LMFDB - Embedded newform 160.4.u.a.43.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,4,Mod(43,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 6]))

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

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

chi := DirichletCharacter("160.43");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	160.u (of order $8$, degree $4$, 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:	$9.44030560092$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$70$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			43.10
Character	$\chi$	$=$	160.43
Dual form			160.4.u.a.67.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.56149 + 1.19949i) q^{2} +(0.532873 - 1.28647i) q^{3} +(5.12247 - 6.14494i) q^{4} +(-11.0603 + 1.63392i) q^{5} +(0.178152 + 3.93445i) q^{6} +4.38872i q^{7} +(-5.75039 + 21.8845i) q^{8} +(17.7208 + 17.7208i) q^{9} +(26.3710 - 17.4519i) q^{10} +(6.98321 - 16.8590i) q^{11} +(-5.17565 - 9.86438i) q^{12} +(10.4110 - 25.1344i) q^{13} +(-5.26421 - 11.2417i) q^{14} +(-3.79175 + 15.0994i) q^{15} +(-11.5206 - 62.9546i) q^{16} +(-87.0870 - 87.0870i) q^{17} +(-66.6476 - 24.1359i) q^{18} +(37.5516 + 90.6575i) q^{19} +(-46.6157 + 76.3346i) q^{20} +(5.64596 + 2.33863i) q^{21} +(2.33465 + 51.5604i) q^{22} -194.901i q^{23} +(25.0896 + 19.0594i) q^{24} +(119.661 - 36.1433i) q^{25} +(3.48065 + 76.8695i) q^{26} +(66.9749 - 27.7419i) q^{27} +(26.9684 + 22.4811i) q^{28} +(-53.8252 - 129.945i) q^{29} +(-8.39900 - 43.2252i) q^{30} -299.439i q^{31} +(105.023 + 147.439i) q^{32} +(-17.9674 - 17.9674i) q^{33} +(327.532 + 118.613i) q^{34} +(-7.17082 - 48.5406i) q^{35} +(199.668 - 18.1191i) q^{36} +(51.1973 + 123.601i) q^{37} +(-204.930 - 187.176i) q^{38} +(-26.7869 - 26.7869i) q^{39} +(27.8435 - 251.445i) q^{40} +(276.236 - 276.236i) q^{41} +(-17.2672 + 0.781859i) q^{42} +(-18.7517 + 7.76720i) q^{43} +(-67.8261 - 129.271i) q^{44} +(-224.952 - 167.043i) q^{45} +(233.781 + 499.237i) q^{46} +(-138.163 + 138.163i) q^{47} +(-87.1281 - 18.7259i) q^{48} +323.739 q^{49} +(-263.156 + 236.112i) q^{50} +(-158.441 + 65.6284i) q^{51} +(-101.119 - 192.725i) q^{52} +(-136.689 - 329.995i) q^{53} +(-138.280 + 151.396i) q^{54} +(-49.6902 + 197.875i) q^{55} +(-96.0452 - 25.2369i) q^{56} +136.638 q^{57} +(293.740 + 268.291i) q^{58} +(-324.305 + 782.941i) q^{59} +(73.3619 + 100.646i) q^{60} +(573.445 - 237.529i) q^{61} +(359.172 + 767.009i) q^{62} +(-77.7718 + 77.7718i) q^{63} +(-445.866 - 251.689i) q^{64} +(-74.0814 + 295.005i) q^{65} +(67.5749 + 24.4717i) q^{66} +(-753.754 - 312.215i) q^{67} +(-981.245 + 89.0440i) q^{68} +(-250.734 - 103.858i) q^{69} +(76.5917 + 115.735i) q^{70} +(-282.902 + 282.902i) q^{71} +(-489.714 + 285.911i) q^{72} -488.899 q^{73} +(-279.399 - 255.193i) q^{74} +(17.2667 - 173.200i) q^{75} +(749.442 + 233.638i) q^{76} +(73.9893 + 30.6474i) q^{77} +(100.745 + 36.4839i) q^{78} -358.166i q^{79} +(230.284 + 677.473i) q^{80} +575.704i q^{81} +(-376.235 + 1038.92i) q^{82} +(58.6897 + 24.3101i) q^{83} +(43.2920 - 22.7145i) q^{84} +(1105.50 + 820.915i) q^{85} +(38.7156 - 42.3880i) q^{86} -195.853 q^{87} +(328.795 + 249.770i) q^{88} +(627.946 - 627.946i) q^{89} +(776.579 + 158.053i) q^{90} +(110.308 + 45.6911i) q^{91} +(-1197.66 - 998.375i) q^{92} +(-385.219 - 159.563i) q^{93} +(188.178 - 519.626i) q^{94} +(-563.459 - 941.343i) q^{95} +(245.639 - 56.5428i) q^{96} +(747.095 - 747.095i) q^{97} +(-829.255 + 388.320i) q^{98} +(422.503 - 175.007i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} + 80 q^{8} + 8 q^{10} - 8 q^{11} + 44 q^{12} - 4 q^{13} + 64 q^{14} - 8 q^{15} - 8 q^{16} + 28 q^{18} - 48 q^{19} - 312 q^{20} - 8 q^{21} - 436 q^{22} + 736 q^{24}+ \cdots + 3480 q^{98}+O(q^{100}) $ 280 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 + 80 * q^8 + 8 * q^10 - 8 * q^11 + 44 * q^12 - 4 * q^13 + 64 * q^14 - 8 * q^15 - 8 * q^16 + 28 * q^18 - 48 * q^19 - 312 * q^20 - 8 * q^21 - 436 * q^22 + 736 * q^24 - 4 * q^25 - 8 * q^26 - 112 * q^27 + 252 * q^28 - 1696 * q^30 - 344 * q^32 - 8 * q^33 + 696 * q^34 + 952 * q^35 - 8 * q^36 - 4 * q^37 - 172 * q^38 + 816 * q^40 - 8 * q^41 - 460 * q^42 + 860 * q^43 + 1232 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 + 3496 * q^48 - 11368 * q^49 - 36 * q^50 + 1480 * q^51 - 328 * q^52 - 4 * q^53 + 2968 * q^54 - 292 * q^55 - 344 * q^56 - 8 * q^57 - 2020 * q^58 + 252 * q^60 + 1816 * q^61 - 440 * q^62 + 2744 * q^63 + 816 * q^64 - 8 * q^65 + 552 * q^66 + 1844 * q^67 + 1224 * q^68 + 216 * q^69 + 1764 * q^70 - 232 * q^71 - 3432 * q^72 - 8 * q^73 + 104 * q^75 + 824 * q^76 + 1368 * q^77 - 5968 * q^78 - 1800 * q^80 + 588 * q^82 + 2676 * q^83 + 2744 * q^84 - 4 * q^85 - 1192 * q^86 + 2568 * q^87 - 5880 * q^88 - 84 * q^90 - 8 * q^91 - 3284 * q^92 + 104 * q^93 + 416 * q^94 + 6168 * q^96 - 8 * q^97 + 3480 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

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

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

$2$	−2.56149	+	1.19949i	−0.905624	+	0.424082i
$2$	−2.56149	+	1.19949i	−0.905624	+	0.424082i
$3$	0.532873	−	1.28647i	0.102551	−	0.247581i	−0.864273	−	0.503023i	$-0.832221\pi$
$3$	0.532873	−	1.28647i	0.102551	−	0.247581i	0.966824	+	0.255442i	$0.0822210\pi$
$4$	5.12247	−	6.14494i	0.640309	−	0.768118i
$5$	−11.0603	+	1.63392i	−0.989264	+	0.146142i
$5$	−11.0603	+	1.63392i	−0.989264	+	0.146142i
$6$	0.178152	+	3.93445i	0.0121217	+	0.267706i
$7$			4.38872i			0.236969i	0.992956	+	0.118484i	$0.0378035\pi$
$7$			4.38872i			0.236969i	−0.992956	+	0.118484i	$0.962196\pi$
$8$	−5.75039	+	21.8845i	−0.254134	+	0.967169i
$9$	17.7208	+	17.7208i	0.656327	+	0.656327i
$10$	26.3710	−	17.4519i	0.833924	−	0.551879i
$11$	6.98321	−	16.8590i	0.191411	−	0.462106i	−0.798816	−	0.601576i	$-0.794540\pi$
$11$	6.98321	−	16.8590i	0.191411	−	0.462106i	0.990226	+	0.139470i	$0.0445397\pi$
$12$	−5.17565	−	9.86438i	−0.124507	−	0.237300i
$13$	10.4110	−	25.1344i	0.222115	−	0.536234i	−0.773062	−	0.634331i	$-0.781276\pi$
$13$	10.4110	−	25.1344i	0.222115	−	0.536234i	0.995177	+	0.0980973i	$0.0312756\pi$
$14$	−5.26421	−	11.2417i	−0.100494	−	0.214605i
$15$	−3.79175	+	15.0994i	−0.0652684	+	0.259910i
$16$	−11.5206	−	62.9546i	−0.180010	−	0.983665i
$17$	−87.0870	−	87.0870i	−1.24245	−	1.24245i	−0.958980	−	0.283472i	$-0.908514\pi$
$17$	−87.0870	−	87.0870i	−1.24245	−	1.24245i	−0.283472	−	0.958980i	$-0.591486\pi$
$18$	−66.6476	−	24.1359i	−0.872722	−	0.316049i
$19$	37.5516	+	90.6575i	0.453417	+	1.09464i	0.971014	+	0.239021i	$0.0768264\pi$
$19$	37.5516	+	90.6575i	0.453417	+	1.09464i	−0.517598	+	0.855624i	$0.673174\pi$
$20$	−46.6157	+	76.3346i	−0.521180	+	0.853447i
$21$	5.64596	+	2.33863i	0.0586690	+	0.0243015i
$22$	2.33465	+	51.5604i	0.0226250	+	0.499668i
$23$		−	194.901i		−	1.76694i	−0.468485	−	0.883471i	$-0.655200\pi$
$23$		−	194.901i		−	1.76694i	0.468485	−	0.883471i	$-0.344800\pi$
$24$	25.0896	+	19.0594i	0.213391	+	0.162103i
$25$	119.661	−	36.1433i	0.957285	−	0.289146i
$26$	3.48065	+	76.8695i	0.0262543	+	0.579821i
$27$	66.9749	−	27.7419i	0.477383	−	0.197738i
$28$	26.9684	+	22.4811i	0.182020	+	0.151733i
$29$	−53.8252	−	129.945i	−0.344658	−	0.832078i	−0.997232	−	0.0743529i	$-0.976311\pi$
$29$	−53.8252	−	129.945i	−0.344658	−	0.832078i	0.652574	−	0.757725i	$-0.273689\pi$
$30$	−8.39900	−	43.2252i	−0.0511147	−	0.263060i
$31$		−	299.439i		−	1.73486i	−0.497556	−	0.867432i	$-0.665769\pi$
$31$		−	299.439i		−	1.73486i	0.497556	−	0.867432i	$-0.334231\pi$
$32$	105.023	+	147.439i	0.580176	+	0.814491i
$33$	−17.9674	−	17.9674i	−0.0947794	−	0.0947794i
$34$	327.532	+	118.613i	1.65210	+	0.598293i
$35$	−7.17082	−	48.5406i	−0.0346311	−	0.234425i
$36$	199.668	−	18.1191i	0.924388	−	0.0838845i
$37$	51.1973	+	123.601i	0.227480	+	0.549186i	0.995869	−	0.0907967i	$-0.0289413\pi$
$37$	51.1973	+	123.601i	0.227480	+	0.549186i	−0.768389	+	0.639983i	$0.778941\pi$
$38$	−204.930	−	187.176i	−0.874844	−	0.799050i
$39$	−26.7869	−	26.7869i	−0.109983	−	0.109983i
$40$	27.8435	−	251.445i	0.110061	−	0.993925i
$41$	276.236	−	276.236i	1.05222	−	1.05222i	0.0536571	−	0.998559i	$-0.482912\pi$
$41$	276.236	−	276.236i	1.05222	−	1.05222i	0.998559	−	0.0536571i	$-0.0170878\pi$
$42$	−17.2672	+	0.781859i	−0.0634379	+	0.00287246i
$43$	−18.7517	+	7.76720i	−0.0665025	+	0.0275462i	−0.415687	−	0.909508i	$-0.636459\pi$
$43$	−18.7517	+	7.76720i	−0.0665025	+	0.0275462i	0.349184	+	0.937054i	$0.386459\pi$
$44$	−67.8261	−	129.271i	−0.232390	−	0.442917i
$45$	−224.952	−	167.043i	−0.745198	−	0.553363i
$46$	233.781	+	499.237i	0.749329	+	1.60019i
$47$	−138.163	+	138.163i	−0.428789	+	0.428789i	−0.888216	−	0.459427i	$-0.848055\pi$
$47$	−138.163	+	138.163i	−0.428789	+	0.428789i	0.459427	+	0.888216i	$0.348055\pi$
$48$	−87.1281	−	18.7259i	−0.261997	−	0.0563093i
$49$	323.739			0.943846
$50$	−263.156	+	236.112i	−0.744318	+	0.667825i
$51$	−158.441	+	65.6284i	−0.435023	+	0.180193i
$52$	−101.119	−	192.725i	−0.269668	−	0.513966i
$53$	−136.689	−	329.995i	−0.354257	−	0.855252i	−0.996085	−	0.0884030i	$-0.971824\pi$
$53$	−136.689	−	329.995i	−0.354257	−	0.855252i	0.641828	−	0.766849i	$-0.278176\pi$
$54$	−138.280	+	151.396i	−0.348472	+	0.381526i
$55$	−49.6902	+	197.875i	−0.121822	+	0.485118i
$56$	−96.0452	−	25.2369i	−0.229189	−	0.0602218i
$57$	136.638			0.317512
$58$	293.740	+	268.291i	0.665000	+	0.607386i
$59$	−324.305	+	782.941i	−0.715609	+	1.72763i	−0.0301226	+	0.999546i	$0.509590\pi$
