LMFDB - Embedded newform 266.2.u.c.225.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [266,2,Mod(43,266)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(266, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("266.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 266 = 2 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	266.u (of order $9$, degree $6$, 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:	$2.12402069377$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 24 x^{16} - 35 x^{15} + 264 x^{14} - 276 x^{13} + 1919 x^{12} - 801 x^{11} + \cdots + 1 $ x^18 - 3x^17 + 24x^16 - 35x^15 + 264x^14 - 276x^13 + 1919x^12 - 801x^11 + 8532x^10 - 414x^9 + 28392x^8 + 8547x^7 + 58143x^6 + 26301x^5 + 84828x^4 + 43250x^3 + 43896x^2 + 210*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			225.1
Root			$1.09378 - 1.89448i$ of defining polynomial
Character	$\chi$	$=$	266.225
Dual form			266.2.u.c.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(-2.05563 + 0.748188i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.106991 + 0.606779i) q^{5} +(-2.05563 - 0.748188i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.36770 - 1.14763i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(-2.05563 + 0.748188i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.106991 + 0.606779i) q^{5} +(-2.05563 - 0.748188i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.36770 - 1.14763i) q^{9} +(-0.471990 + 0.396047i) q^{10} +(-1.71499 + 2.97045i) q^{11} +(-1.09378 - 1.89448i) q^{12} +(-5.99629 - 2.18247i) q^{13} +(-0.173648 + 0.984808i) q^{14} +(-0.234050 - 1.32736i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.89978 + 1.59411i) q^{17} +1.78540 q^{18} +(-4.18460 + 1.22028i) q^{19} -0.616139 q^{20} +(-1.67576 - 1.40613i) q^{21} +(-3.22313 + 1.17312i) q^{22} +(0.469766 + 2.66417i) q^{23} +(0.379865 - 2.15432i) q^{24} +(4.34173 + 1.58026i) q^{25} +(-3.19056 - 5.52621i) q^{26} +(1.32850 - 2.30104i) q^{27} +(-0.766044 + 0.642788i) q^{28} +(4.59639 - 3.85683i) q^{29} +(0.673919 - 1.16726i) q^{30} +(3.86322 + 6.69129i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(1.30293 - 7.38929i) q^{33} +(0.430646 + 2.44232i) q^{34} +(-0.578982 + 0.210732i) q^{35} +(1.36770 + 1.14763i) q^{36} +4.26808 q^{37} +(-3.98998 - 1.75502i) q^{38} +13.9591 q^{39} +(-0.471990 - 0.396047i) q^{40} +(1.21080 - 0.440697i) q^{41} +(-0.379865 - 2.15432i) q^{42} +(-1.79871 + 10.2010i) q^{43} +(-3.22313 - 1.17312i) q^{44} +(0.550027 + 0.952675i) q^{45} +(-1.35264 + 2.34283i) q^{46} +(1.17779 - 0.988284i) q^{47} +(1.67576 - 1.40613i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(2.31019 + 4.00136i) q^{50} +(-5.09795 - 1.85550i) q^{51} +(1.10807 - 6.28418i) q^{52} +(-0.887703 - 5.03442i) q^{53} +(2.49677 - 0.908750i) q^{54} +(-1.61892 - 1.35843i) q^{55} -1.00000 q^{56} +(7.68899 - 5.63932i) q^{57} +6.00017 q^{58} +(9.78756 + 8.21274i) q^{59} +(1.26655 - 0.460988i) q^{60} +(-0.963038 - 5.46166i) q^{61} +(-1.34168 + 7.60906i) q^{62} +(1.67773 + 0.610642i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.96583 - 3.40492i) q^{65} +(5.74784 - 4.82301i) q^{66} +(3.19043 - 2.67709i) q^{67} +(-1.24000 + 2.14774i) q^{68} +(-2.95897 - 5.12508i) q^{69} +(-0.578982 - 0.210732i) q^{70} +(0.00424929 - 0.0240989i) q^{71} +(0.310031 + 1.75827i) q^{72} +(-12.2794 + 4.46934i) q^{73} +(3.26954 + 2.74347i) q^{74} -10.1073 q^{75} +(-1.92839 - 3.90913i) q^{76} -3.42998 q^{77} +(10.6933 + 8.97271i) q^{78} +(-2.78415 + 1.01335i) q^{79} +(-0.106991 - 0.606779i) q^{80} +(-1.93940 + 10.9989i) q^{81} +(1.21080 + 0.440697i) q^{82} +(-6.47125 - 11.2085i) q^{83} +(1.09378 - 1.89448i) q^{84} +(-1.17053 + 0.982193i) q^{85} +(-7.93498 + 6.65824i) q^{86} +(-6.56285 + 11.3672i) q^{87} +(-1.71499 - 2.97045i) q^{88} +(11.7001 + 4.25848i) q^{89} +(-0.191022 + 1.08334i) q^{90} +(-1.10807 - 6.28418i) q^{91} +(-2.54212 + 0.925258i) q^{92} +(-12.9477 - 10.8644i) q^{93} +1.53750 q^{94} +(-0.292725 - 2.66969i) q^{95} +2.18756 q^{96} +(-1.16220 - 0.975198i) q^{97} +(-0.939693 + 0.342020i) q^{98} +(1.06340 + 6.03085i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} - 6 q^{5} + 3 q^{6} + 9 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 - 6 * q^5 + 3 * q^6 + 9 * q^7 - 9 * q^8 - 3 * q^9	\( 18 q + 3 q^{3} - 6 q^{5} + 3 q^{6} + 9 q^{7} - 9 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{11} - 3 q^{12} - 6 q^{13} - 21 q^{17} + 24 q^{18} - 18 q^{19} + 6 q^{20} + 6 q^{21} - 15 q^{22} + 6 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} - 24 q^{27} + 21 q^{29} + 6 q^{30} - 9 q^{31} - 24 q^{33} + 24 q^{34} - 3 q^{35} - 3 q^{36} + 18 q^{37} + 12 q^{38} + 66 q^{39} + 3 q^{40} - 24 q^{41} - 3 q^{42} - 6 q^{43} - 15 q^{44} - 18 q^{45} - 6 q^{46} - 9 q^{47} - 6 q^{48} - 9 q^{49} + 18 q^{51} + 3 q^{52} - 9 q^{53} + 9 q^{54} - 27 q^{55} - 18 q^{56} + 27 q^{57} - 12 q^{58} + 45 q^{59} + 9 q^{60} + 6 q^{61} - 15 q^{62} - 15 q^{63} - 9 q^{64} + 3 q^{65} + 39 q^{66} + 27 q^{67} - 12 q^{68} - 6 q^{69} - 3 q^{70} - 27 q^{71} - 12 q^{72} + 21 q^{73} - 24 q^{74} - 6 q^{75} + 15 q^{76} + 6 q^{77} + 36 q^{78} - 6 q^{79} - 6 q^{80} - 99 q^{81} - 24 q^{82} - 9 q^{83} + 3 q^{84} + 36 q^{85} - 6 q^{86} + 3 q^{87} + 3 q^{88} + 54 q^{89} - 63 q^{90} - 3 q^{91} - 12 q^{92} - 75 q^{93} + 42 q^{94} + 57 q^{95} + 6 q^{96} + 60 q^{97} - 27 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 - 6 * q^5 + 3 * q^6 + 9 * q^7 - 9 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^11 - 3 * q^12 - 6 * q^13 - 21 * q^17 + 24 * q^18 - 18 * q^19 + 6 * q^20 + 6 * q^21 - 15 * q^22 + 6 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 - 24 * q^27 + 21 * q^29 + 6 * q^30 - 9 * q^31 - 24 * q^33 + 24 * q^34 - 3 * q^35 - 3 * q^36 + 18 * q^37 + 12 * q^38 + 66 * q^39 + 3 * q^40 - 24 * q^41 - 3 * q^42 - 6 * q^43 - 15 * q^44 - 18 * q^45 - 6 * q^46 - 9 * q^47 - 6 * q^48 - 9 * q^49 + 18 * q^51 + 3 * q^52 - 9 * q^53 + 9 * q^54 - 27 * q^55 - 18 * q^56 + 27 * q^57 - 12 * q^58 + 45 * q^59 + 9 * q^60 + 6 * q^61 - 15 * q^62 - 15 * q^63 - 9 * q^64 + 3 * q^65 + 39 * q^66 + 27 * q^67 - 12 * q^68 - 6 * q^69 - 3 * q^70 - 27 * q^71 - 12 * q^72 + 21 * q^73 - 24 * q^74 - 6 * q^75 + 15 * q^76 + 6 * q^77 + 36 * q^78 - 6 * q^79 - 6 * q^80 - 99 * q^81 - 24 * q^82 - 9 * q^83 + 3 * q^84 + 36 * q^85 - 6 * q^86 + 3 * q^87 + 3 * q^88 + 54 * q^89 - 63 * q^90 - 3 * q^91 - 12 * q^92 - 75 * q^93 + 42 * q^94 + 57 * q^95 + 6 * q^96 + 60 * q^97 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/266\mathbb{Z}\right)^\times$.

$n$	$115$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	−2.05563	+	0.748188i	−1.18682	+	0.431967i	−0.858605	−	0.512637i	$-0.828669\pi$
$3$	−2.05563	+	0.748188i	−1.18682	+	0.431967i	−0.328213	+	0.944604i	$0.606446\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.106991	+	0.606779i	−0.0478480	+	0.271360i	−0.999340	−	0.0363124i	$-0.988439\pi$
$5$	−0.106991	+	0.606779i	−0.0478480	+	0.271360i	0.951492	+	0.307672i	$0.0995500\pi$
$6$	−2.05563	−	0.748188i	−0.839207	−	0.305446i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	1.36770	−	1.14763i	0.455898	−	0.382544i
$10$	−0.471990	+	0.396047i	−0.149256	+	0.125241i
$11$	−1.71499	+	2.97045i	−0.517089	+	0.895625i	0.482714	+	0.875778i	$0.339651\pi$
$11$	−1.71499	+	2.97045i	−0.517089	+	0.895625i	−0.999803	+	0.0198468i	$0.993682\pi$
$12$	−1.09378	−	1.89448i	−0.315746	−	0.546889i
$13$	−5.99629	−	2.18247i	−1.66307	−	0.605309i	−0.672231	−	0.740341i	$-0.734664\pi$
$13$	−5.99629	−	2.18247i	−1.66307	−	0.605309i	−0.990841	+	0.135032i	$0.956886\pi$
$14$	−0.173648	+	0.984808i	−0.0464094	+	0.263201i
$15$	−0.234050	−	1.32736i	−0.0604314	−	0.342723i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	1.89978	+	1.59411i	0.460765	+	0.386628i	0.843413	−	0.537267i	$-0.180543\pi$
$17$	1.89978	+	1.59411i	0.460765	+	0.386628i	−0.382647	+	0.923895i	$0.624988\pi$
$18$	1.78540			0.420823
$19$	−4.18460	+	1.22028i	−0.960014	+	0.279952i
$19$	−4.18460	+	1.22028i	−0.960014	+	0.279952i
$20$	−0.616139			−0.137773
$21$	−1.67576	−	1.40613i	−0.365682	−	0.306844i
$22$	−3.22313	+	1.17312i	−0.687174	+	0.250111i
$23$	0.469766	+	2.66417i	0.0979529	+	0.555518i	0.993802	+	0.111161i	$0.0354569\pi$
$23$	0.469766	+	2.66417i	0.0979529	+	0.555518i	−0.895850	+	0.444358i	$0.853432\pi$
$24$	0.379865	−	2.15432i	0.0775396	−	0.439749i
$25$	4.34173	+	1.58026i	0.868346	+	0.316052i
$26$	−3.19056	−	5.52621i	−0.625720	−	1.08378i
$27$	1.32850	−	2.30104i	0.255671	−	0.442834i
$28$	−0.766044	+	0.642788i	−0.144769	+	0.121475i
$29$	4.59639	−	3.85683i	0.853529	−	0.716196i	−0.107035	−	0.994255i	$-0.534136\pi$
$29$	4.59639	−	3.85683i	0.853529	−	0.716196i	0.960564	+	0.278059i	$0.0896912\pi$
$30$	0.673919	−	1.16726i	0.123040	−	0.213112i
$31$	3.86322	+	6.69129i	0.693855	+	1.20179i	0.970565	+	0.240838i	$0.0774224\pi$
$31$	3.86322	+	6.69129i	0.693855	+	1.20179i	−0.276711	+	0.960953i	$0.589244\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	1.30293	−	7.38929i	0.226811	−	1.28631i
$34$	0.430646	+	2.44232i	0.0738552	+	0.418854i
$35$	−0.578982	+	0.210732i	−0.0978657	+	0.0356202i
$36$	1.36770	+	1.14763i	0.227949	+	0.191272i
$37$	4.26808			0.701669			0.350834	−	0.936438i	$-0.385898\pi$
$37$	4.26808			0.701669			0.350834	+	0.936438i	$0.385898\pi$
$38$	−3.98998	−	1.75502i	−0.647260	−	0.284702i
$39$	13.9591			2.23524
$40$	−0.471990	−	0.396047i	−0.0746282	−	0.0626205i
$41$	1.21080	−	0.440697i	0.189096	−	0.0688253i	−0.245737	−	0.969337i	$-0.579030\pi$
$41$	1.21080	−	0.440697i	0.189096	−	0.0688253i	0.434832	+	0.900511i	$0.356808\pi$
$42$	−0.379865	−	2.15432i	−0.0586144	−	0.332419i
$43$	−1.79871	+	10.2010i	−0.274301	+	1.55564i	0.466871	+	0.884325i	$0.345381\pi$
$43$	−1.79871	+	10.2010i	−0.274301	+	1.55564i	−0.741172	+	0.671315i	$0.765730\pi$
$44$	−3.22313	−	1.17312i	−0.485905	−	0.176855i
