LMFDB - Embedded newform 140.3.x.a.103.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,3,Mod(3,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("140.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	140.x (of order $12$, degree $4$, 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:	$3.81472370104$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.25
Character	$\chi$	$=$	140.103
Dual form			140.3.x.a.87.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.236130 - 1.98601i) q^{2} +(-0.412261 + 1.53858i) q^{3} +(-3.88849 - 0.937915i) q^{4} +(3.53079 + 3.54027i) q^{5} +(2.95829 + 1.18206i) q^{6} +(-0.696881 + 6.96522i) q^{7} +(-2.78090 + 7.50111i) q^{8} +(5.59696 + 3.23141i) q^{9} +O(q^{10})$	\(q+(0.236130 - 1.98601i) q^{2} +(-0.412261 + 1.53858i) q^{3} +(-3.88849 - 0.937915i) q^{4} +(3.53079 + 3.54027i) q^{5} +(2.95829 + 1.18206i) q^{6} +(-0.696881 + 6.96522i) q^{7} +(-2.78090 + 7.50111i) q^{8} +(5.59696 + 3.23141i) q^{9} +(7.86475 - 6.17622i) q^{10} +(-3.33107 + 1.92319i) q^{11} +(3.04613 - 5.59608i) q^{12} +(6.09582 - 6.09582i) q^{13} +(13.6685 + 3.02871i) q^{14} +(-6.90260 + 3.97289i) q^{15} +(14.2406 + 7.29413i) q^{16} +(1.46435 - 5.46505i) q^{17} +(7.73922 - 10.3526i) q^{18} +(8.53627 + 4.92842i) q^{19} +(-10.4089 - 17.0779i) q^{20} +(-10.4293 - 3.94370i) q^{21} +(3.03292 + 7.06967i) q^{22} +(4.92763 + 18.3902i) q^{23} +(-10.3946 - 7.37105i) q^{24} +(-0.0670535 + 24.9999i) q^{25} +(-10.6670 - 13.5458i) q^{26} +(-17.4161 + 17.4161i) q^{27} +(9.24260 - 26.4306i) q^{28} -33.2500i q^{29} +(6.26028 + 14.6468i) q^{30} +(-24.1791 - 41.8793i) q^{31} +(17.8489 - 26.5597i) q^{32} +(-1.58572 - 5.91798i) q^{33} +(-10.5079 - 4.19869i) q^{34} +(-27.1193 + 22.1256i) q^{35} +(-18.7329 - 17.8147i) q^{36} +(13.8489 + 51.6848i) q^{37} +(11.8036 - 15.7894i) q^{38} +(6.86584 + 11.8920i) q^{39} +(-36.3747 + 16.6397i) q^{40} -9.69355i q^{41} +(-10.2949 + 19.7814i) q^{42} +(-9.19050 + 9.19050i) q^{43} +(14.7566 - 4.35405i) q^{44} +(8.32163 + 31.2242i) q^{45} +(37.6866 - 5.44386i) q^{46} +(-4.02744 - 15.0306i) q^{47} +(-17.0935 + 18.9033i) q^{48} +(-48.0287 - 9.70787i) q^{49} +(49.6343 + 6.03640i) q^{50} +(7.80472 + 4.50605i) q^{51} +(-29.4209 + 17.9862i) q^{52} +(-2.53927 + 9.47670i) q^{53} +(30.4760 + 38.7009i) q^{54} +(-18.5699 - 5.00250i) q^{55} +(-50.3089 - 24.5970i) q^{56} +(-11.1019 + 11.1019i) q^{57} +(-66.0348 - 7.85132i) q^{58} +(54.0889 - 31.2283i) q^{59} +(30.5669 - 8.97445i) q^{60} +(-12.2964 - 7.09934i) q^{61} +(-88.8823 + 38.1309i) q^{62} +(-26.4079 + 36.7322i) q^{63} +(-48.5332 - 41.7196i) q^{64} +(43.1039 + 0.0578055i) q^{65} +(-12.1276 + 1.75184i) q^{66} +(28.3455 - 105.787i) q^{67} +(-10.8199 + 19.8773i) q^{68} -30.3262 q^{69} +(37.5380 + 59.0838i) q^{70} -44.9500i q^{71} +(-39.8037 + 32.9972i) q^{72} +(4.30831 + 1.15441i) q^{73} +(105.917 - 15.2997i) q^{74} +(-38.4367 - 10.4097i) q^{75} +(-28.5707 - 27.1704i) q^{76} +(-11.0741 - 24.5419i) q^{77} +(25.2389 - 10.8276i) q^{78} +(66.8115 - 115.721i) q^{79} +(24.4574 + 76.1698i) q^{80} +(9.46662 + 16.3967i) q^{81} +(-19.2515 - 2.28894i) q^{82} +(109.770 + 109.770i) q^{83} +(36.8552 + 25.1168i) q^{84} +(24.5181 - 14.1117i) q^{85} +(16.0823 + 20.4226i) q^{86} +(51.1577 + 13.7077i) q^{87} +(-5.16272 - 30.3349i) q^{88} +(77.1545 - 133.635i) q^{89} +(63.9766 - 9.15388i) q^{90} +(38.2107 + 46.7068i) q^{91} +(-1.91261 - 76.1316i) q^{92} +(74.4028 - 19.9362i) q^{93} +(-30.8020 + 4.44936i) q^{94} +(12.6918 + 47.6219i) q^{95} +(33.5058 + 38.4115i) q^{96} +(-123.109 - 123.109i) q^{97} +(-30.6210 + 93.0933i) q^{98} -24.8585 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8}+O(q^{10}) $ 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8	$ 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8} - 6 q^{10} - 6 q^{12} - 28 q^{16} - 12 q^{17} - 36 q^{18} - 32 q^{21} - 24 q^{22} - 4 q^{25} - 12 q^{26} + 114 q^{28} + 28 q^{30} + 58 q^{32} - 156 q^{33} - 144 q^{36} - 4 q^{37} + 192 q^{38} + 54 q^{40} - 218 q^{42} - 12 q^{45} + 68 q^{46} - 332 q^{50} - 264 q^{52} - 4 q^{53} - 300 q^{56} - 24 q^{57} - 146 q^{58} - 434 q^{60} - 24 q^{61} + 92 q^{65} - 660 q^{66} - 72 q^{68} + 488 q^{70} - 80 q^{72} - 12 q^{73} - 156 q^{77} + 688 q^{78} + 588 q^{80} + 288 q^{81} + 798 q^{82} + 272 q^{85} - 72 q^{86} + 588 q^{88} + 524 q^{92} + 164 q^{93} + 1080 q^{96} - 766 q^{98}+O(q^{100}) $ 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8 - 6 * q^10 - 6 * q^12 - 28 * q^16 - 12 * q^17 - 36 * q^18 - 32 * q^21 - 24 * q^22 - 4 * q^25 - 12 * q^26 + 114 * q^28 + 28 * q^30 + 58 * q^32 - 156 * q^33 - 144 * q^36 - 4 * q^37 + 192 * q^38 + 54 * q^40 - 218 * q^42 - 12 * q^45 + 68 * q^46 - 332 * q^50 - 264 * q^52 - 4 * q^53 - 300 * q^56 - 24 * q^57 - 146 * q^58 - 434 * q^60 - 24 * q^61 + 92 * q^65 - 660 * q^66 - 72 * q^68 + 488 * q^70 - 80 * q^72 - 12 * q^73 - 156 * q^77 + 688 * q^78 + 588 * q^80 + 288 * q^81 + 798 * q^82 + 272 * q^85 - 72 * q^86 + 588 * q^88 + 524 * q^92 + 164 * q^93 + 1080 * q^96 - 766 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.236130	−	1.98601i	0.118065	−	0.993006i
$2$	0.236130	−	1.98601i	0.118065	−	0.993006i
$3$	−0.412261	+	1.53858i	−0.137420	+	0.512860i	0.862556	+	0.505962i	$0.168862\pi$
$3$	−0.412261	+	1.53858i	−0.137420	+	0.512860i	−0.999976	+	0.00689806i	$0.997804\pi$
$4$	−3.88849	−	0.937915i	−0.972121	−	0.234479i
$5$	3.53079	+	3.54027i	0.706158	+	0.708054i
$5$	3.53079	+	3.54027i	0.706158	+	0.708054i
$6$	2.95829	+	1.18206i	0.493048	+	0.197010i
$7$	−0.696881	+	6.96522i	−0.0995544	+	0.995032i
$7$	−0.696881	+	6.96522i	−0.0995544	+	0.995032i
$8$	−2.78090	+	7.50111i	−0.347612	+	0.937638i
$9$	5.59696	+	3.23141i	0.621884	+	0.359045i
$10$	7.86475	−	6.17622i	0.786475	−	0.617622i
$11$	−3.33107	+	1.92319i	−0.302825	+	0.174836i	−0.643711	−	0.765269i	$-0.722606\pi$
$11$	−3.33107	+	1.92319i	−0.302825	+	0.174836i	0.340886	+	0.940104i	$0.389273\pi$
$12$	3.04613	−	5.59608i	0.253844	−	0.466340i
$13$	6.09582	−	6.09582i	0.468910	−	0.468910i	−0.432652	−	0.901561i	$-0.642422\pi$
$13$	6.09582	−	6.09582i	0.468910	−	0.468910i	0.901561	+	0.432652i	$0.142422\pi$
$14$	13.6685	+	3.02871i	0.976319	+	0.216337i
$15$	−6.90260	+	3.97289i	−0.460173	+	0.264859i
$16$	14.2406	+	7.29413i	0.890039	+	0.455883i
$17$	1.46435	−	5.46505i	0.0861385	−	0.321473i	−0.909389	−	0.415947i	$-0.863450\pi$
$17$	1.46435	−	5.46505i	0.0861385	−	0.321473i	0.995527	+	0.0944737i	$0.0301168\pi$
$18$	7.73922	−	10.3526i	0.429957	−	0.575144i
$19$	8.53627	+	4.92842i	0.449277	+	0.259390i	0.707525	−	0.706688i	$-0.249812\pi$
$19$	8.53627	+	4.92842i	0.449277	+	0.259390i	−0.258248	+	0.966079i	$0.583145\pi$
$20$	−10.4089	−	17.0779i	−0.520447	−	0.853894i
$21$	−10.4293	−	3.94370i	−0.496631	−	0.187795i
$22$	3.03292	+	7.06967i	0.137860	+	0.321349i
$23$	4.92763	+	18.3902i	0.214245	+	0.799572i	0.986431	+	0.164176i	$0.0524966\pi$
$23$	4.92763	+	18.3902i	0.214245	+	0.799572i	−0.772186	+	0.635396i	$0.780837\pi$
$24$	−10.3946	−	7.37105i	−0.433108	−	0.307127i
$25$	−0.0670535	+	24.9999i	−0.00268214	+	0.999996i
$26$	−10.6670	−	13.5458i	−0.410268	−	0.520992i
$27$	−17.4161	+	17.4161i	−0.645039	+	0.645039i
$28$	9.24260	−	26.4306i	0.330093	−	0.943948i
$29$		−	33.2500i		−	1.14655i	−0.819363	−	0.573275i	$-0.805673\pi$
$29$		−	33.2500i		−	1.14655i	0.819363	−	0.573275i	$-0.194327\pi$
$30$	6.26028	+	14.6468i	0.208676	+	0.488225i
$31$	−24.1791	−	41.8793i	−0.779969	−	1.35095i	−0.931959	−	0.362564i	$-0.881901\pi$
$31$	−24.1791	−	41.8793i	−0.779969	−	1.35095i	0.151989	−	0.988382i	$-0.451432\pi$
$32$	17.8489	−	26.5597i	0.557778	−	0.829991i
$33$	−1.58572	−	5.91798i	−0.0480520	−	0.179333i
$34$	−10.5079	−	4.19869i	−0.309055	−	0.123491i
$35$	−27.1193	+	22.1256i	−0.774838	+	0.632160i
$36$	−18.7329	−	17.8147i	−0.520359	−	0.494854i
$37$	13.8489	+	51.6848i	0.374295	+	1.39689i	0.854373	+	0.519661i	$0.173942\pi$
$37$	13.8489	+	51.6848i	0.374295	+	1.39689i	−0.480078	+	0.877226i	$0.659392\pi$
$38$	11.8036	−	15.7894i	0.310620	−	0.415510i
$39$	6.86584	+	11.8920i	0.176047	+	0.304923i
$40$	−36.3747	+	16.6397i	−0.909368	+	0.415992i
$41$		−	9.69355i		−	0.236428i	−0.992988	−	0.118214i	$-0.962283\pi$
$41$		−	9.69355i		−	0.236428i	0.992988	−	0.118214i	$-0.0377169\pi$
$42$	−10.2949	+	19.7814i	−0.245117	+	0.470986i
$43$	−9.19050	+	9.19050i	−0.213733	+	0.213733i	−0.805851	−	0.592118i	$-0.798292\pi$
$43$	−9.19050	+	9.19050i	−0.213733	+	0.213733i	0.592118	+	0.805851i	$0.298292\pi$
$44$	14.7566	−	4.35405i	0.335378	−	0.0989558i
$45$	8.32163	+	31.2242i	0.184925	+	0.693870i
$46$	37.6866	−	5.44386i	0.819275	−	0.118345i
$47$	−4.02744	−	15.0306i	−0.0856902	−	0.319800i	0.909754	−	0.415148i	$-0.136270\pi$
$47$	−4.02744	−	15.0306i	−0.0856902	−	0.319800i	−0.995444	+	0.0953480i	$0.969604\pi$
$48$	−17.0935	+	18.9033i	−0.356114	+	0.393818i
$49$	−48.0287	−	9.70787i	−0.980178	−	0.198120i
$50$	49.6343	+	6.03640i	0.992686	+	0.120728i
$51$	7.80472	+	4.50605i	0.153034	+	0.0883540i
$52$	−29.4209	+	17.9862i	−0.565786	+	0.345888i
$53$	−2.53927	+	9.47670i	−0.0479108	+	0.178806i	−0.985735	−	0.168305i	$-0.946171\pi$
$53$	−2.53927	+	9.47670i	−0.0479108	+	0.178806i	0.937824	+	0.347111i	$0.112837\pi$
$54$	30.4760	+	38.7009i	0.564371	+	0.716684i
$55$	−18.5699	−	5.00250i	−0.337635	−	0.0909546i
$56$	−50.3089	−	24.5970i	−0.898374	−	0.439231i
$57$	−11.1019	+	11.1019i	−0.194771	+	0.194771i
$58$	−66.0348	−	7.85132i	−1.13853	−	0.135368i
$59$	54.0889	−	31.2283i	0.916762	−	0.529293i	0.0341612	−	0.999416i	$-0.489124\pi$
$59$	54.0889	−	31.2283i	0.916762	−	0.529293i	0.882601	+	0.470124i	$0.155791\pi$
$60$	30.5669	−	8.97445i	0.509448	−	0.149574i
$61$	−12.2964	−	7.09934i	−0.201581	−	0.116383i	0.395812	−	0.918332i	$-0.370463\pi$
