LMFDB - Embedded newform 140.3.x.a.103.13

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			103.13
Character	$\chi$	$=$	140.103
Dual form			140.3.x.a.87.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19750 - 1.60187i) q^{2} +(0.412261 - 1.53858i) q^{3} +(-1.13198 + 3.83648i) q^{4} +(3.53079 + 3.54027i) q^{5} +(-2.95829 + 1.18206i) q^{6} +(0.696881 - 6.96522i) q^{7} +(7.50111 - 2.78090i) q^{8} +(5.59696 + 3.23141i) q^{9} +O(q^{10})$	\(q+(-1.19750 - 1.60187i) q^{2} +(0.412261 - 1.53858i) q^{3} +(-1.13198 + 3.83648i) q^{4} +(3.53079 + 3.54027i) q^{5} +(-2.95829 + 1.18206i) q^{6} +(0.696881 - 6.96522i) q^{7} +(7.50111 - 2.78090i) q^{8} +(5.59696 + 3.23141i) q^{9} +(1.44294 - 9.89535i) q^{10} +(3.33107 - 1.92319i) q^{11} +(5.43607 + 3.32328i) q^{12} +(6.09582 - 6.09582i) q^{13} +(-11.9919 + 7.22455i) q^{14} +(6.90260 - 3.97289i) q^{15} +(-13.4372 - 8.68568i) q^{16} +(1.46435 - 5.46505i) q^{17} +(-1.52607 - 12.8352i) q^{18} +(-8.53627 - 4.92842i) q^{19} +(-17.5790 + 9.53828i) q^{20} +(-10.4293 - 3.94370i) q^{21} +(-7.06967 - 3.03292i) q^{22} +(-4.92763 - 18.3902i) q^{23} +(-1.18622 - 12.6875i) q^{24} +(-0.0670535 + 24.9999i) q^{25} +(-17.0645 - 2.46497i) q^{26} +(17.4161 - 17.4161i) q^{27} +(25.9331 + 10.5581i) q^{28} -33.2500i q^{29} +(-14.6299 - 6.29955i) q^{30} +(24.1791 + 41.8793i) q^{31} +(2.17774 + 31.9258i) 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} +(2.32750 + 19.5758i) q^{38} +(-6.86584 - 11.8920i) q^{39} +(36.3300 + 16.7372i) q^{40} -9.69355i q^{41} +(6.17174 + 21.4289i) q^{42} +(9.19050 - 9.19050i) q^{43} +(3.60759 + 14.9566i) q^{44} +(8.32163 + 31.2242i) q^{45} +(-23.5578 + 29.9157i) q^{46} +(4.02744 + 15.0306i) q^{47} +(-18.9033 + 17.0935i) q^{48} +(-48.0287 - 9.70787i) q^{49} +(40.1269 - 29.8300i) q^{50} +(-7.80472 - 4.50605i) q^{51} +(16.4862 + 30.2869i) q^{52} +(-2.53927 + 9.47670i) q^{53} +(-48.7540 - 7.04255i) q^{54} +(18.5699 + 5.00250i) q^{55} +(-14.1422 - 54.1849i) q^{56} +(-11.1019 + 11.1019i) q^{57} +(-53.2622 + 39.8169i) q^{58} +(-54.0889 + 31.2283i) q^{59} +(7.42827 + 30.9790i) q^{60} +(-12.2964 - 7.09934i) q^{61} +(38.1309 - 88.8823i) q^{62} +(26.4079 - 36.7322i) q^{63} +(48.5332 - 41.7196i) q^{64} +(43.1039 + 0.0578055i) q^{65} +(-7.58094 + 9.62690i) q^{66} +(-28.3455 + 105.787i) q^{67} +(19.3089 + 11.8043i) q^{68} -30.3262 q^{69} +(-67.9178 - 16.9463i) q^{70} +44.9500i q^{71} +(50.9696 + 8.67455i) q^{72} +(4.30831 + 1.15441i) q^{73} +(66.2083 - 84.0767i) q^{74} +(38.4367 + 10.4097i) q^{75} +(28.5707 - 27.1704i) q^{76} +(-11.0741 - 24.5419i) q^{77} +(-10.8276 + 25.2389i) q^{78} +(-66.8115 + 115.721i) q^{79} +(-16.6943 - 78.2387i) q^{80} +(9.46662 + 16.3967i) q^{81} +(-15.5278 + 11.6080i) q^{82} +(-109.770 - 109.770i) q^{83} +(26.9357 - 35.5475i) q^{84} +(24.5181 - 14.1117i) q^{85} +(-25.7276 - 3.71637i) q^{86} +(-51.1577 - 13.7077i) q^{87} +(19.6385 - 23.6895i) q^{88} +(77.1545 - 133.635i) q^{89} +(40.0520 - 50.7211i) q^{90} +(-38.2107 - 46.7068i) q^{91} +(76.1316 + 1.91261i) q^{92} +(74.4028 - 19.9362i) q^{93} +(19.2542 - 24.4506i) q^{94} +(-12.6918 - 47.6219i) q^{95} +(50.0182 + 9.81116i) q^{96} +(-123.109 - 123.109i) q^{97} +(41.9637 + 88.5610i) 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 $

$2$	−1.19750	−	1.60187i	−0.598750	−	0.800936i
$2$	−1.19750	−	1.60187i	−0.598750	−	0.800936i
$3$	0.412261	−	1.53858i	0.137420	−	0.512860i	−0.862556	−	0.505962i	$-0.831138\pi$
$3$	0.412261	−	1.53858i	0.137420	−	0.512860i	0.999976	−	0.00689806i	$-0.00219574\pi$
$4$	−1.13198	+	3.83648i	−0.282996	+	0.959121i
$5$	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
$8$	7.50111	−	2.78090i	0.937638	−	0.347612i
$9$	5.59696	+	3.23141i	0.621884	+	0.359045i
$10$	1.44294	−	9.89535i	0.144294	−	0.989535i
$11$	3.33107	−	1.92319i	0.302825	−	0.174836i	−0.340886	−	0.940104i	$-0.610727\pi$
$11$	3.33107	−	1.92319i	0.302825	−	0.174836i	0.643711	+	0.765269i	$0.277394\pi$
$12$	5.43607	+	3.32328i	0.453005	+	0.276940i
$13$	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	$0.142422\pi$
$14$	−11.9919	+	7.22455i	−0.856565	+	0.516039i
$15$	6.90260	−	3.97289i	0.460173	−	0.264859i
$16$	−13.4372	−	8.68568i	−0.839826	−	0.542855i
$17$	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	$0.0301168\pi$
$18$	−1.52607	−	12.8352i	−0.0847814	−	0.713068i
$19$	−8.53627	−	4.92842i	−0.449277	−	0.259390i	0.258248	−	0.966079i	$-0.416855\pi$
$19$	−8.53627	−	4.92842i	−0.449277	−	0.259390i	−0.707525	+	0.706688i	$0.750188\pi$
$20$	−17.5790	+	9.53828i	−0.878950	+	0.476914i
$21$	−10.4293	−	3.94370i	−0.496631	−	0.187795i
$22$	−7.06967	−	3.03292i	−0.321349	−	0.137860i
$23$	−4.92763	−	18.3902i	−0.214245	−	0.799572i	−0.986431	−	0.164176i	$-0.947503\pi$
$23$	−4.92763	−	18.3902i	−0.214245	−	0.799572i	0.772186	−	0.635396i	$-0.219163\pi$
$24$	−1.18622	−	12.6875i	−0.0494258	−	0.528646i
$25$	−0.0670535	+	24.9999i	−0.00268214	+	0.999996i
$26$	−17.0645	−	2.46497i	−0.656326	−	0.0948067i
$27$	17.4161	−	17.4161i	0.645039	−	0.645039i
$28$	25.9331	+	10.5581i	0.926183	+	0.377075i
$29$		−	33.2500i		−	1.14655i	−0.819363	−	0.573275i	$-0.805673\pi$
$29$		−	33.2500i		−	1.14655i	0.819363	−	0.573275i	$-0.194327\pi$
$30$	−14.6299	−	6.29955i	−0.487664	−	0.209985i
$31$	24.1791	+	41.8793i	0.779969	+	1.35095i	0.931959	+	0.362564i	$0.118099\pi$
$31$	24.1791	+	41.8793i	0.779969	+	1.35095i	−0.151989	+	0.988382i	$0.548568\pi$
$32$	2.17774	+	31.9258i	0.0680543	+	0.997682i
$33$	−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	$0.659392\pi$
$38$	2.32750	+	19.5758i	0.0612499	+	0.515152i
$39$	−6.86584	−	11.8920i	−0.176047	−	0.304923i
$40$	36.3300	+	16.7372i	0.908249	+	0.418430i
$41$		−	9.69355i		−	0.236428i	−0.992988	−	0.118214i	$-0.962283\pi$
$41$		−	9.69355i		−	0.236428i	0.992988	−	0.118214i	$-0.0377169\pi$
$42$	6.17174	+	21.4289i	0.146946	+	0.510212i
$43$	9.19050	−	9.19050i	0.213733	−	0.213733i	−0.592118	−	0.805851i	$-0.701708\pi$
$43$	9.19050	−	9.19050i	0.213733	−	0.213733i	0.805851	+	0.592118i	$0.201708\pi$
$44$	3.60759	+	14.9566i	0.0819906	+	0.339923i
$45$	8.32163	+	31.2242i	0.184925	+	0.693870i
$46$	−23.5578	+	29.9157i	−0.512127	+	0.650341i
$47$	4.02744	+	15.0306i	0.0856902	+	0.319800i	0.995444	−	0.0953480i	$-0.0303964\pi$
$47$	4.02744	+	15.0306i	0.0856902	+	0.319800i	−0.909754	+	0.415148i	$0.863730\pi$
$48$	−18.9033	+	17.0935i	−0.393818	+	0.356114i
$49$	−48.0287	−	9.70787i	−0.980178	−	0.198120i
$50$	40.1269	−	29.8300i	0.802539	−	0.596600i
$51$	−7.80472	−	4.50605i	−0.153034	−	0.0883540i
$52$	16.4862	+	30.2869i	0.317041	+	0.582441i
$53$	−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	$0.112837\pi$
$54$	−48.7540	−	7.04255i	−0.902852	−	0.130418i
$55$	18.5699	+	5.00250i	0.337635	+	0.0909546i
$56$	−14.1422	−	54.1849i	−0.252539	−	0.967587i
$57$	−11.1019	+	11.1019i	−0.194771	+	0.194771i
$58$	−53.2622	+	39.8169i	−0.918313	+	0.686498i
$59$	−54.0889	+	31.2283i	−0.916762	+	0.529293i	−0.882601	−	0.470124i	$-0.844209\pi$
$59$	−54.0889	+	31.2283i	−0.916762	+	0.529293i	−0.0341612	+	0.999416i	$0.510876\pi$
$60$	7.42827	+	30.9790i	0.123805	+	0.516316i
$61$	−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	$0.703797\pi$
$62$	38.1309	−	88.8823i	0.615014	−	1.43359i
$63$	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
$66$	−7.58094	+	9.62690i	−0.114863	+	0.145862i
$67$	−28.3455	+	105.787i	−0.423067	+	1.57891i	0.345040	+	0.938588i	$0.387865\pi$
$67$	−28.3455	+	105.787i	−0.423067	+	1.57891i	−0.768108	+	0.640321i	$0.778801\pi$
$68$	19.3089	+	11.8043i	0.283955	+	0.173593i
$69$	−30.3262			−0.439510
$70$	−67.9178	−	16.9463i	−0.970254	−	0.242090i
$71$			44.9500i			0.633099i	0.948576	+	0.316550i	$0.102524\pi$
$71$			44.9500i			0.633099i	−0.948576	+	0.316550i	$0.897476\pi$
$72$	50.9696	+	8.67455i	0.707911	+	0.120480i
