LMFDB - Embedded newform 784.2.x.p.557.3

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			557.3
Character	$\chi$	$=$	784.557
Dual form			784.2.x.p.373.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37372 + 0.335982i) q^{2} +(-2.82735 + 0.757585i) q^{3} +(1.77423 - 0.923092i) q^{4} +(-3.60930 - 0.967109i) q^{5} +(3.62946 - 1.99065i) q^{6} +(-2.12716 + 1.86418i) q^{8} +(4.82188 - 2.78391i) q^{9} +O(q^{10})$	\(q+(-1.37372 + 0.335982i) q^{2} +(-2.82735 + 0.757585i) q^{3} +(1.77423 - 0.923092i) q^{4} +(-3.60930 - 0.967109i) q^{5} +(3.62946 - 1.99065i) q^{6} +(-2.12716 + 1.86418i) q^{8} +(4.82188 - 2.78391i) q^{9} +(5.28311 + 0.115881i) q^{10} +(0.249975 + 0.932921i) q^{11} +(-4.31705 + 3.95403i) q^{12} +(4.19543 + 4.19543i) q^{13} +10.9374 q^{15} +(2.29580 - 3.27556i) q^{16} +(0.729395 - 1.26335i) q^{17} +(-5.68858 + 5.44439i) q^{18} +(-0.981760 + 3.66398i) q^{19} +(-7.29647 + 1.61584i) q^{20} +(-0.656842 - 1.19759i) q^{22} +(-1.55739 + 0.899162i) q^{23} +(4.60195 - 6.88220i) q^{24} +(7.76162 + 4.48117i) q^{25} +(-7.17296 - 4.35378i) q^{26} +(-5.31479 + 5.31479i) q^{27} +(-0.295765 - 0.295765i) q^{29} +(-15.0250 + 3.67477i) q^{30} +(0.581757 - 1.00763i) q^{31} +(-2.05327 + 5.27106i) q^{32} +(-1.41353 - 2.44831i) q^{33} +(-0.577524 + 1.98056i) q^{34} +(5.98533 - 9.39035i) q^{36} +(-0.0674694 - 0.0180784i) q^{37} +(0.117637 - 5.36315i) q^{38} +(-15.0403 - 8.68355i) q^{39} +(9.48044 - 4.67120i) q^{40} -10.1128i q^{41} +(-4.55032 + 4.55032i) q^{43} +(1.30469 + 1.42447i) q^{44} +(-20.0960 + 5.38470i) q^{45} +(1.83733 - 1.75846i) q^{46} +(5.54377 + 9.60208i) q^{47} +(-4.00951 + 11.0004i) q^{48} +(-12.1679 - 3.54813i) q^{50} +(-1.10516 + 4.12450i) q^{51} +(11.3164 + 3.57090i) q^{52} +(-0.152952 - 0.570826i) q^{53} +(5.51538 - 9.08672i) q^{54} -3.60895i q^{55} -11.1031i q^{57} +(0.505672 + 0.306928i) q^{58} +(-1.37168 - 5.11916i) q^{59} +(19.4055 - 10.0962i) q^{60} +(2.57044 - 9.59300i) q^{61} +(-0.460627 + 1.57967i) q^{62} +(1.04964 - 7.93084i) q^{64} +(-11.0851 - 19.2000i) q^{65} +(2.76439 + 2.88838i) q^{66} +(-11.5083 + 3.08364i) q^{67} +(0.127928 - 2.91477i) q^{68} +(3.72210 - 3.72210i) q^{69} +2.89148i q^{71} +(-5.06720 + 14.9107i) q^{72} +(-0.554447 - 0.320110i) q^{73} +(0.0987583 + 0.00216619i) q^{74} +(-25.3397 - 6.78974i) q^{75} +(1.64032 + 7.40701i) q^{76} +(23.5788 + 6.87551i) q^{78} +(0.374910 + 0.649363i) q^{79} +(-11.4541 + 9.60219i) q^{80} +(2.64861 - 4.58752i) q^{81} +(3.39772 + 13.8922i) q^{82} +(-4.51473 - 4.51473i) q^{83} +(-3.85440 + 3.85440i) q^{85} +(4.72206 - 7.77971i) q^{86} +(1.06030 + 0.612164i) q^{87} +(-2.27087 - 1.51847i) q^{88} +(-13.3985 + 7.73562i) q^{89} +(25.7971 - 14.1490i) q^{90} +(-1.93317 + 3.03294i) q^{92} +(-0.881461 + 3.28966i) q^{93} +(-10.8417 - 11.3280i) q^{94} +(7.08694 - 12.2749i) q^{95} +(1.81202 - 16.4586i) 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 $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.37372	+	0.335982i	−0.971369	+	0.237575i
$2$	−1.37372	+	0.335982i	−0.971369	+	0.237575i
$3$	−2.82735	+	0.757585i	−1.63237	+	0.437392i	−0.954602	−	0.297884i	$-0.903719\pi$
$3$	−2.82735	+	0.757585i	−1.63237	+	0.437392i	−0.677768	+	0.735276i	$0.737052\pi$
$4$	1.77423	−	0.923092i	0.887116	−	0.461546i
$5$	−3.60930	−	0.967109i	−1.61413	−	0.432504i	−0.664859	−	0.746969i	$-0.731508\pi$
$5$	−3.60930	−	0.967109i	−1.61413	−	0.432504i	−0.949269	+	0.314465i	$0.898175\pi$
$6$	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
$10$	5.28311	+	0.115881i	1.67067	+	0.0366448i
$11$	0.249975	+	0.932921i	0.0753704	+	0.281286i	0.993317	−	0.115418i	$-0.0368206\pi$
$11$	0.249975	+	0.932921i	0.0753704	+	0.281286i	−0.917947	+	0.396704i	$0.870154\pi$
$12$	−4.31705	+	3.95403i	−1.24622	+	1.14143i
$13$	4.19543	+	4.19543i	1.16360	+	1.16360i	0.983681	+	0.179924i	$0.0575851\pi$
$13$	4.19543	+	4.19543i	1.16360	+	1.16360i	0.179924	+	0.983681i	$0.442415\pi$
$14$		0			0
$15$	10.9374			2.82403
$16$	2.29580	−	3.27556i	0.573950	−	0.818890i
$17$	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	$0.110058\pi$
$18$	−5.68858	+	5.44439i	−1.34081	+	1.28326i
$19$	−0.981760	+	3.66398i	−0.225231	+	0.840575i	0.757080	+	0.653322i	$0.226625\pi$
$19$	−0.981760	+	3.66398i	−0.225231	+	0.840575i	−0.982312	+	0.187253i	$0.940042\pi$
$20$	−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	−0.653503	−	0.756924i	$-0.726701\pi$
$23$	−1.55739	+	0.899162i	−0.324739	+	0.187488i	0.328764	+	0.944412i	$0.393368\pi$
$24$	4.60195	−	6.88220i	0.939369	−	1.40482i
$25$	7.76162	+	4.48117i	1.55232	+	0.896235i
$26$	−7.17296	−	4.35378i	−1.40673	−	0.853846i
$27$	−5.31479	+	5.31479i	−1.02283	+	1.02283i
$28$		0			0
$29$	−0.295765	−	0.295765i	−0.0549222	−	0.0549222i	0.679112	−	0.734034i	$-0.262365\pi$
$29$	−0.295765	−	0.295765i	−0.0549222	−	0.0549222i	−0.734034	+	0.679112i	$0.762365\pi$
$30$	−15.0250	+	3.67477i	−2.74317	+	0.670918i
$31$	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	$0.133347\pi$
$32$	−2.05327	+	5.27106i	−0.362970	+	0.931801i
$33$	−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
$37$	−0.0674694	−	0.0180784i	−0.0110919	−	0.00297207i	0.253269	−	0.967396i	$-0.418494\pi$
$37$	−0.0674694	−	0.0180784i	−0.0110919	−	0.00297207i	−0.264361	+	0.964424i	$0.585161\pi$
$38$	0.117637	−	5.36315i	0.0190832	−	0.870018i
$39$	−15.0403	−	8.68355i	−2.40838	−	1.39048i
$40$	9.48044	−	4.67120i	1.49899	−	0.738582i
$41$		−	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	−0.963092	−	0.269174i	$-0.913249\pi$
$43$	−4.55032	+	4.55032i	−0.693918	+	0.693918i	0.269174	+	0.963092i	$0.413249\pi$
$44$	1.30469	+	1.42447i	0.196689	+	0.214747i
$45$	−20.0960	+	5.38470i	−2.99573	+	0.802703i
$46$	1.83733	−	1.75846i	0.270899	−	0.259270i
$47$	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
$51$	−1.10516	+	4.12450i	−0.154753	+	0.577546i
$52$	11.3164	+	3.57090i	1.56931	+	0.495195i
$53$	−0.152952	−	0.570826i	−0.0210096	−	0.0784090i	0.954625	−	0.297810i	$-0.0962563\pi$
$53$	−0.152952	−	0.570826i	−0.0210096	−	0.0784090i	−0.975635	+	0.219401i	$0.929590\pi$
$54$	5.51538	−	9.08672i	0.750548	−	1.23655i
$55$		−	3.60895i		−	0.486630i
$56$		0			0
$57$		−	11.1031i		−	1.47064i
$58$	0.505672	+	0.306928i	0.0663979	+	0.0403016i
$59$	−1.37168	−	5.11916i	−0.178577	−	0.666458i	−0.995915	−	0.0902992i	$-0.971218\pi$
$59$	−1.37168	−	5.11916i	−0.178577	−	0.666458i	0.817338	−	0.576159i	$-0.195449\pi$
$60$	19.4055	−	10.0962i	2.50524	−	1.30342i
$61$	2.57044	−	9.59300i	0.329111	−	1.22826i	−0.581003	−	0.813901i	$-0.697340\pi$
$61$	2.57044	−	9.59300i	0.329111	−	1.22826i	0.910114	−	0.414357i	$-0.135994\pi$
$62$	−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
$66$	2.76439	+	2.88838i	0.340273	+	0.355535i
$67$	−11.5083	+	3.08364i	−1.40596	+	0.376727i	−0.880483	−	0.474078i	$-0.842781\pi$
$67$	−11.5083	+	3.08364i	−1.40596	+	0.376727i	−0.525482	+	0.850805i	$0.676115\pi$
$68$	0.127928	−	2.91477i	0.0155136	−	0.353468i
$69$	3.72210	−	3.72210i	0.448089	−	0.448089i
$70$		0			0
$71$			2.89148i			0.343156i	0.985171	+	0.171578i	$0.0548865\pi$
$71$			2.89148i			0.343156i	−0.985171	+	0.171578i	$0.945113\pi$
