LMFDB - Embedded newform 392.3.j.e.117.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(117,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("392.117");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.j (of order $6$, degree $2$, 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:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			117.2
Character	$\chi$	$=$	392.117
Dual form			392.3.j.e.325.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87135 - 0.705725i) q^{2} +(0.126628 + 0.219326i) q^{3} +(3.00390 + 2.64132i) q^{4} +(-1.78589 + 3.09325i) q^{5} +(-0.0821813 - 0.499801i) q^{6} +(-3.75731 - 7.06276i) q^{8} +(4.46793 - 7.73868i) q^{9} +O(q^{10})$	\(q+(-1.87135 - 0.705725i) q^{2} +(0.126628 + 0.219326i) q^{3} +(3.00390 + 2.64132i) q^{4} +(-1.78589 + 3.09325i) q^{5} +(-0.0821813 - 0.499801i) q^{6} +(-3.75731 - 7.06276i) q^{8} +(4.46793 - 7.73868i) q^{9} +(5.52501 - 4.52821i) q^{10} +(-6.82675 + 3.94142i) q^{11} +(-0.198932 + 0.993300i) q^{12} -18.1529 q^{13} -0.904575 q^{15} +(2.04687 + 15.8685i) q^{16} +(8.26180 - 4.76995i) q^{17} +(-13.8224 + 11.3287i) q^{18} +(12.4094 - 21.4938i) q^{19} +(-13.5349 + 4.57472i) q^{20} +(15.5568 - 2.55798i) q^{22} +(2.14949 - 3.72303i) q^{23} +(1.07327 - 1.71842i) q^{24} +(6.12120 + 10.6022i) q^{25} +(33.9704 + 12.8110i) q^{26} +4.54237 q^{27} -28.3630i q^{29} +(1.69278 + 0.638381i) q^{30} +(28.2372 - 16.3027i) q^{31} +(7.36842 - 31.1401i) q^{32} +(-1.72891 - 0.998189i) q^{33} +(-18.8270 + 3.09569i) q^{34} +(33.8616 - 11.4450i) q^{36} +(25.9006 + 14.9537i) q^{37} +(-38.3911 + 31.4648i) q^{38} +(-2.29867 - 3.98141i) q^{39} +(28.5570 + 0.991016i) q^{40} -45.2606i q^{41} -24.9109i q^{43} +(-30.9174 - 6.19196i) q^{44} +(15.9585 + 27.6409i) q^{45} +(-6.64990 + 5.45015i) q^{46} +(-44.0432 - 25.4284i) q^{47} +(-3.22119 + 2.45833i) q^{48} +(-3.97264 - 24.1604i) q^{50} +(2.09235 + 1.20802i) q^{51} +(-54.5296 - 47.9476i) q^{52} +(-54.3930 + 31.4038i) q^{53} +(-8.50036 - 3.20566i) q^{54} -28.1558i q^{55} +6.28554 q^{57} +(-20.0165 + 53.0771i) q^{58} +(-37.0048 - 64.0942i) q^{59} +(-2.71725 - 2.38927i) q^{60} +(25.2994 - 43.8198i) q^{61} +(-64.3469 + 10.5804i) q^{62} +(-35.7653 + 53.0740i) q^{64} +(32.4191 - 56.1515i) q^{65} +(2.53096 + 3.08810i) q^{66} +(108.673 - 62.7422i) q^{67} +(37.4166 + 7.49357i) q^{68} +1.08875 q^{69} -5.33822 q^{71} +(-71.4439 - 2.47932i) q^{72} +(23.6569 - 13.6583i) q^{73} +(-37.9159 - 46.2624i) q^{74} +(-1.55023 + 2.68508i) q^{75} +(94.0487 - 31.7880i) q^{76} +(1.49183 + 9.07283i) q^{78} +(51.5380 - 89.2664i) q^{79} +(-52.7408 - 22.0080i) q^{80} +(-39.6362 - 68.6519i) q^{81} +(-31.9415 + 84.6984i) q^{82} +51.5695 q^{83} +34.0744i q^{85} +(-17.5802 + 46.6170i) q^{86} +(6.22075 - 3.59155i) q^{87} +(53.4875 + 33.4066i) q^{88} +(-133.222 - 76.9158i) q^{89} +(-10.3570 - 62.9880i) q^{90} +(16.2906 - 5.50613i) q^{92} +(7.15123 + 4.12877i) q^{93} +(64.4749 + 78.6678i) q^{94} +(44.3238 + 76.7711i) q^{95} +(7.76289 - 2.32712i) q^{96} +47.0436i q^{97} +70.4400i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 4 * q^4 - 20 * q^8 - 32 * q^9	$ 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9} - 24 q^{10} + 18 q^{12} + 28 q^{15} + 16 q^{16} + 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} + 30 q^{24} - 32 q^{25} + 30 q^{26} + 22 q^{30} + 6 q^{31} + 88 q^{32} + 6 q^{33} + 256 q^{36} - 6 q^{38} - 20 q^{39} - 102 q^{40} - 42 q^{44} + 68 q^{46} + 294 q^{47} + 400 q^{50} + 168 q^{52} - 330 q^{54} + 124 q^{57} - 22 q^{58} - 62 q^{60} - 520 q^{64} - 52 q^{65} + 306 q^{66} + 456 q^{68} - 136 q^{71} + 96 q^{72} - 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} - 276 q^{80} - 18 q^{81} + 642 q^{82} + 168 q^{86} - 48 q^{87} + 50 q^{88} + 150 q^{89} + 1020 q^{92} - 618 q^{94} + 290 q^{95} - 1044 q^{96}+O(q^{100}) $ 28 * q - 2 * q^2 - 4 * q^4 - 20 * q^8 - 32 * q^9 - 24 * q^10 + 18 * q^12 + 28 * q^15 + 16 * q^16 + 6 * q^17 - 42 * q^18 - 92 * q^22 + 30 * q^23 + 30 * q^24 - 32 * q^25 + 30 * q^26 + 22 * q^30 + 6 * q^31 + 88 * q^32 + 6 * q^33 + 256 * q^36 - 6 * q^38 - 20 * q^39 - 102 * q^40 - 42 * q^44 + 68 * q^46 + 294 * q^47 + 400 * q^50 + 168 * q^52 - 330 * q^54 + 124 * q^57 - 22 * q^58 - 62 * q^60 - 520 * q^64 - 52 * q^65 + 306 * q^66 + 456 * q^68 - 136 * q^71 + 96 * q^72 - 234 * q^73 - 138 * q^74 - 956 * q^78 - 162 * q^79 - 276 * q^80 - 18 * q^81 + 642 * q^82 + 168 * q^86 - 48 * q^87 + 50 * q^88 + 150 * q^89 + 1020 * q^92 - 618 * q^94 + 290 * q^95 - 1044 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.87135	−	0.705725i	−0.935675	−	0.352863i
$2$	−1.87135	−	0.705725i	−0.935675	−	0.352863i
$3$	0.126628	+	0.219326i	0.0422093	+	0.0731087i	0.886358	−	0.463000i	$-0.153227\pi$
$3$	0.126628	+	0.219326i	0.0422093	+	0.0731087i	−0.844149	+	0.536109i	$0.819894\pi$
$4$	3.00390	+	2.64132i	0.750976	+	0.660330i
$5$	−1.78589	+	3.09325i	−0.357178	+	0.618650i	−0.987488	−	0.157693i	$-0.949594\pi$
$5$	−1.78589	+	3.09325i	−0.357178	+	0.618650i	0.630310	+	0.776343i	$0.282928\pi$
$6$	−0.0821813	−	0.499801i	−0.0136969	−	0.0833001i
$7$		0			0
$7$		0			0
$8$	−3.75731	−	7.06276i	−0.469664	−	0.882845i
$9$	4.46793	−	7.73868i	0.496437	−	0.859854i
$10$	5.52501	−	4.52821i	0.552501	−	0.452821i
$11$	−6.82675	+	3.94142i	−0.620613	+	0.358311i	−0.777108	−	0.629368i	$-0.783314\pi$
$11$	−6.82675	+	3.94142i	−0.620613	+	0.358311i	0.156494	+	0.987679i	$0.449981\pi$
$12$	−0.198932	+	0.993300i	−0.0165777	+	0.0827750i
$13$	−18.1529			−1.39638			−0.698189	−	0.715914i	$-0.746010\pi$
$13$	−18.1529			−1.39638			−0.698189	+	0.715914i	$0.746010\pi$
$14$		0			0
$15$	−0.904575			−0.0603050
$16$	2.04687	+	15.8685i	0.127929	+	0.991783i
$17$	8.26180	−	4.76995i	0.485988	−	0.280585i	−0.236920	−	0.971529i	$-0.576138\pi$
$17$	8.26180	−	4.76995i	0.485988	−	0.280585i	0.722909	+	0.690944i	$0.242805\pi$
$18$	−13.8224	+	11.3287i	−0.767914	+	0.629370i
$19$	12.4094	−	21.4938i	0.653129	−	1.13125i	−0.329231	−	0.944250i	$-0.606789\pi$
$19$	12.4094	−	21.4938i	0.653129	−	1.13125i	0.982359	−	0.187003i	$-0.0598773\pi$
$20$	−13.5349	+	4.57472i	−0.676745	+	0.228736i
$21$		0			0
$22$	15.5568	−	2.55798i	0.707127	−	0.116272i
$23$	2.14949	−	3.72303i	0.0934563	−	0.161871i	−0.815507	−	0.578747i	$-0.803542\pi$
$23$	2.14949	−	3.72303i	0.0934563	−	0.161871i	0.908963	+	0.416876i	$0.136875\pi$
$24$	1.07327	−	1.71842i	0.0447195	−	0.0716008i
$25$	6.12120	+	10.6022i	0.244848	+	0.424089i
$26$	33.9704	+	12.8110i	1.30656	+	0.492729i
$27$	4.54237			0.168236
$28$		0			0
$29$		−	28.3630i		−	0.978035i	−0.872274	−	0.489017i	$-0.837356\pi$
$29$		−	28.3630i		−	0.978035i	0.872274	−	0.489017i	$-0.162644\pi$
$30$	1.69278	+	0.638381i	0.0564259	+	0.0212794i
$31$	28.2372	−	16.3027i	0.910876	−	0.525895i	0.0301634	−	0.999545i	$-0.490397\pi$
$31$	28.2372	−	16.3027i	0.910876	−	0.525895i	0.880713	+	0.473650i	$0.157064\pi$
$32$	7.36842	−	31.1401i	0.230263	−	0.973128i
$33$	−1.72891	−	0.998189i	−0.0523914	−	0.0302482i
$34$	−18.8270	+	3.09569i	−0.553735	+	0.0910497i
$35$		0			0
$36$	33.8616	−	11.4450i	0.940599	−	0.317917i
$37$	25.9006	+	14.9537i	0.700017	+	0.404155i	0.807354	−	0.590068i	$-0.200899\pi$
$37$	25.9006	+	14.9537i	0.700017	+	0.404155i	−0.107337	+	0.994223i	$0.534232\pi$
$38$	−38.3911	+	31.4648i	−1.01029	+	0.828020i
$39$	−2.29867	−	3.98141i	−0.0589402	−	0.102087i
$40$	28.5570	+	0.991016i	0.713926	+	0.0247754i
$41$		−	45.2606i		−	1.10392i	−0.833872	−	0.551958i	$-0.813881\pi$
$41$		−	45.2606i		−	1.10392i	0.833872	−	0.551958i	$-0.186119\pi$
$42$		0			0
$43$		−	24.9109i		−	0.579323i	−0.957129	−	0.289661i	$-0.906457\pi$
$43$		−	24.9109i		−	0.579323i	0.957129	−	0.289661i	$-0.0935427\pi$
$44$	−30.9174	−	6.19196i	−0.702669	−	0.140726i
$45$	15.9585	+	27.6409i	0.354632	+	0.614242i
$46$	−6.64990	+	5.45015i	−0.144563	+	0.118481i
$47$	−44.0432	−	25.4284i	−0.937090	−	0.541029i	−0.0480430	−	0.998845i	$-0.515298\pi$
$47$	−44.0432	−	25.4284i	−0.937090	−	0.541029i	−0.889047	+	0.457816i	$0.848632\pi$
$48$	−3.22119	+	2.45833i	−0.0671082	+	0.0512153i
$49$		0			0
$50$	−3.97264	−	24.1604i	−0.0794529	−	0.483207i
$51$	2.09235	+	1.20802i	0.0410265	+	0.0236867i
$52$	−54.5296	−	47.9476i	−1.04865	−	0.922069i
$53$	−54.3930	+	31.4038i	−1.02628	+	0.592525i	−0.915918	−	0.401366i	$-0.868535\pi$
$53$	−54.3930	+	31.4038i	−1.02628	+	0.592525i	−0.110365	+	0.993891i	$0.535202\pi$
$54$	−8.50036	−	3.20566i	−0.157414	−	0.0593641i
$55$		−	28.1558i		−	0.511924i
$56$		0			0
$57$	6.28554			0.110273
$58$	−20.0165	+	53.0771i	−0.345112	+	0.915123i
$59$	−37.0048	−	64.0942i	−0.627200	−	1.08634i	−0.988111	−	0.153741i	$-0.950868\pi$
$59$	−37.0048	−	64.0942i	−0.627200	−	1.08634i	0.360912	−	0.932600i	$-0.382466\pi$
$60$	−2.71725	−	2.38927i	−0.0452876	−	0.0398212i
