LMFDB - Embedded newform 63.3.k.a.61.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(31,63)]

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, 1]))

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

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

chi := DirichletCharacter("63.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.k (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			61.12
Character	$\chi$	$=$	63.61
Dual form			63.3.k.a.31.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41697 + 2.45427i) q^{2} +(0.222472 + 2.99174i) q^{3} +(-2.01561 + 3.49114i) q^{4} -2.39855i q^{5} +(-7.02729 + 4.78521i) q^{6} +(0.0107242 - 6.99999i) q^{7} -0.0884848 q^{8} +(-8.90101 + 1.33116i) q^{9} +O(q^{10})$	\(q+(1.41697 + 2.45427i) q^{2} +(0.222472 + 2.99174i) q^{3} +(-2.01561 + 3.49114i) q^{4} -2.39855i q^{5} +(-7.02729 + 4.78521i) q^{6} +(0.0107242 - 6.99999i) q^{7} -0.0884848 q^{8} +(-8.90101 + 1.33116i) q^{9} +(5.88667 - 3.39867i) q^{10} +11.3906 q^{11} +(-10.8930 - 5.25350i) q^{12} +(-13.4628 + 7.77278i) q^{13} +(17.1950 - 9.89246i) q^{14} +(7.17583 - 0.533610i) q^{15} +(7.93707 + 13.7474i) q^{16} +(10.4807 - 6.05105i) q^{17} +(-15.8795 - 19.9592i) q^{18} +(-13.8576 - 8.00071i) q^{19} +(8.37367 + 4.83454i) q^{20} +(20.9445 - 1.52522i) q^{21} +(16.1401 + 27.9555i) q^{22} -16.0566 q^{23} +(-0.0196854 - 0.264724i) q^{24} +19.2470 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} +(11.4776 + 16.8553i) q^{30} +(-36.7194 - 21.1999i) q^{31} +(-22.6701 + 39.2658i) q^{32} +(2.53408 + 34.0776i) 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} -45.3471i q^{38} +(-26.2492 - 38.5481i) q^{39} +0.212235i q^{40} +(-7.55990 + 4.36471i) q^{41} +(33.4211 + 49.2423i) q^{42} +(-22.2113 + 38.4711i) q^{43} +(-22.9590 + 39.7661i) q^{44} +(3.19284 + 21.3495i) q^{45} +(-22.7518 - 39.4072i) q^{46} +(-22.8382 + 13.1856i) q^{47} +(-39.3629 + 26.8040i) q^{48} +(-48.9998 - 0.150138i) q^{49} +(27.2724 + 47.2372i) q^{50} +(20.4348 + 30.0094i) q^{51} -62.6676i q^{52} +(34.0624 + 58.9979i) q^{53} +(56.1801 - 51.9477i) q^{54} -27.3208i q^{55} +(-0.000948925 + 0.619393i) q^{56} +(20.8531 - 43.2384i) q^{57} +92.0120 q^{58} +(82.4104 + 47.5797i) q^{59} +(-12.6008 + 26.1274i) q^{60} +(-42.8184 + 24.7212i) q^{61} -120.159i q^{62} +(9.22264 + 62.3213i) q^{63} -64.9952 q^{64} +(18.6434 + 32.2913i) q^{65} +(-80.0448 + 54.5063i) q^{66} +(40.9350 - 70.9015i) q^{67} +48.7863i q^{68} +(-3.57215 - 48.0372i) q^{69} +(-23.7275 - 41.2431i) q^{70} -112.881 q^{71} +(0.787605 - 0.117787i) q^{72} +(58.8056 - 33.9514i) q^{73} -20.4840 q^{74} +(4.28192 + 57.5819i) q^{75} +(55.8633 - 32.2527i) q^{76} +(0.122154 - 79.7339i) q^{77} +(57.4129 - 119.044i) q^{78} +(-68.4439 - 118.548i) q^{79} +(32.9738 - 19.0374i) q^{80} +(77.4560 - 23.6973i) q^{81} +(-21.4243 - 12.3693i) q^{82} +(18.8674 + 10.8931i) q^{83} +(-36.8913 + 76.1946i) q^{84} +(-14.5137 - 25.1385i) q^{85} -125.891 q^{86} +(87.7333 + 42.3122i) q^{87} -1.00789 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} +(55.2557 - 114.571i) q^{93} +(-64.7220 - 37.3673i) q^{94} +(-19.1901 + 33.2382i) q^{95} +(-122.517 - 59.0876i) 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 + q^{2} - 3 q^{3} - 23 q^{4} + 12 q^{6} - 16 q^{8} + 9 q^{9}+O(q^{10}) $ 28 * q + q^2 - 3 * q^3 - 23 * q^4 + 12 * q^6 - 16 * q^8 + 9 * q^9	\( 28 q + q^{2} - 3 q^{3} - 23 q^{4} + 12 q^{6} - 16 q^{8} + 9 q^{9} - 6 q^{10} - 14 q^{11} - 3 q^{12} + 15 q^{13} - 11 q^{14} - 18 q^{15} - 27 q^{16} - 33 q^{17} + 33 q^{18} - 6 q^{19} + 108 q^{20} + 12 q^{21} - 10 q^{22} - 68 q^{23} + 42 q^{24} - 62 q^{25} + 54 q^{26} - 81 q^{27} - 16 q^{28} + 70 q^{29} - 6 q^{30} + 45 q^{31} + 153 q^{32} - 114 q^{33} + 12 q^{34} + 18 q^{35} - 174 q^{36} + 9 q^{37} - 120 q^{39} - 234 q^{41} - 51 q^{42} + 30 q^{43} + 51 q^{44} + 276 q^{45} - 22 q^{46} - 111 q^{47} + 147 q^{48} + 34 q^{49} + 241 q^{50} - 6 q^{51} + 148 q^{53} + 378 q^{54} - 412 q^{56} + 189 q^{57} - 34 q^{58} + 42 q^{59} + 456 q^{60} + 120 q^{61} - 222 q^{63} - 48 q^{64} + 114 q^{65} - 447 q^{66} - 34 q^{67} + 78 q^{69} + 264 q^{70} - 350 q^{71} - 339 q^{72} - 6 q^{73} - 718 q^{74} - 123 q^{75} + 72 q^{76} - 32 q^{77} - 375 q^{78} - 82 q^{79} - 609 q^{80} - 3 q^{81} - 18 q^{82} + 738 q^{83} + 609 q^{84} + 3 q^{85} - 34 q^{86} + 3 q^{87} - 50 q^{88} + 21 q^{89} - 543 q^{90} + 39 q^{91} + 288 q^{92} + 252 q^{93} - 3 q^{94} + 507 q^{95} - 582 q^{96} - 57 q^{97} + 811 q^{98} - 162 q^{99}+O(q^{100}) \) 28 * q + q^2 - 3 * q^3 - 23 * q^4 + 12 * q^6 - 16 * q^8 + 9 * q^9 - 6 * q^10 - 14 * q^11 - 3 * q^12 + 15 * q^13 - 11 * q^14 - 18 * q^15 - 27 * q^16 - 33 * q^17 + 33 * q^18 - 6 * q^19 + 108 * q^20 + 12 * q^21 - 10 * q^22 - 68 * q^23 + 42 * q^24 - 62 * q^25 + 54 * q^26 - 81 * q^27 - 16 * q^28 + 70 * q^29 - 6 * q^30 + 45 * q^31 + 153 * q^32 - 114 * q^33 + 12 * q^34 + 18 * q^35 - 174 * q^36 + 9 * q^37 - 120 * q^39 - 234 * q^41 - 51 * q^42 + 30 * q^43 + 51 * q^44 + 276 * q^45 - 22 * q^46 - 111 * q^47 + 147 * q^48 + 34 * q^49 + 241 * q^50 - 6 * q^51 + 148 * q^53 + 378 * q^54 - 412 * q^56 + 189 * q^57 - 34 * q^58 + 42 * q^59 + 456 * q^60 + 120 * q^61 - 222 * q^63 - 48 * q^64 + 114 * q^65 - 447 * q^66 - 34 * q^67 + 78 * q^69 + 264 * q^70 - 350 * q^71 - 339 * q^72 - 6 * q^73 - 718 * q^74 - 123 * q^75 + 72 * q^76 - 32 * q^77 - 375 * q^78 - 82 * q^79 - 609 * q^80 - 3 * q^81 - 18 * q^82 + 738 * q^83 + 609 * q^84 + 3 * q^85 - 34 * q^86 + 3 * q^87 - 50 * q^88 + 21 * q^89 - 543 * q^90 + 39 * q^91 + 288 * q^92 + 252 * q^93 - 3 * q^94 + 507 * q^95 - 582 * 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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.41697	+	2.45427i	0.708485	+	1.22713i	0.965419	+	0.260704i	$0.0839545\pi$
$2$	1.41697	+	2.45427i	0.708485	+	1.22713i	−0.256934	+	0.966429i	$0.582712\pi$
$3$	0.222472	+	2.99174i	0.0741574	+	0.997247i
$3$	0.222472	+	2.99174i	0.0741574	+	0.997247i
$4$	−2.01561	+	3.49114i	−0.503903	+	0.872785i
$5$		−	2.39855i		−	0.479709i	−0.970809	−	0.239855i	$-0.922900\pi$
$5$		−	2.39855i		−	0.479709i	0.970809	−	0.239855i	$-0.0770998\pi$
$6$	−7.02729	+	4.78521i	−1.17121	+	0.797535i
$7$	0.0107242	−	6.99999i	0.00153202	−	0.999999i
$7$	0.0107242	−	6.99999i	0.00153202	−	0.999999i
$8$	−0.0884848			−0.0110606
$9$	−8.90101	+	1.33116i	−0.989001	+	0.147906i
$10$	5.88667	−	3.39867i	0.588667	−	0.339867i
$11$	11.3906			1.03551			0.517753	−	0.855530i	$-0.326769\pi$
$11$	11.3906			1.03551			0.517753	+	0.855530i	$0.326769\pi$
$12$	−10.8930	−	5.25350i	−0.907750	−	0.437792i
$13$	−13.4628	+	7.77278i	−1.03560	+	0.597906i	−0.918585	−	0.395224i	$-0.870667\pi$
$13$	−13.4628	+	7.77278i	−1.03560	+	0.597906i	−0.117019	+	0.993130i	$0.537334\pi$
$14$	17.1950	−	9.89246i	1.22822	−	0.706604i
$15$	7.17583	−	0.533610i	0.478388	−	0.0355740i
$16$	7.93707	+	13.7474i	0.496067	+	0.859213i
$17$	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	$0.217493\pi$
$18$	−15.8795	−	19.9592i	−0.882194	−	1.10885i
$19$	−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
$21$	20.9445	−	1.52522i	0.997359	−	0.0726295i
$22$	16.1401	+	27.9555i	0.733641	+	1.27070i
$23$	−16.0566			−0.698114			−0.349057	−	0.937102i	$-0.613498\pi$
$23$	−16.0566			−0.698114			−0.349057	+	0.937102i	$0.613498\pi$
$24$	−0.0196854	−	0.264724i	−0.000820225	−	0.0110301i
$25$	19.2470			0.769879
$26$	−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	−0.437723	−	0.899110i	$-0.644215\pi$
$29$	16.2339	−	28.1180i	0.559791	−	0.969586i	0.997513	−	0.0704760i	$-0.0224518\pi$
$30$	11.4776	+	16.8553i	0.382585	+	0.561842i
$31$	−36.7194	−	21.1999i	−1.18450	−	0.683869i	−0.227445	−	0.973791i	$-0.573037\pi$
$31$	−36.7194	−	21.1999i	−1.18450	−	0.683869i	−0.957050	+	0.289922i	$0.906371\pi$
$32$	−22.6701	+	39.2658i	−0.708442	+	1.22706i
$33$	2.53408	+	34.0776i	0.0767904	+	1.03266i
$34$	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	$0.197808\pi$
$38$		−	45.3471i		−	1.19335i
$39$	−26.2492	−	38.5481i	−0.673057	−	0.988413i
$40$			0.212235i			0.00530587i
$41$	−7.55990	+	4.36471i	−0.184388	+	0.106456i	−0.589353	−	0.807876i	$-0.700617\pi$
$41$	−7.55990	+	4.36471i	−0.184388	+	0.106456i	0.404965	+	0.914332i	$0.367284\pi$
$42$	33.4211	+	49.2423i	0.795740	+	1.17243i
$43$	−22.2113	+	38.4711i	−0.516542	+	0.894676i	0.483274	+	0.875469i	$0.339448\pi$
$43$	−22.2113	+	38.4711i	−0.516542	+	0.894676i	−0.999816	+	0.0192072i	$0.993886\pi$
$44$	−22.9590	+	39.7661i	−0.521795	+	0.903775i
