LMFDB - Embedded newform 392.3.k.j.67.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(67,392)]

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([3, 3, 4]))

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

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

chi := DirichletCharacter("392.67");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.k (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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.796594176.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 18x^{6} - 40x^{5} + 83x^{4} - 104x^{3} + 22x^{2} + 24x + 4 $ x^8 - 4x^7 + 18x^6 - 40x^5 + 83x^4 - 104x^3 + 22x^2 + 24*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			67.3
Root			$-0.207107 + 0.0981308i$ of defining polynomial
Character	$\chi$	$=$	392.67
Dual form			392.3.k.j.275.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26663 - 1.54779i) q^{2} +(1.70711 - 2.95680i) q^{3} +(-0.791288 - 3.92095i) q^{4} +(1.34221 - 0.774923i) q^{5} +(-2.41421 - 6.38741i) q^{6} +(-7.07107 - 3.74166i) q^{8} +(-1.32843 - 2.30090i) q^{9} +O(q^{10})$	\(q+(1.26663 - 1.54779i) q^{2} +(1.70711 - 2.95680i) q^{3} +(-0.791288 - 3.92095i) q^{4} +(1.34221 - 0.774923i) q^{5} +(-2.41421 - 6.38741i) q^{6} +(-7.07107 - 3.74166i) q^{8} +(-1.32843 - 2.30090i) q^{9} +(0.500665 - 3.05899i) q^{10} +(2.24264 - 3.88437i) q^{11} +(-12.9443 - 4.35381i) q^{12} -1.54985i q^{13} -5.29150i q^{15} +(-14.7477 + 6.20520i) q^{16} +(11.8284 - 20.4874i) q^{17} +(-5.24394 - 0.858275i) q^{18} +(-12.4350 - 21.5381i) q^{19} +(-4.10051 - 4.64954i) q^{20} +(-3.17157 - 8.39119i) q^{22} +(-30.5055 + 17.6124i) q^{23} +(-23.1344 + 14.5203i) q^{24} +(-11.2990 + 19.5704i) q^{25} +(-2.39883 - 1.96308i) q^{26} +21.6569 q^{27} +22.4499i q^{29} +(-8.19012 - 6.70239i) q^{30} +(40.4569 + 23.3578i) q^{31} +(-9.07561 + 30.6860i) q^{32} +(-7.65685 - 13.2621i) q^{33} +(-16.7279 - 44.2579i) q^{34} +(-7.97056 + 7.02938i) q^{36} +(50.7340 - 29.2913i) q^{37} +(-49.0870 - 8.03407i) q^{38} +(-4.58258 - 2.64575i) q^{39} +(-12.3903 + 0.457458i) q^{40} +26.9706 q^{41} -17.1716 q^{43} +(-17.0050 - 5.71963i) q^{44} +(-3.56604 - 2.05886i) q^{45} +(-11.3791 + 69.5245i) q^{46} +(-31.2918 + 18.0663i) q^{47} +(-6.82843 + 54.1990i) q^{48} +(15.9792 + 42.2769i) q^{50} +(-40.3848 - 69.9485i) q^{51} +(-6.07687 + 1.22637i) q^{52} +(84.7102 + 48.9075i) q^{53} +(27.4313 - 33.5202i) q^{54} -6.95149i q^{55} -84.9117 q^{57} +(34.7477 + 28.4358i) q^{58} +(30.7782 - 53.3094i) q^{59} +(-20.7477 + 4.18710i) q^{60} +(-32.6340 + 18.8412i) q^{61} +(87.3970 - 33.0329i) q^{62} +(36.0000 + 52.9150i) q^{64} +(-1.20101 - 2.08021i) q^{65} +(-30.2253 - 4.94697i) q^{66} +(16.6863 - 28.9015i) q^{67} +(-89.6899 - 30.1672i) q^{68} +120.265i q^{69} -102.199i q^{71} +(0.784207 + 21.2404i) q^{72} +(34.6569 - 60.0274i) q^{73} +(18.9246 - 115.627i) q^{74} +(38.5772 + 66.8176i) q^{75} +(-74.6102 + 65.8000i) q^{76} +(-9.89949 + 3.74166i) q^{78} +(-33.5156 + 19.3503i) q^{79} +(-14.9859 + 19.7570i) q^{80} +(48.9264 - 84.7430i) q^{81} +(34.1618 - 41.7447i) q^{82} -3.61522 q^{83} -36.6645i q^{85} +(-21.7501 + 26.5779i) q^{86} +(66.3799 + 38.3245i) q^{87} +(-30.3918 + 19.0754i) q^{88} +(22.0294 + 38.1561i) q^{89} +(-7.70354 + 2.91166i) q^{90} +(93.1960 + 105.674i) q^{92} +(138.129 - 79.7486i) q^{93} +(-11.6724 + 71.3164i) q^{94} +(-33.3807 - 19.2724i) q^{95} +(75.2393 + 79.2191i) q^{96} -96.1076 q^{97} -11.9167 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} + 12 q^{4} - 8 q^{6} + 12 q^{9}+O(q^{10}) $ 8 * q + 8 * q^3 + 12 * q^4 - 8 * q^6 + 12 * q^9	$ 8 q + 8 q^{3} + 12 q^{4} - 8 q^{6} + 12 q^{9} - 28 q^{10} - 16 q^{11} - 24 q^{12} - 8 q^{16} + 72 q^{17} - 16 q^{18} + 8 q^{19} - 112 q^{20} - 48 q^{22} - 40 q^{24} + 68 q^{25} + 28 q^{26} + 128 q^{27} - 16 q^{33} - 32 q^{34} + 72 q^{36} - 76 q^{38} + 56 q^{40} + 80 q^{41} - 160 q^{43} + 48 q^{44} - 224 q^{46} - 32 q^{48} + 224 q^{50} - 176 q^{51} - 56 q^{52} - 16 q^{54} - 272 q^{57} + 168 q^{58} + 184 q^{59} - 56 q^{60} + 224 q^{62} + 288 q^{64} - 168 q^{65} - 32 q^{66} + 224 q^{67} - 216 q^{68} + 160 q^{72} + 232 q^{73} + 280 q^{74} + 88 q^{75} + 48 q^{76} - 336 q^{80} + 52 q^{81} - 48 q^{82} - 176 q^{83} - 8 q^{86} - 240 q^{88} + 312 q^{89} - 616 q^{90} + 112 q^{92} - 112 q^{94} + 176 q^{96} + 272 q^{97} - 480 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 + 12 * q^4 - 8 * q^6 + 12 * q^9 - 28 * q^10 - 16 * q^11 - 24 * q^12 - 8 * q^16 + 72 * q^17 - 16 * q^18 + 8 * q^19 - 112 * q^20 - 48 * q^22 - 40 * q^24 + 68 * q^25 + 28 * q^26 + 128 * q^27 - 16 * q^33 - 32 * q^34 + 72 * q^36 - 76 * q^38 + 56 * q^40 + 80 * q^41 - 160 * q^43 + 48 * q^44 - 224 * q^46 - 32 * q^48 + 224 * q^50 - 176 * q^51 - 56 * q^52 - 16 * q^54 - 272 * q^57 + 168 * q^58 + 184 * q^59 - 56 * q^60 + 224 * q^62 + 288 * q^64 - 168 * q^65 - 32 * q^66 + 224 * q^67 - 216 * q^68 + 160 * q^72 + 232 * q^73 + 280 * q^74 + 88 * q^75 + 48 * q^76 - 336 * q^80 + 52 * q^81 - 48 * q^82 - 176 * q^83 - 8 * q^86 - 240 * q^88 + 312 * q^89 - 616 * q^90 + 112 * q^92 - 112 * q^94 + 176 * q^96 + 272 * q^97 - 480 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.26663	−	1.54779i	0.633316	−	0.773893i
$2$	1.26663	−	1.54779i	0.633316	−	0.773893i
$3$	1.70711	−	2.95680i	0.569036	−	0.985599i	−0.427626	−	0.903956i	$-0.640650\pi$
$3$	1.70711	−	2.95680i	0.569036	−	0.985599i	0.996662	−	0.0816428i	$-0.0260167\pi$
$4$	−0.791288	−	3.92095i	−0.197822	−	0.980238i
$5$	1.34221	−	0.774923i	0.268441	−	0.154985i	−0.359738	−	0.933053i	$-0.617134\pi$
$5$	1.34221	−	0.774923i	0.268441	−	0.154985i	0.628179	+	0.778069i	$0.283801\pi$
$6$	−2.41421	−	6.38741i	−0.402369	−	1.06457i
$7$		0			0
$7$		0			0
$8$	−7.07107	−	3.74166i	−0.883883	−	0.467707i
$9$	−1.32843	−	2.30090i	−0.147603	−	0.255656i
$10$	0.500665	−	3.05899i	0.0500665	−	0.305899i
$11$	2.24264	−	3.88437i	0.203876	−	0.353124i	−0.745898	−	0.666060i	$-0.767979\pi$
$11$	2.24264	−	3.88437i	0.203876	−	0.353124i	0.949774	+	0.312936i	$0.101313\pi$
$12$	−12.9443	−	4.35381i	−1.07869	−	0.362817i
$13$		−	1.54985i		−	0.119219i	−0.998222	−	0.0596094i	$-0.981014\pi$
$13$		−	1.54985i		−	0.119219i	0.998222	−	0.0596094i	$-0.0189855\pi$
$14$		0			0
$15$		−	5.29150i		−	0.352767i
$16$	−14.7477	+	6.20520i	−0.921733	+	0.387825i
$17$	11.8284	−	20.4874i	0.695790	−	1.20514i	−0.274124	−	0.961694i	$-0.588388\pi$
$17$	11.8284	−	20.4874i	0.695790	−	1.20514i	0.969914	−	0.243449i	$-0.0782788\pi$
$18$	−5.24394	−	0.858275i	−0.291330	−	0.0476820i
$19$	−12.4350	−	21.5381i	−0.654475	−	1.13358i	−0.982025	−	0.188750i	$-0.939556\pi$
$19$	−12.4350	−	21.5381i	−0.654475	−	1.13358i	0.327550	−	0.944834i	$-0.393777\pi$
$20$	−4.10051	−	4.64954i	−0.205025	−	0.232477i
$21$		0			0
$22$	−3.17157	−	8.39119i	−0.144162	−	0.381418i
$23$	−30.5055	+	17.6124i	−1.32633	+	0.765756i	−0.984730	−	0.174090i	$-0.944301\pi$
$23$	−30.5055	+	17.6124i	−1.32633	+	0.765756i	−0.341598	+	0.939846i	$0.610968\pi$
$24$	−23.1344	+	14.5203i	−0.963933	+	0.605012i
$25$	−11.2990	+	19.5704i	−0.451960	+	0.782817i
$26$	−2.39883	−	1.96308i	−0.0922627	−	0.0755032i
$27$	21.6569			0.802106
$28$		0			0
$29$			22.4499i			0.774136i	0.922051	+	0.387068i	$0.126512\pi$
$29$			22.4499i			0.774136i	−0.922051	+	0.387068i	$0.873488\pi$
$30$	−8.19012	−	6.70239i	−0.273004	−	0.223413i
$31$	40.4569	+	23.3578i	1.30506	+	0.753478i	0.981268	−	0.192649i	$-0.0617079\pi$
$31$	40.4569	+	23.3578i	1.30506	+	0.753478i	0.323795	+	0.946127i	$0.395041\pi$
$32$	−9.07561	+	30.6860i	−0.283613	+	0.958939i
$33$	−7.65685	−	13.2621i	−0.232026	−	0.401881i
$34$	−16.7279	−	44.2579i	−0.491998	−	1.30170i
$35$		0			0
$36$	−7.97056	+	7.02938i	−0.221405	+	0.195260i
$37$	50.7340	−	29.2913i	1.37119	−	0.791657i	0.380111	−	0.924941i	$-0.375886\pi$
$37$	50.7340	−	29.2913i	1.37119	−	0.791657i	0.991078	+	0.133284i	$0.0425523\pi$
$38$	−49.0870	−	8.03407i	−1.29176	−	0.211423i
$39$	−4.58258	−	2.64575i	−0.117502	−	0.0678398i
$40$	−12.3903	+	0.457458i	−0.309758	+	0.0114364i
$41$	26.9706			0.657819			0.328909	−	0.944362i	$-0.393319\pi$
$41$	26.9706			0.657819			0.328909	+	0.944362i	$0.393319\pi$
$42$		0			0
$43$	−17.1716			−0.399339			−0.199669	−	0.979863i	$-0.563987\pi$
$43$	−17.1716			−0.399339			−0.199669	+	0.979863i	$0.563987\pi$
$44$	−17.0050	−	5.71963i	−0.386477	−	0.129992i
$45$	−3.56604	−	2.05886i	−0.0792454	−	0.0457524i
$46$	−11.3791	+	69.5245i	−0.247371	+	1.51140i
$47$	−31.2918	+	18.0663i	−0.665783	+	0.384390i	−0.794477	−	0.607295i	$-0.792255\pi$
$47$	−31.2918	+	18.0663i	−0.665783	+	0.384390i	0.128694	+	0.991684i	$0.458921\pi$
$48$	−6.82843	+	54.1990i	−0.142259	+	1.12915i
$49$		0			0
$50$	15.9792	+	42.2769i	0.319584	+	0.845539i
$51$	−40.3848	−	69.9485i	−0.791858	−	1.37154i
$52$	−6.07687	+	1.22637i	−0.116863	+	0.0235841i
$53$	84.7102	+	48.9075i	1.59831	+	0.922782i	0.991814	+	0.127693i	$0.0407571\pi$
