LMFDB - Embedded newform 784.2.m.l.197.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(197,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("784.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.m (of order $4$, degree $2$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.15
Character	$\chi$	$=$	784.197
Dual form			784.2.m.l.589.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.395893 + 1.35767i) q^{2} +(-2.06976 + 2.06976i) q^{3} +(-1.68654 + 1.07498i) q^{4} +(-2.64219 - 2.64219i) q^{5} +(-3.62946 - 1.99065i) q^{6} +(-2.12716 - 1.86418i) q^{8} -5.56783i q^{9} +O(q^{10})$	\(q+(0.395893 + 1.35767i) q^{2} +(-2.06976 + 2.06976i) q^{3} +(-1.68654 + 1.07498i) q^{4} +(-2.64219 - 2.64219i) q^{5} +(-3.62946 - 1.99065i) q^{6} +(-2.12716 - 1.86418i) q^{8} -5.56783i q^{9} +(2.54120 - 4.63325i) q^{10} +(0.682946 + 0.682946i) q^{11} +(1.26577 - 5.71569i) q^{12} +(-4.19543 + 4.19543i) q^{13} +10.9374 q^{15} +(1.68882 - 3.62600i) q^{16} +1.45879 q^{17} +(7.55927 - 2.20426i) q^{18} +(2.68222 - 2.68222i) q^{19} +(7.29647 + 1.61584i) q^{20} +(-0.656842 + 1.19759i) q^{22} +1.79832i q^{23} +(8.26113 - 0.544304i) q^{24} +8.96235i q^{25} +(-7.35696 - 4.03507i) q^{26} +(5.31479 + 5.31479i) q^{27} +(-0.295765 + 0.295765i) q^{29} +(4.33004 + 14.8494i) q^{30} +1.16351 q^{31} +(5.59151 + 0.857349i) q^{32} -2.82707 q^{33} +(0.577524 + 1.98056i) q^{34} +(5.98533 + 9.39035i) q^{36} +(0.0493910 + 0.0493910i) q^{37} +(4.70344 + 2.57970i) q^{38} -17.3671i q^{39} +(0.694841 + 10.5459i) q^{40} -10.1128i q^{41} +(-4.55032 - 4.55032i) q^{43} +(-1.88597 - 0.417658i) q^{44} +(-14.7113 + 14.7113i) q^{45} +(-2.44153 + 0.711944i) q^{46} +11.0875 q^{47} +(4.00951 + 11.0004i) q^{48} +(-12.1679 + 3.54813i) q^{50} +(-3.01935 + 3.01935i) q^{51} +(2.56573 - 11.5858i) q^{52} +(-0.417874 - 0.417874i) q^{53} +(-5.11164 + 9.31982i) q^{54} -3.60895i q^{55} +11.1031i q^{57} +(-0.518643 - 0.284460i) q^{58} +(3.74749 + 3.74749i) q^{59} +(-18.4464 + 11.7575i) q^{60} +(-7.02257 + 7.02257i) q^{61} +(0.460627 + 1.57967i) q^{62} +(1.04964 + 7.93084i) q^{64} +22.1703 q^{65} +(-1.11922 - 3.83823i) q^{66} +(8.42467 - 8.42467i) q^{67} +(-2.46030 + 1.56818i) q^{68} +(-3.72210 - 3.72210i) q^{69} -2.89148i q^{71} +(-10.3795 + 11.8437i) q^{72} +0.640221i q^{73} +(-0.0475032 + 0.0866103i) q^{74} +(-18.5499 - 18.5499i) q^{75} +(-1.64032 + 7.40701i) q^{76} +(23.5788 - 6.87551i) q^{78} -0.749820 q^{79} +(-14.0428 + 5.11841i) q^{80} -5.29721 q^{81} +(13.7299 - 4.00359i) q^{82} +(4.51473 - 4.51473i) q^{83} +(-3.85440 - 3.85440i) q^{85} +(4.37640 - 7.97928i) q^{86} -1.22433i q^{87} +(-0.179600 - 2.72587i) q^{88} -15.4712i q^{89} +(-25.7971 - 14.1490i) q^{90} +(-1.93317 - 3.03294i) q^{92} +(-2.40820 + 2.40820i) q^{93} +(4.38947 + 15.0532i) q^{94} -14.1739 q^{95} +(-13.3476 + 9.79858i) q^{96} +13.7459 q^{97} +(3.80252 - 3.80252i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} - 8 q^{11} + 32 q^{15} + 36 q^{16} + 20 q^{18} - 28 q^{22} - 16 q^{29} + 96 q^{30} + 40 q^{32} + 40 q^{36} - 16 q^{37} + 8 q^{43} + 4 q^{44} + 64 q^{46} - 28 q^{50} + 16 q^{53} - 20 q^{58} + 8 q^{60} + 44 q^{64} + 40 q^{67} - 196 q^{72} - 28 q^{74} + 56 q^{78} + 80 q^{79} - 48 q^{81} - 108 q^{86} - 100 q^{88} - 128 q^{95} - 40 q^{99}+O(q^{100}) $ 48 * q - 4 * q^4 - 8 * q^11 + 32 * q^15 + 36 * q^16 + 20 * q^18 - 28 * q^22 - 16 * q^29 + 96 * q^30 + 40 * q^32 + 40 * q^36 - 16 * q^37 + 8 * q^43 + 4 * q^44 + 64 * q^46 - 28 * q^50 + 16 * q^53 - 20 * q^58 + 8 * q^60 + 44 * q^64 + 40 * q^67 - 196 * q^72 - 28 * q^74 + 56 * q^78 + 80 * q^79 - 48 * q^81 - 108 * q^86 - 100 * q^88 - 128 * q^95 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	0.395893	+	1.35767i	0.279939	+	0.960018i
$2$	0.395893	+	1.35767i	0.279939	+	0.960018i
$3$	−2.06976	+	2.06976i	−1.19498	+	1.19498i	−0.219326	+	0.975652i	$0.570386\pi$
$3$	−2.06976	+	2.06976i	−1.19498	+	1.19498i	−0.975652	+	0.219326i	$0.929614\pi$
$4$	−1.68654	+	1.07498i	−0.843269	+	0.537492i
$5$	−2.64219	−	2.64219i	−1.18162	−	1.18162i	−0.979324	−	0.202300i	$-0.935158\pi$
$5$	−2.64219	−	2.64219i	−1.18162	−	1.18162i	−0.202300	−	0.979324i	$-0.564842\pi$
$6$	−3.62946	−	1.99065i	−1.48172	−	0.812679i
$7$		0			0
$7$		0			0
$8$	−2.12716	−	1.86418i	−0.752065	−	0.659088i
$9$		−	5.56783i		−	1.85594i
$10$	2.54120	−	4.63325i	0.803598	−	1.46516i
$11$	0.682946	+	0.682946i	0.205916	+	0.205916i	0.802529	−	0.596613i	$-0.203487\pi$
$11$	0.682946	+	0.682946i	0.205916	+	0.205916i	−0.596613	+	0.802529i	$0.703487\pi$
$12$	1.26577	−	5.71569i	0.365396	−	1.64998i
$13$	−4.19543	+	4.19543i	−1.16360	+	1.16360i	−0.179924	+	0.983681i	$0.557585\pi$
$13$	−4.19543	+	4.19543i	−1.16360	+	1.16360i	−0.983681	+	0.179924i	$0.942415\pi$
$14$		0			0
$15$	10.9374			2.82403
$16$	1.68882	−	3.62600i	0.422205	−	0.906501i
$17$	1.45879			0.353808			0.176904	−	0.984228i	$-0.443392\pi$
$17$	1.45879			0.353808			0.176904	+	0.984228i	$0.443392\pi$
$18$	7.55927	−	2.20426i	1.78174	−	0.519550i
$19$	2.68222	−	2.68222i	0.615343	−	0.615343i	−0.328990	−	0.944333i	$-0.606708\pi$
$19$	2.68222	−	2.68222i	0.615343	−	0.615343i	0.944333	+	0.328990i	$0.106708\pi$
$20$	7.29647	+	1.61584i	1.63154	+	0.361313i
$21$		0			0
$22$	−0.656842	+	1.19759i	−0.140039	+	0.255327i
$23$			1.79832i			0.374977i	0.982267	+	0.187488i	$0.0600347\pi$
$23$			1.79832i			0.374977i	−0.982267	+	0.187488i	$0.939965\pi$
$24$	8.26113	−	0.544304i	1.68630	−	0.111106i
$25$			8.96235i			1.79247i
$26$	−7.35696	−	4.03507i	−1.44282	−	0.791343i
$27$	5.31479	+	5.31479i	1.02283	+	1.02283i
$28$		0			0
$29$	−0.295765	+	0.295765i	−0.0549222	+	0.0549222i	−0.734034	−	0.679112i	$-0.762365\pi$
$29$	−0.295765	+	0.295765i	−0.0549222	+	0.0549222i	0.679112	+	0.734034i	$0.262365\pi$
$30$	4.33004	+	14.8494i	0.790554	+	2.71112i
$31$	1.16351			0.208973			0.104487	−	0.994526i	$-0.466680\pi$
$31$	1.16351			0.208973			0.104487	+	0.994526i	$0.466680\pi$
$32$	5.59151	+	0.857349i	0.988448	+	0.151559i
$33$	−2.82707			−0.492130
$34$	0.577524	+	1.98056i	0.0990446	+	0.339662i
$35$		0			0
$36$	5.98533	+	9.39035i	0.997554	+	1.56506i
$37$	0.0493910	+	0.0493910i	0.00811983	+	0.00811983i	0.711155	−	0.703035i	$-0.248172\pi$
$37$	0.0493910	+	0.0493910i	0.00811983	+	0.00811983i	−0.703035	+	0.711155i	$0.748172\pi$
$38$	4.70344	+	2.57970i	0.762999	+	0.418482i
$39$		−	17.3671i		−	2.78096i
$40$	0.694841	+	10.5459i	0.109864	+	1.66745i
$41$		−	10.1128i		−	1.57935i	−0.613522	−	0.789677i	$-0.710248\pi$
$41$		−	10.1128i		−	1.57935i	0.613522	−	0.789677i	$-0.289752\pi$
$42$		0			0
$43$	−4.55032	−	4.55032i	−0.693918	−	0.693918i	0.269174	−	0.963092i	$-0.413249\pi$
$43$	−4.55032	−	4.55032i	−0.693918	−	0.693918i	−0.963092	+	0.269174i	$0.913249\pi$
$44$	−1.88597	−	0.417658i	−0.284321	−	0.0629643i
$45$	−14.7113	+	14.7113i	−2.19303	+	2.19303i
$46$	−2.44153	+	0.711944i	−0.359984	+	0.104970i
$47$	11.0875			1.61728			0.808641	−	0.588302i	$-0.200203\pi$
$47$	11.0875			1.61728			0.808641	+	0.588302i	$0.200203\pi$
$48$	4.00951	+	11.0004i	0.578723	+	1.58777i
$49$		0			0
$50$	−12.1679	+	3.54813i	−1.72080	+	0.501781i
$51$	−3.01935	+	3.01935i	−0.422793	+	0.422793i
$52$	2.56573	−	11.5858i	0.355803	−	1.60666i
$53$	−0.417874	−	0.417874i	−0.0573994	−	0.0573994i	0.677824	−	0.735224i	$-0.262923\pi$
$53$	−0.417874	−	0.417874i	−0.0573994	−	0.0573994i	−0.735224	+	0.677824i	$0.762923\pi$
$54$	−5.11164	+	9.31982i	−0.695607	+	1.26827i
$55$		−	3.60895i		−	0.486630i
$56$		0			0
$57$			11.1031i			1.47064i
$58$	−0.518643	−	0.284460i	−0.0681012	−	0.0373515i
$59$	3.74749	+	3.74749i	0.487881	+	0.487881i	0.907637	−	0.419756i	$-0.137884\pi$
$59$	3.74749	+	3.74749i	0.487881	+	0.487881i	−0.419756	+	0.907637i	$0.637884\pi$
$60$	−18.4464	+	11.7575i	−2.38141	+	1.51789i
$61$	−7.02257	+	7.02257i	−0.899148	+	0.899148i	−0.995361	−	0.0962132i	$-0.969327\pi$
$61$	−7.02257	+	7.02257i	−0.899148	+	0.899148i	0.0962132	+	0.995361i	$0.469327\pi$
$62$	0.460627	+	1.57967i	0.0584997	+	0.200618i
$63$		0			0
$64$	1.04964	+	7.93084i	0.131205	+	0.991355i
$65$	22.1703			2.74988
$66$	−1.11922	−	3.83823i	−0.137766	−	0.472453i
$67$	8.42467	−	8.42467i	1.02924	−	1.02924i	0.0296779	−	0.999560i	$-0.490552\pi$
