LMFDB - Embedded newform 230.2.j.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(9,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 10]))

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

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

chi := DirichletCharacter("230.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.j (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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			29.1
Character	$\chi$	$=$	230.29
Dual form			230.2.j.a.119.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909632 - 0.415415i) q^{2} +(-0.768680 + 2.61788i) q^{3} +(0.654861 + 0.755750i) q^{4} +(1.33202 + 1.79603i) q^{5} +(1.78672 - 2.06199i) q^{6} +(1.27046 + 0.182665i) q^{7} +(-0.281733 - 0.959493i) q^{8} +(-3.73869 - 2.40271i) q^{9} +O(q^{10})$	\(q+(-0.909632 - 0.415415i) q^{2} +(-0.768680 + 2.61788i) q^{3} +(0.654861 + 0.755750i) q^{4} +(1.33202 + 1.79603i) q^{5} +(1.78672 - 2.06199i) q^{6} +(1.27046 + 0.182665i) q^{7} +(-0.281733 - 0.959493i) q^{8} +(-3.73869 - 2.40271i) q^{9} +(-0.465548 - 2.18707i) q^{10} +(1.03946 + 2.27610i) q^{11} +(-2.48184 + 1.13342i) q^{12} +(-1.02038 + 0.146709i) q^{13} +(-1.07977 - 0.693928i) q^{14} +(-5.72570 + 2.10650i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-3.98282 - 3.45113i) q^{17} +(2.40271 + 3.73869i) q^{18} +(0.540257 + 0.623490i) q^{19} +(-0.485063 + 2.18282i) q^{20} +(-1.45478 + 3.18552i) q^{21} -2.50222i q^{22} +(-2.14681 + 4.28850i) q^{23} +2.72840 q^{24} +(-1.45145 + 4.78469i) q^{25} +(0.989116 + 0.290431i) q^{26} +(2.97791 - 2.58037i) q^{27} +(0.693928 + 1.07977i) q^{28} +(1.11568 - 1.28757i) q^{29} +(6.08335 + 0.462404i) q^{30} +(7.72564 - 2.26845i) q^{31} +(0.540641 - 0.841254i) q^{32} +(-6.75757 + 0.971592i) q^{33} +(2.18925 + 4.79378i) q^{34} +(1.36421 + 2.52511i) q^{35} +(-0.632474 - 4.39895i) q^{36} +(5.04755 - 7.85414i) q^{37} +(-0.232428 - 0.791577i) q^{38} +(0.400281 - 2.78401i) q^{39} +(1.34801 - 1.78406i) q^{40} +(-3.34958 + 2.15265i) q^{41} +(2.64662 - 2.29331i) q^{42} +(2.74268 - 9.34069i) q^{43} +(-1.03946 + 2.27610i) q^{44} +(-0.664663 - 9.91526i) q^{45} +(3.73431 - 3.00914i) q^{46} +10.1453i q^{47} +(-2.48184 - 1.13342i) q^{48} +(-5.13574 - 1.50799i) q^{49} +(3.30792 - 3.74935i) q^{50} +(12.0962 - 7.77374i) q^{51} +(-0.779083 - 0.675079i) q^{52} +(3.94642 + 0.567409i) q^{53} +(-3.78072 + 1.11012i) q^{54} +(-2.70336 + 4.89870i) q^{55} +(-0.182665 - 1.27046i) q^{56} +(-2.04751 + 0.935066i) q^{57} +(-1.54974 + 0.707741i) q^{58} +(1.11256 + 7.73803i) q^{59} +(-5.34152 - 2.94773i) q^{60} +(-3.40094 + 0.998606i) q^{61} +(-7.96983 - 1.14589i) q^{62} +(-4.31098 - 3.73549i) q^{63} +(-0.841254 + 0.540641i) q^{64} +(-1.62266 - 1.63722i) q^{65} +(6.55051 + 1.92340i) q^{66} +(13.0761 + 5.97166i) q^{67} -5.27002i q^{68} +(-9.57658 - 8.91658i) q^{69} +(-0.191962 - 2.86363i) q^{70} +(2.65819 - 5.82062i) q^{71} +(-1.25207 + 4.26417i) q^{72} +(12.6363 - 10.9494i) q^{73} +(-7.85414 + 5.04755i) q^{74} +(-11.4101 - 7.47764i) q^{75} +(-0.117409 + 0.816598i) q^{76} +(0.904831 + 3.08157i) q^{77} +(-1.52063 + 2.36614i) q^{78} +(1.01786 + 7.07936i) q^{79} +(-1.96732 + 1.06286i) q^{80} +(-1.07250 - 2.34844i) q^{81} +(3.94113 - 0.566649i) q^{82} +(2.41287 - 3.75450i) q^{83} +(-3.36013 + 0.986624i) q^{84} +(0.893151 - 11.7502i) q^{85} +(-6.37509 + 7.35725i) q^{86} +(2.51310 + 3.91046i) q^{87} +(1.89105 - 1.63860i) q^{88} +(6.62662 + 1.94575i) q^{89} +(-3.51435 + 9.29535i) q^{90} -1.32316 q^{91} +(-4.64689 + 1.18592i) q^{92} +21.9685i q^{93} +(4.21451 - 9.22849i) q^{94} +(-0.400175 + 1.80082i) q^{95} +(1.78672 + 2.06199i) q^{96} +(8.57591 + 13.3444i) q^{97} +(4.04519 + 3.50518i) q^{98} +(1.58259 - 11.0071i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41} - 8 q^{44} + 16 q^{45} - 4 q^{46} - 58 q^{49} + 12 q^{50} - 24 q^{51} - 6 q^{54} - 36 q^{55} + 22 q^{56} - 102 q^{59} - 38 q^{60} + 72 q^{61} + 12 q^{64} - 138 q^{65} + 80 q^{66} - 212 q^{69} - 108 q^{70} + 176 q^{71} - 88 q^{74} - 100 q^{75} + 16 q^{76} - 104 q^{79} - 22 q^{80} - 28 q^{81} - 22 q^{84} + 2 q^{85} + 62 q^{86} + 48 q^{89} + 24 q^{90} - 56 q^{91} + 24 q^{94} + 18 q^{95} - 4 q^{96} + 188 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−0.909632	−	0.415415i	−0.643207	−	0.293743i
$2$	−0.909632	−	0.415415i	−0.643207	−	0.293743i
$3$	−0.768680	+	2.61788i	−0.443798	+	1.51144i	0.369300	+	0.929310i	$0.379597\pi$
$3$	−0.768680	+	2.61788i	−0.443798	+	1.51144i	−0.813098	+	0.582126i	$0.802221\pi$
$4$	0.654861	+	0.755750i	0.327430	+	0.377875i
$5$	1.33202	+	1.79603i	0.595697	+	0.803209i
$5$	1.33202	+	1.79603i	0.595697	+	0.803209i
$6$	1.78672	−	2.06199i	0.729427	−	0.841804i
$7$	1.27046	+	0.182665i	0.480190	+	0.0690410i	0.378160	−	0.925740i	$-0.376557\pi$
$7$	1.27046	+	0.182665i	0.480190	+	0.0690410i	0.102031	+	0.994781i	$0.467466\pi$
$8$	−0.281733	−	0.959493i	−0.0996075	−	0.339232i
$9$	−3.73869	−	2.40271i	−1.24623	−	0.800904i
$10$	−0.465548	−	2.18707i	−0.147219	−	0.691611i
$11$	1.03946	+	2.27610i	0.313408	+	0.686269i	0.999135	−	0.0415907i	$-0.0132426\pi$
$11$	1.03946	+	2.27610i	0.313408	+	0.686269i	−0.685726	+	0.727860i	$0.740515\pi$
$12$	−2.48184	+	1.13342i	−0.716447	+	0.327190i
$13$	−1.02038	+	0.146709i	−0.283003	+	0.0406897i	−0.282355	−	0.959310i	$-0.591115\pi$
$13$	−1.02038	+	0.146709i	−0.283003	+	0.0406897i	−0.000648289		1.00000i	$0.500206\pi$
$14$	−1.07977	−	0.693928i	−0.288582	−	0.185460i
$15$	−5.72570	+	2.10650i	−1.47837	+	0.543895i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−3.98282	−	3.45113i	−0.965975	−	0.837022i	0.0206904	−	0.999786i	$-0.493414\pi$
$17$	−3.98282	−	3.45113i	−0.965975	−	0.837022i	−0.986665	+	0.162764i	$0.947959\pi$
$18$	2.40271	+	3.73869i	0.566324	+	0.881218i
$19$	0.540257	+	0.623490i	0.123943	+	0.143038i	0.814330	−	0.580403i	$-0.197105\pi$
$19$	0.540257	+	0.623490i	0.123943	+	0.143038i	−0.690386	+	0.723441i	$0.742559\pi$
$20$	−0.485063	+	2.18282i	−0.108463	+	0.488094i
$21$	−1.45478	+	3.18552i	−0.317459	+	0.695137i
$22$		−	2.50222i		−	0.533474i
$23$	−2.14681	+	4.28850i	−0.447640	+	0.894214i
$23$	−2.14681	+	4.28850i	−0.447640	+	0.894214i
$24$	2.72840			0.556933
$25$	−1.45145	+	4.78469i	−0.290291	+	0.956938i
$26$	0.989116	+	0.290431i	0.193982	+	0.0569582i
$27$	2.97791	−	2.58037i	0.573098	−	0.496592i
$28$	0.693928	+	1.07977i	0.131140	+	0.204058i
$29$	1.11568	−	1.28757i	0.207177	−	0.239095i	−0.642646	−	0.766163i	$-0.722163\pi$
$29$	1.11568	−	1.28757i	0.207177	−	0.239095i	0.849823	+	0.527068i	$0.176709\pi$
$30$	6.08335	+	0.462404i	1.11066	+	0.0844230i
$31$	7.72564	−	2.26845i	1.38757	−	0.407426i	0.499169	−	0.866504i	$-0.333639\pi$
$31$	7.72564	−	2.26845i	1.38757	−	0.407426i	0.888396	+	0.459079i	$0.151820\pi$
$32$	0.540641	−	0.841254i	0.0955727	−	0.148714i
$33$	−6.75757	+	0.971592i	−1.17634	+	0.169132i
$34$	2.18925	+	4.79378i	0.375452	+	0.822126i
$35$	1.36421	+	2.52511i	0.230594	+	0.426821i
$36$	−0.632474	−	4.39895i	−0.105412	−	0.733159i
$37$	5.04755	−	7.85414i	0.829812	−	1.29121i	−0.124446	−	0.992226i	$-0.539715\pi$
$37$	5.04755	−	7.85414i	0.829812	−	1.29121i	0.954258	−	0.298986i	$-0.0966483\pi$
$38$	−0.232428	−	0.791577i	−0.0377048	−	0.128411i
$39$	0.400281	−	2.78401i	0.0640962	−	0.445799i
$40$	1.34801	−	1.78406i	0.213138	−	0.282085i
$41$	−3.34958	+	2.15265i	−0.523117	+	0.336187i	−0.775404	−	0.631466i	$-0.782454\pi$
$41$	−3.34958	+	2.15265i	−0.523117	+	0.336187i	0.252287	+	0.967652i	$0.418817\pi$
$42$	2.64662	−	2.29331i	0.408383	−	0.353866i