$53$	84.7102	+	48.9075i	1.59831	+	0.922782i	0.606492	+	0.795090i	$0.292576\pi$
$54$	27.4313	−	33.5202i	0.507986	−	0.620744i
$55$		−	6.95149i		−	0.126391i
$56$		0			0
$57$	−84.9117			−1.48968
$58$	34.7477	+	28.4358i	0.599099	+	0.490273i
$59$	30.7782	−	53.3094i	0.521664	−	0.903549i	−0.478018	−	0.878350i	$-0.658645\pi$
$59$	30.7782	−	53.3094i	0.521664	−	0.903549i	0.999682	−	0.0251987i	$-0.00802186\pi$
$60$	−20.7477	+	4.18710i	−0.345795	+	0.0697850i
$61$	−32.6340	+	18.8412i	−0.534983	+	0.308873i	−0.743043	−	0.669243i	$-0.766618\pi$
$61$	−32.6340	+	18.8412i	−0.534983	+	0.308873i	0.208060	+	0.978116i	$0.433285\pi$
$62$	87.3970	−	33.0329i	1.40963	−	0.532790i
$63$		0			0
$64$	36.0000	+	52.9150i	0.562500	+	0.826797i
$65$	−1.20101	−	2.08021i	−0.0184771	−	0.0320032i
$66$	−30.2253	−	4.94697i	−0.457958	−	0.0749541i
$67$	16.6863	−	28.9015i	0.249049	−	0.431366i	−0.714213	−	0.699928i	$-0.753215\pi$
$67$	16.6863	−	28.9015i	0.249049	−	0.431366i	0.963262	+	0.268563i	$0.0865486\pi$
$68$	−89.6899	−	30.1672i	−1.31897	−	0.443636i
$69$			120.265i			1.74297i
$70$		0			0
$71$		−	102.199i		−	1.43942i	−0.694277	−	0.719708i	$-0.744276\pi$
$71$		−	102.199i		−	1.43942i	0.694277	−	0.719708i	$-0.255724\pi$
$72$	0.784207	+	21.2404i	0.0108918	+	0.295005i
$73$	34.6569	−	60.0274i	0.474751	−	0.822294i	−0.524830	−	0.851207i	$-0.675871\pi$
$73$	34.6569	−	60.0274i	0.474751	−	0.822294i	0.999582	+	0.0289132i	$0.00920463\pi$
$74$	18.9246	−	115.627i	0.255738	−	1.56252i
$75$	38.5772	+	66.8176i	0.514362	+	0.890901i
$76$	−74.6102	+	65.8000i	−0.981713	+	0.865789i
$77$		0			0
$78$	−9.89949	+	3.74166i	−0.126917	+	0.0479700i
$79$	−33.5156	+	19.3503i	−0.424248	+	0.244940i	−0.696893	−	0.717175i	$-0.745435\pi$
$79$	−33.5156	+	19.3503i	−0.424248	+	0.244940i	0.272645	+	0.962115i	$0.412102\pi$
$80$	−14.9859	+	19.7570i	−0.187324	+	0.246963i
$81$	48.9264	−	84.7430i	0.604030	−	1.04621i
$82$	34.1618	−	41.7447i	0.416607	−	0.509081i
$83$	−3.61522			−0.0435569			−0.0217785	−	0.999763i	$-0.506933\pi$
$83$	−3.61522			−0.0435569			−0.0217785	+	0.999763i	$0.506933\pi$
$84$		0			0
$85$		−	36.6645i		−	0.431347i
$86$	−21.7501	+	26.5779i	−0.252908	+	0.309046i
$87$	66.3799	+	38.3245i	0.762987	+	0.440511i
$88$	−30.3918	+	19.0754i	−0.345362	+	0.216766i
$89$	22.0294	+	38.1561i	0.247522	+	0.428720i	0.962838	−	0.270081i	$-0.0870505\pi$
$89$	22.0294	+	38.1561i	0.247522	+	0.428720i	−0.715316	+	0.698801i	$0.753717\pi$
$90$	−7.70354	+	2.91166i	−0.0855948	+	0.0323518i
$91$		0			0
$92$	93.1960	+	105.674i	1.01300	+	1.14863i
$93$	138.129	−	79.7486i	1.48525	−	0.857512i
$94$	−11.6724	+	71.3164i	−0.124174	+	0.758685i
$95$	−33.3807	−	19.2724i	−0.351376	−	0.202867i
$96$	75.2393	+	79.2191i	0.783743	+	0.825199i
$97$	−96.1076			−0.990800			−0.495400	−	0.868665i	$-0.664979\pi$
$97$	−96.1076			−0.990800			−0.495400	+	0.868665i	$0.664979\pi$
$98$		0			0
$99$	−11.9167			−0.120371
$100$	85.6754	+	28.8170i	0.856754	+	0.288170i
$101$	−16.9881	−	9.80808i	−0.168199	−	0.0971097i	0.413537	−	0.910487i	$-0.364293\pi$
$101$	−16.9881	−	9.80808i	−0.168199	−	0.0971097i	−0.581736	+	0.813377i	$0.697626\pi$
$102$	−159.418	−	26.0920i	−1.56292	−	0.255803i
$103$	37.3120	−	21.5421i	0.362252	−	0.209146i	−0.307816	−	0.951446i	$-0.599598\pi$
$103$	37.3120	−	21.5421i	0.362252	−	0.209146i	0.670068	+	0.742300i	$0.266265\pi$
$104$	−5.79899	+	10.9591i	−0.0557595	+	0.105376i
$105$		0			0
$106$	182.995	−	69.1656i	1.72637	−	0.652506i
$107$	−7.79899	−	13.5082i	−0.0728878	−	0.126245i	0.827278	−	0.561793i	$-0.189888\pi$
$107$	−7.79899	−	13.5082i	−0.0728878	−	0.126245i	−0.900166	+	0.435547i	$0.856555\pi$
$108$	−17.1368	−	84.9155i	−0.158674	−	0.786254i
$109$	3.33576	+	1.92590i	0.0306033	+	0.0176688i	0.515224	−	0.857056i	$-0.327709\pi$
$109$	3.33576	+	1.92590i	0.0306033	+	0.0176688i	−0.484620	+	0.874725i	$0.661042\pi$
$110$	−10.7594	−	8.80498i	−0.0978130	−	0.0800453i
$111$		−	200.013i		−	1.80192i
$112$		0			0
$113$	−13.7746			−0.121899			−0.0609496	−	0.998141i	$-0.519413\pi$
$113$	−13.7746			−0.121899			−0.0609496	+	0.998141i	$0.519413\pi$
$114$	−107.552	+	131.425i	−0.943437	+	1.15285i
$115$	−27.2965	+	47.2789i	−0.237361	+	0.411121i
$116$	88.0252	−	17.7644i	0.758838	−	0.153141i
$117$	−3.56604	+	2.05886i	−0.0304790	+	0.0175971i
$118$	−43.5269	−	115.161i	−0.368872	−	0.975944i
$119$		0			0
$120$	−19.7990	+	37.4166i	−0.164992	+	0.311805i
$121$	50.4411	+	87.3666i	0.416869	+	0.722038i
$122$	−12.1730	+	74.3754i	−0.0997789	+	0.609634i
$123$	46.0416	−	79.7464i	0.374322	−	0.648345i
$124$	59.5718	−	177.112i	0.480418	−	1.42833i
$125$			73.7695i			0.590156i
$126$		0			0
$127$		−	125.025i		−	0.984445i	−0.870469	−	0.492223i	$-0.836185\pi$
$127$		−	125.025i		−	0.984445i	0.870469	−	0.492223i	$-0.163815\pi$
$128$	127.500	+	11.3035i	0.996093	+	0.0883088i
$129$	−29.3137	+	50.7728i	−0.227238	+	0.393588i
$130$	−4.74096	−	0.775953i	−0.0364689	−	0.00596887i
$131$	50.1751	+	86.9059i	0.383016	+	0.663404i	0.991492	−	0.130169i	$-0.0415519\pi$
$131$	50.1751	+	86.9059i	0.383016	+	0.663404i	−0.608475	+	0.793573i	$0.708219\pi$
$132$	−45.9411	+	40.5163i	−0.348039	+	0.306941i
$133$		0			0
$134$	−23.5980	−	62.4344i	−0.176104	−	0.465928i
$135$	29.0679	−	16.7824i	0.215318	−	0.124314i
$136$	−160.297	+	100.610i	−1.17865	+	0.739780i
$137$	−28.6569	+	49.6351i	−0.209174	+	0.362300i	−0.951455	−	0.307789i	$-0.900411\pi$
$137$	−28.6569	+	49.6351i	−0.209174	+	0.362300i	0.742280	+	0.670089i	$0.233744\pi$
$138$	186.144	+	152.331i	1.34887	+	1.10385i
$139$	183.664			1.32132			0.660662	−	0.750684i	$-0.270276\pi$
$139$	183.664			1.32132			0.660662	+	0.750684i	$0.270276\pi$
$140$		0			0
$141$			123.365i			0.874926i
$142$	−158.182	−	129.448i	−1.11395	−	0.911605i
$143$	−6.02017	−	3.47575i	−0.0420991	−	0.0243059i
$144$	33.8689	+	25.6899i	0.235200	+	0.178402i
$145$	17.3970	+	30.1324i	0.119979	+	0.207810i
$146$	−49.0122	−	129.674i	−0.335700	−	0.888179i
$147$		0			0
$148$	−154.995	−	175.748i	−1.04726	−	1.18748i
$149$	−166.545	+	96.1549i	−1.11775	+	0.645335i	−0.940826	−	0.338889i	$-0.889949\pi$
$149$	−166.545	+	96.1549i	−1.11775	+	0.645335i	−0.176927	+	0.984224i	$0.556616\pi$
$150$	152.282	+	24.9241i	1.01522	+	0.166161i
$151$	−99.3791	−	57.3765i	−0.658140	−	0.379977i	0.133428	−	0.991058i	$-0.457401\pi$
$151$	−99.3791	−	57.3765i	−0.658140	−	0.379977i	−0.791568	+	0.611081i	$0.790735\pi$
$152$	7.34073	+	198.825i	0.0482943	+	1.30806i
$153$	−62.8528			−0.410803
$154$		0			0
$155$	72.4020			0.467110
$156$	−6.74773	+	20.0616i	−0.0432547	+	0.128600i
$157$	183.724	+	106.073i	1.17022	+	0.675625i	0.953731	−	0.300661i	$-0.0972071\pi$
$157$	183.724	+	106.073i	1.17022	+	0.675625i	0.216486	+	0.976286i	$0.430540\pi$
$158$	−12.5019	+	76.3847i	−0.0791259	+	0.483447i
$159$	289.219	−	166.981i	1.81899	−	1.05019i
$160$	11.5980	+	48.2199i	0.0724874	+	0.301374i
$161$		0			0
$162$	−69.1924	−	183.066i	−0.427114	−	1.13004i
$163$	120.267	+	208.309i	0.737835	+	1.27797i	0.953469	+	0.301493i	$0.0974849\pi$
$163$	120.267	+	208.309i	0.737835	+	1.27797i	−0.215634	+	0.976474i	$0.569182\pi$
$164$	−21.3415	−	105.750i	−0.130131	−	0.644819i
$165$	−20.5541	−	11.8669i	−0.124571	−	0.0719208i
$166$	−4.57916	+	5.59560i	−0.0275853	+	0.0337084i
$167$		−	212.101i		−	1.27006i	−0.772486	−	0.635032i	$-0.780987\pi$
$167$		−	212.101i		−	1.27006i	0.772486	−	0.635032i	$-0.219013\pi$
$168$		0			0
$169$	166.598			0.985787
$170$	−56.7488	−	46.4404i	−0.333816	−	0.273179i
$171$	−33.0381	+	57.2236i	−0.193205	+	0.334641i
$172$	13.5877	+	67.3289i	0.0789980	+	0.391447i
$173$	−157.801	+	91.1065i	−0.912145	+	0.526627i	−0.881121	−	0.472891i	$-0.843210\pi$
$173$	−157.801	+	91.1065i	−0.912145	+	0.526627i	−0.0310245	+	0.999519i	$0.509877\pi$
$174$	143.397	−	54.1990i	0.824121	−	0.311488i
$175$		0			0
$176$	−8.97056	+	71.2016i	−0.0509691	+	0.404555i
$177$	−105.083	−	182.010i	−0.593691	−	1.02830i
$178$	86.9607	+	14.2329i	0.488543	+	0.0799599i
$179$	−28.6030	+	49.5419i	−0.159793	+	0.276770i	−0.934794	−	0.355190i	$-0.884416\pi$
$179$	−28.6030	+	49.5419i	−0.159793	+	0.276770i	0.775001	+	0.631960i	$0.217749\pi$
$180$	−5.25091	+	15.6114i	−0.0291717	+	0.0867302i
$181$			326.212i			1.80228i	0.433533	+	0.901138i	$0.357267\pi$
$181$			326.212i			1.80228i	−0.433533	+	0.901138i	$0.642733\pi$
$182$		0			0
$183$			128.656i			0.703039i
$184$	281.606	−	10.3971i	1.53047	−	0.0565058i
$185$	45.3970	−	78.6299i	0.245389	−	0.425026i
$186$	51.5243	−	314.806i	0.277012	−	1.69250i
$187$	−53.0538	−	91.8919i	−0.283710	−	0.491401i
$188$	95.5980	+	108.398i	0.508500	+	0.576585i
$189$		0			0
$190$	−72.1106	+	27.2552i	−0.379530	+	0.143449i
$191$	−84.0589	+	48.5314i	−0.440099	+	0.254091i	−0.703639	−	0.710557i	$-0.748443\pi$
$191$	−84.0589	+	48.5314i	−0.440099	+	0.254091i	0.263541	+	0.964648i	$0.415110\pi$
$192$	217.915	−	16.1130i	1.13497	−	0.0839221i
$193$	−78.6518	+	136.229i	−0.407522	+	0.705849i	−0.994611	−	0.103673i	$-0.966940\pi$
