LMFDB - Embedded newform 138.2.f.a.65.1

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			65.1
Character	$\chi$	$=$	138.65
Dual form			138.2.f.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909632 + 0.415415i) q^{2} +(-1.72827 + 0.114314i) q^{3} +(0.654861 - 0.755750i) q^{4} +(-1.19773 - 0.769732i) q^{5} +(1.52461 - 0.821935i) q^{6} +(3.68797 - 0.530250i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(2.97386 - 0.395131i) q^{9} +O(q^{10})$	\(q+(-0.909632 + 0.415415i) q^{2} +(-1.72827 + 0.114314i) q^{3} +(0.654861 - 0.755750i) q^{4} +(-1.19773 - 0.769732i) q^{5} +(1.52461 - 0.821935i) q^{6} +(3.68797 - 0.530250i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(2.97386 - 0.395131i) q^{9} +(1.40925 + 0.202619i) q^{10} +(2.16359 - 4.73760i) q^{11} +(-1.04539 + 1.38100i) q^{12} +(0.0252260 - 0.175451i) q^{13} +(-3.13442 + 2.01437i) q^{14} +(2.15799 + 1.19339i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(4.04561 + 4.66888i) q^{17} +(-2.54098 + 1.59481i) q^{18} +(-3.14485 - 2.72503i) q^{19} +(-1.36607 + 0.401114i) q^{20} +(-6.31321 + 1.33800i) q^{21} +5.20826i q^{22} +(2.80913 - 3.88700i) q^{23} +(0.377228 - 1.69047i) q^{24} +(-1.23501 - 2.70430i) q^{25} +(0.0499385 + 0.170075i) q^{26} +(-5.09449 + 1.02285i) q^{27} +(2.01437 - 3.13442i) q^{28} +(-1.92187 + 1.66531i) q^{29} +(-2.45873 - 0.189085i) q^{30} +(-2.86031 - 0.839864i) q^{31} +(0.540641 + 0.841254i) q^{32} +(-3.19770 + 8.43520i) q^{33} +(-5.61954 - 2.56636i) q^{34} +(-4.82533 - 2.20366i) q^{35} +(1.64885 - 2.50625i) q^{36} +(5.03596 + 7.83610i) q^{37} +(3.99267 + 1.17235i) q^{38} +(-0.0235410 + 0.306111i) q^{39} +(1.07599 - 0.932352i) q^{40} +(-1.83979 + 2.86277i) q^{41} +(5.18687 - 3.83970i) q^{42} +(-0.117381 - 0.399763i) q^{43} +(-2.16359 - 4.73760i) q^{44} +(-3.86602 - 1.81582i) q^{45} +(-0.940555 + 4.70270i) q^{46} -0.926457i q^{47} +(0.359109 + 1.69441i) q^{48} +(6.60353 - 1.93897i) q^{49} +(2.24682 + 1.94688i) q^{50} +(-7.52564 - 7.60664i) q^{51} +(-0.116077 - 0.133960i) q^{52} +(-0.0855320 - 0.594888i) q^{53} +(4.20920 - 3.04674i) q^{54} +(-6.23807 + 4.00896i) q^{55} +(-0.530250 + 3.68797i) q^{56} +(5.74667 + 4.35009i) q^{57} +(1.05640 - 2.31319i) q^{58} +(14.9640 + 2.15150i) q^{59} +(2.31509 - 0.849396i) q^{60} +(1.56365 - 5.32531i) q^{61} +(2.95072 - 0.424250i) q^{62} +(10.7580 - 3.03413i) q^{63} +(-0.841254 - 0.540641i) q^{64} +(-0.165264 + 0.190725i) q^{65} +(-0.595376 - 9.00130i) q^{66} +(0.822269 - 0.375518i) q^{67} +6.17782 q^{68} +(-4.41061 + 7.03893i) q^{69} +5.30471 q^{70} +(-8.13332 + 3.71436i) q^{71} +(-0.458709 + 2.96472i) q^{72} +(-7.53110 + 8.69136i) q^{73} +(-7.83610 - 5.03596i) q^{74} +(2.44358 + 4.53260i) q^{75} +(-4.11887 + 0.592205i) q^{76} +(5.46714 - 18.6194i) q^{77} +(-0.105749 - 0.288227i) q^{78} +(3.47110 + 0.499068i) q^{79} +(-0.591443 + 1.29508i) q^{80} +(8.68774 - 2.35013i) q^{81} +(0.484294 - 3.36834i) q^{82} +(-12.4026 + 7.97068i) q^{83} +(-3.12308 + 5.64742i) q^{84} +(-1.25175 - 8.70608i) q^{85} +(0.272841 + 0.314875i) q^{86} +(3.13115 - 3.09781i) q^{87} +(3.93614 + 3.41068i) q^{88} +(-2.47074 + 0.725476i) q^{89} +(4.27098 + 0.0457245i) q^{90} -0.660433i q^{91} +(-1.09801 - 4.66844i) q^{92} +(5.03941 + 1.12454i) q^{93} +(0.384864 + 0.842735i) q^{94} +(1.66913 + 5.68453i) q^{95} +(-1.03054 - 1.39211i) q^{96} +(-4.87143 + 7.58010i) q^{97} +(-5.20130 + 4.50695i) q^{98} +(4.56225 - 14.9439i) 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 $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−0.909632	+	0.415415i	−0.643207	+	0.293743i
$2$	−0.909632	+	0.415415i	−0.643207	+	0.293743i
$3$	−1.72827	+	0.114314i	−0.997820	+	0.0659991i
$3$	−1.72827	+	0.114314i	−0.997820	+	0.0659991i
$4$	0.654861	−	0.755750i	0.327430	−	0.377875i
$5$	−1.19773	−	0.769732i	−0.535640	−	0.344235i	0.244692	−	0.969601i	$-0.421313\pi$
$5$	−1.19773	−	0.769732i	−0.535640	−	0.344235i	−0.780331	+	0.625366i	$0.784950\pi$
$6$	1.52461	−	0.821935i	0.622418	−	0.335553i
$7$	3.68797	−	0.530250i	1.39392	−	0.200416i	0.595907	−	0.803053i	$-0.296792\pi$
$7$	3.68797	−	0.530250i	1.39392	−	0.200416i	0.798015	+	0.602637i	$0.205883\pi$
$8$	−0.281733	+	0.959493i	−0.0996075	+	0.339232i
$9$	2.97386	−	0.395131i	0.991288	−	0.131710i
$10$	1.40925	+	0.202619i	0.445644	+	0.0640739i
$11$	2.16359	−	4.73760i	0.652347	−	1.42844i	−0.237139	−	0.971476i	$-0.576210\pi$
$11$	2.16359	−	4.73760i	0.652347	−	1.42844i	0.889485	−	0.456964i	$-0.151063\pi$
$12$	−1.04539	+	1.38100i	−0.301777	+	0.398661i
$13$	0.0252260	−	0.175451i	0.00699643	−	0.0486613i	−0.986024	−	0.166602i	$-0.946720\pi$
$13$	0.0252260	−	0.175451i	0.00699643	−	0.0486613i	0.993021	+	0.117941i	$0.0376294\pi$
$14$	−3.13442	+	2.01437i	−0.837710	+	0.538364i
$15$	2.15799	+	1.19339i	0.557191	+	0.308132i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	4.04561	+	4.66888i	0.981204	+	1.13237i	0.991194	+	0.132420i	$0.0422748\pi$
$17$	4.04561	+	4.66888i	0.981204	+	1.13237i	−0.00998944	+	0.999950i	$0.503180\pi$
$18$	−2.54098	+	1.59481i	−0.598915	+	0.375901i
$19$	−3.14485	−	2.72503i	−0.721478	−	0.625164i	0.214705	−	0.976679i	$-0.431121\pi$
$19$	−3.14485	−	2.72503i	−0.721478	−	0.625164i	−0.936182	+	0.351515i	$0.885667\pi$
$20$	−1.36607	+	0.401114i	−0.305462	+	0.0896918i
$21$	−6.31321	+	1.33800i	−1.37766	+	0.291977i
$22$			5.20826i			1.11040i
$23$	2.80913	−	3.88700i	0.585744	−	0.810496i
$23$	2.80913	−	3.88700i	0.585744	−	0.810496i
$24$	0.377228	−	1.69047i	0.0770013	−	0.345066i
$25$	−1.23501	−	2.70430i	−0.247003	−	0.540860i
$26$	0.0499385	+	0.170075i	0.00979374	+	0.0333544i
$27$	−5.09449	+	1.02285i	−0.980434	+	0.196847i
$28$	2.01437	−	3.13442i	0.380681	−	0.592350i
$29$	−1.92187	+	1.66531i	−0.356882	+	0.309240i	−0.814786	−	0.579761i	$-0.803146\pi$
$29$	−1.92187	+	1.66531i	−0.356882	+	0.309240i	0.457904	+	0.889002i	$0.348600\pi$
$30$	−2.45873	−	0.189085i	−0.448901	−	0.0345221i
$31$	−2.86031	−	0.839864i	−0.513728	−	0.150844i	0.0145856	−	0.999894i	$-0.495357\pi$
$31$	−2.86031	−	0.839864i	−0.513728	−	0.150844i	−0.528313	+	0.849050i	$0.677175\pi$
$32$	0.540641	+	0.841254i	0.0955727	+	0.148714i
$33$	−3.19770	+	8.43520i	−0.556649	+	1.46838i
$34$	−5.61954	−	2.56636i	−0.963743	−	0.440127i
$35$	−4.82533	−	2.20366i	−0.815630	−	0.372486i
$36$	1.64885	−	2.50625i	0.274808	−	0.417709i
$37$	5.03596	+	7.83610i	0.827906	+	1.28825i	0.955074	+	0.296366i	$0.0957748\pi$
$37$	5.03596	+	7.83610i	0.827906	+	1.28825i	−0.127168	+	0.991881i	$0.540589\pi$
$38$	3.99267	+	1.17235i	0.647697	+	0.190181i
$39$	−0.0235410	+	0.306111i	−0.00376958	+	0.0490169i
$40$	1.07599	−	0.932352i	0.170129	−	0.147418i
$41$	−1.83979	+	2.86277i	−0.287327	+	0.447089i	−0.954672	−	0.297659i	$-0.903794\pi$
$41$	−1.83979	+	2.86277i	−0.287327	+	0.447089i	0.667346	+	0.744748i	$0.267430\pi$
$42$	5.18687	−	3.83970i	0.800352	−	0.592478i
$43$	−0.117381	−	0.399763i	−0.0179004	−	0.0609633i	0.950058	−	0.312072i	$-0.101023\pi$
$43$	−0.117381	−	0.399763i	−0.0179004	−	0.0609633i	−0.967959	+	0.251109i	$0.919205\pi$
$44$	−2.16359	−	4.73760i	−0.326173	−	0.714220i
$45$	−3.86602	−	1.81582i	−0.576313	−	0.270687i
$46$	−0.940555	+	4.70270i	−0.138677	+	0.693375i
$47$		−	0.926457i		−	0.135138i	−0.997715	−	0.0675688i	$-0.978476\pi$
$47$		−	0.926457i		−	0.135138i	0.997715	−	0.0675688i	$-0.0215242\pi$
$48$	0.359109	+	1.69441i	0.0518330	+	0.244568i
$49$	6.60353	−	1.93897i	0.943361	−	0.276996i
$50$	2.24682	+	1.94688i	0.317748	+	0.275330i
$51$	−7.52564	−	7.60664i	−1.05380	−	1.06514i
$52$	−0.116077	−	0.133960i	−0.0160970	−	0.0185769i
$53$	−0.0855320	−	0.594888i	−0.0117487	−	0.0817141i	0.983103	−	0.183051i	$-0.0585972\pi$
$53$	−0.0855320	−	0.594888i	−0.0117487	−	0.0817141i	−0.994852	+	0.101336i	$0.967688\pi$
$54$	4.20920	−	3.04674i	0.572800	−	0.414609i
$55$	−6.23807	+	4.00896i	−0.841141	+	0.540569i
$56$	−0.530250	+	3.68797i	−0.0708577	+	0.492826i
$57$	5.74667	+	4.35009i	0.761165	+	0.576184i
$58$	1.05640	−	2.31319i	0.138712	−	0.303737i
$59$	14.9640	+	2.15150i	1.94815	+	0.280101i	0.999359	−	0.0358128i	$-0.0114020\pi$
$59$	14.9640	+	2.15150i	1.94815	+	0.280101i	0.948788	+	0.315914i	$0.102311\pi$
$60$	2.31509	−	0.849396i	0.298877	−	0.109657i
$61$	1.56365	−	5.32531i	0.200205	−	0.681837i	−0.796782	−	0.604267i	$-0.793466\pi$
$61$	1.56365	−	5.32531i	0.200205	−	0.681837i	0.996987	−	0.0775694i	$-0.0247159\pi$
$62$	2.95072	−	0.424250i	0.374742	−	0.0538798i
$63$	10.7580	−	3.03413i	1.35538	−	0.382264i
$64$	−0.841254	−	0.540641i	−0.105157	−	0.0675801i
$65$	−0.165264	+	0.190725i	−0.0204985	+	0.0236565i
$66$	−0.595376	−	9.00130i	−0.0732857	−	1.10798i
$67$	0.822269	−	0.375518i	0.100456	−	0.0458768i	−0.364553	−	0.931183i	$-0.618778\pi$
$67$	0.822269	−	0.375518i	0.100456	−	0.0458768i	0.465009	+	0.885306i	$0.346051\pi$
$68$	6.17782			0.749170
$69$	−4.41061	+	7.03893i	−0.530975	+	0.847388i
$70$	5.30471			0.634034
$71$	−8.13332	+	3.71436i	−0.965247	+	0.440814i	−0.834746	−	0.550635i	$-0.814386\pi$
$71$	−8.13332	+	3.71436i	−0.965247	+	0.440814i	−0.130501	+	0.991448i	$0.541658\pi$
$72$	−0.458709	+	2.96472i	−0.0540594	+	0.349396i
$73$	−7.53110	+	8.69136i	−0.881449	+	1.01725i	0.118257	+	0.992983i	$0.462269\pi$
$73$	−7.53110	+	8.69136i	−0.881449	+	1.01725i	−0.999706	+	0.0242633i	$0.992276\pi$
$74$	−7.83610	−	5.03596i	−0.910928	−	0.585418i
$75$	2.44358	+	4.53260i	0.282160	+	0.523379i
$76$	−4.11887	+	0.592205i	−0.472467	+	0.0679305i