$43$	2.74268	−	9.34069i	0.418254	−	1.42444i	−0.433810	−	0.901004i	$-0.642831\pi$
$43$	2.74268	−	9.34069i	0.418254	−	1.42444i	0.852064	−	0.523438i	$-0.175351\pi$
$44$	−1.03946	+	2.27610i	−0.156704	+	0.343134i
$45$	−0.664663	−	9.91526i	−0.0990821	−	1.47808i
$46$	3.73431	−	3.00914i	0.550594	−	0.443673i
$47$			10.1453i			1.47984i	0.672693	+	0.739922i	$0.265138\pi$
$47$			10.1453i			1.47984i	−0.672693	+	0.739922i	$0.734862\pi$
$48$	−2.48184	−	1.13342i	−0.358223	−	0.163595i
$49$	−5.13574	−	1.50799i	−0.733677	−	0.215427i
$50$	3.30792	−	3.74935i	0.467811	−	0.530239i
$51$	12.0962	−	7.77374i	1.69380	−	1.08854i
$52$	−0.779083	−	0.675079i	−0.108039	−	0.0936166i
$53$	3.94642	+	0.567409i	0.542082	+	0.0779396i	0.407916	−	0.913019i	$-0.366255\pi$
$53$	3.94642	+	0.567409i	0.542082	+	0.0779396i	0.134166	+	0.990959i	$0.457165\pi$
$54$	−3.78072	+	1.11012i	−0.514491	+	0.151068i
$55$	−2.70336	+	4.89870i	−0.364521	+	0.660541i
$56$	−0.182665	−	1.27046i	−0.0244097	−	0.169773i
$57$	−2.04751	+	0.935066i	−0.271199	+	0.123853i
$58$	−1.54974	+	0.707741i	−0.203490	+	0.0929310i
$59$	1.11256	+	7.73803i	0.144843	+	1.00741i	0.924495	+	0.381193i	$0.124487\pi$
$59$	1.11256	+	7.73803i	0.144843	+	1.00741i	−0.779652	+	0.626213i	$0.784604\pi$
$60$	−5.34152	−	2.94773i	−0.689587	−	0.380551i
$61$	−3.40094	+	0.998606i	−0.435446	+	0.127858i	−0.492106	−	0.870535i	$-0.663773\pi$
$61$	−3.40094	+	0.998606i	−0.435446	+	0.127858i	0.0566607	+	0.998393i	$0.481955\pi$
$62$	−7.96983	−	1.14589i	−1.01217	−	0.145528i
$63$	−4.31098	−	3.73549i	−0.543133	−	0.470627i
$64$	−0.841254	+	0.540641i	−0.105157	+	0.0675801i
$65$	−1.62266	−	1.63722i	−0.201266	−	0.203072i
$66$	6.55051	+	1.92340i	0.806313	+	0.236755i
$67$	13.0761	+	5.97166i	1.59750	+	0.729555i	0.997515	−	0.0704553i	$-0.0224452\pi$
$67$	13.0761	+	5.97166i	1.59750	+	0.729555i	0.599987	+	0.800010i	$0.295172\pi$
$68$		−	5.27002i		−	0.639084i
$69$	−9.57658	−	8.91658i	−1.15289	−	1.07343i
$70$	−0.191962	−	2.86363i	−0.0229438	−	0.342269i
$71$	2.65819	−	5.82062i	0.315469	−	0.690781i	−0.683773	−	0.729694i	$-0.739662\pi$
$71$	2.65819	−	5.82062i	0.315469	−	0.690781i	0.999243	+	0.0389133i	$0.0123896\pi$
$72$	−1.25207	+	4.26417i	−0.147558	+	0.502537i
$73$	12.6363	−	10.9494i	1.47896	−	1.28153i	0.604343	−	0.796724i	$-0.293436\pi$
$73$	12.6363	−	10.9494i	1.47896	−	1.28153i	0.874621	−	0.484806i	$-0.161110\pi$
$74$	−7.85414	+	5.04755i	−0.913025	+	0.586766i
$75$	−11.4101	−	7.47764i	−1.31752	−	0.863443i
$76$	−0.117409	+	0.816598i	−0.0134677	+	0.0936702i
$77$	0.904831	+	3.08157i	0.103115	+	0.351178i
$78$	−1.52063	+	2.36614i	−0.172177	+	0.267913i
$79$	1.01786	+	7.07936i	0.114518	+	0.796490i	0.963431	+	0.267957i	$0.0863486\pi$
$79$	1.01786	+	7.07936i	0.114518	+	0.796490i	−0.848913	+	0.528533i	$0.822742\pi$
$80$	−1.96732	+	1.06286i	−0.219953	+	0.118831i
$81$	−1.07250	−	2.34844i	−0.119166	−	0.260938i
$82$	3.94113	−	0.566649i	0.435225	−	0.0625759i
$83$	2.41287	−	3.75450i	0.264847	−	0.412110i	−0.683204	−	0.730227i	$-0.739414\pi$
$83$	2.41287	−	3.75450i	0.264847	−	0.412110i	0.948051	+	0.318117i	$0.103051\pi$
$84$	−3.36013	+	0.986624i	−0.366620	+	0.107649i
$85$	0.893151	−	11.7502i	0.0968758	−	1.27449i
$86$	−6.37509	+	7.35725i	−0.687444	+	0.793352i
$87$	2.51310	+	3.91046i	0.269433	+	0.419245i
$88$	1.89105	−	1.63860i	0.201586	−	0.174676i
$89$	6.62662	+	1.94575i	0.702421	+	0.206249i	0.613391	−	0.789780i	$-0.289805\pi$
$89$	6.62662	+	1.94575i	0.702421	+	0.206249i	0.0890300	+	0.996029i	$0.471623\pi$
$90$	−3.51435	+	9.29535i	−0.370445	+	0.979816i
$91$	−1.32316			−0.138705
$92$	−4.64689	+	1.18592i	−0.484472	+	0.123641i
$93$			21.9685i			2.27803i
$94$	4.21451	−	9.22849i	0.434694	−	0.951846i
$95$	−0.400175	+	1.80082i	−0.0410571	+	0.184760i
$96$	1.78672	+	2.06199i	0.182357	+	0.210451i
$97$	8.57591	+	13.3444i	0.870752	+	1.35492i	0.934132	+	0.356927i	$0.116175\pi$
$97$	8.57591	+	13.3444i	0.870752	+	1.35492i	−0.0633809	+	0.997989i	$0.520188\pi$
$98$	4.04519	+	3.50518i	0.408626	+	0.354076i
$99$	1.58259	−	11.0071i	0.159056	−	1.10626i
$100$	−4.56653	+	2.03637i	−0.456653	+	0.203637i
$101$	10.5636	+	6.78883i	1.05112	+	0.675514i	0.947713	−	0.319125i	$-0.103389\pi$
$101$	10.5636	+	6.78883i	1.05112	+	0.675514i	0.103407	+	0.994639i	$0.467025\pi$
$102$	−14.2324	+	2.04631i	−1.40922	+	0.202615i
$103$	−5.37237	+	2.45348i	−0.529356	+	0.241749i	−0.662118	−	0.749399i	$-0.730342\pi$
$103$	−5.37237	+	2.45348i	−0.529356	+	0.241749i	0.132763	+	0.991148i	$0.457615\pi$
$104$	0.428241	+	0.937716i	0.0419924	+	0.0919506i
$105$	−7.65908	+	1.63034i	−0.747450	+	0.159105i
$106$	−3.35408	−	2.15553i	−0.325777	−	0.209364i
$107$	0.0366346	+	0.124766i	0.00354160	+	0.0120616i	0.961245	−	0.275696i	$-0.0889084\pi$
$107$	0.0366346	+	0.124766i	0.00354160	+	0.0120616i	−0.957703	+	0.287758i	$0.907090\pi$
$108$	3.90023	+	0.560768i	0.375300	+	0.0539599i
$109$	−3.33469	+	3.84844i	−0.319405	+	0.368613i	−0.892634	−	0.450782i	$-0.851145\pi$
$109$	−3.33469	+	3.84844i	−0.319405	+	0.368613i	0.573229	+	0.819395i	$0.305691\pi$
$110$	4.49406	−	3.33300i	0.428492	−	0.317789i
$111$	16.6813	+	19.2512i	1.58332	+	1.82724i
$112$	−0.361612	+	1.23154i	−0.0341691	+	0.116369i
$113$	−13.7000	−	6.25659i	−1.28879	−	0.588571i	−0.351196	−	0.936302i	$-0.614225\pi$
$113$	−13.7000	−	6.25659i	−1.28879	−	0.588571i	−0.937594	+	0.347731i	$0.886952\pi$
$114$	2.25092			0.210818
$115$	−10.5619	+	1.85662i	−0.984899	+	0.173131i
$116$	1.70370			0.158184
$117$	4.16739	+	1.90318i	0.385275	+	0.175949i
$118$	2.20247	−	7.50094i	0.202754	−	0.690517i
$119$	−4.42962	−	5.11206i	−0.406063	−	0.468622i
$120$	3.63428	+	4.90030i	0.331763	+	0.447334i
$121$	3.10333	−	3.58143i	0.282121	−	0.325585i
$122$	3.50844	+	0.504437i	0.317639	+	0.0456696i
$123$	−3.06062	−	10.4235i	−0.275967	−	0.939857i
$124$	6.77360	+	4.35313i	0.608287	+	0.390922i
$125$	−10.5268	+	3.76644i	−0.941547	+	0.336881i
$126$	2.36963	+	5.18877i	0.211103	+	0.462252i
$127$	−14.1820	+	6.47670i	−1.25845	+	0.574715i	−0.929217	−	0.369534i	$-0.879517\pi$
$127$	−14.1820	+	6.47670i	−1.25845	+	0.574715i	−0.329232	+	0.944249i	$0.606790\pi$
$128$	0.989821	−	0.142315i	0.0874887	−	0.0125790i
$129$	22.3446	+	14.3600i	1.96733	+	1.26433i
$130$	0.795899	+	2.16334i	0.0698049	+	0.189738i
$131$	1.62591	−	11.3084i	0.142056	−	0.988023i	−0.786701	−	0.617334i	$-0.788213\pi$
$131$	1.62591	−	11.3084i	0.142056	−	0.988023i	0.928757	−	0.370689i	$-0.120878\pi$
$132$	−5.15955	−	4.47077i	−0.449081	−	0.389131i
$133$	0.572487	+	0.890808i	0.0496410	+	0.0772428i
$134$	−9.41374	−	10.8640i	−0.813223	−	0.938509i
$135$	8.60105	+	1.91131i	0.740261	+	0.164499i
$136$	−2.18925	+	4.79378i	−0.187726	+	0.411063i
$137$			7.19734i			0.614910i	0.951563	+	0.307455i	$0.0994774\pi$
$137$			7.19734i			0.614910i	−0.951563	+	0.307455i	$0.900523\pi$
$138$	5.00709	+	12.0891i	0.426231	+	1.02909i
$139$	10.1060			0.857182			0.428591	−	0.903499i	$-0.359010\pi$
$139$	10.1060			0.857182			0.428591	+	0.903499i	$0.359010\pi$
$140$	−1.01498	+	2.68459i	−0.0857816	+	0.226890i
$141$	−26.5592	−	7.79849i	−2.23669	−	0.656752i
$142$	−4.83595	+	4.19037i	−0.405824	+	0.351648i
$143$	−1.39457	−	2.16999i	−0.116620	−	0.181464i
$144$	2.91033	−	3.35869i	0.242527	−	0.279891i
$145$	3.79862	+	0.288739i	0.315459	+	0.0239784i
$146$	−16.0429	+	4.71062i	−1.32772	+	0.389854i
$147$	7.89548	−	12.2856i	0.651208	−	1.01330i
$148$	9.24120	−	1.32868i	0.759622	−	0.109217i
$149$	−5.82013	−	12.7443i	−0.476804	−	1.04405i	−0.983330	−	0.181830i	$-0.941798\pi$
$149$	−5.82013	−	12.7443i	−0.476804	−	1.04405i	0.506527	−	0.862224i	$-0.330929\pi$
