LMFDB - Embedded newform 52.3.c.a.27.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,3,Mod(27,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("52.27");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	52.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.41689737467$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 3 x^{10} + 2 x^{9} - 8 x^{8} + 16 x^{7} + 16 x^{6} + 64 x^{5} - 128 x^{4} + \cdots + 4096 $ x^12 - 2x^11 + 3x^10 + 2x^9 - 8x^8 + 16x^7 + 16x^6 + 64x^5 - 128x^4 + 128x^3 + 768x^2 - 2048*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			27.9
Root			$-1.23130 - 1.57604i$ of defining polynomial
Character	$\chi$	$=$	52.27
Dual form			52.3.c.a.27.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23130 - 1.57604i) q^{2} -0.974116i q^{3} +(-0.967819 - 3.88115i) q^{4} +0.497818 q^{5} +(-1.53525 - 1.19943i) q^{6} +3.22044i q^{7} +(-7.30853 - 3.25352i) q^{8} +8.05110 q^{9} +O(q^{10})$	\(q+(1.23130 - 1.57604i) q^{2} -0.974116i q^{3} +(-0.967819 - 3.88115i) q^{4} +0.497818 q^{5} +(-1.53525 - 1.19943i) q^{6} +3.22044i q^{7} +(-7.30853 - 3.25352i) q^{8} +8.05110 q^{9} +(0.612961 - 0.784582i) q^{10} +11.3937i q^{11} +(-3.78069 + 0.942769i) q^{12} -3.60555 q^{13} +(5.07555 + 3.96532i) q^{14} -0.484932i q^{15} +(-14.1267 + 7.51251i) q^{16} +6.58692 q^{17} +(9.91329 - 12.6889i) q^{18} +10.1874i q^{19} +(-0.481798 - 1.93210i) q^{20} +3.13708 q^{21} +(17.9569 + 14.0290i) q^{22} +3.14016i q^{23} +(-3.16931 + 7.11936i) q^{24} -24.7522 q^{25} +(-4.43950 + 5.68250i) q^{26} -16.6097i q^{27} +(12.4990 - 3.11681i) q^{28} -15.8820 q^{29} +(-0.764274 - 0.597095i) q^{30} -54.6094i q^{31} +(-5.55406 + 31.5143i) q^{32} +11.0987 q^{33} +(8.11044 - 10.3813i) q^{34} +1.60319i q^{35} +(-7.79201 - 31.2475i) q^{36} -42.6198 q^{37} +(16.0557 + 12.5437i) q^{38} +3.51223i q^{39} +(-3.63831 - 1.61966i) q^{40} +36.3748 q^{41} +(3.86268 - 4.94418i) q^{42} -69.6406i q^{43} +(44.2205 - 11.0270i) q^{44} +4.00798 q^{45} +(4.94903 + 3.86647i) q^{46} +41.0455i q^{47} +(7.31805 + 13.7610i) q^{48} +38.6288 q^{49} +(-30.4773 + 39.0105i) q^{50} -6.41642i q^{51} +(3.48952 + 13.9937i) q^{52} -31.3848 q^{53} +(-26.1777 - 20.4515i) q^{54} +5.67196i q^{55} +(10.4778 - 23.5367i) q^{56} +9.92368 q^{57} +(-19.5555 + 25.0307i) q^{58} +102.954i q^{59} +(-1.88209 + 0.469327i) q^{60} -40.1855 q^{61} +(-86.0668 - 67.2404i) q^{62} +25.9281i q^{63} +(42.8292 + 47.5569i) q^{64} -1.79491 q^{65} +(13.6658 - 17.4921i) q^{66} +51.2039i q^{67} +(-6.37495 - 25.5648i) q^{68} +3.05888 q^{69} +(2.52670 + 1.97400i) q^{70} +79.3434i q^{71} +(-58.8417 - 26.1944i) q^{72} +95.2115 q^{73} +(-52.4777 + 67.1707i) q^{74} +24.1115i q^{75} +(39.5387 - 9.85953i) q^{76} -36.6926 q^{77} +(5.53542 + 4.32459i) q^{78} -75.8021i q^{79} +(-7.03249 + 3.73986i) q^{80} +56.2801 q^{81} +(44.7881 - 57.3282i) q^{82} -131.877i q^{83} +(-3.03613 - 12.1755i) q^{84} +3.27908 q^{85} +(-109.757 - 85.7482i) q^{86} +15.4709i q^{87} +(37.0695 - 83.2709i) q^{88} +78.1466 q^{89} +(4.93501 - 6.31674i) q^{90} -11.6115i q^{91} +(12.1874 - 3.03911i) q^{92} -53.1959 q^{93} +(64.6894 + 50.5391i) q^{94} +5.07145i q^{95} +(30.6986 + 5.41030i) q^{96} -35.2166 q^{97} +(47.5634 - 60.8806i) q^{98} +91.7314i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 2 q^{4} + 12 q^{6} + 16 q^{8} - 28 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 2 * q^4 + 12 * q^6 + 16 * q^8 - 28 * q^9	$ 12 q - 2 q^{2} - 2 q^{4} + 12 q^{6} + 16 q^{8} - 28 q^{9} - 6 q^{10} - 2 q^{12} + 14 q^{14} + 2 q^{16} - 24 q^{17} - 34 q^{18} - 84 q^{20} - 16 q^{21} - 40 q^{22} + 36 q^{24} + 76 q^{25} + 16 q^{29} + 90 q^{30} + 8 q^{32} + 32 q^{33} - 52 q^{34} + 152 q^{36} + 96 q^{37} - 44 q^{38} - 118 q^{40} - 120 q^{41} + 178 q^{42} + 44 q^{44} - 128 q^{45} + 212 q^{46} + 30 q^{48} - 4 q^{49} - 230 q^{50} + 52 q^{52} - 24 q^{53} - 148 q^{54} - 78 q^{56} + 144 q^{57} - 8 q^{58} + 72 q^{60} - 40 q^{61} - 184 q^{62} - 134 q^{64} + 288 q^{66} - 350 q^{68} + 64 q^{69} - 292 q^{70} - 432 q^{72} - 88 q^{73} + 10 q^{74} + 384 q^{76} + 136 q^{77} - 130 q^{78} + 420 q^{80} - 164 q^{81} + 124 q^{82} + 52 q^{84} - 208 q^{85} + 156 q^{86} + 456 q^{88} - 168 q^{89} + 72 q^{90} - 428 q^{92} + 432 q^{93} + 614 q^{94} + 516 q^{96} + 200 q^{97} + 718 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 - 2 * q^4 + 12 * q^6 + 16 * q^8 - 28 * q^9 - 6 * q^10 - 2 * q^12 + 14 * q^14 + 2 * q^16 - 24 * q^17 - 34 * q^18 - 84 * q^20 - 16 * q^21 - 40 * q^22 + 36 * q^24 + 76 * q^25 + 16 * q^29 + 90 * q^30 + 8 * q^32 + 32 * q^33 - 52 * q^34 + 152 * q^36 + 96 * q^37 - 44 * q^38 - 118 * q^40 - 120 * q^41 + 178 * q^42 + 44 * q^44 - 128 * q^45 + 212 * q^46 + 30 * q^48 - 4 * q^49 - 230 * q^50 + 52 * q^52 - 24 * q^53 - 148 * q^54 - 78 * q^56 + 144 * q^57 - 8 * q^58 + 72 * q^60 - 40 * q^61 - 184 * q^62 - 134 * q^64 + 288 * q^66 - 350 * q^68 + 64 * q^69 - 292 * q^70 - 432 * q^72 - 88 * q^73 + 10 * q^74 + 384 * q^76 + 136 * q^77 - 130 * q^78 + 420 * q^80 - 164 * q^81 + 124 * q^82 + 52 * q^84 - 208 * q^85 + 156 * q^86 + 456 * q^88 - 168 * q^89 + 72 * q^90 - 428 * q^92 + 432 * q^93 + 614 * q^94 + 516 * q^96 + 200 * q^97 + 718 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.23130	−	1.57604i	0.615648	−	0.788021i
$2$	1.23130	−	1.57604i	0.615648	−	0.788021i
$3$		−	0.974116i		−	0.324705i	−0.986733	−	0.162353i	$-0.948092\pi$
$3$		−	0.974116i		−	0.324705i	0.986733	−	0.162353i	$-0.0519082\pi$
$4$	−0.967819	−	3.88115i	−0.241955	−	0.970288i
$5$	0.497818			0.0995635			0.0497818	−	0.998760i	$-0.484147\pi$
$5$	0.497818			0.0995635			0.0497818	+	0.998760i	$0.484147\pi$
$6$	−1.53525	−	1.19943i	−0.255875	−	0.199904i
$7$			3.22044i			0.460063i	0.973183	+	0.230032i	$0.0738829\pi$
$7$			3.22044i			0.460063i	−0.973183	+	0.230032i	$0.926117\pi$
$8$	−7.30853	−	3.25352i	−0.913566	−	0.406690i
$9$	8.05110			0.894566
$10$	0.612961	−	0.784582i	0.0612961	−	0.0784582i
$11$			11.3937i			1.03579i	0.855445	+	0.517893i	$0.173284\pi$
$11$			11.3937i			1.03579i	−0.855445	+	0.517893i	$0.826716\pi$
$12$	−3.78069	+	0.942769i	−0.315058	+	0.0785640i
$13$	−3.60555			−0.277350
$13$	−3.60555			−0.277350
$14$	5.07555	+	3.96532i	0.362540	+	0.283237i
$15$		−	0.484932i		−	0.0323288i
$16$	−14.1267	+	7.51251i	−0.882916	+	0.469532i
$17$	6.58692			0.387466			0.193733	−	0.981054i	$-0.437941\pi$
$17$	6.58692			0.387466			0.193733	+	0.981054i	$0.437941\pi$
$18$	9.91329	−	12.6889i	0.550738	−	0.704937i
$19$			10.1874i			0.536177i	0.963394	+	0.268089i	$0.0863920\pi$
$19$			10.1874i			0.536177i	−0.963394	+	0.268089i	$0.913608\pi$
$20$	−0.481798	−	1.93210i	−0.0240899	−	0.0966052i
$21$	3.13708			0.149385
$22$	17.9569	+	14.0290i	0.816222	+	0.637680i
$23$			3.14016i			0.136529i	0.997667	+	0.0682644i	$0.0217461\pi$
$23$			3.14016i			0.136529i	−0.997667	+	0.0682644i	$0.978254\pi$
$24$	−3.16931	+	7.11936i	−0.132054	+	0.296640i
$25$	−24.7522			−0.990087
$26$	−4.43950	+	5.68250i	−0.170750	+	0.218558i
$27$		−	16.6097i		−	0.615176i
$28$	12.4990	−	3.11681i	0.446394	−	0.111315i
$29$	−15.8820			−0.547656			−0.273828	−	0.961779i	$-0.588290\pi$
$29$	−15.8820			−0.547656			−0.273828	+	0.961779i	$0.588290\pi$
$30$	−0.764274	−	0.597095i	−0.0254758	−	0.0199032i
$31$		−	54.6094i		−	1.76159i	−0.473494	−	0.880797i	$-0.657007\pi$
$31$		−	54.6094i		−	1.76159i	0.473494	−	0.880797i	$-0.342993\pi$
$32$	−5.55406	+	31.5143i	−0.173565	+	0.984822i
$33$	11.0987			0.336326
$34$	8.11044	−	10.3813i	0.238542	−	0.305331i
$35$			1.60319i			0.0458055i
$36$	−7.79201	−	31.2475i	−0.216445	−	0.867987i
$37$	−42.6198			−1.15189			−0.575944	−	0.817489i	$-0.695365\pi$
$37$	−42.6198			−1.15189			−0.575944	+	0.817489i	$0.695365\pi$
$38$	16.0557	+	12.5437i	0.422519	+	0.330096i
$39$			3.51223i			0.0900571i
$40$	−3.63831	−	1.61966i	−0.0909579	−	0.0404915i
$41$	36.3748			0.887190			0.443595	−	0.896227i	$-0.353703\pi$
$41$	36.3748			0.887190			0.443595	+	0.896227i	$0.353703\pi$
$42$	3.86268	−	4.94418i	0.0919686	−	0.117719i
$43$		−	69.6406i		−	1.61955i	−0.586741	−	0.809775i	$-0.699589\pi$
$43$		−	69.6406i		−	1.61955i	0.586741	−	0.809775i	$-0.300411\pi$
$44$	44.2205	−	11.0270i	1.00501	−	0.250614i
$45$	4.00798			0.0890662
$46$	4.94903	+	3.86647i	0.107588	+	0.0840537i
$47$			41.0455i			0.873308i	0.899630	+	0.436654i	$0.143837\pi$
