LMFDB - Embedded newform 27.4.e.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,4,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, 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:	$1.59305157015$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			16.1
Character	$\chi$	$=$	27.16
Dual form			27.4.e.a.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.58593 - 3.00895i) q^{2} +(-2.57206 + 4.51492i) q^{3} +(2.41590 + 13.7013i) q^{4} +(2.94522 + 1.07197i) q^{5} +(22.8084 - 8.45097i) q^{6} +(-5.29680 + 30.0397i) q^{7} +(13.8388 - 23.9695i) q^{8} +(-13.7690 - 23.2253i) q^{9} +O(q^{10})$	\(q+(-3.58593 - 3.00895i) q^{2} +(-2.57206 + 4.51492i) q^{3} +(2.41590 + 13.7013i) q^{4} +(2.94522 + 1.07197i) q^{5} +(22.8084 - 8.45097i) q^{6} +(-5.29680 + 30.0397i) q^{7} +(13.8388 - 23.9695i) q^{8} +(-13.7690 - 23.2253i) q^{9} +(-7.33583 - 12.7060i) q^{10} +(-49.0358 + 17.8476i) q^{11} +(-68.0740 - 24.3329i) q^{12} +(11.6707 - 9.79286i) q^{13} +(109.382 - 91.7822i) q^{14} +(-12.4152 + 10.5403i) q^{15} +(-17.1590 + 6.24538i) q^{16} +(35.3229 + 61.1810i) q^{17} +(-20.5091 + 124.714i) q^{18} +(32.0937 - 55.5879i) q^{19} +(-7.57202 + 42.9431i) q^{20} +(-122.003 - 101.178i) q^{21} +(229.541 + 83.5461i) q^{22} +(9.07464 + 51.4649i) q^{23} +(72.6261 + 124.132i) q^{24} +(-88.2303 - 74.0341i) q^{25} -71.3164 q^{26} +(140.275 - 2.42909i) q^{27} -424.378 q^{28} +(20.2760 + 17.0136i) q^{29} +(76.2350 - 0.440005i) q^{30} +(18.8621 + 106.972i) q^{31} +(-127.744 - 46.4951i) q^{32} +(45.5427 - 267.298i) q^{33} +(57.4254 - 325.675i) q^{34} +(-47.8020 + 82.7954i) q^{35} +(284.951 - 244.763i) q^{36} +(175.269 + 303.574i) q^{37} +(-282.346 + 102.766i) q^{38} +(14.1963 + 77.8800i) q^{39} +(66.4530 - 55.7607i) q^{40} +(147.723 - 123.955i) q^{41} +(133.053 + 729.919i) q^{42} +(132.385 - 48.1843i) q^{43} +(-363.000 - 628.734i) q^{44} +(-15.6559 - 83.1637i) q^{45} +(122.314 - 211.854i) q^{46} +(-20.0049 + 113.454i) q^{47} +(15.9367 - 93.5352i) q^{48} +(-552.010 - 200.915i) q^{49} +(93.6228 + 530.961i) q^{50} +(-367.080 + 2.11867i) q^{51} +(162.370 + 136.245i) q^{52} -3.24190 q^{53} +(-510.325 - 413.370i) q^{54} -163.553 q^{55} +(646.734 + 542.674i) q^{56} +(168.428 + 287.876i) q^{57} +(-21.5153 - 122.019i) q^{58} +(725.956 + 264.226i) q^{59} +(-174.409 - 144.639i) q^{60} +(32.0329 - 181.668i) q^{61} +(254.236 - 440.349i) q^{62} +(770.612 - 290.596i) q^{63} +(391.221 + 677.615i) q^{64} +(44.8704 - 16.3315i) q^{65} +(-967.597 + 821.474i) q^{66} +(-349.715 + 293.446i) q^{67} +(-752.921 + 631.776i) q^{68} +(-255.700 - 91.3995i) q^{69} +(420.541 - 153.065i) q^{70} +(88.2401 + 152.836i) q^{71} +(-747.245 + 8.62602i) q^{72} +(23.6217 - 40.9140i) q^{73} +(284.939 - 1615.97i) q^{74} +(561.192 - 207.933i) q^{75} +(839.159 + 305.429i) q^{76} +(-276.402 - 1567.55i) q^{77} +(183.430 - 321.988i) q^{78} +(-240.365 - 201.690i) q^{79} -57.2321 q^{80} +(-349.829 + 639.579i) q^{81} -902.697 q^{82} +(-36.6934 - 30.7894i) q^{83} +(1091.53 - 1916.03i) q^{84} +(38.4493 + 218.057i) q^{85} +(-619.708 - 225.555i) q^{86} +(-128.966 + 47.7846i) q^{87} +(-250.799 + 1422.35i) q^{88} +(-306.581 + 531.013i) q^{89} +(-194.094 + 345.326i) q^{90} +(232.357 + 402.454i) q^{91} +(-683.210 + 248.668i) q^{92} +(-531.485 - 189.978i) q^{93} +(413.112 - 346.642i) q^{94} +(154.112 - 129.315i) q^{95} +(538.488 - 457.167i) q^{96} +(-1046.19 + 380.782i) q^{97} +(1374.92 + 2381.44i) q^{98} +(1089.69 + 893.127i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−3.58593	−	3.00895i	−1.26782	−	1.06382i	−0.994804	−	0.101813i	$-0.967536\pi$
$2$	−3.58593	−	3.00895i	−1.26782	−	1.06382i	−0.273013	−	0.962010i	$-0.588020\pi$
$3$	−2.57206	+	4.51492i	−0.494993	+	0.868897i
$3$	−2.57206	+	4.51492i	−0.494993	+	0.868897i
$4$	2.41590	+	13.7013i	0.301988	+	1.71266i
$5$	2.94522	+	1.07197i	0.263429	+	0.0958802i	0.470358	−	0.882476i	$-0.344125\pi$
$5$	2.94522	+	1.07197i	0.263429	+	0.0958802i	−0.206929	+	0.978356i	$0.566347\pi$
$6$	22.8084	−	8.45097i	1.55191	−	0.575016i
$7$	−5.29680	+	30.0397i	−0.286000	+	1.62199i	0.415690	+	0.909507i	$0.363540\pi$
$7$	−5.29680	+	30.0397i	−0.286000	+	1.62199i	−0.701690	+	0.712482i	$0.747571\pi$
$8$	13.8388	−	23.9695i	0.611594	−	1.05931i
$9$	−13.7690	−	23.2253i	−0.509963	−	0.860196i
$10$	−7.33583	−	12.7060i	−0.231979	−	0.401800i
$11$	−49.0358	+	17.8476i	−1.34408	+	0.489204i	−0.911094	−	0.412199i	$-0.864761\pi$
$11$	−49.0358	+	17.8476i	−1.34408	+	0.489204i	−0.432982	+	0.901402i	$0.642539\pi$
$12$	−68.0740	−	24.3329i	−1.63761	−	0.585358i
$13$	11.6707	−	9.79286i	0.248990	−	0.208927i	−0.509748	−	0.860324i	$-0.670261\pi$
$13$	11.6707	−	9.79286i	0.248990	−	0.208927i	0.758737	+	0.651397i	$0.225817\pi$
$14$	109.382	−	91.7822i	2.08811	−	1.75213i
$15$	−12.4152	+	10.5403i	−0.213705	+	0.181432i
$16$	−17.1590	+	6.24538i	−0.268110	+	0.0975840i
$17$	35.3229	+	61.1810i	0.503945	+	0.872858i	0.999990	+	0.00456086i	$0.00145177\pi$
$17$	35.3229	+	61.1810i	0.503945	+	0.872858i	−0.496045	+	0.868297i	$0.665215\pi$
$18$	−20.5091	+	124.714i	−0.268558	+	1.63308i
$19$	32.0937	−	55.5879i	0.387515	−	0.671196i	−0.604599	−	0.796530i	$-0.706667\pi$
$19$	32.0937	−	55.5879i	0.387515	−	0.671196i	0.992115	+	0.125333i	$0.0400001\pi$
$20$	−7.57202	+	42.9431i	−0.0846578	+	0.480118i
$21$	−122.003	−	101.178i	−1.26777	−	1.05138i
$22$	229.541	+	83.5461i	2.22447	+	0.809640i
$23$	9.07464	+	51.4649i	0.0822693	+	0.466572i	0.997913	+	0.0645805i	$0.0205709\pi$
$23$	9.07464	+	51.4649i	0.0822693	+	0.466572i	−0.915643	+	0.401992i	$0.868318\pi$
$24$	72.6261	+	124.132i	0.617698	+	1.05576i
$25$	−88.2303	−	74.0341i	−0.705843	−	0.592272i
$26$	−71.3164			−0.537935
$27$	140.275	−	2.42909i	0.999850	−	0.0173140i
$28$	−424.378			−2.86428
$29$	20.2760	+	17.0136i	0.129833	+	0.108943i	0.705392	−	0.708817i	$-0.250771\pi$
$29$	20.2760	+	17.0136i	0.129833	+	0.108943i	−0.575559	+	0.817760i	$0.695215\pi$
$30$	76.2350	−	0.440005i	0.463951	−	0.00267778i
$31$	18.8621	+	106.972i	0.109282	+	0.619766i	0.989423	+	0.145056i	$0.0463362\pi$
$31$	18.8621	+	106.972i	0.109282	+	0.619766i	−0.880142	+	0.474711i	$0.842553\pi$
$32$	−127.744	−	46.4951i	−0.705694	−	0.256852i
$33$	45.5427	−	267.298i	0.240241	−	1.41002i
$34$	57.4254	−	325.675i	0.289658	−	1.64273i
$35$	−47.8020	+	82.7954i	−0.230857	+	0.399857i
$36$	284.951	−	244.763i	1.31922	−	1.13316i
$37$	175.269	+	303.574i	0.778756	+	1.34885i	0.932659	+	0.360760i	$0.117482\pi$
$37$	175.269	+	303.574i	0.778756	+	1.34885i	−0.153903	+	0.988086i	$0.549184\pi$
$38$	−282.346	+	102.766i	−1.20533	+	0.438705i
$39$	14.1963	+	77.8800i	0.0582879	+	0.319764i
$40$	66.4530	−	55.7607i	0.262678	−	0.220413i
$41$	147.723	−	123.955i	0.562695	−	0.472157i	−0.316518	−	0.948587i	$-0.602514\pi$
$41$	147.723	−	123.955i	0.562695	−	0.472157i	0.879213	+	0.476429i	$0.158069\pi$
$42$	133.053	+	729.919i	0.488821	+	2.68164i
$43$	132.385	−	48.1843i	0.469501	−	0.170885i	−0.0964251	−	0.995340i	$-0.530741\pi$
$43$	132.385	−	48.1843i	0.469501	−	0.170885i	0.565926	+	0.824456i	$0.308519\pi$
$44$	−363.000	−	628.734i	−1.24373	−	2.15421i
$45$	−15.6559	−	83.1637i	−0.0518632	−	0.275496i
$46$	122.314	−	211.854i	0.392049	−	0.679048i
$47$	−20.0049	+	113.454i	−0.0620855	+	0.352104i	0.937901	+	0.346903i	$0.112767\pi$
$47$	−20.0049	+	113.454i	−0.0620855	+	0.352104i	−0.999986	+	0.00520123i	$0.998344\pi$
$48$	15.9367	−	93.5352i	0.0479222	−	0.281263i
$49$	−552.010	−	200.915i	−1.60936	−	0.585759i
$50$	93.6228	+	530.961i	0.264805	+	1.50178i
$51$	−367.080	+	2.11867i	−1.00787	+	0.00581713i
$52$	162.370	+	136.245i	0.433013	+	0.363341i
$53$	−3.24190			−0.00840206			−0.00420103	−	0.999991i	$-0.501337\pi$
$53$	−3.24190			−0.00840206			−0.00420103	+	0.999991i	$0.501337\pi$
$54$	−510.325	−	413.370i	−1.28605	−	1.04171i
$55$	−163.553			−0.400973
$56$	646.734	+	542.674i	1.54328	+	1.29496i
$57$	168.428	+	287.876i	0.391383	+	0.668949i
$58$	−21.5153	−	122.019i	−0.0487085	−	0.276239i
$59$	725.956	+	264.226i	1.60189	+	0.583039i	0.979813	−	0.199918i	$-0.0640677\pi$
$59$	725.956	+	264.226i	1.60189	+	0.583039i	0.622075	+	0.782958i	$0.286290\pi$
$60$	−174.409	−	144.639i	−0.375268	−	0.311214i
$61$	32.0329	−	181.668i	0.0672360	−	0.381314i	−0.932558	−	0.361020i	$-0.882429\pi$
$61$	32.0329	−	181.668i	0.0672360	−	0.381314i	0.999794	−	0.0202943i	$-0.00646030\pi$
$62$	254.236	−	440.349i	0.520773	−	0.902006i
$63$	770.612	−	290.596i	1.54108	−	0.581138i
$64$	391.221	+	677.615i	0.764104	+	1.32347i
$65$	44.8704	−	16.3315i	0.0856230	−	0.0311642i
$66$	−967.597	+	821.474i	−1.80459	+	1.53207i
$67$	−349.715	+	293.446i	−0.637679	+	0.535076i	−0.903304	−	0.429000i	$-0.858866\pi$
$67$	−349.715	+	293.446i	−0.637679	+	0.535076i	0.265625	+	0.964076i	$0.414422\pi$
$68$	−752.921	+	631.776i	−1.34272	+	1.12668i
$69$	−255.700	−	91.3995i	−0.446126	−	0.159467i
$70$	420.541	−	153.065i	0.718062	−	0.261353i
$71$	88.2401	+	152.836i	0.147495	+	0.255469i	0.930301	−	0.366797i	$-0.119546\pi$
$71$	88.2401	+	152.836i	0.147495	+	0.255469i	−0.782806	+	0.622266i	$0.786212\pi$
$72$	−747.245	+	8.62602i	−1.22311	+	0.0141193i
$73$	23.6217	−	40.9140i	0.0378728	−	0.0655976i	−0.846468	−	0.532440i	$-0.821275\pi$
$73$	23.6217	−	40.9140i	0.0378728	−	0.0655976i	0.884340	+	0.466843i	$0.154609\pi$