$59$	−324.305	+	782.941i	−0.715609	+	1.72763i	−0.685486	+	0.728086i	$0.740410\pi$
$60$	73.3619	+	100.646i	0.157850	+	0.216557i
$61$	573.445	−	237.529i	1.20364	−	0.498564i	0.311467	−	0.950257i	$-0.399180\pi$
$61$	573.445	−	237.529i	1.20364	−	0.498564i	0.892174	+	0.451693i	$0.149180\pi$
$62$	359.172	+	767.009i	0.735725	+	1.57113i
$63$	−77.7718	+	77.7718i	−0.155529	+	0.155529i
$64$	−445.866	−	251.689i	−0.870832	−	0.491581i
$65$	−74.0814	+	295.005i	−0.141364	+	0.562937i
$66$	67.5749	+	24.4717i	0.126029	+	0.0456402i
$67$	−753.754	−	312.215i	−1.37441	−	0.569301i	−0.431432	−	0.902146i	$-0.641991\pi$
$67$	−753.754	−	312.215i	−1.37441	−	0.569301i	−0.942982	+	0.332845i	$0.891991\pi$
$68$	−981.245	+	89.0440i	−1.74990	+	0.158797i
$69$	−250.734	−	103.858i	−0.437462	−	0.181203i
$70$	76.5917	+	115.735i	0.130778	+	0.197614i
$71$	−282.902	+	282.902i	−0.472877	+	0.472877i	−0.902844	−	0.429968i	$-0.858525\pi$
$71$	−282.902	+	282.902i	−0.472877	+	0.472877i	0.429968	+	0.902844i	$0.358525\pi$
$72$	−489.714	+	285.911i	−0.801574	+	0.467984i
$73$	−488.899			−0.783853			−0.391927	−	0.919996i	$-0.628191\pi$
$73$	−488.899			−0.783853			−0.391927	+	0.919996i	$0.628191\pi$
$74$	−279.399	−	255.193i	−0.438912	−	0.400886i
$75$	17.2667	−	173.200i	0.0265838	−	0.266658i
$76$	749.442	+	233.638i	1.13114	+	0.352633i
$77$	73.9893	+	30.6474i	0.109505	+	0.0453584i
$78$	100.745	+	36.4839i	0.146245	+	0.0529614i
$79$		−	358.166i		−	0.510086i	−0.966930	−	0.255043i	$-0.917910\pi$
$79$		−	358.166i		−	0.510086i	0.966930	−	0.255043i	$-0.0820897\pi$
$80$	230.284	+	677.473i	0.321832	+	0.946797i
$81$			575.704i			0.789717i
$82$	−376.235	+	1038.92i	−0.506686	+	1.39914i
$83$	58.6897	+	24.3101i	0.0776148	+	0.0321491i	0.421153	−	0.906990i	$-0.361626\pi$
$83$	58.6897	+	24.3101i	0.0776148	+	0.0321491i	−0.343538	+	0.939139i	$0.611626\pi$
$84$	43.2920	−	22.7145i	0.0562327	−	0.0295042i
$85$	1105.50	+	820.915i	1.41069	+	1.04754i
$86$	38.7156	−	42.3880i	0.0485443	−	0.0531490i
$87$	−195.853			−0.241352
$88$	328.795	+	249.770i	0.398291	+	0.302563i
$89$	627.946	−	627.946i	0.747889	−	0.747889i	−0.226193	−	0.974082i	$-0.572628\pi$
$89$	627.946	−	627.946i	0.747889	−	0.747889i	0.974082	+	0.226193i	$0.0726281\pi$
$90$	776.579	+	158.053i	0.909540	+	0.185114i
$91$	110.308	+	45.6911i	0.127071	+	0.0526344i
$92$	−1197.66	−	998.375i	−1.35722	−	1.13139i
$93$	−385.219	−	159.563i	−0.429520	−	0.177913i
$94$	188.178	−	519.626i	0.206480	−	0.570163i
$95$	−563.459	−	941.343i	−0.608523	−	1.01663i
$96$	245.639	−	56.5428i	0.261151	−	0.0601133i
$97$	747.095	−	747.095i	0.782021	−	0.782021i	−0.198150	−	0.980172i	$-0.563493\pi$
$97$	747.095	−	747.095i	0.782021	−	0.782021i	0.980172	+	0.198150i	$0.0634935\pi$
$98$	−829.255	+	388.320i	−0.854769	+	0.400268i
$99$	422.503	−	175.007i	0.428921	−	0.177665i
$100$	390.859	−	920.450i	0.390859	−	0.920450i
$101$	93.2268	−	225.069i	0.0918457	−	0.221735i	−0.871280	−	0.490786i	$-0.836710\pi$
$101$	93.2268	−	225.069i	0.0918457	−	0.221735i	0.963126	+	0.269051i	$0.0867099\pi$
$102$	327.125	−	358.154i	0.317551	−	0.347672i
$103$	−859.746			−0.822459			−0.411230	−	0.911532i	$-0.634901\pi$
$103$	−859.746			−0.822459			−0.411230	+	0.911532i	$0.634901\pi$
$104$	490.188	+	372.373i	0.462182	+	0.351098i
$105$	−66.2671	−	16.6409i	−0.0615906	−	0.0154666i
$106$	745.951	+	681.324i	0.683520	+	0.624302i
$107$	536.672	+	1295.64i	0.484879	+	1.17060i	0.957266	+	0.289209i	$0.0933923\pi$
$107$	536.672	+	1295.64i	0.484879	+	1.17060i	−0.472387	+	0.881391i	$0.656608\pi$
$108$	172.605	−	553.664i	0.153786	−	0.493300i
$109$	−700.242	+	290.050i	−0.615330	+	0.254878i	−0.668506	−	0.743707i	$-0.733066\pi$
$109$	−700.242	+	290.050i	−0.615330	+	0.254878i	0.0531754	+	0.998585i	$0.483066\pi$
$110$	−110.067	−	566.459i	−0.0954047	−	0.490997i
$111$	186.291			0.159297
$112$	276.290	−	50.5608i	0.233098	−	0.0426566i
$113$	658.201	−	658.201i	0.547950	−	0.547950i	−0.377897	−	0.925848i	$-0.623353\pi$
$113$	658.201	−	658.201i	0.547950	−	0.547950i	0.925848	+	0.377897i	$0.123353\pi$
$114$	−349.998	+	163.896i	−0.287546	+	0.134651i
$115$	318.453	+	2155.67i	0.258225	+	1.74797i
$116$	−1074.22	−	334.889i	−0.859821	−	0.268049i
$117$	629.895	−	260.911i	0.497725	−	0.206164i
$118$	−108.423	−	2394.50i	−0.0845857	−	1.86806i
$119$	382.201	−	382.201i	0.294422	−	0.294422i
$120$	−308.640	−	169.808i	−0.234790	−	0.129177i
$121$	705.700	+	705.700i	0.530203	+	0.530203i
$122$	−1183.96	+	1296.27i	−0.878613	+	0.961954i
$123$	−208.171	−	502.569i	−0.152603	−	0.368415i
$124$	−1840.03	−	1533.87i	−1.33258	−	1.11085i
$125$	−1264.43	+	595.272i	−0.904751	+	0.425942i
$126$	105.926	−	292.498i	0.0748937	−	0.206808i
$127$	959.974	+	959.974i	0.670739	+	0.670739i	0.957886	−	0.287147i	$-0.0927069\pi$
$127$	959.974	+	959.974i	0.670739	+	0.670739i	−0.287147	+	0.957886i	$0.592707\pi$
$128$	1443.98	+	109.890i	0.997117	+	0.0758828i
$129$			28.2624i			0.0192897i
$130$	−164.096	−	844.513i	−0.110709	−	0.569759i
$131$	−685.015	−	1653.77i	−0.456870	−	1.10298i	−0.969658	−	0.244467i	$-0.921387\pi$
$131$	−685.015	−	1653.77i	−0.456870	−	1.10298i	0.512787	−	0.858516i	$-0.328613\pi$
$132$	−202.446	+	18.3711i	−0.133490	+	0.0121137i
$133$	−397.870	+	164.803i	−0.259397	+	0.107446i
$134$	2305.23	−	104.381i	1.48613	−	0.0672920i
$135$	−695.435	+	416.266i	−0.443359	+	0.265381i
$136$	2406.64	−	1405.07i	1.51741	−	0.885913i
$137$			698.957i			0.435883i	0.975962	+	0.217941i	$0.0699341\pi$
$137$			698.957i			0.435883i	−0.975962	+	0.217941i	$0.930066\pi$
$138$	766.829	−	34.7220i	0.473021	−	0.0214183i
$139$	−690.919	−	286.188i	−0.421604	−	0.174634i	0.161787	−	0.986826i	$-0.448274\pi$
$139$	−690.919	−	286.188i	−0.421604	−	0.174634i	−0.583391	+	0.812192i	$0.698274\pi$
$140$	−335.011	−	204.583i	−0.202240	−	0.123503i
$141$	104.119	+	251.365i	0.0621871	+	0.150133i
$142$	385.313	−	1063.99i	0.227710	−	0.628787i
$143$	−351.038	−	351.038i	−0.205282	−	0.205282i
$144$	911.452	−	1319.76i	0.527461	−	0.763751i
$145$	807.643	+	1349.29i	0.462559	+	0.772775i
$146$	1252.31	−	586.427i	0.709876	−	0.332418i
$147$	172.512	−	416.481i	0.0967928	−	0.233678i
$148$	1021.78	+	318.539i	0.567498	+	0.176917i
$149$	−197.771	+	477.461i	−0.108738	+	0.262518i	−0.968877	−	0.247543i	$-0.920377\pi$
$149$	−197.771	+	477.461i	−0.108738	+	0.262518i	0.860139	+	0.510060i	$0.170377\pi$
$150$	163.522	+	464.360i	0.0890101	+	0.252766i
$151$	177.952	+	177.952i	0.0959039	+	0.0959039i	0.753431	−	0.657527i	$-0.228397\pi$
$151$	177.952	+	177.952i	0.0959039	+	0.0959039i	−0.657527	+	0.753431i	$0.728397\pi$
$152$	−2199.93	+	300.483i	−1.17394	+	0.160344i
$153$		−	3086.51i		−	1.63091i
$154$	−226.284	+	10.2461i	−0.118406	+	0.00536141i
$155$	489.259	+	3311.88i	0.253537	+	1.71624i
$156$	−301.819	+	27.3889i	−0.154903	+	0.0140568i
$157$	1042.15	−	2515.97i	0.529762	−	1.27896i	−0.401917	−	0.915676i	$-0.631656\pi$
$157$	1042.15	−	2515.97i	0.529762	−	1.27896i	0.931679	−	0.363283i	$-0.118344\pi$
$158$	429.615	+	917.439i	0.216319	+	0.461946i
$159$	−497.367			−0.248074
$160$	−1402.49	−	1459.12i	−0.692978	−	0.720959i
$161$	855.367			0.418710
$162$	−690.549	−	1474.66i	−0.334905	−	0.715187i
$163$	−53.3116	+	128.706i	−0.0256177	+	0.0618466i	−0.936171	−	0.351546i	$-0.885656\pi$
$163$	−53.3116	+	128.706i	−0.0256177	+	0.0618466i	0.910553	+	0.413392i	$0.135656\pi$
$164$	−282.444	−	3112.47i	−0.134483	−	1.48197i
$165$	228.082	+	169.367i	0.107613	+	0.0799105i
$166$	−179.493	+	8.12742i	−0.0839237	+	0.00380006i
$167$		−	203.594i		−	0.0943389i	−0.998887	−	0.0471695i	$-0.984980\pi$
$167$		−	203.594i		−	0.0943389i	0.998887	−	0.0471695i	$-0.0150201\pi$
$168$	−83.6463	+	110.111i	−0.0384134	+	0.0505670i
$169$	1030.16	+	1030.16i	0.468895	+	0.468895i
$170$	−3816.41	−	776.734i	−1.72180	−	0.350428i
$171$	−941.081	+	2271.97i	−0.420855	+	1.01603i
$172$	−48.3259	+	155.015i	−0.0214234	+	0.0687198i
$173$	−944.292	+	2279.72i	−0.414990	+	1.00187i	0.568788	+	0.822484i	$0.307412\pi$
$173$	−944.292	+	2279.72i	−0.414990	+	1.00187i	−0.983778	+	0.179390i	$0.942588\pi$
$174$	501.675	−	234.923i	0.218574	−	0.102353i
$175$	158.623	+	525.157i	0.0685187	+	0.226847i
$176$	−1141.80	−	245.399i	−0.489014	−	0.105100i
$177$	834.417	+	834.417i	0.354342	+	0.354342i
$178$	−855.266	+	2361.69i	−0.360140	+	0.994473i
$179$	134.345	+	324.337i	0.0560973	+	0.135431i	0.949443	−	0.313939i	$-0.101649\pi$
$179$	134.345	+	324.337i	0.0560973	+	0.135431i	−0.893346	+	0.449370i	$0.851649\pi$
$180$	−2178.78	+	526.644i	−0.902205	+	0.218076i
$181$	−1693.34	−	701.403i	−0.695386	−	0.288038i	0.00685640	−	0.999976i	$-0.497818\pi$
$181$	−1693.34	−	701.403i	−0.695386	−	0.288038i	−0.702242	+	0.711938i	$0.747818\pi$
$182$	−337.359	+	15.2756i	−0.137399	+	0.00622144i
$183$		−	864.292i		−	0.349127i
$184$	4265.32	+	1120.76i	1.70893	+	0.449040i
$185$	−768.212	−	1283.41i	−0.305298	−	0.510046i
$186$	1178.13	−	53.3456i	0.464433	−	0.0210295i
$187$	−2076.34	+	860.050i	−0.811964	+	0.336327i
$188$	141.267	+	1556.73i	0.0548031	+	0.603918i
$189$	121.752	+	293.934i	0.0468578	+	0.113125i
$190$	2572.42	+	1735.38i	0.982227	+	0.662620i
$191$			689.819i			0.261327i	0.991427	+	0.130664i	$0.0417108\pi$
$191$			689.819i			0.261327i	−0.991427	+	0.130664i	$0.958289\pi$
$192$	−561.381	+	439.475i	−0.211011	+	0.165189i
$193$	1080.44	+	1080.44i	0.402963	+	0.402963i	0.879276	−	0.476313i	$-0.158027\pi$
$193$	1080.44	+	1080.44i	0.402963	+	0.402963i	−0.476313	+	0.879276i	$0.658027\pi$