$150$	7.27264	+	11.5418i	0.593809	+	0.942385i
$151$	−1.82735	−	12.7095i	−0.148707	−	1.03428i	−0.918339	−	0.395795i	$-0.870469\pi$
$151$	−1.82735	−	12.7095i	−0.148707	−	1.03428i	0.769632	−	0.638488i	$-0.220440\pi$
$152$	0.446026	−	0.694030i	0.0361775	−	0.0562933i
$153$	6.59845	+	22.4723i	0.533453	+	1.81677i
$154$	0.457068	−	3.17898i	0.0368316	−	0.256169i
$155$	14.3649	+	10.8539i	1.15382	+	0.871803i
$156$	2.36614	−	1.52063i	0.189443	−	0.121748i
$157$	9.49942	−	8.23130i	0.758136	−	0.656929i	−0.187460	−	0.982272i	$-0.560025\pi$
$157$	9.49942	−	8.23130i	0.758136	−	0.656929i	0.945596	+	0.325343i	$0.105480\pi$
$158$	2.01500	−	6.86245i	0.160304	−	0.545947i
$159$	−4.51894	+	9.89511i	−0.358376	+	0.784733i
$160$	2.23106	−	0.149558i	0.176381	−	0.0118236i
$161$	−3.51080	+	5.05624i	−0.276690	+	0.398487i
$162$			2.58174i			0.202841i
$163$	−8.89411	−	4.06181i	−0.696641	−	0.318145i	0.0354316	−	0.999372i	$-0.488719\pi$
$163$	−8.89411	−	4.06181i	−0.696641	−	0.318145i	−0.732072	+	0.681227i	$0.761447\pi$
$164$	−3.82037	−	1.12176i	−0.298321	−	0.0875949i
$165$	−10.7462	−	10.8426i	−0.836592	−	0.844097i
$166$	−3.75450	+	2.41287i	−0.291406	+	0.187275i
$167$	−13.7420	−	11.9075i	−1.06339	−	0.921429i	−0.0663062	−	0.997799i	$-0.521121\pi$
$167$	−13.7420	−	11.9075i	−1.06339	−	0.921429i	−0.997080	+	0.0763704i	$0.975667\pi$
$168$	3.46634	+	0.498385i	0.267434	+	0.0384512i
$169$	−11.4538	+	3.36313i	−0.881058	+	0.258702i
$170$	−5.69366	+	10.3174i	−0.436684	+	0.791305i
$171$	−0.521788	−	3.62912i	−0.0399021	−	0.277525i
$172$	8.85530	−	4.04408i	0.675210	−	0.308358i
$173$	4.26160	−	1.94621i	0.324004	−	0.147968i	−0.246772	−	0.969074i	$-0.579370\pi$
$173$	4.26160	−	1.94621i	0.324004	−	0.147968i	0.570776	+	0.821106i	$0.306643\pi$
$174$	−0.661533	−	4.60106i	−0.0501507	−	0.348805i
$175$	−2.71802	+	5.81365i	−0.205463	+	0.439471i
$176$	−2.40086	+	0.704956i	−0.180972	+	0.0531380i
$177$	−21.1125	−	3.03552i	−1.58691	−	0.228163i
$178$	−5.21949	−	4.52272i	−0.391218	−	0.338992i
$179$	−7.44686	+	4.78581i	−0.556605	+	0.357708i	−0.788502	−	0.615032i	$-0.789143\pi$
$179$	−7.44686	+	4.78581i	−0.556605	+	0.357708i	0.231897	+	0.972740i	$0.425507\pi$
$180$	7.05819	−	6.99543i	0.526086	−	0.521409i
$181$	−19.9039	−	5.84430i	−1.47944	−	0.434404i	−0.560287	−	0.828298i	$-0.689309\pi$
$181$	−19.9039	−	5.84430i	−1.47944	−	0.434404i	−0.919156	+	0.393895i	$0.871128\pi$
$182$	1.20359	+	0.549659i	0.0892157	+	0.0407434i
$183$		−	9.67087i		−	0.714892i
$184$	4.71961	+	0.851638i	0.347934	+	0.0627836i
$185$	20.8297	−	1.39630i	1.53143	−	0.102658i
$186$	9.12606	−	19.9833i	0.669155	−	1.46525i
$187$	3.71513	−	12.6526i	0.271677	−	0.925248i
$188$	−7.66731	+	6.64376i	−0.559196	+	0.484546i
$189$	4.25467	−	2.73431i	0.309482	−	0.198892i
$190$	1.11210	−	1.47184i	0.0806801	−	0.106779i
$191$	2.32093	−	16.1424i	0.167937	−	1.16803i	−0.715203	−	0.698917i	$-0.753666\pi$
$191$	2.32093	−	16.1424i	0.167937	−	1.16803i	0.883140	−	0.469110i	$-0.155425\pi$
$192$	−0.768680	−	2.61788i	−0.0554747	−	0.188930i
$193$	5.16166	−	8.03169i	0.371544	−	0.578134i	−0.604258	−	0.796789i	$-0.706530\pi$
$193$	5.16166	−	8.03169i	0.371544	−	0.578134i	0.975802	+	0.218655i	$0.0701668\pi$
$194$	−2.25747	−	15.7010i	−0.162077	−	1.12727i
$195$	5.53335	−	2.98944i	0.396252	−	0.214078i
$196$	−2.22353	−	4.86885i	−0.158824	−	0.347775i
$197$	5.03127	−	0.723387i	0.358463	−	0.0515392i	0.0392691	−	0.999229i	$-0.487497\pi$
$197$	5.03127	−	0.723387i	0.358463	−	0.0515392i	0.319194	+	0.947689i	$0.396588\pi$
$198$	−6.01210	+	9.35501i	−0.427261	+	0.664832i
$199$	−0.513963	+	0.150913i	−0.0364338	+	0.0106979i	−0.299899	−	0.953971i	$-0.596953\pi$
$199$	−0.513963	+	0.150913i	−0.0364338	+	0.0106979i	0.263465	+	0.964669i	$0.415135\pi$
$200$	4.99980	+	0.0446559i	0.353539	+	0.00315765i
$201$	−25.6845	+	29.6415i	−1.81164	+	2.09075i
$202$	−6.78883	−	10.5636i	−0.477660	−	0.743254i
$203$	1.65263	−	1.43201i	0.115992	−	0.100508i
$204$	13.7963	+	4.05096i	0.965934	+	0.283624i
$205$	−8.32792	−	3.14859i	−0.581647	−	0.219907i
$206$	5.90610			0.411497
$207$	18.3303	−	10.8752i	1.27404	−	0.755879i
$208$		−	1.03087i		−	0.0714782i
$209$	−0.857548	+	1.87777i	−0.0593178	+	0.129888i
$210$	7.64421	+	1.69868i	0.527501	+	0.117220i
$211$	3.43509	+	3.96431i	0.236482	+	0.272914i	0.861569	−	0.507640i	$-0.169482\pi$
$211$	3.43509	+	3.96431i	0.236482	+	0.272914i	−0.625087	+	0.780555i	$0.714937\pi$
$212$	2.15553	+	3.35408i	0.148043	+	0.230359i
$213$	13.1944	+	11.4330i	0.904067	+	0.783379i
$214$	0.0185057	−	0.128710i	0.00126502	−	0.00879842i
$215$	20.4295	−	7.51605i	1.39328	−	0.512590i
$216$	−3.31482	−	2.13031i	−0.225545	−	0.144949i
$217$	10.2295	−	1.47078i	0.694425	−	0.0998432i
$218$	4.63204	−	2.11538i	0.313721	−	0.143272i
$219$	18.9510	+	41.4969i	1.28059	+	2.80410i
$220$	−5.47252	+	1.16490i	−0.368957	+	0.0785377i
$221$	4.57030	+	2.93715i	0.307432	+	0.197574i
$222$	−7.17658	−	24.4412i	−0.481660	−	1.64038i
$223$	5.24366	+	0.753925i	0.351142	+	0.0504866i	0.315629	−	0.948883i	$-0.397784\pi$
$223$	5.24366	+	0.753925i	0.351142	+	0.0504866i	0.0355127	+	0.999369i	$0.488694\pi$
$224$	0.840533	−	0.970027i	0.0561605	−	0.0648126i
$225$	16.9228	−	14.4011i	1.12818	−	0.960071i
$226$	9.86290	+	11.3824i	0.656070	+	0.757146i
$227$	−1.89321	+	6.44767i	−0.125657	+	0.427947i	−0.998158	−	0.0606642i	$-0.980678\pi$
$227$	−1.89321	+	6.44767i	−0.125657	+	0.427947i	0.872502	+	0.488611i	$0.162496\pi$
$228$	−2.04751	−	0.935066i	−0.135600	−	0.0619263i
$229$	11.2865			0.745830			0.372915	−	0.927866i	$-0.378358\pi$
$229$	11.2865			0.745830			0.372915	+	0.927866i	$0.378358\pi$
$230$	10.3787	+	2.69871i	0.684350	+	0.177948i
$231$	−8.76273			−0.576545
$232$	−1.54974	−	0.707741i	−0.101745	−	0.0464655i
$233$	1.25006	−	4.25733i	0.0818945	−	0.278907i	−0.908358	−	0.418194i	$-0.862663\pi$
$233$	1.25006	−	4.25733i	0.0818945	−	0.278907i	0.990252	+	0.139288i	$0.0444812\pi$
$234$	−3.00018	−	3.46239i	−0.196128	−	0.226344i
$235$	−18.2213	+	13.5137i	−1.18862	+	0.881538i
$236$	−5.11944	+	5.90815i	−0.333247	+	0.384588i
$237$	−19.3154	−	2.77713i	−1.25467	−	0.180394i
$238$	1.90570	+	6.49023i	0.123528	+	0.420699i
$239$	−15.2662	−	9.81100i	−0.987489	−	0.634621i	−0.0560155	−	0.998430i	$-0.517840\pi$
$239$	−15.2662	−	9.81100i	−0.987489	−	0.634621i	−0.931473	+	0.363809i	$0.881476\pi$
$240$	−1.27020	−	5.96720i	−0.0819913	−	0.385181i
$241$	7.55301	+	16.5388i	0.486532	+	1.06536i	0.980616	+	0.195942i	$0.0627764\pi$
$241$	7.55301	+	16.5388i	0.486532	+	1.06536i	−0.494084	+	0.869414i	$0.664496\pi$
$242$	−4.31067	+	1.96862i	−0.277100	+	0.126547i
$243$	18.6730	−	2.68478i	1.19788	−	0.172228i
$244$	−2.98184	−	1.91631i	−0.190893	−	0.122679i
$245$	−4.13250	−	11.2326i	−0.264016	−	0.717625i
$246$	−1.54605	+	10.7530i	−0.0985724	+	0.685586i
$247$	−0.642739	−	0.556937i	−0.0408965	−	0.0354370i
$248$	−4.35313	−	6.77360i	−0.276424	−	0.430124i
$249$	7.97412	+	9.20263i	0.505339	+	0.583193i
$250$	11.1402	+	0.946921i	0.704566	+	0.0598886i
$251$	3.33161	−	7.29521i	0.210289	−	0.460470i	−0.774868	−	0.632123i	$-0.782184\pi$
$251$	3.33161	−	7.29521i	0.210289	−	0.460470i	0.985157	+	0.171654i	$0.0549110\pi$
$252$		−	5.70425i		−	0.359334i
$253$	−11.9926	−	0.428628i	−0.753965	−	0.0269476i
$254$	15.5909			0.978262
$255$	30.0742	+	11.3703i	1.88332	+	0.712038i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	5.88681	−	5.10095i	0.367209	−	0.318189i	−0.451637	−	0.892202i	$-0.649160\pi$
$257$	5.88681	−	5.10095i	0.367209	−	0.318189i	0.818846	+	0.574013i	$0.194614\pi$
