LMFDB - Embedded newform 138.2.f.a.17.1

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			17.1
Character	$\chi$	$=$	138.17
Dual form			138.2.f.a.65.1

$q$-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 $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{7}{22}\right)$

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	−0.780331	−	0.625366i	$-0.784950\pi$
$5$	−1.19773	+	0.769732i	−0.535640	+	0.344235i	0.244692	+	0.969601i	$0.421313\pi$
$6$	1.52461	+	0.821935i	0.622418	+	0.335553i
$7$	3.68797	+	0.530250i	1.39392	+	0.200416i	0.798015	−	0.602637i	$-0.205883\pi$
$7$	3.68797	+	0.530250i	1.39392	+	0.200416i	0.595907	+	0.803053i	$0.296792\pi$
$8$	−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	0.889485	+	0.456964i	$0.151063\pi$
$11$	2.16359	+	4.73760i	0.652347	+	1.42844i	−0.237139	+	0.971476i	$0.576210\pi$
$12$	−1.04539	−	1.38100i	−0.301777	−	0.398661i
$13$	0.0252260	+	0.175451i	0.00699643	+	0.0486613i	0.993021	−	0.117941i	$-0.0376294\pi$
$13$	0.0252260	+	0.175451i	0.00699643	+	0.0486613i	−0.986024	+	0.166602i	$0.946720\pi$
$14$	−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	−0.00998944	−	0.999950i	$-0.503180\pi$
$17$	4.04561	−	4.66888i	0.981204	−	1.13237i	0.991194	−	0.132420i	$-0.0422748\pi$
$18$	−2.54098	−	1.59481i	−0.598915	−	0.375901i
$19$	−3.14485	+	2.72503i	−0.721478	+	0.625164i	−0.936182	−	0.351515i	$-0.885667\pi$
$19$	−3.14485	+	2.72503i	−0.721478	+	0.625164i	0.214705	+	0.976679i	$0.431121\pi$
$20$	−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	0.457904	−	0.889002i	$-0.348600\pi$
$29$	−1.92187	−	1.66531i	−0.356882	−	0.309240i	−0.814786	+	0.579761i	$0.803146\pi$
$30$	−2.45873	+	0.189085i	−0.448901	+	0.0345221i
$31$	−2.86031	+	0.839864i	−0.513728	+	0.150844i	−0.528313	−	0.849050i	$-0.677175\pi$
$31$	−2.86031	+	0.839864i	−0.513728	+	0.150844i	0.0145856	+	0.999894i	$0.495357\pi$
$32$	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	−0.127168	−	0.991881i	$-0.540589\pi$
$37$	5.03596	−	7.83610i	0.827906	−	1.28825i	0.955074	−	0.296366i	$-0.0957748\pi$
$38$	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	0.667346	−	0.744748i	$-0.267430\pi$
$41$	−1.83979	−	2.86277i	−0.287327	−	0.447089i	−0.954672	+	0.297659i	$0.903794\pi$
$42$	5.18687	+	3.83970i	0.800352	+	0.592478i
$43$	−0.117381	+	0.399763i	−0.0179004	+	0.0609633i	−0.967959	−	0.251109i	$-0.919205\pi$
$43$	−0.117381	+	0.399763i	−0.0179004	+	0.0609633i	0.950058	+	0.312072i	$0.101023\pi$
$44$	−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	$0.0215242\pi$
$47$			0.926457i			0.135138i	−0.997715	+	0.0675688i	$0.978476\pi$
$48$	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	−0.994852	−	0.101336i	$-0.967688\pi$
$53$	−0.0855320	+	0.594888i	−0.0117487	+	0.0817141i	0.983103	+	0.183051i	$0.0585972\pi$
$54$	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	0.948788	−	0.315914i	$-0.102311\pi$
$59$	14.9640	−	2.15150i	1.94815	−	0.280101i	0.999359	+	0.0358128i	$0.0114020\pi$
$60$	2.31509	+	0.849396i	0.298877	+	0.109657i
$61$	1.56365	+	5.32531i	0.200205	+	0.681837i	0.996987	+	0.0775694i	$0.0247159\pi$
$61$	1.56365	+	5.32531i	0.200205	+	0.681837i	−0.796782	+	0.604267i	$0.793466\pi$
$62$	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	0.465009	−	0.885306i	$-0.346051\pi$
$67$	0.822269	+	0.375518i	0.100456	+	0.0458768i	−0.364553	+	0.931183i	$0.618778\pi$
$68$	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	−0.130501	−	0.991448i	$-0.541658\pi$
$71$	−8.13332	−	3.71436i	−0.965247	−	0.440814i	−0.834746	+	0.550635i	$0.814386\pi$
$72$	−0.458709	−	2.96472i	−0.0540594	−	0.349396i
$73$	−7.53110	−	8.69136i	−0.881449	−	1.01725i	−0.999706	−	0.0242633i	$-0.992276\pi$
$73$	−7.53110	−	8.69136i	−0.881449	−	1.01725i	0.118257	−	0.992983i	$-0.462269\pi$
$74$	−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	0.0557462	−	0.998445i	$-0.482246\pi$
