LMFDB - Embedded newform 135.2.q.a.32.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			32.4
Character	$\chi$	$=$	135.32
Dual form			135.2.q.a.38.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.162710 + 1.85978i) q^{2} +(0.207283 - 1.71960i) q^{3} +(-1.46269 - 0.257912i) q^{4} +(1.63097 - 1.52968i) q^{5} +(3.16436 + 0.665296i) q^{6} +(1.79546 - 2.56418i) q^{7} +(-0.248717 + 0.928224i) q^{8} +(-2.91407 - 0.712888i) q^{9} +O(q^{10})$	\(q+(-0.162710 + 1.85978i) q^{2} +(0.207283 - 1.71960i) q^{3} +(-1.46269 - 0.257912i) q^{4} +(1.63097 - 1.52968i) q^{5} +(3.16436 + 0.665296i) q^{6} +(1.79546 - 2.56418i) q^{7} +(-0.248717 + 0.928224i) q^{8} +(-2.91407 - 0.712888i) q^{9} +(2.57950 + 3.28215i) q^{10} +(-1.21790 + 3.34616i) q^{11} +(-0.746697 + 2.46179i) q^{12} +(1.89596 - 0.165875i) q^{13} +(4.47667 + 3.75637i) q^{14} +(-2.29237 - 3.12170i) q^{15} +(-4.47719 - 1.62956i) q^{16} +(0.886863 + 3.30982i) q^{17} +(1.79996 - 5.30353i) q^{18} +(-5.00990 + 2.89247i) q^{19} +(-2.78013 + 1.81680i) q^{20} +(-4.03720 - 3.61898i) q^{21} +(-6.02495 - 2.80948i) q^{22} +(1.06979 - 0.749079i) q^{23} +(1.54462 + 0.620099i) q^{24} +(0.320150 - 4.98974i) q^{25} +3.55306i q^{26} +(-1.82992 + 4.86327i) q^{27} +(-3.28753 + 3.28753i) q^{28} +(-0.0144398 + 0.0121164i) q^{29} +(6.17867 - 3.75538i) q^{30} +(0.260357 - 1.47656i) q^{31} +(2.94687 - 6.31958i) q^{32} +(5.50161 + 2.78791i) q^{33} +(-6.29984 + 1.11083i) q^{34} +(-0.994032 - 6.92858i) q^{35} +(4.07852 + 1.79431i) q^{36} +(9.77656 - 2.61962i) q^{37} +(-4.56420 - 9.78795i) q^{38} +(0.107761 - 3.29468i) q^{39} +(1.01424 + 1.89437i) q^{40} +(-6.39065 + 7.61608i) q^{41} +(7.38740 - 6.91946i) q^{42} +(-6.93786 + 3.23518i) q^{43} +(2.64443 - 4.58028i) q^{44} +(-5.84326 + 3.29489i) q^{45} +(1.21906 + 2.11147i) q^{46} +(-9.02466 - 6.31914i) q^{47} +(-3.73025 + 7.36121i) q^{48} +(-0.957202 - 2.62989i) q^{49} +(9.22773 + 1.40729i) q^{50} +(5.87541 - 0.838984i) q^{51} +(-2.81599 - 0.246367i) q^{52} +(-3.54041 - 3.54041i) q^{53} +(-8.74687 - 4.19455i) q^{54} +(3.13219 + 7.32049i) q^{55} +(1.93357 + 2.30434i) q^{56} +(3.93543 + 9.21460i) q^{57} +(-0.0201844 - 0.0288263i) q^{58} +(5.27046 - 1.91829i) q^{59} +(2.54791 + 5.15732i) q^{60} +(1.47697 + 8.37633i) q^{61} +(2.70371 + 0.724458i) q^{62} +(-7.06005 + 6.19223i) q^{63} +(3.02114 + 1.74425i) q^{64} +(2.83853 - 3.17075i) q^{65} +(-6.08006 + 9.77816i) q^{66} +(0.0194833 + 0.222695i) q^{67} +(-0.443565 - 5.06998i) q^{68} +(-1.06637 - 1.99489i) q^{69} +(13.0474 - 0.721334i) q^{70} +(-0.428964 - 0.247662i) q^{71} +(1.38650 - 2.52760i) q^{72} +(7.75123 + 2.07694i) q^{73} +(3.28118 + 18.6085i) q^{74} +(-8.51401 - 1.58482i) q^{75} +(8.07394 - 2.93867i) q^{76} +(6.39345 + 9.13079i) q^{77} +(6.10985 + 0.736488i) q^{78} +(-1.13950 - 1.35801i) q^{79} +(-9.79489 + 4.19090i) q^{80} +(7.98358 + 4.15481i) q^{81} +(-13.1244 - 13.1244i) q^{82} +(-7.35695 - 0.643650i) q^{83} +(4.97180 + 6.33469i) q^{84} +(6.50942 + 4.04161i) q^{85} +(-4.88786 - 13.4293i) q^{86} +(0.0178423 + 0.0273422i) q^{87} +(-2.80307 - 1.96273i) q^{88} +(-4.43260 - 7.67748i) q^{89} +(-5.17702 - 11.4033i) q^{90} +(2.97878 - 5.15940i) q^{91} +(-1.75798 + 0.819758i) q^{92} +(-2.48513 - 0.753777i) q^{93} +(13.2206 - 15.7557i) q^{94} +(-3.74646 + 12.3811i) q^{95} +(-10.2563 - 6.37738i) q^{96} +(3.23451 + 6.93643i) q^{97} +(5.04676 - 1.35228i) q^{98} +(5.93448 - 8.88270i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.162710	+	1.85978i	−0.115053	+	1.31506i	0.690842	+	0.723005i	$0.257240\pi$
$2$	−0.162710	+	1.85978i	−0.115053	+	1.31506i	−0.805896	+	0.592058i	$0.798316\pi$
$3$	0.207283	−	1.71960i	0.119675	−	0.992813i
$3$	0.207283	−	1.71960i	0.119675	−	0.992813i
$4$	−1.46269	−	0.257912i	−0.731346	−	0.128956i
$5$	1.63097	−	1.52968i	0.729394	−	0.684094i
$5$	1.63097	−	1.52968i	0.729394	−	0.684094i
$6$	3.16436	+	0.665296i	1.29184	+	0.271606i
$7$	1.79546	−	2.56418i	0.678619	−	0.969168i	−0.321136	−	0.947033i	$-0.604065\pi$
$7$	1.79546	−	2.56418i	0.678619	−	0.969168i	0.999755	−	0.0221350i	$-0.00704638\pi$
$8$	−0.248717	+	0.928224i	−0.0879347	+	0.328177i
$9$	−2.91407	−	0.712888i	−0.971356	−	0.237629i
$10$	2.57950	+	3.28215i	0.815708	+	1.03791i
$11$	−1.21790	+	3.34616i	−0.367211	+	1.00890i	0.609206	+	0.793012i	$0.291488\pi$
$11$	−1.21790	+	3.34616i	−0.367211	+	1.00890i	−0.976417	+	0.215892i	$0.930734\pi$
$12$	−0.746697	+	2.46179i	−0.215553	+	0.710657i
$13$	1.89596	−	0.165875i	0.525845	−	0.0460055i	0.178857	−	0.983875i	$-0.442760\pi$
$13$	1.89596	−	0.165875i	0.525845	−	0.0460055i	0.346988	+	0.937870i	$0.387205\pi$
$14$	4.47667	+	3.75637i	1.19644	+	1.00393i
$15$	−2.29237	−	3.12170i	−0.591888	−	0.806020i
$16$	−4.47719	−	1.62956i	−1.11930	−	0.407391i
$17$	0.886863	+	3.30982i	0.215096	+	0.802749i	0.986133	+	0.165958i	$0.0530718\pi$
$17$	0.886863	+	3.30982i	0.215096	+	0.802749i	−0.771037	+	0.636791i	$0.780262\pi$
$18$	1.79996	−	5.30353i	0.424255	−	1.25005i
$19$	−5.00990	+	2.89247i	−1.14935	+	0.663578i	−0.948729	−	0.316091i	$-0.897629\pi$
$19$	−5.00990	+	2.89247i	−1.14935	+	0.663578i	−0.200622	+	0.979669i	$0.564296\pi$
$20$	−2.78013	+	1.81680i	−0.621657	+	0.406250i
$21$	−4.03720	−	3.61898i	−0.880989	−	0.789727i
$22$	−6.02495	−	2.80948i	−1.28452	−	0.598983i
$23$	1.06979	−	0.749079i	0.223068	−	0.156194i	−0.456701	−	0.889620i	$-0.650969\pi$
$23$	1.06979	−	0.749079i	0.223068	−	0.156194i	0.679769	+	0.733427i	$0.262080\pi$
$24$	1.54462	+	0.620099i	0.315295	+	0.126577i
$25$	0.320150	−	4.98974i	0.0640300	−	0.997948i
$26$			3.55306i			0.696812i
$27$	−1.82992	+	4.86327i	−0.352168	+	0.935937i
$28$	−3.28753	+	3.28753i	−0.621285	+	0.621285i
$29$	−0.0144398	+	0.0121164i	−0.00268140	+	0.00224996i	−0.644127	−	0.764918i	$-0.722779\pi$
$29$	−0.0144398	+	0.0121164i	−0.00268140	+	0.00224996i	0.641446	+	0.767168i	$0.278335\pi$
$30$	6.17867	−	3.75538i	1.12807	−	0.685635i
$31$	0.260357	−	1.47656i	0.0467616	−	0.265198i	−0.952459	−	0.304666i	$-0.901455\pi$
$31$	0.260357	−	1.47656i	0.0467616	−	0.265198i	0.999221	+	0.0394679i	$0.0125663\pi$
$32$	2.94687	−	6.31958i	0.520938	−	1.11715i
$33$	5.50161	+	2.78791i	0.957707	+	0.485312i
$34$	−6.29984	+	1.11083i	−1.08041	+	0.190506i
$35$	−0.994032	−	6.92858i	−0.168022	−	1.17114i
$36$	4.07852	+	1.79431i	0.679753	+	0.299051i
$37$	9.77656	−	2.61962i	1.60726	−	0.430663i	0.660033	−	0.751237i	$-0.270542\pi$
$37$	9.77656	−	2.61962i	1.60726	−	0.430663i	0.947224	+	0.320574i	$0.103876\pi$
$38$	−4.56420	−	9.78795i	−0.740410	−	1.58781i
$39$	0.107761	−	3.29468i	0.0172555	−	0.527571i
$40$	1.01424	+	1.89437i	0.160365	+	0.299526i
$41$	−6.39065	+	7.61608i	−0.998051	+	1.18943i	−0.0161828	+	0.999869i	$0.505151\pi$
$41$	−6.39065	+	7.61608i	−0.998051	+	1.18943i	−0.981869	+	0.189562i	$0.939293\pi$
$42$	7.38740	−	6.91946i	1.13990	−	1.06770i
$43$	−6.93786	+	3.23518i	−1.05801	+	0.493360i	−0.872162	−	0.489218i	$-0.837282\pi$
$43$	−6.93786	+	3.23518i	−1.05801	+	0.493360i	−0.185852	+	0.982578i	$0.559505\pi$
$44$	2.64443	−	4.58028i	0.398662	−	0.690503i
$45$	−5.84326	+	3.29489i	−0.871062	+	0.491174i
$46$	1.21906	+	2.11147i	0.179740	+	0.311319i
$47$	−9.02466	−	6.31914i	−1.31638	−	0.921741i	−0.316741	−	0.948512i	$-0.602589\pi$
$47$	−9.02466	−	6.31914i	−1.31638	−	0.921741i	−0.999642	+	0.0267711i	$0.991477\pi$
$48$	−3.73025	+	7.36121i	−0.538415	+	1.06250i
$49$	−0.957202	−	2.62989i	−0.136743	−	0.375699i
$50$	9.22773	+	1.40729i	1.30500	+	0.199020i
$51$	5.87541	−	0.838984i	0.822721	−	0.117481i
$52$	−2.81599	−	0.246367i	−0.390507	−	0.0341649i
$53$	−3.54041	−	3.54041i	−0.486312	−	0.486312i	0.420828	−	0.907140i	$-0.361740\pi$
$53$	−3.54041	−	3.54041i	−0.486312	−	0.486312i	−0.907140	+	0.420828i	$0.861740\pi$
$54$	−8.74687	−	4.19455i	−1.19030	−	0.570806i
$55$	3.13219	+	7.32049i	0.422344	+	0.987095i
$56$	1.93357	+	2.30434i	0.258384	+	0.307930i
$57$	3.93543	+	9.21460i	0.521261	+	1.22050i
$58$	−0.0201844	−	0.0288263i	−0.00265034	−	0.00378507i
$59$	5.27046	−	1.91829i	0.686155	−	0.249740i	0.0246670	−	0.999696i	$-0.492147\pi$
$59$	5.27046	−	1.91829i	0.686155	−	0.249740i	0.661488	+	0.749956i	$0.269925\pi$
$60$	2.54791	+	5.15732i	0.328933	+	0.665807i
$61$	1.47697	+	8.37633i	0.189107	+	1.07248i	0.920564	+	0.390591i	$0.127729\pi$
$61$	1.47697	+	8.37633i	0.189107	+	1.07248i	−0.731457	+	0.681887i	$0.761159\pi$
$62$	2.70371	+	0.724458i	0.343372	+	0.0920063i
$63$	−7.06005	+	6.19223i	−0.889483	+	0.780147i
$64$	3.02114	+	1.74425i	0.377642	+	0.218032i
$65$	2.83853	−	3.17075i	0.352076	−	0.393284i
$66$	−6.08006	+	9.77816i	−0.748403	+	1.20361i
$67$	0.0194833	+	0.222695i	0.00238026	+	0.0272065i	0.997292	−	0.0735444i	$-0.0234311\pi$
$67$	0.0194833	+	0.222695i	0.00238026	+	0.0272065i	−0.994912	+	0.100751i	$0.967876\pi$
$68$	−0.443565	−	5.06998i	−0.0537902	−	0.614825i
$69$	−1.06637	−	1.99489i	−0.128376	−	0.240157i
$70$	13.0474	−	0.721334i	1.55946	−	0.0862159i
$71$	−0.428964	−	0.247662i	−0.0509086	−	0.0293921i	0.474330	−	0.880347i	$-0.342690\pi$
$71$	−0.428964	−	0.247662i	−0.0509086	−	0.0293921i	−0.525238	+	0.850955i	$0.676024\pi$
$72$	1.38650	−	2.52760i	0.163400	−	0.297881i
$73$	7.75123	+	2.07694i	0.907213	+	0.243087i	0.682111	−	0.731248i	$-0.261062\pi$
$73$	7.75123	+	2.07694i	0.907213	+	0.243087i	0.225102	+	0.974335i	$0.427729\pi$
$74$	3.28118	+	18.6085i	0.381429	+	2.16319i
$75$	−8.51401	−	1.58482i	−0.983113	−	0.182999i
$76$	8.07394	−	2.93867i	0.926145	−	0.337089i
$77$	6.39345	+	9.13079i	0.728601	+	1.04055i