$61$	−12.2964	−	7.09934i	−0.201581	−	0.116383i	−0.597393	+	0.801949i	$0.703797\pi$
$62$	−88.8823	+	38.1309i	−1.43359	+	0.615014i
$63$	−26.4079	+	36.7322i	−0.419173	+	0.583050i
$64$	−48.5332	−	41.7196i	−0.758331	−	0.651869i
$65$	43.1039	+	0.0578055i	0.663138	+	0.000889316i
$66$	−12.1276	+	1.75184i	−0.183752	+	0.0265430i
$67$	28.3455	−	105.787i	0.423067	−	1.57891i	−0.345040	−	0.938588i	$-0.612135\pi$
$67$	28.3455	−	105.787i	0.423067	−	1.57891i	0.768108	−	0.640321i	$-0.221199\pi$
$68$	−10.8199	+	19.8773i	−0.159116	+	0.292313i
$69$	−30.3262			−0.439510
$70$	37.5380	+	59.0838i	0.536257	+	0.844055i
$71$		−	44.9500i		−	0.633099i	−0.948576	−	0.316550i	$-0.897476\pi$
$71$		−	44.9500i		−	0.633099i	0.948576	−	0.316550i	$-0.102524\pi$
$72$	−39.8037	+	32.9972i	−0.552829	+	0.458294i
$73$	4.30831	+	1.15441i	0.0590179	+	0.0158138i	0.288207	−	0.957568i	$-0.406941\pi$
$73$	4.30831	+	1.15441i	0.0590179	+	0.0158138i	−0.229189	+	0.973382i	$0.573607\pi$
$74$	105.917	−	15.2997i	1.43131	−	0.206753i
$75$	−38.4367	−	10.4097i	−0.512490	−	0.138796i
$76$	−28.5707	−	27.1704i	−0.375930	−	0.357505i
$77$	−11.0741	−	24.5419i	−0.143820	−	0.318726i
$78$	25.2389	−	10.8276i	0.323575	−	0.138815i
$79$	66.8115	−	115.721i	0.845715	−	1.46482i	−0.0392841	−	0.999228i	$-0.512508\pi$
$79$	66.8115	−	115.721i	0.845715	−	1.46482i	0.884999	−	0.465593i	$-0.154159\pi$
$80$	24.4574	+	76.1698i	0.305718	+	0.952122i
$81$	9.46662	+	16.3967i	0.116872	+	0.202428i
$82$	−19.2515	−	2.28894i	−0.234774	−	0.0279139i
$83$	109.770	+	109.770i	1.32253	+	1.32253i	0.911726	+	0.410799i	$0.134750\pi$
$83$	109.770	+	109.770i	1.32253	+	1.32253i	0.410799	+	0.911726i	$0.365250\pi$
$84$	36.8552	+	25.1168i	0.438752	+	0.299009i
$85$	24.5181	−	14.1117i	0.288448	−	0.166020i
$86$	16.0823	+	20.4226i	0.187003	+	0.237472i
$87$	51.1577	+	13.7077i	0.588020	+	0.157560i
$88$	−5.16272	−	30.3349i	−0.0586673	−	0.344715i
$89$	77.1545	−	133.635i	0.866904	−	1.50152i	0.00176032	−	0.999998i	$-0.499440\pi$
$89$	77.1545	−	133.635i	0.866904	−	1.50152i	0.865144	−	0.501524i	$-0.167227\pi$
$90$	63.9766	−	9.15388i	0.710851	−	0.101710i
$91$	38.2107	+	46.7068i	0.419898	+	0.513262i
$92$	−1.91261	−	76.1316i	−0.0207892	−	0.827517i
$93$	74.4028	−	19.9362i	0.800030	−	0.214367i
$94$	−30.8020	+	4.44936i	−0.327680	+	0.0473336i
$95$	12.6918	+	47.6219i	0.133598	+	0.501283i
$96$	33.5058	+	38.4115i	0.349019	+	0.400119i
$97$	−123.109	−	123.109i	−1.26916	−	1.26916i	−0.946521	−	0.322642i	$-0.895429\pi$
$97$	−123.109	−	123.109i	−1.26916	−	1.26916i	−0.322642	−	0.946521i	$-0.604571\pi$
$98$	−30.6210	+	93.0933i	−0.312459	+	0.949931i
$99$	−24.8585			−0.251096
$100$	23.7085	−	97.1489i	0.237085	−	0.971489i
$101$	−7.45212	+	4.30248i	−0.0737834	+	0.0425988i	−0.536438	−	0.843940i	$-0.680230\pi$
$101$	−7.45212	+	4.30248i	−0.0737834	+	0.0425988i	0.462654	+	0.886539i	$0.346897\pi$
$102$	10.7920	−	14.4362i	0.105804	−	0.141532i
$103$	−91.0780	+	24.4043i	−0.884253	+	0.236935i	−0.672241	−	0.740332i	$-0.734668\pi$
$103$	−91.0780	+	24.4043i	−0.884253	+	0.236935i	−0.212012	+	0.977267i	$0.568001\pi$
$104$	28.7736	+	62.6773i	0.276669	+	0.602666i
$105$	−22.8617	−	50.8468i	−0.217731	−	0.484255i
$106$	18.2212	+	7.28076i	0.171898	+	0.0686864i
$107$	169.056	−	45.2985i	1.57997	−	0.423351i	0.641051	−	0.767498i	$-0.278499\pi$
$107$	169.056	−	45.2985i	1.57997	−	0.423351i	0.938915	+	0.344148i	$0.111832\pi$
$108$	84.0569	−	51.3873i	0.778304	−	0.475808i
$109$	−95.1784	+	54.9513i	−0.873197	+	0.504140i	−0.868409	−	0.495848i	$-0.834857\pi$
$109$	−95.1784	+	54.9513i	−0.873197	+	0.504140i	−0.00478754	+	0.999989i	$0.501524\pi$
$110$	−14.3200	+	35.6989i	−0.130181	+	0.324535i
$111$	−85.2306			−0.767843
$112$	−60.7293	+	94.1061i	−0.542226	+	0.840233i
$113$	101.736	+	101.736i	0.900315	+	0.900315i	0.995463	−	0.0951484i	$-0.0303326\pi$
$113$	101.736	+	101.736i	0.900315	+	0.900315i	−0.0951484	+	0.995463i	$0.530333\pi$
$114$	19.4271	+	24.6701i	0.170413	+	0.216404i
$115$	−47.7078	+	82.3769i	−0.414850	+	0.716321i
$116$	−31.1856	+	129.292i	−0.268842	+	1.11459i
$117$	53.8162	−	14.4200i	0.459967	−	0.123248i
$118$	−49.2477	−	114.795i	−0.417353	−	0.972841i
$119$	37.0448	+	14.0080i	0.311301	+	0.117715i
$120$	−10.6056	−	62.8253i	−0.0883800	−	0.523544i
$121$	−53.1026	+	91.9765i	−0.438865	+	0.760136i
$122$	−17.0029	+	22.7445i	−0.139368	+	0.186430i
$123$	14.9143	+	3.99627i	0.121254	+	0.0324900i
$124$	54.7406	+	185.525i	0.441457	+	1.49617i
$125$	−88.7432	+	88.0320i	−0.709946	+	0.704256i
$126$	66.7148	+	61.1199i	0.529483	+	0.485079i
$127$	−0.562872	−	0.562872i	−0.00443206	−	0.00443206i	0.704887	−	0.709319i	$-0.250998\pi$
$127$	−0.562872	−	0.562872i	−0.00443206	−	0.00443206i	−0.709319	+	0.704887i	$0.750998\pi$
$128$	−94.3158	+	86.5363i	−0.736842	+	0.676064i
$129$	−10.3514	−	17.9292i	−0.0802437	−	0.138986i
$130$	10.2929	−	85.5913i	0.0791765	−	0.658395i
$131$	82.3509	−	142.636i	0.628633	−	1.08882i	−0.359193	−	0.933263i	$-0.616948\pi$
$131$	82.3509	−	142.636i	0.628633	−	1.08882i	0.987826	−	0.155561i	$-0.0497185\pi$
$132$	0.615480	+	24.4992i	0.00466273	+	0.185600i
$133$	−40.2763	+	56.0225i	−0.302829	+	0.421222i
$134$	−203.401	−	81.2740i	−1.51792	−	0.606522i
$135$	−123.150	−	0.165153i	−0.912222	−	0.00122336i
$136$	36.9217	+	26.1820i	0.271483	+	0.192515i
$137$	−87.1793	−	23.3596i	−0.636345	−	0.170508i	−0.0737977	−	0.997273i	$-0.523512\pi$
$137$	−87.1793	−	23.3596i	−0.636345	−	0.170508i	−0.562547	+	0.826765i	$0.690179\pi$
$138$	−7.16094	+	60.2282i	−0.0518908	+	0.436436i
$139$		−	147.258i		−	1.05941i	−0.848183	−	0.529704i	$-0.822303\pi$
$139$		−	147.258i		−	1.05941i	0.848183	−	0.529704i	$-0.177697\pi$
$140$	126.205	−	60.5994i	0.901465	−	0.432853i
$141$	24.7862			0.175788
$142$	−89.2713	−	10.6141i	−0.628671	−	0.0747469i
$143$	−8.58217	+	32.0291i	−0.0600151	+	0.223980i
$144$	56.1339	+	86.8422i	0.389819	+	0.603071i
$145$	117.714	−	117.399i	0.811820	−	0.809646i
$146$	3.30999	−	8.28376i	0.0226711	−	0.0567381i
$147$	34.7367	−	69.8939i	0.236304	−	0.475468i
$148$	−5.37531	−	213.965i	−0.0363196	−	1.44571i
$149$	213.389	+	123.200i	1.43214	+	0.826848i	0.997284	−	0.0736510i	$-0.0234651\pi$
$149$	213.389	+	123.200i	1.43214	+	0.826848i	0.434858	+	0.900499i	$0.356798\pi$
$150$	−29.7498	+	73.8777i	−0.198332	+	0.492518i
$151$	−163.002	+	94.1095i	−1.07949	+	0.623242i	−0.930758	−	0.365637i	$-0.880851\pi$
$151$	−163.002	+	94.1095i	−1.07949	+	0.623242i	−0.148728	+	0.988878i	$0.547518\pi$
$152$	−60.7071	+	50.3260i	−0.399389	+	0.331092i
$153$	25.8557	−	25.8557i	0.168992	−	0.168992i
$154$	−51.3554	+	16.1983i	−0.333477	+	0.105183i
$155$	62.8931	−	233.468i	0.405762	−	1.50624i
$156$	−15.5441	−	52.6814i	−0.0996414	−	0.337701i
$157$	−1.20523	+	4.49798i	−0.00767663	+	0.0286496i	−0.969658	−	0.244466i	$-0.921387\pi$
$157$	−1.20523	+	4.49798i	−0.00767663	+	0.0286496i	0.961981	+	0.273115i	$0.0880541\pi$
$158$	−214.047	−	160.014i	−1.35473	−	1.01274i
$159$	−13.5338	−	7.81375i	−0.0851183	−	0.0491431i
$160$	157.049	−	30.5868i	0.981557	−	0.191167i
$161$	−131.526	+	21.5063i	−0.816929	+	0.133579i
$162$	34.7993	−	14.9291i	0.214811	−	0.0921547i
$163$	33.9820	+	126.823i	0.208478	+	0.778052i	0.988361	+	0.152126i	$0.0486121\pi$
$163$	33.9820	+	126.823i	0.208478	+	0.778052i	−0.779883	+	0.625926i	$0.784721\pi$
$164$	−9.09172	+	37.6932i	−0.0554373	+	0.229837i
$165$	15.3524	−	26.5090i	0.0930450	−	0.160661i
$166$	243.924	−	192.084i	1.46942	−	1.15713i
$167$	−194.593	+	194.593i	−1.16523	+	1.16523i	−0.181916	+	0.983314i	$0.558230\pi$
$167$	−194.593	+	194.593i	−1.16523	+	1.16523i	−0.983314	+	0.181916i	$0.941770\pi$
$168$	58.5848	−	67.2640i	0.348719	−	0.400381i
$169$			94.6819i			0.560248i
$170$	−22.2366	−	52.0254i	−0.130803	−	0.306032i
$171$	31.8514	+	55.1683i	0.186266	+	0.322622i
$172$	44.3570	−	27.1172i	0.257890	−	0.157658i
$173$	−75.5868	−	282.094i	−0.436918	−	1.63060i	−0.736435	−	0.676508i	$-0.763492\pi$
$173$	−75.5868	−	282.094i	−0.436918	−	1.63060i	0.299518	−	0.954091i	$-0.403174\pi$
$174$	39.3035	−	98.3631i	0.225882	−	0.565305i
$175$	−174.083	−	17.8890i	−0.994762	−	0.102223i
$176$	−61.4646	+	3.09023i	−0.349231	+	0.0175581i
$177$	25.7484	+	96.0944i	0.145471	+	0.542906i
$178$	−247.183	−	184.785i	−1.38867	−	1.03812i
$179$	80.2797	+	139.049i	0.448490	+	0.776807i	0.998288	−	0.0584903i	$-0.0186287\pi$
$179$	80.2797	+	139.049i	0.448490	+	0.776807i	−0.549798	+	0.835298i	$0.685295\pi$
$180$	−3.07291	−	129.220i	−0.0170717	−	0.717887i
$181$			22.5735i			0.124715i	0.998054	+	0.0623577i	$0.0198619\pi$
$181$			22.5735i			0.124715i	−0.998054	+	0.0623577i	$0.980138\pi$
$182$	101.783	−	64.8580i	0.559248	−	0.356363i
$183$	15.9922	−	15.9922i	0.0873893	−	0.0873893i
$184$	−151.650	−	14.1785i	−0.824184	−	0.0770571i
$185$	−134.081	+	231.517i	−0.724761	+	1.25144i
$186$	−22.0247	−	152.472i	−0.118412	−	0.819744i
$187$	5.63248	+	21.0207i	0.0301202	+	0.112410i
$188$	1.56321	+	62.2237i	0.00831494	+	0.330977i
$189$	−109.170	−	133.444i	−0.577618	−	0.706051i
$190$	97.5746	−	13.9611i	0.513551	−	0.0734797i
$191$	−238.958	−	137.962i	−1.25109	−	0.722316i	−0.279763	−	0.960069i	$-0.590256\pi$
$191$	−238.958	−	137.962i	−1.25109	−	0.722316i	−0.971326	+	0.237753i	$0.923589\pi$
$192$	84.1974	−	57.4728i	0.438528	−	0.299338i
$193$	−22.0375	+	82.2450i	−0.114184	+	0.426140i	−0.999225	−	0.0393738i	$-0.987464\pi$
$193$	−22.0375	+	82.2450i	−0.114184	+	0.426140i	0.885041	+	0.465514i	$0.154130\pi$
$194$	−273.565	+	215.426i	−1.41013	+	1.11044i
$195$	−17.8590	+	66.2950i	−0.0915848	+	0.339975i
$196$	177.654	+	82.7957i	0.906397	+	0.422427i
$197$	32.1978	−	32.1978i	0.163441	−	0.163441i	−0.620648	−	0.784089i	$-0.713131\pi$
