LMFDB - Embedded newform 140.3.x.a.103.29

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			103.29
Character	$\chi$	$=$	140.103
Dual form			140.3.x.a.87.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.861255 + 1.80506i) q^{2} +(-1.33089 + 4.96696i) q^{3} +(-2.51648 + 3.10923i) q^{4} +(4.98997 - 0.316518i) q^{5} +(-10.1119 + 1.87547i) q^{6} +(4.17892 + 5.61575i) q^{7} +(-7.77968 - 1.86456i) q^{8} +(-15.1051 - 8.72096i) q^{9} +O(q^{10})$	\(q+(0.861255 + 1.80506i) q^{2} +(-1.33089 + 4.96696i) q^{3} +(-2.51648 + 3.10923i) q^{4} +(4.98997 - 0.316518i) q^{5} +(-10.1119 + 1.87547i) q^{6} +(4.17892 + 5.61575i) q^{7} +(-7.77968 - 1.86456i) q^{8} +(-15.1051 - 8.72096i) q^{9} +(4.86897 + 8.73459i) q^{10} +(7.11059 - 4.10530i) q^{11} +(-12.0943 - 16.6373i) q^{12} +(13.5515 - 13.5515i) q^{13} +(-6.53765 + 12.3798i) q^{14} +(-5.06898 + 25.2062i) q^{15} +(-3.33465 - 15.6486i) q^{16} +(-0.501070 + 1.87002i) q^{17} +(2.73247 - 34.7767i) q^{18} +(-20.9442 - 12.0921i) q^{19} +(-11.5730 + 16.3115i) q^{20} +(-33.4549 + 13.2825i) q^{21} +(13.5343 + 9.29933i) q^{22} +(0.290099 + 1.08266i) q^{23} +(19.6151 - 36.1598i) q^{24} +(24.7996 - 3.15884i) q^{25} +(36.1326 + 12.7900i) q^{26} +(30.6953 - 30.6953i) q^{27} +(-27.9768 - 1.13870i) q^{28} +41.0549i q^{29} +(-49.8644 + 12.5592i) q^{30} +(9.66176 + 16.7347i) q^{31} +(25.3748 - 19.4967i) q^{32} +(10.9274 + 40.7817i) q^{33} +(-3.80704 + 0.706101i) q^{34} +(22.6302 + 26.6997i) q^{35} +(65.1273 - 25.0193i) q^{36} +(6.15098 + 22.9558i) q^{37} +(3.78874 - 48.2199i) q^{38} +(49.2741 + 85.3453i) q^{39} +(-39.4106 - 6.84167i) q^{40} -37.5431i q^{41} +(-52.7889 - 48.9484i) q^{42} +(1.24558 - 1.24558i) q^{43} +(-5.12933 + 32.4394i) q^{44} +(-78.1346 - 38.7363i) q^{45} +(-1.70442 + 1.45610i) q^{46} +(-18.5185 - 69.1119i) q^{47} +(82.1642 + 4.26359i) q^{48} +(-14.0733 + 46.9355i) q^{49} +(27.0607 + 42.0443i) q^{50} +(-8.62142 - 4.97758i) q^{51} +(8.03267 + 76.2368i) q^{52} +(-3.32775 + 12.4193i) q^{53} +(81.8434 + 28.9704i) q^{54} +(34.1822 - 22.7360i) q^{55} +(-22.0398 - 51.4806i) q^{56} +(87.9356 - 87.9356i) q^{57} +(-74.1065 + 35.3587i) q^{58} +(-24.9083 + 14.3808i) q^{59} +(-65.6160 - 79.1916i) q^{60} +(-50.5877 - 29.2069i) q^{61} +(-21.8858 + 31.8528i) q^{62} +(-14.1484 - 121.271i) q^{63} +(57.0469 + 29.0113i) q^{64} +(63.3323 - 71.9109i) q^{65} +(-64.2021 + 54.8481i) q^{66} +(-11.5741 + 43.1952i) q^{67} +(-4.55339 - 6.26381i) q^{68} -5.76364 q^{69} +(-28.7043 + 63.8441i) q^{70} -41.0340i q^{71} +(101.252 + 96.0107i) q^{72} +(59.3322 + 15.8980i) q^{73} +(-36.1390 + 30.8737i) q^{74} +(-17.3158 + 127.383i) q^{75} +(90.3029 - 34.6907i) q^{76} +(52.7689 + 22.7756i) q^{77} +(-111.616 + 162.447i) q^{78} +(25.2837 - 43.7926i) q^{79} +(-21.5929 - 77.0308i) q^{80} +(33.1216 + 57.3683i) q^{81} +(67.7675 - 32.3342i) q^{82} +(-50.9762 - 50.9762i) q^{83} +(42.8900 - 137.444i) q^{84} +(-1.90843 + 9.48993i) q^{85} +(3.32111 + 1.17559i) q^{86} +(-203.918 - 54.6396i) q^{87} +(-62.9727 + 18.6798i) q^{88} +(42.4612 - 73.5450i) q^{89} +(2.62752 - 174.399i) q^{90} +(132.732 + 19.4712i) q^{91} +(-4.09628 - 1.82252i) q^{92} +(-95.9790 + 25.7175i) q^{93} +(108.802 - 92.9499i) q^{94} +(-108.338 - 53.7102i) q^{95} +(63.0683 + 151.983i) q^{96} +(-15.7389 - 15.7389i) q^{97} +(-96.8421 + 15.0203i) q^{98} -143.209 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 $

$2$	0.861255	+	1.80506i	0.430627	+	0.902530i
$2$	0.861255	+	1.80506i	0.430627	+	0.902530i
$3$	−1.33089	+	4.96696i	−0.443631	+	1.65565i	0.275897	+	0.961187i	$0.411025\pi$
$3$	−1.33089	+	4.96696i	−0.443631	+	1.65565i	−0.719527	+	0.694464i	$0.755641\pi$
$4$	−2.51648	+	3.10923i	−0.629120	+	0.777308i
$5$	4.98997	−	0.316518i	0.997994	−	0.0633037i
$5$	4.98997	−	0.316518i	0.997994	−	0.0633037i
$6$	−10.1119	+	1.87547i	−1.68531	+	0.312579i
$7$	4.17892	+	5.61575i	0.596988	+	0.802250i
$7$	4.17892	+	5.61575i	0.596988	+	0.802250i
$8$	−7.77968	−	1.86456i	−0.972460	−	0.233070i
$9$	−15.1051	−	8.72096i	−1.67835	−	0.968995i
$10$	4.86897	+	8.73459i	0.486897	+	0.873459i
$11$	7.11059	−	4.10530i	0.646417	−	0.373209i	−0.140665	−	0.990057i	$-0.544924\pi$
$11$	7.11059	−	4.10530i	0.646417	−	0.373209i	0.787082	+	0.616848i	$0.211591\pi$
$12$	−12.0943	−	16.6373i	−1.00785	−	1.38644i
$13$	13.5515	−	13.5515i	1.04242	−	1.04242i	0.0433636	−	0.999059i	$-0.486193\pi$
$13$	13.5515	−	13.5515i	1.04242	−	1.04242i	0.999059	−	0.0433636i	$-0.0138074\pi$
$14$	−6.53765	+	12.3798i	−0.466975	+	0.884270i
$15$	−5.06898	+	25.2062i	−0.337932	+	1.68041i
$16$	−3.33465	−	15.6486i	−0.208416	−	0.978040i
$17$	−0.501070	+	1.87002i	−0.0294747	+	0.110001i	−0.979096	−	0.203399i	$-0.934801\pi$
$17$	−0.501070	+	1.87002i	−0.0294747	+	0.110001i	0.949621	+	0.313400i	$0.101468\pi$
$18$	2.73247	−	34.7767i	0.151804	−	1.93204i
$19$	−20.9442	−	12.0921i	−1.10233	−	0.636428i	−0.165495	−	0.986211i	$-0.552922\pi$
$19$	−20.9442	−	12.0921i	−1.10233	−	0.636428i	−0.936831	+	0.349782i	$0.886256\pi$
$20$	−11.5730	+	16.3115i	−0.578652	+	0.815575i
$21$	−33.4549	+	13.2825i	−1.59309	+	0.632502i
$22$	13.5343	+	9.29933i	0.615197	+	0.422697i
$23$	0.290099	+	1.08266i	0.0126130	+	0.0470724i	0.971946	−	0.235206i	$-0.0755765\pi$
$23$	0.290099	+	1.08266i	0.0126130	+	0.0470724i	−0.959333	+	0.282278i	$0.908910\pi$
$24$	19.6151	−	36.1598i	0.817295	−	1.50666i
$25$	24.7996	−	3.15884i	0.991985	−	0.126353i
$26$	36.1326	+	12.7900i	1.38971	+	0.491922i
$27$	30.6953	−	30.6953i	1.13686	−	1.13686i
$28$	−27.9768	−	1.13870i	−0.999173	−	0.0406679i
$29$			41.0549i			1.41569i	0.706370	+	0.707843i	$0.250331\pi$
$29$			41.0549i			1.41569i	−0.706370	+	0.707843i	$0.749669\pi$
$30$	−49.8644	+	12.5592i	−1.66215	+	0.418639i
$31$	9.66176	+	16.7347i	0.311670	+	0.539827i	0.978724	−	0.205182i	$-0.0657785\pi$
$31$	9.66176	+	16.7347i	0.311670	+	0.539827i	−0.667054	+	0.745009i	$0.732445\pi$
$32$	25.3748	−	19.4967i	0.792961	−	0.609272i
$33$	10.9274	+	40.7817i	0.331134	+	1.23581i
$34$	−3.80704	+	0.706101i	−0.111972	+	0.0207677i
$35$	22.6302	+	26.6997i	0.646576	+	0.762849i
$36$	65.1273	−	25.0193i	1.80909	−	0.694980i
$37$	6.15098	+	22.9558i	0.166243	+	0.620427i	0.997878	+	0.0651049i	$0.0207382\pi$
$37$	6.15098	+	22.9558i	0.166243	+	0.620427i	−0.831636	+	0.555322i	$0.812595\pi$
$38$	3.78874	−	48.2199i	0.0997037	−	1.26895i
$39$	49.2741	+	85.3453i	1.26344	+	2.18834i
$40$	−39.4106	−	6.84167i	−0.985264	−	0.171042i
$41$		−	37.5431i		−	0.915685i	−0.889033	−	0.457843i	$-0.848622\pi$
$41$		−	37.5431i		−	0.915685i	0.889033	−	0.457843i	$-0.151378\pi$
$42$	−52.7889	−	48.9484i	−1.25688	−	1.16544i
$43$	1.24558	−	1.24558i	0.0289670	−	0.0289670i	−0.692475	−	0.721442i	$-0.743480\pi$
$43$	1.24558	−	1.24558i	0.0289670	−	0.0289670i	0.721442	+	0.692475i	$0.243480\pi$
$44$	−5.12933	+	32.4394i	−0.116576	+	0.737259i
$45$	−78.1346	−	38.7363i	−1.73632	−	0.860806i
$46$	−1.70442	+	1.45610i	−0.0370527	+	0.0316543i
$47$	−18.5185	−	69.1119i	−0.394010	−	1.47047i	−0.823460	−	0.567375i	$-0.807959\pi$
$47$	−18.5185	−	69.1119i	−0.394010	−	1.47047i	0.429450	−	0.903091i	$-0.358708\pi$
$48$	82.1642	+	4.26359i	1.71175	+	0.0888248i
$49$	−14.0733	+	46.9355i	−0.287210	+	0.957868i
$50$	27.0607	+	42.0443i	0.541214	+	0.840885i
$51$	−8.62142	−	4.97758i	−0.169048	−	0.0975996i
$52$	8.03267	+	76.2368i	0.154475	+	1.46609i
$53$	−3.32775	+	12.4193i	−0.0627878	+	0.234327i	−0.990188	−	0.139744i	$-0.955372\pi$
$53$	−3.32775	+	12.4193i	−0.0627878	+	0.234327i	0.927400	+	0.374072i	$0.122039\pi$
$54$	81.8434	+	28.9704i	1.51562	+	0.536489i
$55$	34.1822	−	22.7360i	0.621495	−	0.413381i
$56$	−22.0398	−	51.4806i	−0.393567	−	0.919296i
$57$	87.9356	−	87.9356i	1.54273	−	1.54273i
$58$	−74.1065	+	35.3587i	−1.27770	+	0.609633i
$59$	−24.9083	+	14.3808i	−0.422175	+	0.243743i	−0.696007	−	0.718035i	$-0.745042\pi$
$59$	−24.9083	+	14.3808i	−0.422175	+	0.243743i	0.273832	+	0.961777i	$0.411709\pi$
$60$	−65.6160	−	79.1916i	−1.09360	−	1.31986i
$61$	−50.5877	−	29.2069i	−0.829307	−	0.478801i	0.0243081	−	0.999705i	$-0.492262\pi$
$61$	−50.5877	−	29.2069i	−0.829307	−	0.478801i	−0.853615	+	0.520904i	$0.825595\pi$
$62$	−21.8858	+	31.8528i	−0.352997	+	0.513756i
$63$	−14.1484	−	121.271i	−0.224578	−	1.92493i
$64$	57.0469	+	29.0113i	0.891357	+	0.453302i
$65$	63.3323	−	71.9109i	0.974343	−	1.10632i
$66$	−64.2021	+	54.8481i	−0.972759	+	0.831031i
$67$	−11.5741	+	43.1952i	−0.172748	+	0.644704i	0.824176	+	0.566333i	$0.191638\pi$
$67$	−11.5741	+	43.1952i	−0.172748	+	0.644704i	−0.996924	+	0.0783709i	$0.975028\pi$
$68$	−4.55339	−	6.26381i	−0.0669616	−	0.0921148i
$69$	−5.76364			−0.0835310
$70$	−28.7043	+	63.8441i	−0.410061	+	0.912058i
$71$		−	41.0340i		−	0.577943i	−0.957338	−	0.288971i	$-0.906687\pi$
$71$		−	41.0340i		−	0.577943i	0.957338	−	0.288971i	$-0.0933133\pi$
$72$	101.252	+	96.0107i	1.40628	+	1.33348i
$73$	59.3322	+	15.8980i	0.812769	+	0.217781i	0.641183	−	0.767388i	$-0.278444\pi$
$73$	59.3322	+	15.8980i	0.812769	+	0.217781i	0.171586	+	0.985169i	$0.445111\pi$
$74$	−36.1390	+	30.8737i	−0.488365	+	0.417212i
$75$	−17.3158	+	127.383i	−0.230878	+	1.69844i
$76$	90.3029	−	34.6907i	1.18820	−	0.456457i
$77$	52.7689	+	22.7756i	0.685310	+	0.295787i
$78$	−111.616	+	162.447i	−1.43097	+	2.08265i
$79$	25.2837	−	43.7926i	0.320047	−	0.554337i	−0.660451	−	0.750869i	$-0.729635\pi$