$194$	−1017.55	+	2809.81i	−0.376576	+	1.03986i
$195$	340.039	+	252.504i	0.124875	+	0.0927291i
$196$	1658.34	−	1989.36i	0.604353	−	0.724985i
$197$	−870.009	−	2100.39i	−0.314647	−	0.759626i	−0.999521	−	0.0309637i	$-0.990142\pi$
$197$	−870.009	−	2100.39i	−0.314647	−	0.759626i	0.684873	−	0.728662i	$-0.259858\pi$
$198$	−872.320	+	955.064i	−0.313097	+	0.342795i
$199$	−3536.09	−	3536.09i	−1.25963	−	1.25963i	−0.951269	−	0.308363i	$-0.900219\pi$
$199$	−3536.09	−	3536.09i	−1.25963	−	1.25963i	−0.308363	−	0.951269i	$-0.599781\pi$
$200$	102.884	+	2826.56i	0.0363751	+	0.999338i
$201$	−803.310	+	803.310i	−0.281896	+	0.281896i
$202$	31.1679	+	688.337i	0.0108563	+	0.239759i
$203$	570.294	−	236.224i	0.197176	−	0.0816732i
$204$	−408.327	+	1309.79i	−0.140140	+	0.449528i
$205$	−2603.91	+	3506.61i	−0.887146	+	1.19469i
$206$	2202.23	−	1031.25i	0.744838	−	0.348790i
$207$	3453.81	−	3453.81i	1.15969	−	1.15969i
$208$	−1702.27	−	365.857i	−0.567457	−	0.121960i
$209$	1790.62			0.592631
$210$	189.703	−	36.8609i	0.0623370	−	0.0121126i
$211$	−107.274	+	44.4344i	−0.0350003	+	0.0144976i	−0.400115	−	0.916465i	$-0.631030\pi$
$211$	−107.274	+	44.4344i	−0.0350003	+	0.0144976i	0.365115	+	0.930963i	$0.381030\pi$
$212$	−2727.98	−	850.448i	−0.883768	−	0.275514i
$213$	213.194	+	514.695i	0.0685811	+	0.165570i
$214$	−2928.78	−	2675.04i	−0.935548	−	0.854495i
$215$	194.708	−	116.546i	0.0617628	−	0.0369693i
$216$	221.987	+	1625.24i	0.0699274	+	0.511962i
$217$	1314.15			0.411108
$218$	1445.75	−	1582.89i	0.449168	−	0.491774i
$219$	−260.521	+	628.954i	−0.0803853	+	0.194067i
$220$	961.395	+	1318.95i	0.294624	+	0.404199i
$221$	−3095.55	+	1282.22i	−0.942213	+	0.390277i
$222$	−477.182	+	223.453i	−0.144263	+	0.0675549i
$223$	2187.91	−	2187.91i	0.657010	−	0.657010i	−0.297661	−	0.954672i	$-0.596207\pi$
$223$	2187.91	−	2187.91i	0.657010	−	0.657010i	0.954672	+	0.297661i	$0.0962066\pi$
$224$	−647.067	+	460.917i	−0.193009	+	0.137483i
$225$	2760.98	+	1480.00i	0.818067	+	0.438517i
$226$	−896.474	+	2475.48i	−0.263861	+	0.728613i
$227$	4010.25	+	1661.10i	1.17255	+	0.485688i	0.882036	−	0.471182i	$-0.156172\pi$
$227$	4010.25	+	1661.10i	1.17255	+	0.485688i	0.290518	+	0.956870i	$0.406172\pi$
$228$	699.926	−	839.634i	0.203306	−	0.243887i
$229$	−84.3136	−	34.9238i	−0.0243301	−	0.0100779i	0.370485	−	0.928838i	$-0.379191\pi$
$229$	−84.3136	−	34.9238i	−0.0243301	−	0.0100779i	−0.394815	+	0.918761i	$0.629191\pi$
$230$	−3401.40	−	5139.74i	−0.975139	−	1.47350i
$231$	78.8539	−	78.8539i	0.0224598	−	0.0224598i
$232$	3153.31	−	430.702i	0.892349	−	0.121883i
$233$	−2349.23			−0.660528			−0.330264	−	0.943889i	$-0.607138\pi$
$233$	−2349.23			−0.660528			−0.330264	+	0.943889i	$0.607138\pi$
$234$	−1300.51	+	1423.87i	−0.363321	+	0.397784i
$235$	1302.37	−	1753.87i	0.361521	−	0.486849i
$236$	3149.89	+	6003.43i	0.868814	+	1.65589i
$237$	−460.770	−	190.857i	−0.126288	−	0.0523101i
$238$	−520.559	+	1437.45i	−0.141777	+	0.391495i
$239$			2812.35i			0.761154i	0.924749	+	0.380577i	$0.124275\pi$
$239$			2812.35i			0.761154i	−0.924749	+	0.380577i	$0.875725\pi$
$240$	994.260	+	64.7534i	0.267413	+	0.0174159i
$241$		−	5243.52i		−	1.40151i	−0.713400	−	0.700757i	$-0.752846\pi$
$241$		−	5243.52i		−	1.40151i	0.713400	−	0.700757i	$-0.247154\pi$
$242$	−2654.12	−	961.167i	−0.705013	−	0.255315i
$243$	2548.95	+	1055.81i	0.672902	+	0.278725i
$244$	1477.85	−	4740.52i	0.387745	−	1.24377i
$245$	−3580.65	+	528.964i	−0.933712	+	0.137936i
$246$	1136.05	+	1037.63i	0.294439	+	0.268930i
$247$	2669.57			0.687696
$248$	6553.08	+	1721.89i	1.67791	+	0.440887i
$249$	62.5483	−	62.5483i	0.0159190	−	0.0159190i
$250$	2524.80	−	3041.45i	0.638729	−	0.769432i
$251$	519.263	+	215.086i	0.130580	+	0.0540880i	0.447017	−	0.894526i	$-0.352486\pi$
$251$	519.263	+	215.086i	0.130580	+	0.0540880i	−0.316437	+	0.948614i	$0.602486\pi$
$252$	79.5195	+	876.287i	0.0198780	+	0.219051i
$253$	−3285.83	−	1361.04i	−0.816516	−	0.338212i
$254$	−3610.44	−	1307.49i	−0.891886	−	0.322989i
$255$	1645.17	−	984.751i	0.404019	−	0.241833i
$256$	−3830.55	+	1450.55i	−0.935193	+	0.354138i
$257$	811.327	−	811.327i	0.196923	−	0.196923i	−0.601757	−	0.798679i	$-0.705532\pi$
$257$	811.327	−	811.327i	0.196923	−	0.196923i	0.798679	+	0.601757i	$0.205532\pi$
$258$	−33.9003	−	72.3939i	−0.00818040	−	0.0174692i
$259$	−542.451	+	224.691i	−0.130140	+	0.0539058i
$260$	1433.31	+	1966.38i	0.341885	+	0.469038i
$261$	1348.91	−	3256.57i	0.319907	−	0.772324i
$262$	3738.33	+	3414.46i	0.881508	+	0.805137i
$263$	−4405.00			−1.03279			−0.516396	−	0.856350i	$-0.672727\pi$
$263$	−4405.00			−1.03279			−0.516396	+	0.856350i	$0.672727\pi$
$264$	496.527	−	289.888i	0.115754	−	0.0675811i
$265$	2051.00	+	3426.51i	0.475442	+	0.794297i
$266$	821.462	−	899.382i	0.189350	−	0.207311i
$267$	−473.218	−	1142.45i	−0.108466	−	0.261860i
$268$	−5779.63	+	3032.46i	−1.31734	+	0.691183i
$269$	−4183.57	+	1732.89i	−0.948241	+	0.392774i	−0.802569	−	0.596559i	$-0.796534\pi$
$269$	−4183.57	+	1732.89i	−0.948241	+	0.392774i	−0.145671	+	0.989333i	$0.546534\pi$
$270$	1282.05	−	1900.43i	0.288973	−	0.428356i
$271$	−2858.16			−0.640667			−0.320333	−	0.947305i	$-0.603795\pi$
$271$	−2858.16			−0.640667			−0.320333	+	0.947305i	$0.603795\pi$
$272$	−4479.23	+	6485.82i	−0.998504	+	1.44581i
$273$	117.560	−	117.560i	0.0260626	−	0.0260626i
$274$	−838.389	−	1790.37i	−0.184850	−	0.394746i
$275$	226.277	−	2269.75i	0.0496182	−	0.497713i
$276$	−1922.58	+	1008.74i	−0.419296	+	0.219997i
$277$	−2133.15	+	883.582i	−0.462703	+	0.191658i	−0.601842	−	0.798615i	$-0.705566\pi$
$277$	−2133.15	+	883.582i	−0.462703	+	0.191658i	0.139139	+	0.990273i	$0.455566\pi$
$278$	2113.06	−	95.6792i	0.455874	−	0.0206419i
$279$	5306.30	−	5306.30i	1.13864	−	1.13864i
$280$	1103.52	+	122.197i	0.235529	+	0.0260810i
$281$	−3977.03	−	3977.03i	−0.844305	−	0.844305i	0.145110	−	0.989416i	$-0.453646\pi$
$281$	−3977.03	−	3977.03i	−0.844305	−	0.844305i	−0.989416	+	0.145110i	$0.953646\pi$
$282$	−568.208	−	518.980i	−0.119987	−	0.109592i
$283$	2664.72	+	6433.20i	0.559721	+	1.35129i	0.909987	+	0.414636i	$0.136091\pi$
$283$	2664.72	+	6433.20i	0.559721	+	1.35129i	−0.350266	+	0.936650i	$0.613909\pi$
$284$	289.259	+	3187.57i	0.0604379	+	0.666012i
$285$	−1511.26	+	223.256i	−0.314103	+	0.0464019i
$286$	1320.25	+	478.116i	0.272964	+	0.0988517i
$287$	1212.32	+	1212.32i	0.249342	+	0.249342i
$288$	−751.641	+	4473.83i	−0.153788	+	0.915358i
$289$			10255.3i			2.08738i
$290$	−3687.22	−	2487.44i	−0.746625	−	0.503680i
$291$	−563.008	−	1359.22i	−0.113416	−	0.273811i
$292$	−2504.37	+	3004.26i	−0.501908	+	0.602092i
$293$	5022.19	−	2080.26i	1.00136	−	0.414778i	0.179066	−	0.983837i	$-0.442692\pi$
$293$	5022.19	−	2080.26i	1.00136	−	0.414778i	0.822297	+	0.569059i	$0.192692\pi$
$294$	57.6747	+	1273.74i	0.0114410	+	0.252673i
$295$	2307.65	−	9189.46i	0.455445	−	1.81366i
$296$	−2999.36	+	409.674i	−0.588967	+	0.0804453i
$297$		−	1322.86i		−	0.258451i
$298$	−66.1194	−	1460.24i	−0.0128530	−	0.283856i
$299$	−4898.73	−	2029.12i	−0.947494	−	0.392465i
$300$	−975.853	−	993.312i	−0.187803	−	0.191163i
$301$	−34.0881	−	82.2960i	−0.00652759	−	0.0157590i
$302$	−669.271	−	242.371i	−0.127524	−	0.0461817i
$303$	−239.867	−	239.867i	−0.0454785	−	0.0454785i
$304$	5274.68	−	3408.47i	0.995144	−	0.643057i
$305$	−5954.37	+	3564.10i	−1.11786	+	0.669114i
$306$	3702.22	+	7906.06i	0.691640	+	1.47699i
$307$	−657.943	+	1588.41i	−0.122315	+	0.295295i	−0.973163	−	0.230117i	$-0.926089\pi$
$307$	−657.943	+	1588.41i	−0.122315	+	0.295295i	0.850848	+	0.525412i	$0.176089\pi$
$308$	567.334	−	297.670i	0.104957	−	0.0550692i
$309$	−458.136	+	1106.04i	−0.0843444	+	0.203625i
$310$	−5225.79	−	7896.50i	−0.957435	−	1.44674i
$311$	−4402.87	−	4402.87i	−0.802778	−	0.802778i	0.180751	−	0.983529i	$-0.442147\pi$
$311$	−4402.87	−	4402.87i	−0.802778	−	0.802778i	−0.983529	+	0.180751i	$0.942147\pi$
$312$	740.255	−	432.184i	0.134323	−	0.0784218i
$313$		−	10630.6i		−	1.91974i	−0.280448	−	0.959869i	$-0.590483\pi$
$313$		−	10630.6i		−	1.91974i	0.280448	−	0.959869i	$-0.409517\pi$
$314$	348.415	+	7694.69i	0.0626185	+	1.38292i
$315$	733.107	−	987.253i	0.131130	−	0.176589i
$316$	−2200.91	−	1834.69i	−0.391806	−	0.326613i
$317$	270.066	−	651.998i	0.0478500	−	0.115520i	−0.898147	−	0.439695i	$-0.855087\pi$
$317$	270.066	−	651.998i	0.0478500	−	0.115520i	0.945997	+	0.324175i	$0.105087\pi$
$318$	1274.00	−	596.584i	0.224662	−	0.105204i
$319$	−2566.62			−0.450480
$320$	5342.65	+	2055.25i	0.933323	+	0.359037i
$321$	1952.78			0.339544
$322$	−2191.01	+	1026.00i	−0.379194	+	0.177568i
$323$	4624.83	−	11165.3i	0.796696	−	1.92339i
$324$	3537.67	+	2949.03i	0.606596	+	0.505663i
$325$	337.348	−	3383.89i	0.0575775	−	0.577552i
$326$	−17.8233	−	393.625i	−0.00302804	−	0.0668738i
$327$			1055.40i			0.178482i
$328$	4456.84	+	7633.77i	0.750268	+	1.28508i
$329$	−606.357	−	606.357i	−0.101610	−	0.101610i
$330$	−787.384	−	160.252i	−0.131346	−	0.0267321i
$331$	−1170.83	+	2826.63i	−0.194424	+	0.469382i	−0.990786	−	0.135439i	$-0.956755\pi$
$331$	−1170.83	+	2826.63i	−0.194424	+	0.469382i	0.796361	+	0.604821i	$0.206755\pi$
$332$	450.020	−	236.117i	0.0743917	−	0.0390320i
$333$	−1283.06	+	3097.57i	−0.211144	+	0.509748i
$334$	244.208	+	521.505i	0.0400075	+	0.0854356i
$335$	8846.88	+	2221.62i	1.44286	+	0.362329i
$336$	82.1827	−	382.381i	0.0133435	−	0.0620851i
$337$	−2095.81	−	2095.81i	−0.338771	−	0.338771i	0.517133	−	0.855905i	$-0.326999\pi$
