	+	0.535249i	−0.0533232	+	0.998577i	$0.516981\pi$
$770$	0.284402	−	1.97806i	0.0102491	−	0.0712843i
$771$	0.249026	−	1.73201i	0.00896846	−	0.0623770i
$772$	14.7877	+	9.50346i	0.532220	+	0.342037i
$773$	−5.94154	−	6.85690i	−0.213702	−	0.246626i	0.638770	−	0.769398i	$-0.279443\pi$
$773$	−5.94154	−	6.85690i	−0.213702	−	0.246626i	−0.852473	+	0.522772i	$0.824898\pi$
$774$	−0.697393	−	1.52708i	−0.0250673	−	0.0548896i
$775$	13.7683	−	8.84838i	0.494573	−	0.317843i
$776$	−10.9821	−	3.22465i	−0.394236	−	0.115758i
$777$	−1.31759	+	1.52058i	−0.0472683	+	0.0545505i
$778$	−22.8397	+	6.70634i	−0.818842	+	0.240434i
$779$	−18.6575	+	40.8541i	−0.668473	+	1.46375i
$780$	−0.489075	−	3.40159i	−0.0175117	−	0.121796i
$781$	−4.04466			−0.144729
$782$	18.2280	−	13.3212i	0.651832	−	0.476365i
$783$	−1.11204			−0.0397411
$784$	0.778622	+	5.41543i	0.0278079	+	0.193408i
$785$	−5.69263	+	12.4651i	−0.203179	+	0.444899i
$786$	−18.1799	+	5.33810i	−0.648456	+	0.190404i
$787$	34.0644	−	39.3125i	1.21427	−	1.40134i	0.323901	−	0.946091i	$-0.395006\pi$
$787$	34.0644	−	39.3125i	1.21427	−	1.40134i	0.890365	−	0.455247i	$-0.150449\pi$
$788$	−1.17212	−	0.344166i	−0.0417551	−	0.0122604i
$789$	−14.0110	+	9.00435i	−0.498806	+	0.320563i
$790$	13.0215	+	28.5132i	0.463285	+	1.01445i
$791$	−1.10319	−	1.27315i	−0.0392248	−	0.0452679i
$792$	−0.524075	−	0.336803i	−0.0186222	−	0.0119678i
$793$	−2.70963	+	18.8459i	−0.0962219	+	0.669238i
$794$	3.14876	−	21.9001i	0.111745	−	0.777207i
$795$	24.5613	+	15.7846i	0.871098	+	0.559821i
$796$	0.0656352	+	0.0757470i	0.00232638	+	0.00268478i
$797$	11.0146	+	24.1187i	0.390158	+	0.854328i	0.998174	+	0.0604028i	$0.0192385\pi$
$797$	11.0146	+	24.1187i	0.390158	+	0.854328i	−0.608016	+	0.793925i	$0.708034\pi$
$798$	−3.94253	+	2.53371i	−0.139564	+	0.0896924i
$799$	−31.3697	−	9.21096i	−1.10978	−	0.325861i
$800$	−1.13334	+	1.30794i	−0.0400696	+	0.0462428i
$801$	−3.24788	+	0.953664i	−0.114758	+	0.0336961i
$802$	−4.43980	+	9.72180i	−0.156775	+	0.343289i
$803$	−1.16053	−	8.07167i	−0.0409543	−	0.284843i
$804$	−6.12125			−0.215880
$805$	−12.4210	+	9.07735i	−0.437781	+	0.319934i
$806$	−12.5268			−0.441237
$807$	3.80021	+	26.4311i	0.133774	+	0.930418i
$808$	−0.740992	+	1.62255i	−0.0260680	+	0.0570810i
$809$	20.2221	−	5.93775i	0.710972	−	0.208760i	0.0938028	−	0.995591i	$-0.470098\pi$
$809$	20.2221	−	5.93775i	0.710972	−	0.208760i	0.617169	+	0.786831i	$0.288280\pi$
$810$	1.69894	−	1.96068i	0.0596946	−	0.0688913i
$811$	33.9380	+	9.96510i	1.19173	+	0.349922i	0.816684	−	0.577086i	$-0.195810\pi$
$811$	33.9380	+	9.96510i	1.19173	+	0.349922i	0.375042	+	0.927008i	$0.377628\pi$