$79$	25.2837	−	43.7926i	0.320047	−	0.554337i	0.980497	+	0.196532i	$0.0629681\pi$
$80$	−21.5929	−	77.0308i	−0.269911	−	0.962885i
$81$	33.1216	+	57.3683i	0.408909	+	0.708251i
$82$	67.7675	−	32.3342i	0.826433	−	0.394319i
$83$	−50.9762	−	50.9762i	−0.614171	−	0.614171i	0.329859	−	0.944030i	$-0.392999\pi$
$83$	−50.9762	−	50.9762i	−0.614171	−	0.614171i	−0.944030	+	0.329859i	$0.892999\pi$
$84$	42.8900	−	137.444i	0.510595	−	1.63624i
$85$	−1.90843	+	9.48993i	−0.0224521	+	0.111646i
$86$	3.32111	+	1.17559i	0.0386176	+	0.0136696i
$87$	−203.918	−	54.6396i	−2.34388	−	0.628041i
$88$	−62.9727	+	18.6798i	−0.715599	+	0.212271i
$89$	42.4612	−	73.5450i	0.477093	−	0.826349i	−0.522563	−	0.852601i	$-0.675024\pi$
$89$	42.4612	−	73.5450i	0.477093	−	0.826349i	0.999655	+	0.0262521i	$0.00835727\pi$
$90$	2.62752	−	174.399i	0.0291946	−	1.93777i
$91$	132.732	+	19.4712i	1.45860	+	0.213970i
$92$	−4.09628	−	1.82252i	−0.0445248	−	0.0198100i
$93$	−95.9790	+	25.7175i	−1.03203	+	0.276532i
$94$	108.802	−	92.9499i	1.15747	−	0.988828i
$95$	−108.338	−	53.7102i	−1.14040	−	0.565370i
$96$	63.0683	+	151.983i	0.656961	+	1.58316i
$97$	−15.7389	−	15.7389i	−0.162257	−	0.162257i	0.621309	−	0.783566i	$-0.286601\pi$
$97$	−15.7389	−	15.7389i	−0.162257	−	0.162257i	−0.783566	+	0.621309i	$0.786601\pi$
$98$	−96.8421	+	15.0203i	−0.988185	+	0.153268i
$99$	−143.209			−1.44655
$100$	−52.5862	+	85.0570i	−0.525862	+	0.850570i
$101$	−3.80953	+	2.19943i	−0.0377181	+	0.0217766i	−0.518740	−	0.854932i	$-0.673599\pi$
$101$	−3.80953	+	2.19943i	−0.0377181	+	0.0217766i	0.481022	+	0.876708i	$0.340266\pi$
$102$	1.55959	−	19.8492i	0.0152901	−	0.194600i
$103$	55.2430	−	14.8023i	0.536340	−	0.143712i	0.0195254	−	0.999809i	$-0.493784\pi$
$103$	55.2430	−	14.8023i	0.536340	−	0.143712i	0.516814	+	0.856098i	$0.327118\pi$
$104$	−130.694	+	80.1588i	−1.25667	+	0.770758i
$105$	−162.735	+	76.8686i	−1.54985	+	0.732082i
$106$	−25.2837	+	4.68943i	−0.238526	+	0.0442399i
$107$	−64.5692	+	17.3013i	−0.603450	+	0.161694i	−0.547593	−	0.836745i	$-0.684456\pi$
$107$	−64.5692	+	17.3013i	−0.603450	+	0.161694i	−0.0558572	+	0.998439i	$0.517789\pi$
$108$	18.1947	+	172.683i	0.168470	+	1.59892i
$109$	43.0454	−	24.8522i	0.394912	−	0.228002i	−0.289375	−	0.957216i	$-0.593447\pi$
$109$	43.0454	−	24.8522i	0.394912	−	0.228002i	0.684286	+	0.729214i	$0.260114\pi$
$110$	70.4794	+	42.1195i	0.640722	+	0.382905i
$111$	−122.207			−1.10096
$112$	73.9437	−	84.1210i	0.660211	−	0.751080i
$113$	12.8519	+	12.8519i	0.113734	+	0.113734i	0.761683	−	0.647950i	$-0.224373\pi$
$113$	12.8519	+	12.8519i	0.113734	+	0.113734i	−0.647950	+	0.761683i	$0.724373\pi$
$114$	234.464	+	82.9940i	2.05670	+	0.728018i
$115$	1.79027	+	5.31064i	0.0155676	+	0.0461795i
$116$	−127.649	−	103.314i	−1.10042	−	0.890636i
$117$	−322.879	+	86.5153i	−2.75965	+	0.739447i
$118$	−47.4107	−	32.5755i	−0.401785	−	0.276063i
$119$	−12.5955	+	5.00077i	−0.105844	+	0.0420232i
$120$	86.4334	−	186.645i	0.720279	−	1.55537i
$121$	−26.7930	+	46.4069i	−0.221430	+	0.383528i
$122$	9.15117	−	116.468i	0.0750096	−	0.954659i
$123$	186.475	+	49.9658i	1.51606	+	0.406226i
$124$	−76.3455	−	12.0718i	−0.615690	−	0.0973531i
$125$	122.750	−	23.6120i	0.981997	−	0.188896i
$126$	206.716	−	129.984i	1.64060	−	1.03162i
$127$	140.522	+	140.522i	1.10647	+	1.10647i	0.993611	+	0.112863i	$0.0360021\pi$
$127$	140.522	+	140.522i	1.10647	+	1.10647i	0.112863	+	0.993611i	$0.463998\pi$
$128$	−3.23526	+	127.959i	−0.0252755	+	0.999681i
$129$	4.52902	+	7.84449i	0.0351087	+	0.0608100i
$130$	184.349	+	52.3850i	1.41807	+	0.402961i
$131$	35.7024	−	61.8383i	0.272537	−	0.472048i	−0.696974	−	0.717097i	$-0.745471\pi$
$131$	35.7024	−	61.8383i	0.272537	−	0.472048i	0.969511	+	0.245048i	$0.0788039\pi$
$132$	−154.298	−	68.6504i	−1.16893	−	0.520079i
$133$	−19.6176	−	168.149i	−0.147501	−	1.26428i
$134$	−87.9381	+	16.3101i	−0.656255	+	0.121717i
$135$	143.453	−	162.885i	1.06262	−	1.20655i
$136$	7.38492	−	13.6139i	0.0543008	−	0.100102i
$137$	126.001	+	33.7618i	0.919714	+	0.246437i	0.687463	−	0.726219i	$-0.258724\pi$
$137$	126.001	+	33.7618i	0.919714	+	0.246437i	0.232251	+	0.972656i	$0.425391\pi$
$138$	−4.96396	−	10.4037i	−0.0359707	−	0.0753892i
$139$			179.518i			1.29149i	0.763552	+	0.645746i	$0.223454\pi$
$139$			179.518i			1.29149i	−0.763552	+	0.645746i	$0.776546\pi$
$140$	−139.964	+	3.17309i	−0.999743	+	0.0226649i
$141$	367.922			2.60937
$142$	74.0687	−	35.3407i	0.521611	−	0.248878i
$143$	40.7262	−	151.992i	0.284798	−	1.06288i
$144$	−86.1008	+	265.456i	−0.597922	+	1.84345i
$145$	12.9946	+	204.863i	0.0896181	+	1.41285i
$146$	22.4033	+	120.790i	0.153447	+	0.827331i
$147$	−214.397	−	132.368i	−1.45848	−	0.900459i
$148$	−86.8537	−	38.6429i	−0.586849	−	0.261101i
$149$	−193.026	−	111.444i	−1.29548	−	0.747944i	−0.315858	−	0.948806i	$-0.602292\pi$
$149$	−193.026	−	111.444i	−1.29548	−	0.747944i	−0.979620	+	0.200862i	$0.935626\pi$
$150$	−244.847	+	78.4529i	−1.63231	+	0.523019i
$151$	−151.374	+	87.3957i	−1.00248	+	0.578780i	−0.908980	−	0.416840i	$-0.863137\pi$
$151$	−151.374	+	87.3957i	−1.00248	+	0.578780i	−0.0934957	+	0.995620i	$0.529804\pi$
$152$	140.393	+	133.125i	0.923636	+	0.875820i
$153$	23.8771	−	23.8771i	0.156059	−	0.156059i
$154$	4.33619	+	114.867i	0.0281571	+	0.745887i
$155$	53.5087	+	80.4473i	0.345217	+	0.519015i
$156$	−389.356	−	61.5650i	−2.49587	−	0.394648i
$157$	31.0868	−	116.018i	0.198005	−	0.738966i	−0.793463	−	0.608618i	$-0.791724\pi$
$157$	31.0868	−	116.018i	0.198005	−	0.738966i	0.991468	−	0.130348i	$-0.0416093\pi$
$158$	100.824	+	7.92195i	0.638126	+	0.0501389i
$159$	−57.2575	−	33.0576i	−0.360110	−	0.207910i
$160$	120.448	−	105.320i	0.752801	−	0.658248i
$161$	−4.86767	+	6.15349i	−0.0302340	+	0.0382204i
$162$	−75.0271	+	109.195i	−0.463130	+	0.674044i
$163$	13.5668	+	50.6319i	0.0832318	+	0.310625i	0.994973	−	0.100139i	$-0.0319287\pi$
$163$	13.5668	+	50.6319i	0.0832318	+	0.310625i	−0.911742	+	0.410764i	$0.865262\pi$
$164$	116.730	+	94.4765i	0.711770	+	0.576076i
$165$	67.4357	+	200.041i	0.408701	+	1.21237i
$166$	48.1116	−	135.919i	0.289829	−	0.818787i
$167$	153.804	−	153.804i	0.920980	−	0.920980i	−0.0761191	−	0.997099i	$-0.524253\pi$
$167$	153.804	−	153.804i	0.920980	−	0.920980i	0.997099	+	0.0761191i	$0.0242529\pi$
$168$	285.034	−	40.9554i	1.69663	−	0.243782i
$169$		−	198.286i		−	1.17329i
$170$	−18.7735	+	4.72842i	−0.110433	+	0.0278142i
$171$	210.910	+	365.307i	1.23339	+	2.13630i
$172$	0.738321	+	7.00729i	0.00429257	+	0.0407401i
$173$	−38.3238	−	143.027i	−0.221525	−	0.826743i	−0.983767	−	0.179451i	$-0.942568\pi$
$173$	−38.3238	−	143.027i	−0.221525	−	0.826743i	0.762242	−	0.647292i	$-0.224099\pi$
$174$	−76.9974	−	415.142i	−0.442514	−	2.38588i
$175$	121.375	+	126.068i	0.693571	+	0.720389i
$176$	−87.9537	−	97.5813i	−0.499737	−	0.554439i
$177$	−38.2786	−	142.858i	−0.216264	−	0.807107i
$178$	169.323	+	13.3041i	0.951254	+	0.0747420i
$179$	−160.907	−	278.699i	−0.898921	−	1.55698i	−0.828876	−	0.559433i	$-0.811019\pi$
$179$	−160.907	−	278.699i	−0.898921	−	1.55698i	−0.0700450	−	0.997544i	$-0.522314\pi$
$180$	317.064	−	145.459i	1.76147	−	0.808108i
$181$			175.218i			0.968056i	0.875052	+	0.484028i	$0.160827\pi$
$181$			175.218i			0.968056i	−0.875052	+	0.484028i	$0.839173\pi$
$182$	79.1697	+	256.360i	0.434998	+	1.40857i
$183$	212.396	−	212.396i	1.16063	−	1.16063i
$184$	−0.238189	−	8.96369i	−0.00129451	−	0.0487157i
$185$	37.9592	+	112.602i	0.205185	+	0.608658i
$186$	−129.084	−	151.099i	−0.694000	−	0.812358i
$187$	4.11408	+	15.3540i	0.0220004	+	0.0821068i
$188$	261.486	+	116.340i	1.39088	+	0.618832i
$189$	300.651	+	44.1041i	1.59074	+	0.233355i
$190$	3.64321	−	241.815i	0.0191748	−	1.27271i
$191$	131.100	+	75.6906i	0.686387	+	0.396286i	0.802257	−	0.596979i	$-0.203632\pi$
$191$	131.100	+	75.6906i	0.686387	+	0.396286i	−0.115870	+	0.993264i	$0.536966\pi$
$192$	−220.021	+	244.738i	−1.14594	+	1.27468i
$193$	2.64295	−	9.86364i	0.0136941	−	0.0511069i	−0.958741	−	0.284282i	$-0.908245\pi$
$193$	2.64295	−	9.86364i	0.0136941	−	0.0511069i	0.972435	+	0.233175i	$0.0749115\pi$
$194$	14.8545	−	41.9650i	0.0765695	−	0.216314i
$195$	272.890	+	410.274i	1.39943	+	2.10397i
$196$	−110.518	−	161.869i	−0.563868	−	0.825865i
$197$	−101.109	+	101.109i	−0.513246	+	0.513246i	−0.915519	−	0.402274i	$-0.868220\pi$
$197$	−101.109	+	101.109i	−0.513246	+	0.513246i	0.402274	+	0.915519i	$0.368220\pi$
$198$	−123.339	−	258.500i	−0.622925	−	1.30556i
$199$	315.085	−	181.914i	1.58334	−	0.914142i	0.588974	−	0.808152i	$-0.299532\pi$
$199$	315.085	−	181.914i	1.58334	−	0.914142i	0.994367	−	0.105990i	$-0.0338011\pi$
$200$	−198.823	−	21.6656i	−0.994115	−	0.108328i
$201$	−199.145	−	114.976i	−0.990769	−	0.572021i
$202$	−7.25108	−	4.98216i	−0.0358965	−	0.0246641i
$203$	−230.554	+	171.565i	−1.13573	+	0.845147i
$204$	37.1721	−	14.2800i	0.182216	−	0.0700001i
$205$	−11.8831	−	187.339i	−0.0579662	−	0.913849i
$206$	74.2973	+	86.9683i	0.360667	+	0.422176i
$207$	5.05988	−	18.8837i	0.0244439	−	0.0912258i
$208$	−257.252	−	166.873i	−1.23679	−	0.802274i
$209$	−198.567			−0.950083
$210$	−278.908	−	227.542i	−1.32814	−	1.08353i
$211$		−	74.6821i		−	0.353944i	−0.984216	−	0.176972i	$-0.943370\pi$
$211$		−	74.6821i		−	0.353944i	0.984216	−	0.176972i	$-0.0566301\pi$
