LMFDB - Embedded newform 729.2.k.a.4.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(4,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(486))

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

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

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

chi := DirichletCharacter("729.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.k (of order $243$, degree $162$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12960$
Relative dimension:	$80$ over $\Q(\zeta_{243})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{243}]$

Embedding invariants

Embedding label			4.19
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68750 - 0.0218178i) q^{2} +(-0.499964 + 1.65832i) q^{3} +(0.847837 + 0.0219272i) q^{4} +(0.0353662 + 0.0108375i) q^{5} +(0.879869 - 2.78751i) q^{6} +(-1.23579 + 3.08161i) q^{7} +(1.94249 + 0.0753776i) q^{8} +(-2.50007 - 1.65820i) q^{9} +O(q^{10})$	\(q+(-1.68750 - 0.0218178i) q^{2} +(-0.499964 + 1.65832i) q^{3} +(0.847837 + 0.0219272i) q^{4} +(0.0353662 + 0.0108375i) q^{5} +(0.879869 - 2.78751i) q^{6} +(-1.23579 + 3.08161i) q^{7} +(1.94249 + 0.0753776i) q^{8} +(-2.50007 - 1.65820i) q^{9} +(-0.0594438 - 0.0190599i) q^{10} +(-1.55843 - 0.886380i) q^{11} +(-0.460250 + 1.39502i) q^{12} +(-1.61511 - 3.61500i) q^{13} +(2.15263 - 5.17325i) q^{14} +(-0.0356539 + 0.0532302i) q^{15} +(-4.97028 - 0.257260i) q^{16} +(-2.25299 - 1.02411i) q^{17} +(4.18268 + 2.85276i) q^{18} +(3.01767 + 4.39988i) q^{19} +(0.0297471 + 0.00996393i) q^{20} +(-4.49246 - 3.59004i) q^{21} +(2.61051 + 1.52976i) q^{22} +(0.500513 - 1.52697i) q^{23} +(-1.09618 + 3.18360i) q^{24} +(-4.14044 - 2.80055i) q^{25} +(2.64661 + 6.13554i) q^{26} +(3.99978 - 3.31688i) q^{27} +(-1.11532 + 2.58561i) q^{28} +(1.72071 - 1.10013i) q^{29} +(0.0613272 - 0.0890478i) q^{30} +(1.29438 + 4.76898i) q^{31} +(4.50193 + 0.291419i) q^{32} +(2.24906 - 2.14123i) q^{33} +(3.77956 + 1.77733i) q^{34} +(-0.0771023 + 0.0955919i) q^{35} +(-2.08329 - 1.46071i) q^{36} +(-8.92589 - 1.75299i) q^{37} +(-4.99632 - 7.49062i) q^{38} +(6.80234 - 0.870996i) q^{39} +(0.0678816 + 0.0237176i) q^{40} +(5.48293 - 2.07628i) q^{41} +(7.50268 + 6.15620i) q^{42} +(-9.84639 + 4.32302i) q^{43} +(-1.30186 - 0.785677i) q^{44} +(-0.0704471 - 0.0857389i) q^{45} +(-0.877929 + 2.56584i) q^{46} +(2.14880 - 7.91697i) q^{47} +(2.91158 - 8.11371i) q^{48} +(-2.90870 - 2.77997i) q^{49} +(6.92587 + 4.81626i) q^{50} +(2.82471 - 3.22416i) q^{51} +(-1.29008 - 3.10035i) q^{52} +(8.40178 - 8.90536i) q^{53} +(-6.82199 + 5.50997i) q^{54} +(-0.0455096 - 0.0482374i) q^{55} +(-2.63281 + 5.89286i) q^{56} +(-8.80515 + 2.80450i) q^{57} +(-2.92769 + 1.81892i) q^{58} +(12.7754 - 2.16760i) q^{59} +(-0.0313959 + 0.0443487i) q^{60} +(1.40446 - 2.58470i) q^{61} +(-2.08021 - 8.07588i) q^{62} +(8.19952 - 5.65506i) q^{63} +(2.33331 + 0.181359i) q^{64} +(-0.0179424 - 0.145352i) q^{65} +(-3.84201 + 3.56425i) q^{66} +(6.00414 - 3.11323i) q^{67} +(-1.88771 - 0.917678i) q^{68} +(2.28198 + 1.59344i) q^{69} +(0.132196 - 0.159629i) q^{70} +(-7.03273 - 5.45078i) q^{71} +(-4.73138 - 3.40950i) q^{72} +(13.6316 - 4.37080i) q^{73} +(15.0242 + 3.15290i) q^{74} +(6.71429 - 5.46601i) q^{75} +(2.46202 + 3.79655i) q^{76} +(4.65738 - 3.70711i) q^{77} +(-11.4979 + 1.32139i) q^{78} +(-0.852216 + 4.49271i) q^{79} +(-0.172992 - 0.0629638i) q^{80} +(3.50072 + 8.29126i) q^{81} +(-9.29773 + 3.38410i) q^{82} +(-0.245341 - 1.50492i) q^{83} +(-3.73015 - 3.14228i) q^{84} +(-0.0685807 - 0.0606356i) q^{85} +(16.7101 - 7.08026i) q^{86} +(0.964072 + 3.40352i) q^{87} +(-2.96043 - 1.83926i) q^{88} +(-7.06426 - 2.88607i) q^{89} +(0.117009 + 0.146221i) q^{90} +(13.1360 - 0.509736i) q^{91} +(0.457835 - 1.28365i) q^{92} +(-8.55566 - 0.237820i) q^{93} +(-3.79882 + 13.3130i) q^{94} +(0.0590398 + 0.188311i) q^{95} +(-2.73407 + 7.31995i) q^{96} +(1.41808 - 6.16055i) q^{97} +(4.84777 + 4.75466i) q^{98} +(2.42640 + 4.80021i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) $ 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{243}\right)$

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 $

$2$	−1.68750	−	0.0218178i	−1.19324	−	0.0154275i	−0.586246	−	0.810133i	$-0.699395\pi$
$2$	−1.68750	−	0.0218178i	−1.19324	−	0.0154275i	−0.606995	+	0.794706i	$0.707625\pi$
$3$	−0.499964	+	1.65832i	−0.288654	+	0.957433i
$3$	−0.499964	+	1.65832i	−0.288654	+	0.957433i
$4$	0.847837	+	0.0219272i	0.423918	+	0.0109636i
$5$	0.0353662	+	0.0108375i	0.0158162	+	0.00484669i	0.300888	−	0.953660i	$-0.402717\pi$
$5$	0.0353662	+	0.0108375i	0.0158162	+	0.00484669i	−0.285072	+	0.958506i	$0.592017\pi$
$6$	0.879869	−	2.78751i	0.359205	−	1.13799i
$7$	−1.23579	+	3.08161i	−0.467086	+	1.16474i	0.489164	+	0.872192i	$0.337302\pi$
$7$	−1.23579	+	3.08161i	−0.467086	+	1.16474i	−0.956251	+	0.292549i	$0.905497\pi$
$8$	1.94249	+	0.0753776i	0.686775	+	0.0266500i
$9$	−2.50007	−	1.65820i	−0.833357	−	0.552735i
$10$	−0.0594438	−	0.0190599i	−0.0187978	−	0.00602727i
$11$	−1.55843	−	0.886380i	−0.469885	−	0.267253i	0.241048	−	0.970513i	$-0.422509\pi$
$11$	−1.55843	−	0.886380i	−0.469885	−	0.267253i	−0.710933	+	0.703260i	$0.751727\pi$
$12$	−0.460250	+	1.39502i	−0.132863	+	0.402709i
$13$	−1.61511	−	3.61500i	−0.447950	−	1.00262i	−0.987055	−	0.160383i	$-0.948727\pi$
$13$	−1.61511	−	3.61500i	−0.447950	−	1.00262i	0.539105	−	0.842238i	$-0.318763\pi$
$14$	2.15263	−	5.17325i	0.575315	−	1.38261i
$15$	−0.0356539	+	0.0532302i	−0.00920580	+	0.0137440i
$16$	−4.97028	−	0.257260i	−1.24257	−	0.0643149i
$17$	−2.25299	−	1.02411i	−0.546429	−	0.248383i	0.121520	−	0.992589i	$-0.461223\pi$
$17$	−2.25299	−	1.02411i	−0.546429	−	0.248383i	−0.667950	+	0.744206i	$0.732828\pi$
$18$	4.18268	+	2.85276i	0.985868	+	0.672402i
$19$	3.01767	+	4.39988i	0.692302	+	1.00940i	0.998352	+	0.0573857i	$0.0182765\pi$
$19$	3.01767	+	4.39988i	0.692302	+	1.00940i	−0.306050	+	0.952015i	$0.599007\pi$
$20$	0.0297471	+	0.00996393i	0.00665165	+	0.00222800i
$21$	−4.49246	−	3.59004i	−0.980335	−	0.783411i
$22$	2.61051	+	1.52976i	0.556563	+	0.326147i
$23$	0.500513	−	1.52697i	0.104364	−	0.318396i	−0.884642	−	0.466271i	$-0.845597\pi$
$23$	0.500513	−	1.52697i	0.104364	−	0.318396i	0.989006	+	0.147875i	$0.0472433\pi$
$24$	−1.09618	+	3.18360i	−0.223756	+	0.649849i
$25$	−4.14044	−	2.80055i	−0.828087	−	0.560111i
$26$	2.64661	+	6.13554i	0.519044	+	1.20328i
$27$	3.99978	−	3.31688i	0.769759	−	0.638335i
$28$	−1.11532	+	2.58561i	−0.210776	+	0.488634i
$29$	1.72071	−	1.10013i	0.319528	−	0.204288i	−0.369125	−	0.929380i	$-0.620343\pi$
$29$	1.72071	−	1.10013i	0.319528	−	0.204288i	0.688652	+	0.725092i	$0.258203\pi$
$30$	0.0613272	−	0.0890478i	0.0111968	−	0.0162578i
$31$	1.29438	+	4.76898i	0.232477	+	0.856534i	0.981094	+	0.193531i	$0.0619941\pi$
$31$	1.29438	+	4.76898i	0.232477	+	0.856534i	−0.748617	+	0.663003i	$0.769282\pi$
$32$	4.50193	+	0.291419i	0.795835	+	0.0515160i
$33$	2.24906	−	2.14123i	0.391512	−	0.372740i
$34$	3.77956	+	1.77733i	0.648190	+	0.304810i
$35$	−0.0771023	+	0.0955919i	−0.0130327	+	0.0161580i
$36$	−2.08329	−	1.46071i	−0.347216	−	0.243451i
$37$	−8.92589	−	1.75299i	−1.46741	−	0.288189i	−0.605740	−	0.795663i	$-0.707123\pi$
$37$	−8.92589	−	1.75299i	−1.46741	−	0.288189i	−0.861667	+	0.507473i	$0.830580\pi$
$38$	−4.99632	−	7.49062i	−0.810510	−	1.21514i
$39$	6.80234	−	0.870996i	1.08925	−	0.139471i
$40$	0.0678816	+	0.0237176i	0.0107330	+	0.00375009i
$41$	5.48293	−	2.07628i	0.856290	−	0.324261i	0.113298	−	0.993561i	$-0.463859\pi$
$41$	5.48293	−	2.07628i	0.856290	−	0.324261i	0.742992	+	0.669300i	$0.233406\pi$
$42$	7.50268	+	6.15620i	1.15769	+	0.949922i
$43$	−9.84639	+	4.32302i	−1.50156	+	0.659255i	−0.980901	−	0.194509i	$-0.937689\pi$
