LMFDB - Embedded newform 392.3.j.e.117.13

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			117.13
Character	$\chi$	$=$	392.117
Dual form			392.3.j.e.325.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.82837 - 0.810594i) q^{2} +(-1.16781 - 2.02271i) q^{3} +(2.68588 - 2.96413i) q^{4} +(1.55055 - 2.68563i) q^{5} +(-3.77480 - 2.75165i) q^{6} +(2.50807 - 7.59668i) q^{8} +(1.77242 - 3.06992i) q^{9} +O(q^{10})$	\(q+(1.82837 - 0.810594i) q^{2} +(-1.16781 - 2.02271i) q^{3} +(2.68588 - 2.96413i) q^{4} +(1.55055 - 2.68563i) q^{5} +(-3.77480 - 2.75165i) q^{6} +(2.50807 - 7.59668i) q^{8} +(1.77242 - 3.06992i) q^{9} +(0.658023 - 6.16719i) q^{10} +(-4.06604 + 2.34753i) q^{11} +(-9.13219 - 1.97120i) q^{12} +6.88097 q^{13} -7.24301 q^{15} +(-1.57215 - 15.9226i) q^{16} +(-14.7184 + 8.49765i) q^{17} +(0.752180 - 7.04966i) q^{18} +(13.1099 - 22.7070i) q^{19} +(-3.79598 - 11.8093i) q^{20} +(-5.53134 + 7.58806i) q^{22} +(-12.9403 + 22.4132i) q^{23} +(-18.2949 + 3.79841i) q^{24} +(7.69160 + 13.3222i) q^{25} +(12.5810 - 5.57767i) q^{26} -29.3001 q^{27} -42.2701i q^{29} +(-13.2429 + 5.87114i) q^{30} +(-15.9024 + 9.18126i) q^{31} +(-15.7812 - 27.8380i) q^{32} +(9.49676 + 5.48296i) q^{33} +(-20.0225 + 27.4675i) q^{34} +(-4.33915 - 13.4991i) q^{36} +(43.1997 + 24.9413i) q^{37} +(5.56358 - 52.1436i) q^{38} +(-8.03569 - 13.9182i) q^{39} +(-16.5130 - 18.5148i) q^{40} +10.7844i q^{41} -24.1791i q^{43} +(-3.96249 + 18.3575i) q^{44} +(-5.49645 - 9.52013i) q^{45} +(-5.49159 + 51.4689i) q^{46} +(-11.8480 - 6.84046i) q^{47} +(-30.3708 + 21.7746i) q^{48} +(24.8620 + 18.1232i) q^{50} +(34.3766 + 19.8474i) q^{51} +(18.4814 - 20.3961i) q^{52} +(6.03948 - 3.48690i) q^{53} +(-53.5714 + 23.7505i) q^{54} +14.5598i q^{55} -61.2396 q^{57} +(-34.2639 - 77.2854i) q^{58} +(53.0922 + 91.9584i) q^{59} +(-19.4538 + 21.4692i) q^{60} +(46.7304 - 80.9395i) q^{61} +(-21.6332 + 29.6771i) q^{62} +(-51.4192 - 38.1060i) q^{64} +(10.6693 - 18.4797i) q^{65} +(21.8081 + 2.32686i) q^{66} +(-77.2753 + 44.6149i) q^{67} +(-14.3435 + 66.4508i) q^{68} +60.4473 q^{69} +81.7898 q^{71} +(-18.8759 - 21.1641i) q^{72} +(119.473 - 68.9780i) q^{73} +(99.2023 + 10.5846i) q^{74} +(17.9647 - 31.1158i) q^{75} +(-32.0950 - 99.8475i) q^{76} +(-25.9743 - 18.9340i) q^{78} +(6.55090 - 11.3465i) q^{79} +(-45.1998 - 20.4665i) q^{80} +(18.2653 + 31.6364i) q^{81} +(8.74179 + 19.7179i) q^{82} -2.15689 q^{83} +52.7041i q^{85} +(-19.5994 - 44.2083i) q^{86} +(-85.5003 + 49.3636i) q^{87} +(7.63553 + 36.7762i) q^{88} +(87.8261 + 50.7064i) q^{89} +(-17.7665 - 12.9509i) q^{90} +(31.6797 + 98.5556i) q^{92} +(37.1421 + 21.4440i) q^{93} +(-27.2074 - 2.90296i) q^{94} +(-40.6550 - 70.4166i) q^{95} +(-37.8788 + 64.4305i) q^{96} +88.9318i q^{97} +16.6432i 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 $

$2$	1.82837	−	0.810594i	0.914185	−	0.405297i
$2$	1.82837	−	0.810594i	0.914185	−	0.405297i
$3$	−1.16781	−	2.02271i	−0.389271	−	0.674238i	0.603080	−	0.797680i	$-0.293940\pi$
$3$	−1.16781	−	2.02271i	−0.389271	−	0.674238i	−0.992352	+	0.123443i	$0.960607\pi$
$4$	2.68588	−	2.96413i	0.671469	−	0.741033i
$5$	1.55055	−	2.68563i	0.310110	−	0.537126i	−0.668276	−	0.743913i	$-0.732968\pi$
$5$	1.55055	−	2.68563i	0.310110	−	0.537126i	0.978386	+	0.206787i	$0.0663009\pi$
$6$	−3.77480	−	2.75165i	−0.629133	−	0.458608i
$7$		0			0
$7$		0			0
$8$	2.50807	−	7.59668i	0.313509	−	0.949585i
$9$	1.77242	−	3.06992i	0.196936	−	0.341102i
$10$	0.658023	−	6.16719i	0.0658023	−	0.616719i
$11$	−4.06604	+	2.34753i	−0.369640	+	0.213412i	−0.673301	−	0.739368i	$-0.735124\pi$
$11$	−4.06604	+	2.34753i	−0.369640	+	0.213412i	0.303661	+	0.952780i	$0.401791\pi$
$12$	−9.13219	−	1.97120i	−0.761016	−	0.164267i
$13$	6.88097			0.529305			0.264653	−	0.964344i	$-0.414743\pi$
$13$	6.88097			0.529305			0.264653	+	0.964344i	$0.414743\pi$
$14$		0			0
$15$	−7.24301			−0.482868
$16$	−1.57215	−	15.9226i	−0.0982592	−	0.995161i
$17$	−14.7184	+	8.49765i	−0.865786	+	0.499862i	−0.865946	−	0.500138i	$-0.833283\pi$
$17$	−14.7184	+	8.49765i	−0.865786	+	0.499862i	0.000159428		1.00000i	$0.499949\pi$
$18$	0.752180	−	7.04966i	0.0417878	−	0.391648i
$19$	13.1099	−	22.7070i	0.689994	−	1.19510i	−0.281845	−	0.959460i	$-0.590947\pi$
$19$	13.1099	−	22.7070i	0.689994	−	1.19510i	0.971839	−	0.235645i	$-0.0757201\pi$
$20$	−3.79598	−	11.8093i	−0.189799	−	0.590465i
$21$		0			0
$22$	−5.53134	+	7.58806i	−0.251424	+	0.344912i
$23$	−12.9403	+	22.4132i	−0.562620	+	0.974486i	0.434647	+	0.900601i	$0.356873\pi$
$23$	−12.9403	+	22.4132i	−0.562620	+	0.974486i	−0.997267	+	0.0738851i	$0.976460\pi$
$24$	−18.2949	+	3.79841i	−0.762286	+	0.158267i
$25$	7.69160	+	13.3222i	0.307664	+	0.532889i
$26$	12.5810	−	5.57767i	0.483883	−	0.214526i
$27$	−29.3001			−1.08519
$28$		0			0
$29$		−	42.2701i		−	1.45759i	−0.684732	−	0.728795i	$-0.740081\pi$
$29$		−	42.2701i		−	1.45759i	0.684732	−	0.728795i	$-0.259919\pi$
$30$	−13.2429	+	5.87114i	−0.441430	+	0.195705i
$31$	−15.9024	+	9.18126i	−0.512981	+	0.296170i	−0.734058	−	0.679087i	$-0.762376\pi$
$31$	−15.9024	+	9.18126i	−0.512981	+	0.296170i	0.221077	+	0.975256i	$0.429043\pi$
$32$	−15.7812	−	27.8380i	−0.493163	−	0.869937i
$33$	9.49676	+	5.48296i	0.287781	+	0.166150i
$34$	−20.0225	+	27.4675i	−0.588896	+	0.807867i
$35$		0			0
$36$	−4.33915	−	13.4991i	−0.120532	−	0.374975i
$37$	43.1997	+	24.9413i	1.16756	+	0.674090i	0.953104	−	0.302644i	$-0.0978692\pi$
$37$	43.1997	+	24.9413i	1.16756	+	0.674090i	0.214455	+	0.976734i	$0.431203\pi$
$38$	5.56358	−	52.1436i	0.146410	−	1.37220i
$39$	−8.03569	−	13.9182i	−0.206043	−	0.356878i
$40$	−16.5130	−	18.5148i	−0.412825	−	0.462869i
$41$			10.7844i			0.263035i	0.991314	+	0.131517i	$0.0419849\pi$
$41$			10.7844i			0.263035i	−0.991314	+	0.131517i	$0.958015\pi$
$42$		0			0
$43$		−	24.1791i		−	0.562304i	−0.959663	−	0.281152i	$-0.909284\pi$
$43$		−	24.1791i		−	0.562304i	0.959663	−	0.281152i	$-0.0907165\pi$
$44$	−3.96249	+	18.3575i	−0.0900567	+	0.417215i
$45$	−5.49645	−	9.52013i	−0.122143	−	0.211558i
$46$	−5.49159	+	51.4689i	−0.119382	+	1.11889i
$47$	−11.8480	−	6.84046i	−0.252086	−	0.145542i	0.368633	−	0.929575i	$-0.379826\pi$
$47$	−11.8480	−	6.84046i	−0.252086	−	0.145542i	−0.620719	+	0.784033i	$0.713159\pi$
$48$	−30.3708	+	21.7746i	−0.632726	+	0.453638i
$49$		0			0
$50$	24.8620	+	18.1232i	0.497240	+	0.362464i
$51$	34.3766	+	19.8474i	0.674052	+	0.389164i
$52$	18.4814	−	20.3961i	0.355412	−	0.392233i
$53$	6.03948	−	3.48690i	0.113952	−	0.0657905i	−0.441940	−	0.897044i	$-0.645710\pi$
$53$	6.03948	−	3.48690i	0.113952	−	0.0657905i	0.555893	+	0.831254i	$0.312376\pi$
$54$	−53.5714	+	23.7505i	−0.992063	+	0.439823i
$55$			14.5598i			0.264724i
$56$		0			0
$57$	−61.2396			−1.07438
$58$	−34.2639	−	77.2854i	−0.590757	−	1.33251i
$59$	53.0922	+	91.9584i	0.899868	+	1.55862i	0.827662	+	0.561227i	$0.189671\pi$
$59$	53.0922	+	91.9584i	0.899868	+	1.55862i	0.0722059	+	0.997390i	$0.476996\pi$
$60$	−19.4538	+	21.4692i	−0.324230	+	0.357821i
$61$	46.7304	−	80.9395i	0.766073	−	1.32688i	−0.173605	−	0.984815i	$-0.555542\pi$
$61$	46.7304	−	80.9395i	0.766073	−	1.32688i	0.939678	−	0.342062i	$-0.111125\pi$
$62$	−21.6332	+	29.6771i	−0.348923	+	0.478663i
$63$		0			0
$64$	−51.4192	−	38.1060i	−0.803425	−	0.595406i
$65$	10.6693	−	18.4797i	0.164143	−	0.284304i
$66$	21.8081	+	2.32686i	0.330425	+	0.0352555i
$67$	−77.2753	+	44.6149i	−1.15336	+	0.665894i	−0.949705	−	0.313147i	$-0.898617\pi$
$67$	−77.2753	+	44.6149i	−1.15336	+	0.665894i	−0.203659	+	0.979042i	$0.565283\pi$
$68$	−14.3435	+	66.4508i	−0.210934	+	0.977218i
$69$	60.4473			0.876047
$70$		0			0
$71$	81.7898			1.15197			0.575984	−	0.817461i	$-0.304619\pi$
$71$	81.7898			1.15197			0.575984	+	0.817461i	$0.304619\pi$
$72$	−18.8759	−	21.1641i	−0.262165	−	0.293946i
$73$	119.473	−	68.9780i	1.63662	−	0.944904i	0.654637	−	0.755943i	$-0.272821\pi$
$73$	119.473	−	68.9780i	1.63662	−	0.944904i	0.981985	−	0.188961i	$-0.0605120\pi$
$74$	99.2023	+	10.5846i	1.34057	+	0.143035i
$75$	17.9647	−	31.1158i	0.239529	−	0.414877i
$76$	−32.0950	−	99.8475i	−0.422302	−	1.31378i
$77$		0			0
$78$	−25.9743	−	18.9340i	−0.333003	−	0.242744i
$79$	6.55090	−	11.3465i	0.0829228	−	0.143627i	−0.821581	−	0.570091i	$-0.806908\pi$
$79$	6.55090	−	11.3465i	0.0829228	−	0.143627i	0.904504	+	0.426465i	$0.140241\pi$
$80$	−45.1998	−	20.4665i	−0.564998	−	0.255832i