$193$	−78.6518	+	136.229i	−0.407522	+	0.705849i	0.587089	+	0.809522i	$0.300274\pi$
$194$	−121.733	+	148.754i	−0.627490	+	0.766774i
$195$	−8.20101			−0.0420565
$196$		0			0
$197$			124.117i			0.630034i	0.949086	+	0.315017i	$0.102010\pi$
$197$			124.117i			0.630034i	−0.949086	+	0.315017i	$0.897990\pi$
$198$	−15.0941	+	18.4446i	−0.0762329	+	0.0931544i
$199$	−156.729	−	90.4874i	−0.787581	−	0.454710i	0.0515289	−	0.998672i	$-0.483591\pi$
$199$	−156.729	−	90.4874i	−0.787581	−	0.454710i	−0.839110	+	0.543961i	$0.816924\pi$
$200$	153.122	−	96.1069i	0.765609	−	0.480534i
$201$	−56.9706	−	98.6759i	−0.283436	−	0.490925i
$202$	−36.6985	+	13.8707i	−0.181676	+	0.0686669i
$203$		0			0
$204$	−242.309	+	213.696i	−1.18779	+	1.04753i
$205$	36.2000	−	20.9001i	0.176586	−	0.101952i
$206$	13.9180	−	85.0368i	0.0675630	−	0.412800i
$207$	81.0488	+	46.7935i	0.391540	+	0.226056i
$208$	9.61710	+	22.8567i	0.0462361	+	0.109888i
$209$	−111.549			−0.533728
$210$		0			0
$211$	164.049			0.777482			0.388741	−	0.921347i	$-0.372910\pi$
$211$	164.049			0.777482			0.388741	+	0.921347i	$0.372910\pi$
$212$	124.734	−	370.844i	0.588366	−	1.74927i
$213$	−302.180	−	174.464i	−1.41869	−	0.819079i
$214$	−30.7863	−	5.03880i	−0.143861	−	0.0235458i
$215$	−23.0478	+	13.3066i	−0.107199	+	0.0618913i
$216$	−153.137	−	81.0325i	−0.708968	−	0.375151i
$217$		0			0
$218$	7.20606	−	2.72363i	0.0330553	−	0.0124937i
$219$	−118.326	−	204.946i	−0.540301	−	0.935829i
$220$	−27.2565	+	5.50063i	−0.123893	+	0.0250029i
$221$	−31.7524	−	18.3322i	−0.143676	−	0.0829513i
$222$	−309.578	−	253.343i	−1.39450	−	1.14119i
$223$			10.5830i			0.0474574i	0.999718	+	0.0237287i	$0.00755379\pi$
$223$			10.5830i			0.0474574i	−0.999718	+	0.0237287i	$0.992446\pi$
$224$		0			0
$225$	60.0395			0.266842
$226$	−17.4474	+	21.3201i	−0.0772007	+	0.0943369i
$227$	52.9031	−	91.6308i	0.233053	−	0.403660i	−0.725652	−	0.688062i	$-0.758462\pi$
$227$	52.9031	−	91.6308i	0.233053	−	0.403660i	0.958705	+	0.284402i	$0.0917951\pi$
$228$	67.1896	+	332.935i	0.294691	+	1.46024i
$229$	64.8469	−	37.4394i	0.283174	−	0.163491i	−0.351685	−	0.936118i	$-0.614391\pi$
$229$	64.8469	−	37.4394i	0.283174	−	0.163491i	0.634860	+	0.772628i	$0.281058\pi$
$230$	38.6030	+	102.134i	0.167839	+	0.444061i
$231$		0			0
$232$	84.0000	−	158.745i	0.362069	−	0.684246i
$233$	209.569	+	362.983i	0.899436	+	1.55787i	0.828217	+	0.560408i	$0.189356\pi$
$233$	209.569	+	362.983i	0.899436	+	1.55787i	0.0712190	+	0.997461i	$0.477311\pi$
$234$	−1.33019	+	8.12729i	−0.00568459	+	0.0347320i
$235$	−28.0000	+	48.4974i	−0.119149	+	0.206372i
$236$	−233.378	−	78.4967i	−0.988889	−	0.332613i
$237$			132.132i			0.557518i
$238$		0			0
$239$			148.318i			0.620577i	0.950642	+	0.310288i	$0.100426\pi$
$239$			148.318i			0.620577i	−0.950642	+	0.310288i	$0.899574\pi$
$240$	32.8348	+	78.0376i	0.136812	+	0.325157i
$241$	−229.936	+	398.261i	−0.954092	+	1.65254i	−0.217658	+	0.976025i	$0.569842\pi$
$241$	−229.936	+	398.261i	−0.954092	+	1.65254i	−0.736433	+	0.676510i	$0.763492\pi$
$242$	199.115	+	32.5892i	0.822790	+	0.134666i
$243$	−69.5894	−	120.532i	−0.286376	−	0.496018i
$244$	99.6985	+	113.047i	0.408600	+	0.463309i
$245$		0			0
$246$	−65.1127	−	172.272i	−0.264686	−	0.700293i
$247$	−33.3807	+	19.2724i	−0.135145	+	0.0780258i
$248$	−198.677	−	316.541i	−0.801116	−	1.27637i
$249$	−6.17157	+	10.6895i	−0.0247854	+	0.0429296i
$250$	114.179	+	93.4388i	0.456718	+	0.373755i
$251$	−124.919			−0.497685			−0.248842	−	0.968544i	$-0.580050\pi$
$251$	−124.919			−0.497685			−0.248842	+	0.968544i	$0.580050\pi$
$252$		0			0
$253$			157.993i			0.624478i
$254$	−193.511	−	158.360i	−0.761856	−	0.623465i
$255$	−108.409	−	62.5902i	−0.425135	−	0.245452i
$256$	178.991	−	183.025i	0.699183	−	0.714943i
$257$	−213.676	−	370.098i	−0.831425	−	1.44007i	−0.896908	−	0.442216i	$-0.854192\pi$
$257$	−213.676	−	370.098i	−0.831425	−	1.44007i	0.0654835	−	0.997854i	$-0.479141\pi$
$258$	41.4558	+	109.682i	0.160682	+	0.425123i
$259$		0			0
$260$	−7.20606	+	6.35515i	−0.0277156	+	0.0244429i
$261$	51.6552	−	29.8231i	0.197912	−	0.114265i
$262$	198.065	+	32.4173i	0.755974	+	0.123730i
$263$	−223.109	−	128.812i	−0.848322	−	0.489779i	0.0117625	−	0.999931i	$-0.496256\pi$
$263$	−223.109	−	128.812i	−0.848322	−	0.489779i	−0.860084	+	0.510152i	$0.829589\pi$
$264$	4.52005	+	122.426i	0.0171214	+	0.463736i
$265$	151.598			0.572068
$266$		0			0
$267$	150.426			0.563395
$268$	−126.525	−	42.5567i	−0.472108	−	0.158794i
$269$	−186.408	−	107.623i	−0.692968	−	0.400085i	0.111755	−	0.993736i	$-0.464353\pi$
$269$	−186.408	−	107.623i	−0.692968	−	0.400085i	−0.804723	+	0.593650i	$0.797686\pi$
$270$	10.8428	−	66.2481i	0.0401586	−	0.245363i
$271$	−327.833	+	189.275i	−1.20972	+	0.698431i	−0.962698	−	0.270580i	$-0.912785\pi$
$271$	−327.833	+	189.275i	−1.20972	+	0.698431i	−0.247020	+	0.969010i	$0.579451\pi$
$272$	−47.3137	+	375.541i	−0.173947	+	1.38067i
$273$		0			0
$274$	40.5269	+	107.224i	0.147908	+	0.391329i
$275$	50.6791	+	87.7789i	0.184288	+	0.319196i
$276$	471.553	−	95.1641i	1.70852	−	0.344798i
$277$	144.149	+	83.2243i	0.520393	+	0.300449i	0.737095	−	0.675789i	$-0.236197\pi$
$277$	144.149	+	83.2243i	0.520393	+	0.300449i	−0.216703	+	0.976238i	$0.569530\pi$
$278$	232.635	−	284.273i	0.836815	−	1.02256i
$279$		−	124.117i		−	0.444863i
$280$		0			0
$281$	−421.765			−1.50094			−0.750471	−	0.660904i	$-0.770173\pi$
$281$	−421.765			−1.50094			−0.750471	+	0.660904i	$0.770173\pi$
$282$	190.942	+	156.257i	0.677099	+	0.554104i
$283$	−172.719	+	299.159i	−0.610316	+	1.05710i	0.380872	+	0.924628i	$0.375624\pi$
$283$	−172.719	+	299.159i	−0.610316	+	1.05710i	−0.991187	+	0.132470i	$0.957709\pi$
$284$	−400.716	+	80.8685i	−1.41097	+	0.284748i
$285$	−113.969	+	65.8000i	−0.399891	+	0.230877i
$286$	−13.0051	+	4.91545i	−0.0454722	+	0.0171869i
$287$		0			0
$288$	82.6619	−	19.8821i	0.287021	−	0.0690350i
$289$	−135.323	−	234.387i	−0.468247	−	0.811028i
$290$	68.6741	+	11.2399i	0.236807	+	0.0387583i
$291$	−164.066	+	284.171i	−0.563801	+	0.976532i
$292$	−262.788	−	88.3889i	−0.899960	−	0.302702i
$293$		−	511.038i		−	1.74416i	−0.489365	−	0.872079i	$-0.662771\pi$
$293$		−	511.038i		−	1.74416i	0.489365	−	0.872079i	$-0.337229\pi$
$294$		0			0
$295$		−	95.4028i		−	0.323399i
$296$	−468.342	+	17.2914i	−1.58224	+	0.0584170i
$297$	48.5685	−	84.1232i	0.163530	−	0.283243i
$298$	−62.1241	+	379.569i	−0.208470	+	1.27372i
$299$	27.2965	+	47.2789i	0.0912925	+	0.158123i
$300$	231.463	−	204.131i	0.771543	−	0.680437i
$301$		0			0
$302$	−214.683	+	81.1427i	−0.710872	+	0.268684i
$303$	−58.0010	+	33.4869i	−0.191422	+	0.110518i
$304$	317.037	+	240.476i	1.04288	+	0.791040i
$305$	−29.2010	+	50.5776i	−0.0957410	+	0.165828i
$306$	−79.6114	+	97.2828i	−0.260168	+	0.317917i
$307$	−223.331			−0.727462			−0.363731	−	0.931504i	$-0.618497\pi$
$307$	−223.331			−0.727462			−0.363731	+	0.931504i	$0.618497\pi$
$308$		0			0
$309$		−	147.098i		−	0.476047i
$310$	91.7067	−	112.063i	0.295828	−	0.361493i
$311$	−10.7376	−	6.19938i	−0.0345262	−	0.0199337i	0.482638	−	0.875820i	$-0.339679\pi$
$311$	−10.7376	−	6.19938i	−0.0345262	−	0.0199337i	−0.517164	+	0.855886i	$0.673012\pi$
$312$	22.5042	+	35.8547i	0.0721289	+	0.114919i
$313$	205.024	+	355.113i	0.655030	+	1.13455i	0.981886	+	0.189471i	$0.0606774\pi$
$313$	205.024	+	355.113i	0.655030	+	1.13455i	−0.326856	+	0.945074i	$0.605989\pi$
$314$	396.889	−	150.010i	1.26398	−	0.477739i
$315$		0			0
$316$	102.392	+	116.102i	0.324025	+	0.367410i
$317$	−112.857	+	65.1580i	−0.356016	+	0.205546i	−0.667332	−	0.744761i	$-0.732564\pi$
$317$	−112.857	+	65.1580i	−0.356016	+	0.205546i	0.311316	+	0.950306i	$0.399230\pi$
$318$	107.883	−	659.152i	0.339256	−	2.07280i
$319$	87.2038	+	50.3472i	0.273366	+	0.157828i
$320$	89.3244	+	43.1256i	0.279139	+	0.134768i
$321$	−53.2548			−0.165903
$322$		0			0
$323$	−588.347			−1.82151
$324$	−370.988	−	124.782i	−1.14503	−	0.385130i
$325$	30.3311	+	17.5117i	0.0933266	+	0.0538821i
$326$	474.751	+	77.7026i	1.45629	+	0.238351i
$327$	11.3890	−	6.57544i	0.0348287	−	0.0201084i
$328$	−190.711	−	100.915i	−0.581435	−	0.307666i
$329$		0			0
$330$	−44.4020	+	16.7824i	−0.134552	+	0.0508557i
$331$	−107.130	−	185.555i	−0.323655	−	0.560588i	0.657584	−	0.753381i	$-0.271579\pi$
$331$	−107.130	−	185.555i	−0.323655	−	0.560588i	−0.981239	+	0.192794i	$0.938245\pi$
$332$	2.86068	+	14.1751i	0.00861651	+	0.0426961i
$333$	−134.793	−	77.8227i	−0.404783	−	0.233702i
$334$	−328.287	−	268.653i	−0.982894	−	0.804352i
$335$		−	51.7223i		−	0.154395i
$336$		0			0
$337$	164.049			0.486792			0.243396	−	0.969927i	$-0.421739\pi$
$337$	164.049			0.486792			0.243396	+	0.969927i	$0.421739\pi$
$338$	211.018	−	257.858i	0.624314	−	0.762894i
$339$	−23.5147	+	40.7287i	−0.0693650	+	0.120144i
$340$	−143.760	+	29.0121i	−0.422822	+	0.0853298i
$341$	181.461	−	104.766i	0.532143	−	0.307233i