$74$	284.939	−	1615.97i	0.447614	−	2.53855i
$75$	561.192	−	207.933i	0.864011	−	0.320134i
$76$	839.159	+	305.429i	1.26655	+	0.460988i
$77$	−276.402	−	1567.55i	−0.409077	−	2.31999i
$78$	183.430	−	321.988i	0.266274	−	0.467410i
$79$	−240.365	−	201.690i	−0.342319	−	0.287240i	0.455378	−	0.890298i	$-0.349504\pi$
$79$	−240.365	−	201.690i	−0.342319	−	0.287240i	−0.797697	+	0.603058i	$0.793949\pi$
$80$	−57.2321			−0.0799842
$81$	−349.829	+	639.579i	−0.479875	+	0.877337i
$82$	−902.697			−1.21569
$83$	−36.6934	−	30.7894i	−0.0485256	−	0.0407178i	0.618202	−	0.786019i	$-0.287861\pi$
$83$	−36.6934	−	30.7894i	−0.0485256	−	0.0407178i	−0.666728	+	0.745301i	$0.732306\pi$
$84$	1091.53	−	1916.03i	1.41780	−	2.48877i
$85$	38.4493	+	218.057i	0.0490637	+	0.278254i
$86$	−619.708	−	225.555i	−0.777032	−	0.282817i
$87$	−128.966	+	47.7846i	−0.158927	+	0.0588856i
$88$	−250.799	+	1422.35i	−0.303810	+	1.72299i
$89$	−306.581	+	531.013i	−0.365140	+	0.632441i	−0.988799	−	0.149256i	$-0.952312\pi$
$89$	−306.581	+	531.013i	−0.365140	+	0.632441i	0.623658	+	0.781697i	$0.285646\pi$
$90$	−194.094	+	345.326i	−0.227326	+	0.404451i
$91$	232.357	+	402.454i	0.267666	+	0.463612i
$92$	−683.210	+	248.668i	−0.774235	+	0.281798i
$93$	−531.485	−	189.978i	−0.592607	−	0.211826i
$94$	413.112	−	346.642i	0.453290	−	0.380355i
$95$	154.112	−	129.315i	0.166437	−	0.139657i
$96$	538.488	−	457.167i	0.572491	−	0.486035i
$97$	−1046.19	+	380.782i	−1.09510	+	0.398583i	−0.825507	−	0.564392i	$-0.809111\pi$
$97$	−1046.19	+	380.782i	−1.09510	+	0.398583i	−0.269590	+	0.962975i	$0.586888\pi$
$98$	1374.92	+	2381.44i	1.41723	+	2.45471i
$99$	1089.69	+	893.127i	1.10624	+	0.906693i
$100$	801.204	−	1387.73i	0.801204	−	1.38773i
$101$	−23.1067	+	131.044i	−0.0227644	+	0.129103i	−0.994072	−	0.108723i	$-0.965324\pi$
$101$	−23.1067	+	131.044i	−0.0227644	+	0.129103i	0.971308	+	0.237826i	$0.0764349\pi$
$102$	1322.70	+	1096.93i	1.28399	+	1.06482i
$103$	−1093.03	−	397.830i	−1.04562	−	0.380576i	−0.238615	−	0.971114i	$-0.576693\pi$
$103$	−1093.03	−	397.830i	−1.04562	−	0.380576i	−0.807010	+	0.590538i	$0.798915\pi$
$104$	−73.2218	−	415.262i	−0.0690384	−	0.391536i
$105$	−250.865	−	428.777i	−0.233161	−	0.398518i
$106$	11.6252	+	9.75471i	0.0106523	+	0.00893831i
$107$	61.0084			0.0551206			0.0275603	−	0.999620i	$-0.491226\pi$
$107$	61.0084			0.0551206			0.0275603	+	0.999620i	$0.491226\pi$
$108$	372.173	+	1916.08i	0.331596	+	1.70717i
$109$	1788.84			1.57192			0.785961	−	0.618276i	$-0.212169\pi$
$109$	1788.84			1.57192			0.785961	+	0.618276i	$0.212169\pi$
$110$	586.490	+	492.124i	0.508360	+	0.426565i
$111$	−1821.41	+	10.5126i	−1.55749	+	0.00898933i
$112$	−96.7210	−	548.532i	−0.0816007	−	0.462780i
$113$	309.662	+	112.708i	0.257792	+	0.0938287i	0.467683	−	0.883896i	$-0.345089\pi$
$113$	309.662	+	112.708i	0.257792	+	0.0938287i	−0.209891	+	0.977725i	$0.567311\pi$
$114$	262.233	−	1539.09i	0.215442	−	1.26447i
$115$	−28.4421	+	161.303i	−0.0230630	+	0.130797i
$116$	−184.123	+	318.911i	−0.147374	+	0.255260i
$117$	−388.136	−	136.217i	−0.306694	−	0.107635i
$118$	−1808.18	−	3131.86i	−1.41065	−	2.44331i
$119$	−2024.96	+	737.024i	−1.55989	+	0.567755i
$120$	80.8338	+	443.450i	0.0614924	+	0.337344i
$121$	1066.37	−	894.787i	0.801176	−	0.672267i
$122$	−661.497	+	555.062i	−0.490894	+	0.411909i
$123$	179.692	+	985.777i	0.131726	+	0.722639i
$124$	−1420.08	+	516.869i	−1.02845	+	0.374324i
$125$	−376.385	−	651.919i	−0.269320	−	0.466475i
$126$	−3637.75	−	1276.67i	−2.57203	−	0.902660i
$127$	442.097	−	765.734i	0.308896	−	0.535023i	−0.669225	−	0.743060i	$-0.733374\pi$
$127$	442.097	−	765.734i	0.308896	−	0.535023i	0.978121	+	0.208036i	$0.0667072\pi$
$128$	447.169	−	2536.02i	0.308785	−	1.75121i
$129$	−122.955	+	721.642i	−0.0839190	+	0.492535i
$130$	−210.043	−	76.4493i	−0.141707	−	0.0515773i
$131$	288.996	+	1638.98i	0.192746	+	1.09311i	0.915593	+	0.402106i	$0.131722\pi$
$131$	288.996	+	1638.98i	0.192746	+	1.09311i	−0.722847	+	0.691008i	$0.757167\pi$
$132$	3772.34	−	21.7728i	2.48743	−	0.0143567i
$133$	1499.85	+	1258.52i	0.977843	+	0.820508i
$134$	2137.02			1.37769
$135$	415.745	+	143.217i	0.265049	+	0.0913048i
$136$	1955.30			1.23284
$137$	−143.746	−	120.618i	−0.0896429	−	0.0752194i	0.596865	−	0.802342i	$-0.296413\pi$
$137$	−143.746	−	120.618i	−0.0896429	−	0.0752194i	−0.686508	+	0.727122i	$0.740857\pi$
$138$	641.906	+	1097.14i	0.395961	+	0.676774i
$139$	−241.747	−	1371.02i	−0.147516	−	0.836605i	−0.965312	−	0.261097i	$-0.915916\pi$
$139$	−241.747	−	1371.02i	−0.147516	−	0.836605i	0.817796	−	0.575508i	$-0.195195\pi$
$140$	−1249.89	−	454.922i	−0.754534	−	0.274628i
$141$	−460.780	−	382.130i	−0.275210	−	0.228235i
$142$	143.454	−	813.570i	0.0847776	−	0.480797i
$143$	−397.502	+	688.494i	−0.232453	+	0.402621i
$144$	381.314	+	312.531i	0.220668	+	0.180863i
$145$	41.4793	+	71.8442i	0.0237563	+	0.0411472i
$146$	−207.814	+	75.6380i	−0.117800	+	0.0428757i
$147$	2326.92	−	1975.52i	1.30559	−	1.10842i
$148$	−3735.92	+	3134.81i	−2.07494	+	1.74108i
$149$	1579.49	−	1325.35i	0.868437	−	0.728705i	−0.0953311	−	0.995446i	$-0.530391\pi$
$149$	1579.49	−	1325.35i	0.868437	−	0.728705i	0.963768	+	0.266740i	$0.0859465\pi$
$150$	−2638.05	−	942.965i	−1.43597	−	0.513285i
$151$	1455.04	−	529.591i	0.784169	−	0.285414i	0.0812590	−	0.996693i	$-0.474106\pi$
$151$	1455.04	−	529.591i	0.784169	−	0.285414i	0.702910	+	0.711279i	$0.251884\pi$
$152$	−888.275	−	1538.54i	−0.474004	−	0.820999i
$153$	934.587	−	1662.79i	0.493836	−	0.878617i
$154$	−3725.53	+	6452.81i	−1.94943	+	3.37651i
$155$	−59.1183	+	335.276i	−0.0306354	+	0.173742i
$156$	−1032.76	+	382.658i	−0.530044	+	0.196392i
$157$	342.298	+	124.586i	0.174002	+	0.0633316i	0.427552	−	0.903991i	$-0.359376\pi$
$157$	342.298	+	124.586i	0.174002	+	0.0633316i	−0.253550	+	0.967322i	$0.581598\pi$
$158$	255.056	+	1446.49i	0.128425	+	0.728335i
$159$	8.33836	−	14.6369i	0.00415896	−	0.00730052i
$160$	−326.394	−	273.877i	−0.161273	−	0.135324i
$161$	−1594.05			−0.780304
$162$	3178.92	−	1240.86i	1.54173	−	0.601799i
$163$	2054.66			0.987321			0.493660	−	0.869655i	$-0.335659\pi$
$163$	2054.66			0.987321			0.493660	+	0.869655i	$0.335659\pi$
$164$	2055.22	+	1724.53i	0.978571	+	0.821119i
$165$	420.669	−	738.430i	0.198479	−	0.348404i
$166$	38.9360	+	220.817i	0.0182049	+	0.103245i
$167$	−3515.68	−	1279.60i	−1.62905	−	0.592926i	−0.643975	−	0.765047i	$-0.722716\pi$
$167$	−3515.68	−	1279.60i	−1.62905	−	0.592926i	−0.985076	+	0.172121i	$0.944938\pi$
$168$	−4113.57	+	1524.16i	−1.88910	+	0.699950i
$169$	−341.200	+	1935.04i	−0.155303	+	0.880766i
$170$	518.246	−	897.628i	0.233810	−	0.404970i
$171$	−1732.94	+	20.0047i	−0.774979	+	0.00894618i
$172$	980.016	+	1697.44i	0.434451	+	0.752490i
$173$	3861.34	−	1405.41i	1.69695	−	0.617640i	0.701479	−	0.712690i	$-0.252523\pi$
$173$	3861.34	−	1405.41i	1.69695	−	0.617640i	0.995472	+	0.0950505i	$0.0303013\pi$
$174$	606.245	+	216.701i	0.264134	+	0.0944141i
$175$	2691.30	−	2258.27i	1.16253	−	0.975479i
$176$	729.942	−	612.494i	0.312622	−	0.262321i
$177$	−3060.16	+	2598.03i	−1.29952	+	1.10327i
$178$	2697.17	−	981.688i	1.13574	−	0.413374i
$179$	−2025.01	−	3507.41i	−0.845564	−	1.46456i	−0.885130	−	0.465343i	$-0.845931\pi$
$179$	−2025.01	−	3507.41i	−0.845564	−	1.46456i	0.0395661	−	0.999217i	$-0.487402\pi$
$180$	1101.62	−	415.421i	0.456168	−	0.172020i
$181$	−487.694	+	844.711i	−0.200276	+	0.346889i	−0.948617	−	0.316425i	$-0.897517\pi$
$181$	−487.694	+	844.711i	−0.200276	+	0.346889i	0.748341	+	0.663314i	$0.230851\pi$
$182$	377.749	−	2142.32i	0.153850	−	0.872524i
$183$	737.825	+	611.887i	0.298041	+	0.247169i
$184$	1359.17	+	494.697i	0.544561	+	0.198204i
$185$	190.782	+	1081.98i	0.0758192	+	0.429992i
$186$	1334.23	+	2280.46i	0.525971	+	0.898985i
$187$	−2824.02	−	2369.63i	−1.10435	−	0.926656i
$188$	−1602.79			−0.621783
$189$	−670.040	+	4226.68i	−0.257874	+	1.62670i
$190$	−941.735			−0.359582
$191$	3422.73	+	2872.01i	1.29665	+	1.08802i	0.990713	+	0.135967i	$0.0434142\pi$
$191$	3422.73	+	2872.01i	1.29665	+	1.08802i	0.305937	+	0.952052i	$0.401030\pi$
$192$	−4065.62	+	23.4655i	−1.52818	+	0.00882019i
$193$	871.661	+	4943.44i	0.325096	+	1.84371i	0.508998	+	0.860768i	$0.330016\pi$
$193$	871.661	+	4943.44i	0.325096	+	1.84371i	−0.183902	+	0.982945i	$0.558873\pi$
$194$	4897.31	+	1782.47i	1.81240	+	0.659661i
$195$	−41.6741	+	244.592i	−0.0153043	+	0.0898236i
$196$	1419.19	−	8048.63i	0.517198	−	2.93317i
$197$	573.953	−	994.116i	0.207576	−	0.359532i	−0.743374	−	0.668876i	$-0.766776\pi$
$197$	573.953	−	994.116i	0.207576	−	0.359532i	0.950950	+	0.309343i	$0.100109\pi$
$198$	−1220.17	−	6481.50i	−0.437948	−	2.32637i
$199$	−1535.19	−	2659.03i	−0.546869	−	0.947206i	−0.998487	−	0.0549939i	$-0.982486\pi$
$199$	−1535.19	−	2659.03i	−0.546869	−	0.947206i	0.451617	−	0.892212i	$-0.350847\pi$
$200$	−2995.56	+	1090.29i	−1.05909	+	0.385477i
$201$	−425.396	−	2333.70i	−0.149279	−	0.818937i
$202$	477.165	−	400.389i	0.166204	−	0.139462i
$203$	−618.481	+	518.967i	−0.213837	+	0.179430i
$204$	−915.858	−	5024.34i	−0.314328	−	1.72438i
$205$	567.954	−	206.718i	0.193501	−	0.0704284i
$206$	2722.47	+	4715.45i	0.920793	+	1.59486i
$207$	1070.34	−	919.381i	0.359389	−	0.308703i
$208$	−139.098	+	240.924i	−0.0463686	+	0.0803128i
$209$	−581.630	+	3298.59i	−0.192498	+	1.09171i
