LMFDB - Embedded newform 138.2.f.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(5,138)]

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([11, 1]))

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

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

chi := DirichletCharacter("138.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.f (of order $22$, 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:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	138.11
Dual form			138.2.f.a.113.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540641 - 0.841254i) q^{2} +(1.29667 - 1.14833i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-1.43749 + 0.422085i) q^{5} +(-1.66706 - 0.469995i) q^{6} +(3.34037 - 2.89445i) q^{7} +(0.989821 - 0.142315i) q^{8} +(0.362698 - 2.97799i) q^{9} +O(q^{10})$	\(q+(-0.540641 - 0.841254i) q^{2} +(1.29667 - 1.14833i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-1.43749 + 0.422085i) q^{5} +(-1.66706 - 0.469995i) q^{6} +(3.34037 - 2.89445i) q^{7} +(0.989821 - 0.142315i) q^{8} +(0.362698 - 2.97799i) q^{9} +(1.13225 + 0.981098i) q^{10} +(-1.75207 - 1.12599i) q^{11} +(0.505898 + 1.65652i) q^{12} +(-2.50409 + 2.88987i) q^{13} +(-4.24090 - 1.24524i) q^{14} +(-1.37926 + 2.19801i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(1.53425 + 3.35954i) q^{17} +(-2.70134 + 1.30490i) q^{18} +(0.806590 + 0.368357i) q^{19} +(0.213213 - 1.48293i) q^{20} +(1.00759 - 7.58897i) q^{21} +2.08269i q^{22} +(4.39445 + 1.92063i) q^{23} +(1.12005 - 1.32117i) q^{24} +(-2.31804 + 1.48972i) q^{25} +(3.78493 + 0.544191i) q^{26} +(-2.94941 - 4.27797i) q^{27} +(1.24524 + 4.24090i) q^{28} +(4.85145 - 2.21558i) q^{29} +(2.59477 - 0.0280297i) q^{30} +(1.34101 + 9.32693i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(-3.56486 + 0.551916i) q^{33} +(1.99675 - 3.10700i) q^{34} +(-3.58005 + 5.57066i) q^{35} +(2.55821 + 1.56702i) q^{36} +(-0.717497 + 2.44357i) q^{37} +(-0.126194 - 0.877696i) q^{38} +(0.0715413 + 6.62272i) q^{39} +(-1.36279 + 0.622366i) q^{40} +(-0.0613750 - 0.209024i) q^{41} +(-6.92899 + 3.25527i) q^{42} +(-3.01815 - 0.433944i) q^{43} +(1.75207 - 1.12599i) q^{44} +(0.735594 + 4.43393i) q^{45} +(-0.760086 - 4.73522i) q^{46} +9.62337i q^{47} +(-1.71698 - 0.227963i) q^{48} +(1.78404 - 12.4083i) q^{49} +(2.50646 + 1.14466i) q^{50} +(5.84727 + 2.59439i) q^{51} +(-1.58848 - 3.47830i) q^{52} +(-8.08324 - 9.32856i) q^{53} +(-2.00428 + 4.79404i) q^{54} +(2.99385 + 0.879075i) q^{55} +(2.89445 - 3.34037i) q^{56} +(1.46887 - 0.448591i) q^{57} +(-4.48676 - 2.88346i) q^{58} +(-6.92648 - 6.00183i) q^{59} +(-1.42642 - 2.16770i) q^{60} +(6.28652 - 0.903865i) q^{61} +(7.12131 - 6.17065i) q^{62} +(-7.40810 - 10.9974i) q^{63} +(0.959493 - 0.281733i) q^{64} +(2.37983 - 5.21111i) q^{65} +(2.39161 + 2.70056i) q^{66} +(-1.67331 - 2.60371i) q^{67} -3.69330 q^{68} +(7.90365 - 2.55584i) q^{69} +6.62186 q^{70} +(6.11097 + 9.50886i) q^{71} +(-0.0648069 - 2.99930i) q^{72} +(-1.78840 + 3.91604i) q^{73} +(2.44357 - 0.717497i) q^{74} +(-1.29505 + 4.59353i) q^{75} +(-0.670139 + 0.580679i) q^{76} +(-9.11169 + 1.31006i) q^{77} +(5.53271 - 3.64070i) q^{78} +(-9.86473 - 8.54784i) q^{79} +(1.26035 + 0.809976i) q^{80} +(-8.73690 - 2.16022i) q^{81} +(-0.142660 + 0.164639i) q^{82} +(-3.42714 - 1.00630i) q^{83} +(6.48460 + 4.06910i) q^{84} +(-3.62349 - 4.18173i) q^{85} +(1.26668 + 2.77364i) q^{86} +(3.74651 - 8.44392i) q^{87} +(-1.89449 - 0.865182i) q^{88} +(1.50592 - 10.4739i) q^{89} +(3.33237 - 3.01598i) q^{90} +16.9012i q^{91} +(-3.57258 + 3.19948i) q^{92} +(12.4492 + 10.5540i) q^{93} +(8.09570 - 5.20279i) q^{94} +(-1.31494 - 0.189061i) q^{95} +(0.736496 + 1.56766i) q^{96} +(-1.95376 - 6.65389i) q^{97} +(-11.4031 + 5.20760i) q^{98} +(-3.98866 + 4.80927i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.540641	−	0.841254i	−0.382291	−	0.594856i
$2$	−0.540641	−	0.841254i	−0.382291	−	0.594856i
$3$	1.29667	−	1.14833i	0.748632	−	0.662986i
$3$	1.29667	−	1.14833i	0.748632	−	0.662986i
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	−1.43749	+	0.422085i	−0.642866	+	0.188762i	−0.586886	−	0.809670i	$-0.699646\pi$
$5$	−1.43749	+	0.422085i	−0.642866	+	0.188762i	−0.0559796	+	0.998432i	$0.517828\pi$
$6$	−1.66706	−	0.469995i	−0.680576	−	0.191875i
$7$	3.34037	−	2.89445i	1.26254	−	1.09400i	0.271223	−	0.962517i	$-0.412572\pi$
$7$	3.34037	−	2.89445i	1.26254	−	1.09400i	0.991319	−	0.131481i	$-0.0419734\pi$
$8$	0.989821	−	0.142315i	0.349955	−	0.0503159i
$9$	0.362698	−	2.97799i	0.120899	−	0.992665i
$10$	1.13225	+	0.981098i	0.358048	+	0.310250i
$11$	−1.75207	−	1.12599i	−0.528270	−	0.339499i	0.249166	−	0.968461i	$-0.419844\pi$
$11$	−1.75207	−	1.12599i	−0.528270	−	0.339499i	−0.777436	+	0.628962i	$0.783480\pi$
$12$	0.505898	+	1.65652i	0.146040	+	0.478197i
$13$	−2.50409	+	2.88987i	−0.694510	+	0.801507i	−0.988000	−	0.154455i	$-0.950638\pi$
$13$	−2.50409	+	2.88987i	−0.694510	+	0.801507i	0.293490	+	0.955962i	$0.405183\pi$
$14$	−4.24090	−	1.24524i	−1.13343	−	0.332805i
$15$	−1.37926	+	2.19801i	−0.356123	+	0.567524i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	1.53425	+	3.35954i	0.372111	+	0.814809i	0.999352	+	0.0359844i	$0.0114567\pi$
$17$	1.53425	+	3.35954i	0.372111	+	0.814809i	−0.627241	+	0.778825i	$0.715816\pi$
$18$	−2.70134	+	1.30490i	−0.636711	+	0.307569i
$19$	0.806590	+	0.368357i	0.185045	+	0.0845070i	0.505783	−	0.862661i	$-0.331204\pi$
$19$	0.806590	+	0.368357i	0.185045	+	0.0845070i	−0.320738	+	0.947168i	$0.603931\pi$
$20$	0.213213	−	1.48293i	0.0476759	−	0.331593i
$21$	1.00759	−	7.58897i	0.219873	−	1.65605i
$22$			2.08269i			0.444032i
$23$	4.39445	+	1.92063i	0.916306	+	0.400478i
$23$	4.39445	+	1.92063i	0.916306	+	0.400478i
$24$	1.12005	−	1.32117i	0.228629	−	0.269683i
$25$	−2.31804	+	1.48972i	−0.463609	+	0.297943i
$26$	3.78493	+	0.544191i	0.742286	+	0.106725i
$27$	−2.94941	−	4.27797i	−0.567614	−	0.823295i
$28$	1.24524	+	4.24090i	0.235329	+	0.801456i
$29$	4.85145	−	2.21558i	0.900891	−	0.411423i	0.0895408	−	0.995983i	$-0.471460\pi$
$29$	4.85145	−	2.21558i	0.900891	−	0.411423i	0.811351	+	0.584560i	$0.198733\pi$
$30$	2.59477	−	0.0280297i	0.473738	−	0.00511751i
$31$	1.34101	+	9.32693i	0.240852	+	1.67517i	0.647874	+	0.761747i	$0.275658\pi$
$31$	1.34101	+	9.32693i	0.240852	+	1.67517i	−0.407022	+	0.913418i	$0.633433\pi$
$32$	−0.281733	+	0.959493i	−0.0498038	+	0.169616i
$33$	−3.56486	+	0.551916i	−0.620563	+	0.0960762i
$34$	1.99675	−	3.10700i	0.342440	−	0.532847i
$35$	−3.58005	+	5.57066i	−0.605139	+	0.941614i
$36$	2.55821	+	1.56702i	0.426368	+	0.261171i
$37$	−0.717497	+	2.44357i	−0.117956	+	0.401720i	−0.997211	−	0.0746301i	$-0.976222\pi$
$37$	−0.717497	+	2.44357i	−0.117956	+	0.401720i	0.879256	+	0.476350i	$0.158041\pi$
$38$	−0.126194	−	0.877696i	−0.0204713	−	0.142381i
$39$	0.0715413	+	6.62272i	0.0114558	+	1.06048i
$40$	−1.36279	+	0.622366i	−0.215476	+	0.0984046i
$41$	−0.0613750	−	0.209024i	−0.00958517	−	0.0326441i	0.954562	−	0.298014i	$-0.0963242\pi$
$41$	−0.0613750	−	0.209024i	−0.00958517	−	0.0326441i	−0.964147	+	0.265370i	$0.914506\pi$
$42$	−6.92899	+	3.25527i	−1.06917	+	0.502299i
$43$	−3.01815	−	0.433944i	−0.460263	−	0.0661759i	−0.0917167	−	0.995785i	$-0.529235\pi$
$43$	−3.01815	−	0.433944i	−0.460263	−	0.0661759i	−0.368547	+	0.929609i	$0.620144\pi$
$44$	1.75207	−	1.12599i	0.264135	−	0.169749i
$45$	0.735594	+	4.43393i	0.109656	+	0.660971i
$46$	−0.760086	−	4.73522i	−0.112069	−	0.698169i