$43$	−9.84639	+	4.32302i	−1.50156	+	0.659255i	−0.520660	+	0.853764i	$0.674314\pi$
$44$	−1.30186	−	0.785677i	−0.196263	−	0.118445i
$45$	−0.0704471	−	0.0857389i	−0.0105016	−	0.0127812i
$46$	−0.877929	+	2.56584i	−0.129444	+	0.378313i
$47$	2.14880	−	7.91697i	0.313434	−	1.15481i	−0.616582	−	0.787291i	$-0.711483\pi$
$47$	2.14880	−	7.91697i	0.313434	−	1.15481i	0.930016	−	0.367519i	$-0.119793\pi$
$48$	2.91158	−	8.11371i	0.420250	−	1.17111i
$49$	−2.90870	−	2.77997i	−0.415528	−	0.397139i
$50$	6.92587	+	4.81626i	0.979466	+	0.681122i
$51$	2.82471	−	3.22416i	0.395539	−	0.451473i
$52$	−1.29008	−	3.10035i	−0.178902	−	0.429941i
$53$	8.40178	−	8.90536i	1.15407	−	1.22325i	0.183349	−	0.983048i	$-0.441306\pi$
$53$	8.40178	−	8.90536i	1.15407	−	1.22325i	0.970724	−	0.240198i	$-0.0772123\pi$
$54$	−6.82199	+	5.50997i	−0.928355	+	0.749811i
$55$	−0.0455096	−	0.0482374i	−0.00613652	−	0.00650433i
$56$	−2.63281	+	5.89286i	−0.351823	+	0.787467i
$57$	−8.80515	+	2.80450i	−1.16627	+	0.371465i
$58$	−2.92769	+	1.81892i	−0.384425	+	0.238835i
$59$	12.7754	−	2.16760i	1.66322	−	0.282197i	0.741758	−	0.670667i	$-0.233992\pi$
$59$	12.7754	−	2.16760i	1.66322	−	0.282197i	0.921461	+	0.388470i	$0.126996\pi$
$60$	−0.0313959	+	0.0443487i	−0.00405319	+	0.00572539i
$61$	1.40446	−	2.58470i	0.179823	−	0.330937i	−0.773030	−	0.634369i	$-0.781260\pi$
$61$	1.40446	−	2.58470i	0.179823	−	0.330937i	0.952853	+	0.303432i	$0.0981324\pi$
$62$	−2.08021	−	8.07588i	−0.264187	−	1.02564i
$63$	8.19952	−	5.65506i	1.03304	−	0.712470i
$64$	2.33331	+	0.181359i	0.291664	+	0.0226699i
$65$	−0.0179424	−	0.145352i	−0.00222548	−	0.0180288i
$66$	−3.84201	+	3.56425i	−0.472918	+	0.438728i
$67$	6.00414	−	3.11323i	0.733522	−	0.380342i	−0.0524341	−	0.998624i	$-0.516698\pi$
$67$	6.00414	−	3.11323i	0.733522	−	0.380342i	0.785956	+	0.618282i	$0.212171\pi$
$68$	−1.88771	−	0.917678i	−0.228918	−	0.111285i
$69$	2.28198	+	1.59344i	0.274718	+	0.191828i
$70$	0.132196	−	0.159629i	0.0158004	−	0.0190793i
$71$	−7.03273	−	5.45078i	−0.834632	−	0.646888i	0.102937	−	0.994688i	$-0.467176\pi$
$71$	−7.03273	−	5.45078i	−0.834632	−	0.646888i	−0.937569	+	0.347800i	$0.886929\pi$
$72$	−4.73138	−	3.40950i	−0.557599	−	0.401813i
$73$	13.6316	−	4.37080i	1.59546	−	0.511563i	0.630997	−	0.775786i	$-0.282646\pi$
$73$	13.6316	−	4.37080i	1.59546	−	0.511563i	0.964462	+	0.264222i	$0.0851153\pi$
$74$	15.0242	+	3.15290i	1.74652	+	0.366518i
$75$	6.71429	−	5.46601i	0.775300	−	0.631160i
$76$	2.46202	+	3.79655i	0.282413	+	0.435494i
$77$	4.65738	−	3.70711i	0.530758	−	0.422464i
$78$	−11.4979	+	1.32139i	−1.30188	+	0.149618i
$79$	−0.852216	+	4.49271i	−0.0958818	+	0.505470i	0.901476	+	0.432828i	$0.142484\pi$
$79$	−0.852216	+	4.49271i	−0.0958818	+	0.505470i	−0.997358	+	0.0726412i	$0.976857\pi$
$80$	−0.172992	−	0.0629638i	−0.0193411	−	0.00703957i
$81$	3.50072	+	8.29126i	0.388969	+	0.921251i
$82$	−9.29773	+	3.38410i	−1.02676	+	0.373711i
$83$	−0.245341	−	1.50492i	−0.0269297	−	0.165186i	0.970044	−	0.242931i	$-0.0781088\pi$
$83$	−0.245341	−	1.50492i	−0.0269297	−	0.165186i	−0.996973	+	0.0777446i	$0.975228\pi$
$84$	−3.73015	−	3.14228i	−0.406993	−	0.342850i
$85$	−0.0685807	−	0.0606356i	−0.00743862	−	0.00657685i
$86$	16.7101	−	7.08026i	1.80189	−	0.763484i
$87$	0.964072	+	3.40352i	0.103359	+	0.364895i
$88$	−2.96043	−	1.83926i	−0.315583	−	0.196065i
$89$	−7.06426	−	2.88607i	−0.748811	−	0.305923i	−0.0285181	−	0.999593i	$-0.509079\pi$
$89$	−7.06426	−	2.88607i	−0.748811	−	0.305923i	−0.720292	+	0.693670i	$0.755992\pi$
$90$	0.117009	+	0.146221i	0.0123338	+	0.0154131i
$91$	13.1360	−	0.509736i	1.37702	−	0.0534348i
$92$	0.457835	−	1.28365i	0.0477326	−	0.133830i
$93$	−8.55566	−	0.237820i	−0.887180	−	0.0246607i
$94$	−3.79882	+	13.3130i	−0.391818	+	1.37313i
$95$	0.0590398	+	0.188311i	0.00605736	+	0.0193203i
$96$	−2.73407	+	7.31995i	−0.279045	+	0.747089i
$97$	1.41808	−	6.16055i	0.143984	−	0.625509i	−0.850973	−	0.525210i	$-0.823987\pi$
$97$	1.41808	−	6.16055i	0.143984	−	0.625509i	0.994957	−	0.100300i	$-0.0319802\pi$
$98$	4.84777	+	4.75466i	0.489698	+	0.480293i
$99$	2.42640	+	4.80021i	0.243862	+	0.482440i
$100$	−3.44901	−	2.46520i	−0.344901	−	0.246520i
$101$	−1.73472	+	11.5817i	−0.172611	+	1.15242i	0.717461	+	0.696598i	$0.245304\pi$
$101$	−1.73472	+	11.5817i	−0.172611	+	1.15242i	−0.890072	+	0.455820i	$0.849346\pi$
$102$	−4.83704	+	5.37913i	−0.478938	+	0.532614i
$103$	−5.20047	−	14.5808i	−0.512418	−	1.43668i	−0.865413	−	0.501060i	$-0.832944\pi$
$103$	−5.20047	−	14.5808i	−0.512418	−	1.43668i	0.352995	−	0.935625i	$-0.385163\pi$
$104$	−2.86484	−	7.14386i	−0.280921	−	0.700513i
$105$	−0.119974	−	0.175653i	−0.0117083	−	0.0171420i
$106$	−14.3723	+	14.8445i	−1.39596	+	1.44182i
$107$	−0.730592	−	12.5438i	−0.0706290	−	1.21265i	−0.828402	−	0.560135i	$-0.810749\pi$
$107$	−0.730592	−	12.5438i	−0.0706290	−	1.21265i	0.757773	−	0.652519i	$-0.226288\pi$
$108$	3.46389	−	2.72447i	0.333313	−	0.262163i
$109$	0.101469	−	1.74216i	0.00971901	−	0.166869i	−0.989956	−	0.141376i	$-0.954847\pi$
$109$	0.101469	−	1.74216i	0.00971901	−	0.166869i	0.999675	−	0.0254931i	$-0.00811559\pi$
$110$	0.0757449	+	0.0823934i	0.00722199	+	0.00785590i
$111$	7.36964	−	13.9256i	0.699496	−	1.32176i
$112$	6.93501	−	14.9986i	0.655297	−	1.41723i
$113$	−16.0614	+	11.7967i	−1.51093	+	1.10974i	−0.549221	+	0.835677i	$0.685075\pi$
$113$	−16.0614	+	11.7967i	−1.51093	+	1.10974i	−0.961712	+	0.274063i	$0.911632\pi$
$114$	14.9198	−	4.54047i	1.39737	−	0.425254i
$115$	0.0342498	−	0.0485789i	0.00319381	−	0.00453000i
$116$	1.48300	−	0.894997i	0.137693	−	0.0830984i
$117$	−1.95653	+	11.7159i	−0.180881	+	1.08314i
$118$	−21.6058	+	3.37908i	−1.98897	+	0.311070i
$119$	5.94013	−	5.67725i	0.544531	−	0.520432i
$120$	−0.0732699	+	0.100712i	−0.00668859	+	0.00919368i
$121$	−3.97965	−	6.69165i	−0.361786	−	0.608332i
$122$	−2.42641	+	4.33103i	−0.219677	+	0.392113i
$123$	0.701881	+	10.1305i	0.0632865	+	0.913440i
$124$	0.992852	+	4.07170i	0.0891608	+	0.365650i
$125$	−0.232192	−	0.287873i	−0.0207679	−	0.0257482i
$126$	−13.9600	+	9.36399i	−1.24366	+	0.834211i
$127$	−0.0833120	−	4.29555i	−0.00739275	−	0.381168i	−0.985176	−	0.171548i	$-0.945123\pi$
$127$	−0.0833120	−	4.29555i	−0.00739275	−	0.381168i	0.977783	−	0.209620i	$-0.0672226\pi$
$128$	−12.9193	−	1.17238i	−1.14191	−	0.103624i
$129$	−2.24613	−	18.4899i	−0.197760	−	1.62794i
$130$	0.0271065	+	0.245673i	0.00237740	+	0.0215470i
$131$	−18.7077	+	1.69766i	−1.63450	+	0.148325i	−0.868898	−	0.494992i	$-0.835171\pi$
$131$	−18.7077	+	1.69766i	−1.63450	+	0.148325i	−0.765600	+	0.643316i	$0.777558\pi$
$132$	1.95379	−	1.76610i	0.170056	−	0.153719i
$133$	−17.2879	+	3.86197i	−1.49906	+	0.334875i
$134$	−10.1999	+	5.12257i	−0.881136	+	0.442523i
$135$	0.177404	−	0.0739577i	0.0152685	−	0.00636527i
$136$	−4.29922	−	2.15915i	−0.368655	−	0.185145i
$137$	7.08221	+	1.77552i	0.605074	+	0.151693i	0.533582	−	0.845748i	$-0.320845\pi$
$137$	7.08221	+	1.77552i	0.605074	+	0.151693i	0.0714917	+	0.997441i	$0.477224\pi$
$138$	−3.81606	−	2.73872i	−0.324845	−	0.233135i
$139$	11.1369	+	1.59457i	0.944623	+	0.135250i	0.596871	−	0.802337i	$-0.296410\pi$
$139$	11.1369	+	1.59457i	0.944623	+	0.135250i	0.347752	+	0.937587i	$0.386945\pi$
$140$	−0.0674663	+	0.0793557i	−0.00570194	+	0.00670678i
$141$	12.0546	+	7.52160i	1.01518	+	0.633433i
$142$	11.7488	+	9.35161i	0.985936	+	0.784769i
$143$	−0.687229	+	7.06533i	−0.0574690	+	0.590833i
$144$	11.9995	+	8.88490i	0.999956	+	0.740409i
$145$	0.0727775	−	0.0202590i	0.00604384	−	0.00168242i
$146$	−23.0986	+	7.07829i	−1.91166	+	0.585804i
$147$	6.06434	−	3.43368i	0.500178	−	0.283205i
$148$	−7.52926	−	1.68197i	−0.618901	−	0.138257i