$258$	−14.3600	−	22.3446i	−0.894015	−	1.39112i
$259$	7.84741	−	9.05639i	0.487614	−	0.562737i
$260$	0.174710	−	2.29847i	0.0108351	−	0.142545i
$261$	−7.26485	+	2.13315i	−0.449683	+	0.132039i
$262$	−6.17668	+	9.61110i	−0.381596	+	0.593775i
$263$	8.47255	−	1.21817i	0.522440	−	0.0751155i	0.123950	−	0.992288i	$-0.460444\pi$
$263$	8.47255	−	1.21817i	0.522440	−	0.0751155i	0.398490	+	0.917173i	$0.369535\pi$
$264$	2.83606	+	6.21011i	0.174548	+	0.382206i
$265$	4.23762	+	7.84369i	0.260315	+	0.481834i
$266$	−0.150698	−	1.04813i	−0.00923988	−	0.0642648i
$267$	−10.1875	+	15.8521i	−0.623466	+	0.970131i
$268$	4.04995	+	13.7929i	0.247390	+	0.842534i
$269$	1.74040	−	12.1047i	0.106114	−	0.738039i	−0.865404	−	0.501074i	$-0.832938\pi$
$269$	1.74040	−	12.1047i	0.106114	−	0.738039i	0.971518	−	0.236965i	$-0.0761526\pi$
$270$	−7.02980	−	5.31159i	−0.427820	−	0.323253i
$271$	−25.9284	+	16.6632i	−1.57504	+	1.01222i	−0.597394	+	0.801948i	$0.703797\pi$
$271$	−25.9284	+	16.6632i	−1.57504	+	1.01222i	−0.977644	+	0.210267i	$0.932567\pi$
$272$	3.98282	−	3.45113i	0.241494	−	0.209255i
$273$	1.01708	−	3.46387i	0.0615568	−	0.209643i
$274$	2.98988	−	6.54693i	0.180625	−	0.395515i
$275$	−12.3991	+	1.66984i	−0.747697	+	0.100695i
$276$	0.467374	−	13.0766i	0.0281326	−	0.787120i
$277$		−	17.6756i		−	1.06202i	−0.847365	−	0.531011i	$-0.821812\pi$
$277$		−	17.6756i		−	1.06202i	0.847365	−	0.531011i	$-0.178188\pi$
$278$	−9.19276	−	4.19819i	−0.551345	−	0.251791i
$279$	−34.3342	−	10.0814i	−2.05553	−	0.603559i
$280$	2.03848	−	2.02035i	0.121822	−	0.120739i
$281$	20.7971	−	13.3655i	1.24065	−	0.797316i	0.255133	−	0.966906i	$-0.417881\pi$
$281$	20.7971	−	13.3655i	1.24065	−	0.797316i	0.985515	+	0.169590i	$0.0542442\pi$
$282$	20.9195	+	18.1269i	1.24574	+	1.07944i
$283$	−28.1706	−	4.05032i	−1.67457	−	0.240767i	−0.761381	−	0.648305i	$-0.775478\pi$
$283$	−28.1706	−	4.05032i	−1.67457	−	0.240767i	−0.913188	+	0.407538i	$0.866387\pi$
$284$	6.13968	−	1.80277i	0.364323	−	0.106975i
$285$	−4.40673	−	2.43186i	−0.261032	−	0.144051i
$286$	0.367097	+	2.55321i	0.0217069	+	0.150975i
$287$	−4.64874	+	2.12301i	−0.274406	+	0.125317i
$288$	−4.04258	+	1.84618i	−0.238211	+	0.108787i
$289$	1.53317	+	10.6635i	0.0901866	+	0.627262i
$290$	−3.33540	−	1.84065i	−0.195862	−	0.108087i
$291$	−41.5262	+	12.1932i	−2.43431	+	0.714777i
$292$	16.5500	+	2.37953i	0.968516	+	0.139252i
$293$	16.9987	+	14.7294i	0.993073	+	0.860502i	0.990223	−	0.139494i	$-0.0445475\pi$
$293$	16.9987	+	14.7294i	0.993073	+	0.860502i	0.00284964	+	0.999996i	$0.499093\pi$
$294$	−12.2856	+	7.89548i	−0.716511	+	0.460474i
$295$	−12.4158	+	12.3054i	−0.722875	+	0.716448i
$296$	−8.95805	−	2.63032i	−0.520676	−	0.152884i
$297$	8.96858	+	4.09581i	0.520410	+	0.237663i
$298$			14.0104i			0.811600i
$299$	1.56140	−	4.69086i	0.0902983	−	0.271279i
$300$	−1.82079	−	13.5200i	−0.105123	−	0.780576i
$301$	5.19069	−	11.3660i	0.299186	−	0.655127i
$302$	−3.61749	+	12.3201i	−0.208163	+	0.708940i
$303$	−25.8924	+	22.4359i	−1.48748	+	1.28891i
$304$	−0.694030	+	0.446026i	−0.0398054	+	0.0255814i
$305$	−6.32364	−	4.77803i	−0.362091	−	0.273589i
$306$	3.33315	−	23.1826i	0.190544	−	1.32526i
$307$	8.44127	+	28.7483i	0.481769	+	1.64075i	0.738487	+	0.674267i	$0.235540\pi$
$307$	8.44127	+	28.7483i	0.481769	+	1.64075i	−0.256719	+	0.966486i	$0.582641\pi$
$308$	−1.73636	+	2.70183i	−0.0989382	+	0.153951i
$309$	−2.29329	−	15.9502i	−0.130461	−	0.907375i
$310$	−8.55791	−	15.8404i	−0.486057	−	0.899675i
$311$	2.66200	+	5.82897i	0.150948	+	0.330531i	0.969967	−	0.243236i	$-0.0782089\pi$
$311$	2.66200	+	5.82897i	0.150948	+	0.330531i	−0.819019	+	0.573767i	$0.805482\pi$
$312$	−2.78401	+	0.400281i	−0.157614	+	0.0226614i
$313$	−1.17207	+	1.82377i	−0.0662491	+	0.103086i	−0.872798	−	0.488082i	$-0.837697\pi$
$313$	−1.17207	+	1.82377i	−0.0662491	+	0.103086i	0.806548	+	0.591168i	$0.201333\pi$
$314$	−12.0604	+	3.54125i	−0.680607	+	0.199844i
$315$	0.966743	−	12.7184i	0.0544698	−	0.716600i
$316$	−4.68367	+	5.40524i	−0.263477	+	0.304069i
$317$	−4.76371	−	7.41248i	−0.267557	−	0.416326i	0.681314	−	0.731991i	$-0.261409\pi$
$317$	−4.76371	−	7.41248i	−0.267557	−	0.416326i	−0.948871	+	0.315665i	$0.897772\pi$
$318$	8.22115	−	7.12367i	0.461019	−	0.399476i
$319$	4.09034	+	1.20103i	0.229015	+	0.0672448i
$320$	−2.09157	−	0.790774i	−0.116922	−	0.0442056i
$321$	−0.354784			−0.0198021
$322$	5.29398	−	3.14087i	0.295022	−	0.175034i
$323$		−	4.34774i		−	0.241915i
$324$	1.07250	−	2.34844i	0.0595831	−	0.130469i
$325$	0.779080	−	5.09515i	0.0432156	−	0.282628i
$326$	6.40304	+	7.38950i	0.354631	+	0.409266i
$327$	−7.51145	−	11.6880i	−0.415384	−	0.646351i
$328$	3.00914	+	2.60743i	0.166152	+	0.143971i
$329$	−1.85319	+	12.8892i	−0.102170	+	0.710607i
$330$	5.27091	+	14.3269i	0.290154	+	0.788672i
$331$	−0.696634	−	0.447699i	−0.0382905	−	0.0246078i	0.521356	−	0.853340i	$-0.325427\pi$
$331$	−0.696634	−	0.447699i	−0.0382905	−	0.0246078i	−0.559646	+	0.828732i	$0.689063\pi$
$332$	4.41756	−	0.635149i	0.242445	−	0.0348583i
$333$	−37.7424	+	17.2364i	−2.06827	+	0.944549i
$334$	7.55359	+	16.5401i	0.413314	+	0.905031i
$335$	6.69234	+	31.4395i	0.365642	+	1.71772i
$336$	−2.94606	−	1.89332i	−0.160721	−	0.103289i
$337$	2.40619	+	8.19473i	0.131074	+	0.446395i	0.998709	−	0.0508063i	$-0.0161791\pi$
$337$	2.40619	+	8.19473i	0.131074	+	0.446395i	−0.867635	+	0.497202i	$0.834361\pi$
$338$	11.8158	+	1.69885i	0.642694	+	0.0924055i
$339$	26.9100	−	31.0558i	1.46155	−	1.68672i
$340$	9.46512	−	7.01976i	0.513318	−	0.380700i
$341$	13.1937	+	15.2263i	0.714478	+	0.824552i
$342$	−1.03295	+	3.51792i	−0.0558558	+	0.190227i
$343$	−14.4221	−	6.58635i	−0.778720	−	0.355629i
$344$	−9.73503			−0.524878
$345$	3.25827	−	29.0769i	0.175419	−	1.56545i
$346$	−4.68498			−0.251866
$347$	3.39729	+	1.55149i	0.182376	+	0.0832885i	0.504511	−	0.863406i	$-0.331673\pi$
$347$	3.39729	+	1.55149i	0.182376	+	0.0832885i	−0.322134	+	0.946694i	$0.604400\pi$
$348$	−1.30960	+	4.46008i	−0.0702018	+	0.239085i
$349$	−3.56479	−	4.11399i	−0.190819	−	0.220217i	0.652276	−	0.757981i	$-0.273814\pi$
$349$	−3.56479	−	4.11399i	−0.190819	−	0.220217i	−0.843095	+	0.537765i	$0.819269\pi$
$350$	4.88747	−	4.15918i	0.261246	−	0.222317i
$351$	−2.66004	+	3.06985i	−0.141982	+	0.163856i
$352$	2.47675	+	0.356103i	0.132011	+	0.0189803i
$353$	−5.00056	−	17.0304i	−0.266153	−	0.906434i	−0.978784	−	0.204895i	$-0.934315\pi$
$353$	−5.00056	−	17.0304i	−0.266153	−	0.906434i	0.712631	−	0.701539i	$-0.247504\pi$
$354$	17.9436	+	11.5316i	0.953691	+	0.612900i
$355$	13.9948	−	2.97899i	0.742766	−	0.158108i
$356$	2.86901	+	6.28227i	0.152057	+	0.332959i
$357$	16.7877	−	7.66671i	0.888502	−	0.405765i
$358$	8.76200	−	1.25979i	0.463086	−	0.0665817i
$359$	−14.6196	−	9.39543i	−0.771592	−	0.495872i	0.0946415	−	0.995511i	$-0.469830\pi$
$359$	−14.6196	−	9.39543i	−0.771592	−	0.495872i	−0.866234	+	0.499639i	$0.833466\pi$
$360$	−9.32636	+	3.43119i	−0.491543	+	0.180840i
$361$	2.60712	−	18.1329i	0.137217	−	0.954364i
$362$	15.6774	+	13.5845i	0.823985	+	0.713987i
$363$	6.99031	+	10.8771i	0.366896	+	0.570901i
$364$	−0.866483	−	0.999975i	−0.0454161	−	0.0524129i
$365$	36.4972	+	8.11035i	1.91035	+	0.424515i
$366$	−4.01743	+	8.79694i	−0.209994	+	0.459823i
$367$			26.4546i			1.38092i	0.723372	+	0.690458i	$0.242591\pi$
$367$			26.4546i			1.38092i	−0.723372	+	0.690458i	$0.757409\pi$
$368$	−3.93932	−	2.73527i	−0.205351	−	0.142586i
$369$	17.6952			0.921177
$370$	−19.5274	−	7.38285i	−1.01518	−	0.383816i
$371$	4.91014	+	1.44175i	0.254922	+	0.0748517i