$45$	3.19284	+	21.3495i	0.0709521	+	0.474433i
$46$	−22.7518	−	39.4072i	−0.494603	−	0.856678i
$47$	−22.8382	+	13.1856i	−0.485919	+	0.280545i	−0.722880	−	0.690974i	$-0.757182\pi$
$47$	−22.8382	+	13.1856i	−0.485919	+	0.280545i	0.236961	+	0.971519i	$0.423849\pi$
$48$	−39.3629	+	26.8040i	−0.820060	+	0.558418i
$49$	−48.9998	−	0.150138i	−0.999995	−	0.00306404i
$50$	27.2724	+	47.2372i	0.545448	+	0.944744i
$51$	20.4348	+	30.0094i	0.400683	+	0.588420i
$52$		−	62.6676i		−	1.20515i
$53$	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	$0.611153\pi$
$54$	56.1801	−	51.9477i	1.04037	−	0.961994i
$55$		−	27.3208i		−	0.496742i
$56$	−0.000948925		0.619393i	−1.69451e−5		0.0110606i
$57$	20.8531	−	43.2384i	0.365844	−	0.758568i
$58$	92.0120			1.58641
$59$	82.4104	+	47.5797i	1.39679	+	0.806435i	0.994055	−	0.108883i	$-0.0347274\pi$
$59$	82.4104	+	47.5797i	1.39679	+	0.806435i	0.402732	+	0.915318i	$0.368061\pi$
$60$	−12.6008	+	26.1274i	−0.210013	+	0.435456i
$61$	−42.8184	+	24.7212i	−0.701941	+	0.405266i	−0.808070	−	0.589087i	$-0.799488\pi$
$61$	−42.8184	+	24.7212i	−0.701941	+	0.405266i	0.106129	+	0.994352i	$0.466154\pi$
$62$		−	120.159i		−	1.93804i
$63$	9.22264	+	62.3213i	0.146391	+	0.989227i
$64$	−64.9952			−1.01555
$65$	18.6434	+	32.2913i	0.286821	+	0.496789i
$66$	−80.0448	+	54.5063i	−1.21280	+	0.825853i
$67$	40.9350	−	70.9015i	0.610971	−	1.05823i	−0.380107	−	0.924943i	$-0.624113\pi$
$67$	40.9350	−	70.9015i	0.610971	−	1.05823i	0.991077	−	0.133289i	$-0.0425539\pi$
$68$			48.7863i			0.717445i
$69$	−3.57215	−	48.0372i	−0.0517703	−	0.696192i
$70$	−23.7275	−	41.2431i	−0.338965	−	0.589187i
$71$	−112.881			−1.58987			−0.794936	−	0.606694i	$-0.792496\pi$
$71$	−112.881			−1.58987			−0.794936	+	0.606694i	$0.792496\pi$
$72$	0.787605	−	0.117787i	0.0109390	−	0.00163593i
$73$	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	$0.179356\pi$
$74$	−20.4840			−0.276811
$75$	4.28192	+	57.5819i	0.0570922	+	0.767759i
$76$	55.8633	−	32.2527i	0.735043	−	0.424377i
$77$	0.122154	−	79.7339i	0.00158642	−	1.03551i
$78$	57.4129	−	119.044i	0.736063	−	1.52621i
$79$	−68.4439	−	118.548i	−0.866379	−	1.50061i	−0.865671	−	0.500613i	$-0.833108\pi$
$79$	−68.4439	−	118.548i	−0.866379	−	1.50061i	−0.000707812	−	1.00000i	$-0.500225\pi$
$80$	32.9738	−	19.0374i	0.412172	−	0.237968i
$81$	77.4560	−	23.6973i	0.956247	−	0.292559i
$82$	−21.4243	−	12.3693i	−0.261272	−	0.150846i
$83$	18.8674	+	10.8931i	0.227318	+	0.131242i	0.609334	−	0.792913i	$-0.291437\pi$
$83$	18.8674	+	10.8931i	0.227318	+	0.131242i	−0.382016	+	0.924156i	$0.624770\pi$
$84$	−36.8913	+	76.1946i	−0.439182	+	0.907079i
$85$	−14.5137	−	25.1385i	−0.170750	−	0.295747i
$86$	−125.891			−1.46385
$87$	87.7333	+	42.3122i	1.00843	+	0.486347i
$88$	−1.00789			−0.0114533
$89$	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
$93$	55.2557	−	114.571i	0.594147	−	1.23195i
$94$	−64.7220	−	37.3673i	−0.688532	−	0.397524i
$95$	−19.1901	+	33.2382i	−0.202001	+	0.349876i
$96$	−122.517	−	59.0876i	−1.27622	−	0.615496i
$97$	96.5982	+	55.7710i	0.995857	+	0.574959i	0.907020	−	0.421088i	$-0.138351\pi$
$97$	96.5982	+	55.7710i	0.995857	+	0.574959i	0.0888375	+	0.996046i	$0.471685\pi$
$98$	−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
$101$			76.8626i			0.761016i	0.924778	+	0.380508i	$0.124251\pi$
$101$			76.8626i			0.761016i	−0.924778	+	0.380508i	$0.875749\pi$
$102$	−44.6955	+	92.6750i	−0.438191	+	0.908578i
$103$			150.781i			1.46389i	0.681362	+	0.731946i	$0.261388\pi$
$103$			150.781i			1.46389i	−0.681362	+	0.731946i	$0.738612\pi$
$104$	1.19126	−	0.687773i	0.0114544	−	0.00661320i
$105$	−3.65831	−	50.2365i	−0.0348410	−	0.478442i
$106$	−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	$0.283196\pi$
$108$	103.952	+	32.2612i	0.962519	+	0.298715i
$109$	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	$0.796460\pi$
$110$	67.0525	−	38.7128i	0.609568	−	0.351934i
$111$	−19.5315	−	9.41970i	−0.175960	−	0.0848622i
$112$	96.3168	−	55.4120i	0.859972	−	0.494750i
$113$	37.0748	+	64.2154i	0.328095	+	0.568277i	0.982134	−	0.188184i	$-0.0602600\pi$
$113$	37.0748	+	64.2154i	0.328095	+	0.568277i	−0.654039	+	0.756461i	$0.726927\pi$
$114$	135.667	−	10.0885i	1.19006	−	0.0884953i
$115$			38.5125i			0.334892i
$116$	65.4426	+	113.350i	0.564160	+	0.977154i
$117$	109.486	−	87.1068i	0.935779	−	0.744502i
$118$			269.676i			2.28539i
$119$	−42.2449	−	73.4299i	−0.354999	−	0.617058i
$120$	−0.634952	+	0.0472164i	−0.00529127	+	0.000393470i
$121$	8.74506			0.0722732
$122$	−121.345	−	70.0585i	−0.994629	−	0.574250i
$123$	−14.7400	−	21.6462i	−0.119837	−	0.175986i
$124$	148.024	−	85.4617i	1.19374	−	0.689207i
$125$		−	106.128i		−	0.849027i
$126$	−139.885	+	110.942i	−1.11020	+	0.880494i
$127$	52.2864			0.411704			0.205852	−	0.978583i	$-0.434003\pi$
$127$	52.2864			0.411704			0.205852	+	0.978583i	$0.434003\pi$
$128$	−1.41571	−	2.45209i	−0.0110603	−	0.0191569i
$129$	−120.037	−	57.8917i	−0.930518	−	0.448773i
$130$	−52.8342	+	91.5116i	−0.406417	+	0.703935i
$131$		−	186.539i		−	1.42396i	−0.702198	−	0.711982i	$-0.747798\pi$
$131$		−	186.539i		−	1.42396i	0.702198	−	0.711982i	$-0.252202\pi$
$132$	−124.078	−	59.8404i	−0.939981	−	0.453336i
$133$	−56.1535	+	96.9176i	−0.422207	+	0.728704i
$134$	232.015			1.73145
$135$	−63.1618	+	14.3018i	−0.467865	+	0.105939i
$136$	−0.927385	+	0.535426i	−0.00681901	+	0.00393696i
$137$	−153.374			−1.11952			−0.559760	−	0.828655i	$-0.689107\pi$
$137$	−153.374			−1.11952			−0.559760	+	0.828655i	$0.689107\pi$
$138$	112.834	−	76.8343i	0.817641	−	0.556771i
$139$	−79.0232	+	45.6241i	−0.568513	+	0.328231i	−0.756555	−	0.653930i	$-0.773119\pi$
$139$	−79.0232	+	45.6241i	−0.568513	+	0.328231i	0.188043	+	0.982161i	$0.439786\pi$
$140$	33.9315	−	58.5637i	0.242368	−	0.418312i
$141$	−44.5288	−	65.3924i	−0.315807	−	0.463776i
$142$	−159.949	−	277.040i	−1.12640	−	1.95098i
$143$	−153.349	+	88.5364i	−1.07237	+	0.619135i
$144$	−88.9479	−	111.800i	−0.617694	−	0.776391i
$145$	−67.4423	−	38.9378i	−0.465119	−	0.268537i
$146$	166.652	+	96.2164i	1.14145	+	0.659016i
$147$	−10.4519	−	146.628i	−0.0711014	−	0.997469i
$148$	−14.5691	−	25.2344i	−0.0984396	−	0.170502i
$149$	112.412			0.754445			0.377223	−	0.926123i	$-0.376879\pi$
$149$	112.412			0.754445			0.377223	+	0.926123i	$0.376879\pi$
$150$	−135.254	+	92.1009i	−0.901693	+	0.614006i
$151$	28.1969			0.186734			0.0933671	−	0.995632i	$-0.470237\pi$
$151$	28.1969			0.186734			0.0933671	+	0.995632i	$0.470237\pi$
$152$	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
$156$	187.485	−	13.9418i	1.20183	−	0.0893705i
$157$	−8.87726	−	5.12529i	−0.0565431	−	0.0326452i	0.471462	−	0.881886i	$-0.343726\pi$
$157$	−8.87726	−	5.12529i	−0.0565431	−	0.0326452i	−0.528005	+	0.849241i	$0.677060\pi$
$158$	193.966	−	335.959i	1.22763	−	2.12632i
$159$	−168.928	+	115.031i	−1.06244	+	0.723468i
$160$	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	$-0.0168179\pi$
$164$		−	35.1903i		−	0.214575i
$165$	81.7368	−	6.07812i	0.495374	−	0.0368371i
$166$			61.7409i			0.371933i
$167$	53.9725	−	31.1611i	0.323189	−	0.186593i	−0.329624	−	0.944112i	$-0.606922\pi$
$167$	53.9725	−	31.1611i	0.323189	−	0.186593i	0.652813	+	0.757519i	$0.273589\pi$
$168$	−1.85327	+	0.134959i	−0.0110314	+	0.000803326i
$169$	36.3322	−	62.9292i	0.214983	−	0.372362i
$170$	41.1311	−	71.2411i	0.241947	−	0.419065i
$171$	133.997	+	52.7678i	0.783610	+	0.308583i
$172$	−89.5387	−	155.086i	−0.520574	−	0.901660i
$173$	76.2216	−	44.0066i	0.440587	−	0.254373i	−0.263259	−	0.964725i	$-0.584797\pi$
$173$	76.2216	−	44.0066i	0.440587	−	0.254373i	0.703847	+	0.710352i	$0.251464\pi$
$174$	20.4701	+	275.276i	0.117644	+	1.58205i
$175$	0.206408	−	134.729i	0.00117947	−	0.769878i
$176$	90.4077	+	156.591i	0.513680	+	0.889720i
$177$	−124.012	+	257.136i	−0.700632	+	1.45274i
$178$			307.290i			1.72635i
$179$	−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	$0.844852\pi$
$180$	−80.9696	−	31.8856i	−0.449831	−	0.177142i
$181$		−	225.852i		−	1.24780i	−0.781503	−	0.623901i	$-0.785547\pi$
$181$		−	225.852i		−	1.24780i	0.781503	−	0.623901i	$-0.214453\pi$
$182$	−154.602	+	266.834i	−0.849462	+	1.46612i
$183$	−83.4853	−	122.602i	−0.456204	−	0.669955i
$184$	1.42077			0.00772156
$185$	15.0143	+	8.66848i	0.0811581	+	0.0468567i
$186$	359.484	−	26.7320i	1.93271	−	0.143720i
$187$	119.381	−	68.9249i	0.638404	−	0.368582i
$188$		−	106.308i		−	0.565470i
$189$	−184.397	+	41.4565i	−0.975647	+	0.219346i
$190$	−108.767			−0.572459
$191$	−51.9453	−	89.9718i	−0.271965	−	0.471057i	0.697400	−	0.716682i	$-0.254340\pi$