$210$	−390.584	+	2292.40i	−0.128347	+	0.753290i
$211$	−5105.91	−	1858.40i	−1.66590	−	0.606339i	−0.674630	−	0.738156i	$-0.735697\pi$
$211$	−5105.91	−	1858.40i	−1.66590	−	0.606339i	−0.991274	+	0.131817i	$0.957919\pi$
$212$	−7.83212	−	44.4181i	−0.00253732	−	0.0143899i
$213$	−917.003	+	5.29266i	−0.294986	+	0.00170257i
$214$	−218.771	−	183.571i	−0.0698828	−	0.0586386i
$215$	441.556			0.140065
$216$	1883.01	−	3395.94i	0.593161	−	1.06974i
$217$	−3313.31			−1.03651
$218$	−6414.64	−	5382.52i	−1.99291	−	1.67225i
$219$	123.967	+	211.883i	0.0382507	+	0.0653779i
$220$	−395.129	−	2240.89i	−0.121089	−	0.686730i
$221$	1011.38	+	368.112i	0.307841	+	0.112045i
$222$	6563.09	+	5442.85i	1.98417	+	1.64549i
$223$	−748.910	+	4247.28i	−0.224891	+	1.27542i	0.638002	+	0.770034i	$0.279761\pi$
$223$	−748.910	+	4247.28i	−0.224891	+	1.27542i	−0.862893	+	0.505386i	$0.831350\pi$
$224$	2073.33	−	3591.12i	0.618439	−	1.07117i
$225$	−504.619	+	3068.55i	−0.149517	+	0.909200i
$226$	−771.292	−	1335.92i	−0.227016	−	0.393203i
$227$	−1685.55	+	613.489i	−0.492836	+	0.179377i	−0.576469	−	0.817119i	$-0.695570\pi$
$227$	−1685.55	+	613.489i	−0.492836	+	0.179377i	0.0836333	+	0.996497i	$0.473348\pi$
$228$	−3537.36	+	3003.16i	−1.02749	+	0.872319i
$229$	1480.39	−	1242.20i	0.427192	−	0.358457i	−0.403699	−	0.914892i	$-0.632276\pi$
$229$	1480.39	−	1242.20i	0.427192	−	0.358457i	0.830891	+	0.556435i	$0.187831\pi$
$230$	587.344	−	492.840i	0.168384	−	0.141291i
$231$	7788.30	+	2783.91i	2.21832	+	0.792934i
$232$	688.403	−	250.558i	0.194810	−	0.0709050i
$233$	−1836.39	−	3180.72i	−0.516335	−	0.894318i	−0.999820	−	0.0189653i	$-0.993963\pi$
$233$	−1836.39	−	3180.72i	−0.516335	−	0.894318i	0.483486	−	0.875352i	$-0.339371\pi$
$234$	981.956	+	1656.34i	0.274327	+	0.462729i
$235$	−180.538	+	312.701i	−0.0501149	+	0.0868016i
$236$	−1866.40	+	10584.9i	−0.514797	+	2.91956i
$237$	1528.85	−	566.470i	0.419027	−	0.155258i
$238$	9479.01	+	3450.08i	2.58165	+	0.939644i
$239$	−263.444	−	1494.07i	−0.0713003	−	0.404364i	−0.999480	−	0.0322329i	$-0.989738\pi$
$239$	−263.444	−	1494.07i	−0.0713003	−	0.404364i	0.928180	−	0.372131i	$-0.121373\pi$
$240$	147.204	−	258.398i	0.0395917	−	0.0694980i
$241$	3731.32	+	3130.95i	0.997326	+	0.836856i	0.986612	−	0.163086i	$-0.0521449\pi$
$241$	3731.32	+	3130.95i	0.997326	+	0.836856i	0.0107145	+	0.999943i	$0.496589\pi$
$242$	−6516.28			−1.73092
$243$	−1987.86	−	3224.48i	−0.524780	−	0.851238i
$244$	2566.47			0.673366
$245$	−1410.42	−	1183.48i	−0.367789	−	0.308611i
$246$	2321.79	−	4075.61i	0.601756	−	1.05631i
$247$	−169.809	−	963.037i	−0.0437438	−	0.248083i
$248$	2825.09	+	1028.25i	0.723362	+	0.263282i
$249$	233.389	−	86.4755i	0.0593994	−	0.0220087i
$250$	−611.900	+	3470.26i	−0.154800	+	0.877913i
$251$	−1277.75	+	2213.14i	−0.321319	+	0.556542i	−0.980761	−	0.195215i	$-0.937460\pi$
$251$	−1277.75	+	2213.14i	−0.321319	+	0.556542i	0.659441	+	0.751756i	$0.270793\pi$
$252$	5843.26	+	9856.30i	1.46068	+	2.46384i
$253$	−1363.50	−	2361.66i	−0.338825	−	0.586862i
$254$	−3889.38	+	1415.62i	−0.960794	+	0.349700i
$255$	−1083.40	−	387.260i	−0.266060	−	0.0951026i
$256$	−4439.19	+	3724.92i	−1.08379	+	0.909405i
$257$	672.124	−	563.979i	0.163136	−	0.136887i	−0.557565	−	0.830133i	$-0.688264\pi$
$257$	672.124	−	563.979i	0.163136	−	0.136887i	0.720701	+	0.693246i	$0.243820\pi$
$258$	2612.29	−	2217.79i	0.630364	−	0.535169i
$259$	−10047.6	+	3657.04i	−2.41054	+	0.877364i
$260$	332.165	+	575.327i	0.0792307	+	0.137232i
$261$	115.965	−	705.177i	0.0275022	−	0.167239i
$262$	3895.28	−	6746.82i	0.918515	−	1.59091i
$263$	970.761	−	5505.46i	0.227603	−	1.29080i	−0.630042	−	0.776561i	$-0.716962\pi$
$263$	970.761	−	5505.46i	0.227603	−	1.29080i	0.857645	−	0.514242i	$-0.171927\pi$
$264$	−5776.73	−	4790.71i	−1.34672	−	1.11685i
$265$	−9.54812	−	3.47523i	−0.00221334	−	0.000805591i
$266$	−1591.51	−	9025.92i	−0.366849	−	2.08051i
$267$	−1608.94	−	2749.99i	−0.368784	−	0.630323i
$268$	−4865.46	−	4082.60i	−1.10897	−	0.930540i
$269$	4914.12			1.11383			0.556913	−	0.830571i	$-0.311986\pi$
$269$	4914.12			1.11383			0.556913	+	0.830571i	$0.311986\pi$
$270$	−1059.90	−	1764.52i	−0.238901	−	0.397723i
$271$	−2629.84			−0.589487			−0.294744	−	0.955576i	$-0.595234\pi$
$271$	−2629.84			−0.589487			−0.294744	+	0.955576i	$0.595234\pi$
$272$	−988.206	−	829.203i	−0.220290	−	0.184845i
$273$	−2414.68	+	13.9368i	−0.535324	+	0.00308972i
$274$	152.532	+	865.051i	0.0336306	+	0.190729i
$275$	5647.77	+	2055.62i	1.23845	+	0.450758i
$276$	634.541	−	3724.23i	0.138387	−	0.812218i
$277$	919.152	−	5212.77i	0.199374	−	1.13070i	−0.706677	−	0.707536i	$-0.749807\pi$
$277$	919.152	−	5212.77i	0.199374	−	1.13070i	0.906051	−	0.423169i	$-0.139082\pi$
$278$	−3258.43	+	5643.77i	−0.702977	+	1.21759i
$279$	2224.75	−	1910.98i	0.477391	−	0.410062i
$280$	1323.04	+	2291.58i	0.282382	+	0.489100i
$281$	1902.69	−	692.524i	0.403933	−	0.147020i	−0.132060	−	0.991242i	$-0.542159\pi$
$281$	1902.69	−	692.524i	0.403933	−	0.147020i	0.535994	+	0.844222i	$0.319937\pi$
$282$	502.512	+	2756.75i	0.106114	+	0.582136i
$283$	5187.82	−	4353.10i	1.08970	−	0.914363i	0.0930064	−	0.995666i	$-0.470352\pi$
$283$	5187.82	−	4353.10i	1.08970	−	0.914363i	0.996690	+	0.0813021i	$0.0259078\pi$
$284$	−1880.87	+	1578.24i	−0.392990	+	0.329758i
$285$	187.463	+	1028.41i	0.0389625	+	0.213746i
$286$	3497.05	−	1272.82i	0.723025	−	0.263160i
$287$	2941.09	+	5094.12i	0.604903	+	1.04772i
$288$	679.049	+	3607.09i	0.138935	+	0.738020i
$289$	−38.9128	+	67.3989i	−0.00792037	+	0.0137185i
$290$	67.4340	−	382.437i	0.0136547	−	0.0774396i
$291$	971.663	−	5702.85i	0.195738	−	1.14882i
$292$	617.641	+	224.803i	0.123783	+	0.0450534i
$293$	−272.936	−	1547.90i	−0.0544201	−	0.308632i	0.945432	−	0.325819i	$-0.105640\pi$
$293$	−272.936	−	1547.90i	−0.0544201	−	0.308632i	−0.999852	+	0.0171872i	$0.994529\pi$
$294$	−14288.4	+	82.4682i	−2.83441	+	0.0163593i
$295$	1854.86	+	1556.41i	0.366081	+	0.307179i
$296$	9702.02			1.90513
$297$	−6835.14	+	2622.68i	−1.33540	+	0.512402i
$298$	−9651.86			−1.87623
$299$	609.896	+	511.763i	0.117964	+	0.0989834i
$300$	4204.73	+	7186.69i	0.809200	+	1.38308i
$301$	746.221	+	4232.03i	0.142895	+	0.810399i
$302$	−6811.18	−	2479.07i	−1.29781	−	0.472365i
$303$	−532.224	−	441.379i	−0.100909	−	0.0836851i
$304$	−203.529	+	1154.27i	−0.0383987	+	0.217770i
$305$	289.087	−	500.714i	0.0542724	−	0.0940025i
$306$	−8354.60	+	3150.51i	−1.56079	+	0.588570i
$307$	4253.71	+	7367.64i	0.790788	+	1.36968i	0.925480	+	0.378797i	$0.123662\pi$
$307$	4253.71	+	7367.64i	0.790788	+	1.36968i	−0.134692	+	0.990888i	$0.543005\pi$
$308$	20809.7	−	7574.11i	3.84981	−	1.40122i
$309$	4607.51	−	3911.69i	0.848258	−	0.720157i
$310$	1220.82	−	1024.39i	0.223671	−	0.187682i
$311$	−6795.24	+	5701.88i	−1.23898	+	1.03963i	−0.241377	+	0.970432i	$0.577599\pi$
$311$	−6795.24	+	5701.88i	−1.23898	+	1.03963i	−0.997603	+	0.0691959i	$0.977957\pi$
$312$	2063.20	+	737.487i	0.374378	+	0.133821i
$313$	4568.17	−	1662.68i	0.824946	−	0.300256i	0.105163	−	0.994455i	$-0.466464\pi$
$313$	4568.17	−	1662.68i	0.824946	−	0.300256i	0.719783	+	0.694199i	$0.244241\pi$
$314$	−852.581	−	1476.71i	−0.153229	−	0.265401i
$315$	2581.13	−	29.7960i	0.461684	−	0.00532957i
$316$	2182.72	−	3780.57i	0.388568	−	0.673019i
$317$	−892.835	+	5063.52i	−0.158191	+	0.897147i	0.797619	+	0.603162i	$0.206093\pi$
$317$	−892.835	+	5063.52i	−0.158191	+	0.897147i	−0.955810	+	0.293985i	$0.905018\pi$
$318$	−73.9425	+	27.3972i	−0.0130393	+	0.00483131i
$319$	−1297.90	−	472.398i	−0.227801	−	0.0829128i
$320$	425.848	+	2415.10i	0.0743926	+	0.421901i
$321$	−156.917	+	275.448i	−0.0272843	+	0.0478941i
$322$	5716.16	+	4796.42i	0.989282	+	0.830106i
$323$	4534.56			0.781145
$324$	−9608.19	−	3247.94i	−1.64749	−	0.556917i
$325$	−1754.71			−0.299489
$326$	−7367.85	−	6182.36i	−1.25174	−	1.05034i
$327$	−4601.00	+	8076.46i	−0.778091	+	1.36584i
$328$	−926.815	−	5256.23i	−0.156021	−	0.884838i
$329$	−3302.14	−	1201.88i	−0.553353	−	0.201404i
$330$	−3730.39	+	1382.18i	−0.622276	+	0.230566i
$331$	73.9029	−	419.124i	0.0122721	−	0.0695987i	−0.978057	−	0.208339i	$-0.933194\pi$
$331$	73.9029	−	419.124i	0.0122721	−	0.0695987i	0.990329	+	0.138740i	$0.0443054\pi$
$332$	333.206	−	577.130i	0.0550815	−	0.0954040i
$333$	4637.33	−	8250.58i	0.763135	−	1.35774i
$334$	8756.71	+	15167.1i	1.43457	+	2.48474i
$335$	−1344.55	+	489.378i	−0.219286	+	0.0798137i
$336$	2725.35	+	974.170i	0.442500	+	0.158171i
$337$	−6033.36	+	5062.59i	−0.975247	+	0.818329i	−0.983366	−	0.181638i	$-0.941860\pi$
$337$	−6033.36	+	5062.59i	−0.975247	+	0.818329i	0.00811862	+	0.999967i	$0.497416\pi$
$338$	7045.97	−	5912.27i	1.13388	−	0.951435i
$339$	−1305.33	+	1108.21i	−0.209133	+	0.177550i
$340$	−2894.77	+	1053.61i	−0.461738	+	0.168059i
$341$	−2834.11	−	4908.82i	−0.450075	−	0.779552i
$342$	6274.40	+	5142.60i	0.992048	+	0.813099i
$343$	3728.04	−	6457.15i	0.586866	−	1.01648i
$344$	677.099	−	3840.02i	0.106124	−	0.601860i
$345$	−655.116	−	543.296i	−0.102233	−	0.0847828i
$346$	−18075.3	−	6578.88i	−2.80848	−	1.02220i
$347$	1576.05	+	8938.23i	0.243824	+	1.38279i	0.823209	+	0.567739i	$0.192182\pi$
$347$	1576.05	+	8938.23i	0.243824	+	1.38279i	−0.579385	+	0.815054i	$0.696707\pi$
$348$	−966.280	−	1651.56i	−0.148845	−	0.254405i