$77$	5.46714	−	18.6194i	0.623039	−	2.12188i
$78$	−0.105749	−	0.288227i	−0.0119737	−	0.0326353i
$79$	3.47110	+	0.499068i	0.390529	+	0.0561496i	0.334783	−	0.942295i	$-0.391337\pi$
$79$	3.47110	+	0.499068i	0.390529	+	0.0561496i	0.0557462	+	0.998445i	$0.482246\pi$
$80$	−0.591443	+	1.29508i	−0.0661254	+	0.144794i
$81$	8.68774	−	2.35013i	0.965305	−	0.261126i
$82$	0.484294	−	3.36834i	0.0534813	−	0.371971i
$83$	−12.4026	+	7.97068i	−1.36136	+	0.874896i	−0.998380	−	0.0568991i	$-0.981879\pi$
$83$	−12.4026	+	7.97068i	−1.36136	+	0.874896i	−0.362985	+	0.931795i	$0.618242\pi$
$84$	−3.12308	+	5.64742i	−0.340756	+	0.616184i
$85$	−1.25175	−	8.70608i	−0.135771	−	0.944307i
$86$	0.272841	+	0.314875i	0.0294212	+	0.0339539i
$87$	3.13115	−	3.09781i	0.335694	−	0.332120i
$88$	3.93614	+	3.41068i	0.419594	+	0.363580i
$89$	−2.47074	+	0.725476i	−0.261898	+	0.0769003i	−0.410046	−	0.912065i	$-0.634487\pi$
$89$	−2.47074	+	0.725476i	−0.261898	+	0.0769003i	0.148147	+	0.988965i	$0.452669\pi$
$90$	4.27098	+	0.0457245i	0.450201	+	0.00481978i
$91$		−	0.660433i		−	0.0692322i
$92$	−1.09801	−	4.66844i	−0.114476	−	0.486719i
$93$	5.03941	+	1.12454i	0.522563	+	0.116610i
$94$	0.384864	+	0.842735i	0.0396957	+	0.0869214i
$95$	1.66913	+	5.68453i	0.171249	+	0.583220i
$96$	−1.03054	−	1.39211i	−0.105179	−	0.142082i
$97$	−4.87143	+	7.58010i	−0.494619	+	0.769642i	−0.995387	−	0.0959391i	$-0.969415\pi$
$97$	−4.87143	+	7.58010i	−0.494619	+	0.769642i	0.500768	+	0.865581i	$0.333051\pi$
$98$	−5.20130	+	4.50695i	−0.525411	+	0.455271i
$99$	4.56225	−	14.9439i	0.458523	−	1.50192i
$100$	−2.85254	−	0.837580i	−0.285254	−	0.0837580i
$101$	−1.33671	−	2.07995i	−0.133007	−	0.206963i	0.768361	−	0.640017i	$-0.221073\pi$
$101$	−1.33671	−	2.07995i	−0.133007	−	0.206963i	−0.901368	+	0.433053i	$0.857436\pi$
$102$	10.0055	+	3.79298i	0.990690	+	0.375561i
$103$	11.1690	+	5.10071i	1.10051	+	0.502588i	0.881045	−	0.473032i	$-0.156840\pi$
$103$	11.1690	+	5.10071i	1.10051	+	0.502588i	0.219468	+	0.975620i	$0.429568\pi$
$104$	0.161237	+	0.0736343i	0.0158106	+	0.00722044i
$105$	8.59141	+	3.25692i	0.838436	+	0.317843i
$106$	0.324928	+	0.505598i	0.0315598	+	0.0491080i
$107$	−3.30948	−	0.971752i	−0.319940	−	0.0939428i	0.117819	−	0.993035i	$-0.462410\pi$
$107$	−3.30948	−	0.971752i	−0.319940	−	0.0939428i	−0.437759	+	0.899092i	$0.644228\pi$
$108$	−2.56316	+	4.51998i	−0.246640	+	0.434935i
$109$	−4.07200	+	3.52841i	−0.390027	+	0.337960i	−0.827697	−	0.561176i	$-0.810349\pi$
$109$	−4.07200	+	3.52841i	−0.390027	+	0.337960i	0.437670	+	0.899136i	$0.355804\pi$
$110$	4.00896	−	6.23807i	0.382240	−	0.594777i
$111$	−9.59929	−	12.9673i	−0.911124	−	1.23080i
$112$	−1.04971	−	3.57497i	−0.0991879	−	0.337803i
$113$	−5.92458	−	12.9730i	−0.557338	−	1.22040i	−0.953270	−	0.302120i	$-0.902306\pi$
$113$	−5.92458	−	12.9730i	−0.557338	−	1.22040i	0.395932	−	0.918280i	$-0.370422\pi$
$114$	−7.03445	−	1.56973i	−0.658836	−	0.147019i
$115$	−6.35652	+	2.49329i	−0.592749	+	0.232500i
$116$			2.54300i			0.236111i
$117$	0.00569267	−	0.531734i	0.000526288	−	0.0491588i
$118$	−14.5055	+	4.25920i	−1.33534	+	0.392091i
$119$	17.3958	+	15.0735i	1.59467	+	1.38179i
$120$	−1.75303	+	1.73436i	−0.160029	+	0.158325i
$121$	−10.5603	−	12.1872i	−0.960023	−	1.10793i
$122$	0.789866	+	5.49364i	0.0715111	+	0.497371i
$123$	2.85240	−	5.15796i	0.257193	−	0.465077i
$124$	−2.50783	+	1.61169i	−0.225210	+	0.144734i
$125$	−1.61548	+	11.2359i	−0.144493	+	1.00497i
$126$	−8.52541	+	7.22898i	−0.759504	+	0.644009i
$127$	−7.14589	+	15.6473i	−0.634095	+	1.38847i	0.270716	+	0.962659i	$0.412740\pi$
$127$	−7.14589	+	15.6473i	−0.634095	+	1.38847i	−0.904810	+	0.425815i	$0.859988\pi$
$128$	0.989821	+	0.142315i	0.0874887	+	0.0125790i
$129$	0.248565	+	0.677482i	0.0218849	+	0.0596489i
$130$	0.0710994	−	0.242142i	0.00623583	−	0.0212373i
$131$	−8.06318	+	1.15931i	−0.704484	+	0.101289i	−0.485240	−	0.874381i	$-0.661268\pi$
$131$	−8.06318	+	1.15931i	−0.704484	+	0.101289i	−0.219243	+	0.975670i	$0.570359\pi$
$132$	4.28085	+	7.94054i	0.372600	+	0.691135i
$133$	−13.0431	−	8.38226i	−1.13098	−	0.726835i
$134$	−0.591967	+	0.683166i	−0.0511381	+	0.0590165i
$135$	6.88912	+	2.69630i	0.592921	+	0.232060i
$136$	−5.61954	+	2.56636i	−0.481871	+	0.220063i
$137$	−8.66200			−0.740044			−0.370022	−	0.929023i	$-0.620650\pi$
$137$	−8.66200			−0.740044			−0.370022	+	0.929023i	$0.620650\pi$
$138$	1.08795	−	8.23507i	0.0926128	−	0.701016i
$139$	−7.72875			−0.655544			−0.327772	−	0.944757i	$-0.606298\pi$
$139$	−7.72875			−0.655544			−0.327772	+	0.944757i	$0.606298\pi$
$140$	−4.82533	+	2.20366i	−0.407815	+	0.186243i
$141$	0.105907	+	1.60117i	0.00891896	+	0.134843i
$142$	5.85532	−	6.75740i	0.491368	−	0.567069i
$143$	−0.776636	−	0.499114i	−0.0649456	−	0.0417380i
$144$	−0.814334	−	2.88736i	−0.0678612	−	0.240614i
$145$	3.58372	−	0.515261i	0.297611	−	0.0427901i
$146$	3.24001	−	11.0345i	0.268145	−	0.913219i
$147$	−11.1911	+	4.10595i	−0.923023	+	0.338653i
$148$	9.21998	+	1.32563i	0.757878	+	0.108966i
$149$	−2.20569	+	4.82978i	−0.180697	+	0.395671i	−0.978206	−	0.207635i	$-0.933423\pi$
$149$	−2.20569	+	4.82978i	−0.180697	+	0.395671i	0.797509	+	0.603307i	$0.206151\pi$
$150$	−4.10567	−	3.10789i	−0.335226	−	0.253759i
$151$	2.78222	−	19.3508i	0.226414	−	1.57474i	−0.486620	−	0.873614i	$-0.661770\pi$
$151$	2.78222	−	19.3508i	0.226414	−	1.57474i	0.713034	−	0.701130i	$-0.247321\pi$
$152$	3.50065	−	2.24973i	0.283940	−	0.182477i
$153$	13.8759	+	12.2861i	1.12180	+	0.993270i
$154$	2.76168	+	19.2079i	0.222543	+	1.54782i
$155$	2.77940	+	3.20760i	0.223247	+	0.257641i
$156$	0.215927	+	0.218251i	0.0172880	+	0.0174741i
$157$	7.81203	+	6.76917i	0.623468	+	0.540238i	0.908289	−	0.418342i	$-0.137389\pi$
$157$	7.81203	+	6.76917i	0.623468	+	0.540238i	−0.284821	+	0.958581i	$0.591934\pi$
$158$	−3.36474	+	0.987977i	−0.267684	+	0.0785992i
$159$	0.215827	+	1.01835i	0.0171162	+	0.0807606i
$160$		−	1.42374i		−	0.112557i
$161$	8.29891	−	15.8247i	0.654046	−	1.24716i
$162$	−6.92637	+	5.74678i	−0.544187	+	0.451509i
$163$	2.45650	+	5.37899i	0.192408	+	0.421315i	0.981107	−	0.193464i	$-0.0619724\pi$
$163$	2.45650	+	5.37899i	0.192408	+	0.421315i	−0.788699	+	0.614779i	$0.789245\pi$
$164$	0.958729	+	3.26513i	0.0748642	+	0.254964i
$165$	10.3228	−	7.64169i	0.803630	−	0.594905i
$166$	7.97068	−	12.4026i	0.618645	−	0.962630i
$167$	2.85764	−	2.47616i	0.221130	−	0.191611i	−0.537249	−	0.843423i	$-0.680537\pi$
$167$	2.85764	−	2.47616i	0.221130	−	0.191611i	0.758380	+	0.651813i	$0.225991\pi$
$168$	0.494832	−	6.43444i	0.0381771	−	0.496428i
$169$	12.4433	+	3.65367i	0.957174	+	0.281052i
$170$	4.75526	+	7.39934i	0.364712	+	0.567503i
$171$	−10.4291	−	6.86123i	−0.797533	−	0.524691i
$172$	−0.378989	−	0.173078i	−0.0288976	−	0.0131971i
$173$	19.5306	+	8.91933i	1.48488	+	0.678124i	0.982456	−	0.186495i	$-0.0597127\pi$
$173$	19.5306	+	8.91933i	1.48488	+	0.678124i	0.502429	+	0.864619i	$0.332440\pi$
$174$	−1.56132	+	4.11859i	−0.118363	+	0.312230i
$175$	−5.98865	−	9.31853i	−0.452700	−	0.704414i
$176$	−4.99729	−	1.46734i	−0.376685	−	0.110605i
$177$	−26.1078	−	2.00779i	−1.96239	−	0.150915i
$178$	1.94609	−	1.68630i	0.145866	−	0.126394i
$179$	8.96942	−	13.9567i	0.670406	−	1.04317i	−0.324839	−	0.945769i	$-0.605310\pi$
$179$	8.96942	−	13.9567i	0.670406	−	1.04317i	0.995245	−	0.0974027i	$-0.0310535\pi$
$180$	−3.90401	+	1.73264i	−0.290988	+	0.129143i
$181$	4.87903	+	16.6164i	0.362655	+	1.23509i	0.915674	+	0.401922i	$0.131658\pi$
$181$	4.87903	+	16.6164i	0.362655	+	1.23509i	−0.553019	+	0.833169i	$0.686524\pi$
$182$	0.274354	+	0.600751i	0.0203365	+	0.0445306i
$183$	−2.09367	+	9.38235i	−0.154768	+	0.693563i
$184$	2.93813	+	3.79044i	0.216602	+	0.279435i
$185$		−	13.2618i		−	0.975030i
$186$	−5.05116	+	1.07053i	−0.370369	+	0.0784950i
$187$	30.8723	−	9.06493i	2.25761	−	0.662893i
$188$	−0.700169	−	0.606700i	−0.0510651	−	0.0442482i
$189$	−18.2460	+	6.47359i	−1.32720	+	0.470885i
$190$	−3.87973	−	4.47745i	−0.281465	−	0.324828i
$191$	0.988482	+	6.87504i	0.0715240	+	0.497461i	0.993822	+	0.110982i	$0.0353996\pi$
$191$	0.988482	+	6.87504i	0.0715240	+	0.497461i	−0.922298	+	0.386479i	$0.873691\pi$
$192$	1.51572	+	0.838209i	0.109388	+	0.0604925i
$193$	18.3676	−	11.8041i	1.32213	−	0.849678i	0.326692	−	0.945131i	$-0.394066\pi$
$193$	18.3676	−	11.8041i	1.32213	−	0.849678i	0.995434	+	0.0954525i	$0.0304298\pi$
$194$	1.28233	−	8.91877i	0.0920656	−	0.640330i
$195$	0.263819	−	0.348517i	0.0188925	−	0.0249578i
$196$	2.85901	−	6.26037i	0.204215	−	0.447169i
$197$	1.87474	+	0.269548i	0.133570	+	0.0192045i	0.208776	−	0.977964i	$-0.433052\pi$
$197$	1.87474	+	0.269548i	0.133570	+	0.0192045i	−0.0752055	+	0.997168i	$0.523961\pi$
$198$	2.05795	+	15.4887i	0.146252	+	1.10073i
$199$	3.07889	−	10.4857i	0.218257	−	0.743314i	−0.775461	−	0.631396i	$-0.782482\pi$
$199$	3.07889	−	10.4857i	0.218257	−	0.743314i	0.993717	−	0.111918i	$-0.0356995\pi$
$200$	2.94270	−	0.423097i	0.208080	−	0.0299175i
$201$	−1.37818	+	0.742994i	−0.0972093	+	0.0524068i
$202$	2.07995	+	1.33671i	0.146345	+	0.0940503i
$203$	−6.20477	+	7.16069i	−0.435489	+	0.502582i
$204$	−10.6770	+	0.706210i	−0.747537	+	0.0494446i
$205$	4.40713	−	2.01267i	0.307807	−	0.140571i
$206$	−12.2786			−0.855490
$207$	6.81810	−	12.6694i	0.473890	−	0.880584i
$208$	−0.177255			−0.0122904
$209$	−19.7142	+	9.00319i	−1.36366	+	0.622764i
$210$	−9.16800	+	0.606402i	−0.632652	+	0.0418457i
