LMFDB - Embedded newform 57.3.g.b.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,3,Mod(31,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("57.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	57.g (of order $6$, degree $2$, 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:	$1.55313750685$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.92607408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 $ x^6 - 3x^5 + 20x^4 - 35x^3 + 94x^2 - 77*x + 43
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$0.500000 + 2.93068i$ of defining polynomial
Character	$\chi$	$=$	57.31
Dual form			57.3.g.b.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.78805 + 1.03233i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.131406 - 0.227602i) q^{4} +(-3.20750 - 5.55555i) q^{5} +(1.78805 - 3.09699i) q^{6} -2.26281 q^{7} -7.71601i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.78805 + 1.03233i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.131406 - 0.227602i) q^{4} +(-3.20750 - 5.55555i) q^{5} +(1.78805 - 3.09699i) q^{6} -2.26281 q^{7} -7.71601i q^{8} +(1.50000 - 2.59808i) q^{9} +(11.4703 + 6.62239i) q^{10} -20.0928 q^{11} +0.455204i q^{12} +(-0.135471 - 0.0782143i) q^{13} +(4.04601 - 2.33597i) q^{14} +(9.62250 + 5.55555i) q^{15} +(8.49109 + 14.7070i) q^{16} +(12.3133 + 21.3272i) q^{17} +6.19397i q^{18} +(-18.9317 - 1.60945i) q^{19} -1.68594 q^{20} +(3.39422 - 1.95965i) q^{21} +(35.9269 - 20.7424i) q^{22} +(-2.62250 + 4.54230i) q^{23} +(6.68226 + 11.5740i) q^{24} +(-8.07609 + 13.9882i) q^{25} +0.322972 q^{26} +5.19615i q^{27} +(-0.297347 + 0.515021i) q^{28} +(-31.4573 - 18.1619i) q^{29} -22.9406 q^{30} -17.1105i q^{31} +(-3.63586 - 2.09917i) q^{32} +(30.1392 - 17.4009i) q^{33} +(-44.0334 - 25.4227i) q^{34} +(7.25797 + 12.5712i) q^{35} +(-0.394218 - 0.682806i) q^{36} -42.7124i q^{37} +(35.5123 - 16.6660i) q^{38} +0.270942 q^{39} +(-42.8667 + 24.7491i) q^{40} +(30.0928 - 17.3741i) q^{41} +(-4.04601 + 7.00790i) q^{42} +(12.5553 + 21.7464i) q^{43} +(-2.64032 + 4.57316i) q^{44} -19.2450 q^{45} -10.8291i q^{46} +(-14.6778 + 25.4227i) q^{47} +(-25.4733 - 14.7070i) q^{48} -43.8797 q^{49} -33.3487i q^{50} +(-36.9398 - 21.3272i) q^{51} +(-0.0356035 + 0.0205557i) q^{52} +(48.4176 + 27.9539i) q^{53} +(-5.36414 - 9.29096i) q^{54} +(64.4476 + 111.627i) q^{55} +17.4599i q^{56} +(29.7914 - 13.9812i) q^{57} +74.9962 q^{58} +(-29.9269 + 17.2783i) q^{59} +(2.52891 - 1.46007i) q^{60} +(27.3805 - 47.4244i) q^{61} +(17.6637 + 30.5944i) q^{62} +(-3.39422 + 5.87896i) q^{63} -59.2606 q^{64} +1.00349i q^{65} +(-35.9269 + 62.2272i) q^{66} +(66.0698 + 38.1454i) q^{67} +6.47216 q^{68} -9.08459i q^{69} +(-25.9552 - 14.9852i) q^{70} +(63.6080 - 36.7241i) q^{71} +(-20.0468 - 11.5740i) q^{72} +(-45.9053 - 79.5103i) q^{73} +(44.0932 + 76.3717i) q^{74} -27.9764i q^{75} +(-2.85406 + 4.09740i) q^{76} +45.4662 q^{77} +(-0.484457 + 0.279702i) q^{78} +(-53.1300 + 30.6746i) q^{79} +(54.4703 - 94.3453i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-35.8716 + 62.1313i) q^{82} -148.793 q^{83} -1.03004i q^{84} +(78.9897 - 136.814i) q^{85} +(-44.8990 - 25.9224i) q^{86} +62.9147 q^{87} +155.036i q^{88} +(-62.7829 - 36.2477i) q^{89} +(34.4109 - 19.8672i) q^{90} +(0.306546 + 0.176984i) q^{91} +(0.689224 + 1.19377i) q^{92} +(14.8181 + 25.6657i) q^{93} -60.6093i q^{94} +(51.7820 + 110.338i) q^{95} +7.27172 q^{96} +(-70.0326 + 40.4334i) q^{97} +(78.4589 - 45.2983i) q^{98} +(-30.1392 + 52.2026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 9 q^{3} + 5 q^{4} + 4 q^{5} - 3 q^{6} - 22 q^{7} + 9 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 9 * q^3 + 5 * q^4 + 4 * q^5 - 3 * q^6 - 22 * q^7 + 9 * q^9	$ 6 q + 3 q^{2} - 9 q^{3} + 5 q^{4} + 4 q^{5} - 3 q^{6} - 22 q^{7} + 9 q^{9} + 54 q^{10} - 36 q^{11} - 3 q^{13} - 57 q^{14} - 12 q^{15} - 23 q^{16} + 38 q^{17} - 10 q^{19} + 32 q^{20} + 33 q^{21} + 36 q^{22} + 54 q^{23} + 39 q^{24} - 21 q^{25} + 118 q^{26} - 101 q^{28} - 102 q^{29} - 108 q^{30} - 63 q^{32} + 54 q^{33} - 150 q^{34} - 24 q^{35} - 15 q^{36} + 119 q^{38} + 6 q^{39} + 30 q^{40} + 96 q^{41} + 57 q^{42} + 107 q^{43} - 94 q^{44} + 24 q^{45} - 50 q^{47} + 69 q^{48} - 48 q^{49} - 114 q^{51} + 399 q^{52} - 90 q^{53} + 9 q^{54} + 148 q^{55} - 3 q^{57} - 116 q^{58} - 48 q^{60} + 27 q^{61} - 121 q^{62} - 33 q^{63} + 46 q^{64} - 36 q^{66} - 39 q^{67} - 388 q^{68} - 354 q^{70} + 84 q^{71} - 117 q^{72} - 77 q^{73} + 219 q^{74} + 215 q^{76} + 260 q^{77} - 177 q^{78} + 9 q^{79} + 312 q^{80} - 27 q^{81} - 4 q^{82} - 348 q^{83} + 68 q^{85} + 249 q^{86} + 204 q^{87} - 72 q^{89} + 162 q^{90} - 393 q^{91} - 118 q^{92} + 129 q^{93} + 104 q^{95} + 126 q^{96} - 228 q^{97} + 540 q^{98} - 54 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 9 * q^3 + 5 * q^4 + 4 * q^5 - 3 * q^6 - 22 * q^7 + 9 * q^9 + 54 * q^10 - 36 * q^11 - 3 * q^13 - 57 * q^14 - 12 * q^15 - 23 * q^16 + 38 * q^17 - 10 * q^19 + 32 * q^20 + 33 * q^21 + 36 * q^22 + 54 * q^23 + 39 * q^24 - 21 * q^25 + 118 * q^26 - 101 * q^28 - 102 * q^29 - 108 * q^30 - 63 * q^32 + 54 * q^33 - 150 * q^34 - 24 * q^35 - 15 * q^36 + 119 * q^38 + 6 * q^39 + 30 * q^40 + 96 * q^41 + 57 * q^42 + 107 * q^43 - 94 * q^44 + 24 * q^45 - 50 * q^47 + 69 * q^48 - 48 * q^49 - 114 * q^51 + 399 * q^52 - 90 * q^53 + 9 * q^54 + 148 * q^55 - 3 * q^57 - 116 * q^58 - 48 * q^60 + 27 * q^61 - 121 * q^62 - 33 * q^63 + 46 * q^64 - 36 * q^66 - 39 * q^67 - 388 * q^68 - 354 * q^70 + 84 * q^71 - 117 * q^72 - 77 * q^73 + 219 * q^74 + 215 * q^76 + 260 * q^77 - 177 * q^78 + 9 * q^79 + 312 * q^80 - 27 * q^81 - 4 * q^82 - 348 * q^83 + 68 * q^85 + 249 * q^86 + 204 * q^87 - 72 * q^89 + 162 * q^90 - 393 * q^91 - 118 * q^92 + 129 * q^93 + 104 * q^95 + 126 * q^96 - 228 * q^97 + 540 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.78805	+	1.03233i	−0.894023	+	0.516164i	−0.875256	−	0.483659i	$-0.839307\pi$
$2$	−1.78805	+	1.03233i	−0.894023	+	0.516164i	−0.0187668	+	0.999824i	$0.505974\pi$
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$	0.131406	−	0.227602i	0.0328515	−	0.0569005i
$5$	−3.20750	−	5.55555i	−0.641500	−	1.11111i	−0.985098	−	0.171993i	$-0.944979\pi$
$5$	−3.20750	−	5.55555i	−0.641500	−	1.11111i	0.343598	−	0.939117i	$-0.388354\pi$
$6$	1.78805	−	3.09699i	0.298008	−	0.516164i
$7$	−2.26281			−0.323259			−0.161629	−	0.986852i	$-0.551675\pi$
$7$	−2.26281			−0.323259			−0.161629	+	0.986852i	$0.551675\pi$
$8$		−	7.71601i		−	0.964502i
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$	11.4703	+	6.62239i	1.14703	+	0.662239i
$11$	−20.0928			−1.82662			−0.913309	−	0.407267i	$-0.866482\pi$
$11$	−20.0928			−1.82662			−0.913309	+	0.407267i	$0.866482\pi$
$12$			0.455204i			0.0379337i
$13$	−0.135471	−	0.0782143i	−0.0104209	−	0.00601649i	0.494781	−	0.869018i	$-0.335248\pi$
$13$	−0.135471	−	0.0782143i	−0.0104209	−	0.00601649i	−0.505201	+	0.863001i	$0.668582\pi$
$14$	4.04601	−	2.33597i	0.289001	−	0.166855i
$15$	9.62250	+	5.55555i	0.641500	+	0.370370i
$16$	8.49109	+	14.7070i	0.530693	+	0.919187i
$17$	12.3133	+	21.3272i	0.724311	+	1.25454i	0.959257	+	0.282534i	$0.0911752\pi$
$17$	12.3133	+	21.3272i	0.724311	+	1.25454i	−0.234947	+	0.972008i	$0.575492\pi$
$18$			6.19397i			0.344110i
$19$	−18.9317	−	1.60945i	−0.996406	−	0.0847081i
$19$	−18.9317	−	1.60945i	−0.996406	−	0.0847081i
$20$	−1.68594			−0.0842970
$21$	3.39422	−	1.95965i	0.161629	−	0.0933168i
$22$	35.9269	−	20.7424i	1.63304	−	0.942836i
$23$	−2.62250	+	4.54230i	−0.114022	+	0.197491i	−0.917388	−	0.397994i	$-0.869707\pi$
$23$	−2.62250	+	4.54230i	−0.114022	+	0.197491i	0.803367	+	0.595485i	$0.203040\pi$
$24$	6.68226	+	11.5740i	0.278428	+	0.482251i
$25$	−8.07609	+	13.9882i	−0.323044	+	0.559528i
$26$	0.322972			0.0124220
$27$			5.19615i			0.192450i
$28$	−0.297347	+	0.515021i	−0.0106195	+	0.0183936i
$29$	−31.4573	−	18.1619i	−1.08474	−	0.626272i	−0.152566	−	0.988293i	$-0.548754\pi$
$29$	−31.4573	−	18.1619i	−1.08474	−	0.626272i	−0.932170	+	0.362021i	$0.882087\pi$
$30$	−22.9406			−0.764687
$31$		−	17.1105i		−	0.551952i	−0.961165	−	0.275976i	$-0.910999\pi$
$31$		−	17.1105i		−	0.551952i	0.961165	−	0.275976i	$-0.0890010\pi$
$32$	−3.63586	−	2.09917i	−0.113621	−	0.0655989i
$33$	30.1392	−	17.4009i	0.913309	−	0.527299i
$34$	−44.0334	−	25.4227i	−1.29510	−	0.747727i
$35$	7.25797	+	12.5712i	0.207370	+	0.359176i
$36$	−0.394218	−	0.682806i	−0.0109505	−	0.0189668i
$37$		−	42.7124i		−	1.15439i	−0.816607	−	0.577194i	$-0.804148\pi$
$37$		−	42.7124i		−	1.15439i	0.816607	−	0.577194i	$-0.195852\pi$
$38$	35.5123	−	16.6660i	0.934533	−	0.438578i
$39$	0.270942			0.00694724
$40$	−42.8667	+	24.7491i	−1.07167	+	0.618728i
$41$	30.0928	−	17.3741i	0.733971	−	0.423758i	−0.0859022	−	0.996304i	$-0.527377\pi$
$41$	30.0928	−	17.3741i	0.733971	−	0.423758i	0.819873	+	0.572545i	$0.194044\pi$
$42$	−4.04601	+	7.00790i	−0.0963336	+	0.166855i
$43$	12.5553	+	21.7464i	0.291984	+	0.505731i	0.974279	−	0.225346i	$-0.0723512\pi$
$43$	12.5553	+	21.7464i	0.291984	+	0.505731i	−0.682295	+	0.731077i	$0.739018\pi$
$44$	−2.64032	+	4.57316i	−0.0600072	+	0.103936i
$45$	−19.2450			−0.427666
$46$		−	10.8291i		−	0.235415i
