LMFDB - Embedded newform 229.4.g.a.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [229,4,Mod(16,229)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(229, base_ring=CyclotomicField(38))

chi = DirichletCharacter(H, H._module([14]))

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

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

chi := DirichletCharacter("229.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 229 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	229.g (of order $19$, degree $18$, 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:	$13.5114373913$
Analytic rank:	$0$
Dimension:	$1026$
Relative dimension:	$57$ over $\Q(\zeta_{19})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{19}]$

Embedding invariants

Embedding label			16.3
Character	$\chi$	$=$	229.16
Dual form			229.4.g.a.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.54340 + 3.84916i) q^{2} +(-0.642373 + 1.46446i) q^{3} +(-1.59970 - 19.3055i) q^{4} +(-15.3330 - 5.26382i) q^{5} +(-3.36076 - 7.66177i) q^{6} +(-0.615535 - 2.43069i) q^{7} +(46.9494 + 36.5422i) q^{8} +(16.5546 + 17.9831i) q^{9} +O(q^{10})$	\(q+(-3.54340 + 3.84916i) q^{2} +(-0.642373 + 1.46446i) q^{3} +(-1.59970 - 19.3055i) q^{4} +(-15.3330 - 5.26382i) q^{5} +(-3.36076 - 7.66177i) q^{6} +(-0.615535 - 2.43069i) q^{7} +(46.9494 + 36.5422i) q^{8} +(16.5546 + 17.9831i) q^{9} +(74.5922 - 40.3673i) q^{10} +(20.0169 - 30.6382i) q^{11} +(29.2998 + 10.0586i) q^{12} +(20.1090 + 6.90342i) q^{13} +(11.5372 + 6.24362i) q^{14} +(17.5582 - 19.0732i) q^{15} +(-154.157 + 25.7243i) q^{16} +(-23.2211 - 7.97182i) q^{17} -127.879 q^{18} +(39.1602 - 13.4437i) q^{19} +(-77.0927 + 304.432i) q^{20} +(3.95506 + 0.659983i) q^{21} +(47.0032 + 185.611i) q^{22} +(-115.494 - 62.5021i) q^{23} +(-83.6737 + 45.2819i) q^{24} +(108.750 + 84.6437i) q^{25} +(-97.8265 + 52.9411i) q^{26} +(-77.8074 + 26.7113i) q^{27} +(-45.9411 + 15.7716i) q^{28} +(52.6731 + 208.001i) q^{29} +(11.2004 + 135.168i) q^{30} +(78.5324 - 120.203i) q^{31} +(186.901 - 286.074i) q^{32} +(32.0101 + 48.9951i) q^{33} +(112.967 - 61.1344i) q^{34} +(-3.35674 + 40.5099i) q^{35} +(320.691 - 348.363i) q^{36} +(-185.463 - 30.9483i) q^{37} +(-87.0133 + 198.370i) q^{38} +(-23.0273 + 25.0143i) q^{39} +(-527.524 - 807.435i) q^{40} +(-267.473 + 290.553i) q^{41} +(-16.5547 + 12.8851i) q^{42} +(-123.794 - 20.6576i) q^{43} +(-623.507 - 337.425i) q^{44} +(-159.172 - 362.875i) q^{45} +(649.821 - 223.084i) q^{46} +(138.500 + 150.451i) q^{47} +(61.3542 - 242.282i) q^{48} +(296.130 - 160.258i) q^{49} +(-711.153 + 118.670i) q^{50} +(26.5910 - 28.8856i) q^{51} +(101.106 - 399.258i) q^{52} +(-56.5392 + 128.896i) q^{53} +(172.887 - 394.142i) q^{54} +(-468.193 + 364.409i) q^{55} +(59.9239 - 136.613i) q^{56} +(-5.46763 + 65.9845i) q^{57} +(-987.271 - 534.285i) q^{58} +(-558.054 + 93.1227i) q^{59} +(-396.307 - 308.458i) q^{60} +(538.291 + 584.740i) q^{61} +(184.408 + 728.210i) q^{62} +(33.5214 - 51.3084i) q^{63} +(131.944 + 521.034i) q^{64} +(-271.993 - 211.700i) q^{65} +(-302.014 - 50.3973i) q^{66} +(141.454 + 153.660i) q^{67} +(-116.753 + 461.049i) q^{68} +(165.722 - 128.987i) q^{69} +(-144.035 - 156.463i) q^{70} +(610.415 + 934.310i) q^{71} +(120.087 + 1449.24i) q^{72} +(-247.751 - 192.833i) q^{73} +(776.295 - 604.215i) q^{74} +(-193.816 + 104.888i) q^{75} +(-322.183 - 734.503i) q^{76} +(-86.7931 - 29.7961i) q^{77} +(-14.6891 - 177.271i) q^{78} +(49.9859 - 197.390i) q^{79} +(2499.10 + 417.026i) q^{80} +(-43.6349 + 526.594i) q^{81} +(-170.621 - 2059.09i) q^{82} +(-797.315 + 133.048i) q^{83} +(6.41440 - 77.4103i) q^{84} +(314.087 + 244.464i) q^{85} +(518.165 - 403.304i) q^{86} +(-338.446 - 56.4766i) q^{87} +(2059.37 - 706.982i) q^{88} +658.346 q^{89} +(1960.77 + 673.134i) q^{90} +(4.40232 - 53.1281i) q^{91} +(-1021.88 + 2329.65i) q^{92} +(125.585 + 192.223i) q^{93} -1069.87 q^{94} -671.209 q^{95} +(298.884 + 457.476i) q^{96} +(-483.957 + 376.679i) q^{97} +(-432.450 + 1707.71i) q^{98} +(882.340 - 147.237i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1026 q - 15 q^{2} - 21 q^{3} - 257 q^{4} + 57 q^{5} + 3 q^{6} + 7 q^{7} + 23 q^{8} - 470 q^{9}+O(q^{10}) $ 1026 * q - 15 * q^2 - 21 * q^3 - 257 * q^4 + 57 * q^5 + 3 * q^6 + 7 * q^7 + 23 * q^8 - 470 * q^9	\( 1026 q - 15 q^{2} - 21 q^{3} - 257 q^{4} + 57 q^{5} + 3 q^{6} + 7 q^{7} + 23 q^{8} - 470 q^{9} + 55 q^{10} - 53 q^{11} + 13 q^{12} - 791 q^{13} - 73 q^{14} - 59 q^{15} - 21 q^{16} - 49 q^{17} - 1952 q^{18} + 23 q^{19} - 3 q^{20} - 71 q^{21} - q^{22} - 961 q^{23} + 55 q^{24} - 2184 q^{25} - 1211 q^{26} - 63 q^{27} - 255 q^{28} + 199 q^{29} - 4574 q^{30} + 447 q^{31} + 281 q^{32} - 1055 q^{33} + 151 q^{34} - 929 q^{35} - 1471 q^{36} - 99 q^{37} + 57 q^{38} + 861 q^{39} + 6909 q^{40} + 1223 q^{41} + 5705 q^{42} + 2731 q^{43} + 2514 q^{44} - 2035 q^{45} - 839 q^{46} + 227 q^{47} - 4335 q^{48} - 4532 q^{49} + 697 q^{50} + 861 q^{51} - 69 q^{52} + 233 q^{53} + 5334 q^{54} + 521 q^{55} + 13105 q^{56} + 2379 q^{57} + 1513 q^{58} - 3747 q^{59} + 1737 q^{60} + 251 q^{61} + 1477 q^{62} + 3439 q^{63} - 4281 q^{64} - 451 q^{65} + 5051 q^{66} + 919 q^{67} - 1779 q^{68} + 1895 q^{69} + 2029 q^{70} - 4731 q^{71} - 2849 q^{72} + 791 q^{73} - 2111 q^{74} - 14005 q^{75} - 541 q^{76} - 1987 q^{77} + 6837 q^{78} + 4501 q^{79} + 26178 q^{80} + 3716 q^{81} - 13749 q^{82} + 2585 q^{83} - 19881 q^{84} - 19 q^{85} + 1791 q^{86} - 3563 q^{87} + 2293 q^{88} - 1948 q^{89} - 24399 q^{90} - 13663 q^{91} - 4349 q^{92} - 8273 q^{93} + 14024 q^{94} - 6750 q^{95} + 28165 q^{96} + 4087 q^{97} + 9143 q^{98} - 3109 q^{99}+O(q^{100}) \) 1026 * q - 15 * q^2 - 21 * q^3 - 257 * q^4 + 57 * q^5 + 3 * q^6 + 7 * q^7 + 23 * q^8 - 470 * q^9 + 55 * q^10 - 53 * q^11 + 13 * q^12 - 791 * q^13 - 73 * q^14 - 59 * q^15 - 21 * q^16 - 49 * q^17 - 1952 * q^18 + 23 * q^19 - 3 * q^20 - 71 * q^21 - q^22 - 961 * q^23 + 55 * q^24 - 2184 * q^25 - 1211 * q^26 - 63 * q^27 - 255 * q^28 + 199 * q^29 - 4574 * q^30 + 447 * q^31 + 281 * q^32 - 1055 * q^33 + 151 * q^34 - 929 * q^35 - 1471 * q^36 - 99 * q^37 + 57 * q^38 + 861 * q^39 + 6909 * q^40 + 1223 * q^41 + 5705 * q^42 + 2731 * q^43 + 2514 * q^44 - 2035 * q^45 - 839 * q^46 + 227 * q^47 - 4335 * q^48 - 4532 * q^49 + 697 * q^50 + 861 * q^51 - 69 * q^52 + 233 * q^53 + 5334 * q^54 + 521 * q^55 + 13105 * q^56 + 2379 * q^57 + 1513 * q^58 - 3747 * q^59 + 1737 * q^60 + 251 * q^61 + 1477 * q^62 + 3439 * q^63 - 4281 * q^64 - 451 * q^65 + 5051 * q^66 + 919 * q^67 - 1779 * q^68 + 1895 * q^69 + 2029 * q^70 - 4731 * q^71 - 2849 * q^72 + 791 * q^73 - 2111 * q^74 - 14005 * q^75 - 541 * q^76 - 1987 * q^77 + 6837 * q^78 + 4501 * q^79 + 26178 * q^80 + 3716 * q^81 - 13749 * q^82 + 2585 * q^83 - 19881 * q^84 - 19 * q^85 + 1791 * q^86 - 3563 * q^87 + 2293 * q^88 - 1948 * q^89 - 24399 * q^90 - 13663 * q^91 - 4349 * q^92 - 8273 * q^93 + 14024 * q^94 - 6750 * q^95 + 28165 * q^96 + 4087 * q^97 + 9143 * q^98 - 3109 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/229\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{7}{19}\right)$