$73$	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	$0.573607\pi$
$74$	66.2083	−	84.0767i	0.894707	−	1.13617i
$75$	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
$78$	−10.8276	+	25.2389i	−0.138815	+	0.323575i
$79$	−66.8115	+	115.721i	−0.845715	+	1.46482i	0.0392841	+	0.999228i	$0.487492\pi$
$79$	−66.8115	+	115.721i	−0.845715	+	1.46482i	−0.884999	+	0.465593i	$0.845841\pi$
$80$	−16.6943	−	78.2387i	−0.208679	−	0.977984i
$81$	9.46662	+	16.3967i	0.116872	+	0.202428i
$82$	−15.5278	+	11.6080i	−0.189364	+	0.141561i
$83$	−109.770	−	109.770i	−1.32253	−	1.32253i	−0.911726	−	0.410799i	$-0.865250\pi$
$83$	−109.770	−	109.770i	−1.32253	−	1.32253i	−0.410799	−	0.911726i	$-0.634750\pi$
$84$	26.9357	−	35.5475i	0.320663	−	0.423184i
$85$	24.5181	−	14.1117i	0.288448	−	0.166020i
$86$	−25.7276	−	3.71637i	−0.299159	−	0.0432136i
$87$	−51.1577	−	13.7077i	−0.588020	−	0.157560i
$88$	19.6385	−	23.6895i	0.223165	−	0.269198i
$89$	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	$-0.167227\pi$
$90$	40.0520	−	50.7211i	0.445022	−	0.563568i
$91$	−38.2107	−	46.7068i	−0.419898	−	0.513262i
$92$	76.1316	+	1.91261i	0.827517	+	0.0207892i
$93$	74.4028	−	19.9362i	0.800030	−	0.214367i
$94$	19.2542	−	24.4506i	0.204832	−	0.260113i
$95$	−12.6918	−	47.6219i	−0.133598	−	0.501283i
$96$	50.0182	+	9.81116i	0.521023	+	0.102200i
$97$	−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	$-0.604571\pi$
$98$	41.9637	+	88.5610i	0.428201	+	0.903684i
$99$	24.8585			0.251096
$100$	−95.8359	−	28.5568i	−0.958359	−	0.285568i
$101$	−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	$0.346897\pi$
$102$	2.12803	+	17.8982i	0.0208631	+	0.175472i
$103$	91.0780	−	24.4043i	0.884253	−	0.236935i	0.212012	−	0.977267i	$-0.431999\pi$
$103$	91.0780	−	24.4043i	0.884253	−	0.236935i	0.672241	+	0.740332i	$0.265332\pi$
$104$	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	−0.938915	−	0.344148i	$-0.888168\pi$
$107$	−169.056	+	45.2985i	−1.57997	+	0.423351i	−0.641051	+	0.767498i	$0.721501\pi$
$108$	47.1017	+	86.5311i	0.436127	+	0.801214i
$109$	−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	$0.501524\pi$
$110$	−14.2242	−	35.7372i	−0.129310	−	0.324883i
$111$	85.2306			0.767843
$112$	−69.8619	+	87.5404i	−0.623767	+	0.781611i
$113$	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	$0.530333\pi$
$114$	31.0785	+	4.48930i	0.272618	+	0.0393798i
$115$	47.7078	−	82.3769i	0.414850	−	0.716321i
$116$	127.563	+	37.6385i	1.09968	+	0.324469i
$117$	53.8162	−	14.4200i	0.459967	−	0.123248i
$118$	114.795	+	49.2477i	0.972841	+	0.417353i
$119$	−37.0448	−	14.0080i	−0.311301	−	0.117715i
$120$	40.7290	−	48.9965i	0.339408	−	0.408304i
$121$	−53.1026	+	91.9765i	−0.438865	+	0.760136i
$122$	3.35274	+	28.1987i	0.0274815	+	0.231137i
$123$	−14.9143	−	3.99627i	−0.121254	−	0.0324900i
$124$	−188.040	+	45.3558i	−1.51645	+	0.365772i
$125$	−88.7432	+	88.0320i	−0.709946	+	0.704256i
$126$	−90.4637	+	1.68477i	−0.717966	+	0.0133712i
$127$	0.562872	+	0.562872i	0.00443206	+	0.00443206i	0.709319	−	0.704887i	$-0.249002\pi$
$127$	0.562872	+	0.562872i	0.00443206	+	0.00443206i	−0.704887	+	0.709319i	$0.749002\pi$
$128$	−124.948	−	27.7847i	−0.976157	−	0.217068i
$129$	−10.3514	−	17.9292i	−0.0802437	−	0.138986i
$130$	−51.5244	−	69.1162i	−0.396342	−	0.531663i
$131$	−82.3509	+	142.636i	−0.628633	+	1.08882i	0.359193	+	0.933263i	$0.383052\pi$
$131$	−82.3509	+	142.636i	−0.628633	+	1.08882i	−0.987826	+	0.155561i	$0.950282\pi$
$132$	24.4992	+	0.615480i	0.185600	+	0.00466273i
$133$	−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
$136$	−4.21346	−	45.0661i	−0.0309813	−	0.331369i
$137$	−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	$0.690179\pi$
$138$	36.3157	+	48.5787i	0.263157	+	0.352020i
$139$			147.258i			1.05941i	0.848183	+	0.529704i	$0.177697\pi$
$139$			147.258i			1.05941i	−0.848183	+	0.529704i	$0.822303\pi$
$140$	54.1858	+	129.089i	0.387042	+	0.922062i
$141$	24.7862			0.175788
$142$	72.0042	−	53.8277i	0.507072	−	0.379068i
$143$	8.58217	−	32.0291i	0.0600151	−	0.223980i
$144$	−47.1406	−	92.0345i	−0.327365	−	0.639129i
$145$	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
$148$	−213.965	−	5.37531i	−1.44571	−	0.0363196i
$149$	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	$0.356798\pi$
$150$	−29.3531	−	74.0363i	−0.195687	−	0.493575i
$151$	163.002	−	94.1095i	1.07949	−	0.623242i	0.148728	−	0.988878i	$-0.452482\pi$
$151$	163.002	−	94.1095i	1.07949	−	0.623242i	0.930758	+	0.365637i	$0.119149\pi$
$152$	−77.7369	−	13.2301i	−0.511427	−	0.0870400i
$153$	25.8557	−	25.8557i	0.168992	−	0.168992i
$154$	−26.0517	+	47.1283i	−0.169167	+	0.306028i
$155$	−62.8931	+	233.468i	−0.405762	+	1.50624i
$156$	53.3954	−	12.8791i	0.342278	−	0.0825586i
$157$	−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	$0.0880541\pi$
$158$	265.377	−	31.5524i	1.67960	−	0.199699i
$159$	13.5338	+	7.81375i	0.0851183	+	0.0491431i
$160$	−105.337	+	120.433i	−0.658356	+	0.752707i
$161$	−131.526	+	21.5063i	−0.816929	+	0.133579i
$162$	14.9291	−	34.7993i	0.0921547	−	0.214811i
$163$	−33.9820	−	126.823i	−0.208478	−	0.778052i	−0.988361	−	0.152126i	$-0.951388\pi$
$163$	−33.9820	−	126.823i	−0.208478	−	0.778052i	0.779883	−	0.625926i	$-0.215279\pi$
$164$	37.1891	+	10.9729i	0.226763	+	0.0669082i
$165$	15.3524	−	26.5090i	0.0930450	−	0.160661i
$166$	−44.3876	+	307.286i	−0.267395	+	1.85112i
$167$	194.593	−	194.593i	1.16523	−	1.16523i	0.181916	−	0.983314i	$-0.441770\pi$
$167$	194.593	−	194.593i	1.16523	−	1.16523i	0.983314	−	0.181916i	$-0.0582298\pi$
$168$	−89.1980	−	0.579403i	−0.530941	−	0.00344883i
$169$			94.6819i			0.560248i
$170$	−51.9656	−	22.3760i	−0.305680	−	0.131624i
$171$	−31.8514	−	55.1683i	−0.186266	−	0.322622i
$172$	24.8557	+	45.6627i	0.144510	+	0.265481i
$173$	−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
$178$	−306.459	+	36.4370i	−1.72168	+	0.204702i
$179$	−80.2797	−	139.049i	−0.448490	−	0.776807i	0.549798	−	0.835298i	$-0.314705\pi$
$179$	−80.2797	−	139.049i	−0.448490	−	0.776807i	−0.998288	+	0.0584903i	$0.981371\pi$
$180$	−129.211	−	3.41949i	−0.717839	−	0.0189972i
$181$			22.5735i			0.124715i	0.998054	+	0.0623577i	$0.0198619\pi$
$181$			22.5735i			0.124715i	−0.998054	+	0.0623577i	$0.980138\pi$
$182$	−29.0610	+	117.140i	−0.159676	+	0.643627i
$183$	−15.9922	+	15.9922i	−0.0873893	+	0.0873893i
$184$	−88.1039	−	124.243i	−0.478825	−	0.675236i
$185$	−134.081	+	231.517i	−0.724761	+	1.25144i
$186$	−121.033	−	95.3102i	−0.650713	−	0.512420i
$187$	−5.63248	−	21.0207i	−0.0301202	−	0.112410i
$188$	−62.2237	−	1.56321i	−0.330977	−	0.00831494i
$189$	−109.170	−	133.444i	−0.577618	−	0.706051i
$190$	−61.0857	+	77.3579i	−0.321504	+	0.407147i
$191$	238.958	+	137.962i	1.25109	+	0.722316i	0.971326	−	0.237753i	$-0.0764109\pi$
$191$	238.958	+	137.962i	1.25109	+	0.722316i	0.279763	+	0.960069i	$0.409744\pi$
$192$	−44.1806	−	91.8716i	−0.230107	−	0.478498i
$193$	−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	$0.154130\pi$
$194$	−49.7816	+	344.627i	−0.256606	+	1.77643i
$195$	17.8590	−	66.2950i	0.0915848	−	0.339975i
$196$	91.6118	−	173.272i	0.467407	−	0.884042i
$197$	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	$0.213131\pi$
$198$	−29.7681	−	39.8201i	−0.150344	−	0.201112i
$199$	36.3381	−	20.9798i	0.182604	−	0.105426i	−0.405912	−	0.913912i	$-0.633046\pi$
$199$	36.3381	−	20.9798i	0.182604	−	0.105426i	0.588515	+	0.808486i	$0.299713\pi$
$200$	69.0192	+	187.713i	0.345096	+	0.938567i
$201$	151.076	+	87.2237i	0.751621	+	0.433949i
$202$	15.8159	+	6.78511i	0.0782968	+	0.0335897i
$203$	−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
$206$	−148.159	−	116.671i	−0.719216	−	0.566365i
$207$	31.8463	−	118.852i	0.153847	−	0.574165i
$208$	−134.857	+	28.9646i	−0.648353	+	0.139253i
$209$	−37.9132			−0.181403