$67$	8.42467	−	8.42467i	1.02924	−	1.02924i	0.999560	−	0.0296779i	$-0.00944816\pi$
$68$	−2.46030	+	1.56818i	−0.298356	+	0.190169i
$69$	−3.72210	−	3.72210i	−0.448089	−	0.448089i
$70$		0			0
$71$		−	2.89148i		−	0.343156i	−0.985171	−	0.171578i	$-0.945113\pi$
$71$		−	2.89148i		−	0.343156i	0.985171	−	0.171578i	$-0.0548865\pi$
$72$	−10.3795	+	11.8437i	−1.22323	+	1.39579i
$73$			0.640221i			0.0749322i	0.999298	+	0.0374661i	$0.0119286\pi$
$73$			0.640221i			0.0749322i	−0.999298	+	0.0374661i	$0.988071\pi$
$74$	−0.0475032	+	0.0866103i	−0.00552213	+	0.0100682i
$75$	−18.5499	−	18.5499i	−2.14196	−	2.14196i
$76$	−1.64032	+	7.40701i	−0.188158	+	0.849642i
$77$		0			0
$78$	23.5788	−	6.87551i	2.66977	−	0.778498i
$79$	−0.749820			−0.0843613			−0.0421807	−	0.999110i	$-0.513431\pi$
$79$	−0.749820			−0.0843613			−0.0421807	+	0.999110i	$0.513431\pi$
$80$	−14.0428	+	5.11841i	−1.57003	+	0.572256i
$81$	−5.29721			−0.588579
$82$	13.7299	−	4.00359i	1.51621	−	0.442122i
$83$	4.51473	−	4.51473i	0.495556	−	0.495556i	−0.414495	−	0.910051i	$-0.636042\pi$
$83$	4.51473	−	4.51473i	0.495556	−	0.495556i	0.910051	+	0.414495i	$0.136042\pi$
$84$		0			0
$85$	−3.85440	−	3.85440i	−0.418068	−	0.418068i
$86$	4.37640	−	7.97928i	0.471919	−	0.860428i
$87$		−	1.22433i		−	0.131262i
$88$	−0.179600	−	2.72587i	−0.0191455	−	0.290579i
$89$		−	15.4712i		−	1.63995i	−0.572401	−	0.819974i	$-0.693988\pi$
$89$		−	15.4712i		−	1.63995i	0.572401	−	0.819974i	$-0.306012\pi$
$90$	−25.7971	−	14.1490i	−2.71926	−	1.49143i
$91$		0			0
$92$	−1.93317	−	3.03294i	−0.201547	−	0.316206i
$93$	−2.40820	+	2.40820i	−0.249718	+	0.249718i
$94$	4.38947	+	15.0532i	0.452740	+	1.55262i
$95$	−14.1739			−1.45421
$96$	−13.3476	+	9.79858i	−1.36228	+	1.00006i
$97$	13.7459			1.39569			0.697843	−	0.716250i	$-0.254143\pi$
$97$	13.7459			1.39569			0.697843	+	0.716250i	$0.254143\pi$
$98$		0			0
$99$	3.80252	−	3.80252i	0.382168	−	0.382168i
$100$	−9.63438	−	15.1153i	−0.963438	−	1.51153i
$101$	3.27564	+	3.27564i	0.325938	+	0.325938i	0.851040	−	0.525101i	$-0.175973\pi$
$101$	3.27564	+	3.27564i	0.325938	+	0.325938i	−0.525101	+	0.851040i	$0.675973\pi$
$102$	−5.29462	−	2.90394i	−0.524245	−	0.287533i
$103$			8.74763i			0.861930i	0.902369	+	0.430965i	$0.141827\pi$
$103$			8.74763i			0.861930i	−0.902369	+	0.430965i	$0.858173\pi$
$104$	16.7454	−	1.10331i	1.64202	−	0.108189i
$105$		0			0
$106$	0.401901	−	0.732768i	0.0390361	−	0.0711727i
$107$	−3.17643	−	3.17643i	−0.307078	−	0.307078i	0.536697	−	0.843775i	$-0.319672\pi$
$107$	−3.17643	−	3.17643i	−0.307078	−	0.307078i	−0.843775	+	0.536697i	$0.819672\pi$
$108$	−14.6769	−	3.25028i	−1.41229	−	0.312758i
$109$	4.35303	−	4.35303i	0.416945	−	0.416945i	−0.467204	−	0.884149i	$-0.654739\pi$
$109$	4.35303	−	4.35303i	0.416945	−	0.416945i	0.884149	+	0.467204i	$0.154739\pi$
$110$	4.89976	−	1.42876i	0.467174	−	0.136227i
$111$	−0.204455			−0.0194060
$112$		0			0
$113$	0.0896489			0.00843346			0.00421673	−	0.999991i	$-0.498658\pi$
$113$	0.0896489			0.00843346			0.00421673	+	0.999991i	$0.498658\pi$
$114$	−15.0744	+	4.39564i	−1.41184	+	0.411690i
$115$	4.75152	−	4.75152i	0.443081	−	0.443081i
$116$	0.180876	−	0.816762i	0.0167939	−	0.0758345i
$117$	23.3595	+	23.3595i	2.15958	+	2.15958i
$118$	−3.60425	+	6.57145i	−0.331798	+	0.604951i
$119$		0			0
$120$	−23.2657	−	20.3893i	−2.12385	−	1.86128i
$121$		−	10.0672i		−	0.915197i
$122$	−12.3145	−	6.75415i	−1.11490	−	0.611492i
$123$	20.9311	+	20.9311i	1.88729	+	1.88729i
$124$	−1.96231	+	1.25076i	−0.176221	+	0.112321i
$125$	10.4693	−	10.4693i	0.936401	−	0.936401i
$126$		0			0
$127$	−17.0084			−1.50925			−0.754624	−	0.656157i	$-0.772181\pi$
$127$	−17.0084			−1.50925			−0.754624	+	0.656157i	$0.772181\pi$
$128$	−10.3519	+	4.56483i	−0.914989	+	0.403478i
$129$	18.8362			1.65843
$130$	8.77706	+	30.0999i	0.769799	+	2.63994i
$131$	14.0070	−	14.0070i	1.22379	−	1.22379i	0.257521	−	0.966273i	$-0.417094\pi$
$131$	14.0070	−	14.0070i	1.22379	−	1.22379i	0.966273	−	0.257521i	$-0.0829057\pi$
$132$	4.76796	−	3.03905i	0.414997	−	0.264516i
$133$		0			0
$134$	14.7732	+	8.10266i	1.27621	+	0.699963i
$135$		−	28.0854i		−	2.41720i
$136$	−3.10308	−	2.71945i	−0.266087	−	0.233191i
$137$		−	0.915437i		−	0.0782111i	−0.999235	−	0.0391055i	$-0.987549\pi$
$137$		−	0.915437i		−	0.0782111i	0.999235	−	0.0391055i	$-0.0124509\pi$
$138$	3.57983	−	6.52694i	0.304736	−	0.555610i
$139$	2.74533	+	2.74533i	0.232856	+	0.232856i	0.813884	−	0.581028i	$-0.197349\pi$
$139$	2.74533	+	2.74533i	0.232856	+	0.232856i	−0.581028	+	0.813884i	$0.697349\pi$
$140$		0			0
$141$	−22.9485	+	22.9485i	−1.93262	+	1.93262i
$142$	3.92568	−	1.14472i	0.329436	−	0.0960625i
$143$	−5.73051			−0.479209
$144$	−20.1890	−	9.40305i	−1.68241	−	0.783587i
$145$	1.56294			0.129795
$146$	−0.869209	+	0.253459i	−0.0719362	+	0.0209764i
$147$		0			0
$148$	−0.136394	−	0.0302052i	−0.0112115	−	0.00248286i
$149$	−5.96683	−	5.96683i	−0.488822	−	0.488822i	0.419112	−	0.907934i	$-0.362341\pi$
$149$	−5.96683	−	5.96683i	−0.488822	−	0.488822i	−0.907934	+	0.419112i	$0.862341\pi$
$150$	17.8409	−	32.5285i	1.45670	−	2.65594i
$151$		−	5.07755i		−	0.413206i	−0.978425	−	0.206603i	$-0.933759\pi$
$151$		−	5.07755i		−	0.413206i	0.978425	−	0.206603i	$-0.0662408\pi$
$152$	−10.7057	+	0.705367i	−0.868344	+	0.0572129i
$153$		−	8.12229i		−	0.656648i
$154$		0			0
$155$	−3.07423	−	3.07423i	−0.246928	−	0.246928i
$156$	18.6694	+	29.2903i	1.49474	+	2.34510i
$157$	−3.69391	+	3.69391i	−0.294806	+	0.294806i	−0.838976	−	0.544169i	$-0.816845\pi$
$157$	−3.69391	+	3.69391i	−0.294806	+	0.294806i	0.544169	+	0.838976i	$0.316845\pi$
$158$	−0.296848	−	1.01801i	−0.0236160	−	0.0809884i
$159$	1.72980			0.137182
$160$	−12.5085	−	17.0391i	−0.988888	−	1.34706i
$161$		0			0
$162$	−2.09713	−	7.19187i	−0.164766	−	0.565047i
$163$	8.19576	−	8.19576i	0.641941	−	0.641941i	−0.309091	−	0.951032i	$-0.600025\pi$
$163$	8.19576	−	8.19576i	0.641941	−	0.641941i	0.951032	+	0.309091i	$0.100025\pi$
$164$	10.8711	+	17.0556i	0.848891	+	1.33182i
$165$	7.46966	+	7.46966i	0.581512	+	0.581512i
$166$	7.91686	+	4.34216i	0.614468	+	0.337017i
$167$			13.7471i			1.06378i	0.846813	+	0.531891i	$0.178518\pi$
$167$			13.7471i			1.06378i	−0.846813	+	0.531891i	$0.821482\pi$
$168$		0			0
$169$		−	22.2033i		−	1.70795i
$170$	3.70708	−	6.75894i	0.284320	−	0.518387i
$171$	−14.9341	−	14.9341i	−1.14204	−	1.14204i
$172$	12.5658	+	2.78277i	0.958135	+	0.212184i
$173$	5.58305	−	5.58305i	0.424472	−	0.424472i	−0.462268	−	0.886740i	$-0.652964\pi$
$173$	5.58305	−	5.58305i	0.424472	−	0.424472i	0.886740	+	0.462268i	$0.152964\pi$
$174$	1.66223	−	0.484703i	0.126014	−	0.0367452i
$175$		0			0
$176$	3.62973	−	1.32299i	0.273601	−	0.0997242i
$177$	−15.5128			−1.16601
$178$	21.0048	−	6.12495i	1.57438	−	0.459085i
$179$	6.82530	−	6.82530i	0.510147	−	0.510147i	−0.404424	−	0.914571i	$-0.632528\pi$
$179$	6.82530	−	6.82530i	0.510147	−	0.510147i	0.914571	+	0.404424i	$0.132528\pi$
$180$	8.99672	−	40.6255i	0.670576	−	3.02804i
$181$	−15.1263	−	15.1263i	−1.12433	−	1.12433i	−0.991083	−	0.133250i	$-0.957459\pi$
$181$	−15.1263	−	15.1263i	−1.12433	−	1.12433i	−0.133250	−	0.991083i	$-0.542541\pi$
$182$		0			0
$183$		−	29.0701i		−	2.14892i
$184$	3.35241	−	3.82533i	0.247143	−	0.282007i
$185$		−	0.261001i		−	0.0191892i
$186$	−4.22292	−	2.31615i	−0.309640	−	0.169828i
$187$	0.996274	+	0.996274i	0.0728548	+	0.0728548i
$188$	−18.6995	+	11.9189i	−1.36380	+	0.869277i
$189$		0			0
$190$	−5.61134	−	19.2434i	−0.407089	−	1.39607i
$191$	19.8728			1.43794			0.718971	−	0.695040i	$-0.244613\pi$
$191$	19.8728			1.43794			0.718971	+	0.695040i	$0.244613\pi$
$192$	−18.5875	−	14.2424i	−1.34143	−	1.02786i
$193$	−11.8829			−0.855352			−0.427676	−	0.903932i	$-0.640668\pi$
$193$	−11.8829			−0.855352			−0.427676	+	0.903932i	$0.640668\pi$
$194$	5.44191	+	18.6624i	0.390707	+	1.33988i
$195$	−45.8872	+	45.8872i	−3.28605	+	3.28605i
$196$		0			0
$197$	6.61994	+	6.61994i	0.471651	+	0.471651i	0.902449	−	0.430797i	$-0.141768\pi$
$197$	6.61994	+	6.61994i	0.471651	+	0.471651i	−0.430797	+	0.902449i	$0.641768\pi$
$198$	6.66796	+	3.65718i	0.473872	+	0.259904i
$199$		−	24.0632i		−	1.70579i	−0.522079	−	0.852897i	$-0.674843\pi$
$199$		−	24.0632i		−	1.70579i	0.522079	−	0.852897i	$-0.325157\pi$
$200$	16.7075	−	19.0644i	1.18140	−	1.34805i