$47$	−14.6778	+	25.4227i	−0.312294	+	0.540909i	−0.978859	−	0.204538i	$-0.934431\pi$
$47$	−14.6778	+	25.4227i	−0.312294	+	0.540909i	0.666565	+	0.745447i	$0.267764\pi$
$48$	−25.4733	−	14.7070i	−0.530693	−	0.306396i
$49$	−43.8797			−0.895504
$50$		−	33.3487i		−	0.666975i
$51$	−36.9398	−	21.3272i	−0.724311	−	0.418181i
$52$	−0.0356035	+	0.0205557i	−0.000684682	+	0.000395301i
$53$	48.4176	+	27.9539i	0.913540	+	0.527433i	0.881568	−	0.472056i	$-0.156488\pi$
$53$	48.4176	+	27.9539i	0.913540	+	0.527433i	0.0319716	+	0.999489i	$0.489821\pi$
$54$	−5.36414	−	9.29096i	−0.0993359	−	0.172055i
$55$	64.4476	+	111.627i	1.17178	+	2.02957i
$56$			17.4599i			0.311784i
$57$	29.7914	−	13.9812i	0.522656	−	0.245284i
$58$	74.9962			1.29304
$59$	−29.9269	+	17.2783i	−0.507235	+	0.292852i	−0.731696	−	0.681631i	$-0.761271\pi$
$59$	−29.9269	+	17.2783i	−0.507235	+	0.292852i	0.224461	+	0.974483i	$0.427938\pi$
$60$	2.52891	−	1.46007i	0.0421485	−	0.0243344i
$61$	27.3805	−	47.4244i	0.448860	−	0.777448i	−0.549452	−	0.835525i	$-0.685164\pi$
$61$	27.3805	−	47.4244i	0.448860	−	0.777448i	0.998312	+	0.0580769i	$0.0184968\pi$
$62$	17.6637	+	30.5944i	0.284898	+	0.493457i
$63$	−3.39422	+	5.87896i	−0.0538765	+	0.0933168i
$64$	−59.2606			−0.925947
$65$			1.00349i			0.0154383i
$66$	−35.9269	+	62.2272i	−0.544346	+	0.942836i
$67$	66.0698	+	38.1454i	0.986117	+	0.569335i	0.904111	−	0.427297i	$-0.140534\pi$
$67$	66.0698	+	38.1454i	0.986117	+	0.569335i	0.0820054	+	0.996632i	$0.473868\pi$
$68$	6.47216			0.0951788
$69$		−	9.08459i		−	0.131661i
$70$	−25.9552	−	14.9852i	−0.370788	−	0.214075i
$71$	63.6080	−	36.7241i	0.895887	−	0.517240i	0.0200233	−	0.999800i	$-0.493626\pi$
$71$	63.6080	−	36.7241i	0.895887	−	0.517240i	0.875863	+	0.482559i	$0.160293\pi$
$72$	−20.0468	−	11.5740i	−0.278428	−	0.160750i
$73$	−45.9053	−	79.5103i	−0.628840	−	1.08918i	−0.987785	−	0.155824i	$-0.950197\pi$
$73$	−45.9053	−	79.5103i	−0.628840	−	1.08918i	0.358945	−	0.933359i	$-0.383137\pi$
$74$	44.0932	+	76.3717i	0.595854	+	1.03205i
$75$		−	27.9764i		−	0.373019i
$76$	−2.85406	+	4.09740i	−0.0375534	+	0.0539132i
$77$	45.4662			0.590471
$78$	−0.484457	+	0.279702i	−0.00621099	+	0.00358592i
$79$	−53.1300	+	30.6746i	−0.672531	+	0.388286i	−0.797035	−	0.603933i	$-0.793599\pi$
$79$	−53.1300	+	30.6746i	−0.672531	+	0.388286i	0.124504	+	0.992219i	$0.460266\pi$
$80$	54.4703	−	94.3453i	0.680879	−	1.17932i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−35.8716	+	62.1313i	−0.437458	+	0.757699i
$83$	−148.793			−1.79268			−0.896342	−	0.443363i	$-0.853785\pi$
$83$	−148.793			−1.79268			−0.896342	+	0.443363i	$0.853785\pi$
$84$		−	1.03004i		−	0.0122624i
$85$	78.9897	−	136.814i	0.929290	−	1.60958i
$86$	−44.8990	−	25.9224i	−0.522081	−	0.301424i
$87$	62.9147			0.723157
$88$			155.036i			1.76178i
$89$	−62.7829	−	36.2477i	−0.705426	−	0.407278i	0.103939	−	0.994584i	$-0.466855\pi$
$89$	−62.7829	−	36.2477i	−0.705426	−	0.407278i	−0.809365	+	0.587306i	$0.800189\pi$
$90$	34.4109	−	19.8672i	0.382344	−	0.220746i
$91$	0.306546	+	0.176984i	0.00336864	+	0.00194488i
$92$	0.689224	+	1.19377i	0.00749156	+	0.0129758i
$93$	14.8181	+	25.6657i	0.159335	+	0.275976i
$94$		−	60.6093i		−	0.644780i
$95$	51.7820	+	110.338i	0.545074	+	1.16146i
$96$	7.27172			0.0757471
$97$	−70.0326	+	40.4334i	−0.721986	+	0.416839i	−0.815483	−	0.578781i	$-0.803529\pi$
$97$	−70.0326	+	40.4334i	−0.721986	+	0.416839i	0.0934972	+	0.995620i	$0.470195\pi$
$98$	78.4589	−	45.2983i	0.800601	−	0.462227i
$99$	−30.1392	+	52.2026i	−0.304436	+	0.527299i
$100$	2.12250	+	3.67627i	0.0212250	+	0.0367627i
$101$	−76.6770	+	132.809i	−0.759178	+	1.31494i	0.184092	+	0.982909i	$0.441066\pi$
$101$	−76.6770	+	132.809i	−0.759178	+	1.31494i	−0.943270	+	0.332027i	$0.892268\pi$
$102$	88.0669			0.863401
$103$		−	168.948i		−	1.64027i	−0.572169	−	0.820136i	$-0.693898\pi$
$103$		−	168.948i		−	1.64027i	0.572169	−	0.820136i	$-0.306102\pi$
$104$	−0.603503	+	1.04530i	−0.00580291	+	0.0100509i
$105$	−21.7739	−	12.5712i	−0.207370	−	0.119725i
$106$	−115.431			−1.08897
$107$		−	139.060i		−	1.29963i	−0.760093	−	0.649815i	$-0.774846\pi$
$107$		−	139.060i		−	1.29963i	0.760093	−	0.649815i	$-0.225154\pi$
$108$	1.18265	+	0.682806i	0.0109505	+	0.00632228i
$109$	−9.15888	+	5.28788i	−0.0840264	+	0.0485127i	−0.541424	−	0.840749i	$-0.682115\pi$
$109$	−9.15888	+	5.28788i	−0.0840264	+	0.0485127i	0.457398	+	0.889262i	$0.348781\pi$
$110$	−230.471	−	133.062i	−2.09519	−	1.20966i
$111$	36.9900	+	64.0685i	0.333243	+	0.577194i
$112$	−19.2137	−	33.2792i	−0.171551	−	0.297135i
$113$			69.1581i			0.612018i	0.952029	+	0.306009i	$0.0989938\pi$
$113$			69.1581i			0.612018i	−0.952029	+	0.306009i	$0.901006\pi$
$114$	−38.8352	+	55.7535i	−0.340660	+	0.489066i
$115$	33.6466			0.292579
$116$	−8.26737	+	4.77317i	−0.0712704	+	0.0411480i
$117$	−0.406413	+	0.234643i	−0.00347362	+	0.00200550i
$118$	35.6737	−	61.7887i	0.302320	−	0.523633i
$119$	−27.8626	−	48.2595i	−0.234140	−	0.405542i
$120$	42.8667	−	74.2473i	0.357223	−	0.618728i
$121$	282.721			2.33654
$122$			113.063i			0.926742i
$123$	−30.0928	+	52.1223i	−0.244657	+	0.423758i
$124$	−3.89438	−	2.24842i	−0.0314063	−	0.0181324i
$125$	−56.7587			−0.454070
$126$		−	14.0158i		−	0.111236i
$127$	−25.6547	−	14.8118i	−0.202006	−	0.116628i	0.395585	−	0.918429i	$-0.370542\pi$
$127$	−25.6547	−	14.8118i	−0.202006	−	0.116628i	−0.597591	+	0.801801i	$0.703875\pi$
$128$	120.504	−	69.5731i	0.941438	−	0.543540i
$129$	−37.6659	−	21.7464i	−0.291984	−	0.168577i
$130$	−1.03593	−	1.79428i	−0.00796870	−	0.0138022i
$131$	−28.6526	−	49.6278i	−0.218722	−	0.378838i	0.735695	−	0.677313i	$-0.236856\pi$
$131$	−28.6526	−	49.6278i	−0.218722	−	0.378838i	−0.954418	+	0.298474i	$0.903522\pi$
$132$		−	9.14633i		−	0.0692903i
$133$	42.8389	+	3.64189i	0.322097	+	0.0273826i
$134$	−157.514			−1.17548
$135$	28.8675	−	16.6667i	0.213833	−	0.123457i
$136$	164.561	−	95.0094i	1.21001	−	0.698599i
$137$	47.4499	−	82.1856i	0.346349	−	0.599895i	−0.639249	−	0.769000i	$-0.720755\pi$
$137$	47.4499	−	82.1856i	0.346349	−	0.599895i	0.985598	+	0.169105i	$0.0540879\pi$
$138$	9.37829	+	16.2437i	0.0679586	+	0.117708i
$139$	−91.2747	+	158.092i	−0.656652	+	1.13736i	0.324824	+	0.945774i	$0.394695\pi$
$139$	−91.2747	+	158.092i	−0.656652	+	1.13736i	−0.981477	+	0.191581i	$0.938639\pi$
$140$	3.81496			0.0272497
$141$		−	50.8454i		−	0.360606i
$142$	−75.8226	+	131.329i	−0.533962	+	0.924850i
$143$	2.72200	+	1.57155i	0.0190349	+	0.0109898i
$144$	50.9465			0.353795
$145$			233.017i			1.60701i
$146$	164.162	+	94.7788i	1.12439	+	0.649170i
$147$	65.8195	−	38.0009i	0.447752	−	0.258510i
$148$	−9.72142	−	5.61266i	−0.0656852	−	0.0379234i
$149$	−5.50439	−	9.53389i	−0.0369422	−	0.0639858i	0.846963	−	0.531652i	$-0.178428\pi$
$149$	−5.50439	−	9.53389i	−0.0369422	−	0.0639858i	−0.883905	+	0.467666i	$0.845095\pi$
$150$	28.8809	+	50.0231i	0.192539	+	0.333487i
$151$			238.846i			1.58176i	0.611968	+	0.790882i	$0.290378\pi$
$151$			238.846i			1.58176i	−0.611968	+	0.790882i	$0.709622\pi$
$152$	−12.4186	+	146.077i	−0.0817011	+	0.961035i
$153$	73.8797			0.482874
$154$	−81.2957	+	46.9361i	−0.527894	+	0.304780i
$155$	−95.0582	+	54.8819i	−0.613279	+	0.354077i
$156$	0.0356035	−	0.0616670i	0.000228227	−	0.000395301i
$157$	22.8125	+	39.5124i	0.145303	+	0.251671i	0.929486	−	0.368858i	$-0.120251\pi$
$157$	22.8125	+	39.5124i	0.145303	+	0.251671i	−0.784183	+	0.620529i	$0.786918\pi$
$158$	63.3326	−	109.695i	0.400839	−	0.694273i
$159$	−96.8353			−0.609027
$160$			26.9323i			0.168327i
$161$	5.93421	−	10.2784i	0.0368585	−	0.0638407i
$162$	16.0924	+	9.29096i	0.0993359	+	0.0573516i
$163$	5.89159			0.0361447			0.0180724	−	0.999837i	$-0.494247\pi$
$163$	5.89159			0.0361447			0.0180724	+	0.999837i	$0.494247\pi$
$164$		−	9.13224i		−	0.0556844i
$165$	−193.343	−	111.627i	−1.17178	−	0.676525i
$166$	266.048	−	153.603i	1.60270	−	0.925320i
$167$	142.140	+	82.0646i	0.851138	+	0.491405i	0.861035	−	0.508546i	$-0.169817\pi$
$167$	142.140	+	82.0646i	0.851138	+	0.491405i	−0.00989689	+	0.999951i	$0.503150\pi$
$168$	−15.1207	−	26.1898i	−0.0900042	−	0.155892i
$169$	−84.4878	−	146.337i	−0.499928	−	0.865900i
$170$			326.173i			1.91867i
$171$	−32.5790	+	46.7718i	−0.190521	+	0.273520i
$172$	6.59938			0.0383685
$173$	234.355	−	135.305i	1.35465	−	0.782109i	0.365755	−	0.930711i	$-0.380811\pi$
$173$	234.355	−	135.305i	1.35465	−	0.782109i	0.988897	+	0.148603i	$0.0474775\pi$
$174$	−112.494	+	64.9486i	−0.646519	+	0.373268i
$175$	18.2747	−	31.6527i	0.104427	−	0.180872i
$176$	−170.610	−	295.505i	−0.969374	−	1.67900i
$177$	29.9269	−	51.8349i	0.169078	−	0.292852i
$178$	149.678			0.840890
$179$		−	186.439i		−	1.04156i	−0.853691	−	0.520779i	$-0.825641\pi$
$179$		−	186.439i		−	1.04156i	0.853691	−	0.520779i	$-0.174359\pi$
$180$	−2.52891	+	4.38020i	−0.0140495	+	0.0243344i
$181$	−40.1939	−	23.2059i	−0.222066	−	0.128210i	0.384841	−	0.922983i	$-0.374256\pi$
$181$	−40.1939	−	23.2059i	−0.222066	−	0.128210i	−0.606906	+	0.794773i	$0.707590\pi$
$182$	−0.730824			−0.00401552
$183$			94.8487i			0.518299i
$184$	35.0484	+	20.2352i	0.190481	+	0.109974i
$185$	−237.291	+	137.000i	−1.28265	+	0.740539i
$186$	−52.9910	−	30.5944i	−0.284898	−	0.164486i