$210$	−54.0731	+	97.5106i	−0.257491	+	0.464336i
$211$		−	254.539i		−	1.20635i	−0.797610	−	0.603174i	$-0.793902\pi$
$211$		−	254.539i		−	1.20635i	0.797610	−	0.603174i	$-0.206098\pi$
$212$	−33.4828	−	20.4694i	−0.157938	−	0.0965535i
$213$	69.1592	+	18.5312i	0.324691	+	0.0870007i
$214$	275.008	+	216.562i	1.28508	+	1.01197i
$215$	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
$218$	202.001	+	86.6594i	0.926611	+	0.397520i
$219$	3.55230	−	6.15276i	0.0162205	−	0.0280948i
$220$	−40.2129	+	65.5805i	−0.182786	+	0.298093i
$221$	−24.3875	−	42.2404i	−0.110351	−	0.191133i
$222$	−102.064	−	136.528i	−0.459746	−	0.614993i
$223$	61.8244	+	61.8244i	0.277240	+	0.277240i	0.832006	−	0.554766i	$-0.187192\pi$
$223$	61.8244	+	61.8244i	0.277240	+	0.277240i	−0.554766	+	0.832006i	$0.687192\pi$
$224$	223.888	+	7.08007i	0.999500	+	0.0316075i
$225$	−81.1602	+	139.707i	−0.360712	+	0.620919i
$226$	41.1389	−	284.796i	0.182031	−	1.26016i
$227$	−81.8329	−	21.9271i	−0.360497	−	0.0965950i	0.0740241	−	0.997256i	$-0.476416\pi$
$227$	−81.8329	−	21.9271i	−0.360497	−	0.0965950i	−0.434522	+	0.900661i	$0.643083\pi$
$228$	−30.0252	−	55.1596i	−0.131689	−	0.241928i
$229$	−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	$0.975948\pi$
$230$	−189.087	+	22.2247i	−0.822119	+	0.0966293i
$231$	−42.3251	+	6.92075i	−0.183226	+	0.0299600i
$232$	−92.4648	−	249.412i	−0.398555	−	1.07505i
$233$	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	$0.349571\pi$
$234$	−87.5439	−	68.9386i	−0.374119	−	0.294609i
$235$	−38.9924	+	67.3281i	−0.165925	+	0.286503i
$236$	−58.5789	−	242.861i	−0.248216	−	1.02907i
$237$	150.502	+	150.502i	0.635030	+	0.635030i
$238$	21.9221	+	76.1157i	0.0921096	+	0.319814i
$239$	160.228			0.670410			0.335205	−	0.942145i	$-0.391194\pi$
$239$	160.228			0.670410			0.335205	+	0.942145i	$0.391194\pi$
$240$	−127.259	−	6.56925i	−0.530246	−	0.0273719i
$241$	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	$0.107117\pi$
$242$	210.925	−	25.0783i	0.871591	−	0.103629i
$243$	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
$248$	297.832	+	246.902i	1.20093	+	0.995572i
$249$	−214.143	+	123.636i	−0.860012	+	0.496528i
$250$	247.286	+	36.7369i	0.989144	+	0.146947i
$251$	−246.177			−0.980785			−0.490393	−	0.871502i	$-0.663147\pi$
$251$	−246.177			−0.980785			−0.490393	+	0.871502i	$0.663147\pi$
$252$	111.029	+	142.894i	0.440592	+	0.567038i
$253$	−51.7822	−	51.7822i	−0.204673	−	0.204673i
$254$	0.227609	−	1.57569i	0.000896099	−	0.00620350i
$255$	−11.6041	−	43.5407i	−0.0455065	−	0.170748i
$256$	105.118	+	233.423i	0.410617	+	0.911808i
$257$	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	$0.338222\pi$
$258$	−16.3244	+	38.0519i	−0.0632730	+	0.147488i
$259$	369.647	−	60.4426i	1.42721	−	0.233369i
$260$	−49.0148	+	165.302i	−0.188518	+	0.635778i
$261$	107.444	−	186.099i	0.411663	−	0.713022i
$262$	327.100	−	38.8911i	1.24847	−	0.148439i
$263$	−204.891	−	54.9005i	−0.779054	−	0.208747i	−0.152687	−	0.988275i	$-0.548793\pi$
$263$	−204.891	−	54.9005i	−0.779054	−	0.208747i	−0.626368	+	0.779528i	$0.715459\pi$
$264$	−28.3519	−	39.9817i	−0.107394	−	0.151446i
$265$	−42.5157	+	24.4705i	−0.160437	+	0.0923415i
$266$	137.972	−	2.56954i	0.518691	−	0.00965993i
$267$	−173.801	−	173.801i	−0.650940	−	0.650940i
$268$	−373.763	−	228.496i	−1.39464	−	0.852598i
$269$	−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	$0.889655\pi$
$270$	−147.208	−	197.468i	−0.545214	−	0.731364i
$271$	51.4065	−	89.0387i	0.189692	−	0.328556i	−0.755456	−	0.655200i	$-0.772584\pi$
$271$	51.4065	−	89.0387i	0.189692	−	0.328556i	0.945148	+	0.326644i	$0.105918\pi$
$272$	−67.1445	+	60.7161i	−0.246855	+	0.223221i
$273$	−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
$276$	34.3288	−	116.346i	0.124380	−	0.421544i
$277$	−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	$0.617648\pi$
$278$	235.888	−	176.341i	0.848517	−	0.634321i
$279$			312.529i			1.12018i
$280$	141.896	−	241.383i	0.506771	−	0.862081i
$281$	−251.305			−0.894324			−0.447162	−	0.894453i	$-0.647565\pi$
$281$	−251.305			−0.894324			−0.447162	+	0.894453i	$0.647565\pi$
$282$	−29.6814	−	39.7042i	−0.105253	−	0.140795i
$283$	−53.9869	+	201.482i	−0.190767	+	0.711950i	0.802556	+	0.596577i	$0.203473\pi$
$283$	−53.9869	+	201.482i	−0.190767	+	0.711950i	−0.993322	+	0.115373i	$0.963194\pi$
$284$	−172.450	−	50.8827i	−0.607219	−	0.179165i
$285$	−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
$288$	−90.9766	+	185.725i	−0.315891	+	0.644877i
$289$	222.559	+	128.494i	0.770100	+	0.444618i
$290$	−329.020	−	47.9777i	−1.13455	−	0.165440i
$291$	−240.166	+	138.660i	−0.825312	+	0.476494i
$292$	−9.30580	+	15.2220i	−0.0318692	+	0.0521301i
$293$	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	$0.168866\pi$
$294$	153.558	−	28.0542i	0.522307	−	0.0954224i
$295$	−301.533	−	81.2291i	−1.02215	−	0.275353i
$296$	247.612	+	349.181i	0.836528	+	1.17966i
$297$	24.5197	−	91.5086i	0.0825577	−	0.308110i
$298$	−58.1826	−	489.355i	−0.195244	−	1.64213i
$299$	−142.141	−	82.0652i	−0.475389	−	0.274466i
$300$	−83.4463	+	135.678i	−0.278154	+	0.452261i
$301$	−57.6092	−	70.4186i	−0.191393	−	0.233949i
$302$	−345.947	−	148.413i	−1.14552	−	0.491433i
$303$	3.54750	+	13.2394i	0.0117079	+	0.0436945i
$304$	71.8971	+	140.368i	0.236504	+	0.461735i
$305$	−18.2825	−	68.5989i	−0.0599425	−	0.224915i
$306$	−72.3798	−	10.4553i	−0.236535	−	0.0341676i
$307$	−123.314	+	123.314i	−0.401674	+	0.401674i	−0.878823	−	0.477149i	$-0.841670\pi$
$307$	−123.314	+	123.314i	−0.401674	+	0.401674i	0.477149	+	0.878823i	$0.341670\pi$
$308$	106.690	−	14.7047i	0.346397	−	0.0477424i
$309$		−	150.192i		−	0.486058i
$310$	449.300	−	178.831i	1.44935	−	0.576874i
$311$	80.5882	+	139.583i	0.259126	+	0.448819i	0.966008	−	0.258512i	$-0.0832322\pi$
$311$	80.5882	+	139.583i	0.259126	+	0.448819i	−0.706882	+	0.707331i	$0.749899\pi$
$312$	−84.5718	−	70.1099i	−0.271064	−	0.224711i
$313$	−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	$-0.192231\pi$
$318$	−3.69012	−	31.0364i	−0.0116042	−	0.0975987i
$319$	−63.9462	−	110.758i	−0.200458	−	0.347204i
$320$	319.059	+	24.5175i	0.997061	+	0.0766173i
$321$			278.782i			0.868479i
$322$	191.952	+	184.933i	0.596125	+	0.574327i
$323$	−39.4342	+	39.4342i	−0.122087	+	0.122087i
$324$	−73.6216	+	17.7578i	−0.227227	+	0.0548079i
$325$	151.986	+	152.804i	0.467650	+	0.470166i
$326$	−162.460	+	206.305i	−0.498343	+	0.632837i
$327$	45.3086	+	169.094i	0.138558	+	0.517107i
$328$	−26.9568	−	72.7123i	−0.0821853	−	0.221684i
$329$	107.498	−	17.5775i	0.326742	−	0.0534270i
$330$	−60.8486	+	7.15195i	−0.184390	+	0.0216726i
$331$	−86.4453	−	49.9092i	−0.261164	−	0.150783i	0.363701	−	0.931516i	$-0.381513\pi$
$331$	−86.4453	−	49.9092i	−0.261164	−	0.150783i	−0.624865	+	0.780732i	$0.714846\pi$
$332$	545.387	−	296.872i	1.64273	−	0.894192i
$333$	−89.5028	+	334.029i	−0.268777	+	1.00309i
$334$	−544.739	−	78.6879i	−1.63096	−	0.235593i
$335$	−474.596	+	273.160i	−1.41671	+	0.815404i
$336$	105.887	+	143.578i	0.315139	+	0.427314i
$337$	−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	$0.497170\pi$
$338$	151.668	−	113.382i	0.448722	−	0.335448i
$339$	198.470	−	114.587i	0.585457	−	0.338014i
$340$	26.3853	+	110.037i	0.0776038	+	0.323640i
$341$	161.084	+	93.0020i	0.472388	+	0.272733i
$342$	−50.2304	+	117.086i	−0.146873	+	0.342357i
$343$	−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
$346$	−361.363	+	458.888i	−1.04440	+	1.32626i
$347$	−29.0666	+	108.478i	−0.0837654	+	0.312617i	−0.995078	−	0.0990994i	$-0.968404\pi$
$347$	−29.0666	+	108.478i	−0.0837654	+	0.312617i	0.911312	+	0.411716i	$0.135070\pi$
$348$	110.499	−	180.749i	0.317526	−	0.519394i
$349$	416.788			1.19424			0.597118	−	0.802153i	$-0.296312\pi$
$349$	416.788			1.19424			0.597118	+	0.802153i	$0.296312\pi$
