LMFDB - Embedded newform 322.2.i.c.141.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 9 x^{19} + 41 x^{18} - 119 x^{17} + 245 x^{16} - 404 x^{15} + 623 x^{14} - 898 x^{13} + \cdots + 1 $ x^20 - 9x^19 + 41x^18 - 119x^17 + 245x^16 - 404x^15 + 623x^14 - 898x^13 + 1048x^12 - 693x^11 + 859x^10 - 935x^9 + 620x^8 + 679x^7 + 1220x^6 + 2241x^5 + 1750x^4 + 1079x^3 + 534x^2 + 38*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			141.1
Root			$1.45482 + 0.934959i$ of defining polynomial
Character	$\chi$	$=$	322.141
Dual form			322.2.i.c.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(-1.13381 + 2.48271i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.36481 + 2.72913i) q^{5} +(2.61880 + 0.768948i) q^{6} +(0.841254 - 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.91372 - 3.36261i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(-1.13381 + 2.48271i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.36481 + 2.72913i) q^{5} +(2.61880 + 0.768948i) q^{6} +(0.841254 - 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.91372 - 3.36261i) q^{9} +(3.03790 + 1.95234i) q^{10} +(0.471909 - 3.28220i) q^{11} +(0.388428 - 2.70157i) q^{12} +(-4.79116 - 3.07909i) q^{13} +(-0.654861 - 0.755750i) q^{14} +(-4.09439 - 8.96545i) q^{15} +(0.841254 - 0.540641i) q^{16} +(4.13709 + 1.21476i) q^{17} +(-2.91372 + 3.36261i) q^{18} +(-4.49676 + 1.32037i) q^{19} +(1.50013 - 3.28483i) q^{20} +(0.388428 + 2.70157i) q^{21} -3.31595 q^{22} +(-4.09468 + 2.49671i) q^{23} -2.72935 q^{24} +(-1.14428 - 7.95863i) q^{25} +(-2.36590 + 5.18059i) q^{26} +(3.79561 - 1.11449i) q^{27} +(-0.654861 + 0.755750i) q^{28} +(4.68606 + 1.37595i) q^{29} +(-8.29151 + 5.32863i) q^{30} +(0.704600 + 1.54286i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(7.61368 + 4.89301i) q^{33} +(0.613625 - 4.26785i) q^{34} +(-0.513922 + 3.57440i) q^{35} +(3.74305 + 2.40551i) q^{36} +(-5.93203 - 6.84592i) q^{37} +(1.94689 + 4.26309i) q^{38} +(13.0768 - 8.40392i) q^{39} +(-3.46488 - 1.01738i) q^{40} +(-1.90857 + 2.20261i) q^{41} +(2.61880 - 0.768948i) q^{42} +(-4.01355 + 8.78846i) q^{43} +(0.471909 + 3.28220i) q^{44} +16.0674 q^{45} +(3.05404 + 3.69768i) q^{46} -1.64420 q^{47} +(0.388428 + 2.70157i) q^{48} +(0.415415 - 0.909632i) q^{49} +(-7.71478 + 2.26526i) q^{50} +(-7.70658 + 8.89386i) q^{51} +(5.46456 + 1.60454i) q^{52} +(-5.65574 + 3.63472i) q^{53} +(-1.64332 - 3.59836i) q^{54} +(7.84158 + 9.04966i) q^{55} +(0.841254 + 0.540641i) q^{56} +(1.82041 - 12.6612i) q^{57} +(0.695051 - 4.83418i) q^{58} +(-1.22113 - 0.784771i) q^{59} +(6.45439 + 7.44877i) q^{60} +(-3.05716 - 6.69425i) q^{61} +(1.42688 - 0.917000i) q^{62} +(-4.26914 - 1.25353i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(19.7334 - 5.79425i) q^{65} +(3.75967 - 8.23253i) q^{66} +(1.33512 + 9.28594i) q^{67} -4.31174 q^{68} +(-1.55600 - 12.9967i) q^{69} +3.61116 q^{70} +(0.754000 + 5.24418i) q^{71} +(1.84834 - 4.04729i) q^{72} +(-12.4680 + 3.66094i) q^{73} +(-5.93203 + 6.84592i) q^{74} +(21.0564 + 6.18270i) q^{75} +(3.94262 - 2.53377i) q^{76} +(-1.37749 - 3.01629i) q^{77} +(-10.1794 - 11.7477i) q^{78} +(-8.52523 - 5.47883i) q^{79} +(-0.513922 + 3.57440i) q^{80} +(0.363076 - 2.52525i) q^{81} +(2.45181 + 1.57568i) q^{82} +(8.50221 + 9.81207i) q^{83} +(-1.13381 - 2.48271i) q^{84} +(-13.0986 + 8.41799i) q^{85} +(9.27019 + 2.72197i) q^{86} +(-8.72921 + 10.0740i) q^{87} +(3.18163 - 0.934210i) q^{88} +(2.46513 - 5.39787i) q^{89} +(-2.28663 - 15.9038i) q^{90} -5.69526 q^{91} +(3.22541 - 3.54919i) q^{92} -4.62935 q^{93} +(0.233994 + 1.62747i) q^{94} +(7.03052 - 15.3947i) q^{95} +(2.61880 - 0.768948i) q^{96} +(2.45857 - 2.83734i) q^{97} +(-0.959493 - 0.281733i) q^{98} +(-12.4118 + 7.97655i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9	\( 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9} + 6 q^{10} + 6 q^{11} + 4 q^{12} + 14 q^{13} - 2 q^{14} + 13 q^{15} - 2 q^{16} + 7 q^{17} - 12 q^{18} - 2 q^{19} + 6 q^{20} + 4 q^{21} - 16 q^{22} + 9 q^{23} - 18 q^{24} + 23 q^{25} + 3 q^{26} - 47 q^{27} - 2 q^{28} + 2 q^{29} - 20 q^{30} + 28 q^{31} - 2 q^{32} + 26 q^{33} + 18 q^{34} - 5 q^{35} + 10 q^{36} - 17 q^{37} + 9 q^{38} + 36 q^{39} - 5 q^{40} - 7 q^{41} + 4 q^{42} - 17 q^{43} + 6 q^{44} + 90 q^{45} + 9 q^{46} - 68 q^{47} + 4 q^{48} - 2 q^{49} - 43 q^{50} - 15 q^{51} + 14 q^{52} - 35 q^{53} + 19 q^{54} + 8 q^{55} - 2 q^{56} - 20 q^{57} + 24 q^{58} - 60 q^{59} + 13 q^{60} - 48 q^{61} - 5 q^{62} + 10 q^{63} - 2 q^{64} + 40 q^{65} - 29 q^{66} - 57 q^{67} + 18 q^{68} + 4 q^{69} + 6 q^{70} - 39 q^{71} - q^{72} - 30 q^{73} - 17 q^{74} + 57 q^{75} - 2 q^{76} + 6 q^{77} - 19 q^{78} - 18 q^{79} - 5 q^{80} - 90 q^{81} + 26 q^{82} + 28 q^{83} + 4 q^{84} - 13 q^{85} - 6 q^{86} + 13 q^{87} + 6 q^{88} + 34 q^{89} - 20 q^{90} - 30 q^{91} - 2 q^{92} - 16 q^{93} + 9 q^{94} + 110 q^{95} + 4 q^{96} - 2 q^{98} - 28 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9 + 6 * q^10 + 6 * q^11 + 4 * q^12 + 14 * q^13 - 2 * q^14 + 13 * q^15 - 2 * q^16 + 7 * q^17 - 12 * q^18 - 2 * q^19 + 6 * q^20 + 4 * q^21 - 16 * q^22 + 9 * q^23 - 18 * q^24 + 23 * q^25 + 3 * q^26 - 47 * q^27 - 2 * q^28 + 2 * q^29 - 20 * q^30 + 28 * q^31 - 2 * q^32 + 26 * q^33 + 18 * q^34 - 5 * q^35 + 10 * q^36 - 17 * q^37 + 9 * q^38 + 36 * q^39 - 5 * q^40 - 7 * q^41 + 4 * q^42 - 17 * q^43 + 6 * q^44 + 90 * q^45 + 9 * q^46 - 68 * q^47 + 4 * q^48 - 2 * q^49 - 43 * q^50 - 15 * q^51 + 14 * q^52 - 35 * q^53 + 19 * q^54 + 8 * q^55 - 2 * q^56 - 20 * q^57 + 24 * q^58 - 60 * q^59 + 13 * q^60 - 48 * q^61 - 5 * q^62 + 10 * q^63 - 2 * q^64 + 40 * q^65 - 29 * q^66 - 57 * q^67 + 18 * q^68 + 4 * q^69 + 6 * q^70 - 39 * q^71 - q^72 - 30 * q^73 - 17 * q^74 + 57 * q^75 - 2 * q^76 + 6 * q^77 - 19 * q^78 - 18 * q^79 - 5 * q^80 - 90 * q^81 + 26 * q^82 + 28 * q^83 + 4 * q^84 - 13 * q^85 - 6 * q^86 + 13 * q^87 + 6 * q^88 + 34 * q^89 - 20 * q^90 - 30 * q^91 - 2 * q^92 - 16 * q^93 + 9 * q^94 + 110 * q^95 + 4 * q^96 - 2 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	−1.13381	+	2.48271i	−0.654608	+	1.43339i	0.232854	+	0.972512i	$0.425193\pi$
$3$	−1.13381	+	2.48271i	−0.654608	+	1.43339i	−0.887462	+	0.460880i	$0.847534\pi$
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−2.36481	+	2.72913i	−1.05757	+	1.22051i	−0.0829739	+	0.996552i	$0.526442\pi$
$5$	−2.36481	+	2.72913i	−1.05757	+	1.22051i	−0.974600	+	0.223953i	$0.928104\pi$
$6$	2.61880	+	0.768948i	1.06912	+	0.313922i
$7$	0.841254	−	0.540641i	0.317964	−	0.204343i
$7$	0.841254	−	0.540641i	0.317964	−	0.204343i
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	−2.91372	−	3.36261i	−0.971239	−	1.12087i
$10$	3.03790	+	1.95234i	0.960669	+	0.617384i
$11$	0.471909	−	3.28220i	0.142286	−	0.989619i	−0.786126	−	0.618066i	$-0.787916\pi$
$11$	0.471909	−	3.28220i	0.142286	−	0.989619i	0.928412	−	0.371553i	$-0.121175\pi$
$12$	0.388428	−	2.70157i	0.112129	−	0.779877i
$13$	−4.79116	−	3.07909i	−1.32883	−	0.853986i	−0.332797	−	0.942998i	$-0.607993\pi$
$13$	−4.79116	−	3.07909i	−1.32883	−	0.853986i	−0.996031	+	0.0890126i	$0.971629\pi$
$14$	−0.654861	−	0.755750i	−0.175019	−	0.201983i
$15$	−4.09439	−	8.96545i	−1.05717	−	2.31487i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	4.13709	+	1.21476i	1.00339	+	0.294622i	0.741847	−	0.670570i	$-0.233950\pi$
$17$	4.13709	+	1.21476i	1.00339	+	0.294622i	0.261544	+	0.965192i	$0.415768\pi$
$18$	−2.91372	+	3.36261i	−0.686770	+	0.792575i
$19$	−4.49676	+	1.32037i	−1.03163	+	0.302913i	−0.753373	−	0.657594i	$-0.771574\pi$
$19$	−4.49676	+	1.32037i	−1.03163	+	0.302913i	−0.278256	+	0.960507i	$0.589756\pi$
$20$	1.50013	−	3.28483i	0.335439	−	0.734510i
$21$	0.388428	+	2.70157i	0.0847618	+	0.589531i
$22$	−3.31595			−0.706962
$23$	−4.09468	+	2.49671i	−0.853800	+	0.520601i
$23$	−4.09468	+	2.49671i	−0.853800	+	0.520601i
$24$	−2.72935			−0.557127
$25$	−1.14428	−	7.95863i	−0.228856	−	1.59173i
$26$	−2.36590	+	5.18059i	−0.463990	+	1.01600i
$27$	3.79561	−	1.11449i	0.730465	−	0.214484i
$28$	−0.654861	+	0.755750i	−0.123757	+	0.142823i
$29$	4.68606	+	1.37595i	0.870180	+	0.255508i	0.686192	−	0.727421i	$-0.259281\pi$
$29$	4.68606	+	1.37595i	0.870180	+	0.255508i	0.183988	+	0.982928i	$0.441099\pi$
$30$	−8.29151	+	5.32863i	−1.51381	+	0.972870i
$31$	0.704600	+	1.54286i	0.126550	+	0.277106i	0.962293	−	0.272015i	$-0.0876900\pi$
$31$	0.704600	+	1.54286i	0.126550	+	0.277106i	−0.835743	+	0.549121i	$0.814963\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	7.61368	+	4.89301i	1.32537	+	0.851764i
$34$	0.613625	−	4.26785i	0.105236	−	0.731931i
$35$	−0.513922	+	3.57440i	−0.0868686	+	0.604184i
$36$	3.74305	+	2.40551i	0.623841	+	0.400919i
$37$	−5.93203	−	6.84592i	−0.975219	−	1.12546i	−0.992080	−	0.125605i	$-0.959913\pi$
$37$	−5.93203	−	6.84592i	−0.975219	−	1.12546i	0.0168612	−	0.999858i	$-0.494633\pi$
$38$	1.94689	+	4.26309i	0.315827	+	0.691564i
$39$	13.0768	−	8.40392i	2.09396	−	1.34570i
$40$	−3.46488	−	1.01738i	−0.547846	−	0.160862i
$41$	−1.90857	+	2.20261i	−0.298069	+	0.343989i	−0.884952	−	0.465682i	$-0.845809\pi$
$41$	−1.90857	+	2.20261i	−0.298069	+	0.343989i	0.586884	+	0.809671i	$0.300355\pi$
$42$	2.61880	−	0.768948i	0.404089	−	0.118651i
$43$	−4.01355	+	8.78846i	−0.612061	+	1.34023i	0.309094	+	0.951031i	$0.399974\pi$
$43$	−4.01355	+	8.78846i	−0.612061	+	1.34023i	−0.921155	+	0.389195i	$0.872753\pi$
$44$	0.471909	+	3.28220i	0.0711429	+	0.494810i
$45$	16.0674			2.39518
$46$	3.05404	+	3.69768i	0.450293	+	0.545194i
$47$	−1.64420			−0.239832			−0.119916	−	0.992784i	$-0.538262\pi$
$47$	−1.64420			−0.239832			−0.119916	+	0.992784i	$0.538262\pi$
$48$	0.388428	+	2.70157i	0.0560647	+	0.389938i
$49$	0.415415	−	0.909632i	0.0593450	−	0.129947i
$50$	−7.71478	+	2.26526i	−1.09103	+	0.320357i
$51$	−7.70658	+	8.89386i	−1.07914	+	1.24539i