$191$	−51.9453	−	89.9718i	−0.271965	−	0.471057i	−0.969365	+	0.245625i	$0.921007\pi$
$192$	−14.4596	−	194.449i	−0.0753105	−	1.01275i
$193$	−81.1711	+	140.592i	−0.420575	+	0.728458i	−0.995996	−	0.0893998i	$-0.971505\pi$
$193$	−81.1711	+	140.592i	−0.420575	+	0.728458i	0.575420	+	0.817858i	$0.304838\pi$
$194$			316.103i			1.62940i
$195$	−92.4594	+	62.9600i	−0.474151	+	0.322872i
$196$	99.2887	−	170.763i	0.506575	−	0.871237i
$197$	301.595			1.53094			0.765470	−	0.643472i	$-0.222507\pi$
$197$	301.595			1.53094			0.765470	+	0.643472i	$0.222507\pi$
$198$	−180.876	−	227.347i	−0.913517	−	1.14822i
$199$	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	$0.286942\pi$
$200$	−1.70307			−0.00851533
$201$	221.226	+	106.693i	1.10063	+	0.530813i
$202$	−188.641	+	108.912i	−0.933868	+	0.539169i
$203$	−196.652	−	113.939i	−0.968727	−	0.561276i
$204$	−145.956	+	10.8536i	−0.715470	+	0.0532039i
$205$	10.4690	+	18.1328i	0.0510681	+	0.0884526i
$206$	−370.056	+	213.652i	−1.79639	+	1.03715i
$207$	142.920	−	21.3739i	0.690436	−	0.103256i
$208$	−213.711	−	123.386i	−1.02746	−	0.593202i
$209$	−157.846	−	91.1327i	−0.755246	−	0.436042i
$210$	118.110	−	80.1620i	0.562428	−	0.381724i
$211$	−21.2197	−	36.7535i	−0.100567	−	0.174187i	0.811351	−	0.584559i	$-0.198732\pi$
$211$	−21.2197	−	36.7535i	−0.100567	−	0.174187i	−0.911918	+	0.410371i	$0.865399\pi$
$212$	−274.627			−1.29541
$213$	−25.1129	−	337.710i	−0.117901	−	1.58549i
$214$	−217.092			−1.01445
$215$	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
$219$	114.656	+	168.378i	0.523545	+	0.768848i
$220$	95.3808	+	55.0681i	0.433549	+	0.250310i
$221$	−94.0670	+	162.929i	−0.425642	+	0.737234i
$222$	−4.55713	−	61.2829i	−0.0205276	−	0.276049i
$223$	166.212	+	95.9625i	0.745345	+	0.430325i	0.824009	−	0.566576i	$-0.191732\pi$
$223$	166.212	+	95.9625i	0.745345	+	0.430325i	−0.0786645	+	0.996901i	$0.525066\pi$
$224$	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
$227$		−	224.779i		−	0.990216i	−0.868831	−	0.495108i	$-0.835128\pi$
$227$		−	224.779i		−	0.990216i	0.868831	−	0.495108i	$-0.164872\pi$
$228$	108.920	+	159.953i	0.477718	+	0.701548i
$229$		−	160.148i		−	0.699338i	−0.936873	−	0.349669i	$-0.886294\pi$
$229$		−	160.148i		−	0.699338i	0.936873	−	0.349669i	$-0.113706\pi$
$230$	−94.5200	+	54.5712i	−0.410957	+	0.237266i
$231$	238.570	−	17.3731i	1.03277	−	0.0752083i
$232$	−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	$-0.0108336\pi$
$234$	368.922	+	145.280i	1.57659	+	0.620856i
$235$	31.6263	+	54.7784i	0.134580	+	0.233100i
$236$	−332.215	+	191.804i	−1.40769	+	0.812730i
$237$	339.439	−	231.140i	1.43223	−	0.975275i
$238$	120.357	−	207.728i	0.505700	−	0.872808i
$239$	−110.141	−	190.769i	−0.460839	−	0.798197i	0.538164	−	0.842840i	$-0.319118\pi$
$239$	−110.141	−	190.769i	−0.460839	−	0.798197i	−0.999003	+	0.0446434i	$0.985785\pi$
$240$	64.2908	+	94.4137i	0.267878	+	0.393390i
$241$			263.598i			1.09377i	0.837209	+	0.546883i	$0.184186\pi$
$241$			263.598i			1.09377i	−0.837209	+	0.546883i	$0.815814\pi$
$242$	12.3915	+	21.4627i	0.0512045	+	0.0886889i
$243$	88.1280	+	226.456i	0.362667	+	0.931919i
$244$		−	199.313i		−	0.816858i
$245$	−0.360113	+	117.528i	−0.00146985	+	0.479707i
$246$	32.2395	−	66.8478i	0.131055	−	0.271739i
$247$	248.751			1.00709
$248$	3.24911	+	1.87587i	0.0131012	+	0.00756400i
$249$	−28.3919	+	58.8699i	−0.114024	+	0.236425i
$250$	260.467	−	150.381i	1.04187	−	0.601523i
$251$		−	23.0003i		−	0.0916348i	−0.998950	−	0.0458174i	$-0.985411\pi$
$251$		−	23.0003i		−	0.0916348i	0.998950	−	0.0458174i	$-0.0145892\pi$
$252$	−236.162	−	93.4180i	−0.937150	−	0.370706i
$253$	−182.894			−0.722901
$254$	74.0883	+	128.325i	0.291686	+	0.505215i
$255$	71.9790	−	49.0139i	0.282271	−	0.192211i
$256$	−125.978	+	218.201i	−0.492103	+	0.852347i
$257$		−	17.8170i		−	0.0693270i	−0.999399	−	0.0346635i	$-0.988964\pi$
$257$		−	17.8170i		−	0.0693270i	0.999399	−	0.0346635i	$-0.0110359\pi$
$258$	−28.0072	−	376.633i	−0.108555	−	1.45982i
$259$	43.7793	+	25.3655i	0.169032	+	0.0979363i
$260$	−150.311			−0.578120
$261$	−107.069	+	271.889i	−0.410226	+	1.04172i
$262$	457.817	−	264.321i	1.74739	−	1.00886i
$263$	−363.008			−1.38026			−0.690130	−	0.723685i	$-0.742447\pi$
$263$	−363.008			−1.38026			−0.690130	+	0.723685i	$0.742447\pi$
$264$	−0.224228	−	3.01535i	−0.000849349	−	0.0114218i
$265$	141.509	−	81.7004i	0.533997	−	0.308303i
$266$	−317.429	−	0.486310i	−1.19334	−	0.00182823i
$267$	−141.309	+	293.001i	−0.529248	+	1.09738i
$268$	165.018	+	285.820i	0.615740	+	1.06649i
$269$	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	$0.214537\pi$
$270$	−124.599	−	134.751i	−0.461477	−	0.499076i
$271$	−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
$273$	−270.118	+	183.331i	−0.989443	+	0.671542i
$274$	−217.327	−	376.421i	−0.793163	−	1.37380i
$275$	219.234			0.797214
$276$	174.905	+	84.3535i	0.633713	+	0.305629i
$277$	−215.451			−0.777801			−0.388901	−	0.921280i	$-0.627145\pi$
$277$	−215.451			−0.777801			−0.388901	+	0.921280i	$0.627145\pi$
$278$	−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	−0.625713	−	0.780053i	$-0.715192\pi$
$281$	101.916	−	176.523i	0.362689	−	0.628196i	0.988402	+	0.151857i	$0.0485254\pi$
$282$	97.3943	−	201.945i	0.345370	−	0.716116i
$283$	−104.320	−	60.2294i	−0.368624	−	0.212825i	0.304233	−	0.952598i	$-0.401600\pi$
$283$	−104.320	−	60.2294i	−0.368624	−	0.212825i	−0.672857	+	0.739773i	$0.734933\pi$
$284$	227.524	−	394.083i	0.801141	−	1.38762i
$285$	−103.709	−	50.0172i	−0.363892	−	0.175499i
$286$	−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
$290$		−	220.695i		−	0.761018i
$291$	−145.362	+	301.404i	−0.499525	+	1.03575i
$292$			273.732i			0.937437i
$293$	151.688	−	87.5769i	0.517705	−	0.298897i	−0.218290	−	0.975884i	$-0.570048\pi$
$293$	151.688	−	87.5769i	0.517705	−	0.298897i	0.735995	+	0.676987i	$0.236715\pi$
$294$	345.054	−	233.419i	1.17365	−	0.793943i
$295$	114.122	−	197.665i	0.386854	−	0.670051i
$296$	0.319789	−	0.553891i	0.00108037	−	0.00187125i
$297$	−67.9186	−	299.952i	−0.228682	−	1.00994i
$298$	159.285	+	275.890i	0.534513	+	0.925804i
$299$	216.168	−	124.805i	0.722969	−	0.417406i
$300$	−209.657	−	101.114i	−0.698858	−	0.337047i
$301$	269.059	+	155.891i	0.893884	+	0.517912i
$302$	39.9541	+	69.2026i	0.132298	+	0.229148i
$303$	−229.953	+	17.0998i	−0.758921	+	0.0564350i
$304$		−	254.009i		−	0.835555i
$305$	59.2950	+	102.702i	0.194410	+	0.336728i
$306$	−287.203	−	113.100i	−0.938572	−	0.369607i
$307$			18.3665i			0.0598259i	0.999553	+	0.0299129i	$0.00952300\pi$
$307$			18.3665i			0.0598259i	−0.999553	+	0.0299129i	$0.990477\pi$
$308$	278.116	+	161.139i	0.902974	+	0.523179i
$309$	−451.097	+	33.5446i	−1.45986	+	0.108558i
$310$	−288.206			−0.929698
$311$	353.193	+	203.916i	1.13567	+	0.655679i	0.945355	−	0.326044i	$-0.105716\pi$
$311$	353.193	+	203.916i	1.13567	+	0.655679i	0.190315	+	0.981723i	$0.439049\pi$
$312$	2.32266	+	3.41092i	0.00744442	+	0.0109324i
$313$	−348.791	+	201.374i	−1.11435	+	0.643369i	−0.939952	−	0.341307i	$-0.889130\pi$
$313$	−348.791	+	201.374i	−1.11435	+	0.643369i	−0.174396	+	0.984676i	$0.555797\pi$
$314$		−	29.0495i		−	0.0925145i
$315$	149.481	−	22.1209i	0.474541	−	0.0702252i
$316$	551.826			1.74628
$317$	148.273	+	256.817i	0.467739	+	0.810149i	0.999320	−	0.0368589i	$-0.0117352\pi$
$317$	148.273	+	256.817i	0.467739	+	0.810149i	−0.531581	+	0.847007i	$0.678402\pi$
$318$	−521.684	−	251.599i	−1.64052	−	0.791192i
$319$	184.914	−	320.280i	0.579667	−	1.00401i
$320$			155.894i			0.487169i
$321$	−206.997	−	99.8311i	−0.644851	−	0.311000i
$322$	−276.094	+	158.840i	−0.857435	+	0.493290i
$323$	−193.651			−0.599539
$324$	−73.3907	+	318.175i	−0.226514	+	0.982020i
$325$	−259.119	+	149.602i	−0.797289	+	0.460315i
$326$	503.541			1.54460
$327$	−62.4806	+	42.5460i	−0.191072	+	0.130110i
$328$	0.668937	−	0.386211i	0.00203944	−	0.00117747i
$329$	92.0543	+	160.008i	0.279800	+	0.486348i
$330$	130.736	+	191.991i	0.396169	+	0.581791i
$331$	−266.479	−	461.556i	−0.805074	−	1.39443i	−0.916241	−	0.400627i	$-0.868792\pi$
$331$	−266.479	−	461.556i	−0.805074	−	1.39443i	0.111167	−	0.993802i	$-0.464541\pi$
$332$	−76.0588	+	43.9126i	−0.229093	+	0.132267i
$333$	23.8361	−	60.5288i	0.0715798	−	0.181768i
$334$	152.955	+	88.3086i	0.457949	+	0.264397i
$335$	−170.061	−	98.1846i	−0.507644	−	0.293088i
$336$	187.206	+	275.827i	0.557161	+	0.820914i
$337$	149.044	+	258.152i	0.442267	+	0.766029i	0.997857	−	0.0654274i	$-0.0208411\pi$
