LMFDB - Embedded newform 162.2.g.b.97.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			97.3
Character	$\chi$	$=$	162.97
Dual form			162.2.g.b.157.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.973045 + 0.230616i) q^{2} +(0.190350 + 1.72156i) q^{3} +(0.893633 + 0.448799i) q^{4} +(-1.06995 + 1.43719i) q^{5} +(-0.211800 + 1.71905i) q^{6} +(-0.983264 - 0.646703i) q^{7} +(0.766044 + 0.642788i) q^{8} +(-2.92753 + 0.655396i) q^{9} +O(q^{10})$	\(q+(0.973045 + 0.230616i) q^{2} +(0.190350 + 1.72156i) q^{3} +(0.893633 + 0.448799i) q^{4} +(-1.06995 + 1.43719i) q^{5} +(-0.211800 + 1.71905i) q^{6} +(-0.983264 - 0.646703i) q^{7} +(0.766044 + 0.642788i) q^{8} +(-2.92753 + 0.655396i) q^{9} +(-1.37255 + 1.15170i) q^{10} +(3.61528 - 0.422566i) q^{11} +(-0.602532 + 1.62387i) q^{12} +(1.84593 - 6.16584i) q^{13} +(-0.807620 - 0.856027i) q^{14} +(-2.67787 - 1.56841i) q^{15} +(0.597159 + 0.802123i) q^{16} +(0.461322 + 2.61629i) q^{17} +(-2.99977 - 0.0374058i) q^{18} +(-0.128292 + 0.727580i) q^{19} +(-1.60115 + 0.804128i) q^{20} +(0.926174 - 1.81585i) q^{21} +(3.61528 + 0.422566i) q^{22} +(3.51483 - 2.31174i) q^{23} +(-0.960781 + 1.44115i) q^{24} +(0.513291 + 1.71451i) q^{25} +(3.21811 - 5.57394i) q^{26} +(-1.68556 - 4.91517i) q^{27} +(-0.588437 - 1.01920i) q^{28} +(-1.71661 + 1.81950i) q^{29} +(-2.24399 - 2.14369i) q^{30} +(-0.374563 - 6.43100i) q^{31} +(0.396080 + 0.918216i) q^{32} +(1.41564 + 6.14349i) q^{33} +(-0.154470 + 2.65215i) q^{34} +(1.98148 - 0.721198i) q^{35} +(-2.91028 - 0.728191i) q^{36} +(-7.73114 - 2.81391i) q^{37} +(-0.292625 + 0.678382i) q^{38} +(10.9662 + 2.00421i) q^{39} +(-1.74344 + 0.413202i) q^{40} +(-9.76678 + 2.31477i) q^{41} +(1.31997 - 1.55331i) q^{42} +(2.11947 - 4.91348i) q^{43} +(3.42038 + 1.24492i) q^{44} +(2.19038 - 4.90866i) q^{45} +(3.95321 - 1.43885i) q^{46} +(-0.160028 + 2.74758i) q^{47} +(-1.26723 + 1.18073i) q^{48} +(-2.22397 - 5.15575i) q^{49} +(0.104062 + 1.78667i) q^{50} +(-4.41628 + 1.29220i) q^{51} +(4.41681 - 4.68154i) q^{52} +(4.71775 + 8.17138i) q^{53} +(-0.506608 - 5.17140i) q^{54} +(-3.26086 + 5.64797i) q^{55} +(-0.337531 - 1.12743i) q^{56} +(-1.27699 - 0.0823677i) q^{57} +(-2.08995 + 1.37458i) q^{58} +(-9.18819 - 1.07395i) q^{59} +(-1.68913 - 2.60341i) q^{60} +(-10.4142 + 5.23023i) q^{61} +(1.11862 - 6.34403i) q^{62} +(3.30239 + 1.24882i) q^{63} +(0.173648 + 0.984808i) q^{64} +(6.88643 + 9.25008i) q^{65} +(-0.0393048 + 6.30436i) q^{66} +(1.44376 + 1.53030i) q^{67} +(-0.761935 + 2.54504i) q^{68} +(4.64885 + 5.61095i) q^{69} +(2.09438 - 0.244798i) q^{70} +(8.87851 - 7.44995i) q^{71} +(-2.66390 - 1.37972i) q^{72} +(6.70365 + 5.62503i) q^{73} +(-6.87382 - 4.52098i) q^{74} +(-2.85393 + 1.21002i) q^{75} +(-0.441183 + 0.592612i) q^{76} +(-3.82805 - 1.92252i) q^{77} +(10.2084 + 4.47918i) q^{78} +(5.84449 + 1.38517i) q^{79} -1.79173 q^{80} +(8.14091 - 3.83739i) q^{81} -10.0373 q^{82} +(-0.953883 - 0.226074i) q^{83} +(1.64261 - 1.20703i) q^{84} +(-4.25369 - 2.13628i) q^{85} +(3.19546 - 4.29225i) q^{86} +(-3.45914 - 2.60891i) q^{87} +(3.04109 + 2.00015i) q^{88} +(-4.23002 - 3.54941i) q^{89} +(3.26335 - 4.27121i) q^{90} +(-5.80250 + 4.86888i) q^{91} +(4.17847 - 0.488394i) q^{92} +(11.0001 - 1.86897i) q^{93} +(-0.789350 + 2.63661i) q^{94} +(-0.908405 - 0.962853i) q^{95} +(-1.50537 + 0.856657i) q^{96} +(10.4945 + 14.0966i) q^{97} +(-0.975029 - 5.52966i) q^{98} +(-10.3069 + 3.60652i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{27}\right)$

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 $

$2$	0.973045	+	0.230616i	0.688047	+	0.163070i
$2$	0.973045	+	0.230616i	0.688047	+	0.163070i
$3$	0.190350	+	1.72156i	0.109898	+	0.993943i
$3$	0.190350	+	1.72156i	0.109898	+	0.993943i
$4$	0.893633	+	0.448799i	0.446816	+	0.224400i
$5$	−1.06995	+	1.43719i	−0.478495	+	0.642731i	−0.974180	−	0.225772i	$-0.927510\pi$
$5$	−1.06995	+	1.43719i	−0.478495	+	0.642731i	0.495685	+	0.868502i	$0.334917\pi$
$6$	−0.211800	+	1.71905i	−0.0864671	+	0.701800i
$7$	−0.983264	−	0.646703i	−0.371639	−	0.244431i	0.349926	−	0.936777i	$-0.386207\pi$
$7$	−0.983264	−	0.646703i	−0.371639	−	0.244431i	−0.721565	+	0.692347i	$0.756577\pi$
$8$	0.766044	+	0.642788i	0.270838	+	0.227260i
$9$	−2.92753	+	0.655396i	−0.975845	+	0.218465i
$10$	−1.37255	+	1.15170i	−0.434037	+	0.364200i
$11$	3.61528	−	0.422566i	1.09005	−	0.127408i	0.447971	−	0.894048i	$-0.352147\pi$
$11$	3.61528	−	0.422566i	1.09005	−	0.127408i	0.642077	+	0.766640i	$0.278073\pi$
$12$	−0.602532	+	1.62387i	−0.173936	+	0.468771i
$13$	1.84593	−	6.16584i	0.511969	−	1.71010i	−0.176030	−	0.984385i	$-0.556326\pi$
$13$	1.84593	−	6.16584i	0.511969	−	1.71010i	0.687999	−	0.725711i	$-0.258489\pi$
$14$	−0.807620	−	0.856027i	−0.215846	−	0.228783i
$15$	−2.67787	−	1.56841i	−0.691423	−	0.404962i
$16$	0.597159	+	0.802123i	0.149290	+	0.200531i
$17$	0.461322	+	2.61629i	0.111887	+	0.634543i	0.988245	+	0.152882i	$0.0488553\pi$
$17$	0.461322	+	2.61629i	0.111887	+	0.634543i	−0.876358	+	0.481661i	$0.840034\pi$
$18$	−2.99977	−	0.0374058i	−0.707052	−	0.00881663i
$19$	−0.128292	+	0.727580i	−0.0294322	+	0.166918i	−0.995981	−	0.0895643i	$-0.971453\pi$
$19$	−0.128292	+	0.727580i	−0.0294322	+	0.166918i	0.966549	+	0.256483i	$0.0825637\pi$
$20$	−1.60115	+	0.804128i	−0.358028	+	0.179808i
$21$	0.926174	−	1.81585i	0.202108	−	0.396250i
$22$	3.61528	+	0.422566i	0.770780	+	0.0900913i
$23$	3.51483	−	2.31174i	0.732893	−	0.482031i	−0.127387	−	0.991853i	$-0.540659\pi$
$23$	3.51483	−	2.31174i	0.732893	−	0.482031i	0.860280	+	0.509822i	$0.170289\pi$
$24$	−0.960781	+	1.44115i	−0.196119	+	0.294173i
$25$	0.513291	+	1.71451i	0.102658	+	0.342902i
$26$	3.21811	−	5.57394i	0.631124	−	1.09314i
$27$	−1.68556	−	4.91517i	−0.324386	−	0.945925i
$28$	−0.588437	−	1.01920i	−0.111204	−	0.192611i
$29$	−1.71661	+	1.81950i	−0.318767	+	0.337873i	−0.866867	−	0.498540i	$-0.833870\pi$
$29$	−1.71661	+	1.81950i	−0.318767	+	0.337873i	0.548100	+	0.836413i	$0.315351\pi$
$30$	−2.24399	−	2.14369i	−0.409694	−	0.391383i
$31$	−0.374563	−	6.43100i	−0.0672735	−	1.15504i	−0.847939	−	0.530093i	$-0.822157\pi$
$31$	−0.374563	−	6.43100i	−0.0672735	−	1.15504i	0.780666	−	0.624949i	$-0.214880\pi$
$32$	0.396080	+	0.918216i	0.0700177	+	0.162319i
$33$	1.41564	+	6.14349i	0.246431	+	1.06944i
$34$	−0.154470	+	2.65215i	−0.0264914	+	0.454840i
$35$	1.98148	−	0.721198i	0.334931	−	0.121905i
$36$	−2.91028	−	0.728191i	−0.485047	−	0.121365i
$37$	−7.73114	−	2.81391i	−1.27099	−	0.462603i	−0.383549	−	0.923521i	$-0.625298\pi$
$37$	−7.73114	−	2.81391i	−1.27099	−	0.462603i	−0.887443	+	0.460917i	$0.847520\pi$
$38$	−0.292625	+	0.678382i	−0.0474701	+	0.110048i
$39$	10.9662	+	2.00421i	1.75600	+	0.320931i
$40$	−1.74344	+	0.413202i	−0.275661	+	0.0653329i
$41$	−9.76678	+	2.31477i	−1.52532	+	0.361506i	−0.905878	−	0.423540i	$-0.860787\pi$
$41$	−9.76678	+	2.31477i	−1.52532	+	0.361506i	−0.619438	+	0.785046i	$0.712639\pi$
$42$	1.31997	−	1.55331i	0.203676	−	0.239681i
$43$	2.11947	−	4.91348i	0.323216	−	0.749299i	−0.676699	−	0.736260i	$-0.736590\pi$
$43$	2.11947	−	4.91348i	0.323216	−	0.749299i	0.999915	−	0.0130390i	$-0.00415056\pi$
$44$	3.42038	+	1.24492i	0.515642	+	0.187678i
$45$	2.19038	−	4.90866i	0.326523	−	0.731740i
$46$	3.95321	−	1.43885i	0.582869	−	0.212147i
$47$	−0.160028	+	2.74758i	−0.0233425	+	0.400775i	0.966318	+	0.257349i	$0.0828490\pi$
$47$	−0.160028	+	2.74758i	−0.0233425	+	0.400775i	−0.989661	+	0.143426i	$0.954188\pi$
$48$	−1.26723	+	1.18073i	−0.182909	+	0.170423i