$337$	−2095.81	−	2095.81i	−0.338771	−	0.338771i	−0.855905	+	0.517133i	$0.826999\pi$
$338$	−3874.42	−	1403.09i	−0.623493	−	0.225793i
$339$	−496.018	−	1197.49i	−0.0794691	−	0.191855i
$340$	10707.4	−	2588.13i	1.70791	−	0.412827i
$341$	−5048.23	−	2091.04i	−0.801692	−	0.332072i
$342$	−314.625	−	6948.45i	−0.0497456	−	1.09862i
$343$			2926.13i			0.460631i
$344$	−62.1521	−	455.036i	−0.00974133	−	0.0713195i
$345$	2942.89	+	739.016i	0.459246	+	0.115325i
$346$	−315.699	−	6972.15i	−0.0490522	−	1.08331i
$347$	5881.56	−	2436.22i	0.909909	−	0.376897i	0.121887	−	0.992544i	$-0.461105\pi$
$347$	5881.56	−	2436.22i	0.909909	−	0.376897i	0.788022	+	0.615647i	$0.211105\pi$
$348$	−1003.25	+	1203.50i	−0.154540	+	0.185387i
$349$	1022.77	+	2469.20i	0.156871	+	0.378719i	0.982701	−	0.185199i	$-0.0592931\pi$
$349$	1022.77	+	2469.20i	0.156871	+	0.378719i	−0.825830	+	0.563919i	$0.809293\pi$
$350$	−1036.23	−	1154.92i	−0.158254	−	0.176380i
$351$		−	1972.20i		−	0.299909i
$352$	3219.06	−	740.984i	0.487434	−	0.112200i
$353$	−2600.94	−	2600.94i	−0.392164	−	0.392164i	0.483294	−	0.875458i	$-0.339440\pi$
$353$	−2600.94	−	2600.94i	−0.392164	−	0.392164i	−0.875458	+	0.483294i	$0.839440\pi$
$354$	−3138.22	−	1136.48i	−0.471171	−	0.170631i
$355$	2666.74	−	3591.22i	0.398692	−	0.536907i
$356$	−642.057	−	7075.33i	−0.0955870	−	1.05335i
$357$	−288.025	−	695.354i	−0.0427000	−	0.103087i
$358$	−733.161	−	669.642i	−0.108237	−	0.0988595i
$359$	380.108	+	380.108i	0.0558812	+	0.0558812i	0.734495	−	0.678614i	$-0.237419\pi$
$359$	380.108	+	380.108i	0.0558812	+	0.0558812i	−0.678614	+	0.734495i	$0.737419\pi$
$360$	4949.23	−	3962.41i	0.724576	−	0.580104i
$361$	−1958.61	+	1958.61i	−0.285554	+	0.285554i
$362$	5178.79	−	234.495i	0.751909	−	0.0340464i
$363$	1283.91	−	531.813i	0.185641	−	0.0768951i
$364$	845.819	−	443.785i	0.121794	−	0.0639029i
$365$	5407.37	−	798.822i	0.775438	−	0.114554i
$366$	1036.71	+	2213.88i	0.148059	+	0.316178i
$367$	1761.24	−	1761.24i	0.250507	−	0.250507i	−0.570672	−	0.821178i	$-0.693317\pi$
$367$	1761.24	−	1761.24i	0.250507	−	0.250507i	0.821178	+	0.570672i	$0.193317\pi$
$368$	−12269.9	+	2245.38i	−1.73808	+	0.318067i
$369$	9790.28			1.38120
$370$	3507.20	+	2365.99i	0.492786	+	0.332438i
$371$	1448.26	−	599.888i	0.202668	−	0.0839478i
$372$	−2953.78	+	1549.79i	−0.411683	+	0.216002i
$373$	3327.94	+	8034.36i	0.461969	+	1.11529i	0.967588	+	0.252534i	$0.0812641\pi$
$373$	3327.94	+	8034.36i	0.461969	+	1.11529i	−0.505619	+	0.862757i	$0.668736\pi$
$374$	4286.92	−	4693.55i	0.592704	−	0.648925i
$375$	92.0197	+	1943.85i	0.0126717	+	0.267680i
$376$	−2229.13	−	3818.11i	−0.305742	−	0.523681i
$377$	−3826.48			−0.522742
$378$	−664.436	−	606.871i	−0.0904098	−	0.0825769i
$379$	−1500.77	+	3623.17i	−0.203402	+	0.491055i	−0.992358	−	0.123395i	$-0.960622\pi$
$379$	−1500.77	+	3623.17i	−0.203402	+	0.491055i	0.788956	+	0.614450i	$0.210622\pi$
$380$	−8670.80	−	1359.58i	−1.17053	−	0.183539i
$381$	1746.52	−	723.433i	0.234848	−	0.0972771i
$382$	−827.427	−	1766.96i	−0.110824	−	0.236664i
$383$	2216.63	−	2216.63i	0.295730	−	0.295730i	−0.543609	−	0.839339i	$-0.682942\pi$
$383$	2216.63	−	2216.63i	0.295730	−	0.295730i	0.839339	+	0.543609i	$0.182942\pi$
$384$	910.828	−	1799.08i	0.121043	−	0.239085i
$385$	−868.420	−	218.077i	−0.114958	−	0.0288681i
$386$	−4063.51	−	1471.57i	−0.535822	−	0.194043i
$387$	−469.937	−	194.654i	−0.0617267	−	0.0255680i
$388$	−763.884	−	8417.83i	−0.0999493	−	1.10142i
$389$	14139.1	+	5856.61i	1.84288	+	0.763347i	0.949226	+	0.314596i	$0.101869\pi$
$389$	14139.1	+	5856.61i	1.84288	+	0.763347i	0.893657	+	0.448751i	$0.148131\pi$
$390$	−1173.88	−	238.914i	−0.152415	−	0.0310202i
$391$	−16973.3	+	16973.3i	−2.19534	+	2.19534i
$392$	−1861.63	+	7084.88i	−0.239863	+	0.912858i
$393$	−2492.55			−0.319931
$394$	4747.90	+	4336.56i	0.607096	+	0.554499i
$395$	585.215	+	3961.43i	0.0745452	+	0.504610i
$396$	1088.86	−	3492.72i	0.138174	−	0.443222i
$397$	−2906.41	−	1203.87i	−0.367427	−	0.152193i	0.191328	−	0.981526i	$-0.438721\pi$
$397$	−2906.41	−	1203.87i	−0.367427	−	0.152193i	−0.558755	+	0.829333i	$0.688721\pi$
$398$	13299.1	+	4816.17i	1.67494	+	0.606565i
$399$			599.668i			0.0752404i
$400$	−3653.95	−	7116.79i	−0.456744	−	0.889598i
$401$			3501.36i			0.436034i	0.975945	+	0.218017i	$0.0699588\pi$
$401$			3501.36i			0.436034i	−0.975945	+	0.218017i	$0.930041\pi$
$402$	1094.11	−	3021.23i	0.135745	−	0.374839i
$403$	−7526.22	−	3117.46i	−0.930292	−	0.385340i
$404$	−905.487	−	1725.78i	−0.111509	−	0.212527i
$405$	−940.654	−	6367.46i	−0.115411	−	0.781239i
$406$	−1177.46	+	1289.14i	−0.143932	+	0.157584i
$407$	2441.31			0.297325
$408$	−525.150	−	3844.80i	−0.0637226	−	0.466534i
$409$	−2554.77	+	2554.77i	−0.308864	+	0.308864i	−0.844469	−	0.535605i	$-0.820084\pi$
$409$	−2554.77	+	2554.77i	−0.308864	+	0.308864i	0.535605	+	0.844469i	$0.320084\pi$
$410$	2463.77	−	12105.5i	0.296773	−	1.45816i
$411$	899.187	+	372.455i	0.107916	+	0.0447004i
$412$	−4404.02	+	5283.09i	−0.526628	+	0.631745i
$413$	−3436.11	−	1423.28i	−0.409395	−	0.169577i
$414$	−4704.11	+	12989.7i	−0.558440	+	1.54205i
$415$	−688.846	−	172.982i	−0.0814798	−	0.0204611i
$416$	4799.18	−	1104.71i	0.565624	−	0.130199i
$417$	−736.344	+	736.344i	−0.0864722	+	0.0864722i
$418$	−4586.66	+	2147.83i	−0.536701	+	0.251324i
$419$	−3963.99	+	1641.94i	−0.462181	+	0.191442i	−0.601609	−	0.798791i	$-0.705474\pi$
$419$	−3963.99	+	1641.94i	−0.462181	+	0.191442i	0.139428	+	0.990232i	$0.455474\pi$
$420$	−441.709	+	321.965i	−0.0513171	+	0.0374054i
$421$	2849.62	−	6879.60i	0.329886	−	0.796416i	−0.668714	−	0.743520i	$-0.733155\pi$
$421$	2849.62	−	6879.60i	0.329886	−	0.796416i	0.998600	−	0.0528961i	$-0.0168452\pi$
$422$	221.483	−	242.492i	0.0255489	−	0.0279723i
$423$	−4896.71			−0.562852
$424$	8007.81	−	1093.76i	0.917202	−	0.125278i
$425$	−13568.5	−	7273.27i	−1.54863	−	0.830130i
$426$	−1163.46	−	1062.66i	−0.132324	−	0.120860i
$427$	1042.45	+	2516.69i	0.118144	+	0.285225i
$428$	10710.7	+	3339.06i	1.20963	+	0.377102i
$429$	−638.659	+	264.541i	−0.0718759	+	0.0297720i
$430$	−358.948	+	532.082i	−0.0402558	+	0.0596728i
$431$	16102.3			1.79958			0.899789	−	0.436325i	$-0.143720\pi$
$431$	16102.3			1.79958			0.899789	+	0.436325i	$0.143720\pi$
$432$	−2518.07	−	3896.77i	−0.280442	−	0.433990i
$433$	−10666.3	+	10666.3i	−1.18381	+	1.18381i	−0.205062	+	0.978749i	$0.565740\pi$
$433$	−10666.3	+	10666.3i	−1.18381	+	1.18381i	−0.978749	+	0.205062i	$0.934260\pi$
$434$	−3366.19	+	1576.31i	−0.372310	+	0.174344i
$435$	2166.19	−	320.008i	0.238761	−	0.0352717i
$436$	−1804.63	+	5788.72i	−0.198225	+	0.635847i
$437$	17669.2	−	7318.84i	1.93417	−	0.801161i
$438$	−87.0983	−	1923.55i	−0.00950163	−	0.209842i
$439$	−7409.97	+	7409.97i	−0.805601	+	0.805601i	−0.983965	−	0.178364i	$-0.942920\pi$
$439$	−7409.97	+	7409.97i	−0.805601	+	0.805601i	0.178364	+	0.983965i	$0.442920\pi$
$440$	−4044.67	−	2225.31i	−0.438232	−	0.241108i
$441$	5736.93	+	5736.93i	0.619472	+	0.619472i
$442$	6391.21	−	6997.45i	0.687781	−	0.753020i
$443$	1271.21	+	3068.97i	0.136336	+	0.329144i	0.977272	−	0.211991i	$-0.0679947\pi$
$443$	1271.21	+	3068.97i	0.136336	+	0.329144i	−0.840936	+	0.541135i	$0.817995\pi$
$444$	954.269	−	1144.75i	0.101999	−	0.122359i
$445$	−5919.26	+	7971.29i	−0.630561	+	0.849158i
$446$	−2979.95	+	8228.68i	−0.316378	+	0.873630i
$447$	508.853	+	508.853i	0.0538432	+	0.0538432i
$448$	1104.59	−	1956.78i	0.116489	−	0.206360i
$449$			9677.29i			1.01715i	0.861018	+	0.508574i	$0.169827\pi$
$449$			9677.29i			1.01715i	−0.861018	+	0.508574i	$0.830173\pi$
$450$	−8847.45	−	479.247i	−0.926828	−	0.0502043i
$451$	−2728.04	−	6586.08i	−0.284830	−	0.687642i
$452$	−672.993	−	7416.23i	−0.0700330	−	0.771748i
$453$	323.755	−	134.104i	0.0335791	−	0.0139089i
$454$	−12264.7	+	555.344i	−1.26786	+	0.0574088i
$455$	−1294.70	−	325.123i	−0.133398	−	0.0334989i
$456$	−785.724	+	2990.27i	−0.0806905	+	0.307088i
$457$		−	3725.75i		−	0.381364i	−0.981652	−	0.190682i	$-0.938930\pi$
$457$		−	3725.75i		−	0.381364i	0.981652	−	0.190682i	$-0.0610699\pi$
$458$	257.859	−	11.6758i	0.0263078	−	0.00119121i
$459$	−8248.61	−	3416.69i	−0.838806	−	0.347445i
$460$	14877.7	+	9085.46i	1.50799	+	0.920895i
$461$	1245.99	+	3008.08i	0.125881	+	0.303905i	0.974239	−	0.225520i	$-0.0724080\pi$
$461$	1245.99	+	3008.08i	0.125881	+	0.303905i	−0.848357	+	0.529424i	$0.822408\pi$
$462$	−107.399	+	296.567i	−0.0108153	+	0.0298649i
$463$	9723.04	+	9723.04i	0.975957	+	0.975957i	0.999718	−	0.0237606i	$-0.00756395\pi$
$463$	9723.04	+	9723.04i	0.975957	+	0.975957i	−0.0237606	+	0.999718i	$0.507564\pi$
$464$	−7560.56	+	4885.59i	−0.756444	+	0.488810i
$465$	4521.35	+	1135.40i	0.450909	+	0.113232i
$466$	6017.53	−	2817.87i	0.598190	−	0.280118i
$467$	−2481.47	+	5990.80i	−0.245886	+	0.593621i	−0.997847	−	0.0655865i	$-0.979108\pi$
$467$	−2481.47	+	5990.80i	−0.245886	+	0.593621i	0.751961	+	0.659208i	$0.229108\pi$
$468$	1623.34	−	5207.18i	0.160339	−	0.514320i
$469$	1370.23	−	3308.02i	0.134906	−	0.325693i
$470$	−1232.28	+	6054.69i	−0.120938	+	0.594217i
$471$	−2681.39	−	2681.39i	−0.262318	−	0.262318i
$472$	−15269.4	−	11599.5i	−1.48905	−	1.13116i
$473$			370.374i			0.0360039i
$474$	1409.19	−	63.8080i	0.136553	−	0.00618311i
$475$	7770.10	+	9490.89i	0.750562	+	0.916783i
$476$	−390.789	−	4306.41i	−0.0376298	−	0.414672i
$477$	3425.56	−	8270.03i	0.328817	−	0.793833i
$478$	−3373.37	−	7203.81i	−0.322792	−	0.689319i
$479$	11217.1			1.06999			0.534993	−	0.844856i	$-0.320314\pi$
