LMFDB - Embedded newform 280.2.b.d.141.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(141,280)]

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([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("280.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.b (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:	$12$
Coefficient field:	12.0.8272021826830336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 4x^{9} + 4x^{8} - 12x^{7} + 10x^{6} - 24x^{5} + 16x^{4} - 32x^{3} + 48x^{2} + 64 $ x^12 + 3x^10 - 4x^9 + 4x^8 - 12x^7 + 10x^6 - 24x^5 + 16x^4 - 32x^3 + 48*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			141.7
Root			$1.39608 + 0.225774i$ of defining polynomial
Character	$\chi$	$=$	280.141
Dual form			280.2.b.d.141.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.225774 - 1.39608i) q^{2} +2.07981i q^{3} +(-1.89805 + 0.630396i) q^{4} -1.00000i q^{5} +(2.90357 - 0.469568i) q^{6} +1.00000 q^{7} +(1.30861 + 2.50750i) q^{8} -1.32561 q^{9} +O(q^{10})$	\(q+(-0.225774 - 1.39608i) q^{2} +2.07981i q^{3} +(-1.89805 + 0.630396i) q^{4} -1.00000i q^{5} +(2.90357 - 0.469568i) q^{6} +1.00000 q^{7} +(1.30861 + 2.50750i) q^{8} -1.32561 q^{9} +(-1.39608 + 0.225774i) q^{10} +5.25869i q^{11} +(-1.31110 - 3.94759i) q^{12} +1.61722i q^{13} +(-0.225774 - 1.39608i) q^{14} +2.07981 q^{15} +(3.20520 - 2.39305i) q^{16} +1.92810 q^{17} +(0.299289 + 1.85065i) q^{18} +2.71629i q^{19} +(0.630396 + 1.89805i) q^{20} +2.07981i q^{21} +(7.34153 - 1.18728i) q^{22} +3.77110 q^{23} +(-5.21512 + 2.72166i) q^{24} -1.00000 q^{25} +(2.25776 - 0.365127i) q^{26} +3.48241i q^{27} +(-1.89805 + 0.630396i) q^{28} +1.73339i q^{29} +(-0.469568 - 2.90357i) q^{30} +4.86801 q^{31} +(-4.06453 - 3.93441i) q^{32} -10.9371 q^{33} +(-0.435315 - 2.69177i) q^{34} -1.00000i q^{35} +(2.51608 - 0.835659i) q^{36} -7.77110i q^{37} +(3.79215 - 0.613269i) q^{38} -3.36352 q^{39} +(2.50750 - 1.30861i) q^{40} -9.39750 q^{41} +(2.90357 - 0.469568i) q^{42} -12.9818i q^{43} +(-3.31506 - 9.98127i) q^{44} +1.32561i q^{45} +(-0.851419 - 5.26475i) q^{46} -7.83744 q^{47} +(4.97709 + 6.66621i) q^{48} +1.00000 q^{49} +(0.225774 + 1.39608i) q^{50} +4.01008i q^{51} +(-1.01949 - 3.06957i) q^{52} -3.07483i q^{53} +(4.86171 - 0.786240i) q^{54} +5.25869 q^{55} +(1.30861 + 2.50750i) q^{56} -5.64938 q^{57} +(2.41994 - 0.391354i) q^{58} +9.60638i q^{59} +(-3.94759 + 1.31110i) q^{60} +2.70839i q^{61} +(-1.09907 - 6.79610i) q^{62} -1.32561 q^{63} +(-4.57507 + 6.56268i) q^{64} +1.61722 q^{65} +(2.46931 + 15.2690i) q^{66} -10.5374i q^{67} +(-3.65963 + 1.21546i) q^{68} +7.84318i q^{69} +(-1.39608 + 0.225774i) q^{70} +0.391947 q^{71} +(-1.73471 - 3.32396i) q^{72} +2.39195 q^{73} +(-10.8490 + 1.75452i) q^{74} -2.07981i q^{75} +(-1.71234 - 5.15567i) q^{76} +5.25869i q^{77} +(0.759396 + 4.69572i) q^{78} +15.9647 q^{79} +(-2.39305 - 3.20520i) q^{80} -11.2196 q^{81} +(2.12171 + 13.1196i) q^{82} -4.52158i q^{83} +(-1.31110 - 3.94759i) q^{84} -1.92810i q^{85} +(-18.1236 + 2.93096i) q^{86} -3.60511 q^{87} +(-13.1861 + 6.88158i) q^{88} +2.27852 q^{89} +(1.85065 - 0.299289i) q^{90} +1.61722i q^{91} +(-7.15775 + 2.37729i) q^{92} +10.1245i q^{93} +(1.76949 + 10.9417i) q^{94} +2.71629 q^{95} +(8.18283 - 8.45345i) q^{96} +11.0129 q^{97} +(-0.225774 - 1.39608i) q^{98} -6.97097i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9	$ 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9} + 16 q^{12} - 2 q^{14} + 2 q^{16} - 2 q^{18} + 4 q^{20} + 12 q^{22} + 8 q^{23} - 24 q^{24} - 12 q^{25} + 6 q^{28} + 12 q^{30} + 24 q^{31} - 2 q^{32} - 24 q^{33} - 20 q^{34} - 18 q^{36} + 12 q^{38} - 48 q^{39} + 12 q^{40} - 16 q^{41} + 16 q^{44} - 48 q^{46} - 16 q^{47} + 20 q^{48} + 12 q^{49} + 2 q^{50} + 4 q^{52} + 44 q^{54} - 8 q^{55} + 10 q^{56} + 40 q^{57} + 4 q^{58} - 8 q^{60} + 8 q^{62} - 20 q^{63} - 6 q^{64} + 8 q^{65} + 64 q^{66} - 56 q^{68} - 32 q^{71} - 46 q^{72} - 8 q^{73} - 32 q^{74} - 12 q^{76} - 24 q^{78} + 8 q^{80} + 60 q^{81} - 28 q^{82} + 16 q^{84} - 76 q^{86} + 48 q^{87} - 40 q^{88} - 48 q^{89} + 24 q^{90} + 12 q^{94} + 28 q^{96} + 32 q^{97} - 2 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9 + 16 * q^12 - 2 * q^14 + 2 * q^16 - 2 * q^18 + 4 * q^20 + 12 * q^22 + 8 * q^23 - 24 * q^24 - 12 * q^25 + 6 * q^28 + 12 * q^30 + 24 * q^31 - 2 * q^32 - 24 * q^33 - 20 * q^34 - 18 * q^36 + 12 * q^38 - 48 * q^39 + 12 * q^40 - 16 * q^41 + 16 * q^44 - 48 * q^46 - 16 * q^47 + 20 * q^48 + 12 * q^49 + 2 * q^50 + 4 * q^52 + 44 * q^54 - 8 * q^55 + 10 * q^56 + 40 * q^57 + 4 * q^58 - 8 * q^60 + 8 * q^62 - 20 * q^63 - 6 * q^64 + 8 * q^65 + 64 * q^66 - 56 * q^68 - 32 * q^71 - 46 * q^72 - 8 * q^73 - 32 * q^74 - 12 * q^76 - 24 * q^78 + 8 * q^80 + 60 * q^81 - 28 * q^82 + 16 * q^84 - 76 * q^86 + 48 * q^87 - 40 * q^88 - 48 * q^89 + 24 * q^90 + 12 * q^94 + 28 * q^96 + 32 * q^97 - 2 * q^98

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 $

$2$	−0.225774	−	1.39608i	−0.159647	−	0.987174i
$2$	−0.225774	−	1.39608i	−0.159647	−	0.987174i
$3$			2.07981i			1.20078i	0.799708	+	0.600389i	$0.204988\pi$
$3$			2.07981i			1.20078i	−0.799708	+	0.600389i	$0.795012\pi$
$4$	−1.89805	+	0.630396i	−0.949026	+	0.315198i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	2.90357	−	0.469568i	1.18538	−	0.191700i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	1.30861	+	2.50750i	0.462664	+	0.886534i
$9$	−1.32561			−0.441870
$10$	−1.39608	+	0.225774i	−0.441478	+	0.0713961i
$11$			5.25869i			1.58556i	0.609511	+	0.792778i	$0.291366\pi$
$11$			5.25869i			1.58556i	−0.609511	+	0.792778i	$0.708634\pi$
$12$	−1.31110	−	3.94759i	−0.378483	−	1.13957i
$13$			1.61722i			0.448537i	0.974527	+	0.224268i	$0.0719992\pi$
$13$			1.61722i			0.448537i	−0.974527	+	0.224268i	$0.928001\pi$
$14$	−0.225774	−	1.39608i	−0.0603407	−	0.373117i
$15$	2.07981			0.537005
$16$	3.20520	−	2.39305i	0.801301	−	0.598262i
$17$	1.92810			0.467632			0.233816	−	0.972281i	$-0.424879\pi$
$17$	1.92810			0.467632			0.233816	+	0.972281i	$0.424879\pi$
$18$	0.299289	+	1.85065i	0.0705430	+	0.436203i
$19$			2.71629i			0.623161i	0.950220	+	0.311580i	$0.100858\pi$
$19$			2.71629i			0.623161i	−0.950220	+	0.311580i	$0.899142\pi$
$20$	0.630396	+	1.89805i	0.140961	+	0.424417i
$21$			2.07981i			0.453852i
$22$	7.34153	−	1.18728i	1.56522	−	0.253128i
$23$	3.77110			0.786330			0.393165	−	0.919468i	$-0.371380\pi$
$23$	3.77110			0.786330			0.393165	+	0.919468i	$0.371380\pi$
$24$	−5.21512	+	2.72166i	−1.06453	+	0.555557i
$25$	−1.00000			−0.200000
$26$	2.25776	−	0.365127i	0.442784	−	0.0716074i
$27$			3.48241i			0.670191i
$28$	−1.89805	+	0.630396i	−0.358698	+	0.119134i
$29$			1.73339i			0.321882i	0.986964	+	0.160941i	$0.0514529\pi$
$29$			1.73339i			0.321882i	−0.986964	+	0.160941i	$0.948547\pi$
$30$	−0.469568	−	2.90357i	−0.0857309	−	0.530117i
$31$	4.86801			0.874320			0.437160	−	0.899384i	$-0.355984\pi$
$31$	4.86801			0.874320			0.437160	+	0.899384i	$0.355984\pi$
$32$	−4.06453	−	3.93441i	−0.718514	−	0.695513i
$33$	−10.9371			−1.90390
$34$	−0.435315	−	2.69177i	−0.0746559	−	0.461634i
$35$		−	1.00000i		−	0.169031i
$36$	2.51608	−	0.835659i	0.419346	−	0.139276i
$37$		−	7.77110i		−	1.27756i	−0.769389	−	0.638781i	$-0.779439\pi$
$37$		−	7.77110i		−	1.27756i	0.769389	−	0.638781i	$-0.220561\pi$
$38$	3.79215	−	0.613269i	0.615168	−	0.0994854i
$39$	−3.36352			−0.538594
$40$	2.50750	−	1.30861i	0.396470	−	0.206910i
$41$	−9.39750			−1.46764			−0.733821	−	0.679343i	$-0.762265\pi$
$41$	−9.39750			−1.46764			−0.733821	+	0.679343i	$0.762265\pi$
$42$	2.90357	−	0.469568i	0.448031	−	0.0724559i
$43$		−	12.9818i		−	1.97971i	−0.142096	−	0.989853i	$-0.545384\pi$
$43$		−	12.9818i		−	1.97971i	0.142096	−	0.989853i	$-0.454616\pi$
$44$	−3.31506	−	9.98127i	−0.499764	−	1.50473i
$45$			1.32561i			0.197610i
$46$	−0.851419	−	5.26475i	−0.125535	−	0.776244i
$47$	−7.83744			−1.14321			−0.571604	−	0.820529i	$-0.693679\pi$
$47$	−7.83744			−1.14321			−0.571604	+	0.820529i	$0.693679\pi$
$48$	4.97709	+	6.66621i	0.718380	+	0.962185i
$49$	1.00000			0.142857
$50$	0.225774	+	1.39608i	0.0319293	+	0.197435i
$51$			4.01008i			0.561523i
$52$	−1.01949	−	3.06957i	−0.141378	−	0.425673i