$49$	−2.22397	−	5.15575i	−0.317711	−	0.736536i
$50$	0.104062	+	1.78667i	0.0147165	+	0.252673i
$51$	−4.41628	+	1.29220i	−0.618403	+	0.180945i
$52$	4.41681	−	4.68154i	0.612501	−	0.649213i
$53$	4.71775	+	8.17138i	0.648033	+	1.12243i	0.983592	+	0.180407i	$0.0577413\pi$
$53$	4.71775	+	8.17138i	0.648033	+	1.12243i	−0.335559	+	0.942019i	$0.608925\pi$
$54$	−0.506608	−	5.17140i	−0.0689406	−	0.703738i
$55$	−3.26086	+	5.64797i	−0.439694	+	0.761572i
$56$	−0.337531	−	1.12743i	−0.0451045	−	0.150660i
$57$	−1.27699	−	0.0823677i	−0.169142	−	0.0109099i
$58$	−2.08995	+	1.37458i	−0.274424	+	0.180491i
$59$	−9.18819	−	1.07395i	−1.19620	−	0.139816i	−0.505415	−	0.862876i	$-0.668661\pi$
$59$	−9.18819	−	1.07395i	−1.19620	−	0.139816i	−0.690785	+	0.723060i	$0.742735\pi$
$60$	−1.68913	−	2.60341i	−0.218066	−	0.336099i
$61$	−10.4142	+	5.23023i	−1.33341	+	0.669662i	−0.965549	−	0.260220i	$-0.916205\pi$
$61$	−10.4142	+	5.23023i	−1.33341	+	0.669662i	−0.367857	+	0.929882i	$0.619909\pi$
$62$	1.11862	−	6.34403i	0.142065	−	0.805693i
$63$	3.30239	+	1.24882i	0.416061	+	0.157336i
$64$	0.173648	+	0.984808i	0.0217060	+	0.123101i
$65$	6.88643	+	9.25008i	0.854156	+	1.14733i
$66$	−0.0393048	+	6.30436i	−0.00483808	+	0.776013i
$67$	1.44376	+	1.53030i	0.176383	+	0.186955i	0.809534	−	0.587073i	$-0.199720\pi$
$67$	1.44376	+	1.53030i	0.176383	+	0.186955i	−0.633150	+	0.774029i	$0.718239\pi$
$68$	−0.761935	+	2.54504i	−0.0923982	+	0.308631i
$69$	4.64885	+	5.61095i	0.559655	+	0.675479i
$70$	2.09438	−	0.244798i	0.250327	−	0.0292590i
$71$	8.87851	−	7.44995i	1.05369	−	0.884147i	0.0602090	−	0.998186i	$-0.480823\pi$
$71$	8.87851	−	7.44995i	1.05369	−	0.884147i	0.993476	+	0.114039i	$0.0363789\pi$
$72$	−2.66390	−	1.37972i	−0.313944	−	0.162602i
$73$	6.70365	+	5.62503i	0.784603	+	0.658360i	0.944403	−	0.328789i	$-0.106641\pi$
$73$	6.70365	+	5.62503i	0.784603	+	0.658360i	−0.159800	+	0.987149i	$0.551085\pi$
$74$	−6.87382	−	4.52098i	−0.799065	−	0.525553i
$75$	−2.85393	+	1.21002i	−0.329543	+	0.139721i
$76$	−0.441183	+	0.592612i	−0.0506072	+	0.0679773i
$77$	−3.82805	−	1.92252i	−0.436247	−	0.219091i
$78$	10.2084	+	4.47918i	1.15588	+	0.507167i
$79$	5.84449	+	1.38517i	0.657556	+	0.155844i	0.545831	−	0.837895i	$-0.316214\pi$
$79$	5.84449	+	1.38517i	0.657556	+	0.155844i	0.111726	+	0.993739i	$0.464362\pi$
$80$	−1.79173			−0.200322
$81$	8.14091	−	3.83739i	0.904546	−	0.426377i
$82$	−10.0373			−1.10844
$83$	−0.953883	−	0.226074i	−0.104702	−	0.0248149i	0.177931	−	0.984043i	$-0.443060\pi$
$83$	−0.953883	−	0.226074i	−0.104702	−	0.0248149i	−0.282633	+	0.959228i	$0.591208\pi$
$84$	1.64261	−	1.20703i	0.179223	−	0.131698i
$85$	−4.25369	−	2.13628i	−0.461377	−	0.231712i
$86$	3.19546	−	4.29225i	0.344576	−	0.462846i
$87$	−3.45914	−	2.60891i	−0.370859	−	0.279704i
$88$	3.04109	+	2.00015i	0.324181	+	0.213217i
$89$	−4.23002	−	3.54941i	−0.448381	−	0.376236i	0.390454	−	0.920623i	$-0.372318\pi$
$89$	−4.23002	−	3.54941i	−0.448381	−	0.376236i	−0.838835	+	0.544386i	$0.816763\pi$
$90$	3.26335	−	4.27121i	0.343988	−	0.450225i
$91$	−5.80250	+	4.86888i	−0.608268	+	0.510397i
$92$	4.17847	−	0.488394i	0.435636	−	0.0509186i
$93$	11.0001	−	1.86897i	1.14065	−	0.193803i
$94$	−0.789350	+	2.63661i	−0.0814152	+	0.271946i
$95$	−0.908405	−	0.962853i	−0.0932004	−	0.0987866i
$96$	−1.50537	+	0.856657i	−0.153641	+	0.0874322i
$97$	10.4945	+	14.0966i	1.06556	+	1.43129i	0.895065	+	0.445936i	$0.147129\pi$
$97$	10.4945	+	14.0966i	1.06556	+	1.43129i	0.170494	+	0.985359i	$0.445464\pi$
$98$	−0.975029	−	5.52966i	−0.0984928	−	0.558580i
$99$	−10.3069	+	3.60652i	−1.03588	+	0.362469i
$100$	−0.310778	+	1.76251i	−0.0310778	+	0.176251i
$101$	−7.07386	+	3.55263i	−0.703876	+	0.353500i	−0.764467	−	0.644663i	$-0.776998\pi$
$101$	−7.07386	+	3.55263i	−0.703876	+	0.353500i	0.0605912	+	0.998163i	$0.480701\pi$
$102$	−4.59524	+	0.238906i	−0.454997	+	0.0236553i
$103$	8.41247	+	0.983277i	0.828905	+	0.0968851i	0.519956	−	0.854193i	$-0.325948\pi$
$103$	8.41247	+	0.983277i	0.828905	+	0.0968851i	0.308950	+	0.951078i	$0.400023\pi$
$104$	5.37739	−	3.53676i	0.527296	−	0.346808i
$105$	1.61876	+	3.27395i	0.157975	+	0.319505i
$106$	2.70613	+	9.03911i	0.262843	+	0.877956i
$107$	−5.50285	+	9.53121i	−0.531980	+	0.921417i	0.467323	+	0.884087i	$0.345219\pi$
$107$	−5.50285	+	9.53121i	−0.531980	+	0.921417i	−0.999303	+	0.0373303i	$0.988115\pi$
$108$	0.699654	−	5.14883i	0.0673242	−	0.495447i
$109$	1.31433	+	2.27648i	0.125890	+	0.218047i	0.922080	−	0.386998i	$-0.126488\pi$
$109$	1.31433	+	2.27648i	0.125890	+	0.218047i	−0.796191	+	0.605046i	$0.793155\pi$
$110$	−4.47547	+	4.74372i	−0.426719	+	0.452296i
$111$	3.37269	−	13.8452i	0.320121	−	1.31413i
$112$	−0.0684291	−	1.17488i	−0.00646595	−	0.111016i
$113$	0.121350	+	0.281321i	0.0114156	+	0.0264644i	0.923829	−	0.382806i	$-0.125042\pi$
$113$	0.121350	+	0.281321i	0.0114156	+	0.0264644i	−0.912413	+	0.409271i	$0.865783\pi$
$114$	−1.22358	−	0.374642i	−0.114598	−	0.0350885i
$115$	−0.438277	+	7.52492i	−0.0408695	+	0.701702i
$116$	−2.35061	+	0.855553i	−0.218249	+	0.0794361i
$117$	−1.36296	+	19.2605i	−0.126005	+	1.78064i
$118$	−8.69285	−	3.16394i	−0.800242	−	0.291264i
$119$	1.23836	−	2.87084i	0.113520	−	0.263169i
$120$	−1.04321	−	2.92277i	−0.0952319	−	0.266812i
$121$	2.18820	−	0.518613i	0.198927	−	0.0471467i
$122$	−11.3397	+	2.68756i	−1.02665	+	0.243320i
$123$	−5.84412	−	16.3735i	−0.526946	−	1.47635i
$124$	2.55151	−	5.91506i	0.229132	−	0.531188i
$125$	−11.4317	−	4.16078i	−1.02248	−	0.372152i
$126$	2.92537	+	1.97674i	0.260613	+	0.176102i
$127$	5.43508	−	1.97821i	0.482285	−	0.175538i	−0.0894241	−	0.995994i	$-0.528503\pi$
$127$	5.43508	−	1.97821i	0.482285	−	0.175538i	0.571710	+	0.820456i	$0.306280\pi$
$128$	−0.0581448	+	0.998308i	−0.00513933	+	0.0882388i
$129$	8.86229	+	2.71351i	0.780281	+	0.238911i
$130$	4.56759	+	10.5889i	0.400604	+	0.928705i
$131$	−1.07690	−	18.4897i	−0.0940894	−	1.61545i	−0.633728	−	0.773556i	$-0.718476\pi$
$131$	−1.07690	−	18.4897i	−0.0940894	−	1.61545i	0.539639	−	0.841897i	$-0.318561\pi$
$132$	−1.49213	+	6.12536i	−0.129873	+	0.533144i
$133$	0.596673	−	0.632437i	0.0517381	−	0.0548392i
$134$	1.05193	+	1.82200i	0.0908731	+	0.157397i
$135$	8.86749	+	2.83651i	0.763192	+	0.244128i
$136$	−1.32832	+	2.30072i	−0.113903	+	0.197285i
$137$	−1.37081	−	4.57884i	−0.117117	−	0.391197i	0.879250	−	0.476360i	$-0.158044\pi$
$137$	−1.37081	−	4.57884i	−0.117117	−	0.391197i	−0.996367	+	0.0851632i	$0.972859\pi$
$138$	3.22956	+	6.53180i	0.274918	+	0.556024i
$139$	−16.2013	+	10.6558i	−1.37418	+	0.903812i	−0.999725	−	0.0234336i	$-0.992540\pi$
$139$	−16.2013	+	10.6558i	−1.37418	+	0.903812i	−0.374454	+	0.927246i	$0.622170\pi$
$140$	2.09438	+	0.244798i	0.177008	+	0.0206892i
$141$	−4.76058	+	0.247502i	−0.400913	+	0.0208435i
$142$	10.3573	−	5.20161i	0.869162	−	0.436510i
$143$	4.06809	−	23.0713i	0.340191	−	1.92932i
$144$	−2.27391	−	1.95687i	−0.189493	−	0.163072i
$145$	−0.778285	−	4.41387i	−0.0646330	−	0.366552i
$146$	5.22573	+	7.01938i	0.432485	+	0.580928i
$147$	8.45260	−	4.81010i	0.697159	−	0.396730i
$148$	−5.64592	−	5.98433i	−0.464092	−	0.491909i
$149$	5.34018	−	17.8374i	0.437484	−	1.46130i	−0.400851	−	0.916143i	$-0.631285\pi$
$149$	5.34018	−	17.8374i	0.437484	−	1.46130i	0.838335	−	0.545156i	$-0.183529\pi$
$150$	−3.05605	+	0.519240i	−0.249525	+	0.0423958i
$151$	−6.76364	+	0.790556i	−0.550417	+	0.0643345i	−0.386756	−	0.922182i	$-0.626404\pi$
$151$	−6.76364	+	0.790556i	−0.550417	+	0.0643345i	−0.163661	+	0.986517i	$0.552330\pi$
$152$	−0.565957	+	0.474894i	−0.0459052	+	0.0385190i