$79$	3.47110	−	0.499068i	0.390529	−	0.0561496i	0.334783	+	0.942295i	$0.391337\pi$
$80$	−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	−0.362985	−	0.931795i	$-0.618242\pi$
$83$	−12.4026	−	7.97068i	−1.36136	−	0.874896i	−0.998380	+	0.0568991i	$0.981879\pi$
$84$	−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	0.148147	−	0.988965i	$-0.452669\pi$
$89$	−2.47074	−	0.725476i	−0.261898	−	0.0769003i	−0.410046	+	0.912065i	$0.634487\pi$
$90$	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	0.500768	−	0.865581i	$-0.333051\pi$
$97$	−4.87143	−	7.58010i	−0.494619	−	0.769642i	−0.995387	+	0.0959391i	$0.969415\pi$
$98$	−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	−0.901368	−	0.433053i	$-0.857436\pi$
$101$	−1.33671	+	2.07995i	−0.133007	+	0.206963i	0.768361	+	0.640017i	$0.221073\pi$
$102$	10.0055	−	3.79298i	0.990690	−	0.375561i
$103$	11.1690	−	5.10071i	1.10051	−	0.502588i	0.219468	−	0.975620i	$-0.429568\pi$
$103$	11.1690	−	5.10071i	1.10051	−	0.502588i	0.881045	+	0.473032i	$0.156840\pi$
$104$	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	−0.437759	−	0.899092i	$-0.644228\pi$
$107$	−3.30948	+	0.971752i	−0.319940	+	0.0939428i	0.117819	+	0.993035i	$0.462410\pi$
$108$	−2.56316	−	4.51998i	−0.246640	−	0.434935i
$109$	−4.07200	−	3.52841i	−0.390027	−	0.337960i	0.437670	−	0.899136i	$-0.355804\pi$
$109$	−4.07200	−	3.52841i	−0.390027	−	0.337960i	−0.827697	+	0.561176i	$0.810349\pi$
$110$	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	0.395932	+	0.918280i	$0.370422\pi$
$113$	−5.92458	+	12.9730i	−0.557338	+	1.22040i	−0.953270	+	0.302120i	$0.902306\pi$
$114$	−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	−0.904810	−	0.425815i	$-0.859988\pi$
$127$	−7.14589	−	15.6473i	−0.634095	−	1.38847i	0.270716	−	0.962659i	$-0.412740\pi$
$128$	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	−0.219243	−	0.975670i	$-0.570359\pi$
$131$	−8.06318	−	1.15931i	−0.704484	−	0.101289i	−0.485240	+	0.874381i	$0.661268\pi$
$132$	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	0.797509	−	0.603307i	$-0.206151\pi$
$149$	−2.20569	−	4.82978i	−0.180697	−	0.395671i	−0.978206	+	0.207635i	$0.933423\pi$
$150$	−4.10567	+	3.10789i	−0.335226	+	0.253759i
$151$	2.78222	+	19.3508i	0.226414	+	1.57474i	0.713034	+	0.701130i	$0.247321\pi$
$151$	2.78222	+	19.3508i	0.226414	+	1.57474i	−0.486620	+	0.873614i	$0.661770\pi$
$152$	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	−0.284821	−	0.958581i	$-0.591934\pi$
$157$	7.81203	−	6.76917i	0.623468	−	0.540238i	0.908289	+	0.418342i	$0.137389\pi$
$158$	−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	−0.788699	−	0.614779i	$-0.789245\pi$
$163$	2.45650	−	5.37899i	0.192408	−	0.421315i	0.981107	+	0.193464i	$0.0619724\pi$
$164$	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	0.758380	−	0.651813i	$-0.225991\pi$
$167$	2.85764	+	2.47616i	0.221130	+	0.191611i	−0.537249	+	0.843423i	$0.680537\pi$
$168$	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	0.502429	−	0.864619i	$-0.332440\pi$
$173$	19.5306	−	8.91933i	1.48488	−	0.678124i	0.982456	+	0.186495i	$0.0597127\pi$
$174$	−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	0.995245	+	0.0974027i	$0.0310535\pi$
$179$	8.96942	+	13.9567i	0.670406	+	1.04317i	−0.324839	+	0.945769i	$0.605310\pi$
$180$	−3.90401	−	1.73264i	−0.290988	−	0.129143i
$181$	4.87903	−	16.6164i	0.362655	−	1.23509i	−0.553019	−	0.833169i	$-0.686524\pi$
$181$	4.87903	−	16.6164i	0.362655	−	1.23509i	0.915674	−	0.401922i	$-0.131658\pi$
$182$	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	−0.922298	−	0.386479i	$-0.873691\pi$
$191$	0.988482	−	6.87504i	0.0715240	−	0.497461i	0.993822	−	0.110982i	$-0.0353996\pi$
$192$	1.51572	−	0.838209i	0.109388	−	0.0604925i
$193$	18.3676	+	11.8041i	1.32213	+	0.849678i	0.995434	−	0.0954525i	$-0.0304298\pi$
