LMFDB - Embedded newform 52.3.c.a.27.10

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

$q$-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	$0.0519082\pi$
$3$			0.974116i			0.324705i	−0.986733	+	0.162353i	$0.948092\pi$
$4$	−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	$-0.926117\pi$
$7$		−	3.22044i		−	0.460063i	0.973183	−	0.230032i	$-0.0738829\pi$
$8$	−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	$-0.826716\pi$
$11$		−	11.3937i		−	1.03579i	0.855445	−	0.517893i	$-0.173284\pi$
$12$	−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	$-0.913608\pi$
$19$		−	10.1874i		−	0.536177i	0.963394	−	0.268089i	$-0.0863920\pi$
$20$	−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	$-0.978254\pi$
$23$		−	3.14016i		−	0.136529i	0.997667	−	0.0682644i	$-0.0217461\pi$
$24$	−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	$0.342993\pi$
$31$			54.6094i			1.76159i	−0.473494	+	0.880797i	$0.657007\pi$
$32$	−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	$0.300411\pi$
$43$			69.6406i			1.61955i	−0.586741	+	0.809775i	$0.699589\pi$
$44$	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	$-0.856163\pi$
$47$		−	41.0455i		−	0.873308i	0.899630	−	0.436654i	$-0.143837\pi$
$48$	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	$-0.662500\pi$
$59$		−	102.954i		−	1.74499i	0.488622	−	0.872496i	$-0.337500\pi$
$60$	−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	$-0.875195\pi$
$67$		−	51.2039i		−	0.764237i	0.924113	−	0.382119i	$-0.124805\pi$
$68$	−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	$-0.811279\pi$
$71$		−	79.3434i		−	1.11751i	0.829332	−	0.558756i	$-0.188721\pi$
$72$	−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	$0.159276\pi$
$79$			75.8021i			0.959520i	−0.877400	+	0.479760i	$0.840724\pi$
$80$	−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	$0.292235\pi$
$83$			131.877i			1.58888i	−0.607345	+	0.794438i	$0.707765\pi$
$84$	−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	$0.348293\pi$
$103$			183.043i			1.77712i	−0.458761	+	0.888560i	$0.651707\pi$
$104$	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	$0.100907\pi$
$107$			66.7095i			0.623453i	−0.950172	+	0.311727i	$0.899093\pi$
$108$	−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	$-0.824737\pi$
$127$		−	132.893i		−	1.04640i	0.852208	−	0.523202i	$-0.175263\pi$
$128$	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	$0.0481776\pi$
$131$			39.5036i			0.301554i	−0.988568	+	0.150777i	$0.951822\pi$
$132$	−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	$0.0605401\pi$
$139$			52.5553i			0.378096i	−0.981968	+	0.189048i	$0.939460\pi$
$140$	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	$-0.867347\pi$
$151$		−	122.245i		−	0.809569i	0.914412	−	0.404784i	$-0.132653\pi$
$152$	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	$0.0186971\pi$
$163$			19.1378i			0.117410i	−0.998275	+	0.0587051i	$0.981303\pi$
$164$	−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	$0.148133\pi$
$167$			149.885i			0.897513i	−0.893654	+	0.448757i	$0.851867\pi$
$168$	−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	$-0.711895\pi$
$179$		−	281.564i		−	1.57298i	0.617601	−	0.786492i	$-0.288105\pi$
$180$	−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	$0.228701\pi$
$191$			251.450i			1.31649i	−0.752804	+	0.658245i	$0.771299\pi$
$192$	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	$-0.756016\pi$
$199$		−	276.060i		−	1.38724i	0.720343	−	0.693618i	$-0.243984\pi$
$200$	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	$-0.826314\pi$
$211$		−	219.008i		−	1.03795i	0.854789	−	0.518976i	$-0.173686\pi$
$212$	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	$0.0621109\pi$
$223$			86.4756i			0.387783i	−0.981023	+	0.193891i	$0.937889\pi$
$224$	−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	$-0.999689\pi$
$227$		−	0.443002i		−	0.00195155i	1.00000		0.000975775i	$-0.000310599\pi$
$228$	−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	$-0.871580\pi$
$239$		−	187.657i		−	0.785175i	0.919715	−	0.392588i	$-0.128420\pi$
$240$	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	$-0.930175\pi$
$251$		−	109.239i		−	0.435214i	0.976036	−	0.217607i	$-0.0698251\pi$
$252$	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	$0.158776\pi$