$149$	9.05136	−	2.26919i	0.741516	−	0.185899i	0.146047	−	0.989278i	$-0.453345\pi$
$149$	9.05136	−	2.26919i	0.741516	−	0.185899i	0.595469	+	0.803378i	$0.296966\pi$
$150$	−11.4496	+	9.07737i	−0.934856	+	0.741164i
$151$	5.42703	+	6.38343i	0.441646	+	0.519476i	0.937054	−	0.349184i	$-0.113541\pi$
$151$	5.42703	+	6.38343i	0.441646	+	0.519476i	−0.495408	+	0.868660i	$0.664982\pi$
$152$	5.53016	+	8.77420i	0.448555	+	0.711681i
$153$	3.93445	+	6.29625i	0.318081	+	0.509022i
$154$	−7.94019	+	6.15412i	−0.639839	+	0.495913i
$155$	−0.00590671	+	0.182688i	−0.000474439	+	0.0146739i
$156$	5.78637	−	0.589307i	0.463280	−	0.0471823i
$157$	−1.60963	+	13.0397i	−0.128462	+	1.04068i	0.780895	+	0.624663i	$0.214764\pi$
$157$	−1.60963	+	13.0397i	−0.128462	+	1.04068i	−0.909357	+	0.416017i	$0.863426\pi$
$158$	1.53613	−	7.56284i	0.122208	−	0.601667i
$159$	10.5674	+	18.3852i	0.838048	+	1.45804i
$160$	0.156058	+	0.0590961i	0.0123374	+	0.00467196i
$161$	4.08701	+	3.42941i	0.322102	+	0.270275i
$162$	−5.72655	−	14.0678i	−0.449921	−	1.10527i
$163$	−16.2319	+	13.6202i	−1.27138	+	1.06682i	−0.277011	+	0.960867i	$0.589344\pi$
$163$	−16.2319	+	13.6202i	−1.27138	+	1.06682i	−0.994372	+	0.105949i	$0.966212\pi$
$164$	4.69416	−	1.64013i	0.366552	−	0.128072i
$165$	0.102746	−	0.0513527i	0.00799879	−	0.00399780i
$166$	0.381178	+	2.54489i	0.0295852	+	0.197522i
$167$	2.88288	−	5.64895i	0.223084	−	0.437129i	−0.751939	−	0.659233i	$-0.770881\pi$
$167$	2.88288	−	5.64895i	0.223084	−	0.437129i	0.975023	+	0.222104i	$0.0712926\pi$
$168$	−8.45596	−	7.31226i	−0.652392	−	0.564153i
$169$	−1.78598	+	1.99388i	−0.137383	+	0.153375i
$170$	0.114407	+	0.103819i	0.00877460	+	0.00796252i
$171$	−0.248509	−	16.0039i	−0.0190040	−	1.22385i
$172$	−8.44293	+	3.44931i	−0.643767	+	0.263008i
$173$	−17.1837	−	2.91554i	−1.30645	−	0.221665i	−0.527932	−	0.849287i	$-0.677032\pi$
$173$	−17.1837	−	2.91554i	−1.30645	−	0.221665i	−0.778518	+	0.627622i	$0.784028\pi$
$174$	−1.55261	−	5.76445i	−0.117703	−	0.437002i
$175$	13.7470	−	9.29832i	1.03917	−	0.702887i
$176$	7.51782	+	4.80648i	0.566677	+	0.362302i
$177$	−2.79268	+	22.2695i	−0.209911	+	1.67388i
$178$	11.8580	+	5.02436i	0.888791	+	0.376592i
$179$	−5.80960	−	12.1498i	−0.434230	−	0.908115i	−0.996690	−	0.0812910i	$-0.974096\pi$
$179$	−5.80960	−	12.1498i	−0.434230	−	0.908115i	0.562460	−	0.826824i	$-0.309855\pi$
$180$	−0.0578477	−	0.0742373i	−0.00431171	−	0.00553332i
$181$	3.19497	+	0.889381i	0.237480	+	0.0661072i	0.384868	−	0.922972i	$-0.374247\pi$
$181$	3.19497	+	0.889381i	0.237480	+	0.0661072i	−0.147388	+	0.989079i	$0.547086\pi$
$182$	−22.1780	+	0.573579i	−1.64395	+	0.0425165i
$183$	3.58409	+	3.62131i	0.264944	+	0.267695i
$184$	1.08734	−	2.92841i	0.0801599	−	0.215885i
$185$	−0.296676	−	0.158731i	−0.0218121	−	0.0116701i
$186$	14.4325	+	0.587985i	1.05824	+	0.0431132i
$187$	2.60338	+	3.59300i	0.190378	+	0.262747i
$188$	1.99543	−	6.66518i	0.145531	−	0.486109i
$189$	5.27845	+	16.4248i	0.383951	+	1.19473i
$190$	−0.0955209	−	0.319062i	−0.00692982	−	0.0231472i
$191$	−11.2638	+	14.7284i	−0.815018	+	1.06571i	0.181587	+	0.983375i	$0.441877\pi$
$191$	−11.2638	+	14.7284i	−0.815018	+	1.06571i	−0.996604	+	0.0823382i	$0.973761\pi$
$192$	−1.46732	+	3.77871i	−0.105895	+	0.272705i
$193$	−2.53788	+	1.19344i	−0.182681	+	0.0859054i	−0.514712	−	0.857363i	$-0.672101\pi$
$193$	−2.53788	+	1.19344i	−0.182681	+	0.0859054i	0.332032	+	0.943268i	$0.392266\pi$
$194$	−2.52742	+	10.3650i	−0.181458	+	0.744162i
$195$	0.250012	+	0.0429167i	0.0179037	+	0.00307333i
$196$	−2.40515	−	2.42074i	−0.171796	−	0.172910i
$197$	−9.21293	+	1.80936i	−0.656394	+	0.128912i	−0.509811	−	0.860287i	$-0.670285\pi$
$197$	−9.21293	+	1.80936i	−0.656394	+	0.128912i	−0.146584	+	0.989198i	$0.546828\pi$
$198$	−3.98981	−	8.15328i	−0.283543	−	0.579428i
$199$	−2.62559	+	1.44874i	−0.186123	+	0.102698i	−0.573437	−	0.819249i	$-0.694390\pi$
$199$	−2.62559	+	1.44874i	−0.186123	+	0.102698i	0.387314	+	0.921948i	$0.373403\pi$
$200$	−7.83167	−	5.75215i	−0.553783	−	0.406739i
$201$	2.16089	+	11.5133i	0.152418	+	0.812086i
$202$	3.18002	−	19.5062i	0.223745	−	1.37245i
$203$	1.26372	+	6.66209i	0.0886959	+	0.467587i
$204$	2.46559	−	2.67163i	0.172626	−	0.187051i
$205$	0.216412	−	0.0140088i	0.0151149	−	0.000978416i
$206$	8.45766	+	24.7184i	0.589273	+	1.72222i
$207$	−3.78335	+	2.98759i	−0.262961	+	0.207652i
$208$	7.09753	+	18.3831i	0.492125	+	1.27464i
$209$	−0.802883	−	9.53172i	−0.0555366	−	0.659323i
$210$	0.198623	+	0.299032i	0.0137063	+	0.0206351i
$211$	12.3616	−	18.5328i	0.851007	−	1.27585i	−0.108480	−	0.994099i	$-0.534598\pi$
$211$	12.3616	−	18.5328i	0.851007	−	1.27585i	0.959487	−	0.281754i	$-0.0909162\pi$
$212$	7.31861	−	7.36607i	0.502644	−	0.505904i
$213$	12.5553	−	8.93735i	0.860273	−	0.612377i
$214$	0.959194	+	21.1835i	0.0655692	+	1.44808i
$215$	−0.395080	+	0.0461782i	−0.0269442	+	0.00314933i
$216$	8.01957	−	6.14153i	0.545663	−	0.417878i
$217$	−16.2957	−	1.90470i	−1.10623	−	0.129299i
$218$	−0.209240	+	2.93768i	−0.0141715	+	0.198965i
$219$	0.432884	+	24.7908i	0.0292516	+	1.67521i
$220$	−0.0375270	−	0.0418953i	−0.00253007	−	0.00282458i
$221$	−0.0633408	+	9.79859i	−0.00426076	+	0.659125i
$222$	−12.7401	+	23.3386i	−0.855058	+	1.56638i
$223$	−6.27672	+	5.54956i	−0.420321	+	0.371626i	−0.845942	−	0.533275i	$-0.820961\pi$
$223$	−6.27672	+	5.54956i	−0.420321	+	0.371626i	0.425621	+	0.904901i	$0.360056\pi$
$224$	−6.46149	+	13.5131i	−0.431726	+	0.902879i
$225$	5.70750	+	13.8673i	0.380500	+	0.924485i
$226$	27.3610	−	19.5565i	1.82003	−	1.30088i
$227$	−4.68976	−	9.18949i	−0.311271	−	0.609928i	0.681244	−	0.732057i	$-0.261439\pi$
$227$	−4.68976	−	9.18949i	−0.311271	−	0.609928i	−0.992514	+	0.122129i	$0.961028\pi$
$228$	−7.52682	+	2.18469i	−0.498476	+	0.144684i
$229$	−11.7868	−	15.4124i	−0.778896	−	1.01848i	−0.999074	−	0.0430206i	$-0.986302\pi$
$229$	−11.7868	−	15.4124i	−0.778896	−	1.01848i	0.220179	−	0.975460i	$-0.429336\pi$
$230$	−0.0588564	+	0.0812295i	−0.00388087	+	0.00535611i
$231$	3.81906	+	9.57686i	0.251276	+	0.630111i
$232$	3.42539	−	2.00728i	0.224888	−	0.131785i
$233$	−2.07717	−	9.58928i	−0.136080	−	0.628215i	−0.993523	−	0.113635i	$-0.963750\pi$
$233$	−2.07717	−	9.58928i	−0.136080	−	0.628215i	0.857443	−	0.514580i	$-0.172052\pi$
$234$	3.55725	−	19.7279i	0.232545	−	1.28965i
$235$	0.161795	−	0.256705i	0.0105543	−	0.0167456i
$236$	10.8790	−	1.55764i	0.708163	−	0.101394i
$237$	−7.02429	−	3.65944i	−0.456277	−	0.237706i
$238$	−10.1478	+	9.45073i	−0.657785	+	0.612600i
$239$	1.73438	+	3.19187i	0.112188	+	0.206465i	0.928671	−	0.370904i	$-0.120952\pi$
$239$	1.73438	+	3.19187i	0.112188	+	0.206465i	−0.816484	+	0.577369i	$0.804080\pi$
$240$	0.190904	−	0.255396i	0.0123228	−	0.0164858i
$241$	−4.75684	+	7.99847i	−0.306415	+	0.515227i	−0.973181	−	0.230040i	$-0.926114\pi$
$241$	−4.75684	+	7.99847i	−0.306415	+	0.515227i	0.666766	+	0.745267i	$0.267678\pi$
$242$	6.56965	+	11.3790i	0.422313	+	0.731468i
$243$	−15.4998	+	1.65999i	−0.994314	+	0.106489i
$244$	1.24743	−	2.16061i	0.0798584	−	0.138319i
$245$	−0.0727415	−	0.129840i	−0.00464728	−	0.00829518i
$246$	−0.963396	−	17.1106i	−0.0614239	−	1.09093i
$247$	11.0317	−	18.0152i	0.701930	−	1.14628i
$248$	2.15485	+	9.36128i	0.136833	+	0.594442i
$249$	2.61830	+	0.345550i	0.165928	+	0.0218983i
$250$	0.385543	+	0.490851i	0.0243839	+	0.0310441i
$251$	3.16882	+	6.01585i	0.200014	+	0.379717i	0.964158	−	0.265328i	$-0.0854803\pi$
$251$	3.16882	+	6.01585i	0.200014	+	0.379717i	−0.764144	+	0.645046i	$0.776838\pi$
$252$	7.07585	−	4.61477i	0.445737	−	0.290703i
$253$	−2.13349	+	1.93604i	−0.134132	+	0.121718i
$254$	0.0468694	+	7.25054i	0.00294085	+	0.454939i
$255$	0.134841	−	0.0834133i	0.00844409	−	0.00522355i
$256$	17.1200	+	1.77701i	1.07000	+	0.111063i