$153$	−3.06524	−	7.35692i	−0.247810	−	0.594772i
$154$	−3.28150	−	2.75351i	−0.264431	−	0.221884i
$155$	9.64333	+	6.34252i	0.774571	+	0.509443i
$156$	8.90029	+	6.71267i	0.712594	+	0.537443i
$157$	14.4791	−	19.4488i	1.15556	−	1.55218i	0.375085	−	0.926990i	$-0.377613\pi$
$157$	14.4791	−	19.4488i	1.15556	−	1.55218i	0.780471	−	0.625192i	$-0.214979\pi$
$158$	5.36751	+	2.69566i	0.427016	+	0.214456i
$159$	−13.1695	+	9.67731i	−1.04441	+	0.767460i
$160$	−1.74344	−	0.413202i	−0.137831	−	0.0326665i
$161$	−4.95102			−0.390195
$162$	8.80644	−	1.85653i	0.691899	−	0.145863i
$163$	12.0798			0.946163			0.473082	−	0.881019i	$-0.343142\pi$
$163$	12.0798			0.946163			0.473082	+	0.881019i	$0.343142\pi$
$164$	−9.76678	−	2.31477i	−0.762658	−	0.180753i
$165$	−10.3440	−	4.53867i	−0.805280	−	0.353335i
$166$	−0.876034	−	0.439961i	−0.0679935	−	0.0341476i
$167$	−11.4508	+	15.3811i	−0.886090	+	1.19023i	0.0947675	+	0.995499i	$0.469789\pi$
$167$	−11.4508	+	15.3811i	−0.886090	+	1.19023i	−0.980858	+	0.194726i	$0.937618\pi$
$168$	1.87669	−	0.795687i	0.144790	−	0.0613886i
$169$	−23.7488	−	15.6198i	−1.82683	−	1.20152i
$170$	−3.64637	−	3.05967i	−0.279664	−	0.234666i
$171$	−0.101274	−	2.21410i	−0.00774463	−	0.169316i
$172$	4.09919	−	3.43963i	0.312560	−	0.262269i
$173$	2.67346	−	0.312482i	0.203259	−	0.0237576i	−0.0138540	−	0.999904i	$-0.504410\pi$
$173$	2.67346	−	0.312482i	0.203259	−	0.0237576i	0.217113	+	0.976146i	$0.430336\pi$
$174$	−2.76424	−	3.33632i	−0.209557	−	0.252926i
$175$	0.604079	−	2.01776i	0.0456641	−	0.152529i
$176$	2.49785	+	2.64756i	0.188282	+	0.199567i
$177$	0.0998925	−	16.0224i	0.00750838	−	1.20432i
$178$	−3.29745	−	4.42924i	−0.247154	−	0.331986i
$179$	2.19379	+	12.4416i	0.163972	+	0.929931i	0.950118	+	0.311890i	$0.100962\pi$
$179$	2.19379	+	12.4416i	0.163972	+	0.929931i	−0.786146	+	0.618040i	$0.787927\pi$
$180$	4.16040	−	3.40350i	0.310098	−	0.253682i
$181$	1.55173	−	8.80030i	0.115339	−	0.654121i	−0.871243	−	0.490853i	$-0.836685\pi$
$181$	1.55173	−	8.80030i	0.115339	−	0.654121i	0.986582	−	0.163268i	$-0.0522036\pi$
$182$	−6.76894	+	3.39949i	−0.501747	+	0.251987i
$183$	−10.9865	−	16.9332i	−0.812145	−	1.25174i
$184$	4.17847	+	0.488394i	0.308041	+	0.0360049i
$185$	12.3160	−	8.10038i	0.905493	−	0.595552i
$186$	11.1346	+	0.718194i	0.816426	+	0.0526605i
$187$	2.77336	+	9.26367i	0.202808	+	0.677427i
$188$	−1.37612	+	2.38350i	−0.100364	+	0.173835i
$189$	−1.52131	+	5.92296i	−0.110659	+	0.430832i
$190$	−0.661869	−	1.14639i	−0.0480171	−	0.0831680i
$191$	16.0171	−	16.9771i	1.15895	−	1.22842i	0.189838	−	0.981815i	$-0.439204\pi$
$191$	16.0171	−	16.9771i	1.15895	−	1.22842i	0.969116	−	0.246605i	$-0.0793149\pi$
$192$	−1.66235	+	0.486403i	−0.119970	+	0.0351031i
$193$	0.783836	+	13.4579i	0.0564217	+	0.968724i	0.901144	+	0.433519i	$0.142728\pi$
$193$	0.783836	+	13.4579i	0.0564217	+	0.968724i	−0.844722	+	0.535205i	$0.820235\pi$
$194$	6.96076	+	16.1368i	0.499753	+	1.15856i
$195$	−14.6137	+	13.6161i	−1.04651	+	0.975072i
$196$	0.326481	−	5.60547i	0.0233201	−	0.400391i
$197$	−15.4354	+	5.61801i	−1.09972	+	0.400267i	−0.827214	−	0.561886i	$-0.810076\pi$
$197$	−15.4354	+	5.61801i	−1.09972	+	0.400267i	−0.272509	+	0.962153i	$0.587854\pi$
$198$	−10.8608	+	1.13237i	−0.771844	+	0.0804738i
$199$	−1.00917	−	0.367309i	−0.0715384	−	0.0260378i	0.306003	−	0.952031i	$-0.401008\pi$
$199$	−1.00917	−	0.367309i	−0.0715384	−	0.0260378i	−0.377541	+	0.925993i	$0.623230\pi$
$200$	−0.708863	+	1.64333i	−0.0501242	+	0.116201i
$201$	−2.35968	+	2.77681i	−0.166439	+	0.195861i
$202$	−7.70248	+	1.82552i	−0.541945	+	0.128443i
$203$	2.86456	−	0.678914i	0.201053	−	0.0476504i
$204$	−4.52647	−	0.827269i	−0.316916	−	0.0579204i
$205$	7.12319	−	16.5134i	0.497505	−	1.15335i
$206$	7.95895	+	2.89682i	0.554526	+	0.201831i
$207$	−8.77468	+	9.07131i	−0.609882	+	0.630499i
$208$	6.04808	−	2.20132i	0.419359	−	0.152634i
$209$	−0.156361	+	2.68462i	−0.0108157	+	0.185699i
$210$	0.820100	+	3.55901i	0.0565923	+	0.245595i
$211$	9.19140	+	21.3081i	0.632762	+	1.46691i	0.868800	+	0.495164i	$0.164892\pi$
$211$	9.19140	+	21.3081i	0.632762	+	1.46691i	−0.236037	+	0.971744i	$0.575849\pi$
$212$	0.548625	+	9.41954i	0.0376798	+	0.646936i
$213$	14.5156	+	13.8668i	0.994590	+	0.950137i
$214$	−7.55257	+	8.00525i	−0.516283	+	0.547228i
$215$	4.79388	+	8.30325i	0.326940	+	0.566277i
$216$	1.86820	−	4.84869i	0.127115	−	0.329912i
$217$	−3.79065	+	6.56560i	−0.257326	+	0.445702i
$218$	0.753907	+	2.51822i	0.0510610	+	0.170556i
$219$	−8.40779	+	12.6115i	−0.568146	+	0.852204i
$220$	−5.44881	+	3.58374i	−0.367359	+	0.241616i
$221$	16.9832	+	1.98505i	1.14241	+	0.133529i
$222$	6.47471	−	12.6943i	0.434554	−	0.851982i
$223$	0.407187	−	0.204497i	0.0272673	−	0.0136941i	−0.435113	−	0.900376i	$-0.643292\pi$
$223$	0.407187	−	0.204497i	0.0272673	−	0.0136941i	0.462381	+	0.886682i	$0.346995\pi$
$224$	0.204362	−	1.15899i	0.0136545	−	0.0774386i
$225$	−2.62636	−	4.68288i	−0.175091	−	0.312192i
$226$	0.0532019	+	0.301723i	0.00353893	+	0.0200703i
$227$	−3.04738	−	4.09334i	−0.202262	−	0.271685i	0.689406	−	0.724375i	$-0.257872\pi$
$227$	−3.04738	−	4.09334i	−0.202262	−	0.271685i	−0.891668	+	0.452691i	$0.850464\pi$
$228$	−1.10420	−	0.646720i	−0.0731272	−	0.0428301i
$229$	−12.2467	−	12.9808i	−0.809285	−	0.857792i	0.182827	−	0.983145i	$-0.441475\pi$
$229$	−12.2467	−	12.9808i	−0.809285	−	0.857792i	−0.992112	+	0.125353i	$0.959994\pi$
$230$	−2.16183	+	7.22101i	−0.142547	+	0.476139i
$231$	2.58106	−	6.95617i	0.169821	−	0.457682i
$232$	−2.48456	+	0.290403i	−0.163119	+	0.0190659i
$233$	−1.21666	+	1.02090i	−0.0797058	+	0.0668811i	−0.681770	−	0.731567i	$-0.738790\pi$
$233$	−1.21666	+	1.02090i	−0.0797058	+	0.0668811i	0.602064	+	0.798448i	$0.294345\pi$
$234$	−5.76800	+	18.4270i	−0.377066	+	1.20461i
$235$	−3.77757	−	3.16976i	−0.246421	−	0.206772i
$236$	−7.72888	−	5.08336i	−0.503107	−	0.330899i
$237$	−1.27216	+	10.3253i	−0.0826354	+	0.670700i
$238$	1.86704	−	2.50787i	0.121022	−	0.162561i
$239$	0.320055	+	0.160738i	0.0207026	+	0.0103972i	0.459120	−	0.888374i	$-0.348165\pi$
$239$	0.320055	+	0.160738i	0.0207026	+	0.0103972i	−0.438418	+	0.898771i	$0.644461\pi$
$240$	−0.341055	−	3.08457i	−0.0220150	−	0.199108i
$241$	9.12041	+	2.16158i	0.587497	+	0.139239i	0.513605	−	0.858027i	$-0.328310\pi$
$241$	9.12041	+	2.16158i	0.587497	+	0.139239i	0.0738924	+	0.997266i	$0.476458\pi$
$242$	2.24882			0.144560
$243$	8.15591	+	13.2846i	0.523202	+	0.852209i
$244$	−11.6538			−0.746060
$245$	9.78933	+	2.32011i	0.625417	+	0.148227i
$246$	−1.91060	−	17.2799i	−0.121816	−	1.10172i
$247$	4.24932	+	2.13409i	0.270378	+	0.135789i
$248$	3.84684	−	5.16720i	0.244274	−	0.328117i
$249$	0.207629	−	1.68520i	0.0131580	−	0.106795i
$250$	−10.1640	−	6.68495i	−0.642826	−	0.422793i
$251$	12.8852	+	10.8119i	0.813304	+	0.682443i	0.951394	−	0.307977i	$-0.0996518\pi$
$251$	12.8852	+	10.8119i	0.813304	+	0.682443i	−0.138090	+	0.990420i	$0.544096\pi$
$252$	2.39065	+	2.59809i	0.150597	+	0.163664i
$253$	11.7302	−	9.84284i	0.737474	−	0.618814i
$254$	5.74478	−	0.671469i	0.360460	−	0.0421317i
$255$	2.86805	−	7.72962i	0.179604	−	0.484048i
$256$	−0.286803	+	0.957990i	−0.0179252	+	0.0598743i
$257$	12.9520	+	13.7283i	0.807923	+	0.856348i	0.991957	−	0.126572i	$-0.0403974\pi$
$257$	12.9520	+	13.7283i	0.807923	+	0.856348i	−0.184035	+	0.982920i	$0.558916\pi$
$258$	7.99763	+	4.68415i	0.497910	+	0.291623i
$259$	5.78199	+	7.76656i	0.359276	+	0.482591i
$260$	2.00251	+	11.3568i	0.124190	+	0.704319i
$261$	3.83295	−	6.45172i	0.237253	−	0.399351i
