LMFDB - Embedded newform 784.2.x.p.165.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not 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:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.18
Character	$\chi$	$=$	784.165
Dual form			784.2.x.p.765.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.977831 - 1.02169i) q^{2} +(0.757585 + 2.82735i) q^{3} +(-0.0876948 - 1.99808i) q^{4} +(0.967109 - 3.60930i) q^{5} +(3.62946 + 1.99065i) q^{6} +(-2.12716 - 1.86418i) q^{8} +(-4.82188 + 2.78391i) q^{9} +O(q^{10})$	\(q+(0.977831 - 1.02169i) q^{2} +(0.757585 + 2.82735i) q^{3} +(-0.0876948 - 1.99808i) q^{4} +(0.967109 - 3.60930i) q^{5} +(3.62946 + 1.99065i) q^{6} +(-2.12716 - 1.86418i) q^{8} +(-4.82188 + 2.78391i) q^{9} +(-2.74191 - 4.51737i) q^{10} +(-0.932921 + 0.249975i) q^{11} +(5.58282 - 1.76166i) q^{12} +(4.19543 - 4.19543i) q^{13} +10.9374 q^{15} +(-3.98462 + 0.350442i) q^{16} +(0.729395 - 1.26335i) q^{17} +(-1.87069 + 7.64865i) q^{18} +(3.66398 + 0.981760i) q^{19} +(-7.29647 - 1.61584i) q^{20} +(-0.656842 + 1.19759i) q^{22} +(1.55739 - 0.899162i) q^{23} +(3.65919 - 7.42650i) q^{24} +(-7.76162 - 4.48117i) q^{25} +(-0.184003 - 8.38885i) q^{26} +(-5.31479 - 5.31479i) q^{27} +(-0.295765 + 0.295765i) q^{29} +(10.6949 - 11.1746i) q^{30} +(0.581757 - 1.00763i) q^{31} +(-3.53824 + 4.41371i) q^{32} +(-1.41353 - 2.44831i) q^{33} +(-0.577524 - 1.98056i) q^{34} +(5.98533 + 9.39035i) q^{36} +(0.0180784 - 0.0674694i) q^{37} +(4.58580 - 2.78345i) q^{38} +(15.0403 + 8.68355i) q^{39} +(-8.78560 + 5.87470i) q^{40} +10.1128i q^{41} +(-4.55032 - 4.55032i) q^{43} +(0.581282 + 1.84213i) q^{44} +(5.38470 + 20.0960i) q^{45} +(0.604204 - 2.47040i) q^{46} +(5.54377 + 9.60208i) q^{47} +(-4.00951 - 11.0004i) q^{48} +(-12.1679 + 3.54813i) q^{50} +(4.12450 + 1.10516i) q^{51} +(-8.75072 - 8.01488i) q^{52} +(0.570826 - 0.152952i) q^{53} +(-10.6270 + 0.233096i) q^{54} +3.60895i q^{55} +11.1031i q^{57} +(0.0129717 + 0.591388i) q^{58} +(5.11916 - 1.37168i) q^{59} +(-0.959154 - 21.8538i) q^{60} +(-9.59300 - 2.57044i) q^{61} +(-0.460627 - 1.57967i) q^{62} +(1.04964 + 7.93084i) q^{64} +(-11.0851 - 19.2000i) q^{65} +(-3.88361 - 0.949844i) q^{66} +(3.08364 + 11.5083i) q^{67} +(-2.58823 - 1.34660i) q^{68} +(3.72210 + 3.72210i) q^{69} -2.89148i q^{71} +(15.4466 + 3.06703i) q^{72} +(0.554447 + 0.320110i) q^{73} +(-0.0512551 - 0.0844441i) q^{74} +(6.78974 - 25.3397i) q^{75} +(1.64032 - 7.40701i) q^{76} +(23.5788 - 6.87551i) q^{78} +(0.374910 + 0.649363i) q^{79} +(-2.58871 + 14.7206i) q^{80} +(2.64861 - 4.58752i) q^{81} +(10.3321 + 9.88861i) q^{82} +(-4.51473 + 4.51473i) q^{83} +(-3.85440 - 3.85440i) q^{85} +(-9.09846 + 0.199568i) q^{86} +(-1.06030 - 0.612164i) q^{87} +(2.45047 + 1.20740i) q^{88} +(13.3985 - 7.73562i) q^{89} +(25.7971 + 14.1490i) q^{90} +(-1.93317 - 3.03294i) q^{92} +(3.28966 + 0.881461i) q^{93} +(15.2312 + 3.72521i) q^{94} +(7.08694 - 12.2749i) q^{95} +(-15.1596 - 6.66007i) q^{96} -13.7459 q^{97} +(3.80252 - 3.80252i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{4}+O(q^{10}) $ 96 * q + 4 * q^4	$ 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) $ 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.977831	−	1.02169i	0.691431	−	0.722443i
$2$	0.977831	−	1.02169i	0.691431	−	0.722443i
$3$	0.757585	+	2.82735i	0.437392	+	1.63237i	0.735276	+	0.677768i	$0.237052\pi$
$3$	0.757585	+	2.82735i	0.437392	+	1.63237i	−0.297884	+	0.954602i	$0.596281\pi$
$4$	−0.0876948	−	1.99808i	−0.0438474	−	0.999038i
$5$	0.967109	−	3.60930i	0.432504	−	1.61413i	−0.314465	−	0.949269i	$-0.601825\pi$
$5$	0.967109	−	3.60930i	0.432504	−	1.61413i	0.746969	−	0.664859i	$-0.231508\pi$
$6$	3.62946	+	1.99065i	1.48172	+	0.812679i
$7$		0			0
$7$		0			0
$8$	−2.12716	−	1.86418i	−0.752065	−	0.659088i
$9$	−4.82188	+	2.78391i	−1.60729	+	0.927971i
$10$	−2.74191	−	4.51737i	−0.867069	−	1.42852i
$11$	−0.932921	+	0.249975i	−0.281286	+	0.0753704i	−0.396704	−	0.917947i	$-0.629846\pi$
$11$	−0.932921	+	0.249975i	−0.281286	+	0.0753704i	0.115418	+	0.993317i	$0.463179\pi$
$12$	5.58282	−	1.76166i	1.61162	−	0.508547i
$13$	4.19543	−	4.19543i	1.16360	−	1.16360i	0.179924	−	0.983681i	$-0.442415\pi$
$13$	4.19543	−	4.19543i	1.16360	−	1.16360i	0.983681	−	0.179924i	$-0.0575851\pi$
$14$		0			0
$15$	10.9374			2.82403
$16$	−3.98462	+	0.350442i	−0.996155	+	0.0876105i
$17$	0.729395	−	1.26335i	0.176904	−	0.306407i	−0.763914	−	0.645318i	$-0.776725\pi$
$17$	0.729395	−	1.26335i	0.176904	−	0.306407i	0.940819	+	0.338911i	$0.110058\pi$
$18$	−1.87069	+	7.64865i	−0.440926	+	1.80281i
$19$	3.66398	+	0.981760i	0.840575	+	0.225231i	0.653322	−	0.757080i	$-0.273375\pi$
$19$	3.66398	+	0.981760i	0.840575	+	0.225231i	0.187253	+	0.982312i	$0.440042\pi$
$20$	−7.29647	−	1.61584i	−1.63154	−	0.361313i
$21$		0			0
$22$	−0.656842	+	1.19759i	−0.140039	+	0.255327i
$23$	1.55739	−	0.899162i	0.324739	−	0.187488i	−0.328764	−	0.944412i	$-0.606632\pi$
$23$	1.55739	−	0.899162i	0.324739	−	0.187488i	0.653503	+	0.756924i	$0.273299\pi$
$24$	3.65919	−	7.42650i	0.746928	−	1.51593i
$25$	−7.76162	−	4.48117i	−1.55232	−	0.896235i
$26$	−0.184003	−	8.38885i	−0.0360860	−	1.64519i
$27$	−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	$0.262365\pi$
$30$	10.6949	−	11.1746i	1.95262	−	2.04020i
$31$	0.581757	−	1.00763i	0.104487	−	0.180976i	−0.809042	−	0.587751i	$-0.800013\pi$
$31$	0.581757	−	1.00763i	0.104487	−	0.180976i	0.913528	+	0.406775i	$0.133347\pi$
$32$	−3.53824	+	4.41371i	−0.625478	+	0.780242i
$33$	−1.41353	−	2.44831i	−0.246065	−	0.426197i
$34$	−0.577524	−	1.98056i	−0.0990446	−	0.339662i
$35$		0			0
$36$	5.98533	+	9.39035i	0.997554	+	1.56506i
$37$	0.0180784	−	0.0674694i	0.00297207	−	0.0110919i	−0.964424	−	0.264361i	$-0.914839\pi$
$37$	0.0180784	−	0.0674694i	0.00297207	−	0.0110919i	0.967396	+	0.253269i	$0.0815057\pi$
$38$	4.58580	−	2.78345i	0.743916	−	0.451535i
$39$	15.0403	+	8.68355i	2.40838	+	1.39048i
$40$	−8.78560	+	5.87470i	−1.38912	+	0.928872i
$41$			10.1128i			1.57935i	0.613522	+	0.789677i	$0.289752\pi$
$41$			10.1128i			1.57935i	−0.613522	+	0.789677i	$0.710248\pi$
$42$		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	$0.913249\pi$
$44$	0.581282	+	1.84213i	0.0876316	+	0.277711i
$45$	5.38470	+	20.0960i	0.802703	+	2.99573i
$46$	0.604204	−	2.47040i	0.0890851	−	0.364241i
$47$	5.54377	+	9.60208i	0.808641	+	1.40061i	0.913805	+	0.406153i	$0.133130\pi$
$47$	5.54377	+	9.60208i	0.808641	+	1.40061i	−0.105164	+	0.994455i	$0.533537\pi$
$48$	−4.00951	−	11.0004i	−0.578723	−	1.58777i
$49$		0			0
$50$	−12.1679	+	3.54813i	−1.72080	+	0.501781i
$51$	4.12450	+	1.10516i	0.577546	+	0.154753i
$52$	−8.75072	−	8.01488i	−1.21351	−	1.11146i
$53$	0.570826	−	0.152952i	0.0784090	−	0.0210096i	−0.219401	−	0.975635i	$-0.570410\pi$
$53$	0.570826	−	0.152952i	0.0784090	−	0.0210096i	0.297810	+	0.954625i	$0.403744\pi$
$54$	−10.6270	+	0.233096i	−1.44615	+	0.0317203i
$55$			3.60895i			0.486630i
$56$		0			0
$57$			11.1031i			1.47064i
$58$	0.0129717	+	0.591388i	0.00170326	+	0.0776531i
$59$	5.11916	−	1.37168i	0.666458	−	0.178577i	0.0902992	−	0.995915i	$-0.471218\pi$
$59$	5.11916	−	1.37168i	0.666458	−	0.178577i	0.576159	+	0.817338i	$0.304551\pi$
$60$	−0.959154	−	21.8538i	−0.123826	−	2.82131i
$61$	−9.59300	−	2.57044i	−1.22826	−	0.329111i	−0.414357	−	0.910114i	$-0.635994\pi$
$61$	−9.59300	−	2.57044i	−1.22826	−	0.329111i	−0.813901	+	0.581003i	$0.802660\pi$
$62$	−0.460627	−	1.57967i	−0.0584997	−	0.200618i
$63$		0			0
$64$	1.04964	+	7.93084i	0.131205	+	0.991355i
$65$	−11.0851	−	19.2000i	−1.37494	−	2.38147i
$66$	−3.88361	−	0.949844i	−0.478039	−	0.116918i
$67$	3.08364	+	11.5083i	0.376727	+	1.40596i	0.850805	+	0.525482i	$0.176115\pi$
$67$	3.08364	+	11.5083i	0.376727	+	1.40596i	−0.474078	+	0.880483i	$0.657219\pi$
$68$	−2.58823	−	1.34660i	−0.313869	−	0.163299i
$69$	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	$-0.0548865\pi$
$72$	15.4466	+	3.06703i	1.82040	+	0.361453i
$73$	0.554447	+	0.320110i	0.0648932	+	0.0374661i	0.532096	−	0.846684i	$-0.321405\pi$
$73$	0.554447	+	0.320110i	0.0648932	+	0.0374661i	−0.467202	+	0.884150i	$0.654738\pi$