$187$	−247.408	−	428.524i	−1.32304	−	2.29157i
$188$	3.85751	+	6.68140i	0.0205187	+	0.0355393i
$189$		−	11.7579i		−	0.0622112i
$190$	−206.494	−	143.834i	−1.08681	−	0.757021i
$191$	−36.7222			−0.192263			−0.0961315	−	0.995369i	$-0.530647\pi$
$191$	−36.7222			−0.192263			−0.0961315	+	0.995369i	$0.530647\pi$
$192$	88.8909	−	51.3212i	0.462973	−	0.267298i
$193$	−173.472	+	100.154i	−0.898817	+	0.518932i	−0.876816	−	0.480826i	$-0.840337\pi$
$193$	−173.472	+	100.154i	−0.898817	+	0.518932i	−0.0220009	+	0.999758i	$0.507004\pi$
$194$	83.4811	−	144.593i	0.430315	−	0.745327i
$195$	−0.869047	−	1.50523i	−0.00445665	−	0.00771915i
$196$	−5.76606	+	9.98710i	−0.0294187	+	0.0509546i
$197$	−171.512			−0.870620			−0.435310	−	0.900281i	$-0.643361\pi$
$197$	−171.512			−0.870620			−0.435310	+	0.900281i	$0.643361\pi$
$198$		−	124.454i		−	0.628557i
$199$	−43.7500	+	75.7772i	−0.219849	+	0.380790i	−0.954762	−	0.297372i	$-0.903890\pi$
$199$	−43.7500	+	75.7772i	−0.219849	+	0.380790i	0.734913	+	0.678162i	$0.237223\pi$
$200$	107.933	+	62.3152i	0.539666	+	0.311576i
$201$	−132.140			−0.657411
$202$		−	316.624i		−	1.56744i
$203$	71.1820	+	41.0970i	0.350650	+	0.202448i
$204$	−9.70824	+	5.60505i	−0.0475894	+	0.0274758i
$205$	−193.045	−	111.455i	−0.941684	−	0.543682i
$206$	174.410	+	302.087i	0.846650	+	1.46644i
$207$	7.86749	+	13.6269i	0.0380072	+	0.0658304i
$208$		−	2.65650i		−	0.0127716i
$209$	380.391	+	32.3384i	1.82005	+	0.154729i
$210$	51.9103			0.247192
$211$	16.3950	−	9.46566i	0.0777014	−	0.0448609i	−0.460646	−	0.887584i	$-0.652382\pi$
$211$	16.3950	−	9.46566i	0.0777014	−	0.0448609i	0.538347	+	0.842723i	$0.319049\pi$
$212$	12.7247	−	7.34663i	0.0600224	−	0.0346539i
$213$	−63.6080	+	110.172i	−0.298629	+	0.517240i
$214$	143.556	+	248.646i	0.670823	+	1.16190i
$215$	80.5423	−	139.503i	0.374615	−	0.648853i
$216$	40.0936			0.185618
$217$			38.7178i			0.178423i
$218$	10.9177	−	18.9100i	0.0500810	−	0.0867429i
$219$	137.716	+	79.5103i	0.628840	+	0.363061i
$220$	33.8752			0.153978
$221$		−	3.85230i		−	0.0174312i
$222$	−132.280	−	76.3717i	−0.595854	−	0.344016i
$223$	−224.162	+	129.420i	−1.00521	+	0.580358i	−0.909786	−	0.415078i	$-0.863754\pi$
$223$	−224.162	+	129.420i	−1.00521	+	0.580358i	−0.0954244	+	0.995437i	$0.530421\pi$
$224$	8.22727	+	4.75002i	0.0367289	+	0.0212054i
$225$	24.2283	+	41.9646i	0.107681	+	0.186509i
$226$	−71.3939	−	123.658i	−0.315902	−	0.547159i
$227$		−	129.054i		−	0.568522i	−0.958747	−	0.284261i	$-0.908252\pi$
$227$		−	129.054i		−	0.568522i	0.958747	−	0.284261i	$-0.0917482\pi$
$228$	0.732630	−	8.61779i	0.00321329	−	0.0377973i
$229$	−98.8946			−0.431854			−0.215927	−	0.976409i	$-0.569277\pi$
$229$	−98.8946			−0.431854			−0.215927	+	0.976409i	$0.569277\pi$
$230$	−60.1617	+	34.7344i	−0.261572	+	0.151019i
$231$	−68.1994	+	39.3749i	−0.295235	+	0.170454i
$232$	−140.137	+	242.725i	−0.604041	+	1.04623i
$233$	174.731	+	302.644i	0.749920	+	1.29890i	0.947861	+	0.318685i	$0.103241\pi$
$233$	174.731	+	302.644i	0.749920	+	1.29890i	−0.197941	+	0.980214i	$0.563425\pi$
$234$	0.484457	−	0.839105i	0.00207033	−	0.00358592i
$235$	188.316			0.801346
$236$			9.08189i			0.0384826i
$237$	53.1300	−	92.0238i	0.224177	−	0.388286i
$238$	99.6394	+	57.5268i	0.418653	+	0.241709i
$239$	301.091			1.25979			0.629897	−	0.776679i	$-0.283097\pi$
$239$	301.091			1.25979			0.629897	+	0.776679i	$0.283097\pi$
$240$			188.691i			0.786211i
$241$	110.242	+	63.6485i	0.457438	+	0.264102i	0.710966	−	0.703226i	$-0.248258\pi$
$241$	110.242	+	63.6485i	0.457438	+	0.264102i	−0.253529	+	0.967328i	$0.581591\pi$
$242$	−505.518	+	291.861i	−2.08892	+	1.20604i
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$	−7.19592	−	12.4637i	−0.0294915	−	0.0510807i
$245$	140.744	+	243.776i	0.574465	+	0.995003i
$246$		−	124.263i		−	0.505133i
$247$	2.43882	+	1.69877i	0.00987376	+	0.00687759i
$248$	−132.025			−0.532358
$249$	223.189	−	128.858i	0.896342	−	0.517503i
$250$	101.487	−	58.5937i	0.405949	−	0.234375i
$251$	177.023	−	306.613i	0.705271	−	1.22157i	−0.261322	−	0.965252i	$-0.584159\pi$
$251$	177.023	−	306.613i	0.705271	−	1.22157i	0.966594	−	0.256314i	$-0.0825081\pi$
$252$	0.892042	+	1.54506i	0.00353985	+	0.00613120i
$253$	52.6933	−	91.2675i	0.208274	−	0.360741i
$254$	61.1625			0.240797
$255$			273.628i			1.07305i
$256$	−25.1234	+	43.5151i	−0.0981384	+	0.169981i
$257$	−236.669	−	136.641i	−0.920889	−	0.531676i	−0.0369706	−	0.999316i	$-0.511771\pi$
$257$	−236.669	−	136.641i	−0.920889	−	0.531676i	−0.883919	+	0.467641i	$0.845104\pi$
$258$	89.7979			0.348054
$259$			96.6500i			0.373166i
$260$	0.228396	+	0.131865i	0.000878447	+	0.000507171i
$261$	−94.3720	+	54.4857i	−0.361579	+	0.208757i
$262$	102.464	+	59.1579i	0.391086	+	0.225793i
$263$	−75.5642	−	130.881i	−0.287316	−	0.497646i	0.685852	−	0.727741i	$-0.259430\pi$
$263$	−75.5642	−	130.881i	−0.287316	−	0.497646i	−0.973168	+	0.230095i	$0.926096\pi$
$264$	−134.265	−	232.555i	−0.508581	−	0.880889i
$265$		−	358.649i		−	1.35339i
$266$	−80.3576	+	37.7120i	−0.302096	+	0.141774i
$267$	125.566			0.470284
$268$	17.3639	−	10.0251i	0.0647909	−	0.0374070i
$269$	58.9364	−	34.0269i	0.219094	−	0.126494i	−0.386437	−	0.922316i	$-0.626294\pi$
$269$	58.9364	−	34.0269i	0.219094	−	0.126494i	0.605531	+	0.795822i	$0.292961\pi$
$270$	−34.4109	+	59.6015i	−0.127448	+	0.220746i
$271$	56.8991	+	98.5521i	0.209960	+	0.363661i	0.951702	−	0.307025i	$-0.0993334\pi$
$271$	56.8991	+	98.5521i	0.209960	+	0.363661i	−0.741742	+	0.670685i	$0.766000\pi$
$272$	−209.106	+	362.183i	−0.768773	+	1.33155i
$273$	−0.613092			−0.00224576
$274$			195.935i			0.715093i
$275$	162.271	−	281.062i	0.590078	−	1.02204i
$276$	−2.06767	−	1.19377i	−0.00749156	−	0.00432526i
$277$	440.910			1.59173			0.795867	−	0.605472i	$-0.207016\pi$
$277$	440.910			1.59173			0.795867	+	0.605472i	$0.207016\pi$
$278$		−	376.902i		−	1.35576i
$279$	−44.4544	−	25.6657i	−0.159335	−	0.0919919i
$280$	96.9993	−	56.0026i	0.346426	−	0.200009i
$281$	78.0928	+	45.0869i	0.277910	+	0.160452i	0.632477	−	0.774579i	$-0.282038\pi$
$281$	78.0928	+	45.0869i	0.277910	+	0.160452i	−0.354567	+	0.935031i	$0.615372\pi$
$282$	52.4892	+	90.9140i	0.186132	+	0.322390i
$283$	34.5331	+	59.8131i	0.122025	+	0.211354i	0.920566	−	0.390587i	$-0.127728\pi$
$283$	34.5331	+	59.8131i	0.122025	+	0.211354i	−0.798541	+	0.601940i	$0.794394\pi$
$284$		−	19.3031i		−	0.0679685i
$285$	−173.229	−	120.663i	−0.607821	−	0.423379i
$286$	−6.48941			−0.0226902
$287$	−68.0944	+	39.3143i	−0.237263	+	0.136984i
$288$	−10.9076	+	6.29750i	−0.0378736	+	0.0218663i
$289$	−158.734	+	274.935i	−0.549252	+	0.951332i
$290$	−240.550	−	416.645i	−0.829484	−	1.43671i
$291$	70.0326	−	121.300i	0.240662	−	0.416839i
$292$	−24.1289			−0.0826334
$293$			410.238i			1.40013i	0.714079	+	0.700065i	$0.246846\pi$
$293$			410.238i			1.40013i	−0.714079	+	0.700065i	$0.753154\pi$
$294$	−78.4589	+	135.895i	−0.266867	+	0.462227i
$295$	191.981	+	110.840i	0.650782	+	0.375729i
$296$	−329.569			−1.11341
$297$		−	104.405i		−	0.351533i
$298$	19.6842	+	11.3647i	0.0660544	+	0.0381365i
$299$	0.710545	−	0.410233i	0.00237640	−	0.00137202i
$300$	−6.36749	−	3.67627i	−0.0212250	−	0.0122542i
$301$	−28.4103	−	49.2081i	−0.0943864	−	0.163482i
$302$	−246.568	−	427.068i	−0.816451	−	1.41413i
$303$		−	265.617i		−	0.876624i
$304$	−137.081	−	292.095i	−0.450923	−	0.960838i
$305$	−351.291			−1.15177
$306$	−132.100	+	76.2681i	−0.431700	+	0.249242i
$307$	−201.882	+	116.556i	−0.657595	+	0.379663i	−0.791360	−	0.611350i	$-0.790627\pi$
$307$	−201.882	+	116.556i	−0.657595	+	0.379663i	0.133765	+	0.991013i	$0.457293\pi$
$308$	5.97454	−	10.3482i	0.0193979	−	0.0335981i
$309$	146.313	+	253.422i	0.473506	+	0.820136i
$310$	113.312	−	196.263i	0.365524	−	0.633106i
$311$	−441.280			−1.41891			−0.709454	−	0.704752i	$-0.751058\pi$
$311$	−441.280			−1.41891			−0.709454	+	0.704752i	$0.751058\pi$
$312$		−	2.09059i		−	0.00670062i
$313$	−60.6339	+	105.021i	−0.193719	+	0.335530i	−0.946480	−	0.322763i	$-0.895388\pi$
$313$	−60.6339	+	105.021i	−0.193719	+	0.335530i	0.752761	+	0.658294i	$0.228722\pi$
$314$	−81.5796	−	47.1000i	−0.259808	−	0.150000i
$315$	43.5478			0.138247
$316$			16.1233i			0.0510232i
$317$	286.409	+	165.358i	0.903499	+	0.521635i	0.878334	−	0.478048i	$-0.158656\pi$
$317$	286.409	+	165.358i	0.903499	+	0.521635i	0.0251649	+	0.999683i	$0.491989\pi$
$318$	173.146	−	99.9658i	0.544484	−	0.314358i
$319$	632.066	+	364.924i	1.98140	+	1.14396i
$320$	190.078	+	329.225i	0.593995	+	1.02883i
$321$	120.430	+	208.591i	0.375171	+	0.649815i
$322$			24.5042i			0.0761001i
$323$	−198.786	−	423.579i	−0.615437	−	1.31139i
$324$	−2.36531			−0.00730034
$325$	2.18816	−	1.26333i	0.00673279	−	0.00388718i
$326$	−10.5344	+	6.08206i	−0.0323142	+	0.0186566i
$327$	9.15888	−	15.8636i	0.0280088	−	0.0485127i
$328$	−134.059	−	232.197i	−0.408716	−	0.707916i
$329$	33.2131	−	57.5268i	0.100952	−	0.174854i
$330$	460.941			1.39679
$331$		−	436.308i		−	1.31815i	−0.752077	−	0.659075i	$-0.770948\pi$
$331$		−	436.308i		−	1.31815i	0.752077	−	0.659075i	$-0.229052\pi$
$332$	−19.5523	+	33.8655i	−0.0588924	+	0.102005i
$333$	−110.970	−	64.0685i	−0.333243	−	0.192398i