$81$	18.2653	+	31.6364i	0.225497	+	0.390573i
$82$	8.74179	+	19.7179i	0.106607	+	0.240463i
$83$	−2.15689			−0.0259867			−0.0129933	−	0.999916i	$-0.504136\pi$
$83$	−2.15689			−0.0259867			−0.0129933	+	0.999916i	$0.504136\pi$
$84$		0			0
$85$			52.7041i			0.620048i
$86$	−19.5994	−	44.2083i	−0.227900	−	0.514050i
$87$	−85.5003	+	49.3636i	−0.982762	+	0.567398i
$88$	7.63553	+	36.7762i	0.0867674	+	0.417911i
$89$	87.8261	+	50.7064i	0.986810	+	0.569735i	0.904319	−	0.426857i	$-0.140379\pi$
$89$	87.8261	+	50.7064i	0.986810	+	0.569735i	0.0824908	+	0.996592i	$0.473712\pi$
$90$	−17.7665	−	12.9509i	−0.197405	−	0.143899i
$91$		0			0
$92$	31.6797	+	98.5556i	0.344344	+	1.07126i
$93$	37.1421	+	21.4440i	0.399378	+	0.230581i
$94$	−27.2074	−	2.90296i	−0.289440	−	0.0308825i
$95$	−40.6550	−	70.4166i	−0.427948	−	0.741227i
$96$	−37.8788	+	64.4305i	−0.394570	+	0.671151i
$97$			88.9318i			0.916823i	0.888740	+	0.458412i	$0.151581\pi$
$97$			88.9318i			0.916823i	−0.888740	+	0.458412i	$0.848419\pi$
$98$		0			0
$99$			16.6432i			0.168114i
$100$	60.1475	+	12.9830i	0.601475	+	0.129830i
$101$	10.4239	+	18.0546i	0.103206	+	0.178759i	0.913004	−	0.407951i	$-0.133756\pi$
$101$	10.4239	+	18.0546i	0.103206	+	0.178759i	−0.809798	+	0.586709i	$0.800423\pi$
$102$	78.9414	+	8.42283i	0.773935	+	0.0825768i
$103$	−2.97469	−	1.71744i	−0.0288805	−	0.0166741i	0.485490	−	0.874242i	$-0.338641\pi$
$103$	−2.97469	−	1.71744i	−0.0288805	−	0.0166741i	−0.514371	+	0.857568i	$0.671974\pi$
$104$	17.2579	−	52.2725i	0.165942	−	0.502621i
$105$		0			0
$106$	8.21595	−	11.2709i	0.0775090	−	0.106329i
$107$	58.4603	+	33.7521i	0.546358	+	0.315440i	0.747652	−	0.664091i	$-0.231181\pi$
$107$	58.4603	+	33.7521i	0.546358	+	0.315440i	−0.201294	+	0.979531i	$0.564515\pi$
$108$	−78.6964	+	86.8493i	−0.728670	+	0.804160i
$109$	116.961	−	67.5273i	1.07303	−	0.619516i	0.144025	−	0.989574i	$-0.453995\pi$
$109$	116.961	−	67.5273i	1.07303	−	0.619516i	0.929009	+	0.370058i	$0.120662\pi$
$110$	11.8021	+	26.6208i	0.107292	+	0.242007i
$111$		−	116.507i		−	1.04962i
$112$		0			0
$113$	136.328			1.20645			0.603223	−	0.797573i	$-0.293883\pi$
$113$	136.328			1.20645			0.603223	+	0.797573i	$0.293883\pi$
$114$	−111.969	+	49.6405i	−0.982182	+	0.435443i
$115$	40.1290	+	69.5055i	0.348948	+	0.604395i
$116$	−125.294	−	113.532i	−1.08012	−	0.978726i
$117$	12.1960	−	21.1240i	0.104239	−	0.180547i
$118$	171.613	+	125.098i	1.45435	+	1.06015i
$119$		0			0
$120$	−18.1660	+	55.0229i	−0.151383	+	0.458524i
$121$	−49.4782	+	85.6988i	−0.408911	+	0.708254i
$122$	19.8315	−	185.867i	0.162553	−	1.52350i
$123$	21.8138	−	12.5942i	0.177348	−	0.102392i
$124$	−15.4974	+	71.7965i	−0.124979	+	0.579004i
$125$	125.232			1.00186
$126$		0			0
$127$	−6.39702			−0.0503702			−0.0251851	−	0.999683i	$-0.508018\pi$
$127$	−6.39702			−0.0503702			−0.0251851	+	0.999683i	$0.508018\pi$
$128$	−124.902	−	27.9918i	−0.975795	−	0.218686i
$129$	−48.9073	+	28.2366i	−0.379126	+	0.218889i
$130$	4.52784	−	42.4363i	0.0348295	−	0.326433i
$131$	−86.8472	+	150.424i	−0.662956	+	1.14827i	0.316879	+	0.948466i	$0.397365\pi$
$131$	−86.8472	+	150.424i	−0.662956	+	1.14827i	−0.979835	+	0.199807i	$0.935968\pi$
$132$	41.7593	−	13.4231i	0.316359	−	0.101690i
$133$		0			0
$134$	−105.123	+	144.212i	−0.784502	+	1.07621i
$135$	−45.4312	+	78.6892i	−0.336528	+	0.582883i
$136$	27.6393	+	133.123i	0.203230	+	0.978849i
$137$	38.2926	+	66.3247i	0.279508	+	0.484122i	0.971262	−	0.238011i	$-0.0764954\pi$
$137$	38.2926	+	66.3247i	0.279508	+	0.484122i	−0.691755	+	0.722133i	$0.743162\pi$
$138$	110.520	−	48.9982i	0.800869	−	0.355059i
$139$	72.4724			0.521384			0.260692	−	0.965422i	$-0.416049\pi$
$139$	72.4724			0.521384			0.260692	+	0.965422i	$0.416049\pi$
$140$		0			0
$141$			31.9535i			0.226621i
$142$	149.542	−	66.2983i	1.05311	−	0.466889i
$143$	−27.9783	+	16.1533i	−0.195653	+	0.112960i
$144$	−51.6675	−	23.3951i	−0.358802	−	0.162466i
$145$	−113.522	−	65.5419i	−0.782909	−	0.452013i
$146$	162.528	−	222.962i	1.11321	−	1.52714i
$147$		0			0
$148$	189.958	−	61.0601i	1.28350	−	0.412569i
$149$	−211.542	−	122.134i	−1.41974	−	0.819690i	−0.423469	−	0.905911i	$-0.639188\pi$
$149$	−211.542	−	122.134i	−1.41974	−	0.819690i	−0.996276	+	0.0862205i	$0.972521\pi$
$150$	7.62387	−	71.4533i	0.0508258	−	0.476355i
$151$	−103.109	−	178.590i	−0.682841	−	1.18272i	−0.974110	−	0.226074i	$-0.927411\pi$
$151$	−103.109	−	178.590i	−0.682841	−	1.18272i	0.291269	−	0.956641i	$-0.405923\pi$
$152$	−139.617	−	156.542i	−0.918535	−	1.02988i
$153$			60.2456i			0.393762i
$154$		0			0
$155$			56.9440i			0.367380i
$156$	−62.8383	−	13.5638i	−0.402810	−	0.0869473i
$157$	−37.2714	−	64.5559i	−0.237397	−	0.411184i	0.722569	−	0.691298i	$-0.242961\pi$
$157$	−37.2714	−	64.5559i	−0.237397	−	0.411184i	−0.959967	+	0.280114i	$0.909628\pi$
$158$	2.78008	−	26.0557i	0.0175954	−	0.164910i
$159$	−14.1060	−	8.14409i	−0.0887169	−	0.0512207i
$160$	−99.2321	−	0.781686i	−0.620200	−	0.00488554i
$161$		0			0
$162$	59.0400	+	43.0373i	0.364444	+	0.265662i
$163$	85.1169	+	49.1422i	0.522189	+	0.301486i	0.737830	−	0.674987i	$-0.235851\pi$
$163$	85.1169	+	49.1422i	0.522189	+	0.301486i	−0.215641	+	0.976473i	$0.569184\pi$
$164$	31.9665	+	28.9656i	0.194917	+	0.176620i
$165$	29.4504	−	17.0032i	0.178487	−	0.103050i
$166$	−3.94360	+	1.74837i	−0.0237566	+	0.0105323i
$167$		−	252.539i		−	1.51221i	−0.654449	−	0.756106i	$-0.727099\pi$
$167$		−	252.539i		−	1.51221i	0.654449	−	0.756106i	$-0.272901\pi$
$168$		0			0
$169$	−121.652			−0.719836
$170$	42.7216	+	96.3626i	0.251304	+	0.566839i
$171$	−46.4724	−	80.4926i	−0.271769	−	0.470717i
$172$	−71.6699	−	64.9419i	−0.416685	−	0.377569i
$173$	−75.1889	+	130.231i	−0.434618	+	0.752781i	−0.997264	−	0.0739171i	$-0.976450\pi$
$173$	−75.1889	+	130.231i	−0.434618	+	0.752781i	0.562646	+	0.826698i	$0.309783\pi$
$174$	−116.312	+	159.561i	−0.668462	+	0.917017i
$175$		0			0
$176$	43.7711	+	61.0512i	0.248700	+	0.346882i
$177$	124.004	−	214.781i	0.700586	−	1.21345i
$178$	201.681	+	21.5188i	1.13304	+	0.120892i
$179$	−89.6246	+	51.7448i	−0.500696	+	0.289077i	−0.729001	−	0.684513i	$-0.760015\pi$
$179$	−89.6246	+	51.7448i	−0.500696	+	0.289077i	0.228305	+	0.973590i	$0.426682\pi$
$180$	−42.9817	−	9.27768i	−0.238787	−	0.0515427i
$181$	−95.1121			−0.525481			−0.262741	−	0.964867i	$-0.584626\pi$
$181$	−95.1121			−0.525481			−0.262741	+	0.964867i	$0.584626\pi$
$182$		0			0
$183$	−218.290			−1.19284
$184$	137.811	+	154.517i	0.748972	+	0.839765i
$185$	133.966	−	77.3455i	0.724143	−	0.418084i
$186$	85.2919	+	9.10042i	0.458559	+	0.0489270i
$187$	39.8970	−	69.1036i	0.213353	−	0.369538i
$188$	−52.0983	+	16.7465i	−0.277119	+	0.0890770i
$189$		0			0
$190$	−131.412	−	95.7929i	−0.691640	−	0.504173i
$191$	−1.97252	+	3.41650i	−0.0103273	+	0.0178874i	−0.871143	−	0.491030i	$-0.836621\pi$
$191$	−1.97252	+	3.41650i	−0.0103273	+	0.0178874i	0.860816	+	0.508917i	$0.169954\pi$
$192$	−17.0295	+	148.507i	−0.0886951	+	0.773474i
$193$	146.091	+	253.037i	0.756949	+	1.31107i	0.944399	+	0.328800i	$0.106644\pi$
$193$	146.091	+	253.037i	0.756949	+	1.31107i	−0.187450	+	0.982274i	$0.560022\pi$
$194$	72.0876	+	162.600i	0.371586	+	0.838146i
$195$	−49.8390			−0.255584
$196$		0			0
$197$			160.503i			0.814735i	0.913264	+	0.407367i	$0.133553\pi$
$197$			160.503i			0.814735i	−0.913264	+	0.407367i	$0.866447\pi$
$198$	13.4909	+	30.4300i	0.0681359	+	0.153687i
$199$	−174.461	+	100.725i	−0.876688	+	0.506156i	−0.869565	−	0.493819i	$-0.835601\pi$
$199$	−174.461	+	100.725i	−0.876688	+	0.506156i	−0.00712311	+	0.999975i	$0.502267\pi$
$200$	120.496	−	25.0175i	0.602479	−	0.125088i
$201$	180.486	+	104.204i	0.897943	+	0.518427i
$202$	33.6936	+	24.5611i	0.166800	+	0.121589i
$203$		0			0
$204$	151.162	−	48.5893i	0.740988	−	0.238183i
$205$	28.9630	+	16.7218i	0.141283	+	0.0815697i
$206$	−6.83098	−	0.728847i	−0.0331601	−	0.00353809i
$207$	45.8711	+	79.4511i	0.221600	+	0.383822i
$208$	−10.8179	−	109.563i	−0.0520091	−	0.526744i
$209$			123.103i			0.589012i
$210$		0			0
$211$		−	170.542i		−	0.808256i	−0.914702	−	0.404128i	$-0.867575\pi$
$211$		−	170.542i		−	0.808256i	0.914702	−	0.404128i	$-0.132425\pi$
$212$	5.88568	−	27.2672i	0.0277626	−	0.128619i
$213$	−95.5152	−	165.437i	−0.448428	−	0.776701i
$214$	134.246	+	14.3237i	0.627319	+	0.0669333i
$215$	−64.9360	−	37.4908i	−0.302028	−	0.174376i