$74$	−0.0512551	−	0.0844441i	−0.00595829	−	0.00981643i
$75$	6.78974	−	25.3397i	0.784012	−	2.92597i
$76$	1.64032	−	7.40701i	0.188158	−	0.849642i
$77$		0			0
$78$	23.5788	−	6.87551i	2.66977	−	0.778498i
$79$	0.374910	+	0.649363i	0.0421807	+	0.0730590i	0.886345	−	0.463025i	$-0.153236\pi$
$79$	0.374910	+	0.649363i	0.0421807	+	0.0730590i	−0.844164	+	0.536085i	$0.819903\pi$
$80$	−2.58871	+	14.7206i	−0.289427	+	1.64581i
$81$	2.64861	−	4.58752i	0.294290	−	0.509725i
$82$	10.3321	+	9.88861i	1.14099	+	1.09201i
$83$	−4.51473	+	4.51473i	−0.495556	+	0.495556i	−0.910051	−	0.414495i	$-0.863958\pi$
$83$	−4.51473	+	4.51473i	−0.495556	+	0.495556i	0.414495	+	0.910051i	$0.363958\pi$
$84$		0			0
$85$	−3.85440	−	3.85440i	−0.418068	−	0.418068i
$86$	−9.09846	+	0.199568i	−0.981112	+	0.0215200i
$87$	−1.06030	−	0.612164i	−0.113676	−	0.0656308i
$88$	2.45047	+	1.20740i	0.261221	+	0.128709i
$89$	13.3985	−	7.73562i	1.42024	−	0.819974i	0.423918	−	0.905701i	$-0.360654\pi$
$89$	13.3985	−	7.73562i	1.42024	−	0.819974i	0.996319	+	0.0857266i	$0.0273212\pi$
$90$	25.7971	+	14.1490i	2.71926	+	1.49143i
$91$		0			0
$92$	−1.93317	−	3.03294i	−0.201547	−	0.316206i
$93$	3.28966	+	0.881461i	0.341122	+	0.0914032i
$94$	15.2312	+	3.72521i	1.57098	+	0.384226i
$95$	7.08694	−	12.2749i	0.727104	−	1.25938i
$96$	−15.1596	−	6.66007i	−1.54722	−	0.679740i
$97$	−13.7459			−1.39569			−0.697843	−	0.716250i	$-0.745857\pi$
$97$	−13.7459			−1.39569			−0.697843	+	0.716250i	$0.745857\pi$
$98$		0			0
$99$	3.80252	−	3.80252i	0.382168	−	0.382168i
$100$	−8.27307	+	15.9013i	−0.827307	+	1.59013i
$101$	4.47461	−	1.19897i	0.445240	−	0.119302i	−0.0292314	−	0.999573i	$-0.509306\pi$
$101$	4.47461	−	1.19897i	0.445240	−	0.119302i	0.474471	+	0.880271i	$0.342639\pi$
$102$	5.16219	−	3.13330i	0.511133	−	0.310243i
$103$	−7.57567	+	4.37382i	−0.746453	+	0.430965i	−0.824411	−	0.565992i	$-0.808493\pi$
$103$	−7.57567	+	4.37382i	−0.746453	+	0.430965i	0.0779578	+	0.996957i	$0.475160\pi$
$104$	−16.7454	+	1.10331i	−1.64202	+	0.108189i
$105$		0			0
$106$	0.401901	−	0.732768i	0.0390361	−	0.0711727i
$107$	−1.16266	+	4.33909i	−0.112398	+	0.419476i	−0.999079	−	0.0429061i	$-0.986338\pi$
$107$	−1.16266	+	4.33909i	−0.112398	+	0.419476i	0.886681	+	0.462382i	$0.153005\pi$
$108$	−10.1533	+	11.0854i	−0.976999	+	1.06670i
$109$	1.59332	+	5.94636i	0.152613	+	0.569558i	0.999298	+	0.0374639i	$0.0119279\pi$
$109$	1.59332	+	5.94636i	0.152613	+	0.569558i	−0.846685	+	0.532094i	$0.821405\pi$
$110$	3.68722	+	3.52894i	0.351562	+	0.336471i
$111$	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	$0.498658\pi$
$114$	11.3439	+	10.8570i	1.06246	+	1.01685i
$115$	−1.73918	−	6.49069i	−0.162179	−	0.605260i
$116$	0.616899	+	0.565025i	0.0572776	+	0.0524612i
$117$	−8.55015	+	31.9096i	−0.790462	+	2.95004i
$118$	3.60425	−	6.57145i	0.331798	−	0.604951i
$119$		0			0
$120$	−23.2657	−	20.3893i	−2.12385	−	1.86128i
$121$	−8.71843	+	5.03359i	−0.792584	+	0.457599i
$122$	−12.0065	+	7.28761i	−1.08702	+	0.659789i
$123$	−28.5924	+	7.66131i	−2.57809	+	0.690797i
$124$	−2.06434	−	1.07403i	−0.185384	−	0.0964508i
$125$	−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	$0.772181\pi$
$128$	9.12922	+	6.68261i	0.806917	+	0.590665i
$129$	9.41809	−	16.3126i	0.829216	−	1.43624i
$130$	−30.4558	−	7.44881i	−2.67115	−	0.653304i
$131$	19.1339	+	5.12690i	1.67173	+	0.447940i	0.965577	−	0.260116i	$-0.0837610\pi$
$131$	19.1339	+	5.12690i	1.67173	+	0.447940i	0.706156	+	0.708056i	$0.250428\pi$
$132$	−4.76796	+	3.03905i	−0.414997	+	0.264516i
$133$		0			0
$134$	14.7732	+	8.10266i	1.27621	+	0.699963i
$135$	−24.3227	+	14.0427i	−2.09336	+	1.20860i
$136$	−3.90665	+	1.32762i	−0.334993	+	0.113843i
$137$	0.792792	+	0.457719i	0.0677328	+	0.0391055i	0.533484	−	0.845810i	$-0.320882\pi$
$137$	0.792792	+	0.457719i	0.0677328	+	0.0391055i	−0.465751	+	0.884916i	$0.654216\pi$
$138$	7.44242	−	0.163244i	0.633541	−	0.0138962i
$139$	−2.74533	−	2.74533i	−0.232856	−	0.232856i	0.581028	−	0.813884i	$-0.302651\pi$
$139$	−2.74533	−	2.74533i	−0.232856	−	0.232856i	−0.813884	+	0.581028i	$0.802651\pi$
$140$		0			0
$141$	−22.9485	+	22.9485i	−1.93262	+	1.93262i
$142$	−2.95419	−	2.82738i	−0.247910	−	0.237268i
$143$	−2.86525	+	4.96276i	−0.239605	+	0.415007i
$144$	18.2378	−	12.7826i	1.51981	−	1.06522i
$145$	0.781469	+	1.35354i	0.0648974	+	0.112406i
$146$	0.869209	−	0.253459i	0.0719362	−	0.0209764i
$147$		0			0
$148$	−0.136394	−	0.0302052i	−0.0112115	−	0.00248286i
$149$	−2.18401	+	8.15084i	−0.178921	+	0.667743i	0.816929	+	0.576738i	$0.195675\pi$
$149$	−2.18401	+	8.15084i	−0.178921	+	0.667743i	−0.995850	+	0.0910051i	$0.970992\pi$
$150$	−19.2500	−	31.7149i	−1.57176	−	2.58951i
$151$	4.39729	+	2.53878i	0.357846	+	0.206603i	0.668136	−	0.744039i	$-0.267093\pi$
$151$	4.39729	+	2.53878i	0.357846	+	0.206603i	−0.310289	+	0.950642i	$0.600426\pi$
$152$	−5.96370	−	8.91869i	−0.483720	−	0.723402i
$153$			8.12229i			0.656648i
$154$		0			0
$155$	−3.07423	−	3.07423i	−0.246928	−	0.246928i
$156$	16.0314	−	30.8133i	1.28354	−	2.46704i
$157$	1.35207	+	5.04598i	0.107907	+	0.402713i	0.998659	−	0.0517765i	$-0.0164883\pi$
$157$	1.35207	+	5.04598i	0.107907	+	0.402713i	−0.890752	+	0.454490i	$0.849822\pi$
$158$	1.03005	+	0.251926i	0.0819460	+	0.0200421i
$159$	0.864899	+	1.49805i	0.0685909	+	0.118803i
$160$	12.5085	+	17.0391i	0.988888	+	1.34706i
$161$		0			0
$162$	−2.09713	−	7.19187i	−0.164766	−	0.565047i
$163$	−11.1956	−	2.99986i	−0.876908	−	0.234967i	−0.207835	−	0.978164i	$-0.566642\pi$
$163$	−11.1956	−	2.99986i	−0.876908	−	0.234967i	−0.669073	+	0.743197i	$0.733309\pi$
$164$	20.2062	−	0.886841i	1.57784	−	0.0692506i
$165$	−10.2037	+	2.73408i	−0.794360	+	0.212848i
$166$	0.198007	+	9.02729i	0.0153683	+	0.700653i
$167$		−	13.7471i		−	1.06378i	−0.846813	−	0.531891i	$-0.821482\pi$
$167$		−	13.7471i		−	1.06378i	0.846813	−	0.531891i	$-0.178518\pi$
$168$		0			0
$169$		−	22.2033i		−	1.70795i
$170$	−7.70695	+	0.169046i	−0.591096	+	0.0129652i
$171$	−20.4004	+	5.46627i	−1.56006	+	0.418016i
$172$	−8.69286	+	9.49094i	−0.662824	+	0.723677i
$173$	7.62659	+	2.04354i	0.579839	+	0.155367i	0.536805	−	0.843706i	$-0.319631\pi$
$173$	7.62659	+	2.04354i	0.579839	+	0.155367i	0.0430338	+	0.999074i	$0.486298\pi$
$174$	−1.66223	+	0.484703i	−0.126014	+	0.0367452i
$175$		0			0
$176$	3.62973	−	1.32299i	0.273601	−	0.0997242i
$177$	7.75640	+	13.4345i	0.583007	+	1.00980i
$178$	5.19806	−	21.2532i	0.389611	−	1.59299i
$179$	2.49823	+	9.32354i	0.186727	+	0.696874i	0.994254	+	0.107044i	$0.0341386\pi$
$179$	2.49823	+	9.32354i	0.186727	+	0.696874i	−0.807527	+	0.589830i	$0.799195\pi$
$180$	39.6811	−	12.5213i	2.95765	−	0.933286i
$181$	15.1263	+	15.1263i	1.12433	+	1.12433i	0.991083	+	0.133250i	$0.0425412\pi$
$181$	15.1263	+	15.1263i	1.12433	+	1.12433i	0.133250	+	0.991083i	$0.457459\pi$
$182$		0			0
$183$		−	29.0701i		−	2.14892i
$184$	−4.98903	−	0.990605i	−0.367797	−	0.0730284i
$185$	−0.226034	−	0.130501i	−0.0166183	−	0.00959459i
$186$	4.11731	−	2.49909i	0.301896	−	0.183242i
$187$	−0.364661	+	1.36094i	−0.0266667	+	0.0995214i
$188$	18.6995	−	11.9189i	1.36380	−	0.869277i
$189$		0			0
$190$	−5.61134	−	19.2434i	−0.407089	−	1.39607i
$191$	−9.93638	−	17.2103i	−0.718971	−	1.24529i	−0.961408	−	0.275127i	$-0.911280\pi$
$191$	−9.93638	−	17.2103i	−0.718971	−	1.24529i	0.242437	−	0.970167i	$-0.422053\pi$
$192$	−21.6281	+	8.97599i	−1.56087	+	0.647786i
$193$	5.94147	−	10.2909i	0.427676	−	0.740757i	−0.568990	−	0.822344i	$-0.692666\pi$
$193$	5.94147	−	10.2909i	0.427676	−	0.740757i	0.996666	+	0.0815877i	$0.0259991\pi$
$194$	−13.4412	+	14.0440i	−0.965020	+	1.00830i
$195$	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	$0.641768\pi$
$198$	−0.166771	−	7.60322i	−0.0118519	−	0.540337i
$199$	−20.8393	−	12.0316i	−1.47726	−	0.852897i	−0.477591	−	0.878582i	$-0.658490\pi$
$199$	−20.8393	−	12.0316i	−1.47726	−	0.852897i	−0.999670	+	0.0256852i	$0.991823\pi$
$200$	8.15650	+	24.0013i	0.576752	+	1.69715i
$201$	−30.2019	+	17.4371i	−2.13028	+	1.22992i
$202$	3.15044	−	5.74404i	0.221664	−	0.404149i
$203$		0			0
$204$	1.84649	−	8.33799i	0.129280	−	0.583776i