$52$	5.46456	+	1.60454i	0.757798	+	0.222510i
$53$	−5.65574	+	3.63472i	−0.776876	+	0.499268i	−0.867995	−	0.496572i	$-0.834592\pi$
$53$	−5.65574	+	3.63472i	−0.776876	+	0.499268i	0.0911195	+	0.995840i	$0.470955\pi$
$54$	−1.64332	−	3.59836i	−0.223627	−	0.489675i
$55$	7.84158	+	9.04966i	1.05736	+	1.22026i
$56$	0.841254	+	0.540641i	0.112417	+	0.0722462i
$57$	1.82041	−	12.6612i	0.241119	−	1.67702i
$58$	0.695051	−	4.83418i	0.0912646	−	0.634759i
$59$	−1.22113	−	0.784771i	−0.158977	−	0.102169i	0.458733	−	0.888574i	$-0.348303\pi$
$59$	−1.22113	−	0.784771i	−0.158977	−	0.102169i	−0.617711	+	0.786405i	$0.711940\pi$
$60$	6.45439	+	7.44877i	0.833259	+	0.961632i
$61$	−3.05716	−	6.69425i	−0.391430	−	0.857112i	−0.998068	−	0.0621334i	$-0.980210\pi$
$61$	−3.05716	−	6.69425i	−0.391430	−	0.857112i	0.606638	−	0.794978i	$-0.292518\pi$
$62$	1.42688	−	0.917000i	0.181214	−	0.116459i
$63$	−4.26914	−	1.25353i	−0.537861	−	0.157930i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	19.7334	−	5.79425i	2.44763	−	0.718688i
$66$	3.75967	−	8.23253i	0.462783	−	1.01335i
$67$	1.33512	+	9.28594i	0.163110	+	1.13446i	0.892726	+	0.450600i	$0.148790\pi$
$67$	1.33512	+	9.28594i	0.163110	+	1.13446i	−0.729616	+	0.683858i	$0.760301\pi$
$68$	−4.31174			−0.522875
$69$	−1.55600	−	12.9967i	−0.187321	−	1.56462i
$70$	3.61116			0.431616
$71$	0.754000	+	5.24418i	0.0894833	+	0.622370i	0.984375	+	0.176086i	$0.0563438\pi$
$71$	0.754000	+	5.24418i	0.0894833	+	0.622370i	−0.894891	+	0.446284i	$0.852747\pi$
$72$	1.84834	−	4.04729i	0.217828	−	0.476978i
$73$	−12.4680	+	3.66094i	−1.45927	+	0.428481i	−0.912595	−	0.408864i	$-0.865925\pi$
$73$	−12.4680	+	3.66094i	−1.45927	+	0.428481i	−0.546675	+	0.837345i	$0.684107\pi$
$74$	−5.93203	+	6.84592i	−0.689584	+	0.795822i
$75$	21.0564	+	6.18270i	2.43138	+	0.713917i
$76$	3.94262	−	2.53377i	0.452250	−	0.290643i
$77$	−1.37749	−	3.01629i	−0.156980	−	0.343738i
$78$	−10.1794	−	11.7477i	−1.15259	−	1.33016i
$79$	−8.52523	−	5.47883i	−0.959163	−	0.616417i	−0.0353970	−	0.999373i	$-0.511270\pi$
$79$	−8.52523	−	5.47883i	−0.959163	−	0.616417i	−0.923766	+	0.382956i	$0.874906\pi$
$80$	−0.513922	+	3.57440i	−0.0574582	+	0.399630i
$81$	0.363076	−	2.52525i	0.0403417	−	0.280583i
$82$	2.45181	+	1.57568i	0.270757	+	0.174005i
$83$	8.50221	+	9.81207i	0.933239	+	1.07702i	0.996871	+	0.0790417i	$0.0251860\pi$
$83$	8.50221	+	9.81207i	0.933239	+	1.07702i	−0.0636324	+	0.997973i	$0.520269\pi$
$84$	−1.13381	−	2.48271i	−0.123709	−	0.270886i
$85$	−13.0986	+	8.41799i	−1.42075	+	0.913059i
$86$	9.27019	+	2.72197i	0.999630	+	0.293518i
$87$	−8.72921	+	10.0740i	−0.935870	+	1.08005i
$88$	3.18163	−	0.934210i	0.339163	−	0.0995872i
$89$	2.46513	−	5.39787i	0.261303	−	0.572174i	−0.732821	−	0.680421i	$-0.761797\pi$
$89$	2.46513	−	5.39787i	0.261303	−	0.572174i	0.994124	+	0.108248i	$0.0345240\pi$
$90$	−2.28663	−	15.9038i	−0.241032	−	1.67641i
$91$	−5.69526			−0.597025
$92$	3.22541	−	3.54919i	0.336272	−	0.370028i
$93$	−4.62935			−0.480041
$94$	0.233994	+	1.62747i	0.0241347	+	0.167860i
$95$	7.03052	−	15.3947i	0.721316	−	1.57946i
$96$	2.61880	−	0.768948i	0.267280	−	0.0784804i
$97$	2.45857	−	2.83734i	0.249630	−	0.288089i	−0.617080	−	0.786900i	$-0.711685\pi$
$97$	2.45857	−	2.83734i	0.249630	−	0.288089i	0.866710	+	0.498812i	$0.166230\pi$
$98$	−0.959493	−	0.281733i	−0.0969234	−	0.0284593i
$99$	−12.4118	+	7.97655i	−1.24743	+	0.801673i
$100$	3.34013	+	7.31387i	0.334013	+	0.731387i
$101$	−0.252564	−	0.291474i	−0.0251310	−	0.0290028i	0.743045	−	0.669242i	$-0.233381\pi$
$101$	−0.252564	−	0.291474i	−0.0251310	−	0.0290028i	−0.768176	+	0.640239i	$0.778835\pi$
$102$	9.90010	+	6.36240i	0.980256	+	0.629972i
$103$	0.292549	−	2.03473i	0.0288258	−	0.200488i	−0.970319	−	0.241827i	$-0.922253\pi$
$103$	0.292549	−	2.03473i	0.0288258	−	0.200488i	0.999145	+	0.0413394i	$0.0131625\pi$
$104$	0.810520	−	5.63729i	0.0794780	−	0.552782i
$105$	−8.29151	−	5.32863i	−0.809168	−	0.520021i
$106$	4.40262	+	5.08090i	0.427621	+	0.493501i
$107$	1.90603	+	4.17363i	0.184263	+	0.403480i	0.979110	−	0.203329i	$-0.0651762\pi$
$107$	1.90603	+	4.17363i	0.184263	+	0.403480i	−0.794847	+	0.606810i	$0.792449\pi$
$108$	−3.32787	+	2.13869i	−0.320224	+	0.205796i
$109$	16.5478	+	4.85887i	1.58499	+	0.465395i	0.951319	−	0.308208i	$-0.0997293\pi$
$109$	16.5478	+	4.85887i	1.58499	+	0.465395i	0.633671	+	0.773603i	$0.281547\pi$
$110$	7.84158	−	9.04966i	0.747665	−	0.862851i
$111$	23.7222	−	6.96548i	2.25162	−	0.661134i
$112$	0.415415	−	0.909632i	0.0392530	−	0.0859521i
$113$	−1.13909	−	7.92252i	−0.107156	−	0.745288i	−0.970575	−	0.240800i	$-0.922590\pi$
$113$	−1.13909	−	7.92252i	−0.107156	−	0.745288i	0.863419	−	0.504488i	$-0.168319\pi$
$114$	−12.7914			−1.19802
$115$	2.86926	−	17.0792i	0.267560	−	1.59264i
$116$	−4.88389			−0.453458
$117$	3.60630	+	25.0824i	0.333403	+	2.31887i
$118$	−0.602999	+	1.32038i	−0.0555106	+	0.121551i
$119$	4.13709	−	1.21476i	0.379246	−	0.111357i
$120$	6.45439	−	7.44877i	0.589203	−	0.679976i
$121$	0.00430932	+	0.00126533i	0.000391757	+	0.000115030i
$122$	−6.19104	+	3.97874i	−0.560510	+	0.360218i
$123$	−3.30446	−	7.23577i	−0.297954	−	0.652427i
$124$	−1.11073	−	1.28185i	−0.0997467	−	0.115114i
$125$	9.23666	+	5.93604i	0.826152	+	0.530936i
$126$	−0.633211	+	4.40408i	−0.0564110	+	0.392347i
$127$	−2.51559	+	17.4963i	−0.223222	+	1.55254i	0.502513	+	0.864570i	$0.332409\pi$
$127$	−2.51559	+	17.4963i	−0.223222	+	1.55254i	−0.725735	+	0.687974i	$0.758500\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	−17.2685	−	19.9290i	−1.52041	−	1.75465i
$130$	−8.54363	−	18.7079i	−0.749326	−	1.64079i
$131$	−12.5641	+	8.07446i	−1.09773	+	0.705469i	−0.958586	−	0.284803i	$-0.908072\pi$
$131$	−12.5641	+	8.07446i	−1.09773	+	0.705469i	−0.139145	+	0.990272i	$0.544435\pi$
$132$	−8.68379	−	2.54979i	−0.755827	−	0.221931i
$133$	−3.06907	+	3.54190i	−0.266122	+	0.307122i
$134$	9.00141	−	2.64305i	0.777603	−	0.228325i
$135$	−5.93428	+	12.9943i	−0.510742	+	1.11837i
$136$	0.613625	+	4.26785i	0.0526179	+	0.365965i
$137$	21.3865			1.82718			0.913588	−	0.406641i	$-0.133300\pi$
$137$	21.3865			1.82718			0.913588	+	0.406641i	$0.133300\pi$
$138$	−12.6430	+	3.38979i	−1.07624	+	0.288558i
$139$	−13.8100			−1.17135			−0.585675	−	0.810546i	$-0.699170\pi$
$139$	−13.8100			−1.17135			−0.585675	+	0.810546i	$0.699170\pi$
$140$	−0.513922	−	3.57440i	−0.0434343	−	0.302092i
$141$	1.86422	−	4.08207i	0.156996	−	0.343773i
$142$	5.08350	−	1.49265i	0.426598	−	0.125260i
$143$	−12.3672	+	14.2725i	−1.03419	+	1.19352i
$144$	−4.26914	−	1.25353i	−0.355762	−	0.104461i
$145$	−14.8368	+	9.53502i	−1.23213	+	0.791841i
$146$	5.39806	+	11.8201i	0.446747	+	0.978239i
$147$	1.78735	+	2.06271i	0.147418	+	0.170129i
$148$	7.62046	+	4.89737i	0.626398	+	0.402561i
$149$	−1.77803	+	12.3665i	−0.145662	+	1.01310i	0.777553	+	0.628817i	$0.216460\pi$
$149$	−1.77803	+	12.3665i	−0.145662	+	1.01310i	−0.923215	+	0.384283i	$0.874449\pi$
$150$	3.12314	−	21.7219i	0.255003	−	1.77359i
$151$	−18.3368	−	11.7844i	−1.49223	−	0.958998i	−0.995861	−	0.0908865i	$-0.971030\pi$
$151$	−18.3368	−	11.7844i	−1.49223	−	0.958998i	−0.496369	−	0.868112i	$-0.665334\pi$
$152$	−3.06907	−	3.54190i	−0.248935	−	0.287286i
$153$	−7.96954	−	17.4509i	−0.644299	−	1.41082i
$154$	−2.78955	+	1.79274i	−0.224789	+	0.144463i
$155$	−5.87691	−	1.72562i	−0.472045	−	0.138605i
$156$	−10.1794	+	11.7477i	−0.815004	+	0.940565i
$157$	−5.94565	+	1.74580i	−0.474515	+	0.139330i	−0.510241	−	0.860032i	$-0.670444\pi$
$157$	−5.94565	+	1.74580i	−0.474515	+	0.139330i	0.0357262	+	0.999362i	$0.488626\pi$
$158$	−4.20980	+	9.21818i	−0.334914	+	0.733359i
$159$	−2.61140	−	18.1627i	−0.207097	−	1.44039i
$160$	3.61116			0.285487
$161$	−2.09484	+	4.31412i	−0.165096	+	0.340000i
$162$	−2.55121			−0.200442
$163$	1.15849	+	8.05749i	0.0907401	+	0.631111i	0.983544	+	0.180667i	$0.0578255\pi$
$163$	1.15849	+	8.05749i	0.0907401	+	0.631111i	−0.892804	+	0.450445i	$0.851265\pi$
$164$	1.21071	−	2.65109i	0.0945408	−	0.207016i
$165$	−31.3585	+	9.20770i	−2.44126	+	0.716819i
$166$	8.50221	−	9.81207i	0.659900	−	0.761565i
$167$	3.12841	+	0.918584i	0.242084	+	0.0710821i	0.400524	−	0.916286i	$-0.368828\pi$
$167$	3.12841	+	0.918584i	0.242084	+	0.0710821i	−0.158440	+	0.987369i	$0.550646\pi$
$168$	−2.29608	+	1.47560i	−0.177146	+	0.113845i
$169$	8.07400	+	17.6796i	0.621077	+	1.35997i
$170$	10.1964	+	11.7673i	0.782031	+	0.902512i
$171$	17.5422	+	11.2737i	1.34148	+	0.862120i
$172$	1.37498	−	9.56321i	0.104841	−	0.729188i
$173$	−2.16313	+	15.0449i	−0.164460	+	1.14385i	0.725638	+	0.688076i	$0.241545\pi$
$173$	−2.16313	+	15.0449i	−0.164460	+	1.14385i	−0.890098	+	0.455769i	$0.849364\pi$
$174$	11.2138	+	7.20667i	0.850116	+	0.546337i
$175$	−5.26539	−	6.07659i	−0.398026	−	0.459347i
$176$	−1.37749	−	3.01629i	−0.103833	−	0.227362i
$177$	3.33289	−	2.14192i	0.250515	−	0.160996i
$178$	−5.69376	−	1.67184i	−0.426765	−	0.125310i
$179$	−1.75139	+	2.02121i	−0.130905	+	0.151073i	−0.817418	−	0.576045i	$-0.804595\pi$
$179$	−1.75139	+	2.02121i	−0.130905	+	0.151073i	0.686513	+	0.727118i	$0.259141\pi$
$180$	−15.4165	+	4.52671i	−1.14908	+	0.337401i
$181$	7.69514	−	16.8500i	0.571976	−	1.25245i	−0.373763	−	0.927524i	$-0.621933\pi$
$181$	7.69514	−	16.8500i	0.571976	−	1.25245i	0.945739	−	0.324928i	$-0.105340\pi$
$182$	0.810520	+	5.63729i	0.0600797	+	0.417864i
$183$	20.0861			1.48481
$184$	−3.97208	−	2.68748i	−0.292826	−	0.198124i
$185$	32.7115			2.40500
$186$	0.658825	+	4.58223i	0.0483074	+	0.335986i
$187$	5.93940	−	13.0055i	0.434332	−	0.951054i
$188$	1.57760	−	0.463225i	0.115058	−	0.0337842i
$189$	2.59053	−	2.98963i	0.188433	−	0.217463i
$190$	−16.2385	−	4.76806i	−1.17807	−	0.345912i
$191$	−12.4431	+	7.99670i	−0.900351	+	0.578621i	−0.906894	−	0.421358i	$-0.861554\pi$