$201$			34.8741i			2.45983i
$202$	−3.15044	+	5.74404i	−0.221664	+	0.404149i
$203$		0			0
$204$	1.84649	−	8.33799i	0.129280	−	0.583776i
$205$	−26.7200	+	26.7200i	−1.86620	+	1.86620i
$206$	−11.8764	+	3.46313i	−0.827468	+	0.241287i
$207$	10.0128			0.695935
$208$	8.12733	+	22.2980i	0.563529	+	1.54609i
$209$	3.66362			0.253418
$210$		0			0
$211$	−18.2158	+	18.2158i	−1.25403	+	1.25403i	−0.300133	+	0.953897i	$0.597031\pi$
$211$	−18.2158	+	18.2158i	−1.25403	+	1.25403i	−0.953897	+	0.300133i	$0.902969\pi$
$212$	1.15397	+	0.255552i	0.0792548	+	0.0175514i
$213$	5.98468	+	5.98468i	0.410063	+	0.410063i
$214$	3.05502	−	5.57008i	0.208837	−	0.380763i
$215$			24.0457i			1.63990i
$216$	−1.39768	−	21.2132i	−0.0950999	−	1.44337i
$217$		0			0
$218$	7.63332	+	4.18665i	0.516994	+	0.283556i
$219$	−1.32510	−	1.32510i	−0.0895423	−	0.0895423i
$220$	3.87956	+	6.08662i	0.261560	+	0.410360i
$221$	−6.12026	+	6.12026i	−0.411693	+	0.411693i
$222$	−0.0809424	−	0.277583i	−0.00543250	−	0.0186301i
$223$	8.33457			0.558124			0.279062	−	0.960273i	$-0.409976\pi$
$223$	8.33457			0.558124			0.279062	+	0.960273i	$0.409976\pi$
$224$		0			0
$225$	49.9008			3.32672
$226$	0.0354914	+	0.121714i	0.00236085	+	0.00809627i
$227$	−7.87294	+	7.87294i	−0.522545	+	0.522545i	−0.918339	−	0.395794i	$-0.870469\pi$
$227$	−7.87294	+	7.87294i	−0.522545	+	0.522545i	0.395794	+	0.918339i	$0.370469\pi$
$228$	−11.9357	−	18.7258i	−0.790459	−	1.24015i
$229$	−8.97014	−	8.97014i	−0.592763	−	0.592763i	0.345614	−	0.938377i	$-0.387671\pi$
$229$	−8.97014	−	8.97014i	−0.592763	−	0.592763i	−0.938377	+	0.345614i	$0.887671\pi$
$230$	8.33209	+	4.56990i	0.549401	+	0.301330i
$231$		0			0
$232$	1.18050	−	0.0777801i	0.0775037	−	0.00510651i
$233$			22.5390i			1.47658i	0.674483	+	0.738291i	$0.264367\pi$
$233$			22.5390i			1.47658i	−0.674483	+	0.738291i	$0.735633\pi$
$234$	−22.4666	+	40.9623i	−1.46869	+	2.67779i
$235$	−29.2954	−	29.2954i	−1.91102	−	1.91102i
$236$	−10.3488	−	2.29179i	−0.673647	−	0.149183i
$237$	1.55195	−	1.55195i	0.100810	−	0.100810i
$238$		0			0
$239$	13.3677			0.864687			0.432344	−	0.901709i	$-0.357687\pi$
$239$	13.3677			0.864687			0.432344	+	0.901709i	$0.357687\pi$
$240$	18.4713	−	39.6591i	1.19232	−	2.55998i
$241$	−19.3942			−1.24929			−0.624645	−	0.780909i	$-0.714756\pi$
$241$	−19.3942			−1.24929			−0.624645	+	0.780909i	$0.714756\pi$
$242$	13.6679	−	3.98552i	0.878606	−	0.256199i
$243$	−4.98040	+	4.98040i	−0.319493	+	0.319493i
$244$	4.29467	−	19.3930i	0.274938	−	1.24151i
$245$		0			0
$246$	−20.1311	+	36.7040i	−1.28351	+	2.34016i
$247$			22.5062i			1.43203i
$248$	−2.47498	−	2.16900i	−0.157162	−	0.137732i
$249$			18.6888i			1.18436i
$250$	18.3585	+	10.0691i	1.16110	+	0.636827i
$251$	−8.09990	−	8.09990i	−0.511261	−	0.511261i	0.403652	−	0.914913i	$-0.367741\pi$
$251$	−8.09990	−	8.09990i	−0.511261	−	0.511261i	−0.914913	+	0.403652i	$0.867741\pi$
$252$		0			0
$253$	−1.22816	+	1.22816i	−0.0772136	+	0.0772136i
$254$	−6.73349	−	23.0918i	−0.422497	−	1.44891i
$255$	15.9554			0.999165
$256$	−10.2958	−	12.2473i	−0.643487	−	0.765457i
$257$	−16.9823			−1.05932			−0.529662	−	0.848209i	$-0.677681\pi$
$257$	−16.9823			−1.05932			−0.529662	+	0.848209i	$0.677681\pi$
$258$	7.45711	+	25.5733i	0.464259	+	1.59212i
$259$		0			0
$260$	−37.3910	+	23.8327i	−2.31889	+	1.47804i
$261$	1.64677	+	1.64677i	0.101933	+	0.101933i
$262$	24.5621	+	13.4716i	1.51745	+	0.832277i
$263$		−	4.39734i		−	0.271152i	−0.990767	−	0.135576i	$-0.956712\pi$
$263$		−	4.39734i		−	0.271152i	0.990767	−	0.135576i	$-0.0432884\pi$
$264$	6.01363	+	5.27018i	0.370114	+	0.324357i
$265$			2.20820i			0.135649i
$266$		0			0
$267$	32.0218	+	32.0218i	1.95970	+	1.95970i
$268$	−5.15214	+	23.2649i	−0.314717	+	1.42113i
$269$	7.71509	−	7.71509i	0.470397	−	0.470397i	−0.431646	−	0.902043i	$-0.642067\pi$
$269$	7.71509	−	7.71509i	0.470397	−	0.470397i	0.902043	+	0.431646i	$0.142067\pi$
$270$	38.1307	−	11.1188i	2.32056	−	0.676669i
$271$	−16.7376			−1.01674			−0.508369	−	0.861139i	$-0.669752\pi$
$271$	−16.7376			−1.01674			−0.508369	+	0.861139i	$0.669752\pi$
$272$	2.46363	−	5.28957i	0.149380	−	0.320728i
$273$		0			0
$274$	1.24286	−	0.362415i	0.0750840	−	0.0218943i
$275$	−6.12080	+	6.12080i	−0.369098	+	0.369098i
$276$	10.2787	+	2.27626i	0.618703	+	0.137015i
$277$	−13.6141	−	13.6141i	−0.817989	−	0.817989i	0.167827	−	0.985816i	$-0.446325\pi$
$277$	−13.6141	−	13.6141i	−0.817989	−	0.817989i	−0.985816	+	0.167827i	$0.946325\pi$
$278$	−2.64040	+	4.81411i	−0.158360	+	0.288731i
$279$		−	6.47824i		−	0.387842i
$280$		0			0
$281$		−	14.9711i		−	0.893100i	−0.894759	−	0.446550i	$-0.852652\pi$
$281$		−	14.9711i		−	0.893100i	0.894759	−	0.446550i	$-0.147348\pi$
$282$	−40.2417	−	22.0714i	−2.39636	−	1.31433i
$283$	6.66191	+	6.66191i	0.396010	+	0.396010i	0.876823	−	0.480813i	$-0.159659\pi$
$283$	6.66191	+	6.66191i	0.396010	+	0.396010i	−0.480813	+	0.876823i	$0.659659\pi$
$284$	3.10830	+	4.87659i	0.184444	+	0.289373i
$285$	29.3365	−	29.3365i	1.73775	−	1.73775i
$286$	−2.26867	−	7.78014i	−0.134149	−	0.460049i
$287$		0			0
$288$	4.77357	−	31.1325i	0.281285	−	1.83450i
$289$	−14.8719			−0.874820
$290$	0.618756	+	2.12195i	0.0363346	+	0.124605i
$291$	−28.4508	+	28.4508i	−1.66781	+	1.66781i
$292$	−0.688227	−	1.07976i	−0.0402754	−	0.0631880i
$293$	1.24795	+	1.24795i	0.0729060	+	0.0729060i	0.742620	−	0.669714i	$-0.233583\pi$
$293$	1.24795	+	1.24795i	0.0729060	+	0.0729060i	−0.669714	+	0.742620i	$0.733583\pi$
$294$		0			0
$295$		−	19.8031i		−	1.15298i
$296$	−0.0129888	−	0.197137i	−0.000754959	−	0.0114583i
$297$			7.25942i			0.421234i
$298$	5.73876	−	10.4632i	0.332438	−	0.606118i
$299$	−7.54475	−	7.54475i	−0.436324	−	0.436324i
$300$	51.2260	+	11.3443i	2.95754	+	0.654962i
$301$		0			0
$302$	6.89365	−	2.01017i	0.396685	−	0.115672i
$303$	−13.5596			−0.778978
$304$	−5.19595	−	14.2555i	−0.298008	−	0.817610i
$305$	37.1099			2.12491
$306$	11.0274	−	3.21556i	0.630394	−	0.183821i
$307$	17.4736	−	17.4736i	0.997273	−	0.997273i	−0.00272350	−	0.999996i	$-0.500867\pi$
$307$	17.4736	−	17.4736i	0.997273	−	0.997273i	0.999996	+	0.00272350i	$0.000866918\pi$
$308$		0			0
$309$	−18.1055	−	18.1055i	−1.02999	−	1.02999i
$310$	2.95672	−	5.39085i	0.167930	−	0.306180i
$311$			28.4805i			1.61498i	0.589880	+	0.807491i	$0.299175\pi$
$311$			28.4805i			1.61498i	−0.589880	+	0.807491i	$0.700825\pi$
$312$	−32.3755	+	36.9426i	−1.83290	+	2.09147i
$313$		−	15.6876i		−	0.886714i	−0.896345	−	0.443357i	$-0.853787\pi$
$313$		−	15.6876i		−	0.886714i	0.896345	−	0.443357i	$-0.146213\pi$
$314$	−6.47751	−	3.55272i	−0.365547	−	0.200492i
$315$		0			0
$316$	1.26460	−	0.806044i	0.0711393	−	0.0453435i
$317$	11.9478	−	11.9478i	0.671054	−	0.671054i	−0.286905	−	0.957959i	$-0.592626\pi$
$317$	11.9478	−	11.9478i	0.671054	−	0.671054i	0.957959	+	0.286905i	$0.0926263\pi$
$318$	0.684815	+	2.34849i	0.0384025	+	0.131697i
$319$	−0.403983			−0.0226187
$320$	18.1815	−	23.7282i	1.01637	−	1.32644i
$321$	13.1489			0.733901
$322$		0			0
$323$	3.91279	−	3.91279i	0.217714	−	0.217714i
$324$	8.93395	−	5.69442i	0.496331	−	0.316357i
$325$	−37.6009	−	37.6009i	−2.08573	−	2.08573i
$326$	14.3718	+	7.88250i	0.795979	+	0.436571i
$327$			18.0195i			0.996480i
$328$	−18.8521	+	21.5116i	−1.04093	+	1.18778i
$329$		0			0
$330$	−7.18415	+	13.0985i	−0.395474	+	0.721050i
$331$	21.0571	+	21.0571i	1.15741	+	1.15741i	0.985032	+	0.172374i	$0.0551437\pi$
$331$	21.0571	+	21.0571i	1.15741	+	1.15741i	0.172374	+	0.985032i	$0.444856\pi$
$332$	−2.76100	+	12.4675i	−0.151529	+	0.684244i
$333$	0.275001	−	0.275001i	0.0150699	−	0.0150699i
$334$	−18.6640	+	5.44237i	−1.02125	+	0.297793i
$335$	−44.5192			−2.43234
$336$		0			0
$337$	−1.90123			−0.103567			−0.0517833	−	0.998658i	$-0.516491\pi$
$337$	−1.90123			−0.103567			−0.0517833	+	0.998658i	$0.516491\pi$
$338$	30.1448	−	8.79015i	1.63966	−	0.478121i
$339$	−0.185552	+	0.185552i	−0.0100778	+	0.0100778i
$340$	10.6440	+	2.35717i	0.577253	+	0.127836i
$341$	0.794617	+	0.794617i	0.0430309	+	0.0430309i
$342$	14.3633	−	26.1879i	0.776679	−	1.41608i
$343$		0			0
$344$	1.19664	+	18.1619i	0.0645185	+	0.979225i
$345$			19.6690i			1.05894i
$346$	9.79024	+	5.36965i	0.526326	+	0.288674i
