LMFDB - Embedded newform 280.2.h.b.251.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(251,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("280.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.h (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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 2x^{12} + 6x^{11} - 12x^{9} + 8x^{8} - 24x^{7} + 48x^{5} - 32x^{4} - 128x + 256 $ x^16 - x^15 - 2x^12 + 6x^11 - 12x^9 + 8x^8 - 24x^7 + 48x^5 - 32x^4 - 128x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.14
Root			$1.14218 - 0.833926i$ of defining polynomial
Character	$\chi$	$=$	280.251
Dual form			280.2.h.b.251.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14218 + 0.833926i) q^{2} +0.586834i q^{3} +(0.609136 + 1.90498i) q^{4} +1.00000 q^{5} +(-0.489376 + 0.670268i) q^{6} +(-2.52442 + 0.792014i) q^{7} +(-0.892871 + 2.68380i) q^{8} +2.65563 q^{9} +O(q^{10})$	\(q+(1.14218 + 0.833926i) q^{2} +0.586834i q^{3} +(0.609136 + 1.90498i) q^{4} +1.00000 q^{5} +(-0.489376 + 0.670268i) q^{6} +(-2.52442 + 0.792014i) q^{7} +(-0.892871 + 2.68380i) q^{8} +2.65563 q^{9} +(1.14218 + 0.833926i) q^{10} -0.580189 q^{11} +(-1.11791 + 0.357462i) q^{12} +1.14766 q^{13} +(-3.54382 - 1.20056i) q^{14} +0.586834i q^{15} +(-3.25791 + 2.32079i) q^{16} +1.82880i q^{17} +(3.03319 + 2.21459i) q^{18} -4.72462i q^{19} +(0.609136 + 1.90498i) q^{20} +(-0.464781 - 1.48142i) q^{21} +(-0.662679 - 0.483835i) q^{22} -2.79961i q^{23} +(-1.57494 - 0.523967i) q^{24} +1.00000 q^{25} +(1.31083 + 0.957061i) q^{26} +3.31891i q^{27} +(-3.04649 - 4.32653i) q^{28} -7.40518i q^{29} +(-0.489376 + 0.670268i) q^{30} +4.73007 q^{31} +(-5.65647 - 0.0661016i) q^{32} -0.340475i q^{33} +(-1.52509 + 2.08882i) q^{34} +(-2.52442 + 0.792014i) q^{35} +(1.61764 + 5.05892i) q^{36} -4.35175i q^{37} +(3.93998 - 5.39635i) q^{38} +0.673485i q^{39} +(-0.892871 + 2.68380i) q^{40} +8.46264i q^{41} +(0.704530 - 2.07963i) q^{42} -4.32314 q^{43} +(-0.353414 - 1.10525i) q^{44} +2.65563 q^{45} +(2.33466 - 3.19765i) q^{46} +3.56830 q^{47} +(-1.36192 - 1.91185i) q^{48} +(5.74543 - 3.99876i) q^{49} +(1.14218 + 0.833926i) q^{50} -1.07320 q^{51} +(0.699080 + 2.18627i) q^{52} -5.48977i q^{53} +(-2.76773 + 3.79079i) q^{54} -0.580189 q^{55} +(0.128378 - 7.48221i) q^{56} +2.77257 q^{57} +(6.17537 - 8.45803i) q^{58} -13.2957i q^{59} +(-1.11791 + 0.357462i) q^{60} +0.275184 q^{61} +(5.40258 + 3.94453i) q^{62} +(-6.70392 + 2.10329i) q^{63} +(-6.40556 - 4.79257i) q^{64} +1.14766 q^{65} +(0.283931 - 0.388882i) q^{66} -7.71818 q^{67} +(-3.48384 + 1.11399i) q^{68} +1.64291 q^{69} +(-3.54382 - 1.20056i) q^{70} +1.13454i q^{71} +(-2.37113 + 7.12717i) q^{72} -1.78121i q^{73} +(3.62904 - 4.97047i) q^{74} +0.586834i q^{75} +(9.00031 - 2.87794i) q^{76} +(1.46464 - 0.459518i) q^{77} +(-0.561636 + 0.769239i) q^{78} +10.0108i q^{79} +(-3.25791 + 2.32079i) q^{80} +6.01923 q^{81} +(-7.05721 + 9.66583i) q^{82} +15.6230i q^{83} +(2.53896 - 1.78778i) q^{84} +1.82880i q^{85} +(-4.93780 - 3.60518i) q^{86} +4.34561 q^{87} +(0.518034 - 1.55711i) q^{88} -15.3393i q^{89} +(3.03319 + 2.21459i) q^{90} +(-2.89717 + 0.908961i) q^{91} +(5.33320 - 1.70534i) q^{92} +2.77577i q^{93} +(4.07563 + 2.97569i) q^{94} -4.72462i q^{95} +(0.0387907 - 3.31941i) q^{96} +14.9759i q^{97} +(9.89696 + 0.223972i) q^{98} -1.54077 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9	$ 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9} + q^{10} - 4 q^{11} + 14 q^{12} - q^{14} + 9 q^{16} - 15 q^{18} + q^{20} - 4 q^{21} + 6 q^{22} + 22 q^{24} + 16 q^{25} - 20 q^{26} + q^{28} - 16 q^{31} - 19 q^{32} - 14 q^{34} + 15 q^{36} - 30 q^{38} + q^{40} + 44 q^{42} - 4 q^{43} - 20 q^{44} - 16 q^{45} + 6 q^{46} - 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} - 38 q^{52} + 26 q^{54} - 4 q^{55} + 33 q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} - 8 q^{61} + 28 q^{62} + 28 q^{63} - 23 q^{64} + 46 q^{66} + 20 q^{67} + 12 q^{68} - 40 q^{69} - q^{70} - 13 q^{72} - 28 q^{74} + 34 q^{76} - 4 q^{77} - 6 q^{78} + 9 q^{80} + 24 q^{81} - 16 q^{82} - 42 q^{84} - 24 q^{86} + 72 q^{87} - 44 q^{88} - 15 q^{90} - 32 q^{91} - 30 q^{92} - 58 q^{94} - 30 q^{96} + 5 q^{98} + 20 q^{99}+O(q^{100}) $ 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9 + q^10 - 4 * q^11 + 14 * q^12 - q^14 + 9 * q^16 - 15 * q^18 + q^20 - 4 * q^21 + 6 * q^22 + 22 * q^24 + 16 * q^25 - 20 * q^26 + q^28 - 16 * q^31 - 19 * q^32 - 14 * q^34 + 15 * q^36 - 30 * q^38 + q^40 + 44 * q^42 - 4 * q^43 - 20 * q^44 - 16 * q^45 + 6 * q^46 - 34 * q^48 - 8 * q^49 + q^50 - 40 * q^51 - 38 * q^52 + 26 * q^54 - 4 * q^55 + 33 * q^56 - 16 * q^57 + 18 * q^58 + 14 * q^60 - 8 * q^61 + 28 * q^62 + 28 * q^63 - 23 * q^64 + 46 * q^66 + 20 * q^67 + 12 * q^68 - 40 * q^69 - q^70 - 13 * q^72 - 28 * q^74 + 34 * q^76 - 4 * q^77 - 6 * q^78 + 9 * q^80 + 24 * q^81 - 16 * q^82 - 42 * q^84 - 24 * q^86 + 72 * q^87 - 44 * q^88 - 15 * q^90 - 32 * q^91 - 30 * q^92 - 58 * q^94 - 30 * q^96 + 5 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	1.14218	+	0.833926i	0.807641	+	0.589674i
$2$	1.14218	+	0.833926i	0.807641	+	0.589674i
$3$			0.586834i			0.338809i	0.985547	+	0.169404i	$0.0541844\pi$
$3$			0.586834i			0.338809i	−0.985547	+	0.169404i	$0.945816\pi$
$4$	0.609136	+	1.90498i	0.304568	+	0.952491i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.489376	+	0.670268i	−0.199787	+	0.273636i
$7$	−2.52442	+	0.792014i	−0.954142	+	0.299353i
$7$	−2.52442	+	0.792014i	−0.954142	+	0.299353i
$8$	−0.892871	+	2.68380i	−0.315677	+	0.948867i
$9$	2.65563			0.885209
$10$	1.14218	+	0.833926i	0.361188	+	0.263710i
$11$	−0.580189			−0.174934			−0.0874668	−	0.996167i	$-0.527877\pi$
$11$	−0.580189			−0.174934			−0.0874668	+	0.996167i	$0.527877\pi$
$12$	−1.11791	+	0.357462i	−0.322712	+	0.103190i
$13$	1.14766			0.318303			0.159152	−	0.987254i	$-0.449124\pi$
$13$	1.14766			0.318303			0.159152	+	0.987254i	$0.449124\pi$
$14$	−3.54382	−	1.20056i	−0.947125	−	0.320864i
$15$			0.586834i			0.151520i
$16$	−3.25791	+	2.32079i	−0.814476	+	0.580197i
$17$			1.82880i			0.443550i	0.975098	+	0.221775i	$0.0711851\pi$
$17$			1.82880i			0.443550i	−0.975098	+	0.221775i	$0.928815\pi$
$18$	3.03319	+	2.21459i	0.714931	+	0.521985i
$19$		−	4.72462i		−	1.08390i	−0.840410	−	0.541951i	$-0.817686\pi$
$19$		−	4.72462i		−	1.08390i	0.840410	−	0.541951i	$-0.182314\pi$
$20$	0.609136	+	1.90498i	0.136207	+	0.425967i
$21$	−0.464781	−	1.48142i	−0.101423	−	0.323272i
$22$	−0.662679	−	0.483835i	−0.141284	−	0.103154i
$23$		−	2.79961i		−	0.583759i	−0.956455	−	0.291879i	$-0.905719\pi$
$23$		−	2.79961i		−	0.583759i	0.956455	−	0.291879i	$-0.0942806\pi$
$24$	−1.57494	−	0.523967i	−0.321484	−	0.106954i
$25$	1.00000			0.200000
$26$	1.31083	+	0.957061i	0.257075	+	0.187695i
$27$			3.31891i			0.638725i
$28$	−3.04649	−	4.32653i	−0.575732	−	0.817638i
$29$		−	7.40518i		−	1.37511i	−0.726133	−	0.687554i	$-0.758684\pi$
$29$		−	7.40518i		−	1.37511i	0.726133	−	0.687554i	$-0.241316\pi$
$30$	−0.489376	+	0.670268i	−0.0893474	+	0.122374i
$31$	4.73007			0.849546			0.424773	−	0.905300i	$-0.360354\pi$
$31$	4.73007			0.849546			0.424773	+	0.905300i	$0.360354\pi$
$32$	−5.65647	−	0.0661016i	−0.999932	−	0.0116852i
$33$		−	0.340475i		−	0.0592691i
$34$	−1.52509	+	2.08882i	−0.261550	+	0.358229i
$35$	−2.52442	+	0.792014i	−0.426705	+	0.133875i
$36$	1.61764	+	5.05892i	0.269606	+	0.843153i
$37$		−	4.35175i		−	0.715423i	−0.933832	−	0.357712i	$-0.883557\pi$
$37$		−	4.35175i		−	0.715423i	0.933832	−	0.357712i	$-0.116443\pi$
$38$	3.93998	−	5.39635i	0.639149	−	0.875404i
$39$			0.673485i			0.107844i
$40$	−0.892871	+	2.68380i	−0.141175	+	0.424346i
$41$			8.46264i			1.32164i	0.750544	+	0.660821i	$0.229792\pi$
$41$			8.46264i			1.32164i	−0.750544	+	0.660821i	$0.770208\pi$
$42$	0.704530	−	2.07963i	0.108711	−	0.320894i
$43$	−4.32314			−0.659273			−0.329637	−	0.944108i	$-0.606926\pi$
$43$	−4.32314			−0.659273			−0.329637	+	0.944108i	$0.606926\pi$
$44$	−0.353414	−	1.10525i	−0.0532792	−	0.166623i
$45$	2.65563			0.395877
$46$	2.33466	−	3.19765i	0.344228	−	0.471468i
$47$	3.56830			0.520490			0.260245	−	0.965543i	$-0.416197\pi$
$47$	3.56830			0.520490			0.260245	+	0.965543i	$0.416197\pi$
$48$	−1.36192	−	1.91185i	−0.196576	−	0.275952i
$49$	5.74543	−	3.99876i	0.820775	−	0.571251i
$50$	1.14218	+	0.833926i	0.161528	+	0.117935i
$51$	−1.07320			−0.150279
$52$	0.699080	+	2.18627i	0.0969450	+	0.303181i