$212$	−30.2404	−	41.5998i	−0.142643	−	0.196226i
$213$	203.814	+	54.6117i	0.956872	+	0.256393i
$214$	−86.8403	−	101.650i	−0.405796	−	0.475002i
$215$	5.82117	−	6.60967i	0.0270752	−	0.0307427i
$216$	−296.033	+	181.567i	−1.37052	+	0.840587i
$217$	−53.6019	+	124.191i	−0.247014	+	0.572308i
$218$	81.9328	+	56.2953i	0.375839	+	0.258235i
$219$	−157.929	+	273.542i	−0.721139	+	1.24905i
$220$	−15.3275	+	163.495i	−0.0696706	+	0.743160i
$221$	18.5513	+	32.1318i	0.0839425	+	0.145393i
$222$	−105.251	−	220.590i	−0.474104	−	0.993650i
$223$	−1.23417	−	1.23417i	−0.00553440	−	0.00553440i	0.704334	−	0.709869i	$-0.251246\pi$
$223$	−1.23417	−	1.23417i	−0.00553440	−	0.00553440i	−0.709869	+	0.704334i	$0.751246\pi$
$224$	215.528	+	61.0231i	0.962177	+	0.272425i
$225$	−402.150	−	168.562i	−1.78733	−	0.749164i
$226$	−12.1297	+	34.2672i	−0.0536712	+	0.151625i
$227$	292.901	+	78.4827i	1.29031	+	0.345739i	0.837780	−	0.546008i	$-0.183853\pi$
$227$	292.901	+	78.4827i	1.29031	+	0.345739i	0.452535	+	0.891747i	$0.350520\pi$
$228$	52.1240	+	494.700i	0.228614	+	2.16974i
$229$	−176.064	+	304.951i	−0.768836	+	1.33166i	0.169358	+	0.985555i	$0.445831\pi$
$229$	−176.064	+	304.951i	−0.768836	+	1.33166i	−0.938194	+	0.346109i	$0.887503\pi$
$230$	−8.04415	+	7.80536i	−0.0349746	+	0.0339363i
$231$	−183.355	+	231.789i	−0.793744	+	1.00342i
$232$	76.5491	−	319.394i	0.329953	−	1.37670i
$233$	−19.6378	+	5.26194i	−0.0842825	+	0.0225834i	−0.300714	−	0.953714i	$-0.597225\pi$
$233$	−19.6378	+	5.26194i	−0.0842825	+	0.0225834i	0.216431	+	0.976298i	$0.430558\pi$
$234$	−434.247	−	508.305i	−1.85575	−	2.17224i
$235$	−114.282	−	339.005i	−0.486306	−	1.44257i
$236$	17.9680	−	113.635i	0.0761355	−	0.481504i
$237$	183.866	+	183.866i	0.775806	+	0.775806i
$238$	−19.8746	−	18.4287i	−0.0835067	−	0.0774313i
$239$	−402.188			−1.68279			−0.841397	−	0.540418i	$-0.818266\pi$
$239$	−402.188			−1.68279			−0.841397	+	0.540418i	$0.818266\pi$
$240$	411.346	−	4.73129i	1.71394	−	0.0197137i
$241$	−277.789	+	160.382i	−1.15265	+	0.665484i	−0.949532	−	0.313669i	$-0.898442\pi$
$241$	−277.789	+	160.382i	−1.15265	+	0.665484i	−0.203121	+	0.979154i	$0.565108\pi$
$242$	−106.843	−	8.39486i	−0.441499	−	0.0346895i
$243$	48.3486	−	12.9550i	0.198965	−	0.0533126i
$244$	218.114	−	83.7906i	0.893910	−	0.343404i
$245$	−55.3694	+	238.661i	−0.225998	+	0.974128i
$246$	70.4111	+	379.632i	0.286224	+	1.54322i
$247$	−447.692	+	119.959i	−1.81252	+	0.485663i
$248$	−43.9627	−	148.205i	−0.177269	−	0.597601i
$249$	321.040	−	185.353i	1.28932	−	0.744388i
$250$	148.340	+	201.234i	0.593359	+	0.804938i
$251$	−407.511			−1.62355			−0.811774	−	0.583971i	$-0.801498\pi$
$251$	−407.511			−1.62355			−0.811774	+	0.583971i	$0.801498\pi$
$252$	412.664	+	261.185i	1.63755	+	1.03645i
$253$	6.50744	+	6.50744i	0.0257211	+	0.0257211i
$254$	−132.625	+	374.676i	−0.522148	+	1.47510i
$255$	−44.5962	−	22.1092i	−0.174887	−	0.0867026i
$256$	−233.760	+	104.366i	−0.913126	+	0.407678i
$257$	−5.08625	+	1.36286i	−0.0197909	+	0.00530294i	−0.268701	−	0.963224i	$-0.586594\pi$
$257$	−5.08625	+	1.36286i	−0.0197909	+	0.00530294i	0.248910	+	0.968527i	$0.419928\pi$
$258$	−10.2591	+	14.9312i	−0.0397641	+	0.0578731i
$259$	−103.209	+	130.473i	−0.398492	+	0.503756i
$260$	64.2132	+	377.877i	0.246974	+	1.45337i
$261$	358.038	−	620.140i	1.37179	−	2.37601i
$262$	142.371	+	11.1864i	0.543400	+	0.0426960i
$263$	6.94528	+	1.86098i	0.0264079	+	0.00707598i	0.271999	−	0.962298i	$-0.412315\pi$
$263$	6.94528	+	1.86098i	0.0264079	+	0.00707598i	−0.245591	+	0.969374i	$0.578982\pi$
$264$	−8.97208	−	337.643i	−0.0339851	−	1.27895i
$265$	−12.6744	+	63.0255i	−0.0478281	+	0.237832i
$266$	286.624	−	180.230i	1.07753	−	0.677558i
$267$	308.784	+	308.784i	1.15649	+	1.15649i
$268$	−105.178	−	144.686i	−0.392455	−	0.539875i
$269$	−26.4379	−	45.7917i	−0.0982821	−	0.170230i	0.812692	−	0.582694i	$-0.198001\pi$
$269$	−26.4379	−	45.7917i	−0.0982821	−	0.170230i	−0.910974	+	0.412465i	$0.864668\pi$
$270$	417.566	+	118.657i	1.54654	+	0.439469i
$271$	114.514	−	198.344i	0.422561	−	0.731898i	−0.573628	−	0.819116i	$-0.694464\pi$
$271$	114.514	−	198.344i	0.422561	−	0.731898i	0.996189	+	0.0872183i	$0.0277978\pi$
$272$	30.9341	+	1.60521i	0.113728	+	0.00590149i
$273$	−273.365	+	633.362i	−1.00134	+	2.32001i
$274$	47.5767	+	256.516i	0.173638	+	0.936191i
$275$	163.372	−	124.271i	0.594080	−	0.451895i
$276$	14.5041	−	17.9205i	0.0525510	−	0.0649293i
$277$	102.874	+	27.5649i	0.371385	+	0.0995124i	0.439684	−	0.898153i	$-0.355090\pi$
$277$	102.874	+	27.5649i	0.371385	+	0.0995124i	−0.0682987	+	0.997665i	$0.521757\pi$
$278$	−324.040	+	154.610i	−1.16561	+	0.556152i
$279$		−	337.039i		−	1.20803i
$280$	−126.272	−	249.911i	−0.450973	−	0.892538i
$281$	−449.848			−1.60088			−0.800441	−	0.599412i	$-0.795401\pi$
$281$	−449.848			−1.60088			−0.800441	+	0.599412i	$0.795401\pi$
$282$	316.874	+	664.121i	1.12367	+	2.35504i
$283$	4.85726	−	18.1275i	0.0171635	−	0.0640549i	−0.956813	−	0.290704i	$-0.906110\pi$
$283$	4.85726	−	18.1275i	0.0171635	−	0.0640549i	0.973976	+	0.226649i	$0.0727771\pi$
$284$	127.584	+	103.261i	0.449240	+	0.363596i
$285$	410.963	−	466.629i	1.44197	−	1.63730i
$286$	309.430	−	57.3908i	1.08192	−	0.200667i
$287$	210.833	−	156.890i	0.734609	−	0.546653i
$288$	−553.319	+	73.2085i	−1.92125	+	0.254196i
$289$	247.035	+	142.626i	0.854794	+	0.493516i
$290$	−358.598	+	199.895i	−1.23654	+	0.689293i
$291$	99.1214	−	57.2278i	0.340623	−	0.196659i
$292$	−198.739	+	144.470i	−0.680612	+	0.494762i
$293$	−74.8254	+	74.8254i	−0.255377	+	0.255377i	−0.823171	−	0.567794i	$-0.807797\pi$
$293$	−74.8254	+	74.8254i	−0.255377	+	0.255377i	0.567794	+	0.823171i	$0.307797\pi$
$294$	54.2813	−	501.001i	0.184630	−	1.70408i
$295$	−119.740	+	79.6439i	−0.405898	+	0.269979i
$296$	−5.05033	−	190.058i	−0.0170619	−	0.642086i
$297$	92.2484	−	344.276i	0.310601	−	1.15918i
$298$	34.9178	−	444.405i	0.117174	−	1.49129i
$299$	18.6030	+	10.7404i	0.0622174	+	0.0359212i
$300$	−352.488	−	374.395i	−1.17496	−	1.24798i
$301$	12.2001	+	1.78969i	0.0405318	+	0.00594583i
$302$	−288.126	−	197.969i	−0.954059	−	0.655526i
$303$	−5.85441	−	21.8490i	−0.0193215	−	0.0721088i
$304$	−119.384	+	368.071i	−0.392710	+	1.21076i
$305$	−261.676	−	129.729i	−0.857954	−	0.425342i
$306$	63.6638	+	22.5353i	0.208052	+	0.0736448i
$307$	−157.540	+	157.540i	−0.513158	+	0.513158i	−0.915493	−	0.402335i	$-0.868199\pi$
$307$	−157.540	+	157.540i	−0.513158	+	0.513158i	0.402335	+	0.915493i	$0.368199\pi$
$308$	−203.606	+	106.756i	−0.661060	+	0.346612i
$309$			294.090i			0.951747i
$310$	−99.1276	+	165.872i	−0.319766	+	0.535071i
$311$	−288.131	−	499.058i	−0.926466	−	1.60469i	−0.789186	−	0.614155i	$-0.789497\pi$
$311$	−288.131	−	499.058i	−0.926466	−	1.60469i	−0.137281	−	0.990532i	$-0.543836\pi$
$312$	−224.206	−	755.833i	−0.718608	−	2.42254i
$313$	20.9917	+	78.3422i	0.0670662	+	0.250295i	0.991317	−	0.131490i	$-0.0419762\pi$
$313$	20.9917	+	78.3422i	0.0670662	+	0.250295i	−0.924251	+	0.381785i	$0.875310\pi$
$314$	236.192	−	43.8072i	0.752205	−	0.139513i
$315$	−108.985	−	600.660i	−0.345983	−	1.90686i
$316$	72.5355	+	188.816i	0.229543	+	0.597519i
$317$	−22.8638	−	85.3290i	−0.0721257	−	0.269177i	0.920441	−	0.390883i	$-0.127830\pi$
$317$	−22.8638	−	85.3290i	−0.0721257	−	0.269177i	−0.992566	+	0.121706i	$0.961164\pi$
$318$	10.3577	−	131.824i	0.0325714	−	0.414541i
$319$	168.543	+	291.924i	0.528347	+	0.915123i
$320$	293.845	+	126.709i	0.918265	+	0.395966i
$321$		−	343.738i		−	1.07084i
$322$	−15.2997	−	3.48672i	−0.0475147	−	0.0108283i
$323$	33.1070	−	33.1070i	0.102498	−	0.102498i
$324$	−261.721	−	41.3835i	−0.807782	−	0.127727i
$325$	293.265	−	378.879i	0.902355	−	1.16578i
$326$	−79.7092	+	68.0958i	−0.244507	+	0.208883i
$327$	66.1513	+	246.880i	0.202298	+	0.754985i
$328$	−70.0012	+	292.073i	−0.213418	+	0.890467i
$329$	310.728	−	392.808i	0.944462	−	1.19395i
$330$	−303.006	+	294.011i	−0.918200	+	0.890944i
$331$	335.818	+	193.884i	1.01455	+	0.585753i	0.912522	−	0.409028i	$-0.134132\pi$
$331$	335.818	+	193.884i	1.01455	+	0.585753i	0.102033	+	0.994781i	$0.467465\pi$
$332$	286.778	−	30.2162i	0.863788	−	0.0910128i
$333$	107.285	−	400.393i	0.322177	−	1.20238i
$334$	410.089	+	145.161i	1.22781	+	0.434613i
$335$	−44.0824	+	219.206i	−0.131589	+	0.654347i
$336$	319.414	+	479.231i	0.950637	+	1.42628i
$337$	160.589	−	160.589i	0.476524	−	0.476524i	−0.427494	−	0.904018i	$-0.640604\pi$
$337$	160.589	−	160.589i	0.476524	−	0.476524i	0.904018	+	0.427494i	$0.140604\pi$
$338$	357.918	−	170.775i	1.05893	−	0.505251i
$339$	−80.9394	+	46.7304i	−0.238759	+	0.137848i
$340$	−24.7039	−	29.8150i	−0.0726585	−	0.0876911i
$341$	137.402	+	79.3288i	0.402937	+	0.232636i
$342$	−477.753	+	695.327i	−1.39694	+	2.03312i
$343$	−322.389	+	117.107i	−0.939910	+	0.341421i
$344$	−12.0127	+	7.36778i	−0.0349206	+	0.0214180i
$345$	−28.7604	+	1.82430i	−0.0833634	+	0.00528782i
$346$	225.165	−	192.359i	0.650765	−	0.555951i
$347$	20.6315	−	76.9976i	0.0594566	−	0.221895i	−0.929805	−	0.368054i	$-0.880024\pi$
$347$	20.6315	−	76.9976i	0.0594566	−	0.221895i	0.989261	+	0.146158i	$0.0466909\pi$
$348$	683.042	−	496.528i	1.96276	−	1.42680i
$349$	−517.525			−1.48288			−0.741439	−	0.671020i	$-0.765856\pi$
$349$	−517.525			−1.48288			−0.741439	+	0.671020i	$0.765856\pi$