$53$		−	3.07483i		−	0.422360i	−0.977447	−	0.211180i	$-0.932269\pi$
$53$		−	3.07483i		−	0.422360i	0.977447	−	0.211180i	$-0.0677306\pi$
$54$	4.86171	−	0.786240i	0.661595	−	0.106994i
$55$	5.25869			0.709082
$56$	1.30861	+	2.50750i	0.174871	+	0.335078i
$57$	−5.64938			−0.748278
$58$	2.41994	−	0.391354i	0.317753	−	0.0513873i
$59$			9.60638i			1.25064i	0.780367	+	0.625322i	$0.215032\pi$
$59$			9.60638i			1.25064i	−0.780367	+	0.625322i	$0.784968\pi$
$60$	−3.94759	+	1.31110i	−0.509631	+	0.169263i
$61$			2.70839i			0.346773i	0.984854	+	0.173387i	$0.0554710\pi$
$61$			2.70839i			0.346773i	−0.984854	+	0.173387i	$0.944529\pi$
$62$	−1.09907	−	6.79610i	−0.139582	−	0.863106i
$63$	−1.32561			−0.167011
$64$	−4.57507	+	6.56268i	−0.571884	+	0.820334i
$65$	1.61722			0.200592
$66$	2.46931	+	15.2690i	0.303951	+	1.87948i
$67$		−	10.5374i		−	1.28735i	−0.765300	−	0.643674i	$-0.777409\pi$
$67$		−	10.5374i		−	1.28735i	0.765300	−	0.643674i	$-0.222591\pi$
$68$	−3.65963	+	1.21546i	−0.443795	+	0.147397i
$69$			7.84318i			0.944208i
$70$	−1.39608	+	0.225774i	−0.166863	+	0.0269852i
$71$	0.391947			0.0465156			0.0232578	−	0.999730i	$-0.492596\pi$
$71$	0.391947			0.0465156			0.0232578	+	0.999730i	$0.492596\pi$
$72$	−1.73471	−	3.32396i	−0.204437	−	0.391733i
$73$	2.39195			0.279956			0.139978	−	0.990155i	$-0.455297\pi$
$73$	2.39195			0.279956			0.139978	+	0.990155i	$0.455297\pi$
$74$	−10.8490	+	1.75452i	−1.26118	+	0.203958i
$75$		−	2.07981i		−	0.240156i
$76$	−1.71234	−	5.15567i	−0.196419	−	0.591396i
$77$			5.25869i			0.599283i
$78$	0.759396	+	4.69572i	0.0859846	+	0.531686i
$79$	15.9647			1.79617			0.898085	−	0.439822i	$-0.144959\pi$
$79$	15.9647			1.79617			0.898085	+	0.439822i	$0.144959\pi$
$80$	−2.39305	−	3.20520i	−0.267551	−	0.358352i
$81$	−11.2196			−1.24662
$82$	2.12171	+	13.1196i	0.234304	+	1.44882i
$83$		−	4.52158i		−	0.496308i	−0.968721	−	0.248154i	$-0.920176\pi$
$83$		−	4.52158i		−	0.496308i	0.968721	−	0.248154i	$-0.0798239\pi$
$84$	−1.31110	−	3.94759i	−0.143053	−	0.430717i
$85$		−	1.92810i		−	0.209131i
$86$	−18.1236	+	2.93096i	−1.95431	+	0.316053i
$87$	−3.60511			−0.386509
$88$	−13.1861	+	6.88158i	−1.40565	+	0.733579i
$89$	2.27852			0.241522			0.120761	−	0.992682i	$-0.461466\pi$
$89$	2.27852			0.241522			0.120761	+	0.992682i	$0.461466\pi$
$90$	1.85065	−	0.299289i	0.195076	−	0.0315478i
$91$			1.61722i			0.169531i
$92$	−7.15775	+	2.37729i	−0.746247	+	0.247849i
$93$			10.1245i			1.04986i
$94$	1.76949	+	10.9417i	0.182509	+	1.12855i
$95$	2.71629			0.278686
$96$	8.18283	−	8.45345i	0.835157	−	0.862776i
$97$	11.0129			1.11819			0.559095	−	0.829104i	$-0.311149\pi$
$97$	11.0129			1.11819			0.559095	+	0.829104i	$0.311149\pi$
$98$	−0.225774	−	1.39608i	−0.0228067	−	0.141025i
$99$		−	6.97097i		−	0.700609i
$100$	1.89805	−	0.630396i	0.189805	−	0.0630396i
$101$		−	16.8522i		−	1.67685i	−0.545015	−	0.838426i	$-0.683476\pi$
$101$		−	16.8522i		−	1.67685i	0.545015	−	0.838426i	$-0.316524\pi$
$102$	5.59837	−	0.905372i	0.554321	−	0.0896452i
$103$	−14.4660			−1.42537			−0.712686	−	0.701483i	$-0.752522\pi$
$103$	−14.4660			−1.42537			−0.712686	+	0.701483i	$0.752522\pi$
$104$	−4.05518	+	2.11632i	−0.397643	+	0.207522i
$105$	2.07981			0.202969
$106$	−4.29269	+	0.694217i	−0.416943	+	0.0674283i
$107$		−	0.945190i		−	0.0913749i	−0.998956	−	0.0456875i	$-0.985452\pi$
$107$		−	0.945190i		−	0.0913749i	0.998956	−	0.0456875i	$-0.0145478\pi$
$108$	−2.19530	−	6.60980i	−0.211243	−	0.636028i
$109$			1.22597i			0.117427i	0.998275	+	0.0587135i	$0.0186998\pi$
$109$			1.22597i			0.117427i	−0.998275	+	0.0587135i	$0.981300\pi$
$110$	−1.18728	−	7.34153i	−0.113202	−	0.699987i
$111$	16.1624			1.53407
$112$	3.20520	−	2.39305i	0.302863	−	0.226122i
$113$	−2.33225			−0.219400			−0.109700	−	0.993965i	$-0.534989\pi$
$113$	−2.33225			−0.219400			−0.109700	+	0.993965i	$0.534989\pi$
$114$	1.27548	+	7.88695i	0.119460	+	0.738681i
$115$		−	3.77110i		−	0.351657i
$116$	−1.09272	−	3.29006i	−0.101456	−	0.305474i
$117$		−	2.14381i		−	0.198195i
$118$	13.4112	−	2.16887i	1.23460	−	0.199661i
$119$	1.92810			0.176748
$120$	2.72166	+	5.21512i	0.248453	+	0.476073i
$121$	−16.6538			−1.51398
$122$	3.78111	−	0.611484i	0.342326	−	0.0553612i
$123$		−	19.5450i		−	1.76231i
$124$	−9.23973	+	3.06877i	−0.829752	+	0.275584i
$125$			1.00000i			0.0894427i
$126$	0.299289	+	1.85065i	0.0266628	+	0.164869i
$127$	19.7202			1.74988			0.874941	−	0.484230i	$-0.160900\pi$
$127$	19.7202			1.74988			0.874941	+	0.484230i	$0.160900\pi$
$128$	10.1949	+	4.90546i	0.901112	+	0.433586i
$129$	26.9997			2.37719
$130$	−0.365127	−	2.25776i	−0.0320238	−	0.198019i
$131$			7.26786i			0.634996i	0.948259	+	0.317498i	$0.102843\pi$
$131$			7.26786i			0.634996i	−0.948259	+	0.317498i	$0.897157\pi$
$132$	20.7591	−	6.89469i	1.80685	−	0.600106i
$133$			2.71629i			0.235533i
$134$	−14.7110	+	2.37907i	−1.27084	+	0.205521i
$135$	3.48241			0.299718
$136$	2.52313	+	4.83470i	0.216357	+	0.414572i
$137$	19.1214			1.63365			0.816826	−	0.576884i	$-0.195732\pi$
$137$	19.1214			1.63365			0.816826	+	0.576884i	$0.195732\pi$
$138$	10.9497	−	1.77079i	0.932098	−	0.150740i
$139$			13.4626i			1.14188i	0.820992	+	0.570940i	$0.193421\pi$
$139$			13.4626i			1.14188i	−0.820992	+	0.570940i	$0.806579\pi$
$140$	0.630396	+	1.89805i	0.0532782	+	0.160415i
$141$		−	16.3004i		−	1.37274i
$142$	−0.0884917	−	0.547188i	−0.00742605	−	0.0459190i
$143$	−8.50448			−0.711180
$144$	−4.24885	+	3.17225i	−0.354071	+	0.264354i
$145$	1.73339			0.143950
$146$	−0.540040	−	3.33934i	−0.0446941	−	0.276366i
$147$			2.07981i			0.171540i
$148$	4.89887	+	14.7500i	0.402685	+	1.21244i
$149$		−	7.50840i		−	0.615112i	−0.951530	−	0.307556i	$-0.900489\pi$
$149$		−	7.50840i		−	0.615112i	0.951530	−	0.307556i	$-0.0995112\pi$
$150$	−2.90357	+	0.469568i	−0.237076	+	0.0383400i
$151$	−7.68709			−0.625567			−0.312783	−	0.949824i	$-0.601261\pi$
$151$	−7.68709			−0.625567			−0.312783	+	0.949824i	$0.601261\pi$
$152$	−6.81110	+	3.55457i	−0.552453	+	0.288314i
$153$	−2.55590			−0.206633
$154$	7.34153	−	1.18728i	0.591597	−	0.0956735i
$155$		−	4.86801i		−	0.391008i
$156$	6.38413	−	2.12035i	0.511139	−	0.169764i
$157$		−	23.4720i		−	1.87327i	−0.350308	−	0.936635i	$-0.613923\pi$
$157$		−	23.4720i		−	1.87327i	0.350308	−	0.936635i	$-0.386077\pi$
$158$	−3.60442	−	22.2879i	−0.286752	−	1.77313i
$159$	6.39505			0.507161
$160$	−3.93441	+	4.06453i	−0.311043	+	0.321329i
$161$	3.77110			0.297205
$162$	2.53309	+	15.6634i	0.199019	+	1.23063i
$163$			19.9958i			1.56619i	0.621901	+	0.783096i	$0.286361\pi$
$163$			19.9958i			1.56619i	−0.621901	+	0.783096i	$0.713639\pi$
$164$	17.8369	−	5.92414i	1.39283	−	0.462598i
$165$			10.9371i			0.851450i
$166$	−6.31247	+	1.02086i	−0.489943	+	0.0792339i
$167$	−15.2315			−1.17865			−0.589325	−	0.807896i	$-0.700606\pi$
$167$	−15.2315			−1.17865			−0.589325	+	0.807896i	$0.700606\pi$
$168$	−5.21512	+	2.72166i	−0.402355	+	0.209981i
$169$	10.3846			0.798815
$170$	−2.69177	+	0.435315i	−0.206449	+	0.0333871i
$171$		−	3.60075i		−	0.275356i
$172$	8.18367	+	24.6401i	0.623999	+	1.87879i
$173$			14.8218i			1.12688i	0.826156	+	0.563441i	$0.190523\pi$
$173$			14.8218i			1.12688i	−0.826156	+	0.563441i	$0.809477\pi$
$174$	0.813942	+	5.03301i	0.0617048	+	0.381552i
$175$	−1.00000			−0.0755929
$176$	12.5843	+	16.8552i	0.948577	+	1.27051i
$177$	−19.9794			−1.50175
$178$	−0.514431	−	3.18098i	−0.0385582	−	0.238425i
$179$		−	14.4532i		−	1.08028i	−0.841574	−	0.540142i	$-0.818371\pi$
$179$		−	14.4532i		−	1.08028i	0.841574	−	0.540142i	$-0.181629\pi$
$180$	−0.835659	−	2.51608i	−0.0622863	−	0.187537i
$181$		−	21.4426i		−	1.59381i	−0.604103	−	0.796906i	$-0.706468\pi$
$181$		−	21.4426i		−	1.59381i	0.604103	−	0.796906i	$-0.293532\pi$
$182$	2.25776	−	0.365127i	0.167357	−	0.0270650i
$183$	−5.63293			−0.416398
$184$	4.93491	+	9.45603i	0.363806	+	0.697108i
$185$	−7.77110			−0.571343
$186$	14.1346	−	2.28586i	1.03640	−	0.167607i
$187$			10.1393i			0.741457i
$188$	14.8759	−	4.94069i	1.08493	−	0.360337i
$189$			3.48241i			0.253308i
$190$	−0.613269	−	3.79215i	−0.0444912	−	0.275112i
$191$	−23.8209			−1.72362			−0.861810	−	0.507231i	$-0.830669\pi$
$191$	−23.8209			−1.72362			−0.861810	+	0.507231i	$0.830669\pi$