$372$	−16.6027	+	14.3863i	−0.860811	+	0.745897i
$373$	−6.35988	−	9.89617i	−0.329302	−	0.512404i	0.636640	−	0.771161i	$-0.280324\pi$
$373$	−6.35988	−	9.89617i	−0.329302	−	0.512404i	−0.965943	+	0.258757i	$0.916687\pi$
$374$	−8.63547	+	9.96587i	−0.446530	+	0.515323i
$375$	−1.76836	−	30.4532i	−0.0913175	−	1.57260i
$376$	9.73435	−	2.85826i	0.502011	−	0.147404i
$377$	−0.949526	+	1.47749i	−0.0489031	+	0.0760947i
$378$	−5.00606	+	0.719762i	−0.257484	+	0.0370206i
$379$	−0.218894	−	0.479311i	−0.0112438	−	0.0246205i	0.903927	−	0.427687i	$-0.140672\pi$
$379$	−0.218894	−	0.479311i	−0.0112438	−	0.0246205i	−0.915171	+	0.403067i	$0.867944\pi$
$380$	−1.62303	+	0.876853i	−0.0832595	+	0.0449816i
$381$	−6.05384	−	42.1054i	−0.310148	−	2.15712i
$382$	−8.81701	+	13.7195i	−0.451118	+	0.701953i
$383$	−0.866849	−	2.95222i	−0.0442939	−	0.150851i	0.934377	−	0.356286i	$-0.115957\pi$
$383$	−0.866849	−	2.95222i	−0.0442939	−	0.150851i	−0.978671	+	0.205435i	$0.934139\pi$
$384$	−0.388292	+	2.70063i	−0.0198150	+	0.137816i
$385$	−4.32935	+	5.72982i	−0.220644	+	0.292018i
$386$	−8.03169	+	5.16166i	−0.408802	+	0.262721i
$387$	−32.6970	+	28.3321i	−1.66208	+	1.44020i
$388$	−4.46898	+	15.2199i	−0.226878	+	0.772676i
$389$	−8.17077	+	17.8915i	−0.414275	+	0.907135i	0.581347	+	0.813656i	$0.302526\pi$
$389$	−8.17077	+	17.8915i	−0.414275	+	0.907135i	−0.995621	+	0.0934789i	$0.970201\pi$
$390$	−6.27517	+	0.420652i	−0.317756	+	0.0213005i
$391$	23.3505	−	9.67138i	1.18089	−	0.489103i
$392$			5.35255i			0.270345i
$393$	28.3544	+	12.9490i	1.43029	+	0.653192i
$394$	−4.87711	−	1.43205i	−0.245705	−	0.0721455i
$395$	−11.3589	+	11.2579i	−0.571530	+	0.566449i
$396$	9.35501	−	6.01210i	0.470107	−	0.302119i
$397$	−20.5192	−	17.7800i	−1.02983	−	0.892350i	−0.0355698	−	0.999367i	$-0.511325\pi$
$397$	−20.5192	−	17.7800i	−1.02983	−	0.892350i	−0.994257	+	0.107017i	$0.965870\pi$
$398$	0.530208	+	0.0762325i	0.0265769	+	0.00382119i
$399$	−2.77209	+	0.813960i	−0.138778	+	0.0407490i
$400$	−4.52943	−	2.11761i	−0.226471	−	0.105881i
$401$	2.38450	+	16.5846i	0.119076	+	0.828195i	0.958577	+	0.284835i	$0.0919389\pi$
$401$	2.38450	+	16.5846i	0.119076	+	0.828195i	−0.839500	+	0.543360i	$0.817152\pi$
$402$	35.6769	−	16.2931i	1.77940	−	0.812626i
$403$	−7.55029	+	3.44810i	−0.376107	+	0.171762i
$404$	1.78705	+	12.4292i	0.0889090	+	0.618375i
$405$	2.78928	−	5.05440i	0.138601	−	0.251155i
$406$	−2.09817	+	0.616077i	−0.104130	+	0.0305754i
$407$	23.1235	+	3.32466i	1.14619	+	0.164797i
$408$	−10.8667	−	9.41608i	−0.537983	−	0.466165i
$409$	17.1243	−	11.0051i	0.846744	−	0.544170i	−0.0438134	−	0.999040i	$-0.513951\pi$
$409$	17.1243	−	11.0051i	0.846744	−	0.544170i	0.890558	+	0.454870i	$0.150314\pi$
$410$	6.26738	+	6.32360i	0.309524	+	0.312300i
$411$	−18.8418	−	5.53245i	−0.929398	−	0.272896i
$412$	−5.37237	−	2.45348i	−0.264678	−	0.120874i
$413$			10.0341i			0.493747i
$414$	−21.1915	+	2.27777i	−1.04151	+	0.111946i
$415$	9.95719	−	0.667473i	0.488779	−	0.0327650i
$416$	−0.428241	+	0.937716i	−0.0209962	+	0.0459753i
$417$	−7.76830	+	26.4564i	−0.380415	+	1.29558i
$418$	1.56011	−	1.35184i	0.0763073	−	0.0661207i
$419$	15.4046	−	9.89992i	0.752562	−	0.483642i	−0.107263	−	0.994231i	$-0.534209\pi$
$419$	15.4046	−	9.89992i	0.752562	−	0.483642i	0.859825	+	0.510588i	$0.170572\pi$
$420$	−6.24776	−	4.72070i	−0.304860	−	0.230347i
$421$	−1.11885	+	7.78178i	−0.0545295	+	0.379261i	0.944222	+	0.329309i	$0.106816\pi$
$421$	−1.11885	+	7.78178i	−0.0545295	+	0.379261i	−0.998752	+	0.0499517i	$0.984093\pi$
$422$	−1.47784	−	5.03305i	−0.0719400	−	0.245005i
$423$	24.3762	−	37.9301i	1.18521	−	1.84423i
$424$	−0.567409	−	3.94642i	−0.0275558	−	0.191655i
$425$	22.2935	−	14.0474i	1.08139	−	0.681399i
$426$	−7.25262	−	15.8810i	−0.351390	−	0.769438i
$427$	−4.50318	+	0.647460i	−0.217924	+	0.0313328i
$428$	−0.0703014	+	0.109391i	−0.00339814	+	0.00528762i
$429$	6.75275	−	1.98279i	0.326026	−	0.0957299i
$430$	−21.7056	−	1.64987i	−1.04674	−	0.0795638i
$431$	−14.5740	+	16.8193i	−0.702006	+	0.810158i	−0.989022	−	0.147768i	$-0.952791\pi$
$431$	−14.5740	+	16.8193i	−0.702006	+	0.810158i	0.287016	+	0.957926i	$0.407337\pi$
$432$	2.13031	+	3.31482i	0.102494	+	0.159484i
$433$	−18.8350	+	16.3206i	−0.905152	+	0.784319i	−0.977032	−	0.213095i	$-0.931646\pi$
$433$	−18.8350	+	16.3206i	−0.905152	+	0.784319i	0.0718794	+	0.997413i	$0.477100\pi$
$434$	−9.91608	−	2.91162i	−0.475987	−	0.139762i
$435$	−3.67581	+	9.72241i	−0.176242	+	0.466154i
$436$	−5.09221			−0.243873
$437$	−3.83366	+	0.978378i	−0.183389	+	0.0468022i
$438$		−	45.6195i		−	2.17978i
$439$	−0.884648	+	1.93711i	−0.0422219	+	0.0924531i	−0.929568	−	0.368652i	$-0.879820\pi$
$439$	−0.884648	+	1.93711i	−0.0422219	+	0.0924531i	0.887346	+	0.461105i	$0.152547\pi$
$440$	5.46189	+	1.21373i	0.260386	+	0.0578624i
$441$	15.5777	+	17.9776i	0.741794	+	0.856076i
$442$	−2.93715	−	4.57030i	−0.139706	−	0.217387i
$443$	9.52095	+	8.24995i	0.452354	+	0.391967i	0.851023	−	0.525128i	$-0.175982\pi$
$443$	9.52095	+	8.24995i	0.452354	+	0.391967i	−0.398669	+	0.917095i	$0.630528\pi$
$444$	−3.62519	+	25.2137i	−0.172044	+	1.19659i
$445$	5.33215	+	14.4934i	0.252768	+	0.687053i
$446$	−4.45661	−	2.86409i	−0.211027	−	0.135619i
$447$	37.8369	−	5.44013i	1.78963	−	0.257309i
$448$	−1.16754	+	0.533197i	−0.0551610	+	0.0251912i
$449$	−6.38566	−	13.9826i	−0.301358	−	0.659882i	0.697006	−	0.717066i	$-0.254515\pi$
$449$	−6.38566	−	13.9826i	−0.301358	−	0.659882i	−0.998364	+	0.0571837i	$0.981788\pi$
$450$	−21.3759	+	6.06970i	−1.00767	+	0.286128i
$451$	−8.38138	−	5.38639i	−0.394664	−	0.253635i
$452$	−4.24319	−	14.4510i	−0.199583	−	0.679717i
$453$	34.6766	+	4.98574i	1.62925	+	0.234251i
$454$	4.40058	−	5.07854i	0.206530	−	0.238348i
$455$	−1.76247	−	2.37643i	−0.0826258	−	0.111409i
$456$	1.47404	+	1.70113i	0.0690282	+	0.0796628i
$457$	−0.512479	+	1.74534i	−0.0239728	+	0.0816438i	−0.970611	−	0.240656i	$-0.922638\pi$
$457$	−0.512479	+	1.74534i	−0.0239728	+	0.0816438i	0.946638	+	0.322299i	$0.104456\pi$
$458$	−10.2665	−	4.68856i	−0.479723	−	0.219082i
$459$	−20.7656			−0.969257
$460$	−8.31969	−	6.76629i	−0.387908	−	0.315480i
$461$	6.04815			0.281690			0.140845	−	0.990032i	$-0.455018\pi$
$461$	6.04815			0.281690			0.140845	+	0.990032i	$0.455018\pi$
$462$	7.97086	+	3.64017i	0.370838	+	0.169356i
$463$	9.21629	−	31.3878i	0.428317	−	1.45871i	−0.409271	−	0.912413i	$-0.634217\pi$
$463$	9.21629	−	31.3878i	0.428317	−	1.45871i	0.837589	−	0.546302i	$-0.183965\pi$
$464$	1.11568	+	1.28757i	0.0517943	+	0.0597739i
$465$	−39.4562	+	29.2625i	−1.82974	+	1.35702i
$466$	−2.90566	+	3.35331i	−0.134602	+	0.155339i
$467$	−30.0199	−	4.31621i	−1.38915	−	0.199730i	−0.593184	−	0.805067i	$-0.702130\pi$
$467$	−30.0199	−	4.31621i	−1.38915	−	0.199730i	−0.795970	+	0.605336i	$0.793039\pi$
$468$	1.29073	+	4.39582i	0.0596640	+	0.203197i
$469$	15.5219	+	9.97534i	0.716736	+	0.460618i
$470$	22.1885	−	4.72313i	1.02348	−	0.217862i
$471$	14.2466	+	31.1956i	0.656447	+	1.43742i
$472$	7.11114	−	3.24755i	0.327317	−	0.149481i
$473$	24.1112	−	3.46667i	1.10863	−	0.159398i
$474$	16.4162	+	10.5501i	0.754021	+	0.484580i
$475$	−3.76736	+	1.68000i	−0.172859	+	0.0770835i
$476$	0.962649	−	6.69537i	0.0441230	−	0.306882i
$477$	−13.3911	−	11.6035i	−0.613137	−	0.531286i
$478$	9.81100	+	15.2662i	0.448745	+	0.698260i
$479$	−25.7751	−	29.7461i	−1.17769	−	1.35913i	−0.919525	−	0.393033i	$-0.871426\pi$
$479$	−25.7751	−	29.7461i	−1.17769	−	1.35913i	−0.258170	−	0.966099i	$-0.583119\pi$
$480$	−1.32345	+	5.95562i	−0.0604069	+	0.271836i