$350$	−123.026	+	327.666i	−0.351502	+	0.936187i
$351$		−	831.936i		−	2.37019i
$352$	100.390	−	242.804i	0.285198	−	0.689784i
$353$	555.250	+	148.779i	1.57295	+	0.421470i	0.936734	−	0.350043i	$-0.113833\pi$
$353$	555.250	+	148.779i	1.57295	+	0.421470i	0.636214	+	0.771513i	$0.280500\pi$
$354$	224.899	−	192.132i	0.635309	−	0.542746i
$355$	−12.9880	−	204.758i	−0.0365859	−	0.576784i
$356$	121.816	+	317.097i	0.342179	+	0.890721i
$357$	−8.07536	−	69.2167i	−0.0226201	−	0.193884i
$358$	364.486	−	530.477i	1.01812	−	1.48178i
$359$	352.879	−	611.204i	0.982949	−	1.70252i	0.332230	−	0.943198i	$-0.392199\pi$
$359$	352.879	−	611.204i	0.982949	−	1.70252i	0.650719	−	0.759319i	$-0.274468\pi$
$360$	535.636	+	447.042i	1.48788	+	1.24178i
$361$	111.940	+	193.885i	0.310082	+	0.537077i
$362$	−316.279	+	150.907i	−0.873700	+	0.416871i
$363$	−194.842	−	194.842i	−0.536756	−	0.536756i
$364$	−394.559	+	363.697i	−1.08395	+	0.999167i
$365$	301.098	+	60.5509i	0.824925	+	0.165893i
$366$	566.314	+	200.460i	1.54731	+	0.547706i
$367$	−573.668	−	153.714i	−1.56313	−	0.418839i	−0.629476	−	0.777020i	$-0.716730\pi$
$367$	−573.668	−	153.714i	−1.56313	−	0.418839i	−0.933652	+	0.358181i	$0.883397\pi$
$368$	15.9749	−	8.14997i	0.0434099	−	0.0221466i
$369$	−327.412	+	567.094i	−0.887295	+	1.53684i
$370$	−170.560	+	165.497i	−0.460974	+	0.447290i
$371$	−83.6504	+	33.2116i	−0.225473	+	0.0895191i
$372$	161.568	−	363.139i	0.434322	−	0.976179i
$373$	−350.158	+	93.8246i	−0.938762	+	0.251541i	−0.695587	−	0.718442i	$-0.744856\pi$
$373$	−350.158	+	93.8246i	−0.938762	+	0.251541i	−0.243175	+	0.969982i	$0.578189\pi$
$374$	−24.1716	+	20.6498i	−0.0646298	+	0.0552135i
$375$	−46.0865	+	641.117i	−0.122897	+	1.70965i
$376$	15.2048	+	572.197i	0.0404383	+	1.52180i
$377$	556.355	+	556.355i	1.47574	+	1.47574i
$378$	179.326	+	580.677i	0.474408	+	1.53618i
$379$	205.160			0.541319			0.270660	−	0.962675i	$-0.412758\pi$
$379$	205.160			0.541319			0.270660	+	0.962675i	$0.412758\pi$
$380$	439.629	−	201.688i	1.15692	−	0.530759i
$381$	−884.987	+	510.947i	−2.32280	+	1.34107i
$382$	−23.7156	+	301.832i	−0.0620827	+	0.790136i
$383$	−85.4211	+	22.8885i	−0.223032	+	0.0597611i	−0.368604	−	0.929586i	$-0.620164\pi$
$383$	−85.4211	+	22.8885i	−0.223032	+	0.0597611i	0.145573	+	0.989348i	$0.453498\pi$
$384$	−631.261	−	186.369i	−1.64391	−	0.485336i
$385$	270.524	+	96.9472i	0.702660	+	0.251811i
$386$	20.0807	−	3.72442i	0.0520226	−	0.00964875i
$387$	−29.6774	+	7.95203i	−0.0766857	+	0.0205479i
$388$	88.5428	−	9.32928i	0.228203	−	0.0240445i
$389$	−272.183	+	157.145i	−0.699699	+	0.403972i	−0.807235	−	0.590230i	$-0.799037\pi$
$389$	−272.183	+	157.145i	−0.699699	+	0.403972i	0.107536	+	0.994201i	$0.465704\pi$
$390$	−505.542	+	845.933i	−1.29626	+	2.16906i
$391$	−2.16996			−0.00554977
$392$	197.000	−	338.903i	0.502550	−	0.864548i
$393$	259.632	+	259.632i	0.660642	+	0.660642i
$394$	−269.589	−	95.4275i	−0.684237	−	0.242202i
$395$	112.304	−	226.527i	0.284313	−	0.573485i
$396$	360.382	−	445.269i	0.910055	−	1.12442i
$397$	−494.981	+	132.630i	−1.24680	+	0.334080i	−0.821101	−	0.570783i	$-0.806640\pi$
$397$	−494.981	+	132.630i	−1.24680	+	0.334080i	−0.425703	+	0.904863i	$0.639973\pi$
$398$	599.734	+	412.072i	1.50687	+	1.03536i
$399$	861.300	+	126.349i	2.15865	+	0.316663i
$400$	−132.130	−	377.547i	−0.330324	−	0.943868i
$401$	−102.204	+	177.023i	−0.254873	+	0.441454i	−0.964861	−	0.262760i	$-0.915367\pi$
$401$	−102.204	+	177.023i	−0.254873	+	0.441454i	0.709988	+	0.704214i	$0.248700\pi$
$402$	36.0247	−	458.492i	0.0896136	−	1.14053i
$403$	357.711	+	95.8483i	0.887620	+	0.237837i
$404$	2.74806	−	17.3795i	0.00680213	−	0.0430187i
$405$	183.434	+	275.783i	0.452923	+	0.680945i
$406$	−508.251	−	268.402i	−1.25185	−	0.661090i
$407$	137.977	+	137.977i	0.339011	+	0.339011i
$408$	57.7909	+	54.7991i	0.141644	+	0.134312i
$409$	−307.492	−	532.592i	−0.751815	−	1.30218i	−0.946942	−	0.321403i	$-0.895845\pi$
$409$	−307.492	−	532.592i	−0.751815	−	1.30218i	0.195128	−	0.980778i	$-0.437488\pi$
$410$	327.924	−	182.796i	0.799814	−	0.445845i
$411$	−335.387	+	580.907i	−0.816026	+	1.41340i
$412$	−92.9941	+	209.013i	−0.225714	+	0.507313i
$413$	−184.849	−	79.7826i	−0.447576	−	0.193178i
$414$	38.4441	−	7.13032i	0.0928602	−	0.0172230i
$415$	−270.505	−	238.235i	−0.651819	−	0.574060i
$416$	79.6563	−	608.076i	0.191481	−	1.46172i
$417$	−891.655	−	238.918i	−2.13826	−	0.572946i
$418$	−171.017	−	358.426i	−0.409132	−	0.857478i
$419$			172.040i			0.410596i	0.978699	+	0.205298i	$0.0658164\pi$
$419$			172.040i			0.410596i	−0.978699	+	0.205298i	$0.934184\pi$
$420$	170.516	−	699.418i	0.405991	−	1.66528i
$421$	−234.277			−0.556477			−0.278239	−	0.960512i	$-0.589751\pi$
$421$	−234.277			−0.556477			−0.278239	+	0.960512i	$0.589751\pi$
$422$	134.806	−	64.3203i	0.319445	−	0.152418i
$423$	−322.998	+	1205.44i	−0.763588	+	2.84975i
$424$	49.0454	−	90.4138i	0.115673	−	0.213240i
$425$	−6.51927	+	47.9585i	−0.0153395	+	0.112844i
$426$	76.9581	+	414.931i	0.180653	+	0.974016i
$427$	−47.3836	−	406.141i	−0.110969	−	0.951150i
$428$	108.693	−	244.299i	0.253957	−	0.570792i
$429$	700.736	+	404.570i	1.63342	+	0.943054i
$430$	16.9444	+	4.81495i	0.0394055	+	0.0111976i
$431$	296.293	−	171.065i	0.687454	−	0.396902i	−0.115203	−	0.993342i	$-0.536752\pi$
$431$	296.293	−	171.065i	0.687454	−	0.396902i	0.802658	+	0.596440i	$0.203419\pi$
$432$	−582.699	−	377.982i	−1.34884	−	0.874959i
$433$	401.113	−	401.113i	0.926357	−	0.926357i	−0.0711115	−	0.997468i	$-0.522655\pi$
$433$	401.113	−	401.113i	0.926357	−	0.926357i	0.997468	+	0.0711115i	$0.0226546\pi$
$434$	−270.337	+	10.2051i	−0.622895	+	0.0235142i
$435$	−1034.84	−	208.106i	−2.37894	−	0.478405i
$436$	−31.0514	+	196.378i	−0.0712188	+	0.450409i
$437$	7.01584	−	26.1835i	0.0160545	−	0.0599164i
$438$	−629.776	−	49.4828i	−1.43785	−	0.112975i
$439$	−9.23376	−	5.33111i	−0.0210336	−	0.0121438i	0.489446	−	0.872033i	$-0.337199\pi$
$439$	−9.23376	−	5.33111i	−0.0210336	−	0.0121438i	−0.510480	+	0.859890i	$0.670532\pi$
$440$	−308.319	+	113.144i	−0.700726	+	0.257145i
$441$	621.902	−	586.235i	1.41021	−	1.32933i
$442$	−42.0224	+	61.1598i	−0.0950733	+	0.138371i
$443$	91.1694	+	340.249i	0.205800	+	0.768056i	0.989204	+	0.146544i	$0.0468149\pi$
$443$	91.1694	+	340.249i	0.205800	+	0.768056i	−0.783404	+	0.621513i	$0.786518\pi$
$444$	307.531	−	379.969i	0.692637	−	0.855786i
$445$	188.602	−	380.427i	0.423825	−	0.854893i
$446$	1.16482	−	3.29069i	0.00261170	−	0.00737823i
$447$	810.433	−	810.433i	1.81305	−	1.81305i
$448$	75.4738	+	441.597i	0.168468	+	0.985707i
$449$			53.8323i			0.119894i	0.998202	+	0.0599469i	$0.0190931\pi$
$449$			53.8323i			0.119894i	−0.998202	+	0.0599469i	$0.980907\pi$
$450$	−42.0894	−	871.080i	−0.0935319	−	1.93573i
$451$	−154.126	−	266.954i	−0.341742	−	0.591915i
$452$	−72.3012	+	7.61799i	−0.159958	+	0.0168540i
$453$	−232.628	−	868.181i	−0.513529	−	1.91651i
$454$	110.597	+	596.298i	0.243605	+	1.31343i
$455$	668.494	+	55.1487i	1.46922	+	0.121206i
$456$	−848.071	+	520.150i	−1.85981	+	1.14068i
$457$	31.6038	+	117.947i	0.0691549	+	0.258090i	0.991844	−	0.127454i	$-0.0406805\pi$
$457$	31.6038	+	117.947i	0.0691549	+	0.258090i	−0.922690	+	0.385544i	$0.874014\pi$
$458$	−702.090	−	55.1647i	−1.53295	−	0.120447i
$459$	42.0203	+	72.7813i	0.0915476	+	0.158565i
$460$	−21.0172	−	7.79777i	−0.0456896	−	0.0169517i
$461$			301.000i			0.652928i	0.945210	+	0.326464i	$0.105857\pi$
$461$			301.000i			0.652928i	−0.945210	+	0.326464i	$0.894143\pi$
$462$	−576.308	−	131.337i	−1.24742	−	0.284280i
$463$	−360.363	+	360.363i	−0.778321	+	0.778321i	−0.979545	−	0.201224i	$-0.935508\pi$
$463$	−360.363	+	360.363i	−0.778321	+	0.778321i	0.201224	+	0.979545i	$0.435508\pi$
$464$	642.453	−	136.904i	1.38460	−	0.295051i
$465$	−470.793	+	158.709i	−1.01246	+	0.341309i
$466$	−26.4113	−	30.9156i	−0.0566766	−	0.0663425i
$467$	−50.9926	−	190.307i	−0.109192	−	0.407510i	0.889595	−	0.456750i	$-0.150987\pi$
$467$	−50.9926	−	190.307i	−0.109192	−	0.407510i	−0.998787	+	0.0492402i	$0.984320\pi$
$468$	543.524	−	1221.62i	1.16138	−	2.61030i
$469$	−290.941	+	115.512i	−0.620342	+	0.246294i
$470$	513.498	−	498.255i	1.09255	−	1.06012i
$471$	534.881	+	308.814i	1.13563	+	0.655656i
$472$	220.593	−	65.4353i	0.467357	−	0.138634i
$473$	3.74333	−	13.9703i	0.00791403	−	0.0295356i
$474$	−173.534	+	490.245i	−0.366105	+	1.03427i
$475$	−557.605	−	233.721i	−1.17391	−	0.492045i
$476$	16.1477	−	51.7466i	0.0339238	−	0.108711i
$477$	158.575	−	158.575i	0.332442	−	0.332442i
$478$	−346.386	−	725.973i	−0.724657	−	1.51877i
$479$	−373.896	+	215.869i	−0.780577	+	0.450666i	−0.836635	−	0.547761i	$-0.815480\pi$
$479$	−373.896	+	215.869i	−0.780577	+	0.450666i	0.0560577	+	0.998428i	$0.482147\pi$
$480$	362.814	+	738.430i	0.755863	+	1.53840i
$481$	394.440	+	227.730i	0.820042	+	0.473452i
$482$	−528.746	−	363.297i	−1.09698	−	0.753728i
$483$	−24.0858	−	32.3671i	−0.0498670	−	0.0670127i
$484$	−76.8656	−	200.088i	−0.158813	−	0.413404i
$485$	−83.5185	−	73.5552i	−0.172203	−	0.151660i
$486$	65.0249	+	76.1145i	0.133796	+	0.156614i
$487$	−235.372	+	878.421i	−0.483311	+	1.80374i	0.104240	+	0.994552i	$0.466759\pi$
$487$	−235.372	+	878.421i	−0.483311	+	1.80374i	−0.587551	+	0.809187i	$0.699908\pi$