$205$	36.5002	+	9.78019i	2.54928	+	0.683078i
$206$	−2.93905	+	12.0168i	−0.204773	+	0.837252i
$207$	−5.00638	+	8.67130i	−0.347967	+	0.602697i
$208$	−15.2470	+	18.1875i	−1.05719	+	1.26107i
$209$	−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	$0.902969\pi$
$212$	−0.355669	−	1.12714i	−0.0244274	−	0.0774123i
$213$	8.17522	−	2.19054i	0.560157	−	0.150094i
$214$	3.29632	+	5.43077i	0.225332	+	0.371240i
$215$	−20.8241	+	12.0228i	−1.42019	+	0.819950i
$216$	1.39768	+	21.2132i	0.0950999	+	1.44337i
$217$		0			0
$218$	7.63332	+	4.18665i	0.516994	+	0.283556i
$219$	−0.485022	+	1.81013i	−0.0327747	+	0.122317i
$220$	7.21095	−	0.316486i	0.486162	−	0.0213375i
$221$	−2.24017	−	8.36042i	−0.150690	−	0.562383i
$222$	0.199923	−	0.208890i	0.0134179	−	0.0140198i
$223$	−8.33457			−0.558124			−0.279062	−	0.960273i	$-0.590024\pi$
$223$	−8.33457			−0.558124			−0.279062	+	0.960273i	$0.590024\pi$
$224$		0			0
$225$	49.9008			3.32672
$226$	0.0876615	−	0.0915933i	0.00583115	−	0.00609269i
$227$	2.88170	+	10.7546i	0.191265	+	0.713810i	0.993202	+	0.116402i	$0.0371361\pi$
$227$	2.88170	+	10.7546i	0.191265	+	0.713810i	−0.801937	+	0.597408i	$0.796197\pi$
$228$	22.1849	−	0.973685i	1.46923	−	0.0644839i
$229$	3.28330	−	12.2534i	0.216966	−	0.809730i	−0.768499	−	0.639851i	$-0.778996\pi$
$229$	3.28330	−	12.2534i	0.216966	−	0.809730i	0.985465	−	0.169878i	$-0.0543375\pi$
$230$	−8.33209	−	4.56990i	−0.549401	−	0.301330i
$231$		0			0
$232$	1.18050	−	0.0777801i	0.0775037	−	0.00510651i
$233$	19.5194	−	11.2695i	1.27876	−	0.738291i	0.302137	−	0.953265i	$-0.402300\pi$
$233$	19.5194	−	11.2695i	1.27876	−	0.738291i	0.976620	+	0.214974i	$0.0689667\pi$
$234$	24.2411	+	39.9378i	1.58469	+	2.61081i
$235$	40.0182	−	10.7229i	2.61050	−	0.699482i
$236$	−3.18964	−	10.1082i	−0.207628	−	0.657987i
$237$	−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	$0.357687\pi$
$240$	−43.5814	+	3.83293i	−2.81317	+	0.247414i
$241$	−9.69709	+	16.7959i	−0.624645	+	1.08192i	0.363965	+	0.931413i	$0.381423\pi$
$241$	−9.69709	+	16.7959i	−0.624645	+	1.08192i	−0.988609	+	0.150504i	$0.951910\pi$
$242$	−3.38239	+	13.8295i	−0.217428	+	0.888995i
$243$	−6.80335	−	1.82295i	−0.436435	−	0.116942i
$244$	−4.29467	+	19.3930i	−0.274938	+	1.24151i
$245$		0			0
$246$	−20.1311	+	36.7040i	−1.28351	+	2.34016i
$247$	19.4909	−	11.2531i	1.24018	−	0.716016i
$248$	−3.11590	+	1.05890i	−0.197860	+	0.0672400i
$249$	−16.1850	−	9.34441i	−1.02568	−	0.592178i
$250$	0.459161	+	20.9335i	0.0290399	+	1.32395i
$251$	8.09990	+	8.09990i	0.511261	+	0.511261i	0.914913	−	0.403652i	$-0.132259\pi$
$251$	8.09990	+	8.09990i	0.511261	+	0.511261i	−0.403652	+	0.914913i	$0.632259\pi$
$252$		0			0
$253$	−1.22816	+	1.22816i	−0.0772136	+	0.0772136i
$254$	−16.6313	+	17.3773i	−1.04354	+	1.09035i
$255$	7.97769	−	13.8178i	0.499582	−	0.865302i
$256$	15.7544	−	2.79276i	0.984649	−	0.174547i
$257$	−8.49113	−	14.7071i	−0.529662	−	0.917401i	−0.999401	−	0.0345963i	$-0.988985\pi$
$257$	−8.49113	−	14.7071i	−0.529662	−	0.917401i	0.469739	−	0.882805i	$-0.344348\pi$
$258$	−7.45711	−	25.5733i	−0.464259	−	1.59212i
$259$		0			0
$260$	−37.3910	+	23.8327i	−2.31889	+	1.47804i
$261$	0.602760	−	2.24953i	0.0373099	−	0.139242i
$262$	23.9478	−	14.5356i	1.47950	−	0.898013i
$263$	3.80821	+	2.19867i	0.234824	+	0.135576i	0.612796	−	0.790241i	$-0.290045\pi$
$263$	3.80821	+	2.19867i	0.234824	+	0.135576i	−0.377971	+	0.925817i	$0.623378\pi$
$264$	−1.55729	+	7.84305i	−0.0958445	+	0.482706i
$265$		−	2.20820i		−	0.135649i
$266$		0			0
$267$	32.0218	+	32.0218i	1.95970	+	1.95970i
$268$	22.7241	−	7.17058i	1.38809	−	0.438013i
$269$	−2.82392	−	10.5390i	−0.172177	−	0.642575i	−0.997015	−	0.0772054i	$-0.975400\pi$
$269$	−2.82392	−	10.5390i	−0.172177	−	0.642575i	0.824838	−	0.565369i	$-0.191266\pi$
$270$	−9.43618	+	38.5815i	−0.574267	+	2.34800i
$271$	−8.36882	−	14.4952i	−0.508369	−	0.880522i	−0.999953	−	0.00969131i	$-0.996915\pi$
$271$	−8.36882	−	14.4952i	−0.508369	−	0.880522i	0.491584	−	0.870830i	$-0.336418\pi$
$272$	−2.46363	+	5.28957i	−0.149380	+	0.320728i
$273$		0			0
$274$	1.24286	−	0.362415i	0.0750840	−	0.0218943i
$275$	8.36116	+	2.24037i	0.504197	+	0.135099i
$276$	7.11064	−	7.76346i	0.428010	−	0.467305i
$277$	18.5971	−	4.98309i	1.11739	−	0.299405i	0.347566	−	0.937656i	$-0.387008\pi$
$277$	18.5971	−	4.98309i	1.11739	−	0.299405i	0.769828	+	0.638251i	$0.220342\pi$
$278$	−5.48934	+	0.120405i	−0.329229	+	0.00722138i
$279$			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	$-0.147348\pi$
$282$	1.00648	+	45.8861i	0.0599348	+	2.73247i
$283$	9.10034	−	2.43843i	0.540959	−	0.144950i	0.0220149	−	0.999758i	$-0.492992\pi$
$283$	9.10034	−	2.43843i	0.540959	−	0.144950i	0.518944	+	0.854808i	$0.326325\pi$
$284$	−5.77740	+	0.253568i	−0.342826	+	0.0150465i
$285$	40.0745	+	10.7379i	2.37381	+	0.636059i
$286$	2.26867	+	7.78014i	0.134149	+	0.460049i
$287$		0			0
$288$	4.77357	−	31.1325i	0.281285	−	1.83450i
$289$	7.43597	+	12.8795i	0.437410	+	0.757616i
$290$	2.14704	+	0.525118i	0.126079	+	0.0308360i
$291$	−10.4137	−	38.8645i	−0.610462	−	2.27828i
$292$	0.590983	−	1.13590i	0.0345847	−	0.0664735i
$293$	−1.24795	−	1.24795i	−0.0729060	−	0.0729060i	0.669714	−	0.742620i	$-0.266417\pi$
$293$	−1.24795	−	1.24795i	−0.0729060	−	0.0729060i	−0.742620	+	0.669714i	$0.766417\pi$
$294$		0			0
$295$		−	19.8031i		−	1.15298i
$296$	−0.164231	+	0.109817i	−0.00954573	+	0.00638298i
$297$	6.28684	+	3.62971i	0.364800	+	0.210617i
$298$	6.19203	+	10.2015i	0.358695	+	0.590958i
$299$	2.76157	−	10.3063i	0.159706	−	0.596030i
$300$	−51.2260	−	11.3443i	−2.95754	−	0.654962i
$301$		0			0
$302$	6.89365	−	2.01017i	0.396685	−	0.115672i
$303$	6.77979	+	11.7429i	0.389489	+	0.674614i
$304$	−14.9436	−	2.62793i	−0.857075	−	0.150722i
$305$	−18.5550	+	32.1381i	−1.06245	+	1.84022i
$306$	8.29845	+	7.94222i	0.474391	+	0.454027i
$307$	−17.4736	+	17.4736i	−0.997273	+	0.997273i	−0.999996	−	0.00272350i	$-0.999133\pi$
$307$	−17.4736	+	17.4736i	−0.997273	+	0.997273i	0.00272350	+	0.999996i	$0.499133\pi$
$308$		0			0
$309$	−18.1055	−	18.1055i	−1.02999	−	1.02999i
$310$	−6.14697	+	0.134829i	−0.349125	+	0.00765779i
$311$	24.6649	+	14.2403i	1.39862	+	0.807491i	0.994248	−	0.107106i	$-0.0341583\pi$
$311$	24.6649	+	14.2403i	1.39862	+	0.807491i	0.404368	+	0.914596i	$0.367492\pi$
$312$	−15.8055	−	46.5093i	−0.894812	−	2.63307i
$313$	13.5858	−	7.84379i	0.767917	−	0.443357i	−0.0642141	−	0.997936i	$-0.520454\pi$
$313$	13.5858	−	7.84379i	0.767917	−	0.443357i	0.832131	+	0.554579i	$0.187121\pi$
$314$	6.47751	+	3.55272i	0.365547	+	0.200492i
$315$		0			0
$316$	1.26460	−	0.806044i	0.0711393	−	0.0453435i
$317$	−16.3210	−	4.37319i	−0.916677	−	0.245623i	−0.230513	−	0.973069i	$-0.574040\pi$
$317$	−16.3210	−	4.37319i	−0.916677	−	0.245623i	−0.686165	+	0.727446i	$0.740707\pi$
$318$	2.37626	+	0.581181i	0.133254	+	0.0325910i
$319$	0.201992	−	0.349860i	0.0113094	−	0.0195884i
$320$	29.6399	+	3.88152i	1.65692	+	0.216984i
$321$	−13.1489			−0.733901
$322$		0			0
$323$	3.91279	−	3.91279i	0.217714	−	0.217714i
$324$	−9.39849	−	4.88982i	−0.522138	−	0.271657i
$325$	−51.3638	+	13.7629i	−2.84915	+	0.763428i
$326$	−14.0123	+	8.50508i	−0.776071	+	0.471053i
$327$	−15.6053	+	9.00974i	−0.862977	+	0.498240i
$328$	18.8521	−	21.5116i	1.04093	−	1.18778i
$329$		0			0
$330$	−7.18415	+	13.0985i	−0.395474	+	0.721050i
$331$	7.70745	−	28.7646i	0.423640	−	1.58105i	−0.343236	−	0.939249i	$-0.611523\pi$
$331$	7.70745	−	28.7646i	0.423640	−	1.58105i	0.766876	−	0.641796i	$-0.221810\pi$
$332$	9.41669	+	8.62486i	0.516808	+	0.473350i
$333$	0.100657	+	0.375658i	0.00551598	+	0.0205859i
$334$	−14.0452	−	13.4423i	−0.768521	−	0.735531i
$335$	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	$0.516491\pi$
$338$	−22.6849	−	21.7111i	−1.23390	−	1.18093i
$339$	0.0679167	+	0.253469i	0.00368873	+	0.0137665i
$340$	−7.36338	+	8.03940i	−0.399335	+	0.435998i
$341$	−0.290850	+	1.08547i	−0.0157504	+	0.0587813i
$342$	−14.3633	+	26.1879i	−0.776679	+	1.41608i
$343$		0			0
$344$	1.19664	+	18.1619i	0.0645185	+	0.979225i
$345$	17.0339	−	9.83451i	0.917073	−	0.529472i