$216$	−73.4866	+	222.583i	−0.340216	+	1.03048i
$217$		0			0
$218$	159.110	−	218.273i	0.729864	−	1.00125i
$219$	−279.045	−	161.107i	−1.27418	−	0.735648i
$220$	43.1573	+	39.1059i	0.196169	+	0.177754i
$221$	−101.277	+	58.4721i	−0.458265	+	0.264580i
$222$	−94.4402	−	213.019i	−0.425406	−	0.959544i
$223$			143.446i			0.643255i	0.946866	+	0.321628i	$0.104230\pi$
$223$			143.446i			0.643255i	−0.946866	+	0.321628i	$0.895770\pi$
$224$		0			0
$225$	54.5309			0.242360
$226$	249.259	−	110.507i	1.10291	−	0.488969i
$227$	11.7597	+	20.3683i	0.0518047	+	0.0897284i	0.890765	−	0.454464i	$-0.150169\pi$
$227$	11.7597	+	20.3683i	0.0518047	+	0.0897284i	−0.838960	+	0.544193i	$0.816836\pi$
$228$	−164.482	+	181.522i	−0.721412	+	0.796150i
$229$	30.7040	−	53.1809i	0.134079	−	0.232231i	−0.791167	−	0.611601i	$-0.790526\pi$
$229$	30.7040	−	53.1809i	0.134079	−	0.232231i	0.925245	+	0.379370i	$0.123859\pi$
$230$	129.711	+	94.5534i	0.563962	+	0.411102i
$231$		0			0
$232$	−321.113	−	106.016i	−1.38411	−	0.456967i
$233$	−52.0991	+	90.2384i	−0.223601	+	0.387289i	−0.955899	−	0.293696i	$-0.905115\pi$
$233$	−52.0991	+	90.2384i	−0.223601	+	0.387289i	0.732297	+	0.680985i	$0.238448\pi$
$234$	5.17573	−	48.5085i	0.0221185	−	0.207301i
$235$	−36.7419	+	21.2129i	−0.156348	+	0.0902678i
$236$	415.176	+	89.6165i	1.75922	+	0.379731i
$237$	−30.6010			−0.129118
$238$		0			0
$239$	104.695			0.438056			0.219028	−	0.975719i	$-0.429711\pi$
$239$	104.695			0.438056			0.219028	+	0.975719i	$0.429711\pi$
$240$	11.3871	+	115.327i	0.0474462	+	0.480531i
$241$	142.650	−	82.3591i	0.591910	−	0.341739i	−0.173943	−	0.984756i	$-0.555651\pi$
$241$	142.650	−	82.3591i	0.591910	−	0.341739i	0.765852	+	0.643017i	$0.222317\pi$
$242$	−20.9976	+	196.796i	−0.0867669	+	0.813206i
$243$	−89.1895	+	154.481i	−0.367035	+	0.635723i
$244$	−114.403	−	355.909i	−0.468865	−	1.45864i
$245$		0			0
$246$	29.6749	−	40.7090i	0.120630	−	0.165484i
$247$	90.2087	−	156.246i	0.365217	−	0.632575i
$248$	29.8628	+	143.833i	0.120414	+	0.579971i
$249$	2.51885	+	4.36278i	0.0101159	+	0.0175212i
$250$	228.971	−	101.512i	0.915884	−	0.406050i
$251$	−399.066			−1.58990			−0.794952	−	0.606672i	$-0.792504\pi$
$251$	−399.066			−1.58990			−0.794952	+	0.606672i	$0.792504\pi$
$252$		0			0
$253$		−	121.511i		−	0.480279i
$254$	−11.6961	+	5.18538i	−0.0460477	+	0.0204149i
$255$	106.605	−	61.5486i	0.418060	−	0.241367i
$256$	−251.057	+	50.0653i	−0.980690	+	0.195567i
$257$	−2.12341	−	1.22595i	−0.00826231	−	0.00477025i	0.495863	−	0.868401i	$-0.334852\pi$
$257$	−2.12341	−	1.22595i	−0.00826231	−	0.00477025i	−0.504125	+	0.863630i	$0.668185\pi$
$258$	−66.5322	+	91.2710i	−0.257877	+	0.353764i
$259$		0			0
$260$	−26.1200	−	81.2594i	−0.100462	−	0.312536i
$261$	−129.766	−	74.9204i	−0.497187	−	0.287051i
$262$	−36.8563	+	345.428i	−0.140673	+	1.31843i
$263$	−28.7798	−	49.8481i	−0.109429	−	0.189536i	0.806110	−	0.591766i	$-0.201569\pi$
$263$	−28.7798	−	49.8481i	−0.109429	−	0.189536i	−0.915539	+	0.402229i	$0.868236\pi$
$264$	65.4708	−	58.3923i	0.247996	−	0.221183i
$265$		−	21.6264i		−	0.0816091i
$266$		0			0
$267$		−	236.863i		−	0.887126i
$268$	−75.3074	+	348.884i	−0.280998	+	1.30181i
$269$	−120.201	−	208.195i	−0.446845	−	0.773958i	0.551334	−	0.834285i	$-0.314119\pi$
$269$	−120.201	−	208.195i	−0.446845	−	0.773958i	−0.998179	+	0.0603267i	$0.980786\pi$
$270$	−19.2801	+	180.699i	−0.0714079	+	0.669256i
$271$	−116.507	−	67.2655i	−0.429916	−	0.248212i	0.269395	−	0.963030i	$-0.413176\pi$
$271$	−116.507	−	67.2655i	−0.429916	−	0.248212i	−0.699311	+	0.714818i	$0.746510\pi$
$272$	158.444	+	220.995i	0.582514	+	0.812481i
$273$		0			0
$274$	123.775	+	90.2263i	0.451735	+	0.329293i
$275$	−62.5487	−	36.1125i	−0.227450	−	0.131318i
$276$	162.354	−	179.174i	0.588238	−	0.649180i
$277$	95.6097	−	55.2003i	0.345161	−	0.199279i	−0.317391	−	0.948295i	$-0.602807\pi$
$277$	95.6097	−	55.2003i	0.345161	−	0.199279i	0.662552	+	0.749016i	$0.269473\pi$
$278$	132.506	−	58.7457i	0.476642	−	0.211315i
$279$			65.0922i			0.233305i
$280$		0			0
$281$	−154.087			−0.548351			−0.274175	−	0.961680i	$-0.588405\pi$
$281$	−154.087			−0.548351			−0.274175	+	0.961680i	$0.588405\pi$
$282$	25.9013	+	58.4229i	0.0918487	+	0.207173i
$283$	−15.4714	−	26.7972i	−0.0546692	−	0.0946899i	0.837396	−	0.546597i	$-0.184077\pi$
$283$	−15.4714	−	26.7972i	−0.0546692	−	0.0946899i	−0.892065	+	0.451907i	$0.850744\pi$
$284$	219.677	−	242.436i	0.773511	−	0.853646i
$285$	−94.9551	+	164.467i	−0.333176	+	0.577077i
$286$	−38.0610	+	52.2132i	−0.133080	+	0.182564i
$287$		0			0
$288$	−113.431	−	0.893539i	−0.393859	−	0.00310257i
$289$	−0.0797964	+	0.138211i	−0.000276112	+	0.000478240i
$290$	−260.688	−	27.8147i	−0.898923	−	0.0959127i
$291$	179.884	−	103.856i	0.618157	−	0.356893i
$292$	116.431	−	539.401i	0.398736	−	1.84726i
$293$	−511.686			−1.74637			−0.873184	−	0.487390i	$-0.837949\pi$
$293$	−511.686			−1.74637			−0.873184	+	0.487390i	$0.837949\pi$
$294$		0			0
$295$	329.288			1.11623
$296$	297.819	−	265.620i	1.00615	−	0.897364i
$297$	119.135	−	68.7828i	0.401129	−	0.231592i
$298$	−485.778	−	51.8312i	−1.63013	−	0.173930i
$299$	−89.0415	+	154.224i	−0.297798	+	0.515801i
$300$	−43.9803	−	136.823i	−0.146601	−	0.456076i
$301$		0			0
$302$	−333.285	−	242.949i	−1.10359	−	0.804468i
$303$	24.3463	−	42.1689i	0.0803507	−	0.139171i
$304$	−382.164	−	173.044i	−1.25712	−	0.569225i
$305$	−144.916	−	251.001i	−0.475133	−	0.822955i
$306$	48.8347	+	110.151i	0.159591	+	0.359972i
$307$	−51.2670			−0.166993			−0.0834967	−	0.996508i	$-0.526609\pi$
$307$	−51.2670			−0.166993			−0.0834967	+	0.996508i	$0.526609\pi$
$308$		0			0
$309$			8.02259i			0.0259631i
$310$	46.1584	+	104.115i	0.148898	+	0.335854i
$311$	17.7940	−	10.2734i	0.0572153	−	0.0330333i	−0.471119	−	0.882069i	$-0.656150\pi$
$311$	17.7940	−	10.2734i	0.0572153	−	0.0330333i	0.528335	+	0.849036i	$0.322817\pi$
$312$	−125.886	+	26.1368i	−0.403482	+	0.0837716i
$313$	−291.960	−	168.563i	−0.932780	−	0.538541i	−0.0450905	−	0.998983i	$-0.514358\pi$
$313$	−291.960	−	168.563i	−0.932780	−	0.538541i	−0.887690	+	0.460442i	$0.847691\pi$
$314$	−120.475	−	87.8202i	−0.383677	−	0.279682i
$315$		0			0
$316$	−16.0376	−	49.8930i	−0.0507519	−	0.157889i
$317$	80.7634	+	46.6288i	0.254774	+	0.147094i	0.621948	−	0.783058i	$-0.286341\pi$
$317$	80.7634	+	46.6288i	0.254774	+	0.147094i	−0.367174	+	0.930152i	$0.619675\pi$
$318$	−32.3925	−	3.45620i	−0.101863	−	0.0108685i
$319$	99.2304	+	171.872i	0.311067	+	0.538784i
$320$	−182.067	+	79.0077i	−0.568958	+	0.246899i
$321$		−	157.665i		−	0.491167i
$322$		0			0
$323$			445.613i			1.37961i
$324$	142.833	+	30.8307i	0.440842	+	0.0951566i
$325$	52.9256	+	91.6699i	0.162848	+	0.282061i
$326$	195.460	+	20.8550i	0.599569	+	0.0639724i
$327$	−273.177	−	157.719i	−0.835403	−	0.482320i
$328$	81.9259	+	27.0481i	0.249774	+	0.0824637i
$329$		0			0
$330$	40.0635	−	54.9604i	0.121405	−	0.166547i
$331$	−64.9939	−	37.5242i	−0.196356	−	0.113366i	0.398599	−	0.917125i	$-0.369497\pi$
$331$	−64.9939	−	37.5242i	−0.196356	−	0.113366i	−0.594955	+	0.803759i	$0.702830\pi$
$332$	−5.79315	+	6.39332i	−0.0174492	+	0.0192570i
$333$	153.136	−	88.4130i	0.459867	−	0.265505i
$334$	−204.707	−	461.736i	−0.612895	−	1.38244i
$335$			276.711i			0.826002i
$336$		0			0
$337$	−140.105			−0.415743			−0.207872	−	0.978156i	$-0.566654\pi$
$337$	−140.105			−0.415743			−0.207872	+	0.978156i	$0.566654\pi$
$338$	−222.425	+	98.6106i	−0.658063	+	0.291747i
$339$	−159.206	−	275.753i	−0.469635	−	0.813431i
$340$	156.222	+	141.557i	0.459476	+	0.416343i
$341$	43.1066	−	74.6628i	0.126412	−	0.218952i
$342$	−150.216	−	109.500i	−0.439227	−	0.320176i
$343$		0			0
$344$	−183.681	−	60.6427i	−0.533955	−	0.176287i
$345$	93.7264	−	162.339i	0.271671	−	0.470548i
$346$	−31.9087	+	299.058i	−0.0922217	+	0.864330i
$347$	−64.9715	+	37.5113i	−0.187238	+	0.108102i	−0.590689	−	0.806899i	$-0.701144\pi$
$347$	−64.9715	+	37.5113i	−0.187238	+	0.108102i	0.403451	+	0.915001i	$0.367811\pi$
$348$	−83.3229	+	386.019i	−0.239434	+	1.10925i
$349$	603.618			1.72956			0.864782	−	0.502148i	$-0.167457\pi$
$349$	603.618			1.72956			0.864782	+	0.502148i	$0.167457\pi$
$350$		0			0
$351$	−201.613			−0.574396
$352$	129.518	+	76.1436i	0.367948	+	0.216317i
$353$	−337.515	+	194.864i	−0.956132	+	0.552023i	−0.894980	−	0.446106i	$-0.852811\pi$