$488$	339.099	+	321.544i	0.694874	+	0.658901i
$489$	−269.542			−0.551212
$490$	−478.485	+	105.603i	−0.976500	+	0.215516i
$491$			445.372i			0.907072i	0.891238	+	0.453536i	$0.149838\pi$
$491$			445.372i			0.907072i	−0.891238	+	0.453536i	$0.850162\pi$
$492$	−624.616	+	454.056i	−1.26954	+	0.922878i
$493$	−76.7733	−	20.5714i	−0.155727	−	0.0417269i
$494$	−602.109	−	704.795i	−1.21884	−	1.42671i
$495$	−714.607	+	45.3282i	−1.44365	+	0.0915720i
$496$	229.656	−	206.998i	0.463016	−	0.417334i
$497$	230.436	−	171.477i	0.463655	−	0.345025i
$498$	611.070	+	419.861i	1.22705	+	0.843094i
$499$	142.325	−	246.515i	0.285221	−	0.494018i	−0.687441	−	0.726240i	$-0.741266\pi$
$499$	142.325	−	246.515i	0.285221	−	0.494018i	0.972663	+	0.232222i	$0.0745995\pi$
$500$	−235.482	+	441.076i	−0.470963	+	0.882153i
$501$	559.240	+	968.631i	1.11625	+	1.93340i
$502$	−350.971	−	735.581i	−0.699145	−	1.46530i
$503$	−119.937	−	119.937i	−0.238443	−	0.238443i	0.577762	−	0.816205i	$-0.303926\pi$
$503$	−119.937	−	119.937i	−0.238443	−	0.238443i	−0.816205	+	0.577762i	$0.803926\pi$
$504$	−116.046	+	969.829i	−0.230250	+	1.92426i
$505$	−18.3133	+	12.1809i	−0.0362639	+	0.0241206i
$506$	−6.14175	+	17.3509i	−0.0121378	+	0.0342903i
$507$	984.879	+	263.898i	1.94256	+	0.520508i
$508$	−790.537	+	83.2947i	−1.55618	+	0.163966i
$509$	277.902	−	481.340i	0.545976	−	0.945658i	−0.452569	−	0.891729i	$-0.649492\pi$
$509$	277.902	−	481.340i	0.545976	−	0.945658i	0.998545	−	0.0539284i	$-0.0171743\pi$
$510$	1.49968	−	99.5403i	0.00294056	−	0.195177i
$511$	158.665	+	399.631i	0.310499	+	0.782057i
$512$	−389.713	−	332.066i	−0.761158	−	0.648566i
$513$	−1014.06	+	271.717i	−1.97673	+	0.529663i
$514$	−6.84059	−	8.00722i	−0.0133085	−	0.0155782i
$515$	270.976	−	91.3485i	0.526166	−	0.177376i
$516$	−35.7875	−	5.65874i	−0.0693557	−	0.0109665i
$517$	−415.402	−	415.402i	−0.803486	−	0.803486i
$518$	−324.401	−	73.9291i	−0.626256	−	0.142720i
$519$	761.411			1.46707
$520$	−626.787	+	441.357i	−1.20536	+	0.848764i
$521$	835.784	−	482.540i	1.60419	−	0.926181i	0.613557	−	0.789651i	$-0.289738\pi$
$521$	835.784	−	482.540i	1.60419	−	0.926181i	0.990636	−	0.136530i	$-0.0435951\pi$
$522$	1427.75	+	112.181i	2.73516	+	0.214907i
$523$	328.159	−	87.9300i	0.627456	−	0.168126i	0.0689408	−	0.997621i	$-0.478038\pi$
$523$	328.159	−	87.9300i	0.627456	−	0.168126i	0.558515	+	0.829495i	$0.311371\pi$
$524$	102.425	+	266.622i	0.195468	+	0.508820i
$525$	−787.711	+	435.081i	−1.50040	+	0.828725i
$526$	2.62247	+	14.1394i	0.00498569	+	0.0268810i
$527$	−36.1353	+	9.68243i	−0.0685679	+	0.0183727i
$528$	601.739	−	306.992i	1.13966	−	0.581424i
$529$	457.039	−	263.872i	0.863969	−	0.498813i
$530$	−124.681	+	31.4029i	−0.235247	+	0.0592507i
$531$	501.658			0.944743
$532$	572.183	+	362.149i	1.07553	+	0.680731i
$533$	−508.765	−	508.765i	−0.954531	−	0.954531i
$534$	−291.431	+	823.314i	−0.545752	+	1.54179i
$535$	−316.722	+	106.770i	−0.592004	+	0.199570i
$536$	170.583	−	314.464i	0.318251	−	0.586687i
$537$	1598.43	−	428.299i	2.97660	−	0.797577i
$538$	59.8871	−	87.1603i	0.111314	−	0.162008i
$539$	92.6149	+	391.514i	0.171827	+	0.726371i
$540$	145.449	+	855.925i	0.269349	+	1.58505i
$541$	211.314	−	366.007i	0.390599	−	0.676538i	−0.601930	−	0.798549i	$-0.705601\pi$
$541$	211.314	−	366.007i	0.390599	−	0.676538i	0.992529	+	0.122012i	$0.0389345\pi$
$542$	456.649	+	35.8799i	0.842526	+	0.0661990i
$543$	−870.301	−	233.196i	−1.60276	−	0.429459i
$544$	23.7447	+	57.2204i	0.0436483	+	0.105185i
$545$	206.929	−	137.637i	0.379686	−	0.252544i
$546$	−1378.69	+	52.0453i	−2.52508	+	0.0953211i
$547$	379.060	+	379.060i	0.692981	+	0.692981i	0.962887	−	0.269906i	$-0.0869927\pi$
$547$	379.060	+	379.060i	0.692981	+	0.692981i	−0.269906	+	0.962887i	$0.586993\pi$
$548$	−422.052	+	306.805i	−0.770167	+	0.559863i
$549$	509.423	+	882.347i	0.927912	+	1.60719i
$550$	365.022	+	187.867i	0.663676	+	0.341577i
$551$	496.441	−	859.861i	0.900982	−	1.56055i
$552$	44.8393	+	10.7466i	0.0812305	+	0.0194685i
$553$	351.587	−	41.0189i	0.635781	−	0.0741752i
$554$	38.8441	+	209.434i	0.0701158	+	0.378039i
$555$	−609.808	+	38.6806i	−1.09875	+	0.0696949i
$556$	−558.162	−	451.752i	−1.00389	−	0.812504i
$557$	−924.112	−	247.615i	−1.65909	−	0.444551i	−0.696952	−	0.717118i	$-0.745461\pi$
$557$	−924.112	−	247.615i	−1.65909	−	0.444551i	−0.962137	+	0.272567i	$0.912127\pi$
$558$	608.376	−	290.277i	1.09028	−	0.520209i
$559$		−	33.7590i		−	0.0603918i
$560$	342.351	−	443.166i	0.611341	−	0.791367i
$561$	−81.7379			−0.145700
$562$	−387.433	−	812.002i	−0.689383	−	1.44484i
$563$	−202.985	+	757.549i	−0.360541	+	1.34556i	0.512825	+	0.858493i	$0.328599\pi$
$563$	−202.985	+	757.549i	−0.360541	+	1.34556i	−0.873366	+	0.487064i	$0.838068\pi$
$564$	−925.868	+	1143.95i	−1.64161	+	2.02829i
$565$	68.1986	+	60.0628i	0.120705	+	0.106306i
$566$	36.9046	−	6.84479i	0.0652025	−	0.0120933i
$567$	−183.754	+	425.740i	−0.324080	+	0.750864i
$568$	−76.5101	+	319.231i	−0.134701	+	0.562026i
$569$	201.442	+	116.303i	0.354029	+	0.204399i	0.666458	−	0.745542i	$-0.267809\pi$
$569$	201.442	+	116.303i	0.354029	+	0.204399i	−0.312429	+	0.949941i	$0.601143\pi$
$570$	1196.24	+	339.926i	2.09866	+	0.596361i
$571$	522.066	−	301.415i	0.914302	−	0.527873i	0.0324892	−	0.999472i	$-0.489657\pi$
$571$	522.066	−	301.415i	0.914302	−	0.527873i	0.881813	+	0.471600i	$0.156323\pi$
$572$	370.092	+	509.112i	0.647014	+	0.890056i
$573$	−550.431	+	550.431i	−0.960613	+	0.960613i
$574$	464.776	+	245.444i	0.809713	+	0.427602i
$575$	10.6143	+	25.9333i	0.0184597	+	0.0451014i
$576$	−608.695	−	935.723i	−1.05676	−	1.62452i
$577$	−167.006	+	623.276i	−0.289439	+	1.08020i	0.656095	+	0.754678i	$0.272207\pi$
$577$	−167.006	+	623.276i	−0.289439	+	1.08020i	−0.945534	+	0.325522i	$0.894460\pi$
$578$	−44.6880	+	568.751i	−0.0773148	+	0.983998i
$579$	45.4748	+	26.2549i	0.0785402	+	0.0453452i
$580$	−669.666	−	475.130i	−1.15460	−	0.819189i
$581$	73.2443	−	499.295i	0.126066	−	0.859372i
$582$	188.668	+	129.632i	0.324172	+	0.222736i
$583$	27.3229	+	101.970i	0.0468660	+	0.174906i
$584$	−431.942	−	234.310i	−0.739628	−	0.401215i
$585$	−1583.78	+	533.906i	−2.70731	+	0.912660i
$586$	−199.508	−	70.6206i	−0.340457	−	0.120513i
$587$	−168.260	+	168.260i	−0.286644	+	0.286644i	−0.835752	−	0.549108i	$-0.814968\pi$
$587$	−168.260	+	168.260i	−0.286644	+	0.286644i	0.549108	+	0.835752i	$0.314968\pi$
$588$	951.086	−	333.508i	1.61749	−	0.567191i
$589$		−	467.325i		−	0.793421i
$590$	−246.889	−	147.544i	−0.418455	−	0.250075i
$591$	−367.640	−	636.772i	−0.622065	−	1.07745i
$592$	338.716	−	172.804i	0.572155	−	0.291899i
$593$	35.8252	+	133.701i	0.0604134	+	0.225466i	0.989531	−	0.144317i	$-0.0460986\pi$
$593$	35.8252	+	133.701i	0.0604134	+	0.225466i	−0.929118	+	0.369783i	$0.879432\pi$
$594$	700.887	−	129.995i	1.17994	−	0.218847i
$595$	−61.2683	+	28.9404i	−0.102972	+	0.0486393i
$596$	832.251	−	319.717i	1.39639	−	0.536438i
$597$	484.216	+	1807.12i	0.811083	+	3.02700i
$598$	−3.36523	+	42.8298i	−0.00562747	+	0.0716217i
$599$	66.7826	+	115.671i	0.111490	+	0.193107i	0.916371	−	0.400329i	$-0.131104\pi$
$599$	66.7826	+	115.671i	0.111490	+	0.193107i	−0.804881	+	0.593436i	$0.797771\pi$
$600$	372.224	−	958.711i	0.620373	−	1.59785i
$601$		−	762.252i		−	1.26831i	−0.773208	−	0.634153i	$-0.781349\pi$
$601$		−	762.252i		−	1.26831i	0.773208	−	0.634153i	$-0.218651\pi$
$602$	7.27686	+	23.5632i	0.0120878	+	0.0391416i
$603$	551.532	−	551.532i	0.914647	−	0.914647i
$604$	109.196	−	690.586i	0.180788	−	1.14335i
$605$	−119.008	+	240.049i	−0.196707	+	0.396776i
$606$	34.3966	−	29.3851i	0.0567600	−	0.0484903i
$607$	−159.743	−	596.170i	−0.263169	−	0.982159i	−0.963362	−	0.268205i	$-0.913569\pi$
$607$	−159.743	−	596.170i	−0.263169	−	0.982159i	0.700193	−	0.713953i	$-0.253097\pi$
$608$	−767.211	+	101.508i	−1.26186	+	0.166954i
$609$	−545.313	−	1373.49i	−0.895424	−	2.25531i
$610$	8.79967	−	584.071i	0.0144257	−	0.957493i
$611$	−1187.52	−	685.616i	−1.94357	−	1.12212i
$612$	14.1532	+	134.326i	0.0231261	+	0.219486i
$613$	84.3991	−	314.982i	0.137682	−	0.513837i	−0.862290	−	0.506414i	$-0.830971\pi$
$613$	84.3991	−	314.982i	0.137682	−	0.513837i	0.999972	−	0.00742237i	$-0.00236263\pi$
$614$	−420.050	−	148.687i	−0.684121	−	0.242161i
$615$	946.319	+	190.305i	1.53873	+	0.309439i
$616$	−368.059	−	275.577i	−0.597498	−	0.447366i
$617$	−710.167	+	710.167i	−1.15100	+	1.15100i	−0.164648	+	0.986352i	$0.552649\pi$
$617$	−710.167	+	710.167i	−1.15100	+	1.15100i	−0.986352	+	0.164648i	$0.947351\pi$
$618$	−530.849	+	253.286i	−0.858980	+	0.409848i
$619$	254.105	−	146.708i	0.410509	−	0.237008i	−0.280499	−	0.959854i	$-0.590500\pi$
$619$	254.105	−	146.708i	0.410509	−	0.237008i	0.691008	+	0.722847i	$0.257167\pi$
$620$	−384.783	−	36.0731i	−0.620618	−	0.0581824i
$621$	42.1375	+	24.3281i	0.0678542	+	0.0391756i
$622$	652.675	−	949.910i	1.04932	−	1.52719i
$623$	590.453	−	68.8869i	0.947757	−	0.110573i
$624$	1171.23	−	1055.67i	1.87696	−	1.69178i
$625$	605.044	−	156.676i	0.968070	−	0.250681i
$626$	−123.333	+	105.364i	−0.197018	+	0.168313i
$627$	264.272	−	986.275i	0.421486	−	1.57301i
$628$	282.496	+	388.612i	0.449835	+	0.618810i
$629$	−46.0098			−0.0731475
$630$	990.364	−	714.045i	1.57201	−	1.13340i
$631$			795.520i			1.26073i	0.776299	+	0.630365i	$0.217095\pi$