$191$	−12.4431	+	7.99670i	−0.900351	+	0.578621i	0.00654309	+	0.999979i	$0.497917\pi$
$192$	−1.13381	−	2.48271i	−0.0818260	−	0.179174i
$193$	6.18404	+	7.13676i	0.445137	+	0.513715i	0.933330	−	0.359020i	$-0.116889\pi$
$193$	6.18404	+	7.13676i	0.445137	+	0.513715i	−0.488193	+	0.872736i	$0.662344\pi$
$194$	−3.15835	−	2.02975i	−0.226757	−	0.145728i
$195$	−7.98859	+	55.5619i	−0.572075	+	3.97887i
$196$	−0.142315	+	0.989821i	−0.0101653	+	0.0707015i
$197$	−12.8875	−	8.28227i	−0.918194	−	0.590087i	−0.00606085	−	0.999982i	$-0.501929\pi$
$197$	−12.8875	−	8.28227i	−0.918194	−	0.590087i	−0.912133	+	0.409894i	$0.865566\pi$
$198$	9.66174	+	11.1502i	0.686630	+	0.792413i
$199$	−2.88180	−	6.31027i	−0.204286	−	0.447323i	0.779563	−	0.626323i	$-0.215441\pi$
$199$	−2.88180	−	6.31027i	−0.204286	−	0.447323i	−0.983849	+	0.179000i	$0.942714\pi$
$200$	6.76408	−	4.34701i	0.478293	−	0.307380i
$201$	−24.5680	−	7.21383i	−1.73290	−	0.508824i
$202$	−0.252564	+	0.291474i	−0.0177703	+	0.0205080i
$203$	4.68606	−	1.37595i	0.328897	−	0.0965729i
$204$	4.88871	−	10.7048i	0.342278	−	0.749485i
$205$	−1.49781	−	10.4175i	−0.104611	−	0.727588i
$206$	−2.05565			−0.143224
$207$	20.3262	+	6.49409i	1.41277	+	0.451371i
$208$	−5.69526			−0.394895
$209$	2.21165	+	15.3824i	0.152983	+	1.06402i
$210$	−4.09439	+	8.96545i	−0.282539	+	0.618675i
$211$	25.1701	−	7.39060i	1.73278	−	0.508790i	0.745326	−	0.666700i	$-0.232294\pi$
$211$	25.1701	−	7.39060i	1.73278	−	0.508790i	0.987453	+	0.157910i	$0.0504757\pi$
$212$	4.40262	−	5.08090i	0.302373	−	0.348958i
$213$	−13.8747	−	4.07397i	−0.950677	−	0.279144i
$214$	3.85989	−	2.48060i	0.263857	−	0.169571i
$215$	−14.4936	−	31.7365i	−0.988454	−	2.16441i
$216$	2.59053	+	2.98963i	0.176263	+	0.203418i
$217$	1.42688	+	0.917000i	0.0968629	+	0.0622500i
$218$	2.45442	−	17.0708i	0.166234	−	1.15618i
$219$	5.04737	−	35.1053i	0.341070	−	2.37219i
$220$	−10.0735	−	6.47386i	−0.679157	−	0.436467i
$221$	−16.0811	−	18.5586i	−1.08173	−	1.24838i
$222$	−10.2706	−	22.4895i	−0.689318	−	1.50940i
$223$	2.01320	−	1.29380i	0.134814	−	0.0866395i	−0.471496	−	0.881868i	$-0.656286\pi$
$223$	2.01320	−	1.29380i	0.134814	−	0.0866395i	0.606309	+	0.795229i	$0.292649\pi$
$224$	−0.959493	−	0.281733i	−0.0641088	−	0.0188240i
$225$	−23.4277	+	27.0370i	−1.56185	+	1.80247i
$226$	−7.67977	+	2.25498i	−0.510851	+	0.149999i
$227$	4.25188	−	9.31031i	0.282207	−	0.617947i	−0.714447	−	0.699690i	$-0.753321\pi$
$227$	4.25188	−	9.31031i	0.282207	−	0.617947i	0.996653	+	0.0817432i	$0.0260487\pi$
$228$	1.82041	+	12.6612i	0.120559	+	0.838509i
$229$	7.48570			0.494669			0.247335	−	0.968930i	$-0.420445\pi$
$229$	7.48570			0.494669			0.247335	+	0.968930i	$0.420445\pi$
$230$	−17.3137	−	0.409440i	−1.14163	−	0.0269976i
$231$	9.05039			0.595472
$232$	0.695051	+	4.83418i	0.0456323	+	0.317380i
$233$	2.67039	−	5.84735i	0.174943	−	0.383072i	−0.801766	−	0.597638i	$-0.796106\pi$
$233$	2.67039	−	5.84735i	0.174943	−	0.383072i	0.976710	+	0.214565i	$0.0688335\pi$
$234$	24.3139	−	7.13919i	1.58945	−	0.466704i
$235$	3.88822	−	4.48725i	0.253640	−	0.292716i
$236$	1.39276	+	0.408951i	0.0906609	+	0.0266205i
$237$	23.2684	−	14.9537i	1.51144	−	0.971345i
$238$	−1.79116	−	3.92210i	−0.116104	−	0.254232i
$239$	8.06304	+	9.30525i	0.521555	+	0.601907i	0.954020	−	0.299744i	$-0.0969014\pi$
$239$	8.06304	+	9.30525i	0.521555	+	0.601907i	−0.432465	+	0.901651i	$0.642356\pi$
$240$	−8.29151	−	5.32863i	−0.535214	−	0.343961i
$241$	2.25061	−	15.6533i	0.144974	−	1.00832i	−0.779317	−	0.626630i	$-0.784434\pi$
$241$	2.25061	−	15.6533i	0.144974	−	1.00832i	0.924291	−	0.381688i	$-0.124657\pi$
$242$	0.000639172	−	0.00444554i	4.10875e−5	−	0.000285770i
$243$	15.8414	+	10.1806i	1.01623	+	0.653089i
$244$	4.81932	+	5.56179i	0.308525	+	0.356057i
$245$	1.50013	+	3.28483i	0.0958398	+	0.209860i
$246$	−6.69184	+	4.30059i	−0.426656	+	0.274195i
$247$	25.6102	+	7.51985i	1.62954	+	0.478476i
$248$	−1.11073	+	1.28185i	−0.0705316	+	0.0813978i
$249$	−34.0004	+	9.98343i	−2.15469	+	0.632674i
$250$	4.56111	−	9.98743i	0.288470	−	0.631661i
$251$	1.69370	+	11.7799i	0.106905	+	0.743542i	0.970804	+	0.239876i	$0.0771067\pi$
$251$	1.69370	+	11.7799i	0.106905	+	0.743542i	−0.863898	+	0.503666i	$0.831984\pi$
$252$	4.44937			0.280284
$253$	6.26239	+	14.6178i	0.393713	+	0.919011i
$254$	17.6762			1.10910
$255$	−6.04797	−	42.0645i	−0.378738	−	2.63418i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−2.48034	+	0.728294i	−0.154719	+	0.0454297i	−0.358175	−	0.933654i	$-0.616601\pi$
$257$	−2.48034	+	0.728294i	−0.154719	+	0.0454297i	0.203456	+	0.979084i	$0.434783\pi$
$258$	−17.2685	+	19.9290i	−1.07509	+	1.24072i
$259$	−8.69152	−	2.55206i	−0.540065	−	0.158577i
$260$	−17.3016	+	11.1191i	−1.07300	+	0.689576i
$261$	−9.02707	−	19.7665i	−0.558762	−	1.22352i
$262$	9.78033	+	11.2871i	0.604231	+	0.697320i
$263$	−10.5950	−	6.80899i	−0.653315	−	0.419860i	0.171561	−	0.985174i	$-0.445119\pi$
$263$	−10.5950	−	6.80899i	−0.653315	−	0.419860i	−0.824876	+	0.565313i	$0.808755\pi$
$264$	−1.28801	+	8.95827i	−0.0792712	+	0.551344i
$265$	3.45509	−	24.0307i	0.212245	−	1.47619i
$266$	3.94262	+	2.53377i	0.241738	+	0.155355i
$267$	10.6063	+	12.2404i	0.649098	+	0.749099i
$268$	−3.89718	−	8.53364i	−0.238058	−	0.521275i
$269$	−12.0908	+	7.77031i	−0.737192	+	0.473764i	−0.854579	−	0.519322i	$-0.826185\pi$
$269$	−12.0908	+	7.77031i	−0.737192	+	0.473764i	0.117387	+	0.993086i	$0.462548\pi$
$270$	13.7065	+	4.02460i	0.834153	+	0.244929i
$271$	13.1499	−	15.1757i	0.798797	−	0.921861i	−0.199518	−	0.979894i	$-0.563938\pi$
$271$	13.1499	−	15.1757i	0.798797	−	0.921861i	0.998315	+	0.0580336i	$0.0184831\pi$
$272$	4.13709	−	1.21476i	0.250848	−	0.0736555i
$273$	6.45737	−	14.1397i	0.390818	−	0.855771i
$274$	−3.04362	−	21.1689i	−0.183872	−	1.27886i
$275$	−26.6618			−1.60777
$276$	5.15457	+	12.0319i	0.310269	+	0.724234i
$277$	−28.5599			−1.71600			−0.857998	−	0.513652i	$-0.828292\pi$
$277$	−28.5599			−1.71600			−0.857998	+	0.513652i	$0.828292\pi$
$278$	1.96537	+	13.6694i	0.117875	+	0.819838i
$279$	3.13503	−	6.86475i	0.187689	−	0.410982i
$280$	−3.46488	+	1.01738i	−0.207066	+	0.0608002i
$281$	18.5294	−	21.3840i	1.10537	−	1.27566i	0.147310	−	0.989090i	$-0.452938\pi$
$281$	18.5294	−	21.3840i	1.10537	−	1.27566i	0.958058	−	0.286573i	$-0.0925161\pi$
$282$	−4.30583	−	1.26431i	−0.256408	−	0.0752883i
$283$	12.9871	−	8.34629i	0.772002	−	0.496135i	−0.0943686	−	0.995537i	$-0.530083\pi$
$283$	12.9871	−	8.34629i	0.772002	−	0.496135i	0.866370	+	0.499402i	$0.166447\pi$
$284$	−2.20091	−	4.81933i	−0.130600	−	0.285975i
$285$	30.2492	+	34.9094i	1.79181	+	2.06786i
$286$	15.8872	+	10.2101i	0.939431	+	0.603736i
$287$	−0.414772	+	2.88480i	−0.0244832	+	0.170284i
$288$	−0.633211	+	4.40408i	−0.0373123	+	0.259513i
$289$	1.33853	+	0.860220i	0.0787370	+	0.0506012i
$290$	11.5495	+	13.3288i	0.678208	+	0.782694i
$291$	4.25673	+	9.32094i	0.249534	+	0.546403i
$292$	10.9316	−	7.02529i	0.639721	−	0.411124i
$293$	−2.15484	−	0.632717i	−0.125887	−	0.0369637i	0.218182	−	0.975908i	$-0.429987\pi$
$293$	−2.15484	−	0.632717i	−0.125887	−	0.0369637i	−0.344069	+	0.938944i	$0.611805\pi$
$294$	1.78735	−	2.06271i	0.104240	−	0.120300i
$295$	5.02948	−	1.47679i	0.292827	−	0.0859819i
$296$	3.76302	−	8.23986i	0.218721	−	0.478932i
$297$	−1.86680	−	12.9839i	−0.108323	−	0.753400i
$298$	12.4936			0.723737
$299$	27.3059	+	0.645738i	1.57914	+	0.0373440i
$300$	−21.9453			−1.26701
$301$	1.37498	+	9.56321i	0.0792526	+	0.551214i
$302$	−9.05482	+	19.8273i	−0.521046	+	1.14093i
$303$	1.01001	−	0.296564i	0.0580233	−	0.0170372i
$304$	−3.06907	+	3.54190i	−0.176023	+	0.203142i
$305$	25.4991	+	7.48721i	1.46007	+	0.428717i
$306$	−16.1391	+	10.3719i	−0.922609	+	0.592924i
$307$	0.294755	+	0.645422i	0.0168225	+	0.0368362i	0.917857	−	0.396912i	$-0.129918\pi$
$307$	0.294755	+	0.645422i	0.0168225	+	0.0368362i	−0.901034	+	0.433748i	$0.857191\pi$
$308$	2.17148	+	2.50603i	0.123732	+	0.142794i
$309$	4.71993	+	3.03332i	0.268508	+	0.172559i
$310$	−0.871680	+	6.06267i	−0.0495081	+	0.344337i
$311$	−2.70121	+	18.7873i	−0.153172	+	1.06533i	0.757688	+	0.652617i	$0.226329\pi$
$311$	−2.70121	+	18.7873i	−0.153172	+	1.06533i	−0.910860	+	0.412716i	$0.864580\pi$
$312$	13.0768	+	8.40392i	0.740326	+	0.475779i
$313$	10.4200	+	12.0253i	0.588972	+	0.679710i	0.969509	−	0.245056i	$-0.0788063\pi$
$313$	10.4200	+	12.0253i	0.588972	+	0.679710i	−0.380537	+	0.924766i	$0.624261\pi$
$314$	2.57419	+	5.63668i	0.145270	+	0.318096i
$315$	13.5167	−	8.68669i	0.761582	−	0.489439i
$316$	9.72347	+	2.85507i	0.546988	+	0.160610i
$317$	−4.28071	+	4.94021i	−0.240429	+	0.277470i	−0.863121	−	0.504997i	$-0.831493\pi$
$317$	−4.28071	+	4.94021i	−0.240429	+	0.277470i	0.622692	+	0.782467i	$0.286039\pi$
$318$	−17.6061	+	5.16963i	−0.987304	+	0.289898i
$319$	6.72754	−	14.7313i	0.376670	−	0.824792i
$320$	−0.513922	−	3.57440i	−0.0287291	−	0.199815i
$321$	−12.5230			−0.698966
$322$	4.56834	+	1.45955i	0.254583	+	0.0813377i
$323$	−20.2074			−1.12437
$324$	0.363076	+	2.52525i	0.0201709	+	0.140291i
$325$	−19.0229	+	41.6544i	−1.05520	+	2.31057i
$326$	7.81061	−	2.29340i	0.432589	−	0.127020i
$327$	−30.8252	+	35.5742i	−1.70464	+	1.96726i
$328$	−2.79641	−	0.821100i	−0.154406	−	0.0453377i
$329$	−1.38319	+	0.888923i	−0.0762578	+	0.0490079i
$330$	13.5768	+	29.7290i	0.747376	+	1.63653i
$331$	−3.85973	−	4.45437i	−0.212150	−	0.244834i	0.639694	−	0.768630i	$-0.279061\pi$
$331$	−3.85973	−	4.45437i	−0.212150	−	0.244834i	−0.851844	+	0.523796i	$0.824516\pi$
$332$	−10.9222	−	7.01927i	−0.599433	−	0.385232i
$333$	−5.73592	+	39.8942i	−0.314326	+	2.18619i
$334$	0.464015	−	3.22729i	0.0253898	−	0.176590i
$335$	−28.4998	−	18.3157i	−1.55711	−	1.00070i
$336$	1.78735	+	2.06271i	0.0975077	+	0.112530i
$337$	11.1926	+	24.5084i	0.609700	+	1.33506i	0.922779	+	0.385330i	$0.125912\pi$