$78$	6.10985	+	0.736488i	0.691804	+	0.0833908i
$79$	−1.13950	−	1.35801i	−0.128204	−	0.152788i	0.698124	−	0.715977i	$-0.254019\pi$
$79$	−1.13950	−	1.35801i	−0.128204	−	0.152788i	−0.826328	+	0.563190i	$0.809574\pi$
$80$	−9.79489	+	4.19090i	−1.09510	+	0.468557i
$81$	7.98358	+	4.15481i	0.887065	+	0.461645i
$82$	−13.1244	−	13.1244i	−1.44935	−	1.44935i
$83$	−7.35695	−	0.643650i	−0.807531	−	0.0706498i	−0.324089	−	0.946027i	$-0.605058\pi$
$83$	−7.35695	−	0.643650i	−0.807531	−	0.0706498i	−0.483441	+	0.875377i	$0.660613\pi$
$84$	4.97180	+	6.33469i	0.542468	+	0.691172i
$85$	6.50942	+	4.04161i	0.706046	+	0.438374i
$86$	−4.88786	−	13.4293i	−0.527072	−	1.44812i
$87$	0.0178423	+	0.0273422i	0.00191290	+	0.00293139i
$88$	−2.80307	−	1.96273i	−0.298808	−	0.209228i
$89$	−4.43260	−	7.67748i	−0.469854	−	0.813812i	0.529552	−	0.848278i	$-0.322360\pi$
$89$	−4.43260	−	7.67748i	−0.469854	−	0.813812i	−0.999406	+	0.0344662i	$0.989027\pi$
$90$	−5.17702	−	11.4033i	−0.545706	−	1.20201i
$91$	2.97878	−	5.15940i	0.312261	−	0.540852i
$92$	−1.75798	+	0.819758i	−0.183282	+	0.0854656i
$93$	−2.48513	−	0.753777i	−0.257696	−	0.0781630i
$94$	13.2206	−	15.7557i	1.36360	−	1.62508i
$95$	−3.74646	+	12.3811i	−0.384379	+	1.27027i
$96$	−10.2563	−	6.37738i	−1.04678	−	0.650889i
$97$	3.23451	+	6.93643i	0.328415	+	0.704288i	0.999305	−	0.0372686i	$-0.0118657\pi$
$97$	3.23451	+	6.93643i	0.328415	+	0.704288i	−0.670890	+	0.741556i	$0.734088\pi$
$98$	5.04676	−	1.35228i	0.509800	−	0.136601i
$99$	5.93448	−	8.88270i	0.596438	−	0.892745i
$100$	−1.75519	+	7.21588i	−0.175519	+	0.721588i
$101$	16.6975	−	2.94423i	1.66147	−	0.292961i	0.737475	−	0.675374i	$-0.236018\pi$
$101$	16.6975	−	2.94423i	1.66147	−	0.292961i	0.923992	+	0.382413i	$0.124907\pi$
$102$	0.604341	+	11.0635i	0.0598387	+	1.09545i
$103$	0.931271	−	1.99712i	0.0917609	−	0.196782i	−0.855071	−	0.518511i	$-0.826486\pi$
$103$	0.931271	−	1.99712i	0.0917609	−	0.196782i	0.946832	+	0.321730i	$0.104264\pi$
$104$	−0.317588	+	1.80113i	−0.0311421	+	0.176616i
$105$	−12.1205	+	0.273166i	−1.18284	+	0.0266582i
$106$	7.16044	−	6.00832i	0.695483	−	0.583579i
$107$	13.8021	−	13.8021i	1.33430	−	1.33430i	0.432826	−	0.901477i	$-0.357516\pi$
$107$	13.8021	−	13.8021i	1.33430	−	1.33430i	0.901477	−	0.432826i	$-0.142484\pi$
$108$	3.93090	−	6.64150i	0.378251	−	0.639079i
$109$		−	14.9196i		−	1.42903i	−0.699618	−	0.714517i	$-0.746646\pi$
$109$		−	14.9196i		−	1.42903i	0.699618	−	0.714517i	$-0.253354\pi$
$110$	−14.1241	+	4.63407i	−1.34668	+	0.441841i
$111$	−2.47820	−	17.3548i	−0.235220	−	1.64724i
$112$	−12.2171	+	8.55450i	−1.15441	+	0.808324i
$113$	−6.41164	−	2.98979i	−0.603156	−	0.281256i	0.0969568	−	0.995289i	$-0.469089\pi$
$113$	−6.41164	−	2.98979i	−0.603156	−	0.281256i	−0.700113	+	0.714032i	$0.746867\pi$
$114$	−17.7775	+	5.81973i	−1.66501	+	0.545068i
$115$	0.598956	−	2.85817i	0.0558529	−	0.266526i
$116$	0.0242459	−	0.0139984i	0.00225118	−	0.00129972i
$117$	−5.64321	−	0.868236i	−0.521715	−	0.0802685i
$118$	2.71004	+	10.1140i	0.249480	+	0.931070i
$119$	10.0793	+	3.66856i	0.923967	+	0.336296i
$120$	3.46779	−	1.35141i	0.316565	−	0.123367i
$121$	−1.28699	−	1.07991i	−0.116999	−	0.0981738i
$122$	−15.8184	+	1.38393i	−1.43213	+	0.125296i
$123$	11.7720	+	12.5681i	1.06144	+	1.13322i
$124$	−0.761645	+	2.09260i	−0.0683978	+	0.187921i
$125$	−7.11056	−	8.62786i	−0.635987	−	0.771699i
$126$	−10.3674	−	14.1377i	−0.923605	−	1.25948i
$127$	0.370667	−	1.38335i	0.0328914	−	0.122752i	−0.947528	−	0.319672i	$-0.896427\pi$
$127$	0.370667	−	1.38335i	0.0328914	−	0.122752i	0.980420	+	0.196920i	$0.0630939\pi$
$128$	4.26347	−	6.08886i	0.376841	−	0.538184i
$129$	4.12512	+	12.6010i	0.363197	+	1.10945i
$130$	5.43505	+	5.79495i	0.476685	+	0.508250i
$131$	−5.99175	−	1.05651i	−0.523502	−	0.0923075i	−0.0943485	−	0.995539i	$-0.530077\pi$
$131$	−5.99175	−	1.05651i	−0.523502	−	0.0923075i	−0.429153	+	0.903232i	$0.641188\pi$
$132$	−7.32812	−	5.49678i	−0.637831	−	0.478433i
$133$	−1.57826	+	18.0396i	−0.136852	+	1.56423i
$134$	−0.417333			−0.0360521
$135$	4.45470	+	10.7311i	0.383400	+	0.923583i
$136$	−3.29283			−0.282358
$137$	0.0905225	−	1.03468i	0.00773386	−	0.0883984i	−0.991347	−	0.131269i	$-0.958095\pi$
$137$	0.0905225	−	1.03468i	0.00773386	−	0.0883984i	0.999081	+	0.0428707i	$0.0136504\pi$
$138$	3.88357	−	1.65862i	0.330592	−	0.141191i
$139$	18.7473	+	3.30565i	1.59012	+	0.280381i	0.897532	−	0.440950i	$-0.145358\pi$
$139$	18.7473	+	3.30565i	1.59012	+	0.280381i	0.692590	+	0.721331i	$0.256469\pi$
$140$	−0.333001	+	10.3907i	−0.0281438	+	0.878179i
$141$	−12.7371	+	14.2090i	−1.07265	+	1.19661i
$142$	0.530394	−	0.757481i	0.0445097	−	0.0635664i
$143$	−1.75405	+	6.54620i	−0.146681	+	0.547421i
$144$	11.8851	+	7.94040i	0.990428	+	0.661700i
$145$	−0.00501665	+	0.0418498i	−0.000416610	+	0.00347544i
$146$	−5.12385	+	14.0777i	−0.424052	+	1.16507i
$147$	−4.72078	+	1.10088i	−0.389363	+	0.0907988i
$148$	−14.9757	+	1.31021i	−1.23100	+	0.107698i
$149$	−2.25551	−	1.89260i	−0.184779	−	0.155048i	0.545706	−	0.837977i	$-0.316261\pi$
$149$	−2.25551	−	1.89260i	−0.184779	−	0.155048i	−0.730485	+	0.682929i	$0.760706\pi$
$150$	4.33272	−	15.5763i	0.353765	−	1.27180i
$151$	−16.5766	−	6.03340i	−1.34899	−	0.490992i	−0.436356	−	0.899774i	$-0.643731\pi$
$151$	−16.5766	−	6.03340i	−1.34899	−	0.490992i	−0.912632	+	0.408782i	$0.865953\pi$
$152$	−1.43881	−	5.36972i	−0.116703	−	0.435542i
$153$	−0.224850	−	10.2773i	−0.0181781	−	0.830868i
$154$	−18.0215	+	10.4047i	−1.45222	+	0.838438i
$155$	−1.83403	−	2.80650i	−0.147313	−	0.225423i
$156$	−1.00736	+	4.79131i	−0.0806532	+	0.383612i
$157$	7.82751	+	3.65003i	0.624703	+	0.291304i	0.709078	−	0.705130i	$-0.249111\pi$
$157$	7.82751	+	3.65003i	0.624703	+	0.291304i	−0.0843747	+	0.996434i	$0.526889\pi$
$158$	2.71100	−	1.89826i	0.215676	−	0.151018i
$159$	−6.82196	+	5.35423i	−0.541016	+	0.424618i
$160$	−4.86068	−	14.8148i	−0.384270	−	1.17122i
$161$		−	4.08808i		−	0.322186i
$162$	−9.02603	+	14.1717i	−0.709152	+	1.11343i
$163$	7.31819	−	7.31819i	0.573205	−	0.573205i	−0.359818	−	0.933023i	$-0.617161\pi$
$163$	7.31819	−	7.31819i	0.573205	−	0.573205i	0.933023	+	0.359818i	$0.117161\pi$
$164$	11.3118	−	9.49174i	0.883305	−	0.741181i
$165$	13.2376	−	3.86871i	1.03054	−	0.301178i
$166$	2.39409	−	13.5776i	0.185818	−	1.05382i
$167$	−2.98173	+	6.39434i	−0.230733	+	0.494809i	−0.987252	−	0.159163i	$-0.949121\pi$
$167$	−2.98173	+	6.39434i	−0.230733	+	0.494809i	0.756519	+	0.653971i	$0.226898\pi$
$168$	4.36335	−	2.84732i	0.336639	−	0.219676i
$169$	−9.23535	+	1.62844i	−0.710411	+	0.125265i
$170$	−8.57565	+	11.4485i	−0.657722	+	0.878058i
$171$	16.6612	−	4.85735i	1.27411	−	0.371451i
$172$	10.9823	−	2.94271i	0.837396	−	0.224379i
$173$	1.56841	+	3.36346i	0.119244	+	0.255719i	0.956865	−	0.290532i	$-0.0938323\pi$
$173$	1.56841	+	3.36346i	0.119244	+	0.255719i	−0.837622	+	0.546251i	$0.816055\pi$
$174$	−0.0537536	+	0.0287339i	−0.00407505	+	0.00217831i
$175$	−12.2198	−	9.77978i	−0.923727	−	0.739282i
$176$	10.9056	−	12.9967i	0.822037	−	0.979666i
$177$	−2.20622	−	9.46072i	−0.165830	−	0.711111i
$178$	14.9997	−	6.99445i	1.12427	−	0.524256i
$179$	−2.76656	+	4.79182i	−0.206782	+	0.358157i	−0.950699	−	0.310115i	$-0.899632\pi$
$179$	−2.76656	+	4.79182i	−0.206782	+	0.358157i	0.743917	+	0.668272i	$0.232966\pi$
$180$	9.39668	−	3.31237i	0.700387	−	0.246889i
$181$	7.47188	+	12.9417i	0.555381	+	0.961948i	0.997874	+	0.0651757i	$0.0207608\pi$
$181$	7.47188	+	12.9417i	0.555381	+	0.961948i	−0.442493	+	0.896772i	$0.645906\pi$
$182$	9.11067	+	6.37936i	0.675328	+	0.472870i
$183$	14.7101	−	0.803538i	1.08740	−	0.0593993i
$184$	0.429237	+	1.17932i	0.0316437	+	0.0869405i
$185$	11.9381	−	19.2276i	0.877708	−	1.41364i
$186$	1.80621	−	4.49915i	0.132438	−	0.329894i
$187$	−12.1553	−	1.06345i	−0.888882	−	0.0777671i
$188$	11.5705	+	11.5705i	0.843867	+	0.843867i
$189$	9.18475	+	13.4240i	0.668092	+	0.976454i
$190$	−22.4165	−	8.98212i	−1.62627	−	0.651632i
$191$	−1.79674	−	2.14127i	−0.130008	−	0.154937i	0.697113	−	0.716961i	$-0.254467\pi$
$191$	−1.79674	−	2.14127i	−0.130008	−	0.154937i	−0.827121	+	0.562024i	$0.810023\pi$
$192$	3.62565	−	4.83360i	0.261659	−	0.348835i
$193$	−6.82607	−	9.74863i	−0.491351	−	0.701722i	0.494532	−	0.869160i	$-0.335340\pi$
$193$	−6.82607	−	9.74863i	−0.491351	−	0.701722i	−0.985883	+	0.167438i	$0.946451\pi$
$194$	−13.4265	+	4.88685i	−0.963968	+	0.350856i
$195$	−4.86406	−	5.53838i	−0.348323	−	0.396612i
$196$	0.721811	+	4.09359i	0.0515579	+	0.292399i
$197$	18.9450	+	5.07629i	1.34977	+	0.361671i	0.860051	−	0.510208i	$-0.170432\pi$
$197$	18.9450	+	5.07629i	1.34977	+	0.361671i	0.489722	+	0.871879i	$0.337098\pi$
$198$	15.5543	+	12.4821i	1.10539	+	0.887066i
$199$	−10.1682	−	5.87060i	−0.720802	−	0.416156i	0.0942455	−	0.995549i	$-0.469956\pi$
$199$	−10.1682	−	5.87060i	−0.720802	−	0.416156i	−0.815048	+	0.579393i	$0.803289\pi$
$200$	4.55197	+	1.53820i	0.321873	+	0.108767i
$201$	0.386985	+	0.0126573i	0.0272958	+	0.000892776i
$202$	2.75876	+	31.5328i	0.194106	+	2.21864i
$203$	0.00514264	+	0.0587806i	0.000360943	+	0.00412559i
$204$	−8.81029	−	0.288162i	−0.616844	−	0.0201754i
$205$	1.22719	+	22.1973i	0.0857109	+	1.55032i
$206$	3.56267	+	2.05691i	0.248223	+	0.143312i
$207$	−3.65146	+	1.42022i	−0.253794	+	0.0987122i
$208$	−8.75888	−	2.34694i	−0.607319	−	0.162731i
$209$	−3.57709	−	20.2867i	−0.247432	−	1.40326i
$210$	1.46409	−	22.5858i	0.101032	−	1.55857i
$211$	−5.77638	+	2.10243i	−0.397662	+	0.144737i	−0.533107	−	0.846048i	$-0.678976\pi$