$45$	0.550027	+	0.952675i	0.0819932	+	0.142016i
$46$	−1.35264	+	2.34283i	−0.199435	+	0.345432i
$47$	1.17779	−	0.988284i	0.171799	−	0.144156i	−0.552834	−	0.833291i	$-0.686454\pi$
$47$	1.17779	−	0.988284i	0.171799	−	0.144156i	0.724633	+	0.689135i	$0.242009\pi$
$48$	1.67576	−	1.40613i	0.241876	−	0.202958i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	2.31019	+	4.00136i	0.326710	+	0.565878i
$51$	−5.09795	−	1.85550i	−0.713855	−	0.259822i
$52$	1.10807	−	6.28418i	0.153662	−	0.871459i
$53$	−0.887703	−	5.03442i	−0.121935	−	0.691530i	−0.983081	−	0.183172i	$-0.941364\pi$
$53$	−0.887703	−	5.03442i	−0.121935	−	0.691530i	0.861146	−	0.508358i	$-0.169748\pi$
$54$	2.49677	−	0.908750i	0.339767	−	0.123665i
$55$	−1.61892	−	1.35843i	−0.218295	−	0.183171i
$56$	−1.00000			−0.133631
$57$	7.68899	−	5.63932i	1.01843	−	0.746946i
$58$	6.00017			0.787860
$59$	9.78756	+	8.21274i	1.27423	+	1.06921i	0.994012	+	0.109272i	$0.0348518\pi$
$59$	9.78756	+	8.21274i	1.27423	+	1.06921i	0.280220	+	0.959936i	$0.409593\pi$
$60$	1.26655	−	0.460988i	0.163511	−	0.0595133i
$61$	−0.963038	−	5.46166i	−0.123304	−	0.699294i	−0.982301	−	0.187312i	$-0.940023\pi$
$61$	−0.963038	−	5.46166i	−0.123304	−	0.699294i	0.858996	−	0.511982i	$-0.171089\pi$
$62$	−1.34168	+	7.60906i	−0.170394	+	0.966351i
$63$	1.67773	+	0.610642i	0.211374	+	0.0769337i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.96583	−	3.40492i	0.243831	−	0.422328i
$66$	5.74784	−	4.82301i	0.707511	−	0.593672i
$67$	3.19043	−	2.67709i	0.389773	−	0.327059i	−0.426752	−	0.904369i	$-0.640342\pi$
$67$	3.19043	−	2.67709i	0.389773	−	0.327059i	0.816525	+	0.577310i	$0.195898\pi$
$68$	−1.24000	+	2.14774i	−0.150372	+	0.260451i
$69$	−2.95897	−	5.12508i	−0.356218	−	0.616987i
$70$	−0.578982	−	0.210732i	−0.0692015	−	0.0251873i
$71$	0.00424929	−	0.0240989i	0.000504298	−	0.00286002i	−0.984555	−	0.175078i	$-0.943982\pi$
$71$	0.00424929	−	0.0240989i	0.000504298	−	0.00286002i	0.985059	+	0.172218i	$0.0550933\pi$
$72$	0.310031	+	1.75827i	0.0365375	+	0.207215i
$73$	−12.2794	+	4.46934i	−1.43719	+	0.523096i	−0.938984	−	0.343960i	$-0.888232\pi$
$73$	−12.2794	+	4.46934i	−1.43719	+	0.523096i	−0.498211	+	0.867056i	$0.666009\pi$
$74$	3.26954	+	2.74347i	0.380076	+	0.318922i
$75$	−10.1073			−1.16709
$76$	−1.92839	−	3.90913i	−0.221202	−	0.448408i
$77$	−3.42998			−0.390883
$78$	10.6933	+	8.97271i	1.21077	+	1.01596i
$79$	−2.78415	+	1.01335i	−0.313241	+	0.114010i	−0.493857	−	0.869543i	$-0.664413\pi$
$79$	−2.78415	+	1.01335i	−0.313241	+	0.114010i	0.180615	+	0.983554i	$0.442191\pi$
$80$	−0.106991	−	0.606779i	−0.0119620	−	0.0678399i
$81$	−1.93940	+	10.9989i	−0.215489	+	1.22210i
$82$	1.21080	+	0.440697i	0.133711	+	0.0486668i
$83$	−6.47125	−	11.2085i	−0.710312	−	1.23030i	−0.964740	−	0.263205i	$-0.915220\pi$
$83$	−6.47125	−	11.2085i	−0.710312	−	1.23030i	0.254427	−	0.967092i	$-0.418113\pi$
$84$	1.09378	−	1.89448i	0.119341	−	0.206705i
$85$	−1.17053	+	0.982193i	−0.126962	+	0.106534i
$86$	−7.93498	+	6.65824i	−0.855651	+	0.717976i
$87$	−6.56285	+	11.3672i	−0.703611	+	1.21869i
$88$	−1.71499	−	2.97045i	−0.182819	−	0.316651i
$89$	11.7001	+	4.25848i	1.24020	+	0.451398i	0.877081	−	0.480343i	$-0.159488\pi$
$89$	11.7001	+	4.25848i	1.24020	+	0.451398i	0.363124	+	0.931741i	$0.381710\pi$
$90$	−0.191022	+	1.08334i	−0.0201355	+	0.114194i
$91$	−1.10807	−	6.28418i	−0.116157	−	0.658761i
$92$	−2.54212	+	0.925258i	−0.265035	+	0.0964648i
$93$	−12.9477	−	10.8644i	−1.34261	−	1.12659i
$94$	1.53750			0.158581
$95$	−0.292725	−	2.66969i	−0.0300330	−	0.273904i
$96$	2.18756			0.223266
$97$	−1.16220	−	0.975198i	−0.118003	−	0.0990164i	0.581877	−	0.813277i	$-0.302319\pi$
$97$	−1.16220	−	0.975198i	−0.118003	−	0.0990164i	−0.699880	+	0.714261i	$0.746763\pi$
$98$	−0.939693	+	0.342020i	−0.0949233	+	0.0345493i
$99$	1.06340	+	6.03085i	0.106876	+	0.606124i
$100$	−0.802319	+	4.55018i	−0.0802319	+	0.455018i
$101$	9.32949	+	3.39566i	0.928319	+	0.337880i	0.761543	−	0.648114i	$-0.224442\pi$
$101$	9.32949	+	3.39566i	0.928319	+	0.337880i	0.166776	+	0.985995i	$0.446664\pi$
$102$	−2.71256	−	4.69829i	−0.268583	−	0.465200i
$103$	−4.17494	+	7.23121i	−0.411369	+	0.712512i	−0.995040	−	0.0994782i	$-0.968283\pi$
$103$	−4.17494	+	7.23121i	−0.411369	+	0.712512i	0.583671	+	0.811991i	$0.301616\pi$
$104$	4.88822	−	4.10171i	0.479330	−	0.402205i
$105$	1.03250	−	0.866374i	0.100762	−	0.0845495i
$106$	2.55604	−	4.42719i	0.248265	−	0.430007i
$107$	−6.77811	−	11.7400i	−0.655264	−	1.13495i	−0.981827	−	0.189776i	$-0.939224\pi$
$107$	−6.77811	−	11.7400i	−0.655264	−	1.13495i	0.326563	−	0.945175i	$-0.394109\pi$
$108$	2.49677	+	0.908750i	0.240252	+	0.0874445i
$109$	0.0969481	−	0.549820i	0.00928594	−	0.0526632i	−0.979813	−	0.199918i	$-0.935933\pi$
$109$	0.0969481	−	0.549820i	0.00928594	−	0.0526632i	0.989099	+	0.147254i	$0.0470436\pi$
$110$	−0.366979	−	2.08124i	−0.0349901	−	0.198439i
$111$	−8.77360	+	3.19333i	−0.832753	+	0.303097i
$112$	−0.766044	−	0.642788i	−0.0723844	−	0.0607377i
$113$	10.0986			0.949999			0.474999	−	0.879986i	$-0.342448\pi$
$113$	10.0986			0.949999			0.474999	+	0.879986i	$0.342448\pi$
$114$	9.51500	+	0.622419i	0.891161	+	0.0582948i
$115$	−1.66682			−0.155432
$116$	4.59639	+	3.85683i	0.426764	+	0.358098i
$117$	−10.7058	+	3.89658i	−0.989749	+	0.360239i
$118$	2.21866	+	12.5826i	0.204244	+	1.15833i
$119$	−0.430646	+	2.44232i	−0.0394773	+	0.223887i
$120$	1.26655	+	0.460988i	0.115620	+	0.0420823i
$121$	−0.382392	−	0.662322i	−0.0347629	−	0.0602111i
$122$	2.77296	−	4.80290i	0.251052	−	0.434834i
$123$	−2.15924	+	1.81182i	−0.194692	+	0.163366i
$124$	−5.91880	+	4.96646i	−0.531524	+	0.446001i
$125$	−2.96374	+	5.13336i	−0.265085	+	0.459141i
$126$	0.892700	+	1.54620i	0.0795280	+	0.137747i
$127$	−4.17800	−	1.52067i	−0.370737	−	0.134937i	0.149931	−	0.988696i	$-0.452095\pi$
$127$	−4.17800	−	1.52067i	−0.370737	−	0.134937i	−0.520668	+	0.853759i	$0.674317\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	−3.93479	−	22.3153i	−0.346439	−	1.96475i
$130$	3.69455	−	1.34471i	0.324034	−	0.117939i
$131$	5.49394	+	4.60997i	0.480008	+	0.402775i	0.850429	−	0.526089i	$-0.176342\pi$
$131$	5.49394	+	4.60997i	0.480008	+	0.402775i	−0.370421	+	0.928864i	$0.620787\pi$
$132$	7.50328			0.653077
$133$	−3.14910	−	3.01383i	−0.273061	−	0.261332i
$134$	4.16481			0.359785
$135$	1.25408	+	1.05230i	0.107934	+	0.0905675i
$136$	−2.33043	+	0.848207i	−0.199833	+	0.0727332i
$137$	−2.91855	−	16.5519i	−0.249349	−	1.41413i	−0.810173	−	0.586191i	$-0.800627\pi$
$137$	−2.91855	−	16.5519i	−0.249349	−	1.41413i	0.560824	−	0.827935i	$-0.310484\pi$
$138$	1.02764	−	5.82803i	0.0874784	−	0.496115i
$139$	12.7391	+	4.63664i	1.08051	+	0.393275i	0.820099	−	0.572222i	$-0.193918\pi$
$139$	12.7391	+	4.63664i	1.08051	+	0.393275i	0.260415	+	0.965497i	$0.416141\pi$
$140$	−0.308070	−	0.533592i	−0.0260366	−	0.0450968i
$141$	−1.68168	+	2.91276i	−0.141623	+	0.245298i
$142$	0.0187456	−	0.0157295i	0.00157310	−	0.00131999i
$143$	16.7665	−	14.0688i	1.40209	−	1.17649i
$144$	−0.892700	+	1.54620i	−0.0743916	+	0.128850i
$145$	1.84847	+	3.20164i	0.153507	+	0.265882i
$146$	−12.2794	−	4.46934i	−1.01625	−	0.369885i
$147$	0.379865	−	2.15432i	0.0313307	−	0.177685i
$148$	0.741145	+	4.20324i	0.0609217	+	0.345504i
$149$	−12.7789	+	4.65114i	−1.04689	+	0.381036i	−0.807487	−	0.589885i	$-0.799173\pi$
$149$	−12.7789	+	4.65114i	−1.04689	+	0.381036i	−0.239401	+	0.970921i	$0.576951\pi$
$150$	−7.74266	−	6.49686i	−0.632185	−	0.530466i
$151$	−20.2325			−1.64650			−0.823250	−	0.567679i	$-0.807841\pi$
$151$	−20.2325			−1.64650			−0.823250	+	0.567679i	$0.807841\pi$
$152$	1.03551	−	4.23411i	0.0839905	−	0.343432i
$153$	4.42778			0.357964
$154$	−2.62752	−	2.20475i	−0.211732	−	0.177664i
$155$	−4.47347	+	1.62821i	−0.359317	+	0.130781i
$156$	2.42397	+	13.7470i	0.194073	+	1.10064i
$157$	−1.92917	+	10.9409i	−0.153965	+	0.873178i	0.805761	+	0.592241i	$0.201757\pi$
$157$	−1.92917	+	10.9409i	−0.153965	+	0.873178i	−0.959726	+	0.280938i	$0.909355\pi$
$158$	−2.78415	−	1.01335i	−0.221495	−	0.0806176i
$159$	5.59148	+	9.68472i	0.443433	+	0.768049i
$160$	0.308070	−	0.533592i	0.0243550	−	0.0421842i
$161$	−2.07236	+	1.73892i	−0.163325	+	0.137046i
$162$	−8.55560	+	7.17900i	−0.672192	+	0.564036i
$163$	5.14015	−	8.90300i	0.402608	−	0.697337i	−0.591432	−	0.806355i	$-0.701437\pi$
$163$	5.14015	−	8.90300i	0.402608	−	0.697337i	0.994040	+	0.109018i	$0.0347705\pi$
$164$	0.644255	+	1.11588i	0.0503079	+	0.0871358i
$165$	4.34426	+	1.58118i	0.338200	+	0.123095i
$166$	2.24744	−	12.7459i	0.174435	−	0.989272i
$167$	−2.20096	−	12.4822i	−0.170315	−	0.965905i	−0.943413	−	0.331619i	$-0.892405\pi$
$167$	−2.20096	−	12.4822i	−0.170315	−	0.965905i	0.773098	−	0.634286i	$-0.218706\pi$
$168$	2.05563	−	0.748188i	0.158595	−	0.0577240i
$169$	21.2338	+	17.8172i	1.63337	+	1.37056i
$170$	−1.52802			−0.117194
$171$	−4.32282	+	6.47136i	−0.330575	+	0.494878i
$172$	−10.3584			−0.789819
$173$	4.78347	+	4.01381i	0.363680	+	0.305164i	0.806256	−	0.591567i	$-0.201491\pi$
$173$	4.78347	+	4.01381i	0.363680	+	0.305164i	−0.442575	+	0.896731i	$0.645935\pi$
$174$	−12.3341	+	4.48925i	−0.935047	+	0.340329i
$175$	0.802319	+	4.55018i	0.0606496	+	0.343961i
$176$	0.595610	−	3.37787i	0.0448958	−	0.254617i
$177$	−26.2643	−	9.55941i	−1.97414	−	0.718530i
$178$	6.22548	+	10.7828i	0.466619	+	0.808208i
$179$	−8.89880	+	15.4132i	−0.665128	+	1.15204i	0.314123	+	0.949382i	$0.398290\pi$
$179$	−8.89880	+	15.4132i	−0.665128	+	1.15204i	−0.979251	+	0.202653i	$0.935044\pi$
$180$	−0.842691	+	0.707101i	−0.0628105	+	0.0527042i
$181$	−4.54078	+	3.81017i	−0.337514	+	0.283208i	−0.795753	−	0.605621i	$-0.792925\pi$
$181$	−4.54078	+	3.81017i	−0.337514	+	0.283208i	0.458239	+	0.888829i	$0.348480\pi$
$182$	3.19056	−	5.52621i	0.236500	−	0.409630i
$183$	6.06600	+	10.5066i	0.448412	+	0.776672i
$184$	−2.54212	−	0.925258i	−0.187408	−	0.0682109i