$337$	11.1926	+	24.5084i	0.609700	+	1.33506i	−0.313079	+	0.949727i	$0.601360\pi$
$338$	16.3506	−	10.5079i	0.889355	−	0.571553i
$339$	20.9608	+	6.15465i	1.13843	+	0.334275i
$340$	10.1964	−	11.7673i	0.552979	−	0.638172i
$341$	5.39647	−	1.58455i	0.292235	−	0.0858080i
$342$	8.66242	−	18.9680i	0.468410	−	1.02567i
$343$	−0.142315	−	0.989821i	−0.00768428	−	0.0534453i
$344$	−9.66155			−0.520916
$345$	39.1494	+	26.4882i	2.10773	+	1.42607i
$346$	15.1996			0.817138
$347$	0.711924	+	4.95154i	0.0382181	+	0.265812i	0.999967	−	0.00811985i	$-0.00258466\pi$
$347$	0.711924	+	4.95154i	0.0382181	+	0.265812i	−0.961749	+	0.273932i	$0.911676\pi$
$348$	5.53743	−	12.1253i	0.296837	−	0.649983i
$349$	15.8130	−	4.64312i	0.846452	−	0.248541i	0.170382	−	0.985378i	$-0.445500\pi$
$349$	15.8130	−	4.64312i	0.846452	−	0.248541i	0.676070	+	0.736838i	$0.263682\pi$
$350$	−5.26539	+	6.07659i	−0.281447	+	0.324807i
$351$	−21.6170	−	6.34731i	−1.15383	−	0.338794i
$352$	−2.78955	+	1.79274i	−0.148684	+	0.0955532i
$353$	4.01373	+	8.78885i	0.213629	+	0.467783i	0.985863	−	0.167556i	$-0.0535875\pi$
$353$	4.01373	+	8.78885i	0.213629	+	0.467783i	−0.772233	+	0.635339i	$0.780860\pi$
$354$	−2.59444	−	2.99414i	−0.137893	−	0.159137i
$355$	−16.0951	−	10.3437i	−0.854241	−	0.548987i
$356$	−0.844515	+	5.87373i	−0.0447592	+	0.311307i
$357$	−1.67480	+	11.6485i	−0.0886398	+	0.616503i
$358$	2.24989	+	1.44592i	0.118910	+	0.0764190i
$359$	−15.5401	−	17.9342i	−0.820173	−	0.946530i	0.179131	−	0.983825i	$-0.442671\pi$
$359$	−15.5401	−	17.9342i	−0.820173	−	0.946530i	−0.999304	+	0.0372950i	$0.988126\pi$
$360$	6.67463	+	14.6154i	0.351784	+	0.770300i
$361$	2.49370	−	1.60260i	0.131247	−	0.0843476i
$362$	−17.7736	−	5.21881i	−0.934162	−	0.274295i
$363$	−0.00802742	+	0.00926414i	−0.000421330	+	0.000486241i
$364$	5.46456	−	1.60454i	0.286421	−	0.0841007i
$365$	19.4933	−	42.6843i	1.02032	−	2.23420i
$366$	−2.85855	−	19.8817i	−0.149419	−	1.03923i
$367$	5.96215			0.311221			0.155611	−	0.987818i	$-0.450265\pi$
$367$	5.96215			0.311221			0.155611	+	0.987818i	$0.450265\pi$
$368$	−2.09484	+	4.31412i	−0.109201	+	0.224889i
$369$	12.9675			0.675063
$370$	−4.65534	−	32.3786i	−0.242019	−	1.68328i
$371$	−2.79283	+	6.11545i	−0.144997	+	0.317498i
$372$	4.44183	−	1.30424i	0.230298	−	0.0676217i
$373$	13.0004	−	15.0033i	0.673135	−	0.776839i	−0.311728	−	0.950171i	$-0.600908\pi$
$373$	13.0004	−	15.0033i	0.673135	−	0.776839i	0.984863	+	0.173332i	$0.0554534\pi$
$374$	−13.7184	−	4.02807i	−0.709359	−	0.208287i
$375$	−25.2101	+	16.2016i	−1.30184	+	0.836645i
$376$	−0.683026	−	1.49562i	−0.0352244	−	0.0771307i
$377$	−18.2150	−	21.0212i	−0.938119	−	1.08265i
$378$	−3.32787	−	2.13869i	−0.171167	−	0.110002i
$379$	1.89395	−	13.1727i	0.0972857	−	0.676637i	−0.881565	−	0.472062i	$-0.843510\pi$
$379$	1.89395	−	13.1727i	0.0972857	−	0.676637i	0.978851	−	0.204575i	$-0.0655812\pi$
$380$	−2.40855	+	16.7518i	−0.123556	+	0.859350i
$381$	−40.5859	−	26.0830i	−2.07928	−	1.33627i
$382$	9.68614	+	11.1784i	0.495586	+	0.571937i
$383$	3.98924	+	8.73522i	0.203841	+	0.446349i	0.983750	−	0.179544i	$-0.0574621\pi$
$383$	3.98924	+	8.73522i	0.203841	+	0.446349i	−0.779909	+	0.625893i	$0.784735\pi$
$384$	−2.29608	+	1.47560i	−0.117171	+	0.0753014i
$385$	11.4894	+	3.37358i	0.585552	+	0.171934i
$386$	6.18404	−	7.13676i	0.314759	−	0.363252i
$387$	41.2465	−	12.1111i	2.09668	−	0.615640i
$388$	−1.55961	+	3.41507i	−0.0791772	+	0.173374i
$389$	1.22093	+	8.49172i	0.0619034	+	0.430547i	0.997080	+	0.0763654i	$0.0243316\pi$
$389$	1.22093	+	8.49172i	0.0619034	+	0.430547i	−0.935177	+	0.354182i	$0.884759\pi$
$390$	56.1332			2.84242
$391$	−19.9730	+	5.35508i	−1.01008	+	0.270818i
$392$	1.00000			0.0505076
$393$	−5.80116	−	40.3479i	−0.292630	−	2.03528i
$394$	−6.36389	+	13.9350i	−0.320608	+	0.702034i
$395$	35.1130	−	10.3101i	1.76673	−	0.518758i
$396$	9.66174	−	11.1502i	0.485521	−	0.560321i
$397$	−33.9481	−	9.96805i	−1.70380	−	0.500282i	−0.722277	−	0.691604i	$-0.756905\pi$
$397$	−33.9481	−	9.96805i	−1.70380	−	0.500282i	−0.981527	+	0.191321i	$0.938723\pi$
$398$	−5.83592	+	3.75052i	−0.292528	+	0.187996i
$399$	−5.31374	−	11.6355i	−0.266020	−	0.582502i
$400$	−5.26539	−	6.07659i	−0.263270	−	0.303829i
$401$	1.92618	+	1.23788i	0.0961889	+	0.0618168i	0.587851	−	0.808969i	$-0.299974\pi$
$401$	1.92618	+	1.23788i	0.0961889	+	0.0618168i	−0.491662	+	0.870786i	$0.663610\pi$
$402$	−3.64400	+	25.3446i	−0.181746	+	1.26407i
$403$	1.37475	−	9.56160i	0.0684812	−	0.476297i
$404$	0.324451	+	0.208512i	0.0161420	+	0.0103739i
$405$	6.03313	+	6.96260i	0.299788	+	0.345974i
$406$	−2.02884	−	4.44255i	−0.100690	−	0.220480i
$407$	−25.2690	+	16.2394i	−1.25254	+	0.804958i
$408$	−11.2916	−	3.31550i	−0.559016	−	0.164142i
$409$	−9.90272	+	11.4284i	−0.489658	+	0.565096i	−0.945774	−	0.324825i	$-0.894695\pi$
$409$	−9.90272	+	11.4284i	−0.489658	+	0.565096i	0.456116	+	0.889920i	$0.349240\pi$
$410$	−10.0983	+	2.96512i	−0.498719	+	0.146437i
$411$	−24.2484	+	53.0965i	−1.19608	+	2.61906i
$412$	0.292549	+	2.03473i	0.0144129	+	0.100244i
$413$	−1.45156			−0.0714265
$414$	3.53527	−	21.0435i	0.173749	−	1.03423i
$415$	−46.8845			−2.30147
$416$	0.810520	+	5.63729i	0.0397390	+	0.276391i
$417$	15.6580	−	34.2862i	0.766775	−	1.67900i
$418$	14.9110	−	4.37828i	0.729323	−	0.214148i
$419$	−17.3388	+	20.0101i	−0.847058	+	0.977557i	−0.999943	−	0.0106871i	$-0.996598\pi$
$419$	−17.3388	+	20.0101i	−0.847058	+	0.977557i	0.152885	+	0.988244i	$0.451144\pi$
$420$	9.45689	+	2.77679i	0.461449	+	0.135494i
$421$	11.5680	−	7.43431i	0.563790	−	0.362326i	−0.227489	−	0.973781i	$-0.573052\pi$
$421$	11.5680	−	7.43431i	0.563790	−	0.362326i	0.791280	+	0.611455i	$0.209415\pi$
$422$	−10.8975	−	23.8621i	−0.530480	−	1.16159i
$423$	4.79074	+	5.52881i	0.232934	+	0.268820i
$424$	−5.65574	−	3.63472i	−0.274667	−	0.176518i
$425$	4.93383	−	34.3156i	0.239326	−	1.66455i
$426$	−2.05793	+	14.3132i	−0.0997071	+	0.693478i
$427$	−6.19104	−	3.97874i	−0.299605	−	0.192545i
$428$	−3.00467	−	3.46758i	−0.145236	−	0.167612i
$429$	−21.4123	−	46.8864i	−1.03380	−	2.26370i
$430$	−29.3508	+	18.8626i	−1.41542	+	0.909637i
$431$	6.36599	+	1.86922i	0.306639	+	0.0900373i	0.431432	−	0.902146i	$-0.358009\pi$
$431$	6.36599	+	1.86922i	0.306639	+	0.0900373i	−0.124793	+	0.992183i	$0.539827\pi$
$432$	2.59053	−	2.98963i	0.124637	−	0.143839i
$433$	−8.21455	+	2.41201i	−0.394766	+	0.115914i	−0.473090	−	0.881014i	$-0.656861\pi$
$433$	−8.21455	+	2.41201i	−0.394766	+	0.115914i	0.0783236	+	0.996928i	$0.475043\pi$
$434$	0.704600	−	1.54286i	0.0338219	−	0.0740596i
$435$	−6.85051	−	47.6463i	−0.328457	−	2.28447i
$436$	−17.2464			−0.825952
$437$	15.1162	−	16.6336i	0.723107	−	0.795694i
$438$	−35.4662			−1.69464
$439$	3.99371	+	27.7769i	0.190609	+	1.32572i	0.830400	+	0.557168i	$0.188112\pi$
$439$	3.99371	+	27.7769i	0.190609	+	1.32572i	−0.639790	+	0.768550i	$0.720979\pi$
$440$	−4.97435	+	10.8923i	−0.237143	+	0.519271i
$441$	−4.26914	+	1.25353i	−0.203292	+	0.0596920i
$442$	−16.0811	+	18.5586i	−0.764899	+	0.882740i
$443$	5.73644	+	1.68437i	0.272547	+	0.0800269i	0.415150	−	0.909753i	$-0.363729\pi$
$443$	5.73644	+	1.68437i	0.272547	+	0.0800269i	−0.142603	+	0.989780i	$0.545547\pi$
$444$	−20.7989	+	13.3667i	−0.987073	+	0.634353i
$445$	8.90197	+	19.4926i	0.421994	+	0.924037i
$446$	−1.56714	−	1.80858i	−0.0742064	−	0.0856387i
$447$	−28.6864	−	18.4356i	−1.35682	−	0.871974i
$448$	−0.142315	+	0.989821i	−0.00672374	+	0.0467647i
$449$	−2.84484	+	19.7863i	−0.134256	+	0.933773i	0.805662	+	0.592375i	$0.201810\pi$
$449$	−2.84484	+	19.7863i	−0.134256	+	0.933773i	−0.939919	+	0.341398i	$0.889100\pi$
$450$	30.0959	+	19.3415i	1.41873	+	0.911765i
$451$	6.32872	+	7.30373i	0.298008	+	0.343919i
$452$	3.32498	+	7.28068i	0.156394	+	0.342454i
$453$	50.0477	−	32.1637i	2.35145	−	1.51118i
$454$	−9.82065	−	2.88360i	−0.460906	−	0.135334i
$455$	13.4682	−	15.5431i	0.631398	−	0.728673i
$456$	12.2733	−	3.60375i	0.574748	−	0.168761i
$457$	−10.3656	+	22.6974i	−0.484881	+	1.06174i	0.496211	+	0.868202i	$0.334724\pi$
$457$	−10.3656	+	22.6974i	−0.484881	+	1.06174i	−0.981092	+	0.193540i	$0.938003\pi$
$458$	−1.06533	−	7.40951i	−0.0497794	−	0.346224i
$459$	17.0566			0.796133
$460$	2.05872	+	17.1957i	0.0959883	+	0.801754i
$461$	−16.3493			−0.761464			−0.380732	−	0.924686i	$-0.624328\pi$
$461$	−16.3493			−0.761464			−0.380732	+	0.924686i	$0.624328\pi$
$462$	−1.28801	−	8.95827i	−0.0599234	−	0.416777i
$463$	−1.79721	+	3.93533i	−0.0835232	+	0.182890i	−0.946785	−	0.321865i	$-0.895690\pi$
$463$	−1.79721	+	3.93533i	−0.0835232	+	0.182890i	0.863262	+	0.504756i	$0.168417\pi$
$464$	4.68606	−	1.37595i	0.217545	−	0.0638770i
$465$	10.9475	−	12.6341i	0.507679	−	0.585893i
$466$	−6.16786	−	1.81105i	−0.285721	−	0.0838952i
$467$	29.3524	−	18.8636i	1.35827	−	0.872904i	0.360069	−	0.932926i	$-0.382753\pi$
$467$	29.3524	−	18.8636i	1.35827	−	0.872904i	0.998197	+	0.0600214i	$0.0191169\pi$
$468$	−10.5267	−	23.0504i	−0.486599	−	1.06550i
$469$	6.14353	+	7.09001i	0.283682	+	0.327386i
$470$	−4.99492	−	3.21004i	−0.230399	−	0.148068i
$471$	2.40695	−	16.7407i	0.110907	−	0.771372i
$472$	0.206578	−	1.43678i	0.00950853	−	0.0661333i
$473$	26.9514	+	17.3206i	1.23923	+	0.796403i
$474$	−18.1129	−	20.9034i	−0.831953	−	0.960125i
$475$	15.6539	+	34.2772i	0.718250	+	1.57275i
$476$	−3.62727	+	2.33110i	−0.166256	+	0.106846i
$477$	28.7014	+	8.42749i	1.31415	+	0.385868i
$478$	8.06304	−	9.30525i	0.368795	−	0.425612i
$479$	12.8343	−	3.76850i	0.586415	−	0.172187i	0.0249517	−	0.999689i	$-0.492057\pi$
$479$	12.8343	−	3.76850i	0.586415	−	0.172187i	0.561463	+	0.827502i	$0.310239\pi$
$480$	−4.09439	+	8.96545i	−0.186882	+	0.409215i
$481$	7.34206	+	51.0651i	0.334769	+	2.32837i
$482$	−15.8143			−0.720321
$483$	−8.33554	−	10.0923i	−0.379280	−	0.459215i
$484$	−0.00449125			−0.000204148