$262$	3.21614	−	18.2397i	0.198694	−	1.12685i
$263$	0.0777083	−	0.0390266i	0.00479170	−	0.00240648i	−0.446402	−	0.894833i	$-0.647295\pi$
$263$	0.0777083	−	0.0390266i	0.00479170	−	0.00240648i	0.451193	+	0.892426i	$0.350998\pi$
$264$	−2.86451	+	5.61614i	−0.176299	+	0.345649i
$265$	−16.7916	−	1.96265i	−1.03150	−	0.120565i
$266$	0.726440	−	0.477787i	0.0445409	−	0.0292950i
$267$	5.30533	−	7.95786i	0.324681	−	0.487013i
$268$	0.603395	+	2.01548i	0.0368582	+	0.123115i
$269$	−13.9803	+	24.2145i	−0.852392	+	1.47639i	0.0266520	+	0.999645i	$0.491515\pi$
$269$	−13.9803	+	24.2145i	−0.852392	+	1.47639i	−0.879044	+	0.476741i	$0.841818\pi$
$270$	7.97432	+	4.80503i	0.485302	+	0.292425i
$271$	8.66520	+	15.0086i	0.526373	+	0.911705i	0.999528	+	0.0307258i	$0.00978186\pi$
$271$	8.66520	+	15.0086i	0.526373	+	0.911705i	−0.473155	+	0.880979i	$0.656885\pi$
$272$	−1.82310	+	1.93238i	−0.110542	+	0.117167i
$273$	−9.48657	−	9.06257i	−0.574153	−	0.548491i
$274$	−0.277911	−	4.77155i	−0.0167892	−	0.288260i
$275$	2.58019	+	5.98154i	0.155591	+	0.360701i
$276$	1.63617	+	7.10053i	0.0984858	+	0.427402i
$277$	−0.361549	+	6.20756i	−0.0217234	+	0.372976i	0.969873	+	0.243609i	$0.0783314\pi$
$277$	−0.361549	+	6.20756i	−0.0217234	+	0.372976i	−0.991597	+	0.129367i	$0.958706\pi$
$278$	−18.2220	+	6.63227i	−1.09288	+	0.397777i
$279$	5.31140	+	18.5815i	0.317985	+	1.11244i
$280$	1.98148	+	0.721198i	0.118416	+	0.0430998i
$281$	−7.21907	+	16.7357i	−0.430653	+	0.998367i	0.555346	+	0.831619i	$0.312586\pi$
$281$	−7.21907	+	16.7357i	−0.430653	+	0.998367i	−0.986000	+	0.166748i	$0.946673\pi$
$282$	−4.68934	−	0.857034i	−0.279246	−	0.0510357i
$283$	8.73861	−	2.07109i	0.519456	−	0.123113i	0.0374796	−	0.999297i	$-0.488067\pi$
$283$	8.73861	−	2.07109i	0.519456	−	0.123113i	0.481977	+	0.876184i	$0.339919\pi$
$284$	11.2777	−	2.67285i	0.669206	−	0.158605i
$285$	1.48469	−	1.74715i	0.0879457	−	0.103492i
$286$	9.27903	−	21.5112i	0.548681	−	1.27198i
$287$	11.1003	+	4.04018i	0.655230	+	0.238484i
$288$	−1.76133	−	2.42852i	−0.103788	−	0.143102i
$289$	9.34264	−	3.40044i	0.549567	−	0.200026i
$290$	0.260603	−	4.47438i	0.0153031	−	0.262745i
$291$	−22.2705	+	20.7503i	−1.30552	+	1.21640i
$292$	3.46609	+	8.03531i	0.202838	+	0.470231i
$293$	−0.0639623	−	1.09819i	−0.00373672	−	0.0641570i	0.995924	−	0.0901933i	$-0.0287485\pi$
$293$	−0.0639623	−	1.09819i	−0.00373672	−	0.0641570i	−0.999661	+	0.0260363i	$0.991711\pi$
$294$	9.33405	−	2.73114i	0.544373	−	0.159283i
$295$	11.3743	−	12.0561i	0.662240	−	0.701933i
$296$	−4.11366	−	7.12506i	−0.239101	−	0.414136i
$297$	−8.17075	−	17.0575i	−0.474115	−	0.989774i
$298$	9.30983	−	16.1251i	0.539304	−	0.934101i
$299$	−7.76568	−	25.9392i	−0.449101	−	1.50010i
$300$	−3.09342	−	0.199530i	−0.178599	−	0.0115198i
$301$	−5.26156	+	3.46058i	−0.303271	+	0.199465i
$302$	−6.76364	−	0.790556i	−0.389204	−	0.0454914i
$303$	−7.46257	−	11.5018i	−0.428713	−	0.660763i
$304$	−0.660220	+	0.331575i	−0.0378662	+	0.0190171i
$305$	3.62587	−	20.5633i	0.207616	−	1.17745i
$306$	−1.28599	−	7.86551i	−0.0735154	−	0.449641i
$307$	−4.44355	−	25.2006i	−0.253607	−	1.43828i	−0.799624	−	0.600502i	$-0.794968\pi$
$307$	−4.44355	−	25.2006i	−0.253607	−	1.43828i	0.546017	−	0.837774i	$-0.316143\pi$
$308$	−2.55805	−	3.43605i	−0.145758	−	0.195787i
$309$	−0.0914590	+	14.6697i	−0.00520292	+	0.834532i
$310$	7.92071	+	8.39546i	0.449866	+	0.476830i
$311$	−6.83294	+	22.8236i	−0.387460	+	1.29421i	0.512670	+	0.858586i	$0.328657\pi$
$311$	−6.83294	+	22.8236i	−0.387460	+	1.29421i	−0.900130	+	0.435622i	$0.856529\pi$
$312$	7.11234	+	8.58427i	0.402657	+	0.485989i
$313$	−24.6494	+	2.88110i	−1.39327	+	0.162849i	−0.779383	−	0.626548i	$-0.784467\pi$
$313$	−24.6494	+	2.88110i	−1.39327	+	0.162849i	−0.613883	+	0.789397i	$0.710393\pi$
$314$	18.5740	−	15.5854i	1.04819	−	0.879537i
$315$	−5.32817	+	3.40998i	−0.300208	+	0.192131i
$316$	4.60116	+	3.86083i	0.258836	+	0.217189i
$317$	−12.8790	−	8.47067i	−0.723359	−	0.475760i	0.133672	−	0.991026i	$-0.457323\pi$
$317$	−12.8790	−	8.47067i	−0.723359	−	0.475760i	−0.857031	+	0.515265i	$0.827693\pi$
$318$	−15.0463	+	6.37936i	−0.843752	+	0.357737i
$319$	−5.43718	+	7.30340i	−0.304424	+	0.408912i
$320$	−1.60115	−	0.804128i	−0.0895070	−	0.0449521i
$321$	−17.4560	−	7.65922i	−0.974300	−	0.427496i
$322$	−4.81756	−	1.14178i	−0.268472	−	0.0636291i
$323$	−1.96274			−0.109210
$324$	8.99720	+	0.224417i	0.499845	+	0.0124676i
$325$	11.5189			0.638954
$326$	11.7542	+	2.78579i	0.651004	+	0.154291i
$327$	−3.66892	+	2.69602i	−0.202892	+	0.149090i
$328$	−8.96970	−	4.50475i	−0.495269	−	0.248733i
$329$	1.93422	−	2.59810i	0.106637	−	0.143238i
$330$	−9.01850	−	6.80182i	−0.496452	−	0.374428i
$331$	−18.9769	−	12.4813i	−1.04306	−	0.686034i	−0.0922311	−	0.995738i	$-0.529400\pi$
$331$	−18.9769	−	12.4813i	−1.04306	−	0.686034i	−0.950833	+	0.309703i	$0.899770\pi$
$332$	−0.750959	−	0.630129i	−0.0412142	−	0.0345828i
$333$	24.4774	+	3.17084i	1.34135	+	0.173761i
$334$	−14.6893	+	12.3258i	−0.803761	+	0.674436i
$335$	−3.74407	+	0.437619i	−0.204560	+	0.0239097i
$336$	2.00961	−	0.341443i	0.109633	−	0.0186273i
$337$	3.49968	−	11.6897i	0.190639	−	0.636780i	−0.808213	−	0.588890i	$-0.799565\pi$
$337$	3.49968	−	11.6897i	0.190639	−	0.636780i	0.998853	−	0.0478901i	$-0.0152497\pi$
$338$	−19.5064	−	20.6756i	−1.06101	−	1.12461i
$339$	−0.461211	+	0.262460i	−0.0250496	+	0.0142549i
$340$	−2.84247	−	3.81811i	−0.154155	−	0.207066i
$341$	−4.07167	−	23.0916i	−0.220493	−	1.25048i
$342$	0.412062	−	2.17777i	0.0222818	−	0.117760i
$343$	−2.57802	+	14.6207i	−0.139200	+	0.789443i
$344$	4.78193	−	2.40158i	0.257824	−	0.129484i
$345$	−13.0380	+	0.677846i	−0.701944	+	0.0364940i
$346$	2.67346	+	0.312482i	0.143726	+	0.0167992i
$347$	2.40626	−	1.58262i	0.129175	−	0.0849597i	−0.483277	−	0.875467i	$-0.660554\pi$
$347$	2.40626	−	1.58262i	0.129175	−	0.0849597i	0.612452	+	0.790508i	$0.290183\pi$
$348$	−1.92032	−	3.88387i	−0.102940	−	0.208197i
$349$	1.42792	+	4.76957i	0.0764346	+	0.255309i	0.987664	−	0.156591i	$-0.0500504\pi$
$349$	1.42792	+	4.76957i	0.0764346	+	0.255309i	−0.911229	+	0.411900i	$0.864865\pi$
$350$	1.05312	−	1.82407i	0.0562919	−	0.0975004i
$351$	−33.4176	+	1.31982i	−1.78370	+	0.0704468i
$352$	1.81995	+	3.15224i	0.0970035	+	0.168015i
$353$	17.1705	−	18.1997i	0.913896	−	0.968673i	−0.0857222	−	0.996319i	$-0.527320\pi$
$353$	17.1705	−	18.1997i	0.913896	−	0.968673i	0.999618	+	0.0276463i	$0.00880123\pi$
$354$	3.79223	−	15.5675i	0.201555	−	0.827404i
$355$	1.20745	+	20.7312i	0.0640849	+	1.10030i
$356$	−2.18711	−	5.07029i	−0.115917	−	0.268725i
$357$	5.17804	+	1.58545i	0.274051	+	0.0839107i
$358$	−0.734576	+	12.6122i	−0.0388235	+	0.666575i
$359$	−12.8993	+	4.69497i	−0.680800	+	0.247791i	−0.659191	−	0.751976i	$-0.729101\pi$
$359$	−12.8993	+	4.69497i	−0.680800	+	0.247791i	−0.0216088	+	0.999767i	$0.506879\pi$
$360$	4.83316	−	2.35230i	0.254730	−	0.123977i
$361$	17.3412	+	6.31170i	0.912697	+	0.332195i
$362$	3.53939	−	8.20523i	0.186026	−	0.431257i
$363$	1.30935	+	3.66840i	0.0687229	+	0.192541i
$364$	−7.37045	+	1.74683i	−0.386317	+	0.0915588i
$365$	−15.2568	+	3.61593i	−0.798577	+	0.189266i
$366$	−6.78530	−	19.0104i	−0.354673	−	0.993689i
$367$	10.8698	−	25.1991i	0.567400	−	1.31538i	−0.357052	−	0.934084i	$-0.616218\pi$
$367$	10.8698	−	25.1991i	0.567400	−	1.31538i	0.924452	−	0.381297i	$-0.124523\pi$
$368$	3.95321	+	1.43885i	0.206075	+	0.0750053i
$369$	27.0755	−	13.1777i	1.40949	−	0.686003i
$370$	13.8521	−	5.04176i	0.720138	−	0.262109i