$346$	9.54537	−	5.79377i	0.513163	−	0.311475i
$347$	27.6994	−	7.42203i	1.48698	−	0.398436i	0.578265	−	0.815849i	$-0.303730\pi$
$347$	27.6994	−	7.42203i	1.48698	−	0.398436i	0.908717	+	0.417413i	$0.137063\pi$
$348$	−1.13017	+	2.17224i	−0.0605833	+	0.116444i
$349$	5.48808	−	5.48808i	0.293770	−	0.293770i	−0.544797	−	0.838568i	$-0.683393\pi$
$349$	5.48808	−	5.48808i	0.293770	−	0.293770i	0.838568	+	0.544797i	$0.183393\pi$
$350$		0			0
$351$	−44.5957			−2.38034
$352$	2.19758	−	5.00212i	0.117131	−	0.266614i
$353$	1.05144	−	1.82115i	0.0559627	−	0.0969303i	−0.836687	−	0.547682i	$-0.815511\pi$
$353$	1.05144	−	1.82115i	0.0559627	−	0.0969303i	0.892650	+	0.450751i	$0.148844\pi$
$354$	21.3103	+	5.21202i	1.13263	+	0.277016i
$355$	−10.4362	−	2.79638i	−0.553897	−	0.148416i
$356$	−16.6313	−	26.0928i	−0.881459	−	1.38292i
$357$		0			0
$358$	11.9686	+	6.56442i	0.632560	+	0.346941i
$359$	−9.27572	+	5.35534i	−0.489554	+	0.282644i	−0.724389	−	0.689391i	$-0.757878\pi$
$359$	−9.27572	+	5.35534i	−0.489554	+	0.282644i	0.234836	+	0.972035i	$0.424545\pi$
$360$	26.0084	−	52.7854i	1.37076	−	2.78204i
$361$	−3.99359	−	2.30570i	−0.210189	−	0.121353i
$362$	30.2454	−	0.663410i	1.58966	−	0.0348681i
$363$	−20.8366	−	20.8366i	−1.09364	−	1.09364i
$364$		0			0
$365$	1.69159	−	1.69159i	0.0885416	−	0.0885416i
$366$	−29.7006	−	28.4256i	−1.55247	−	1.48583i
$367$	9.09452	−	15.7522i	0.474730	−	0.822257i	−0.524851	−	0.851194i	$-0.675879\pi$
$367$	9.09452	−	15.7522i	0.474730	−	0.822257i	0.999581	+	0.0289374i	$0.00921235\pi$
$368$	−5.89052	+	4.12860i	−0.307065	+	0.215218i
$369$	−28.1532	−	48.7627i	−1.46560	−	2.53849i
$370$	−0.354353	+	0.103328i	−0.0184220	+	0.00537179i
$371$		0			0
$372$	1.47274	−	6.65029i	0.0763580	−	0.344801i
$373$	−0.252883	+	0.943772i	−0.0130938	+	0.0488667i	−0.972164	−	0.234303i	$-0.924719\pi$
$373$	−0.252883	+	0.943772i	−0.0130938	+	0.0488667i	0.959070	+	0.283170i	$0.0913859\pi$
$374$	1.03387	+	1.70333i	0.0534604	+	0.0880773i
$375$	−37.5317	−	21.6689i	−1.93813	−	1.11898i
$376$	6.10755	−	30.7598i	0.314973	−	1.58631i
$377$			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	$0.527968\pi$
$380$	−25.1477	−	13.0838i	−1.29005	−	0.671184i
$381$	−12.8853	−	48.0886i	−0.660133	−	2.46365i
$382$	−27.2997	−	6.67689i	−1.39677	−	0.341619i
$383$	5.62521	+	9.74315i	0.287435	+	0.497852i	0.973197	−	0.229974i	$-0.0738642\pi$
$383$	5.62521	+	9.74315i	0.287435	+	0.497852i	−0.685762	+	0.727826i	$0.740531\pi$
$384$	−11.9779	+	30.8741i	−0.611245	+	1.57554i
$385$		0			0
$386$	−4.70437	−	16.1331i	−0.239446	−	0.821153i
$387$	34.6088	+	9.27341i	1.75927	+	0.471394i
$388$	1.20545	+	27.4654i	0.0611972	+	1.39434i
$389$	−34.3310	+	9.19898i	−1.74065	+	0.466407i	−0.982592	−	0.185777i	$-0.940520\pi$
$389$	−34.3310	+	9.19898i	−1.74065	+	0.466407i	−0.758061	+	0.652184i	$0.773853\pi$
$390$	−2.01252	−	91.7523i	−0.101908	−	4.64606i
$391$		−	2.62338i		−	0.132670i
$392$		0			0
$393$			57.9821i			2.92481i
$394$	13.2367	−	0.290337i	0.666856	−	0.0146270i
$395$	2.70632	−	0.725158i	0.136170	−	0.0364866i
$396$	−7.93119	−	7.26427i	−0.398557	−	0.365043i
$397$	−2.96120	−	0.793452i	−0.148619	−	0.0398222i	0.183743	−	0.982974i	$-0.441179\pi$
$397$	−2.96120	−	0.793452i	−0.148619	−	0.0398222i	−0.332361	+	0.943152i	$0.607845\pi$
$398$	−32.6699	+	9.52645i	−1.63759	+	0.477518i
$399$		0			0
$400$	32.4975	+	15.1358i	1.62487	+	0.756789i
$401$	−10.6817	−	18.5012i	−0.533416	−	0.923904i	−0.999238	−	0.0390256i	$-0.987575\pi$
$401$	−10.6817	−	18.5012i	−0.533416	−	0.923904i	0.465822	−	0.884878i	$-0.345759\pi$
$402$	−11.7171	+	47.9074i	−0.584394	+	2.38940i
$403$	−1.78673	−	6.66818i	−0.0890035	−	0.332166i
$404$	−2.78803	−	8.83546i	−0.138710	−	0.439581i
$405$	−13.9963	−	13.9963i	−0.695479	−	0.695479i
$406$		0			0
$407$			0.0674628i			0.00334400i
$408$	−6.71327	−	10.0397i	−0.332357	−	0.497038i
$409$	8.76082	+	5.05806i	0.433195	+	0.250105i	0.700707	−	0.713449i	$-0.252868\pi$
$409$	8.76082	+	5.05806i	0.433195	+	0.250105i	−0.267512	+	0.963555i	$0.586201\pi$
$410$	45.6833	−	27.7284i	2.25614	−	1.36941i
$411$	−0.693522	+	2.58826i	−0.0342089	+	0.127669i
$412$	9.40357	+	14.7532i	0.463280	+	0.726839i
$413$		0			0
$414$	3.96398	+	13.5940i	0.194819	+	0.668110i
$415$	11.9288	+	20.6612i	0.585561	+	1.01422i
$416$	3.67299	+	33.3619i	0.180083	+	1.63570i
$417$	5.68218	−	9.84182i	0.278257	−	0.481956i
$418$	−3.58240	+	3.74308i	−0.175221	+	0.183080i
$419$	−17.7452	+	17.7452i	−0.866909	+	0.866909i	−0.992129	−	0.125220i	$-0.960036\pi$
$419$	−17.7452	+	17.7452i	−0.866909	+	0.866909i	0.125220	+	0.992129i	$0.460036\pi$
$420$		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	$0.966915\pi$
$422$	0.798910	+	36.4229i	0.0388903	+	1.77304i
$423$	−53.4627	−	30.8667i	−2.59945	−	1.50079i
$424$	−1.49937	−	0.738770i	−0.0728159	−	0.0358778i
$425$	−11.3226	+	6.53709i	−0.549225	+	0.317095i
$426$	5.75593	−	10.4945i	0.278876	−	0.508461i
$427$		0			0
$428$	8.77179	+	1.94256i	0.424001	+	0.0938972i
$429$	−16.2021	−	4.34135i	−0.782246	−	0.209602i
$430$	−8.07890	+	33.0321i	−0.389599	+	1.59295i
$431$	−11.1720	+	19.3505i	−0.538136	+	0.932080i	0.460868	+	0.887469i	$0.347538\pi$
$431$	−11.1720	+	19.3505i	−0.538136	+	0.932080i	−0.999004	+	0.0446110i	$0.985795\pi$
$432$	23.0399	+	19.3149i	1.10851	+	0.929288i
$433$	9.86560			0.474111			0.237055	−	0.971496i	$-0.423818\pi$
$433$	9.86560			0.474111			0.237055	+	0.971496i	$0.423818\pi$
$434$		0			0
$435$	−3.23491	+	3.23491i	−0.155102	+	0.155102i
$436$	11.7415	−	3.70504i	0.562318	−	0.177439i
$437$	6.58902	−	1.76552i	0.315196	−	0.0844565i
$438$	1.37512	+	2.26554i	0.0657056	+	0.108252i
$439$	16.8323	−	9.71811i	0.803360	−	0.463820i	−0.0412847	−	0.999147i	$-0.513145\pi$
$439$	16.8323	−	9.71811i	0.803360	−	0.463820i	0.844645	+	0.535327i	$0.179812\pi$
$440$	6.72774	−	7.67681i	0.320732	−	0.365978i
$441$		0			0
$442$	−10.7323	−	5.88632i	−0.510481	−	0.279984i
$443$	6.53942	−	24.4055i	0.310697	−	1.15954i	−0.617232	−	0.786781i	$-0.711746\pi$
$443$	6.53942	−	24.4055i	0.310697	−	1.15954i	0.927929	−	0.372757i	$-0.121587\pi$
$444$	−0.0179297	−	0.408517i	−0.000850904	−	0.0193874i
$445$	−14.9624	−	55.8403i	−0.709285	−	2.64709i
$446$	−8.14980	+	8.51533i	−0.385904	+	0.403213i
$447$	−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	$0.647125\pi$
$450$	48.7945	−	50.9831i	2.30020	−	2.40337i
$451$	−2.52795	−	9.43445i	−0.119037	−	0.444251i
$452$	−0.00786175	−	0.179125i	−0.000369785	−	0.00842535i
$453$	−3.84668	+	14.3560i	−0.180733	+	0.674504i
$454$	13.8057	+	7.57202i	0.647934	+	0.355372i
$455$		0			0
$456$	20.6982	−	23.6181i	0.969284	−	1.10602i
$457$	7.98948	−	4.61273i	0.373732	−	0.215774i	−0.301356	−	0.953512i	$-0.597439\pi$
$457$	7.98948	−	4.61273i	0.373732	−	0.215774i	0.675088	+	0.737738i	$0.264106\pi$
$458$	−9.30868	−	15.3363i	−0.434966	−	0.716618i
$459$	−10.5910	+	2.83785i	−0.494346	+	0.132460i
$460$	−12.8164	+	4.04421i	−0.597567	+	0.188562i
$461$	10.6272	−	10.6272i	0.494960	−	0.494960i	−0.414905	−	0.909865i	$-0.636185\pi$
$461$	10.6272	−	10.6272i	0.494960	−	0.494960i	0.909865	+	0.414905i	$0.136185\pi$
$462$		0			0
$463$	32.4877			1.50983			0.754916	−	0.655821i	$-0.227678\pi$
$463$	32.4877			1.50983			0.754916	+	0.655821i	$0.227678\pi$
$464$	1.07486	−	1.28216i	0.0498993	−	0.0595228i
$465$	6.36291	−	11.0209i	0.295073	−	0.511082i
$466$	7.57271	−	30.9624i	0.350799	−	1.43431i
$467$	16.9836	+	4.55073i	0.785905	+	0.210583i	0.629387	−	0.777092i	$-0.283306\pi$
$467$	16.9836	+	4.55073i	0.785905	+	0.210583i	0.156519	+	0.987675i	$0.449973\pi$
$468$	64.5076	+	14.2856i	2.98187	+	0.660350i
$469$		0			0
$470$	28.1756	−	51.3713i	1.29964	−	2.36958i
$471$	−13.2424	+	7.64552i	−0.610179	+	0.352287i
$472$	−13.4463	−	6.62528i	−0.618918	−	0.304953i
$473$	5.38256	+	3.10762i	0.247490	+	0.142889i
$474$	0.0680653	+	3.10315i	0.00312634	+	0.142532i
$475$	−24.0390	−	24.0390i	−1.10298	−	1.10298i
$476$		0			0
$477$	−2.32665	+	2.32665i	−0.106530	+	0.106530i
$478$	13.0714	−	13.6577i	0.597871	−	0.624687i
$479$	−18.1404	+	31.4201i	−0.828857	+	1.43562i	0.0700792	+	0.997541i	$0.477675\pi$
$479$	−18.1404	+	31.4201i	−0.828857	+	1.43562i	−0.898936	+	0.438080i	$0.855659\pi$