$53$		−	5.48977i		−	0.754079i	−0.926197	−	0.377039i	$-0.876942\pi$
$53$		−	5.48977i		−	0.754079i	0.926197	−	0.377039i	$-0.123058\pi$
$54$	−2.76773	+	3.79079i	−0.376640	+	0.515861i
$55$	−0.580189			−0.0782327
$56$	0.128378	−	7.48221i	0.0171552	−	0.999853i
$57$	2.77257			0.367235
$58$	6.17537	−	8.45803i	0.810866	−	1.11059i
$59$		−	13.2957i		−	1.73095i	−0.500948	−	0.865477i	$-0.667015\pi$
$59$		−	13.2957i		−	1.73095i	0.500948	−	0.865477i	$-0.332985\pi$
$60$	−1.11791	+	0.357462i	−0.144321	+	0.0461481i
$61$	0.275184			0.0352337			0.0176168	−	0.999845i	$-0.494392\pi$
$61$	0.275184			0.0352337			0.0176168	+	0.999845i	$0.494392\pi$
$62$	5.40258	+	3.94453i	0.686128	+	0.500955i
$63$	−6.70392	+	2.10329i	−0.844615	+	0.264990i
$64$	−6.40556	−	4.79257i	−0.800695	−	0.599072i
$65$	1.14766			0.142349
$66$	0.283931	−	0.388882i	0.0349494	−	0.0478681i
$67$	−7.71818			−0.942925			−0.471463	−	0.881886i	$-0.656274\pi$
$67$	−7.71818			−0.942925			−0.471463	+	0.881886i	$0.656274\pi$
$68$	−3.48384	+	1.11399i	−0.422477	+	0.135091i
$69$	1.64291			0.197783
$70$	−3.54382	−	1.20056i	−0.423567	−	0.143495i
$71$			1.13454i			0.134645i	0.997731	+	0.0673224i	$0.0214456\pi$
$71$			1.13454i			0.134645i	−0.997731	+	0.0673224i	$0.978554\pi$
$72$	−2.37113	+	7.12717i	−0.279440	+	0.839945i
$73$		−	1.78121i		−	0.208474i	−0.994552	−	0.104237i	$-0.966760\pi$
$73$		−	1.78121i		−	0.208474i	0.994552	−	0.104237i	$-0.0332401\pi$
$74$	3.62904	−	4.97047i	0.421867	−	0.577805i
$75$			0.586834i			0.0677617i
$76$	9.00031	−	2.87794i	1.03241	−	0.330122i
$77$	1.46464	−	0.459518i	0.166912	−	0.0523669i
$78$	−0.561636	+	0.769239i	−0.0635928	+	0.0870991i
$79$			10.0108i			1.12630i	0.826355	+	0.563149i	$0.190410\pi$
$79$			10.0108i			1.12630i	−0.826355	+	0.563149i	$0.809590\pi$
$80$	−3.25791	+	2.32079i	−0.364245	+	0.259472i
$81$	6.01923			0.668803
$82$	−7.05721	+	9.66583i	−0.779338	+	1.06741i
$83$			15.6230i			1.71485i	0.514607	+	0.857426i	$0.327938\pi$
$83$			15.6230i			1.71485i	−0.514607	+	0.857426i	$0.672062\pi$
$84$	2.53896	−	1.78778i	0.277023	−	0.195063i
$85$			1.82880i			0.198362i
$86$	−4.93780	−	3.60518i	−0.532456	−	0.388757i
$87$	4.34561			0.465899
$88$	0.518034	−	1.55711i	0.0552226	−	0.165989i
$89$		−	15.3393i		−	1.62596i	−0.582293	−	0.812979i	$-0.697844\pi$
$89$		−	15.3393i		−	1.62596i	0.582293	−	0.812979i	$-0.302156\pi$
$90$	3.03319	+	2.21459i	0.319727	+	0.233439i
$91$	−2.89717	+	0.908961i	−0.303706	+	0.0952850i
$92$	5.33320	−	1.70534i	0.556025	−	0.177794i
$93$			2.77577i			0.287833i
$94$	4.07563	+	2.97569i	0.420369	+	0.306919i
$95$		−	4.72462i		−	0.484736i
$96$	0.0387907	−	3.31941i	0.00395906	−	0.338786i
$97$			14.9759i			1.52058i	0.649585	+	0.760289i	$0.274943\pi$
$97$			14.9759i			1.52058i	−0.649585	+	0.760289i	$0.725057\pi$
$98$	9.89696	+	0.223972i	0.999744	+	0.0226246i
$99$	−1.54077			−0.154853
$100$	0.609136	+	1.90498i	0.0609136	+	0.190498i
$101$	−12.7803			−1.27169			−0.635845	−	0.771817i	$-0.719348\pi$
$101$	−12.7803			−1.27169			−0.635845	+	0.771817i	$0.719348\pi$
$102$	−1.22579	−	0.894973i	−0.121371	−	0.0886155i
$103$	−15.1439			−1.49217			−0.746085	−	0.665851i	$-0.768069\pi$
$103$	−15.1439			−1.49217			−0.746085	+	0.665851i	$0.768069\pi$
$104$	−1.02471	+	3.08008i	−0.100481	+	0.302027i
$105$	−0.464781	−	1.48142i	−0.0453579	−	0.144572i
$106$	4.57806	−	6.27029i	0.444661	−	0.609025i
$107$	6.70224			0.647930			0.323965	−	0.946069i	$-0.394984\pi$
$107$	6.70224			0.647930			0.323965	+	0.946069i	$0.394984\pi$
$108$	−6.32247	+	2.02167i	−0.608380	+	0.194535i
$109$			11.2152i			1.07422i	0.843511	+	0.537112i	$0.180485\pi$
$109$			11.2152i			1.07422i	−0.843511	+	0.537112i	$0.819515\pi$
$110$	−0.662679	−	0.483835i	−0.0631839	−	0.0461318i
$111$	2.55376			0.242392
$112$	6.38624	−	8.43895i	0.603443	−	0.797406i
$113$	1.41012			0.132653			0.0663265	−	0.997798i	$-0.478872\pi$
$113$	1.41012			0.132653			0.0663265	+	0.997798i	$0.478872\pi$
$114$	3.16676	+	2.31211i	0.296594	+	0.216549i
$115$		−	2.79961i		−	0.261065i
$116$	14.1067	−	4.51077i	1.30978	−	0.418814i
$117$	3.04775			0.281765
$118$	11.0876	−	15.1861i	1.02070	−	1.39799i
$119$	−1.44844	−	4.61668i	−0.132778	−	0.423210i
$120$	−1.57494	−	0.523967i	−0.143772	−	0.0478314i
$121$	−10.6634			−0.969398
$122$	0.314309	+	0.229483i	0.0284562	+	0.0207764i
$123$	−4.96616			−0.447784
$124$	2.88126	+	9.01069i	0.258745	+	0.809184i
$125$	1.00000			0.0894427
$126$	−9.41106	−	3.18824i	−0.838404	−	0.284031i
$127$			15.7103i			1.39406i	0.717041	+	0.697031i	$0.245496\pi$
$127$			15.7103i			1.39406i	−0.717041	+	0.697031i	$0.754504\pi$
$128$	−3.31964	−	10.8157i	−0.293417	−	0.955984i
$129$		−	2.53697i		−	0.223368i
$130$	1.31083	+	0.957061i	0.114967	+	0.0839398i
$131$		−	5.01749i		−	0.438380i	−0.975682	−	0.219190i	$-0.929658\pi$
$131$		−	5.01749i		−	0.438380i	0.975682	−	0.219190i	$-0.0703415\pi$
$132$	0.648598	−	0.207396i	0.0564532	−	0.0180515i
$133$	3.74196	+	11.9269i	0.324469	+	1.03420i
$134$	−8.81552	−	6.43638i	−0.761545	−	0.556019i
$135$			3.31891i			0.285647i
$136$	−4.90815	−	1.63289i	−0.420870	−	0.140019i
$137$	−14.8703			−1.27045			−0.635226	−	0.772326i	$-0.719093\pi$
$137$	−14.8703			−1.27045			−0.635226	+	0.772326i	$0.719093\pi$
$138$	1.87649	+	1.37006i	0.159737	+	0.116627i
$139$		−	0.148572i		−	0.0126017i	−0.999980	−	0.00630086i	$-0.997994\pi$
$139$		−	0.148572i		−	0.0126017i	0.999980	−	0.00630086i	$-0.00200564\pi$
$140$	−3.04649	−	4.32653i	−0.257475	−	0.365659i
$141$			2.09400i			0.176346i
$142$	−0.946120	+	1.29584i	−0.0793966	+	0.108745i
$143$	−0.665859			−0.0556819
$144$	−8.65178	+	6.16314i	−0.720982	+	0.513595i
$145$		−	7.40518i		−	0.614967i
$146$	1.48539	−	2.03445i	0.122932	−	0.168372i
$147$	2.34661	+	3.37161i	0.193545	+	0.278086i
$148$	8.29000	−	2.65081i	0.681434	−	0.217895i
$149$			8.85493i			0.725424i	0.931901	+	0.362712i	$0.118149\pi$
$149$			8.85493i			0.725424i	−0.931901	+	0.362712i	$0.881851\pi$
$150$	−0.489376	+	0.670268i	−0.0399574	+	0.0547272i
$151$			12.3932i			1.00855i	0.863544	+	0.504273i	$0.168239\pi$
$151$			12.3932i			1.00855i	−0.863544	+	0.504273i	$0.831761\pi$
$152$	12.6799	+	4.21847i	1.02848	+	0.342163i
$153$			4.85662i			0.392635i
$154$	2.05609	+	0.696553i	0.165684	+	0.0561298i
$155$	4.73007			0.379928
$156$	−1.28298	+	0.410244i	−0.102720	+	0.0328458i
$157$	−15.6090			−1.24574			−0.622869	−	0.782326i	$-0.714033\pi$
$157$	−15.6090			−1.24574			−0.622869	+	0.782326i	$0.714033\pi$
$158$	−8.34822	+	11.4341i	−0.664149	+	0.909644i
$159$	3.22159			0.255488
$160$	−5.65647	−	0.0661016i	−0.447183	−	0.00522579i
$161$	2.21733	+	7.06740i	0.174750	+	0.556989i
$162$	6.87502	+	5.01959i	0.540153	+	0.394376i
$163$	−5.60110			−0.438712			−0.219356	−	0.975645i	$-0.570396\pi$
$163$	−5.60110			−0.438712			−0.219356	+	0.975645i	$0.570396\pi$
$164$	−16.1212	+	5.15490i	−1.25885	+	0.402530i
$165$		−	0.340475i		−	0.0265059i
$166$	−13.0285	+	17.8443i	−1.01120	+	1.38498i
$167$	9.34952			0.723488			0.361744	−	0.932278i	$-0.382181\pi$
$167$	9.34952			0.723488			0.361744	+	0.932278i	$0.382181\pi$
$168$	4.39082	+	0.0753363i	0.338759	+	0.00581232i
$169$	−11.6829			−0.898683
$170$	−1.52509	+	2.08882i	−0.116969	+	0.160205i
$171$		−	12.5468i		−	0.959479i
$172$	−2.63338	−	8.23551i	−0.200794	−	0.627952i
$173$	23.5706			1.79204			0.896018	−	0.444018i	$-0.146447\pi$
$173$	23.5706			1.79204			0.896018	+	0.444018i	$0.146447\pi$
$174$	4.96346	+	3.62392i	0.376279	+	0.274729i
$175$	−2.52442	+	0.792014i	−0.190828	+	0.0598706i
$176$	1.89020	−	1.34650i	0.142479	−	0.101496i
$177$	7.80238			0.586463
$178$	12.7918	−	17.5202i	0.958786	−	1.31319i
$179$	19.7086			1.47309			0.736546	−	0.676387i	$-0.236455\pi$
$179$	19.7086			1.47309			0.736546	+	0.676387i	$0.236455\pi$
$180$	1.61764	+	5.05892i	0.120572	+	0.377069i
$181$	−21.0102			−1.56168			−0.780839	−	0.624732i	$-0.785208\pi$
$181$	−21.0102			−1.56168			−0.780839	+	0.624732i	$0.785208\pi$
$182$	−4.06709	−	1.37783i	−0.301473	−	0.102132i
$183$			0.161487i			0.0119375i
$184$	7.51359	+	2.49969i	0.553909	+	0.184279i
$185$		−	4.35175i		−	0.319947i
$186$	−2.31478	+	3.17042i	−0.169728	+	0.232466i
$187$		−	1.06105i		−	0.0775919i
$188$	2.17358	+	6.79754i	0.158525	+	0.495761i
$189$	−2.62862	−	8.37834i	−0.191204	−	0.609435i
$190$	3.93998	−	5.39635i	0.285836	−	0.391492i
$191$		−	16.9750i		−	1.22827i	−0.789201	−	0.614135i	$-0.789505\pi$
$191$		−	16.9750i		−	1.22827i	0.789201	−	0.614135i	$-0.210495\pi$