$349$	−4507.96	−	3782.63i	−0.691420	−	0.580170i	0.227898	−	0.973685i	$-0.426815\pi$
$349$	−4507.96	−	3782.63i	−0.691420	−	0.580170i	−0.919318	+	0.393515i	$0.871259\pi$
$350$	−16445.8			−2.51161
$351$	1613.32	−	1402.04i	0.245335	−	0.213207i
$352$	7093.86			1.07416
$353$	1206.41	+	1012.30i	0.181900	+	0.152633i	0.729191	−	0.684310i	$-0.239896\pi$
$353$	1206.41	+	1012.30i	0.181900	+	0.152633i	−0.547291	+	0.836942i	$0.684341\pi$
$354$	18790.8	−	108.455i	2.82125	−	0.0162834i
$355$	96.0502	+	544.728i	0.0143600	+	0.0814399i
$356$	−8016.22	−	2917.67i	−1.19342	−	0.434371i
$357$	1880.71	−	11038.2i	0.278817	−	1.63642i
$358$	−3292.10	+	18670.5i	−0.486014	+	2.75632i
$359$	−1288.44	+	2231.64i	−0.189419	+	0.328082i	−0.945057	−	0.326907i	$-0.893994\pi$
$359$	−1288.44	+	2231.64i	−0.189419	+	0.328082i	0.755638	+	0.654989i	$0.227327\pi$
$360$	−2210.05	−	775.621i	−0.323555	−	0.113552i
$361$	1369.49	+	2372.03i	0.199664	+	0.345828i
$362$	4290.53	−	1561.62i	0.622942	−	0.226732i
$363$	1297.13	+	7116.00i	0.187554	+	1.02891i
$364$	−4952.78	+	4155.88i	−0.713176	+	0.598426i
$365$	113.430	−	95.1790i	0.0162663	−	0.0136490i
$366$	−804.649	−	4414.26i	−0.114917	−	0.630429i
$367$	7370.16	−	2682.52i	1.04828	−	0.381543i	0.240267	−	0.970707i	$-0.422765\pi$
$367$	7370.16	−	2682.52i	1.04828	−	0.381543i	0.808014	+	0.589164i	$0.200543\pi$
$368$	−477.130	−	826.413i	−0.0675872	−	0.117065i
$369$	−4912.88	−	1724.19i	−0.693102	−	0.243245i
$370$	2571.48	−	4453.94i	0.361311	−	0.625809i
$371$	17.1717	−	97.3856i	0.00240299	−	0.0136280i
$372$	1318.92	−	7740.99i	0.183825	−	1.07890i
$373$	742.689	+	270.317i	0.103096	+	0.0375240i	0.393053	−	0.919516i	$-0.371419\pi$
$373$	742.689	+	270.317i	0.103096	+	0.0375240i	−0.289957	+	0.957040i	$0.593641\pi$
$374$	2996.61	+	16994.6i	0.414308	+	2.34966i
$375$	3911.45	−	22.5757i	0.538630	−	0.00310881i
$376$	2442.58	+	2049.57i	0.335017	+	0.281113i
$377$	403.247			0.0550883
$378$	15120.6	−	13140.4i	2.05746	−	1.78802i
$379$	2352.16			0.318792			0.159396	−	0.987215i	$-0.449045\pi$
$379$	2352.16			0.318792			0.159396	+	0.987215i	$0.449045\pi$
$380$	2144.10	+	1799.11i	0.289447	+	0.242875i
$381$	2320.13	+	3965.55i	0.311979	+	0.533231i
$382$	−3631.92	−	20597.7i	−0.486454	−	2.75882i
$383$	−2407.58	−	876.286i	−0.321205	−	0.116909i	0.176386	−	0.984321i	$-0.443559\pi$
$383$	−2407.58	−	876.286i	−0.321205	−	0.116909i	−0.497590	+	0.867412i	$0.665782\pi$
$384$	10299.8	+	8541.73i	1.36877	+	1.13514i
$385$	866.310	−	4913.09i	0.114679	−	0.650374i
$386$	11748.8	−	20349.6i	1.54922	−	2.68333i
$387$	−2941.91	−	2411.24i	−0.386423	−	0.316718i
$388$	−7744.68	−	13414.2i	−1.01334	−	1.75516i
$389$	4602.57	−	1675.20i	0.599896	−	0.218344i	−0.0241805	−	0.999708i	$-0.507698\pi$
$389$	4602.57	−	1675.20i	0.599896	−	0.218344i	0.624076	+	0.781363i	$0.285475\pi$
$390$	885.405	−	751.694i	0.114960	−	0.0975987i
$391$	−2828.13	+	2373.08i	−0.365792	+	0.306936i
$392$	−12455.0	+	10451.0i	−1.60478	+	1.34657i
$393$	−8143.16	−	2910.75i	−1.04521	−	0.373608i
$394$	−5049.40	+	1837.83i	−0.645647	+	0.234996i
$395$	−491.723	−	851.688i	−0.0626361	−	0.108489i
$396$	−9604.39	+	17087.8i	−1.21878	+	2.16842i
$397$	−2389.95	+	4139.51i	−0.302136	+	0.523315i	−0.976620	−	0.214975i	$-0.931033\pi$
$397$	−2389.95	+	4139.51i	−0.302136	+	0.523315i	0.674484	+	0.738290i	$0.264366\pi$
$398$	−2495.81	+	14154.4i	−0.314330	+	1.78266i
$399$	−9539.82	+	3534.70i	−1.19696	+	0.443499i
$400$	1976.32	+	719.321i	0.247040	+	0.0899151i
$401$	−1985.67	−	11261.3i	−0.247281	−	1.40240i	−0.815134	−	0.579272i	$-0.803337\pi$
$401$	−1985.67	−	11261.3i	−0.247281	−	1.40240i	0.567853	−	0.823130i	$-0.307774\pi$
$402$	−5496.53	+	9648.46i	−0.681946	+	1.19707i
$403$	1267.70	+	1063.72i	0.156696	+	0.131484i
$404$	−1851.30			−0.227984
$405$	−1715.94	+	1508.69i	−0.210532	+	0.185105i
$406$	3779.37			0.461988
$407$	−14012.5	−	11757.9i	−1.70657	−	1.43198i
$408$	−5029.16	+	8828.04i	−0.610246	+	1.07121i
$409$	127.051	+	720.541i	0.0153600	+	0.0871111i	0.991524	−	0.129923i	$-0.0414729\pi$
$409$	127.051	+	720.541i	0.0153600	+	0.0871111i	−0.976164	+	0.217034i	$0.930362\pi$
$410$	−2658.64	−	967.667i	−0.320247	−	0.116560i
$411$	914.303	−	338.768i	0.109731	−	0.0406574i
$412$	2810.12	−	15937.0i	0.336031	−	1.90573i
$413$	−11782.5	+	20407.9i	−1.40382	+	2.43149i
$414$	−6604.52	+	76.2411i	−0.784045	+	0.00905083i
$415$	−75.0648	−	130.016i	−0.00887900	−	0.0153789i
$416$	−1946.18	+	708.353i	−0.229374	+	0.0834852i
$417$	6811.82	+	2434.87i	0.799943	+	0.285938i
$418$	12011.0	−	10078.4i	1.40544	−	1.17931i
$419$	9216.88	−	7733.88i	1.07464	−	0.901730i	0.0791753	−	0.996861i	$-0.474771\pi$
$419$	9216.88	−	7733.88i	1.07464	−	0.901730i	0.995465	+	0.0951306i	$0.0303269\pi$
$420$	5268.72	−	4473.05i	0.612113	−	0.519673i
$421$	9190.64	−	3345.12i	1.06395	−	0.387247i	0.250041	−	0.968235i	$-0.419556\pi$
$421$	9190.64	−	3345.12i	1.06395	−	0.387247i	0.813912	+	0.580988i	$0.197334\pi$
$422$	12717.6	+	22027.5i	1.46702	+	2.54095i
$423$	2910.44	−	1097.52i	0.334540	−	0.126155i
$424$	−44.8640	+	77.7067i	−0.00513865	+	0.00890040i
$425$	1412.93	−	8013.12i	0.161264	−	0.914573i
$426$	3304.23	+	2740.23i	0.375799	+	0.311654i
$427$	5287.56	+	1924.52i	0.599258	+	0.218112i
$428$	147.390	+	835.892i	0.0166457	+	0.0944027i
$429$	−2086.09	−	3565.54i	−0.234773	−	0.401272i
$430$	−1583.39	−	1328.62i	−0.177576	−	0.149004i
$431$	13216.3			1.47704			0.738521	−	0.674230i	$-0.235525\pi$
$431$	13216.3			1.47704			0.738521	+	0.674230i	$0.235525\pi$
$432$	−2391.81	+	917.752i	−0.266380	+	0.102211i
$433$	−8013.78			−0.889417			−0.444708	−	0.895675i	$-0.646693\pi$
$433$	−8013.78			−0.889417			−0.444708	+	0.895675i	$0.646693\pi$
$434$	11881.3	+	9969.59i	1.31410	+	1.10266i
$435$	−431.058	+	2.48793i	−0.0475119	+	0.000274224i
$436$	4321.66	+	24509.3i	0.474702	+	2.69217i
$437$	3152.06	+	1147.26i	0.345042	+	0.125585i
$438$	193.010	−	1132.81i	0.0210557	−	0.123579i
$439$	1447.64	−	8209.96i	0.157385	−	0.892575i	−0.799188	−	0.601081i	$-0.794737\pi$
$439$	1447.64	−	8209.96i	0.157385	−	0.892575i	0.956573	−	0.291493i	$-0.0941521\pi$
$440$	−2263.38	+	3920.29i	−0.245233	+	0.424756i
$441$	2934.32	+	15587.0i	0.316846	+	1.68308i
$442$	−2519.10	−	4363.21i	−0.271089	−	0.469540i
$443$	−9943.42	+	3619.11i	−1.06642	+	0.388147i	−0.814838	−	0.579688i	$-0.803174\pi$
$443$	−9943.42	+	3619.11i	−1.06642	+	0.388147i	−0.251586	+	0.967835i	$0.580952\pi$
$444$	−4544.40	−	24930.3i	−0.485738	−	2.66473i
$445$	−1472.18	+	1235.31i	−0.156827	+	0.131594i
$446$	15465.4	−	12977.0i	1.64194	−	1.37775i
$447$	1921.31	+	10540.2i	0.203299	+	1.11529i
$448$	−22427.5	+	8162.96i	−2.36518	+	0.860856i
$449$	4046.22	+	7008.25i	0.425285	+	0.736614i	0.996447	−	0.0842226i	$-0.0268407\pi$
$449$	4046.22	+	7008.25i	0.425285	+	0.736614i	−0.571162	+	0.820837i	$0.693507\pi$
$450$	11042.6	−	9485.22i	1.15679	−	0.993640i
$451$	−5031.44	+	8714.71i	−0.525324	+	0.909888i
$452$	−796.125	+	4515.05i	−0.0828464	+	0.469845i
$453$	−1351.39	+	7931.53i	−0.140163	+	0.822640i
$454$	7890.20	+	2871.80i	0.815651	+	0.296873i
$455$	252.923	+	1434.40i	0.0260598	+	0.147792i
$456$	9231.07	−	53.2789i	0.947992	−	0.00547152i
$457$	−10258.7	−	8608.05i	−1.05007	−	0.881111i	−0.0569661	−	0.998376i	$-0.518143\pi$
$457$	−10258.7	−	8608.05i	−1.05007	−	0.881111i	−0.993101	+	0.117266i	$0.962587\pi$
$458$	−9046.27			−0.922936
$459$	5103.54	+	8496.37i	0.518982	+	0.864002i
$460$	−2278.77			−0.230975
$461$	−1578.04	−	1324.13i	−0.159428	−	0.133776i	0.559584	−	0.828774i	$-0.310961\pi$
$461$	−1578.04	−	1324.13i	−0.159428	−	0.133776i	−0.719012	+	0.694997i	$0.755405\pi$
$462$	−19551.6	−	33417.5i	−1.96888	−	3.36520i
$463$	1067.23	+	6052.56i	0.107124	+	0.607530i	0.990351	+	0.138584i	$0.0442550\pi$
$463$	1067.23	+	6052.56i	0.107124	+	0.607530i	−0.883227	+	0.468946i	$0.844634\pi$
$464$	−454.174	−	165.306i	−0.0454407	−	0.0165391i
$465$	−1361.69	−	1129.27i	−0.135800	−	0.112620i
$466$	−2985.47	+	16931.4i	−0.296779	+	1.68312i
$467$	6632.44	−	11487.7i	0.657200	−	1.13830i	−0.324137	−	0.946010i	$-0.605074\pi$
$467$	6632.44	−	11487.7i	0.657200	−	1.13830i	0.981337	−	0.192294i	$-0.0615928\pi$
$468$	928.647	−	5647.04i	0.0917238	−	0.557766i
$469$	−6962.64	−	12059.6i	−0.685511	−	1.18734i
$470$	1588.30	−	578.093i	0.155878	−	0.0567350i
$471$	−1442.91	+	1225.00i	−0.141159	+	0.119841i
$472$	16379.7	−	13744.2i	1.59732	−	1.34031i
$473$	−5631.64	+	4725.51i	−0.547448	+	0.459364i
$474$	−7186.82	−	2568.91i	−0.696417	−	0.248933i
$475$	−6947.03	+	2528.51i	−0.671056	+	0.244244i
$476$	−14990.3	−	25963.9i	−1.44344	−	2.50011i
$477$	44.6377	+	75.2941i	0.00428474	+	0.00722742i
$478$	−3550.88	+	6150.30i	−0.339777	+	0.588511i
$479$	1327.47	−	7528.44i	0.126625	−	0.718128i	−0.853704	−	0.520759i	$-0.825649\pi$
$479$	1327.47	−	7528.44i	0.126625	−	0.718128i	0.980329	−	0.197369i	$-0.0632397\pi$
$480$	2076.04	−	769.214i	0.197412	−	0.0731451i
$481$	5018.36	+	1826.54i	0.475713	+	0.173145i
$482$	−3959.37	−	22454.7i	−0.374159	−	2.12196i
$483$	4100.00	−	7197.02i	0.386245	−	0.678004i
$484$	14836.0	+	12448.8i	1.39331	+	1.16913i
$485$	−3489.45			−0.326696
$486$	−2573.97	+	17544.1i	−0.240242	+	1.63749i
$487$	11505.9			1.07060			0.535298	−	0.844663i	$-0.320199\pi$
$487$	11505.9			1.07060			0.535298	+	0.844663i	$0.320199\pi$
$488$	−3911.19	−	3281.87i	−0.362810	−	0.304433i