$211$	−4.77496	+	5.51060i	−0.328722	+	0.379365i	−0.895920	−	0.444216i	$-0.853482\pi$
$211$	−4.77496	+	5.51060i	−0.328722	+	0.379365i	0.567198	+	0.823582i	$0.308028\pi$
$212$	−0.505598	−	0.324928i	−0.0347246	−	0.0223161i
$213$	13.6320	−	7.34918i	0.934049	−	0.503558i
$214$	3.41409	−	0.490872i	0.233383	−	0.0335553i
$215$	−0.167120	+	0.569159i	−0.0113975	+	0.0388163i
$216$	0.453866	−	5.17629i	0.0308817	−	0.352202i
$217$	−10.9941	−	1.58071i	−0.746328	−	0.107306i
$218$	2.23827	−	4.90112i	0.151595	−	0.331946i
$219$	12.0223	−	15.8820i	0.812390	−	1.07320i
$220$	−1.05529	+	7.33973i	−0.0711479	+	0.494845i
$221$	0.921213	−	0.592027i	0.0619675	−	0.0398241i
$222$	14.1186	+	7.80774i	0.947579	+	0.524021i
$223$	−1.23570	−	8.59451i	−0.0827489	−	0.575531i	−0.988442	−	0.151598i	$-0.951558\pi$
$223$	−1.23570	−	8.59451i	−0.0827489	−	0.575531i	0.905693	−	0.423933i	$-0.139351\pi$
$224$	2.43994	+	2.81585i	0.163026	+	0.188142i
$225$	−4.74132	−	7.55424i	−0.316088	−	0.503616i
$226$	10.7784	+	9.33952i	0.716967	+	0.621256i
$227$	−20.7863	+	6.10342i	−1.37964	+	0.405098i	−0.885643	−	0.464367i	$-0.846282\pi$
$227$	−20.7863	+	6.10342i	−1.37964	+	0.405098i	−0.493994	+	0.869465i	$0.664464\pi$
$228$	7.05085	−	1.49434i	0.466954	−	0.0989648i
$229$			9.76977i			0.645604i	0.946466	+	0.322802i	$0.104625\pi$
$229$			9.76977i			0.645604i	−0.946466	+	0.322802i	$0.895375\pi$
$230$	4.74635	−	4.90857i	0.312965	−	0.323662i
$231$	−7.32027	+	32.8044i	−0.481638	+	2.15837i
$232$	−1.05640	−	2.31319i	−0.0693560	−	0.151868i
$233$	−2.24536	−	7.64698i	−0.147098	−	0.500971i	0.852671	−	0.522448i	$-0.174981\pi$
$233$	−2.24536	−	7.64698i	−0.147098	−	0.500971i	−0.999769	+	0.0214775i	$0.993163\pi$
$234$	0.215712	+	0.486047i	0.0141015	+	0.0317739i
$235$	−0.713124	+	1.10964i	−0.0465191	+	0.0723851i
$236$	11.4253	−	9.90010i	0.743725	−	0.644442i
$237$	−6.05606	−	0.465733i	−0.393383	−	0.0302526i
$238$	−22.0855	−	6.48489i	−1.43159	−	0.420353i
$239$	15.7022	+	24.4331i	1.01569	+	1.58045i	0.796382	+	0.604794i	$0.206745\pi$
$239$	15.7022	+	24.4331i	1.01569	+	1.58045i	0.219311	+	0.975655i	$0.429619\pi$
$240$	0.874131	−	2.30586i	0.0564249	−	0.148843i
$241$	−3.65934	−	1.67116i	−0.235719	−	0.107649i	0.294054	−	0.955789i	$-0.404995\pi$
$241$	−3.65934	−	1.67116i	−0.235719	−	0.107649i	−0.529773	+	0.848140i	$0.677723\pi$
$242$	14.6687	+	6.69896i	0.942939	+	0.430626i
$243$	−14.7462	+	5.05480i	−0.945966	+	0.324266i
$244$	−3.00063	−	4.66907i	−0.192096	−	0.298907i
$245$	−9.40171	−	2.76059i	−0.600653	−	0.176368i
$246$	−0.451945	+	5.87677i	−0.0288150	+	0.374689i
$247$	−0.557439	+	0.483024i	−0.0354690	+	0.0307341i
$248$	1.61169	−	2.50783i	0.102342	−	0.159248i
$249$	20.5240	−	15.1933i	1.30065	−	0.962837i
$250$	−3.19807	−	10.8916i	−0.202264	−	0.688846i
$251$	−2.09183	−	4.58048i	−0.132035	−	0.289117i	0.832054	−	0.554694i	$-0.187165\pi$
$251$	−2.09183	−	4.58048i	−0.132035	−	0.289117i	−0.964090	+	0.265577i	$0.914438\pi$
$252$	4.75196	−	10.1173i	0.299345	−	0.637330i
$253$	−12.3373	−	21.7184i	−0.775637	−	1.36542i
$254$		−	17.2018i		−	1.07934i
$255$	3.15858	+	14.9034i	0.197798	+	0.933287i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	−11.3840	−	9.86431i	−0.710116	−	0.615319i	0.223032	−	0.974811i	$-0.428404\pi$
$257$	−11.3840	−	9.86431i	−0.710116	−	0.615319i	−0.933148	+	0.359492i	$0.882950\pi$
$258$	−0.507539	−	0.513002i	−0.0315980	−	0.0319381i
$259$	22.7276	+	26.2290i	1.41222	+	1.62979i
$260$	0.0359153	+	0.249796i	0.00222737	+	0.0154917i
$261$	−5.05736	+	5.71179i	−0.313043	+	0.353551i
$262$	6.85293	−	4.40411i	0.423376	−	0.272087i
$263$	−3.59455	+	25.0007i	−0.221650	+	1.54161i	0.510149	+	0.860086i	$0.329590\pi$
$263$	−3.59455	+	25.0007i	−0.221650	+	1.54161i	−0.731799	+	0.681521i	$0.761319\pi$
$264$	−7.19262	−	5.44464i	−0.442675	−	0.335095i
$265$	−0.355461	+	0.778350i	−0.0218358	+	0.0478137i
$266$	15.3465	+	2.20649i	0.940954	+	0.135289i
$267$	4.18719	−	1.53626i	0.256252	−	0.0940177i
$268$	0.254674	−	0.867341i	0.0155567	−	0.0529813i
$269$	13.5861	−	1.95339i	0.828360	−	0.119100i	0.284923	−	0.958550i	$-0.408032\pi$
$269$	13.5861	−	1.95339i	0.828360	−	0.119100i	0.543437	+	0.839450i	$0.317123\pi$
$270$	−7.38665	+	0.409207i	−0.449537	+	0.0249036i
$271$	16.6069	+	10.6726i	1.00880	+	0.648313i	0.937081	−	0.349112i	$-0.113517\pi$
$271$	16.6069	+	10.6726i	1.00880	+	0.648313i	0.0717144	+	0.997425i	$0.477153\pi$
$272$	4.04561	−	4.66888i	0.245301	−	0.283093i
$273$	0.0754966	+	1.14141i	0.00456926	+	0.0690813i
$274$	7.87923	−	3.59832i	0.476002	−	0.217383i
$275$	−15.4840			−0.933718
$276$	2.43133	+	7.94283i	0.146349	+	0.478102i
$277$	19.8811			1.19454			0.597270	−	0.802041i	$-0.296252\pi$
$277$	19.8811			1.19454			0.597270	+	0.802041i	$0.296252\pi$
$278$	7.03032	−	3.21064i	0.421651	−	0.192561i
$279$	−8.83804	−	1.36744i	−0.529120	−	0.0818666i
$280$	3.47385	−	4.00903i	0.207602	−	0.239586i
$281$	7.48487	+	4.81024i	0.446510	+	0.286955i	0.744510	−	0.667611i	$-0.232683\pi$
$281$	7.48487	+	4.81024i	0.446510	+	0.286955i	−0.298000	+	0.954566i	$0.596320\pi$
$282$	−0.761487	−	1.41248i	−0.0453459	−	0.0841120i
$283$	−21.9899	+	3.16167i	−1.30716	+	0.187942i	−0.760460	−	0.649385i	$-0.775026\pi$
$283$	−21.9899	+	3.16167i	−1.30716	+	0.187942i	−0.546703	+	0.837327i	$0.684117\pi$
$284$	−2.51906	+	8.57914i	−0.149479	+	0.509078i
$285$	−3.53453	−	9.63362i	−0.209368	−	0.570646i
$286$	0.913792	+	0.131384i	0.0540337	+	0.00776887i
$287$	−5.26710	+	11.5333i	−0.310907	+	0.680792i
$288$	1.94020	+	2.28815i	0.114327	+	0.134831i
$289$	−3.01215	+	20.9500i	−0.177185	+	1.23235i
$290$	−3.04582	+	1.95743i	−0.178856	+	0.114944i
$291$	7.55266	−	13.6574i	0.442745	−	0.800609i
$292$	1.63667	+	11.3833i	0.0957786	+	0.666155i
$293$	−8.70390	−	10.0448i	−0.508487	−	0.586825i	0.442224	−	0.896905i	$-0.354190\pi$
$293$	−8.70390	−	10.0448i	−0.508487	−	0.586825i	−0.950711	+	0.310079i	$0.899644\pi$
$294$	8.47407	−	8.38383i	0.494218	−	0.488955i
$295$	−16.2667	−	14.0952i	−0.947084	−	0.820653i
$296$	−8.93748	+	2.62428i	−0.519480	+	0.152533i
$297$	−6.17652	+	26.3487i	−0.358398	+	1.52890i
$298$		−	5.30960i		−	0.307577i
$299$	−0.611114	−	0.590917i	−0.0353416	−	0.0341736i
$300$	5.02571	+	1.12148i	0.290160	+	0.0647489i
$301$	−0.644872	−	1.41207i	−0.0371698	−	0.0813906i
$302$	5.50780	+	18.7579i	0.316939	+	1.07939i
$303$	2.54796	+	3.44193i	0.146377	+	0.197734i
$304$	−2.24973	+	3.50065i	−0.129031	+	0.200776i
$305$	−5.97190	+	5.17468i	−0.341950	+	0.296301i
$306$	−17.7258	−	5.41154i	−1.01332	−	0.309357i
$307$	−22.7446	−	6.67843i	−1.29811	−	0.381158i	−0.441561	−	0.897231i	$-0.645575\pi$
$307$	−22.7446	−	6.67843i	−1.29811	−	0.381158i	−0.856544	+	0.516073i	$0.827393\pi$
$308$	−10.4914	−	16.3249i	−0.597801	−	0.930197i
$309$	−19.8862	−	7.53866i	−1.13128	−	0.428859i
$310$	−3.86072	−	1.76313i	−0.219274	−	0.100139i
$311$	11.0277	+	5.03616i	0.625321	+	0.285575i	0.702765	−	0.711422i	$-0.251949\pi$
$311$	11.0277	+	5.03616i	0.625321	+	0.285575i	−0.0774437	+	0.996997i	$0.524676\pi$
$312$	−0.287079	−	0.108829i	−0.0162526	−	0.00616121i
$313$	−15.0820	−	23.4680i	−0.852485	−	1.32649i	−0.943748	−	0.330666i	$-0.892727\pi$
$313$	−15.0820	−	23.4680i	−0.852485	−	1.32649i	0.0912631	−	0.995827i	$-0.470910\pi$
$314$	−9.91809	−	2.91221i	−0.559710	−	0.164346i
$315$	−15.2206	−	4.64674i	−0.857585	−	0.261814i
$316$	2.65025	−	2.29646i	0.149088	−	0.129186i
$317$	3.14599	−	4.89525i	0.176696	−	0.274945i	−0.741597	−	0.670846i	$-0.765931\pi$
$317$	3.14599	−	4.89525i	0.176696	−	0.274945i	0.918293	+	0.395901i	$0.129568\pi$
$318$	−0.619362	−	0.836668i	−0.0347321	−	0.0469180i
$319$	3.73143	+	12.7081i	0.208920	+	0.711516i
$320$	0.591443	+	1.29508i	0.0330627	+	0.0723972i
$321$	5.83078	+	1.30113i	0.325442	+	0.0726222i
$322$	−0.975134	+	17.8421i	−0.0543421	+	0.994304i
$323$		−	25.7073i		−	1.43039i
$324$	3.91315	−	8.10477i	0.217397	−	0.450265i
$325$	−0.505626	+	0.148465i	−0.0280471	+	0.00823537i
$326$	−4.46902	−	3.87243i	−0.247516	−	0.214474i
$327$	6.63419	−	6.56354i	0.366871	−	0.362965i
$328$	−2.22848	−	2.57180i	−0.123047	−	0.142004i
$329$	−0.491254	−	3.41675i	−0.0270837	−	0.188371i
$330$	−6.21549	+	11.2394i	−0.342152	+	0.618707i
$331$	−15.7671	+	10.1329i	−0.866640	+	0.556956i	−0.896723	−	0.442592i	$-0.854059\pi$
$331$	−15.7671	+	10.1329i	−0.866640	+	0.556956i	0.0300834	+	0.999547i	$0.490423\pi$
$332$	−2.09815	+	14.5930i	−0.115151	+	0.800893i
$333$	18.0725	+	21.3136i	0.990369	+	1.16798i
$334$	−1.57076	+	3.43949i	−0.0859484	+	0.188201i
$335$	−1.27390	−	0.183159i	−0.0696007	−	0.0100071i
$336$	2.22285	+	6.05854i	0.121266	+	0.330520i
$337$	−1.87769	+	6.39484i	−0.102285	+	0.348349i	−0.994694	−	0.102877i	$-0.967195\pi$
$337$	−1.87769	+	6.39484i	−0.102285	+	0.348349i	0.892410	+	0.451226i	$0.149013\pi$
$338$	−12.8366	+	1.84562i	−0.698218	+	0.100389i
$339$	11.7223	+	21.7437i	0.636668	+	1.18096i
$340$	−7.39934	−	4.75526i	−0.401285	−	0.257890i
$341$	−10.1675	+	11.7339i	−0.550600	+	0.635426i
$342$	12.3369	+	1.90879i	0.667103	+	0.103216i
$343$	−0.398877	+	0.182161i	−0.0215373	+	0.00983577i
$344$	0.416640			0.0224637
$345$	10.7008	−	5.03573i	0.576111	−	0.271114i
$346$	−21.4709			−1.15428
$347$	7.72113	−	3.52612i	0.414492	−	0.189292i	−0.197244	−	0.980355i	$-0.563199\pi$
$347$	7.72113	−	3.52612i	0.414492	−	0.189292i	0.611735	+	0.791062i	$0.290472\pi$
$348$	−0.290700	−	4.39500i	−0.0155831	−	0.235597i