$350$	−179.809	−	300.281i	−0.513740	−	0.857946i
$351$		−	212.330i		−	0.604930i
$352$	68.6537	+	102.159i	0.195039	+	0.290224i
$353$	−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	$0.613191\pi$
$354$	123.097	−	156.319i	0.347732	−	0.441578i
$355$	−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
$358$	−126.603	+	295.108i	−0.353639	+	0.824325i
$359$	−170.211	+	294.814i	−0.474125	+	0.821209i	−0.999561	−	0.0296242i	$-0.990569\pi$
$359$	−170.211	+	294.814i	−0.474125	+	0.821209i	0.525436	+	0.850833i	$0.323902\pi$
$360$	149.253	+	211.074i	0.414591	+	0.586317i
$361$	−131.921	−	228.495i	−0.365433	−	0.632949i
$362$	36.1598	−	27.0317i	0.0998889	−	0.0746733i
$363$	119.621	+	119.621i	0.329534	+	0.329534i
$364$	222.444	−	93.7234i	0.611110	−	0.257482i
$365$	11.1248	+	19.3285i	0.0304789	+	0.0529549i
$366$	44.7682	+	6.46680i	0.122318	+	0.0176688i
$367$	625.453	+	167.590i	1.70423	+	0.456647i	0.973999	−	0.226551i	$-0.0727451\pi$
$367$	625.453	+	167.590i	1.70423	+	0.456647i	0.730232	+	0.683199i	$0.239412\pi$
$368$	−93.5175	+	289.913i	−0.254124	+	0.787806i
$369$	31.3238	−	54.2544i	0.0848883	−	0.147031i
$370$	531.422	−	62.4617i	1.43628	−	0.168815i
$371$	64.2377	+	24.2907i	0.173148	+	0.0654737i
$372$	−7.73802	+	308.013i	−0.0208011	+	0.827991i
$373$	−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	$0.829834\pi$
$374$	−26.9276	+	34.1948i	−0.0719988	+	0.0914300i
$375$	98.8589	+	172.831i	0.263624	+	0.460882i
$376$	72.0089	+	101.546i	0.191513	+	0.270070i
$377$	−202.686	−	202.686i	−0.537629	−	0.537629i
$378$	−83.0287	+	334.675i	−0.219653	+	0.885383i
$379$	93.4538			0.246580			0.123290	−	0.992371i	$-0.460655\pi$
$379$	93.4538			0.246580			0.123290	+	0.992371i	$0.460655\pi$
$380$	197.068	+	5.21527i	0.518599	+	0.0137244i
$381$	1.09807	−	0.633973i	0.00288208	−	0.00166397i
$382$	−65.1542	−	547.990i	−0.170561	−	1.43453i
$383$	247.189	−	66.2342i	0.645403	−	0.172935i	0.0787534	−	0.996894i	$-0.474906\pi$
$383$	247.189	−	66.2342i	0.645403	−	0.172935i	0.566649	+	0.823959i	$0.308239\pi$
$384$	−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
$388$	611.662	−	332.948i	1.57645	−	0.858113i
$389$	−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	$0.403019\pi$
$390$	−127.582	+	50.7805i	−0.327134	+	0.130206i
$391$	−107.719			−0.275496
$392$	−387.265	+	60.7432i	−0.987921	+	0.154957i
$393$	185.507	+	185.507i	0.472027	+	0.472027i
$394$	−90.1337	−	13.0199i	−0.228766	−	0.0330453i
$395$	−645.581	+	172.055i	−1.63438	+	0.435583i
$396$	−28.1394	+	95.3692i	−0.0710592	+	0.240831i
$397$	−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	$0.651847\pi$
$398$	−77.1219	−	33.0856i	−0.193774	−	0.0831297i
$399$	69.5908	+	85.0642i	0.174413	+	0.213194i
$400$	218.042	−	335.347i	0.545106	−	0.838367i
$401$	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	$0.115447\pi$
$402$	−41.1923	−	346.454i	−0.102468	−	0.861827i
$403$	402.680	+	107.898i	0.999207	+	0.267737i
$404$	−8.07073	−	33.4603i	−0.0199770	−	0.0828225i
$405$	−24.6240	+	91.4076i	−0.0608000	+	0.225698i
$406$	240.216	+	398.731i	0.591665	+	0.982095i
$407$	145.532	+	145.532i	0.357572	+	0.357572i
$408$	−71.0749	−	12.0963i	−0.174203	−	0.0296477i
$409$	−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	$-0.436224\pi$
$410$	−95.9210	−	13.9872i	−0.233954	−	0.0341151i
$411$	−71.8813	+	124.502i	−0.174894	+	0.302925i
$412$	−9.47227	+	377.045i	−0.0229909	+	0.915157i
$413$	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
$416$	207.889	+	181.339i	0.499734	+	0.435911i
$417$	226.568	+	60.7086i	0.543328	+	0.145584i
$418$	45.4011	+	60.7321i	0.108615	+	0.145292i
$419$		−	563.142i		−	1.34401i	−0.740545	−	0.672007i	$-0.765433\pi$
$419$		−	563.142i		−	1.34401i	0.740545	−	0.672007i	$-0.234567\pi$
$420$	220.952	−	30.1510i	0.526076	−	0.0717880i
$421$	317.578			0.754343			0.377171	−	0.926143i	$-0.376897\pi$
$421$	317.578			0.754343			0.377171	+	0.926143i	$0.376897\pi$
$422$	−407.740	+	304.811i	−0.966207	+	0.722301i
$423$	−26.0286	+	97.1400i	−0.0615333	+	0.229645i
$424$	7.30637	+	78.1472i	0.0172320	+	0.184309i
$425$	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
$428$	17.5822	−	699.859i	0.0410798	−	1.63519i
$429$	−45.7412	−	26.4087i	−0.106623	−	0.0615587i
$430$	−77.6819	−	104.205i	−0.180656	−	0.242336i
$431$	103.372	−	59.6818i	0.239842	−	0.138473i	−0.375262	−	0.926919i	$-0.622447\pi$
$431$	103.372	−	59.6818i	0.239842	−	0.138473i	0.615104	+	0.788446i	$0.289114\pi$
$432$	−385.294	+	82.7531i	−0.891884	+	0.191558i
$433$	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	$0.175327\pi$
$434$	−592.512	−	327.531i	−1.36524	−	0.754679i
$435$	−132.098	−	229.511i	−0.303674	−	0.527612i
$436$	−103.079	−	427.355i	−0.236420	−	0.980171i
$437$	−48.5708	+	181.269i	−0.111146	+	0.414803i
$438$	−14.1098	+	1.67761i	−0.0322142	+	0.00383016i
$439$	−610.466	−	352.453i	−1.39058	−	0.802853i	−0.397203	−	0.917731i	$-0.630019\pi$
$439$	−610.466	−	352.453i	−1.39058	−	0.802853i	−0.993380	+	0.114877i	$0.963352\pi$
$440$	153.207	−	14.1168i	0.348197	−	0.0320837i
$441$	−237.445	−	209.535i	−0.538423	−	0.475136i
$442$	−38.4596	+	89.6486i	−0.0870128	+	0.202825i
$443$	42.4566	+	158.450i	0.0958388	+	0.357675i	0.997145	−	0.0755066i	$-0.0240574\pi$
$443$	42.4566	+	158.450i	0.0958388	+	0.357675i	−0.901306	+	0.433182i	$0.857391\pi$
$444$	−96.4797	+	326.986i	−0.217297	+	0.736454i
$445$	745.522	−	198.691i	1.67533	−	0.446496i
$446$	25.0000	−	173.070i	0.0560538	−	0.388049i
$447$	277.526	−	277.526i	0.620863	−	0.620863i
$448$	−256.765	−	367.118i	−0.573136	−	0.819461i
$449$		−	152.026i		−	0.338589i	−0.985566	−	0.169295i	$-0.945851\pi$
$449$		−	152.026i		−	0.338589i	0.985566	−	0.169295i	$-0.0541489\pi$
$450$	320.982	−	37.2908i	0.713293	−	0.0828685i
$451$	−18.6426	−	32.2899i	−0.0413361	−	0.0715962i
$452$	−505.470	+	275.144i	−1.11830	+	0.608725i
$453$	−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	$0.822889\pi$
$458$	512.965	−	60.9899i	1.12001	−	0.133166i
$459$	−69.6763	−	120.683i	−0.151800	−	0.262926i
$460$	262.033	+	276.280i	0.569638	+	0.600608i
$461$			323.443i			0.701611i	0.936448	+	0.350806i	$0.114092\pi$
$461$			323.443i			0.701611i	−0.936448	+	0.350806i	$0.885908\pi$
$462$	61.7705	+	59.5118i	0.133702	+	0.128813i
$463$	15.5188	−	15.5188i	0.0335179	−	0.0335179i	−0.690149	−	0.723667i	$-0.742455\pi$
$463$	15.5188	−	15.5188i	0.0335179	−	0.0335179i	0.723667	+	0.690149i	$0.242455\pi$
$464$	−288.799	+	446.787i	−0.622411	+	0.962904i
$465$	333.280	+	193.016i	0.716731	+	0.415088i
$466$	−153.202	−	120.643i	−0.328760	−	0.258890i
$467$	−83.6945	−	312.352i	−0.179217	−	0.668848i	−0.995795	−	0.0916121i	$-0.970798\pi$
$467$	−83.6945	−	312.352i	−0.179217	−	0.668848i	0.816577	−	0.577236i	$-0.195869\pi$
$468$	−5.59697	+	222.788i	−0.0119593	+	0.476043i
$469$	717.076	+	271.154i	1.52895	+	0.578153i
$470$	154.544	−	18.1647i	0.328818	−	0.0386482i
$471$	6.42364	+	3.70869i	0.0136383	+	0.00787407i
$472$	−318.884	+	384.662i	−0.675602	+	0.814963i
$473$	12.9391	−	48.2893i	0.0273554	−	0.102092i
$474$	60.8586	−	421.311i	0.128394	−	0.888842i
$475$	123.782	−	213.075i	0.260594	−	0.448580i
$476$	95.6758	−	126.265i	0.201000	−	0.265262i
$477$	−44.8353	+	44.8353i	−0.0939942	+	0.0939942i
$478$	−191.873	−	256.664i	−0.401408	−	0.536955i
$479$	351.573	−	202.981i	0.733973	−	0.423759i	−0.0859010	−	0.996304i	$-0.527377\pi$
$479$	351.573	−	202.981i	0.733973	−	0.423759i	0.819874	+	0.572544i	$0.194044\pi$
$480$	141.870	+	211.719i	0.295562	+	0.441082i
$481$	399.482	+	230.641i	0.830524	+	0.479503i
$482$	−577.927	−	247.933i	−1.19902	−	0.514384i
$483$	−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
$486$	−395.695	−	311.600i	−0.814188	−	0.641153i
$487$	69.1207	−	257.962i	0.141932	−	0.529696i	−0.857941	−	0.513748i	$-0.828257\pi$