$211$	−5.77638	+	2.10243i	−0.397662	+	0.144737i	0.135445	+	0.990785i	$0.456754\pi$
$212$	4.26541	+	6.09163i	0.292949	+	0.418375i
$213$	−0.514798	+	0.686311i	−0.0352734	+	0.0470253i
$214$	23.4232	+	27.9147i	1.60118	+	1.90821i
$215$	−6.36668	+	15.8892i	−0.434204	+	1.08364i
$216$	−4.05907	−	2.90815i	−0.276185	−	0.197875i
$217$	−3.31870	−	3.31870i	−0.225288	−	0.225288i
$218$	27.7471	+	2.42756i	1.87927	+	0.164415i
$219$	5.17820	−	12.8985i	0.349911	−	0.871602i
$220$	−2.69338	−	11.5154i	−0.181588	−	0.776371i
$221$	2.23047	+	6.12818i	0.150038	+	0.412226i
$222$	32.6793	−	1.78511i	2.19329	−	0.119808i
$223$	−7.89767	−	5.53001i	−0.528867	−	0.370317i	0.278435	−	0.960455i	$-0.410184\pi$
$223$	−7.89767	−	5.53001i	−0.528867	−	0.370317i	−0.807302	+	0.590138i	$0.799073\pi$
$224$	−10.9135	−	18.9028i	−0.729192	−	1.26300i
$225$	−4.49006	+	14.3122i	−0.299338	+	0.954147i
$226$	6.60360	−	11.4378i	0.439265	−	0.760829i
$227$	−0.828704	+	0.386431i	−0.0550030	+	0.0256483i	−0.449925	−	0.893066i	$-0.648549\pi$
$227$	−0.828704	+	0.386431i	−0.0550030	+	0.0256483i	0.394922	+	0.918715i	$0.370772\pi$
$228$	−3.37976	−	14.4931i	−0.223830	−	0.959830i
$229$	−3.03966	+	3.62252i	−0.200866	+	0.239383i	−0.857069	−	0.515201i	$-0.827717\pi$
$229$	−3.03966	+	3.62252i	−0.200866	+	0.239383i	0.656203	+	0.754585i	$0.272162\pi$
$230$	5.21812	+	1.57898i	0.344072	+	0.104115i
$231$	17.0266	−	9.10154i	1.12027	−	0.598837i
$232$	−0.00765533	−	0.0164169i	−0.000502597	−	0.00107782i
$233$	−3.91060	+	1.04784i	−0.256192	+	0.0686464i	−0.384629	−	0.923071i	$-0.625671\pi$
$233$	−3.91060	+	1.04784i	−0.256192	+	0.0686464i	0.128437	+	0.991718i	$0.459004\pi$
$234$	2.53293	−	10.3539i	0.165583	−	0.676853i
$235$	−24.3853	+	3.49851i	−1.59072	+	0.228218i
$236$	−8.20380	+	1.44655i	−0.534022	+	0.0941625i
$237$	−2.57143	+	1.67800i	−0.167032	+	0.108998i
$238$	−8.46271	+	18.1483i	−0.548556	+	1.17638i
$239$	−2.52463	+	14.3179i	−0.163305	+	0.926146i	0.787491	+	0.616327i	$0.211380\pi$
$239$	−2.52463	+	14.3179i	−0.163305	+	0.926146i	−0.950795	+	0.309820i	$0.899731\pi$
$240$	5.17637	+	17.7120i	0.334133	+	1.14331i
$241$	−12.3103	+	10.3295i	−0.792974	+	0.665384i	−0.946480	−	0.322764i	$-0.895388\pi$
$241$	−12.3103	+	10.3295i	−0.792974	+	0.665384i	0.153506	+	0.988148i	$0.450944\pi$
$242$	2.21780	−	2.21780i	0.142566	−	0.142566i
$243$	8.79948	−	12.8674i	0.564487	−	0.825442i
$244$		−	12.6329i		−	0.808739i
$245$	−5.58407	−	2.82507i	−0.356753	−	0.180487i
$246$	−25.2892	+	19.8483i	−1.61238	+	1.26548i
$247$	−9.01879	+	6.31502i	−0.573852	+	0.401815i
$248$	1.30582	+	0.608915i	0.0829199	+	0.0386662i
$249$	−2.63179	+	12.5176i	−0.166783	+	0.793272i
$250$	17.2029	−	11.8202i	1.08801	−	0.747577i
$251$	5.03670	−	2.90794i	0.317914	−	0.183547i	−0.332549	−	0.943086i	$-0.607909\pi$
$251$	5.03670	−	2.90794i	0.317914	−	0.183547i	0.650462	+	0.759539i	$0.274575\pi$
$252$	11.9237	−	7.23645i	0.751124	−	0.455853i
$253$	1.20363	+	4.49200i	0.0756715	+	0.282410i
$254$	2.51241	+	0.914443i	0.157643	+	0.0573773i
$255$	8.29925	−	10.3559i	0.519719	−	0.648509i
$256$	15.9749	+	13.4046i	0.998434	+	0.837785i
$257$	−10.8182	+	0.946469i	−0.674820	+	0.0590391i	−0.419414	−	0.907795i	$-0.637765\pi$
$257$	−10.8182	+	0.946469i	−0.674820	+	0.0590391i	−0.255406	+	0.966834i	$0.582209\pi$
$258$	−24.1062	+	5.62152i	−1.50079	+	0.349981i
$259$	10.8362	−	29.7722i	0.673329	−	1.84996i
$260$	−4.96966	+	3.90574i	−0.308205	+	0.242224i
$261$	0.0507161	−	0.0250141i	0.00313925	−	0.00154833i
$262$	2.93979	−	10.9714i	0.181621	−	0.677817i
$263$	−7.24249	+	10.3433i	−0.446591	+	0.637798i	−0.977824	−	0.209428i	$-0.932840\pi$
$263$	−7.24249	+	10.3433i	−0.446591	+	0.637798i	0.531233	+	0.847226i	$0.321729\pi$
$264$	−3.95614	+	4.41333i	−0.243484	+	0.271621i
$265$	−11.1900	−	0.358616i	−0.687396	−	0.0220296i
$266$	−33.2929	−	5.87043i	−2.04132	−	0.359939i
$267$	−14.1210	+	6.03090i	−0.864193	+	0.369085i
$268$	0.0289376	−	0.330759i	0.00176765	−	0.0202043i
$269$	0.247995			0.0151205			0.00756025	−	0.999971i	$-0.497593\pi$
$269$	0.247995			0.0151205			0.00756025	+	0.999971i	$0.497593\pi$
$270$	−20.6822	+	6.53872i	−1.25868	+	0.397934i
$271$	10.3307			0.627548			0.313774	−	0.949498i	$-0.398407\pi$
$271$	10.3307			0.627548			0.313774	+	0.949498i	$0.398407\pi$
$272$	1.42291	−	16.2639i	0.0862764	−	0.986143i
$273$	−8.25467	−	6.19178i	−0.499595	−	0.374743i
$274$	1.90954	+	0.336704i	0.115360	+	0.0203410i
$275$	16.3065	+	7.14828i	0.983321	+	0.431058i
$276$	1.04526	+	3.19294i	0.0629172	+	0.192193i
$277$	8.26002	−	11.7965i	0.496297	−	0.708785i	−0.490375	−	0.871512i	$-0.663140\pi$
$277$	8.26002	−	11.7965i	0.496297	−	0.708785i	0.986671	+	0.162727i	$0.0520289\pi$
$278$	−9.19814	+	34.3279i	−0.551668	+	2.05885i
$279$	−1.81132	+	4.11719i	−0.108441	+	0.246490i
$280$	6.67851	+	0.800570i	0.399117	+	0.0478432i
$281$	3.43244	−	9.43056i	0.204762	−	0.562580i	−0.794223	−	0.607627i	$-0.792122\pi$
$281$	3.43244	−	9.43056i	0.204762	−	0.562580i	0.998985	+	0.0450472i	$0.0143438\pi$
$282$	−24.3531	−	26.0001i	−1.45021	−	1.54828i
$283$	−21.5718	+	1.88728i	−1.28231	+	0.112187i	−0.707860	−	0.706353i	$-0.750339\pi$
$283$	−21.5718	+	1.88728i	−1.28231	+	0.112187i	−0.574449	+	0.818541i	$0.694783\pi$
$284$	0.563566	+	0.472888i	0.0334415	+	0.0280608i
$285$	20.5140	+	9.00882i	1.21514	+	0.533636i
$286$	−11.8891	−	4.32727i	−0.703017	−	0.255877i
$287$	8.05485	+	30.0611i	0.475462	+	1.77445i
$288$	−13.0925	+	16.3149i	−0.771484	+	0.961364i
$289$	4.55406	−	2.62929i	0.267886	−	0.154664i
$290$	−0.0770152	−	0.0161392i	−0.00452249	−	0.000947728i
$291$	12.5984	−	4.12427i	0.738529	−	0.241769i
$292$	−10.8020	−	5.03705i	−0.632139	−	0.294771i
$293$	−11.7339	+	8.21615i	−0.685500	+	0.479992i	−0.863703	−	0.504001i	$-0.831861\pi$
$293$	−11.7339	+	8.21615i	−0.685500	+	0.479992i	0.178203	+	0.983994i	$0.442972\pi$
$294$	−1.27927	−	8.95873i	−0.0746086	−	0.522484i
$295$	5.66160	−	11.1908i	0.329631	−	0.651554i
$296$			9.72638i			0.565334i
$297$	−14.0446	−	12.0462i	−0.814950	−	0.698990i
$298$	3.88681	−	3.88681i	0.225157	−	0.225157i
$299$	1.90404	−	1.59768i	0.110113	−	0.0923960i
$300$	12.0446	+	4.51396i	0.695397	+	0.260614i
$301$	−4.16106	+	23.5985i	−0.239839	+	1.36020i
$302$	13.9180	−	29.8472i	0.800890	−	1.71751i
$303$	−1.60179	−	29.3234i	−0.0920204	−	1.68459i
$304$	27.1438	−	4.78618i	1.55680	−	0.274506i
$305$	15.2220	+	11.4023i	0.871610	+	0.652892i
$306$	19.1500	+	1.25404i	1.09474	+	0.0716887i
$307$	11.2937	−	3.02613i	0.644564	−	0.172710i	0.0782941	−	0.996930i	$-0.475053\pi$
$307$	11.2937	−	3.02613i	0.644564	−	0.172710i	0.566270	+	0.824220i	$0.308386\pi$
$308$	−6.99670	−	15.0045i	−0.398674	−	0.854959i
$309$	−3.24121	−	2.01538i	−0.184386	−	0.114651i
$310$	5.51788	−	2.95425i	0.313394	−	0.167790i
$311$	16.3947	−	19.5384i	0.929657	−	1.10792i	−0.0642755	−	0.997932i	$-0.520474\pi$
$311$	16.3947	−	19.5384i	0.929657	−	1.10792i	0.993933	−	0.109990i	$-0.0350819\pi$
$312$	3.03140	+	0.919469i	0.171619	+	0.0520547i
$313$	27.0049	−	12.5926i	1.52641	−	0.711775i	0.535276	−	0.844677i	$-0.320207\pi$
$313$	27.0049	−	12.5926i	1.52641	−	0.711775i	0.991129	+	0.132902i	$0.0424297\pi$
$314$	−8.06186	+	13.9635i	−0.454957	+	0.788008i
$315$	−2.04262	+	20.8990i	−0.115089	+	1.17752i
$316$	1.31649	+	2.28023i	0.0740586	+	0.128273i
$317$	−20.6398	−	14.4521i	−1.15925	−	0.811713i	−0.174321	−	0.984689i	$-0.555773\pi$
$317$	−20.6398	−	14.4521i	−1.15925	−	0.811713i	−0.984926	+	0.172976i	$0.944662\pi$
$318$	−8.84769	−	13.5585i	−0.496154	−	0.760324i
$319$	−0.0229572	−	0.0630743i	−0.00128536	−	0.00353148i
$320$	7.59555	−	1.77654i	0.424604	−	0.0993118i
$321$	−20.8733	−	26.5952i	−1.16503	−	1.48440i
$322$	7.60293	+	0.665170i	0.423695	+	0.0370685i
$323$	−14.0166	−	14.0166i	−0.779907	−	0.779907i
$324$	−10.6059	−	8.13626i	−0.589219	−	0.452014i
$325$	−0.220682	−	9.51346i	−0.0122412	−	0.527712i
$326$	12.4195	+	14.8010i	0.687852	+	0.819750i
$327$	−25.6557	−	3.09257i	−1.41876	−	0.171019i
$328$	−5.47996	−	7.82620i	−0.302580	−	0.432130i
$329$	−32.4068	+	11.7951i	−1.78664	+	0.650285i
$330$	5.04106	+	25.2485i	0.277501	+	1.38988i
$331$	4.41876	+	25.0600i	0.242877	+	1.37742i	0.825372	+	0.564589i	$0.190965\pi$
$331$	4.41876	+	25.0600i	0.242877	+	1.37742i	−0.582495	+	0.812834i	$0.697924\pi$
$332$	10.5949	+	2.83891i	0.581473	+	0.155805i
$333$	−30.3571	+	0.664163i	−1.66356	+	0.0363959i
$334$	−11.4069	−	6.58578i	−0.624158	−	0.360358i
$335$	0.372429	+	0.333406i	0.0203479	+	0.0182159i
$336$	12.1780	+	22.7817i	0.664362	+	1.24285i
$337$	−1.37458	−	15.7115i	−0.0748780	−	0.855859i	−0.937039	−	0.349225i	$-0.886445\pi$
$337$	−1.37458	−	15.7115i	−0.0748780	−	0.855859i	0.862161	−	0.506634i	$-0.169111\pi$
$338$	−1.52586	−	17.4407i	−0.0829959	−	0.948648i
$339$	−6.47028	+	10.4057i	−0.351417	+	0.565162i
$340$	−8.47889	−	7.59048i	−0.459832	−	0.411652i
$341$	4.62371	+	2.66950i	0.250388	+	0.144562i
$342$	6.32266	+	31.7765i	0.341891	+	1.71828i
$343$	12.7032	+	3.40382i	0.685910	+	0.183789i
$344$	−1.27741	−	7.24453i	−0.0688731	−	0.390599i
$345$	−4.79077	−	1.62242i	−0.257926	−	0.0873480i
$346$	−6.51048	+	2.36962i	−0.350006	+	0.127392i
$347$	−6.38852	−	9.12375i	−0.342954	−	0.489788i	0.610212	−	0.792238i	$-0.291084\pi$
$347$	−6.38852	−	9.12375i	−0.342954	−	0.489788i	−0.953165	+	0.302450i	$0.902195\pi$
$348$	−0.0190459	−	0.0445949i	−0.00102097	−	0.00239054i
$349$	0.156572	+	0.186596i	0.00838112	+	0.00998823i	0.770219	−	0.637780i	$-0.220147\pi$
$349$	0.156572	+	0.186596i	0.00838112	+	0.00998823i	−0.761838	+	0.647768i	$0.775703\pi$