$72$	−5.06720	+	14.9107i	−0.597175	+	1.75724i
$73$	−0.554447	−	0.320110i	−0.0648932	−	0.0374661i	0.467202	−	0.884150i	$-0.345262\pi$
$73$	−0.554447	−	0.320110i	−0.0648932	−	0.0374661i	−0.532096	+	0.846684i	$0.678595\pi$
$74$	0.0987583	+	0.00216619i	0.0114804	+	0.000251814i
$75$	−25.3397	−	6.78974i	−2.92597	−	0.784012i
$76$	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	$0.819903\pi$
$80$	−11.4541	+	9.60219i	−1.28060	+	1.07356i
$81$	2.64861	−	4.58752i	0.294290	−	0.509725i
$82$	3.39772	+	13.8922i	0.375215	+	1.53414i
$83$	−4.51473	−	4.51473i	−0.495556	−	0.495556i	0.414495	−	0.910051i	$-0.363958\pi$
$83$	−4.51473	−	4.51473i	−0.495556	−	0.495556i	−0.910051	+	0.414495i	$0.863958\pi$
$84$		0			0
$85$	−3.85440	+	3.85440i	−0.418068	+	0.418068i
$86$	4.72206	−	7.77971i	0.509193	−	0.838908i
$87$	1.06030	+	0.612164i	0.113676	+	0.0656308i
$88$	−2.27087	−	1.51847i	−0.242076	−	0.161870i
$89$	−13.3985	+	7.73562i	−1.42024	+	0.819974i	−0.996319	−	0.0857266i	$-0.972679\pi$
$89$	−13.3985	+	7.73562i	−1.42024	+	0.819974i	−0.423918	+	0.905701i	$0.639346\pi$
$90$	25.7971	−	14.1490i	2.71926	−	1.49143i
$91$		0			0
$92$	−1.93317	+	3.03294i	−0.201547	+	0.316206i
$93$	−0.881461	+	3.28966i	−0.0914032	+	0.341122i
$94$	−10.8417	−	11.3280i	−1.11824	−	1.16839i
$95$	7.08694	−	12.2749i	0.727104	−	1.25938i
$96$	1.81202	−	16.4586i	0.184938	−	1.67980i
$97$	−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
$100$	17.9075	+	0.785952i	1.79075	+	0.0785952i
$101$	−1.19897	−	4.47461i	−0.119302	−	0.445240i	0.880271	−	0.474471i	$-0.157361\pi$
$101$	−1.19897	−	4.47461i	−0.119302	−	0.445240i	−0.999573	+	0.0292314i	$0.990694\pi$
$102$	0.132422	−	6.03724i	0.0131118	−	0.597776i
$103$	7.57567	−	4.37382i	0.746453	−	0.430965i	−0.0779578	−	0.996957i	$-0.524840\pi$
$103$	7.57567	−	4.37382i	0.746453	−	0.430965i	0.824411	+	0.565992i	$0.191507\pi$
$104$	−16.7454	−	1.10331i	−1.64202	−	0.108189i
$105$		0			0
$106$	0.401901	+	0.732768i	0.0390361	+	0.0711727i
$107$	4.33909	+	1.16266i	0.419476	+	0.112398i	0.462382	−	0.886681i	$-0.346995\pi$
$107$	4.33909	+	1.16266i	0.419476	+	0.112398i	−0.0429061	+	0.999079i	$0.513662\pi$
$108$	−4.52363	+	14.3357i	−0.435287	+	1.37945i
$109$	−5.94636	+	1.59332i	−0.569558	+	0.152613i	−0.532094	−	0.846685i	$-0.678595\pi$
$109$	−5.94636	+	1.59332i	−0.569558	+	0.152613i	−0.0374639	+	0.999298i	$0.511928\pi$
$110$	1.21254	+	4.95769i	0.115611	+	0.472697i
$111$	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	$0.498658\pi$
$114$	3.73044	+	15.2526i	0.349388	+	1.42854i
$115$	6.49069	−	1.73918i	0.605260	−	0.162179i
$116$	−0.797775	−	0.251738i	−0.0740716	−	0.0233733i
$117$	31.9096	+	8.55015i	2.95004	+	0.790462i
$118$	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
$122$	−0.307995	+	14.0418i	−0.0278846	+	1.27128i
$123$	7.66131	+	28.5924i	0.690797	+	2.57809i
$124$	0.102034	−	2.32479i	0.00916294	−	0.208772i
$125$	−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	$0.772181\pi$
$128$	1.22270	+	11.2474i	0.108073	+	0.994143i
$129$	9.41809	−	16.3126i	0.829216	−	1.43624i
$130$	21.6788	+	22.6511i	1.90135	+	1.98663i
$131$	−5.12690	+	19.1339i	−0.447940	+	1.67173i	0.260116	+	0.965577i	$0.416239\pi$
$131$	−5.12690	+	19.1339i	−0.447940	+	1.67173i	−0.708056	+	0.706156i	$0.750428\pi$
$132$	−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
$136$	0.803573	+	4.04707i	0.0689058	+	0.347034i
$137$	−0.792792	−	0.457719i	−0.0677328	−	0.0391055i	0.465751	−	0.884916i	$-0.345784\pi$
$137$	−0.792792	−	0.457719i	−0.0677328	−	0.0391055i	−0.533484	+	0.845810i	$0.679118\pi$
$138$	−3.86258	+	6.36370i	−0.328805	+	0.541714i
$139$	−2.74533	+	2.74533i	−0.232856	+	0.232856i	−0.813884	−	0.581028i	$-0.802651\pi$
$139$	−2.74533	+	2.74533i	−0.232856	+	0.232856i	0.581028	+	0.813884i	$0.302651\pi$
$140$		0			0
$141$	−22.9485	−	22.9485i	−1.93262	−	1.93262i
$142$	−0.971485	−	3.97210i	−0.0815252	−	0.333331i
$143$	−2.86525	+	4.96276i	−0.239605	+	0.415007i
$144$	1.95120	−	22.1857i	0.162600	−	1.84881i
$145$	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
$149$	8.15084	+	2.18401i	0.667743	+	0.178921i	0.576738	−	0.816929i	$-0.304325\pi$
$149$	8.15084	+	2.18401i	0.667743	+	0.178921i	0.0910051	+	0.995850i	$0.470992\pi$
$150$	37.0909	+	0.813562i	3.02846	+	0.0664270i
$151$	−4.39729	−	2.53878i	−0.357846	−	0.206603i	0.310289	−	0.950642i	$-0.399574\pi$
$151$	−4.39729	−	2.53878i	−0.357846	−	0.206603i	−0.668136	+	0.744039i	$0.732907\pi$
$152$	−4.74197	−	9.62406i	−0.384624	−	0.780615i
$153$		−	8.12229i		−	0.656648i
$154$		0			0
$155$	−3.07423	+	3.07423i	−0.246928	+	0.246928i
$156$	−34.7008	−	1.52300i	−2.77829	−	0.121938i
$157$	−5.04598	+	1.35207i	−0.402713	+	0.107907i	−0.454490	−	0.890752i	$-0.650178\pi$
$157$	−5.04598	+	1.35207i	−0.402713	+	0.107907i	0.0517765	+	0.998659i	$0.483512\pi$
$158$	−0.733197	−	0.766082i	−0.0583300	−	0.0609462i
$159$	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
$163$	2.99986	−	11.1956i	0.234967	−	0.876908i	−0.743197	−	0.669073i	$-0.766691\pi$
$163$	2.99986	−	11.1956i	0.234967	−	0.876908i	0.978164	−	0.207835i	$-0.0666419\pi$
$164$	−9.33505	−	17.9425i	−0.728945	−	1.40107i
$165$	2.73408	+	10.2037i	0.212848	+	0.794360i
$166$	7.71886	+	4.68512i	0.599099	+	0.363636i
$167$			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
$170$	3.99987	−	6.58989i	0.306776	−	0.505421i
$171$	5.46627	+	20.4004i	0.418016	+	1.56006i
$172$	−3.87296	+	12.2737i	−0.295311	+	0.935861i
$173$	−2.04354	+	7.62659i	−0.155367	+	0.579839i	0.843706	+	0.536805i	$0.180369\pi$
$173$	−2.04354	+	7.62659i	−0.155367	+	0.579839i	−0.999074	+	0.0430338i	$0.986298\pi$
$174$	−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
$178$	15.8068	−	15.1282i	1.18477	−	1.13391i
$179$	−9.32354	+	2.49823i	−0.696874	+	0.186727i	−0.589830	−	0.807527i	$-0.700805\pi$
$179$	−9.32354	+	2.49823i	−0.696874	+	0.186727i	−0.107044	+	0.994254i	$0.534139\pi$
$180$	−30.6843	+	28.1041i	−2.28707	+	2.09476i
$181$	15.1263	−	15.1263i	1.12433	−	1.12433i	0.133250	−	0.991083i	$-0.457459\pi$
$181$	15.1263	−	15.1263i	1.12433	−	1.12433i	0.991083	−	0.133250i	$-0.0425412\pi$
$182$		0			0
$183$			29.0701i			2.14892i
$184$	1.63663	−	4.81593i	0.120654	−	0.355035i
$185$	0.226034	+	0.130501i	0.0166183	+	0.00959459i
$186$	0.105619	−	4.81523i	0.00774433	−	0.353070i
$187$	1.36094	+	0.364661i	0.0995214	+	0.0266667i
$188$	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	$-0.422053\pi$
$192$	3.04059	+	23.2184i	0.219436	+	1.67565i
$193$	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	$0.0259991\pi$
$194$	18.8831	−	4.61838i	1.35573	−	0.331580i
$195$	45.8872	+	45.8872i	3.28605	+	3.28605i
$196$		0			0
$197$	6.61994	−	6.61994i	0.471651	−	0.471651i	−0.430797	−	0.902449i	$-0.641768\pi$
$197$	6.61994	−	6.61994i	0.471651	−	0.471651i	0.902449	+	0.430797i	$0.141768\pi$
$198$	−6.50119	−	3.94604i	−0.462020	−	0.280433i
$199$	20.8393	+	12.0316i	1.47726	+	0.852897i	0.999670	−	0.0256852i	$-0.00817674\pi$
$199$	20.8393	+	12.0316i	1.47726	+	0.852897i	0.477591	+	0.878582i	$0.341510\pi$
$200$	−24.8640	+	4.93690i	−1.75815	+	0.349092i
$201$	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
$205$	−9.78019	+	36.5002i	−0.683078	+	2.54928i