$192$	−13.6491	−	9.51528i	−0.985040	−	0.686706i
$193$	−2.59039			−0.186461			−0.0932303	−	0.995645i	$-0.529719\pi$
$193$	−2.59039			−0.186461			−0.0932303	+	0.995645i	$0.529719\pi$
$194$	−2.48643	−	15.3748i	−0.178515	−	1.10385i
$195$			3.36352i			0.240866i
$196$	−1.89805	+	0.630396i	−0.135575	+	0.0450283i
$197$			3.91491i			0.278926i	0.990227	+	0.139463i	$0.0445376\pi$
$197$			3.91491i			0.278926i	−0.990227	+	0.139463i	$0.955462\pi$
$198$	−9.73200	+	1.57387i	−0.691623	+	0.111850i
$199$	−8.94099			−0.633810			−0.316905	−	0.948457i	$-0.602644\pi$
$199$	−8.94099			−0.633810			−0.316905	+	0.948457i	$0.602644\pi$
$200$	−1.30861	−	2.50750i	−0.0925328	−	0.177307i
$201$	21.9158			1.54582
$202$	−23.5269	+	3.80479i	−1.65535	+	0.267704i
$203$			1.73339i			0.121660i
$204$	−2.52793	−	7.61133i	−0.176991	−	0.532900i
$205$			9.39750i			0.656350i
$206$	3.26604	+	20.1956i	0.227556	+	1.40709i
$207$	−4.99901			−0.347455
$208$	3.87009	+	5.18353i	0.268343	+	0.359413i
$209$	−14.2841			−0.988055
$210$	−0.469568	−	2.90357i	−0.0324032	−	0.200365i
$211$		−	6.26552i		−	0.431336i	−0.976467	−	0.215668i	$-0.930807\pi$
$211$		−	6.26552i		−	0.431336i	0.976467	−	0.215668i	$-0.0691930\pi$
$212$	1.93836	+	5.83618i	0.133127	+	0.400830i
$213$			0.815176i			0.0558549i
$214$	−1.31956	+	0.213400i	−0.0902030	+	0.0145877i
$215$	−12.9818			−0.885351
$216$	−8.73214	+	4.55713i	−0.594147	+	0.310073i
$217$	4.86801			0.330462
$218$	1.71155	−	0.276793i	0.115921	−	0.0187468i
$219$			4.97480i			0.336166i
$220$	−9.98127	+	3.31506i	−0.672937	+	0.223501i
$221$			3.11816i			0.209750i
$222$	−3.64906	−	22.5640i	−0.244909	−	1.51439i
$223$	7.40134			0.495630			0.247815	−	0.968807i	$-0.420287\pi$
$223$	7.40134			0.495630			0.247815	+	0.968807i	$0.420287\pi$
$224$	−4.06453	−	3.93441i	−0.271573	−	0.262879i
$225$	1.32561			0.0883740
$226$	0.526563	+	3.25600i	0.0350264	+	0.216586i
$227$			14.6056i			0.969405i	0.874679	+	0.484703i	$0.161072\pi$
$227$			14.6056i			0.969405i	−0.874679	+	0.484703i	$0.838928\pi$
$228$	10.7228	−	3.56134i	0.710135	−	0.235856i
$229$		−	8.10717i		−	0.535737i	−0.963456	−	0.267868i	$-0.913681\pi$
$229$		−	8.10717i		−	0.535737i	0.963456	−	0.267868i	$-0.0863192\pi$
$230$	−5.26475	+	0.851419i	−0.347147	+	0.0561409i
$231$	−10.9371			−0.719607
$232$	−4.34646	+	2.26833i	−0.285359	+	0.148923i
$233$	−7.08479			−0.464140			−0.232070	−	0.972699i	$-0.574550\pi$
$233$	−7.08479			−0.464140			−0.232070	+	0.972699i	$0.574550\pi$
$234$	−2.99291	+	0.484016i	−0.195653	+	0.0316411i
$235$			7.83744i			0.511258i
$236$	−6.05582	−	18.2334i	−0.394200	−	1.18689i
$237$			33.2036i			2.15680i
$238$	−0.435315	−	2.69177i	−0.0282173	−	0.174481i
$239$	−2.79026			−0.180487			−0.0902434	−	0.995920i	$-0.528765\pi$
$239$	−2.79026			−0.180487			−0.0902434	+	0.995920i	$0.528765\pi$
$240$	6.66621	−	4.97709i	0.430302	−	0.321269i
$241$	15.2931			0.985117			0.492559	−	0.870279i	$-0.336062\pi$
$241$	15.2931			0.985117			0.492559	+	0.870279i	$0.336062\pi$
$242$	3.76001	+	23.2500i	0.241702	+	1.49457i
$243$		−	12.8874i		−	0.826725i
$244$	−1.70736	−	5.14066i	−0.109302	−	0.329097i
$245$		−	1.00000i		−	0.0638877i
$246$	−27.2863	+	4.41276i	−1.73971	+	0.281347i
$247$	−4.39285			−0.279510
$248$	6.37033	+	12.2065i	0.404516	+	0.775114i
$249$	9.40403			0.595956
$250$	1.39608	−	0.225774i	0.0882955	−	0.0142792i
$251$			2.02527i			0.127834i	0.997955	+	0.0639170i	$0.0203593\pi$
$251$			2.02527i			0.127834i	−0.997955	+	0.0639170i	$0.979641\pi$
$252$	2.51608	−	0.835659i	0.158498	−	0.0526416i
$253$			19.8311i			1.24677i
$254$	−4.45231	−	27.5308i	−0.279363	−	1.72744i
$255$	4.01008			0.251121
$256$	4.54664	−	15.3404i	0.284165	−	0.958775i
$257$	25.8114			1.61007			0.805036	−	0.593226i	$-0.202146\pi$
$257$	25.8114			1.61007			0.805036	+	0.593226i	$0.202146\pi$
$258$	−6.09583	−	37.6936i	−0.379510	−	2.34670i
$259$		−	7.77110i		−	0.482873i
$260$	−3.06957	+	1.01949i	−0.190367	+	0.0632261i
$261$		−	2.29779i		−	0.142230i
$262$	10.1465	−	1.64090i	0.626852	−	0.101375i
$263$	−6.61956			−0.408180			−0.204090	−	0.978952i	$-0.565423\pi$
$263$	−6.61956			−0.408180			−0.204090	+	0.978952i	$0.565423\pi$
$264$	−14.3124	−	27.4247i	−0.880866	−	1.68787i
$265$	−3.07483			−0.188885
$266$	3.79215	−	0.613269i	0.232512	−	0.0376020i
$267$			4.73888i			0.290015i
$268$	6.64273	+	20.0005i	0.405769	+	1.22173i
$269$			8.42794i			0.513861i	0.966430	+	0.256930i	$0.0827111\pi$
$269$			8.42794i			0.513861i	−0.966430	+	0.256930i	$0.917289\pi$
$270$	−0.786240	−	4.86171i	−0.0478490	−	0.295874i
$271$	5.07199			0.308102			0.154051	−	0.988063i	$-0.450768\pi$
$271$	5.07199			0.308102			0.154051	+	0.988063i	$0.450768\pi$
$272$	6.17994	−	4.61403i	0.374714	−	0.279767i
$273$	−3.36352			−0.203569
$274$	−4.31712	−	26.6949i	−0.260807	−	1.61270i
$275$		−	5.25869i		−	0.317111i
$276$	−4.94431	−	14.8868i	−0.297612	−	0.896078i
$277$		−	19.2571i		−	1.15705i	−0.815665	−	0.578524i	$-0.803629\pi$
$277$		−	19.2571i		−	1.15705i	0.815665	−	0.578524i	$-0.196371\pi$
$278$	18.7948	−	3.03950i	1.12723	−	0.182297i
$279$	−6.45308			−0.386336
$280$	2.50750	−	1.30861i	0.149852	−	0.0782045i
$281$	23.8936			1.42537			0.712686	−	0.701483i	$-0.247478\pi$
$281$	23.8936			1.42537			0.712686	+	0.701483i	$0.247478\pi$
$282$	−22.7566	+	3.68021i	−1.35513	+	0.219153i
$283$		−	21.9571i		−	1.30521i	−0.757697	−	0.652606i	$-0.773676\pi$
$283$		−	21.9571i		−	1.30521i	0.757697	−	0.652606i	$-0.226324\pi$
$284$	−0.743936	+	0.247082i	−0.0441445	+	0.0146616i
$285$			5.64938i			0.334640i
$286$	1.92009	+	11.8729i	0.113537	+	0.702059i
$287$	−9.39750			−0.554717
$288$	5.38798	+	5.21550i	0.317490	+	0.307326i
$289$	−13.2824			−0.781320
$290$	−0.391354	−	2.41994i	−0.0229811	−	0.142104i
$291$			22.9047i			1.34270i
$292$	−4.54004	+	1.50787i	−0.265686	+	0.0882416i
$293$			4.16841i			0.243521i	0.992559	+	0.121761i	$0.0388540\pi$
$293$			4.16841i			0.243521i	−0.992559	+	0.121761i	$0.961146\pi$
$294$	2.90357	−	0.469568i	0.169340	−	0.0273857i
$295$	9.60638			0.559305
$296$	19.4860	−	10.1694i	1.13260	−	0.591082i
$297$	−18.3129			−1.06262
$298$	−10.4823	+	1.69520i	−0.607223	+	0.0982005i
$299$			6.09872i			0.352698i
$300$	1.31110	+	3.94759i	0.0756966	+	0.227914i
$301$		−	12.9818i		−	0.748258i
$302$	1.73555	+	10.7318i	0.0998696	+	0.617543i
$303$	35.0493			2.01353
$304$	6.50022	+	8.70627i	0.372813	+	0.499339i
$305$	2.70839			0.155082
$306$	0.577057	+	3.56823i	0.0329882	+	0.203982i
$307$			6.24377i			0.356351i	0.983999	+	0.178175i	$0.0570194\pi$
$307$			6.24377i			0.356351i	−0.983999	+	0.178175i	$0.942981\pi$
$308$	−3.31506	−	9.98127i	−0.188893	−	0.568736i
$309$		−	30.0864i		−	1.71156i
$310$	−6.79610	+	1.09907i	−0.385993	+	0.0624230i
$311$	−20.9360			−1.18717			−0.593585	−	0.804771i	$-0.702288\pi$
$311$	−20.9360			−1.18717			−0.593585	+	0.804771i	$0.702288\pi$
$312$	−4.40154	−	8.43400i	−0.249188	−	0.477481i
$313$	−3.63577			−0.205506			−0.102753	−	0.994707i	$-0.532765\pi$
$313$	−3.63577			−0.205506			−0.102753	+	0.994707i	$0.532765\pi$
$314$	−32.7687	+	5.29937i	−1.84924	+	0.299061i
$315$			1.32561i			0.0746896i
$316$	−30.3018	+	10.0641i	−1.70461	+	0.566149i
$317$		−	5.11860i		−	0.287489i	−0.989615	−	0.143745i	$-0.954086\pi$
$317$		−	5.11860i		−	0.287489i	0.989615	−	0.143745i	$-0.0459144\pi$
$318$	−1.44384	−	8.92797i	−0.0809665	−	0.500656i
$319$	−9.11534			−0.510361
$320$	6.56268	+	4.57507i	0.366865	+	0.255754i
$321$	1.96581			0.109721
$322$	−0.851419	−	5.26475i	−0.0474477	−	0.293393i
$323$			5.23728i			0.291410i
$324$	21.2954	−	7.07278i	1.18308	−	0.392932i
$325$		−	1.61722i		−	0.0897074i
$326$	27.9156	−	4.51454i	1.54610	−	0.250037i
$327$	−2.54979			−0.141004
$328$	−12.2977	−	23.5642i	−0.679025	−	1.30111i
$329$	−7.83744			−0.432092
$330$	15.2690	−	2.46931i	0.840530	−	0.135931i
$331$			9.52804i			0.523708i	0.965107	+	0.261854i	$0.0843339\pi$
$331$			9.52804i			0.523708i	−0.965107	+	0.261854i	$0.915666\pi$
$332$	2.85039	+	8.58220i	0.156435	+	0.471009i
$333$			10.3015i			0.564516i
$334$	3.43888	+	21.2643i	0.188167	+	1.16353i
$335$	−10.5374			−0.575720
$336$	4.97709	+	6.66621i	0.271522	+	0.363672i
$337$	−31.1900			−1.69903			−0.849515	−	0.527564i	$-0.823105\pi$