$371$	0.645663	−	11.0856i	0.0335212	−	0.575536i
$372$	10.6688	+	3.26664i	0.553152	+	0.169367i
$373$	−6.48302	−	15.0293i	−0.335678	−	0.778189i	−0.999540	−	0.0303339i	$-0.990343\pi$
$373$	−6.48302	−	15.0293i	−0.335678	−	0.778189i	0.663862	−	0.747855i	$-0.268916\pi$
$374$	0.562255	+	9.65355i	0.0290735	+	0.499173i
$375$	4.98702	−	20.4723i	0.257529	−	1.05718i
$376$	−1.88870	+	2.00190i	−0.0974022	+	0.103240i
$377$	8.05001	+	13.9430i	0.414597	+	0.718103i
$378$	−2.84623	+	5.41247i	−0.146394	+	0.278388i
$379$	−9.26188	+	16.0420i	−0.475751	+	0.824024i	−0.999614	−	0.0277779i	$-0.991157\pi$
$379$	−9.26188	+	16.0420i	−0.475751	+	0.824024i	0.523863	+	0.851802i	$0.324490\pi$
$380$	−0.379653	−	1.26813i	−0.0194758	−	0.0650536i
$381$	4.44017	+	8.98026i	0.227477	+	0.460073i
$382$	19.5005	−	12.8257i	0.997733	−	0.656219i
$383$	26.9481	+	3.14979i	1.37699	+	0.160947i	0.772169	−	0.635418i	$-0.219172\pi$
$383$	26.9481	+	3.14979i	1.37699	+	0.160947i	0.604817	+	0.796364i	$0.293246\pi$
$384$	−1.72971	+	0.0899278i	−0.0882691	+	0.00458911i
$385$	6.85884	−	3.44464i	0.349559	−	0.175555i
$386$	−2.34091	+	13.2759i	−0.119149	+	0.675728i
$387$	−2.98454	+	15.7735i	−0.151713	+	0.801811i
$388$	3.05172	+	17.3071i	0.154927	+	0.878637i
$389$	−3.51381	−	4.71987i	−0.178157	−	0.239307i	0.704070	−	0.710131i	$-0.251364\pi$
$389$	−3.51381	−	4.71987i	−0.178157	−	0.239307i	−0.882227	+	0.470824i	$0.843957\pi$
$390$	−17.3599	+	9.87896i	−0.879054	+	0.500241i
$391$	7.66964	+	8.12935i	0.387871	+	0.411119i
$392$	1.61039	−	5.37908i	0.0813370	−	0.271685i
$393$	31.6261	−	5.37346i	1.59533	−	0.271055i
$394$	−16.3149	+	1.90694i	−0.821933	+	0.0960702i
$395$	−8.24405	+	6.91758i	−0.414803	+	0.348061i
$396$	−10.8292	−	1.40283i	−0.544187	−	0.0704949i
$397$	17.9372	+	15.0511i	0.900243	+	0.755393i	0.970238	−	0.242154i	$-0.0778539\pi$
$397$	17.9372	+	15.0511i	0.900243	+	0.755393i	−0.0699952	+	0.997547i	$0.522298\pi$
$398$	−0.897263	−	0.590139i	−0.0449757	−	0.0295810i
$399$	1.20235	+	0.906824i	0.0601930	+	0.0453980i
$400$	−1.06873	+	1.43556i	−0.0534367	+	0.0717779i
$401$	3.31607	+	1.66539i	0.165597	+	0.0831657i	0.529667	−	0.848206i	$-0.322317\pi$
$401$	3.31607	+	1.66539i	0.165597	+	0.0831657i	−0.364070	+	0.931371i	$0.618613\pi$
$402$	−2.93645	+	2.15778i	−0.146457	+	0.107620i
$403$	−40.3439	−	9.56169i	−2.00968	−	0.476302i
$404$	−7.91585			−0.393828
$405$	−3.19529	+	15.8058i	−0.158775	+	0.785399i
$406$	2.94392			0.146104
$407$	−29.1393	−	6.90614i	−1.44438	−	0.342325i
$408$	−4.21368	−	1.84885i	−0.208608	−	0.0915315i
$409$	9.23834	+	4.63967i	0.456807	+	0.229417i	0.662296	−	0.749243i	$-0.269582\pi$
$409$	9.23834	+	4.63967i	0.456807	+	0.229417i	−0.205489	+	0.978659i	$0.565879\pi$
$410$	10.7394	−	14.4256i	0.530383	−	0.712428i
$411$	7.62181	−	3.23152i	0.375956	−	0.159399i
$412$	7.07636	+	4.65420i	0.348627	+	0.229296i
$413$	8.33989	+	6.99800i	0.410379	+	0.344349i
$414$	−10.6301	+	6.80321i	−0.522443	+	0.334359i
$415$	1.34552	−	1.12902i	0.0660488	−	0.0554215i
$416$	6.39271	−	0.747200i	0.313428	−	0.0366345i
$417$	−21.4285	−	25.8632i	−1.04936	−	1.26653i
$418$	−0.771262	+	2.57619i	−0.0377237	+	0.126006i
$419$	−9.51027	−	10.0803i	−0.464607	−	0.492455i	0.452127	−	0.891954i	$-0.350666\pi$
$419$	−9.51027	−	10.0803i	−0.464607	−	0.492455i	−0.916734	+	0.399499i	$0.869184\pi$
$420$	−0.0227698	+	3.65221i	−0.00111105	+	0.178209i
$421$	5.20311	+	6.98898i	0.253584	+	0.340622i	0.910626	−	0.413232i	$-0.135600\pi$
$421$	5.20311	+	6.98898i	0.253584	+	0.340622i	−0.657042	+	0.753854i	$0.728193\pi$
$422$	4.02967	+	22.8534i	0.196161	+	1.11249i
$423$	−1.33226	−	8.14851i	−0.0647769	−	0.396194i
$424$	−1.63846	+	9.29215i	−0.0795705	+	0.451267i
$425$	−4.24886	+	2.13386i	−0.206100	+	0.103507i
$426$	10.9264	+	16.8405i	0.529385	+	0.815926i
$427$	13.6223	+	1.59222i	0.659232	+	0.0770531i
$428$	−9.19513	+	6.04773i	−0.444463	+	0.292328i
$429$	40.4929	+	2.61185i	1.95502	+	0.126101i
$430$	2.74980	+	9.18498i	0.132607	+	0.442939i
$431$	10.7815	−	18.6742i	0.519328	−	0.899503i	−0.480420	−	0.877039i	$-0.659516\pi$
$431$	10.7815	−	18.6742i	0.519328	−	0.899503i	0.999748	−	0.0224638i	$-0.00715106\pi$
$432$	2.93603	−	4.28716i	0.141260	−	0.206266i
$433$	−3.07025	−	5.31783i	−0.147547	−	0.255558i	0.782773	−	0.622307i	$-0.213804\pi$
$433$	−3.07025	−	5.31783i	−0.147547	−	0.255558i	−0.930320	+	0.366748i	$0.880471\pi$
$434$	−5.20261	+	5.51444i	−0.249733	+	0.264702i
$435$	7.45060	−	2.18004i	0.357229	−	0.104525i
$436$	0.152843	+	2.62421i	0.00731984	+	0.125677i
$437$	1.23105	+	2.85390i	0.0588892	+	0.136521i
$438$	−11.0896	+	10.3325i	−0.529880	+	0.493708i
$439$	−0.719298	+	12.3499i	−0.0343302	+	0.589427i	0.936650	+	0.350267i	$0.113909\pi$
$439$	−0.719298	+	12.3499i	−0.0343302	+	0.589427i	−0.970980	+	0.239160i	$0.923128\pi$
$440$	−6.12840	+	2.23056i	−0.292160	+	0.106338i
$441$	9.88982	+	13.6361i	0.470944	+	0.649336i
$442$	16.0676	+	5.84813i	0.764258	+	0.278167i
$443$	6.40801	−	14.8554i	0.304454	−	0.705803i	−0.695465	−	0.718560i	$-0.744802\pi$
$443$	6.40801	−	14.8554i	0.304454	−	0.705803i	0.999919	+	0.0127572i	$0.00406086\pi$
$444$	9.22768	−	10.8589i	0.437926	−	0.515341i
$445$	9.62707	−	2.28166i	0.456367	−	0.108161i
$446$	0.443372	−	0.105081i	0.0209943	−	0.00497573i
$447$	31.7247	+	5.79808i	1.50053	+	0.274240i
$448$	0.466136	−	1.08062i	0.0220229	−	0.0510547i
$449$	−12.4608	−	4.53535i	−0.588060	−	0.214036i	0.0308157	−	0.999525i	$-0.490189\pi$
$449$	−12.4608	−	4.53535i	−0.588060	−	0.214036i	−0.618876	+	0.785489i	$0.712412\pi$
$450$	−1.47562	−	5.16234i	−0.0695614	−	0.243355i
$451$	−34.3315	+	12.4957i	−1.61661	+	0.588397i
$452$	−0.0178143	+	0.305859i	−0.000837912	+	0.0143864i
$453$	−2.64844	−	11.4935i	−0.124435	−	0.540013i
$454$	−2.02125	−	4.68578i	−0.0948618	−	0.219914i
$455$	−0.789124	−	13.5487i	−0.0369947	−	0.635175i
$456$	−0.925288	−	0.883933i	−0.0433306	−	0.0413939i
$457$	−1.21778	+	1.29077i	−0.0569654	+	0.0603798i	−0.755230	−	0.655460i	$-0.772475\pi$
$457$	−1.21778	+	1.29077i	−0.0569654	+	0.0603798i	0.698264	+	0.715840i	$0.253956\pi$
$458$	−8.92303	−	15.4551i	−0.416946	−	0.722171i
$459$	12.0819	−	6.67738i	0.563935	−	0.311673i
$460$	−3.76884	+	6.52782i	−0.175723	+	0.304361i
$461$	−0.0152579	−	0.0509649i	−0.000710630	−	0.00237367i	0.957633	−	0.287990i	$-0.0929869\pi$
$461$	−0.0152579	−	0.0509649i	−0.000710630	−	0.00237367i	−0.958344	+	0.285616i	$0.907802\pi$
$462$	4.11569	−	6.17343i	0.191479	−	0.287214i
$463$	−8.70742	+	5.72696i	−0.404668	+	0.266154i	−0.735486	−	0.677540i	$-0.763046\pi$
$463$	−8.70742	+	5.72696i	−0.404668	+	0.266154i	0.330817	+	0.943695i	$0.392676\pi$
$464$	−2.48456	−	0.290403i	−0.115343	−	0.0134816i
$465$	−9.08342	+	17.8089i	−0.421234	+	0.825866i
$466$	−1.41930	+	0.712797i	−0.0657476	+	0.0330197i
$467$	−5.23134	+	29.6684i	−0.242078	+	1.37289i	0.585105	+	0.810957i	$0.301053\pi$
$467$	−5.23134	+	29.6684i	−0.242078	+	1.37289i	−0.827183	+	0.561933i	$0.810058\pi$
$468$	−9.86209	+	16.6001i	−0.455875	+	0.767341i
$469$	−0.429950	−	2.43837i	−0.0198532	−	0.112593i
$470$	−2.94475	−	3.95548i	−0.135831	−	0.182453i
$471$	36.2383	+	21.2245i	1.66977	+	0.977975i
$472$	−6.34824	−	6.72874i	−0.292202	−	0.309716i
$473$	5.58621	−	18.6592i	0.256854	−	0.857952i
$474$	−3.61904	+	9.75360i	−0.166228	+	0.447998i
$475$	−1.31330	+	0.153502i	−0.0602581	+	0.00704317i
$476$	2.39507	−	2.00970i	0.109778	−	0.0921145i
$477$	−19.1669	−	20.8300i	−0.877591	−	0.953740i
$478$	0.274359	+	0.230215i	0.0125489	+	0.0105298i
$479$	2.50288	+	1.64617i	0.114359	+	0.0752154i	0.605400	−	0.795921i	$-0.293013\pi$
