LMFDB - Embedded newform 31.5.h.a.11.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,5,Mod(3,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.3"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	31.h (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.20446885560$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	31.11
Dual form			31.5.h.a.17.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.970390 + 2.98655i) q^{2} +(3.96725 - 3.57213i) q^{3} +(4.96643 - 3.60832i) q^{4} +(13.2322 + 22.9188i) q^{5} +(14.5181 + 8.38205i) q^{6} +(-5.15690 - 49.0646i) q^{7} +(56.2440 + 40.8637i) q^{8} +(-5.48783 + 52.2132i) q^{9} +(-55.6079 + 61.7588i) q^{10} +(-55.9128 + 125.582i) q^{11} +(6.81368 - 32.0559i) q^{12} +(-55.1111 - 259.277i) q^{13} +(141.530 - 63.0131i) q^{14} +(134.364 + 43.6576i) q^{15} +(-37.1108 + 114.215i) q^{16} +(-212.733 - 477.805i) q^{17} +(-161.263 + 34.2775i) q^{18} +(-35.5978 - 7.56655i) q^{19} +(148.415 + 66.0787i) q^{20} +(-195.724 - 176.230i) q^{21} +(-429.315 - 45.1228i) q^{22} +(-279.407 + 384.571i) q^{23} +(369.105 - 38.7945i) q^{24} +(-37.6817 + 65.2666i) q^{25} +(720.866 - 416.192i) q^{26} +(418.908 + 576.578i) q^{27} +(-202.652 - 225.068i) q^{28} +(-859.313 + 279.208i) q^{29} +443.651i q^{30} +(-806.998 + 521.799i) q^{31} +735.221 q^{32} +(226.776 + 697.944i) q^{33} +(1220.56 - 1098.99i) q^{34} +(1056.27 - 767.422i) q^{35} +(161.147 + 279.115i) q^{36} +(969.351 + 559.655i) q^{37} +(-11.9459 - 113.657i) q^{38} +(-1144.81 - 831.754i) q^{39} +(-192.316 + 1829.76i) q^{40} +(530.399 - 589.067i) q^{41} +(336.393 - 755.552i) q^{42} +(174.735 - 822.062i) q^{43} +(175.454 + 825.447i) q^{44} +(-1269.28 + 565.120i) q^{45} +(-1419.68 - 461.281i) q^{46} +(-16.9627 + 52.2059i) q^{47} +(260.764 + 585.685i) q^{48} +(-32.2080 + 6.84602i) q^{49} +(-231.488 - 49.2043i) q^{50} +(-2550.75 - 1135.67i) q^{51} +(-1209.26 - 1088.82i) q^{52} +(1005.95 + 105.729i) q^{53} +(-1315.48 + 1810.60i) q^{54} +(-3618.04 + 380.272i) q^{55} +(1714.92 - 2970.32i) q^{56} +(-168.254 + 97.1416i) q^{57} +(-1667.74 - 2295.44i) q^{58} +(2048.95 + 2275.59i) q^{59} +(824.843 - 268.008i) q^{60} -3291.45i q^{61} +(-2341.48 - 1903.79i) q^{62} +2590.12 q^{63} +(1307.22 + 4023.22i) q^{64} +(5213.09 - 4693.89i) q^{65} +(-1864.39 + 1354.56i) q^{66} +(4033.66 + 6986.50i) q^{67} +(-2780.60 - 1605.38i) q^{68} +(265.259 + 2523.77i) q^{69} +(3316.94 + 2409.89i) q^{70} +(830.831 - 7904.83i) q^{71} +(-2442.28 + 2712.43i) q^{72} +(-1679.33 + 3771.83i) q^{73} +(-730.791 + 3438.10i) q^{74} +(83.6480 + 393.533i) q^{75} +(-204.097 + 90.8696i) q^{76} +(6449.97 + 2095.72i) q^{77} +(1373.16 - 4226.17i) q^{78} +(1193.65 + 2680.97i) q^{79} +(-3108.74 + 660.782i) q^{80} +(-438.112 - 93.1237i) q^{81} +(2273.97 + 1012.44i) q^{82} +(809.495 + 728.873i) q^{83} +(-1607.95 - 169.002i) q^{84} +(8135.82 - 11198.0i) q^{85} +(2624.69 - 275.866i) q^{86} +(-2411.74 + 4177.26i) q^{87} +(-8276.51 + 4778.45i) q^{88} +(-2807.44 - 3864.11i) q^{89} +(-2919.46 - 3242.39i) q^{90} +(-12437.1 + 4041.07i) q^{91} +2918.14i q^{92} +(-1337.63 + 4952.81i) q^{93} -172.376 q^{94} +(-297.621 - 915.982i) q^{95} +(2916.81 - 2626.31i) q^{96} +(6120.59 - 4446.87i) q^{97} +(-51.7003 - 89.5475i) q^{98} +(-6250.21 - 3608.56i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{2} - 16 q^{3} - 138 q^{4} - q^{5} - 9 q^{6} + 288 q^{7} - 221 q^{8} - 182 q^{9} + 102 q^{10} - 49 q^{11} - 159 q^{12} + 527 q^{13} - 740 q^{14} + 1060 q^{15} - 1970 q^{16} + 848 q^{17} + 3 q^{18}+ \cdots + 75228 q^{99}+O(q^{100}) $ 80 * q - 6 * q^2 - 16 * q^3 - 138 * q^4 - q^5 - 9 * q^6 + 288 * q^7 - 221 * q^8 - 182 * q^9 + 102 * q^10 - 49 * q^11 - 159 * q^12 + 527 * q^13 - 740 * q^14 + 1060 * q^15 - 1970 * q^16 + 848 * q^17 + 3 * q^18 + 1534 * q^19 + 1165 * q^20 + 1367 * q^21 + 4579 * q^22 - 1375 * q^23 - 3828 * q^24 - 5997 * q^25 - 2547 * q^26 - 3235 * q^27 - 1564 * q^28 - 1150 * q^29 - 3587 * q^31 + 15718 * q^32 - 5029 * q^33 + 5958 * q^34 + 4959 * q^35 + 13555 * q^36 + 3462 * q^37 + 6118 * q^38 - 8143 * q^39 - 13011 * q^40 - 7290 * q^41 - 24735 * q^42 + 4687 * q^43 + 17051 * q^44 - 6093 * q^45 - 16530 * q^46 - 4302 * q^47 + 40344 * q^48 + 14300 * q^49 + 30081 * q^50 + 1348 * q^51 - 14433 * q^52 + 17996 * q^53 - 42200 * q^54 - 5289 * q^55 - 32470 * q^56 - 35847 * q^57 - 38475 * q^58 + 3552 * q^59 - 26585 * q^60 - 6327 * q^62 + 35814 * q^63 + 231 * q^64 + 18280 * q^65 + 85992 * q^66 + 2185 * q^67 + 56694 * q^68 + 57836 * q^69 + 6338 * q^70 - 3708 * q^71 - 25127 * q^72 + 5344 * q^73 + 5247 * q^74 + 13921 * q^75 - 10354 * q^76 - 37000 * q^77 - 98345 * q^78 + 53300 * q^79 + 65286 * q^80 + 20439 * q^81 - 26142 * q^82 - 59542 * q^83 - 77120 * q^84 + 4525 * q^85 - 100990 * q^86 - 55761 * q^87 - 82191 * q^88 - 26395 * q^89 - 61689 * q^90 - 12450 * q^91 + 9029 * q^93 + 67112 * q^94 - 3972 * q^95 + 210490 * q^96 + 5883 * q^97 + 107722 * q^98 + 75228 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{23}{30}\right)$

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 $

$2$	0.970390	+	2.98655i	0.242597	+	0.746638i	0.996022	+	0.0891042i	$0.0284004\pi$
$2$	0.970390	+	2.98655i	0.242597	+	0.746638i	−0.753425	+	0.657534i	$0.771600\pi$
$3$	3.96725	−	3.57213i	0.440806	−	0.396903i	−0.418622	−	0.908161i	$-0.637487\pi$
$3$	3.96725	−	3.57213i	0.440806	−	0.396903i	0.859428	+	0.511257i	$0.170820\pi$
$4$	4.96643	−	3.60832i	0.310402	−	0.225520i
$5$	13.2322	+	22.9188i	0.529288	+	0.916753i	0.999417	+	0.0341552i	$0.0108741\pi$
$5$	13.2322	+	22.9188i	0.529288	+	0.916753i	−0.470129	+	0.882598i	$0.655793\pi$
$6$	14.5181	+	8.38205i	0.403281	+	0.232835i
$7$	−5.15690	−	49.0646i	−0.105243	−	1.00132i	−0.911932	−	0.410342i	$-0.865409\pi$
$7$	−5.15690	−	49.0646i	−0.105243	−	1.00132i	0.806689	−	0.590976i	$-0.201257\pi$
$8$	56.2440	+	40.8637i	0.878813	+	0.638495i
$9$	−5.48783	+	52.2132i	−0.0677510	+	0.644607i
$10$	−55.6079	+	61.7588i	−0.556079	+	0.617588i
$11$	−55.9128	+	125.582i	−0.462089	+	1.03787i	0.520801	+	0.853678i	$0.325633\pi$
$11$	−55.9128	+	125.582i	−0.462089	+	1.03787i	−0.982890	+	0.184191i	$0.941033\pi$
$12$	6.81368	−	32.0559i	0.0473172	−	0.222610i
$13$	−55.1111	−	259.277i	−0.326101	−	1.53419i	−0.769962	−	0.638090i	$-0.779725\pi$
$13$	−55.1111	−	259.277i	−0.326101	−	1.53419i	0.443861	−	0.896096i	$-0.353608\pi$
$14$	141.530	−	63.0131i	0.722091	−	0.321496i
$15$	134.364	+	43.6576i	0.597175	+	0.194034i
$16$	−37.1108	+	114.215i	−0.144964	+	0.446153i
$17$	−212.733	−	477.805i	−0.736099	−	1.65331i	−0.756907	−	0.653522i	$-0.773291\pi$
$17$	−212.733	−	477.805i	−0.736099	−	1.65331i	0.0208081	−	0.999783i	$-0.493376\pi$
$18$	−161.263	+	34.2775i	−0.497725	+	0.105795i
$19$	−35.5978	−	7.56655i	−0.0986089	−	0.0209600i	0.158343	−	0.987384i	$-0.449385\pi$
$19$	−35.5978	−	7.56655i	−0.0986089	−	0.0209600i	−0.256952	+	0.966424i	$0.582718\pi$
$20$	148.415	+	66.0787i	0.371038	+	0.165197i
$21$	−195.724	−	176.230i	−0.443818	−	0.399616i
$22$	−429.315	−	45.1228i	−0.887014	−	0.0932290i
$23$	−279.407	+	384.571i	−0.528180	+	0.726977i	−0.986852	−	0.161628i	$-0.948325\pi$
$23$	−279.407	+	384.571i	−0.528180	+	0.726977i	0.458672	+	0.888606i	$0.348325\pi$
$24$	369.105	−	38.7945i	0.640807	−	0.0673515i
$25$	−37.6817	+	65.2666i	−0.0602907	+	0.104427i
$26$	720.866	−	416.192i	1.06637	−	0.615669i
$27$	418.908	+	576.578i	0.574634	+	0.790916i
$28$	−202.652	−	225.068i	−0.258485	−	0.287077i
$29$	−859.313	+	279.208i	−1.02178	+	0.331995i	−0.771534	−	0.636189i	$-0.780510\pi$
$29$	−859.313	+	279.208i	−1.02178	+	0.331995i	−0.250241	+	0.968183i	$0.580510\pi$
$30$			443.651i			0.492946i
$31$	−806.998	+	521.799i	−0.839749	+	0.542975i
$31$	−806.998	+	521.799i	−0.839749	+	0.542975i
$32$	735.221			0.717990
$33$	226.776	+	697.944i	0.208242	+	0.640903i
$34$	1220.56	−	1098.99i	1.05585	−	0.950688i
$35$	1056.27	−	767.422i	0.862258	−	0.626467i
$36$	161.147	+	279.115i	0.124342	+	0.215367i
$37$	969.351	+	559.655i	0.708073	+	0.408806i	0.810347	−	0.585950i	$-0.199279\pi$
$37$	969.351	+	559.655i	0.708073	+	0.408806i	−0.102274	+	0.994756i	$0.532612\pi$
$38$	−11.9459	−	113.657i	−0.00827275	−	0.0787100i
$39$	−1144.81	−	831.754i	−0.752670	−	0.546847i
$40$	−192.316	+	1829.76i	−0.120197	+	1.14360i
$41$	530.399	−	589.067i	0.315526	−	0.350427i	−0.564431	−	0.825480i	$-0.690905\pi$
$41$	530.399	−	589.067i	0.315526	−	0.350427i	0.879957	+	0.475053i	$0.157571\pi$
$42$	336.393	−	755.552i	0.190699	−	0.428317i
$43$	174.735	−	822.062i	0.0945023	−	0.444598i	−0.905301	−	0.424770i	$-0.860355\pi$
$43$	174.735	−	822.062i	0.0945023	−	0.444598i	0.999803	−	0.0198278i	$-0.00631181\pi$
$44$	175.454	+	825.447i	0.0906271	+	0.426367i
$45$	−1269.28	+	565.120i	−0.626806	+	0.279072i
$46$	−1419.68	−	461.281i	−0.670924	−	0.217996i
$47$	−16.9627	+	52.2059i	−0.00767891	+	0.0236333i	−0.954823	−	0.297177i	$-0.903955\pi$
