LMFDB - Embedded newform 280.2.h.b.251.13

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

$q$-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	$-0.945816\pi$
$3$		−	0.586834i		−	0.338809i	0.985547	−	0.169404i	$-0.0541844\pi$
$4$	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	$-0.928815\pi$
$17$		−	1.82880i		−	0.443550i	0.975098	−	0.221775i	$-0.0711851\pi$
$18$	3.03319	−	2.21459i	0.714931	−	0.521985i
$19$			4.72462i			1.08390i	0.840410	+	0.541951i	$0.182314\pi$
$19$			4.72462i			1.08390i	−0.840410	+	0.541951i	$0.817686\pi$
$20$	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	$0.0942806\pi$
$23$			2.79961i			0.583759i	−0.956455	+	0.291879i	$0.905719\pi$
$24$	−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	$0.241316\pi$
$29$			7.40518i			1.37511i	−0.726133	+	0.687554i	$0.758684\pi$
$30$	−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	$0.116443\pi$
$37$			4.35175i			0.715423i	−0.933832	+	0.357712i	$0.883557\pi$
$38$	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	$-0.770208\pi$
$41$		−	8.46264i		−	1.32164i	0.750544	−	0.660821i	$-0.229792\pi$
$42$	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	$0.123058\pi$
$53$			5.48977i			0.754079i	−0.926197	+	0.377039i	$0.876942\pi$
$54$	−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	$0.332985\pi$
$59$			13.2957i			1.73095i	−0.500948	+	0.865477i	$0.667015\pi$
$60$	−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	$-0.978554\pi$
$71$		−	1.13454i		−	0.134645i	0.997731	−	0.0673224i	$-0.0214456\pi$
$72$	−2.37113	−	7.12717i	−0.279440	−	0.839945i
$73$			1.78121i			0.208474i	0.994552	+	0.104237i	$0.0332401\pi$
$73$			1.78121i			0.208474i	−0.994552	+	0.104237i	$0.966760\pi$
$74$	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	$-0.809590\pi$
$79$		−	10.0108i		−	1.12630i	0.826355	−	0.563149i	$-0.190410\pi$
$80$	−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	$-0.672062\pi$
$83$		−	15.6230i		−	1.71485i	0.514607	−	0.857426i	$-0.327938\pi$
$84$	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	$0.302156\pi$
$89$			15.3393i			1.62596i	−0.582293	+	0.812979i	$0.697844\pi$
$90$	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	$-0.725057\pi$
$97$		−	14.9759i		−	1.52058i	0.649585	−	0.760289i	$-0.274943\pi$
$98$	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	$-0.819515\pi$
$109$		−	11.2152i		−	1.07422i	0.843511	−	0.537112i	$-0.180485\pi$
$110$	−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	$-0.754504\pi$
$127$		−	15.7103i		−	1.39406i	0.717041	−	0.697031i	$-0.245496\pi$
$128$	−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	$0.0703415\pi$
$131$			5.01749i			0.438380i	−0.975682	+	0.219190i	$0.929658\pi$
$132$	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	$0.00200564\pi$
$139$			0.148572i			0.0126017i	−0.999980	+	0.00630086i	$0.997994\pi$
$140$	−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	$-0.881851\pi$
$149$		−	8.85493i		−	0.725424i	0.931901	−	0.362712i	$-0.118149\pi$
$150$	−0.489376	−	0.670268i	−0.0399574	−	0.0547272i
$151$		−	12.3932i		−	1.00855i	−0.863544	−	0.504273i	$-0.831761\pi$
$151$		−	12.3932i		−	1.00855i	0.863544	−	0.504273i	$-0.168239\pi$
$152$	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	$0.210495\pi$
$191$			16.9750i			1.22827i	−0.789201	+	0.614135i	$0.789505\pi$
$192$	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	$-0.927857\pi$
$197$		−	6.30785i		−	0.449416i	0.974426	−	0.224708i	$-0.0721428\pi$
$198$	−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	$0.165469\pi$
$227$			14.9683i			0.993478i	−0.867900	+	0.496739i	$0.834531\pi$
$228$	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	$0.270988\pi$
$239$			23.2562i			1.50432i	−0.658981	+	0.752160i	$0.729012\pi$
$240$	−1.36192	+	1.91185i	−0.0879113	+	0.123409i
$241$		−	20.9056i		−	1.34665i	−0.739347	−	0.673324i	$-0.764866\pi$
$241$		−	20.9056i		−	1.34665i	0.739347	−	0.673324i	$-0.235134\pi$
$242$	−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	$-0.966418\pi$
$251$		−	3.33668i		−	0.210610i	0.994440	−	0.105305i	$-0.0335818\pi$
$252$	−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	$0.275605\pi$
$257$			24.4200i			1.52328i	−0.648002	+	0.761639i	$0.724395\pi$
$258$	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	$0.315041\pi$
$263$			27.1113i			1.67176i	−0.548915	+	0.835878i	$0.684959\pi$