$197$	32.1978	−	32.1978i	0.163441	−	0.163441i	0.784089	+	0.620648i	$0.213131\pi$
$198$	−5.86984	+	49.3693i	−0.0296457	+	0.249340i
$199$	−36.3381	+	20.9798i	−0.182604	+	0.105426i	−0.588515	−	0.808486i	$-0.700287\pi$
$199$	−36.3381	+	20.9798i	−0.182604	+	0.105426i	0.405912	+	0.913912i	$0.366954\pi$
$200$	−187.341	−	70.0252i	−0.936703	−	0.350126i
$201$	151.076	+	87.2237i	0.751621	+	0.433949i
$202$	6.78511	+	15.8159i	0.0335897	+	0.0782968i
$203$	231.594	+	23.1713i	1.14085	+	0.114144i
$204$	−26.1222	−	24.8419i	−0.128050	−	0.121774i
$205$	34.3178	−	34.2259i	0.167404	−	0.166955i
$206$	26.9609	+	186.645i	0.130878	+	0.906042i
$207$	−31.8463	+	118.852i	−0.153847	+	0.574165i
$208$	131.272	−	42.3446i	0.631116	−	0.203580i
$209$	−37.9132			−0.181403
$210$	−106.381	+	33.3972i	−0.506575	+	0.159034i
$211$			254.539i			1.20635i	0.797610	+	0.603174i	$0.206098\pi$
$211$			254.539i			1.20635i	−0.797610	+	0.603174i	$0.793902\pi$
$212$	18.7623	−	34.4684i	0.0885012	−	0.162587i
$213$	69.1592	+	18.5312i	0.324691	+	0.0870007i
$214$	−50.0441	−	346.444i	−0.233851	−	1.61890i
$215$	−64.9866	−	0.0871518i	−0.302263	−	0.000405357i
$216$	−82.2074	−	179.072i	−0.380590	−	0.829037i
$217$	308.549	−	139.228i	1.42188	−	0.641602i
$218$	86.6594	+	202.001i	0.397520	+	0.926611i
$219$	−3.55230	+	6.15276i	−0.0162205	+	0.0280948i
$220$	67.5170	+	36.8692i	0.306896	+	0.167587i
$221$	−24.3875	−	42.2404i	−0.110351	−	0.191133i
$222$	−20.1255	+	169.269i	−0.0906555	+	0.762473i
$223$	−61.8244	−	61.8244i	−0.277240	−	0.277240i	0.554766	−	0.832006i	$-0.312808\pi$
$223$	−61.8244	−	61.8244i	−0.277240	−	0.277240i	−0.832006	+	0.554766i	$0.812808\pi$
$224$	172.556	+	142.830i	0.770338	+	0.637636i
$225$	−81.1602	+	139.707i	−0.360712	+	0.620919i
$226$	226.071	−	178.025i	1.00031	−	0.787722i
$227$	81.8329	+	21.9271i	0.360497	+	0.0965950i	0.434522	−	0.900661i	$-0.356917\pi$
$227$	81.8329	+	21.9271i	0.360497	+	0.0965950i	−0.0740241	+	0.997256i	$0.523584\pi$
$228$	53.5824	−	32.7570i	0.235010	−	0.143671i
$229$	−129.145	+	223.685i	−0.563950	+	0.976791i	0.433196	+	0.901300i	$0.357386\pi$
$229$	−129.145	+	223.685i	−0.563950	+	0.976791i	−0.997146	+	0.0754909i	$0.975948\pi$
$230$	152.336	+	114.200i	0.662332	+	0.496521i
$231$	42.3251	−	6.92075i	0.183226	−	0.0299600i
$232$	249.412	+	92.4648i	1.07505	+	0.398555i
$233$	94.1784	−	25.2350i	0.404199	−	0.108305i	−0.0509910	−	0.998699i	$-0.516238\pi$
$233$	94.1784	−	25.2350i	0.404199	−	0.108305i	0.455190	+	0.890394i	$0.349571\pi$
$234$	−15.9307	−	110.285i	−0.0680797	−	0.471301i
$235$	38.9924	−	67.3281i	0.165925	−	0.286503i
$236$	−239.613	+	70.6998i	−1.01531	+	0.299576i
$237$	150.502	+	150.502i	0.635030	+	0.635030i
$238$	36.5675	−	70.2637i	0.153645	−	0.295226i
$239$	−160.228			−0.670410			−0.335205	−	0.942145i	$-0.608806\pi$
$239$	−160.228			−0.670410			−0.335205	+	0.942145i	$0.608806\pi$
$240$	−127.276	+	6.22790i	−0.530317	+	0.0259496i
$241$	272.306	−	157.216i	1.12990	−	0.652349i	0.185991	−	0.982551i	$-0.440451\pi$
$241$	272.306	−	157.216i	1.12990	−	0.652349i	0.943910	+	0.330203i	$0.107117\pi$
$242$	170.127	+	127.181i	0.703005	+	0.525541i
$243$	−243.247	+	65.1779i	−1.00102	+	0.268222i
$244$	41.1559	+	39.1387i	0.168672	+	0.160404i
$245$	−135.211	−	204.311i	−0.551881	−	0.833923i
$246$	11.4584	−	28.6763i	0.0465787	−	0.116570i
$247$	82.0783	−	21.9928i	0.332301	−	0.0890398i
$248$	381.381	−	64.9074i	1.53783	−	0.261724i
$249$	−214.143	+	123.636i	−0.860012	+	0.496528i
$250$	153.878	+	197.032i	0.615511	+	0.788129i
$251$	246.177			0.980785			0.490393	−	0.871502i	$-0.336853\pi$
$251$	246.177			0.980785			0.490393	+	0.871502i	$0.336853\pi$
$252$	137.138	−	118.064i	0.544200	−	0.468509i
$253$	−51.7822	−	51.7822i	−0.204673	−	0.204673i
$254$	−1.25078	+	0.984959i	−0.00492434	+	0.00387779i
$255$	11.6041	+	43.5407i	0.0455065	+	0.170748i
$256$	149.591	+	207.746i	0.584341	+	0.811509i
$257$	121.120	−	32.4539i	0.471283	−	0.126280i	−0.0153577	−	0.999882i	$-0.504889\pi$
$257$	121.120	−	32.4539i	0.471283	−	0.126280i	0.486641	+	0.873602i	$0.338222\pi$
$258$	−38.0519	+	16.3244i	−0.147488	+	0.0632730i
$259$	−369.647	+	60.4426i	−1.42721	+	0.233369i
$260$	−167.555	−	40.6526i	−0.644442	−	0.156356i
$261$	107.444	−	186.099i	0.411663	−	0.713022i
$262$	−263.831	−	197.231i	−1.00699	−	0.752788i
$263$	204.891	+	54.9005i	0.779054	+	0.208747i	0.626368	−	0.779528i	$-0.284541\pi$
$263$	204.891	+	54.9005i	0.779054	+	0.208747i	0.152687	+	0.988275i	$0.451207\pi$
$264$	48.8011	+	4.56266i	0.184853	+	0.0172828i
$265$	−42.5157	+	24.4705i	−0.160437	+	0.0923415i
$266$	101.751	+	93.2178i	0.382522	+	0.350443i
$267$	173.801	+	173.801i	0.650940	+	0.650940i
$268$	−209.440	+	384.765i	−0.781493	+	1.43569i
$269$	−47.3491	−	82.0110i	−0.176019	−	0.304874i	0.764495	−	0.644630i	$-0.222989\pi$
$269$	−47.3491	−	82.0110i	−0.176019	−	0.304874i	−0.940513	+	0.339757i	$0.889655\pi$
$270$	−29.4074	+	244.538i	−0.108916	+	0.905698i
$271$	−51.4065	+	89.0387i	−0.189692	+	0.328556i	−0.945148	−	0.326644i	$-0.894082\pi$
$271$	−51.4065	+	89.0387i	−0.189692	+	0.328556i	0.755456	+	0.655200i	$0.227416\pi$
$272$	60.7161	−	67.1445i	0.223221	−	0.246855i
$273$	−87.6150	+	39.5348i	−0.320934	+	0.144816i
$274$	−66.9781	+	167.623i	−0.244446	+	0.611763i
$275$	−47.8563	−	83.4054i	−0.174023	−	0.303292i
$276$	117.923	+	28.4434i	0.427257	+	0.103056i
$277$	−57.5754	−	15.4273i	−0.207853	−	0.0556941i	0.153390	−	0.988166i	$-0.450981\pi$
$277$	−57.5754	−	15.4273i	−0.207853	−	0.0556941i	−0.361243	+	0.932472i	$0.617648\pi$
$278$	−292.455	−	34.7720i	−1.05200	−	0.125079i
$279$		−	312.529i		−	1.12018i
$280$	−90.5503	−	264.954i	−0.323394	−	0.946264i
$281$	−251.305			−0.894324			−0.447162	−	0.894453i	$-0.647565\pi$
$281$	−251.305			−0.894324			−0.447162	+	0.894453i	$0.647565\pi$
$282$	5.85276	−	49.2256i	0.0207545	−	0.174559i
$283$	53.9869	−	201.482i	0.190767	−	0.711950i	−0.802556	−	0.596577i	$-0.796527\pi$
$283$	53.9869	−	201.482i	0.190767	−	0.711950i	0.993322	−	0.115373i	$-0.0368064\pi$
$284$	−42.1593	+	174.788i	−0.148448	+	0.615449i
$285$	−78.5025	−	0.105278i	−0.275447	−	0.000369395i
$286$	61.5836	+	24.6073i	0.215327	+	0.0860396i
$287$	67.5177	+	6.75525i	0.235253	+	0.0235375i
$288$	185.725	−	90.9766i	0.644877	−	0.315891i
$289$	222.559	+	128.494i	0.770100	+	0.444618i
$290$	−205.359	−	261.503i	−0.708135	−	0.901733i
$291$	240.166	−	138.660i	0.825312	−	0.476494i
$292$	−15.6700	−	8.52972i	−0.0536646	−	0.0292114i
$293$	104.478	−	104.478i	0.356580	−	0.356580i	−0.505971	−	0.862551i	$-0.668866\pi$
$293$	104.478	−	104.478i	0.356580	−	0.356580i	0.862551	+	0.505971i	$0.168866\pi$
$294$	−130.608	−	85.4916i	−0.444244	−	0.290788i
$295$	301.533	+	81.2291i	1.02215	+	0.275353i
$296$	−426.206	−	39.8481i	−1.43988	−	0.134622i
$297$	24.5197	−	91.5086i	0.0825577	−	0.308110i
$298$	295.065	−	394.702i	0.990151	−	1.32450i
$299$	142.141	+	82.0652i	0.475389	+	0.274466i
$300$	139.697	+	76.5282i	0.465657	+	0.255094i
$301$	−57.6092	−	70.4186i	−0.191393	−	0.233949i
$302$	148.413	+	345.947i	0.491433	+	1.14552i
$303$	−3.54750	−	13.2394i	−0.0117079	−	0.0436945i
$304$	85.6133	+	132.448i	0.281623	+	0.435686i
$305$	−18.2825	−	68.5989i	−0.0599425	−	0.224915i
$306$	−45.2444	−	57.4551i	−0.147858	−	0.187762i
$307$	123.314	−	123.314i	0.401674	−	0.401674i	−0.477149	−	0.878823i	$-0.658330\pi$
$307$	123.314	−	123.314i	0.401674	−	0.401674i	0.878823	+	0.477149i	$0.158330\pi$
$308$	20.0434	+	105.817i	0.0650758	+	0.343563i
$309$		−	150.192i		−	0.486058i
$310$	−448.818	−	180.035i	−1.44780	−	0.580759i
$311$	−80.5882	−	139.583i	−0.259126	−	0.448819i	0.706882	−	0.707331i	$-0.250101\pi$
$311$	−80.5882	−	139.583i	−0.259126	−	0.448819i	−0.966008	+	0.258512i	$0.916768\pi$
$312$	−108.296	+	18.4310i	−0.347103	+	0.0590737i
$313$	−78.8707	−	294.349i	−0.251983	−	0.940413i	−0.969744	−	0.244124i	$-0.921500\pi$
$313$	−78.8707	−	294.349i	−0.251983	−	0.940413i	0.717761	−	0.696289i	$-0.245167\pi$
$314$	8.64845	+	3.45571i	0.0275428	+	0.0110055i
$315$	−223.283	+	36.2025i	−0.708834	+	0.114928i
$316$	−368.332	+	387.315i	−1.16561	+	1.22568i
$317$	−55.0488	−	205.445i	−0.173655	−	0.648091i	−0.996777	−	0.0802254i	$-0.974436\pi$
$317$	−55.0488	−	205.445i	−0.173655	−	0.648091i	0.823121	−	0.567866i	$-0.192231\pi$
$318$	−18.7139	+	25.0332i	−0.0588489	+	0.0787209i
$319$	63.9462	+	110.758i	0.200458	+	0.347204i
$320$	−23.6617	−	319.124i	−0.0739427	−	0.997262i
$321$			278.782i			0.868479i
$322$	11.6546	+	266.290i	0.0361944	+	0.826987i
$323$	39.4342	−	39.4342i	0.122087	−	0.122087i
$324$	−21.4321	−	72.6371i	−0.0661486	−	0.224188i
$325$	151.986	+	152.804i	0.467650	+	0.470166i
$326$	259.895	−	37.5420i	0.797225	−	0.115160i
$327$	−45.3086	−	169.094i	−0.138558	−	0.517107i
$328$	72.7123	+	26.9568i	0.221684	+	0.0821853i
$329$	107.498	−	17.5775i	0.326742	−	0.0534270i
$330$	−49.0220	−	36.7497i	−0.148552	−	0.111363i
$331$	86.4453	+	49.9092i	0.261164	+	0.150783i	0.624865	−	0.780732i	$-0.285154\pi$
$331$	86.4453	+	49.9092i	0.261164	+	0.150783i	−0.363701	+	0.931516i	$0.618487\pi$
$332$	−323.883	−	529.792i	−0.975551	−	1.59576i
$333$	−89.5028	+	334.029i	−0.268777	+	1.00309i
$334$	340.515	+	432.414i	1.01951	+	1.29465i
$335$	474.596	−	273.160i	1.41671	−	0.815404i
$336$	−119.753	−	132.233i	−0.356409	−	0.393551i
$337$	−333.991	+	333.991i	−0.991071	+	0.991071i	−0.999960	−	0.00888916i	$-0.997170\pi$
$337$	−333.991	+	333.991i	−0.991071	+	0.991071i	0.00888916	+	0.999960i	$0.497170\pi$
$338$	188.039	+	22.3572i	0.556329	+	0.0661457i
$339$	−198.470	+	114.587i	−0.585457	+	0.338014i
$340$	−108.574	+	31.8773i	−0.319335	+	0.0937568i
$341$	161.084	+	93.0020i	0.472388	+	0.272733i
$342$	117.086	−	50.2304i	0.342357	−	0.146873i
$343$	101.088	−	327.766i	0.294717	−	0.955585i