$487$	69.1207	−	257.962i	0.141932	−	0.529696i	0.999873	−	0.0159483i	$-0.00507672\pi$
$488$	−111.979	−	19.0578i	−0.229466	−	0.0390529i
$489$	−209.136			−0.427681
$490$	−165.365	+	461.253i	−0.337480	+	0.941333i
$491$			34.9926i			0.0712680i	0.999365	+	0.0356340i	$0.0113451\pi$
$491$			34.9926i			0.0712680i	−0.999365	+	0.0356340i	$0.988655\pi$
$492$	32.2144	−	52.6948i	0.0654764	−	0.107103i
$493$	−181.713	−	48.6898i	−0.368586	−	0.0987622i
$494$	133.519	+	105.143i	0.270280	+	0.212839i
$495$	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
$498$	454.485	+	194.976i	0.912620	+	0.391518i
$499$	319.252	−	552.961i	0.639784	−	1.10814i	−0.345697	−	0.938346i	$-0.612357\pi$
$499$	319.252	−	552.961i	0.639784	−	1.10814i	0.985480	−	0.169791i	$-0.0543093\pi$
$500$	−237.278	−	440.113i	−0.474555	−	0.880226i
$501$	−219.174	−	379.621i	−0.437473	−	0.757726i
$502$	294.797	+	394.344i	0.587245	+	0.785546i
$503$	263.613	+	263.613i	0.524082	+	0.524082i	0.918802	−	0.394719i	$-0.129158\pi$
$503$	263.613	+	263.613i	0.524082	+	0.524082i	−0.394719	+	0.918802i	$0.629158\pi$
$504$	95.9399	−	348.970i	0.190357	−	0.692400i
$505$	−41.5438	−	11.1914i	−0.0822650	−	0.0221611i
$506$	−20.9392	+	144.958i	−0.0413818	+	0.286477i
$507$	145.676	+	39.0337i	0.287329	+	0.0769895i
$508$	−2.79661	+	1.52229i	−0.00550514	+	0.00299663i
$509$	−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	$0.260735\pi$
$510$	−55.8507	+	70.7284i	−0.109511	+	0.138683i
$511$	11.0431	−	29.2038i	0.0216107	−	0.0571504i
$512$	248.035	−	447.909i	0.484443	−	0.874823i
$513$	−234.502	+	62.8345i	−0.457118	+	0.122484i
$514$	−197.028	−	155.155i	−0.383323	−	0.301857i
$515$	407.975	+	236.275i	0.792185	+	0.458786i
$516$	80.5028	−	19.4175i	0.156013	−	0.0376309i
$517$	42.3225	+	42.3225i	0.0818617	+	0.0818617i
$518$	−539.474	−	519.747i	−1.04146	−	1.00337i
$519$	−465.185			−0.896310
$520$	323.488	−	119.434i	0.622092	−	0.229681i
$521$	−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	$0.424863\pi$
$522$	−426.771	+	50.7416i	−0.817568	+	0.0972062i
$523$	26.8371	−	7.19097i	0.0513137	−	0.0137495i	−0.233071	−	0.972460i	$-0.574877\pi$
$523$	26.8371	−	7.19097i	0.0513137	−	0.0137495i	0.284385	+	0.958710i	$0.408211\pi$
$524$	−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
$528$	−30.0940	+	93.2942i	−0.0569963	+	0.176694i
$529$	144.211	−	83.2601i	0.272610	−	0.157392i
$530$	90.1112	+	38.8013i	0.170021	+	0.0732100i
$531$	−403.645			−0.760160
$532$	−169.337	−	217.936i	−0.318303	−	0.409654i
$533$	−59.0902	−	59.0902i	−0.110863	−	0.110863i
$534$	−70.2801	+	486.534i	−0.131611	+	0.911112i
$535$	−757.272	−	438.566i	−1.41546	−	0.819750i
$536$	81.5599	+	872.345i	0.152164	+	1.62751i
$537$	−247.033	+	66.1924i	−0.460025	+	0.123263i
$538$	−74.6705	+	174.055i	−0.138793	+	0.323523i
$539$	−178.657	+	60.0310i	−0.331460	+	0.111375i
$540$	−140.038	+	472.276i	−0.259329	+	0.874585i
$541$	−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	$0.244312\pi$
$542$	−204.188	+	24.2773i	−0.376730	+	0.0447920i
$543$	34.7311	+	9.30617i	0.0639615	+	0.0171384i
$544$	177.665	+	34.8493i	0.326590	+	0.0640612i
$545$	−530.598	−	142.936i	−0.973574	−	0.262268i
$546$	168.249	+	93.0050i	0.308148	+	0.170339i
$547$	643.986	+	643.986i	1.17731	+	1.17731i	0.980428	+	0.196878i	$0.0630804\pi$
$547$	643.986	+	643.986i	1.17731	+	1.17731i	0.196878	+	0.980428i	$0.436920\pi$
$548$	188.304	−	308.019i	0.343621	−	0.562079i
$549$	−45.8817	−	79.4694i	−0.0835732	−	0.144753i
$550$	76.2968	−	176.538i	0.138721	−	0.320978i
$551$	−163.870	+	283.831i	−0.297404	+	0.515119i
$552$	−227.480	+	84.3341i	−0.412102	+	0.152779i
$553$	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
$556$	−564.952	−	166.693i	−1.01610	−	0.299808i
$557$	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	$0.360545\pi$
$558$	500.632	−	374.254i	0.897190	−	0.670706i
$559$		−	112.047i		−	0.200443i
$560$	−556.584	+	61.7566i	−0.993901	+	0.110280i
$561$	−34.6641			−0.0617898
$562$	300.938	+	402.559i	0.535477	+	0.716296i
$563$	−44.8183	+	167.264i	−0.0796062	+	0.297094i	−0.994238	−	0.107193i	$-0.965814\pi$
$563$	−44.8183	+	167.264i	−0.0796062	+	0.297094i	0.914632	+	0.404287i	$0.132480\pi$
$564$	−28.0575	+	95.0917i	−0.0497474	+	0.168602i
$565$	−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
$568$	125.001	+	337.175i	0.220073	+	0.593618i
$569$	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	$0.587363\pi$
$570$	93.8381	+	125.877i	0.164628	+	0.220837i
$571$	492.711	−	284.467i	0.862892	−	0.498191i	−0.00208773	−	0.999998i	$-0.500665\pi$
$571$	492.711	−	284.467i	0.862892	−	0.498191i	0.864980	+	0.501807i	$0.167331\pi$
$572$	113.164	+	69.1818i	0.197839	+	0.120947i
$573$	310.779	−	310.779i	0.542372	−	0.542372i
$574$	70.0315	+	116.244i	0.122006	+	0.202516i
$575$	460.083	−	121.957i	0.800144	−	0.212099i
$576$	406.451	−	76.6726i	0.705645	−	0.133112i
$577$	−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	$0.0951673\pi$
$578$	−60.6828	−	510.383i	−0.104988	−	0.883016i
$579$	117.455	+	67.8128i	0.202859	+	0.117121i
$580$	317.148	+	584.501i	0.546806	+	1.00776i
$581$	−841.066	+	688.073i	−1.44762	+	1.18429i
$582$	509.714	+	218.670i	0.875797	+	0.375721i
$583$	9.76703	+	36.4511i	0.0167531	+	0.0625233i
$584$	35.5274	−	3.32163i	0.0608345	−	0.00568772i
$585$	241.064	+	139.610i	0.412076	+	0.238649i
$586$	−292.473	−	42.2479i	−0.499100	−	0.0720953i
$587$	330.283	−	330.283i	0.562662	−	0.562662i	−0.367400	−	0.930063i	$-0.619752\pi$
$587$	330.283	−	330.283i	0.562662	−	0.562662i	0.930063	+	0.367400i	$0.119752\pi$
$588$	−228.825	−	212.386i	−0.389159	−	0.361200i
$589$		−	476.658i		−	0.809266i
$590$	230.968	+	580.289i	0.391470	+	0.983541i
$591$	−36.2650	−	62.8128i	−0.0613621	−	0.106282i
$592$	262.827	−	814.787i	0.443964	−	1.37633i
$593$	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
$598$	38.7562	+	325.965i	0.0648096	+	0.545092i
$599$	169.733	+	293.986i	0.283360	+	0.490795i	0.972210	−	0.234109i	$-0.0752174\pi$
$599$	169.733	+	293.986i	0.283360	+	0.490795i	−0.688850	+	0.724904i	$0.741884\pi$
$600$	317.266	−	28.8046i	0.528777	−	0.0480077i
$601$			52.8008i			0.0878549i	0.999035	+	0.0439274i	$0.0139870\pi$
$601$			52.8008i			0.0878549i	−0.999035	+	0.0439274i	$0.986013\pi$
$602$	−43.8145	+	176.609i	−0.0727815	+	0.293370i
$603$	−500.489	+	500.489i	−0.829998	+	0.829998i
$604$	176.533	+	731.887i	0.292274	+	1.21173i
$605$	−513.116	+	136.752i	−0.848126	+	0.226036i
$606$	16.9597	−	21.5369i	0.0279864	−	0.0355394i
$607$	−30.9598	−	115.543i	−0.0510045	−	0.190352i	0.935723	−	0.352735i	$-0.114748\pi$
$607$	−30.9598	−	115.543i	−0.0510045	−	0.190352i	−0.986728	+	0.162384i	$0.948082\pi$
$608$	138.754	−	283.260i	0.228214	−	0.465888i
$609$	−131.128	+	346.773i	−0.215317	+	0.569413i
$610$	−87.9934	+	111.433i	−0.144251	+	0.182678i
$611$	116.175	+	67.0734i	0.190138	+	0.109776i
$612$	69.9268	+	128.463i	0.114259	+	0.209907i
$613$	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	$0.0743111\pi$
$614$	345.202	+	49.8646i	0.562218	+	0.0812127i
$615$	−38.5114	−	66.9107i	−0.0626201	−	0.108798i
$616$	−151.317	−	153.295i	−0.245644	−	0.248856i
$617$	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	$-0.00248338\pi$
$618$	−240.588	+	179.855i	−0.389301	+	0.291027i
$619$	227.656	−	131.437i	0.367780	−	0.212338i	−0.304708	−	0.952446i	$-0.598559\pi$
$619$	227.656	−	131.437i	0.367780	−	0.212338i	0.672488	+	0.740108i	$0.265226\pi$
$620$	−824.501	−	505.570i	−1.32984	−	0.815436i
$621$	−406.104	−	234.464i	−0.653952	−	0.377559i
$622$	127.089	−	296.242i	0.204324	−	0.476274i
$623$	−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
$626$	−377.062	+	478.824i	−0.602336	+	0.764895i
$627$	−15.6302	+	58.3325i	−0.0249285	+	0.0930343i
$628$	−15.8921	−	9.71549i	−0.0253059	−	0.0154705i
$629$	302.740			0.481303
$630$	−325.373	−	314.317i	−0.516465	−	0.498917i