$334$	−338.870			−1.01458
$335$		−	489.406i		−	1.46091i
$336$	57.6412	+	33.2792i	0.171551	+	0.0990452i
$337$	−217.027	+	125.301i	−0.643997	+	0.371812i	−0.786153	−	0.618033i	$-0.787930\pi$
$337$	−217.027	+	125.301i	−0.643997	+	0.371812i	0.142156	+	0.989844i	$0.454597\pi$
$338$	302.136	+	174.438i	0.893894	+	0.516090i
$339$	−59.8927	−	103.737i	−0.176675	−	0.306009i
$340$	−20.7594	−	35.9564i	−0.0610572	−	0.105754i
$341$			343.798i			1.00821i
$342$	9.96891	−	117.263i	0.0291489	−	0.342873i
$343$	210.169			0.612738
$344$	167.796	−	96.8770i	0.487779	−	0.281619i
$345$	−50.4699	+	29.1388i	−0.146290	+	0.0844603i
$346$	−279.358	+	483.862i	−0.807393	+	1.39845i
$347$	−83.6670	−	144.915i	−0.241115	−	0.417624i	0.719917	−	0.694060i	$-0.244180\pi$
$347$	−83.6670	−	144.915i	−0.241115	−	0.417624i	−0.961032	+	0.276436i	$0.910846\pi$
$348$	8.26737	−	14.3195i	0.0237568	−	0.0411480i
$349$	−486.776			−1.39477			−0.697387	−	0.716695i	$-0.745654\pi$
$349$	−486.776			−1.39477			−0.697387	+	0.716695i	$0.745654\pi$
$350$			75.4619i			0.215605i
$351$	0.406413	−	0.703929i	0.00115787	−	0.00200550i
$352$	73.0547	+	42.1781i	0.207542	+	0.119824i
$353$	30.1507			0.0854128			0.0427064	−	0.999088i	$-0.486402\pi$
$353$	30.1507			0.0854128			0.0427064	+	0.999088i	$0.486402\pi$
$354$			123.577i			0.349089i
$355$	−408.045	−	235.585i	−1.14942	−	0.663619i
$356$	−16.5001	+	9.52635i	−0.0463486	+	0.0267594i
$357$	83.5879	+	48.2595i	0.234140	+	0.135181i
$358$	192.466	+	333.361i	0.537615	+	0.931177i
$359$	−75.0088	−	129.919i	−0.208938	−	0.361891i	0.742442	−	0.669910i	$-0.233667\pi$
$359$	−75.0088	−	129.919i	−0.208938	−	0.361891i	−0.951380	+	0.308019i	$0.900334\pi$
$360$			148.495i			0.412485i
$361$	355.819	+	60.9394i	0.985649	+	0.168807i
$362$	95.8247			0.264709
$363$	−424.081	+	244.843i	−1.16827	+	0.674500i
$364$	0.0805640	−	0.0465136i	0.000221330	−	0.000127785i
$365$	−294.482	+	510.058i	−0.806801	+	1.39742i
$366$	−97.9151	−	169.594i	−0.267527	−	0.463371i
$367$	248.090	−	429.704i	0.675994	−	1.17086i	−0.300183	−	0.953882i	$-0.597048\pi$
$367$	248.090	−	429.704i	0.675994	−	1.17086i	0.976177	−	0.216975i	$-0.0696189\pi$
$368$	−89.0714			−0.242042
$369$		−	104.245i		−	0.282506i
$370$	282.858	−	489.924i	0.764480	−	1.32412i
$371$	−109.560	−	63.2545i	−0.295310	−	0.170497i
$372$	7.78877			0.0209375
$373$			449.613i			1.20540i	0.797969	+	0.602698i	$0.205908\pi$
$373$			449.613i			1.20540i	−0.797969	+	0.602698i	$0.794092\pi$
$374$	884.755	+	510.814i	2.36566	+	1.36581i
$375$	85.1381	−	49.1545i	0.227035	−	0.131079i
$376$	196.162	+	113.254i	0.521707	+	0.301208i
$377$	2.84104	+	4.92083i	0.00753592	+	0.0130526i
$378$	12.1380	+	21.0237i	0.0321112	+	0.0556182i
$379$		−	471.336i		−	1.24363i	−0.783163	−	0.621816i	$-0.786395\pi$
$379$		−	471.336i		−	1.24363i	0.783163	−	0.621816i	$-0.213605\pi$
$380$	31.9177	+	2.71344i	0.0839940	+	0.00714064i
$381$	51.3095			0.134670
$382$	65.6611	−	37.9094i	0.171888	−	0.0992393i
$383$	−23.4258	+	13.5249i	−0.0611641	+	0.0353131i	−0.530270	−	0.847829i	$-0.677910\pi$
$383$	−23.4258	+	13.5249i	−0.0611641	+	0.0353131i	0.469106	+	0.883142i	$0.344576\pi$
$384$	−120.504	+	208.719i	−0.313813	+	0.543540i
$385$	−145.833	−	252.590i	−0.378787	−	0.656078i
$386$	206.784	−	358.160i	0.535709	−	0.927875i
$387$	75.3319			0.194656
$388$			21.2528i			0.0547752i
$389$	177.144	−	306.822i	0.455382	−	0.788745i	−0.543328	−	0.839520i	$-0.682836\pi$
$389$	177.144	−	306.822i	0.455382	−	0.788745i	0.998710	+	0.0507758i	$0.0161694\pi$
$390$	3.10779	+	1.79428i	0.00796870	+	0.00460073i
$391$	−129.166			−0.330348
$392$			338.576i			0.863715i
$393$	85.9579	+	49.6278i	0.218722	+	0.126279i
$394$	306.672	−	177.057i	0.778354	−	0.449383i
$395$	340.829	+	196.777i	0.862857	+	0.498171i
$396$	7.92095	+	13.7195i	0.0200024	+	0.0346452i
$397$	−79.5105	−	137.716i	−0.200278	−	0.346892i	0.748340	−	0.663316i	$-0.230851\pi$
$397$	−79.5105	−	137.716i	−0.200278	−	0.346892i	−0.948618	+	0.316423i	$0.897518\pi$
$398$		−	180.657i		−	0.453913i
$399$	−67.4123	+	31.6367i	−0.168953	+	0.0792901i
$400$	−274.299			−0.685748
$401$	−277.534	+	160.234i	−0.692105	+	0.399587i	−0.804400	−	0.594088i	$-0.797513\pi$
$401$	−277.534	+	160.234i	−0.692105	+	0.399587i	0.112295	+	0.993675i	$0.464180\pi$
$402$	236.272	−	136.412i	0.587741	−	0.339332i
$403$	−1.33829	+	2.31798i	−0.00332081	+	0.00575181i
$404$	20.1517	+	34.9037i	0.0498803	+	0.0863953i
$405$	−28.8675	+	50.0000i	−0.0712777	+	0.123457i
$406$	−169.702			−0.417986
$407$			858.211i			2.10863i
$408$	−164.561	+	285.028i	−0.403336	+	0.698599i
$409$	−251.776	−	145.363i	−0.615590	−	0.355411i	0.159560	−	0.987188i	$-0.448992\pi$
$409$	−251.776	−	145.363i	−0.615590	−	0.355411i	−0.775150	+	0.631777i	$0.782326\pi$
$410$	460.232			1.12252
$411$			164.371i			0.399930i
$412$	−38.4529	−	22.2008i	−0.0933323	−	0.0538854i
$413$	67.7189	−	39.0975i	0.163968	−	0.0946671i
$414$	−28.1349	−	16.2437i	−0.0679586	−	0.0392359i
$415$	477.253	+	826.626i	1.15001	+	1.99187i
$416$	0.328370	+	0.568753i	0.000789350	+	0.00136719i
$417$		−	316.185i		−	0.758237i
$418$	−713.541	+	334.866i	−1.70704	+	0.801115i
$419$	−141.846			−0.338535			−0.169267	−	0.985570i	$-0.554140\pi$
$419$	−141.846			−0.338535			−0.169267	+	0.985570i	$0.554140\pi$
$420$	−5.72245	+	3.30386i	−0.0136249	+	0.00786632i
$421$	98.6666	−	56.9652i	0.234362	−	0.135309i	−0.378220	−	0.925716i	$-0.623464\pi$
$421$	98.6666	−	56.9652i	0.234362	−	0.135309i	0.612583	+	0.790406i	$0.290131\pi$
$422$	−19.5433	+	33.8501i	−0.0463112	+	0.0802134i
$423$	44.0334	+	76.2681i	0.104098	+	0.180303i
$424$	215.693	−	373.591i	0.508710	−	0.881111i
$425$	−397.773			−0.935936
$426$		−	262.657i		−	0.616567i
$427$	−61.9568	+	107.312i	−0.145098	+	0.251317i
$428$	−31.6504	−	18.2734i	−0.0739496	−	0.0426948i
$429$	−5.44399			−0.0126900
$430$			332.585i			0.773453i
$431$	229.263	+	132.365i	0.531932	+	0.307111i	0.741803	−	0.670618i	$-0.233971\pi$
$431$	229.263	+	132.365i	0.531932	+	0.307111i	−0.209871	+	0.977729i	$0.567304\pi$
$432$	−76.4198	+	44.1210i	−0.176898	+	0.102132i
$433$	−631.333	−	364.500i	−1.45804	−	0.841802i	−0.459129	−	0.888369i	$-0.651839\pi$
$433$	−631.333	−	364.500i	−1.45804	−	0.841802i	−0.998915	+	0.0465669i	$0.985172\pi$
$434$	−39.9695	−	69.2293i	−0.0920957	−	0.159514i
$435$	−201.799	−	349.526i	−0.463905	−	0.803507i
$436$			2.77944i			0.00637486i
$437$	56.9589	−	81.7726i	0.130341	−	0.187123i
$438$	−328.323			−0.749596
$439$	319.591	−	184.516i	0.727998	−	0.420310i	−0.0896911	−	0.995970i	$-0.528588\pi$
$439$	319.591	−	184.516i	0.727998	−	0.420310i	0.817689	+	0.575660i	$0.195255\pi$
$440$	861.312	−	497.279i	1.95753	−	1.13018i
$441$	−65.8195	+	114.003i	−0.149251	+	0.258510i
$442$	3.97684	+	6.88809i	0.00899738	+	0.0155839i
$443$	−291.547	+	504.975i	−0.658120	+	1.13990i	0.322982	+	0.946405i	$0.395315\pi$
$443$	−291.547	+	504.975i	−0.658120	+	1.13990i	−0.981102	+	0.193492i	$0.938019\pi$
$444$	19.4428			0.0437902
$445$			465.058i			1.04507i
$446$	267.208	−	462.818i	0.599121	−	1.03771i
$447$	16.5132	+	9.53389i	0.0369422	+	0.0213286i
$448$	134.096			0.299321
$449$		−	314.423i		−	0.700273i	−0.936699	−	0.350137i	$-0.886135\pi$
$449$		−	314.423i		−	0.700273i	0.936699	−	0.350137i	$-0.113865\pi$
$450$	−86.6426	−	50.0231i	−0.192539	−	0.111162i
$451$	−604.649	+	349.094i	−1.34068	+	0.774045i
$452$	15.7405	+	9.08779i	0.0348242	+	0.0201057i
$453$	−206.847	−	358.270i	−0.456616	−	0.790882i
$454$	133.227	+	230.755i	0.293451	+	0.508272i
$455$		−	2.27071i		−	0.00499057i
$456$	−107.879	−	229.871i	−0.236576	−	0.504103i
$457$	505.253			1.10559			0.552793	−	0.833319i	$-0.313562\pi$
$457$	505.253			1.10559			0.552793	+	0.833319i	$0.313562\pi$
$458$	176.828	−	102.092i	0.386088	−	0.222908i
$459$	−110.820	+	63.9817i	−0.241437	+	0.139394i
$460$	4.42137	−	7.65803i	0.00961167	−	0.0166479i
$461$	136.902	+	237.122i	0.296968	+	0.514364i	0.975441	−	0.220262i	$-0.0706912\pi$
$461$	136.902	+	237.122i	0.296968	+	0.514364i	−0.678473	+	0.734626i	$0.737358\pi$
$462$	81.2957	−	140.808i	0.175965	−	0.304780i
$463$	319.780			0.690669			0.345334	−	0.938480i	$-0.387765\pi$
$463$	319.780			0.690669			0.345334	+	0.938480i	$0.387765\pi$
$464$		−	616.857i		−	1.32943i
$465$	95.0582	−	164.646i	0.204426	−	0.354077i
$466$	−624.855	−	360.760i	−1.34089	−	0.774164i
$467$	−295.510			−0.632785			−0.316392	−	0.948628i	$-0.602472\pi$
$467$	−295.510			−0.632785			−0.316392	+	0.948628i	$0.602472\pi$
$468$			0.123334i			0.000263534i
$469$	−149.504	−	86.3159i	−0.318771	−	0.184042i
$470$	−336.718	+	194.404i	−0.716421	+	0.413626i
$471$	−68.4375	−	39.5124i	−0.145303	−	0.0838905i
$472$	133.319	+	230.916i	0.282457	+	0.489229i
$473$	−252.271	−	436.947i	−0.533344	−	0.923778i
$474$			219.390i			0.462849i
$475$	175.408	−	251.822i	0.369279	−	0.530153i
$476$	−14.6453			−0.0307674
$477$	145.253	−	83.8618i	0.304513	−	0.175811i
$478$	−538.364	+	310.825i	−1.12629	+	0.650261i
$479$	204.559	−	354.306i	0.427054	−	0.739679i	−0.569556	−	0.821953i	$-0.692885\pi$
$479$	204.559	−	354.306i	0.427054	−	0.739679i	0.996610	+	0.0822735i	$0.0262181\pi$
$480$	−23.3240	−	40.3984i	−0.0485917	−	0.0841634i
$481$	−3.34072	+	5.78629i	−0.00694536	+	0.0120297i