$337$	149.044	+	258.152i	0.442267	+	0.766029i	−0.555590	+	0.831456i	$0.687508\pi$
$338$	205.926			0.609250
$339$	−183.868	+	125.204i	−0.542382	+	0.369334i
$340$	117.016			0.344165
$341$	−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
$345$	−115.220	+	8.56797i	−0.333970	+	0.0248347i
$346$	216.008	+	124.712i	0.624300	+	0.360439i
$347$	90.4019	−	156.581i	0.260524	−	0.451241i	−0.705857	−	0.708354i	$-0.749438\pi$
$347$	90.4019	−	156.581i	0.260524	−	0.451241i	0.966381	+	0.257113i	$0.0827712\pi$
$348$	−324.554	+	221.004i	−0.932627	+	0.635070i
$349$	151.888	+	87.6925i	0.435209	+	0.251268i	0.701563	−	0.712607i	$-0.252486\pi$
$349$	151.888	+	87.6925i	0.435209	+	0.251268i	−0.266354	+	0.963875i	$0.585819\pi$
$350$	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
$353$		−	39.3099i		−	0.111359i	−0.998449	−	0.0556797i	$-0.982267\pi$
$353$		−	39.3099i		−	0.111359i	0.998449	−	0.0556797i	$-0.0177326\pi$
$354$	−806.800	+	59.9954i	−2.27910	+	0.169479i
$355$			270.750i			0.762676i
$356$	−378.552	+	218.557i	−1.06335	+	0.613924i
$357$	210.285	−	142.722i	0.589033	−	0.399781i
$358$	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	$0.278758\pi$
$360$	−0.282518	−	1.88911i	−0.000784773	−	0.00524752i
$361$	−52.4771	−	90.8930i	−0.145366	−	0.251781i
$362$	554.302	−	320.026i	1.53122	−	0.884050i
$363$	1.94553	+	26.1630i	0.00535959	+	0.0720742i
$364$	−438.673	−	0.672057i	−1.20514	−	0.00184631i
$365$	−81.4341	−	141.048i	−0.223107	−	0.386433i
$366$	182.601	−	378.618i	0.498909	−	1.03448i
$367$		−	396.795i		−	1.08119i	−0.841284	−	0.540593i	$-0.818200\pi$
$367$		−	396.795i		−	1.08119i	0.841284	−	0.540593i	$-0.181800\pi$
$368$	−127.442	−	220.737i	−0.346311	−	0.599828i
$369$	61.4807	−	48.9138i	0.166614	−	0.132558i
$370$			49.1319i			0.132789i
$371$	413.350	−	237.804i	1.11415	−	0.640981i
$372$	288.610	+	423.836i	0.775834	+	1.13935i
$373$	373.141			1.00038			0.500189	−	0.865916i	$-0.333264\pi$
$373$	373.141			1.00038			0.500189	+	0.865916i	$0.333264\pi$
$374$	338.320	+	195.329i	0.904599	+	0.522271i
$375$	317.509	−	23.6106i	0.846690	−	0.0629617i
$376$	2.02083	−	1.16673i	0.00537455	−	0.00310300i
$377$			504.731i			1.33881i
$378$	−363.031	−	393.817i	−0.960399	−	1.04184i
$379$	548.285			1.44666			0.723331	−	0.690502i	$-0.242610\pi$
$379$	548.285			1.44666			0.723331	+	0.690502i	$0.242610\pi$
$380$	−77.3595	−	133.991i	−0.203578	−	0.352607i
$381$	11.6323	+	156.427i	0.0305309	+	0.410570i
$382$	147.210	−	254.975i	0.385366	−	0.667474i
$383$			4.66627i			0.0121835i	0.999981	+	0.00609174i	$0.00193907\pi$
$383$			4.66627i			0.0121835i	−0.999981	+	0.00609174i	$0.998061\pi$
$384$	7.02105	−	4.78097i	0.0182840	−	0.0124504i
$385$	−191.245	−	0.292993i	−0.496741	−	0.000761020i
$386$	−460.068			−1.19189
$387$	146.492	−	371.998i	0.378532	−	0.961236i
$388$	−389.409	+	224.825i	−1.00363	+	0.579447i
$389$	−672.626			−1.72912			−0.864558	−	0.502533i	$-0.832401\pi$
$389$	−672.626			−1.72912			−0.864558	+	0.502533i	$0.832401\pi$
$390$	−285.533	−	137.707i	−0.732136	−	0.353096i
$391$	−168.285	+	97.1594i	−0.430397	+	0.248490i
$392$	4.33574	+	0.0132849i	0.0110606	+	3.38902e-5i
$393$	558.077	−	41.4998i	1.42004	−	0.105597i
$394$	427.351	+	740.194i	1.08465	+	1.87867i
$395$	−284.344	+	164.166i	−0.719858	+	0.415610i
$396$	151.423	−	384.520i	0.382382	−	0.971011i
$397$	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
$399$	−302.445	−	146.435i	−0.758007	−	0.367006i
$400$	152.765	+	264.596i	0.381911	+	0.661490i
$401$	−298.393			−0.744122			−0.372061	−	0.928208i	$-0.621349\pi$
$401$	−298.393			−0.744122			−0.372061	+	0.928208i	$0.621349\pi$
$402$	51.6169	+	694.128i	0.128400	+	1.72669i
$403$	659.130			1.63556
$404$	−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
$408$	−1.80817	−	2.65538i	−0.00443180	−	0.00650828i
$409$	−570.795	−	329.549i	−1.39559	−	0.805743i	−0.401661	−	0.915789i	$-0.631567\pi$
$409$	−570.795	−	329.549i	−1.39559	−	0.805743i	−0.993927	+	0.110046i	$0.964900\pi$
$410$	−29.6684	+	51.3872i	−0.0723620	+	0.125335i
$411$	−34.1215	−	458.856i	−0.0830207	−	1.11644i
$412$	−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
$416$		−	704.840i		−	1.69433i
$417$	−154.076	−	226.267i	−0.369486	−	0.542606i
$418$		−	516.529i		−	1.23572i
$419$	−485.296	+	280.186i	−1.15822	+	0.668701i	−0.950878	−	0.309566i	$-0.899816\pi$
$419$	−485.296	+	280.186i	−1.15822	+	0.668701i	−0.207346	+	0.978268i	$0.566483\pi$
$420$	182.756	+	88.4855i	0.435134	+	0.210680i
$421$	57.9969	−	100.454i	0.137760	−	0.238607i	−0.788889	−	0.614536i	$-0.789343\pi$
$421$	57.9969	−	100.454i	0.137760	−	0.238607i	0.926648	+	0.375929i	$0.122676\pi$
$422$	60.1353	−	104.157i	0.142501	−	0.246818i
$423$	185.731	−	147.767i	0.439080	−	0.349330i
$424$	−3.01401	−	5.22042i	−0.00710851	−	0.0123123i
$425$	201.722	−	116.464i	0.474641	−	0.274034i
$426$	793.246	−	540.159i	1.86208	−	1.26798i
$427$	172.589	+	299.993i	0.404190	+	0.702561i
$428$	−154.405	−	267.437i	−0.360759	−	0.624852i
$429$	−298.994	−	439.085i	−0.696955	−	1.02351i
$430$			301.955i			0.702222i
$431$	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	$0.711272\pi$
$432$	314.689	−	290.981i	0.728447	−	0.673568i
$433$			117.316i			0.270937i	0.990782	+	0.135468i	$0.0432539\pi$
$433$			117.316i			0.270937i	−0.990782	+	0.135468i	$0.956746\pi$
$434$	−841.110	−	1.28860i	−1.93804	−	0.00296913i
$435$	101.488	−	210.432i	0.233305	−	0.483753i
$436$	−101.575			−0.232969
$437$	222.507	+	128.464i	0.509169	+	0.293969i
$438$	−250.779	+	519.984i	−0.572555	+	1.18718i
$439$	−187.788	+	108.419i	−0.427763	+	0.246969i	−0.698393	−	0.715714i	$-0.746101\pi$
$439$	−187.788	+	108.419i	−0.427763	+	0.246969i	0.270630	+	0.962683i	$0.412768\pi$
$440$			2.41748i			0.00549427i
$441$	436.347	−	63.8900i	0.989450	−	0.144875i
$442$	−533.160			−1.20625
$443$	74.8709	+	129.680i	0.169009	+	0.292732i	0.938072	−	0.346441i	$-0.112610\pi$
$443$	74.8709	+	129.680i	0.169009	+	0.292732i	−0.769063	+	0.639173i	$0.779277\pi$
$444$	72.2534	−	49.2008i	0.162733	−	0.110813i
$445$	130.040	−	225.235i	0.292224	−	0.506147i
$446$			543.904i			1.21952i
$447$	25.0086	+	336.308i	0.0559477	+	0.752368i
$448$	−0.697019	+	454.966i	−0.00155585	+	1.01555i
$449$	−263.767			−0.587455			−0.293727	−	0.955889i	$-0.594896\pi$
$449$	−263.767			−0.587455			−0.293727	+	0.955889i	$0.594896\pi$
$450$	−305.632	−	384.155i	−0.679182	−	0.853677i
$451$	−86.1116	+	49.7166i	−0.190935	+	0.110236i
$452$	−298.913			−0.661312
$453$	6.27302	+	84.3577i	0.0138477	+	0.186220i
$454$	551.668	−	318.505i	1.21513	−	0.701554i
$455$	226.239	−	130.157i	0.497228	−	0.286060i
$456$	−1.84518	+	3.82594i	−0.00404646	+	0.00839023i
$457$	109.396	+	189.480i	0.239379	+	0.414617i	0.960536	−	0.278154i	$-0.0897227\pi$
$457$	109.396	+	189.480i	0.239379	+	0.414617i	−0.721157	+	0.692772i	$0.756389\pi$
$458$	393.047	−	226.926i	0.858180	−	0.495471i
$459$	−221.838	−	239.912i	−0.483307	−	0.522685i
$460$	−134.453	−	77.6263i	−0.292289	−	0.168753i
$461$	334.892	+	193.350i	0.726446	+	0.419414i	0.817121	−	0.576467i	$-0.195569\pi$
$461$	334.892	+	193.350i	0.726446	+	0.419414i	−0.0906743	+	0.995881i	$0.528902\pi$
$462$	380.685	+	560.897i	0.823994	+	1.21406i
$463$	241.881	+	418.950i	0.522421	+	0.904860i	0.999660	+	0.0260863i	$0.00830447\pi$
$463$	241.881	+	418.950i	0.522421	+	0.904860i	−0.477238	+	0.878774i	$0.658362\pi$
$464$	515.399			1.11077
$465$	−274.804	−	132.533i	−0.590977	−	0.285018i
$466$	698.843			1.49966
$467$	−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
$471$	13.3586	−	27.6987i	0.0283622	−	0.0588083i
$472$	−7.29207	−	4.21008i	−0.0154493	−	0.00891966i
$473$	−252.999	+	438.208i	−0.534882	+	0.926443i
$474$	1048.25	+	505.555i	2.21151	+	1.06657i
$475$	−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
$479$			455.647i			0.951246i	0.879649	+	0.475623i	$0.157777\pi$
$479$			455.647i			0.951246i	−0.879649	+	0.475623i	$0.842223\pi$
$480$	−141.724	+	293.862i	−0.295259	+	0.612212i
$481$		−	112.365i		−	0.233607i
$482$	−646.939	+	373.510i	−1.34220	+	0.774918i
$483$	−336.298	+	24.4899i	−0.696270	+	0.0507037i
$484$	−17.6267	+	30.5303i	−0.0364187	+	0.0630790i
$485$	133.769	−	231.695i	0.275813	−	0.477722i
$486$	−430.909	+	537.171i	−0.886644	+	1.10529i
$487$	−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	$0.941507\pi$
$488$	3.78878	−	2.18745i	0.00776389	−	0.00448248i
$489$	480.126	+	231.556i	0.981852	+	0.473530i
$490$	−288.956	+	165.650i	−0.589706	+	0.338062i
$491$	−155.221	−	268.850i	−0.316132	−	0.547557i	0.663545	−	0.748136i	$-0.269051\pi$
