LMFDB - Embedded newform 63.3.t.a.40.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(40,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("63.40");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.t (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:	$1.71662566547$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			40.3
Character	$\chi$	$=$	63.40
Dual form			63.3.t.a.52.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.83394 q^{2} +(-2.47969 - 1.68854i) q^{3} +4.03122 q^{4} +(-2.07720 + 1.19927i) q^{5} +(7.02729 + 4.78521i) q^{6} +(6.05681 + 3.50928i) q^{7} -0.0884848 q^{8} +(3.29769 + 8.37408i) q^{9} +O(q^{10})$	\(q-2.83394 q^{2} +(-2.47969 - 1.68854i) q^{3} +4.03122 q^{4} +(-2.07720 + 1.19927i) q^{5} +(7.02729 + 4.78521i) q^{6} +(6.05681 + 3.50928i) q^{7} -0.0884848 q^{8} +(3.29769 + 8.37408i) q^{9} +(5.88667 - 3.39867i) q^{10} +(-5.69528 + 9.86452i) q^{11} +(-9.99617 - 6.80687i) q^{12} +(13.4628 + 7.77278i) q^{13} +(-17.1646 - 9.94510i) q^{14} +(7.17583 + 0.533610i) q^{15} -15.8741 q^{16} +(10.4807 - 6.05105i) q^{17} +(-9.34546 - 23.7317i) q^{18} +(-13.8576 - 8.00071i) q^{19} +(-8.37367 + 4.83454i) q^{20} +(-9.09343 - 18.9291i) q^{21} +(16.1401 - 27.9555i) q^{22} +(8.02831 + 13.9054i) q^{23} +(0.219415 + 0.149410i) q^{24} +(-9.62349 + 16.6684i) q^{25} +(-38.1529 - 22.0276i) q^{26} +(5.96270 - 26.3334i) q^{27} +(24.4163 + 14.1467i) q^{28} +(16.2339 + 28.1180i) q^{29} +(-20.3359 - 1.51222i) q^{30} +42.3999i q^{31} +45.3403 q^{32} +(30.7791 - 14.8442i) q^{33} +(-29.7018 + 17.1483i) q^{34} +(-16.7898 - 0.0257224i) q^{35} +(13.2937 + 33.7578i) q^{36} +(-3.61406 + 6.25973i) q^{37} +(39.2718 + 22.6736i) q^{38} +(-20.2590 - 42.0066i) q^{39} +(0.183801 - 0.106117i) q^{40} +(7.55990 + 4.36471i) q^{41} +(25.7703 + 53.6439i) q^{42} +(-22.2113 - 38.4711i) q^{43} +(-22.9590 + 39.7661i) q^{44} +(-16.8928 - 13.4398i) q^{45} +(-22.7518 - 39.4072i) q^{46} -26.3712i q^{47} +(39.3629 + 26.8040i) q^{48} +(24.3699 + 42.5101i) q^{49} +(27.2724 - 47.2372i) q^{50} +(-36.2063 - 2.69238i) q^{51} +(54.2717 + 31.3338i) q^{52} +(34.0624 + 58.9979i) q^{53} +(-16.8980 + 74.6272i) q^{54} -27.3208i q^{55} +(-0.535936 - 0.310518i) q^{56} +(20.8531 + 43.2384i) q^{57} +(-46.0060 - 79.6847i) q^{58} -95.1593i q^{59} +(28.9274 + 2.15110i) q^{60} -49.4424i q^{61} -120.159i q^{62} +(-9.41355 + 62.2927i) q^{63} -64.9952 q^{64} -37.2867 q^{65} +(-87.2262 + 42.0677i) q^{66} -81.8700 q^{67} +(42.2502 - 24.3931i) q^{68} +(3.57215 - 48.0372i) q^{69} +(47.5813 + 0.0728958i) q^{70} -112.881 q^{71} +(-0.291796 - 0.740979i) q^{72} +(58.8056 - 33.9514i) q^{73} +(10.2420 - 17.7397i) q^{74} +(52.0084 - 25.0827i) q^{75} +(-55.8633 - 32.2527i) q^{76} +(-69.1127 + 39.7612i) q^{77} +(57.4129 + 119.044i) q^{78} +136.888 q^{79} +(32.9738 - 19.0374i) q^{80} +(-59.2505 + 55.2302i) q^{81} +(-21.4243 - 12.3693i) q^{82} +(-18.8674 + 10.8931i) q^{83} +(-36.6577 - 76.3073i) q^{84} +(-14.5137 + 25.1385i) q^{85} +(62.9455 + 109.025i) q^{86} +(7.22320 - 97.1354i) q^{87} +(0.503946 - 0.872861i) q^{88} +(93.9050 + 54.2161i) q^{89} +(47.8732 + 38.0877i) q^{90} +(54.2650 + 94.3232i) q^{91} +(32.3639 + 56.0559i) q^{92} +(71.5937 - 105.138i) q^{93} +74.7346i q^{94} +38.3802 q^{95} +(-112.430 - 76.5587i) q^{96} +(-96.5982 + 55.7710i) q^{97} +(-69.0628 - 120.471i) q^{98} +(-101.388 - 15.1626i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 3 q^{3} + 46 q^{4} - 3 q^{5} - 12 q^{6} - 16 q^{8} - 15 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 3 * q^3 + 46 * q^4 - 3 * q^5 - 12 * q^6 - 16 * q^8 - 15 * q^9	\( 28 q - 2 q^{2} - 3 q^{3} + 46 q^{4} - 3 q^{5} - 12 q^{6} - 16 q^{8} - 15 q^{9} - 6 q^{10} + 7 q^{11} - 30 q^{12} - 15 q^{13} + 10 q^{14} - 18 q^{15} + 54 q^{16} - 33 q^{17} - 42 q^{18} - 6 q^{19} - 108 q^{20} + 21 q^{21} - 10 q^{22} + 34 q^{23} - 78 q^{24} + 31 q^{25} + 54 q^{26} + 81 q^{27} - 16 q^{28} + 70 q^{29} - 27 q^{30} - 306 q^{32} - 3 q^{33} - 12 q^{34} + 18 q^{35} - 174 q^{36} + 9 q^{37} + 87 q^{38} + 129 q^{39} - 102 q^{40} + 234 q^{41} + 306 q^{42} + 30 q^{43} + 51 q^{44} + 273 q^{45} - 22 q^{46} - 147 q^{48} - 38 q^{49} + 241 q^{50} + 12 q^{51} - 219 q^{52} + 148 q^{53} + 171 q^{54} + 110 q^{56} + 189 q^{57} + 17 q^{58} + 33 q^{60} - 471 q^{63} - 48 q^{64} - 228 q^{65} + 258 q^{66} + 68 q^{67} - 18 q^{68} - 78 q^{69} - 225 q^{70} - 350 q^{71} + 162 q^{72} - 6 q^{73} + 359 q^{74} - 510 q^{75} - 72 q^{76} - 224 q^{77} - 375 q^{78} + 164 q^{79} - 609 q^{80} - 435 q^{81} - 18 q^{82} - 738 q^{83} - 21 q^{84} + 3 q^{85} + 17 q^{86} - 561 q^{87} + 25 q^{88} + 21 q^{89} + 543 q^{90} + 39 q^{91} + 288 q^{92} - 222 q^{93} - 1014 q^{95} + 231 q^{96} + 57 q^{97} + 811 q^{98} - 162 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 3 * q^3 + 46 * q^4 - 3 * q^5 - 12 * q^6 - 16 * q^8 - 15 * q^9 - 6 * q^10 + 7 * q^11 - 30 * q^12 - 15 * q^13 + 10 * q^14 - 18 * q^15 + 54 * q^16 - 33 * q^17 - 42 * q^18 - 6 * q^19 - 108 * q^20 + 21 * q^21 - 10 * q^22 + 34 * q^23 - 78 * q^24 + 31 * q^25 + 54 * q^26 + 81 * q^27 - 16 * q^28 + 70 * q^29 - 27 * q^30 - 306 * q^32 - 3 * q^33 - 12 * q^34 + 18 * q^35 - 174 * q^36 + 9 * q^37 + 87 * q^38 + 129 * q^39 - 102 * q^40 + 234 * q^41 + 306 * q^42 + 30 * q^43 + 51 * q^44 + 273 * q^45 - 22 * q^46 - 147 * q^48 - 38 * q^49 + 241 * q^50 + 12 * q^51 - 219 * q^52 + 148 * q^53 + 171 * q^54 + 110 * q^56 + 189 * q^57 + 17 * q^58 + 33 * q^60 - 471 * q^63 - 48 * q^64 - 228 * q^65 + 258 * q^66 + 68 * q^67 - 18 * q^68 - 78 * q^69 - 225 * q^70 - 350 * q^71 + 162 * q^72 - 6 * q^73 + 359 * q^74 - 510 * q^75 - 72 * q^76 - 224 * q^77 - 375 * q^78 + 164 * q^79 - 609 * q^80 - 435 * q^81 - 18 * q^82 - 738 * q^83 - 21 * q^84 + 3 * q^85 + 17 * q^86 - 561 * q^87 + 25 * q^88 + 21 * q^89 + 543 * q^90 + 39 * q^91 + 288 * q^92 - 222 * q^93 - 1014 * q^95 + 231 * q^96 + 57 * q^97 + 811 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.83394			−1.41697			−0.708485	−	0.705726i	$-0.750621\pi$
$2$	−2.83394			−1.41697			−0.708485	+	0.705726i	$0.750621\pi$
$3$	−2.47969	−	1.68854i	−0.826562	−	0.562845i
$3$	−2.47969	−	1.68854i	−0.826562	−	0.562845i
$4$	4.03122			1.00781
$5$	−2.07720	+	1.19927i	−0.415440	+	0.239855i	−0.693125	−	0.720818i	$-0.743766\pi$
$5$	−2.07720	+	1.19927i	−0.415440	+	0.239855i	0.277684	+	0.960672i	$0.410433\pi$
$6$	7.02729	+	4.78521i	1.17121	+	0.797535i
$7$	6.05681	+	3.50928i	0.865258	+	0.501326i
$7$	6.05681	+	3.50928i	0.865258	+	0.501326i
$8$	−0.0884848			−0.0110606
$9$	3.29769	+	8.37408i	0.366410	+	0.930454i
$10$	5.88667	−	3.39867i	0.588667	−	0.339867i
$11$	−5.69528	+	9.86452i	−0.517753	+	0.896775i	0.482034	+	0.876152i	$0.339898\pi$
$11$	−5.69528	+	9.86452i	−0.517753	+	0.896775i	−0.999787	+	0.0206223i	$0.993435\pi$
$12$	−9.99617	−	6.80687i	−0.833014	−	0.567239i
$13$	13.4628	+	7.77278i	1.03560	+	0.597906i	0.918585	−	0.395224i	$-0.129333\pi$
$13$	13.4628	+	7.77278i	1.03560	+	0.597906i	0.117019	+	0.993130i	$0.462666\pi$
$14$	−17.1646	−	9.94510i	−1.22605	−	0.710364i
$15$	7.17583	+	0.533610i	0.478388	+	0.0355740i
$16$	−15.8741			−0.992133
$17$	10.4807	−	6.05105i	0.616513	−	0.355944i	−0.158997	−	0.987279i	$-0.550826\pi$
$17$	10.4807	−	6.05105i	0.616513	−	0.355944i	0.775510	+	0.631335i	$0.217493\pi$
$18$	−9.34546	−	23.7317i	−0.519192	−	1.31843i
$19$	−13.8576	−	8.00071i	−0.729350	−	0.421090i	0.0888345	−	0.996046i	$-0.471686\pi$
$19$	−13.8576	−	8.00071i	−0.729350	−	0.421090i	−0.818184	+	0.574956i	$0.805019\pi$
$20$	−8.37367	+	4.83454i	−0.418683	+	0.241727i
$21$	−9.09343	−	18.9291i	−0.433021	−	0.901384i
$22$	16.1401	−	27.9555i	0.733641	−	1.27070i
$23$	8.02831	+	13.9054i	0.349057	+	0.604584i	0.986082	−	0.166259i	$-0.0531686\pi$
$23$	8.02831	+	13.9054i	0.349057	+	0.604584i	−0.637025	+	0.770843i	$0.719835\pi$
$24$	0.219415	+	0.149410i	0.00914228	+	0.00622541i
$25$	−9.62349	+	16.6684i	−0.384939	+	0.666735i
$26$	−38.1529	−	22.0276i	−1.46742	−	0.847215i
$27$	5.96270	−	26.3334i	0.220841	−	0.975310i
$28$	24.4163	+	14.1467i	0.872012	+	0.505239i
$29$	16.2339	+	28.1180i	0.559791	+	0.969586i	0.997513	+	0.0704760i	$0.0224518\pi$
$29$	16.2339	+	28.1180i	0.559791	+	0.969586i	−0.437723	+	0.899110i	$0.644215\pi$
$30$	−20.3359	−	1.51222i	−0.677862	−	0.0504073i
$31$			42.3999i			1.36774i	0.729605	+	0.683869i	$0.239704\pi$
$31$			42.3999i			1.36774i	−0.729605	+	0.683869i	$0.760296\pi$
$32$	45.3403			1.41688
$33$	30.7791	−	14.8442i	0.932701	−	0.449825i
$34$	−29.7018	+	17.1483i	−0.873581	+	0.504362i
$35$	−16.7898	−	0.0257224i	−0.479709	−	0.000734926i
$36$	13.2937	+	33.7578i	0.369270	+	0.937716i
$37$	−3.61406	+	6.25973i	−0.0976772	+	0.169182i	−0.910723	−	0.413018i	$-0.864475\pi$
$37$	−3.61406	+	6.25973i	−0.0976772	+	0.169182i	0.813046	+	0.582200i	$0.197808\pi$
$38$	39.2718	+	22.6736i	1.03347	+	0.596673i
$39$	−20.2590	−	42.0066i	−0.519462	−	1.07709i
$40$	0.183801	−	0.106117i	0.00459502	−	0.00265294i
$41$	7.55990	+	4.36471i	0.184388	+	0.106456i	0.589353	−	0.807876i	$-0.299383\pi$
$41$	7.55990	+	4.36471i	0.184388	+	0.106456i	−0.404965	+	0.914332i	$0.632716\pi$
$42$	25.7703	+	53.6439i	0.613578	+	1.27723i
$43$	−22.2113	−	38.4711i	−0.516542	−	0.894676i	−0.999816	−	0.0192072i	$-0.993886\pi$
$43$	−22.2113	−	38.4711i	−0.516542	−	0.894676i	0.483274	−	0.875469i	$-0.339448\pi$
$44$	−22.9590	+	39.7661i	−0.521795	+	0.903775i
$45$	−16.8928	−	13.4398i	−0.375395	−	0.298663i
$46$	−22.7518	−	39.4072i	−0.494603	−	0.856678i
$47$		−	26.3712i		−	0.561090i	−0.959841	−	0.280545i	$-0.909485\pi$
$47$		−	26.3712i		−	0.561090i	0.959841	−	0.280545i	$-0.0905153\pi$