$482$	−262.825			−0.545280
$483$			20.5567i			0.0425605i
$484$	37.1512	−	64.3478i	0.0767588	−	0.132950i
$485$	449.259	+	259.380i	0.926308	+	0.534804i
$486$	−32.1848			−0.0662239
$487$		−	638.208i		−	1.31049i	−0.755417	−	0.655244i	$-0.772566\pi$
$487$		−	638.208i		−	1.31049i	0.755417	−	0.655244i	$-0.227434\pi$
$488$	−365.927	−	211.268i	−0.749850	−	0.432926i
$489$	−8.83738	+	5.10227i	−0.0180724	+	0.0104341i
$490$	−503.314	−	290.588i	−1.02717	−	0.593037i
$491$	−173.278	−	300.126i	−0.352908	−	0.611255i	0.633850	−	0.773456i	$-0.281474\pi$
$491$	−173.278	−	300.126i	−0.352908	−	0.611255i	−0.986758	+	0.162202i	$0.948141\pi$
$492$	7.90876	+	13.6984i	0.0160747	+	0.0278422i
$493$		−	894.530i		−	1.81446i
$494$	−6.11440	−	0.519808i	−0.0123773	−	0.00105224i
$495$	386.686			0.781184
$496$	251.644	−	145.287i	0.507347	−	0.292917i
$497$	−143.933	+	83.0997i	−0.289603	+	0.167203i
$498$	−266.048	+	460.809i	−0.534234	+	0.925320i
$499$	−40.3510	−	69.8900i	−0.0808638	−	0.140060i	0.822757	−	0.568393i	$-0.192435\pi$
$499$	−40.3510	−	69.8900i	−0.0808638	−	0.140060i	−0.903621	+	0.428333i	$0.859101\pi$
$500$	−7.45844	+	12.9184i	−0.0149169	+	0.0258368i
$501$	−284.280			−0.567425
$502$			730.984i			1.45614i
$503$	−247.050	+	427.903i	−0.491153	+	0.850701i	−0.999948	−	0.0101862i	$-0.996758\pi$
$503$	−247.050	+	427.903i	−0.491153	+	0.850701i	0.508796	+	0.860887i	$0.330091\pi$
$504$	45.3621	+	26.1898i	0.0900042	+	0.0519640i
$505$	983.766			1.94805
$506$			217.587i			0.430014i
$507$	253.463	+	146.337i	0.499928	+	0.288633i
$508$	−6.74237	+	3.89271i	−0.0132724	+	0.00766282i
$509$	63.9084	+	36.8975i	0.125557	+	0.0724902i	0.561463	−	0.827502i	$-0.310239\pi$
$509$	63.9084	+	36.8975i	0.125557	+	0.0724902i	−0.435906	+	0.899992i	$0.643572\pi$
$510$	−282.474	−	489.260i	−0.553871	−	0.959333i
$511$	103.875	+	179.917i	0.203278	+	0.352088i
$512$			452.842i			0.884457i
$513$	8.36297	−	98.3721i	0.0163021	−	0.191758i
$514$	564.232			1.09773
$515$	−938.599	+	541.900i	−1.82252	+	1.05223i
$516$	−9.89907	+	5.71523i	−0.0191842	+	0.0110760i
$517$	294.918	−	510.814i	0.570442	−	0.988034i
$518$	−99.7746	−	172.815i	−0.192615	−	0.333619i
$519$	−234.355	+	405.914i	−0.451551	+	0.782109i
$520$	7.74294			0.0148903
$521$		−	357.582i		−	0.686337i	−0.939274	−	0.343169i	$-0.888500\pi$
$521$		−	357.582i		−	0.686337i	0.939274	−	0.343169i	$-0.111500\pi$
$522$	112.494	−	194.846i	0.215506	−	0.373268i
$523$	382.935	+	221.088i	0.732190	+	0.422730i	0.819223	−	0.573475i	$-0.194405\pi$
$523$	382.935	+	221.088i	0.732190	+	0.422730i	−0.0870328	+	0.996205i	$0.527739\pi$
$524$	−15.0605			−0.0287415
$525$			63.3053i			0.120582i
$526$	270.225	+	156.014i	0.513735	+	0.296605i
$527$	364.919	−	210.686i	0.692447	−	0.399784i
$528$	511.829	+	295.505i	0.969374	+	0.559668i
$529$	250.745	+	434.303i	0.473998	+	0.820989i
$530$	370.243	+	641.281i	0.698573	+	1.20996i
$531$			103.670i			0.195235i
$532$	6.45819	−	9.27165i	0.0121395	−	0.0174279i
$533$	−5.43561			−0.0101981
$534$	−224.518	+	129.625i	−0.420445	+	0.242744i
$535$	−772.557	+	446.036i	−1.44403	+	0.833712i
$536$	294.331	−	509.796i	0.549124	−	0.951111i
$537$	161.461	+	279.658i	0.300672	+	0.520779i
$538$	−70.2539	+	121.683i	−0.130584	+	0.226177i
$539$	881.666			1.63574
$540$		−	8.76040i		−	0.0162230i
$541$	−487.737	+	844.785i	−0.901547	+	1.56152i	−0.0760596	+	0.997103i	$0.524234\pi$
$541$	−487.737	+	844.785i	−0.901547	+	1.56152i	−0.825487	+	0.564421i	$0.809099\pi$
$542$	−203.476	−	117.477i	−0.375418	−	0.216747i
$543$	80.3877			0.148044
$544$		−	103.390i		−	0.190056i
$545$	58.7542	+	33.9217i	0.107806	+	0.0622417i
$546$	1.09624	−	0.632912i	0.00200776	−	0.00115918i
$547$	350.050	+	202.102i	0.639945	+	0.369473i	0.784594	−	0.620010i	$-0.212872\pi$
$547$	350.050	+	202.102i	0.639945	+	0.369473i	−0.144648	+	0.989483i	$0.546205\pi$
$548$	−12.4704	−	21.5994i	−0.0227562	−	0.0394149i
$549$	−82.1414	−	142.273i	−0.149620	−	0.259149i
$550$			670.070i			1.21831i
$551$	566.310	+	394.465i	1.02779	+	0.715907i
$552$	−70.0968			−0.126987
$553$	120.223	−	69.4109i	0.217402	−	0.125517i
$554$	−788.368	+	455.164i	−1.42305	+	0.821596i
$555$	237.291	−	410.999i	0.427551	−	0.740539i
$556$	23.9881	+	41.5486i	0.0431441	+	0.0747277i
$557$	−29.9352	+	51.8492i	−0.0537435	+	0.0930866i	−0.891646	−	0.452734i	$-0.850449\pi$
$557$	−29.9352	+	51.8492i	−0.0537435	+	0.0930866i	0.837902	+	0.545821i	$0.183782\pi$
$558$	105.982			0.189932
$559$		−	3.92802i		−	0.00702687i
$560$	−123.256	+	213.486i	−0.220100	+	0.381225i
$561$	742.225	+	428.524i	1.32304	+	0.763857i
$562$	−186.178			−0.331278
$563$			247.579i			0.439749i	0.975528	+	0.219874i	$0.0705648\pi$
$563$			247.579i			0.439749i	−0.975528	+	0.219874i	$0.929435\pi$
$564$	−11.5725	−	6.68140i	−0.0205187	−	0.0118464i
$565$	384.211	−	221.824i	0.680020	−	0.392610i
$566$	−123.494	−	71.2990i	−0.218186	−	0.125970i
$567$	10.1827	+	17.6369i	0.0179588	+	0.0311056i
$568$	−283.363	−	490.800i	−0.498879	−	0.864084i
$569$		−	76.4991i		−	0.134445i	−0.997738	−	0.0672224i	$-0.978586\pi$
$569$		−	76.4991i		−	0.134445i	0.997738	−	0.0672224i	$-0.0214137\pi$
$570$	434.305	+	36.9219i	0.761939	+	0.0647752i
$571$	−624.523			−1.09373			−0.546867	−	0.837219i	$-0.684180\pi$
$571$	−624.523			−1.09373			−0.546867	+	0.837219i	$0.684180\pi$
$572$	0.715374	−	0.413021i	0.00125065	−	0.000722065i
$573$	55.0834	−	31.8024i	0.0961315	−	0.0555016i
$574$	81.1706	−	140.592i	0.141412	−	0.244933i
$575$	−42.3590	−	73.3680i	−0.0736679	−	0.127597i
$576$	−88.8909	+	153.964i	−0.154324	+	0.267298i
$577$	185.550			0.321577			0.160789	−	0.986989i	$-0.448596\pi$
$577$	185.550			0.321577			0.160789	+	0.986989i	$0.448596\pi$
$578$		−	655.462i		−	1.13402i
$579$	173.472	−	300.462i	0.299606	−	0.518932i
$580$	53.0352	+	30.6199i	0.0914399	+	0.0527929i
$581$	336.690			0.579501
$582$			289.187i			0.496885i
$583$	−972.846	−	561.673i	−1.66869	−	0.963418i
$584$	−613.503	+	354.206i	−1.05052	+	0.606517i
$585$	2.60714	+	1.50523i	0.00445665	+	0.00257305i
$586$	−423.501	−	733.525i	−0.722698	−	1.25175i
$587$	−130.891	−	226.710i	−0.222983	−	0.386218i	0.732729	−	0.680520i	$-0.238246\pi$
$587$	−130.891	−	226.710i	−0.222983	−	0.386218i	−0.955712	+	0.294302i	$0.904913\pi$
$588$		−	19.9742i		−	0.0339697i
$589$	−27.5386	+	323.931i	−0.0467548	+	0.549968i
$590$	−457.694			−0.775752
$591$	257.268	−	148.534i	0.435310	−	0.251326i
$592$	628.170	−	362.674i	1.06110	−	0.612626i
$593$	−124.254	+	215.215i	−0.209535	+	0.362925i	−0.951568	−	0.307438i	$-0.900528\pi$
$593$	−124.254	+	215.215i	−0.209535	+	0.362925i	0.742033	+	0.670363i	$0.233862\pi$
$594$	107.781	+	186.681i	0.181449	+	0.314279i
$595$	−178.739	+	309.585i	−0.300401	+	0.520310i
$596$	−2.89324			−0.00485443
$597$		−	151.554i		−	0.253860i
$598$	−0.846992	+	1.46703i	−0.00141637	+	0.00245323i
$599$	−167.646	−	96.7905i	−0.279877	−	0.161587i	0.353491	−	0.935438i	$-0.384995\pi$
$599$	−167.646	−	96.7905i	−0.279877	−	0.161587i	−0.633368	+	0.773851i	$0.718328\pi$
$600$	−215.866			−0.359777
$601$		−	675.975i		−	1.12475i	−0.826882	−	0.562375i	$-0.809888\pi$
$601$		−	675.975i		−	1.12475i	0.826882	−	0.562375i	$-0.190112\pi$
$602$	101.598	+	58.6576i	0.168767	+	0.0974378i
$603$	198.209	−	114.436i	0.328706	−	0.189778i
$604$	54.3619	+	31.3859i	0.0900032	+	0.0519634i
$605$	−906.827	−	1570.67i	−1.49889	−	2.59615i
$606$	274.204	+	474.935i	0.452482	+	0.783722i
$607$			383.052i			0.631057i	0.948916	+	0.315528i	$0.102182\pi$
$607$			383.052i			0.631057i	−0.948916	+	0.315528i	$0.897818\pi$
$608$	65.4546	+	45.5925i	0.107656	+	0.0749877i
$609$	−142.364			−0.233767
$610$	628.125	−	362.648i	1.02971	−	0.594505i
$611$	3.97684	−	2.29603i	0.00650874	−	0.00375782i
$612$	9.70824	−	16.8152i	0.0158631	−	0.0274758i
$613$	−27.5410	−	47.7025i	−0.0449283	−	0.0778180i	0.842687	−	0.538404i	$-0.180973\pi$
$613$	−27.5410	−	47.7025i	−0.0449283	−	0.0778180i	−0.887615	+	0.460586i	$0.847639\pi$
$614$	240.649	−	416.817i	0.391937	−	0.678854i
$615$	386.091			0.627789
$616$		−	350.818i		−	0.569510i
$617$	−51.7851	+	89.6944i	−0.0839305	+	0.145372i	−0.904935	−	0.425550i	$-0.860081\pi$
$617$	−51.7851	+	89.6944i	−0.0839305	+	0.145372i	0.821004	+	0.570922i	$0.193414\pi$
$618$	−523.230	−	302.087i	−0.846650	−	0.488814i
$619$	−263.102			−0.425043			−0.212521	−	0.977156i	$-0.568168\pi$
$619$	−263.102			−0.425043			−0.212521	+	0.977156i	$0.568168\pi$
$620$			28.8473i			0.0465278i
$621$	−23.6025	−	13.6269i	−0.0380072	−	0.0219435i
$622$	789.030	−	455.547i	1.26854	−	0.732390i
$623$	142.066	+	82.0218i	0.228035	+	0.131656i
$624$	2.30060	+	3.98475i	0.00368685	+	0.00638581i
$625$	383.956	+	665.031i	0.614329	+	1.06405i
$626$		−	250.377i		−	0.399963i
$627$	−598.593	+	280.921i	−0.954693	+	0.448039i
$628$	11.9908			0.0190936
$629$	910.936	−	525.929i	1.44823	−	0.836135i
$630$	−77.8655	+	44.9557i	−0.123596	+	0.0713582i
$631$	72.5474	−	125.656i	0.114972	−	0.199137i	−0.802797	−	0.596253i	$-0.796655\pi$
$631$	72.5474	−	125.656i	0.114972	−	0.199137i	0.917769	+	0.397116i	$0.129989\pi$
$632$	236.686	+	409.952i	0.374503	+	0.648658i
$633$	−16.3950	+	28.3970i	−0.0259005	+	0.0448609i
$634$	−682.817			−1.07700