$185$	−0.456648	+	2.58978i	−0.0335735	+	0.190405i
$186$	−2.93500	−	16.6452i	−0.215205	−	1.22049i
$187$	−7.99334	+	2.90934i	−0.584531	+	0.212752i
$188$	1.17779	+	0.988284i	0.0858993	+	0.0720780i
$189$	2.65701			0.193269
$190$	1.49180	−	2.23326i	0.108227	−	0.162018i
$191$	16.3567			1.18353			0.591764	−	0.806111i	$-0.298432\pi$
$191$	16.3567			1.18353			0.591764	+	0.806111i	$0.298432\pi$
$192$	1.67576	+	1.40613i	0.120938	+	0.101479i
$193$	−18.7831	+	6.83648i	−1.35203	+	0.492100i	−0.913582	−	0.406654i	$-0.866695\pi$
$193$	−18.7831	+	6.83648i	−1.35203	+	0.492100i	−0.438452	+	0.898754i	$0.644473\pi$
$194$	−0.263448	−	1.49409i	−0.0189145	−	0.107269i
$195$	−1.49350	+	8.47006i	−0.106952	+	0.606554i
$196$	−0.939693	−	0.342020i	−0.0671209	−	0.0244300i
$197$	1.72215	+	2.98285i	0.122698	+	0.212519i	0.920831	−	0.389962i	$-0.127512\pi$
$197$	1.72215	+	2.98285i	0.122698	+	0.212519i	−0.798133	+	0.602482i	$0.794179\pi$
$198$	−3.06194	+	5.30344i	−0.217603	+	0.376899i
$199$	2.39792	−	2.01210i	0.169984	−	0.142634i	−0.553827	−	0.832632i	$-0.686833\pi$
$199$	2.39792	−	2.01210i	0.169984	−	0.142634i	0.723811	+	0.689998i	$0.242389\pi$
$200$	−3.53941	+	2.96992i	−0.250274	+	0.210005i
$201$	−4.55538	+	7.89015i	−0.321312	+	0.556528i
$202$	4.96412	+	8.59810i	0.349274	+	0.604960i
$203$	5.63831	+	2.05218i	0.395732	+	0.144035i
$204$	0.942062	−	5.34270i	0.0659575	−	0.374064i
$205$	0.137860	+	0.781841i	0.00962854	+	0.0546061i
$206$	−7.84632	+	2.85583i	−0.546679	+	0.198975i
$207$	3.69999	+	3.10466i	0.257167	+	0.215789i
$208$	6.38112			0.442451
$209$	3.55176	−	14.5229i	0.245681	−	1.00457i
$210$	1.34784			0.0930097
$211$	−12.7919	−	10.7337i	−0.880634	−	0.738940i	0.0856754	−	0.996323i	$-0.472695\pi$
$211$	−12.7919	−	10.7337i	−0.880634	−	0.738940i	−0.966309	+	0.257383i	$0.917140\pi$
$212$	4.80378	−	1.74843i	0.329925	−	0.120083i
$213$	0.00929556	+	0.0527177i	0.000636921	+	0.00361216i
$214$	2.35401	−	13.3503i	0.160917	−	0.912605i
$215$	−5.99731	−	2.18284i	−0.409013	−	0.148869i
$216$	1.32850	+	2.30104i	0.0903932	+	0.156566i
$217$	−3.86322	+	6.69129i	−0.262252	+	0.454235i
$218$	0.427684	−	0.358870i	0.0289664	−	0.0243057i
$219$	21.8980	−	18.3746i	1.47973	−	1.24164i
$220$	1.05667	−	1.83021i	0.0712409	−	0.123393i
$221$	−7.91257	−	13.7050i	−0.532257	−	0.921896i
$222$	−8.77360	−	3.19333i	−0.588845	−	0.214322i
$223$	2.53255	−	14.3628i	0.169592	−	0.961803i	−0.774611	−	0.632438i	$-0.782054\pi$
$223$	2.53255	−	14.3628i	0.169592	−	0.961803i	0.944203	−	0.329365i	$-0.106835\pi$
$224$	−0.173648	−	0.984808i	−0.0116024	−	0.0658002i
$225$	7.75172	−	2.82140i	0.516781	−	0.188093i
$226$	7.73599	+	6.49127i	0.514591	+	0.431793i
$227$	−4.73333			−0.314162			−0.157081	−	0.987586i	$-0.550208\pi$
$227$	−4.73333			−0.314162			−0.157081	+	0.987586i	$0.550208\pi$
$228$	6.88883	+	6.59292i	0.456224	+	0.436627i
$229$	14.8611			0.982051			0.491026	−	0.871145i	$-0.336622\pi$
$229$	14.8611			0.982051			0.491026	+	0.871145i	$0.336622\pi$
$230$	−1.27686	−	1.07141i	−0.0841938	−	0.0706470i
$231$	7.05078	−	2.56627i	0.463907	−	0.168848i
$232$	1.04192	+	5.90901i	0.0684053	+	0.387946i
$233$	−0.758410	+	4.30115i	−0.0496851	+	0.281778i	−0.999520	−	0.0309730i	$-0.990139\pi$
$233$	−0.758410	+	4.30115i	−0.0496851	+	0.281778i	0.949835	+	0.312751i	$0.101251\pi$
$234$	−10.7058	−	3.89658i	−0.699859	−	0.254728i
$235$	0.473656	+	0.820397i	0.0308979	+	0.0535168i
$236$	−6.38838	+	11.0650i	−0.415848	+	0.720270i
$237$	4.96501	−	4.16613i	0.322512	−	0.270620i
$238$	−1.89978	+	1.59411i	−0.123145	+	0.103331i
$239$	12.1108	−	20.9766i	0.783385	−	1.35686i	−0.146575	−	0.989200i	$-0.546825\pi$
$239$	12.1108	−	20.9766i	0.783385	−	1.35686i	0.929959	−	0.367663i	$-0.119842\pi$
$240$	0.673919	+	1.16726i	0.0435013	+	0.0753465i
$241$	16.0696	+	5.84886i	1.03514	+	0.376758i	0.803034	−	0.595933i	$-0.203218\pi$
$241$	16.0696	+	5.84886i	1.03514	+	0.376758i	0.232101	+	0.972692i	$0.425440\pi$
$242$	0.132803	−	0.753164i	0.00853691	−	0.0484152i
$243$	−2.85839	−	16.2107i	−0.183366	−	1.03992i
$244$	5.21146	−	1.89681i	0.333629	−	0.121431i
$245$	−0.471990	−	0.396047i	−0.0301543	−	0.0253025i
$246$	−2.81869			−0.179713
$247$	27.7553	+	1.81560i	1.76603	+	0.115524i
$248$	−7.72644			−0.490629
$249$	21.6886	+	18.1989i	1.37446	+	1.15331i
$250$	−5.57002	+	2.02732i	−0.352279	+	0.128219i
$251$	4.74226	+	26.8947i	0.299329	+	1.69758i	0.649067	+	0.760731i	$0.275159\pi$
$251$	4.74226	+	26.8947i	0.299329	+	1.69758i	−0.349738	+	0.936847i	$0.613730\pi$
$252$	−0.310031	+	1.75827i	−0.0195301	+	0.110761i
$253$	−8.71944	−	3.17362i	−0.548187	−	0.199524i
$254$	−2.22307	−	3.85046i	−0.139488	−	0.241600i
$255$	1.67131	−	2.89480i	0.104662	−	0.181280i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−7.63606	+	6.40742i	−0.476325	+	0.399684i	−0.849095	−	0.528240i	$-0.822852\pi$
$257$	−7.63606	+	6.40742i	−0.476325	+	0.399684i	0.372771	+	0.927923i	$0.378408\pi$
$258$	11.3298	−	19.6237i	0.705360	−	1.22172i
$259$	2.13404	+	3.69627i	0.132603	+	0.229675i
$260$	3.69455	+	1.34471i	0.229126	+	0.0833952i
$261$	1.86024	−	10.5499i	0.115146	−	0.653025i
$262$	1.24538	+	7.06288i	0.0769396	+	0.436346i
$263$	23.4279	−	8.52705i	1.44462	−	0.525800i	0.503540	−	0.863972i	$-0.332031\pi$
$263$	23.4279	−	8.52705i	1.44462	−	0.525800i	0.941084	+	0.338172i	$0.109808\pi$
$264$	5.74784	+	4.82301i	0.353755	+	0.296836i
$265$	3.14975			0.193488
$266$	−0.475096	−	4.33293i	−0.0291300	−	0.265669i
$267$	−27.2371			−1.66689
$268$	3.19043	+	2.67709i	0.194887	+	0.163529i
$269$	24.1186	−	8.77845i	1.47054	−	0.535231i	0.522290	−	0.852768i	$-0.325078\pi$
$269$	24.1186	−	8.77845i	1.47054	−	0.535231i	0.948246	+	0.317536i	$0.102856\pi$
$270$	0.284277	+	1.61222i	0.0173005	+	0.0981163i
$271$	3.26396	−	18.5108i	0.198271	−	1.12445i	−0.709411	−	0.704795i	$-0.751039\pi$
$271$	3.26396	−	18.5108i	0.198271	−	1.12445i	0.907682	−	0.419658i	$-0.137850\pi$
$272$	−2.33043	−	0.848207i	−0.141303	−	0.0514301i
$273$	6.97953	+	12.0889i	0.422420	+	0.731653i
$274$	8.40363	−	14.5555i	0.507682	−	0.879331i
$275$	−12.1401	+	10.1868i	−0.732077	+	0.614285i
$276$	4.53340	−	3.80397i	0.272879	−	0.228972i
$277$	−9.93724	+	17.2118i	−0.597071	+	1.03416i	0.396180	+	0.918173i	$0.370336\pi$
$277$	−9.93724	+	17.2118i	−0.597071	+	1.03416i	−0.993251	+	0.115985i	$0.962998\pi$
$278$	6.77831	+	11.7404i	0.406536	+	0.704142i
$279$	12.9629	+	4.71809i	0.776066	+	0.282465i
$280$	0.106991	−	0.606779i	0.00639396	−	0.0362620i
$281$	−3.69772	−	20.9708i	−0.220587	−	1.25101i	−0.870943	−	0.491384i	$-0.836491\pi$
$281$	−3.69772	−	20.9708i	−0.220587	−	1.25101i	0.650356	−	0.759630i	$-0.274620\pi$
$282$	−3.16053	+	1.15034i	−0.188207	+	0.0685016i
$283$	−2.89155	−	2.42630i	−0.171885	−	0.144229i	0.552787	−	0.833323i	$-0.313564\pi$
$283$	−2.89155	−	2.42630i	−0.171885	−	0.144229i	−0.724672	+	0.689094i	$0.758009\pi$
$284$	0.0244707			0.00145207
$285$	2.59916	+	5.26888i	0.153961	+	0.312101i
$286$	21.8871			1.29421
$287$	0.987057	+	0.828239i	0.0582641	+	0.0488894i
$288$	−1.67773	+	0.610642i	−0.0988610	+	0.0359825i
$289$	−1.88402	−	10.6848i	−0.110825	−	0.628518i
$290$	−0.641967	+	3.64077i	−0.0376976	+	0.213794i
$291$	3.11868	+	1.13511i	0.182820	+	0.0665411i
$292$	−6.53373	−	11.3168i	−0.382358	−	0.662263i
$293$	8.47920	−	14.6864i	0.495360	−	0.857989i	−0.504625	−	0.863338i	$-0.668369\pi$
$293$	8.47920	−	14.6864i	0.495360	−	0.857989i	0.999986	+	0.00534920i	$0.00170271\pi$
$294$	1.67576	−	1.40613i	0.0977326	−	0.0820074i
$295$	−6.03050	+	5.06019i	−0.351109	+	0.294616i
$296$	−2.13404	+	3.69627i	−0.124039	+	0.214841i
$297$	4.55674	+	7.89251i	0.264409	+	0.457970i
$298$	−12.7789	−	4.65114i	−0.740262	−	0.269433i
$299$	2.99763	−	17.0004i	0.173358	−	0.983159i
$300$	−1.75512	−	9.95377i	−0.101332	−	0.574681i
$301$	−9.73369	+	3.54278i	−0.561041	+	0.204202i
$302$	−15.4990	−	13.0052i	−0.891868	−	0.748366i
$303$	−21.7186			−1.24770
$304$	3.51488	−	2.57791i	0.201592	−	0.147853i
$305$	3.41706			0.195660
$306$	3.39187	+	2.84612i	0.193900	+	0.162702i
$307$	2.52387	−	0.918614i	0.144045	−	0.0524281i	−0.268992	−	0.963143i	$-0.586690\pi$
$307$	2.52387	−	0.918614i	0.144045	−	0.0524281i	0.413037	+	0.910714i	$0.364468\pi$
$308$	−0.595610	−	3.37787i	−0.0339380	−	0.192472i
$309$	3.17183	−	17.9883i	0.180439	−	1.02332i
$310$	−4.47347	−	1.62821i	−0.254076	−	0.0924760i
$311$	−0.885396	−	1.53355i	−0.0502062	−	0.0869597i	0.839830	−	0.542849i	$-0.182655\pi$
$311$	−0.885396	−	1.53355i	−0.0502062	−	0.0869597i	−0.890036	+	0.455890i	$0.849321\pi$
$312$	−6.97953	+	12.0889i	−0.395138	+	0.684399i
$313$	6.04967	−	5.07628i	0.341948	−	0.286928i	−0.455599	−	0.890185i	$-0.650575\pi$
$313$	6.04967	−	5.07628i	0.341948	−	0.286928i	0.797547	+	0.603257i	$0.206131\pi$
$314$	−8.51050	+	7.14116i	−0.480275	+	0.402999i
$315$	−0.550027	+	0.952675i	−0.0309905	+	0.0536772i
$316$	−1.48141	−	2.56589i	−0.0833361	−	0.144342i
$317$	10.9194	+	3.97435i	0.613296	+	0.223222i	0.629945	−	0.776640i	$-0.283077\pi$
$317$	10.9194	+	3.97435i	0.613296	+	0.223222i	−0.0166485	+	0.999861i	$0.505300\pi$
$318$	−1.94190	+	11.0131i	−0.108896	+	0.617582i
$319$	3.57376	+	20.2678i	0.200092	+	1.13478i
$320$	0.578982	−	0.210732i	0.0323661	−	0.0117803i
$321$	22.7170	+	19.0618i	1.26794	+	1.06393i
$322$	−2.70527			−0.150759
$323$	−9.89511	−	4.35243i	−0.550579	−	0.242176i
$324$	−11.1685			−0.620475
$325$	−22.5854	−	18.9514i	−1.25281	−	1.05124i
$326$	9.66032	−	3.51607i	0.535036	−	0.194737i
$327$	0.212079	+	1.20276i	0.0117280	+	0.0665129i
$328$	−0.223748	+	1.26894i	−0.0123544	+	0.0700652i
$329$	1.44477	+	0.525855i	0.0796530	+	0.0289913i
$330$	2.31153	+	4.00369i	0.127246	+	0.220396i
$331$	0.576760	−	0.998978i	0.0317016	−	0.0549088i	−0.849739	−	0.527203i	$-0.823241\pi$
$331$	0.576760	−	0.998978i	0.0317016	−	0.0549088i	0.881441	+	0.472294i	$0.156574\pi$
$332$	9.91454	−	8.31928i	0.544131	−	0.456580i