$489$	−5284.71	+	9276.62i	−0.488717	+	0.857880i
$490$	1496.62	+	8487.74i	0.137980	+	0.782525i
$491$	−2048.18	−	745.475i	−0.188254	−	0.0685190i	0.246173	−	0.969226i	$-0.420827\pi$
$491$	−2048.18	−	745.475i	−0.188254	−	0.0685190i	−0.434427	+	0.900707i	$0.643049\pi$
$492$	−13072.3	+	4843.55i	−1.19785	+	0.443829i
$493$	−324.702	+	1841.48i	−0.0296630	+	0.168227i
$494$	−2288.81	+	3964.33i	−0.208458	+	0.361060i
$495$	2251.97	+	3798.58i	0.204482	+	0.344916i
$496$	−991.736	−	1717.74i	−0.0897788	−	0.155501i
$497$	−5058.54	+	1841.16i	−0.456552	+	0.166171i
$498$	−1097.12	−	392.162i	−0.0987209	−	0.0352875i
$499$	−8175.54	+	6860.09i	−0.733442	+	0.615431i	−0.931068	−	0.364847i	$-0.881121\pi$
$499$	−8175.54	+	6860.09i	−0.733442	+	0.615431i	0.197626	+	0.980278i	$0.436677\pi$
$500$	8022.80	−	6731.93i	0.717581	−	0.602122i
$501$	14819.8	−	12581.8i	1.32156	−	1.12198i
$502$	11241.1	−	4091.44i	0.999436	−	0.363765i
$503$	−6253.53	−	10831.4i	−0.554336	−	0.960138i	−0.997955	−	0.0639225i	$-0.979639\pi$
$503$	−6253.53	−	10831.4i	−0.554336	−	0.960138i	0.443619	−	0.896216i	$-0.353694\pi$
$504$	3698.89	−	22492.7i	0.326908	−	1.98790i
$505$	−208.530	+	361.185i	−0.0183752	+	0.0318268i
$506$	−2216.69	+	12571.4i	−0.194750	+	1.10448i
$507$	−7858.98	−	6517.54i	−0.688421	−	0.570916i
$508$	11559.6	+	4207.35i	1.00959	+	0.367462i
$509$	−2383.89	−	13519.7i	−0.207592	−	1.17731i	−0.893309	−	0.449442i	$-0.851623\pi$
$509$	−2383.89	−	13519.7i	−0.207592	−	1.17731i	0.685718	−	0.727868i	$-0.259488\pi$
$510$	2719.76	+	4648.59i	0.236143	+	0.403614i
$511$	1103.92	+	926.301i	0.0955669	+	0.0801901i
$512$	6525.55			0.563264
$513$	4366.91	−	7875.55i	0.375836	−	0.677805i
$514$	−4107.17			−0.352450
$515$	−2792.75	−	2343.39i	−0.238958	−	0.200509i
$516$	−10184.5	+	58.7815i	−0.868887	+	0.00501494i
$517$	−1043.91	−	5920.32i	−0.0888031	−	0.503628i
$518$	47033.9	+	17118.9i	3.98948	+	1.45205i
$519$	−3586.28	+	21048.5i	−0.303314	+	1.78020i
$520$	229.495	−	1301.53i	0.0193539	−	0.109761i
$521$	−1364.30	+	2363.03i	−0.114723	+	0.198707i	−0.917669	−	0.397345i	$-0.869931\pi$
$521$	−1364.30	+	2363.03i	−0.114723	+	0.198707i	0.802946	+	0.596052i	$0.203265\pi$
$522$	−2537.69	+	2179.78i	−0.212781	+	0.182771i
$523$	3952.82	+	6846.49i	0.330487	+	0.572421i	0.982607	−	0.185695i	$-0.0594536\pi$
$523$	3952.82	+	6846.49i	0.330487	+	0.572421i	−0.652120	+	0.758116i	$0.726120\pi$
$524$	−21757.9	+	7919.21i	−1.81392	+	0.660214i
$525$	3273.71	+	17959.4i	0.272146	+	1.49297i
$526$	−20046.7	+	16821.2i	−1.66175	+	1.39437i
$527$	−5878.40	+	4932.56i	−0.485896	+	0.407715i
$528$	887.906	+	4871.00i	0.0731840	+	0.401483i
$529$	8866.96	−	3227.31i	0.728771	−	0.265251i
$530$	23.7820	+	41.1917i	0.00194911	+	0.00337595i
$531$	−3858.95	−	20498.7i	−0.315375	−	1.67527i
$532$	−13619.8	+	23590.3i	−1.10995	+	1.92250i
$533$	510.161	−	2893.27i	0.0414588	−	0.235124i
$534$	−2505.03	+	14702.5i	−0.203003	+	1.19146i
$535$	179.683	+	65.3993i	0.0145203	+	0.00528497i
$536$	2194.11	+	12443.4i	0.176812	+	1.00275i
$537$	21044.1	−	121.460i	1.69110	−	0.00976051i
$538$	−17621.7	−	14786.3i	−1.41213	−	1.18491i
$539$	30654.1			2.44966
$540$	−957.853	+	6042.23i	−0.0763323	+	0.481512i
$541$	15190.8			1.20721			0.603606	−	0.797283i	$-0.293730\pi$
$541$	15190.8			1.20721			0.603606	+	0.797283i	$0.293730\pi$
$542$	9430.39	+	7913.04i	0.747362	+	0.627111i
$543$	−2559.42	−	4374.55i	−0.202275	−	0.345727i
$544$	−1667.68	−	9457.87i	−0.131436	−	0.745410i
$545$	5268.52	+	1917.59i	0.414089	+	0.150716i
$546$	8700.81	+	7215.68i	0.681979	+	0.565573i
$547$	−808.572	+	4585.64i	−0.0632030	+	0.358442i	0.936761	+	0.349970i	$0.113808\pi$
$547$	−808.572	+	4585.64i	−0.0632030	+	0.358442i	−0.999964	+	0.00847267i	$0.997303\pi$
$548$	1305.34	−	2260.91i	0.101754	−	0.176243i
$549$	−4660.35	+	1757.41i	−0.362293	+	0.136620i
$550$	−14067.2	−	24365.1i	−1.09060	−	1.88897i
$551$	1596.48	−	581.072i	0.123435	−	0.0449265i
$552$	−5729.38	+	4864.15i	−0.441773	+	0.375058i
$553$	7331.88	−	6152.18i	0.563803	−	0.473087i
$554$	−18981.0	+	15926.9i	−1.45564	+	1.22143i
$555$	−5375.74	−	1921.55i	−0.411149	−	0.146964i
$556$	18200.6	−	6624.48i	1.38827	−	0.505289i
$557$	−2359.71	−	4087.14i	−0.179505	−	0.310911i	0.762206	−	0.647334i	$-0.224116\pi$
$557$	−2359.71	−	4087.14i	−0.179505	−	0.310911i	−0.941711	+	0.336423i	$0.890783\pi$
$558$	−13727.8	+	158.471i	−1.04148	+	0.0120226i
$559$	1073.16	−	1858.77i	0.0811985	−	0.140640i
$560$	303.147	−	1719.23i	0.0228755	−	0.129734i
$561$	17962.2	−	6655.37i	1.35181	−	0.500874i
$562$	−8906.69	−	3241.77i	−0.668516	−	0.243320i
$563$	3316.99	+	18811.6i	0.248303	+	1.40820i	0.812695	+	0.582689i	$0.198000\pi$
$563$	3316.99	+	18811.6i	0.248303	+	1.40820i	−0.564392	+	0.825507i	$0.690889\pi$
$564$	4122.47	−	7236.46i	0.307779	−	0.540266i
$565$	791.203	+	663.898i	0.0589136	+	0.0494343i
$566$	−31701.4			−2.35426
$567$	−17359.7	−	13896.5i	−1.28579	−	1.02927i
$568$	4884.54			0.360829
$569$	14399.9	+	12083.0i	1.06094	+	0.890237i	0.994201	−	0.107534i	$-0.0342954\pi$
$569$	14399.9	+	12083.0i	1.06094	+	0.890237i	0.0667412	+	0.997770i	$0.478740\pi$
$570$	2422.20	−	4251.86i	0.177991	−	0.312440i
$571$	−2425.55	−	13756.0i	−0.177769	−	1.00818i	−0.934899	−	0.354914i	$-0.884510\pi$
$571$	−2425.55	−	13756.0i	−0.177769	−	1.00818i	0.757130	−	0.653265i	$-0.226601\pi$
$572$	−10393.6	−	3782.95i	−0.759750	−	0.276526i
$573$	−21770.4	+	8066.37i	−1.58721	+	0.588093i
$574$	4781.41	−	27116.7i	0.347687	−	1.97183i
$575$	3009.49	−	5212.60i	0.218269	−	0.378053i
$576$	10351.1	−	18416.3i	0.748776	−	1.33220i
$577$	−5985.88	−	10367.9i	−0.431881	−	0.748041i	0.565154	−	0.824985i	$-0.308817\pi$
$577$	−5985.88	−	10367.9i	−0.431881	−	0.748041i	−0.997035	+	0.0769449i	$0.975483\pi$
$578$	342.338	−	124.601i	0.0246356	−	0.00896663i
$579$	−24561.2	−	8779.34i	−1.76292	−	0.630150i
$580$	−884.147	+	741.887i	−0.0632969	+	0.0531124i
$581$	1119.26	−	939.171i	0.0799221	−	0.0670626i
$582$	−20643.9	+	17526.3i	−1.47030	+	1.24826i
$583$	158.969	−	57.8600i	0.0112930	−	0.00411032i
$584$	−653.792	−	1132.40i	−0.0463255	−	0.0802381i
$585$	−997.125	−	817.261i	−0.0704719	−	0.0577599i
$586$	−3678.81	+	6371.89i	−0.259335	+	0.449182i
$587$	215.649	−	1223.01i	0.0151632	−	0.0859946i	−0.976287	−	0.216480i	$-0.930542\pi$
$587$	215.649	−	1223.01i	0.0151632	−	0.0859946i	0.991450	+	0.130485i	$0.0416535\pi$
$588$	32688.7	+	27109.1i	2.29262	+	1.90129i
$589$	6551.70	+	2384.63i	0.458333	+	0.166820i
$590$	−1968.22	−	11162.3i	−0.137340	−	0.778892i
$591$	3012.11	+	5148.28i	0.209648	+	0.358328i
$592$	−4903.38	−	4114.42i	−0.340418	−	0.285645i
$593$	−19788.2			−1.37033			−0.685164	−	0.728389i	$-0.740270\pi$
$593$	−19788.2			−1.37033			−0.685164	+	0.728389i	$0.740270\pi$
$594$	32401.8	+	11161.9i	2.23815	+	0.771004i
$595$	−6754.01			−0.465357
$596$	21974.9	+	18439.1i	1.51028	+	1.26728i
$597$	15953.9	−	92.0812i	1.09372	−	0.00631262i
$598$	−647.171	−	3670.29i	−0.0442555	−	0.250985i
$599$	−10203.7	−	3713.84i	−0.696013	−	0.253328i	−0.0303055	−	0.999541i	$-0.509648\pi$
$599$	−10203.7	−	3713.84i	−0.696013	−	0.253328i	−0.665708	+	0.746213i	$0.731870\pi$
$600$	2782.17	−	16329.0i	0.189303	−	1.11105i
$601$	2149.42	−	12190.0i	0.145885	−	0.827353i	−0.820768	−	0.571262i	$-0.806454\pi$
$601$	2149.42	−	12190.0i	0.145885	−	0.827353i	0.966653	−	0.256091i	$-0.0824347\pi$
$602$	10058.1	−	17421.1i	0.680957	−	1.17945i
$603$	11630.6	+	4081.78i	0.785464	+	0.275660i
$604$	10771.3	+	18656.5i	0.725627	+	1.25682i
$605$	4099.87	−	1492.23i	0.275510	−	0.100277i
$606$	580.427	+	3184.19i	0.0389080	+	0.213447i
$607$	−437.013	+	366.698i	−0.0292221	+	0.0245203i	−0.657282	−	0.753645i	$-0.728294\pi$
$607$	−437.013	+	366.698i	−0.0292221	+	0.0245203i	0.628060	+	0.778165i	$0.283849\pi$
$608$	−6684.35	+	5608.83i	−0.445865	+	0.374125i
$609$	−752.325	−	4127.21i	−0.0500587	−	0.274619i
$610$	−2543.27	+	925.673i	−0.168810	+	0.0614417i
$611$	877.564	+	1519.99i	0.0581055	+	0.100642i
$612$	25040.2	+	8787.89i	1.65390	+	0.580440i
$613$	−6020.22	+	10427.3i	−0.396663	+	0.687040i	−0.993312	−	0.115462i	$-0.963165\pi$
$613$	−6020.22	+	10427.3i	−0.396663	+	0.687040i	0.596649	+	0.802502i	$0.296498\pi$
$614$	6915.36	−	39219.0i	0.454530	−	2.57777i
$615$	−527.495	+	3095.96i	−0.0345864	+	0.202994i
$616$	−41398.5	−	15067.8i	−2.70778	−	0.985552i
$617$	2860.54	+	16222.9i	0.186647	+	1.05853i	0.923821	+	0.382824i	$0.125048\pi$
$617$	2860.54	+	16222.9i	0.186647	+	1.05853i	−0.737174	+	0.675702i	$0.763840\pi$
$618$	−28292.3	+	163.294i	−1.84156	+	0.0106289i
$619$	16324.7	+	13698.0i	1.06001	+	0.889451i	0.994110	−	0.108375i	$-0.0345647\pi$
$619$	16324.7	+	13698.0i	1.06001	+	0.889451i	0.0658968	+	0.997826i	$0.479009\pi$
$620$	−4736.53			−0.306813
$621$	1397.96	+	7197.19i	0.0903352	+	0.465078i
$622$	41523.9			2.67678
$623$	−14327.6	−	12022.2i	−0.921383	−	0.773132i
$624$	−729.985	−	1247.69i	−0.0468314	−	0.0800439i
$625$	2090.33	+	11854.8i	0.133781	+	0.758709i
$626$	−21384.0	−	7783.14i	−1.36530	−	0.496928i
$627$	−13396.9	−	11110.2i	−0.853300	−	0.707652i
$628$	−880.031	+	4990.91i	−0.0559189	+	0.317132i
$629$	−12382.0	+	21446.2i	−0.784900	+	1.35949i
$630$	−9345.41	−	7659.65i	−0.591000	−	0.484394i
$631$	4125.03	+	7144.76i	0.260245	+	0.450758i	0.966307	−	0.257392i	$-0.0828632\pi$