$347$	−20.2774	−	20.2774i	−1.08855	−	1.08855i	−0.995678	−	0.0928678i	$-0.970397\pi$
$347$	−20.2774	−	20.2774i	−1.08855	−	1.08855i	−0.0928678	−	0.995678i	$-0.529603\pi$
$348$	1.31613	+	2.06487i	0.0705521	+	0.110689i
$349$	−5.48808	+	5.48808i	−0.293770	+	0.293770i	−0.838568	−	0.544797i	$-0.816607\pi$
$349$	−5.48808	+	5.48808i	−0.293770	+	0.293770i	0.544797	+	0.838568i	$0.316607\pi$
$350$		0			0
$351$	−44.5957			−2.38034
$352$	3.23317	+	4.40422i	0.172329	+	0.234746i
$353$	2.10289			0.111925			0.0559627	−	0.998433i	$-0.482177\pi$
$353$	2.10289			0.111925			0.0559627	+	0.998433i	$0.482177\pi$
$354$	−6.14141	−	21.0613i	−0.326412	−	1.11939i
$355$	−7.63985	+	7.63985i	−0.405481	+	0.405481i
$356$	16.6313	+	26.0928i	0.881459	+	1.38292i
$357$		0			0
$358$	11.9686	+	6.56442i	0.632560	+	0.346941i
$359$		−	10.7107i		−	0.565288i	−0.959225	−	0.282644i	$-0.908789\pi$
$359$		−	10.7107i		−	0.565288i	0.959225	−	0.282644i	$-0.0912115\pi$
$360$	58.7177	−	3.86875i	3.09470	−	0.203901i
$361$			4.61140i			0.242705i
$362$	14.5482	−	26.5250i	0.764635	−	1.39412i
$363$	20.8366	+	20.8366i	1.09364	+	1.09364i
$364$		0			0
$365$	1.69159	−	1.69159i	0.0885416	−	0.0885416i
$366$	39.4676	−	11.5086i	2.06300	−	0.601566i
$367$	18.1890			0.949460			0.474730	−	0.880131i	$-0.342546\pi$
$367$	18.1890			0.949460			0.474730	+	0.880131i	$0.342546\pi$
$368$	6.52073	+	3.03704i	0.339916	+	0.158317i
$369$	−56.3063			−2.93119
$370$	0.354353	−	0.103328i	0.0184220	−	0.00537179i
$371$		0			0
$372$	1.47274	−	6.65029i	0.0763580	−	0.344801i
$373$	−0.690889	−	0.690889i	−0.0357729	−	0.0357729i	0.688994	−	0.724767i	$-0.258053\pi$
$373$	−0.690889	−	0.690889i	−0.0357729	−	0.0357729i	−0.724767	+	0.688994i	$0.758053\pi$
$374$	−0.958194	+	1.74703i	−0.0495470	+	0.0903367i
$375$			43.3378i			2.23796i
$376$	−23.5850	−	20.6692i	−1.21630	−	1.06593i
$377$		−	2.48173i		−	0.127816i
$378$		0			0
$379$	17.6845	+	17.6845i	0.908391	+	0.908391i	0.996142	−	0.0877516i	$-0.0279682\pi$
$379$	17.6845	+	17.6845i	0.908391	+	0.908391i	−0.0877516	+	0.996142i	$0.527968\pi$
$380$	23.9048	−	15.2367i	1.22629	−	0.781626i
$381$	35.2033	−	35.2033i	1.80352	−	1.80352i
$382$	7.86749	+	26.9807i	0.402536	+	1.38045i
$383$	11.2504			0.574869			0.287435	−	0.957800i	$-0.407198\pi$
$383$	11.2504			0.574869			0.287435	+	0.957800i	$0.407198\pi$
$384$	11.9779	−	30.8741i	0.611245	−	1.57554i
$385$		0			0
$386$	−4.70437	−	16.1331i	−0.239446	−	0.821153i
$387$	−25.3354	+	25.3354i	−1.28787	+	1.28787i
$388$	−23.1830	+	14.7766i	−1.17694	+	0.750171i
$389$	25.1321	+	25.1321i	1.27425	+	1.27425i	0.943838	+	0.330408i	$0.107186\pi$
$389$	25.1321	+	25.1321i	1.27425	+	1.27425i	0.330408	+	0.943838i	$0.392814\pi$
$390$	−80.4661	−	44.1333i	−4.07456	−	2.23478i
$391$			2.62338i			0.132670i
$392$		0			0
$393$			57.9821i			2.92481i
$394$	−6.36691	+	11.6085i	−0.320760	+	0.584827i
$395$	1.98117	+	1.98117i	0.0996834	+	0.0996834i
$396$	−2.32545	+	10.5007i	−0.116858	+	0.527682i
$397$	−2.16775	+	2.16775i	−0.108796	+	0.108796i	−0.759409	−	0.650613i	$-0.774512\pi$
$397$	−2.16775	+	2.16775i	−0.108796	+	0.108796i	0.650613	+	0.759409i	$0.274512\pi$
$398$	32.6699	−	9.52645i	1.63759	−	0.477518i
$399$		0			0
$400$	32.4975	+	15.1358i	1.62487	+	0.756789i
$401$	21.3633			1.06683			0.533416	−	0.845853i	$-0.320908\pi$
$401$	21.3633			1.06683			0.533416	+	0.845853i	$0.320908\pi$
$402$	−47.3476	+	13.8064i	−2.36148	+	0.688602i
$403$	−4.88145	+	4.88145i	−0.243162	+	0.243162i
$404$	−9.04575	−	2.00323i	−0.450043	−	0.0996643i
$405$	13.9963	+	13.9963i	0.695479	+	0.695479i
$406$		0			0
$407$			0.0674628i			0.00334400i
$408$	12.0513	−	0.794025i	0.596626	−	0.0393101i
$409$			10.1161i			0.500210i	0.968219	+	0.250105i	$0.0804652\pi$
$409$			10.1161i			0.500210i	−0.968219	+	0.250105i	$0.919535\pi$
$410$	−46.8551	−	25.6987i	−2.31401	−	1.26917i
$411$	1.89474	+	1.89474i	0.0934605	+	0.0934605i
$412$	−9.40357	−	14.7532i	−0.463280	−	0.726839i
$413$		0			0
$414$	3.96398	+	13.5940i	0.194819	+	0.668110i
$415$	−23.8576			−1.17112
$416$	−27.0558	+	19.8618i	−1.32652	+	0.973807i
$417$	−11.3644			−0.556515
$418$	1.45040	+	4.97399i	0.0709414	+	0.243286i
$419$	17.7452	−	17.7452i	0.866909	−	0.866909i	−0.125220	−	0.992129i	$-0.539964\pi$
$419$	17.7452	−	17.7452i	0.866909	−	0.866909i	0.992129	+	0.125220i	$0.0399637\pi$
$420$		0			0
$421$	−18.2787	−	18.2787i	−0.890851	−	0.890851i	0.103752	−	0.994603i	$-0.466915\pi$
$421$	−18.2787	−	18.2787i	−0.890851	−	0.890851i	−0.994603	+	0.103752i	$0.966915\pi$
$422$	−31.9426	−	17.5196i	−1.55494	−	0.852840i
$423$		−	61.7334i		−	3.00158i
$424$	0.109892	+	1.66788i	0.00533683	+	0.0809993i
$425$			13.0742i			0.634191i
$426$	−5.75593	+	10.4945i	−0.278876	+	0.508461i
$427$		0			0
$428$	8.77179	+	1.94256i	0.424001	+	0.0938972i
$429$	11.8608	−	11.8608i	0.572644	−	0.572644i
$430$	−32.6461	+	9.51950i	−1.57433	+	0.459071i
$431$	22.3440			1.07627			0.538136	−	0.842858i	$-0.319128\pi$
$431$	22.3440			1.07627			0.538136	+	0.842858i	$0.319128\pi$
$432$	28.2472	−	10.2957i	1.35904	−	0.495353i
$433$	−9.86560			−0.474111			−0.237055	−	0.971496i	$-0.576182\pi$
$433$	−9.86560			−0.474111			−0.237055	+	0.971496i	$0.576182\pi$
$434$		0			0
$435$	−3.23491	+	3.23491i	−0.155102	+	0.155102i
$436$	−2.66211	+	12.0210i	−0.127492	+	0.575702i
$437$	4.82350	+	4.82350i	0.230739	+	0.230739i
$438$	1.27446	−	2.32365i	0.0608958	−	0.111028i
$439$		−	19.4362i		−	0.927640i	−0.885929	−	0.463820i	$-0.846478\pi$
$439$		−	19.4362i		−	0.927640i	0.885929	−	0.463820i	$-0.153522\pi$
$440$	−6.72774	+	7.67681i	−0.320732	+	0.365978i
$441$		0			0
$442$	−10.7323	−	5.88632i	−0.510481	−	0.279984i
$443$	17.8660	+	17.8660i	0.848841	+	0.848841i	0.989989	−	0.141148i	$-0.0450792\pi$
$443$	17.8660	+	17.8660i	0.848841	+	0.848841i	−0.141148	+	0.989989i	$0.545079\pi$
$444$	0.344822	−	0.219786i	0.0163645	−	0.0104306i
$445$	−40.8780	+	40.8780i	−1.93780	+	1.93780i
$446$	3.29960	+	11.3156i	0.156240	+	0.535809i
$447$	24.6998			1.16826
$448$		0			0
$449$	−18.8980			−0.891850			−0.445925	−	0.895070i	$-0.647125\pi$
$449$	−18.8980			−0.891850			−0.445925	+	0.895070i	$0.647125\pi$
$450$	19.7554	+	67.7488i	0.931277	+	3.19371i
$451$	6.90650	−	6.90650i	0.325214	−	0.325214i
$452$	−0.151196	+	0.0963712i	−0.00711167	+	0.00453292i
$453$	10.5093	+	10.5093i	0.493771	+	0.493771i
$454$	−13.8057	−	7.57202i	−0.647934	−	0.355372i
$455$		0			0
$456$	20.6982	−	23.6181i	0.969284	−	1.10602i
$457$			9.22546i			0.431549i	0.976443	+	0.215774i	$0.0692275\pi$
$457$			9.22546i			0.431549i	−0.976443	+	0.215774i	$0.930772\pi$
$458$	8.62727	−	15.7297i	0.403126	−	0.735001i
$459$	7.75316	+	7.75316i	0.361886	+	0.361886i
$460$	−2.90581	+	13.1214i	−0.135484	+	0.611789i
$461$	−10.6272	+	10.6272i	−0.494960	+	0.494960i	−0.909865	−	0.414905i	$-0.863815\pi$
$461$	−10.6272	+	10.6272i	−0.494960	+	0.494960i	0.414905	+	0.909865i	$0.363815\pi$
$462$		0			0
$463$	32.4877			1.50983			0.754916	−	0.655821i	$-0.227678\pi$
$463$	32.4877			1.50983			0.754916	+	0.655821i	$0.227678\pi$
$464$	0.572952	+	1.57194i	0.0265986	+	0.0729755i
$465$	12.7258			0.590146
$466$	−30.6006	+	8.92304i	−1.41754	+	0.413352i
$467$	12.4328	−	12.4328i	0.575323	−	0.575323i	−0.358288	−	0.933611i	$-0.616640\pi$
$467$	12.4328	−	12.4328i	0.575323	−	0.575323i	0.933611	+	0.358288i	$0.116640\pi$
$468$	−64.5076	−	14.2856i	−2.98187	−	0.660350i
$469$		0			0
$470$	28.1756	−	51.3713i	1.29964	−	2.36958i
$471$		−	15.2910i		−	0.704574i
$472$	−0.985510	−	14.9575i	−0.0453618	−	0.688475i
$473$		−	6.21525i		−	0.285777i
$474$	2.72144	+	1.49263i	0.125000	+	0.0685587i
$475$	24.0390	+	24.0390i	1.10298	+	1.10298i
$476$		0			0
$477$	−2.32665	+	2.32665i	−0.106530	+	0.106530i
$478$	5.29220	+	18.1490i	0.242059	+	0.830115i
$479$	−36.2808			−1.65771			−0.828857	−	0.559461i	$-0.811008\pi$
$479$	−36.2808			−1.65771			−0.828857	+	0.559461i	$0.811008\pi$
$480$	61.1566	+	9.37718i	2.79140	+	0.428008i
$481$	−0.414434			−0.0188965
$482$	−7.67802	−	26.3309i	−0.349724	−	1.19934i
$483$		0			0
$484$	10.8220	+	16.9787i	0.491911	+	0.771757i
$485$	−36.3193	−	36.3193i	−1.64918	−	1.64918i
$486$	−8.73344	−	4.79003i	−0.396157	−	0.217280i
$487$		−	7.29888i		−	0.330744i	−0.986231	−	0.165372i	$-0.947118\pi$
$487$		−	7.29888i		−	0.330744i	0.986231	−	0.165372i	$-0.0528824\pi$