$349$	5.73202	−	6.61510i	0.306828	−	0.354098i	−0.581304	−	0.813686i	$-0.697457\pi$
$349$	5.73202	−	6.61510i	0.306828	−	0.354098i	0.888132	+	0.459588i	$0.152003\pi$
$350$	9.31853	+	5.98865i	0.498096	+	0.320107i
$351$	0.0509460	+	0.919633i	0.00271930	+	0.0490864i
$352$	5.15525	−	0.741212i	0.274776	−	0.0395068i
$353$	7.14421	−	24.3310i	0.380248	−	1.29501i	−0.517948	−	0.855412i	$-0.673304\pi$
$353$	7.14421	−	24.3310i	0.380248	−	1.29501i	0.898196	−	0.439594i	$-0.144878\pi$
$354$	24.5826	−	9.01924i	1.30655	−	0.479367i
$355$	12.6006	+	1.81169i	0.668768	+	0.0961543i
$356$	−1.06971	+	2.34235i	−0.0566948	+	0.124144i
$357$	−31.7878	−	24.0626i	−1.68239	−	1.27353i
$358$	−2.36105	+	16.4215i	−0.124786	+	0.867902i
$359$	6.91139	−	4.44168i	0.364769	−	0.234423i	−0.345398	−	0.938456i	$-0.612256\pi$
$359$	6.91139	−	4.44168i	0.364769	−	0.234423i	0.710167	+	0.704034i	$0.248620\pi$
$360$	2.83145	−	3.19785i	0.149231	−	0.168541i
$361$	−0.239682	−	1.66703i	−0.0126148	−	0.0877382i
$362$	−11.3408	−	13.0880i	−0.596061	−	0.687891i
$363$	19.6442	+	19.8556i	1.03105	+	1.04215i
$364$	−0.499122	−	0.432492i	−0.0261611	−	0.0226687i
$365$	15.7102	−	4.61294i	0.822311	−	0.241452i
$366$	−1.99311	−	9.40423i	−0.104181	−	0.491567i
$367$		−	7.70363i		−	0.402126i	−0.979578	−	0.201063i	$-0.935560\pi$
$367$		−	7.70363i		−	0.402126i	0.979578	−	0.201063i	$-0.0644396\pi$
$368$	−4.24722	−	2.22736i	−0.221402	−	0.116109i
$369$	−4.34011	+	9.24043i	−0.225937	+	0.481038i
$370$	5.50917	+	12.0634i	0.286408	+	0.627146i
$371$	−0.630879	−	2.14858i	−0.0327536	−	0.111549i
$372$	4.14999	−	3.07212i	0.215167	−	0.159282i
$373$	−7.68769	+	11.9623i	−0.398054	+	0.619384i	−0.981202	−	0.192982i	$-0.938184\pi$
$373$	−7.68769	+	11.9623i	−0.398054	+	0.619384i	0.583149	+	0.812365i	$0.301820\pi$
$374$	−24.3167	+	21.0706i	−1.25739	+	1.08953i
$375$	1.50757	−	19.6034i	0.0778506	−	1.01231i
$376$	0.888929	+	0.261013i	0.0458430	+	0.0134607i
$377$	0.243698	+	0.379202i	0.0125511	+	0.0195299i
$378$	13.9079	−	13.4682i	0.715344	−	0.692731i
$379$	−17.1252	−	7.82084i	−0.879665	−	0.401729i	−0.0762074	−	0.997092i	$-0.524281\pi$
$379$	−17.1252	−	7.82084i	−0.879665	−	0.401729i	−0.803457	+	0.595363i	$0.797008\pi$
$380$	5.38913	+	2.46113i	0.276456	+	0.126253i
$381$	10.5613	−	27.8597i	0.541074	−	1.42730i
$382$	−3.75515	−	5.84313i	−0.192130	−	0.298960i
$383$	−19.9933	−	5.87055i	−1.02161	−	0.299971i	−0.272313	−	0.962209i	$-0.587789\pi$
$383$	−19.9933	−	5.87055i	−1.02161	−	0.299971i	−0.749294	+	0.662238i	$0.769607\pi$
$384$	−1.72695	−	0.132809i	−0.0881281	−	0.00677737i
$385$	−20.8801	+	18.0927i	−1.06415	+	0.922089i
$386$	−11.8041	+	18.3676i	−0.600813	+	0.934884i
$387$	−0.507034	−	1.14246i	−0.0257740	−	0.0580745i
$388$	2.53855	+	8.64549i	0.128875	+	0.438908i
$389$	4.41133	+	9.65948i	0.223664	+	0.489755i	0.987883	−	0.155202i	$-0.0496027\pi$
$389$	4.41133	+	9.65948i	0.223664	+	0.489755i	−0.764219	+	0.644957i	$0.776875\pi$
$390$	−0.0951991	+	0.426616i	−0.00482059	+	0.0216025i
$391$	29.5126	−	2.60980i	1.49252	−	0.131983i
$392$			6.88231i			0.347609i
$393$	13.8029	−	2.92534i	0.696263	−	0.147564i
$394$	−1.81730	+	0.533608i	−0.0915543	+	0.0268828i
$395$	−3.77328	−	3.26956i	−0.189854	−	0.164510i
$396$	−8.30619	−	13.2341i	−0.417402	−	0.665037i
$397$	−8.46553	−	9.76974i	−0.424873	−	0.490329i	0.502443	−	0.864611i	$-0.332435\pi$
$397$	−8.46553	−	9.76974i	−0.424873	−	0.490329i	−0.927315	+	0.374282i	$0.877889\pi$
$398$	1.55528	+	10.8172i	0.0779589	+	0.542216i
$399$	23.5002	+	12.9959i	1.17648	+	0.650606i
$400$	−2.50102	+	1.60730i	−0.125051	+	0.0803652i
$401$	0.00577400	−	0.0401590i	0.000288340	−	0.00200545i	−0.989677	−	0.143317i	$-0.954223\pi$
$401$	0.00577400	−	0.0401590i	0.000288340	−	0.00200545i	0.989965	+	0.141312i	$0.0451321\pi$
$402$	0.944985	−	1.24837i	0.0471316	−	0.0622629i
$403$	−0.219509	+	0.480657i	−0.0109345	+	0.0239433i
$404$	−2.44728	−	0.351866i	−0.121757	−	0.0175060i
$405$	−12.2145	−	3.87242i	−0.606944	−	0.192422i
$406$	2.66940	−	9.09114i	0.132480	−	0.451186i
$407$	48.0200	−	6.90424i	2.38027	−	0.342230i
$408$	9.41873	−	5.07776i	0.466297	−	0.251387i
$409$	8.41485	+	5.40790i	0.416088	+	0.267403i	0.731891	−	0.681421i	$-0.238638\pi$
$409$	8.41485	+	5.40790i	0.416088	+	0.267403i	−0.315804	+	0.948824i	$0.602274\pi$
$410$	−3.17277	+	3.66157i	−0.156692	+	0.180832i
$411$	14.9703	−	0.990186i	0.738431	−	0.0488423i
$412$	11.1690	−	5.10071i	0.550257	−	0.251294i
$413$	56.3276			2.77170
$414$	−0.938901	+	14.3568i	−0.0461445	+	0.705600i
$415$	20.9902			1.03037
$416$	0.161237	−	0.0736343i	0.00790528	−	0.00361022i
$417$	13.3574	−	0.883503i	0.654115	−	0.0432653i
$418$	14.1926	−	16.3792i	0.694185	−	0.801132i
$419$	7.61634	+	4.89473i	0.372083	+	0.239123i	0.713296	−	0.700863i	$-0.247202\pi$
$419$	7.61634	+	4.89473i	0.372083	+	0.239123i	−0.341213	+	0.939986i	$0.610838\pi$
$420$	8.08759	−	4.36013i	0.394634	−	0.212752i
$421$	9.75720	−	1.40287i	0.475537	−	0.0683719i	0.0996206	−	0.995025i	$-0.468237\pi$
$421$	9.75720	−	1.40287i	0.475537	−	0.0683719i	0.375916	+	0.926654i	$0.377328\pi$
$422$	2.05427	−	6.99621i	0.100000	−	0.340570i
$423$	−0.366072	−	2.75516i	−0.0177990	−	0.133960i
$424$	0.594888	+	0.0855320i	0.0288903	+	0.00415380i
$425$	7.62968	−	16.7067i	0.370094	−	0.810393i
$426$	−9.34714	+	12.3480i	−0.452870	+	0.598262i
$427$	2.94296	−	20.4687i	0.142420	−	0.990552i
$428$	−2.90165	+	1.86478i	−0.140257	+	0.0901375i
$429$	1.39930	+	0.773825i	0.0675586	+	0.0373606i
$430$	−0.0844193	−	0.587149i	−0.00407106	−	0.0283148i
$431$	−21.0639	−	24.3090i	−1.01461	−	1.17093i	−0.985209	−	0.171358i	$-0.945185\pi$
$431$	−21.0639	−	24.3090i	−1.01461	−	1.17093i	−0.0294037	−	0.999568i	$-0.509361\pi$
$432$	1.73746	+	4.89706i	0.0835935	+	0.235610i
$433$	5.12637	+	4.44203i	0.246358	+	0.213470i	0.769283	−	0.638908i	$-0.220614\pi$
$433$	5.12637	+	4.44203i	0.246358	+	0.213470i	−0.522925	+	0.852379i	$0.675159\pi$
$434$	10.6572	−	3.12925i	0.511564	−	0.150209i
$435$	−6.13474	+	1.30018i	−0.294138	+	0.0623389i
$436$			5.38803i			0.258040i
$437$	−19.4265	+	4.56908i	−0.929294	+	0.218569i
$438$	−4.33824	+	19.4410i	−0.207289	+	0.928925i
$439$	−11.4480	−	25.0676i	−0.546382	−	1.19641i	−0.958451	−	0.285257i	$-0.907921\pi$
$439$	−11.4480	−	25.0676i	−0.546382	−	1.19641i	0.412069	−	0.911153i	$-0.364806\pi$
$440$	−2.08911	−	7.11484i	−0.0995942	−	0.339187i
$441$	18.8718	−	8.37550i	0.898659	−	0.398833i
$442$	−0.592027	+	0.921213i	−0.0281599	+	0.0438176i
$443$	2.89251	−	2.50637i	0.137427	−	0.119081i	−0.583435	−	0.812160i	$-0.698292\pi$
$443$	2.89251	−	2.50637i	0.137427	−	0.119081i	0.720862	+	0.693079i	$0.243746\pi$
$444$	−16.0862	−	1.23709i	−0.763417	−	0.0587095i
$445$	3.51770	+	1.03289i	0.166755	+	0.0489636i
$446$	4.69433	+	7.30451i	0.222283	+	0.345879i
$447$	3.25992	−	8.59933i	0.154189	−	0.406734i
$448$	−3.38920	−	1.54779i	−0.160124	−	0.0731264i
$449$	−16.9525	−	7.74195i	−0.800038	−	0.365365i	−0.0269281	−	0.999637i	$-0.508573\pi$
$449$	−16.9525	−	7.74195i	−0.800038	−	0.365365i	−0.773110	+	0.634272i	$0.781300\pi$
$450$	7.45100	+	4.90196i	0.351243	+	0.231081i
$451$	9.58209	+	14.9100i	0.451203	+	0.702085i
$452$	−13.6841	−	4.01803i	−0.643648	−	0.188992i
$453$	−2.59638	+	33.7615i	−0.121989	+	1.58625i
$454$	16.3725	−	14.1868i	0.768398	−	0.665820i
$455$	−0.508357	+	0.791019i	−0.0238321	+	0.0370835i
$456$	−5.79291	+	4.28832i	−0.271278	+	0.200819i
$457$	7.02484	+	23.9244i	0.328608	+	1.11914i	0.943733	+	0.330707i	$0.107287\pi$
$457$	7.02484	+	23.9244i	0.328608	+	1.11914i	−0.615125	+	0.788429i	$0.710895\pi$
$458$	−4.05851	−	8.88689i	−0.189642	−	0.415257i
$459$	−25.3859	−	19.6475i	−1.18491	−	0.917067i
$460$	−2.27833	+	6.43670i	−0.106228	+	0.300113i
$461$			11.0295i			0.513693i	0.966452	+	0.256847i	$0.0826835\pi$
$461$			11.0295i			0.513693i	−0.966452	+	0.256847i	$0.917317\pi$
$462$	−6.96867	−	32.8809i	−0.324212	−	1.52976i
$463$	−28.1962	+	8.27914i	−1.31039	+	0.384764i	−0.861014	−	0.508581i	$-0.830170\pi$
$463$	−28.1962	+	8.27914i	−1.31039	+	0.384764i	−0.449372	+	0.893345i	$0.648352\pi$
$464$	1.92187	+	1.66531i	0.0892205	+	0.0773100i
$465$	−5.17025	−	5.22589i	−0.239764	−	0.242345i
$466$	5.21912	+	6.02319i	0.241771	+	0.279019i
$467$	3.33349	+	23.1849i	0.154255	+	1.07287i	0.908984	+	0.416832i	$0.136860\pi$
$467$	3.33349	+	23.1849i	0.154255	+	1.07287i	−0.754728	+	0.656038i	$0.772231\pi$
$468$	−0.398130	−	0.352514i	−0.0184036	−	0.0162950i
$469$	2.83339	−	1.82091i	0.130834	−	0.0840817i
$470$	0.187718	−	1.30561i	0.00865879	−	0.0602232i
$471$	−14.2751	−	10.8060i	−0.657764	−	0.497912i
$472$	−6.28019	+	13.7517i	−0.289069	+	0.632973i
$473$	−2.14788	−	0.308819i	−0.0987597	−	0.0141995i
$474$	5.70225	−	2.09213i	0.261913	−	0.0960948i
$475$	−3.48536	+	11.8701i	−0.159919	+	0.544636i
$476$	22.7836	−	3.27579i	1.04429	−	0.150146i
$477$	−0.489419	−	1.73532i	−0.0224090	−	0.0794548i
$478$	−24.4331	−	15.7022i	−1.11755	−	0.718203i
$479$	0.272929	−	0.314976i	0.0124704	−	0.0143916i	−0.749480	−	0.662027i	$-0.769696\pi$
$479$	0.272929	−	0.314976i	0.0124704	−	0.0143916i	0.761951	+	0.647635i	$0.224242\pi$
$480$	0.162753	+	2.46061i	0.00742863	+	0.112311i
$481$	1.50189	−	0.685888i	0.0684801	−	0.0312738i
$482$	4.02288			0.183237
$483$	−12.5338	+	28.2981i	−0.570308	+	1.28761i
$484$	−16.1260			−0.732998
$485$	11.6693	−	5.32919i	0.529875	−	0.241986i
$486$	11.3137	−	10.7238i	0.513201	−	0.486441i
$487$	−15.6934	+	18.1112i	−0.711136	+	0.820695i	−0.990212	−	0.139575i	$-0.955427\pi$