$333$	5.83744	−	4.89819i	0.319890	−	0.268419i
$334$	6.33740	−	10.9767i	0.346767	−	0.600618i
$335$	1.28305	+	2.22231i	0.0701006	+	0.121418i
$336$	2.05563	+	0.748188i	0.112144	+	0.0408170i
$337$	−1.27031	+	7.20430i	−0.0691983	+	0.392443i	0.930462	+	0.366388i	$0.119406\pi$
$337$	−1.27031	+	7.20430i	−0.0691983	+	0.392443i	−0.999661	+	0.0260553i	$0.991705\pi$
$338$	4.81330	+	27.2976i	0.261809	+	1.48479i
$339$	−20.7590	+	7.55567i	−1.12748	+	0.410368i
$340$	−1.17053	−	0.982193i	−0.0634810	−	0.0532669i
$341$	−26.5016			−1.43514
$342$	−7.47119	+	2.17869i	−0.403996	+	0.117810i
$343$	−1.00000			−0.0539949
$344$	−7.93498	−	6.65824i	−0.427825	−	0.358988i
$345$	3.42637	−	1.24710i	0.184470	−	0.0671415i
$346$	1.08432	+	6.14951i	0.0582936	+	0.330600i
$347$	−5.44741	+	30.8938i	−0.292432	+	1.65846i	0.385028	+	0.922905i	$0.374192\pi$
$347$	−5.44741	+	30.8938i	−0.292432	+	1.65846i	−0.677460	+	0.735560i	$0.736919\pi$
$348$	−12.3341	−	4.48925i	−0.661178	−	0.240649i
$349$	1.16983	+	2.02621i	0.0626197	+	0.108460i	0.895636	−	0.444788i	$-0.146721\pi$
$349$	1.16983	+	2.02621i	0.0626197	+	0.108460i	−0.833016	+	0.553249i	$0.813388\pi$
$350$	−2.31019	+	4.00136i	−0.123485	+	0.213882i
$351$	−12.9880	+	10.8983i	−0.693250	+	0.581706i
$352$	2.62752	−	2.20475i	0.140047	−	0.117514i
$353$	3.32480	−	5.75873i	0.176961	−	0.306506i	−0.763877	−	0.645362i	$-0.776707\pi$
$353$	3.32480	−	5.75873i	0.176961	−	0.306506i	0.940838	+	0.338856i	$0.110040\pi$
$354$	−13.9749	−	24.2053i	−0.742759	−	1.28650i
$355$	0.0141681	+	0.00515676i	0.000751963	+	0.000273692i
$356$	−2.16208	+	12.2618i	−0.114590	+	0.649874i
$357$	−0.942062	−	5.34270i	−0.0498592	−	0.282766i
$358$	−16.7243	+	6.08714i	−0.883906	+	0.321715i
$359$	17.8186	+	14.9516i	0.940429	+	0.789114i	0.977660	−	0.210193i	$-0.0674093\pi$
$359$	17.8186	+	14.9516i	0.940429	+	0.789114i	−0.0372310	+	0.999307i	$0.511854\pi$
$360$	−1.10005			−0.0579780
$361$	16.0218	−	10.2128i	0.843253	−	0.537516i
$362$	−5.92757			−0.311546
$363$	1.28160	+	1.07539i	0.0672664	+	0.0564432i
$364$	5.99629	−	2.18247i	0.314291	−	0.114393i
$365$	−1.39811	−	7.92906i	−0.0731803	−	0.415026i
$366$	−2.10670	+	11.9477i	−0.110119	+	0.624516i
$367$	−10.0043	−	3.64125i	−0.522218	−	0.190072i	0.0674424	−	0.997723i	$-0.478516\pi$
$367$	−10.0043	−	3.64125i	−0.522218	−	0.190072i	−0.589660	+	0.807651i	$0.700738\pi$
$368$	−1.35264	−	2.34283i	−0.0705110	−	0.122129i
$369$	1.15025	−	1.99230i	0.0598798	−	0.103715i
$370$	−2.01449	+	1.69036i	−0.104728	+	0.0878776i
$371$	3.91608	−	3.28598i	0.203313	−	0.170600i
$372$	8.45101	−	14.6376i	0.438164	−	0.758923i
$373$	14.4397	+	25.0103i	0.747659	+	1.29498i	0.948942	+	0.315450i	$0.102156\pi$
$373$	14.4397	+	25.0103i	0.747659	+	1.29498i	−0.201283	+	0.979533i	$0.564511\pi$
$374$	−7.99334	−	2.90934i	−0.413326	−	0.150438i
$375$	2.25165	−	12.7697i	0.116274	−	0.659425i
$376$	0.266984	+	1.51414i	0.0137686	+	0.0780858i
$377$	−35.9788	+	13.0952i	−1.85300	+	0.674437i
$378$	2.03539	+	1.70789i	0.104689	+	0.0878444i
$379$	−33.1311			−1.70183			−0.850916	−	0.525302i	$-0.823952\pi$
$379$	−33.1311			−1.70183			−0.850916	+	0.525302i	$0.823952\pi$
$380$	2.57830	−	0.751865i	0.132264	−	0.0385698i
$381$	9.72616			0.498286
$382$	12.5299	+	10.5139i	0.641087	+	0.537936i
$383$	3.43384	−	1.24981i	0.175461	−	0.0638625i	−0.252796	−	0.967520i	$-0.581350\pi$
$383$	3.43384	−	1.24981i	0.175461	−	0.0638625i	0.428257	+	0.903657i	$0.359128\pi$
$384$	0.379865	+	2.15432i	0.0193849	+	0.109937i
$385$	0.366979	−	2.08124i	0.0187030	−	0.106070i
$386$	−18.7831	−	6.83648i	−0.956033	−	0.347968i
$387$	9.24692	+	16.0161i	0.470047	+	0.814146i
$388$	0.758570	−	1.31388i	0.0385105	−	0.0667022i
$389$	−7.08651	+	5.94629i	−0.359300	+	0.301489i	−0.804512	−	0.593937i	$-0.797573\pi$
$389$	−7.08651	+	5.94629i	−0.359300	+	0.301489i	0.445212	+	0.895425i	$0.353128\pi$
$390$	−6.58854	+	5.52844i	−0.333624	+	0.279943i
$391$	−3.35453	+	5.81021i	−0.169646	+	0.293835i
$392$	−0.500000	−	0.866025i	−0.0252538	−	0.0437409i
$393$	−14.7426	−	5.36588i	−0.743668	−	0.270673i
$394$	−0.598097	+	3.39197i	−0.0301317	+	0.170885i
$395$	−0.316997	−	1.79778i	−0.0159499	−	0.0904562i
$396$	−5.75457	+	2.09449i	−0.289178	+	0.105252i
$397$	14.7317	+	12.3614i	0.739365	+	0.620401i	0.932667	−	0.360739i	$-0.117475\pi$
$397$	14.7317	+	12.3614i	0.739365	+	0.620401i	−0.193302	+	0.981139i	$0.561920\pi$
$398$	3.13027			0.156906
$399$	8.72829	+	3.83920i	0.436961	+	0.192201i
$400$	−4.62037			−0.231019
$401$	−22.6313	−	18.9899i	−1.13015	−	0.948310i	−0.131079	−	0.991372i	$-0.541844\pi$
$401$	−22.6313	−	18.9899i	−1.13015	−	0.948310i	−0.999072	+	0.0430619i	$0.986289\pi$
$402$	−8.56131	+	3.11606i	−0.426999	+	0.155415i
$403$	−8.56144	−	48.5543i	−0.426476	−	2.41866i
$404$	−1.72402	+	9.77740i	−0.0857732	+	0.486444i
$405$	−6.46638	−	2.35357i	−0.321317	−	0.116950i
$406$	3.00008	+	5.19630i	0.148892	+	0.257888i
$407$	−7.31973	+	12.6781i	−0.362825	+	0.628432i
$408$	4.15588	−	3.48720i	0.205747	−	0.172642i
$409$	−30.5625	+	25.6450i	−1.51122	+	1.26806i	−0.649875	+	0.760041i	$0.725179\pi$
$409$	−30.5625	+	25.6450i	−1.51122	+	1.26806i	−0.861344	+	0.508022i	$0.830377\pi$
$410$	−0.396951	+	0.687539i	−0.0196040	+	0.0339552i
$411$	18.3834	+	31.8410i	0.906787	+	1.57060i
$412$	−7.84632	−	2.85583i	−0.386561	−	0.140697i
$413$	−2.21866	+	12.5826i	−0.109173	+	0.619152i
$414$	0.838719	+	4.75661i	0.0412208	+	0.233775i
$415$	7.49347	−	2.72740i	0.367840	−	0.133883i
$416$	4.88822	+	4.10171i	0.239665	+	0.201103i
$417$	−29.6559			−1.45225
$418$	12.0560	−	8.84219i	0.589677	−	0.432486i
$419$	−34.5562			−1.68818			−0.844090	−	0.536201i	$-0.819859\pi$
$419$	−34.5562			−1.68818			−0.844090	+	0.536201i	$0.819859\pi$
$420$	1.03250	+	0.866374i	0.0503811	+	0.0422747i
$421$	27.1243	−	9.87245i	1.32196	−	0.481154i	0.417873	−	0.908505i	$-0.362776\pi$
$421$	27.1243	−	9.87245i	1.32196	−	0.481154i	0.904085	+	0.427352i	$0.140553\pi$
$422$	−2.89970	−	16.4450i	−0.141155	−	0.800531i
$423$	0.476672	−	2.70334i	0.0231766	−	0.131441i
$424$	4.80378	+	1.74843i	0.233292	+	0.0849115i
$425$	5.72924	+	9.92334i	0.277909	+	0.481353i
$426$	−0.0267655	+	0.0463592i	−0.00129679	+	0.00224611i
$427$	4.24842	−	3.56485i	0.205595	−	0.172515i
$428$	10.3847	−	8.71377i	0.501962	−	0.421196i
$429$	−23.9397	+	41.4647i	−1.15582	+	2.00194i
$430$	−3.19110	−	5.52715i	−0.153889	−	0.266543i
$431$	18.3126	+	6.66525i	0.882089	+	0.321054i	0.743052	−	0.669233i	$-0.233377\pi$
$431$	18.3126	+	6.66525i	0.882089	+	0.321054i	0.139036	+	0.990287i	$0.455600\pi$
$432$	−0.461384	+	2.61664i	−0.0221984	+	0.125893i
$433$	−0.250445	−	1.42034i	−0.0120356	−	0.0682573i	0.978198	−	0.207673i	$-0.0665888\pi$
$433$	−0.250445	−	1.42034i	−0.0120356	−	0.0682573i	−0.990234	+	0.139415i	$0.955478\pi$
$434$	−7.26048	+	2.64260i	−0.348514	+	0.126849i
$435$	−6.19520	−	5.19839i	−0.297037	−	0.249244i
$436$	0.558302			0.0267378
$437$	−5.21683	−	10.5753i	−0.249555	−	0.505883i
$438$	28.5858			1.36588
$439$	12.6799	+	10.6397i	0.605180	+	0.507806i	0.893106	−	0.449846i	$-0.148521\pi$
$439$	12.6799	+	10.6397i	0.605180	+	0.507806i	−0.287926	+	0.957653i	$0.592966\pi$
$440$	1.98590	−	0.722807i	0.0946739	−	0.0344585i
$441$	0.310031	+	1.75827i	0.0147634	+	0.0837274i
$442$	2.74801	−	15.5847i	0.130709	−	0.741289i
$443$	−2.90147	−	1.05605i	−0.137853	−	0.0501744i	0.272172	−	0.962249i	$-0.412258\pi$
$443$	−2.90147	−	1.05605i	−0.137853	−	0.0501744i	−0.410025	+	0.912074i	$0.634480\pi$
$444$	−4.66833	−	8.08579i	−0.221549	−	0.383735i
$445$	−3.83576	+	6.64373i	−0.181832	+	0.314943i
$446$	11.1723	−	9.37464i	0.529022	−	0.443902i
$447$	22.7888	−	19.1220i	1.07787	−	0.904441i
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	8.95405	+	15.5089i	0.422568	+	0.731909i	0.996190	−	0.0872114i	$-0.0277956\pi$
$449$	8.95405	+	15.5089i	0.422568	+	0.731909i	−0.573622	+	0.819120i	$0.694462\pi$
$450$	7.75172	+	2.82140i	0.365420	+	0.133002i
$451$	−0.767450	+	4.35243i	−0.0361378	+	0.204948i
$452$	1.75361	+	9.94520i	0.0824828	+	0.467783i
$453$	41.5906	−	15.1377i	1.95410	−	0.711233i
$454$	−3.62594	−	3.04253i	−0.170174	−	0.142793i
$455$	3.93166			0.184319
$456$	1.03930	+	9.47853i	0.0486696	+	0.443873i
$457$	31.2954			1.46394			0.731970	−	0.681337i	$-0.238601\pi$
$457$	31.2954			1.46394			0.731970	+	0.681337i	$0.238601\pi$
$458$	11.3843	+	9.55255i	0.531953	+	0.446361i
$459$	6.19197	−	2.25369i	0.289016	−	0.105193i
$460$	−0.289441	−	1.64150i	−0.0134953	−	0.0765354i
$461$	−2.01579	+	11.4321i	−0.0938845	+	0.532446i	0.901199	+	0.433406i	$0.142688\pi$
$461$	−2.01579	+	11.4321i	−0.0938845	+	0.532446i	−0.995083	+	0.0990400i	$0.968423\pi$
$462$	7.05078	+	2.56627i	0.328032	+	0.119394i
$463$	−2.07566	−	3.59515i	−0.0964640	−	0.167081i	0.813755	−	0.581209i	$-0.197420\pi$
$463$	−2.07566	−	3.59515i	−0.0964640	−	0.167081i	−0.910219	+	0.414128i	$0.864087\pi$
$464$	−3.00008	+	5.19630i	−0.139275	+	0.241232i
$465$	7.97758	−	6.69399i	0.369952	−	0.310426i
$466$	−3.34570	+	2.80738i	−0.154987	+	0.130049i
$467$	12.4598	−	21.5810i	0.576570	−	0.998649i	−0.419299	−	0.907848i	$-0.637724\pi$
$467$	12.4598	−	21.5810i	0.576570	−	0.998649i	0.995869	−	0.0908009i	$-0.0289427\pi$
$468$	−5.69643	−	9.86650i	−0.263317	−	0.456079i
$469$	3.91364	+	1.42445i	0.180715	+	0.0657750i
$470$	−0.164499	+	0.932921i	−0.00758778	+	0.0430324i
$471$	−4.22018	−	23.9338i	−0.194455	−	1.10281i
$472$	−12.0062	+	4.36991i	−0.552631	+	0.201141i
$473$	−27.2168	−	22.8376i	−1.25143	−	1.05008i
$474$	6.48135			0.297698
$475$	−20.0968	−	1.31462i	−0.922104	−	0.0603189i
$476$	−2.47999			−0.113670
$477$	−6.99177	−	5.86679i	−0.320131	−	0.268622i
$478$	22.7609	−	8.28430i	1.04106	−	0.378915i
$479$	−3.29546	−	18.6895i	−0.150573	−	0.853944i	−0.962722	−	0.270493i	$-0.912813\pi$
$479$	−3.29546	−	18.6895i	−0.150573	−	0.853944i	0.812149	−	0.583451i	$-0.198298\pi$
$480$	−0.234050	+	1.32736i	−0.0106829	+	0.0605855i