$631$			472.941i			0.749510i	0.927124	+	0.374755i	$0.122273\pi$
$631$			472.941i			0.749510i	−0.927124	+	0.374755i	$0.877727\pi$
$632$	−179.352	+	1053.83i	−0.283785	+	1.66745i
$633$	−391.629	−	104.937i	−0.618688	−	0.165777i
$634$	−263.175	+	334.201i	−0.415103	+	0.527132i
$635$	−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
$638$	−100.845	+	235.066i	−0.158064	+	0.368443i
$639$	−145.252	+	251.583i	−0.227311	+	0.393714i
$640$	−342.800	−	540.452i	−0.535625	−	0.844456i
$641$	−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	$-0.496414\pi$
$642$	446.572	−	333.841i	0.695596	−	0.520002i
$643$	642.845	+	642.845i	0.999759	+	0.999759i	1.00000		0.000241112i	$-7.67484e-5\pi$
$643$	642.845	+	642.845i	0.999759	+	0.999759i	−0.000241112		1.00000i	$0.500077\pi$
$644$	66.3764	−	528.941i	0.103069	−	0.821336i
$645$	26.9256	−	99.9512i	0.0417450	−	0.154963i
$646$	110.391	+	15.9460i	0.170884	+	0.0246842i
$647$	−498.113	−	133.469i	−0.769880	−	0.206289i	−0.147562	−	0.989053i	$-0.547143\pi$
$647$	−498.113	−	133.469i	−0.769880	−	0.206289i	−0.622319	+	0.782764i	$0.713809\pi$
$648$	116.608	+	96.6674i	0.179950	+	0.149178i
$649$	−120.116	+	208.047i	−0.185079	+	0.320566i
$650$	62.7684	−	426.445i	0.0965667	−	0.656069i
$651$	−87.0100	−	532.125i	−0.133656	−	0.817397i
$652$	525.020	+	13.1898i	0.805245	+	0.0202297i
$653$	−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	$0.449736\pi$
$654$	216.610	−	275.069i	0.331208	−	0.420594i
$655$	−795.734	+	212.073i	−1.21486	+	0.323775i
$656$	−84.1951	+	130.254i	−0.128346	+	0.198558i
$657$	20.3831	+	20.3831i	0.0310244	+	0.0310244i
$658$	−156.886	−	151.149i	−0.238429	−	0.229710i
$659$	542.902			0.823826			0.411913	−	0.911223i	$-0.364861\pi$
$659$	542.902			0.823826			0.411913	+	0.911223i	$0.364861\pi$
$660$	84.3227	+	88.9071i	0.127762	+	0.134708i
$661$	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	$0.112707\pi$
$662$	23.5701	+	198.241i	0.0356044	+	0.299457i
$663$	−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
$668$	526.278	+	966.831i	0.787841	+	1.44735i
$669$	120.610	−	69.6340i	0.180284	−	0.104087i
$670$	1005.90	+	433.133i	1.50134	+	0.646467i
$671$	−54.6136			−0.0813914
$672$	103.194	−	341.551i	0.153562	−	0.508260i
$673$	−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	$-0.560141\pi$
$674$	934.965	+	135.056i	1.38719	+	0.200380i
$675$	434.232	+	436.568i	0.643307	+	0.646767i
$676$	−363.245	−	107.178i	−0.537345	−	0.158548i
$677$	−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	$0.630376\pi$
$678$	−421.221	−	180.706i	−0.621270	−	0.266528i
$679$	−943.273	+	771.688i	−1.38921	+	1.13651i
$680$	144.670	−	174.036i	0.212749	−	0.255935i
$681$	−67.4731	+	116.867i	−0.0990794	+	0.171611i
$682$	−43.9212	−	369.406i	−0.0644006	−	0.541651i
$683$	76.1113	+	20.3939i	0.111437	+	0.0298594i	0.314106	−	0.949388i	$-0.398295\pi$
$683$	76.1113	+	20.3939i	0.111437	+	0.0298594i	−0.202670	+	0.979247i	$0.564962\pi$
$684$	247.708	−	59.7478i	0.362146	−	0.0873507i
$685$	−225.112	−	391.116i	−0.328631	−	0.570973i
$686$	646.091	−	230.570i	0.941824	−	0.336108i
$687$	290.916	+	290.916i	0.423459	+	0.423459i
$688$	−203.321	+	43.6690i	−0.295524	+	0.0634724i
$689$	42.2893	+	73.2472i	0.0613778	+	0.106309i
$690$	−43.7589	+	300.088i	−0.0634186	+	0.434911i
$691$	−20.0504	+	34.7283i	−0.0290165	+	0.0502580i	−0.880169	−	0.474660i	$-0.842571\pi$
$691$	−20.0504	+	34.7283i	−0.0290165	+	0.0502580i	0.851153	+	0.524918i	$0.175904\pi$
$692$	1167.81	+	29.3382i	1.68759	+	0.0423963i
$693$	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
$696$	−421.859	+	39.4418i	−0.606120	+	0.0566692i
$697$	−52.9757	−	14.1948i	−0.0760053	−	0.0203656i
$698$	−499.104	−	667.641i	−0.715049	−	0.956506i
$699$		−	155.304i		−	0.222181i
$700$	−265.690	+	647.618i	−0.379558	+	0.925168i
$701$	1039.18			1.48243			0.741216	−	0.671266i	$-0.234249\pi$
$701$	1039.18			1.48243			0.741216	+	0.671266i	$0.234249\pi$
$702$	−340.126	+	254.266i	−0.484510	+	0.362202i
$703$	136.506	−	509.448i	0.194177	−	0.724678i
$704$	81.4326	−	232.310i	0.115671	−	0.329986i
$705$	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
$708$	−397.811	−	9.99398i	−0.561880	−	0.0141158i
$709$	−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	$0.907330\pi$
$710$	444.796	+	64.8601i	0.626474	+	0.0913523i
$711$	−747.882	+	431.790i	−1.05187	+	0.607300i
$712$	207.117	−	1216.97i	0.290895	−	1.70923i
$713$	651.023	−	651.023i	0.913075	−	0.913075i
$714$	126.148	−	2.34933i	0.176677	−	0.00329038i
$715$	143.693	−	82.7047i	0.200970	−	0.115671i
$716$	624.333	−	150.591i	0.871973	−	0.210323i
$717$	66.0558	−	246.523i	0.0921280	−	0.343826i
$718$	676.082	−	80.3839i	0.941618	−	0.111955i
$719$	897.643	+	518.254i	1.24846	+	0.720799i	0.970802	−	0.239882i	$-0.0771086\pi$
$719$	897.643	+	518.254i	1.24846	+	0.720799i	0.277658	+	0.960680i	$0.410442\pi$
$720$	159.384	−	491.845i	0.221366	−	0.683118i
$721$	−106.511	−	651.386i	−0.147726	−	0.903448i
$722$	−208.043	+	484.944i	−0.288148	+	0.671667i
$723$	−129.628	−	483.779i	−0.179292	−	0.669127i
$724$	−86.6028	−	25.5528i	−0.119617	−	0.0352939i
$725$	831.246	+	2.22953i	1.14655	+	0.00307521i
$726$	48.3713	−	334.864i	0.0666271	−	0.461245i
$727$	−721.945	+	721.945i	−0.993047	+	0.993047i	−0.999976	−	0.00692882i	$-0.997794\pi$
$727$	−721.945	+	721.945i	−0.993047	+	0.993047i	0.00692882	+	0.999976i	$0.497794\pi$
$728$	−416.510	−	244.093i	−0.572129	−	0.335292i
$729$		−	230.727i		−	0.316497i
$730$	17.6399	−	40.9665i	0.0241642	−	0.0561184i
$731$	−36.7684	−	63.6847i	−0.0502987	−	0.0871199i
$732$	−43.2510	−	79.4569i	−0.0590861	−	0.108548i
$733$	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
$738$	−124.419	+	14.7930i	−0.168589	+	0.0200447i
$739$	142.841	+	247.407i	0.193289	+	0.334786i	0.946338	−	0.323178i	$-0.104751\pi$
$739$	142.841	+	247.407i	0.193289	+	0.334786i	−0.753049	+	0.657964i	$0.771418\pi$
$740$	−736.434	−	776.472i	−0.995181	−	1.04929i
$741$			135.351i			0.182660i
$742$	−38.0141	−	131.989i	−0.0512319	−	0.177882i
$743$	669.758	−	669.758i	0.901424	−	0.901424i	−0.0941353	−	0.995559i	$-0.530009\pi$
$743$	669.758	−	669.758i	0.901424	−	0.901424i	0.995559	+	0.0941353i	$0.0300086\pi$
$744$	502.663	−	356.450i	0.675622	−	0.479100i
$745$	317.270	+	1190.45i	0.425865	+	1.59792i
$746$	1128.84	+	888.932i	1.51319	+	1.19160i
$747$	−259.666	−	969.086i	−0.347611	−	1.29730i
$748$	87.0215	+	2.18619i	0.116339	+	0.00292271i
$749$	197.702	+	1209.08i	0.263955	+	1.61426i
$750$	158.469	−	365.324i	0.211292	−	0.487099i
$751$	−773.228	−	446.424i	−1.02960	−	0.594439i	−0.112729	−	0.993626i	$-0.535959\pi$
$751$	−773.228	−	446.424i	−1.02960	−	0.594439i	−0.916870	+	0.399187i	$0.869292\pi$
$752$	76.4335	−	236.951i	0.101640	−	0.315094i
$753$	−101.489	+	378.763i	−0.134780	+	0.503006i
$754$	−81.9603	+	567.393i	−0.108701	+	0.752511i
$755$	908.700	+	244.792i	1.20358	+	0.324228i
$756$	635.533	−	267.772i	0.840652	−	0.354196i
$757$	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	$0.112569\pi$
$758$	−111.911	−	149.701i	−0.147640	−	0.197495i
$759$	−101.019	+	58.3232i	−0.133095	+	0.0768422i
$760$	−227.634	−	321.922i	−0.299519	−	0.423582i
$761$	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	$0.471133\pi$
$762$	−2.33049	−	0.999790i	−0.00305838	−	0.00131206i
$763$	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
$766$	−402.108	−	316.650i	−0.524945	−	0.413381i
$767$	−139.355	+	520.079i	−0.181688	+	0.678069i
$768$	402.476	−	65.5011i	0.524057	−	0.0852878i
$769$	96.1772			0.125068			0.0625340	−	0.998043i	$-0.480082\pi$
$769$	96.1772			0.125068			0.0625340	+	0.998043i	$0.480082\pi$
$770$	−258.830	+	74.1699i	−0.336143	+	0.0963245i
$771$		−	199.732i		−	0.259056i
$772$	−290.585	−	177.646i	−0.376406	−	0.230112i