$344$	−43.3811	−	94.4968i	−0.126108	−	0.274700i
$345$	−107.075	−	107.363i	−0.310364	−	0.311197i
$346$	−578.090	+	83.5054i	−1.67078	+	0.241345i
$347$	29.0666	−	108.478i	0.0837654	−	0.312617i	−0.911312	−	0.411716i	$-0.864930\pi$
$347$	29.0666	−	108.478i	0.0837654	−	0.312617i	0.995078	+	0.0990994i	$0.0315962\pi$
$348$	−186.070	−	101.284i	−0.534682	−	0.291045i
$349$	416.788			1.19424			0.597118	−	0.802153i	$-0.296312\pi$
$349$	416.788			1.19424			0.597118	+	0.802153i	$0.296312\pi$
$350$	−76.6341	+	341.507i	−0.218955	+	0.975735i
$351$			212.330i			0.604930i
$352$	−8.37642	+	122.799i	−0.0237966	+	0.348861i
$353$	−63.8724	−	17.1146i	−0.180942	−	0.0484832i	0.167210	−	0.985921i	$-0.446524\pi$
$353$	−63.8724	−	17.1146i	−0.180942	−	0.0484832i	−0.348152	+	0.937438i	$0.613191\pi$
$354$	196.925	−	28.4459i	0.556284	−	0.0803555i
$355$	159.135	−	158.709i	0.448269	−	0.447068i
$356$	−425.353	+	447.275i	−1.19481	+	1.25639i
$357$	−36.8246	+	51.2214i	−0.103150	+	0.143477i
$358$	295.108	−	126.603i	0.824325	−	0.353639i
$359$	170.211	−	294.814i	0.474125	−	0.821209i	−0.525436	−	0.850833i	$-0.676098\pi$
$359$	170.211	−	294.814i	0.474125	−	0.821209i	0.999561	+	0.0296242i	$0.00943106\pi$
$360$	−257.357	−	24.4098i	−0.714882	−	0.0678051i
$361$	−131.921	−	228.495i	−0.365433	−	0.632949i
$362$	44.8312	+	5.33028i	0.123843	+	0.0147245i
$363$	−119.621	−	119.621i	−0.329534	−	0.329534i
$364$	−104.775	−	217.457i	−0.287843	−	0.597410i
$365$	11.1248	+	19.3285i	0.0304789	+	0.0529549i
$366$	−27.9845	−	35.5370i	−0.0764604	−	0.0970957i
$367$	−625.453	−	167.590i	−1.70423	−	0.456647i	−0.730232	−	0.683199i	$-0.760588\pi$
$367$	−625.453	−	167.590i	−1.70423	−	0.456647i	−0.973999	+	0.226551i	$0.927255\pi$
$368$	−63.9678	+	297.830i	−0.173825	+	0.809322i
$369$	31.3238	−	54.2544i	0.0848883	−	0.147031i
$370$	428.135	+	320.954i	1.15712	+	0.867443i
$371$	−64.2377	−	24.2907i	−0.173148	−	0.0654737i
$372$	−308.013	+	7.73802i	−0.827991	+	0.0208011i
$373$	−693.935	+	185.939i	−1.86042	+	0.498497i	−0.999940	−	0.0109939i	$-0.996500\pi$
$373$	−693.935	+	185.939i	−1.86042	+	0.498497i	−0.860476	+	0.509491i	$0.829834\pi$
$374$	43.0774	−	6.22255i	0.115180	−	0.0166378i
$375$	−98.8589	−	172.831i	−0.263624	−	0.460882i
$376$	123.946	+	11.5883i	0.329644	+	0.0308201i
$377$	−202.686	−	202.686i	−0.537629	−	0.537629i
$378$	−290.799	+	185.302i	−0.769309	+	0.490218i
$379$	−93.4538			−0.246580			−0.123290	−	0.992371i	$-0.539345\pi$
$379$	−93.4538			−0.246580			−0.123290	+	0.992371i	$0.539345\pi$
$380$	−4.68669	−	197.081i	−0.0123334	−	0.518634i
$381$	1.09807	−	0.633973i	0.00288208	−	0.00166397i
$382$	−330.420	+	441.996i	−0.864974	+	1.15706i
$383$	−247.189	+	66.2342i	−0.645403	+	0.172935i	−0.566649	−	0.823959i	$-0.691761\pi$
$383$	−247.189	+	66.2342i	−0.645403	+	0.172935i	−0.0787534	+	0.996894i	$0.525094\pi$
$384$	−94.2602	−	180.788i	−0.245469	−	0.470802i
$385$	47.7846	−	125.858i	0.124116	−	0.326903i
$386$	158.136	+	63.1872i	0.409678	+	0.163697i
$387$	−81.1371	+	21.7406i	−0.209657	+	0.0561773i
$388$	363.241	+	594.172i	0.936189	+	1.53137i
$389$	−146.329	+	84.4829i	−0.376166	+	0.217180i	−0.676149	−	0.736765i	$-0.736352\pi$
$389$	−146.329	+	84.4829i	−0.376166	+	0.217180i	0.299983	+	0.953945i	$0.403019\pi$
$390$	127.446	+	51.1225i	0.326784	+	0.131083i
$391$	107.719			0.275496
$392$	206.383	−	333.272i	0.526487	−	0.850183i
$393$	185.507	+	185.507i	0.472027	+	0.472027i
$394$	−56.3424	−	71.5481i	−0.143001	−	0.181594i
$395$	645.581	−	172.055i	1.63438	−	0.435583i
$396$	96.6619	+	23.3151i	0.244096	+	0.0588766i
$397$	−516.485	+	138.392i	−1.30097	+	0.348594i	−0.841817	−	0.539763i	$-0.818514\pi$
$397$	−516.485	+	138.392i	−1.30097	+	0.348594i	−0.459153	+	0.888357i	$0.651847\pi$
$398$	33.0856	+	77.1219i	0.0831297	+	0.193774i
$399$	−69.5908	−	85.0642i	−0.174413	−	0.213194i
$400$	−183.308	+	355.525i	−0.458269	+	0.888814i
$401$	64.2479	−	111.281i	0.160219	−	0.277508i	−0.774728	−	0.632295i	$-0.782113\pi$
$401$	64.2479	−	111.281i	0.160219	−	0.277508i	0.934947	+	0.354787i	$0.115447\pi$
$402$	208.901	−	279.442i	0.519654	−	0.695130i
$403$	−402.680	−	107.898i	−0.999207	−	0.267737i
$404$	33.0128	−	9.74069i	0.0817149	−	0.0241106i
$405$	−24.6240	+	91.4076i	−0.0608000	+	0.225698i
$406$	100.705	−	454.476i	0.248041	−	1.11940i
$407$	−145.532	−	145.532i	−0.357572	−	0.357572i
$408$	−55.5045	+	46.0131i	−0.136040	+	0.112777i
$409$	−306.419	−	530.733i	−0.749190	−	1.29763i	−0.948211	−	0.317640i	$-0.897110\pi$
$409$	−306.419	−	530.733i	−0.749190	−	1.29763i	0.199022	−	0.979995i	$-0.436224\pi$
$410$	−59.8695	−	76.2373i	−0.146023	−	0.185945i
$411$	71.8813	−	124.502i	0.174894	−	0.302925i
$412$	377.045	−	9.47227i	0.915157	−	0.0229909i
$413$	179.818	+	398.504i	0.435395	+	0.964901i
$414$	228.522	+	91.3118i	0.551985	+	0.220560i
$415$	−1.04092	+	776.187i	−0.00250825	+	1.87033i
$416$	−53.0996	−	270.707i	−0.127643	−	0.650738i
$417$	226.568	+	60.7086i	0.543328	+	0.145584i
$418$	−8.95246	+	75.2961i	−0.0214174	+	0.180134i
$419$			563.142i			1.34401i	0.740545	+	0.672007i	$0.234567\pi$
$419$			563.142i			1.34401i	−0.740545	+	0.672007i	$0.765433\pi$
$420$	41.2076	+	219.159i	0.0981134	+	0.521808i
$421$	317.578			0.754343			0.377171	−	0.926143i	$-0.376897\pi$
$421$	317.578			0.754343			0.377171	+	0.926143i	$0.376897\pi$
$422$	505.518	+	60.1045i	1.19791	+	0.142428i
$423$	26.0286	−	97.1400i	0.0615333	−	0.229645i
$424$	−64.0242	−	45.4011i	−0.151001	−	0.107078i
$425$	136.527	+	36.9752i	0.321241	+	0.0870005i
$426$	53.1337	−	132.975i	0.124727	−	0.312149i
$427$	58.0176	−	80.6999i	0.135873	−	0.188993i
$428$	−699.859	+	17.5822i	−1.63519	+	0.0410798i
$429$	−45.7412	−	26.4087i	−0.106623	−	0.0615587i
$430$	−15.5184	+	129.044i	−0.0360893	+	0.300101i
$431$	−103.372	+	59.6818i	−0.239842	+	0.138473i	−0.615104	−	0.788446i	$-0.710886\pi$
$431$	−103.372	+	59.6818i	−0.239842	+	0.138473i	0.375262	+	0.926919i	$0.377553\pi$
$432$	−375.051	+	120.981i	−0.868173	+	0.280048i
$433$	142.340	−	142.340i	0.328730	−	0.328730i	−0.523373	−	0.852104i	$-0.675327\pi$
$433$	142.340	−	142.340i	0.328730	−	0.328730i	0.852104	+	0.523373i	$0.175327\pi$
$434$	−203.650	−	645.658i	−0.469239	−	1.48769i
$435$	132.098	+	229.511i	0.303674	+	0.527612i
$436$	421.640	−	124.408i	0.967063	−	0.285340i
$437$	−48.5708	+	181.269i	−0.111146	+	0.414803i
$438$	11.3806	+	8.50775i	0.0259832	+	0.0194241i
$439$	610.466	+	352.453i	1.39058	+	0.802853i	0.993380	−	0.114877i	$-0.0366475\pi$
$439$	610.466	+	352.453i	1.39058	+	0.802853i	0.397203	+	0.917731i	$0.369981\pi$
$440$	89.1654	−	125.384i	0.202649	−	0.284963i
$441$	−237.445	−	209.535i	−0.538423	−	0.475136i
$442$	−89.6486	+	38.4596i	−0.202825	+	0.0870128i
$443$	−42.4566	−	158.450i	−0.0958388	−	0.357675i	0.901306	−	0.433182i	$-0.142609\pi$
$443$	−42.4566	−	158.450i	−0.0958388	−	0.357675i	−0.997145	+	0.0755066i	$0.975943\pi$
$444$	331.418	+	79.9390i	0.746437	+	0.180043i
$445$	745.522	−	198.691i	1.67533	−	0.446496i
$446$	−137.383	+	108.185i	−0.308033	+	0.242568i
$447$	−277.526	+	277.526i	−0.620863	+	0.620863i
$448$	324.408	−	308.971i	0.724126	−	0.689668i
$449$		−	152.026i		−	0.338589i	−0.985566	−	0.169295i	$-0.945851\pi$
$449$		−	152.026i		−	0.338589i	0.985566	−	0.169295i	$-0.0541489\pi$
$450$	258.295	+	194.174i	0.573989	+	0.431498i
$451$	18.6426	+	32.2899i	0.0413361	+	0.0715962i
$452$	−300.178	−	491.016i	−0.664110	−	1.08632i
$453$	−77.5954	−	289.590i	−0.171292	−	0.639271i
$454$	62.8706	−	157.343i	0.138482	−	0.346572i
$455$	−30.4409	+	300.188i	−0.0669032	+	0.659755i
$456$	−52.4035	−	114.150i	−0.114920	−	0.250329i
$457$	68.6898	+	256.354i	0.150306	+	0.560949i	0.999462	+	0.0328067i	$0.0104446\pi$
$457$	68.6898	+	256.354i	0.150306	+	0.560949i	−0.849156	+	0.528142i	$0.822889\pi$
$458$	413.746	+	309.302i	0.903376	+	0.675331i
$459$	69.6763	+	120.683i	0.151800	+	0.262926i
$460$	262.773	−	275.576i	0.571247	−	0.599078i
$461$			323.443i			0.701611i	0.936448	+	0.350806i	$0.114092\pi$
$461$			323.443i			0.701611i	−0.936448	+	0.350806i	$0.885908\pi$
$462$	−3.75046	−	85.6924i	−0.00811788	−	0.185481i
$463$	−15.5188	+	15.5188i	−0.0335179	+	0.0335179i	−0.723667	−	0.690149i	$-0.757545\pi$
$463$	−15.5188	+	15.5188i	−0.0335179	+	0.0335179i	0.690149	+	0.723667i	$0.257545\pi$
$464$	242.530	−	473.501i	0.522693	−	1.02048i
$465$	333.280	+	193.016i	0.716731	+	0.415088i
$466$	−27.8787	−	192.998i	−0.0598255	−	0.414159i
$467$	83.6945	+	312.352i	0.179217	+	0.668848i	0.995795	+	0.0916121i	$0.0292020\pi$
$467$	83.6945	+	312.352i	0.179217	+	0.668848i	−0.816577	+	0.577236i	$0.804131\pi$
$468$	−222.788	+	5.59697i	−0.476043	+	0.0119593i
$469$	717.076	+	271.154i	1.52895	+	0.578153i
$470$	−124.507	−	93.3376i	−0.264909	−	0.198591i
$471$	−6.42364	−	3.70869i	−0.0136383	−	0.00787407i
$472$	83.8307	+	492.570i	0.177607	+	1.04358i
$473$	12.9391	−	48.2893i	0.0273554	−	0.102092i
$474$	334.437	−	263.361i	0.705563	−	0.555613i
$475$	−123.782	+	213.075i	−0.260594	+	0.448580i
$476$	−130.910	−	89.2149i	−0.275021	−	0.187426i
$477$	−44.8353	+	44.8353i	−0.0939942	+	0.0939942i
$478$	−37.8346	+	318.214i	−0.0791520	+	0.665721i
$479$	−351.573	+	202.981i	−0.733973	+	0.423759i	−0.819874	−	0.572544i	$-0.805956\pi$
$479$	−351.573	+	202.981i	−0.733973	+	0.423759i	0.0859010	+	0.996304i	$0.472623\pi$
$480$	−17.6851	+	254.243i	−0.0368439	+	0.529672i
$481$	399.482	+	230.641i	0.830524	+	0.479503i
$482$	−247.933	−	577.927i	−0.514384	−	1.19902i
$483$	21.1338	−	211.229i	0.0437552	−	0.437327i
$484$	292.755	−	307.843i	0.604866	−	0.636040i
$485$	1.16742	−	870.510i	0.00240705	−	1.79487i
$486$	72.0061	+	498.482i	0.148161	+	1.02568i
$487$	−69.1207	+	257.962i	−0.141932	+	0.529696i	0.857941	+	0.513748i	$0.171743\pi$