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 $

$2$	−3.54340	+	3.84916i	−1.25278	+	1.36088i	−0.346588	+	0.938017i	$0.612660\pi$
$2$	−3.54340	+	3.84916i	−1.25278	+	1.36088i	−0.906193	+	0.422865i	$0.861024\pi$
$3$	−0.642373	+	1.46446i	−0.123625	+	0.281836i	−0.966679	−	0.255993i	$-0.917598\pi$
$3$	−0.642373	+	1.46446i	−0.123625	+	0.281836i	0.843054	+	0.537829i	$0.180755\pi$
$4$	−1.59970	−	19.3055i	−0.199963	−	2.41319i
$5$	−15.3330	−	5.26382i	−1.37142	−	0.470811i	−0.462074	−	0.886841i	$-0.652895\pi$
$5$	−15.3330	−	5.26382i	−1.37142	−	0.470811i	−0.909351	+	0.416031i	$0.863421\pi$
$6$	−3.36076	−	7.66177i	−0.228671	−	0.521317i
$7$	−0.615535	−	2.43069i	−0.0332358	−	0.131245i	0.950559	−	0.310545i	$-0.100512\pi$
$7$	−0.615535	−	2.43069i	−0.0332358	−	0.131245i	−0.983794	+	0.179300i	$0.942617\pi$
$8$	46.9494	+	36.5422i	2.07489	+	1.61495i
$9$	16.5546	+	17.9831i	0.613133	+	0.666040i
$10$	74.5922	−	40.3673i	2.35881	−	1.27653i
$11$	20.0169	−	30.6382i	0.548666	−	0.839796i	−0.449914	−	0.893072i	$-0.648545\pi$
$11$	20.0169	−	30.6382i	0.548666	−	0.839796i	0.998580	+	0.0532763i	$0.0169664\pi$
$12$	29.2998	+	10.0586i	0.704844	+	0.241973i
$13$	20.1090	+	6.90342i	0.429018	+	0.147282i	0.530747	−	0.847530i	$-0.321911\pi$
$13$	20.1090	+	6.90342i	0.429018	+	0.147282i	−0.101730	+	0.994812i	$0.532438\pi$
$14$	11.5372	+	6.24362i	0.220246	+	0.119191i
$15$	17.5582	−	19.0732i	0.302233	−	0.328313i
$16$	−154.157	+	25.7243i	−2.40871	+	0.401942i
$17$	−23.2211	−	7.97182i	−0.331291	−	0.113732i	0.154035	−	0.988065i	$-0.450773\pi$
$17$	−23.2211	−	7.97182i	−0.331291	−	0.113732i	−0.485327	+	0.874333i	$0.661299\pi$
$18$	−127.879			−1.67452
$19$	39.1602	−	13.4437i	0.472841	−	0.162326i	−0.0779717	−	0.996956i	$-0.524844\pi$
$19$	39.1602	−	13.4437i	0.472841	−	0.162326i	0.550812	+	0.834629i	$0.314318\pi$
$20$	−77.0927	+	304.432i	−0.861922	+	3.40365i
$21$	3.95506	+	0.659983i	0.0410983	+	0.00685810i
$22$	47.0032	+	185.611i	0.455505	+	1.79875i
$23$	−115.494	−	62.5021i	−1.04705	−	0.566634i	−0.141088	−	0.989997i	$-0.545060\pi$
$23$	−115.494	−	62.5021i	−1.04705	−	0.566634i	−0.905960	+	0.423363i	$0.860850\pi$
$24$	−83.6737	+	45.2819i	−0.711659	+	0.385131i
$25$	108.750	+	84.6437i	0.870002	+	0.677150i
$26$	−97.8265	+	52.9411i	−0.737898	+	0.399331i
$27$	−77.8074	+	26.7113i	−0.554594	+	0.190393i
$28$	−45.9411	+	15.7716i	−0.310074	+	0.106448i
$29$	52.6731	+	208.001i	0.337281	+	1.33189i	0.873093	+	0.487554i	$0.162111\pi$
$29$	52.6731	+	208.001i	0.337281	+	1.33189i	−0.535812	+	0.844337i	$0.679994\pi$
$30$	11.2004	+	135.168i	0.0681632	+	0.822608i
$31$	78.5324	−	120.203i	0.454995	−	0.696421i	−0.533815	−	0.845601i	$-0.679242\pi$
$31$	78.5324	−	120.203i	0.454995	−	0.696421i	0.988810	+	0.149180i	$0.0476633\pi$
$32$	186.901	−	286.074i	1.03249	−	1.58035i
$33$	32.0101	+	48.9951i	0.168856	+	0.258453i
$34$	112.967	−	61.1344i	0.569812	−	0.308367i
$35$	−3.35674	+	40.5099i	−0.0162112	+	0.195641i
$36$	320.691	−	348.363i	1.48468	−	1.61279i
$37$	−185.463	−	30.9483i	−0.824053	−	0.137510i	−0.262480	−	0.964937i	$-0.584540\pi$
$37$	−185.463	−	30.9483i	−0.824053	−	0.137510i	−0.561573	+	0.827427i	$0.689804\pi$
$38$	−87.0133	+	198.370i	−0.371458	+	0.846840i
$39$	−23.0273	+	25.0143i	−0.0945465	+	0.102705i
$40$	−527.524	−	807.435i	−2.08522	−	3.19167i
$41$	−267.473	+	290.553i	−1.01883	+	1.10675i	−0.0245806	+	0.999698i	$0.507825\pi$
$41$	−267.473	+	290.553i	−1.01883	+	1.10675i	−0.994254	+	0.107051i	$0.965859\pi$
$42$	−16.5547	+	12.8851i	−0.0608203	+	0.0473383i
$43$	−123.794	−	20.6576i	−0.439032	−	0.0732616i	−0.0590495	−	0.998255i	$-0.518807\pi$
$43$	−123.794	−	20.6576i	−0.439032	−	0.0732616i	−0.379983	+	0.924994i	$0.624070\pi$
$44$	−623.507	−	337.425i	−2.13630	−	1.15611i
$45$	−159.172	−	362.875i	−0.527287	−	1.20209i
$46$	649.821	−	223.084i	2.08285	−	0.715042i
$47$	138.500	+	150.451i	0.429836	+	0.466927i	0.912618	−	0.408814i	$-0.134058\pi$
$47$	138.500	+	150.451i	0.429836	+	0.466927i	−0.482781	+	0.875741i	$0.660373\pi$
$48$	61.3542	−	242.282i	0.184494	−	0.728550i
$49$	296.130	−	160.258i	0.863353	−	0.467223i
$50$	−711.153	+	118.670i	−2.01144	+	0.335651i
$51$	26.5910	−	28.8856i	0.0730096	−	0.0793096i
$52$	101.106	−	399.258i	0.269632	−	1.06475i
$53$	−56.5392	+	128.896i	−0.146533	+	0.334062i	−0.973678	−	0.227926i	$-0.926805\pi$
$53$	−56.5392	+	128.896i	−0.146533	+	0.334062i	0.827145	+	0.561988i	$0.189963\pi$
$54$	172.887	−	394.142i	0.435683	−	0.993258i
$55$	−468.193	+	364.409i	−1.14784	+	0.893399i
$56$	59.9239	−	136.613i	0.142994	−	0.325993i
$57$	−5.46763	+	65.9845i	−0.0127054	+	0.153331i
$58$	−987.271	−	534.285i	−2.23509	−	1.20957i
$59$	−558.054	+	93.1227i	−1.23140	+	0.205484i	−0.744289	−	0.667858i	$-0.767211\pi$
$59$	−558.054	+	93.1227i	−1.23140	+	0.205484i	−0.487108	+	0.873342i	$0.661948\pi$
$60$	−396.307	−	308.458i	−0.852717	−	0.663696i
$61$	538.291	+	584.740i	1.12985	+	1.22735i	0.970752	+	0.240086i	$0.0771757\pi$
$61$	538.291	+	584.740i	1.12985	+	1.22735i	0.159102	+	0.987262i	$0.449140\pi$
$62$	184.408	+	728.210i	0.377739	+	1.49166i
$63$	33.5214	−	51.3084i	0.0670366	−	0.102607i
$64$	131.944	+	521.034i	0.257703	+	1.01765i
$65$	−271.993	−	211.700i	−0.519023	−	0.403972i
$66$	−302.014	−	50.3973i	−0.563264	−	0.0939921i
$67$	141.454	+	153.660i	0.257931	+	0.280187i	0.851228	−	0.524796i	$-0.175858\pi$
$67$	141.454	+	153.660i	0.257931	+	0.280187i	−0.593297	+	0.804983i	$0.702174\pi$
$68$	−116.753	+	461.049i	−0.208212	+	0.822211i
$69$	165.722	−	128.987i	0.289139	−	0.225046i
$70$	−144.035	−	156.463i	−0.245935	−	0.267156i
$71$	610.415	+	934.310i	1.02032	+	1.56172i	0.811997	+	0.583661i	$0.198380\pi$
$71$	610.415	+	934.310i	1.02032	+	1.56172i	0.208326	+	0.978060i	$0.433199\pi$
$72$	120.087	+	1449.24i	0.196561	+	2.37214i
$73$	−247.751	−	192.833i	−0.397220	−	0.309169i	0.395831	−	0.918323i	$-0.370456\pi$
$73$	−247.751	−	192.833i	−0.397220	−	0.309169i	−0.793052	+	0.609154i	$0.791509\pi$
$74$	776.295	−	604.215i	1.21949	−	0.949170i
$75$	−193.816	+	104.888i	−0.298399	+	0.161485i
$76$	−322.183	−	734.503i	−0.486275	−	1.10860i
$77$	−86.7931	−	29.7961i	−0.128454	−	0.0440984i
$78$	−14.6891	−	177.271i	−0.0213232	−	0.257333i
$79$	49.9859	−	197.390i	0.0711880	−	0.281115i	−0.923562	−	0.383449i	$-0.874736\pi$
$79$	49.9859	−	197.390i	0.0711880	−	0.281115i	0.994750	+	0.102334i	$0.0326310\pi$
$80$	2499.10	+	417.026i	3.49260	+	0.582812i
$81$	−43.6349	+	526.594i	−0.0598558	+	0.722352i
$82$	−170.621	−	2059.09i	−0.229780	−	2.77303i
$83$	−797.315	+	133.048i	−1.05442	+	0.175951i	−0.666319	−	0.745667i	$-0.732131\pi$
$83$	−797.315	+	133.048i	−1.05442	+	0.175951i	−0.388099	+	0.921618i	$0.626868\pi$
$84$	6.41440	−	77.4103i	0.00833177	−	0.100549i
$85$	314.087	+	244.464i	0.400794	+	0.311951i
$86$	518.165	−	403.304i	0.649712	−	0.505691i
$87$	−338.446	−	56.4766i	−0.417071	−	0.0695969i
$88$	2059.37	−	706.982i	2.49465	−	0.856415i
$89$	658.346			0.784095			0.392048	−	0.919945i	$-0.371767\pi$
$89$	658.346			0.784095			0.392048	+	0.919945i	$0.371767\pi$
$90$	1960.77	+	673.134i	2.29648	+	0.788384i
$91$	4.40232	−	53.1281i	0.00507130	−	0.0612015i
$92$	−1021.88	+	2329.65i	−1.15803	+	2.64003i
$93$	125.585	+	192.223i	0.140028	+	0.214329i
$94$	−1069.87			−1.17392
$95$	−671.209			−0.724890
$96$	298.884	+	457.476i	0.317757	+	0.486364i
$97$	−483.957	+	376.679i	−0.506581	+	0.394288i	−0.835005	−	0.550243i	$-0.814535\pi$
$97$	−483.957	+	376.679i	−0.506581	+	0.394288i	0.328424	+	0.944531i	$0.393483\pi$
$98$	−432.450	+	1707.71i	−0.445756	+	1.76025i
$99$	882.340	−	147.237i	0.895743	−	0.149473i
$100$	1460.12	−	2234.89i	1.46012	−	2.23489i
$101$	1178.83	+	637.949i	1.16136	+	0.628498i	0.938136	−	0.346268i	$-0.112551\pi$
$101$	1178.83	+	637.949i	1.16136	+	0.628498i	0.223228	+	0.974766i	$0.428341\pi$
$102$	16.9624	+	204.706i	0.0164660	+	0.198715i
$103$	457.821	+	1807.89i	0.437965	+	1.72949i	0.657112	+	0.753793i	$0.271778\pi$
$103$	457.821	+	1807.89i	0.437965	+	1.72949i	−0.219146	+	0.975692i	$0.570327\pi$
$104$	691.839	+	1058.94i	0.652311	+	0.998437i
$105$	−57.1689	−	30.9383i	−0.0531344	−	0.0287549i
$106$	−295.802	−	674.360i	−0.271045	−	0.617921i
$107$	−1487.12			−1.34360			−0.671802	−	0.740731i	$-0.734479\pi$
$107$	−1487.12			−1.34360			−0.671802	+	0.740731i	$0.734479\pi$
$108$	640.145	+	1459.38i	0.570352	+	1.30027i
$109$	−733.782	+	122.447i	−0.644804	+	0.107599i	−0.477956	−	0.878384i	$-0.658622\pi$
$109$	−733.782	+	122.447i	−0.644804	+	0.107599i	−0.166848	+	0.985983i	$0.553359\pi$
$110$	256.326	−	3093.40i	0.222179	−	2.68131i
$111$	164.459	−	251.723i	0.140629	−	0.215248i
$112$	157.417	+	358.875i	0.132808	+	0.302772i
$113$	−1022.19	+	350.920i	−0.850972	+	0.292139i	−0.715475	−	0.698638i	$-0.753790\pi$
$113$	−1022.19	+	350.920i	−0.850972	+	0.292139i	−0.135498	+	0.990778i	$0.543263\pi$
$114$	−234.611	−	254.855i	−0.192748	−	0.209381i
$115$	1441.87	+	1566.28i	1.16917	+	1.27006i
$116$	3931.31	−	1349.62i	3.14667	−	1.08025i
$117$	208.751	+	475.905i	0.164949	+	0.376046i
$118$	1618.96	−	2478.01i	1.26303	−	1.93321i
$119$	−5.08364	+	61.3504i	−0.00391610	+	0.0472603i
$120$	1521.32	−	253.864i	1.15731	−	0.193121i
$121$	−3.36340	−	7.66777i	−0.00252697	−	0.00576091i
$122$	−4158.13			−3.08574
$123$	−253.686	−	578.346i	−0.185968	−	0.423965i
$124$	−2446.21	−	1323.82i	−1.77158	−	0.958731i
$125$	−113.570	−	173.832i	−0.0812643	−	0.124384i
$126$	78.7142	+	310.835i	0.0556541	+	0.219773i
$127$	22.6894	+	273.820i	0.0158532	+	0.191320i	0.999909	+	0.0134618i	$0.00428514\pi$
$127$	22.6894	+	273.820i	0.0158532	+	0.191320i	−0.984056	+	0.177858i	$0.943083\pi$
$128$	−68.8260	−	37.2468i	−0.0475267	−	0.0257201i
$129$	109.774	−	168.022i	0.0749230	−	0.114678i
$130$	1778.65	−	296.804i	1.19998	−	0.200241i
$131$	244.064	−	963.788i	0.162779	−	0.642798i	−0.833181	−	0.553000i	$-0.813483\pi$
$131$	244.064	−	963.788i	0.162779	−	0.642798i	0.995960	−	0.0897982i	$-0.0286222\pi$
$132$	894.670	−	696.349i	0.589932	−	0.459162i
$133$	−56.7820	−	86.9114i	−0.0370198	−	0.0566630i
$134$	−1092.69			−0.704433
$135$	1333.62			0.850223
$136$	−798.910	−	1222.82i	−0.503721	−	0.771002i
$137$	−361.426	+	823.969i	−0.225392	+	0.513843i	−0.991691	−	0.128642i	$-0.958938\pi$
$137$	−361.426	+	823.969i	−0.225392	+	0.513843i	0.766299	+	0.642484i	$0.222096\pi$
$138$	−90.7294	+	1094.94i	−0.0559667	+	0.675417i
$139$	544.827	+	187.039i	0.332458	+	0.114133i	0.485874	−	0.874029i	$-0.338501\pi$
$139$	544.827	+	187.039i	0.332458	+	0.114133i	−0.153417	+	0.988162i	$0.549028\pi$
$140$	787.434			0.475360
$141$	−309.299	+	106.182i	−0.184735	+	0.0634196i
$142$	−5759.25	−	961.049i	−3.40356	−	0.567954i
$143$	614.028	−	477.917i	0.359074	−	0.279479i
$144$	−3014.62	−	2346.37i	−1.74457	−	1.35785i
$145$	287.246	−	3466.54i	0.164514	−	1.98538i
$146$	1620.12	−	270.351i	0.918373	−	0.153249i
$147$	44.4653	+	536.616i	0.0249485	+	0.301084i
$148$	−300.788	+	3629.97i	−0.167058	+	2.01609i
$149$	−2342.04	−	390.817i	−1.28770	−	0.214879i	−0.519157	−	0.854679i	$-0.673754\pi$
$149$	−2342.04	−	390.817i	−1.28770	−	0.214879i	−0.768541	+	0.639800i	$0.779017\pi$
$150$	283.037	−	1117.69i	0.154066	−	0.608392i
$151$	−21.9540	−	264.945i	−0.0118317	−	0.142788i	0.988108	−	0.153761i	$-0.0491386\pi$