$47$	−16.9627	+	52.2059i	−0.00767891	+	0.0236333i	0.947144	+	0.320810i	$0.103955\pi$
$48$	260.764	+	585.685i	0.113179	+	0.254204i
$49$	−32.2080	+	6.84602i	−0.0134144	+	0.00285132i
$50$	−231.488	−	49.2043i	−0.0925952	−	0.0196817i
$51$	−2550.75	−	1135.67i	−0.980679	−	0.436627i
$52$	−1209.26	−	1088.82i	−0.447212	−	0.402672i
$53$	1005.95	+	105.729i	0.358116	+	0.0376395i	0.281878	−	0.959450i	$-0.409043\pi$
$53$	1005.95	+	105.729i	0.358116	+	0.0376395i	0.0762378	+	0.997090i	$0.475709\pi$
$54$	−1315.48	+	1810.60i	−0.451123	+	0.620918i
$55$	−3618.04	+	380.272i	−1.19605	+	0.125710i
$56$	1714.92	−	2970.32i	0.546848	−	0.947169i
$57$	−168.254	+	97.1416i	−0.0517864	+	0.0298989i
$58$	−1667.74	−	2295.44i	−0.495760	−	0.682355i
$59$	2048.95	+	2275.59i	0.588609	+	0.653716i	0.961708	−	0.274075i	$-0.0883717\pi$
$59$	2048.95	+	2275.59i	0.588609	+	0.653716i	−0.373100	+	0.927791i	$0.621705\pi$
$60$	824.843	−	268.008i	0.229123	−	0.0744466i
$61$		−	3291.45i		−	0.884560i	−0.896877	−	0.442280i	$-0.854170\pi$
$61$		−	3291.45i		−	0.884560i	0.896877	−	0.442280i	$-0.145830\pi$
$62$	−2341.48	−	1903.79i	−0.609127	−	0.495264i
$63$	2590.12			0.652587
$64$	1307.22	+	4023.22i	0.319146	+	0.982232i
$65$	5213.09	−	4693.89i	1.23387	−	1.11098i
$66$	−1864.39	+	1354.56i	−0.428004	+	0.310963i
$67$	4033.66	+	6986.50i	0.898565	+	1.55636i	0.829330	+	0.558759i	$0.188722\pi$
$67$	4033.66	+	6986.50i	0.898565	+	1.55636i	0.0692346	+	0.997600i	$0.477944\pi$
$68$	−2780.60	−	1605.38i	−0.601340	−	0.347184i
$69$	265.259	+	2523.77i	0.0557149	+	0.530092i
$70$	3316.94	+	2409.89i	0.676926	+	0.491815i
$71$	830.831	−	7904.83i	0.164815	−	1.56811i	−0.529421	−	0.848359i	$-0.677591\pi$
$71$	830.831	−	7904.83i	0.164815	−	1.56811i	0.694236	−	0.719748i	$-0.255742\pi$
$72$	−2442.28	+	2712.43i	−0.471119	+	0.523231i
$73$	−1679.33	+	3771.83i	−0.315130	+	0.707793i	−0.999778	−	0.0210807i	$-0.993289\pi$
$73$	−1679.33	+	3771.83i	−0.315130	+	0.707793i	0.684648	+	0.728874i	$0.259956\pi$
$74$	−730.791	+	3438.10i	−0.133453	+	0.627849i
$75$	83.6480	+	393.533i	0.0148708	+	0.0699614i
$76$	−204.097	+	90.8696i	−0.0353353	+	0.0157323i
$77$	6449.97	+	2095.72i	1.08787	+	0.353470i
$78$	1373.16	−	4226.17i	0.225701	−	0.694636i
$79$	1193.65	+	2680.97i	0.191259	+	0.429574i	0.983566	−	0.180548i	$-0.0577870\pi$
$79$	1193.65	+	2680.97i	0.191259	+	0.429574i	−0.792307	+	0.610122i	$0.791120\pi$
$80$	−3108.74	+	660.782i	−0.485740	+	0.103247i
$81$	−438.112	−	93.1237i	−0.0667753	−	0.0141935i
$82$	2273.97	+	1012.44i	0.338188	+	0.150571i
$83$	809.495	+	728.873i	0.117505	+	0.105802i	0.725789	−	0.687918i	$-0.241475\pi$
$83$	809.495	+	728.873i	0.117505	+	0.105802i	−0.608283	+	0.793720i	$0.708142\pi$
$84$	−1607.95	−	169.002i	−0.227883	−	0.0239515i
$85$	8135.82	−	11198.0i	1.12606	−	1.54990i
$86$	2624.69	−	275.866i	0.354880	−	0.0372994i
$87$	−2411.74	+	4177.26i	−0.318634	+	0.551891i
$88$	−8276.51	+	4778.45i	−1.06876	+	0.617051i
$89$	−2807.44	−	3864.11i	−0.354430	−	0.487831i	0.594156	−	0.804350i	$-0.297486\pi$
$89$	−2807.44	−	3864.11i	−0.354430	−	0.487831i	−0.948586	+	0.316518i	$0.897486\pi$
$90$	−2919.46	−	3242.39i	−0.360427	−	0.400295i
$91$	−12437.1	+	4041.07i	−1.50189	+	0.487993i
$92$			2918.14i			0.344770i
$93$	−1337.63	+	4952.81i	−0.154657	+	0.572646i
$94$	−172.376			−0.0195084
$95$	−297.621	−	915.982i	−0.0329773	−	0.101494i
$96$	2916.81	−	2626.31i	0.316494	−	0.284972i
$97$	6120.59	−	4446.87i	0.650504	−	0.472619i	−0.212939	−	0.977065i	$-0.568304\pi$
$97$	6120.59	−	4446.87i	0.650504	−	0.472619i	0.863443	+	0.504447i	$0.168304\pi$
$98$	−51.7003	−	89.5475i	−0.00538320	−	0.00932398i
$99$	−6250.21	−	3608.56i	−0.637711	−	0.368183i
$100$	48.3595	+	460.110i	0.00483595	+	0.0460110i
$101$	9425.58	+	6848.08i	0.923986	+	0.671315i	0.944513	−	0.328474i	$-0.106534\pi$
$101$	9425.58	+	6848.08i	0.923986	+	0.671315i	−0.0205273	+	0.999789i	$0.506534\pi$
$102$	916.507	−	8719.98i	0.0880918	−	0.838137i
$103$	−3763.93	+	4180.27i	−0.354786	+	0.394030i	−0.893947	−	0.448173i	$-0.852075\pi$
$103$	−3763.93	+	4180.27i	−0.354786	+	0.394030i	0.539161	+	0.842203i	$0.318742\pi$
$104$	7495.36	−	16834.8i	0.692988	−	1.55648i
$105$	1449.14	−	6817.67i	0.131441	−	0.618383i
$106$	660.395	+	3106.92i	0.0587750	+	0.276514i
$107$	−10950.8	+	4875.59i	−0.956482	+	0.425853i	−0.824791	−	0.565438i	$-0.808707\pi$
$107$	−10950.8	+	4875.59i	−0.956482	+	0.425853i	−0.131691	+	0.991291i	$0.542041\pi$
$108$	4160.96	+	1351.98i	0.356735	+	0.115910i
$109$	−860.846	+	2649.41i	−0.0724557	+	0.222996i	−0.980726	−	0.195388i	$-0.937403\pi$
$109$	−860.846	+	2649.41i	−0.0724557	+	0.222996i	0.908270	+	0.418384i	$0.137403\pi$
$110$	−4646.62	−	10436.5i	−0.384018	−	0.862518i
$111$	5844.82	−	1242.36i	0.474379	−	0.100832i
$112$	5795.30	+	1231.83i	0.461998	+	0.0982007i
$113$	−15434.5	−	6871.86i	−1.20874	−	0.538167i	−0.299366	−	0.954138i	$-0.596775\pi$
$113$	−15434.5	−	6871.86i	−1.20874	−	0.538167i	−0.909378	+	0.415971i	$0.863442\pi$
$114$	−453.390	−	408.235i	−0.0348869	−	0.0314123i
$115$	−12511.1	−	1314.97i	−0.946018	−	0.0994305i
$116$	−3260.25	+	4487.34i	−0.242289	+	0.333483i
$117$	13840.1	−	1454.66i	1.01104	−	0.106265i
$118$	−4807.88	+	8327.49i	−0.345294	+	0.598067i
$119$	−22346.3	+	12901.6i	−1.57802	+	0.911068i
$120$	5773.19	+	7946.11i	0.400916	+	0.551813i
$121$	−2847.90	−	3162.91i	−0.194515	−	0.216031i
$122$	9830.08	−	3193.99i	0.660446	−	0.214592i
$123$		−	4231.63i		−	0.279703i
$124$	−2125.08	+	5503.39i	−0.138208	+	0.357921i
$125$	14545.8			0.930931
$126$	2513.43	+	7735.53i	0.158316	+	0.487247i
$127$	18265.0	−	16445.9i	1.13243	−	1.01965i	0.132838	−	0.991138i	$-0.457591\pi$
$127$	18265.0	−	16445.9i	1.13243	−	1.01965i	0.999594	−	0.0285082i	$-0.00907566\pi$
$128$	−1230.14	+	893.750i	−0.0750819	+	0.0545502i
$129$	−2243.30	−	3885.50i	−0.134805	−	0.233490i
$130$	19077.3	+	11014.3i	1.12883	+	0.651732i
$131$	2053.12	+	19534.1i	0.119639	+	1.13829i	0.875387	+	0.483423i	$0.160607\pi$
$131$	2053.12	+	19534.1i	0.119639	+	1.13829i	−0.755748	+	0.654863i	$0.772726\pi$
$132$	3644.67	+	2648.01i	0.209175	+	0.151975i
$133$	−187.675	+	1785.61i	−0.0106097	+	0.100945i
$134$	−16951.3	+	18826.4i	−0.944048	+	1.04847i
$135$	−7671.41	+	17230.3i	−0.420928	+	0.945419i
$136$	7559.94	−	35566.7i	0.408734	−	1.92294i
$137$	3809.67	+	17923.1i	0.202977	+	0.954930i	0.955186	+	0.296006i	$0.0956549\pi$
$137$	3809.67	+	17923.1i	0.202977	+	0.954930i	−0.752209	+	0.658924i	$0.771012\pi$
$138$	−7279.96	+	3241.25i	−0.382271	+	0.170198i
$139$	−5325.99	−	1730.52i	−0.275658	−	0.0895667i	0.167926	−	0.985800i	$-0.446293\pi$
$139$	−5325.99	−	1730.52i	−0.275658	−	0.0895667i	−0.443584	+	0.896233i	$0.646293\pi$
$140$	2476.76	−	7622.70i	0.126366	−	0.388913i
$141$	119.191	+	267.707i	0.00599521	+	0.0134655i
$142$	24414.4	−	5189.44i	1.21079	−	0.257362i
$143$	35642.0	+	7575.95i	1.74297	+	0.370480i
$144$	−5759.89	−	2564.47i	−0.277772	−	0.123672i
$145$	−17769.7	−	15999.9i	−0.845170	−	0.760995i
$146$	−12894.4	−	1355.25i	−0.604915	−	0.0635791i
$147$	−103.322	+	142.211i	−0.00478145	+	0.00658110i
$148$	6833.63	−	718.244i	0.311981	−	0.0327905i
$149$	642.099	−	1112.15i	0.0289221	−	0.0500945i	−0.851202	−	0.524838i	$-0.824126\pi$
$149$	642.099	−	1112.15i	0.0289221	−	0.0500945i	0.880124	+	0.474744i	$0.157459\pi$
$150$	−1094.14	+	631.699i	−0.0486282	+	0.0280755i
$151$	−13540.2	−	18636.5i	−0.593843	−	0.817355i	0.401284	−	0.915954i	$-0.368564\pi$
$151$	−13540.2	−	18636.5i	−0.593843	−	0.817355i	−0.995127	+	0.0985984i	$0.968564\pi$
$152$	−1692.97	−	1880.23i	−0.0732759	−	0.0813812i
$153$	26115.2	−	8485.34i	1.11560	−	0.362482i
$154$			21296.9i			0.897995i
$155$	−22637.4	−	11590.9i	−0.942243	−	0.482452i
$156$	−8686.87			−0.356955
$157$	−14825.2	−	45627.1i	−0.601450	−	1.85107i	−0.519562	−	0.854433i	$-0.673905\pi$
$157$	−14825.2	−	45627.1i	−0.601450	−	1.85107i	−0.0818885	−	0.996641i	$-0.526095\pi$
$158$	−6848.57	+	6166.48i	−0.274338	+	0.247015i
$159$	4368.53	−	3173.92i	0.172799	−	0.125546i
$160$	9728.59	+	16850.4i	0.380023	+	0.658219i
$161$	20309.7	+	11725.8i	0.783523	+	0.452367i
$162$	−147.021	−	1398.81i	−0.00560208	−	0.0533003i
$163$	−13366.1	−	9711.05i	−0.503072	−	0.365503i	0.307117	−	0.951672i	$-0.400636\pi$
$163$	−13366.1	−	9711.05i	−0.503072	−	0.365503i	−0.810189	+	0.586169i	$0.800636\pi$
$164$	508.643	−	4839.41i	0.0189115	−	0.179931i
$165$	−12995.3	+	14432.8i	−0.477330	+	0.530129i
$166$	−1391.29	+	3124.89i	−0.0504896	+	0.113401i
$167$	−2304.34	+	10841.1i	−0.0826254	+	0.388722i	−0.999956	−	0.00940483i	$-0.997006\pi$
$167$	−2304.34	+	10841.1i	−0.0826254	+	0.388722i	0.917330	+	0.398127i	$0.130340\pi$
$168$	−3806.87	−	17909.9i	−0.134881	−	0.634563i
$169$	−38095.7	+	16961.3i	−1.33384	+	0.593862i
$170$	41338.3	+	13431.6i	1.43039	+	0.464762i
$171$	590.428	−	1817.15i	0.0201918	−	0.0621440i
$172$	−2098.46	−	4713.21i	−0.0709322	−	0.159316i
$173$	−56592.4	+	12029.1i	−1.89089	+	0.401921i	−0.998757	−	0.0498534i	$-0.984125\pi$