$48$	39.3629	+	26.8040i	0.820060	+	0.558418i
$49$	24.3699	+	42.5101i	0.497344	+	0.867553i
$50$	27.2724	−	47.2372i	0.545448	−	0.944744i
$51$	−36.2063	−	2.69238i	−0.709928	−	0.0527918i
$52$	54.2717	+	31.3338i	1.04369	+	0.602573i
$53$	34.0624	+	58.9979i	0.642688	+	1.11317i	0.984830	+	0.173520i	$0.0555140\pi$
$53$	34.0624	+	58.9979i	0.642688	+	1.11317i	−0.342143	+	0.939648i	$0.611153\pi$
$54$	−16.8980	+	74.6272i	−0.312925	+	1.38199i
$55$		−	27.3208i		−	0.496742i
$56$	−0.535936	−	0.310518i	−0.00957028	−	0.00554497i
$57$	20.8531	+	43.2384i	0.365844	+	0.758568i
$58$	−46.0060	−	79.6847i	−0.793207	−	1.37387i
$59$		−	95.1593i		−	1.61287i	−0.591323	−	0.806435i	$-0.701394\pi$
$59$		−	95.1593i		−	1.61287i	0.591323	−	0.806435i	$-0.298606\pi$
$60$	28.9274	+	2.15110i	0.482123	+	0.0358517i
$61$		−	49.4424i		−	0.810531i	−0.914199	−	0.405266i	$-0.867179\pi$
$61$		−	49.4424i		−	0.810531i	0.914199	−	0.405266i	$-0.132821\pi$
$62$		−	120.159i		−	1.93804i
$63$	−9.41355	+	62.2927i	−0.149421	+	0.988774i
$64$	−64.9952			−1.01555
$65$	−37.2867			−0.573642
$66$	−87.2262	+	42.0677i	−1.32161	+	0.637389i
$67$	−81.8700			−1.22194			−0.610971	−	0.791653i	$-0.709221\pi$
$67$	−81.8700			−1.22194			−0.610971	+	0.791653i	$0.709221\pi$
$68$	42.2502	−	24.3931i	0.621326	−	0.358723i
$69$	3.57215	−	48.0372i	0.0517703	−	0.696192i
$70$	47.5813	+	0.0728958i	0.679733	+	0.00104137i
$71$	−112.881			−1.58987			−0.794936	−	0.606694i	$-0.792496\pi$
$71$	−112.881			−1.58987			−0.794936	+	0.606694i	$0.792496\pi$
$72$	−0.291796	−	0.740979i	−0.00405272	−	0.0102914i
$73$	58.8056	−	33.9514i	0.805556	−	0.465088i	−0.0398541	−	0.999206i	$-0.512689\pi$
$73$	58.8056	−	33.9514i	0.805556	−	0.465088i	0.845410	+	0.534117i	$0.179356\pi$
$74$	10.2420	−	17.7397i	0.138406	−	0.239726i
$75$	52.0084	−	25.0827i	0.693445	−	0.334436i
$76$	−55.8633	−	32.2527i	−0.735043	−	0.424377i
$77$	−69.1127	+	39.7612i	−0.897567	+	0.516379i
$78$	57.4129	+	119.044i	0.736063	+	1.52621i
$79$	136.888			1.73276			0.866379	−	0.499387i	$-0.166441\pi$
$79$	136.888			1.73276			0.866379	+	0.499387i	$0.166441\pi$
$80$	32.9738	−	19.0374i	0.412172	−	0.237968i
$81$	−59.2505	+	55.2302i	−0.731487	+	0.681855i
$82$	−21.4243	−	12.3693i	−0.261272	−	0.150846i
$83$	−18.8674	+	10.8931i	−0.227318	+	0.131242i	−0.609334	−	0.792913i	$-0.708563\pi$
$83$	−18.8674	+	10.8931i	−0.227318	+	0.131242i	0.382016	+	0.924156i	$0.375230\pi$
$84$	−36.6577	−	76.3073i	−0.436401	−	0.908420i
$85$	−14.5137	+	25.1385i	−0.170750	+	0.295747i
$86$	62.9455	+	109.025i	0.731924	+	1.26773i
$87$	7.22320	−	97.1354i	0.0830252	−	1.11650i
$88$	0.503946	−	0.872861i	0.00572666	−	0.00991887i
$89$	93.9050	+	54.2161i	1.05511	+	0.609169i	0.924076	−	0.382208i	$-0.124836\pi$
$89$	93.9050	+	54.2161i	1.05511	+	0.609169i	0.131036	+	0.991378i	$0.458170\pi$
$90$	47.8732	+	38.0877i	0.531924	+	0.423197i
$91$	54.2650	+	94.3232i	0.596319	+	1.03652i
$92$	32.3639	+	56.0559i	0.351782	+	0.609304i
$93$	71.5937	−	105.138i	0.769825	−	1.13052i
$94$			74.7346i			0.795049i
$95$	38.3802			0.404002
$96$	−112.430	−	76.5587i	−1.17114	−	0.797487i
$97$	−96.5982	+	55.7710i	−0.995857	+	0.574959i	−0.907020	−	0.421088i	$-0.861649\pi$
$97$	−96.5982	+	55.7710i	−0.995857	+	0.574959i	−0.0888375	+	0.996046i	$0.528315\pi$
$98$	−69.0628	−	120.471i	−0.704722	−	1.22930i
$99$	−101.388	−	15.1626i	−1.02412	−	0.153158i
$100$	−38.7944	+	67.1939i	−0.387944	+	0.671939i
$101$	−66.5650	−	38.4313i	−0.659059	−	0.380508i	0.132859	−	0.991135i	$-0.457584\pi$
$101$	−66.5650	−	38.4313i	−0.659059	−	0.380508i	−0.791919	+	0.610627i	$0.790918\pi$
$102$	102.607	+	7.63005i	1.00595	+	0.0748044i
$103$	130.580	−	75.3905i	1.26777	−	0.731946i	0.293203	−	0.956050i	$-0.405279\pi$
$103$	130.580	−	75.3905i	1.26777	−	0.731946i	0.974565	+	0.224104i	$0.0719456\pi$
$104$	−1.19126	−	0.687773i	−0.0114544	−	0.00661320i
$105$	41.5900	+	28.4140i	0.396095	+	0.270609i
$106$	−96.5310	−	167.197i	−0.910669	−	1.57733i
$107$	−38.3022	+	66.3413i	−0.357964	+	0.620013i	−0.987621	−	0.156861i	$-0.949862\pi$
$107$	−38.3022	+	66.3413i	−0.357964	+	0.620013i	0.629656	+	0.776874i	$0.283196\pi$
$108$	24.0370	−	106.156i	0.222565	−	0.982923i
$109$	12.5985	+	21.8212i	0.115582	+	0.200195i	0.918012	−	0.396552i	$-0.129793\pi$
$109$	12.5985	+	21.8212i	0.115582	+	0.200195i	−0.802430	+	0.596746i	$0.796460\pi$
$110$			77.4256i			0.703869i
$111$	19.5315	−	9.41970i	0.175960	−	0.0848622i
$112$	−96.1466	−	55.7068i	−0.858452	−	0.497382i
$113$	37.0748	−	64.2154i	0.328095	−	0.568277i	−0.654039	−	0.756461i	$-0.726927\pi$
$113$	37.0748	−	64.2154i	0.328095	−	0.568277i	0.982134	+	0.188184i	$0.0602600\pi$
$114$	−59.0965	−	122.535i	−0.518390	−	1.07487i
$115$	−33.3528	−	19.2563i	−0.290025	−	0.167446i
$116$	65.4426	+	113.350i	0.564160	+	0.977154i
$117$	−20.6936	+	138.371i	−0.176868	+	1.18266i
$118$			269.676i			2.28539i
$119$	84.7146	+	0.129785i	0.711888	+	0.00109063i
$120$	−0.634952	−	0.0472164i	−0.00529127	−	0.000393470i
$121$	−4.37253	−	7.57345i	−0.0361366	−	0.0625905i
$122$			140.117i			1.14850i
$123$	−11.3762	−	23.5883i	−0.0924896	−	0.191775i
$124$			170.923i			1.37841i
$125$		−	106.128i		−	0.849027i
$126$	26.6774	−	176.534i	0.211726	−	1.40106i
$127$	52.2864			0.411704			0.205852	−	0.978583i	$-0.434003\pi$
$127$	52.2864			0.411704			0.205852	+	0.978583i	$0.434003\pi$
$128$	2.83143			0.0221205
$129$	−9.88279	+	132.901i	−0.0766108	+	1.03024i
$130$	105.668			0.812834
$131$	−161.548	+	93.2696i	−1.23319	+	0.711982i	−0.967693	−	0.252131i	$-0.918869\pi$
$131$	−161.548	+	93.2696i	−1.23319	+	0.711982i	−0.265495	+	0.964112i	$0.585535\pi$
$132$	124.078	−	59.8404i	0.939981	−	0.453336i
$133$	−55.8563	−	97.0892i	−0.419972	−	0.729994i
$134$	232.015			1.73145
$135$	19.1952	+	61.8506i	0.142186	+	0.458153i
$136$	−0.927385	+	0.535426i	−0.00681901	+	0.00393696i
$137$	76.6871	−	132.826i	0.559760	−	0.969533i	−0.437756	−	0.899094i	$-0.644227\pi$
$137$	76.6871	−	132.826i	0.559760	−	0.969533i	0.997516	−	0.0704389i	$-0.0224400\pi$
$138$	−10.1233	+	136.135i	−0.0733570	+	0.986483i
$139$	79.0232	+	45.6241i	0.568513	+	0.328231i	0.756555	−	0.653930i	$-0.226881\pi$
$139$	79.0232	+	45.6241i	0.568513	+	0.328231i	−0.188043	+	0.982161i	$0.560214\pi$
$140$	−67.6835	−	0.103693i	−0.483453	−	0.000740662i
$141$	−44.5288	+	65.3924i	−0.315807	+	0.463776i
$142$	319.898			2.25280
$143$	−153.349	+	88.5364i	−1.07237	+	0.619135i
$144$	−52.3480	−	132.931i	−0.363528	−	0.923134i
$145$	−67.4423	−	38.9378i	−0.465119	−	0.268537i
$146$	−166.652	+	96.2164i	−1.14145	+	0.659016i
$147$	11.3503	−	146.561i	0.0772126	−	0.997015i
$148$	−14.5691	+	25.2344i	−0.0984396	+	0.170502i
$149$	−56.2062	−	97.3519i	−0.377223	−	0.653369i	0.613434	−	0.789746i	$-0.289787\pi$
$149$	−56.2062	−	97.3519i	−0.377223	−	0.653369i	−0.990657	+	0.136377i	$0.956454\pi$
$150$	−147.389	+	71.0830i	−0.982591	+	0.473886i
$151$	−14.0984	+	24.4192i	−0.0933671	+	0.161717i	−0.908926	−	0.416958i	$-0.863096\pi$
$151$	−14.0984	+	24.4192i	−0.0933671	+	0.161717i	0.815559	+	0.578674i	$0.196430\pi$
$152$	1.22619	+	0.707942i	0.00806705	+	0.00465751i
$153$	85.2342	+	67.8120i	0.557086	+	0.443216i
$154$	195.861	−	112.681i	1.27183	−	0.731693i
$155$	−50.8490	−	88.0731i	−0.328058	−	0.568214i
$156$	−81.6686	−	169.338i	−0.523517	−	1.08550i
$157$			10.2506i			0.0652903i	0.999467	+	0.0326452i	$0.0103931\pi$
$157$			10.2506i			0.0652903i	−0.999467	+	0.0326452i	$0.989607\pi$
$158$	−387.932			−2.45527
$159$	15.1559	−	203.812i	0.0953201	−	1.28184i
$160$	−94.1810	+	54.3754i	−0.588631	+	0.339846i
$161$	−0.172194	+	112.396i	−0.00106953	+	0.698113i
$162$	167.912	−	156.519i	1.03650	−	0.966168i
$163$	88.8411	−	153.877i	0.545037	−	0.944033i	−0.453567	−	0.891222i	$-0.649849\pi$
$163$	88.8411	−	153.877i	0.545037	−	0.944033i	0.998605	−	0.0528105i	$-0.0168179\pi$
$164$	30.4757	+	17.5951i	0.185827	+	0.107287i
$165$	−46.1322	+	67.7470i	−0.279589	+	0.410588i
$166$	53.4692	−	30.8705i	0.322104	−	0.185967i
$167$	−53.9725	−	31.1611i	−0.323189	−	0.186593i	0.329624	−	0.944112i	$-0.393078\pi$
$167$	−53.9725	−	31.1611i	−0.323189	−	0.186593i	−0.652813	+	0.757519i	$0.726411\pi$
$168$	0.804631	+	1.67494i	0.00478947	+	0.00996985i
$169$	36.3322	+	62.9292i	0.214983	+	0.372362i
$170$	41.1311	−	71.2411i	0.241947	−	0.419065i
$171$	21.3004	−	142.429i	0.124564	−	0.832918i
$172$	−89.5387	−	155.086i	−0.520574	−	0.901660i
$173$			88.0132i			0.508747i	0.967106	+	0.254373i	$0.0818692\pi$
$173$			88.0132i			0.508747i	−0.967106	+	0.254373i	$0.918131\pi$
$174$	−20.4701	+	275.276i	−0.117644	+	1.58205i
$175$	−116.782	+	67.1856i	−0.667324	+	0.383918i
$176$	90.4077	−	156.591i	0.513680	−	0.889720i
$177$	−160.680	+	235.965i	−0.907797	+	1.33314i
$178$	−266.121	−	153.645i	−1.49506	−	0.863175i
$179$	−6.47603	−	11.2168i	−0.0361789	−	0.0626638i	0.847369	−	0.531005i	$-0.178185\pi$
$179$	−6.47603	−	11.2168i	−0.0361789	−	0.0626638i	−0.883548	+	0.468341i	$0.844852\pi$
$180$	−68.0986	−	54.1790i	−0.378325	−	0.300994i
$181$		−	225.852i		−	1.24780i	−0.781503	−	0.623901i	$-0.785547\pi$
$181$		−	225.852i		−	1.24780i	0.781503	−	0.623901i	$-0.214453\pi$
$182$	−153.784	−	267.306i	−0.844966	−	1.46872i
$183$	−83.4853	+	122.602i	−0.456204	+	0.669955i
$184$	−0.710384	−	1.23042i	−0.00386078	−	0.00668707i
$185$		−	17.3370i		−	0.0937133i
$186$	−202.892	+	297.956i	−1.09082	+	1.60191i
$187$			137.850i			0.737165i
$188$		−	106.308i		−	0.565470i
$189$	128.526	−	138.571i	0.680033	−	0.733182i
$190$	−108.767			−0.572459
$191$	103.891			0.543929			0.271965	−	0.962307i	$-0.412327\pi$
$191$	103.891			0.543929			0.271965	+	0.962307i	$0.412327\pi$