$47$			41.0455i			0.873308i	−0.899630	+	0.436654i	$0.856163\pi$
$48$	7.31805	+	13.7610i	0.152459	+	0.286687i
$49$	38.6288			0.788342
$50$	−30.4773	+	39.0105i	−0.609545	+	0.780210i
$51$		−	6.41642i		−	0.125812i
$52$	3.48952	+	13.9937i	0.0671062	+	0.269109i
$53$	−31.3848			−0.592165			−0.296083	−	0.955162i	$-0.595680\pi$
$53$	−31.3848			−0.592165			−0.296083	+	0.955162i	$0.595680\pi$
$54$	−26.1777	−	20.4515i	−0.484772	−	0.378732i
$55$			5.67196i			0.103127i
$56$	10.4778	−	23.5367i	0.187103	−	0.420298i
$57$	9.92368			0.174100
$58$	−19.5555	+	25.0307i	−0.337163	+	0.431564i
$59$			102.954i			1.74499i	0.488622	+	0.872496i	$0.337500\pi$
$59$			102.954i			1.74499i	−0.488622	+	0.872496i	$0.662500\pi$
$60$	−1.88209	+	0.469327i	−0.0313682	+	0.00782211i
$61$	−40.1855			−0.658779			−0.329389	−	0.944194i	$-0.606843\pi$
$61$	−40.1855			−0.658779			−0.329389	+	0.944194i	$0.606843\pi$
$62$	−86.0668	−	67.2404i	−1.38817	−	1.08452i
$63$			25.9281i			0.411557i
$64$	42.8292	+	47.5569i	0.669206	+	0.743077i
$65$	−1.79491			−0.0276139
$66$	13.6658	−	17.4921i	0.207058	−	0.265032i
$67$			51.2039i			0.764237i	0.924113	+	0.382119i	$0.124805\pi$
$67$			51.2039i			0.764237i	−0.924113	+	0.382119i	$0.875195\pi$
$68$	−6.37495	−	25.5648i	−0.0937492	−	0.375953i
$69$	3.05888			0.0443316
$70$	2.52670	+	1.97400i	0.0360957	+	0.0282001i
$71$			79.3434i			1.11751i	0.829332	+	0.558756i	$0.188721\pi$
$71$			79.3434i			1.11751i	−0.829332	+	0.558756i	$0.811279\pi$
$72$	−58.8417	−	26.1944i	−0.817246	−	0.363811i
$73$	95.2115			1.30427			0.652134	−	0.758104i	$-0.273874\pi$
$73$	95.2115			1.30427			0.652134	+	0.758104i	$0.273874\pi$
$74$	−52.4777	+	67.1707i	−0.709158	+	0.907712i
$75$			24.1115i			0.321487i
$76$	39.5387	−	9.85953i	0.520246	−	0.129731i
$77$	−36.6926			−0.476527
$78$	5.53542	+	4.32459i	0.0709669	+	0.0554435i
$79$		−	75.8021i		−	0.959520i	−0.877400	−	0.479760i	$-0.840724\pi$
$79$		−	75.8021i		−	0.959520i	0.877400	−	0.479760i	$-0.159276\pi$
$80$	−7.03249	+	3.73986i	−0.0879062	+	0.0467482i
$81$	56.2801			0.694816
$82$	44.7881	−	57.3282i	0.546197	−	0.699124i
$83$		−	131.877i		−	1.58888i	−0.607345	−	0.794438i	$-0.707765\pi$
$83$		−	131.877i		−	1.58888i	0.607345	−	0.794438i	$-0.292235\pi$
$84$	−3.03613	−	12.1755i	−0.0361444	−	0.144946i
$85$	3.27908			0.0385774
$86$	−109.757	−	85.7482i	−1.27624	−	0.997073i
$87$			15.4709i			0.177827i
$88$	37.0695	−	83.2709i	0.421244	−	0.946260i
$89$	78.1466			0.878052			0.439026	−	0.898474i	$-0.355324\pi$
$89$	78.1466			0.878052			0.439026	+	0.898474i	$0.355324\pi$
$90$	4.93501	−	6.31674i	0.0548334	−	0.0701860i
$91$		−	11.6115i		−	0.127599i
$92$	12.1874	−	3.03911i	0.132472	−	0.0330338i
$93$	−53.1959			−0.571999
$94$	64.6894	+	50.5391i	0.688185	+	0.537650i
$95$			5.07145i			0.0533837i
$96$	30.6986	+	5.41030i	0.319777	+	0.0563573i
$97$	−35.2166			−0.363057			−0.181529	−	0.983386i	$-0.558105\pi$
$97$	−35.2166			−0.363057			−0.181529	+	0.983386i	$0.558105\pi$
$98$	47.5634	−	60.8806i	0.485341	−	0.621230i
$99$			91.7314i			0.926580i
$100$	23.9556	+	96.0669i	0.239556	+	0.960669i
$101$	134.379			1.33049			0.665244	−	0.746626i	$-0.268327\pi$
$101$	134.379			1.33049			0.665244	+	0.746626i	$0.268327\pi$
$102$	−10.1126	−	7.90051i	−0.0991427	−	0.0774560i
$103$		−	183.043i		−	1.77712i	−0.458761	−	0.888560i	$-0.651707\pi$
$103$		−	183.043i		−	1.77712i	0.458761	−	0.888560i	$-0.348293\pi$
$104$	26.3513	+	11.7307i	0.253378	+	0.112796i
$105$	1.56170			0.0148733
$106$	−38.6439	+	49.4637i	−0.364565	+	0.466639i
$107$		−	66.7095i		−	0.623453i	−0.950172	−	0.311727i	$-0.899093\pi$
$107$		−	66.7095i		−	0.623453i	0.950172	−	0.311727i	$-0.100907\pi$
$108$	−64.4649	+	16.0752i	−0.596897	+	0.148845i
$109$	−182.098			−1.67062			−0.835311	−	0.549778i	$-0.814712\pi$
$109$	−182.098			−1.67062			−0.835311	+	0.549778i	$0.814712\pi$
$110$	8.93925	+	6.98386i	0.0812659	+	0.0634897i
$111$			41.5167i			0.374024i
$112$	−24.1936	−	45.4941i	−0.216014	−	0.406197i
$113$	−143.730			−1.27195			−0.635975	−	0.771709i	$-0.719402\pi$
$113$	−143.730			−1.27195			−0.635975	+	0.771709i	$0.719402\pi$
$114$	12.2190	−	15.6401i	0.107184	−	0.137194i
$115$			1.56323i			0.0135933i
$116$	15.3709	+	61.6405i	0.132508	+	0.531384i
$117$	−29.0286			−0.248108
$118$	162.261	+	126.767i	1.37509	+	1.07430i
$119$			21.2128i			0.178259i
$120$	−1.57774	+	3.54414i	−0.0131478	+	0.0295345i
$121$	−8.81537			−0.0728543
$122$	−49.4803	+	63.3341i	−0.405576	+	0.519132i
$123$		−	35.4332i		−	0.288075i
$124$	−211.947	+	52.8521i	−1.70925	+	0.426226i
$125$	−24.7675			−0.198140
$126$	40.8638	+	31.9252i	0.324316	+	0.253374i
$127$			132.893i			1.04640i	0.852208	+	0.523202i	$0.175263\pi$
$127$			132.893i			1.04640i	−0.852208	+	0.523202i	$0.824737\pi$
$128$	127.687	−	8.94401i	0.997556	−	0.0698751i
$129$	−67.8381			−0.525876
$130$	−2.21006	+	2.82885i	−0.0170005	+	0.0217604i
$131$		−	39.5036i		−	0.301554i	−0.988568	−	0.150777i	$-0.951822\pi$
$131$		−	39.5036i		−	0.301554i	0.988568	−	0.150777i	$-0.0481776\pi$
$132$	−10.7416	−	43.0759i	−0.0813756	−	0.326332i
$133$	−32.8078			−0.246675
$134$	80.6995	+	63.0472i	0.602235	+	0.470501i
$135$		−	8.26862i		−	0.0612491i
$136$	−48.1407	−	21.4307i	−0.353976	−	0.157578i
$137$	146.437			1.06888			0.534441	−	0.845205i	$-0.320522\pi$
$137$	146.437			1.06888			0.534441	+	0.845205i	$0.320522\pi$
$138$	3.76639	−	4.82093i	0.0272927	−	0.0349343i
$139$		−	52.5553i		−	0.378096i	−0.981968	−	0.189048i	$-0.939460\pi$
$139$		−	52.5553i		−	0.378096i	0.981968	−	0.189048i	$-0.0605401\pi$
$140$	6.22223	−	1.55160i	0.0444445	−	0.0110829i
$141$	39.9830			0.283568
$142$	125.049	+	97.6952i	0.880623	+	0.687994i
$143$		−	41.0804i		−	0.287276i
$144$	−113.735	+	60.4839i	−0.789827	+	0.420027i
$145$	−7.90635			−0.0545265
$146$	117.234	−	150.057i	0.802970	−	1.02779i
$147$		−	37.6289i		−	0.255979i
$148$	41.2483	+	165.414i	0.278705	+	1.11766i
$149$	52.6480			0.353342			0.176671	−	0.984270i	$-0.443467\pi$
$149$	52.6480			0.353342			0.176671	+	0.984270i	$0.443467\pi$
$150$	38.0007	+	29.6884i	0.253338	+	0.197923i
$151$			122.245i			0.809569i	0.914412	+	0.404784i	$0.132653\pi$
$151$			122.245i			0.809569i	−0.914412	+	0.404784i	$0.867347\pi$
$152$	33.1448	−	74.4547i	0.218058	−	0.489833i
$153$	53.0319			0.346614
$154$	−45.1795	+	57.8291i	−0.293373	+	0.375514i
$155$		−	27.1855i		−	0.175391i
$156$	13.6315	−	3.39920i	0.0873812	−	0.0217897i
$157$	−42.2402			−0.269046			−0.134523	−	0.990910i	$-0.542950\pi$
$157$	−42.2402			−0.269046			−0.134523	+	0.990910i	$0.542950\pi$
$158$	−119.467	−	93.3348i	−0.756122	−	0.590727i
$159$			30.5724i			0.192279i
$160$	−2.76491	+	15.6884i	−0.0172807	+	0.0980524i
$161$	−10.1127			−0.0628119
$162$	69.2974	−	88.6998i	0.427762	−	0.547529i
$163$		−	19.1378i		−	0.117410i	−0.998275	−	0.0587051i	$-0.981303\pi$
$163$		−	19.1378i		−	0.117410i	0.998275	−	0.0587051i	$-0.0186971\pi$
$164$	−35.2042	−	141.176i	−0.214660	−	0.860829i
$165$	5.52515			0.0334858
$166$	−207.843	−	162.379i	−1.25207	−	0.978189i
$167$		−	149.885i		−	0.897513i	−0.893654	−	0.448757i	$-0.851867\pi$
$167$		−	149.885i		−	0.897513i	0.893654	−	0.448757i	$-0.148133\pi$
$168$	−22.9275	−	10.2066i	−0.136473	−	0.0607534i
$169$	13.0000			0.0769231
$170$	4.03752	−	5.16797i	0.0237501	−	0.0303998i
$171$			82.0195i			0.479646i
$172$	−270.286	+	67.3996i	−1.57143	+	0.391858i
$173$	−58.8026			−0.339899			−0.169950	−	0.985453i	$-0.554361\pi$
$173$	−58.8026			−0.339899			−0.169950	+	0.985453i	$0.554361\pi$
$174$	24.3828	+	19.0493i	0.140131	+	0.109479i
$175$		−	79.7130i		−	0.455503i
$176$	−85.5949	−	160.954i	−0.486335	−	0.914512i
$177$	100.290			0.566608
$178$	96.2216	−	123.162i	0.540571	−	0.691924i
$179$			281.564i			1.57298i	0.617601	+	0.786492i	$0.288105\pi$
$179$			281.564i			1.57298i	−0.617601	+	0.786492i	$0.711895\pi$
$180$	−3.87900	−	15.5556i	−0.0215500	−	0.0864198i
$181$	119.904			0.662455			0.331227	−	0.943551i	$-0.392537\pi$
$181$	119.904			0.662455			0.331227	+	0.943551i	$0.392537\pi$
$182$	−18.3002	−	14.2972i	−0.100550	−	0.0785558i
$183$			39.1454i			0.213909i
$184$	10.2166	−	22.9500i	0.0555249	−	0.124728i
$185$	−21.2169			−0.114686
$186$	−65.4999	+	83.8390i	−0.352150	+	0.450748i
$187$			75.0490i			0.401332i
$188$	159.304	−	39.7246i	0.847360	−	0.211301i