$487$	−69.1207	+	257.962i	−0.141932	+	0.529696i	−0.999873	+	0.0159483i	$0.994923\pi$
$488$	87.4480	−	72.4942i	0.179197	−	0.148554i
$489$	−209.136			−0.427681
$490$	−437.692	+	220.286i	−0.893248	+	0.449564i
$491$		−	34.9926i		−	0.0712680i	−0.999365	−	0.0356340i	$-0.988655\pi$
$491$		−	34.9926i		−	0.0712680i	0.999365	−	0.0356340i	$-0.0113451\pi$
$492$	−54.2459	−	29.5278i	−0.110256	−	0.0600158i
$493$	−181.713	−	48.6898i	−0.368586	−	0.0987622i
$494$	−24.2968	−	168.202i	−0.0491839	−	0.340489i
$495$	−87.7701	−	88.0058i	−0.177313	−	0.177790i
$496$	−38.8514	−	772.754i	−0.0783294	−	1.55797i
$497$	313.087	+	31.3248i	0.629954	+	0.0630278i
$498$	194.976	+	454.485i	0.391518	+	0.912620i
$499$	−319.252	+	552.961i	−0.639784	+	1.10814i	0.345697	+	0.938346i	$0.387643\pi$
$499$	−319.252	+	552.961i	−0.639784	+	1.10814i	−0.985480	+	0.169791i	$0.945691\pi$
$500$	427.643	−	259.078i	0.855287	−	0.518155i
$501$	−219.174	−	379.621i	−0.437473	−	0.757726i
$502$	58.1298	−	488.911i	0.115797	−	0.973925i
$503$	−263.613	−	263.613i	−0.524082	−	0.524082i	0.394719	−	0.918802i	$-0.370842\pi$
$503$	−263.613	−	263.613i	−0.524082	−	0.524082i	−0.918802	+	0.394719i	$0.870842\pi$
$504$	−202.094	−	300.237i	−0.400981	−	0.595708i
$505$	−41.5438	−	11.1914i	−0.0822650	−	0.0221611i
$506$	−115.067	+	90.6126i	−0.227406	+	0.179076i
$507$	−145.676	−	39.0337i	−0.287329	−	0.0769895i
$508$	1.66079	+	2.71665i	0.00326928	+	0.00534773i
$509$	−148.242	+	256.763i	−0.291242	+	0.504446i	−0.974104	−	0.226102i	$-0.927402\pi$
$509$	−148.242	+	256.763i	−0.291242	+	0.504446i	0.682862	+	0.730548i	$0.260735\pi$
$510$	89.2125	−	12.7647i	0.174927	−	0.0250288i
$511$	−11.0431	+	29.2038i	−0.0216107	+	0.0571504i
$512$	447.909	−	248.035i	0.874823	−	0.484443i
$513$	−234.502	+	62.8345i	−0.457118	+	0.122484i
$514$	−35.8539	−	248.209i	−0.0697546	−	0.482896i
$515$	−407.975	−	236.275i	−0.792185	−	0.458786i
$516$	23.4353	+	79.4262i	0.0454173	+	0.153927i
$517$	42.3225	+	42.3225i	0.0818617	+	0.0818617i
$518$	32.7547	+	748.396i	0.0632331	+	1.44478i
$519$	465.185			0.896310
$520$	−120.301	+	323.167i	−0.231349	+	0.621474i
$521$	−255.924	+	147.758i	−0.491217	+	0.283604i	−0.725079	−	0.688666i	$-0.758197\pi$
$521$	−255.924	+	147.758i	−0.491217	+	0.283604i	0.233862	+	0.972270i	$0.424863\pi$
$522$	−344.223	−	257.329i	−0.659432	−	0.492967i
$523$	−26.8371	+	7.19097i	−0.0513137	+	0.0137495i	−0.284385	−	0.958710i	$-0.591789\pi$
$523$	−26.8371	+	7.19097i	−0.0513137	+	0.0137495i	0.233071	+	0.972460i	$0.425123\pi$
$524$	−454.001	+	477.400i	−0.866413	+	0.911068i
$525$	99.2915	−	260.466i	0.189127	−	0.496126i
$526$	157.414	−	393.953i	0.299266	−	0.748960i
$527$	−264.279	+	70.8134i	−0.501479	+	0.134371i
$528$	20.5849	−	95.8422i	0.0389866	−	0.181519i
$529$	144.211	−	83.2601i	0.272610	−	0.157392i
$530$	38.5594	+	90.2149i	0.0727537	+	0.170217i
$531$	403.645			0.760160
$532$	209.158	−	180.067i	0.393154	−	0.338472i
$533$	−59.0902	−	59.0902i	−0.110863	−	0.110863i
$534$	386.211	−	304.131i	0.723241	−	0.569534i
$535$	757.272	+	438.566i	1.41546	+	0.819750i
$536$	714.693	+	506.805i	1.33338	+	0.945532i
$537$	−247.033	+	66.1924i	−0.460025	+	0.123263i
$538$	−174.055	+	74.6705i	−0.323523	+	0.138793i
$539$	178.657	−	60.0310i	0.331460	−	0.111375i
$540$	478.712	+	116.146i	0.886504	+	0.215086i
$541$	−130.662	+	226.313i	−0.241519	+	0.418323i	−0.961147	−	0.276037i	$-0.910979\pi$
$541$	−130.662	+	226.313i	−0.241519	+	0.418323i	0.719628	+	0.694359i	$0.244312\pi$
$542$	164.693	+	123.119i	0.303862	+	0.227156i
$543$	−34.7311	−	9.30617i	−0.0639615	−	0.0171384i
$544$	−119.013	−	136.438i	−0.218774	−	0.250805i
$545$	−530.598	−	142.936i	−0.973574	−	0.262268i
$546$	57.8281	+	183.340i	0.105912	+	0.335787i
$547$	−643.986	−	643.986i	−1.17731	−	1.17731i	−0.980428	−	0.196878i	$-0.936920\pi$
$547$	−643.986	−	643.986i	−1.17731	−	1.17731i	−0.196878	−	0.980428i	$-0.563080\pi$
$548$	317.086	+	172.600i	0.578624	+	0.314964i
$549$	−45.8817	−	79.4694i	−0.0835732	−	0.144753i
$550$	−176.944	+	75.3487i	−0.321717	+	0.136998i
$551$	163.870	−	283.831i	0.297404	−	0.515119i
$552$	84.3341	−	227.480i	0.152779	−	0.412102i
$553$	759.462	+	546.001i	1.37335	+	0.987343i
$554$	−44.2340	+	110.703i	−0.0798448	+	0.199824i
$555$	−300.931	−	301.739i	−0.542218	−	0.543675i
$556$	−138.115	+	572.609i	−0.248408	+	1.02987i
$557$	693.131	+	185.724i	1.24440	+	0.333436i	0.820171	−	0.572118i	$-0.193878\pi$
$557$	693.131	+	185.724i	1.24440	+	0.333436i	0.424230	+	0.905554i	$0.360545\pi$
$558$	−620.687	−	73.7976i	−1.11234	−	0.132254i
$559$			112.047i			0.200443i
$560$	−547.583	+	117.270i	−0.977828	+	0.209411i
$561$	−34.6641			−0.0617898
$562$	−59.3407	+	499.095i	−0.105588	+	0.888069i
$563$	44.8183	−	167.264i	0.0796062	−	0.297094i	−0.914632	−	0.404287i	$-0.867520\pi$
$563$	44.8183	−	167.264i	0.0796062	−	0.297094i	0.994238	+	0.107193i	$0.0341863\pi$
$564$	−96.3806	−	23.2473i	−0.170888	−	0.0412186i
$565$	−0.964739	+	719.378i	−0.00170750	+	1.27324i
$566$	−387.398	−	154.795i	−0.684448	−	0.273489i
$567$	−120.804	+	54.5106i	−0.213057	+	0.0961386i
$568$	337.175	+	125.001i	0.593618	+	0.220073i
$569$	243.006	+	140.299i	0.427075	+	0.246572i	0.698100	−	0.716000i	$-0.254029\pi$
$569$	243.006	+	140.299i	0.427075	+	0.246572i	−0.271025	+	0.962572i	$0.587363\pi$
$570$	−18.7459	+	155.882i	−0.0328875	+	0.273477i
$571$	−492.711	+	284.467i	−0.862892	+	0.498191i	−0.864980	−	0.501807i	$-0.832669\pi$
$571$	−492.711	+	284.467i	−0.862892	+	0.498191i	0.00208773	+	0.999998i	$0.499335\pi$
$572$	63.4122	−	116.495i	0.110860	−	0.203663i
$573$	310.779	−	310.779i	0.542372	−	0.542372i
$574$	29.3590	−	132.496i	0.0511480	−	0.230829i
$575$	−460.083	+	121.957i	−0.800144	+	0.212099i
$576$	−136.825	−	390.334i	−0.237544	−	0.677662i
$577$	−11.1015	+	41.4315i	−0.0192401	+	0.0718050i	−0.974878	−	0.222738i	$-0.928501\pi$
$577$	−11.1015	+	41.4315i	−0.0192401	+	0.0718050i	0.955638	+	0.294543i	$0.0951673\pi$
$578$	307.744	−	411.663i	0.532430	−	0.712220i
$579$	−117.455	−	67.8128i	−0.202859	−	0.117121i
$580$	−567.839	+	346.097i	−0.979033	+	0.596719i
$581$	−841.066	+	688.073i	−1.44762	+	1.18429i
$582$	−218.670	−	509.714i	−0.375721	−	0.875797i
$583$	−9.76703	−	36.4511i	−0.0167531	−	0.0625233i
$584$	−20.6403	+	29.1068i	−0.0353430	+	0.0498404i
$585$	241.064	+	139.610i	0.412076	+	0.238649i
$586$	−182.824	−	232.165i	−0.311987	−	0.396186i
$587$	−330.283	+	330.283i	−0.562662	+	0.562662i	−0.930063	−	0.367400i	$-0.880248\pi$
$587$	−330.283	+	330.283i	−0.562662	+	0.562662i	0.367400	+	0.930063i	$0.380248\pi$
$588$	−200.628	+	239.201i	−0.341203	+	0.406805i
$589$		−	476.658i		−	0.809266i
$590$	232.523	−	579.668i	0.394107	−	0.982488i
$591$	36.2650	+	62.8128i	0.0613621	+	0.106282i
$592$	−179.779	+	837.040i	−0.303680	+	1.41392i
$593$	111.158	+	414.846i	0.187450	+	0.699571i	0.994093	+	0.108533i	$0.0346153\pi$
$593$	111.158	+	414.846i	0.187450	+	0.699571i	−0.806643	+	0.591039i	$0.798718\pi$
$594$	−175.947	−	70.3043i	−0.296208	−	0.118357i
$595$	81.2051	+	180.608i	0.136479	+	0.303543i
$596$	−714.209	−	679.204i	−1.19834	−	1.13960i
$597$	−17.2983	−	64.5582i	−0.0289754	−	0.108138i
$598$	196.546	−	262.916i	0.328673	−	0.439659i
$599$	−169.733	−	293.986i	−0.283360	−	0.490795i	0.688850	−	0.724904i	$-0.258116\pi$
$599$	−169.733	−	293.986i	−0.283360	−	0.490795i	−0.972210	+	0.234109i	$0.924783\pi$
$600$	184.973	−	259.370i	0.308288	−	0.432283i
$601$			52.8008i			0.0878549i	0.999035	+	0.0439274i	$0.0139870\pi$
$601$			52.8008i			0.0878549i	−0.999035	+	0.0439274i	$0.986013\pi$
$602$	−153.455	+	97.7846i	−0.254909	+	0.162433i
$603$	500.489	−	500.489i	0.829998	−	0.829998i
$604$	722.099	−	213.061i	1.19553	−	0.352750i
$605$	−513.116	+	136.752i	−0.848126	+	0.226036i
$606$	−27.1313	+	3.91914i	−0.0447712	+	0.00646722i
$607$	30.9598	+	115.543i	0.0510045	+	0.190352i	0.986728	−	0.162384i	$-0.0519183\pi$
$607$	30.9598	+	115.543i	0.0510045	+	0.190352i	−0.935723	+	0.352735i	$0.885252\pi$
$608$	283.260	−	138.754i	0.465888	−	0.228214i
$609$	−131.128	+	346.773i	−0.215317	+	0.569413i
$610$	−140.555	+	20.1109i	−0.230419	+	0.0329687i
$611$	−116.175	−	67.0734i	−0.190138	−	0.109776i
$612$	−124.790	+	76.2891i	−0.203905	+	0.124655i
$613$	8.99270	−	33.5612i	0.0146700	−	0.0547492i	−0.958203	−	0.286090i	$-0.907644\pi$
$613$	8.99270	−	33.5612i	0.0146700	−	0.0547492i	0.972873	+	0.231341i	$0.0743111\pi$
$614$	−215.785	−	274.021i	−0.351441	−	0.446288i
$615$	38.5114	+	66.9107i	0.0626201	+	0.108798i
$616$	214.887	−	14.8197i	0.348843	−	0.0240579i
$617$	621.795	−	621.795i	1.00777	−	1.00777i	0.00780168	−	0.999970i	$-0.497517\pi$
$617$	621.795	−	621.795i	1.00777	−	1.00777i	0.999970	−	0.00780168i	$-0.00248338\pi$
$618$	−298.283	−	35.4648i	−0.482658	−	0.0573864i
$619$	−227.656	+	131.437i	−0.367780	+	0.212338i	−0.672488	−	0.740108i	$-0.734774\pi$
$619$	−227.656	+	131.437i	−0.367780	+	0.212338i	0.304708	+	0.952446i	$0.401441\pi$
$620$	−463.532	+	848.847i	−0.747632	+	1.36911i
$621$	−406.104	−	234.464i	−0.653952	−	0.377559i
$622$	−296.242	+	127.089i	−0.476274	+	0.204324i
$623$	877.034	+	630.526i	1.40776	+	1.01208i
$624$	11.0322	+	219.430i	0.0176798	+	0.351650i
$625$	−624.991	−	3.35266i	−0.999986	−	0.00536426i
$626$	−603.205	+	87.1333i	−0.963586	+	0.139191i
$627$	15.6302	−	58.3325i	0.0249285	−	0.0930343i
$628$	8.90524	−	16.3599i	0.0141803	−	0.0260508i
$629$	302.740			0.481303
$630$	19.1748	+	451.990i	0.0304362	+	0.717445i
$631$		−	472.941i		−	0.749510i	−0.927124	−	0.374755i	$-0.877727\pi$
$631$		−	472.941i		−	0.749510i	0.927124	−	0.374755i	$-0.122273\pi$
$632$	682.239	+	822.968i	1.07949	+	1.30216i
$633$	−391.629	−	104.937i	−0.618688	−	0.165777i
$634$	−421.015	+	60.8158i	−0.664061	+	0.0959240i