$488$	28.0295	−	1.84679i	1.26884	−	0.0836002i
$489$			33.9265i			1.53421i
$490$		0			0
$491$	11.4241	+	11.4241i	0.515561	+	0.515561i	0.916225	−	0.400664i	$-0.131221\pi$
$491$	11.4241	+	11.4241i	0.515561	+	0.515561i	−0.400664	+	0.916225i	$0.631221\pi$
$492$	−57.8017	−	12.8005i	−2.60590	−	0.577090i
$493$	−0.431459	+	0.431459i	−0.0194320	+	0.0194320i
$494$	−30.5559	+	8.91003i	−1.37478	+	0.400881i
$495$	−20.0940			−0.903157
$496$	1.96496	−	4.21890i	0.0882294	−	0.189434i
$497$		0			0
$498$	−25.3733	+	7.39877i	−1.13700	+	0.331547i
$499$	16.3221	−	16.3221i	0.730679	−	0.730679i	−0.240076	−	0.970754i	$-0.577172\pi$
$499$	16.3221	−	16.3221i	0.730679	−	0.730679i	0.970754	+	0.240076i	$0.0771722\pi$
$500$	−6.40253	+	28.9112i	−0.286330	+	1.29295i
$501$	−28.4532	−	28.4532i	−1.27119	−	1.27119i
$502$	7.79030	−	14.2037i	0.347698	−	0.633941i
$503$		−	11.6303i		−	0.518568i	−0.965801	−	0.259284i	$-0.916513\pi$
$503$		−	11.6303i		−	0.518568i	0.965801	−	0.259284i	$-0.0834866\pi$
$504$		0			0
$505$		−	17.3097i		−	0.770273i
$506$	−2.15365	−	1.18121i	−0.0957415	−	0.0525114i
$507$	45.9556	+	45.9556i	2.04096	+	2.04096i
$508$	28.6853	−	18.2837i	1.27270	−	0.811209i
$509$	19.8640	−	19.8640i	0.880457	−	0.880457i	−0.113124	−	0.993581i	$-0.536086\pi$
$509$	19.8640	−	19.8640i	0.880457	−	0.880457i	0.993581	+	0.113124i	$0.0360858\pi$
$510$	6.31662	+	21.6621i	0.279705	+	0.959216i
$511$		0			0
$512$	12.5518	−	18.8269i	0.554716	−	0.832040i
$513$	28.5109			1.25879
$514$	−6.72315	−	23.0563i	−0.296546	−	1.01697i
$515$	23.1129	−	23.1129i	1.01848	−	1.01848i
$516$	−31.7679	+	20.2486i	−1.39850	+	0.891394i
$517$	7.57218	+	7.57218i	0.333024	+	0.333024i
$518$		0			0
$519$			23.1112i			1.01447i
$520$	−47.1598	−	41.3295i	−2.06809	−	1.81242i
$521$			6.68809i			0.293010i	0.989210	+	0.146505i	$0.0468025\pi$
$521$			6.68809i			0.293010i	−0.989210	+	0.146505i	$0.953197\pi$
$522$	−1.58383	+	2.88772i	−0.0693222	+	0.126392i
$523$	9.25913	+	9.25913i	0.404874	+	0.404874i	0.879946	−	0.475073i	$-0.157578\pi$
$523$	9.25913	+	9.25913i	0.404874	+	0.404874i	−0.475073	+	0.879946i	$0.657578\pi$
$524$	−8.56600	+	38.6805i	−0.374208	+	1.68977i
$525$		0			0
$526$	5.97014	−	1.74088i	0.260310	−	0.0759058i
$527$	1.69732			0.0739365
$528$	−4.77440	+	10.2510i	−0.207779	+	0.446116i
$529$	19.7660			0.859393
$530$	−2.99801	+	0.874212i	−0.130225	+	0.0379734i
$531$	20.8654	−	20.8654i	0.905479	−	0.905479i
$532$		0			0
$533$	42.4276	+	42.4276i	1.83774	+	1.83774i
$534$	−30.7978	+	56.1522i	−1.33275	+	2.42994i
$535$			16.7855i			0.725700i
$536$	−33.6258	+	2.21551i	−1.45241	+	0.0956955i
$537$			28.2535i			1.21923i
$538$	13.5289	+	7.42020i	0.583272	+	0.319908i
$539$		0			0
$540$	30.1913	+	47.3670i	1.29923	+	2.03835i
$541$	13.4444	−	13.4444i	0.578019	−	0.578019i	−0.356338	−	0.934357i	$-0.615975\pi$
$541$	13.4444	−	13.4444i	0.578019	−	0.578019i	0.934357	+	0.356338i	$0.115975\pi$
$542$	−6.62631	−	22.7242i	−0.284624	−	0.976088i
$543$	62.6158			2.68710
$544$	8.15683	+	1.25069i	0.349721	+	0.0536230i
$545$	−23.0031			−0.985345
$546$		0			0
$547$	−12.0842	+	12.0842i	−0.516683	+	0.516683i	−0.916566	−	0.399883i	$-0.869051\pi$
$547$	−12.0842	+	12.0842i	−0.516683	+	0.516683i	0.399883	+	0.916566i	$0.369051\pi$
$548$	0.984080	+	1.54392i	0.0420378	+	0.0659530i
$549$	39.1004	+	39.1004i	1.66877	+	1.66877i
$550$	−10.7332	−	5.88684i	−0.457665	−	0.251016i
$551$			1.58662i			0.0675921i
$552$	0.978835	+	14.8562i	0.0416620	+	0.632322i
$553$		0			0
$554$	13.0937	−	23.8731i	0.556298	−	1.01427i
$555$	0.540210	+	0.540210i	0.0229306	+	0.0229306i
$556$	−7.58129	−	1.67892i	−0.321518	−	0.0712019i
$557$	23.8656	−	23.8656i	1.01122	−	1.01122i	0.0112795	−	0.999936i	$-0.496410\pi$
$557$	23.8656	−	23.8656i	1.01122	−	1.01122i	0.999936	−	0.0112795i	$-0.00359046\pi$
$558$	8.79532	−	2.56469i	0.372336	−	0.108572i
$559$	38.1812			1.61489
$560$		0			0
$561$	−4.12410			−0.174120
$562$	20.3258	−	5.92695i	0.857392	−	0.250013i
$563$	20.6614	−	20.6614i	0.870774	−	0.870774i	−0.121783	−	0.992557i	$-0.538861\pi$
$563$	20.6614	−	20.6614i	0.870774	−	0.870774i	0.992557	+	0.121783i	$0.0388612\pi$
$564$	14.0343	−	63.3729i	0.590949	−	2.66848i
$565$	−0.236870	−	0.236870i	−0.00996518	−	0.00996518i
$566$	−6.40728	+	11.6821i	−0.269318	+	0.491035i
$567$		0			0
$568$	−5.39025	+	6.15065i	−0.226170	+	0.258076i
$569$		−	26.4857i		−	1.11034i	−0.831738	−	0.555169i	$-0.812654\pi$
$569$		−	26.4857i		−	1.11034i	0.831738	−	0.555169i	$-0.187346\pi$
$570$	51.4435	+	28.2152i	2.15473	+	1.18181i
$571$	23.7561	+	23.7561i	0.994161	+	0.994161i	0.999983	−	0.00582227i	$-0.00185330\pi$
$571$	23.7561	+	23.7561i	0.994161	+	0.994161i	−0.00582227	+	0.999983i	$0.501853\pi$
$572$	9.66471	−	6.16020i	0.404102	−	0.257571i
$573$	−41.1319	+	41.1319i	−1.71831	+	1.71831i
$574$		0			0
$575$	−16.1172			−0.672134
$576$	44.1576	−	5.84421i	1.83990	−	0.243509i
$577$	27.5648			1.14754			0.573770	−	0.819017i	$-0.305480\pi$
$577$	27.5648			1.14754			0.573770	+	0.819017i	$0.305480\pi$
$578$	−5.88769	−	20.1912i	−0.244896	−	0.839842i
$579$	24.5948	−	24.5948i	1.02213	−	1.02213i
$580$	−2.63595	+	1.68013i	−0.109452	+	0.0697637i
$581$		0			0
$582$	−49.8902	−	27.3633i	−2.06802	−	1.13425i
$583$		−	0.570770i		−	0.0236389i
$584$	1.19349	−	1.36185i	0.0493869	−	0.0563539i
$585$		−	123.440i		−	5.10363i
$586$	−1.20025	+	2.18836i	−0.0495818	+	0.0904002i
$587$	−23.6471	−	23.6471i	−0.976018	−	0.976018i	0.0237007	−	0.999719i	$-0.492455\pi$
$587$	−23.6471	−	23.6471i	−0.976018	−	0.976018i	−0.999719	+	0.0237007i	$0.992455\pi$
$588$		0			0
$589$	3.12080	−	3.12080i	0.128590	−	0.128590i
$590$	26.8861	−	7.83993i	1.10689	−	0.322765i
$591$	−27.4034			−1.12723
$592$	0.262504	−	0.0956795i	0.0107889	−	0.00393240i
$593$	−41.8302			−1.71776			−0.858881	−	0.512175i	$-0.828840\pi$
$593$	−41.8302			−1.71776			−0.858881	+	0.512175i	$0.828840\pi$
$594$	−9.85590	+	2.87395i	−0.404393	+	0.117920i
$595$		0			0
$596$	16.4775	+	3.64904i	0.674946	+	0.149470i
$597$	49.8051	+	49.8051i	2.03839	+	2.03839i
$598$	7.25637	−	13.2302i	0.296735	−	0.541023i
$599$			27.7720i			1.13473i	0.823465	+	0.567367i	$0.192038\pi$
$599$			27.7720i			1.13473i	−0.823465	+	0.567367i	$0.807962\pi$
$600$	4.87824	+	74.0392i	0.199153	+	3.02264i
$601$			26.3860i			1.07631i	0.842846	+	0.538154i	$0.180878\pi$
$601$			26.3860i			1.07631i	−0.842846	+	0.538154i	$0.819122\pi$
$602$		0			0
$603$	−46.9071	−	46.9071i	−1.91021	−	1.91021i
$604$	5.45829	+	8.56349i	0.222095	+	0.348443i
$605$	−26.5994	+	26.5994i	−1.08142	+	1.08142i
$606$	−5.36814	−	18.4094i	−0.218066	−	0.747832i
$607$	−18.9982			−0.771113			−0.385557	−	0.922684i	$-0.625991\pi$
$607$	−18.9982			−0.771113			−0.385557	+	0.922684i	$0.625991\pi$
$608$	17.2972	−	12.6981i	0.701496	−	0.514974i
$609$		0			0
$610$	14.6916	+	50.3830i	0.594844	+	2.03995i
$611$	−46.5170	+	46.5170i	−1.88188	+	1.88188i
$612$	8.73133	+	13.6985i	0.352943	+	0.553731i
$613$	−3.03271	−	3.03271i	−0.122490	−	0.122490i	0.643204	−	0.765694i	$-0.277605\pi$
$613$	−3.03271	−	3.03271i	−0.122490	−	0.122490i	−0.765694	+	0.643204i	$0.777605\pi$
$614$	30.6411	+	16.8057i	1.23657	+	0.678225i
$615$		−	110.608i		−	4.46014i
$616$		0			0
$617$		−	1.11707i		−	0.0449717i	−0.999747	−	0.0224859i	$-0.992842\pi$
$617$		−	1.11707i		−	0.0449717i	0.999747	−	0.0224859i	$-0.00715808\pi$
$618$	17.4135	−	31.7492i	0.700473	−	1.27714i
$619$	−5.95717	−	5.95717i	−0.239439	−	0.239439i	0.577179	−	0.816618i	$-0.304154\pi$
$619$	−5.95717	−	5.95717i	−0.239439	−	0.239439i	−0.816618	+	0.577179i	$0.804154\pi$
$620$	8.48954	+	1.88005i	0.340948	+	0.0755048i
$621$	−9.55772	+	9.55772i	−0.383538	+	0.383538i
$622$	−38.6672	+	11.2752i	−1.55041	+	0.452096i
$623$		0			0
$624$	−62.9731	−	29.3299i	−2.52094	−	1.17413i
$625$	−10.5119			−0.420478
$626$	21.2986	−	6.21060i	0.851261	−	0.248225i
$627$	−7.58282	+	7.58282i	−0.302829	+	0.302829i
$628$	2.25903	−	10.2008i	0.0901449	−	0.407057i
$629$	0.0720511	+	0.0720511i	0.00287287	+	0.00287287i
$630$		0			0
$631$		−	12.4799i		−	0.496819i	−0.968655	−	0.248409i	$-0.920092\pi$
$631$		−	12.4799i		−	0.496819i	0.968655	−	0.248409i	$-0.0799078\pi$
$632$	1.59499	+	1.39780i	0.0634452	+	0.0556016i
$633$		−	75.4049i		−	2.99708i