$173$	−56592.4	+	12029.1i	−1.89089	+	0.401921i	−0.892132	+	0.451774i	$0.850791\pi$
$174$	−14815.9	−	3149.23i	−0.489363	−	0.104017i
$175$	3396.60	+	1512.26i	0.110909	+	0.0493800i
$176$	−12268.4	−	11046.5i	−0.396063	−	0.356616i
$177$	16257.4	+	1708.72i	0.518924	+	0.0545411i
$178$	8816.06	−	12134.3i	0.278250	−	0.382978i
$179$	−28065.1	+	2949.76i	−0.875912	+	0.0920621i	−0.531803	−	0.846868i	$-0.678485\pi$
$179$	−28065.1	+	2949.76i	−0.875912	+	0.0920621i	−0.344109	+	0.938930i	$0.611819\pi$
$180$	−4264.66	+	7386.61i	−0.131625	+	0.227982i
$181$	29779.7	−	17193.3i	0.908998	−	0.524810i	0.0288891	−	0.999583i	$-0.490803\pi$
$181$	29779.7	−	17193.3i	0.908998	−	0.524810i	0.880108	+	0.474773i	$0.157470\pi$
$182$	−24137.7	−	33222.7i	−0.728708	−	1.00298i
$183$	−11757.5	−	13058.0i	−0.351085	−	0.389919i
$184$	−31430.0	+	10212.2i	−0.928343	+	0.301637i
$185$			29621.9i			0.865504i
$186$	−16089.9	+	811.253i	−0.465079	+	0.0234493i
$187$	71898.3			2.05606
$188$	104.132	+	320.484i	0.00294623	+	0.00906756i
$189$	26129.3	−	23526.9i	0.731482	−	0.658630i
$190$	2446.82	−	1777.72i	0.0677789	−	0.0492443i
$191$	13253.8	+	22956.3i	0.363308	+	0.629268i	0.988503	−	0.151200i	$-0.0483139\pi$
$191$	13253.8	+	22956.3i	0.363308	+	0.629268i	−0.625195	+	0.780469i	$0.714981\pi$
$192$	19557.6	+	11291.6i	0.530533	+	0.306303i
$193$	5581.11	+	53100.8i	0.149833	+	1.42556i	0.768470	+	0.639886i	$0.221018\pi$
$193$	5581.11	+	53100.8i	0.149833	+	1.42556i	−0.618638	+	0.785676i	$0.712315\pi$
$194$	19220.2	+	13964.3i	0.510686	+	0.371035i
$195$	3914.47	−	37243.7i	0.102945	−	0.979452i
$196$	−135.256	+	150.217i	−0.00352083	+	0.00391027i
$197$	22967.0	−	51584.8i	0.591797	−	1.32920i	−0.330898	−	0.943667i	$-0.607352\pi$
$197$	22967.0	−	51584.8i	0.591797	−	1.32920i	0.922695	−	0.385531i	$-0.125982\pi$
$198$	4712.01	−	22168.3i	0.120192	−	0.565460i
$199$	−3894.97	−	18324.4i	−0.0983554	−	0.462726i	−0.999569	−	0.0293509i	$-0.990656\pi$
$199$	−3894.97	−	18324.4i	−0.0983554	−	0.462726i	0.901214	−	0.433375i	$-0.142677\pi$
$200$	−4786.40	+	2131.04i	−0.119660	+	0.0532761i
$201$	40959.2	+	13308.5i	1.01382	+	0.329409i
$202$	−11305.7	+	34795.3i	−0.277073	+	0.852742i
$203$	18130.6	+	40722.0i	0.439967	+	0.988182i
$204$	−16766.0	+	3563.71i	−0.402873	+	0.0856333i
$205$	20519.1	+	4361.46i	0.488258	+	0.103783i
$206$	−16137.1	−	7184.68i	−0.380268	−	0.169306i
$207$	−18546.3	−	16699.2i	−0.432830	−	0.389722i
$208$	31658.6	+	3327.46i	0.731755	+	0.0769105i
$209$	2940.60	−	4047.38i	0.0673198	−	0.0926577i
$210$	21767.6	−	2287.86i	0.493596	−	0.0518790i
$211$	−20467.6	+	35451.0i	−0.459730	+	0.796275i	−0.998946	−	0.0458918i	$-0.985387\pi$
$211$	−20467.6	+	35451.0i	−0.459730	+	0.796275i	0.539217	+	0.842167i	$0.318720\pi$
$212$	5377.48	−	3104.69i	0.119648	−	0.0690790i
$213$	−24940.9	−	34328.3i	−0.549735	−	0.756646i
$214$	−25187.7	−	27973.8i	−0.549998	−	0.610835i
$215$	21152.8	−	6872.97i	0.457606	−	0.148685i
$216$			49547.2i			1.06197i
$217$	29763.5	+	36904.2i	0.632069	+	0.783711i
$218$	−8747.96			−0.184075
$219$	6811.15	+	20962.6i	0.142014	+	0.437075i
$220$	−16596.6	+	14943.7i	−0.342905	+	0.308753i
$221$	−112160.	+	81489.1i	−2.29643	+	1.66846i
$222$	9382.11	+	16250.3i	0.190368	+	0.329728i
$223$	74488.0	+	43005.7i	1.49788	+	0.864800i	0.999997	−	0.00244471i	$-0.000778176\pi$
$223$	74488.0	+	43005.7i	1.49788	+	0.864800i	0.497881	+	0.867245i	$0.334112\pi$
$224$	−3791.46	−	36073.3i	−0.0755632	−	0.718936i
$225$	−3200.99	−	2325.65i	−0.0632294	−	0.0459388i
$226$	5545.74	−	52764.2i	0.108578	−	1.03305i
$227$	23713.8	−	26336.8i	0.460203	−	0.511107i	−0.467721	−	0.883876i	$-0.654925\pi$
$227$	23713.8	−	26336.8i	0.460203	−	0.511107i	0.927924	+	0.372769i	$0.121592\pi$
$228$	−485.104	+	1089.56i	−0.00933180	+	0.0209596i
$229$	11145.2	−	52434.3i	0.212529	−	0.999872i	−0.734471	−	0.678640i	$-0.762570\pi$
$229$	11145.2	−	52434.3i	0.212529	−	0.999872i	0.947001	−	0.321232i	$-0.104097\pi$
$230$	−8213.41	−	38641.0i	−0.155263	−	0.730455i
$231$	33074.9	−	14725.9i	0.619832	−	0.275967i
$232$	−59740.7	−	19410.9i	−1.10993	−	0.360637i
$233$	1619.96	−	4985.73i	0.0298396	−	0.0918368i	−0.935028	−	0.354575i	$-0.884626\pi$
$233$	1619.96	−	4985.73i	0.0298396	−	0.0918368i	0.964867	+	0.262738i	$0.0846256\pi$
$234$	17774.7	+	39922.7i	0.324617	+	0.729102i
$235$	−1420.95	+	302.033i	−0.0257302	+	0.00546913i
$236$	18387.0	+	3908.28i	0.330131	+	0.0701716i
$237$	14312.3	+	6372.24i	0.254808	+	0.113448i
$238$	−60216.0	−	54218.7i	−1.06306	−	0.957184i
$239$	−34561.3	−	3632.54i	−0.605055	−	0.0635938i	−0.202952	−	0.979189i	$-0.565054\pi$
$239$	−34561.3	−	3632.54i	−0.605055	−	0.0635938i	−0.402102	+	0.915595i	$0.631720\pi$
$240$	−9972.74	+	13726.3i	−0.173138	+	0.238304i
$241$	−67803.6	+	7126.45i	−1.16740	+	0.122698i	−0.668330	−	0.743865i	$-0.732991\pi$
$241$	−67803.6	+	7126.45i	−1.16740	+	0.122698i	−0.499067	+	0.866563i	$0.666324\pi$
$242$	6682.64	−	11574.7i	0.114108	−	0.197641i
$243$	−52064.5	+	30059.5i	−0.881717	+	0.509060i
$244$	−11876.6	−	16346.7i	−0.199486	−	0.274569i
$245$	−583.085	−	647.581i	−0.00971403	−	0.0107885i
$246$	12638.0	−	4106.33i	0.208837	−	0.0678553i
$247$			9646.70i			0.158119i
$248$	−66711.5	−	3628.83i	−1.08467	−	0.0590015i
$249$	5815.10			0.0937904
$250$	14115.1	+	43441.8i	0.225841	+	0.695068i
$251$	28140.2	−	25337.6i	0.446663	−	0.402177i	−0.414868	−	0.909881i	$-0.636172\pi$
$251$	28140.2	−	25337.6i	0.446663	−	0.402177i	0.861532	+	0.507704i	$0.169506\pi$
$252$	12863.6	−	9345.99i	0.202564	−	0.147172i
$253$	−32672.8	−	56591.0i	−0.510441	−	0.884110i
$254$	66840.6	+	38590.4i	1.03603	+	0.598153i
$255$	−7723.84	−	73487.5i	−0.118783	−	1.13014i
$256$	50894.8	+	36977.2i	0.776592	+	0.564227i
$257$	4750.33	−	45196.4i	0.0719213	−	0.684286i	−0.897855	−	0.440291i	$-0.854875\pi$
$257$	4750.33	−	45196.4i	0.0719213	−	0.684286i	0.969777	−	0.243995i	$-0.0784580\pi$
$258$	9427.38	−	10470.2i	0.141629	−	0.157295i
$259$	22460.4	−	50446.9i	0.334825	−	0.752030i
$260$	8953.39	−	42122.4i	0.132447	−	0.623112i
$261$	−9862.56	−	46399.7i	−0.144780	−	0.681137i
$262$	−56347.4	+	25087.5i	−0.820864	+	0.365472i
$263$	624.416	+	202.885i	0.00902740	+	0.00293318i	0.313527	−	0.949579i	$-0.398489\pi$
$263$	624.416	+	202.885i	0.00902740	+	0.00293318i	−0.304500	+	0.952512i	$0.598489\pi$
$264$	−15765.8	+	48522.1i	−0.226208	+	0.696196i
$265$	10887.7	+	24454.2i	0.155040	+	0.348226i
$266$	−5514.94	+	1172.24i	−0.0779431	+	0.0165673i
$267$	−24940.9	−	5301.36i	−0.349857	−	0.0743643i
$268$	45242.4	+	20143.2i	0.629907	+	0.280453i
$269$	63188.9	+	56895.5i	0.873245	+	0.786273i	0.978083	−	0.208216i	$-0.0667658\pi$
$269$	63188.9	+	56895.5i	0.873245	+	0.786273i	−0.104838	+	0.994489i	$0.533432\pi$
$270$	−58903.4	−	6190.99i	−0.808002	−	0.0849245i
$271$	−19068.9	+	26246.1i	−0.259650	+	0.357377i	−0.918862	−	0.394580i	$-0.870890\pi$
$271$	−19068.9	+	26246.1i	−0.259650	+	0.357377i	0.659212	+	0.751957i	$0.270890\pi$
$272$	62467.3	−	6565.58i	0.844336	−	0.0887433i
$273$	−34906.0	+	60459.0i	−0.468355	+	0.811214i
$274$	−49831.4	+	28770.2i	−0.663746	+	0.383214i
$275$	−6089.43	−	8381.38i	−0.0805214	−	0.110828i
$276$	10424.0	+	11577.0i	0.136841	+	0.151977i
$277$	116865.	−	37971.9i	1.52309	−	0.494883i	0.576441	−	0.817139i	$-0.304441\pi$
$277$	116865.	−	37971.9i	1.52309	−	0.494883i	0.946653	+	0.322255i	$0.104441\pi$
$278$		−	17585.6i		−	0.227545i
$279$	−22816.1	−	44999.5i	−0.293112	−	0.578095i
$280$	90768.3			1.15776
$281$	−2159.07	−	6644.94i	−0.0273435	−	0.0841547i	0.936453	−	0.350792i	$-0.114088\pi$
$281$	−2159.07	−	6644.94i	−0.0273435	−	0.0841547i	−0.963797	+	0.266637i	$0.914088\pi$
$282$	−683.859	+	615.750i	−0.00859941	+	0.00774294i
$283$	28629.0	−	20800.2i	0.357465	−	0.259714i	−0.394529	−	0.918884i	$-0.629092\pi$
$283$	28629.0	−	20800.2i	0.357465	−	0.259714i	0.751994	+	0.659170i	$0.229092\pi$
$284$	−24396.9	−	42256.7i	−0.302481	−	0.523912i
$285$	−4452.74	−	2570.79i	−0.0548198	−	0.0316502i
$286$	11960.7	+	113798.i	0.146226	+	1.39125i
$287$	−31637.6	−	22986.0i	−0.384095	−	0.279062i
$288$	−4034.77	+	38388.3i	−0.0486445	+	0.462821i
$289$	−127156.	+	141221.i	−1.52245	+	1.69085i
$290$	30541.0	−	68596.3i	0.363151	−	0.815652i
$291$	8397.13	−	39505.4i	0.0991619	−	0.466520i
$292$	5269.72	+	24792.1i	0.0618048	+	0.290769i
$293$	−29912.0	+	13317.7i	−0.348426	+	0.155129i	−0.573485	−	0.819216i	$-0.694409\pi$
$293$	−29912.0	+	13317.7i	−0.348426	+	0.155129i	0.225059	+	0.974345i	$0.427742\pi$
$294$	−524.983	−	170.577i	−0.00607367	−	0.00197345i
$295$	−25041.7	+	77070.4i	−0.287753	+	0.885612i
$296$	31650.7	+	71088.5i	0.361243	+	0.811365i
$297$	−95830.2	+	20369.3i	−1.08640	+	0.230921i
$298$	3944.58	+	838.445i	0.0444189	+	0.00944153i
$299$	115109.	+	51249.8i	1.28756	+	0.573258i
$300$	1835.43	+	1652.62i	0.0203936	+	0.0183625i
$301$	−41235.2	−	4334.00i	−0.455130	−	0.0478361i
$302$	42519.7	−	58523.3i	0.466204	−	0.641674i