$812$	1.15673	−	0.743388i	0.0405934	−	0.0260878i
$813$	11.1779	+	24.4763i	0.392028	+	0.858421i
$814$	−0.663836	−	0.766107i	−0.0232674	−	0.0268520i
$815$	−19.8404	−	12.7506i	−0.694978	−	0.446635i
$816$	0.669961	−	4.65968i	0.0234533	−	0.163122i
$817$	0.905539	−	6.29816i	0.0316808	−	0.220345i
$818$	−13.3592	−	8.58542i	−0.467093	−	0.300182i
$819$	−1.07259	−	1.23783i	−0.0374792	−	0.0432533i
$820$	12.7708	+	27.9642i	0.445977	+	0.976554i
$821$	−41.4714	+	26.6520i	−1.44736	+	0.930163i	−0.448015	+	0.894026i	$0.647869\pi$
$821$	−41.4714	+	26.6520i	−1.44736	+	0.930163i	−0.999347	+	0.0361365i	$0.988495\pi$
$822$	10.9344	+	3.21064i	0.381382	+	0.111984i
$823$	8.11057	−	9.36009i	0.282717	−	0.326272i	−0.596574	−	0.802558i	$-0.703472\pi$
$823$	8.11057	−	9.36009i	0.282717	−	0.326272i	0.879291	+	0.476286i	$0.158017\pi$
$824$	−19.0464	+	5.59253i	−0.663513	+	0.194825i
$825$	−0.447879	+	0.980717i	−0.0155931	+	0.0341442i
$826$	−1.71505	−	11.9284i	−0.0596741	−	0.415043i
$827$	30.0768			1.04587			0.522936	−	0.852372i	$-0.324837\pi$
$827$	30.0768			1.04587			0.522936	+	0.852372i	$0.324837\pi$
$828$	0.965501	+	4.69764i	0.0335535	+	0.163254i
$829$	48.4553			1.68292			0.841462	−	0.540317i	$-0.181696\pi$
$829$	48.4553			1.68292			0.841462	+	0.540317i	$0.181696\pi$
$830$	2.72875	+	18.9789i	0.0947163	+	0.658766i
$831$	−0.887800	+	1.94401i	−0.0307975	+	0.0674370i
$832$	1.27098	−	0.373193i	0.0440632	−	0.0129381i
$833$	−16.8665	+	19.4650i	−0.584389	+	0.674421i
$834$	−5.08787	−	1.49393i	−0.176179	−	0.0517307i
$835$	−6.28104	+	4.03658i	−0.217364	+	0.139692i
$836$	−0.980868	−	2.14780i	−0.0339240	−	0.0742833i
$837$	−6.19288	−	7.14696i	−0.214057	−	0.247035i
$838$	−3.89512	−	2.50324i	−0.134555	−	0.0864731i
$839$	6.45239	−	44.8773i	0.222761	−	1.54934i	−0.504764	−	0.863257i	$-0.668421\pi$
$839$	6.45239	−	44.8773i	0.222761	−	1.54934i	0.727525	−	0.686081i	$-0.240670\pi$
$840$	−0.456526	+	3.17521i	−0.0157516	+	0.109555i
$841$	−23.3560	−	15.0100i	−0.805380	−	0.517587i
$842$	6.88183	+	7.94206i	0.237164	+	0.273701i
$843$	−11.5426	−	25.2747i	−0.397548	−	0.870509i
$844$	−14.0465	+	9.02714i	−0.483501	+	0.310727i
$845$	−27.9926	−	8.21937i	−0.962975	−	0.282755i
$846$	4.54797	−	5.24864i	0.156362	−	0.180452i
$847$	−12.5899	+	3.69673i	−0.432594	+	0.127021i
$848$	−4.67495	+	10.2367i	−0.160539	+	0.351530i
$849$	−3.34175	−	23.2423i	−0.114688	−	0.797675i
$850$	−8.14724			−0.279448
$851$	−0.646144	+	7.77705i	−0.0221495	+	0.266594i
$852$	6.49255			0.222431
$853$	2.06419	+	14.3568i	0.0706765	+	0.491566i	0.994159	+	0.107925i	$0.0344207\pi$