$193$	18.3676	+	11.8041i	1.32213	+	0.849678i	0.326692	+	0.945131i	$0.394066\pi$
$194$	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	−0.0752055	−	0.997168i	$-0.523961\pi$
$197$	1.87474	−	0.269548i	0.133570	−	0.0192045i	0.208776	+	0.977964i	$0.433052\pi$
$198$	2.05795	−	15.4887i	0.146252	−	1.10073i
$199$	3.07889	+	10.4857i	0.218257	+	0.743314i	0.993717	+	0.111918i	$0.0356995\pi$
$199$	3.07889	+	10.4857i	0.218257	+	0.743314i	−0.775461	+	0.631396i	$0.782482\pi$
$200$	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	0.567198	−	0.823582i	$-0.308028\pi$
$211$	−4.77496	−	5.51060i	−0.328722	−	0.379365i	−0.895920	+	0.444216i	$0.853482\pi$
$212$	−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	0.905693	+	0.423933i	$0.139351\pi$
$223$	−1.23570	+	8.59451i	−0.0827489	+	0.575531i	−0.988442	+	0.151598i	$0.951558\pi$
$224$	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	−0.493994	−	0.869465i	$-0.664464\pi$
$227$	−20.7863	−	6.10342i	−1.37964	−	0.405098i	−0.885643	+	0.464367i	$0.846282\pi$
$228$	7.05085	+	1.49434i	0.466954	+	0.0989648i
$229$		−	9.76977i		−	0.645604i	−0.946466	−	0.322802i	$-0.895375\pi$
$229$		−	9.76977i		−	0.645604i	0.946466	−	0.322802i	$-0.104625\pi$
$230$	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	−0.999769	−	0.0214775i	$-0.993163\pi$
$233$	−2.24536	+	7.64698i	−0.147098	+	0.500971i	0.852671	+	0.522448i	$0.174981\pi$
$234$	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	0.219311	−	0.975655i	$-0.429619\pi$
$239$	15.7022	−	24.4331i	1.01569	−	1.58045i	0.796382	−	0.604794i	$-0.206745\pi$
$240$	0.874131	+	2.30586i	0.0564249	+	0.148843i
$241$	−3.65934	+	1.67116i	−0.235719	+	0.107649i	−0.529773	−	0.848140i	$-0.677723\pi$
$241$	−3.65934	+	1.67116i	−0.235719	+	0.107649i	0.294054	+	0.955789i	$0.404995\pi$
$242$	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	−0.964090	−	0.265577i	$-0.914438\pi$
$251$	−2.09183	+	4.58048i	−0.132035	+	0.289117i	0.832054	+	0.554694i	$0.187165\pi$
$252$	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	−0.933148	−	0.359492i	$-0.882950\pi$
$257$	−11.3840	+	9.86431i	−0.710116	+	0.615319i	0.223032	+	0.974811i	$0.428404\pi$
$258$	−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	−0.731799	−	0.681521i	$-0.761319\pi$
$263$	−3.59455	−	25.0007i	−0.221650	−	1.54161i	0.510149	−	0.860086i	$-0.329590\pi$
$264$	−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	0.543437	−	0.839450i	$-0.317123\pi$
$269$	13.5861	+	1.95339i	0.828360	+	0.119100i	0.284923	+	0.958550i	$0.408032\pi$
$270$	−7.38665	−	0.409207i	−0.449537	−	0.0249036i
$271$	16.6069	−	10.6726i	1.00880	−	0.648313i	0.0717144	−	0.997425i	$-0.477153\pi$
$271$	16.6069	−	10.6726i	1.00880	−	0.648313i	0.937081	+	0.349112i	$0.113517\pi$
$272$	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	−0.298000	−	0.954566i	$-0.596320\pi$
$281$	7.48487	−	4.81024i	0.446510	−	0.286955i	0.744510	+	0.667611i	$0.232683\pi$
$282$	−0.761487	+	1.41248i	−0.0453459	+	0.0841120i
$283$	−21.9899	−	3.16167i	−1.30716	−	0.187942i	−0.546703	−	0.837327i	$-0.684117\pi$
$283$	−21.9899	−	3.16167i	−1.30716	−	0.187942i	−0.760460	+	0.649385i	$0.775026\pi$
$284$	−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	−0.950711	−	0.310079i	$-0.899644\pi$
$293$	−8.70390	+	10.0448i	−0.508487	+	0.586825i	0.442224	+	0.896905i	$0.354190\pi$
$294$	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	−0.856544	−	0.516073i	$-0.827393\pi$
$307$	−22.7446	+	6.67843i	−1.29811	+	0.381158i	−0.441561	+	0.897231i	$0.645575\pi$
$308$	−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	−0.0774437	−	0.996997i	$-0.524676\pi$
$311$	11.0277	−	5.03616i	0.625321	−	0.285575i	0.702765	+	0.711422i	$0.251949\pi$
$312$	−0.287079	+	0.108829i	−0.0162526	+	0.00616121i
$313$	−15.0820	+	23.4680i	−0.852485	+	1.32649i	0.0912631	+	0.995827i	$0.470910\pi$