$189$	53.4907			0.283020
$190$	7.99282	+	6.24446i	0.0420675	+	0.0328656i
$191$		−	251.450i		−	1.31649i	−0.752804	−	0.658245i	$-0.771299\pi$
$191$		−	251.450i		−	1.31649i	0.752804	−	0.658245i	$-0.228701\pi$
$192$	46.3259	−	41.7206i	0.241281	−	0.217295i
$193$	−184.734			−0.957171			−0.478586	−	0.878041i	$-0.658850\pi$
$193$	−184.734			−0.957171			−0.478586	+	0.878041i	$0.658850\pi$
$194$	−43.3620	+	55.5028i	−0.223516	+	0.286097i
$195$			1.74845i			0.00896640i
$196$	−37.3857	−	149.924i	−0.190743	−	0.764918i
$197$	255.417			1.29653			0.648266	−	0.761414i	$-0.275494\pi$
$197$	255.417			1.29653			0.648266	+	0.761414i	$0.275494\pi$
$198$	144.573	+	112.949i	0.730165	+	0.570447i
$199$			276.060i			1.38724i	0.720343	+	0.693618i	$0.243984\pi$
$199$			276.060i			1.38724i	−0.720343	+	0.693618i	$0.756016\pi$
$200$	180.902	+	80.5317i	0.904510	+	0.402659i
$201$	49.8786			0.248152
$202$	165.461	−	211.788i	0.819113	−	1.04845i
$203$		−	51.1471i		−	0.251956i
$204$	−24.9031	+	6.20994i	−0.122074	+	0.0304409i
$205$	18.1080			0.0883317
$206$	−288.484	−	225.380i	−1.40041	−	1.09408i
$207$			25.2818i			0.122134i
$208$	50.9344	−	27.0867i	0.244877	−	0.130225i
$209$	−116.071			−0.555365
$210$	1.92291	−	2.46130i	0.00915671	−	0.0117205i
$211$			219.008i			1.03795i	0.854789	+	0.518976i	$0.173686\pi$
$211$			219.008i			1.03795i	−0.854789	+	0.518976i	$0.826314\pi$
$212$	30.3748	+	121.809i	0.143277	+	0.574570i
$213$	77.2896			0.362862
$214$	−105.137	−	82.1391i	−0.491294	−	0.383828i
$215$		−	34.6683i		−	0.161248i
$216$	−54.0402	+	121.393i	−0.250186	+	0.562004i
$217$	175.867			0.810445
$218$	−224.216	+	286.994i	−1.02851	+	1.31649i
$219$		−	92.7471i		−	0.423503i
$220$	22.0137	−	5.48943i	0.100062	−	0.0249520i
$221$	−23.7495			−0.107464
$222$	65.4321	+	51.1193i	0.294739	+	0.230267i
$223$		−	86.4756i		−	0.387783i	−0.981023	−	0.193891i	$-0.937889\pi$
$223$		−	86.4756i		−	0.387783i	0.981023	−	0.193891i	$-0.0621109\pi$
$224$	−101.490	−	17.8865i	−0.453081	−	0.0798506i
$225$	−199.282			−0.885699
$226$	−176.975	+	226.525i	−0.783074	+	1.00232i
$227$			0.443002i			0.00195155i	1.00000		0.000975775i	$0.000310599\pi$
$227$			0.443002i			0.00195155i	−1.00000		0.000975775i	$0.999689\pi$
$228$	−9.60433	−	38.5153i	−0.0421243	−	0.168927i
$229$	179.865			0.785438			0.392719	−	0.919658i	$-0.371534\pi$
$229$	179.865			0.785438			0.392719	+	0.919658i	$0.371534\pi$
$230$	2.46371	+	1.92480i	0.0107118	+	0.00836868i
$231$			35.7429i			0.154731i
$232$	116.074	+	51.6725i	0.500320	+	0.222726i
$233$	−265.436			−1.13921			−0.569605	−	0.821919i	$-0.692904\pi$
$233$	−265.436			−1.13921			−0.569605	+	0.821919i	$0.692904\pi$
$234$	−35.7429	+	45.7504i	−0.152747	+	0.195514i
$235$			20.4332i			0.0869496i
$236$	399.582	−	99.6414i	1.69314	−	0.422209i
$237$	−73.8400			−0.311561
$238$	33.4322	+	26.1192i	0.140472	+	0.109745i
$239$			187.657i			0.785175i	0.919715	+	0.392588i	$0.128420\pi$
$239$			187.657i			0.785175i	−0.919715	+	0.392588i	$0.871580\pi$
$240$	3.64305	+	6.85047i	0.0151794	+	0.0285436i
$241$	−54.3754			−0.225624			−0.112812	−	0.993616i	$-0.535986\pi$
$241$	−54.3754			−0.225624			−0.112812	+	0.993616i	$0.535986\pi$
$242$	−10.8543	+	13.8934i	−0.0448526	+	0.0574108i
$243$		−	204.311i		−	0.840786i
$244$	38.8923	+	155.966i	0.159395	+	0.639205i
$245$	19.2301			0.0784901
$246$	−55.8443	−	43.6288i	−0.227009	−	0.177353i
$247$		−	36.7311i		−	0.148709i
$248$	−177.673	+	399.115i	−0.716423	+	1.60933i
$249$	−128.463			−0.515917
$250$	−30.4961	+	39.0346i	−0.121985	+	0.156139i
$251$			109.239i			0.435214i	0.976036	+	0.217607i	$0.0698251\pi$
$251$			109.239i			0.435214i	−0.976036	+	0.217607i	$0.930175\pi$
$252$	100.631	−	25.0937i	0.399329	−	0.0995782i
$253$	−35.7779			−0.141415
$254$	209.446	+	163.631i	0.824589	+	0.644217i
$255$		−	3.19421i		−	0.0125263i
$256$	143.125	−	212.253i	0.559080	−	0.829114i
$257$	−245.998			−0.957191			−0.478595	−	0.878036i	$-0.658854\pi$
$257$	−245.998			−0.957191			−0.478595	+	0.878036i	$0.658854\pi$
$258$	−83.5287	+	106.916i	−0.323755	+	0.414402i
$259$		−	137.255i		−	0.529941i
$260$	1.73715	+	6.96630i	0.00668133	+	0.0267935i
$261$	−127.868			−0.489915
$262$	−62.2594	−	48.6407i	−0.237631	−	0.185651i
$263$		−	251.629i		−	0.956763i	−0.878152	−	0.478382i	$-0.841224\pi$
$263$		−	251.629i		−	0.956763i	0.878152	−	0.478382i	$-0.158776\pi$
$264$	−81.1155	−	36.1100i	−0.307256	−	0.136780i
$265$	−15.6239			−0.0589580
$266$	−40.3962	+	51.7065i	−0.151865	+	0.194385i
$267$		−	76.1239i		−	0.285108i
$268$	198.730	−	49.5561i	0.741530	−	0.184911i
$269$	171.392			0.637145			0.318572	−	0.947899i	$-0.396797\pi$
$269$	171.392			0.637145			0.318572	+	0.947899i	$0.396797\pi$
$270$	−13.0317	−	10.1811i	−0.0482656	−	0.0377079i
$271$			147.640i			0.544796i	0.962185	+	0.272398i	$0.0878168\pi$
$271$			147.640i			0.544796i	−0.962185	+	0.272398i	$0.912183\pi$
$272$	−93.0511	+	49.4842i	−0.342099	+	0.181927i
$273$	−11.3109			−0.0414319
$274$	180.307	−	230.791i	0.658056	−	0.842302i
$275$		−	282.018i		−	1.02552i
$276$	−2.96045	−	11.8720i	−0.0107263	−	0.0430144i
$277$	373.877			1.34973			0.674867	−	0.737939i	$-0.264201\pi$
$277$	373.877			1.34973			0.674867	+	0.737939i	$0.264201\pi$
$278$	−82.8294	−	64.7111i	−0.297947	−	0.232774i
$279$		−	439.666i		−	1.57586i
$280$	5.21602	−	11.7170i	0.0186286	−	0.0418464i
$281$	−233.238			−0.830030			−0.415015	−	0.909815i	$-0.636224\pi$
$281$	−233.238			−0.830030			−0.415015	+	0.909815i	$0.636224\pi$
$282$	49.2310	−	63.0150i	0.174578	−	0.223457i
$283$		−	232.768i		−	0.822503i	−0.911522	−	0.411252i	$-0.865092\pi$
$283$		−	232.768i		−	0.822503i	0.911522	−	0.411252i	$-0.134908\pi$
$284$	307.943	−	76.7900i	1.08431	−	0.270387i
$285$	4.94018			0.0173340
$286$	−64.7445	−	50.5821i	−0.226379	−	0.176861i
$287$			117.143i			0.408163i
$288$	−44.7163	+	253.725i	−0.155265	+	0.880989i
$289$	−245.613			−0.849870
$290$	−9.73506	+	12.4607i	−0.0335692	+	0.0429681i
$291$			34.3050i			0.117887i
$292$	−92.1476	−	369.530i	−0.315574	−	1.26551i
$293$	−68.4639			−0.233665			−0.116833	−	0.993152i	$-0.537274\pi$
$293$	−68.4639			−0.233665			−0.116833	+	0.993152i	$0.537274\pi$
$294$	−59.3047	−	46.3323i	−0.201717	−	0.157593i
$295$			51.2526i			0.173737i
$296$	311.488	+	138.665i	1.05233	+	0.468461i
$297$	189.246			0.637191
$298$	64.8253	−	82.9754i	0.217534	−	0.278441i
$299$		−	11.3220i		−	0.0378663i
$300$	93.5803	−	23.3356i	0.311934	−	0.0777852i
$301$	224.274			0.745095
$302$	192.663	+	150.520i	0.637957	+	0.498409i
$303$		−	130.901i		−	0.432017i
$304$	−76.5327	−	143.913i	−0.251752	−	0.473399i
$305$	−20.0051			−0.0655903
$306$	65.2980	−	83.5805i	0.213392	−	0.273139i
$307$		−	58.8784i		−	0.191786i	−0.995392	−	0.0958931i	$-0.969429\pi$
$307$		−	58.8784i		−	0.191786i	0.995392	−	0.0958931i	$-0.0305707\pi$
$308$	35.5118	+	142.410i	0.115298	+	0.462369i
$309$	−178.305			−0.577040
$310$	−42.8456	−	33.4734i	−0.138211	−	0.107979i
$311$			495.582i			1.59351i	0.604302	+	0.796755i	$0.293452\pi$
$311$			495.582i			1.59351i	−0.604302	+	0.796755i	$0.706548\pi$
$312$	11.4271	−	25.6692i	0.0366253	−	0.0822731i
$313$	497.622			1.58985			0.794924	−	0.606710i	$-0.207511\pi$
$313$	497.622			1.58985			0.794924	+	0.606710i	$0.207511\pi$
$314$	−52.0102	+	66.5724i	−0.165638	+	0.212014i
$315$			12.9075i			0.0409761i
$316$	−294.199	+	73.3627i	−0.931010	+	0.232161i
$317$	−30.0346			−0.0947464			−0.0473732	−	0.998877i	$-0.515085\pi$
$317$	−30.0346			−0.0947464			−0.0473732	+	0.998877i	$0.515085\pi$
$318$	48.1834	+	37.6437i	0.151520	+	0.118376i
$319$		−	180.954i		−	0.567255i
$320$	21.3211	+	23.6747i	0.0666285	+	0.0739833i
$321$	−64.9828			−0.202439
$322$	−12.4517	+	15.9381i	−0.0386700	+	0.0494971i
$323$			67.1033i			0.207750i
$324$	−54.4689	−	218.431i	−0.168114	−	0.674171i
$325$	89.2452			0.274601
$326$	−30.1621	−	23.5644i	−0.0925217	−	0.0722833i
$327$			177.384i			0.542460i
$328$	−265.846	−	118.346i	−0.810506	−	0.360811i
$329$	−132.185			−0.401777
$330$	6.80309	−	8.70787i	0.0206154	−	0.0263875i
$331$			230.896i			0.697571i	0.937203	+	0.348786i	$0.113406\pi$
$331$			230.896i			0.697571i	−0.937203	+	0.348786i	$0.886594\pi$
$332$	−511.833	+	127.633i	−1.54167	+	0.384436i
$333$	−343.137			−1.03044
$334$	−236.225	−	184.552i	−0.707259	−	0.552552i
$335$			25.4902i			0.0760902i