$479$	11217.1			1.06999			0.534993	+	0.844856i	$0.320314\pi$
$480$	−2624.46	+	1026.74i	−0.249562	+	0.0976330i
$481$	3639.66			0.345019
$482$	6289.52	+	13431.2i	0.594357	+	1.26924i
$483$	455.802	−	1100.40i	0.0429394	−	0.103665i
$484$	7951.41	−	721.558i	0.746751	−	0.0677647i
$485$	−7042.41	+	9483.80i	−0.659339	+	0.887911i
$486$	−7795.54	+	352.982i	−0.727598	+	0.0329456i
$487$			8810.28i			0.819778i	0.912135	+	0.409889i	$0.134433\pi$
$487$			8810.28i			0.819778i	−0.912135	+	0.409889i	$0.865567\pi$
$488$	1900.67	+	13915.5i	0.176310	+	1.29083i
$489$	137.167	+	137.167i	0.0126849	+	0.0126849i
$490$	8537.32	−	5649.88i	0.787096	−	0.520889i
$491$	−5828.62	+	14071.5i	−0.535727	+	1.29336i	0.391954	+	0.919985i	$0.371799\pi$
$491$	−5828.62	+	14071.5i	−0.535727	+	1.29336i	−0.927681	+	0.373375i	$0.878201\pi$
$492$	−4154.60	−	1295.20i	−0.380699	−	0.118683i
$493$	−6629.08	+	16004.0i	−0.605596	+	1.46204i
$494$	−6838.09	+	3202.12i	−0.622794	+	0.291640i
$495$	−4387.07	+	2625.96i	−0.398352	+	0.238441i
$496$	−18851.0	+	3449.72i	−1.70652	+	0.312292i
$497$	−1241.58	−	1241.58i	−0.112057	−	0.112057i
$498$	−85.1911	+	235.243i	−0.00766567	+	0.0211676i
$499$	−7242.18	−	17484.2i	−0.649709	−	1.56854i	−0.813196	−	0.581990i	$-0.802274\pi$
$499$	−7242.18	−	17484.2i	−0.649709	−	1.56854i	0.163487	−	0.986545i	$-0.447726\pi$
$500$	−2819.08	+	10819.1i	−0.252146	+	0.967689i
$501$	−261.918	−	108.490i	−0.0233565	−	0.00967460i
$502$	−1588.08	+	71.9082i	−0.141194	+	0.00639326i
$503$			2667.87i			0.236490i	0.992984	+	0.118245i	$0.0377268\pi$
$503$			2667.87i			0.236490i	−0.992984	+	0.118245i	$0.962273\pi$
$504$	−1254.78	−	2149.22i	−0.110898	−	0.189948i
$505$	−663.371	+	2641.66i	−0.0584547	+	0.232777i
$506$	10049.2	−	455.026i	0.882886	−	0.0399770i
$507$	1874.22	−	776.327i	0.164176	−	0.0680038i
$508$	10816.4	−	981.546i	0.944687	−	0.0857265i
$509$	−2186.69	−	5279.15i	−0.190419	−	0.459713i	0.799619	−	0.600507i	$-0.205035\pi$
$509$	−2186.69	−	5279.15i	−0.190419	−	0.459713i	−0.990039	+	0.140794i	$0.955035\pi$
$510$	−3032.91	+	4495.79i	−0.263332	+	0.390347i
$511$		−	2145.64i		−	0.185749i
$512$	8072.01	−	8310.26i	0.696749	−	0.717315i
$513$	5030.03	+	5030.03i	0.432907	+	0.432907i
$514$	−1105.03	+	3051.38i	−0.0948265	+	0.261849i
$515$	9509.05	−	1404.76i	0.813629	−	0.120196i
$516$	173.671	+	144.773i	0.0148167	+	0.0123513i
$517$	1364.46	+	3294.10i	0.116071	+	0.280221i
$518$	1119.97	−	1226.20i	0.0949974	−	0.104008i
$519$	2429.61	+	2429.61i	0.205487	+	0.205487i
$520$	−6030.06	−	3317.63i	−0.508530	−	0.279784i
$521$	10176.2	−	10176.2i	0.855713	−	0.855713i	−0.135117	−	0.990830i	$-0.543141\pi$
$521$	10176.2	−	10176.2i	0.855713	−	0.855713i	0.990830	+	0.135117i	$0.0431409\pi$
$522$	450.973	+	9959.67i	0.0378133	+	0.835101i
$523$	1426.49	−	590.871i	0.119266	−	0.0494015i	−0.322253	−	0.946654i	$-0.604440\pi$
$523$	1426.49	−	590.871i	0.119266	−	0.0494015i	0.441518	+	0.897252i	$0.354440\pi$
$524$	−13671.3	−	4262.02i	−1.13976	−	0.355319i
$525$	760.125	+	75.7786i	0.0631896	+	0.00629952i
$526$	11283.4	−	5283.74i	0.935320	−	0.437988i
$527$	−26077.2	+	26077.2i	−2.15549	+	2.15549i
$528$	−924.133	+	1338.12i	−0.0761700	+	0.110292i
$529$	−25819.4			−2.12209
$530$	−9363.67	−	6316.83i	−0.767419	−	0.517708i
$531$	−19621.3	+	8127.42i	−1.60357	+	0.664218i
$532$	−1025.37	+	3289.09i	−0.0835630	+	0.268045i
$533$	−4067.14	−	9818.95i	−0.330521	−	0.797947i
$534$	2582.49	+	2358.75i	0.209280	+	0.191148i
$535$	−8052.72	−	13453.3i	−0.650747	−	1.08717i
$536$	11167.1	−	14700.2i	0.899895	−	1.18461i
$537$	488.839			0.0392830
$538$	8637.60	−	9456.92i	0.692181	−	0.757837i
$539$	2260.74	−	5457.91i	0.180662	−	0.436157i
$540$	−1004.42	+	6405.72i	−0.0800429	+	0.510478i
$541$	−4024.70	+	1667.09i	−0.319844	+	0.132484i	−0.536829	−	0.843691i	$-0.680378\pi$
$541$	−4024.70	+	1667.09i	−0.319844	+	0.132484i	0.216985	+	0.976175i	$0.430378\pi$
$542$	7321.14	−	3428.32i	0.580203	−	0.271695i
$543$	−1804.67	+	1804.67i	−0.142626	+	0.142626i
$544$	3693.85	−	21986.1i	0.291126	−	1.73281i
$545$	7270.97	−	4352.18i	0.571475	−	0.342067i
$546$	−160.118	+	442.142i	−0.0125502	+	0.0346555i
$547$	−7683.09	−	3182.44i	−0.600558	−	0.248759i	0.0616277	−	0.998099i	$-0.480371\pi$
$547$	−7683.09	−	3182.44i	−0.600558	−	0.248759i	−0.662185	+	0.749340i	$0.730371\pi$
$548$	4295.05	+	3580.39i	0.334809	+	0.279099i
$549$	14371.1	+	5952.71i	1.11720	+	0.462761i
$550$	2142.93	+	6085.36i	0.166136	+	0.471783i
$551$	9759.30	−	9759.30i	0.754556	−	0.754556i
$552$	3714.70	−	4889.98i	0.286427	−	0.377050i
$553$	1571.89			0.120875
$554$	4404.21	−	4821.97i	0.337756	−	0.369794i
$555$	−2060.43	+	304.384i	−0.157586	+	0.0232800i
$556$	−5297.82	+	2779.67i	−0.404096	+	0.212022i
$557$	10501.9	+	4350.01i	0.798883	+	0.330908i	0.744509	−	0.667612i	$-0.232684\pi$
$557$	10501.9	+	4350.01i	0.798883	+	0.330908i	0.0543741	+	0.998521i	$0.482684\pi$
$558$	−7227.21	+	19956.9i	−0.548302	+	1.51405i
$559$			552.178i			0.0417793i
$560$	−2973.24	+	1010.65i	−0.224361	+	0.0762641i
$561$			3129.45i			0.235518i
$562$	14957.5	+	5416.74i	1.12268	+	0.406568i
$563$	23610.3	+	9779.70i	1.76742	+	0.732087i	0.995326	+	0.0965736i	$0.0307883\pi$
$563$	23610.3	+	9779.70i	1.76742	+	0.732087i	0.772089	+	0.635514i	$0.219212\pi$
$564$	2077.97	+	647.806i	0.155139	+	0.0483644i
$565$	−6204.46	+	8355.36i	−0.461989	+	0.622146i
$566$	−14542.2	−	13282.3i	−1.07995	−	0.986389i
$567$	−2526.60			−0.187138
$568$	−4564.38	−	7817.96i	−0.337178	−	0.577525i
$569$	14640.3	−	14640.3i	1.07865	−	1.07865i	0.0820220	−	0.996631i	$-0.473862\pi$
$569$	14640.3	−	14640.3i	1.07865	−	1.07865i	0.996631	−	0.0820220i	$-0.0261378\pi$
$570$	3603.29	−	2384.60i	0.264781	−	0.175228i
$571$	9537.59	+	3950.60i	0.699012	+	0.289540i	0.703749	−	0.710449i	$-0.251508\pi$
$571$	9537.59	+	3950.60i	0.699012	+	0.289540i	−0.00473738	+	0.999989i	$0.501508\pi$
$572$	−3955.29	+	358.927i	−0.289124	+	0.0262369i
$573$	887.431	+	367.586i	0.0646997	+	0.0267995i
$574$	−4559.52	−	1651.19i	−0.331552	−	0.120069i
$575$	−7044.37	−	23322.0i	−0.510905	−	1.69147i
$576$	−3440.97	−	12361.3i	−0.248913	−	0.894188i
$577$	5329.12	−	5329.12i	0.384496	−	0.384496i	−0.488223	−	0.872719i	$-0.662355\pi$
$577$	5329.12	−	5329.12i	0.384496	−	0.384496i	0.872719	+	0.488223i	$0.162355\pi$
$578$	−12301.1	−	26268.8i	−0.885220	−	1.89038i
$579$	1965.69	−	814.216i	0.141090	−	0.0584416i
$580$	12428.4	+	1948.78i	0.889763	+	0.139515i
$581$	−106.690	+	257.573i	−0.00761833	+	0.0183923i
$582$	3072.51	+	2806.32i	0.218831	+	0.199872i
$583$	−6517.91			−0.463026
$584$	2811.36	−	10699.3i	0.199204	−	0.758119i
$585$	−6540.52	+	3914.95i	−0.462252	+	0.276690i
$586$	−10369.0	+	11352.6i	−0.730958	+	0.800293i
$587$	−7340.17	−	17720.7i	−0.516118	−	1.24602i	−0.940271	−	0.340428i	$-0.889428\pi$
$587$	−7340.17	−	17720.7i	−0.516118	−	1.24602i	0.424153	−	0.905591i	$-0.360572\pi$
$588$	−1675.56	−	3193.48i	−0.117515	−	0.223975i
$589$	27146.4	−	11244.4i	1.89906	−	0.786616i
$590$	5111.60	+	26306.7i	0.356680	+	1.83564i
$591$	−3165.69			−0.220337
$592$	7191.43	−	4647.06i	0.499267	−	0.322623i
$593$	6821.87	−	6821.87i	0.472413	−	0.472413i	−0.430282	−	0.902695i	$-0.641586\pi$
$593$	6821.87	−	6821.87i	0.472413	−	0.472413i	0.902695	+	0.430282i	$0.141586\pi$
$594$	1586.75	+	3388.48i	0.109604	+	0.234059i
$595$	−3602.77	+	4851.74i	−0.248234	+	0.334289i
$596$	1920.90	+	3661.07i	0.132018	+	0.251616i
$597$	−6433.36	+	2664.78i	−0.441038	+	0.182684i
$598$	14981.9	−	678.382i	1.02451	−	0.0463898i
$599$	−4493.46	+	4493.46i	−0.306507	+	0.306507i	−0.843553	−	0.537046i	$-0.819540\pi$
$599$	−4493.46	+	4493.46i	−0.306507	+	0.306507i	0.537046	+	0.843553i	$0.319540\pi$
$600$	3691.10	+	1373.84i	0.251148	+	0.0934778i
$601$	−2816.44	−	2816.44i	−0.191157	−	0.191157i	0.605039	−	0.796196i	$-0.293157\pi$
$601$	−2816.44	−	2816.44i	−0.191157	−	0.191157i	−0.796196	+	0.605039i	$0.793157\pi$
$602$	186.029	+	169.912i	0.0125947	+	0.0115035i
$603$	−7824.44	−	18889.9i	−0.528417	−	1.27571i
$604$	2005.05	−	181.950i	0.135074	−	0.0122574i
$605$	−8958.31	−	6652.19i	−0.601995	−	0.447025i
$606$	902.133	+	326.700i	0.0604730	+	0.0218998i
$607$	9851.85	+	9851.85i	0.658772	+	0.658772i	0.955089	−	0.296318i	$-0.0957587\pi$
$607$	9851.85	+	9851.85i	0.658772	+	0.658772i	−0.296318	+	0.955089i	$0.595759\pi$
$608$	−9422.64	+	15057.7i	−0.628517	+	1.00439i
$609$		−	859.544i		−	0.0571929i
$610$	10977.0	−	16271.6i	0.728598	−	1.08003i
$611$	2034.22	+	4911.05i	0.134690	+	0.325172i
$612$	−18966.4	−	15810.5i	−1.25273	−	1.04429i
$613$	26460.6	−	10960.3i	1.74345	−	0.722159i	0.744963	−	0.667106i	$-0.232467\pi$
$613$	26460.6	−	10960.3i	1.74345	−	0.722159i	0.998483	−	0.0550534i	$-0.0175329\pi$
$614$	−219.966	−	4857.90i	−0.0144578	−	0.319298i
$615$	3123.59	+	5218.43i	0.204805	+	0.342158i
$616$	−1096.17	+	1442.99i	−0.0716981	+	0.0943825i
$617$		−	3562.11i		−	0.232423i	−0.993224	−	0.116211i	$-0.962925\pi$
$617$		−	3562.11i		−	0.232423i	0.993224	−	0.116211i	$-0.0370750\pi$
$618$	−153.165	−	3382.63i	−0.00996960	−	0.220177i
$619$	−18858.4	−	7811.41i	−1.22453	−	0.507217i	−0.325682	−	0.945479i	$-0.605594\pi$
$619$	−18858.4	−	7811.41i	−1.22453	−	0.507217i	−0.898847	+	0.438263i	$0.855594\pi$
$620$	22857.5	+	13958.6i	1.48061	+	0.904176i
$621$	−5406.93	−	13053.5i	−0.349392	−	0.843508i
$622$	16559.1	+	5996.73i	1.06746	+	0.386571i
$623$	2755.88	+	2755.88i	0.177226	+	0.177226i
$624$	−1377.76	+	1994.96i	−0.0883885	+	0.127985i
$625$	13012.3	−	8649.86i	0.832789	−	0.553591i