$206$	−8.93736	+	8.55370i	−0.622695	+	0.595965i
$207$	−5.00638	+	8.67130i	−0.347967	+	0.602697i
$208$	23.3743	−	4.11052i	1.62072	−	0.285013i
$209$	−3.66362			−0.253418
$210$		0			0
$211$	−18.2158	−	18.2158i	−1.25403	−	1.25403i	−0.953897	−	0.300133i	$-0.902969\pi$
$211$	−18.2158	−	18.2158i	−1.25403	−	1.25403i	−0.300133	−	0.953897i	$-0.597031\pi$
$212$	−0.798298	−	0.871589i	−0.0548273	−	0.0598610i
$213$	−2.19054	−	8.17522i	−0.150094	−	0.560157i
$214$	−6.35134	−	0.139312i	−0.434169	−	0.00952317i
$215$	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
$219$	1.81013	+	0.485022i	0.122317	+	0.0327747i
$220$	−3.33139	−	6.40311i	−0.224602	−	0.431697i
$221$	8.36042	−	2.24017i	0.562383	−	0.150690i
$222$	−0.280865	+	0.0686933i	−0.0188504	+	0.00461039i
$223$	−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
$226$	−0.123153	+	0.0301204i	−0.00819200	+	0.00200358i
$227$	−10.7546	+	2.88170i	−0.713810	+	0.191265i	−0.597408	−	0.801937i	$-0.703803\pi$
$227$	−10.7546	+	2.88170i	−0.713810	+	0.191265i	−0.116402	+	0.993202i	$0.537136\pi$
$228$	−10.2492	−	19.6995i	−0.678770	−	1.30463i
$229$	−12.2534	−	3.28330i	−0.809730	−	0.216966i	−0.169878	−	0.985465i	$-0.554337\pi$
$229$	−12.2534	−	3.28330i	−0.809730	−	0.216966i	−0.639851	+	0.768499i	$0.721004\pi$
$230$	−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	−0.976620	−	0.214974i	$-0.931033\pi$
$233$	−19.5194	+	11.2695i	−1.27876	+	0.738291i	−0.302137	+	0.953265i	$0.597700\pi$
$234$	−46.7077	−	1.02450i	−3.05338	−	0.0669735i
$235$	−10.7229	−	40.0182i	−0.699482	−	2.61050i
$236$	−7.15913	−	7.81640i	−0.466020	−	0.508804i
$237$	−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	$0.357687\pi$
$240$	25.1101	−	35.8262i	1.62085	−	2.31257i
$241$	−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	$0.951910\pi$
$242$	−10.2855	+	9.84399i	−0.661178	+	0.632795i
$243$	1.82295	−	6.80335i	0.116942	−	0.436435i
$244$	−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
$248$	0.640920	+	3.22790i	0.0406985	+	0.204972i
$249$	16.1850	+	9.34441i	1.02568	+	0.592178i
$250$	17.8994	+	10.8644i	1.13206	+	0.687126i
$251$	8.09990	−	8.09990i	0.511261	−	0.511261i	−0.403652	−	0.914913i	$-0.632259\pi$
$251$	8.09990	−	8.09990i	0.511261	−	0.511261i	0.914913	+	0.403652i	$0.132259\pi$
$252$		0			0
$253$	−1.22816	−	1.22816i	−0.0772136	−	0.0772136i
$254$	23.3648	−	5.71450i	1.46604	−	0.358560i
$255$	7.97769	−	13.8178i	0.499582	−	0.865302i
$256$	−5.45859	−	15.0401i	−0.341162	−	0.940004i
$257$	−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
$261$	−2.24953	−	0.602760i	−0.139242	−	0.0373099i
$262$	0.614317	−	28.0072i	0.0379526	−	1.73029i
$263$	−3.80821	−	2.19867i	−0.234824	−	0.135576i	0.377971	−	0.925817i	$-0.376622\pi$
$263$	−3.80821	−	2.19867i	−0.234824	−	0.135576i	−0.612796	+	0.790241i	$0.709955\pi$
$264$	7.57092	+	2.57287i	0.465958	+	0.158349i
$265$			2.20820i			0.135649i
$266$		0			0
$267$	32.0218	−	32.0218i	1.95970	−	1.95970i
$268$	−17.5719	+	16.0943i	−1.07338	+	0.983118i
$269$	10.5390	−	2.82392i	0.642575	−	0.172177i	0.0772054	−	0.997015i	$-0.475400\pi$
$269$	10.5390	−	2.82392i	0.642575	−	0.172177i	0.565369	+	0.824838i	$0.308734\pi$
$270$	−28.6945	+	27.4627i	−1.74629	+	1.67133i
$271$	−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
$275$	−2.24037	+	8.36116i	−0.135099	+	0.504197i
$276$	3.16803	−	10.0397i	0.190693	−	0.604320i
$277$	−4.98309	−	18.5971i	−0.299405	−	1.11739i	−0.937656	−	0.347566i	$-0.887008\pi$
$277$	−4.98309	−	18.5971i	−0.299405	−	1.11739i	0.638251	−	0.769828i	$-0.279658\pi$
$278$	2.84894	−	4.69370i	0.170868	−	0.281510i
$279$		−	6.47824i		−	0.387842i
$280$		0			0
$281$			14.9711i			0.893100i	0.894759	+	0.446550i	$0.147348\pi$
$281$			14.9711i			0.893100i	−0.894759	+	0.446550i	$0.852652\pi$
$282$	39.2353	+	23.8147i	2.33643	+	1.41814i
$283$	−2.43843	−	9.10034i	−0.144950	−	0.540959i	−0.999758	−	0.0220149i	$-0.992992\pi$
$283$	−2.43843	−	9.10034i	−0.144950	−	0.540959i	0.854808	−	0.518944i	$-0.173675\pi$
$284$	2.66910	+	5.13016i	0.158382	+	0.304419i
$285$	−10.7379	+	40.0745i	−0.636059	+	2.37381i
$286$	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
$290$	−1.52829	−	1.59683i	−0.0897441	−	0.0937694i
$291$	38.8645	−	10.4137i	2.27828	−	0.610462i
$292$	−1.27921	−	0.0561440i	−0.0748601	−	0.00328558i
$293$	−1.24795	+	1.24795i	−0.0729060	+	0.0729060i	−0.742620	−	0.669714i	$-0.766417\pi$
$293$	−1.24795	+	1.24795i	−0.0729060	+	0.0729060i	0.669714	+	0.742620i	$0.266417\pi$
$294$		0			0
$295$			19.8031i			1.15298i
$296$	0.177220	−	0.0873197i	0.0103007	−	0.00507535i
$297$	−6.28684	−	3.62971i	−0.364800	−	0.210617i
$298$	−11.9308	−	0.261693i	−0.691132	−	0.0151595i
$299$	−10.3063	−	2.76157i	−0.596030	−	0.159706i
$300$	−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
$304$	9.74766	+	11.6276i	0.559067	+	0.666888i
$305$	−18.5550	+	32.1381i	−1.06245	+	1.84022i
$306$	2.72894	+	11.1578i	0.156003	+	0.637848i
$307$	−17.4736	−	17.4736i	−0.997273	−	0.997273i	0.00272350	−	0.999996i	$-0.499133\pi$
$307$	−17.4736	−	17.4736i	−0.997273	−	0.997273i	−0.999996	+	0.00272350i	$0.999133\pi$
$308$		0			0
$309$	−18.1055	+	18.1055i	−1.02999	+	1.02999i
$310$	3.19025	−	5.25602i	0.181194	−	0.298522i
$311$	−24.6649	−	14.2403i	−1.39862	−	0.807491i	−0.404368	−	0.914596i	$-0.632508\pi$
$311$	−24.6649	−	14.2403i	−1.39862	−	0.807491i	−0.994248	+	0.107106i	$0.965842\pi$
$312$	48.1810	−	9.56665i	2.72771	−	0.541605i
$313$	−13.5858	+	7.84379i	−0.767917	+	0.443357i	−0.832131	−	0.554579i	$-0.812879\pi$
$313$	−13.5858	+	7.84379i	−0.767917	+	0.443357i	0.0642141	+	0.997936i	$0.479546\pi$
$314$	6.47751	−	3.55272i	0.365547	−	0.200492i
$315$		0			0
$316$	1.26460	+	0.806044i	0.0711393	+	0.0453435i
$317$	4.37319	−	16.3210i	0.245623	−	0.916677i	−0.727446	−	0.686165i	$-0.759293\pi$
$317$	4.37319	−	16.3210i	0.245623	−	0.916677i	0.973069	−	0.230513i	$-0.0740404\pi$
$318$	−1.69145	−	1.76731i	−0.0948517	−	0.0991061i
$319$	0.201992	−	0.349860i	0.0113094	−	0.0195884i
$320$	−11.4585	+	27.6097i	−0.640547	+	1.54343i
$321$	−13.1489			−0.733901
$322$		0			0
$323$	3.91279	+	3.91279i	0.217714	+	0.217714i
$324$	0.464538	−	10.5842i	0.0258077	−	0.588013i
$325$	13.7629	+	51.3638i	0.763428	+	2.84915i
$326$	−0.359449	+	16.3876i	−0.0199081	+	0.907624i
$327$	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
$331$	−28.7646	−	7.70745i	−1.58105	−	0.423640i	−0.641796	−	0.766876i	$-0.721810\pi$
$331$	−28.7646	−	7.70745i	−1.58105	−	0.423640i	−0.939249	+	0.343236i	$0.888477\pi$
$332$	−12.1777	−	3.84267i	−0.668338	−	0.210894i
$333$	−0.375658	+	0.100657i	−0.0205859	+	0.00551598i
$334$	−4.61877	−	18.8847i	−0.252728	−	1.03332i
$335$	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	$0.516491\pi$
$338$	−7.45992	−	30.5013i	−0.405766	−	1.65905i
$339$	−0.253469	+	0.0679167i	−0.0137665	+	0.00368873i
$340$	−3.28063	+	10.3966i	−0.177917	+	0.563833i
$341$	1.08547	+	0.290850i	0.0587813	+	0.0157504i
$342$	−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
$346$	0.244861	−	11.1634i	0.0131638	−	0.600149i
$347$	−7.42203	−	27.6994i	−0.398436	−	1.48698i	−0.815849	−	0.578265i	$-0.803730\pi$