$257$	−1.75802	+	0.228558i	−0.109662	+	0.0142571i	−0.183558	−	0.983009i	$-0.558761\pi$
$257$	−1.75802	+	0.228558i	−0.109662	+	0.0142571i	0.0738954	+	0.997266i	$0.476457\pi$
$258$	3.38692	+	31.2506i	0.210861	+	1.94558i
$259$	16.4326	−	25.3398i	1.02107	−	1.57454i
$260$	−0.0120251	−	0.123629i	−0.000745764	−	0.00766712i
$261$	−6.12613	−	0.102893i	−0.379198	−	0.00636890i
$262$	31.6062	−	2.45663i	1.95264	−	0.151771i
$263$	−3.34370	−	16.4621i	−0.206181	−	1.01509i	−0.941407	−	0.337271i	$-0.890496\pi$
$263$	−3.34370	−	16.4621i	−0.206181	−	1.01509i	0.735226	−	0.677822i	$-0.237076\pi$
$264$	4.53019	−	3.98979i	0.278814	−	0.245555i
$265$	0.393651	−	0.223894i	0.0241818	−	0.0137537i
$266$	29.2576	−	6.13987i	1.79390	−	0.376460i
$267$	8.31792	−	10.2719i	0.509048	−	0.628630i
$268$	5.15879	−	2.50786i	0.315123	−	0.153192i
$269$	15.6096	−	20.9673i	0.951732	−	1.27840i	−0.00872278	−	0.999962i	$-0.502777\pi$
$269$	15.6096	−	20.9673i	0.951732	−	1.27840i	0.960455	−	0.278436i	$-0.0898160\pi$
$270$	−0.300982	+	0.120933i	−0.0183172	+	0.00735974i
$271$	−10.7419	−	14.4289i	−0.652526	−	0.876494i	0.345556	−	0.938398i	$-0.387690\pi$
$271$	−10.7419	−	14.4289i	−0.652526	−	0.876494i	−0.998082	+	0.0619039i	$0.980283\pi$
$272$	10.9345	+	5.66970i	0.663002	+	0.343776i
$273$	−5.72221	+	22.0385i	−0.346324	+	1.33383i
$274$	−11.9125	−	3.15070i	−0.719658	−	0.190341i
$275$	3.97024	+	8.03448i	0.239414	+	0.484497i
$276$	1.89981	+	1.40102i	0.114355	+	0.0843314i
$277$	−1.89988	+	1.32118i	−0.114153	+	0.0793820i	−0.626621	−	0.779324i	$-0.715563\pi$
$277$	−1.89988	+	1.32118i	−0.114153	+	0.0793820i	0.512468	+	0.858706i	$0.328731\pi$
$278$	−18.7588	−	2.93382i	−1.12508	−	0.175959i
$279$	4.67190	−	14.0691i	0.279699	−	0.842298i
$280$	−0.156976	+	0.179875i	−0.00938113	+	0.0107496i
$281$	4.02250	−	8.14023i	0.239962	−	0.485605i	−0.743029	−	0.669259i	$-0.766612\pi$
$281$	4.02250	−	8.14023i	0.239962	−	0.485605i	0.982991	+	0.183654i	$0.0587926\pi$
$282$	−20.1780	−	12.9557i	−1.20158	−	0.771499i
$283$	−19.0007	+	16.3667i	−1.12947	+	0.972898i	−0.999826	−	0.0186627i	$-0.994059\pi$
$283$	−19.0007	+	16.3667i	−1.12947	+	0.972898i	−0.129646	+	0.991560i	$0.541384\pi$
$284$	−5.84309	−	4.77558i	−0.346724	−	0.283378i
$285$	−0.341798	+	0.00375839i	−0.0202464	+	0.000222628i
$286$	1.31385	−	11.9077i	0.0776894	−	0.704119i
$287$	−0.377468	+	19.4621i	−0.0222812	+	1.14881i
$288$	−10.7719	−	8.19368i	−0.634741	−	0.482817i
$289$	−7.15071	−	8.19381i	−0.420630	−	0.481989i
$290$	−0.123254	+	0.0325992i	−0.00723771	+	0.00191429i
$291$	9.50720	+	5.43169i	0.557322	+	0.318412i
$292$	11.6532	−	3.40682i	0.681953	−	0.199369i
$293$	0.656907	−	7.79871i	0.0383769	−	0.455606i	−0.950894	−	0.309516i	$-0.899833\pi$
$293$	0.656907	−	7.79871i	0.0383769	−	0.455606i	0.989271	−	0.146090i	$-0.0466690\pi$
$294$	−10.3085	+	5.66201i	−0.601202	+	0.330215i
$295$	0.475309	+	0.0617944i	0.0276736	+	0.00359781i
$296$	−17.2063	−	4.07798i	−1.00010	−	0.237028i
$297$	−9.17342	+	1.62382i	−0.532296	+	0.0942234i
$298$	−15.3237	+	3.63177i	−0.887675	+	0.210383i
$299$	−6.32839	+	0.656870i	−0.365980	+	0.0379878i
$300$	5.81248	−	4.48706i	0.335584	−	0.259060i
$301$	−1.15378	−	35.6851i	−0.0665027	−	2.05686i
$302$	−9.01883	−	10.8904i	−0.518975	−	0.626673i
$303$	−18.3388	−	8.66714i	−1.05354	−	0.497914i
$304$	−13.8668	−	22.6449i	−0.795314	−	1.29878i
$305$	0.0776821	−	0.0761901i	0.00444807	−	0.00436263i
$306$	−6.50200	−	10.7107i	−0.371694	−	0.612293i
$307$	−0.780621	+	1.13817i	−0.0445524	+	0.0649590i	−0.846311	−	0.532689i	$-0.821182\pi$
$307$	−0.780621	+	1.13817i	−0.0445524	+	0.0649590i	0.801759	+	0.597648i	$0.203898\pi$
$308$	4.02999	−	3.04090i	0.229630	−	0.173271i
$309$	26.7797	−	1.33421i	1.52344	−	0.0759005i
$310$	0.0139534	−	0.308157i	0.000792501	−	0.0175022i
$311$	0.430242	+	6.04051i	0.0243968	+	0.342526i	0.994859	+	0.101272i	$0.0322912\pi$
$311$	0.430242	+	6.04051i	0.0243968	+	0.342526i	−0.970462	+	0.241254i	$0.922441\pi$
$312$	13.2791	−	1.17916i	0.751784	−	0.0667568i
$313$	−0.592718	−	1.59630i	−0.0335024	−	0.0902280i	0.919625	−	0.392798i	$-0.128493\pi$
$313$	−0.592718	−	1.59630i	−0.0335024	−	0.0902280i	−0.953127	+	0.302570i	$0.902155\pi$
$314$	3.00074	−	21.9693i	0.169341	−	1.23980i
$315$	0.351272	−	0.111135i	0.0197919	−	0.00626176i
$316$	−0.821052	+	3.79040i	−0.0461878	+	0.213227i
$317$	−6.60325	−	20.1453i	−0.370876	−	1.13147i	−0.948933	−	0.315478i	$-0.897835\pi$
$317$	−6.60325	−	20.1453i	−0.370876	−	1.13147i	0.578057	−	0.815996i	$-0.303811\pi$
$318$	−17.4313	−	31.2556i	−0.977499	−	1.75272i
$319$	−3.65674	+	0.189271i	−0.204738	+	0.0105972i
$320$	0.0805547	+	0.0317013i	0.00450314	+	0.00177215i
$321$	21.1669	+	5.05988i	1.18142	+	0.282415i
$322$	−6.82200	−	5.87629i	−0.380175	−	0.327473i
$323$	−2.29283	−	13.0033i	−0.127577	−	0.723522i
$324$	2.78623	+	7.10640i	0.154791	+	0.394800i
$325$	−3.43677	+	19.4909i	−0.190638	+	1.08116i
$326$	27.6885	−	22.6299i	1.53352	−	1.25335i
$327$	2.83834	+	1.03929i	0.156961	+	0.0574728i
$328$	10.8071	−	3.61988i	0.596721	−	0.199874i
$329$	21.7416	+	16.4055i	1.19865	+	0.904465i
$330$	−0.174505	+	0.0844158i	−0.00960616	+	0.00464694i
$331$	−16.3238	+	8.73374i	−0.897238	+	0.480050i	−0.854746	−	0.519047i	$-0.826287\pi$
$331$	−16.3238	+	8.73374i	−0.897238	+	0.480050i	−0.0424922	+	0.999097i	$0.513530\pi$
$332$	−0.175011	−	1.28130i	−0.00960495	−	0.0703207i
$333$	19.4086	+	19.1835i	1.06358	+	1.05125i
$334$	−4.98810	+	9.46968i	−0.272937	+	0.518158i
$335$	0.246083	−	0.0450331i	0.0134449	−	0.00246042i
$336$	21.4052	+	18.9992i	1.16775	+	1.03649i
$337$	−19.9881	−	20.6448i	−1.08882	−	1.12459i	−0.991602	−	0.129328i	$-0.958718\pi$
$337$	−19.9881	−	20.6448i	−1.08882	−	1.12459i	−0.0972168	−	0.995263i	$-0.530994\pi$
$338$	3.05734	−	3.32569i	0.166297	−	0.180894i
$339$	−11.5326	−	32.5330i	−0.626365	−	1.76695i
$340$	−0.0568157	−	0.0529128i	−0.00308126	−	0.00286960i
$341$	2.20992	−	8.57945i	0.119674	−	0.464603i
$342$	0.0701884	+	27.0120i	0.00379535	+	1.46064i
$343$	−8.99656	+	4.08944i	−0.485769	+	0.220809i
$344$	−19.4524	+	7.65525i	−1.04880	+	0.412743i
$345$	0.0634358	+	0.0810850i	0.00341527	+	0.00436547i
$346$	28.9338	+	5.29488i	1.55549	+	0.284654i
$347$	−1.31499	+	1.67416i	−0.0705921	+	0.0898738i	−0.820427	−	0.571751i	$-0.806264\pi$
$347$	−1.31499	+	1.67416i	−0.0705921	+	0.0898738i	0.749835	+	0.661625i	$0.230133\pi$
$348$	0.742746	+	2.90677i	0.0398154	+	0.155819i
$349$	7.26946	+	25.4759i	0.389125	+	1.36369i	0.872643	+	0.488358i	$0.162404\pi$
$349$	7.26946	+	25.4759i	0.389125	+	1.36369i	−0.483518	+	0.875335i	$0.660641\pi$
$350$	−23.4008	+	15.3909i	−1.25083	+	0.822681i
$351$	−18.4506	−	9.10211i	−0.984821	−	0.485835i
$352$	−6.75764	−	4.44457i	−0.360184	−	0.236896i
$353$	−3.40240	+	10.8522i	−0.181092	+	0.577602i	0.818902	+	0.573934i	$0.194583\pi$
$353$	−3.40240	+	10.8522i	−0.181092	+	0.577602i	−0.999993	+	0.00366830i	$0.998832\pi$
$354$	5.19851	−	37.5188i	0.276297	−	1.99410i
$355$	−0.189648	−	0.268990i	−0.0100655	−	0.0142765i
$356$	−5.92606	−	2.60182i	−0.314081	−	0.137896i
$357$	6.44486	+	12.6891i	0.341098	+	0.671577i
$358$	9.53860	+	20.6294i	0.504131	+	1.09030i
$359$	−5.80652	−	3.20390i	−0.306456	−	0.169095i	0.322429	−	0.946594i	$-0.395501\pi$
$359$	−5.80652	−	3.20390i	−0.306456	−	0.169095i	−0.628885	+	0.777498i	$0.716488\pi$
$360$	−0.130380	−	0.171857i	−0.00687164	−	0.00905768i
$361$	−3.40919	+	8.83001i	−0.179431	+	0.464737i
$362$	−5.37210	−	1.57053i	−0.282351	−	0.0825455i
$363$	13.0866	−	3.25396i	0.686869	−	0.170789i
$364$	11.1483	−	0.144138i	0.584332	−	0.00755488i
$365$	0.529466	−	0.00684551i	0.0277135	−	0.000358310i
$366$	−5.96913	−	6.18914i	−0.312012	−	0.323512i
$367$	17.4458	+	5.10029i	0.910664	+	0.266233i	0.702352	−	0.711830i	$-0.252133\pi$