$336$	−44.3165	+	23.5674i	−0.131894	+	0.0701410i
$337$	18.1729			0.0539255			0.0269627	−	0.999636i	$-0.491416\pi$
$337$	18.1729			0.0539255			0.0269627	+	0.999636i	$0.491416\pi$
$338$	16.0069	−	20.4886i	0.0473575	−	0.0606170i
$339$			140.010i			0.413009i
$340$	−3.17356	−	12.7266i	−0.00933400	−	0.0374312i
$341$	622.201			1.82464
$342$	129.266	+	100.990i	0.377971	+	0.295293i
$343$			282.203i			0.822750i
$344$	−226.577	+	508.971i	−0.658655	+	1.47957i
$345$	1.52277			0.00441381
$346$	−72.4034	+	92.6754i	−0.209258	+	0.267848i
$347$			627.142i			1.80733i	0.428245	+	0.903663i	$0.359132\pi$
$347$			627.142i			1.80733i	−0.428245	+	0.903663i	$0.640868\pi$
$348$	60.0450	−	14.9731i	0.172543	−	0.0430261i
$349$	−31.9065			−0.0914227			−0.0457114	−	0.998955i	$-0.514555\pi$
$349$	−31.9065			−0.0914227			−0.0457114	+	0.998955i	$0.514555\pi$
$350$	−125.631	−	98.1503i	−0.358946	−	0.280429i
$351$			59.8873i			0.170619i
$352$	−359.063	−	63.2811i	−1.02007	−	0.179776i
$353$	−595.247			−1.68625			−0.843126	−	0.537716i	$-0.819287\pi$
$353$	−595.247			−1.68625			−0.843126	+	0.537716i	$0.819287\pi$
$354$	123.486	−	158.061i	0.348831	−	0.446499i
$355$			39.4985i			0.111263i
$356$	−75.6318	−	303.299i	−0.212449	−	0.851963i
$357$	20.6637			0.0578815
$358$	443.757	+	346.689i	1.23954	+	0.968404i
$359$		−	395.000i		−	1.10028i	−0.835073	−	0.550139i	$-0.814575\pi$
$359$		−	395.000i		−	1.10028i	0.835073	−	0.550139i	$-0.185425\pi$
$360$	−29.2924	−	13.0400i	−0.0813678	−	0.0362223i
$361$	257.218			0.712514
$362$	147.638	−	188.974i	0.407839	−	0.522028i
$363$			8.58720i			0.0236562i
$364$	−45.0659	+	11.2378i	−0.123807	+	0.0308731i
$365$	47.3980			0.129857
$366$	61.6947	+	48.1995i	0.168565	+	0.131693i
$367$			315.669i			0.860133i	0.902797	+	0.430066i	$0.141510\pi$
$367$			315.669i			0.860133i	−0.902797	+	0.430066i	$0.858490\pi$
$368$	−23.5905	−	44.3600i	−0.0641046	−	0.120543i
$369$	292.857			0.793650
$370$	−26.1243	+	33.4387i	−0.0706062	+	0.0903750i
$371$		−	101.073i		−	0.272433i
$372$	51.4841	+	206.461i	0.138398	+	0.555004i
$373$	−7.32792			−0.0196459			−0.00982295	−	0.999952i	$-0.503127\pi$
$373$	−7.32792			−0.0196459			−0.00982295	+	0.999952i	$0.503127\pi$
$374$	118.280	+	92.4076i	0.316258	+	0.247079i
$375$			24.1264i			0.0643371i
$376$	133.542	−	299.982i	0.355166	−	0.797824i
$377$	57.2634			0.151892
$378$	65.8629	−	84.3037i	0.174241	−	0.223026i
$379$			231.814i			0.611648i	0.952088	+	0.305824i	$0.0989319\pi$
$379$			231.814i			0.611648i	−0.952088	+	0.305824i	$0.901068\pi$
$380$	19.6831	−	4.90825i	0.0517975	−	0.0129164i
$381$	129.454			0.339773
$382$	−396.295	−	309.609i	−1.03742	−	0.810495i
$383$			336.472i			0.878516i	0.898361	+	0.439258i	$0.144759\pi$
$383$			336.472i			0.878516i	−0.898361	+	0.439258i	$0.855241\pi$
$384$	−8.71251	−	124.382i	−0.0226888	−	0.323912i
$385$	−18.2662			−0.0474447
$386$	−227.462	+	291.149i	−0.589281	+	0.754271i
$387$		−	560.683i		−	1.44879i
$388$	34.0833	+	136.681i	0.0878435	+	0.352270i
$389$	704.538			1.81115			0.905576	−	0.424184i	$-0.139439\pi$
$389$	704.538			1.81115			0.905576	+	0.424184i	$0.139439\pi$
$390$	2.75563	+	2.15286i	0.00706571	+	0.00552015i
$391$			20.6840i			0.0529002i
$392$	−282.319	−	125.679i	−0.720203	−	0.320611i
$393$	−38.4811			−0.0979163
$394$	314.494	−	402.548i	0.798207	−	1.02169i
$395$		−	37.7356i		−	0.0955332i
$396$	356.023	−	88.7795i	0.899049	−	0.224191i
$397$	−535.675			−1.34931			−0.674653	−	0.738135i	$-0.735707\pi$
$397$	−535.675			−1.34931			−0.674653	+	0.738135i	$0.735707\pi$
$398$	435.082	+	339.911i	1.09317	+	0.854049i
$399$			31.9586i			0.0800968i
$400$	349.665	−	185.951i	0.874163	−	0.464877i
$401$	−178.181			−0.444342			−0.222171	−	0.975008i	$-0.571314\pi$
$401$	−178.181			−0.444342			−0.222171	+	0.975008i	$0.571314\pi$
$402$	61.4153	−	78.6107i	0.152774	−	0.195549i
$403$			196.897i			0.488578i
$404$	−130.055	−	521.546i	−0.321918	−	1.29096i
$405$	28.0172			0.0691783
$406$	−80.6100	−	62.9773i	−0.198547	−	0.155116i
$407$		−	485.596i		−	1.19311i
$408$	−20.8760	+	46.8946i	−0.0511666	+	0.114938i
$409$	258.068			0.630973			0.315487	−	0.948930i	$-0.397832\pi$
$409$	258.068			0.630973			0.315487	+	0.948930i	$0.397832\pi$
$410$	22.2963	−	28.5390i	0.0543812	−	0.0696073i
$411$		−	142.647i		−	0.347072i
$412$	−710.418	+	177.153i	−1.72432	+	0.429983i
$413$	−331.559			−0.802806
$414$	39.8451	+	31.1293i	0.0962442	+	0.0751916i
$415$		−	65.6505i		−	0.158194i
$416$	20.0255	−	113.626i	0.0481381	−	0.273141i
$417$	−51.1950			−0.122770
$418$	−142.918	+	182.933i	−0.341910	+	0.437640i
$419$		−	631.259i		−	1.50659i	−0.657685	−	0.753293i	$-0.728464\pi$
$419$		−	631.259i		−	1.50659i	0.657685	−	0.753293i	$-0.271536\pi$
$420$	−1.51144	−	6.06118i	−0.00359867	−	0.0144314i
$421$	−223.747			−0.531466			−0.265733	−	0.964047i	$-0.585614\pi$
$421$	−223.747			−0.531466			−0.265733	+	0.964047i	$0.585614\pi$
$422$	345.165	+	269.663i	0.817928	+	0.639013i
$423$			330.461i			0.781232i
$424$	229.376	+	102.111i	0.540982	+	0.240828i
$425$	−163.041			−0.383625
$426$	95.1664	−	121.812i	0.223395	−	0.285943i
$427$		−	129.415i		−	0.303080i
$428$	−258.909	+	64.5627i	−0.604929	+	0.150848i
$429$	−40.0171			−0.0932799
$430$	−54.6388	−	42.6870i	−0.127067	−	0.0992720i
$431$		−	359.581i		−	0.834295i	−0.908839	−	0.417148i	$-0.863030\pi$
$431$		−	359.581i		−	0.834295i	0.908839	−	0.417148i	$-0.136970\pi$
$432$	124.781	+	234.640i	0.288844	+	0.543148i
$433$	−71.0809			−0.164159			−0.0820795	−	0.996626i	$-0.526156\pi$
$433$	−71.0809			−0.164159			−0.0820795	+	0.996626i	$0.526156\pi$
$434$	216.544	−	277.173i	0.498949	−	0.638648i
$435$			7.70170i			0.0177051i
$436$	176.238	+	706.749i	0.404215	+	1.62098i
$437$	−31.9900			−0.0732036
$438$	−146.173	−	114.199i	−0.333729	−	0.260729i
$439$		−	742.515i		−	1.69138i	−0.533675	−	0.845689i	$-0.679190\pi$
$439$		−	742.515i		−	1.69138i	0.533675	−	0.845689i	$-0.320810\pi$
$440$	18.4538	−	41.4537i	0.0419406	−	0.0942129i
$441$	311.004			0.705224
$442$	−29.2426	+	37.4302i	−0.0661598	+	0.0846836i
$443$		−	146.551i		−	0.330814i	−0.986225	−	0.165407i	$-0.947106\pi$
$443$		−	146.551i		−	0.330814i	0.986225	−	0.165407i	$-0.0528938\pi$
$444$	161.132	−	40.1807i	0.362911	−	0.0904970i
$445$	38.9028			0.0874219
$446$	−136.289	−	106.477i	−0.305581	−	0.238738i
$447$		−	51.2852i		−	0.114732i
$448$	−153.154	+	137.929i	−0.341862	+	0.307877i
$449$	−115.227			−0.256629			−0.128315	−	0.991734i	$-0.540957\pi$
$449$	−115.227			−0.256629			−0.128315	+	0.991734i	$0.540957\pi$
$450$	−245.375	+	314.077i	−0.545279	+	0.697949i
$451$			414.442i			0.918939i
$452$	139.105	+	557.839i	0.307755	+	1.23416i
$453$	119.081			0.262871
$454$	0.698190	+	0.545467i	0.00153786	+	0.00120147i
$455$		−	5.78039i		−	0.0127042i
$456$	−72.5275	−	32.2869i	−0.159052	−	0.0708046i
$457$	−503.039			−1.10074			−0.550371	−	0.834920i	$-0.685514\pi$
$457$	−503.039			−1.10074			−0.550371	+	0.834920i	$0.685514\pi$
$458$	221.467	−	283.475i	0.483553	−	0.618942i
$459$		−	109.407i		−	0.238360i
$460$	6.06712	−	1.51292i	0.0131894	−	0.00328896i
$461$	−607.835			−1.31852			−0.659258	−	0.751917i	$-0.729129\pi$
$461$	−607.835			−1.31852			−0.659258	+	0.751917i	$0.729129\pi$
$462$	56.3323	+	44.0100i	0.121931	+	0.0952598i
$463$		−	300.263i		−	0.648515i	−0.945969	−	0.324258i	$-0.894886\pi$
$463$		−	300.263i		−	0.648515i	0.945969	−	0.324258i	$-0.105114\pi$
$464$	224.360	−	119.314i	0.483534	−	0.257142i
$465$	−26.4819			−0.0569502
$466$	−326.830	+	418.338i	−0.701352	+	0.897722i
$467$			785.840i			1.68274i	0.540459	+	0.841371i	$0.318251\pi$
$467$			785.840i			1.68274i	−0.540459	+	0.841371i	$0.681749\pi$
$468$	28.0945	+	112.665i	0.0600310	+	0.240736i
$469$	−164.899			−0.351597
$470$	32.2035	+	25.1593i	0.0685181	+	0.0535303i
$471$			41.1469i			0.0873607i
$472$	334.965	−	752.446i	0.709671	−	1.59417i
$473$	793.461			1.67751
$474$	−90.9190	+	116.375i	−0.191812	+	0.245517i
$475$		−	252.160i		−	0.530862i
$476$	82.3300	−	20.5301i	0.172962	−	0.0431305i
$477$	−252.682			−0.529731
$478$	295.755	+	231.061i	0.618735	+	0.483392i
$479$			77.7614i			0.162341i	0.996700	+	0.0811706i	$0.0258659\pi$
$479$			77.7614i			0.162341i	−0.996700	+	0.0811706i	$0.974134\pi$
$480$	15.2823	+	2.69334i	0.0318381	+	0.00561113i
$481$	153.668			0.319476