$313$	−15.0820	+	23.4680i	−0.852485	+	1.32649i	−0.943748	+	0.330666i	$0.892727\pi$
$314$	−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	0.918293	−	0.395901i	$-0.129568\pi$
$317$	3.14599	+	4.89525i	0.176696	+	0.274945i	−0.741597	+	0.670846i	$0.765931\pi$
$318$	−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	0.0300834	−	0.999547i	$-0.490423\pi$
$331$	−15.7671	−	10.1329i	−0.866640	−	0.556956i	−0.896723	+	0.442592i	$0.854059\pi$
$332$	−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	0.892410	−	0.451226i	$-0.149013\pi$
$337$	−1.87769	−	6.39484i	−0.102285	−	0.348349i	−0.994694	+	0.102877i	$0.967195\pi$
$338$	−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	0.611735	−	0.791062i	$-0.290472\pi$
$347$	7.72113	+	3.52612i	0.414492	+	0.189292i	−0.197244	+	0.980355i	$0.563199\pi$
$348$	−0.290700	+	4.39500i	−0.0155831	+	0.235597i
$349$	5.73202	+	6.61510i	0.306828	+	0.354098i	0.888132	−	0.459588i	$-0.152003\pi$
$349$	5.73202	+	6.61510i	0.306828	+	0.354098i	−0.581304	+	0.813686i	$0.697457\pi$
$350$	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	0.898196	+	0.439594i	$0.144878\pi$
$353$	7.14421	+	24.3310i	0.380248	+	1.29501i	−0.517948	+	0.855412i	$0.673304\pi$
$354$	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	0.710167	−	0.704034i	$-0.248620\pi$
$359$	6.91139	+	4.44168i	0.364769	+	0.234423i	−0.345398	+	0.938456i	$0.612256\pi$
$360$	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	$0.0644396\pi$
$367$			7.70363i			0.402126i	−0.979578	+	0.201063i	$0.935560\pi$
$368$	−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	0.583149	−	0.812365i	$-0.301820\pi$
$373$	−7.68769	−	11.9623i	−0.398054	−	0.619384i	−0.981202	+	0.192982i	$0.938184\pi$
$374$	−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	−0.803457	−	0.595363i	$-0.797008\pi$
$379$	−17.1252	+	7.82084i	−0.879665	+	0.401729i	−0.0762074	+	0.997092i	$0.524281\pi$
$380$	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	−0.749294	−	0.662238i	$-0.769607\pi$
$383$	−19.9933	+	5.87055i	−1.02161	+	0.299971i	−0.272313	+	0.962209i	$0.587789\pi$
$384$	−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	−0.764219	−	0.644957i	$-0.776875\pi$
$389$	4.41133	−	9.65948i	0.223664	−	0.489755i	0.987883	+	0.155202i	$0.0496027\pi$
$390$	−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	−0.927315	−	0.374282i	$-0.877889\pi$
$397$	−8.46553	+	9.76974i	−0.424873	+	0.490329i	0.502443	+	0.864611i	$0.332435\pi$
$398$	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	0.989965	−	0.141312i	$-0.0451321\pi$
$401$	0.00577400	+	0.0401590i	0.000288340	+	0.00200545i	−0.989677	+	0.143317i	$0.954223\pi$
$402$	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	−0.315804	−	0.948824i	$-0.602274\pi$
$409$	8.41485	−	5.40790i	0.416088	−	0.267403i	0.731891	+	0.681421i	$0.238638\pi$
$410$	−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	−0.341213	−	0.939986i	$-0.610838\pi$
$419$	7.61634	−	4.89473i	0.372083	−	0.239123i	0.713296	+	0.700863i	$0.247202\pi$
$420$	8.08759	+	4.36013i	0.394634	+	0.212752i
$421$	9.75720	+	1.40287i	0.475537	+	0.0683719i	0.375916	−	0.926654i	$-0.377328\pi$
$421$	9.75720	+	1.40287i	0.475537	+	0.0683719i	0.0996206	+	0.995025i	$0.468237\pi$
$422$	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	−0.0294037	+	0.999568i	$0.509361\pi$
$431$	−21.0639	+	24.3090i	−1.01461	+	1.17093i	−0.985209	+	0.171358i	$0.945185\pi$
$432$	1.73746	−	4.89706i	0.0835935	−	0.235610i
$433$	5.12637	−	4.44203i	0.246358	−	0.213470i	−0.522925	−	0.852379i	$-0.675159\pi$
$433$	5.12637	−	4.44203i	0.246358	−	0.213470i	0.769283	+	0.638908i	$0.220614\pi$
$434$	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	0.412069	+	0.911153i	$0.364806\pi$
$439$	−11.4480	+	25.0676i	−0.546382	+	1.19641i	−0.958451	+	0.285257i	$0.907921\pi$