$61$	25.2994	−	43.8198i	0.414743	−	0.718357i	−0.580658	−	0.814148i	$-0.697205\pi$
$61$	25.2994	−	43.8198i	0.414743	−	0.718357i	0.995401	+	0.0957908i	$0.0305380\pi$
$62$	−64.3469	+	10.5804i	−1.03785	+	0.170652i
$63$		0			0
$64$	−35.7653	+	53.0740i	−0.558832	+	0.829281i
$65$	32.4191	−	56.1515i	0.498755	−	0.863869i
$66$	2.53096	+	3.08810i	0.0383478	+	0.0467894i
$67$	108.673	−	62.7422i	1.62198	−	0.936451i	0.635592	−	0.772025i	$-0.280756\pi$
$67$	108.673	−	62.7422i	1.62198	−	0.936451i	0.986389	−	0.164426i	$-0.0525772\pi$
$68$	37.4166	+	7.49357i	0.550244	+	0.110200i
$69$	1.08875			0.0157789
$70$		0			0
$71$	−5.33822			−0.0751863			−0.0375931	−	0.999293i	$-0.511969\pi$
$71$	−5.33822			−0.0751863			−0.0375931	+	0.999293i	$0.511969\pi$
$72$	−71.4439	−	2.47932i	−0.992276	−	0.0344350i
$73$	23.6569	−	13.6583i	0.324067	−	0.187100i	−0.329137	−	0.944282i	$-0.606758\pi$
$73$	23.6569	−	13.6583i	0.324067	−	0.187100i	0.653204	+	0.757182i	$0.273424\pi$
$74$	−37.9159	−	46.2624i	−0.512378	−	0.625168i
$75$	−1.55023	+	2.68508i	−0.0206697	+	0.0358010i
$76$	94.0487	−	31.7880i	1.23748	−	0.418263i
$77$		0			0
$78$	1.49183	+	9.07283i	0.0191260	+	0.116318i
$79$	51.5380	−	89.2664i	0.652380	−	1.12995i	−0.330164	−	0.943924i	$-0.607104\pi$
$79$	51.5380	−	89.2664i	0.652380	−	1.12995i	0.982544	−	0.186031i	$-0.0595626\pi$
$80$	−52.7408	−	22.0080i	−0.659261	−	0.275100i
$81$	−39.6362	−	68.6519i	−0.489336	−	0.847554i
$82$	−31.9415	+	84.6984i	−0.389531	+	1.03291i
$83$	51.5695			0.621319			0.310660	−	0.950521i	$-0.399450\pi$
$83$	51.5695			0.621319			0.310660	+	0.950521i	$0.399450\pi$
$84$		0			0
$85$			34.0744i			0.400876i
$86$	−17.5802	+	46.6170i	−0.204421	+	0.542058i
$87$	6.22075	−	3.59155i	0.0715029	−	0.0412822i
$88$	53.4875	+	33.4066i	0.607813	+	0.379620i
$89$	−133.222	−	76.9158i	−1.49688	−	0.864222i	−0.496883	−	0.867818i	$-0.665522\pi$
$89$	−133.222	−	76.9158i	−1.49688	−	0.864222i	−0.999994	+	0.00359545i	$0.998856\pi$
$90$	−10.3570	−	62.9880i	−0.115078	−	0.699867i
$91$		0			0
$92$	16.2906	−	5.50613i	0.177072	−	0.0598493i
$93$	7.15123	+	4.12877i	0.0768950	+	0.0443953i
$94$	64.4749	+	78.6678i	0.685903	+	0.836892i
$95$	44.3238	+	76.7711i	0.466566	+	0.808117i
$96$	7.76289	−	2.32712i	0.0808634	−	0.0242409i
$97$			47.0436i			0.484986i	0.970153	+	0.242493i	$0.0779651\pi$
$97$			47.0436i			0.484986i	−0.970153	+	0.242493i	$0.922035\pi$
$98$		0			0
$99$			70.4400i			0.711516i
$100$	−9.61637	+	48.0161i	−0.0961637	+	0.480161i
$101$	74.6727	+	129.337i	0.739333	+	1.28056i	0.952796	+	0.303612i	$0.0981926\pi$
$101$	74.6727	+	129.337i	0.739333	+	1.28056i	−0.213462	+	0.976951i	$0.568474\pi$
$102$	−3.06299	−	3.73725i	−0.0300293	−	0.0366397i
$103$	17.1847	+	9.92160i	0.166842	+	0.0963262i	0.581096	−	0.813835i	$-0.302624\pi$
$103$	17.1847	+	9.92160i	0.166842	+	0.0963262i	−0.414254	+	0.910161i	$0.635957\pi$
$104$	68.2061	+	128.210i	0.655827	+	1.23279i
$105$		0			0
$106$	123.951	−	20.3810i	1.16935	−	0.192274i
$107$	7.91877	+	4.57190i	0.0740072	+	0.0427281i	0.536547	−	0.843870i	$-0.319728\pi$
$107$	7.91877	+	4.57190i	0.0740072	+	0.0427281i	−0.462540	+	0.886599i	$0.653062\pi$
$108$	13.6448	+	11.9978i	0.126341	+	0.111091i
$109$	−103.229	+	59.5992i	−0.947053	+	0.546781i	−0.892164	−	0.451711i	$-0.850814\pi$
$109$	−103.229	+	59.5992i	−0.947053	+	0.546781i	−0.0548888	+	0.998492i	$0.517480\pi$
$110$	−19.8703	+	52.6894i	−0.180639	+	0.478994i
$111$			7.57425i			0.0682365i
$112$		0			0
$113$	−124.011			−1.09744			−0.548720	−	0.836006i	$-0.684885\pi$
$113$	−124.011			−1.09744			−0.548720	+	0.836006i	$0.684885\pi$
$114$	−11.7624	−	4.43586i	−0.103179	−	0.0389111i
$115$	7.67752	+	13.2979i	0.0667611	+	0.115634i
$116$	74.9157	−	85.1997i	0.645825	−	0.734480i
$117$	−81.1059	+	140.480i	−0.693213	+	1.20068i
$118$	24.0160	+	146.058i	0.203526	+	1.23778i
$119$		0			0
$120$	3.39877	+	6.38880i	0.0283231	+	0.0532400i
$121$	−29.4303	+	50.9749i	−0.243226	+	0.421280i
$122$	−78.2687	+	64.1477i	−0.641546	+	0.525801i
$123$	9.92683	−	5.73126i	0.0807059	−	0.0465956i
$124$	127.882	+	25.6115i	1.03131	+	0.206545i
$125$	−133.022			−1.06417
$126$		0			0
$127$	−57.6144			−0.453656			−0.226828	−	0.973935i	$-0.572836\pi$
$127$	−57.6144			−0.453656			−0.226828	+	0.973935i	$0.572836\pi$
$128$	104.385	−	74.0795i	0.815508	−	0.578746i
$129$	5.46361	−	3.15441i	0.0423535	−	0.0244528i
$130$	−100.295	+	82.2001i	−0.771500	+	0.632309i
$131$	62.1497	−	107.646i	0.474425	−	0.821728i	−0.525146	−	0.851012i	$-0.675989\pi$
$131$	62.1497	−	107.646i	0.474425	−	0.821728i	0.999571	+	0.0292837i	$0.00932261\pi$
$132$	−2.55696	−	7.56508i	−0.0193709	−	0.0573112i
$133$		0			0
$134$	−247.644	+	40.7196i	−1.84809	+	0.303877i
$135$	−8.11216	+	14.0507i	−0.0600901	+	0.104079i
$136$	−64.7312	−	40.4290i	−0.475965	−	0.297272i
$137$	84.7404	+	146.775i	0.618543	+	1.07135i	0.989752	+	0.142799i	$0.0456102\pi$
$137$	84.7404	+	146.775i	0.618543	+	1.07135i	−0.371208	+	0.928550i	$0.621056\pi$
$138$	−2.03742	−	0.768355i	−0.0147639	−	0.00556779i
$139$	266.497			1.91725			0.958624	−	0.284677i	$-0.0918862\pi$
$139$	266.497			1.91725			0.958624	+	0.284677i	$0.0918862\pi$
$140$		0			0
$141$		−	12.8798i		−	0.0913459i
$142$	9.98969	+	3.76732i	0.0703499	+	0.0265304i
$143$	123.925	−	71.5483i	0.866610	−	0.500338i
$144$	131.947	+	55.0594i	0.916297	+	0.382357i
$145$	87.7339	+	50.6532i	0.605061	+	0.349332i
$146$	−53.9093	+	8.86421i	−0.369242	+	0.0607138i
$147$		0			0
$148$	38.3054	+	113.331i	0.258820	+	0.765753i
$149$	26.6902	+	15.4096i	0.179129	+	0.103420i	0.586883	−	0.809672i	$-0.300355\pi$
$149$	26.6902	+	15.4096i	0.179129	+	0.103420i	−0.407754	+	0.913092i	$0.633688\pi$
$150$	4.79595	−	3.93068i	0.0319730	−	0.0262046i
$151$	−11.7448	−	20.3425i	−0.0777800	−	0.134719i	0.824512	−	0.565845i	$-0.191450\pi$
$151$	−11.7448	−	20.3425i	−0.0777800	−	0.134719i	−0.902292	+	0.431126i	$0.858116\pi$
$152$	−198.432	−	6.88618i	−1.30547	−	0.0453038i
$153$		−	85.2473i		−	0.557172i
$154$		0			0
$155$			116.460i			0.751352i
$156$	3.61119	−	18.0313i	0.0231487	−	0.115585i
$157$	63.8147	+	110.530i	0.406463	+	0.704015i	0.994491	−	0.104826i	$-0.0334287\pi$
$157$	63.8147	+	110.530i	0.406463	+	0.704015i	−0.588028	+	0.808841i	$0.700095\pi$
$158$	−159.443	+	130.677i	−1.00913	+	0.827070i
$159$	−13.7754	−	7.95320i	−0.0866374	−	0.0500202i
$160$	83.1650	+	78.4052i	0.519781	+	0.490032i
$161$		0			0
$162$	25.7238	+	156.444i	0.158789	+	0.965704i
$163$	−138.291	−	79.8421i	−0.848409	−	0.489829i	0.0117050	−	0.999931i	$-0.496274\pi$
$163$	−138.291	−	79.8421i	−0.848409	−	0.489829i	−0.860114	+	0.510103i	$0.829607\pi$
$164$	119.548	−	135.958i	0.728949	−	0.829015i
$165$	6.17530	−	3.56531i	0.0374261	−	0.0216080i
$166$	−96.5046	−	36.3939i	−0.581353	−	0.219240i
$167$			142.792i			0.855042i	0.904005	+	0.427521i	$0.140613\pi$
$167$			142.792i			0.855042i	−0.904005	+	0.427521i	$0.859387\pi$
$168$		0			0
$169$	160.528			0.949869
$170$	24.0472	−	63.7652i	0.141454	−	0.375089i
$171$	−110.889	−	192.066i	−0.648474	−	1.12319i
$172$	65.7976	−	74.8299i	0.382544	−	0.435057i
$173$	−97.8898	+	169.550i	−0.565837	+	0.980059i	0.431134	+	0.902288i	$0.358114\pi$
$173$	−97.8898	+	169.550i	−0.565837	+	0.980059i	−0.996971	+	0.0777710i	$0.975220\pi$
$174$	−14.1758	+	2.33091i	−0.0814704	+	0.0133960i
$175$		0			0
$176$	−76.5181	−	100.263i	−0.434762	−	0.569675i
$177$	9.37168	−	16.2322i	0.0529474	−	0.0917075i
$178$	195.024	+	237.955i	1.09564	+	1.33682i
$179$	129.477	−	74.7535i	0.723334	−	0.417617i	−0.0926444	−	0.995699i	$-0.529532\pi$
$179$	129.477	−	74.7535i	0.723334	−	0.417617i	0.815979	+	0.578082i	$0.196199\pi$
$180$	−25.0707	+	125.182i	−0.139282	+	0.695455i
$181$	−91.2994			−0.504417			−0.252208	−	0.967673i	$-0.581157\pi$
$181$	−91.2994			−0.504417			−0.252208	+	0.967673i	$0.581157\pi$
$182$		0			0
$183$	12.8144			0.0700242
$184$	−34.3712	−	1.19279i	−0.186800	−	0.00648253i
$185$	−92.5114	+	53.4115i	−0.500062	+	0.288711i
$186$	−10.4687	−	12.7732i	−0.0562833	−	0.0686730i
$187$	−37.6008	+	65.1265i	−0.201074	+	0.348270i
$188$	−65.1372	−	192.717i	−0.346474	−	1.02509i
$189$		0			0
$190$	−28.7661	−	174.946i	−0.151400	−	0.920769i
$191$	−13.9140	+	24.0997i	−0.0728480	+	0.126176i	−0.900148	−	0.435583i	$-0.856542\pi$
$191$	−13.9140	+	24.0997i	−0.0728480	+	0.126176i	0.827300	+	0.561760i	$0.189875\pi$
$192$	−16.1694	−	1.12361i	−0.0842156	−	0.00585212i
$193$	−121.192	−	209.911i	−0.627938	−	1.08762i	−0.987965	−	0.154678i	$-0.950566\pi$
$193$	−121.192	−	209.911i	−0.627938	−	1.08762i	0.360027	−	0.932942i	$-0.382767\pi$
$194$	33.1999	−	88.0351i	0.171133	−	0.453789i
$195$	16.4207			0.0842085
$196$		0			0
$197$		−	94.7050i		−	0.480736i	−0.970682	−	0.240368i	$-0.922732\pi$
$197$		−	94.7050i		−	0.480736i	0.970682	−	0.240368i	$-0.0772682\pi$
$198$	49.7113	−	131.818i	0.251067	−	0.665747i