$491$	−155.221	−	268.850i	−0.316132	−	0.547557i	−0.979678	+	0.200579i	$0.935718\pi$
$492$	105.280	−	7.82885i	0.213984	−	0.0159123i
$493$		−	392.929i		−	0.797017i
$494$	352.473	+	610.501i	0.713508	+	1.23583i
$495$	36.3683	+	243.183i	0.0734713	+	0.491279i
$496$		−	673.061i		−	1.35698i
$497$	−1.21055	+	790.165i	−0.00243572	+	1.58987i
$498$	−184.713	+	13.7356i	−0.370909	+	0.0275816i
$499$	−774.220			−1.55154			−0.775771	−	0.631014i	$-0.782639\pi$
$499$	−774.220			−1.55154			−0.775771	+	0.631014i	$0.782639\pi$
$500$	370.509	+	213.914i	0.741019	+	0.427827i
$501$	105.233	+	154.539i	0.210046	+	0.308462i
$502$	56.4489	−	32.5908i	0.112448	−	0.0649219i
$503$		−	106.472i		−	0.211674i	−0.994384	−	0.105837i	$-0.966248\pi$
$503$		−	106.472i		−	0.211674i	0.994384	−	0.105837i	$-0.0337521\pi$
$504$	−0.816063	−	5.51449i	−0.00161917	−	0.0109414i
$505$	184.359			0.365067
$506$	−259.155	−	448.870i	−0.512165	−	0.887096i
$507$	196.351	+	94.6964i	0.387279	+	0.186778i
$508$	−105.389	+	182.539i	−0.207459	+	0.359329i
$509$		−	338.626i		−	0.665276i	−0.943055	−	0.332638i	$-0.892061\pi$
$509$		−	338.626i		−	0.665276i	0.943055	−	0.332638i	$-0.107939\pi$
$510$	222.285	+	107.204i	0.435853	+	0.210204i
$511$	−237.029	−	412.003i	−0.463853	−	0.806268i
$512$	−725.356			−1.41671
$513$	−128.057	+	412.624i	−0.249623	+	0.804336i
$514$	43.7277	−	25.2462i	0.0850734	−	0.0491172i
$515$	361.655			0.702243
$516$	444.056	−	302.379i	0.860573	−	0.586005i
$517$	−260.140	+	150.192i	−0.503172	+	0.290506i
$518$	−0.219674	+	143.388i	−0.000424081	+	0.276811i
$519$	148.613	+	218.245i	0.286346	+	0.420511i
$520$	−1.64966	−	2.85729i	−0.00317241	−	0.00549478i
$521$	−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	$0.363057\pi$
$522$	−819.000	+	122.482i	−1.56897	+	0.234641i
$523$	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
$525$	403.119	−	29.3559i	0.767846	−	0.0559159i
$526$	−514.372	−	890.919i	−0.977894	−	1.69376i
$527$	−513.128			−0.973677
$528$	−448.365	+	305.313i	−0.849177	+	0.578245i
$529$	−271.185			−0.512637
$530$	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
$534$	−919.333	+	68.3635i	−1.72160	+	0.128022i
$535$	159.123	+	91.8696i	0.297426	+	0.171719i
$536$	−3.62213	+	6.27371i	−0.00675770	+	0.0117047i
$537$	32.1170	−	21.8700i	0.0598083	−	0.0407263i
$538$	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	$-0.0127723\pi$
$542$		−	270.051i		−	0.498249i
$543$	675.691	−	50.2459i	1.24437	−	0.0925338i
$544$			548.713i			1.00866i
$545$	52.3392	−	30.2181i	0.0960352	−	0.0554460i
$546$	−832.692	−	403.166i	−1.52508	−	0.738400i
$547$	110.283	−	191.016i	0.201615	−	0.349207i	−0.747434	−	0.664336i	$-0.768714\pi$
$547$	110.283	−	191.016i	0.201615	−	0.349207i	0.949049	+	0.315129i	$0.102048\pi$
$548$	309.143	−	535.451i	0.564129	−	0.977101i
$549$	348.219	−	277.042i	0.634279	−	0.504630i
$550$	310.648	+	538.058i	0.564815	+	0.978288i
$551$	−449.928	+	259.766i	−0.816566	+	0.471445i
$552$	0.316081	+	4.25057i	0.000572611	+	0.00770030i
$553$	−830.572	+	477.836i	−1.50194	+	0.864079i
$554$	−305.288	−	528.774i	−0.551061	−	0.954465i
$555$	−22.5936	+	46.8472i	−0.0407092	+	0.0844094i
$556$		−	367.842i		−	0.661586i
$557$	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	$0.728711\pi$
$558$	159.950	+	1069.53i	0.286649	+	1.91673i
$559$		−	690.574i		−	1.23537i
$560$	−132.908	−	231.020i	−0.237336	−	0.412536i
$561$	232.764	+	341.824i	0.414910	+	0.609313i
$562$	577.646			1.02784
$563$	854.592	+	493.399i	1.51792	+	0.876374i	0.999778	+	0.0210827i	$0.00671133\pi$
$563$	854.592	+	493.399i	1.51792	+	0.876374i	0.518147	+	0.855292i	$0.326622\pi$
$564$	318.047	−	23.6507i	0.563913	−	0.0419338i
$565$	154.024	−	88.9255i	0.272608	−	0.157390i
$566$		−	341.373i		−	0.603133i
$567$	−165.050	−	542.446i	−0.291094	−	0.956694i
$568$	9.98825			0.0175849
$569$	−41.8937	−	72.5620i	−0.0736269	−	0.127525i	0.826861	−	0.562406i	$-0.190124\pi$
$569$	−41.8937	−	72.5620i	−0.0736269	−	0.127525i	−0.900488	+	0.434880i	$0.856791\pi$
$570$	−24.1977	−	325.403i	−0.0424520	−	0.570883i
$571$	175.350	−	303.715i	0.307093	−	0.531901i	−0.670632	−	0.741790i	$-0.733977\pi$
$571$	175.350	−	303.715i	0.307093	−	0.531901i	0.977725	+	0.209889i	$0.0673103\pi$
$572$		−	713.820i		−	1.24794i
$573$	257.616	−	175.423i	0.449592	−	0.306148i
$574$	−86.8150	+	149.837i	−0.151246	+	0.261041i
$575$	−309.041			−0.537463
$576$	578.523	−	86.5189i	1.00438	−	0.150206i
$577$	−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	$0.559792\pi$
$578$	−403.947			−0.698871
$579$	−438.674	−	211.565i	−0.757641	−	0.365397i
$580$	271.875	−	156.967i	0.468750	−	0.270633i
$581$	76.4541	−	131.955i	0.131590	−	0.227117i
$582$	−945.699	+	70.3242i	−1.62491	+	0.120832i
$583$	387.991	+	672.019i	0.665507	+	1.15269i
$584$	−5.20340	+	3.00419i	−0.00890994	+	0.00514416i
$585$	−208.930	−	262.608i	−0.357145	−	0.448902i
$586$	429.874	+	248.188i	0.733573	+	0.423528i
$587$	−112.348	−	64.8642i	−0.191394	−	0.110501i	0.401241	−	0.915972i	$-0.368579\pi$
$587$	−112.348	−	64.8642i	−0.191394	−	0.110501i	−0.592635	+	0.805471i	$0.701912\pi$
$588$	532.966	+	259.056i	0.906405	+	0.440571i
$589$	339.229	+	587.562i	0.575941	+	0.997559i
$590$	646.830			1.09632
$591$	67.0965	+	902.294i	0.113530	+	1.52672i
$592$	−114.740			−0.193818
$593$	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
$597$	97.5990	+	143.328i	0.163482	+	0.240081i
$598$	612.607	+	353.689i	1.02443	+	0.591453i
$599$	141.278	−	244.701i	0.235857	−	0.408516i	−0.723664	−	0.690152i	$-0.757544\pi$
$599$	141.278	−	244.701i	0.235857	−	0.408516i	0.959521	+	0.281636i	$0.0908770\pi$
$600$	−0.378885	−	5.09513i	−0.000631474	−	0.00849188i
$601$	−159.905	−	92.3214i	−0.266065	−	0.153613i	0.361033	−	0.932553i	$-0.382424\pi$
$601$	−159.905	−	92.3214i	−0.266065	−	0.153613i	−0.627098	+	0.778940i	$0.715758\pi$
$602$	−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
$605$		−	20.9754i		−	0.0346702i
$606$	−367.804	−	540.136i	−0.606938	−	0.891313i
$607$		−	1045.66i		−	1.72267i	−0.508040	−	0.861333i	$-0.669630\pi$
$607$		−	1045.66i		−	1.72267i	0.508040	−	0.861333i	$-0.330370\pi$
$608$	628.310	−	362.755i	1.03340	−	0.596636i
$609$	297.126	−	613.679i	0.487892	−	1.00768i
$610$	−168.038	+	291.051i	−0.275473	+	0.477133i
$611$	204.978	−	355.032i	0.335479	−	0.581067i
$612$	−64.9422	−	434.247i	−0.106115	−	0.709554i
$613$	−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	$0.860714\pi$
$614$	−45.0764	+	26.0248i	−0.0734143	+	0.0423857i
$615$	−51.9195	+	35.3545i	−0.0844220	+	0.0574869i
$616$	−0.0108088	+	7.05524i	−1.75468e−5	+	0.0114533i
$617$	269.908	+	467.495i	0.437452	+	0.757690i	0.997492	−	0.0707759i	$-0.0225475\pi$
$617$	269.908	+	467.495i	0.437452	+	0.757690i	−0.560040	+	0.828466i	$0.689214\pi$
$618$	−721.519	−	1059.58i	−1.16751	−	1.71453i
$619$			1117.89i			1.80596i	0.429678	+	0.902982i	$0.358627\pi$
$619$			1117.89i			1.80596i	−0.429678	+	0.902982i	$0.641373\pi$
$620$	−204.984	−	355.042i	−0.330619	−	0.572649i
$621$	95.7409	+	422.825i	0.154172	+	0.680877i
$622$			1155.77i			1.85816i
$623$	380.519	−	656.753i	0.610785	−	1.05418i
$624$	321.594	−	666.818i	0.515376	−	1.06862i
$625$	226.620			0.362593
$626$	−988.452	−	570.683i	−1.57900	−	0.911635i
$627$	237.529	−	492.510i	0.378834	−	0.785502i
$628$	35.7862	−	20.6612i	0.0569845	−	0.0329000i
$629$			87.4754i			0.139071i
$630$	266.100	+	335.520i	0.422381	+	0.532572i
$631$	−710.879			−1.12659			−0.563296	−	0.826255i	$-0.690467\pi$
$631$	−710.879			−1.12659			−0.563296	+	0.826255i	$0.690467\pi$
$632$	6.05625	+	10.4897i	0.00958268	+	0.0165977i
$633$	105.236	−	71.6603i	0.166250	−	0.113207i
$634$	−420.198	+	727.805i	−0.662773	+	1.14796i
$635$		−	125.411i		−	0.197498i
$636$	−61.0968	−	821.611i	−0.0960641	−	1.29184i
$637$	660.843	−	378.843i	1.03743	−	0.594730i
$638$	1048.07			1.64274
$639$	1004.75	−	150.262i	1.57239	−	0.235152i
$640$	−5.88145	+	3.39566i	−0.00918977	+	0.00530571i
$641$	1070.78			1.67048			0.835240	−	0.549885i	$-0.185328\pi$
$641$	1070.78			1.67048			0.835240	+	0.549885i	$0.185328\pi$
$642$	−48.2970	−	649.484i	−0.0752290	−	1.01166i
$643$	−664.371	+	383.575i	−1.03324	+	0.596539i	−0.917910	−	0.396788i	$-0.870125\pi$
$643$	−664.371	+	383.575i	−1.03324	+	0.596539i	−0.115326	+	0.993328i	$0.536791\pi$
$644$	−392.044	−	227.148i	−0.608764	−	0.352715i
$645$	−138.856	+	287.914i	−0.215280	+	0.446378i
$646$	−274.398	−	475.271i	−0.424764	−	0.735713i
$647$	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	$0.329125\pi$