$485$	1.92944	+	13.4195i	0.0876113	+	0.609350i
$486$	7.82255	−	17.1290i	0.354838	−	0.776987i
$487$	−27.1492	+	7.97173i	−1.23025	+	0.361234i	−0.831344	−	0.555759i	$-0.812428\pi$
$487$	−27.1492	+	7.97173i	−1.23025	+	0.361234i	−0.398905	+	0.916992i	$0.630610\pi$
$488$	4.81932	−	5.56179i	0.218160	−	0.251770i
$489$	−21.3179	−	6.25950i	−0.964029	−	0.283064i
$490$	3.03790	−	1.95234i	0.137238	−	0.0881977i
$491$	−9.23157	−	20.2143i	−0.416615	−	0.912259i	−0.995312	−	0.0967168i	$-0.969166\pi$
$491$	−9.23157	−	20.2143i	−0.416615	−	0.912259i	0.578697	−	0.815543i	$-0.303561\pi$
$492$	5.20916	+	6.01169i	0.234847	+	0.271028i
$493$	17.7152	+	11.3849i	0.797852	+	0.512748i
$494$	3.79859	−	26.4198i	0.170906	−	1.18868i
$495$	7.58234	−	52.7363i	0.340801	−	2.37032i
$496$	1.42688	+	0.917000i	0.0640688	+	0.0411745i
$497$	3.46952	+	4.00405i	0.155629	+	0.179606i
$498$	14.7206	+	32.2336i	0.659645	+	1.44442i
$499$	11.8813	−	7.63567i	0.531881	−	0.341819i	−0.246975	−	0.969022i	$-0.579437\pi$
$499$	11.8813	−	7.63567i	0.531881	−	0.341819i	0.778856	+	0.627202i	$0.215800\pi$
$500$	−10.5349	−	3.09332i	−0.471135	−	0.138338i
$501$	−5.82761	+	6.72542i	−0.260358	+	0.300470i
$502$	11.4190	−	3.35291i	0.509654	−	0.149648i
$503$	−4.81758	+	10.5490i	−0.214805	+	0.470358i	−0.986107	−	0.166112i	$-0.946879\pi$
$503$	−4.81758	+	10.5490i	−0.214805	+	0.470358i	0.771302	+	0.636470i	$0.219606\pi$
$504$	−0.633211	−	4.40408i	−0.0282055	−	0.196173i
$505$	1.39274			0.0619759
$506$	13.5777	−	8.27898i	0.603605	−	0.368045i
$507$	−53.0477			−2.35593
$508$	−2.51559	−	17.4963i	−0.111611	−	0.776272i
$509$	3.58025	−	7.83965i	0.158692	−	0.347486i	−0.813539	−	0.581510i	$-0.802462\pi$
$509$	3.58025	−	7.83965i	0.158692	−	0.347486i	0.972231	+	0.234024i	$0.0751894\pi$
$510$	−40.7757	+	11.9728i	−1.80558	+	0.530165i
$511$	−8.50951	+	9.82049i	−0.376438	+	0.434433i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	−15.5964	+	10.0232i	−0.688598	+	0.442535i
$514$	1.07387	+	2.35145i	0.0473664	+	0.103718i
$515$	4.86121	+	5.61014i	0.214211	+	0.247212i
$516$	22.1837	+	14.2566i	0.976582	+	0.627611i
$517$	−0.775913	+	5.39659i	−0.0341246	+	0.237342i
$518$	−1.28915	+	8.96625i	−0.0566421	+	0.393955i
$519$	−34.8996	−	22.4286i	−1.53192	−	0.984506i
$520$	13.4682	+	15.5431i	0.590619	+	0.681611i
$521$	1.19514	+	2.61700i	0.0523602	+	0.114653i	0.934004	−	0.357263i	$-0.116290\pi$
$521$	1.19514	+	2.61700i	0.0523602	+	0.114653i	−0.881644	+	0.471916i	$0.843563\pi$
$522$	−18.2807	+	11.7483i	−0.800122	+	0.514207i
$523$	−1.87025	−	0.549154i	−0.0817802	−	0.0240128i	0.240586	−	0.970628i	$-0.422660\pi$
$523$	−1.87025	−	0.549154i	−0.0817802	−	0.0240128i	−0.322367	+	0.946615i	$0.604478\pi$
$524$	9.78033	−	11.2871i	0.427256	−	0.493079i
$525$	21.0564	−	6.18270i	0.918975	−	0.269835i
$526$	−5.23186	+	11.4562i	−0.228120	+	0.499513i
$527$	1.04079	+	7.23886i	0.0453375	+	0.315330i
$528$	9.05039			0.393868
$529$	10.5328	−	20.4465i	0.457949	−	0.888978i
$530$	−24.2778			−1.05456
$531$	0.919143	+	6.39278i	0.0398874	+	0.277423i
$532$	1.94689	−	4.26309i	0.0844082	−	0.184828i
$533$	15.9263	−	4.67638i	0.689844	−	0.202556i
$534$	10.6063	−	12.2404i	0.458981	−	0.529693i
$535$	−15.8978	−	4.66802i	−0.687322	−	0.201816i
$536$	−7.89216	+	5.07198i	−0.340889	+	0.219076i
$537$	−3.03233	−	6.63987i	−0.130855	−	0.286532i
$538$	9.41193	+	10.8619i	0.405777	+	0.468292i
$539$	−2.78955	−	1.79274i	−0.120155	−	0.0772186i
$540$	2.03299	−	14.1398i	0.0874861	−	0.608479i
$541$	4.85157	−	33.7434i	0.208585	−	1.45074i	−0.569192	−	0.822204i	$-0.692744\pi$
$541$	4.85157	−	33.7434i	0.208585	−	1.45074i	0.777778	−	0.628539i	$-0.216347\pi$
$542$	−16.8927	−	10.8563i	−0.725603	−	0.466317i
$543$	33.1088	+	38.2096i	1.42083	+	1.63973i
$544$	−1.79116	−	3.92210i	−0.0767954	−	0.168159i
$545$	−52.3928	+	33.6708i	−2.24426	+	1.44230i
$546$	−14.9147	−	4.37936i	−0.638291	−	0.187419i
$547$	−0.632257	+	0.729663i	−0.0270333	+	0.0311981i	−0.769105	−	0.639122i	$-0.779298\pi$
$547$	−0.632257	+	0.729663i	−0.0270333	+	0.0311981i	0.742072	+	0.670320i	$0.233843\pi$
$548$	−20.5202	+	6.02529i	−0.876581	+	0.257387i
$549$	−13.6025	+	29.7852i	−0.580539	+	1.27120i
$550$	3.79437	+	26.3904i	0.161792	+	1.12529i
$551$	−22.8889			−0.975099
$552$	11.1758	−	6.81442i	0.475675	−	0.290041i
$553$	−10.1340			−0.430940
$554$	4.06449	+	28.2692i	0.172684	+	1.20104i
$555$	−37.0888	+	81.2131i	−1.57433	+	3.44731i
$556$	13.2506	−	3.89073i	0.561951	−	0.165004i
$557$	11.7127	−	13.5172i	0.496283	−	0.572742i	−0.451250	−	0.892397i	$-0.649022\pi$
$557$	11.7127	−	13.5172i	0.496283	−	0.572742i	0.947534	+	0.319656i	$0.103567\pi$
$558$	−7.24104	−	2.12616i	−0.306538	−	0.0900075i
$559$	46.2900	−	29.7488i	1.95786	−	1.25824i
$560$	1.50013	+	3.28483i	0.0633921	+	0.138809i
$561$	25.5546	+	29.4916i	1.07892	+	1.24514i
$562$	−23.8034	−	15.2975i	−1.00408	−	0.645286i
$563$	0.185078	−	1.28724i	0.00780009	−	0.0542508i	−0.985550	−	0.169387i	$-0.945821\pi$
$563$	0.185078	−	1.28724i	0.00780009	−	0.0542508i	0.993350	+	0.115136i	$0.0367304\pi$
$564$	−0.638653	+	4.44193i	−0.0268922	+	0.187039i
$565$	24.3153	+	15.6265i	1.02295	+	0.657412i
$566$	−10.1096	−	11.6671i	−0.424938	−	0.490404i
$567$	−1.05981	−	2.32067i	−0.0445079	−	0.0974588i
$568$	−4.45705	+	2.86437i	−0.187014	+	0.120187i
$569$	14.9139	+	4.37912i	0.625223	+	0.183582i	0.578972	−	0.815348i	$-0.303454\pi$
$569$	14.9139	+	4.37912i	0.625223	+	0.183582i	0.0462518	+	0.998930i	$0.485272\pi$
$570$	30.2492	−	34.9094i	1.26700	−	1.46220i
$571$	−36.5264	+	10.7251i	−1.52858	+	0.448832i	−0.934616	−	0.355658i	$-0.884257\pi$
$571$	−36.5264	+	10.7251i	−1.52858	+	0.448832i	−0.593966	+	0.804490i	$0.702439\pi$
$572$	7.84519	−	17.1786i	0.328024	−	0.718272i
$573$	−5.74529	−	39.9594i	−0.240013	−	1.66933i
$574$	2.91447			0.121647
$575$	24.5559	+	29.7311i	1.02405	+	1.23987i
$576$	4.44937			0.185390
$577$	2.77337	+	19.2892i	0.115457	+	0.803020i	0.962458	+	0.271430i	$0.0874965\pi$
$577$	2.77337	+	19.2892i	0.115457	+	0.803020i	−0.847001	+	0.531591i	$0.821594\pi$
$578$	0.660972	−	1.44733i	0.0274928	−	0.0602009i
$579$	−24.7300	+	7.26140i	−1.02775	+	0.301773i
$580$	11.5495	−	13.3288i	0.479565	−	0.553448i
$581$	12.4573	+	3.65780i	0.516817	+	0.151751i
$582$	8.62027	−	5.53991i	0.357322	−	0.229637i
$583$	9.26089	+	20.2785i	0.383547	+	0.839850i
$584$	−8.50951	−	9.82049i	−0.352126	−	0.406375i
$585$	−76.9814	−	49.4729i	−3.18279	−	2.04545i
$586$	−0.319612	+	2.22295i	−0.0132030	+	0.0918292i
$587$	1.05618	−	7.34592i	0.0435934	−	0.303199i	−0.956347	−	0.292235i	$-0.905601\pi$
$587$	1.05618	−	7.34592i	0.0435934	−	0.303199i	0.999940	−	0.0109636i	$-0.00348989\pi$
$588$	−2.29608	−	1.47560i	−0.0946887	−	0.0608527i
$589$	−5.20556	−	6.00754i	−0.214491	−	0.247536i
$590$	−2.17753	−	4.76812i	−0.0896473	−	0.196300i
$591$	35.1744	−	22.6052i	1.44688	−	0.929856i
$592$	−8.69152	−	2.55206i	−0.357219	−	0.104889i
$593$	−31.4359	+	36.2789i	−1.29092	+	1.48980i	−0.517848	+	0.855473i	$0.673267\pi$
$593$	−31.4359	+	36.2789i	−1.29092	+	1.48980i	−0.773068	+	0.634324i	$0.781279\pi$
$594$	−12.5860	+	3.69559i	−0.516411	+	0.151632i
$595$	−6.46817	+	14.1633i	−0.265169	+	0.580640i
$596$	−1.77803	−	12.3665i	−0.0728309	−	0.506550i
$597$	18.9340			0.774916
$598$	−3.24686	−	27.1198i	−0.132774	−	1.10901i
$599$	−19.7297			−0.806133			−0.403067	−	0.915171i	$-0.632056\pi$
$599$	−19.7297			−0.806133			−0.403067	+	0.915171i	$0.632056\pi$
$600$	3.12314	+	21.7219i	0.127502	+	0.886794i
$601$	−18.1016	+	39.6369i	−0.738379	+	1.61682i	0.0478244	+	0.998856i	$0.484771\pi$
$601$	−18.1016	+	39.6369i	−0.738379	+	1.61682i	−0.786203	+	0.617968i	$0.787956\pi$
$602$	9.27019	−	2.72197i	0.377825	−	0.110939i
$603$	27.3348	−	31.5461i	1.11316	−	1.28466i
$604$	20.9141	+	6.14093i	0.850983	+	0.249871i
$605$	−0.0136440	+	0.00876845i	−0.000554706	+	0.000356488i
$606$	−0.437285	−	0.957520i	−0.0177635	−	0.0388966i
$607$	13.3615	+	15.4200i	0.542326	+	0.625877i	0.959078	−	0.283143i	$-0.0913771\pi$
$607$	13.3615	+	15.4200i	0.542326	+	0.625877i	−0.416752	+	0.909020i	$0.636832\pi$
$608$	3.94262	+	2.53377i	0.159894	+	0.102758i
$609$	−1.89704	+	13.1942i	−0.0768719	+	0.534656i
$610$	3.78210	−	26.3051i	0.153133	−	1.06506i
$611$	7.87763	+	5.06265i	0.318695	+	0.204813i
$612$	12.5632	+	14.4987i	0.507837	+	0.586075i
$613$	−7.68875	−	16.8360i	−0.310546	−	0.680000i	0.688428	−	0.725305i	$-0.258301\pi$
$613$	−7.68875	−	16.8360i	−0.310546	−	0.680000i	−0.998973	+	0.0453051i	$0.985574\pi$
$614$	0.596905	−	0.383608i	0.0240891	−	0.0154811i
$615$	27.5618	+	8.09287i	1.11140	+	0.326336i
$616$	2.17148	−	2.50603i	0.0874916	−	0.100971i
$617$	−24.3378	+	7.14622i	−0.979803	+	0.287696i	−0.732143	−	0.681151i	$-0.761480\pi$
$617$	−24.3378	+	7.14622i	−0.979803	+	0.287696i	−0.247660	+	0.968847i	$0.579662\pi$
$618$	2.33073	−	5.10358i	0.0937555	−	0.205296i
$619$	−3.80527	−	26.4663i	−0.152947	−	1.06377i	−0.911246	−	0.411862i	$-0.864879\pi$
$619$	−3.80527	−	26.4663i	−0.152947	−	1.06377i	0.758299	−	0.651906i	$-0.226031\pi$
$620$	6.12501			0.245986
$621$	−12.7592	+	14.0400i	−0.512010	+	0.563407i
$622$	18.9805			0.761050
$623$	−0.844515	−	5.87373i	−0.0338348	−	0.235326i
$624$	6.45737	−	14.1397i	0.258502	−	0.566039i
$625$	0.530733	−	0.155837i	0.0212293	−	0.00623349i
$626$	10.4200	−	12.0253i	0.416466	−	0.480627i
$627$	−40.6975	−	11.9499i	−1.62530	−	0.477231i
$628$	5.21296	−	3.35017i	0.208020	−	0.133686i
$629$	−16.2252	−	35.5281i	−0.646940	−	1.41660i
$630$	−10.5219	−	12.1429i	−0.419203	−	0.483786i
$631$	21.0875	+	13.5521i	0.839481	+	0.539502i	0.888278	−	0.459307i	$-0.151902\pi$
$631$	21.0875	+	13.5521i	0.839481	+	0.539502i	−0.0487965	+	0.998809i	$0.515539\pi$
$632$	1.44221	−	10.0308i	0.0573682	−	0.399004i
$633$	−10.1895	+	70.8695i	−0.404996	+	2.81681i
$634$	5.49913	+	3.53408i	0.218398	+	0.140356i
$635$	−41.8008	−	48.2407i	−1.65881	−	1.91437i