$151$	−21.9540	−	264.945i	−0.0118317	−	0.142788i	−0.999940	+	0.0109734i	$0.996507\pi$
$152$	2329.81	+	799.826i	1.24324	+	0.426805i
$153$	−241.058	−	549.558i	−0.127375	−	0.290386i
$154$	422.232	−	228.501i	0.220938	−	0.119566i
$155$	−1836.86	+	1429.69i	−0.951873	+	0.740873i
$156$	519.751	+	404.538i	0.266752	+	0.207622i
$157$	174.563	+	2106.66i	0.0887364	+	1.07089i	0.884892	+	0.465797i	$0.154232\pi$
$157$	174.563	+	2106.66i	0.0887364	+	1.07089i	−0.796155	+	0.605092i	$0.793136\pi$
$158$	582.664	+	891.834i	0.293381	+	0.449054i
$159$	−152.445	−	165.599i	−0.0760355	−	0.0825966i
$160$	−4371.60	+	3402.55i	−2.16003	+	1.68122i
$161$	−80.8330	+	319.202i	−0.0395685	+	0.156253i
$162$	−1872.33	−	2033.89i	−0.908050	−	0.986405i
$163$	355.456	+	59.3151i	0.170806	+	0.0285026i	0.249380	−	0.968406i	$-0.419773\pi$
$163$	355.456	+	59.3151i	0.170806	+	0.0285026i	−0.0785732	+	0.996908i	$0.525036\pi$
$164$	6037.15	+	4698.90i	2.87453	+	2.23733i
$165$	−232.909	−	919.737i	−0.109891	−	0.433948i
$166$	2313.08	−	3540.43i	1.08151	−	1.65537i
$167$	254.056	+	1003.25i	0.117721	+	0.464871i	0.999983	−	0.00588878i	$-0.00187447\pi$
$167$	254.056	+	1003.25i	0.117721	+	0.464871i	−0.882261	+	0.470760i	$0.843980\pi$
$168$	161.571	+	175.512i	0.0741991	+	0.0806017i
$169$	−1377.03	−	1071.78i	−0.626776	−	0.487840i
$170$	−2053.92	+	342.738i	−0.926636	+	0.154628i
$171$	890.041	+	481.666i	0.398030	+	0.215403i
$172$	−200.772	+	2422.95i	−0.0890040	+	1.07412i
$173$	544.255	−	1240.78i	0.239184	−	0.545286i	−0.754654	−	0.656123i	$-0.772195\pi$
$173$	544.255	−	1240.78i	0.239184	−	0.545286i	0.993839	+	0.110837i	$0.0353532\pi$
$174$	1416.64	−	1102.61i	0.617212	−	0.480395i
$175$	138.803	−	316.440i	0.0599574	−	0.136689i
$176$	−2297.61	+	5238.02i	−0.984027	+	2.24335i
$177$	222.104	−	877.068i	0.0943183	−	0.372455i
$178$	−2332.78	+	2534.08i	−0.982300	+	1.06706i
$179$	−422.385	+	70.4836i	−0.176372	+	0.0294312i	−0.252121	−	0.967696i	$-0.581128\pi$
$179$	−422.385	+	70.4836i	−0.176372	+	0.0294312i	0.0757495	+	0.997127i	$0.475865\pi$
$180$	−6750.87	+	3653.39i	−2.79544	+	1.51282i
$181$	75.0786	−	296.479i	0.0308318	−	0.121752i	−0.952071	−	0.305877i	$-0.901050\pi$
$181$	75.0786	−	296.479i	0.0308318	−	0.121752i	0.982903	+	0.184125i	$0.0589451\pi$
$182$	188.899	+	205.199i	0.0769348	+	0.0835735i
$183$	−1202.11	+	412.686i	−0.485589	+	0.166703i
$184$	−3138.40	−	7154.83i	−1.25742	−	2.86664i
$185$	2680.80	+	1450.78i	1.06539	+	0.576558i
$186$	−1184.89	−	197.724i	−0.467100	−	0.0779453i
$187$	−709.057	+	551.881i	−0.277280	+	0.215816i
$188$	2682.98	−	2914.49i	1.04083	−	1.13064i
$189$	112.820	+	172.684i	0.0434205	+	0.0664600i
$190$	2378.36	−	2583.59i	0.908128	−	0.986490i
$191$	−1753.66	+	3997.95i	−0.664348	+	1.51456i	0.182769	+	0.983156i	$0.441494\pi$
$191$	−1753.66	+	3997.95i	−0.664348	+	1.51456i	−0.847117	+	0.531406i	$0.821664\pi$
$192$	−847.792	−	141.472i	−0.318667	−	0.0531762i
$193$	3122.14	−	3391.55i	1.16444	−	1.26492i	0.206340	−	0.978480i	$-0.433845\pi$
$193$	3122.14	−	3391.55i	1.16444	−	1.26492i	0.958099	−	0.286437i	$-0.0924710\pi$
$194$	264.956	−	3197.55i	0.0980555	−	1.18335i
$195$	484.748	−	262.332i	0.178018	−	0.0963385i
$196$	−3567.58	−	5460.58i	−1.30014	−	1.99001i
$197$	2166.80	−	3316.54i	0.783646	−	1.19946i	−0.192276	−	0.981341i	$-0.561587\pi$
$197$	2166.80	−	3316.54i	0.783646	−	1.19946i	0.975922	−	0.218119i	$-0.0699920\pi$
$198$	−2559.75	+	3917.98i	−0.918754	+	1.40626i
$199$	−128.348	−	1548.93i	−0.0457202	−	0.551761i	−0.980498	−	0.196528i	$-0.937033\pi$
$199$	−128.348	−	1548.93i	−0.0457202	−	0.551761i	0.934778	−	0.355233i	$-0.115598\pi$
$200$	2012.69	+	7947.95i	0.711595	+	2.81002i
$201$	−315.895	+	108.447i	−0.110853	+	0.0380560i
$202$	−6632.62	+	2276.98i	−2.31025	+	0.793109i
$203$	473.165	−	256.064i	0.163594	−	0.0885329i
$204$	−600.189	−	467.146i	−0.205988	−	0.160327i
$205$	5630.57	−	3047.11i	1.91832	−	1.03814i
$206$	−8581.11	−	4643.86i	−2.90230	−	1.57065i
$207$	−787.972	−	3111.63i	−0.264579	−	1.04480i
$208$	−3277.53	−	546.924i	−1.09258	−	0.182319i
$209$	371.976	−	1468.90i	0.123110	−	0.486152i
$210$	321.658	−	110.425i	0.105698	−	0.0362861i
$211$	1312.38			0.428189			0.214095	−	0.976813i	$-0.431320\pi$
$211$	1312.38			0.428189			0.214095	+	0.976813i	$0.431320\pi$
$212$	2578.86	+	885.323i	0.835456	+	0.286813i
$213$	−1760.37	+	293.755i	−0.566286	+	0.0944964i
$214$	5269.47	−	5724.17i	1.68324	−	1.82849i
$215$	1789.39	+	968.371i	0.567608	+	0.307174i
$216$	−4629.11	−	1589.17i	−1.45820	−	0.500600i
$217$	−340.515	−	116.899i	−0.106524	−	0.0365697i
$218$	2128.77	−	3258.32i	0.661368	−	1.01230i
$219$	441.545	−	238.952i	0.136241	−	0.0737300i
$220$	7784.08	+	8455.77i	2.38547	+	2.59131i
$221$	−411.920	−	320.610i	−0.125379	−	0.0975864i
$222$	386.179	+	1524.99i	0.116751	+	0.461038i
$223$	2301.21	+	5246.22i	0.691032	+	1.57539i	0.812607	+	0.582812i	$0.198047\pi$
$223$	2301.21	+	5246.22i	0.691032	+	1.57539i	−0.121575	+	0.992582i	$0.538795\pi$
$224$	−810.402	−	278.211i	−0.241729	−	0.0829856i
$225$	278.161	+	3356.91i	0.0824182	+	0.994640i
$226$	2271.30	−	5178.03i	0.668515	−	1.52406i
$227$	3125.90	−	3395.64i	0.913980	−	0.992847i	−0.0860142	−	0.996294i	$-0.527413\pi$
$227$	3125.90	−	3395.64i	0.913980	−	0.992847i	0.999994	+	0.00344710i	$0.00109725\pi$
$228$	1282.61			0.372557
$229$	−2503.01	+	2396.65i	−0.722285	+	0.691595i
$229$	−2503.01	+	2396.65i	−0.722285	+	0.691595i
$230$	−11138.0			−3.19311
$231$	99.3887	−	107.965i	0.0283087	−	0.0307514i
$232$	−5127.85	+	11690.3i	−1.45112	+	3.30822i
$233$	−23.8788	−	288.174i	−0.00671395	−	0.0810253i	0.992404	−	0.123024i	$-0.0392591\pi$
$233$	−23.8788	−	288.174i	−0.00671395	−	0.0810253i	−0.999118	+	0.0419984i	$0.986628\pi$
$234$	−2571.52	−	882.805i	−0.718400	−	0.246627i
$235$	−1331.67	−	3035.91i	−0.369654	−	0.842726i
$236$	2690.50	+	10624.6i	0.742105	+	2.93051i
$237$	256.960	+	200.000i	0.0704277	+	0.0548160i
$238$	−218.134	−	236.957i	−0.0594097	−	0.0645362i
$239$	4893.39	−	2648.17i	1.32438	−	0.716719i	0.348974	−	0.937133i	$-0.386530\pi$
$239$	4893.39	−	2648.17i	1.32438	−	0.716719i	0.975406	+	0.220414i	$0.0707408\pi$
$240$	−2216.07	+	3391.95i	−0.596029	+	0.912290i
$241$	4279.81	+	1469.26i	1.14393	+	0.392711i	0.830565	−	0.556922i	$-0.188018\pi$
$241$	4279.81	+	1469.26i	1.14393	+	0.392711i	0.313364	+	0.949633i	$0.398544\pi$
$242$	41.4323	+	14.2237i	0.0110057	+	0.00377825i
$243$	−2696.59	−	1459.32i	−0.711878	−	0.385249i
$244$	10427.6	−	11327.4i	2.73590	−	2.97198i
$245$	−5384.13	+	898.452i	−1.40400	+	0.234286i
$246$	3125.06	+	1072.83i	0.809945	+	0.278054i
$247$	880.280			0.226765
$248$	8079.52	−	2773.70i	2.06875	−	0.710203i
$249$	317.329	−	1253.10i	0.0807627	−	0.318925i
$250$	1071.53	+	178.807i	0.271079	+	0.0452351i
$251$	−709.281	−	2800.89i	−0.178364	−	0.704344i	−0.992350	−	0.123459i	$-0.960601\pi$
$251$	−709.281	−	2800.89i	−0.178364	−	0.704344i	0.813986	−	0.580885i	$-0.197293\pi$
$252$	−1044.16	−	565.071i	−0.261015	−	0.141254i
$253$	−4226.78	+	2287.42i	−1.05034	+	0.568414i
$254$	−1134.37	−	882.918i	−0.280224	−	0.218107i
$255$	−559.769	+	302.932i	−0.137467	+	0.0743934i
$256$	−3679.63	+	1263.22i	−0.898346	+	0.308403i
$257$	−3984.30	+	1367.81i	−0.967057	+	0.331991i	−0.762590	−	0.646882i	$-0.776072\pi$
$257$	−3984.30	+	1367.81i	−0.967057	+	0.331991i	−0.204467	+	0.978873i	$0.565546\pi$
$258$	257.769	+	1017.91i	0.0622014	+	0.245628i
$259$	38.9332	+	469.854i	0.00934051	+	0.112723i
$260$	−3651.88	+	5589.62i	−0.871077	+	1.33328i
$261$	−2868.52	+	4390.60i	−0.680295	+	1.04127i
$262$	2844.95	+	4354.53i	0.670847	+	1.02681i
$263$	6657.56	−	3602.89i	1.56092	−	0.844729i	0.561067	−	0.827770i	$-0.310391\pi$
$263$	6657.56	−	3602.89i	1.56092	−	0.844729i	0.999856	−	0.0169591i	$-0.00539850\pi$
$264$	−287.533	+	3470.01i	−0.0670320	+	0.808956i
$265$	1545.40	−	1678.76i	0.358239	−	0.389151i
$266$	535.737	+	89.3987i	0.123489	+	0.0206067i
$267$	−422.903	+	964.122i	−0.0969335	+	0.220986i
$268$	2740.20	−	2976.65i	0.624569	−	0.678463i
$269$	1531.77	+	2344.55i	0.347188	+	0.531411i	0.967476	−	0.252964i	$-0.0814053\pi$
$269$	1531.77	+	2344.55i	0.347188	+	0.531411i	−0.620288	+	0.784374i	$0.712984\pi$
$270$	−4725.56	+	5133.33i	−1.06514	+	1.15705i
$271$	−1698.25	+	1321.80i	−0.380669	+	0.296286i	−0.786414	−	0.617700i	$-0.788065\pi$
$271$	−1698.25	+	1321.80i	−0.380669	+	0.296286i	0.405745	+	0.913986i	$0.367012\pi$
$272$	3784.78	+	631.567i	0.843698	+	0.140788i
$273$	74.9761	+	40.5750i	0.0166218	+	0.00899529i
$274$	−1890.91	−	4310.84i	−0.416912	−	0.950465i
$275$	4770.17	−	1637.60i	1.04601	−	0.359095i
$276$	−2755.26	−	2993.01i	−0.600896	−	0.652747i
$277$	−1276.79	+	5041.91i	−0.276948	+	1.09364i	0.661978	+	0.749523i	$0.269717\pi$
$277$	−1276.79	+	5041.91i	−0.276948	+	1.09364i	−0.938926	+	0.344119i	$0.888177\pi$
$278$	−2650.48	+	1434.37i	−0.571818	+	0.309452i
$279$	3461.69	−	577.654i	0.742817	−	0.123954i
$280$	−1637.92	+	1779.25i	−0.349587	+	0.379752i
$281$	−1740.92	+	6874.74i	−0.369590	+	1.45948i	0.453342	+	0.891337i	$0.350232\pi$
$281$	−1740.92	+	6874.74i	−0.369590	+	1.45948i	−0.822932	+	0.568140i	$0.807663\pi$
$282$	687.256	−	1566.79i	0.145126	−	0.330854i
$283$	−3457.27	+	7881.78i	−0.726196	+	1.65556i	0.0285924	+	0.999591i	$0.490898\pi$
$283$	−3457.27	+	7881.78i	−0.726196	+	1.65556i	−0.754788	+	0.655969i	$0.772260\pi$
$284$	17060.9	−	13279.0i	3.56470	−	2.77452i
$285$	431.166	−	982.960i	0.0896143	−	0.204300i
$286$	−336.168	+	4056.94i	−0.0695035	+	0.838783i
$287$	870.883	+	471.298i	0.179117	+	0.0969333i
$288$	8238.57	−	1374.77i	1.68563	−	0.281282i
$289$	−3401.38	−	2647.40i	−0.692322	−	0.538856i
$290$	12325.4	+	13389.0i	2.49578	+	2.71114i
$291$	−240.751	−	950.704i	−0.0484985	−	0.191516i
$292$	−3326.41	+	5091.44i	−0.666655	+	1.02039i
$293$	−491.189	−	1939.66i	−0.0979371	−	0.386745i	0.900949	−	0.433924i	$-0.142871\pi$
$293$	−491.189	−	1939.66i	−0.0979371	−	0.386745i	−0.998886	+	0.0471794i	$0.984977\pi$
$294$	−2223.08	−	1730.29i	−0.440995	−	0.343240i
$295$	9046.82	+	1509.65i	1.78551	+	0.297949i
$296$	−7576.47	−	8230.24i	−1.48775	−	1.61613i
$297$	−739.078	+	2918.55i	−0.144396	+	0.570208i
$298$	9803.08	−	7630.04i	1.90563	−	1.48321i
$299$	−1890.98	−	2054.16i	−0.365747	−	0.397307i
$300$	2334.96	+	3573.93i	0.449364	+	0.687802i
$301$	25.9873	+	313.620i	0.00497636	+	0.0600558i
$302$	1097.61	+	854.302i	0.209140	+	0.162780i
$303$	−1691.50	+	1316.55i	−0.320707	+	0.249616i
$304$	−5691.00	+	3079.82i	−1.07369	+	0.581052i
$305$	−5175.64	−	11799.3i	−0.971661	−	2.21516i
$306$	2969.50	+	1019.43i	0.554755	+	0.190448i
$307$	−329.528	−	3976.81i	−0.0612610	−	0.739311i	−0.956123	−	0.292967i	$-0.905357\pi$
$307$	−329.528	−	3976.81i	−0.0612610	−	0.739311i	0.894862	−	0.446344i	$-0.147274\pi$
$308$	−436.386	+	1723.25i	−0.0807319	+	0.318803i
$309$	−2941.68	−	490.880i	−0.541574	−	0.0903728i
$310$	1005.64	−	12136.3i	0.184248	−	2.22354i
$311$	−109.325	−	1319.36i	−0.0199333	−	0.240559i	−0.999266	−	0.0383040i	$-0.987804\pi$
$311$	−109.325	−	1319.36i	−0.0199333	−	0.240559i	0.979333	−	0.202255i	$-0.0648271\pi$
$312$	−1995.19	+	332.939i	−0.362037	+	0.0604133i
$313$	−838.469	+	10118.8i	−0.151416	+	1.82731i	0.322302	+	0.946637i	$0.395543\pi$
$313$	−838.469	+	10118.8i	−0.151416	+	1.82731i	−0.473717	+	0.880677i	$0.657088\pi$