$303$	61855.9	−	6501.31i	0.673745	−	0.0708135i
$304$	2185.28	−	3785.01i	0.0236461	−	0.0409562i
$305$	75436.1	−	43553.0i	0.810923	−	0.468186i
$306$	50683.8	+	69760.3i	0.541286	+	0.745016i
$307$	−66534.3	−	73893.8i	−0.705941	−	0.784027i	0.278369	−	0.960474i	$-0.410206\pi$
$307$	−66534.3	−	73893.8i	−0.705941	−	0.784027i	−0.984310	+	0.176447i	$0.943540\pi$
$308$	39595.4	−	12865.3i	0.417391	−	0.135619i
$309$			30029.4i			0.314507i
$310$	12649.8	−	78855.4i	0.131631	−	0.820556i
$311$	−19696.7			−0.203644			−0.101822	−	0.994803i	$-0.532467\pi$
$311$	−19696.7			−0.203644			−0.101822	+	0.994803i	$0.532467\pi$
$312$	−30400.3	−	93562.4i	−0.312297	−	0.961153i
$313$	−51942.2	+	46769.0i	−0.530190	+	0.477386i	−0.890204	−	0.455561i	$-0.849439\pi$
$313$	−51942.2	+	46769.0i	−0.530190	+	0.477386i	0.360014	+	0.932947i	$0.382772\pi$
$314$	121882.	−	88552.2i	1.23617	−	0.898132i
$315$	34273.0	+	59362.5i	0.345406	+	0.598261i
$316$	15602.0	+	9007.81i	0.156245	+	0.0902080i
$317$	−6662.37	−	63388.2i	−0.0662995	−	0.630798i	−0.976334	−	0.216266i	$-0.930612\pi$
$317$	−6662.37	−	63388.2i	−0.0662995	−	0.630798i	0.910035	−	0.414531i	$-0.136055\pi$
$318$	13718.3	+	9966.90i	0.135658	+	0.0985612i
$319$	12983.1	−	123526.i	0.127584	−	1.21388i
$320$	−74910.1	+	83196.1i	−0.731544	+	0.812462i
$321$	−26028.2	+	58460.2i	−0.252600	+	0.567349i
$322$	−15311.4	+	72034.6i	−0.147674	+	0.694751i
$323$	3957.48	+	18618.5i	0.0379327	+	0.178459i
$324$	−2511.88	+	1118.36i	−0.0239281	+	0.0106535i
$325$	18998.8	+	6173.09i	0.179870	+	0.0584435i
$326$	16032.2	−	49342.1i	0.150855	−	0.464283i
$327$	6048.85	+	13585.9i	0.0565688	+	0.127056i
$328$	53903.2	−	11457.5i	0.501034	−	0.106498i
$329$	2648.94	+	563.049i	0.0244726	+	0.00520181i
$330$	−55714.7	−	24805.8i	−0.511613	−	0.227785i
$331$	15689.9	+	14127.2i	0.143207	+	0.128944i	0.737621	−	0.675215i	$-0.235949\pi$
$331$	15689.9	+	14127.2i	0.143207	+	0.128944i	−0.594414	+	0.804159i	$0.702616\pi$
$332$	6650.31	+	698.976i	0.0603345	+	0.00634141i
$333$	−34541.0	+	47541.6i	−0.311492	+	0.428732i
$334$	−34613.5	+	3638.03i	−0.310279	+	0.0326117i
$335$	−106748.	+	184893.i	−0.951198	+	1.64752i
$336$	27391.7	−	15814.6i	0.242627	−	0.140081i
$337$	8919.15	+	12276.2i	0.0785350	+	0.108094i	0.846477	−	0.532425i	$-0.178719\pi$
$337$	8919.15	+	12276.2i	0.0785350	+	0.108094i	−0.767942	+	0.640519i	$0.778719\pi$
$338$	−87623.5	−	97315.8i	−0.766986	−	0.851824i
$339$	−85779.5	+	27871.5i	−0.746422	+	0.242527i
$340$		−	84970.7i		−	0.735041i
$341$	−20407.2	−	130520.i	−0.175499	−	1.12245i
$342$	5999.96			0.0512975
$343$	−36102.0	−	111111.i	−0.306862	−	0.944424i
$344$	43420.3	−	39095.8i	0.366924	−	0.330379i
$345$	−54331.9	+	39474.4i	−0.456474	+	0.331648i
$346$	−90842.2	−	157343.i	−0.758814	−	1.31430i
$347$	30972.7	+	17882.1i	0.257229	+	0.148511i	0.623070	−	0.782166i	$-0.285885\pi$
$347$	30972.7	+	17882.1i	0.257229	+	0.148511i	−0.365841	+	0.930677i	$0.619219\pi$
$348$	3095.16	+	29448.4i	0.0255578	+	0.243167i
$349$	24301.7	+	17656.2i	0.199520	+	0.144960i	0.683059	−	0.730363i	$-0.260649\pi$
$349$	24301.7	+	17656.2i	0.199520	+	0.144960i	−0.483540	+	0.875323i	$0.660649\pi$
$350$	−1220.43	+	11611.6i	−0.00996268	+	0.0947886i
$351$	126407.	−	140389.i	1.02602	−	1.13951i
$352$	−41108.3	+	92330.7i	−0.331775	+	0.745179i
$353$	5572.62	−	26217.1i	0.0447209	−	0.210395i	−0.950114	−	0.311903i	$-0.899033\pi$
$353$	5572.62	−	26217.1i	0.0447209	−	0.210395i	0.994835	+	0.101508i	$0.0323668\pi$
$354$	10672.8	+	50211.6i	0.0851672	+	0.400680i
$355$	192163.	−	85556.5i	1.52480	−	0.678885i
$356$	−27885.9	−	9060.69i	−0.220032	−	0.0714926i
$357$	−42567.0	+	131008.i	−0.333993	+	1.02792i
$358$	−36043.7	−	80955.5i	−0.281231	−	0.631655i
$359$	32252.4	−	6855.46i	0.250250	−	0.0531922i	−0.0810788	−	0.996708i	$-0.525837\pi$
$359$	32252.4	−	6855.46i	0.250250	−	0.0531922i	0.331328	+	0.943516i	$0.392503\pi$
$360$	−94482.4	−	20082.9i	−0.729031	−	0.154960i
$361$	−117844.	−	52467.6i	−0.904261	−	0.402603i
$362$	80246.6	+	72254.4i	0.612364	+	0.551375i
$363$	−22596.7	−	2375.01i	−0.171487	−	0.0180240i
$364$	−47186.7	+	64946.9i	−0.356137	+	0.490180i
$365$	−108667.	+	11421.4i	−0.815666	+	0.0857299i
$366$	27589.1	−	47785.7i	0.205956	−	0.356727i
$367$	−172828.	+	99782.5i	−1.28317	+	0.740837i	−0.977426	−	0.211278i	$-0.932237\pi$
$367$	−172828.	+	99782.5i	−1.28317	+	0.740837i	−0.305741	+	0.952115i	$0.598904\pi$
$368$	−33554.9	−	46184.3i	−0.247776	−	0.341035i
$369$	27846.4	+	30926.5i	0.204510	+	0.227132i
$370$	−88467.2	+	28744.7i	−0.646218	+	0.209969i
$371$		−	49901.7i		−	0.362549i
$372$	11228.1	+	29424.4i	0.0811372	+	0.212629i
$373$	29629.0			0.212961			0.106480	−	0.994315i	$-0.466042\pi$
$373$	29629.0			0.212961			0.106480	+	0.994315i	$0.466042\pi$
$374$	69769.4	+	214728.i	0.498795	+	1.53513i
$375$	57706.8	−	51959.5i	0.410360	−	0.369489i
$376$	−3087.38	+	2243.11i	−0.0218381	+	0.0158663i
$377$	119750.	+	207413.i	0.842544	+	1.45933i
$378$	95619.9	+	55206.2i	0.669214	+	0.386371i
$379$	−25903.0	−	246451.i	−0.180332	−	1.71574i	−0.593287	−	0.804991i	$-0.702170\pi$
$379$	−25903.0	−	246451.i	−0.180332	−	1.71574i	0.412955	−	0.910751i	$-0.364497\pi$
$380$	−4783.27	−	3475.25i	−0.0331251	−	0.0240668i
$381$	13715.0	−	130490.i	0.0944815	−	0.898932i
$382$	−55698.9	+	61859.9i	−0.381698	+	0.423919i
$383$	6825.22	−	15329.7i	0.0465285	−	0.104505i	−0.888786	−	0.458323i	$-0.848450\pi$
$383$	6825.22	−	15329.7i	0.0465285	−	0.104505i	0.935314	+	0.353818i	$0.115117\pi$
$384$	−1687.69	+	7939.95i	−0.0114454	+	0.0538463i
$385$	37315.8	+	175557.i	0.251751	+	1.18439i
$386$	−153172.	+	68196.7i	−1.02803	+	0.457708i
$387$	41963.6	+	13634.8i	0.280189	+	0.0910388i
$388$	14351.7	−	44170.1i	0.0953326	−	0.293403i
$389$	−34040.9	−	76457.1i	−0.224958	−	0.505264i	0.765440	−	0.643507i	$-0.222521\pi$
$389$	−34040.9	−	76457.1i	−0.224958	−	0.505264i	−0.990398	+	0.138243i	$0.955855\pi$
$390$	115029.	−	24450.1i	0.756270	−	0.160750i
$391$	243189.	+	51691.4i	1.59071	+	0.338116i
$392$	−2091.26	−	931.089i	−0.0136093	−	0.00605925i
$393$	77923.7	+	70162.8i	0.504527	+	0.454278i
$394$	176348.	+	18534.9i	1.13600	+	0.119398i
$395$	−45650.2	+	62832.1i	−0.292583	+	0.402706i
$396$	−44062.1	+	4631.11i	−0.280979	+	0.0295321i
$397$	111528.	−	193173.i	0.707627	−	1.22565i	−0.258108	−	0.966116i	$-0.583099\pi$
$397$	111528.	−	193173.i	0.707627	−	1.22565i	0.965735	−	0.259530i	$-0.0835675\pi$
$398$	50947.1	−	29414.3i	0.321628	−	0.185692i
$399$	5633.88	+	7754.37i	0.0353885	+	0.0487080i
$400$	−6056.04	−	6725.92i	−0.0378503	−	0.0420370i
$401$	100879.	−	32777.6i	0.627353	−	0.203839i	0.0219509	−	0.999759i	$-0.493012\pi$
$401$	100879.	−	32777.6i	0.627353	−	0.203839i	0.605402	+	0.795920i	$0.293012\pi$
$402$			135241.i			0.836868i
$403$	179765.	+	180479.i	1.10687	+	1.11126i
$404$	71521.6			0.438202
$405$	−3662.90	−	11273.3i	−0.0223314	−	0.0687289i
$406$	−104025.	+	93664.2i	−0.631079	+	0.568226i
$407$	−124482.	+	90441.4i	−0.751480	+	0.545982i
$408$	−97056.8	−	168107.i	−0.583050	−	1.00987i
$409$	−170262.	−	98300.9i	−1.01782	−	0.587639i	−0.104349	−	0.994541i	$-0.533276\pi$
$409$	−170262.	−	98300.9i	−1.01782	−	0.587639i	−0.913472	+	0.406901i	$0.866609\pi$
$410$	6885.75	+	65513.6i	0.0409623	+	0.389730i
$411$	79137.5	+	57496.8i	0.468488	+	0.340377i
$412$	−3609.54	+	34342.5i	−0.0212646	+	0.202319i
$413$	101084.	−	112266.i	0.592631	−	0.658183i
$414$	31875.9	−	71594.4i	0.185978	−	0.417713i
$415$	−5993.51	+	28197.3i	−0.0348005	+	0.163723i
$416$	−40518.9	−	190626.i	−0.234137	−	1.10153i
$417$	−27311.2	+	12159.7i	−0.157061	+	0.0699280i
$418$	14941.2	+	4854.70i	0.0855134	+	0.0277850i
$419$	54219.2	−	166870.i	0.308834	−	0.950494i	−0.669384	−	0.742916i	$-0.733442\pi$
$419$	54219.2	−	166870.i	0.308834	−	0.950494i	0.978219	−	0.207578i	$-0.0665580\pi$
$420$	−17403.3	−	39088.5i	−0.0986582	−	0.221590i
$421$	−13879.9	+	2950.27i	−0.0783109	+	0.0166455i	−0.246901	−	0.969041i	$-0.579412\pi$
$421$	−13879.9	+	2950.27i	−0.0783109	+	0.0166455i	0.168590	+	0.985686i	$0.446079\pi$
$422$	−125738.	−	26726.4i	−0.706059	−	0.150077i
$423$	−2632.75	−	1172.17i	−0.0147139	−	0.00655106i
$424$	52258.1	+	47053.4i	0.290684	+	0.261733i
$425$	39200.8	+	4120.17i	0.217029	+	0.0228107i
$426$	78320.7	−	107799.i	0.431576	−	0.594014i
$427$	−161493.	+	16973.6i	−0.885726	+	0.0930935i
$428$	−36793.5	+	63728.2i	−0.200855	+	0.347892i
$429$	168463.	−	97262.2i	0.915356	−	0.528481i
$430$	41053.0	+	56504.5i	0.222028	+	0.305595i
$431$	64089.8	+	71179.0i	0.345012	+	0.383175i	0.890530	−	0.454924i	$-0.150334\pi$
$431$	64089.8	+	71179.0i	0.345012	+	0.383175i	−0.545518	+	0.838099i	$0.683667\pi$
$432$	−81400.0	+	26448.5i	−0.436171	+	0.141721i
$433$			85303.7i			0.454980i	0.973780	+	0.227490i	$0.0730519\pi$
$433$			85303.7i			0.454980i	−0.973780	+	0.227490i	$0.926948\pi$
$434$	−81334.1	+	124702.i	−0.431811	+	0.662053i
$435$	−127651.			−0.674597
$436$	5284.60	+	16264.3i	0.0277996	+	0.0855585i