$264$	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	$-0.994673\pi$
$277$		−	0.557017i		−	0.0334679i	0.999860	−	0.0167340i	$-0.00532683\pi$
$278$	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	$-0.950209\pi$
$283$		−	5.24149i		−	0.311574i	0.987791	−	0.155787i	$-0.0497914\pi$
$284$	−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	$0.162083\pi$
$307$			17.0826i			0.974957i	−0.873135	+	0.487479i	$0.837917\pi$
$308$	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	$0.264887\pi$
$313$			26.1624i			1.47879i	−0.673275	+	0.739393i	$0.735113\pi$
$314$	−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	$0.0514149\pi$
$317$			5.72675i			0.321646i	−0.986983	+	0.160823i	$0.948585\pi$
$318$	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	$-0.948269\pi$
$353$		−	6.08004i		−	0.323608i	0.986823	−	0.161804i	$-0.0517312\pi$
$354$	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	$-0.857669\pi$
$359$		−	16.3854i		−	0.864787i	0.901685	−	0.432394i	$-0.142331\pi$
$360$	−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	$-0.995448\pi$
$373$		−	0.552362i		−	0.0286002i	0.999898	−	0.0143001i	$-0.00455202\pi$
$374$	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	$-0.888492\pi$
$389$		−	13.5376i		−	0.686385i	0.939265	−	0.343192i	$-0.111508\pi$
$390$	−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	$-0.760296\pi$
$409$		−	27.6608i		−	1.36774i	0.729605	−	0.683868i	$-0.239704\pi$
$410$	−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	$-0.916647\pi$
$419$		−	10.5982i		−	0.517755i	0.965910	−	0.258877i	$-0.0833526\pi$
$420$	2.53896	+	1.78778i	0.123888	+	0.0872349i
$421$		−	25.5951i		−	1.24743i	−0.781652	−	0.623715i	$-0.785623\pi$
$421$		−	25.5951i		−	1.24743i	0.781652	−	0.623715i	$-0.214377\pi$
$422$	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	$-0.710843\pi$
$431$		−	32.7406i		−	1.57706i	0.614997	−	0.788529i	$-0.289157\pi$
$432$	−7.70249	+	10.8127i	−0.370586	+	0.520227i
$433$			16.8933i			0.811840i	0.913909	+	0.405920i	$0.133049\pi$
$433$			16.8933i			0.811840i	−0.913909	+	0.405920i	$0.866951\pi$
$434$	−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	$-0.970412\pi$
$463$		−	3.99447i		−	0.185639i	0.995683	−	0.0928193i	$-0.0295879\pi$
$464$	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	$-0.971195\pi$
$467$		−	3.90589i		−	0.180743i	0.995908	−	0.0903716i	$-0.0288055\pi$
$468$	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	$-0.838537\pi$
$487$		−	21.4403i		−	0.971552i	0.874083	−	0.485776i	$-0.161463\pi$
$488$	−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	$-0.909435\pi$
$521$		−	12.8139i		−	0.561388i	0.959797	−	0.280694i	$-0.0905646\pi$
$522$	16.3995	+	22.4614i	0.717786	+	0.983107i
$523$			8.05393i			0.352174i	0.984375	+	0.176087i	$0.0563439\pi$
$523$			8.05393i			0.352174i	−0.984375	+	0.176087i	$0.943656\pi$
$524$	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	$0.111107\pi$
$541$			15.9099i			0.684018i	−0.939697	+	0.342009i	$0.888893\pi$
$542$	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	$-0.783455\pi$
$557$		−	29.6910i		−	1.25805i	0.777386	−	0.629024i	$-0.216545\pi$
$558$	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	$0.182948\pi$
$563$			25.7978i			1.08725i	−0.839329	+	0.543624i	$0.817052\pi$
$564$	−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	$-0.612718\pi$
$577$		−	45.0609i		−	1.87591i	0.346760	−	0.937954i	$-0.387282\pi$
$578$	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	$0.00485278\pi$
$587$			0.738708i			0.0304897i	−0.999884	+	0.0152449i	$0.995147\pi$
$588$	−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	$0.0361522\pi$
$593$			5.51961i			0.226663i	−0.993557	+	0.113332i	$0.963848\pi$
$594$	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	$-0.999052\pi$
$599$		−	0.145815i		−	0.00595785i	0.999996	−	0.00297893i	$-0.000948223\pi$
$600$	−1.57494	+	0.523967i	−0.0642969	+	0.0213909i
$601$			21.7269i			0.886257i	0.896458	+	0.443128i	$0.146131\pi$
$601$			21.7269i			0.886257i	−0.896458	+	0.443128i	$0.853869\pi$
$602$	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	$0.401664\pi$
$613$			47.1735i			1.90532i	−0.304041	+	0.952659i	$0.598336\pi$
$614$	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	$-0.792148\pi$
$619$		−	30.2319i		−	1.21512i	0.794273	−	0.607561i	$-0.207852\pi$