$192$	161.168	+	109.747i	0.839415	+	0.571598i
$193$	162.342			0.841151			0.420575	−	0.907258i	$-0.361828\pi$
$193$	162.342			0.841151			0.420575	+	0.907258i	$0.361828\pi$
$194$	273.754	−	158.052i	1.41110	−	0.814699i
$195$	92.4594	+	62.9600i	0.474151	+	0.322872i
$196$	98.2404	+	171.368i	0.501226	+	0.874325i
$197$	301.595			1.53094			0.765470	−	0.643472i	$-0.222507\pi$
$197$	301.595			1.53094			0.765470	+	0.643472i	$0.222507\pi$
$198$	287.326	+	42.9700i	1.45114	+	0.217020i
$199$	50.0571	−	28.9005i	0.251543	−	0.145229i	−0.368927	−	0.929458i	$-0.620275\pi$
$199$	50.0571	−	28.9005i	0.251543	−	0.145229i	0.620471	+	0.784230i	$0.286942\pi$
$200$	0.851533	−	1.47490i	0.00425766	−	0.00737449i
$201$	203.012	+	138.241i	1.01001	+	0.687764i
$202$	188.641	+	108.912i	0.933868	+	0.539169i
$203$	−0.348191	+	227.275i	−0.00171522	+	1.11958i
$204$	−145.956	−	10.8536i	−0.715470	−	0.0532039i
$205$	−20.9379			−0.102136
$206$	−370.056	+	213.652i	−1.79639	+	1.03715i
$207$	−89.9704	+	113.086i	−0.434640	+	0.546307i
$208$	−213.711	−	123.386i	−1.02746	−	0.593202i
$209$	157.846	−	91.1327i	0.755246	−	0.436042i
$210$	−117.864	−	80.5236i	−0.561256	−	0.383446i
$211$	−21.2197	+	36.7535i	−0.100567	+	0.174187i	−0.911918	−	0.410371i	$-0.865399\pi$
$211$	−21.2197	+	36.7535i	−0.100567	+	0.174187i	0.811351	+	0.584559i	$0.198732\pi$
$212$	137.313	+	237.834i	0.647704	+	1.12186i
$213$	279.909	+	190.603i	1.31413	+	0.894852i
$214$	108.546	−	188.007i	0.507225	−	0.878540i
$215$	92.2747	+	53.2748i	0.429185	+	0.247790i
$216$	−0.527609	+	2.33010i	−0.00244263	+	0.0107875i
$217$	−148.793	+	256.808i	−0.685683	+	1.18345i
$218$	−35.7034	−	61.8400i	−0.163777	−	0.283670i
$219$	−203.148	−	15.1065i	−0.927615	−	0.0689794i
$220$		−	110.136i		−	0.500619i
$221$	188.134			0.851285
$222$	−55.3511	+	26.6949i	−0.249329	+	0.120247i
$223$	−166.212	+	95.9625i	−0.745345	+	0.430325i	−0.824009	−	0.566576i	$-0.808268\pi$
$223$	−166.212	+	95.9625i	−0.745345	+	0.430325i	0.0786645	+	0.996901i	$0.474934\pi$
$224$	274.618	+	159.112i	1.22597	+	0.710321i
$225$	−171.318	−	25.6208i	−0.761411	−	0.113870i
$226$	−105.068	+	181.983i	−0.464901	+	0.805233i
$227$	194.664	+	112.390i	0.857552	+	0.495108i	0.863192	−	0.504876i	$-0.168462\pi$
$227$	194.664	+	112.390i	0.857552	+	0.495108i	−0.00563942	+	0.999984i	$0.501795\pi$
$228$	84.0636	+	174.304i	0.368700	+	0.764490i
$229$	−138.693	+	80.0742i	−0.605644	+	0.349669i	−0.771259	−	0.636522i	$-0.780373\pi$
$229$	−138.693	+	80.0742i	−0.605644	+	0.349669i	0.165614	+	0.986191i	$0.447039\pi$
$230$	94.5200	+	54.5712i	0.410957	+	0.237266i
$231$	238.516	+	18.1040i	1.03254	+	0.0783724i
$232$	−1.43646	−	2.48802i	−0.00619162	−	0.0107242i
$233$	123.299	−	213.560i	0.529180	−	0.916566i	−0.470241	−	0.882538i	$-0.655833\pi$
$233$	123.299	−	213.560i	0.529180	−	0.916566i	0.999421	−	0.0340281i	$-0.0108336\pi$
$234$	58.6444	−	392.136i	0.250617	−	1.67579i
$235$	31.6263	+	54.7784i	0.134580	+	0.233100i
$236$		−	383.608i		−	1.62546i
$237$	−339.439	−	231.140i	−1.43223	−	0.975275i
$238$	−240.076	−	0.367803i	−1.00872	−	0.00154539i
$239$	−110.141	+	190.769i	−0.460839	+	0.798197i	−0.999003	−	0.0446434i	$-0.985785\pi$
$239$	−110.141	+	190.769i	−0.460839	+	0.798197i	0.538164	+	0.842840i	$0.319118\pi$
$240$	−113.910	−	8.47059i	−0.474625	−	0.0352941i
$241$	−228.282	−	131.799i	−0.947230	−	0.546883i	−0.0550106	−	0.998486i	$-0.517519\pi$
$241$	−228.282	−	131.799i	−0.947230	−	0.546883i	−0.892219	+	0.451602i	$0.850853\pi$
$242$	12.3915	+	21.4627i	0.0512045	+	0.0886889i
$243$	240.181	−	36.9071i	0.988399	−	0.151881i
$244$		−	199.313i		−	0.816858i
$245$	−101.602	−	59.0760i	−0.414704	−	0.241126i
$246$	32.2395	+	66.8478i	0.131055	+	0.271739i
$247$	−124.376	−	215.425i	−0.503545	−	0.872165i
$248$		−	3.75175i		−	0.0151280i
$249$	65.1787	+	4.84683i	0.261762	+	0.0194652i
$250$			300.762i			1.20305i
$251$		−	23.0003i		−	0.0916348i	−0.998950	−	0.0458174i	$-0.985411\pi$
$251$		−	23.0003i		−	0.0916348i	0.998950	−	0.0458174i	$-0.0145892\pi$
$252$	−37.9481	+	251.116i	−0.150588	+	0.996492i
$253$	−182.894			−0.722901
$254$	−148.177			−0.583372
$255$	78.4368	−	37.8287i	0.307595	−	0.148348i
$256$	251.957			0.984206
$257$	−15.4300	+	8.90852i	−0.0600389	+	0.0346635i	−0.529719	−	0.848173i	$-0.677703\pi$
$257$	−15.4300	+	8.90852i	−0.0600389	+	0.0346635i	0.469680	+	0.882837i	$0.344369\pi$
$258$	28.0072	−	376.633i	0.108555	−	1.45982i
$259$	−43.8568	+	25.2312i	−0.169331	+	0.0974179i
$260$	−150.311			−0.578120
$261$	−181.928	+	228.669i	−0.697042	+	0.876125i
$262$	457.817	−	264.321i	1.74739	−	1.00886i
$263$	181.504	−	314.375i	0.690130	−	1.19534i	−0.281665	−	0.959513i	$-0.590887\pi$
$263$	181.504	−	314.375i	0.690130	−	1.19534i	0.971795	−	0.235828i	$-0.0757801\pi$
$264$	−2.72349	+	1.31349i	−0.0103162	+	0.00497534i
$265$	−141.509	−	81.7004i	−0.533997	−	0.308303i
$266$	158.294	+	275.145i	0.595089	+	1.03438i
$267$	−141.309	−	293.001i	−0.529248	−	1.09738i
$268$	−330.036			−1.23148
$269$	169.879	−	98.0794i	0.631519	−	0.364607i	−0.149821	−	0.988713i	$-0.547870\pi$
$269$	169.879	−	98.0794i	0.631519	−	0.364607i	0.781340	+	0.624106i	$0.214537\pi$
$270$	−54.3980	−	175.281i	−0.201474	−	0.649189i
$271$	−82.5249	−	47.6458i	−0.304520	−	0.175815i	0.339952	−	0.940443i	$-0.389589\pi$
$271$	−82.5249	−	47.6458i	−0.304520	−	0.175815i	−0.644472	+	0.764628i	$0.722923\pi$
$272$	−166.372	+	96.0552i	−0.611663	+	0.353144i
$273$	24.7079	−	325.520i	0.0905052	−	1.19238i
$274$	−217.327	+	376.421i	−0.793163	+	1.37380i
$275$	−109.617	−	189.862i	−0.398607	−	0.690408i
$276$	14.4001	−	193.649i	0.0521744	−	0.701626i
$277$	107.725	−	186.586i	0.388901	−	0.673596i	−0.603401	−	0.797438i	$-0.706188\pi$
$277$	107.725	−	186.586i	0.388901	−	0.673596i	0.992302	+	0.123842i	$0.0395216\pi$
$278$	−223.947	−	129.296i	−0.805566	−	0.465093i
$279$	−355.060	+	139.822i	−1.27262	+	0.501153i
$280$	1.48564	+	0.00227604i	0.00530587	+	8.12872e-6i
$281$	101.916	+	176.523i	0.362689	+	0.628196i	0.988402	−	0.151857i	$-0.0485254\pi$
$281$	101.916	+	176.523i	0.362689	+	0.628196i	−0.625713	+	0.780053i	$0.715192\pi$
$282$	126.192	−	185.318i	0.447490	−	0.657157i
$283$			120.459i			0.425650i	0.977090	+	0.212825i	$0.0682664\pi$
$283$			120.459i			0.425650i	−0.977090	+	0.212825i	$0.931734\pi$
$284$	−455.048			−1.60228
$285$	−95.1708	−	64.8063i	−0.333933	−	0.227391i
$286$	434.583	−	250.907i	1.51952	−	0.877297i
$287$	30.4719	+	52.9661i	0.106174	+	0.184551i
$288$	149.518	+	379.683i	0.519161	+	1.31834i
$289$	−71.2696	+	123.442i	−0.246607	+	0.427137i
$290$	191.128	+	110.348i	0.659061	+	0.380509i
$291$	333.705	+	24.8150i	1.14675	+	0.0852749i
$292$	237.059	−	136.866i	0.811844	−	0.468719i
$293$	−151.688	−	87.5769i	−0.517705	−	0.298897i	0.218290	−	0.975884i	$-0.429952\pi$
$293$	−151.688	−	87.5769i	−0.517705	−	0.298897i	−0.735995	+	0.676987i	$0.763285\pi$
$294$	−32.1660	+	415.346i	−0.109408	+	1.41274i
$295$	114.122	+	197.665i	0.386854	+	0.670051i
$296$	0.319789	−	0.553891i	0.00108037	−	0.00187125i
$297$	225.807	+	208.795i	0.760292	+	0.703014i
$298$	159.285	+	275.890i	0.534513	+	0.925804i
$299$			249.609i			0.834813i
$300$	209.657	−	101.114i	0.698858	−	0.337047i
$301$	0.476395	−	310.958i	0.00158271	−	1.03308i
$302$	39.9541	−	69.2026i	0.132298	−	0.229148i
$303$	100.168	+	207.695i	0.330586	+	0.685462i
$304$	219.978	+	127.004i	0.723612	+	0.417778i
$305$	59.2950	+	102.702i	0.194410	+	0.336728i
$306$	−241.549	−	192.175i	−0.789375	−	0.628023i
$307$			18.3665i			0.0598259i	0.999553	+	0.0299129i	$0.00952300\pi$
$307$			18.3665i			0.0598259i	−0.999553	+	0.0299129i	$0.990477\pi$
$308$	−278.609	+	160.286i	−0.904573	+	0.520409i
$309$	−451.097	−	33.5446i	−1.45986	−	0.108558i
$310$	144.103	+	249.594i	0.464849	+	0.805142i
$311$		−	407.832i		−	1.31136i	−0.755040	−	0.655679i	$-0.772383\pi$
$311$		−	407.832i		−	1.31136i	0.755040	−	0.655679i	$-0.227617\pi$
$312$	1.79262	+	3.71694i	0.00574556	+	0.0119133i
$313$		−	402.749i		−	1.28674i	−0.765556	−	0.643369i	$-0.777536\pi$
$313$		−	402.749i		−	1.28674i	0.765556	−	0.643369i	$-0.222464\pi$
$314$		−	29.0495i		−	0.0925145i
$315$	−55.1522	−	140.684i	−0.175086	−	0.446616i
$316$	551.826			1.74628
$317$	−296.547			−0.935479			−0.467739	−	0.883866i	$-0.654931\pi$
$317$	−296.547			−0.935479			−0.467739	+	0.883866i	$0.654931\pi$
$318$	−42.9509	+	577.591i	−0.135066	+	1.81632i
$319$	−369.827			−1.15933
$320$	135.008	−	77.9470i	0.421901	−	0.243584i
$321$	206.997	−	99.8311i	0.644851	−	0.311000i
$322$	0.487987	−	318.524i	0.00151549	−	0.989206i
$323$	−193.651			−0.599539
$324$	−238.852	+	222.645i	−0.737197	+	0.687177i
$325$	−259.119	+	149.602i	−0.797289	+	0.460315i
$326$	−251.770	+	436.079i	−0.772302	+	1.33767i
$327$	5.60562	−	75.3828i	0.0171426	−	0.230528i
$328$	−0.668937	−	0.386211i	−0.00203944	−	0.00117747i
$329$	92.5442	−	159.726i	0.281289	−	0.485488i
$330$	130.736	−	191.991i	0.396169	−	0.581791i
$331$	532.959			1.61015			0.805074	−	0.593175i	$-0.202126\pi$
$331$	532.959			1.61015			0.805074	+	0.593175i	$0.202126\pi$
$332$	−76.0588	+	43.9126i	−0.229093	+	0.132267i
$333$	−64.3375	−	9.62176i	−0.193206	−	0.0288942i
$334$	152.955	+	88.3086i	0.457949	+	0.264397i
$335$	170.061	−	98.1846i	0.507644	−	0.293088i
$336$	144.350	+	300.482i	0.429614	+	0.894293i
$337$	149.044	−	258.152i	0.442267	−	0.766029i	−0.555590	−	0.831456i	$-0.687508\pi$
$337$	149.044	−	258.152i	0.442267	−	0.766029i	0.997857	+	0.0654274i	$0.0208411\pi$
$338$	−102.963	−	178.338i	−0.304625	−	0.527626i
$339$	−200.364	+	96.6319i	−0.591043	+	0.285050i