$635$	0.00533761	−	3.98010i	8.40568e−6	−	0.00626788i
$636$	45.2974	+	43.0772i	0.0712223	+	0.0677315i
$637$	−351.952	+	233.597i	−0.552515	+	0.366715i
$638$	235.066	−	100.845i	0.368443	−	0.158064i
$639$	145.252	−	251.583i	0.227311	−	0.393714i
$640$	−639.371	−	28.3624i	−0.999018	−	0.0443163i
$641$	−551.476	−	955.185i	−0.860337	−	1.49015i	−0.871604	−	0.490211i	$-0.836920\pi$
$641$	−551.476	−	955.185i	−0.860337	−	1.49015i	0.0112668	−	0.999937i	$-0.496414\pi$
$642$	553.664	+	65.8288i	0.862404	+	0.102537i
$643$	−642.845	−	642.845i	−0.999759	−	0.999759i	0.000241112	−	1.00000i	$-0.499923\pi$
$643$	−642.845	−	642.845i	−0.999759	−	0.999759i	−1.00000		0.000241112i	$0.999923\pi$
$644$	531.606	+	39.7329i	0.825476	+	0.0616971i
$645$	26.9256	−	99.9512i	0.0417450	−	0.154963i
$646$	−69.0051	−	87.6283i	−0.106819	−	0.135648i
$647$	498.113	+	133.469i	0.769880	+	0.206289i	0.622319	−	0.782764i	$-0.286191\pi$
$647$	498.113	+	133.469i	0.769880	+	0.206289i	0.147562	+	0.989053i	$0.452857\pi$
$648$	−149.319	+	25.4127i	−0.230430	+	0.0392171i
$649$	−120.116	+	208.047i	−0.185079	+	0.320566i
$650$	339.359	−	265.765i	0.522090	−	0.408869i
$651$	87.0100	+	532.125i	0.133656	+	0.817397i
$652$	−13.1898	−	525.020i	−0.0202297	−	0.805245i
$653$	−130.824	+	35.0542i	−0.200343	+	0.0536817i	−0.357595	−	0.933877i	$-0.616403\pi$
$653$	−130.824	+	35.0542i	−0.200343	+	0.0536817i	0.157252	+	0.987559i	$0.449736\pi$
$654$	−346.521	+	50.0552i	−0.529849	+	0.0765370i
$655$	795.734	−	212.073i	1.21486	−	0.323775i
$656$	70.7060	−	138.042i	0.107784	−	0.210430i
$657$	20.3831	+	20.3831i	0.0310244	+	0.0310244i
$658$	−9.52550	−	217.643i	−0.0144764	−	0.330765i
$659$	−542.902			−0.823826			−0.411913	−	0.911223i	$-0.635139\pi$
$659$	−542.902			−0.823826			−0.411913	+	0.911223i	$0.635139\pi$
$660$	−84.5608	+	88.6806i	−0.128122	+	0.134365i
$661$	731.512	−	422.339i	1.10667	−	0.638939i	0.168709	−	0.985666i	$-0.446040\pi$
$661$	731.512	−	422.339i	1.10667	−	0.638939i	0.937966	+	0.346727i	$0.112707\pi$
$662$	119.533	−	159.896i	0.180563	−	0.241535i
$663$	75.0443	−	20.1081i	0.113189	−	0.0303289i
$664$	−1128.65	+	518.135i	−1.69978	+	0.780324i
$665$	−340.542	+	55.2146i	−0.512093	+	0.0830295i
$666$	642.251	+	256.628i	0.964341	+	0.385327i
$667$	611.472	−	163.844i	0.916750	−	0.245643i
$668$	939.186	−	574.161i	1.40597	−	0.859523i
$669$	120.610	−	69.6340i	0.180284	−	0.104087i
$670$	−430.433	−	1007.06i	−0.642438	−	1.50307i
$671$	54.6136			0.0813914
$672$	−290.894	+	206.607i	−0.432878	+	0.307451i
$673$	−787.425	−	787.425i	−1.17002	−	1.17002i	−0.982204	−	0.187818i	$-0.939859\pi$
$673$	−787.425	−	787.425i	−1.17002	−	1.17002i	−0.187818	−	0.982204i	$-0.560141\pi$
$674$	584.445	+	742.175i	0.867129	+	1.10115i
$675$	−434.232	−	436.568i	−0.643307	−	0.646767i
$676$	88.8035	−	368.169i	0.131366	−	0.544629i
$677$	−813.588	+	218.000i	−1.20175	+	0.322009i	−0.803522	−	0.595275i	$-0.797043\pi$
$677$	−813.588	+	218.000i	−1.20175	+	0.322009i	−0.398233	+	0.917284i	$0.630376\pi$
$678$	180.706	+	421.221i	0.266528	+	0.621270i
$679$	943.273	−	771.688i	1.38921	−	1.13651i
$680$	37.6712	+	223.156i	0.0553988	+	0.328171i
$681$	−67.4731	+	116.867i	−0.0990794	+	0.171611i
$682$	222.740	−	297.955i	0.326598	−	0.436884i
$683$	−76.1113	−	20.3939i	−0.111437	−	0.0298594i	0.202670	−	0.979247i	$-0.435038\pi$
$683$	−76.1113	−	20.3939i	−0.111437	−	0.0298594i	−0.314106	+	0.949388i	$0.601705\pi$
$684$	−72.1106	−	244.395i	−0.105425	−	0.357303i
$685$	−225.112	−	391.116i	−0.328631	−	0.570973i
$686$	−627.076	−	278.157i	−0.914106	−	0.405476i
$687$	−290.916	−	290.916i	−0.423459	−	0.423459i
$688$	−197.915	+	63.8418i	−0.287668	+	0.0927933i
$689$	42.2893	+	73.2472i	0.0613778	+	0.106309i
$690$	−238.508	+	187.301i	−0.345664	+	0.271451i
$691$	20.0504	−	34.7283i	0.0290165	−	0.0502580i	−0.851153	−	0.524918i	$-0.824096\pi$
$691$	20.0504	−	34.7283i	0.0290165	−	0.0502580i	0.880169	+	0.474660i	$0.157429\pi$
$692$	29.3382	+	1167.81i	0.0423963	+	1.68759i
$693$	17.3234	−	173.145i	0.0249977	−	0.249848i
$694$	−208.575	−	83.3415i	−0.300540	−	0.120089i
$695$	521.332	−	519.936i	0.750118	−	0.748109i
$696$	−245.087	+	345.620i	−0.352137	+	0.496581i
$697$	−52.9757	−	14.1948i	−0.0760053	−	0.0203656i
$698$	98.4163	−	827.747i	0.140998	−	1.18588i
$699$			155.304i			0.222181i
$700$	660.142	+	232.836i	0.943060	+	0.332623i
$701$	1039.18			1.48243			0.741216	−	0.671266i	$-0.234249\pi$
$701$	1039.18			1.48243			0.741216	+	0.671266i	$0.234249\pi$
$702$	421.691	+	50.1376i	0.600699	+	0.0714211i
$703$	−136.506	+	509.448i	−0.194177	+	0.724678i
$704$	241.903	+	45.6322i	0.343612	+	0.0648185i
$705$	87.5147	+	87.7497i	0.124134	+	0.124468i
$706$	−49.0719	+	122.810i	−0.0695069	+	0.173952i
$707$	−24.7745	−	54.9040i	−0.0350418	−	0.0776577i
$708$	−9.99398	−	397.811i	−0.0141158	−	0.561880i
$709$	−842.505	−	486.420i	−1.18830	−	0.686065i	−0.230380	−	0.973101i	$-0.573997\pi$
$709$	−842.505	−	486.420i	−1.18830	−	0.686065i	−0.957920	+	0.287035i	$0.907330\pi$
$710$	−277.621	−	353.521i	−0.391016	−	0.497916i
$711$	747.882	−	431.790i	1.05187	−	0.607300i
$712$	787.855	+	950.371i	1.10654	+	1.33479i
$713$	651.023	−	651.023i	0.913075	−	0.913075i
$714$	93.0309	+	85.2291i	0.130295	+	0.119368i
$715$	−143.693	+	82.7047i	−0.200970	+	0.115671i
$716$	−181.751	−	615.984i	−0.253842	−	0.860312i
$717$	66.0558	−	246.523i	0.0921280	−	0.343826i
$718$	−545.312	−	407.655i	−0.759488	−	0.567765i
$719$	−897.643	−	518.254i	−1.24846	−	0.720799i	−0.277658	−	0.960680i	$-0.589558\pi$
$719$	−897.643	−	518.254i	−1.24846	−	0.720799i	−0.970802	+	0.239882i	$0.922891\pi$
$720$	−109.248	+	505.351i	−0.151733	+	0.701876i
$721$	−106.511	−	651.386i	−0.147726	−	0.903448i
$722$	−484.944	+	208.043i	−0.671667	+	0.288148i
$723$	129.628	+	483.779i	0.179292	+	0.669127i
$724$	21.1720	−	87.7766i	0.0292431	−	0.121238i
$725$	831.246	+	2.22953i	1.14655	+	0.00307521i
$726$	−265.815	+	209.323i	−0.366136	+	0.288323i
$727$	721.945	−	721.945i	0.993047	−	0.993047i	−0.00692882	−	0.999976i	$-0.502206\pi$
$727$	721.945	−	721.945i	0.993047	−	0.993047i	0.999976	+	0.00692882i	$0.00220553\pi$
$728$	−456.613	+	156.736i	−0.627216	+	0.215296i
$729$		−	230.727i		−	0.316497i
$730$	41.0136	−	17.5299i	0.0561830	−	0.0240136i
$731$	36.7684	+	63.6847i	0.0502987	+	0.0871199i
$732$	−77.1849	+	47.1862i	−0.105444	+	0.0644621i
$733$	189.522	+	707.304i	0.258556	+	0.964944i	0.966078	+	0.258252i	$0.0831466\pi$
$733$	189.522	+	707.304i	0.258556	+	0.964944i	−0.707522	+	0.706692i	$0.750187\pi$
$734$	−480.523	+	1202.58i	−0.654664	+	1.63840i
$735$	370.091	−	123.803i	0.503526	−	0.168440i
$736$	576.390	+	197.368i	0.783138	+	0.268162i
$737$	109.028	+	406.898i	0.147935	+	0.552100i
$738$	−100.353	−	75.0205i	−0.135980	−	0.101654i
$739$	−142.841	−	247.407i	−0.193289	−	0.334786i	0.753049	−	0.657964i	$-0.228582\pi$
$739$	−142.841	−	247.407i	−0.193289	−	0.334786i	−0.946338	+	0.323178i	$0.895249\pi$
$740$	738.514	−	774.494i	0.997992	−	1.04661i
$741$			135.351i			0.182660i
$742$	−63.4102	+	121.841i	−0.0854584	+	0.164206i
$743$	−669.758	+	669.758i	−0.901424	+	0.901424i	−0.995559	−	0.0941353i	$-0.969991\pi$
$743$	−669.758	+	669.758i	−0.901424	+	0.901424i	0.0941353	+	0.995559i	$0.469991\pi$
$744$	−57.3633	+	613.544i	−0.0771012	+	0.824656i
$745$	317.270	+	1190.45i	0.425865	+	1.59792i
$746$	205.419	+	1422.07i	0.275360	+	1.90626i
$747$	259.666	+	969.086i	0.347611	+	1.29730i
$748$	−2.18619	−	87.0215i	−0.00292271	−	0.116339i
$749$	197.702	+	1209.08i	0.263955	+	1.61426i
$750$	−366.588	+	155.524i	−0.488783	+	0.207366i
$751$	773.228	+	446.424i	1.02960	+	0.594439i	0.916870	−	0.399187i	$-0.130708\pi$
$751$	773.228	+	446.424i	1.02960	+	0.594439i	0.112729	+	0.993626i	$0.464041\pi$
$752$	52.2820	−	243.422i	0.0695239	−	0.323700i
$753$	−101.489	+	378.763i	−0.134780	+	0.503006i
$754$	−450.397	+	354.676i	−0.597343	+	0.470393i
$755$	−908.700	−	244.792i	−1.20358	−	0.324228i
$756$	299.346	+	621.286i	0.395961	+	0.821806i
$757$	447.990	−	447.990i	0.591797	−	0.591797i	−0.346320	−	0.938117i	$-0.612569\pi$
$757$	447.990	−	447.990i	0.591797	−	0.591797i	0.938117	+	0.346320i	$0.112569\pi$
$758$	−22.0673	+	185.600i	−0.0291125	+	0.244855i
$759$	101.019	−	58.3232i	0.133095	−	0.0768422i
$760$	−392.512	−	37.2289i	−0.516463	−	0.0489855i
$761$	759.715	+	438.622i	0.998311	+	0.576375i	0.907748	−	0.419515i	$-0.137800\pi$
$761$	759.715	+	438.622i	0.998311	+	0.576375i	0.0905632	+	0.995891i	$0.471133\pi$
$762$	−0.999790	−	2.33049i	−0.00131206	−	0.00305838i
$763$	−316.420	−	701.234i	−0.414705	−	0.919048i
$764$	799.787	+	760.587i	1.04684	+	0.995532i
$765$	182.827	+	0.245185i	0.238990	+	0.000320503i
$766$	73.1730	+	506.561i	0.0955261	+	0.661306i
$767$	139.355	−	520.079i	0.181688	−	0.678069i
$768$	−381.305	+	144.512i	−0.496491	+	0.188167i
$769$	96.1772			0.125068			0.0625340	−	0.998043i	$-0.480082\pi$
$769$	96.1772			0.125068			0.0625340	+	0.998043i	$0.480082\pi$
$770$	−238.671	−	124.620i	−0.309963	−	0.161844i
$771$			199.732i			0.259056i
$772$	162.831	−	299.139i	0.210921	−	0.387486i
$773$	125.402	+	33.6015i	0.162228	+	0.0434689i	0.339019	−	0.940780i	$-0.389905\pi$
$773$	125.402	+	33.6015i	0.162228	+	0.0434689i	−0.176791	+	0.984248i	$0.556572\pi$
$774$	24.0182	+	166.273i	0.0310313	+	0.214823i
$775$	1048.60	−	601.666i	1.35303	−	0.776343i
$776$	1265.81	−	581.099i	1.63119	−	0.748839i
$777$	59.3956	−	593.650i	0.0764422	−	0.764028i
$778$	133.231	+	310.559i	0.171249	+	0.399176i
$779$	47.7738	−	82.7467i	0.0613271	−	0.106222i
$780$	131.624	−	241.037i	0.168748	−	0.309022i
$781$	86.4477	+	149.732i	0.110688	+	0.191718i
$782$	25.4357	−	213.931i	0.0325265	−	0.273569i
$783$	579.083	+	579.083i	0.739570	+	0.739570i
$784$	−613.149	−	488.574i	−0.782077	−	0.623181i