$353$	−337.515	+	194.864i	−0.956132	+	0.552023i	−0.0611514	+	0.998129i	$0.519477\pi$
$354$	52.6247	−	493.215i	0.148657	−	1.39326i
$355$	126.819	−	219.657i	0.357237	−	0.618752i
$356$	386.190	−	124.137i	1.08480	−	0.348699i
$357$		0			0
$358$	−121.923	+	167.258i	−0.340567	+	0.467200i
$359$	−69.2214	+	119.895i	−0.192817	+	0.333969i	−0.946183	−	0.323633i	$-0.895096\pi$
$359$	−69.2214	+	119.895i	−0.192817	+	0.333969i	0.753366	+	0.657602i	$0.228429\pi$
$360$	−86.1068	+	17.8776i	−0.239186	+	0.0496601i
$361$	−163.238	−	282.737i	−0.452183	−	0.783204i
$362$	−173.900	+	77.0973i	−0.480387	+	0.212976i
$363$	231.125			0.636709
$364$		0			0
$365$		−	427.815i		−	1.17210i
$366$	−399.115	+	176.944i	−1.09048	+	0.483455i
$367$	408.823	−	236.034i	1.11396	−	0.643145i	0.174108	−	0.984727i	$-0.444296\pi$
$367$	408.823	−	236.034i	1.11396	−	0.643145i	0.939852	+	0.341581i	$0.110963\pi$
$368$	377.219	+	170.805i	1.02505	+	0.464145i
$369$	33.1073	+	19.1145i	0.0897218	+	0.0518009i
$370$	182.244	−	250.009i	0.492552	−	0.675699i
$371$		0			0
$372$	163.322	−	52.4982i	0.439038	−	0.141124i
$373$	−30.5419	−	17.6334i	−0.0818818	−	0.0472745i	0.458500	−	0.888694i	$-0.348387\pi$
$373$	−30.5419	−	17.6334i	−0.0818818	−	0.0472745i	−0.540382	+	0.841420i	$0.681720\pi$
$374$	16.9315	−	158.687i	0.0452714	−	0.424298i
$375$	−146.248	−	253.309i	−0.389995	−	0.675491i
$376$	−81.6804	+	72.8493i	−0.217235	+	0.193748i
$377$		−	290.859i		−	0.771510i
$378$		0			0
$379$			230.447i			0.608039i	0.952666	+	0.304019i	$0.0983287\pi$
$379$			230.447i			0.608039i	−0.952666	+	0.304019i	$0.901671\pi$
$380$	−317.918	−	68.6233i	−0.836627	−	0.180588i
$381$	7.47053	+	12.9393i	0.0196077	+	0.0339615i
$382$	−0.837098	+	7.84554i	−0.00219136	+	0.0205381i
$383$	480.020	+	277.140i	1.25332	+	0.723602i	0.971766	−	0.235945i	$-0.0758184\pi$
$383$	480.020	+	277.140i	1.25332	+	0.723602i	0.281549	+	0.959547i	$0.409152\pi$
$384$	89.2427	+	285.330i	0.232403	+	0.743046i
$385$		0			0
$386$	472.219	+	344.225i	1.22337	+	0.891776i
$387$	−74.2278	−	42.8554i	−0.191803	−	0.110738i
$388$	263.606	+	238.860i	0.679396	+	0.615618i
$389$	−344.401	+	198.840i	−0.885349	+	0.511157i	−0.872418	−	0.488760i	$-0.837450\pi$
$389$	−344.401	+	198.840i	−0.885349	+	0.511157i	−0.0129310	+	0.999916i	$0.504116\pi$
$390$	−91.1241	+	40.3991i	−0.233651	+	0.103588i
$391$		−	439.847i		−	1.12493i
$392$		0			0
$393$	405.686			1.03228
$394$	130.103	+	293.458i	0.330209	+	0.744818i
$395$	−20.3150	−	35.1866i	−0.0514304	−	0.0890800i
$396$	49.3327	+	44.7017i	0.124578	+	0.112883i
$397$	60.9545	−	105.576i	0.153538	−	0.265935i	−0.778988	−	0.627039i	$-0.784267\pi$
$397$	60.9545	−	105.576i	0.153538	−	0.265935i	0.932526	+	0.361104i	$0.117600\pi$
$398$	−237.332	+	325.580i	−0.596312	+	0.818039i
$399$		0			0
$400$	200.032	−	143.415i	0.500080	−	0.358536i
$401$	−124.337	+	215.358i	−0.310067	+	0.537051i	−0.978377	−	0.206832i	$-0.933685\pi$
$401$	−124.337	+	215.358i	−0.310067	+	0.537051i	0.668310	+	0.743883i	$0.267018\pi$
$402$	414.463	+	44.2221i	1.03100	+	0.110005i
$403$	−109.424	+	63.1760i	−0.271524	+	0.156764i
$404$	81.5135	+	17.5949i	0.201766	+	0.0435516i
$405$	113.285			0.279716
$406$		0			0
$407$	−234.202			−0.575435
$408$	236.993	−	211.370i	0.580865	−	0.518063i
$409$	−582.721	+	336.434i	−1.42475	+	0.822578i	−0.996700	−	0.0811790i	$-0.974131\pi$
$409$	−582.721	+	336.434i	−1.42475	+	0.822578i	−0.428047	+	0.903757i	$0.640798\pi$
$410$	66.5096	+	7.09640i	0.162219	+	0.0173083i
$411$	89.4372	−	154.910i	0.217609	−	0.376909i
$412$	−13.0804	+	4.20455i	−0.0317484	+	0.0102052i
$413$		0			0
$414$	148.272	+	108.083i	0.358145	+	0.261071i
$415$	−3.34437	+	5.79262i	−0.00805872	+	0.0139581i
$416$	−108.590	−	191.552i	−0.261034	−	0.460462i
$417$	−84.6343	−	146.591i	−0.202960	−	0.351537i
$418$	99.7869	+	225.079i	0.238725	+	0.538466i
$419$	178.795			0.426718			0.213359	−	0.976974i	$-0.431560\pi$
$419$	178.795			0.426718			0.213359	+	0.976974i	$0.431560\pi$
$420$		0			0
$421$			212.470i			0.504679i	0.967639	+	0.252340i	$0.0812000\pi$
$421$			212.470i			0.504679i	−0.967639	+	0.252340i	$0.918800\pi$
$422$	−138.240	−	311.814i	−0.327584	−	0.738896i
$423$	−41.9993	+	24.2483i	−0.0992892	+	0.0573247i
$424$	−11.3414	−	54.6254i	−0.0267486	−	0.128833i
$425$	−226.415	−	130.721i	−0.532742	−	0.307579i
$426$	−308.740	−	225.056i	−0.724741	−	0.528302i
$427$		0			0
$428$	257.063	−	82.6301i	0.600614	−	0.193061i
$429$	65.3470	+	37.7281i	0.152324	+	0.0879442i
$430$	−149.117	−	15.9104i	−0.346783	−	0.0370009i
$431$	345.732	+	598.826i	0.802163	+	1.38939i	0.918190	+	0.396141i	$0.129651\pi$
$431$	345.732	+	598.826i	0.802163	+	1.38939i	−0.116027	+	0.993246i	$0.537016\pi$
$432$	46.0640	+	466.533i	0.106630	+	1.07994i
$433$		−	99.8389i		−	0.230575i	−0.993332	−	0.115287i	$-0.963221\pi$
$433$		−	99.8389i		−	0.230575i	0.993332	−	0.115287i	$-0.0367789\pi$
$434$		0			0
$435$			306.163i			0.703823i
$436$	113.982	−	528.057i	0.261427	−	1.21114i
$437$	339.290	+	587.668i	0.776408	+	1.34478i
$438$	−640.791	−	68.3707i	−1.46299	−	0.156097i
$439$	599.369	+	346.046i	1.36530	+	0.788259i	0.990324	−	0.138774i	$-0.0443161\pi$
$439$	599.369	+	346.046i	1.36530	+	0.788259i	0.374980	+	0.927033i	$0.377649\pi$
$440$	110.607	+	36.5171i	0.251378	+	0.0829934i
$441$		0			0
$442$	−137.774	+	189.003i	−0.311706	+	0.427608i
$443$	233.569	+	134.851i	0.527244	+	0.304405i	0.739893	−	0.672724i	$-0.234876\pi$
$443$	233.569	+	134.851i	0.527244	+	0.304405i	−0.212649	+	0.977129i	$0.568209\pi$
$444$	−345.343	−	312.924i	−0.777800	−	0.704785i
$445$	272.357	−	157.246i	0.612039	−	0.353361i
$446$	116.276	+	262.272i	0.260709	+	0.588054i
$447$			570.519i			1.27633i
$448$		0			0
$449$	−76.6510			−0.170715			−0.0853575	−	0.996350i	$-0.527203\pi$
$449$	−76.6510			−0.170715			−0.0853575	+	0.996350i	$0.527203\pi$
$450$	99.7028	−	44.2024i	0.221562	−	0.0982277i
$451$	−25.3168	−	43.8500i	−0.0561348	−	0.0972283i
$452$	366.161	−	404.095i	0.810090	−	0.894016i
$453$	−240.824	+	417.120i	−0.531621	+	0.920795i
$454$	38.0115	+	27.7086i	0.0837257	+	0.0610320i
$455$		0			0
$456$	−153.593	+	465.218i	−0.336827	+	1.02022i
$457$	175.616	−	304.177i	0.384281	−	0.665594i	−0.607388	−	0.794405i	$-0.707783\pi$
$457$	175.616	−	304.177i	0.384281	−	0.665594i	0.991669	+	0.128811i	$0.0411160\pi$
$458$	13.0302	−	122.123i	0.0284502	−	0.266644i
$459$	431.249	−	248.982i	0.939541	−	0.542444i
$460$	313.805	+	67.7354i	0.682184	+	0.147251i
$461$	−296.940			−0.644122			−0.322061	−	0.946719i	$-0.604376\pi$
$461$	−296.940			−0.644122			−0.322061	+	0.946719i	$0.604376\pi$
$462$		0			0
$463$	25.5350			0.0551513			0.0275756	−	0.999620i	$-0.491221\pi$
$463$	25.5350			0.0551513			0.0275756	+	0.999620i	$0.491221\pi$
$464$	−673.049	+	66.4548i	−1.45054	+	0.143222i
$465$	115.181	−	66.5000i	0.247702	−	0.143011i
$466$	−22.1099	+	207.220i	−0.0474461	+	0.444679i
$467$	−62.7601	+	108.704i	−0.134390	+	0.232770i	−0.925364	−	0.379079i	$-0.876241\pi$
$467$	−62.7601	+	108.704i	−0.134390	+	0.232770i	0.790974	+	0.611849i	$0.209574\pi$
$468$	−29.8576	−	92.8870i	−0.0637982	−	0.198476i
$469$		0			0
$470$	−49.9827	+	68.5678i	−0.106346	+	0.145889i
$471$	−87.0521	+	150.779i	−0.184824	+	0.320125i
$472$	831.738	−	172.687i	1.76216	−	0.365862i
$473$	56.7611	+	98.3131i	0.120002	+	0.207850i
$474$	−55.9499	+	24.8049i	−0.118038	+	0.0523311i
$475$	403.344			0.849145
$476$		0			0
$477$		−	24.7210i		−	0.0518259i
$478$	191.422	−	84.8654i	0.400464	−	0.177543i
$479$	150.188	−	86.7108i	0.313544	−	0.181025i	−0.334967	−	0.942230i	$-0.608725\pi$
$479$	150.188	−	86.7108i	0.313544	−	0.181025i	0.648511	+	0.761205i	$0.275392\pi$
$480$	114.303	+	201.631i	0.238132	+	0.420064i
$481$	297.256	+	171.621i	0.617995	+	0.356800i
$482$	194.058	−	266.214i	0.402609	−	0.552312i
$483$		0			0
$484$	121.130	+	376.836i	0.250269	+	0.778587i
$485$	238.838	+	137.893i	0.492449	+	0.284316i
$486$	−37.8503	+	354.744i	−0.0778812	+	0.729927i
$487$	340.756	+	590.206i	0.699704	+	1.21192i	0.968569	+	0.248744i	$0.0800179\pi$
$487$	340.756	+	590.206i	0.699704	+	1.21192i	−0.268866	+	0.963178i	$0.586649\pi$
$488$	−497.669	−	557.998i	−1.01981	−	1.14344i
$489$		−	229.556i		−	0.469440i
$490$		0			0
$491$		−	278.104i		−	0.566404i	−0.959060	−	0.283202i	$-0.908603\pi$
$491$		−	278.104i		−	0.566404i	0.959060	−	0.283202i	$-0.0913966\pi$
$492$	21.2583	−	98.4855i	0.0432079	−	0.200174i