$342$	46.7229	+	123.617i	0.136617	+	0.361454i
$343$		0			0
$344$	121.421	+	64.2501i	0.352969	+	0.186774i
$345$	93.1960	+	161.420i	0.270133	+	0.467884i
$346$	−58.8625	+	359.641i	−0.170123	+	1.03942i
$347$	54.8457	−	94.9955i	0.158057	−	0.273762i	−0.776111	−	0.630596i	$-0.782810\pi$
$347$	54.8457	−	94.9955i	0.158057	−	0.273762i	0.934168	+	0.356834i	$0.116144\pi$
$348$	97.7427	−	290.598i	0.280870	−	0.835052i
$349$		−	463.479i		−	1.32802i	−0.747723	−	0.664010i	$-0.768853\pi$
$349$		−	463.479i		−	1.32802i	0.747723	−	0.664010i	$-0.231147\pi$
$350$		0			0
$351$		−	33.5648i		−	0.0956261i
$352$	98.8425	+	104.071i	0.280803	+	0.295656i
$353$	39.0488	−	67.6345i	0.110620	−	0.191599i	−0.805401	−	0.592731i	$-0.798050\pi$
$353$	39.0488	−	67.6345i	0.110620	−	0.191599i	0.916020	+	0.401132i	$0.131383\pi$
$354$	−414.814	−	67.8926i	−1.17179	−	0.191787i
$355$	−79.1960	−	137.171i	−0.223087	−	0.386398i
$356$	132.177	−	116.569i	0.371283	−	0.327441i
$357$		0			0
$358$	40.4508	+	107.023i	0.112991	+	0.298946i
$359$	−316.198	+	182.557i	−0.880774	+	0.508515i	−0.870913	−	0.491437i	$-0.836472\pi$
$359$	−316.198	+	182.557i	−0.880774	+	0.508515i	−0.00986020	+	0.999951i	$0.503139\pi$
$360$	17.5122	+	27.9012i	0.0486450	+	0.0775034i
$361$	−128.760	+	223.019i	−0.356676	+	0.617780i
$362$	504.906	+	413.190i	1.39477	+	1.14141i
$363$	344.434			0.948853
$364$		0			0
$365$		−	107.426i		−	0.294316i
$366$	199.132	+	162.960i	0.544077	+	0.445245i
$367$	191.165	+	110.369i	0.520887	+	0.300734i	0.737297	−	0.675568i	$-0.236102\pi$
$367$	191.165	+	110.369i	0.520887	+	0.300734i	−0.216411	+	0.976302i	$0.569435\pi$
$368$	340.599	−	449.036i	0.925541	−	1.22021i
$369$	−35.8284	−	62.0567i	−0.0970960	−	0.168175i
$370$	−64.2010	−	169.860i	−0.173516	−	0.459081i
$371$		0			0
$372$	−421.990	−	478.492i	−1.13438	−	1.28627i
$373$	217.852	−	125.777i	0.584052	−	0.337203i	−0.178690	−	0.983905i	$-0.557186\pi$
$373$	217.852	−	125.777i	0.584052	−	0.337203i	0.762742	+	0.646703i	$0.223853\pi$
$374$	−209.429	−	34.2772i	−0.559970	−	0.0916503i
$375$	218.121	+	125.932i	0.581657	+	0.335820i
$376$	288.864	−	10.6650i	0.768256	−	0.0283645i
$377$	34.7939			0.0922916
$378$		0			0
$379$	286.024			0.754682			0.377341	−	0.926074i	$-0.376839\pi$
$379$	286.024			0.754682			0.377341	+	0.926074i	$0.376839\pi$
$380$	−49.1523	+	146.134i	−0.129348	+	0.384564i
$381$	−369.672	−	213.430i	−0.970268	−	0.560184i
$382$	−31.3554	+	191.577i	−0.0820821	+	0.501509i
$383$	92.5727	−	53.4468i	0.241704	−	0.139548i	−0.374256	−	0.927326i	$-0.622102\pi$
$383$	92.5727	−	53.4468i	0.241704	−	0.139548i	0.615960	+	0.787778i	$0.288768\pi$
$384$	251.078	−	357.695i	0.653850	−	0.931497i
$385$		0			0
$386$	111.230	+	294.288i	0.288162	+	0.762404i
$387$	22.8112	+	39.5101i	0.0589436	+	0.102093i
$388$	76.0488	+	376.833i	0.196002	+	0.971220i
$389$	−66.8405	−	38.5904i	−0.171826	−	0.0992040i	0.411620	−	0.911355i	$-0.364963\pi$
$389$	−66.8405	−	38.5904i	−0.171826	−	0.0992040i	−0.583447	+	0.812151i	$0.698296\pi$
$390$	−10.3877	+	12.6934i	−0.0266350	+	0.0325472i
$391$			833.307i			2.13122i
$392$		0			0
$393$	342.617			0.871800
$394$	192.106	+	157.210i	0.487579	+	0.399010i
$395$	−29.9899	+	51.9440i	−0.0759238	+	0.131504i
$396$	9.42957	+	46.7250i	0.0238120	+	0.117992i
$397$	569.424	−	328.757i	1.43432	−	0.828103i	0.436870	−	0.899525i	$-0.356087\pi$
$397$	569.424	−	328.757i	1.43432	−	0.828103i	0.997446	+	0.0714218i	$0.0227536\pi$
$398$	−338.573	+	127.968i	−0.850685	+	0.321529i
$399$		0			0
$400$	45.1960	−	358.732i	0.112990	−	0.896830i
$401$	−159.397	−	276.084i	−0.397499	−	0.688488i	0.595918	−	0.803045i	$-0.296788\pi$
$401$	−159.397	−	276.084i	−0.397499	−	0.688488i	−0.993417	+	0.114557i	$0.963455\pi$
$402$	−224.890	−	36.8078i	−0.559428	−	0.0915616i
$403$	36.2010	−	62.7020i	0.0898288	−	0.155588i
$404$	−25.0145	+	74.3705i	−0.0619172	+	0.184085i
$405$		−	151.657i		−	0.374461i
$406$		0			0
$407$		−	262.759i		−	0.645600i
$408$	23.8402	+	645.716i	0.0584319	+	1.58264i
$409$	72.6325	−	125.803i	0.177585	−	0.307587i	−0.763468	−	0.645846i	$-0.776505\pi$
$409$	72.6325	−	125.803i	0.177585	−	0.307587i	0.941053	+	0.338259i	$0.109838\pi$
$410$	13.5032	−	82.5027i	0.0329347	−	0.201226i
$411$	97.8406	+	169.465i	0.238055	+	0.412323i
$412$	−113.990	−	129.252i	−0.276675	−	0.313719i
$413$		0			0
$414$	175.085	−	66.1760i	0.422911	−	0.159846i
$415$	−4.85237	+	2.80152i	−0.0116925	+	0.00675065i
$416$	47.5586	+	14.0658i	0.114324	+	0.0338120i
$417$	313.534	−	543.057i	0.751880	−	1.30229i
$418$	−141.292	+	172.654i	−0.338019	+	0.413049i
$419$	−707.012			−1.68738			−0.843690	−	0.536831i	$-0.819621\pi$
$419$	−707.012			−1.68738			−0.843690	+	0.536831i	$0.819621\pi$
$420$		0			0
$421$		−	121.989i		−	0.289761i	−0.989449	−	0.144880i	$-0.953720\pi$
$421$		−	121.989i		−	0.289761i	0.989449	−	0.144880i	$-0.0462798\pi$
$422$	207.789	−	253.913i	0.492392	−	0.601688i
$423$	83.1377	+	47.9996i	0.196543	+	0.113474i
$424$	−415.997	−	662.784i	−0.981124	−	1.56317i
$425$	267.299	+	462.975i	0.628938	+	1.08935i
$426$	−652.784	+	246.729i	−1.53236	+	0.579176i
$427$		0			0
$428$	−46.7939	+	41.2684i	−0.109332	+	0.0964214i
$429$	−20.5541	+	11.8669i	−0.0479118	+	0.0276619i
$430$	−8.59720	+	52.5277i	−0.0199935	+	0.122157i
$431$	−509.969	−	294.431i	−1.18322	−	0.683133i	−0.226464	−	0.974020i	$-0.572717\pi$
$431$	−509.969	−	294.431i	−1.18322	−	0.683133i	−0.956758	+	0.290886i	$0.906050\pi$
$432$	−319.389	+	134.385i	−0.739327	+	0.311077i
$433$	−137.696			−0.318004			−0.159002	−	0.987278i	$-0.550828\pi$
$433$	−137.696			−0.318004			−0.159002	+	0.987278i	$0.550828\pi$
$434$		0			0
$435$	118.794			0.273090
$436$	4.91182	−	14.6033i	0.0112656	−	0.0334938i
$437$	758.675	+	438.021i	1.73610	+	1.00234i
$438$	−467.089	−	76.4485i	−1.06641	−	0.174540i
$439$	−381.522	+	220.272i	−0.869070	+	0.501758i	−0.867039	−	0.498240i	$-0.833980\pi$
$439$	−381.522	+	220.272i	−0.869070	+	0.501758i	−0.00203069	+	0.999998i	$0.500646\pi$
$440$	−26.0101	+	49.1545i	−0.0591139	+	0.111715i
$441$		0			0
$442$	−68.5929	+	25.9257i	−0.155188	+	0.0586554i
$443$	243.529	+	421.805i	0.549727	+	0.952155i	0.998293	+	0.0584052i	$0.0186015\pi$
$443$	243.529	+	421.805i	0.549727	+	0.952155i	−0.448566	+	0.893750i	$0.648065\pi$
$444$	−784.243	+	158.268i	−1.76631	+	0.356460i
$445$	59.1361	+	34.1422i	0.132890	+	0.0767241i
$446$	16.3802	+	13.4048i	0.0367270	+	0.0300555i
$447$			656.587i			1.46887i
$448$		0			0
$449$	264.039			0.588059			0.294030	−	0.955796i	$-0.405004\pi$
$449$	264.039			0.588059			0.294030	+	0.955796i	$0.405004\pi$
$450$	76.0480	−	92.9284i	0.168996	−	0.206508i
$451$	60.4853	−	104.764i	0.134114	−	0.232292i
$452$	10.8997	+	54.0096i	0.0241143	+	0.119490i
$453$	−339.301	+	195.896i	−0.749010	+	0.432441i
$454$	−74.8162	−	197.945i	−0.164793	−	0.436003i
$455$		0			0
$456$	600.416	+	317.710i	1.31670	+	0.696733i
$457$	257.161	+	445.417i	0.562717	+	0.974654i	0.997258	+	0.0740019i	$0.0235771\pi$
$457$	257.161	+	445.417i	0.562717	+	0.974654i	−0.434542	+	0.900652i	$0.643090\pi$
$458$	24.1890	−	147.791i	0.0528144	−	0.322688i
$459$	256.167	−	443.693i	0.558097	−	0.966652i
$460$	206.978	+	69.6169i	0.449951	+	0.151341i
$461$		−	202.224i		−	0.438664i	−0.975650	−	0.219332i	$-0.929612\pi$
$461$		−	202.224i		−	0.438664i	0.975650	−	0.219332i	$-0.0703878\pi$
$462$		0			0
$463$			722.653i			1.56081i	0.625277	+	0.780403i	$0.284986\pi$
$463$			722.653i			1.56081i	−0.625277	+	0.780403i	$0.715014\pi$
$464$	−139.306	−	331.086i	−0.300229	−	0.713547i
$465$	123.598	−	214.078i	0.265802	−	0.460383i
$466$	827.267	+	135.399i	1.77525	+	0.290555i
$467$	−173.641	−	300.755i	−0.371822	−	0.644015i	0.618023	−	0.786160i	$-0.287934\pi$
$467$	−173.641	−	300.755i	−0.371822	−	0.644015i	−0.989846	+	0.142144i	$0.954600\pi$
$468$	10.8944	+	12.3531i	0.0232787	+	0.0263956i
$469$		0			0
$470$	39.5980	+	104.766i	0.0842510	+	0.222907i
$471$	627.273	−	362.156i	1.33179	−	0.768910i
$472$	−417.100	+	261.793i	−0.883686	+	0.554646i
$473$	−38.5097	+	66.7007i	−0.0814158	+	0.141016i
$474$	204.512	+	167.362i	0.431460	+	0.353085i
$475$	562.013			1.18319
$476$		0			0
$477$		−	259.880i		−	0.544822i
$478$	229.564	+	187.864i	0.480260	+	0.393021i
$479$	−25.2716	−	14.5906i	−0.0527591	−	0.0304605i	0.473388	−	0.880854i	$-0.343031\pi$
$479$	−25.2716	−	14.5906i	−0.0527591	−	0.0304605i	−0.526148	+	0.850393i	$0.676364\pi$
$480$	162.375	+	48.0236i	0.338282	+	0.100049i
$481$	−45.3970	−	78.6299i	−0.0943804	−	0.163472i
$482$	325.179	+	860.342i	0.674645	+	1.78494i
$483$		0			0
$484$	302.647	−	266.909i	0.625303	−	0.551466i
$485$	−128.996	+	74.4760i	−0.265972	+	0.153559i
$486$	−274.702	−	44.9606i	−0.565231	−	0.0925114i
$487$	607.640	+	350.821i	1.24772	+	0.720372i	0.970654	−	0.240478i	$-0.0773043\pi$
$487$	607.640	+	350.821i	1.24772	+	0.720372i	0.277067	+	0.960851i	$0.410638\pi$
$488$	301.255	−	11.1225i	0.617325	−	0.0227920i