$263$			251.629i			0.956763i	−0.878152	+	0.478382i	$0.841224\pi$
$264$	−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	$-0.912183\pi$
$271$		−	147.640i		−	0.544796i	0.962185	−	0.272398i	$-0.0878168\pi$
$272$	−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	$0.134908\pi$
$283$			232.768i			0.822503i	−0.911522	+	0.411252i	$0.865092\pi$
$284$	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	$0.0305707\pi$
$307$			58.8784i			0.191786i	−0.995392	+	0.0958931i	$0.969429\pi$
$308$	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	$-0.706548\pi$
$311$		−	495.582i		−	1.59351i	0.604302	−	0.796755i	$-0.293452\pi$
$312$	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	$-0.886594\pi$
$331$		−	230.896i		−	0.697571i	0.937203	−	0.348786i	$-0.113406\pi$
$332$	−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	$-0.640868\pi$
$347$		−	627.142i		−	1.80733i	0.428245	−	0.903663i	$-0.359132\pi$
$348$	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	$0.185425\pi$
$359$			395.000i			1.10028i	−0.835073	+	0.550139i	$0.814575\pi$
$360$	−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	$-0.858490\pi$
$367$		−	315.669i		−	0.860133i	0.902797	−	0.430066i	$-0.141510\pi$
$368$	−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	$-0.901068\pi$
$379$		−	231.814i		−	0.611648i	0.952088	−	0.305824i	$-0.0989319\pi$
$380$	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	$-0.855241\pi$
$383$		−	336.472i		−	0.878516i	0.898361	−	0.439258i	$-0.144759\pi$
$384$	−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	$0.271536\pi$
$419$			631.259i			1.50659i	−0.657685	+	0.753293i	$0.728464\pi$
$420$	−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	$0.136970\pi$
$431$			359.581i			0.834295i	−0.908839	+	0.417148i	$0.863030\pi$
$432$	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	$0.320810\pi$
$439$			742.515i			1.69138i	−0.533675	+	0.845689i	$0.679190\pi$
$440$	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	$0.0528938\pi$
$443$			146.551i			0.330814i	−0.986225	+	0.165407i	$0.947106\pi$
$444$	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	$0.105114\pi$
$463$			300.263i			0.648515i	−0.945969	+	0.324258i	$0.894886\pi$
$464$	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	$-0.681749\pi$
$467$		−	785.840i		−	1.68274i	0.540459	−	0.841371i	$-0.318251\pi$
$468$	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	$-0.974134\pi$
$479$		−	77.7614i		−	0.162341i	0.996700	−	0.0811706i	$-0.0258659\pi$
$480$	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	$-0.943144\pi$
$487$		−	173.050i		−	0.355339i	0.984090	−	0.177670i	$-0.0568558\pi$
$488$	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	$0.156104\pi$
$491$			462.515i			0.941985i	−0.882137	+	0.470993i	$0.843896\pi$
$492$	−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	$0.120929\pi$
$499$			370.096i			0.741675i	−0.928698	+	0.370838i	$0.879071\pi$
$500$	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	$-0.814675\pi$
$503$		−	553.175i		−	1.09975i	0.835246	−	0.549876i	$-0.185325\pi$
$504$	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	$-0.808391\pi$
$523$		−	592.304i		−	1.13251i	0.824229	−	0.566256i	$-0.191609\pi$
$524$	−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	$-0.986787\pi$
$547$		−	45.3981i		−	0.0829947i	0.999139	−	0.0414973i	$-0.0132128\pi$
$548$	−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	$0.0412063\pi$
$563$			145.358i			0.258184i	−0.991633	+	0.129092i	$0.958794\pi$
$564$	−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	$0.158128\pi$
$571$			544.266i			0.953181i	−0.879125	+	0.476590i	$0.841872\pi$
$572$	−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	$0.176128\pi$
$587$			616.956i			1.05103i	−0.850784	+	0.525516i	$0.823872\pi$
$588$	−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	$-0.847772\pi$
$599$		−	551.338i		−	0.920431i	0.887807	−	0.460216i	$-0.152228\pi$
$600$	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	$-0.973818\pi$
$607$		−	99.7418i		−	0.164319i	0.996619	−	0.0821597i	$-0.0261817\pi$
$608$	−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	$0.0285302\pi$
$619$			110.814i			0.179020i	−0.995986	+	0.0895102i	$0.971470\pi$
$620$	−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	$0.159277\pi$