$773$	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	$0.556572\pi$
$774$	−131.987	−	103.937i	−0.170526	−	0.134285i
$775$	−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
$778$	310.559	+	133.231i	0.399176	+	0.171249i
$779$	−47.7738	+	82.7467i	−0.0613271	+	0.106222i
$780$	234.124	+	143.561i	0.300159	+	0.184052i
$781$	86.4477	+	149.732i	0.110688	+	0.191718i
$782$	128.993	+	172.552i	0.164953	+	0.220655i
$783$	−579.083	−	579.083i	−0.739570	−	0.739570i
$784$	561.053	+	547.609i	0.715629	+	0.698481i
$785$	−20.1795	+	11.6146i	−0.0257064	+	0.0147956i
$786$	75.0135	−	519.302i	0.0954371	−	0.660690i
$787$	−1193.80	−	319.877i	−1.51690	−	0.406451i	−0.598177	−	0.801364i	$-0.704108\pi$
$787$	−1193.80	−	319.877i	−1.51690	−	0.406451i	−0.918718	+	0.394913i	$0.870775\pi$
$788$	87.0790	+	159.974i	0.110506	+	0.203012i
$789$	−168.938	+	292.608i	−0.214116	+	0.370860i
$790$	1048.69	+	828.101i	1.32746	+	1.04823i
$791$	779.509	−	637.713i	0.985472	−	0.806212i
$792$	186.466	−	69.1289i	0.235437	−	0.0872840i
$793$	−118.233	+	31.6805i	−0.149096	+	0.0399501i
$794$	840.177	+	661.618i	1.05816	+	0.833273i
$795$	20.1222	+	75.5021i	0.0253110	+	0.0949712i
$796$	39.3546	+	163.159i	0.0494404	+	0.204974i
$797$	−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	$0.964475\pi$
$798$	52.9270	−	213.340i	0.0663245	−	0.267343i
$799$	88.0406			0.110188
$800$	−798.288	+	52.3025i	−0.997861	+	0.0653781i
$801$	863.661	−	498.635i	1.07823	−	0.622515i
$802$	−255.194	+	30.3418i	−0.318197	+	0.0378326i
$803$	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
$808$	−43.9344	+	52.9970i	−0.0543742	+	0.0655903i
$809$	−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	$0.445833\pi$
$810$	175.910	−	70.0161i	0.217173	−	0.0864396i
$811$	281.861			0.347548			0.173774	−	0.984786i	$-0.444404\pi$
$811$	281.861			0.347548			0.173774	+	0.984786i	$0.444404\pi$
$812$	351.057	−	862.275i	0.432336	−	1.06192i
$813$	−115.800	−	115.800i	−0.142436	−	0.142436i
$814$	58.8487	−	407.397i	0.0722957	−	0.500488i
$815$	329.003	−	568.089i	0.403685	−	0.697042i
$816$	65.7355	+	128.338i	0.0805583	+	0.157277i
$817$	−123.747	+	33.1580i	−0.151465	+	0.0405850i
$818$	−483.229	+	1126.40i	−0.590745	+	1.37701i
$819$	−62.9351	−	384.891i	−0.0768438	−	0.469952i
$820$	92.4598	+	170.403i	0.112756	+	0.207808i
$821$	−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	$0.193272\pi$
$822$	285.514	−	33.9467i	0.347341	−	0.0412977i
$823$	−523.143	−	140.176i	−0.635654	−	0.170323i	−0.0734197	−	0.997301i	$-0.523391\pi$
$823$	−523.143	−	140.176i	−0.635654	−	0.170323i	−0.562234	+	0.826978i	$0.690058\pi$
$824$	615.320	−	436.338i	0.746748	−	0.529536i
$825$	148.055	−	39.2460i	0.179461	−	0.0475709i
$826$	423.020	−	765.255i	0.512130	−	0.926458i
$827$	−577.230	−	577.230i	−0.697981	−	0.697981i	0.265994	−	0.963975i	$-0.414300\pi$
$827$	−577.230	−	577.230i	−0.697981	−	0.697981i	−0.963975	+	0.265994i	$0.914300\pi$
$828$	419.925	+	256.717i	0.507156	+	0.310044i
$829$	−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	$-0.424590\pi$
$830$	−1244.60	+	927.818i	−1.49952	+	1.11785i
$831$	−47.4722	+	82.2243i	−0.0571266	+	0.0989462i
$832$	41.5344	−	550.165i	0.0499211	−	0.661256i
$833$	−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
$836$	42.9172	−	145.453i	0.0513363	−	0.173987i
$837$	1150.48	+	308.269i	1.37452	+	0.368303i
$838$	−902.080	+	674.362i	−1.07647	+	0.804728i
$839$			431.185i			0.513927i	0.966421	+	0.256963i	$0.0827220\pi$
$839$			431.185i			0.513927i	−0.966421	+	0.256963i	$0.917278\pi$
$840$	−312.888	−	317.831i	−0.372486	−	0.378370i
$841$	−264.561			−0.314579
$842$	−380.300	−	508.720i	−0.451663	−	0.604180i
$843$	−103.603	+	386.653i	−0.122898	+	0.458663i
$844$	976.537	+	288.135i	1.15703	+	0.341392i
$845$	−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
$848$	116.432	−	105.285i	0.137302	−	0.124157i
$849$	287.739	+	166.126i	0.338916	+	0.195673i
$850$	−104.262	−	262.977i	−0.122661	−	0.309385i
$851$	882.250	−	509.367i	1.03672	−	0.598551i
$852$	−149.382	+	244.351i	−0.175331	+	0.286797i
$853$	−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	$0.282273\pi$
$854$	198.747	−	3.70140i	0.232725	−	0.00433419i
$855$	82.8501	−	307.550i	0.0969007	−	0.359708i
$856$	−1142.14	+	809.918i	−1.33428	+	0.946166i
$857$	−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	$0.907636\pi$
$858$	12.4718	+	104.896i	0.0145359	+	0.122256i
$859$	−453.573	−	261.870i	−0.528024	−	0.304855i	0.212187	−	0.977229i	$-0.431941\pi$
$859$	−453.573	−	261.870i	−0.528024	−	0.304855i	−0.740212	+	0.672374i	$0.765275\pi$
$860$	−73.8982	+	249.221i	−0.0859281	+	0.289792i
$861$	−38.2284	+	101.097i	−0.0444000	+	0.117418i
$862$	−219.391	−	94.1196i	−0.254513	−	0.109187i
$863$	−300.705	−	1122.25i	−0.348442	−	1.30040i	−0.888540	−	0.458800i	$-0.848279\pi$
$863$	−300.705	−	1122.25i	−0.348442	−	1.30040i	0.540098	−	0.841602i	$-0.318387\pi$
$864$	593.949	+	518.094i	0.687441	+	0.599646i
$865$	731.807	−	1263.61i	0.846020	−	1.46082i
$866$	−398.463	−	57.5582i	−0.460119	−	0.0664645i
$867$	289.451	−	289.451i	0.333854	−	0.333854i
$868$	184.872	+	1341.35i	0.212986	+	1.54533i
$869$			513.966i			0.591445i
$870$	−209.460	+	486.444i	−0.240758	+	0.559132i
$871$	472.069	+	817.647i	0.541985	+	0.938746i
$872$	−561.130	+	676.877i	−0.643497	+	0.776235i
$873$	−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	$-0.387212\pi$
$878$	166.449	+	1399.95i	0.189578	+	1.59448i
$879$	−117.676	−	203.820i	−0.133874	−	0.231877i
$880$	−206.078	−	228.512i	−0.234180	−	0.259673i
$881$			1428.72i			1.62170i	0.585253	+	0.810851i	$0.300995\pi$
$881$			1428.72i			1.62170i	−0.585253	+	0.810851i	$0.699005\pi$
$882$	−51.3076	+	631.274i	−0.0581719	+	0.715730i
$883$	341.650	−	341.650i	0.386920	−	0.386920i	−0.486667	−	0.873587i	$-0.661788\pi$
$883$	341.650	−	341.650i	0.386920	−	0.386920i	0.873587	+	0.486667i	$0.161788\pi$
$884$	189.661	−	45.7468i	0.214549	−	0.0517498i
$885$	−249.288	+	430.445i	−0.281681	+	0.486379i
$886$	202.975	−	257.754i	0.229091	−	0.290919i
$887$	−237.427	−	886.090i	−0.267674	−	0.998975i	−0.960593	−	0.277959i	$-0.910342\pi$
$887$	−237.427	−	886.090i	−0.267674	−	0.998975i	0.692919	−	0.721016i	$-0.256325\pi$
$888$	639.324	−	237.018i	0.719959	−	0.266912i
$889$	4.31278	−	3.52828i	0.00485128	−	0.00396881i
$890$	−1211.04	−	956.298i	−1.36072	−	1.07449i
$891$	63.0680	+	36.4123i	0.0707833	+	0.0408668i
$892$	−307.173	+	167.204i	−0.344364	+	0.187449i
$893$	39.6978	−	148.154i	0.0444544	−	0.165906i
$894$	−776.898	−	112.223i	−0.869013	−	0.125529i
$895$	208.819	−	775.163i	0.233317	−	0.866104i
$896$	−280.600	+	850.929i	−0.313170	+	0.949697i
$897$	−184.863	+	184.863i	−0.206091	+	0.206091i
$898$	−243.527	+	182.052i	−0.271188	+	0.202730i
$899$	1392.49	−	803.953i	1.54893	−	0.894274i
$900$	−444.111	−	469.516i	−0.493457	−	0.521684i
$901$	48.0722	+	27.7545i	0.0533543	+	0.0308041i
$902$	−29.3998	+	68.5302i	−0.0325940	+	0.0759758i
$903$	−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
$906$	−370.965	+	471.082i	−0.409454	+	0.519958i
$907$	−288.292	+	1075.92i	−0.317852	+	1.18624i	0.603452	+	0.797399i	$0.293791\pi$
$907$	−288.292	+	1075.92i	−0.317852	+	1.18624i	−0.921305	+	0.388842i	$0.872875\pi$
$908$	176.756	−	289.130i	0.194666	−	0.318425i
$909$	−55.6123			−0.0611796
$910$	−517.316	+	310.713i	−0.568479	+	0.341443i
$911$			1377.04i			1.51157i	0.654817	+	0.755787i	$0.272746\pi$
$911$			1377.04i			1.51157i	−0.654817	+	0.755787i	$0.727254\pi$
$912$	245.607	−	52.7513i	0.269306	−	0.0578413i
$913$	−576.759	−	154.542i	−0.631718	−	0.169268i
$914$	328.390	−	417.016i	0.359288	−	0.456254i
$915$	−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
$918$	−109.881	+	256.130i	−0.119696	+	0.279009i
$919$	−284.636	+	493.004i	−0.309724	+	0.536457i	−0.978302	−	0.207185i	$-0.933570\pi$