$337$	−31.1900			−1.69903			−0.849515	+	0.527564i	$0.823105\pi$
$338$	−2.34457	−	14.4977i	−0.127528	−	0.788569i
$339$		−	4.85064i		−	0.263451i
$340$	1.21546	+	3.65963i	0.0659178	+	0.198471i
$341$			25.5993i			1.38628i
$342$	−5.02691	+	0.812956i	−0.271824	+	0.0439596i
$343$	1.00000			0.0539949
$344$	32.5518	−	16.9881i	1.75508	−	0.915939i
$345$	7.84318			0.422263
$346$	20.6924	−	3.34639i	1.11243	−	0.179903i
$347$		−	1.18431i		−	0.0635770i	−0.999495	−	0.0317885i	$-0.989880\pi$
$347$		−	1.18431i		−	0.0635770i	0.999495	−	0.0317885i	$-0.0101203\pi$
$348$	6.84269	−	2.27265i	0.366807	−	0.121827i
$349$			23.6788i			1.26750i	0.773538	+	0.633750i	$0.218485\pi$
$349$			23.6788i			1.26750i	−0.773538	+	0.633750i	$0.781515\pi$
$350$	0.225774	+	1.39608i	0.0120681	+	0.0746234i
$351$	−5.63184			−0.300605
$352$	20.6899	−	21.3741i	1.10277	−	1.13924i
$353$	30.7056			1.63430			0.817148	−	0.576428i	$-0.195554\pi$
$353$	30.7056			1.63430			0.817148	+	0.576428i	$0.195554\pi$
$354$	4.51084	+	27.8928i	0.239749	+	1.48249i
$355$		−	0.391947i		−	0.0208024i
$356$	−4.32474	+	1.43637i	−0.229211	+	0.0761274i
$357$			4.01008i			0.212236i
$358$	−20.1778	+	3.26316i	−1.06643	+	0.172464i
$359$	20.1053			1.06111			0.530557	−	0.847649i	$-0.321983\pi$
$359$	20.1053			1.06111			0.530557	+	0.847649i	$0.321983\pi$
$360$	−3.32396	+	1.73471i	−0.175188	+	0.0914271i
$361$	11.6217			0.611671
$362$	−29.9354	+	4.84118i	−1.57337	+	0.254447i
$363$		−	34.6368i		−	1.81796i
$364$	−1.01949	−	3.06957i	−0.0534358	−	0.160889i
$365$		−	2.39195i		−	0.125200i
$366$	1.27177	+	7.86399i	0.0664765	+	0.411058i
$367$	−27.0373			−1.41134			−0.705668	−	0.708542i	$-0.749353\pi$
$367$	−27.0373			−1.41134			−0.705668	+	0.708542i	$0.749353\pi$
$368$	12.0872	−	9.02443i	0.630086	−	0.470431i
$369$	12.4574			0.648507
$370$	1.75452	+	10.8490i	0.0912129	+	0.564015i
$371$		−	3.07483i		−	0.159637i
$372$	−6.38246	−	19.2169i	−0.330915	−	0.996349i
$373$			5.98325i			0.309801i	0.987930	+	0.154900i	$0.0495057\pi$
$373$			5.98325i			0.309801i	−0.987930	+	0.154900i	$0.950494\pi$
$374$	14.1552	−	2.28919i	0.731947	−	0.118371i
$375$	−2.07981			−0.107401
$376$	−10.2562	−	19.6524i	−0.528921	−	1.01349i
$377$	−2.80327			−0.144376
$378$	4.86171	−	0.786240i	0.250059	−	0.0404398i
$379$		−	27.8998i		−	1.43312i	−0.697527	−	0.716558i	$-0.745716\pi$
$379$		−	27.8998i		−	1.43312i	0.697527	−	0.716558i	$-0.254284\pi$
$380$	−5.15567	+	1.71234i	−0.264480	+	0.0878412i
$381$			41.0142i			2.10122i
$382$	5.37815	+	33.2558i	0.275170	+	1.70151i
$383$	−11.9794			−0.612121			−0.306060	−	0.952012i	$-0.599011\pi$
$383$	−11.9794			−0.612121			−0.306060	+	0.952012i	$0.599011\pi$
$384$	−10.2024	+	21.2035i	−0.520640	+	1.08204i
$385$	5.25869			0.268008
$386$	0.584845	+	3.61639i	0.0297678	+	0.184069i
$387$			17.2088i			0.874772i
$388$	−20.9030	+	6.94248i	−1.06119	+	0.352451i
$389$			2.72987i			0.138410i	0.997602	+	0.0692050i	$0.0220463\pi$
$389$			2.72987i			0.138410i	−0.997602	+	0.0692050i	$0.977954\pi$
$390$	4.69572	−	0.759396i	0.237777	−	0.0384535i
$391$	7.27105			0.367713
$392$	1.30861	+	2.50750i	0.0660949	+	0.126648i
$393$	−15.1158			−0.762490
$394$	5.46551	−	0.883886i	0.275348	−	0.0445295i
$395$		−	15.9647i		−	0.803272i
$396$	4.39447	+	13.2313i	0.220831	+	0.664896i
$397$			1.56760i			0.0786756i	0.999226	+	0.0393378i	$0.0125248\pi$
$397$			1.56760i			0.0786756i	−0.999226	+	0.0393378i	$0.987475\pi$
$398$	2.01865	+	12.4823i	0.101186	+	0.625681i
$399$	−5.64938			−0.282823
$400$	−3.20520	+	2.39305i	−0.160260	+	0.119652i
$401$	−7.77401			−0.388216			−0.194108	−	0.980980i	$-0.562181\pi$
$401$	−7.77401			−0.388216			−0.194108	+	0.980980i	$0.562181\pi$
$402$	−4.94802	−	30.5961i	−0.246785	−	1.52599i
$403$			7.87265i			0.392165i
$404$	10.6235	+	31.9863i	0.528541	+	1.59138i
$405$			11.2196i			0.557506i
$406$	2.41994	−	0.391354i	0.120099	−	0.0194226i
$407$	40.8658			2.02564
$408$	−10.0552	+	5.24763i	−0.497809	+	0.259796i
$409$	−15.7180			−0.777206			−0.388603	−	0.921405i	$-0.627042\pi$
$409$	−15.7180			−0.777206			−0.388603	+	0.921405i	$0.627042\pi$
$410$	13.1196	−	2.12171i	0.647931	−	0.104784i
$411$			39.7689i			1.96165i
$412$	27.4571	−	9.11928i	1.35272	−	0.449275i
$413$			9.60638i			0.472699i
$414$	1.12865	+	6.97900i	0.0554701	+	0.342999i
$415$	−4.52158			−0.221956
$416$	6.36282	−	6.57325i	0.311963	−	0.322280i
$417$	−27.9996			−1.37115
$418$	3.22499	+	19.9417i	0.157740	+	0.975383i
$419$			25.4331i			1.24249i	0.783617	+	0.621244i	$0.213372\pi$
$419$			25.4331i			1.24249i	−0.783617	+	0.621244i	$0.786628\pi$
$420$	−3.94759	+	1.31110i	−0.192623	+	0.0639753i
$421$		−	15.7703i		−	0.768597i	−0.923209	−	0.384299i	$-0.874443\pi$
$421$		−	15.7703i		−	0.768597i	0.923209	−	0.384299i	$-0.125557\pi$
$422$	−8.74714	+	1.41459i	−0.425804	+	0.0688614i
$423$	10.3894			0.505149
$424$	7.71011	−	4.02375i	0.374436	−	0.195411i
$425$	−1.92810			−0.0935264
$426$	1.13805	−	0.184046i	0.0551386	−	0.00891705i
$427$			2.70839i			0.131068i
$428$	0.595844	+	1.79402i	0.0288012	+	0.0867172i
$429$		−	17.6877i		−	0.853970i
$430$	2.93096	+	18.1236i	0.141343	+	0.873996i
$431$	−20.6075			−0.992629			−0.496315	−	0.868143i	$-0.665314\pi$
$431$	−20.6075			−0.992629			−0.496315	+	0.868143i	$0.665314\pi$
$432$	8.33358	+	11.1618i	0.400950	+	0.537024i
$433$	−27.4378			−1.31858			−0.659289	−	0.751889i	$-0.729143\pi$
$433$	−27.4378			−1.31858			−0.659289	+	0.751889i	$0.729143\pi$
$434$	−1.09907	−	6.79610i	−0.0527571	−	0.326223i
$435$			3.60511i			0.172852i
$436$	−0.772849	−	2.32696i	−0.0370127	−	0.111441i
$437$			10.2434i			0.490010i
$438$	6.94519	−	1.12318i	0.331854	−	0.0536677i
$439$	29.5378			1.40976			0.704882	−	0.709324i	$-0.251000\pi$
$439$	29.5378			1.40976			0.704882	+	0.709324i	$0.251000\pi$
$440$	6.88158	+	13.1861i	0.328067	+	0.628625i
$441$	−1.32561			−0.0631243
$442$	4.35319	−	0.704001i	0.207060	−	0.0334859i
$443$		−	28.5613i		−	1.35699i	−0.734606	−	0.678494i	$-0.762633\pi$
$443$		−	28.5613i		−	1.35699i	0.734606	−	0.678494i	$-0.237367\pi$
$444$	−30.6771	+	10.1887i	−1.45587	+	0.483535i
$445$		−	2.27852i		−	0.108012i
$446$	−1.67103	−	10.3328i	−0.0791257	−	0.489274i
$447$	15.6160			0.738614
$448$	−4.57507	+	6.56268i	−0.216152	+	0.310057i
$449$	26.7334			1.26163			0.630813	−	0.775935i	$-0.282722\pi$
$449$	26.7334			1.26163			0.630813	+	0.775935i	$0.282722\pi$
$450$	−0.299289	−	1.85065i	−0.0141086	−	0.0872405i
$451$		−	49.4185i		−	2.32703i
$452$	4.42674	−	1.47024i	0.208216	−	0.0691544i
$453$		−	15.9877i		−	0.751167i
$454$	20.3905	−	3.29756i	0.956972	−	0.154762i
$455$	1.61722			0.0758166
$456$	−7.39284	−	14.1658i	−0.346201	−	0.663374i
$457$	−6.28041			−0.293785			−0.146893	−	0.989152i	$-0.546927\pi$
$457$	−6.28041			−0.293785			−0.146893	+	0.989152i	$0.546927\pi$
$458$	−11.3182	+	1.83039i	−0.528865	+	0.0855285i
$459$			6.71443i			0.313403i
$460$	2.37729	+	7.15775i	0.110842	+	0.333732i
$461$		−	25.3778i		−	1.18196i	−0.806685	−	0.590982i	$-0.798740\pi$
$461$		−	25.3778i		−	1.18196i	0.806685	−	0.590982i	$-0.201260\pi$
$462$	2.46931	+	15.2690i	0.114883	+	0.710377i
$463$	−36.8574			−1.71291			−0.856454	−	0.516224i	$-0.827337\pi$
$463$	−36.8574			−1.71291			−0.856454	+	0.516224i	$0.827337\pi$
$464$	4.14808	+	5.55585i	0.192570	+	0.257924i
$465$	10.1245			0.469514
$466$	1.59956	+	9.89091i	0.0740984	+	0.458187i
$467$		−	23.5698i		−	1.09068i	−0.838214	−	0.545341i	$-0.816400\pi$
$467$		−	23.5698i		−	1.09068i	0.838214	−	0.545341i	$-0.183600\pi$
$468$	1.35145	+	4.06906i	0.0624706	+	0.188092i
$469$		−	10.5374i		−	0.486572i
$470$	10.9417	−	1.76949i	0.504701	−	0.0816206i
$471$	48.8173			2.24938
$472$	−24.0880	+	12.5710i	−1.10874	+	0.578628i
$473$	68.2673			3.13893
$474$	46.3547	−	7.49651i	2.12914	−	0.344326i
$475$		−	2.71629i		−	0.124632i
$476$	−3.65963	+	1.21546i	−0.167739	+	0.0557107i
$477$			4.07602i			0.186628i
$478$	0.629969	+	3.89541i	0.0288141	+	0.178172i
$479$	−11.6447			−0.532058			−0.266029	−	0.963965i	$-0.585712\pi$
$479$	−11.6447			−0.532058			−0.266029	+	0.963965i	$0.585712\pi$
$480$	−8.45345	−	8.18283i	−0.385845	−	0.373494i
$481$	12.5676			0.573034
$482$	−3.45280	−	21.3504i	−0.157271	−	0.972482i