$340$	−58.5081	+	101.339i	−0.172083	+	0.298056i
$341$	−418.255	−	241.479i	−1.22655	−	0.708151i
$342$	−60.3642	+	403.635i	−0.176503	+	1.18022i
$343$	−1.57645	+	342.996i	−0.00459605	+	0.999989i
$344$	1.96536	+	3.40411i	0.00571326	+	0.00989566i
$345$	50.1897	+	104.067i	0.145477	+	0.301644i
$346$		−	249.424i		−	0.720879i
$347$	−180.804			−0.521049			−0.260524	−	0.965467i	$-0.583895\pi$
$347$	−180.804			−0.521049			−0.260524	+	0.965467i	$0.583895\pi$
$348$	29.1183	−	391.574i	0.0836733	−	1.12521i
$349$	−151.888	+	87.6925i	−0.435209	+	0.251268i	−0.701563	−	0.712607i	$-0.747514\pi$
$349$	−151.888	+	87.6925i	−0.435209	+	0.251268i	0.266354	+	0.963875i	$0.414181\pi$
$350$	330.952	−	190.400i	0.945578	−	0.544000i
$351$	284.958	−	308.175i	0.811847	−	0.877992i
$352$	−258.226	+	447.260i	−0.733596	+	1.27063i
$353$	34.0434	+	19.6549i	0.0964401	+	0.0556797i	0.547444	−	0.836842i	$-0.315601\pi$
$353$	34.0434	+	19.6549i	0.0964401	+	0.0556797i	−0.451004	+	0.892522i	$0.648934\pi$
$354$	455.358	−	668.712i	1.28632	−	1.88902i
$355$	234.476	−	135.375i	0.660497	−	0.381338i
$356$	378.552	+	218.557i	1.06335	+	0.613924i
$357$	−209.847	−	143.366i	−0.587805	−	0.401584i
$358$	18.3527	+	31.7878i	0.0512645	+	0.0887927i
$359$	−123.823	+	214.468i	−0.344912	+	0.597405i	−0.985338	−	0.170615i	$-0.945425\pi$
$359$	−123.823	+	214.468i	−0.344912	+	0.597405i	0.640426	+	0.768020i	$0.278758\pi$
$360$	1.49475	+	1.18922i	0.00415210	+	0.00330339i
$361$	−52.4771	−	90.8930i	−0.145366	−	0.251781i
$362$			640.052i			1.76810i
$363$	−1.94553	+	26.1630i	−0.00535959	+	0.0720742i
$364$	218.754	+	380.238i	0.600974	+	1.04461i
$365$	−81.4341	+	141.048i	−0.223107	+	0.386433i
$366$	236.592	−	347.446i	0.646428	−	0.949306i
$367$	343.635	+	198.398i	0.936334	+	0.540593i	0.888809	−	0.458277i	$-0.151533\pi$
$367$	343.635	+	198.398i	0.936334	+	0.540593i	0.0475248	+	0.998870i	$0.484867\pi$
$368$	−127.442	−	220.737i	−0.346311	−	0.599828i
$369$	−11.6202	+	77.7007i	−0.0314912	+	0.210571i
$370$			49.1319i			0.132789i
$371$	−0.730582	+	476.874i	−0.00196922	+	1.28537i
$372$	288.610	−	423.836i	0.775834	−	1.13935i
$373$	−186.570	−	323.149i	−0.500189	−	0.866352i	−1.00000		0.000217836i	$-0.999931\pi$
$373$	−186.570	−	323.149i	−0.500189	−	0.866352i	0.499811	−	0.866134i	$-0.333403\pi$
$374$		−	390.658i		−	1.04454i
$375$	−179.202	+	263.165i	−0.477871	+	0.701774i
$376$			2.33346i			0.00620600i
$377$			504.731i			1.33881i
$378$	−364.236	+	392.703i	−0.963587	+	1.03890i
$379$	548.285			1.44666			0.723331	−	0.690502i	$-0.242610\pi$
$379$	548.285			1.44666			0.723331	+	0.690502i	$0.242610\pi$
$380$	154.719			0.407155
$381$	−129.654	−	88.2874i	−0.340299	−	0.231726i
$382$	−294.420			−0.770732
$383$	4.04111	−	2.33314i	0.0105512	−	0.00609174i	−0.494715	−	0.869055i	$-0.664728\pi$
$383$	4.04111	−	2.33314i	0.0105512	−	0.00609174i	0.505266	+	0.862963i	$0.331394\pi$
$384$	−7.02105	−	4.78097i	−0.0182840	−	0.0124504i
$385$	95.8765	−	165.477i	0.249030	−	0.429810i
$386$	−460.068			−1.19189
$387$	248.914	−	312.865i	0.643189	−	0.808436i
$388$	−389.409	+	224.825i	−1.00363	+	0.579447i
$389$	336.313	−	582.511i	0.864558	−	1.49746i	−0.00292782	−	0.999996i	$-0.500932\pi$
$389$	336.313	−	582.511i	0.864558	−	1.49746i	0.867486	−	0.497462i	$-0.165735\pi$
$390$	−262.025	−	178.425i	−0.671858	−	0.457500i
$391$	168.285	+	97.1594i	0.430397	+	0.248490i
$392$	−2.15636	−	3.76150i	−0.00550093	−	0.00959566i
$393$	558.077	+	41.4998i	1.42004	+	0.105597i
$394$	−854.703			−2.16930
$395$	−284.344	+	164.166i	−0.719858	+	0.415610i
$396$	−408.716	−	61.1240i	−1.03211	−	0.154354i
$397$	92.0332	+	53.1354i	0.231822	+	0.133842i	0.611412	−	0.791312i	$-0.290602\pi$
$397$	92.0332	+	53.1354i	0.231822	+	0.133842i	−0.379591	+	0.925155i	$0.623935\pi$
$398$	−141.859	+	81.9023i	−0.356429	+	0.205785i
$399$	−25.4325	+	335.066i	−0.0637405	+	0.839765i
$400$	152.765	−	264.596i	0.381911	−	0.661490i
$401$	149.197	+	258.416i	0.372061	+	0.644429i	0.989882	−	0.141890i	$-0.0453178\pi$
$401$	149.197	+	258.416i	0.372061	+	0.644429i	−0.617821	+	0.786319i	$0.711985\pi$
$402$	−575.324	−	391.766i	−1.43115	−	0.974541i
$403$	−329.565	+	570.823i	−0.817779	+	1.41643i
$404$	−268.338	−	154.925i	−0.664204	−	0.383478i
$405$	56.8391	−	185.782i	0.140343	−	0.458721i
$406$	0.986752	−	644.083i	0.00243042	−	1.58641i
$407$	−41.1662	−	71.3019i	−0.101145	−	0.175189i
$408$	3.20371	+	0.238235i	0.00785224	+	0.000583909i
$409$			659.097i			1.61149i	0.592266	+	0.805743i	$0.298234\pi$
$409$			659.097i			1.61149i	−0.592266	+	0.805743i	$0.701766\pi$
$410$	59.3369			0.144724
$411$	−414.441	+	199.878i	−1.00837	+	0.486321i
$412$	526.398	−	303.916i	1.27766	−	0.737660i
$413$	333.941	−	576.362i	0.808574	−	1.39555i
$414$	254.971	−	320.478i	0.615872	−	0.774101i
$415$	26.1276	−	45.2544i	0.0629582	−	0.109047i
$416$	610.409	+	352.420i	1.46733	+	0.847164i
$417$	−118.915	−	246.567i	−0.285168	−	0.591288i
$418$	−447.328	+	258.265i	−1.07016	+	0.617858i
$419$	485.296	+	280.186i	1.15822	+	0.668701i	0.950878	−	0.309566i	$-0.100184\pi$
$419$	485.296	+	280.186i	1.15822	+	0.668701i	0.207346	+	0.978268i	$0.433517\pi$
$420$	167.659	+	114.543i	0.399187	+	0.272722i
$421$	57.9969	+	100.454i	0.137760	+	0.238607i	0.926648	−	0.375929i	$-0.122676\pi$
$421$	57.9969	+	100.454i	0.137760	+	0.238607i	−0.788889	+	0.614536i	$0.789343\pi$
$422$	60.1353	−	104.157i	0.142501	−	0.246818i
$423$	220.835	−	86.9642i	0.522069	−	0.205589i
$424$	−3.01401	−	5.22042i	−0.00710851	−	0.0123123i
$425$			232.929i			0.548068i
$426$	−793.246	−	540.159i	−1.86208	−	1.26798i
$427$	173.507	−	299.463i	0.406341	−	0.701319i
$428$	−154.405	+	267.437i	−0.360759	+	0.624852i
$429$	529.756	+	39.3938i	1.23486	+	0.0918269i
$430$	−261.501	−	150.978i	−0.608142	−	0.351111i
$431$	161.254	+	279.299i	0.374138	+	0.648027i	0.990198	−	0.139673i	$-0.0446052\pi$
$431$	161.254	+	279.299i	0.374138	+	0.648027i	−0.616059	+	0.787700i	$0.711272\pi$
$432$	−94.6528	+	418.019i	−0.219104	+	0.967637i
$433$			117.316i			0.270937i	0.990782	+	0.135468i	$0.0432539\pi$
$433$			117.316i			0.270937i	−0.990782	+	0.135468i	$0.956746\pi$
$434$	421.671	−	727.779i	0.971592	−	1.67691i
$435$	101.488	+	210.432i	0.233305	+	0.483753i
$436$	50.7873	+	87.9662i	0.116485	+	0.201757i
$437$		−	256.929i		−	0.587938i
$438$	575.709	+	42.8109i	1.31440	+	0.0977418i
$439$		−	216.839i		−	0.493938i	−0.969023	−	0.246969i	$-0.920565\pi$
$439$		−	216.839i		−	0.493938i	0.969023	−	0.246969i	$-0.0794346\pi$
$440$			2.41748i			0.00549427i
$441$	−275.619	+	344.260i	−0.624986	+	0.780636i
$442$	−533.160			−1.20625
$443$	−149.742			−0.338018			−0.169009	−	0.985615i	$-0.554057\pi$
$443$	−149.742			−0.338018			−0.169009	+	0.985615i	$0.554057\pi$
$444$	78.7359	−	37.9729i	0.177333	−	0.0855246i
$445$	−260.080			−0.584448
$446$	471.035	−	271.952i	1.05613	−	0.609758i
$447$	−25.0086	+	336.308i	−0.0559477	+	0.752368i
$448$	−393.664	−	228.087i	−0.878713	−	0.509122i
$449$	−263.767			−0.587455			−0.293727	−	0.955889i	$-0.594896\pi$
$449$	−263.767			−0.587455			−0.293727	+	0.955889i	$0.594896\pi$
$450$	485.504	+	72.6077i	1.07890	+	0.161350i
$451$	−86.1116	+	49.7166i	−0.190935	+	0.110236i
$452$	149.457	−	258.866i	0.330656	−	0.572713i
$453$	76.1924	−	36.7462i	0.168195	−	0.0811175i
$454$	−551.668	−	318.505i	−1.21513	−	0.701554i
$455$	−225.839	−	130.850i	−0.496349	−	0.287582i
$456$	−1.84518	−	3.82594i	−0.00404646	−	0.00839023i
$457$	−218.793			−0.478759			−0.239379	−	0.970926i	$-0.576944\pi$
$457$	−218.793			−0.478759			−0.239379	+	0.970926i	$0.576944\pi$
$458$	393.047	−	226.926i	0.858180	−	0.495471i
$459$	−96.8511	−	312.073i	−0.211004	−	0.679899i
$460$	−134.453	−	77.6263i	−0.292289	−	0.168753i
$461$	−334.892	+	193.350i	−0.726446	+	0.419414i	−0.817121	−	0.576467i	$-0.804431\pi$
$461$	−334.892	+	193.350i	−0.726446	+	0.419414i	0.0906743	+	0.995881i	$0.471098\pi$
$462$	−675.940	−	51.3057i	−1.46307	−	0.111051i
$463$	241.881	−	418.950i	0.522421	−	0.904860i	−0.477238	−	0.878774i	$-0.658362\pi$
$463$	241.881	−	418.950i	0.522421	−	0.904860i	0.999660	−	0.0260863i	$-0.00830447\pi$
$464$	−257.700	−	446.349i	−0.555387	−	0.961959i
$465$	−22.6250	+	304.254i	−0.0486559	+	0.654310i
$466$	−349.422	+	605.216i	−0.749832	+	1.29875i
$467$	−100.042	−	57.7593i	−0.214223	−	0.123682i	0.389049	−	0.921217i	$-0.372804\pi$
$467$	−100.042	−	57.7593i	−0.214223	−	0.123682i	−0.603272	+	0.797535i	$0.706137\pi$
$468$	−83.4205	+	557.805i	−0.178249	+	1.19189i
$469$	−495.871	−	287.305i	−1.05729	−	0.612591i
$470$	−89.6272	−	155.239i	−0.190696	−	0.330295i
$471$	17.3085	−	25.4182i	0.0367484	−	0.0539665i
$472$			8.42016i			0.0178393i
$473$	505.999			1.06976
$474$	961.950	+	655.038i	2.02943	+	1.38194i
$475$	266.718	−	153.990i	0.561511	−	0.324189i
$476$	341.504	+	0.523192i	0.717444	+	0.00109914i
$477$	−381.726	+	479.798i	−0.800264	+	1.00587i
$478$	312.132	−	540.628i	0.652996	−	1.13102i
$479$	−394.602	−	227.823i	−0.823803	−	0.475623i	0.0279230	−	0.999610i	$-0.491111\pi$
$479$	−394.602	−	227.823i	−0.823803	−	0.475623i	−0.851726	+	0.523987i	$0.824444\pi$
$480$	325.354	+	24.1940i	0.677821	+	0.0504042i
$481$	−97.3110	+	56.1825i	−0.202310	+	0.116804i
$482$	646.939	+	373.510i	1.34220	+	0.774918i
$483$	190.212	−	278.417i	0.393814	−	0.576432i
$484$	−17.6267	−	30.5303i	−0.0364187	−	0.0630790i
$485$	133.769	−	231.695i	0.275813	−	0.477722i
$486$	−680.659	+	104.593i	−1.40053	+	0.215211i
$487$	−162.334	−	281.171i	−0.333335	−	0.577354i	0.649828	−	0.760081i	$-0.274841\pi$
$487$	−162.334	−	281.171i	−0.333335	−	0.577354i	−0.983164	+	0.182727i	$0.941507\pi$
$488$			4.37490i			0.00896497i