$482$	−66.9522	+	85.6979i	−0.138905	+	0.177796i
$483$			9.85095i			0.0203953i
$484$	8.53169	+	34.2138i	0.0176275	+	0.0706897i
$485$	−17.5314			−0.0361473
$486$	−322.003	−	251.567i	−0.662557	−	0.517628i
$487$			173.050i			0.355339i	0.984090	+	0.177670i	$0.0568558\pi$
$487$			173.050i			0.355339i	−0.984090	+	0.177670i	$0.943144\pi$
$488$	293.697	+	130.744i	0.601838	+	0.267919i
$489$	−18.6425			−0.0381237
$490$	23.6779	−	30.3074i	0.0483223	−	0.0618519i
$491$		−	462.515i		−	0.941985i	−0.882137	−	0.470993i	$-0.843896\pi$
$491$		−	462.515i		−	0.941985i	0.882137	−	0.470993i	$-0.156104\pi$
$492$	−137.522	+	34.2930i	−0.279516	+	0.0697012i
$493$	−104.614			−0.212198
$494$	−57.8897	−	45.2268i	−0.117186	−	0.0915523i
$495$			45.6655i			0.0922536i
$496$	410.254	+	771.448i	0.827124	+	1.55534i
$497$	−255.521			−0.514126
$498$	−158.176	+	202.464i	−0.317623	+	0.406553i
$499$		−	370.096i		−	0.741675i	−0.928698	−	0.370838i	$-0.879071\pi$
$499$		−	370.096i		−	0.741675i	0.928698	−	0.370838i	$-0.120929\pi$
$500$	23.9705	+	96.1264i	0.0479410	+	0.192253i
$501$	−146.005			−0.291427
$502$	172.165	+	134.505i	0.342958	+	0.267939i
$503$			553.175i			1.09975i	0.835246	+	0.549876i	$0.185325\pi$
$503$			553.175i			1.09975i	−0.835246	+	0.549876i	$0.814675\pi$
$504$	84.3576	−	189.496i	0.167376	−	0.375985i
$505$	66.8964			0.132468
$506$	−44.0532	+	56.3875i	−0.0870617	+	0.111438i
$507$		−	12.6635i		−	0.0249773i
$508$	515.779	−	128.617i	1.01531	−	0.253183i
$509$	493.932			0.970397			0.485198	−	0.874404i	$-0.338747\pi$
$509$	493.932			0.970397			0.485198	+	0.874404i	$0.338747\pi$
$510$	−5.03421	−	3.93301i	−0.00987099	−	0.00771179i
$511$			306.623i			0.600046i
$512$	−158.291	−	486.917i	−0.309162	−	0.951009i
$513$	169.210			0.329843
$514$	−302.896	+	387.703i	−0.589293	+	0.754287i
$515$		−	91.1222i		−	0.176936i
$516$	65.6550	+	263.290i	0.127238	+	0.510251i
$517$	−467.658			−0.904561
$518$	−216.319	−	169.001i	−0.417605	−	0.326257i
$519$			57.2806i			0.110367i
$520$	13.1181	+	5.83977i	0.0252272	+	0.0112303i
$521$	567.493			1.08924			0.544619	−	0.838684i	$-0.316674\pi$
$521$	567.493			1.08924			0.544619	+	0.838684i	$0.316674\pi$
$522$	−157.443	+	201.525i	−0.301615	+	0.386063i
$523$			592.304i			1.13251i	0.824229	+	0.566256i	$0.191609\pi$
$523$			592.304i			1.13251i	−0.824229	+	0.566256i	$0.808391\pi$
$524$	−153.320	+	38.2324i	−0.292594	+	0.0729626i
$525$	−77.6497			−0.147904
$526$	−396.578	−	309.829i	−0.753950	−	0.589029i
$527$		−	359.708i		−	0.682557i
$528$	−156.788	+	83.3794i	−0.296947	+	0.157915i
$529$	519.139			0.981360
$530$	−19.2376	+	24.6239i	−0.0362974	+	0.0464602i
$531$			828.897i			1.56101i
$532$	31.7521	+	127.332i	0.0596843	+	0.239346i
$533$	−131.151			−0.246062
$534$	−119.974	−	93.7311i	−0.224671	−	0.175526i
$535$		−	33.2091i		−	0.0620732i
$536$	166.593	−	374.225i	0.310808	−	0.698182i
$537$	274.276			0.510756
$538$	211.034	−	270.121i	0.392257	−	0.502084i
$539$			440.123i			0.816554i
$540$	−32.0918	+	8.00254i	−0.0594292	+	0.0148195i
$541$	−969.868			−1.79273			−0.896366	−	0.443315i	$-0.853802\pi$
$541$	−969.868			−1.79273			−0.896366	+	0.443315i	$0.853802\pi$
$542$	232.687	+	181.788i	0.429311	+	0.335403i
$543$		−	116.801i		−	0.215103i
$544$	−36.5842	+	207.582i	−0.0672503	+	0.381585i
$545$	−90.6515			−0.166333
$546$	−13.9271	+	17.8265i	−0.0255075	+	0.0326492i
$547$			45.3981i			0.0829947i	0.999139	+	0.0414973i	$0.0132128\pi$
$547$			45.3981i			0.0829947i	−0.999139	+	0.0414973i	$0.986787\pi$
$548$	−141.725	−	568.344i	−0.258621	−	1.03712i
$549$	−323.537			−0.589321
$550$	−444.472	−	347.247i	−0.808131	−	0.631359i
$551$		−	161.796i		−	0.293641i
$552$	−22.3559	−	9.95214i	−0.0404999	−	0.0180292i
$553$	244.116			0.441440
$554$	460.353	−	589.245i	0.830962	−	1.06362i
$555$			20.6677i			0.0372392i
$556$	−203.975	+	50.8640i	−0.366861	+	0.0914821i
$557$	381.228			0.684431			0.342215	−	0.939622i	$-0.388823\pi$
$557$	381.228			0.684431			0.342215	+	0.939622i	$0.388823\pi$
$558$	−692.932	−	541.359i	−1.24181	−	0.970177i
$559$			251.093i			0.449182i
$560$	−12.0440	−	22.6477i	−0.0215071	−	0.0404424i
$561$	73.1065			0.130315
$562$	−287.185	+	367.593i	−0.511006	+	0.654081i
$563$		−	145.358i		−	0.258184i	−0.991633	−	0.129092i	$-0.958794\pi$
$563$		−	145.358i		−	0.258184i	0.991633	−	0.129092i	$-0.0412063\pi$
$564$	−38.6964	−	155.180i	−0.0686106	−	0.275142i
$565$	−71.5515			−0.126640
$566$	−366.853	−	286.607i	−0.648150	−	0.506373i
$567$			181.247i			0.319659i
$568$	258.145	−	579.883i	0.454481	−	1.02092i
$569$	−169.835			−0.298480			−0.149240	−	0.988801i	$-0.547683\pi$
$569$	−169.835			−0.298480			−0.149240	+	0.988801i	$0.547683\pi$
$570$	6.08283	−	7.78594i	0.0106716	−	0.0136595i
$571$		−	544.266i		−	0.953181i	−0.879125	−	0.476590i	$-0.841872\pi$
$571$		−	544.266i		−	0.953181i	0.879125	−	0.476590i	$-0.158128\pi$
$572$	−159.439	+	39.7584i	−0.278740	+	0.0695077i
$573$	−244.941			−0.427472
$574$	184.622	+	144.238i	0.321641	+	0.251285i
$575$		−	77.7258i		−	0.135175i
$576$	344.822	+	382.885i	0.598650	+	0.664731i
$577$	529.542			0.917750			0.458875	−	0.888501i	$-0.348253\pi$
$577$	529.542			0.917750			0.458875	+	0.888501i	$0.348253\pi$
$578$	−302.422	+	387.096i	−0.523221	+	0.669716i
$579$			179.952i			0.310799i
$580$	7.65192	+	30.6857i	0.0131930	+	0.0529064i
$581$	424.701			0.730983
$582$	54.0662	+	42.2397i	0.0928972	+	0.0725767i
$583$		−	357.587i		−	0.613357i
$584$	−695.856	−	309.773i	−1.19153	−	0.530433i
$585$	−14.4510			−0.0247025
$586$	−84.2993	+	107.902i	−0.143855	+	0.184133i
$587$		−	616.956i		−	1.05103i	−0.850784	−	0.525516i	$-0.823872\pi$
$587$		−	616.956i		−	1.05103i	0.850784	−	0.525516i	$-0.176128\pi$
$588$	−146.043	+	36.4180i	−0.248373	+	0.0619353i
$589$	556.326			0.944527
$590$	80.7762	+	63.1071i	0.136909	+	0.106961i
$591$		−	248.806i		−	0.420991i
$592$	602.076	−	320.182i	1.01702	−	0.540848i
$593$	658.198			1.10995			0.554973	−	0.831868i	$-0.312728\pi$
$593$	658.198			1.10995			0.554973	+	0.831868i	$0.312728\pi$
$594$	233.018	−	298.259i	0.392285	−	0.502120i
$595$			10.5601i			0.0177481i
$596$	−50.9537	−	204.335i	−0.0854928	−	0.342843i
$597$	268.914			0.450443
$598$	−17.8440	−	13.9408i	−0.0298394	−	0.0233123i
$599$			551.338i			0.920431i	0.887807	+	0.460216i	$0.152228\pi$
$599$			551.338i			0.920431i	−0.887807	+	0.460216i	$0.847772\pi$
$600$	78.4472	−	176.220i	0.130745	−	0.293699i
$601$	95.6870			0.159213			0.0796065	−	0.996826i	$-0.474634\pi$
$601$	95.6870			0.159213			0.0796065	+	0.996826i	$0.474634\pi$
$602$	276.147	−	353.465i	0.458716	−	0.587151i
$603$			412.248i			0.683661i
$604$	474.451	−	118.311i	0.785514	−	0.195879i
$605$	−4.38845			−0.00725363
$606$	−206.306	−	161.178i	−0.340438	−	0.265970i
$607$			99.7418i			0.164319i	0.996619	+	0.0821597i	$0.0261817\pi$
$607$			99.7418i			0.164319i	−0.996619	+	0.0821597i	$0.973818\pi$
$608$	−321.048	−	56.5813i	−0.528039	−	0.0930613i
$609$	−49.8232			−0.0818116
$610$	−24.6321	+	31.5288i	−0.0403806	+	0.0516866i
$611$		−	147.992i		−	0.242212i
$612$	−51.3253	−	205.825i	−0.0838649	−	0.336315i
$613$	407.424			0.664639			0.332320	−	0.943167i	$-0.392169\pi$
$613$	407.424			0.664639			0.332320	+	0.943167i	$0.392169\pi$
$614$	−92.7948	−	72.4967i	−0.151132	−	0.118073i
$615$		−	17.6393i		−	0.0286818i
$616$	268.169	+	119.380i	0.435339	+	0.193799i
$617$	−361.949			−0.586627			−0.293313	−	0.956016i	$-0.594758\pi$
$617$	−361.949			−0.586627			−0.293313	+	0.956016i	$0.594758\pi$
$618$	−219.547	+	281.017i	−0.355254	+	0.454720i
$619$		−	110.814i		−	0.179020i	−0.995986	−	0.0895102i	$-0.971470\pi$
$619$		−	110.814i		−	0.179020i	0.995986	−	0.0895102i	$-0.0285302\pi$
$620$	−105.511	+	26.3107i	−0.170179	+	0.0424366i
$621$	52.1573			0.0839892
$622$	781.058	+	610.208i	1.25572	+	0.981042i
$623$			251.667i			0.403959i
$624$	−26.3856	−	49.6160i	−0.0422846	−	0.0795128i
$625$	606.475			0.970360
$626$	612.720	−	784.274i	0.978786	−	1.25283i
$627$			113.067i			0.180330i
$628$	40.8809	+	163.941i	0.0650970	+	0.261052i
$629$	−280.733			−0.446317
$630$	20.3427	+	15.8929i	0.0322900	+	0.0252268i
$631$		−	605.458i		−	0.959522i	−0.877399	−	0.479761i	$-0.840723\pi$
$631$		−	605.458i		−	0.959522i	0.877399	−	0.479761i	$-0.159277\pi$
$632$	−246.624	+	554.002i	−0.390227	+	0.876585i
$633$	213.339			0.337028