$493$	359.197	+	622.147i	0.728594	+	1.26196i
$494$	38.2828	−	358.798i	0.0774956	−	0.726312i
$495$	44.6976	+	25.8062i	0.0902981	+	0.0521336i
$496$	171.190	+	238.773i	0.345142	+	0.481397i
$497$		0			0
$498$	8.14184	+	5.93501i	0.0163491	+	0.0119177i
$499$	355.447	+	205.217i	0.712319	+	0.411258i	0.811919	−	0.583770i	$-0.198423\pi$
$499$	355.447	+	205.217i	0.712319	+	0.411258i	−0.0996002	+	0.995028i	$0.531756\pi$
$500$	336.358	−	371.205i	0.672716	−	0.742410i
$501$	−510.815	+	294.919i	−1.01959	+	0.588661i
$502$	−729.641	+	323.481i	−1.45347	+	0.644384i
$503$			554.042i			1.10148i	0.834678	+	0.550738i	$0.185654\pi$
$503$			554.042i			1.10148i	−0.834678	+	0.550738i	$0.814346\pi$
$504$		0			0
$505$	64.6508			0.128021
$506$	−98.4957	−	222.166i	−0.194656	−	0.439064i
$507$	142.067	+	246.068i	0.280212	+	0.485341i
$508$	−17.1816	+	18.9616i	−0.0338220	+	0.0373260i
$509$	−22.0971	+	38.2733i	−0.0434127	+	0.0751931i	−0.886915	−	0.461932i	$-0.847156\pi$
$509$	−22.0971	+	38.2733i	−0.0434127	+	0.0751931i	0.843503	+	0.537125i	$0.180490\pi$
$510$	145.023	−	198.947i	0.284359	−	0.390093i
$511$		0			0
$512$	−418.442	+	295.043i	−0.817270	+	0.576256i
$513$	−384.121	+	665.317i	−0.748773	+	1.29691i
$514$	−4.87614	−	0.520271i	−0.00948665	−	0.00101220i
$515$	−9.22480	+	5.32594i	−0.0179122	+	0.0103416i
$516$	−47.6618	+	220.808i	−0.0923679	+	0.427922i
$517$	64.2327			0.124241
$518$		0			0
$519$	351.227			0.676738
$520$	−113.625	−	127.400i	−0.218510	−	0.244999i
$521$	−363.862	+	210.076i	−0.698392	+	0.403217i	−0.806748	−	0.590895i	$-0.798775\pi$
$521$	−363.862	+	210.076i	−0.698392	+	0.403217i	0.108356	+	0.994112i	$0.465441\pi$
$522$	−297.990	−	31.7947i	−0.570862	−	0.0609095i
$523$	137.447	−	238.065i	0.262805	−	0.455191i	−0.704181	−	0.710020i	$-0.748686\pi$
$523$	137.447	−	238.065i	0.262805	−	0.455191i	0.966986	+	0.254829i	$0.0820192\pi$
$524$	212.615	+	661.446i	0.405754	+	1.26230i
$525$		0			0
$526$	−93.0267	−	67.8120i	−0.176857	−	0.128920i
$527$	156.038	−	270.266i	0.296088	−	0.512839i
$528$	72.3725	−	159.833i	0.137069	−	0.302714i
$529$	−70.4004	−	121.937i	−0.133082	−	0.230505i
$530$	−17.5302	−	39.5411i	−0.0330759	−	0.0746058i
$531$	376.407			0.708864
$532$		0			0
$533$			74.2073i			0.139226i
$534$	−191.999	−	433.073i	−0.359550	−	0.810998i
$535$	181.291	−	104.668i	0.338862	−	0.195642i
$536$	145.114	+	698.933i	0.270735	+	1.30398i
$537$	209.330	+	120.857i	0.389813	+	0.225059i
$538$	−388.534	−	283.223i	−0.722182	−	0.526436i
$539$		0			0
$540$	111.222	+	346.013i	0.205967	+	0.640766i
$541$	485.358	+	280.221i	0.897149	+	0.517969i	0.876274	−	0.481813i	$-0.160022\pi$
$541$	485.358	+	280.221i	0.897149	+	0.517969i	0.0208748	+	0.999782i	$0.493355\pi$
$542$	−267.543	−	28.5462i	−0.493623	−	0.0526682i
$543$	111.073	+	192.385i	0.204555	+	0.354299i
$544$	468.831	+	275.626i	0.861822	+	0.506666i
$545$		−	418.818i		−	0.768473i
$546$		0			0
$547$		−	655.564i		−	1.19847i	−0.800573	−	0.599235i	$-0.795471\pi$
$547$		−	655.564i		−	1.19847i	0.800573	−	0.599235i	$-0.204529\pi$
$548$	299.444	+	64.6356i	0.546431	+	0.117948i
$549$	−165.652	−	286.917i	−0.301734	−	0.522618i
$550$	−143.635	−	15.3254i	−0.261154	−	0.0278645i
$551$	−959.826	−	554.156i	−1.74197	−	1.00573i
$552$	151.606	−	459.199i	0.274648	−	0.831882i
$553$		0			0
$554$	130.065	−	178.427i	0.234774	−	0.322071i
$555$	−312.896	−	180.650i	−0.563776	−	0.325496i
$556$	194.652	−	214.818i	0.350093	−	0.386363i
$557$	−650.172	+	375.377i	−1.16728	+	0.673927i	−0.953037	−	0.302855i	$-0.902060\pi$
$557$	−650.172	+	375.377i	−1.16728	+	0.673927i	−0.214239	+	0.976781i	$0.568727\pi$
$558$	52.7633	+	119.013i	0.0945579	+	0.213284i
$559$		−	166.375i		−	0.297630i
$560$		0			0
$561$	−186.369			−0.332209
$562$	−281.727	+	124.902i	−0.501294	+	0.222245i
$563$	317.191	+	549.391i	0.563394	+	0.975827i	0.997197	+	0.0748195i	$0.0238381\pi$
$563$	317.191	+	549.391i	0.563394	+	0.975827i	−0.433803	+	0.901008i	$0.642829\pi$
$564$	94.7145	+	85.8232i	0.167933	+	0.152169i
$565$	211.384	−	366.127i	0.374130	−	0.648013i
$566$	−50.0091	−	36.4542i	−0.0883553	−	0.0644068i
$567$		0			0
$568$	205.134	−	621.331i	0.361152	−	1.09389i
$569$	−196.482	+	340.317i	−0.345312	+	0.598097i	−0.985410	−	0.170195i	$-0.945560\pi$
$569$	−196.482	+	340.317i	−0.345312	+	0.598097i	0.640099	+	0.768293i	$0.278893\pi$
$570$	−40.2971	+	377.676i	−0.0706966	+	0.662590i
$571$	466.776	−	269.493i	0.817471	−	0.471967i	−0.0320728	−	0.999486i	$-0.510211\pi$
$571$	466.776	−	269.493i	0.817471	−	0.471967i	0.849543	+	0.527519i	$0.176878\pi$
$572$	−27.2658	+	126.317i	−0.0476675	+	0.220834i
$573$	9.21414			0.0160805
$574$		0			0
$575$	−398.125			−0.692391
$576$	−208.119	+	90.3130i	−0.361317	+	0.156793i
$577$	301.353	−	173.986i	0.522276	−	0.301536i	−0.215589	−	0.976484i	$-0.569167\pi$
$577$	301.353	−	173.986i	0.522276	−	0.301536i	0.737865	+	0.674948i	$0.235834\pi$
$578$	−0.0338640	+	0.317384i	−5.85883e−5	+	0.000549107i
$579$	341.215	−	591.001i	0.589317	−	1.02073i
$580$	−499.180	+	160.456i	−0.860655	+	0.276649i
$581$		0			0
$582$	244.709	−	335.700i	0.420462	−	0.576803i
$583$	−16.3712	+	28.3557i	−0.0280809	+	0.0486376i
$584$	−224.357	−	1080.60i	−0.384172	−	1.85035i
$585$	−37.8209	−	65.5077i	−0.0646511	−	0.111979i
$586$	−935.551	+	414.769i	−1.59650	+	0.707798i
$587$	258.936			0.441118			0.220559	−	0.975374i	$-0.429212\pi$
$587$	258.936			0.441118			0.220559	+	0.975374i	$0.429212\pi$
$588$		0			0
$589$			481.461i			0.817421i
$590$	602.061	−	266.919i	1.02044	−	0.452405i
$591$	324.651	−	187.437i	0.549325	−	0.317153i
$592$	329.214	−	727.061i	0.556105	−	1.22814i
$593$	−66.6525	−	38.4819i	−0.112399	−	0.0648935i	0.442747	−	0.896647i	$-0.354004\pi$
$593$	−66.6525	−	38.4819i	−0.112399	−	0.0648935i	−0.555146	+	0.831753i	$0.687337\pi$
$594$	162.069	−	222.331i	0.272843	−	0.374294i
$595$		0			0
$596$	−930.196	+	299.002i	−1.56073	+	0.501681i
$597$	407.476	+	235.256i	0.682539	+	0.394064i
$598$	−37.7875	+	354.156i	−0.0631898	+	0.592234i
$599$	−579.488	−	1003.70i	−0.967426	−	1.67563i	−0.702951	−	0.711239i	$-0.748135\pi$
$599$	−579.488	−	1003.70i	−0.967426	−	1.67563i	−0.264475	−	0.964392i	$-0.585199\pi$
$600$	−191.320	−	214.513i	−0.318867	−	0.357521i
$601$			976.895i			1.62545i	0.582648	+	0.812724i	$0.302017\pi$
$601$			976.895i			1.62545i	−0.582648	+	0.812724i	$0.697983\pi$
$602$		0			0
$603$			316.306i			0.524553i
$604$	−806.302	−	174.042i	−1.33494	−	0.288149i
$605$	153.437	+	265.760i	0.253614	+	0.439273i
$606$	10.3321	−	96.8354i	0.0170496	−	0.159794i
$607$	684.187	+	395.015i	1.12716	+	0.650767i	0.943219	−	0.332170i	$-0.107781\pi$
$607$	684.187	+	395.015i	1.12716	+	0.650767i	0.183942	+	0.982937i	$0.441114\pi$
$608$	−839.007	−	6.60916i	−1.37994	−	0.0108703i
$609$		0			0
$610$	−468.420	−	341.456i	−0.767901	−	0.559763i
$611$	−81.5259	−	47.0690i	−0.133430	−	0.0770360i
$612$	178.576	+	161.812i	0.291791	+	0.264399i
$613$	−233.690	+	134.921i	−0.381223	+	0.220099i	−0.678350	−	0.734739i	$-0.737305\pi$
$613$	−233.690	+	134.921i	−0.381223	+	0.220099i	0.297127	+	0.954838i	$0.403971\pi$
$614$	−93.7350	+	41.5567i	−0.152663	+	0.0676819i
$615$		−	78.1118i		−	0.127011i
$616$		0			0
$617$	701.515			1.13698			0.568489	−	0.822691i	$-0.307528\pi$
$617$	701.515			1.13698			0.568489	+	0.822691i	$0.307528\pi$
$618$	6.50306	+	14.6683i	0.0105228	+	0.0237351i
$619$	−434.760	−	753.026i	−0.702358	−	1.21652i	−0.967636	−	0.252349i	$-0.918797\pi$
$619$	−434.760	−	753.026i	−0.702358	−	1.21652i	0.265278	−	0.964172i	$-0.414536\pi$
$620$	168.789	+	152.944i	0.272241	+	0.246685i
$621$	379.151	−	656.708i	0.610548	−	1.05750i
$622$	24.2064	−	33.2072i	0.0389171	−	0.0533877i
$623$		0			0
$624$	−208.981	+	149.830i	−0.334905	+	0.240113i
$625$	1.88880	−	3.27149i	0.00302208	−	0.00523439i
$626$	−670.448	−	71.5350i	−1.07100	−	0.114273i
$627$	249.003	−	143.762i	0.397134	−	0.229285i
$628$	−291.459	−	62.9119i	−0.464106	−	0.100178i
$629$	−847.771			−1.34781
$630$		0			0
$631$	100.362			0.159052			0.0795258	−	0.996833i	$-0.474659\pi$
$631$	100.362			0.159052			0.0795258	+	0.996833i	$0.474659\pi$
$632$	−69.7656	−	78.2229i	−0.110389	−	0.123770i
$633$	−344.958	+	199.162i	−0.544957	+	0.314631i
$634$	185.462	+	19.7883i	0.292527	+	0.0312119i
$635$	−9.91889	+	17.1800i	−0.0156203	+	0.0270552i
$636$	−62.0271	+	19.9380i	−0.0975269	+	0.0313490i
$637$		0			0