$314$	−8727.40	−	6792.81i	−1.56852	−	1.22083i
$315$	−784.062	+	610.260i	−0.140244	+	0.109156i
$316$	−3890.67	−	649.239i	−0.692619	−	0.115578i
$317$	3924.82	−	1347.39i	0.695394	−	0.238729i	0.0457336	−	0.998954i	$-0.485437\pi$
$317$	3924.82	−	1347.39i	0.695394	−	0.238729i	0.649660	+	0.760225i	$0.274911\pi$
$318$	1177.59			0.207660
$319$	7427.13	+	2549.74i	1.30357	+	0.447517i
$320$	719.539	−	8683.55i	0.125698	−	1.51695i
$321$	955.287	−	2177.83i	0.166102	−	0.378676i
$322$	−942.236	−	1442.20i	−0.163071	−	0.249598i
$323$	−1016.52			−0.175110
$324$	10236.0			1.75514
$325$	1602.53	+	2452.85i	0.273514	+	0.418645i
$326$	−1487.84	+	1158.03i	−0.252772	+	0.196740i
$327$	292.043	−	1153.25i	0.0493885	−	0.195031i
$328$	−23175.1	+	3867.24i	−3.90132	+	0.651015i
$329$	280.449	−	429.259i	0.0469959	−	0.0719326i
$330$	4365.50	+	2362.49i	0.728221	+	0.394094i
$331$	−660.892	−	7975.79i	−0.109746	−	1.32444i	−0.799619	−	0.600507i	$-0.794965\pi$
$331$	−660.892	−	7975.79i	−0.109746	−	1.32444i	0.689873	−	0.723930i	$-0.257666\pi$
$332$	3844.03	+	15179.7i	0.635448	+	2.50933i
$333$	−2513.72	−	3847.54i	−0.413667	−	0.633165i
$334$	−4761.88	−	2577.00i	−0.780114	−	0.422177i
$335$	−1360.07	−	3100.66i	−0.221817	−	0.505692i
$336$	−626.679			−0.101750
$337$	562.099	+	1281.46i	0.0908590	+	0.207138i	0.955327	−	0.295549i	$-0.0955027\pi$
$337$	562.099	+	1281.46i	0.0908590	+	0.207138i	−0.864468	+	0.502687i	$0.832345\pi$
$338$	9004.82	−	1502.64i	1.44911	−	0.241813i
$339$	142.721	−	1722.38i	0.0228659	−	0.275950i
$340$	4217.06	−	6454.69i	0.672653	−	1.02957i
$341$	−2110.82	−	4812.17i	−0.335211	−	0.764205i
$342$	−5007.78	+	1719.17i	−0.791783	+	0.271819i
$343$	−1154.31	−	1253.91i	−0.181711	−	0.197390i
$344$	−5057.18	−	5493.56i	−0.792631	−	0.861026i
$345$	−3219.98	+	1105.42i	−0.502486	+	0.172504i
$346$	2847.43	+	6491.48i	0.442424	+	1.00863i
$347$	−577.122	+	883.350i	−0.0892839	+	0.136659i	−0.879015	−	0.476794i	$-0.841799\pi$
$347$	−577.122	+	883.350i	−0.0892839	+	0.136659i	0.789731	+	0.613453i	$0.210220\pi$
$348$	−548.898	+	6624.22i	−0.0845518	+	1.02039i
$349$	−11600.9	+	1935.84i	−1.77931	+	0.296914i	−0.960731	−	0.277480i	$-0.910501\pi$
$349$	−11600.9	+	1935.84i	−1.77931	+	0.296914i	−0.818579	+	0.574394i	$0.805238\pi$
$350$	726.191	+	1655.55i	0.110904	+	0.252837i
$351$	−1749.03			−0.265972
$352$	−5023.59	−	11452.6i	−0.760676	−	1.73417i
$353$	−12.7532	−	6.90169i	−0.00192290	−	0.00104062i	0.474986	−	0.879994i	$-0.342453\pi$
$353$	−12.7532	−	6.90169i	−0.00192290	−	0.00104062i	−0.476909	+	0.878953i	$0.658243\pi$
$354$	2588.97	+	3962.71i	0.388707	+	0.594960i
$355$	−4441.45	−	17538.9i	−0.664021	−	2.62216i
$356$	−1053.16	−	12709.7i	−0.156790	−	1.89217i
$357$	−86.5797	−	46.8546i	−0.0128355	−	0.00694624i
$358$	1225.38	−	1875.58i	0.180903	−	0.276892i
$359$	7931.69	−	1323.56i	1.16607	−	0.194582i	0.450272	−	0.892892i	$-0.351327\pi$
$359$	7931.69	−	1323.56i	1.16607	−	0.194582i	0.715796	+	0.698309i	$0.246064\pi$
$360$	5787.23	−	22853.3i	0.847261	−	3.34576i
$361$	−4059.93	+	3159.97i	−0.591912	+	0.460704i
$362$	875.160	+	1339.53i	0.127065	+	0.194487i
$363$	13.3897			0.00193603
$364$	−1032.71			−0.148705
$365$	2783.73	+	4260.82i	0.399198	+	0.611018i
$366$	2671.07	−	6089.43i	0.381473	−	0.869671i
$367$	−721.454	+	8706.65i	−0.102615	+	1.23838i	0.729582	+	0.683894i	$0.239715\pi$
$367$	−721.454	+	8706.65i	−0.102615	+	1.23838i	−0.832196	+	0.554481i	$0.812917\pi$
$368$	19412.0	+	6664.16i	2.74979	+	0.944004i
$369$	−9652.93			−1.36182
$370$	−15083.4	+	5178.14i	−2.11932	+	0.727564i
$371$	348.109	+	58.0892i	0.0487141	+	0.00812895i
$372$	3510.06	−	2731.99i	0.489216	−	0.380772i
$373$	−9209.27	−	7167.86i	−1.27839	−	0.995007i	−0.999397	−	0.0347126i	$-0.988948\pi$
$373$	−9209.27	−	7167.86i	−1.27839	−	0.995007i	−0.278988	−	0.960295i	$-0.589999\pi$
$374$	388.194	−	4684.81i	0.0536712	−	0.647716i
$375$	327.525	−	54.6543i	0.0451022	−	0.00752623i
$376$	1004.68	+	12124.7i	0.137799	+	1.66299i
$377$	−376.719	+	4546.32i	−0.0514642	+	0.621080i
$378$	−1064.46	−	177.626i	−0.144841	−	0.0241696i
$379$	2615.21	−	10327.2i	0.354444	−	1.39967i	−0.493575	−	0.869703i	$-0.664310\pi$
$379$	2615.21	−	10327.2i	0.354444	−	1.39967i	0.848019	−	0.529965i	$-0.177795\pi$
$380$	1073.73	+	12958.0i	0.144951	+	1.74930i
$381$	−415.574	−	142.667i	−0.0558806	−	0.0191838i
$382$	−9174.80	−	20916.4i	−1.22886	−	2.80151i
$383$	7596.40	−	4110.97i	1.01347	−	0.548461i	0.117730	−	0.993046i	$-0.462438\pi$
$383$	7596.40	−	4110.97i	1.01347	−	0.548461i	0.895737	+	0.444585i	$0.146649\pi$
$384$	98.7584	−	76.8667i	0.0131243	−	0.0102151i
$385$	1173.96	+	913.727i	0.155403	+	0.120955i
$386$	1991.62	+	24035.2i	0.262618	+	3.16933i
$387$	−1677.87	−	2568.17i	−0.220390	−	0.337332i
$388$	8046.17	+	8740.47i	1.05279	+	1.14363i
$389$	684.263	−	532.583i	0.0891864	−	0.0694166i	−0.568638	−	0.822588i	$-0.692529\pi$
$389$	684.263	−	532.583i	0.0891864	−	0.0694166i	0.657824	+	0.753171i	$0.271477\pi$
$390$	−707.896	+	2795.42i	−0.0919121	+	0.362953i
$391$	2183.64	+	2372.06i	0.282433	+	0.306804i
$392$	19759.3	+	3297.24i	2.54591	+	0.424837i
$393$	1254.65	+	976.533i	0.161040	+	0.125342i
$394$	5088.03	+	20092.2i	0.650587	+	2.56911i
$395$	−1805.46	+	2763.46i	−0.229981	+	0.352012i
$396$	−4253.96	−	16798.5i	−0.539822	−	2.13171i
$397$	897.061	+	974.468i	0.113406	+	0.123192i	0.789844	−	0.613308i	$-0.210161\pi$
$397$	897.061	+	974.468i	0.113406	+	0.123192i	−0.676438	+	0.736500i	$0.736477\pi$
$398$	6416.84	+	4994.43i	0.808159	+	0.629016i
$399$	163.754	−	27.3257i	0.0205462	−	0.00342856i
$400$	−18942.1	−	10250.9i	−2.36776	−	1.28137i
$401$	−139.676	+	1685.64i	−0.0173942	+	0.209917i	0.982345	+	0.187079i	$0.0599019\pi$
$401$	−139.676	+	1685.64i	−0.0173942	+	0.209917i	−0.999739	+	0.0228385i	$0.992730\pi$
$402$	701.914	−	1600.20i	0.0870853	−	0.198534i
$403$	2409.02	−	1875.01i	0.297771	−	0.231764i
$404$	10430.2	−	23778.4i	1.28446	−	2.92827i
$405$	3440.95	−	7844.58i	0.422179	−	0.962470i
$406$	−690.982	+	2728.62i	−0.0844651	+	0.333545i
$407$	−4660.60	+	5062.76i	−0.567610	+	0.616589i
$408$	2303.98	−	384.466i	0.279568	−	0.0466517i
$409$	−10882.8	+	5889.48i	−1.31570	+	0.712020i	−0.973733	−	0.227692i	$-0.926882\pi$
$409$	−10882.8	+	5889.48i	−1.31570	+	0.712020i	−0.341965	+	0.939713i	$0.611092\pi$
$410$	−8222.55	+	32470.1i	−0.990445	+	3.91118i
$411$	−974.501	−	1058.59i	−0.116955	−	0.127047i
$412$	34170.0	−	11730.6i	4.08600	−	1.40273i
$413$	569.854	+	1299.14i	0.0678952	+	0.154785i
$414$	14769.3	+	7992.72i	1.75331	+	0.948843i
$415$	12925.6	+	2156.90i	1.52889	+	0.255127i
$416$	5733.29	−	4462.40i	0.675715	−	0.525930i
$417$	−623.894	+	677.729i	−0.0732667	+	0.0795888i
$418$	4335.96	+	6636.69i	0.507366	+	0.776581i
$419$	−4946.45	+	5373.28i	−0.576730	+	0.626496i	−0.954072	−	0.299578i	$-0.903154\pi$
$419$	−4946.45	+	5373.28i	−0.576730	+	0.626496i	0.377342	+	0.926074i	$0.376838\pi$
$420$	−505.826	+	1153.17i	−0.0587662	+	0.133973i
$421$	14400.5	+	2403.01i	1.66707	+	0.278185i	0.921538	−	0.388287i	$-0.126933\pi$
$421$	14400.5	+	2403.01i	1.66707	+	0.278185i	0.745530	+	0.666472i	$0.232196\pi$
$422$	−4650.28	+	5051.55i	−0.536427	+	0.582715i
$423$	−412.764	+	4981.32i	−0.0474450	+	0.572576i
$424$	−7364.64	+	3985.54i	−0.843534	+	0.456498i
$425$	−1850.54	−	2832.46i	−0.211210	−	0.323281i
$426$	5107.00	−	7816.85i	0.580834	−	0.889032i
$427$	1089.99	−	1668.35i	0.123532	−	0.189080i
$428$	2378.95	+	28709.7i	0.268671	+	3.24237i
$429$	305.457	+	1206.22i	0.0343767	+	0.135750i
$430$	−10067.9	+	3456.33i	−1.12912	+	0.387626i
$431$	−8967.89	+	3078.68i	−1.00225	+	0.344071i	−0.776502	−	0.630115i	$-0.783008\pi$
$431$	−8967.89	+	3078.68i	−1.00225	+	0.344071i	−0.225744	+	0.974187i	$0.572481\pi$
$432$	11307.5	−	6119.29i	1.25933	−	0.681515i
$433$	3694.16	+	2875.28i	0.410000	+	0.319116i	0.798126	−	0.602490i	$-0.205825\pi$
$433$	3694.16	+	2875.28i	0.410000	+	0.319116i	−0.388126	+	0.921606i	$0.626877\pi$
$434$	1656.55	−	896.478i	0.183218	−	0.0991528i
$435$	4892.10	+	2647.47i	0.539215	+	0.291808i
$436$	3537.73	+	13970.2i	0.388593	+	1.53452i
$437$	−5363.02	−	894.930i	−0.587067	−	0.0979641i
$438$	−644.805	+	2546.28i	−0.0703424	+	0.277776i
$439$	−7624.69	+	2617.56i	−0.828945	+	0.284577i	−0.706335	−	0.707878i	$-0.749653\pi$
$439$	−7624.69	+	2617.56i	−0.828945	+	0.284577i	−0.122610	+	0.992455i	$0.539126\pi$
$440$	−35297.7			−3.82444
$441$	7784.24	+	2672.33i	0.840540	+	0.288558i
$442$	2693.68	−	449.495i	0.289876	−	0.0483718i
$443$	−6666.18	+	7241.40i	−0.714943	+	0.776635i	−0.982371	−	0.186943i	$-0.940142\pi$
$443$	−6666.18	+	7241.40i	−0.714943	+	0.776635i	0.267428	+	0.963578i	$0.413826\pi$
$444$	−5122.74	−	2772.29i	−0.547555	−	0.296322i
$445$	−10094.4	−	3465.41i	−1.07533	−	0.369160i
$446$	−28347.6	−	9731.75i	−3.00964	−	1.03321i
$447$	2076.80	−	3178.77i	0.219752	−	0.336355i
$448$	1185.26	−	641.430i	0.124996	−	0.0676445i
$449$	3833.67	+	4164.48i	0.402945	+	0.437715i	0.903890	−	0.427764i	$-0.140699\pi$
$449$	3833.67	+	4164.48i	0.402945	+	0.437715i	−0.500946	+	0.865479i	$0.667014\pi$
$450$	−13906.9	−	10824.2i	−1.45684	−	1.13390i
$451$	3548.02	+	14010.8i	0.370443	+	1.46285i
$452$	8409.89	+	19172.6i	0.875151	+	1.99514i
$453$	402.105	+	138.043i	0.0417054	+	0.0143175i
$454$	1994.02	+	24064.2i	0.206132	+	2.48764i
$455$	−347.157	+	791.439i	−0.0357692	+	0.0815456i
$456$	−2667.92	+	2898.14i	−0.273984	+	0.297626i
$457$	−15694.2			−1.60644			−0.803218	−	0.595685i	$-0.796881\pi$
$457$	−15694.2			−1.60644			−0.803218	+	0.595685i	$0.796881\pi$
$458$	−355.943	−	18126.8i	−0.0363146	−	1.84936i
$459$	2019.71			0.205386
$460$	27931.4	−	30341.6i	2.83110	−	3.07540i
$461$	−3861.32	+	8802.93i	−0.390108	+	0.889357i	0.605510	+	0.795838i	$0.292969\pi$
$461$	−3861.32	+	8802.93i	−0.390108	+	0.889357i	−0.995618	+	0.0935186i	$0.970189\pi$
$462$	63.4001	+	765.126i	0.00638450	+	0.0770495i
$463$	5887.71	+	2021.25i	0.590983	+	0.202885i	0.603938	−	0.797031i	$-0.293597\pi$
$463$	5887.71	+	2021.25i	0.590983	+	0.202885i	−0.0129549	+	0.999916i	$0.504124\pi$
$464$	−13470.6	−	30709.9i	−1.34775	−	3.07257i
$465$	−913.773	−	3608.41i	−0.0911295	−	0.359862i
$466$	1193.84	+	929.202i	0.118677	+	0.0923701i
$467$	−6347.28	−	6894.99i	−0.628945	−	0.683216i	0.337136	−	0.941456i	$-0.390542\pi$
$467$	−6347.28	−	6894.99i	−0.628945	−	0.683216i	−0.966081	+	0.258240i	$0.916858\pi$
$468$	8853.66	−	4791.36i	0.874488	−	0.473249i
$469$	286.430	−	438.414i	0.0282007	−	0.0431644i
$470$	16404.3	+	5631.61i	1.60995	+	0.552696i
$471$	−3197.25	−	1097.62i	−0.312785	−	0.107379i
$472$	−29603.2	−	16020.5i	−2.88686	−	1.56229i
$473$	−3110.88	+	3379.32i	−0.302407	+	0.328501i
$474$	−1680.34	+	280.400i	−0.162829	+	0.0271713i
$475$	5396.61	+	1852.66i	0.521292	+	0.178960i
$476$	1192.53			0.114831
$477$	−3253.94	+	1117.08i	−0.312343	+	0.107227i
$478$	−7146.00	+	28218.9i	−0.683788	+	2.70022i
$479$	1891.01	+	315.554i	0.180381	+	0.0301002i	0.254095	−	0.967179i	$-0.418222\pi$
$479$	1891.01	+	315.554i	0.180381	+	0.0301002i	−0.0737147	+	0.997279i	$0.523485\pi$
$480$	−2174.71	−	8587.75i	−0.206795	−	0.816615i
$481$	−3515.83	−	1902.67i	−0.333281	−	0.180362i
$482$	−20820.5	+	11267.5i	−1.96753	+	1.06477i
$483$	−415.535	−	323.423i	−0.0391459	−	0.0304685i