$483$			7.84318i			0.356877i
$484$	31.6098	−	10.4985i	1.43681	−	0.477205i
$485$		−	11.0129i		−	0.500070i
$486$	−17.9917	+	2.90964i	−0.816122	+	0.131984i
$487$	33.8751			1.53503			0.767513	−	0.641033i	$-0.221494\pi$
$487$	33.8751			1.53503			0.767513	+	0.641033i	$0.221494\pi$
$488$	−6.79127	+	3.54423i	−0.307426	+	0.160440i
$489$	−41.5875			−1.88065
$490$	−1.39608	+	0.225774i	−0.0630682	+	0.0101994i
$491$			36.1406i			1.63100i	0.578755	+	0.815501i	$0.303539\pi$
$491$			36.1406i			1.63100i	−0.578755	+	0.815501i	$0.696461\pi$
$492$	12.3211	+	37.0974i	0.555478	+	1.67248i
$493$			3.34214i			0.150522i
$494$	0.991793	+	6.13275i	0.0446229	+	0.275926i
$495$	−6.97097			−0.313322
$496$	15.6029	−	11.6494i	0.700593	−	0.523072i
$497$	0.391947			0.0175812
$498$	−2.12319	−	13.1287i	−0.0951424	−	0.588313i
$499$		−	15.8739i		−	0.710614i	−0.934750	−	0.355307i	$-0.884376\pi$
$499$		−	15.8739i		−	0.710614i	0.934750	−	0.355307i	$-0.115624\pi$
$500$	−0.630396	−	1.89805i	−0.0281922	−	0.0848835i
$501$		−	31.6786i		−	1.41530i
$502$	2.82743	−	0.457254i	0.126194	−	0.0204082i
$503$	26.4296			1.17844			0.589218	−	0.807974i	$-0.299436\pi$
$503$	26.4296			1.17844			0.589218	+	0.807974i	$0.299436\pi$
$504$	−1.73471	−	3.32396i	−0.0772700	−	0.148061i
$505$	−16.8522			−0.749911
$506$	27.6857	−	4.47735i	1.23078	−	0.199042i
$507$			21.5980i			0.959200i
$508$	−37.4299	+	12.4315i	−1.66068	+	0.551559i
$509$		−	13.4167i		−	0.594687i	−0.954771	−	0.297343i	$-0.903899\pi$
$509$		−	13.4167i		−	0.594687i	0.954771	−	0.297343i	$-0.0961006\pi$
$510$	−0.905372	−	5.59837i	−0.0400905	−	0.247900i
$511$	2.39195			0.105814
$512$	−22.4429	−	2.88398i	−0.991844	−	0.127455i
$513$	−9.45926			−0.417636
$514$	−5.82756	−	36.0347i	−0.257042	−	1.58942i
$515$			14.4660i			0.637446i
$516$	−51.2468	+	17.0205i	−2.25601	+	0.749285i
$517$		−	41.2147i		−	1.81262i
$518$	−10.8490	+	1.75452i	−0.476680	+	0.0770890i
$519$	−30.8266			−1.35314
$520$	2.11632	+	4.05518i	0.0928066	+	0.177831i
$521$	−16.9530			−0.742724			−0.371362	−	0.928488i	$-0.621109\pi$
$521$	−16.9530			−0.742724			−0.371362	+	0.928488i	$0.621109\pi$
$522$	−3.20789	+	0.518783i	−0.140406	+	0.0227065i
$523$		−	7.63582i		−	0.333891i	−0.985966	−	0.166946i	$-0.946610\pi$
$523$		−	7.63582i		−	0.333891i	0.985966	−	0.166946i	$-0.0533904\pi$
$524$	−4.58163	−	13.7948i	−0.200149	−	0.602628i
$525$		−	2.07981i		−	0.0907704i
$526$	1.49453	+	9.24140i	0.0651645	+	0.402944i
$527$	9.38599			0.408860
$528$	−35.0555	+	26.1730i	−1.52560	+	1.13903i
$529$	−8.77877			−0.381686
$530$	0.694217	+	4.29269i	0.0301548	+	0.186462i
$531$		−	12.7343i		−	0.552622i
$532$	−1.71234	−	5.15567i	−0.0742394	−	0.223526i
$533$		−	15.1978i		−	0.658292i
$534$	6.61584	−	1.06992i	0.286295	−	0.0462999i
$535$	−0.945190			−0.0408641
$536$	26.4225	−	13.7894i	1.14128	−	0.595610i
$537$	30.0599			1.29718
$538$	11.7660	−	1.90281i	0.507270	−	0.0820361i
$539$			5.25869i			0.226508i
$540$	−6.60980	+	2.19530i	−0.284441	+	0.0944706i
$541$			17.5194i			0.753218i	0.926372	+	0.376609i	$0.122910\pi$
$541$			17.5194i			0.753218i	−0.926372	+	0.376609i	$0.877090\pi$
$542$	−1.14513	−	7.08088i	−0.0491874	−	0.304150i
$543$	44.5964			1.91382
$544$	−7.83680	−	7.58593i	−0.336000	−	0.325244i
$545$	1.22597			0.0525149
$546$	0.759396	+	4.69572i	0.0324991	+	0.200958i
$547$			10.2911i			0.440017i	0.975498	+	0.220009i	$0.0706086\pi$
$547$			10.2911i			0.440017i	−0.975498	+	0.220009i	$0.929391\pi$
$548$	−36.2934	+	12.0541i	−1.55038	+	0.514924i
$549$		−	3.59026i		−	0.153229i
$550$	−7.34153	+	1.18728i	−0.313044	+	0.0506257i
$551$	−4.70839			−0.200584
$552$	−19.6667	+	10.2637i	−0.837072	+	0.436851i
$553$	15.9647			0.678888
$554$	−26.8844	+	4.34776i	−1.14221	+	0.184719i
$555$		−	16.1624i		−	0.686057i
$556$	−8.48675	−	25.5527i	−0.359918	−	1.08367i
$557$			17.5375i			0.743087i	0.928415	+	0.371544i	$0.121171\pi$
$557$			17.5375i			0.743087i	−0.928415	+	0.371544i	$0.878829\pi$
$558$	1.45694	+	9.00898i	0.0616772	+	0.381381i
$559$	20.9945			0.887971
$560$	−2.39305	−	3.20520i	−0.101125	−	0.135445i
$561$	−21.0877			−0.890325
$562$	−5.39456	−	33.3573i	−0.227556	−	1.40709i
$563$			2.83611i			0.119528i	0.998213	+	0.0597639i	$0.0190348\pi$
$563$			2.83611i			0.119528i	−0.998213	+	0.0597639i	$0.980965\pi$
$564$	10.2757	+	30.9390i	0.432685	+	1.30277i
$565$			2.33225i			0.0981186i
$566$	−30.6537	+	4.95734i	−1.28847	+	0.208373i
$567$	−11.2196			−0.471178
$568$	0.512907	+	0.982806i	0.0215211	+	0.0412376i
$569$	−29.7733			−1.24816			−0.624080	−	0.781360i	$-0.714526\pi$
$569$	−29.7733			−1.24816			−0.624080	+	0.781360i	$0.714526\pi$
$570$	7.88695	−	1.27548i	0.330348	−	0.0534241i
$571$			17.7803i			0.744083i	0.928216	+	0.372041i	$0.121342\pi$
$571$			17.7803i			0.744083i	−0.928216	+	0.372041i	$0.878658\pi$
$572$	16.1419	−	5.36119i	0.674928	−	0.224162i
$573$		−	49.5429i		−	2.06969i
$574$	2.12171	+	13.1196i	0.0885586	+	0.547602i
$575$	−3.77110			−0.157266
$576$	6.06476	−	8.69955i	0.252698	−	0.362481i
$577$	−10.3384			−0.430393			−0.215196	−	0.976571i	$-0.569039\pi$
$577$	−10.3384			−0.430393			−0.215196	+	0.976571i	$0.569039\pi$
$578$	2.99883	+	18.5433i	0.124735	+	0.771299i
$579$		−	5.38753i		−	0.223898i
$580$	−3.29006	+	1.09272i	−0.136612	+	0.0453727i
$581$		−	4.52158i		−	0.187587i
$582$	31.9767	−	5.17130i	1.32548	−	0.214357i
$583$	16.1696			0.669675
$584$	3.13013	+	5.99780i	0.129526	+	0.248191i
$585$	−2.14381			−0.0886355
$586$	5.81942	−	0.941121i	0.240398	−	0.0388773i
$587$		−	8.50906i		−	0.351206i	−0.984461	−	0.175603i	$-0.943812\pi$
$587$		−	8.50906i		−	0.351206i	0.984461	−	0.175603i	$-0.0561876\pi$
$588$	−1.31110	−	3.94759i	−0.0540690	−	0.162796i
$589$			13.2229i			0.544842i
$590$	−2.16887	−	13.4112i	−0.0892911	−	0.552131i
$591$	−8.14227			−0.334928
$592$	−18.5966	−	24.9080i	−0.764317	−	1.02371i
$593$	−35.8995			−1.47422			−0.737108	−	0.675775i	$-0.763809\pi$
$593$	−35.8995			−1.47422			−0.737108	+	0.675775i	$0.763809\pi$
$594$	4.13459	+	25.5662i	0.169644	+	1.04900i
$595$		−	1.92810i		−	0.0790443i
$596$	4.73326	+	14.2513i	0.193882	+	0.583757i
$597$		−	18.5956i		−	0.761065i
$598$	8.51427	−	1.37693i	0.348174	−	0.0563070i
$599$	−18.2323			−0.744954			−0.372477	−	0.928042i	$-0.621491\pi$
$599$	−18.2323			−0.744954			−0.372477	+	0.928042i	$0.621491\pi$
$600$	5.21512	−	2.72166i	0.212906	−	0.111111i
$601$	41.2871			1.68414			0.842069	−	0.539370i	$-0.181338\pi$
$601$	41.2871			1.68414			0.842069	+	0.539370i	$0.181338\pi$
$602$	−18.1236	+	2.93096i	−0.738661	+	0.119457i
$603$			13.9685i			0.568840i
$604$	14.5905	−	4.84591i	0.593679	−	0.197177i
$605$			16.6538i			0.677075i
$606$	−7.91323	−	48.9315i	−0.321453	−	1.98770i
$607$	−7.18370			−0.291577			−0.145789	−	0.989316i	$-0.546572\pi$
$607$	−7.18370			−0.291577			−0.145789	+	0.989316i	$0.546572\pi$
$608$	10.6870	−	11.0405i	0.433416	−	0.447749i
$609$	−3.60511			−0.146087
$610$	−0.611484	−	3.78111i	−0.0247583	−	0.153093i
$611$		−	12.6749i		−	0.512771i
$612$	4.85124	−	1.61123i	0.196100	−	0.0651302i
$613$			9.26275i			0.374119i	0.982349	+	0.187060i	$0.0598957\pi$
$613$			9.26275i			0.374119i	−0.982349	+	0.187060i	$0.940104\pi$
$614$	8.71677	−	1.40968i	0.351780	−	0.0568901i
$615$	−19.5450			−0.788131
$616$	−13.1861	+	6.88158i	−0.531285	+	0.277267i
$617$	−4.99750			−0.201192			−0.100596	−	0.994927i	$-0.532075\pi$
$617$	−4.99750			−0.201192			−0.100596	+	0.994927i	$0.532075\pi$
$618$	−42.0029	+	6.79274i	−1.68961	+	0.273244i
$619$			23.2237i			0.933440i	0.884405	+	0.466720i	$0.154564\pi$
$619$			23.2237i			0.933440i	−0.884405	+	0.466720i	$0.845436\pi$
$620$	3.06877	+	9.23973i	0.123245	+	0.371076i
$621$			13.1325i			0.526991i
$622$	4.72680	+	29.2282i	0.189528	+	1.17194i
$623$	2.27852			0.0912869
$624$	−10.7807	+	8.04906i	−0.431575	+	0.322220i
$625$	1.00000			0.0400000
$626$	0.820864	+	5.07581i	0.0328083	+	0.202870i
$627$		−	29.7083i		−	1.18644i
$628$	14.7966	+	44.5511i	0.590451	+	1.77778i
$629$		−	14.9834i		−	0.597429i
$630$	1.85065	−	0.299289i	0.0737317	−	0.0119239i
$631$	15.6997			0.624995			0.312498	−	0.949919i	$-0.398834\pi$
$631$	15.6997			0.624995			0.312498	+	0.949919i	$0.398834\pi$
$632$	20.8916	+	40.0314i	0.831023	+	1.59236i