$47$			9.62337i			1.40371i	0.712318	+	0.701856i	$0.247645\pi$
$47$			9.62337i			1.40371i	−0.712318	+	0.701856i	$0.752355\pi$
$48$	−1.71698	−	0.227963i	−0.247825	−	0.0329037i
$49$	1.78404	−	12.4083i	0.254863	−	1.77261i
$50$	2.50646	+	1.14466i	0.354467	+	0.161879i
$51$	5.84727	+	2.59439i	0.818781	+	0.363288i
$52$	−1.58848	−	3.47830i	−0.220283	−	0.482353i
$53$	−8.08324	−	9.32856i	−1.11032	−	1.28138i	−0.956004	−	0.293354i	$-0.905228\pi$
$53$	−8.08324	−	9.32856i	−1.11032	−	1.28138i	−0.154315	−	0.988022i	$-0.549317\pi$
$54$	−2.00428	+	4.79404i	−0.272748	+	0.652387i
$55$	2.99385	+	0.879075i	0.403691	+	0.118534i
$56$	2.89445	−	3.34037i	0.386787	−	0.446376i
$57$	1.46887	−	0.448591i	0.194557	−	0.0594173i
$58$	−4.48676	−	2.88346i	−0.589140	−	0.378617i
$59$	−6.92648	−	6.00183i	−0.901751	−	0.781372i	0.0746787	−	0.997208i	$-0.476207\pi$
$59$	−6.92648	−	6.00183i	−0.901751	−	0.781372i	−0.976430	+	0.215836i	$0.930752\pi$
$60$	−1.42642	−	2.16770i	−0.184150	−	0.279849i
$61$	6.28652	−	0.903865i	0.804906	−	0.115728i	0.272433	−	0.962175i	$-0.412172\pi$
$61$	6.28652	−	0.903865i	0.804906	−	0.115728i	0.532473	+	0.846447i	$0.321263\pi$
$62$	7.12131	−	6.17065i	0.904407	−	0.783673i
$63$	−7.40810	−	10.9974i	−0.933333	−	1.38554i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	2.37983	−	5.21111i	0.295182	−	0.646358i
$66$	2.39161	+	2.70056i	0.294387	+	0.332416i
$67$	−1.67331	−	2.60371i	−0.204427	−	0.318094i	0.723869	−	0.689938i	$-0.242362\pi$
$67$	−1.67331	−	2.60371i	−0.204427	−	0.318094i	−0.928295	+	0.371843i	$0.878726\pi$
$68$	−3.69330			−0.447879
$69$	7.90365	−	2.55584i	0.951487	−	0.307687i
$70$	6.62186			0.791464
$71$	6.11097	+	9.50886i	0.725239	+	1.12849i	0.986585	+	0.163249i	$0.0521972\pi$
$71$	6.11097	+	9.50886i	0.725239	+	1.12849i	−0.261346	+	0.965245i	$0.584166\pi$
$72$	−0.0648069	−	2.99930i	−0.00763756	−	0.353471i
$73$	−1.78840	+	3.91604i	−0.209316	+	0.458338i	−0.984949	−	0.172846i	$-0.944704\pi$
$73$	−1.78840	+	3.91604i	−0.209316	+	0.458338i	0.775633	+	0.631184i	$0.217431\pi$
$74$	2.44357	−	0.717497i	0.284059	−	0.0834073i
$75$	−1.29505	+	4.59353i	−0.149540	+	0.530416i
$76$	−0.670139	+	0.580679i	−0.0768703	+	0.0666085i
$77$	−9.11169	+	1.31006i	−1.03837	+	0.149296i
$78$	5.53271	−	3.64070i	0.626456	−	0.412228i
$79$	−9.86473	−	8.54784i	−1.10987	−	0.961707i	−0.110387	−	0.993889i	$-0.535209\pi$
$79$	−9.86473	−	8.54784i	−1.10987	−	0.961707i	−0.999482	+	0.0321821i	$0.989754\pi$
$80$	1.26035	+	0.809976i	0.140911	+	0.0905581i
$81$	−8.73690	−	2.16022i	−0.970767	−	0.240025i
$82$	−0.142660	+	0.164639i	−0.0157542	+	0.0181813i
$83$	−3.42714	−	1.00630i	−0.376177	−	0.110456i	0.0881777	−	0.996105i	$-0.471896\pi$
$83$	−3.42714	−	1.00630i	−0.376177	−	0.110456i	−0.464355	+	0.885649i	$0.653714\pi$
$84$	6.48460	+	4.06910i	0.707528	+	0.443976i
$85$	−3.62349	−	4.18173i	−0.393023	−	0.453572i
$86$	1.26668	+	2.77364i	0.136589	+	0.299089i
$87$	3.74651	−	8.44392i	0.401668	−	0.905283i
$88$	−1.89449	−	0.865182i	−0.201953	−	0.0922287i
$89$	1.50592	−	10.4739i	0.159627	−	1.11023i	−0.739694	−	0.672943i	$-0.765030\pi$
$89$	1.50592	−	10.4739i	0.159627	−	1.11023i	0.899322	−	0.437288i	$-0.144061\pi$
$90$	3.33237	−	3.01598i	0.351262	−	0.317913i
$91$			16.9012i			1.77173i
$92$	−3.57258	+	3.19948i	−0.372468	+	0.333568i
$93$	12.4492	+	10.5540i	1.29092	+	1.09440i
$94$	8.09570	−	5.20279i	0.835007	−	0.536627i
$95$	−1.31494	−	0.189061i	−0.134910	−	0.0193972i
$96$	0.736496	+	1.56766i	0.0751684	+	0.159999i
$97$	−1.95376	−	6.65389i	−0.198374	−	0.675600i	−0.997250	−	0.0741047i	$-0.976390\pi$
$97$	−1.95376	−	6.65389i	−0.198374	−	0.675600i	0.798876	−	0.601495i	$-0.205428\pi$
$98$	−11.4031	+	5.20760i	−1.15188	+	0.526047i
$99$	−3.98866	+	4.80927i	−0.400876	+	0.483350i
$100$	−0.392143	−	2.72742i	−0.0392143	−	0.272742i
$101$	−2.92436	+	9.95947i	−0.290985	+	0.991004i	0.676155	+	0.736760i	$0.263645\pi$
$101$	−2.92436	+	9.95947i	−0.290985	+	0.991004i	−0.967140	+	0.254245i	$0.918173\pi$
$102$	−0.978728	−	6.32167i	−0.0969085	−	0.625939i
$103$	10.4440	−	16.2512i	1.02908	−	1.60127i	0.256299	−	0.966597i	$-0.417497\pi$
$103$	10.4440	−	16.2512i	1.02908	−	1.60127i	0.772777	−	0.634677i	$-0.218867\pi$
$104$	−2.06733	+	3.21683i	−0.202718	+	0.315436i
$105$	1.75480	+	11.3344i	0.171251	+	1.10612i
$106$	−3.47755	+	11.8435i	−0.337770	+	1.15034i
$107$	0.778146	+	5.41213i	0.0752262	+	0.523210i	0.992238	+	0.124351i	$0.0396847\pi$
$107$	0.778146	+	5.41213i	0.0752262	+	0.523210i	−0.917012	+	0.398859i	$0.869406\pi$
$108$	5.11660	−	0.905744i	0.492345	−	0.0871553i
$109$	−8.78378	+	4.01142i	−0.841334	+	0.384224i	−0.788991	−	0.614405i	$-0.789396\pi$
$109$	−8.78378	+	4.01142i	−0.841334	+	0.384224i	−0.0523429	+	0.998629i	$0.516669\pi$
$110$	−0.879075	−	2.99385i	−0.0838165	−	0.285453i
$111$	1.87566	+	3.99242i	0.178029	+	0.378944i
$112$	−4.37495	−	0.629023i	−0.413394	−	0.0594371i
$113$	5.05558	−	3.24902i	0.475589	−	0.305642i	−0.280798	−	0.959767i	$-0.590599\pi$
$113$	5.05558	−	3.24902i	0.475589	−	0.305642i	0.756387	+	0.654124i	$0.226963\pi$
$114$	−1.17151	−	0.993169i	−0.109722	−	0.0930188i
$115$	−7.12765	−	0.906049i	−0.664657	−	0.0844895i
$116$			5.33342i			0.495196i
$117$	7.69780	+	8.50532i	0.711662	+	0.786317i
$118$	−1.30432	+	9.07176i	−0.120073	+	0.835123i
$119$	14.8490	+	6.78131i	1.36121	+	0.621642i
$120$	−1.05241	+	2.37193i	−0.0960714	+	0.216526i
$121$	−2.76766	−	6.06032i	−0.251605	−	0.550938i
$122$	−4.15913	−	4.79989i	−0.376550	−	0.434561i
$123$	−0.319611	−	0.200556i	−0.0288183	−	0.0180836i
$124$	−9.04115	−	2.65472i	−0.811919	−	0.238401i
$125$	7.60887	−	8.78110i	0.680558	−	0.785406i
$126$	−5.24649	+	12.1777i	−0.467394	+	1.08488i
$127$	11.1438	+	7.16167i	0.988850	+	0.635495i	0.931837	−	0.362878i	$-0.118206\pi$
$127$	11.1438	+	7.16167i	0.988850	+	0.635495i	0.0570134	+	0.998373i	$0.481842\pi$
$128$	−0.755750	−	0.654861i	−0.0667995	−	0.0578821i
$129$	−4.41185	+	2.90313i	−0.388441	+	0.255607i
$130$	−5.67050	+	0.815294i	−0.497336	+	0.0715061i
$131$	5.82456	−	5.04701i	0.508894	−	0.440959i	−0.362182	−	0.932107i	$-0.617968\pi$
$131$	5.82456	−	5.04701i	0.508894	−	0.440959i	0.871076	+	0.491148i	$0.163423\pi$
$132$	0.978856	−	3.47199i	0.0851985	−	0.302198i
$133$	3.76050	−	1.10418i	0.326077	−	0.0957448i
$134$	−1.28573	+	2.81535i	−0.111070	+	0.243209i
$135$	6.04542	+	4.90464i	0.520306	+	0.422124i
$136$	1.99675	+	3.10700i	0.171220	+	0.266423i
$137$	−16.0060			−1.36748			−0.683741	−	0.729725i	$-0.739648\pi$
$137$	−16.0060			−1.36748			−0.683741	+	0.729725i	$0.739648\pi$
$138$	−6.42315	−	5.26718i	−0.546775	−	0.448372i
$139$	0.415789			0.0352668			0.0176334	−	0.999845i	$-0.494387\pi$
$139$	0.415789			0.0352668			0.0176334	+	0.999845i	$0.494387\pi$
$140$	−3.58005	−	5.57066i	−0.302569	−	0.470807i
$141$	11.0508	+	12.4783i	0.930642	+	1.05086i
$142$	4.69552	−	10.2818i	0.394039	−	0.862825i
$143$	7.64132	−	2.24369i	0.638999	−	0.187627i
$144$	−2.48813	+	1.67606i	−0.207345	+	0.139672i
$145$	−6.03875	+	5.23261i	−0.501491	+	0.434544i
$146$	4.26126	−	0.612677i	0.352665	−	0.0507055i
$147$	−11.9354	−	18.1381i	−0.984419	−	1.49601i
$148$	−1.92469	−	1.66775i	−0.158209	−	0.137088i
$149$	2.64950	+	1.70273i	0.217055	+	0.139493i	0.644651	−	0.764477i	$-0.277003\pi$
$149$	2.64950	+	1.70273i	0.217055	+	0.139493i	−0.427595	+	0.903970i	$0.640639\pi$
$150$	4.56449	−	1.39398i	0.372689	−	0.113818i
$151$	3.12657	−	3.60826i	0.254437	−	0.293636i	−0.614133	−	0.789203i	$-0.710494\pi$