$481$	−25.5927	−	9.31497i	−1.16693	−	0.424726i
$482$	8.55047	+	14.8098i	0.389463	+	0.674570i
$483$	2.95897	−	5.12508i	0.134638	−	0.233199i
$484$	0.585858	−	0.491593i	0.0266299	−	0.0223451i
$485$	0.716075	−	0.600858i	0.0325153	−	0.0272836i
$486$	8.23040	−	14.2555i	0.373338	−	0.646641i
$487$	−18.0754	−	31.3075i	−0.819074	−	1.41868i	−0.906365	−	0.422496i	$-0.861154\pi$
$487$	−18.0754	−	31.3075i	−0.819074	−	1.41868i	0.0872906	−	0.996183i	$-0.472179\pi$
$488$	5.21146	+	1.89681i	0.235912	+	0.0858648i
$489$	−3.90513	+	22.1471i	−0.176596	+	1.00153i
$490$	−0.106991	−	0.606779i	−0.00483338	−	0.0274115i
$491$	−2.90134	+	1.05600i	−0.130936	+	0.0476566i	−0.406657	−	0.913581i	$-0.633306\pi$
$491$	−2.90134	+	1.05600i	−0.130936	+	0.0476566i	0.275721	+	0.961238i	$0.411083\pi$
$492$	−2.15924	−	1.81182i	−0.0973461	−	0.0816831i
$493$	14.8804			0.670178
$494$	20.0948	+	19.2316i	0.904107	+	0.865272i
$495$	−3.77317			−0.169591
$496$	−5.91880	−	4.96646i	−0.265762	−	0.223001i
$497$	0.0229949	−	0.00836947i	0.00103146	−	0.000375422i
$498$	4.91641	+	27.8823i	0.220309	+	1.24944i
$499$	5.37602	−	30.4890i	0.240664	−	1.36487i	−0.589687	−	0.807632i	$-0.700749\pi$
$499$	5.37602	−	30.4890i	0.240664	−	1.36487i	0.830351	−	0.557241i	$-0.188140\pi$
$500$	−5.57002	−	2.02732i	−0.249099	−	0.0906645i
$501$	13.8634	+	24.0121i	0.619372	+	1.07278i
$502$	−13.6548	+	23.6508i	−0.609443	+	1.05559i
$503$	2.90536	−	2.43789i	0.129544	−	0.108700i	−0.575714	−	0.817651i	$-0.695276\pi$
$503$	2.90536	−	2.43789i	0.129544	−	0.108700i	0.705258	+	0.708951i	$0.250831\pi$
$504$	−1.36770	+	1.14763i	−0.0609220	+	0.0511196i
$505$	−3.05859	+	5.29763i	−0.136105	+	0.235741i
$506$	−4.63952	−	8.03588i	−0.206252	−	0.357239i
$507$	−56.9794	−	20.7388i	−2.53055	−	0.921043i
$508$	0.772063	−	4.37859i	0.0342547	−	0.194268i
$509$	6.25599	+	35.4795i	0.277292	+	1.57260i	0.731586	+	0.681749i	$0.238780\pi$
$509$	6.25599	+	35.4795i	0.277292	+	1.57260i	−0.454294	+	0.890852i	$0.650108\pi$
$510$	3.14104	−	1.14325i	0.139088	−	0.0506238i
$511$	−10.0103	−	8.39960i	−0.442828	−	0.371577i
$512$	1.00000			0.0441942
$513$	−2.75134	+	11.2501i	−0.121475	+	0.496703i
$514$	−9.96817			−0.439677
$515$	−3.94106	−	3.30694i	−0.173664	−	0.145721i
$516$	21.2930	−	7.75002i	0.937372	−	0.341175i
$517$	0.915749	+	5.19347i	0.0402746	+	0.228409i
$518$	−0.741145	+	4.20324i	−0.0325640	+	0.184680i
$519$	−12.8361	−	4.67197i	−0.563443	−	0.205077i
$520$	1.96583	+	3.40492i	0.0862073	+	0.149315i
$521$	−3.95514	+	6.85050i	−0.173278	+	0.300126i	−0.939564	−	0.342374i	$-0.888769\pi$
$521$	−3.95514	+	6.85050i	−0.173278	+	0.300126i	0.766286	+	0.642499i	$0.222102\pi$
$522$	8.20640	−	6.88599i	0.359184	−	0.301391i
$523$	−25.3465	+	21.2683i	−1.10833	+	0.929997i	−0.997957	−	0.0638939i	$-0.979648\pi$
$523$	−25.3465	+	21.2683i	−1.10833	+	0.929997i	−0.110370	+	0.993891i	$0.535204\pi$
$524$	−3.58592	+	6.21099i	−0.156652	+	0.271328i
$525$	−5.05366	−	8.75320i	−0.220560	−	0.382021i
$526$	23.4279	+	8.52705i	1.02150	+	0.371797i
$527$	−3.32736	+	18.8704i	−0.144942	+	0.822008i
$528$	1.30293	+	7.38929i	0.0567028	+	0.321577i
$529$	14.7358	−	5.36339i	0.640687	−	0.233191i
$530$	2.41285	+	2.02462i	0.104808	+	0.0879440i
$531$	22.8116			0.989939
$532$	2.42121	−	3.62460i	0.104973	−	0.157146i
$533$	−8.22215			−0.356141
$534$	−20.8649	−	17.5077i	−0.902911	−	0.757632i
$535$	7.84880	−	2.85673i	0.339333	−	0.123507i
$536$	0.723212	+	4.10154i	0.0312380	+	0.177159i
$537$	6.76069	−	38.3418i	0.291745	−	1.65457i
$538$	24.1186	+	8.77845i	1.03983	+	0.378466i
$539$	−1.71499	−	2.97045i	−0.0738699	−	0.127946i
$540$	−0.818543	+	1.41776i	−0.0352245	+	0.0610106i
$541$	7.14100	−	5.99201i	0.307016	−	0.257617i	−0.476242	−	0.879315i	$-0.658001\pi$
$541$	7.14100	−	5.99201i	0.307016	−	0.257617i	0.783257	+	0.621698i	$0.213557\pi$
$542$	14.3989	−	12.0821i	0.618484	−	0.518970i
$543$	6.48344	−	11.2297i	0.278231	−	0.481910i
$544$	−1.24000	−	2.14774i	−0.0531644	−	0.0920834i
$545$	0.323246	+	0.117652i	0.0138464	+	0.00503966i
$546$	−2.42397	+	13.7470i	−0.103736	+	0.588317i
$547$	−4.74851	−	26.9302i	−0.203032	−	1.15145i	−0.900507	−	0.434842i	$-0.856804\pi$
$547$	−4.74851	−	26.9302i	−0.203032	−	1.15145i	0.697475	−	0.716609i	$-0.254307\pi$
$548$	15.7937	−	5.74842i	0.674672	−	0.245560i
$549$	−7.58512	−	6.36467i	−0.323725	−	0.271638i
$550$	−15.8478			−0.675752
$551$	−14.5277	+	21.7482i	−0.618899	+	0.926505i
$552$	5.91793			0.251884
$553$	−2.26966	−	1.90447i	−0.0965157	−	0.0809863i
$554$	−18.6759	+	6.79748i	−0.793463	+	0.288797i
$555$	−0.998944	−	5.66529i	−0.0424028	−	0.240478i
$556$	−2.35408	+	13.3507i	−0.0998354	+	0.566195i
$557$	15.5014	+	5.64206i	0.656817	+	0.239062i	0.648861	−	0.760907i	$-0.275246\pi$
$557$	15.5014	+	5.64206i	0.656817	+	0.239062i	0.00795525	+	0.999968i	$0.497468\pi$
$558$	6.89739	+	11.9466i	0.291990	+	0.505741i
$559$	33.0490	−	57.2426i	1.39783	−	2.42111i
$560$	0.471990	−	0.396047i	0.0199452	−	0.0167360i
$561$	14.2546	−	11.9610i	0.601830	−	0.504995i
$562$	10.6472	−	18.4414i	0.449123	−	0.777904i
$563$	17.7341	+	30.7163i	0.747401	+	1.29454i	0.949064	+	0.315082i	$0.102032\pi$
$563$	17.7341	+	30.7163i	0.747401	+	1.29454i	−0.201663	+	0.979455i	$0.564635\pi$
$564$	−3.16053	−	1.15034i	−0.133082	−	0.0484379i
$565$	−1.08047	+	6.12763i	−0.0454556	+	0.257791i
$566$	−0.655462	−	3.71731i	−0.0275511	−	0.156250i
$567$	−10.4950	+	3.81987i	−0.440749	+	0.160419i
$568$	0.0187456	+	0.0157295i	0.000786549	+	0.000659993i
$569$	−43.3131			−1.81578			−0.907889	−	0.419210i	$-0.862307\pi$
$569$	−43.3131			−1.81578			−0.907889	+	0.419210i	$0.862307\pi$
$570$	−1.39569	+	5.70690i	−0.0584592	+	0.239036i
$571$	1.18471			0.0495787			0.0247893	−	0.999693i	$-0.492108\pi$
$571$	1.18471			0.0495787			0.0247893	+	0.999693i	$0.492108\pi$
$572$	16.7665	+	14.0688i	0.701043	+	0.588245i
$573$	−33.6233	+	12.2379i	−1.40463	+	0.511244i
$574$	0.223748	+	1.26894i	0.00933904	+	0.0529643i
$575$	−2.17049	+	12.3095i	−0.0905158	+	0.513340i
$576$	−1.67773	−	0.610642i	−0.0699053	−	0.0254434i
$577$	−6.47773	−	11.2198i	−0.269671	−	0.467085i	0.699106	−	0.715018i	$-0.253582\pi$
$577$	−6.47773	−	11.2198i	−0.269671	−	0.467085i	−0.968777	+	0.247934i	$0.920248\pi$
$578$	5.42482	−	9.39606i	0.225643	−	0.390825i
$579$	33.4961	−	28.1065i	1.39205	−	1.16807i
$580$	−2.83202	+	2.37635i	−0.117593	+	0.0986724i
$581$	6.47125	−	11.2085i	0.268473	−	0.465009i
$582$	1.65941	+	2.87419i	0.0687849	+	0.119139i
$583$	16.4769	+	5.99710i	0.682403	+	0.248374i
$584$	2.26914	−	12.8689i	0.0938977	−	0.532520i
$585$	−1.21894	−	6.91294i	−0.0503969	−	0.285815i
$586$	15.9357	−	5.80012i	0.658297	−	0.239601i
$587$	27.9150	+	23.4235i	1.15218	+	0.966791i	0.999768	−	0.0215266i	$-0.00685267\pi$
$587$	27.9150	+	23.4235i	1.15218	+	0.966791i	0.152408	+	0.988318i	$0.451297\pi$
$588$	2.18756			0.0902133
$589$	−24.3313	−	23.2862i	−1.00255	−	0.959490i
$590$	−7.87226			−0.324096
$591$	−5.77184	−	4.84315i	−0.237422	−	0.199220i
$592$	−4.01069	+	1.45977i	−0.164838	+	0.0599962i
$593$	5.50142	+	31.2001i	0.225916	+	1.28124i	0.860926	+	0.508731i	$0.169885\pi$
$593$	5.50142	+	31.2001i	0.225916	+	1.28124i	−0.635009	+	0.772504i	$0.719004\pi$
$594$	−1.58254	+	8.97503i	−0.0649324	+	0.368250i
$595$	−1.43587	−	0.522614i	−0.0588649	−	0.0214251i
$596$	−6.79951	−	11.7771i	−0.278519	−	0.482409i
$597$	−3.42381	+	5.93022i	−0.140127	+	0.242708i
$598$	13.2240	−	11.0962i	0.540769	−	0.453759i
$599$	3.99428	−	3.35160i	0.163202	−	0.136943i	−0.557529	−	0.830157i	$-0.688251\pi$
$599$	3.99428	−	3.35160i	0.163202	−	0.136943i	0.720731	+	0.693215i	$0.243806\pi$
$600$	5.05366	−	8.75320i	0.206315	−	0.357348i
$601$	4.21615	+	7.30259i	0.171981	+	0.297879i	0.939112	−	0.343611i	$-0.111650\pi$
$601$	4.21615	+	7.30259i	0.171981	+	0.297879i	−0.767132	+	0.641490i	$0.778317\pi$
$602$	−9.73369	−	3.54278i	−0.396716	−	0.144393i
$603$	1.29122	−	7.32288i	0.0525826	−	0.298211i
$604$	−3.51334	−	19.9251i	−0.142956	−	0.810743i
$605$	0.442795	−	0.161164i	0.0180022	−	0.00655226i
$606$	−16.6374	−	13.9604i	−0.675848	−	0.567103i
$607$	18.8481			0.765022			0.382511	−	0.923951i	$-0.375059\pi$
$607$	18.8481			0.765022			0.382511	+	0.923951i	$0.375059\pi$
$608$	4.34960	+	0.284527i	0.176400	+	0.0115391i
$609$	−13.1257			−0.531880
$610$	2.61762	+	2.19644i	0.105984	+	0.0889313i
$611$	−9.21929	+	3.35555i	−0.372972	+	0.135751i
$612$	0.768875	+	4.36051i	0.0310799	+	0.176263i
$613$	2.57333	−	14.5941i	0.103936	−	0.589449i	−0.887704	−	0.460414i	$-0.847701\pi$
$613$	2.57333	−	14.5941i	0.103936	−	0.589449i	0.991640	−	0.129035i	$-0.0411880\pi$
$614$	2.52387	+	0.918614i	0.101855	+	0.0370722i
$615$	−0.868353	−	1.50403i	−0.0350154	−	0.0606484i
$616$	1.71499	−	2.97045i	0.0690990	−	0.119683i
$617$	10.9435	−	9.18271i	0.440570	−	0.369682i	−0.395353	−	0.918529i	$-0.629378\pi$
$617$	10.9435	−	9.18271i	0.440570	−	0.369682i	0.835923	+	0.548847i	$0.184933\pi$
$618$	13.9924	−	11.7411i	0.562859	−	0.472294i
$619$	13.9441	−	24.1518i	0.560459	−	0.970744i	−0.436997	−	0.899463i	$-0.643958\pi$
$619$	13.9441	−	24.1518i	0.560459	−	0.970744i	0.997456	−	0.0712809i	$-0.0227087\pi$
$620$	−2.38028	−	4.12277i	−0.0955944	−	0.165574i
$621$	6.75444	+	2.45842i	0.271046	+	0.0986528i
$622$	0.307495	−	1.74389i	0.0123294	−	0.0699236i
$623$	2.16208	+	12.2618i	0.0866221	+	0.491258i
$624$	−13.1172	+	4.77428i	−0.525109	+	0.191124i
$625$	14.8993	+	12.5020i	0.595973	+	0.500081i
$626$	7.89729			0.315639
$627$	3.56478	+	32.5112i	0.142364	+	1.29837i
$628$	−11.1097			−0.443324
$629$	8.10844	+	6.80379i	0.323305	+	0.271285i
$630$	−1.03371	+	0.376241i	−0.0411841	+	0.0149898i
$631$	4.58051	+	25.9774i	0.182347	+	1.03414i	0.929317	+	0.369284i	$0.120397\pi$
$631$	4.58051	+	25.9774i	0.182347	+	1.03414i	−0.746969	+	0.664859i	$0.768492\pi$
$632$	0.514490	−	2.91782i	0.0204653	−	0.116065i
$633$	34.3263	+	12.4938i	1.36435	+	0.496583i
$634$	5.81011	+	10.0634i	0.230749	+	0.399669i