$350$	20.1765	−	21.1348i	1.07848	−	1.12970i
$351$	−2.66276	+	9.52411i	−0.142128	+	0.508359i
$352$	17.5573	+	17.5573i	0.935807	+	0.935807i
$353$	−14.0660	−	1.23061i	−0.748656	−	0.0654989i	−0.293559	−	0.955941i	$-0.594840\pi$
$353$	−14.0660	−	1.23061i	−0.748656	−	0.0654989i	−0.455097	+	0.890442i	$0.650395\pi$
$354$	17.9538	−	2.56374i	0.954235	−	0.136261i
$355$	−1.07847	+	0.252247i	−0.0572394	+	0.0133879i
$356$	4.50341	+	12.3730i	0.238680	+	0.655768i
$357$	8.39773	−	16.5719i	0.444455	−	0.877080i
$358$	−8.46158	−	5.92486i	−0.447208	−	0.313139i
$359$	0.501469	+	0.868570i	0.0264665	+	0.0458414i	0.878955	−	0.476904i	$-0.158241\pi$
$359$	0.501469	+	0.868570i	0.0264665	+	0.0458414i	−0.852489	+	0.522746i	$0.824908\pi$
$360$	−1.60508	−	6.24335i	−0.0845953	−	0.329053i
$361$	7.23275	−	12.5275i	0.380671	−	0.659341i
$362$	−25.2844	+	11.7903i	−1.32892	+	0.619686i
$363$	−2.12379	+	1.98926i	−0.111470	+	0.104409i
$364$	−5.68771	+	6.77835i	−0.298117	+	0.355282i
$365$	15.8191	−	8.46949i	0.828010	−	0.443313i
$366$	−0.899072	+	27.4883i	−0.0469952	+	1.43684i
$367$	−6.15484	−	13.1991i	−0.321280	−	0.688987i	0.677643	−	0.735391i	$-0.263002\pi$
$367$	−6.15484	−	13.1991i	−0.321280	−	0.688987i	−0.998923	+	0.0464043i	$0.985224\pi$
$368$	−6.01035	+	1.61047i	−0.313311	+	0.0839514i
$369$	24.0522	−	17.6379i	1.25211	−	0.918195i
$370$	33.8166	+	25.3308i	1.75804	+	1.31689i
$371$	−15.4349	+	2.72159i	−0.801339	+	0.141298i
$372$	3.44057	+	1.74349i	0.178385	+	0.0903956i
$373$	15.0887	−	32.3578i	0.781262	−	1.67542i	0.0447484	−	0.998998i	$-0.485751\pi$
$373$	15.0887	−	32.3578i	0.781262	−	1.67542i	0.736513	−	0.676423i	$-0.236471\pi$
$374$	3.95556	−	22.4331i	0.204537	−	1.15999i
$375$	−16.3104	+	10.4389i	−0.842265	+	0.539064i
$376$	8.11016	−	6.80523i	0.418250	−	0.350953i
$377$	−0.0253674	+	0.0253674i	−0.00130649	+	0.00130649i
$378$	−26.4602	+	14.8974i	−1.36097	+	0.766239i
$379$			33.2247i			1.70664i	0.521388	+	0.853320i	$0.325415\pi$
$379$			33.2247i			1.70664i	−0.521388	+	0.853320i	$0.674585\pi$
$380$	8.67315	−	17.1435i	0.444923	−	0.879441i
$381$	−2.30198	−	0.924144i	−0.117934	−	0.0473453i
$382$	4.27464	−	2.99314i	0.218710	−	0.153142i
$383$	29.7492	+	13.8723i	1.52012	+	0.708842i	0.990258	−	0.139245i	$-0.0444676\pi$
$383$	29.7492	+	13.8723i	1.52012	+	0.708842i	0.529858	+	0.848087i	$0.322245\pi$
$384$	−9.58668	−	8.59358i	−0.489218	−	0.438539i
$385$	24.3948	+	5.11214i	1.24327	+	0.260539i
$386$	19.2410	−	11.1088i	0.979340	−	0.565422i
$387$	22.5237	−	4.48161i	1.14495	−	0.227813i
$388$	−2.94210	−	10.9801i	−0.149363	−	0.557429i
$389$	5.02600	+	1.82931i	0.254828	+	0.0927498i	0.466276	−	0.884640i	$-0.345596\pi$
$389$	5.02600	+	1.82931i	0.254828	+	0.0927498i	−0.211447	+	0.977389i	$0.567818\pi$
$390$	11.0916	−	8.14493i	0.561645	−	0.412435i
$391$	3.42808	+	2.87650i	0.173365	+	0.145471i
$392$	2.67920	−	0.234400i	0.135320	−	0.0118390i
$393$	−3.05876	+	10.0844i	−0.154294	+	0.508692i
$394$	−12.5233	+	34.4075i	−0.630915	+	1.73343i
$395$	−3.93582	−	0.471797i	−0.198032	−	0.0237387i
$396$	−10.9713	+	11.4621i	−0.551327	+	0.575991i
$397$	−7.94953	+	29.6681i	−0.398976	+	1.48900i	0.415926	+	0.909398i	$0.363458\pi$
$397$	−7.94953	+	29.6681i	−0.398976	+	1.48900i	−0.814902	+	0.579599i	$0.803209\pi$
$398$	12.5725	−	17.9554i	0.630201	−	0.900021i
$399$	30.6938	+	6.45327i	1.53661	+	0.323068i
$400$	−9.56447	+	21.8183i	−0.478224	+	1.09092i
$401$	−0.473405	−	0.0834740i	−0.0236407	−	0.00416849i	0.161815	−	0.986821i	$-0.448265\pi$
$401$	−0.473405	−	0.0834740i	−0.0236407	−	0.00416849i	−0.185456	+	0.982653i	$0.559376\pi$
$402$	−0.0865060	+	0.717647i	−0.00431452	+	0.0357930i
$403$	0.248703	−	2.84269i	0.0123888	−	0.141604i
$404$	−25.1827			−1.25289
$405$	19.3765	−	5.43596i	0.962828	−	0.270115i
$406$	−0.110156			−0.00546694
$407$	−3.14122	+	35.9043i	−0.155705	+	1.77971i
$408$	−0.682547	+	5.66236i	−0.0337911	+	0.280329i
$409$	−22.3819	−	3.94653i	−1.10671	−	0.195144i	−0.409714	−	0.912214i	$-0.634371\pi$
$409$	−22.3819	−	3.94653i	−1.10671	−	0.195144i	−0.697000	+	0.717071i	$0.745482\pi$
$410$	−41.4817	−	1.32940i	−2.04864	−	0.0656544i
$411$	−1.76047	−	0.370133i	−0.0868375	−	0.0182573i
$412$	−1.87724	+	2.68098i	−0.0924851	+	0.132082i
$413$	4.54404	−	16.9586i	0.223598	−	0.834478i
$414$	−2.04717	−	7.02200i	−0.100613	−	0.345113i
$415$	−12.9836	+	10.2040i	−0.637339	+	0.500896i
$416$	4.53888	−	12.4705i	0.222537	−	0.611416i
$417$	9.57039	−	31.5526i	0.468664	−	1.54514i
$418$	38.3107	−	3.35176i	1.87384	−	0.163940i
$419$	8.25865	+	6.92983i	0.403462	+	0.338544i	0.821830	−	0.569733i	$-0.192953\pi$
$419$	8.25865	+	6.92983i	0.403462	+	0.338544i	−0.418368	+	0.908277i	$0.637398\pi$
$420$	17.7989	+	2.72645i	0.868499	+	0.133037i
$421$	−23.5375	−	8.56694i	−1.14715	−	0.417527i	−0.302657	−	0.953099i	$-0.597874\pi$
$421$	−23.5375	−	8.56694i	−1.14715	−	0.417527i	−0.844489	+	0.535572i	$0.820096\pi$
$422$	−2.97018	−	11.0849i	−0.144586	−	0.539603i
$423$	21.7936	+	24.8480i	1.05964	+	1.20815i
$424$	4.16685	−	2.40573i	0.202360	−	0.116833i
$425$	16.7991	−	3.36558i	0.814874	−	0.163255i
$426$	−1.19263	−	1.06908i	−0.0577829	−	0.0517971i
$427$	24.1302	+	11.2521i	1.16774	+	0.544528i
$428$	−23.7480	+	16.6285i	−1.14790	+	0.803771i
$429$	10.8933	+	4.37318i	0.525932	+	0.211139i
$430$	−28.5145	−	14.4259i	−1.37509	−	0.695681i
$431$			14.1259i			0.680421i	0.940349	+	0.340210i	$0.110498\pi$
$431$			14.1259i			0.680421i	−0.940349	+	0.340210i	$0.889502\pi$
$432$	16.1179	−	18.7918i	0.775473	−	0.904122i
$433$	1.82757	−	1.82757i	0.0878275	−	0.0878275i	−0.661828	−	0.749656i	$-0.730219\pi$
$433$	1.82757	−	1.82757i	0.0878275	−	0.0878275i	0.749656	+	0.661828i	$0.230219\pi$
$434$	6.71204	−	5.63207i	0.322188	−	0.270348i
$435$	0.0709252	+	0.0173014i	0.00340060	+	0.000829538i
$436$	−3.84793	+	21.8227i	−0.184283	+	1.04512i
$437$	−3.19288	+	6.84716i	−0.152736	+	0.327544i
$438$	23.1459	+	11.7290i	1.10595	+	0.560435i
$439$	−24.0637	+	4.24307i	−1.14850	+	0.202511i	−0.715319	−	0.698798i	$-0.753719\pi$
$439$	−24.0637	+	4.24307i	−1.14850	+	0.202511i	−0.433177	+	0.901309i	$0.642607\pi$
$440$	−7.57408	+	1.08664i	−0.361080	+	0.0518036i
$441$	0.914534	+	8.34606i	0.0435492	+	0.397431i
$442$	−11.7600	+	3.15108i	−0.559365	+	0.149881i
$443$	12.5019	+	26.8103i	0.593981	+	1.27380i	0.941781	+	0.336227i	$0.109151\pi$
$443$	12.5019	+	26.8103i	0.593981	+	1.27380i	−0.347800	+	0.937569i	$0.613071\pi$
$444$	−0.851174	+	26.0239i	−0.0403949	+	1.23504i
$445$	−18.9736	−	5.74131i	−0.899433	−	0.272164i
$446$	11.5696	−	13.7881i	0.547838	−	0.652888i
$447$	−3.72205	+	3.48628i	−0.176047	+	0.164895i
$448$	9.89690	−	4.61500i	0.467584	−	0.218038i
$449$	15.2444	−	26.4040i	0.719426	−	1.24608i	−0.241802	−	0.970326i	$-0.577738\pi$
$449$	15.2444	−	26.4040i	0.719426	−	1.24608i	0.961228	−	0.275756i	$-0.0889283\pi$
$450$	−25.8870	−	10.6793i	−1.22032	−	0.503425i
$451$	−17.7014	−	30.6597i	−0.833527	−	1.44371i
$452$	8.60714	+	6.02678i	0.404846	+	0.283476i
$453$	−13.8111	+	27.2546i	−0.648903	+	1.28053i
$454$	−0.583838	−	1.60408i	−0.0274009	−	0.0752833i
$455$	−3.03393	−	12.9714i	−0.142233	−	0.608110i
$456$	−9.53202	+	1.36113i	−0.446378	+	0.0637410i
$457$	9.32149	+	0.815525i	0.436041	+	0.0381486i	0.303063	−	0.952970i	$-0.401991\pi$
$457$	9.32149	+	0.815525i	0.436041	+	0.0381486i	0.132978	+	0.991119i	$0.457546\pi$
$458$	−6.24252	−	6.24252i	−0.291694	−	0.291694i
$459$	−17.7194	−	1.74365i	−0.827072	−	0.0813865i
$460$	−1.61324	+	4.02615i	−0.0752179	+	0.187720i
$461$	−4.16189	−	4.95995i	−0.193839	−	0.231008i	0.660367	−	0.750943i	$-0.270401\pi$
$461$	−4.16189	−	4.95995i	−0.193839	−	0.231008i	−0.854206	+	0.519935i	$0.825956\pi$
$462$	14.1565	+	33.1466i	0.658619	+	1.54212i
$463$	7.62562	+	10.8905i	0.354393	+	0.506125i	0.956279	−	0.292457i	$-0.0944728\pi$
$463$	7.62562	+	10.8905i	0.354393	+	0.506125i	−0.601886	+	0.798582i	$0.705584\pi$
$464$	0.0843941	−	0.0307169i	0.00391790	−	0.00142600i
$465$	−5.20622	+	2.57207i	−0.241433	+	0.119277i
$466$	−1.31246	−	7.44335i	−0.0607987	−	0.344806i
$467$	−21.1655	−	5.67127i	−0.979421	−	0.262435i	−0.266620	−	0.963802i	$-0.585907\pi$
$467$	−21.1655	−	5.67127i	−0.979421	−	0.262435i	−0.712801	+	0.701367i	$0.752574\pi$
$468$	8.03034	+	2.72541i	0.371203	+	0.125982i
$469$	0.606010	+	0.349880i	0.0279829	+	0.0161560i
$470$	−2.53875	−	45.9204i	−0.117104	−	2.11815i
$471$	7.89910	−	12.7036i	0.363971	−	0.585352i
$472$	0.469751	+	5.36927i	0.0216220	+	0.247141i
$473$	−2.37578	−	27.1553i	−0.109239	−	1.24860i
$474$	−2.70231	−	5.05532i	−0.124121	−	0.232199i
$475$	12.8287	+	25.9241i	0.588623	+	1.18948i
$476$	−13.7967	−	7.96554i	−0.632372	−	0.365100i
$477$	7.79307	+	12.8409i	0.356820	+	0.587944i
$478$	−26.2173	−	7.02491i	−1.19915	−	0.321312i
$479$	2.75645	+	15.6326i	0.125945	+	0.714272i	0.980742	+	0.195309i	$0.0625709\pi$
$479$	2.75645	+	15.6326i	0.125945	+	0.714272i	−0.854796	+	0.518964i	$0.826318\pi$
$480$	−26.4832	+	5.28758i	−1.20879	+	0.241344i
$481$	18.1014	−	6.58839i	0.825355	−	0.300405i
$482$	−17.2077	−	24.5751i	−0.783788	−	1.11936i
$483$	−7.02988	−	0.847389i	−0.319871	−	0.0385575i
$484$	1.60395	+	1.91151i	0.0729066	+	0.0868867i
$485$	15.8859	+	6.36537i	0.721343	+	0.289036i
$486$	22.4987	+	18.4587i	1.02056	+	0.837305i
$487$	−9.67948	−	9.67948i	−0.438619	−	0.438619i	0.452928	−	0.891547i	$-0.350379\pi$
$487$	−9.67948	−	9.67948i	−0.438619	−	0.438619i	−0.891547	+	0.452928i	$0.850379\pi$
$488$	−8.14245	−	0.712372i	−0.368592	−	0.0322476i
$489$	−11.0674	−	14.1013i	−0.500487	−	0.637684i