$347$	−7.42203	−	27.6994i	−0.398436	−	1.48698i	0.417413	−	0.908717i	$-0.362937\pi$
$348$	2.44630	+	0.107367i	0.131135	+	0.00575548i
$349$	5.48808	+	5.48808i	0.293770	+	0.293770i	0.838568	−	0.544797i	$-0.183393\pi$
$349$	5.48808	+	5.48808i	0.293770	+	0.293770i	−0.544797	+	0.838568i	$0.683393\pi$
$350$		0			0
$351$	−44.5957			−2.38034
$352$	−5.43075	−	0.597900i	−0.289460	−	0.0318682i
$353$	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	$0.148844\pi$
$354$	−15.1689	−	15.8493i	−0.806218	−	0.842378i
$355$	2.79638	−	10.4362i	0.148416	−	0.553897i
$356$	−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	−0.234836	−	0.972035i	$-0.575455\pi$
$359$	9.27572	−	5.35534i	0.489554	−	0.282644i	0.724389	+	0.689391i	$0.242122\pi$
$360$	32.7093	−	48.9167i	1.72393	−	2.57814i
$361$	3.99359	+	2.30570i	0.210189	+	0.121353i
$362$	−15.6972	+	25.8616i	−0.825028	+	1.35925i
$363$	−20.8366	+	20.8366i	−1.09364	+	1.09364i
$364$		0			0
$365$	1.69159	+	1.69159i	0.0885416	+	0.0885416i
$366$	−9.76702	−	39.9342i	−0.510530	−	2.08740i
$367$	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	$0.00921235\pi$
$368$	−0.630208	+	7.16564i	−0.0328519	+	0.373535i
$369$	−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
$373$	0.943772	+	0.252883i	0.0488667	+	0.0130938i	0.283170	−	0.959070i	$-0.408614\pi$
$373$	0.943772	+	0.252883i	0.0488667	+	0.0130938i	−0.234303	+	0.972164i	$0.575281\pi$
$374$	−1.99207	−	0.0436945i	−0.103007	−	0.00225939i
$375$	37.5317	+	21.6689i	1.93813	+	1.11898i
$376$	−29.6925	−	10.0906i	−1.53128	−	0.520383i
$377$		−	2.48173i		−	0.127816i
$378$		0			0
$379$	17.6845	−	17.6845i	0.908391	−	0.908391i	−0.0877516	−	0.996142i	$-0.527968\pi$
$379$	17.6845	−	17.6845i	0.908391	−	0.908391i	0.996142	+	0.0877516i	$0.0279682\pi$
$380$	1.24298	−	28.3205i	0.0637633	−	1.45281i
$381$	48.0886	−	12.8853i	2.46365	−	0.660133i
$382$	19.4322	+	20.3038i	0.994237	+	1.03883i
$383$	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
$387$	−9.27341	+	34.6088i	−0.471394	+	1.75927i
$388$	−24.3885	+	12.6888i	−1.23814	+	0.644174i
$389$	9.19898	+	34.3310i	0.466407	+	1.74065i	0.652184	+	0.758061i	$0.273853\pi$
$389$	9.19898	+	34.3310i	0.466407	+	1.74065i	−0.185777	+	0.982592i	$0.559480\pi$
$390$	−78.4536	−	47.6191i	−3.97265	−	2.41128i
$391$			2.62338i			0.132670i
$392$		0			0
$393$		−	57.9821i		−	2.92481i
$394$	−6.86979	+	11.3182i	−0.346095	+	0.570200i
$395$	−0.725158	−	2.70632i	−0.0364866	−	0.136170i
$396$	10.2566	+	3.23648i	0.515415	+	0.162639i
$397$	0.793452	−	2.96120i	0.0398222	−	0.148619i	−0.943152	−	0.332361i	$-0.892155\pi$
$397$	0.793452	−	2.96120i	0.0398222	−	0.148619i	0.982974	+	0.183743i	$0.0588213\pi$
$398$	−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	$-0.345759\pi$
$402$	−35.6305	+	34.1010i	−1.77709	+	1.70080i
$403$	6.66818	−	1.78673i	0.332166	−	0.0890035i
$404$	−6.25772	−	6.83223i	−0.311333	−	0.339916i
$405$	−13.9963	+	13.9963i	−0.695479	+	0.695479i
$406$		0			0
$407$		−	0.0674628i		−	0.00334400i
$408$	−5.33798	−	10.8337i	−0.264270	−	0.536348i
$409$	−8.76082	−	5.05806i	−0.433195	−	0.250105i	0.267512	−	0.963555i	$-0.413799\pi$
$409$	−8.76082	−	5.05806i	−0.433195	−	0.250105i	−0.700707	+	0.713449i	$0.747132\pi$
$410$	1.17188	−	53.4271i	0.0578752	−	2.63858i
$411$	2.58826	+	0.693522i	0.127669	+	0.0342089i
$412$	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
$416$	−30.7287	+	13.5000i	−1.50660	+	0.661894i
$417$	5.68218	−	9.84182i	0.278257	−	0.481956i
$418$	5.03280	−	1.23091i	0.246162	−	0.0602058i
$419$	−17.7452	−	17.7452i	−0.866909	−	0.866909i	0.125220	−	0.992129i	$-0.460036\pi$
$419$	−17.7452	−	17.7452i	−0.866909	−	0.866909i	−0.992129	+	0.125220i	$0.960036\pi$
$420$		0			0
$421$	−18.2787	+	18.2787i	−0.890851	+	0.890851i	−0.994603	−	0.103752i	$-0.966915\pi$
$421$	−18.2787	+	18.2787i	−0.890851	+	0.890851i	0.103752	+	0.994603i	$0.466915\pi$
$422$	31.1437	+	18.9033i	1.51605	+	0.920200i
$423$	53.4627	+	30.8667i	2.59945	+	1.50079i
$424$	1.38948	+	0.929108i	0.0674791	+	0.0451215i
$425$	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
$429$	4.34135	−	16.2021i	0.209602	−	0.782246i
$430$	−24.5672	+	23.5126i	−1.18473	+	1.13388i
$431$	−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	$0.985795\pi$
$432$	5.20721	+	29.6106i	0.250532	+	1.42464i
$433$	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
$436$	−9.07944	+	8.31596i	−0.434826	+	0.398262i
$437$	−1.76552	−	6.58902i	−0.0844565	−	0.315196i
$438$	−2.64957	−	0.0581164i	−0.126601	−	0.00277691i
$439$	−16.8323	+	9.71811i	−0.803360	+	0.463820i	−0.844645	−	0.535327i	$-0.820188\pi$
$439$	−16.8323	+	9.71811i	−0.803360	+	0.463820i	0.0412847	+	0.999147i	$0.486855\pi$
$440$	6.72774	+	7.67681i	0.320732	+	0.365978i
$441$		0			0
$442$	−10.7323	+	5.88632i	−0.510481	+	0.279984i
$443$	−24.4055	−	6.53942i	−1.15954	−	0.310697i	−0.372757	−	0.927929i	$-0.621587\pi$
$443$	−24.4055	−	6.53942i	−1.15954	−	0.310697i	−0.786781	+	0.617232i	$0.788254\pi$
$444$	0.362751	−	0.188731i	0.0172154	−	0.00895678i
$445$	55.8403	−	14.9624i	2.64709	−	0.709285i
$446$	11.4494	−	2.80026i	0.542145	−	0.132596i
$447$	−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	$0.647125\pi$
$450$	−68.5499	+	16.7658i	−3.23147	+	0.790346i
$451$	9.43445	−	2.52795i	0.444251	−	0.119037i
$452$	0.159058	−	0.0827542i	0.00748146	−	0.00389243i
$453$	14.3560	+	3.84668i	0.674504	+	0.180733i
$454$	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	−0.675088	−	0.737738i	$-0.735894\pi$
$457$	−7.98948	+	4.61273i	−0.373732	+	0.215774i	0.301356	+	0.953512i	$0.402561\pi$
$458$	17.9360	+	0.393412i	0.838092	+	0.0183829i
$459$	2.83785	+	10.5910i	0.132460	+	0.494346i
$460$	9.91058	−	9.07721i	0.462083	−	0.423227i
$461$	10.6272	+	10.6272i	0.494960	+	0.494960i	0.909865	−	0.414905i	$-0.136185\pi$
$461$	10.6272	+	10.6272i	0.494960	+	0.494960i	−0.414905	+	0.909865i	$0.636185\pi$
$462$		0			0
$463$	32.4877			1.50983			0.754916	−	0.655821i	$-0.227678\pi$
$463$	32.4877			1.50983			0.754916	+	0.655821i	$0.227678\pi$
$464$	−1.64782	+	0.289779i	−0.0764979	+	0.0134526i
$465$	6.36291	−	11.0209i	0.295073	−	0.511082i
$466$	23.0279	−	22.0394i	1.06675	−	1.02095i
$467$	−4.55073	+	16.9836i	−0.210583	+	0.785905i	0.777092	+	0.629387i	$0.216694\pi$
$467$	−4.55073	+	16.9836i	−0.210583	+	0.785905i	−0.987675	+	0.156519i	$0.949973\pi$
$468$	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
$472$	12.4608	+	8.33223i	0.573556	+	0.383522i
$473$	−5.38256	−	3.10762i	−0.247490	−	0.142889i
$474$	2.65337	+	1.61052i	0.121874	+	0.0739737i
$475$	−24.0390	+	24.0390i	−1.10298	+	1.10298i
$476$		0			0
$477$	−2.32665	−	2.32665i	−0.106530	−	0.106530i
$478$	−18.3636	+	4.49132i	−0.839931	+	0.205428i
$479$	−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	$0.855659\pi$
$480$	−22.4574	+	57.6518i	−1.02504	+	2.63143i
$481$	−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
$485$	49.6132	+	13.2938i	2.25282	+	0.603641i
$486$	−0.218430	+	9.95840i	−0.00990819	+	0.451722i
$487$	−6.32101	−	3.64944i	−0.286432	−	0.165372i	0.349899	−	0.936787i	$-0.386216\pi$
$487$	−6.32101	−	3.64944i	−0.286432	−	0.165372i	−0.636332	+	0.771415i	$0.719549\pi$
$488$	12.4154	+	25.1976i	0.562018	+	1.14064i