$437$	12856.2	−	11575.7i	0.0673206	−	0.0606158i
$438$	−55996.4	+	40683.7i	−0.291885	+	0.212067i
$439$	147959.	+	256272.i	0.767736	+	1.32976i	0.938788	+	0.344496i	$0.111950\pi$
$439$	147959.	+	256272.i	0.767736	+	1.32976i	−0.171052	+	0.985262i	$0.554716\pi$
$440$	−219033.	−	126459.i	−1.13137	−	0.653195i
$441$	−180.701	−	1719.25i	−0.000929143	−	0.00884020i
$442$	−352211.	−	255896.i	−1.80284	−	1.30984i
$443$	−29113.1	+	276993.i	−0.148348	+	1.41143i	0.626566	+	0.779368i	$0.284460\pi$
$443$	−29113.1	+	276993.i	−0.148348	+	1.41143i	−0.774914	+	0.632067i	$0.782207\pi$
$444$	24545.1	−	27260.1i	0.124508	−	0.138281i
$445$	51412.3	−	115474.i	0.259625	−	0.583128i
$446$	−56156.3	+	264195.i	−0.282312	+	1.32817i
$447$	−1425.37	−	6705.83i	−0.00713366	−	0.0335612i
$448$	190657.	−	84885.7i	0.949939	−	0.422940i
$449$	−345001.	−	112098.i	−1.71131	−	0.556037i	−0.720757	−	0.693188i	$-0.756206\pi$
$449$	−345001.	−	112098.i	−1.71131	−	0.556037i	−0.990550	+	0.137150i	$0.956206\pi$
$450$	3839.48	−	11816.7i	0.0189604	−	0.0583541i
$451$	44320.3	+	99545.0i	0.217896	+	0.489403i
$452$	−101450.	+	21563.9i	−0.496564	+	0.105548i
$453$	−120290.	−	25568.3i	−0.586181	−	0.124597i
$454$	101668.	+	45265.5i	0.493256	+	0.219612i
$455$	−257187.	−	231572.i	−1.24230	−	1.11857i
$456$	−13432.9	−	1411.85i	−0.0646009	−	0.00678983i
$457$	63211.4	−	87003.0i	0.302666	−	0.416583i	−0.630411	−	0.776262i	$-0.717114\pi$
$457$	63211.4	−	87003.0i	0.302666	−	0.416583i	0.933076	+	0.359678i	$0.117114\pi$
$458$	167413.	−	17595.8i	0.798102	−	0.0838839i
$459$	186376.	−	322813.i	0.884638	−	1.53224i
$460$	−66880.3	+	38613.3i	−0.316069	+	0.182483i
$461$	42868.0	+	59002.7i	0.201712	+	0.277632i	0.897874	−	0.440252i	$-0.145111\pi$
$461$	42868.0	+	59002.7i	0.201712	+	0.277632i	−0.696163	+	0.717884i	$0.745111\pi$
$462$	76075.1	+	84490.0i	0.356417	+	0.395841i
$463$	−168906.	+	54880.7i	−0.787920	+	0.256011i	−0.675218	−	0.737618i	$-0.735950\pi$
$463$	−168906.	+	54880.7i	−0.787920	+	0.256011i	−0.112702	+	0.993629i	$0.535950\pi$
$464$		−	108508.i		−	0.503996i
$465$	−131212.	+	34879.6i	−0.606833	+	0.161312i
$466$	16462.1			0.0758079
$467$	17095.5	+	52614.6i	0.0783879	+	0.241253i	0.982570	−	0.185895i	$-0.0595184\pi$
$467$	17095.5	+	52614.6i	0.0783879	+	0.241253i	−0.904182	+	0.427148i	$0.859518\pi$
$468$	63487.2	−	57164.1i	0.289864	−	0.260995i
$469$	321989.	−	233938.i	1.46384	−	1.06354i
$470$	−2280.91	−	3950.66i	−0.0103255	−	0.0178844i
$471$	−221801.	−	128057.i	−0.999820	−	0.577246i
$472$	22252.2	+	211716.i	0.0998824	+	0.950318i
$473$	93466.4	+	67907.3i	0.417766	+	0.303525i
$474$	−5142.53	+	48927.9i	−0.0228887	+	0.217771i
$475$	1835.23	−	2038.23i	0.00813397	−	0.00903369i
$476$	−64428.0	+	144708.i	−0.284355	+	0.638672i
$477$	−11040.9	+	51943.6i	−0.0485254	+	0.228294i
$478$	−22689.2	−	106744.i	−0.0993031	−	0.467185i
$479$	−36433.8	+	16221.4i	−0.158794	+	0.0706996i	−0.484595	−	0.874739i	$-0.661033\pi$
$479$	−36433.8	+	16221.4i	−0.158794	+	0.0706996i	0.325801	+	0.945438i	$0.394366\pi$
$480$	98787.6	+	32098.0i	0.428766	+	0.139314i
$481$	91683.9	−	282174.i	0.396281	−	1.21963i
$482$	−87079.4	−	195584.i	−0.374819	−	0.841857i
$483$	122460.	−	26029.6i	0.524927	−	0.111577i
$484$	−25556.7	−	5432.25i	−0.109097	−	0.0231894i
$485$	182906.	+	81434.9i	0.777578	+	0.346200i
$486$	−140297.	−	126324.i	−0.593986	−	0.534827i
$487$	−142070.	−	14932.1i	−0.599023	−	0.0629599i	−0.199836	−	0.979829i	$-0.564041\pi$
$487$	−142070.	−	14932.1i	−0.599023	−	0.0629599i	−0.399187	+	0.916869i	$0.630708\pi$
$488$	134501.	−	185124.i	0.564787	−	0.777363i
$489$	−87715.8	+	9219.31i	−0.366826	+	0.0385550i
$490$	1368.22	−	2369.82i	0.00569853	−	0.00987014i
$491$	71152.9	−	41080.1i	0.295141	−	0.170400i	−0.345117	−	0.938560i	$-0.612161\pi$
$491$	71152.9	−	41080.1i	0.295141	−	0.170400i	0.640258	+	0.768160i	$0.278827\pi$
$492$	−15269.1	−	21016.1i	−0.0630787	−	0.0868204i
$493$	316211.	+	351188.i	1.30102	+	1.44493i
$494$	−28810.4	+	9361.06i	−0.118058	+	0.0383593i
$495$		−	190997.i		−	0.779498i
$496$	−29649.1	−	111536.i	−0.120517	−	0.453369i
$497$	−392132.			−1.58752
$498$	5642.91	+	17367.1i	0.0227533	+	0.0700275i
$499$	−211403.	+	190348.i	−0.849006	+	0.764449i	−0.973721	−	0.227744i	$-0.926865\pi$
$499$	−211403.	+	190348.i	−0.849006	+	0.764449i	0.124715	+	0.992193i	$0.460198\pi$
$500$	72240.7	−	52485.9i	0.288963	−	0.209944i
$501$	29583.8	+	51240.7i	0.117863	+	0.204145i
$502$	102979.	+	59455.0i	0.408640	+	0.235929i
$503$	39863.3	+	379274.i	0.157557	+	1.49906i	0.732447	+	0.680824i	$0.238378\pi$
$503$	39863.3	+	379274.i	0.157557	+	1.49906i	−0.574890	+	0.818231i	$0.694955\pi$
$504$	145679.	+	105842.i	0.573502	+	0.416674i
$505$	−32229.0	+	306638.i	−0.126376	+	1.20239i
$506$	137307.	−	152494.i	0.536279	−	0.595598i
$507$	−90547.3	+	203373.i	−0.352257	+	0.791182i
$508$	31369.8	−	147583.i	0.121558	−	0.571886i
$509$	21430.5	+	100823.i	0.0827175	+	0.389155i	0.999958	−	0.00917896i	$-0.00292179\pi$
$509$	21430.5	+	100823.i	0.0827175	+	0.389155i	−0.917240	+	0.398334i	$0.869588\pi$
$510$	211979.	−	94379.1i	0.814990	−	0.362857i
$511$	193723.	+	62944.5i	0.741891	+	0.241055i
$512$	−68564.6	+	211020.i	−0.261553	+	0.804978i
$513$	−10549.5	−	23694.6i	−0.0400864	−	0.0900356i
$514$	139591.	−	29671.0i	0.528362	−	0.112307i
$515$	−145612.	−	30950.7i	−0.549012	−	0.116696i
$516$	−25161.3	−	11202.5i	−0.0945005	−	0.0420743i
$517$	−5607.70	−	5049.19i	−0.0209799	−	0.0188904i
$518$	172458.	+	18126.0i	0.642722	+	0.0675528i
$519$	−181547.	+	249878.i	−0.673991	+	0.927669i
$520$	485015.	−	50977.1i	1.79369	−	0.188525i
$521$	137142.	−	237538.i	0.505238	−	0.875098i	−0.494743	−	0.869039i	$-0.664738\pi$
$521$	137142.	−	237538.i	0.505238	−	0.875098i	0.999982	−	0.00605932i	$-0.00192875\pi$
$522$	129005.	−	74480.9i	0.473439	−	0.273340i
$523$	−202738.	−	279045.i	−0.741195	−	1.02017i	−0.998549	−	0.0538497i	$-0.982851\pi$
$523$	−202738.	−	279045.i	−0.741195	−	1.02017i	0.257355	−	0.966317i	$-0.417149\pi$
$524$	80682.1	+	89606.6i	0.293843	+	0.326345i
$525$	18877.2	−	6133.56i	0.0684886	−	0.0222533i
$526$			2061.73i			0.00745178i
$527$	420993.	+	274584.i	1.51584	+	0.988678i
$528$	−88131.7			−0.316129
$529$	16649.1	+	51240.8i	0.0594950	+	0.183107i
$530$	−62468.4	+	56246.8i	−0.222387	+	0.200238i
$531$	−130060.	+	94494.0i	−0.461269	+	0.335132i
$532$	5510.99	+	9545.31i	0.0194718	+	0.0337261i
$533$	−181963.	−	105056.i	−0.640513	−	0.369800i
$534$	−8369.64	−	79631.8i	−0.0293511	−	0.279257i
$535$	−256645.	−	186464.i	−0.896656	−	0.651459i
$536$	−58624.9	+	557779.i	−0.204058	+	1.94148i
$537$	−100804.	+	111955.i	−0.349567	+	0.388234i
$538$	−108604.	+	243928.i	−0.375215	+	0.842746i
$539$	941.100	−	4427.53i	0.00323935	−	0.0152400i
$540$	24072.9	+	113254.i	0.0825544	+	0.388388i
$541$	−134265.	+	59778.5i	−0.458741	+	0.204245i	−0.623078	−	0.782160i	$-0.714118\pi$
$541$	−134265.	+	59778.5i	−0.458741	+	0.204245i	0.164337	+	0.986404i	$0.447451\pi$
$542$	−96889.8	−	31481.4i	−0.329822	−	0.107166i
$543$	56726.7	−	174587.i	0.192393	−	0.592123i
$544$	−156406.	−	351293.i	−0.528512	−	1.18706i
$545$	−72112.3	+	15327.9i	−0.242782	+	0.0516049i
$546$	−214436.	−	45579.9i	−0.719305	−	0.152893i
$547$	−416232.	−	185318.i	−1.39111	−	0.619361i	−0.431863	−	0.901939i	$-0.642144\pi$
$547$	−416232.	−	185318.i	−1.39111	−	0.619361i	−0.959244	+	0.282578i	$0.908810\pi$
$548$	83592.8	+	75267.3i	0.278360	+	0.250637i
$549$	171857.	+	18062.9i	0.570194	+	0.0599298i
$550$	19122.3	−	26319.6i	0.0632143	−	0.0870070i
$551$	32702.3	−	3437.15i	0.107715	−	0.0113213i
$552$	−88211.3	+	152786.i	−0.289498	+	0.501426i
$553$	125385.	−	72391.3i	0.410012	−	0.236721i
$554$	226810.	+	312177.i	0.738998	+	1.01714i
$555$	105813.	+	117517.i	0.343521	+	0.381519i
$556$	−32695.4	+	10623.4i	−0.105764	+	0.0343648i
$557$		−	499392.i		−	1.60965i	−0.593513	−	0.804824i	$-0.702260\pi$
$557$		−	499392.i		−	1.60965i	0.593513	−	0.804824i	$-0.297740\pi$
$558$	112253.	−	111809.i	0.360520	−	0.359093i
$559$	−222772.			−0.712913
$560$	48452.4	+	149121.i	0.154504	+	0.475514i
$561$	285239.	−	256830.i	0.906322	−	0.816056i
$562$	17750.3	−	12896.4i	0.0561996	−	0.0408314i
$563$	−263678.	−	456703.i	−0.831872	−	1.44084i	−0.896552	−	0.442938i	$-0.853936\pi$
$563$	−263678.	−	456703.i	−0.831872	−	1.44084i	0.0646806	−	0.997906i	$-0.479397\pi$
$564$	1557.93	+	899.469i	0.00489766	+	0.00282767i
$565$	−46736.6	−	444669.i	−0.146407	−	1.39296i
$566$	89902.3	+	65317.8i	0.280632	+	0.203891i
$567$	−2309.77	+	21976.0i	−0.00718461	+	0.0683570i
$568$	369750.	−	410649.i	1.14607	−	1.27284i
$569$	−115555.	+	259541.i	−0.356915	+	0.801645i	0.642461	+	0.766319i	$0.277914\pi$
$569$	−115555.	+	259541.i	−0.356915	+	0.801645i	−0.999376	+	0.0353259i	$0.988753\pi$
$570$	3356.91	−	15793.0i	0.0103321	−	0.0486088i
$571$	34385.1	+	161769.i	0.105462	+	0.496161i	0.998896	+	0.0469671i	$0.0149556\pi$