$785$	−20.1795	+	11.6146i	−0.0257064	+	0.0147956i
$786$	412.222	−	324.615i	0.524456	−	0.412996i
$787$	1193.80	+	319.877i	1.51690	+	0.406451i	0.918718	−	0.394913i	$-0.129225\pi$
$787$	1193.80	+	319.877i	1.51690	+	0.406451i	0.598177	+	0.801364i	$0.295892\pi$
$788$	−155.400	+	95.0019i	−0.197208	+	0.120561i
$789$	−168.938	+	292.608i	−0.214116	+	0.370860i
$790$	−189.263	−	1322.76i	−0.239573	−	1.67438i
$791$	−779.509	+	637.713i	−0.985472	+	0.806212i
$792$	69.1289	−	186.466i	0.0872840	−	0.235437i
$793$	−118.233	+	31.6805i	−0.149096	+	0.0399501i
$794$	152.890	+	1058.42i	0.192557	+	1.33303i
$795$	−20.1222	−	75.5021i	−0.0253110	−	0.0949712i
$796$	160.977	−	47.4976i	0.202233	−	0.0596704i
$797$	−703.276	−	703.276i	−0.882405	−	0.882405i	0.111374	−	0.993779i	$-0.464475\pi$
$797$	−703.276	−	703.276i	−0.882405	−	0.882405i	−0.993779	+	0.111374i	$0.964475\pi$
$798$	−185.371	+	118.122i	−0.232295	+	0.148022i
$799$	−88.0406			−0.110188
$800$	662.793	+	448.001i	0.828491	+	0.560002i
$801$	863.661	−	498.635i	1.07823	−	0.622515i
$802$	−205.834	−	153.874i	−0.256651	−	0.191863i
$803$	−16.5714	+	4.44030i	−0.0206369	+	0.00552964i
$804$	−505.648	−	480.864i	−0.628915	−	0.598090i
$805$	−540.527	−	389.702i	−0.671463	−	0.484102i
$806$	−309.371	+	774.250i	−0.383836	+	0.960608i
$807$	145.701	−	39.0404i	0.180546	−	0.0483772i
$808$	−11.5498	−	67.8639i	−0.0142943	−	0.0839900i
$809$	−484.986	+	280.007i	−0.599489	+	0.346115i	−0.768840	−	0.639441i	$-0.779166\pi$
$809$	−484.986	+	280.007i	−0.599489	+	0.346115i	0.169352	+	0.985556i	$0.445833\pi$
$810$	175.722	+	70.4877i	0.216941	+	0.0870218i
$811$	−281.861			−0.347548			−0.173774	−	0.984786i	$-0.555596\pi$
$811$	−281.861			−0.347548			−0.173774	+	0.984786i	$0.555596\pi$
$812$	−878.815	−	307.316i	−1.08228	−	0.378468i
$813$	−115.800	−	115.800i	−0.142436	−	0.142436i
$814$	−323.392	+	254.663i	−0.397287	+	0.312854i
$815$	−329.003	+	568.089i	−0.403685	+	0.697042i
$816$	78.2763	+	121.098i	0.0959269	+	0.148404i
$817$	−123.747	+	33.1580i	−0.151465	+	0.0405850i
$818$	−1126.40	+	483.229i	−1.37701	+	0.590745i
$819$	62.9351	+	384.891i	0.0768438	+	0.469952i
$820$	−165.545	+	100.900i	−0.201884	+	0.123048i
$821$	−68.5408	+	118.716i	−0.0834845	+	0.144599i	−0.904744	−	0.425955i	$-0.859938\pi$
$821$	−68.5408	+	118.716i	−0.0834845	+	0.144599i	0.821260	+	0.570554i	$0.193272\pi$
$822$	−230.289	−	172.156i	−0.280157	−	0.209435i
$823$	523.143	+	140.176i	0.635654	+	0.170323i	0.562234	−	0.826978i	$-0.309942\pi$
$823$	523.143	+	140.176i	0.635654	+	0.170323i	0.0734197	+	0.997301i	$0.476609\pi$
$824$	70.2196	−	751.052i	0.0852180	−	0.911471i
$825$	148.055	−	39.2460i	0.179461	−	0.0475709i
$826$	833.894	−	263.022i	1.00956	−	0.318429i
$827$	577.230	+	577.230i	0.697981	+	0.697981i	0.963975	−	0.265994i	$-0.0857001\pi$
$827$	577.230	+	577.230i	0.697981	+	0.697981i	−0.265994	+	0.963975i	$0.585700\pi$
$828$	235.307	−	432.286i	0.284187	−	0.522084i
$829$	−600.599	−	1040.27i	−0.724486	−	1.25485i	−0.959185	−	0.282779i	$-0.908744\pi$
$829$	−600.599	−	1040.27i	−0.724486	−	1.25485i	0.234699	−	0.972068i	$-0.424590\pi$
$830$	1541.27	+	185.349i	1.85695	+	0.223312i
$831$	47.4722	−	82.2243i	0.0571266	−	0.0989462i
$832$	−550.165	+	41.5344i	−0.661256	+	0.0499211i
$833$	−123.385	+	248.263i	−0.148121	+	0.298035i
$834$	174.068	−	435.631i	0.208714	−	0.522339i
$835$	−1375.98	−	1.84529i	−1.64788	−	0.00220993i
$836$	147.425	+	35.5594i	0.176346	+	0.0425351i
$837$	1150.48	+	308.269i	1.37452	+	0.368303i
$838$	1118.41	+	132.975i	1.33461	+	0.158681i
$839$		−	431.185i		−	0.513927i	−0.966421	−	0.256963i	$-0.917278\pi$
$839$		−	431.185i		−	0.513927i	0.966421	−	0.256963i	$-0.0827220\pi$
$840$	444.983	−	30.0887i	0.529742	−	0.0358198i
$841$	−264.561			−0.314579
$842$	74.9898	−	630.714i	0.0890615	−	0.749067i
$843$	103.603	−	386.653i	0.122898	−	0.458663i
$844$	238.736	−	989.773i	0.282863	−	1.17272i
$845$	−335.200	+	334.302i	−0.396686	+	0.395623i
$846$	−186.775	−	74.6308i	−0.220774	−	0.0882160i
$847$	−603.631	−	433.969i	−0.712669	−	0.512360i
$848$	−105.285	+	116.432i	−0.124157	+	0.137302i
$849$	287.739	+	166.126i	0.338916	+	0.195673i
$850$	105.671	−	262.414i	0.124319	−	0.308723i
$851$	−882.250	+	509.367i	−1.03672	+	0.598551i
$852$	−251.544	−	136.924i	−0.295239	−	0.160708i
$853$	−122.098	+	122.098i	−0.143140	+	0.143140i	−0.775045	−	0.631906i	$-0.782273\pi$
$853$	−122.098	+	122.098i	−0.143140	+	0.143140i	0.631906	+	0.775045i	$0.282273\pi$
$854$	−146.571	−	134.279i	−0.171629	−	0.157236i
$855$	−82.8501	+	307.550i	−0.0969007	+	0.359708i
$856$	−130.340	+	1394.08i	−0.152266	+	1.62860i
$857$	−232.617	+	868.138i	−0.271432	+	1.01300i	0.686763	+	0.726881i	$0.259031\pi$
$857$	−232.617	+	868.138i	−0.271432	+	1.01300i	−0.958195	+	0.286116i	$0.907636\pi$
$858$	−63.2489	+	84.6067i	−0.0737166	+	0.0986092i
$859$	453.573	+	261.870i	0.528024	+	0.304855i	0.740212	−	0.672374i	$-0.234725\pi$
$859$	453.573	+	261.870i	0.528024	+	0.304855i	−0.212187	+	0.977229i	$0.568059\pi$
$860$	252.618	+	61.2908i	0.293742	+	0.0712683i
$861$	−38.2284	+	101.097i	−0.0444000	+	0.117418i
$862$	94.1196	+	219.391i	0.109187	+	0.254513i
$863$	300.705	+	1122.25i	0.348442	+	1.30040i	0.888540	+	0.458800i	$0.151721\pi$
$863$	300.705	+	1122.25i	0.348442	+	1.30040i	−0.540098	+	0.841602i	$0.681613\pi$
$864$	151.708	+	773.422i	0.175588	+	0.895165i
$865$	731.807	−	1263.61i	0.846020	−	1.46082i
$866$	−249.079	−	316.300i	−0.287620	−	0.365243i
$867$	−289.451	+	289.451i	−0.333854	+	0.333854i
$868$	−1330.37	+	251.992i	−1.53269	+	0.290313i
$869$			513.966i			0.591445i
$870$	487.004	−	208.154i	0.559775	−	0.239258i
$871$	−472.069	−	817.647i	−0.541985	−	0.938746i
$872$	−147.514	−	866.758i	−0.169167	−	0.993988i
$873$	−291.220	−	1086.85i	−0.333586	−	1.24496i
$874$	348.533	+	139.265i	0.398779	+	0.159342i
$875$	−551.319	−	679.464i	−0.630079	−	0.776531i
$876$	19.5838	−	20.5932i	0.0223559	−	0.0235082i
$877$	−370.492	−	1382.70i	−0.422454	−	1.57662i	−0.769421	−	0.638743i	$-0.779455\pi$
$877$	−370.492	−	1382.70i	−0.422454	−	1.57662i	0.346966	−	0.937878i	$-0.387212\pi$
$878$	844.124	−	1129.17i	0.961417	−	1.28607i
$879$	117.676	+	203.820i	0.133874	+	0.231877i
$880$	−227.959	−	206.690i	−0.259044	−	0.234876i
$881$			1428.72i			1.62170i	0.585253	+	0.810851i	$0.300995\pi$
$881$			1428.72i			1.62170i	−0.585253	+	0.810851i	$0.699005\pi$
$882$	−472.206	+	422.090i	−0.535381	+	0.478561i
$883$	−341.650	+	341.650i	−0.386920	+	0.386920i	−0.873587	−	0.486667i	$-0.838212\pi$
$883$	−341.650	+	341.650i	−0.386920	+	0.386920i	0.486667	+	0.873587i	$0.338212\pi$
$884$	55.2126	+	187.125i	0.0624577	+	0.211679i
$885$	−249.288	+	430.445i	−0.281681	+	0.486379i
$886$	−324.709	+	46.9044i	−0.366489	+	0.0529395i
$887$	237.427	+	886.090i	0.267674	+	0.998975i	0.960593	+	0.277959i	$0.0896578\pi$
$887$	237.427	+	886.090i	0.267674	+	0.998975i	−0.692919	+	0.721016i	$0.743675\pi$
$888$	237.018	−	639.324i	0.266912	−	0.719959i
$889$	4.31278	−	3.52828i	0.00485128	−	0.00396881i
$890$	−218.562	−	1527.53i	−0.245575	−	1.71633i
$891$	−63.0680	−	36.4123i	−0.0707833	−	0.0408668i
$892$	182.417	+	298.390i	0.204504	+	0.334517i
$893$	39.6978	−	148.154i	0.0444544	−	0.165906i
$894$	485.637	+	616.702i	0.543218	+	0.689823i
$895$	−208.819	+	775.163i	−0.233317	+	0.866104i
$896$	−537.018	−	717.236i	−0.599350	−	0.800487i
$897$	−184.863	+	184.863i	−0.206091	+	0.206091i
$898$	−301.926	−	35.8980i	−0.336221	−	0.0399755i
$899$	−1392.49	+	803.953i	−1.54893	+	0.894274i
$900$	446.623	−	467.126i	0.496248	−	0.519029i
$901$	48.0722	+	27.7545i	0.0533543	+	0.0308041i
$902$	68.5302	−	29.3998i	0.0759758	−	0.0325940i
$903$	132.095	−	59.6055i	0.146284	−	0.0660084i
$904$	−1046.05	+	480.213i	−1.15713	+	0.531209i
$905$	−79.9162	+	79.7022i	−0.0883052	+	0.0880687i
$906$	−593.452	+	85.7244i	−0.655024	+	0.0946186i
$907$	288.292	−	1075.92i	0.317852	−	1.18624i	−0.603452	−	0.797399i	$-0.706209\pi$
$907$	288.292	−	1075.92i	0.317852	−	1.18624i	0.921305	−	0.388842i	$-0.127125\pi$
$908$	−297.640	−	162.015i	−0.327798	−	0.178431i
$909$	−55.6123			−0.0611796
$910$	588.990	+	131.340i	0.647241	+	0.144329i
$911$		−	1377.04i		−	1.51157i	−0.654817	−	0.755787i	$-0.727254\pi$
$911$		−	1377.04i		−	1.51157i	0.654817	−	0.755787i	$-0.272746\pi$
$912$	−239.078	+	77.1196i	−0.262147	+	0.0845609i
$913$	−576.759	−	154.542i	−0.631718	−	0.169268i
$914$	525.341	−	75.8858i	0.574771	−	0.0830261i
$915$	113.082	+	0.151651i	0.123587	+	0.000165739i
$916$	711.974	−	748.669i	0.777265	−	0.817325i
$917$	936.103	+	672.993i	1.02083	+	0.733907i
$918$	256.130	−	109.881i	0.279009	−	0.119696i
$919$	284.636	−	493.004i	0.309724	−	0.536457i	−0.668578	−	0.743642i	$-0.733097\pi$
$919$	284.636	−	493.004i	0.309724	−	0.536457i	0.978302	+	0.207185i	$0.0664301\pi$
$920$	−485.248	−	586.943i	−0.527443	−	0.637982i
$921$	138.891	+	240.566i	0.150804	+	0.261201i
$922$	642.361	+	76.3746i	0.696704	+	0.0828358i
$923$	−274.007	−	274.007i	−0.296866	−	0.296866i
$924$	−171.072	−	12.7861i	−0.185142	−	0.0138378i
$925$	−1293.04	+	342.756i	−1.39789	+	0.370547i
$926$	27.1560	+	34.4849i	0.0293262	+	0.0372407i
$927$	−588.620	−	157.720i	−0.634973	−	0.170141i
$928$	−883.109	−	593.475i	−0.951626	−	0.639520i
$929$	428.086	−	741.466i	0.460803	−	0.798133i	−0.538199	−	0.842818i	$-0.680895\pi$
$929$	428.086	−	741.466i	0.460803	−	0.798133i	0.999001	+	0.0446847i	$0.0142283\pi$
$930$	462.029	−	616.321i	0.496806	−	0.662711i
$931$	−362.142	−	319.574i	−0.388981	−	0.343259i
$932$	−389.880	+	9.79471i	−0.418326	+	0.0105093i
$933$	247.983	−	66.4468i	0.265791	−	0.0712184i
$934$	640.098	−	92.4624i	0.685329	−	0.0989962i
$935$	−54.5319	+	94.1602i	−0.0583229	+	0.100706i
$936$	−41.4913	+	443.781i	−0.0443284	+	0.474125i