$853$	2.06419	+	14.3568i	0.0706765	+	0.491566i	−0.923482	+	0.383641i	$0.874670\pi$
$854$	7.38301	−	16.1665i	0.252641	−	0.553207i
$855$	9.43479	−	2.77030i	0.322663	−	0.0947424i
$856$	2.85468	−	3.29448i	0.0975710	−	0.112603i
$857$	−47.8893	−	14.0616i	−1.63587	−	0.480334i	−0.670648	−	0.741776i	$-0.733984\pi$
$857$	−47.8893	−	14.0616i	−1.63587	−	0.480334i	−0.965219	+	0.261442i	$0.915802\pi$
$858$	0.694209	−	0.446141i	0.0236999	−	0.0152310i
$859$	22.8565	+	50.0487i	0.779853	+	1.70764i	0.703650	+	0.710547i	$0.251552\pi$
$859$	22.8565	+	50.0487i	0.779853	+	1.70764i	0.0762029	+	0.997092i	$0.475720\pi$
$860$	−2.85215	−	3.29156i	−0.0972576	−	0.112241i
$861$	12.3260	+	7.92144i	0.420069	+	0.269962i
$862$	−1.93953	+	13.4897i	−0.0660606	+	0.459461i
$863$	−5.67710	+	39.4851i	−0.193251	+	1.34409i	0.630081	+	0.776529i	$0.283022\pi$
$863$	−5.67710	+	39.4851i	−0.193251	+	1.34409i	−0.823332	+	0.567560i	$0.807888\pi$
$864$	0.841254	+	0.540641i	0.0286200	+	0.0183930i
$865$	23.2121	+	26.7882i	0.789234	+	0.910825i
$866$	−3.57691	−	7.83233i	−0.121548	−	0.266154i
$867$	4.34212	−	2.79051i	0.147466	−	0.0947707i
$868$	11.2195	+	3.29433i	0.380813	+	0.111817i
$869$	−4.92909	+	5.68848i	−0.167208	+	0.192968i
$870$	−2.76816	+	0.812804i	−0.0938493	+	0.0275566i
$871$	3.36836	−	7.37568i	0.114133	−	0.249916i
$872$	−0.920120	−	6.39957i	−0.0311592	−	0.216717i
$873$	11.4458			0.387381
$874$	−6.54758	+	16.9569i	−0.221475	+	0.573577i
$875$	−10.4876			−0.354545
$876$	1.86290	+	12.9568i	0.0629416	+	0.437769i
$877$	1.58544	−	3.47164i	0.0535366	−	0.117229i	−0.880973	−	0.473166i	$-0.843111\pi$
$877$	1.58544	−	3.47164i	0.0535366	−	0.117229i	0.934510	+	0.355937i	$0.115838\pi$
$878$	35.5322	−	10.4332i	1.19915	−	0.352103i
$879$	12.4295	−	14.3444i	0.419236	−	0.483824i
$880$	−1.55073	−	0.455337i	−0.0522752	−	0.0153494i
$881$	17.4153	−	11.1921i	0.586736	−	0.377072i	−0.213334	−	0.976979i	$-0.568432\pi$
$881$	17.4153	−	11.1921i	0.586736	−	0.377072i	0.800070	+	0.599907i	$0.204796\pi$
$882$	−2.27279	−	4.97671i	−0.0765287	−	0.167574i
$883$	−11.8661	−	13.6942i	−0.399327	−	0.460848i	0.520102	−	0.854104i	$-0.325894\pi$
$883$	−11.8661	−	13.6942i	−0.399327	−	0.460848i	−0.919429	+	0.393257i	$0.871348\pi$
$884$	5.24593	+	3.37135i	0.176440	+	0.113391i
$885$	−3.59847	+	25.0279i	−0.120961	+	0.841305i
$886$	−2.04943	+	14.2541i	−0.0688519	+	0.478875i
$887$	−23.7101	−	15.2376i	−0.796109	−	0.511628i	0.0782352	−	0.996935i	$-0.475071\pi$
$887$	−23.7101	−	15.2376i	−0.796109	−	0.511628i	−0.874344	+	0.485307i	$0.838708\pi$
$888$	1.06560	+	1.22977i	0.0357592	+	0.0412683i