$490$	6.16259	−	9.92547i	0.278397	−	0.448387i
$491$	9.36638	+	25.7339i	0.422699	+	1.16136i	0.950156	+	0.311774i	$0.100923\pi$
$491$	9.36638	+	25.7339i	0.422699	+	1.16136i	−0.527458	+	0.849581i	$0.676855\pi$
$492$	−13.9773	−	21.4193i	−0.630145	−	0.965657i
$493$	−0.0529092	−	0.0370474i	−0.00238291	−	0.00166853i
$494$	−10.2771	−	17.8005i	−0.462389	−	0.800881i
$495$	−3.90872	−	23.5653i	−0.175684	−	1.05918i
$496$	−3.57182	+	6.18657i	−0.160379	+	0.277785i
$497$	−1.40524	+	0.655272i	−0.0630335	+	0.0293930i
$498$	−22.8518	−	6.93129i	−1.02401	−	0.310599i
$499$	−2.84438	+	3.38980i	−0.127332	+	0.151749i	−0.825944	−	0.563753i	$-0.809357\pi$
$499$	−2.84438	+	3.38980i	−0.127332	+	0.151749i	0.698612	+	0.715501i	$0.253802\pi$
$500$	8.17532	+	14.4538i	0.365611	+	0.646393i
$501$	10.3777	+	6.45283i	0.463640	+	0.288291i
$502$	4.58861	+	9.84030i	0.204800	+	0.439194i
$503$	20.3350	−	5.44875i	0.906693	−	0.242948i	0.224805	−	0.974404i	$-0.427826\pi$
$503$	20.3350	−	5.44875i	0.906693	−	0.242948i	0.681889	+	0.731456i	$0.261159\pi$
$504$	−3.99182	−	8.09342i	−0.177810	−	0.360510i
$505$	22.7295	−	30.3439i	1.01145	−	1.35028i
$506$	−8.54998	+	1.50759i	−0.380093	+	0.0670207i
$507$	0.885944	+	16.2187i	0.0393462	+	0.720297i
$508$	−0.898953	+	1.92781i	−0.0398846	+	0.0855328i
$509$	−3.28136	+	18.6095i	−0.145444	+	0.824851i	0.821566	+	0.570113i	$0.193101\pi$
$509$	−3.28136	+	18.6095i	−0.145444	+	0.824851i	−0.967010	+	0.254739i	$0.918011\pi$
$510$	17.9093	+	17.1198i	0.793035	+	0.758077i
$511$	19.2426	−	16.1465i	0.851244	−	0.714279i
$512$	−17.0168	+	17.0168i	−0.752043	+	0.752043i
$513$	−4.89914	−	29.6575i	−0.216302	−	1.30941i
$514$		−	20.2735i		−	0.894224i
$515$	−1.53607	−	4.68179i	−0.0676875	−	0.206305i
$516$	−2.78384	−	19.4952i	−0.122552	−	0.858230i
$517$	32.1360	−	22.5018i	1.41334	−	0.989630i
$518$	53.6067	+	24.9972i	2.35534	+	1.09831i
$519$	6.10891	−	1.99985i	0.268151	−	0.0877836i
$520$	2.23718	+	3.42341i	0.0981068	+	0.150126i
$521$	−20.9815	+	12.1137i	−0.919216	+	0.530709i	−0.883385	−	0.468648i	$-0.844741\pi$
$521$	−20.9815	+	12.1137i	−0.919216	+	0.530709i	−0.0358309	+	0.999358i	$0.511408\pi$
$522$	0.0382687	+	0.0983909i	0.00167498	+	0.00430645i
$523$	8.39124	+	31.3165i	0.366923	+	1.36938i	0.864795	+	0.502125i	$0.167448\pi$
$523$	8.39124	+	31.3165i	0.366923	+	1.36938i	−0.497872	+	0.867251i	$0.665885\pi$
$524$	8.49159	+	3.09069i	0.370957	+	0.135017i
$525$	−19.3503	+	18.9860i	−0.844516	+	0.828615i
$526$	−18.0579	−	15.1524i	−0.787363	−	0.660676i
$527$	5.11805	−	0.447771i	0.222946	−	0.0195052i
$528$	−20.0887	−	21.4472i	−0.874248	−	0.933370i
$529$	−7.28312	+	20.0102i	−0.316657	+	0.870009i
$530$	2.48767	−	20.7526i	0.108057	−	0.901435i
$531$	−16.7260	+	1.83278i	−0.725846	+	0.0795359i
$532$	6.96113	−	25.9793i	0.301803	−	1.12634i
$533$	−10.8531	+	15.4998i	−0.470100	+	0.671372i
$534$	−8.91851	−	27.2433i	−0.385942	−	1.17893i
$535$	1.39805	−	43.6238i	0.0604430	−	1.88602i
$536$	−0.211556	−	0.0373031i	−0.00913784	−	0.00161125i
$537$	7.66656	+	5.75064i	0.330837	+	0.248158i
$538$	−0.0403511	+	0.461216i	−0.00173966	+	0.0198844i
$539$	9.96580			0.429258
$540$	−3.74819	−	16.8451i	−0.161296	−	0.724900i
$541$	−31.6739			−1.36177			−0.680885	−	0.732391i	$-0.738404\pi$
$541$	−31.6739			−1.36177			−0.680885	+	0.732391i	$0.738404\pi$
$542$	−1.68091	+	19.2129i	−0.0722013	+	0.825265i
$543$	23.8033	−	10.1661i	1.02150	−	0.436268i
$544$	23.5301	+	4.14900i	1.00885	+	0.177887i
$545$	−22.8222	−	24.3334i	−0.977595	−	1.04233i
$546$	12.8585	−	14.3444i	0.550291	−	0.613884i
$547$	−3.05247	+	4.35939i	−0.130514	+	0.186394i	−0.879090	−	0.476655i	$-0.841849\pi$
$547$	−3.05247	+	4.35939i	−0.130514	+	0.186394i	0.748576	+	0.663049i	$0.230738\pi$
$548$	−0.399262	+	1.49007i	−0.0170556	+	0.0636525i
$549$	1.66738	−	25.4621i	0.0711622	−	1.08670i
$550$	−15.9475	+	29.1635i	−0.680002	+	1.24353i
$551$	0.0372955	−	0.102469i	0.00158884	−	0.00436531i
$552$	2.11693	−	0.493664i	0.0901026	−	0.0210117i
$553$	−5.52810	+	0.483646i	−0.235079	+	0.0205667i
$554$	20.5950	+	17.2812i	0.874996	+	0.734209i
$555$	−30.5892	−	24.5144i	−1.29844	−	1.04058i
$556$	−26.5689	−	9.67029i	−1.12677	−	0.410111i
$557$	−1.56986	−	5.85880i	−0.0665171	−	0.248245i	0.924659	−	0.380796i	$-0.124350\pi$
$557$	−1.56986	−	5.85880i	−0.0665171	−	0.248245i	−0.991176	+	0.132551i	$0.957683\pi$
$558$	−7.36235	−	4.03857i	−0.311673	−	0.170966i
$559$	−12.6173	+	7.28459i	−0.533654	+	0.308105i
$560$	−6.84010	+	32.6404i	−0.289047	+	1.37931i
$561$	−4.34829	+	20.6818i	−0.183585	+	0.873187i
$562$	16.9803	+	7.91803i	0.716269	+	0.334002i
$563$	10.3919	−	7.27648i	0.437966	−	0.306667i	−0.333718	−	0.942673i	$-0.608303\pi$
$563$	10.3919	−	7.27648i	0.437966	−	0.306667i	0.771684	+	0.636006i	$0.219415\pi$
$564$	22.2951	−	17.4983i	0.938791	−	0.736812i
$565$	−15.0306	+	4.93148i	−0.632344	+	0.207469i
$566$		−	40.4258i		−	1.69922i
$567$	24.9878	−	13.0115i	1.04939	−	0.546434i
$568$	0.336577	−	0.336577i	0.0141224	−	0.0141224i
$569$	−10.4685	+	8.78410i	−0.438862	+	0.368249i	−0.835283	−	0.549820i	$-0.814696\pi$
$569$	−10.4685	+	8.78410i	−0.438862	+	0.368249i	0.396421	+	0.918069i	$0.370252\pi$
$570$	−20.0922	+	36.6857i	−0.841571	+	1.53659i
$571$	0.567607	−	3.21906i	0.0237536	−	0.134713i	−0.970625	−	0.240598i	$-0.922656\pi$
$571$	0.567607	−	3.21906i	0.0237536	−	0.134713i	0.994378	+	0.105885i	$0.0337675\pi$
$572$	4.25397	−	9.12268i	0.177868	−	0.381438i
$573$	−4.05457	+	2.64583i	−0.169382	+	0.110531i
$574$	−57.2176	+	10.0890i	−2.38822	+	0.421107i
$575$	−3.39521	−	5.57782i	−0.141590	−	0.232611i
$576$	−7.56034	−	7.23661i	−0.315014	−	0.301525i
$577$	−14.4385	+	3.86877i	−0.601081	+	0.161059i	−0.546513	−	0.837451i	$-0.684045\pi$
$577$	−14.4385	+	3.86877i	−0.601081	+	0.161059i	−0.0545684	+	0.998510i	$0.517378\pi$
$578$	4.14890	+	8.89735i	0.172572	+	0.370081i
$579$	−18.1787	+	9.71740i	−0.755481	+	0.403841i
$580$	0.0181314	−	0.0599195i	0.000752864	−	0.00248802i
$581$	−14.8595	+	17.7089i	−0.616477	+	0.734689i
$582$	5.62036	+	24.1012i	0.232972	+	0.999029i
$583$	16.1586	−	7.53489i	0.669222	−	0.312063i
$584$	−3.85572	+	6.67831i	−0.159551	+	0.276350i
$585$	−10.5320	+	7.21624i	−0.435447	+	0.298355i
$586$	−13.3710	−	23.1593i	−0.552351	−	0.956700i
$587$	23.5519	+	16.4912i	0.972091	+	0.680666i	0.947742	−	0.319038i	$-0.103360\pi$
$587$	23.5519	+	16.4912i	0.972091	+	0.680666i	0.0243494	+	0.999704i	$0.492249\pi$
$588$	7.18897	−	0.392697i	0.296468	−	0.0161945i
$589$	2.96654	+	8.15050i	0.122234	+	0.335836i
$590$	19.8912	+	12.3502i	0.818909	+	0.508449i
$591$	12.6562	−	31.5256i	0.520605	−	1.29679i
$592$	−48.0404	−	4.20299i	−1.97445	−	0.172742i
$593$	21.0591	+	21.0591i	0.864795	+	0.864795i	0.991891	−	0.127095i	$-0.0405654\pi$
$593$	21.0591	+	21.0591i	0.864795	+	0.864795i	−0.127095	+	0.991891i	$0.540565\pi$
$594$	24.6884	−	24.1598i	1.01298	−	0.991290i
$595$	22.0508	−	9.43477i	0.903994	−	0.386788i
$596$	2.81099	+	3.35001i	0.115143	+	0.137222i
$597$	−12.2028	+	16.2683i	−0.499426	+	0.665819i
$598$	2.66152	+	3.80104i	0.108838	+	0.155436i
$599$	−18.9188	+	6.88587i	−0.773000	+	0.281349i	−0.698251	−	0.715853i	$-0.746038\pi$
$599$	−18.9188	+	6.88587i	−0.773000	+	0.281349i	−0.0747495	+	0.997202i	$0.523816\pi$
$600$	3.58864	−	7.50874i	0.146506	−	0.306543i
$601$	3.78086	+	21.4423i	0.154225	+	0.874652i	0.959491	+	0.281739i	$0.0909111\pi$
$601$	3.78086	+	21.4423i	0.154225	+	0.874652i	−0.805267	+	0.592913i	$0.797978\pi$
$602$	−43.2110	−	11.5784i	−1.76115	−	0.471899i
$603$	0.101981	−	0.662837i	0.00415298	−	0.0269928i
$604$	22.6904	+	13.1003i	0.923260	+	0.533045i
$605$	−3.75097	+	0.207375i	−0.152498	+	0.00843100i
$606$	54.7957	+	1.79223i	2.22592	+	0.0728043i
$607$	−2.20037	−	25.1503i	−0.0893101	−	1.02082i	−0.900158	−	0.435563i	$-0.856549\pi$
$607$	−2.20037	−	25.1503i	−0.0893101	−	1.02082i	0.810848	−	0.585257i	$-0.199006\pi$
$608$	3.51566	+	40.1842i	0.142579	+	1.62968i
$609$	0.102145	+	0.00334091i	0.00413914	+	0.000135381i
$610$	−23.6825	+	26.4543i	−0.958876	+	1.07110i
$611$	−18.1586	−	10.4839i	−0.734618	−	0.424132i
$612$	−2.32174	+	15.0905i	−0.0938510	+	0.609996i
$613$	27.4201	+	7.34719i	1.10749	+	0.296750i	0.765810	−	0.643067i	$-0.222338\pi$
$613$	27.4201	+	7.34719i	1.10749	+	0.296750i	0.341677	+	0.939817i	$0.389005\pi$
$614$	3.79035	+	21.4961i	0.152966	+	0.867513i
$615$	38.4249	+	2.49083i	1.54944	+	0.100440i
$616$	−10.0656	+	3.66357i	−0.405554	+	0.147609i
$617$	13.1265	+	18.7465i	0.528452	+	0.754707i	0.991285	−	0.131738i	$-0.0420559\pi$
$617$	13.1265	+	18.7465i	0.528452	+	0.754707i	−0.462833	+	0.886446i	$0.653167\pi$
$618$	4.27555	−	5.70002i	0.171988	−	0.229288i
$619$	18.4274	+	21.9609i	0.740658	+	0.882682i	0.996462	−	0.0840469i	$-0.0267846\pi$
$619$	18.4274	+	21.9609i	0.740658	+	0.882682i	−0.255804	+	0.966729i	$0.582340\pi$
$620$	1.95879	+	4.57805i	0.0786670	+	0.183859i
$621$	1.68533	+	6.57346i	0.0676300	+	0.263784i
$622$	33.6696	+	33.6696i	1.35003	+	1.35003i
$623$	−27.6450	−	2.41862i	−1.10757	−	0.0969000i
$624$	−5.85136	+	14.5753i	−0.234242	+	0.583480i
$625$	−24.7950	−	3.19493i	−0.991800	−	0.127797i
$626$	19.0255	+	52.2720i	0.760411	+	2.08921i
$627$	−35.6265	+	1.94609i	−1.42278	+	0.0777194i
$628$	−10.5078	−	7.35767i	−0.419308	−	0.293603i
$629$	17.3409	+	30.0354i	0.691429	+	1.19759i
$630$	−38.5352	−	7.19930i	−1.53528	−	0.286827i
$631$	−3.00683	+	5.20799i	−0.119700	+	0.207327i	−0.919649	−	0.392742i	$-0.871527\pi$
$631$	−3.00683	+	5.20799i	−0.119700	+	0.207327i	0.799949	+	0.600068i	$0.204860\pi$