$151$	3.12657	−	3.60826i	0.254437	−	0.293636i	0.868570	+	0.495567i	$0.165040\pi$
$152$	0.850803	+	0.249818i	0.0690092	+	0.0202629i
$153$	10.5612	−	3.35050i	0.853820	−	0.270872i
$154$	6.02825	+	6.95697i	0.485770	+	0.560608i
$155$	−5.86445	−	12.8414i	−0.471044	−	1.03144i
$156$	−6.05395	−	2.68610i	−0.484704	−	0.215060i
$157$	−2.06181	−	0.941599i	−0.164551	−	0.0751477i	0.331437	−	0.943477i	$-0.392467\pi$
$157$	−2.06181	−	0.941599i	−0.164551	−	0.0751477i	−0.495988	+	0.868330i	$0.665194\pi$
$158$	−1.85762	+	12.9200i	−0.147784	+	1.02786i
$159$	−21.1935	−	2.81385i	−1.68075	−	0.223153i
$160$		−	1.49818i		−	0.118441i
$161$	20.2382	−	6.30390i	1.59500	−	0.496817i
$162$	2.90623	+	8.51785i	0.228335	+	0.669226i
$163$	−10.2526	+	6.58893i	−0.803043	+	0.516085i	−0.876608	−	0.481206i	$-0.840199\pi$
$163$	−10.2526	+	6.58893i	−0.803043	+	0.516085i	0.0735643	+	0.997290i	$0.476563\pi$
$164$	0.215631	+	0.0310031i	0.0168380	+	0.00242093i
$165$	4.89150	−	2.29805i	0.380803	−	0.178903i
$166$	1.00630	+	3.42714i	0.0781039	+	0.265998i
$167$	−8.04885	+	3.67579i	−0.622839	+	0.284441i	−0.701731	−	0.712442i	$-0.747589\pi$
$167$	−8.04885	+	3.67579i	−0.622839	+	0.284441i	0.0788919	+	0.996883i	$0.474862\pi$
$168$	−0.0826937	−	7.65512i	−0.00637996	−	0.590605i
$169$	−0.230811	−	1.60533i	−0.0177547	−	0.123487i
$170$	−1.55889	+	5.30909i	−0.119561	+	0.407188i
$171$	1.38951	−	2.26842i	0.106259	−	0.173470i
$172$	1.64851	−	2.56514i	0.125698	−	0.195590i
$173$	−9.50005	+	14.7824i	−0.722276	+	1.12388i	0.264905	+	0.964275i	$0.414659\pi$
$173$	−9.50005	+	14.7824i	−0.722276	+	1.12388i	−0.987180	+	0.159608i	$0.948977\pi$
$174$	−9.12899	+	1.41336i	−0.692067	+	0.107147i
$175$	−3.43122	+	11.6857i	−0.259376	+	0.883352i
$176$	0.296398	+	2.06150i	0.0223419	+	0.155391i
$177$	−15.8734	+	0.171471i	−1.19312	+	0.0128885i
$178$	−9.62536	+	4.39576i	−0.721452	+	0.329476i
$179$	3.55735	+	12.1152i	0.265889	+	0.905534i	0.978893	+	0.204374i	$0.0655159\pi$
$179$	3.55735	+	12.1152i	0.265889	+	0.905534i	−0.713004	+	0.701160i	$0.752666\pi$
$180$	−4.33882	−	1.17280i	−0.323397	−	0.0874155i
$181$	18.0950	+	2.60167i	1.34499	+	0.193380i	0.776920	−	0.629600i	$-0.216781\pi$
$181$	18.0950	+	2.60167i	1.34499	+	0.193380i	0.568070	+	0.822980i	$0.307690\pi$
$182$	14.2182	−	9.13748i	1.05392	−	0.677315i
$183$	7.11360	−	8.39098i	0.525852	−	0.620279i
$184$	4.62306	+	1.27568i	0.340816	+	0.0940445i
$185$		−	3.81545i		−	0.280518i
$186$	2.14806	−	16.1789i	0.157504	−	1.18629i
$187$	1.09469	−	7.61372i	0.0800515	−	0.556770i
$188$	−8.75373	−	3.99769i	−0.638431	−	0.291562i
$189$	−22.2345	−	5.75308i	−1.61732	−	0.418475i
$190$	0.551865	+	1.20842i	0.0400365	+	0.0876677i
$191$	9.55402	+	11.0259i	0.691305	+	0.797808i	0.987550	−	0.157304i	$-0.0502801\pi$
$191$	9.55402	+	11.0259i	0.691305	+	0.797808i	−0.296246	+	0.955112i	$0.595735\pi$
$192$	0.920624	−	1.46712i	0.0664403	−	0.105881i
$193$	0.392170	+	0.115152i	0.0282290	+	0.00828880i	0.295817	−	0.955245i	$-0.404408\pi$
$193$	0.392170	+	0.115152i	0.0282290	+	0.00828880i	−0.267588	+	0.963534i	$0.586226\pi$
$194$	−4.54132	+	5.24097i	−0.326048	+	0.376280i
$195$	−2.89819	−	9.48990i	−0.207544	−	0.679586i
$196$	10.5459	+	6.77742i	0.753276	+	0.484101i
$197$	−13.2726	−	11.5008i	−0.945637	−	0.819399i	0.0380522	−	0.999276i	$-0.487885\pi$
$197$	−13.2726	−	11.5008i	−0.945637	−	0.819399i	−0.983689	+	0.179877i	$0.942430\pi$
$198$	6.20225	+	0.755388i	0.440775	+	0.0536831i
$199$	8.87881	−	1.27658i	0.629403	−	0.0904944i	0.179771	−	0.983709i	$-0.442464\pi$
$199$	8.87881	−	1.27658i	0.629403	−	0.0904944i	0.449632	+	0.893214i	$0.351555\pi$
$200$	−2.08244	+	1.80444i	−0.147251	+	0.127593i
$201$	−5.15963	−	1.45466i	−0.363933	−	0.102603i
$202$	9.95947	−	2.92436i	0.700746	−	0.205758i
$203$	9.79275	−	21.4431i	0.687316	−	1.50501i
$204$	−4.78899	+	4.24111i	−0.335296	+	0.296937i
$205$	0.176452	+	0.274565i	0.0123239	+	0.0191764i
$206$	−19.3178			−1.34593
$207$	7.31347	−	12.3900i	0.508321	−	0.861167i
$208$	3.82385			0.265136
$209$	−0.998439	−	1.55360i	−0.0690635	−	0.107465i
$210$	8.58636	−	7.60405i	0.592515	−	0.524729i
$211$	5.24063	−	11.4754i	0.360780	−	0.789998i	−0.639004	−	0.769204i	$-0.720653\pi$
$211$	5.24063	−	11.4754i	0.360780	−	0.789998i	0.999784	−	0.0207943i	$-0.00661951\pi$
$212$	11.8435	−	3.47755i	0.813412	−	0.238839i
$213$	18.8432	+	5.31245i	1.29111	+	0.364003i
$214$	4.13227	−	3.58063i	0.282476	−	0.244767i
$215$	4.52172	−	0.650126i	0.308379	−	0.0443382i
$216$	−3.52821	−	3.81468i	−0.240064	−	0.259556i
$217$	31.4758	+	27.2739i	2.13671	+	1.85147i
$218$	8.12349	+	5.22065i	0.550192	+	0.353587i
$219$	2.17793	+	7.13147i	0.147171	+	0.481900i
$220$	−2.04333	+	2.35812i	−0.137761	+	0.158985i
$221$	−13.5506	−	3.97880i	−0.911510	−	0.267643i
$222$	2.34458	−	3.73637i	0.157358	−	0.250769i
$223$	−9.65557	−	11.1431i	−0.646585	−	0.746198i	0.333940	−	0.942594i	$-0.391622\pi$
$223$	−9.65557	−	11.1431i	−0.646585	−	0.746198i	−0.980525	+	0.196396i	$0.937076\pi$
$224$	1.83611	+	4.02052i	0.122680	+	0.268632i
$225$	3.59562	+	7.44344i	0.239708	+	0.496229i
$226$	−5.46651	−	2.49647i	−0.363627	−	0.166063i
$227$	1.98541	−	13.8089i	0.131777	−	0.916526i	−0.811461	−	0.584407i	$-0.801327\pi$
$227$	1.98541	−	13.8089i	0.131777	−	0.916526i	0.943237	−	0.332119i	$-0.107764\pi$
$228$	−0.202140	+	1.52249i	−0.0133871	+	0.100829i
$229$			4.45353i			0.294298i	0.989114	+	0.147149i	$0.0470096\pi$
$229$			4.45353i			0.294298i	−0.989114	+	0.147149i	$0.952990\pi$
$230$	3.09128	+	6.48601i	0.203833	+	0.427675i
$231$	−10.3105	+	12.1619i	−0.678379	+	0.800194i
$232$	4.48676	−	2.88346i	0.294570	−	0.189309i
$233$	−8.57581	−	1.23301i	−0.561820	−	0.0807775i	−0.144446	−	0.989513i	$-0.546140\pi$
$233$	−8.57581	−	1.23301i	−0.561820	−	0.0807775i	−0.417373	+	0.908735i	$0.637049\pi$
$234$	2.99338	−	11.0741i	0.195683	−	0.723938i
$235$	−4.06189	−	13.8335i	−0.264968	−	0.902399i
$236$	8.33682	−	3.80730i	0.542681	−	0.247834i
$237$	−22.6070	+	0.244210i	−1.46848	+	0.0158631i
$238$	−2.32317	−	16.1580i	−0.150589	−	1.04737i
$239$	6.42524	−	21.8824i	0.415614	−	1.41545i	−0.440075	−	0.897961i	$-0.645048\pi$
$239$	6.42524	−	21.8824i	0.415614	−	1.41545i	0.855689	−	0.517491i	$-0.173134\pi$
$240$	2.56437	−	0.397019i	0.165529	−	0.0256274i
$241$	−10.5755	+	16.4557i	−0.681225	+	1.06001i	0.312689	+	0.949855i	$0.398770\pi$
$241$	−10.5755	+	16.4557i	−0.681225	+	1.06001i	−0.993915	+	0.110152i	$0.964866\pi$
$242$	−3.60196	+	5.60476i	−0.231543	+	0.360287i
$243$	−13.8095	+	7.23171i	−0.885880	+	0.463915i
$244$	−1.78933	+	6.09390i	−0.114550	+	0.390122i
$245$	2.67282	+	18.5898i	0.170760	+	1.18766i
$246$	0.00407578	+	0.377303i	0.000259862	+	0.0240559i
$247$	−3.08428	+	1.40854i	−0.196248	+	0.0896235i
$248$	2.65472	+	9.04115i	0.168575	+	0.574113i
$249$	−5.59942	+	2.63063i	−0.354849	+	0.166710i
$250$	−11.5008	−	1.65357i	−0.727374	−	0.104581i
$251$	11.8661	−	7.62590i	0.748983	−	0.481342i	−0.109626	−	0.993973i	$-0.534965\pi$
$251$	11.8661	−	7.62590i	0.748983	−	0.481342i	0.858609	+	0.512631i	$0.171329\pi$
$252$	13.0810	−	2.17016i	0.824028	−	0.136707i
$253$	−5.53680	−	8.31318i	−0.348095	−	0.522645i
$254$		−	13.2466i		−	0.831167i
$255$	−9.50045	−	1.26137i	−0.594941	−	0.0789902i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−7.29558	−	3.33178i	−0.455086	−	0.207831i	0.174665	−	0.984628i	$-0.444116\pi$
$257$	−7.29558	−	3.33178i	−0.455086	−	0.207831i	−0.629751	+	0.776797i	$0.716843\pi$
$258$	4.82750	+	2.14193i	0.300547	+	0.133351i
$259$	4.67608	+	10.2392i	0.290557	+	0.636232i