$634$	20.9512	+	11.4911i	0.832078	+	0.456370i
$635$	44.9394	+	44.9394i	1.78336	+	1.78336i
$636$	−2.91737	+	1.85951i	−0.115681	+	0.0737342i
$637$		0			0
$638$	−0.159934	−	0.548476i	−0.00633185	−	0.0217144i
$639$	−16.0993			−0.636877
$640$	39.4129	+	15.2906i	1.55793	+	0.604414i
$641$	−10.1980			−0.402797			−0.201398	−	0.979509i	$-0.564549\pi$
$641$	−10.1980			−0.402797			−0.201398	+	0.979509i	$0.564549\pi$
$642$	5.20557	+	17.8519i	0.205447	+	0.704559i
$643$	−10.9741	+	10.9741i	−0.432777	+	0.432777i	−0.889572	−	0.456795i	$-0.848997\pi$
$643$	−10.9741	+	10.9741i	−0.432777	+	0.432777i	0.456795	+	0.889572i	$0.348997\pi$
$644$		0			0
$645$	−49.7688	−	49.7688i	−1.95964	−	1.95964i
$646$	6.86133	+	3.76324i	0.269955	+	0.148063i
$647$			6.58567i			0.258909i	0.991585	+	0.129455i	$0.0413227\pi$
$647$			6.58567i			0.258909i	−0.991585	+	0.129455i	$0.958677\pi$
$648$	11.2680	+	9.87498i	0.442650	+	0.387926i
$649$			5.11866i			0.200925i
$650$	36.1637	−	65.9356i	1.41846	−	2.58621i
$651$		0			0
$652$	−5.01214	+	22.6328i	−0.196291	+	0.886367i
$653$	3.62950	−	3.62950i	0.142033	−	0.142033i	−0.632515	−	0.774548i	$-0.717977\pi$
$653$	3.62950	−	3.62950i	0.142033	−	0.142033i	0.774548	+	0.632515i	$0.217977\pi$
$654$	−24.4645	+	7.13379i	−0.956639	+	0.278953i
$655$	−74.0181			−2.89213
$656$	−36.6691	−	17.0787i	−1.43169	−	0.666811i
$657$	3.56464			0.139070
$658$		0			0
$659$	−5.78706	+	5.78706i	−0.225432	+	0.225432i	−0.810781	−	0.585349i	$-0.800957\pi$
$659$	−5.78706	+	5.78706i	−0.225432	+	0.225432i	0.585349	+	0.810781i	$0.300957\pi$
$660$	−20.6276	−	4.56809i	−0.802929	−	0.177813i
$661$	−19.4549	−	19.4549i	−0.756709	−	0.756709i	0.219013	−	0.975722i	$-0.429716\pi$
$661$	−19.4549	−	19.4549i	−0.756709	−	0.756709i	−0.975722	+	0.219013i	$0.929716\pi$
$662$	−20.2523	+	36.9250i	−0.787127	+	1.43513i
$663$		−	25.3349i		−	0.983928i
$664$	−18.0198	+	1.18728i	−0.699306	+	0.0460754i
$665$		0			0
$666$	0.482231	+	0.264489i	0.0186861	+	0.0102488i
$667$	−0.531882	−	0.531882i	−0.0205946	−	0.0205946i
$668$	−14.7779	−	23.1850i	−0.571774	−	0.897053i
$669$	−17.2506	+	17.2506i	−0.666946	+	0.666946i
$670$	−17.6248	−	60.4424i	−0.680907	−	2.33509i
$671$	−9.59206			−0.370297
$672$		0			0
$673$	−37.3667			−1.44038			−0.720190	−	0.693776i	$-0.755946\pi$
$673$	−37.3667			−1.44038			−0.720190	+	0.693776i	$0.755946\pi$
$674$	−0.752683	−	2.58124i	−0.0289923	−	0.0994258i
$675$	−47.6330	+	47.6330i	−1.83339	+	1.83339i
$676$	23.8682	+	37.4468i	0.918009	+	1.44026i
$677$	−16.1658	−	16.1658i	−0.621303	−	0.621303i	0.324561	−	0.945865i	$-0.394783\pi$
$677$	−16.1658	−	16.1658i	−0.621303	−	0.621303i	−0.945865	+	0.324561i	$0.894783\pi$
$678$	−0.325377	−	0.178460i	−0.0124960	−	0.00685370i
$679$		0			0
$680$	1.01363	+	15.3842i	0.0388708	+	0.589959i
$681$		−	32.5902i		−	1.24886i
$682$	−0.764244	+	1.39341i	−0.0292644	+	0.0533564i
$683$	13.2551	+	13.2551i	0.507192	+	0.507192i	0.913663	−	0.406472i	$-0.133241\pi$
$683$	13.2551	+	13.2551i	0.507192	+	0.507192i	−0.406472	+	0.913663i	$0.633241\pi$
$684$	41.2409	+	9.13302i	1.57689	+	0.349210i
$685$	−2.41876	+	2.41876i	−0.0924161	+	0.0924161i
$686$		0			0
$687$	37.1321			1.41668
$688$	−24.1842	+	8.81482i	−0.922012	+	0.336062i
$689$	3.50632			0.133580
$690$	−26.7040	+	7.78682i	−1.01661	+	0.296439i
$691$	−6.24472	+	6.24472i	−0.237560	+	0.237560i	−0.815839	−	0.578279i	$-0.803725\pi$
$691$	−6.24472	+	6.24472i	−0.237560	+	0.237560i	0.578279	+	0.815839i	$0.303725\pi$
$692$	−3.41433	+	15.4177i	−0.129794	+	0.586094i
$693$		0			0
$694$	19.5023	−	35.5577i	0.740298	−	1.34975i
$695$		−	14.5074i		−	0.550296i
$696$	−2.28237	+	2.60434i	−0.0865130	+	0.0987174i
$697$		−	14.7525i		−	0.558789i
$698$	−9.62370	−	5.27831i	−0.364262	−	0.199787i
$699$	−46.6504	−	46.6504i	−1.76448	−	1.76448i
$700$		0			0
$701$	28.1681	−	28.1681i	1.06389	−	1.06389i	0.0660783	−	0.997814i	$-0.478951\pi$
$701$	28.1681	−	28.1681i	1.06389	−	1.06389i	0.997814	−	0.0660783i	$-0.0210487\pi$
$702$	−17.6551	−	60.5463i	−0.666350	−	2.28517i
$703$	0.264955			0.00999297
$704$	−4.69949	+	6.13318i	−0.177119	+	0.231153i
$705$	121.269			4.56725
$706$	0.832519	+	2.85503i	0.0313322	+	0.107450i
$707$		0			0
$708$	26.1629	−	16.6760i	0.983263	−	0.626723i
$709$	10.8738	+	10.8738i	0.408376	+	0.408376i	0.881172	−	0.472796i	$-0.156755\pi$
$709$	10.8738	+	10.8738i	0.408376	+	0.408376i	−0.472796	+	0.881172i	$0.656755\pi$
$710$	−13.3970	−	7.34783i	−0.502779	−	0.275759i
$711$			4.17487i			0.156570i
$712$	−28.8412	+	32.9098i	−1.08087	+	1.23335i
$713$			2.09238i			0.0783601i
$714$		0			0
$715$	15.1411	+	15.1411i	0.566245	+	0.566245i
$716$	−4.17404	+	18.8482i	−0.155991	+	0.704391i
$717$	−27.6680	+	27.6680i	−1.03328	+	1.03328i
$718$	14.5416	−	4.24028i	0.542686	−	0.158246i
$719$	−21.4416			−0.799638			−0.399819	−	0.916594i	$-0.630927\pi$
$719$	−21.4416			−0.799638			−0.399819	+	0.916594i	$0.630927\pi$
$720$	28.4984	+	78.1877i	1.06207	+	2.91388i
$721$		0			0
$722$	−6.26076	+	1.82562i	−0.233001	+	0.0679425i
$723$	40.1413	−	40.1413i	1.49287	−	1.49287i
$724$	41.7717	+	9.25056i	1.55243	+	0.343795i
$725$	−2.65075	−	2.65075i	−0.0984465	−	0.0984465i
$726$	−20.0402	+	36.5384i	−0.743762	+	1.35607i
$727$			30.4747i			1.13024i	0.825007	+	0.565122i	$0.191171\pi$
$727$			30.4747i			1.13024i	−0.825007	+	0.565122i	$0.808829\pi$
$728$		0			0
$729$		−	36.5081i		−	1.35215i
$730$	2.96630	+	1.62693i	0.109788	+	0.0602153i
$731$	−6.63796	−	6.63796i	−0.245514	−	0.245514i
$732$	31.2499	+	49.0278i	1.15503	+	1.81212i
$733$	32.8283	−	32.8283i	1.21254	−	1.21254i	0.242351	−	0.970189i	$-0.422081\pi$
$733$	32.8283	−	32.8283i	1.21254	−	1.21254i	0.970189	−	0.242351i	$-0.0779186\pi$
$734$	7.20091	+	24.6947i	0.265791	+	0.911499i
$735$		0			0
$736$	−1.54179	+	10.0553i	−0.0568312	+	0.370645i
$737$	11.5072			0.423873
$738$	−22.2913	−	76.4455i	−0.820554	−	2.81400i
$739$	−15.4736	+	15.4736i	−0.569207	+	0.569207i	−0.931906	−	0.362699i	$-0.881855\pi$
$739$	−15.4736	+	15.4736i	−0.569207	+	0.569207i	0.362699	+	0.931906i	$0.381855\pi$
$740$	0.280572	+	0.440188i	0.0103140	+	0.0161816i
$741$	−46.5824	−	46.5824i	−1.71125	−	1.71125i
$742$		0			0
$743$		−	19.2071i		−	0.704639i	−0.935880	−	0.352320i	$-0.885393\pi$
$743$		−	19.2071i		−	0.704639i	0.935880	−	0.352320i	$-0.114607\pi$
$744$	9.61194	−	0.633305i	0.352391	−	0.0232181i
$745$			31.5310i			1.15521i
$746$	0.664482	−	1.21152i	0.0243284	−	0.0443568i
$747$	−25.1372	−	25.1372i	−0.919723	−	0.919723i
$748$	−2.75123	−	0.609275i	−0.100595	−	0.0222773i
$749$		0			0
$750$	−58.8385	+	17.1571i	−2.14848	+	0.626490i
$751$	−35.8573			−1.30845			−0.654225	−	0.756300i	$-0.727005\pi$
$751$	−35.8573			−1.30845			−0.654225	+	0.756300i	$0.727005\pi$
$752$	18.7248	−	40.2034i	0.682824	−	1.46607i
$753$	33.5297			1.22189
$754$	3.36937	−	0.982499i	0.122705	−	0.0357805i
$755$	−13.4159	+	13.4159i	−0.488253	+	0.488253i
$756$		0			0
$757$	22.1772	+	22.1772i	0.806045	+	0.806045i	0.984033	−	0.177988i	$-0.0569587\pi$
$757$	22.1772	+	22.1772i	0.806045	+	0.806045i	−0.177988	+	0.984033i	$0.556959\pi$
$758$	−17.0085	+	31.0109i	−0.617778	+	1.12636i
$759$		−	5.08399i		−	0.184537i
$760$	30.1501	+	26.4227i	1.09366	+	0.958452i
$761$		−	29.5689i		−	1.07187i	−0.844258	−	0.535936i	$-0.819959\pi$
$761$		−	29.5689i		−	1.07187i	0.844258	−	0.535936i	$-0.180041\pi$
$762$	61.7312	+	33.8577i	2.23628	+	1.22654i
$763$		0			0
$764$	−33.5162	+	21.3629i	−1.21257	+	0.772883i
$765$	−21.4606	+	21.4606i	−0.775911	+	0.775911i
$766$	4.45396	+	15.2744i	0.160928	+	0.551885i
$767$	−31.4447			−1.13540
$768$	46.6589	+	4.03920i	1.68366	+	0.145752i
$769$	30.8038			1.11081			0.555406	−	0.831579i	$-0.312563\pi$
$769$	30.8038			1.11081			0.555406	+	0.831579i	$0.312563\pi$
$770$		0			0
$771$	35.1492	−	35.1492i	1.26587	−	1.26587i
$772$	20.0410	−	12.7740i	0.721292	−	0.459745i
$773$	−36.3527	−	36.3527i	−1.30752	−	1.30752i	−0.923203	−	0.384313i	$-0.874438\pi$
$773$	−36.3527	−	36.3527i	−1.30752	−	1.30752i	−0.384313	−	0.923203i	$-0.625562\pi$
$774$	−44.4273	−	24.3670i	−1.59690	−	0.875855i
$775$			10.4278i			0.374578i
$776$	−29.2398	−	25.6249i	−1.04965	−	0.919881i
$777$		0			0
$778$	−24.1715	+	44.0707i	−0.866589	+	1.58001i
$779$	−27.1248	−	27.1248i	−0.971845	−	0.971845i