$631$	4125.03	+	7144.76i	0.260245	+	0.450758i	−0.706062	+	0.708150i	$0.749530\pi$
$632$	−8160.78	+	2970.28i	−0.513637	+	0.186949i
$633$	21523.3	−	18272.9i	1.35146	−	1.14736i
$634$	18437.5	−	15470.9i	1.15496	−	0.969130i
$635$	2122.92	−	1781.34i	0.132670	−	0.111323i
$636$	220.689	+	78.8848i	0.0137593	+	0.00491821i
$637$	−8409.87	+	3060.94i	−0.523095	+	0.190391i
$638$	3232.76	+	5599.30i	0.200605	+	0.347459i
$639$	2334.69	−	4153.81i	0.144537	−	0.257155i
$640$	4035.56	−	6989.79i	0.249249	−	0.431712i
$641$	−4518.42	+	25625.2i	−0.278419	+	1.57899i	0.449467	+	0.893297i	$0.351614\pi$
$641$	−4518.42	+	25625.2i	−0.278419	+	1.57899i	−0.727887	+	0.685697i	$0.759497\pi$
$642$	1391.50	−	515.580i	0.0855424	−	0.0316952i
$643$	8192.22	+	2981.72i	0.502441	+	0.182874i	0.580792	−	0.814052i	$-0.302743\pi$
$643$	8192.22	+	2981.72i	0.502441	+	0.182874i	−0.0783505	+	0.996926i	$0.524965\pi$
$644$	−3851.08	−	21840.6i	−0.235642	−	1.33639i
$645$	−1135.71	+	1993.59i	−0.0693310	+	0.121702i
$646$	−16260.6	−	13644.3i	−0.990348	−	0.831001i
$647$	−23287.2			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$647$	−23287.2			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$648$	10489.2	+	17236.2i	0.635885	+	1.04491i
$649$	−40313.6			−2.43828
$650$	6292.27	+	5279.84i	0.379697	+	0.318604i
$651$	8522.05	−	14959.3i	0.513065	−	0.900619i
$652$	4963.86	+	28151.4i	0.298159	+	1.69094i
$653$	−14922.9	−	5431.50i	−0.894302	−	0.325499i	−0.146335	−	0.989235i	$-0.546748\pi$
$653$	−14922.9	−	5431.50i	−0.894302	−	0.325499i	−0.747967	+	0.663736i	$0.768970\pi$
$654$	40800.5	−	15117.4i	2.43949	−	0.903880i
$655$	−905.782	+	5136.94i	−0.0540333	+	0.306438i
$656$	−1760.65	+	3049.53i	−0.104789	+	0.181500i
$657$	−1275.49	+	14.7239i	−0.0757405	+	0.000874330i
$658$	8224.84	+	14245.8i	0.487291	+	0.844013i
$659$	19553.5	−	7116.89i	1.15584	−	0.420690i	0.308228	−	0.951313i	$-0.400264\pi$
$659$	19553.5	−	7116.89i	1.15584	−	0.420690i	0.847608	+	0.530623i	$0.178042\pi$
$660$	11133.7	+	3979.72i	0.656636	+	0.234713i
$661$	−13949.0	+	11704.6i	−0.820809	+	0.688740i	−0.953161	−	0.302462i	$-0.902191\pi$
$661$	−13949.0	+	11704.6i	−0.820809	+	0.688740i	0.132353	+	0.991203i	$0.457747\pi$
$662$	−1526.13	+	1280.58i	−0.0895995	+	0.0751829i
$663$	−4263.33	+	3619.49i	−0.249734	+	0.212020i
$664$	−1245.80	+	453.433i	−0.0728108	+	0.0265010i
$665$	3068.28	+	5314.42i	0.178922	+	0.309901i
$666$	−41454.7	+	15632.5i	−2.41192	+	0.909530i
$667$	−691.605	+	1197.90i	−0.0401485	+	0.0695393i
$668$	9038.64	−	51260.7i	0.523526	−	2.96906i
$669$	−17249.9	−	14305.5i	−0.996889	−	0.826732i
$670$	6293.99	+	2290.82i	0.362922	+	0.132093i
$671$	1671.57	+	9479.93i	0.0961701	+	0.545408i
$672$	10880.9	+	18597.5i	0.624611	+	1.06758i
$673$	8520.19	+	7149.29i	0.488008	+	0.409487i	0.853312	−	0.521401i	$-0.174590\pi$
$673$	8520.19	+	7149.29i	0.488008	+	0.409487i	−0.365304	+	0.930888i	$0.619035\pi$
$674$	36868.3			2.10699
$675$	−12556.4	−	10170.8i	−0.715992	−	0.579963i
$676$	−27336.9			−1.55535
$677$	26623.1	+	22339.4i	1.51139	+	1.26820i	0.861003	+	0.508600i	$0.169837\pi$
$677$	26623.1	+	22339.4i	1.51139	+	1.26820i	0.650385	+	0.759605i	$0.274608\pi$
$678$	8015.37	−	46.2622i	0.454024	−	0.00262049i
$679$	−5897.10	−	33444.1i	−0.333299	−	1.89023i
$680$	5758.81	+	2096.03i	0.324765	+	0.118205i
$681$	1565.48	−	9188.04i	0.0880898	−	0.517014i
$682$	−4607.48	+	26130.3i	−0.258695	+	1.46713i
$683$	3589.24	−	6216.75i	0.201081	−	0.348283i	−0.747796	−	0.663929i	$-0.768888\pi$
$683$	3589.24	−	6216.75i	0.201081	−	0.348283i	0.948877	+	0.315646i	$0.102221\pi$
$684$	−4460.71	−	23695.2i	−0.249356	−	1.32457i
$685$	−294.066	−	509.338i	−0.0164025	−	0.0284099i
$686$	−32797.7	+	11937.4i	−1.82540	+	0.664390i
$687$	1800.76	+	9878.85i	0.100005	+	0.548619i
$688$	−1970.67	+	1653.59i	−0.109202	+	0.0916317i
$689$	−37.8352	+	31.7475i	−0.00209203	+	0.00175542i
$690$	714.450	+	3919.43i	0.0394183	+	0.216247i
$691$	−24197.2	+	8807.08i	−1.33214	+	0.484858i	−0.907328	−	0.420424i	$-0.861881\pi$
$691$	−24197.2	+	8807.08i	−1.33214	+	0.484858i	−0.424810	+	0.905283i	$0.639659\pi$
$692$	28584.6	+	49510.0i	1.57026	+	2.71978i
$693$	−32601.1	+	28003.2i	−1.78703	+	1.53500i
$694$	21243.1	−	36794.1i	1.16192	−	2.01251i
$695$	757.694	−	4297.09i	0.0413539	−	0.234530i
$696$	−639.364	+	3752.54i	−0.0348205	+	0.204367i
$697$	12801.7	+	4659.43i	0.695693	+	0.253212i
$698$	4783.47	+	27128.4i	0.259394	+	1.47110i
$699$	19084.0	−	110.147i	1.03265	−	0.00596015i
$700$	37443.0	+	31418.4i	2.02173	+	1.69644i
$701$	27202.1			1.46563			0.732817	−	0.680426i	$-0.238205\pi$
$701$	27202.1			1.46563			0.732817	+	0.680426i	$0.238205\pi$
$702$	−10003.9	+	173.234i	−0.537854	+	0.00931381i
$703$	22500.1			1.20712
$704$	−31277.6	−	26245.0i	−1.67446	−	1.40504i
$705$	−947.466	−	1619.40i	−0.0506151	−	0.0865109i
$706$	−1280.14	−	7260.06i	−0.0682421	−	0.387020i
$707$	−3814.14	−	1388.23i	−0.202893	−	0.0738471i
$708$	−42989.3	−	35651.5i	−2.28197	−	1.89247i
$709$	−1745.24	+	9897.72i	−0.0924453	+	0.524283i	0.903055	+	0.429525i	$0.141319\pi$
$709$	−1745.24	+	9897.72i	−0.0924453	+	0.524283i	−0.995500	+	0.0947584i	$0.969792\pi$
$710$	1294.63	−	2242.36i	0.0684318	−	0.118527i
$711$	−1374.73	+	8359.63i	−0.0725125	+	0.440943i
$712$	8485.41	+	14697.2i	0.446635	+	0.773595i
$713$	−5334.14	+	1941.47i	−0.280175	+	0.101976i
$714$	−39957.4	+	33923.1i	−2.09435	+	1.77807i
$715$	−1908.78	+	1601.66i	−0.0998382	+	0.0837742i
$716$	43163.8	−	36218.7i	2.25294	−	1.89044i
$717$	7423.18	+	2653.40i	0.386644	+	0.138205i
$718$	11335.1	−	4125.66i	0.589170	−	0.214440i
$719$	−11693.7	−	20254.0i	−0.606537	−	1.05055i	−0.991806	−	0.127749i	$-0.959225\pi$
$719$	−11693.7	−	20254.0i	−0.606537	−	1.05055i	0.385269	−	0.922804i	$-0.374109\pi$
$720$	788.029	+	1329.23i	0.0407890	+	0.0688021i
$721$	17740.2	−	30727.0i	0.916339	−	1.58715i
$722$	2226.42	−	12626.7i	0.114763	−	0.650853i
$723$	−23733.2	+	8793.63i	−1.22081	+	0.452335i
$724$	−12751.8	−	4641.29i	−0.654583	−	0.238249i
$725$	−529.375	−	3002.23i	−0.0271179	−	0.153793i
$726$	16760.3	−	29420.5i	0.856793	−	1.50399i
$727$	−15563.4	−	13059.3i	−0.793970	−	0.666220i	0.152755	−	0.988264i	$-0.451185\pi$
$727$	−15563.4	−	13059.3i	−0.793970	−	0.666220i	−0.946725	+	0.322045i	$0.895630\pi$
$728$	12862.2			0.654812
$729$	19671.2	−	681.481i	0.999400	−	0.0346228i
$730$	−693.140			−0.0351428
$731$	7624.19	+	6397.46i	0.385761	+	0.323692i
$732$	−6601.11	+	11587.4i	−0.333311	+	0.585085i
$733$	84.3528	+	478.388i	0.00425053	+	0.0241060i	0.986859	−	0.161582i	$-0.0516597\pi$
$733$	84.3528	+	478.388i	0.00425053	+	0.0241060i	−0.982609	+	0.185688i	$0.940549\pi$
$734$	−34500.4	−	12557.1i	−1.73492	−	0.631460i
$735$	8971.00	−	3323.94i	0.450204	−	0.166810i
$736$	1233.63	−	6996.27i	0.0617829	−	0.350388i
$737$	11911.3	−	20630.9i	0.595328	−	1.03114i
$738$	12429.2	+	20965.4i	0.619955	+	1.04573i
$739$	−6592.06	−	11417.8i	−0.328137	−	0.568349i	0.654006	−	0.756490i	$-0.273087\pi$
$739$	−6592.06	−	11417.8i	−0.328137	−	0.568349i	−0.982142	+	0.188141i	$0.939754\pi$
$740$	−14363.5	+	5227.90i	−0.713533	+	0.259705i
$741$	4784.80	+	1710.31i	0.237212	+	0.0847908i
$742$	−354.605	+	297.549i	−0.0175444	+	0.0147215i
$743$	14943.7	−	12539.3i	0.737864	−	0.619141i	−0.194399	−	0.980922i	$-0.562276\pi$
$743$	14943.7	−	12539.3i	0.737864	−	0.619141i	0.932263	+	0.361781i	$0.117831\pi$
$744$	−11908.8	+	10110.4i	−0.586824	+	0.498204i
$745$	6072.70	−	2210.28i	0.298640	−	0.108696i
$746$	−1849.86	−	3204.05i	−0.0907883	−	0.157250i
$747$	−209.862	+	1276.15i	−0.0102790	+	0.0625061i
$748$	25644.4	−	44417.4i	1.25355	−	2.17121i
$749$	−323.149	+	1832.67i	−0.0157645	+	0.0894050i
$750$	−14094.1	−	11688.4i	−0.686191	−	0.569066i
$751$	20744.4	+	7550.33i	1.00795	+	0.366865i	0.792646	−	0.609682i	$-0.208703\pi$
$751$	20744.4	+	7550.33i	1.00795	+	0.366865i	0.215306	+	0.976547i	$0.430925\pi$
$752$	−365.295	−	2071.69i	−0.0177140	−	0.100461i
$753$	−6705.67	−	11461.3i	−0.324526	−	0.554678i
$754$	−1446.01	−	1213.35i	−0.0698418	−	0.0586042i
$755$	4853.13			0.233938
$756$	−59529.6	+	1030.85i	−2.86385	+	0.0495922i
$757$	−17820.4			−0.855604			−0.427802	−	0.903872i	$-0.640712\pi$
$757$	−17820.4			−0.855604			−0.427802	+	0.903872i	$0.640712\pi$
$758$	−8434.67	−	7077.52i	−0.404170	−	0.339139i
$759$	14169.7	−	81.7832i	0.677639	−	0.00391112i
$760$	−966.896	−	5483.54i	−0.0461487	−	0.261722i
$761$	21698.4	+	7897.57i	1.03360	+	0.376198i	0.802449	−	0.596721i	$-0.203530\pi$
$761$	21698.4	+	7897.57i	1.03360	+	0.376198i	0.231147	+	0.972919i	$0.425752\pi$
$762$	3612.32	−	21201.3i	0.171733	−	1.00793i
$763$	−9475.12	+	53736.1i	−0.449570	+	2.54964i
$764$	−31081.2	+	53834.3i	−1.47183	+	2.54929i
$765$	4535.03	−	3895.42i	0.214332	−	0.184104i
$766$	5996.69	+	10386.6i	0.282858	+	0.489924i
$767$	11059.9	−	4025.48i	0.520666	−	0.189507i
$768$	−5399.86	−	29623.3i	−0.253712	−	1.39185i
$769$	−16860.1	+	14147.3i	−0.790624	+	0.663412i	−0.945900	−	0.324459i	$-0.894818\pi$
$769$	−16860.1	+	14147.3i	−0.790624	+	0.663412i	0.155276	+	0.987871i	$0.450373\pi$
$770$	−17889.7	+	15011.3i	−0.837275	+	0.702557i
$771$	817.576	+	4485.17i	0.0381897	+	0.209507i
$772$	−65625.5	+	23885.7i	−3.05947	+	1.11356i
$773$	−13045.8	−	22595.9i	−0.607016	−	1.05138i	−0.991729	−	0.128346i	$-0.959033\pi$
$773$	−13045.8	−	22595.9i	−0.607016	−	1.05138i	0.384714	−	0.923036i	$-0.374300\pi$