$440$	−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	0.720862	−	0.693079i	$-0.243746\pi$
$443$	2.89251	+	2.50637i	0.137427	+	0.119081i	−0.583435	+	0.812160i	$0.698292\pi$
$444$	−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	−0.773110	−	0.634272i	$-0.781300\pi$
$449$	−16.9525	+	7.74195i	−0.800038	+	0.365365i	−0.0269281	+	0.999637i	$0.508573\pi$
$450$	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	−0.615125	−	0.788429i	$-0.710895\pi$
$457$	7.02484	−	23.9244i	0.328608	−	1.11914i	0.943733	−	0.330707i	$-0.107287\pi$
$458$	−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	$-0.917317\pi$
$461$		−	11.0295i		−	0.513693i	0.966452	−	0.256847i	$-0.0826835\pi$
$462$	−6.96867	+	32.8809i	−0.324212	+	1.52976i
$463$	−28.1962	−	8.27914i	−1.31039	−	0.384764i	−0.449372	−	0.893345i	$-0.648352\pi$
$463$	−28.1962	−	8.27914i	−1.31039	−	0.384764i	−0.861014	+	0.508581i	$0.830170\pi$
$464$	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	−0.754728	−	0.656038i	$-0.772231\pi$
$467$	3.33349	−	23.1849i	0.154255	−	1.07287i	0.908984	−	0.416832i	$-0.136860\pi$
$468$	−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	0.761951	−	0.647635i	$-0.224242\pi$
$479$	0.272929	+	0.314976i	0.0124704	+	0.0143916i	−0.749480	+	0.662027i	$0.769696\pi$
$480$	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	0.279076	−	0.960269i	$-0.409972\pi$
$487$	−15.6934	−	18.1112i	−0.711136	−	0.820695i	−0.990212	+	0.139575i	$0.955427\pi$
$488$	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	−0.999917	−	0.0129118i	$-0.995890\pi$
$491$	−3.67197	−	12.5056i	−0.165714	−	0.564370i	0.834203	−	0.551458i	$-0.185928\pi$
$492$	−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	−0.0317731	+	0.999495i	$0.510115\pi$
$499$	−6.31900	+	43.9496i	−0.282877	+	1.96746i	−0.251104	+	0.967960i	$0.580794\pi$
$500$	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	0.580037	−	0.814590i	$-0.303038\pi$
$503$	14.0755	+	4.13293i	0.627595	+	0.184278i	0.0475577	+	0.998868i	$0.484856\pi$
$504$	−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	−0.902536	−	0.430614i	$-0.858297\pi$
$509$	2.01996	−	6.87934i	0.0895331	−	0.304922i	0.992069	+	0.125692i	$0.0401152\pi$
$510$	−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	−0.420563	−	0.907263i	$-0.638167\pi$
$521$	−6.47921	+	1.90247i	−0.283860	+	0.0833487i	0.136703	+	0.990612i	$0.456349\pi$
$522$	2.22757	+	7.29654i	0.0974983	+	0.319361i
$523$	13.3559	+	11.5730i	0.584013	+	0.506051i	0.896011	−	0.444032i	$-0.146453\pi$
$523$	13.3559	+	11.5730i	0.584013	+	0.506051i	−0.311997	+	0.950083i	$0.600998\pi$
$524$	−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	0.992338	−	0.123554i	$-0.0394292\pi$
$541$	5.79436	+	12.6879i	0.249119	+	0.545494i	−0.743219	+	0.669048i	$0.766702\pi$
$542$	−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	−0.172033	−	0.985091i	$-0.555034\pi$
$547$	15.2624	−	9.80854i	0.652573	−	0.419383i	0.824605	+	0.565708i	$0.191397\pi$
$548$	−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	0.274368	−	0.961625i	$-0.411531\pi$
$557$	29.8095	−	19.1574i	1.26307	−	0.811725i	0.988701	+	0.149900i	$0.0478951\pi$
$558$	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	0.987939	+	0.154840i	$0.0494864\pi$
$563$	10.8672	+	23.7958i	0.457997	+	1.00287i	−0.529942	+	0.848034i	$0.677786\pi$
$564$	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	−0.440744	−	0.897633i	$-0.645285\pi$
$569$	12.1768	−	14.0527i	0.510477	−	0.589122i	0.951221	+	0.308511i	$0.0998308\pi$
$570$	7.21707	−	7.29475i	0.302290	−	0.305543i
$571$	20.6801	−	17.9194i	0.865436	−	0.749905i	−0.104174	−	0.994559i	$-0.533220\pi$
$571$	20.6801	−	17.9194i	0.865436	−	0.749905i	0.969610	+	0.244654i	$0.0786744\pi$
$572$	−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	−0.963477	−	0.267790i	$-0.913707\pi$