$480$	−38.6992	+	48.2746i	−1.76637	+	2.20342i
$481$	−0.207217	−	0.358910i	−0.00944827	−	0.0163649i
$482$	7.67802	+	26.3309i	0.349724	+	1.19934i
$483$		0			0
$484$	10.8220	+	16.9787i	0.491911	+	0.771757i
$485$	−13.2938	+	49.6132i	−0.603641	+	2.25282i
$486$	−8.51501	+	5.16837i	−0.386249	+	0.234442i
$487$	6.32101	+	3.64944i	0.286432	+	0.165372i	0.636332	−	0.771415i	$-0.280451\pi$
$487$	6.32101	+	3.64944i	0.286432	+	0.165372i	−0.349899	+	0.936787i	$0.613784\pi$
$488$	15.6141	+	23.3509i	0.706818	+	1.05704i
$489$		−	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	$0.631221\pi$
$492$	17.8153	+	56.4580i	0.803176	+	2.54532i
$493$	0.157925	+	0.589384i	0.00711259	+	0.0265445i
$494$	7.56166	−	30.9172i	0.340215	−	1.39103i
$495$	−10.0470	−	17.4019i	−0.451579	−	0.782157i
$496$	−1.96496	+	4.21890i	−0.0882294	+	0.189434i
$497$		0			0
$498$	−25.3733	+	7.39877i	−1.13700	+	0.331547i
$499$	−22.2964	−	5.97431i	−0.998126	−	0.267447i	−0.277466	−	0.960736i	$-0.589494\pi$
$499$	−22.2964	−	5.97431i	−0.998126	−	0.267447i	−0.720660	+	0.693289i	$0.756161\pi$
$500$	21.8365	+	20.0003i	0.976559	+	0.894442i
$501$	38.8678	−	10.4146i	1.73648	−	0.465289i
$502$	16.1959	−	0.355245i	0.722858	−	0.0158554i
$503$			11.6303i			0.518568i	0.965801	+	0.259284i	$0.0834866\pi$
$503$			11.6303i			0.518568i	−0.965801	+	0.259284i	$0.916513\pi$
$504$		0			0
$505$		−	17.3097i		−	0.770273i
$506$	0.0538645	+	2.45572i	0.00239457	+	0.109170i
$507$	62.7766	−	16.8209i	2.78800	−	0.747044i
$508$	1.49155	+	33.9840i	0.0661766	+	1.50780i
$509$	27.1347	+	7.27073i	1.20273	+	0.322270i	0.803904	−	0.594759i	$-0.202752\pi$
$509$	27.1347	+	7.27073i	1.20273	+	0.322270i	0.398822	+	0.917028i	$0.369419\pi$
$510$	−6.31662	−	21.6621i	−0.279705	−	0.959216i
$511$		0			0
$512$	12.5518	−	18.8269i	0.554716	−	0.832040i
$513$	−14.2554	−	24.6911i	−0.629393	−	1.09014i
$514$	−23.3289	−	5.70573i	−1.02899	−	0.251669i
$515$	8.45992	+	31.5728i	0.372788	+	1.39127i
$516$	−33.4197	−	17.3875i	−1.47122	−	0.765443i
$517$	−7.57218	−	7.57218i	−0.333024	−	0.333024i
$518$		0			0
$519$			23.1112i			1.01447i
$520$	−12.2125	+	61.5063i	−0.535553	+	2.69723i
$521$	5.79205	+	3.34404i	0.253755	+	0.146505i	0.621482	−	0.783428i	$-0.286531\pi$
$521$	5.79205	+	3.34404i	0.253755	+	0.146505i	−0.367728	+	0.929934i	$0.619864\pi$
$522$	−1.70892	−	2.81549i	−0.0747975	−	0.123231i
$523$	−3.38908	+	12.6482i	−0.148194	+	0.553068i	0.851398	+	0.524520i	$0.175755\pi$
$523$	−3.38908	+	12.6482i	−0.148194	+	0.553068i	−0.999592	+	0.0285481i	$0.990912\pi$
$524$	8.56600	−	38.6805i	0.374208	−	1.68977i
$525$		0			0
$526$	5.97014	−	1.74088i	0.260310	−	0.0759058i
$527$	−0.848661	−	1.46992i	−0.0369682	−	0.0640309i
$528$	6.49039	+	9.26024i	0.282458	+	0.403000i
$529$	−9.88301	+	17.1179i	−0.429696	+	0.744256i
$530$	−2.25610	−	2.15925i	−0.0979986	−	0.0937918i
$531$	−20.8654	+	20.8654i	−0.905479	+	0.905479i
$532$		0			0
$533$	42.4276	+	42.4276i	1.83774	+	1.83774i
$534$	64.0282	−	1.40441i	2.77077	−	0.0607748i
$535$	14.5367	+	8.39275i	0.628475	+	0.362850i
$536$	14.8942	−	30.2285i	0.643331	−	1.30567i
$537$	−24.4682	+	14.1268i	−1.05588	+	0.609614i
$538$	−13.5289	−	7.42020i	−0.583272	−	0.319908i
$539$		0			0
$540$	30.1913	+	47.3670i	1.29923	+	2.03835i
$541$	−18.3654	−	4.92099i	−0.789589	−	0.211570i	−0.158581	−	0.987346i	$-0.550692\pi$
$541$	−18.3654	−	4.92099i	−0.789589	−	0.211570i	−0.631008	+	0.775776i	$0.717359\pi$
$542$	−22.9929	−	5.62354i	−0.987629	−	0.241552i
$543$	−31.3079	+	54.2269i	−1.34355	+	2.32710i
$544$	2.99528	+	7.68937i	0.128422	+	0.329679i
$545$	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	$0.369051\pi$
$548$	0.845033	−	1.62420i	0.0360980	−	0.0693823i
$549$	53.4122	−	14.3118i	2.27958	−	0.610811i
$550$	10.4648	−	6.35180i	0.446219	−	0.270842i
$551$	−1.37405	+	0.793308i	−0.0585365	+	0.0337960i
$552$	−0.978835	−	14.8562i	−0.0416620	−	0.632322i
$553$		0			0
$554$	13.0937	−	23.8731i	0.556298	−	1.01427i
$555$	0.197731	−	0.737941i	0.00839320	−	0.0313238i
$556$	−5.24463	+	5.72613i	−0.222422	+	0.242842i
$557$	8.73540	+	32.6010i	0.370131	+	1.38135i	0.860331	+	0.509737i	$0.170257\pi$
$557$	8.73540	+	32.6010i	0.370131	+	1.38135i	−0.490200	+	0.871610i	$0.663076\pi$
$558$	6.61875	+	6.33462i	0.280194	+	0.268166i
$559$	−38.1812			−1.61489
$560$		0			0
$561$	−4.12410			−0.174120
$562$	−15.2958	−	14.6392i	−0.645214	−	0.617517i
$563$	−7.56259	−	28.2240i	−0.318725	−	1.18950i	−0.920471	−	0.390811i	$-0.872195\pi$
$563$	−7.56259	−	28.2240i	−0.318725	−	1.18950i	0.601746	−	0.798688i	$-0.294472\pi$
$564$	47.8654	+	43.8405i	2.01550	+	1.84602i
$565$	0.0867003	−	0.323570i	0.00364751	−	0.0136127i
$566$	6.40728	−	11.6821i	0.269318	−	0.491035i
$567$		0			0
$568$	−5.39025	+	6.15065i	−0.226170	+	0.258076i
$569$	−22.9373	+	13.2428i	−0.961581	+	0.555169i	−0.896659	−	0.442722i	$-0.854013\pi$
$569$	−22.9373	+	13.2428i	−0.961581	+	0.555169i	−0.0649214	+	0.997890i	$0.520680\pi$
$570$	50.1568	−	30.4437i	2.10084	−	1.27515i
$571$	−32.4514	+	8.69533i	−1.35805	+	0.363888i	−0.863100	−	0.505034i	$-0.831480\pi$
$571$	−32.4514	+	8.69533i	−1.35805	+	0.363888i	−0.494949	+	0.868922i	$0.664813\pi$
$572$	10.1673	+	5.28979i	0.425114	+	0.221177i
$573$	41.1319	−	41.1319i	1.71831	−	1.71831i
$574$		0			0
$575$	−16.1172			−0.672134
$576$	−27.1400	−	35.3195i	−1.13083	−	1.47164i
$577$	13.7824	−	23.8719i	0.573770	−	0.993799i	−0.422404	−	0.906408i	$-0.638814\pi$
$577$	13.7824	−	23.8719i	0.573770	−	0.993799i	0.996174	−	0.0873910i	$-0.0278529\pi$
$578$	20.4299	+	4.99670i	0.849773	+	0.207835i
$579$	33.5972	+	9.00233i	1.39625	+	0.374124i
$580$	2.63595	−	1.68013i	0.109452	−	0.0697637i
$581$		0			0
$582$	−49.8902	−	27.3633i	−2.06802	−	1.13425i
$583$	−0.494301	+	0.285385i	−0.0204719	+	0.0118194i
$584$	−0.582655	−	1.71452i	−0.0241104	−	0.0709473i
$585$	106.902	+	61.7201i	4.41987	+	2.55181i
$586$	−2.49530	+	0.0547325i	−0.103080	+	0.00226098i
$587$	23.6471	+	23.6471i	0.976018	+	0.976018i	0.999719	−	0.0237007i	$-0.00754488\pi$
$587$	23.6471	+	23.6471i	0.976018	+	0.976018i	−0.0237007	+	0.999719i	$0.507545\pi$
$588$		0			0
$589$	3.12080	−	3.12080i	0.128590	−	0.128590i
$590$	−20.2326	−	19.3641i	−0.832965	−	0.797208i
$591$	−13.7017	+	23.7321i	−0.563613	+	0.976206i
$592$	−0.0483913	+	0.275175i	−0.00198887	+	0.0113096i
$593$	−20.9151	−	36.2261i	−0.858881	−	1.48763i	−0.872997	−	0.487725i	$-0.837827\pi$
$593$	−20.9151	−	36.2261i	−0.858881	−	1.48763i	0.0141161	−	0.999900i	$-0.495507\pi$
$594$	9.85590	−	2.87395i	0.404393	−	0.117920i
$595$		0			0
$596$	16.4775	+	3.64904i	0.674946	+	0.149470i
$597$	18.2299	−	68.0350i	0.746101	−	2.78449i
$598$	−7.82950	−	12.8993i	−0.320172	−	0.527492i
$599$	−24.0513	−	13.8860i	−0.982708	−	0.567367i	−0.0796214	−	0.996825i	$-0.525371\pi$
$599$	−24.0513	−	13.8860i	−0.982708	−	0.567367i	−0.903087	+	0.429458i	$0.858704\pi$
$600$	−61.6807	+	41.2443i	−2.51810	+	1.68379i
$601$		−	26.3860i		−	1.07631i	−0.842846	−	0.538154i	$-0.819122\pi$
$601$		−	26.3860i		−	1.07631i	0.842846	−	0.538154i	$-0.180878\pi$
$602$		0			0
$603$	−46.9071	−	46.9071i	−1.91021	−	1.91021i
$604$	4.68705	−	9.00876i	0.190713	−	0.366561i
$605$	9.73605	+	36.3354i	0.395827	+	1.47725i
$606$	18.6271	+	4.55577i	0.756675	+	0.185066i
$607$	−9.49910	−	16.4529i	−0.385557	−	0.667804i	0.606290	−	0.795244i	$-0.292657\pi$
$607$	−9.49910	−	16.4529i	−0.385557	−	0.667804i	−0.991846	+	0.127440i	$0.959324\pi$
$608$	−17.2972	+	12.6981i	−0.701496	+	0.514974i
$609$		0			0
$610$	14.6916	+	50.3830i	0.594844	+	2.03995i
$611$	63.5434	+	17.0264i	2.57069	+	0.688815i
$612$	16.2290	−	0.712282i	0.656016	−	0.0287923i
$613$	4.14276	−	1.11005i	0.167324	−	0.0448344i	−0.174184	−	0.984713i	$-0.555729\pi$
$613$	4.14276	−	1.11005i	0.167324	−	0.0448344i	0.341509	+	0.939879i	$0.389062\pi$
$614$	0.766358	+	34.9389i	0.0309277	+	1.41002i
$615$			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	$-0.00715808\pi$
$618$	−36.2023	+	0.794071i	−1.45627	+	0.0319422i
$619$	−8.13764	+	2.18047i	−0.327079	+	0.0876407i	−0.418622	−	0.908160i	$-0.637487\pi$