$631$			795.520i			1.26073i	−0.776299	+	0.630365i	$0.782905\pi$
$632$	−278.353	+	293.550i	−0.440431	+	0.464477i
$633$	370.943	+	99.3938i	0.586007	+	0.157020i
$634$	134.332	−	114.761i	0.211881	−	0.181010i
$635$	745.679	+	656.724i	1.17430	+	1.03421i
$636$	246.871	−	94.8379i	0.388162	−	0.149116i
$637$	445.332	+	826.761i	0.699109	+	1.29790i
$638$	−381.783	+	555.651i	−0.598406	+	0.870926i
$639$	−357.855	+	619.824i	−0.560024	+	0.969990i
$640$	24.3575	+	639.536i	0.0380587	+	0.999276i
$641$	291.596	+	505.060i	0.454909	+	0.787925i	0.998683	−	0.0513065i	$-0.0163385\pi$
$641$	291.596	+	505.060i	0.454909	+	0.787925i	−0.543774	+	0.839232i	$0.683005\pi$
$642$	620.468	−	296.046i	0.966462	−	0.461131i
$643$	−191.432	−	191.432i	−0.297717	−	0.297717i	0.542402	−	0.840119i	$-0.317515\pi$
$643$	−191.432	−	191.432i	−0.297717	−	0.297717i	−0.840119	+	0.542402i	$0.817515\pi$
$644$	−6.88322	−	30.6199i	−0.0106882	−	0.0475464i
$645$	25.0826	+	37.7103i	0.0388877	+	0.0584655i
$646$	88.2737	+	31.2466i	0.136647	+	0.0483693i
$647$	419.564	+	112.422i	0.648476	+	0.173758i	0.568040	−	0.823001i	$-0.307702\pi$
$647$	419.564	+	112.422i	0.648476	+	0.173758i	0.0804360	+	0.996760i	$0.474369\pi$
$648$	−150.709	−	508.064i	−0.232576	−	0.784050i
$649$	−118.075	+	204.512i	−0.181934	+	0.315119i
$650$	936.476	+	203.050i	1.44073	+	0.312384i
$651$	−545.511	−	431.523i	−0.837959	−	0.662862i
$652$	−191.567	−	85.2320i	−0.293814	−	0.130724i
$653$	264.563	−	70.8894i	0.405150	−	0.108560i	−0.0504882	−	0.998725i	$-0.516078\pi$
$653$	264.563	−	70.8894i	0.405150	−	0.108560i	0.455638	+	0.890165i	$0.349411\pi$
$654$	−388.660	+	332.034i	−0.594281	+	0.507697i
$655$	158.581	−	319.872i	0.242108	−	0.488354i
$656$	−587.499	+	125.193i	−0.895577	+	0.190843i
$657$	−757.575	−	757.575i	−1.15308	−	1.15308i
$658$	976.658	+	222.575i	1.48428	+	0.338259i
$659$	193.657			0.293865			0.146933	−	0.989147i	$-0.453060\pi$
$659$	193.657			0.293865			0.146933	+	0.989147i	$0.453060\pi$
$660$	−791.674	−	293.725i	−1.19951	−	0.445039i
$661$	−550.039	+	317.565i	−0.832132	+	0.480431i	−0.854582	−	0.519316i	$-0.826187\pi$
$661$	−550.039	+	317.565i	−0.832132	+	0.480431i	0.0224503	+	0.999748i	$0.492853\pi$
$662$	−60.7484	+	773.155i	−0.0917649	+	1.16791i
$663$	−184.287	+	49.3795i	−0.277959	+	0.0744789i
$664$	301.531	+	491.627i	0.454112	+	0.740402i
$665$	−151.114	−	832.851i	−0.227239	−	1.25241i
$666$	815.133	−	151.185i	1.22392	−	0.227004i
$667$	−44.4487	+	11.9100i	−0.0666397	+	0.0178560i
$668$	91.1673	+	865.255i	0.136478	+	1.29529i
$669$	7.77262	−	4.48753i	0.0116183	−	0.00670781i
$670$	−433.646	+	109.221i	−0.647233	+	0.163016i
$671$	−479.612			−0.714771
$672$	−589.943	+	989.301i	−0.877892	+	1.47217i
$673$	870.139	+	870.139i	1.29293	+	1.29293i	0.932969	+	0.359956i	$0.117208\pi$
$673$	870.139	+	870.139i	1.29293	+	1.29293i	0.359956	+	0.932969i	$0.382792\pi$
$674$	428.180	+	151.564i	0.635282	+	0.224873i
$675$	664.272	−	858.195i	0.984106	−	1.27140i
$676$	616.518	+	498.983i	0.912009	+	0.738141i
$677$	45.4465	−	12.1774i	0.0671292	−	0.0179872i	−0.225098	−	0.974336i	$-0.572270\pi$
$677$	45.4465	−	12.1774i	0.0671292	−	0.0179872i	0.292227	+	0.956349i	$0.405604\pi$
$678$	−154.061	−	105.854i	−0.227228	−	0.156126i
$679$	22.6142	−	154.158i	0.0333052	−	0.227036i
$680$	32.5415	−	70.2703i	0.0478551	−	0.103339i
$681$	−779.640	+	1350.38i	−1.14485	+	1.98293i
$682$	−24.8555	+	316.340i	−0.0364450	+	0.463842i
$683$	−754.857	−	202.263i	−1.10521	−	0.296140i	−0.340324	−	0.940308i	$-0.610537\pi$
$683$	−754.857	−	202.263i	−1.10521	−	0.296140i	−0.764884	+	0.644168i	$0.777204\pi$
$684$	−1666.58	−	263.519i	−2.43651	−	0.385262i
$685$	639.426	+	128.589i	0.933469	+	0.187721i
$686$	−489.045	−	481.072i	−0.712894	−	0.701272i
$687$	−1280.36	−	1280.36i	−1.86369	−	1.86369i
$688$	−23.6453	−	15.3381i	−0.0343681	−	0.0222937i
$689$	123.205	+	213.397i	0.178817	+	0.309720i
$690$	−28.0630	−	50.3430i	−0.0406710	−	0.0729609i
$691$	−366.696	+	635.136i	−0.530674	+	0.919155i	0.468685	+	0.883365i	$0.344728\pi$
$691$	−366.696	+	635.136i	−0.530674	+	0.919155i	−0.999359	+	0.0357895i	$0.988605\pi$
$692$	541.144	+	240.766i	0.782000	+	0.347927i
$693$	−598.457	−	804.224i	−0.863574	−	1.16050i
$694$	156.754	−	29.0736i	0.225871	−	0.0418928i
$695$	56.8206	+	895.787i	0.0817563	+	1.28890i
$696$	1484.54	+	805.295i	2.13295	+	1.15703i
$697$	70.2063	+	18.8117i	0.100726	+	0.0269895i
$698$	−445.720	−	934.163i	−0.638568	−	1.33834i
$699$		−	104.543i		−	0.149561i
$700$	−697.412	+	60.1348i	−0.996303	+	0.0859069i
$701$	235.306			0.335671			0.167836	−	0.985815i	$-0.446322\pi$
$701$	235.306			0.335671			0.167836	+	0.985815i	$0.446322\pi$
$702$	1501.69	−	716.509i	2.13917	−	1.02067i
$703$	148.757	−	555.169i	0.211603	−	0.789714i
$704$	524.737	−	27.9070i	0.745365	−	0.0396406i
$705$	1835.92	−	116.454i	2.60414	−	0.165183i
$706$	209.657	+	1130.40i	0.296965	+	1.60113i
$707$	−28.2712	−	12.2021i	−0.0399875	−	0.0172590i
$708$	540.506	+	240.482i	0.763426	+	0.339664i
$709$	−688.468	−	397.487i	−0.971041	−	0.560631i	−0.0714875	−	0.997441i	$-0.522775\pi$
$709$	−688.468	−	397.487i	−0.971041	−	0.560631i	−0.899553	+	0.436811i	$0.856108\pi$
$710$	358.415	−	199.793i	0.504810	−	0.281399i
$711$	−763.827	+	440.996i	−1.07430	+	0.620247i
$712$	−467.464	+	492.986i	−0.656550	+	0.692395i
$713$	−15.3151	+	15.3151i	−0.0214799	+	0.0214799i
$714$	117.985	−	74.1897i	0.165245	−	0.103907i
$715$	155.114	−	771.327i	0.216943	−	1.07878i
$716$	1271.46	+	201.043i	1.77578	+	0.280787i
$717$	535.268	−	1997.65i	0.746539	−	2.78612i
$718$	1407.18	+	110.565i	1.95986	+	0.153990i
$719$	36.9887	+	21.3554i	0.0514447	+	0.0297016i	0.525502	−	0.850793i	$-0.323878\pi$
$719$	36.9887	+	21.3554i	0.0514447	+	0.0297016i	−0.474057	+	0.880494i	$0.657211\pi$
$720$	−345.619	+	1351.87i	−0.480026	+	1.87760i
$721$	313.982	+	248.373i	0.435481	+	0.344484i
$722$	−253.565	+	369.042i	−0.351199	+	0.511138i
$723$	−426.901	−	1593.22i	−0.590458	−	2.20362i
$724$	−544.794	−	440.933i	−0.752478	−	0.609024i
$725$	129.686	+	1018.15i	0.178877	+	1.40434i
$726$	183.893	−	519.511i	0.253296	−	0.715580i
$727$	−370.230	+	370.230i	−0.509257	+	0.509257i	−0.914298	−	0.405041i	$-0.867257\pi$
$727$	−370.230	+	370.230i	−0.509257	+	0.509257i	0.405041	+	0.914298i	$0.367257\pi$
$728$	−996.311	−	398.967i	−1.36856	−	0.548032i
$729$			853.576i			1.17089i
$730$	150.024	+	595.649i	0.205512	+	0.815958i
$731$	1.70514	+	2.95339i	0.00233261	+	0.00404020i
$732$	125.898	+	1194.88i	0.171992	+	1.63235i
$733$	276.381	+	1031.47i	0.377055	+	1.40719i	0.850319	+	0.526267i	$0.176409\pi$
$733$	276.381	+	1031.47i	0.377055	+	1.40719i	−0.473264	+	0.880920i	$0.656924\pi$
$734$	−216.612	−	1167.89i	−0.295111	−	1.59113i
$735$	−1111.73	−	592.650i	−1.51256	−	0.806326i
$736$	28.4696	+	21.8164i	0.0386815	+	0.0296418i
$737$	95.0304	+	354.658i	0.128942	+	0.481219i
$738$	−1305.62	−	102.586i	−1.76914	−	0.139005i
$739$	−719.106	−	1245.53i	−0.973079	−	1.68542i	−0.686133	−	0.727476i	$-0.740693\pi$
$739$	−719.106	−	1245.53i	−0.973079	−	1.68542i	−0.286946	−	0.957947i	$-0.592640\pi$
$740$	−445.629	−	165.336i	−0.602201	−	0.223428i
$741$		−	2383.32i		−	3.21635i
$742$	−131.993	−	122.390i	−0.177888	−	0.164946i
$743$	−459.601	+	459.601i	−0.618574	+	0.618574i	−0.945166	−	0.326591i	$-0.894100\pi$
$743$	−459.601	+	459.601i	−0.618574	+	0.618574i	0.326591	+	0.945166i	$0.394100\pi$
$744$	794.638	−	21.1156i	1.06806	−	0.0283812i
$745$	−998.469	−	495.005i	−1.34023	−	0.664436i
$746$	−470.935	−	551.250i	−0.631280	−	0.738941i
$747$	325.442	+	1214.56i	0.435665	+	1.62592i
$748$	−58.0921	−	25.8463i	−0.0776632	−	0.0345539i
$749$	−366.989	−	290.304i	−0.489972	−	0.387589i
$750$	−1196.95	+	468.976i	−1.59593	+	0.625302i
$751$	297.095	+	171.528i	0.395599	+	0.228399i	0.684583	−	0.728935i	$-0.259984\pi$
$751$	297.095	+	171.528i	0.395599	+	0.228399i	−0.288984	+	0.957334i	$0.593318\pi$
$752$	−1019.75	+	520.253i	−1.35606	+	0.691826i
$753$	542.353	−	2024.09i	0.720256	−	2.68803i
$754$	−525.091	+	1483.42i	−0.696407	+	1.96740i
$755$	−727.689	+	484.015i	−0.963826	+	0.641079i
$756$	−893.711	+	823.806i	−1.18216	+	1.08969i
$757$	505.150	−	505.150i	0.667306	−	0.667306i	−0.289786	−	0.957092i	$-0.593584\pi$
$757$	505.150	−	505.150i	0.667306	−	0.667306i	0.957092	+	0.289786i	$0.0935841\pi$
$758$	176.695	+	370.326i	0.233107	+	0.488557i
$759$	−40.9828	+	23.6615i	−0.0539958	+	0.0311745i
$760$	742.692	+	619.851i	0.977226	+	0.815594i
$761$	−584.540	−	337.484i	−0.768121	−	0.443475i	0.0640828	−	0.997945i	$-0.479588\pi$
$761$	−584.540	−	337.484i	−0.768121	−	0.443475i	−0.832204	+	0.554470i	$0.812921\pi$
$762$	−1684.49	−	1157.40i	−2.21062	−	1.51890i
$763$	319.447	+	137.876i	0.418672	+	0.180703i
$764$	−565.250	+	217.146i	−0.739856	+	0.284223i
$765$	111.588	−	126.703i	0.145867	−	0.165625i
$766$	−114.884	−	134.477i	−0.149980	−	0.175558i
$767$	−142.663	+	532.427i	−0.186002	+	0.694168i
$768$	−207.269	−	1299.98i	−0.269882	−	1.69268i
$769$	824.304			1.07192			0.535959	−	0.844244i	$-0.319950\pi$
$769$	824.304			1.07192			0.535959	+	0.844244i	$0.319950\pi$
$770$	57.9948	+	571.809i	0.0753180	+	0.742608i
$771$		−	27.0770i		−	0.0351193i
$772$	24.0174	+	33.0392i	0.0311106	+	0.0427969i
$773$	877.809	+	235.208i	1.13559	+	0.304280i	0.777175	−	0.629284i	$-0.216652\pi$