$648$	−6.85368	+	2.09685i	−0.0105767	+	0.00323588i
$649$	938.701	+	541.959i	1.44638	+	0.835068i
$650$	−734.328	−	423.965i	−1.12974	−	0.652253i
$651$	−801.405	−	388.018i	−1.23104	−	0.596034i
$652$	358.138	+	620.314i	0.549292	+	0.951402i
$653$	−968.287			−1.48283			−0.741414	−	0.671048i	$-0.765845\pi$
$653$	−968.287			−1.48283			−0.741414	+	0.671048i	$0.765845\pi$
$654$	−192.952	−	93.0575i	−0.295034	−	0.142290i
$655$	−447.423			−0.683088
$656$	−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	−0.248665	−	0.968589i	$-0.579992\pi$
$659$	470.849	−	815.535i	0.714490	−	1.23753i	0.963156	−	0.268944i	$-0.0866747\pi$
$660$	−143.530	+	297.606i	−0.217470	+	0.450918i
$661$	4.75875	+	2.74747i	0.00719933	+	0.00415653i	0.503595	−	0.863940i	$-0.332010\pi$
$661$	4.75875	+	2.74747i	0.00719933	+	0.00415653i	−0.496396	+	0.868096i	$0.665344\pi$
$662$	755.187	−	1308.02i	1.14077	−	1.97586i
$663$	−508.368	−	245.177i	−0.766769	−	0.369799i
$664$	−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
$668$			251.234i			0.376099i
$669$	−250.117	+	518.612i	−0.373867	+	0.775205i
$670$		−	556.499i		−	0.830595i
$671$	−487.726	+	281.589i	−0.726864	+	0.419655i
$672$	−414.927	+	856.982i	−0.617451	+	1.27527i
$673$	329.366	−	570.479i	0.489400	−	0.847666i	−0.510525	−	0.859863i	$-0.670549\pi$
$673$	329.366	−	570.479i	0.489400	−	0.847666i	0.999926	+	0.0121964i	$0.00388233\pi$
$674$	−422.382	+	731.587i	−0.626679	+	1.08544i
$675$	−114.764	−	506.838i	−0.170021	−	0.750871i
$676$	146.463	+	253.681i	0.216661	+	0.375268i
$677$	−730.516	+	421.763i	−1.07905	+	0.622989i	−0.930639	−	0.365937i	$-0.880748\pi$
$677$	−730.516	+	421.763i	−1.07905	+	0.622989i	−0.148409	+	0.988926i	$0.547415\pi$
$678$	−567.819	−	273.849i	−0.837491	−	0.403907i
$679$	391.432	−	675.588i	0.576484	−	0.994975i
$680$	1.28424	+	2.22438i	0.00188860	+	0.00327114i
$681$	672.481	−	50.0071i	0.987490	−	0.0734319i
$682$		−	1368.68i		−	2.00686i
$683$	−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	$0.973131\pi$
$684$	−454.306	+	361.444i	−0.664190	+	0.528427i
$685$			367.875i			0.537044i
$686$	−844.038	+	482.147i	−1.23038	+	0.702838i
$687$	479.122	−	35.6286i	0.697412	−	0.0518611i
$688$	−705.170			−1.02496
$689$	−917.155	−	529.520i	−1.33114	−	0.768534i
$690$	−184.291	−	270.639i	−0.267088	−	0.392230i
$691$	−976.744	+	563.924i	−1.41352	+	0.816098i	−0.995718	−	0.0924390i	$-0.970534\pi$
$691$	−976.744	+	563.924i	−1.41352	+	0.816098i	−0.417805	+	0.908537i	$0.637200\pi$
$692$			354.801i			0.512718i
$693$	105.051	+	709.875i	0.151589	+	1.02435i
$694$	512.388			0.738311
$695$	109.432	+	189.541i	0.157455	+	0.272721i
$696$	−7.76307	−	3.74399i	−0.0111538	−	0.00537930i
$697$	−52.8222	+	91.4907i	−0.0757851	+	0.131264i
$698$			497.031i			0.712078i
$699$	666.346	+	321.367i	0.953285	+	0.459752i
$700$	469.941	+	272.281i	0.671344	+	0.388973i
$701$	352.754			0.503216			0.251608	−	0.967829i	$-0.419041\pi$
$701$	352.754			0.503216			0.251608	+	0.967829i	$0.419041\pi$
$702$	−352.566	+	1136.04i	−0.502231	+	1.61829i
$703$	100.165	−	57.8301i	0.142482	−	0.0822618i
$704$	−740.332			−1.05161
$705$	−156.847	+	106.804i	−0.222478	+	0.151496i
$706$	96.4769	−	55.7009i	0.136653	−	0.0788965i
$707$	538.038	+	0.824287i	0.761015	+	0.00116589i
$708$	−647.737	−	951.229i	−0.914883	−	1.34354i
$709$	396.038	+	685.959i	0.558587	+	0.967502i	0.997615	+	0.0690279i	$0.0219898\pi$
$709$	396.038	+	685.959i	0.558587	+	0.967502i	−0.439027	+	0.898474i	$0.644677\pi$
$710$	−664.492	+	383.645i	−0.935905	+	0.540345i
$711$	767.027	+	964.091i	1.07880	+	1.35596i
$712$	−8.30917	−	4.79730i	−0.0116702	−	0.00673778i
$713$	589.589	+	340.399i	0.826913	+	0.477418i
$714$	648.245	+	313.862i	0.907906	+	0.439583i
$715$	212.359	+	367.816i	0.297005	+	0.514428i
$716$	52.2126			0.0729227
$717$	546.228	−	371.953i	0.761824	−	0.518762i
$718$	−701.816			−0.977460
$719$	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
$723$	−788.616	+	58.6432i	−1.09076	+	0.0811109i
$724$	788.483	+	455.231i	1.08906	+	0.628772i
$725$	312.454	−	541.186i	0.430971	−	0.746464i
$726$	−61.4541	+	41.8470i	−0.0846475	+	0.0576405i
$727$	−113.839	−	65.7248i	−0.156587	−	0.0904055i	0.419659	−	0.907682i	$-0.362150\pi$
$727$	−113.839	−	65.7248i	−0.156587	−	0.0904055i	−0.576246	+	0.817276i	$0.695483\pi$
$728$	−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
$731$			537.607i			0.735440i
$732$	596.294	−	44.3417i	0.814609	−	0.0605761i
$733$		−	1279.26i		−	1.74524i	−0.488400	−	0.872620i	$-0.662419\pi$
$733$		−	1279.26i		−	1.74524i	0.488400	−	0.872620i	$-0.337581\pi$
$734$	973.840	−	562.247i	1.32676	−	0.766004i
$735$	−351.694	+	25.0694i	−0.478495	+	0.0341080i
$736$	364.006	−	630.477i	0.494573	−	0.856626i
$737$	466.273	−	807.609i	0.632664	−	1.09581i
$738$	207.164	+	81.5805i	0.280710	+	0.110543i
$739$	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	$0.829053\pi$
$740$	−60.5258	+	34.9446i	−0.0817916	+	0.0472224i
$741$	55.3402	+	744.199i	0.0746831	+	1.00432i
$742$	1169.34	+	677.509i	1.57593	+	0.913085i
$743$	729.663	+	1263.81i	0.982050	+	1.70096i	0.654374	+	0.756171i	$0.272932\pi$
$743$	729.663	+	1263.81i	0.982050	+	1.70096i	0.327677	+	0.944790i	$0.393734\pi$
$744$	−4.88929	+	10.1378i	−0.00657162	+	0.0136261i
$745$		−	269.626i		−	0.361914i
$746$	528.729	+	915.786i	0.708753	+	1.22760i
$747$	−182.440	−	71.8442i	−0.244230	−	0.0961770i
$748$			555.703i			0.742919i
$749$	463.978	+	268.826i	0.619463	+	0.358914i
$750$	507.847	+	745.795i	0.677130	+	0.994393i
$751$	−989.823			−1.31801			−0.659003	−	0.752140i	$-0.729022\pi$
$751$	−989.823			−1.31801			−0.659003	+	0.752140i	$0.729022\pi$
$752$	−362.536	−	209.310i	−0.482096	−	0.278338i
$753$	68.8110	−	5.11693i	0.0913824	−	0.00679539i
$754$	−1238.74	+	715.189i	−1.64290	+	0.948527i
$755$		−	67.6315i		−	0.0895781i
$756$	226.943	−	727.317i	0.300189	−	0.962060i
$757$	−499.688			−0.660089			−0.330045	−	0.943965i	$-0.607064\pi$
$757$	−499.688			−0.660089			−0.330045	+	0.943965i	$0.607064\pi$
$758$	776.903	+	1345.64i	1.02494	+	1.77525i
$759$	−40.6888	−	547.171i	−0.0536085	−	0.720911i
$760$	1.69803	−	2.94108i	0.00223425	−	0.00386984i
$761$		−	685.947i		−	0.901376i	−0.892682	−	0.450688i	$-0.851179\pi$
$761$		−	685.947i		−	0.901376i	0.892682	−	0.450688i	$-0.148821\pi$
$762$	−367.431	+	250.201i	−0.482193	+	0.328348i
$763$	152.883	−	87.9553i	0.200371	−	0.115276i
$764$	418.806			0.548175
$765$	162.650	+	204.438i	0.212615	+	0.267239i
$766$	−11.4523	+	6.61197i	−0.0149507	+	0.00863182i
$767$	−1479.30			−1.92869
$768$	−680.827	−	328.351i	−0.886494	−	0.427540i
$769$	586.160	−	338.420i	0.762237	−	0.440078i	−0.0678613	−	0.997695i	$-0.521618\pi$
$769$	586.160	−	338.420i	0.762237	−	0.440078i	0.830098	+	0.557617i	$0.188284\pi$
$770$	−270.270	−	469.782i	−0.351000	−	0.610107i
$771$	53.3039	−	3.96379i	0.0691361	−	0.00514111i
$772$	−327.219	−	566.759i	−0.423858	−	0.734144i
$773$	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	$0.227410\pi$
$774$	1120.56	−	167.581i	1.44775	−	0.216513i
$775$	−706.737	−	408.035i	−0.911918	−	0.526496i
$776$	−8.54747	−	4.93489i	−0.0110148	−	0.00635939i
$777$	−66.1473	+	136.619i	−0.0851316	+	0.175829i
$778$	−953.091	−	1650.80i	−1.22505	−	2.12185i
$779$	139.683			0.179311
$780$	−33.4401	−	449.692i	−0.0428719	−	0.576528i
$781$	−1285.78			−1.64632
$782$	−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
$786$	892.630	+	1310.86i	1.13566	+	1.66777i
$787$	−16.0382	−	9.25964i	−0.0203789	−	0.0117657i	0.489776	−	0.871848i	$-0.337079\pi$
$787$	−16.0382	−	9.25964i	−0.0203789	−	0.0117657i	−0.510155	+	0.860083i	$0.670412\pi$
$788$	−607.898	+	1052.91i	−0.771445	+	1.33618i
$789$	−80.7593	−	1086.03i	−0.102356	−	1.37646i
$790$	−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
$794$			301.165i			0.379301i
$795$	275.908	+	405.183i	0.347054	+	0.509664i
$796$			233.009i			0.292724i
$797$	−615.232	+	355.205i	−0.771935	+	0.445677i	−0.833565	−	0.552422i	$-0.813704\pi$
$797$	−615.232	+	355.205i	−0.771935	+	0.445677i	0.0616293	+	0.998099i	$0.480370\pi$
$798$	−69.1643	−	949.774i	−0.0866720	−	1.19019i
$799$	−159.574	+	276.390i	−0.199717	+	0.345920i
$800$	−436.332	+	755.749i	−0.545415	+	0.944686i
$801$	−908.020	−	357.576i	−1.13361	−	0.446411i
$802$	−422.814	−	732.336i	−0.527200	−	0.913137i
$803$	669.829	−	386.726i	0.834159	−	0.481602i
$804$	−818.387	+	557.279i	−1.01789	+	0.693133i
$805$	269.588	+	0.413015i	0.334891	+	0.000513062i
$806$	933.967	+	1617.68i	1.15877	+	2.00705i