$636$	7.62263	+	16.6912i	0.302257	+	0.661850i
$637$	−4.79116	+	3.07909i	−0.189833	+	0.121998i
$638$	−15.5387	−	4.56258i	−0.615184	−	0.180634i
$639$	15.4372	−	17.8155i	0.610686	−	0.704769i
$640$	−3.46488	+	1.01738i	−0.136962	+	0.0402155i
$641$	5.04774	−	11.0530i	0.199374	−	0.436567i	−0.783366	−	0.621560i	$-0.786499\pi$
$641$	5.04774	−	11.0530i	0.199374	−	0.436567i	0.982740	+	0.184993i	$0.0592263\pi$
$642$	1.78221	+	12.3955i	0.0703382	+	0.489213i
$643$	17.7362			0.699446			0.349723	−	0.936853i	$-0.386276\pi$
$643$	17.7362			0.699446			0.349723	+	0.936853i	$0.386276\pi$
$644$	0.794555	−	4.72955i	0.0313098	−	0.186371i
$645$	95.2255			3.74950
$646$	2.87582	+	20.0017i	0.113148	+	0.786958i
$647$	−19.7580	+	43.2641i	−0.776769	+	1.70089i	−0.0656205	+	0.997845i	$0.520903\pi$
$647$	−19.7580	+	43.2641i	−0.776769	+	1.70089i	−0.711148	+	0.703042i	$0.751825\pi$
$648$	2.44787	−	0.718760i	0.0961615	−	0.0282356i
$649$	−3.15203	+	3.63764i	−0.123728	+	0.142790i
$650$	43.9377	+	12.9013i	1.72338	+	0.506029i
$651$	−3.89446	+	2.50282i	−0.152636	+	0.0980931i
$652$	−3.38162	−	7.40472i	−0.132435	−	0.289991i
$653$	13.7924	+	15.9173i	0.539738	+	0.622891i	0.958461	−	0.285223i	$-0.0920676\pi$
$653$	13.7924	+	15.9173i	0.539738	+	0.622891i	−0.418723	+	0.908114i	$0.637522\pi$
$654$	39.5990	+	25.4488i	1.54844	+	0.995125i
$655$	7.67541	−	53.3836i	0.299903	−	2.08587i
$656$	−0.414772	+	2.88480i	−0.0161941	+	0.112633i
$657$	48.6386	+	31.2581i	1.89757	+	1.21950i
$658$	1.07672	+	1.24261i	0.0419750	+	0.0484418i
$659$	0.228094	+	0.499456i	0.00888528	+	0.0194560i	0.914023	−	0.405663i	$-0.132959\pi$
$659$	0.228094	+	0.499456i	0.00888528	+	0.0194560i	−0.905137	+	0.425119i	$0.860232\pi$
$660$	27.4942	−	17.6694i	1.07021	−	0.687782i
$661$	−5.34331	−	1.56894i	−0.207831	−	0.0610246i	0.176160	−	0.984362i	$-0.443632\pi$
$661$	−5.34331	−	1.56894i	−0.207831	−	0.0610246i	−0.383991	+	0.923337i	$0.625451\pi$
$662$	−3.85973	+	4.45437i	−0.150013	+	0.173124i
$663$	64.3084	−	18.8827i	2.49753	−	0.733341i
$664$	−5.39343	+	11.8100i	−0.209306	+	0.458316i
$665$	−2.40855	−	16.7518i	−0.0933995	−	0.649608i
$666$	40.3044			1.56176
$667$	−22.6233	+	6.06568i	−0.875977	+	0.234864i
$668$	−3.26048			−0.126152
$669$	0.929543	+	6.46512i	0.0359382	+	0.249956i
$670$	−14.0734	+	30.8164i	−0.543701	+	1.19054i
$671$	−23.4146	+	6.87513i	−0.903909	+	0.265412i
$672$	1.78735	−	2.06271i	0.0689484	−	0.0795707i
$673$	−35.2629	−	10.3541i	−1.35928	−	0.399122i	−0.480773	−	0.876845i	$-0.659644\pi$
$673$	−35.2629	−	10.3541i	−1.35928	−	0.399122i	−0.878510	+	0.477723i	$0.841462\pi$
$674$	22.6661	−	14.5666i	0.873064	−	0.561084i
$675$	−13.2131	−	28.9325i	−0.508571	−	1.11361i
$676$	−12.7279	−	14.6887i	−0.489533	−	0.564951i
$677$	−19.9133	−	12.7975i	−0.765332	−	0.491849i	0.0988044	−	0.995107i	$-0.468498\pi$
$677$	−19.9133	−	12.7975i	−0.765332	−	0.491849i	−0.864136	+	0.503258i	$0.832135\pi$
$678$	3.10897	−	21.6234i	0.119399	−	0.830440i
$679$	0.534299	−	3.71613i	0.0205045	−	0.142612i
$680$	−13.0986	−	8.41799i	−0.502310	−	0.322815i
$681$	18.2939	+	21.1123i	0.701025	+	0.809026i
$682$	−2.33642	−	5.11604i	−0.0894660	−	0.195903i
$683$	24.4035	−	15.6831i	0.933772	−	0.600099i	0.0171497	−	0.999853i	$-0.494541\pi$
$683$	24.4035	−	15.6831i	0.933772	−	0.600099i	0.916622	+	0.399754i	$0.130904\pi$
$684$	−20.0078	−	5.87481i	−0.765016	−	0.224629i
$685$	−50.5750	+	58.3667i	−1.93237	+	2.23008i
$686$	−0.959493	+	0.281733i	−0.0366336	+	0.0107566i
$687$	−8.48740	+	18.5848i	−0.323814	+	0.709055i
$688$	1.37498	+	9.56321i	0.0524207	+	0.364594i
$689$	38.2892			1.45870
$690$	20.6470	−	42.5206i	0.786018	−	1.61873i
$691$	−13.5473			−0.515362			−0.257681	−	0.966230i	$-0.582958\pi$
$691$	−13.5473			−0.515362			−0.257681	+	0.966230i	$0.582958\pi$
$692$	−2.16313	−	15.0449i	−0.0822301	−	0.571923i
$693$	−6.12898	+	13.4206i	−0.232821	+	0.509806i
$694$	4.79982	−	1.40935i	0.182199	−	0.0534984i
$695$	32.6580	−	37.6893i	1.23879	−	1.42964i
$696$	−12.7899	−	3.75546i	−0.484801	−	0.142350i
$697$	−10.5716	+	6.79392i	−0.400426	+	0.257338i
$698$	−6.84629	−	14.9913i	−0.259136	−	0.567428i
$699$	11.4895	+	13.2596i	0.434573	+	0.501524i
$700$	6.76408	+	4.34701i	0.255658	+	0.164301i
$701$	−1.20755	+	8.39870i	−0.0456086	+	0.317214i	0.954227	+	0.299083i	$0.0966808\pi$
$701$	−1.20755	+	8.39870i	−0.0456086	+	0.317214i	−0.999836	+	0.0181313i	$0.994228\pi$
$702$	−3.20629	+	22.3002i	−0.121014	+	0.841668i
$703$	35.7141	+	22.9520i	1.34698	+	0.865653i
$704$	2.17148	+	2.50603i	0.0818409	+	0.0944494i
$705$	6.73200	+	14.7410i	0.253542	+	0.555179i
$706$	8.12818	−	5.22366i	0.305908	−	0.196595i
$707$	−0.370053	−	0.108657i	−0.0139173	−	0.00408648i
$708$	−2.59444	+	2.99414i	−0.0975049	+	0.112527i
$709$	−9.41555	+	2.76466i	−0.353608	+	0.103829i	−0.453712	−	0.891148i	$-0.649901\pi$
$709$	−9.41555	+	2.76466i	−0.353608	+	0.103829i	0.100104	+	0.994977i	$0.468082\pi$
$710$	−7.94785	+	17.4034i	−0.298278	+	0.653137i
$711$	6.41694	+	44.6308i	0.240654	+	1.67379i
$712$	5.93413			0.222391
$713$	−6.73719	−	4.55833i	−0.252310	−	0.170711i
$714$	11.7683			0.440416
$715$	−9.70550	−	67.5033i	−0.362965	−	2.52448i
$716$	1.11101	−	2.43276i	0.0415203	−	0.0909167i
$717$	−32.2442	+	9.46775i	−1.20418	+	0.353580i
$718$	−15.5401	+	17.9342i	−0.579950	+	0.669298i
$719$	−11.9974	−	3.52275i	−0.447427	−	0.131376i	0.0502541	−	0.998736i	$-0.483997\pi$
$719$	−11.9974	−	3.52275i	−0.447427	−	0.131376i	−0.497681	+	0.867360i	$0.665815\pi$
$720$	13.5167	−	8.68669i	0.503739	−	0.323734i
$721$	−0.853948	−	1.86988i	−0.0318027	−	0.0696382i
$722$	−1.94118	−	2.24024i	−0.0722433	−	0.0833733i
$723$	36.3108	+	23.3356i	1.35041	+	0.867858i
$724$	−2.63624	+	18.3354i	−0.0979751	+	0.681431i
$725$	5.58854	−	38.8691i	0.207553	−	1.44356i
$726$	0.0103123	+	0.00662729i	0.000382724	+	0.000245962i
$727$	9.41270	+	10.8628i	0.349098	+	0.402880i	0.902958	−	0.429730i	$-0.141391\pi$
$727$	9.41270	+	10.8628i	0.349098	+	0.402880i	−0.553860	+	0.832610i	$0.686846\pi$
$728$	−2.36590	−	5.18059i	−0.0876859	−	0.192005i
$729$	−36.7981	+	23.6487i	−1.36289	+	0.875878i
$730$	−45.0240	−	13.2202i	−1.66641	−	0.489303i
$731$	−27.2803	+	31.4831i	−1.00900	+	1.16444i
$732$	−19.2725	+	5.65892i	−0.712332	+	0.209160i
$733$	7.66442	−	16.7827i	0.283092	−	0.619884i	−0.713654	−	0.700499i	$-0.752961\pi$
$733$	7.66442	−	16.7827i	0.283092	−	0.619884i	0.996745	+	0.0806144i	$0.0256882\pi$
$734$	−0.848502	−	5.90146i	−0.0313188	−	0.217827i
$735$	−9.85613			−0.363549
$736$	4.56834	+	1.45955i	0.168391	+	0.0537998i
$737$	31.1083			1.14589
$738$	−1.84547	−	12.8356i	−0.0679328	−	0.472483i
$739$	−12.3473	+	27.0368i	−0.454203	+	0.994565i	0.534568	+	0.845125i	$0.320474\pi$
$739$	−12.3473	+	27.0368i	−0.454203	+	0.994565i	−0.988771	+	0.149440i	$0.952253\pi$
$740$	−31.3865	+	9.21590i	−1.15379	+	0.338783i
$741$	−47.7068	+	55.0566i	−1.75255	+	2.02256i
$742$	6.45067	+	1.89409i	0.236811	+	0.0695341i
$743$	6.67877	−	4.29218i	0.245020	−	0.157465i	−0.412367	−	0.911018i	$-0.635298\pi$
$743$	6.67877	−	4.29218i	0.245020	−	0.157465i	0.657387	+	0.753553i	$0.271662\pi$
$744$	−1.92310	−	4.21101i	−0.0705044	−	0.154383i
$745$	−29.5450	−	34.0968i	−1.08245	−	1.24921i
$746$	−16.7007	−	10.7329i	−0.611456	−	0.392959i
$747$	8.22113	−	57.1792i	0.300796	−	2.09208i
$748$	−2.03475	+	14.1520i	−0.0743977	+	0.517448i
$749$	3.85989	+	2.48060i	0.141037	+	0.0906393i
$750$	19.6244	+	22.6478i	0.716583	+	0.826980i
$751$	−1.69045	−	3.70157i	−0.0616854	−	0.135072i	0.876279	−	0.481805i	$-0.160018\pi$
$751$	−1.69045	−	3.70157i	−0.0616854	−	0.135072i	−0.937964	+	0.346732i	$0.887291\pi$
$752$	−1.38319	+	0.888923i	−0.0504398	+	0.0324157i
$753$	−31.1664	−	9.15129i	−1.13577	−	0.333491i
$754$	−18.2150	+	21.0212i	−0.663350	+	0.765547i
$755$	75.5242	−	22.1759i	2.74861	−	0.807063i
$756$	−1.64332	+	3.59836i	−0.0597669	+	0.130871i
$757$	3.17940	+	22.1132i	0.115557	+	0.803719i	0.962353	+	0.271801i	$0.0876193\pi$
$757$	3.17940	+	22.1132i	0.115557	+	0.803719i	−0.846796	+	0.531918i	$0.821472\pi$
$758$	−13.3082			−0.483375
$759$	−43.3920	−	1.02615i	−1.57503	−	0.0372469i
$760$	16.9241			0.613901
$761$	−4.78724	−	33.2960i	−0.173537	−	1.20698i	−0.871337	−	0.490686i	$-0.836746\pi$
$761$	−4.78724	−	33.2960i	−0.173537	−	1.20698i	0.697799	−	0.716293i	$-0.254163\pi$
$762$	−20.0415	+	43.8848i	−0.726028	+	1.58978i
$763$	16.5478	−	4.85887i	0.599070	−	0.175903i
$764$	9.68614	−	11.1784i	0.350432	−	0.404420i
$765$	66.4722	+	19.5180i	2.40331	+	0.705674i
$766$	8.07858	−	5.19179i	0.291891	−	0.187587i
$767$	3.43424	+	7.51993i	0.124003	+	0.271529i
$768$	1.78735	+	2.06271i	0.0644953	+	0.0744316i
$769$	15.2326	+	9.78943i	0.549303	+	0.353016i	0.785668	−	0.618649i	$-0.212320\pi$
$769$	15.2326	+	9.78943i	0.549303	+	0.353016i	−0.236364	+	0.971664i	$0.575956\pi$
$770$	1.70414	−	11.8525i	0.0614128	−	0.427136i
$771$	1.00411	−	6.98371i	0.0361620	−	0.251512i
$772$	−7.94420	−	5.10543i	−0.285918	−	0.183748i
$773$	9.82196	+	11.3351i	0.353271	+	0.407697i	0.904374	−	0.426741i	$-0.140338\pi$
$773$	9.82196	+	11.3351i	0.353271	+	0.407697i	−0.551103	+	0.834437i	$0.685793\pi$
$774$	−17.8578	−	39.1031i	−0.641885	−	1.40553i
$775$	11.4728	−	7.37311i	0.412115	−	0.264850i
$776$	3.60227	+	1.05772i	0.129314	+	0.0379700i
$777$	16.1906	−	18.6849i	0.580834	−	0.670319i
$778$	8.23153	−	2.41700i	0.295115	−	0.0866535i
$779$	5.67413	−	12.4246i	0.203297	−	0.445158i
$780$	−7.98859	−	55.5619i	−0.286037	−	1.98943i
$781$	17.5683			0.628642
$782$	8.14302	+	19.0075i	0.291194	+	0.679709i
$783$	19.3199			0.690438
$784$	−0.142315	−	0.989821i	−0.00508267	−	0.0353508i
$785$	9.29580	−	20.3550i	0.331781	−	0.726500i
$786$	−39.1117	+	11.4842i	−1.39507	+	0.409629i
$787$	10.0221	−	11.5662i	0.357250	−	0.412289i	−0.548466	−	0.836173i	$-0.684788\pi$