$260$	3.75157	+	4.32954i	0.232663	+	0.268507i
$261$	−4.83838	−	15.2512i	−0.299488	−	0.944024i
$262$	−7.39481	−	2.17131i	−0.456853	−	0.134144i
$263$	−12.4722	+	14.3937i	−0.769069	+	0.887553i	−0.996270	−	0.0862953i	$-0.972497\pi$
$263$	−12.4722	+	14.3937i	−0.769069	+	0.887553i	0.227201	+	0.973848i	$0.427043\pi$
$264$	−3.45003	+	1.05363i	−0.212335	+	0.0648465i
$265$	15.5570	+	9.99790i	0.955661	+	0.614166i
$266$	−2.96198	−	2.56657i	−0.181611	−	0.157366i
$267$	−10.0748	−	15.3105i	−0.616566	−	0.936985i
$268$	3.06354	−	0.440470i	0.187135	−	0.0269060i
$269$	−1.95976	+	1.69814i	−0.119489	+	0.103537i	−0.712556	−	0.701616i	$-0.752462\pi$
$269$	−1.95976	+	1.69814i	−0.119489	+	0.103537i	0.593067	+	0.805153i	$0.297917\pi$
$270$	0.857644	−	7.73737i	0.0521946	−	0.470882i
$271$	−1.61521	+	0.474268i	−0.0981170	+	0.0288098i	−0.330423	−	0.943833i	$-0.607191\pi$
$271$	−1.61521	+	0.474268i	−0.0981170	+	0.0288098i	0.232306	+	0.972643i	$0.425373\pi$
$272$	1.53425	−	3.35954i	0.0930277	−	0.203702i
$273$	19.4081	+	21.9153i	1.17463	+	1.32637i
$274$	8.65347	+	13.4651i	0.522775	+	0.813454i
$275$	5.73879			0.346062
$276$	−0.958416	+	8.25115i	−0.0576899	+	0.496661i
$277$	−12.1413			−0.729498			−0.364749	−	0.931106i	$-0.618845\pi$
$277$	−12.1413			−0.729498			−0.364749	+	0.931106i	$0.618845\pi$
$278$	−0.224793	−	0.349784i	−0.0134822	−	0.0209787i
$279$	28.2619	−	0.610665i	1.69200	−	0.0365595i
$280$	−2.75082	+	6.02346i	−0.164393	+	0.359970i
$281$	−14.4675	+	4.24804i	−0.863059	+	0.253417i	−0.683161	−	0.730268i	$-0.739395\pi$
$281$	−14.4675	+	4.24804i	−0.863059	+	0.253417i	−0.179899	+	0.983685i	$0.557577\pi$
$282$	4.52294	−	16.0428i	0.269337	−	0.955334i
$283$	−18.9926	+	16.4572i	−1.12899	+	0.978278i	−0.999911	−	0.0133560i	$-0.995749\pi$
$283$	−18.9926	+	16.4572i	−1.12899	+	0.978278i	−0.129082	+	0.991634i	$0.541203\pi$
$284$	−11.1881	+	1.60861i	−0.663895	+	0.0954536i
$285$	−1.92215	+	1.26484i	−0.113858	+	0.0749224i
$286$	−6.01872	−	5.21525i	−0.355894	−	0.308384i
$287$	−0.810025	−	0.520571i	−0.0478142	−	0.0307283i
$288$	2.75518	+	1.18700i	0.162351	+	0.0699449i
$289$	2.20002	−	2.53896i	0.129413	−	0.149351i
$290$	7.66674	+	2.25116i	0.450207	+	0.132193i
$291$	−10.1742	−	6.38433i	−0.596422	−	0.374256i
$292$	−2.81923	−	3.25357i	−0.164983	−	0.190401i
$293$	10.0554	+	22.0182i	0.587443	+	1.28632i	0.936975	+	0.349396i	$0.113613\pi$
$293$	10.0554	+	22.0182i	0.587443	+	1.28632i	−0.349533	+	0.936924i	$0.613660\pi$
$294$	−8.80596	+	19.8469i	−0.513574	+	1.15750i
$295$	12.4900	+	5.70401i	0.727198	+	0.332100i
$296$	−0.362437	+	2.52081i	−0.0210662	+	0.146519i
$297$	0.350636	+	10.8163i	0.0203459	+	0.627626i
$298$		−	3.14946i		−	0.182443i
$299$	−16.5545	+	7.88999i	−0.957369	+	0.456290i
$300$	−3.64044	−	3.08625i	−0.210181	−	0.178185i
$301$	−11.3378	+	7.28634i	−0.653498	+	0.419977i
$302$	−4.72581	−	0.679469i	−0.271940	−	0.0390990i
$303$	7.64478	+	16.2723i	0.439181	+	0.934816i
$304$	−0.249818	−	0.850803i	−0.0143281	−	0.0487969i
$305$	−8.65530	+	3.95274i	−0.495601	+	0.226334i
$306$	−8.52842	−	7.07321i	−0.487537	−	0.404349i
$307$	1.99118	+	13.8489i	0.113642	+	0.790401i	0.964325	+	0.264721i	$0.0852799\pi$
$307$	1.99118	+	13.8489i	0.113642	+	0.790401i	−0.850683	+	0.525680i	$0.823811\pi$
$308$	2.59346	−	8.83251i	0.147776	−	0.503279i
$309$	−5.11923	−	33.0655i	−0.291223	−	1.88103i
$310$	−7.63227	+	11.8761i	−0.433484	+	0.674514i
$311$	4.32275	−	6.72633i	0.245121	−	0.381415i	−0.696792	−	0.717273i	$-0.745390\pi$
$311$	4.32275	−	6.72633i	0.245121	−	0.381415i	0.941913	+	0.335858i	$0.109026\pi$
$312$	1.01332	+	6.54513i	0.0573682	+	0.370545i
$313$	2.64169	−	8.99677i	0.149317	−	0.508527i	−0.850532	−	0.525924i	$-0.823720\pi$
$313$	2.64169	−	8.99677i	0.149317	−	0.508527i	0.999849	+	0.0173966i	$0.00553780\pi$
$314$	0.322577	+	2.24357i	0.0182041	+	0.126612i
$315$	15.2909	+	12.6818i	0.861546	+	0.714540i
$316$	11.8733	−	5.42237i	0.667928	−	0.305032i
$317$	−5.80350	−	19.7649i	−0.325957	−	1.11011i	−0.945629	−	0.325246i	$-0.894553\pi$
$317$	−5.80350	−	19.7649i	−0.325957	−	1.11011i	0.619673	−	0.784860i	$-0.287265\pi$
$318$	9.09091	+	19.3504i	0.509793	+	1.08512i
$319$	−10.9948	−	1.58082i	−0.615592	−	0.0885087i
$320$	−1.26035	+	0.809976i	−0.0704556	+	0.0452790i
$321$	7.22388	+	6.12417i	0.403198	+	0.341818i
$322$	−16.2448	−	13.6173i	−0.905287	−	0.758865i
$323$			3.27493i			0.182222i
$324$	5.59445	−	7.04998i	0.310803	−	0.391665i
$325$	1.49950	−	10.4292i	0.0831771	−	0.578510i
$326$	11.0859	+	5.06277i	0.613992	+	0.280401i
$327$	−6.78324	+	15.2881i	−0.375114	+	0.845435i
$328$	−0.0904975	−	0.198162i	−0.00499689	−	0.0109417i
$329$	27.8543	+	32.1456i	1.53566	+	1.77225i
$330$	−4.57779	−	2.87257i	−0.251999	−	0.158130i
$331$	12.4601	+	3.65863i	0.684871	+	0.201096i	0.605615	−	0.795758i	$-0.292927\pi$
$331$	12.4601	+	3.65863i	0.684871	+	0.201096i	0.0792563	+	0.996854i	$0.474745\pi$
$332$	2.33905	−	2.69940i	0.128372	−	0.148149i
$333$	7.01670	+	3.02298i	0.384513	+	0.165658i
$334$	7.44381	+	4.78384i	0.407307	+	0.261760i
$335$	3.50435	+	3.03654i	0.191463	+	0.165904i
$336$	−6.39519	+	4.20824i	−0.348886	+	0.229578i
$337$	3.56137	−	0.512047i	0.194000	−	0.0278930i	−0.0446298	−	0.999004i	$-0.514211\pi$
$337$	3.56137	−	0.512047i	0.194000	−	0.0278930i	0.238630	+	0.971111i	$0.423302\pi$
$338$	−1.22570	+	1.06208i	−0.0666693	+	0.0577693i
$339$	2.82447	−	10.0184i	0.153404	−	0.544122i
$340$	5.30909	−	1.55889i	0.287926	−	0.0845426i
$341$	8.15247	−	17.8514i	0.441481	−	0.966709i
$342$	−2.65954	+	0.0574656i	−0.143812	+	0.00310739i
$343$	−13.2286	−	20.5841i	−0.714276	−	1.11144i
$344$	−3.04918			−0.164401
$345$	−10.2826	+	7.01002i	−0.553599	+	0.377407i
$346$	17.5718			0.944668
$347$	10.3610	+	16.1220i	0.556207	+	0.865475i	0.999523	−	0.0308903i	$-0.00983425\pi$
$347$	10.3610	+	16.1220i	0.556207	+	0.865475i	−0.443316	+	0.896366i	$0.646198\pi$
$348$	6.12450	+	6.91568i	0.328308	+	0.370719i
$349$	3.67410	−	8.04515i	0.196670	−	0.430647i	−0.785444	−	0.618932i	$-0.787566\pi$
$349$	3.67410	−	8.04515i	0.196670	−	0.430647i	0.982114	+	0.188285i	$0.0602929\pi$
$350$	11.6857	−	3.43122i	0.624624	−	0.183406i
$351$	19.7484	+	2.18899i	1.05409	+	0.116840i
$352$	1.57400	−	1.36387i	0.0838942	−	0.0726948i
$353$	17.0199	−	2.44709i	0.905878	−	0.130246i	0.326399	−	0.945232i	$-0.394165\pi$
$353$	17.0199	−	2.44709i	0.905878	−	0.130246i	0.579480	+	0.814987i	$0.303256\pi$
$354$	8.72606	+	13.2609i	0.463785	+	0.704806i
$355$	−12.7980	−	11.0895i	−0.679248	−	0.588572i
$356$	8.90181	+	5.72085i	0.471795	+	0.303204i
$357$	27.0414	−	8.25837i	1.43118	−	0.437079i
$358$	8.26872	−	9.54262i	0.437016	−	0.504343i
$359$	−25.0701	−	7.36126i	−1.32315	−	0.388512i	−0.457522	−	0.889198i	$-0.651263\pi$
$359$	−25.0701	−	7.36126i	−1.32315	−	0.388512i	−0.865629	+	0.500686i	$0.833081\pi$
$360$	1.35912	+	4.28411i	0.0716319	+	0.225793i
$361$	−11.9275	−	13.7650i	−0.627761	−	0.724474i
$362$	−7.59423	−	16.6290i	−0.399144	−	0.874003i
$363$	−10.5479	−	4.68006i	−0.553624	−	0.245639i
$364$	−15.3739	−	7.02101i	−0.805810	−	0.368001i
$365$	0.917900	−	6.38413i	0.0480451	−	0.334161i
$366$	−10.9048	−	1.44783i	−0.570005	−	0.0756794i
$367$		−	10.8935i		−	0.568637i	−0.958730	−	0.284318i	$-0.908233\pi$
$367$		−	10.8935i		−	0.568637i	0.958730	−	0.284318i	$-0.0917673\pi$
$368$	−1.42624	−	4.57885i	−0.0743479	−	0.238689i
$369$	−0.644733	+	0.106962i	−0.0335635	+	0.00556821i
$370$	−3.20976	+	2.06279i	−0.166868	+	0.107239i
$371$	−54.0020	−	7.76432i	−2.80365	−	0.403103i