$367$	17.4458	+	5.10029i	0.910664	+	0.266233i	0.208312	+	0.978063i	$0.433203\pi$
$368$	−2.88052	+	7.46073i	−0.150157	+	0.388917i
$369$	−17.1506	−	3.90096i	−0.892826	−	0.203076i
$370$	0.497177	+	0.274331i	0.0258470	+	0.0142618i
$371$	17.0600	+	36.8962i	0.885712	+	1.91556i
$372$	−7.24859	−	0.389234i	−0.375822	−	0.0201808i
$373$	11.1835	+	4.91008i	0.579060	+	0.254234i	0.670910	−	0.741539i	$-0.265904\pi$
$373$	11.1835	+	4.91008i	0.579060	+	0.254234i	−0.0918504	+	0.995773i	$0.529278\pi$
$374$	−4.31480	−	6.11998i	−0.223113	−	0.316457i
$375$	0.593475	−	0.241124i	0.0306469	−	0.0124516i
$376$	4.77078	−	15.2167i	0.246034	−	0.784741i
$377$	−6.75608	−	4.44355i	−0.347956	−	0.228854i
$378$	−8.54901	−	27.8319i	−0.439714	−	1.43152i
$379$	23.3324	−	15.3460i	1.19851	−	0.788269i	0.216345	−	0.976317i	$-0.430586\pi$
$379$	23.3324	−	15.3460i	1.19851	−	0.788269i	0.982160	+	0.188048i	$0.0602160\pi$
$380$	0.0459270	+	0.160952i	0.00235600	+	0.00825664i
$381$	7.16506	+	2.00946i	0.367077	+	0.102948i
$382$	19.3289	−	24.6085i	0.988953	−	1.25908i
$383$	27.7239	+	5.07346i	1.41662	+	0.259242i	0.833221	−	0.552941i	$-0.186494\pi$
$383$	27.7239	+	5.07346i	1.41662	+	0.259242i	0.583403	+	0.812183i	$0.301721\pi$
$384$	8.40335	−	20.8382i	0.428832	−	1.06339i
$385$	0.204890	−	0.0806316i	0.0104421	−	0.00410937i
$386$	4.30871	−	1.95855i	0.219307	−	0.0996874i
$387$	31.7851	+	5.51946i	1.61573	+	0.280570i
$388$	1.33739	−	5.19205i	0.0678955	−	0.263586i
$389$	−14.3858	−	13.3976i	−0.729387	−	0.679284i	0.226170	−	0.974088i	$-0.427379\pi$
$389$	−14.3858	−	13.3976i	−0.729387	−	0.679284i	−0.955558	+	0.294804i	$0.904746\pi$
$390$	−0.420958	−	0.0778764i	−0.0213160	−	0.00394343i
$391$	−2.69143	+	2.92767i	−0.136112	+	0.148059i
$392$	−5.44058	−	5.61933i	−0.274791	−	0.283819i
$393$	6.53791	−	31.8722i	0.329794	−	1.60774i
$394$	15.5863	−	2.85228i	0.785225	−	0.143696i
$395$	−0.0788295	+	0.149654i	−0.00396634	+	0.00752991i
$396$	1.95193	+	4.12300i	0.0980883	+	0.207189i
$397$	−1.56298	−	11.4431i	−0.0784440	−	0.574311i	−0.987498	−	0.157633i	$-0.949614\pi$
$397$	−1.56298	−	11.4431i	−0.0784440	−	0.574311i	0.909054	−	0.416679i	$-0.136806\pi$
$398$	4.46228	−	2.38746i	0.223674	−	0.119672i
$399$	2.23896	−	30.5998i	0.112088	−	1.53191i
$400$	19.8587	+	14.9847i	0.992933	+	0.749235i
$401$	−9.65287	+	3.23328i	−0.482042	+	0.161462i	−0.548200	−	0.836347i	$-0.684687\pi$
$401$	−9.65287	+	3.23328i	−0.482042	+	0.161462i	0.0661589	+	0.997809i	$0.478926\pi$
$402$	−3.39531	−	19.4758i	−0.169343	−	0.971365i
$403$	15.1493	−	12.3816i	0.754641	−	0.616771i
$404$	−1.72471	+	9.78132i	−0.0858076	+	0.486639i
$405$	0.0339503	+	0.331169i	0.00168700	+	0.0164559i
$406$	−1.98717	−	11.2698i	−0.0986218	−	0.559312i
$407$	12.3566	+	10.6436i	0.612493	+	0.527586i
$408$	5.73002	−	6.04999i	0.283678	−	0.299519i
$409$	−21.2291	−	8.35444i	−1.04971	−	0.413100i	−0.222466	−	0.974941i	$-0.571410\pi$
$409$	−21.2291	−	8.35444i	−1.04971	−	0.413100i	−0.827246	+	0.561840i	$0.810094\pi$
$410$	−0.365500	+	0.0189182i	−0.0180508	+	0.000934301i
$411$	−6.48524	+	10.8569i	−0.319893	+	0.535531i
$412$	−4.08944	−	12.4761i	−0.201472	−	0.614655i
$413$	−9.10810	+	42.0477i	−0.448180	+	2.06903i
$414$	6.44958	−	4.95901i	0.316979	−	0.243722i
$415$	0.00763281	−	0.0558820i	0.000374680	−	0.00274314i
$416$	−6.21761	−	16.7451i	−0.304843	−	0.820998i
$417$	−8.21238	+	17.6714i	−0.402162	+	0.865373i
$418$	1.14690	+	16.1023i	0.0560968	+	0.787587i
$419$	0.790200	−	17.4513i	0.0386038	−	0.852554i	−0.884159	−	0.467186i	$-0.845268\pi$
$419$	0.790200	−	17.4513i	0.0386038	−	0.852554i	0.922763	−	0.385368i	$-0.125925\pi$
$420$	−0.0978667	−	0.151556i	−0.00477541	−	0.00739517i
$421$	−7.26516	+	5.48206i	−0.354082	+	0.267179i	−0.764371	−	0.644776i	$-0.776950\pi$
$421$	−7.26516	+	5.48206i	−0.354082	+	0.267179i	0.410289	+	0.911956i	$0.365428\pi$
$422$	−21.2645	+	31.0044i	−1.03514	+	1.50927i
$423$	−18.5001	+	16.2299i	−0.899506	+	0.789123i
$424$	16.9917	−	16.6653i	0.825188	−	0.809339i
$425$	6.46028	+	10.5499i	0.313369	+	0.511744i
$426$	−21.3820	+	14.8078i	−1.03596	+	0.717441i
$427$	6.22943	+	7.52216i	0.301463	+	0.364023i
$428$	−0.344373	−	10.6511i	−0.0166459	−	0.514841i
$429$	−11.3730	−	4.67206i	−0.549095	−	0.225569i
$430$	0.667703	−	0.0693058i	0.0321995	−	0.00334222i
$431$	16.3624	−	3.87797i	0.788151	−	0.186795i	0.183219	−	0.983072i	$-0.441348\pi$
$431$	16.3624	−	3.87797i	0.788151	−	0.186795i	0.604932	+	0.796277i	$0.293200\pi$
$432$	−20.7333	+	15.4569i	−0.997534	+	0.743669i
$433$	3.60901	+	0.855350i	0.173438	+	0.0411055i	0.316417	−	0.948620i	$-0.397520\pi$
$433$	3.60901	+	0.855350i	0.173438	+	0.0411055i	−0.142979	+	0.989726i	$0.545668\pi$
$434$	27.4575	+	3.56971i	1.31800	+	0.171352i
$435$	−0.00279016	+	0.130817i	−0.000133778	+	0.00627222i
$436$	0.124230	−	1.47485i	0.00594955	−	0.0706323i
$437$	8.22888	−	2.40572i	0.393641	−	0.115081i
$438$	−0.189608	−	41.8439i	−0.00905984	−	1.99938i
$439$	21.8044	−	5.76702i	1.04067	−	0.275245i	0.304834	−	0.952405i	$-0.401399\pi$
$439$	21.8044	−	5.76702i	1.04067	−	0.275245i	0.735835	+	0.677161i	$0.236790\pi$
$440$	−0.0847661	−	0.0971312i	−0.00404107	−	0.00463055i
$441$	2.66219	+	11.7733i	0.126771	+	0.560636i
$442$	0.320671	−	16.5337i	0.0152528	−	0.786428i
$443$	0.290723	−	2.63490i	0.0138127	−	0.125188i	−0.985089	−	0.172046i	$-0.944962\pi$
$443$	0.290723	−	2.63490i	0.0138127	−	0.125188i	0.998902	+	0.0468584i	$0.0149210\pi$
$444$	6.55360	−	11.6450i	0.311020	−	0.552648i
$445$	−0.218558	−	0.178628i	−0.0103606	−	0.00846780i
$446$	10.7130	−	9.22792i	0.507277	−	0.436955i
$447$	−0.762303	+	16.1446i	−0.0360557	+	0.763613i
$448$	−3.44237	+	6.96623i	−0.162637	+	0.329124i
$449$	−6.45434	+	7.39585i	−0.304599	+	0.349032i	−0.885246	−	0.465124i	$-0.846010\pi$
$449$	−6.45434	+	7.39585i	−0.304599	+	0.349032i	0.580646	+	0.814156i	$0.302800\pi$
$450$	−9.32883	−	23.5255i	−0.439765	−	1.10900i
$451$	−10.3852	−	1.62421i	−0.489018	−	0.0764811i
$452$	−13.8761	+	9.64949i	−0.652679	+	0.453874i
$453$	−13.2991	+	5.80829i	−0.624847	+	0.272897i
$454$	7.71347	+	15.6096i	0.362011	+	0.732593i
$455$	0.470093	+	0.124334i	0.0220383	+	0.00582887i
$456$	−17.3153	+	4.78401i	−0.810865	+	0.224032i
$457$	12.8203	+	6.64752i	0.599709	+	0.310958i	0.733116	−	0.680103i	$-0.238065\pi$
$457$	12.8203	+	6.64752i	0.599709	+	0.310958i	−0.133407	+	0.991061i	$0.542592\pi$
$458$	19.5540	+	26.2655i	0.913697	+	1.22731i
$459$	−12.4083	+	3.37669i	−0.579170	+	0.157610i
$460$	0.0301035	−	0.0404360i	0.00140358	−	0.00188534i
$461$	−26.5220	+	12.8932i	−1.23525	+	0.600496i	−0.935434	−	0.353501i	$-0.884991\pi$
$461$	−26.5220	+	12.8932i	−1.23525	+	0.600496i	−0.299816	+	0.953997i	$0.596925\pi$
$462$	−6.23570	−	16.2442i	−0.290111	−	0.755751i
$463$	2.17836	−	0.457141i	0.101237	−	0.0212451i	−0.154488	−	0.987995i	$-0.549373\pi$
$463$	2.17836	−	0.457141i	0.101237	−	0.0212451i	0.255725	+	0.966749i	$0.417686\pi$
$464$	−8.83542	+	5.02526i	−0.410174	+	0.233292i
$465$	−0.300003	−	0.101133i	−0.0139123	−	0.00468993i
$466$	3.29600	+	16.2272i	0.152684	+	0.751710i
$467$	−26.6360	+	2.07031i	−1.23257	+	0.0958027i	−0.677198	−	0.735801i	$-0.736806\pi$
$467$	−26.6360	+	2.07031i	−1.23257	+	0.0958027i	−0.555369	+	0.831604i	$0.687423\pi$
$468$	−1.91572	+	9.89030i	−0.0885540	+	0.457179i
$469$	2.17391	+	22.3497i	0.100382	+	1.03202i
$470$	−0.278629	+	0.429659i	−0.0128522	+	0.0198187i
$471$	−20.8192	−	9.18865i	−0.959300	−	0.423391i
$472$	24.9796	−	3.24757i	1.14978	−	0.149481i
$473$	19.1768	+	1.99050i	0.881749	+	0.0915232i
$474$	11.7736	+	6.32855i	0.540781	+	0.290680i
$475$	−0.172393	−	26.6686i	−0.00790993	−	1.22364i
$476$	5.16075	−	4.68313i	0.236543	−	0.214651i
$477$	−35.7720	+	8.33219i	−1.63789	+	0.381505i