$577$	−3.12636	+	6.84577i	−0.130152	+	0.284993i	0.833325	+	0.552783i	$0.186434\pi$
$578$	−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	−0.557303	−	0.830309i	$-0.688164\pi$
$587$	−7.14131	+	3.26133i	−0.294753	+	0.134609i	0.262550	+	0.964918i	$0.415437\pi$
$588$	−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	−0.798741	−	0.601676i	$-0.794500\pi$
$593$	−24.6982	−	38.4312i	−1.01424	−	1.57818i	−0.215495	−	0.976505i	$-0.569136\pi$
$594$	−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	$0.404460\pi$
$599$			46.7606i			1.91059i	−0.295662	+	0.955293i	$0.595540\pi$
$600$	−5.03743	−	1.06762i	−0.205652	−	0.0435853i
$601$	20.8538	+	6.12322i	0.850643	+	0.249771i	0.677862	−	0.735189i	$-0.262907\pi$
$601$	20.8538	+	6.12322i	0.850643	+	0.249771i	0.172781	+	0.984960i	$0.444725\pi$
$602$	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	0.707286	−	0.706928i	$-0.249919\pi$
$607$	8.82162	+	5.66931i	0.358058	+	0.230110i	−0.349227	+	0.937038i	$0.613556\pi$
$608$	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	0.968874	−	0.247554i	$-0.0796268\pi$
$613$	0.494372	+	1.68368i	0.0199675	+	0.0680030i	−0.948907	+	0.315557i	$0.897809\pi$
$614$	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	0.799902	−	0.600130i	$-0.204885\pi$
$617$	2.28628	+	2.63851i	0.0920423	+	0.106222i	−0.707860	+	0.706353i	$0.750339\pi$
$618$	21.2208	+	1.40361i	0.853624	+	0.0564615i
$619$	−18.8744	−	8.61963i	−0.758625	−	0.346452i	−0.00173796	−	0.999998i	$-0.500553\pi$
$619$	−18.8744	−	8.61963i	−0.758625	−	0.346452i	−0.756887	+	0.653546i	$0.773280\pi$
$620$	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	0.521701	−	0.853129i	$-0.325298\pi$
$631$	31.7167	−	4.56018i	1.26262	−	0.181538i	0.740922	+	0.671591i	$0.234389\pi$
$632$	−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	−0.455517	−	0.890227i	$-0.650545\pi$
$641$	−33.4201	−	9.81303i	−1.32001	−	0.387591i	−0.864498	+	0.502636i	$0.832364\pi$
$642$	−5.84437	−	1.23864i	−0.230659	−	0.0488852i
$643$			26.7667i			1.05557i	0.849377	+	0.527787i	$0.176978\pi$
$643$			26.7667i			1.05557i	−0.849377	+	0.527787i	$0.823022\pi$
$644$	−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	0.835612	+	0.549320i	$0.185113\pi$
$647$	−4.18004	+	14.2359i	−0.164334	+	0.559672i	−0.999946	+	0.0103516i	$0.996705\pi$
$648$	−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	−0.413983	−	0.910285i	$-0.635863\pi$
$653$	14.9750	−	23.3015i	0.586016	−	0.911858i	0.999999	−	0.00157377i	$-0.000500946\pi$
$654$	−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	−0.538549	−	0.842594i	$-0.681027\pi$
$659$	−13.7613	+	4.04069i	−0.536065	+	0.157403i	0.00248404	+	0.999997i	$0.499209\pi$
$660$	0.984805	+	12.8057i	0.0383335	+	0.498461i
$661$	−11.7371	−	10.1703i	−0.456521	−	0.395577i	0.396017	−	0.918243i	$-0.370392\pi$
$661$	−11.7371	−	10.1703i	−0.456521	−	0.395577i	−0.852538	+	0.522666i	$0.824938\pi$
$662$	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	−0.728273	−	0.685287i	$-0.759677\pi$
$673$	1.39266	−	1.60721i	0.0536829	−	0.0619534i	0.781956	+	0.623334i	$0.214222\pi$
$674$	−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	0.811924	+	0.583763i	$0.198420\pi$
$677$	5.13499	+	35.7146i	0.197354	+	1.37263i	−0.614570	+	0.788862i	$0.710671\pi$
$678$	−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	−0.395415	−	0.918503i	$-0.629399\pi$
$683$	−27.0120	−	3.88374i	−1.03359	−	0.148607i	−0.638170	+	0.769895i	$0.720308\pi$
$684$	−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	0.959748	+	0.280863i	$0.0906208\pi$
$701$	14.3902	+	31.5101i	0.543509	+	1.19012i	−0.416239	+	0.909255i	$0.636652\pi$
$702$	−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	−0.910671	−	0.413133i	$-0.864434\pi$
$709$	−16.8108	+	14.5667i	−0.631344	+	0.547063i	0.279326	+	0.960196i	$0.409889\pi$