$199$	−267.738	+	154.579i	−1.34542	+	0.776778i	−0.987597	−	0.157011i	$-0.949814\pi$
$199$	−267.738	+	154.579i	−1.34542	+	0.776778i	−0.357823	+	0.933790i	$0.616481\pi$
$200$	51.8818	−	83.0684i	0.259409	−	0.415342i
$201$	27.5220	+	15.8899i	0.136926	+	0.0790540i
$202$	−48.4624	−	294.733i	−0.239913	−	1.45907i
$203$		0			0
$204$	3.09445	+	9.15534i	0.0151689	+	0.0448791i
$205$	140.002	+	80.8304i	0.682938	+	0.394295i
$206$	−25.1567	−	30.6945i	−0.122120	−	0.149002i
$207$	−19.2076	−	33.2685i	−0.0927903	−	0.160717i
$208$	−37.1566	−	288.060i	−0.178637	−	1.38490i
$209$			195.644i			0.936094i
$210$		0			0
$211$		−	125.864i		−	0.596514i	−0.954486	−	0.298257i	$-0.903595\pi$
$211$		−	125.864i		−	0.596514i	0.954486	−	0.298257i	$-0.0964052\pi$
$212$	−246.339	−	49.3352i	−1.16198	−	0.232713i
$213$	−0.675969	−	1.17081i	−0.00317356	−	0.00549677i
$214$	−11.5923	−	14.1441i	−0.0541695	−	0.0660940i
$215$	77.0556	+	44.4881i	0.358398	+	0.206921i
$216$	−17.0671	−	32.0817i	−0.0790142	−	0.148526i
$217$		0			0
$218$	235.238	−	38.6797i	1.07907	−	0.177430i
$219$	5.99125	+	3.45905i	0.0273573	+	0.0157947i
$220$	74.3684	−	84.5773i	0.338038	−	0.384442i
$221$	−149.976	+	86.5885i	−0.678623	+	0.391803i
$222$	5.34534	−	14.1741i	0.0240781	−	0.0638472i
$223$		−	8.94619i		−	0.0401174i	−0.999799	−	0.0200587i	$-0.993615\pi$
$223$		−	8.94619i		−	0.0401174i	0.999799	−	0.0200587i	$-0.00638532\pi$
$224$		0			0
$225$	109.396			0.486206
$226$	232.067	+	87.5175i	1.02685	+	0.387246i
$227$	−136.347	−	236.160i	−0.600647	−	1.04035i	−0.992723	−	0.120419i	$-0.961576\pi$
$227$	−136.347	−	236.160i	−0.600647	−	1.04035i	0.392076	−	0.919933i	$-0.371757\pi$
$228$	18.8811	+	16.6021i	0.0828120	+	0.0728162i
$229$	165.611	−	286.846i	0.723191	−	1.25260i	−0.236523	−	0.971626i	$-0.576008\pi$
$229$	165.611	−	286.846i	0.723191	−	1.25260i	0.959714	−	0.280978i	$-0.0906588\pi$
$230$	−4.98269	−	30.3032i	−0.0216639	−	0.131753i
$231$		0			0
$232$	−200.321	+	106.569i	−0.863453	+	0.459347i
$233$	−79.1185	+	137.037i	−0.339564	+	0.588143i	−0.984351	−	0.176220i	$-0.943613\pi$
$233$	−79.1185	+	137.037i	−0.339564	+	0.588143i	0.644786	+	0.764363i	$0.276946\pi$
$234$	250.918	−	205.648i	1.07230	−	0.878837i
$235$	157.313	−	90.8245i	0.669416	−	0.386487i
$236$	58.1343	−	290.274i	0.246332	−	1.22997i
$237$	26.1046			0.110146
$238$		0			0
$239$	48.9981			0.205013			0.102507	−	0.994732i	$-0.467314\pi$
$239$	48.9981			0.205013			0.102507	+	0.994732i	$0.467314\pi$
$240$	−1.85154	−	14.3543i	−0.00771477	−	0.0598095i
$241$	−170.914	+	98.6771i	−0.709186	+	0.409449i	−0.810759	−	0.585379i	$-0.800946\pi$
$241$	−170.914	+	98.6771i	−0.709186	+	0.409449i	0.101574	+	0.994828i	$0.467612\pi$
$242$	91.0487	−	74.6221i	0.376234	−	0.308356i
$243$	30.4787	−	52.7907i	0.125427	−	0.217246i
$244$	191.739	−	64.8067i	0.785815	−	0.265601i
$245$		0			0
$246$	−22.6213	+	3.71957i	−0.0919564	+	0.0151202i
$247$	−225.267	+	390.175i	−0.912014	+	1.57965i
$248$	−221.238	−	138.178i	−0.892089	−	0.557170i
$249$	6.53014	+	11.3105i	0.0262255	+	0.0454239i
$250$	248.930	+	93.8767i	0.995720	+	0.375507i
$251$	−315.497			−1.25696			−0.628480	−	0.777826i	$-0.716323\pi$
$251$	−315.497			−1.25696			−0.628480	+	0.777826i	$0.716323\pi$
$252$		0			0
$253$			33.8883i			0.133946i
$254$	107.817	+	40.6599i	0.424475	+	0.160078i
$255$	−7.47341	+	4.31478i	−0.0293075	+	0.0169207i
$256$	−247.621	+	64.9616i	−0.967268	+	0.253756i
$257$	329.533	+	190.256i	1.28223	+	0.740296i	0.977256	−	0.212065i	$-0.0680188\pi$
$257$	329.533	+	190.256i	1.28223	+	0.740296i	0.304974	+	0.952361i	$0.401352\pi$
$258$	−12.4505	+	2.04721i	−0.0482576	+	0.00793492i
$259$		0			0
$260$	245.698	−	83.0445i	0.944991	−	0.319402i
$261$	−219.492	−	126.724i	−0.840967	−	0.485532i
$262$	−192.273	+	157.584i	−0.733865	+	0.601464i
$263$	−98.1636	−	170.024i	−0.373246	−	0.646480i	0.616817	−	0.787106i	$-0.288422\pi$
$263$	−98.1636	−	170.024i	−0.373246	−	0.646480i	−0.990063	+	0.140626i	$0.955088\pi$
$264$	−0.553910	+	15.9614i	−0.00209814	+	0.0604599i
$265$		−	224.335i		−	0.846547i
$266$		0			0
$267$		−	38.9588i		−	0.145913i
$268$	492.165	+	98.5678i	1.83644	+	0.367790i
$269$	−51.1557	−	88.6043i	−0.190170	−	0.329384i	0.755137	−	0.655568i	$-0.227571\pi$
$269$	−51.1557	−	88.6043i	−0.190170	−	0.329384i	−0.945306	+	0.326184i	$0.894237\pi$
$270$	25.0966	−	20.5688i	0.0929504	−	0.0761807i
$271$	221.981	+	128.161i	0.819118	+	0.472918i	0.850112	−	0.526602i	$-0.176534\pi$
$271$	221.981	+	128.161i	0.819118	+	0.472918i	−0.0309944	+	0.999520i	$0.509867\pi$
$272$	92.6030	+	121.339i	0.340452	+	0.446100i
$273$		0			0
$274$	−54.9964	−	334.470i	−0.200717	−	1.22070i
$275$	−83.5757	−	48.2525i	−0.303912	−	0.175464i
$276$	3.27048	+	2.87572i	0.0118496	+	0.0104193i
$277$	−170.372	+	98.3646i	−0.615063	+	0.355107i	−0.774944	−	0.632029i	$-0.782222\pi$
$277$	−170.372	+	98.3646i	−0.615063	+	0.355107i	0.159881	+	0.987136i	$0.448889\pi$
$278$	−498.710	−	188.074i	−1.79392	−	0.676525i
$279$		−	291.358i		−	1.04429i
$280$		0			0
$281$	−70.2923			−0.250151			−0.125075	−	0.992147i	$-0.539917\pi$
$281$	−70.2923			−0.250151			−0.125075	+	0.992147i	$0.539917\pi$
$282$	−9.08959	+	24.1026i	−0.0322326	+	0.0854701i
$283$	148.495	+	257.201i	0.524718	+	0.908838i	0.999586	+	0.0287807i	$0.00916244\pi$
$283$	148.495	+	257.201i	0.524718	+	0.908838i	−0.474868	+	0.880057i	$0.657504\pi$
$284$	−16.0355	−	14.1000i	−0.0564631	−	0.0496477i
$285$	−11.2253	+	19.4427i	−0.0393869	+	0.0682201i
$286$	−282.401	+	46.4347i	−0.987416	+	0.162359i
$287$		0			0
$288$	−208.062	−	196.154i	−0.722437	−	0.681089i
$289$	−98.9951	+	171.465i	−0.342544	+	0.593303i
$290$	−128.434	−	156.706i	−0.442874	−	0.540365i
$291$	−10.3179	+	5.95704i	−0.0354567	+	0.0204709i
$292$	107.139	+	21.4571i	0.366914	+	0.0734834i
$293$	−135.561			−0.462665			−0.231333	−	0.972875i	$-0.574309\pi$
$293$	−135.561			−0.462665			−0.231333	+	0.972875i	$0.574309\pi$
$294$		0			0
$295$	264.346			0.896087
$296$	8.29805	−	239.116i	0.0280339	−	0.807824i
$297$	−31.0096	+	17.9034i	−0.104409	+	0.0602808i
$298$	−39.0718	−	47.6727i	−0.131113	−	0.159976i
$299$	−39.0196	+	67.5839i	−0.130500	+	0.226033i
$300$	−11.7489	+	3.97106i	−0.0391630	+	0.0132369i
$301$		0			0
$302$	7.62233	+	46.3566i	0.0252395	+	0.153499i
$303$	−18.9113	+	32.7553i	−0.0624136	+	0.108103i
$304$	366.475	+	152.925i	1.20551	+	0.503042i
$305$	90.3637	+	156.515i	0.296274	+	0.513162i
$306$	−60.1612	+	159.527i	−0.196605	+	0.521332i
$307$	−76.2052			−0.248225			−0.124113	−	0.992268i	$-0.539608\pi$
$307$	−76.2052			−0.248225			−0.124113	+	0.992268i	$0.539608\pi$
$308$		0			0
$309$			5.02541i			0.0162635i
$310$	82.1885	−	217.937i	0.265124	−	0.703021i
$311$	171.554	−	99.0468i	0.551621	−	0.318479i	−0.198154	−	0.980171i	$-0.563495\pi$
$311$	171.554	−	99.0468i	0.551621	−	0.318479i	0.749776	+	0.661692i	$0.230161\pi$
$312$	−19.4829	+	31.1943i	−0.0624453	+	0.0999817i
$313$	47.9693	+	27.6951i	0.153257	+	0.0884827i	0.574667	−	0.818387i	$-0.305132\pi$
$313$	47.9693	+	27.6951i	0.153257	+	0.0884827i	−0.421411	+	0.906870i	$0.638465\pi$
$314$	−41.4156	−	251.877i	−0.131897	−	0.802155i
$315$		0			0
$316$	390.596	−	132.019i	1.23606	−	0.417783i
$317$	−259.080	−	149.580i	−0.817289	−	0.471862i	0.0321920	−	0.999482i	$-0.489751\pi$
$317$	−259.080	−	149.580i	−0.817289	−	0.471862i	−0.849481	+	0.527620i	$0.823085\pi$
$318$	20.1657	+	24.6048i	0.0634143	+	0.0773737i
$319$	111.791	+	193.627i	0.350441	+	0.606981i
$320$	−100.298	−	205.415i	−0.313432	−	0.641923i
$321$			2.31572i			0.00721409i
$322$		0			0
$323$		−	236.770i		−	0.733034i
$324$	62.2683	−	310.915i	0.192186	−	0.959616i
$325$	−111.117	−	192.461i	−0.341900	−	0.592188i
$326$	202.444	+	247.008i	0.620992	+	0.757693i
$327$	−26.1433	−	15.0938i	−0.0799490	−	0.0461586i
$328$	−319.665	+	170.058i	−0.974588	+	0.518469i
$329$		0			0
$330$	−14.0723	+	2.31388i	−0.0426433	+	0.00701176i
$331$	325.087	+	187.689i	0.982135	+	0.567036i	0.902914	−	0.429821i	$-0.141423\pi$
$331$	325.087	+	187.689i	0.982135	+	0.567036i	0.0792209	+	0.996857i	$0.474757\pi$
$332$	154.910	+	136.212i	0.466596	+	0.410276i
$333$	231.445	−	133.625i	0.695029	−	0.401275i
$334$	100.772	−	267.214i	0.301712	−	0.800041i
$335$			448.203i			1.33792i
$336$		0			0
$337$	−4.99043			−0.0148084			−0.00740419	−	0.999973i	$-0.502357\pi$
$337$	−4.99043			−0.0148084			−0.00740419	+	0.999973i	$0.502357\pi$
$338$	−300.404	−	113.289i	−0.888769	−	0.335173i
$339$	−15.7032	−	27.1988i	−0.0463222	−	0.0802324i
$340$	−90.0014	+	102.356i	−0.264710	+	0.301048i
$341$	−128.512	+	222.589i	−0.376868	+	0.652755i
$342$	71.9668	+	437.679i	0.210429	+	1.27976i
$343$		0			0
$344$	−175.940	+	93.5978i	−0.511452	+	0.272087i
$345$	−1.94438	+	3.36776i	−0.00563588	+	0.00976163i
$346$	302.842	−	248.204i	0.875266	−	0.717354i