$626$	12751.3	+	27230.2i	0.814127	+	1.73856i
$627$	954.174	−	2303.58i	0.0607752	−	0.146724i
$628$	−10122.1	−	19292.0i	−0.643180	−	1.22585i
$629$	6305.43	−	15222.7i	0.399704	−	0.964972i
$630$	−693.651	+	3408.19i	−0.0438662	+	0.215533i
$631$	7732.51	+	7732.51i	0.487839	+	0.487839i	0.907624	−	0.419785i	$-0.137894\pi$
$631$	7732.51	+	7732.51i	0.487839	+	0.487839i	−0.419785	+	0.907624i	$0.637894\pi$
$632$	7838.30	+	2059.59i	0.493340	+	0.129630i
$633$			161.683i			0.0101522i
$634$	90.2895	+	1994.03i	0.00565592	+	0.124910i
$635$	−12186.1	−	9049.08i	−0.761561	−	0.565515i
$636$	−2547.75	+	3056.29i	−0.158844	+	0.190550i
$637$	3370.46	−	8137.00i	0.209643	−	0.506122i
$638$	6574.37	−	3078.62i	0.407965	−	0.191040i
$639$	−10026.5			−0.620723
$640$	−16150.4	+	1143.93i	−0.997501	+	0.0706528i
$641$	10687.2			0.658534			0.329267	−	0.944237i	$-0.393198\pi$
$641$	10687.2			0.658534			0.329267	+	0.944237i	$0.393198\pi$
$642$	−5002.03	+	2342.33i	−0.307499	+	0.143994i
$643$	5562.66	−	13429.4i	0.341166	−	0.823648i	−0.656432	−	0.754385i	$-0.727935\pi$
$643$	5562.66	−	13429.4i	0.341166	−	0.823648i	0.997598	−	0.0692630i	$-0.0220648\pi$
$644$	4381.59	−	5256.18i	0.268104	−	0.321619i
$645$	−46.1785	−	312.591i	−0.00281904	−	0.0190826i
$646$	1546.19	+	34147.3i	0.0941703	+	2.07973i
$647$			6534.02i			0.397031i	0.980098	+	0.198515i	$0.0636120\pi$
$647$			6534.02i			0.397031i	−0.980098	+	0.198515i	$0.936388\pi$
$648$	−12599.0	−	3310.52i	−0.763790	−	0.200694i
$649$	10934.9	+	10934.9i	0.661375	+	0.661375i
$650$	3194.81	+	9072.45i	0.192786	+	0.547463i
$651$	700.277	−	1690.62i	0.0421598	−	0.101783i
$652$	517.801	+	986.887i	0.0311022	+	0.0592783i
$653$	−1572.19	+	3795.61i	−0.0942186	+	0.227464i	−0.963962	−	0.266041i	$-0.914284\pi$
$653$	−1572.19	+	3795.61i	−0.0942186	+	0.227464i	0.869743	+	0.493505i	$0.164284\pi$
$654$	−1265.94	−	2703.40i	−0.0756912	−	0.161638i
$655$	10278.6	+	17172.0i	0.613158	+	1.02437i
$656$	−20572.8	−	14207.9i	−1.22444	−	0.845619i
$657$	−8663.70	−	8663.70i	−0.514464	−	0.514464i
$658$	2280.49	+	825.861i	0.135111	+	0.0489292i
$659$	−9693.56	−	23402.3i	−0.573000	−	1.38335i	−0.898989	−	0.437972i	$-0.855697\pi$
$659$	−9693.56	−	23402.3i	−0.573000	−	1.38335i	0.325988	−	0.945374i	$-0.394303\pi$
$660$	2209.10	−	533.971i	0.130286	−	0.0314921i
$661$	21979.2	+	9104.09i	1.29333	+	0.535716i	0.919977	−	0.391973i	$-0.128207\pi$
$661$	21979.2	+	9104.09i	1.29333	+	0.535716i	0.373355	+	0.927688i	$0.378207\pi$
$662$	−391.434	−	8644.76i	−0.0229812	−	0.507535i
$663$			4665.59i			0.273298i
$664$	−869.503	+	1144.60i	−0.0508182	+	0.0668965i
$665$	4131.29	−	2472.86i	0.240909	−	0.144201i
$666$	−428.956	−	9473.41i	−0.0249575	−	0.551182i
$667$	−25326.5	+	10490.6i	−1.47023	+	0.608991i
$668$	−1251.08	−	1042.91i	−0.0724634	−	0.0604060i
$669$	−1648.80	−	3980.56i	−0.0952860	−	0.230041i
$670$	−25326.0	+	4921.05i	−1.46034	+	0.283756i
$671$		−	11326.4i		−	0.651641i
$672$	248.151	+	1078.04i	0.0142450	+	0.0618845i
$673$	1163.20	+	1163.20i	0.0666242	+	0.0666242i	0.739634	−	0.673010i	$-0.234999\pi$
$673$	1163.20	+	1163.20i	0.0666242	+	0.0666242i	−0.673010	+	0.739634i	$0.734999\pi$
$674$	7882.28	+	2854.50i	0.450466	+	0.163132i
$675$	7011.58	−	5740.31i	0.399816	−	0.327326i
$676$	11607.3	−	1053.31i	0.660405	−	0.0599291i
$677$	−1872.95	−	4521.71i	−0.106327	−	0.256696i	0.861757	−	0.507321i	$-0.169364\pi$
$677$	−1872.95	−	4521.71i	−0.106327	−	0.256696i	−0.968084	+	0.250625i	$0.919364\pi$
$678$	2706.92	+	2472.40i	0.153331	+	0.140047i
$679$	3278.79	+	3278.79i	0.185315	+	0.185315i
$680$	−24322.4	+	19472.8i	−1.37165	+	1.09816i
$681$	4273.91	−	4273.91i	0.240494	−	0.240494i
$682$	15439.2	−	699.085i	0.866857	−	0.0392512i
$683$	11049.7	−	4576.96i	0.619044	−	0.256416i	−0.0510461	−	0.998696i	$-0.516256\pi$
$683$	11049.7	−	4576.96i	0.619044	−	0.256416i	0.670090	+	0.742280i	$0.266256\pi$
$684$	9140.47	+	17421.0i	0.510957	+	0.973842i
$685$	−1142.04	−	7730.68i	−0.0637009	−	0.431203i
$686$	−3509.85	−	7495.26i	−0.195345	−	0.417158i
$687$	−89.8569	+	89.8569i	−0.00499018	+	0.00499018i
$688$	705.012	+	1091.02i	0.0390673	+	0.0604575i
$689$	−9717.31			−0.537301
$690$	−8424.63	+	1636.97i	−0.464812	+	0.0903167i
$691$	10285.8	−	4260.53i	0.566269	−	0.234556i	−0.0811353	−	0.996703i	$-0.525855\pi$
$691$	10285.8	−	4260.53i	0.566269	−	0.234556i	0.647404	+	0.762147i	$0.275855\pi$
$692$	9171.66	+	17480.4i	0.503835	+	0.960269i
$693$	768.055	+	1854.25i	0.0421010	+	0.101641i
$694$	−12143.3	+	13295.2i	−0.664200	+	0.727203i
$695$	8109.38	+	2036.42i	0.442599	+	0.111145i
$696$	1126.23	−	4286.15i	0.0613357	−	0.233428i
$697$	−48113.2			−2.61466
$698$	−5581.59	−	5098.02i	−0.302674	−	0.276451i
$699$	−1251.84	+	3022.21i	−0.0677382	+	0.163534i
$700$	4039.60	+	1715.37i	0.218118	+	0.0926214i
$701$	15593.9	−	6459.21i	0.840191	−	0.348018i	0.0792621	−	0.996854i	$-0.474744\pi$
$701$	15593.9	−	6459.21i	0.840191	−	0.348018i	0.760929	+	0.648835i	$0.224744\pi$
$702$	2365.62	+	5051.77i	0.127186	+	0.271605i
$703$	−9282.83	+	9282.83i	−0.498021	+	0.498021i
$704$	−7356.80	+	5759.24i	−0.393849	+	0.308323i
$705$	−1562.30	−	2610.05i	−0.0834602	−	0.139433i
$706$	9782.07	+	3542.49i	0.521463	+	0.188843i
$707$	987.767	+	409.146i	0.0525443	+	0.0217645i
$708$	9401.72	−	853.168i	0.499065	−	0.0452882i
$709$	−5467.01	−	2264.51i	−0.289588	−	0.119951i	0.233160	−	0.972438i	$-0.425093\pi$
$709$	−5467.01	−	2264.51i	−0.289588	−	0.119951i	−0.522748	+	0.852487i	$0.675093\pi$
$710$	−2523.21	+	12397.6i	−0.133373	+	0.655314i
$711$	6347.00	−	6347.00i	0.334784	−	0.334784i
$712$	10131.4	+	17353.2i	0.533271	+	0.913399i
$713$	−58360.9			−3.06541
$714$	1571.84	+	1435.66i	0.0823875	+	0.0752497i
$715$	4456.16	+	3309.02i	0.233078	+	0.173077i
$716$	2681.21	+	835.867i	0.139946	+	0.0436282i
$717$	3618.00	+	1498.63i	0.188447	+	0.0780574i
$718$	−1429.58	−	517.710i	−0.0743056	−	0.0269091i
$719$		−	15105.7i		−	0.783514i	−0.920069	−	0.391757i	$-0.871867\pi$
$719$		−	15105.7i		−	0.783514i	0.920069	−	0.391757i	$-0.128133\pi$
$720$	−7924.55	+	16086.2i	−0.410181	+	0.832635i
$721$		−	3773.19i		−	0.194897i
$722$	2667.64	−	7366.30i	0.137506	−	0.379702i
$723$	−6745.63	−	2794.13i	−0.346988	−	0.143727i
$724$	−12984.2	+	6812.54i	−0.666509	+	0.349705i
$725$	−11137.4	−	13603.9i	−0.570528	−	0.696879i
$726$	−2650.82	+	2902.26i	−0.135511	+	0.148365i
$727$	−25073.0			−1.27910			−0.639550	−	0.768749i	$-0.720879\pi$
$727$	−25073.0			−1.27910			−0.639550	+	0.768749i	$0.720879\pi$
$728$	−1634.24	+	2151.30i	−0.0831993	+	0.109523i
$729$	−8274.74	+	8274.74i	−0.420400	+	0.420400i
$730$	−12892.8	+	8532.24i	−0.653674	+	0.432592i
$731$	2309.45	+	956.606i	0.116851	+	0.0484013i
$732$	−5311.02	−	4427.31i	−0.268171	−	0.223549i
$733$	20663.8	+	8559.23i	1.04125	+	0.431299i	0.836760	−	0.547570i	$-0.184447\pi$
$733$	20663.8	+	8559.23i	1.04125	+	0.431299i	0.204488	+	0.978869i	$0.434447\pi$
$734$	−2398.82	+	6623.98i	−0.120629	+	0.333100i
$735$	−1227.54	+	4888.27i	−0.0616033	+	0.245315i
$736$	28736.0	−	20469.1i	1.43916	−	1.02514i
$737$	−10527.2	+	10527.2i	−0.526155	+	0.526155i
$738$	−25077.7	+	11743.3i	−1.25084	+	0.585741i
$739$	−6694.29	+	2772.86i	−0.333225	+	0.138026i	−0.543022	−	0.839719i	$-0.682720\pi$
$739$	−6694.29	+	2772.86i	−0.333225	+	0.138026i	0.209797	+	0.977745i	$0.432720\pi$
$740$	−11821.6	−	1853.63i	−0.587260	−	0.0920822i
$741$	1422.54	−	3434.33i	0.0705243	−	0.170261i
$742$	−2990.14	+	3273.77i	−0.147940	+	0.161973i
$743$	25936.0			1.28062			0.640309	−	0.768117i	$-0.278806\pi$
$743$	25936.0			1.28062			0.640309	+	0.768117i	$0.278806\pi$
$744$	5707.12	−	7512.79i	0.281227	−	0.370204i
$745$	1407.27	−	5604.01i	0.0692060	−	0.275591i
$746$	−18161.6	−	16588.1i	−0.891345	−	0.814122i
$747$	609.235	+	1470.82i	0.0298404	+	0.0720410i
$748$	−5351.05	+	17164.6i	−0.261569	+	0.839037i
$749$	−5686.20	+	2355.30i	−0.277396	+	0.114901i
$750$	−2567.33	−	4868.78i	−0.124994	−	0.237044i
$751$	−8285.64			−0.402593			−0.201296	−	0.979530i	$-0.564515\pi$
$751$	−8285.64			−0.402593			−0.201296	+	0.979530i	$0.564515\pi$
$752$	10289.7	+	7106.24i	0.498971	+	0.344598i
$753$	553.403	−	553.403i	0.0267824	−	0.0267824i
$754$	9801.49	−	4589.81i	0.473408	−	0.221686i
$755$	−2258.96	−	1677.44i	−0.108890	−	0.0808586i
$756$	2429.88	+	757.514i	0.116897	+	0.0364425i
$757$	−1015.10	+	420.467i	−0.0487375	+	0.0201877i	−0.406919	−	0.913464i	$-0.633397\pi$
$757$	−1015.10	+	420.467i	−0.0487375	+	0.0201877i	0.358182	+	0.933652i	$0.383397\pi$
$758$	−501.741	−	11080.9i	−0.0240423	−	0.530970i
$759$	−3501.86	+	3501.86i	−0.167470	+	0.167470i
$760$	23841.0	−	6917.94i	1.13790	−	0.330184i
$761$	27010.0	+	27010.0i	1.28661	+	1.28661i	0.936831	+	0.349781i	$0.113744\pi$
$761$	27010.0	+	27010.0i	1.28661	+	1.28661i	0.349781	+	0.936831i	$0.386256\pi$
$762$	−3605.95	+	3947.99i	−0.171430	+	0.187691i
$763$	−1272.95	−	3073.17i	−0.0603982	−	0.145814i
$764$	4238.90	+	3533.57i	0.200730	+	0.167330i
$765$	5043.11	+	34137.7i	0.238345	+	1.61340i
$766$	−3019.07	+	8336.70i	−0.142406	+	0.393234i
$767$	16302.4	+	16302.4i	0.767467	+	0.767467i
$768$	−175.110	+	5700.85i	−0.00822750	+	0.267854i
$769$			8525.03i			0.399766i	0.979820	+	0.199883i	$0.0640563\pi$
$769$			8525.03i			0.399766i	−0.979820	+	0.199883i	$0.935944\pi$
$770$	2486.03	−	483.055i	0.116351	−	0.0226079i
$771$	−611.413	−	1476.08i	−0.0285597	−	0.0689491i
$772$	12173.8	−	1104.72i	0.567543	−	0.0515023i
$773$	−9347.35	+	3871.80i	−0.434930	+	0.180154i	−0.589396	−	0.807844i	$-0.700634\pi$