$489$	821.235			1.67942
$490$		0			0
$491$	−59.9512			−0.122100			−0.0610501	−	0.998135i	$-0.519445\pi$
$491$	−59.9512			−0.122100			−0.0610501	+	0.998135i	$0.519445\pi$
$492$	−349.114	−	117.425i	−0.709582	−	0.238668i
$493$	459.942	+	265.548i	0.932945	+	0.538636i
$494$	−12.4516	+	76.0772i	−0.0252056	+	0.154003i
$495$	−15.9947	+	9.23455i	−0.0323125	+	0.0186557i
$496$	−741.588	−	93.4313i	−1.49514	−	0.188370i
$497$		0			0
$498$	8.72792	+	23.0919i	0.0175259	+	0.0463693i
$499$	42.1421	+	72.9923i	0.0844532	+	0.146277i	0.905158	−	0.425075i	$-0.139752\pi$
$499$	42.1421	+	72.9923i	0.0844532	+	0.146277i	−0.820705	+	0.571352i	$0.806419\pi$
$500$	289.247	−	58.3729i	0.578493	−	0.116746i
$501$	−627.138	−	362.079i	−1.25177	−	0.722712i
$502$	−158.226	+	193.348i	−0.315192	+	0.385155i
$503$			409.987i			0.815083i	0.913187	+	0.407542i	$0.133614\pi$
$503$			409.987i			0.815083i	−0.913187	+	0.407542i	$0.866386\pi$
$504$		0			0
$505$	−30.4020			−0.0602020
$506$	244.539	+	200.119i	0.483280	+	0.395492i
$507$	284.401	−	492.596i	0.560948	−	0.971590i
$508$	−490.215	+	98.9304i	−0.964991	+	0.194745i
$509$	413.123	−	238.516i	0.811636	−	0.468598i	−0.0358878	−	0.999356i	$-0.511426\pi$
$509$	413.123	−	238.516i	0.811636	−	0.468598i	0.847524	+	0.530758i	$0.178093\pi$
$510$	−234.191	+	88.5158i	−0.459198	+	0.173560i
$511$		0			0
$512$	−56.5685	−	508.865i	−0.110485	−	0.993878i
$513$	−269.304	−	466.448i	−0.524958	−	0.909254i
$514$	−843.482	−	138.053i	−1.64102	−	0.268585i
$515$	33.3869	−	57.8278i	0.0648289	−	0.112287i
$516$	222.273	+	74.7617i	0.430762	+	0.144887i
$517$			162.065i			0.313472i
$518$		0			0
$519$			622.114i			1.19868i
$520$	0.708989	+	19.2031i	0.00136344	+	0.0369290i
$521$	105.437	−	182.621i	0.202373	−	0.350521i	−0.746919	−	0.664915i	$-0.768468\pi$
$521$	105.437	−	182.621i	0.202373	−	0.350521i	0.949293	+	0.314394i	$0.101801\pi$
$522$	19.2682	−	117.726i	0.0369123	−	0.225529i
$523$	255.783	+	443.030i	0.489069	+	0.847093i	0.999921	−	0.0125761i	$-0.00400319\pi$
$523$	255.783	+	443.030i	0.489069	+	0.847093i	−0.510852	+	0.859669i	$0.670670\pi$
$524$	301.051	−	265.502i	0.574525	−	0.506683i
$525$		0			0
$526$	−481.970	+	182.167i	−0.916292	+	0.346326i
$527$	957.084	−	552.573i	1.81610	−	1.04852i
$528$	195.215	+	148.073i	0.369725	+	0.280441i
$529$	355.892	−	616.423i	0.672764	−	1.16526i
$530$	192.019	−	234.641i	0.362300	−	0.442720i
$531$	−163.546			−0.307997
$532$		0			0
$533$		−	41.8002i		−	0.0784244i
$534$	190.535	−	232.828i	0.356807	−	0.436007i
$535$	−20.9357	−	12.0872i	−0.0391321	−	0.0225929i
$536$	−226.129	+	141.930i	−0.421883	+	0.264795i
$537$	97.6569	+	169.147i	0.181856	+	0.314984i
$538$	−402.688	+	152.202i	−0.748491	+	0.282903i
$539$		0			0
$540$	−88.8040	−	100.694i	−0.164452	−	0.186471i
$541$	−296.542	+	171.208i	−0.548136	+	0.316466i	−0.748370	−	0.663282i	$-0.769163\pi$
$541$	−296.542	+	171.208i	−0.548136	+	0.316466i	0.200234	+	0.979748i	$0.435830\pi$
$542$	−122.287	+	747.157i	−0.225622	+	1.37852i
$543$	964.542	+	556.878i	1.77632	+	1.02556i
$544$	521.328	+	548.904i	0.958324	+	1.00901i
$545$	5.96970			0.0109536
$546$		0			0
$547$	−441.976			−0.807999			−0.404000	−	0.914759i	$-0.632380\pi$
$547$	−441.976			−0.807999			−0.404000	+	0.914759i	$0.632380\pi$
$548$	217.293	+	73.0865i	0.396520	+	0.133369i
$549$	86.7038	+	50.0584i	0.157930	+	0.0911811i
$550$	200.055	+	32.7430i	0.363736	+	0.0595327i
$551$	483.529	−	279.166i	0.877548	−	0.506653i
$552$	449.990	−	850.401i	0.815199	−	1.54058i
$553$		0			0
$554$	311.397	−	117.697i	0.562088	−	0.212449i
$555$	−154.995	−	268.459i	−0.279270	−	0.483710i
$556$	−145.331	−	720.138i	−0.261387	−	1.29521i
$557$	316.714	+	182.855i	0.568607	+	0.328285i	0.756593	−	0.653886i	$-0.226863\pi$
$557$	316.714	+	182.855i	0.568607	+	0.328285i	−0.187986	+	0.982172i	$0.560196\pi$
$558$	−192.106	−	157.210i	−0.344276	−	0.281739i
$559$			26.6133i			0.0476087i
$560$		0			0
$561$	−362.274			−0.645765
$562$	−534.220	+	652.802i	−0.950570	+	1.16157i
$563$	403.194	−	698.353i	0.716154	−	1.24041i	−0.246359	−	0.969179i	$-0.579234\pi$
$563$	403.194	−	698.353i	0.716154	−	1.24041i	0.962513	−	0.271236i	$-0.0874323\pi$
$564$	483.706	−	97.6169i	0.857636	−	0.173080i
$565$	−18.4883	+	10.6743i	−0.0327227	+	0.0188925i
$566$	244.262	+	646.256i	0.431558	+	1.14180i
$567$		0			0
$568$	−382.392	+	722.653i	−0.673225	+	1.27228i
$569$	−111.446	−	193.030i	−0.195862	−	0.339244i	0.751320	−	0.659938i	$-0.229417\pi$
$569$	−111.446	−	193.030i	−0.195862	−	0.339244i	−0.947183	+	0.320694i	$0.896084\pi$
$570$	−42.5123	+	259.744i	−0.0745830	+	0.455691i
$571$	−286.541	+	496.304i	−0.501823	+	0.869184i	0.498174	+	0.867077i	$0.334004\pi$
$571$	−286.541	+	496.304i	−0.501823	+	0.869184i	−0.999998	+	0.00210683i	$0.999329\pi$
$572$	−8.86455	+	26.3551i	−0.0154975	+	0.0460754i
$573$			331.393i			0.578348i
$574$		0			0
$575$		−	796.008i		−	1.38436i
$576$	73.9290	−	153.126i	0.128349	−	0.265844i
$577$	−361.950	+	626.916i	−0.627297	+	1.08651i	0.360795	+	0.932645i	$0.382505\pi$
$577$	−361.950	+	626.916i	−0.627297	+	1.08651i	−0.988092	+	0.153865i	$0.950828\pi$
$578$	−534.186	−	87.4302i	−0.924197	−	0.151263i
$579$	268.534	+	465.115i	0.463789	+	0.803307i
$580$	104.382	−	92.0561i	0.179969	−	0.158717i
$581$		0			0
$582$	232.024	+	613.879i	0.398667	+	1.05477i
$583$	379.949	−	219.364i	0.651714	−	0.376267i
$584$	−469.663	+	294.784i	−0.804218	+	0.504767i
$585$	−3.19091	+	5.52682i	−0.00545455	+	0.00944755i
$586$	−790.978	−	647.297i	−1.34979	−	1.10460i
$587$	−21.1198			−0.0359793			−0.0179896	−	0.999838i	$-0.505727\pi$
$587$	−21.1198			−0.0359793			−0.0179896	+	0.999838i	$0.505727\pi$
$588$		0			0
$589$		−	1161.82i		−	1.97253i
$590$	−147.663	−	120.840i	−0.250277	−	0.204814i
$591$	366.988	+	211.880i	0.620960	+	0.358512i
$592$	−566.453	+	746.795i	−0.956846	+	1.26148i
$593$	−64.3726	−	111.497i	−0.108554	−	0.188021i	0.806631	−	0.591056i	$-0.201289\pi$
$593$	−64.3726	−	111.497i	−0.108554	−	0.188021i	−0.915185	+	0.403035i	$0.867955\pi$
$594$	−68.6863	−	181.727i	−0.115633	−	0.305937i
$595$		0			0
$596$	508.804	+	576.930i	0.853698	+	0.968003i
$597$	−535.105	+	308.943i	−0.896324	+	0.517493i
$598$	107.752	+	17.6358i	0.180188	+	0.0294913i
$599$	−280.705	−	162.065i	−0.468623	−	0.270559i	0.247040	−	0.969005i	$-0.420542\pi$
$599$	−280.705	−	162.065i	−0.468623	−	0.270559i	−0.715663	+	0.698446i	$0.753875\pi$
$600$	−22.7731	−	616.814i	−0.0379552	−	1.02802i
$601$	721.862			1.20110			0.600551	−	0.799587i	$-0.294948\pi$
$601$	721.862			1.20110			0.600551	+	0.799587i	$0.294948\pi$
$602$		0			0
$603$	−88.6661			−0.147042
$604$	−146.333	+	435.062i	−0.242273	+	0.720301i
$605$	135.405	+	78.1759i	0.223809	+	0.129216i
$606$	−21.6353	+	132.189i	−0.0357019	+	0.218133i
$607$	−611.413	+	353.000i	−1.00727	+	0.581548i	−0.910391	−	0.413748i	$-0.864219\pi$
$607$	−611.413	+	353.000i	−1.00727	+	0.581548i	−0.0968795	+	0.995296i	$0.530886\pi$
$608$	773.775	−	186.110i	1.27266	−	0.306103i
$609$		0			0
$610$	41.2965	+	109.260i	0.0676991	+	0.179115i
$611$	28.0000	+	48.4974i	0.0458265	+	0.0793739i
$612$	49.7347	+	246.443i	0.0812658	+	0.402684i
$613$	−18.9026	−	10.9134i	−0.0308363	−	0.0178033i	0.484503	−	0.874790i	$-0.339001\pi$
$613$	−18.9026	−	10.9134i	−0.0308363	−	0.0178033i	−0.515339	+	0.856986i	$0.672334\pi$
$614$	−282.878	+	345.669i	−0.460713	+	0.562978i
$615$		−	142.715i		−	0.232057i
$616$		0			0
$617$	−699.578			−1.13384			−0.566919	−	0.823774i	$-0.691865\pi$
$617$	−699.578			−1.13384			−0.566919	+	0.823774i	$0.691865\pi$
$618$	−227.677	−	186.320i	−0.368409	−	0.301488i
$619$	48.0990	−	83.3100i	0.0777044	−	0.134588i	−0.824555	−	0.565782i	$-0.808574\pi$
$619$	48.0990	−	83.3100i	0.0777044	−	0.134588i	0.902259	+	0.431194i	$0.141908\pi$
$620$	−57.2908	−	283.885i	−0.0924046	−	0.457879i
$621$	−660.654	+	381.429i	−1.06386	+	0.614217i
$622$	−23.1960	+	8.76725i	−0.0372925	+	0.0140953i
$623$		0			0
$624$	84.0000	+	10.5830i	0.134615	+	0.0169599i
$625$	−225.309	−	390.247i	−0.360495	−	0.624395i
$626$	809.329	+	132.463i	1.29286	+	0.211602i
$627$	−190.426	+	329.828i	−0.303710	+	0.526042i
$628$	270.529	−	804.308i	0.430779	−	1.28074i
$629$		−	1385.88i		−	2.20331i
$630$		0			0
$631$			269.399i			0.426940i	0.976950	+	0.213470i	$0.0684766\pi$
$631$			269.399i			0.426940i	−0.976950	+	0.213470i	$0.931523\pi$
$632$	309.393	−	11.4230i	0.489546	−	0.0180743i
$633$	280.049	−	485.059i	0.442415	−	0.766285i
$634$	−42.0975	+	257.210i	−0.0663999	+	0.405694i
$635$	−96.8843	−	167.809i	−0.152574	−	0.264266i
$636$	−883.578	−	1001.88i	−1.38927	−	1.57529i
$637$		0			0
$638$	188.382	−	71.2016i	0.295269	−	0.111601i
$639$	−235.149	+	135.763i	−0.367995	+	0.212462i
$640$	179.890	−	83.6309i	0.281079	−	0.130673i
$641$	−317.907	+	550.630i	−0.495954	+	0.859018i	−0.999989	−	0.00466541i	$-0.998515\pi$
$641$	−317.907	+	550.630i	−0.495954	+	0.859018i	0.504035	+	0.863683i	$0.331848\pi$