$889$	−1.77476	−	3.88619i	−0.0595237	−	0.130339i
$890$	−7.38778	+	4.74784i	−0.247639	+	0.159148i
$891$	0.597735	+	0.175511i	0.0200249	+	0.00587983i
$892$	−11.9238	+	13.7608i	−0.399238	+	0.460746i
$893$	25.2564	−	7.41596i	0.845174	−	0.248166i
$894$	5.74044	−	12.5698i	0.191989	−	0.420397i
$895$	−7.53181	−	52.3849i	−0.251761	−	1.75103i
$896$	−1.23648			−0.0413079
$897$	−6.19162	−	1.42162i	−0.206732	−	0.0474666i
$898$	14.7629			0.492646
$899$	1.49663	+	10.4093i	0.0499153	+	0.347169i
$900$	0.718941	−	1.57426i	0.0239647	−	0.0524754i
$901$	−50.8319	+	14.9256i	−1.69346	+	0.497244i
$902$	−4.83420	+	5.57896i	−0.160961	+	0.185759i
$903$	−1.99170	−	0.584816i	−0.0662796	−	0.0194614i
$904$	−1.14615	+	0.736584i	−0.0381203	+	0.0244984i
$905$	−10.2779	−	22.5054i	−0.341648	−	0.748104i
$906$	3.55918	+	4.10752i	0.118246	+	0.136463i
$907$	20.8735	+	13.4146i	0.693092	+	0.445423i	0.839184	−	0.543848i	$-0.183033\pi$
$907$	20.8735	+	13.4146i	0.693092	+	0.445423i	−0.146092	+	0.989271i	$0.546670\pi$
$908$	−2.27494	+	15.8226i	−0.0754966	+	0.525090i
$909$	0.253852	−	1.76558i	0.00841975	−	0.0585607i
$910$	−3.57469	−	2.29731i	−0.118500	−	0.0761552i
$911$	24.6656	+	28.4657i	0.817209	+	0.943110i	0.999192	−	0.0401918i	$-0.0127969\pi$
$911$	24.6656	+	28.4657i	0.817209	+	0.943110i	−0.181983	+	0.983302i	$0.558251\pi$
$912$	1.57450	+	3.44768i	0.0521370	+	0.114164i
$913$	−3.87328	+	2.48920i	−0.128187	+	0.0823806i
$914$	−6.35610	−	1.86632i	−0.210241	−	0.0617324i
$915$	−24.4198	+	28.1819i	−0.807294	+	0.931666i
$916$	17.0134	−	4.99560i	0.562140	−	0.165059i
$917$	−9.73237	+	21.3109i	−0.321391	+	0.703749i
$918$	0.669961	+	4.65968i	0.0221120	+	0.153792i
$919$	51.5748			1.70129			0.850647	−	0.525737i	$-0.176210\pi$
$919$	51.5748			1.70129			0.850647	+	0.525737i	$0.176210\pi$
$920$	5.83695	+	10.9880i	0.192439	+	0.362262i
$921$	14.9115			0.491350
$922$	−1.04691	−	7.28139i	−0.0344780	−	0.239800i
$923$	−3.57267	+	7.82306i	−0.117596	+	0.257499i
$924$	−0.739087	+	0.217015i	−0.0243142	+	0.00713928i
$925$	1.84419	−	2.12831i	0.0606365	−	0.0699782i
$926$	−33.2328	−	9.75804i	−1.09210	−	0.320669i
$927$	16.6993	−	10.7320i	0.548477	−	0.352485i
$928$	−0.461958	−	1.01155i	−0.0151645	−	0.0332056i
$929$	8.90537	+	10.2773i	0.292176	+	0.337189i	0.882792	−	0.469764i	$-0.155661\pi$
$929$	8.90537	+	10.2773i	0.292176	+	0.337189i	−0.590617	+	0.806952i	$0.701115\pi$
$930$	−20.6395	−	13.2642i	−0.676796	−	0.434950i
$931$	2.95113	−	20.5255i	0.0967193	−	0.672698i
$932$	1.32986	−	9.24935i	0.0435609	−	0.302973i
$933$	−4.44887	−	2.85911i	−0.145649	−	0.0936031i