$347$	−320.772	+	185.198i	−0.924414	+	0.533711i	−0.885041	−	0.465514i	$-0.845870\pi$
$347$	−320.772	+	185.198i	−0.924414	+	0.533711i	−0.0393734	+	0.999225i	$0.512536\pi$
$348$	28.1730	+	5.64231i	0.0809568	+	0.0162135i
$349$	−25.6801			−0.0735821			−0.0367910	−	0.999323i	$-0.511714\pi$
$349$	−25.6801			−0.0735821			−0.0367910	+	0.999323i	$0.511714\pi$
$350$		0			0
$351$	−82.4571			−0.234921
$352$	72.4340	+	241.628i	0.205779	+	0.686442i
$353$	229.938	−	132.755i	0.651383	−	0.376076i	−0.137603	−	0.990487i	$-0.543940\pi$
$353$	229.938	−	132.755i	0.651383	−	0.376076i	0.788986	+	0.614411i	$0.210606\pi$
$354$	−28.9932	+	23.7624i	−0.0819017	+	0.0671253i
$355$	9.53348	−	16.5125i	0.0268549	−	0.0465140i
$356$	−197.027	−	582.929i	−0.553446	−	1.63744i
$357$		0			0
$358$	−295.052	+	48.5148i	−0.824167	+	0.135516i
$359$	275.228	−	476.709i	0.766651	−	1.32788i	−0.172718	−	0.984971i	$-0.555255\pi$
$359$	275.228	−	476.709i	0.766651	−	1.32788i	0.939369	−	0.342908i	$-0.111412\pi$
$360$	135.260	−	216.566i	0.375722	−	0.601573i
$361$	−127.489	−	220.817i	−0.353155	−	0.611682i
$362$	170.853	+	64.4323i	0.471970	+	0.177990i
$363$	−14.9068			−0.0410656
$364$		0			0
$365$			97.5689i			0.267312i
$366$	−23.9803	−	9.04347i	−0.0655199	−	0.0247089i
$367$	−180.099	+	103.980i	−0.490732	+	0.283324i	−0.724878	−	0.688877i	$-0.758104\pi$
$367$	−180.099	+	103.980i	−0.490732	+	0.283324i	0.234146	+	0.972201i	$0.424771\pi$
$368$	63.4788	+	26.4888i	0.172497	+	0.0719803i
$369$	−350.257	−	202.221i	−0.949207	−	0.548025i
$370$	210.815	−	34.6639i	0.569770	−	0.0936863i
$371$		0			0
$372$	10.5762	+	31.2911i	0.0284307	+	0.0841159i
$373$	393.539	+	227.210i	1.05507	+	0.609142i	0.924063	−	0.382240i	$-0.124847\pi$
$373$	393.539	+	227.210i	1.05507	+	0.609142i	0.131002	+	0.991382i	$0.458180\pi$
$374$	116.326	−	95.3387i	0.311031	−	0.254916i
$375$	−16.8443	−	29.1751i	−0.0449180	−	0.0778003i
$376$	−14.1106	+	406.609i	−0.0375281	+	1.08141i
$377$			514.871i			1.36570i
$378$		0			0
$379$			373.244i			0.984813i	0.870365	+	0.492406i	$0.163883\pi$
$379$			373.244i			0.984813i	−0.870365	+	0.492406i	$0.836117\pi$
$380$	−69.6325	+	347.686i	−0.183243	+	0.914964i
$381$	−7.29559	−	12.6363i	−0.0191485	−	0.0331662i
$382$	43.0457	−	35.2796i	0.112685	−	0.0923549i
$383$	270.298	+	156.056i	0.705738	+	0.407458i	0.809481	−	0.587146i	$-0.199749\pi$
$383$	270.298	+	156.056i	0.705738	+	0.407458i	−0.103743	+	0.994604i	$0.533082\pi$
$384$	29.4656	+	13.5138i	0.0767334	+	0.0351922i
$385$		0			0
$386$	78.6533	+	478.345i	0.203765	+	1.23923i
$387$	−192.777	−	111.300i	−0.498133	−	0.287597i
$388$	−124.257	+	141.314i	−0.320251	+	0.364213i
$389$	439.628	−	253.819i	1.13015	−	0.652492i	0.186177	−	0.982516i	$-0.440390\pi$
$389$	439.628	−	253.819i	1.13015	−	0.652492i	0.943973	+	0.330024i	$0.107057\pi$
$390$	−30.7288	−	11.5885i	−0.0787918	−	0.0297140i
$391$		−	41.0120i		−	0.104890i
$392$		0			0
$393$	31.4796			0.0801007
$394$	−66.8358	+	177.226i	−0.169634	+	0.449813i
$395$	184.082	+	318.840i	0.466031	+	0.807190i
$396$	−186.055	+	211.595i	−0.469835	+	0.534331i
$397$	95.6487	−	165.668i	0.240929	−	0.417301i	−0.720050	−	0.693922i	$-0.755881\pi$
$397$	95.6487	−	165.668i	0.240929	−	0.417301i	0.960979	+	0.276621i	$0.0892146\pi$
$398$	610.123	−	100.321i	1.53297	−	0.252064i
$399$		0			0
$400$	−155.712	+	118.836i	−0.389281	+	0.297089i
$401$	61.2011	−	106.004i	0.152621	−	0.264348i	−0.779569	−	0.626316i	$-0.784562\pi$
$401$	61.2011	−	106.004i	0.152621	−	0.264348i	0.932190	+	0.361968i	$0.117895\pi$
$402$	−40.2895	−	49.1585i	−0.100223	−	0.122285i
$403$	−512.587	+	295.942i	−1.27193	+	0.734347i
$404$	−117.310	+	585.750i	−0.290372	+	1.44988i
$405$	283.143			0.699120
$406$		0			0
$407$	−235.756			−0.579254
$408$	0.670347	−	19.3167i	0.00164301	−	0.0473448i
$409$	4.57744	−	2.64279i	0.0111918	−	0.00646158i	−0.494394	−	0.869238i	$-0.664610\pi$
$409$	4.57744	−	2.64279i	0.0111918	−	0.00646158i	0.505585	+	0.862777i	$0.331277\pi$
$410$	−204.949	−	250.065i	−0.499877	−	0.609915i
$411$	−21.4610	+	37.1716i	−0.0522166	+	0.0904418i
$412$	25.4151	+	75.1939i	0.0616872	+	0.182509i
$413$		0			0
$414$	12.4657	+	75.8123i	0.0301103	+	0.183122i
$415$	−92.0975	+	159.517i	−0.221922	+	0.384379i
$416$	−133.758	+	565.283i	−0.321534	+	1.35885i
$417$	33.7460	+	58.4498i	0.0809257	+	0.140167i
$418$	138.071	−	366.118i	0.330313	−	0.875880i
$419$	34.7160			0.0828545			0.0414272	−	0.999142i	$-0.486810\pi$
$419$	34.7160			0.0828545			0.0414272	+	0.999142i	$0.486810\pi$
$420$		0			0
$421$		−	394.337i		−	0.936669i	−0.883551	−	0.468334i	$-0.844854\pi$
$421$		−	394.337i		−	0.936669i	0.883551	−	0.468334i	$-0.155146\pi$
$422$	−88.8257	+	235.536i	−0.210487	+	0.558143i
$423$	−393.564	+	227.224i	−0.930412	+	0.537173i
$424$	426.169	+	266.171i	1.00512	+	0.627762i
$425$	101.144	+	58.3956i	0.237986	+	0.137401i
$426$	0.438702	+	2.66805i	0.00102982	+	0.00626302i
$427$		0			0
$428$	11.7114	+	34.6495i	0.0273630	+	0.0809569i
$429$	31.3848	+	18.1200i	0.0731581	+	0.0422378i
$430$	−112.802	−	137.633i	−0.262329	−	0.320076i
$431$	215.872	+	373.901i	0.500862	+	0.867519i	1.00000		0.000995912i	$0.000317009\pi$
$431$	215.872	+	373.901i	0.500862	+	0.867519i	−0.499137	+	0.866523i	$0.666350\pi$
$432$	9.29762	+	72.0807i	0.0215223	+	0.166853i
$433$		−	318.535i		−	0.735647i	−0.929896	−	0.367823i	$-0.880103\pi$
$433$		−	318.535i		−	0.735647i	0.929896	−	0.367823i	$-0.119897\pi$
$434$		0			0
$435$			25.6565i			0.0589803i
$436$	−467.510	−	93.6300i	−1.07227	−	0.214748i
$437$	−53.3481	−	92.4016i	−0.122078	−	0.211445i
$438$	−8.77058	−	10.7013i	−0.0200242	−	0.0244321i
$439$	−532.799	−	307.612i	−1.21366	−	0.700710i	−0.250109	−	0.968218i	$-0.580467\pi$
$439$	−532.799	−	307.612i	−1.21366	−	0.700710i	−0.963556	+	0.267508i	$0.913800\pi$
$440$	−198.858	+	105.790i	−0.451949	+	0.240432i
$441$		0			0
$442$	341.765	−	56.1957i	0.773223	−	0.127140i
$443$	−86.4553	−	49.9150i	−0.195159	−	0.112675i	0.399237	−	0.916848i	$-0.369275\pi$
$443$	−86.4553	−	49.9150i	−0.195159	−	0.112675i	−0.594395	+	0.804173i	$0.702609\pi$
$444$	−20.0060	+	22.7523i	−0.0450586	+	0.0512440i
$445$	475.840	−	274.726i	1.06930	−	0.617362i
$446$	−6.31355	+	16.7415i	−0.0141559	+	0.0375369i
$447$			7.80515i			0.0174612i
$448$		0			0
$449$	−75.3168			−0.167743			−0.0838717	−	0.996477i	$-0.526729\pi$
$449$	−75.3168			−0.167743			−0.0838717	+	0.996477i	$0.526729\pi$
$450$	−204.719	−	77.2038i	−0.454931	−	0.171564i
$451$	178.391	+	308.983i	0.395546	+	0.685105i
$452$	−372.516	−	327.552i	−0.824151	−	0.724672i
$453$	2.97443	−	5.15187i	0.00656608	−	0.0113728i
$454$	88.4889	+	538.161i	0.194909	+	1.18538i
$455$		0			0
$456$	−23.6167	−	44.3932i	−0.0517910	−	0.0973536i
$457$	104.447	−	180.907i	0.228549	−	0.395858i	−0.728830	−	0.684695i	$-0.759935\pi$
$457$	104.447	−	180.907i	0.228549	−	0.395858i	0.957378	+	0.288837i	$0.0932687\pi$
$458$	−512.351	+	419.914i	−1.11867	+	0.916843i
$459$	37.5281	−	21.6669i	0.0817606	−	0.0472045i
$460$	−12.0614	+	60.2243i	−0.0262203	+	0.130922i
$461$	751.461			1.63007			0.815034	−	0.579413i	$-0.196718\pi$
$461$	751.461			1.63007			0.815034	+	0.579413i	$0.196718\pi$
$462$		0			0
$463$	−3.56075			−0.00769060			−0.00384530	−	0.999993i	$-0.501224\pi$
$463$	−3.56075			−0.00769060			−0.00384530	+	0.999993i	$0.501224\pi$
$464$	450.079	−	58.0553i	0.969998	−	0.125119i
$465$	−25.5426	+	14.7470i	−0.0549304	+	0.0317141i
$466$	244.769	−	200.609i	0.525256	−	0.430491i
$467$	−206.945	+	358.440i	−0.443138	+	0.767537i	−0.997920	−	0.0644583i	$-0.979468\pi$
$467$	−206.945	+	358.440i	−0.443138	+	0.767537i	0.554783	+	0.831995i	$0.312801\pi$
$468$	−614.686	+	207.760i	−1.31343	+	0.443932i
$469$		0			0
$470$	−358.484	+	58.9449i	−0.762733	+	0.125415i
$471$	−16.1615	+	27.9925i	−0.0343131	+	0.0594320i
$472$	−313.643	+	502.177i	−0.664499	+	1.06394i
$473$	98.1843	+	170.060i	0.207578	+	0.359535i
$474$	−48.8509	−	18.4227i	−0.103061	−	0.0388664i
$475$	303.843			0.639669
$476$		0			0
$477$			561.240i			1.17660i
$478$	−91.6927	−	34.5792i	−0.191826	−	0.0723415i
$479$	785.798	−	453.681i	1.64050	−	0.947142i	0.659841	−	0.751405i	$-0.270624\pi$
$479$	785.798	−	453.681i	1.64050	−	0.947142i	0.980657	−	0.195737i	$-0.0627098\pi$
$480$	−6.66529	+	28.1686i	−0.0138860	+	0.0586845i
$481$	−470.172	−	271.454i	−0.977488	−	0.564353i
$482$	389.478	−	64.0412i	0.808047	−	0.132866i
$483$		0			0
$484$	−223.047	+	75.3886i	−0.460840	+	0.155762i
$485$	−145.518	−	84.0147i	−0.300037	−	0.173226i
$486$	−94.2922	+	77.2803i	−0.194017	+	0.159013i
$487$	−421.452	−	729.977i	−0.865405	−	1.49893i	−0.866644	−	0.498926i	$-0.833728\pi$
$487$	−421.452	−	729.977i	−0.865405	−	1.49893i	0.00123943	−	0.999999i	$-0.499605\pi$
$488$	−404.546	−	14.0390i	−0.828988	−	0.0287684i
$489$		−	40.4410i		−	0.0827014i
$490$		0			0