$642$	−67.4543	+	82.4271i	−0.105069	+	0.128391i
$643$	−1281.70			−1.99332			−0.996658	−	0.0816828i	$-0.973971\pi$
$643$	−1281.70			−1.99332			−0.996658	+	0.0816828i	$0.973971\pi$
$644$		0			0
$645$			90.8634i			0.140874i
$646$	−745.219	+	910.636i	−1.15359	+	1.40965i
$647$	−225.826	−	130.381i	−0.349035	−	0.201516i	0.315225	−	0.949017i	$-0.397920\pi$
$647$	−225.826	−	130.381i	−0.349035	−	0.201516i	−0.664260	+	0.747501i	$0.731253\pi$
$648$	−663.041	+	416.158i	−1.02321	+	0.642219i
$649$	−138.049	−	239.107i	−0.212710	−	0.368424i
$650$	65.5227	−	24.7653i	0.100804	−	0.0381004i
$651$		0			0
$652$	721.602	−	636.393i	1.10675	−	0.976063i
$653$	−944.471	+	545.291i	−1.44636	+	0.835055i	−0.998262	−	0.0589313i	$-0.981231\pi$
$653$	−944.471	+	545.291i	−1.44636	+	0.835055i	−0.448095	+	0.893986i	$0.647897\pi$
$654$	4.24828	−	25.9564i	0.00649585	−	0.0396887i
$655$	134.691	+	77.7637i	0.205635	+	0.118723i
$656$	−397.754	+	167.358i	−0.606333	+	0.255119i
$657$	−184.156			−0.280299
$658$		0			0
$659$	−362.780			−0.550500			−0.275250	−	0.961373i	$-0.588761\pi$
$659$	−362.780			−0.550500			−0.275250	+	0.961373i	$0.588761\pi$
$660$	−30.2655	+	89.9820i	−0.0458567	+	0.136336i
$661$	102.047	+	58.9169i	0.154383	+	0.0891330i	0.575201	−	0.818012i	$-0.304924\pi$
$661$	102.047	+	58.9169i	0.154383	+	0.0891330i	−0.420818	+	0.907145i	$0.638257\pi$
$662$	−422.893	−	69.2149i	−0.638811	−	0.104554i
$663$	−108.409	+	62.5902i	−0.163513	+	0.0944045i
$664$	25.5635	+	13.5269i	0.0384992	+	0.0203719i
$665$		0			0
$666$	−291.186	+	110.058i	−0.437216	+	0.165252i
$667$	−395.397	−	684.848i	−0.592799	−	1.02676i
$668$	−831.637	+	167.833i	−1.24496	+	0.251247i
$669$	31.2918	+	18.0663i	0.0467740	+	0.0270050i
$670$	−80.0552	−	65.5132i	−0.119485	−	0.0977808i
$671$			169.017i			0.251888i
$672$		0			0
$673$	−6.56854			−0.00976009			−0.00488005	−	0.999988i	$-0.501553\pi$
$673$	−6.56854			−0.00976009			−0.00488005	+	0.999988i	$0.501553\pi$
$674$	207.789	−	253.913i	0.308293	−	0.376725i
$675$	−244.701	+	423.834i	−0.362519	+	0.627902i
$676$	−131.827	−	653.223i	−0.195010	−	0.966306i
$677$	−108.942	+	62.8978i	−0.160919	+	0.0929066i	−0.578297	−	0.815826i	$-0.696282\pi$
$677$	−108.942	+	62.8978i	−0.160919	+	0.0929066i	0.417378	+	0.908733i	$0.362949\pi$
$678$	33.2548	+	87.9840i	0.0490484	+	0.129770i
$679$		0			0
$680$	−137.186	+	259.257i	−0.201744	+	0.381260i
$681$	−180.622	−	312.847i	−0.265231	−	0.459394i
$682$	67.6879	−	413.563i	0.0992491	−	0.606397i
$683$	276.887	−	479.583i	0.405399	−	0.702171i	−0.588969	−	0.808156i	$-0.700466\pi$
$683$	276.887	−	479.583i	0.405399	−	0.702171i	0.994368	+	0.105984i	$0.0337994\pi$
$684$	250.514	+	84.2603i	0.366248	+	0.123188i
$685$			88.8274i			0.129675i
$686$		0			0
$687$		−	255.652i		−	0.372128i
$688$	253.242	−	106.553i	0.368084	−	0.154874i
$689$	75.7990	−	131.288i	0.110013	−	0.190548i
$690$	367.889	+	60.2124i	0.533172	+	0.0872644i
$691$	−523.413	−	906.577i	−0.757471	−	1.31198i	−0.944136	−	0.329555i	$-0.893101\pi$
$691$	−523.413	−	906.577i	−0.757471	−	1.31198i	0.186665	−	0.982424i	$-0.440232\pi$
$692$	482.090	+	546.639i	0.696662	+	0.789941i
$693$		0			0
$694$	−77.5635	−	205.214i	−0.111763	−	0.295697i
$695$	246.515	−	142.325i	0.354698	−	0.204785i
$696$	−325.980	−	519.366i	−0.468362	−	0.746215i
$697$	319.019	−	552.558i	0.457703	−	0.792766i
$698$	−717.367	−	587.058i	−1.02775	−	0.841057i
$699$	1431.02			2.04724
$700$		0			0
$701$		−	625.993i		−	0.893000i	−0.894784	−	0.446500i	$-0.852670\pi$
$701$		−	625.993i		−	0.893000i	0.894784	−	0.446500i	$-0.147330\pi$
$702$	−51.9511	−	42.5142i	−0.0740044	−	0.0605615i
$703$	−1261.76	−	728.476i	−1.79482	−	1.03624i
$704$	286.276	−	21.1678i	0.406643	−	0.0300680i
$705$	95.5980	+	165.581i	0.135600	+	0.234866i
$706$	−55.2233	−	146.107i	−0.0782200	−	0.206951i
$707$		0			0
$708$	−630.500	+	556.048i	−0.890536	+	0.785379i
$709$	513.979	−	296.746i	0.724935	−	0.418541i	−0.0916314	−	0.995793i	$-0.529208\pi$
$709$	513.979	−	296.746i	0.724935	−	0.418541i	0.816566	+	0.577252i	$0.195875\pi$
$710$	−312.624	−	51.1672i	−0.440316	−	0.0720665i
$711$	89.0461	+	51.4108i	0.125241	+	0.0723077i
$712$	−13.0046	−	352.231i	−0.0182649	−	0.494706i
$713$	−1645.55			−2.30792
$714$		0			0
$715$	−10.7737			−0.0150682
$716$	216.885	+	72.9492i	0.302912	+	0.101884i
$717$	438.546	+	253.194i	0.611640	+	0.353130i
$718$	−117.947	+	720.639i	−0.164272	+	1.00368i
$719$	529.578	−	305.752i	0.736549	−	0.425247i	−0.0842645	−	0.996443i	$-0.526854\pi$
$719$	529.578	−	305.752i	0.736549	−	0.425247i	0.820813	+	0.571197i	$0.193521\pi$
$720$	65.3667	+	8.23543i	0.0907870	+	0.0114381i
$721$		0			0
$722$	182.094	+	481.775i	0.252208	+	0.667279i
$723$	785.051	+	1359.75i	1.08582	+	1.88070i
$724$	1279.06	−	258.127i	1.76666	−	0.356530i
$725$	−439.355	−	253.662i	−0.606007	−	0.349878i
$726$	436.270	−	533.110i	0.600924	−	0.734311i
$727$		−	944.144i		−	1.29868i	−0.760496	−	0.649342i	$-0.775044\pi$
$727$		−	944.144i		−	1.29868i	0.760496	−	0.649342i	$-0.224956\pi$
$728$		0			0
$729$	405.489			0.556227
$730$	−166.272	−	136.069i	−0.227770	−	0.186395i
$731$	−203.113	+	351.802i	−0.277856	+	0.481261i
$732$	504.454	−	101.804i	0.689145	−	0.139076i
$733$	189.014	−	109.127i	0.257863	−	0.148878i	−0.365496	−	0.930813i	$-0.619101\pi$
$733$	189.014	−	109.127i	0.257863	−	0.148878i	0.623360	+	0.781935i	$0.285767\pi$
$734$	412.965	−	156.086i	0.562622	−	0.212651i
$735$		0			0
$736$	−263.598	−	1095.94i	−0.358149	−	1.48905i
$737$	−74.8427	−	129.631i	−0.101550	−	0.175891i
$738$	−141.432	−	23.1482i	−0.191642	−	0.0313661i
$739$	3.64971	−	6.32149i	0.00493872	−	0.00855411i	−0.863545	−	0.504271i	$-0.831761\pi$
$739$	3.64971	−	6.32149i	0.00493872	−	0.00855411i	0.868484	+	0.495717i	$0.165095\pi$
$740$	−344.226	−	115.780i	−0.465170	−	0.156460i
$741$			131.600i			0.177598i
$742$		0			0
$743$		−	106.867i		−	0.143832i	−0.997411	−	0.0719159i	$-0.977089\pi$
$743$		−	106.867i		−	0.143832i	0.997411	−	0.0719159i	$-0.0229113\pi$
$744$	−1275.11	+	47.0778i	−1.71386	+	0.0632766i
$745$	−149.025	+	258.119i	−0.200034	+	0.346469i
$746$	81.2623	−	496.500i	0.108931	−	0.665550i
$747$	4.80256	+	8.31828i	0.00642913	+	0.0111356i
$748$	−318.323	+	280.734i	−0.425565	+	0.375313i
$749$		0			0
$750$	471.196	−	178.095i	0.628261	−	0.237460i
$751$	110.387	−	63.7317i	0.146986	−	0.0848624i	−0.424703	−	0.905333i	$-0.639622\pi$
$751$	110.387	−	63.7317i	0.146986	−	0.0848624i	0.571689	+	0.820470i	$0.306288\pi$
$752$	349.378	−	460.609i	0.464598	−	0.612512i
$753$	−213.250	+	369.359i	−0.283200	+	0.490517i
$754$	44.0711	−	53.8536i	0.0584497	−	0.0714239i
$755$	−177.849			−0.235562
$756$		0			0
$757$			704.275i			0.930350i	0.885219	+	0.465175i	$0.154009\pi$
$757$			704.275i			0.930350i	−0.885219	+	0.465175i	$0.845991\pi$
$758$	362.288	−	442.705i	0.477952	−	0.584043i
$759$	467.153	+	269.711i	0.615485	+	0.355350i
$760$	163.927	+	261.175i	0.215693	+	0.343652i
$761$	−501.465	−	868.563i	−0.658955	−	1.14134i	−0.980886	−	0.194581i	$-0.937665\pi$
$761$	−501.465	−	868.563i	−0.658955	−	1.14134i	0.321931	−	0.946763i	$-0.395668\pi$
$762$	−798.583	+	301.836i	−1.04801	+	0.396110i
$763$		0			0
$764$	256.804	+	291.188i	0.336131	+	0.381137i
$765$	−84.3614	+	48.7061i	−0.110276	+	0.0636681i
$766$	34.5311	−	210.980i	0.0450798	−	0.275431i
$767$	−82.6213	−	47.7014i	−0.107720	−	0.0621922i
$768$	−235.612	−	841.683i	−0.306786	−	1.09594i
$769$	646.950			0.841288			0.420644	−	0.907226i	$-0.361804\pi$
$769$	646.950			0.841288			0.420644	+	0.907226i	$0.361804\pi$
$770$		0			0
$771$	−1459.07			−1.89244
$772$	596.383	+	200.594i	0.772517	+	0.259836i
$773$	−488.668	−	282.132i	−0.632170	−	0.364984i	0.149422	−	0.988774i	$-0.452259\pi$
$773$	−488.668	−	282.132i	−0.632170	−	0.364984i	−0.781592	+	0.623790i	$0.785592\pi$
$774$	90.0466	+	14.7379i	0.116339	+	0.0190413i
$775$	−914.245	+	527.840i	−1.17967	+	0.681083i
$776$	679.584	+	359.602i	0.875752	+	0.463404i
$777$		0			0
$778$	−144.392	+	54.5750i	−0.185594	+	0.0701478i
$779$	−335.380	−	580.895i	−0.430526	−	0.745693i
$780$	6.48936	+	32.1558i	0.00831969	+	0.0412253i
$781$	−396.977	−	229.195i	−0.508293	−	0.293463i
$782$	1289.78	+	1055.49i	1.64934	+	1.34974i
$783$			486.195i			0.620939i
$784$		0			0
$785$	328.794			0.418846
$786$	433.970	−	530.299i	0.552125	−	0.674680i
$787$	461.673	−	799.640i	0.586623	−	1.01606i	−0.408048	−	0.912961i	$-0.633790\pi$
$787$	461.673	−	799.640i	0.586623	−	1.01606i	0.994671	−	0.103101i	$-0.0328764\pi$
$788$	486.655	−	98.2120i	0.617583	−	0.124635i
$789$	−761.740	+	439.791i	−0.965451	+	0.557403i
$790$	42.4121	+	112.212i	0.0536862	+	0.142040i
$791$		0			0
$792$	84.2641	+	44.5884i	0.106394	+	0.0562984i
$793$	29.2010	+	50.5776i	0.0368235	+	0.0637801i
$794$	212.404	−	1297.76i	0.267512	−	1.63446i
$795$	258.794	−	448.244i	0.325527	−	0.563829i
$796$	−230.779	+	686.127i	−0.289923	+	0.861969i
$797$			207.983i			0.260957i	0.991451	+	0.130479i	$0.0416514\pi$