$773$	877.809	+	235.208i	1.13559	+	0.304280i	0.358412	+	0.933564i	$0.383318\pi$
$774$	−39.9137	−	46.7207i	−0.0515680	−	0.0603627i
$775$	292.470	+	384.493i	0.377381	+	0.496120i
$776$	93.0978	+	151.790i	0.119971	+	0.195606i
$777$	−510.691	−	686.282i	−0.657261	−	0.883246i
$778$	−518.075	−	355.965i	−0.665906	−	0.457538i
$779$	−453.976	+	786.310i	−0.582768	+	1.00938i
$780$	−1962.36	−	183.970i	−2.51585	−	0.235858i
$781$	−168.457	−	291.776i	−0.215694	−	0.373592i
$782$	−1.86889	−	3.91691i	−0.00238988	−	0.00500884i
$783$	1260.19	+	1260.19i	1.60944	+	1.60944i
$784$	781.407	+	63.7146i	0.996692	+	0.0812686i
$785$	118.401	−	588.764i	0.150829	−	0.750018i
$786$	−245.042	+	692.261i	−0.311758	+	0.880739i
$787$	−33.0716	−	8.86150i	−0.0420223	−	0.0112599i	0.237747	−	0.971327i	$-0.423591\pi$
$787$	−33.0716	−	8.86150i	−0.0420223	−	0.0112599i	−0.279769	+	0.960067i	$0.590258\pi$
$788$	−59.9328	−	568.812i	−0.0760568	−	0.721843i
$789$	−18.4868	+	32.0201i	−0.0234307	+	0.0405832i
$790$	505.616	+	7.61766i	0.640020	+	0.00964261i
$791$	−18.4661	+	125.880i	−0.0233452	+	0.159141i
$792$	1114.12	+	267.021i	1.40671	+	0.337147i
$793$	−1081.34	+	289.743i	−1.36360	+	0.365376i
$794$	−665.710	−	779.243i	−0.838425	−	0.981414i
$795$	−296.176	−	146.833i	−0.372549	−	0.184696i
$796$	−227.291	+	1437.46i	−0.285541	+	1.80585i
$797$	−762.713	−	762.713i	−0.956980	−	0.956980i	0.0421325	−	0.999112i	$-0.486585\pi$
$797$	−762.713	−	762.713i	−0.956980	−	0.956980i	−0.999112	+	0.0421325i	$0.986585\pi$
$798$	513.731	+	1663.52i	0.643774	+	2.08461i
$799$	138.519			0.173366
$800$	567.698	−	563.666i	0.709622	−	0.704583i
$801$	−1282.77	+	740.606i	−1.60146	+	0.924601i
$802$	−407.561	−	32.0229i	−0.508181	−	0.0399288i
$803$	487.153	−	130.532i	0.606666	−	0.162556i
$804$	858.631	−	329.852i	1.06795	−	0.410263i
$805$	−22.3419	+	32.2464i	−0.0277539	+	0.0400577i
$806$	135.068	+	728.239i	0.167578	+	0.903523i
$807$	262.631	−	70.3719i	0.325442	−	0.0872018i
$808$	33.7379	−	10.0078i	0.0417548	−	0.0123859i
$809$	−613.277	+	354.076i	−0.758068	+	0.437671i	−0.828602	−	0.559839i	$-0.810863\pi$
$809$	−613.277	+	354.076i	−0.758068	+	0.437671i	0.0705338	+	0.997509i	$0.477530\pi$
$810$	−339.821	+	568.628i	−0.419532	+	0.702010i
$811$	1268.64			1.56429			0.782147	−	0.623094i	$-0.214125\pi$
$811$	1268.64			1.56429			0.782147	+	0.623094i	$0.214125\pi$
$812$	46.7493	−	1148.59i	0.0575730	−	1.41451i
$813$	832.761	+	832.761i	1.02431	+	1.02431i
$814$	−130.224	+	367.891i	−0.159980	+	0.451955i
$815$	83.7238	+	248.358i	0.102729	+	0.304733i
$816$	−49.1430	+	151.512i	−0.0602242	+	0.185677i
$817$	−41.1495	+	11.0260i	−0.0503666	+	0.0134957i
$818$	696.531	−	1013.74i	0.851505	−	1.23929i
$819$	−1835.13	−	1451.67i	−2.24070	−	1.77249i
$820$	612.384	+	434.488i	0.746810	+	0.529863i
$821$	−7.86332	+	13.6197i	−0.00957774	+	0.0165891i	−0.870775	−	0.491683i	$-0.836382\pi$
$821$	−7.86332	+	13.6197i	−0.00957774	+	0.0165891i	0.861197	+	0.508272i	$0.169715\pi$
$822$	−1337.42	−	105.084i	−1.62704	−	0.127840i
$823$	1237.02	+	331.459i	1.50306	+	0.402744i	0.914124	−	0.405434i	$-0.132880\pi$
$823$	1237.02	+	331.459i	1.50306	+	0.402744i	0.588938	+	0.808178i	$0.299546\pi$
$824$	−457.372	+	12.1536i	−0.555064	+	0.0147495i
$825$	399.819	+	976.853i	0.484629	+	1.18406i
$826$	−15.1896	−	402.377i	−0.0183894	−	0.487139i
$827$	70.4321	+	70.4321i	0.0851658	+	0.0851658i	0.748406	−	0.663241i	$-0.230819\pi$
$827$	70.4321	+	70.4321i	0.0851658	+	0.0851658i	−0.663241	+	0.748406i	$0.730819\pi$
$828$	45.9808	+	63.2529i	0.0555324	+	0.0763924i
$829$	518.410	+	897.913i	0.625344	+	1.08313i	0.988474	+	0.151389i	$0.0483747\pi$
$829$	518.410	+	897.913i	0.625344	+	1.08313i	−0.363130	+	0.931738i	$0.618292\pi$
$830$	197.055	−	693.458i	0.237415	−	0.835492i
$831$	−273.828	+	474.283i	−0.329516	+	0.570738i
$832$	1166.22	−	379.924i	1.40170	−	0.456639i
$833$	−80.7185	−	49.8353i	−0.0969010	−	0.0598263i
$834$	−336.681	−	1815.26i	−0.403694	−	2.17657i
$835$	718.794	−	816.157i	0.860831	−	0.977434i
$836$	499.691	−	617.392i	0.597717	−	0.738507i
$837$	810.247	+	217.105i	0.968037	+	0.259385i
$838$	−310.542	+	148.170i	−0.370575	+	0.176814i
$839$			891.282i			1.06232i	0.847273	+	0.531158i	$0.178243\pi$
$839$			891.282i			1.06232i	−0.847273	+	0.531158i	$0.821757\pi$
$840$	1409.35	−	294.585i	1.67780	−	0.350696i
$841$	−844.503			−1.00417
$842$	−201.772	−	422.884i	−0.239634	−	0.502237i
$843$	598.698	−	2234.37i	0.710200	−	2.65050i
$844$	232.204	+	187.936i	0.275123	+	0.222673i
$845$	−62.7612	−	989.443i	−0.0742737	−	1.17094i
$846$	−2454.08	+	455.164i	−2.90080	+	0.538019i
$847$	−372.575	+	43.4676i	−0.439876	+	0.0513194i
$848$	205.443	+	10.6607i	0.242268	+	0.0125715i
$849$	83.5742	+	48.2516i	0.0984384	+	0.0568334i
$850$	−92.1828	+	29.5369i	−0.108450	+	0.0347492i
$851$	−23.0690	+	13.3189i	−0.0271081	+	0.0156509i
$852$	−682.694	+	496.275i	−0.801284	+	0.582482i
$853$	−427.944	+	427.944i	−0.501693	+	0.501693i	−0.911964	−	0.410271i	$-0.865434\pi$
$853$	−427.944	+	427.944i	−0.501693	+	0.501693i	0.410271	+	0.911964i	$0.365434\pi$
$854$	692.300	−	435.321i	0.810655	−	0.509744i
$855$	1168.06	+	1756.11i	1.36615	+	2.05393i
$856$	534.587	−	14.2054i	0.624517	−	0.0165951i
$857$	−244.237	+	911.506i	−0.284991	+	1.06360i	0.663855	+	0.747861i	$0.268919\pi$
$857$	−244.237	+	911.506i	−0.284991	+	1.06360i	−0.948846	+	0.315739i	$0.897747\pi$
$858$	−126.761	+	1613.31i	−0.147740	+	1.88031i
$859$	−1154.68	−	666.658i	−1.34422	−	0.776086i	−0.356796	−	0.934182i	$-0.616131\pi$
$859$	−1154.68	−	666.658i	−1.34422	−	0.776086i	−0.987424	+	0.158097i	$0.949464\pi$
$860$	5.90214	+	34.7325i	0.00686295	+	0.0403866i
$861$	498.668	+	1256.00i	0.579173	+	1.45877i
$862$	563.966	+	387.496i	0.654252	+	0.449531i
$863$	209.718	+	782.679i	0.243011	+	0.906928i	0.974373	+	0.224939i	$0.0722182\pi$
$863$	209.718	+	782.679i	0.243011	+	0.906928i	−0.731362	+	0.681989i	$0.761115\pi$
$864$	180.428	−	1377.35i	0.208829	−	1.59415i
$865$	−236.505	−	701.568i	−0.273417	−	0.811062i
$866$	1069.49	+	378.572i	1.23498	+	0.437150i
$867$	−1037.19	+	1037.19i	−1.19630	+	1.19630i
$868$	−251.250	−	479.184i	−0.289458	−	0.552056i
$869$		−	415.188i		−	0.477777i
$870$	−515.615	−	2047.18i	−0.592661	−	2.35308i
$871$	428.513	+	742.206i	0.491978	+	0.852131i
$872$	−381.218	+	113.082i	−0.437176	+	0.129681i
$873$	100.480	+	374.998i	0.115098	+	0.429550i
$874$	53.3051	−	9.88662i	0.0609898	−	0.0113119i
$875$	645.560	+	590.659i	0.737783	+	0.675038i
$876$	−453.078	−	1179.40i	−0.517213	−	1.34635i
$877$	−29.7005	−	110.844i	−0.0338660	−	0.126390i	0.946923	−	0.321459i	$-0.104173\pi$
$877$	−29.7005	−	110.844i	−0.0338660	−	0.126390i	−0.980789	+	0.195070i	$0.937507\pi$
$878$	1.67036	−	21.2589i	0.00190246	−	0.0242129i
$879$	−272.070	−	471.239i	−0.309522	−	0.536108i
$880$	−469.773	−	459.089i	−0.533833	−	0.521692i
$881$			84.2997i			0.0956863i	0.998855	+	0.0478432i	$0.0152348\pi$
$881$			84.2997i			0.0956863i	−0.998855	+	0.0478432i	$0.984765\pi$
$882$	1593.80	+	617.672i	1.80704	+	0.700309i
$883$	−281.794	+	281.794i	−0.319133	+	0.319133i	−0.848434	−	0.529301i	$-0.822454\pi$
$883$	−281.794	+	281.794i	−0.319133	+	0.319133i	0.529301	+	0.848434i	$0.322454\pi$
$884$	−146.589	−	23.1787i	−0.165825	−	0.0262203i
$885$	−236.227	−	700.741i	−0.266923	−	0.791797i
$886$	−535.649	+	457.607i	−0.604570	+	0.516487i
$887$	73.7241	+	275.142i	0.0831162	+	0.310194i	0.994951	−	0.100364i	$-0.0320007\pi$
$887$	73.7241	+	275.142i	0.0831162	+	0.310194i	−0.911835	+	0.410558i	$0.865334\pi$
$888$	950.729	+	227.861i	1.07064	+	0.256600i
$889$	−201.907	+	1376.37i	−0.227117	+	1.54822i
$890$	849.129	+	12.7931i	0.954077	+	0.0143742i
$891$	471.028	+	271.948i	0.528651	+	0.305217i
$892$	6.94309	−	0.731557i	0.00778374	−	0.000820132i
$893$	−447.856	+	1671.42i	−0.501518	+	1.87169i
$894$	2160.87	+	764.891i	2.41708	+	0.855582i
$895$	−891.134	−	1339.77i	−0.995680	−	1.49695i
$896$	−732.106	+	516.562i	−0.817083	+	0.576520i
$897$	−78.1059	+	78.1059i	−0.0870746	+	0.0870746i
$898$	−97.1705	+	46.3633i	−0.108208	+	0.0516295i
$899$	−687.039	+	396.662i	−0.764226	+	0.441226i
$900$	1536.10	−	826.195i	1.70678	−	0.917995i
$901$	−21.5570	−	12.4459i	−0.0239256	−	0.0138134i
$902$	349.126	−	508.121i	0.387057	−	0.563327i
$903$	−25.1263	+	58.2153i	−0.0278254	+	0.0644688i
$904$	−76.0207	−	123.947i	−0.0840937	−	0.137109i
$905$	55.4598	+	874.334i	0.0612815	+	0.966115i
$906$	1366.77	−	1167.63i	1.50857	−	1.28878i
$907$	48.3959	−	180.616i	0.0533583	−	0.199136i	−0.934101	−	0.357008i	$-0.883797\pi$
$907$	48.3959	−	180.616i	0.0533583	−	0.199136i	0.987460	+	0.157872i	$0.0504635\pi$
$908$	−981.102	+	713.198i	−1.08051	+	0.785461i
$909$	76.7247			0.0844056
$910$	476.197	+	1254.17i	0.523293	+	1.37821i
$911$		−	208.768i		−	0.229163i	−0.993414	−	0.114582i	$-0.963447\pi$
$911$		−	208.768i		−	0.229163i	0.993414	−	0.114582i	$-0.0365528\pi$
$912$	−1669.31	−	1082.84i	−1.83038	−	1.18732i
$913$	−571.743	−	153.198i	−0.626225	−	0.167796i
$914$	−185.682	+	158.629i	−0.203154	+	0.173555i
$915$	992.622	−	1127.08i	1.08483	−	1.23178i
$916$	−505.103	−	1314.83i	−0.551423	−	1.43540i
$917$	496.466	−	57.9216i	0.541402	−	0.0631643i
$918$	−95.1845	+	138.532i	−0.103687	+	0.150907i
$919$	739.876	−	1281.50i	0.805088	−	1.39445i	−0.111144	−	0.993804i	$-0.535451\pi$