$487$	−15.6934	+	18.1112i	−0.711136	+	0.820695i	0.279076	+	0.960269i	$0.409972\pi$
$488$	4.66907	+	3.00063i	0.211359	+	0.135832i
$489$	−4.86040	−	9.01555i	−0.219795	−	0.407697i
$490$	9.69889	−	1.39449i	0.438151	−	0.0629966i
$491$	−3.67197	+	12.5056i	−0.165714	+	0.564370i	0.834203	+	0.551458i	$0.185928\pi$
$491$	−3.67197	+	12.5056i	−0.165714	+	0.564370i	−0.999917	+	0.0129118i	$0.995890\pi$
$492$	−2.03020	−	5.53345i	−0.0915283	−	0.249467i
$493$	−15.5503	−	2.23579i	−0.700349	−	0.100695i
$494$	0.306409	−	0.670943i	0.0137860	−	0.0301871i
$495$	−16.9671	+	14.3870i	−0.762615	+	0.646646i
$496$	−0.424250	+	2.95072i	−0.0190494	+	0.132491i
$497$	−28.0259	+	18.0112i	−1.25713	+	0.807911i
$498$	−12.3577	+	22.3463i	−0.553763	+	1.00136i
$499$	−6.31900	−	43.9496i	−0.282877	−	1.96746i	−0.251104	−	0.967960i	$-0.580794\pi$
$499$	−6.31900	−	43.9496i	−0.282877	−	1.96746i	−0.0317731	−	0.999495i	$-0.510115\pi$
$500$	7.43361	+	8.57884i	0.332441	+	0.383657i
$501$	−4.65572	+	4.60614i	−0.208002	+	0.205787i
$502$	3.80560	+	3.29757i	0.169852	+	0.147178i
$503$	14.0755	−	4.13293i	0.627595	−	0.184278i	0.0475577	−	0.998868i	$-0.484856\pi$
$503$	14.0755	−	4.13293i	0.627595	−	0.184278i	0.580037	+	0.814590i	$0.303038\pi$
$504$	−0.119660	+	11.1771i	−0.00533008	+	0.497865i
$505$			3.52012i			0.156643i
$506$	20.2445	+	14.6307i	0.899978	+	0.650413i
$507$	−21.9230	−	4.89211i	−0.973636	−	0.217266i
$508$	7.14589	+	15.6473i	0.317047	+	0.694237i
$509$	2.01996	+	6.87934i	0.0895331	+	0.304922i	0.992069	−	0.125692i	$-0.0401152\pi$
$509$	2.01996	+	6.87934i	0.0895331	+	0.304922i	−0.902536	+	0.430614i	$0.858297\pi$
$510$	−9.06425	−	12.2445i	−0.401372	−	0.542195i
$511$	−23.1659	+	36.0469i	−1.02480	+	1.59462i
$512$	0.755750	−	0.654861i	0.0333997	−	0.0289410i
$513$	18.8087	+	10.6659i	0.830423	+	0.470911i
$514$	14.4531	+	4.24380i	0.637497	+	0.187186i
$515$	−9.45123	−	14.7064i	−0.416471	−	0.648041i
$516$	0.674782	+	0.255803i	0.0297056	+	0.0112611i
$517$	−4.38918	−	2.00447i	−0.193036	−	0.0881565i
$518$	−31.5696	−	14.4174i	−1.38709	−	0.633463i
$519$	−34.7739	−	13.1824i	−1.52640	−	0.578645i
$520$	−0.136439	−	0.212303i	−0.00598324	−	0.00931010i
$521$	−6.47921	−	1.90247i	−0.283860	−	0.0833487i	0.136703	−	0.990612i	$-0.456349\pi$
$521$	−6.47921	−	1.90247i	−0.283860	−	0.0833487i	−0.420563	+	0.907263i	$0.638167\pi$
$522$	2.22757	−	7.29654i	0.0974983	−	0.319361i
$523$	13.3559	−	11.5730i	0.584013	−	0.506051i	−0.311997	−	0.950083i	$-0.600998\pi$
$523$	13.3559	−	11.5730i	0.584013	−	0.506051i	0.896011	+	0.444032i	$0.146453\pi$
$524$	−4.40411	+	6.85293i	−0.192395	+	0.299372i
$525$	11.4153	+	15.4204i	0.498203	+	0.673001i
$526$	−7.11593	−	24.2346i	−0.310269	−	1.05668i
$527$	−7.65049	−	16.7522i	−0.333260	−	0.729738i
$528$	8.80442	+	1.96470i	0.383163	+	0.0855026i
$529$	−7.21758	−	21.8382i	−0.313808	−	0.949486i
$530$		−	0.855676i		−	0.0371682i
$531$	45.3510	+	0.485522i	1.96807	+	0.0210699i
$532$	−14.8763	+	4.36807i	−0.644969	+	0.189380i
$533$	0.455864	+	0.395008i	0.0197456	+	0.0171097i
$534$	−3.17062	+	3.13685i	−0.137206	+	0.135745i
$535$	3.21587	+	3.71131i	0.139034	+	0.160454i
$536$	0.128647	+	0.894757i	0.00555669	+	0.0386476i
$537$	−13.9062	+	25.1463i	−0.600096	+	1.08514i
$538$	−11.5469	+	7.42074i	−0.497822	+	0.319931i
$539$	5.10125	−	35.4800i	0.219727	−	1.52823i
$540$	6.54914	−	3.44075i	0.281830	−	0.148066i
$541$	5.79436	−	12.6879i	0.249119	−	0.545494i	−0.743219	−	0.669048i	$-0.766702\pi$
$541$	5.79436	−	12.6879i	0.249119	−	0.545494i	0.992338	+	0.123554i	$0.0394292\pi$
$542$	−19.5397	−	2.80938i	−0.839302	−	0.120673i
$543$	−10.3318	−	28.1600i	−0.443379	−	1.20846i
$544$	−1.74049	+	5.92757i	−0.0746230	+	0.254142i
$545$	7.59307	−	1.09172i	0.325251	−	0.0467641i
$546$	−0.542833	−	1.00690i	−0.0232311	−	0.0430914i
$547$	15.2624	+	9.80854i	0.652573	+	0.419383i	0.824605	−	0.565708i	$-0.191397\pi$
$547$	15.2624	+	9.80854i	0.652573	+	0.419383i	−0.172033	+	0.985091i	$0.555034\pi$
$548$	−5.67240	+	6.54630i	−0.242313	+	0.279644i
$549$	2.54590	−	16.4546i	0.108656	−	0.702266i
$550$	14.0847	−	6.43227i	0.600574	−	0.274273i
$551$	10.5820			0.450808
$552$	−5.51119	−	6.21504i	−0.234572	−	0.264530i
$553$	13.0659			0.555620
$554$	−18.0845	+	8.25890i	−0.768336	+	0.350887i
$555$	1.51601	+	22.9201i	0.0643511	+	0.972905i
$556$	−5.06126	+	5.84100i	−0.214645	+	0.247714i
$557$	29.8095	+	19.1574i	1.26307	+	0.811725i	0.988701	−	0.149900i	$-0.0478951\pi$
$557$	29.8095	+	19.1574i	1.26307	+	0.811725i	0.274368	+	0.961625i	$0.411531\pi$
$558$	8.60742	−	2.42759i	0.364381	−	0.102768i
$559$	−0.0730997	+	0.0105102i	−0.00309179	+	0.000444532i
$560$	−1.49451	+	5.08983i	−0.0631546	+	0.215085i
$561$	−52.3196	+	19.1958i	−2.20893	+	0.810448i
$562$	−8.80672	−	1.26622i	−0.371489	−	0.0534121i
$563$	10.8672	−	23.7958i	0.457997	−	1.00287i	−0.529942	−	0.848034i	$-0.677786\pi$
$563$	10.8672	−	23.7958i	0.457997	−	1.00287i	0.987939	−	0.154840i	$-0.0494864\pi$
$564$	1.27944	+	0.968505i	0.0538741	+	0.0407814i
$565$	−2.88973	+	20.0985i	−0.121572	+	0.845550i
$566$	18.6893	−	12.0109i	0.785570	−	0.504855i
$567$	30.7940	−	13.2739i	1.29323	−	0.557452i
$568$	−1.27248	−	8.85032i	−0.0533922	−	0.371351i
$569$	12.1768	+	14.0527i	0.510477	+	0.589122i	0.951221	−	0.308511i	$-0.0998308\pi$
$569$	12.1768	+	14.0527i	0.510477	+	0.589122i	−0.440744	+	0.897633i	$0.645285\pi$
$570$	7.21707	+	7.29475i	0.302290	+	0.305543i
$571$	20.6801	+	17.9194i	0.865436	+	0.749905i	0.969610	−	0.244654i	$-0.0786744\pi$
$571$	20.6801	+	17.9194i	0.865436	+	0.749905i	−0.104174	+	0.994559i	$0.533220\pi$
$572$	−0.885793	+	0.260092i	−0.0370369	+	0.0108750i
$573$	−2.49428	−	11.7690i	−0.104200	−	0.491656i
$574$		−	12.6791i		−	0.529217i
$575$	−13.9809	−	2.79623i	−0.583046	−	0.116611i
$576$	−2.71540	−	1.27539i	−0.113142	−	0.0531411i
$577$	−3.12636	−	6.84577i	−0.130152	−	0.284993i	0.833325	−	0.552783i	$-0.186434\pi$
$577$	−3.12636	−	6.84577i	−0.130152	−	0.284993i	−0.963477	+	0.267790i	$0.913707\pi$
$578$	−5.96298	−	20.3081i	−0.248027	−	0.844704i
$579$	−30.3948	+	22.5004i	−1.26316	+	0.935085i
$580$	1.95743	−	3.04582i	0.0812777	−	0.126471i
$581$	−41.5141	+	35.9722i	−1.72229	+	1.49238i
$582$	−1.19667	+	15.5607i	−0.0496036	+	0.645010i
$583$	−3.00340	−	0.881877i	−0.124388	−	0.0365236i
$584$	−6.21754	−	9.67468i	−0.257284	−	0.400341i
$585$	−0.416111	+	0.632490i	−0.0172041	+	0.0261503i
$586$	12.0901	+	5.52137i	0.499438	+	0.228086i
$587$	−7.14131	−	3.26133i	−0.294753	−	0.134609i	0.262550	−	0.964918i	$-0.415437\pi$
$587$	−7.14131	−	3.26133i	−0.294753	−	0.134609i	−0.557303	+	0.830309i	$0.688164\pi$
$588$	−4.22552	+	11.1465i	−0.174257	+	0.459672i
$589$	6.70660	+	10.4357i	0.276341	+	0.429994i
$590$	20.6521	+	6.06399i	0.850232	+	0.249651i
$591$	−3.27089	−	0.251543i	−0.134546	−	0.0103471i
$592$	7.03965	−	6.09989i	0.289328	−	0.250704i
$593$	−24.6982	+	38.4312i	−1.01424	+	1.57818i	−0.215495	+	0.976505i	$0.569136\pi$
$593$	−24.6982	+	38.4312i	−1.01424	+	1.57818i	−0.798741	+	0.601676i	$0.794500\pi$
$594$	−5.32726	−	26.5334i	−0.218580	−	1.08868i
$595$	−9.23281	−	31.4440i	−0.378508	−	1.28908i
$596$	2.20569	+	4.82978i	0.0903485	+	0.197836i
$597$	−4.12250	+	18.4742i	−0.168723	+	0.756099i
$598$	0.801365	+	0.283651i	0.0327702	+	0.0115994i
$599$		−	46.7606i		−	1.91059i	−0.295662	−	0.955293i	$-0.595540\pi$
$599$		−	46.7606i		−	1.91059i	0.295662	−	0.955293i	$-0.404460\pi$
$600$	−5.03743	+	1.06762i	−0.205652	+	0.0435853i
$601$	20.8538	−	6.12322i	0.850643	−	0.249771i	0.172781	−	0.984960i	$-0.444725\pi$
$601$	20.8538	−	6.12322i	0.850643	−	0.249771i	0.677862	+	0.735189i	$0.262907\pi$
$602$	1.17319	+	1.01658i	0.0478158	+	0.0414326i
$603$	2.29694	−	1.44164i	0.0935386	−	0.0587082i
$604$	−12.8024	−	14.7747i	−0.520921	−	0.601175i
$605$	3.26743	+	22.7255i	0.132840	+	0.923923i
$606$	−3.74754	−	2.07243i	−0.152233	−	0.0841866i
$607$	8.82162	−	5.66931i	0.358058	−	0.230110i	−0.349227	−	0.937038i	$-0.613556\pi$
$607$	8.82162	−	5.66931i	0.358058	−	0.230110i	0.707286	+	0.706928i	$0.249919\pi$
$608$	0.592205	−	4.11887i	0.0240171	−	0.167042i
$609$	9.90498	−	13.0849i	0.401370	−	0.530228i
$610$	3.28259	−	7.18787i	0.132908	−	0.291028i
$611$	−0.162547	−	0.0233708i	−0.00657596	−	0.000945481i
$612$	18.3720	−	2.44105i	0.742644	−	0.0986735i
$613$	0.494372	−	1.68368i	0.0199675	−	0.0680030i	−0.948907	−	0.315557i	$-0.897809\pi$
$613$	0.494372	−	1.68368i	0.0199675	−	0.0680030i	0.968874	+	0.247554i	$0.0796268\pi$
$614$	23.4636	−	3.37355i	0.946913	−	0.136146i
$615$	−7.38665	+	3.98224i	−0.297858	+	0.160579i
$616$	16.3249	+	10.4914i	0.657749	+	0.422709i
$617$	2.28628	−	2.63851i	0.0920423	−	0.106222i	−0.707860	−	0.706353i	$-0.750339\pi$
$617$	2.28628	−	2.63851i	0.0920423	−	0.106222i	0.799902	+	0.600130i	$0.204885\pi$
$618$	21.2208	−	1.40361i	0.853624	−	0.0564615i
$619$	−18.8744	+	8.61963i	−0.758625	+	0.346452i	−0.756887	−	0.653546i	$-0.773280\pi$
$619$	−18.8744	+	8.61963i	−0.758625	+	0.346452i	−0.00173796	+	0.999998i	$0.500553\pi$
$620$	4.24427			0.170454
$621$	−10.3353	+	22.6756i	−0.414739	+	0.909940i
$622$	−12.1232			−0.486096
$623$	−8.72735	+	3.98565i	−0.349654	+	0.159682i
$624$	0.306345	−	0.0202627i	0.0122636	−	0.000811156i
$625$	0.849145	−	0.979966i	0.0339658	−	0.0391986i
$626$	23.4680	+	15.0820i	0.937972	+	0.602798i
$627$	33.0424	−	17.8136i	1.31959	−	0.711406i
$628$	10.2316	−	1.47108i	0.408285	−	0.0587025i