$632$	1.54395	−	0.719954i	0.0614149	−	0.0286382i
$633$	2.41800	+	10.3689i	0.0961069	+	0.412126i
$634$	30.2361	−	36.0340i	1.20083	−	1.43109i
$635$	−1.51153	−	2.82321i	−0.0599834	−	0.112036i
$636$	11.3593	−	6.07212i	0.450427	−	0.240775i
$637$	−2.25105	−	4.82739i	−0.0891899	−	0.191268i
$638$	0.121040	−	0.0324325i	0.00479201	−	0.00128401i
$639$	1.07347	+	1.02751i	0.0424660	+	0.0406476i
$640$	−2.36042	−	16.4525i	−0.0933036	−	0.650343i
$641$	−7.56572	+	1.33404i	−0.298828	+	0.0526914i	−0.321052	−	0.947062i	$-0.604036\pi$
$641$	−7.56572	+	1.33404i	−0.298828	+	0.0526914i	0.0222240	+	0.999753i	$0.492925\pi$
$642$	52.8574	−	34.4924i	2.08612	−	1.36131i
$643$	−12.3056	+	26.3895i	−0.485286	+	1.04070i	0.499402	+	0.866370i	$0.333553\pi$
$643$	−12.3056	+	26.3895i	−0.485286	+	1.04070i	−0.984688	+	0.174328i	$0.944225\pi$
$644$	−1.05437	+	5.97960i	−0.0415478	+	0.235629i
$645$	26.0034	+	14.2417i	1.02388	+	0.560767i
$646$	28.3485	−	23.7872i	1.11536	−	0.935896i
$647$	−12.6122	+	12.6122i	−0.495836	+	0.495836i	−0.910139	−	0.414303i	$-0.864025\pi$
$647$	−12.6122	+	12.6122i	−0.495836	+	0.495836i	0.414303	+	0.910139i	$0.364025\pi$
$648$	−5.84224	+	6.37718i	−0.229505	+	0.250519i
$649$			19.9721i			0.783972i
$650$	17.7288	+	1.13751i	0.695382	+	0.0446169i
$651$	−6.39476	+	5.01894i	−0.250630	+	0.196708i
$652$	−12.5917	+	8.81681i	−0.493129	+	0.345293i
$653$	2.60484	+	1.21466i	0.101935	+	0.0475332i	0.472917	−	0.881107i	$-0.343201\pi$
$653$	2.60484	+	1.21466i	0.101935	+	0.0475332i	−0.370982	+	0.928640i	$0.620979\pi$
$654$	9.92593	−	47.2108i	0.388135	−	1.84609i
$655$	−11.3885	+	7.44233i	−0.444986	+	0.290796i
$656$	41.0230	−	23.6847i	1.60168	−	0.924731i
$657$	−21.1070	−	11.5781i	−0.823462	−	0.451704i
$658$	−16.6634	−	62.1887i	−0.649607	−	2.42437i
$659$	27.2829	+	9.93016i	1.06279	+	0.386824i	0.813476	−	0.581599i	$-0.197573\pi$
$659$	27.2829	+	9.93016i	1.06279	+	0.386824i	0.249314	+	0.968423i	$0.419795\pi$
$660$	−20.3603	+	2.24459i	−0.792523	+	0.0873706i
$661$	−1.29090	−	1.08319i	−0.0502100	−	0.0421312i	0.617337	−	0.786699i	$-0.288211\pi$
$661$	−1.29090	−	1.08319i	−0.0502100	−	0.0421312i	−0.667547	+	0.744567i	$0.732656\pi$
$662$	−47.3251	+	4.14041i	−1.83934	+	0.160922i
$663$	11.0004	−	2.56526i	0.427219	−	0.0996266i
$664$	2.42725	−	6.66881i	0.0941955	−	0.258800i
$665$	25.0207	+	31.8363i	0.970262	+	1.23456i
$666$	3.70419	−	56.5655i	0.143534	−	2.19187i
$667$	−0.00637146	+	0.0237786i	−0.000246704	+	0.000920711i
$668$	6.01053	−	8.58392i	0.232554	−	0.332122i
$669$	−11.1465	+	12.4346i	−0.430948	+	0.480749i
$670$	−0.680659	+	0.638387i	−0.0262962	+	0.0246630i
$671$	−29.8273	−	5.25936i	−1.15147	−	0.203035i
$672$	−34.7675	+	14.8487i	−1.34119	+	0.572803i
$673$	1.87350	−	21.4142i	0.0722182	−	0.825458i	−0.870565	−	0.492053i	$-0.836247\pi$
$673$	1.87350	−	21.4142i	0.0722182	−	0.825458i	0.942784	−	0.333405i	$-0.108198\pi$
$674$	29.4436			1.13412
$675$	23.6806	+	10.6878i	0.911467	+	0.411374i
$676$	13.9285			0.535710
$677$	1.02266	−	11.6890i	0.0393039	−	0.449245i	−0.950888	−	0.309534i	$-0.899827\pi$
$677$	1.02266	−	11.6890i	0.0393039	−	0.449245i	0.990192	−	0.139711i	$-0.0446175\pi$
$678$	−18.2996	−	13.7264i	−0.702792	−	0.527160i
$679$	23.5937	+	4.16020i	0.905442	+	0.159654i
$680$	−5.37052	+	5.03698i	−0.205950	+	0.193159i
$681$	0.492732	+	1.50514i	0.0188815	+	0.0576771i
$682$	−5.71701	+	8.16473i	−0.218916	+	0.312644i
$683$	8.76191	−	32.6999i	0.335265	−	1.25123i	−0.568316	−	0.822810i	$-0.692405\pi$
$683$	8.76191	−	32.6999i	0.335265	−	1.25123i	0.903581	−	0.428416i	$-0.140928\pi$
$684$	−25.6230	+	2.80768i	−0.979718	+	0.107354i
$685$	−1.43509	−	1.82600i	−0.0548318	−	0.0697679i
$686$	−8.39729	+	23.0714i	−0.320610	+	0.880869i
$687$	5.59923	+	5.97789i	0.213624	+	0.228071i
$688$	36.3341	−	3.17882i	1.38522	−	0.121191i
$689$	−7.29974	−	6.12521i	−0.278098	−	0.233352i
$690$	3.79684	−	8.64579i	0.144543	−	0.329140i
$691$	26.6550	+	9.70163i	1.01400	+	0.369067i	0.794969	−	0.606650i	$-0.207487\pi$
$691$	26.6550	+	9.70163i	1.01400	+	0.369067i	0.219035	+	0.975717i	$0.429709\pi$
$692$	−1.42662	−	5.32421i	−0.0542318	−	0.202396i
$693$	−12.1217	−	31.1656i	−0.460466	−	1.18388i
$694$	18.0076	−	10.3967i	0.683561	−	0.394654i
$695$	35.6329	−	23.2859i	1.35163	−	0.883285i
$696$	−0.0298174	+	0.00976118i	−0.00113022	+	0.000369997i
$697$	−30.8755	−	14.3975i	−1.16949	−	0.545343i
$698$	−0.372502	+	0.260829i	−0.0140994	+	0.00987252i
$699$	0.991272	+	6.94188i	0.0374934	+	0.262566i
$700$	15.3514	+	17.4564i	0.580229	+	0.659791i
$701$		−	44.1563i		−	1.66776i	−0.551945	−	0.833880i	$-0.686114\pi$
$701$		−	44.1563i		−	1.66776i	0.551945	−	0.833880i	$-0.313886\pi$
$702$	−17.2795	−	6.50181i	−0.652172	−	0.245395i
$703$	−41.4024	+	41.4024i	−1.56152	+	1.56152i
$704$	−9.51599	+	7.98487i	−0.358648	+	0.300941i
$705$	0.961411	+	42.6581i	0.0362088	+	1.60660i
$706$	4.57734	−	25.9594i	0.172270	−	0.976994i
$707$	22.4302	−	48.1017i	0.843574	−	1.80905i
$708$	0.786988	+	14.4071i	0.0295768	+	0.541453i
$709$	16.3732	−	2.88704i	0.614909	−	0.108425i	0.142486	−	0.989797i	$-0.454490\pi$
$709$	16.3732	−	2.88704i	0.614909	−	0.108425i	0.472423	+	0.881372i	$0.343379\pi$
$710$	−0.293646	−	2.04677i	−0.0110203	−	0.0768137i
$711$	2.35248	+	4.76966i	0.0882249	+	0.178876i
$712$	8.22888	−	2.20492i	0.308390	−	0.0826330i
$713$	−0.827531	−	1.77465i	−0.0309913	−	0.0664610i
$714$	29.4538	+	18.3143i	1.10228	+	0.685397i
$715$	7.15279	+	13.3598i	0.267499	+	0.499629i
$716$	5.28248	−	6.29542i	0.197416	−	0.235271i
$717$	24.0978	+	7.30921i	0.899947	+	0.272967i
$718$	−1.69694	+	0.791297i	−0.0633293	+	0.0295310i
$719$	24.0796	−	41.7071i	0.898017	−	1.55541i	0.0679908	−	0.997686i	$-0.478341\pi$
$719$	24.0796	−	41.7071i	0.898017	−	1.55541i	0.830026	−	0.557725i	$-0.188326\pi$
$720$	31.5306	−	5.22990i	1.17508	−	0.194907i
$721$	−3.44891	−	5.97368i	−0.128444	−	0.222472i
$722$	22.1215	+	15.4897i	0.823278	+	0.576466i
$723$	15.2110	+	23.3099i	0.565703	+	0.866904i
$724$	−7.59124	−	20.8568i	−0.282126	−	0.775136i
$725$	0.0558348	+	0.0759298i	0.00207365	+	0.00281996i
$726$	−3.35403	−	4.27345i	−0.124480	−	0.158603i
$727$	−25.2483	−	2.20894i	−0.936407	−	0.0819250i	−0.391274	−	0.920274i	$-0.627965\pi$
$727$	−25.2483	−	2.20894i	−0.936407	−	0.0819250i	−0.545133	+	0.838349i	$0.683521\pi$
$728$	4.04821	+	4.04821i	0.150037	+	0.150037i
$729$	−20.3028	−	17.7988i	−0.751955	−	0.659214i
$730$	13.1775	+	30.7981i	0.487720	+	1.13989i
$731$	−16.8608	−	20.0939i	−0.623619	−	0.743200i
$732$	−21.7236	−	2.61858i	−0.802927	−	0.0967856i
$733$	8.53910	+	12.1951i	0.315399	+	0.450436i	0.945282	−	0.326253i	$-0.105786\pi$
$733$	8.53910	+	12.1951i	0.315399	+	0.450436i	−0.629883	+	0.776690i	$0.716897\pi$
$734$	25.5488	−	9.29902i	0.943025	−	0.343233i
$735$	−6.01548	+	9.01679i	−0.221884	+	0.332589i
$736$	−1.58132	−	8.96809i	−0.0582881	−	0.330568i
$737$	−0.768900	−	0.206026i	−0.0283228	−	0.00758907i
$738$	28.8892	+	47.6016i	1.06343	+	1.75224i
$739$	−23.0919	−	13.3321i	−0.849450	−	0.490430i	0.0110150	−	0.999939i	$-0.496494\pi$
$739$	−23.0919	−	13.3321i	−0.849450	−	0.490430i	−0.860465	+	0.509509i	$0.829827\pi$
$740$	−22.4208	+	25.0450i	−0.824205	+	0.920672i
$741$	8.98989	+	16.8177i	0.330252	+	0.617815i
$742$	−2.55015	−	29.1483i	−0.0936188	−	1.07007i
$743$	0.0585912	+	0.669700i	0.00214950	+	0.0245689i	0.997194	−	0.0748647i	$-0.0238525\pi$
$743$	0.0585912	+	0.669700i	0.00214950	+	0.0245689i	−0.995044	+	0.0994336i	$0.968297\pi$
$744$	1.31777	−	2.11928i	0.0483117	−	0.0776966i
$745$	−6.57375	+	0.363435i	−0.240844	+	0.0133152i
$746$	57.7232	+	33.3265i	2.11340	+	1.22017i
$747$	20.9798	+	7.12032i	0.767611	+	0.260519i
$748$	17.5051	+	4.69049i	0.640052	+	0.171501i
$749$	−10.6100	−	60.1723i	−0.387681	−	2.19865i
$750$	−16.7602	−	32.0322i	−0.611998	−	1.16965i
$751$	9.08514	−	3.30672i	0.331521	−	0.120664i	−0.170896	−	0.985289i	$-0.554666\pi$
$751$	9.08514	−	3.30672i	0.331521	−	0.120664i	0.502417	+	0.864625i	$0.332444\pi$
$752$	30.1077	+	42.9983i	1.09791	+	1.56799i
$753$	−3.95648	−	9.26389i	−0.144182	−	0.337595i
$754$	−0.0430503	−	0.0513054i	−0.00156780	−	0.00186843i
$755$	−36.2653	+	15.5167i	−1.31983	+	0.564709i
$756$	−9.97223	−	22.0041i	−0.362687	−	0.800280i
$757$	17.1950	+	17.1950i	0.624963	+	0.624963i	0.946796	−	0.321833i	$-0.104299\pi$
$757$	17.1950	+	17.1950i	0.624963	+	0.624963i	−0.321833	+	0.946796i	$0.604299\pi$
$758$	−61.7907	−	5.40599i	−2.24434	−	0.196354i
$759$	7.97396	−	1.13865i	0.289436	−	0.0413303i
$760$	−10.5606	−	6.55694i	−0.383074	−	0.237845i
$761$	−13.4878	−	37.0575i	−0.488933	−	1.34333i	−0.901647	−	0.432472i	$-0.857642\pi$
$761$	−13.4878	−	37.0575i	−0.488933	−	1.34333i	0.412715	−	0.910860i	$-0.364581\pi$
$762$	2.09326	−	4.13080i	0.0758307	−	0.149643i
$763$	−38.2564	−	26.7874i	−1.38498	−	0.969770i
$764$	2.07582	+	3.59542i	0.0751005	+	0.130078i
$765$	−16.0877	−	16.4180i	−0.581651	−	0.593594i
$766$	−30.6399	+	53.0699i	−1.10707	+	1.91749i
$767$	9.67438	−	4.51124i	0.349322	−	0.162891i
$768$	26.3619	−	24.6920i	0.951251	−	0.890996i
$769$	−33.2031	+	39.5700i	−1.19734	+	1.42693i	−0.319756	+	0.947500i	$0.603601\pi$
$769$	−33.2031	+	39.5700i	−1.19734	+	1.42693i	−0.877580	+	0.479429i	$0.840844\pi$
$770$	−13.4767	+	44.5371i	−0.485667	+	1.60500i
$771$	−0.614873	+	18.7992i	−0.0221441	+	0.677036i
$772$	7.47014	+	16.0198i	0.268856	+	0.576564i
$773$	−30.3870	+	8.14217i	−1.09294	+	0.292853i	−0.759888	−	0.650054i	$-0.774746\pi$
$773$	−30.3870	+	8.14217i	−1.09294	+	0.292853i	−0.333056	+	0.942907i	$0.608080\pi$