$787$	10.0221	−	11.5662i	0.357250	−	0.412289i	0.905717	+	0.423884i	$0.139334\pi$
$788$	14.6988	+	4.31596i	0.523624	+	0.153750i
$789$	28.9175	−	18.5841i	1.02949	−	0.661613i
$790$	−15.2023	−	33.2883i	−0.540872	−	1.18434i
$791$	−5.24150	−	6.04901i	−0.186366	−	0.215078i
$792$	−12.4118	−	7.97655i	−0.441032	−	0.283434i
$793$	−5.96486	+	41.4865i	−0.211818	+	1.47323i
$794$	−5.03528	+	35.0211i	−0.178695	+	1.24285i
$795$	55.7437	+	35.8243i	1.97703	+	1.27056i
$796$	4.54288	+	5.24276i	0.161018	+	0.185825i
$797$	−9.17470	−	20.0898i	−0.324984	−	0.711617i	0.674664	−	0.738125i	$-0.264288\pi$
$797$	−9.17470	−	20.0898i	−0.324984	−	0.711617i	−0.999649	+	0.0265082i	$0.991561\pi$
$798$	−10.7608	+	6.91555i	−0.380929	+	0.244808i
$799$	−6.80220	−	1.99731i	−0.240645	−	0.0706597i
$800$	−5.26539	+	6.07659i	−0.186160	+	0.214840i
$801$	−25.3336	+	7.43863i	−0.895120	+	0.262831i
$802$	0.951157	−	2.08274i	0.0335865	−	0.0735442i
$803$	6.13216	+	42.6501i	0.216399	+	1.50509i
$804$	25.6052			0.903027
$805$	−6.81992	−	15.9192i	−0.240371	−	0.561077i
$806$	−9.65993			−0.340256
$807$	−5.58264	−	38.8281i	−0.196518	−	1.36681i
$808$	0.160215	−	0.350823i	0.00563636	−	0.0123419i
$809$	10.7161	−	3.14652i	0.376757	−	0.110626i	−0.0878711	−	0.996132i	$-0.528006\pi$
$809$	10.7161	−	3.14652i	0.376757	−	0.110626i	0.464628	+	0.885506i	$0.346188\pi$
$810$	6.03313	−	6.96260i	0.211982	−	0.244641i
$811$	−4.96653	−	1.45831i	−0.174399	−	0.0512081i	0.193367	−	0.981126i	$-0.438059\pi$
$811$	−4.96653	−	1.45831i	−0.174399	−	0.0512081i	−0.367766	+	0.929918i	$0.619877\pi$
$812$	−4.10859	+	2.64043i	−0.144183	+	0.0926610i
$813$	22.7674	+	49.8537i	0.798489	+	1.74845i
$814$	19.6703	+	22.7007i	0.689443	+	0.795660i
$815$	−24.7296	−	15.8927i	−0.866239	−	0.556698i
$816$	−1.67480	+	11.6485i	−0.0586297	+	0.407778i
$817$	6.44400	−	44.8190i	0.225447	−	1.56802i
$818$	12.7213	+	8.17550i	0.444791	+	0.285850i
$819$	16.5944	+	19.1509i	0.579855	+	0.669188i
$820$	4.37208	+	9.57352i	0.152680	+	0.334322i
$821$	−9.46810	+	6.08478i	−0.330439	+	0.212360i	−0.695331	−	0.718690i	$-0.744742\pi$
$821$	−9.46810	+	6.08478i	−0.330439	+	0.212360i	0.364892	+	0.931050i	$0.381106\pi$
$822$	56.0070	+	16.4451i	1.95347	+	0.573590i
$823$	29.4973	−	34.0417i	1.02821	−	1.18662i	0.0459806	−	0.998942i	$-0.485359\pi$
$823$	29.4973	−	34.0417i	1.02821	−	1.18662i	0.982231	−	0.187677i	$-0.0600958\pi$
$824$	1.97238	−	0.579143i	0.0687112	−	0.0201754i
$825$	30.2295	−	66.1934i	1.05246	−	2.30456i
$826$	0.206578	+	1.43678i	0.00718778	+	0.0499921i
$827$	0.0591853			0.00205807			0.00102904	−	0.999999i	$-0.499672\pi$
$827$	0.0591853			0.00205807			0.00102904	+	0.999999i	$0.499672\pi$
$828$	−21.3325	−	0.504477i	−0.741354	−	0.0175318i
$829$	51.8203			1.79980			0.899898	−	0.436101i	$-0.143641\pi$
$829$	51.8203			1.79980			0.899898	+	0.436101i	$0.143641\pi$
$830$	6.67237	+	46.4073i	0.231601	+	1.61082i
$831$	32.3816	−	70.9058i	1.12331	−	2.45970i
$832$	5.46456	−	1.60454i	0.189450	−	0.0556274i
$833$	2.82359	−	3.25860i	0.0978316	−	0.112904i
$834$	−36.1656	−	10.6192i	−1.25231	−	0.367712i
$835$	−9.90502	+	6.36557i	−0.342777	+	0.220290i
$836$	−6.45577	−	14.1362i	−0.223278	−	0.488910i
$837$	4.39388	+	5.07081i	0.151875	+	0.175273i
$838$	22.2740	+	14.3146i	0.769442	+	0.494491i
$839$	4.93705	−	34.3379i	0.170446	−	1.18548i	−0.707499	−	0.706714i	$-0.750177\pi$
$839$	4.93705	−	34.3379i	0.170446	−	1.18548i	0.877945	−	0.478762i	$-0.158914\pi$
$840$	1.40267	−	9.75581i	0.0483968	−	0.336607i
$841$	−4.33042	−	2.78299i	−0.149325	−	0.0959652i
$842$	−9.00494	−	10.3923i	−0.310331	−	0.358141i
$843$	32.0814	+	70.2485i	1.10494	+	2.41949i
$844$	−22.0683	+	14.1825i	−0.759624	+	0.488180i
$845$	−67.3434	−	19.7738i	−2.31668	−	0.680239i
$846$	4.79074	−	5.52881i	0.164709	−	0.190084i
$847$	0.00430932	−	0.00126533i	0.000148070	−	4.34773e-5i
$848$	−2.79283	+	6.11545i	−0.0959063	+	0.210005i
$849$	5.99646	+	41.7063i	0.205798	+	1.43136i
$850$	−34.6684			−1.18912
$851$	41.3821	+	13.2213i	1.41856	+	0.453220i
$852$	14.4604			0.495406
$853$	−6.81098	−	47.3714i	−0.233204	−	1.62197i	−0.684098	−	0.729390i	$-0.739804\pi$
$853$	−6.81098	−	47.3714i	−0.233204	−	1.62197i	0.450894	−	0.892577i	$-0.351105\pi$
$854$	−3.05716	+	6.69425i	−0.104614	+	0.229073i
$855$	−72.2513	+	21.2149i	−2.47094	+	0.725534i
$856$	−3.00467	+	3.46758i	−0.102698	+	0.118519i
$857$	−20.4622	−	6.00825i	−0.698976	−	0.205238i	−0.0871092	−	0.996199i	$-0.527763\pi$
$857$	−20.4622	−	6.00825i	−0.698976	−	0.205238i	−0.611867	+	0.790961i	$0.709581\pi$
$858$	−43.3619	+	27.8670i	−1.48035	+	0.951363i
$859$	6.28235	+	13.7564i	0.214351	+	0.469363i	0.986013	−	0.166670i	$-0.0533014\pi$
$859$	6.28235	+	13.7564i	0.214351	+	0.469363i	−0.771662	+	0.636033i	$0.780574\pi$
$860$	22.8477	+	26.3677i	0.779100	+	0.899129i
$861$	−6.69184	−	4.30059i	−0.228057	−	0.146564i
$862$	0.944222	−	6.56721i	0.0321603	−	0.223680i
$863$	1.05581	−	7.34332i	0.0359402	−	0.249970i	−0.963929	−	0.266161i	$-0.914245\pi$
$863$	1.05581	−	7.34332i	0.0359402	−	0.249970i	0.999869	+	0.0161909i	$0.00515395\pi$
$864$	−3.32787	−	2.13869i	−0.113216	−	0.0727597i
$865$	−35.9442	−	41.4818i	−1.22214	−	1.41042i
$866$	3.55651	+	7.78768i	0.120855	+	0.264636i
$867$	−3.65332	+	2.34785i	−0.124073	+	0.0797370i
$868$	−1.62743	−	0.477856i	−0.0552386	−	0.0162195i
$869$	−22.0057	+	25.3960i	−0.746493	+	0.861499i
$870$	−46.1864	+	13.5616i	−1.56587	+	0.459780i
$871$	22.1955	−	48.6013i	0.752065	−	1.64679i
$872$	2.45442	+	17.0708i	0.0831170	+	0.578091i
$873$	−16.7045			−0.565360
$874$	−18.6156	−	12.5952i	−0.629682	−	0.426038i
$875$	10.9796			0.371180
$876$	5.04737	+	35.1053i	0.170535	+	1.18610i
$877$	2.74050	−	6.00085i	0.0925400	−	0.202634i	−0.857702	−	0.514147i	$-0.828108\pi$
$877$	2.74050	−	6.00085i	0.0925400	−	0.202634i	0.950242	+	0.311513i	$0.100836\pi$
$878$	26.9258	−	7.90612i	0.908701	−	0.266819i
$879$	4.01404	−	4.63245i	0.135390	−	0.156249i
$880$	11.4894	+	3.37358i	0.387307	+	0.113723i
$881$	−28.3872	+	18.2434i	−0.956391	+	0.614635i	−0.922997	−	0.384807i	$-0.874268\pi$
$881$	−28.3872	+	18.2434i	−0.956391	+	0.614635i	−0.0333937	+	0.999442i	$0.510632\pi$
$882$	1.84834	+	4.04729i	0.0622367	+	0.136279i
$883$	3.43571	+	3.96502i	0.115621	+	0.133434i	0.810609	−	0.585587i	$-0.199136\pi$
$883$	3.43571	+	3.96502i	0.115621	+	0.133434i	−0.694989	+	0.719021i	$0.744591\pi$
$884$	20.6582	+	13.2762i	0.694811	+	0.446528i
$885$	−2.03606	+	14.1611i	−0.0684415	+	0.476021i
$886$	0.850846	−	5.91776i	0.0285847	−	0.198811i
$887$	−33.7289	−	21.6762i	−1.13250	−	0.727816i	−0.166423	−	0.986054i	$-0.553222\pi$
$887$	−33.7289	−	21.6762i	−1.13250	−	0.727816i	−0.966081	+	0.258238i	$0.916858\pi$
$888$	16.1906	+	18.6849i	0.543321	+	0.627026i
$889$	7.34296	+	16.0788i	0.246275	+	0.539267i
$890$	18.0273	−	11.5854i	0.604276	−	0.388345i
$891$	−8.11701	−	2.38337i	−0.271930	−	0.0798459i
$892$	−1.56714	+	1.80858i	−0.0524718	+	0.0605557i
$893$	7.39359	−	2.17095i	0.247417	−	0.0726482i
$894$	−14.1655	+	31.0180i	−0.473764	+	1.03740i
$895$	−1.37446	−	9.55956i	−0.0459430	−	0.319541i
$896$	1.00000			0.0334077
$897$	−32.5630	+	67.0603i	−1.08725	+	2.23908i
$898$	19.9898			0.667067
$899$	1.17890	+	8.19943i	0.0393185	+	0.273466i
$900$	14.8615	−	32.5421i	0.495383	−	1.08474i
$901$	−27.8136	+	8.16681i	−0.926605	+	0.272076i
$902$	6.32872	−	7.30373i	0.210723	−	0.243188i
$903$	−25.3016	−	7.42923i	−0.841985	−	0.247229i
$904$	6.73338	−	4.32728i	0.223949	−	0.143923i
$905$	27.7884	+	60.8481i	0.923718	+	2.02266i
$906$	−38.9589	−	44.9609i	−1.29432	−	1.49373i
$907$	−23.2349	−	14.9322i	−0.771504	−	0.495815i	0.0947002	−	0.995506i	$-0.469811\pi$
$907$	−23.2349	−	14.9322i	−0.771504	−	0.495815i	−0.866204	+	0.499690i	$0.833447\pi$
$908$	−1.45663	+	10.1311i	−0.0483399	+	0.336211i
$909$	−0.244214	+	1.69855i	−0.00810007	+	0.0563372i
$910$	−17.3016	−	11.1191i	−0.573544	−	0.368594i
$911$	−9.38550	−	10.8314i	−0.310955	−	0.358862i	0.578663	−	0.815567i	$-0.303575\pi$
$911$	−9.38550	−	10.8314i	−0.310955	−	0.358862i	−0.889618	+	0.456705i	$0.849029\pi$
$912$	−5.31374	−	11.6355i	−0.175956	−	0.385289i
$913$	36.2174	−	23.2755i	1.19862	−	0.770307i
$914$	23.9416	+	7.02988i	0.791917	+	0.232528i
$915$	−47.4998	+	54.8177i	−1.57030	+	1.81222i
$916$	−7.18248	+	2.10897i	−0.237316	+	0.0696822i
$917$	−6.20422	+	13.5853i	−0.204881	+	0.448627i
$918$	−2.42740	−	16.8830i	−0.0801163	−	0.557221i
$919$	37.3401			1.23173			0.615867	−	0.787850i	$-0.288806\pi$
$919$	37.3401			1.23173			0.615867	+	0.787850i	$0.288806\pi$
$920$	16.7277	−	4.48497i	0.551496	−	0.147865i
$921$	−1.93659			−0.0638129
$922$	2.32675	+	16.1829i	0.0766274	+	0.532956i
$923$	12.5348	−	27.4473i	0.412587	−	0.903440i
$924$	−8.68379	+	2.54979i	−0.285676	+	0.0838819i
$925$	−47.6963	+	55.0445i	−1.56824	+	1.80985i
$926$	4.15105	+	1.21886i	0.136412	+	0.0400541i
$927$	−7.69440	+	4.94489i	−0.252717	+	0.162411i
$928$	−2.02884	−	4.44255i	−0.0666000	−	0.145834i
$929$	−23.5556	−	27.1846i	−0.772833	−	0.891897i	0.223737	−	0.974650i	$-0.428174\pi$
$929$	−23.5556	−	27.1846i	−0.772833	−	0.891897i	−0.996570	+	0.0827525i	$0.973629\pi$
$930$	−14.0635	−	9.03807i	−0.461161	−	0.296370i
$931$	−0.666973	+	4.63890i	−0.0218592	+	0.152034i
$932$	−0.914836	+	6.36282i	−0.0299664	+	0.208421i
$933$	−43.5808	−	28.0077i	−1.42677	−	0.916930i
$934$	−22.8489	−	26.3690i	−0.747639	−	0.862821i
$935$	21.4481	+	46.9648i	0.701429	+	1.53591i
$936$	−21.3176	+	13.7000i	−0.696789	+	0.447799i
$937$	−18.4128	−	5.40650i	−0.601521	−	0.176623i	−0.0332267	−	0.999448i	$-0.510578\pi$
$937$	−18.4128	−	5.40650i	−0.601521	−	0.176623i	−0.568294	+	0.822825i	$0.692397\pi$
$938$	6.14353	−	7.09001i	0.200593	−	0.231497i
$939$	−41.6696	+	12.2353i	−1.35984	+	0.399284i
$940$	−2.46652	+	5.40092i	−0.0804489	+	0.176159i
$941$	−1.15156	−	8.00927i	−0.0375398	−	0.261095i	0.962405	−	0.271619i	$-0.0875591\pi$