$491$		−	144.126i		−	0.293535i	−0.989171	−	0.146768i	$-0.953113\pi$
$491$		−	144.126i		−	0.293535i	0.989171	−	0.146768i	$-0.0468870\pi$
$492$	44.9573	+	9.00378i	0.0913766	+	0.0183004i
$493$	−135.290	−	234.329i	−0.274422	−	0.475313i
$494$	696.911	−	571.177i	1.41075	−	1.15623i
$495$	−217.889	−	125.798i	−0.440179	−	0.254138i
$496$	316.498	+	414.713i	0.638101	+	0.836115i
$497$		0			0
$498$	−4.23805	−	25.7745i	−0.00851014	−	0.0517560i
$499$	330.101	+	190.584i	0.661526	+	0.381932i	0.792858	−	0.609406i	$-0.208592\pi$
$499$	330.101	+	190.584i	0.661526	+	0.381932i	−0.131332	+	0.991338i	$0.541926\pi$
$500$	−399.584	−	351.352i	−0.799168	−	0.702705i
$501$	−31.3180	+	18.0815i	−0.0625110	+	0.0360908i
$502$	590.405	+	222.654i	1.17611	+	0.443534i
$503$		−	936.429i		−	1.86169i	−0.365418	−	0.930843i	$-0.619074\pi$
$503$		−	936.429i		−	1.86169i	0.365418	−	0.930843i	$-0.380926\pi$
$504$		0			0
$505$	−533.429			−1.05629
$506$	23.9158	−	63.4168i	0.0472645	−	0.125330i
$507$	20.3273	+	35.2080i	0.0400933	+	0.0694437i
$508$	−173.068	−	152.178i	−0.340685	−	0.299563i
$509$	167.592	−	290.278i	0.329258	−	0.570291i	−0.653107	−	0.757265i	$-0.726535\pi$
$509$	167.592	−	290.278i	0.329258	−	0.570291i	0.982365	+	0.186975i	$0.0598682\pi$
$510$	17.0304	−	2.80028i	0.0333930	−	0.00549075i
$511$		0			0
$512$	509.230	+	53.1863i	0.994590	+	0.103880i
$513$	56.3682	−	97.6327i	0.109880	−	0.190317i
$514$	−482.403	−	588.596i	−0.938528	−	1.14513i
$515$	−61.3800	+	35.4378i	−0.119185	+	0.0688112i
$516$	24.7440	+	4.95557i	0.0479534	+	0.00960382i
$517$	400.896			0.775427
$518$		0			0
$519$	−49.5824			−0.0955345
$520$	−518.393	−	17.9898i	−0.996910	−	0.0345958i
$521$	421.675	−	243.454i	0.809357	−	0.467283i	−0.0373754	−	0.999301i	$-0.511900\pi$
$521$	421.675	−	243.454i	0.809357	−	0.467283i	0.846733	+	0.532019i	$0.178566\pi$
$522$	321.315	+	392.046i	0.615545	+	0.751046i
$523$	−86.3132	+	149.499i	−0.165035	+	0.285849i	−0.936668	−	0.350220i	$-0.886107\pi$
$523$	−86.3132	+	149.499i	−0.165035	+	0.285849i	0.771633	+	0.636068i	$0.219440\pi$
$524$	471.020	−	159.202i	0.898894	−	0.303821i
$525$		0			0
$526$	63.7080	+	387.452i	0.121118	+	0.736600i
$527$	155.527	−	269.380i	0.295117	−	0.511157i
$528$	12.3009	−	29.4785i	0.0232972	−	0.0558305i
$529$	255.259	+	442.122i	0.482532	+	0.835770i
$530$	−158.319	+	419.809i	−0.298715	+	0.792093i
$531$	−661.339			−1.24546
$532$		0			0
$533$			821.611i			1.54148i
$534$	−27.4942	+	72.9055i	−0.0514872	+	0.136527i
$535$	−28.2841	+	16.3298i	−0.0528675	+	0.0305230i
$536$	−851.451	−	531.788i	−1.58853	−	0.992142i
$537$	32.7908	+	18.9318i	0.0610629	+	0.0352547i
$538$	33.1999	+	201.912i	0.0617099	+	0.375300i
$539$		0			0
$540$	−61.4805	+	20.7801i	−0.113853	+	0.0384816i
$541$	−500.736	−	289.100i	−0.925574	−	0.534381i	−0.0401652	−	0.999193i	$-0.512788\pi$
$541$	−500.736	−	289.100i	−0.925574	−	0.534381i	−0.885409	+	0.464812i	$0.846122\pi$
$542$	−324.958	−	396.491i	−0.599553	−	0.731534i
$543$	−11.5611	−	20.0244i	−0.0212911	−	0.0368773i
$544$	−87.6604	−	292.420i	−0.161140	−	0.537537i
$545$		−	425.750i		−	0.781193i
$546$		0			0
$547$			454.579i			0.831040i	0.909584	+	0.415520i	$0.136400\pi$
$547$			454.579i			0.831040i	−0.909584	+	0.415520i	$0.863600\pi$
$548$	−133.127	+	664.724i	−0.242932	+	1.21300i
$549$	−226.071	−	391.567i	−0.411788	−	0.713237i
$550$	122.346	+	149.279i	0.222448	+	0.271416i
$551$	−609.629	−	351.969i	−1.10640	−	0.638783i
$552$	−4.09075	−	7.68955i	−0.00741078	−	0.0139303i
$553$		0			0
$554$	388.245	−	63.8384i	0.700803	−	0.115232i
$555$	−23.4291	−	13.5268i	−0.0422145	−	0.0243726i
$556$	800.532	+	703.905i	1.43981	+	1.26602i
$557$	−25.2401	+	14.5724i	−0.0453143	+	0.0261622i	−0.522486	−	0.852648i	$-0.674995\pi$
$557$	−25.2401	+	14.5724i	−0.0453143	+	0.0261622i	0.477172	+	0.878810i	$0.341662\pi$
$558$	−205.619	+	545.233i	−0.368492	+	0.977120i
$559$			452.205i			0.808953i
$560$		0			0
$561$	−19.0453			−0.0339488
$562$	131.542	+	49.6071i	0.234060	+	0.0882688i
$563$	514.005	+	890.283i	0.912975	+	1.58132i	0.809839	+	0.586652i	$0.199554\pi$
$563$	514.005	+	890.283i	0.912975	+	1.58132i	0.103136	+	0.994667i	$0.467112\pi$
$564$	34.0196	−	38.6896i	0.0603184	−	0.0685986i
$565$	221.469	−	383.596i	0.391981	−	0.678931i
$566$	−96.3730	−	586.110i	−0.170270	−	1.03553i
$567$		0			0
$568$	20.0574	+	37.7026i	0.0353122	+	0.0663778i
$569$	409.852	−	709.885i	0.720303	−	1.24760i	−0.240576	−	0.970630i	$-0.577336\pi$
$569$	409.852	−	709.885i	0.720303	−	1.24760i	0.960878	−	0.276971i	$-0.0893305\pi$
$570$	34.7277	−	28.4622i	0.0609257	−	0.0499337i
$571$	−140.820	+	81.3023i	−0.246620	+	0.142386i	−0.618215	−	0.786009i	$-0.712144\pi$
$571$	−140.820	+	81.3023i	−0.246620	+	0.142386i	0.371596	+	0.928395i	$0.378811\pi$
$572$	561.241	+	112.402i	0.981191	+	0.196507i
$573$	−7.04760			−0.0122995
$574$		0			0
$575$	52.6299			0.0915303
$576$	250.926	+	513.907i	0.435635	+	0.892199i
$577$	−131.878	+	76.1400i	−0.228559	+	0.131958i	−0.609907	−	0.792473i	$-0.708793\pi$
$577$	−131.878	+	76.1400i	−0.228559	+	0.131958i	0.381348	+	0.924431i	$0.375460\pi$
$578$	306.261	−	251.007i	0.529864	−	0.434268i
$579$	30.6926	−	53.1611i	0.0530097	−	0.0918154i
$580$	129.753	+	383.890i	0.223712	+	0.661880i
$581$		0			0
$582$	23.5124	−	3.86611i	0.0403994	−	0.00664279i
$583$	247.551	−	428.772i	0.424617	−	0.735457i
$584$	−185.352	−	115.764i	−0.317383	−	0.198227i
$585$	−289.692	−	501.762i	−0.495201	−	0.857713i
$586$	253.682	+	95.6688i	0.432905	+	0.163257i
$587$	−894.404			−1.52369			−0.761843	−	0.647761i	$-0.775705\pi$
$587$	−894.404			−1.52369			−0.761843	+	0.647761i	$0.775705\pi$
$588$		0			0
$589$		−	809.232i		−	1.37391i
$590$	−494.684	−	186.556i	−0.838447	−	0.316196i
$591$	20.7713	−	11.9923i	0.0351460	−	0.0202916i
$592$	−184.279	+	441.614i	−0.311282	+	0.745969i
$593$	−164.729	−	95.1064i	−0.277789	−	0.160382i	0.354633	−	0.935006i	$-0.384606\pi$
$593$	−164.729	−	95.1064i	−0.277789	−	0.160382i	−0.632422	+	0.774624i	$0.717939\pi$
$594$	70.6647	−	11.6193i	0.118964	−	0.0195610i
$595$		0			0
$596$	39.4731	+	116.786i	0.0662301	+	0.195950i
$597$	−67.8064	−	39.1480i	−0.113579	−	0.0655746i
$598$	120.715	−	98.9360i	0.201864	−	0.165445i
$599$	146.832	+	254.320i	0.245128	+	0.424574i	0.962168	−	0.272458i	$-0.0878366\pi$
$599$	146.832	+	254.320i	0.245128	+	0.424574i	−0.717040	+	0.697033i	$0.754503\pi$
$600$	24.7888	+	0.860245i	0.0413146	+	0.00143374i
$601$			597.574i			0.994299i	0.867665	+	0.497150i	$0.165620\pi$
$601$			597.574i			0.994299i	−0.867665	+	0.497150i	$0.834380\pi$
$602$		0			0
$603$		−	1121.31i		−	1.85956i
$604$	18.4510	−	92.1287i	0.0305480	−	0.152531i
$605$	−105.119	−	182.071i	−0.173750	−	0.300944i
$606$	58.5060	−	47.9505i	0.0965445	−	0.0791263i
$607$	10.6620	+	6.15569i	0.0175650	+	0.0101412i	0.508757	−	0.860910i	$-0.330105\pi$
$607$	10.6620	+	6.15569i	0.0175650	+	0.0101412i	−0.491192	+	0.871051i	$0.663439\pi$
$608$	−577.881	−	544.807i	−0.950462	−	0.896064i
$609$		0			0
$610$	−58.6458	−	356.665i	−0.0961407	−	0.584697i
$611$	799.512	+	461.599i	1.30853	+	0.755481i
$612$	225.165	−	256.075i	0.367917	−	0.418422i
$613$	118.897	−	68.6451i	0.193959	−	0.111982i	−0.399876	−	0.916569i	$-0.630947\pi$
$613$	118.897	−	68.6451i	0.193959	−	0.111982i	0.593835	+	0.804587i	$0.297613\pi$
$614$	142.607	+	53.7800i	0.232258	+	0.0875895i
$615$			40.9416i			0.0665717i
$616$		0			0
$617$	290.516			0.470853			0.235427	−	0.971892i	$-0.424351\pi$
$617$	290.516			0.470853			0.235427	+	0.971892i	$0.424351\pi$
$618$	3.54656	−	9.40430i	0.00573877	−	0.0152173i
$619$	−51.1586	−	88.6092i	−0.0826471	−	0.143149i	0.821739	−	0.569864i	$-0.193004\pi$
$619$	−51.1586	−	88.6092i	−0.0826471	−	0.143149i	−0.904386	+	0.426715i	$0.859671\pi$
$620$	−307.607	+	349.833i	−0.496140	+	0.564247i
$621$	9.76379	−	16.9114i	0.0157227	−	0.0272325i
$622$	−390.938	+	64.2812i	−0.628517	+	0.103346i
$623$		0			0
$624$	58.4740	−	44.6259i	0.0937083	−	0.0715158i
$625$	84.5320	−	146.414i	0.135251	−	0.234262i
$626$	−70.2222	−	85.6804i	−0.112176	−	0.136870i
$627$	−42.9098	+	24.7740i	−0.0684366	+	0.0395119i
$628$	−100.253	+	500.577i	−0.159638	+	0.797097i
$629$	285.315			0.453600
$630$		0			0
$631$	−562.739			−0.891820			−0.445910	−	0.895078i	$-0.647120\pi$
$631$	−562.739			−0.891820			−0.445910	+	0.895078i	$0.647120\pi$
$632$	−824.112	−	28.5992i	−1.30397	−	0.0452519i
$633$	27.6054	−	15.9380i	0.0436104	−	0.0251785i
$634$	379.268	+	462.757i	0.598214	+	0.729900i
$635$	102.893	−	178.216i	0.162036	−	0.280655i
$636$	−20.3729	−	60.2758i	−0.0320328	−	0.0947732i
$637$		0			0
$638$	−72.5519	−	441.237i	−0.113718	−	0.691595i
$639$	−23.8508	+	41.3108i	−0.0373252	+	0.0646492i
$640$	42.7265	+	455.187i	0.0667602	+	0.711229i
$641$	376.275	+	651.727i	0.587012	+	1.01673i	0.994621	+	0.103578i	$0.0330291\pi$