$934$	9.23548	+	10.6583i	0.302194	+	0.348751i
$935$	−3.16066	−	6.92087i	−0.103365	−	0.226337i
$936$	−1.11435	+	0.716152i	−0.0364238	+	0.0234081i
$937$	10.0520	+	2.95153i	0.328385	+	0.0964224i	0.441769	−	0.897129i	$-0.354351\pi$
$937$	10.0520	+	2.95153i	0.328385	+	0.0964224i	−0.113385	+	0.993551i	$0.536169\pi$
$938$	−4.95651	+	5.72012i	−0.161836	+	0.186768i
$939$	8.51109	−	2.49908i	0.277749	−	0.0815544i
$940$	7.48479	−	16.3894i	0.244127	−	0.534563i
$941$	−2.04257	−	14.2064i	−0.0665858	−	0.463114i	−0.995648	−	0.0931913i	$-0.970293\pi$
$941$	−2.04257	−	14.2064i	−0.0665858	−	0.463114i	0.929062	−	0.369923i	$-0.120616\pi$
$942$	5.28204			0.172098
$943$	56.7274	−	3.40241i	1.84730	−	0.110798i
$944$	−9.74629			−0.317215
$945$	−0.456526	−	3.17521i	−0.0148508	−	0.103290i
$946$	0.434454	−	0.951323i	0.0141253	−	0.0309302i
$947$	2.12191	−	0.623050i	0.0689529	−	0.0202464i	−0.247074	−	0.968997i	$-0.579469\pi$
$947$	2.12191	−	0.623050i	0.0689529	−	0.0202464i	0.316027	+	0.948750i	$0.397651\pi$
$948$	7.91225	−	9.13122i	0.256978	−	0.296568i
$949$	−16.6371	−	4.88510i	−0.540063	−	0.158577i
$950$	5.51823	−	3.54635i	0.179035	−	0.115059i
$951$	1.26274	+	2.76502i	0.0409472	+	0.0896618i
$952$	−3.81184	−	4.39910i	−0.123543	−	0.142576i
$953$	19.3483	+	12.4344i	0.626753	+	0.402790i	0.815106	−	0.579312i	$-0.196679\pi$
$953$	19.3483	+	12.4344i	0.626753	+	0.402790i	−0.188353	+	0.982101i	$0.560315\pi$
$954$	1.60157	−	11.1391i	0.0518527	−	0.360643i
$955$	0.588172	−	4.09083i	0.0190328	−	0.132376i
$956$	−4.21387	−	2.70809i	−0.136286	−	0.0875859i
$957$	−0.453666	−	0.523558i	−0.0146649	−	0.0169242i
$958$	−7.08182	−	15.5070i	−0.228803	−	0.501009i
$959$	11.8541	−	7.61815i	0.382788	−	0.246003i
$960$	2.48926	+	0.730913i	0.0803406	+	0.0235901i
$961$	−38.2640	+	44.1590i	−1.23432	+	1.42449i
$962$	−2.06815	+	0.607265i	−0.0666799	+	0.0195790i
$963$	−1.81089	+	3.96529i	−0.0583550	+	0.127780i
$964$	−2.07440	−	14.4278i	−0.0668120	−	0.464688i
$965$	−45.6039			−1.46804
$966$	5.17158	+	2.90155i	0.166393	+	0.0933558i
$967$	−8.31090			−0.267261			−0.133630	−	0.991031i	$-0.542663\pi$
$967$	−8.31090			−0.267261			−0.133630	+	0.991031i	$0.542663\pi$
$968$	1.51023	+	10.5039i	0.0485407	+	0.337608i
$969$	−7.41213	+	16.2303i	−0.238112	+	0.521393i
$970$	28.4915	−	8.36587i	0.914808	−	0.268612i
$971$	−9.81765	+	11.3302i	−0.315063	+	0.363602i	−0.891089	−	0.453829i	$-0.850058\pi$
$971$	−9.81765	+	11.3302i	−0.315063	+	0.363602i	0.576025	+	0.817432i	$0.304603\pi$
$972$	−0.959493	−	0.281733i	−0.0307758	−	0.00903658i
$973$	−5.51579	+	3.54479i	−0.176828	+	0.113641i