$489$	−480.126	+	231.556i	−0.981852	+	0.473530i
$490$	287.935	+	167.418i	0.587623	+	0.341669i
$491$	−155.221	+	268.850i	−0.316132	+	0.547557i	−0.979678	−	0.200579i	$-0.935718\pi$
$491$	−155.221	+	268.850i	−0.316132	+	0.547557i	0.663545	+	0.748136i	$0.269051\pi$
$492$	−45.8601	−	95.0897i	−0.0932115	−	0.193272i
$493$	340.287	+	196.465i	0.690237	+	0.398509i
$494$	352.473	+	610.501i	0.713508	+	1.23583i
$495$	228.787	−	90.0956i	0.462195	−	0.182011i
$496$		−	673.061i		−	1.35698i
$497$	−683.698	−	396.131i	−1.37565	−	0.797044i
$498$	−184.713	−	13.7356i	−0.370909	−	0.0275816i
$499$	387.110	+	670.494i	0.775771	+	1.34368i	0.934360	+	0.356331i	$0.115972\pi$
$499$	387.110	+	670.494i	0.775771	+	1.34368i	−0.158589	+	0.987345i	$0.550694\pi$
$500$		−	427.827i		−	0.855655i
$501$	81.2184	+	168.404i	0.162113	+	0.336136i
$502$			65.1816i			0.129844i
$503$		−	106.472i		−	0.211674i	−0.994384	−	0.105837i	$-0.966248\pi$
$503$		−	106.472i		−	0.211674i	0.994384	−	0.105837i	$-0.0337521\pi$
$504$	0.832956	−	5.51196i	0.00165269	−	0.0109364i
$505$	184.359			0.365067
$506$	518.311			1.02433
$507$	16.1658	−	217.393i	0.0318852	−	0.428783i
$508$	210.778			0.414917
$509$	−293.258	+	169.313i	−0.576146	+	0.332638i	−0.759600	−	0.650390i	$-0.774605\pi$
$509$	−293.258	+	169.313i	−0.576146	+	0.332638i	0.183454	+	0.983028i	$0.441272\pi$
$510$	−222.285	+	107.204i	−0.435853	+	0.210204i
$511$	475.319	+	0.728201i	0.930175	+	0.00142505i
$512$	−725.356			−1.41671
$513$	−293.315	+	317.213i	−0.571764	+	0.618348i
$514$	43.7277	−	25.2462i	0.0850734	−	0.0491172i
$515$	−180.828	+	313.202i	−0.351121	+	0.608160i
$516$	−39.8397	+	535.753i	−0.0772088	+	1.03828i
$517$	260.140	+	150.192i	0.503172	+	0.290506i
$518$	124.288	−	71.5038i	0.239938	−	0.138038i
$519$	148.613	−	218.245i	0.286346	−	0.420511i
$520$	3.29931			0.00634483
$521$	−84.1424	+	48.5796i	−0.161502	+	0.0932431i	−0.578573	−	0.815631i	$-0.696390\pi$
$521$	−84.1424	+	48.5796i	−0.161502	+	0.0932431i	0.417071	+	0.908874i	$0.363057\pi$
$522$	515.573	−	648.034i	0.987688	−	1.24144i
$523$	513.773	+	296.627i	0.982357	+	0.567164i	0.902981	−	0.429681i	$-0.141374\pi$
$523$	513.773	+	296.627i	0.982357	+	0.567164i	0.0793761	+	0.996845i	$0.474707\pi$
$524$	−651.235	+	375.990i	−1.24281	+	0.717539i
$525$	403.027	+	30.5909i	0.767671	+	0.0582684i
$526$	−514.372	+	890.919i	−0.977894	+	1.69376i
$527$	256.564	+	444.382i	0.486838	+	0.843229i
$528$	−488.592	+	235.639i	−0.925363	+	0.446286i
$529$	135.592	−	234.853i	0.256319	−	0.443957i
$530$	401.029	+	231.534i	0.756658	+	0.436857i
$531$	796.872	−	313.806i	1.50070	−	0.590972i
$532$	−225.169	−	391.388i	−0.423251	−	0.735692i
$533$	67.8519	+	117.523i	0.127302	+	0.220493i
$534$	400.462	+	830.347i	0.749928	+	1.55496i
$535$		−	183.739i		−	0.343438i
$536$	7.24426			0.0135154
$537$	−2.88147	+	38.7492i	−0.00536587	+	0.0721586i
$538$	−481.426	+	277.951i	−0.894843	+	0.516638i
$539$	−558.135	−	1.71016i	−1.03550	−	0.00317283i
$540$	77.3800	+	249.334i	0.143296	+	0.461729i
$541$	289.077	−	500.696i	0.534338	−	0.925500i	−0.464857	−	0.885386i	$-0.653894\pi$
$541$	289.077	−	500.696i	0.534338	−	0.925500i	0.999195	−	0.0401146i	$-0.0127723\pi$
$542$	233.871	+	135.025i	0.431496	+	0.249124i
$543$	−381.360	+	560.043i	−0.702320	+	1.03139i
$544$	475.199	−	274.356i	0.873528	−	0.504332i
$545$	−52.3392	−	30.2181i	−0.0960352	−	0.0554460i
$546$	−70.0208	+	922.506i	−0.128243	+	1.68957i
$547$	110.283	+	191.016i	0.201615	+	0.349207i	0.949049	−	0.315129i	$-0.102048\pi$
$547$	110.283	+	191.016i	0.201615	+	0.349207i	−0.747434	+	0.664336i	$0.768714\pi$
$548$	309.143	−	535.451i	0.564129	−	0.977101i
$549$	414.035	−	163.046i	0.754162	−	0.296987i
$550$	310.648	+	538.058i	0.564815	+	0.978288i
$551$		−	519.532i		−	0.942890i
$552$	−0.316081	+	4.25057i	−0.000572611	+	0.00770030i
$553$	829.104	+	480.378i	1.49928	+	0.868677i
$554$	−305.288	+	528.774i	−0.551061	+	0.954465i
$555$	−29.2741	+	42.9902i	−0.0527461	+	0.0774599i
$556$	318.560	+	183.921i	0.572950	+	0.330793i
$557$	179.797	+	311.417i	0.322795	+	0.559098i	0.981064	−	0.193686i	$-0.0620442\pi$
$557$	179.797	+	311.417i	0.322795	+	0.559098i	−0.658268	+	0.752783i	$0.728711\pi$
$558$	1006.22	−	396.246i	1.80326	−	0.710119i
$559$		−	690.574i		−	1.23537i
$560$	266.524	+	0.408321i	0.475935	+	0.000729144i
$561$	232.764	−	341.824i	0.414910	−	0.609313i
$562$	−288.823	−	500.256i	−0.513920	−	0.890135i
$563$		−	986.797i		−	1.75275i	−0.481631	−	0.876374i	$-0.659955\pi$
$563$		−	986.797i		−	1.75275i	0.481631	−	0.876374i	$-0.340045\pi$
$564$	−179.506	+	263.611i	−0.318272	+	0.467396i
$565$			177.851i			0.314781i
$566$		−	341.373i		−	0.603133i
$567$	−552.687	+	126.592i	−0.974757	+	0.223267i
$568$	9.98825			0.0175849
$569$	83.7874			0.147254			0.0736269	−	0.997286i	$-0.476543\pi$
$569$	83.7874			0.147254			0.0736269	+	0.997286i	$0.476543\pi$
$570$	269.708	+	183.657i	0.473173	+	0.322206i
$571$	−350.700			−0.614186			−0.307093	−	0.951679i	$-0.599356\pi$
$571$	−350.700			−0.614186			−0.307093	+	0.951679i	$0.599356\pi$
$572$	−618.186	+	356.910i	−1.08074	+	0.623968i
$573$	−257.616	−	175.423i	−0.449592	−	0.306148i
$574$	−86.3555	−	150.103i	−0.150445	−	0.261503i
$575$	−309.041			−0.537463
$576$	−214.334	−	544.275i	−0.372108	−	0.944922i
$577$	−652.529	+	376.738i	−1.13090	+	0.652925i	−0.944161	−	0.329485i	$-0.893125\pi$
$577$	−652.529	+	376.738i	−1.13090	+	0.652925i	−0.186738	+	0.982410i	$0.559792\pi$
$578$	201.974	−	349.829i	0.349436	−	0.605240i
$579$	−402.558	−	274.121i	−0.695263	−	0.473438i
$580$	−271.875	−	156.967i	−0.468750	−	0.270633i
$581$	−152.503	−	0.233639i	−0.262484	−	0.000402133i
$582$	−945.699	−	70.3242i	−1.62491	−	0.120832i
$583$	−775.981			−1.33101
$584$	−5.20340	+	3.00419i	−0.00890994	+	0.00514416i
$585$	−122.960	−	312.242i	−0.210188	−	0.533747i
$586$	429.874	+	248.188i	0.733573	+	0.423528i
$587$	112.348	−	64.8642i	0.191394	−	0.110501i	−0.401241	−	0.915972i	$-0.631421\pi$
$587$	112.348	−	64.8642i	0.191394	−	0.110501i	0.592635	+	0.805471i	$0.298088\pi$
$588$	45.7554	−	590.821i	0.0778153	−	1.00480i
$589$	339.229	−	587.562i	0.575941	−	0.997559i
$590$	−323.415	−	560.172i	−0.548161	−	0.949443i
$591$	−747.861	−	509.254i	−1.26542	−	0.861682i
$592$	57.3700	−	99.3678i	0.0969088	−	0.167851i
$593$	435.912	+	251.674i	0.735096	+	0.424408i	0.820283	−	0.571957i	$-0.193816\pi$
$593$	435.912	+	251.674i	0.735096	+	0.424408i	−0.0851878	+	0.996365i	$0.527149\pi$
$594$	−639.923	−	591.713i	−1.07731	−	0.996151i
$595$	−176.125	+	101.326i	−0.296008	+	0.170296i
$596$	−226.580	−	392.447i	−0.380167	−	0.658469i
$597$	−172.925	−	12.8591i	−0.289657	−	0.0215395i
$598$		−	707.377i		−	1.18291i
$599$	−282.557			−0.471714			−0.235857	−	0.971788i	$-0.575790\pi$
$599$	−282.557			−0.471714			−0.235857	+	0.971788i	$0.575790\pi$
$600$	−4.60195	+	2.21944i	−0.00766992	+	0.00369907i
$601$	159.905	−	92.3214i	0.266065	−	0.153613i	−0.361033	−	0.932553i	$-0.617576\pi$
$601$	159.905	−	92.3214i	0.266065	−	0.153613i	0.627098	+	0.778940i	$0.284242\pi$
$602$	−1.35008	+	881.236i	−0.00224265	+	1.46385i
$603$	−269.982	−	685.586i	−0.447731	−	1.13696i
$604$	−56.8339	+	98.4392i	−0.0940959	+	0.162979i
$605$	18.1653	+	10.4877i	0.0300252	+	0.0173351i
$606$	−283.869	−	588.596i	−0.468431	−	0.971280i
$607$	−905.567	+	522.829i	−1.49187	+	0.861333i	−0.999957	−	0.00930928i	$-0.997037\pi$
$607$	−905.567	+	522.829i	−1.49187	+	0.861333i	−0.491916	+	0.870643i	$0.663703\pi$
$608$	−628.310	−	362.755i	−1.03340	−	0.596636i
$609$	384.625	−	562.982i	0.631568	−	0.924437i
$610$	−168.038	−	291.051i	−0.275473	−	0.477133i
$611$	204.978	−	355.032i	0.335479	−	0.581067i
$612$	343.598	+	273.365i	0.561435	+	0.446675i
$613$	−52.6647	−	91.2179i	−0.0859131	−	0.148806i	0.819867	−	0.572554i	$-0.194047\pi$
$613$	−52.6647	−	91.2179i	−0.0859131	−	0.148806i	−0.905780	+	0.423748i	$0.860714\pi$
$614$		−	52.0497i		−	0.0847715i
$615$	51.9195	+	35.3545i	0.0844220	+	0.0574869i
$616$	6.11542	−	3.51826i	0.00992763	−	0.00571146i
$617$	269.908	−	467.495i	0.437452	−	0.757690i	−0.560040	−	0.828466i	$-0.689214\pi$
$617$	269.908	−	467.495i	0.437452	−	0.757690i	0.997492	+	0.0707759i	$0.0225475\pi$
$618$	1278.38	+	95.0633i	2.06858	+	0.153824i
$619$	−968.123	−	558.946i	−1.56401	−	0.902982i	−0.996845	−	0.0793787i	$-0.974706\pi$
$619$	−968.123	−	558.946i	−1.56401	−	0.902982i	−0.567166	−	0.823603i	$-0.691960\pi$
$620$	−204.984	−	355.042i	−0.330619	−	0.572649i
$621$	414.047	−	128.498i	0.666743	−	0.206922i
$622$			1155.77i			1.85816i
$623$	378.505	+	657.916i	0.607552	+	1.05604i
$624$	321.594	+	666.818i	0.515376	+	1.06862i
$625$	−113.310	−	196.259i	−0.181296	−	0.314014i
$626$			1141.37i			1.82327i
$627$	−545.291	−	40.5490i	−0.869682	−	0.0646714i
$628$			41.3224i			0.0658000i
$629$			87.4754i			0.139071i
$630$	156.298	+	398.690i	0.248092	+	0.632842i
$631$	−710.879			−1.12659			−0.563296	−	0.826255i	$-0.690467\pi$
$631$	−710.879			−1.12659			−0.563296	+	0.826255i	$0.690467\pi$
$632$	−12.1125			−0.0191654
$633$	114.678	−	55.3070i	0.181165	−	0.0873729i
$634$	840.396			1.32555
$635$	−108.609	+	62.7057i	−0.171038	+	0.0987491i
$636$	61.0968	−	821.611i	0.0960641	−	1.29184i
$637$	−2.33398	+	761.729i	−0.00366402	+	1.19581i
$638$	1048.07			1.64274
$639$	−372.246	−	945.274i	−0.582545	−	1.47930i
$640$	−5.88145	+	3.39566i	−0.00918977	+	0.00530571i
$641$	−535.389	+	927.321i	−0.835240	+	1.44668i	0.0585942	+	0.998282i	$0.481338\pi$
$641$	−535.389	+	927.321i	−0.835240	+	1.44668i	−0.893835	+	0.448397i	$0.851995\pi$
$642$	−586.618	+	282.915i	−0.913735	+	0.440678i