$192$	2.81244	−	3.75900i	0.202971	−	0.271283i
$193$	14.8445			1.06853			0.534266	−	0.845317i	$-0.320588\pi$
$193$	14.8445			1.06853			0.534266	+	0.845317i	$0.320588\pi$
$194$	−12.4888	+	17.1052i	−0.896645	+	1.22808i
$195$			0.673485i			0.0482292i
$196$	11.1173	+	8.50914i	0.794093	+	0.607796i
$197$			6.30785i			0.449416i	0.974426	+	0.224708i	$0.0721428\pi$
$197$			6.30785i			0.449416i	−0.974426	+	0.224708i	$0.927857\pi$
$198$	−1.75983	−	1.28488i	−0.125065	−	0.0913127i
$199$	11.9770			0.849030			0.424515	−	0.905421i	$-0.360445\pi$
$199$	11.9770			0.849030			0.424515	+	0.905421i	$0.360445\pi$
$200$	−0.892871	+	2.68380i	−0.0631355	+	0.189773i
$201$		−	4.52929i		−	0.319471i
$202$	−14.5974	−	10.6578i	−1.02707	−	0.749883i
$203$	5.86501	+	18.6938i	0.411643	+	1.31205i
$204$	−0.653728	−	2.04443i	−0.0457701	−	0.143139i
$205$			8.46264i			0.591056i
$206$	−17.2970	−	12.6289i	−1.20514	−	0.879895i
$207$		−	7.43471i		−	0.516748i
$208$	−3.73896	+	2.66347i	−0.259250	+	0.184678i
$209$			2.74117i			0.189611i
$210$	0.704530	−	2.07963i	0.0486172	−	0.143508i
$211$	10.8525			0.747120			0.373560	−	0.927606i	$-0.378137\pi$
$211$	10.8525			0.747120			0.373560	+	0.927606i	$0.378137\pi$
$212$	10.4579	−	3.34402i	0.718253	−	0.229668i
$213$	−0.665785			−0.0456189
$214$	7.65515	+	5.58917i	0.523295	+	0.382068i
$215$	−4.32314			−0.294836
$216$	−8.90730	−	2.96336i	−0.606065	−	0.201631i
$217$	−11.9407	+	3.74628i	−0.810588	+	0.254314i
$218$	−9.35267	+	12.8098i	−0.633443	+	0.867588i
$219$	1.04527			0.0706329
$220$	−0.353414	−	1.10525i	−0.0238272	−	0.0745159i
$221$			2.09884i			0.141183i
$222$	2.91684	+	2.12964i	0.195766	+	0.142932i
$223$	−14.0737			−0.942445			−0.471223	−	0.882014i	$-0.656187\pi$
$223$	−14.0737			−0.942445			−0.471223	+	0.882014i	$0.656187\pi$
$224$	14.3317	−	4.31313i	0.957575	−	0.288183i
$225$	2.65563			0.177042
$226$	1.61061	+	1.17594i	0.107136	+	0.0782221i
$227$		−	14.9683i		−	0.993478i	−0.867900	−	0.496739i	$-0.834531\pi$
$227$		−	14.9683i		−	0.993478i	0.867900	−	0.496739i	$-0.165469\pi$
$228$	1.68887	+	5.28169i	0.111848	+	0.349788i
$229$	21.5684			1.42528			0.712641	−	0.701529i	$-0.247499\pi$
$229$	21.5684			1.42528			0.712641	+	0.701529i	$0.247499\pi$
$230$	2.33466	−	3.19765i	0.153943	−	0.210847i
$231$	0.269661	+	0.859503i	0.0177424	+	0.0565511i
$232$	19.8740	+	6.61187i	1.30479	+	0.434091i
$233$	−19.5888			−1.28331			−0.641653	−	0.766995i	$-0.721751\pi$
$233$	−19.5888			−1.28331			−0.641653	+	0.766995i	$0.721751\pi$
$234$	3.48107	+	2.54160i	0.227565	+	0.166149i
$235$	3.56830			0.232770
$236$	25.3281	−	8.09891i	1.64872	−	0.527194i
$237$	−5.87465			−0.381600
$238$	2.19559	−	6.48095i	0.142319	−	0.420098i
$239$		−	23.2562i		−	1.50432i	−0.658981	−	0.752160i	$-0.729012\pi$
$239$		−	23.2562i		−	1.50432i	0.658981	−	0.752160i	$-0.270988\pi$
$240$	−1.36192	−	1.91185i	−0.0879113	−	0.123409i
$241$			20.9056i			1.34665i	0.739347	+	0.673324i	$0.235134\pi$
$241$			20.9056i			1.34665i	−0.739347	+	0.673324i	$0.764866\pi$
$242$	−12.1795	−	8.89247i	−0.782926	−	0.571629i
$243$			13.4890i			0.865321i
$244$	0.167624	+	0.524220i	0.0107311	+	0.0335597i
$245$	5.74543	−	3.99876i	0.367062	−	0.255471i
$246$	−5.67224	−	4.14141i	−0.361649	−	0.264047i
$247$		−	5.42225i		−	0.345009i
$248$	−4.22334	+	12.6946i	−0.268182	+	0.806105i
$249$	−9.16813			−0.581007
$250$	1.14218	+	0.833926i	0.0722376	+	0.0527421i
$251$			3.33668i			0.210610i	0.994440	+	0.105305i	$0.0335818\pi$
$251$			3.33668i			0.210610i	−0.994440	+	0.105305i	$0.966418\pi$
$252$	−8.09034	−	11.4897i	−0.509643	−	0.723780i
$253$			1.62430i			0.102119i
$254$	−13.1012	+	17.9439i	−0.822043	+	1.12590i
$255$	−1.07320			−0.0672067
$256$	5.22790	−	15.1218i	0.326744	−	0.945113i
$257$		−	24.4200i		−	1.52328i	−0.648002	−	0.761639i	$-0.724395\pi$
$257$		−	24.4200i		−	1.52328i	0.648002	−	0.761639i	$-0.275605\pi$
$258$	2.11564	−	2.89767i	0.131714	−	0.180401i
$259$	3.44665	+	10.9857i	0.214164	+	0.682616i
$260$	0.699080	+	2.18627i	0.0433551	+	0.135587i
$261$		−	19.6654i		−	1.21726i
$262$	4.18422	−	5.73087i	0.258502	−	0.354054i
$263$		−	27.1113i		−	1.67176i	−0.548915	−	0.835878i	$-0.684959\pi$
$263$		−	27.1113i		−	1.67176i	0.548915	−	0.835878i	$-0.315041\pi$
$264$	0.913766	+	0.304000i	0.0562384	+	0.0187099i
$265$		−	5.48977i		−	0.337234i
$266$	−5.67219	+	16.7432i	−0.347785	+	1.02659i
$267$	9.00160			0.550889
$268$	−4.70142	−	14.7030i	−0.287185	−	0.898128i
$269$	−18.5701			−1.13224			−0.566121	−	0.824322i	$-0.691556\pi$
$269$	−18.5701			−1.13224			−0.566121	+	0.824322i	$0.691556\pi$
$270$	−2.76773	+	3.79079i	−0.168438	+	0.230700i
$271$	12.9119			0.784344			0.392172	−	0.919892i	$-0.371724\pi$
$271$	12.9119			0.784344			0.392172	+	0.919892i	$0.371724\pi$
$272$	−4.24427	−	5.95807i	−0.257346	−	0.361261i
$273$	−0.533409	−	1.70016i	−0.0322834	−	0.102898i
$274$	−16.9845	−	12.4007i	−1.02607	−	0.749153i
$275$	−0.580189			−0.0349867
$276$	1.00075	+	3.12970i	0.0602383	+	0.188386i
$277$			0.557017i			0.0334679i	0.999860	+	0.0167340i	$0.00532683\pi$
$277$			0.557017i			0.0334679i	−0.999860	+	0.0167340i	$0.994673\pi$
$278$	0.123898	−	0.169696i	0.00743091	−	0.0101777i
$279$	12.5613			0.752025
$280$	0.128378	−	7.48221i	0.00767203	−	0.447148i
$281$	−27.3862			−1.63372			−0.816860	−	0.576835i	$-0.804287\pi$
$281$	−27.3862			−1.63372			−0.816860	+	0.576835i	$0.804287\pi$
$282$	−1.74624	+	2.39172i	−0.103987	+	0.142425i
$283$			5.24149i			0.311574i	0.987791	+	0.155787i	$0.0497914\pi$
$283$			5.24149i			0.311574i	−0.987791	+	0.155787i	$0.950209\pi$
$284$	−2.16127	+	0.691088i	−0.128248	+	0.0410085i
$285$	2.77257			0.164233
$286$	−0.760529	−	0.555277i	−0.0449710	−	0.0328342i
$287$	−6.70253	−	21.3633i	−0.395638	−	1.26103i
$288$	−15.0215	−	0.175541i	−0.885148	−	0.0103439i
$289$	13.6555			0.803263
$290$	6.17537	−	8.45803i	0.362630	−	0.496673i
$291$	−8.78840			−0.515185
$292$	3.39316	−	1.08500i	0.198570	−	0.0634947i
$293$	6.66098			0.389138			0.194569	−	0.980889i	$-0.437669\pi$
$293$	6.66098			0.389138			0.194569	+	0.980889i	$0.437669\pi$
$294$	−0.131435	+	5.80787i	−0.00766542	+	0.338722i
$295$		−	13.2957i		−	0.774107i
$296$	11.6792	+	3.88555i	0.678841	+	0.225843i
$297$		−	1.92560i		−	0.111735i
$298$	−7.38435	+	10.1139i	−0.427764	+	0.585882i
$299$		−	3.21299i		−	0.185812i
$300$	−1.11791	+	0.357462i	−0.0645424	+	0.0206381i
$301$	10.9134	−	3.42399i	0.629041	−	0.197355i
$302$	−10.3350	+	14.1552i	−0.594714	+	0.814543i
$303$		−	7.49993i		−	0.430860i
$304$	10.9648	+	15.3924i	0.628876	+	0.882812i
$305$	0.275184			0.0157570
$306$	−4.05006	+	5.54712i	−0.231527	+	0.317108i
$307$		−	17.0826i		−	0.974957i	−0.873135	−	0.487479i	$-0.837917\pi$
$307$		−	17.0826i		−	0.974957i	0.873135	−	0.487479i	$-0.162083\pi$
$308$	1.76754	+	2.51021i	0.100715	+	0.143032i
$309$		−	8.88694i		−	0.505560i
$310$	5.40258	+	3.94453i	0.306846	+	0.224034i
$311$	29.4721			1.67121			0.835604	−	0.549332i	$-0.185118\pi$
$311$	29.4721			1.67121			0.835604	+	0.549332i	$0.185118\pi$
$312$	−1.80750	−	0.601335i	−0.102329	−	0.0340439i
$313$		−	26.1624i		−	1.47879i	−0.673275	−	0.739393i	$-0.735113\pi$
$313$		−	26.1624i		−	1.47879i	0.673275	−	0.739393i	$-0.264887\pi$
$314$	−17.8283	−	13.0168i	−1.00611	−	0.734580i
$315$	−6.70392	+	2.10329i	−0.377723	+	0.118507i
$316$	−19.0703	+	6.09792i	−1.07279	+	0.343035i
$317$		−	5.72675i		−	0.321646i	−0.986983	−	0.160823i	$-0.948585\pi$
$317$		−	5.72675i		−	0.321646i	0.986983	−	0.160823i	$-0.0514149\pi$
$318$	3.67962	+	2.68656i	0.206343	+	0.150655i
$319$			4.29641i			0.240553i
$320$	−6.40556	−	4.79257i	−0.358082	−	0.267913i
$321$			3.93310i			0.219524i
$322$	−3.36110	+	9.92131i	−0.187307	+	0.552893i
$323$	8.64040			0.480765
$324$	3.66653	+	11.4665i	0.203696	+	0.637028i
$325$	1.14766			0.0636606
$326$	−6.39745	−	4.67090i	−0.354322	−	0.258697i
$327$	−6.58148			−0.363957
$328$	−22.7120	−	7.55604i	−1.25406	−	0.417213i
$329$	−9.00789	+	2.82614i	−0.496621	+	0.155810i
$330$	0.283931	−	0.388882i	0.0156299	−	0.0214073i
$331$	17.6047			0.967641			0.483820	−	0.875167i	$-0.339249\pi$
$331$	17.6047			0.967641			0.483820	+	0.875167i	$0.339249\pi$
$332$	−29.7616	+	9.51657i	−1.63338	+	0.522289i
$333$		−	11.5566i		−	0.633299i
$334$	10.6788	+	7.79681i	0.584318	+	0.426622i
$335$	−7.71818			−0.421689
$336$	4.95227	+	3.74766i	0.270168	+	0.204452i
$337$	24.3443			1.32612			0.663059	−	0.748567i	$-0.269258\pi$
$337$	24.3443			1.32612			0.663059	+	0.748567i	$0.269258\pi$