$629$	−16.2123	+	55.2141i	−0.646427	+	2.20153i
$630$	15.7755	−	2.09606i	0.628511	−	0.0835089i
$631$	31.7167	+	4.56018i	1.26262	+	0.181538i	0.740922	−	0.671591i	$-0.234389\pi$
$631$	31.7167	+	4.56018i	1.26262	+	0.181538i	0.521701	+	0.853129i	$0.325298\pi$
$632$	−1.45677	+	3.18989i	−0.0579473	+	0.126887i
$633$	7.62251	−	10.0697i	0.302967	−	0.400234i
$634$	−0.828130	+	5.75977i	−0.0328892	+	0.228750i
$635$	20.6031	−	13.2408i	0.817607	−	0.525444i
$636$	0.910956	+	0.503768i	0.0361217	+	0.0199757i
$637$	−0.173613	−	1.20751i	−0.00687880	−	0.0478431i
$638$	−8.67336	−	10.0096i	−0.343382	−	0.396283i
$639$	−22.7197	+	14.2597i	−0.898778	+	0.564106i
$640$	−1.07599	−	0.932352i	−0.0425323	−	0.0368544i
$641$	−33.4201	+	9.81303i	−1.32001	+	0.387591i	−0.864498	−	0.502636i	$-0.832364\pi$
$641$	−33.4201	+	9.81303i	−1.32001	+	0.387591i	−0.455517	+	0.890227i	$0.650545\pi$
$642$	−5.84437	+	1.23864i	−0.230659	+	0.0488852i
$643$		−	26.7667i		−	1.05557i	−0.849377	−	0.527787i	$-0.823022\pi$
$643$		−	26.7667i		−	1.05557i	0.849377	−	0.527787i	$-0.176978\pi$
$644$	−6.52488	−	16.6349i	−0.257116	−	0.655506i
$645$	0.223767	−	1.00277i	0.00881080	−	0.0394839i
$646$	10.6792	+	23.3842i	0.420168	+	0.920039i
$647$	−4.18004	−	14.2359i	−0.164334	−	0.559672i	−0.999946	−	0.0103516i	$-0.996705\pi$
$647$	−4.18004	−	14.2359i	−0.164334	−	0.559672i	0.835612	−	0.549320i	$-0.185113\pi$
$648$	−0.192683	+	8.99794i	−0.00756932	+	0.353472i
$649$	42.5689	−	66.2385i	1.67097	−	2.60009i
$650$	0.398259	−	0.345093i	0.0156210	−	0.0135357i
$651$	19.1815	+	1.47513i	0.751783	+	0.0578148i
$652$	5.67383	+	1.66599i	0.222204	+	0.0652451i
$653$	14.9750	+	23.3015i	0.586016	+	0.911858i	0.999999	+	0.00157377i	$0.000500946\pi$
$653$	14.9750	+	23.3015i	0.586016	+	0.911858i	−0.413983	+	0.910285i	$0.635863\pi$
$654$	−3.30807	+	8.72635i	−0.129356	+	0.341227i
$655$	10.5498	+	4.81795i	0.412217	+	0.188253i
$656$	3.09546	+	1.41365i	0.120857	+	0.0551936i
$657$	−18.9623	+	28.8227i	−0.739788	+	1.12448i
$658$	1.86623	+	2.90391i	0.0727532	+	0.113206i
$659$	−13.7613	−	4.04069i	−0.536065	−	0.157403i	0.00248404	−	0.999997i	$-0.499209\pi$
$659$	−13.7613	−	4.04069i	−0.536065	−	0.157403i	−0.538549	+	0.842594i	$0.681027\pi$
$660$	0.984805	−	12.8057i	0.0383335	−	0.498461i
$661$	−11.7371	+	10.1703i	−0.456521	+	0.395577i	−0.852538	−	0.522666i	$-0.824938\pi$
$661$	−11.7371	+	10.1703i	−0.456521	+	0.395577i	0.396017	+	0.918243i	$0.370392\pi$
$662$	10.1329	−	15.7671i	0.393827	−	0.612807i
$663$	−1.52443	+	1.12849i	−0.0592040	+	0.0438270i
$664$	−4.15359	−	14.1458i	−0.161191	−	0.548965i
$665$	9.16992	+	20.0793i	0.355594	+	0.778643i
$666$	−25.2934	−	11.8800i	−0.980098	−	0.460339i
$667$	1.07428	+	12.1484i	0.0415963	+	0.470387i
$668$		−	3.78119i		−	0.146299i
$669$	3.11811	+	14.7124i	0.120553	+	0.568815i
$670$	1.23487	−	0.362590i	0.0477072	−	0.0140081i
$671$	−21.8461	−	18.9298i	−0.843359	−	0.730775i
$672$	−4.53878	−	4.58763i	−0.175087	−	0.176972i
$673$	1.39266	+	1.60721i	0.0536829	+	0.0619534i	0.781956	−	0.623334i	$-0.214222\pi$
$673$	1.39266	+	1.60721i	0.0536829	+	0.0619534i	−0.728273	+	0.685287i	$0.759677\pi$
$674$	−0.948501	−	6.59697i	−0.0365349	−	0.254106i
$675$	9.05785	+	12.5138i	0.348637	+	0.481656i
$676$	10.9099	−	7.01134i	0.419610	−	0.269667i
$677$	5.13499	−	35.7146i	0.197354	−	1.37263i	−0.614570	−	0.788862i	$-0.710671\pi$
$677$	5.13499	−	35.7146i	0.197354	−	1.37263i	0.811924	−	0.583763i	$-0.198420\pi$
$678$	−19.6956	−	14.9091i	−0.756406	−	0.572582i
$679$	−13.9464	+	30.5383i	−0.535212	+	1.17195i
$680$	8.70608	+	1.25175i	0.333863	+	0.0480022i
$681$	35.2268	−	12.9245i	1.34989	−	0.495270i
$682$	4.37423	−	14.8973i	0.167498	−	0.570445i
$683$	−27.0120	+	3.88374i	−1.03359	+	0.148607i	−0.638170	−	0.769895i	$-0.720308\pi$
$683$	−27.0120	+	3.88374i	−1.03359	+	0.148607i	−0.395415	+	0.918503i	$0.629399\pi$
$684$	−12.0150	+	3.38863i	−0.459404	+	0.129568i
$685$	10.3747	+	6.66742i	0.396397	+	0.254749i
$686$	0.287159	−	0.331399i	0.0109638	−	0.0126529i
$687$	−1.11682	−	16.8848i	−0.0426093	−	0.644197i
$688$	−0.378989	+	0.173078i	−0.0144488	+	0.00659855i
$689$	−0.106531			−0.00405851
$690$	−7.64187	+	9.02593i	−0.290921	+	0.343611i
$691$	7.06754			0.268862			0.134431	−	0.990923i	$-0.457079\pi$
$691$	7.06754			0.268862			0.134431	+	0.990923i	$0.457079\pi$
$692$	19.5306	−	8.91933i	0.742442	−	0.339062i
$693$	8.90145	−	57.5318i	0.338138	−	2.18545i
$694$	−5.55858	+	6.41494i	−0.211001	+	0.243508i
$695$	9.25693	+	5.94907i	0.351135	+	0.225661i
$696$	2.09018	+	3.87707i	0.0792280	+	0.146960i
$697$	−20.8090	+	2.99188i	−0.788196	+	0.113325i
$698$	−2.46602	+	8.39848i	−0.0933401	+	0.317887i
$699$	4.75475	+	12.9594i	0.179841	+	0.490170i
$700$	−10.9642	−	1.57641i	−0.414408	−	0.0595829i
$701$	14.3902	−	31.5101i	0.543509	−	1.19012i	−0.416239	−	0.909255i	$-0.636652\pi$
$701$	14.3902	−	31.5101i	0.543509	−	1.19012i	0.959748	−	0.280863i	$-0.0906208\pi$
$702$	−0.428372	−	0.815364i	−0.0161678	−	0.0307739i
$703$	5.51626	−	38.3665i	0.208050	−	1.44702i
$704$	−4.38147	+	2.81580i	−0.165133	+	0.106124i
$705$	1.10563	−	1.99929i	0.0416403	−	0.0752975i
$706$	3.60884	+	25.1000i	0.135820	+	0.944652i
$707$	−6.03263	−	6.96203i	−0.226880	−	0.261834i
$708$	−18.6144	+	18.4162i	−0.699571	+	0.692122i
$709$	−16.8108	−	14.5667i	−0.631344	−	0.547063i	0.279326	−	0.960196i	$-0.409889\pi$
$709$	−16.8108	−	14.5667i	−0.631344	−	0.547063i	−0.910671	+	0.413133i	$0.864434\pi$
$710$	−12.2145	+	3.58649i	−0.458401	+	0.134599i
$711$	10.5198	+	0.112623i	0.394522	+	0.00422370i
$712$		−	2.57505i		−	0.0965041i
$713$	−11.2995	+	8.75876i	−0.423171	+	0.328018i
$714$	38.9111	+	8.68300i	1.45621	+	0.324953i
$715$	0.546014	+	1.19560i	0.0204198	+	0.0447130i
$716$	−4.67404	−	15.9183i	−0.174677	−	0.594896i
$717$	−29.9308	−	40.4322i	−1.11779	−	1.50997i
$718$	−4.44168	+	6.91139i	−0.165762	+	0.257931i
$719$	−3.63258	+	3.14765i	−0.135472	+	0.117387i	−0.719961	−	0.694014i	$-0.755840\pi$
$719$	−3.63258	+	3.14765i	−0.135472	+	0.117387i	0.584489	+	0.811402i	$0.301295\pi$
$720$	−1.24715	+	4.08509i	−0.0464784	+	0.152242i
$721$	43.8956	+	12.8889i	1.63476	+	0.480008i
$722$	0.910530	+	1.41681i	0.0338864	+	0.0527283i
$723$	6.51538	+	2.46992i	0.242310	+	0.0918572i
$724$	15.7530	+	7.19413i	0.585454	+	0.267368i
$725$	6.87703	+	3.14064i	0.255407	+	0.116640i
$726$	−26.1173	−	9.90082i	−0.969304	−	0.367454i
$727$	16.0082	+	24.9093i	0.593712	+	0.923833i	0.999949	+	0.0100660i	$0.00320416\pi$
$727$	16.0082	+	24.9093i	0.593712	+	0.923833i	−0.406238	+	0.913767i	$0.633159\pi$
$728$	0.633681	+	0.186066i	0.0234858	+	0.00689605i
$729$	24.9076	−	10.4218i	0.922502	−	0.385992i
$730$	−12.3742	+	10.7223i	−0.457991	+	0.396852i
$731$	1.39157	−	2.16532i	0.0514690	−	0.0800873i
$732$	5.71965	+	7.72642i	0.211404	+	0.285577i
$733$	−1.67520	−	5.70521i	−0.0618749	−	0.210727i	0.922753	−	0.385392i	$-0.125934\pi$
$733$	−1.67520	−	5.70521i	−0.0618749	−	0.210727i	−0.984628	+	0.174665i	$0.944116\pi$
$734$	3.20020	+	7.00747i	0.118122	+	0.258650i
$735$	16.5643	+	3.69631i	0.610984	+	0.136341i
$736$	4.78868	+	0.261718i	0.176513	+	0.00964705i
$737$		−	4.70805i		−	0.173423i
$738$	0.109289	−	10.2083i	0.00402299	−	0.375774i
$739$	−4.25778	+	1.25020i	−0.156625	+	0.0459893i	−0.359105	−	0.933297i	$-0.616918\pi$
$739$	−4.25778	+	1.25020i	−0.156625	+	0.0459893i	0.202480	+	0.979286i	$0.435100\pi$
$740$	−10.0226	−	8.68466i	−0.368439	−	0.319255i
$741$	0.908192	−	0.898521i	0.0333633	−	0.0330080i
$742$	1.46642	+	1.69234i	0.0538339	+	0.0621277i
$743$	4.49128	+	31.2376i	0.164769	+	1.14600i	0.889491	+	0.456953i	$0.151059\pi$
$743$	4.49128	+	31.2376i	0.164769	+	1.14600i	−0.724721	+	0.689042i	$0.758032\pi$
$744$	−2.49876	+	4.51846i	−0.0916089	+	0.165655i
$745$	6.35945	−	4.08697i	0.232992	−	0.149735i
$746$	2.02366	−	14.0749i	0.0740914	−	0.515317i
$747$	−33.7343	+	28.6044i	−1.23427	+	1.04658i
$748$	13.3663	−	29.2680i	0.488719	−	1.07014i
$749$	−12.7206	−	1.82894i	−0.464799	−	0.0668280i
$750$	6.77220	+	18.4581i	0.247286	+	0.673995i
$751$	−1.59683	+	5.43829i	−0.0582690	+	0.198446i	−0.983483	−	0.180999i	$-0.942067\pi$
$751$	−1.59683	+	5.43829i	−0.0582690	+	0.198446i	0.925214	+	0.379445i	$0.123885\pi$
$752$	−0.917027	+	0.131849i	−0.0334405	+	0.00480802i
$753$	4.13888	+	7.67720i	0.150829	+	0.279773i
$754$	−0.379202	−	0.243698i	−0.0138097	−	0.00887498i
$755$	−18.2273	+	21.0354i	−0.663358	+	0.765556i
$756$	−7.05615	+	18.0287i	−0.256630	+	0.655697i
$757$	20.8632	−	9.52792i	0.758287	−	0.346298i	0.00153402	−	0.999999i	$-0.499512\pi$
$757$	20.8632	−	9.52792i	0.758287	−	0.346298i	0.756753	+	0.653701i	$0.226784\pi$
$758$	18.8266			0.683811
$759$	23.8049	+	36.1250i	0.864062	+	1.31126i
$760$	−5.92451			−0.214905
$761$	11.4464	−	5.22740i	0.414932	−	0.189493i	−0.197000	−	0.980403i	$-0.563120\pi$
$761$	11.4464	−	5.22740i	0.414932	−	0.189493i	0.611932	+	0.790910i	$0.290393\pi$
$762$	1.96640	+	29.7294i	0.0712353	+	1.07698i
$763$	−13.1465	+	15.1719i	−0.475935	+	0.549258i
$764$	5.84313	+	3.75515i	0.211397	+	0.135857i
$765$	−7.16257	−	25.3961i	−0.258963	−	0.918198i
$766$	20.6252	−	2.96546i	0.745219	−	0.107146i
$767$	0.754963	−	2.57117i	0.0272601	−	0.0928395i
$768$	1.62606	−	0.596594i	0.0586754	−	0.0215277i
$769$	−29.9806	−	4.31056i	−1.08113	−	0.155443i	−0.421347	−	0.906900i	$-0.638443\pi$
$769$	−29.9806	−	4.31056i	−1.08113	−	0.155443i	−0.659783	+	0.751457i	$0.729352\pi$