$571$	34385.1	+	161769.i	0.105462	+	0.496161i	−0.893434	+	0.449194i	$0.851711\pi$
$572$	204350.	−	90982.5i	0.624572	−	0.278078i
$573$	134584.	+	43729.1i	0.409907	+	0.133187i
$574$	37948.2	−	116793.i	0.115178	−	0.354480i
$575$	−14571.1	−	32727.2i	−0.0440714	−	0.0989860i
$576$	−217239.	+	46175.6i	−0.654776	+	0.139177i
$577$	545736.	+	116000.i	1.63920	+	0.348422i	0.933079	−	0.359671i	$-0.117111\pi$
$577$	545736.	+	116000.i	1.63920	+	0.348422i	0.706119	+	0.708094i	$0.250445\pi$
$578$	−545156.	−	242719.i	−1.63179	−	0.726522i
$579$	211824.	+	190728.i	0.631857	+	0.568927i
$580$	−145985.	−	15343.6i	−0.433962	−	0.0456113i
$581$	31587.4	−	43476.3i	0.0935752	−	0.128795i
$582$	126133.	−	13257.2i	0.372378	−	0.0391385i
$583$	−69523.1	+	120418.i	−0.204546	+	0.354285i
$584$	−248583.	+	143519.i	−0.728863	+	0.420809i
$585$	216474.	+	297951.i	0.632550	+	0.870630i
$586$	−68800.3	−	76410.4i	−0.200353	−	0.222514i
$587$	−192712.	+	62616.0i	−0.559285	+	0.181723i	−0.574999	−	0.818154i	$-0.694998\pi$
$587$	−192712.	+	62616.0i	−0.559285	+	0.181723i	0.0157144	+	0.999877i	$0.494998\pi$
$588$			1079.10i			0.00312110i
$589$	32675.6	−	12468.7i	0.0941874	−	0.0359411i
$590$	−254475.			−0.731040
$591$	−93151.6	−	286691.i	−0.266695	−	0.820804i
$592$	−99894.6	+	89945.5i	−0.285035	+	0.256647i
$593$	37663.4	−	27364.1i	0.107105	−	0.0778164i	−0.532944	−	0.846151i	$-0.678914\pi$
$593$	37663.4	−	27364.1i	0.107105	−	0.0778164i	0.640049	+	0.768334i	$0.278914\pi$
$594$	−153827.	−	266436.i	−0.435972	−	0.755126i
$595$	−591381.	−	341434.i	−1.67045	−	0.964434i
$596$	−824.049	−	7840.31i	−0.00231985	−	0.0220719i
$597$	−80909.5	−	58784.2i	−0.227013	−	0.164935i
$598$	−41359.7	+	393511.i	−0.115658	+	1.10041i
$599$	271497.	−	301528.i	0.756677	−	0.840375i	−0.234610	−	0.972090i	$-0.575381\pi$
$599$	271497.	−	301528.i	0.756677	−	0.840375i	0.991288	+	0.131714i	$0.0420481\pi$
$600$	−11376.5	+	25552.0i	−0.0316014	+	0.0709779i
$601$	−83268.0	+	391745.i	−0.230531	+	1.08456i	0.698801	+	0.715316i	$0.253717\pi$
$601$	−83268.0	+	391745.i	−0.230531	+	1.08456i	−0.929332	+	0.369246i	$0.879616\pi$
$602$	−27070.5	−	127357.i	−0.0746971	−	0.351422i
$603$	−386923.	+	172269.i	−1.06412	+	0.473777i
$604$	−134493.	−	43699.5i	−0.368660	−	0.119785i
$605$	34806.3	−	107123.i	0.0950927	−	0.292665i
$606$	79440.8	+	178427.i	0.216321	+	0.485865i
$607$	128511.	−	27315.9i	0.348790	−	0.0741376i	−0.0301854	−	0.999544i	$-0.509610\pi$
$607$	128511.	−	27315.9i	0.348790	−	0.0741376i	0.378976	+	0.925407i	$0.376276\pi$
$608$	−26172.3	−	5563.09i	−0.0708002	−	0.0150490i
$609$	217393.	+	96789.5i	0.586153	+	0.260972i
$610$	203276.	+	183030.i	0.546294	+	0.491885i
$611$	14470.6	+	1520.93i	0.0387619	+	0.00407404i
$612$	99081.4	−	136374.i	0.264539	−	0.364106i
$613$	−173251.	+	18209.4i	−0.461058	+	0.0484592i	−0.332211	−	0.943205i	$-0.607794\pi$
$613$	−173251.	+	18209.4i	−0.461058	+	0.0484592i	−0.128848	+	0.991664i	$0.541128\pi$
$614$	156124.	−	270414.i	0.414125	−	0.717286i
$615$	96984.0	−	55993.7i	0.256419	−	0.148043i
$616$	277134.	+	381442.i	0.730344	+	1.00523i
$617$	−37529.7	−	41681.0i	−0.0985838	−	0.109488i	0.691834	−	0.722057i	$-0.256803\pi$
$617$	−37529.7	−	41681.0i	−0.0985838	−	0.109488i	−0.790418	+	0.612568i	$0.790136\pi$
$618$	−89684.4	+	29140.2i	−0.234823	+	0.0762985i
$619$			137474.i			0.358790i	0.983777	+	0.179395i	$0.0574140\pi$
$619$			137474.i			0.358790i	−0.983777	+	0.179395i	$0.942586\pi$
$620$	−154251.	+	24117.6i	−0.401277	+	0.0627408i
$621$	−338781.			−0.878488
$622$	−19113.5	−	58825.2i	−0.0494036	−	0.152049i
$623$	−175113.	+	157673.i	−0.451173	+	0.406238i
$624$	137484.	−	99887.9i	0.353088	−	0.256533i
$625$	216024.	+	374164.i	0.553021	+	0.957860i
$626$	−190082.	−	109744.i	−0.485057	−	0.280048i
$627$	−2791.69	−	26561.2i	−0.00710121	−	0.0675635i
$628$	−238266.	−	173110.i	−0.604146	−	0.438938i
$629$	61193.6	−	582218.i	0.154670	−	1.47158i
$630$	−144031.	+	159963.i	−0.362890	+	0.403030i
$631$	158437.	−	355855.i	0.397921	−	0.893746i	−0.597826	−	0.801626i	$-0.703969\pi$
$631$	158437.	−	355855.i	0.397921	−	0.893746i	0.995748	−	0.0921206i	$-0.0293645\pi$
$632$	−42419.0	+	199566.i	−0.106200	+	0.499634i
$633$	45435.2	+	213756.i	0.113393	+	0.533471i
$634$	182847.	−	81408.8i	0.454893	−	0.202532i
$635$	618606.	+	200997.i	1.53415	+	0.498474i
$636$	10243.5	−	31526.1i	0.0253240	−	0.0779393i
$637$	3550.03	+	7973.51i	0.00874890	+	0.0196504i
$638$	381514.	−	81093.4i	0.937281	−	0.199225i
$639$	408177.	+	86760.7i	0.999647	+	0.212481i
$640$	−36761.2	−	16367.1i	−0.0897489	−	0.0399588i
$641$	307431.	+	276812.i	0.748225	+	0.673705i	0.952270	−	0.305257i	$-0.0987423\pi$
$641$	307431.	+	276812.i	0.748225	+	0.673705i	−0.204045	+	0.978961i	$0.565409\pi$
$642$	−199852.	−	21005.3i	−0.484885	−	0.0509634i
$643$	−217005.	+	298682.i	−0.524865	+	0.722415i	−0.986337	−	0.164740i	$-0.947321\pi$
$643$	−217005.	+	298682.i	−0.524865	+	0.722415i	0.461472	+	0.887155i	$0.347321\pi$
$644$	143177.	−	15048.5i	0.345225	−	0.0362846i
$645$	59367.4	−	102827.i	0.142702	−	0.247166i
$646$	−51764.8	+	29886.4i	−0.124042	+	0.0716157i
$647$	177510.	+	244322.i	0.424048	+	0.583652i	0.966574	−	0.256387i	$-0.0825321\pi$
$647$	177510.	+	244322.i	0.424048	+	0.583652i	−0.542526	+	0.840039i	$0.682532\pi$
$648$	−20835.8	−	23140.5i	−0.0496205	−	0.0551091i
$649$	−400335.	+	130077.i	−0.950461	+	0.308824i
$650$			62731.3i			0.148476i
$651$	249906.	+	40089.2i	0.589677	+	0.0945943i
$652$	−101422.			−0.238583
$653$	−207605.	−	638941.i	−0.486867	−	1.49842i	−0.829258	−	0.558866i	$-0.811237\pi$
$653$	−207605.	−	638941.i	−0.486867	−	1.49842i	0.342390	−	0.939558i	$-0.388763\pi$
$654$	−34705.4	+	31248.9i	−0.0811412	+	0.0730598i
$655$	−420532.	+	305534.i	−0.980204	+	0.712160i
$656$	47597.0	+	82440.4i	0.110604	+	0.191572i
$657$	−187723.	−	108382.i	−0.434898	−	0.251089i
$658$	888.926	+	8457.56i	0.00205312	+	0.0195341i
$659$	608308.	+	441962.i	1.40072	+	1.01769i	0.994591	+	0.103872i	$0.0331233\pi$
$659$	608308.	+	441962.i	1.40072	+	1.01769i	0.406134	+	0.913814i	$0.366877\pi$
$660$	−12462.3	+	118571.i	−0.0286094	+	0.272201i
$661$	258761.	−	287383.i	0.592238	−	0.657747i	−0.370294	−	0.928915i	$-0.620743\pi$
$661$	258761.	−	287383.i	0.592238	−	0.657747i	0.962532	+	0.271168i	$0.0874098\pi$
$662$	−26966.4	+	60567.5i	−0.0615328	+	0.138205i
$663$	−153878.	+	723938.i	−0.350065	+	1.64693i
$664$	15744.8	+	74073.7i	0.0357110	+	0.168007i
$665$	−43407.5	+	19326.3i	−0.0981570	+	0.0437023i
$666$	−175504.	−	57024.7i	−0.395675	−	0.128563i
$667$	132723.	−	408479.i	0.298328	−	0.918160i
$668$	27673.7	+	62156.2i	0.0620176	+	0.139294i
$669$	449134.	−	95466.5i	1.00352	−	0.213304i
$670$	−655781.	−	139391.i	−1.46086	−	0.310516i
$671$	413347.	+	184034.i	0.918057	+	0.408745i
$672$	−143900.	−	129568.i	−0.318657	−	0.286920i
$673$	677149.	+	71171.2i	1.49504	+	0.157136i	0.816467	−	0.577393i	$-0.195930\pi$
$673$	677149.	+	71171.2i	1.49504	+	0.157136i	0.678578	+	0.734528i	$0.262597\pi$
$674$	−28008.3	+	38550.2i	−0.0616549	+	0.0848607i
$675$	−53416.4	+	5614.29i	−0.117238	+	0.0123222i
$676$	−127998.	+	221699.i	−0.280098	+	0.485143i
$677$	149245.	−	86166.4i	0.325627	−	0.188001i	−0.328271	−	0.944584i	$-0.606466\pi$
$677$	149245.	−	86166.4i	0.325627	−	0.188001i	0.653898	+	0.756583i	$0.273132\pi$
$678$	−166479.	−	229139.i	−0.362160	−	0.498470i
$679$	−249747.	−	277372.i	−0.541702	−	0.601621i
$680$	915183.	−	297361.i	1.97920	−	0.643081i
$681$		−	189194.i		−	0.407955i
$682$	370002.	−	187602.i	0.795490	−	0.403338i
$683$	564794.			1.21073			0.605366	−	0.795947i	$-0.293027\pi$
$683$	564794.			1.21073			0.605366	+	0.795947i	$0.293027\pi$
$684$	−3624.55	−	11155.2i	−0.00774714	−	0.0238433i
$685$	−360366.	+	324475.i	−0.768002	+	0.691512i
$686$	296804.	−	215641.i	0.630699	−	0.458230i
$687$	−143086.	−	247832.i	−0.303168	−	0.525103i
$688$	87407.5	+	50464.7i	0.184660	+	0.106613i
$689$	−28025.7	−	266646.i	−0.0590361	−	0.561691i
$690$	−170615.	−	123959.i	−0.358361	−	0.260364i
$691$	−49095.3	+	467110.i	−0.102821	+	0.978281i	0.814508	+	0.580152i	$0.197007\pi$
$691$	−49095.3	+	467110.i	−0.102821	+	0.978281i	−0.917330	+	0.398129i	$0.869660\pi$
$692$	−237657.	+	263945.i	−0.496294	+	0.551191i
$693$	−144821.	+	325273.i	−0.301554	+	0.677300i
$694$	−23350.2	+	109854.i	−0.0484811	+	0.228085i
$695$	−30813.0	−	144964.i	−0.0637918	−	0.300117i
$696$	−306345.	+	136393.i	−0.632400	+	0.281563i
$697$	−394293.	−	128113.i	−0.811621	−	0.263712i
$698$	−29149.1	+	89711.7i	−0.0598294	+	0.184136i
$699$	−11382.9	−	25566.4i	−0.0232969	−	0.0523256i
$700$	22325.7	−	4745.47i	0.0455627	−	0.00968464i
$701$	−841242.	−	178811.i	−1.71193	−	0.363881i	−0.755340	−	0.655333i	$-0.772528\pi$
$701$	−841242.	−	178811.i	−1.71193	−	0.363881i	−0.956585	+	0.291452i	$0.905862\pi$
$702$	541944.	+	241289.i	1.09971	+	0.489625i
$703$	−30272.1	−	27257.1i	−0.0612537	−	0.0551531i
$704$	−578335.	−	60785.5i	−1.16690	−	0.122646i