$638$	320.748	+	233.810i	0.502740	+	0.366474i
$639$	144.966	−	251.088i	0.226863	−	0.392939i
$640$	−268.842	+	292.037i	−0.420066	+	0.456308i
$641$	−530.571	−	918.977i	−0.827724	−	1.43366i	−0.899819	−	0.436263i	$-0.856302\pi$
$641$	−530.571	−	918.977i	−0.827724	−	1.43366i	0.0720947	−	0.997398i	$-0.477032\pi$
$642$	−127.802	−	288.269i	−0.199068	−	0.449017i
$643$	132.853			0.206615			0.103308	−	0.994649i	$-0.467057\pi$
$643$	132.853			0.206615			0.103308	+	0.994649i	$0.467057\pi$
$644$		0			0
$645$			175.129i			0.271518i
$646$	361.211	+	814.745i	0.559150	+	1.26122i
$647$	−998.259	+	576.345i	−1.54290	+	0.890796i	−0.544250	+	0.838923i	$0.683186\pi$
$647$	−998.259	+	576.345i	−1.54290	+	0.890796i	−0.998654	+	0.0518730i	$0.983481\pi$
$648$	286.142	−	59.4093i	0.441578	−	0.0916810i
$649$	−431.750	−	249.271i	−0.665255	−	0.384085i
$650$	171.075	+	124.705i	0.263192	+	0.191854i
$651$		0			0
$652$	374.277	−	120.308i	0.574045	−	0.184521i
$653$	25.1758	+	14.5352i	0.0385540	+	0.0222592i	0.519153	−	0.854681i	$-0.326247\pi$
$653$	25.1758	+	14.5352i	0.0385540	+	0.0222592i	−0.480599	+	0.876940i	$0.659581\pi$
$654$	−627.314	−	66.9327i	−0.959196	−	0.102344i
$655$	269.322	+	466.479i	0.411178	+	0.712181i
$656$	171.716	−	16.9547i	0.261762	−	0.0258456i
$657$		−	489.032i		−	0.744341i
$658$		0			0
$659$		−	705.504i		−	1.07057i	−0.844672	−	0.535283i	$-0.820205\pi$
$659$		−	705.504i		−	1.07057i	0.844672	−	0.535283i	$-0.179795\pi$
$660$	28.7004	−	132.963i	0.0434854	−	0.201460i
$661$	63.6678	+	110.276i	0.0963204	+	0.166832i	0.910159	−	0.414259i	$-0.135959\pi$
$661$	63.6678	+	110.276i	0.0963204	+	0.166832i	−0.813838	+	0.581091i	$0.802626\pi$
$662$	−149.250	−	15.9246i	−0.225453	−	0.0240552i
$663$	236.545	+	136.569i	0.356779	+	0.205987i
$664$	−5.40964	+	16.3852i	−0.00814705	+	0.0246766i
$665$		0			0
$666$	208.322	−	285.783i	0.312796	−	0.429103i
$667$	947.407	+	546.986i	1.42040	+	0.820069i
$668$	−748.560	−	678.289i	−1.12060	−	1.01540i
$669$	290.150	−	167.518i	0.433707	−	0.250401i
$670$	224.300	+	505.929i	0.334776	+	0.755118i
$671$			438.805i			0.653956i
$672$		0			0
$673$	−463.380			−0.688528			−0.344264	−	0.938873i	$-0.611872\pi$
$673$	−463.380			−0.688528			−0.344264	+	0.938873i	$0.611872\pi$
$674$	−256.165	+	113.569i	−0.380066	+	0.168499i
$675$	−225.364	−	390.343i	−0.333873	−	0.578285i
$676$	−326.743	+	360.593i	−0.483347	+	0.533422i
$677$	188.138	−	325.864i	0.277899	−	0.481335i	−0.692963	−	0.720973i	$-0.743695\pi$
$677$	188.138	−	325.864i	0.277899	−	0.481335i	0.970862	+	0.239637i	$0.0770286\pi$
$678$	−514.612	−	375.127i	−0.759014	−	0.553285i
$679$		0			0
$680$	400.376	+	132.185i	0.588789	+	0.194390i
$681$	27.4662	−	47.5729i	0.0403322	−	0.0698574i
$682$	18.2936	−	171.453i	0.0268234	−	0.251398i
$683$	−897.932	+	518.421i	−1.31469	+	0.759035i	−0.982869	−	0.184308i	$-0.940996\pi$
$683$	−897.932	+	518.421i	−1.31469	+	0.759035i	−0.331819	+	0.943343i	$0.607662\pi$
$684$	−363.410	−	78.4427i	−0.531301	−	0.114682i
$685$	237.498			0.346712
$686$		0			0
$687$	−143.426			−0.208772
$688$	−384.993	+	38.0130i	−0.559583	+	0.0552515i
$689$	41.5575	−	23.9932i	0.0603157	−	0.0348233i
$690$	39.7757	−	372.790i	0.0576459	−	0.540275i
$691$	177.535	−	307.499i	0.256924	−	0.445006i	−0.708492	−	0.705719i	$-0.750624\pi$
$691$	177.535	−	307.499i	0.256924	−	0.445006i	0.965416	+	0.260713i	$0.0839575\pi$
$692$	184.074	+	572.654i	0.266003	+	0.827535i
$693$		0			0
$694$	−88.3856	+	121.250i	−0.127357	+	0.174712i
$695$	112.372	−	194.634i	0.161686	−	0.280049i
$696$	160.559	+	773.326i	0.230689	+	1.11110i
$697$	−91.6423	−	158.729i	−0.131481	−	0.227732i
$698$	1103.64	−	489.289i	1.58114	−	0.700987i
$699$	243.368			0.348167
$700$		0			0
$701$		−	1278.63i		−	1.82400i	−0.410185	−	0.912002i	$-0.634536\pi$
$701$		−	1278.63i		−	1.82400i	0.410185	−	0.912002i	$-0.365464\pi$
$702$	−368.623	+	163.426i	−0.525104	+	0.232801i
$703$	1132.69	−	653.956i	1.61122	−	0.930236i
$704$	298.528	+	34.2325i	0.424045	+	0.0486257i
$705$	85.8154	+	49.5455i	0.121724	+	0.0702774i
$706$	−459.146	+	629.871i	−0.650348	+	0.892168i
$707$		0			0
$708$	−303.580	−	944.437i	−0.428785	−	1.33395i
$709$	−1040.03	−	600.464i	−1.46690	−	0.846917i	−0.467589	−	0.883946i	$-0.654877\pi$
$709$	−1040.03	−	600.464i	−1.46690	−	0.846917i	−0.999314	+	0.0370292i	$0.988211\pi$
$710$	53.8195	−	504.413i	0.0758021	−	0.710441i
$711$	−23.2219	−	40.2215i	−0.0326609	−	0.0565704i
$712$	605.474	−	540.012i	0.850385	−	0.758444i
$713$		−	475.231i		−	0.666524i
$714$		0			0
$715$			100.186i			0.140120i
$716$	−87.3422	+	404.639i	−0.121986	+	0.565138i
$717$	−122.265	−	211.769i	−0.170523	−	0.295354i
$718$	−29.3762	+	275.323i	−0.0409140	+	0.383458i
$719$	6.39954	+	3.69478i	0.00890061	+	0.00513877i	0.504444	−	0.863445i	$-0.331698\pi$
$719$	6.39954	+	3.69478i	0.00890061	+	0.00513877i	−0.495543	+	0.868583i	$0.665031\pi$
$720$	−142.944	+	102.485i	−0.198533	+	0.142340i
$721$		0			0
$722$	−527.644	−	384.628i	−0.730809	−	0.532725i
$723$	−333.178	−	192.360i	−0.460827	−	0.266059i
$724$	−255.459	+	281.925i	−0.352844	+	0.389399i
$725$	563.132	−	325.125i	0.776734	−	0.448448i
$726$	422.583	−	187.349i	0.582070	−	0.258056i
$727$		−	1184.67i		−	1.62953i	−0.579788	−	0.814767i	$-0.696865\pi$
$727$		−	1184.67i		−	1.62953i	0.579788	−	0.814767i	$-0.303135\pi$
$728$		0			0
$729$	745.402			1.02250
$730$	−346.784	−	782.204i	−0.475047	−	1.07151i
$731$	205.465	+	355.876i	0.281074	+	0.486835i
$732$	−586.299	+	647.040i	−0.800956	+	0.883934i
$733$	−469.714	+	813.569i	−0.640810	+	1.10992i	0.344442	+	0.938808i	$0.388068\pi$
$733$	−469.714	+	813.569i	−0.640810	+	1.10992i	−0.985252	+	0.171108i	$0.945265\pi$
$734$	556.153	−	762.948i	0.757701	−	1.03944i
$735$		0			0
$736$	828.151	+	6.52364i	1.12520	+	0.00886364i
$737$	209.470	−	362.812i	0.284220	−	0.492283i
$738$	76.0266	+	8.11184i	0.103017	+	0.0109917i
$739$	984.945	−	568.658i	1.33281	−	0.769497i	0.347079	−	0.937836i	$-0.387174\pi$
$739$	984.945	−	568.658i	1.33281	−	0.769497i	0.985729	+	0.168339i	$0.0538404\pi$
$740$	130.555	−	604.834i	0.176425	−	0.817344i
$741$	−421.388			−0.568675
$742$		0			0
$743$	−455.212			−0.612667			−0.306333	−	0.951924i	$-0.599102\pi$
$743$	−455.212			−0.612667			−0.306333	+	0.951924i	$0.599102\pi$
$744$	256.058	−	228.374i	0.344164	−	0.306954i
$745$	−656.012	+	378.749i	−0.880554	+	0.508388i
$746$	−70.1355	−	7.48327i	−0.0940154	−	0.0100312i
$747$	−3.82292	+	6.62150i	−0.00511770	+	0.00886412i
$748$	−97.6739	−	303.864i	−0.130580	−	0.406235i
$749$		0			0
$750$	−472.726	−	344.595i	−0.630301	−	0.459460i
$751$	−94.2623	+	163.267i	−0.125516	+	0.217400i	−0.921934	−	0.387346i	$-0.873392\pi$
$751$	−94.2623	+	163.267i	−0.125516	+	0.217400i	0.796419	+	0.604746i	$0.206725\pi$
$752$	−90.2909	+	199.405i	−0.120068	+	0.265167i
$753$	466.035	+	807.196i	0.618905	+	1.07197i
$754$	−235.769	−	531.798i	−0.312691	−	0.705303i
$755$	−639.502			−0.847023
$756$		0			0
$757$		−	199.539i		−	0.263591i	−0.991277	−	0.131796i	$-0.957926\pi$
$757$		−	199.539i		−	0.263591i	0.991277	−	0.131796i	$-0.0420743\pi$
$758$	186.799	+	421.342i	0.246436	+	0.555860i
$759$	−245.781	+	141.902i	−0.323822	+	0.186959i
$760$	−636.898	+	132.234i	−0.838024	+	0.173992i
$761$	−292.734	−	169.010i	−0.384670	−	0.222089i	0.295178	−	0.955442i	$-0.404621\pi$
$761$	−292.734	−	169.010i	−0.384670	−	0.222089i	−0.679848	+	0.733353i	$0.737954\pi$
$762$	24.1474	+	17.6023i	0.0316896	+	0.0231002i
$763$		0			0
$764$	4.82902	+	15.0231i	0.00632071	+	0.0196637i
$765$	161.797	+	93.4138i	0.211500	+	0.122110i
$766$	1102.30	+	117.613i	1.43904	+	0.153541i
$767$	365.326	+	632.763i	0.476305	+	0.824984i
$768$	394.455	+	449.349i	0.513614	+	0.585090i
$769$			604.446i			0.786015i	0.919535	+	0.393008i	$0.128565\pi$
$769$			604.446i			0.786015i	−0.919535	+	0.393008i	$0.871435\pi$
$770$		0			0
$771$			5.72674i			0.00742768i
$772$	1142.42	+	246.593i	1.47982	+	0.319422i
$773$	390.213	+	675.869i	0.504804	+	0.874346i	0.999985	+	0.00555593i	$0.00176852\pi$
$773$	390.213	+	675.869i	0.504804	+	0.874346i	−0.495181	+	0.868790i	$0.664898\pi$
$774$	−170.454	−	18.1870i	−0.220225	−	0.0234974i
$775$	−244.630	−	141.237i	−0.315651	−	0.182241i
$776$	675.587	+	223.047i	0.870602	+	0.287432i
$777$		0			0
$778$	−468.514	+	642.722i	−0.602203	+	0.826121i
$779$	244.882	+	141.383i	0.314354	+	0.181492i