$770$	11.4772	−	25.1316i	0.413610	−	0.905680i
$771$	20.8023	+	15.7469i	0.749178	+	0.567110i
$772$	3.10724	−	21.6113i	0.111832	−	0.777808i
$773$	15.4317	−	9.91733i	0.555038	−	0.356702i	−0.232857	−	0.972511i	$-0.574807\pi$
$773$	15.4317	−	9.91733i	0.555038	−	0.356702i	0.787895	+	0.615810i	$0.211171\pi$
$774$	0.935809	+	0.828589i	0.0336370	+	0.0297830i
$775$	1.26128	+	8.77239i	0.0453065	+	0.315114i
$776$	−5.90061	−	6.80967i	−0.211820	−	0.244453i
$777$	−42.2778	−	42.7329i	−1.51671	−	1.53303i
$778$	−8.02538	−	6.95403i	−0.287724	−	0.249314i
$779$	13.5870	−	3.98949i	0.486803	−	0.142938i
$780$	−0.0906266	−	0.427611i	−0.00324495	−	0.0153109i
$781$			46.5687i			1.66636i
$782$	−25.7615	+	14.6339i	−0.921228	+	0.523308i
$783$	8.08757	−	10.4497i	0.289026	−	0.373441i
$784$	−2.85901	−	6.26037i	−0.102108	−	0.223585i
$785$	−4.14624	−	14.1208i	−0.147986	−	0.503992i
$786$	−11.3403	+	8.39490i	−0.404495	+	0.299436i
$787$	3.71957	−	5.78777i	0.132588	−	0.206312i	−0.768611	−	0.639717i	$-0.779052\pi$
$787$	3.71957	−	5.78777i	0.132588	−	0.206312i	0.901199	+	0.433405i	$0.142688\pi$
$788$	1.43141	−	1.24032i	0.0509918	−	0.0441846i
$789$	3.35445	−	43.6189i	0.119422	−	1.55287i
$790$	4.79052	+	1.40662i	0.170439	+	0.0500454i
$791$	−28.7287	−	44.7027i	−1.02147	−	1.58944i
$792$	13.0532	+	8.58762i	0.463826	+	0.305148i
$793$	−0.894885	−	0.408680i	−0.0317783	−	0.0145127i
$794$	11.7590	+	5.37016i	0.417312	+	0.190580i
$795$	0.525357	−	1.38584i	0.0186325	−	0.0491505i
$796$	−5.90835	−	9.19357i	−0.209416	−	0.325857i
$797$	10.7851	+	3.16679i	0.382028	+	0.112174i	0.467107	−	0.884201i	$-0.345296\pi$
$797$	10.7851	+	3.16679i	0.382028	+	0.112174i	−0.0850793	+	0.996374i	$0.527114\pi$
$798$	−26.7752	−	2.05911i	−0.947832	−	0.0728917i
$799$	4.32552	−	3.74808i	0.153026	−	0.132598i
$800$	1.60730	−	2.50102i	0.0568268	−	0.0884242i
$801$	−7.06100	+	3.13373i	−0.249488	+	0.110725i
$802$	0.0114305	+	0.0389286i	0.000403623	+	0.00137462i
$803$	24.8819	+	54.4839i	0.878065	+	1.92269i
$804$	−0.340998	+	1.52812i	−0.0120261	+	0.0538925i
$805$	−22.1206	+	12.5657i	−0.779649	+	0.442884i
$806$		−	0.528409i		−	0.0186124i
$807$	−23.2572	+	4.92907i	−0.818694	+	0.173512i
$808$	2.37229	−	0.696569i	0.0834570	−	0.0245052i
$809$	15.5590	+	13.4819i	0.547024	+	0.473999i	0.883982	−	0.467521i	$-0.154853\pi$
$809$	15.5590	+	13.4819i	0.547024	+	0.473999i	−0.336958	+	0.941520i	$0.609398\pi$
$810$	12.7194	−	1.55162i	0.446913	−	0.0545183i
$811$	12.6718	+	14.6240i	0.444967	+	0.513519i	0.933280	−	0.359149i	$-0.116933\pi$
$811$	12.6718	+	14.6240i	0.444967	+	0.513519i	−0.488313	+	0.872668i	$0.662388\pi$
$812$	1.34843	+	9.37850i	0.0473205	+	0.329121i
$813$	−29.9213	−	16.5468i	−1.04938	−	0.580320i
$814$	−40.8124	+	26.2286i	−1.43048	+	0.919311i
$815$	1.19816	−	8.33340i	0.0419698	−	0.291906i
$816$	−6.45820	+	8.53158i	−0.226082	+	0.298665i
$817$	−0.720219	+	1.57706i	−0.0251973	+	0.0551743i
$818$	−9.90094	−	1.42354i	−0.346178	−	0.0497729i
$819$	−0.260958	−	1.96404i	−0.00911860	−	0.0686291i
$820$	1.36498	−	4.64870i	0.0476672	−	0.162340i
$821$	23.9736	−	3.44689i	0.836685	−	0.120297i	0.289363	−	0.957219i	$-0.406556\pi$
$821$	23.9736	−	3.44689i	0.836685	−	0.120297i	0.547322	+	0.836922i	$0.315647\pi$
$822$	−13.2061	+	7.11960i	−0.460617	+	0.248324i
$823$	−28.5116	−	18.3233i	−0.993853	−	0.638710i	−0.0606870	−	0.998157i	$-0.519329\pi$
$823$	−28.5116	−	18.3233i	−0.993853	−	0.638710i	−0.933166	+	0.359447i	$0.882966\pi$
$824$	−8.04076	+	9.27954i	−0.280113	+	0.323268i
$825$	26.7605	−	1.77003i	0.931682	−	0.0616245i
$826$	−51.2374	+	23.3993i	−1.78278	+	0.814167i
$827$	43.2784			1.50494			0.752469	−	0.658628i	$-0.228863\pi$
$827$	43.2784			1.50494			0.752469	+	0.658628i	$0.228863\pi$
$828$	−5.10999	−	13.4495i	−0.177584	−	0.467401i
$829$	−43.4745			−1.50993			−0.754967	−	0.655763i	$-0.772347\pi$
$829$	−43.4745			−1.50993			−0.754967	+	0.655763i	$0.772347\pi$
$830$	−19.0934	+	8.71966i	−0.662742	+	0.302664i
$831$	−34.3600	+	2.27268i	−1.19193	+	0.0788385i
$832$	−0.116077	+	0.133960i	−0.00402425	+	0.00464424i
$833$	35.7681	+	22.9868i	1.23929	+	0.796444i
$834$	−11.7833	+	6.35253i	−0.408022	+	0.219970i
$835$	−5.32864	+	0.766143i	−0.184405	+	0.0265135i
$836$	−6.10592	+	20.7949i	−0.211178	+	0.719205i
$837$	15.4309	+	1.35301i	0.533369	+	0.0467667i
$838$	−8.96141	−	1.28846i	−0.309567	−	0.0445090i
$839$	−5.16784	+	11.3160i	−0.178414	+	0.390672i	−0.977618	−	0.210388i	$-0.932527\pi$
$839$	−5.16784	+	11.3160i	−0.178414	+	0.390672i	0.799204	+	0.601060i	$0.205255\pi$
$840$	−5.54547	+	7.32582i	−0.191337	+	0.252765i
$841$	−3.20680	+	22.3038i	−0.110579	+	0.769097i
$842$	−8.29269	+	5.32939i	−0.285785	+	0.183663i
$843$	−13.4858	−	7.45778i	−0.464475	−	0.256860i
$844$	1.03770	+	7.21735i	0.0357191	+	0.248431i
$845$	−12.0913	−	13.9541i	−0.415953	−	0.480035i
$846$	1.47752	+	2.35411i	0.0507983	+	0.0809359i
$847$	−45.4082	−	39.3464i	−1.56024	−	1.35196i
$848$	−0.576660	+	0.169323i	−0.0198026	+	0.00581457i
$849$	37.6431	−	7.97797i	1.29191	−	0.273803i
$850$			18.3664i			0.629963i
$851$	44.6056	+	2.43785i	1.52906	+	0.0835683i
$852$	3.37292	−	15.1151i	0.115554	−	0.517834i
$853$	−20.8249	−	45.6003i	−0.713032	−	1.56132i	−0.823419	−	0.567434i	$-0.807936\pi$
$853$	−20.8249	−	45.6003i	−0.713032	−	1.56132i	0.110387	−	0.993889i	$-0.464791\pi$
$854$	5.82601	+	19.8416i	0.199362	+	0.678965i
$855$	7.20989	+	16.2455i	0.246573	+	0.555584i
$856$	1.86478	−	2.90165i	0.0637368	−	0.0991764i
$857$	−2.44036	+	2.11458i	−0.0833611	+	0.0722328i	−0.695545	−	0.718483i	$-0.744837\pi$
$857$	−2.44036	+	2.11458i	−0.0833611	+	0.0722328i	0.612183	+	0.790716i	$0.290291\pi$
$858$	−1.59430	−	0.122608i	−0.0544286	−	0.00418576i
$859$	−0.414426	−	0.121687i	−0.0141400	−	0.00415189i	0.274655	−	0.961543i	$-0.411436\pi$
$859$	−0.414426	−	0.121687i	−0.0141400	−	0.00415189i	−0.288795	+	0.957391i	$0.593255\pi$
$860$	0.320701	+	0.499021i	0.0109358	+	0.0170165i
$861$	7.78458	−	20.5349i	0.265298	−	0.699827i
$862$	29.2587	+	13.3620i	0.996557	+	0.455112i
$863$	−10.1035	−	4.61411i	−0.343927	−	0.157066i	0.235961	−	0.971763i	$-0.424176\pi$
$863$	−10.1035	−	4.61411i	−0.343927	−	0.157066i	−0.579888	+	0.814696i	$0.696904\pi$
$864$	−3.61476	−	3.73276i	−0.122977	−	0.126991i
$865$	−16.5268	−	25.7163i	−0.561929	−	0.874379i
$866$	−6.50840	−	1.91104i	−0.221164	−	0.0649397i
$867$	2.81095	−	36.5516i	0.0954650	−	1.24136i
$868$	−8.39423	+	7.27364i	−0.284919	+	0.246883i
$869$	9.87441	−	15.3649i	0.334966	−	0.521218i
$870$	5.04024	−	3.73115i	0.170880	−	0.126498i
$871$	−0.0451423	−	0.153740i	−0.00152959	−	0.00520930i
$872$	−2.23827	−	4.90112i	−0.0757973	−	0.165973i
$873$	−11.4919	+	24.4670i	−0.388940	+	0.828084i
$874$	15.7729	−	12.2262i	0.533525	−	0.413558i
$875$			42.2943i			1.42981i
$876$	−4.12987	−	19.4863i	−0.139535	−	0.658381i
$877$	−23.1675	+	6.80260i	−0.782311	+	0.229707i	−0.648414	−	0.761288i	$-0.724567\pi$
$877$	−23.1675	+	6.80260i	−0.782311	+	0.229707i	−0.133897	+	0.990995i	$0.542749\pi$
$878$	20.8269	+	18.0466i	0.702874	+	0.609043i
$879$	16.1910	+	16.3653i	0.546108	+	0.551986i
$880$	4.85593	+	5.60404i	0.163693	+	0.188912i
$881$	−0.107225	−	0.745769i	−0.00361251	−	0.0251256i	0.987935	−	0.154866i	$-0.0494946\pi$
$881$	−0.107225	−	0.745769i	−0.00361251	−	0.0251256i	−0.991548	+	0.129741i	$0.958586\pi$
$882$	−13.6871	+	15.4583i	−0.460870	+	0.520507i
$883$	31.6790	−	20.3589i	1.06608	−	0.685130i	0.114781	−	0.993391i	$-0.463383\pi$
$883$	31.6790	−	20.3589i	1.06608	−	0.685130i	0.951302	+	0.308261i	$0.0997468\pi$
$884$	0.155842	−	1.08390i	0.00524152	−	0.0364556i
$885$	29.7246	+	22.5008i	0.999181	+	0.756357i
$886$	−1.58993	+	3.48147i	−0.0534148	+	0.116962i
$887$	−41.2961	−	5.93749i	−1.38659	−	0.199361i	−0.591720	−	0.806144i	$-0.701551\pi$
$887$	−41.2961	−	5.93749i	−1.38659	−	0.199361i	−0.794868	+	0.606782i	$0.792460\pi$
$888$	15.1464	−	5.55715i	0.508281	−	0.186486i
$889$	−18.0568	+	61.4960i	−0.605607	+	2.06251i
$890$	−3.62889	+	0.521755i	−0.121641	+	0.0174893i
$891$	7.66271	−	46.2438i	0.256711	−	1.54922i
$892$	−7.30451	−	4.69433i	−0.244573	−	0.157178i
$893$	−2.52462	+	2.91357i	−0.0844831	+	0.0974987i
$894$	0.606961	+	9.17645i	0.0202998	+	0.306906i
$895$	−21.4858	+	9.81225i	−0.718192	+	0.327987i
$896$	3.72590			0.124473
$897$	1.12372	+	0.951408i	0.0375200	+	0.0317666i
$898$	18.6367			0.621913
$899$	6.89578	−	3.14920i	0.229987	−	0.105032i
$900$	−8.81401	−	1.36372i	−0.293800	−	0.0454575i
$901$	2.43143	−	2.80602i	0.0810028	−	0.0934822i
$902$	−14.9100	−	9.58209i	−0.496449	−	0.319049i
$903$	1.27594	+	2.36673i	0.0424605	+	0.0787599i
$904$	14.1167	−	2.02967i	0.469514	−	0.0675059i
$905$	6.94647	−	23.6575i	0.230908	−	0.786402i
$906$	−11.6633	−	31.7891i	−0.387487	−	1.05612i
$907$	−7.63423	−	1.09764i	−0.253490	−	0.0364464i	0.0143980	−	0.999896i	$-0.495417\pi$
$907$	−7.63423	−	1.09764i	−0.253490	−	0.0364464i	−0.267889	+	0.963450i	$0.586326\pi$
$908$	−8.99950	+	19.7061i	−0.298659	+	0.653971i
$909$	−4.79704	−	5.65733i	−0.159108	−	0.187642i
$910$	0.133817	−	0.930715i	0.00443598	−	0.0308529i
$911$	22.1642	−	14.2441i	0.734333	−	0.471927i	−0.119263	−	0.992863i	$-0.538053\pi$
$911$	22.1642	−	14.2441i	0.734333	−	0.471927i	0.853596	+	0.520936i	$0.174417\pi$
$912$	3.48798	−	6.30726i	0.115499	−	0.208854i
$913$	10.9277	+	76.0039i	0.361655	+	2.51536i
$914$	−16.3286	−	18.8442i	−0.540101	−	0.623310i
$915$	9.72954	−	9.62593i	0.321649	−	0.318224i