$797$			207.983i			0.260957i	−0.991451	+	0.130479i	$0.958349\pi$
$798$		0			0
$799$			854.785i			1.06982i
$800$	−497.994	−	524.335i	−0.622492	−	0.655419i
$801$	58.5290	−	101.375i	0.0730699	−	0.126561i
$802$	−629.216	−	102.984i	−0.784558	−	0.128409i
$803$	−155.446	−	269.240i	−0.193581	−	0.335293i
$804$	−341.823	+	301.460i	−0.425153	+	0.374950i
$805$		0			0
$806$	−51.1960	−	135.452i	−0.0635186	−	0.168054i
$807$	−636.438	+	367.448i	−0.788647	+	0.455326i
$808$	83.4255	+	132.917i	0.103249	+	0.164502i
$809$	−170.270	+	294.916i	−0.210470	+	0.364544i	−0.951862	−	0.306528i	$-0.900833\pi$
$809$	−170.270	+	294.916i	−0.210470	+	0.364544i	0.741392	+	0.671072i	$0.234166\pi$
$810$	−234.732	−	192.093i	−0.289793	−	0.237152i
$811$	907.380			1.11884			0.559420	−	0.828884i	$-0.311024\pi$
$811$	907.380			1.11884			0.559420	+	0.828884i	$0.311024\pi$
$812$		0			0
$813$			1292.45i			1.58973i
$814$	−406.695	−	332.819i	−0.499626	−	0.408869i
$815$	322.846	+	186.395i	0.396130	+	0.228706i
$816$	1029.63	+	780.985i	1.26180	+	0.957090i
$817$	213.529	+	369.843i	0.261357	+	0.452684i
$818$	−102.718	−	271.766i	−0.125572	−	0.332232i
$819$		0			0
$820$	−110.593	−	125.401i	−0.134869	−	0.152928i
$821$	548.560	−	316.711i	0.668161	−	0.385763i	−0.127219	−	0.991875i	$-0.540605\pi$
$821$	548.560	−	316.711i	0.668161	−	0.385763i	0.795379	+	0.606112i	$0.207272\pi$
$822$	386.224	+	63.2132i	0.469858	+	0.0769018i
$823$	124.404	+	71.8247i	0.151159	+	0.0872718i	0.573672	−	0.819085i	$-0.305518\pi$
$823$	124.404	+	71.8247i	0.151159	+	0.0872718i	−0.422513	+	0.906357i	$0.638852\pi$
$824$	−344.438	+	12.7169i	−0.418008	+	0.0154331i
$825$	346.059			0.419465
$826$		0			0
$827$	1545.57			1.86888			0.934442	−	0.356114i	$-0.115899\pi$
$827$	1545.57			1.86888			0.934442	+	0.356114i	$0.115899\pi$
$828$	119.342	−	354.815i	0.144133	−	0.428521i
$829$	−644.285	−	371.978i	−0.777183	−	0.448707i	0.0582482	−	0.998302i	$-0.481449\pi$
$829$	−644.285	−	371.978i	−0.777183	−	0.448707i	−0.835431	+	0.549595i	$0.814782\pi$
$830$	−1.81002	+	11.0589i	−0.00218074	+	0.0133240i
$831$	492.155	−	284.146i	0.592244	−	0.341932i
$832$	82.0101	−	55.7944i	0.0985698	−	0.0670606i
$833$		0			0
$834$	−443.404	−	1173.14i	−0.531660	−	1.40664i
$835$	−164.362	−	284.683i	−0.196840	−	0.340937i
$836$	88.2675	+	437.379i	0.105583	+	0.523181i
$837$	876.170	+	505.857i	1.04680	+	0.604369i
$838$	−895.524	+	1094.30i	−1.06864	+	1.30585i
$839$		−	96.3107i		−	0.114792i	−0.998351	−	0.0573961i	$-0.981720\pi$
$839$		−	96.3107i		−	0.114792i	0.998351	−	0.0573961i	$-0.0182798\pi$
$840$		0			0
$841$	337.000			0.400713
$842$	−188.814	−	154.516i	−0.224244	−	0.183510i
$843$	−719.997	+	1247.07i	−0.854089	+	1.47933i
$844$	−129.810	−	643.227i	−0.153803	−	0.762118i
$845$	223.609	−	129.101i	0.264626	−	0.152782i
$846$	179.598	−	67.8817i	0.212291	−	0.0802384i
$847$		0			0
$848$	−1552.76	−	195.630i	−1.83109	−	0.230696i
$849$	589.701	+	1021.39i	0.694583	+	1.20305i
$850$	1055.15	+	172.697i	1.24136	+	0.203173i
$851$	−1031.78	+	1787.09i	−1.21243	+	2.09999i
$852$	−444.953	+	1322.89i	−0.522245	+	1.55268i
$853$			904.866i			1.06080i	0.847746	+	0.530402i	$0.177959\pi$
$853$			904.866i			1.06080i	−0.847746	+	0.530402i	$0.822041\pi$
$854$		0			0
$855$			102.408i			0.119775i
$856$	4.60396	+	124.699i	0.00537845	+	0.145676i
$857$	80.4659	−	139.371i	0.0938926	−	0.162627i	−0.815253	−	0.579105i	$-0.803402\pi$
$857$	80.4659	−	139.371i	0.0938926	−	0.162627i	0.909146	+	0.416478i	$0.136736\pi$
$858$	−7.66704	+	46.8445i	−0.00893594	+	0.0545973i
$859$	115.846	+	200.652i	0.134862	+	0.233587i	0.925545	−	0.378638i	$-0.123608\pi$
$859$	115.846	+	200.652i	0.134862	+	0.233587i	−0.790683	+	0.612226i	$0.790274\pi$
$860$	70.4121	+	79.8398i	0.0818746	+	0.0928370i
$861$		0			0
$862$	−1101.66	+	416.388i	−1.27803	+	0.483048i
$863$	−1158.18	+	668.674i	−1.34204	+	0.774825i	−0.987106	−	0.160068i	$-0.948829\pi$
$863$	−1158.18	+	668.674i	−1.34204	+	0.774825i	−0.354931	+	0.934893i	$0.615495\pi$
$864$	−196.549	+	664.563i	−0.227487	+	0.769170i
$865$	−141.201	+	244.567i	−0.163238	+	0.282737i
$866$	−174.410	+	213.123i	−0.201397	+	0.246101i
$867$	−924.046			−1.06580
$868$		0			0
$869$			173.583i			0.199750i
$870$	150.468	−	183.868i	0.172952	−	0.211342i
$871$	−44.7929	−	25.8612i	−0.0514269	−	0.0296914i
$872$	−16.3813	−	26.0994i	−0.0187859	−	0.0299305i
$873$	127.672	+	221.134i	0.146245	+	0.253304i
$874$	1638.92	−	619.455i	1.87520	−	0.708759i
$875$		0			0
$876$	−709.955	+	626.122i	−0.810451	+	0.714751i
$877$	1243.73	−	718.068i	1.41816	−	0.818777i	0.422026	−	0.906584i	$-0.361319\pi$
$877$	1243.73	−	718.068i	1.41816	−	0.818777i	0.996138	+	0.0878061i	$0.0279856\pi$
$878$	−142.314	+	869.517i	−0.162089	+	0.990338i
$879$	−1511.04	−	872.397i	−1.71904	−	0.992488i
$880$	43.1354	+	102.519i	0.0490175	+	0.116499i
$881$	186.706			0.211926			0.105963	−	0.994370i	$-0.466208\pi$
$881$	186.706			0.211926			0.105963	+	0.994370i	$0.466208\pi$
$882$		0			0
$883$	1277.99			1.44733			0.723664	−	0.690153i	$-0.242457\pi$
$883$	1277.99			1.44733			0.723664	+	0.690153i	$0.242457\pi$
$884$	−46.7545	+	139.006i	−0.0528898	+	0.157246i
$885$	−282.087	−	162.863i	−0.318742	−	0.184026i
$886$	961.325	+	157.340i	1.08502	+	0.177585i
$887$	849.326	−	490.359i	0.957526	−	0.552828i	0.0621155	−	0.998069i	$-0.480215\pi$
$887$	849.326	−	490.359i	0.957526	−	0.552828i	0.895411	+	0.445241i	$0.146882\pi$
$888$	−748.382	+	1414.31i	−0.842772	+	1.59269i
$889$		0			0
$890$	127.748	−	48.2844i	0.143538	−	0.0542521i
$891$	−219.449	−	380.096i	−0.246295	−	0.426595i
$892$	41.4955	−	8.37420i	0.0465196	−	0.00938812i
$893$	778.228	+	449.310i	0.871476	+	0.503147i
$894$	1016.26	+	831.654i	1.13675	+	0.930262i
$895$			88.6605i			0.0990621i
$896$		0			0
$897$	186.392			0.207795
$898$	334.440	−	408.676i	0.372427	−	0.455095i
$899$	−524.382	+	908.256i	−0.583295	+	1.01030i
$900$	−47.5086	−	235.412i	−0.0527873	−	0.261569i
$901$	2003.98	−	1157.00i	2.22417	−	1.28412i
$902$	−85.5391	−	226.315i	−0.0948327	−	0.250904i
$903$		0			0
$904$	97.4012	+	51.5398i	0.107745	+	0.0570131i
$905$	252.789	+	437.843i	0.279325	+	0.483805i
$906$	−126.565	+	773.294i	−0.139697	+	0.853525i
$907$	329.186	−	570.167i	0.362939	−	0.628629i	−0.625504	−	0.780221i	$-0.715107\pi$
$907$	329.186	−	570.167i	0.362939	−	0.628629i	0.988443	+	0.151592i	$0.0484399\pi$
$908$	−401.142	−	134.924i	−0.441786	−	0.148595i
$909$			52.1173i			0.0573348i
$910$		0			0
$911$		−	276.507i		−	0.303520i	−0.988417	−	0.151760i	$-0.951506\pi$
$911$		−	276.507i		−	0.303520i	0.988417	−	0.151760i	$-0.0484941\pi$
$912$	1252.25	−	526.894i	1.37309	−	0.577735i
$913$	−8.10765	+	14.0429i	−0.00888023	+	0.0153810i
$914$	1015.14	+	166.148i	1.11066	+	0.181781i
$915$	99.6985	+	172.683i	0.108960	+	0.188724i
$916$	−198.111	−	224.636i	−0.216278	−	0.245236i
$917$		0			0
$918$	−362.274	−	958.487i	−0.394634	−	1.04410i
$919$	−1160.24	+	669.867i	−1.26251	+	0.728908i	−0.973559	−	0.228437i	$-0.926639\pi$
$919$	−1160.24	+	669.867i	−1.26251	+	0.728908i	−0.288948	+	0.957345i	$0.593305\pi$
$920$	369.916	−	232.178i	0.402083	−	0.252367i
$921$	−381.250	+	660.344i	−0.413952	+	0.716986i
$922$	−313.000	−	256.144i	−0.339479	−	0.277813i
$923$	−158.392			−0.171606
$924$		0			0
$925$			1323.85i			1.43119i
$926$	1118.51	+	915.335i	1.20790	+	0.988483i
$927$	−99.1324	−	57.2341i	−0.106939	−	0.0617412i
$928$	−688.900	−	203.747i	−0.742349	−	0.219555i
$929$	17.7006	+	30.6583i	0.0190534	+	0.0330014i	0.875395	−	0.483409i	$-0.160601\pi$
$929$	17.7006	+	30.6583i	0.0190534	+	0.0330014i	−0.856342	+	0.516410i	$0.827268\pi$
$930$	−174.794	−	462.461i	−0.187950	−	0.497270i
$931$		0			0
$932$	1257.41	−	1108.93i	1.34915	−	1.18984i
$933$	−36.6606	+	21.1660i	−0.0392933	+	0.0226860i
$934$	−685.444	−	112.187i	−0.733880	−	0.120114i
$935$	−142.418	−	82.2252i	−0.152319	−	0.0879414i
$936$	32.9193	−	1.21540i	0.0351702	−	0.00129850i
$937$	−610.235			−0.651265			−0.325633	−	0.945496i	$-0.605577\pi$
$937$	−610.235			−0.651265			−0.325633	+	0.945496i	$0.605577\pi$
$938$		0			0
$939$	1399.99			1.49094
$940$	212.312	+	71.4112i	0.225864	+	0.0759694i
$941$	−1604.66	−	926.450i	−1.70527	−	0.984537i	−0.940222	−	0.340563i	$-0.889382\pi$
$941$	−1604.66	−	926.450i	−1.70527	−	0.984537i	−0.765047	−	0.643975i	$-0.777284\pi$
$942$	233.983	−	1429.60i	0.248390	−	1.51763i
$943$	−822.752	+	475.016i	−0.872483	+	0.503728i
$944$	−123.113	+	977.177i	−0.130416	+	1.03514i
$945$		0			0
$946$	54.4609	+	144.090i	0.0575697	+	0.152315i
$947$	916.448	+	1587.33i	0.967738	+	1.67617i	0.702072	+	0.712106i	$0.252259\pi$
$947$	916.448	+	1587.33i	0.967738	+	1.67617i	0.265666	+	0.964065i	$0.414408\pi$
$948$	518.082	−	104.554i	0.546500	−	0.110289i
$949$	−93.0332	−	53.7128i	−0.0980329	−	0.0565993i
$950$	711.864	−	869.876i	0.749330	−	0.915659i
$951$			444.927i			0.467852i
$952$		0			0