$974$	−5.12118	−	11.2138i	−0.164093	−	0.359314i
$975$	1.50126	+	1.73255i	0.0480788	+	0.0554859i
$976$	−12.0918	−	7.77093i	−0.387049	−	0.248741i
$977$	7.45385	−	51.8426i	0.238470	−	1.65859i	−0.421148	−	0.906992i	$-0.638373\pi$
$977$	7.45385	−	51.8426i	0.238470	−	1.65859i	0.659618	−	0.751601i	$-0.270718\pi$
$978$	−1.29373	+	8.99811i	−0.0413690	+	0.287728i
$979$	−1.77399	−	1.14008i	−0.0566971	−	0.0364370i
$980$	−9.29510	−	10.7271i	−0.296921	−	0.342665i
$981$	2.68582	+	5.88112i	0.0857515	+	0.187770i
$982$	−5.46304	+	3.51089i	−0.174333	+	0.112037i
$983$	28.9296	+	8.49451i	0.922712	+	0.270933i	0.708382	−	0.705829i	$-0.249425\pi$
$983$	28.9296	+	8.49451i	0.922712	+	0.270933i	0.214329	+	0.976761i	$0.431243\pi$
$984$	7.75992	−	8.95543i	0.247377	−	0.285489i
$985$	3.04090	−	0.892887i	0.0968910	−	0.0284498i
$986$	2.17471	−	4.76196i	0.0692570	−	0.151652i
$987$	−1.22210	−	8.49987i	−0.0388998	−	0.270554i
$988$	−5.02062			−0.159727
$989$	−7.57538	+	2.72671i	−0.240883	+	0.0867044i
$990$	1.61620			0.0513663
$991$	−0.384388	−	2.67348i	−0.0122105	−	0.0849258i	0.982805	−	0.184647i	$-0.0591141\pi$
$991$	−0.384388	−	2.67348i	−0.0122105	−	0.0849258i	−0.995015	+	0.0997209i	$0.968205\pi$
$992$	3.92849	−	8.60219i	0.124730	−	0.273120i
$993$	−1.57478	+	0.462397i	−0.0499741	+	0.0146737i
$994$	5.25715	−	6.06708i	0.166747	−	0.192436i
$995$	−0.249493	−	0.0732577i	−0.00790946	−	0.00232243i
$996$	6.21744	−	3.99571i	0.197007	−	0.126609i
$997$	3.76854	+	8.25196i	0.119351	+	0.261342i	0.959873	−	0.280435i	$-0.0904788\pi$
$997$	3.76854	+	8.25196i	0.119351	+	0.261342i	−0.840522	+	0.541778i	$0.817752\pi$
$998$	8.90642	+	10.2786i	0.281928	+	0.325362i
$999$	−1.36890	−	0.879739i	−0.0433101	−	0.0278337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.e.a.49.1	yes	10
3.2	odd	2		414.2.i.d.325.1		10
23.8	even	11	inner	138.2.e.a.31.1	✓	10
23.10	odd	22		3174.2.a.bd.1.4		5
23.13	even	11		3174.2.a.bc.1.2		5
69.8	odd	22		414.2.i.d.307.1		10
69.56	even	22		9522.2.a.bq.1.2		5
69.59	odd	22		9522.2.a.bt.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.a.31.1	✓	10	23.8	even	11	inner
138.2.e.a.49.1	yes	10	1.1	even	1	trivial
414.2.i.d.307.1		10	69.8	odd	22
414.2.i.d.325.1		10	3.2	odd	2
3174.2.a.bc.1.2		5	23.13	even	11
3174.2.a.bd.1.4		5	23.10	odd	22
9522.2.a.bq.1.2		5	69.56	even	22
9522.2.a.bt.1.4		5	69.59	odd	22