$643$	664.371	+	383.575i	1.03324	+	0.596539i	0.917910	−	0.396788i	$-0.129875\pi$
$643$	664.371	+	383.575i	1.03324	+	0.596539i	0.115326	+	0.993328i	$0.463209\pi$
$644$	−0.694151	+	453.094i	−0.00107787	+	0.703562i
$645$	−138.856	−	287.914i	−0.215280	−	0.446378i
$646$	548.795			0.849528
$647$	14.8163	−	8.55422i	0.0229001	−	0.0132214i	−0.488506	−	0.872560i	$-0.662458\pi$
$647$	14.8163	−	8.55422i	0.0229001	−	0.0132214i	0.511406	+	0.859339i	$0.329125\pi$
$648$	5.24277	−	4.88704i	0.00809069	−	0.00754173i
$649$	938.701	+	541.959i	1.44638	+	0.835068i
$650$	734.328	−	423.965i	1.12974	−	0.652253i
$651$	802.590	−	385.560i	1.23286	−	0.592259i
$652$	358.138	−	620.314i	0.549292	−	0.951402i
$653$	484.144	+	838.561i	0.741414	+	1.28417i	0.951851	+	0.306560i	$0.0991779\pi$
$653$	484.144	+	838.561i	0.741414	+	1.28417i	−0.210437	+	0.977607i	$0.567489\pi$
$654$	−15.8860	+	213.630i	−0.0242905	+	0.326652i
$655$	223.711	−	387.480i	0.341544	−	0.591572i
$656$	−120.007	−	69.2860i	−0.182937	−	0.105619i
$657$	478.235	+	380.482i	0.727907	+	0.579120i
$658$	−262.265	+	452.653i	−0.398579	+	0.687923i
$659$	470.849	+	815.535i	0.714490	+	1.23753i	0.963156	+	0.268944i	$0.0866747\pi$
$659$	470.849	+	815.535i	0.714490	+	1.23753i	−0.248665	+	0.968589i	$0.579992\pi$
$660$	−185.969	+	273.103i	−0.281771	+	0.413793i
$661$		−	5.49494i		−	0.00831307i	−0.999991	−	0.00415653i	$-0.998677\pi$
$661$		−	5.49494i		−	0.00831307i	0.999991	−	0.00415653i	$-0.00132307\pi$
$662$	−1510.37			−2.28153
$663$	−466.513	−	317.671i	−0.703640	−	0.479142i
$664$	1.66948	−	0.963876i	0.00251428	−	0.00145162i
$665$	232.461	+	134.687i	0.349566	+	0.202537i
$666$	182.329	+	27.2675i	0.273767	+	0.0409422i
$667$	−260.662	+	451.480i	−0.390798	+	0.676881i
$668$	−217.575	−	125.617i	−0.325712	−	0.188050i
$669$	574.190	+	42.6980i	0.858280	+	0.0638236i
$670$	−481.942	+	278.249i	−0.719316	+	0.415297i
$671$	487.726	+	281.589i	0.726864	+	0.419655i
$672$	−412.299	−	858.249i	−0.613540	−	1.27716i
$673$	329.366	+	570.479i	0.489400	+	0.847666i	0.999926	−	0.0121964i	$-0.00388233\pi$
$673$	329.366	+	570.479i	0.489400	+	0.847666i	−0.510525	+	0.859863i	$0.670549\pi$
$674$	−422.382	+	731.587i	−0.626679	+	1.08544i
$675$	381.552	+	352.807i	0.565263	+	0.522678i
$676$	146.463	+	253.681i	0.216661	+	0.375268i
$677$		−	843.527i		−	1.24598i	−0.782231	−	0.622989i	$-0.785918\pi$
$677$		−	843.527i		−	1.24598i	0.782231	−	0.622989i	$-0.214082\pi$
$678$	567.819	−	273.849i	0.837491	−	0.403907i
$679$	−780.793	−	1.19619i	−1.14992	−	0.00176170i
$680$	1.28424	−	2.22438i	0.00188860	−	0.00327114i
$681$	−292.933	−	607.389i	−0.430151	−	0.891907i
$682$	1185.31	+	684.338i	1.73799	+	1.00343i
$683$	−290.414	−	503.012i	−0.425203	−	0.736474i	0.571236	−	0.820786i	$-0.306464\pi$
$683$	−290.414	−	503.012i	−0.425203	−	0.736474i	−0.996439	+	0.0843121i	$0.973131\pi$
$684$	85.8668	−	574.163i	0.125536	−	0.839419i
$685$			367.875i			0.537044i
$686$	4.46756	−	972.032i	0.00651247	−	1.41696i
$687$	479.122	+	35.6286i	0.697412	+	0.0518611i
$688$	352.585	+	610.695i	0.512478	+	0.887638i
$689$			1059.04i			1.53707i
$690$	−142.235	−	294.920i	−0.206137	−	0.427420i
$691$		−	1127.85i		−	1.63220i	−0.577914	−	0.816098i	$-0.696133\pi$
$691$		−	1127.85i		−	1.63220i	0.577914	−	0.816098i	$-0.303867\pi$
$692$			354.801i			0.512718i
$693$	−560.875	−	447.635i	−0.809344	−	0.645938i
$694$	512.388			0.738311
$695$	−218.863			−0.314911
$696$	−0.639143	+	8.59501i	−0.000918309	+	0.0123492i
$697$	105.644			0.151570
$698$	430.441	−	248.515i	0.616678	−	0.356039i
$699$	−666.346	+	321.367i	−0.953285	+	0.459752i
$700$	−470.773	+	270.840i	−0.672533	+	0.386914i
$701$	352.754			0.503216			0.251608	−	0.967829i	$-0.419041\pi$
$701$	352.754			0.503216			0.251608	+	0.967829i	$0.419041\pi$
$702$	−807.555	+	873.351i	−1.15036	+	1.24409i
$703$	100.165	−	57.8301i	0.142482	−	0.0822618i
$704$	370.166	−	641.147i	0.525804	−	0.910720i
$705$	14.0720	−	189.236i	0.0199602	−	0.268419i
$706$	−96.4769	−	55.7009i	−0.136653	−	0.0788965i
$707$	−268.305	−	466.367i	−0.379498	−	0.659642i
$708$	−647.737	+	951.229i	−0.914883	+	1.34354i
$709$	−792.077			−1.11717			−0.558587	−	0.829446i	$-0.688656\pi$
$709$	−792.077			−1.11717			−0.558587	+	0.829446i	$0.688656\pi$
$710$	−664.492	+	383.645i	−0.935905	+	0.540345i
$711$	451.414	+	1146.31i	0.634900	+	1.61225i
$712$	−8.30917	−	4.79730i	−0.0116702	−	0.00673778i
$713$	−589.589	+	340.399i	−0.826913	+	0.477418i
$714$	594.693	+	406.290i	0.832903	+	0.569033i
$715$	212.359	−	367.816i	0.297005	−	0.514428i
$716$	−26.1063	−	45.2175i	−0.0364613	−	0.0631529i
$717$	595.235	−	287.071i	0.830174	−	0.400378i
$718$	350.908	−	607.791i	0.488730	−	0.846505i
$719$	473.277	+	273.247i	0.658244	+	0.380037i	0.791608	−	0.611030i	$-0.209244\pi$
$719$	473.277	+	273.247i	0.658244	+	0.380037i	−0.133364	+	0.991067i	$0.542578\pi$
$720$	268.158	+	213.346i	0.372442	+	0.296313i
$721$	1055.47	+	1.61700i	1.46389	+	0.00224272i
$722$	148.717	+	257.586i	0.205979	+	0.356767i
$723$	343.522	+	712.283i	0.475134	+	0.985177i
$724$		−	910.461i		−	1.25754i
$725$	−624.908			−0.861942
$726$	5.51353	−	74.1443i	0.00759439	−	0.102127i
$727$	113.839	−	65.7248i	0.156587	−	0.0904055i	−0.419659	−	0.907682i	$-0.637850\pi$
$727$	113.839	−	65.7248i	0.156587	−	0.0904055i	0.576246	+	0.817276i	$0.304517\pi$
$728$	−4.80163	−	8.34617i	−0.00659565	−	0.0114645i
$729$	−657.892	−	314.036i	−0.902459	−	0.430777i
$730$	230.779	−	399.722i	0.316136	−	0.547564i
$731$	−465.581	−	268.803i	−0.636910	−	0.367720i
$732$	−336.548	+	494.235i	−0.459765	+	0.675184i
$733$	−1107.87	+	639.630i	−1.51142	+	0.872620i	−0.511511	+	0.859277i	$0.670914\pi$
$733$	−1107.87	+	639.630i	−1.51142	+	0.872620i	−0.999911	+	0.0133434i	$0.995753\pi$
$734$	−973.840	−	562.247i	−1.32676	−	0.766004i
$735$	152.190	+	318.049i	0.207061	+	0.432720i
$736$	364.006	+	630.477i	0.494573	+	0.856626i
$737$	466.273	−	807.609i	0.632664	−	1.09581i
$738$	32.9311	−	220.199i	0.0446221	−	0.298373i
$739$	9.93656	+	17.2106i	0.0134460	+	0.0232891i	0.872670	−	0.488310i	$-0.162387\pi$
$739$	9.93656	+	17.2106i	0.0134460	+	0.0232891i	−0.859224	+	0.511599i	$0.829053\pi$
$740$		−	69.8892i		−	0.0944448i
$741$	−55.3402	+	744.199i	−0.0746831	+	1.00432i
$742$	2.07043	−	1351.43i	0.00279033	−	1.82134i
$743$	729.663	−	1263.81i	0.982050	−	1.70096i	0.327677	−	0.944790i	$-0.393734\pi$
$743$	729.663	−	1263.81i	0.982050	−	1.70096i	0.654374	−	0.756171i	$-0.272932\pi$
$744$	−6.33496	+	9.30315i	−0.00851473	+	0.0125042i
$745$	233.503	+	134.813i	0.313427	+	0.180957i
$746$	528.729	+	915.786i	0.708753	+	1.22760i
$747$	−153.439	−	122.075i	−0.205407	−	0.163421i
$748$			555.703i			0.742919i
$749$	−464.800	+	267.404i	−0.620560	+	0.357014i
$750$	507.847	−	745.795i	0.677130	−	0.994393i
$751$	494.911	+	857.211i	0.659003	+	1.14143i	0.980874	+	0.194643i	$0.0623549\pi$
$751$	494.911	+	857.211i	0.659003	+	1.14143i	−0.321871	+	0.946784i	$0.604312\pi$
$752$			418.621i			0.556676i
$753$	−38.8369	+	57.0336i	−0.0515762	+	0.0757418i
$754$		−	1430.38i		−	1.89705i
$755$		−	67.6315i		−	0.0895781i
$756$	518.118	−	558.612i	0.685341	−	0.738905i
$757$	−499.688			−0.660089			−0.330045	−	0.943965i	$-0.607064\pi$
$757$	−499.688			−0.660089			−0.330045	+	0.943965i	$0.607064\pi$
$758$	−1553.81			−2.04988
$759$	453.520	+	308.823i	0.597523	+	0.406882i
$760$	−3.39606			−0.00446850
$761$	−594.048	+	342.974i	−0.780614	+	0.450688i	−0.836648	−	0.547741i	$-0.815488\pi$
$761$	−594.048	+	342.974i	−0.780614	+	0.450688i	0.0560336	+	0.998429i	$0.482155\pi$
$762$	367.431	+	250.201i	0.482193	+	0.328348i
$763$	−0.270216	+	176.379i	−0.000354150	+	0.231165i
$764$	418.806			0.548175
$765$	−258.374	−	38.6401i	−0.337743	−	0.0505100i
$766$	−11.4523	+	6.61197i	−0.0149507	+	0.00863182i
$767$	739.652	−	1281.12i	0.964345	−	1.67029i
$768$	−624.774	−	425.438i	−0.813507	−	0.553956i
$769$	−586.160	−	338.420i	−0.762237	−	0.440078i	0.0678613	−	0.997695i	$-0.478382\pi$
$769$	−586.160	−	338.420i	−0.762237	−	0.440078i	−0.830098	+	0.557617i	$0.811716\pi$
$770$	−271.708	+	468.952i	−0.352868	+	0.609028i
$771$	53.3039	+	3.96379i	0.0691361	+	0.00514111i
$772$	654.437			0.847717
$773$	437.359	−	252.509i	0.565794	−	0.326661i	−0.189674	−	0.981847i	$-0.560743\pi$
$773$	437.359	−	252.509i	0.565794	−	0.326661i	0.755468	+	0.655186i	$0.227410\pi$
$774$	−705.408	+	886.641i	−0.911380	+	1.14553i
$775$	−706.737	−	408.035i	−0.911918	−	0.526496i
$776$	8.54747	−	4.93489i	0.0110148	−	0.00635939i
$777$	151.355	+	11.4883i	0.194794	+	0.0147854i
$778$	−953.091	+	1650.80i	−1.22505	+	2.12185i
$779$	−69.8416	−	120.969i	−0.0896555	−	0.155288i
$780$	372.725	+	253.806i	0.477852	+	0.325392i
$781$	642.889	−	1113.52i	0.823161	−	1.42576i
$782$	−476.910	−	275.344i	−0.609859	−	0.352102i
$783$	837.240	−	259.835i	1.06927	−	0.331845i
$784$	−386.850	−	674.811i	−0.493432	−	0.860729i
$785$	−12.2932	−	21.2925i	−0.0156602	−	0.0271242i
$786$	−1581.56	−	117.608i	−2.01216	−	0.149628i
$787$			18.5193i			0.0235315i	0.999931	+	0.0117657i	$0.00374524\pi$
$787$			18.5193i			0.0235315i	−0.999931	+	0.0117657i	$0.996255\pi$
$788$	1215.80			1.54289
$789$	−980.906	+	473.074i	−1.24323	+	0.599587i
$790$	805.814	−	465.237i	1.02002	−	0.588907i
$791$	449.905	−	258.834i	0.568779	−	0.327224i
$792$	8.97126	+	1.34166i	0.0113274	+	0.00169402i
$793$	384.305	−	665.636i	0.484622	−	0.839389i
$794$	−260.817	−	150.583i	−0.328484	−	0.189651i
$795$	212.944	+	441.535i	0.267855	+	0.555390i
$796$	201.791	−	116.504i	0.253507	−	0.146362i
$797$	615.232	+	355.205i	0.771935	+	0.445677i	0.833565	−	0.552422i	$-0.186296\pi$