$372$	−14.7719	+	6.93989i	−0.765885	+	0.359816i
$373$	−4.61692	−	15.7238i	−0.239055	−	0.814147i	−0.988388	−	0.151953i	$-0.951444\pi$
$373$	−4.61692	−	15.7238i	−0.239055	−	0.814147i	0.749333	−	0.662194i	$-0.230374\pi$
$374$	−6.99690	+	3.19538i	−0.361801	+	0.165229i
$375$	−0.217384	−	20.1236i	−0.0112256	−	1.03918i
$376$	1.36955	+	9.52542i	0.0706291	+	0.491236i
$377$	−5.74571	+	19.5681i	−0.295919	+	1.00781i
$378$	7.18105	+	21.8152i	0.369354	+	1.12205i
$379$	−4.54460	+	7.07153i	−0.233440	+	0.363240i	−0.938135	−	0.346271i	$-0.887448\pi$
$379$	−4.54460	+	7.07153i	−0.233440	+	0.363240i	0.704694	+	0.709511i	$0.251084\pi$
$380$	0.718223	−	1.11758i	0.0368441	−	0.0573305i
$381$	22.6737	−	3.51037i	1.16161	−	0.179842i
$382$	4.11031	−	13.9984i	0.210302	−	0.716222i
$383$	2.07801	+	14.4529i	0.106181	+	0.738506i	0.971458	+	0.237212i	$0.0762336\pi$
$383$	2.07801	+	14.4529i	0.106181	+	0.738506i	−0.865277	+	0.501294i	$0.832857\pi$
$384$	−1.73195	+	0.0187092i	−0.0883832	+	0.000954751i
$385$	12.5450	−	5.72912i	0.639353	−	0.291983i
$386$	−0.115152	−	0.392170i	−0.00586106	−	0.0199610i
$387$	−2.38696	+	8.83064i	−0.121336	+	0.448887i
$388$	6.86421	+	0.986924i	0.348477	+	0.0501035i
$389$	1.39589	−	0.897083i	0.0707743	−	0.0454839i	−0.504775	−	0.863251i	$-0.668425\pi$
$389$	1.39589	−	0.897083i	0.0707743	−	0.0454839i	0.575549	+	0.817767i	$0.304788\pi$
$390$	−6.41653	+	7.56874i	−0.324914	+	0.383258i
$391$	0.289769	+	17.7101i	0.0146542	+	0.895637i
$392$		−	12.5359i		−	0.633158i
$393$	1.75691	−	13.2328i	0.0886246	−	0.667506i
$394$	−2.49937	+	17.3835i	−0.125916	+	0.875767i
$395$	17.7884	+	8.12368i	0.895030	+	0.408747i
$396$	−2.71772	−	5.62606i	−0.136570	−	0.282720i
$397$	−0.289503	−	0.633922i	−0.0145297	−	0.0318156i	0.902228	−	0.431259i	$-0.141931\pi$
$397$	−0.289503	−	0.633922i	−0.0145297	−	0.0318156i	−0.916758	+	0.399444i	$0.869203\pi$
$398$	−5.87418	−	6.77916i	−0.294446	−	0.339809i
$399$	3.60816	−	5.75004i	0.180634	−	0.287862i
$400$	2.64385	+	0.776304i	0.132192	+	0.0388152i
$401$	6.66635	−	7.69338i	0.332902	−	0.384189i	−0.564478	−	0.825448i	$-0.690923\pi$
$401$	6.66635	−	7.69338i	0.332902	−	0.384189i	0.897380	+	0.441259i	$0.145468\pi$
$402$	1.56578	+	5.12701i	0.0780938	+	0.255712i
$403$	−30.3116	−	19.4801i	−1.50993	−	0.970374i
$404$	−7.84463	−	6.79741i	−0.390285	−	0.338184i
$405$	13.4710	−	0.582417i	0.669380	−	0.0289405i
$406$	−23.3335	+	3.35485i	−1.15802	+	0.166498i
$407$	4.00854	−	3.47342i	0.198696	−	0.172171i
$408$	6.15697	+	1.73583i	0.304816	+	0.0859366i
$409$	6.83524	−	2.00701i	0.337981	−	0.0992402i	−0.108338	−	0.994114i	$-0.534553\pi$
$409$	6.83524	−	2.00701i	0.337981	−	0.0992402i	0.446319	+	0.894874i	$0.352735\pi$
$410$	0.135581	−	0.296882i	0.00669589	−	0.0146620i
$411$	−20.7544	+	18.3800i	−1.02374	+	0.906621i
$412$	10.4440	+	16.2512i	0.514538	+	0.800637i
$413$	−40.5090			−1.99332
$414$	−14.3771	+	0.546080i	−0.706597	+	0.0268384i
$415$	5.35123			0.262681
$416$	−2.06733	−	3.21683i	−0.101359	−	0.157718i
$417$	0.539141	−	0.477461i	0.0264018	−	0.0233814i
$418$	−0.767176	+	1.67988i	−0.0375238	+	0.0821657i
$419$	28.9174	−	8.49091i	1.41271	−	0.414808i	0.515678	−	0.856782i	$-0.327540\pi$
$419$	28.9174	−	8.49091i	1.41271	−	0.414808i	0.897028	+	0.441974i	$0.145722\pi$
$420$	−11.0391	−	3.11224i	−0.538651	−	0.151862i
$421$	1.45761	−	1.26303i	0.0710398	−	0.0615563i	−0.618617	−	0.785693i	$-0.712307\pi$
$421$	1.45761	−	1.26303i	0.0710398	−	0.0615563i	0.689657	+	0.724136i	$0.257761\pi$
$422$	−12.4870	+	1.79536i	−0.607858	+	0.0873968i
$423$	28.6583	+	3.49037i	1.39342	+	0.169708i
$424$	−9.32856	−	8.08324i	−0.453035	−	0.392557i
$425$	−8.56123	−	5.50197i	−0.415281	−	0.266885i
$426$	−5.71827	−	18.7240i	−0.277051	−	0.907181i
$427$	18.3831	−	21.2152i	0.889621	−	1.02668i
$428$	−5.24630	−	1.54045i	−0.253589	−	0.0744605i
$429$	7.33176	−	11.6840i	0.353981	−	0.564111i
$430$	−2.99155	−	3.45243i	−0.144265	−	0.166491i
$431$	7.36638	+	16.1301i	0.354826	+	0.776960i	0.999917	+	0.0128549i	$0.00409195\pi$
$431$	7.36638	+	16.1301i	0.354826	+	0.776960i	−0.645092	+	0.764105i	$0.723181\pi$
$432$	−1.30162	+	5.03049i	−0.0626242	+	0.242029i
$433$	11.7875	+	5.38317i	0.566471	+	0.258699i	0.677999	−	0.735063i	$-0.262847\pi$
$433$	11.7875	+	5.38317i	0.566471	+	0.258699i	−0.111528	+	0.993761i	$0.535575\pi$
$434$	5.92719	−	41.2245i	0.284514	−	1.97884i
$435$	−1.82152	+	13.7194i	−0.0873352	+	0.657795i
$436$		−	9.65641i		−	0.462458i
$437$	2.83704	+	3.16789i	0.135714	+	0.151541i
$438$	4.82189	−	5.68776i	0.230399	−	0.271772i
$439$	30.1165	−	19.3547i	1.43738	−	0.923748i	0.437683	−	0.899129i	$-0.355799\pi$
$439$	30.1165	−	19.3547i	1.43738	−	0.923748i	0.999697	−	0.0246192i	$-0.00783731\pi$
$440$	3.08849	+	0.444057i	0.147238	+	0.0211696i
$441$	−36.3048	−	9.81333i	−1.72880	−	0.467302i
$442$	3.97880	+	13.5506i	0.189252	+	0.644535i
$443$	27.0628	−	12.3591i	1.28579	−	0.587201i	0.349010	−	0.937119i	$-0.386518\pi$
$443$	27.0628	−	12.3591i	1.28579	−	0.587201i	0.936780	+	0.349918i	$0.113791\pi$
$444$	−4.41081	+	0.0476473i	−0.209328	+	0.00226124i
$445$	2.25613	+	15.6918i	0.106951	+	0.743861i
$446$	−4.15399	+	14.1472i	−0.196697	+	0.669890i
$447$	5.39080	−	0.834611i	0.254976	−	0.0394757i
$448$	2.38960	−	3.71829i	0.112898	−	0.175673i
$449$	19.2115	−	29.8936i	0.906645	−	1.41077i	−0.00509021	−	0.999987i	$-0.501620\pi$
$449$	19.2115	−	29.8936i	0.906645	−	1.41077i	0.911735	−	0.410779i	$-0.134743\pi$
$450$	4.31788	−	7.04905i	0.203547	−	0.332295i
$451$	−0.127825	+	0.435333i	−0.00601906	+	0.0204990i
$452$	0.855252	+	5.94841i	0.0402277	+	0.279790i
$453$	−0.0893254	−	8.26903i	−0.00419687	−	0.388513i
$454$	−12.6902	+	5.79540i	−0.595578	+	0.271991i
$455$	−7.13375	−	24.2953i	−0.334435	−	1.13898i
$456$	1.39008	−	0.653067i	0.0650966	−	0.0305827i
$457$	−31.1612	−	4.48030i	−1.45766	−	0.209580i	−0.632535	−	0.774532i	$-0.717986\pi$
$457$	−31.1612	−	4.48030i	−1.45766	−	0.209580i	−0.825124	+	0.564952i	$0.808895\pi$
$458$	3.74655	−	2.40776i	0.175065	−	0.112507i
$459$	9.84688	−	16.4721i	0.459613	−	0.768854i
$460$	3.78510	−	6.10715i	0.176481	−	0.284748i
$461$			12.6427i			0.588831i	0.955678	+	0.294415i	$0.0951249\pi$
$461$			12.6427i			0.588831i	−0.955678	+	0.294415i	$0.904875\pi$
$462$	15.8055	+	2.09849i	0.735338	+	0.0976306i
$463$	0.769592	−	5.35263i	0.0357660	−	0.248758i	−0.964093	−	0.265566i	$-0.914441\pi$
$463$	0.769592	−	5.35263i	0.0357660	−	0.248758i	0.999859	+	0.0168079i	$0.00535039\pi$
$464$	−4.85145	−	2.21558i	−0.225223	−	0.102856i
$465$	−22.3503	−	9.91668i	−1.03647	−	0.459875i
$466$	3.59915	+	7.88105i	0.166728	+	0.365082i
$467$	8.57841	+	9.90001i	0.396961	+	0.458118i	0.918682	−	0.394999i	$-0.129255\pi$
$467$	8.57841	+	9.90001i	0.396961	+	0.458118i	−0.521720	+	0.853117i	$0.674710\pi$
$468$	−10.9345	+	3.46893i	−0.505447	+	0.160351i
$469$	−13.1258	−	3.85408i	−0.606092	−	0.177965i
$470$	−9.44147	+	10.8960i	−0.435503	+	0.502597i
$471$	−3.75475	+	1.14669i	−0.173010	+	0.0528368i
$472$	−7.71013	−	4.95500i	−0.354887	−	0.228072i
$473$	4.79940	+	4.15870i	0.220677	+	0.191217i
$474$	12.4277	+	18.8862i	0.570823	+	0.867470i
$475$	−2.41846	+	0.347722i	−0.110967	+	0.0159546i
$476$	−12.3370	+	10.6901i	−0.565465	+	0.489978i
$477$	−30.7122	+	20.6884i	−1.40621	+	0.947257i
$478$	−21.8824	+	6.42524i	−1.00088	+	0.293884i
$479$	−8.56405	+	18.7527i	−0.391302	+	0.856831i	0.606777	+	0.794872i	$0.292462\pi$
$479$	−8.56405	+	18.7527i	−0.391302	+	0.856831i	−0.998079	+	0.0619589i	$0.980265\pi$