$773$	−9347.35	+	3871.80i	−0.434930	+	0.180154i	0.154466	+	0.987998i	$0.450634\pi$
$774$	1437.22	−	65.0774i	0.0667441	−	0.00302217i
$775$	−10822.7	−	35831.0i	−0.501630	−	1.66076i
$776$	12053.7	+	20645.9i	0.557609	+	0.955085i
$777$			817.578i			0.0377483i
$778$	−43242.1	+	1958.00i	−1.99268	+	0.0902284i
$779$	35416.0	+	14669.8i	1.62890	+	0.674711i
$780$	3293.46	−	796.078i	0.151186	−	0.0365438i
$781$	2793.87	+	6744.99i	0.128006	+	0.309033i
$782$	23117.8	−	63836.4i	1.05715	−	2.91916i
$783$	−7209.87	−	7209.87i	−0.329068	−	0.329068i
$784$	−3729.67	−	20380.9i	−0.169901	−	0.928428i
$785$	−7415.60	+	29530.2i	−0.337164	+	1.34265i
$786$	6384.65	−	2989.78i	0.289737	−	0.135677i
$787$	5650.30	−	13641.0i	0.255923	−	0.617853i	−0.742738	−	0.669582i	$-0.766473\pi$
$787$	5650.30	−	13641.0i	0.255923	−	0.617853i	0.998661	+	0.0517291i	$0.0164732\pi$
$788$	−17363.3	−	5413.01i	−0.784954	−	0.244709i
$789$	−2347.31	+	5666.90i	−0.105914	+	0.255700i
$790$	−6250.69	−	9445.20i	−0.281506	−	0.425373i
$791$	2888.66	+	2888.66i	0.129847	+	0.129847i
$792$	1400.38	+	10252.6i	0.0628287	+	0.459990i
$793$		−	16886.1i		−	0.756171i
$794$	8888.76	−	402.483i	0.397293	−	0.0179894i
$795$	5501.02	−	812.657i	0.245410	−	0.0362541i
$796$	−39842.6	+	3615.55i	−1.77410	+	0.160992i
$797$	−13193.1	+	31851.0i	−0.586354	+	1.41558i	0.300610	+	0.953747i	$0.402810\pi$
$797$	−13193.1	+	31851.0i	−0.586354	+	1.41558i	−0.886964	+	0.461838i	$0.847190\pi$
$798$	−719.292	−	1536.04i	−0.0319081	−	0.0681395i
$799$	24064.3			1.06550
$800$	17896.0	+	13846.7i	0.790901	+	0.611945i
$801$	22255.5			0.981720
$802$	−4199.83	−	8968.70i	−0.184914	−	0.394883i
$803$	−3414.09	+	8242.33i	−0.150038	+	0.362224i
$804$	821.362	+	9051.23i	0.0360289	+	0.397030i
$805$	−9460.62	+	1397.60i	−0.414215	+	0.0611913i
$806$	23017.7	−	1042.24i	1.00591	−	0.0455476i
$807$			6305.45i			0.275046i
$808$	4389.45	+	3334.46i	0.191114	+	0.145181i
$809$	10514.0	+	10514.0i	0.456924	+	0.456924i	0.897645	−	0.440720i	$-0.145277\pi$
$809$	10514.0	+	10514.0i	0.456924	+	0.456924i	−0.440720	+	0.897645i	$0.645277\pi$
$810$	10047.2	+	15181.9i	0.435828	+	0.658564i
$811$	−8209.30	+	19819.0i	−0.355447	+	0.858125i	0.640481	+	0.767974i	$0.278735\pi$
$811$	−8209.30	+	19819.0i	−0.355447	+	0.858125i	−0.995928	+	0.0901508i	$0.971265\pi$
$812$	1469.73	−	4714.47i	0.0635192	−	0.203751i
$813$	−1523.04	+	3676.93i	−0.0657013	+	0.158617i
$814$	−6253.39	+	2928.31i	−0.269264	+	0.126090i
$815$	379.348	−	1510.63i	0.0163043	−	0.0649264i
$816$	5956.95	+	9218.51i	0.255557	+	0.395481i
$817$	−1408.31	−	1408.31i	−0.0603067	−	0.0603067i
$818$	3479.61	−	9608.43i	0.148731	−	0.410698i
$819$	1145.07	+	2764.43i	0.0488545	+	0.117945i
$820$	8209.44	+	33963.4i	0.349617	+	1.44640i
$821$	−21991.9	−	9109.36i	−0.934865	−	0.387234i	−0.137343	−	0.990524i	$-0.543856\pi$
$821$	−21991.9	−	9109.36i	−0.934865	−	0.387234i	−0.797522	+	0.603290i	$0.793856\pi$
$822$	−2750.01	+	124.520i	−0.116688	+	0.00528364i
$823$			26861.4i			1.13770i	0.822441	+	0.568850i	$0.192612\pi$
$823$			26861.4i			1.13770i	−0.822441	+	0.568850i	$0.807388\pi$
$824$	4943.87	−	18815.1i	0.209015	−	0.795457i
$825$	−2799.39	−	1500.59i	−0.118136	−	0.0633258i
$826$	10508.8	−	475.837i	0.442672	−	0.0200442i
$827$	10125.7	−	4194.21i	0.425763	−	0.176357i	−0.159504	−	0.987197i	$-0.550990\pi$
$827$	10125.7	−	4194.21i	0.425763	−	0.176357i	0.585267	+	0.810840i	$0.300990\pi$
$828$	−3531.42	−	38915.5i	−0.148219	−	1.63334i
$829$	−11895.1	−	28717.2i	−0.498350	−	1.20312i	−0.950372	−	0.311117i	$-0.899297\pi$
$829$	−11895.1	−	28717.2i	−0.498350	−	1.20312i	0.452022	−	0.892007i	$-0.350703\pi$
$830$	1971.96	−	383.168i	0.0824673	−	0.0160241i
$831$			3215.08i			0.134211i
$832$	−10968.0	+	8586.25i	−0.457027	+	0.357782i
$833$	−28193.5	−	28193.5i	−1.17268	−	1.17268i
$834$	1002.90	−	2769.37i	0.0416400	−	0.114983i
$835$	332.657	+	2251.81i	0.0137869	+	0.0933261i
$836$	9172.41	−	11003.3i	0.379467	−	0.455210i
$837$	−8307.01	−	20054.9i	−0.343049	−	0.828194i
$838$	8184.25	−	8960.57i	0.337375	−	0.369377i
$839$	3865.38	+	3865.38i	0.159056	+	0.159056i	0.782148	−	0.623093i	$-0.214124\pi$
$839$	3865.38	+	3865.38i	0.159056	+	0.159056i	−0.623093	+	0.782148i	$0.714124\pi$
$840$	745.241	−	1354.53i	0.0306110	−	0.0556379i
$841$	3256.96	−	3256.96i	0.133542	−	0.133542i
$842$	952.695	+	21040.1i	0.0389929	+	0.861152i
$843$	−7235.58	+	2997.08i	−0.295619	+	0.122449i
$844$	−276.462	+	886.807i	−0.0112751	+	0.0361673i
$845$	−13077.1	−	9710.71i	−0.532387	−	0.395336i
$846$	12542.9	−	5873.53i	0.509732	−	0.238695i
$847$	−3097.12	+	3097.12i	−0.125641	+	0.125641i
$848$	−19200.0	+	12406.9i	−0.777511	+	0.502423i
$849$	9696.08			0.391953
$850$	43479.8	+	2355.20i	1.75452	+	0.0950386i
$851$	24090.0	−	9978.40i	0.970381	−	0.401945i
$852$	4254.85	+	1326.45i	0.171090	+	0.0533372i
$853$	15711.3	+	37930.5i	0.630651	+	1.52253i	0.838807	+	0.544429i	$0.183254\pi$
$853$	15711.3	+	37930.5i	0.630651	+	1.52253i	−0.208156	+	0.978096i	$0.566746\pi$
$854$	−5688.95	−	5196.08i	−0.227953	−	0.208204i
$855$	6696.42	−	26666.3i	0.267851	−	1.06663i
$856$	−31440.6	+	4294.37i	−1.25539	+	0.171470i
$857$	−15626.7			−0.622870			−0.311435	−	0.950267i	$-0.600810\pi$
$857$	−15626.7			−0.622870			−0.311435	+	0.950267i	$0.600810\pi$
$858$	1318.61	−	1443.68i	0.0524667	−	0.0574435i
$859$	13908.1	−	33577.2i	0.552433	−	1.33369i	−0.363213	−	0.931706i	$-0.618320\pi$
$859$	13908.1	−	33577.2i	0.552433	−	1.33369i	0.915646	−	0.401985i	$-0.131680\pi$
$860$	281.217	−	1793.48i	0.0111505	−	0.0711129i
$861$	2205.63	−	913.604i	0.0873029	−	0.0361621i
$862$	−41245.8	+	19314.4i	−1.62974	+	0.763169i
$863$	−28444.4	+	28444.4i	−1.12197	+	1.12197i	−0.130522	+	0.991445i	$0.541665\pi$
$863$	−28444.4	+	28444.4i	−1.12197	+	1.12197i	−0.991445	+	0.130522i	$0.958335\pi$
$864$	11124.1	+	6961.16i	0.438022	+	0.274101i
$865$	6719.27	−	26757.3i	0.264118	−	1.05176i
$866$	14527.6	−	40115.7i	0.570054	−	1.57412i
$867$	13193.1	+	5464.77i	0.516795	+	0.214064i
$868$	6731.71	−	8075.39i	0.263236	−	0.315780i
$869$	−6038.31	−	2501.15i	−0.235714	−	0.0976360i
$870$	−5164.83	+	3418.01i	−0.201269	+	0.133197i
$871$	−15694.7	+	15694.7i	−0.610556	+	0.610556i
$872$	−2320.94	−	16992.4i	−0.0901341	−	0.659902i
$873$	26478.3			1.02652
$874$	−36480.8	+	39941.1i	−1.41188	+	1.54580i
$875$	−2612.48	−	5549.22i	−0.100935	−	0.214398i
$876$	2530.37	+	4822.68i	0.0975951	+	0.186008i
$877$	17259.8	+	7149.22i	0.664562	+	0.275270i	0.689357	−	0.724422i	$-0.257893\pi$
$877$	17259.8	+	7149.22i	0.664562	+	0.275270i	−0.0247951	+	0.999693i	$0.507893\pi$
$878$	10092.4	−	27868.7i	0.387930	−	1.07121i
$879$		−	7569.40i		−	0.290455i
$880$	13029.6	+	848.583i	0.499123	+	0.0325065i
$881$		−	18203.4i		−	0.696126i	−0.937471	−	0.348063i	$-0.886839\pi$
$881$		−	18203.4i		−	0.696126i	0.937471	−	0.348063i	$-0.113161\pi$
$882$	−21576.4	−	7813.72i	−0.823715	−	0.298301i
$883$	18005.4	+	7458.09i	0.686218	+	0.284241i	0.698424	−	0.715685i	$-0.253885\pi$
$883$	18005.4	+	7458.09i	0.686218	+	0.284241i	−0.0122053	+	0.999926i	$0.503885\pi$
$884$	−7977.69	+	25590.1i	−0.303528	+	0.973628i
$885$	−10592.3	−	7865.53i	−0.402323	−	0.298754i
$886$	−6937.37	−	6336.33i	−0.263054	−	0.240263i
$887$	35176.9			1.33159			0.665797	−	0.746133i	$-0.268092\pi$
$887$	35176.9			1.33159			0.665797	+	0.746133i	$0.268092\pi$
$888$	−1071.24	+	4076.89i	−0.0404827	+	0.154067i
$889$	−4213.06	+	4213.06i	−0.158944	+	0.158944i
$890$	5600.69	−	27518.4i	0.210939	−	1.03643i
$891$	9705.78	+	4020.26i	0.364933	+	0.151160i
$892$	−2237.08	−	24652.1i	−0.0839718	−	0.925351i
$893$	−17713.7	−	7337.25i	−0.663792	−	0.274951i
$894$	−1913.78	−	693.060i	−0.0715956	−	0.0259277i
$895$	−2015.84	−	3367.76i	−0.0752872	−	0.125779i
$896$	−482.277	+	6337.22i	−0.0179818	+	0.236285i
$897$	−5220.80	+	5220.80i	−0.194334	+	0.194334i
$898$	−11607.8	−	24788.3i	−0.431354	−	0.921153i
$899$	−38910.7	+	16117.3i	−1.44354	+	0.597935i
$900$	23237.5	−	9384.80i	0.860648	−	0.347585i
$901$	−16834.5	+	40642.1i	−0.622462	+	1.50276i
$902$	14887.8	+	13597.9i	0.549566	+	0.501953i
$903$	−124.036			−0.00457105
$904$	10619.5	+	18189.4i	0.390708	+	0.669213i
$905$	19874.9	+	4990.96i	0.730014	+	0.183320i
$906$	−668.440	+	731.844i	−0.0245115	+	0.0268365i
$907$	−8009.21	−	19335.9i	−0.293210	−	0.707872i	−1.00000		0.000448085i	$-0.999857\pi$
$907$	−8009.21	−	19335.9i	−0.293210	−	0.707872i	0.706790	−	0.707424i	$-0.250143\pi$
$908$	30749.8	−	16133.8i	1.12386	−	0.589669i
$909$	5640.47	−	2336.36i	0.205812	−	0.0852499i
$910$	3706.33	−	720.170i	0.135015	−	0.0262345i
$911$	36146.4			1.31458			0.657291	−	0.753637i	$-0.271702\pi$
$911$	36146.4			1.31458			0.657291	+	0.753637i	$0.271702\pi$
$912$	−1574.16	−	8602.00i	−0.0571552	−	0.312325i
$913$	819.685	−	819.685i	0.0297126	−	0.0297126i
$914$	4468.99	+	9543.48i	0.161730	+	0.345372i
$915$	1412.18	+	9559.33i	0.0510223	+	0.345379i
$916$	−646.499	+	339.206i	−0.0233198	+	0.0122355i
$917$	7257.95	−	3006.34i	0.261372	−	0.108264i
$918$	25227.0	−	1142.28i	0.906988	−	0.0410684i
$919$	25024.4	−	25024.4i	0.898236	−	0.898236i	−0.0970439	−	0.995280i	$-0.530939\pi$
$919$	25024.4	−	25024.4i	0.898236	−	0.898236i	0.995280	+	0.0970439i	$0.0309387\pi$
$920$	−49007.0	−	5426.72i	−1.75621	−	0.194471i
$921$	1692.85	+	1692.85i	0.0605659	+	0.0605659i
$922$	−6799.73	−	6210.62i	−0.242882	−	0.221839i
$923$	4165.28	+	10055.9i	0.148539	+	0.358605i
$924$	−80.6259	−	888.479i	−0.00287056	−	0.0316329i