$633$	13.0311			0.517940
$634$	−7.14595	+	1.15565i	−0.283802	+	0.0458967i
$635$		−	19.7202i		−	0.782571i
$636$	−12.1381	+	4.03141i	−0.481309	+	0.159856i
$637$			1.61722i			0.0640767i
$638$	2.05801	+	12.7257i	0.0814774	+	0.503816i
$639$	−0.519569			−0.0205538
$640$	4.90546	−	10.1949i	0.193905	−	0.402990i
$641$	6.27829			0.247978			0.123989	−	0.992284i	$-0.460431\pi$
$641$	6.27829			0.247978			0.123989	+	0.992284i	$0.460431\pi$
$642$	−0.443830	−	2.74443i	−0.0175166	−	0.108314i
$643$			18.2552i			0.719917i	0.932968	+	0.359958i	$0.117209\pi$
$643$			18.2552i			0.719917i	−0.932968	+	0.359958i	$0.882791\pi$
$644$	−7.15775	+	2.37729i	−0.282055	+	0.0936783i
$645$		−	26.9997i		−	1.06311i
$646$	7.31163	−	1.18244i	0.287672	−	0.0465226i
$647$	33.3239			1.31010			0.655048	−	0.755587i	$-0.272648\pi$
$647$	33.3239			1.31010			0.655048	+	0.755587i	$0.272648\pi$
$648$	−14.6821	−	28.1331i	−0.576767	−	1.10517i
$649$	−50.5170			−1.98296
$650$	−2.25776	+	0.365127i	−0.0885568	+	0.0143215i
$651$			10.1245i			0.396812i
$652$	−12.6053	−	37.9531i	−0.493660	−	1.48636i
$653$			22.5233i			0.881406i	0.897653	+	0.440703i	$0.145271\pi$
$653$			22.5233i			0.881406i	−0.897653	+	0.440703i	$0.854729\pi$
$654$	0.575677	+	3.55970i	0.0225108	+	0.139195i
$655$	7.26786			0.283979
$656$	−30.1209	+	22.4887i	−1.17602	+	0.878035i
$657$	−3.17079			−0.123704
$658$	1.76949	+	10.9417i	0.0689820	+	0.426550i
$659$			21.1940i			0.825600i	0.910822	+	0.412800i	$0.135449\pi$
$659$			21.1940i			0.825600i	−0.910822	+	0.412800i	$0.864551\pi$
$660$	−6.89469	−	20.7591i	−0.268375	−	0.808049i
$661$			0.783517i			0.0304753i	0.999884	+	0.0152376i	$0.00485048\pi$
$661$			0.783517i			0.0304753i	−0.999884	+	0.0152376i	$0.995150\pi$
$662$	13.3019	−	2.15119i	0.516991	−	0.0836082i
$663$	−6.48518			−0.251864
$664$	11.3379	−	5.91700i	0.439994	−	0.229624i
$665$	2.71629			0.105333
$666$	14.3816	−	2.32580i	0.557276	−	0.0901230i
$667$			6.53678i			0.253105i
$668$	28.9102	−	9.60188i	1.11857	−	0.371508i
$669$			15.3934i			0.595143i
$670$	2.37907	+	14.7110i	0.0919116	+	0.568335i
$671$	−14.2426			−0.549828
$672$	8.18283	−	8.45345i	0.315660	−	0.326099i
$673$	−13.4096			−0.516902			−0.258451	−	0.966024i	$-0.583212\pi$
$673$	−13.4096			−0.516902			−0.258451	+	0.966024i	$0.583212\pi$
$674$	7.04191	+	43.5437i	0.271244	+	1.67724i
$675$		−	3.48241i		−	0.134038i
$676$	−19.7105	+	6.54640i	−0.758096	+	0.251785i
$677$		−	9.92960i		−	0.381626i	−0.981626	−	0.190813i	$-0.938888\pi$
$677$		−	9.92960i		−	0.381626i	0.981626	−	0.190813i	$-0.0611123\pi$
$678$	−6.77186	+	1.09515i	−0.260072	+	0.0420590i
$679$	11.0129			0.422636
$680$	4.83470	−	2.52313i	0.185402	−	0.0967576i
$681$	−30.3768			−1.16404
$682$	35.7386	−	5.77967i	1.36850	−	0.221315i
$683$			18.4011i			0.704098i	0.935981	+	0.352049i	$0.114515\pi$
$683$			18.4011i			0.704098i	−0.935981	+	0.352049i	$0.885485\pi$
$684$	2.26990	+	6.83440i	0.0867916	+	0.261320i
$685$		−	19.1214i		−	0.730591i
$686$	−0.225774	−	1.39608i	−0.00862010	−	0.0533024i
$687$	16.8614			0.643301
$688$	−31.0661	−	41.6093i	−1.18438	−	1.58634i
$689$	4.97268			0.189444
$690$	−1.77079	−	10.9497i	−0.0674128	−	0.416847i
$691$		−	47.1017i		−	1.79183i	−0.444224	−	0.895916i	$-0.646521\pi$
$691$		−	47.1017i		−	1.79183i	0.444224	−	0.895916i	$-0.353479\pi$
$692$	−9.34361	−	28.1326i	−0.355191	−	1.06944i
$693$		−	6.97097i		−	0.264805i
$694$	−1.65338	+	0.267386i	−0.0627616	+	0.0101498i
$695$	13.4626			0.510664
$696$	−4.71769	−	9.03981i	−0.178824	−	0.342653i
$697$	−18.1193			−0.686317
$698$	33.0575	−	5.34608i	1.25124	−	0.202352i
$699$		−	14.7350i		−	0.557330i
$700$	1.89805	−	0.630396i	0.0717396	−	0.0238267i
$701$			14.5973i			0.551334i	0.961253	+	0.275667i	$0.0888986\pi$
$701$			14.5973i			0.551334i	−0.961253	+	0.275667i	$0.911101\pi$
$702$	1.27152	+	7.86247i	0.0479906	+	0.296750i
$703$	21.1086			0.796126
$704$	−34.5111	−	24.0589i	−1.30069	−	0.906754i
$705$	−16.3004			−0.613908
$706$	−6.93254	−	42.8674i	−0.260910	−	1.61334i
$707$		−	16.8522i		−	0.633791i
$708$	37.9220	−	12.5950i	1.42520	−	0.473347i
$709$			8.68547i			0.326190i	0.986610	+	0.163095i	$0.0521477\pi$
$709$			8.68547i			0.326190i	−0.986610	+	0.163095i	$0.947852\pi$
$710$	−0.547188	+	0.0884917i	−0.0205356	+	0.00332103i
$711$	−21.1630			−0.793673
$712$	2.98169	+	5.71337i	0.111744	+	0.214118i
$713$	18.3578			0.687504
$714$	5.59837	−	0.905372i	0.209514	−	0.0338827i
$715$			8.50448i			0.318049i
$716$	9.11125	+	27.4329i	0.340503	+	1.02522i
$717$		−	5.80321i		−	0.216725i
$718$	−4.53925	−	28.0684i	−0.169403	−	1.04751i
$719$	−40.2390			−1.50066			−0.750330	−	0.661063i	$-0.770106\pi$
$719$	−40.2390			−1.50066			−0.750330	+	0.661063i	$0.770106\pi$
$720$	3.17225	+	4.24885i	0.118223	+	0.158345i
$721$	−14.4660			−0.538740
$722$	−2.62389	−	16.2248i	−0.0976512	−	0.603826i
$723$			31.8068i			1.18291i
$724$	13.5173	+	40.6991i	0.502366	+	1.51257i
$725$		−	1.73339i		−	0.0643764i
$726$	−48.3556	+	7.82010i	−1.79464	+	0.290231i
$727$	−7.08169			−0.262645			−0.131323	−	0.991340i	$-0.541922\pi$
$727$	−7.08169			−0.262645			−0.131323	+	0.991340i	$0.541922\pi$
$728$	−4.05518	+	2.11632i	−0.150295	+	0.0784359i
$729$	−6.85548			−0.253907
$730$	−3.33934	+	0.540040i	−0.123594	+	0.0199878i
$731$		−	25.0302i		−	0.925774i
$732$	10.6916	−	3.55098i	0.395173	−	0.131248i
$733$			13.3996i			0.494925i	0.968898	+	0.247462i	$0.0795967\pi$
$733$			13.3996i			0.494925i	−0.968898	+	0.247462i	$0.920403\pi$
$734$	6.10433	+	37.7461i	0.225315	+	1.39324i
$735$	2.07981			0.0767149
$736$	−15.3278	−	14.8371i	−0.564989	−	0.546902i
$737$	55.4129			2.04116
$738$	−2.81256	−	17.3915i	−0.103532	−	0.640189i
$739$			12.9152i			0.475095i	0.971376	+	0.237547i	$0.0763435\pi$
$739$			12.9152i			0.475095i	−0.971376	+	0.237547i	$0.923657\pi$
$740$	14.7500	−	4.89887i	0.542219	−	0.180086i
$741$		−	9.13630i		−	0.335630i
$742$	−4.29269	+	0.694217i	−0.157590	+	0.0254855i
$743$	8.35561			0.306538			0.153269	−	0.988185i	$-0.451020\pi$
$743$	8.35561			0.306538			0.153269	+	0.988185i	$0.451020\pi$
$744$	−25.3872	+	13.2491i	−0.930741	+	0.485735i
$745$	−7.50840			−0.275087
$746$	8.35307	−	1.35086i	0.305828	−	0.0494587i
$747$			5.99386i			0.219304i
$748$	−6.39175	−	19.2449i	−0.233706	−	0.703661i
$749$		−	0.945190i		−	0.0345365i
$750$	0.469568	+	2.90357i	0.0171462	+	0.106023i
$751$	12.0765			0.440678			0.220339	−	0.975423i	$-0.429284\pi$
$751$	12.0765			0.440678			0.220339	+	0.975423i	$0.429284\pi$
$752$	−25.1206	+	18.7554i	−0.916053	+	0.683938i
$753$	−4.21218			−0.153500
$754$	0.632907	+	3.91358i	0.0230491	+	0.142524i
$755$			7.68709i			0.279762i
$756$	−2.19530	−	6.60980i	−0.0798423	−	0.240396i
$757$			28.0120i			1.01811i	0.860733	+	0.509056i	$0.170006\pi$
$757$			28.0120i			1.01811i	−0.860733	+	0.509056i	$0.829994\pi$
$758$	−38.9502	+	6.29906i	−1.41474	+	0.228792i
$759$	−41.2449			−1.49709
$760$	3.55457	+	6.81110i	0.128938	+	0.247064i
$761$	−11.6693			−0.423012			−0.211506	−	0.977377i	$-0.567837\pi$
$761$	−11.6693			−0.423012			−0.211506	+	0.977377i	$0.567837\pi$
$762$	57.2589	−	9.25995i	2.07427	−	0.335453i
$763$			1.22597i			0.0443832i
$764$	45.2133	−	15.0166i	1.63576	−	0.543281i
$765$			2.55590i			0.0924089i
$766$	2.70465	+	16.7242i	0.0977230	+	0.604270i
$767$	−15.5357			−0.560960
$768$	31.9051	+	9.45615i	1.15128	+	0.341219i
$769$	−16.5785			−0.597835			−0.298918	−	0.954279i	$-0.596626\pi$
$769$	−16.5785			−0.597835			−0.298918	+	0.954279i	$0.596626\pi$
$770$	−1.18728	−	7.34153i	−0.0427865	−	0.264570i
$771$			53.6828i			1.93334i
$772$	4.91670	−	1.63297i	0.176956	−	0.0587720i
$773$			33.0454i			1.18856i	0.804257	+	0.594281i	$0.202563\pi$
$773$			33.0454i			1.18856i	−0.804257	+	0.594281i	$0.797437\pi$
$774$	24.0248	−	3.88530i	0.863553	−	0.139654i
$775$	−4.86801			−0.174864
$776$	14.4116	+	27.6148i	0.517346	+	0.991313i
$777$	16.1624			0.579824
$778$	3.81111	−	0.616335i	0.136635	−	0.0220967i
$779$		−	25.5264i		−	0.914577i
$780$	−2.12035	−	6.38413i	−0.0759206	−	0.228588i
$781$			2.06113i			0.0737530i
$782$	−1.64162	−	10.1509i	−0.0587041	−	0.362997i
$783$	−6.03637			−0.215722
$784$	3.20520	−	2.39305i	0.114472	−	0.0854660i
$785$	−23.4720			−0.837751