$619$	−8.13764	+	2.18047i	−0.327079	+	0.0876407i	0.0915428	+	0.995801i	$0.470820\pi$
$620$	−5.87294	+	6.41213i	−0.235863	+	0.257517i
$621$	−13.0561	−	3.49837i	−0.523923	−	0.140385i
$622$	38.6672	−	11.2752i	1.55041	−	0.452096i
$623$		0			0
$624$	−62.9731	−	29.3299i	−2.52094	−	1.17413i
$625$	5.25597	+	9.10361i	0.210239	+	0.364145i
$626$	5.27074	−	21.5504i	0.210661	−	0.861327i
$627$	−2.77550	−	10.3583i	−0.110843	−	0.413672i
$628$	9.96369	−	3.14404i	0.397594	−	0.125461i
$629$	−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	$-0.0799078\pi$
$632$	0.413038	−	2.08020i	0.0164297	−	0.0827460i
$633$	−65.3026	−	37.7025i	−2.59554	−	1.49854i
$634$	−20.4272	+	12.3987i	−0.811267	+	0.492416i
$635$	−16.4489	+	61.3883i	−0.652757	+	2.43612i
$636$	2.91737	−	1.85951i	0.115681	−	0.0737342i
$637$		0			0
$638$	−0.159934	−	0.548476i	−0.00633185	−	0.0217144i
$639$	8.04963	+	13.9424i	0.318439	+	0.551552i
$640$	32.9485	−	26.4873i	1.30240	−	1.04700i
$641$	5.09900	−	8.83173i	0.201398	−	0.348832i	−0.747581	−	0.664171i	$-0.768785\pi$
$641$	5.09900	−	8.83173i	0.201398	−	0.348832i	0.948979	+	0.315339i	$0.102118\pi$
$642$	−12.8574	+	13.4341i	−0.507442	+	0.530202i
$643$	10.9741	−	10.9741i	0.432777	−	0.432777i	−0.456795	−	0.889572i	$-0.651003\pi$
$643$	10.9741	−	10.9741i	0.432777	−	0.432777i	0.889572	+	0.456795i	$0.151003\pi$
$644$		0			0
$645$	−49.7688	−	49.7688i	−1.95964	−	1.95964i
$646$	−0.171607	−	7.82371i	−0.00675179	−	0.307820i
$647$	5.70335	+	3.29283i	0.224222	+	0.129455i	0.607904	−	0.794011i	$-0.292011\pi$
$647$	5.70335	+	3.29283i	0.224222	+	0.129455i	−0.383682	+	0.923465i	$0.625344\pi$
$648$	−14.1860	+	4.82091i	−0.557279	+	0.189383i
$649$	−4.43289	+	2.55933i	−0.174006	+	0.100462i
$650$	−36.1637	+	65.9356i	−1.41846	+	2.58621i
$651$		0			0
$652$	−5.01214	+	22.6328i	−0.196291	+	0.886367i
$653$	−4.95799	−	1.32849i	−0.194021	−	0.0519878i	0.160500	−	0.987036i	$-0.448689\pi$
$653$	−4.95799	−	1.32849i	−0.194021	−	0.0519878i	−0.354521	+	0.935048i	$0.615356\pi$
$654$	−6.05422	+	24.7538i	−0.236739	+	0.967950i
$655$	37.0091	−	64.1016i	1.44606	−	2.50466i
$656$	−3.54395	−	40.2957i	−0.138368	−	1.57328i
$657$	−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	$0.300957\pi$
$660$	6.35772	+	20.1481i	0.247474	+	0.784263i
$661$	−26.5759	+	7.12099i	−1.03368	+	0.276975i	−0.735493	−	0.677532i	$-0.763050\pi$
$661$	−26.5759	+	7.12099i	−1.03368	+	0.276975i	−0.298190	+	0.954507i	$0.596383\pi$
$662$	−21.8519	−	36.0015i	−0.849297	−	1.39924i
$663$	21.9407	−	12.6675i	0.852106	−	0.491964i
$664$	18.0198	−	1.18728i	0.699306	−	0.0460754i
$665$		0			0
$666$	0.482231	+	0.264489i	0.0186861	+	0.0102488i
$667$	−0.194682	+	0.726564i	−0.00753813	+	0.0281327i
$668$	−27.4677	+	1.20555i	−1.06276	+	0.0466441i
$669$	−6.31415	−	23.5647i	−0.244119	−	0.911065i
$670$	43.5322	−	45.4847i	1.68180	−	1.75723i
$671$	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	$0.755946\pi$
$674$	−1.85908	+	1.94246i	−0.0716091	+	0.0748209i
$675$	17.4349	+	65.0679i	0.671069	+	2.50446i
$676$	−44.3640	+	1.94712i	−1.70631	+	0.0748892i
$677$	5.91710	−	22.0829i	0.227413	−	0.848716i	−0.754011	−	0.656862i	$-0.771883\pi$
$677$	5.91710	−	22.0829i	0.227413	−	0.848716i	0.981424	−	0.191854i	$-0.0614500\pi$
$678$	0.325377	+	0.178460i	0.0124960	+	0.00685370i
$679$		0			0
$680$	1.01363	+	15.3842i	0.0388708	+	0.589959i
$681$	−28.2240	+	16.2951i	−1.08154	+	0.624430i
$682$	0.824607	+	1.35856i	0.0315758	+	0.0520220i
$683$	−18.1068	+	4.85170i	−0.692837	+	0.185645i	−0.588020	−	0.808847i	$-0.700092\pi$
$683$	−18.1068	+	4.85170i	−0.692837	+	0.185645i	−0.104817	+	0.994492i	$0.533426\pi$
$684$	12.7110	+	40.2822i	0.486019	+	1.54023i
$685$	2.41876	−	2.41876i	0.0924161	−	0.0924161i
$686$		0			0
$687$	37.1321			1.41668
$688$	19.7259	+	16.5367i	0.752044	+	0.630455i
$689$	1.75316	−	3.03656i	0.0667901	−	0.115684i
$690$	6.60843	−	27.0198i	0.251579	−	1.02863i
$691$	−8.53045	−	2.28573i	−0.324514	−	0.0869532i	0.0928845	−	0.995677i	$-0.470391\pi$
$691$	−8.53045	−	2.28573i	−0.324514	−	0.0869532i	−0.417398	+	0.908724i	$0.637058\pi$
$692$	3.41433	−	15.4177i	0.129794	−	0.586094i
$693$		0			0
$694$	19.5023	−	35.5577i	0.740298	−	1.34975i
$695$	−12.5637	+	7.25368i	−0.476570	+	0.275148i
$696$	1.11424	+	3.27876i	0.0422352	+	0.124281i
$697$	12.7760	+	7.37623i	0.483925	+	0.279395i
$698$	−0.240696	−	10.9735i	−0.00911048	−	0.415354i
$699$	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	$-0.0210487\pi$
$702$	−43.6070	+	45.5629i	−1.64584	+	1.71966i
$703$	0.132478	−	0.229458i	0.00499649	−	0.00865417i
$704$	−2.96175	−	7.13646i	−0.111625	−	0.268966i
$705$	60.6344	+	105.022i	2.28363	+	3.95536i
$706$	−0.832519	−	2.85503i	−0.0313322	−	0.107450i
$707$		0			0
$708$	26.1629	−	16.6760i	0.983263	−	0.626723i
$709$	3.98010	−	14.8540i	0.149476	−	0.557852i	−0.850039	−	0.526719i	$-0.823422\pi$
$709$	3.98010	−	14.8540i	0.149476	−	0.557852i	0.999515	−	0.0311326i	$-0.00991142\pi$
$710$	−13.0619	+	7.92819i	−0.490204	+	0.297540i
$711$	−3.61554	−	2.08743i	−0.135593	−	0.0782849i
$712$	−42.9214	−	8.52232i	−1.60855	−	0.319387i
$713$		−	2.09238i		−	0.0783601i
$714$		0			0
$715$	15.1411	+	15.1411i	0.566245	+	0.566245i
$716$	18.4101	−	5.80929i	0.688016	−	0.217103i
$717$	10.1272	+	37.7952i	0.378207	+	1.41149i
$718$	−3.59859	+	14.7135i	−0.134298	+	0.549103i
$719$	−10.7208	−	18.5690i	−0.399819	−	0.692506i	0.593884	−	0.804550i	$-0.297594\pi$
$719$	−10.7208	−	18.5690i	−0.399819	−	0.692506i	−0.993703	+	0.112044i	$0.964260\pi$
$720$	−28.4984	−	78.1877i	−1.06207	−	2.91388i
$721$		0			0
$722$	−6.26076	+	1.82562i	−0.233001	+	0.0679425i
$723$	−54.8341	−	14.6928i	−2.03930	−	0.546429i
$724$	28.8971	−	31.5501i	1.07395	−	1.17255i
$725$	3.62099	−	0.970243i	0.134480	−	0.0360339i
$726$	−41.6633	+	0.913853i	−1.54627	+	0.0339163i
$727$		−	30.4747i		−	1.13024i	−0.825007	−	0.565122i	$-0.808829\pi$
$727$		−	30.4747i		−	1.13024i	0.825007	−	0.565122i	$-0.191171\pi$
$728$		0			0
$729$		−	36.5081i		−	1.35215i
$730$	−0.0741895	−	3.38236i	−0.00274588	−	0.125187i
$731$	−9.06763	+	2.42966i	−0.335378	+	0.0898644i
$732$	−58.0842	+	2.54930i	−2.14686	+	0.0942247i
$733$	44.8442	+	12.0160i	1.65636	+	0.443820i	0.961384	−	0.275212i	$-0.0887481\pi$
$733$	44.8442	+	12.0160i	1.65636	+	0.443820i	0.694976	+	0.719032i	$0.255415\pi$
$734$	−7.20091	−	24.6947i	−0.265791	−	0.911499i
$735$		0			0
$736$	−1.54179	+	10.0553i	−0.0568312	+	0.370645i
$737$	−5.75359	−	9.96551i	−0.211936	−	0.367084i
$738$	−77.3493	−	18.9179i	−2.84727	−	0.696378i
$739$	−5.66375	−	21.1374i	−0.208344	−	0.777552i	−0.988404	−	0.151847i	$-0.951478\pi$
$739$	−5.66375	−	21.1374i	−0.208344	−	0.777552i	0.780060	−	0.625705i	$-0.215189\pi$
$740$	−0.240928	+	0.463077i	−0.00885669	+	0.0170230i
$741$	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	$-0.114607\pi$
$744$	−5.35443	−	8.00754i	−0.196303	−	0.293570i
$745$	27.3067	+	15.7655i	1.00044	+	0.577604i
$746$	0.716965	+	1.18122i	0.0262499	+	0.0432474i
$747$	9.20086	−	34.3381i	0.336642	−	1.25637i
$748$	2.75123	+	0.609275i	0.100595	+	0.0222773i
$749$		0			0
$750$	−58.8385	+	17.1571i	−2.14848	+	0.626490i
$751$	17.9286	+	31.0533i	0.654225	+	1.13315i	0.982087	+	0.188426i	$0.0603385\pi$
$751$	17.9286	+	31.0533i	0.654225	+	1.13315i	−0.327862	+	0.944726i	$0.606328\pi$
$752$	−25.4548	−	36.3179i	−0.928240	−	1.32438i
$753$	−16.7649	+	29.0376i	−0.610945	+	1.05819i
$754$	2.53555	+	2.42671i	0.0923394	+	0.0883756i
$755$	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	$0.556959\pi$
$758$	35.3605	−	0.775605i	1.28435	−	0.0281712i
$759$	−4.40286	−	2.54199i	−0.159814	−	0.0922685i
$760$	−37.9578	+	12.8994i	−1.37687	+	0.467911i
$761$	25.6074	−	14.7845i	0.928269	−	0.535936i	0.0420051	−	0.999117i	$-0.486625\pi$
$761$	25.6074	−	14.7845i	0.928269	−	0.535936i	0.886264	+	0.463181i	$0.153292\pi$
$762$	−61.7312	−	33.8577i	−2.23628	−	1.22654i
$763$		0			0
$764$	−33.5162	+	21.3629i	−1.21257	+	0.772883i
$765$	29.3158	+	7.85514i	1.05991	+	0.284003i
$766$	15.4550	+	3.77994i	0.558410	+	0.136575i
$767$	15.7223	−	27.2319i	0.567701	−	0.983286i
$768$	19.8314	+	42.4274i	0.715603	+	1.53097i