$338$	−13.3439	−	9.74265i	−0.725813	−	0.529930i
$339$			0.827507i			0.0449440i
$340$	−3.48384	+	1.11399i	−0.188938	+	0.0604147i
$341$	−2.74434			−0.148614
$342$	10.4631	−	14.3307i	0.565780	−	0.774915i
$343$	−11.3368	+	14.6450i	−0.612131	+	0.790756i
$344$	3.86001	−	11.6025i	0.208118	−	0.625562i
$345$	1.64291			0.0884510
$346$	26.9217	+	19.6561i	1.44732	+	1.05672i
$347$	16.7400			0.898650			0.449325	−	0.893368i	$-0.351664\pi$
$347$	16.7400			0.898650			0.449325	+	0.893368i	$0.351664\pi$
$348$	2.64707	+	8.27831i	0.141898	+	0.443764i
$349$	−14.2317			−0.761807			−0.380903	−	0.924615i	$-0.624387\pi$
$349$	−14.2317			−0.761807			−0.380903	+	0.924615i	$0.624387\pi$
$350$	−3.54382	−	1.20056i	−0.189425	−	0.0641727i
$351$			3.80898i			0.203308i
$352$	3.28182	+	0.0383515i	0.174922	+	0.00204414i
$353$			6.08004i			0.323608i	0.986823	+	0.161804i	$0.0517312\pi$
$353$			6.08004i			0.323608i	−0.986823	+	0.161804i	$0.948269\pi$
$354$	8.91170	+	6.50660i	0.473651	+	0.345822i
$355$			1.13454i			0.0602150i
$356$	29.2210	−	9.34370i	1.54871	−	0.495215i
$357$	2.70922	−	0.849993i	0.143387	−	0.0449864i
$358$	22.5107	+	16.4355i	1.18973	+	0.868645i
$359$			16.3854i			0.864787i	0.901685	+	0.432394i	$0.142331\pi$
$359$			16.3854i			0.864787i	−0.901685	+	0.432394i	$0.857669\pi$
$360$	−2.37113	+	7.12717i	−0.124970	+	0.375635i
$361$	−3.32202			−0.174843
$362$	−23.9974	−	17.5210i	−1.26128	−	0.920882i
$363$		−	6.25763i		−	0.328441i
$364$	−3.49633	−	4.96538i	−0.183257	−	0.260257i
$365$		−	1.78121i		−	0.0932326i
$366$	−0.134668	+	0.184447i	−0.00703922	+	0.00964119i
$367$	13.1245			0.685092			0.342546	−	0.939501i	$-0.388711\pi$
$367$	13.1245			0.685092			0.342546	+	0.939501i	$0.388711\pi$
$368$	6.49729	+	9.12086i	0.338695	+	0.475458i
$369$			22.4736i			1.16993i
$370$	3.62904	−	4.97047i	0.188665	−	0.258402i
$371$	4.34798	+	13.8585i	0.225736	+	0.719498i
$372$	−5.28778	+	1.69082i	−0.274159	+	0.0876649i
$373$			0.552362i			0.0286002i	0.999898	+	0.0143001i	$0.00455202\pi$
$373$			0.552362i			0.0286002i	−0.999898	+	0.0143001i	$0.995448\pi$
$374$	0.884839	−	1.21191i	0.0457539	−	0.0626664i
$375$			0.586834i			0.0303040i
$376$	−3.18603	+	9.57659i	−0.164307	+	0.493875i
$377$		−	8.49862i		−	0.437701i
$378$	3.98456	−	11.7616i	0.204944	−	0.604953i
$379$	−29.1600			−1.49785			−0.748925	−	0.662655i	$-0.769430\pi$
$379$	−29.1600			−1.49785			−0.748925	+	0.662655i	$0.769430\pi$
$380$	9.00031	−	2.87794i	0.461706	−	0.147635i
$381$	−9.21933			−0.472320
$382$	14.1559	−	19.3885i	0.724280	−	0.992002i
$383$	−5.89451			−0.301195			−0.150598	−	0.988595i	$-0.548120\pi$
$383$	−5.89451			−0.301195			−0.150598	+	0.988595i	$0.548120\pi$
$384$	6.34704	−	1.94808i	0.323896	−	0.0994124i
$385$	1.46464	−	0.459518i	0.0746451	−	0.0234192i
$386$	16.9551	+	12.3792i	0.862990	+	0.630085i
$387$	−11.4807			−0.583594
$388$	−28.5289	+	9.12240i	−1.44834	+	0.463120i
$389$			13.5376i			0.686385i	0.939265	+	0.343192i	$0.111508\pi$
$389$			13.5376i			0.686385i	−0.939265	+	0.343192i	$0.888492\pi$
$390$	−0.561636	+	0.769239i	−0.0284395	+	0.0389519i
$391$	5.11994			0.258926
$392$	5.60194	+	18.9900i	0.282941	+	0.959137i
$393$	2.94444			0.148527
$394$	−5.26028	+	7.20468i	−0.265009	+	0.362967i
$395$			10.0108i			0.503696i
$396$	−0.938536	−	2.93513i	−0.0471632	−	0.147496i
$397$	−4.22501			−0.212047			−0.106024	−	0.994364i	$-0.533812\pi$
$397$	−4.22501			−0.212047			−0.106024	+	0.994364i	$0.533812\pi$
$398$	13.6799	+	9.98796i	0.685711	+	0.500651i
$399$	−6.99913	+	2.19591i	−0.350395	+	0.109933i
$400$	−3.25791	+	2.32079i	−0.162895	+	0.116039i
$401$	8.09225			0.404108			0.202054	−	0.979374i	$-0.435238\pi$
$401$	8.09225			0.404108			0.202054	+	0.979374i	$0.435238\pi$
$402$	3.77709	−	5.17325i	0.188384	−	0.258018i
$403$	5.42850			0.270413
$404$	−7.78496	−	24.3463i	−0.387316	−	1.21127i
$405$	6.01923			0.299098
$406$	−8.89038	+	26.2426i	−0.441222	+	1.30240i
$407$			2.52484i			0.125152i
$408$	0.958233	−	2.88027i	0.0474396	−	0.142594i
$409$			27.6608i			1.36774i	0.729605	+	0.683868i	$0.239704\pi$
$409$			27.6608i			1.36774i	−0.729605	+	0.683868i	$0.760296\pi$
$410$	−7.05721	+	9.66583i	−0.348531	+	0.477361i
$411$		−	8.72637i		−	0.430440i
$412$	−9.22468	−	28.8488i	−0.454468	−	1.42128i
$413$	10.5304	+	33.5640i	0.518167	+	1.65158i
$414$	6.20000	−	8.49176i	0.304713	−	0.417347i
$415$			15.6230i			0.766905i
$416$	−6.49169	−	0.0758621i	−0.318281	−	0.00371944i
$417$	0.0871872			0.00426957
$418$	−2.28593	+	3.13090i	−0.111809	+	0.153138i
$419$			10.5982i			0.517755i	0.965910	+	0.258877i	$0.0833526\pi$
$419$			10.5982i			0.517755i	−0.965910	+	0.258877i	$0.916647\pi$
$420$	2.53896	−	1.78778i	0.123888	−	0.0872349i
$421$			25.5951i			1.24743i	0.781652	+	0.623715i	$0.214377\pi$
$421$			25.5951i			1.24743i	−0.781652	+	0.623715i	$0.785623\pi$
$422$	12.3955	+	9.05021i	0.603405	+	0.440557i
$423$	9.47606			0.460742
$424$	14.7335	+	4.90166i	0.715520	+	0.238046i
$425$			1.82880i			0.0887101i
$426$	−0.760445	−	0.555215i	−0.0368437	−	0.0269003i
$427$	−0.694680	+	0.217949i	−0.0336179	+	0.0105473i
$428$	4.08258	+	12.7676i	0.197339	+	0.617147i
$429$		−	0.390749i		−	0.0188655i
$430$	−4.93780	−	3.60518i	−0.238122	−	0.173857i
$431$			32.7406i			1.57706i	0.614997	+	0.788529i	$0.289157\pi$
$431$			32.7406i			1.57706i	−0.614997	+	0.788529i	$0.710843\pi$
$432$	−7.70249	−	10.8127i	−0.370586	−	0.520227i
$433$		−	16.8933i		−	0.811840i	−0.913909	−	0.405920i	$-0.866951\pi$
$433$		−	16.8933i		−	0.811840i	0.913909	−	0.405920i	$-0.133049\pi$
$434$	−16.7625	−	5.67874i	−0.804626	−	0.272588i
$435$	4.34561			0.208356
$436$	−21.3648	+	6.83161i	−1.02319	+	0.327175i
$437$	−13.2271			−0.632737
$438$	1.19389	+	0.871679i	0.0570461	+	0.0416504i
$439$	−31.6749			−1.51176			−0.755881	−	0.654709i	$-0.772791\pi$
$439$	−31.6749			−1.51176			−0.755881	+	0.654709i	$0.772791\pi$
$440$	0.518034	−	1.55711i	0.0246963	−	0.0742324i
$441$	15.2577	−	10.6192i	0.726558	−	0.505676i
$442$	−1.75028	+	2.39725i	−0.0832522	+	0.114026i
$443$	−12.8303			−0.609587			−0.304794	−	0.952418i	$-0.598587\pi$
$443$	−12.8303			−0.609587			−0.304794	+	0.952418i	$0.598587\pi$
$444$	1.55559	+	4.86486i	0.0738248	+	0.230876i
$445$		−	15.3393i		−	0.727151i
$446$	−16.0747	−	11.7364i	−0.761157	−	0.555736i
$447$	−5.19637			−0.245780
$448$	19.9661	+	7.02519i	0.943311	+	0.331909i
$449$	9.10148			0.429525			0.214763	−	0.976666i	$-0.431102\pi$
$449$	9.10148			0.429525			0.214763	+	0.976666i	$0.431102\pi$
$450$	3.03319	+	2.21459i	0.142986	+	0.104397i
$451$		−	4.90993i		−	0.231200i
$452$	0.858956	+	2.68625i	0.0404019	+	0.126351i
$453$	−7.27276			−0.341704
$454$	12.4824	−	17.0964i	0.585828	−	0.802373i
$455$	−2.89717	+	0.908961i	−0.135822	+	0.0426127i
$456$	−2.47554	+	7.44101i	−0.115928	+	0.348457i
$457$	−5.29969			−0.247909			−0.123954	−	0.992288i	$-0.539558\pi$
$457$	−5.29969			−0.247909			−0.123954	+	0.992288i	$0.539558\pi$
$458$	24.6350	+	17.9865i	1.15112	+	0.840452i
$459$	−6.06964			−0.283307
$460$	5.33320	−	1.70534i	0.248662	−	0.0795120i
$461$	0.755725			0.0351976			0.0175988	−	0.999845i	$-0.494398\pi$
$461$	0.755725			0.0351976			0.0175988	+	0.999845i	$0.494398\pi$
$462$	−0.408761	+	1.20658i	−0.0190173	+	0.0561352i
$463$			3.99447i			0.185639i	0.995683	+	0.0928193i	$0.0295879\pi$
$463$			3.99447i			0.185639i	−0.995683	+	0.0928193i	$0.970412\pi$
$464$	17.1859	+	24.1254i	0.797833	+	1.11999i
$465$			2.77577i			0.128723i
$466$	−22.3739	−	16.3356i	−1.03645	−	0.756733i
$467$			3.90589i			0.180743i	0.995908	+	0.0903716i	$0.0288055\pi$
$467$			3.90589i			0.180743i	−0.995908	+	0.0903716i	$0.971195\pi$
$468$	1.85650	+	5.80591i	0.0858165	+	0.268378i
$469$	19.4839	−	6.11290i	0.899685	−	0.282268i
$470$	4.07563	+	2.97569i	0.187995	+	0.137259i
$471$		−	9.15992i		−	0.422067i
$472$	35.6830	+	11.8714i	1.64245	+	0.546423i
$473$	2.50824			0.115329
$474$	−6.70989	−	4.89902i	−0.308196	−	0.225020i
$475$		−	4.72462i		−	0.216780i
$476$	7.91239	−	5.57143i	0.362664	−	0.255366i
$477$		−	14.5788i		−	0.667517i
$478$	19.3940	−	26.5627i	0.887059	−	1.21495i
$479$	9.21055			0.420841			0.210420	−	0.977611i	$-0.432517\pi$
$479$	9.21055			0.420841			0.210420	+	0.977611i	$0.432517\pi$
$480$	0.0387907	−	3.31941i	0.00177054	−	0.151510i
$481$		−	4.99432i		−	0.227721i
$482$	−17.4337	+	23.8779i	−0.794084	+	1.08761i
$483$	−4.14739	+	1.30120i	−0.188713	+	0.0592068i
$484$	−6.49545	−	20.3135i	−0.295248	−	0.923343i