$479$	2.50288	+	1.64617i	0.114359	+	0.0752154i	−0.491041	+	0.871137i	$0.663383\pi$
$480$	0.379489	−	3.08008i	0.0173212	−	0.140586i
$481$	−31.6212	+	42.4747i	−1.44180	+	1.93668i
$482$	8.37608	+	4.20662i	0.381520	+	0.191606i
$483$	−0.942424	−	8.52347i	−0.0428818	−	0.387831i
$484$	2.18820	+	0.518613i	0.0994637	+	0.0235733i
$485$	−31.4881			−1.42980
$486$	4.87243	+	14.8074i	0.221018	+	0.671678i
$487$	5.17613			0.234553			0.117276	−	0.993099i	$-0.462584\pi$
$487$	5.17613			0.234553			0.117276	+	0.993099i	$0.462584\pi$
$488$	−11.3397	−	2.68756i	−0.513324	−	0.121660i
$489$	2.29939	+	20.7961i	0.103982	+	0.940432i
$490$	8.99040	+	4.51515i	0.406145	+	0.203974i
$491$	−23.8549	+	32.0427i	−1.07656	+	1.44607i	−0.190966	+	0.981597i	$0.561162\pi$
$491$	−23.8549	+	32.0427i	−1.07656	+	1.44607i	−0.885589	+	0.464469i	$0.846245\pi$
$492$	2.12591	−	17.2547i	0.0958435	−	0.777903i
$493$	−5.55225	−	3.65177i	−0.250061	−	0.164468i
$494$	3.64263	+	3.05653i	0.163890	+	0.137520i
$495$	5.84461	−	18.6718i	0.262696	−	0.839234i
$496$	4.93478	−	4.14077i	0.221578	−	0.185926i
$497$	−13.5478	+	1.58351i	−0.607703	+	0.0710303i
$498$	0.590666	−	1.59189i	0.0264684	−	0.0713344i
$499$	4.79308	−	16.0100i	0.214568	−	0.716706i	−0.781157	−	0.624335i	$-0.785370\pi$
$499$	4.79308	−	16.0100i	0.214568	−	0.716706i	0.995725	−	0.0923714i	$-0.0294447\pi$
$500$	−8.34835	−	8.84873i	−0.373349	−	0.395727i
$501$	−28.6591	−	16.7855i	−1.28040	−	0.749919i
$502$	10.0444	+	13.4920i	0.448305	+	0.602178i
$503$	−0.0162598	−	0.0922139i	−0.000724989	−	0.00411162i	0.984443	−	0.175704i	$-0.0562200\pi$
$503$	−0.0162598	−	0.0922139i	−0.000724989	−	0.00411162i	−0.985168	+	0.171592i	$0.945109\pi$
$504$	1.72705	+	3.07938i	0.0769289	+	0.137167i
$505$	2.46287	−	13.9676i	0.109596	−	0.621550i
$506$	13.6840	−	6.87234i	0.608326	−	0.305513i
$507$	22.3699	−	43.8581i	0.993480	−	1.94781i
$508$	5.74478	+	0.671469i	0.254884	+	0.0297916i
$509$	−24.4077	+	16.0532i	−1.08185	+	0.711545i	−0.959717	−	0.280968i	$-0.909344\pi$
$509$	−24.4077	+	16.0532i	−1.08185	+	0.711545i	−0.122135	+	0.992513i	$0.538974\pi$
$510$	4.57332	−	6.85985i	0.202510	−	0.303759i
$511$	−2.95374	−	9.86617i	−0.130666	−	0.436453i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	3.79242	−	0.595802i	0.167440	−	0.0263053i
$514$	9.43690	+	16.3452i	0.416244	+	0.720955i
$515$	−10.4141	+	11.0383i	−0.458898	+	0.486404i
$516$	6.70181	+	6.40227i	0.295031	+	0.281844i
$517$	0.582485	+	10.0009i	0.0256177	+	0.439839i
$518$	3.83505	+	8.89064i	0.168502	+	0.390632i
$519$	1.04685	+	4.54304i	0.0459516	+	0.199417i
$520$	−0.670526	+	11.5125i	−0.0294045	+	0.504856i
$521$	13.5587	−	4.93498i	0.594019	−	0.216205i	−0.0274771	−	0.999622i	$-0.508747\pi$
$521$	13.5587	−	4.93498i	0.594019	−	0.216205i	0.621496	+	0.783417i	$0.286525\pi$
$522$	5.21750	−	5.39387i	0.228364	−	0.236083i
$523$	−31.0775	−	11.3113i	−1.35893	−	0.494609i	−0.443204	−	0.896421i	$-0.646158\pi$
$523$	−31.0775	−	11.3113i	−1.35893	−	0.494609i	−0.915722	+	0.401812i	$0.868380\pi$
$524$	7.33581	−	17.0063i	0.320466	−	0.742924i
$525$	3.58869	+	0.655877i	0.156623	+	0.0286248i
$526$	0.0846138	−	0.0200538i	0.00368934	−	0.000874389i
$527$	16.6526	−	3.94673i	0.725397	−	0.171922i
$528$	−4.08247	+	4.80415i	−0.177667	+	0.209074i
$529$	−2.09994	+	4.86822i	−0.0913019	+	0.211662i
$530$	−15.8863	−	5.78215i	−0.690058	−	0.251161i
$531$	27.6026	−	2.87789i	1.19785	−	0.124890i
$532$	0.817044	−	0.297380i	0.0354233	−	0.0128930i
$533$	−3.75631	+	64.4933i	−0.162704	+	2.79352i
$534$	6.99754	−	6.51986i	0.302813	−	0.282142i
$535$	−7.81040	−	18.1065i	−0.337673	−	0.782814i
$536$	0.122329	+	2.10030i	0.00528380	+	0.0907194i
$537$	−21.0014	+	6.14500i	−0.906278	+	0.265177i
$538$	−19.1877	+	20.3378i	−0.827240	+	0.876823i
$539$	−10.2189	−	17.6997i	−0.440161	−	0.762381i
$540$	6.65126	+	6.51452i	0.286224	+	0.280340i
$541$	13.8125	−	23.9240i	0.593846	−	1.02857i	−0.399863	−	0.916575i	$-0.630942\pi$
$541$	13.8125	−	23.9240i	0.593846	−	1.02857i	0.993709	−	0.111996i	$-0.0357245\pi$
$542$	4.97041	+	16.6023i	0.213498	+	0.713131i
$543$	15.4456	+	0.996262i	0.662834	+	0.0427537i
$544$	−2.21960	+	1.45985i	−0.0951644	+	0.0625906i
$545$	−4.67800	−	0.546779i	−0.200383	−	0.0234215i
$546$	−7.14088	−	11.0060i	−0.305602	−	0.471015i
$547$	29.3813	−	14.7559i	1.25626	−	0.630915i	0.308899	−	0.951095i	$-0.400040\pi$
$547$	29.3813	−	14.7559i	1.25626	−	0.630915i	0.947357	+	0.320180i	$0.103743\pi$
$548$	0.829975	−	4.70702i	0.0354548	−	0.201074i
$549$	27.0602	−	22.1371i	1.15490	−	0.944789i
$550$	1.13120	+	6.41534i	0.0482344	+	0.273551i
$551$	−1.10361	−	1.48240i	−0.0470152	−	0.0631524i
$552$	−0.0454277	+	7.28646i	−0.00193353	+	0.310132i
$553$	−4.85088	−	5.14164i	−0.206281	−	0.218645i
$554$	−1.78336	+	5.95685i	−0.0757679	+	0.253082i
$555$	16.2896	+	19.6609i	0.691457	+	0.834558i
$556$	−19.2603	+	2.25121i	−0.816821	+	0.0954727i
$557$	11.2025	−	9.40005i	0.474667	−	0.398293i	−0.373827	−	0.927499i	$-0.621954\pi$
$557$	11.2025	−	9.40005i	0.474667	−	0.398293i	0.848494	+	0.529206i	$0.177510\pi$
$558$	0.883046	+	19.3055i	0.0373823	+	0.817268i
$559$	−26.3833	−	22.1382i	−1.11590	−	0.936348i
$560$	1.76175	+	1.15872i	0.0744473	+	0.0489648i
$561$	−15.4201	+	6.53784i	−0.651035	+	0.276028i
$562$	−10.8840	+	14.6197i	−0.459113	+	0.616696i
$563$	12.5877	+	6.32179i	0.530509	+	0.266432i	0.693827	−	0.720142i	$-0.255923\pi$
$563$	12.5877	+	6.32179i	0.530509	+	0.266432i	−0.163318	+	0.986573i	$0.552220\pi$
$564$	−4.36529	−	1.91537i	−0.183812	−	0.0806516i
$565$	−0.534149	−	0.126596i	−0.0224718	−	0.00532592i
$566$	8.98069			0.377486
$567$	−10.4863	−	1.49158i	−0.440384	−	0.0626406i
$568$	11.5901			0.486309
$569$	22.1272	+	5.24425i	0.927621	+	0.219850i	0.666542	−	0.745467i	$-0.267774\pi$
$569$	22.1272	+	5.24425i	0.927621	+	0.219850i	0.261079	+	0.965318i	$0.415922\pi$
$570$	1.84759	−	1.35766i	0.0773872	−	0.0568662i
$571$	11.3254	+	5.68783i	0.473953	+	0.238028i	0.669708	−	0.742625i	$-0.266419\pi$
$571$	11.3254	+	5.68783i	0.473953	+	0.238028i	−0.195755	+	0.980653i	$0.562716\pi$
$572$	13.9897	−	18.7915i	0.584940	−	0.785711i
$573$	32.2759	+	24.3428i	1.34835	+	1.01693i
$574$	9.86936	+	6.49118i	0.411939	+	0.270936i
$575$	5.76764	+	4.83962i	0.240527	+	0.201826i
$576$	−1.15380	−	2.76925i	−0.0480750	−	0.115385i
$577$	1.95448	−	1.64000i	0.0813660	−	0.0682742i	−0.601197	−	0.799100i	$-0.705309\pi$
$577$	1.95448	−	1.64000i	0.0813660	−	0.0682742i	0.682564	+	0.730826i	$0.260865\pi$
$578$	9.87500	−	1.15422i	0.410746	−	0.0480093i
$579$	−23.0194	+	3.91113i	−0.956656	+	0.162541i
$580$	1.28544	−	4.29367i	0.0533750	−	0.178285i
$581$	0.791716	+	0.839170i	0.0328459	+	0.0348146i
$582$	−26.4556	+	15.0550i	−1.09662	+	0.624050i
$583$	20.5089	+	27.5483i	0.849393	+	1.14093i
$584$	1.51960	+	8.61805i	0.0628813	+	0.356618i
$585$	−26.2227	−	22.5666i	−1.08418	−	0.933013i
$586$	0.191022	−	1.08334i	0.00789104	−	0.0447523i
$587$	−2.66520	+	1.33851i	−0.110005	+	0.0552464i	−0.502951	−	0.864315i	$-0.667752\pi$
$587$	−2.66520	+	1.33851i	−0.110005	+	0.0552464i	0.392946	+	0.919562i	$0.371456\pi$
$588$	9.71229	−	0.504942i	0.400528	−	0.0208234i
$589$	4.72712	+	0.552522i	0.194778	+	0.0227663i
$590$	13.8481	−	9.10802i	0.570116	−	0.374971i
$591$	−12.6099	−	25.5035i	−0.518700	−	1.04907i
$592$	−2.35962	−	7.88168i	−0.0969798	−	0.323935i
$593$	20.6292	−	35.7308i	0.847140	−	1.46729i	−0.0366105	−	0.999330i	$-0.511656\pi$
$593$	20.6292	−	35.7308i	0.847140	−	1.46729i	0.883750	−	0.467959i	$-0.155011\pi$
$594$	−4.01679	−	18.4820i	−0.164811	−	0.758325i