$480$	−1.72040	−	1.94264i	−0.0785250	−	0.0886690i
$481$	−5.26493	−	8.19239i	−0.240060	−	0.373541i
$482$	19.5610			0.890978
$483$	19.0034	−	31.4142i	0.864683	−	1.42939i
$484$	6.66239			0.302836
$485$	5.61702	+	8.74025i	0.255056	+	0.396874i
$486$	13.5497	+	7.70753i	0.614626	+	0.349621i
$487$	−14.7470	+	32.2913i	−0.668249	+	1.46326i	0.206382	+	0.978471i	$0.433831\pi$
$487$	−14.7470	+	32.2913i	−0.668249	+	1.46326i	−0.874631	+	0.484789i	$0.838896\pi$
$488$	6.09390	−	1.78933i	0.275858	−	0.0809991i
$489$	−5.72795	+	20.3169i	−0.259027	+	0.918764i
$490$	14.1937	−	12.2989i	0.641208	−	0.555609i
$491$	−4.90904	+	0.705814i	−0.221542	+	0.0318529i	−0.252192	−	0.967677i	$-0.581151\pi$
$491$	−4.90904	+	0.705814i	−0.221542	+	0.0318529i	0.0306499	+	0.999530i	$0.490242\pi$
$492$	0.315204	−	0.207414i	0.0142105	−	0.00935095i
$493$	14.8867	+	12.8994i	0.670463	+	0.580960i
$494$	2.85243	+	1.83315i	0.128337	+	0.0824771i
$495$	3.70374	−	8.59684i	0.166471	−	0.386399i
$496$	6.17065	−	7.12131i	0.277070	−	0.319756i
$497$	47.9358	+	14.0752i	2.15021	+	0.631360i
$498$	5.24031	+	3.28830i	0.234824	+	0.147352i
$499$	15.2358	+	17.5831i	0.682050	+	0.787128i	0.986211	−	0.165493i	$-0.0529215\pi$
$499$	15.2358	+	17.5831i	0.682050	+	0.787128i	−0.304161	+	0.952621i	$0.598376\pi$
$500$	4.82673	+	10.5691i	0.215858	+	0.472663i
$501$	−6.21569	+	14.0090i	−0.277697	+	0.625875i
$502$	−12.8306	−	5.85955i	−0.572659	−	0.261525i
$503$	−1.77720	+	12.3607i	−0.0792414	+	0.551136i	0.911068	+	0.412256i	$0.135259\pi$
$503$	−1.77720	+	12.3607i	−0.0792414	+	0.551136i	−0.990309	+	0.138880i	$0.955650\pi$
$504$	−8.89779	−	9.83119i	−0.396339	−	0.437916i
$505$		−	15.5510i		−	0.692010i
$506$	−4.00008	+	9.15230i	−0.177825	+	0.406869i
$507$	−2.14272	−	1.81653i	−0.0951616	−	0.0806749i
$508$	−11.1438	+	7.16167i	−0.494425	+	0.317748i
$509$	−6.78322	−	0.975280i	−0.300661	−	0.0432285i	−0.00966659	−	0.999953i	$-0.503077\pi$
$509$	−6.78322	−	0.975280i	−0.300661	−	0.0432285i	−0.290994	+	0.956725i	$0.593986\pi$
$510$	4.07520	+	8.67424i	0.180453	+	0.384102i
$511$	5.36087	+	18.2574i	0.237151	+	0.807662i
$512$	0.909632	−	0.415415i	0.0402004	−	0.0183589i
$513$	−0.803143	−	4.53700i	−0.0354596	−	0.200314i
$514$	1.14142	+	7.93872i	0.0503457	+	0.350162i
$515$	−8.15376	+	27.7692i	−0.359298	+	1.22366i
$516$	−0.808037	−	5.21916i	−0.0355718	−	0.229761i
$517$	10.8358	−	16.8609i	0.476559	−	0.741540i
$518$	6.08567	−	9.46949i	0.267389	−	0.416065i
$519$	4.65655	+	30.0770i	0.204400	+	1.32023i
$520$	1.61399	−	5.49675i	0.0707782	−	0.241049i
$521$	−6.08273	−	42.3063i	−0.266489	−	1.85347i	−0.480961	−	0.876742i	$-0.659712\pi$
$521$	−6.08273	−	42.3063i	−0.266489	−	1.85347i	0.214472	−	0.976730i	$-0.431197\pi$
$522$	−10.2143	+	12.3157i	−0.447067	+	0.539044i
$523$	23.6188	−	10.7863i	1.03278	−	0.471654i	0.174402	−	0.984675i	$-0.444201\pi$
$523$	23.6188	−	10.7863i	1.03278	−	0.471654i	0.858376	+	0.513021i	$0.171474\pi$
$524$	2.17131	+	7.39481i	0.0948542	+	0.323044i
$525$	8.96978	+	19.0926i	0.391473	+	0.833268i
$526$	18.8517	+	2.71047i	0.821974	+	0.118182i
$527$	−29.2768	+	18.8150i	−1.27532	+	0.819596i
$528$	2.75160	+	2.33271i	0.119748	+	0.101518i
$529$	15.6224	+	16.8802i	0.679234	+	0.733921i
$530$		−	18.4927i		−	0.803271i
$531$	−20.3856	+	18.4502i	−0.884661	+	0.800669i
$532$	−0.557769	+	3.87937i	−0.0241823	+	0.168192i
$533$	0.757742	+	0.346049i	0.0328214	+	0.0149891i
$534$	−7.43315	+	16.7529i	−0.321664	+	0.724968i
$535$	−3.40296	−	7.45144i	−0.147123	−	0.322154i
$536$	−2.02682	−	2.33908i	−0.0875453	−	0.101033i
$537$	18.5249	+	11.6244i	0.799409	+	0.501631i
$538$	2.48809	+	0.730570i	0.107269	+	0.0314971i
$539$	−17.0974	+	19.7314i	−0.736437	+	0.849893i
$540$	−6.97277	+	3.46164i	−0.300060	+	0.148965i
$541$	−9.67306	−	6.21650i	−0.415877	−	0.267268i	0.315926	−	0.948784i	$-0.397685\pi$
$541$	−9.67306	−	6.21650i	−0.415877	−	0.267268i	−0.731803	+	0.681516i	$0.761321\pi$
$542$	1.27223	+	1.10239i	0.0546469	+	0.0473518i
$543$	26.4508	−	17.4054i	1.13511	−	0.746939i
$544$	−3.65571	+	0.525612i	−0.156737	+	0.0225354i
$545$	10.9334	−	9.47389i	0.468337	−	0.405817i
$546$	7.94348	−	28.1754i	0.339950	−	1.20580i
$547$	−13.8188	+	4.05757i	−0.590849	+	0.173489i	−0.563471	−	0.826136i	$-0.690534\pi$
$547$	−13.8188	+	4.05757i	−0.590849	+	0.173489i	−0.0273786	+	0.999625i	$0.508716\pi$
$548$	6.64911	−	14.5595i	0.284036	−	0.621952i
$549$	−0.411599	−	19.0490i	−0.0175666	−	0.812993i
$550$	−3.10262	−	4.82777i	−0.132296	−	0.205857i
$551$	4.72926			0.201473
$552$	7.45947	−	3.65464i	0.317496	−	0.155552i
$553$	−57.6931			−2.45336
$554$	6.56406	+	10.2139i	0.278880	+	0.433946i
$555$	−4.38138	−	4.94738i	−0.185979	−	0.210005i
$556$	−0.172725	+	0.378215i	−0.00732518	+	0.0160399i
$557$	−10.8451	+	3.18441i	−0.459522	+	0.134928i	−0.503297	−	0.864114i	$-0.667880\pi$
$557$	−10.8451	+	3.18441i	−0.459522	+	0.134928i	0.0437750	+	0.999041i	$0.486062\pi$
$558$	−15.7933	−	23.4453i	−0.668582	−	0.992518i
$559$	8.81176	−	7.63543i	0.372698	−	0.322944i
$560$	6.55446	−	0.942389i	0.276976	−	0.0398232i
$561$	−7.32358	−	11.1295i	−0.309202	−	0.469889i
$562$	11.3954	+	9.87418i	0.480686	+	0.416517i
$563$	7.28347	+	4.68080i	0.306962	+	0.197272i	0.685048	−	0.728498i	$-0.259781\pi$
$563$	7.28347	+	4.68080i	0.306962	+	0.197272i	−0.378086	+	0.925770i	$0.623418\pi$
$564$	−15.9413	+	4.86844i	−0.671251	+	0.204998i
$565$	−5.89599	+	6.80433i	−0.248046	+	0.286260i
$566$	24.1128	+	7.08017i	1.01354	+	0.297602i
$567$	−35.4371	+	18.0726i	−1.48822	+	0.758976i
$568$	7.40202	+	8.54239i	0.310582	+	0.358431i
$569$	4.99059	+	10.9279i	0.209216	+	0.458120i	0.984927	−	0.172968i	$-0.0553359\pi$
$569$	4.99059	+	10.9279i	0.209216	+	0.458120i	−0.775711	+	0.631088i	$0.782609\pi$
$570$	2.10324	+	0.933194i	0.0880950	+	0.0390872i
$571$	25.9567	+	11.8540i	1.08626	+	0.496076i	0.876364	−	0.481649i	$-0.159962\pi$
$571$	25.9567	+	11.8540i	1.08626	+	0.496076i	0.209891	+	0.977725i	$0.432689\pi$
$572$	−1.13338	+	7.88285i	−0.0473891	+	0.329598i
$573$	25.0498	+	3.32585i	1.04647	+	0.138939i
$574$			0.962878i			0.0401898i
$575$	−13.0477	+	2.09439i	−0.544127	+	0.0873421i
$576$	−0.490992	−	2.95955i	−0.0204580	−	0.123315i
$577$	−11.5536	+	7.42507i	−0.480984	+	0.309110i	−0.758570	−	0.651591i	$-0.774102\pi$
$577$	−11.5536	+	7.42507i	−0.480984	+	0.309110i	0.277587	+	0.960701i	$0.410465\pi$
$578$	−3.32533	−	0.478111i	−0.138316	−	0.0198868i
$579$	0.640747	−	0.301026i	0.0266285	−	0.0125102i
$580$	−2.25116	−	7.66674i	−0.0934743	−	0.318344i
$581$	−14.3606	+	6.55826i	−0.595778	+	0.272083i
$582$	0.129745	+	12.0107i	0.00537809	+	0.497860i
$583$	3.65858	+	25.4460i	0.151523	+	1.05386i
$584$	−1.21288	+	4.13070i	−0.0501894	+	0.170930i
$585$	−14.6555	−	8.97719i	−0.605930	−	0.371161i
$586$	13.0866	−	20.3631i	0.540601	−	0.841192i
$587$	−19.5497	+	30.4200i	−0.806904	+	1.25557i	0.156544	+	0.987671i	$0.449965\pi$
$587$	−19.5497	+	30.4200i	−0.806904	+	1.25557i	−0.963448	+	0.267896i	$0.913672\pi$
$588$	21.4572	−	3.32202i	0.884879	−	0.136998i
$589$	−2.35400	+	8.01698i	−0.0969948	+	0.330334i
$590$	−1.95411	−	13.5911i	−0.0804493	−	0.559537i
$591$	−30.4169	+	0.328576i	−1.25118	+	0.0135158i
$592$	2.31659	−	1.05795i	0.0952111	−	0.0434815i
$593$	4.24596	+	14.4604i	0.174361	+	0.593818i	0.999579	+	0.0290042i	$0.00923363\pi$
$593$	4.24596	+	14.4604i	0.174361	+	0.593818i	−0.825219	+	0.564813i	$0.808948\pi$
$594$	8.90969	−	6.14271i	0.365569	−	0.252039i
$595$	−24.2076	−	3.48053i	−0.992415	−	0.142688i
$596$	−2.64950	+	1.70273i	−0.108528	+	0.0697465i