$769$	−30.8038			−1.11081			−0.555406	−	0.831579i	$-0.687437\pi$
$769$	−30.8038			−1.11081			−0.555406	+	0.831579i	$0.687437\pi$
$770$		0			0
$771$	35.1492	−	35.1492i	1.26587	−	1.26587i
$772$	−21.0831	−	10.9690i	−0.758797	−	0.394784i
$773$	−49.6587	+	13.3060i	−1.78610	+	0.478584i	−0.991674	−	0.128777i	$-0.958895\pi$
$773$	−49.6587	+	13.3060i	−1.78610	+	0.478584i	−0.794426	+	0.607361i	$0.792228\pi$
$774$	43.3161	−	26.2916i	1.55696	−	0.945033i
$775$	−9.03075	+	5.21391i	−0.324394	+	0.187289i
$776$	29.2398	+	25.6249i	1.04965	+	0.919881i
$777$		0			0
$778$	−24.1715	+	44.0707i	−0.866589	+	1.58001i
$779$	−9.92835	+	37.0531i	−0.355720	+	1.32757i
$780$	−95.7102	−	87.6621i	−3.42697	−	3.13881i
$781$	0.722799	+	2.69752i	0.0258638	+	0.0965250i
$782$	−2.68027	−	2.56522i	−0.0958464	−	0.0917320i
$783$	3.14386			0.112352
$784$		0			0
$785$	19.5201			0.696701
$786$	59.2397	+	56.6967i	2.11301	+	2.02230i
$787$	2.69273	+	10.0494i	0.0959855	+	0.358223i	0.997167	−	0.0752192i	$-0.0239656\pi$
$787$	2.69273	+	10.0494i	0.0959855	+	0.358223i	−0.901182	+	0.433442i	$0.857299\pi$
$788$	12.6466	−	13.8077i	0.450517	−	0.491879i
$789$	−3.33136	+	12.4328i	−0.118600	+	0.442620i
$790$	1.90544	−	3.47410i	0.0677926	−	0.123603i
$791$		0			0
$792$	−15.1772	+	0.999984i	−0.539298	+	0.0355329i
$793$	−51.0309	+	29.4627i	−1.81216	+	1.04625i
$794$	−3.70622	+	2.24957i	−0.131529	+	0.0798341i
$795$	6.24336	−	1.67290i	0.221429	−	0.0593318i
$796$	−22.2125	+	42.6937i	−0.787303	+	1.51324i
$797$	−18.5924	+	18.5924i	−0.658577	+	0.658577i	−0.955043	−	0.296466i	$-0.904192\pi$
$797$	−18.5924	+	18.5924i	−0.658577	+	0.658577i	0.296466	+	0.955043i	$0.404192\pi$
$798$		0			0
$799$	16.1744			0.572208
$800$	47.2411	−	18.4021i	1.67022	−	0.650612i
$801$	−43.0706	+	74.6004i	−1.52182	+	2.63588i
$802$	−29.3473	−	7.17768i	−1.03629	−	0.253453i
$803$	−0.597275	−	0.160039i	−0.0210774	−	0.00564767i
$804$	37.4891	+	58.8165i	1.32214	+	2.07430i
$805$		0			0
$806$	−8.55992	−	4.69486i	−0.301510	−	0.165370i
$807$	27.6581	−	15.9684i	0.973611	−	0.562114i
$808$	−11.7533	−	5.79109i	−0.413480	−	0.203730i
$809$	−38.5540	−	22.2591i	−1.35548	−	0.782589i	−0.366473	−	0.930429i	$-0.619435\pi$
$809$	−38.5540	−	22.2591i	−1.35548	−	0.782589i	−0.989011	+	0.147839i	$0.952768\pi$
$810$	−27.9858	+	0.613847i	−0.983320	+	0.0215684i
$811$	−20.8814	−	20.8814i	−0.733246	−	0.733246i	0.238015	−	0.971261i	$-0.423503\pi$
$811$	−20.8814	−	20.8814i	−0.733246	−	0.733246i	−0.971261	+	0.238015i	$0.923503\pi$
$812$		0			0
$813$	34.6429	−	34.6429i	1.21498	−	1.21498i
$814$	0.0689259	+	0.0659671i	0.00241585	+	0.00231215i
$815$	−21.6548	+	37.5071i	−0.758533	+	1.31382i
$816$	−16.8219	−	2.95823i	−0.588883	−	0.103559i
$817$	−12.2050	−	21.1396i	−0.426998	−	0.739582i
$818$	13.7344	−	4.00490i	0.480211	−	0.140028i
$819$		0			0
$820$	16.3407	−	73.7878i	0.570641	−	2.57678i
$821$	−6.30073	+	23.5147i	−0.219897	+	0.820667i	0.764488	+	0.644638i	$0.222992\pi$
$821$	−6.30073	+	23.5147i	−0.219897	+	0.820667i	−0.984385	+	0.176029i	$0.943675\pi$
$822$	1.96625	+	3.23944i	0.0685807	+	0.112988i
$823$	27.4622	+	15.8553i	0.957273	+	0.552682i	0.895333	−	0.445398i	$-0.146938\pi$
$823$	27.4622	+	15.8553i	0.957273	+	0.552682i	0.0619404	+	0.998080i	$0.480271\pi$
$824$	24.2683	+	4.81862i	0.845426	+	0.167865i
$825$			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	$-0.505795\pi$
$828$	17.7650	+	9.24270i	0.617375	+	0.321206i
$829$	0.0813215	+	0.303496i	0.00282441	+	0.0105409i	0.967324	−	0.253545i	$-0.0815965\pi$
$829$	0.0813215	+	0.303496i	0.00282441	+	0.0105409i	−0.964499	+	0.264086i	$0.914930\pi$
$830$	32.7737	+	8.01571i	1.13759	+	0.278229i
$831$	28.1778	+	48.8055i	0.977479	+	1.69304i
$832$	37.6770	+	28.8696i	1.30622	+	1.00087i
$833$		0			0
$834$	−4.49907	−	15.4290i	−0.155790	−	0.534264i
$835$	−49.6173	−	13.2949i	−1.71708	−	0.460090i
$836$	0.321280	+	7.32019i	0.0111117	+	0.253174i
$837$	−8.44727	+	2.26344i	−0.291980	+	0.0782359i
$838$	0.778267	+	35.4818i	0.0268848	+	1.22570i
$839$		−	1.52778i		−	0.0527447i	−0.999652	−	0.0263723i	$-0.991604\pi$
$839$		−	1.52778i		−	0.0527447i	0.999652	−	0.0263723i	$-0.00839555\pi$
$840$		0			0
$841$			28.8250i			0.993967i
$842$	−36.5487	+	0.801668i	−1.25955	+	0.0276273i
$843$	42.3285	−	11.3419i	1.45787	−	0.390635i
$844$	37.9941	+	34.7992i	1.30781	+	1.19784i
$845$	−80.1385	−	21.4731i	−2.75685	−	0.738696i
$846$	−83.8137	+	24.4398i	−2.88157	+	0.840259i
$847$		0			0
$848$	−2.22092	+	0.809498i	−0.0762668	+	0.0277983i
$849$	13.7886	+	23.8825i	0.473223	+	0.819645i
$850$	−4.39269	+	17.9603i	−0.150668	+	0.616033i
$851$	−0.0325108	−	0.121332i	−0.00111445	−	0.00415920i
$852$	−5.09380	−	16.1426i	−0.174511	−	0.553037i
$853$	−35.7996	−	35.7996i	−1.22576	−	1.22576i	−0.965554	−	0.260202i	$-0.916211\pi$
$853$	−35.7996	−	35.7996i	−1.22576	−	1.22576i	−0.260202	−	0.965554i	$-0.583789\pi$
$854$		0			0
$855$			78.9177i			2.69893i
$856$	10.5620	−	7.06255i	0.361002	−	0.241393i
$857$	−6.57388	−	3.79543i	−0.224560	−	0.129650i	0.383500	−	0.923541i	$-0.374719\pi$
$857$	−6.57388	−	3.79543i	−0.224560	−	0.129650i	−0.608060	+	0.793891i	$0.708052\pi$
$858$	−20.2784	+	12.3084i	−0.692295	+	0.420203i
$859$	7.47395	−	27.8932i	0.255008	−	0.951703i	−0.713078	−	0.701085i	$-0.752699\pi$
$859$	7.47395	−	27.8932i	0.255008	−	0.951703i	0.968086	−	0.250618i	$-0.0806339\pi$
$860$	25.8487	+	40.5539i	0.881433	+	1.38288i
$861$		0			0
$862$	8.84583	+	30.3358i	0.301290	+	1.03324i
$863$	4.36905	+	7.56742i	0.148724	+	0.257598i	0.930756	−	0.365640i	$-0.119150\pi$
$863$	4.36905	+	7.56742i	0.148724	+	0.257598i	−0.782032	+	0.623238i	$0.785817\pi$
$864$	42.2630	−	4.65295i	1.43781	−	0.158297i
$865$	14.7515	−	25.5503i	0.501566	−	0.868737i
$866$	9.64689	−	10.0796i	0.327815	−	0.342518i
$867$	−30.7814	+	30.7814i	−1.04539	+	1.04539i
$868$		0			0
$869$	−0.512086	−	0.512086i	−0.0173713	−	0.0173713i
$870$	0.141876	+	6.46826i	0.00481006	+	0.219295i
$871$	61.2196	+	35.3452i	2.07435	+	1.19762i
$872$	7.69585	−	15.6191i	0.260614	−	0.528930i
$873$	66.2812	−	38.2674i	2.24328	−	1.29516i
$874$	4.63913	−	8.45831i	0.156921	−	0.286107i
$875$		0			0
$876$	3.65930	+	0.810372i	0.123636	+	0.0273799i
$877$	−21.8518	−	5.85518i	−0.737884	−	0.197715i	−0.129746	−	0.991547i	$-0.541416\pi$
$877$	−21.8518	−	5.85518i	−0.737884	−	0.197715i	−0.608137	+	0.793832i	$0.708083\pi$
$878$	6.53022	−	26.7000i	0.220384	−	0.901081i
$879$	2.58296	−	4.47381i	0.0871210	−	0.150898i
$880$	−1.26473	−	14.3803i	−0.0426339	−	0.484759i
$881$	−19.9839			−0.673273			−0.336637	−	0.941635i	$-0.609289\pi$
$881$	−19.9839			−0.673273			−0.336637	+	0.941635i	$0.609289\pi$
$882$		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	$0.255881\pi$
$884$	−16.5083	+	5.20920i	−0.555235	+	0.175204i
$885$	55.9904	−	15.0026i	1.88210	−	0.504306i
$886$	−18.5403	−	30.5457i	−0.622875	−	1.02620i
$887$	−24.6075	+	14.2071i	−0.826239	+	0.477029i	−0.852563	−	0.522624i	$-0.824953\pi$
$887$	−24.6075	+	14.2071i	−0.826239	+	0.477029i	0.0263244	+	0.999653i	$0.491620\pi$
$888$	−0.434910	−	0.381142i	−0.0145946	−	0.0127903i
$889$		0			0
$890$	−71.6821	−	39.3155i	−2.40279	−	1.31786i
$891$	−1.32417	+	4.94188i	−0.0443615	+	0.165559i
$892$	0.730899	+	16.6531i	0.0244723	+	0.557587i
$893$	10.8853	+	40.6245i	0.364263	+	1.35945i
$894$	−24.1523	+	25.2355i	−0.807772	+	0.844003i
$895$	36.0675			1.20560
$896$		0			0
$897$	31.2317			1.04280
$898$	−18.4790	+	19.3078i	−0.616652	+	0.644310i
$899$	0.125959	+	0.470086i	0.00420098	+	0.0156783i
$900$	−4.37604	−	99.7056i	−0.145868	−	3.32352i
$901$	0.223125	−	0.832715i	0.00743338	−	0.0277418i
$902$	−12.1110	−	6.64251i	−0.403251	−	0.221171i
$903$		0			0
$904$	−0.190698	−	0.167122i	−0.00634251	−	0.00555840i
$905$	69.2243	−	39.9667i	2.30109	−	1.32854i
$906$	10.9060	+	17.9679i	0.362326	+	0.596942i
$907$	−13.2020	+	3.53747i	−0.438366	+	0.117460i	−0.471251	−	0.881999i	$-0.656197\pi$
$907$	−13.2020	+	3.53747i	−0.438366	+	0.117460i	0.0328844	+	0.999459i	$0.489531\pi$
$908$	21.2359	−	6.70098i	0.704737	−	0.222380i
$909$	−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	$0.845506\pi$
$912$	−3.89100	−	44.2417i	−0.128844	−	1.46499i