$635$	1.36972	−	2.37242i	0.0543556	−	0.0941467i
$636$	−8.56664	+	7.18827i	−0.339689	+	0.285033i
$637$	4.88822	−	4.10171i	0.193678	−	0.162516i
$638$	−10.2902	+	17.8232i	−0.407394	+	0.705628i
$639$	−0.0218450	−	0.0378366i	−0.000864174	−	0.00149679i
$640$	0.578982	+	0.210732i	0.0228863	+	0.00832992i
$641$	6.79783	−	38.5524i	0.268498	−	1.52273i	−0.490387	−	0.871505i	$-0.663144\pi$
$641$	6.79783	−	38.5524i	0.268498	−	1.52273i	0.758885	−	0.651225i	$-0.225744\pi$
$642$	5.14953	+	29.2044i	0.203236	+	1.15261i
$643$	5.82827	−	2.12132i	0.229845	−	0.0836566i	−0.224530	−	0.974467i	$-0.572085\pi$
$643$	5.82827	−	2.12132i	0.229845	−	0.0836566i	0.454375	+	0.890810i	$0.349863\pi$
$644$	−2.07236	−	1.73892i	−0.0816624	−	0.0685229i
$645$	13.9614			0.549731
$646$	−4.78240	−	9.69461i	−0.188161	−	0.381429i
$647$	−2.11530			−0.0831610			−0.0415805	−	0.999135i	$-0.513239\pi$
$647$	−2.11530			−0.0831610			−0.0415805	+	0.999135i	$0.513239\pi$
$648$	−8.55560	−	7.17900i	−0.336096	−	0.282018i
$649$	−41.1811	+	14.9887i	−1.61650	+	0.588358i
$650$	−5.11970	−	29.0352i	−0.200811	−	1.13886i
$651$	2.93500	−	16.6452i	0.115032	−	0.652378i
$652$	9.66032	+	3.51607i	0.378328	+	0.137700i
$653$	10.1015	+	17.4963i	0.395301	+	0.684682i	0.993140	−	0.116935i	$-0.0373069\pi$
$653$	10.1015	+	17.4963i	0.395301	+	0.684682i	−0.597838	+	0.801617i	$0.703974\pi$
$654$	−0.610658	+	1.05769i	−0.0238786	+	0.0413590i
$655$	−3.38503	+	2.84038i	−0.132264	+	0.110983i
$656$	−0.987057	+	0.828239i	−0.0385381	+	0.0323373i
$657$	−11.6653	+	20.2049i	−0.455107	+	0.788269i
$658$	0.768749	+	1.33151i	0.0299689	+	0.0519077i
$659$	21.9025	+	7.97187i	0.853202	+	0.310540i	0.731345	−	0.682008i	$-0.238893\pi$
$659$	21.9025	+	7.97187i	0.853202	+	0.310540i	0.121857	+	0.992548i	$0.461115\pi$
$660$	−0.802787	+	4.55283i	−0.0312484	+	0.177219i
$661$	−4.93695	−	27.9988i	−0.192025	−	1.08903i	−0.916592	−	0.399823i	$-0.869071\pi$
$661$	−4.93695	−	27.9988i	−0.192025	−	1.08903i	0.724567	−	0.689204i	$-0.242040\pi$
$662$	1.08395	−	0.394527i	0.0421291	−	0.0153337i
$663$	26.5192	+	22.2522i	1.02992	+	0.864206i
$664$	12.9425			0.502267
$665$	2.16566	−	1.58835i	0.0839805	−	0.0615936i
$666$	7.62023			0.295278
$667$	12.4345	+	10.4338i	0.481466	+	0.403998i
$668$	11.9104	−	4.33504i	0.460828	−	0.167728i
$669$	5.54009	+	31.4194i	0.214192	+	1.21474i
$670$	−0.445599	+	2.52712i	−0.0172150	+	0.0976311i
$671$	17.8752	+	6.50604i	0.690065	+	0.251163i
$672$	1.09378	+	1.89448i	0.0421934	+	0.0730811i
$673$	4.74349	−	8.21596i	0.182848	−	0.316702i	−0.760001	−	0.649922i	$-0.774802\pi$
$673$	4.74349	−	8.21596i	0.182848	−	0.316702i	0.942849	+	0.333220i	$0.108135\pi$
$674$	−5.60395	+	4.70227i	−0.215856	+	0.181125i
$675$	9.40424	−	7.89109i	0.361969	−	0.303728i
$676$	−13.8594	+	24.0051i	−0.533052	+	0.923274i
$677$	−21.6433	−	37.4873i	−0.831820	−	1.44075i	−0.896593	−	0.442855i	$-0.853966\pi$
$677$	−21.6433	−	37.4873i	−0.831820	−	1.44075i	0.0647731	−	0.997900i	$-0.479368\pi$
$678$	−20.7590	−	7.55567i	−0.797246	−	0.290174i
$679$	0.263448	−	1.49409i	0.0101102	−	0.0573379i
$680$	−0.265338	−	1.50481i	−0.0101752	−	0.0577067i
$681$	9.72997	−	3.54142i	0.372853	−	0.135708i
$682$	−20.3014	−	17.0349i	−0.777380	−	0.652299i
$683$	−16.3891			−0.627110			−0.313555	−	0.949570i	$-0.601520\pi$
$683$	−16.3891			−0.627110			−0.313555	+	0.949570i	$0.601520\pi$
$684$	−7.12370	−	3.13341i	−0.272381	−	0.119809i
$685$	10.3556			0.395668
$686$	−0.766044	−	0.642788i	−0.0292477	−	0.0245417i
$687$	−30.5490	+	11.1189i	−1.16552	+	0.424213i
$688$	−1.79871	−	10.2010i	−0.0685753	−	0.388910i
$689$	−5.66454	+	32.1252i	−0.215802	+	1.22387i
$690$	3.42637	+	1.24710i	0.130440	+	0.0474762i
$691$	−20.7128	−	35.8757i	−0.787953	−	1.36478i	−0.927219	−	0.374520i	$-0.877808\pi$
$691$	−20.7128	−	35.8757i	−0.787953	−	1.36478i	0.139266	−	0.990255i	$-0.455526\pi$
$692$	−3.12219	+	5.40779i	−0.118688	+	0.205573i
$693$	−4.69117	+	3.93636i	−0.178203	+	0.149530i
$694$	−24.0311	+	20.1645i	−0.912208	+	0.765433i
$695$	−4.17639	+	7.23371i	−0.158419	+	0.274390i
$696$	−6.56285	−	11.3672i	−0.248764	−	0.430872i
$697$	3.00278	+	1.09292i	0.113739	+	0.0413975i
$698$	−0.406279	+	2.30412i	−0.0153779	+	0.0872122i
$699$	−1.65906	−	9.40902i	−0.0627515	−	0.355882i
$700$	−4.34173	+	1.58026i	−0.164102	+	0.0597282i
$701$	35.3214	+	29.6382i	1.33407	+	1.11942i	0.983108	+	0.183028i	$0.0585899\pi$
$701$	35.3214	+	29.6382i	1.33407	+	1.11942i	0.350962	+	0.936390i	$0.385855\pi$
$702$	−16.9547			−0.639913
$703$	−17.8602	+	5.20827i	−0.673612	+	0.196434i
$704$	3.42998			0.129272
$705$	−1.58747	−	1.33205i	−0.0597877	−	0.0501678i
$706$	6.24858	−	2.27430i	0.235169	−	0.0855943i
$707$	1.72402	+	9.77740i	0.0648384	+	0.367717i
$708$	4.85344	−	27.5252i	0.182404	−	1.03446i
$709$	25.4027	+	9.24581i	0.954017	+	0.347234i	0.771686	−	0.636004i	$-0.219414\pi$
$709$	25.4027	+	9.24581i	0.954017	+	0.347234i	0.182331	+	0.983237i	$0.441636\pi$
$710$	0.00753868	+	0.0130574i	0.000282921	+	0.000490034i
$711$	−2.64492	+	4.58113i	−0.0991921	+	0.171806i
$712$	−9.53798	+	8.00332i	−0.357451	+	0.299937i
$713$	−16.0120	+	13.4356i	−0.599652	+	0.503168i
$714$	2.71256	−	4.69829i	0.101515	−	0.175829i
$715$	6.74276	+	11.6788i	0.252165	+	0.436763i
$716$	−16.7243	−	6.08714i	−0.625016	−	0.227487i
$717$	−9.20096	+	52.1813i	−0.343616	+	1.94875i
$718$	4.03915	+	22.9071i	0.150740	+	0.854887i
$719$	44.9579	−	16.3633i	1.67665	−	0.610249i	0.683802	−	0.729668i	$-0.260325\pi$
$719$	44.9579	−	16.3633i	1.67665	−	0.610249i	0.992844	+	0.119418i	$0.0381030\pi$
$720$	−0.842691	−	0.707101i	−0.0314052	−	0.0263521i
$721$	−8.34988			−0.310966
$722$	18.8381	+	2.47516i	0.701081	+	0.0921159i
$723$	−37.4092			−1.39126
$724$	−4.54078	−	3.81017i	−0.168757	−	0.141604i
$725$	26.0511	−	9.48183i	0.967514	−	0.352146i
$726$	0.290514	+	1.64759i	0.0107820	+	0.0611478i
$727$	0.852060	−	4.83227i	0.0316012	−	0.179219i	−0.964922	−	0.262537i	$-0.915441\pi$
$727$	0.852060	−	4.83227i	0.0316012	−	0.179219i	0.996523	+	0.0833183i	$0.0265518\pi$
$728$	5.99629	+	2.18247i	0.222237	+	0.0808878i
$729$	1.25163	+	2.16789i	0.0463568	+	0.0802923i
$730$	4.02569	−	6.97270i	0.148997	−	0.258071i
$731$	−19.6787	+	16.5124i	−0.727843	+	0.610732i
$732$	−9.29365	+	7.79830i	−0.343503	+	0.288233i
$733$	−26.2850	+	45.5269i	−0.970858	+	1.68157i	−0.277880	+	0.960616i	$0.589632\pi$
$733$	−26.2850	+	45.5269i	−0.970858	+	1.68157i	−0.692978	+	0.720959i	$0.743702\pi$
$734$	−5.32315	−	9.21997i	−0.196481	−	0.340315i
$735$	1.26655	+	0.460988i	0.0467176	+	0.0170038i
$736$	0.469766	−	2.66417i	0.0173158	−	0.0982027i
$737$	2.48060	+	14.0682i	0.0913742	+	0.518209i
$738$	2.16177	−	0.786820i	0.0795758	−	0.0289632i
$739$	19.3190	+	16.2106i	0.710661	+	0.596316i	0.924785	−	0.380491i	$-0.124245\pi$
$739$	19.3190	+	16.2106i	0.710661	+	0.596316i	−0.214123	+	0.976807i	$0.568689\pi$
$740$	−2.62973			−0.0966709
$741$	−58.4131	+	17.0340i	−2.14586	+	0.625760i
$742$	5.11208			0.187670
$743$	4.27593	+	3.58793i	0.156869	+	0.131628i	0.717844	−	0.696204i	$-0.245129\pi$
$743$	4.27593	+	3.58793i	0.156869	+	0.131628i	−0.560975	+	0.827833i	$0.689574\pi$
$744$	15.8827	−	5.78083i	0.582288	−	0.211935i
$745$	−1.45498	−	8.25160i	−0.0533063	−	0.302315i
$746$	−5.01485	+	28.4406i	−0.183607	+	1.04129i
$747$	−21.7140	−	7.90325i	−0.794473	−	0.289165i
$748$	−4.25316	−	7.36670i	−0.155511	−	0.269353i
$749$	6.77811	−	11.7400i	0.247667	−	0.428971i
$750$	9.93308	−	8.33484i	0.362705	−	0.304345i
$751$	19.7275	−	16.5533i	0.719866	−	0.604039i	−0.207483	−	0.978239i	$-0.566527\pi$
$751$	19.7275	−	16.5533i	0.719866	−	0.604039i	0.927348	+	0.374200i	$0.122083\pi$
$752$	−0.768749	+	1.33151i	−0.0280334	+	0.0485552i
$753$	−29.8706	−	51.7374i	−1.08855	−	1.88542i
$754$	−35.9788	−	13.0952i	−1.31027	−	0.476899i
$755$	2.16471	−	12.2767i	0.0787818	−	0.446794i
$756$	0.461384	+	2.61664i	0.0167804	+	0.0951663i
$757$	42.6135	−	15.5100i	1.54881	−	0.563722i	0.580674	−	0.814136i	$-0.302789\pi$
$757$	42.6135	−	15.5100i	1.54881	−	0.563722i	0.968139	+	0.250414i	$0.0805668\pi$
$758$	−25.3799	−	21.2963i	−0.921840	−	0.773516i
$759$	20.2984			0.736786
$760$	2.45838	+	1.08134i	0.0891748	+	0.0392242i
$761$	−24.9534			−0.904560			−0.452280	−	0.891876i	$-0.649389\pi$
$761$	−24.9534			−0.904560			−0.452280	+	0.891876i	$0.649389\pi$
$762$	7.45067	+	6.25186i	0.269909	+	0.226481i
$763$	0.524632	−	0.190950i	0.0189930	−	0.00691287i
$764$	2.84031	+	16.1082i	0.102759	+	0.582773i
$765$	−0.473734	+	2.68668i	−0.0171279	+	0.0971371i
$766$	3.43384	+	1.24981i	0.124070	+	0.0451576i
$767$	−40.7650	−	70.6071i	−1.47194	−	2.54947i
$768$	−1.09378	+	1.89448i	−0.0394683	+	0.0683611i
$769$	9.90193	−	8.30871i	0.357073	−	0.299620i	−0.446550	−	0.894759i	$-0.647347\pi$
$769$	9.90193	−	8.30871i	0.357073	−	0.299620i	0.803623	+	0.595139i	$0.202903\pi$
$770$	1.61892	−	1.35843i	0.0583417	−	0.0489545i
$771$	10.9030	−	18.8845i	0.392661	−	0.680108i
$772$	−9.99426	−	17.3106i	−0.359701	−	0.623021i
$773$	−13.1749	−	4.79528i	−0.473869	−	0.172474i	0.0940349	−	0.995569i	$-0.470023\pi$
$773$	−13.1749	−	4.79528i	−0.473869	−	0.172474i	−0.567904	+	0.823095i	$0.692246\pi$
$774$	−3.21142	+	18.2129i	−0.115432	+	0.654649i
$775$	6.19907	+	35.1567i	0.222677	+	1.26287i
$776$	1.42564	−	0.518892i	0.0511777	−	0.0186271i
$777$	−7.15230	−	6.00150i	−0.256587	−	0.215302i
$778$	−9.25078			−0.331657
$779$	−4.52896	+	3.32167i	−0.162267	+	0.119011i
$780$	−8.60072			−0.307955
$781$	0.0642972	+	0.0539518i	0.00230073	+	0.00193055i
$782$	−6.30445	+	2.29463i	−0.225447	+	0.0820558i
$783$	−2.76838	−	15.7003i	−0.0989339	−	0.561082i
$784$	0.173648	−	0.984808i	0.00620172	−	0.0351717i
$785$	−6.43230	−	2.34116i	−0.229578	−	0.0835597i
$786$	−7.84439	−	13.5869i	−0.279800	−	0.484628i
$787$	2.06886	−	3.58337i	0.0737468	−	0.127733i	−0.826794	−	0.562505i	$-0.809838\pi$