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.69894 - 1.96068i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-1.04019 + 0.668491i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.69894 - 1.96068i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-1.04019 + 0.668491i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-2.18251 - 1.40261i) q^{10} +(0.0886578 - 0.616629i) q^{11} +(-0.142315 + 0.989821i) q^{12} +(-1.11435 - 0.716152i) q^{13} +(0.809721 + 0.934468i) q^{14} +(-1.07773 - 2.35990i) q^{15} +(0.841254 - 0.540641i) q^{16} +(4.51691 + 1.32628i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(-3.63667 + 1.06782i) q^{19} +(-1.07773 + 2.35990i) q^{20} +(0.175969 + 1.22389i) q^{21} -0.622970 q^{22} +(3.35197 + 3.42992i) q^{23} +1.00000 q^{24} +(-0.246298 - 1.71304i) q^{25} +(-0.550273 + 1.20493i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(0.809721 - 0.934468i) q^{28} +(1.06699 + 0.313298i) q^{29} +(-2.18251 + 1.40261i) q^{30} +(3.92849 + 8.60219i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-0.524075 - 0.336803i) q^{33} +(0.669961 - 4.65968i) q^{34} +(-0.456526 + 3.17521i) q^{35} +(0.841254 + 0.540641i) q^{36} +(1.06560 + 1.22977i) q^{37} +(1.57450 + 3.44768i) q^{38} +(-1.11435 + 0.716152i) q^{39} +(2.48926 + 0.730913i) q^{40} +(7.75992 - 8.95543i) q^{41} +(1.18639 - 0.348356i) q^{42} +(-0.697393 + 1.52708i) q^{43} +(0.0886578 + 0.616629i) q^{44} -2.59435 q^{45} +(2.91797 - 3.80598i) q^{46} -6.94494 q^{47} +(-0.142315 - 0.989821i) q^{48} +(-2.27279 + 4.97671i) q^{49} +(-1.66055 + 0.487583i) q^{50} +(3.08282 - 3.55777i) q^{51} +(1.27098 + 0.373193i) q^{52} +(-9.46721 + 6.08421i) q^{53} +(0.415415 + 0.909632i) q^{54} +(-1.05839 - 1.22144i) q^{55} +(-1.04019 - 0.668491i) q^{56} +(-0.539401 + 3.75162i) q^{57} +(0.158260 - 1.10072i) q^{58} +(-8.19910 - 5.26924i) q^{59} +(1.69894 + 1.96068i) q^{60} +(-5.97099 - 13.0746i) q^{61} +(7.95555 - 5.11272i) q^{62} +(1.18639 + 0.348356i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-3.29736 + 0.968193i) q^{65} +(-0.258791 + 0.566673i) q^{66} +(0.871145 + 6.05895i) q^{67} -4.70760 q^{68} +(4.51242 - 1.62422i) q^{69} +3.20786 q^{70} +(-0.923986 - 6.42646i) q^{71} +(0.415415 - 0.909632i) q^{72} +(12.5598 - 3.68788i) q^{73} +(1.06560 - 1.22977i) q^{74} +(-1.66055 - 0.487583i) q^{75} +(3.18852 - 2.04913i) q^{76} +(0.319990 + 0.700679i) q^{77} +(0.867451 + 1.00109i) q^{78} +(-10.1643 - 6.53221i) q^{79} +(0.369215 - 2.56794i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-9.96863 - 6.40645i) q^{82} +(-4.83987 - 5.58551i) q^{83} +(-0.513652 - 1.12474i) q^{84} +(10.2744 - 6.60294i) q^{85} +(1.61078 + 0.472968i) q^{86} +(0.728231 - 0.840423i) q^{87} +(0.597735 - 0.175511i) q^{88} +(1.40618 - 3.07910i) q^{89} +(0.369215 + 2.56794i) q^{90} +1.63788 q^{91} +(-4.18251 - 