$478$	−2.85712	−	5.42411i	−0.130682	−	0.248093i
$479$	−26.7501	−	34.0567i	−1.22224	−	1.55609i	−0.725564	−	0.688154i	$-0.758421\pi$
$479$	−26.7501	−	34.0567i	−1.22224	−	1.55609i	−0.496678	−	0.867935i	$-0.665447\pi$
$480$	−0.176024	+	0.229248i	−0.00803434	+	0.0104637i
$481$	8.07920	+	35.0984i	0.368380	+	1.60035i
$482$	8.20166	−	13.3936i	0.373575	−	0.610062i
$483$	−7.73043	+	5.06301i	−0.351747	+	0.230375i
$484$	−3.22737	−	5.76069i	−0.146698	−	0.261850i
$485$	0.116917	−	0.202507i	0.00530894	−	0.00919535i
$486$	26.1921	−	2.46306i	1.18810	−	0.111727i
$487$	−12.9531	−	22.4354i	−0.586959	−	1.01664i	−0.994628	−	0.103513i	$-0.966992\pi$
$487$	−12.9531	−	22.4354i	−0.586959	−	1.01664i	0.407669	−	0.913130i	$-0.366342\pi$
$488$	2.92298	−	4.91490i	0.132317	−	0.222487i
$489$	−14.4713	−	33.7274i	−0.654415	−	1.52520i
$490$	0.119918	+	0.220692i	0.00541735	+	0.00996983i
$491$	−18.9596	+	17.6572i	−0.855634	+	0.796858i	−0.980747	−	0.195284i	$-0.937437\pi$
$491$	−18.9596	+	17.6572i	−0.855634	+	0.796858i	0.125112	+	0.992143i	$0.460071\pi$
$492$	0.372947	+	8.60444i	0.0168137	+	0.387918i
$493$	−5.00338	+	0.716377i	−0.225341	+	0.0322640i
$494$	−19.0090	+	30.1598i	−0.855256	+	1.35696i
$495$	0.0337899	+	0.196061i	0.00151874	+	0.00881230i
$496$	−5.20656	−	24.0362i	−0.233782	−	1.07926i
$497$	25.4882	−	14.9361i	1.14330	−	0.669977i
$498$	−4.41083	−	0.640240i	−0.197654	−	0.0286898i
$499$	5.51855	−	7.61632i	0.247044	−	0.340953i	−0.668106	−	0.744066i	$-0.732895\pi$
$499$	5.51855	−	7.61632i	0.247044	−	0.340953i	0.915150	+	0.403113i	$0.132072\pi$
$500$	−0.190549	−	0.249161i	−0.00852161	−	0.0111428i
$501$	7.92644	+	7.60503i	0.354127	+	0.339767i
$502$	−5.21612	−	10.2209i	−0.232807	−	0.456180i
$503$	19.6496	−	14.0447i	0.876134	−	0.626223i	−0.0519273	−	0.998651i	$-0.516536\pi$
$503$	19.6496	−	14.0447i	0.876134	−	0.626223i	0.928061	+	0.372428i	$0.121475\pi$
$504$	16.3538	−	10.3669i	0.728455	−	0.461776i
$505$	−0.186867	+	0.390799i	−0.00831546	+	0.0173903i
$506$	3.64250	−	3.22052i	0.161929	−	0.143169i
$507$	−2.41356	−	3.95860i	−0.107190	−	0.175808i
$508$	0.0235542	−	3.64375i	0.00104505	−	0.161665i
$509$	5.04815	+	5.63577i	0.223755	+	0.249801i	0.846204	−	0.532859i	$-0.178883\pi$
$509$	5.04815	+	5.63577i	0.223755	+	0.249801i	−0.622448	+	0.782661i	$0.713862\pi$
$510$	−0.229364	+	0.137818i	−0.0101564	+	0.00610267i
$511$	−3.37674	+	47.4087i	−0.149378	+	2.09724i
$512$	−3.08182	−	0.360214i	−0.136199	−	0.0159193i
$513$	26.6639	+	7.58928i	1.17724	+	0.335075i
$514$	2.97164	−	0.347335i	0.131073	−	0.0153203i
$515$	−0.0259014	−	0.572026i	−0.00114135	−	0.0252065i
$516$	−1.49892	−	15.7256i	−0.0659862	−	0.692282i
$517$	−10.3662	+	10.4334i	−0.455905	+	0.458861i
$518$	−28.2828	+	42.4023i	−1.24267	+	1.86305i
$519$	13.4261	−	27.0384i	0.589342	−	1.18685i
$520$	−0.0238967	−	0.283699i	−0.00104794	−	0.0124410i
$521$	−9.94614	−	25.7611i	−0.435748	−	1.12862i	−0.960726	−	0.277500i	$-0.910494\pi$
$521$	−9.94614	−	25.7611i	−0.435748	−	1.12862i	0.524978	−	0.851116i	$-0.324074\pi$
$522$	10.3356	+	0.307290i	0.452376	+	0.0134497i
$523$	7.18242	+	20.9914i	0.314065	+	0.917891i	0.984417	+	0.175848i	$0.0562666\pi$
$523$	7.18242	+	20.9914i	0.314065	+	0.917891i	−0.670352	+	0.742043i	$0.733857\pi$
$524$	−15.8983	+	1.02913i	−0.694520	+	0.0449577i
$525$	8.54663	+	27.4457i	0.373006	+	1.19783i
$526$	5.28332	+	27.8526i	0.230364	+	1.21443i
$527$	1.96773	−	12.0700i	0.0857158	−	0.525779i
$528$	−11.7293	+	10.0639i	−0.510454	+	0.437975i
$529$	16.4561	+	12.0866i	0.715482	+	0.525503i
$530$	−0.669169	+	0.369232i	−0.0290668	+	0.0160384i
$531$	−35.5338	−	15.7651i	−1.54204	−	0.684148i
$532$	−14.7420	+	2.89524i	−0.639149	+	0.125525i
$533$	−16.3613	−	16.4674i	−0.708686	−	0.713282i
$534$	−14.2606	+	17.1523i	−0.617115	+	0.742254i
$535$	0.110105	−	0.451543i	0.00476027	−	0.0195219i
$536$	11.8977	−	5.59486i	0.513901	−	0.241661i
$537$	23.0528	−	3.55976i	0.994802	−	0.153615i
$538$	−26.7985	+	35.0417i	−1.15537	+	1.51075i
$539$	2.06890	+	6.91061i	0.0891139	+	0.297661i
$540$	0.152031	−	0.0588141i	0.00654238	−	0.00253096i
$541$	−2.21599	+	7.40191i	−0.0952727	+	0.318233i	−0.992319	−	0.123703i	$-0.960523\pi$
$541$	−2.21599	+	7.40191i	−0.0952727	+	0.318233i	0.897047	+	0.441936i	$0.145708\pi$
$542$	17.8122	+	24.5831i	0.765098	+	1.05593i
$543$	−3.07225	+	4.85364i	−0.131843	+	0.208289i
$544$	−9.84433	−	5.26702i	−0.422072	−	0.225822i
$545$	0.0224693	−	0.0605140i	0.000962480	−	0.00259213i
$546$	10.1370	−	37.0651i	0.433825	−	1.58624i
$547$	26.7787	−	0.692563i	1.14497	−	0.0296118i	0.551292	−	0.834313i	$-0.314135\pi$
$547$	26.7787	−	0.692563i	1.14497	−	0.0296118i	0.593681	+	0.804701i	$0.297674\pi$
$548$	5.96563	+	1.66065i	0.254839	+	0.0709393i
$549$	−7.79722	+	4.13306i	−0.332777	+	0.176395i
$550$	−6.52447	−	13.6448i	−0.278204	−	0.581815i
$551$	10.0330	+	4.25109i	0.427419	+	0.181102i
$552$	4.31262	+	3.26726i	0.183557	+	0.139064i
$553$	−12.7916	−	8.17826i	−0.543956	−	0.347775i
$554$	3.23486	−	2.18803i	0.137436	−	0.0929607i
$555$	0.411555	−	0.412626i	0.0174695	−	0.0175150i
$556$	9.40734	+	1.59614i	0.398960	+	0.0676913i
$557$	7.94152	−	3.24447i	0.336493	−	0.137472i	−0.203655	−	0.979043i	$-0.565282\pi$
$557$	7.94152	−	3.24447i	0.336493	−	0.137472i	0.540148	+	0.841570i	$0.318368\pi$
$558$	−8.19078	+	23.6397i	−0.346743	+	1.00075i
$559$	31.5307	+	28.6126i	1.33361	+	1.21018i
$560$	0.407812	−	0.455283i	0.0172332	−	0.0192392i
$561$	−7.25996	+	2.52087i	−0.306516	+	0.106431i
$562$	−6.96555	+	13.6488i	−0.293824	+	0.575742i
$563$	0.0928289	+	0.619762i	0.00391227	+	0.0261199i	0.990838	−	0.135056i	$-0.0431215\pi$
$563$	0.0928289	+	0.619762i	0.00391227	+	0.0261199i	−0.986926	+	0.161176i	$0.948471\pi$
$564$	10.0554	+	6.64141i	0.423408	+	0.279654i
$565$	−0.695878	+	0.243138i	−0.0292758	+	0.0102289i
$566$	32.4206	−	27.2041i	1.36274	−	1.14348i
$567$	−29.8766	+	0.541578i	−1.25470	+	0.0227442i
$568$	−13.2502	−	11.1182i	−0.555965	−	0.466510i
$569$	−2.49748	−	0.945750i	−0.104700	−	0.0396479i	0.301235	−	0.953550i	$-0.402601\pi$
$569$	−2.49748	−	0.945750i	−0.104700	−	0.0396479i	−0.405935	+	0.913902i	$0.633054\pi$
$570$	0.576865	+	0.00111502i	0.0241622	+	4.67029e-5i
$571$	−3.54397	+	17.4480i	−0.148311	+	0.730178i	0.835289	+	0.549811i	$0.185300\pi$
$571$	−3.54397	+	17.4480i	−0.148311	+	0.730178i	−0.983599	+	0.180367i	$0.942272\pi$
$572$	−0.737581	+	5.97518i	−0.0308398	+	0.249835i
$573$	−18.7930	−	26.0427i	−0.785091	−	1.08795i
$574$	1.06160	−	32.8341i	0.0443102	−	1.37047i
$575$	−6.34872	+	4.92063i	−0.264760	+	0.205204i
$576$	−5.53271	−	4.32251i	−0.230530	−	0.180105i
$577$	5.69329	+	9.03302i	0.237015	+	0.376050i	0.943334	−	0.331843i	$-0.107671\pi$
$577$	5.69329	+	9.03302i	0.237015	+	0.376050i	−0.706320	+	0.707893i	$0.749646\pi$
$578$	11.8880	+	13.9830i	0.494477	+	0.581618i
$579$	−0.710252	−	4.80531i	−0.0295171	−	0.199702i
$580$	0.0621477	−	0.0155805i	0.00258054	−	0.000646946i
$581$	4.94076	+	1.10372i	0.204977	+	0.0457901i
$582$	−15.9249	−	9.37339i	−0.660107	−	0.388539i
$583$	−20.9871	+	6.43125i	−0.869199	+	0.266355i
$584$	26.8088	−	7.46273i	1.10935	−	0.308810i
$585$	−0.196167	+	0.393144i	−0.00811049	+	0.0162545i
$586$	−1.27868	+	13.1460i	−0.0528218	+	0.543055i
$587$	11.8469	+	9.42972i	0.488975	+	0.389206i	0.836069	−	0.548624i	$-0.184848\pi$
$587$	11.8469	+	9.42972i	0.488975	+	0.389206i	−0.347095	+	0.937830i	$0.612832\pi$
$588$	5.21686	−	2.77822i	0.215140	−	0.114572i
$589$	−17.0769	+	20.0863i	−0.703642	+	0.827644i
$590$	−0.800735	−	0.114648i	−0.0329657	−	0.00471999i
$591$	1.60563	−	16.1826i	0.0660468	−	0.665665i
$592$	43.9132	+	11.0091i	1.80482	+	0.452472i
$593$	25.1268	+	12.6192i	1.03184	+	0.518207i	0.882368	−	0.470560i	$-0.155948\pi$