$705$	−4558.37	+	6274.06i	−0.00917131	+	0.0126232i
$706$	83706.5	−	8797.91i	0.167938	−	0.0176510i
$707$	287392.	−	497777.i	0.574957	−	0.995855i
$708$	86906.7	−	50175.6i	0.173375	−	0.100098i
$709$	−306488.	−	421844.i	−0.609706	−	0.839188i	0.386847	−	0.922144i	$-0.373564\pi$
$709$	−306488.	−	421844.i	−0.609706	−	0.839188i	−0.996553	+	0.0829554i	$0.973564\pi$
$710$	441992.	+	490882.i	0.876794	+	0.973779i
$711$	−146533.	+	47611.4i	−0.289865	+	0.0941828i
$712$		−	332056.i		−	0.655015i
$713$	24812.3	−	456143.i	0.0488076	−	0.897267i
$714$	−432568.			−0.848513
$715$	297990.	+	917120.i	0.582894	+	1.79396i
$716$	−128740.	+	115918.i	−0.251123	+	0.226112i
$717$	−150089.	+	109046.i	−0.291952	+	0.212116i
$718$	51771.6	+	89671.1i	0.100425	+	0.173942i
$719$	−336139.	−	194070.i	−0.650221	−	0.375405i	0.138320	−	0.990388i	$-0.455830\pi$
$719$	−336139.	−	194070.i	−0.650221	−	0.375405i	−0.788541	+	0.614982i	$0.789163\pi$
$720$	−17441.3	−	165943.i	−0.0336446	−	0.320107i
$721$	224513.	+	163118.i	0.431888	+	0.313785i
$722$	42342.5	−	402862.i	0.0812273	−	0.772826i
$723$	−243537.	+	270476.i	−0.465896	+	0.517430i
$724$	85859.7	−	192844.i	0.163799	−	0.367899i
$725$	14157.4	−	66605.4i	0.0269344	−	0.126717i
$726$	−14834.5	−	69790.9i	−0.0281449	−	0.132411i
$727$	857791.	−	381913.i	1.62298	−	0.722596i	0.624678	−	0.780883i	$-0.285230\pi$
$727$	857791.	−	381913.i	1.62298	−	0.722596i	0.998300	+	0.0582865i	$0.0185637\pi$
$728$	−864647.	−	280941.i	−1.63146	−	0.530093i
$729$	−87965.6	+	270730.i	−0.165523	+	0.509427i
$730$	−139560.	−	313457.i	−0.261888	−	0.588209i
$731$	−429957.	+	91390.3i	−0.804620	+	0.171027i
$732$	−105510.	−	22426.9i	−0.196912	−	0.0418549i
$733$	−288529.	−	128462.i	−0.537010	−	0.239092i	0.120267	−	0.992742i	$-0.461625\pi$
$733$	−288529.	−	128462.i	−0.537010	−	0.239092i	−0.657277	+	0.753650i	$0.728292\pi$
$734$	−465717.	−	419333.i	−0.864430	−	0.778336i
$735$	−4626.49	−	486.263i	−0.00856400	−	0.000900113i
$736$	−205426.	+	282745.i	−0.379228	+	0.521962i
$737$	−1.10291e6	+	115921.i	−2.03051	+	0.213416i
$738$	−65341.8	+	113175.i	−0.119972	+	0.207797i
$739$	234550.	−	135417.i	0.429483	−	0.247962i	−0.269643	−	0.962960i	$-0.586906\pi$
$739$	234550.	−	135417.i	0.429483	−	0.247962i	0.699126	+	0.714998i	$0.253572\pi$
$740$	106885.	+	147115.i	0.195189	+	0.268654i
$741$	34459.3	+	38270.9i	0.0627581	+	0.0696999i
$742$	149034.	−	48424.1i	0.270693	−	0.0879536i
$743$		−	74500.5i		−	0.134953i	−0.997721	−	0.0674764i	$-0.978505\pi$
$743$		−	74500.5i		−	0.134953i	0.997721	−	0.0674764i	$-0.0214947\pi$
$744$	−277624.	+	223906.i	−0.501546	+	0.404501i
$745$	33985.5			0.0612324
$746$	28751.7	+	88488.5i	0.0516637	+	0.159004i
$747$	−42499.1	+	38266.4i	−0.0761621	+	0.0685767i
$748$	357078.	−	259432.i	0.638205	−	0.463683i
$749$	295691.	+	512152.i	0.527077	+	0.912925i
$750$	211178.	+	121924.i	0.375427	+	0.216753i
$751$	−63700.8	−	606072.i	−0.112944	−	1.07459i	−0.893363	−	0.449337i	$-0.851660\pi$
$751$	−63700.8	−	606072.i	−0.112944	−	1.07459i	0.780418	−	0.625258i	$-0.215006\pi$
$752$	−5333.21	−	3874.80i	−0.00943090	−	0.00685195i
$753$	21130.3	−	201041.i	0.0372662	−	0.354564i
$754$	−503245.	+	558911.i	−0.885191	+	0.983104i
$755$	247960.	−	556928.i	0.434999	−	0.977024i
$756$	44876.6	−	211128.i	0.0785192	−	0.369404i
$757$	110555.	+	520120.i	0.192924	+	0.907636i	0.962962	+	0.269638i	$0.0869040\pi$
$757$	110555.	+	520120.i	0.192924	+	0.907636i	−0.770038	+	0.637998i	$0.779763\pi$
$758$	710903.	−	316514.i	1.23729	−	0.550877i
$759$	−331772.	−	107799.i	−0.575912	−	0.187125i
$760$	20691.0	−	63680.4i	0.0358224	−	0.110250i
$761$	162121.	+	364129.i	0.279943	+	0.628762i	0.997718	−	0.0675126i	$-0.0215063\pi$
$761$	162121.	+	364129.i	0.279943	+	0.628762i	−0.717776	+	0.696275i	$0.754840\pi$
$762$	403024.	−	85665.3i	0.694098	−	0.147535i
$763$	134432.	+	28574.3i	0.230915	+	0.0490825i
$764$	148658.	+	66186.9i	0.254684	+	0.113393i
$765$	540035.	+	486250.i	0.922782	+	0.830877i
$766$	52406.1	+	5508.10i	0.0893149	+	0.00938738i
$767$	477088.	−	656655.i	0.810976	−	1.11621i
$768$	334000.	−	35104.8i	0.566270	−	0.0595174i
$769$	−392795.	+	680340.i	−0.664222	+	1.15047i	0.315274	+	0.949001i	$0.397904\pi$
$769$	−392795.	+	680340.i	−0.664222	+	1.15047i	−0.979496	+	0.201465i	$0.935430\pi$
$770$	−488099.	+	281804.i	−0.823240	+	0.475298i
$771$	−142602.	−	196274.i	−0.239892	−	0.330183i
$772$	219323.	+	243583.i	0.368001	+	0.408707i
$773$	−247652.	+	80467.1i	−0.414461	+	0.134666i	−0.508822	−	0.860872i	$-0.669919\pi$
$773$	−247652.	+	80467.1i	−0.414461	+	0.134666i	0.0943616	+	0.995538i	$0.469919\pi$
$774$			138557.i			0.231285i
$775$	−3647.00	−	72332.3i	−0.00607202	−	0.120428i
$776$	525962.			0.873436
$777$	−91096.8	−	280367.i	−0.150890	−	0.464392i
$778$	195310.	−	175858.i	0.322675	−	0.290538i
$779$	−23338.2	+	16956.2i	−0.0384586	+	0.0279418i
$780$	−114946.	−	199093.i	−0.188932	−	0.327240i
$781$	946251.	+	546318.i	1.55133	+	0.895661i
$782$	81609.0	+	776458.i	0.133452	+	1.26971i
$783$	−520958.	−	378498.i	−0.849727	−	0.617363i
$784$	413.344	−	3932.70i	0.000672480	−	0.00639822i
$785$	849551.	−	943522.i	1.37864	−	1.53113i
$786$	−133929.	+	300808.i	−0.216784	+	0.486906i
$787$	107368.	−	505128.i	0.173351	−	0.815553i	−0.802420	−	0.596760i	$-0.796455\pi$
$787$	107368.	−	505128.i	0.173351	−	0.815553i	0.975771	−	0.218793i	$-0.0702121\pi$
$788$	−72070.5	−	339065.i	−0.116066	−	0.546048i
$789$	3201.95	−	1425.60i	0.00514352	−	0.00229004i
$790$	−231950.	−	75365.1i	−0.371655	−	0.120758i
$791$	−257571.	+	792722.i	−0.411665	+	1.26698i
$792$	−204078.	−	458366.i	−0.325346	−	0.730739i
$793$	−853397.	+	181395.i	−1.35708	+	0.288456i
$794$	685147.	+	145632.i	1.08678	+	0.231003i
$795$	130548.	+	58123.6i	0.206555	+	0.0919641i
$796$	−85464.5	−	76952.5i	−0.134884	−	0.121450i
$797$	832740.	+	87524.5i	1.31097	+	0.137788i	0.734096	−	0.679045i	$-0.237606\pi$
$797$	832740.	+	87524.5i	1.31097	+	0.137788i	0.576873	+	0.816834i	$0.304273\pi$
$798$	−17691.8	+	24350.6i	−0.0277821	+	0.0382388i
$799$	28552.8	−	3001.02i	0.0447255	−	0.00470084i
$800$	−27704.4	+	47985.4i	−0.0432881	+	0.0749772i
$801$	217164.	−	125380.i	0.338473	−	0.195417i
$802$	195784.	+	269473.i	0.304389	+	0.418955i
$803$	−379779.	−	421787.i	−0.588979	−	0.654127i
$804$	251442.	−	81698.5i	0.388979	−	0.126387i
$805$			620632.i			0.957729i
$806$	−364569.	+	712014.i	−0.561190	+	1.09602i
$807$	453924.			0.697006
$808$	250295.	+	770328.i	0.383379	+	1.17992i
$809$	−954087.	+	859063.i	−1.45778	+	1.31259i	−0.598448	+	0.801162i	$0.704216\pi$
$809$	−954087.	+	859063.i	−1.45778	+	1.31259i	−0.859328	+	0.511426i	$0.829118\pi$
$810$	30113.7	−	21878.9i	0.0458981	−	0.0333469i
$811$	−536372.	−	929023.i	−0.815500	−	1.41249i	−0.908968	−	0.416866i	$-0.863129\pi$
$811$	−536372.	−	929023.i	−0.815500	−	1.41249i	0.0934679	−	0.995622i	$-0.470205\pi$
$812$	236982.	+	136822.i	0.359422	+	0.207512i
$813$	18103.3	+	172242.i	0.0273891	+	0.260590i
$814$	−390904.	−	284008.i	−0.589958	−	0.428630i
$815$	45702.9	−	434834.i	0.0688063	−	0.654649i
$816$	224371.	−	249189.i	0.336966	−	0.374238i
$817$	−12440.3	+	27941.5i	−0.0186375	+	0.0418606i
$818$	128360.	−	603887.i	0.191833	−	0.902504i
$819$	−142744.	−	671559.i	−0.212809	−	1.00119i
$820$	117644.	−	52378.5i	0.174961	−	0.0778978i
$821$	86958.3	+	28254.5i	0.129010	+	0.0419180i	0.372811	−	0.927907i	$-0.378394\pi$
$821$	86958.3	+	28254.5i	0.129010	+	0.0419180i	−0.243800	+	0.969825i	$0.578394\pi$
$822$	−94922.9	+	292143.i	−0.140484	+	0.432366i
$823$	434449.	+	975788.i	0.641414	+	1.44064i	0.882583	+	0.470157i	$0.155803\pi$
$823$	434449.	+	975788.i	0.641414	+	1.44064i	−0.241168	+	0.970483i	$0.577531\pi$
$824$	−382520.	+	81307.0i	−0.563377	+	0.119750i
$825$	−54097.7	−	11498.8i	−0.0794824	−	0.0168945i
$826$	433379.	+	192953.i	0.635196	+	0.282807i
$827$	645366.	+	581090.i	0.943615	+	0.849635i	0.988785	−	0.149344i	$-0.0477163\pi$
$827$	645366.	+	581090.i	0.943615	+	0.849635i	−0.0451701	+	0.998979i	$0.514383\pi$
$828$	−152365.	−	16014.2i	−0.222242	−	0.0233585i
$829$	−445792.	+	613580.i	−0.648669	+	0.892816i	−0.999041	−	0.0437948i	$-0.986055\pi$
$829$	−445792.	+	613580.i	−0.648669	+	0.892816i	0.350372	+	0.936611i	$0.386055\pi$
$830$	−90028.6	+	9462.39i	−0.130685	+	0.0137355i
$831$	327994.	−	568103.i	0.474968	−	0.822668i
$832$	971088.	−	560658.i	1.40285	−	0.809937i
$833$	10122.8	+	13932.8i	0.0145884	+	0.0200793i
$834$	−62818.1	−	69766.6i	−0.0903135	−	0.100303i
$835$	−278956.	+	90638.3i	−0.400095	+	0.129999i
$836$		−	30711.7i		−	0.0439431i
$837$	−638916.	−	246711.i	−0.911996	−	0.352158i
$838$	550979.			0.784597
$839$	151448.	+	466108.i	0.215148	+	0.662159i	0.999143	+	0.0413912i	$0.0131790\pi$
$839$	151448.	+	466108.i	0.215148	+	0.662159i	−0.783995	+	0.620768i	$0.786821\pi$
$840$	360101.	−	324236.i	0.510347	−	0.459518i
$841$	88259.2	−	64124.1i	0.124787	−	0.0906628i
$842$	−22280.0	−	38590.2i	−0.0314262	−	0.0544318i