$710$	−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	0.584489	−	0.811402i	$-0.301295\pi$
$719$	−3.63258	−	3.14765i	−0.135472	−	0.117387i	−0.719961	+	0.694014i	$0.755840\pi$
$720$	−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	−0.406238	−	0.913767i	$-0.633159\pi$
$727$	16.0082	−	24.9093i	0.593712	−	0.923833i	0.999949	−	0.0100660i	$-0.00320416\pi$
$728$	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	−0.984628	−	0.174665i	$-0.944116\pi$
$733$	−1.67520	+	5.70521i	−0.0618749	+	0.210727i	0.922753	+	0.385392i	$0.125934\pi$
$734$	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	0.202480	−	0.979286i	$-0.435100\pi$
$739$	−4.25778	−	1.25020i	−0.156625	−	0.0459893i	−0.359105	+	0.933297i	$0.616918\pi$
$740$	−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	−0.724721	−	0.689042i	$-0.758032\pi$
$743$	4.49128	−	31.2376i	0.164769	−	1.14600i	0.889491	−	0.456953i	$-0.151059\pi$
$744$	−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	0.925214	−	0.379445i	$-0.123885\pi$
$751$	−1.59683	−	5.43829i	−0.0582690	−	0.198446i	−0.983483	+	0.180999i	$0.942067\pi$
$752$	−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	0.756753	−	0.653701i	$-0.226784\pi$
$757$	20.8632	+	9.52792i	0.758287	+	0.346298i	0.00153402	+	0.999999i	$0.499512\pi$
$758$	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	0.611932	−	0.790910i	$-0.290393\pi$
$761$	11.4464	+	5.22740i	0.414932	+	0.189493i	−0.197000	+	0.980403i	$0.563120\pi$
$762$	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	−0.659783	−	0.751457i	$-0.729352\pi$
$769$	−29.9806	+	4.31056i	−1.08113	+	0.155443i	−0.421347	+	0.906900i	$0.638443\pi$
$770$	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	0.787895	−	0.615810i	$-0.211171\pi$
$773$	15.4317	+	9.91733i	0.555038	+	0.356702i	−0.232857	+	0.972511i	$0.574807\pi$
$774$	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	0.901199	−	0.433405i	$-0.142688\pi$
$787$	3.71957	+	5.78777i	0.132588	+	0.206312i	−0.768611	+	0.639717i	$0.779052\pi$
$788$	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	−0.0850793	−	0.996374i	$-0.527114\pi$
$797$	10.7851	−	3.16679i	0.382028	−	0.112174i	0.467107	+	0.884201i	$0.345296\pi$
$798$	−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	−0.336958	−	0.941520i	$-0.609398\pi$
$809$	15.5590	−	13.4819i	0.547024	−	0.473999i	0.883982	+	0.467521i	$0.154853\pi$
$810$	12.7194	+	1.55162i	0.446913	+	0.0545183i
$811$	12.6718	−	14.6240i	0.444967	−	0.513519i	−0.488313	−	0.872668i	$-0.662388\pi$
$811$	12.6718	−	14.6240i	0.444967	−	0.513519i	0.933280	+	0.359149i	$0.116933\pi$
$812$	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	0.547322	−	0.836922i	$-0.315647\pi$
$821$	23.9736	+	3.44689i	0.836685	+	0.120297i	0.289363	+	0.957219i	$0.406556\pi$
$822$	−13.2061	−	7.11960i	−0.460617	−	0.248324i
$823$	−28.5116	+	18.3233i	−0.993853	+	0.638710i	−0.933166	−	0.359447i	$-0.882966\pi$
$823$	−28.5116	+	18.3233i	−0.993853	+	0.638710i	−0.0606870	+	0.998157i	$0.519329\pi$
$824$	−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	0.799204	−	0.601060i	$-0.205255\pi$
$839$	−5.16784	−	11.3160i	−0.178414	−	0.390672i	−0.977618	+	0.210388i	$0.932527\pi$
$840$	−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	0.110387	+	0.993889i	$0.464791\pi$
$853$	−20.8249	+	45.6003i	−0.713032	+	1.56132i	−0.823419	+	0.567434i	$0.807936\pi$
$854$	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	0.612183	−	0.790716i	$-0.290291\pi$
$857$	−2.44036	−	2.11458i	−0.0833611	−	0.0722328i	−0.695545	+	0.718483i	$0.744837\pi$
$858$	−1.59430	+	0.122608i	−0.0544286	+	0.00418576i
$859$	−0.414426	+	0.121687i	−0.0141400	+	0.00415189i	−0.288795	−	0.957391i	$-0.593255\pi$
$859$	−0.414426	+	0.121687i	−0.0141400	+	0.00415189i	0.274655	+	0.961543i	$0.411436\pi$
$860$	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	−0.579888	−	0.814696i	$-0.696904\pi$