$593$	25.1268	+	12.6192i	1.03184	+	0.518207i	0.149467	+	0.988767i	$0.452244\pi$
$594$	15.5155	−	2.54004i	0.636610	−	0.104219i
$595$	0.271607	−	0.136406i	0.0111348	−	0.00559211i
$596$	7.72384	−	1.72543i	0.316381	−	0.0706765i
$597$	−1.08978	−	5.07839i	−0.0446016	−	0.207845i
$598$	10.6935	−	0.970395i	0.437289	−	0.0396824i
$599$	3.06139	+	27.7461i	0.125085	+	1.13368i	0.879039	+	0.476750i	$0.158185\pi$
$599$	3.06139	+	27.7461i	0.125085	+	1.13368i	−0.753954	+	0.656927i	$0.771856\pi$
$600$	13.4545	−	10.1116i	0.549277	−	0.412803i
$601$	23.0784	+	2.09428i	0.941387	+	0.0854275i	0.550338	−	0.834942i	$-0.314499\pi$
$601$	23.0784	+	2.09428i	0.941387	+	0.0854275i	0.391049	+	0.920370i	$0.372112\pi$
$602$	1.16843	+	60.2437i	0.0476215	+	2.45535i
$603$	−20.1731	−	2.17277i	−0.821514	−	0.0884822i
$604$	4.46127	+	5.53111i	0.181526	+	0.225057i
$605$	−0.0682240	−	0.279788i	−0.00277370	−	0.0113750i
$606$	30.7576	+	15.0259i	1.24944	+	0.610384i
$607$	0.931207	−	1.66216i	0.0377965	−	0.0674650i	−0.852866	−	0.522129i	$-0.825138\pi$
$607$	0.931207	−	1.66216i	0.0377965	−	0.0674650i	0.890663	+	0.454664i	$0.150241\pi$
$608$	12.3031	+	20.6873i	0.498958	+	0.838982i
$609$	−11.6797	−	1.23515i	−0.473286	−	0.0500506i
$610$	−0.132751	+	0.126876i	−0.00537492	+	0.00513705i
$611$	−32.0904	+	5.01885i	−1.29824	+	0.203041i
$612$	3.19771	+	5.42447i	0.129260	+	0.219271i
$613$	−18.8067	+	11.3499i	−0.759595	+	0.458418i	−0.842876	−	0.538108i	$-0.819139\pi$
$613$	−18.8067	+	11.3499i	−0.759595	+	0.458418i	0.0832809	+	0.996526i	$0.473460\pi$
$614$	1.34213	−	1.90363i	0.0541639	−	0.0768244i
$615$	−0.0849672	+	0.365885i	−0.00342621	+	0.0147539i
$616$	9.32636	−	6.84997i	0.375770	−	0.275993i
$617$	−8.38641	+	18.1375i	−0.337624	+	0.730190i	−0.999817	−	0.0191439i	$-0.993906\pi$
$617$	−8.38641	+	18.1375i	−0.337624	+	0.730190i	0.662193	+	0.749334i	$0.269626\pi$
$618$	−45.2197	+	1.66720i	−1.81900	+	0.0670646i
$619$	−25.9769	−	28.2570i	−1.04410	−	1.13574i	−0.990546	−	0.137178i	$-0.956197\pi$
$619$	−25.9769	−	28.2570i	−1.04410	−	1.13574i	−0.0535521	−	0.998565i	$-0.517054\pi$
$620$	−0.00901377	+	0.154760i	−0.000362002	+	0.00621533i
$621$	−3.06285	−	7.76771i	−0.122908	−	0.311707i
$622$	−0.594241	−	10.2027i	−0.0238269	−	0.409092i
$623$	17.6237	−	18.2027i	0.706080	−	0.729278i
$624$	−34.0336	+	2.57913i	−1.36243	+	0.103248i
$625$	9.29756	+	23.1847i	0.371902	+	0.927387i
$626$	0.965381	+	2.70668i	0.0385844	+	0.108181i
$627$	16.2081	+	3.43408i	0.647289	+	0.137144i
$628$	−1.65063	+	11.0202i	−0.0658671	+	0.439755i
$629$	18.3147	+	13.0905i	0.730253	+	0.521954i
$630$	−0.595195	+	0.179876i	−0.0237132	+	0.00716644i
$631$	10.1188	+	9.92447i	0.402824	+	0.395087i	0.873186	−	0.487386i	$-0.162050\pi$
$631$	10.1188	+	9.92447i	0.402824	+	0.395087i	−0.470363	+	0.882473i	$0.655877\pi$
$632$	−1.99407	+	8.66282i	−0.0793200	+	0.344589i
$633$	24.5531	+	29.7653i	0.975897	+	1.18306i
$634$	10.7034	+	34.1393i	0.425088	+	1.35584i
$635$	0.0436066	−	0.152820i	0.00173048	−	0.00606447i
$636$	8.55628	+	15.8194i	0.339279	+	0.627279i
$637$	−5.35175	+	15.0049i	−0.212044	+	0.594516i
$638$	6.17486	−	0.239613i	0.244465	−	0.00948636i
$639$	8.54383	+	25.2890i	0.337989	+	1.00042i
$640$	−0.444199	−	0.181475i	−0.0175585	−	0.00717344i
$641$	−10.9890	−	6.82727i	−0.434041	−	0.269661i	0.293189	−	0.956054i	$-0.405283\pi$
$641$	−10.9890	−	6.82727i	−0.434041	−	0.269661i	−0.727230	+	0.686394i	$0.759193\pi$
$642$	−35.6087	−	9.00035i	−1.40536	−	0.355216i
$643$	−35.9504	+	15.2326i	−1.41775	+	0.600716i	−0.957853	−	0.287259i	$-0.907256\pi$
$643$	−35.9504	+	15.2326i	−1.41775	+	0.600716i	−0.459893	+	0.887975i	$0.652112\pi$
$644$	3.38992	+	2.99720i	0.133582	+	0.118106i
$645$	0.120947	−	0.678258i	0.00476230	−	0.0267064i
$646$	3.58544	+	21.9930i	0.141067	+	0.865304i
$647$	20.9429	−	7.62260i	0.823351	−	0.299675i	0.104224	−	0.994554i	$-0.466764\pi$
$647$	20.9429	−	7.62260i	0.823351	−	0.299675i	0.719127	+	0.694878i	$0.244542\pi$
$648$	6.17515	+	16.3696i	0.242583	+	0.643058i
$649$	−21.8310	−	7.94583i	−0.856941	−	0.311901i
$650$	6.22478	−	32.8158i	0.244156	−	1.28714i
$651$	11.3059	−	26.0713i	0.443113	−	1.02182i
$652$	−14.0607	+	11.1918i	−0.550658	+	0.438304i
$653$	5.54059	+	8.54384i	0.216820	+	0.334346i	0.930609	−	0.366014i	$-0.119278\pi$
$653$	5.54059	+	8.54384i	0.216820	+	0.334346i	−0.713789	+	0.700360i	$0.753023\pi$
$654$	−4.76701	−	1.81572i	−0.186405	−	0.0710003i
$655$	−0.680017	−	0.142705i	−0.0265705	−	0.00557596i
$656$	−27.7859	+	8.90918i	−1.08486	+	0.347845i
$657$	−41.3277	−	11.6767i	−1.61235	−	0.455550i
$658$	−36.3309	−	28.1586i	−1.41633	−	1.09774i
$659$	−19.2490	+	23.2435i	−0.749833	+	0.905439i	−0.997996	−	0.0632795i	$-0.979844\pi$
$659$	−19.2490	+	23.2435i	−0.749833	+	0.905439i	0.248163	+	0.968718i	$0.420173\pi$
$660$	0.0882382	−	0.0412858i	0.00343467	−	0.00160705i
$661$	−26.9583	−	13.1053i	−1.04856	−	0.509738i	−0.169041	−	0.985609i	$-0.554067\pi$
$661$	−26.9583	−	13.1053i	−1.04856	−	0.509738i	−0.879515	+	0.475871i	$0.842133\pi$
$662$	27.7369	−	14.3820i	1.07803	−	0.558973i
$663$	−16.2176	−	5.00398i	−0.629838	−	0.194339i
$664$	−0.363136	−	2.94178i	−0.0140924	−	0.114163i
$665$	−0.653262	−	0.0507756i	−0.0253324	−	0.00196899i
$666$	−32.3333	−	32.7956i	−1.25289	−	1.27080i
$667$	−0.818627	−	3.17811i	−0.0316974	−	0.123057i
$668$	2.56808	−	4.72617i	0.0993620	−	0.182861i
$669$	−6.06483	−	13.1834i	−0.234480	−	0.509700i
$670$	−0.416247	+	0.0706243i	−0.0160810	+	0.00272845i
$671$	−4.47979	+	2.78320i	−0.172940	+	0.107444i
$672$	−19.1785	−	17.4713i	−0.739827	−	0.673969i
$673$	9.79765	−	21.9295i	0.377672	−	0.845321i	−0.620461	−	0.784237i	$-0.713054\pi$
$673$	9.79765	−	21.9295i	0.377672	−	0.845321i	0.998133	−	0.0610842i	$-0.0194558\pi$
$674$	33.2793	+	35.2740i	1.28187	+	1.35871i
$675$	−25.8500	+	2.53174i	−0.994966	+	0.0974466i
$676$	−1.55794	+	1.65132i	−0.0599208	+	0.0635123i
$677$	−14.1122	−	33.9148i	−0.542377	−	1.30345i	−0.925147	−	0.379608i	$-0.876059\pi$
$677$	−14.1122	−	33.9148i	−0.542377	−	1.30345i	0.382771	−	0.923843i	$-0.374970\pi$
$678$	18.7514	+	55.1509i	0.720144	+	2.11806i
$679$	17.2320	+	11.9832i	0.661303	+	0.459871i
$680$	−0.128647	−	0.122954i	−0.00493339	−	0.00471506i
$681$	17.5839	−	3.18273i	0.673815	−	0.121962i
$682$	−3.91642	+	14.4296i	−0.149968	+	0.552537i
$683$	−12.3984	+	36.2356i	−0.474411	+	1.38652i	0.406680	+	0.913571i	$0.366687\pi$
$683$	−12.3984	+	36.2356i	−0.474411	+	1.38652i	−0.881091	+	0.472948i	$0.843190\pi$
$684$	0.140226	−	13.5742i	0.00536166	−	0.519021i
$685$	0.231228	+	0.139547i	0.00883478	+	0.00533182i
$686$	15.2709	−	6.70463i	0.583045	−	0.255984i
$687$	31.4517	−	11.8407i	1.19996	−	0.451752i
$688$	50.0515	−	18.9536i	1.90819	−	0.722597i
$689$	−45.7627	−	15.9893i	−1.74342	−	0.609145i
$690$	−0.105279	−	0.138215i	−0.00400789	−	0.00526174i
$691$	−7.02183	−	10.5273i	−0.267123	−	0.400478i	0.673899	−	0.738824i	$-0.264618\pi$
$691$	−7.02183	−	10.5273i	−0.267123	−	0.400478i	−0.941022	+	0.338346i	$0.890133\pi$
$692$	−14.5050	−	2.84869i	−0.551398	−	0.108291i
$693$	−17.7909	+	1.54514i	−0.675821	+	0.0586952i
$694$	2.25556	−	2.79646i	0.0856199	−	0.106152i
$695$	0.376590	+	0.177091i	0.0142849	+	0.00671743i
$696$	1.61615	+	6.68398i	0.0612602	+	0.253355i
$697$	−14.4793	−	0.937275i	−0.548443	−	0.0355018i
$698$	−11.7114	−	43.1491i	−0.443282	−	1.63322i
$699$	16.9406	+	1.34968i	0.640754	+	0.0510495i
$700$	11.8591	−	7.58202i	0.448230	−	0.286574i
$701$	−0.514053	+	1.19171i	−0.0194155	+	0.0450102i	−0.927648	−	0.373456i	$-0.878173\pi$
$701$	−0.514053	+	1.19171i	−0.0194155	+	0.0450102i	0.908233	+	0.418466i	$0.137432\pi$
$702$	30.9368	+	15.7623i	1.16763	+	0.594911i
$703$	−19.2225	−	44.5628i	−0.724990	−	1.68072i
$704$	−3.47555	−	2.35083i	−0.130990	−	0.0886003i