$481$	−3.99815	+	8.75473i	−0.182300	+	0.399181i
$482$		−	18.1818i		−	0.828160i
$483$	−10.5380	−	13.0775i	−0.479494	−	0.595047i
$484$	4.73891			0.215405
$485$	−12.5436	+	33.1775i	−0.569577	+	1.50651i
$486$	−18.1009	−	5.31490i	−0.821073	−	0.241089i
$487$	20.2402	−	17.5383i	0.917172	−	0.794734i	−0.0619349	−	0.998080i	$-0.519727\pi$
$487$	20.2402	−	17.5383i	0.917172	−	0.794734i	0.979107	+	0.203346i	$0.0651817\pi$
$488$	1.91631	+	2.98184i	0.0867473	+	0.134981i
$489$	17.4701	−	20.1615i	0.790024	−	0.911736i
$490$	−0.907138	+	11.9342i	−0.0409803	+	0.539134i
$491$	−12.5811	+	3.69414i	−0.567777	+	0.166714i	−0.553007	−	0.833177i	$-0.686520\pi$
$491$	−12.5811	+	3.69414i	−0.567777	+	0.166714i	−0.0147699	+	0.999891i	$0.504702\pi$
$492$	5.87329	−	9.13902i	0.264788	−	0.412019i
$493$	−8.88713	+	1.27778i	−0.400256	+	0.0575481i
$494$	0.353296	+	0.773611i	0.0158956	+	0.0348064i
$495$	21.8772	−	11.8193i	0.983307	−	0.531240i
$496$	1.14589	+	7.96983i	0.0514519	+	0.357856i
$497$	4.44036	−	6.90934i	0.199177	−	0.309926i
$498$	−3.43061	−	11.6836i	−0.153729	−	0.523553i
$499$	−1.11596	+	7.76167i	−0.0499572	+	0.347460i	0.949477	+	0.313836i	$0.101614\pi$
$499$	−1.11596	+	7.76167i	−0.0499572	+	0.347460i	−0.999435	+	0.0336244i	$0.989295\pi$
$500$	−9.74009	−	5.48914i	−0.435590	−	0.245482i
$501$	41.7356	−	26.8218i	1.86461	−	1.19831i
$502$	−6.06108	+	5.25195i	−0.270519	+	0.234406i
$503$	−4.20705	+	14.3279i	−0.187583	+	0.638850i	0.810970	+	0.585087i	$0.198940\pi$
$503$	−4.20705	+	14.3279i	−0.187583	+	0.638850i	−0.998554	+	0.0537629i	$0.982878\pi$
$504$	−2.36963	+	5.18877i	−0.105552	+	0.231126i
$505$	1.87800	+	28.0154i	0.0835697	+	1.24667i
$506$	10.7307	+	5.37178i	0.477040	+	0.238805i
$507$		−	32.5698i		−	1.44647i
$508$	−14.1820	−	6.47670i	−0.629225	−	0.287357i
$509$	−8.09490	−	2.37688i	−0.358800	−	0.105353i	0.0973641	−	0.995249i	$-0.468959\pi$
$509$	−8.09490	−	2.37688i	−0.358800	−	0.105353i	−0.456164	+	0.889896i	$0.650777\pi$
$510$	−22.6330	−	22.8361i	−1.00221	−	1.01120i
$511$	18.0540	−	11.6026i	0.798663	−	0.513270i
$512$	0.755750	+	0.654861i	0.0333997	+	0.0289410i
$513$	3.21767	+	0.462631i	0.142064	+	0.0204257i
$514$	−7.47384	+	2.19452i	−0.329657	+	0.0967961i
$515$	−11.5626	−	6.38087i	−0.509510	−	0.281175i
$516$	3.78004	+	26.2907i	0.166407	+	1.15739i
$517$	−23.0917	+	10.5456i	−1.01557	+	0.463796i
$518$	−10.9004	+	4.97805i	−0.478937	+	0.218723i
$519$	1.81914	+	12.6524i	0.0798514	+	0.555379i
$520$	−1.11374	+	2.01819i	−0.0488408	+	0.0885034i
$521$	34.8812	−	10.2420i	1.52817	−	0.448712i	0.593682	−	0.804700i	$-0.297674\pi$
$521$	34.8812	−	10.2420i	1.52817	−	0.448712i	0.934490	+	0.355988i	$0.115856\pi$
$522$	7.49449	+	1.07754i	0.328025	+	0.0471628i
$523$	11.2685	+	9.76418i	0.492736	+	0.426958i	0.865455	−	0.500986i	$-0.167029\pi$
$523$	11.2685	+	9.76418i	0.492736	+	0.426958i	−0.372720	+	0.927944i	$0.621575\pi$
$524$	9.61110	−	6.17668i	0.419863	−	0.269829i
$525$	−13.1302	−	11.5843i	−0.573048	−	0.505580i
$526$	−8.21295	−	2.41154i	−0.358102	−	0.105148i
$527$	−38.5985	−	17.6273i	−1.68138	−	0.767859i
$528$		−	6.82706i		−	0.297110i
$529$	−13.7824	−	18.4132i	−0.599236	−	0.800572i
$530$	−0.596286	−	8.89524i	−0.0259010	−	0.386384i
$531$	14.4327	−	31.6033i	0.626327	−	1.37147i
$532$	−0.298328	+	1.01601i	−0.0129342	+	0.0440497i
$533$	3.10204	−	2.68793i	0.134364	−	0.116427i
$534$	15.8521	−	10.1875i	0.685986	−	0.440857i
$535$	−0.175286	+	0.231988i	−0.00757827	+	0.0100297i
$536$	2.04580	−	14.2289i	0.0883651	−	0.614593i
$537$	−6.80444	−	23.1738i	−0.293633	−	1.00002i
$538$	−6.61162	+	10.2879i	−0.285047	+	0.443542i
$539$	−1.90606	−	13.2569i	−0.0820997	−	0.571016i
$540$	4.18802	+	7.75188i	0.180224	+	0.333588i
$541$	−15.8763	−	34.7642i	−0.682575	−	1.49463i	−0.859891	−	0.510477i	$-0.829469\pi$
$541$	−15.8763	−	34.7642i	−0.682575	−	1.49463i	0.177316	−	0.984154i	$-0.443258\pi$
$542$	30.5074	−	4.38631i	1.31041	−	0.188408i
$543$	30.5994	−	47.6136i	1.31315	−	2.04330i
$544$	−5.05655	+	1.48474i	−0.216798	+	0.0636575i
$545$	−11.3538	−	0.863016i	−0.486342	−	0.0369676i
$546$	−2.36412	+	2.72834i	−0.101175	+	0.116762i
$547$	−8.28852	−	12.8972i	−0.354392	−	0.551444i	0.617590	−	0.786500i	$-0.288109\pi$
$547$	−8.28852	−	12.8972i	−0.354392	−	0.551444i	−0.971982	+	0.235056i	$0.924473\pi$
$548$	−5.43939	+	4.71326i	−0.232359	+	0.201340i
$549$	15.1144	+	4.43799i	0.645068	+	0.189409i
$550$	11.9723	+	3.63185i	0.510502	+	0.154863i
$551$	1.40554			0.0598781
$552$	−5.85736	+	11.7008i	−0.249306	+	0.498017i
$553$			9.18000i			0.390374i
$554$	−7.34270	+	16.0783i	−0.311961	+	0.683100i
$555$	−12.3560	+	55.6031i	−0.524484	+	2.36022i
$556$	6.61804	+	7.63762i	0.280667	+	0.323907i
$557$	−4.05660	−	6.31220i	−0.171884	−	0.267456i	0.744615	−	0.667494i	$-0.232633\pi$
$557$	−4.05660	−	6.31220i	−0.171884	−	0.267456i	−0.916498	+	0.400038i	$0.868997\pi$
$558$	27.0435	+	23.4333i	1.14484	+	0.992012i
$559$	−1.42821	+	9.93344i	−0.0604070	+	0.420140i
$560$	−2.69355	+	0.990964i	−0.113823	+	0.0418759i
$561$	30.2672	+	19.4516i	1.27788	+	0.821246i
$562$	−24.4699	+	3.51824i	−1.03220	+	0.148408i
$563$	8.69523	−	3.97098i	0.366460	−	0.167357i	−0.223670	−	0.974665i	$-0.571804\pi$
$563$	8.69523	−	3.97098i	0.366460	−	0.167357i	0.590130	+	0.807308i	$0.299076\pi$
$564$	−11.4989	−	25.1791i	−0.484191	−	1.06023i
$565$	−7.01166	−	32.9396i	−0.294983	−	1.38578i
$566$	23.9423	+	15.3868i	1.00637	+	0.646755i
$567$	−0.933590	−	3.17951i	−0.0392071	−	0.133527i
$568$	−6.33375	−	0.910655i	−0.265758	−	0.0382102i
$569$	−22.0675	+	25.4672i	−0.925117	+	1.06764i	0.0724108	+	0.997375i	$0.476931\pi$
$569$	−22.0675	+	25.4672i	−0.925117	+	1.06764i	−0.997528	+	0.0702675i	$0.977615\pi$
$570$	2.99827	+	4.04272i	0.125584	+	0.169331i
$571$	16.9259	+	19.5336i	0.708328	+	0.817454i	0.989852	−	0.142100i	$-0.0453855\pi$
$571$	16.9259	+	19.5336i	0.708328	+	0.817454i	−0.281525	+	0.959554i	$0.590840\pi$
$572$	0.726721	−	2.47498i	0.0303857	−	0.103484i
$573$	40.4750	+	18.4843i	1.69087	+	0.772194i
$574$	5.11057			0.213311
$575$	−17.4032	−	16.4964i	−0.725762	−	0.687946i
$576$	4.44419			0.185175
$577$	−39.1801	−	17.8929i	−1.63109	−	0.744893i	−0.631551	−	0.775334i	$-0.717581\pi$
$577$	−39.1801	−	17.8929i	−1.63109	−	0.744893i	−0.999537	+	0.0304413i	$0.990309\pi$
$578$	3.03513	−	10.3367i	0.126245	−	0.429951i
$579$	17.0584	+	19.6864i	0.708922	+	0.818140i
$580$	2.26936	+	3.05989i	0.0942299	+	0.127055i
$581$	3.75128	−	4.32921i	0.155629	−	0.179606i
$582$	42.8388	+	6.15928i	1.77572	+	0.255311i
$583$	2.81066	+	9.57222i	0.116406	+	0.396441i
$584$	−14.0659	−	9.03962i	−0.582052	−	0.374062i
$585$	2.13286	+	10.0198i	0.0881831	+	0.414269i
$586$	−9.34370	−	20.4599i	−0.385985	−	0.845189i
$587$	36.7829	−	16.7982i	1.51819	−	0.693335i	0.530205	−	0.847869i	$-0.322115\pi$
$587$	36.7829	−	16.7982i	1.51819	−	0.693335i	0.987987	+	0.154534i	$0.0493876\pi$
$588$	14.4553	−	2.07836i	0.596126	−	0.0857099i
$589$	5.58818	+	3.59131i	0.230257	+	0.147977i
$590$	16.4057	−	6.03568i	0.675410	−	0.248485i
$591$	−1.97369	+	13.7273i	−0.0811868	+	0.564667i
$592$	7.05585	+	6.11393i	0.289994	+	0.251281i
$593$	7.43652	+	11.5715i	0.305381	+	0.475183i	0.959696	−	0.281039i	$-0.0906792\pi$
$593$	7.43652	+	11.5715i	0.305381	+	0.475183i	−0.654315	+	0.756222i	$0.727043\pi$
$594$	−6.45664	−	7.45137i	−0.264919	−	0.305733i
$595$	3.28107	−	14.7651i	0.134511	−	0.605310i
$596$	5.82013	−	12.7443i	0.238402	−	0.522027i
$597$		−	1.46150i		−	0.0598152i
$598$	−3.36895	+	3.61832i	−0.137767	+	0.147964i
$599$	−12.9013			−0.527132			−0.263566	−	0.964641i	$-0.584899\pi$