$595$	2.80096	+	4.85140i	0.114828	+	0.198888i
$596$	12.7776	−	13.5434i	0.523390	−	0.554761i
$597$	0.440248	−	1.80727i	0.0180182	−	0.0739666i
$598$	−1.57437	−	27.0309i	−0.0643808	−	1.10538i
$599$	−5.96114	−	13.8195i	−0.243565	−	0.564648i	0.751953	−	0.659217i	$-0.229112\pi$
$599$	−5.96114	−	13.8195i	−0.243565	−	0.564648i	−0.995518	+	0.0945686i	$0.969853\pi$
$600$	−2.96402	−	0.907543i	−0.121006	−	0.0370503i
$601$	−1.13397	+	19.4696i	−0.0462558	+	0.794181i	0.892808	+	0.450438i	$0.148732\pi$
$601$	−1.13397	+	19.4696i	−0.0462558	+	0.794181i	−0.939064	+	0.343743i	$0.888305\pi$
$602$	−5.91780	+	2.15390i	−0.241191	+	0.0877865i
$603$	−5.22960	−	3.53376i	−0.212966	−	0.143906i
$604$	−6.39901	−	2.32905i	−0.260372	−	0.0947676i
$605$	−1.59592	+	3.69975i	−0.0648832	+	0.150416i
$606$	−4.60891	−	12.9128i	−0.187224	−	0.524546i
$607$	−11.6570	+	2.76275i	−0.473141	+	0.112137i	−0.460267	−	0.887781i	$-0.652246\pi$
$607$	−11.6570	+	2.76275i	−0.473141	+	0.112137i	−0.0128744	+	0.999917i	$0.504098\pi$
$608$	−0.718890	+	0.170380i	−0.0291548	+	0.00690982i
$609$	1.71406	+	4.80228i	0.0694571	+	0.194598i
$610$	8.27036	−	19.1728i	0.334857	−	0.776286i
$611$	16.6457	+	6.05855i	0.673414	+	0.245103i
$612$	0.562581	−	7.95006i	0.0227410	−	0.321362i
$613$	−18.2405	+	6.63900i	−0.736727	+	0.268147i	−0.683010	−	0.730409i	$-0.739329\pi$
$613$	−18.2405	+	6.63900i	−0.736727	+	0.268147i	−0.0537175	+	0.998556i	$0.517107\pi$
$614$	1.48789	−	25.5461i	0.0600464	−	1.03096i
$615$	29.7847	+	9.11967i	1.20103	+	0.367741i
$616$	−1.69669	−	3.93336i	−0.0683614	−	0.158480i
$617$	0.236895	+	4.06733i	0.00953704	+	0.163745i	0.999714	+	0.0239233i	$0.00761576\pi$
$617$	0.236895	+	4.06733i	0.00953704	+	0.163745i	−0.990177	+	0.139821i	$0.955347\pi$
$618$	−3.47207	+	14.2532i	−0.139667	+	0.573348i
$619$	30.8347	−	32.6828i	1.23935	−	1.31363i	0.307163	−	0.951657i	$-0.400620\pi$
$619$	30.8347	−	32.6828i	1.23935	−	1.31363i	0.932187	−	0.361977i	$-0.117898\pi$
$620$	5.77108	+	9.99580i	0.231772	+	0.401441i
$621$	−17.2871	−	13.3794i	−0.693705	−	0.536897i
$622$	−11.9122	+	20.6326i	−0.477637	+	0.827292i
$623$	1.86381	+	6.22557i	0.0746721	+	0.249422i
$624$	4.94095	+	9.99310i	0.197796	+	0.400044i
$625$	10.7348	−	7.06036i	0.429390	−	0.282414i
$626$	−24.6494	−	2.88110i	−0.985188	−	0.115152i
$627$	−4.65149	+	0.241831i	−0.185763	+	0.00965780i
$628$	21.6676	−	10.8819i	0.864631	−	0.434234i
$629$	3.79544	−	21.5250i	0.151334	−	0.858258i
$630$	−5.97094	+	2.08931i	−0.237888	+	0.0832400i
$631$	−7.98428	−	45.2811i	−0.317849	−	1.80261i	−0.555780	−	0.831330i	$-0.687580\pi$
$631$	−7.98428	−	45.2811i	−0.317849	−	1.80261i	0.237931	−	0.971282i	$-0.423531\pi$
$632$	3.58677	+	4.81787i	0.142674	+	0.191644i
$633$	−34.9335	+	19.8795i	−1.38848	+	0.790140i
$634$	−10.5784	−	11.2125i	−0.420122	−	0.445304i
$635$	−2.97219	+	9.92782i	−0.117948	+	0.393973i
$636$	−16.1119	+	2.73750i	−0.638877	+	0.108549i
$637$	−35.8948	+	4.19551i	−1.42221	+	0.166232i
$638$	−6.97490	+	5.85263i	−0.276139	+	0.231708i
$639$	−21.1095	+	27.6289i	−0.835078	+	1.09298i
$640$	−1.37255	−	1.15170i	−0.0542546	−	0.0455251i
$641$	20.1660	+	13.2634i	0.796510	+	0.523873i	0.881318	−	0.472524i	$-0.156657\pi$
$641$	20.1660	+	13.2634i	0.796510	+	0.523873i	−0.0848075	+	0.996397i	$0.527028\pi$
$642$	−15.2191	−	11.4784i	−0.600652	−	0.453016i
$643$	13.9752	−	18.7719i	0.551127	−	0.740292i	−0.436050	−	0.899922i	$-0.643623\pi$
$643$	13.9752	−	18.7719i	0.551127	−	0.740292i	0.987177	+	0.159631i	$0.0510304\pi$
$644$	−4.42439	−	2.22201i	−0.174345	−	0.0875595i
$645$	−13.3820	+	9.83347i	−0.526916	+	0.387193i
$646$	−1.90984	−	0.452640i	−0.0751415	−	0.0178089i
$647$	11.2246			0.441285			0.220643	−	0.975355i	$-0.429185\pi$
$647$	11.2246			0.441285			0.220643	+	0.975355i	$0.429185\pi$
$648$	8.70293	+	2.29327i	0.341883	+	0.0900880i
$649$	−33.6717			−1.32173
$650$	11.2084	+	2.65644i	0.439630	+	0.104194i
$651$	−12.0246	−	5.27608i	−0.471282	−	0.206786i
$652$	10.7949	+	5.42141i	0.422761	+	0.212319i
$653$	−5.07586	+	6.81807i	−0.198634	+	0.266812i	−0.890269	−	0.455436i	$-0.849483\pi$
$653$	−5.07586	+	6.81807i	−0.198634	+	0.266812i	0.691635	+	0.722247i	$0.256891\pi$
$654$	−4.19177	+	1.77724i	−0.163911	+	0.0694955i
$655$	27.7254	+	18.2353i	1.08332	+	0.712512i
$656$	−7.68905	−	6.45188i	−0.300207	−	0.251904i
$657$	−23.3118	−	12.0739i	−0.909480	−	0.471049i
$658$	2.48124	−	2.08201i	0.0967289	−	0.0811652i
$659$	−35.8975	+	4.19582i	−1.39837	+	0.163446i	−0.781640	−	0.623730i	$-0.785617\pi$
$659$	−35.8975	+	4.19582i	−1.39837	+	0.163446i	−0.616729	+	0.787176i	$0.711543\pi$
$660$	−7.20680	−	8.69829i	−0.280524	−	0.338580i
$661$	−6.73818	+	22.5071i	−0.262085	+	0.875425i	0.721103	+	0.692828i	$0.243635\pi$
$661$	−6.73818	+	22.5071i	−0.262085	+	0.875425i	−0.983188	+	0.182597i	$0.941550\pi$
$662$	−15.5870	−	16.5212i	−0.605805	−	0.642116i
$663$	−0.184638	+	29.6154i	−0.00717076	+	1.15017i
$664$	−0.585399	−	0.786327i	−0.0227179	−	0.0305154i
$665$	0.270522	+	1.53421i	0.0104904	+	0.0594940i
$666$	23.0864	+	8.73025i	0.894579	+	0.338290i
$667$	−1.82738	+	10.3636i	−0.0707566	+	0.401281i
$668$	−17.1358	+	8.60594i	−0.663006	+	0.332974i
$669$	0.429562	+	0.662071i	0.0166078	+	0.0255972i
$670$	−3.74407	−	0.437619i	−0.144646	−	0.0169067i
$671$	−35.4403	+	23.3094i	−1.36816	+	0.899851i
$672$	2.03418	+	0.131207i	0.0784701	+	0.00506143i
$673$	12.6137	+	42.1326i	0.486221	+	1.62409i	0.751368	+	0.659884i	$0.229394\pi$
$673$	12.6137	+	42.1326i	0.486221	+	1.62409i	−0.265147	+	0.964208i	$0.585420\pi$
$674$	6.10118	−	10.5676i	0.235009	−	0.407047i
$675$	7.56193	−	5.41282i	0.291059	−	0.208340i
$676$	−14.2125	−	24.6168i	−0.546635	−	0.946800i
$677$	−17.6888	+	18.7490i	−0.679836	+	0.720584i	−0.971790	−	0.235848i	$-0.924213\pi$
$677$	−17.6888	+	18.7490i	−0.679836	+	0.720584i	0.291954	+	0.956432i	$0.405695\pi$
$678$	−0.509307	+	0.149023i	−0.0195598	+	0.00572319i
$679$	−1.20258	−	20.6475i	−0.0461509	−	0.792380i
$680$	−1.88534	−	4.37071i	−0.0722995	−	0.167609i
$681$	6.46686	−	6.02541i	0.247811	−	0.230894i
$682$	1.36337	−	23.4082i	0.0522061	−	0.896345i
$683$	8.21143	−	2.98872i	0.314202	−	0.114360i	−0.180106	−	0.983647i	$-0.557644\pi$
$683$	8.21143	−	2.98872i	0.314202	−	0.114360i	0.494307	+	0.869287i	$0.335422\pi$
$684$	0.903183	−	2.02404i	0.0345341	−	0.0773912i
$685$	8.04736	+	2.92900i	0.307474	+	0.111911i
$686$	−5.88029	+	13.6320i	−0.224511	+	0.520474i
$687$	20.0160	−	23.5543i	0.763657	−	0.898653i
$688$	5.20688	−	1.23405i	0.198510	−	0.0470478i
$689$	59.0921	−	14.0051i	2.25123	−	0.533551i
$690$	−12.8429	−	2.34720i	−0.488921	−	0.0893564i
$691$	14.5352	−	33.6963i	0.552943	−	1.28187i	−0.381043	−	0.924557i	$-0.624435\pi$
$691$	14.5352	−	33.6963i	0.552943	−	1.28187i	0.933986	−	0.357309i	$-0.116306\pi$
$692$	2.52933	+	0.920601i	0.0961507	+	0.0349960i
$693$	12.4668	+	3.11935i	0.473573	+	0.118494i
$694$	2.70638	−	0.985041i	0.102733	−	0.0373917i
$695$	2.02020	−	34.6855i	0.0766306	−	1.31570i
$696$	−0.972880	−	4.22203i	−0.0368769	−	0.160036i
$697$	−10.5617	−	24.4849i	−0.400054	−	0.927430i
$698$	0.289488	+	4.97031i	0.0109573	+	0.188129i
$699$	−1.98912	−	1.90022i	−0.0752355	−	0.0718729i
$700$	1.44540	−	1.53203i	0.0546308	−	0.0579053i
$701$	4.33269	+	7.50444i	0.163643	+	0.283439i	0.936173	−	0.351540i	$-0.114342\pi$
$701$	4.33269	+	7.50444i	0.163643	+	0.283439i	−0.772529	+	0.634979i	$0.781009\pi$
$702$	−32.8212	−	6.42238i	−1.23876	−	0.242397i
$703$	3.03919	−	5.26402i	0.114625	−	0.198536i
$704$	1.04393	+	3.48698i	0.0393447	+	0.131420i