2.34662i) q^{92} +9.45679 q^{93} +(0.988368 + 6.87425i) q^{94} +(-4.08482 + 8.94450i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(-7.49539 + 8.65015i) q^{97} +(5.24950 + 1.54139i) q^{98} +(-0.524075 + 0.336803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{3} - q^{4} + 8 q^{5} - q^{6} + 8 q^{7} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 - q^3 - q^4 + 8 * q^5 - q^6 + 8 * q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} + 8 q^{5} - q^{6} + 8 q^{7} - q^{8} - q^{9} - 3 q^{10} + 7 q^{11} - q^{12} + 3 q^{13} - 3 q^{14} - 3 q^{15} - q^{16} + 4 q^{17} - q^{18} - 3 q^{20} - 3 q^{21} - 26 q^{22} - 12 q^{23} + 10 q^{24} - 15 q^{25} + 3 q^{26} - q^{27} - 3 q^{28} - 25 q^{29} - 3 q^{30} + 6 q^{31} - q^{32} - 4 q^{33} - 7 q^{34} + 2 q^{35} - q^{36} + 9 q^{37} + 11 q^{38} + 3 q^{39} - 3 q^{40} + 24 q^{41} + 8 q^{42} - 30 q^{43} + 7 q^{44} - 14 q^{45} + 21 q^{46} - 48 q^{47} - q^{48} + 9 q^{49} + 7 q^{50} + 15 q^{51} + 14 q^{52} + 15 q^{53} - q^{54} - 23 q^{55} + 8 q^{56} - 11 q^{57} - 3 q^{58} + 5 q^{59} + 8 q^{60} + 12 q^{61} + 28 q^{62} + 8 q^{63} - q^{64} - 13 q^{65} + 18 q^{66} + 18 q^{67} - 18 q^{68} - q^{69} + 2 q^{70} + 28 q^{71} - q^{72} + 19 q^{73} + 9 q^{74} + 7 q^{75} + 22 q^{76} - 12 q^{77} - 8 q^{78} - 52 q^{79} + 8 q^{80} - q^{81} - 20 q^{82} + 7 q^{83} - 3 q^{84} + 23 q^{85} + 14 q^{86} + 30 q^{87} - 4 q^{88} + 3 q^{89} + 8 q^{90} + 42 q^{91} - 23 q^{92} - 16 q^{93} + 29 q^{94} + 22 q^{95} - q^{96} + 51 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 + 8 * q^5 - q^6 + 8 * q^7 - q^8 - q^9 - 3 * q^10 + 7 * q^11 - q^12 + 3 * q^13 - 3 * q^14 - 3 * q^15 - q^16 + 4 * q^17 - q^18 - 3 * q^20 - 3 * q^21 - 26 * q^22 - 12 * q^23 + 10 * q^24 - 15 * q^25 + 3 * q^26 - q^27 - 3 * q^28 - 25 * q^29 - 3 * q^30 + 6 * q^31 - q^32 - 4 * q^33 - 7 * q^34 + 2 * q^35 - q^36 + 9 * q^37 + 11 * q^38 + 3 * q^39 - 3 * q^40 + 24 * q^41 + 8 * q^42 - 30 * q^43 + 7 * q^44 - 14 * q^45 + 21 * q^46 - 48 * q^47 - q^48 + 9 * q^49 + 7 * q^50 + 15 * q^51 + 14 * q^52 + 15 * q^53 - q^54 - 23 * q^55 + 8 * q^56 - 11 * q^57 - 3 * q^58 + 5 * q^59 + 8 * q^60 + 12 * q^61 + 28 * q^62 + 8 * q^63 - q^64 - 13 * q^65 + 18 * q^66 + 18 * q^67 - 18 * q^68 - q^69 + 2 * q^70 + 28 * q^71 - q^72 + 19 * q^73 + 9 * q^74 + 7 * q^75 + 22 * q^76 - 12 * q^77 - 8 * q^78 - 52 * q^79 + 8 * q^80 - q^81 - 20 * q^82 + 7 * q^83 - 3 * q^84 + 23 * q^85 + 14 * q^86 + 30 * q^87 - 4 * q^88 + 3 * q^89 + 8 * q^90 + 42 * q^91 - 23 * q^92 - 16 * q^93 + 29 * q^94 + 22 * q^95 - q^96 + 51 * q^97 - 2 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more