$484$	−142.650	+	77.1983i	−0.0133969	+	0.00725003i
$485$	9403.28	−	3228.15i	0.880373	−	0.302232i
$486$	15172.3	−	5208.64i	1.41611	−	0.486150i
$487$	3690.22	+	14572.4i	0.343367	+	1.35593i	0.864578	+	0.502499i	$0.167586\pi$
$487$	3690.22	+	14572.4i	0.343367	+	1.35593i	−0.521210	+	0.853428i	$0.674519\pi$
$488$	3904.77	+	47123.5i	0.362214	+	4.37127i
$489$	−315.200	+	482.449i	−0.0291489	+	0.0446158i
$490$	15619.8	−	23907.9i	1.44007	−	2.20418i
$491$	−6930.49	−	10607.9i	−0.637003	−	0.975006i	−0.999081	−	0.0428581i	$-0.986354\pi$
$491$	−6930.49	−	10607.9i	−0.637003	−	0.975006i	0.362078	−	0.932148i	$-0.382067\pi$
$492$	−10759.5	+	5822.73i	−0.985923	+	0.533555i
$493$	435.021	−	5249.92i	0.0397411	−	0.479604i
$494$	−3119.18	+	3388.34i	−0.284086	+	0.308600i
$495$	−14303.9	−	2386.91i	−1.29882	−	0.216734i
$496$	−9014.21	+	20550.3i	−0.816028	+	1.86036i
$497$	1895.29	−	2058.83i	0.171057	−	0.185817i
$498$	3698.97	+	5661.70i	0.332841	+	0.509451i
$499$	7182.39	−	7802.15i	0.644344	−	0.699945i	−0.324982	−	0.945720i	$-0.605358\pi$
$499$	7182.39	−	7802.15i	0.644344	−	0.699945i	0.969327	+	0.245775i	$0.0790426\pi$
$500$	−3174.25	+	2470.62i	−0.283913	+	0.220979i
$501$	−1632.41	−	272.402i	−0.145571	−	0.0242914i
$502$	13294.3	+	7194.52i	1.18198	+	0.639656i
$503$	−5188.44	−	11828.4i	−0.459922	−	1.04852i	−0.980823	−	0.194900i	$-0.937562\pi$
$503$	−5188.44	−	11828.4i	−0.459922	−	1.04852i	0.520901	−	0.853617i	$-0.325596\pi$
$504$	3448.73	−	1183.95i	0.304799	−	0.104638i
$505$	−14716.9	−	15986.8i	−1.29682	−	1.40872i
$506$	6172.53	−	24374.8i	0.542297	−	2.14148i
$507$	2454.15	−	1328.12i	0.214976	−	0.116339i
$508$	5249.94	−	876.060i	0.458521	−	0.0765136i
$509$	11000.2	−	11949.4i	0.957907	−	1.04056i	−0.0412348	−	0.999149i	$-0.513129\pi$
$509$	11000.2	−	11949.4i	0.957907	−	1.04056i	0.999142	−	0.0414151i	$-0.0131866\pi$
$510$	817.452	−	3228.05i	0.0709753	−	0.280275i
$511$	−316.217	+	720.903i	−0.0273750	+	0.0624087i
$512$	8427.55	−	19212.9i	0.727439	−	1.65839i
$513$	−2687.86	+	2092.04i	−0.231329	+	0.180051i
$514$	8853.03	−	20182.9i	0.759709	−	1.73196i
$515$	2496.67	−	30130.3i	0.213624	−	2.57806i
$516$	−3419.35	−	1850.46i	−0.291722	−	0.157872i
$517$	7381.89	−	1231.82i	0.627959	−	0.104788i
$518$	−1946.50	−	1515.02i	−0.165105	−	0.128506i
$519$	1467.45	+	1594.08i	0.124112	+	0.134821i
$520$	−5033.90	−	19878.4i	−0.424521	−	1.67640i
$521$	361.417	−	553.189i	0.0303915	−	0.0465176i	−0.821648	−	0.569996i	$-0.806945\pi$
$521$	361.417	−	553.189i	0.0303915	−	0.0465176i	0.852039	+	0.523478i	$0.175366\pi$
$522$	−6735.79	−	26599.0i	−0.564785	−	2.23029i
$523$	15226.7	+	11851.4i	1.27307	+	0.990871i	0.999580	+	0.0289965i	$0.00923117\pi$
$523$	15226.7	+	11851.4i	1.27307	+	0.990871i	0.273491	+	0.961874i	$0.411821\pi$
$524$	−18996.9	−	3170.02i	−1.58374	−	0.264280i
$525$	374.251	+	406.544i	0.0311117	+	0.0337963i
$526$	−9722.30	+	38392.5i	−0.805917	+	3.18249i
$527$	−2781.85	+	2165.20i	−0.229941	+	0.178971i
$528$	−6194.96	−	6729.52i	−0.510608	−	0.554668i
$529$	2777.58	+	4251.40i	0.228288	+	0.349421i
$530$	985.814	+	11897.0i	0.0807944	+	0.975043i
$531$	−10913.0	−	8493.92i	−0.891871	−	0.694171i
$532$	−1587.04	+	1235.24i	−0.129336	+	0.100666i
$533$	−7384.41	+	3996.24i	−0.600102	+	0.324759i
$534$	−2212.54	−	5044.09i	−0.179300	−	0.408762i
$535$	22802.0	+	7827.95i	1.84265	+	0.632583i
$536$	1026.11	+	12383.3i	0.0826887	+	0.997904i
$537$	168.108	−	663.844i	0.0135091	−	0.0533463i
$538$	−14452.2	−	2411.64i	−1.15814	−	0.193259i
$539$	1017.61	−	12280.7i	0.0813203	−	0.981390i
$540$	−2133.40	−	25746.3i	−0.170013	−	2.05175i
$541$	−8595.88	+	1434.40i	−0.683116	+	0.113992i	−0.495969	−	0.868340i	$-0.665187\pi$
$541$	−8595.88	+	1434.40i	−0.683116	+	0.113992i	−0.187147	+	0.982332i	$0.559924\pi$
$542$	929.756	−	11220.5i	0.0736835	−	0.889227i
$543$	385.953	+	300.399i	0.0305025	+	0.0237410i
$544$	−6620.59	+	5153.01i	−0.521793	+	0.406128i
$545$	11895.6	+	1985.03i	0.934958	+	0.156017i
$546$	−421.850	+	144.821i	−0.0330650	+	0.0113512i
$547$	10174.0			0.795265			0.397633	−	0.917545i	$-0.369832\pi$
$547$	10174.0			0.795265			0.397633	+	0.917545i	$0.369832\pi$
$548$	16485.3	+	5659.42i	1.28507	+	0.441165i
$549$	−1604.24	+	19360.3i	−0.124712	+	1.50506i
$550$	−10599.2	+	24163.8i	−0.821733	+	1.87336i
$551$	4859.00	+	7437.25i	0.375681	+	0.575023i
$552$	12494.0			0.963370
$553$	−510.562			−0.0392609
$554$	−14882.9	−	22780.0i	−1.14136	−	1.74699i
$555$	−3846.68	+	2993.99i	−0.294203	+	0.228987i
$556$	2739.33	−	10817.4i	0.208945	−	0.825106i
$557$	−18051.0	+	3012.18i	−1.37315	+	0.229139i	−0.804751	−	0.593612i	$-0.797701\pi$
$557$	−18051.0	+	3012.18i	−1.37315	+	0.229139i	−0.568402	+	0.822751i	$0.692438\pi$
$558$	−10042.7	+	15371.4i	−0.761899	+	1.16617i
$559$	−2346.76	−	1270.00i	−0.177563	−	0.0960920i
$560$	−524.622	−	6331.24i	−0.0395881	−	0.477757i
$561$	−352.730	−	1392.90i	−0.0265460	−	0.104828i
$562$	−20293.2	−	31061.0i	−1.52316	−	2.33137i
$563$	4321.20	+	2338.52i	0.323476	+	0.175056i	0.629568	−	0.776946i	$-0.283232\pi$
$563$	4321.20	+	2338.52i	0.323476	+	0.175056i	−0.306092	+	0.952002i	$0.599021\pi$
$564$	2544.69	+	5801.31i	0.189984	+	0.433119i
$565$	17520.5			1.30459
$566$	−18087.7	−	41235.9i	−1.34326	−	3.06232i
$567$	1306.85	−	218.074i	0.0967945	−	0.0161521i
$568$	−5483.10	+	66171.2i	−0.405046	+	4.88817i
$569$	−10121.4	+	15492.0i	−0.745717	+	1.14140i	0.239634	+	0.970863i	$0.422973\pi$
$569$	−10121.4	+	15492.0i	−0.745717	+	1.14140i	−0.985351	+	0.170541i	$0.945448\pi$
$570$	2255.77	+	5142.64i	0.165761	+	0.377898i
$571$	7132.57	−	2448.61i	0.522747	−	0.179459i	−0.0506814	−	0.998715i	$-0.516139\pi$
$571$	7132.57	−	2448.61i	0.522747	−	0.179459i	0.573429	+	0.819255i	$0.305613\pi$
$572$	−10208.7	−	11089.6i	−0.746236	−	0.810629i
$573$	−4728.34	−	5136.34i	−0.344728	−	0.374474i
$574$	−4899.99	+	1682.17i	−0.356309	+	0.122321i
$575$	−7269.57	−	16572.9i	−0.527238	−	1.20198i
$576$	−7185.53	+	10998.3i	−0.519787	+	0.795593i
$577$	−100.574	+	1213.74i	−0.00725639	+	0.0875716i	−0.999250	−	0.0387138i	$-0.987674\pi$
$577$	−100.574	+	1213.74i	−0.00725639	+	0.0875716i	0.991994	+	0.126285i	$0.0403055\pi$
$578$	22242.7	−	3711.65i	1.60065	−	0.267101i
$579$	2961.22	+	6750.90i	0.212546	+	0.484556i
$580$	−67383.0			−4.82401
$581$	814.175	+	1856.13i	0.0581371	+	0.132539i
$582$	4512.49	+	2442.04i	0.321389	+	0.173927i
$583$	2817.41	+	4312.36i	0.200146	+	0.306346i
$584$	−4585.25	−	18106.8i	−0.324896	−	1.28298i
$585$	−695.702	−	8395.88i	−0.0491688	−	0.593379i
$586$	9206.55	+	4982.33i	0.649008	+	0.351226i
$587$	−359.762	+	550.656i	−0.0252963	+	0.0387189i	−0.849591	−	0.527442i	$-0.823151\pi$
$587$	−359.762	+	550.656i	−0.0252963	+	0.0387189i	0.824294	+	0.566161i	$0.191572\pi$
$588$	10288.5	−	1716.85i	0.721585	−	0.120411i
$589$	1459.37	−	5762.93i	0.102092	−	0.403154i
$590$	−37867.3	+	29473.3i	−2.64233	+	2.05661i
$591$	3465.05	+	5303.65i	0.241173	+	0.369142i
$592$	29386.6			2.04018
$593$	−1931.21			−0.133736			−0.0668680	−	0.997762i	$-0.521301\pi$
$593$	−1931.21			−0.133736			−0.0668680	+	0.997762i	$0.521301\pi$
$594$	−8615.13	−	13186.4i	−0.595089	−	0.910852i
$595$	400.885	−	913.925i	0.0276213	−	0.0629702i
$596$	−3798.36	+	45839.4i	−0.261052	+	3.15043i
$597$	2350.79	+	807.027i	0.161158	+	0.0553257i
$598$	14607.3			0.998890
$599$	−4758.93	+	1633.74i	−0.324615	+	0.111440i	−0.482190	−	0.876066i	$-0.660159\pi$
$599$	−4758.93	+	1633.74i	−0.324615	+	0.111440i	0.157575	+	0.987507i	$0.449632\pi$
$600$	−12932.4	−	2158.03i	−0.879936	−	0.146835i
$601$	12497.0	−	9726.77i	0.848189	−	0.660172i	−0.0938830	−	0.995583i	$-0.529928\pi$
$601$	12497.0	−	9726.77i	0.848189	−	0.660172i	0.942072	+	0.335411i	$0.108875\pi$
$602$	−1299.26	−	1011.25i	−0.0879631	−	0.0684645i
$603$	−421.567	+	5087.56i	−0.0284702	+	0.343584i
$604$	−5079.79	+	847.666i	−0.342208	+	0.0571044i
$605$	11.2091	+	135.274i	0.000753250	+	0.00909038i
$606$	926.061	−	11175.9i	0.0620770	−	0.749158i
$607$	14660.3	+	2446.37i	0.980301	+	0.163583i	0.632984	−	0.774165i	$-0.281830\pi$
$607$	14660.3	+	2446.37i	0.980301	+	0.163583i	0.347317	+	0.937748i	$0.387093\pi$
$608$	3473.20	−	13715.4i	0.231673	−	0.914854i
$609$	71.0479	+	857.421i	0.00472743	+	0.0570516i
$610$	63756.7	+	21887.7i	4.23185	+	1.45280i
$611$	1746.47	+	3981.54i	0.115637	+	0.263627i
$612$	−10223.9	+	5532.89i	−0.675287	+	0.365447i
$613$	18603.5	−	14479.7i	1.22576	−	0.954044i	0.225958	−	0.974137i	$-0.427449\pi$
$613$	18603.5	−	14479.7i	1.22576	−	0.954044i	0.999798	+	0.0200931i	$0.00639626\pi$
$614$	16475.0	+	12823.0i	1.08286	+	0.842825i
$615$	845.456	+	10203.1i	0.0554343	+	0.668993i
$616$	−2986.07	−	4570.52i	−0.195312	−	0.298947i
$617$	−13142.9	−	14277.0i	−0.857557	−	0.931555i	0.140731	−	0.990048i	$-0.455055\pi$
$617$	−13142.9	−	14277.0i	−0.857557	−	0.931555i	−0.998288	+	0.0584931i	$0.981370\pi$
$618$	12313.0	−	9583.61i	0.801461	−	0.623802i
$619$	1947.78	−	7691.62i	0.126475	−	0.499438i	−0.873447	−	0.486920i	$-0.838120\pi$
$619$	1947.78	−	7691.62i	0.126475	−	0.499438i	0.999922	−	0.0125184i	$-0.00398482\pi$
$620$	30539.3	+	33174.5i	1.97821	+	2.14891i
$621$	10655.8	+	1778.14i	0.688570	+	0.114902i
$622$	5465.80	+	4254.20i	0.352345	+	0.274241i
$623$	−405.235	−	1600.24i	−0.0260600	−	0.102909i
$624$	2906.35	−	4448.49i	0.186453	−	0.285388i
$625$	−3402.40	−	13435.8i	−0.217754	−	0.859889i
$626$	−35977.9	−	39082.4i	−2.29707	−	2.49528i
$627$	1912.20	+	1488.32i	0.121796	+	0.0947974i
$628$	40390.9	−	6740.05i	2.56652	−	0.428276i
$629$	4059.95	+	2197.14i	0.257362	+	0.139277i
$630$	429.258	−	5180.37i	0.0271461	−	0.327605i
$631$	10558.3	−	24070.5i	0.666116	−	1.51859i	−0.178908	−	0.983866i	$-0.557257\pi$
$631$	10558.3	−	24070.5i	0.666116	−	1.51859i	0.845025	−	0.534727i	$-0.179586\pi$
$632$	9559.86	−	7440.74i	0.601694	−	0.468318i
$633$	−843.036	+	1921.93i	−0.0529347	+	0.120679i
$634$	−8720.88	+	19881.6i	−0.546294	+	1.24542i
$635$	1093.44	−	4317.91i	0.0683339	−	0.269844i
$636$	−2953.11	+	3207.93i	−0.184117	+	0.200004i
$637$	7061.20	−	1178.31i	0.439207	−	0.0732907i
$638$	−36131.6	+	19553.4i	−2.24211	+	1.21337i
$639$	−6696.60	+	26444.3i	−0.414575	+	1.63712i
$640$	859.248	+	933.392i	0.0530699	+	0.0576493i
$641$	26186.2	−	8989.73i	1.61356	−	0.553936i	0.637315	−	0.770603i	$-0.280045\pi$
$641$	26186.2	−	8989.73i	1.61356	−	0.553936i	0.976246	+	0.216667i	$0.0695186\pi$
$642$	4997.86	+	11394.0i	0.307243	+	0.700443i
$643$	−10320.8	−	5585.33i	−0.632990	−	0.342557i	0.127565	−	0.991830i	$-0.459284\pi$
$643$	−10320.8	−	5585.33i	−0.632990	−	0.342557i	−0.760555	+	0.649273i	$0.775073\pi$
$644$	6291.67	+	1049.89i	0.384979	+	0.0642417i
$645$	−2567.60	+	1998.44i	−0.156743	+	0.121998i
$646$	3601.92	−	3912.73i	0.219374	−	0.238304i
$647$	11810.9	+	18078.0i	0.717675	+	1.09848i	0.990645	+	0.136461i	$0.0435728\pi$
$647$	11810.9	+	18078.0i	0.717675	+	1.09848i	−0.272970	+	0.962022i	$0.588006\pi$
$648$	−21291.6	+	23128.8i	−1.29076	+	1.40214i
$649$	−8317.40	+	18961.8i	−0.503061	+	1.14686i
$650$	−15119.8	−	2523.05i	−0.912380	−	0.152249i
$651$	389.932	−	423.579i	0.0234756	−	0.0255013i
$652$	576.486	−	6957.15i	0.0346272	−	0.417888i
$653$	2154.15	−	1165.77i	0.129094	−	0.0698621i	−0.410117	−	0.912033i	$-0.634512\pi$
$653$	2154.15	−	1165.77i	0.129094	−	0.0698621i	0.539211	+	0.842171i	$0.318723\pi$