$941$	−1.15156	−	8.00927i	−0.0375398	−	0.261095i	−0.999945	+	0.0105242i	$0.996650\pi$
$942$	−16.9129			−0.551051
$943$	2.31570	−	13.7841i	0.0754097	−	0.448873i
$944$	−1.45156			−0.0472442
$945$	2.03299	+	14.1398i	0.0661333	+	0.459967i
$946$	13.3087	−	29.1421i	0.432704	−	0.947490i
$947$	−2.86107	+	0.840085i	−0.0929722	+	0.0272991i	−0.327888	−	0.944717i	$-0.606337\pi$
$947$	−2.86107	+	0.840085i	−0.0929722	+	0.0272991i	0.234916	+	0.972016i	$0.424519\pi$
$948$	−18.1129	+	20.9034i	−0.588280	+	0.678911i
$949$	71.0086	+	20.8500i	2.30504	+	0.676820i
$950$	31.7006	−	20.3727i	1.02850	−	0.660978i
$951$	−7.41155	−	16.2290i	−0.240336	−	0.526263i
$952$	2.82359	+	3.25860i	0.0915131	+	0.105612i
$953$	−7.93152	−	5.09728i	−0.256927	−	0.165117i	0.405837	−	0.913946i	$-0.366980\pi$
$953$	−7.93152	−	5.09728i	−0.256927	−	0.165117i	−0.662764	+	0.748829i	$0.730617\pi$
$954$	4.25708	−	29.6086i	0.137828	−	0.958614i
$955$	7.60149	−	52.8695i	0.245978	−	1.71082i
$956$	−10.3580	−	6.65670i	−0.335003	−	0.215293i
$957$	28.9456	+	33.4050i	0.935679	+	1.07983i
$958$	−5.55665	−	12.1674i	−0.179527	−	0.393110i
$959$	17.9915	−	11.5624i	0.580976	−	0.373371i
$960$	9.45689	+	2.77679i	0.305220	+	0.0896206i
$961$	18.4167	−	21.2540i	0.594088	−	0.685614i
$962$	49.5005	−	14.5347i	1.59596	−	0.468616i
$963$	8.48065	−	18.5700i	0.273285	−	0.598411i
$964$	2.25061	+	15.6533i	0.0724872	+	0.504159i
$965$	−34.1012			−1.09776
$966$	−8.80329	+	9.68698i	−0.283241	+	0.311674i
$967$	−21.7050			−0.697984			−0.348992	−	0.937126i	$-0.613476\pi$
$967$	−21.7050			−0.697984			−0.348992	+	0.937126i	$0.613476\pi$
$968$	0.000639172		0.00444554i	2.05438e−5		0.000142885i
$969$	22.9115	−	50.1691i	0.736023	−	1.61166i
$970$	13.0084	−	3.81960i	0.417673	−	0.122640i
$971$	32.9832	−	38.0646i	1.05848	−	1.22155i	0.0841444	−	0.996454i	$-0.473184\pi$
$971$	32.9832	−	38.0646i	1.05848	−	1.22155i	0.974336	−	0.225098i	$-0.0722702\pi$
$972$	−18.0679	−	5.30522i	−0.579529	−	0.170165i
$973$	−11.6177	+	7.46625i	−0.372447	+	0.239357i
$974$	11.7543	+	25.7384i	0.376633	+	0.824711i
$975$	−81.8472	−	94.4567i	−2.62121	−	3.02504i
$976$	−6.19104	−	3.97874i	−0.198170	−	0.127356i
$977$	−0.600261	+	4.17490i	−0.0192040	+	0.133567i	−0.997168	−	0.0752070i	$-0.976038\pi$
$977$	−0.600261	+	4.17490i	−0.0192040	+	0.133567i	0.977964	+	0.208774i	$0.0669473\pi$
$978$	−3.16193	+	21.9917i	−0.101108	+	0.703218i
$979$	−16.5536	−	10.6383i	−0.529054	−	0.340003i
$980$	−2.36481	−	2.72913i	−0.0755410	−	0.0871789i
$981$	−31.8771	−	69.8011i	−1.01776	−	2.22858i
$982$	−18.6948	+	12.0144i	−0.596574	+	0.383395i
$983$	−15.7889	−	4.63603i	−0.503586	−	0.147866i	0.0200654	−	0.999799i	$-0.493613\pi$
$983$	−15.7889	−	4.63603i	−0.503586	−	0.147866i	−0.523652	+	0.851932i	$0.675431\pi$
$984$	5.20916	−	6.01169i	0.166062	−	0.191646i
$985$	53.0798	−	15.5856i	1.69126	−	0.496599i
$986$	8.74785	−	19.1551i	0.278588	−	0.610023i
$987$	−0.638653	−	4.44193i	−0.0203286	−	0.141388i
$988$	−26.6914			−0.849168
$989$	−5.50805	−	46.0066i	−0.175146	−	1.46293i
$990$	−53.2786			−1.69331
$991$	7.08505	+	49.2776i	0.225064	+	1.56535i	0.718472	+	0.695556i	$0.244842\pi$
$991$	7.08505	+	49.2776i	0.225064	+	1.56535i	−0.493408	+	0.869798i	$0.664249\pi$
$992$	0.704600	−	1.54286i	0.0223711	−	0.0489858i
$993$	15.4351	−	4.53215i	0.489818	−	0.143824i
$994$	3.46952	−	4.00405i	0.110047	−	0.127001i
$995$	24.0365	+	7.05774i	0.762007	+	0.223745i
$996$	29.8105	−	19.1581i	0.944583	−	0.607046i
$997$	−22.1224	−	48.4414i	−0.700625	−	1.53415i	−0.839212	−	0.543804i	$-0.816983\pi$
$997$	−22.1224	−	48.4414i	−0.700625	−	1.53415i	0.138587	−	0.990350i	$-0.455744\pi$
$998$	−9.24884	−	10.6737i	−0.292767	−	0.337871i
$999$	−30.1453	−	19.3732i	−0.953756	−	0.612942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.c.141.1	✓	20
23.8	even	11	inner	322.2.i.c.169.1	yes	20
23.10	odd	22		7406.2.a.bo.1.2		10
23.13	even	11		7406.2.a.bp.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.c.141.1	✓	20	1.1	even	1	trivial
322.2.i.c.169.1	yes	20	23.8	even	11	inner
7406.2.a.bo.1.2		10	23.10	odd	22
7406.2.a.bp.1.2		10	23.13	even	11

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-1.13381 + 2.48271i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.36481 + 2.72913i) q^{5} +(2.61880 + 0.768948i) q^{6} +(0.841254 - 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.91372 - 3.36261i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-1.13381 + 2.48271i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.36481 + 2.72913i) q^{5} +(2.61880 + 0.768948i) q^{6} +(0.841254 - 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.91372 - 3.36261i) q^{9} +(3.03790 + 1.95234i) q^{10} +(0.471909 - 3.28220i) q^{11} +(0.388428 - 2.70157i) q^{12} +(-4.79116 - 3.07909i) q^{13} +(-0.654861 - 0.755750i) q^{14} +(-4.09439 - 8.96545i) q^{15} +(0.841254 - 0.540641i) q^{16} +(4.13709 + 1.21476i) q^{17} +(-2.91372 + 3.36261i) q^{18} +(-4.49676 + 1.32037i) q^{19} +(1.50013 - 3.28483i) q^{20} +(0.388428 + 2.70157i) q^{21} -3.31595 q^{22} +(-4.09468 + 2.49671i) q^{23} -2.72935 q^{24} +(-1.14428 - 7.95863i) q^{25} +(-2.36590 + 5.18059i) q^{26} +(3.79561 - 1.11449i) q^{27} +(-0.654861 + 0.755750i) q^{28} +(4.68606 + 1.37595i) q^{29} +(-8.29151 + 5.32863i) q^{30} +(0.704600 + 1.54286i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(7.61368 + 4.89301i) q^{33} +(0.613625 - 4.26785i) q^{34} +(-0.513922 + 3.57440i) q^{35} +(3.74305 + 2.40551i) q^{36} +(-5.93203 - 6.84592i) q^{37} +(1.94689 + 4.26309i) q^{38} +(13.0768 - 8.40392i) q^{39} +(-3.46488 - 1.01738i) q^{40} +(-1.90857 + 2.20261i) q^{41} +(2.61880 - 0.768948i) q^{42} +(-4.01355 + 8.78846i) q^{43} +(0.471909 + 3.28220i) q^{44} +16.0674 q^{45} +(3.05404 + 3.69768i) q^{46} -1.64420 q^{47} +(0.388428 + 2.70157i) q^{48} +(0.415415 - 0.909632i) q^{49} +(-7.71478 + 2.26526i) q^{50} +(-7.70658 + 8.89386i) q^{51} +(5.46456 + 1.60454i) q^{52} +(-5.65574 + 3.63472i) q^{53} +(-1.64332 - 3.59836i) q^{54} +(7.84158 + 9.04966i) q^{55} +(0.841254 + 0.540641i) q^{56} +(1.82041 - 12.6612i) q^{57} +(0.695051 - 4.83418i) q^{58} +(-1.22113 - 0.784771i) q^{59} +(6.45439 + 7.44877i) q^{60} +(-3.05716 - 6.69425i) q^{61} +(1.42688 - 0.917000i) q^{62} +(-4.26914 - 1.25353i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(19.7334 - 5.79425i) q^{65} +(3.75967 - 8.23253i) q^{66} +(1.33512 + 9.28594i) q^{67} -4.31174 q^{68} +(-1.55600 - 12.9967i) q^{69} +3.61116 q^{70} +(0.754000 + 5.24418i) q^{71} +(1.84834 - 4.04729i) q^{72} +(-12.4680 + 3.66094i) q^{73} +(-5.93203 + 6.84592i) q^{74} +(21.0564 + 6.18270i) q^{75} +(3.94262 - 2.53377i) q^{76} +(-1.37749 - 3.01629i) q^{77} +(-10.1794 - 11.7477i) q^{78} +(-8.52523 - 5.47883i) q^{79} +(-0.513922 + 3.57440i) q^{80} +(0.363076 - 2.52525i) q^{81} +(2.45181 + 1.57568i) q^{82} +(8.50221 + 9.81207i) q^{83} +(-1.13381 - 2.48271i) q^{84} +(-13.0986 + 8.41799i) q^{85} +(9.27019 + 2.72197i) q^{86} +(-8.72921 + 10.0740i) q^{87} +(3.18163 - 0.934210i) q^{88} +(2.46513 - 5.39787i) q^{89} +(-2.28663 - 15.9038i) q^{90} -5.69526 q^{91} +(3.22541 - 3.54919i) q^{92} -4.62935 q^{93} +(0.233994 + 1.62747i) q^{94} +(7.03052 - 15.3947i) q^{95} +(2.61880 - 0.768948i) q^{96} +(2.45857 - 2.83734i) q^{97} +(-0.959493 - 0.281733i) q^{98} +(-12.4118 + 7.97655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9	\( 20 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 5 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{8} - 12 q^{9} + 6 q^{10} + 6 q^{11} + 4 q^{12} + 14 q^{13} - 2 q^{14} + 13 q^{15} - 2 q^{16} + 7 q^{17} - 12 q^{18} - 2 q^{19} + 6 q^{20} + 4 q^{21} - 16 q^{22} + 9 q^{23} - 18 q^{24} + 23 q^{25} + 3 q^{26} - 47 q^{27} - 2 q^{28} + 2 q^{29} - 20 q^{30} + 28 q^{31} - 2 q^{32} + 26 q^{33} + 18 q^{34} - 5 q^{35} + 10 q^{36} - 17 q^{37} + 9 q^{38} + 36 q^{39} - 5 q^{40} - 7 q^{41} + 4 q^{42} - 17 q^{43} + 6 q^{44} + 90 q^{45} + 9 q^{46} - 68 q^{47} + 4 q^{48} - 2 q^{49} - 43 q^{50} - 15 q^{51} + 14 q^{52} - 35 q^{53} + 19 q^{54} + 8 q^{55} - 2 q^{56} - 20 q^{57} + 24 q^{58} - 60 q^{59} + 13 q^{60} - 48 q^{61} - 5 q^{62} + 10 q^{63} - 2 q^{64} + 40 q^{65} - 29 q^{66} - 57 q^{67} + 18 q^{68} + 4 q^{69} + 6 q^{70} - 39 q^{71} - q^{72} - 30 q^{73} - 17 q^{74} + 57 q^{75} - 2 q^{76} + 6 q^{77} - 19 q^{78} - 18 q^{79} - 5 q^{80} - 90 q^{81} + 26 q^{82} + 28 q^{83} + 4 q^{84} - 13 q^{85} - 6 q^{86} + 13 q^{87} + 6 q^{88} + 34 q^{89} - 20 q^{90} - 30 q^{91} - 2 q^{92} - 16 q^{93} + 9 q^{94} + 110 q^{95} + 4 q^{96} - 2 q^{98} - 28 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 5 * q^5 + 4 * q^6 - 2 * q^7 - 2 * q^8 - 12 * q^9 + 6 * q^10 + 6 * q^11 + 4 * q^12 + 14 * q^13 - 2 * q^14 + 13 * q^15 - 2 * q^16 + 7 * q^17 - 12 * q^18 - 2 * q^19 + 6 * q^20 + 4 * q^21 - 16 * q^22 + 9 * q^23 - 18 * q^24 + 23 * q^25 + 3 * q^26 - 47 * q^27 - 2 * q^28 + 2 * q^29 - 20 * q^30 + 28 * q^31 - 2 * q^32 + 26 * q^33 + 18 * q^34 - 5 * q^35 + 10 * q^36 - 17 * q^37 + 9 * q^38 + 36 * q^39 - 5 * q^40 - 7 * q^41 + 4 * q^42 - 17 * q^43 + 6 * q^44 + 90 * q^45 + 9 * q^46 - 68 * q^47 + 4 * q^48 - 2 * q^49 - 43 * q^50 - 15 * q^51 + 14 * q^52 - 35 * q^53 + 19 * q^54 + 8 * q^55 - 2 * q^56 - 20 * q^57 + 24 * q^58 - 60 * q^59 + 13 * q^60 - 48 * q^61 - 5 * q^62 + 10 * q^63 - 2 * q^64 + 40 * q^65 - 29 * q^66 - 57 * q^67 + 18 * q^68 + 4 * q^69 + 6 * q^70 - 39 * q^71 - q^72 - 30 * q^73 - 17 * q^74 + 57 * q^75 - 2 * q^76 + 6 * q^77 - 19 * q^78 - 18 * q^79 - 5 * q^80 - 90 * q^81 + 26 * q^82 + 28 * q^83 + 4 * q^84 - 13 * q^85 - 6 * q^86 + 13 * q^87 + 6 * q^88 + 34 * q^89 - 20 * q^90 - 30 * q^91 - 2 * q^92 - 16 * q^93 + 9 * q^94 + 110 * q^95 + 4 * q^96 - 2 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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