$807$	331.221	+	486.412i	0.410435	+	0.602741i
$808$		−	6.80118i		−	0.00841730i
$809$	−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	$-0.413191\pi$
$810$	375.419	−	402.746i	0.463480	−	0.497217i
$811$			199.736i			0.246283i	0.992389	+	0.123142i	$0.0392970\pi$
$811$			199.736i			0.246283i	−0.992389	+	0.123142i	$0.960703\pi$
$812$	794.150	−	456.882i	0.978018	−	0.562663i
$813$	124.184	−	257.493i	0.152748	−	0.316720i
$814$	−233.325			−0.286640
$815$	−369.082	−	213.090i	−0.452861	−	0.261460i
$816$	−250.359	+	519.113i	−0.306812	+	0.636168i
$817$	615.592	−	355.412i	0.753479	−	0.435021i
$818$		−	1867.84i		−	2.28343i
$819$	−608.573	−	767.336i	−0.743068	−	0.936919i
$820$	−84.4055			−0.102934
$821$	−196.680	−	340.660i	−0.239562	−	0.414933i	0.721027	−	0.692907i	$-0.243670\pi$
$821$	−196.680	−	340.660i	−0.239562	−	0.414933i	−0.960589	+	0.277974i	$0.910337\pi$
$822$	1077.80	−	733.928i	1.31120	−	0.892857i
$823$	424.378	−	735.045i	0.515648	−	0.893128i	−0.484187	−	0.874965i	$-0.660885\pi$
$823$	424.378	−	735.045i	0.515648	−	0.893128i	0.999835	−	0.0181639i	$-0.00578208\pi$
$824$		−	13.3418i		−	0.0161915i
$825$	48.7735	+	655.891i	0.0591193	+	0.795019i
$826$	1887.73	+	2.89205i	2.28539	+	0.00350127i
$827$	495.009			0.598559			0.299280	−	0.954165i	$-0.403254\pi$
$827$	495.009			0.598559			0.299280	+	0.954165i	$0.403254\pi$
$828$	−213.452	+	542.036i	−0.257793	+	0.654633i
$829$	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	$0.139767\pi$
$830$	148.088			0.178420
$831$	−47.9318	−	644.573i	−0.0576797	−	0.775660i
$832$	875.021	−	505.193i	1.05171	−	0.607204i
$833$	−514.462	+	294.927i	−0.617601	+	0.354053i
$834$	336.998	−	698.757i	0.404074	−	0.837838i
$835$	−74.7412	−	129.456i	−0.0895105	−	0.155037i
$836$	636.314	−	367.376i	0.761142	−	0.439445i
$837$	−339.319	+	1093.35i	−0.405399	+	1.30628i
$838$	−1375.30	−	794.030i	−1.64117	−	0.947530i
$839$	−787.270	−	454.531i	−0.938343	−	0.541753i	−0.0489028	−	0.998804i	$-0.515572\pi$
$839$	−787.270	−	454.531i	−0.938343	−	0.541753i	−0.889441	+	0.457051i	$0.848906\pi$
$840$	0.323705	+	4.44516i	0.000385363	+	0.00529186i
$841$	−106.581	−	184.604i	−0.126731	−	0.219505i
$842$	328.720			0.390403
$843$	550.784	+	265.634i	0.653362	+	0.315105i
$844$	171.082			0.202704
$845$	−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
$849$	156.982	−	325.499i	0.184903	−	0.383391i
$850$	571.669	+	330.053i	0.672552	+	0.388298i
$851$	58.0295	−	100.510i	0.0681898	−	0.118108i
$852$	1229.61	+	593.020i	1.44321	+	0.696033i
$853$	768.763	+	443.845i	0.901246	+	0.520335i	0.877604	−	0.479386i	$-0.159141\pi$
$853$	768.763	+	443.845i	0.901246	+	0.520335i	0.0236417	+	0.999720i	$0.492474\pi$
$854$	−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
$857$		−	175.131i		−	0.204354i	−0.994766	−	0.102177i	$-0.967419\pi$
$857$		−	175.131i		−	0.204354i	0.994766	−	0.102177i	$-0.0325808\pi$
$858$	653.965	−	1355.98i	0.762197	−	1.58040i
$859$			1377.03i			1.60306i	0.597953	+	0.801531i	$0.295981\pi$
$859$			1377.03i			1.60306i	−0.597953	+	0.801531i	$0.704019\pi$
$860$	−371.980	+	214.763i	−0.432535	+	0.249724i
$861$	−151.682	+	102.947i	−0.176169	+	0.119567i
$862$	−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	$0.822701\pi$
$864$	1169.18	+	362.851i	1.35321	+	0.419966i
$865$	−105.552	−	182.821i	−0.122025	−	0.211354i
$866$	−287.924	+	166.233i	−0.332475	+	0.191955i
$867$	−385.163	−	185.757i	−0.444248	−	0.214253i
$868$	−596.644	−	1037.08i	−0.687377	−	1.19480i
$869$	−779.616	−	1350.33i	−0.897141	−	1.55389i
$870$	660.262	−	49.0985i	0.758922	−	0.0564351i
$871$			1272.72i			1.46121i
$872$	−1.11477	−	1.93085i	−0.00127841	−	0.00221427i
$873$	−934.062	−	367.831i	−1.06994	−	0.421341i
$874$			728.121i			0.833091i
$875$	−742.898	−	1.13814i	−0.849026	−	0.00130073i
$876$	−818.934	+	60.8977i	−0.934856	+	0.0695179i
$877$	−719.054			−0.819902			−0.409951	−	0.912108i	$-0.634454\pi$
$877$	−719.054			−0.819902			−0.409951	+	0.912108i	$0.634454\pi$
$878$	−532.180	−	307.254i	−0.606128	−	0.349948i
$879$	295.753	+	434.326i	0.336466	+	0.494114i
$880$	375.590	−	216.847i	0.426807	−	0.246417i
$881$		−	1065.56i		−	1.20949i	−0.796418	−	0.604747i	$-0.793274\pi$
$881$		−	1065.56i		−	1.20949i	0.796418	−	0.604747i	$-0.206726\pi$
$882$	775.095	+	980.382i	0.878792	+	1.11154i
$883$	−378.403			−0.428543			−0.214271	−	0.976774i	$-0.568738\pi$
$883$	−378.403			−0.428543			−0.214271	+	0.976774i	$0.568738\pi$
$884$	−379.205	−	656.802i	−0.428965	−	0.742989i
$885$	616.752	+	297.448i	0.696895	+	0.336100i
$886$	−212.180	+	367.506i	−0.239481	+	0.414793i
$887$			1758.17i			1.98216i	0.133277	+	0.991079i	$0.457450\pi$
$887$			1758.17i			1.98216i	−0.133277	+	0.991079i	$0.542550\pi$
$888$	1.72824	+	0.833501i	0.00194622	+	0.000938627i
$889$	0.560727	−	366.004i	0.000630739	−	0.411703i
$890$	737.050			0.828146
$891$	882.268	−	269.926i	0.990200	−	0.302947i
$892$	−670.037	+	386.846i	−0.751163	+	0.433684i
$893$	421.978			0.472539
$894$	−789.953	+	537.917i	−0.883617	+	0.601697i
$895$	−26.9040	+	15.5331i	−0.0300604	+	0.0173554i
$896$	−17.1798	+	9.88369i	−0.0191739	+	0.0110309i
$897$	421.474	+	618.952i	0.469871	+	0.690025i
$898$	−373.750	−	647.355i	−0.416203	−	0.720885i
$899$	−1192.20	+	688.317i	−1.32614	+	0.765647i
$900$	255.864	−	649.735i	0.284293	−	0.721928i
$901$	713.998	+	412.227i	0.792451	+	0.457522i
$902$	−244.035	−	140.894i	−0.270549	−	0.156202i
$903$	−406.528	+	839.636i	−0.450198	+	0.929830i
$904$	−3.28055	−	5.68209i	−0.00362893	−	0.00628549i
$905$	−541.717			−0.598583
$906$	−198.147	+	134.928i	−0.218706	+	0.148927i
$907$	742.349			0.818467			0.409233	−	0.912430i	$-0.365796\pi$
$907$	742.349			0.818467			0.409233	+	0.912430i	$0.365796\pi$
$908$	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	−0.563889	−	0.825851i	$-0.690695\pi$
$911$	394.703	−	683.645i	0.433263	−	0.750434i	0.997152	+	0.0754169i	$0.0240288\pi$
$912$	759.928	−	56.5099i	0.833255	−	0.0619626i
$913$	214.911	+	124.079i	0.235390	+	0.135902i
$914$	−310.023	+	536.975i	−0.339193	+	0.587500i
$915$	−294.066	+	200.243i	−0.321383	+	0.218845i
$916$	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	$0.0919363\pi$
$920$		−	3.40778i		−	0.00370410i
$921$	−54.9479	+	4.08604i	−0.0596611	+	0.00443653i
$922$			1095.88i			1.18859i
$923$	1519.70	−	877.398i	1.64648	−	0.950594i
$924$	−420.213	+	867.900i	−0.454776	+	0.939286i
$925$	−69.5596	+	120.481i	−0.0751996	+	0.130250i
$926$	−685.477	+	1187.28i	−0.740256	+	1.28216i
$927$	−200.713	−	1342.10i	−0.216519	−	1.44779i
$928$	736.051	+	1274.88i	0.793159	+	1.37379i
$929$	−978.107	+	564.711i	−1.05286	+	0.607869i	−0.923449	−	0.383722i	$-0.874642\pi$
$929$	−978.107	+	564.711i	−1.05286	+	0.607869i	−0.129412	+	0.991591i	$0.541309\pi$
$930$	−64.1179	−	862.238i	−0.0689440	−	0.927138i
$931$	677.820	+	394.114i	0.728056	+	0.423323i
$932$	497.045	+	860.908i	0.533310	+	0.923721i
$933$	−531.488	+	1102.03i	−0.569655	+	1.18117i
$934$		−	327.373i		−	0.350507i
$935$	−165.320	−	286.342i	−0.176812	−	0.306248i
$936$	−9.68787	+	7.70763i	−0.0103503	+	0.00823464i
$937$		−	736.130i		−	0.785625i	−0.919619	−	0.392812i	$-0.871502\pi$
$937$		−	736.130i		−	0.785625i	0.919619	−	0.392812i	$-0.128498\pi$
$938$	2.48816	−	1624.10i	0.00265263	−	1.73145i
$939$	−680.056	−	998.691i	−0.724234	−	1.06357i
$940$	−254.986			−0.271261
$941$	75.0157	+	43.3103i	0.0797191	+	0.0460259i	0.539330	−	0.842095i	$-0.318678\pi$
$941$	75.0157	+	43.3103i	0.0797191	+	0.0460259i	−0.459611	+	0.888121i	$0.652011\pi$
$942$	86.9087	−	6.46272i	0.0922597	−	0.00686063i
$943$	121.386	−	70.0825i	0.128724	−	0.0743187i
$944$			1510.57i			1.60018i
$945$	99.4353	+	442.286i	0.105223	+	0.468027i
$946$	−1433.97			−1.51582
$947$	−293.684	−	508.676i	−0.310121	−	0.537145i	0.668268	−	0.743921i	$-0.267036\pi$
$947$	−293.684	−	508.676i	−0.310121	−	0.537145i	−0.978388	+	0.206776i	$0.933703\pi$
$948$	122.766	+	1650.92i	0.129500	+	1.74148i
$949$	−527.794	+	914.166i	−0.556158	+	0.963294i
$950$		−	872.795i		−	0.918731i
$951$	−735.343	+	500.730i	−0.773232	+	0.526530i
$952$	3.73803	+	6.49743i	0.00392651	+	0.00682503i
$953$	−396.549			−0.416106			−0.208053	−	0.978118i	$-0.566713\pi$
$953$	−396.549			−0.416106			−0.208053	+	0.978118i	$0.566713\pi$
$954$	636.658	−	1616.72i	0.667357	−	1.69467i
$955$	−215.802	+	124.593i	−0.225970	+	0.130464i
$956$	888.002			0.928873
$957$	999.332	+	481.960i	1.04423	+	0.503616i
$958$	−1118.28	+	645.638i	−1.16730	+	0.673944i
$959$	−1.64481	+	1073.62i	−0.00171513	+	1.11952i