$597$	10.0469	−	11.8511i	0.411194	−	0.485032i
$598$	15.5875	+	9.66085i	0.637420	+	0.395062i
$599$		−	42.6957i		−	1.74450i	−0.489062	−	0.872249i	$-0.662661\pi$
$599$		−	42.6957i		−	1.74450i	0.489062	−	0.872249i	$-0.337339\pi$
$600$	−0.628145	+	4.73108i	−0.0256439	+	0.193146i
$601$	−4.00534	+	27.8577i	−0.163381	+	1.13634i	0.728821	+	0.684704i	$0.240069\pi$
$601$	−4.00534	+	27.8577i	−0.163381	+	1.13634i	−0.892202	+	0.451636i	$0.850840\pi$
$602$	12.2593	+	5.59864i	0.499652	+	0.228184i
$603$	−8.36075	+	4.03873i	−0.340476	+	0.164470i
$604$	1.98336	+	4.34295i	0.0807018	+	0.176712i
$605$	6.53645	+	7.54347i	0.265745	+	0.306686i
$606$	9.55601	−	15.2286i	0.388186	−	0.618621i
$607$	20.6007	+	6.04891i	0.836156	+	0.245518i	0.671660	−	0.740860i	$-0.265582\pi$
$607$	20.6007	+	6.04891i	0.836156	+	0.245518i	0.164497	+	0.986378i	$0.447400\pi$
$608$	−0.580679	+	0.670139i	−0.0235496	+	0.0271777i
$609$	−11.9257	−	39.0499i	−0.483255	−	1.58238i
$610$	8.00467	+	5.14429i	0.324100	+	0.208286i
$611$	−27.8103	−	24.0978i	−1.12509	−	0.974892i
$612$	−1.33955	+	10.9986i	−0.0541482	+	0.444593i
$613$	−28.8038	+	4.14136i	−1.16337	+	0.167268i	−0.696834	−	0.717232i	$-0.745409\pi$
$613$	−28.8038	+	4.14136i	−1.16337	+	0.167268i	−0.466540	+	0.884500i	$0.654500\pi$
$614$	10.5740	−	9.16239i	0.426730	−	0.369764i
$615$	0.544090	+	0.153395i	0.0219398	+	0.00618549i
$616$	−8.83251	+	2.59346i	−0.355872	+	0.104493i
$617$	9.61666	−	21.0575i	0.387152	−	0.847745i	−0.611261	−	0.791429i	$-0.709337\pi$
$617$	9.61666	−	21.0575i	0.387152	−	0.847745i	0.998413	−	0.0563157i	$-0.0179353\pi$
$618$	−25.0488	+	22.1831i	−1.00761	+	0.892336i
$619$	−0.784765	−	1.22112i	−0.0315424	−	0.0490809i	0.825124	−	0.564951i	$-0.191105\pi$
$619$	−0.784765	−	1.22112i	−0.0315424	−	0.0490809i	−0.856667	+	0.515870i	$0.827469\pi$
$620$	14.1171			0.566956
$621$	−4.74466	−	24.4640i	−0.190396	−	0.981707i
$622$	−7.99561			−0.320595
$623$	−25.2858	−	39.3455i	−1.01305	−	1.57634i
$624$	4.95827	−	4.39102i	0.198490	−	0.175782i
$625$	−1.50800	+	3.30206i	−0.0603201	+	0.132083i
$626$	−8.99677	+	2.64169i	−0.359583	+	0.105583i
$627$	−3.07868	−	0.867973i	−0.122951	−	0.0346635i
$628$	1.71302	−	1.48434i	0.0683568	−	0.0592315i
$629$	−9.31010	+	1.33859i	−0.371218	+	0.0533731i
$630$	2.40173	−	19.7199i	0.0956874	−	0.785658i
$631$	8.63569	+	7.48287i	0.343781	+	0.297888i	0.809588	−	0.586998i	$-0.199690\pi$
$631$	8.63569	+	7.48287i	0.343781	+	0.297888i	−0.465807	+	0.884886i	$0.654236\pi$
$632$	−10.9808	−	7.05693i	−0.436793	−	0.280710i
$633$	−6.38211	−	20.8977i	−0.253666	−	0.830610i
$634$	−13.4897	+	15.5679i	−0.535744	+	0.618281i
$635$	−19.0419	−	5.59121i	−0.755655	−	0.221880i
$636$	11.3637	−	18.1094i	0.450599	−	0.718083i
$637$	31.3910	+	36.2272i	1.24376	+	1.43537i
$638$	4.61438	+	10.1041i	0.182685	+	0.400024i
$639$	30.5338	−	14.7496i	1.20790	−	0.583485i
$640$	1.36279	+	0.622366i	0.0538690	+	0.0246012i
$641$	3.86823	−	26.9041i	0.152786	−	1.06265i	−0.758736	−	0.651398i	$-0.774183\pi$
$641$	3.86823	−	26.9041i	0.152786	−	1.06265i	0.911522	−	0.411251i	$-0.134908\pi$
$642$	1.24645	−	9.38809i	0.0491936	−	0.370518i
$643$			26.1567i			1.03152i	0.856733	+	0.515760i	$0.172490\pi$
$643$			26.1567i			1.03152i	−0.856733	+	0.515760i	$0.827510\pi$
$644$	−2.67304	+	21.0281i	−0.105332	+	0.828623i
$645$	5.11662	−	6.03541i	0.201467	−	0.237644i
$646$	2.75505	−	1.77056i	0.108396	−	0.0696618i
$647$	3.72851	+	0.536079i	0.146583	+	0.0210755i	0.215216	−	0.976567i	$-0.430955\pi$
$647$	3.72851	+	0.536079i	0.146583	+	0.0210755i	−0.0686327	+	0.997642i	$0.521864\pi$
$648$	−8.95540	−	0.894845i	−0.351801	−	0.0351528i
$649$	5.37771	+	18.3148i	0.211093	+	0.718918i
$650$	−9.58432	+	4.37701i	−0.375928	+	0.171681i
$651$	72.1330	−	0.779209i	2.82711	−	0.0305396i
$652$	−1.73443	−	12.0632i	−0.0679254	−	0.472432i
$653$	−2.06178	+	7.02179i	−0.0806839	+	0.274784i	−0.989947	−	0.141437i	$-0.954828\pi$
$653$	−2.06178	+	7.02179i	−0.0806839	+	0.274784i	0.909263	+	0.416221i	$0.136646\pi$
$654$	16.5285	−	2.55896i	0.646315	−	0.100063i
$655$	−6.24248	+	9.71350i	−0.243914	+	0.379538i
$656$	−0.117778	+	0.183266i	−0.00459845	+	0.00715533i
$657$	11.0133	+	6.74617i	0.429670	+	0.263193i
$658$	11.9834	−	40.8118i	0.467163	−	1.59101i
$659$	−5.49519	−	38.2199i	−0.214062	−	1.48884i	−0.759403	−	0.650621i	$-0.774509\pi$
$659$	−5.49519	−	38.2199i	−0.214062	−	1.48884i	0.545340	−	0.838215i	$-0.316400\pi$
$660$	0.0583774	+	5.40411i	0.00227234	+	0.210355i
$661$	44.4075	−	20.2802i	1.72725	−	0.788810i	0.733187	−	0.680027i	$-0.238032\pi$
$661$	44.4075	−	20.2802i	1.72725	−	0.788810i	0.994066	−	0.108782i	$-0.0346951\pi$
$662$	−3.65863	−	12.4601i	−0.142197	−	0.484277i
$663$	−22.1396	+	10.4013i	−0.859829	+	0.403952i
$664$	−3.53547	−	0.508323i	−0.137203	−	0.0197268i
$665$	−4.93963	+	3.17451i	−0.191551	+	0.123102i
$666$	−1.25042	−	7.53717i	−0.0484529	−	0.292059i
$667$	25.5748	−	0.418449i	0.990258	−	0.0162024i
$668$		−	8.84847i		−	0.342358i
$669$	−25.3160	−	3.36120i	−0.978773	−	0.129951i
$670$	0.659903	−	4.58973i	0.0254943	−	0.177317i
$671$	−12.0322	−	5.49491i	−0.464497	−	0.212129i
$672$	6.99769	+	3.10483i	0.269942	+	0.119771i
$673$	−13.5600	−	29.6923i	−0.522701	−	1.14455i	−0.968407	−	0.249376i	$-0.919775\pi$
$673$	−13.5600	−	29.6923i	−0.522701	−	1.14455i	0.445706	−	0.895179i	$-0.352953\pi$
$674$	−2.35618	−	2.71918i	−0.0907567	−	0.104739i
$675$	13.2098	+	5.52273i	0.508446	+	0.212570i
$676$	1.55614	+	0.456923i	0.0598515	+	0.0175740i
$677$	−4.82277	+	5.56578i	−0.185354	+	0.213910i	−0.840820	−	0.541315i	$-0.817927\pi$
$677$	−4.82277	+	5.56578i	−0.185354	+	0.213910i	0.655466	+	0.755225i	$0.272472\pi$
$678$	−9.95500	+	3.04023i	−0.382320	+	0.116759i
$679$	−25.7856	−	16.5714i	−0.989560	−	0.635952i
$680$	−4.18173	−	3.62349i	−0.160362	−	0.138954i
$681$	−13.2826	−	20.1854i	−0.508992	−	0.773507i
$682$	−19.4251	+	2.79291i	−0.743827	+	0.106946i
$683$	25.0432	−	21.7001i	0.958252	−	0.830330i	−0.0273133	−	0.999627i	$-0.508695\pi$
$683$	25.0432	−	21.7001i	0.958252	−	0.830330i	0.985565	+	0.169297i	$0.0541497\pi$
$684$	1.48620	+	2.20628i	0.0568263	+	0.0843593i
$685$	23.0084	−	6.75588i	0.879106	−	0.258129i
$686$	−10.1645	+	22.2572i	−0.388083	+	0.849783i
$687$	5.11410	+	5.77475i	0.195115	+	0.220321i
$688$	1.64851	+	2.56514i	0.0628490	+	0.0977949i
$689$	47.1995			1.79816
$690$	11.4564	+	4.86040i	0.436138	+	0.185032i
$691$	51.7368			1.96816			0.984080	−	0.177724i	$-0.0568734\pi$
$691$	51.7368			1.96816			0.984080	+	0.177724i	$0.0568734\pi$
$692$	−9.50005	−	14.7824i	−0.361138	−	0.561941i
$693$	0.596572	+	27.6097i	0.0226619	+	1.04881i
$694$	7.96113	−	17.4324i	0.302200	−	0.661726i
$695$	−0.597693	+	0.175499i	−0.0226718	+	0.00665704i
$696$	2.50668	−	8.89115i	0.0950155	−	0.337018i
$697$	0.608061	−	0.526888i	0.0230320	−	0.0199573i
$698$	−8.75438	+	1.25869i	−0.331358	+	0.0476421i
$699$	−12.5359	+	8.24901i	−0.474151	+	0.312006i
$700$	−9.20427	−	7.97554i	−0.347889	−	0.301447i
$701$	7.67794	+	4.93431i	0.289992	+	0.186366i	0.677546	−	0.735481i	$-0.263044\pi$
$701$	7.67794	+	4.93431i	0.289992	+	0.186366i	−0.387554	+	0.921847i	$0.626680\pi$
$702$	−8.83527	−	17.7968i	−0.333466	−	0.671698i
$703$	−1.47883	+	1.70666i	−0.0557752	+	0.0643680i
$704$	−1.99833	−	0.586763i	−0.0753149	−	0.0221145i
$705$	−21.1523	−	13.2731i	−0.796641	−	0.499894i
$706$	−11.2603	−	12.9951i	−0.423786	−	0.489076i
$707$	19.0587	+	41.7327i	0.716776	+	1.56952i
$708$	6.43807	−	14.5102i	0.241958	−	0.545326i