$797$	615.232	+	355.205i	0.771935	+	0.445677i	−0.0616293	+	0.998099i	$0.519630\pi$
$798$	72.0741	−	949.558i	0.0903184	−	1.18992i
$799$	−159.574	−	276.390i	−0.199717	−	0.345920i
$800$	−436.332	+	755.749i	−0.545415	+	0.944686i
$801$	−144.340	+	965.156i	−0.180200	+	1.20494i
$802$	−422.814	−	732.336i	−0.527200	−	0.913137i
$803$			773.452i			0.963203i
$804$	818.387	+	557.279i	1.01789	+	0.693133i
$805$	−134.436	−	233.676i	−0.167001	−	0.290281i
$806$	933.967	−	1617.68i	1.15877	−	2.00705i
$807$	−586.856	−	43.6399i	−0.727207	−	0.0540767i
$808$	5.88999	+	3.40059i	0.00728960	+	0.00420865i
$809$	−565.769	−	979.941i	−0.699344	−	1.21130i	−0.968694	−	0.248257i	$-0.920142\pi$
$809$	−565.769	−	979.941i	−0.699344	−	1.21130i	0.269351	−	0.963042i	$-0.413191\pi$
$810$	−161.079	+	526.495i	−0.198862	+	0.649994i
$811$			199.736i			0.246283i	0.992389	+	0.123142i	$0.0392970\pi$
$811$			199.736i			0.246283i	−0.992389	+	0.123142i	$0.960703\pi$
$812$	−1.40363	+	916.195i	−0.00172861	+	1.12832i
$813$	124.184	+	257.493i	0.152748	+	0.316720i
$814$	116.662	+	202.065i	0.143320	+	0.248238i
$815$			426.179i			0.522919i
$816$	574.744	+	42.7392i	0.704343	+	0.0523765i
$817$			710.825i			0.870043i
$818$		−	1867.84i		−	2.28343i
$819$	−610.921	+	765.468i	−0.745935	+	0.934638i
$820$	−84.4055			−0.102934
$821$	393.360			0.479123			0.239562	−	0.970881i	$-0.422996\pi$
$821$	393.360			0.479123			0.239562	+	0.970881i	$0.422996\pi$
$822$	1174.50	−	566.442i	1.42884	−	0.689102i
$823$	−848.757			−1.03130			−0.515648	−	0.856801i	$-0.672449\pi$
$823$	−848.757			−1.03130			−0.515648	+	0.856801i	$0.672449\pi$
$824$	−11.5544	+	6.67091i	−0.0140223	+	0.00809577i
$825$	−48.7735	+	655.891i	−0.0591193	+	0.795019i
$826$	−946.369	+	1633.38i	−1.14573	+	1.97745i
$827$	495.009			0.598559			0.299280	−	0.954165i	$-0.403254\pi$
$827$	495.009			0.598559			0.299280	+	0.954165i	$0.403254\pi$
$828$	−362.691	+	455.873i	−0.438032	+	0.550571i
$829$	820.334	−	473.620i	0.989546	−	0.571315i	0.0844077	−	0.996431i	$-0.473100\pi$
$829$	820.334	−	473.620i	0.989546	−	0.571315i	0.905139	+	0.425116i	$0.139767\pi$
$830$	−74.0442	+	128.248i	−0.0892099	+	0.154516i
$831$	−582.183	+	280.776i	−0.700581	+	0.337878i
$832$	−875.021	−	505.193i	−1.05171	−	0.607204i
$833$	512.645	+	298.074i	0.615420	+	0.357832i
$834$	336.998	+	698.757i	0.404074	+	0.837838i
$835$	149.482			0.179021
$836$	636.314	−	367.376i	0.761142	−	0.439445i
$837$	1116.53	+	252.818i	1.33397	+	0.302052i
$838$	−1375.30	−	794.030i	−1.64117	−	0.947530i
$839$	787.270	−	454.531i	0.938343	−	0.541753i	0.0489028	−	0.998804i	$-0.484428\pi$
$839$	787.270	−	454.531i	0.938343	−	0.541753i	0.889441	+	0.457051i	$0.151094\pi$
$840$	−3.68009	−	2.51421i	−0.00438106	−	0.00299310i
$841$	−106.581	+	184.604i	−0.126731	+	0.219505i
$842$	−164.360	−	284.680i	−0.195202	−	0.338099i
$843$	45.3468	−	609.810i	0.0537921	−	0.723381i
$844$	−85.5412	+	148.162i	−0.101352	+	0.175547i
$845$	−150.939	−	87.1444i	−0.178625	−	0.103129i
$846$	−625.833	+	246.451i	−0.739756	+	0.291314i
$847$	0.0937834	−	61.2154i	0.000110724	−	0.0722732i
$848$	−540.712	−	936.540i	−0.637632	−	1.10441i
$849$	203.399	−	298.700i	0.239575	−	0.351826i
$850$		−	660.107i		−	0.776596i
$851$	−116.059			−0.136380
$852$	1128.38	+	768.365i	1.32439	+	0.901837i
$853$	−768.763	+	443.845i	−0.901246	+	0.520335i	−0.877604	−	0.479386i	$-0.840859\pi$
$853$	−768.763	+	443.845i	−0.901246	+	0.520335i	−0.0236417	+	0.999720i	$0.507526\pi$
$854$	−491.710	+	848.661i	−0.575773	+	0.993749i
$855$	126.566	+	321.399i	0.148030	+	0.375905i
$856$	3.38916	−	5.87020i	0.00395930	−	0.00685771i
$857$	151.668	+	87.5656i	0.176976	+	0.102177i	0.585871	−	0.810404i	$-0.300753\pi$
$857$	151.668	+	87.5656i	0.176976	+	0.102177i	−0.408895	+	0.912581i	$0.634086\pi$
$858$	−1501.30	−	111.640i	−1.74976	−	0.130116i
$859$	1192.54	−	688.515i	1.38829	−	0.801531i	0.395170	−	0.918608i	$-0.370686\pi$
$859$	1192.54	−	688.515i	1.38829	−	0.801531i	0.993123	+	0.117077i	$0.0373525\pi$
$860$	371.980	+	214.763i	0.432535	+	0.249724i
$861$	13.8744	−	182.792i	0.0161143	−	0.212302i
$862$	−456.983	−	791.518i	−0.530143	−	0.918235i
$863$	−761.374	+	1318.74i	−0.882241	+	1.52809i	−0.0333969	+	0.999442i	$0.510633\pi$
$863$	−761.374	+	1318.74i	−0.882241	+	1.52809i	−0.848844	+	0.528644i	$0.822701\pi$
$864$	270.351	−	1193.96i	0.312906	−	1.38190i
$865$	−105.552	−	182.821i	−0.122025	−	0.211354i
$866$		−	332.465i		−	0.383909i
$867$	385.163	−	185.757i	0.444248	−	0.214253i
$868$	−599.818	+	1035.25i	−0.691035	+	1.19268i
$869$	−779.616	+	1350.33i	−0.897141	+	1.55389i
$870$	−287.611	−	596.353i	−0.330587	−	0.685463i
$871$	−1102.20	−	636.358i	−1.26545	−	0.730606i
$872$	−1.11477	−	1.93085i	−0.00127841	−	0.00221427i
$873$	−785.582	−	625.006i	−0.899864	−	0.715929i
$874$			728.121i			0.833091i
$875$	372.435	−	642.800i	0.425640	−	0.734628i
$876$	−818.934	−	60.8977i	−0.934856	−	0.0695179i
$877$	359.527	+	622.719i	0.409951	+	0.710056i	0.994884	−	0.101026i	$-0.0322124\pi$
$877$	359.527	+	622.719i	0.409951	+	0.710056i	−0.584933	+	0.811082i	$0.698879\pi$
$878$			614.509i			0.699896i
$879$	228.261	+	473.293i	0.259682	+	0.538445i
$880$			433.694i			0.492834i
$881$		−	1065.56i		−	1.20949i	−0.796418	−	0.604747i	$-0.793274\pi$
$881$		−	1065.56i		−	1.20949i	0.796418	−	0.604747i	$-0.206726\pi$
$882$	781.088	−	975.614i	0.885587	−	1.10614i
$883$	−378.403			−0.428543			−0.214271	−	0.976774i	$-0.568738\pi$
$883$	−378.403			−0.428543			−0.214271	+	0.976774i	$0.568738\pi$
$884$	758.410			0.857930
$885$	50.7780	−	682.847i	0.0573762	−	0.771578i
$886$	424.360			0.478961
$887$	1522.62	−	879.087i	1.71660	−	0.991079i	0.791661	−	0.610960i	$-0.209217\pi$
$887$	1522.62	−	879.087i	1.71660	−	0.991079i	0.924938	−	0.380118i	$-0.124117\pi$
$888$	−1.72824	+	0.833501i	−0.00194622	+	0.000938627i
$889$	316.689	+	183.488i	0.356230	+	0.206398i
$890$	737.050			0.828146
$891$	−207.372	−	899.030i	−0.232740	−	1.00901i
$892$	−670.037	+	386.846i	−0.751163	+	0.433684i
$893$	−210.989	+	365.443i	−0.236270	+	0.409231i
$894$	70.8729	−	953.078i	0.0792762	−	1.06608i
$895$	26.9040	+	15.5331i	0.0300604	+	0.0173554i
$896$	17.1494	+	9.93628i	0.0191400	+	0.0110896i
$897$	421.474	−	618.952i	0.469871	−	0.690025i
$898$	747.501			0.832406
$899$	−1192.20	+	688.317i	−1.32614	+	0.765647i
$900$	−690.619	−	103.283i	−0.767355	−	0.114759i
$901$	713.998	+	412.227i	0.792451	+	0.457522i
$902$	244.035	−	140.894i	0.270549	−	0.156202i
$903$	−526.245	+	770.273i	−0.582774	+	0.853016i
$904$	−3.28055	+	5.68209i	−0.00362893	+	0.00628549i
$905$	270.859	+	469.141i	0.299291	+	0.518388i
$906$	−215.925	+	104.137i	−0.238328	+	0.114941i
$907$	−371.175	+	642.893i	−0.409233	+	0.708813i	−0.994804	−	0.101808i	$-0.967537\pi$
$907$	−371.175	+	642.893i	−0.409233	+	0.708813i	0.585571	+	0.810621i	$0.300870\pi$
$908$	784.736	+	453.067i	0.864246	+	0.498973i
$909$	102.316	−	684.155i	0.112559	−	0.752646i
$910$	640.014	+	370.820i	0.703312	+	0.407495i
$911$	394.703	+	683.645i	0.433263	+	0.750434i	0.997152	−	0.0754169i	$-0.0240288\pi$
$911$	394.703	+	683.645i	0.433263	+	0.750434i	−0.563889	+	0.825851i	$0.690695\pi$
$912$	−331.025	−	686.372i	−0.362966	−	0.752601i
$913$		−	248.158i		−	0.271805i
$914$	620.046			0.678387
$915$	26.3830	−	354.790i	0.0288338	−	0.387749i
$916$	−559.101	+	322.797i	−0.610372	+	0.352398i
$917$	−1305.77	−	2.00048i	−1.42396	−	0.00218154i
$918$	274.470	+	884.398i	0.298987	+	0.963396i
$919$	213.779	−	370.276i	0.232621	−	0.402912i	−0.725957	−	0.687740i	$-0.758603\pi$
$919$	213.779	−	370.276i	0.232621	−	0.402912i	0.958579	+	0.284828i	$0.0919363\pi$
$920$	2.95122	+	1.70389i	0.00320785	+	0.00185205i
$921$	31.0126	−	45.5433i	0.0336727	−	0.0494498i
$922$	949.064	−	547.942i	1.02935	−	0.594297i
$923$	−1519.70	−	877.398i	−1.64648	−	0.950594i
$924$	961.511	+	72.9814i	1.04060	+	0.0789842i
$925$	−69.5596	−	120.481i	−0.0751996	−	0.130250i
$926$	−685.477	+	1187.28i	−0.740256	+	1.28216i
$927$	1061.94	+	844.874i	1.14556	+	0.911407i
$928$	736.051	+	1274.88i	0.793159	+	1.37379i
$929$		−	1129.42i		−	1.21574i	−0.794037	−	0.607869i	$-0.792024\pi$
$929$		−	1129.42i		−	1.21574i	0.794037	−	0.607869i	$-0.207976\pi$
$930$	64.1179	−	862.238i	0.0689440	−	0.927138i
$931$	2.40242	−	784.066i	0.00258048	−	0.842177i
$932$	497.045	−	860.908i	0.533310	−	0.923721i
$933$	−688.640	+	1011.30i	−0.738092	+	1.08392i
$934$	283.514	+	163.687i	0.303548	+	0.175253i
$935$	−165.320	−	286.342i	−0.176812	−	0.306248i
$936$	1.83107	−	12.2438i	0.00195627	−	0.0130809i
$937$		−	736.130i		−	0.785625i	−0.919619	−	0.392812i	$-0.871502\pi$
$937$		−	736.130i		−	0.785625i	0.919619	−	0.392812i	$-0.128498\pi$
$938$	1405.27	+	814.206i	1.49816	+	0.868024i
$939$	−680.056	+	998.691i	−0.724234	+	1.06357i
$940$	127.493	+	220.824i	0.135631	+	0.234919i
$941$		−	86.6207i		−	0.0920517i	−0.998940	−	0.0460259i	$-0.985344\pi$
$941$		−	86.6207i		−	0.0920517i	0.998940	−	0.0460259i	$-0.0146557\pi$
$942$	−49.0512	+	72.0338i	−0.0520714	+	0.0764690i
$943$			140.165i			0.148637i
$944$			1510.57i			1.60018i
$945$	−100.790	+	441.979i	−0.106656	+	0.467702i
$946$	−1433.97			−1.51582
$947$	587.369			0.620241			0.310121	−	0.950697i	$-0.399631\pi$
$947$	587.369			0.620241			0.310121	+	0.950697i	$0.399631\pi$
$948$	−1368.35	−	931.778i	−1.44341	−	0.982888i
$949$	1055.59			1.11232
$950$	−755.862	+	436.397i	−0.795645	+	0.459366i
$951$	735.343	+	500.730i	0.773232	+	0.526530i
$952$	−7.49596	−	0.0114840i	−0.00787391	−	1.20630e-5i
$953$	−396.549			−0.416106			−0.208053	−	0.978118i	$-0.566713\pi$
$953$	−396.549			−0.416106			−0.208053	+	0.978118i	$0.566713\pi$