$654$	3404.22	+	5210.55i	0.203541	+	0.311542i
$655$	−8815.44	+	13493.0i	−0.525875	+	0.804911i
$656$	33758.6	−	51671.4i	2.00923	−	3.07535i
$657$	−633.698	−	7647.60i	−0.0376300	−	0.454127i
$658$	658.543	+	2600.53i	0.0390162	+	0.154072i
$659$	−28316.6	+	9721.12i	−1.67384	+	0.574630i	−0.988181	−	0.153294i	$-0.951012\pi$
$659$	−28316.6	+	9721.12i	−1.67384	+	0.574630i	−0.685659	+	0.727923i	$0.740486\pi$
$660$	−17383.4	+	5967.74i	−1.02523	+	0.351960i
$661$	−2886.99	+	1562.36i	−0.169881	+	0.0919348i	−0.558663	−	0.829395i	$-0.688685\pi$
$661$	−2886.99	+	1562.36i	−0.169881	+	0.0919348i	0.388782	+	0.921330i	$0.372896\pi$
$662$	33041.9	+	25717.5i	1.93989	+	1.50988i
$663$	734.128	−	397.290i	0.0430033	−	0.0232722i
$664$	−42295.4	−	22889.1i	−2.47195	−	1.33776i
$665$	413.153	+	1631.50i	0.0240923	+	0.0951383i
$666$	23716.9	+	3957.65i	1.37990	+	0.230264i
$667$	6917.10	−	27315.0i	0.401546	−	1.58567i
$668$	18961.8	−	6509.59i	1.09828	−	0.377041i
$669$	−9161.12			−0.529431
$670$	16754.2	+	5751.72i	0.966077	+	0.331654i
$671$	28690.3	−	4787.56i	1.65063	−	0.275442i
$672$	928.010	−	1008.09i	0.0532720	−	0.0578688i
$673$	−18710.4	−	10125.6i	−1.07167	−	0.579959i	−0.158426	−	0.987371i	$-0.550642\pi$
$673$	−18710.4	−	10125.6i	−1.07167	−	0.579959i	−0.913245	+	0.407412i	$0.866431\pi$
$674$	−6924.27	−	2377.10i	−0.395716	−	0.135850i
$675$	−10722.5	−	3681.05i	−0.611423	−	0.209902i
$676$	−18488.5	+	28298.8i	−1.05192	+	1.61008i
$677$	1872.20	−	1013.18i	0.106284	−	0.0575183i	−0.421936	−	0.906626i	$-0.638649\pi$
$677$	1872.20	−	1013.18i	0.106284	−	0.0575183i	0.528220	+	0.849108i	$0.322860\pi$
$678$	6124.01	+	6652.45i	0.346890	+	0.376823i
$679$	1213.48	+	944.492i	0.0685850	+	0.0533818i
$680$	5812.96	+	22954.9i	0.327819	+	1.29453i
$681$	2964.78	+	6759.03i	0.166829	+	0.380333i
$682$	26002.3	+	8926.59i	1.45994	+	0.501198i
$683$	−94.5624	−	1141.20i	−0.00529770	−	0.0639337i	0.993423	−	0.114504i	$-0.0365278\pi$
$683$	−94.5624	−	1141.20i	−0.00529770	−	0.0639337i	−0.998721	+	0.0505700i	$0.983896\pi$
$684$	7875.02	−	17953.2i	0.440218	−	1.00360i
$685$	9878.98	−	10731.4i	0.551031	−	0.598579i
$686$	8916.68			0.496269
$687$	−1901.94	−	5205.10i	−0.105624	−	0.289064i
$688$	19615.1			1.08695
$689$	−2026.77	+	2201.66i	−0.112067	+	0.121737i
$690$	7154.73	−	16311.1i	0.394748	−	0.899934i
$691$	−472.603	−	5703.48i	−0.0260184	−	0.313995i	−0.997150	−	0.0754492i	$-0.975961\pi$
$691$	−472.603	−	5703.48i	−0.0260184	−	0.313995i	0.971131	−	0.238546i	$-0.0766707\pi$
$692$	−24824.5	−	8522.25i	−1.36371	−	0.468161i
$693$	−900.998	−	2054.07i	−0.0493883	−	0.112594i
$694$	−1355.18	−	5351.50i	−0.0741240	−	0.292709i
$695$	−7369.28	−	5735.74i	−0.402205	−	0.313049i
$696$	−13826.0	−	15019.1i	−0.752981	−	0.817956i
$697$	8527.25	−	4614.72i	0.463404	−	0.250782i
$698$	33655.1	−	51513.0i	1.82502	−	2.79340i
$699$	437.359	+	150.145i	0.0236658	+	0.00812449i
$700$	−6331.08	−	2173.46i	−0.341846	−	0.117356i
$701$	4430.16	+	2397.48i	0.238695	+	0.129175i	0.590892	−	0.806751i	$-0.298776\pi$
$701$	4430.16	+	2397.48i	0.238695	+	0.129175i	−0.352197	+	0.935926i	$0.614565\pi$
$702$	6197.51	−	6732.29i	0.333205	−	0.361957i
$703$	−7678.84	+	1281.37i	−0.411967	+	0.0687452i
$704$	18604.6	+	6386.98i	0.996007	+	0.341930i
$705$	5301.40			0.283209
$706$	71.7554	−	24.6336i	0.00382514	−	0.00131317i
$707$	825.050	−	3258.05i	0.0438885	−	0.173312i
$708$	−17287.6	−	2884.78i	−0.917664	−	0.153131i
$709$	−3027.97	−	11957.2i	−0.160392	−	0.633374i	−0.996409	−	0.0846702i	$-0.973016\pi$
$709$	−3027.97	−	11957.2i	−0.160392	−	0.633374i	0.836017	−	0.548703i	$-0.184878\pi$
$710$	83247.7	+	45051.4i	4.40033	+	2.38134i
$711$	4377.17	−	2368.81i	0.230881	−	0.124947i
$712$	30908.9	+	24057.4i	1.62691	+	1.26628i
$713$	−16582.9	+	8974.23i	−0.871018	+	0.471371i
$714$	487.137	−	167.234i	0.0255331	−	0.00876553i
$715$	−11930.6	+	4095.76i	−0.624024	+	0.214228i
$716$	2036.41	+	8041.62i	0.106291	+	0.419734i
$717$	734.765	+	8867.29i	0.0382710	+	0.461862i
$718$	−23010.5	+	35220.2i	−1.19602	+	1.83065i
$719$	8499.26	−	13009.1i	0.440847	−	0.674766i	−0.545749	−	0.837949i	$-0.683755\pi$
$719$	8499.26	−	13009.1i	0.440847	−	0.674766i	0.986596	+	0.163182i	$0.0521758\pi$
$720$	33872.2	+	51845.3i	1.75325	+	2.68355i
$721$	4112.63	−	2225.64i	0.212430	−	0.114962i
$722$	2222.73	−	26824.3i	0.114572	−	1.38268i
$723$	−4900.91	+	5323.81i	−0.252098	+	0.273851i
$724$	−5843.78	−	975.154i	−0.299976	−	0.0500571i
$725$	−11877.8	+	27078.6i	−0.608455	+	1.38714i
$726$	−47.4451	+	51.5391i	−0.00242542	+	0.00263471i
$727$	1994.53	+	3052.85i	0.101751	+	0.155741i	0.884412	−	0.466706i	$-0.154559\pi$
$727$	1994.53	+	3052.85i	0.101751	+	0.155741i	−0.782662	+	0.622448i	$0.786138\pi$
$728$	2148.10	−	2333.46i	0.109360	−	0.118797i
$729$	−7389.16	+	5751.21i	−0.375408	+	0.292192i
$730$	−26264.4	−	4382.76i	−1.33163	−	0.222210i
$731$	2709.96	+	1466.55i	0.137115	+	0.0742031i
$732$	9890.14	+	22547.2i	0.499385	+	1.13848i
$733$	−13283.5	+	4560.22i	−0.669353	+	0.229789i	−0.638369	−	0.769731i	$-0.720391\pi$
$733$	−13283.5	+	4560.22i	−0.669353	+	0.229789i	−0.0309845	+	0.999520i	$0.509864\pi$
$734$	−30956.9	−	33628.1i	−1.55673	−	1.69106i
$735$	2142.87	−	8461.99i	0.107539	−	0.424660i
$736$	−39466.2	+	21358.0i	−1.97655	+	1.06966i
$737$	7539.33	−	1258.09i	0.376818	−	0.0628798i
$738$	34204.2	−	37155.7i	1.70606	−	1.85328i
$739$	−4449.59	+	17571.0i	−0.221490	+	0.874642i	0.754407	+	0.656407i	$0.227925\pi$
$739$	−4449.59	+	17571.0i	−0.221490	+	0.874642i	−0.975896	+	0.218235i	$0.929970\pi$
$740$	23719.5	−	54075.1i	1.17831	−	2.68627i
$741$	−565.468	+	1289.14i	−0.0280337	+	0.0639104i
$742$	−1457.09	+	1134.10i	−0.0720907	+	0.0561104i
$743$	110.438	−	251.772i	0.00545298	−	0.0124315i	−0.913026	−	0.407902i	$-0.866261\pi$
$743$	110.438	−	251.772i	0.00545298	−	0.0124315i	0.918479	+	0.395470i	$0.129418\pi$
$744$	−1128.08	+	13613.9i	−0.0555880	+	0.670847i
$745$	33853.2	+	18320.4i	1.66481	+	0.900952i
$746$	60222.3	−	10049.3i	2.95562	−	0.493207i
$747$	−15591.8	−	12135.6i	−0.763689	−	0.594403i
$748$	11788.6	+	12805.9i	0.576250	+	0.625975i
$749$	915.376	+	3614.74i	0.0446557	+	0.176341i
$750$	−950.180	+	1454.36i	−0.0462609	+	0.0708076i
$751$	4506.76	+	17796.8i	0.218980	+	0.864733i	0.977128	+	0.212650i	$0.0682096\pi$
$751$	4506.76	+	17796.8i	0.218980	+	0.864733i	−0.758148	+	0.652082i	$0.773896\pi$
$752$	−25221.0	−	19630.3i	−1.22303	−	0.951921i
$753$	4557.41	+	760.498i	0.220560	+	0.0368049i
$754$	−16164.6	−	17559.5i	−0.780744	−	0.848114i
$755$	−1058.00	+	4177.96i	−0.0509996	+	0.201393i
$756$	3153.28	−	2454.30i	0.151698	−	0.118071i
$757$	−26489.4	−	28775.2i	−1.27183	−	1.38157i	−0.889100	−	0.457713i	$-0.848669\pi$
$757$	−26489.4	−	28775.2i	−1.27183	−	1.38157i	−0.382729	−	0.923861i	$-0.625016\pi$
$758$	30484.4	+	46659.9i	1.46074	+	2.23583i
$759$	−634.670	−	7659.33i	−0.0303519	−	0.366292i
$760$	−31512.9	−	24527.4i	−1.50407	−	1.17066i
$761$	−25400.5	+	19770.0i	−1.20995	+	0.941738i	−0.999358	−	0.0358365i	$-0.988590\pi$
$761$	−25400.5	+	19770.0i	−1.20995	+	0.941738i	−0.210588	+	0.977575i	$0.567538\pi$
$762$	2021.69	−	1094.08i	0.0961130	−	0.0520138i
$763$	749.299	+	1708.23i	0.0355523	+	0.0810512i
$764$	79987.8	+	27459.8i	3.78777	+	1.30034i
$765$	803.372	+	9695.25i	0.0379686	+	0.458213i
$766$	−11093.3	+	43806.5i	−0.523261	+	2.06631i
$767$	−11864.8	−	1979.88i	−0.558555	−	0.0932063i
$768$	513.757	−	6200.13i	0.0241388	−	0.291312i
$769$	641.851	+	7745.99i	0.0300985	+	0.363235i	0.994945	+	0.100421i	$0.0320189\pi$
$769$	641.851	+	7745.99i	0.0300985	+	0.363235i	−0.964847	+	0.262814i	$0.915349\pi$
$770$	−7676.87	+	1281.04i	−0.359293	+	0.0599553i
$771$	556.296	−	6713.49i	0.0259851	−	0.313594i
$772$	−70470.2	−	54849.1i	−3.28533	−	2.55708i
$773$	19776.5	−	15392.7i	0.920196	−	0.716218i	−0.0389162	−	0.999242i	$-0.512391\pi$
$773$	19776.5	−	15392.7i	0.920196	−	0.716218i	0.959113	+	0.283025i	$0.0913379\pi$
$774$	15830.7	+	2641.67i	0.735170	+	0.122678i
$775$	18714.8	−	6424.81i	0.867428	−	0.297788i
$776$	−36486.2			−1.68786
$777$	−713.093	−	244.805i	−0.0329242	−	0.0113029i
$778$	−374.620	+	4520.99i	−0.0172632	+	0.208336i
$779$	−6568.18	+	14973.9i	−0.302092	+	0.688699i
$780$	−5839.91	−	8938.65i	−0.268080	−	0.410327i
$781$	40844.1			1.87134
$782$	−16868.0			−0.771352
$783$	−9654.35	−	14777.1i	−0.440636	−	0.674444i
$784$	−41528.1	+	32322.6i	−1.89177	+	1.47242i
$785$	8412.51	−	33220.2i	0.382491	−	1.51042i
$786$	−8204.56	+	1369.10i	−0.372324	+	0.0621299i
$787$	543.973	−	832.612i	0.0246385	−	0.0377121i	−0.824635	−	0.565665i	$-0.808619\pi$
$787$	543.973	−	832.612i	0.0246385	−	0.0377121i	0.849273	+	0.527953i	$0.177040\pi$
$788$	−67493.7	−	36525.8i	−3.05122	−	1.65124i
$789$	999.663	+	12064.1i	0.0451064	+	0.544353i
$790$	−4239.53	−	16741.5i	−0.190931	−	0.753971i
$791$	1482.17	+	2268.64i	0.0666246	+	0.101976i
$792$	46805.7	+	25330.0i	2.09996	+	1.13644i
$793$	6787.78	+	15474.6i	0.303961	+	0.692961i
$794$	−6929.53			−0.309723
$795$	1465.75	+	3341.57i	0.0653896	+	0.149073i
$796$	−29697.5	+	4955.64i	−1.32236	+	0.220663i
$797$	2759.81	−	33305.9i	0.122657	−	1.48025i	−0.606053	−	0.795424i	$-0.707248\pi$
$797$	2759.81	−	33305.9i	0.122657	−	1.48025i	0.728710	−	0.684822i	$-0.240120\pi$
$798$	−475.064	+	727.139i	−0.0210740	+	0.0322562i
$799$	−2016.76	−	4597.74i	−0.0892963	−	0.203575i
$800$	44539.9	−	15290.6i	1.96841	−	0.675755i
$801$	10898.6	+	11839.1i	0.480755	+	0.522239i
$802$	−5993.36	−	6510.53i	−0.263882	−	0.286652i
$803$	−10867.2	+	3730.73i	−0.477580	+	0.163953i
$804$	2598.97	+	5925.04i	0.114003	+	0.259901i
$805$	2919.63	−	4468.83i	0.127831	−	0.195659i
$806$	−1318.89	+	15916.6i	−0.0576375	+	0.695581i
$807$	−4417.46	+	737.144i	−0.192692	+	0.0321545i
$808$	32033.2	+	73028.3i	1.39471	+	3.17961i
$809$	6856.50			0.297975			0.148987	−	0.988839i	$-0.452399\pi$
$809$	6856.50			0.297975			0.148987	+	0.988839i	$0.452399\pi$
$810$	18002.4	+	41041.3i	0.780912	+	1.78030i
$811$	33736.5	+	18257.3i	1.46072	+	0.790505i	0.995507	−	0.0946917i	$-0.0301865\pi$
$811$	33736.5	+	18257.3i	1.46072	+	0.790505i	0.465218	+	0.885196i	$0.345976\pi$
$812$	−5700.38	−	8725.08i	−0.246360	−	0.377081i
$813$	−844.817	−	3336.11i	−0.0364441	−	0.143914i
$814$	−2973.00	−	35878.8i	−0.128014	−	1.54490i
$815$	−5137.98	−	2780.53i	−0.220829	−	0.119507i
$816$	−3356.14	+	5136.96i	−0.143981	+	0.220379i
$817$	−5125.51	+	855.296i	−0.219485	+	0.0366255i
$818$	15892.6	−	62758.5i	0.679305	−	2.68252i
$819$	1028.29	−	800.347i	0.0438720	−	0.0341470i
$820$	−67833.4	−	103827.i	−2.88883	−	4.42169i
$821$	−10974.2			−0.466506			−0.233253	−	0.972416i	$-0.574937\pi$
$821$	−10974.2			−0.466506			−0.233253	+	0.972416i	$0.574937\pi$
$822$	7527.73			0.319416
$823$	6843.37	+	10474.6i	0.289848	+	0.443645i	0.952168	−	0.305576i	$-0.0988490\pi$
$823$	6843.37	+	10474.6i	0.289848	+	0.443645i	−0.662320	+	0.749221i	$0.730428\pi$
$824$	−44570.0	+	101609.i	−1.88431	+	4.29579i
$825$	−666.022	+	8037.69i	−0.0281065	+	0.339196i
$826$	−7019.80	−	2409.90i	−0.295702	−	0.101515i
$827$	25880.7			1.08822			0.544111	−	0.839013i	$-0.316867\pi$
$827$	25880.7			1.08822			0.544111	+	0.839013i	$0.316867\pi$
$828$	−58811.2	+	20189.9i	−2.46839	+	0.847400i