$960$	−466.394	+	34.6821i	−0.485828	+	0.0361272i
$961$	418.375	+	724.646i	0.435353	+	0.754054i
$962$	275.774	−	159.218i	0.286667	−	0.165507i
$963$	252.618	−	641.491i	0.262323	−	0.666139i
$964$	−920.257	−	531.311i	−0.954624	−	0.551152i
$965$	337.217	+	194.693i	0.349448	+	0.201754i
$966$	−536.630	−	790.664i	−0.555517	−	0.818493i
$967$	−163.959	−	283.985i	−0.169554	−	0.293676i	0.768709	−	0.639598i	$-0.220899\pi$
$967$	−163.959	−	283.985i	−0.169554	−	0.293676i	−0.938263	+	0.345922i	$0.887566\pi$
$968$	−0.773805			−0.000799386
$969$	−43.0819	−	579.353i	−0.0444602	−	0.597888i
$970$	758.189			0.781638
$971$	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
$975$	−505.218	−	741.934i	−0.518173	−	0.760958i
$976$	−679.705	−	392.428i	−0.696419	−	0.402078i
$977$	−743.417	+	1287.64i	−0.760918	+	1.31795i	0.181460	+	0.983398i	$0.441918\pi$
$977$	−743.417	+	1287.64i	−0.760918	+	1.31795i	−0.942378	+	0.334550i	$0.891416\pi$
$978$	112.024	+	1506.46i	0.114544	+	1.54035i
$979$	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
$983$		−	1106.95i		−	1.12609i	−0.826426	−	0.563045i	$-0.809630\pi$
$983$		−	1106.95i		−	1.12609i	0.826426	−	0.563045i	$-0.190370\pi$
$984$	1.30426	+	1.91536i	0.00132547	+	0.00194651i
$985$		−	723.390i		−	0.734406i
$986$	964.353	−	556.769i	0.978046	−	0.564675i
$987$	−458.224	+	311.000i	−0.464259	+	0.315096i
$988$	−501.386	+	868.425i	−0.507475	+	0.878973i
$989$	356.638	−	617.716i	0.360605	−	0.624586i
$990$	−545.302	+	433.840i	−0.550811	+	0.438223i
$991$	−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	$-0.351444\pi$
$992$	1664.87	−	961.211i	1.67829	−	0.968963i
$993$	1321.57	−	899.920i	1.33089	−	0.906264i
$994$	−1940.99	+	1116.67i	−1.95271	+	1.12341i
$995$	−69.3191	−	120.064i	−0.0696675	−	0.120668i
$996$	−148.296	−	217.779i	−0.148892	−	0.218653i
$997$		−	827.392i		−	0.829882i	−0.909848	−	0.414941i	$-0.863802\pi$
$997$		−	827.392i		−	0.829882i	0.909848	−	0.414941i	$-0.136198\pi$
$998$	−1097.05	−	1900.14i	−1.09925	−	1.90395i
$999$	186.389	+	57.8454i	0.186576	+	0.0579033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.k.a.61.12	yes	28
3.2	odd	2		189.3.k.a.19.3		28
7.2	even	3		441.3.l.a.97.12		28
7.3	odd	6		63.3.t.a.52.3	yes	28
7.4	even	3		441.3.t.a.178.3		28
7.5	odd	6		441.3.l.b.97.12		28
7.6	odd	2		441.3.k.b.313.12		28
9.4	even	3		63.3.t.a.40.3	yes	28
9.5	odd	6		189.3.t.a.145.12		28
21.17	even	6		189.3.t.a.73.12		28
63.4	even	3		441.3.k.b.31.12		28
63.13	odd	6		441.3.t.a.166.3		28
63.31	odd	6	inner	63.3.k.a.31.12	✓	28
63.40	odd	6		441.3.l.a.391.12		28
63.58	even	3		441.3.l.b.391.12		28
63.59	even	6		189.3.k.a.10.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.12	✓	28	63.31	odd	6	inner
63.3.k.a.61.12	yes	28	1.1	even	1	trivial
63.3.t.a.40.3	yes	28	9.4	even	3
63.3.t.a.52.3	yes	28	7.3	odd	6
189.3.k.a.10.3		28	63.59	even	6
189.3.k.a.19.3		28	3.2	odd	2
189.3.t.a.73.12		28	21.17	even	6
189.3.t.a.145.12		28	9.5	odd	6
441.3.k.b.31.12		28	63.4	even	3
441.3.k.b.313.12		28	7.6	odd	2
441.3.l.a.97.12		28	7.2	even	3
441.3.l.a.391.12		28	63.40	odd	6
441.3.l.b.97.12		28	7.5	odd	6
441.3.l.b.391.12		28	63.58	even	3
441.3.t.a.166.3		28	63.13	odd	6
441.3.t.a.178.3		28	7.4	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.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41697 + 2.45427i) q^{2} +(0.222472 + 2.99174i) q^{3} +(-2.01561 + 3.49114i) q^{4} -2.39855i q^{5} +(-7.02729 + 4.78521i) q^{6} +(0.0107242 - 6.99999i) q^{7} -0.0884848 q^{8} +(-8.90101 + 1.33116i) q^{9} +O(q^{10})\)	\(q+(1.41697 + 2.45427i) q^{2} +(0.222472 + 2.99174i) q^{3} +(-2.01561 + 3.49114i) q^{4} -2.39855i q^{5} +(-7.02729 + 4.78521i) q^{6} +(0.0107242 - 6.99999i) q^{7} -0.0884848 q^{8} +(-8.90101 + 1.33116i) q^{9} +(5.88667 - 3.39867i) q^{10} +11.3906 q^{11} +(-10.8930 - 5.25350i) q^{12} +(-13.4628 + 7.77278i) q^{13} +(17.1950 - 9.89246i) q^{14} +(7.17583 - 0.533610i) q^{15} +(7.93707 + 13.7474i) q^{16} +(10.4807 - 6.05105i) q^{17} +(-15.8795 - 19.9592i) q^{18} +(-13.8576 - 8.00071i) q^{19} +(8.37367 + 4.83454i) q^{20} +(20.9445 - 1.52522i) q^{21} +(16.1401 + 27.9555i) q^{22} -16.0566 q^{23} +(-0.0196854 - 0.264724i) q^{24} +19.2470 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} +(11.4776 + 16.8553i) q^{30} +(-36.7194 - 21.1999i) q^{31} +(-22.6701 + 39.2658i) q^{32} +(2.53408 + 34.0776i) 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} -45.3471i q^{38} +(-26.2492 - 38.5481i) q^{39} +0.212235i q^{40} +(-7.55990 + 4.36471i) q^{41} +(33.4211 + 49.2423i) q^{42} +(-22.2113 + 38.4711i) q^{43} +(-22.9590 + 39.7661i) q^{44} +(3.19284 + 21.3495i) q^{45} +(-22.7518 - 39.4072i) q^{46} +(-22.8382 + 13.1856i) q^{47} +(-39.3629 + 26.8040i) q^{48} +(-48.9998 - 0.150138i) q^{49} +(27.2724 + 47.2372i) q^{50} +(20.4348 + 30.0094i) q^{51} -62.6676i q^{52} +(34.0624 + 58.9979i) q^{53} +(56.1801 - 51.9477i) q^{54} -27.3208i q^{55} +(-0.000948925 + 0.619393i) q^{56} +(20.8531 - 43.2384i) q^{57} +92.0120 q^{58} +(82.4104 + 47.5797i) q^{59} +(-12.6008 + 26.1274i) q^{60} +(-42.8184 + 24.7212i) q^{61} -120.159i q^{62} +(9.22264 + 62.3213i) q^{63} -64.9952 q^{64} +(18.6434 + 32.2913i) q^{65} +(-80.0448 + 54.5063i) q^{66} +(40.9350 - 70.9015i) q^{67} +48.7863i q^{68} +(-3.57215 - 48.0372i) q^{69} +(-23.7275 - 41.2431i) q^{70} -112.881 q^{71} +(0.787605 - 0.117787i) q^{72} +(58.8056 - 33.9514i) q^{73} -20.4840 q^{74} +(4.28192 + 57.5819i) q^{75} +(55.8633 - 32.2527i) q^{76} +(0.122154 - 79.7339i) q^{77} +(57.4129 - 119.044i) q^{78} +(-68.4439 - 118.548i) q^{79} +(32.9738 - 19.0374i) q^{80} +(77.4560 - 23.6973i) q^{81} +(-21.4243 - 12.3693i) q^{82} +(18.8674 + 10.8931i) q^{83} +(-36.8913 + 76.1946i) q^{84} +(-14.5137 - 25.1385i) q^{85} -125.891 q^{86} +(87.7333 + 42.3122i) q^{87} -1.00789 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} +(55.2557 - 114.571i) q^{93} +(-64.7220 - 37.3673i) q^{94} +(-19.1901 + 33.2382i) q^{95} +(-122.517 - 59.0876i) q^{96} +(96.5982 + 55.7710i) q^{97} +(-69.0628 - 120.471i) q^{98} +(-101.388 + 15.1626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} - 3 q^{3} - 23 q^{4} + 12 q^{6} - 16 q^{8} + 9 q^{9}+O(q^{10}) \) 28 * q + q^2 - 3 * q^3 - 23 * q^4 + 12 * q^6 - 16 * q^8 + 9 * q^9	\( 28 q + q^{2} - 3 q^{3} - 23 q^{4} + 12 q^{6} - 16 q^{8} + 9 q^{9} - 6 q^{10} - 14 q^{11} - 3 q^{12} + 15 q^{13} - 11 q^{14} - 18 q^{15} - 27 q^{16} - 33 q^{17} + 33 q^{18} - 6 q^{19} + 108 q^{20} + 12 q^{21} - 10 q^{22} - 68 q^{23} + 42 q^{24} - 62 q^{25} + 54 q^{26} - 81 q^{27} - 16 q^{28} + 70 q^{29} - 6 q^{30} + 45 q^{31} + 153 q^{32} - 114 q^{33} + 12 q^{34} + 18 q^{35} - 174 q^{36} + 9 q^{37} - 120 q^{39} - 234 q^{41} - 51 q^{42} + 30 q^{43} + 51 q^{44} + 276 q^{45} - 22 q^{46} - 111 q^{47} + 147 q^{48} + 34 q^{49} + 241 q^{50} - 6 q^{51} + 148 q^{53} + 378 q^{54} - 412 q^{56} + 189 q^{57} - 34 q^{58} + 42 q^{59} + 456 q^{60} + 120 q^{61} - 222 q^{63} - 48 q^{64} + 114 q^{65} - 447 q^{66} - 34 q^{67} + 78 q^{69} + 264 q^{70} - 350 q^{71} - 339 q^{72} - 6 q^{73} - 718 q^{74} - 123 q^{75} + 72 q^{76} - 32 q^{77} - 375 q^{78} - 82 q^{79} - 609 q^{80} - 3 q^{81} - 18 q^{82} + 738 q^{83} + 609 q^{84} + 3 q^{85} - 34 q^{86} + 3 q^{87} - 50 q^{88} + 21 q^{89} - 543 q^{90} + 39 q^{91} + 288 q^{92} + 252 q^{93} - 3 q^{94} + 507 q^{95} - 582 q^{96} - 57 q^{97} + 811 q^{98} - 162 q^{99}+O(q^{100}) \) 28 * q + q^2 - 3 * q^3 - 23 * q^4 + 12 * q^6 - 16 * q^8 + 9 * q^9 - 6 * q^10 - 14 * q^11 - 3 * q^12 + 15 * q^13 - 11 * q^14 - 18 * q^15 - 27 * q^16 - 33 * q^17 + 33 * q^18 - 6 * q^19 + 108 * q^20 + 12 * q^21 - 10 * q^22 - 68 * q^23 + 42 * q^24 - 62 * q^25 + 54 * q^26 - 81 * q^27 - 16 * q^28 + 70 * q^29 - 6 * q^30 + 45 * q^31 + 153 * q^32 - 114 * q^33 + 12 * q^34 + 18 * q^35 - 174 * q^36 + 9 * q^37 - 120 * q^39 - 234 * q^41 - 51 * q^42 + 30 * q^43 + 51 * q^44 + 276 * q^45 - 22 * q^46 - 111 * q^47 + 147 * q^48 + 34 * q^49 + 241 * q^50 - 6 * q^51 + 148 * q^53 + 378 * q^54 - 412 * q^56 + 189 * q^57 - 34 * q^58 + 42 * q^59 + 456 * q^60 + 120 * q^61 - 222 * q^63 - 48 * q^64 + 114 * q^65 - 447 * q^66 - 34 * q^67 + 78 * q^69 + 264 * q^70 - 350 * q^71 - 339 * q^72 - 6 * q^73 - 718 * q^74 - 123 * q^75 + 72 * q^76 - 32 * q^77 - 375 * q^78 - 82 * q^79 - 609 * q^80 - 3 * q^81 - 18 * q^82 + 738 * q^83 + 609 * q^84 + 3 * q^85 - 34 * q^86 + 3 * q^87 - 50 * q^88 + 21 * q^89 - 543 * q^90 + 39 * q^91 + 288 * q^92 + 252 * q^93 - 3 * q^94 + 507 * q^95 - 582 * 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