$953$	349.687			0.366933			0.183467	−	0.983026i	$-0.441268\pi$
$953$	349.687			0.366933			0.183467	+	0.983026i	$0.441268\pi$
$954$	−402.239	−	329.172i	−0.421634	−	0.345044i
$955$	−75.2162	+	130.278i	−0.0787604	+	0.136417i
$956$	581.547	−	117.362i	0.608313	−	0.122764i
$957$	297.733	−	171.896i	0.311110	−	0.179620i
$958$	−54.5929	+	20.6342i	−0.0569864	+	0.0215388i
$959$		0			0
$960$	280.000	−	190.494i	0.291667	−	0.198431i
$961$	610.676	+	1057.72i	0.635459	+	1.10065i
$962$	−179.203	−	29.3302i	−0.186282	−	0.0304888i
$963$	−20.7208	+	35.8894i	−0.0215169	+	0.0372684i
$964$	1743.51	+	586.429i	1.80862	+	0.608329i
$965$			243.796i			0.252639i
$966$		0			0
$967$		−	632.128i		−	0.653700i	−0.945076	−	0.326850i	$-0.894013\pi$
$967$		−	632.128i		−	0.653700i	0.945076	−	0.326850i	$-0.105987\pi$
$968$	−29.7768	−	806.509i	−0.0307611	−	0.833170i
$969$	−1004.37	+	1739.62i	−1.03650	+	1.79528i
$970$	−48.1177	+	293.992i	−0.0496059	+	0.303085i
$971$	328.248	+	568.543i	0.338052	+	0.585523i	0.984066	−	0.177802i	$-0.0568988\pi$
$971$	328.248	+	568.543i	0.338052	+	0.585523i	−0.646014	+	0.763325i	$0.723565\pi$
$972$	−417.536	+	368.232i	−0.429564	+	0.378840i
$973$		0			0
$974$	1312.65	−	496.136i	1.34769	−	0.509380i
$975$	103.557	−	59.7886i	0.106212	−	0.0613217i
$976$	364.363	−	480.366i	0.373323	−	0.492178i
$977$	−84.6569	+	146.630i	−0.0866498	+	0.150082i	−0.906093	−	0.423078i	$-0.860949\pi$
$977$	−84.6569	+	146.630i	−0.0866498	+	0.150082i	0.819443	+	0.573160i	$0.194283\pi$
$978$	1040.20	−	1271.10i	1.06360	−	1.29969i
$979$	197.616			0.201855
$980$		0			0
$981$		−	10.2337i		−	0.0104319i
$982$	−75.9361	+	92.7917i	−0.0773280	+	0.0944926i
$983$	605.012	+	349.304i	0.615475	+	0.355345i	0.775105	−	0.631832i	$-0.217697\pi$
$983$	605.012	+	349.304i	0.615475	+	0.355345i	−0.159630	+	0.987177i	$0.551030\pi$
$984$	−623.947	+	391.621i	−0.634093	+	0.397988i
$985$	96.1808	+	166.590i	0.0976455	+	0.169127i
$986$	993.588	−	375.541i	1.00770	−	0.380873i
$987$		0			0
$988$	101.980	+	115.634i	0.103218	+	0.117039i
$989$	523.828	−	302.432i	0.529654	−	0.305796i
$990$	−5.96629	+	36.4532i	−0.00602656	+	0.0368214i
$991$	−372.133	−	214.851i	−0.375513	−	0.216802i	0.300352	−	0.953829i	$-0.402896\pi$
$991$	−372.133	−	214.851i	−0.375513	−	0.216802i	−0.675864	+	0.737026i	$0.736229\pi$
$992$	−1083.93	+	1029.48i	−1.09267	+	1.03778i
$993$	−731.529			−0.736686
$994$		0			0
$995$	−280.483			−0.281892
$996$	46.7964	+	15.7400i	0.0469844	+	0.0158032i
$997$	−45.3720	−	26.1955i	−0.0455085	−	0.0262743i	0.477073	−	0.878864i	$-0.341698\pi$
$997$	−45.3720	−	26.1955i	−0.0455085	−	0.0262743i	−0.522582	+	0.852589i	$0.675031\pi$
$998$	166.355	+	27.2274i	0.166688	+	0.0272819i
$999$	1098.74	−	634.357i	1.09984	−	0.634992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.k.j.67.3		8
7.2	even	3	inner	392.3.k.j.275.1		8
7.3	odd	6		56.3.g.a.43.4	yes	4
7.4	even	3		392.3.g.h.99.4		4
7.5	odd	6		392.3.k.i.275.1		8
7.6	odd	2		392.3.k.i.67.3		8
8.3	odd	2	inner	392.3.k.j.67.1		8
21.17	even	6		504.3.g.a.379.1		4
28.3	even	6		224.3.g.a.15.1		4
28.11	odd	6		1568.3.g.h.687.4		4
56.3	even	6		56.3.g.a.43.3	✓	4
56.11	odd	6		392.3.g.h.99.3		4
56.19	even	6		392.3.k.i.275.3		8
56.27	even	2		392.3.k.i.67.1		8
56.45	odd	6		224.3.g.a.15.2		4
56.51	odd	6	inner	392.3.k.j.275.3		8
56.53	even	6		1568.3.g.h.687.3		4
84.59	odd	6		2016.3.g.a.1135.3		4
112.3	even	12		1792.3.d.g.1023.1		8
112.45	odd	12		1792.3.d.g.1023.7		8
112.59	even	12		1792.3.d.g.1023.8		8
112.101	odd	12		1792.3.d.g.1023.2		8
168.59	odd	6		504.3.g.a.379.2		4
168.101	even	6		2016.3.g.a.1135.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.a.43.3	✓	4	56.3	even	6
56.3.g.a.43.4	yes	4	7.3	odd	6
224.3.g.a.15.1		4	28.3	even	6
224.3.g.a.15.2		4	56.45	odd	6
392.3.g.h.99.3		4	56.11	odd	6
392.3.g.h.99.4		4	7.4	even	3
392.3.k.i.67.1		8	56.27	even	2
392.3.k.i.67.3		8	7.6	odd	2
392.3.k.i.275.1		8	7.5	odd	6
392.3.k.i.275.3		8	56.19	even	6
392.3.k.j.67.1		8	8.3	odd	2	inner
392.3.k.j.67.3		8	1.1	even	1	trivial
392.3.k.j.275.1		8	7.2	even	3	inner
392.3.k.j.275.3		8	56.51	odd	6	inner
504.3.g.a.379.1		4	21.17	even	6
504.3.g.a.379.2		4	168.59	odd	6
1568.3.g.h.687.3		4	56.53	even	6
1568.3.g.h.687.4		4	28.11	odd	6
1792.3.d.g.1023.1		8	112.3	even	12
1792.3.d.g.1023.2		8	112.101	odd	12
1792.3.d.g.1023.7		8	112.45	odd	12
1792.3.d.g.1023.8		8	112.59	even	12
2016.3.g.a.1135.2		4	168.101	even	6
2016.3.g.a.1135.3		4	84.59	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.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.26663 - 1.54779i) q^{2} +(1.70711 - 2.95680i) q^{3} +(-0.791288 - 3.92095i) q^{4} +(1.34221 - 0.774923i) q^{5} +(-2.41421 - 6.38741i) q^{6} +(-7.07107 - 3.74166i) q^{8} +(-1.32843 - 2.30090i) q^{9} +O(q^{10})\)	\(q+(1.26663 - 1.54779i) q^{2} +(1.70711 - 2.95680i) q^{3} +(-0.791288 - 3.92095i) q^{4} +(1.34221 - 0.774923i) q^{5} +(-2.41421 - 6.38741i) q^{6} +(-7.07107 - 3.74166i) q^{8} +(-1.32843 - 2.30090i) q^{9} +(0.500665 - 3.05899i) q^{10} +(2.24264 - 3.88437i) q^{11} +(-12.9443 - 4.35381i) q^{12} -1.54985i q^{13} -5.29150i q^{15} +(-14.7477 + 6.20520i) q^{16} +(11.8284 - 20.4874i) q^{17} +(-5.24394 - 0.858275i) q^{18} +(-12.4350 - 21.5381i) q^{19} +(-4.10051 - 4.64954i) q^{20} +(-3.17157 - 8.39119i) q^{22} +(-30.5055 + 17.6124i) q^{23} +(-23.1344 + 14.5203i) q^{24} +(-11.2990 + 19.5704i) q^{25} +(-2.39883 - 1.96308i) q^{26} +21.6569 q^{27} +22.4499i q^{29} +(-8.19012 - 6.70239i) q^{30} +(40.4569 + 23.3578i) q^{31} +(-9.07561 + 30.6860i) q^{32} +(-7.65685 - 13.2621i) q^{33} +(-16.7279 - 44.2579i) q^{34} +(-7.97056 + 7.02938i) q^{36} +(50.7340 - 29.2913i) q^{37} +(-49.0870 - 8.03407i) q^{38} +(-4.58258 - 2.64575i) q^{39} +(-12.3903 + 0.457458i) q^{40} +26.9706 q^{41} -17.1716 q^{43} +(-17.0050 - 5.71963i) q^{44} +(-3.56604 - 2.05886i) q^{45} +(-11.3791 + 69.5245i) q^{46} +(-31.2918 + 18.0663i) q^{47} +(-6.82843 + 54.1990i) q^{48} +(15.9792 + 42.2769i) q^{50} +(-40.3848 - 69.9485i) q^{51} +(-6.07687 + 1.22637i) q^{52} +(84.7102 + 48.9075i) q^{53} +(27.4313 - 33.5202i) q^{54} -6.95149i q^{55} -84.9117 q^{57} +(34.7477 + 28.4358i) q^{58} +(30.7782 - 53.3094i) q^{59} +(-20.7477 + 4.18710i) q^{60} +(-32.6340 + 18.8412i) q^{61} +(87.3970 - 33.0329i) q^{62} +(36.0000 + 52.9150i) q^{64} +(-1.20101 - 2.08021i) q^{65} +(-30.2253 - 4.94697i) q^{66} +(16.6863 - 28.9015i) q^{67} +(-89.6899 - 30.1672i) q^{68} +120.265i q^{69} -102.199i q^{71} +(0.784207 + 21.2404i) q^{72} +(34.6569 - 60.0274i) q^{73} +(18.9246 - 115.627i) q^{74} +(38.5772 + 66.8176i) q^{75} +(-74.6102 + 65.8000i) q^{76} +(-9.89949 + 3.74166i) q^{78} +(-33.5156 + 19.3503i) q^{79} +(-14.9859 + 19.7570i) q^{80} +(48.9264 - 84.7430i) q^{81} +(34.1618 - 41.7447i) q^{82} -3.61522 q^{83} -36.6645i q^{85} +(-21.7501 + 26.5779i) q^{86} +(66.3799 + 38.3245i) q^{87} +(-30.3918 + 19.0754i) q^{88} +(22.0294 + 38.1561i) q^{89} +(-7.70354 + 2.91166i) q^{90} +(93.1960 + 105.674i) q^{92} +(138.129 - 79.7486i) q^{93} +(-11.6724 + 71.3164i) q^{94} +(-33.3807 - 19.2724i) q^{95} +(75.2393 + 79.2191i) q^{96} -96.1076 q^{97} -11.9167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} + 12 q^{4} - 8 q^{6} + 12 q^{9}+O(q^{10}) \) 8 * q + 8 * q^3 + 12 * q^4 - 8 * q^6 + 12 * q^9	\( 8 q + 8 q^{3} + 12 q^{4} - 8 q^{6} + 12 q^{9} - 28 q^{10} - 16 q^{11} - 24 q^{12} - 8 q^{16} + 72 q^{17} - 16 q^{18} + 8 q^{19} - 112 q^{20} - 48 q^{22} - 40 q^{24} + 68 q^{25} + 28 q^{26} + 128 q^{27} - 16 q^{33} - 32 q^{34} + 72 q^{36} - 76 q^{38} + 56 q^{40} + 80 q^{41} - 160 q^{43} + 48 q^{44} - 224 q^{46} - 32 q^{48} + 224 q^{50} - 176 q^{51} - 56 q^{52} - 16 q^{54} - 272 q^{57} + 168 q^{58} + 184 q^{59} - 56 q^{60} + 224 q^{62} + 288 q^{64} - 168 q^{65} - 32 q^{66} + 224 q^{67} - 216 q^{68} + 160 q^{72} + 232 q^{73} + 280 q^{74} + 88 q^{75} + 48 q^{76} - 336 q^{80} + 52 q^{81} - 48 q^{82} - 176 q^{83} - 8 q^{86} - 240 q^{88} + 312 q^{89} - 616 q^{90} + 112 q^{92} - 112 q^{94} + 176 q^{96} + 272 q^{97} - 480 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 + 12 * q^4 - 8 * q^6 + 12 * q^9 - 28 * q^10 - 16 * q^11 - 24 * q^12 - 8 * q^16 + 72 * q^17 - 16 * q^18 + 8 * q^19 - 112 * q^20 - 48 * q^22 - 40 * q^24 + 68 * q^25 + 28 * q^26 + 128 * q^27 - 16 * q^33 - 32 * q^34 + 72 * q^36 - 76 * q^38 + 56 * q^40 + 80 * q^41 - 160 * q^43 + 48 * q^44 - 224 * q^46 - 32 * q^48 + 224 * q^50 - 176 * q^51 - 56 * q^52 - 16 * q^54 - 272 * q^57 + 168 * q^58 + 184 * q^59 - 56 * q^60 + 224 * q^62 + 288 * q^64 - 168 * q^65 - 32 * q^66 + 224 * q^67 - 216 * q^68 + 160 * q^72 + 232 * q^73 + 280 * q^74 + 88 * q^75 + 48 * q^76 - 336 * q^80 + 52 * q^81 - 48 * q^82 - 176 * q^83 - 8 * q^86 - 240 * q^88 + 312 * q^89 - 616 * q^90 + 112 * q^92 - 112 * q^94 + 176 * q^96 + 272 * q^97 - 480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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