$705$	0.344809	+	0.396652i	0.0129862	+	0.0149388i
$706$	5.97831	−	18.2387i	0.224997	−	0.686424i
$707$	−33.5464	−	19.6583i	−1.26164	−	0.739325i
$708$	−2.85604	+	18.8197i	−0.107337	+	0.707287i
$709$	19.7475	+	6.61452i	0.741633	+	0.248413i	0.663134	−	0.748501i	$-0.269226\pi$
$709$	19.7475	+	6.61452i	0.741633	+	0.248413i	0.0784989	+	0.996914i	$0.474987\pi$
$710$	0.314161	+	0.458058i	0.0117903	+	0.0171906i
$711$	9.58043	−	9.81895i	0.359294	−	0.368240i
$712$	−13.5047	−	6.13866i	−0.506112	−	0.230056i
$713$	7.92996	+	0.410452i	0.296980	+	0.0153715i
$714$	−10.5988	−	21.5534i	−0.396651	−	0.806615i
$715$	−0.100875	+	0.242426i	−0.00377253	+	0.00906621i
$716$	−4.65919	−	10.4284i	−0.174122	−	0.389728i
$717$	−6.16028	+	1.28034i	−0.230060	+	0.0478153i
$718$	9.72858	+	5.53326i	0.363067	+	0.206499i
$719$	48.3854	+	15.5142i	1.80447	+	0.578580i	0.999884	−	0.0152543i	$-0.00485577\pi$
$719$	48.3854	+	15.5142i	1.80447	+	0.578580i	0.804587	+	0.593835i	$0.202387\pi$
$720$	0.328085	+	0.444269i	0.0122270	+	0.0165569i
$721$	51.3590	+	1.99296i	1.91271	+	0.0742218i
$722$	5.94564	−	14.8262i	0.221274	−	0.551775i
$723$	−10.8858	−	11.8873i	−0.404847	−	0.442095i
$724$	2.68931	+	0.824107i	0.0999475	+	0.0306277i
$725$	−10.2054	−	0.263938i	−0.379021	−	0.00980243i
$726$	−22.1546	+	5.20553i	−0.822234	+	0.193195i
$727$	−50.5230	−	0.653216i	−1.87379	−	0.0242265i	−0.932380	−	0.361479i	$-0.882272\pi$
$727$	−50.5230	−	0.653216i	−1.87379	−	0.0242265i	−0.941414	+	0.337252i	$0.890502\pi$
$728$	25.5550			0.947130
$729$	4.99655	−	26.5336i	0.185057	−	0.982728i
$730$	−0.893621			−0.0330744
$731$	26.6110	+	0.344056i	0.984244	+	0.0127254i
$732$	2.95932	+	3.14887i	0.109380	+	0.116385i
$733$	−32.8372	−	0.849253i	−1.21287	−	0.0313679i	−0.585882	−	0.810396i	$-0.699252\pi$
$733$	−32.8372	−	0.849253i	−1.21287	−	0.0313679i	−0.626989	+	0.779028i	$0.715713\pi$
$734$	−29.3285	−	8.98734i	−1.08253	−	0.331729i
$735$	0.251685	−	0.0557135i	0.00928354	−	0.00205503i
$736$	2.69826	−	6.72846i	0.0994592	−	0.248014i
$737$	−12.1165	−	0.470177i	−0.446319	−	0.0173192i
$738$	28.8565	+	6.95705i	1.06222	+	0.256093i
$739$	20.0558	+	6.43063i	0.737765	+	0.236555i	0.650368	−	0.759619i	$-0.274615\pi$
$739$	20.0558	+	6.43063i	0.737765	+	0.236555i	0.0873962	+	0.996174i	$0.472145\pi$
$740$	−0.248053	−	0.141083i	−0.00911860	−	0.00518632i
$741$	24.3595	+	27.3011i	0.894869	+	1.00293i
$742$	−27.9837	−	62.6345i	−1.02732	−	2.29938i
$743$	15.3846	−	36.9726i	0.564407	−	1.35639i	−0.344261	−	0.938874i	$-0.611870\pi$
$743$	15.3846	−	36.9726i	0.564407	−	1.35639i	0.908667	−	0.417521i	$-0.137101\pi$
$744$	−16.6014	−	1.10687i	−0.608636	−	0.0405797i
$745$	0.344704	+	0.0178418i	0.0126290	+	0.000653672i
$746$	−18.7650	−	8.52973i	−0.687035	−	0.312296i
$747$	−1.88209	+	4.16923i	−0.0688620	+	0.152544i
$748$	2.12846	+	3.10337i	0.0778241	+	0.113470i
$749$	39.5580	+	13.2501i	1.44542	+	0.484149i
$750$	−1.00675	+	0.393947i	−0.0367612	+	0.0143849i
$751$	4.15748	+	2.43629i	0.151708	+	0.0889014i	0.579484	−	0.814984i	$-0.303254\pi$
$751$	4.15748	+	2.43629i	0.151708	+	0.0889014i	−0.427776	+	0.903885i	$0.640703\pi$
$752$	−12.7168	+	38.7968i	−0.463735	+	1.41477i
$753$	−11.5605	+	2.24721i	−0.421289	+	0.0818931i
$754$	11.3039	+	7.64587i	0.411664	+	0.278446i
$755$	0.122753	+	0.284573i	0.00446743	+	0.0103567i
$756$	4.11512	+	14.0413i	0.149665	+	0.510676i
$757$	−16.0084	+	37.1117i	−0.581836	+	1.34885i	0.332197	+	0.943210i	$0.392210\pi$
$757$	−16.0084	+	37.1117i	−0.581836	+	1.34885i	−0.914034	+	0.405638i	$0.867049\pi$
$758$	−39.7082	+	25.3872i	−1.44227	+	0.922104i
$759$	−2.14391	−	4.50597i	−0.0778192	−	0.163557i
$760$	0.100490	+	0.370243i	0.00364516	+	0.0134301i
$761$	−22.5229	−	1.45795i	−0.816454	−	0.0528507i	−0.349283	−	0.937017i	$-0.613575\pi$
$761$	−22.5229	−	1.45795i	−0.816454	−	0.0528507i	−0.467172	+	0.884167i	$0.654727\pi$
$762$	−12.0472	−	3.54728i	−0.436423	−	0.128504i
$763$	5.24328	+	2.46564i	0.189819	+	0.0892623i
$764$	−9.87279	+	12.2403i	−0.357185	+	0.442840i
$765$	0.0709105	+	0.265314i	0.00256377	+	0.00959245i
$766$	−46.6732	−	9.16633i	−1.68637	−	0.331193i
$767$	−28.4696	−

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.k (of order \(243\), degree \(162\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68750 - 0.0218178i) q^{2} +(-0.499964 + 1.65832i) q^{3} +(0.847837 + 0.0219272i) q^{4} +(0.0353662 + 0.0108375i) q^{5} +(0.879869 - 2.78751i) q^{6} +(-1.23579 + 3.08161i) q^{7} +(1.94249 + 0.0753776i) q^{8} +(-2.50007 - 1.65820i) q^{9} +O(q^{10})\)	\(q+(-1.68750 - 0.0218178i) q^{2} +(-0.499964 + 1.65832i) q^{3} +(0.847837 + 0.0219272i) q^{4} +(0.0353662 + 0.0108375i) q^{5} +(0.879869 - 2.78751i) q^{6} +(-1.23579 + 3.08161i) q^{7} +(1.94249 + 0.0753776i) q^{8} +(-2.50007 - 1.65820i) q^{9} +(-0.0594438 - 0.0190599i) q^{10} +(-1.55843 - 0.886380i) q^{11} +(-0.460250 + 1.39502i) q^{12} +(-1.61511 - 3.61500i) q^{13} +(2.15263 - 5.17325i) q^{14} +(-0.0356539 + 0.0532302i) q^{15} +(-4.97028 - 0.257260i) q^{16} +(-2.25299 - 1.02411i) q^{17} +(4.18268 + 2.85276i) q^{18} +(3.01767 + 4.39988i) q^{19} +(0.0297471 + 0.00996393i) q^{20} +(-4.49246 - 3.59004i) q^{21} +(2.61051 + 1.52976i) q^{22} +(0.500513 - 1.52697i) q^{23} +(-1.09618 + 3.18360i) q^{24} +(-4.14044 - 2.80055i) q^{25} +(2.64661 + 6.13554i) q^{26} +(3.99978 - 3.31688i) q^{27} +(-1.11532 + 2.58561i) q^{28} +(1.72071 - 1.10013i) q^{29} +(0.0613272 - 0.0890478i) q^{30} +(1.29438 + 4.76898i) q^{31} +(4.50193 + 0.291419i) q^{32} +(2.24906 - 2.14123i) q^{33} +(3.77956 + 1.77733i) q^{34} +(-0.0771023 + 0.0955919i) q^{35} +(-2.08329 - 1.46071i) q^{36} +(-8.92589 - 1.75299i) q^{37} +(-4.99632 - 7.49062i) q^{38} +(6.80234 - 0.870996i) q^{39} +(0.0678816 + 0.0237176i) q^{40} +(5.48293 - 2.07628i) q^{41} +(7.50268 + 6.15620i) q^{42} +(-9.84639 + 4.32302i) q^{43} +(-1.30186 - 0.785677i) q^{44} +(-0.0704471 - 0.0857389i) q^{45} +(-0.877929 + 2.56584i) q^{46} +(2.14880 - 7.91697i) q^{47} +(2.91158 - 8.11371i) q^{48} +(-2.90870 - 2.77997i) q^{49} +(6.92587 + 4.81626i) q^{50} +(2.82471 - 3.22416i) q^{51} +(-1.29008 - 3.10035i) q^{52} +(8.40178 - 8.90536i) q^{53} +(-6.82199 + 5.50997i) q^{54} +(-0.0455096 - 0.0482374i) q^{55} +(-2.63281 + 5.89286i) q^{56} +(-8.80515 + 2.80450i) q^{57} +(-2.92769 + 1.81892i) q^{58} +(12.7754 - 2.16760i) q^{59} +(-0.0313959 + 0.0443487i) q^{60} +(1.40446 - 2.58470i) q^{61} +(-2.08021 - 8.07588i) q^{62} +(8.19952 - 5.65506i) q^{63} +(2.33331 + 0.181359i) q^{64} +(-0.0179424 - 0.145352i) q^{65} +(-3.84201 + 3.56425i) q^{66} +(6.00414 - 3.11323i) q^{67} +(-1.88771 - 0.917678i) q^{68} +(2.28198 + 1.59344i) q^{69} +(0.132196 - 0.159629i) q^{70} +(-7.03273 - 5.45078i) q^{71} +(-4.73138 - 3.40950i) q^{72} +(13.6316 - 4.37080i) q^{73} +(15.0242 + 3.15290i) q^{74} +(6.71429 - 5.46601i) q^{75} +(2.46202 + 3.79655i) q^{76} +(4.65738 - 3.70711i) q^{77} +(-11.4979 + 1.32139i) q^{78} +(-0.852216 + 4.49271i) q^{79} +(-0.172992 - 0.0629638i) q^{80} +(3.50072 + 8.29126i) q^{81} +(-9.29773 + 3.38410i) q^{82} +(-0.245341 - 1.50492i) q^{83} +(-3.73015 - 3.14228i) q^{84} +(-0.0685807 - 0.0606356i) q^{85} +(16.7101 - 7.08026i) q^{86} +(0.964072 + 3.40352i) q^{87} +(-2.96043 - 1.83926i) q^{88} +(-7.06426 - 2.88607i) q^{89} +(0.117009 + 0.146221i) q^{90} +(13.1360 - 0.509736i) q^{91} +(0.457835 - 1.28365i) q^{92} +(-8.55566 - 0.237820i) q^{93} +(-3.79882 + 13.3130i) q^{94} +(0.0590398 + 0.188311i) q^{95} +(-2.73407 + 7.31995i) q^{96} +(1.41808 - 6.16055i) q^{97} +(4.84777 + 4.75466i) q^{98} +(2.42640 + 4.80021i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Introduction

L-functions

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