$919$	739.876	−	1281.50i	0.805088	−	1.39445i	0.916232	−	0.400649i	$-0.131215\pi$
$920$	−4.02573	−	44.6532i	−0.00437579	−	0.0485361i
$921$	−572.824	−	992.160i	−0.621959	−	1.07726i
$922$	−543.322	+	259.237i	−0.589287	+	0.281169i
$923$	−556.072	−	556.072i	−0.602461	−	0.602461i
$924$	−259.276	−	1153.39i	−0.280602	−	1.24825i
$925$	225.056	+	549.865i	0.243303	+	0.594449i
$926$	−960.840	−	340.112i	−1.03762	−	0.367292i
$927$	−963.543	−	258.181i	−1.03942	−	0.278512i
$928$	800.435	+	1041.76i	0.862538	+	1.12258i
$929$	49.8229	−	86.2958i	0.0536307	−	0.0928911i	−0.837964	−	0.545726i	$-0.816254\pi$
$929$	49.8229	−	86.2958i	0.0536307	−	0.0928911i	0.891594	+	0.452835i	$0.149587\pi$
$930$	−691.951	−	713.120i	−0.744033	−	0.766796i
$931$	862.305	−	812.850i	0.926213	−	0.873094i
$932$	33.0576	−	74.3001i	0.0354696	−	0.0797212i
$933$	2862.27	−	766.942i	3.06781	−	0.822018i
$934$	299.598	−	255.948i	0.320769	−	0.274034i
$935$	25.3890	+	75.3137i	0.0271540	+	0.0805494i
$936$	2673.21	−	71.0343i	2.85599	−	0.0758914i
$937$	416.927	+	416.927i	0.444960	+	0.444960i	0.893675	−	0.448715i	$-0.148118\pi$
$937$	416.927	+	416.927i	0.444960	+	0.444960i	−0.448715	+	0.893675i	$0.648118\pi$
$938$	−459.080	−	425.680i	−0.489424	−	0.453817i
$939$	−417.060			−0.444153
$940$	1341.63	+	497.770i	1.42727	+	0.529543i
$941$	−398.597	+	230.130i	−0.423589	+	0.244559i	−0.696612	−	0.717448i	$-0.745310\pi$
$941$	−398.597	+	230.130i	−0.423589	+	0.244559i	0.273023	+	0.962008i	$0.411977\pi$
$942$	−96.7584	+	1231.46i	−0.102716	+	1.30728i
$943$	40.6466	−	10.8912i	0.0431035	−	0.0115495i
$944$	308.101	+	341.827i	0.326378	+	0.362104i
$945$	1514.20	+	124.917i	1.60233	+	0.132187i
$946$	28.4412	−	5.27506i	0.0300647	−	0.00557617i
$947$	422.151	−	113.115i	0.445778	−	0.119446i	−0.0289454	−	0.999581i	$-0.509215\pi$
$947$	422.151	−	113.115i	0.445778	−	0.119446i	0.474723	+	0.880135i	$0.342548\pi$
$948$	−1034.38	+	108.987i	−1.09112	+	0.114965i
$949$	1019.48	−	588.598i	1.07427	−	0.620230i
$950$	−58.3595	−	1207.80i	−0.0614310	−	1.27137i
$951$	454.255			0.477660
$952$	107.313	−	15.4194i	0.112724	−	0.0161968i
$953$	−961.057	−	961.057i	−1.00845	−	1.00845i	−0.999964	−	0.00849066i	$-0.997297\pi$
$953$	−961.057	−	961.057i	−1.00845	−	1.00845i	−0.00849066	−	0.999964i	$-0.502703\pi$
$954$	422.810	+	149.664i	0.443197	+	0.156880i
$955$	678.142	+	336.198i	0.710097	+	0.352040i
$956$	1012.10	−	1250.49i	1.05868	−	1.30805i
$957$	−1674.29	+	448.624i	−1.74952	+	0.468781i
$958$	−711.677	−	488.987i	−0.742878	−	0.510425i
$959$	336.949	+	848.677i	0.351354	+	0.884960i
$960$	−1020.43	+	1290.88i	−1.06295	+	1.34466i
$961$	293.801	−	508.878i	0.305724	−	0.529530i
$962$	−71.3530	+	908.122i	−0.0741716	+	0.943994i
$963$	1126.21	+	301.767i	1.16948	+	0.313362i
$964$	200.387	−	1267.31i	0.207871	−	1.31464i
$965$	10.0662	−	50.0558i	0.0104313	−	0.0518713i
$966$	37.6807	−	71.3526i	0.0390069	−	0.0738640i
$967$	−573.515	−	573.515i	−0.593087	−	0.593087i	0.345377	−	0.938464i	$-0.387751\pi$
$967$	−573.515	−	573.515i	−0.593087	−	0.593087i	−0.938464	+	0.345377i	$0.887751\pi$
$968$	294.969	−	311.074i	0.304720	−	0.321357i
$969$	120.379	+	208.503i	0.124230	+	0.215173i
$970$	60.8408	−	214.106i	0.0627225	−	0.220728i
$971$	−260.728	+	451.594i	−0.268515	+	0.465081i	−0.968479	−	0.249097i	$-0.919866\pi$
$971$	−260.728	+	451.594i	−0.268515	+	0.465081i	0.699964	+	0.714178i	$0.253199\pi$
$972$	−81.3882	+	182.928i	−0.0837328	+	0.188197i
$973$	−1008.13	+	750.189i	−1.03610	+	0.771006i
$974$	−1788.32	+	331.683i	−1.83606	+	0.340537i
$975$	1491.57	+	1960.88i	1.52982	+	2.01116i
$976$	−288.355	+	889.024i	−0.295446	+	0.910886i
$977$	320.791	+	85.9557i	0.328343	+	0.0879792i	0.419225	−	0.907882i	$-0.362302\pi$
$977$	320.791	+	85.9557i	0.328343	+	0.0879792i	−0.0908820	+	0.995862i	$0.528969\pi$
$978$	−232.145	−	486.540i	−0.237367	−	0.497485i
$979$		−	697.265i		−	0.712221i
$980$	−602.717	−	772.743i	−0.615018	−	0.788513i
$981$	−866.942			−0.883733
$982$	−803.924	+	383.579i	−0.818660	+	0.390610i
$983$	52.2305	−	194.927i	0.0531338	−	0.198298i	−0.934257	−	0.356601i	$-0.883936\pi$
$983$	52.2305	−	194.927i	0.0531338	−	0.198298i	0.987391	+	0.158303i	$0.0506023\pi$
$984$	−1357.55	−	736.411i	−1.37963	−	0.748385i
$985$	−472.530	+	536.536i	−0.479726	+	0.544707i
$986$	−28.9889	−	156.298i	−0.0294005	−	0.158517i
$987$	1537.51	+	2066.16i	1.55777	+	2.09337i
$988$	753.628	−	1693.85i	0.762782	−	1.71442i
$989$	1.70989	+	0.987206i	0.00172891	+	0.000998186i
$990$	−697.279	−	1250.87i	−0.704322	−	1.26350i
$991$	−55.5963	+	32.0985i	−0.0561012	+	0.0323901i	−0.527788	−	0.849376i	$-0.676979\pi$
$991$	−55.5963	+	32.0985i	−0.0561012	+	0.0323901i	0.471687	+	0.881766i	$0.343645\pi$
$992$	571.435	+	236.265i	0.576044	+	0.238171i
$993$	−1409.95	+	1409.95i	−1.41989	+	1.41989i
$994$	507.992	+	268.266i	0.511058	+	0.269885i
$995$	1514.69	−	1007.48i	1.52230	−	1.01254i
$996$	−231.587	+	1464.63i	−0.232517	+	1.47051i
$997$	412.030	−	1537.72i	0.413270	−	1.54234i	−0.375006	−	0.927022i	$-0.622359\pi$
$997$	412.030	−	1537.72i	0.413270	−	1.54234i	0.788276	−	0.615322i	$-0.210974\pi$
$998$	567.553	+	44.5938i	0.568690	+	0.0446832i
$999$	893.442	+	515.829i	0.894337	+	0.516345i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.3.x.a.103.29	yes	176
4.3	odd	2	inner	140.3.x.a.103.23	yes	176
5.2	odd	4	inner	140.3.x.a.47.7	yes	176
7.3	odd	6	inner	140.3.x.a.3.2	✓	176
20.7	even	4	inner	140.3.x.a.47.2	yes	176
28.3	even	6	inner	140.3.x.a.3.7	yes	176
35.17	even	12	inner	140.3.x.a.87.23	yes	176
140.87	odd	12	inner	140.3.x.a.87.29	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.3.x.a.3.2	✓	176	7.3	odd	6	inner
140.3.x.a.3.7	yes	176	28.3	even	6	inner
140.3.x.a.47.2	yes	176	20.7	even	4	inner
140.3.x.a.47.7	yes	176	5.2	odd	4	inner
140.3.x.a.87.23	yes	176	35.17	even	12	inner
140.3.x.a.87.29	yes	176	140.87	odd	12	inner
140.3.x.a.103.23	yes	176	4.3	odd	2	inner
140.3.x.a.103.29	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)

\(f(q)\)	\(=\)	\(q+(0.861255 + 1.80506i) q^{2} +(-1.33089 + 4.96696i) q^{3} +(-2.51648 + 3.10923i) q^{4} +(4.98997 - 0.316518i) q^{5} +(-10.1119 + 1.87547i) q^{6} +(4.17892 + 5.61575i) q^{7} +(-7.77968 - 1.86456i) q^{8} +(-15.1051 - 8.72096i) q^{9} +O(q^{10})\)	\(q+(0.861255 + 1.80506i) q^{2} +(-1.33089 + 4.96696i) q^{3} +(-2.51648 + 3.10923i) q^{4} +(4.98997 - 0.316518i) q^{5} +(-10.1119 + 1.87547i) q^{6} +(4.17892 + 5.61575i) q^{7} +(-7.77968 - 1.86456i) q^{8} +(-15.1051 - 8.72096i) q^{9} +(4.86897 + 8.73459i) q^{10} +(7.11059 - 4.10530i) q^{11} +(-12.0943 - 16.6373i) q^{12} +(13.5515 - 13.5515i) q^{13} +(-6.53765 + 12.3798i) q^{14} +(-5.06898 + 25.2062i) q^{15} +(-3.33465 - 15.6486i) q^{16} +(-0.501070 + 1.87002i) q^{17} +(2.73247 - 34.7767i) q^{18} +(-20.9442 - 12.0921i) q^{19} +(-11.5730 + 16.3115i) q^{20} +(-33.4549 + 13.2825i) q^{21} +(13.5343 + 9.29933i) q^{22} +(0.290099 + 1.08266i) q^{23} +(19.6151 - 36.1598i) q^{24} +(24.7996 - 3.15884i) q^{25} +(36.1326 + 12.7900i) q^{26} +(30.6953 - 30.6953i) q^{27} +(-27.9768 - 1.13870i) q^{28} +41.0549i q^{29} +(-49.8644 + 12.5592i) q^{30} +(9.66176 + 16.7347i) q^{31} +(25.3748 - 19.4967i) q^{32} +(10.9274 + 40.7817i) q^{33} +(-3.80704 + 0.706101i) q^{34} +(22.6302 + 26.6997i) q^{35} +(65.1273 - 25.0193i) q^{36} +(6.15098 + 22.9558i) q^{37} +(3.78874 - 48.2199i) q^{38} +(49.2741 + 85.3453i) q^{39} +(-39.4106 - 6.84167i) q^{40} -37.5431i q^{41} +(-52.7889 - 48.9484i) q^{42} +(1.24558 - 1.24558i) q^{43} +(-5.12933 + 32.4394i) q^{44} +(-78.1346 - 38.7363i) q^{45} +(-1.70442 + 1.45610i) q^{46} +(-18.5185 - 69.1119i) q^{47} +(82.1642 + 4.26359i) q^{48} +(-14.0733 + 46.9355i) q^{49} +(27.0607 + 42.0443i) q^{50} +(-8.62142 - 4.97758i) q^{51} +(8.03267 + 76.2368i) q^{52} +(-3.32775 + 12.4193i) q^{53} +(81.8434 + 28.9704i) q^{54} +(34.1822 - 22.7360i) q^{55} +(-22.0398 - 51.4806i) q^{56} +(87.9356 - 87.9356i) q^{57} +(-74.1065 + 35.3587i) q^{58} +(-24.9083 + 14.3808i) q^{59} +(-65.6160 - 79.1916i) q^{60} +(-50.5877 - 29.2069i) q^{61} +(-21.8858 + 31.8528i) q^{62} +(-14.1484 - 121.271i) q^{63} +(57.0469 + 29.0113i) q^{64} +(63.3323 - 71.9109i) q^{65} +(-64.2021 + 54.8481i) q^{66} +(-11.5741 + 43.1952i) q^{67} +(-4.55339 - 6.26381i) q^{68} -5.76364 q^{69} +(-28.7043 + 63.8441i) q^{70} -41.0340i q^{71} +(101.252 + 96.0107i) q^{72} +(59.3322 + 15.8980i) q^{73} +(-36.1390 + 30.8737i) q^{74} +(-17.3158 + 127.383i) q^{75} +(90.3029 - 34.6907i) q^{76} +(52.7689 + 22.7756i) q^{77} +(-111.616 + 162.447i) q^{78} +(25.2837 - 43.7926i) q^{79} +(-21.5929 - 77.0308i) q^{80} +(33.1216 + 57.3683i) q^{81} +(67.7675 - 32.3342i) q^{82} +(-50.9762 - 50.9762i) q^{83} +(42.8900 - 137.444i) q^{84} +(-1.90843 + 9.48993i) q^{85} +(3.32111 + 1.17559i) q^{86} +(-203.918 - 54.6396i) q^{87} +(-62.9727 + 18.6798i) q^{88} +(42.4612 - 73.5450i) q^{89} +(2.62752 - 174.399i) q^{90} +(132.732 + 19.4712i) q^{91} +(-4.09628 - 1.82252i) q^{92} +(-95.9790 + 25.7175i) q^{93} +(108.802 - 92.9499i) q^{94} +(-108.338 - 53.7102i) q^{95} +(63.0683 + 151.983i) q^{96} +(-15.7389 - 15.7389i) q^{97} +(-96.8421 + 15.0203i) q^{98} -143.209 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

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