$774$	3294.17	+	17498.6i	0.152980	+	0.812626i
$775$	6255.37	−	10834.6i	0.289935	−	0.502182i
$776$	−5350.85	+	30346.2i	−0.247531	+	1.40382i
$777$	9331.88	−	54770.4i	0.430861	−	2.52880i
$778$	−21545.0	−	7841.76i	−0.992837	−	0.361363i
$779$	−2149.39	−	12189.8i	−0.0988572	−	0.560647i
$780$	−3451.90	+	19.9233i	−0.158459	+	0.000914576i
$781$	−7054.68	−	5919.58i	−0.323222	−	0.271215i
$782$	17282.0			0.790283
$783$	2885.55	+	2337.33i	0.131700	+	0.106679i
$784$	10726.8			0.488646
$785$	874.591	+	733.869i	0.0397649	+	0.0333667i
$786$	20442.4	+	34940.1i	0.927682	+	1.58559i
$787$	−2687.28	−	15240.3i	−0.121717	−	0.690290i	−0.983204	−	0.182511i	$-0.941578\pi$
$787$	−2687.28	−	15240.3i	−0.121717	−	0.690290i	0.861487	−	0.507779i	$-0.169533\pi$
$788$	15007.3	+	5462.20i	0.678441	+	0.246932i
$789$	22359.9	+	18543.3i	1.00891	+	0.836703i
$790$	−799.406	+	4533.66i	−0.0360020	+	0.204178i
$791$	−5025.92	+	8705.14i	−0.225918	+	0.391301i
$792$	36487.8	−	13759.5i	1.63704	−	0.617326i
$793$	−1405.20	−	2433.88i	−0.0629258	−	0.108991i
$794$	21025.7	−	7652.74i	0.939768	−	0.342047i
$795$	40.2487	−	34.1705i	0.00179557	−	0.00152440i
$796$	32723.3	−	27458.1i	1.45709	−	1.22265i
$797$	−6124.73	+	5139.26i	−0.272207	+	0.228409i	−0.768664	−	0.639652i	$-0.779078\pi$
$797$	−6124.73	+	5139.26i	−0.272207	+	0.228409i	0.496457	+	0.868061i	$0.334634\pi$
$798$	44844.8	+	16029.7i	1.98933	+	0.711083i
$799$	−7647.84	+	2783.59i	−0.338625	+	0.123249i
$800$	7828.70	+	13559.7i	0.345983	+	0.599260i
$801$	16554.3	−	191.098i	0.730232	−	0.00842963i
$802$	−26764.2	+	46357.0i	−1.17840	+	2.04105i
$803$	−428.094	+	2427.84i	−0.0188133	+	0.106696i
$804$	30946.9	−	11466.4i	1.35748	−	0.502973i
$805$	−4694.84	−	1708.78i	−0.205555	−	0.0748157i
$806$	−1345.18	−	7628.87i	−0.0587863	−	0.333394i
$807$	−12639.4	+	22186.9i	−0.551337	+	0.967800i
$808$	2821.30	+	2367.35i	0.122838	+	0.103073i
$809$	−13390.4			−0.581929			−0.290965	−	0.956734i	$-0.593976\pi$
$809$	−13390.4			−0.581929			−0.290965	+	0.956734i	$0.593976\pi$
$810$	10692.8	−	246.903i	0.463835	−	0.0107102i
$811$	−3713.56			−0.160790			−0.0803950	−	0.996763i	$-0.525618\pi$
$811$	−3713.56			−0.160790			−0.0803950	+	0.996763i	$0.525618\pi$
$812$	−8604.70	−	7220.20i	−0.371879	−	0.312044i
$813$	6764.10	−	11873.5i	0.291792	−	0.512204i
$814$	14868.9	+	84325.7i	0.640239	+	3.63098i
$815$	6051.43	+	2202.54i	0.260089	+	0.0946645i
$816$	6285.51	−	2328.91i	0.269653	−	0.0999119i
$817$	1570.27	−	8905.42i	0.0672419	−	0.381348i
$818$	1712.48	−	2966.09i	0.0731972	−	0.126781i
$819$	6147.79	−	10938.0i	0.262297	−	0.466670i
$820$	4204.42	+	7282.28i	0.179055	+	0.310132i
$821$	−32799.2	+	11937.9i	−1.39427	+	0.507474i	−0.926473	−	0.376360i	$-0.877175\pi$
$821$	−32799.2	+	11937.9i	−1.39427	+	0.507474i	−0.467800	+	0.883834i	$0.654953\pi$
$822$	−4297.96	−	1536.29i	−0.182370	−	0.0651879i
$823$	21639.4	−	18157.6i	0.916527	−	0.769057i	−0.0568227	−	0.998384i	$-0.518097\pi$
$823$	21639.4	−	18157.6i	0.916527	−	0.769057i	0.973349	+	0.229327i	$0.0736525\pi$
$824$	−24662.0	+	20693.8i	−1.04265	+	0.874884i
$825$	−23807.4	+	20212.0i	−1.00469	+	0.852962i
$826$	103658.	−	37728.2i	4.36647	−	1.58927i
$827$	11000.1	+	19052.7i	0.462527	+	0.801120i	0.999086	−	0.0427426i	$-0.0136095\pi$
$827$	11000.1	+	19052.7i	0.462527	+	0.801120i	−0.536559	+	0.843863i	$0.680276\pi$
$828$	15182.5	+	12443.8i	0.637233	+	0.522287i
$829$	−8114.55	+	14054.8i	−0.339964	+	0.588835i	−0.984426	−	0.175802i	$-0.943748\pi$
$829$	−8114.55	+	14054.8i	−0.339964	+	0.588835i	0.644462	+	0.764637i	$0.277082\pi$
$830$	−122.035	+	692.094i	−0.00510348	+	0.0289433i
$831$	21171.1	+	17557.5i	0.883777	+	0.732926i
$832$	11201.6	+	4077.05i	0.466762	+	0.169887i
$833$	−7206.39	−	40869.5i	−0.299744	−	1.69993i
$834$	−17100.3	−	29227.7i	−0.709993	−	1.21351i
$835$	−8982.76	−	7537.43i	−0.372289	−	0.312387i
$836$	−46600.0			−1.92786
$837$	2905.72	+	14959.7i	0.119996	+	0.617781i
$838$	−56321.9			−2.32173
$839$	−180.074	−	151.100i	−0.00740983	−	0.00621759i	0.639075	−	0.769144i	$-0.279317\pi$
$839$	−180.074	−	151.100i	−0.00740983	−	0.00621759i	−0.646485	+	0.762927i	$0.723762\pi$
$840$	−13749.2	+	79.3563i	−0.564754	+	0.00325959i
$841$	−4113.45	−	23328.5i	−0.168660	−	0.956519i
$842$	−43022.2	−	15658.8i	−1.76086	−	0.640900i
$843$	−1767.15	+	10371.7i	−0.0721993	+	0.423750i
$844$	13127.1	−	74447.2i	0.535369	−	3.03623i
$845$	−3079.23	+	5333.38i	−0.125359	+	0.217129i
$846$	−13739.0	−	4821.73i	−0.558342	−	0.195951i
$847$	21230.8	+	36772.8i	0.861273	+	1.49177i
$848$	55.6279	−	20.2469i	0.00225268	−	0.000819907i
$849$	6310.50	+	34619.0i	0.255095	+	1.39944i
$850$	−29177.7	+	24483.0i	−1.17740	+	0.987954i
$851$	−14032.9	+	11775.0i	−0.565266	+	0.474315i
$852$	−2287.91	−	12551.3i	−0.0919981	−	0.504696i
$853$	2924.36	−	1064.38i	0.117384	−	0.0427242i	−0.282661	−	0.959220i	$-0.591217\pi$
$853$	2924.36	−	1064.38i	0.117384	−	0.0427242i	0.400044	+	0.916496i	$0.368995\pi$
$854$	−13170.0	−	22811.2i	−0.527716	−	0.914031i
$855$	−5125.35	−	1798.75i	−0.205009	−	0.0719485i
$856$	844.282	−	1462.34i	0.0337114	−	0.0583899i
$857$	7331.93	−	41581.4i	0.292245	−	1.65740i	−0.385949	−	0.922520i	$-0.626126\pi$
$857$	7331.93	−	41581.4i	0.292245	−	1.65740i	0.678194	−	0.734883i	$-0.262763\pi$
$858$	−3247.94	+	19062.7i	−0.129234	+	0.758496i
$859$	−29900.8	−	10883.0i	−1.18766	−	0.432273i	−0.328759	−	0.944414i	$-0.606630\pi$
$859$	−29900.8	−	10883.0i	−1.18766	−	0.432273i	−0.858902	+	0.512141i	$0.828853\pi$
$860$	1066.76	+	6049.88i	0.0422978	+	0.239883i
$861$	−30564.2	+	176.407i	−1.20979	+	0.00698251i
$862$	−47392.5	−	39767.1i	−1.87262	−	1.57131i
$863$	2920.52			0.115198			0.0575990	−	0.998340i	$-0.481656\pi$
$863$	2920.52			0.115198			0.0575990	+	0.998340i	$0.481656\pi$
$864$	−18032.3	−	6211.80i	−0.710035	−	0.244595i
$865$	12879.1			0.506245
$866$	28736.8	+	24113.0i	1.12762	+	0.946183i
$867$	−204.215	−	349.042i	−0.00799941	−	0.0136725i
$868$	−8004.65	−	45396.6i	−0.313013	−	1.77519i
$869$	15386.2	+	5600.11i	0.600622	+	0.218608i
$870$	1553.23	+	1288.11i	0.0605280	+	0.0501966i
$871$	−1207.74	+	6849.43i	−0.0469835	+	0.266457i
$872$	24755.3	−	42877.5i	0.961378	−	1.66516i
$873$	23248.8	+	19055.1i	0.901319	+	0.738736i
$874$	−7851.02	−	13598.4i	−0.303850	−	0.526283i
$875$	21577.1	−	7853.41i	0.833643	−	0.303421i
$876$	−2603.58	+	2210.39i	−0.100419	+	0.0852538i
$877$	414.658	−	347.940i	0.0159658	−	0.0133969i	−0.634770	−	0.772701i	$-0.718905\pi$
$877$	414.658	−	347.940i	0.0159658	−	0.0133969i	0.650736	+	0.759304i	$0.274461\pi$
$878$	−29894.5	+	25084.4i	−1.14908	+	0.964190i
$879$	7690.64	+	2749.00i	0.295107	+	0.105485i
$880$	2806.42	−	1021.45i	0.107505	−	0.0391286i
$881$	−2134.73	−	3697.46i	−0.0816355	−	0.141397i	0.822317	−	0.569030i	$-0.192681\pi$
$881$	−2134.73	−	3697.46i	−0.0816355	−	0.141397i	−0.903953	+	0.427633i	$0.859348\pi$
$882$	36378.3	−	64723.0i	1.38880	−	2.47090i
$883$	203.423	−	352.338i	0.00775279	−	0.0134282i	−0.862123	−	0.506699i	$-0.830866\pi$
$883$	203.423	−	352.338i	0.00775279	−	0.0134282i	0.869876	+	0.493271i	$0.164199\pi$
$884$	−2600.21	+	14746.5i	−0.0989303	+	0.561062i
$885$	−11797.9	+	4371.35i	−0.448114	+	0.166035i
$886$	46546.1	+	16941.4i	1.76495	+	0.642389i
$887$	5343.16	+	30302.6i	0.202261	+	1.14708i	0.901692	+	0.432380i	$0.142326\pi$
$887$	5343.16	+	30302.6i	0.202261	+	1.14708i	−0.699430	+	0.714701i	$0.746563\pi$
$888$	−24954.2	+	43803.9i	−0.943027	+	1.65536i
$889$	20660.7	+	17336.4i	0.779457	+	0.654042i
$890$	8996.10			0.338820
$891$	5739.21	−	37605.8i	0.215792	−	1.41396i
$892$	−60002.4			−2.25227
$893$	5664.61	+	4753.17i	0.212272	+	0.178117i
$894$	24825.2	−	43577.4i	0.928723	−	1.63025i
$895$	−2204.24	−	12500.9i	−0.0823236	−	0.466880i
$896$	73812.6	+	26865.6i	2.75213	+	1.00169i
$897$	−3879.26	+	1437.34i	−0.144398	+	0.0535023i
$898$	6578.04	−	37305.9i	0.244446	−	1.38632i
$899$	−1437.53	+	2489.88i	−0.0533309	+	0.0923718i
$900$	−43262.2	+	499.408i	−1.60230	+	0.0184966i
$901$	−114.513	−	198.343i	−0.00423417	−	0.00733380i
$902$	44264.5	−	16110.9i	1.63397	−	0.594718i
$903$	−21026.6	−	7515.91i	−0.774885	−	0.276981i
$904$	6986.89	−	5862.69i	0.257058	−	0.215697i
$905$	−2341.88	+	1965.07i	−0.0860183	+	0.0721779i
$906$	28711.6	−	24375.6i	1.05285	−	0.893847i
$907$	8953.27	−	3258.72i	0.327771	−	0.119299i	−0.172893	−	0.984941i	$-0.555311\pi$
$907$	8953.27	−	3258.72i	0.327771	−	0.119299i	0.500664	+	0.865642i	$0.333089\pi$
$908$	−12477.7	−	21612.0i	−0.456043	−	0.789889i
$909$	3361.70	−	1267.69i	0.122663	−	0.0462560i
$910$	3409.06	−	5904.67i	0.124186	−	0.215097i
$911$	−8754.93	+	49651.7i	−0.318402	+	1.80575i	0.234076	+	0.972218i	$0.424793\pi$
$911$	−8754.93	+	49651.7i	−0.318402	+	1.80575i	−0.552478	+	0.833527i	$0.686318\pi$
$912$	−4687.95	−	3887.77i	−0.170212	−	0.141159i
$913$	2348.80	+	854.895i	0.0851414	+	0.0309889i
$914$	10885.7	+	61735.6i	0.393945	+	2.23417i
$915$	1517.13	+	2593.07i	0.0548140	+	0.0936877i
$916$	20596.1	+	17282.2i	0.742921	+	0.623385i
$917$	−50765.0			−1.82814
$918$	7264.25	−	45823.6i	0.261172	−	1.64750i
$919$	40352.3			1.44842			0.724210	−	0.689579i	$-0.242205\pi$
$919$	40352.3			1.44842			0.724210	+	0.689579i	$0.242205\pi$
$920$	3472.75	+	2913.98i	0.124449	+	0.104425i
$921$	−44205.1	+	255.138i	−1.58155	+	0.00912821i