$634$	−36.9815	+	47.3358i	−0.0583305	+	0.0746622i
$635$			66.1567i			0.104184i
$636$	118.656	−	29.5886i	0.186566	−	0.0465229i
$637$	−139.278			−0.218647
$638$	−285.192	−	222.808i	−0.447009	−	0.349229i
$639$			638.801i			0.999689i
$640$	63.5649	−	4.45249i	0.0993202	−	0.00695701i
$641$	−1097.57			−1.71228			−0.856142	−	0.516740i	$-0.827145\pi$
$641$	−1097.57			−1.71228			−0.856142	+	0.516740i	$0.827145\pi$
$642$	−80.0130	+	102.416i	−0.124631	+	0.159526i
$643$		−	224.973i		−	0.349880i	−0.984579	−	0.174940i	$-0.944027\pi$
$643$		−	224.973i		−	0.349880i	0.984579	−	0.174940i	$-0.0559731\pi$
$644$	9.78728	+	39.2489i	0.0151976	+	0.0609456i
$645$	−33.7710			−0.0523581
$646$	105.758	+	82.6241i	0.163712	+	0.127901i
$647$			887.194i			1.37124i	0.727958	+	0.685621i	$0.240469\pi$
$647$			887.194i			1.37124i	−0.727958	+	0.685621i	$0.759531\pi$
$648$	−411.324	−	183.108i	−0.634760	−	0.282575i
$649$	−1173.03			−1.80744
$650$	109.887	−	140.654i	0.169057	−	0.216391i
$651$		−	171.314i		−	0.263156i
$652$	−74.2769	+	18.5220i	−0.113922	+	0.0284079i
$653$	−11.7116			−0.0179350			−0.00896751	−	0.999960i	$-0.502854\pi$
$653$	−11.7116			−0.0179350			−0.00896751	+	0.999960i	$0.502854\pi$
$654$	279.565	+	218.413i	0.427470	+	0.333964i
$655$		−	19.6656i		−	0.0300238i
$656$	−513.854	+	273.266i	−0.783314	+	0.416563i
$657$	766.557			1.16675
$658$	−162.758	+	208.328i	−0.247353	+	0.316609i
$659$		−	887.211i		−	1.34630i	−0.739507	−	0.673149i	$-0.764941\pi$
$659$		−	887.211i		−	1.34630i	0.739507	−	0.673149i	$-0.235059\pi$
$660$	−5.34735	−	21.4439i	−0.00810204	−	0.0324908i
$661$	−1200.76			−1.81658			−0.908290	−	0.418342i	$-0.862611\pi$
$661$	−1200.76			−1.81658			−0.908290	+	0.418342i	$0.862611\pi$
$662$	363.902	+	284.301i	0.549701	+	0.429458i
$663$			23.1347i			0.0348940i
$664$	−429.064	+	963.825i	−0.646180	+	1.45154i
$665$	−16.3323			−0.0245599
$666$	−422.503	+	540.798i	−0.634389	+	0.812009i
$667$		−	49.8721i		−	0.0747708i
$668$	−581.725	+	145.061i	−0.870846	+	0.217158i
$669$	−84.2372			−0.125915
$670$	40.1736	+	31.3860i	0.0599607	+	0.0468448i
$671$		−	457.860i		−	0.682354i
$672$	−17.4236	+	98.8631i	−0.0259279	+	0.147118i
$673$	−50.1168			−0.0744677			−0.0372339	−	0.999307i	$-0.511855\pi$
$673$	−50.1168			−0.0744677			−0.0372339	+	0.999307i	$0.511855\pi$
$674$	22.3762	−	28.6412i	0.0331991	−	0.0424944i
$675$			411.127i			0.609078i
$676$	−12.5817	−	50.4550i	−0.0186119	−	0.0746375i
$677$	−894.970			−1.32196			−0.660982	−	0.750402i	$-0.729860\pi$
$677$	−894.970			−1.32196			−0.660982	+	0.750402i	$0.729860\pi$
$678$	220.662	+	172.394i	0.325460	+	0.254268i
$679$		−	113.413i		−	0.167029i
$680$	−23.9653	−	10.6686i	−0.0352430	−	0.0156891i
$681$	0.431535			0.000633679
$682$	766.114	−	980.615i	1.12333	−	1.43785i
$683$			758.735i			1.11089i	0.831555	+	0.555443i	$0.187451\pi$
$683$			758.735i			1.11089i	−0.831555	+	0.555443i	$0.812549\pi$
$684$	318.330	−	79.3801i	0.465395	−	0.116053i
$685$	72.8989			0.106422
$686$	444.764	+	347.476i	0.648345	+	0.506525i
$687$		−	175.210i		−	0.255036i
$688$	523.176	+	983.789i	0.760430	+	1.42993i
$689$	113.159			0.164237
$690$	1.87498	−	2.39994i	0.00271736	−	0.00347818i
$691$			126.346i			0.182845i	0.995812	+	0.0914227i	$0.0291415\pi$
$691$			126.346i			0.182845i	−0.995812	+	0.0914227i	$0.970859\pi$
$692$	56.9103	+	228.222i	0.0822403	+	0.329800i
$693$	−295.416			−0.426285
$694$	988.402	+	772.197i	1.42421	+	1.11268i
$695$		−	26.1629i		−	0.0376445i
$696$	50.3350	−	113.070i	0.0723204	−	0.162457i
$697$	239.598			0.343755
$698$	−39.2864	+	50.2860i	−0.0562842	+	0.0720430i
$699$			258.565i			0.369908i
$700$	−309.378	+	77.1477i	−0.441968	+	0.110211i
$701$	730.518			1.04211			0.521054	−	0.853524i	$-0.325539\pi$
$701$	730.518			1.04211			0.521054	+	0.853524i	$0.325539\pi$
$702$	94.3849	+	73.7390i	0.134451	+	0.105041i
$703$		−	434.184i		−	0.617616i
$704$	−541.847	+	487.981i	−0.769669	+	0.693155i
$705$	19.9043			0.0282330
$706$	−732.925	+	938.135i	−1.03814	+	1.32880i
$707$			432.761i			0.612109i
$708$	−97.0623	−	389.239i	−0.137094	−	0.549773i
$709$	−906.169			−1.27809			−0.639047	−	0.769167i	$-0.720671\pi$
$709$	−906.169			−1.27809			−0.639047	+	0.769167i	$0.720671\pi$
$710$	62.2513	+	48.6344i	0.0876779	+	0.0684991i
$711$		−	610.290i		−	0.858355i
$712$	−571.137	−	254.252i	−0.802159	−	0.357095i
$713$	171.482			0.240508
$714$	25.4431	−	32.5669i	0.0356347	−	0.0456119i
$715$		−	20.4505i		−	0.0286022i
$716$	1092.79	−	272.503i	1.52625	−	0.380591i
$717$	182.800			0.254951
$718$	−622.536	−	486.361i	−0.867042	−	0.677384i
$719$			264.478i			0.367841i	0.982941	+	0.183921i	$0.0588789\pi$
$719$			264.478i			0.367841i	−0.982941	+	0.183921i	$0.941121\pi$
$720$	−56.6193	+	30.1100i	−0.0786379	+	0.0418194i
$721$	589.480			0.817587
$722$	316.711	−	405.386i	0.438658	−	0.561476i
$723$			52.9679i			0.0732613i
$724$	−116.046	−	465.367i	−0.160284	−	0.642772i
$725$	393.115			0.542227
$726$	13.5338	+	10.5734i	0.0186416	+	0.0145639i
$727$		−	986.166i		−	1.35649i	−0.734838	−	0.678243i	$-0.762742\pi$
$727$		−	986.166i		−	1.35649i	0.734838	−	0.678243i	$-0.237258\pi$
$728$	−37.7782	+	84.8628i	−0.0518931	+	0.116570i
$729$	307.498			0.421808
$730$	58.3609	−	74.7012i	0.0799465	−	0.102330i
$731$		−	458.717i		−	0.627520i
$732$	151.929	−	37.8856i	0.207553	−	0.0517563i
$733$	−718.229			−0.979849			−0.489925	−	0.871765i	$-0.662976\pi$
$733$	−718.229			−0.979849			−0.489925	+	0.871765i	$0.662976\pi$
$734$	497.507	+	388.682i	0.677803	+	0.529539i
$735$		−	18.7323i		−	0.0254862i
$736$	−98.9601	−	17.4407i	−0.134457	−	0.0236966i
$737$	−583.400			−0.791587
$738$	360.593	−	461.555i	0.488609	−	0.625413i
$739$		−	694.891i		−	0.940312i	−0.882583	−	0.470156i	$-0.844198\pi$
$739$		−	694.891i		−	0.940312i	0.882583	−	0.470156i	$-0.155802\pi$
$740$	20.5341	+	82.3460i	0.0277488	+	0.111278i
$741$	−35.7803			−0.0482865
$742$	−159.295	−	124.451i	−0.214683	−	0.167723i
$743$		−	273.958i		−	0.368719i	−0.982859	−	0.184359i	$-0.940979\pi$
$743$		−	273.958i		−	0.368719i	0.982859	−	0.184359i	$-0.0590210\pi$
$744$	388.784	+	173.074i	0.522559	+	0.232626i
$745$	26.2091			0.0351800
$746$	−9.02284	+	11.5491i	−0.0120950	+	0.0154814i
$747$		−	1061.75i		−	1.42136i
$748$	291.277	−	72.6339i	0.389407	−	0.0971042i
$749$	214.834			0.286828
$750$	38.0243	+	29.7068i	0.0506990	+	0.0396090i
$751$			208.045i			0.277024i	0.990361	+	0.138512i	$0.0442319\pi$
$751$			208.045i			0.277024i	−0.990361	+	0.138512i	$0.955768\pi$
$752$	−308.354	−	579.835i	−0.410046	−	0.771057i
$753$	106.411			0.141316
$754$	70.5083	−	90.2496i	0.0935123	−	0.119694i
$755$			60.8556i			0.0806035i
$756$	−51.7694	−	207.606i	−0.0684780	−	0.274611i
$757$	562.324			0.742833			0.371416	−	0.928466i	$-0.378872\pi$
$757$	562.324			0.742833			0.371416	+	0.928466i	$0.378872\pi$
$758$	365.349	+	285.432i	0.481991	+	0.376560i
$759$			34.8519i			0.0459181i
$760$	16.5001	−	37.0648i	0.0217106	−	0.0487695i
$761$	620.270			0.815072			0.407536	−	0.913189i	$-0.366388\pi$
$761$	620.270			0.815072			0.407536	+	0.913189i	$0.366388\pi$
$762$	159.396	−	204.024i	0.209181	−	0.267749i
$763$		−	586.435i		−	0.768591i
$764$	−975.914	+	243.358i	−1.27737	+	0.318531i
$765$	26.4002			0.0345101
$766$	530.294	+	414.296i	0.692289	+	0.540857i
$767$		−	371.208i		−	0.483974i
$768$	−206.759	−	139.420i	−0.269218	−	0.181536i
$769$	−1102.48			−1.43365			−0.716827	−	0.697251i	$-0.754406\pi$
$769$	−1102.48			−1.43365			−0.716827	+	0.697251i	$0.754406\pi$
$770$	−22.4911	+	28.7883i	−0.0292093	+	0.0373875i
$771$			239.631i			0.310805i
$772$	178.789	+	716.980i	0.231592	+	0.928731i
$773$	747.128			0.966531			0.483265	−	0.875474i	$-0.339451\pi$
$773$	747.128			0.966531			0.483265	+	0.875474i	$0.339451\pi$
$774$	−883.661	−	690.367i	−1.14168	−	0.891948i
$775$			1351.70i			1.74413i
$776$	257.381	+	114.578i	0.331677	+	0.147652i
$777$	−133.702			−0.172075
$778$	867.495	−	1110.38i	1.11503	−	1.42723i
$779$			370.563i			0.475691i
$780$	6.78599	−	1.69218i	0.00869998	−	0.00216946i
$781$	−904.011			−1.15750
$782$	32.5988	+	25.4681i	0.0416865	+	0.0325679i
$783$			263.796i			0.336905i
$784$	−545.695	+	290.199i	−0.696039	+	0.370151i
$785$	−21.0279			−0.0267872
$786$	−47.3817	+	60.6479i	−0.0602820	+	0.0771602i
$787$		−	794.505i		−	1.00954i	−0.863255	−	0.504768i	$-0.831578\pi$