$641$	376.275	+	651.727i	0.587012	+	1.01673i	−0.407610	+	0.913156i	$0.633638\pi$
$642$	1.63427	−	4.33353i	0.00254558	−	0.00675005i
$643$	253.143			0.393690			0.196845	−	0.980435i	$-0.436930\pi$
$643$	253.143			0.393690			0.196845	+	0.980435i	$0.436930\pi$
$644$		0			0
$645$			22.5337i			0.0349360i
$646$	−167.095	+	443.079i	−0.258660	+	0.685881i
$647$	−485.492	+	280.299i	−0.750374	+	0.433229i	−0.825829	−	0.563921i	$-0.809292\pi$
$647$	−485.492	+	280.299i	−0.750374	+	0.433229i	0.0754551	+	0.997149i	$0.475959\pi$
$648$	−335.947	+	537.887i	−0.518436	+	0.830073i
$649$	505.244	+	291.703i	0.778497	+	0.449465i
$650$	72.1150	+	438.581i	0.110946	+	0.674739i
$651$		0			0
$652$	−204.523	−	605.108i	−0.313686	−	0.928079i
$653$	602.396	+	347.793i	0.922505	+	0.532609i	0.884433	−	0.466666i	$-0.154545\pi$
$653$	602.396	+	347.793i	0.922505	+	0.532609i	0.0380717	+	0.999275i	$0.487878\pi$
$654$	38.2712	+	46.6959i	0.0585186	+	0.0714004i
$655$	221.985	+	384.489i	0.338908	+	0.587007i
$656$	718.219	−	92.6424i	1.09485	−	0.141223i
$657$		−	244.097i		−	0.371533i
$658$		0			0
$659$		−	323.387i		−	0.490724i	−0.969432	−	0.245362i	$-0.921093\pi$
$659$		−	323.387i		−	0.490724i	0.969432	−	0.245362i	$-0.0789068\pi$
$660$	27.9671	+	5.60109i	0.0423745	+	0.00848650i
$661$	−15.5168	−	26.8758i	−0.0234747	−	0.0406593i	0.854049	−	0.520192i	$-0.174140\pi$
$661$	−15.5168	−	26.8758i	−0.0234747	−	0.0406593i	−0.877524	+	0.479533i	$0.840806\pi$
$662$	−475.894	−	580.654i	−0.718873	−	0.877120i
$663$	−37.9822	−	21.9291i	−0.0572884	−	0.0330755i
$664$	−193.763	−	364.223i	−0.291811	−	0.548529i
$665$		0			0
$666$	−527.416	+	86.7221i	−0.791916	+	0.130213i
$667$	−105.596	−	60.9661i	−0.158315	−	0.0914035i
$668$	−377.159	+	428.933i	−0.564610	+	0.642116i
$669$	1.96213	−	1.13284i	0.00293293	−	0.00169333i
$670$	316.308	−	838.745i	0.472102	−	1.25186i
$671$			398.862i			0.594429i
$672$		0			0
$673$	1011.75			1.50334			0.751670	−	0.659539i	$-0.229249\pi$
$673$	1011.75			1.50334			0.751670	+	0.659539i	$0.229249\pi$
$674$	9.33884	+	3.52187i	0.0138558	+	0.00522533i
$675$	27.8047	+	48.1592i	0.0411922	+	0.0713469i
$676$	482.210	+	424.005i	0.713328	+	0.627227i
$677$	34.7377	−	60.1674i	0.0513112	−	0.0888736i	−0.839229	−	0.543778i	$-0.816993\pi$
$677$	34.7377	−	60.1674i	0.0513112	−	0.0888736i	0.890540	+	0.454905i	$0.150327\pi$
$678$	10.1914	+	61.9806i	0.0150315	+	0.0914169i
$679$		0			0
$680$	240.660	−	128.028i	0.353911	−	0.188277i
$681$	34.5307	−	59.8089i	0.0507058	−	0.0878251i
$682$	397.578	−	325.848i	0.582959	−	0.477784i
$683$	−824.530	+	476.042i	−1.20722	+	0.696987i	−0.962150	−	0.272519i	$-0.912143\pi$
$683$	−824.530	+	476.042i	−1.20722	+	0.696987i	−0.245067	+	0.969506i	$0.578810\pi$
$684$	174.206	−	869.840i	0.254688	−	1.27170i
$685$	−605.348			−0.883720
$686$		0			0
$687$	83.8839			0.122102
$688$	395.299	−	50.9893i	0.574563	−	0.0741123i
$689$	987.391	−	570.070i	1.43308	−	0.827388i
$690$	6.01533	−	4.93007i	0.00871787	−	0.00714502i
$691$	34.0754	−	59.0204i	0.0493132	−	0.0854130i	−0.840315	−	0.542098i	$-0.817630\pi$
$691$	34.0754	−	59.0204i	0.0493132	−	0.0854130i	0.889628	+	0.456685i	$0.150963\pi$
$692$	−741.888	+	250.754i	−1.07209	+	0.362361i
$693$		0			0
$694$	730.975	−	120.193i	1.05328	−	0.173189i
$695$	−475.935	+	824.343i	−0.684798	+	1.18611i
$696$	−48.7395	−	30.4411i	−0.0700281	−	0.0437372i
$697$	−215.891	−	373.934i	−0.309743	−	0.536490i
$698$	48.0565	+	18.1231i	0.0688489	+	0.0259644i
$699$	−40.0745			−0.0573311
$700$		0			0
$701$			1.67276i			0.00238625i	0.999999	+	0.00119312i	$0.000379783\pi$
$701$			1.67276i			0.00238625i	−0.999999	+	0.00119312i	$0.999620\pi$
$702$	154.306	+	58.1921i	0.219809	+	0.0828947i
$703$	642.825	−	371.135i	0.914403	−	0.527931i
$704$	34.9734	−	503.289i	0.0496781	−	0.714899i
$705$	39.8404	+	23.0019i	0.0565112	+	0.0326267i
$706$	−523.984	+	86.1577i	−0.742186	+	0.122036i
$707$		0			0
$708$	71.0261	−	24.0064i	0.100319	−	0.0339074i
$709$	45.7969	+	26.4408i	0.0645936	+	0.0372931i	0.531949	−	0.846776i	$-0.321460\pi$
$709$	45.7969	+	26.4408i	0.0645936	+	0.0372931i	−0.467355	+	0.884070i	$0.654793\pi$
$710$	−29.4937	+	24.1726i	−0.0415405	+	0.0340459i
$711$	−460.536	−	797.673i	−0.647731	−	1.12190i
$712$	−42.6817	+	1229.91i	−0.0599461	+	1.72740i
$713$		−	140.171i		−	0.196593i
$714$		0			0
$715$			511.109i			0.714838i
$716$	586.384	+	117.437i	0.818972	+	0.164019i
$717$	6.20454	+	10.7466i	0.00865347	+	0.0149882i
$718$	−851.473	+	697.853i	−1.18590	+	0.971941i
$719$	824.178	+	475.840i	1.14628	+	0.661808i	0.947979	−	0.318333i	$-0.103123\pi$
$719$	824.178	+	475.840i	1.14628	+	0.661808i	0.198305	+	0.980140i	$0.436456\pi$
$720$	−405.955	+	309.815i	−0.563827	+	0.430298i
$721$		0			0
$722$	82.7399	+	503.198i	0.114598	+	0.696950i
$723$	−43.2849	−	24.9906i	−0.0598685	−	0.0345651i
$724$	−274.255	−	241.151i	−0.378805	−	0.333081i
$725$	300.711	−	173.615i	0.414774	−	0.239470i
$726$	27.8959	+	10.5201i	0.0384241	+	0.0144905i
$727$		−	1061.98i		−	1.46078i	−0.683032	−	0.730388i	$-0.739339\pi$
$727$		−	1061.98i		−	1.46078i	0.683032	−	0.730388i	$-0.260661\pi$
$728$		0			0
$729$	−698.013			−0.957494
$730$	68.8569	−	182.586i	0.0943245	−	0.250117i
$731$	−118.824	−	205.809i	−0.162550	−	0.281544i
$732$	38.4933	+	33.8470i	0.0525865	+	0.0462391i
$733$	0.148102	−	0.256519i	0.000202048	−	0.000349958i	−0.865924	−	0.500175i	$-0.833269\pi$
$733$	0.148102	−	0.256519i	0.000202048	−	0.000349958i	0.866126	+	0.499825i	$0.166602\pi$
$734$	410.409	−	67.4828i	0.559140	−	0.0919384i
$735$		0			0
$736$	−100.097	−	94.3684i	−0.136002	−	0.128218i
$737$	−494.588	+	856.651i	−0.671082	+	1.16235i
$738$	512.741	+	625.612i	0.694772	+	0.847713i
$739$	176.276	−	101.773i	0.238533	−	0.137717i	−0.375969	−	0.926632i	$-0.622690\pi$
$739$	176.276	−	101.773i	0.238533	−	0.137717i	0.614502	+	0.788915i	$0.289357\pi$
$740$	−418.972	−	83.9092i	−0.566178	−	0.113391i
$741$	−114.101			−0.153982
$742$		0			0
$743$	1142.13			1.53718			0.768592	−	0.639739i	$-0.220958\pi$
$743$	1142.13			1.53718			0.768592	+	0.639739i	$0.220958\pi$
$744$	2.29111	−	66.0205i	0.00307945	−	0.0887373i
$745$	−95.3315	+	55.0397i	−0.127962	+	0.0738788i
$746$	−576.102	−	702.920i	−0.772255	−	0.942253i
$747$	230.409	−	399.080i	0.308446	−	0.534244i
$748$	−284.969	+	96.3180i	−0.380975	+	0.128767i
$749$		0			0
$750$	10.9319	+	66.4843i	0.0145759	+	0.0886457i
$751$	396.068	−	686.010i	0.527387	−	0.913462i	−0.472103	−	0.881543i	$-0.656505\pi$
$751$	396.068	−	686.010i	0.527387	−	0.913462i	0.999490	−	0.0319185i	$-0.0101617\pi$
$752$	313.360	−	750.950i	0.416702	−	0.998604i
$753$	−39.9508	−	69.1967i	−0.0530554	−	0.0918947i
$754$	363.357	−	963.503i	0.481906	−	1.27786i
$755$	83.8995			0.111125
$756$		0			0
$757$		−	1179.34i		−	1.55792i	−0.627076	−	0.778958i	$-0.715748\pi$
$757$		−	1179.34i		−	1.55792i	0.627076	−	0.778958i	$-0.284252\pi$
$758$	263.408	−	698.470i	0.347504	−	0.921465i
$759$	−7.43259	+	4.29121i	−0.00979260	+	0.00565376i
$760$	375.678	−	601.501i	0.494313	−	0.791449i
$761$	−197.869	−	114.240i	−0.260011	−	0.150118i	0.364328	−	0.931271i	$-0.381299\pi$
$761$	−197.869	−	114.240i	−0.260011	−	0.150118i	−0.624340	+	0.781153i	$0.714632\pi$
$762$	4.73482	+	28.7957i	0.00621368	+	0.0377896i
$763$		0			0
$764$	−105.451	+	35.6420i	−0.138025	+	0.0466518i
$765$	263.691	+	152.242i	0.344694	+	0.199009i
$766$	−395.689	−	482.792i	−0.516565	−	0.630277i
$767$	671.744	+	1163.49i	0.875807	+	1.51694i
$768$	−45.6035	−	46.0837i	−0.0593795	−	0.0600049i
$769$		−	83.4232i		−	0.108483i	−0.998528	−	0.0542414i	$-0.982726\pi$
$769$		−	83.4232i		−	0.108483i	0.998528	−	0.0542414i	$-0.0172740\pi$
$770$		0			0
$771$			96.3670i			0.124990i
$772$	190.392	−	950.658i	0.246622	−	1.23142i
$773$	285.318	+	494.186i	0.369105	+	0.639309i	0.989426	−	0.145039i	$-0.0463309\pi$
$773$	285.318	+	494.186i	0.369105	+	0.639309i	−0.620321	+	0.784348i	$0.712998\pi$
$774$	282.207	+	344.329i	0.364608	+	0.444870i
$775$	345.691	+	199.585i	0.446052	+	0.257528i
$776$	332.258	−	176.757i	0.428168	−	0.227780i
$777$		0			0
$778$	−1001.83	+	164.728i	−1.28769	+	0.211733i
$779$	−972.822	−	561.659i	−1.24881	−	0.721000i
$780$	49.3261	+	43.3722i	0.0632385	+	0.0556054i
$781$	36.4427	−	21.0402i	0.0466616	−	0.0269401i
$782$	−28.9432	+	76.7477i	−0.0370117	+	0.0981429i
$783$		−	128.835i		−	0.164540i
$784$		0			0
$785$	−455.864			−0.580718
$786$	−58.9093	−	22.2159i	−0.0749482	−	0.0282645i
$787$	−382.719	−	662.888i	−0.486301	−	0.842298i	0.513575	−	0.858045i	$-0.328321\pi$
$787$	−382.719	−	662.888i	−0.486301	−	0.842298i	−0.999876	+	0.0157470i	$0.994987\pi$
$788$	250.146	−	284.485i	0.317444	−	0.361021i
$789$	24.8605	−	43.0597i	0.0315089	−	0.0545750i
$790$	−119.469	−	726.573i	−0.151227	−	0.919713i
$791$		0			0
$792$	497.501	−	264.665i	0.628158	−	0.334173i