$780$	28.0625	−	126.718i	1.00480	−	4.53725i
$781$	1.97472	−	1.97472i	0.0706612	−	0.0706612i
$782$	−3.56168	+	1.03858i	−0.127365	+	0.0371394i
$783$	−3.14386			−0.112352
$784$		0			0
$785$	19.5201			0.696701
$786$	−78.7206	+	22.9547i	−2.80787	+	0.818768i
$787$	−7.35668	+	7.35668i	−0.262237	+	0.262237i	−0.825962	−	0.563725i	$-0.809368\pi$
$787$	−7.35668	+	7.35668i	−0.262237	+	0.262237i	0.563725	+	0.825962i	$0.309368\pi$
$788$	−18.2811	−	4.04845i	−0.651238	−	0.144220i
$789$	9.10145	+	9.10145i	0.324020	+	0.324020i
$790$	−1.90544	+	3.47410i	−0.0677926	+	0.123603i
$791$		0			0
$792$	−15.1772	+	0.999984i	−0.539298	+	0.0355329i
$793$		−	58.9254i		−	2.09250i
$794$	−3.80129	−	2.08490i	−0.134903	−	0.0739902i
$795$	−4.57046	−	4.57046i	−0.162097	−	0.162097i
$796$	25.8675	+	40.5835i	0.916851	+	1.43844i
$797$	18.5924	−	18.5924i	0.658577	−	0.658577i	−0.296466	−	0.955043i	$-0.595808\pi$
$797$	18.5924	−	18.5924i	0.658577	−	0.658577i	0.955043	+	0.296466i	$0.0958082\pi$
$798$		0			0
$799$	16.1744			0.572208
$800$	−7.68386	+	50.1130i	−0.271666	+	1.77176i
$801$	−86.1412			−3.04365
$802$	8.45758	+	29.0043i	0.298648	+	1.02418i
$803$	−0.437236	+	0.437236i	−0.0154297	+	0.0154297i
$804$	−37.4891	−	58.8165i	−1.32214	−	2.07430i
$805$		0			0
$806$	−8.55992	−	4.69486i	−0.301510	−	0.165370i
$807$			31.9368i			1.12423i
$808$	−0.861424	−	13.0742i	−0.0303048	−	0.459949i
$809$			44.5183i			1.56518i	0.622538	+	0.782589i	$0.286102\pi$
$809$			44.5183i			1.56518i	−0.622538	+	0.782589i	$0.713898\pi$
$810$	−13.4613	+	24.5433i	−0.472981	+	0.862364i
$811$	20.8814	+	20.8814i	0.733246	+	0.733246i	0.971261	−	0.238015i	$-0.0764968\pi$
$811$	20.8814	+	20.8814i	0.733246	+	0.733246i	−0.238015	+	0.971261i	$0.576497\pi$
$812$		0			0
$813$	34.6429	−	34.6429i	1.21498	−	1.21498i
$814$	−0.0915922	+	0.0267080i	−0.00321030	+	0.000936116i
$815$	−43.3095			−1.51707
$816$	5.84903	+	16.0473i	0.204757	+	0.561767i
$817$	−24.4099			−0.853996
$818$	−13.7344	+	4.00490i	−0.480211	+	0.140028i
$819$		0			0
$820$	16.3407	−	73.7878i	0.570641	−	2.57678i
$821$	−17.2139	−	17.2139i	−0.600770	−	0.600770i	0.339747	−	0.940517i	$-0.389659\pi$
$821$	−17.2139	−	17.2139i	−0.600770	−	0.600770i	−0.940517	+	0.339747i	$0.889659\pi$
$822$	−1.82231	+	3.32254i	−0.0635605	+	0.115887i
$823$		−	31.7106i		−	1.10536i	−0.833392	−	0.552682i	$-0.813604\pi$
$823$		−	31.7106i		−	1.10536i	0.833392	−	0.552682i	$-0.186396\pi$
$824$	16.3072	−	18.6076i	0.568088	−	0.648228i
$825$		−	25.3372i		−	0.882127i
$826$		0			0
$827$	−29.2764	−	29.2764i	−1.01804	−	1.01804i	−0.999834	−	0.0182049i	$-0.994205\pi$
$827$	−29.2764	−	29.2764i	−1.01804	−	1.01804i	−0.0182049	−	0.999834i	$-0.505795\pi$
$828$	−16.8869	+	10.7636i	−0.586860	+	0.374059i
$829$	−0.222175	+	0.222175i	−0.00771644	+	0.00771644i	−0.710954	−	0.703238i	$-0.751737\pi$
$829$	−0.222175	+	0.222175i	−0.00771644	+	0.00771644i	0.703238	+	0.710954i	$0.251737\pi$
$830$	−9.44504	−	32.3907i	−0.327842	−	1.12430i
$831$	56.3557			1.95496
$832$	−37.6770	−	28.8696i	−1.30622	−	1.00087i
$833$		0			0
$834$	−4.49907	−	15.4290i	−0.155790	−	0.534264i
$835$	36.3224	−	36.3224i	1.25699	−	1.25699i
$836$	−6.17883	+	3.93833i	−0.213699	+	0.136210i
$837$	6.18383	+	6.18383i	0.213744	+	0.213744i
$838$	31.1173	+	17.0669i	1.07493	+	0.589567i
$839$			1.52778i			0.0527447i	0.999652	+	0.0263723i	$0.00839555\pi$
$839$			1.52778i			0.0527447i	−0.999652	+	0.0263723i	$0.991604\pi$
$840$		0			0
$841$			28.8250i			0.993967i
$842$	17.5801	−	32.0529i	0.605849	−	1.10462i
$843$	30.9866	+	30.9866i	1.06723	+	1.06723i
$844$	11.1400	−	50.3034i	0.383453	−	1.73152i
$845$	−58.6655	+	58.6655i	−2.01815	+	2.01815i
$846$	83.8137	−	24.4398i	2.88157	−	0.840259i
$847$		0			0
$848$	−2.22092	+	0.809498i	−0.0762668	+	0.0277983i
$849$	−27.5771			−0.946445
$850$	−17.7504	+	5.17598i	−0.608835	+	0.177534i
$851$	−0.0888211	+	0.0888211i	−0.00304475	+	0.00304475i
$852$	−16.5268	−	3.65995i	−0.566200	−	0.125388i
$853$	35.7996	+	35.7996i	1.22576	+	1.22576i	0.965554	+	0.260202i	$0.0837890\pi$
$853$	35.7996	+	35.7996i	1.22576	+	1.22576i	0.260202	+	0.965554i	$0.416211\pi$
$854$		0			0
$855$			78.9177i			2.69893i
$856$	0.835336	+	12.6782i	0.0285512	+	0.433334i
$857$		−	7.59086i		−	0.259299i	−0.991560	−	0.129650i	$-0.958615\pi$
$857$		−	7.59086i		−	0.259299i	0.991560	−	0.129650i	$-0.0413852\pi$
$858$	20.7986	+	11.4074i	0.710054	+	0.389443i
$859$	−20.4192	−	20.4192i	−0.696695	−	0.696695i	0.267001	−	0.963696i	$-0.413967\pi$
$859$	−20.4192	−	20.4192i	−0.696695	−	0.696695i	−0.963696	+	0.267001i	$0.913967\pi$
$860$	−25.8487	−	40.5539i	−0.881433	−	1.38288i
$861$		0			0
$862$	8.84583	+	30.3358i	0.301290	+	1.03324i
$863$	−8.73810			−0.297449			−0.148724	−	0.988879i	$-0.547517\pi$
$863$	−8.73810			−0.297449			−0.148724	+	0.988879i	$0.547517\pi$
$864$	25.1611	+	34.2743i	0.855996	+	1.16604i
$865$	−29.5030			−1.00313
$866$	−3.90572	−	13.3942i	−0.132722	−	0.455155i
$867$	30.7814	−	30.7814i	1.04539	−	1.04539i
$868$		0			0
$869$	−0.512086	−	0.512086i	−0.0173713	−	0.0173713i
$870$	−5.67261	−	3.11126i	−0.192320	−	0.105482i
$871$			70.6903i			2.39525i
$872$	−17.3745	+	1.14476i	−0.588374	+	0.0387664i
$873$		−	76.5349i		−	2.59031i
$874$	−4.63913	+	8.45831i	−0.156921	+	0.286107i
$875$		0			0
$876$	3.65930	+	0.810372i	0.123636	+	0.0273799i
$877$	15.9966	−	15.9966i	0.540168	−	0.540168i	−0.383410	−	0.923578i	$-0.625250\pi$
$877$	15.9966	−	15.9966i	0.540168	−	0.540168i	0.923578	+	0.383410i	$0.125250\pi$
$878$	26.3880	−	7.69466i	0.890551	−	0.259682i
$879$	−5.16591			−0.174242
$880$	−13.0860	−	6.09485i	−0.441130	−	0.205457i
$881$	19.9839			0.673273			0.336637	−	0.941635i	$-0.390711\pi$
$881$	19.9839			0.673273			0.336637	+	0.941635i	$0.390711\pi$
$882$		0			0
$883$	−0.776332	+	0.776332i	−0.0261257	+	0.0261257i	−0.720049	−	0.693923i	$-0.755881\pi$
$883$	−0.776332	+	0.776332i	−0.0261257	+	0.0261257i	0.693923	+	0.720049i	$0.255881\pi$
$884$	3.74286	−	16.9012i	0.125886	−	0.568450i
$885$	40.9878	+	40.9878i	1.37779	+	1.37779i
$886$	−17.1832	+	31.3292i	−0.577279	+	1.05253i
$887$			28.4143i			0.954058i	0.878887	+	0.477029i	$0.158286\pi$
$887$			28.4143i			0.954058i	−0.878887	+	0.477029i	$0.841714\pi$
$888$	0.434910	+	0.381142i	0.0145946	+	0.0127903i
$889$		0			0
$890$	−71.6821	−	39.3155i	−2.40279	−	1.31786i
$891$	−3.61771	−	3.61771i	−0.121198	−	0.121198i
$892$	−14.0566	+	8.95953i	−0.470649	+	0.299987i
$893$	29.7392	−	29.7392i	0.995184	−	0.995184i
$894$	9.77849	+	33.5342i	0.327042	+	1.12155i
$895$	−36.0675			−1.20560
$896$		0			0
$897$	31.2317			1.04280
$898$	−7.48157	−	25.6572i	−0.249663	−	0.856192i
$899$	−0.344127	+	0.344127i	−0.0114773	+	0.0114773i
$900$	−84.1596	+	53.6426i	−2.80532	+	1.78809i
$901$	−0.609590	−	0.609590i	−0.0203084	−	0.0203084i
$902$	12.1110	+	6.64251i	0.403251	+	0.221171i
$903$		0			0
$904$	−0.190698	−	0.167122i	−0.00634251	−	0.00555840i
$905$			79.9334i			2.65708i
$906$	−10.1076	+	18.4288i	−0.335804	+	0.612255i
$907$	9.66456	+	9.66456i	0.320906	+	0.320906i	0.849115	−	0.528208i	$-0.177136\pi$
$907$	9.66456	+	9.66456i	0.320906	+	0.320906i	−0.528208	+	0.849115i	$0.677136\pi$
$908$	4.81472	−	21.7413i	0.159782	−	0.721510i
$909$	18.2382	−	18.2382i	0.604923	−	0.604923i
$910$		0			0
$911$	−53.3939			−1.76902			−0.884509	−	0.466523i	$-0.845506\pi$
$911$	−53.3939			−1.76902			−0.884509	+	0.466523i	$0.845506\pi$
$912$	40.2599	+	18.7511i	1.33314	+	0.620912i
$913$	6.16663			0.204086
$914$	−12.5251	+	3.65229i	−0.414294	+	0.120807i
$915$	−76.8087	+	76.8087i	−2.53922	+	2.53922i
$916$	24.7712	+	5.48572i	0.818464	+	0.181253i
$917$		0			0
$918$	−7.45681	+	13.5957i	−0.246111	+	0.448723i
$919$			5.20441i			0.171678i	0.996309	+	0.0858388i	$0.0273570\pi$
$919$			5.20441i			0.171678i	−0.996309	+	0.0858388i	$0.972643\pi$
$920$	−18.9649	+	1.24955i	−0.625256	+	0.0411964i
$921$			72.3325i			2.38344i
$922$	−18.6355	−	10.2210i	−0.613729	−	0.336612i
$923$	12.1310	+	12.1310i	0.399297	+	0.399297i
$924$		0			0
$925$	−0.442660	+	0.442660i	−0.0145546	+	0.0145546i
$926$	12.8617	+	44.1076i	0.422660	+	1.44947i
$927$	48.7053			1.59969
$928$	−1.90735	+	1.40020i	−0.0626118	+	0.0459638i
$929$	−9.12328			−0.299325			−0.149663	−	0.988737i	$-0.547819\pi$
$929$	−9.12328			−0.299325			−0.149663	+	0.988737i	$0.547819\pi$