$913$	3.08331	−	5.34046i	0.102043	−	0.176743i
$914$	3.09959	−	12.6732i	0.102525	−	0.419193i
$915$	−104.923	−	28.1139i	−3.46864	−	0.929418i
$916$	−24.7712	−	5.48572i	−0.818464	−	0.181253i
$917$		0			0
$918$	−7.45681	+	13.5957i	−0.246111	+	0.448723i
$919$	4.50715	−	2.60220i	0.148677	−	0.0858388i	−0.423816	−	0.905748i	$-0.639310\pi$
$919$	4.50715	−	2.60220i	0.148677	−	0.0858388i	0.572493	+	0.819910i	$0.305976\pi$
$920$	−8.40033	+	17.0489i	−0.276951	+	0.562086i
$921$	−62.6418	−	36.1663i	−2.06412	−	1.19172i
$922$	−0.466089	−	21.2494i	−0.0153498	−	0.699811i
$923$	−12.1310	−	12.1310i	−0.399297	−	0.399297i
$924$		0			0
$925$	−0.442660	+	0.442660i	−0.0145546	+	0.0145546i
$926$	31.7675	−	33.1923i	1.04394	−	1.09077i
$927$	24.3527	−	42.1800i	0.799846	−	1.38537i
$928$	−0.258934	−	2.35191i	−0.00849994	−	0.0772053i
$929$	−4.56164	−	7.90099i	−0.149663	−	0.259223i	0.781440	−	0.623980i	$-0.214485\pi$
$929$	−4.56164	−	7.90099i	−0.149663	−	0.259223i	−0.931103	+	0.364757i	$0.881152\pi$
$930$	−5.03807	−	17.2775i	−0.165205	−	0.566551i
$931$		0			0
$932$	−24.2291	−	38.0129i	−0.793651	−	1.24515i
$933$	−21.5764	+	80.5243i	−0.706380	+	2.63625i
$934$	21.2565	−	12.9021i	0.695533	−	0.422168i
$935$	4.55936	+	2.63235i	0.149107	+	0.0860869i
$936$	77.6729	−	51.9379i	2.53882	−	1.69764i
$937$		−	7.41975i		−	0.242393i	−0.992629	−	0.121196i	$-0.961327\pi$
$937$		−	7.41975i		−	0.242393i	0.992629	−	0.121196i	$-0.0386731\pi$
$938$		0			0
$939$	32.4695	+	32.4695i	1.05960	+	1.05960i
$940$	−24.9345	−	79.0191i	−0.813273	−	2.57732i
$941$	−0.678902	−	2.53370i	−0.0221316	−	0.0825961i	0.953977	−	0.299880i	$-0.0969468\pi$
$941$	−0.678902	−	2.53370i	−0.0221316	−	0.0825961i	−0.976108	+	0.217284i	$0.930280\pi$
$942$	−5.13751	+	21.0057i	−0.167389	+	0.684402i
$943$	9.09305	+	15.7496i	0.296111	+	0.512878i
$944$	−19.9172	+	7.25957i	−0.648250	+	0.236279i
$945$		0			0
$946$	8.43826	−	2.46057i	0.274351	−	0.0800001i
$947$	−16.9412	−	4.53939i	−0.550516	−	0.147510i	−0.0271703	−	0.999631i	$-0.508650\pi$
$947$	−16.9412	−	4.53939i	−0.550516	−	0.147510i	−0.523346	+	0.852121i	$0.675316\pi$
$948$	3.23701	+	2.96481i	0.105133	+	0.0962927i
$949$	3.66915	−	0.983146i	0.119106	−	0.0319143i
$950$	−48.0664	+	1.05430i	−1.55948	+	0.0342060i
$951$		−	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	$-0.146225\pi$
$954$	0.102042	+	4.65218i	0.00330373	+	0.150620i
$955$	−71.7268	+	19.2191i	−2.32102	+	0.621916i
$956$	−1.17228	−	26.7098i	−0.0379143	−	0.863856i
$957$	1.14220	+	0.306052i	0.0369221	+	0.00989325i
$958$	14.3633	+	49.2574i	0.464058	+	1.59143i
$959$		0			0
$960$	11.4803	+	86.7429i	0.370527	+	2.79961i
$961$	14.8231	+	25.6744i	0.478165	+	0.828206i
$962$	−0.569317	−	0.139242i	−0.0183555	−	0.00448935i
$963$	−6.47347	−	24.1593i	−0.208605	−	0.778523i
$964$	34.4098	+	17.9026i	1.10826	+	0.576605i
$965$	−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	$0.826680\pi$
$968$	27.9290	+	5.54549i	0.897673	+	0.178239i
$969$	14.0271	+	8.09855i	0.450615	+	0.260163i
$970$	37.6901	+	62.0954i	1.21016	+	1.99376i
$971$	−9.06154	+	33.8181i	−0.290799	+	1.08528i	0.653698	+	0.756755i	$0.273217\pi$
$971$	−9.06154	+	33.8181i	−0.290799	+	1.08528i	−0.944497	+	0.328520i	$0.893450\pi$
$972$	−3.04578	+	13.7535i	−0.0976934	+	0.441143i
$973$		0			0
$974$	9.90947	−	2.88957i	0.317520	−	0.0925879i
$975$	−77.8250	−	134.797i	−2.49239	−	4.31695i
$976$	39.1253	+	6.88043i	1.25237	+	0.220237i
$977$	1.57394	−	2.72614i	0.0503548	−	0.0872170i	−0.839749	−	0.542974i	$-0.817298\pi$
$977$	1.57394	−	2.72614i	0.0503548	−	0.0872170i	0.890104	+	0.455757i	$0.150631\pi$
$978$	−34.6623	−	33.1744i	−1.10838	−	1.06080i
$979$	−10.5660	+	10.5660i	−0.337691	+	0.337691i
$980$		0			0
$981$	−24.2369	−	24.2369i	−0.773826	−	0.773826i
$982$	22.8426	−	0.501036i	0.728937	−	0.0159887i
$983$	44.3439	+	25.6020i	1.41435	+	0.816576i	0.995794	−	0.0916152i	$-0.0292030\pi$
$983$	44.3439	+	25.6020i	1.41435	+	0.816576i	0.418556	+	0.908191i	$0.362536\pi$
$984$	75.1028	+	37.0046i	2.39419	+	1.17966i
$985$	30.2956	−	17.4912i	0.965297	−	0.557315i
$986$	0.756591	+	0.414968i	0.0240948	+	0.0132153i
$987$		0			0
$988$	−24.1938	−	37.9575i	−0.769706	−	1.20759i
$989$	−11.1781	−	2.99517i	−0.355444	−	0.0952409i
$990$	−27.6036	−	6.75121i	−0.877299	−	0.214568i
$991$	10.0802	−	17.4594i	0.320207	−	0.554615i	−0.660324	−	0.750981i	$-0.729581\pi$
$991$	10.0802	−	17.4594i	0.320207	−	0.554615i	0.980531	+	0.196367i	$0.0629142\pi$
$992$	2.38900	+	6.13295i	0.0758510	+	0.194721i
$993$	87.1665			2.76615
$994$		0			0
$995$	−63.5795	+	63.5795i	−2.01561	+	2.01561i
$996$	−17.2515	+	33.1583i	−0.546635	+	1.05066i
$997$	−36.6961	+	9.83269i	−1.16218	+	0.311404i	−0.787835	−	0.615886i	$-0.788798\pi$
$997$	−36.6961	+	9.83269i	−1.16218	+	0.311404i	−0.374342	+	0.927291i	$0.622131\pi$
$998$	−27.9060	+	16.9381i	−0.883350	+	0.536168i
$999$	−0.454668	+	0.262503i	−0.0143851	+	0.00830522i

Twists

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

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

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.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.977831 - 1.02169i) q^{2} +(0.757585 + 2.82735i) q^{3} +(-0.0876948 - 1.99808i) q^{4} +(0.967109 - 3.60930i) q^{5} +(3.62946 + 1.99065i) q^{6} +(-2.12716 - 1.86418i) q^{8} +(-4.82188 + 2.78391i) q^{9} +O(q^{10})\)	\(q+(0.977831 - 1.02169i) q^{2} +(0.757585 + 2.82735i) q^{3} +(-0.0876948 - 1.99808i) q^{4} +(0.967109 - 3.60930i) q^{5} +(3.62946 + 1.99065i) q^{6} +(-2.12716 - 1.86418i) q^{8} +(-4.82188 + 2.78391i) q^{9} +(-2.74191 - 4.51737i) q^{10} +(-0.932921 + 0.249975i) q^{11} +(5.58282 - 1.76166i) q^{12} +(4.19543 - 4.19543i) q^{13} +10.9374 q^{15} +(-3.98462 + 0.350442i) q^{16} +(0.729395 - 1.26335i) q^{17} +(-1.87069 + 7.64865i) q^{18} +(3.66398 + 0.981760i) q^{19} +(-7.29647 - 1.61584i) q^{20} +(-0.656842 + 1.19759i) q^{22} +(1.55739 - 0.899162i) q^{23} +(3.65919 - 7.42650i) q^{24} +(-7.76162 - 4.48117i) q^{25} +(-0.184003 - 8.38885i) q^{26} +(-5.31479 - 5.31479i) q^{27} +(-0.295765 + 0.295765i) q^{29} +(10.6949 - 11.1746i) q^{30} +(0.581757 - 1.00763i) q^{31} +(-3.53824 + 4.41371i) q^{32} +(-1.41353 - 2.44831i) q^{33} +(-0.577524 - 1.98056i) q^{34} +(5.98533 + 9.39035i) q^{36} +(0.0180784 - 0.0674694i) q^{37} +(4.58580 - 2.78345i) q^{38} +(15.0403 + 8.68355i) q^{39} +(-8.78560 + 5.87470i) q^{40} +10.1128i q^{41} +(-4.55032 - 4.55032i) q^{43} +(0.581282 + 1.84213i) q^{44} +(5.38470 + 20.0960i) q^{45} +(0.604204 - 2.47040i) q^{46} +(5.54377 + 9.60208i) q^{47} +(-4.00951 - 11.0004i) q^{48} +(-12.1679 + 3.54813i) q^{50} +(4.12450 + 1.10516i) q^{51} +(-8.75072 - 8.01488i) q^{52} +(0.570826 - 0.152952i) q^{53} +(-10.6270 + 0.233096i) q^{54} +3.60895i q^{55} +11.1031i q^{57} +(0.0129717 + 0.591388i) q^{58} +(5.11916 - 1.37168i) q^{59} +(-0.959154 - 21.8538i) q^{60} +(-9.59300 - 2.57044i) q^{61} +(-0.460627 - 1.57967i) q^{62} +(1.04964 + 7.93084i) q^{64} +(-11.0851 - 19.2000i) q^{65} +(-3.88361 - 0.949844i) q^{66} +(3.08364 + 11.5083i) q^{67} +(-2.58823 - 1.34660i) q^{68} +(3.72210 + 3.72210i) q^{69} -2.89148i q^{71} +(15.4466 + 3.06703i) q^{72} +(0.554447 + 0.320110i) q^{73} +(-0.0512551 - 0.0844441i) q^{74} +(6.78974 - 25.3397i) q^{75} +(1.64032 - 7.40701i) q^{76} +(23.5788 - 6.87551i) q^{78} +(0.374910 + 0.649363i) q^{79} +(-2.58871 + 14.7206i) q^{80} +(2.64861 - 4.58752i) q^{81} +(10.3321 + 9.88861i) q^{82} +(-4.51473 + 4.51473i) q^{83} +(-3.85440 - 3.85440i) q^{85} +(-9.09846 + 0.199568i) q^{86} +(-1.06030 - 0.612164i) q^{87} +(2.45047 + 1.20740i) q^{88} +(13.3985 - 7.73562i) q^{89} +(25.7971 + 14.1490i) q^{90} +(-1.93317 - 3.03294i) q^{92} +(3.28966 + 0.881461i) q^{93} +(15.2312 + 3.72521i) q^{94} +(7.08694 - 12.2749i) q^{95} +(-15.1596 - 6.66007i) q^{96} -13.7459 q^{97} +(3.80252 - 3.80252i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{4}+O(q^{10}) \) 96 * q + 4 * q^4	\( 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) \) 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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