$954$	1081.79	−	1359.72i	1.13395	−	1.42528i
$955$	−215.802	+	124.593i	−0.225970	+	0.130464i
$956$	−444.001	+	769.033i	−0.464436	+	0.804427i
$957$	917.056	+	624.467i	0.958261	+	0.652526i
$958$	1118.28	+	645.638i	1.16730	+	0.673944i
$959$	930.603	−	535.385i	0.970389	−	0.558274i
$960$	−466.394	−	34.6821i	−0.485828	−	0.0361272i
$961$	−836.749			−0.870707
$962$	275.774	−	159.218i	0.286667	−	0.165507i
$963$	−681.857	−	101.973i	−0.708055	−	0.105890i
$964$	−920.257	−	531.311i	−0.954624	−	0.551152i
$965$	−337.217	+	194.693i	−0.349448	+	0.201754i
$966$	−539.050	+	789.016i	−0.558023	+	0.816787i
$967$	−163.959	+	283.985i	−0.169554	+	0.293676i	−0.938263	−	0.345922i	$-0.887566\pi$
$967$	−163.959	+	283.985i	−0.169554	+	0.293676i	0.768709	+	0.639598i	$0.220899\pi$
$968$	0.386903	+	0.670135i	0.000399693	+	0.000692288i
$969$	480.194	+	326.987i	0.495556	+	0.337448i
$970$	−379.094	+	656.611i	−0.390819	+	0.676918i
$971$	900.251	+	519.760i	0.927138	+	0.535283i	0.885905	−	0.463866i	$-0.153538\pi$
$971$	900.251	+	519.760i	0.927138	+	0.535283i	0.0412328	+	0.999150i	$0.486871\pi$
$972$	968.223	−	148.781i	0.996114	−	0.153067i
$973$	318.521	+	553.651i	0.327359	+	0.569015i
$974$	460.046	+	796.823i	0.472326	+	0.818093i
$975$	895.143	+	66.5648i	0.918096	+	0.0682716i
$976$			784.855i			0.804155i
$977$	1486.83			1.52184			0.760918	−	0.648848i	$-0.224749\pi$
$977$	1486.83			1.52184			0.760918	+	0.648848i	$0.224749\pi$
$978$	1360.65	−	656.216i	1.39126	−	0.670978i
$979$	−1069.63	+	617.552i	−1.09258	+	0.630799i
$980$	−409.582	−	238.148i	−0.417941	−	0.243009i
$981$	−141.187	+	177.460i	−0.143921	+	0.180897i
$982$	439.887	−	761.906i	0.447950	−	0.775872i
$983$	958.645	+	553.474i	0.975223	+	0.563045i	0.900825	−	0.434183i	$-0.142963\pi$
$983$	958.645	+	553.474i	0.975223	+	0.563045i	0.0743987	+	0.997229i	$0.476296\pi$
$984$	1.00662	+	2.08721i	0.00102299	+	0.00212114i
$985$	−626.474	+	361.695i	−0.636014	+	0.367203i
$986$	−964.353	−	556.769i	−0.978046	−	0.564675i
$987$	−499.183	+	239.805i	−0.505758	+	0.242964i
$988$	−501.386	−	868.425i	−0.507475	−	0.878973i
$989$	356.638	−	617.716i	0.360605	−	0.624586i
$990$	−648.368	+	255.326i	−0.654917	+	0.257905i
$991$	−543.503	−	941.374i	−0.548439	−	0.949924i	−0.998382	−	0.0568665i	$-0.981889\pi$
$991$	−543.503	−	941.374i	−0.548439	−	0.949924i	0.449943	−	0.893057i	$-0.351444\pi$
$992$			1922.42i			1.93793i
$993$	−1321.57	−	899.920i	−1.33089	−	0.906264i
$994$	1937.56	+	1122.61i	1.94926	+	1.12939i
$995$	−69.3191	+	120.064i	−0.0696675	+	0.120668i
$996$	262.750	+	19.5387i	0.263805	+	0.0196171i
$997$	716.543	+	413.696i	0.718699	+	0.414941i	0.814274	−	0.580481i	$-0.197136\pi$
$997$	716.543	+	413.696i	0.718699	+	0.414941i	−0.0955746	+	0.995422i	$0.530469\pi$
$998$	−1097.05	−	1900.14i	−1.09925	−	1.90395i
$999$	143.290	+	132.495i	0.143434	+	0.132628i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.t.a.40.3	yes	28
3.2	odd	2		189.3.t.a.145.12		28
7.2	even	3		441.3.l.b.391.12		28
7.3	odd	6		63.3.k.a.31.12	✓	28
7.4	even	3		441.3.k.b.31.12		28
7.5	odd	6		441.3.l.a.391.12		28
7.6	odd	2		441.3.t.a.166.3		28
9.2	odd	6		189.3.k.a.19.3		28
9.7	even	3		63.3.k.a.61.12	yes	28
21.17	even	6		189.3.k.a.10.3		28
63.16	even	3		441.3.l.a.97.12		28
63.25	even	3		441.3.t.a.178.3		28
63.34	odd	6		441.3.k.b.313.12		28
63.38	even	6		189.3.t.a.73.12		28
63.52	odd	6	inner	63.3.t.a.52.3	yes	28
63.61	odd	6		441.3.l.b.97.12		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.12	✓	28	7.3	odd	6
63.3.k.a.61.12	yes	28	9.7	even	3
63.3.t.a.40.3	yes	28	1.1	even	1	trivial
63.3.t.a.52.3	yes	28	63.52	odd	6	inner
189.3.k.a.10.3		28	21.17	even	6
189.3.k.a.19.3		28	9.2	odd	6
189.3.t.a.73.12		28	63.38	even	6
189.3.t.a.145.12		28	3.2	odd	2
441.3.k.b.31.12		28	7.4	even	3
441.3.k.b.313.12		28	63.34	odd	6
441.3.l.a.97.12		28	63.16	even	3
441.3.l.a.391.12		28	7.5	odd	6
441.3.l.b.97.12		28	63.61	odd	6
441.3.l.b.391.12		28	7.2	even	3
441.3.t.a.166.3		28	7.6	odd	2
441.3.t.a.178.3		28	63.25	even	3

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.83394 q^{2} +(-2.47969 - 1.68854i) q^{3} +4.03122 q^{4} +(-2.07720 + 1.19927i) q^{5} +(7.02729 + 4.78521i) q^{6} +(6.05681 + 3.50928i) q^{7} -0.0884848 q^{8} +(3.29769 + 8.37408i) q^{9} +O(q^{10})\)	\(q-2.83394 q^{2} +(-2.47969 - 1.68854i) q^{3} +4.03122 q^{4} +(-2.07720 + 1.19927i) q^{5} +(7.02729 + 4.78521i) q^{6} +(6.05681 + 3.50928i) q^{7} -0.0884848 q^{8} +(3.29769 + 8.37408i) q^{9} +(5.88667 - 3.39867i) q^{10} +(-5.69528 + 9.86452i) q^{11} +(-9.99617 - 6.80687i) q^{12} +(13.4628 + 7.77278i) q^{13} +(-17.1646 - 9.94510i) q^{14} +(7.17583 + 0.533610i) q^{15} -15.8741 q^{16} +(10.4807 - 6.05105i) q^{17} +(-9.34546 - 23.7317i) q^{18} +(-13.8576 - 8.00071i) q^{19} +(-8.37367 + 4.83454i) q^{20} +(-9.09343 - 18.9291i) q^{21} +(16.1401 - 27.9555i) q^{22} +(8.02831 + 13.9054i) q^{23} +(0.219415 + 0.149410i) q^{24} +(-9.62349 + 16.6684i) q^{25} +(-38.1529 - 22.0276i) q^{26} +(5.96270 - 26.3334i) q^{27} +(24.4163 + 14.1467i) q^{28} +(16.2339 + 28.1180i) q^{29} +(-20.3359 - 1.51222i) q^{30} +42.3999i q^{31} +45.3403 q^{32} +(30.7791 - 14.8442i) q^{33} +(-29.7018 + 17.1483i) q^{34} +(-16.7898 - 0.0257224i) q^{35} +(13.2937 + 33.7578i) q^{36} +(-3.61406 + 6.25973i) q^{37} +(39.2718 + 22.6736i) q^{38} +(-20.2590 - 42.0066i) q^{39} +(0.183801 - 0.106117i) q^{40} +(7.55990 + 4.36471i) q^{41} +(25.7703 + 53.6439i) q^{42} +(-22.2113 - 38.4711i) q^{43} +(-22.9590 + 39.7661i) q^{44} +(-16.8928 - 13.4398i) q^{45} +(-22.7518 - 39.4072i) q^{46} -26.3712i q^{47} +(39.3629 + 26.8040i) q^{48} +(24.3699 + 42.5101i) q^{49} +(27.2724 - 47.2372i) q^{50} +(-36.2063 - 2.69238i) q^{51} +(54.2717 + 31.3338i) q^{52} +(34.0624 + 58.9979i) q^{53} +(-16.8980 + 74.6272i) q^{54} -27.3208i q^{55} +(-0.535936 - 0.310518i) q^{56} +(20.8531 + 43.2384i) q^{57} +(-46.0060 - 79.6847i) q^{58} -95.1593i q^{59} +(28.9274 + 2.15110i) q^{60} -49.4424i q^{61} -120.159i q^{62} +(-9.41355 + 62.2927i) q^{63} -64.9952 q^{64} -37.2867 q^{65} +(-87.2262 + 42.0677i) q^{66} -81.8700 q^{67} +(42.2502 - 24.3931i) q^{68} +(3.57215 - 48.0372i) q^{69} +(47.5813 + 0.0728958i) q^{70} -112.881 q^{71} +(-0.291796 - 0.740979i) q^{72} +(58.8056 - 33.9514i) q^{73} +(10.2420 - 17.7397i) q^{74} +(52.0084 - 25.0827i) q^{75} +(-55.8633 - 32.2527i) q^{76} +(-69.1127 + 39.7612i) q^{77} +(57.4129 + 119.044i) q^{78} +136.888 q^{79} +(32.9738 - 19.0374i) q^{80} +(-59.2505 + 55.2302i) q^{81} +(-21.4243 - 12.3693i) q^{82} +(-18.8674 + 10.8931i) q^{83} +(-36.6577 - 76.3073i) q^{84} +(-14.5137 + 25.1385i) q^{85} +(62.9455 + 109.025i) q^{86} +(7.22320 - 97.1354i) q^{87} +(0.503946 - 0.872861i) q^{88} +(93.9050 + 54.2161i) q^{89} +(47.8732 + 38.0877i) q^{90} +(54.2650 + 94.3232i) q^{91} +(32.3639 + 56.0559i) q^{92} +(71.5937 - 105.138i) q^{93} +74.7346i q^{94} +38.3802 q^{95} +(-112.430 - 76.5587i) q^{96} +(-96.5982 + 55.7710i) q^{97} +(-69.0628 - 120.471i) q^{98} +(-101.388 - 15.1626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 3 q^{3} + 46 q^{4} - 3 q^{5} - 12 q^{6} - 16 q^{8} - 15 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 3 * q^3 + 46 * q^4 - 3 * q^5 - 12 * q^6 - 16 * q^8 - 15 * q^9	\( 28 q - 2 q^{2} - 3 q^{3} + 46 q^{4} - 3 q^{5} - 12 q^{6} - 16 q^{8} - 15 q^{9} - 6 q^{10} + 7 q^{11} - 30 q^{12} - 15 q^{13} + 10 q^{14} - 18 q^{15} + 54 q^{16} - 33 q^{17} - 42 q^{18} - 6 q^{19} - 108 q^{20} + 21 q^{21} - 10 q^{22} + 34 q^{23} - 78 q^{24} + 31 q^{25} + 54 q^{26} + 81 q^{27} - 16 q^{28} + 70 q^{29} - 27 q^{30} - 306 q^{32} - 3 q^{33} - 12 q^{34} + 18 q^{35} - 174 q^{36} + 9 q^{37} + 87 q^{38} + 129 q^{39} - 102 q^{40} + 234 q^{41} + 306 q^{42} + 30 q^{43} + 51 q^{44} + 273 q^{45} - 22 q^{46} - 147 q^{48} - 38 q^{49} + 241 q^{50} + 12 q^{51} - 219 q^{52} + 148 q^{53} + 171 q^{54} + 110 q^{56} + 189 q^{57} + 17 q^{58} + 33 q^{60} - 471 q^{63} - 48 q^{64} - 228 q^{65} + 258 q^{66} + 68 q^{67} - 18 q^{68} - 78 q^{69} - 225 q^{70} - 350 q^{71} + 162 q^{72} - 6 q^{73} + 359 q^{74} - 510 q^{75} - 72 q^{76} - 224 q^{77} - 375 q^{78} + 164 q^{79} - 609 q^{80} - 435 q^{81} - 18 q^{82} - 738 q^{83} - 21 q^{84} + 3 q^{85} + 17 q^{86} - 561 q^{87} + 25 q^{88} + 21 q^{89} + 543 q^{90} + 39 q^{91} + 288 q^{92} - 222 q^{93} - 1014 q^{95} + 231 q^{96} + 57 q^{97} + 811 q^{98} - 162 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 3 * q^3 + 46 * q^4 - 3 * q^5 - 12 * q^6 - 16 * q^8 - 15 * q^9 - 6 * q^10 + 7 * q^11 - 30 * q^12 - 15 * q^13 + 10 * q^14 - 18 * q^15 + 54 * q^16 - 33 * q^17 - 42 * q^18 - 6 * q^19 - 108 * q^20 + 21 * q^21 - 10 * q^22 + 34 * q^23 - 78 * q^24 + 31 * q^25 + 54 * q^26 + 81 * q^27 - 16 * q^28 + 70 * q^29 - 27 * q^30 - 306 * q^32 - 3 * q^33 - 12 * q^34 + 18 * q^35 - 174 * q^36 + 9 * q^37 + 87 * q^38 + 129 * q^39 - 102 * q^40 + 234 * q^41 + 306 * q^42 + 30 * q^43 + 51 * q^44 + 273 * q^45 - 22 * q^46 - 147 * q^48 - 38 * q^49 + 241 * q^50 + 12 * q^51 - 219 * q^52 + 148 * q^53 + 171 * q^54 + 110 * q^56 + 189 * q^57 + 17 * q^58 + 33 * q^60 - 471 * q^63 - 48 * q^64 - 228 * q^65 + 258 * q^66 + 68 * q^67 - 18 * q^68 - 78 * q^69 - 225 * q^70 - 350 * q^71 + 162 * q^72 - 6 * q^73 + 359 * q^74 - 510 * q^75 - 72 * q^76 - 224 * q^77 - 375 * q^78 + 164 * q^79 - 609 * q^80 - 435 * q^81 - 18 * q^82 - 738 * q^83 - 21 * q^84 + 3 * q^85 + 17 * q^86 - 561 * q^87 + 25 * q^88 + 21 * q^89 + 543 * q^90 + 39 * q^91 + 288 * q^92 - 222 * q^93 - 1014 * q^95 + 231 * q^96 + 57 * q^97 + 811 * q^98 - 162 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more