$919$	−284.636	+	493.004i	−0.309724	+	0.536457i	0.668578	+	0.743642i	$0.266903\pi$
$920$	128.779	−	750.589i	0.139977	−	0.815857i
$921$	138.891	+	240.566i	0.150804	+	0.261201i
$922$	518.114	−	387.323i	0.561945	−	0.420090i
$923$	274.007	+	274.007i	0.296866	+	0.296866i
$924$	21.3600	−	170.214i	0.0231169	−	0.184214i
$925$	−1293.04	+	342.756i	−1.39789	+	0.370547i
$926$	−43.4428	−	6.27534i	−0.0469145	−	0.00677683i
$927$	588.620	+	157.720i	0.634973	+	0.170141i
$928$	1061.53	−	72.4097i	1.14389	−	0.0780277i
$929$	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	$0.0142283\pi$
$930$	−89.9167	−	765.008i	−0.0966846	−	0.822590i
$931$	362.142	+	319.574i	0.388981	+	0.343259i
$932$	−9.79471	+	389.880i	−0.0105093	+	0.418326i
$933$	247.983	−	66.4468i	0.265791	−	0.0712184i
$934$	−400.124	+	508.109i	−0.428398	+	0.544014i
$935$	54.5319	−	94.1602i	0.0583229	−	0.100706i
$936$	363.580	−	257.823i	0.388440	−	0.275452i
$937$	−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	$0.786338\pi$
$938$	−424.345	−	1473.37i	−0.452394	−	1.57076i
$939$	−485.395			−0.516928
$940$	−214.165	−	225.808i	−0.227835	−	0.240221i
$941$	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	$0.209903\pi$
$942$	−1.75147	−	14.7310i	−0.00185931	−	0.0156380i
$943$	−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	−0.0835439	−	0.996504i	$-0.526624\pi$
$947$	324.212	−	86.8724i	0.342357	−	0.0917343i	0.425901	+	0.904770i	$0.359957\pi$
$948$	−747.765	+	407.033i	−0.788781	+	0.429359i
$949$	33.2997	−	19.2256i	0.0350893	−	0.0202588i
$950$	−489.549	+	56.8746i	−0.515315	+	0.0598680i
$951$	−338.788			−0.356244
$952$	−316.832	−	2.05804i	−0.332807	−	0.00216181i
$953$	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	$0.593293\pi$
$954$	125.511	+	18.1301i	0.131562	+	0.0190043i
$955$	355.286	+	1333.09i	0.372027	+	1.39591i
$956$	−181.375	+	614.712i	−0.189723	+	0.643004i
$957$	−196.773	+	52.7251i	−0.205614	+	0.0550941i
$958$	−746.158	−	320.105i	−0.778870	−	0.334139i
$959$	−223.459	+	590.944i	−0.233012	+	0.616209i
$960$	169.258	−	480.791i	0.176310	−	0.500824i
$961$	−688.753	+	1192.96i	−0.716704	+	1.24137i
$962$	−108.923	−	916.111i	−0.113225	−	0.952299i
$963$	−1092.58	−	292.756i	−1.13456	−	0.304004i
$964$	294.910	+	1222.66i	0.305924	+	1.26832i
$965$	−368.979	+	212.371i	−0.382362	+	0.220074i
$966$	363.669	−	219.093i	0.376469	−	0.226805i
$967$	−739.981	−	739.981i	−0.765234	−	0.765234i	0.212029	−	0.977263i	$-0.431993\pi$
$967$	−739.981	−	739.981i	−0.765234	−	0.765234i	−0.977263	+	0.212029i	$0.931993\pi$
$968$	−142.551	+	837.598i	−0.147264	+	0.865288i
$969$	44.4154	+	76.9298i	0.0458364	+	0.0793909i
$970$	−1395.84	+	1040.57i	−1.43901	+	1.07275i
$971$	489.851	−	848.447i	0.504481	−	0.873786i	−0.495506	−	0.868605i	$-0.665017\pi$
$971$	489.851	−	848.447i	0.504481	−	0.873786i	0.999987	−	0.00518177i	$-0.00164942\pi$
$972$	−25.2981	+	1006.99i	−0.0260269	+	1.03600i
$973$	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
$976$	103.567	+	202.198i	0.106114	+	0.207170i
$977$	−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	$0.797671\pi$
$978$	250.441	+	335.009i	0.256074	+	0.342545i
$979$		−	593.532i		−	0.606264i
$980$	936.893	−	287.457i	0.956013	−	0.293323i
$981$	−710.280			−0.724037
$982$	56.0536	−	41.9036i	0.0570811	−	0.0426717i
$983$	83.9937	−	313.469i	0.0854462	−	0.318890i	−0.909952	−	0.414713i	$-0.863882\pi$
$983$	83.9937	−	313.469i	0.0854462	−	0.318890i	0.995398	+	0.0958237i	$0.0305485\pi$
$984$	−122.987	+	11.4987i	−0.124987	+	0.0116856i
$985$	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
$988$	8.53629	−	339.788i	0.00863997	−	0.343915i
$989$	−214.302	−	123.727i	−0.216686	−	0.125104i
$990$	35.8693	−	245.983i	0.0362316	−	0.248468i
$991$	1320.96	−	762.658i	1.33296	−	0.769584i	0.347207	−	0.937789i	$-0.387130\pi$
$991$	1320.96	−	762.658i	1.33296	−	0.769584i	0.985752	+	0.168204i	$0.0537969\pi$
$992$	−1284.38	+	863.138i	−1.29473	+	0.870099i
$993$	−112.427	+	112.427i	−0.113220	+	0.113220i
$994$	−324.744	−	539.037i	−0.326704	−	0.542290i
$995$	202.576	+	54.5715i	0.203594	+	0.0548457i
$996$	−231.919	−	961.510i	−0.232851	−	0.965371i
$997$	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	$0.0780058\pi$
$998$	−1268.08	+	150.770i	−1.27062	+	0.151072i
$999$	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.103.13	yes	176
4.3	odd	2	inner	140.3.x.a.103.25	yes	176
5.2	odd	4	inner	140.3.x.a.47.37	yes	176
7.3	odd	6	inner	140.3.x.a.3.43	yes	176
20.7	even	4	inner	140.3.x.a.47.43	yes	176
28.3	even	6	inner	140.3.x.a.3.37	✓	176
35.17	even	12	inner	140.3.x.a.87.25	yes	176
140.87	odd	12	inner	140.3.x.a.87.13	yes	176

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.19750 - 1.60187i) q^{2} +(0.412261 - 1.53858i) q^{3} +(-1.13198 + 3.83648i) q^{4} +(3.53079 + 3.54027i) q^{5} +(-2.95829 + 1.18206i) q^{6} +(0.696881 - 6.96522i) q^{7} +(7.50111 - 2.78090i) q^{8} +(5.59696 + 3.23141i) q^{9} +O(q^{10})\)	\(q+(-1.19750 - 1.60187i) q^{2} +(0.412261 - 1.53858i) q^{3} +(-1.13198 + 3.83648i) q^{4} +(3.53079 + 3.54027i) q^{5} +(-2.95829 + 1.18206i) q^{6} +(0.696881 - 6.96522i) q^{7} +(7.50111 - 2.78090i) q^{8} +(5.59696 + 3.23141i) q^{9} +(1.44294 - 9.89535i) q^{10} +(3.33107 - 1.92319i) q^{11} +(5.43607 + 3.32328i) q^{12} +(6.09582 - 6.09582i) q^{13} +(-11.9919 + 7.22455i) q^{14} +(6.90260 - 3.97289i) q^{15} +(-13.4372 - 8.68568i) q^{16} +(1.46435 - 5.46505i) q^{17} +(-1.52607 - 12.8352i) q^{18} +(-8.53627 - 4.92842i) q^{19} +(-17.5790 + 9.53828i) q^{20} +(-10.4293 - 3.94370i) q^{21} +(-7.06967 - 3.03292i) q^{22} +(-4.92763 - 18.3902i) q^{23} +(-1.18622 - 12.6875i) q^{24} +(-0.0670535 + 24.9999i) q^{25} +(-17.0645 - 2.46497i) q^{26} +(17.4161 - 17.4161i) q^{27} +(25.9331 + 10.5581i) q^{28} -33.2500i q^{29} +(-14.6299 - 6.29955i) q^{30} +(24.1791 + 41.8793i) q^{31} +(2.17774 + 31.9258i) 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} +(2.32750 + 19.5758i) q^{38} +(-6.86584 - 11.8920i) q^{39} +(36.3300 + 16.7372i) q^{40} -9.69355i q^{41} +(6.17174 + 21.4289i) q^{42} +(9.19050 - 9.19050i) q^{43} +(3.60759 + 14.9566i) q^{44} +(8.32163 + 31.2242i) q^{45} +(-23.5578 + 29.9157i) q^{46} +(4.02744 + 15.0306i) q^{47} +(-18.9033 + 17.0935i) q^{48} +(-48.0287 - 9.70787i) q^{49} +(40.1269 - 29.8300i) q^{50} +(-7.80472 - 4.50605i) q^{51} +(16.4862 + 30.2869i) q^{52} +(-2.53927 + 9.47670i) q^{53} +(-48.7540 - 7.04255i) q^{54} +(18.5699 + 5.00250i) q^{55} +(-14.1422 - 54.1849i) q^{56} +(-11.1019 + 11.1019i) q^{57} +(-53.2622 + 39.8169i) q^{58} +(-54.0889 + 31.2283i) q^{59} +(7.42827 + 30.9790i) q^{60} +(-12.2964 - 7.09934i) q^{61} +(38.1309 - 88.8823i) q^{62} +(26.4079 - 36.7322i) q^{63} +(48.5332 - 41.7196i) q^{64} +(43.1039 + 0.0578055i) q^{65} +(-7.58094 + 9.62690i) q^{66} +(-28.3455 + 105.787i) q^{67} +(19.3089 + 11.8043i) q^{68} -30.3262 q^{69} +(-67.9178 - 16.9463i) q^{70} +44.9500i q^{71} +(50.9696 + 8.67455i) q^{72} +(4.30831 + 1.15441i) q^{73} +(66.2083 - 84.0767i) q^{74} +(38.4367 + 10.4097i) q^{75} +(28.5707 - 27.1704i) q^{76} +(-11.0741 - 24.5419i) q^{77} +(-10.8276 + 25.2389i) q^{78} +(-66.8115 + 115.721i) q^{79} +(-16.6943 - 78.2387i) q^{80} +(9.46662 + 16.3967i) q^{81} +(-15.5278 + 11.6080i) q^{82} +(-109.770 - 109.770i) q^{83} +(26.9357 - 35.5475i) q^{84} +(24.5181 - 14.1117i) q^{85} +(-25.7276 - 3.71637i) q^{86} +(-51.1577 - 13.7077i) q^{87} +(19.6385 - 23.6895i) q^{88} +(77.1545 - 133.635i) q^{89} +(40.0520 - 50.7211i) q^{90} +(-38.2107 - 46.7068i) q^{91} +(76.1316 + 1.91261i) q^{92} +(74.4028 - 19.9362i) q^{93} +(19.2542 - 24.4506i) q^{94} +(-12.6918 - 47.6219i) q^{95} +(50.0182 + 9.81116i) q^{96} +(-123.109 - 123.109i) q^{97} +(41.9637 + 88.5610i) 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

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