$774$	4.66998	+	42.6184i	0.167859	+	1.53189i
$775$	−7.28430	−	1.77184i	−0.261660	−	0.0636463i
$776$	−7.24304	+	1.27714i	−0.260010	+	0.0458468i
$777$	−48.9503	−	24.8053i	−1.75608	−	0.889884i
$778$	−4.21990	+	9.04960i	−0.151291	+	0.324444i
$779$	9.98726	−	56.6405i	0.357831	−	2.02936i
$780$	5.68620	+	9.35544i	0.203599	+	0.334978i
$781$	1.35115	−	1.13375i	0.0483480	−	0.0405688i
$782$	−5.90743	+	5.90743i	−0.211249	+	0.211249i
$783$	−0.0325017	−	0.0923966i	−0.00116152	−	0.00330198i
$784$			13.3343i			0.476227i
$785$	18.3498	−	6.02049i	0.654934	−	0.214881i
$786$	−18.2571	−	7.32945i	−0.651211	−	0.261433i
$787$	19.1723	−	13.4246i	0.683419	−	0.478535i	−0.179579	−	0.983744i	$-0.557473\pi$
$787$	19.1723	−	13.4246i	0.683419	−	0.478535i	0.862997	+	0.505209i	$0.168585\pi$
$788$	−26.4014	−	12.3112i	−0.940511	−	0.438567i
$789$	16.2852	+	14.5982i	0.579769	+	0.519710i
$790$	1.51783	−	7.24298i	0.0540021	−	0.257694i
$791$	−19.1782	+	11.0725i	−0.681898	+	0.393694i
$792$	6.76913	+	7.71780i	0.240530	+	0.274240i
$793$	4.18971	+	15.6362i	0.148781	+	0.555257i
$794$	−53.8826	−	19.6117i	−1.91222	−	0.695992i
$795$	−2.93617	+	19.1680i	−0.104135	+	0.679820i
$796$	13.3588	+	11.2094i	0.473490	+	0.397305i
$797$	−6.32065	+	0.552985i	−0.223889	+	0.0195877i	−0.198548	−	0.980091i	$-0.563623\pi$
$797$	−6.32065	+	0.552985i	−0.223889	+	0.0195877i	−0.0253407	+	0.999679i	$0.508067\pi$
$798$	−16.9958	+	56.0336i	−0.601646	+	1.98357i
$799$	12.9116	−	35.4742i	0.456778	−	1.25499i
$800$	−30.5896	−	16.7273i	−1.08151	−	0.591400i
$801$	7.44370	+	25.5327i	0.263010	+	0.902152i
$802$	0.232271	−	0.866846i	0.00820177	−	0.0306094i
$803$	−16.3900	+	23.4073i	−0.578390	+	0.826027i
$804$	−0.562775	−	0.118322i	−0.0198475	−	0.00417289i
$805$	−6.25346	−	6.66755i	−0.220406	−	0.235000i
$806$	5.24631	+	0.925065i	0.184793	+	0.0325840i
$807$	0.0514050	−	0.426452i	0.00180954	−	0.0150118i
$808$	−1.42006	+	16.2313i	−0.0499574	+	0.571016i
$809$	−2.19431			−0.0771479			−0.0385740	−	0.999256i	$-0.512282\pi$
$809$	−2.19431			−0.0771479			−0.0385740	+	0.999256i	$0.512282\pi$
$810$	6.95693	+	36.9206i	0.244442	+	1.29726i
$811$	6.26943			0.220149			0.110075	−	0.993923i	$-0.464891\pi$
$811$	6.26943			0.220149			0.110075	+	0.993923i	$0.464891\pi$
$812$	0.00763813	−	0.0873043i	0.000268046	−	0.00306378i
$813$	2.14138	−	17.7648i	0.0751016	−	0.623037i
$814$	−66.2630	−	11.6840i	−2.32252	−	0.409523i
$815$	0.741276	−	23.1303i	0.0259658	−	0.810218i
$816$	−27.6725	−	5.81806i	−0.968731	−	0.203673i
$817$	25.4004	−	36.2755i	0.888646	−	1.26912i
$818$	10.9814	−	40.9833i	0.383957	−	1.43295i
$819$	−12.3584	+	12.9113i	−0.431839	+	0.451158i
$820$	3.92994	−	32.7843i	0.137239	−	1.14488i
$821$	−0.182595	+	0.501675i	−0.00637260	+	0.0175086i	−0.942838	−	0.333251i	$-0.891854\pi$
$821$	−0.182595	+	0.501675i	−0.00637260	+	0.0175086i	0.936466	+	0.350760i	$0.114077\pi$
$822$	0.974812	−	3.21386i	0.0340005	−	0.112096i
$823$	0.461633	−	0.0403877i	0.0160915	−	0.00140783i	−0.0791071	−	0.996866i	$-0.525207\pi$
$823$	0.461633	−	0.0403877i	0.0160915	−	0.00140783i	0.0951987	+	0.995458i	$0.469651\pi$
$824$	1.62215	+	1.36115i	0.0565103	+	0.0474177i
$825$	15.6723	−	26.5591i	0.545638	−	0.924668i
$826$	30.7999	+	11.2102i	1.07167	+	0.390054i
$827$	−8.01968	−	29.9299i	−0.278872	−	1.04076i	−0.953202	−	0.302333i	$-0.902234\pi$
$827$	−8.01968	−	29.9299i	−0.278872	−	1.04076i	0.674331	−	0.738430i	$-0.264432\pi$
$828$	5.70726	−	1.13559i	0.198341	−	0.0394645i
$829$	35.8944	−	20.7236i	1.24666	−	0.719761i	0.276220	−	0.961094i	$-0.410918\pi$
$829$	35.8944	−	20.7236i	1.24666	−	0.719761i	0.970442	+	0.241334i	$0.0775848\pi$
$830$	−16.8647	−	25.8069i	−0.585381	−	0.895770i
$831$	−18.5732	−	16.6492i	−0.644297	−	0.577553i
$832$	6.01729	+	2.80591i	0.208612	+	0.0972773i
$833$	7.85556	−	5.50052i	0.272179	−	0.190582i
$834$	57.1238	+	22.9327i	1.97803	+	0.794095i
$835$	4.91818	+	14.9901i	0.170201	+	0.518754i
$836$			30.5957i			1.05817i
$837$	6.70448	+	3.96818i	0.231741	+	0.137160i
$838$	−14.2317	+	14.2317i	−0.491627	+	0.491627i
$839$	−23.3960	+	19.6316i	−0.807719	+	0.677757i	−0.950062	−	0.312060i	$-0.898981\pi$
$839$	−23.3960	+	19.6316i	−0.807719	+	0.677757i	0.142343	+	0.989817i	$0.454536\pi$
$840$	2.76100	−	11.3184i	0.0952636	−	0.390523i
$841$	−5.03574	+	28.5591i	−0.173646	+	0.984796i
$842$	19.7624	−	42.3806i	0.681057	−	1.46053i
$843$	−15.5053	−	7.85723i	−0.534032	−	0.270617i
$844$	8.99130	−	1.58541i	0.309493	−	0.0545720i
$845$	−12.5716	+	16.7831i	−0.432477	+	0.577356i
$846$	−49.7578	+	36.4884i	−1.71071	+	1.25450i
$847$	−5.07982	+	1.36113i	−0.174545	+	0.0467691i
$848$	10.0818	+	21.6204i	0.346209	+	0.742447i
$849$	−1.22607	+	37.4861i	−0.0420787	+	1.28652i
$850$	3.52587	+	31.7902i	0.120936	+	1.09039i
$851$	8.49661	−	10.1259i	0.291260	−	0.347110i
$852$	0.929998	−	0.871089i	0.0318612	−	0.0298430i
$853$	−37.9830	+	17.7118i	−1.30051	+	0.606439i	−0.944644	−	0.328097i	$-0.893593\pi$
$853$	−37.9830	+	17.7118i	−1.30051	+	0.606439i	−0.355869	+	0.934536i	$0.615815\pi$
$854$	−24.8527	+	43.0461i	−0.850441	+	1.47301i
$855$	19.7438	−	33.4085i	0.675223	−	1.14255i
$856$	9.37865	+	16.2443i	0.320556	+	0.555219i
$857$	−1.16320	−	0.814484i	−0.0397343	−	0.0278222i	0.553541	−	0.832822i	$-0.313276\pi$
$857$	−1.16320	−	0.814484i	−0.0397343	−	0.0278222i	−0.593275	+	0.805000i	$0.702165\pi$
$858$	−9.90560	+	19.5475i	−0.338171	+	0.667342i
$859$	−7.27047	−	19.9755i	−0.248065	−	0.681554i	−0.999757	−	0.0220394i	$-0.992984\pi$
$859$	−7.27047	−	19.9755i	−0.248065	−	0.681554i	0.751692	−	0.659515i	$-0.229238\pi$
$860$	13.4105	−	21.5990i	0.457294	−	0.736519i
$861$	53.3628	−	7.61999i	1.81860	−	0.259689i
$862$	−26.2711	−	2.29842i	−0.894796	−	0.0782845i
$863$	−17.8190	−	17.8190i	−0.606565	−	0.606565i	0.335482	−	0.942047i	$-0.391101\pi$
$863$	−17.8190	−	17.8190i	−0.606565	−	0.606565i	−0.942047	+	0.335482i	$0.891101\pi$
$864$	25.3413	+	25.8957i	0.862128	+	0.880991i
$865$	7.70304	+	3.08655i	0.261911	+	0.104946i
$866$	3.10152	+	3.69624i	0.105394	+	0.125603i
$867$	−3.57735	−	8.37618i	−0.121493	−	0.284470i
$868$	3.99830	+	5.71017i	0.135711	+	0.193816i
$869$	5.93190	−	2.15904i	0.201226	−	0.0732403i
$870$	−0.0437170	+	0.129090i	−0.00148214	+	0.00437656i
$871$	0.0738790	+	0.418989i	0.00250329	+	0.0141969i
$872$	13.8487	+	3.71075i	0.468976	+	0.125662i
$873$	−4.48069	−	22.5191i	−0.151648	−	0.762155i
$874$	−12.2147	−	7.05216i	−0.413168	−	0.238543i
$875$	−34.8901	+	2.74178i	−1.17950	+	0.0926890i
$876$	−10.9008	+	17.5310i	−0.368304	+	0.592319i
$877$	4.24765	+	48.5508i	0.143433	+	1.63944i	0.637808	+	0.770196i	$0.279841\pi$
$877$	4.24765	+	48.5508i	0.143433	+	1.63944i	−0.494375	+	0.869249i	$0.664603\pi$
$878$	−3.97579	−	45.4435i	−0.134176	−	1.53364i
$879$	11.6963	+	21.8807i	0.394506	+	0.738016i
$880$	−2.09419	−	37.8793i	−0.0705951	−	1.27691i
$881$	−6.73697	−	3.88959i	−0.226974	−	0.131044i	0.382201	−	0.924079i	$-0.375166\pi$
$881$	−6.73697	−	3.88959i	−0.226974	−	0.131044i	−0.609175	+	0.793036i	$0.708499\pi$
$882$	−15.6706	+	0.342848i	−0.527658	+	0.0115443i
$883$	−13.5617	−	3.63385i	−0.456388	−	0.122289i	0.0232990	−	0.999729i	$-0.492583\pi$
$883$	−13.5617	−	3.63385i	−0.456388	−	0.122289i	−0.479687	+	0.877440i	$0.659250\pi$
$884$	−1.68197	−	9.53890i	−0.0565706	−	0.320828i
$885$	−18.0702	−	12.0554i	−0.607422	−	0.405237i
$886$	−51.8954	+	18.8884i	−1.74346	+	0.634568i
$887$	23.1997	+	33.1326i	0.778969	+	1.11248i	0.990821	+	0.135182i	$0.0431618\pi$
$887$	23.1997	+	33.1326i	0.778969	+	1.11248i	−0.211851	+	0.977302i	$0.567949\pi$
$888$	16.7255	+	2.01611i	0.561271	+	0.0676562i
$889$	−2.88163	−	3.43420i	−0.0966469	−	0.115179i
$890$	13.7648	−	34.3525i	0.461396	−	1.15150i
$891$	−23.6258	+	21.6542i	−0.791496	+	0.725442i
$892$	10.1256	+	10.1256i	0.339030	+	0.339030i
$893$	63.4906	+	5.55471i	2.12463	+	0.185881i
$894$	−5.87810	−	7.48944i	−0.196593	−	0.250484i
$895$	2.81777	+	12.0473i	0.0941877	+	0.402696i
$896$	−7.95805	−	21.8646i	−0.265860	−	0.730444i
$897$	−2.35269	−	3.60536i	−0.0785542	−	0.120379i
$898$	46.6252	+	32.6473i	1.55590	+	1.08946i
$899$	0.0141311	+	0.0244758i	0.000471299	+	0.000816314i
$900$	10.2589	−	19.7763i	0.341962	−	0.659210i
$901$	8.57825	−	14.8580i	0.285783	−	0.494990i
$902$	59.9005	−	27.9321i	1.99447	−	0.930037i
$903$	39.7176	+	12.0469i	1.32172	+	0.400897i
$904$	4.36988	−	5.20782i	0.145340	−	0.173210i
$905$	31.9831	+	9.67794i	1.06315	+	0.321706i
$906$	−48.4404	−	30.1202i	−1.60932	−	1.00068i
$907$	−6.55044	−	14.0475i	−0.217504	−	0.466438i	0.767035	−	0.641605i	$-0.221731\pi$
$907$	−6.55044	−	14.0475i	−0.217504	−	0.466438i	−0.984539	+	0.175167i	$0.943953\pi$
$908$	1.31180	−	0.351496i	0.0435337	−	0.0116648i
$909$	−50.7566	−	3.32380i	−1.68349	−	0.110243i
$910$	24.6177	−	3.53186i	0.816068	−	0.117080i
$911$	21.0612	−	3.71365i	0.697788	−	0.123039i	0.186508	−	0.982453i	$-0.440283\pi$
$911$	21.0612	−	3.71365i	0.697788	−	0.123039i	0.511279	+	0.859415i	$0.329172\pi$
$912$	−2.60389	−	47.6686i	−0.0862235	−	1.57846i
$913$	11.1138	−	23.8336i	0.367813	−	0.788777i
$914$	−3.03339	+	17.2032i	−0.100336	+	0.569032i
$915$	22.7626	−	23.8123i	0.752510	−	0.787211i
$916$	5.38037	−	4.51467i	0.177773	−	0.149169i
$917$	−13.4670	+	13.4670i	−0.444720	+	0.444720i
$918$	6.12592	−	32.6705i	0.202186	−	1.07829i
$919$		−	10.8447i		−	0.357733i	−0.983873	−	0.178867i	$-0.942757\pi$
$919$		−	10.8447i		−	0.357733i	0.983873	−	0.178867i	$-0.0572431\pi$
$920$	2.50405	+	1.26684i	0.0825562	+	0.0417665i