$631$			605.458i			0.959522i	−0.877399	+	0.479761i	$0.840723\pi$
$632$	−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	$0.0559731\pi$
$643$			224.973i			0.349880i	−0.984579	+	0.174940i	$0.944027\pi$
$644$	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	$-0.759531\pi$
$647$		−	887.194i		−	1.37124i	0.727958	−	0.685621i	$-0.240469\pi$
$648$	−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	$0.235059\pi$
$659$			887.211i			1.34630i	−0.739507	+	0.673149i	$0.764941\pi$
$660$	−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	$-0.812549\pi$
$683$		−	758.735i		−	1.11089i	0.831555	−	0.555443i	$-0.187451\pi$
$684$	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	$-0.970859\pi$
$691$		−	126.346i		−	0.182845i	0.995812	−	0.0914227i	$-0.0291415\pi$
$692$	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	$-0.941121\pi$
$719$		−	264.478i		−	0.367841i	0.982941	−	0.183921i	$-0.0588789\pi$
$720$	−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	$0.237258\pi$
$727$			986.166i			1.35649i	−0.734838	+	0.678243i	$0.762742\pi$
$728$	−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	$0.155802\pi$
$739$			694.891i			0.940312i	−0.882583	+	0.470156i	$0.844198\pi$
$740$	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	$0.0590210\pi$
$743$			273.958i			0.368719i	−0.982859	+	0.184359i	$0.940979\pi$
$744$	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	$-0.955768\pi$
$751$		−	208.045i		−	0.277024i	0.990361	−	0.138512i	$-0.0442319\pi$
$752$	−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	$0.168422\pi$
$787$			794.505i			1.00954i	−0.863255	+	0.504768i	$0.831578\pi$
$788$	−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	$-0.988207\pi$
$811$		−	60.0777i		−	0.0740786i	0.999314	−	0.0370393i	$-0.0117927\pi$
$812$	−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	$-0.697362\pi$
$823$		−	1339.61i		−	1.62772i	0.581061	−	0.813860i	$-0.302638\pi$
$824$	−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	$-0.853146\pi$
$827$		−	736.299i		−	0.890325i	0.895450	−	0.445162i	$-0.146854\pi$
$828$	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	$-0.780729\pi$
$839$		−	1066.63i		−	1.27132i	0.771971	−	0.635658i	$-0.219271\pi$
$840$	−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	$-0.898688\pi$
$859$		−	537.624i		−	0.625872i	0.949774	−	0.312936i	$-0.101312\pi$
$860$	−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	$-0.876879\pi$
$863$		−	651.088i		−	0.754448i	0.926122	−	0.377224i	$-0.123121\pi$
$864$	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	$0.290088\pi$
$883$			1395.71i			1.58065i	−0.612689	+	0.790324i	$0.709912\pi$
$884$	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	$-0.934048\pi$
$887$		−	364.941i		−	0.411433i	0.978612	−	0.205716i	$-0.0659524\pi$
$888$	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	$-0.801194\pi$
$907$		−	1060.73i		−	1.16949i	0.811216	−	0.584746i	$-0.198806\pi$
$908$	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	$0.104902\pi$
$911$			589.648i			0.647253i	−0.946185	+	0.323627i	$0.895098\pi$
$912$	−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	$0.0684513\pi$
$919$			392.215i			0.426785i	−0.976967	+	0.213393i	$0.931549\pi$
$920$	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	$0.0984271\pi$
$947$			576.370i			0.608627i	−0.952572	+	0.304314i	$0.901573\pi$
$948$	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	$0.299951\pi$
$967$			1564.46i			1.61785i	−0.587911	+	0.808926i	$0.700049\pi$
$968$	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	$0.200927\pi$
$971$			1146.05i			1.18028i	−0.807301	+	0.590139i	$0.799073\pi$
$972$	−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	$0.166083\pi$
$983$			979.875i			0.996821i	−0.866941	+	0.498411i	$0.833917\pi$
$984$	−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	$0.0623045\pi$
$991$			385.475i			0.388976i	−0.980905	+	0.194488i	$0.937696\pi$
$992$	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.27.10	yes	12
3.2	odd	2		468.3.f.a.235.3		12
4.3	odd	2	inner	52.3.c.a.27.9	✓	12
8.3	odd	2		832.3.d.d.703.8		12
8.5	even	2		832.3.d.d.703.5		12
12.11	even	2		468.3.f.a.235.4		12

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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more