$485$			14.9759i			0.680023i
$486$	−11.2488	+	15.4069i	−0.510258	+	0.698869i
$487$			21.4403i			0.971552i	0.874083	+	0.485776i	$0.161463\pi$
$487$			21.4403i			0.971552i	−0.874083	+	0.485776i	$0.838537\pi$
$488$	−0.245703	+	0.738538i	−0.0111225	+	0.0334320i
$489$		−	3.28692i		−	0.148640i
$490$	9.89696	+	0.223972i	0.447099	+	0.0101180i
$491$	19.6672			0.887570			0.443785	−	0.896133i	$-0.353635\pi$
$491$	19.6672			0.887570			0.443785	+	0.896133i	$0.353635\pi$
$492$	−3.02507	−	9.46045i	−0.136381	−	0.426510i
$493$	13.5426			0.609930
$494$	4.52175	−	6.19316i	0.203443	−	0.278644i
$495$	−1.54077			−0.0692523
$496$	−15.4101	+	10.9775i	−0.691935	+	0.492904i
$497$	−0.898570	−	2.86405i	−0.0403064	−	0.128470i
$498$	−10.4716	−	7.64554i	−0.469245	−	0.342605i
$499$	−12.2344			−0.547686			−0.273843	−	0.961774i	$-0.588295\pi$
$499$	−12.2344			−0.547686			−0.273843	+	0.961774i	$0.588295\pi$
$500$	0.609136	+	1.90498i	0.0272414	+	0.0851933i
$501$			5.48662i			0.245124i
$502$	−2.78255	+	3.81108i	−0.124191	+	0.170097i
$503$	5.42742			0.241997			0.120998	−	0.992653i	$-0.461390\pi$
$503$	5.42742			0.241997			0.120998	+	0.992653i	$0.461390\pi$
$504$	0.340923	−	19.8700i	0.0151859	−	0.885078i
$505$	−12.7803			−0.568717
$506$	−1.35455	+	1.85524i	−0.0602170	+	0.0824755i
$507$		−	6.85591i		−	0.304482i
$508$	−29.9278	+	9.56970i	−1.32783	+	0.424587i
$509$	−17.3838			−0.770522			−0.385261	−	0.922808i	$-0.625889\pi$
$509$	−17.3838			−0.770522			−0.385261	+	0.922808i	$0.625889\pi$
$510$	−1.22579	−	0.894973i	−0.0542789	−	0.0396301i
$511$	1.41074	+	4.49652i	0.0624074	+	0.198914i
$512$	18.5816	−	12.9121i	0.821201	−	0.570640i
$513$	15.6806			0.692315
$514$	20.3645	−	27.8920i	0.898238	−	1.23026i
$515$	−15.1439			−0.667319
$516$	4.83288	−	1.54536i	0.212756	−	0.0680307i
$517$	−2.07029			−0.0910511
$518$	−5.22454	+	15.4218i	−0.229553	+	0.677596i
$519$			13.8320i			0.607157i
$520$	−1.02471	+	3.08008i	−0.0449365	+	0.135071i
$521$			12.8139i			0.561388i	0.959797	+	0.280694i	$0.0905646\pi$
$521$			12.8139i			0.561388i	−0.959797	+	0.280694i	$0.909435\pi$
$522$	16.3995	−	22.4614i	0.717786	−	0.983107i
$523$		−	8.05393i		−	0.352174i	−0.984375	−	0.176087i	$-0.943656\pi$
$523$		−	8.05393i		−	0.352174i	0.984375	−	0.176087i	$-0.0563439\pi$
$524$	9.55823	−	3.05634i	0.417553	−	0.133517i
$525$	−0.464781	−	1.48142i	−0.0202847	−	0.0646544i
$526$	22.6088	−	30.9659i	0.985792	−	1.35018i
$527$			8.65037i			0.376816i
$528$	0.790169	+	1.10923i	0.0343877	+	0.0482732i
$529$	15.1622			0.659226
$530$	4.57806	−	6.27029i	0.198858	−	0.272364i
$531$		−	35.3085i		−	1.53226i
$532$	−20.4412	+	14.3935i	−0.886239	+	0.624037i
$533$			9.71221i			0.420683i
$534$	10.2814	+	7.50666i	0.444921	+	0.324845i
$535$	6.70224			0.289763
$536$	6.89133	−	20.7140i	0.297660	−	0.894710i
$537$			11.5657i			0.499096i
$538$	−21.2104	−	15.4861i	−0.914445	−	0.667654i
$539$	−3.33344	+	2.32004i	−0.143581	+	0.0999310i
$540$	−6.32247	+	2.02167i	−0.272076	+	0.0869989i
$541$		−	15.9099i		−	0.684018i	−0.939697	−	0.342009i	$-0.888893\pi$
$541$		−	15.9099i		−	0.684018i	0.939697	−	0.342009i	$-0.111107\pi$
$542$	14.7477	+	10.7676i	0.633469	+	0.462508i
$543$		−	12.3295i		−	0.529110i
$544$	0.120887	−	10.3446i	0.00518299	−	0.443520i
$545$			11.2152i			0.480408i
$546$	0.808560	−	2.38671i	0.0346032	−	0.102142i
$547$	−28.6893			−1.22667			−0.613333	−	0.789825i	$-0.710172\pi$
$547$	−28.6893			−1.22667			−0.613333	+	0.789825i	$0.710172\pi$
$548$	−9.05802	−	28.3276i	−0.386939	−	1.21009i
$549$	0.730785			0.0311891
$550$	−0.662679	−	0.483835i	−0.0282567	−	0.0206308i
$551$	−34.9867			−1.49048
$552$	−1.46690	+	4.40923i	−0.0624355	+	0.187669i
$553$	−7.92866	−	25.2714i	−0.337161	−	1.07465i
$554$	−0.464511	+	0.636212i	−0.0197352	+	0.0270301i
$555$	2.55376			0.108401
$556$	0.283027	−	0.0905007i	0.0120030	−	0.00383808i
$557$			29.6910i			1.25805i	0.777386	+	0.629024i	$0.216545\pi$
$557$			29.6910i			1.25805i	−0.777386	+	0.629024i	$0.783455\pi$
$558$	14.3472	+	10.4752i	0.607366	+	0.443450i
$559$	−4.96149			−0.209849
$560$	6.38624	−	8.43895i	0.269868	−	0.356611i
$561$	0.622662			0.0262888
$562$	−31.2798	−	22.8380i	−1.31946	−	0.963363i
$563$		−	25.7978i		−	1.08725i	−0.839329	−	0.543624i	$-0.817052\pi$
$563$		−	25.7978i		−	1.08725i	0.839329	−	0.543624i	$-0.182948\pi$
$564$	−3.98903	+	1.27553i	−0.167968	+	0.0537095i
$565$	1.41012			0.0593242
$566$	−4.37101	+	5.98671i	−0.183727	+	0.251640i
$567$	−15.1951	+	4.76731i	−0.638133	+	0.200208i
$568$	−3.04487	−	1.01300i	−0.127760	−	0.0425044i
$569$	−6.17604			−0.258913			−0.129457	−	0.991585i	$-0.541323\pi$
$569$	−6.17604			−0.258913			−0.129457	+	0.991585i	$0.541323\pi$
$570$	3.16676	+	2.31211i	0.132641	+	0.0968438i
$571$	−44.7626			−1.87326			−0.936628	−	0.350325i	$-0.886071\pi$
$571$	−44.7626			−1.87326			−0.936628	+	0.350325i	$0.886071\pi$
$572$	−0.405599	−	1.26845i	−0.0169589	−	0.0530365i
$573$	9.96153			0.416149
$574$	10.1599	−	29.9901i	0.424067	−	1.25176i
$575$		−	2.79961i		−	0.116752i
$576$	−17.0108	−	12.7273i	−0.708783	−	0.530303i
$577$			45.0609i			1.87591i	0.346760	+	0.937954i	$0.387282\pi$
$577$			45.0609i			1.87591i	−0.346760	+	0.937954i	$0.612718\pi$
$578$	15.5970	+	11.3876i	0.648748	+	0.473664i
$579$			8.71126i			0.362028i
$580$	14.1067	−	4.51077i	0.585750	−	0.187299i
$581$	−12.3737	−	39.4392i	−0.513346	−	1.63621i
$582$	−10.0379	−	7.32887i	−0.416084	−	0.303791i
$583$			3.18511i			0.131914i
$584$	4.78040	+	1.59039i	0.197814	+	0.0658107i
$585$	3.04775			0.126009
$586$	7.60801	+	5.55476i	0.314284	+	0.229465i
$587$		−	0.738708i		−	0.0304897i	−0.999884	−	0.0152449i	$-0.995147\pi$
$587$		−	0.738708i		−	0.0304897i	0.999884	−	0.0152449i	$-0.00485278\pi$
$588$	−4.99345	+	6.52401i	−0.205927	+	0.269046i
$589$		−	22.3478i		−	0.920824i
$590$	11.0876	−	15.1861i	0.456471	−	0.625200i
$591$	−3.70166			−0.152266
$592$	10.0995	+	14.1776i	0.415086	+	0.582696i
$593$		−	5.51961i		−	0.226663i	−0.993557	−	0.113332i	$-0.963848\pi$
$593$		−	5.51961i		−	0.226663i	0.993557	−	0.113332i	$-0.0361522\pi$
$594$	1.60581	−	2.19937i	0.0658870	−	0.0902414i
$595$	−1.44844	−	4.61668i	−0.0593802	−	0.189265i
$596$	−16.8685	+	5.39386i	−0.690959	+	0.220941i
$597$			7.02853i			0.287659i
$598$	2.67940	−	3.66981i	0.109569	−	0.150070i
$599$			0.145815i			0.00595785i	0.999996	+	0.00297893i	$0.000948223\pi$
$599$			0.145815i			0.00595785i	−0.999996	+	0.00297893i	$0.999052\pi$
$600$	−1.57494	−	0.523967i	−0.0642969	−	0.0213909i
$601$		−	21.7269i		−	0.886257i	−0.896458	−	0.443128i	$-0.853869\pi$
$601$		−	21.7269i		−	0.886257i	0.896458	−	0.443128i	$-0.146131\pi$
$602$	15.3204	+	5.19020i	0.624415	+	0.211537i
$603$	−20.4966			−0.834686
$604$	−23.6088	+	7.54916i	−0.960630	+	0.307171i
$605$	−10.6634			−0.433528
$606$	6.25438	−	8.56624i	0.254067	−	0.347980i
$607$	18.6456			0.756804			0.378402	−	0.925641i	$-0.376474\pi$
$607$	18.6456			0.756804			0.378402	+	0.925641i	$0.376474\pi$
$608$	−0.312305	+	26.7247i	−0.0126656	+	1.08383i
$609$	−10.9702	+	3.44179i	−0.444534	+	0.139468i
$610$	0.314309	+	0.229483i	0.0127260	+	0.00929148i
$611$	4.09518			0.165673
$612$	−9.25177	+	2.95834i	−0.373981	+	0.119584i
$613$		−	47.1735i		−	1.90532i	−0.304041	−	0.952659i	$-0.598336\pi$
$613$		−	47.1735i		−	1.90532i	0.304041	−	0.952659i	$-0.401664\pi$
$614$	14.2456	−	19.5114i	0.574907	−	0.787415i
$615$	−4.96616			−0.200255
$616$	−0.0744833	+	4.34110i	−0.00300102	+	0.174908i
$617$	16.2076			0.652493			0.326246	−	0.945285i	$-0.394216\pi$
$617$	16.2076			0.652493			0.326246	+	0.945285i	$0.394216\pi$
$618$	7.41105	−	10.1505i	0.298116	−	0.408311i
$619$			30.2319i			1.21512i	0.794273	+	0.607561i	$0.207852\pi$
$619$			30.2319i			1.21512i	−0.794273	+	0.607561i	$0.792148\pi$
$620$	2.88126	+	9.01069i	0.115714	+	0.361878i
$621$	9.29166			0.372861
$622$	33.6623	+	24.5775i	1.34974	+	0.985469i
$623$	12.1489	+	38.7228i	0.486736	+	1.55140i
$624$	−1.56301	−	2.19415i	−0.0625706	−	0.0878363i
$625$	1.00000			0.0400000
$626$	21.8175	−	29.8821i	0.872002	−	1.19433i
$627$	−1.60861			−0.0642418
$628$	−9.50804	−	29.7349i	−0.379412	−	1.18655i
$629$	7.95850			0.317326
$630$	−9.41106	−	3.18824i	−0.374945	−	0.127023i
$631$		−	6.27504i		−	0.249806i	−0.992169	−	0.124903i	$-0.960138\pi$
$631$		−	6.27504i		−	0.249806i	0.992169	−	0.124903i	$-0.0398619\pi$
$632$	−26.8669	−	8.93831i	−1.06871	−	0.355547i
$633$			6.36864i			0.253131i
$634$	4.77569	−	6.54096i	0.189667	−	0.259775i