$709$	−11.9108	−	5.43948i	−0.447320	−	0.204284i	0.179002	−	0.983849i	$-0.442713\pi$
$709$	−11.9108	−	5.43948i	−0.447320	−	0.204284i	−0.626322	+	0.779565i	$0.715440\pi$
$710$	−2.40999	+	16.7618i	−0.0904453	+	0.629061i
$711$	−29.0333	+	26.2768i	−1.08883	+	0.985458i
$712$		−	10.5816i		−	0.396562i
$713$	−12.0205	+	43.5623i	−0.450173	+	1.63142i
$714$	−21.5671	−	18.2838i	−0.807127	−	0.684255i
$715$	−10.0373	+	6.45058i	−0.375374	+	0.241238i
$716$	−12.4982	−	1.79697i	−0.467079	−	0.0671558i
$717$	−16.7967	−	35.7524i	−0.627283	−	1.33520i
$718$	7.36126	+	25.0701i	0.274720	+	0.935609i
$719$	10.3331	−	4.71899i	0.385361	−	0.175988i	−0.213308	−	0.976985i	$-0.568424\pi$
$719$	10.3331	−	4.71899i	0.385361	−	0.175988i	0.598669	+	0.800997i	$0.295696\pi$
$720$	2.86923	−	3.45953i	0.106930	−	0.128929i
$721$	−12.1513	−	84.5145i	−0.452540	−	3.14748i
$722$	−5.13140	+	17.4759i	−0.190971	+	0.650387i
$723$	5.18368	+	33.4817i	0.192783	+	1.24520i
$724$	−9.88349	+	15.3790i	−0.367317	+	0.571557i
$725$	−7.94528	+	12.3631i	−0.295080	+	0.459154i
$726$	1.76554	+	11.4037i	0.0655253	+	0.423232i
$727$	−0.576048	+	1.96184i	−0.0213644	+	0.0727606i	−0.969485	−	0.245150i	$-0.921163\pi$
$727$	−0.576048	+	1.96184i	−0.0213644	+	0.0727606i	0.948121	+	0.317910i	$0.102981\pi$
$728$	2.40529	+	16.7292i	0.0891460	+	0.620024i
$729$	−9.60199	+	25.2349i	−0.355629	+	0.934627i
$730$	−5.86693	+	2.67934i	−0.217145	+	0.0991667i
$731$	−3.17275	−	10.8054i	−0.117348	−	0.399652i
$732$	4.67761	+	9.95649i	0.172889	+	0.368003i
$733$	45.4669	+	6.53715i	1.67936	+	0.241455i	0.915033	−	0.403378i	$-0.132164\pi$
$733$	45.4669	+	6.53715i	1.67936	+	0.241455i	0.764323	+	0.644833i	$0.223073\pi$
$734$	−9.16421	+	5.88948i	−0.338257	+	0.217385i
$735$	24.8129	+	21.0356i	0.915239	+	0.775910i
$736$	−3.08089	+	3.67534i	−0.113563	+	0.135475i
$737$			6.44602i			0.237442i
$738$	0.438551	+	0.484556i	0.0161433	+	0.0178368i
$739$	5.99347	−	41.6855i	0.220473	−	1.53343i	−0.515781	−	0.856720i	$-0.672498\pi$
$739$	5.99347	−	41.6855i	0.220473	−	1.53343i	0.736254	−	0.676705i	$-0.236593\pi$
$740$	3.47066	+	1.58500i	0.127584	+	0.0582656i
$741$	−2.38182	+	5.36817i	−0.0874984	+	0.197205i
$742$	22.6639	+	49.6271i	0.832020	+	1.82187i
$743$	−23.1670	−	26.7362i	−0.849915	−	0.980854i	0.150054	−	0.988678i	$-0.452055\pi$
$743$	−23.1670	−	26.7362i	−0.849915	−	0.980854i	−0.999969	+	0.00782329i	$0.997510\pi$
$744$	13.8245	+	8.67489i	0.506830	+	0.318037i
$745$	−4.52733	−	1.32934i	−0.165868	−	0.0487033i
$746$	−10.7316	+	12.3849i	−0.392912	+	0.453444i
$747$	−4.23977	+	9.84102i	−0.155125	+	0.360064i
$748$	6.47094	+	4.15862i	0.236601	+	0.152054i
$749$	18.2644	+	15.8262i	0.667367	+	0.578277i
$750$	−16.8116	+	11.0625i	−0.613871	+	0.403947i
$751$	−1.69293	+	0.243406i	−0.0617758	+	0.00888202i	−0.173133	−	0.984898i	$-0.555389\pi$
$751$	−1.69293	+	0.243406i	−0.0617758	+	0.00888202i	0.111358	+	0.993780i	$0.464480\pi$
$752$	7.27286	−	6.30197i	0.265214	−	0.229809i
$753$	6.62942	−	23.5144i	0.241590	−	0.856914i
$754$	19.5681	−	5.74571i	0.712628	−	0.209246i
$755$	−2.97143	+	6.50652i	−0.108141	+	0.236796i
$756$	14.4697	−	17.8353i	0.526259	−	0.648662i
$757$	7.66632	+	11.9290i	0.278637	+	0.433568i	0.952161	−	0.305598i	$-0.0988563\pi$
$757$	7.66632	+	11.9290i	0.278637	+	0.433568i	−0.673523	+	0.739166i	$0.735220\pi$
$758$	8.40595			0.305318
$759$	−16.7256	−	4.42140i	−0.607102	−	0.160487i
$760$	−1.32847			−0.0481886
$761$	−5.36055	−	8.34118i	−0.194320	−	0.302367i	0.730397	−	0.683022i	$-0.239335\pi$
$761$	−5.36055	−	8.34118i	−0.194320	−	0.302367i	−0.924717	+	0.380655i	$0.875699\pi$
$762$	−15.2114	−	17.1765i	−0.551052	−	0.622238i
$763$	−17.7302	+	38.8238i	−0.641878	+	1.40552i
$764$	−13.9984	+	4.11031i	−0.506445	+	0.148706i
$765$	−13.7674	+	9.27403i	−0.497761	+	0.335303i
$766$	11.0351	−	9.56193i	0.398713	−	0.345487i
$767$	34.6891	−	4.98753i	1.25255	−	0.180089i
$768$	0.952102	+	1.44689i	0.0343560	+	0.0522103i
$769$	6.27029	+	5.43323i	0.226112	+	0.195927i	0.760548	−	0.649282i	$-0.224930\pi$

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.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540641 - 0.841254i) q^{2} +(1.29667 - 1.14833i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-1.43749 + 0.422085i) q^{5} +(-1.66706 - 0.469995i) q^{6} +(3.34037 - 2.89445i) q^{7} +(0.989821 - 0.142315i) q^{8} +(0.362698 - 2.97799i) q^{9} +O(q^{10})\)	\(q+(-0.540641 - 0.841254i) q^{2} +(1.29667 - 1.14833i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-1.43749 + 0.422085i) q^{5} +(-1.66706 - 0.469995i) q^{6} +(3.34037 - 2.89445i) q^{7} +(0.989821 - 0.142315i) q^{8} +(0.362698 - 2.97799i) q^{9} +(1.13225 + 0.981098i) q^{10} +(-1.75207 - 1.12599i) q^{11} +(0.505898 + 1.65652i) q^{12} +(-2.50409 + 2.88987i) q^{13} +(-4.24090 - 1.24524i) q^{14} +(-1.37926 + 2.19801i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(1.53425 + 3.35954i) q^{17} +(-2.70134 + 1.30490i) q^{18} +(0.806590 + 0.368357i) q^{19} +(0.213213 - 1.48293i) q^{20} +(1.00759 - 7.58897i) q^{21} +2.08269i q^{22} +(4.39445 + 1.92063i) q^{23} +(1.12005 - 1.32117i) q^{24} +(-2.31804 + 1.48972i) q^{25} +(3.78493 + 0.544191i) q^{26} +(-2.94941 - 4.27797i) q^{27} +(1.24524 + 4.24090i) q^{28} +(4.85145 - 2.21558i) q^{29} +(2.59477 - 0.0280297i) q^{30} +(1.34101 + 9.32693i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(-3.56486 + 0.551916i) q^{33} +(1.99675 - 3.10700i) q^{34} +(-3.58005 + 5.57066i) q^{35} +(2.55821 + 1.56702i) q^{36} +(-0.717497 + 2.44357i) q^{37} +(-0.126194 - 0.877696i) q^{38} +(0.0715413 + 6.62272i) q^{39} +(-1.36279 + 0.622366i) q^{40} +(-0.0613750 - 0.209024i) q^{41} +(-6.92899 + 3.25527i) q^{42} +(-3.01815 - 0.433944i) q^{43} +(1.75207 - 1.12599i) q^{44} +(0.735594 + 4.43393i) q^{45} +(-0.760086 - 4.73522i) q^{46} +9.62337i q^{47} +(-1.71698 - 0.227963i) q^{48} +(1.78404 - 12.4083i) q^{49} +(2.50646 + 1.14466i) q^{50} +(5.84727 + 2.59439i) q^{51} +(-1.58848 - 3.47830i) q^{52} +(-8.08324 - 9.32856i) q^{53} +(-2.00428 + 4.79404i) q^{54} +(2.99385 + 0.879075i) q^{55} +(2.89445 - 3.34037i) q^{56} +(1.46887 - 0.448591i) q^{57} +(-4.48676 - 2.88346i) q^{58} +(-6.92648 - 6.00183i) q^{59} +(-1.42642 - 2.16770i) q^{60} +(6.28652 - 0.903865i) q^{61} +(7.12131 - 6.17065i) q^{62} +(-7.40810 - 10.9974i) q^{63} +(0.959493 - 0.281733i) q^{64} +(2.37983 - 5.21111i) q^{65} +(2.39161 + 2.70056i) q^{66} +(-1.67331 - 2.60371i) q^{67} -3.69330 q^{68} +(7.90365 - 2.55584i) q^{69} +6.62186 q^{70} +(6.11097 + 9.50886i) q^{71} +(-0.0648069 - 2.99930i) q^{72} +(-1.78840 + 3.91604i) q^{73} +(2.44357 - 0.717497i) q^{74} +(-1.29505 + 4.59353i) q^{75} +(-0.670139 + 0.580679i) q^{76} +(-9.11169 + 1.31006i) q^{77} +(5.53271 - 3.64070i) q^{78} +(-9.86473 - 8.54784i) q^{79} +(1.26035 + 0.809976i) q^{80} +(-8.73690 - 2.16022i) q^{81} +(-0.142660 + 0.164639i) q^{82} +(-3.42714 - 1.00630i) q^{83} +(6.48460 + 4.06910i) q^{84} +(-3.62349 - 4.18173i) q^{85} +(1.26668 + 2.77364i) q^{86} +(3.74651 - 8.44392i) q^{87} +(-1.89449 - 0.865182i) q^{88} +(1.50592 - 10.4739i) q^{89} +(3.33237 - 3.01598i) q^{90} +16.9012i q^{91} +(-3.57258 + 3.19948i) q^{92} +(12.4492 + 10.5540i) q^{93} +(8.09570 - 5.20279i) q^{94} +(-1.31494 - 0.189061i) q^{95} +(0.736496 + 1.56766i) q^{96} +(-1.95376 - 6.65389i) q^{97} +(-11.4031 + 5.20760i) q^{98} +(-3.98866 + 4.80927i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Introduction

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