$863$	−10.1035	+	4.61411i	−0.343927	+	0.157066i	0.235961	+	0.971763i	$0.424176\pi$
$864$	−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	−0.133897	−	0.990995i	$-0.542749\pi$
$877$	−23.1675	−	6.80260i	−0.782311	−	0.229707i	−0.648414	+	0.761288i	$0.724567\pi$
$878$	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	−0.991548	−	0.129741i	$-0.958586\pi$
$881$	−0.107225	+	0.745769i	−0.00361251	+	0.0251256i	0.987935	+	0.154866i	$0.0494946\pi$
$882$	−13.6871	−	15.4583i	−0.460870	−	0.520507i
$883$	31.6790	+	20.3589i	1.06608	+	0.685130i	0.951302	−	0.308261i	$-0.0997468\pi$
$883$	31.6790	+	20.3589i	1.06608	+	0.685130i	0.114781	+	0.993391i	$0.463383\pi$
$884$	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	−0.794868	−	0.606782i	$-0.792460\pi$
$887$	−41.2961	+	5.93749i	−1.38659	+	0.199361i	−0.591720	+	0.806144i	$0.701551\pi$
$888$	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	−0.267889	−	0.963450i	$-0.586326\pi$
$907$	−7.63423	+	1.09764i	−0.253490	+	0.0364464i	0.0143980	+	0.999896i	$0.495417\pi$
$908$	−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	0.853596	−	0.520936i	$-0.174417\pi$
$911$	22.1642	+	14.2441i	0.734333	+	0.471927i	−0.119263	+	0.992863i	$0.538053\pi$
$912$	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	$-0.966509\pi$
$919$		−	6.36736i		−	0.210040i	0.994470	−	0.105020i	$-0.0334906\pi$
$920$	−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	−0.999023	−	0.0441861i	$-0.985931\pi$
$929$	−16.5754	+	25.7918i	−0.543821	+	0.846202i	0.455202	+	0.890388i	$0.349567\pi$
$930$	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	0.860781	−	0.508975i	$-0.169976\pi$
$937$	14.6774	+	12.7180i	0.479488	+	0.415479i	−0.381293	+	0.924454i	$0.624521\pi$
$938$	−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	0.373626	+	0.927579i	$0.378114\pi$
$941$	−17.5485	+	38.4259i	−0.572065	+	1.25265i	−0.945691	+	0.325068i	$0.894613\pi$
$942$	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	−0.210289	−	0.977639i	$-0.567441\pi$
$947$	22.3867	−	19.3982i	0.727471	−	0.630358i	0.937761	+	0.347282i	$0.112895\pi$
$948$	−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	−0.999963	−	0.00857985i	$-0.997269\pi$
$953$	−1.32506	−	9.21596i	−0.0429228	−	0.298534i	0.957040	−	0.289954i	$-0.0936402\pi$
$954$	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	−0.484378	−	0.874859i	$-0.660954\pi$
$971$	3.43406	−	2.20693i	0.110204	−	0.0708239i	0.594582	+	0.804035i	$0.297318\pi$
$972$	−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	−0.805917	−	0.592029i	$-0.798327\pi$
$977$	−22.6794	−	49.6610i	−0.725579	−	1.58880i	0.0803378	−	0.996768i	$-0.474400\pi$
$978$	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	−0.937984	−	0.346677i	$-0.887310\pi$
$983$	−14.4645	+	16.6930i	−0.461347	+	0.532423i	0.476638	+	0.879100i	$0.341855\pi$
$984$	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	−0.970777	−	0.239983i	$-0.922858\pi$
$991$	−4.83807	+	10.5939i	−0.153686	+	0.336526i	0.817091	+	0.576509i	$0.195585\pi$
$992$	−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	0.0444645	−	0.999011i	$-0.485842\pi$
$997$	19.6391	−	5.76656i	0.621977	−	0.182629i	0.577512	+	0.816382i	$0.304024\pi$
$998$	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.17.1	✓	80
3.2	odd	2	inner	138.2.f.a.17.5	yes	80
23.19	odd	22	inner	138.2.f.a.65.5	yes	80
69.65	even	22	inner	138.2.f.a.65.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.17.1	✓	80	1.1	even	1	trivial
138.2.f.a.17.5	yes	80	3.2	odd	2	inner
138.2.f.a.65.1	yes	80	69.65	even	22	inner
138.2.f.a.65.5	yes	80	23.19	odd	22	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

Fields

Representations

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Database

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