$489$			33.9265i			1.53421i
$490$		0			0
$491$	11.4241	−	11.4241i	0.515561	−	0.515561i	−0.400664	−	0.916225i	$-0.631221\pi$
$491$	11.4241	−	11.4241i	0.515561	−	0.515561i	0.916225	+	0.400664i	$0.131221\pi$
$492$	39.9864	+	43.6575i	1.80273	+	1.96823i
$493$	−0.589384	+	0.157925i	−0.0265445	+	0.00711259i
$494$	22.9943	−	22.0072i	1.03456	−	0.990151i
$495$	−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
$499$	5.97431	−	22.2964i	0.267447	−	0.998126i	−0.693289	−	0.720660i	$-0.743839\pi$
$499$	5.97431	−	22.2964i	0.267447	−	0.998126i	0.960736	−	0.277466i	$-0.0894945\pi$
$500$	−28.2391	−	8.91083i	−1.26289	−	0.398504i
$501$	−10.4146	−	38.8678i	−0.465289	−	1.73648i
$502$	−8.40560	+	13.8484i	−0.375160	+	0.618086i
$503$		−	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
$506$	2.09979	+	1.27451i	0.0933470	+	0.0566589i
$507$	−16.8209	−	62.7766i	−0.747044	−	2.78800i
$508$	−30.1768	+	15.7003i	−1.33888	+	0.696588i
$509$	−7.27073	+	27.1347i	−0.322270	+	1.20273i	0.594759	+	0.803904i	$0.297248\pi$
$509$	−7.27073	+	27.1347i	−0.322270	+	1.20273i	−0.917028	+	0.398822i	$0.869419\pi$
$510$	−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
$514$	16.6058	+	17.3506i	0.732449	+	0.765301i
$515$	−31.5728	+	8.45992i	−1.39127	+	0.372788i
$516$	1.65183	−	37.6361i	0.0727180	−	1.65684i
$517$	−7.57218	+	7.57218i	−0.333024	+	0.333024i
$518$		0			0
$519$		−	23.1112i		−	1.01447i
$520$	59.3723	+	20.1768i	2.60365	+	0.884813i
$521$	−5.79205	−	3.34404i	−0.253755	−	0.146505i	0.367728	−	0.929934i	$-0.380136\pi$
$521$	−5.79205	−	3.34404i	−0.253755	−	0.146505i	−0.621482	+	0.783428i	$0.713469\pi$
$522$	3.29275	+	0.0722240i	0.144120	+	0.00316116i
$523$	12.6482	+	3.38908i	0.553068	+	0.148194i	0.524520	−	0.851398i	$-0.324245\pi$
$523$	12.6482	+	3.38908i	0.553068	+	0.148194i	0.0285481	+	0.999592i	$0.490912\pi$
$524$	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
$528$	−11.2648	−	0.990723i	−0.490237	−	0.0431157i
$529$	−9.88301	+	17.1179i	−0.429696	+	0.744256i
$530$	−0.741916	−	3.03346i	−0.0322268	−	0.131765i
$531$	−20.8654	−	20.8654i	−0.905479	−	0.905479i
$532$		0			0
$533$	42.4276	−	42.4276i	1.83774	−	1.83774i
$534$	−33.2303	+	54.7478i	−1.43802	+	2.36917i
$535$	−14.5367	−	8.39275i	−0.628475	−	0.362850i
$536$	18.7316	−	28.0130i	0.809081	−	1.20998i
$537$	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
$541$	4.92099	−	18.3654i	0.211570	−	0.789589i	−0.775776	−	0.631008i	$-0.782641\pi$
$541$	4.92099	−	18.3654i	0.211570	−	0.789589i	0.987346	−	0.158581i	$-0.0506919\pi$
$542$	16.3666	+	17.1006i	0.703004	+	0.734536i
$543$	−31.3079	+	54.2269i	−1.34355	+	2.32710i
$544$	5.16155	+	6.43868i	0.221300	+	0.276056i
$545$	23.0031			0.985345
$546$		0			0
$547$	−12.0842	−	12.0842i	−0.516683	−	0.516683i	0.399883	−	0.916566i	$-0.369051\pi$
$547$	−12.0842	−	12.0842i	−0.516683	−	0.516683i	−0.916566	+	0.399883i	$0.869051\pi$
$548$	−1.82911	−	0.0802791i	−0.0781358	−	0.00342935i
$549$	−14.3118	−	53.4122i	−0.610811	−	2.27958i
$550$	0.268446	−	12.2386i	0.0114466	−	0.521858i
$551$	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
$555$	−0.737941	−	0.197731i	−0.0313238	−	0.00839320i
$556$	−2.33666	+	7.40504i	−0.0990964	+	0.314044i
$557$	−32.6010	+	8.73540i	−1.38135	+	0.370131i	−0.871610	−	0.490200i	$-0.836924\pi$
$557$	−32.6010	+	8.73540i	−1.38135	+	0.370131i	−0.509737	+	0.860331i	$0.670257\pi$
$558$	2.17657	+	8.89931i	0.0921416	+	0.376738i
$559$	−38.1812			−1.61489
$560$		0			0
$561$	−4.12410			−0.174120
$562$	−5.03001	−	20.5661i	−0.212178	−	0.867530i
$563$	28.2240	−	7.56259i	1.18950	−	0.318725i	0.390811	−	0.920471i	$-0.372195\pi$
$563$	28.2240	−	7.56259i	1.18950	−	0.318725i	0.798688	+	0.601746i	$0.205528\pi$
$564$	−61.8997	−	19.5324i	−2.60645	−	0.822464i
$565$	−0.323570	−	0.0867003i	−0.0136127	−	0.00364751i
$566$	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	0.0649214	−	0.997890i	$-0.479320\pi$
$569$	22.9373	−	13.2428i	0.961581	−	0.555169i	0.896659	+	0.442722i	$0.145987\pi$
$570$	1.28664	−	58.6590i	0.0538914	−	2.45695i
$571$	8.69533	+	32.4514i	0.363888	+	1.35805i	0.868922	+	0.494949i	$0.164813\pi$
$571$	8.69533	+	32.4514i	0.363888	+	1.35805i	−0.505034	+	0.863100i	$0.668520\pi$
$572$	−0.502536	+	11.4500i	−0.0210121	+	0.478748i
$573$	41.1319	+	41.1319i	1.71831	+	1.71831i
$574$		0			0
$575$	−16.1172			−0.672134
$576$	−17.0175	−	41.1637i	−0.709064	−	1.71515i
$577$	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	$-0.0278529\pi$
$578$	−14.5422	−	15.1945i	−0.604877	−	0.632007i
$579$	−9.00233	+	33.5972i	−0.374124	+	1.39625i
$580$	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
$584$	1.77614	−	0.352665i	0.0734974	−	0.0145934i
$585$	−106.902	−	61.7201i	−4.41987	−	2.55181i
$586$	1.29505	−	2.13362i	0.0534980	−	0.0881392i
$587$	23.6471	−	23.6471i	0.976018	−	0.976018i	−0.0237007	−	0.999719i	$-0.507545\pi$
$587$	23.6471	−	23.6471i	0.976018	−	0.976018i	0.999719	+	0.0237007i	$0.00754488\pi$
$588$		0			0
$589$	3.12080	+	3.12080i	0.128590	+	0.128590i
$590$	−6.65350	−	27.2040i	−0.273920	−	1.11997i
$591$	−13.7017	+	23.7321i	−0.563613	+	0.976206i
$592$	−0.214113	+	0.179496i	−0.00879999	+	0.00737723i
$593$	−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
$597$	−68.0350	−	18.2299i	−2.78449	−	0.746101i
$598$	15.0859	+	0.330897i	0.616907	+	0.0135314i
$599$	24.0513	+	13.8860i	0.982708	+	0.567367i	0.903087	−	0.429458i	$-0.141296\pi$
$599$	24.0513	+	13.8860i	0.982708	+	0.567367i	0.0796214	+	0.996825i	$0.474629\pi$
$600$	66.5589	−	32.7949i	2.71726	−	1.33885i
$601$			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
$604$	−10.1453	−	0.445275i	−0.412808	−	0.0181180i
$605$	−36.3354	+	9.73605i	−1.47725	+	0.395827i
$606$	−13.2590	−	13.8537i	−0.538609	−	0.562767i
$607$	−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
$611$	−17.0264	+	63.5434i	−0.688815	+	2.57069i
$612$	−7.49762	−	14.4108i	−0.303073	−	0.582523i
$613$	−1.11005	−	4.14276i	−0.0448344	−	0.167324i	0.939879	−	0.341509i	$-0.110938\pi$
$613$	−1.11005	−	4.14276i	−0.0448344	−	0.167324i	−0.984713	+	0.174184i	$0.944271\pi$
$614$	29.8748	+	18.1331i	1.20565	+	0.731793i
$615$		−	110.608i		−	4.46014i
$616$		0			0
$617$			1.11707i			0.0449717i	0.999747	+	0.0224859i	$0.00715808\pi$
$617$			1.11707i			0.0449717i	−0.999747	+	0.0224859i	$0.992842\pi$
$618$	18.7888	−	30.9551i	0.755798	−	1.24520i
$619$	2.18047	+	8.13764i	0.0876407	+	0.327079i	0.995801	−	0.0915428i	$-0.0291798\pi$
$619$	2.18047	+	8.13764i	0.0876407	+	0.327079i	−0.908160	+	0.418622i	$0.862513\pi$
$620$	−2.61660	+	8.29219i	−0.105085	+	0.333022i
$621$	3.49837	−	13.0561i	0.140385	−	0.523923i
$622$	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
$626$	16.0278	−	15.3398i	0.640600	−	0.613101i
$627$	10.3583	−	2.77550i	0.413672	−	0.110843i
$628$	−7.70466	+	7.05679i	−0.307449	+	0.281596i
$629$	−0.0720511	+	0.0720511i	−0.00287287	+	0.00287287i
$630$		0			0
$631$			12.4799i			0.496819i	0.968655	+	0.248409i	$0.0799078\pi$
$631$			12.4799i			0.496819i	−0.968655	+	0.248409i	$0.920092\pi$
$632$	−2.00803	−	0.682400i	−0.0798750	−	0.0271444i
$633$	65.3026	+	37.7025i	2.59554	+	1.49854i
$634$	−0.524005	+	23.8898i	−0.0208109	+	0.948786i