$780$	−133.861	+	147.729i	−0.171617	+	0.189396i
$781$	−332.561	+	192.004i	−0.425814	+	0.245844i
$782$	−356.537	−	804.203i	−0.455930	−	1.02839i
$783$			1238.52i			1.58176i
$784$		0			0
$785$	−231.164			−0.294477
$786$	741.743	−	328.846i	0.943694	−	0.418379i
$787$	−481.905	−	834.684i	−0.612332	−	1.06059i	−0.990846	−	0.134994i	$-0.956898\pi$
$787$	−481.905	−	834.684i	−0.612332	−	1.06059i	0.378515	−	0.925595i	$-0.376435\pi$
$788$	475.751	+	431.090i	0.603745	+	0.547069i
$789$	−67.2189	+	116.427i	−0.0851951	+	0.147562i
$790$	−65.6654	−	47.8669i	−0.0831207	−	0.0605911i
$791$		0			0
$792$	126.433	+	41.7424i	0.159638	+	0.0527050i
$793$	321.551	−	556.942i	0.405486	−	0.702323i
$794$	25.8679	−	242.442i	0.0325792	−	0.305342i
$795$	−43.7440	+	25.2556i	−0.0550239	+	0.0317681i
$796$	−170.018	+	787.660i	−0.213590	+	0.989523i
$797$	−677.191			−0.849675			−0.424837	−	0.905270i	$-0.639669\pi$
$797$	−677.191			−0.849675			−0.424837	+	0.905270i	$0.639669\pi$
$798$		0			0
$799$	232.511			0.291003
$800$	249.482	−	424.359i	0.311852	−	0.530449i
$801$	311.329	−	179.746i	0.388676	−	0.224402i
$802$	−52.7661	+	494.540i	−0.0657931	+	0.616633i
$803$	−323.856	+	560.935i	−0.403308	+	0.698549i
$804$	793.638	−	255.107i	0.987112	−	0.317297i
$805$		0			0
$806$	−148.858	+	204.207i	−0.184687	+	0.253359i
$807$	−280.746	+	486.265i	−0.347888	+	0.602559i
$808$	163.299	−	33.9044i	0.202103	−	0.0419609i
$809$	208.617	+	361.335i	0.257870	+	0.446645i	0.965671	−	0.259767i	$-0.0836459\pi$
$809$	208.617	+	361.335i	0.257870	+	0.446645i	−0.707801	+	0.706412i	$0.750313\pi$
$810$	207.127	−	91.8280i	0.255712	−	0.113368i
$811$	−1431.94			−1.76564			−0.882821	−	0.469709i	$-0.844359\pi$
$811$	−1431.94			−1.76564			−0.882821	+	0.469709i	$0.844359\pi$
$812$		0			0
$813$			314.215i			0.386488i
$814$	−428.208	+	189.843i	−0.526055	+	0.233222i
$815$	263.956	−	152.395i	0.323872	−	0.186988i
$816$	261.976	−	578.567i	0.321049	−	0.709029i
$817$	−549.033	−	316.985i	−0.672012	−	0.387986i
$818$	−792.719	+	1087.48i	−0.969094	+	1.32943i
$819$		0			0
$820$	127.357	−	40.9375i	0.155313	−	0.0499237i
$821$	−15.8963	−	9.17774i	−0.0193621	−	0.0111787i	0.490288	−	0.871561i	$-0.336892\pi$
$821$	−15.8963	−	9.17774i	−0.0193621	−	0.0111787i	−0.509650	+	0.860382i	$0.670225\pi$
$822$	37.9554	−	355.730i	0.0461745	−	0.432761i
$823$	−720.293	−	1247.58i	−0.875204	−	1.51590i	−0.856545	−	0.516073i	$-0.827393\pi$
$823$	−720.293	−	1247.58i	−0.875204	−	1.51590i	−0.0186596	−	0.999826i	$-0.505940\pi$
$824$	−20.5075	+	18.2903i	−0.0248878	+	0.0221970i
$825$			168.691i			0.204474i
$826$		0			0
$827$			240.040i			0.290255i	0.989413	+	0.145127i	$0.0463592\pi$
$827$			240.040i			0.290255i	−0.989413	+	0.145127i	$0.953641\pi$
$828$	358.708	+	77.4278i	0.433222	+	0.0935118i
$829$	−732.065	−	1267.97i	−0.883070	−	1.52952i	−0.847910	−	0.530140i	$-0.822139\pi$
$829$	−732.065	−	1267.97i	−0.883070	−	1.52952i	−0.0351599	−	0.999382i	$-0.511194\pi$
$830$	−1.41929	+	13.3020i	−0.00170998	+	0.0160265i
$831$	−223.309	−	128.927i	−0.268723	−	0.155147i
$832$	−353.814	−	262.206i	−0.425257	−	0.315152i
$833$		0			0
$834$	−273.569	−	199.418i	−0.328020	−	0.239111i
$835$	−678.227	−	391.575i	−0.812248	−	0.468952i
$836$	364.895	+	330.640i	0.436477	+	0.395503i
$837$	465.942	−	269.012i	0.556681	−	0.321400i
$838$	326.903	−	144.930i	0.390099	−	0.172947i
$839$		−	896.568i		−	1.06861i	−0.845290	−	0.534307i	$-0.820573\pi$
$839$		−	896.568i		−	1.06861i	0.845290	−	0.534307i	$-0.179427\pi$
$840$		0			0
$841$	−945.761			−1.12457
$842$	172.227	+	388.474i	0.204545	+	0.461370i
$843$	179.944	+	311.673i	0.213457	+	0.369719i
$844$	−505.509	−	458.055i	−0.598945	−	0.542719i
$845$	−188.628	+	326.713i	−0.223228	+	0.386642i
$846$	−57.1348	+	78.3793i	−0.0675352	+	0.0926470i
$847$		0			0
$848$	−65.0153	−	90.6822i	−0.0766690	−	0.106937i
$849$	−36.1354	+	62.5884i	−0.0425623	+	0.0737201i
$850$	−519.933	−	55.4755i	−0.611686	−	0.0652653i
$851$	−1118.03	+	645.495i	−1.31378	+	0.758513i
$852$	−746.920	−	161.224i	−0.876666	−	0.189230i
$853$	1376.70			1.61395			0.806973	−	0.590588i	$-0.201104\pi$
$853$	1376.70			1.61395			0.806973	+	0.590588i	$0.201104\pi$
$854$		0			0
$855$	−288.231			−0.337112
$856$	403.026	−	359.452i	0.470825	−	0.419920i
$857$	1048.58	−	605.400i	1.22355	−	0.706418i	0.257878	−	0.966177i	$-0.416977\pi$
$857$	1048.58	−	605.400i	1.22355	−	0.706418i	0.965673	+	0.259760i	$0.0836433\pi$
$858$	150.061	+	16.0111i	0.174896	+	0.0186609i
$859$	−287.326	+	497.663i	−0.334488	+	0.579351i	−0.983386	−	0.181524i	$-0.941897\pi$
$859$	−287.326	+	497.663i	−0.334488	+	0.579351i	0.648898	+	0.760875i	$0.275230\pi$
$860$	−285.538	+	91.7832i	−0.332021	+	0.106725i
$861$		0			0
$862$	1117.53	+	814.627i	1.29644	+	0.945043i
$863$	243.335	−	421.468i	0.281964	−	0.488375i	−0.689905	−	0.723900i	$-0.742348\pi$
$863$	243.335	−	421.468i	0.281964	−	0.488375i	0.971868	+	0.235525i	$0.0756809\pi$
$864$	462.391	+	815.655i	0.535174	+	0.944046i
$865$	233.168	+	403.859i	0.269559	+	0.466889i
$866$	−80.9288	−	182.542i	−0.0934513	−	0.210788i
$867$	0.372749			0.000429930
$868$		0			0
$869$			61.5138i			0.0707869i
$870$	248.174	+	559.779i	0.285257	+	0.643424i
$871$	−531.729	+	306.994i	−0.610481	+	0.352462i
$872$	−219.638	−	1057.88i	−0.251878	−	1.21316i
$873$	273.014	+	157.625i	0.312730	+	0.180555i
$874$	1096.71	+	799.449i	1.25482	+	0.914701i
$875$		0			0
$876$	−1227.02	+	394.414i	−1.40071	+	0.450244i
$877$	−1018.25	−	587.886i	−1.16106	−	0.670337i	−0.209500	−	0.977809i	$-0.567184\pi$
$877$	−1018.25	−	587.886i	−1.16106	−	0.670337i	−0.951557	+	0.307472i	$0.900517\pi$
$878$	1376.37	+	146.855i	1.56762	+	0.167261i
$879$	597.554	+	1034.99i	0.679811	+	1.17747i
$880$	231.830	−	22.8902i	0.263443	−	0.0260116i
$881$			197.506i			0.224183i	0.993698	+	0.112092i	$0.0357550\pi$
$881$			197.506i			0.224183i	−0.993698	+	0.112092i	$0.964245\pi$
$882$		0			0
$883$			739.290i			0.837248i	0.908160	+	0.418624i	$0.137487\pi$
$883$			739.290i			0.837248i	−0.908160	+	0.418624i	$0.862513\pi$
$884$	−98.6975	+	457.246i	−0.111649	+	0.517247i
$885$	−384.547	−	666.056i	−0.434517	−	0.752605i
$886$	536.360	+	57.2282i	0.605373	+	0.0645917i
$887$	379.322	+	219.002i	0.427646	+	0.246902i	0.698343	−	0.715763i	$-0.253921\pi$
$887$	379.322	+	219.002i	0.427646	+	0.246902i	−0.270697	+	0.962665i	$0.587254\pi$
$888$	−885.070	−	292.209i	−0.996700	−	0.329064i
$889$		0			0
$890$	370.508	−	508.274i	0.416301	−	0.571095i
$891$	−148.535	−	85.7566i	−0.166706	−	0.0962476i
$892$	425.192	+	385.278i	0.476673	+	0.431926i
$893$	−310.652	+	179.355i	−0.347875	+	0.200846i
$894$	462.459	+	1043.12i	0.517292	+	1.16680i
$895$			320.931i			0.358582i
$896$		0			0
$897$	415.936			0.463696
$898$	−140.146	+	62.1329i	−0.156065	+	0.0691903i
$899$	388.093	+	672.196i	0.431694	+	0.747716i
$900$	146.463	−	161.637i	0.162737	−	0.179597i
$901$	−59.2609	+	102.643i	−0.0657723	+	0.113921i
$902$	−81.8329	−	59.6523i	−0.0907239	−	0.0661334i
$903$		0			0
$904$	341.921	−	1035.64i	0.378231	−	1.14562i
$905$	−147.476	+	255.436i	−0.162957	+	0.282250i
$906$	−102.201	+	957.861i	−0.112805	+	1.05724i
$907$	−1142.72	+	659.752i	−1.25989	+	0.727400i	−0.973054	−	0.230579i	$-0.925938\pi$
$907$	−1142.72	+	659.752i	−1.25989	+	0.727400i	−0.286840	+	0.957979i	$0.592605\pi$
$908$	91.9594	+	19.8496i	0.101277	+	0.0218608i
$909$	73.9018			0.0813001
$910$		0			0
$911$	206.561			0.226741			0.113371	−	0.993553i	$-0.463835\pi$
$911$	206.561			0.226741			0.113371	+	0.993553i	$0.463835\pi$
$912$	96.2777	+	975.093i	0.105568	+	1.06918i
$913$	8.77002	−	5.06338i	0.00960572	−	0.00554587i
$914$	74.5282	−	698.501i	0.0815407	−	0.764224i
$915$	−338.469	+	586.246i	−0.369912	+	0.640706i
$916$	−75.1680	−	233.848i	−0.0820611	−	0.255292i
$917$		0			0
$918$	586.660	−	804.799i	0.639064	−	0.876688i
$919$	−281.693	+	487.906i	−0.306521	+	0.530910i	−0.977599	−	0.210477i	$-0.932498\pi$
$919$	−281.693	+	487.906i	−0.306521	+	0.530910i	0.671078	+	0.741387i	$0.265832\pi$
$920$	628.657	−	130.523i	0.683323	−	0.141873i
$921$	59.8703	+	103.698i	0.0650058	+	0.112593i
$922$	−542.917	+	240.698i	−0.588847	+	0.261061i
$923$	562.793			0.609743
$924$		0			0
$925$			767.355i			0.829573i
$926$	46.6875	−	20.6985i	0.0504185	−	0.0223526i
$927$	−10.5448	+	6.08804i	−0.0113752	+	0.00656746i
$928$	−1176.71	+	667.073i	−1.26801	+	0.718829i