$786$	3.41275	+	21.1028i	0.121729	+	0.752710i
$787$		−	6.71778i		−	0.239463i	−0.992806	−	0.119732i	$-0.961797\pi$
$787$		−	6.71778i		−	0.239463i	0.992806	−	0.119732i	$-0.0382034\pi$
$788$	−2.46794	−	7.43070i	−0.0879168	−	0.264708i
$789$		−	13.7674i		−	0.490133i
$790$	−22.2879	+	3.60442i	−0.792969	+	0.128240i
$791$	−2.33225			−0.0829254
$792$	17.4797	−	9.12229i	0.621114	−	0.324147i
$793$	−4.38007			−0.155541
$794$	2.18849	−	0.353924i	0.0776666	−	0.0125603i
$795$		−	6.39505i		−	0.226809i
$796$	16.9705	−	5.63636i	0.601502	−	0.199776i
$797$			7.18362i			0.254457i	0.991873	+	0.127228i	$0.0406081\pi$
$797$			7.18362i			0.254457i	−0.991873	+	0.127228i	$0.959392\pi$
$798$	1.27548	+	7.88695i	0.0451516	+	0.279195i
$799$	−15.1113			−0.534601
$800$	4.06453	+	3.93441i	0.143703	+	0.139103i
$801$	−3.02042			−0.106721
$802$	1.75517	+	10.8531i	0.0619773	+	0.383236i
$803$			12.5785i			0.443886i
$804$	−41.5973	+	13.8156i	−1.46702	+	0.487239i
$805$		−	3.77110i		−	0.132914i
$806$	10.9908	−	1.77744i	0.387135	−	0.0626077i
$807$	−17.5285			−0.617033
$808$	42.2567	−	22.0529i	1.48659	−	0.775819i
$809$	−8.16384			−0.287025			−0.143513	−	0.989648i	$-0.545840\pi$
$809$	−8.16384			−0.287025			−0.143513	+	0.989648i	$0.545840\pi$
$810$	15.6634	−	2.53309i	0.550355	−	0.0890039i
$811$			36.4183i			1.27882i	0.768866	+	0.639410i	$0.220821\pi$
$811$			36.4183i			1.27882i	−0.768866	+	0.639410i	$0.779179\pi$
$812$	−1.09272	−	3.29006i	−0.0383469	−	0.115458i
$813$			10.5488i			0.369962i
$814$	−9.22646	−	57.0518i	−0.323387	−	1.99966i
$815$	19.9958			0.700422
$816$	9.59630	+	12.8531i	0.335938	+	0.449949i
$817$	35.2624			1.23367
$818$	3.54873	+	21.9435i	0.124078	+	0.767238i
$819$		−	2.14381i		−	0.0749107i
$820$	−5.92414	−	17.8369i	−0.206880	−	0.622893i
$821$			46.7050i			1.63002i	0.579449	+	0.815008i	$0.303268\pi$
$821$			46.7050i			1.63002i	−0.579449	+	0.815008i	$0.696732\pi$
$822$	55.5204	−	8.97879i	1.93649	−	0.313171i
$823$	21.2275			0.739944			0.369972	−	0.929043i	$-0.379367\pi$
$823$	21.2275			0.739944			0.369972	+	0.929043i	$0.379367\pi$
$824$	−18.9303	−	36.2733i	−0.659469	−	1.26364i
$825$	10.9371			0.380780
$826$	13.4112	−	2.16887i	0.466636	−	0.0754648i
$827$		−	25.2582i		−	0.878314i	−0.898410	−	0.439157i	$-0.855277\pi$
$827$		−	25.2582i		−	0.878314i	0.898410	−	0.439157i	$-0.144723\pi$
$828$	9.48839	−	3.15136i	0.329744	−	0.109517i
$829$			7.94868i			0.276069i	0.990427	+	0.138034i	$0.0440785\pi$
$829$			7.94868i			0.276069i	−0.990427	+	0.138034i	$0.955922\pi$
$830$	1.02086	+	6.31247i	0.0354345	+	0.219109i
$831$	40.0512			1.38936
$832$	−10.6133	−	7.39891i	−0.367950	−	0.256511i
$833$	1.92810			0.0668046
$834$	6.32159	+	39.0895i	0.218899	+	1.35356i
$835$			15.2315i			0.527108i
$836$	27.1121	−	9.00467i	0.937690	−	0.311433i
$837$			16.9524i			0.585961i
$838$	35.5065	−	5.74214i	1.22655	−	0.198359i
$839$	29.7468			1.02697			0.513487	−	0.858097i	$-0.328353\pi$
$839$	29.7468			1.02697			0.513487	+	0.858097i	$0.328353\pi$
$840$	2.72166	+	5.21512i	0.0939063	+	0.179939i
$841$	25.9954			0.896392
$842$	−22.0165	+	3.56053i	−0.758740	+	0.122704i
$843$			49.6942i			1.71156i
$844$	3.94976	+	11.8923i	0.135956	+	0.409349i
$845$		−	10.3846i		−	0.357241i
$846$	−2.34566	−	14.5044i	−0.0806454	−	0.498670i
$847$	−16.6538			−0.572232
$848$	−7.35821	−	9.85544i	−0.252682	−	0.338437i
$849$	45.6665			1.56727
$850$	0.435315	+	2.69177i	0.0149312	+	0.0923269i
$851$		−	29.3056i		−	1.00458i
$852$	−0.513884	−	1.54725i	−0.0176054	−	0.0530078i
$853$			33.8558i			1.15920i	0.814901	+	0.579600i	$0.196791\pi$
$853$			33.8558i			1.15920i	−0.814901	+	0.579600i	$0.803209\pi$
$854$	3.78111	−	0.611484i	0.129387	−	0.0209246i
$855$	−3.60075			−0.123143
$856$	2.37006	−	1.23689i	0.0810069	−	0.0422759i
$857$	−5.69589			−0.194568			−0.0972840	−	0.995257i	$-0.531016\pi$
$857$	−5.69589			−0.194568			−0.0972840	+	0.995257i	$0.531016\pi$
$858$	−24.6933	+	3.99343i	−0.843017	+	0.136333i
$859$		−	49.3115i		−	1.68249i	−0.540658	−	0.841243i	$-0.681825\pi$
$859$		−	49.3115i		−	1.68249i	0.540658	−	0.841243i	$-0.318175\pi$
$860$	24.6401	−	8.18367i	0.840221	−	0.279061i
$861$		−	19.5450i		−	0.666092i
$862$	4.65265	+	28.7697i	0.158470	+	0.979898i
$863$	−28.9028			−0.983862			−0.491931	−	0.870634i	$-0.663709\pi$
$863$	−28.9028			−0.983862			−0.491931	+	0.870634i	$0.663709\pi$
$864$	13.7013	−	14.1544i	0.466126	−	0.481541i
$865$	14.8218			0.503957
$866$	6.19476	+	38.3053i	0.210507	+	1.30167i
$867$		−	27.6250i		−	0.938193i
$868$	−9.23973	+	3.06877i	−0.313617	+	0.104161i
$869$			83.9535i			2.84793i
$870$	5.03301	−	0.813942i	0.170635	−	0.0275952i
$871$	17.0413			0.577423
$872$	−3.07412	+	1.60432i	−0.104103	+	0.0543292i
$873$	−14.5988			−0.494094
$874$	14.3006	−	2.31270i	0.483725	−	0.0782283i
$875$			1.00000i			0.0338062i
$876$	−3.13609	−	9.44242i	−0.105959	−	0.319030i
$877$			15.2953i			0.516486i	0.966080	+	0.258243i	$0.0831436\pi$
$877$			15.2953i			0.516486i	−0.966080	+	0.258243i	$0.916856\pi$
$878$	−6.66889	−	41.2370i	−0.225064	−	1.39168i
$879$	−8.66951			−0.292415
$880$	16.8552	−	12.5843i	0.568188	−	0.424217i
$881$	−2.34505			−0.0790069			−0.0395034	−	0.999219i	$-0.512578\pi$
$881$	−2.34505			−0.0790069			−0.0395034	+	0.999219i	$0.512578\pi$
$882$	0.299289	+	1.85065i	0.0100776	+	0.0623147i
$883$			17.0109i			0.572462i	0.958161	+	0.286231i	$0.0924025\pi$
$883$			17.0109i			0.572462i	−0.958161	+	0.286231i	$0.907597\pi$
$884$	−1.96568	−	5.91843i	−0.0661129	−	0.199058i
$885$			19.9794i			0.671602i
$886$	−39.8737	+	6.44841i	−1.33958	+	0.216638i
$887$	−11.6016			−0.389545			−0.194772	−	0.980848i	$-0.562397\pi$
$887$	−11.6016			−0.389545			−0.194772	+	0.980848i	$0.562397\pi$
$888$	21.1503	+	40.5272i	0.709759	+	1.36000i
$889$	19.7202			0.661393
$890$	−3.18098	+	0.514431i	−0.106627	+	0.0172438i
$891$		−	59.0003i		−	1.97659i
$892$	−14.0481	+	4.66577i	−0.470366	+	0.156222i
$893$		−	21.2888i		−	0.712402i
$894$	−3.52570	−	21.8012i	−0.117917	−	0.729140i
$895$	−14.4532			−0.483118
$896$	10.1949	+	4.90546i	0.340588	+	0.163880i
$897$	−12.6842			−0.423512
$898$	−6.03571	−	37.3218i	−0.201414	−	1.24544i
$899$			8.43814i			0.281428i
$900$	−2.51608	+	0.835659i	−0.0838692	+	0.0278553i
$901$		−	5.92856i		−	0.197509i
$902$	−68.9920	+	11.1574i	−2.29718	+	0.371502i
$903$	26.9997			0.898493
$904$	−3.05201	−	5.84812i	−0.101508	−	0.194505i
$905$	−21.4426			−0.712775
$906$	−22.3200	+	3.60961i	−0.741533	+	0.119921i
$907$			13.5367i			0.449479i	0.974419	+	0.224740i	$0.0721532\pi$
$907$			13.5367i			0.449479i	−0.974419	+	0.224740i	$0.927847\pi$
$908$	−9.20729	−	27.7221i	−0.305555	−	0.919991i
$909$			22.3394i			0.740951i
$910$	−0.365127	−	2.25776i	−0.0121039	−	0.0748442i
$911$	36.0383			1.19400			0.597001	−	0.802241i	$-0.296359\pi$
$911$	36.0383			1.19400			0.597001	+	0.802241i	$0.296359\pi$
$912$	−18.1074	+	13.5192i	−0.599596	+	0.447666i
$913$	23.7776			0.786924
$914$	1.41796	+	8.76793i	0.0469018	+	0.290017i
$915$			5.63293i			0.186219i
$916$	5.11072	+	15.3878i	0.168863	+	0.508428i
$917$			7.26786i			0.240006i
$918$	9.37385	−	1.51595i	0.309383	−	0.0500337i
$919$	−20.2560			−0.668183			−0.334091	−	0.942541i	$-0.608429\pi$
$919$	−20.2560			−0.668183			−0.334091	+	0.942541i	$0.608429\pi$
$920$	9.45603	−	4.93491i	0.311756	−	0.162699i
$921$	−12.9858			−0.427898
$922$	−35.4294	+	5.72967i	−1.16680	+	0.188696i
$923$			0.633866i			0.0208640i
$924$	20.7591	−	6.89469i	0.682926	−	0.226819i
$925$			7.77110i			0.255512i
$926$	8.32145	+	51.4557i	0.273460	+	1.69094i
$927$	19.1762			0.629829
$928$	6.81986	−	7.04540i	0.223873	−	0.231276i
$929$	50.6595			1.66209			0.831043	−	0.556208i	$-0.187744\pi$
$929$	50.6595			1.66209			0.831043	+	0.556208i	$0.187744\pi$
$930$	−2.28586	−	14.1346i	−0.0749563	−	0.463492i
$931$			2.71629i			0.0890229i
$932$	13.4473	−	4.46623i	0.440481	−	0.146296i
$933$		−	43.5428i		−	1.42553i
$934$	−32.9053	+	5.32146i	−1.07669	+	0.174124i
$935$	10.1393			0.331589
$936$	5.37559	−	2.80541i	0.175707	−	0.0916977i
$937$	31.4148			1.02628			0.513138	−	0.858306i	$-0.328483\pi$
$937$	31.4148			1.02628			0.513138	+	0.858306i	$0.328483\pi$
$938$	−14.7110	+	2.37907i	−0.480331	+	0.0776795i