$787$		−	794.505i		−	1.00954i	0.863255	−	0.504768i	$-0.168422\pi$
$788$	−247.197	−	991.311i	−0.313702	−	1.25801i
$789$	−245.116			−0.310666
$790$	−59.4729	−	46.4637i	−0.0752822	−	0.0588148i
$791$		−	462.876i		−	0.585178i
$792$	298.450	−	670.422i	0.376831	−	0.846492i
$793$	144.891			0.182712
$794$	−659.574	+	844.246i	−0.830698	+	1.06328i
$795$			15.2195i			0.0191440i
$796$	1071.43	−	267.176i	1.34602	−	0.335648i
$797$	1084.36			1.36056			0.680278	−	0.732954i	$-0.261859\pi$
$797$	1084.36			1.36056			0.680278	+	0.732954i	$0.261859\pi$
$798$	50.3682	+	39.3505i	0.0631180	+	0.0493115i
$799$			270.363i			0.338377i
$800$	137.475	−	780.048i	0.171844	−	0.975060i
$801$	629.166			0.785476
$802$	−219.394	+	280.821i	−0.273558	+	0.350151i
$803$			1084.81i			1.35094i
$804$	−48.2734	−	193.586i	−0.0600416	−	0.240779i
$805$	−5.03428			−0.00625377
$806$	310.318	+	242.439i	0.385010	+	0.300792i
$807$		−	166.956i		−	0.206884i
$808$	−982.115	−	437.206i	−1.21549	−	0.541097i
$809$	−867.148			−1.07188			−0.535938	−	0.844257i	$-0.680042\pi$
$809$	−867.148			−1.07188			−0.535938	+	0.844257i	$0.680042\pi$
$810$	34.4975	−	44.1563i	0.0425895	−	0.0545139i
$811$			60.0777i			0.0740786i	0.999314	+	0.0370393i	$0.0117927\pi$
$811$			60.0777i			0.0740786i	−0.999314	+	0.0370393i	$0.988207\pi$
$812$	−198.510	+	49.5012i	−0.244470	+	0.0609621i
$813$	143.818			0.176898
$814$	−765.320	−	597.912i	−0.940196	−	0.734536i
$815$		−	9.52716i		−	0.0116898i
$816$	48.2034	+	90.6425i	0.0590728	+	0.111082i
$817$	709.455			0.868366
$818$	317.758	−	406.726i	0.388458	−	0.497220i
$819$		−	93.4851i		−	0.114145i
$820$	−17.5253	−	70.2799i	−0.0213723	−	0.0857071i
$821$	553.923			0.674693			0.337347	−	0.941380i	$-0.390471\pi$
$821$	553.923			0.674693			0.337347	+	0.941380i	$0.390471\pi$
$822$	−224.817	−	175.640i	−0.273500	−	0.213674i
$823$			1339.61i			1.62772i	0.581061	+	0.813860i	$0.302638\pi$
$823$			1339.61i			1.62772i	−0.581061	+	0.813860i	$0.697362\pi$
$824$	−595.535	+	1337.78i	−0.722737	+	1.62352i
$825$	−274.718			−0.332992
$826$	−408.247	+	522.551i	−0.494246	+	0.632628i
$827$			736.299i			0.890325i	0.895450	+	0.445162i	$0.146854\pi$
$827$			736.299i			0.890325i	−0.895450	+	0.445162i	$0.853146\pi$
$828$	98.1223	−	24.4682i	0.118505	−	0.0295509i
$829$	1033.43			1.24660			0.623302	−	0.781981i	$-0.285791\pi$
$829$	1033.43			1.24660			0.623302	+	0.781981i	$0.285791\pi$
$830$	−103.468	−	80.8353i	−0.124660	−	0.0973919i
$831$		−	364.199i		−	0.438266i
$832$	−154.423	−	171.469i	−0.185604	−	0.206092i
$833$	254.444			0.305455
$834$	−63.0361	+	80.6854i	−0.0755829	+	0.0967451i
$835$		−	74.6152i		−	0.0893596i
$836$	112.336	+	450.490i	0.134373	+	0.538864i
$837$	−907.049			−1.08369
$838$	−994.892	−	777.267i	−1.18722	−	0.927527i
$839$			1066.63i			1.27132i	0.771971	+	0.635658i	$0.219271\pi$
$839$			1066.63i			1.27132i	−0.771971	+	0.635658i	$0.780729\pi$
$840$	−11.4137	−	5.08101i	−0.0135877	−	0.00604882i
$841$	−588.761			−0.700073
$842$	−275.499	+	352.635i	−0.327196	+	0.418807i
$843$			227.201i			0.269515i
$844$	850.002	−	211.960i	1.00711	−	0.251137i
$845$	6.47163			0.00765873
$846$	520.821	+	406.895i	0.615627	+	0.480964i
$847$		−	28.3894i		−	0.0335176i
$848$	443.361	−	235.778i	0.522832	−	0.278040i
$849$	−226.744			−0.267071
$850$	−200.751	+	256.959i	−0.236178	+	0.302304i
$851$		−	133.833i		−	0.157266i
$852$	−74.8024	−	299.973i	−0.0877963	−	0.352081i
$853$	−49.3291			−0.0578301			−0.0289150	−	0.999582i	$-0.509205\pi$
$853$	−49.3291			−0.0578301			−0.0289150	+	0.999582i	$0.509205\pi$
$854$	−203.964	−	159.348i	−0.238833	−	0.186591i
$855$			40.8307i			0.0477553i
$856$	−217.041	+	487.548i	−0.253552	+	0.569566i
$857$	−1454.64			−1.69736			−0.848681	−	0.528906i	$-0.822602\pi$
$857$	−1454.64			−1.69736			−0.848681	+	0.528906i	$0.822602\pi$
$858$	−49.2729	+	63.0686i	−0.0574276	+	0.0735066i
$859$			537.624i			0.625872i	0.949774	+	0.312936i	$0.101312\pi$
$859$			537.624i			0.625872i	−0.949774	+	0.312936i	$0.898688\pi$
$860$	−134.553	+	33.5527i	−0.156457	+	0.0390147i
$861$	114.111			0.132533
$862$	−566.715	−	442.751i	−0.657442	−	0.513632i
$863$			651.088i			0.754448i	0.926122	+	0.377224i	$0.123121\pi$
$863$			651.088i			0.754448i	−0.926122	+	0.377224i	$0.876879\pi$
$864$	523.445	+	92.2516i	0.605839	+	0.106773i
$865$	−29.2730			−0.0338416
$866$	−87.5216	+	112.026i	−0.101064	+	0.129361i
$867$			239.255i			0.275957i
$868$	−170.207	−	682.564i	−0.196091	−	0.786364i
$869$	863.663			0.993858
$870$	12.1382	+	9.48308i	0.0139520	+	0.0109001i
$871$		−	184.618i		−	0.211961i
$872$	1330.87	+	592.459i	1.52622	+	0.679425i
$873$	−283.532			−0.324779
$874$	−39.3891	+	50.4176i	−0.0450677	+	0.0576860i
$875$		−	79.7623i		−	0.0911569i
$876$	−359.965	+	89.7624i	−0.410919	+	0.102469i
$877$	1423.05			1.62263			0.811314	−	0.584610i	$-0.198753\pi$
$877$	1423.05			1.62263			0.811314	+	0.584610i	$0.198753\pi$
$878$	−1170.24	−	914.256i	−1.33284	−	1.04129i
$879$			66.6918i			0.0758723i
$880$	−42.6106	−	80.1258i	−0.0484212	−	0.0910521i
$881$	773.996			0.878542			0.439271	−	0.898355i	$-0.355237\pi$
$881$	773.996			0.878542			0.439271	+	0.898355i	$0.355237\pi$
$882$	382.938	−	490.155i	0.434170	−	0.555732i
$883$		−	1395.71i		−	1.58065i	−0.612689	−	0.790324i	$-0.709912\pi$
$883$		−	1395.71i		−	1.58065i	0.612689	−	0.790324i	$-0.290088\pi$
$884$	22.9852	+	92.1752i	0.0260013	+	0.104271i
$885$	49.9259			0.0564135
$886$	−230.970	−	180.447i	−0.260689	−	0.203665i
$887$			364.941i			0.411433i	0.978612	+	0.205716i	$0.0659524\pi$
$887$			364.941i			0.411433i	−0.978612	+	0.205716i	$0.934048\pi$
$888$	135.075	−	303.426i	0.152112	−	0.341696i
$889$	−427.975			−0.481412
$890$	47.9008	−	61.3124i	0.0538212	−	0.0688903i
$891$			641.236i			0.719681i
$892$	−335.625	+	83.6927i	−0.376261	+	0.0938259i
$893$	−418.145			−0.468248
$894$	−80.8277	−	63.1473i	−0.0904113	−	0.0706346i
$895$			140.167i			0.156612i
$896$	28.8037	+	411.209i	0.0321470	+	0.458939i
$897$	−11.0290			−0.0122954
$898$	−141.878	+	181.602i	−0.157993	+	0.202229i
$899$			867.308i			0.964748i
$900$	192.869	+	773.444i	0.214299	+	0.859382i
$901$	−206.729			−0.229444
$902$	653.178	+	510.300i	0.724144	+	0.565743i
$903$		−	218.469i		−	0.241936i
$904$	1050.46	+	467.630i	1.16201	+	0.517290i
$905$	59.6905			0.0659563
$906$	146.624	−	187.676i	0.161836	−	0.207148i
$907$			1060.73i			1.16949i	0.811216	+	0.584746i	$0.198806\pi$
$907$			1060.73i			1.16949i	−0.811216	+	0.584746i	$0.801194\pi$
$908$	1.71936	−	0.428746i	0.00189356	−	0.000472187i
$909$	1081.90			1.19021
$910$	−9.11014	−	7.11738i	−0.0100111	−	0.00782129i
$911$		−	589.648i		−	0.647253i	−0.946185	−	0.323627i	$-0.895098\pi$
$911$		−	589.648i		−	0.647253i	0.946185	−	0.323627i	$-0.104902\pi$
$912$	−140.188	+	74.5517i	−0.153715	+	0.0817453i
$913$	1502.56			1.64574
$914$	−619.390	+	792.811i	−0.677670	+	0.867408i
$915$			19.4872i			0.0212975i
$916$	−174.077	−	698.084i	−0.190041	−	0.762101i
$917$	127.219			0.138734
$918$	−172.430	−	134.712i	−0.187832	−	0.146746i
$919$		−	392.215i		−	0.426785i	−0.976967	−	0.213393i	$-0.931549\pi$
$919$		−	392.215i		−	0.426785i	0.976967	−	0.213393i	$-0.0684513\pi$
$920$	5.08599	−	11.4249i	0.00552825	−	0.0124184i
$921$	−57.3544			−0.0622740
$922$	−748.425	+	957.974i	−0.811741	+	1.03902i
$923$		−	286.077i		−	0.309942i
$924$	138.723	−	34.5926i	0.150134	−	0.0374379i
$925$	1054.93			1.14047
$926$	−473.227	−	369.712i	−0.511044	−	0.399257i
$927$		−	1473.70i		−	1.58975i
$928$	88.2098	−	500.511i	0.0950536	−	0.539344i
$929$	−1419.41			−1.52789			−0.763945	−	0.645281i	$-0.776740\pi$
$929$	−1419.41			−1.52789			−0.763945	+	0.645281i	$0.776740\pi$
$930$	−32.6070	+	41.7365i	−0.0350613	+	0.0448780i
$931$			393.525i			0.422691i
$932$	256.894	+	1030.20i	0.275637	+	1.10536i
$933$	482.754			0.517421
$934$	1238.52	+	967.602i	1.32604	+	1.03598i
$935$			37.3607i			0.0399580i
$936$	212.157	+	94.4453i	0.226663	+	0.100903i
$937$	−538.568			−0.574779			−0.287390	−	0.957814i	$-0.592787\pi$
$937$	−538.568			−0.574779			−0.287390	+	0.957814i	$0.592787\pi$
$938$	−203.040	+	259.888i	−0.216460	+	0.277066i
$939$		−	484.742i		−	0.516232i
$940$	79.3041	−	19.7756i	0.0843661	−	0.0210379i
$941$	−998.574			−1.06118			−0.530592	−	0.847627i	$-0.678030\pi$
$941$	−998.574			−1.06118			−0.530592	+	0.847627i	$0.678030\pi$