$921$	−2.86276	−	20.0479i	−0.0943311	−	0.660601i
$922$	9.90159	−	6.93317i	0.326091	−	0.228332i
$923$	−0.854379	−	0.398404i	−0.0281222	−	0.0131136i
$924$	−27.2520	+	8.92138i	−0.896526	+	0.293492i
$925$	−9.94126	−	49.6212i	−0.326867	−	1.63153i
$926$	−21.4947	+	12.4100i	−0.706360	+	0.407817i
$927$	−4.13751	+	5.15584i	−0.135894	+	0.169340i
$928$	0.0340185	+	0.126959i	0.00111671	+	0.00416762i
$929$	−27.6616	−	10.0680i	−0.907549	−	0.330321i	−0.154275	−	0.988028i	$-0.549304\pi$
$929$	−27.6616	−	10.0680i	−0.907549	−	0.330321i	−0.753274	+	0.657707i	$0.771526\pi$
$930$	−3.93638	−	10.1009i	−0.129079	−	0.331222i
$931$	12.4024	+	10.4068i	0.406471	+	0.341070i
$932$	5.99025	−	0.524079i	0.196217	−	0.0171668i
$933$	−30.2000	−	32.2423i	−0.988703	−	1.05557i
$934$	13.9911	−	38.4403i	0.457804	−	1.25781i
$935$	−21.4517	+	16.8593i	−0.701545	+	0.551356i
$936$	2.20948	−	5.02222i	0.0722191	−	0.164156i
$937$	−2.47258	+	9.22780i	−0.0807757	+	0.301459i	−0.994481	−	0.104919i	$-0.966542\pi$
$937$	−2.47258	+	9.22780i	−0.0807757	+	0.301459i	0.913705	+	0.406378i	$0.133208\pi$
$938$	−0.749304	+	1.07012i	−0.0244656	+	0.0349405i
$939$	−16.0566	−	49.0479i	−0.523987	−	1.60062i
$940$	36.5704	+	1.17200i	1.19280	+	0.0382266i
$941$	34.3869	+	6.06333i	1.12098	+	0.197659i	0.703271	−	0.710922i	$-0.251722\pi$
$941$	34.3869	+	6.06333i	1.12098	+	0.197659i	0.417709	+	0.908581i	$0.362833\pi$
$942$	22.3407	+	16.7576i	0.727898	+	0.545992i
$943$	−1.13164	+	12.9347i	−0.0368514	+	0.421213i
$944$	−26.7228			−0.869754
$945$	35.5146	+	7.84450i	1.15529	+	0.255182i
$946$	50.8894			1.65456
$947$	0.792811	−	9.06188i	0.0257629	−	0.294471i	−0.972373	−	0.233434i	$-0.925004\pi$
$947$	0.792811	−	9.06188i	0.0257629	−	0.294471i	0.998135	−	0.0610371i	$-0.0194408\pi$
$948$	4.19398	−	1.79119i	0.136214	−	0.0581753i
$949$	15.0405	+	2.65205i	0.488237	+	0.0860893i
$950$	−50.3005	+	19.6405i	−1.63197	+	0.637223i
$951$	−29.1302	+	32.4966i	−0.944612	+	1.05377i
$952$	−5.91213	+	8.44340i	−0.191613	+	0.273652i
$953$	−1.81201	+	6.76251i	−0.0586968	+	0.219059i	−0.989044	−	0.147620i	$-0.952839\pi$
$953$	−1.81201	+	6.76251i	−0.0586968	+	0.219059i	0.930347	+	0.366679i	$0.119505\pi$
$954$	−25.1493	+	12.4041i	−0.814237	+	0.401596i
$955$	−6.20590	−	0.743918i	−0.200818	−	0.0240726i
$956$	7.38550	−	20.2915i	0.238864	−	0.656274i
$957$	−0.113221	+	0.0264030i	−0.00365993	+	0.000853488i
$958$	−29.5217	+	2.58282i	−0.953803	+	0.0834470i
$959$	−2.49057	−	2.08983i	−0.0804246	−	0.0674842i
$960$	−1.48052	−	13.4296i	−0.0477837	−	0.433438i
$961$	27.0180	+	9.83376i	0.871549	+	0.317218i
$962$	9.30767	+	34.7367i	0.300091	+	1.11996i
$963$	−50.0598	+	30.3810i	−1.61315	+	0.979014i
$964$	20.6702	−	11.9340i	0.665743	−	0.384367i
$965$	−26.0454	−	5.45806i	−0.838432	−	0.175701i
$966$	2.71979	−	12.9361i	0.0875077	−	0.416214i
$967$	11.8805	+	5.53995i	0.382050	+	0.178153i	0.604149	−	0.796871i	$-0.293513\pi$
$967$	11.8805	+	5.53995i	0.382050	+	0.178153i	−0.222099	+	0.975024i	$0.571291\pi$
$968$	1.32250	−	0.926022i	0.0425066	−	0.0297635i
$969$	−27.0085	+	21.1977i	−0.867637	+	0.680967i
$970$	−14.4230	+	28.5086i	−0.463094	+	0.915357i
$971$			10.0161i			0.321431i	0.987001	+	0.160716i	$0.0513802\pi$
$971$			10.0161i			0.321431i	−0.987001	+	0.160716i	$0.948620\pi$
$972$	−16.1896	+	16.5515i	−0.519281	+	0.530890i
$973$	42.1362	−	42.1362i	1.35082	−	1.35082i
$974$	19.5766	−	16.4268i	0.627276	−	0.526347i
$975$	−16.4051	−	1.59249i	−0.525384	−	0.0510005i
$976$	7.03707	−	39.9092i	0.225251	−	1.27746i
$977$	14.9516	−	32.0639i	0.478345	−	1.02581i	−0.508035	−	0.861336i	$-0.669628\pi$
$977$	14.9516	−	32.0639i	0.478345	−	1.02581i	0.986381	−	0.164479i	$-0.0525942\pi$
$978$	28.0261	−	18.2886i	0.896177	−	0.584805i
$979$	31.0885	−	5.48175i	0.993594	−	0.175197i
$980$	7.43915	+	5.57240i	0.237635	+	0.178004i
$981$	−10.6360	+	43.4766i	−0.339581	+	1.38810i
$982$	−49.3834	+	13.2322i	−1.57589	+	0.422258i
$983$	−18.3271	−	39.3025i	−0.584543	−	1.25356i	−0.946903	−	0.321518i	$-0.895807\pi$
$983$	−18.3271	−	39.3025i	−0.584543	−	1.25356i	0.362361	−	0.932038i	$-0.381971\pi$
$984$	−14.5939	+	7.80112i	−0.465235	+	0.248691i
$985$	38.6638	−	20.7005i	1.23193	−	0.659572i
$986$	0.0775089	−	0.0923715i	0.00246839	−	0.00294171i
$987$	13.5655	+	58.1717i	0.431796	+	1.85163i
$988$	14.8204	−	6.91088i	0.471500	−	0.219864i
$989$	−4.99869	+	8.65798i	−0.158949	+	0.275308i
$990$	44.4623	−	3.43505i	1.41310	−	0.109173i
$991$	−2.24550	−	3.88933i	−0.0713308	−	0.123549i	0.828154	−	0.560501i	$-0.189391\pi$
$991$	−2.24550	−	3.88933i	−0.0713308	−	0.123549i	−0.899485	+	0.436952i	$0.856058\pi$
$992$	−8.56400	−	5.99658i	−0.271907	−	0.190392i
$993$	44.0092	−	2.40400i	1.39659	−	0.0762886i
$994$	−0.990017	−	2.72005i	−0.0314014	−	0.0862747i
$995$	−25.5642	+	5.97927i	−0.810438	+	0.189556i
$996$	7.07794	−	17.6306i	0.224273	−	0.558648i
$997$	21.7592	+	1.90368i	0.689121	+	0.0602903i	0.426337	−	0.904564i	$-0.359804\pi$
$997$	21.7592	+	1.90368i	0.689121	+	0.0602903i	0.262784	+	0.964855i	$0.415359\pi$
$998$	−5.84148	−	5.84148i	−0.184909	−	0.184909i
$999$	−5.15039	+	52.3397i	−0.162951	+	1.65596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.32.4	✓	192
3.2	odd	2		405.2.r.a.287.13		192
5.2	odd	4		675.2.ba.b.518.4		192
5.3	odd	4	inner	135.2.q.a.113.13	yes	192
5.4	even	2		675.2.ba.b.32.13		192
15.8	even	4		405.2.r.a.368.4		192
27.11	odd	18	inner	135.2.q.a.92.13	yes	192
27.16	even	9		405.2.r.a.197.4		192
135.38	even	36	inner	135.2.q.a.38.4	yes	192
135.43	odd	36		405.2.r.a.278.13		192
135.92	even	36		675.2.ba.b.443.13		192
135.119	odd	18		675.2.ba.b.632.4		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.4	✓	192	1.1	even	1	trivial
135.2.q.a.38.4	yes	192	135.38	even	36	inner
135.2.q.a.92.13	yes	192	27.11	odd	18	inner
135.2.q.a.113.13	yes	192	5.3	odd	4	inner
405.2.r.a.197.4		192	27.16	even	9
405.2.r.a.278.13		192	135.43	odd	36
405.2.r.a.287.13		192	3.2	odd	2
405.2.r.a.368.4		192	15.8	even	4
675.2.ba.b.32.13		192	5.4	even	2
675.2.ba.b.443.13		192	135.92	even	36
675.2.ba.b.518.4		192	5.2	odd	4
675.2.ba.b.632.4		192	135.119	odd	18

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.162710 + 1.85978i) q^{2} +(0.207283 - 1.71960i) q^{3} +(-1.46269 - 0.257912i) q^{4} +(1.63097 - 1.52968i) q^{5} +(3.16436 + 0.665296i) q^{6} +(1.79546 - 2.56418i) q^{7} +(-0.248717 + 0.928224i) q^{8} +(-2.91407 - 0.712888i) q^{9} +O(q^{10})\)	\(q+(-0.162710 + 1.85978i) q^{2} +(0.207283 - 1.71960i) q^{3} +(-1.46269 - 0.257912i) q^{4} +(1.63097 - 1.52968i) q^{5} +(3.16436 + 0.665296i) q^{6} +(1.79546 - 2.56418i) q^{7} +(-0.248717 + 0.928224i) q^{8} +(-2.91407 - 0.712888i) q^{9} +(2.57950 + 3.28215i) q^{10} +(-1.21790 + 3.34616i) q^{11} +(-0.746697 + 2.46179i) q^{12} +(1.89596 - 0.165875i) q^{13} +(4.47667 + 3.75637i) q^{14} +(-2.29237 - 3.12170i) q^{15} +(-4.47719 - 1.62956i) q^{16} +(0.886863 + 3.30982i) q^{17} +(1.79996 - 5.30353i) q^{18} +(-5.00990 + 2.89247i) q^{19} +(-2.78013 + 1.81680i) q^{20} +(-4.03720 - 3.61898i) q^{21} +(-6.02495 - 2.80948i) q^{22} +(1.06979 - 0.749079i) q^{23} +(1.54462 + 0.620099i) q^{24} +(0.320150 - 4.98974i) q^{25} +3.55306i q^{26} +(-1.82992 + 4.86327i) q^{27} +(-3.28753 + 3.28753i) q^{28} +(-0.0144398 + 0.0121164i) q^{29} +(6.17867 - 3.75538i) q^{30} +(0.260357 - 1.47656i) q^{31} +(2.94687 - 6.31958i) q^{32} +(5.50161 + 2.78791i) q^{33} +(-6.29984 + 1.11083i) q^{34} +(-0.994032 - 6.92858i) q^{35} +(4.07852 + 1.79431i) q^{36} +(9.77656 - 2.61962i) q^{37} +(-4.56420 - 9.78795i) q^{38} +(0.107761 - 3.29468i) q^{39} +(1.01424 + 1.89437i) q^{40} +(-6.39065 + 7.61608i) q^{41} +(7.38740 - 6.91946i) q^{42} +(-6.93786 + 3.23518i) q^{43} +(2.64443 - 4.58028i) q^{44} +(-5.84326 + 3.29489i) q^{45} +(1.21906 + 2.11147i) q^{46} +(-9.02466 - 6.31914i) q^{47} +(-3.73025 + 7.36121i) q^{48} +(-0.957202 - 2.62989i) q^{49} +(9.22773 + 1.40729i) q^{50} +(5.87541 - 0.838984i) q^{51} +(-2.81599 - 0.246367i) q^{52} +(-3.54041 - 3.54041i) q^{53} +(-8.74687 - 4.19455i) q^{54} +(3.13219 + 7.32049i) q^{55} +(1.93357 + 2.30434i) q^{56} +(3.93543 + 9.21460i) q^{57} +(-0.0201844 - 0.0288263i) q^{58} +(5.27046 - 1.91829i) q^{59} +(2.54791 + 5.15732i) q^{60} +(1.47697 + 8.37633i) q^{61} +(2.70371 + 0.724458i) q^{62} +(-7.06005 + 6.19223i) q^{63} +(3.02114 + 1.74425i) q^{64} +(2.83853 - 3.17075i) q^{65} +(-6.08006 + 9.77816i) q^{66} +(0.0194833 + 0.222695i) q^{67} +(-0.443565 - 5.06998i) q^{68} +(-1.06637 - 1.99489i) q^{69} +(13.0474 - 0.721334i) q^{70} +(-0.428964 - 0.247662i) q^{71} +(1.38650 - 2.52760i) q^{72} +(7.75123 + 2.07694i) q^{73} +(3.28118 + 18.6085i) q^{74} +(-8.51401 - 1.58482i) q^{75} +(8.07394 - 2.93867i) q^{76} +(6.39345 + 9.13079i) q^{77} +(6.10985 + 0.736488i) q^{78} +(-1.13950 - 1.35801i) q^{79} +(-9.79489 + 4.19090i) q^{80} +(7.98358 + 4.15481i) q^{81} +(-13.1244 - 13.1244i) q^{82} +(-7.35695 - 0.643650i) q^{83} +(4.97180 + 6.33469i) q^{84} +(6.50942 + 4.04161i) q^{85} +(-4.88786 - 13.4293i) q^{86} +(0.0178423 + 0.0273422i) q^{87} +(-2.80307 - 1.96273i) q^{88} +(-4.43260 - 7.67748i) q^{89} +(-5.17702 - 11.4033i) q^{90} +(2.97878 - 5.15940i) q^{91} +(-1.75798 + 0.819758i) q^{92} +(-2.48513 - 0.753777i) q^{93} +(13.2206 - 15.7557i) q^{94} +(-3.74646 + 12.3811i) q^{95} +(-10.2563 - 6.37738i) q^{96} +(3.23451 + 6.93643i) q^{97} +(5.04676 - 1.35228i) q^{98} +(5.93448 - 8.88270i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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