$793$	−459.257	+	795.456i	−0.579138	+	1.00310i
$794$	−295.909	+	242.522i	−0.372681	+	0.305443i
$795$	49.2025	−	28.4071i	0.0618900	−	0.0357322i
$796$	−1212.55	−	242.843i	−1.52331	−	0.305079i
$797$	−577.729			−0.724880			−0.362440	−	0.932007i	$-0.618056\pi$
$797$	−577.729			−0.724880			−0.362440	+	0.932007i	$0.618056\pi$
$798$		0			0
$799$	−485.168			−0.607220
$800$	375.258	−	112.493i	0.469072	−	0.140616i
$801$	−1190.45	+	687.309i	−1.48621	+	0.858063i
$802$	−189.338	+	155.178i	−0.236082	+	0.193489i
$803$	−107.666	+	186.484i	−0.134080	+	0.232234i
$804$	40.7033	+	120.426i	0.0506260	+	0.149784i
$805$		0			0
$806$	1168.08	−	192.066i	1.44923	−	0.238295i
$807$	12.9555	−	22.4396i	0.0160539	−	0.0278062i
$808$	632.908	−	1013.35i	0.783301	−	1.25415i
$809$	41.4824	+	71.8496i	0.0512761	+	0.0888128i	0.890524	−	0.454936i	$-0.150338\pi$
$809$	41.4824	+	71.8496i	0.0512761	+	0.0888128i	−0.839248	+	0.543749i	$0.817004\pi$
$810$	−529.860	−	199.822i	−0.654149	−	0.246693i
$811$	525.164			0.647552			0.323776	−	0.946134i	$-0.395048\pi$
$811$	525.164			0.647552			0.323776	+	0.946134i	$0.395048\pi$
$812$		0			0
$813$			64.9150i			0.0798462i
$814$	441.182	+	166.379i	0.541993	+	0.204397i
$815$	493.944	−	285.178i	0.606066	−	0.349912i
$816$	−14.8867	+	35.6752i	−0.0182435	+	0.0437196i
$817$	−535.429	−	309.130i	−0.655360	−	0.378372i
$818$	−10.4311	+	1.71516i	−0.0127519	+	0.00209677i
$819$		0			0
$820$	207.055	+	612.598i	0.252506	+	0.747070i
$821$	−506.369	−	292.352i	−0.616771	−	0.356093i	0.158840	−	0.987304i	$-0.449225\pi$
$821$	−506.369	−	292.352i	−0.616771	−	0.356093i	−0.775611	+	0.631211i	$0.782558\pi$
$822$	66.3940	−	54.4155i	0.0807713	−	0.0661989i
$823$	−590.484	−	1022.75i	−0.717478	−	1.24271i	−0.961996	−	0.273063i	$-0.911963\pi$
$823$	−590.484	−	1022.75i	−0.717478	−	1.24271i	0.244518	−	0.969645i	$-0.421370\pi$
$824$	5.50564	−	158.650i	0.00668160	−	0.192537i
$825$		−	24.4405i		−	0.0296248i
$826$		0			0
$827$		−	336.806i		−	0.407262i	−0.979048	−	0.203631i	$-0.934726\pi$
$827$		−	336.806i		−	0.407262i	0.979048	−	0.203631i	$-0.0652743\pi$
$828$	30.1750	−	150.669i	0.0364433	−	0.181967i
$829$	−184.145	−	318.949i	−0.222130	−	0.384740i	0.733325	−	0.679878i	$-0.237967\pi$
$829$	−184.145	−	318.949i	−0.222130	−	0.384740i	−0.955454	+	0.295139i	$0.904634\pi$
$830$	284.922	−	233.518i	0.343280	−	0.281346i
$831$	−43.1479	−	24.9114i	−0.0519228	−	0.0299777i
$832$	649.243	−	963.446i	0.780340	−	1.15799i
$833$		0			0
$834$	−21.9011	−	133.196i	−0.0262603	−	0.159707i
$835$	−441.692	−	255.011i	−0.528972	−	0.305402i
$836$	−516.757	+	587.694i	−0.618131	+	0.702984i
$837$	128.264	−	74.0530i	0.153242	−	0.0884743i
$838$	−64.9658	−	24.5000i	−0.0775249	−	0.0292363i
$839$			709.889i			0.846113i	0.906103	+	0.423056i	$0.139043\pi$
$839$			709.889i			0.846113i	−0.906103	+	0.423056i	$0.860957\pi$
$840$		0			0
$841$	36.5402			0.0434485
$842$	−278.294	+	737.943i	−0.330515	+	0.876417i
$843$	−8.90098	−	15.4169i	−0.0105587	−	0.0182882i
$844$	332.448	−	378.084i	0.393896	−	0.447967i
$845$	−286.685	+	496.553i	−0.339272	+	0.587637i
$846$	896.854	−	147.468i	1.06011	−	0.174312i
$847$		0			0
$848$	−609.668	−	798.858i	−0.718948	−	0.942049i
$849$	−37.6073	+	65.1377i	−0.0442960	+	0.0767229i
$850$	−148.065	−	180.659i	−0.174194	−	0.212540i
$851$	111.347	−	64.2860i	0.130842	−	0.0755417i
$852$	1.06194	−	5.30246i	0.00124641	−	0.00622354i
$853$	−1136.65			−1.33253			−0.666267	−	0.745713i	$-0.732109\pi$
$853$	−1136.65			−1.33253			−0.666267	+	0.745713i	$0.732109\pi$
$854$		0			0
$855$	792.143			0.926483
$856$	2.53701	−	73.1064i	0.00296380	−	0.0854047i
$857$	−578.645	+	334.081i	−0.675198	+	0.389826i	−0.798043	−	0.602600i	$-0.794131\pi$
$857$	−578.645	+	334.081i	−0.675198	+	0.389826i	0.122845	+	0.992426i	$0.460798\pi$
$858$	−45.9442	−	56.0580i	−0.0535480	−	0.0653357i
$859$	−100.378	+	173.859i	−0.116854	+	0.202397i	−0.918519	−	0.395376i	$-0.870614\pi$
$859$	−100.378	+	173.859i	−0.116854	+	0.202397i	0.801665	+	0.597773i	$0.203948\pi$
$860$	113.960	+	337.166i	0.132512	+	0.392054i
$861$		0			0
$862$	−140.100	−	852.045i	−0.162529	−	0.988451i
$863$	−21.7855	+	37.7337i	−0.0252440	+	0.0437238i	−0.878371	−	0.477979i	$-0.841370\pi$
$863$	−21.7855	+	37.7337i	−0.0252440	+	0.0437238i	0.853127	+	0.521703i	$0.174703\pi$
$864$	33.4701	−	141.450i	0.0387385	−	0.163715i
$865$	−349.641	−	605.596i	−0.404209	−	0.700111i
$866$	−224.798	+	596.091i	−0.259582	+	0.688326i
$867$	−50.1422			−0.0578342
$868$		0			0
$869$			812.533i			0.935020i
$870$	18.1064	−	48.0122i	0.0208120	−	0.0551864i
$871$	−1972.73	+	1138.95i	−2.26490	+	1.30764i
$872$	808.797	+	505.148i	0.927520	+	0.579298i
$873$	364.056	+	210.188i	0.417017	+	0.240765i
$874$	34.6228	+	210.565i	0.0396142	+	0.240921i
$875$		0			0
$876$	8.86068	+	26.2154i	0.0101149	+	0.0299263i
$877$	−129.242	−	74.6180i	−0.147368	−	0.0850832i	0.424503	−	0.905427i	$-0.360449\pi$
$877$	−129.242	−	74.6180i	−0.147368	−	0.0850832i	−0.571871	+	0.820343i	$0.693782\pi$
$878$	779.964	+	951.659i	0.888342	+	1.08389i
$879$	−17.1658	−	29.7321i	−0.0195288	−	0.0338249i
$880$	446.791	−	57.6312i	0.507717	−	0.0654900i
$881$			865.257i			0.982130i	0.871123	+	0.491065i	$0.163392\pi$
$881$			865.257i			0.982130i	−0.871123	+	0.491065i	$0.836608\pi$
$882$		0			0
$883$			1476.24i			1.67184i	0.548850	+	0.835921i	$0.315066\pi$
$883$			1476.24i			1.67184i	−0.548850	+	0.835921i	$0.684934\pi$
$884$	−679.220	−	136.030i	−0.768348	−	0.153880i
$885$	33.4736	+	57.9779i	0.0378233	+	0.0655118i
$886$	126.562	+	154.422i	0.142846	+	0.174291i
$887$	518.166	+	299.163i	0.584178	+	0.337275i	0.762792	−	0.646644i	$-0.223828\pi$
$887$	518.166	+	299.163i	0.584178	+	0.337275i	−0.178614	+	0.983919i	$0.557161\pi$
$888$	53.4951	−	28.4588i	0.0602423	−	0.0320482i
$889$		0			0
$890$	−1084.34	+	178.297i	−1.21836	+	0.200333i
$891$	541.172	+	312.446i	0.607376	+	0.350669i
$892$	23.6297	−	26.8735i	0.0264907	−	0.0301272i
$893$	−1093.10	+	631.104i	−1.22408	+	0.706723i
$894$	5.50829	−	14.6062i	0.00616140	−	0.0163380i
$895$			534.006i			0.596655i
$896$		0			0
$897$	−19.7639			−0.0220333
$898$	140.944	+	53.1530i	0.156953	+	0.0591904i
$899$	−462.395	−	800.891i	−0.514343	−	0.890869i
$900$	328.616	+	288.951i	0.365129	+	0.321056i
$901$	−299.589	+	518.904i	−0.332508	+	0.575920i
$902$	−115.775	−	704.110i	−0.128354	−	0.780609i
$903$		0			0
$904$	465.946	+	875.858i	0.515428	+	0.968870i
$905$	163.051	−	282.412i	0.180167	−	0.312058i
$906$	−9.20202	+	7.54182i	−0.0101568	+	0.00832431i
$907$	1463.00	−	844.666i	1.61301	−	0.931274i	0.624348	−	0.781146i	$-0.285365\pi$
$907$	1463.00	−	844.666i	1.61301	−	0.931274i	0.988667	−	0.150128i	$-0.0479687\pi$
$908$	214.200	−	1069.54i	0.235904	−	1.17790i
$909$	1334.53			1.46813
$910$		0			0
$911$	−813.339			−0.892798			−0.446399	−	0.894834i	$-0.647294\pi$
$911$	−813.339			−0.892798			−0.446399	+	0.894834i	$0.647294\pi$
$912$	12.8657	+	99.7422i	0.0141071	+	0.109366i
$913$	−352.052	+	203.257i	−0.385599	+	0.222626i
$914$	−323.127	+	264.830i	−0.353531	+	0.289748i
$915$	−22.8852	+	39.6382i	−0.0250111	+	0.0433205i
$916$	1255.13	−	424.228i	1.37023	−	0.463131i
$917$		0			0
$918$	−85.5191	+	14.0617i	−0.0931581	+	0.0153178i
$919$	−751.489	+	1301.62i	−0.817724	+	1.41634i	0.0896310	+	0.995975i	$0.471431\pi$
$919$	−751.489	+	1301.62i	−0.817724	+	1.41634i	−0.907355	+	0.420365i	$0.861902\pi$
$920$	65.0728	−	104.189i	0.0707313	−	0.113249i
$921$	−9.64971	−	16.7138i	−0.0104774	−	0.0181474i
$922$	−1406.25	−	530.325i	−1.52521	−	0.575190i
$923$	96.9043			0.104988
$924$		0			0
$925$			366.139i			0.395826i
$926$	6.66340	+	2.51291i	0.00719590	+	0.00271373i
$927$	153.560	−	88.6581i	0.165653	−	0.0956398i
$928$	−883.227	−	208.991i	−0.951753	−	0.225205i
$929$	1301.71	+	751.543i	1.40120	+	0.808981i	0.994515	−	0.104589i	$-0.0333528\pi$
$929$	1301.71	+	751.543i	1.40120	+	0.808981i	0.406681	+	0.913570i	$0.366686\pi$
$930$	58.2066	−	9.57080i	0.0625877	−	0.0102912i
$931$		0			0
$932$	−599.623	+	202.669i	−0.643373	+	0.217456i
$933$	43.4471	+	25.0842i	0.0465671	+	0.0268855i
$934$	640.227	−	524.720i	0.685468	−	0.561798i
$935$	−134.302	−	232.618i	−0.143638	−	0.248789i
$936$	1296.91	+	45.0068i	1.38559	+	0.0480842i
$937$		−	419.349i		−	0.447545i	−0.974641	−	0.223772i	$-0.928163\pi$
$937$		−	419.349i		−	0.447545i	0.974641	−	0.223772i	$-0.0718372\pi$
$938$		0			0
$939$			14.0279i			0.0149392i
$940$	712.449	+	142.685i	0.757924	+	0.151792i
$941$	261.680	+	453.243i	0.278087	+	0.481661i	0.970909	−	0.239448i	$-0.0769664\pi$
$941$	261.680	+	453.243i	0.278087	+	0.481661i	−0.692822	+	0.721108i	$0.743633\pi$
$942$	49.9987	−	40.9781i	0.0530772	−	0.0435012i
$943$	−168.507	−	97.2874i	−0.178692	−	0.103168i
$944$	941.336	−	718.404i	0.997178	−	0.761021i
$945$		0			0