$922$	1674.48	+	9496.47i	0.0598115	+	0.339208i
$923$	2526.53	+	919.581i	0.0900993	+	0.0327935i
$924$	−19327.3	+	113435.i	−0.688119	+	4.03868i
$925$	7010.81	−	39760.3i	0.249204	−	1.41331i
$926$	14384.8	−	24915.3i	0.510491	−	0.884197i
$927$	5810.20	+	30863.6i	0.205860	+	1.09352i
$928$	−1799.10	−	3116.13i	−0.0636404	−	0.110228i
$929$	5272.06	−	1918.87i	0.186190	−	0.0677676i	−0.247243	−	0.968954i	$-0.579524\pi$
$929$	5272.06	−	1918.87i	0.186190	−	0.0677676i	0.433433	+	0.901186i	$0.357302\pi$
$930$	1485.02	+	8146.72i	0.0523609	+	0.287249i
$931$	−28884.5	+	24237.0i	−1.01681	+	0.853205i
$932$	39143.4	−	32845.2i	1.37573	−	1.15438i
$933$	−8265.78	−	45345.6i	−0.290042	−	1.59115i
$934$	−58349.4	+	21237.4i	−2.04416	+	0.744015i
$935$	−5777.18	−	10006.4i	−0.202068	−	0.349993i
$936$	−8636.38	+	7418.34i	−0.301591	+	0.259056i
$937$	3778.88	−	6545.21i	0.131751	−	0.228199i	−0.792601	−	0.609741i	$-0.791273\pi$
$937$	3778.88	−	6545.21i	0.131751	−	0.228199i	0.924352	+	0.381542i	$0.124607\pi$
$938$	−11319.3	+	64195.2i	−0.394019	+	2.23459i
$939$	−4242.75	+	24901.4i	−0.147451	+	0.865417i
$940$	−4720.57	−	1718.15i	−0.163796	−	0.0596167i
$941$	−8492.14	−	48161.3i	−0.294193	−	1.66845i	−0.670463	−	0.741943i	$-0.733905\pi$
$941$	−8492.14	−	48161.3i	−0.294193	−	1.66845i	0.376270	−	0.926510i	$-0.377206\pi$
$942$	8860.14	−	51.1380i	0.306453	−	0.00176875i
$943$	7719.84	+	6477.71i	0.266588	+	0.223694i
$944$	−14106.9			−0.486377
$945$	−6504.31	+	11730.3i	−0.223900	+	0.403794i
$946$	34413.4			1.18275
$947$	−20585.6	−	17273.4i	−0.706380	−	0.592724i	0.217201	−	0.976127i	$-0.430307\pi$
$947$	−20585.6	−	17273.4i	−0.706380	−	0.592724i	−0.923581	+	0.383403i	$0.874752\pi$
$948$	11454.9	+	19578.7i	0.392445	+	0.670765i
$949$	−124.984	−	708.818i	−0.00427518	−	0.0242458i
$950$	32519.7	+	11836.2i	1.11061	+	0.404228i
$951$	−20565.0	−	17054.8i	−0.701224	−	0.581534i
$952$	−10356.9	+	58736.7i	−0.352592	+	1.99965i
$953$	11651.1	−	20180.4i	0.396031	−	0.685946i	−0.597201	−	0.802091i	$-0.703721\pi$
$953$	11651.1	−	20180.4i	0.396031	−	0.685946i	0.993232	+	0.116146i	$0.0370540\pi$
$954$	66.4884	−	404.312i	0.00225644	−	0.0137212i
$955$	7001.99	+	12127.8i	0.237255	+	0.410938i
$956$	19834.1	−	7219.04i	0.671006	−	0.244226i
$957$	5471.12	−	4644.89i	0.184803	−	0.156894i
$958$	−27412.9	+	23002.1i	−0.924499	+	0.775747i
$959$	4384.71	−	3679.21i	0.147643	−	0.123887i
$960$	−11999.3	−	4289.13i	−0.403413	−	0.144199i
$961$	16907.1	−	6153.69i	0.567525	−	0.206562i
$962$	−12499.5	−	21649.8i	−0.418920	−	0.725591i
$963$	−840.025	−	1416.94i	−0.0281095	−	0.0474145i
$964$	−33883.5	+	58687.9i	−1.13207	+	1.96080i
$965$	−2732.00	+	15493.9i	−0.0911358	+	0.516857i
$966$	−36357.8	+	13471.3i	−1.21096	+	0.448687i
$967$	−21473.4	−	7815.69i	−0.714104	−	0.259913i	−0.0406836	−	0.999172i	$-0.512954\pi$
$967$	−21473.4	−	7815.69i	−0.714104	−	0.259913i	−0.673421	+	0.739259i	$0.735176\pi$
$968$	−6690.38	−	37943.0i	−0.222146	−	1.25985i
$969$	−11663.2	+	20473.2i	−0.386662	+	0.678734i
$970$	12512.9	+	10499.6i	0.414191	+	0.347547i
$971$	−3397.56			−0.112289			−0.0561446	−	0.998423i	$-0.517881\pi$
$971$	−3397.56			−0.112289			−0.0561446	+	0.998423i	$0.517881\pi$
$972$	39377.0	−	35026.3i	1.29940	−	1.15583i
$973$	42465.3			1.39915
$974$	−41259.2	−	34620.6i	−1.35732	−	1.13893i
$975$	4513.23	−	7922.39i	0.148245	−	0.260225i
$976$	584.930	+	3317.30i	0.0191836	+	0.108795i
$977$	33100.7	+	12047.7i	1.08392	+	0.394513i	0.821364	−	0.570404i	$-0.193213\pi$
$977$	33100.7	+	12047.7i	1.08392	+	0.394513i	0.262553	+	0.964918i	$0.415436\pi$
$978$	46863.4	−	17363.9i	1.53224	−	0.567725i
$979$	5556.13	−	31510.4i	0.181384	−	1.02868i
$980$	12807.8	−	22183.7i	0.417478	−	0.723093i
$981$	−24630.5	−	41546.3i	−0.801623	−	1.35216i
$982$	5101.51	+	8836.07i	0.165780	+	0.287139i
$983$	−57337.1	+	20869.0i	−1.86040	+	0.677129i	−0.881702	+	0.471807i	$0.843602\pi$
$983$	−57337.1	+	20869.0i	−1.86040	+	0.677129i	−0.978694	+	0.205322i	$0.934176\pi$
$984$	26115.3	+	9334.85i	0.846062	+	0.302423i
$985$	2756.09	−	2312.63i	0.0891535	−	0.0748086i
$986$	6705.27	−	5626.39i	0.216571	−	0.181725i
$987$	13919.7	−	11817.6i	0.448905	−	0.381113i
$988$	12784.6	−	4653.21i	0.411672	−	0.149836i
$989$	3681.15	+	6375.93i	0.118356	+	0.204998i
$990$	3354.33	−	20397.5i	0.107684	−	0.654822i
$991$	−676.987	+	1172.58i	−0.0217005	+	0.0375864i	−0.876672	−	0.481089i	$-0.840241\pi$
$991$	−676.987	+	1172.58i	−0.0217005	+	0.0375864i	0.854971	+	0.518675i	$0.173575\pi$
$992$	2564.16	−	14542.1i	0.0820687	−	0.465435i
$993$	1702.23	+	1411.68i	0.0543994	+	0.0451141i
$994$	23679.5	+	8618.63i	0.755602	+	0.275017i
$995$	−1671.07	−	9477.13i	−0.0532428	−	0.301955i
$996$	1748.67	+	2988.81i	0.0556312	+	0.0950845i
$997$	12681.5	+	10641.1i	0.402837	+	0.338020i	0.821589	−	0.570081i	$-0.193088\pi$
$997$	12681.5	+	10641.1i	0.402837	+	0.338020i	−0.418752	+	0.908100i	$0.637532\pi$
$998$	49958.5			1.58458
$999$	25323.2	+	42158.1i	0.801994	+	1.33516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.e.a.16.1	✓	48
3.2	odd	2		81.4.e.a.46.8		48
9.2	odd	6		243.4.e.a.217.8		48
9.4	even	3		243.4.e.c.55.8		48
9.5	odd	6		243.4.e.b.55.1		48
9.7	even	3		243.4.e.d.217.1		48
27.4	even	9		243.4.e.d.28.1		48
27.5	odd	18		81.4.e.a.37.8		48
27.7	even	9		729.4.a.d.1.2		24
27.13	even	9		243.4.e.c.190.8		48
27.14	odd	18		243.4.e.b.190.1		48
27.20	odd	18		729.4.a.c.1.23		24
27.22	even	9	inner	27.4.e.a.22.1	yes	48
27.23	odd	18		243.4.e.a.28.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.16.1	✓	48	1.1	even	1	trivial
27.4.e.a.22.1	yes	48	27.22	even	9	inner
81.4.e.a.37.8		48	27.5	odd	18
81.4.e.a.46.8		48	3.2	odd	2
243.4.e.a.28.8		48	27.23	odd	18
243.4.e.a.217.8		48	9.2	odd	6
243.4.e.b.55.1		48	9.5	odd	6
243.4.e.b.190.1		48	27.14	odd	18
243.4.e.c.55.8		48	9.4	even	3
243.4.e.c.190.8		48	27.13	even	9
243.4.e.d.28.1		48	27.4	even	9
243.4.e.d.217.1		48	9.7	even	3
729.4.a.c.1.23		24	27.20	odd	18
729.4.a.d.1.2		24	27.7	even	9

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.58593 - 3.00895i) q^{2} +(-2.57206 + 4.51492i) q^{3} +(2.41590 + 13.7013i) q^{4} +(2.94522 + 1.07197i) q^{5} +(22.8084 - 8.45097i) q^{6} +(-5.29680 + 30.0397i) q^{7} +(13.8388 - 23.9695i) q^{8} +(-13.7690 - 23.2253i) q^{9} +O(q^{10})\)	\(q+(-3.58593 - 3.00895i) q^{2} +(-2.57206 + 4.51492i) q^{3} +(2.41590 + 13.7013i) q^{4} +(2.94522 + 1.07197i) q^{5} +(22.8084 - 8.45097i) q^{6} +(-5.29680 + 30.0397i) q^{7} +(13.8388 - 23.9695i) q^{8} +(-13.7690 - 23.2253i) q^{9} +(-7.33583 - 12.7060i) q^{10} +(-49.0358 + 17.8476i) q^{11} +(-68.0740 - 24.3329i) q^{12} +(11.6707 - 9.79286i) q^{13} +(109.382 - 91.7822i) q^{14} +(-12.4152 + 10.5403i) q^{15} +(-17.1590 + 6.24538i) q^{16} +(35.3229 + 61.1810i) q^{17} +(-20.5091 + 124.714i) q^{18} +(32.0937 - 55.5879i) q^{19} +(-7.57202 + 42.9431i) q^{20} +(-122.003 - 101.178i) q^{21} +(229.541 + 83.5461i) q^{22} +(9.07464 + 51.4649i) q^{23} +(72.6261 + 124.132i) q^{24} +(-88.2303 - 74.0341i) q^{25} -71.3164 q^{26} +(140.275 - 2.42909i) q^{27} -424.378 q^{28} +(20.2760 + 17.0136i) q^{29} +(76.2350 - 0.440005i) q^{30} +(18.8621 + 106.972i) q^{31} +(-127.744 - 46.4951i) q^{32} +(45.5427 - 267.298i) q^{33} +(57.4254 - 325.675i) q^{34} +(-47.8020 + 82.7954i) q^{35} +(284.951 - 244.763i) q^{36} +(175.269 + 303.574i) q^{37} +(-282.346 + 102.766i) q^{38} +(14.1963 + 77.8800i) q^{39} +(66.4530 - 55.7607i) q^{40} +(147.723 - 123.955i) q^{41} +(133.053 + 729.919i) q^{42} +(132.385 - 48.1843i) q^{43} +(-363.000 - 628.734i) q^{44} +(-15.6559 - 83.1637i) q^{45} +(122.314 - 211.854i) q^{46} +(-20.0049 + 113.454i) q^{47} +(15.9367 - 93.5352i) q^{48} +(-552.010 - 200.915i) q^{49} +(93.6228 + 530.961i) q^{50} +(-367.080 + 2.11867i) q^{51} +(162.370 + 136.245i) q^{52} -3.24190 q^{53} +(-510.325 - 413.370i) q^{54} -163.553 q^{55} +(646.734 + 542.674i) q^{56} +(168.428 + 287.876i) q^{57} +(-21.5153 - 122.019i) q^{58} +(725.956 + 264.226i) q^{59} +(-174.409 - 144.639i) q^{60} +(32.0329 - 181.668i) q^{61} +(254.236 - 440.349i) q^{62} +(770.612 - 290.596i) q^{63} +(391.221 + 677.615i) q^{64} +(44.8704 - 16.3315i) q^{65} +(-967.597 + 821.474i) q^{66} +(-349.715 + 293.446i) q^{67} +(-752.921 + 631.776i) q^{68} +(-255.700 - 91.3995i) q^{69} +(420.541 - 153.065i) q^{70} +(88.2401 + 152.836i) q^{71} +(-747.245 + 8.62602i) q^{72} +(23.6217 - 40.9140i) q^{73} +(284.939 - 1615.97i) q^{74} +(561.192 - 207.933i) q^{75} +(839.159 + 305.429i) q^{76} +(-276.402 - 1567.55i) q^{77} +(183.430 - 321.988i) q^{78} +(-240.365 - 201.690i) q^{79} -57.2321 q^{80} +(-349.829 + 639.579i) q^{81} -902.697 q^{82} +(-36.6934 - 30.7894i) q^{83} +(1091.53 - 1916.03i) q^{84} +(38.4493 + 218.057i) q^{85} +(-619.708 - 225.555i) q^{86} +(-128.966 + 47.7846i) q^{87} +(-250.799 + 1422.35i) q^{88} +(-306.581 + 531.013i) q^{89} +(-194.094 + 345.326i) q^{90} +(232.357 + 402.454i) q^{91} +(-683.210 + 248.668i) q^{92} +(-531.485 - 189.978i) q^{93} +(413.112 - 346.642i) q^{94} +(154.112 - 129.315i) q^{95} +(538.488 - 457.167i) q^{96} +(-1046.19 + 380.782i) q^{97} +(1374.92 + 2381.44i) q^{98} +(1089.69 + 893.127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Introduction

L-functions

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