$925$	10593.6	+	12939.7i	0.376559	+	0.459953i
$926$	−36568.1	−	13242.8i	−1.29774	−	0.469964i
$927$	−15235.4	−	15235.4i	−0.539802	−	0.539802i
$928$	13506.1	−	21583.2i	0.477758	−	0.763472i
$929$			34790.8i			1.22869i	0.789039	+	0.614344i	$0.210579\pi$
$929$			34790.8i			1.22869i	−0.789039	+	0.614344i	$0.789421\pi$
$930$	−12943.3	+	2514.98i	−0.456373	+	0.0886770i
$931$	12156.9	+	29349.4i	0.427955	+	1.03318i
$932$	−12033.9	+	14435.9i	−0.422942	+	0.507363i
$933$	−8010.33	+	3317.99i	−0.281079	+	0.116427i
$934$	−829.613	−	18321.9i	−0.0290640	−	0.641873i
$935$	21559.7	−	12905.0i	0.754095	−	0.451378i
$936$	2087.78	+	15285.3i	0.0729071	+	0.533778i
$937$			44073.0i			1.53661i	0.640085	+	0.768304i	$0.278899\pi$
$937$			44073.0i			1.53661i	−0.640085	+	0.768304i	$0.721101\pi$
$938$	458.098	+	10117.0i	0.0159461	+	0.352167i
$939$	−13676.0	−	5664.77i	−0.475291	−	0.196872i
$940$	−4106.04	−	16987.1i	−0.142473	−	0.589425i
$941$	−9968.74	−	24066.7i	−0.345347	−	0.833742i	−0.997156	−	0.0753588i	$-0.975990\pi$
$941$	−9968.74	−	24066.7i	−0.345347	−	0.833742i	0.651809	−	0.758383i	$-0.274010\pi$
$942$	10084.6	+	3652.07i	0.348806	+	0.126317i
$943$	−53838.8	−	53838.8i	−1.85921	−	1.85921i
$944$	53025.9	+	11396.5i	1.82823	+	0.392929i
$945$	−1826.88	−	3052.07i	−0.0628870	−	0.105062i
$946$	−444.258	−	948.710i	−0.0152686	−	0.0326059i
$947$	−16724.6	+	40376.9i	−0.573894	+	1.38550i	0.324321	+	0.945947i	$0.394864\pi$
$947$	−16724.6	+	40376.9i	−0.573894	+	1.38550i	−0.898215	+	0.439556i	$0.855136\pi$
$948$	−3533.08	+	1853.74i	−0.121044	+	0.0635093i
$949$	−5089.94	+	12288.2i	−0.174106	+	0.420329i
$950$	−31287.2	−	14990.7i	−1.06852	−	0.511961i
$951$	−694.865	−	694.865i	−0.0236935	−	0.0236935i
$952$	6166.48	+	10562.1i	0.209934	+	0.359579i
$953$		−	3266.63i		−	0.111035i	−0.998458	−	0.0555176i	$-0.982319\pi$
$953$		−	3266.63i		−	0.111035i	0.998458	−	0.0555176i	$-0.0176809\pi$
$954$	1145.24	+	25292.5i	0.0388665	+	0.858359i
$955$	−1127.11	−	7629.60i	−0.0381910	−	0.258522i
$956$	17281.7	+	14406.2i	0.584656	+	0.487373i
$957$	−1367.68	+	3301.88i	−0.0461974	+	0.111530i
$958$	−28732.6	+	13454.8i	−0.969005	+	0.453762i
$959$	−3067.53			−0.103291
$960$	5490.97	−	5777.97i	0.184605	−	0.194253i
$961$	−59872.5			−2.00975
$962$	−9322.96	+	4365.72i	−0.312458	+	0.146316i
$963$	−13449.5	+	32470.1i	−0.450058	+	1.08654i
$964$	−32221.1	−	26859.8i	−1.07653	−	0.897401i
$965$	−13715.4	−	10184.6i	−0.457526	−	0.339746i
$966$	152.385	+	3365.40i	0.00507548	+	0.112091i
$967$			19957.7i			0.663698i	0.943333	+	0.331849i	$0.107672\pi$
$967$			19957.7i			0.663698i	−0.943333	+	0.331849i	$0.892328\pi$
$968$	−19502.0	+	11385.9i	−0.647538	+	0.378053i
$969$	−11899.4	−	11899.4i	−0.394494	−	0.394494i
$970$	6663.39	−	32739.9i	0.220565	−	1.08373i
$971$	−6543.01	+	15796.2i	−0.216246	+	0.522065i	−0.994360	−	0.106059i	$-0.966177\pi$
$971$	−6543.01	+	15796.2i	−0.216246	+	0.522065i	0.778113	+	0.628124i	$0.216177\pi$
$972$	19544.8	−	10254.8i	0.644959	−	0.338398i
$973$	1256.00	−	3032.25i	0.0413828	−	0.0999069i
$974$	−10567.8	−	22567.4i	−0.347653	−	0.742410i
$975$	−4173.51	−	2237.17i	−0.137086	−	0.0734839i
$976$	−21559.9	−	33364.5i	−0.707087	−	1.09423i
$977$	26603.6	+	26603.6i	0.871161	+	0.871161i	0.992599	−	0.121438i	$-0.0387505\pi$
$977$	26603.6	+	26603.6i	0.871161	+	0.871161i	−0.121438	+	0.992599i	$0.538751\pi$
$978$	−515.884	−	186.823i	−0.0168672	−	0.00610832i
$979$	−6201.44	−	14971.6i	−0.202450	−	0.488758i
$980$	−15091.3	+	24712.5i	−0.491913	+	0.805522i
$981$	−17548.8	−	7268.95i	−0.571141	−	0.236575i
$982$	−1948.64	−	43035.5i	−0.0633235	−	1.39849i
$983$		−	1333.07i		−	0.0432536i	−0.999766	−	0.0216268i	$-0.993115\pi$
$983$		−	1333.07i		−	0.0432536i	0.999766	−	0.0216268i	$-0.00688457\pi$
$984$	12195.5	−	1665.75i	0.395101	−	0.0539658i
$985$	13054.4	+	21809.4i	0.422283	+	0.705487i
$986$	−2216.26	−	48945.7i	−0.0715821	−	1.58088i
$987$	−1103.17	+	456.948i	−0.0355768	+	0.0147364i
$988$	13674.8	−	16404.4i	0.440338	−	0.528232i
$989$	1513.84	+	3654.72i	0.0486726	+	0.117506i
$990$	8087.63	−	11988.6i	0.259638	−	0.384872i
$991$		−	19096.0i		−	0.612114i	−0.952013	−	0.306057i	$-0.900990\pi$
$991$		−	19096.0i		−	0.612114i	0.952013	−	0.306057i	$-0.0990099\pi$
$992$	44148.9	−	31448.0i	1.41303	−	1.00653i
$993$	3012.47	+	3012.47i	0.0962716	+	0.0962716i
$994$	4669.54	+	1691.03i	0.149003	+	0.0539601i
$995$	44887.9	+	33332.5i	1.43019	+	1.06202i
$996$	−63.9539	−	704.757i	−0.00203459	−	0.0224208i
$997$	4611.95	+	11134.2i	0.146501	+	0.353685i	0.980047	−	0.198765i	$-0.0636930\pi$
$997$	4611.95	+	11134.2i	0.146501	+	0.353685i	−0.833546	+	0.552450i	$0.813693\pi$
$998$	39522.8	+	36098.7i	1.25358	+	1.14497i
$999$	6857.87	+	6857.87i	0.217191	+	0.217191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.4.u.a.43.10	✓	280
5.2	odd	4		160.4.ba.a.107.25	yes	280
32.3	odd	8		160.4.ba.a.3.25	yes	280
160.67	even	8	inner	160.4.u.a.67.10	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.4.u.a.43.10	✓	280	1.1	even	1	trivial
160.4.u.a.67.10	yes	280	160.67	even	8	inner
160.4.ba.a.3.25	yes	280	32.3	odd	8
160.4.ba.a.107.25	yes	280	5.2	odd	4

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	160.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.56149 + 1.19949i) q^{2} +(0.532873 - 1.28647i) q^{3} +(5.12247 - 6.14494i) q^{4} +(-11.0603 + 1.63392i) q^{5} +(0.178152 + 3.93445i) q^{6} +4.38872i q^{7} +(-5.75039 + 21.8845i) q^{8} +(17.7208 + 17.7208i) q^{9} +(26.3710 - 17.4519i) q^{10} +(6.98321 - 16.8590i) q^{11} +(-5.17565 - 9.86438i) q^{12} +(10.4110 - 25.1344i) q^{13} +(-5.26421 - 11.2417i) q^{14} +(-3.79175 + 15.0994i) q^{15} +(-11.5206 - 62.9546i) q^{16} +(-87.0870 - 87.0870i) q^{17} +(-66.6476 - 24.1359i) q^{18} +(37.5516 + 90.6575i) q^{19} +(-46.6157 + 76.3346i) q^{20} +(5.64596 + 2.33863i) q^{21} +(2.33465 + 51.5604i) q^{22} -194.901i q^{23} +(25.0896 + 19.0594i) q^{24} +(119.661 - 36.1433i) q^{25} +(3.48065 + 76.8695i) q^{26} +(66.9749 - 27.7419i) q^{27} +(26.9684 + 22.4811i) q^{28} +(-53.8252 - 129.945i) q^{29} +(-8.39900 - 43.2252i) q^{30} -299.439i q^{31} +(105.023 + 147.439i) q^{32} +(-17.9674 - 17.9674i) q^{33} +(327.532 + 118.613i) q^{34} +(-7.17082 - 48.5406i) q^{35} +(199.668 - 18.1191i) q^{36} +(51.1973 + 123.601i) q^{37} +(-204.930 - 187.176i) q^{38} +(-26.7869 - 26.7869i) q^{39} +(27.8435 - 251.445i) q^{40} +(276.236 - 276.236i) q^{41} +(-17.2672 + 0.781859i) q^{42} +(-18.7517 + 7.76720i) q^{43} +(-67.8261 - 129.271i) q^{44} +(-224.952 - 167.043i) q^{45} +(233.781 + 499.237i) q^{46} +(-138.163 + 138.163i) q^{47} +(-87.1281 - 18.7259i) q^{48} +323.739 q^{49} +(-263.156 + 236.112i) q^{50} +(-158.441 + 65.6284i) q^{51} +(-101.119 - 192.725i) q^{52} +(-136.689 - 329.995i) q^{53} +(-138.280 + 151.396i) q^{54} +(-49.6902 + 197.875i) q^{55} +(-96.0452 - 25.2369i) q^{56} +136.638 q^{57} +(293.740 + 268.291i) q^{58} +(-324.305 + 782.941i) q^{59} +(73.3619 + 100.646i) q^{60} +(573.445 - 237.529i) q^{61} +(359.172 + 767.009i) q^{62} +(-77.7718 + 77.7718i) q^{63} +(-445.866 - 251.689i) q^{64} +(-74.0814 + 295.005i) q^{65} +(67.5749 + 24.4717i) q^{66} +(-753.754 - 312.215i) q^{67} +(-981.245 + 89.0440i) q^{68} +(-250.734 - 103.858i) q^{69} +(76.5917 + 115.735i) q^{70} +(-282.902 + 282.902i) q^{71} +(-489.714 + 285.911i) q^{72} -488.899 q^{73} +(-279.399 - 255.193i) q^{74} +(17.2667 - 173.200i) q^{75} +(749.442 + 233.638i) q^{76} +(73.9893 + 30.6474i) q^{77} +(100.745 + 36.4839i) q^{78} -358.166i q^{79} +(230.284 + 677.473i) q^{80} +575.704i q^{81} +(-376.235 + 1038.92i) q^{82} +(58.6897 + 24.3101i) q^{83} +(43.2920 - 22.7145i) q^{84} +(1105.50 + 820.915i) q^{85} +(38.7156 - 42.3880i) q^{86} -195.853 q^{87} +(328.795 + 249.770i) q^{88} +(627.946 - 627.946i) q^{89} +(776.579 + 158.053i) q^{90} +(110.308 + 45.6911i) q^{91} +(-1197.66 - 998.375i) q^{92} +(-385.219 - 159.563i) q^{93} +(188.178 - 519.626i) q^{94} +(-563.459 - 941.343i) q^{95} +(245.639 - 56.5428i) q^{96} +(747.095 - 747.095i) q^{97} +(-829.255 + 388.320i) q^{98} +(422.503 - 175.007i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} + 80 q^{8} + 8 q^{10} - 8 q^{11} + 44 q^{12} - 4 q^{13} + 64 q^{14} - 8 q^{15} - 8 q^{16} + 28 q^{18} - 48 q^{19} - 312 q^{20} - 8 q^{21} - 436 q^{22} + 736 q^{24}+ \cdots + 3480 q^{98}+O(q^{100}) \) 280 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 + 80 * q^8 + 8 * q^10 - 8 * q^11 + 44 * q^12 - 4 * q^13 + 64 * q^14 - 8 * q^15 - 8 * q^16 + 28 * q^18 - 48 * q^19 - 312 * q^20 - 8 * q^21 - 436 * q^22 + 736 * q^24 - 4 * q^25 - 8 * q^26 - 112 * q^27 + 252 * q^28 - 1696 * q^30 - 344 * q^32 - 8 * q^33 + 696 * q^34 + 952 * q^35 - 8 * q^36 - 4 * q^37 - 172 * q^38 + 816 * q^40 - 8 * q^41 - 460 * q^42 + 860 * q^43 + 1232 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 + 3496 * q^48 - 11368 * q^49 - 36 * q^50 + 1480 * q^51 - 328 * q^52 - 4 * q^53 + 2968 * q^54 - 292 * q^55 - 344 * q^56 - 8 * q^57 - 2020 * q^58 + 252 * q^60 + 1816 * q^61 - 440 * q^62 + 2744 * q^63 + 816 * q^64 - 8 * q^65 + 552 * q^66 + 1844 * q^67 + 1224 * q^68 + 216 * q^69 + 1764 * q^70 - 232 * q^71 - 3432 * q^72 - 8 * q^73 + 104 * q^75 + 824 * q^76 + 1368 * q^77 - 5968 * q^78 - 1800 * q^80 + 588 * q^82 + 2676 * q^83 + 2744 * q^84 - 4 * q^85 - 1192 * q^86 + 2568 * q^87 - 5880 * q^88 - 84 * q^90 - 8 * q^91 - 3284 * q^92 + 104 * q^93 + 416 * q^94 + 6168 * q^96 - 8 * q^97 + 3480 * q^98

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