$599$	−12.9013			−0.527132			−0.263566	+	0.964641i	$0.584899\pi$
$600$	−3.96015	+	13.0546i	−0.161673	+	0.532951i
$601$	14.6759	+	4.30923i	0.598642	+	0.175777i	0.566994	−	0.823722i	$-0.308106\pi$
$601$	14.6759	+	4.30923i	0.598642	+	0.175777i	0.0316482	+	0.999499i	$0.489924\pi$
$602$	−9.44324	+	8.18261i	−0.384878	+	0.333498i
$603$	−34.5394	−	53.7443i	−1.40655	−	2.18864i
$604$	8.40852	−	9.70395i	0.342138	−	0.394848i
$605$	10.5661	+	0.803140i	0.429571	+	0.0326523i
$606$	32.8728	−	9.65232i	1.33537	−	0.392099i
$607$	−16.6331	+	25.8816i	−0.675116	+	1.05050i	0.319571	+	0.947562i	$0.396461\pi$
$607$	−16.6331	+	25.8816i	−0.675116	+	1.05050i	−0.994688	+	0.102939i	$0.967175\pi$
$608$	0.816598	−	0.117409i	0.0331174	−	0.00476157i
$609$	2.47850	+	5.42716i	0.100434	+	0.219920i
$610$	3.76732	+	6.97318i	0.152534	+	0.282336i
$611$	−1.48840	−	10.3521i	−0.0602144	−	0.418800i
$612$	−12.6623	+	19.7030i	−0.511844	+	0.796445i
$613$	4.97950	+	16.9586i	0.201120	+	0.684952i	0.996851	+	0.0793012i	$0.0252689\pi$
$613$	4.97950	+	16.9586i	0.201120	+	0.684952i	−0.795731	+	0.605651i	$0.792913\pi$
$614$	4.26404	−	29.6570i	0.172083	−	1.19686i
$615$	14.6442	−	19.3813i	0.590509	−	0.781529i
$616$	2.70183	−	1.73636i	0.108860	−	0.0699599i
$617$	−8.31028	+	7.20090i	−0.334559	+	0.289897i	−0.805897	−	0.592055i	$-0.798317\pi$
$617$	−8.31028	+	7.20090i	−0.334559	+	0.289897i	0.471338	+	0.881953i	$0.343771\pi$
$618$	−4.53990	+	15.4615i	−0.182622	+	0.621952i
$619$	−8.16958	+	17.8889i	−0.328363	+	0.719015i	−0.999756	−	0.0220866i	$-0.992969\pi$
$619$	−8.16958	+	17.8889i	−0.328363	+	0.719015i	0.671393	+	0.741102i	$0.265696\pi$
$620$	1.20421	+	17.9640i	0.0483621	+	0.721453i
$621$	4.67292	+	18.3103i	0.187518	+	0.734767i
$622$		−	6.40806i		−	0.256940i
$623$	8.06347	+	3.68246i	0.323056	+	0.147535i
$624$	2.69871	+	0.792413i	0.108035	+	0.0317219i
$625$	−20.7866	−	13.8895i	−0.831463	−	0.555581i
$626$	1.82377	−	1.17207i	0.0728926	−	0.0468452i
$627$	−4.25660	−	3.68837i	−0.169992	−	0.147299i
$628$	12.4416	+	1.78883i	0.496474	+	0.0713821i
$629$	−47.2091	+	13.8618i	−1.88235	+	0.552708i
$630$	−6.16279	+	11.1675i	−0.245532	+	0.444922i
$631$	−1.39279	−	9.68707i	−0.0554461	−	0.385636i	−0.998582	−	0.0532297i	$-0.983048\pi$
$631$	−1.39279	−	9.68707i	−0.0554461	−	0.385636i	0.943136	−	0.332407i	$-0.107861\pi$
$632$	6.50583	−	2.97111i	0.258788	−	0.118185i
$633$	−13.0186	+	5.94539i	−0.517443	+	0.236308i
$634$	1.25397	+	8.72155i	0.0498015	+	0.346377i
$635$	−30.5231	−	16.8442i	−1.21127	−	0.668443i
$636$	−10.4375	+	3.06473i	−0.413874	+	0.121524i
$637$	5.46164	+	0.785266i	0.216398	+	0.0311134i
$638$	−3.22177	−	2.79168i	−0.127551	−	0.110524i
$639$	−23.9234	+	15.3747i	−0.946396	+	0.608212i
$640$	1.57406	+	1.58818i	0.0622203	+	0.0627785i
$641$	15.0604	+	4.42214i	0.594851	+	0.174664i	0.565281	−	0.824899i	$-0.308768\pi$
$641$	15.0604	+	4.42214i	0.594851	+	0.174664i	0.0295706	+	0.999563i	$0.490586\pi$
$642$	0.322723	+	0.147382i	0.0127368	+	0.00581672i
$643$			23.5890i			0.930261i	0.885242	+	0.465130i	$0.153993\pi$
$643$			23.5890i			0.930261i	−0.885242	+	0.465130i	$0.846007\pi$
$644$	−6.12034	+	0.657843i	−0.241175	+	0.0259226i
$645$	3.97242	+	59.2594i	0.156414	+	2.33334i
$646$	−1.80612	+	3.95484i	−0.0710607	+	0.155601i
$647$	4.90636	−	16.7095i	0.192889	−	0.656920i	−0.805077	−	0.593171i	$-0.797876\pi$
$647$	4.90636	−	16.7095i	0.192889	−	0.656920i	0.997966	−	0.0637494i	$-0.0203058\pi$
$648$	−1.95115	+	1.69068i	−0.0766485	+	0.0664163i
$649$	−16.4560	+	10.5757i	−0.645956	+	0.415131i
$650$	−2.82528	+	4.31107i	−0.110817	+	0.169094i
$651$	−4.01289	+	27.9102i	−0.157277	+	1.09389i
$652$	−2.75470	−	9.38164i	−0.107882	−	0.367413i
$653$	−15.8004	+	24.5860i	−0.618319	+	0.962123i	0.380976	+	0.924585i	$0.375588\pi$
$653$	−15.8004	+	24.5860i	−0.618319	+	0.962123i	−0.999295	+	0.0375381i	$0.988048\pi$
$654$	1.97727	+	13.7522i	0.0773173	+	0.537753i
$655$	22.4761	−	12.1429i	0.878212	−	0.474461i
$656$	−1.65404	−	3.62184i	−0.0645794	−	0.141409i
$657$	−73.5514	+	10.5751i	−2.86951	+	0.412574i
$658$	7.04011	−	10.9546i	0.274452	−	0.427056i
$659$	9.55859	−	2.80665i	0.372350	−	0.109332i	−0.0902033	−	0.995923i	$-0.528752\pi$
$659$	9.55859	−	2.80665i	0.372350	−	0.109332i	0.462553	+	0.886592i	$0.346934\pi$
$660$	1.15703	−	15.2219i	0.0450375	−	0.592510i
$661$	−4.29992	+	4.96237i	−0.167248	+	0.193014i	−0.833186	−	0.552993i	$-0.813486\pi$
$661$	−4.29992	+	4.96237i	−0.167248	+	0.193014i	0.665939	+	0.746007i	$0.268031\pi$
$662$	0.447699	+	0.696634i	0.0174003	+	0.0270754i
$663$	−11.2022	+	9.70679i	−0.435059	+	0.376980i
$664$	−4.28220	−	1.25737i	−0.166182	−	0.0487953i
$665$	−0.837355	+	2.21478i	−0.0324712	+	0.0858854i
$666$	41.4920			1.60778
$667$	3.12657	+	7.54877i	0.121061	+	0.292290i
$668$		−	18.1832i		−	0.703530i
$669$	−6.00439	+	13.1478i	−0.232143	+	0.508323i
$670$	6.97286	−	31.3784i	0.269385	−	1.21226i
$671$	−5.80806	−	6.70285i	−0.224218	−	0.258761i
$672$	1.89332	+	2.94606i	0.0730363	+	0.113647i
$673$	−0.128416	−	0.111273i	−0.00495006	−	0.00428925i	0.652382	−	0.757890i	$-0.273770\pi$
$673$	−0.128416	−	0.111273i	−0.00495006	−	0.00428925i	−0.657332	+	0.753601i	$0.728315\pi$
$674$	1.21547	−	8.45376i	0.0468180	−	0.325627i
$675$	8.02399	+	17.9937i	0.308843	+	0.692576i
$676$	−10.0423	−	6.45379i	−0.386242	−	0.248223i
$677$	22.7942	−	3.27731i	0.876051	−	0.125957i	0.310404	−	0.950605i	$-0.399536\pi$
$677$	22.7942	−	3.27731i	0.876051	−	0.125957i	0.565647	+	0.824648i	$0.308627\pi$
$678$	−37.3792	+	17.0705i	−1.43554	+	0.655589i
$679$	8.45784	+	18.5201i	0.324582	+	0.710735i
$680$	−11.5259	+	2.45345i	−0.441998	+	0.0940855i
$681$	−15.4240	−	9.91240i	−0.591049	−	0.379844i
$682$	−5.67616	−	19.3312i	−0.217351	−	0.740230i
$683$	−28.6657	−	4.12150i	−1.09686	−	0.157705i	−0.429958	−	0.902849i	$-0.641472\pi$
$683$	−28.6657	−	4.12150i	−1.09686	−	0.157705i	−0.666904	+	0.745144i	$0.732381\pi$
$684$	2.40100	−	2.77091i	0.0918047	−	0.105948i
$685$	−12.9266	+	9.58699i	−0.493902	+	0.366300i
$686$	10.3827	+	11.9823i	0.396414	+	0.457487i
$687$	−8.67568	+	29.5466i	−0.330998	+	1.12727i
$688$	8.85530	+	4.04408i	0.337605	+	0.154179i
$689$	−4.11009			−0.156582
$690$	−15.0428	+	25.0957i	−0.572670	+	0.955378i
$691$	−31.4009			−1.19454			−0.597272	−	0.802038i	$-0.703749\pi$
$691$	−31.4009			−1.19454			−0.597272	+	0.802038i	$0.703749\pi$
$692$	4.26160	+	1.94621i	0.162002	+	0.0739838i
$693$	4.02124	−	13.6951i	0.152754	−	0.520234i
$694$	−2.44577	−	2.82257i	−0.0928403	−	0.107143i
$695$	13.4614	+	18.1507i	0.510621	+	0.688497i
$696$	3.04404	−	3.51301i	0.115384	−	0.133160i
$697$	20.7698	+	2.98625i	0.786713	+	0.113112i
$698$	1.53363	+	5.22308i	0.0580489	+	0.197696i
$699$	10.1843	+	6.54505i	0.385206	+	0.247557i
$700$	−6.17359	+	1.75299i	−0.233340	+	0.0662569i
$701$	−9.54358	−	20.8975i	−0.360456	−	0.789289i	−0.999793	−	0.0203618i	$-0.993518\pi$
$701$	−9.54358	−	20.8975i	−0.360456	−	0.789289i	0.639337	−	0.768927i	$-0.279209\pi$
$702$	3.69491	−	1.68741i	0.139456	−	0.0636872i
$703$	7.62395	−	1.09616i	0.287543	−	0.0413424i
$704$	−2.10500	−	1.35280i	−0.0793351	−	0.0509856i
$705$	−21.3710	−	58.0889i	−0.804880	−	2.18776i
$706$	−2.52599	+	17.5687i	−0.0950670	+	0.661206i
$707$	12.1806	+	10.5546i	0.458100	+	0.396946i
$708$	−11.5316	−	17.9436i	−0.433386	−	0.674361i
$709$	−26.4117	−	30.4807i	−0.991913	−	1.14473i	−0.989471	−	0.144731i	$-0.953768\pi$
$709$	−26.4117	−	30.4807i	−0.991913	−	1.14473i	−0.00244186	−	0.999997i	$-0.500777\pi$
$710$	−13.9676	−	3.10386i	−0.524195	−	0.116486i