$635$			15.7103i			0.623443i
$636$	1.96239	+	6.13706i	0.0778136	+	0.243350i
$637$	6.59379	−	4.58920i	0.261255	−	0.181831i
$638$	−3.58288	+	4.90726i	−0.141848	+	0.194280i
$639$			3.01291i			0.119189i
$640$	−3.31964	−	10.8157i	−0.131220	−	0.427529i
$641$	−0.954180			−0.0376878			−0.0188439	−	0.999822i	$-0.505999\pi$
$641$	−0.954180			−0.0376878			−0.0188439	+	0.999822i	$0.505999\pi$
$642$	−3.27991	+	4.49230i	−0.129448	+	0.177297i
$643$		−	29.7150i		−	1.17184i	−0.810367	−	0.585922i	$-0.800732\pi$
$643$		−	29.7150i		−	1.17184i	0.810367	−	0.585922i	$-0.199268\pi$
$644$	−12.1126	+	8.52898i	−0.477303	+	0.336089i
$645$		−	2.53697i		−	0.0998930i
$646$	9.86887	+	7.20545i	0.388286	+	0.283495i
$647$	22.3760			0.879693			0.439846	−	0.898073i	$-0.355033\pi$
$647$	22.3760			0.879693			0.439846	+	0.898073i	$0.355033\pi$
$648$	−5.37439	+	16.1544i	−0.211126	+	0.634605i
$649$			7.71403i			0.302802i
$650$	1.31083	+	0.957061i	0.0514149	+	0.0375390i
$651$	−2.19844	−	7.00721i	−0.0861638	−	0.274634i
$652$	−3.41184	−	10.6700i	−0.133618	−	0.417869i
$653$		−	3.18538i		−	0.124653i	−0.998056	−	0.0623267i	$-0.980148\pi$
$653$		−	3.18538i		−	0.124653i	0.998056	−	0.0623267i	$-0.0198521\pi$
$654$	−7.51721	−	5.48846i	−0.293946	−	0.214616i
$655$		−	5.01749i		−	0.196050i
$656$	−19.6400	−	27.5705i	−0.766812	−	1.07645i
$657$		−	4.73022i		−	0.184543i
$658$	−12.6454	−	4.28396i	−0.492969	−	0.167006i
$659$	−1.50751			−0.0587242			−0.0293621	−	0.999569i	$-0.509348\pi$
$659$	−1.50751			−0.0587242			−0.0293621	+	0.999569i	$0.509348\pi$
$660$	0.648598	−	0.207396i	0.0252466	−	0.00807286i
$661$	11.0607			0.430210			0.215105	−	0.976591i	$-0.430991\pi$
$661$	11.0607			0.430210			0.215105	+	0.976591i	$0.430991\pi$
$662$	20.1077	+	14.6810i	0.781506	+	0.570593i
$663$	−1.23167			−0.0478342
$664$	−41.9291	−	13.9494i	−1.62717	−	0.541340i
$665$	3.74196	+	11.9269i	0.145107	+	0.462507i
$666$	9.63736	−	13.1997i	0.373440	−	0.511478i
$667$	−20.7316			−0.802731
$668$	5.69513	+	17.8107i	0.220351	+	0.689115i
$669$		−	8.25893i		−	0.319309i
$670$	−8.81552	−	6.43638i	−0.340573	−	0.248659i
$671$	−0.159659			−0.00616355
$672$	2.53109	+	8.41031i	0.0976390	+	0.324435i
$673$	31.5781			1.21725			0.608624	−	0.793459i	$-0.291722\pi$
$673$	31.5781			1.21725			0.608624	+	0.793459i	$0.291722\pi$
$674$	27.8055	+	20.3013i	1.07103	+	0.781977i
$675$			3.31891i			0.127745i
$676$	−7.11647	−	22.2557i	−0.273710	−	0.855987i
$677$	5.96254			0.229159			0.114580	−	0.993414i	$-0.463448\pi$
$677$	5.96254			0.229159			0.114580	+	0.993414i	$0.463448\pi$
$678$	−0.690079	+	0.945159i	−0.0265023	+	0.0362986i
$679$	−11.8612	−	37.8056i	−0.455189	−	1.45085i
$680$	−4.90815	−	1.63289i	−0.188219	−	0.0626183i
$681$	8.78388			0.336599
$682$	−3.13452	−	2.28857i	−0.120027	−	0.0876339i
$683$	32.0466			1.22623			0.613114	−	0.789994i	$-0.289916\pi$
$683$	32.0466			1.22623			0.613114	+	0.789994i	$0.289916\pi$
$684$	23.9015	−	7.64272i	0.913895	−	0.292227i
$685$	−14.8703			−0.568163
$686$	−25.1615	+	7.27313i	−0.960671	+	0.277689i
$687$			12.6571i			0.482898i
$688$	14.0844	−	10.0331i	0.536963	−	0.382508i
$689$		−	6.30038i		−	0.240026i
$690$	1.87649	+	1.37006i	0.0714367	+	0.0521573i
$691$			17.0740i			0.649526i	0.945795	+	0.324763i	$0.105285\pi$
$691$			17.0740i			0.649526i	−0.945795	+	0.324763i	$0.894715\pi$
$692$	14.3577	+	44.9015i	0.545797	+	1.70690i
$693$	3.88955	−	1.22031i	0.147752	−	0.0463557i
$694$	19.1200	+	13.9599i	0.725787	+	0.529911i
$695$		−	0.148572i		−	0.00563566i
$696$	−3.88007	+	11.6628i	−0.147074	+	0.442076i
$697$	−15.4765			−0.586215
$698$	−16.2551	−	11.8682i	−0.615266	−	0.449218i
$699$		−	11.4954i		−	0.434796i
$700$	−3.04649	−	4.32653i	−0.115146	−	0.163528i
$701$			32.7289i			1.23615i	0.786118	+	0.618076i	$0.212088\pi$
$701$			32.7289i			1.23615i	−0.786118	+	0.618076i	$0.787912\pi$
$702$	−3.17640	+	4.35053i	−0.119886	+	0.164200i
$703$	−20.5604			−0.775449
$704$	3.71644	+	2.78060i	0.140069	+	0.104798i
$705$			2.09400i			0.0788645i
$706$	−5.07030	+	6.94448i	−0.190823	+	0.261359i
$707$	32.2629	−	10.1222i	1.21337	−	0.380684i
$708$	4.75271	+	14.8634i	0.178618	+	0.558600i
$709$			20.9447i			0.786594i	0.919412	+	0.393297i	$0.128666\pi$
$709$			20.9447i			0.786594i	−0.919412	+	0.393297i	$0.871334\pi$
$710$	−0.946120	+	1.29584i	−0.0355073	+	0.0486321i
$711$			26.5848i			0.997009i
$712$	41.1675	+	13.6960i	1.54282	+	0.513279i
$713$		−	13.2423i		−	0.495930i
$714$	3.80324	+	1.28845i	0.142333	+	0.0482190i
$715$	−0.665859			−0.0249017
$716$	12.0052	+	37.5446i	0.448657	+	1.40311i
$717$	13.6475			0.509677
$718$	−13.6642	+	18.7150i	−0.509943	+	0.698438i
$719$	−0.417030			−0.0155526			−0.00777630	−	0.999970i	$-0.502475\pi$
$719$	−0.417030			−0.0155526			−0.00777630	+	0.999970i	$0.502475\pi$
$720$	−8.65178	+	6.16314i	−0.322433	+	0.229687i
$721$	38.2295	−	11.9942i	1.42374	−	0.446686i
$722$	−3.79433	−	2.77032i	−0.141210	−	0.103100i
$723$	−12.2681			−0.456256
$724$	−12.7981	−	40.0241i	−0.475638	−	1.48748i
$725$		−	7.40518i		−	0.275022i
$726$	5.21840	−	7.14733i	0.193673	−	0.265262i
$727$	4.48987			0.166520			0.0832601	−	0.996528i	$-0.473467\pi$
$727$	4.48987			0.166520			0.0832601	+	0.996528i	$0.473467\pi$
$728$	0.147334	−	8.58702i	0.00546055	−	0.318256i
$729$	10.1419			0.375624
$730$	1.48539	−	2.03445i	0.0549769	−	0.0752984i
$731$		−	7.90619i		−	0.292421i
$732$	−0.307630	+	0.0983677i	−0.0113703	+	0.00363578i
$733$	22.8948			0.845640			0.422820	−	0.906214i	$-0.361040\pi$
$733$	22.8948			0.845640			0.422820	+	0.906214i	$0.361040\pi$
$734$	14.9905	+	10.9448i	0.553308	+	0.403981i
$735$	2.34661	+	3.37161i	0.0865559	+	0.124364i
$736$	−0.185059	+	15.8359i	−0.00682135	+	0.583719i
$737$	4.47800			0.164949
$738$	−18.7413	+	25.6688i	−0.689877	+	0.944883i
$739$	−0.354985			−0.0130583			−0.00652917	−	0.999979i	$-0.502078\pi$
$739$	−0.354985			−0.0130583			−0.00652917	+	0.999979i	$0.502078\pi$
$740$	8.29000	−	2.65081i	0.304747	−	0.0974457i
$741$	3.18196			0.116892
$742$	−6.59081	+	19.4548i	−0.241956	+	0.714207i
$743$			6.75171i			0.247696i	0.992301	+	0.123848i	$0.0395235\pi$
$743$			6.75171i			0.247696i	−0.992301	+	0.123848i	$0.960476\pi$
$744$	−7.44960	−	2.47840i	−0.273116	−	0.0908626i
$745$			8.85493i			0.324419i
$746$	−0.460629	+	0.630896i	−0.0168648	+	0.0230987i
$747$			41.4890i			1.51800i
$748$	2.02129	−	0.646326i	0.0739055	−	0.0236320i
$749$	−16.9193	+	5.30827i	−0.618218	+	0.193960i
$750$	−0.489376	+	0.670268i	−0.0178695	+	0.0244747i
$751$		−	27.4120i		−	1.00028i	−0.865945	−	0.500139i	$-0.833282\pi$
$751$		−	27.4120i		−	1.00028i	0.865945	−	0.500139i	$-0.166718\pi$
$752$	−11.6252	+	8.28125i	−0.423926	+	0.301986i
$753$	−1.95808			−0.0713564
$754$	7.08721	−	9.70693i	0.258101	−	0.353505i
$755$			12.3932i			0.451035i
$756$	14.3594	−	10.1110i	0.522246	−	0.367735i
$757$		−	27.6550i		−	1.00514i	−0.864537	−	0.502570i	$-0.832388\pi$
$757$		−	27.6550i		−	1.00514i	0.864537	−	0.502570i	$-0.167612\pi$
$758$	−33.3059	−	24.3173i	−1.20973	−	0.883244i
$759$	−0.953196			−0.0345988
$760$	12.6799	+	4.21847i	0.459949	+	0.153020i
$761$			14.1083i			0.511424i	0.966753	+	0.255712i	$0.0823099\pi$
$761$			14.1083i			0.511424i	−0.966753	+	0.255712i	$0.917690\pi$
$762$	−10.5301	−	7.68823i	−0.381465	−	0.278515i
$763$	−8.88262	−	28.3120i	−0.321572	−	1.02496i
$764$	32.3371	−	10.3401i	1.16992	−	0.374092i
$765$			4.85662i			0.175592i
$766$	−6.73258	−	4.91558i	−0.243258	−	0.177607i
$767$		−	15.2589i		−	0.550968i
$768$	8.87399	+	3.06791i	0.320213	+	0.110704i
$769$			2.82610i			0.101912i	0.998701	+	0.0509558i	$0.0162268\pi$
$769$			2.82610i			0.101912i	−0.998701	+	0.0509558i	$0.983773\pi$
$770$	2.05609	+	0.696553i	0.0740962	+	0.0251020i
$771$	14.3305			0.516100
$772$	9.04233	+	28.2785i	0.325441	+	1.01777i
$773$	−44.5587			−1.60266			−0.801332	−	0.598220i	$-0.795875\pi$
$773$	−44.5587			−1.60266			−0.801332	+	0.598220i	$0.795875\pi$
$774$	−13.1129	−	9.57401i	−0.471335	−	0.344131i
$775$	4.73007			0.169909
$776$	−40.1925	−	13.3716i	−1.44282	−	0.480012i
$777$	−6.44676	+	2.02261i	−0.231276	+	0.0725607i
$778$	−11.2894	+	15.4624i	−0.404743	+	0.554352i
$779$	39.9827			1.43253
$780$	−1.28298	+	0.410244i	−0.0459379	+	0.0146891i
$781$		−	0.658247i		−	0.0235539i
$782$	5.84787	+	4.26965i	0.209120	+	0.152682i
$783$	24.5772			0.878316
$784$	−9.43780	+	26.3615i	−0.337064	+	0.941482i
$785$	−15.6090			−0.557111
$786$	3.36307	+	2.45544i	0.119957	+	0.0875827i