$930$	5.03807	+	17.2775i	0.165205	+	0.566551i
$931$		0			0
$932$	−24.2291	−	38.0129i	−0.793651	−	1.24515i
$933$	−58.9479	−	58.9479i	−1.92987	−	1.92987i
$934$	21.8017	+	11.9576i	0.713375	+	0.391265i
$935$		−	5.26469i		−	0.172174i
$936$	−6.14305	−	93.2357i	−0.200792	−	3.04750i
$937$			7.41975i			0.242393i	0.992629	+	0.121196i	$0.0386731\pi$
$937$			7.41975i			0.242393i	−0.992629	+	0.121196i	$0.961327\pi$
$938$		0			0
$939$	32.4695	+	32.4695i	1.05960	+	1.05960i
$940$	80.8998	+	17.9157i	2.63866	+	0.584345i
$941$	1.85479	−	1.85479i	0.0604646	−	0.0604646i	−0.676228	−	0.736692i	$-0.736387\pi$
$941$	1.85479	−	1.85479i	0.0604646	−	0.0604646i	0.736692	+	0.676228i	$0.236387\pi$
$942$	20.7602	−	6.05362i	0.676404	−	0.197237i
$943$	18.1861			0.592221
$944$	19.9172	−	7.25957i	0.648250	−	0.236279i
$945$		0			0
$946$	8.43826	−	2.46057i	0.274351	−	0.0800001i
$947$	12.4018	−	12.4018i	0.403006	−	0.403006i	−0.476285	−	0.879291i	$-0.658017\pi$
$947$	12.4018	−	12.4018i	0.403006	−	0.403006i	0.879291	+	0.476285i	$0.158017\pi$
$948$	−0.949099	+	4.28574i	−0.0308253	+	0.139194i
$949$	−2.68600	−	2.68600i	−0.0871914	−	0.0871914i
$950$	−23.1202	+	42.1539i	−0.750117	+	1.36765i
$951$			49.4581i			1.60379i
$952$		0			0
$953$		−	27.3756i		−	0.886782i	−0.896328	−	0.443391i	$-0.853775\pi$
$953$		−	27.3756i		−	0.886782i	0.896328	−	0.443391i	$-0.146225\pi$
$954$	−4.07992	−	2.23772i	−0.132092	−	0.0724488i
$955$	−52.5076	−	52.5076i	−1.69911	−	1.69911i
$956$	−22.5452	+	14.3701i	−0.729164	+	0.464763i
$957$	0.836149	−	0.836149i	0.0270289	−	0.0270289i
$958$	−14.3633	−	49.2574i	−0.464058	−	1.59143i
$959$		0			0
$960$	11.4803	+	86.7429i	0.370527	+	2.79961i
$961$	−29.6462			−0.956330
$962$	−0.164071	−	0.562664i	−0.00528987	−	0.0181410i
$963$	−17.6858	+	17.6858i	−0.569918	+	0.569918i
$964$	32.7090	−	20.8484i	1.05349	−	0.671483i
$965$	31.3970	+	31.3970i	1.01070	+	1.01070i
$966$		0			0
$967$			32.2156i			1.03598i	0.855385	+	0.517992i	$0.173320\pi$
$967$			32.2156i			1.03598i	−0.855385	+	0.517992i	$0.826680\pi$
$968$	−18.7671	+	21.4145i	−0.603196	+	0.688288i
$969$			16.1971i			0.520326i
$970$	34.9311	−	63.6883i	1.12157	−	2.04491i
$971$	24.7566	+	24.7566i	0.794477	+	0.794477i	0.982218	−	0.187742i	$-0.0601168\pi$
$971$	24.7566	+	24.7566i	0.794477	+	0.794477i	−0.187742	+	0.982218i	$0.560117\pi$
$972$	3.04578	−	13.7535i	0.0976934	−	0.441143i
$973$		0			0
$974$	9.90947	−	2.88957i	0.317520	−	0.0925879i
$975$	155.650			4.98479
$976$	13.6040	+	37.3237i	0.435454	+	1.19470i
$977$	−3.14788			−0.100710			−0.0503548	−	0.998731i	$-0.516035\pi$
$977$	−3.14788			−0.100710			−0.0503548	+	0.998731i	$0.516035\pi$
$978$	−46.0610	+	13.4313i	−1.47287	+	0.429485i
$979$	10.5660	−	10.5660i	0.337691	−	0.337691i
$980$		0			0
$981$	−24.2369	−	24.2369i	−0.773826	−	0.773826i
$982$	−10.9874	+	20.0328i	−0.350622	+	0.639273i
$983$			51.2039i			1.63315i	0.577238	+	0.816576i	$0.304130\pi$
$983$			51.2039i			1.63315i	−0.577238	+	0.816576i	$0.695870\pi$
$984$	−5.50444	−	83.5432i	−0.175475	−	2.66326i
$985$		−	34.9823i		−	1.11463i
$986$	−0.756591	−	0.414968i	−0.0240948	−	0.0132153i
$987$		0			0
$988$	−24.1938	−	37.9575i	−0.769706	−	1.20759i
$989$	8.18296	−	8.18296i	0.260203	−	0.260203i
$990$	−7.95507	−	27.2810i	−0.252829	−	0.867047i
$991$	−20.1603			−0.640414			−0.320207	−	0.947348i	$-0.603752\pi$
$991$	−20.1603			−0.640414			−0.320207	+	0.947348i	$0.603752\pi$
$992$	6.50580	+	0.997538i	0.206559	+	0.0316719i
$993$	−87.1665			−2.76615
$994$		0			0
$995$	−63.5795	+	63.5795i	−2.01561	+	2.01561i
$996$	−20.0902	−	31.5194i	−0.636582	−	0.998731i
$997$	−26.8634	−	26.8634i	−0.850773	−	0.850773i	0.139456	−	0.990228i	$-0.455465\pi$
$997$	−26.8634	−	26.8634i	−0.850773	−	0.850773i	−0.990228	+	0.139456i	$0.955465\pi$
$998$	28.6219	+	15.6983i	0.906010	+	0.496919i
$999$			0.525006i			0.0166104i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.m.l.197.15	✓	48
7.2	even	3		784.2.x.p.165.17		96
7.3	odd	6		784.2.x.p.373.3		96
7.4	even	3		784.2.x.p.373.4		96
7.5	odd	6		784.2.x.p.165.18		96
7.6	odd	2	inner	784.2.m.l.197.16	yes	48
16.13	even	4	inner	784.2.m.l.589.15	yes	48
112.13	odd	4	inner	784.2.m.l.589.16	yes	48
112.45	odd	12		784.2.x.p.765.18		96
112.61	odd	12		784.2.x.p.557.3		96
112.93	even	12		784.2.x.p.557.4		96
112.109	even	12		784.2.x.p.765.17		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.l.197.15	✓	48	1.1	even	1	trivial
784.2.m.l.197.16	yes	48	7.6	odd	2	inner
784.2.m.l.589.15	yes	48	16.13	even	4	inner
784.2.m.l.589.16	yes	48	112.13	odd	4	inner
784.2.x.p.165.17		96	7.2	even	3
784.2.x.p.165.18		96	7.5	odd	6
784.2.x.p.373.3		96	7.3	odd	6
784.2.x.p.373.4		96	7.4	even	3
784.2.x.p.557.3		96	112.61	odd	12
784.2.x.p.557.4		96	112.93	even	12
784.2.x.p.765.17		96	112.109	even	12
784.2.x.p.765.18		96	112.45	odd	12

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.395893 + 1.35767i) q^{2} +(-2.06976 + 2.06976i) q^{3} +(-1.68654 + 1.07498i) q^{4} +(-2.64219 - 2.64219i) q^{5} +(-3.62946 - 1.99065i) q^{6} +(-2.12716 - 1.86418i) q^{8} -5.56783i q^{9} +O(q^{10})\)	\(q+(0.395893 + 1.35767i) q^{2} +(-2.06976 + 2.06976i) q^{3} +(-1.68654 + 1.07498i) q^{4} +(-2.64219 - 2.64219i) q^{5} +(-3.62946 - 1.99065i) q^{6} +(-2.12716 - 1.86418i) q^{8} -5.56783i q^{9} +(2.54120 - 4.63325i) q^{10} +(0.682946 + 0.682946i) q^{11} +(1.26577 - 5.71569i) q^{12} +(-4.19543 + 4.19543i) q^{13} +10.9374 q^{15} +(1.68882 - 3.62600i) q^{16} +1.45879 q^{17} +(7.55927 - 2.20426i) q^{18} +(2.68222 - 2.68222i) q^{19} +(7.29647 + 1.61584i) q^{20} +(-0.656842 + 1.19759i) q^{22} +1.79832i q^{23} +(8.26113 - 0.544304i) q^{24} +8.96235i q^{25} +(-7.35696 - 4.03507i) q^{26} +(5.31479 + 5.31479i) q^{27} +(-0.295765 + 0.295765i) q^{29} +(4.33004 + 14.8494i) q^{30} +1.16351 q^{31} +(5.59151 + 0.857349i) q^{32} -2.82707 q^{33} +(0.577524 + 1.98056i) q^{34} +(5.98533 + 9.39035i) q^{36} +(0.0493910 + 0.0493910i) q^{37} +(4.70344 + 2.57970i) q^{38} -17.3671i q^{39} +(0.694841 + 10.5459i) q^{40} -10.1128i q^{41} +(-4.55032 - 4.55032i) q^{43} +(-1.88597 - 0.417658i) q^{44} +(-14.7113 + 14.7113i) q^{45} +(-2.44153 + 0.711944i) q^{46} +11.0875 q^{47} +(4.00951 + 11.0004i) q^{48} +(-12.1679 + 3.54813i) q^{50} +(-3.01935 + 3.01935i) q^{51} +(2.56573 - 11.5858i) q^{52} +(-0.417874 - 0.417874i) q^{53} +(-5.11164 + 9.31982i) q^{54} -3.60895i q^{55} +11.1031i q^{57} +(-0.518643 - 0.284460i) q^{58} +(3.74749 + 3.74749i) q^{59} +(-18.4464 + 11.7575i) q^{60} +(-7.02257 + 7.02257i) q^{61} +(0.460627 + 1.57967i) q^{62} +(1.04964 + 7.93084i) q^{64} +22.1703 q^{65} +(-1.11922 - 3.83823i) q^{66} +(8.42467 - 8.42467i) q^{67} +(-2.46030 + 1.56818i) q^{68} +(-3.72210 - 3.72210i) q^{69} -2.89148i q^{71} +(-10.3795 + 11.8437i) q^{72} +0.640221i q^{73} +(-0.0475032 + 0.0866103i) q^{74} +(-18.5499 - 18.5499i) q^{75} +(-1.64032 + 7.40701i) q^{76} +(23.5788 - 6.87551i) q^{78} -0.749820 q^{79} +(-14.0428 + 5.11841i) q^{80} -5.29721 q^{81} +(13.7299 - 4.00359i) q^{82} +(4.51473 - 4.51473i) q^{83} +(-3.85440 - 3.85440i) q^{85} +(4.37640 - 7.97928i) q^{86} -1.22433i q^{87} +(-0.179600 - 2.72587i) q^{88} -15.4712i q^{89} +(-25.7971 - 14.1490i) q^{90} +(-1.93317 - 3.03294i) q^{92} +(-2.40820 + 2.40820i) q^{93} +(4.38947 + 15.0532i) q^{94} -14.1739 q^{95} +(-13.3476 + 9.79858i) q^{96} +13.7459 q^{97} +(3.80252 - 3.80252i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} - 8 q^{11} + 32 q^{15} + 36 q^{16} + 20 q^{18} - 28 q^{22} - 16 q^{29} + 96 q^{30} + 40 q^{32} + 40 q^{36} - 16 q^{37} + 8 q^{43} + 4 q^{44} + 64 q^{46} - 28 q^{50} + 16 q^{53} - 20 q^{58} + 8 q^{60} + 44 q^{64} + 40 q^{67} - 196 q^{72} - 28 q^{74} + 56 q^{78} + 80 q^{79} - 48 q^{81} - 108 q^{86} - 100 q^{88} - 128 q^{95} - 40 q^{99}+O(q^{100}) \) 48 * q - 4 * q^4 - 8 * q^11 + 32 * q^15 + 36 * q^16 + 20 * q^18 - 28 * q^22 - 16 * q^29 + 96 * q^30 + 40 * q^32 + 40 * q^36 - 16 * q^37 + 8 * q^43 + 4 * q^44 + 64 * q^46 - 28 * q^50 + 16 * q^53 - 20 * q^58 + 8 * q^60 + 44 * q^64 + 40 * q^67 - 196 * q^72 - 28 * q^74 + 56 * q^78 + 80 * q^79 - 48 * q^81 - 108 * q^86 - 100 * q^88 - 128 * q^95 - 40 * q^99

Introduction

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