$635$	61.3883	+	16.4489i	2.43612	+	0.652757i
$636$	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
$640$	6.46440	−	41.7779i	0.255528	−	1.65142i
$641$	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	$0.102118\pi$
$642$	18.0630	−	4.41780i	0.712889	−	0.174357i
$643$	10.9741	+	10.9741i	0.432777	+	0.432777i	0.889572	−	0.456795i	$-0.151003\pi$
$643$	10.9741	+	10.9741i	0.432777	+	0.432777i	−0.456795	+	0.889572i	$0.651003\pi$
$644$		0			0
$645$	−49.7688	+	49.7688i	−1.95964	+	1.95964i
$646$	−6.68972	−	4.06047i	−0.263204	−	0.159757i
$647$	−5.70335	−	3.29283i	−0.224222	−	0.129455i	0.383682	−	0.923465i	$-0.374656\pi$
$647$	−5.70335	−	3.29283i	−0.224222	−	0.129455i	−0.607904	+	0.794011i	$0.707989\pi$
$648$	2.91796	+	14.6959i	0.114628	+	0.577309i
$649$	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
$653$	1.32849	−	4.95799i	0.0519878	−	0.194021i	−0.935048	−	0.354521i	$-0.884644\pi$
$653$	1.32849	−	4.95799i	0.0519878	−	0.194021i	0.987036	+	0.160500i	$0.0513106\pi$
$654$	−18.4103	+	17.6200i	−0.719900	+	0.688997i
$655$	37.0091	−	64.1016i	1.44606	−	2.50466i
$656$	−33.1251	−	23.2170i	−1.29332	−	0.906471i
$657$	−3.56464			−0.139070
$658$		0			0
$659$	−5.78706	−	5.78706i	−0.225432	−	0.225432i	0.585349	−	0.810781i	$-0.300957\pi$
$659$	−5.78706	−	5.78706i	−0.225432	−	0.225432i	−0.810781	+	0.585349i	$0.800957\pi$
$660$	14.2699	+	15.5800i	0.555455	+	0.606451i
$661$	7.12099	+	26.5759i	0.276975	+	1.03368i	0.954507	+	0.298190i	$0.0963828\pi$
$661$	7.12099	+	26.5759i	0.276975	+	1.03368i	−0.677532	+	0.735493i	$0.736950\pi$
$662$	42.1042	+	0.923523i	1.63642	+	0.0358938i
$663$	−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
$667$	0.726564	+	0.194682i	0.0281327	+	0.00753813i
$668$	12.6898	+	24.3905i	0.490984	+	0.943698i
$669$	23.5647	−	6.31415i	0.911065	−	0.244119i
$670$	−61.1570	+	14.9576i	−2.36270	+	0.577864i
$671$	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	$0.755946\pi$
$674$	2.61176	−	0.638779i	0.100601	−	0.0246048i
$675$	−65.0679	+	17.4349i	−2.50446	+	0.671069i
$676$	20.4957	+	39.3939i	0.788298	+	1.51515i
$677$	−22.0829	−	5.91710i	−0.848716	−	0.227413i	−0.191854	−	0.981424i	$-0.561450\pi$
$677$	−22.0829	−	5.91710i	−0.848716	−	0.227413i	−0.656862	+	0.754011i	$0.728117\pi$
$678$	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
$682$	−1.58885	−	0.0348503i	−0.0608402	−	0.00133449i
$683$	4.85170	+	18.1068i	0.185645	+	0.692837i	0.994492	+	0.104817i	$0.0334256\pi$
$683$	4.85170	+	18.1068i	0.185645	+	0.692837i	−0.808847	+	0.588020i	$0.799908\pi$
$684$	28.5299	+	31.1492i	1.09087	+	1.19102i
$685$	2.41876	+	2.41876i	0.0924161	+	0.0924161i
$686$		0			0
$687$	37.1321			1.41668
$688$	4.45822	+	25.3515i	0.169968	+	0.966517i
$689$	1.75316	−	3.03656i	0.0667901	−	0.115684i
$690$	20.0956	−	19.2330i	0.765027	−	0.732186i
$691$	2.28573	−	8.53045i	0.0869532	−	0.324514i	−0.908724	−	0.417398i	$-0.862942\pi$
$691$	2.28573	−	8.53045i	0.0869532	−	0.324514i	0.995677	+	0.0928845i	$0.0296087\pi$
$692$	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
$696$	−3.39661	+	0.674420i	−0.128748	+	0.0255638i
$697$	−12.7760	−	7.37623i	−0.483925	−	0.279395i
$698$	−9.38301	−	5.69521i	−0.355152	−	0.215567i
$699$	46.6504	−	46.6504i	1.76448	−	1.76448i
$700$		0			0
$701$	28.1681	+	28.1681i	1.06389	+	1.06389i	0.997814	+	0.0660783i	$0.0210487\pi$
$701$	28.1681	+	28.1681i	1.06389	+	1.06389i	0.0660783	+	0.997814i	$0.478951\pi$
$702$	61.2622	−	14.9833i	2.31219	−	0.565510i
$703$	0.132478	−	0.229458i	0.00499649	−	0.00865417i
$704$	7.66123	−	1.00328i	0.288744	−	0.0378127i
$705$	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
$709$	−14.8540	−	3.98010i	−0.557852	−	0.149476i	−0.0311326	−	0.999515i	$-0.509911\pi$
$709$	−14.8540	−	3.98010i	−0.557852	−	0.149476i	−0.526719	+	0.850039i	$0.676578\pi$
$710$	−0.335068	+	15.2760i	−0.0125749	+	0.573299i
$711$	3.61554	+	2.08743i	0.135593	+	0.0782849i
$712$	14.0801	−	41.4322i	0.527676	−	1.55274i
$713$			2.09238i			0.0783601i
$714$		0			0
$715$	15.1411	−	15.1411i	0.566245	−	0.566245i
$716$	−14.2360	+	13.0389i	−0.532025	+	0.487288i
$717$	−37.7952	+	10.1272i	−1.41149	+	0.378207i
$718$	−10.9430	+	10.4732i	−0.408388	+	0.390857i
$719$	−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
$723$	14.6928	−	54.8341i	0.546429	−	2.03930i
$724$	12.8746	−	40.8007i	0.478482	−	1.51634i
$725$	−0.970243	−	3.62099i	−0.0360339	−	0.134480i
$726$	21.6231	−	35.6245i	0.802507	−	1.32215i
$727$			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
$730$	−2.89211	−	1.75543i	−0.107042	−	0.0649713i
$731$	2.42966	+	9.06763i	0.0898644	+	0.335378i
$732$	26.8344	+	51.5771i	0.991827	+	1.90634i
$733$	−12.0160	+	44.8442i	−0.443820	+	1.65636i	0.275212	+	0.961384i	$0.411252\pi$
$733$	−12.0160	+	44.8442i	−0.443820	+	1.65636i	−0.719032	+	0.694976i	$0.755415\pi$
$734$	−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
$738$	55.0581	+	57.5275i	2.02672	+	2.11762i
$739$	21.1374	−	5.66375i	0.777552	−	0.208344i	0.151847	−	0.988404i	$-0.451478\pi$
$739$	21.1374	−	5.66375i	0.777552	−	0.208344i	0.625705	+	0.780060i	$0.284811\pi$
$740$	0.521500	+	0.0228884i	0.0191707	+	0.000841396i
$741$	46.5824	−	46.5824i	1.71125	−	1.71125i
$742$		0			0
$743$			19.2071i			0.704639i	0.935880	+	0.352320i	$0.114607\pi$
$743$			19.2071i			0.704639i	−0.935880	+	0.352320i	$0.885393\pi$
$744$	−4.25751	−	8.64084i	−0.156088	−	0.316789i
$745$	−27.3067	−	15.7655i	−1.00044	−	0.577604i
$746$	−1.38145	−	0.0303010i	−0.0505783	−	0.00110940i
$747$	−34.3381	−	9.20086i	−1.25637	−	0.336642i
$748$	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	$0.606328\pi$
$752$	44.1796	+	3.88554i	1.61106	+	0.141691i
$753$	−16.7649	+	29.0376i	−0.610945	+	1.05819i
$754$	0.833816	+	3.40921i	0.0303658	+	0.124156i
$755$	13.4159	+	13.4159i	0.488253	+	0.488253i
$756$		0			0
$757$	22.1772	−	22.1772i	0.806045	−	0.806045i	−0.177988	−	0.984033i	$-0.556959\pi$
$757$	22.1772	−	22.1772i	0.806045	−	0.806045i	0.984033	+	0.177988i	$0.0569587\pi$
$758$	−18.3519	+	30.2353i	−0.666572	+	1.09819i
$759$	4.40286	+	2.54199i	0.159814	+	0.0922685i
$760$	7.80766	+	39.3221i	0.283214	+	1.42636i
$761$	−25.6074	+	14.7845i	−0.928269	+	0.535936i	−0.886264	−	0.463181i	$-0.846708\pi$
$761$	−25.6074	+	14.7845i	−0.928269	+	0.535936i	−0.0420051	+	0.999117i	$0.513375\pi$
$762$	−61.7312	+	33.8577i	−2.23628	+	1.22654i
$763$		0			0
$764$	−33.5162	−	21.3629i	−1.21257	−	0.772883i
$765$	−7.85514	+	29.3158i	−0.284003	+	1.05991i
$766$	−11.0010	−	11.4944i	−0.397482	−	0.415310i
$767$	15.7223	−	27.2319i	0.567701	−	0.983286i
$768$	26.8275	+	38.3882i	0.968053	+	1.38521i
$769$	−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
$772$	1.04207	−	23.7430i	0.0375050	−	0.854529i
$773$	13.3060	+	49.6587i	0.478584	+	1.78610i	0.607361	+	0.794426i	$0.292228\pi$
$773$	13.3060	+	49.6587i	0.478584	+	1.78610i	−0.128777	+	0.991674i	$0.541105\pi$
$774$	1.11116	−	50.6586i	0.0399398	−	1.82089i
$775$	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
$779$	37.0531	+	9.92835i	1.32757	+	0.355720i
$780$	123.773	+	39.0564i	4.43177	+	1.39844i
$781$	−2.69752	+	0.722799i	−0.0965250	+	0.0258638i
$782$	−0.881407	−	3.60379i	−0.0315190	−	0.128871i