$829$	−39858.1	−	6651.14i	−1.66988	−	0.278654i	−0.747307	−	0.664479i	$-0.768654\pi$
$829$	−39858.1	−	6651.14i	−1.66988	−	0.278654i	−0.922572	+	0.385825i	$0.873917\pi$
$830$	−54102.7	+	42109.8i	−2.26257	+	1.76103i
$831$	−6563.51	−	5108.59i	−0.273990	−	0.213255i
$832$	−943.665	+	11388.3i	−0.0393217	+	0.474543i
$833$	−8154.02	+	1360.67i	−0.339160	+	0.0565957i
$834$	−397.982	−	4802.93i	−0.0165240	−	0.199415i
$835$	1385.46	−	16720.1i	0.0574203	−	0.692960i
$836$	−28952.9	−	4831.39i	−1.19780	−	0.199877i
$837$	−2899.63	+	11450.4i	−0.119744	+	0.472859i
$838$	−3155.34	−	38079.3i	−0.130071	−	1.56972i
$839$	−23417.4	−	8039.20i	−0.963598	−	0.330804i	−0.202385	−	0.979306i	$-0.564869\pi$
$839$	−23417.4	−	8039.20i	−0.963598	−	0.330804i	−0.761213	+	0.648502i	$0.775396\pi$
$840$	−1553.49	−	3541.61i	−0.0638103	−	0.145473i
$841$	−19040.6	+	10304.2i	−0.780704	+	0.422496i
$842$	−60276.2	+	46914.8i	−2.46705	+	1.92018i
$843$	−8949.48	−	6965.66i	−0.365642	−	0.284591i
$844$	−2099.42	−	25336.2i	−0.0856219	−	1.03330i
$845$	15472.3	+	23682.1i	0.629896	+	0.964128i
$846$	−17711.3	−	19239.6i	−0.719771	−	0.781880i
$847$	−16.5677	+	12.8952i	−0.000672106	+	0.000523121i
$848$	5400.16	−	21324.8i	0.218682	−	0.863556i
$849$	−9321.72	−	10126.1i	−0.376820	−	0.409336i
$850$	17459.8	+	2913.52i	0.704548	+	0.117568i
$851$	19485.5	+	15166.2i	0.784906	+	0.610917i
$852$	8487.16	+	33515.0i	0.341274	+	1.34766i
$853$	−12133.2	+	18571.3i	−0.487026	+	0.745449i	−0.993129	−	0.117024i	$-0.962665\pi$
$853$	−12133.2	+	18571.3i	−0.487026	+	0.745449i	0.506103	+	0.862473i	$0.331086\pi$
$854$	2559.48	+	10107.1i	0.102557	+	0.404988i
$855$	−11111.6	−	12070.4i	−0.444454	−	0.482806i
$856$	−69819.5	−	54342.7i	−2.78783	−	2.16986i
$857$	−7983.55	+	1332.22i	−0.318218	+	0.0531012i	−0.321548	−	0.946893i	$-0.604203\pi$
$857$	−7983.55	+	1332.22i	−0.318218	+	0.0531012i	0.00333001	+	0.999994i	$0.498940\pi$
$858$	−5725.29	−	3098.37i	−0.227807	−	0.123283i
$859$	−1416.88	+	17099.2i	−0.0562785	+	0.679180i	0.908802	+	0.417227i	$0.136998\pi$
$859$	−1416.88	+	17099.2i	−0.0562785	+	0.679180i	−0.965081	+	0.261953i	$0.915634\pi$
$860$	15832.4	−	36094.3i	0.627769	−	1.43117i
$861$	−1249.63	+	972.626i	−0.0494626	+	0.0384983i
$862$	19926.5	−	45427.8i	0.787354	−	1.79499i
$863$	900.725	−	2053.45i	0.0355284	−	0.0809967i	−0.897113	−	0.441801i	$-0.854340\pi$
$863$	900.725	−	2053.45i	0.0355284	−	0.0809967i	0.932642	+	0.360804i	$0.117498\pi$
$864$	−6900.91	+	27251.1i	−0.271729	+	1.07303i
$865$	−14876.3	+	16159.9i	−0.584750	+	0.635208i
$866$	−24157.3	+	4031.14i	−0.947919	+	0.158180i
$867$	6061.96	−	3280.57i	0.237457	−	0.128505i
$868$	−1712.08	+	6760.84i	−0.0669489	+	0.264375i
$869$	−5047.09	−	5482.61i	−0.197021	−	0.214021i
$870$	−27525.2	+	9449.42i	−1.07263	+	0.368236i
$871$	1783.72	+	4066.46i	0.0693903	+	0.158194i
$872$	−38925.1	−	21065.2i	−1.51166	−	0.818072i
$873$	−14785.6	−	2467.27i	−0.573213	−	0.0956524i
$874$	22448.1	−	17472.0i	0.868783	−	0.676201i
$875$	−352.627	+	383.055i	−0.0136239	+	0.0147996i
$876$	−5319.43	−	8142.00i	−0.205168	−	0.314033i
$877$	17920.3	−	19466.7i	0.689996	−	0.749535i	−0.288121	−	0.957594i	$-0.593030\pi$
$877$	17920.3	−	19466.7i	0.689996	−	0.749535i	0.978116	+	0.208059i	$0.0667147\pi$
$878$	16941.9	−	38623.7i	0.651210	−	1.48461i
$879$	3156.09	+	526.658i	0.121106	+	0.0202090i
$880$	62801.2	−	68220.3i	2.40571	−	2.61330i
$881$	−291.180	+	3514.02i	−0.0111352	+	0.134382i	−0.999884	−	0.0152005i	$-0.995161\pi$
$881$	−291.180	+	3514.02i	−0.0111352	+	0.134382i	0.988749	+	0.149582i	$0.0477929\pi$
$882$	−37868.9	+	20493.6i	−1.44571	+	0.782377i
$883$	14398.5	+	22038.5i	0.548751	+	0.839927i	0.998585	−	0.0531860i	$-0.0169376\pi$
$883$	14398.5	+	22038.5i	0.548751	+	0.839927i	−0.449833	+	0.893113i	$0.648517\pi$
$884$	−5530.61	+	8465.22i	−0.210424	+	0.322077i
$885$	−8022.25	+	12279.0i	−0.304706	+	0.466387i
$886$	−4252.36	−	51318.3i	−0.161242	−	1.94591i
$887$	8767.93	+	34623.8i	0.331903	+	1.31066i	0.880292	+	0.474433i	$0.157347\pi$
$887$	8767.93	+	34623.8i	0.331903	+	1.31066i	−0.548388	+	0.836224i	$0.684758\pi$
$888$	16919.8	−	5808.57i	0.639404	−	0.219508i
$889$	651.606	−	223.697i	0.0245829	−	0.00843931i
$890$	49107.4	−	26575.6i	1.84953	−	1.00092i
$891$	15260.4	+	11877.7i	0.573787	+	0.446596i
$892$	97599.8	−	52818.4i	3.66355	−	1.98261i
$893$	7446.31	+	4029.74i	0.279039	+	0.151008i
$894$	4876.68	+	19257.6i	0.182439	+	0.720436i
$895$	6847.44	+	1142.64i	0.255737	+	0.0426750i
$896$	−48.1706	+	190.222i	−0.00179606	+	0.00709247i
$897$	4222.95	−	1449.74i	0.157191	−	0.0539637i
$898$	−29614.0			−1.10048
$899$	29138.9	+	10003.4i	1.08102	+	0.371114i
$900$	64361.9	−	10740.1i	2.38377	−	0.397782i
$901$	2340.44	−	2542.40i	0.0865388	−	0.0940062i
$902$	−66502.0	−	35989.1i	−2.45485	−	1.32850i
$903$	−475.979	−	163.404i	−0.0175411	−	0.00602186i
$904$	−60814.8	−	20877.7i	−2.23747	−	0.768123i
$905$	−2711.79	+	4150.70i	−0.0996055	+	0.152458i
$906$	−1956.17	+	1058.62i	−0.0717321	+	0.0388195i
$907$	9124.03	+	9911.34i	0.334023	+	0.362845i	0.880016	−	0.474944i	$-0.157532\pi$
$907$	9124.03	+	9911.34i	0.334023	+	0.362845i	−0.545993	+	0.837790i	$0.683848\pi$
$908$	−70555.0	−	54915.2i	−2.57869	−	2.00708i
$909$	8042.71	+	31759.9i	0.293465	+	1.15887i
$910$	−1816.26	−	4140.65i	−0.0661630	−	0.150836i
$911$	−32325.5	−	11097.4i	−1.17562	−	0.403592i	−0.333433	−	0.942774i	$-0.608207\pi$
$911$	−32325.5	−	11097.4i	−1.17562	−	0.403592i	−0.842189	+	0.539182i	$0.818733\pi$
$912$	−854.531	−	10312.7i	−0.0310267	−	0.374436i
$913$	−11883.4	+	27091.5i	−0.430760	+	0.982034i
$914$	55610.7	−	60409.3i	2.01251	−	2.18617i
$915$	20604.3			0.744433
$916$	50272.7	+	44487.9i	1.81338	+	1.60472i
$917$	−2492.90			−0.0897741
$918$	−7156.65	+	7774.20i	−0.257304	+	0.279506i
$919$	3328.09	−	7587.29i	0.119460	−	0.272341i	−0.845863	−	0.533400i	$-0.820914\pi$
$919$	3328.09	−	7587.29i	0.119460	−	0.272341i	0.965323	+	0.261059i	$0.0840718\pi$
$920$	10459.3	+	126225.i	0.374818	+	4.52339i
$921$	6035.56	+	2072.01i	0.215938	+	0.0741315i
$922$	−20201.7	−	46055.1i	−0.721590	−	1.64506i
$923$	5824.89	+	23002.0i	0.207723	+	0.820281i
$924$	−2243.31	−	1746.04i	−0.0798697	−	0.0621650i
$925$	−17549.6	−	19063.9i	−0.623813	−	0.677642i
$926$	−28642.6	+	15500.6i	−1.01647	+	0.550089i
$927$	−24932.5	+	38162.0i	−0.883376	+	1.35211i
$928$	69348.4	+	23807.3i	2.45310	+	0.842149i
$929$	26543.6	+	9112.42i	0.937423	+	0.321818i	0.750736	−	0.660602i	$-0.229699\pi$
$929$	26543.6	+	9112.42i	0.937423	+	0.321818i	0.186686	+	0.982420i	$0.440225\pi$
$930$	17127.2	+	9268.77i	0.603895	+	0.326812i
$931$	9442.06	−	10256.8i	0.332386	−	0.361067i
$932$	−5525.15	+	921.984i	−0.194187	+	0.0324041i
$933$	2002.38	+	687.417i	0.0702625	+	0.0241211i
$934$	49030.8			1.71771
$935$	13777.0	−	4729.64i	0.481877	−	0.165429i
$936$	−7589.86	+	29971.7i	−0.265045	+	1.04664i
$937$	−28293.0	−	4721.27i	−0.986439	−	0.164608i	−0.350680	−	0.936495i	$-0.614050\pi$
$937$	−28293.0	−	4721.27i	−0.986439	−	0.164608i	−0.635759	+	0.771888i	$0.719313\pi$
$938$	672.589	+	2655.99i	0.0234124	+	0.0924534i
$939$	−14280.0	−	7727.96i	−0.496284	−	0.268575i
$940$	−56479.5	+	30565.2i	−1.95974	+	1.06056i
$941$	−2931.32	−	2281.54i	−0.101550	−	0.0790392i	0.562165	−	0.827025i	$-0.309969\pi$
$941$	−2931.32	−	2281.54i	−0.101550	−	0.0790392i	−0.663715	+	0.747986i	$0.731021\pi$
$942$	15554.1	−	8417.44i	0.537982	−	0.291141i
$943$	49051.6	−	16839.4i	1.69389	−	0.581513i
$944$	83632.6	−	28711.1i	2.88348	−	0.989901i
$945$	−820.893	−	3241.63i	−0.0282578	−	0.111588i
$946$	−1984.43	−	23948.5i	−0.0682024	−	0.823080i
$947$	−6278.53	+	9610.00i	−0.215443	+	0.329760i	−0.928491	−	0.371355i	$-0.878893\pi$
$947$	−6278.53	+	9610.00i	−0.215443	+	0.329760i	0.713048	+	0.701115i	$0.247314\pi$
$948$	3450.05	−	5280.69i	0.118199	−	0.180917i
$949$	−3650.82	−	5588.00i	−0.124880	−	0.191142i
$950$	−26253.5	+	14207.7i	−0.896607	+	0.485220i
$951$	−547.992	+	6613.28i	−0.0186854	+	0.225500i
$952$	−2480.55	+	2694.60i	−0.0844487	+	0.0917357i
$953$	38552.7	+	6433.31i	1.31044	+	0.218673i	0.778250	−	0.627955i	$-0.216108\pi$
$953$	38552.7	+	6433.31i	1.31044	+	0.218673i	0.532185	+	0.846628i	$0.321371\pi$
$954$	7230.19	−	16483.2i	0.245373	−	0.559395i
$955$	47933.4	−	52069.5i	1.62418	−	1.76432i
$956$	−58952.2	−	90233.1i	−1.99441	−	3.05267i
$957$	−8504.97	+	9238.86i	−0.287280	+	0.312069i
$958$	−7915.22	+	6160.66i	−0.266941	+	0.207768i
$959$	2225.29	+	371.335i	0.0749304	+	0.0125037i
$960$	12254.5	+	6631.81i	0.411992	+	0.222959i
$961$	3685.54	+	8402.18i	0.123713	+	0.282038i
$962$	19781.7	−	6791.05i	0.662980	−	0.227601i
$963$	−24618.7	−	26743.0i	−0.823808	−	0.894894i
$964$	21518.4	−	84974.4i	0.718944	−	2.83905i
$965$	−65724.3	+	35568.2i	−2.19248	+	1.18651i
$966$	2717.31	−	453.439i	0.0905053	−	0.0151027i
$967$	−35908.6	+	39007.1i	−1.19415	+	1.29719i	−0.249782	+	0.968302i	$0.580359\pi$
$967$	−35908.6	+	39007.1i	−1.19415	+	1.29719i	−0.944368	+	0.328890i	$0.893325\pi$
$968$	122.288	−	482.904i	0.00406041	−	0.0160342i
$969$	652.981	−	1488.65i	0.0216479	−	0.0493522i
$970$	−20893.9	+	47633.3i	−0.691611	+	1.57672i
$971$	−3690.60	+	2872.51i	−0.121974	+	0.0949364i	−0.673363	−	0.739312i	$-0.735151\pi$
$971$	−3690.60	+	2872.51i	−0.121974	+	0.0949364i	0.551389	+	0.834249i	$0.314098\pi$
$972$	−23859.2	+	54393.6i	−0.787330	+	1.79493i
$973$	119.275	−	1439.44i	0.00392989	−	0.0474267i
$974$	−69167.2	−	37431.4i	−2.27542	−	1.23140i
$975$	−4621.52	+	771.196i	−0.151802	+	0.0253313i
$976$	−98023.5	−	76294.8i	−3.21481	−	2.50219i
$977$	4039.28	+	4387.83i	0.132270	+	0.143684i	0.798343	−	0.602203i	$-0.205710\pi$
$977$	4039.28	+	4387.83i	0.132270	+	0.143684i	−0.666073	+	0.745887i	$0.732026\pi$
$978$	−740.144	−	2922.76i	−0.0241996	−	0.0955621i
$979$	13178.0	−	20170.5i	0.430206	−	0.658480i
$980$	25958.1	+	102506.i	0.846123	+	3.34127i
$981$	−14349.4	−	11168.6i	−0.467015	−	0.363493i
$982$	65389.0	+	10911.5i	2.12489	+	0.354582i
$983$	19733.6	+	21436.4i	0.640288	+	0.695538i	0.968485	−	0.249071i	$-0.0801253\pi$
$983$	19733.6	+	21436.4i	0.640288	+	0.695538i	−0.328197	+	0.944609i	$0.606441\pi$
$984$	9223.63	−	36423.3i	0.298820	−	1.18001i
$985$	−50681.2	+	39446.8i	−1.63943	+	1.27602i
$986$	18666.3	+	20277.0i	0.602898	+	0.654921i
$987$	448.481	+	686.451i	0.0144633	+	0.0221378i
$988$	−1408.19	−	16994.3i	−0.0453445	−	0.547226i
$989$	13006.3	+	10123.2i	0.418176	+	0.325479i
$990$	59872.2	−	46600.4i	1.92208	−	1.49602i
$991$	−29264.4	+	15837.1i	−0.938058	+	0.507651i	−0.871643	−	0.490141i	$-0.836945\pi$
$991$	−29264.4	+	15837.1i	−0.938058	+	0.507651i	−0.0664144	+	0.997792i	$0.521156\pi$
$992$	−19709.1	−	44932.1i	−0.630810	−	1.43810i
$993$	12104.8	+	4155.57i	0.386841	+	0.132803i
$994$	1209.01	+	14590.5i	0.0385788	+	0.465577i
$995$	−6185.32	+	24425.3i	−0.197073	+	0.778224i
$996$	−24699.5	−	4121.61i	−0.785776	−	0.131123i
$997$	95.5908	−	1153.61i	0.00303650	−	0.0366451i	−0.994898	−	0.100888i	$-0.967832\pi$
$997$	95.5908	−	1153.61i	0.00303650	−	0.0366451i	0.997934	+	0.0642428i	$0.0204632\pi$
$998$	4581.65	+	55292.3i	0.145320	+	1.75375i
$999$	15257.1	−	2545.96i	0.483196	−	0.0806312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	229.4.g.a.16.3	✓	1026
229.43	even	19	inner	229.4.g.a.43.3	yes	1026