$787$			30.3744i			1.08273i	0.840788	+	0.541365i	$0.182092\pi$
$787$			30.3744i			1.08273i	−0.840788	+	0.541365i	$0.817908\pi$
$788$	−12.0163	+	3.84234i	−0.428064	+	0.136878i
$789$	15.9098			0.566406
$790$	−8.34822	+	11.4341i	−0.297016	+	0.406805i
$791$	−3.55974	+	1.11684i	−0.126570	+	0.0397101i
$792$	1.37570	−	4.13511i	0.0488835	−	0.146935i
$793$	0.315817			0.0112150
$794$	−4.82571	−	3.52334i	−0.171258	−	0.125039i
$795$	3.22159			0.114258
$796$	7.29565	+	22.8160i	0.258587	+	0.808693i
$797$	43.5064			1.54108			0.770538	−	0.637394i	$-0.219988\pi$
$797$	43.5064			1.54108			0.770538	+	0.637394i	$0.219988\pi$
$798$	−9.82547	−	3.32864i	−0.347818	−	0.117832i
$799$			6.52572i			0.230863i
$800$	−5.65647	−	0.0661016i	−0.199986	−	0.00233705i
$801$		−	40.7353i		−	1.43931i
$802$	9.24278	+	6.74833i	0.326374	+	0.238292i
$803$			1.03344i			0.0364692i
$804$	8.62821	−	2.75895i	0.304293	−	0.0973008i
$805$	2.21733	+	7.06740i	0.0781506	+	0.249093i
$806$	6.20031	+	4.52697i	0.218397	+	0.159456i
$807$		−	10.8976i		−	0.383613i
$808$	11.4112	−	34.2998i	0.401444	−	1.20666i
$809$	−17.7818			−0.625176			−0.312588	−	0.949889i	$-0.601196\pi$
$809$	−17.7818			−0.625176			−0.312588	+	0.949889i	$0.601196\pi$
$810$	6.87502	+	5.01959i	0.241564	+	0.176370i
$811$			7.03219i			0.246934i	0.992349	+	0.123467i	$0.0394012\pi$
$811$			7.03219i			0.246934i	−0.992349	+	0.123467i	$0.960599\pi$
$812$	−32.0388	+	22.5598i	−1.12434	+	0.791694i
$813$			7.57716i			0.265743i
$814$	−2.10553	+	2.88381i	−0.0737987	+	0.101078i
$815$	−5.60110			−0.196198
$816$	3.49640	−	2.49068i	0.122398	−	0.0871912i
$817$			20.4252i			0.714588i
$818$	−23.0670	+	31.5935i	−0.806519	+	1.10464i
$819$	−7.69381	+	2.41386i	−0.268844	+	0.0843471i
$820$	−16.1212	+	5.15490i	−0.562976	+	0.180017i
$821$		−	7.24453i		−	0.252836i	−0.991977	−	0.126418i	$-0.959652\pi$
$821$		−	7.24453i		−	0.252836i	0.991977	−	0.126418i	$-0.0403481\pi$
$822$	7.27715	−	9.96706i	0.253820	−	0.347641i
$823$		−	46.4665i		−	1.61972i	−0.586624	−	0.809860i	$-0.699543\pi$
$823$		−	46.4665i		−	1.61972i	0.586624	−	0.809860i	$-0.300457\pi$
$824$	13.5215	−	40.6431i	0.471045	−	1.41587i
$825$		−	0.340475i		−	0.0118538i
$826$	−15.9623	+	47.1176i	−0.555400	+	1.63943i
$827$	−51.0385			−1.77478			−0.887392	−	0.461016i	$-0.847485\pi$
$827$	−51.0385			−1.77478			−0.887392	+	0.461016i	$0.847485\pi$
$828$	14.1630	−	4.52875i	0.492198	−	0.157385i
$829$	−14.8970			−0.517393			−0.258696	−	0.965959i	$-0.583293\pi$
$829$	−14.8970			−0.517393			−0.258696	+	0.965959i	$0.583293\pi$
$830$	−13.0285	+	17.8443i	−0.452224	+	0.619384i
$831$	−0.326876			−0.0113392
$832$	−7.35140	−	5.50023i	−0.254864	−	0.190686i
$833$	7.31294	+	10.5073i	0.253379	+	0.364055i
$834$	0.0995832	+	0.0727076i	0.00344828	+	0.00251766i
$835$	9.34952			0.323554
$836$	−5.22188	+	1.66975i	−0.180603	+	0.0577494i
$837$			15.6987i			0.542626i
$838$	−8.83809	+	12.1050i	−0.305307	+	0.418160i
$839$	4.53355			0.156516			0.0782578	−	0.996933i	$-0.475064\pi$
$839$	4.53355			0.156516			0.0782578	+	0.996933i	$0.475064\pi$
$840$	4.39082	+	0.0753363i	0.151498	+	0.00259935i
$841$	−25.8367			−0.890922
$842$	−21.3444	+	29.2341i	−0.735577	+	1.00747i
$843$		−	16.0711i		−	0.553519i
$844$	6.61068	+	20.6739i	0.227549	+	0.711625i
$845$	−11.6829			−0.401903
$846$	10.8233	+	7.90233i	0.372114	+	0.271688i
$847$	26.9189	−	8.44554i	0.924944	−	0.290192i
$848$	12.7406	+	17.8852i	0.437514	+	0.614179i
$849$	−3.07588			−0.105564
$850$	−1.52509	+	2.08882i	−0.0523101	+	0.0716459i
$851$	−12.1832			−0.417635
$852$	−0.405554	−	1.26831i	−0.0138941	−	0.0434515i
$853$	−39.0584			−1.33734			−0.668668	−	0.743561i	$-0.733135\pi$
$853$	−39.0584			−1.33734			−0.668668	+	0.743561i	$0.733135\pi$
$854$	−0.975201	−	0.330375i	−0.0333707	−	0.0113052i
$855$		−	12.5468i		−	0.429092i
$856$	−5.98424	+	17.9875i	−0.204537	+	0.614799i
$857$		−	52.9271i		−	1.80795i	−0.427580	−	0.903977i	$-0.640634\pi$
$857$		−	52.9271i		−	1.80795i	0.427580	−	0.903977i	$-0.359366\pi$
$858$	0.325855	−	0.446304i	0.0111245	−	0.0152366i
$859$			25.8556i			0.882182i	0.897462	+	0.441091i	$0.145408\pi$
$859$			25.8556i			0.882182i	−0.897462	+	0.441091i	$0.854592\pi$
$860$	−2.63338	−	8.23551i	−0.0897977	−	0.280829i
$861$	12.5367	−	3.93327i	0.427250	−	0.134045i
$862$	−27.3032	+	37.3955i	−0.929951	+	1.27370i
$863$			31.9510i			1.08762i	0.839207	+	0.543812i	$0.183020\pi$
$863$			31.9510i			1.08762i	−0.839207	+	0.543812i	$0.816980\pi$
$864$	0.219386	−	18.7733i	0.00746365	−	0.638682i
$865$	23.5706			0.801423
$866$	14.0877	−	19.2951i	0.478721	−	0.655675i
$867$			8.01350i			0.272153i
$868$	−14.4101	−	20.4648i	−0.489111	−	0.694621i
$869$		−	5.80813i		−	0.197027i
$870$	4.96346	+	3.62392i	0.168277	+	0.122862i
$871$	−8.85783			−0.300136
$872$	−30.0994	−	10.0138i	−1.01930	−	0.339108i
$873$			39.7705i			1.34603i
$874$	−15.1077	−	11.0304i	−0.511024	−	0.373109i
$875$	−2.52442	+	0.792014i	−0.0853411	+	0.0267750i
$876$	0.636713	+	1.99122i	0.0215125	+	0.0672772i
$877$		−	40.3185i		−	1.36146i	−0.732534	−	0.680730i	$-0.761663\pi$
$877$		−	40.3185i		−	1.36146i	0.732534	−	0.680730i	$-0.238337\pi$
$878$	−36.1784	−	26.4145i	−1.22096	−	0.891447i
$879$			3.90889i			0.131843i
$880$	1.89020	−	1.34650i	0.0637187	−	0.0453904i
$881$			1.03841i			0.0349848i	0.999847	+	0.0174924i	$0.00556829\pi$
$881$			1.03841i			0.0349848i	−0.999847	+	0.0174924i	$0.994432\pi$
$882$	26.2826	+	0.594786i	0.884982	+	0.0200275i
$883$	31.1810			1.04932			0.524662	−	0.851310i	$-0.324192\pi$
$883$	31.1810			1.04932			0.524662	+	0.851310i	$0.324192\pi$
$884$	−3.99825	+	1.27848i	−0.134476	+	0.0430000i
$885$	7.80238			0.262274
$886$	−14.6545	−	10.6995i	−0.492328	−	0.359458i
$887$	−32.4273			−1.08880			−0.544402	−	0.838825i	$-0.683243\pi$
$887$	−32.4273			−1.08880			−0.544402	+	0.838825i	$0.683243\pi$
$888$	−2.28017	+	6.85377i	−0.0765176	+	0.229997i
$889$	−12.4428	−	39.6594i	−0.417317	−	1.33013i
$890$	12.7918	−	17.5202i	0.428782	−	0.587277i
$891$	−3.49229			−0.116996
$892$	−8.57281	−	26.8101i	−0.287039	−	0.897670i
$893$		−	16.8588i		−	0.564160i
$894$	−5.93518	−	4.33339i	−0.198502	−	0.144930i
$895$	19.7086			0.658787
$896$	16.9464	+	24.6743i	0.566139	+	0.824310i
$897$	1.88549			0.0629548
$898$	10.3955	+	7.58996i	0.346902	+	0.253280i
$899$		−	35.0270i		−	1.16822i
$900$	1.61764	+	5.05892i	0.0539213	+	0.168631i
$901$	10.0397			0.334472
$902$	4.09452	−	5.60801i	0.136333	−	0.186726i
$903$	2.00931	+	6.40438i	0.0668658	+	0.213124i
$904$	−1.25906	+	3.78448i	−0.0418756	+	0.125870i
$905$	−21.0102			−0.698404
$906$	−8.30678	−	6.06494i	−0.275974	−	0.201494i
$907$	48.3550			1.60560			0.802801	−	0.596248i	$-0.203342\pi$
$907$	48.3550			1.60560			0.802801	+	0.596248i	$0.203342\pi$
$908$	28.5142	−	9.11771i	0.946278	−	0.302582i
$909$	−33.9398			−1.12571
$910$	−4.06709	−	1.37783i	−0.134823	−	0.0456747i
$911$		−	48.2821i		−	1.59966i	−0.600229	−	0.799828i	$-0.704924\pi$
$911$		−	48.2821i		−	1.59966i	0.600229	−	0.799828i	$-0.295076\pi$
$912$	−9.03276	+	6.43454i	−0.299105	+	0.213069i
$913$		−	9.06432i		−	0.299985i
$914$	−6.05318	−	4.41954i	−0.200221	−	0.146186i
$915$			0.161487i			0.00533860i
$916$	13.1381	+	41.0874i	0.434095	+	1.35757i
$917$	3.97392	+	12.6663i	0.131231	+	0.418277i
$918$	−6.93261	−	5.06163i	−0.228810	−	0.167059i
$919$		−	6.72784i		−	0.221931i	−0.993824	−	0.110965i	$-0.964606\pi$
$919$		−	6.72784i		−	0.221931i	0.993824	−	0.110965i	$-0.0353943\pi$
$920$	7.51359	+	2.49969i	0.247716	+	0.0824123i
$921$	10.0247			0.330324
$922$	0.863172	+	0.630218i	0.0284270	+	0.0207551i
$923$			1.30206i			0.0428579i
$924$	−1.47308	+	1.03725i	−0.0484606	+	0.0341231i
$925$		−	4.35175i		−	0.143085i
$926$	−3.33109	+	4.56239i	−0.109466	+	0.149929i
$927$	−40.2165			−1.32088
$928$	−0.489495	+	41.8872i	−0.0160685	+	1.37501i
$929$			15.7311i			0.516120i	0.966129	+	0.258060i	$0.0830832\pi$
$929$			15.7311i			0.516120i	−0.966129	+	0.258060i	$0.916917\pi$
$930$	−2.31478	+	3.17042i	−0.0759047	+	0.103962i
$931$	−18.8926	−	27.1450i	−0.619180	−	0.889640i
$932$	−11.9323	−	37.3163i	−0.390854	−	1.22234i
$933$			17.2952i			0.566220i
$934$	−3.25722	+	4.46122i	−0.106580	+	0.145976i
$935$		−	1.06105i		−	0.0347001i
$936$	−2.72125	+	8.17955i	−0.0889467	+	0.267357i
$937$			32.8060i			1.07172i	0.844306	+	0.535862i	$0.180013\pi$
$937$			32.8060i			1.07172i	−0.844306	+	0.535862i	$0.819987\pi$
$938$	27.3518	+	9.26615i	0.893069	+	0.302550i
$939$	15.3530			0.501025