$783$	3.14386			0.112352
$784$		0			0
$785$	19.5201			0.696701
$786$	19.4809	+	79.6514i	0.694862	+	2.84107i
$787$	−10.0494	+	2.69273i	−0.358223	+	0.0959855i	−0.433442	−	0.901182i	$-0.642701\pi$
$787$	−10.0494	+	2.69273i	−0.358223	+	0.0959855i	0.0752192	+	0.997167i	$0.476034\pi$
$788$	5.63450	−	17.8561i	0.200721	−	0.636099i
$789$	12.4328	+	3.33136i	0.442620	+	0.118600i
$790$	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
$794$	−0.0950732	+	4.33446i	−0.00337402	+	0.153824i
$795$	−1.67290	−	6.24336i	−0.0593318	−	0.221429i
$796$	48.0801	+	2.11022i	1.70415	+	0.0747947i
$797$	−18.5924	−	18.5924i	−0.658577	−	0.658577i	0.296466	−	0.955043i	$-0.404192\pi$
$797$	−18.5924	−	18.5924i	−0.658577	−	0.658577i	−0.955043	+	0.296466i	$0.904192\pi$
$798$		0			0
$799$	16.1744			0.572208
$800$	−39.5572	+	31.7109i	−1.39856	+	1.12115i
$801$	−43.0706	+	74.6004i	−1.52182	+	2.63588i
$802$	20.8897	+	21.8266i	0.737641	+	0.770726i
$803$	0.160039	−	0.597275i	0.00564767	−	0.0210774i
$804$	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
$808$	10.8919	+	7.28312i	0.383175	+	0.256219i
$809$	38.5540	+	22.2591i	1.35548	+	0.782589i	0.989011	−	0.147839i	$-0.0472318\pi$
$809$	38.5540	+	22.2591i	1.35548	+	0.782589i	0.366473	+	0.930429i	$0.380565\pi$
$810$	14.5245	−	23.9295i	0.510339	−	0.840796i
$811$	−20.8814	+	20.8814i	−0.733246	+	0.733246i	−0.971261	−	0.238015i	$-0.923503\pi$
$811$	−20.8814	+	20.8814i	−0.733246	+	0.733246i	0.238015	+	0.971261i	$0.423503\pi$
$812$		0			0
$813$	34.6429	+	34.6429i	1.21498	+	1.21498i
$814$	0.0226663	+	0.0926752i	0.000794452	+	0.00324826i
$815$	−21.6548	+	37.5071i	−0.758533	+	1.31382i
$816$	10.9728	+	13.0891i	0.384126	+	0.458208i
$817$	−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
$821$	23.5147	+	6.30073i	0.820667	+	0.219897i	0.644638	−	0.764488i	$-0.277008\pi$
$821$	23.5147	+	6.30073i	0.820667	+	0.219897i	0.176029	+	0.984385i	$0.443675\pi$
$822$	−3.78856	−	0.0830993i	−0.132141	−	0.00289842i
$823$	−27.4622	−	15.8553i	−0.957273	−	0.552682i	−0.0619404	−	0.998080i	$-0.519729\pi$
$823$	−27.4622	−	15.8553i	−0.957273	−	0.552682i	−0.895333	+	0.445398i	$0.853062\pi$
$824$	−7.96109	+	23.4263i	−0.277338	+	0.816092i
$825$		−	25.3372i		−	0.882127i
$826$		0			0
$827$	−29.2764	+	29.2764i	−1.01804	+	1.01804i	−0.0182049	+	0.999834i	$0.505795\pi$
$827$	−29.2764	+	29.2764i	−1.01804	+	1.01804i	−0.999834	+	0.0182049i	$0.994205\pi$
$828$	−0.878067	+	20.0063i	−0.0305149	+	0.695266i
$829$	−0.303496	+	0.0813215i	−0.0105409	+	0.00282441i	−0.264086	−	0.964499i	$-0.585070\pi$
$829$	−0.303496	+	0.0813215i	−0.0105409	+	0.00282441i	0.253545	+	0.967324i	$0.418403\pi$
$830$	−23.3286	−	24.3750i	−0.809749	−	0.846068i
$831$	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
$835$	13.2949	−	49.6173i	0.460090	−	1.71708i
$836$	−6.50011	+	3.38186i	−0.224811	+	0.116964i
$837$	2.26344	+	8.44727i	0.0782359	+	0.291980i
$838$	30.3390	+	18.4149i	1.04804	+	0.636133i
$839$			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
$842$	18.9686	−	31.2512i	0.653701	−	1.07699i
$843$	−11.3419	−	42.3285i	−0.390635	−	1.45787i
$844$	−49.1340	−	15.5042i	−1.69126	−	0.533678i
$845$	21.4731	−	80.1385i	0.738696	−	2.75685i
$846$	−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
$850$	−13.3577	+	12.7843i	−0.458167	+	0.438499i
$851$	0.121332	−	0.0325108i	0.00415920	−	0.00111445i
$852$	−11.4330	−	12.4827i	−0.391689	−	0.427649i
$853$	−35.7996	+	35.7996i	−1.22576	+	1.22576i	−0.260202	+	0.965554i	$0.583789\pi$
$853$	−35.7996	+	35.7996i	−1.22576	+	1.22576i	−0.965554	+	0.260202i	$0.916211\pi$
$854$		0			0
$855$		−	78.9177i		−	2.69893i
$856$	−11.3974	+	5.61570i	−0.389554	+	0.191941i
$857$	6.57388	+	3.79543i	0.224560	+	0.129650i	0.608060	−	0.793891i	$-0.291948\pi$
$857$	6.57388	+	3.79543i	0.224560	+	0.129650i	−0.383500	+	0.923541i	$0.625281\pi$
$858$	−0.520190	+	23.7159i	−0.0177590	+	0.809646i
$859$	−27.8932	−	7.47395i	−0.951703	−	0.255008i	−0.250618	−	0.968086i	$-0.580634\pi$
$859$	−27.8932	−	7.47395i	−0.951703	−	0.255008i	−0.701085	+	0.713078i	$0.747301\pi$
$860$	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	$0.785817\pi$
$864$	−17.1019	−	38.9273i	−0.581818	−	1.32433i
$865$	14.7515	−	25.5503i	0.501566	−	0.868737i
$866$	−13.5526	+	3.31466i	−0.460536	+	0.112637i
$867$	−30.7814	−	30.7814i	−1.04539	−	1.04539i
$868$		0			0
$869$	−0.512086	+	0.512086i	−0.0173713	+	0.0173713i
$870$	5.53074	+	3.35700i	0.187510	+	0.113813i
$871$	−61.2196	−	35.3452i	−2.07435	−	1.19762i
$872$	9.67862	−	14.4744i	0.327760	−	0.490163i
$873$	−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
$877$	5.85518	−	21.8518i	0.197715	−	0.737884i	−0.793832	−	0.608137i	$-0.791917\pi$
$877$	5.85518	−	21.8518i	0.197715	−	0.737884i	0.991547	−	0.129746i	$-0.0414163\pi$
$878$	19.8578	−	19.0053i	0.670167	−	0.641399i
$879$	2.58296	−	4.47381i	0.0871210	−	0.150898i
$880$	−11.8213	−	8.28542i	−0.398497	−	0.279301i
$881$	−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	0.693923	−	0.720049i	$-0.255881\pi$
$883$	−0.776332	−	0.776332i	−0.0261257	−	0.0261257i	−0.720049	+	0.693923i	$0.755881\pi$
$884$	12.7655	−	11.6920i	0.429349	−	0.393245i
$885$	−15.0026	−	55.9904i	−0.504306	−	1.88210i
$886$	35.7235	+	0.783568i	1.20015	+	0.0263245i
$887$	24.6075	−	14.2071i	0.826239	−	0.477029i	−0.0263244	−	0.999653i	$-0.508380\pi$
$887$	24.6075	−	14.2071i	0.826239	−	0.477029i	0.852563	+	0.522624i	$0.175047\pi$
$888$	−0.434910	+	0.381142i	−0.0145946	+	0.0127903i
$889$		0			0
$890$	−71.6821	+	39.3155i	−2.40279	+	1.31786i
$891$	4.94188	+	1.32417i	0.165559	+	0.0443615i
$892$	−14.7875	+	7.69358i	−0.495121	+	0.257600i
$893$	−40.6245	+	10.8853i	−1.35945	+	0.364263i
$894$	33.9307	−	8.29870i	1.13481	−	0.277550i
$895$	36.0675			1.20560
$896$		0			0
$897$	31.2317			1.04280
$898$	25.9606	−	6.34937i	0.866315	−	0.211881i
$899$	−0.470086	+	0.125959i	−0.0156783	+	0.00420098i
$900$	88.5356	−	46.0630i	2.95119	−	1.53543i
$901$	−0.832715	−	0.223125i	−0.0277418	−	0.00743338i
$902$	−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
$906$	−21.0136	−	0.460918i	−0.698130	−	0.0153130i
$907$	3.53747	+	13.2020i	0.117460	+	0.438366i	0.999459	−	0.0328844i	$-0.0104693\pi$
$907$	3.53747	+	13.2020i	0.117460	+	0.438366i	−0.881999	+	0.471251i	$0.843803\pi$
$908$	−16.4212	+	15.0403i	−0.544955	+	0.499131i
$909$	−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	$0.845506\pi$
$912$	−36.3689	−	25.4905i	−1.20429	−	0.844076i
$913$	3.08331	−	5.34046i	0.102043	−	0.176743i
$914$	9.42554	−	9.02093i	0.311769	−	0.298386i
$915$	28.1139	−	104.923i	0.929418	−	3.46864i
$916$	−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	−0.572493	−	0.819910i	$-0.694024\pi$
$919$	−4.50715	+	2.60220i	−0.148677	+	0.0858388i	0.423816	+	0.905748i	$0.360690\pi$
$920$	−10.5646	+	15.7994i	−0.348305	+	0.520889i
$921$	62.6418	+	36.1663i	2.06412	+	1.19172i
$922$	−18.1695	−	11.0283i	−0.598379	−	0.363199i
$923$	−12.1310	+	12.1310i	−0.399297	+	0.399297i
$924$		0			0
$925$	−0.442660	−	0.442660i	−0.0145546	−	0.0145546i
$926$	−44.6291	+	10.9153i	−1.46660	+	0.358698i
$927$	24.3527	−	42.1800i	0.799846	−	1.38537i