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
229.4.g.a.16.3	✓	1026	1.1	even	1	trivial
229.4.g.a.43.3	yes	1026	229.43	even	19	inner

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:	\( N \)	\(=\)	\( 229 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	229.g (of order \(19\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.54340 + 3.84916i) q^{2} +(-0.642373 + 1.46446i) q^{3} +(-1.59970 - 19.3055i) q^{4} +(-15.3330 - 5.26382i) q^{5} +(-3.36076 - 7.66177i) q^{6} +(-0.615535 - 2.43069i) q^{7} +(46.9494 + 36.5422i) q^{8} +(16.5546 + 17.9831i) q^{9} +O(q^{10})\)	\(q+(-3.54340 + 3.84916i) q^{2} +(-0.642373 + 1.46446i) q^{3} +(-1.59970 - 19.3055i) q^{4} +(-15.3330 - 5.26382i) q^{5} +(-3.36076 - 7.66177i) q^{6} +(-0.615535 - 2.43069i) q^{7} +(46.9494 + 36.5422i) q^{8} +(16.5546 + 17.9831i) q^{9} +(74.5922 - 40.3673i) q^{10} +(20.0169 - 30.6382i) q^{11} +(29.2998 + 10.0586i) q^{12} +(20.1090 + 6.90342i) q^{13} +(11.5372 + 6.24362i) q^{14} +(17.5582 - 19.0732i) q^{15} +(-154.157 + 25.7243i) q^{16} +(-23.2211 - 7.97182i) q^{17} -127.879 q^{18} +(39.1602 - 13.4437i) q^{19} +(-77.0927 + 304.432i) q^{20} +(3.95506 + 0.659983i) q^{21} +(47.0032 + 185.611i) q^{22} +(-115.494 - 62.5021i) q^{23} +(-83.6737 + 45.2819i) q^{24} +(108.750 + 84.6437i) q^{25} +(-97.8265 + 52.9411i) q^{26} +(-77.8074 + 26.7113i) q^{27} +(-45.9411 + 15.7716i) q^{28} +(52.6731 + 208.001i) q^{29} +(11.2004 + 135.168i) q^{30} +(78.5324 - 120.203i) q^{31} +(186.901 - 286.074i) q^{32} +(32.0101 + 48.9951i) q^{33} +(112.967 - 61.1344i) q^{34} +(-3.35674 + 40.5099i) q^{35} +(320.691 - 348.363i) q^{36} +(-185.463 - 30.9483i) q^{37} +(-87.0133 + 198.370i) q^{38} +(-23.0273 + 25.0143i) q^{39} +(-527.524 - 807.435i) q^{40} +(-267.473 + 290.553i) q^{41} +(-16.5547 + 12.8851i) q^{42} +(-123.794 - 20.6576i) q^{43} +(-623.507 - 337.425i) q^{44} +(-159.172 - 362.875i) q^{45} +(649.821 - 223.084i) q^{46} +(138.500 + 150.451i) q^{47} +(61.3542 - 242.282i) q^{48} +(296.130 - 160.258i) q^{49} +(-711.153 + 118.670i) q^{50} +(26.5910 - 28.8856i) q^{51} +(101.106 - 399.258i) q^{52} +(-56.5392 + 128.896i) q^{53} +(172.887 - 394.142i) q^{54} +(-468.193 + 364.409i) q^{55} +(59.9239 - 136.613i) q^{56} +(-5.46763 + 65.9845i) q^{57} +(-987.271 - 534.285i) q^{58} +(-558.054 + 93.1227i) q^{59} +(-396.307 - 308.458i) q^{60} +(538.291 + 584.740i) q^{61} +(184.408 + 728.210i) q^{62} +(33.5214 - 51.3084i) q^{63} +(131.944 + 521.034i) q^{64} +(-271.993 - 211.700i) q^{65} +(-302.014 - 50.3973i) q^{66} +(141.454 + 153.660i) q^{67} +(-116.753 + 461.049i) q^{68} +(165.722 - 128.987i) q^{69} +(-144.035 - 156.463i) q^{70} +(610.415 + 934.310i) q^{71} +(120.087 + 1449.24i) q^{72} +(-247.751 - 192.833i) q^{73} +(776.295 - 604.215i) q^{74} +(-193.816 + 104.888i) q^{75} +(-322.183 - 734.503i) q^{76} +(-86.7931 - 29.7961i) q^{77} +(-14.6891 - 177.271i) q^{78} +(49.9859 - 197.390i) q^{79} +(2499.10 + 417.026i) q^{80} +(-43.6349 + 526.594i) q^{81} +(-170.621 - 2059.09i) q^{82} +(-797.315 + 133.048i) q^{83} +(6.41440 - 77.4103i) q^{84} +(314.087 + 244.464i) q^{85} +(518.165 - 403.304i) q^{86} +(-338.446 - 56.4766i) q^{87} +(2059.37 - 706.982i) q^{88} +658.346 q^{89} +(1960.77 + 673.134i) q^{90} +(4.40232 - 53.1281i) q^{91} +(-1021.88 + 2329.65i) q^{92} +(125.585 + 192.223i) q^{93} -1069.87 q^{94} -671.209 q^{95} +(298.884 + 457.476i) q^{96} +(-483.957 + 376.679i) q^{97} +(-432.450 + 1707.71i) q^{98} +(882.340 - 147.237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1026 q - 15 q^{2} - 21 q^{3} - 257 q^{4} + 57 q^{5} + 3 q^{6} + 7 q^{7} + 23 q^{8} - 470 q^{9}+O(q^{10}) \) 1026 * q - 15 * q^2 - 21 * q^3 - 257 * q^4 + 57 * q^5 + 3 * q^6 + 7 * q^7 + 23 * q^8 - 470 * q^9	\( 1026 q - 15 q^{2} - 21 q^{3} - 257 q^{4} + 57 q^{5} + 3 q^{6} + 7 q^{7} + 23 q^{8} - 470 q^{9} + 55 q^{10} - 53 q^{11} + 13 q^{12} - 791 q^{13} - 73 q^{14} - 59 q^{15} - 21 q^{16} - 49 q^{17} - 1952 q^{18} + 23 q^{19} - 3 q^{20} - 71 q^{21} - q^{22} - 961 q^{23} + 55 q^{24} - 2184 q^{25} - 1211 q^{26} - 63 q^{27} - 255 q^{28} + 199 q^{29} - 4574 q^{30} + 447 q^{31} + 281 q^{32} - 1055 q^{33} + 151 q^{34} - 929 q^{35} - 1471 q^{36} - 99 q^{37} + 57 q^{38} + 861 q^{39} + 6909 q^{40} + 1223 q^{41} + 5705 q^{42} + 2731 q^{43} + 2514 q^{44} - 2035 q^{45} - 839 q^{46} + 227 q^{47} - 4335 q^{48} - 4532 q^{49} + 697 q^{50} + 861 q^{51} - 69 q^{52} + 233 q^{53} + 5334 q^{54} + 521 q^{55} + 13105 q^{56} + 2379 q^{57} + 1513 q^{58} - 3747 q^{59} + 1737 q^{60} + 251 q^{61} + 1477 q^{62} + 3439 q^{63} - 4281 q^{64} - 451 q^{65} + 5051 q^{66} + 919 q^{67} - 1779 q^{68} + 1895 q^{69} + 2029 q^{70} - 4731 q^{71} - 2849 q^{72} + 791 q^{73} - 2111 q^{74} - 14005 q^{75} - 541 q^{76} - 1987 q^{77} + 6837 q^{78} + 4501 q^{79} + 26178 q^{80} + 3716 q^{81} - 13749 q^{82} + 2585 q^{83} - 19881 q^{84} - 19 q^{85} + 1791 q^{86} - 3563 q^{87} + 2293 q^{88} - 1948 q^{89} - 24399 q^{90} - 13663 q^{91} - 4349 q^{92} - 8273 q^{93} + 14024 q^{94} - 6750 q^{95} + 28165 q^{96} + 4087 q^{97} + 9143 q^{98} - 3109 q^{99}+O(q^{100}) \) 1026 * q - 15 * q^2 - 21 * q^3 - 257 * q^4 + 57 * q^5 + 3 * q^6 + 7 * q^7 + 23 * q^8 - 470 * q^9 + 55 * q^10 - 53 * q^11 + 13 * q^12 - 791 * q^13 - 73 * q^14 - 59 * q^15 - 21 * q^16 - 49 * q^17 - 1952 * q^18 + 23 * q^19 - 3 * q^20 - 71 * q^21 - q^22 - 961 * q^23 + 55 * q^24 - 2184 * q^25 - 1211 * q^26 - 63 * q^27 - 255 * q^28 + 199 * q^29 - 4574 * q^30 + 447 * q^31 + 281 * q^32 - 1055 * q^33 + 151 * q^34 - 929 * q^35 - 1471 * q^36 - 99 * q^37 + 57 * q^38 + 861 * q^39 + 6909 * q^40 + 1223 * q^41 + 5705 * q^42 + 2731 * q^43 + 2514 * q^44 - 2035 * q^45 - 839 * q^46 + 227 * q^47 - 4335 * q^48 - 4532 * q^49 + 697 * q^50 + 861 * q^51 - 69 * q^52 + 233 * q^53 + 5334 * q^54 + 521 * q^55 + 13105 * q^56 + 2379 * q^57 + 1513 * q^58 - 3747 * q^59 + 1737 * q^60 + 251 * q^61 + 1477 * q^62 + 3439 * q^63 - 4281 * q^64 - 451 * q^65 + 5051 * q^66 + 919 * q^67 - 1779 * q^68 + 1895 * q^69 + 2029 * q^70 - 4731 * q^71 - 2849 * q^72 + 791 * q^73 - 2111 * q^74 - 14005 * q^75 - 541 * q^76 - 1987 * q^77 + 6837 * q^78 + 4501 * q^79 + 26178 * q^80 + 3716 * q^81 - 13749 * q^82 + 2585 * q^83 - 19881 * q^84 - 19 * q^85 + 1791 * q^86 - 3563 * q^87 + 2293 * q^88 - 1948 * q^89 - 24399 * q^90 - 13663 * q^91 - 4349 * q^92 - 8273 * q^93 + 14024 * q^94 - 6750 * q^95 + 28165 * q^96 + 4087 * q^97 + 9143 * q^98 - 3109 * q^99

Introduction

L-functions

Modular forms

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Database

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