$937$	−150.947	−	150.947i	−0.161096	−	0.161096i	0.621956	−	0.783052i	$-0.286338\pi$
$937$	−150.947	−	150.947i	−0.161096	−	0.161096i	−0.783052	+	0.621956i	$0.786338\pi$
$938$	707.838	−	1360.09i	0.754624	−	1.44999i
$939$	485.395			0.516928
$940$	−214.769	+	225.233i	−0.228478	+	0.239610i
$941$	616.289	−	355.814i	0.654930	−	0.378124i	−0.135413	−	0.990789i	$-0.543236\pi$
$941$	616.289	−	355.814i	0.654930	−	0.378124i	0.790342	+	0.612666i	$0.209903\pi$
$942$	−8.88231	+	11.8817i	−0.00942921	+	0.0126133i
$943$	178.266	−	47.7662i	0.189041	−	0.0506535i
$944$	998.044	−	50.1782i	1.05725	−	0.0531549i
$945$	86.9712	−	857.652i	0.0920330	−	0.907569i
$946$	−92.8479	−	37.0998i	−0.0981479	−	0.0392175i
$947$	−324.212	+	86.8724i	−0.342357	+	0.0917343i	−0.425901	−	0.904770i	$-0.640043\pi$
$947$	−324.212	+	86.8724i	−0.342357	+	0.0917343i	0.0835439	+	0.996504i	$0.473376\pi$
$948$	−444.067	−	726.383i	−0.468425	−	0.766227i
$949$	33.2997	−	19.2256i	0.0350893	−	0.0202588i
$950$	393.942	+	296.147i	0.414675	+	0.311733i
$951$	338.788			0.356244
$952$	−208.094	+	238.922i	−0.218586	+	0.250969i
$953$	637.030	+	637.030i	0.668447	+	0.668447i	0.957356	−	0.288910i	$-0.0932928\pi$
$953$	637.030	+	637.030i	0.668447	+	0.668447i	−0.288910	+	0.957356i	$0.593293\pi$
$954$	78.4564	+	99.6303i	0.0822394	+	0.104434i
$955$	−355.286	−	1333.09i	−0.372027	−	1.39591i
$956$	623.044	+	150.280i	0.651719	+	0.157197i
$957$	−196.773	+	52.7251i	−0.205614	+	0.0550941i
$958$	320.105	+	746.158i	0.334139	+	0.778870i
$959$	223.459	−	590.944i	0.233012	−	0.616209i
$960$	500.753	+	95.1571i	0.521617	+	0.0991220i
$961$	−688.753	+	1192.96i	−0.716704	+	1.24137i
$962$	552.385	−	738.914i	0.574205	−	0.768102i
$963$	1092.58	+	292.756i	1.13456	+	0.304004i
$964$	−1206.31	+	355.932i	−1.25136	+	0.369224i
$965$	−368.979	+	212.371i	−0.382362	+	0.220074i
$966$	−414.513	−	91.8494i	−0.429102	−	0.0950822i
$967$	739.981	+	739.981i	0.765234	+	0.765234i	0.977263	−	0.212029i	$-0.0680072\pi$
$967$	739.981	+	739.981i	0.765234	+	0.765234i	−0.212029	+	0.977263i	$0.568007\pi$
$968$	−542.252	−	654.106i	−0.560178	−	0.675729i
$969$	44.4154	+	76.9298i	0.0458364	+	0.0793909i
$970$	−1728.57	−	207.872i	−1.78203	−	0.214301i
$971$	−489.851	+	848.447i	−0.504481	+	0.873786i	0.495506	+	0.868605i	$0.334983\pi$
$971$	−489.851	+	848.447i	−0.504481	+	0.873786i	−0.999987	+	0.00518177i	$0.998351\pi$
$972$	1006.99	−	25.2981i	1.03600	−	0.0260269i
$973$	1025.68	+	102.621i	1.05414	+	0.105469i
$974$	495.994	+	198.187i	0.509234	+	0.203478i
$975$	−297.759	+	170.848i	−0.305394	+	0.175229i
$976$	−123.325	−	190.791i	−0.126358	−	0.195482i
$977$	−1177.03	−	315.383i	−1.20473	−	0.322808i	−0.400040	−	0.916498i	$-0.631004\pi$
$977$	−1177.03	−	315.383i	−1.20473	−	0.322808i	−0.804694	+	0.593690i	$0.797671\pi$
$978$	−49.3833	+	415.347i	−0.0504942	+	0.424690i
$979$			593.532i			0.606264i
$980$	334.139	+	921.277i	0.340958	+	0.940079i
$981$	−710.280			−0.724037
$982$	−69.4957	−	8.26281i	−0.0707695	−	0.00841426i
$983$	−83.9937	+	313.469i	−0.0854462	+	0.318890i	−0.995398	−	0.0958237i	$-0.969451\pi$
$983$	−83.9937	+	313.469i	−0.0854462	+	0.318890i	0.909952	+	0.414713i	$0.136118\pi$
$984$	−71.4516	+	100.761i	−0.0726135	+	0.102399i
$985$	227.673	+	0.305326i	0.231140	+	0.000309975i
$986$	−139.606	+	349.386i	−0.141589	+	0.354347i
$987$	−17.2730	+	172.641i	−0.0175005	+	0.174915i
$988$	−339.788	+	8.53629i	−0.343915	+	0.00863997i
$989$	−214.302	−	123.727i	−0.216686	−	0.125104i
$990$	−195.506	+	153.532i	−0.197481	+	0.155082i
$991$	−1320.96	+	762.658i	−1.33296	+	0.769584i	−0.985752	−	0.168204i	$-0.946203\pi$
$991$	−1320.96	+	762.658i	−1.33296	+	0.769584i	−0.347207	+	0.937789i	$0.612870\pi$
$992$	−1543.87	−	105.311i	−1.55632	−	0.106160i
$993$	−112.427	+	112.427i	−0.113220	+	0.113220i
$994$	136.141	−	614.398i	0.136963	−	0.618107i
$995$	−202.576	−	54.5715i	−0.203594	−	0.0548457i
$996$	948.652	−	279.907i	0.952462	−	0.281031i
$997$	8.63734	−	32.2350i	0.00866333	−	0.0323320i	−0.961459	−	0.274949i	$-0.911339\pi$
$997$	8.63734	−	32.2350i	0.00866333	−	0.0323320i	0.970122	+	0.242617i	$0.0780058\pi$
$998$	1022.80	+	764.609i	1.02485	+	0.766141i
$999$	−1141.34	−	658.952i	−1.14248	−	0.659612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.3.x.a.103.25	yes	176
4.3	odd	2	inner	140.3.x.a.103.13	yes	176
5.2	odd	4	inner	140.3.x.a.47.43	yes	176
7.3	odd	6	inner	140.3.x.a.3.37	✓	176
20.7	even	4	inner	140.3.x.a.47.37	yes	176
28.3	even	6	inner	140.3.x.a.3.43	yes	176
35.17	even	12	inner	140.3.x.a.87.13	yes	176
140.87	odd	12	inner	140.3.x.a.87.25	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.3.x.a.3.37	✓	176	7.3	odd	6	inner
140.3.x.a.3.43	yes	176	28.3	even	6	inner
140.3.x.a.47.37	yes	176	20.7	even	4	inner
140.3.x.a.47.43	yes	176	5.2	odd	4	inner
140.3.x.a.87.13	yes	176	35.17	even	12	inner
140.3.x.a.87.25	yes	176	140.87	odd	12	inner
140.3.x.a.103.13	yes	176	4.3	odd	2	inner
140.3.x.a.103.25	yes	176	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	140.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.236130 - 1.98601i) q^{2} +(-0.412261 + 1.53858i) q^{3} +(-3.88849 - 0.937915i) q^{4} +(3.53079 + 3.54027i) q^{5} +(2.95829 + 1.18206i) q^{6} +(-0.696881 + 6.96522i) q^{7} +(-2.78090 + 7.50111i) q^{8} +(5.59696 + 3.23141i) q^{9} +O(q^{10})\)	\(q+(0.236130 - 1.98601i) q^{2} +(-0.412261 + 1.53858i) q^{3} +(-3.88849 - 0.937915i) q^{4} +(3.53079 + 3.54027i) q^{5} +(2.95829 + 1.18206i) q^{6} +(-0.696881 + 6.96522i) q^{7} +(-2.78090 + 7.50111i) q^{8} +(5.59696 + 3.23141i) q^{9} +(7.86475 - 6.17622i) q^{10} +(-3.33107 + 1.92319i) q^{11} +(3.04613 - 5.59608i) q^{12} +(6.09582 - 6.09582i) q^{13} +(13.6685 + 3.02871i) q^{14} +(-6.90260 + 3.97289i) q^{15} +(14.2406 + 7.29413i) q^{16} +(1.46435 - 5.46505i) q^{17} +(7.73922 - 10.3526i) q^{18} +(8.53627 + 4.92842i) q^{19} +(-10.4089 - 17.0779i) q^{20} +(-10.4293 - 3.94370i) q^{21} +(3.03292 + 7.06967i) q^{22} +(4.92763 + 18.3902i) q^{23} +(-10.3946 - 7.37105i) q^{24} +(-0.0670535 + 24.9999i) q^{25} +(-10.6670 - 13.5458i) q^{26} +(-17.4161 + 17.4161i) q^{27} +(9.24260 - 26.4306i) q^{28} -33.2500i q^{29} +(6.26028 + 14.6468i) q^{30} +(-24.1791 - 41.8793i) q^{31} +(17.8489 - 26.5597i) q^{32} +(-1.58572 - 5.91798i) q^{33} +(-10.5079 - 4.19869i) q^{34} +(-27.1193 + 22.1256i) q^{35} +(-18.7329 - 17.8147i) q^{36} +(13.8489 + 51.6848i) q^{37} +(11.8036 - 15.7894i) q^{38} +(6.86584 + 11.8920i) q^{39} +(-36.3747 + 16.6397i) q^{40} -9.69355i q^{41} +(-10.2949 + 19.7814i) q^{42} +(-9.19050 + 9.19050i) q^{43} +(14.7566 - 4.35405i) q^{44} +(8.32163 + 31.2242i) q^{45} +(37.6866 - 5.44386i) q^{46} +(-4.02744 - 15.0306i) q^{47} +(-17.0935 + 18.9033i) q^{48} +(-48.0287 - 9.70787i) q^{49} +(49.6343 + 6.03640i) q^{50} +(7.80472 + 4.50605i) q^{51} +(-29.4209 + 17.9862i) q^{52} +(-2.53927 + 9.47670i) q^{53} +(30.4760 + 38.7009i) q^{54} +(-18.5699 - 5.00250i) q^{55} +(-50.3089 - 24.5970i) q^{56} +(-11.1019 + 11.1019i) q^{57} +(-66.0348 - 7.85132i) q^{58} +(54.0889 - 31.2283i) q^{59} +(30.5669 - 8.97445i) q^{60} +(-12.2964 - 7.09934i) q^{61} +(-88.8823 + 38.1309i) q^{62} +(-26.4079 + 36.7322i) q^{63} +(-48.5332 - 41.7196i) q^{64} +(43.1039 + 0.0578055i) q^{65} +(-12.1276 + 1.75184i) q^{66} +(28.3455 - 105.787i) q^{67} +(-10.8199 + 19.8773i) q^{68} -30.3262 q^{69} +(37.5380 + 59.0838i) q^{70} -44.9500i q^{71} +(-39.8037 + 32.9972i) q^{72} +(4.30831 + 1.15441i) q^{73} +(105.917 - 15.2997i) q^{74} +(-38.4367 - 10.4097i) q^{75} +(-28.5707 - 27.1704i) q^{76} +(-11.0741 - 24.5419i) q^{77} +(25.2389 - 10.8276i) q^{78} +(66.8115 - 115.721i) q^{79} +(24.4574 + 76.1698i) q^{80} +(9.46662 + 16.3967i) q^{81} +(-19.2515 - 2.28894i) q^{82} +(109.770 + 109.770i) q^{83} +(36.8552 + 25.1168i) q^{84} +(24.5181 - 14.1117i) q^{85} +(16.0823 + 20.4226i) q^{86} +(51.1577 + 13.7077i) q^{87} +(-5.16272 - 30.3349i) q^{88} +(77.1545 - 133.635i) q^{89} +(63.9766 - 9.15388i) q^{90} +(38.2107 + 46.7068i) q^{91} +(-1.91261 - 76.1316i) q^{92} +(74.4028 - 19.9362i) q^{93} +(-30.8020 + 4.44936i) q^{94} +(12.6918 + 47.6219i) q^{95} +(33.5058 + 38.4115i) q^{96} +(-123.109 - 123.109i) q^{97} +(-30.6210 + 93.0933i) q^{98} -24.8585 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8}+O(q^{10}) \) 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8	\( 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8} - 6 q^{10} - 6 q^{12} - 28 q^{16} - 12 q^{17} - 36 q^{18} - 32 q^{21} - 24 q^{22} - 4 q^{25} - 12 q^{26} + 114 q^{28} + 28 q^{30} + 58 q^{32} - 156 q^{33} - 144 q^{36} - 4 q^{37} + 192 q^{38} + 54 q^{40} - 218 q^{42} - 12 q^{45} + 68 q^{46} - 332 q^{50} - 264 q^{52} - 4 q^{53} - 300 q^{56} - 24 q^{57} - 146 q^{58} - 434 q^{60} - 24 q^{61} + 92 q^{65} - 660 q^{66} - 72 q^{68} + 488 q^{70} - 80 q^{72} - 12 q^{73} - 156 q^{77} + 688 q^{78} + 588 q^{80} + 288 q^{81} + 798 q^{82} + 272 q^{85} - 72 q^{86} + 588 q^{88} + 524 q^{92} + 164 q^{93} + 1080 q^{96} - 766 q^{98}+O(q^{100}) \) 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8 - 6 * q^10 - 6 * q^12 - 28 * q^16 - 12 * q^17 - 36 * q^18 - 32 * q^21 - 24 * q^22 - 4 * q^25 - 12 * q^26 + 114 * q^28 + 28 * q^30 + 58 * q^32 - 156 * q^33 - 144 * q^36 - 4 * q^37 + 192 * q^38 + 54 * q^40 - 218 * q^42 - 12 * q^45 + 68 * q^46 - 332 * q^50 - 264 * q^52 - 4 * q^53 - 300 * q^56 - 24 * q^57 - 146 * q^58 - 434 * q^60 - 24 * q^61 + 92 * q^65 - 660 * q^66 - 72 * q^68 + 488 * q^70 - 80 * q^72 - 12 * q^73 - 156 * q^77 + 688 * q^78 + 588 * q^80 + 288 * q^81 + 798 * q^82 + 272 * q^85 - 72 * q^86 + 588 * q^88 + 524 * q^92 + 164 * q^93 + 1080 * q^96 - 766 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more