$635$			190.035i			0.299267i
$636$	−12.7247	+	22.0399i	−0.0200075	+	0.0346539i
$637$	5.94443	+	3.43202i	0.00933192	+	0.00538779i
$638$	−1506.88			−2.36189
$639$		−	220.344i		−	0.344827i
$640$	−773.034	−	446.311i	−1.20787	−	0.697361i
$641$	−583.796	+	337.055i	−0.910758	+	0.525826i	−0.880675	−	0.473721i	$-0.842911\pi$
$641$	−583.796	+	337.055i	−0.910758	+	0.525826i	−0.0300832	+	0.999547i	$0.509577\pi$
$642$	−430.668	−	248.646i	−0.670823	−	0.387300i
$643$	0.719856	+	1.24683i	0.00111953	+	0.00193908i	0.866585	−	0.499030i	$-0.166310\pi$
$643$	0.719856	+	1.24683i	0.00111953	+	0.00193908i	−0.865465	+	0.500969i	$0.832977\pi$
$644$	−1.55958	−	2.70128i	−0.00242171	−	0.00419453i
$645$			279.007i			0.432569i
$646$	792.711	+	552.165i	1.22711	+	0.854745i
$647$	−614.044			−0.949063			−0.474532	−	0.880239i	$-0.657383\pi$
$647$	−614.044			−0.949063			−0.474532	+	0.880239i	$0.657383\pi$
$648$	−60.1404	+	34.7221i	−0.0928092	+	0.0535834i
$649$	601.315	−	347.169i	0.926525	−	0.534929i
$650$	−2.60835	+	4.51779i	−0.00401284	+	0.00695045i
$651$	−33.5306	−	58.0768i	−0.0515064	−	0.0892116i
$652$	0.774191	−	1.34094i	0.00118741	−	0.00205665i
$653$	822.374			1.25938			0.629689	−	0.776847i	$-0.283182\pi$
$653$	822.374			1.25938			0.629689	+	0.776847i	$0.283182\pi$
$654$			37.8199i			0.0578286i
$655$	−183.807	+	318.362i	−0.280621	+	0.486049i
$656$	511.041	+	295.050i	0.779027	+	0.449771i
$657$	−275.432			−0.419227
$658$			137.147i			0.208431i
$659$	−549.386	−	317.188i	−0.833666	−	0.481317i	0.0214404	−	0.999770i	$-0.493175\pi$
$659$	−549.386	−	317.188i	−0.833666	−	0.481317i	−0.855106	+	0.518453i	$0.826508\pi$
$660$	−50.8129	+	29.3368i	−0.0769892	+	0.0444497i
$661$	−818.470	−	472.544i	−1.23823	−	0.714893i	−0.269498	−	0.963001i	$-0.586858\pi$
$661$	−818.470	−	472.544i	−1.23823	−	0.714893i	−0.968732	+	0.248108i	$0.920191\pi$
$662$	450.413	+	780.138i	0.680382	+	1.17846i
$663$	3.33619	+	5.77845i	0.00503196	+	0.00871561i
$664$			1148.09i			1.72905i
$665$	−117.173	−	249.675i	−0.176200	−	0.375451i
$666$	264.559			0.397236
$667$	164.993	−	95.2590i	0.247366	−	0.142817i
$668$	37.3561	−	21.5676i	0.0559223	−	0.0322868i
$669$	224.162	−	388.260i	0.335070	−	0.580358i
$670$	505.228	+	875.080i	0.754071	+	1.30609i
$671$	−550.150	+	952.888i	−0.819896	+	1.42010i
$672$	−16.4545			−0.0244859
$673$		−	570.803i		−	0.848147i	−0.905628	−	0.424074i	$-0.860600\pi$
$673$		−	570.803i		−	0.848147i	0.905628	−	0.424074i	$-0.139400\pi$
$674$	258.703	−	448.086i	0.383832	−	0.664817i
$675$	−72.6848	−	41.9646i	−0.107681	−	0.0621698i
$676$	−44.4088			−0.0656935
$677$		−	275.976i		−	0.407646i	−0.979008	−	0.203823i	$-0.934663\pi$
$677$		−	275.976i		−	0.407646i	0.979008	−	0.203823i	$-0.0653367\pi$
$678$	214.182	+	123.658i	0.315902	+	0.182386i
$679$	158.471	−	91.4931i	0.233388	−	0.134747i
$680$	−1055.66	−	609.485i	−1.55244	−	0.896302i
$681$	111.764	+	193.582i	0.164118	+	0.284261i
$682$	−354.913	−	614.727i	−0.520400	−	0.901359i
$683$			106.224i			0.155525i	0.996972	+	0.0777627i	$0.0247776\pi$
$683$			106.224i			0.155525i	−0.996972	+	0.0777627i	$0.975222\pi$
$684$	6.36428	+	13.5612i	0.00930450	+	0.0198263i
$685$	−608.781			−0.888732
$686$	−375.792	+	216.964i	−0.547802	+	0.316274i
$687$	148.342	−	85.6453i	0.215927	−	0.124666i
$688$	−213.217	+	369.302i	−0.309908	+	0.536776i
$689$	−4.37279	−	7.57390i	−0.00634658	−	0.0109926i
$690$	60.1617	−	104.203i	0.0871908	−	0.151019i
$691$	244.177			0.353367			0.176684	−	0.984268i	$-0.443463\pi$
$691$	244.177			0.353367			0.176684	+	0.984268i	$0.443463\pi$
$692$		−	71.1195i		−	0.102774i
$693$	68.1994	−	118.125i	0.0984118	−	0.170454i
$694$	299.201	+	172.744i	0.431125	+	0.248910i
$695$	1171.05			1.68497
$696$		−	485.450i		−	0.697486i
$697$	741.082	+	427.864i	1.06325	+	0.613865i
$698$	870.378	−	502.513i	1.24696	−	0.719932i
$699$	−524.194	−	302.644i	−0.749920	−	0.432966i
$700$	−4.80281	−	8.31871i	−0.00686115	−	0.0118839i
$701$	143.276	+	248.161i	0.204388	+	0.354010i	0.949938	−	0.312440i	$-0.101146\pi$
$701$	143.276	+	248.161i	0.204388	+	0.354010i	−0.745550	+	0.666450i	$0.767813\pi$
$702$			1.67821i			0.00239061i
$703$	−68.7436	+	808.618i	−0.0977860	+	1.15024i
$704$	1190.71			1.69135
$705$	−282.474	+	163.087i	−0.400673	+	0.231329i
$706$	−53.9108	+	31.1254i	−0.0763610	+	0.0440870i
$707$	173.506	−	300.521i	0.245411	−	0.425065i
$708$	−7.86514	−	13.6228i	−0.0111090	−	0.0192413i
$709$	−5.70585	+	9.88282i	−0.00804774	+	0.0139391i	−0.870021	−	0.493014i	$-0.835895\pi$
$709$	−5.70585	+	9.88282i	−0.00804774	+	0.0139391i	0.861973	+	0.506953i	$0.169228\pi$
$710$	972.804			1.37015
$711$			184.048i			0.258857i
$712$	−279.688	+	484.434i	−0.392820	+	0.680385i
$713$	77.7209	+	44.8722i	0.109006	+	0.0629344i
$714$	−199.279			−0.279102
$715$		−	20.1629i		−	0.0281999i
$716$	−42.4339	−	24.4992i	−0.0592652	−	0.0342168i
$717$	−451.636	+	260.752i	−0.629897	+	0.363671i
$718$	268.238	+	154.867i	0.373591	+	0.215693i
$719$	438.491	+	759.488i	0.609862	+	1.05631i	0.991263	+	0.131902i	$0.0421084\pi$
$719$	438.491	+	759.488i	0.609862	+	1.05631i	−0.381401	+	0.924410i	$0.624558\pi$
$720$	−163.411	−	283.036i	−0.226960	−	0.393106i
$721$			382.298i			0.530232i
$722$	−699.131	+	258.360i	−0.968325	+	0.357839i
$723$	−220.485			−0.304958
$724$	−10.5634	+	6.09880i	−0.0145904	+	0.00842376i
$725$	508.105	−	293.354i	0.700834	−	0.404627i
$726$	505.518	−	875.583i	0.696306	−	1.20604i
$727$	−360.167	−	623.827i	−0.495415	−	0.858084i	0.504571	−	0.863370i	$-0.331651\pi$
$727$	−360.167	−	623.827i	−0.495415	−	0.858084i	−0.999986	+	0.00528653i	$0.998317\pi$
$728$	1.36561	−	2.36531i	0.00187584	−	0.00324905i
$729$	−27.0000			−0.0370370
$730$		−	1216.01i		−	1.66577i
$731$	−309.194	+	535.540i	−0.422974	+	0.732613i
$732$	21.5878	+	12.4637i	0.0294915	+	0.0170269i
$733$	−170.651			−0.232812			−0.116406	−	0.993202i	$-0.537137\pi$
$733$	−170.651			−0.232812			−0.116406	+	0.993202i	$0.537137\pi$
$734$			1024.44i			1.39570i
$735$	−422.232	−	243.776i	−0.574465	−	0.331668i
$736$	19.0701	−	11.0101i	0.0259104	−	0.0149594i
$737$	−1327.53	−	766.449i	−1.80126	−	1.03996i
$738$	107.615	+	186.394i	0.145819	+	0.252566i
$739$	530.334	+	918.566i	0.717637	+	1.24298i	0.961933	+	0.273284i	$0.0881098\pi$
$739$	530.334	+	918.566i	0.717637	+	1.24298i	−0.244296	+	0.969701i	$0.578557\pi$
$740$			72.0104i			0.0973114i
$741$	−5.12940	−	0.436069i	−0.00692227	−	0.000588487i
$742$	261.198			0.352019
$743$	290.537	−	167.742i	0.391033	−	0.225763i	−0.291575	−	0.956548i	$-0.594179\pi$
$743$	290.537	−	167.742i	0.391033	−	0.225763i	0.682607	+	0.730785i	$0.260846\pi$
$744$	198.037	−	114.337i	0.266179	−	0.153679i
$745$	−35.3107	+	61.1599i	−0.0473969	+	0.0820938i
$746$	−464.148	−	803.928i	−0.622182	−	1.07765i
$747$	−223.189	+	386.575i	−0.298781	+	0.517503i
$748$	−130.044			−0.173855
$749$			314.668i			0.420117i
$750$	−101.487	+	175.781i	−0.135316	+	0.234375i
$751$	−1128.41	−	651.490i	−1.50255	−	0.867497i	−0.999996	−	0.00295120i	$-0.999061\pi$
$751$	−1128.41	−	651.490i	−1.50255	−	0.867497i	−0.502554	−	0.864546i	$-0.667606\pi$
$752$	−498.522			−0.662929
$753$			613.226i			0.814377i
$754$	−10.1598	−	5.86578i	−0.0134746	−	0.00777955i
$755$	1326.92	−	766.100i	1.75751	−	1.01470i
$756$	−2.67613	−	1.54506i	−0.00353985	−	0.00204373i
$757$	−60.1511	−	104.185i	−0.0794598	−	0.137628i	0.823557	−	0.567233i	$-0.191986\pi$
$757$	−60.1511	−	104.185i	−0.0794598	−	0.137628i	−0.903017	+	0.429605i	$0.858653\pi$
$758$	486.574	+	842.771i	0.641919	+	1.11184i
$759$			182.535i			0.240494i
$760$	851.373	−	399.551i	1.12023	−	0.525725i
$761$	1346.45			1.76932			0.884658	−	0.466240i	$-0.154392\pi$
$761$	1346.45			1.76932			0.884658	+	0.466240i	$0.154392\pi$
$762$	−91.7437	+	52.9682i	−0.120399	+	0.0695121i
$763$	20.7248	−	11.9655i	0.0271623	−	0.0156822i
$764$	−4.82553	+	8.35805i	−0.00631613	+	0.0109399i
$765$	−236.969	−	410.442i	−0.309763	−	0.536526i
$766$	27.9243	−	48.3663i	0.0364547	−	0.0631414i
$767$	5.40564			0.00704777
$768$		−	87.0301i		−	0.113320i
$769$	109.016	−	188.821i	0.141763	−	0.245541i	−0.786398	−	0.617721i	$-0.788056\pi$
$769$	109.016	−	188.821i	0.141763	−	0.245541i	0.928161	+	0.372180i	$0.121390\pi$
$770$	521.512	+	301.095i	0.677288	+	0.391033i
$771$	473.337			0.613926
$772$			52.6433i			0.0681909i
$773$	−48.6422	−	28.0836i	−0.0629266	−	0.0363307i	0.468207	−	0.883619i	$-0.344900\pi$
$773$	−48.6422	−	28.0836i	−0.0629266	−	0.0363307i	−0.531133	+	0.847288i	$0.678234\pi$
$774$	−134.697	+	77.7673i	−0.174027	+	0.100475i
$775$	239.345	+	138.186i	0.308832	+	0.178304i
$776$	311.984	+	540.373i	0.402042	+	0.696357i
$777$	−83.7014	−	144.975i	−0.107724	−	0.186583i
$778$			731.482i			0.940208i
$779$	−597.671	+	280.488i	−0.767229	+	0.360062i
$780$	−0.456792			−0.000585631
$781$	−1278.06	+	737.890i	−1.63644	+	0.944801i
$782$	230.955	−	133.342i	0.295339	−	0.170514i
$783$	94.3720	−	163.457i	0.120526	−	0.208757i
$784$	−372.586	−	645.338i	−0.475238	−	0.823136i
$785$	146.342	−	253.472i	0.186423	−	0.322894i
$786$	−204.929			−0.260724
$787$		−	170.104i		−	0.216142i	−0.994143	−	0.108071i	$-0.965533\pi$
$787$		−	170.104i		−	0.216142i	0.994143	−	0.108071i	$-0.0344674\pi$