$916$	7.38350	+	6.39784i	0.243958	+	0.211391i
$917$	−29.1221	+	8.55101i	−0.961696	+	0.282379i
$918$	31.2537	+	7.32633i	1.03152	+	0.241805i
$919$			6.36736i			0.210040i	0.994470	+	0.105020i	$0.0334906\pi$
$919$			6.36736i			0.210040i	−0.994470	+	0.105020i	$0.966509\pi$
$920$	−0.601455	−	6.80148i	−0.0198294	−	0.224238i
$921$	40.0724	+	8.94213i	1.32043	+	0.294653i
$922$	−4.58180	−	10.0327i	−0.150894	−	0.330411i
$923$	0.446516	+	1.52069i	0.0146973	+	0.0500543i
$924$	19.9981	+	27.0146i	0.657890	+	0.888715i
$925$	14.9717	−	23.2964i	0.492267	−	0.765982i
$926$	22.2088	−	19.2441i	0.729828	−	0.632400i
$927$	35.2305	+	10.7556i	1.15712	+	0.353260i
$928$	−2.43999	−	0.716445i	−0.0800965	−	0.0235185i
$929$	−16.5754	−	25.7918i	−0.543821	−	0.846202i	0.455202	−	0.890388i	$-0.349567\pi$
$929$	−16.5754	−	25.7918i	−0.543821	−	0.846202i	−0.999023	+	0.0441861i	$0.985931\pi$
$930$	6.87394	+	2.60584i	0.225405	+	0.0854490i
$931$	−26.0508	−	11.8970i	−0.853782	−	0.389909i
$932$	−7.24960	−	3.31078i	−0.237469	−	0.108448i
$933$	−19.6345	−	7.44326i	−0.642806	−	0.243681i
$934$	−12.6636	−	19.7050i	−0.414366	−	0.644766i
$935$	−43.9542	−	12.9061i	−1.43746	−	0.422075i
$936$	0.508591	+	0.155269i	0.0166238	+	0.00507512i
$937$	14.6774	−	12.7180i	0.479488	−	0.415479i	−0.381293	−	0.924454i	$-0.624521\pi$
$937$	14.6774	−	12.7180i	0.479488	−	0.415479i	0.860781	+	0.508975i	$0.169976\pi$
$938$	−1.82091	+	2.83339i	−0.0594547	+	0.0925134i
$939$	28.7486	+	38.8351i	0.938173	+	1.26734i
$940$	0.371615	+	1.26560i	0.0121207	+	0.0412794i
$941$	−17.5485	−	38.4259i	−0.572065	−	1.25265i	−0.945691	−	0.325068i	$-0.894613\pi$
$941$	−17.5485	−	38.4259i	−0.572065	−	1.25265i	0.373626	−	0.927579i	$-0.378114\pi$
$942$	17.4741	+	3.89933i	0.569336	+	0.127047i
$943$	5.95937	+	15.1931i	0.194064	+	0.494757i
$944$		−	15.1179i		−	0.492045i
$945$	26.8366	+	6.29091i	0.872995	+	0.204643i
$946$	2.08207	−	0.611351i	0.0676939	−	0.0198767i
$947$	22.3867	+	19.3982i	0.727471	+	0.630358i	0.937761	−	0.347282i	$-0.112895\pi$
$947$	22.3867	+	19.3982i	0.727471	+	0.630358i	−0.210289	+	0.977639i	$0.567441\pi$
$948$	−4.31785	+	4.27187i	−0.140237	+	0.138744i
$949$	1.33492	+	1.54059i	0.0433335	+	0.0500095i
$950$	−1.76060	−	12.2453i	−0.0571215	−	0.397289i
$951$	−4.87754	+	8.81997i	−0.158165	+	0.286007i
$952$	−19.3639	+	12.4444i	−0.627587	+	0.403326i
$953$	−1.32506	+	9.21596i	−0.0429228	+	0.298534i	0.957040	+	0.289954i	$0.0936402\pi$
$953$	−1.32506	+	9.21596i	−0.0429228	+	0.298534i	−0.999963	+	0.00857985i	$0.997269\pi$
$954$	1.16607	+	1.37519i	0.0377529	+	0.0445234i
$955$	4.10801	−	8.99529i	0.132932	−	0.291081i
$956$	28.7481	+	4.13335i	0.929781	+	0.133682i
$957$	−7.90165	−	21.5365i	−0.255424	−	0.696176i
$958$	−0.117419	+	0.399891i	−0.00379362	+	0.0129199i
$959$	−31.9452	+	4.59303i	−1.03156	+	0.148317i
$960$	−1.17022	−	2.17064i	−0.0377687	−	0.0700572i
$961$	−18.6028	−	11.9553i	−0.600091	−	0.385655i
$962$	−1.08124	+	1.24781i	−0.0348604	+	0.0402311i
$963$	−10.2259	−	1.58218i	−0.329526	−	0.0509850i
$964$	−3.65934	+	1.67116i	−0.117859	+	0.0538246i
$965$	−31.0853			−1.00067
$966$	−0.354305	−	30.9476i	−0.0113996	−	0.995723i
$967$	18.0422			0.580197			0.290099	−	0.956997i	$-0.406312\pi$
$967$	18.0422			0.580197			0.290099	+	0.956997i	$0.406312\pi$
$968$	14.6687	−	6.69896i	0.471469	−	0.215313i
$969$	2.93870	+	44.4293i	0.0944046	+	1.42727i
$970$	−8.40094	+	9.69520i	−0.269738	+	0.311294i
$971$	3.43406	+	2.20693i	0.110204	+	0.0708239i	0.594582	−	0.804035i	$-0.297318\pi$
$971$	3.43406	+	2.20693i	0.110204	+	0.0708239i	−0.484378	+	0.874859i	$0.660954\pi$
$972$	−5.83651	+	14.4546i	−0.187206	+	0.463631i
$973$	−28.5034	+	4.09817i	−0.913778	+	0.131381i
$974$	6.75158	−	22.9938i	0.216334	−	0.736768i
$975$	0.856889	−	0.314389i	0.0274424	−	0.0100685i
$976$	−5.49364	−	0.789866i	−0.175847	−	0.0252830i
$977$	−22.6794	+	49.6610i	−0.725579	+	1.58880i	0.0803378	+	0.996768i	$0.474400\pi$
$977$	−22.6794	+	49.6610i	−0.725579	+	1.58880i	−0.805917	+	0.592029i	$0.798327\pi$
$978$	8.16637	+	6.18175i	0.261132	+	0.197671i
$979$	−1.90866	+	13.2750i	−0.0610010	+	0.424272i
$980$	−8.24313	+	5.29754i	−0.263317	+	0.169224i
$981$	−10.7154	+	12.1020i	−0.342116	+	0.386387i
$982$	−1.85487	−	12.9009i	−0.0591912	−	0.411684i
$983$	−14.4645	−	16.6930i	−0.461347	−	0.532423i	0.476638	−	0.879100i	$-0.341855\pi$
$983$	−14.4645	−	16.6930i	−0.461347	−	0.532423i	−0.937984	+	0.346677i	$0.887310\pi$
$984$	4.14541	+	4.19003i	0.132151	+	0.133573i
$985$	−2.03795	−	1.76590i	−0.0649346	−	0.0562661i
$986$	15.0738	−	4.42607i	0.480047	−	0.140955i
$987$	1.23960	+	5.84892i	0.0394570	+	0.186173i
$988$			0.737598i			0.0234661i
$989$	−1.88362	−	0.666726i	−0.0598956	−	0.0212006i
$990$	9.45726	−	20.1352i	0.300572	−	0.639940i
$991$	−4.83807	−	10.5939i	−0.153686	−	0.336526i	0.817091	−	0.576509i	$-0.195585\pi$
$991$	−4.83807	−	10.5939i	−0.153686	−	0.336526i	−0.970777	+	0.239983i	$0.922858\pi$
$992$	−0.839864	−	2.86031i	−0.0266657	−	0.0908151i
$993$	26.0916	−	19.3149i	0.827992	−	0.612939i
$994$	18.0112	−	28.0259i	0.571279	−	0.888928i
$995$	−11.7589	+	10.1891i	−0.372782	+	0.323017i
$996$	1.95800	−	25.4605i	0.0620417	−	0.806747i
$997$	19.6391	+	5.76656i	0.621977	+	0.182629i	0.577512	−	0.816382i	$-0.304024\pi$
$997$	19.6391	+	5.76656i	0.621977	+	0.182629i	0.0444645	+	0.999011i	$0.485842\pi$
$998$	24.0053	+	37.3530i	0.759874	+	1.18239i
$999$	−33.6708	−	34.7699i	−1.06530	−	1.10007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.f.a.65.1	yes	80
3.2	odd	2	inner	138.2.f.a.65.5	yes	80
23.17	odd	22	inner	138.2.f.a.17.5	yes	80
69.17	even	22	inner	138.2.f.a.17.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.17.1	✓	80	69.17	even	22	inner
138.2.f.a.17.5	yes	80	23.17	odd	22	inner
138.2.f.a.65.1	yes	80	1.1	even	1	trivial
138.2.f.a.65.5	yes	80	3.2	odd	2	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.909632 + 0.415415i) q^{2} +(-1.72827 + 0.114314i) q^{3} +(0.654861 - 0.755750i) q^{4} +(-1.19773 - 0.769732i) q^{5} +(1.52461 - 0.821935i) q^{6} +(3.68797 - 0.530250i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(2.97386 - 0.395131i) q^{9} +O(q^{10})\)	\(q+(-0.909632 + 0.415415i) q^{2} +(-1.72827 + 0.114314i) q^{3} +(0.654861 - 0.755750i) q^{4} +(-1.19773 - 0.769732i) q^{5} +(1.52461 - 0.821935i) q^{6} +(3.68797 - 0.530250i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(2.97386 - 0.395131i) q^{9} +(1.40925 + 0.202619i) q^{10} +(2.16359 - 4.73760i) q^{11} +(-1.04539 + 1.38100i) q^{12} +(0.0252260 - 0.175451i) q^{13} +(-3.13442 + 2.01437i) q^{14} +(2.15799 + 1.19339i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(4.04561 + 4.66888i) q^{17} +(-2.54098 + 1.59481i) q^{18} +(-3.14485 - 2.72503i) q^{19} +(-1.36607 + 0.401114i) q^{20} +(-6.31321 + 1.33800i) q^{21} +5.20826i q^{22} +(2.80913 - 3.88700i) q^{23} +(0.377228 - 1.69047i) q^{24} +(-1.23501 - 2.70430i) q^{25} +(0.0499385 + 0.170075i) q^{26} +(-5.09449 + 1.02285i) q^{27} +(2.01437 - 3.13442i) q^{28} +(-1.92187 + 1.66531i) q^{29} +(-2.45873 - 0.189085i) q^{30} +(-2.86031 - 0.839864i) q^{31} +(0.540641 + 0.841254i) q^{32} +(-3.19770 + 8.43520i) q^{33} +(-5.61954 - 2.56636i) q^{34} +(-4.82533 - 2.20366i) q^{35} +(1.64885 - 2.50625i) q^{36} +(5.03596 + 7.83610i) q^{37} +(3.99267 + 1.17235i) q^{38} +(-0.0235410 + 0.306111i) q^{39} +(1.07599 - 0.932352i) q^{40} +(-1.83979 + 2.86277i) q^{41} +(5.18687 - 3.83970i) q^{42} +(-0.117381 - 0.399763i) q^{43} +(-2.16359 - 4.73760i) q^{44} +(-3.86602 - 1.81582i) q^{45} +(-0.940555 + 4.70270i) q^{46} -0.926457i q^{47} +(0.359109 + 1.69441i) q^{48} +(6.60353 - 1.93897i) q^{49} +(2.24682 + 1.94688i) q^{50} +(-7.52564 - 7.60664i) q^{51} +(-0.116077 - 0.133960i) q^{52} +(-0.0855320 - 0.594888i) q^{53} +(4.20920 - 3.04674i) q^{54} +(-6.23807 + 4.00896i) q^{55} +(-0.530250 + 3.68797i) q^{56} +(5.74667 + 4.35009i) q^{57} +(1.05640 - 2.31319i) q^{58} +(14.9640 + 2.15150i) q^{59} +(2.31509 - 0.849396i) q^{60} +(1.56365 - 5.32531i) q^{61} +(2.95072 - 0.424250i) q^{62} +(10.7580 - 3.03413i) q^{63} +(-0.841254 - 0.540641i) q^{64} +(-0.165264 + 0.190725i) q^{65} +(-0.595376 - 9.00130i) q^{66} +(0.822269 - 0.375518i) q^{67} +6.17782 q^{68} +(-4.41061 + 7.03893i) q^{69} +5.30471 q^{70} +(-8.13332 + 3.71436i) q^{71} +(-0.458709 + 2.96472i) q^{72} +(-7.53110 + 8.69136i) q^{73} +(-7.83610 - 5.03596i) q^{74} +(2.44358 + 4.53260i) q^{75} +(-4.11887 + 0.592205i) q^{76} +(5.46714 - 18.6194i) q^{77} +(-0.105749 - 0.288227i) q^{78} +(3.47110 + 0.499068i) q^{79} +(-0.591443 + 1.29508i) q^{80} +(8.68774 - 2.35013i) q^{81} +(0.484294 - 3.36834i) q^{82} +(-12.4026 + 7.97068i) q^{83} +(-3.12308 + 5.64742i) q^{84} +(-1.25175 - 8.70608i) q^{85} +(0.272841 + 0.314875i) q^{86} +(3.13115 - 3.09781i) q^{87} +(3.93614 + 3.41068i) q^{88} +(-2.47074 + 0.725476i) q^{89} +(4.27098 + 0.0457245i) q^{90} -0.660433i q^{91} +(-1.09801 - 4.66844i) q^{92} +(5.03941 + 1.12454i) q^{93} +(0.384864 + 0.842735i) q^{94} +(1.66913 + 5.68453i) q^{95} +(-1.03054 - 1.39211i) q^{96} +(-4.87143 + 7.58010i) q^{97} +(-5.20130 + 4.50695i) q^{98} +(4.56225 - 14.9439i) 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

L-functions

Modular forms

Varieties

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Representations

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Database

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