$787$	2.06886	−	3.58337i	0.0737468	−	0.127733i	0.900541	+	0.434772i	$0.143171\pi$
$788$	−2.63849	+	2.21395i	−0.0939922	+	0.0788688i
$789$	−41.7792	+	35.0569i	−1.48738	+	1.24806i
$790$	0.912758	−	1.58094i	0.0324745	−	0.0562474i
$791$	5.04931	+	8.74566i	0.179533	+	0.310960i
$792$	−5.75457	−	2.09449i	−0.204480	−	0.0744246i
$793$	−6.14526	+	34.8515i	−0.218225	+	1.23761i
$794$	3.33941	+	18.9388i	0.118511	+	0.672111i
$795$	−6.47473	+	2.35661i	−0.229635	+	0.0835802i
$796$	2.39792	+	2.01210i	0.0849921	+	0.0713168i
$797$	53.5733			1.89767			0.948833	−	0.315780i	$-0.102266\pi$
$797$	53.5733			1.89767			0.948833	+	0.315780i	$0.102266\pi$
$798$	4.21847	+	8.55144i	0.149332	+	0.302718i
$799$	3.81298			0.134894
$800$	−3.53941	−	2.96992i	−0.125137	−	0.105002i
$801$	20.8893	−	7.60308i	0.738087	−	0.268642i
$802$	−5.13009	−	29.0942i	−0.181150	−	1.02735i
$803$	7.78312	−	44.1402i	0.274660	−	1.55768i
$804$	−8.56131	−	3.11606i	−0.301934	−	0.109895i
$805$	−0.833412	−	1.44351i	−0.0293739	−	0.0508771i
$806$	24.6517	−	42.6980i	0.868318	−	1.50397i
$807$	−43.0110	+	36.0905i	−1.51406	+	1.27045i
$808$	−7.60547	+	6.38175i	−0.267559	+	0.224509i
$809$	−15.3570	+	26.5990i	−0.539922	+	0.935173i	0.458986	+	0.888444i	$0.348213\pi$
$809$	−15.3570	+	26.5990i	−0.539922	+	0.935173i	−0.998908	+	0.0467288i	$0.985120\pi$
$810$	−3.44069	−	5.95945i	−0.120894	−	0.209394i
$811$	40.9859	+	14.9177i	1.43921	+	0.523830i	0.939556	−	0.342395i	$-0.111238\pi$
$811$	40.9859	+	14.9177i	1.43921	+	0.523830i	0.499654	+	0.866225i	$0.333460\pi$
$812$	−1.04192	+	5.90901i	−0.0365642	+	0.207366i
$813$	7.14009	+	40.4935i	0.250414	+	1.42017i
$814$	−13.7566	+	5.00699i	−0.482168	+	0.175495i
$815$	4.85220	+	4.07148i	0.169965	+	0.142618i
$816$	5.42512			0.189917
$817$	−4.92123	−	44.8821i	−0.172172	−	1.57023i
$818$	−39.8965			−1.39495
$819$	−8.72743	−	7.32318i	−0.304961	−	0.255893i
$820$	−0.746024	+	0.271531i	−0.0260523	+	0.00948226i
$821$	−7.46852	−	42.3561i	−0.260653	−	1.47824i	−0.781134	−	0.624364i	$-0.785358\pi$
$821$	−7.46852	−	42.3561i	−0.260653	−	1.47824i	0.520480	−	0.853874i	$-0.325753\pi$
$822$	−6.38449	+	36.2082i	−0.222685	+	1.26291i
$823$	3.21358	+	1.16965i	0.112018	+	0.0407713i	0.397421	−	0.917636i	$-0.369905\pi$
$823$	3.21358	+	1.16965i	0.112018	+	0.0407713i	−0.285403	+	0.958408i	$0.592127\pi$
$824$	−4.17494	−	7.23121i	−0.145441	−	0.251911i
$825$	17.3340	−	30.0233i	0.603491	−	1.04528i
$826$	−9.78756	+	8.21274i	−0.340553	+	0.285758i
$827$	−21.1725	+	17.7658i	−0.736240	+	0.617779i	−0.931825	−	0.362908i	$-0.881784\pi$
$827$	−21.1725	+	17.7658i	−0.736240	+	0.617779i	0.195585	+	0.980687i	$0.437340\pi$
$828$	−2.41500	+	4.18289i	−0.0839269	+	0.145366i
$829$	−12.8521	−	22.2605i	−0.446373	−	0.773140i	0.551774	−	0.833994i	$-0.313951\pi$
$829$	−12.8521	−	22.2605i	−0.446373	−	0.773140i	−0.998147	+	0.0608535i	$0.980618\pi$
$830$	7.49347	+	2.72740i	0.260102	+	0.0946695i
$831$	7.54962	−	42.8160i	0.261894	−	1.48527i
$832$	1.10807	+	6.28418i	0.0384154	+	0.217865i
$833$	−2.33043	+	0.848207i	−0.0807446	+	0.0293886i
$834$	−22.7177	−	19.0624i	−0.786650	−	0.660078i
$835$	7.80944			0.270257
$836$	14.9191	+	0.975923i	0.515987	+	0.0337530i
$837$	20.5292			0.709593
$838$	−26.4716	−	22.2123i	−0.914446	−	0.767311i
$839$	−34.7540	+	12.6494i	−1.19984	+	0.436706i	−0.863169	−	0.504915i	$-0.831524\pi$
$839$	−34.7540	+	12.6494i	−1.19984	+	0.436706i	−0.336672	+	0.941622i	$0.609301\pi$
$840$	0.234050	+	1.32736i	0.00807548	+	0.0457983i
$841$	1.21588	−	6.89562i	0.0419270	−	0.237780i
$842$	27.1243	+	9.87245i	0.934766	+	0.340227i
$843$	23.2912	+	40.3416i	0.802193	+	1.38944i
$844$	8.34935	−	14.4615i	0.287397	−	0.497785i
$845$	−13.0830	+	10.9779i	−0.450067	+	0.377651i
$846$	2.10283	−	1.76448i	0.0722967	−	0.0606641i
$847$	0.382392	−	0.662322i	0.0131391	−	0.0227576i
$848$	2.55604	+	4.42719i	0.0877748	+	0.152030i
$849$	7.75930	+	2.82415i	0.266298	+	0.0969247i
$850$	−1.98975	+	11.2844i	−0.0682477	+	0.387052i
$851$	2.00500	+	11.3709i	0.0687305	+	0.389790i
$852$	−0.0503027	+	0.0183087i	−0.00172334	+	0.000627245i
$853$	−30.0232	−	25.1924i	−1.02797	−	0.862573i	−0.0373658	−	0.999302i	$-0.511897\pi$
$853$	−30.0232	−	25.1924i	−1.02797	−	0.862573i	−0.990609	+	0.136729i	$0.956341\pi$
$854$	5.54592			0.189777
$855$	−3.46418	−	3.31538i	−0.118472	−	0.113384i
$856$	13.5562			0.463342
$857$	−4.30878	−	3.61549i	−0.147185	−	0.123503i	0.566222	−	0.824253i	$-0.308404\pi$
$857$	−4.30878	−	3.61549i	−0.147185	−	0.123503i	−0.713407	+	0.700750i	$0.752849\pi$
$858$	−44.9919	+	16.3757i	−1.53600	+	0.559057i
$859$	−3.99557	−	22.6600i	−0.136327	−	0.773149i	−0.973926	−	0.226864i	$-0.927153\pi$
$859$	−3.99557	−	22.6600i	−0.136327	−	0.773149i	0.837599	−	0.546285i	$-0.183958\pi$
$860$	1.10826	−	6.28525i	0.0377913	−	0.214325i
$861$	−2.64870	−	0.964048i	−0.0902675	−	0.0328547i
$862$	9.74395	+	16.8770i	0.331880	+	0.574833i
$863$	−5.18337	+	8.97786i	−0.176444	+	0.305610i	−0.940660	−	0.339350i	$-0.889793\pi$
$863$	−5.18337	+	8.97786i	−0.176444	+	0.305610i	0.764216	+	0.644960i	$0.223126\pi$
$864$	−2.03539	+	1.70789i	−0.0692452	+	0.0581036i
$865$	−2.94728	+	2.47306i	−0.100211	+	0.0840867i
$866$	0.721126	−	1.24903i	0.0245049	−	0.0424437i
$867$	11.8671	+	20.5544i	0.403028	+	0.698064i
$868$	−7.26048	−	2.64260i	−0.246437	−	0.0896956i
$869$	1.76469	−	10.0081i	0.0598631	−	0.339500i
$870$	−1.40434	−	7.96439i	−0.0476115	−	0.270018i
$871$	−24.9734	+	9.08959i	−0.846192	+	0.307989i
$872$	0.427684	+	0.358870i	0.0144832	+	0.0121529i
$873$	−2.70870			−0.0916756
$874$	2.80132	−	11.4544i	0.0947562	−	0.387452i
$875$	−5.92749			−0.200386
$876$	21.8980	+	18.3746i	0.739865	+	0.620820i
$877$	35.6224	−	12.9655i	1.20288	−	0.437813i	0.338653	−	0.940911i	$-0.390029\pi$
$877$	35.6224	−	12.9655i	1.20288	−	0.437813i	0.864229	+	0.503098i	$0.167806\pi$
$878$	2.87431	+	16.3010i	0.0970031	+	0.550132i
$879$	−6.44191	+	36.5339i	−0.217280	+	1.23226i
$880$	1.98590	+	0.722807i	0.0669446	+	0.0243658i
$881$	−13.0824	−	22.6594i	−0.440757	−	0.763414i	0.556989	−	0.830520i	$-0.311957\pi$
$881$	−13.0824	−	22.6594i	−0.440757	−	0.763414i	−0.997746	+	0.0671064i	$0.978623\pi$
$882$	−0.892700	+	1.54620i	−0.0300588	+	0.0520633i
$883$	−7.37822	+	6.19106i	−0.248297	+	0.208346i	−0.758438	−	0.651745i	$-0.774037\pi$
$883$	−7.37822	+	6.19106i	−0.248297	+	0.208346i	0.510142	+	0.860090i	$0.329593\pi$
$884$	12.1228	−	10.1722i	0.407732	−	0.342128i
$885$	8.61050	−	14.9138i	0.289439	−	0.501323i
$886$	−1.54384	−	2.67401i	−0.0518663	−	0.0898350i
$887$	−1.84299	−	0.670795i	−0.0618817	−	0.0225231i	0.310894	−	0.950445i	$-0.399372\pi$
$887$	−1.84299	−	0.670795i	−0.0618817	−	0.0225231i	−0.372776	+	0.927922i	$0.621594\pi$
$888$	1.62130	−	9.19482i	0.0544071	−	0.308558i
$889$	−0.772063	−	4.37859i	−0.0258942	−	0.146853i
$890$	−7.20887	+	2.62381i	−0.241642	+	0.0879505i
$891$	−29.3456	−	24.6239i	−0.983114	−	0.824930i
$892$	14.5844			0.488320
$893$	−3.72260	+	5.57282i	−0.124572	+	0.186487i
$894$	29.7486			0.994942
$895$	−8.40029	−	7.04868i	−0.280791	−	0.235612i
$896$	0.939693	−	0.342020i	0.0313929	−	0.0114261i
$897$	6.55749	+	37.1893i	0.218948	+	1.24172i
$898$	−3.10971	+	17.6360i	−0.103772	+	0.588522i
$899$	43.5641	+	15.8560i	1.45294	+	0.528828i
$900$	4.12460	+	7.14402i	0.137487	+	0.238134i
$901$	6.33896	−	10.9794i	0.211181	−	0.365777i
$902$	−3.38559	+	2.84085i	−0.112728	+	0.0945898i
$903$	17.3582	−	14.5653i	0.577645	−	0.484702i
$904$	−5.04931	+	8.74566i	−0.167938	+	0.290876i
$905$	−1.82610	−	3.16290i	−0.0607017	−	0.105139i
$906$	41.5906	+	15.1377i	1.38175	+	0.502918i
$907$	−7.55098	+	42.8237i	−0.250726	+	1.42194i	0.556083	+	0.831127i	$0.312304\pi$
$907$	−7.55098	+	42.8237i	−0.250726	+	1.42194i	−0.806809	+	0.590812i	$0.798807\pi$
$908$	−0.821934	−	4.66142i	−0.0272768	−	0.154695i
$909$	16.6569	−	6.06260i	0.552473	−	0.201084i
$910$	3.01183	+	2.52722i	0.0998411	+	0.0837766i
$911$	−4.93846			−0.163618			−0.0818092	−	0.996648i	$-0.526070\pi$
$911$	−4.93846			−0.163618			−0.0818092	+	0.996648i	$0.526070\pi$
$912$	−5.29653	+	7.92902i	−0.175386	+	0.262556i
$913$	44.3926			1.46918
$914$	23.9737	+	20.1163i	0.792980	+	0.665389i
$915$	−7.02420	+	2.55660i	−0.232213	+	0.0845186i
$916$	2.58061	+	14.6354i	0.0852657	+	0.483566i
$917$	−1.24538	+	7.06288i	−0.0411259	+	0.233237i
$918$	6.19197	+	2.25369i	0.204365	+	0.0743829i
$919$	−0.625827	−	1.08396i	−0.0206441	−	0.0357567i	0.855519	−	0.517772i	$-0.173238\pi$
$919$	−0.625827	−	1.08396i	−0.0206441	−	0.0357567i	−0.876163	+	0.482015i	$0.839905\pi$
$920$	0.833412	−	1.44351i	0.0274768	−	0.0475912i
$921$	−4.50085	+	3.77666i	−0.148308	+	0.124445i
$922$	−8.89259	+	7.46177i	−0.292862	+	0.245740i
$923$	−0.0780752	+	0.135230i	−0.00256988	+	0.00445116i
$924$	3.75164	+	6.49803i	0.123420	+	0.213769i
$925$	18.5309	+	6.74468i	0.609291	+	0.221764i
$926$	0.720868	−	4.08825i	0.0236892	−	0.134348i
$927$	2.58873	+	14.6814i	0.0850249	+	0.482200i
$928$	−5.63831	+	2.05218i	−0.185087	+	0.0673660i
$929$	−29.6544	−	24.8830i	−0.972928	−	0.816384i	0.0100791	−	0.999949i	$-0.496792\pi$
$929$	−29.6544	−	24.8830i	−0.972928	−	0.816384i	−0.983008	+	0.183565i	$0.941236\pi$
$930$	10.4140			0.341488
$931$	1.03551	−	4.23411i	0.0339373	−	0.138768i
$932$	−4.36751			−0.143062
$933$	2.96743	+	2.48997i	0.0971493	+	0.0815180i
$934$	23.4167	−	8.52300i	0.766219	−	0.278881i
$935$	−0.910105	−	5.16146i	−0.0297636	−	0.168798i
$936$	1.97835	−	11.2198i	0.0646643	−	0.366730i
$937$	−17.4287	−	6.34355i	−0.569372	−	0.207235i	0.0412605	−	0.999148i	$-0.486863\pi$
$937$	−17.4287	−	6.34355i	−0.569372	−	0.207235i	−0.610633	+	0.791914i	$0.709085\pi$
$938$	2.08241	+	3.60683i	0.0679930	+	0.117767i
$939$	−8.63788	+	14.9612i	−0.281887	+	0.488242i
$940$	−0.725683	+	0.608921i	−0.0236692	+	0.0198608i
$941$	18.8664	−	15.8308i	0.615026	−	0.516068i	−0.281210	−	0.959646i	$-0.590736\pi$
$941$	18.8664	−	15.8308i	0.615026	−	0.516068i	0.896236	+	0.443579i	$0.146291\pi$