$788$	−22.5377	+	39.0365i	−0.0286012	+	0.0495387i
$789$	226.693	+	130.881i	0.287316	+	0.165882i
$790$	−812.556			−1.02855
$791$		−	156.492i		−	0.197840i
$792$	402.796	+	232.555i	0.508581	+	0.293630i
$793$	−7.41853	+	4.28309i	−0.00935501	+	0.00540112i
$794$	284.337	+	164.162i	0.358107	+	0.206753i
$795$	310.599	+	537.973i	0.390690	+	0.676696i
$796$	11.4980	+	19.9152i	0.0144448	+	0.0250190i
$797$			740.226i			0.928765i	0.885635	+	0.464383i	$0.153724\pi$
$797$			740.226i			0.928765i	−0.885635	+	0.464383i	$0.846276\pi$
$798$	87.8768	−	126.160i	0.110121	−	0.158095i
$799$	−722.928			−0.904791
$800$	58.7271	−	33.9061i	0.0734089	−	0.0423826i
$801$	−188.349	+	108.743i	−0.235142	+	0.135759i
$802$	330.829	−	573.013i	0.412505	−	0.714480i
$803$	922.366	+	1597.59i	1.14865	+	1.98952i
$804$	−17.3639	+	30.0752i	−0.0215970	+	0.0374070i
$805$	−76.1359			−0.0945788
$806$		−	5.52620i		−	0.00685633i
$807$	−58.9364	+	102.081i	−0.0730314	+	0.126494i
$808$	1024.75	+	591.641i	1.26826	+	0.732229i
$809$	−1489.01			−1.84056			−0.920280	−	0.391260i	$-0.872039\pi$
$809$	−1489.01			−1.84056			−0.920280	+	0.391260i	$0.872039\pi$
$810$		−	119.203i		−	0.147164i
$811$	823.672	+	475.547i	1.01563	+	0.586372i	0.912834	−	0.408331i	$-0.133889\pi$
$811$	823.672	+	475.547i	1.01563	+	0.586372i	0.102792	+	0.994703i	$0.467223\pi$
$812$	18.7075	−	10.8008i	0.0230388	−	0.0133015i
$813$	−170.697	−	98.5521i	−0.209960	−	0.121220i
$814$	−885.956	−	1534.52i	−1.08840	−	1.88516i
$815$	−18.8973	−	32.7310i	−0.0231868	−	0.0401608i
$816$		−	724.366i		−	0.887703i
$817$	−202.694	−	431.905i	−0.248095	−	0.528647i
$818$	600.250			0.733802
$819$	0.919637	−	0.530953i	0.00112288	−	0.000648294i
$820$	−50.7346	+	29.2917i	−0.0618715	+	0.0357215i
$821$	790.459	−	1369.12i	0.962801	−	1.66762i	0.247390	−	0.968916i	$-0.420427\pi$
$821$	790.459	−	1369.12i	0.962801	−	1.66762i	0.715411	−	0.698704i	$-0.246240\pi$
$822$	−169.685	−	293.903i	−0.206430	−	0.357546i
$823$	734.523	−	1272.23i	0.892494	−	1.54585i	0.0556192	−	0.998452i	$-0.482287\pi$
$823$	734.523	−	1272.23i	0.892494	−	1.54585i	0.836875	−	0.547394i	$-0.184380\pi$
$824$	−1303.61			−1.58204
$825$			562.124i			0.681363i
$826$	−80.7230	+	139.816i	−0.0977276	+	0.169269i
$827$	−13.7499	−	7.93854i	−0.0166263	−	0.00959920i	0.491664	−	0.870785i	$-0.336389\pi$
$827$	−13.7499	−	7.93854i	−0.0166263	−	0.00959920i	−0.508290	+	0.861186i	$0.669722\pi$
$828$	4.13534			0.00499437
$829$			460.891i			0.555960i	0.960587	+	0.277980i	$0.0896649\pi$
$829$			460.891i			0.555960i	−0.960587	+	0.277980i	$0.910335\pi$
$830$	−1706.70	−	985.363i	−2.05626	−	1.18718i
$831$	−661.365	+	381.839i	−0.795867	+	0.459494i
$832$	8.02810	+	4.63503i	0.00964916	+	0.00557095i
$833$	−540.303	−	935.832i	−0.648623	−	1.12345i
$834$	326.407	+	565.353i	0.391375	+	0.677881i
$835$		−	1052.89i		−	1.26094i
$836$	57.3460	−	82.3283i	0.0685957	−	0.0984789i
$837$	88.9088			0.106223
$838$	253.627	−	146.432i	0.302658	−	0.174740i
$839$	−11.1163	+	6.41800i	−0.0132495	+	0.00764959i	−0.506610	−	0.862175i	$-0.669102\pi$
$839$	−11.1163	+	6.41800i	−0.0132495	+	0.00764959i	0.493361	+	0.869825i	$0.335768\pi$
$840$	−96.9993	+	168.008i	−0.115475	+	0.200009i
$841$	239.209	+	414.323i	0.284434	+	0.492655i
$842$	−117.614	+	203.713i	−0.139684	+	0.241939i
$843$	−156.186			−0.185274
$844$		−	4.97538i		−	0.00589500i
$845$	−541.989	+	938.752i	−0.641407	+	1.11095i
$846$	−157.468	−	90.9140i	−0.186132	−	0.107463i
$847$	−639.744			−0.755306
$848$			949.437i			1.11962i
$849$	−103.599	−	59.8131i	−0.122025	−	0.0704512i
$850$	711.236	−	410.632i	0.836748	−	0.483097i
$851$	194.012	+	112.013i	0.227981	+	0.131625i
$852$	16.7169	+	28.9546i	0.0196208	+	0.0339843i
$853$	321.717	+	557.231i	0.377160	+	0.653260i	0.990648	−	0.136444i	$-0.0435674\pi$
$853$	321.717	+	557.231i	0.377160	+	0.653260i	−0.613488	+	0.789704i	$0.710234\pi$
$854$		−	255.839i		−	0.299578i
$855$	364.341	+	30.9739i	0.426129	+	0.0362268i
$856$	−1072.99			−1.25350
$857$	−115.805	+	66.8603i	−0.135129	+	0.0780167i	−0.566040	−	0.824377i	$-0.691525\pi$
$857$	−115.805	+	66.8603i	−0.135129	+	0.0780167i	0.430912	+	0.902394i	$0.358192\pi$
$858$	9.73411	−	5.61999i	0.0113451	−	0.00655011i
$859$	−49.3229	+	85.4297i	−0.0574189	+	0.0994525i	−0.893306	−	0.449449i	$-0.851620\pi$
$859$	−49.3229	+	85.4297i	−0.0574189	+	0.0994525i	0.835887	+	0.548901i	$0.184954\pi$
$860$	−21.1675	−	36.6632i	−0.0246134	−	0.0426316i
$861$	68.0944	−	117.943i	0.0790875	−	0.136984i
$862$	−546.576			−0.634079
$863$		−	829.585i		−	0.961280i	−0.876918	−	0.480640i	$-0.840404\pi$
$863$		−	829.585i		−	0.961280i	0.876918	−	0.480640i	$-0.159596\pi$
$864$	10.9076	−	18.8925i	0.0126245	−	0.0218663i
$865$	−1503.39	−	867.980i	−1.73802	−	1.00344i
$866$	1505.14			1.73803
$867$		−	549.870i		−	0.634221i
$868$	8.81226	+	5.08776i	0.0101524	+	0.00586147i
$869$	1067.53	−	616.339i	1.22846	−	0.709251i
$870$	721.651	+	416.645i	0.829484	+	0.478903i
$871$	−5.96704	−	10.3352i	−0.00685079	−	0.0118659i
$872$	40.8014	+	70.6700i	0.0467906	+	0.0810436i
$873$			242.600i			0.277893i
$874$	−17.4290	+	205.014i	−0.0199416	+	0.234569i
$875$	128.434			0.146782
$876$	36.1934	−	20.8963i	0.0413167	−	0.0238542i
$877$	157.383	−	90.8649i	0.179456	−	0.103609i	−0.407581	−	0.913169i	$-0.633628\pi$
$877$	157.383	−	90.8649i	0.179456	−	0.103609i	0.587037	+	0.809560i	$0.300294\pi$
$878$	−380.963	+	659.847i	−0.433898	+	0.751534i
$879$	−355.277	−	615.358i	−0.404183	−	0.700065i
$880$	−1094.46	+	1895.66i	−1.24371	+	2.15416i
$881$	−517.816			−0.587759			−0.293880	−	0.955842i	$-0.594946\pi$
$881$	−517.816			−0.587759			−0.293880	+	0.955842i	$0.594946\pi$
$882$		−	271.790i		−	0.308151i
$883$	782.367	−	1355.10i	0.886033	−	1.53465i	0.0415084	−	0.999138i	$-0.486784\pi$
$883$	782.367	−	1355.10i	0.886033	−	1.53465i	0.844525	−	0.535516i	$-0.179883\pi$
$884$	−0.876791	−	0.506216i	−0.000991845	−	0.000572642i
$885$	−383.961			−0.433855
$886$		−	1203.89i		−	1.35879i
$887$	−620.266	−	358.111i	−0.699285	−	0.403732i	0.107796	−	0.994173i	$-0.465621\pi$
$887$	−620.266	−	358.111i	−0.699285	−	0.403732i	−0.807081	+	0.590441i	$0.798954\pi$
$888$	494.354	−	285.415i	0.556705	−	0.321414i
$889$	58.0518	+	33.5162i	0.0653001	+	0.0377011i
$890$	−480.093	−	831.546i	−0.539431	−	0.934321i
$891$	90.4176	+	156.608i	0.101479	+	0.175766i
$892$			68.0262i			0.0762626i
$893$	318.793	−	457.672i	0.356991	−	0.512511i
$894$	−39.3684			−0.0440363
$895$	−1035.77	+	598.003i	−1.15729	+	0.668159i
$896$	−272.678	+	157.431i	−0.304328	+	0.175704i
$897$	−0.710545	+	1.23070i	−0.000792135	+	0.00137202i
$898$	324.588	+	562.202i	0.361456	+	0.626061i
$899$	−310.759	+	538.251i	−0.345672	+	0.598722i
$900$	12.7350			0.0141500
$901$			1376.82i			1.52810i
$902$	720.760	−	1248.39i	0.799069	−	1.38403i
$903$	85.2309	+	49.2081i	0.0943864	+	0.0544940i
$904$	533.625			0.590293
$905$			297.732i			0.328986i
$906$	739.704	+	427.068i	0.816451	+	0.471378i
$907$	240.379	−	138.783i	0.265026	−	0.153013i	−0.361599	−	0.932334i	$-0.617769\pi$
$907$	240.379	−	138.783i	0.265026	−	0.153013i	0.626625	+	0.779321i	$0.284436\pi$
$908$	−29.3731	−	16.9585i	−0.0323492	−	0.0186768i
$909$	230.031	+	398.426i	0.253059	+	0.438312i
$910$	2.34412	+	4.06013i	0.00257595	+	0.00446168i
$911$		−	1630.56i		−	1.78986i	−0.446207	−	0.894930i	$-0.647226\pi$
$911$		−	1630.56i		−	1.78986i	0.446207	−	0.894930i	$-0.352774\pi$
$912$	458.582	+	319.427i	0.502831	+	0.350249i
$913$	2989.66			3.27455
$914$	−903.415	+	521.587i	−0.988419	+	0.570664i
$915$	526.937	−	304.227i	0.575887	−	0.332489i
$916$	−12.9954	+	22.5086i	−0.0141871	+	0.0245727i
$917$	64.8355	+	112.298i	0.0707040	+	0.122463i
$918$	132.100	−	228.804i	0.143900	−	0.249242i
$919$	−48.0409			−0.0522752			−0.0261376	−	0.999658i	$-0.508321\pi$
$919$	−48.0409			−0.0522752			−0.0261376	+	0.999658i	$0.508321\pi$
$920$		−	259.618i		−	0.282193i
$921$	201.882	−	349.669i	0.219198	−	0.379663i
$922$	−489.575	−	282.656i	−0.530993	−	0.306569i
$923$	−11.4894			−0.0124479
$924$			20.6964i			0.0223987i
$925$	597.469	+	344.949i	0.645912	+	0.372918i
$926$	−571.781	+	330.118i	−0.617474	+	0.356499i
$927$	−438.940	−	253.422i	−0.473506	−	0.273379i
$928$	76.2497	+	132.068i	0.0821656	+	0.142315i
$929$	−641.727	−	1111.50i	−0.690772	−	1.19645i	−0.971585	−	0.236690i	$-0.923937\pi$
$929$	−641.727	−	1111.50i	−0.690772	−	1.19645i	0.280813	−	0.959763i	$-0.409396\pi$
$930$			392.525i			0.422070i
$931$	830.717	+	70.6223i	0.892285	+	0.0758564i
$932$	91.8430			0.0985440
$933$	661.921	−	382.160i	0.709454	−	0.409604i
$934$	528.386	−	305.064i	0.565724	−	0.326621i
$935$	−1587.12	+	2748.98i	−1.69746	+	2.94008i
$936$	1.81051	+	3.13589i	0.00193430	+	0.00335031i
$937$	−769.568	+	1332.93i	−0.821311	+	1.42255i	0.0833953	+	0.996517i	$0.473424\pi$
$937$	−769.568	+	1332.93i	−0.821311	+	1.42255i	−0.904706	+	0.426036i	$0.859910\pi$
$938$	356.426			0.379985
$939$		−	210.042i		−	0.223687i
$940$	24.7459	−	42.8611i	0.0263254	−	0.0455970i
$941$	−1281.05	−	739.617i	−1.36138	−	0.785990i	−0.371568	−	0.928406i	$-0.621180\pi$
$941$	−1281.05	−	739.617i	−1.36138	−	0.785990i	−0.989807	+	0.142415i	$0.954513\pi$
$942$	163.159			0.173205
$943$			182.254i			0.193270i