$620$	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	$0.0398619\pi$
$631$			6.27504i			0.249806i	−0.992169	+	0.124903i	$0.960138\pi$
$632$	−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	$0.199268\pi$
$643$			29.7150i			1.17184i	−0.810367	+	0.585922i	$0.800732\pi$
$644$	−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	$0.0198521\pi$
$653$			3.18538i			0.124653i	−0.998056	+	0.0623267i	$0.980148\pi$
$654$	−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	$-0.894715\pi$
$691$		−	17.0740i		−	0.649526i	0.945795	−	0.324763i	$-0.105285\pi$
$692$	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	$-0.787912\pi$
$701$		−	32.7289i		−	1.23615i	0.786118	−	0.618076i	$-0.212088\pi$
$702$	−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	$-0.871334\pi$
$709$		−	20.9447i		−	0.786594i	0.919412	−	0.393297i	$-0.128666\pi$
$710$	−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	$-0.960476\pi$
$743$		−	6.75171i		−	0.247696i	0.992301	−	0.123848i	$-0.0395235\pi$
$744$	−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	$0.166718\pi$
$751$			27.4120i			1.00028i	−0.865945	+	0.500139i	$0.833282\pi$
$752$	−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	$0.167612\pi$
$757$			27.6550i			1.00514i	−0.864537	+	0.502570i	$0.832388\pi$
$758$	−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	$-0.917690\pi$
$761$		−	14.1083i		−	0.511424i	0.966753	−	0.255712i	$-0.0823099\pi$
$762$	−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	$-0.983773\pi$
$769$		−	2.82610i		−	0.101912i	0.998701	−	0.0509558i	$-0.0162268\pi$
$770$	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	$-0.817908\pi$
$787$		−	30.3744i		−	1.08273i	0.840788	−	0.541365i	$-0.182092\pi$
$788$	−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	$-0.960599\pi$
$811$		−	7.03219i		−	0.246934i	0.992349	−	0.123467i	$-0.0394012\pi$
$812$	−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	$0.0403481\pi$
$821$			7.24453i			0.252836i	−0.991977	+	0.126418i	$0.959652\pi$
$822$	7.27715	+	9.96706i	0.253820	+	0.347641i
$823$			46.4665i			1.61972i	0.586624	+	0.809860i	$0.300457\pi$
$823$			46.4665i			1.61972i	−0.586624	+	0.809860i	$0.699543\pi$
$824$	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	$0.359366\pi$
$857$			52.9271i			1.80795i	−0.427580	+	0.903977i	$0.640634\pi$
$858$	0.325855	+	0.446304i	0.0111245	+	0.0152366i
$859$		−	25.8556i		−	0.882182i	−0.897462	−	0.441091i	$-0.854592\pi$
$859$		−	25.8556i		−	0.882182i	0.897462	−	0.441091i	$-0.145408\pi$
$860$	−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	$-0.816980\pi$
$863$		−	31.9510i		−	1.08762i	0.839207	−	0.543812i	$-0.183020\pi$
$864$	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	$0.238337\pi$
$877$			40.3185i			1.36146i	−0.732534	+	0.680730i	$0.761663\pi$
$878$	−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	$-0.994432\pi$
$881$		−	1.03841i		−	0.0349848i	0.999847	−	0.0174924i	$-0.00556829\pi$
$882$	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	$0.295076\pi$
$911$			48.2821i			1.59966i	−0.600229	+	0.799828i	$0.704924\pi$
$912$	−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	$0.0353943\pi$
$919$			6.72784i			0.221931i	−0.993824	+	0.110965i	$0.964606\pi$
$920$	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	$-0.916917\pi$
$929$		−	15.7311i		−	0.516120i	0.966129	−	0.258060i	$-0.0830832\pi$
$930$	−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	$-0.819987\pi$
$937$		−	32.8060i		−	1.07172i	0.844306	−	0.535862i	$-0.180013\pi$
$938$	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	$-0.928831\pi$
$967$		−	13.7899i		−	0.443454i	0.975109	−	0.221727i	$-0.0711693\pi$
$968$	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	$-0.784182\pi$
$971$		−	39.0911i		−	1.25449i	0.778821	−	0.627246i	$-0.215818\pi$
$972$	−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	$-0.918726\pi$
$991$		−	15.9016i		−	0.505132i	0.967580	−	0.252566i	$-0.0812745\pi$
$992$	−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.251.13	yes	16
4.3	odd	2		1120.2.h.b.111.10		16
7.6	odd	2		280.2.h.a.251.13	✓	16
8.3	odd	2		280.2.h.a.251.14	yes	16
8.5	even	2		1120.2.h.a.111.10		16
28.27	even	2		1120.2.h.a.111.7		16
56.13	odd	2		1120.2.h.b.111.7		16
56.27	even	2	inner	280.2.h.b.251.14	yes	16

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

Varieties

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