$942$	12.1515	−	21.0470i	0.395918	−	0.685750i
$943$	1.74289	+	3.01877i	0.0567562	+	0.0983046i
$944$	−12.0062	−	4.36991i	−0.390769	−	0.142228i
$945$	−0.284277	+	1.61222i	−0.00924753	+	0.0524454i
$946$	−6.16956	−	34.9893i	−0.200590	−	1.13760i
$947$	−19.4666	+	7.08527i	−0.632580	+	0.230240i	−0.638354	−	0.769743i	$-0.720384\pi$
$947$	−19.4666	+	7.08527i	−0.632580	+	0.230240i	0.00577360	+	0.999983i	$0.498162\pi$
$948$	4.96501	+	4.16613i	0.161256	+	0.135310i
$949$	83.3851			2.70679
$950$	−14.5500	−	13.9250i	−0.472065	−	0.451787i
$951$	−25.4199			−0.824296
$952$	−1.89978	−	1.59411i	−0.0615724	−	0.0516653i
$953$	40.1024	−	14.5961i	1.29905	−	0.472814i	0.402360	−	0.915482i	$-0.368190\pi$
$953$	40.1024	−	14.5961i	1.29905	−	0.472814i	0.896686	+	0.442668i	$0.145968\pi$
$954$	−1.58490	−	8.98844i	−0.0513132	−	0.291012i
$955$	−1.75002	+	9.92488i	−0.0566295	+	0.321162i
$956$	22.7609	+	8.28430i	0.736141	+	0.267933i
$957$	−22.5105	−	38.9893i	−0.727660	−	1.26034i
$958$	9.48889	−	16.4352i	0.306572	−	0.530999i
$959$	12.8751	−	10.8035i	0.415759	−	0.348863i
$960$	−1.03250	+	0.866374i	−0.0333239	+	0.0279621i
$961$	−14.3489	+	24.8531i	−0.462869	+	0.801712i
$962$	−13.6176	−	23.5863i	−0.439048	−	0.760454i
$963$	−22.7436	−	8.27800i	−0.732903	−	0.266755i
$964$	−2.96955	+	16.8411i	−0.0956426	+	0.542416i
$965$	−2.13860	−	12.1286i	−0.0688440	−	0.390434i
$966$	5.56104	−	2.02405i	0.178923	−	0.0651228i
$967$	35.6778	+	29.9372i	1.14732	+	0.962716i	0.999654	−	0.0263213i	$-0.00837931\pi$
$967$	35.6778	+	29.9372i	1.14732	+	0.962716i	0.147667	+	0.989037i	$0.452824\pi$
$968$	0.764783			0.0245811
$969$	23.5971	+	1.54359i	0.758049	+	0.0495874i
$970$	0.934769			0.0300136
$971$	12.9804	+	10.8919i	0.416561	+	0.349537i	0.826853	−	0.562418i	$-0.190129\pi$
$971$	12.9804	+	10.8919i	0.416561	+	0.349537i	−0.410292	+	0.911954i	$0.634573\pi$
$972$	15.4681	−	5.62992i	0.496139	−	0.180580i
$973$	2.35408	+	13.3507i	0.0754685	+	0.428003i
$974$	6.27752	−	35.6016i	0.201145	−	1.14075i
$975$	60.6065	+	22.0589i	1.94096	+	0.706452i
$976$	2.77296	+	4.80290i	0.0887602	+	0.153737i
$977$	−5.05931	+	8.76298i	−0.161862	+	0.280353i	−0.935536	−	0.353230i	$-0.885083\pi$
$977$	−5.05931	+	8.76298i	−0.161862	+	0.280353i	0.773675	+	0.633583i	$0.218416\pi$
$978$	−17.2274	+	14.4555i	−0.550871	+	0.462235i
$979$	−32.7151	+	27.4512i	−1.04558	+	0.877345i
$980$	0.308070	−	0.533592i	0.00984092	−	0.0170450i
$981$	−0.498396	−	0.863247i	−0.0159126	−	0.0275614i
$982$	−2.90134	−	1.05600i	−0.0925854	−	0.0336983i
$983$	6.40057	−	36.2994i	0.204146	−	1.15777i	−0.694631	−	0.719366i	$-0.744432\pi$
$983$	6.40057	−	36.2994i	0.204146	−	1.15777i	0.898777	−	0.438406i	$-0.144457\pi$
$984$	−0.489460	−	2.77587i	−0.0156034	−	0.0884914i
$985$	−1.99419	+	0.725825i	−0.0635401	+	0.0231267i
$986$	11.3990	+	9.56491i	0.363019	+	0.304609i
$987$	−3.36336			−0.107057
$988$	3.03165	+	27.6490i	0.0964495	+	0.879630i
$989$	−28.0222			−0.891055
$990$	−2.89041	−	2.42535i	−0.0918634	−	0.0770826i
$991$	−47.6030	+	17.3261i	−1.51216	+	0.550381i	−0.959176	−	0.282812i	$-0.908733\pi$
$991$	−47.6030	+	17.3261i	−1.51216	+	0.550381i	−0.552983	+	0.833192i	$0.686511\pi$
$992$	−1.34168	−	7.60906i	−0.0425984	−	0.241588i
$993$	−0.438182	+	2.48505i	−0.0139053	+	0.0788608i
$994$	0.0229949	+	0.00836947i	0.000729355	+	0.000265463i
$995$	0.964340	+	1.67029i	0.0305716	+	0.0529516i
$996$	−14.1562	+	24.5193i	−0.448557	+	0.776924i
$997$	−15.2632	+	12.8073i	−0.483389	+	0.405611i	−0.851650	−	0.524111i	$-0.824398\pi$
$997$	−15.2632	+	12.8073i	−0.483389	+	0.405611i	0.368261	+	0.929722i	$0.379953\pi$
$998$	23.7162	−	19.9003i	0.750723	−	0.629931i
$999$	5.67016	−	9.82101i	0.179396	−	0.310723i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	266.2.u.c.225.1	✓	18
19.5	even	9		5054.2.a.bk.1.7		9
19.6	even	9	inner	266.2.u.c.253.1	yes	18
19.14	odd	18		5054.2.a.bj.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.c.225.1	✓	18	1.1	even	1	trivial
266.2.u.c.253.1	yes	18	19.6	even	9	inner
5054.2.a.bj.1.3		9	19.14	odd	18
5054.2.a.bk.1.7		9	19.5	even	9

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:	\( N \)	\(=\)	\( 266 = 2 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	266.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(-2.05563 + 0.748188i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.106991 + 0.606779i) q^{5} +(-2.05563 - 0.748188i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.36770 - 1.14763i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(-2.05563 + 0.748188i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.106991 + 0.606779i) q^{5} +(-2.05563 - 0.748188i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.36770 - 1.14763i) q^{9} +(-0.471990 + 0.396047i) q^{10} +(-1.71499 + 2.97045i) q^{11} +(-1.09378 - 1.89448i) q^{12} +(-5.99629 - 2.18247i) q^{13} +(-0.173648 + 0.984808i) q^{14} +(-0.234050 - 1.32736i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.89978 + 1.59411i) q^{17} +1.78540 q^{18} +(-4.18460 + 1.22028i) q^{19} -0.616139 q^{20} +(-1.67576 - 1.40613i) q^{21} +(-3.22313 + 1.17312i) q^{22} +(0.469766 + 2.66417i) q^{23} +(0.379865 - 2.15432i) q^{24} +(4.34173 + 1.58026i) q^{25} +(-3.19056 - 5.52621i) q^{26} +(1.32850 - 2.30104i) q^{27} +(-0.766044 + 0.642788i) q^{28} +(4.59639 - 3.85683i) q^{29} +(0.673919 - 1.16726i) q^{30} +(3.86322 + 6.69129i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(1.30293 - 7.38929i) q^{33} +(0.430646 + 2.44232i) q^{34} +(-0.578982 + 0.210732i) q^{35} +(1.36770 + 1.14763i) q^{36} +4.26808 q^{37} +(-3.98998 - 1.75502i) q^{38} +13.9591 q^{39} +(-0.471990 - 0.396047i) q^{40} +(1.21080 - 0.440697i) q^{41} +(-0.379865 - 2.15432i) q^{42} +(-1.79871 + 10.2010i) q^{43} +(-3.22313 - 1.17312i) q^{44} +(0.550027 + 0.952675i) q^{45} +(-1.35264 + 2.34283i) q^{46} +(1.17779 - 0.988284i) q^{47} +(1.67576 - 1.40613i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(2.31019 + 4.00136i) q^{50} +(-5.09795 - 1.85550i) q^{51} +(1.10807 - 6.28418i) q^{52} +(-0.887703 - 5.03442i) q^{53} +(2.49677 - 0.908750i) q^{54} +(-1.61892 - 1.35843i) q^{55} -1.00000 q^{56} +(7.68899 - 5.63932i) q^{57} +6.00017 q^{58} +(9.78756 + 8.21274i) q^{59} +(1.26655 - 0.460988i) q^{60} +(-0.963038 - 5.46166i) q^{61} +(-1.34168 + 7.60906i) q^{62} +(1.67773 + 0.610642i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.96583 - 3.40492i) q^{65} +(5.74784 - 4.82301i) q^{66} +(3.19043 - 2.67709i) q^{67} +(-1.24000 + 2.14774i) q^{68} +(-2.95897 - 5.12508i) q^{69} +(-0.578982 - 0.210732i) q^{70} +(0.00424929 - 0.0240989i) q^{71} +(0.310031 + 1.75827i) q^{72} +(-12.2794 + 4.46934i) q^{73} +(3.26954 + 2.74347i) q^{74} -10.1073 q^{75} +(-1.92839 - 3.90913i) q^{76} -3.42998 q^{77} +(10.6933 + 8.97271i) q^{78} +(-2.78415 + 1.01335i) q^{79} +(-0.106991 - 0.606779i) q^{80} +(-1.93940 + 10.9989i) q^{81} +(1.21080 + 0.440697i) q^{82} +(-6.47125 - 11.2085i) q^{83} +(1.09378 - 1.89448i) q^{84} +(-1.17053 + 0.982193i) q^{85} +(-7.93498 + 6.65824i) q^{86} +(-6.56285 + 11.3672i) q^{87} +(-1.71499 - 2.97045i) q^{88} +(11.7001 + 4.25848i) q^{89} +(-0.191022 + 1.08334i) q^{90} +(-1.10807 - 6.28418i) q^{91} +(-2.54212 + 0.925258i) q^{92} +(-12.9477 - 10.8644i) q^{93} +1.53750 q^{94} +(-0.292725 - 2.66969i) q^{95} +2.18756 q^{96} +(-1.16220 - 0.975198i) q^{97} +(-0.939693 + 0.342020i) q^{98} +(1.06340 + 6.03085i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 6 q^{5} + 3 q^{6} + 9 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 - 6 * q^5 + 3 * q^6 + 9 * q^7 - 9 * q^8 - 3 * q^9	\( 18 q + 3 q^{3} - 6 q^{5} + 3 q^{6} + 9 q^{7} - 9 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{11} - 3 q^{12} - 6 q^{13} - 21 q^{17} + 24 q^{18} - 18 q^{19} + 6 q^{20} + 6 q^{21} - 15 q^{22} + 6 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} - 24 q^{27} + 21 q^{29} + 6 q^{30} - 9 q^{31} - 24 q^{33} + 24 q^{34} - 3 q^{35} - 3 q^{36} + 18 q^{37} + 12 q^{38} + 66 q^{39} + 3 q^{40} - 24 q^{41} - 3 q^{42} - 6 q^{43} - 15 q^{44} - 18 q^{45} - 6 q^{46} - 9 q^{47} - 6 q^{48} - 9 q^{49} + 18 q^{51} + 3 q^{52} - 9 q^{53} + 9 q^{54} - 27 q^{55} - 18 q^{56} + 27 q^{57} - 12 q^{58} + 45 q^{59} + 9 q^{60} + 6 q^{61} - 15 q^{62} - 15 q^{63} - 9 q^{64} + 3 q^{65} + 39 q^{66} + 27 q^{67} - 12 q^{68} - 6 q^{69} - 3 q^{70} - 27 q^{71} - 12 q^{72} + 21 q^{73} - 24 q^{74} - 6 q^{75} + 15 q^{76} + 6 q^{77} + 36 q^{78} - 6 q^{79} - 6 q^{80} - 99 q^{81} - 24 q^{82} - 9 q^{83} + 3 q^{84} + 36 q^{85} - 6 q^{86} + 3 q^{87} + 3 q^{88} + 54 q^{89} - 63 q^{90} - 3 q^{91} - 12 q^{92} - 75 q^{93} + 42 q^{94} + 57 q^{95} + 6 q^{96} + 60 q^{97} - 27 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 - 6 * q^5 + 3 * q^6 + 9 * q^7 - 9 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^11 - 3 * q^12 - 6 * q^13 - 21 * q^17 + 24 * q^18 - 18 * q^19 + 6 * q^20 + 6 * q^21 - 15 * q^22 + 6 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 - 24 * q^27 + 21 * q^29 + 6 * q^30 - 9 * q^31 - 24 * q^33 + 24 * q^34 - 3 * q^35 - 3 * q^36 + 18 * q^37 + 12 * q^38 + 66 * q^39 + 3 * q^40 - 24 * q^41 - 3 * q^42 - 6 * q^43 - 15 * q^44 - 18 * q^45 - 6 * q^46 - 9 * q^47 - 6 * q^48 - 9 * q^49 + 18 * q^51 + 3 * q^52 - 9 * q^53 + 9 * q^54 - 27 * q^55 - 18 * q^56 + 27 * q^57 - 12 * q^58 + 45 * q^59 + 9 * q^60 + 6 * q^61 - 15 * q^62 - 15 * q^63 - 9 * q^64 + 3 * q^65 + 39 * q^66 + 27 * q^67 - 12 * q^68 - 6 * q^69 - 3 * q^70 - 27 * q^71 - 12 * q^72 + 21 * q^73 - 24 * q^74 - 6 * q^75 + 15 * q^76 + 6 * q^77 + 36 * q^78 - 6 * q^79 - 6 * q^80 - 99 * q^81 - 24 * q^82 - 9 * q^83 + 3 * q^84 + 36 * q^85 - 6 * q^86 + 3 * q^87 + 3 * q^88 + 54 * q^89 - 63 * q^90 - 3 * q^91 - 12 * q^92 - 75 * q^93 + 42 * q^94 + 57 * q^95 + 6 * q^96 + 60 * q^97 - 27 * q^99

Introduction

L-functions

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