$940$	2.17358	+	6.79754i	0.0708943	+	0.221711i
$941$	10.5674			0.344488			0.172244	−	0.985054i	$-0.444898\pi$
$941$	10.5674			0.344488			0.172244	+	0.985054i	$0.444898\pi$
$942$	7.63869	−	10.4622i	0.248882	−	0.340878i
$943$	23.6921			0.771520
$944$	30.8565	+	43.3162i	1.00429	+	1.40982i
$945$	−2.62862	−	8.37834i	−0.0855092	−	0.272548i
$946$	2.86486	+	2.09169i	0.0931445	+	0.0680066i
$947$	34.2414			1.11269			0.556347	−	0.830950i	$-0.312202\pi$
$947$	34.2414			1.11269			0.556347	+	0.830950i	$0.312202\pi$
$948$	−3.57846	−	11.1911i	−0.116223	−	0.363470i
$949$		−	2.04421i		−	0.0663580i
$950$	3.93998	−	5.39635i	0.127830	−	0.175081i
$951$	3.36065			0.108977
$952$	13.6835	+	0.234778i	0.443485	+	0.00760918i
$953$	−3.54692			−0.114896			−0.0574480	−	0.998348i	$-0.518296\pi$
$953$	−3.54692			−0.114896			−0.0574480	+	0.998348i	$0.518296\pi$
$954$	12.1576	−	16.6516i	0.393618	−	0.539114i
$955$		−	16.9750i		−	0.549299i
$956$	44.3027	−	14.1662i	1.43285	−	0.458168i
$957$	−2.52128			−0.0815013
$958$	10.5201	+	7.68091i	0.339888	+	0.248159i
$959$	37.5388	−	11.7775i	1.21219	−	0.380314i
$960$	2.81244	−	3.75900i	0.0907713	−	0.121321i
$961$	−8.62644			−0.278272
$962$	4.16489	−	5.70440i	0.134282	−	0.183917i
$963$	17.7986			0.573553
$964$	−39.8248	+	12.7344i	−1.28267	+	0.410146i
$965$	14.8445			0.477862
$966$	−5.82216	−	1.97241i	−0.187325	−	0.0634612i
$967$			13.7899i			0.443454i	0.975109	+	0.221727i	$0.0711693\pi$
$967$			13.7899i			0.443454i	−0.975109	+	0.221727i	$0.928831\pi$
$968$	9.52102	−	28.6184i	0.306017	−	0.919830i
$969$			5.07048i			0.162887i
$970$	−12.4888	+	17.1052i	−0.400992	+	0.549214i
$971$			39.0911i			1.25449i	0.778821	+	0.627246i	$0.215818\pi$
$971$			39.0911i			1.25449i	−0.778821	+	0.627246i	$0.784182\pi$
$972$	−25.6963	+	8.21666i	−0.824211	+	0.263549i
$973$	0.117671	+	0.375059i	0.00377236	+	0.0120238i
$974$	−17.8796	+	24.4886i	−0.572899	+	0.784665i
$975$			0.673485i			0.0215688i
$976$	−0.896523	+	0.638643i	−0.0286970	+	0.0204425i
$977$	−18.1910			−0.581982			−0.290991	−	0.956726i	$-0.593985\pi$
$977$	−18.1910			−0.581982			−0.290991	+	0.956726i	$0.593985\pi$
$978$	2.74104	−	3.75424i	0.0876489	−	0.120047i
$979$			8.89968i			0.284435i
$980$	11.1173	+	8.50914i	0.355129	+	0.271815i
$981$			29.7835i			0.950913i
$982$	22.4635	+	16.4010i	0.716838	+	0.523377i
$983$	44.1968			1.40966			0.704830	−	0.709376i	$-0.251023\pi$
$983$	44.1968			1.40966			0.704830	+	0.709376i	$0.251023\pi$
$984$	4.43414	−	13.3282i	0.141355	−	0.424887i
$985$			6.30785i			0.200985i
$986$	15.4681	+	11.2935i	0.492604	+	0.359660i
$987$	−1.65847	−	5.28614i	−0.0527898	−	0.168260i
$988$	10.3293	−	3.30289i	0.328618	−	0.105079i
$989$			12.1031i			0.384857i
$990$	−1.75983	−	1.28488i	−0.0559310	−	0.0408363i
$991$			15.9016i			0.505132i	0.967580	+	0.252566i	$0.0812745\pi$
$991$			15.9016i			0.505132i	−0.967580	+	0.252566i	$0.918726\pi$
$992$	−26.7555	−	0.312665i	−0.849488	−	0.00992714i
$993$			10.3310i			0.327845i
$994$	1.36208	−	4.02060i	0.0432026	−	0.127526i
$995$	11.9770			0.379698
$996$	−5.58464	−	17.4651i	−0.176956	−	0.553403i
$997$	−13.5139			−0.427988			−0.213994	−	0.976835i	$-0.568647\pi$
$997$	−13.5139			−0.427988			−0.213994	+	0.976835i	$0.568647\pi$
$998$	−13.9738	−	10.2026i	−0.442334	−	0.322957i
$999$	14.4431			0.456959

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.h.b.251.14	yes	16
4.3	odd	2		1120.2.h.b.111.7		16
7.6	odd	2		280.2.h.a.251.14	yes	16
8.3	odd	2		280.2.h.a.251.13	✓	16
8.5	even	2		1120.2.h.a.111.7		16
28.27	even	2		1120.2.h.a.111.10		16
56.13	odd	2		1120.2.h.b.111.10		16
56.27	even	2	inner	280.2.h.b.251.13	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.h.a.251.13	✓	16	8.3	odd	2
280.2.h.a.251.14	yes	16	7.6	odd	2
280.2.h.b.251.13	yes	16	56.27	even	2	inner
280.2.h.b.251.14	yes	16	1.1	even	1	trivial
1120.2.h.a.111.7		16	8.5	even	2
1120.2.h.a.111.10		16	28.27	even	2
1120.2.h.b.111.7		16	4.3	odd	2
1120.2.h.b.111.10		16	56.13	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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14218 + 0.833926i) q^{2} +0.586834i q^{3} +(0.609136 + 1.90498i) q^{4} +1.00000 q^{5} +(-0.489376 + 0.670268i) q^{6} +(-2.52442 + 0.792014i) q^{7} +(-0.892871 + 2.68380i) q^{8} +2.65563 q^{9} +O(q^{10})\)	\(q+(1.14218 + 0.833926i) q^{2} +0.586834i q^{3} +(0.609136 + 1.90498i) q^{4} +1.00000 q^{5} +(-0.489376 + 0.670268i) q^{6} +(-2.52442 + 0.792014i) q^{7} +(-0.892871 + 2.68380i) q^{8} +2.65563 q^{9} +(1.14218 + 0.833926i) q^{10} -0.580189 q^{11} +(-1.11791 + 0.357462i) q^{12} +1.14766 q^{13} +(-3.54382 - 1.20056i) q^{14} +0.586834i q^{15} +(-3.25791 + 2.32079i) q^{16} +1.82880i q^{17} +(3.03319 + 2.21459i) q^{18} -4.72462i q^{19} +(0.609136 + 1.90498i) q^{20} +(-0.464781 - 1.48142i) q^{21} +(-0.662679 - 0.483835i) q^{22} -2.79961i q^{23} +(-1.57494 - 0.523967i) q^{24} +1.00000 q^{25} +(1.31083 + 0.957061i) q^{26} +3.31891i q^{27} +(-3.04649 - 4.32653i) q^{28} -7.40518i q^{29} +(-0.489376 + 0.670268i) q^{30} +4.73007 q^{31} +(-5.65647 - 0.0661016i) q^{32} -0.340475i q^{33} +(-1.52509 + 2.08882i) q^{34} +(-2.52442 + 0.792014i) q^{35} +(1.61764 + 5.05892i) q^{36} -4.35175i q^{37} +(3.93998 - 5.39635i) q^{38} +0.673485i q^{39} +(-0.892871 + 2.68380i) q^{40} +8.46264i q^{41} +(0.704530 - 2.07963i) q^{42} -4.32314 q^{43} +(-0.353414 - 1.10525i) q^{44} +2.65563 q^{45} +(2.33466 - 3.19765i) q^{46} +3.56830 q^{47} +(-1.36192 - 1.91185i) q^{48} +(5.74543 - 3.99876i) q^{49} +(1.14218 + 0.833926i) q^{50} -1.07320 q^{51} +(0.699080 + 2.18627i) q^{52} -5.48977i q^{53} +(-2.76773 + 3.79079i) q^{54} -0.580189 q^{55} +(0.128378 - 7.48221i) q^{56} +2.77257 q^{57} +(6.17537 - 8.45803i) q^{58} -13.2957i q^{59} +(-1.11791 + 0.357462i) q^{60} +0.275184 q^{61} +(5.40258 + 3.94453i) q^{62} +(-6.70392 + 2.10329i) q^{63} +(-6.40556 - 4.79257i) q^{64} +1.14766 q^{65} +(0.283931 - 0.388882i) q^{66} -7.71818 q^{67} +(-3.48384 + 1.11399i) q^{68} +1.64291 q^{69} +(-3.54382 - 1.20056i) q^{70} +1.13454i q^{71} +(-2.37113 + 7.12717i) q^{72} -1.78121i q^{73} +(3.62904 - 4.97047i) q^{74} +0.586834i q^{75} +(9.00031 - 2.87794i) q^{76} +(1.46464 - 0.459518i) q^{77} +(-0.561636 + 0.769239i) q^{78} +10.0108i q^{79} +(-3.25791 + 2.32079i) q^{80} +6.01923 q^{81} +(-7.05721 + 9.66583i) q^{82} +15.6230i q^{83} +(2.53896 - 1.78778i) q^{84} +1.82880i q^{85} +(-4.93780 - 3.60518i) q^{86} +4.34561 q^{87} +(0.518034 - 1.55711i) q^{88} -15.3393i q^{89} +(3.03319 + 2.21459i) q^{90} +(-2.89717 + 0.908961i) q^{91} +(5.33320 - 1.70534i) q^{92} +2.77577i q^{93} +(4.07563 + 2.97569i) q^{94} -4.72462i q^{95} +(0.0387907 - 3.31941i) q^{96} +14.9759i q^{97} +(9.89696 + 0.223972i) q^{98} -1.54077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9	\( 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9} + q^{10} - 4 q^{11} + 14 q^{12} - q^{14} + 9 q^{16} - 15 q^{18} + q^{20} - 4 q^{21} + 6 q^{22} + 22 q^{24} + 16 q^{25} - 20 q^{26} + q^{28} - 16 q^{31} - 19 q^{32} - 14 q^{34} + 15 q^{36} - 30 q^{38} + q^{40} + 44 q^{42} - 4 q^{43} - 20 q^{44} - 16 q^{45} + 6 q^{46} - 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} - 38 q^{52} + 26 q^{54} - 4 q^{55} + 33 q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} - 8 q^{61} + 28 q^{62} + 28 q^{63} - 23 q^{64} + 46 q^{66} + 20 q^{67} + 12 q^{68} - 40 q^{69} - q^{70} - 13 q^{72} - 28 q^{74} + 34 q^{76} - 4 q^{77} - 6 q^{78} + 9 q^{80} + 24 q^{81} - 16 q^{82} - 42 q^{84} - 24 q^{86} + 72 q^{87} - 44 q^{88} - 15 q^{90} - 32 q^{91} - 30 q^{92} - 58 q^{94} - 30 q^{96} + 5 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9 + q^10 - 4 * q^11 + 14 * q^12 - q^14 + 9 * q^16 - 15 * q^18 + q^20 - 4 * q^21 + 6 * q^22 + 22 * q^24 + 16 * q^25 - 20 * q^26 + q^28 - 16 * q^31 - 19 * q^32 - 14 * q^34 + 15 * q^36 - 30 * q^38 + q^40 + 44 * q^42 - 4 * q^43 - 20 * q^44 - 16 * q^45 + 6 * q^46 - 34 * q^48 - 8 * q^49 + q^50 - 40 * q^51 - 38 * q^52 + 26 * q^54 - 4 * q^55 + 33 * q^56 - 16 * q^57 + 18 * q^58 + 14 * q^60 - 8 * q^61 + 28 * q^62 + 28 * q^63 - 23 * q^64 + 46 * q^66 + 20 * q^67 + 12 * q^68 - 40 * q^69 - q^70 - 13 * q^72 - 28 * q^74 + 34 * q^76 - 4 * q^77 - 6 * q^78 + 9 * q^80 + 24 * q^81 - 16 * q^82 - 42 * q^84 - 24 * q^86 + 72 * q^87 - 44 * q^88 - 15 * q^90 - 32 * q^91 - 30 * q^92 - 58 * q^94 - 30 * q^96 + 5 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

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