$929$	1050.66	+	606.600i	1.13096	+	0.652960i	0.944176	−	0.329441i	$-0.106860\pi$
$929$	1050.66	+	606.600i	1.13096	+	0.652960i	0.186784	+	0.982401i	$0.440194\pi$
$930$	156.690	−	214.952i	0.168484	−	0.231131i
$931$		0			0
$932$	127.547	+	396.798i	0.136853	+	0.425749i
$933$	−41.5601	−	23.9947i	−0.0445446	−	0.0257178i
$934$	−26.6342	+	249.624i	−0.0285162	+	0.267263i
$935$	−123.724	−	214.297i	−0.132326	−	0.229195i
$936$	−129.884	−	145.629i	−0.138765	−	0.155587i
$937$			237.201i			0.253149i	0.991957	+	0.126575i	$0.0403983\pi$
$937$			237.201i			0.253149i	−0.991957	+	0.126575i	$0.959602\pi$
$938$		0			0
$939$			787.403i			0.838554i
$940$	−35.8062	+	165.883i	−0.0380917	+	0.176471i
$941$	−59.6021	−	103.234i	−0.0633391	−	0.109707i	0.832617	−	0.553849i	$-0.186842\pi$
$941$	−59.6021	−	103.234i	−0.0633391	−	0.109707i	−0.895956	+	0.444143i	$0.853508\pi$
$942$	−36.9432	+	346.243i	−0.0392179	+	0.367562i
$943$	−241.713	−	139.553i	−0.256324	−	0.147989i
$944$	1380.75	−	989.937i	1.46265	−	1.04866i
$945$		0			0
$946$	183.472	+	133.743i	0.193945	+	0.141377i
$947$	−842.482	−	486.407i	−0.889633	−	0.513630i	−0.0158103	−	0.999875i	$-0.505033\pi$
$947$	−842.482	−	486.407i	−0.889633	−	0.513630i	−0.873822	+	0.486245i	$0.838366\pi$
$948$	−82.1904	+	90.7053i	−0.0866987	+	0.0956807i
$949$	822.093	−	474.636i	0.866273	−	0.500143i
$950$	737.462	−	326.948i	0.776275	−	0.344156i
$951$		−	217.815i		−	0.229038i
$952$		0			0
$953$	−840.555			−0.882010			−0.441005	−	0.897505i	$-0.645378\pi$
$953$	−840.555			−0.882010			−0.441005	+	0.897505i	$0.645378\pi$
$954$	−20.0387	−	45.1991i	−0.0210049	−	0.0473785i
$955$	6.11697	+	10.5949i	0.00640520	+	0.0110941i
$956$	281.199	−	310.331i	0.294141	−	0.324614i
$957$	231.765	−	401.429i	0.242179	−	0.419466i
$958$	204.311	−	280.281i	0.213268	−	0.292568i
$959$		0			0
$960$	372.430	+	276.002i	0.387948	+	0.287502i
$961$	−311.909	+	540.242i	−0.324567	+	0.562167i
$962$	682.608	+	72.8324i	0.709572	+	0.0757094i
$963$	207.232	−	119.646i	0.215195	−	0.124243i
$964$	139.017	−	644.040i	0.144209	−	0.668092i
$965$	906.086			0.938949
$966$		0			0
$967$	1696.40			1.75429			0.877147	−	0.480222i	$-0.159444\pi$
$967$	1696.40			1.75429			0.877147	+	0.480222i	$0.159444\pi$
$968$	526.932	+	590.809i	0.544351	+	0.610339i
$969$	901.347	−	520.393i	0.930183	−	0.537041i
$970$	548.460	+	58.5192i	0.565422	+	0.0603291i
$971$	−644.056	+	1115.54i	−0.663291	+	1.14885i	0.316454	+	0.948608i	$0.397508\pi$
$971$	−644.056	+	1115.54i	−0.663291	+	1.14885i	−0.979746	+	0.200247i	$0.935826\pi$
$972$	218.349	+	679.285i	0.224639	+	0.698853i
$973$		0			0
$974$	1101.44	+	802.901i	1.13085	+	0.824333i
$975$	123.615	−	214.107i	0.126784	−	0.219597i
$976$	−1362.23	−	616.820i	−1.39573	−	0.631988i
$977$	61.9545	+	107.308i	0.0634130	+	0.109835i	0.895989	−	0.444076i	$-0.146468\pi$
$977$	61.9545	+	107.308i	0.0634130	+	0.109835i	−0.832576	+	0.553911i	$0.813135\pi$
$978$	−186.077	−	419.714i	−0.190263	−	0.429155i
$979$	−476.139			−0.486353
$980$		0			0
$981$		−	478.747i		−	0.488019i
$982$	−225.429	−	508.477i	−0.229562	−	0.517798i
$983$	−1425.29	+	822.891i	−1.44994	+	0.837122i	−0.998477	−	0.0551686i	$-0.982430\pi$
$983$	−1425.29	+	822.891i	−1.44994	+	0.837122i	−0.451461	+	0.892291i	$0.649097\pi$
$984$	−40.9637	−	197.300i	−0.0416298	−	0.200508i
$985$	431.051	+	248.867i	0.437615	+	0.252657i
$986$	1161.05	+	846.352i	1.17754	+	0.858369i
$987$		0			0
$988$	−220.844	−	687.048i	−0.223527	−	0.695393i
$989$	541.930	+	312.883i	0.547957	+	0.316363i
$990$	102.642	+	10.9516i	0.103679	+	0.0110623i
$991$	−226.918	−	393.034i	−0.228979	−	0.396603i	0.728527	−	0.685017i	$-0.240205\pi$
$991$	−226.918	−	393.034i	−0.228979	−	0.396603i	−0.957506	+	0.288414i	$0.906872\pi$
$992$	506.547	+	297.800i	0.510632	+	0.300201i
$993$			175.285i			0.176521i
$994$		0			0
$995$			624.717i			0.627856i
$996$	19.6972	+	4.25168i	0.0197763	+	0.00426875i
$997$	−453.413	−	785.334i	−0.454777	−	0.787697i	0.543898	−	0.839151i	$-0.316948\pi$
$997$	−453.413	−	785.334i	−0.454777	−	0.787697i	−0.998675	+	0.0514540i	$0.983614\pi$
$998$	816.237	+	87.0903i	0.817873	+	0.0872648i
$999$	−1265.75	−	730.783i	−1.26702	−	0.731515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.j.e.117.13		28
7.2	even	3		392.3.h.a.293.6		28
7.3	odd	6	inner	392.3.j.e.325.7		28
7.4	even	3		56.3.j.a.45.7	yes	28
7.5	odd	6		392.3.h.a.293.5		28
7.6	odd	2		56.3.j.a.5.13	yes	28
8.5	even	2	inner	392.3.j.e.117.7		28
28.11	odd	6		224.3.n.a.17.10		28
28.19	even	6		1568.3.h.a.881.19		28
28.23	odd	6		1568.3.h.a.881.9		28
28.27	even	2		224.3.n.a.145.5		28
56.5	odd	6		392.3.h.a.293.8		28
56.11	odd	6		224.3.n.a.17.5		28
56.13	odd	2		56.3.j.a.5.7	✓	28
56.19	even	6		1568.3.h.a.881.10		28
56.27	even	2		224.3.n.a.145.10		28
56.37	even	6		392.3.h.a.293.7		28
56.45	odd	6	inner	392.3.j.e.325.13		28
56.51	odd	6		1568.3.h.a.881.20		28
56.53	even	6		56.3.j.a.45.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.7	✓	28	56.13	odd	2
56.3.j.a.5.13	yes	28	7.6	odd	2
56.3.j.a.45.7	yes	28	7.4	even	3
56.3.j.a.45.13	yes	28	56.53	even	6
224.3.n.a.17.5		28	56.11	odd	6
224.3.n.a.17.10		28	28.11	odd	6
224.3.n.a.145.5		28	28.27	even	2
224.3.n.a.145.10		28	56.27	even	2
392.3.h.a.293.5		28	7.5	odd	6
392.3.h.a.293.6		28	7.2	even	3
392.3.h.a.293.7		28	56.37	even	6
392.3.h.a.293.8		28	56.5	odd	6
392.3.j.e.117.7		28	8.5	even	2	inner
392.3.j.e.117.13		28	1.1	even	1	trivial
392.3.j.e.325.7		28	7.3	odd	6	inner
392.3.j.e.325.13		28	56.45	odd	6	inner
1568.3.h.a.881.9		28	28.23	odd	6
1568.3.h.a.881.10		28	56.19	even	6
1568.3.h.a.881.19		28	28.19	even	6
1568.3.h.a.881.20		28	56.51	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)

\(f(q)\)	\(=\)	\(q+(1.82837 - 0.810594i) q^{2} +(-1.16781 - 2.02271i) q^{3} +(2.68588 - 2.96413i) q^{4} +(1.55055 - 2.68563i) q^{5} +(-3.77480 - 2.75165i) q^{6} +(2.50807 - 7.59668i) q^{8} +(1.77242 - 3.06992i) q^{9} +O(q^{10})\)	\(q+(1.82837 - 0.810594i) q^{2} +(-1.16781 - 2.02271i) q^{3} +(2.68588 - 2.96413i) q^{4} +(1.55055 - 2.68563i) q^{5} +(-3.77480 - 2.75165i) q^{6} +(2.50807 - 7.59668i) q^{8} +(1.77242 - 3.06992i) q^{9} +(0.658023 - 6.16719i) q^{10} +(-4.06604 + 2.34753i) q^{11} +(-9.13219 - 1.97120i) q^{12} +6.88097 q^{13} -7.24301 q^{15} +(-1.57215 - 15.9226i) q^{16} +(-14.7184 + 8.49765i) q^{17} +(0.752180 - 7.04966i) q^{18} +(13.1099 - 22.7070i) q^{19} +(-3.79598 - 11.8093i) q^{20} +(-5.53134 + 7.58806i) q^{22} +(-12.9403 + 22.4132i) q^{23} +(-18.2949 + 3.79841i) q^{24} +(7.69160 + 13.3222i) q^{25} +(12.5810 - 5.57767i) q^{26} -29.3001 q^{27} -42.2701i q^{29} +(-13.2429 + 5.87114i) q^{30} +(-15.9024 + 9.18126i) q^{31} +(-15.7812 - 27.8380i) q^{32} +(9.49676 + 5.48296i) q^{33} +(-20.0225 + 27.4675i) q^{34} +(-4.33915 - 13.4991i) q^{36} +(43.1997 + 24.9413i) q^{37} +(5.56358 - 52.1436i) q^{38} +(-8.03569 - 13.9182i) q^{39} +(-16.5130 - 18.5148i) q^{40} +10.7844i q^{41} -24.1791i q^{43} +(-3.96249 + 18.3575i) q^{44} +(-5.49645 - 9.52013i) q^{45} +(-5.49159 + 51.4689i) q^{46} +(-11.8480 - 6.84046i) q^{47} +(-30.3708 + 21.7746i) q^{48} +(24.8620 + 18.1232i) q^{50} +(34.3766 + 19.8474i) q^{51} +(18.4814 - 20.3961i) q^{52} +(6.03948 - 3.48690i) q^{53} +(-53.5714 + 23.7505i) q^{54} +14.5598i q^{55} -61.2396 q^{57} +(-34.2639 - 77.2854i) q^{58} +(53.0922 + 91.9584i) q^{59} +(-19.4538 + 21.4692i) q^{60} +(46.7304 - 80.9395i) q^{61} +(-21.6332 + 29.6771i) q^{62} +(-51.4192 - 38.1060i) q^{64} +(10.6693 - 18.4797i) q^{65} +(21.8081 + 2.32686i) q^{66} +(-77.2753 + 44.6149i) q^{67} +(-14.3435 + 66.4508i) q^{68} +60.4473 q^{69} +81.7898 q^{71} +(-18.8759 - 21.1641i) q^{72} +(119.473 - 68.9780i) q^{73} +(99.2023 + 10.5846i) q^{74} +(17.9647 - 31.1158i) q^{75} +(-32.0950 - 99.8475i) q^{76} +(-25.9743 - 18.9340i) q^{78} +(6.55090 - 11.3465i) q^{79} +(-45.1998 - 20.4665i) q^{80} +(18.2653 + 31.6364i) q^{81} +(8.74179 + 19.7179i) q^{82} -2.15689 q^{83} +52.7041i q^{85} +(-19.5994 - 44.2083i) q^{86} +(-85.5003 + 49.3636i) q^{87} +(7.63553 + 36.7762i) q^{88} +(87.8261 + 50.7064i) q^{89} +(-17.7665 - 12.9509i) q^{90} +(31.6797 + 98.5556i) q^{92} +(37.1421 + 21.4440i) q^{93} +(-27.2074 - 2.90296i) q^{94} +(-40.6550 - 70.4166i) q^{95} +(-37.8788 + 64.4305i) q^{96} +88.9318i q^{97} +16.6432i 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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