$705$	4.73787	−	7.10667i	0.178438	−	0.267653i
$706$	20.9048	−	13.7493i	0.786764	−	0.517463i
$707$	9.25297	+	1.08152i	0.347994	+	0.0406746i
$708$	7.28012	−	14.2733i	0.273604	−	0.536425i
$709$	13.8097	−	6.93551i	0.518636	−	0.260469i	−0.170170	−	0.985415i	$-0.554432\pi$
$709$	13.8097	−	6.93551i	0.518636	−	0.260469i	0.688806	+	0.724946i	$0.258135\pi$
$710$	−3.60603	+	20.4508i	−0.135332	+	0.767505i
$711$	−18.0178	−	0.224674i	−0.675719	−	0.00842592i
$712$	−0.958867	−	5.43801i	−0.0359351	−	0.203798i
$713$	−16.1833	−	21.7380i	−0.606071	−	0.814094i
$714$	4.67284	+	2.73685i	0.174877	+	0.102424i
$715$	28.8051	+	30.5317i	1.07725	+	1.14182i
$716$	−3.62334	+	12.1028i	−0.135411	+	0.452303i
$717$	−0.215797	+	0.581590i	−0.00805908	+	0.0217199i
$718$	−13.6343	+	1.59363i	−0.508829	+	0.0594736i
$719$	11.5092	−	9.65734i	0.429220	−	0.360158i	−0.402438	−	0.915447i	$-0.631837\pi$
$719$	11.5092	−	9.65734i	0.429220	−	0.360158i	0.831657	+	0.555289i	$0.187393\pi$
$720$	5.24536	−	1.17429i	0.195483	−	0.0437634i
$721$	−7.63579	−	6.40719i	−0.284372	−	0.238616i
$722$	15.4182	+	10.1407i	0.573807	+	0.377399i
$723$	−1.98522	+	16.1128i	−0.0738310	+	0.599241i
$724$	5.33624	−	7.16782i	0.198320	−	0.266390i
$725$	−4.00068	−	2.00922i	−0.148582	−	0.0746205i
$726$	0.428062	+	3.87147i	0.0158869	+	0.143684i
$727$	16.5338	+	3.91859i	0.613205	+	0.145332i	0.525471	−	0.850812i	$-0.323889\pi$
$727$	16.5338	+	3.91859i	0.613205	+	0.145332i	0.0877345	+	0.996144i	$0.472037\pi$
$728$	−7.57463			−0.280734
$729$	−21.3178	+	16.5696i	−0.789548	+	0.613689i
$730$	−15.6794			−0.580322
$731$	13.8328	+	3.27844i	0.511626	+	0.121258i
$732$	−2.21830	−	20.0628i	−0.0819908	−	0.741541i
$733$	−25.3695	−	12.7410i	−0.937043	−	0.470600i	−0.0863505	−	0.996265i	$-0.527521\pi$
$733$	−25.3695	−	12.7410i	−0.937043	−	0.470600i	−0.850692	+	0.525664i	$0.823817\pi$
$734$	16.3881	−	22.0131i	0.604897	−	0.812518i
$735$	−2.13082	+	17.2946i	−0.0785965	+	0.637919i
$736$	3.51483	+	2.31174i	0.129558	+	0.0852119i
$737$	5.86625	+	4.92236i	0.216086	+	0.181318i
$738$	29.3847	−	6.57844i	1.08166	−	0.242156i
$739$	1.59783	−	1.34074i	0.0587771	−	0.0493198i	−0.612926	−	0.790140i	$-0.710008\pi$
$739$	1.59783	−	1.34074i	0.0587771	−	0.0493198i	0.671703	+	0.740821i	$0.265563\pi$
$740$	14.6415	−	1.71134i	0.538231	−	0.0629101i
$741$	−2.86511	+	7.72169i	−0.105252	+	0.283663i
$742$	3.18478	−	10.6379i	0.116917	−	0.390529i
$743$	17.6295	+	18.6862i	0.646764	+	0.685529i	0.964931	−	0.262505i	$-0.0845487\pi$
$743$	17.6295	+	18.6862i	0.646764	+	0.685529i	−0.318167	+	0.948035i	$0.603067\pi$
$744$	9.62788	+	5.63898i	0.352975	+	0.206735i
$745$	19.9221	+	26.7600i	0.729888	+	0.980409i
$746$	−2.84227	−	16.1193i	−0.104063	−	0.590169i
$747$	2.94069	+	0.0366691i	0.107594	+	0.00134165i
$748$	−1.67916	+	9.52300i	−0.0613963	+	0.348195i
$749$	11.5746	−	5.81299i	0.422927	−	0.212402i
$750$	9.57383	−	18.7704i	0.349587	−	0.685397i
$751$	−49.3806	−	5.77176i	−1.80192	−	0.210614i	−0.852094	−	0.523388i	$-0.824668\pi$
$751$	−49.3806	−	5.77176i	−1.80192	−	0.210614i	−0.949828	+	0.312774i	$0.898742\pi$
$752$	−2.29946	+	1.51238i	−0.0838526	+	0.0551507i
$753$	−16.1607	+	24.2406i	−0.588929	+	0.883377i
$754$	4.61754	+	15.4237i	0.168161	+	0.561697i
$755$	6.10056	−	10.5665i	0.222022	−	0.384554i
$756$	−4.01771	+	4.61019i	−0.146123	+	0.167671i
$757$	−3.58950	−	6.21720i	−0.130463	−	0.225968i	0.793392	−	0.608711i	$-0.208313\pi$
$757$	−3.58950	−	6.21720i	−0.130463	−	0.225968i	−0.923855	+	0.382743i	$0.874980\pi$
$758$	−12.7118	+	13.4737i	−0.461712	+	0.489387i
$759$	19.1779	+	18.3207i	0.696113	+	0.665000i
$760$	−0.0769686	−	1.32150i	−0.00279194	−	0.0479358i
$761$	−12.0807	−	28.0062i	−0.437924	−	1.01522i	−0.984110	−	0.177559i	$-0.943180\pi$
$761$	−12.0807	−	28.0062i	−0.437924	−	1.01522i	0.546186	−	0.837664i	$-0.316079\pi$
$762$	2.24949	+	9.76217i	0.0814904	+	0.353646i
$763$	0.179877	−	3.08836i	0.00651197	−	0.111806i
$764$	21.9327	−	7.98284i	0.793497	−	0.288809i
$765$	13.8529	+	3.46619i	0.500854	+	0.125320i
$766$	25.4954	+	9.27955i	0.921185	+	0.335284i
$767$	−23.5825	+	54.6705i	−0.851516	+	1.97404i
$768$	−1.70383	−	0.311396i	−0.0614816	−	0.0112365i

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.973045 + 0.230616i) q^{2} +(0.190350 + 1.72156i) q^{3} +(0.893633 + 0.448799i) q^{4} +(-1.06995 + 1.43719i) q^{5} +(-0.211800 + 1.71905i) q^{6} +(-0.983264 - 0.646703i) q^{7} +(0.766044 + 0.642788i) q^{8} +(-2.92753 + 0.655396i) q^{9} +O(q^{10})\)	\(q+(0.973045 + 0.230616i) q^{2} +(0.190350 + 1.72156i) q^{3} +(0.893633 + 0.448799i) q^{4} +(-1.06995 + 1.43719i) q^{5} +(-0.211800 + 1.71905i) q^{6} +(-0.983264 - 0.646703i) q^{7} +(0.766044 + 0.642788i) q^{8} +(-2.92753 + 0.655396i) q^{9} +(-1.37255 + 1.15170i) q^{10} +(3.61528 - 0.422566i) q^{11} +(-0.602532 + 1.62387i) q^{12} +(1.84593 - 6.16584i) q^{13} +(-0.807620 - 0.856027i) q^{14} +(-2.67787 - 1.56841i) q^{15} +(0.597159 + 0.802123i) q^{16} +(0.461322 + 2.61629i) q^{17} +(-2.99977 - 0.0374058i) q^{18} +(-0.128292 + 0.727580i) q^{19} +(-1.60115 + 0.804128i) q^{20} +(0.926174 - 1.81585i) q^{21} +(3.61528 + 0.422566i) q^{22} +(3.51483 - 2.31174i) q^{23} +(-0.960781 + 1.44115i) q^{24} +(0.513291 + 1.71451i) q^{25} +(3.21811 - 5.57394i) q^{26} +(-1.68556 - 4.91517i) q^{27} +(-0.588437 - 1.01920i) q^{28} +(-1.71661 + 1.81950i) q^{29} +(-2.24399 - 2.14369i) q^{30} +(-0.374563 - 6.43100i) q^{31} +(0.396080 + 0.918216i) q^{32} +(1.41564 + 6.14349i) q^{33} +(-0.154470 + 2.65215i) q^{34} +(1.98148 - 0.721198i) q^{35} +(-2.91028 - 0.728191i) q^{36} +(-7.73114 - 2.81391i) q^{37} +(-0.292625 + 0.678382i) q^{38} +(10.9662 + 2.00421i) q^{39} +(-1.74344 + 0.413202i) q^{40} +(-9.76678 + 2.31477i) q^{41} +(1.31997 - 1.55331i) q^{42} +(2.11947 - 4.91348i) q^{43} +(3.42038 + 1.24492i) q^{44} +(2.19038 - 4.90866i) q^{45} +(3.95321 - 1.43885i) q^{46} +(-0.160028 + 2.74758i) q^{47} +(-1.26723 + 1.18073i) q^{48} +(-2.22397 - 5.15575i) q^{49} +(0.104062 + 1.78667i) q^{50} +(-4.41628 + 1.29220i) q^{51} +(4.41681 - 4.68154i) q^{52} +(4.71775 + 8.17138i) q^{53} +(-0.506608 - 5.17140i) q^{54} +(-3.26086 + 5.64797i) q^{55} +(-0.337531 - 1.12743i) q^{56} +(-1.27699 - 0.0823677i) q^{57} +(-2.08995 + 1.37458i) q^{58} +(-9.18819 - 1.07395i) q^{59} +(-1.68913 - 2.60341i) q^{60} +(-10.4142 + 5.23023i) q^{61} +(1.11862 - 6.34403i) q^{62} +(3.30239 + 1.24882i) q^{63} +(0.173648 + 0.984808i) q^{64} +(6.88643 + 9.25008i) q^{65} +(-0.0393048 + 6.30436i) q^{66} +(1.44376 + 1.53030i) q^{67} +(-0.761935 + 2.54504i) q^{68} +(4.64885 + 5.61095i) q^{69} +(2.09438 - 0.244798i) q^{70} +(8.87851 - 7.44995i) q^{71} +(-2.66390 - 1.37972i) q^{72} +(6.70365 + 5.62503i) q^{73} +(-6.87382 - 4.52098i) q^{74} +(-2.85393 + 1.21002i) q^{75} +(-0.441183 + 0.592612i) q^{76} +(-3.82805 - 1.92252i) q^{77} +(10.2084 + 4.47918i) q^{78} +(5.84449 + 1.38517i) q^{79} -1.79173 q^{80} +(8.14091 - 3.83739i) q^{81} -10.0373 q^{82} +(-0.953883 - 0.226074i) q^{83} +(1.64261 - 1.20703i) q^{84} +(-4.25369 - 2.13628i) q^{85} +(3.19546 - 4.29225i) q^{86} +(-3.45914 - 2.60891i) q^{87} +(3.04109 + 2.00015i) q^{88} +(-4.23002 - 3.54941i) q^{89} +(3.26335 - 4.27121i) q^{90} +(-5.80250 + 4.86888i) q^{91} +(4.17847 - 0.488394i) q^{92} +(11.0001 - 1.86897i) q^{93} +(-0.789350 + 2.63661i) q^{94} +(-0.908405 - 0.962853i) q^{95} +(-1.50537 + 0.856657i) q^{96} +(10.4945 + 14.0966i) q^{97} +(-0.975029 - 5.52966i) q^{98} +(-10.3069 + 3.60652i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more