$928$	2.16628	−	0.951712i	0.0711117	−	0.0312415i
$929$	−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
$933$	80.5243	+	21.5764i	2.63625	+	0.706380i
$934$	0.545278	−	24.8597i	0.0178421	−	0.813433i
$935$	−4.55936	−	2.63235i	−0.149107	−	0.0860869i
$936$	−83.8160	+	41.2978i	−2.73961	+	1.34986i
$937$			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
$940$	−55.9653	−	61.1035i	−1.82539	−	1.99297i
$941$	2.53370	−	0.678902i	0.0825961	−	0.0221316i	−0.217284	−	0.976108i	$-0.569720\pi$
$941$	2.53370	−	0.678902i	0.0825961	−	0.0221316i	0.299880	+	0.953977i	$0.403053\pi$
$942$	−15.6227	+	14.9520i	−0.509015	+	0.487164i
$943$	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
$947$	4.53939	−	16.9412i	0.147510	−	0.550516i	−0.852121	−	0.523346i	$-0.824684\pi$
$947$	4.53939	−	16.9412i	0.147510	−	0.550516i	0.999631	−	0.0271703i	$-0.00864965\pi$
$948$	−4.18611	−	1.32093i	−0.135958	−	0.0429017i
$949$	−0.983146	−	3.66915i	−0.0319143	−	0.119106i
$950$	24.9463	−	41.0996i	0.809363	−	1.33345i
$951$			49.4581i			1.60379i
$952$		0			0
$953$			27.3756i			0.886782i	0.896328	+	0.443391i	$0.146225\pi$
$953$			27.3756i			0.886782i	−0.896328	+	0.443391i	$0.853775\pi$
$954$	3.97788	+	2.41446i	0.128789	+	0.0781710i
$955$	19.2191	+	71.7268i	0.621916	+	2.32102i
$956$	23.7175	−	12.3397i	0.767078	−	0.399093i
$957$	−0.306052	+	1.14220i	−0.00989325	+	0.0369221i
$958$	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
$962$	0.405246	+	0.423422i	0.0130657	+	0.0136517i
$963$	24.1593	−	6.47347i	0.778523	−	0.208605i
$964$	−1.70077	+	38.7511i	−0.0547781	+	1.24809i
$965$	−31.3970	+	31.3970i	−1.01070	+	1.01070i
$966$		0			0
$967$		−	32.2156i		−	1.03598i	−0.855385	−	0.517992i	$-0.826680\pi$
$967$		−	32.2156i		−	1.03598i	0.855385	−	0.517992i	$-0.173320\pi$
$968$	−9.16198	+	26.9600i	−0.294477	+	0.866527i
$969$	−14.0271	−	8.09855i	−0.450615	−	0.260163i
$970$	−72.6212	−	1.59289i	−2.33173	−	0.0511447i
$971$	33.8181	+	9.06154i	1.08528	+	0.290799i	0.756755	−	0.653698i	$-0.226783\pi$
$971$	33.8181	+	9.06154i	1.08528	+	0.290799i	0.328520	+	0.944497i	$0.393450\pi$
$972$	−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
$976$	−25.5213	−	30.4433i	−0.816915	−	0.974465i
$977$	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	$0.150631\pi$
$978$	−11.3987	−	46.6057i	−0.364490	−	1.49029i
$979$	−10.5660	−	10.5660i	−0.337691	−	0.337691i
$980$		0			0
$981$	−24.2369	+	24.2369i	−0.773826	+	0.773826i
$982$	−11.8552	+	19.5318i	−0.378315	+	0.623284i
$983$	−44.3439	−	25.6020i	−1.41435	−	0.816576i	−0.418556	−	0.908191i	$-0.637464\pi$
$983$	−44.3439	−	25.6020i	−1.41435	−	0.816576i	−0.995794	+	0.0916152i	$0.970797\pi$
$984$	−69.5984	−	46.5386i	−2.21871	−	1.48360i
$985$	−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
$989$	2.99517	−	11.1781i	0.0952409	−	0.355444i
$990$	19.6485	+	20.5298i	0.624471	+	0.652480i
$991$	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	$0.0629142\pi$
$992$	4.11679	+	5.13542i	0.130708	+	0.163050i
$993$	87.1665			2.76615
$994$		0			0
$995$	−63.5795	−	63.5795i	−2.01561	−	2.01561i
$996$	37.3417	+	1.63891i	1.18322	+	0.0519310i
$997$	9.83269	+	36.6961i	0.311404	+	1.16218i	0.927291	+	0.374342i	$0.122131\pi$
$997$	9.83269	+	36.6961i	0.311404	+	1.16218i	−0.615886	+	0.787835i	$0.711202\pi$
$998$	−0.715855	+	32.6364i	−0.0226600	+	1.03309i
$999$	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.557.3		96
7.2	even	3	inner	784.2.x.p.765.18		96
7.3	odd	6		784.2.m.l.589.15	yes	48
7.4	even	3		784.2.m.l.589.16	yes	48
7.5	odd	6	inner	784.2.x.p.765.17		96
7.6	odd	2	inner	784.2.x.p.557.4		96
16.5	even	4	inner	784.2.x.p.165.18		96
112.5	odd	12	inner	784.2.x.p.373.4		96
112.37	even	12	inner	784.2.x.p.373.3		96
112.53	even	12		784.2.m.l.197.16	yes	48
112.69	odd	4	inner	784.2.x.p.165.17		96
112.101	odd	12		784.2.m.l.197.15	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.l.197.15	✓	48	112.101	odd	12
784.2.m.l.197.16	yes	48	112.53	even	12
784.2.m.l.589.15	yes	48	7.3	odd	6
784.2.m.l.589.16	yes	48	7.4	even	3
784.2.x.p.165.17		96	112.69	odd	4	inner
784.2.x.p.165.18		96	16.5	even	4	inner
784.2.x.p.373.3		96	112.37	even	12	inner
784.2.x.p.373.4		96	112.5	odd	12	inner
784.2.x.p.557.3		96	1.1	even	1	trivial
784.2.x.p.557.4		96	7.6	odd	2	inner
784.2.x.p.765.17		96	7.5	odd	6	inner
784.2.x.p.765.18		96	7.2	even	3	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)

\(f(q)\)	\(=\)	\(q+(-1.37372 + 0.335982i) q^{2} +(-2.82735 + 0.757585i) q^{3} +(1.77423 - 0.923092i) q^{4} +(-3.60930 - 0.967109i) q^{5} +(3.62946 - 1.99065i) q^{6} +(-2.12716 + 1.86418i) q^{8} +(4.82188 - 2.78391i) q^{9} +O(q^{10})\)	\(q+(-1.37372 + 0.335982i) q^{2} +(-2.82735 + 0.757585i) q^{3} +(1.77423 - 0.923092i) q^{4} +(-3.60930 - 0.967109i) q^{5} +(3.62946 - 1.99065i) q^{6} +(-2.12716 + 1.86418i) q^{8} +(4.82188 - 2.78391i) q^{9} +(5.28311 + 0.115881i) q^{10} +(0.249975 + 0.932921i) q^{11} +(-4.31705 + 3.95403i) q^{12} +(4.19543 + 4.19543i) q^{13} +10.9374 q^{15} +(2.29580 - 3.27556i) q^{16} +(0.729395 - 1.26335i) q^{17} +(-5.68858 + 5.44439i) q^{18} +(-0.981760 + 3.66398i) q^{19} +(-7.29647 + 1.61584i) q^{20} +(-0.656842 - 1.19759i) q^{22} +(-1.55739 + 0.899162i) q^{23} +(4.60195 - 6.88220i) q^{24} +(7.76162 + 4.48117i) q^{25} +(-7.17296 - 4.35378i) q^{26} +(-5.31479 + 5.31479i) q^{27} +(-0.295765 - 0.295765i) q^{29} +(-15.0250 + 3.67477i) q^{30} +(0.581757 - 1.00763i) q^{31} +(-2.05327 + 5.27106i) q^{32} +(-1.41353 - 2.44831i) q^{33} +(-0.577524 + 1.98056i) q^{34} +(5.98533 - 9.39035i) q^{36} +(-0.0674694 - 0.0180784i) q^{37} +(0.117637 - 5.36315i) q^{38} +(-15.0403 - 8.68355i) q^{39} +(9.48044 - 4.67120i) q^{40} -10.1128i q^{41} +(-4.55032 + 4.55032i) q^{43} +(1.30469 + 1.42447i) q^{44} +(-20.0960 + 5.38470i) q^{45} +(1.83733 - 1.75846i) q^{46} +(5.54377 + 9.60208i) q^{47} +(-4.00951 + 11.0004i) q^{48} +(-12.1679 - 3.54813i) q^{50} +(-1.10516 + 4.12450i) q^{51} +(11.3164 + 3.57090i) q^{52} +(-0.152952 - 0.570826i) q^{53} +(5.51538 - 9.08672i) q^{54} -3.60895i q^{55} -11.1031i q^{57} +(0.505672 + 0.306928i) q^{58} +(-1.37168 - 5.11916i) q^{59} +(19.4055 - 10.0962i) q^{60} +(2.57044 - 9.59300i) q^{61} +(-0.460627 + 1.57967i) q^{62} +(1.04964 - 7.93084i) q^{64} +(-11.0851 - 19.2000i) q^{65} +(2.76439 + 2.88838i) q^{66} +(-11.5083 + 3.08364i) q^{67} +(0.127928 - 2.91477i) q^{68} +(3.72210 - 3.72210i) q^{69} +2.89148i q^{71} +(-5.06720 + 14.9107i) q^{72} +(-0.554447 - 0.320110i) q^{73} +(0.0987583 + 0.00216619i) q^{74} +(-25.3397 - 6.78974i) q^{75} +(1.64032 + 7.40701i) q^{76} +(23.5788 + 6.87551i) q^{78} +(0.374910 + 0.649363i) q^{79} +(-11.4541 + 9.60219i) q^{80} +(2.64861 - 4.58752i) q^{81} +(3.39772 + 13.8922i) q^{82} +(-4.51473 - 4.51473i) q^{83} +(-3.85440 + 3.85440i) q^{85} +(4.72206 - 7.77971i) q^{86} +(1.06030 + 0.612164i) q^{87} +(-2.27087 - 1.51847i) q^{88} +(-13.3985 + 7.73562i) q^{89} +(25.7971 - 14.1490i) q^{90} +(-1.93317 + 3.03294i) q^{92} +(-0.881461 + 3.28966i) q^{93} +(-10.8417 - 11.3280i) q^{94} +(7.08694 - 12.2749i) q^{95} +(1.81202 - 16.4586i) 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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