$942$	64.8492	+	50.6640i	0.0688421	+	0.0537835i
$943$			114.223i			0.121127i
$944$	−773.446	−	1454.40i	−0.819329	−	1.54068i
$945$	26.6286			0.0281784
$946$	976.986	−	1250.53i	1.03275	−	1.32191i
$947$		−	576.370i		−	0.608627i	−0.952572	−	0.304314i	$-0.901573\pi$
$947$		−	576.370i		−	0.608627i	0.952572	−	0.304314i	$-0.0984271\pi$
$948$	71.4638	+	286.584i	0.0753838	+	0.302304i
$949$	−343.290			−0.361739
$950$	−397.414	−	310.483i	−0.418331	−	0.326824i
$951$			29.2572i			0.0307647i
$952$	69.0162	−	155.034i	0.0724960	−	0.162851i
$953$	−808.634			−0.848514			−0.424257	−	0.905542i	$-0.639465\pi$
$953$	−808.634			−0.848514			−0.424257	+	0.905542i	$0.639465\pi$
$954$	−311.126	+	398.237i	−0.326128	+	0.417439i
$955$		−	125.176i		−	0.131074i
$956$	728.324	−	181.618i	0.761846	−	0.189977i
$957$	−176.270			−0.184191
$958$	122.555	+	95.7473i	0.127928	+	0.0999450i
$959$			471.592i			0.491754i
$960$	23.0619	−	20.7693i	0.0240228	−	0.0216346i
$961$	−2021.19			−2.10322
$962$	189.211	−	242.187i	0.196685	−	0.251754i
$963$		−	537.085i		−	0.557720i
$964$	52.6255	+	211.039i	0.0545908	+	0.218920i
$965$	−91.9638			−0.0952993
$966$	15.5255	+	12.1294i	0.0160720	+	0.0125564i
$967$		−	1564.46i		−	1.61785i	−0.587911	−	0.808926i	$-0.700049\pi$
$967$		−	1564.46i		−	1.61785i	0.587911	−	0.808926i	$-0.299951\pi$
$968$	64.4274	+	28.6810i	0.0665573	+	0.0296291i
$969$	65.3664			0.0674576
$970$	−21.5864	+	27.6303i	−0.0222540	+	0.0284848i
$971$		−	1146.05i		−	1.18028i	−0.807301	−	0.590139i	$-0.799073\pi$
$971$		−	1146.05i		−	1.18028i	0.807301	−	0.590139i	$-0.200927\pi$
$972$	−792.962	+	197.736i	−0.815804	+	0.203432i
$973$	169.251			0.173948
$974$	272.735	+	213.076i	0.280015	+	0.218764i
$975$		−	86.9352i		−	0.0891643i
$976$	567.687	−	301.894i	0.581646	−	0.309317i
$977$	−773.399			−0.791606			−0.395803	−	0.918335i	$-0.629534\pi$
$977$	−773.399			−0.791606			−0.395803	+	0.918335i	$0.629534\pi$
$978$	−22.9544	+	29.3813i	−0.0234708	+	0.0300423i
$979$			890.376i			0.909475i
$980$	−18.6112	−	74.6348i	−0.0189911	−	0.0761580i
$981$	−1466.09			−1.49448
$982$	−728.943	−	569.493i	−0.742304	−	0.579931i
$983$		−	979.875i		−	0.996821i	−0.866941	−	0.498411i	$-0.833917\pi$
$983$		−	979.875i		−	0.996821i	0.866941	−	0.498411i	$-0.166083\pi$
$984$	−115.283	+	258.965i	−0.117157	+	0.263176i
$985$	127.151			0.129087
$986$	−128.810	+	164.875i	−0.130639	+	0.167216i
$987$			128.763i			0.130459i
$988$	−142.559	+	35.5491i	−0.144290	+	0.0359808i
$989$	218.683			0.221115
$990$	71.9708	+	56.2278i	0.0726978	+	0.0567957i
$991$		−	385.475i		−	0.388976i	−0.980905	−	0.194488i	$-0.937696\pi$
$991$		−	385.475i		−	0.388976i	0.980905	−	0.194488i	$-0.0623045\pi$
$992$	1720.98	+	303.304i	1.73486	+	0.305750i
$993$	224.920			0.226505
$994$	−314.622	+	402.711i	−0.316521	+	0.405142i
$995$			137.427i			0.138118i
$996$	124.329	+	498.585i	0.124829	+	0.500587i
$997$	693.031			0.695117			0.347558	−	0.937658i	$-0.387011\pi$
$997$	693.031			0.695117			0.347558	+	0.937658i	$0.387011\pi$
$998$	−583.287	−	455.698i	−0.584456	−	0.456611i
$999$			707.905i			0.708614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	52.3.c.a.27.9	✓	12
3.2	odd	2		468.3.f.a.235.4		12
4.3	odd	2	inner	52.3.c.a.27.10	yes	12
8.3	odd	2		832.3.d.d.703.5		12
8.5	even	2		832.3.d.d.703.8		12
12.11	even	2		468.3.f.a.235.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.3.c.a.27.9	✓	12	1.1	even	1	trivial
52.3.c.a.27.10	yes	12	4.3	odd	2	inner
468.3.f.a.235.3		12	12.11	even	2
468.3.f.a.235.4		12	3.2	odd	2
832.3.d.d.703.5		12	8.3	odd	2
832.3.d.d.703.8		12	8.5	even	2

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:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	52.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23130 - 1.57604i) q^{2} -0.974116i q^{3} +(-0.967819 - 3.88115i) q^{4} +0.497818 q^{5} +(-1.53525 - 1.19943i) q^{6} +3.22044i q^{7} +(-7.30853 - 3.25352i) q^{8} +8.05110 q^{9} +O(q^{10})\)	\(q+(1.23130 - 1.57604i) q^{2} -0.974116i q^{3} +(-0.967819 - 3.88115i) q^{4} +0.497818 q^{5} +(-1.53525 - 1.19943i) q^{6} +3.22044i q^{7} +(-7.30853 - 3.25352i) q^{8} +8.05110 q^{9} +(0.612961 - 0.784582i) q^{10} +11.3937i q^{11} +(-3.78069 + 0.942769i) q^{12} -3.60555 q^{13} +(5.07555 + 3.96532i) q^{14} -0.484932i q^{15} +(-14.1267 + 7.51251i) q^{16} +6.58692 q^{17} +(9.91329 - 12.6889i) q^{18} +10.1874i q^{19} +(-0.481798 - 1.93210i) q^{20} +3.13708 q^{21} +(17.9569 + 14.0290i) q^{22} +3.14016i q^{23} +(-3.16931 + 7.11936i) q^{24} -24.7522 q^{25} +(-4.43950 + 5.68250i) q^{26} -16.6097i q^{27} +(12.4990 - 3.11681i) q^{28} -15.8820 q^{29} +(-0.764274 - 0.597095i) q^{30} -54.6094i q^{31} +(-5.55406 + 31.5143i) q^{32} +11.0987 q^{33} +(8.11044 - 10.3813i) q^{34} +1.60319i q^{35} +(-7.79201 - 31.2475i) q^{36} -42.6198 q^{37} +(16.0557 + 12.5437i) q^{38} +3.51223i q^{39} +(-3.63831 - 1.61966i) q^{40} +36.3748 q^{41} +(3.86268 - 4.94418i) q^{42} -69.6406i q^{43} +(44.2205 - 11.0270i) q^{44} +4.00798 q^{45} +(4.94903 + 3.86647i) q^{46} +41.0455i q^{47} +(7.31805 + 13.7610i) q^{48} +38.6288 q^{49} +(-30.4773 + 39.0105i) q^{50} -6.41642i q^{51} +(3.48952 + 13.9937i) q^{52} -31.3848 q^{53} +(-26.1777 - 20.4515i) q^{54} +5.67196i q^{55} +(10.4778 - 23.5367i) q^{56} +9.92368 q^{57} +(-19.5555 + 25.0307i) q^{58} +102.954i q^{59} +(-1.88209 + 0.469327i) q^{60} -40.1855 q^{61} +(-86.0668 - 67.2404i) q^{62} +25.9281i q^{63} +(42.8292 + 47.5569i) q^{64} -1.79491 q^{65} +(13.6658 - 17.4921i) q^{66} +51.2039i q^{67} +(-6.37495 - 25.5648i) q^{68} +3.05888 q^{69} +(2.52670 + 1.97400i) q^{70} +79.3434i q^{71} +(-58.8417 - 26.1944i) q^{72} +95.2115 q^{73} +(-52.4777 + 67.1707i) q^{74} +24.1115i q^{75} +(39.5387 - 9.85953i) q^{76} -36.6926 q^{77} +(5.53542 + 4.32459i) q^{78} -75.8021i q^{79} +(-7.03249 + 3.73986i) q^{80} +56.2801 q^{81} +(44.7881 - 57.3282i) q^{82} -131.877i q^{83} +(-3.03613 - 12.1755i) q^{84} +3.27908 q^{85} +(-109.757 - 85.7482i) q^{86} +15.4709i q^{87} +(37.0695 - 83.2709i) q^{88} +78.1466 q^{89} +(4.93501 - 6.31674i) q^{90} -11.6115i q^{91} +(12.1874 - 3.03911i) q^{92} -53.1959 q^{93} +(64.6894 + 50.5391i) q^{94} +5.07145i q^{95} +(30.6986 + 5.41030i) q^{96} -35.2166 q^{97} +(47.5634 - 60.8806i) q^{98} +91.7314i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 2 q^{4} + 12 q^{6} + 16 q^{8} - 28 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 2 * q^4 + 12 * q^6 + 16 * q^8 - 28 * q^9	\( 12 q - 2 q^{2} - 2 q^{4} + 12 q^{6} + 16 q^{8} - 28 q^{9} - 6 q^{10} - 2 q^{12} + 14 q^{14} + 2 q^{16} - 24 q^{17} - 34 q^{18} - 84 q^{20} - 16 q^{21} - 40 q^{22} + 36 q^{24} + 76 q^{25} + 16 q^{29} + 90 q^{30} + 8 q^{32} + 32 q^{33} - 52 q^{34} + 152 q^{36} + 96 q^{37} - 44 q^{38} - 118 q^{40} - 120 q^{41} + 178 q^{42} + 44 q^{44} - 128 q^{45} + 212 q^{46} + 30 q^{48} - 4 q^{49} - 230 q^{50} + 52 q^{52} - 24 q^{53} - 148 q^{54} - 78 q^{56} + 144 q^{57} - 8 q^{58} + 72 q^{60} - 40 q^{61} - 184 q^{62} - 134 q^{64} + 288 q^{66} - 350 q^{68} + 64 q^{69} - 292 q^{70} - 432 q^{72} - 88 q^{73} + 10 q^{74} + 384 q^{76} + 136 q^{77} - 130 q^{78} + 420 q^{80} - 164 q^{81} + 124 q^{82} + 52 q^{84} - 208 q^{85} + 156 q^{86} + 456 q^{88} - 168 q^{89} + 72 q^{90} - 428 q^{92} + 432 q^{93} + 614 q^{94} + 516 q^{96} + 200 q^{97} + 718 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 - 2 * q^4 + 12 * q^6 + 16 * q^8 - 28 * q^9 - 6 * q^10 - 2 * q^12 + 14 * q^14 + 2 * q^16 - 24 * q^17 - 34 * q^18 - 84 * q^20 - 16 * q^21 - 40 * q^22 + 36 * q^24 + 76 * q^25 + 16 * q^29 + 90 * q^30 + 8 * q^32 + 32 * q^33 - 52 * q^34 + 152 * q^36 + 96 * q^37 - 44 * q^38 - 118 * q^40 - 120 * q^41 + 178 * q^42 + 44 * q^44 - 128 * q^45 + 212 * q^46 + 30 * q^48 - 4 * q^49 - 230 * q^50 + 52 * q^52 - 24 * q^53 - 148 * q^54 - 78 * q^56 + 144 * q^57 - 8 * q^58 + 72 * q^60 - 40 * q^61 - 184 * q^62 - 134 * q^64 + 288 * q^66 - 350 * q^68 + 64 * q^69 - 292 * q^70 - 432 * q^72 - 88 * q^73 + 10 * q^74 + 384 * q^76 + 136 * q^77 - 130 * q^78 + 420 * q^80 - 164 * q^81 + 124 * q^82 + 52 * q^84 - 208 * q^85 + 156 * q^86 + 456 * q^88 - 168 * q^89 + 72 * q^90 - 428 * q^92 + 432 * q^93 + 614 * q^94 + 516 * q^96 + 200 * q^97 + 718 * q^98

Introduction

L-functions

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