$944$	−508.223	−	293.423i	−0.538372	−	0.310829i
$945$	−65.3217	+	37.7135i	−0.0691235	+	0.0399085i
$946$	902.146	+	520.854i	0.953643	+	0.550586i
$947$	349.924	+	606.086i	0.369508	+	0.640006i	0.989489	−	0.144611i	$-0.0461930\pi$
$947$	349.924	+	606.086i	0.369508	+	0.640006i	−0.619981	+	0.784617i	$0.712860\pi$
$948$	−13.9632	−	24.1850i	−0.0147291	−	0.0255116i
$949$			14.3618i			0.0151336i
$950$	−53.6733	+	631.349i	−0.0564982	+	0.664577i
$951$	−572.818			−0.602332
$952$	−372.371	+	214.989i	−0.391146	+	0.225828i
$953$	−354.907	+	204.906i	−0.372411	+	0.215011i	−0.674511	−	0.738265i	$-0.735646\pi$
$953$	−354.907	+	204.906i	−0.372411	+	0.215011i	0.302100	+	0.953276i	$0.402312\pi$
$954$	−173.146	+	299.898i	−0.181495	+	0.314358i
$955$	117.787	+	204.012i	0.123337	+	0.213625i
$956$	39.5652	−	68.5289i	0.0413862	−	0.0716829i
$957$	−1264.13			−1.32093
$958$			844.688i			0.881720i
$959$	−107.370	+	185.971i	−0.111960	+	0.193921i
$960$	−570.235	−	329.225i	−0.593995	−	0.342943i
$961$	668.231			0.695349
$962$		−	13.7949i		−	0.0143398i
$963$	−361.289	−	208.591i	−0.375171	−	0.216605i
$964$	28.9731	−	16.7276i	0.0300550	−	0.0173523i
$965$	1112.82	+	642.487i	1.15318	+	0.665790i
$966$	−21.2213	−	36.7564i	−0.0219682	−	0.0380501i
$967$	92.4602	+	160.146i	0.0956155	+	0.165611i	0.909865	−	0.414904i	$-0.136185\pi$
$967$	92.4602	+	160.146i	0.0956155	+	0.165611i	−0.814250	+	0.580515i	$0.802851\pi$
$968$		−	2181.48i		−	2.25359i
$969$	665.009	+	463.214i	0.686284	+	0.478033i
$970$	−1071.06			−1.10419
$971$	218.148	−	125.948i	0.224663	−	0.129709i	−0.383445	−	0.923564i	$-0.625262\pi$
$971$	218.148	−	125.948i	0.224663	−	0.129709i	0.608107	+	0.793855i	$0.291929\pi$
$972$	3.54796	−	2.04842i	0.00365017	−	0.00210743i
$973$	206.537	−	357.733i	0.212269	−	0.367660i
$974$	658.840	+	1141.14i	0.676427	+	1.17161i
$975$	−2.18816	+	3.79000i	−0.00224426	+	0.00388718i
$976$	929.960			0.952828
$977$		−	372.639i		−	0.381411i	−0.981647	−	0.190706i	$-0.938922\pi$
$977$		−	372.639i		−	0.381411i	0.981647	−	0.190706i	$-0.0610776\pi$
$978$	10.5344	−	18.2462i	0.0107714	−	0.0186566i
$979$	1261.49	+	728.319i	1.28854	+	0.743942i
$980$	73.9785			0.0754882
$981$			31.7273i			0.0323418i
$982$	619.658	+	357.760i	0.631016	+	0.364317i
$983$	137.328	−	79.2861i	0.139702	−	0.0806573i	−0.428520	−	0.903532i	$-0.640965\pi$
$983$	137.328	−	79.2861i	0.139702	−	0.0806573i	0.568222	+	0.822875i	$0.307631\pi$
$984$	402.176	+	232.197i	0.408716	+	0.235972i
$985$	550.125	+	952.844i	0.558503	+	0.967355i
$986$	923.450	+	1599.46i	0.936561	+	1.62217i
$987$			115.054i			0.116569i
$988$	0.707118	−	0.331852i	0.000715706	−	0.000335882i
$989$	−131.705			−0.133170
$990$	−691.412	+	399.187i	−0.698396	+	0.403219i
$991$	1489.96	−	860.227i	1.50349	−	0.868039i	0.503496	−	0.863998i	$-0.332047\pi$
$991$	1489.96	−	860.227i	1.50349	−	0.868039i	0.999992	−	0.00404127i	$-0.00128638\pi$
$992$	−35.9178	+	62.2114i	−0.0362074	+	0.0627131i
$993$	377.854	+	654.462i	0.380517	+	0.659075i
$994$	171.572	−	297.172i	0.172608	−	0.298966i
$995$	561.312			0.564132
$996$		−	67.7311i		−	0.0680031i
$997$	−261.532	+	452.987i	−0.262319	+	0.454350i	−0.966858	−	0.255316i	$-0.917821\pi$
$997$	−261.532	+	452.987i	−0.262319	+	0.454350i	0.704539	+	0.709666i	$0.251154\pi$
$998$	144.299	+	83.3111i	0.144588	+	0.0834780i
$999$	221.940			0.222162

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.3.g.b.31.1	✓	6
3.2	odd	2		171.3.p.c.145.3		6
4.3	odd	2		912.3.be.f.145.1		6
19.8	odd	6	inner	57.3.g.b.46.1	yes	6
57.8	even	6		171.3.p.c.46.3		6
76.27	even	6		912.3.be.f.673.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.g.b.31.1	✓	6	1.1	even	1	trivial
57.3.g.b.46.1	yes	6	19.8	odd	6	inner
171.3.p.c.46.3		6	57.8	even	6
171.3.p.c.145.3		6	3.2	odd	2
912.3.be.f.145.1		6	4.3	odd	2
912.3.be.f.673.1		6	76.27	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	57.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.78805 + 1.03233i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.131406 - 0.227602i) q^{4} +(-3.20750 - 5.55555i) q^{5} +(1.78805 - 3.09699i) q^{6} -2.26281 q^{7} -7.71601i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.78805 + 1.03233i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.131406 - 0.227602i) q^{4} +(-3.20750 - 5.55555i) q^{5} +(1.78805 - 3.09699i) q^{6} -2.26281 q^{7} -7.71601i q^{8} +(1.50000 - 2.59808i) q^{9} +(11.4703 + 6.62239i) q^{10} -20.0928 q^{11} +0.455204i q^{12} +(-0.135471 - 0.0782143i) q^{13} +(4.04601 - 2.33597i) q^{14} +(9.62250 + 5.55555i) q^{15} +(8.49109 + 14.7070i) q^{16} +(12.3133 + 21.3272i) q^{17} +6.19397i q^{18} +(-18.9317 - 1.60945i) q^{19} -1.68594 q^{20} +(3.39422 - 1.95965i) q^{21} +(35.9269 - 20.7424i) q^{22} +(-2.62250 + 4.54230i) q^{23} +(6.68226 + 11.5740i) q^{24} +(-8.07609 + 13.9882i) q^{25} +0.322972 q^{26} +5.19615i q^{27} +(-0.297347 + 0.515021i) q^{28} +(-31.4573 - 18.1619i) q^{29} -22.9406 q^{30} -17.1105i q^{31} +(-3.63586 - 2.09917i) q^{32} +(30.1392 - 17.4009i) q^{33} +(-44.0334 - 25.4227i) q^{34} +(7.25797 + 12.5712i) q^{35} +(-0.394218 - 0.682806i) q^{36} -42.7124i q^{37} +(35.5123 - 16.6660i) q^{38} +0.270942 q^{39} +(-42.8667 + 24.7491i) q^{40} +(30.0928 - 17.3741i) q^{41} +(-4.04601 + 7.00790i) q^{42} +(12.5553 + 21.7464i) q^{43} +(-2.64032 + 4.57316i) q^{44} -19.2450 q^{45} -10.8291i q^{46} +(-14.6778 + 25.4227i) q^{47} +(-25.4733 - 14.7070i) q^{48} -43.8797 q^{49} -33.3487i q^{50} +(-36.9398 - 21.3272i) q^{51} +(-0.0356035 + 0.0205557i) q^{52} +(48.4176 + 27.9539i) q^{53} +(-5.36414 - 9.29096i) q^{54} +(64.4476 + 111.627i) q^{55} +17.4599i q^{56} +(29.7914 - 13.9812i) q^{57} +74.9962 q^{58} +(-29.9269 + 17.2783i) q^{59} +(2.52891 - 1.46007i) q^{60} +(27.3805 - 47.4244i) q^{61} +(17.6637 + 30.5944i) q^{62} +(-3.39422 + 5.87896i) q^{63} -59.2606 q^{64} +1.00349i q^{65} +(-35.9269 + 62.2272i) q^{66} +(66.0698 + 38.1454i) q^{67} +6.47216 q^{68} -9.08459i q^{69} +(-25.9552 - 14.9852i) q^{70} +(63.6080 - 36.7241i) q^{71} +(-20.0468 - 11.5740i) q^{72} +(-45.9053 - 79.5103i) q^{73} +(44.0932 + 76.3717i) q^{74} -27.9764i q^{75} +(-2.85406 + 4.09740i) q^{76} +45.4662 q^{77} +(-0.484457 + 0.279702i) q^{78} +(-53.1300 + 30.6746i) q^{79} +(54.4703 - 94.3453i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-35.8716 + 62.1313i) q^{82} -148.793 q^{83} -1.03004i q^{84} +(78.9897 - 136.814i) q^{85} +(-44.8990 - 25.9224i) q^{86} +62.9147 q^{87} +155.036i q^{88} +(-62.7829 - 36.2477i) q^{89} +(34.4109 - 19.8672i) q^{90} +(0.306546 + 0.176984i) q^{91} +(0.689224 + 1.19377i) q^{92} +(14.8181 + 25.6657i) q^{93} -60.6093i q^{94} +(51.7820 + 110.338i) q^{95} +7.27172 q^{96} +(-70.0326 + 40.4334i) q^{97} +(78.4589 - 45.2983i) q^{98} +(-30.1392 + 52.2026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 9 q^{3} + 5 q^{4} + 4 q^{5} - 3 q^{6} - 22 q^{7} + 9 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 9 * q^3 + 5 * q^4 + 4 * q^5 - 3 * q^6 - 22 * q^7 + 9 * q^9	\( 6 q + 3 q^{2} - 9 q^{3} + 5 q^{4} + 4 q^{5} - 3 q^{6} - 22 q^{7} + 9 q^{9} + 54 q^{10} - 36 q^{11} - 3 q^{13} - 57 q^{14} - 12 q^{15} - 23 q^{16} + 38 q^{17} - 10 q^{19} + 32 q^{20} + 33 q^{21} + 36 q^{22} + 54 q^{23} + 39 q^{24} - 21 q^{25} + 118 q^{26} - 101 q^{28} - 102 q^{29} - 108 q^{30} - 63 q^{32} + 54 q^{33} - 150 q^{34} - 24 q^{35} - 15 q^{36} + 119 q^{38} + 6 q^{39} + 30 q^{40} + 96 q^{41} + 57 q^{42} + 107 q^{43} - 94 q^{44} + 24 q^{45} - 50 q^{47} + 69 q^{48} - 48 q^{49} - 114 q^{51} + 399 q^{52} - 90 q^{53} + 9 q^{54} + 148 q^{55} - 3 q^{57} - 116 q^{58} - 48 q^{60} + 27 q^{61} - 121 q^{62} - 33 q^{63} + 46 q^{64} - 36 q^{66} - 39 q^{67} - 388 q^{68} - 354 q^{70} + 84 q^{71} - 117 q^{72} - 77 q^{73} + 219 q^{74} + 215 q^{76} + 260 q^{77} - 177 q^{78} + 9 q^{79} + 312 q^{80} - 27 q^{81} - 4 q^{82} - 348 q^{83} + 68 q^{85} + 249 q^{86} + 204 q^{87} - 72 q^{89} + 162 q^{90} - 393 q^{91} - 118 q^{92} + 129 q^{93} + 104 q^{95} + 126 q^{96} - 228 q^{97} + 540 q^{98} - 54 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 9 * q^3 + 5 * q^4 + 4 * q^5 - 3 * q^6 - 22 * q^7 + 9 * q^9 + 54 * q^10 - 36 * q^11 - 3 * q^13 - 57 * q^14 - 12 * q^15 - 23 * q^16 + 38 * q^17 - 10 * q^19 + 32 * q^20 + 33 * q^21 + 36 * q^22 + 54 * q^23 + 39 * q^24 - 21 * q^25 + 118 * q^26 - 101 * q^28 - 102 * q^29 - 108 * q^30 - 63 * q^32 + 54 * q^33 - 150 * q^34 - 24 * q^35 - 15 * q^36 + 119 * q^38 + 6 * q^39 + 30 * q^40 + 96 * q^41 + 57 * q^42 + 107 * q^43 - 94 * q^44 + 24 * q^45 - 50 * q^47 + 69 * q^48 - 48 * q^49 - 114 * q^51 + 399 * q^52 - 90 * q^53 + 9 * q^54 + 148 * q^55 - 3 * q^57 - 116 * q^58 - 48 * q^60 + 27 * q^61 - 121 * q^62 - 33 * q^63 + 46 * q^64 - 36 * q^66 - 39 * q^67 - 388 * q^68 - 354 * q^70 + 84 * q^71 - 117 * q^72 - 77 * q^73 + 219 * q^74 + 215 * q^76 + 260 * q^77 - 177 * q^78 + 9 * q^79 + 312 * q^80 - 27 * q^81 - 4 * q^82 - 348 * q^83 + 68 * q^85 + 249 * q^86 + 204 * q^87 - 72 * q^89 + 162 * q^90 - 393 * q^91 - 118 * q^92 + 129 * q^93 + 104 * q^95 + 126 * q^96 - 228 * q^97 + 540 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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