$711$	13.2042	−	28.9132i	0.495196	−	1.08433i
$712$		−	6.90638i		−	0.258828i
$713$	−6.85721	+	38.0013i	−0.256805	+	1.42316i
$714$	−18.4555			−0.690681
$715$	2.03978	−	5.39515i	0.0762833	−	0.201767i
$716$	−8.49353	−	2.49393i	−0.317418	−	0.0932024i
$717$	37.4189	−	32.4237i	1.39743	−	1.21088i
$718$	9.39543	+	14.6196i	0.350635	+	0.545598i
$719$	−5.20115	+	6.00245i	−0.193970	+	0.223854i	−0.844401	−	0.535712i	$-0.820043\pi$
$719$	−5.20115	+	6.00245i	−0.193970	+	0.223854i	0.650430	+	0.759566i	$0.274589\pi$
$720$	9.90893	+	0.753191i	0.369284	+	0.0280698i
$721$	−7.27358	+	2.13571i	−0.270882	+	0.0795382i
$722$	−9.90421	+	15.4112i	−0.368596	+	0.573547i
$723$	−49.1025	+	7.05987i	−1.82614	+	0.262559i
$724$	−8.61743	−	18.8695i	−0.320264	−	0.701281i
$725$	4.54125	+	7.20705i	0.168658	+	0.267663i
$726$	−1.84008	−	12.7981i	−0.0682919	−	0.474981i
$727$	−8.95902	+	13.9405i	−0.332272	+	0.517025i	−0.966685	−	0.255969i	$-0.917605\pi$
$727$	−8.95902	+	13.9405i	−0.332272	+	0.517025i	0.634413	+	0.772994i	$0.281242\pi$
$728$	0.372776	+	1.26956i	0.0138160	+	0.0470530i
$729$	−6.22289	+	43.2812i	−0.230478	+	1.60301i
$730$	−29.8299	−	22.5389i	−1.10405	−	0.834203i
$731$	−43.1595	+	27.7369i	−1.59631	+	1.02589i
$732$	7.30876	−	6.33308i	0.270140	−	0.234077i
$733$	−4.19248	+	14.2783i	−0.154853	+	0.527380i	−0.999974	−	0.00719467i	$-0.997710\pi$
$733$	−4.19248	+	14.2783i	−0.154853	+	0.527380i	0.845121	+	0.534574i	$0.179528\pi$
$734$	10.9896	−	24.0639i	0.405634	−	0.888215i
$735$	32.5823	−	2.18413i	1.20181	−	0.0805628i
$736$	2.44706	+	4.12455i	0.0901999	+	0.152033i
$737$			35.9698i			1.32496i
$738$	−16.0962	−	7.35087i	−0.592508	−	0.270589i
$739$	45.9414	+	13.4896i	1.68998	+	0.496223i	0.978459	−	0.206441i	$-0.0661882\pi$
$739$	45.9414	+	13.4896i	1.68998	+	0.496223i	0.711522	+	0.702664i	$0.248006\pi$
$740$	14.6958	+	14.8277i	0.540229	+	0.545075i
$741$	1.95206	−	1.25451i	0.0717106	−	0.0460856i
$742$	−3.86750	−	3.35120i	−0.141980	−	0.123027i
$743$	−6.21778	−	0.893982i	−0.228108	−	0.0327970i	0.0273127	−	0.999627i	$-0.491305\pi$
$743$	−6.21778	−	0.893982i	−0.228108	−	0.0327970i	−0.255421	+	0.966830i	$0.582214\pi$
$744$	21.0787	−	6.18925i	0.772781	−	0.226909i
$745$	15.1366	−	27.4288i	0.554564	−	1.00491i
$746$	1.67413	+	11.6439i	0.0612944	+	0.426312i
$747$	−18.0420	+	8.23948i	−0.660121	+	0.301467i
$748$	11.9951	−	5.47797i	0.438583	−	0.200294i
$749$	0.0237526	+	0.165203i	0.000867900	+	0.00603638i
$750$	−11.0422	+	28.4358i	−0.403203	+	1.03833i
$751$	−13.7749	+	4.04468i	−0.502654	+	0.147593i	−0.523223	−	0.852196i	$-0.675271\pi$
$751$	−13.7749	+	4.04468i	−0.502654	+	0.147593i	0.0205686	+	0.999788i	$0.493452\pi$
$752$	−10.0420	−	1.44383i	−0.366195	−	0.0526510i
$753$	16.5371	+	14.3295i	0.602644	+	0.522194i
$754$	1.47749	−	0.949526i	0.0538070	−	0.0345797i
$755$	20.3926	−	20.2112i	0.742161	−	0.735562i
$756$	4.85267	+	1.42487i	0.176490	+	0.0518221i
$757$	25.9541	+	11.8528i	0.943318	+	0.430799i	0.826867	−	0.562398i	$-0.190121\pi$
$757$	25.9541	+	11.8528i	0.943318	+	0.430799i	0.116451	+	0.993196i	$0.462848\pi$
$758$			0.526928i			0.0191389i
$759$	10.3405	−	31.0656i	0.375338	−	1.12761i
$760$	1.84061	−	0.123384i	0.0667661	−	0.00447562i
$761$	22.6426	−	49.5805i	0.820795	−	1.79729i	0.269446	−	0.963015i	$-0.413159\pi$
$761$	22.6426	−	49.5805i	0.820795	−	1.79729i	0.551349	−	0.834275i	$-0.314113\pi$
$762$	−11.9844	+	40.8152i	−0.434150	+	1.47858i
$763$	−4.93958	+	4.28017i	−0.178825	+	0.154953i
$764$	13.7195	−	8.81701i	0.496355	−	0.318988i
$765$	−31.5716	+	41.7845i	−1.14147	+	1.51072i
$766$	−0.437881	+	3.04553i	−0.0158213	+	0.110040i
$767$	−2.27047	−	7.73252i	−0.0819820	−	0.279205i
$768$	1.47509	−	2.29528i	0.0532276	−	0.0828238i
$769$	3.75398	+	26.1095i

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.909632 - 0.415415i) q^{2} +(-0.768680 + 2.61788i) q^{3} +(0.654861 + 0.755750i) q^{4} +(1.33202 + 1.79603i) q^{5} +(1.78672 - 2.06199i) q^{6} +(1.27046 + 0.182665i) q^{7} +(-0.281733 - 0.959493i) q^{8} +(-3.73869 - 2.40271i) q^{9} +O(q^{10})\)	\(q+(-0.909632 - 0.415415i) q^{2} +(-0.768680 + 2.61788i) q^{3} +(0.654861 + 0.755750i) q^{4} +(1.33202 + 1.79603i) q^{5} +(1.78672 - 2.06199i) q^{6} +(1.27046 + 0.182665i) q^{7} +(-0.281733 - 0.959493i) q^{8} +(-3.73869 - 2.40271i) q^{9} +(-0.465548 - 2.18707i) q^{10} +(1.03946 + 2.27610i) q^{11} +(-2.48184 + 1.13342i) q^{12} +(-1.02038 + 0.146709i) q^{13} +(-1.07977 - 0.693928i) q^{14} +(-5.72570 + 2.10650i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-3.98282 - 3.45113i) q^{17} +(2.40271 + 3.73869i) q^{18} +(0.540257 + 0.623490i) q^{19} +(-0.485063 + 2.18282i) q^{20} +(-1.45478 + 3.18552i) q^{21} -2.50222i q^{22} +(-2.14681 + 4.28850i) q^{23} +2.72840 q^{24} +(-1.45145 + 4.78469i) q^{25} +(0.989116 + 0.290431i) q^{26} +(2.97791 - 2.58037i) q^{27} +(0.693928 + 1.07977i) q^{28} +(1.11568 - 1.28757i) q^{29} +(6.08335 + 0.462404i) q^{30} +(7.72564 - 2.26845i) q^{31} +(0.540641 - 0.841254i) q^{32} +(-6.75757 + 0.971592i) q^{33} +(2.18925 + 4.79378i) q^{34} +(1.36421 + 2.52511i) q^{35} +(-0.632474 - 4.39895i) q^{36} +(5.04755 - 7.85414i) q^{37} +(-0.232428 - 0.791577i) q^{38} +(0.400281 - 2.78401i) q^{39} +(1.34801 - 1.78406i) q^{40} +(-3.34958 + 2.15265i) q^{41} +(2.64662 - 2.29331i) q^{42} +(2.74268 - 9.34069i) q^{43} +(-1.03946 + 2.27610i) q^{44} +(-0.664663 - 9.91526i) q^{45} +(3.73431 - 3.00914i) q^{46} +10.1453i q^{47} +(-2.48184 - 1.13342i) q^{48} +(-5.13574 - 1.50799i) q^{49} +(3.30792 - 3.74935i) q^{50} +(12.0962 - 7.77374i) q^{51} +(-0.779083 - 0.675079i) q^{52} +(3.94642 + 0.567409i) q^{53} +(-3.78072 + 1.11012i) q^{54} +(-2.70336 + 4.89870i) q^{55} +(-0.182665 - 1.27046i) q^{56} +(-2.04751 + 0.935066i) q^{57} +(-1.54974 + 0.707741i) q^{58} +(1.11256 + 7.73803i) q^{59} +(-5.34152 - 2.94773i) q^{60} +(-3.40094 + 0.998606i) q^{61} +(-7.96983 - 1.14589i) q^{62} +(-4.31098 - 3.73549i) q^{63} +(-0.841254 + 0.540641i) q^{64} +(-1.62266 - 1.63722i) q^{65} +(6.55051 + 1.92340i) q^{66} +(13.0761 + 5.97166i) q^{67} -5.27002i q^{68} +(-9.57658 - 8.91658i) q^{69} +(-0.191962 - 2.86363i) q^{70} +(2.65819 - 5.82062i) q^{71} +(-1.25207 + 4.26417i) q^{72} +(12.6363 - 10.9494i) q^{73} +(-7.85414 + 5.04755i) q^{74} +(-11.4101 - 7.47764i) q^{75} +(-0.117409 + 0.816598i) q^{76} +(0.904831 + 3.08157i) q^{77} +(-1.52063 + 2.36614i) q^{78} +(1.01786 + 7.07936i) q^{79} +(-1.96732 + 1.06286i) q^{80} +(-1.07250 - 2.34844i) q^{81} +(3.94113 - 0.566649i) q^{82} +(2.41287 - 3.75450i) q^{83} +(-3.36013 + 0.986624i) q^{84} +(0.893151 - 11.7502i) q^{85} +(-6.37509 + 7.35725i) q^{86} +(2.51310 + 3.91046i) q^{87} +(1.89105 - 1.63860i) q^{88} +(6.62662 + 1.94575i) q^{89} +(-3.51435 + 9.29535i) q^{90} -1.32316 q^{91} +(-4.64689 + 1.18592i) q^{92} +21.9685i q^{93} +(4.21451 - 9.22849i) q^{94} +(-0.400175 + 1.80082i) q^{95} +(1.78672 + 2.06199i) q^{96} +(8.57591 + 13.3444i) q^{97} +(4.04519 + 3.50518i) q^{98} +(1.58259 - 11.0071i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41} - 8 q^{44} + 16 q^{45} - 4 q^{46} - 58 q^{49} + 12 q^{50} - 24 q^{51} - 6 q^{54} - 36 q^{55} + 22 q^{56} - 102 q^{59} - 38 q^{60} + 72 q^{61} + 12 q^{64} - 138 q^{65} + 80 q^{66} - 212 q^{69} - 108 q^{70} + 176 q^{71} - 88 q^{74} - 100 q^{75} + 16 q^{76} - 104 q^{79} - 22 q^{80} - 28 q^{81} - 22 q^{84} + 2 q^{85} + 62 q^{86} + 48 q^{89} + 24 q^{90} - 56 q^{91} + 24 q^{94} + 18 q^{95} - 4 q^{96} + 188 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

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