$946$	−63.7214	−	387.533i	−0.0673588	−	0.409655i
$947$	311.949	+	180.104i	0.329408	+	0.190184i	0.655578	−	0.755127i	$-0.272425\pi$
$947$	311.949	+	180.104i	0.329408	+	0.190184i	−0.326170	+	0.945311i	$0.605758\pi$
$948$	78.4157	+	68.9506i	0.0827170	+	0.0727327i
$949$	−429.441	+	247.938i	−0.452520	+	0.261262i
$950$	−568.596	−	214.430i	−0.598522	−	0.225715i
$951$		−	75.7642i		−	0.0796679i
$952$		0			0
$953$	1242.81			1.30410			0.652051	−	0.758175i	$-0.273909\pi$
$953$	1242.81			1.30410			0.652051	+	0.758175i	$0.273909\pi$
$954$	396.081	−	1050.28i	0.415180	−	1.10092i
$955$	−49.6976	−	86.0789i	−0.0520394	−	0.0901349i
$956$	147.186	+	129.420i	0.153960	+	0.135376i
$957$	−28.3116	+	49.0372i	−0.0295838	+	0.0512406i
$958$	−1790.68	+	294.438i	−1.86918	+	0.307346i
$959$		0			0
$960$	32.3524	−	48.0094i	0.0337004	−	0.0500098i
$961$	51.0585	−	88.4359i	0.0531306	−	0.0920248i
$962$	688.284	+	839.797i	0.715472	+	0.872970i
$963$	70.7610	−	40.8539i	0.0734798	−	0.0424236i
$964$	−774.046	−	155.021i	−0.802952	−	0.160810i
$965$	865.742			0.897142
$966$		0			0
$967$	81.8793			0.0846735			0.0423368	−	0.999103i	$-0.486520\pi$
$967$	81.8793			0.0846735			0.0423368	+	0.999103i	$0.486520\pi$
$968$	470.602	+	16.3313i	0.486159	+	0.0168712i
$969$	51.9298	−	29.9817i	0.0535912	−	0.0309409i
$970$	213.023	+	259.917i	0.219612	+	0.267955i
$971$	409.052	−	708.499i	0.421269	−	0.729660i	−0.574795	−	0.818298i	$-0.694918\pi$
$971$	409.052	−	708.499i	0.421269	−	0.729660i	0.996064	+	0.0886380i	$0.0282514\pi$
$972$	230.992	−	78.0742i	0.237646	−	0.0803232i
$973$		0			0
$974$	273.522	+	1663.47i	0.280823	+	1.70788i
$975$	28.1412	−	48.7419i	0.0288627	−	0.0499917i
$976$	747.140	+	311.770i	0.765512	+	0.319437i
$977$	−448.155	−	776.227i	−0.458705	−	0.794500i	0.540188	−	0.841544i	$-0.318353\pi$
$977$	−448.155	−	776.227i	−0.458705	−	0.794500i	−0.998893	+	0.0470441i	$0.985020\pi$
$978$	−28.5402	+	75.6793i	−0.0291823	+	0.0773817i
$979$	1212.63			1.23864
$980$		0			0
$981$			1065.14i			1.08577i
$982$	−101.713	+	269.710i	−0.103578	+	0.274654i
$983$	−852.404	+	492.136i	−0.867146	+	0.500647i	−0.866399	−	0.499353i	$-0.833571\pi$
$983$	−852.404	+	492.136i	−0.867146	+	0.500647i	−0.000746983		1.00000i	$0.500238\pi$
$984$	−77.7767	−	48.5767i	−0.0790413	−	0.0493666i
$985$	292.947	+	169.133i	0.297408	+	0.171708i
$986$	87.8030	+	533.990i	0.0890497	+	0.541572i
$987$		0			0
$988$	−1707.26	+	577.044i	−1.72799	+	0.584052i
$989$	−92.7440	−	53.5458i	−0.0937756	−	0.0541414i
$990$	318.967	+	389.182i	0.322189	+	0.393113i
$991$	612.037	+	1060.08i	0.617596	+	1.06971i	0.989923	+	0.141606i	$0.0452265\pi$
$991$	612.037	+	1060.08i	0.617596	+	1.06971i	−0.372327	+	0.928101i	$0.621440\pi$
$992$	−299.606	−	999.434i	−0.302022	−	1.00749i
$993$			95.0667i			0.0957368i
$994$		0			0
$995$		−	1104.24i		−	1.10979i
$996$	−10.2588	+	51.2240i	−0.0103000	+	0.0514297i
$997$	186.825	+	323.590i	0.187387	+	0.324563i	0.944378	−	0.328861i	$-0.106665\pi$
$997$	186.825	+	323.590i	0.187387	+	0.324563i	−0.756991	+	0.653425i	$0.773332\pi$
$998$	−483.235	−	589.610i	−0.484203	−	0.590792i
$999$	117.650	+	67.9254i	0.117768	+	0.0679934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.j.e.117.2		28
7.2	even	3		392.3.h.a.293.15		28
7.3	odd	6	inner	392.3.j.e.325.12		28
7.4	even	3		56.3.j.a.45.12	yes	28
7.5	odd	6		392.3.h.a.293.16		28
7.6	odd	2		56.3.j.a.5.2	✓	28
8.5	even	2	inner	392.3.j.e.117.12		28
28.11	odd	6		224.3.n.a.17.7		28
28.19	even	6		1568.3.h.a.881.14		28
28.23	odd	6		1568.3.h.a.881.16		28
28.27	even	2		224.3.n.a.145.8		28
56.5	odd	6		392.3.h.a.293.13		28
56.11	odd	6		224.3.n.a.17.8		28
56.13	odd	2		56.3.j.a.5.12	yes	28
56.19	even	6		1568.3.h.a.881.15		28
56.27	even	2		224.3.n.a.145.7		28
56.37	even	6		392.3.h.a.293.14		28
56.45	odd	6	inner	392.3.j.e.325.2		28
56.51	odd	6		1568.3.h.a.881.13		28
56.53	even	6		56.3.j.a.45.2	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.2	✓	28	7.6	odd	2
56.3.j.a.5.12	yes	28	56.13	odd	2
56.3.j.a.45.2	yes	28	56.53	even	6
56.3.j.a.45.12	yes	28	7.4	even	3
224.3.n.a.17.7		28	28.11	odd	6
224.3.n.a.17.8		28	56.11	odd	6
224.3.n.a.145.7		28	56.27	even	2
224.3.n.a.145.8		28	28.27	even	2
392.3.h.a.293.13		28	56.5	odd	6
392.3.h.a.293.14		28	56.37	even	6
392.3.h.a.293.15		28	7.2	even	3
392.3.h.a.293.16		28	7.5	odd	6
392.3.j.e.117.2		28	1.1	even	1	trivial
392.3.j.e.117.12		28	8.5	even	2	inner
392.3.j.e.325.2		28	56.45	odd	6	inner
392.3.j.e.325.12		28	7.3	odd	6	inner
1568.3.h.a.881.13		28	56.51	odd	6
1568.3.h.a.881.14		28	28.19	even	6
1568.3.h.a.881.15		28	56.19	even	6
1568.3.h.a.881.16		28	28.23	odd	6

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.87135 - 0.705725i) q^{2} +(0.126628 + 0.219326i) q^{3} +(3.00390 + 2.64132i) q^{4} +(-1.78589 + 3.09325i) q^{5} +(-0.0821813 - 0.499801i) q^{6} +(-3.75731 - 7.06276i) q^{8} +(4.46793 - 7.73868i) q^{9} +O(q^{10})\)	\(q+(-1.87135 - 0.705725i) q^{2} +(0.126628 + 0.219326i) q^{3} +(3.00390 + 2.64132i) q^{4} +(-1.78589 + 3.09325i) q^{5} +(-0.0821813 - 0.499801i) q^{6} +(-3.75731 - 7.06276i) q^{8} +(4.46793 - 7.73868i) q^{9} +(5.52501 - 4.52821i) q^{10} +(-6.82675 + 3.94142i) q^{11} +(-0.198932 + 0.993300i) q^{12} -18.1529 q^{13} -0.904575 q^{15} +(2.04687 + 15.8685i) q^{16} +(8.26180 - 4.76995i) q^{17} +(-13.8224 + 11.3287i) q^{18} +(12.4094 - 21.4938i) q^{19} +(-13.5349 + 4.57472i) q^{20} +(15.5568 - 2.55798i) q^{22} +(2.14949 - 3.72303i) q^{23} +(1.07327 - 1.71842i) q^{24} +(6.12120 + 10.6022i) q^{25} +(33.9704 + 12.8110i) q^{26} +4.54237 q^{27} -28.3630i q^{29} +(1.69278 + 0.638381i) q^{30} +(28.2372 - 16.3027i) q^{31} +(7.36842 - 31.1401i) q^{32} +(-1.72891 - 0.998189i) q^{33} +(-18.8270 + 3.09569i) q^{34} +(33.8616 - 11.4450i) q^{36} +(25.9006 + 14.9537i) q^{37} +(-38.3911 + 31.4648i) q^{38} +(-2.29867 - 3.98141i) q^{39} +(28.5570 + 0.991016i) q^{40} -45.2606i q^{41} -24.9109i q^{43} +(-30.9174 - 6.19196i) q^{44} +(15.9585 + 27.6409i) q^{45} +(-6.64990 + 5.45015i) q^{46} +(-44.0432 - 25.4284i) q^{47} +(-3.22119 + 2.45833i) q^{48} +(-3.97264 - 24.1604i) q^{50} +(2.09235 + 1.20802i) q^{51} +(-54.5296 - 47.9476i) q^{52} +(-54.3930 + 31.4038i) q^{53} +(-8.50036 - 3.20566i) q^{54} -28.1558i q^{55} +6.28554 q^{57} +(-20.0165 + 53.0771i) q^{58} +(-37.0048 - 64.0942i) q^{59} +(-2.71725 - 2.38927i) q^{60} +(25.2994 - 43.8198i) q^{61} +(-64.3469 + 10.5804i) q^{62} +(-35.7653 + 53.0740i) q^{64} +(32.4191 - 56.1515i) q^{65} +(2.53096 + 3.08810i) q^{66} +(108.673 - 62.7422i) q^{67} +(37.4166 + 7.49357i) q^{68} +1.08875 q^{69} -5.33822 q^{71} +(-71.4439 - 2.47932i) q^{72} +(23.6569 - 13.6583i) q^{73} +(-37.9159 - 46.2624i) q^{74} +(-1.55023 + 2.68508i) q^{75} +(94.0487 - 31.7880i) q^{76} +(1.49183 + 9.07283i) q^{78} +(51.5380 - 89.2664i) q^{79} +(-52.7408 - 22.0080i) q^{80} +(-39.6362 - 68.6519i) q^{81} +(-31.9415 + 84.6984i) q^{82} +51.5695 q^{83} +34.0744i q^{85} +(-17.5802 + 46.6170i) q^{86} +(6.22075 - 3.59155i) q^{87} +(53.4875 + 33.4066i) q^{88} +(-133.222 - 76.9158i) q^{89} +(-10.3570 - 62.9880i) q^{90} +(16.2906 - 5.50613i) q^{92} +(7.15123 + 4.12877i) q^{93} +(64.4749 + 78.6678i) q^{94} +(44.3238 + 76.7711i) q^{95} +(7.76289 - 2.32712i) q^{96} +47.0436i q^{97} +70.4400i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 4 * q^4 - 20 * q^8 - 32 * q^9	\( 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9} - 24 q^{10} + 18 q^{12} + 28 q^{15} + 16 q^{16} + 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} + 30 q^{24} - 32 q^{25} + 30 q^{26} + 22 q^{30} + 6 q^{31} + 88 q^{32} + 6 q^{33} + 256 q^{36} - 6 q^{38} - 20 q^{39} - 102 q^{40} - 42 q^{44} + 68 q^{46} + 294 q^{47} + 400 q^{50} + 168 q^{52} - 330 q^{54} + 124 q^{57} - 22 q^{58} - 62 q^{60} - 520 q^{64} - 52 q^{65} + 306 q^{66} + 456 q^{68} - 136 q^{71} + 96 q^{72} - 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} - 276 q^{80} - 18 q^{81} + 642 q^{82} + 168 q^{86} - 48 q^{87} + 50 q^{88} + 150 q^{89} + 1020 q^{92} - 618 q^{94} + 290 q^{95} - 1044 q^{96}+O(q^{100}) \) 28 * q - 2 * q^2 - 4 * q^4 - 20 * q^8 - 32 * q^9 - 24 * q^10 + 18 * q^12 + 28 * q^15 + 16 * q^16 + 6 * q^17 - 42 * q^18 - 92 * q^22 + 30 * q^23 + 30 * q^24 - 32 * q^25 + 30 * q^26 + 22 * q^30 + 6 * q^31 + 88 * q^32 + 6 * q^33 + 256 * q^36 - 6 * q^38 - 20 * q^39 - 102 * q^40 - 42 * q^44 + 68 * q^46 + 294 * q^47 + 400 * q^50 + 168 * q^52 - 330 * q^54 + 124 * q^57 - 22 * q^58 - 62 * q^60 - 520 * q^64 - 52 * q^65 + 306 * q^66 + 456 * q^68 - 136 * q^71 + 96 * q^72 - 234 * q^73 - 138 * q^74 - 956 * q^78 - 162 * q^79 - 276 * q^80 - 18 * q^81 + 642 * q^82 + 168 * q^86 - 48 * q^87 + 50 * q^88 + 150 * q^89 + 1020 * q^92 - 618 * q^94 + 290 * q^95 - 1044 * q^96

Introduction

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