$939$		−	7.56171i		−	0.246767i
$940$	−4.94069	−	14.8759i	−0.161148	−	0.485197i
$941$			38.3927i			1.25157i	0.779997	+	0.625784i	$0.215221\pi$
$941$			38.3927i			1.25157i	−0.779997	+	0.625784i	$0.784779\pi$
$942$	−11.0217	−	68.1526i	−0.359106	−	2.22053i
$943$	−35.4389			−1.15405
$944$	22.9885	+	30.7904i	0.748213	+	1.00214i
$945$	3.48241			0.113283
$946$	−15.4130	−	95.3062i	−0.501120	−	3.09867i
$947$		−	11.7665i		−	0.382359i	−0.981555	−	0.191180i	$-0.938769\pi$
$947$		−	11.7665i		−	0.382359i	0.981555	−	0.191180i	$-0.0612313\pi$
$948$	−20.9314	−	63.0221i	−0.679820	−	2.04686i
$949$			3.86831i			0.125571i
$950$	−3.79215	+	0.613269i	−0.123034	+	0.0198971i
$951$	10.6457			0.345211
$952$	2.52313	+	4.83470i	0.0817751	+	0.156693i
$953$	46.7227			1.51350			0.756748	−	0.653707i	$-0.226787\pi$
$953$	46.7227			1.51350			0.756748	+	0.653707i	$0.226787\pi$
$954$	5.69043	−	0.920260i	0.184234	−	0.0297945i
$955$			23.8209i			0.770826i
$956$	5.29606	−	1.75897i	0.171287	−	0.0568891i
$957$		−	18.9582i		−	0.612831i
$958$	2.62907	+	16.2568i	0.0849413	+	0.525234i
$959$	19.1214			0.617462
$960$	−9.51528	+	13.6491i	−0.307104	+	0.440523i
$961$	−7.30251			−0.235565
$962$	−2.83744	−	17.5453i	−0.0914828	−	0.565684i
$963$			1.25295i			0.0403758i
$964$	−29.0272	+	9.64073i	−0.934902	+	0.310507i
$965$			2.59039i			0.0833877i
$966$	10.9497	−	1.77079i	0.352300	−	0.0569742i
$967$	−43.4540			−1.39739			−0.698693	−	0.715421i	$-0.746235\pi$
$967$	−43.4540			−1.39739			−0.698693	+	0.715421i	$0.746235\pi$
$968$	−21.7934	−	41.7594i	−0.700466	−	1.34220i
$969$	−10.8925			−0.349919
$970$	−15.3748	+	2.48643i	−0.493656	+	0.0798344i
$971$		−	19.3682i		−	0.621556i	−0.950482	−	0.310778i	$-0.899410\pi$
$971$		−	19.3682i		−	0.621556i	0.950482	−	0.310778i	$-0.100590\pi$
$972$	8.12415	+	24.4609i	0.260582	+	0.784584i
$973$			13.4626i			0.431590i
$974$	−7.64812	−	47.2922i	−0.245062	−	1.51534i
$975$	3.36352			0.107719
$976$	6.48130	+	8.68093i	0.207461	+	0.277870i
$977$	−19.2547			−0.616012			−0.308006	−	0.951384i	$-0.599662\pi$
$977$	−19.2547			−0.616012			−0.308006	+	0.951384i	$0.599662\pi$
$978$	9.38938	+	58.0592i	0.300239	+	1.85653i
$979$			11.9820i			0.382947i
$980$	0.630396	+	1.89805i	0.0201373	+	0.0606310i
$981$		−	1.62516i		−	0.0518874i
$982$	50.4550	−	8.15962i	1.61008	−	0.260384i
$983$	−22.2368			−0.709245			−0.354622	−	0.935010i	$-0.615391\pi$
$983$	−22.2368			−0.709245			−0.354622	+	0.935010i	$0.615391\pi$
$984$	49.0090	−	25.5768i	1.56235	−	0.815359i
$985$	3.91491			0.124739
$986$	4.66587	−	0.754569i	0.148592	−	0.0240304i
$987$		−	16.3004i		−	0.518847i
$988$	8.33786	−	2.76924i	0.265263	−	0.0881011i
$989$		−	48.9557i		−	1.55670i
$990$	1.57387	+	9.73200i	0.0500208	+	0.309303i
$991$	−7.27082			−0.230965			−0.115483	−	0.993310i	$-0.536841\pi$
$991$	−7.27082			−0.230965			−0.115483	+	0.993310i	$0.536841\pi$
$992$	−19.7861	−	19.1528i	−0.628211	−	0.608101i
$993$	−19.8165			−0.628858
$994$	−0.0884917	−	0.547188i	−0.00280678	−	0.0173557i
$995$			8.94099i			0.283448i
$996$	−17.8493	+	5.92826i	−0.565578	+	0.187844i
$997$		−	61.0812i		−	1.93446i	−0.253903	−	0.967230i	$-0.581714\pi$
$997$		−	61.0812i		−	1.93446i	0.253903	−	0.967230i	$-0.418286\pi$
$998$	−22.1612	+	3.58392i	−0.701500	+	0.113447i
$999$	27.0622			0.856210

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.b.d.141.7	✓	12
4.3	odd	2		1120.2.b.d.561.3		12
8.3	odd	2		1120.2.b.d.561.10		12
8.5	even	2	inner	280.2.b.d.141.8	yes	12
16.3	odd	4		8960.2.a.cd.1.5		6
16.5	even	4		8960.2.a.cf.1.5		6
16.11	odd	4		8960.2.a.cg.1.2		6
16.13	even	4		8960.2.a.ca.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.b.d.141.7	✓	12	1.1	even	1	trivial
280.2.b.d.141.8	yes	12	8.5	even	2	inner
1120.2.b.d.561.3		12	4.3	odd	2
1120.2.b.d.561.10		12	8.3	odd	2
8960.2.a.ca.1.2		6	16.13	even	4
8960.2.a.cd.1.5		6	16.3	odd	4
8960.2.a.cf.1.5		6	16.5	even	4
8960.2.a.cg.1.2		6	16.11	odd	4

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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.225774 - 1.39608i) q^{2} +2.07981i q^{3} +(-1.89805 + 0.630396i) q^{4} -1.00000i q^{5} +(2.90357 - 0.469568i) q^{6} +1.00000 q^{7} +(1.30861 + 2.50750i) q^{8} -1.32561 q^{9} +O(q^{10})\)	\(q+(-0.225774 - 1.39608i) q^{2} +2.07981i q^{3} +(-1.89805 + 0.630396i) q^{4} -1.00000i q^{5} +(2.90357 - 0.469568i) q^{6} +1.00000 q^{7} +(1.30861 + 2.50750i) q^{8} -1.32561 q^{9} +(-1.39608 + 0.225774i) q^{10} +5.25869i q^{11} +(-1.31110 - 3.94759i) q^{12} +1.61722i q^{13} +(-0.225774 - 1.39608i) q^{14} +2.07981 q^{15} +(3.20520 - 2.39305i) q^{16} +1.92810 q^{17} +(0.299289 + 1.85065i) q^{18} +2.71629i q^{19} +(0.630396 + 1.89805i) q^{20} +2.07981i q^{21} +(7.34153 - 1.18728i) q^{22} +3.77110 q^{23} +(-5.21512 + 2.72166i) q^{24} -1.00000 q^{25} +(2.25776 - 0.365127i) q^{26} +3.48241i q^{27} +(-1.89805 + 0.630396i) q^{28} +1.73339i q^{29} +(-0.469568 - 2.90357i) q^{30} +4.86801 q^{31} +(-4.06453 - 3.93441i) q^{32} -10.9371 q^{33} +(-0.435315 - 2.69177i) q^{34} -1.00000i q^{35} +(2.51608 - 0.835659i) q^{36} -7.77110i q^{37} +(3.79215 - 0.613269i) q^{38} -3.36352 q^{39} +(2.50750 - 1.30861i) q^{40} -9.39750 q^{41} +(2.90357 - 0.469568i) q^{42} -12.9818i q^{43} +(-3.31506 - 9.98127i) q^{44} +1.32561i q^{45} +(-0.851419 - 5.26475i) q^{46} -7.83744 q^{47} +(4.97709 + 6.66621i) q^{48} +1.00000 q^{49} +(0.225774 + 1.39608i) q^{50} +4.01008i q^{51} +(-1.01949 - 3.06957i) q^{52} -3.07483i q^{53} +(4.86171 - 0.786240i) q^{54} +5.25869 q^{55} +(1.30861 + 2.50750i) q^{56} -5.64938 q^{57} +(2.41994 - 0.391354i) q^{58} +9.60638i q^{59} +(-3.94759 + 1.31110i) q^{60} +2.70839i q^{61} +(-1.09907 - 6.79610i) q^{62} -1.32561 q^{63} +(-4.57507 + 6.56268i) q^{64} +1.61722 q^{65} +(2.46931 + 15.2690i) q^{66} -10.5374i q^{67} +(-3.65963 + 1.21546i) q^{68} +7.84318i q^{69} +(-1.39608 + 0.225774i) q^{70} +0.391947 q^{71} +(-1.73471 - 3.32396i) q^{72} +2.39195 q^{73} +(-10.8490 + 1.75452i) q^{74} -2.07981i q^{75} +(-1.71234 - 5.15567i) q^{76} +5.25869i q^{77} +(0.759396 + 4.69572i) q^{78} +15.9647 q^{79} +(-2.39305 - 3.20520i) q^{80} -11.2196 q^{81} +(2.12171 + 13.1196i) q^{82} -4.52158i q^{83} +(-1.31110 - 3.94759i) q^{84} -1.92810i q^{85} +(-18.1236 + 2.93096i) q^{86} -3.60511 q^{87} +(-13.1861 + 6.88158i) q^{88} +2.27852 q^{89} +(1.85065 - 0.299289i) q^{90} +1.61722i q^{91} +(-7.15775 + 2.37729i) q^{92} +10.1245i q^{93} +(1.76949 + 10.9417i) q^{94} +2.71629 q^{95} +(8.18283 - 8.45345i) q^{96} +11.0129 q^{97} +(-0.225774 - 1.39608i) q^{98} -6.97097i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9	\( 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9} + 16 q^{12} - 2 q^{14} + 2 q^{16} - 2 q^{18} + 4 q^{20} + 12 q^{22} + 8 q^{23} - 24 q^{24} - 12 q^{25} + 6 q^{28} + 12 q^{30} + 24 q^{31} - 2 q^{32} - 24 q^{33} - 20 q^{34} - 18 q^{36} + 12 q^{38} - 48 q^{39} + 12 q^{40} - 16 q^{41} + 16 q^{44} - 48 q^{46} - 16 q^{47} + 20 q^{48} + 12 q^{49} + 2 q^{50} + 4 q^{52} + 44 q^{54} - 8 q^{55} + 10 q^{56} + 40 q^{57} + 4 q^{58} - 8 q^{60} + 8 q^{62} - 20 q^{63} - 6 q^{64} + 8 q^{65} + 64 q^{66} - 56 q^{68} - 32 q^{71} - 46 q^{72} - 8 q^{73} - 32 q^{74} - 12 q^{76} - 24 q^{78} + 8 q^{80} + 60 q^{81} - 28 q^{82} + 16 q^{84} - 76 q^{86} + 48 q^{87} - 40 q^{88} - 48 q^{89} + 24 q^{90} + 12 q^{94} + 28 q^{96} + 32 q^{97} - 2 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9 + 16 * q^12 - 2 * q^14 + 2 * q^16 - 2 * q^18 + 4 * q^20 + 12 * q^22 + 8 * q^23 - 24 * q^24 - 12 * q^25 + 6 * q^28 + 12 * q^30 + 24 * q^31 - 2 * q^32 - 24 * q^33 - 20 * q^34 - 18 * q^36 + 12 * q^38 - 48 * q^39 + 12 * q^40 - 16 * q^41 + 16 * q^44 - 48 * q^46 - 16 * q^47 + 20 * q^48 + 12 * q^49 + 2 * q^50 + 4 * q^52 + 44 * q^54 - 8 * q^55 + 10 * q^56 + 40 * q^57 + 4 * q^58 - 8 * q^60 + 8 * q^62 - 20 * q^63 - 6 * q^64 + 8 * q^65 + 64 * q^66 - 56 * q^68 - 32 * q^71 - 46 * q^72 - 8 * q^73 - 32 * q^74 - 12 * q^76 - 24 * q^78 + 8 * q^80 + 60 * q^81 - 28 * q^82 + 16 * q^84 - 76 * q^86 + 48 * q^87 - 40 * q^88 - 48 * q^89 + 24 * q^90 + 12 * q^94 + 28 * q^96 + 32 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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