$843$	−32302.2	−	18649.7i	−0.0454545	−	0.0262431i
$844$	26267.5	+	249919.i	0.0368752	+	0.350844i
$845$	−892823.	−	648674.i	−1.25041	−	0.908475i
$846$	945.970	−	9000.31i	0.00132171	−	0.0125753i
$847$	−140501.	+	156042.i	−0.195845	+	0.217508i
$848$	−49407.4	+	110971.i	−0.0687070	+	0.154318i
$849$	39277.5	−	184786.i	0.0544915	−	0.256362i
$850$	25735.0	+	121074.i	0.0356194	+	0.167576i
$851$	−486071.	+	216413.i	−0.671182	+	0.298830i
$852$	−247735.	−	80494.0i	−0.341278	−	0.110888i
$853$	−154656.	+	475982.i	−0.212554	+	0.654173i	0.786765	+	0.617253i	$0.211755\pi$
$853$	−154656.	+	475982.i	−0.212554	+	0.654173i	−0.999318	+	0.0369198i	$0.988245\pi$
$854$	−207404.	−	465838.i	−0.284382	−	0.638732i
$855$	49459.6	−	10513.0i	0.0676579	−	0.0143811i
$856$	−815150.	−	173265.i	−1.11247	−	0.236464i
$857$	65549.1	+	29184.3i	0.0892493	+	0.0397363i	0.450876	−	0.892587i	$-0.351112\pi$
$857$	65549.1	+	29184.3i	0.0892493	+	0.0397363i	−0.361626	+	0.932323i	$0.617778\pi$
$858$	453954.	+	408742.i	0.616647	+	0.555232i
$859$	−225694.	−	23721.4i	−0.305867	−	0.0321479i	−0.0496484	−	0.998767i	$-0.515810\pi$
$859$	−225694.	−	23721.4i	−0.305867	−	0.0321479i	−0.256219	+	0.966619i	$0.582477\pi$
$860$	80254.1	−	110460.i	0.108510	−	0.149351i
$861$	−207623.	+	21822.1i	−0.280072	+	0.0294367i
$862$	−150388.	+	260479.i	−0.202394	+	0.350557i
$863$	−798951.	+	461275.i	−1.07275	+	0.619353i	−0.928932	−	0.370251i	$-0.879272\pi$
$863$	−798951.	+	461275.i	−1.07275	+	0.619353i	−0.143819	+	0.989604i	$0.545938\pi$
$864$	307990.	+	423912.i	0.412581	+	0.567869i
$865$	−1.02453e6	−	1.13786e6i	−1.36929	−	1.52075i
$866$	−254764.	+	82777.9i	−0.339705	+	0.110377i
$867$			1.01448e6i			1.34960i
$868$	280980.	+	75885.8i	0.372938	+	0.100721i
$869$	−403423.			−0.534221
$870$	−123871.	−	381235.i	−0.163656	−	0.503680i
$871$	1.58914e6	−	1.43087e6i	2.09472	−	1.88610i
$872$	−156682.	+	113836.i	−0.206057	+	0.149709i
$873$	198596.	+	343979.i	0.260581	+	0.451340i
$874$	47047.0	+	27162.6i	0.0615899	+	0.0355589i
$875$	−75011.1	−	713683.i	−0.0979737	−	0.932158i
$876$	109467.	+	79532.3i	0.142651	+	0.103642i
$877$	38092.1	−	362422.i	0.0495263	−	0.471212i	−0.941448	−	0.337159i	$-0.890534\pi$
$877$	38092.1	−	362422.i	0.0495263	−	0.471212i	0.990974	−	0.134053i	$-0.0427992\pi$
$878$	−621793.	+	690571.i	−0.806597	+	0.895817i
$879$	−71096.0	+	159684.i	−0.0920168	+	0.206673i
$880$	90835.6	−	427348.i	0.117298	−	0.551844i
$881$	−165276.	−	777560.i	−0.212940	−	1.00180i	−0.946631	−	0.322320i	$-0.895537\pi$
$881$	−165276.	−	777560.i	−0.212940	−	1.00180i	0.733691	−	0.679483i	$-0.237796\pi$
$882$	4959.29	−	2208.02i	0.00637503	−	0.00283834i
$883$	1.08598e6	+	352857.i	1.39284	+	0.452561i	0.906868	−	0.421415i	$-0.138466\pi$
$883$	1.08598e6	+	352857.i	1.39284	+	0.452561i	0.485970	+	0.873975i	$0.338466\pi$
$884$	−262997.	+	809420.i	−0.336547	+	1.03578i
$885$	175959.	+	395210.i	0.224659	+	0.504593i
$886$	−855504.	+	181843.i	−1.08982	+	0.231648i
$887$	−156826.	−	33334.4i	−0.199329	−	0.0423687i	0.107165	−	0.994241i	$-0.465823\pi$
$887$	−156826.	−	33334.4i	−0.199329	−	0.0423687i	−0.306494	+	0.951873i	$0.599156\pi$
$888$	379504.	+	168966.i	0.481271	+	0.214276i
$889$	−901100.	−	811355.i	−1.14017	−	1.02661i
$890$	394759.	+	41490.8i	0.498370	+	0.0523808i
$891$	36190.8	−	49812.3i	0.0455871	−	0.0627453i
$892$	525118.	−	55192.1i	0.659974	−	0.0693661i
$893$	998.854	−	1730.07i	0.00125256	−	0.00216950i
$894$	18644.2	−	10764.2i	0.0233275	−	0.0134681i
$895$	−438968.	−	604187.i	−0.548007	−	0.754268i
$896$	50195.2	+	55747.4i	0.0625239	+	0.0694398i
$897$	639737.	−	207863.i	0.795091	−	0.258341i
$898$		−	1.13914e6i		−	1.41262i
$899$	547774.	−	673709.i	0.677769	−	0.833591i
$900$	−24289.2			−0.0299866
$901$	−163480.	−	503140.i	−0.201379	−	0.619782i
$902$	−254288.	+	228962.i	−0.312546	+	0.281417i
$903$	−179072.	+	130103.i	−0.219610	+	0.159556i
$904$	−587286.	−	1.01721e6i	−0.718643	−	1.24473i
$905$	788100.	+	455010.i	0.962242	+	0.555551i
$906$	−40366.6	−	384062.i	−0.0491774	−	0.467892i
$907$	408085.	+	296491.i	0.496062	+	0.360410i	0.807511	−	0.589853i	$-0.200814\pi$
$907$	408085.	+	296491.i	0.496062	+	0.360410i	−0.311449	+	0.950263i	$0.600814\pi$
$908$	22741.1	−	216367.i	0.0275829	−	0.262434i
$909$	−409286.	+	454558.i	−0.495335	+	0.550126i
$910$	442031.	−	992818.i	0.533789	−	1.19891i
$911$	−195120.	+	917969.i	−0.235107	+	1.10609i	0.689238	+	0.724535i	$0.257945\pi$
$911$	−195120.	+	917969.i	−0.235107	+	1.10609i	−0.924345	+	0.381557i	$0.875388\pi$
$912$	−4851.01	−	22822.2i	−0.00583233	−	0.0274390i
$913$	−136795.	+	60904.8i	−0.164107	+	0.0730652i
$914$	321179.	+	104357.i	0.384463	+	0.124920i
$915$	143697.	−	442253.i	0.171635	−	0.528237i
$916$	−133848.	−	300627.i	−0.159522	−	0.358292i
$917$	947846.	−	201471.i	1.12720	−	0.239593i
$918$	1.14496e6	+	243368.i	1.35864	+	0.288788i
$919$	−266068.	−	118461.i	−0.315036	−	0.140263i	0.243127	−	0.969995i	$-0.421827\pi$
$919$	−266068.	−	118461.i	−0.315036	−	0.140263i	−0.558163	+	0.829731i	$0.688494\pi$
$920$	−649940.	−	585208.i	−0.767887	−	0.691409i
$921$	−527916.	−	55486.2i	−0.622366	−	0.0654133i
$922$	−134616.	+	185283.i	−0.158356	+	0.217959i
$923$	−2.09533e6	+	220228.i	−2.45951	+	0.258505i
$924$	111128.	−	192480.i	0.130161	−	0.225445i
$925$	−73053.6	+	42177.5i	−0.0853804	+	0.0492944i
$926$	−327808.	−	451190.i	−0.382295	−	0.526183i
$927$	−197609.	−	219467.i	−0.229958	−	0.255394i
$928$	−631785.	+	205279.i	−0.733624	+	0.238369i
$929$			1.09772e6i			1.27192i	0.771723	+	0.635959i	$0.219395\pi$
$929$			1.09772e6i			1.27192i	−0.771723	+	0.635959i	$0.780605\pi$
$930$	−231497.	−	358026.i	−0.267658	−	0.413951i
$931$	1198.33			0.00138254
$932$	−9944.70	−	30606.6i	−0.0114488	−	0.0352358i
$933$	−78141.7	+	70359.1i	−0.0897676	+	0.0808271i
$934$	−140547.	+	102113.i	−0.161112	+	0.117055i
$935$	951372.	+	1.64782e6i	1.08825	+	1.88490i
$936$	837868.	+	483743.i	0.956365	+	0.552158i
$937$	71641.7	+	681625.i	0.0815993	+	0.776365i	0.956435	+	0.291946i	$0.0943026\pi$
$937$	71641.7	+	681625.i	0.0815993	+	0.776365i	−0.874836	+	0.484420i	$0.839031\pi$
$938$	1.01112e6	+	734624.i	1.14921	+	0.834948i
$939$	−39003.0	+	371089.i	−0.0442351	+	0.420869i
$940$	−5967.23	+	6627.28i	−0.00675331	+	0.00750031i
$941$	−74768.9	+	167934.i	−0.0844387	+	0.189652i	−0.950830	−	0.309713i	$-0.899767\pi$
$941$	−74768.9	+	167934.i	−0.0844387	+	0.189652i	0.866391	+	0.499366i	$0.166434\pi$
$942$	167215.	−	786686.i	0.188440	−	0.886542i
$943$	78341.0	+	368566.i	0.0880980	+	0.414468i
$944$	−335945.	+	149572.i	−0.376985	+	0.167844i
$945$	884957.	+	287540.i	0.990965	+	0.321984i
$946$	−112110.	+	345039.i	−0.125274	+	0.385555i
$947$	298108.	+	669561.i	0.332409	+	0.746604i	0.999998	+	0.00207328i	$0.000659945\pi$
$947$	298108.	+	669561.i	0.332409	+	0.746604i	−0.667588	+	0.744531i	$0.732673\pi$
$948$	94074.1	−	19996.1i	0.104677	−	0.0222499i
$949$	1.07050e6	+	227542.i	1.18865	+	0.252655i
$950$	7868.16	+	3503.13i	0.00871818	+	0.00388158i
$951$	−252862.	−	227678.i	−0.279591	−	0.251745i
$952$	−1.78405e6	−	187512.i	−1.96849	−	0.206897i
$953$	−113653.	+	156430.i	−0.125139	+	0.172240i	−0.866990	−	0.498326i	$-0.833948\pi$
$953$	−113653.	+	156430.i	−0.125139	+	0.172240i	0.741851	+	0.670565i	$0.233948\pi$
$954$	−165846.	+	17431.1i	−0.182225	+	0.0191527i
$955$	−350755.	+	607525.i	−0.384589	+	0.666128i
$956$	−184754.	+	106668.i	−0.202152	+	0.116712i
$957$	−389742.	−	536434.i	−0.425553	−	0.585724i
$958$	−83801.1	−	93070.5i	−0.0913100	−	0.101410i
$959$	859743.	−	279347.i	0.934827	−	0.303744i
$960$			597648.i			0.648490i
$961$	378972.	−	842182.i	0.410355	−	0.911926i
$962$	931697.			1.00676
$963$	−194474.	−	598531.i	−0.209706	−	0.645407i
$964$	−311027.	+	280050.i	−0.334691	+	0.301357i
$965$	−1.14316e6	+	830552.i	−1.22758	+	0.891892i
$966$	196573.	+	340474.i	0.210653	+	0.364863i
$967$	998876.	+	576701.i	1.06821	+	0.616734i	0.927693	−	0.373343i	$-0.121789\pi$
$967$	998876.	+	576701.i	1.06821	+	0.616734i	0.140522	+	0.990078i	$0.455122\pi$
$968$	−30929.1	−	294271.i	−0.0330078	−	0.314048i
$969$	82207.9	+	59727.5i	0.0875520	+	0.0636102i
$970$	−65719.7	+	625281.i	−0.0698477	+	0.664557i
$971$	−531967.	+	590810.i	−0.564217	+	0.626627i	−0.955977	−	0.293441i	$-0.905200\pi$
$971$	−531967.	+	590810.i	−0.564217	+	0.626627i	0.391760	+	0.920068i	$0.371866\pi$
$972$	−150111.	+	337154.i	−0.158883	+	0.356858i
$973$	−57441.6	+	270241.i	−0.0606738	+	0.285448i
$974$	−93267.4	−	438789.i	−0.0983132	−	0.462527i
$975$	97424.2	−	43376.0i	0.102484	−	0.0456290i
$976$	375933.	+	122148.i	0.394649	+	0.128229i
$977$	495654.	−	1.52547e6i	0.519265	−	1.59813i	−0.256120	−	0.966645i	$-0.582444\pi$
$977$	495654.	−	1.52547e6i	0.519265	−	1.59813i	0.775385	−	0.631489i	$-0.217556\pi$
$978$	−112653.	−	253022.i	−0.117778	−	0.264533i
$979$	642236.	−	136511.i	0.670084	−	0.142431i
$980$	−5232.53	−	1112.21i	−0.00544828	−	0.00115807i
$981$	−133610.	−	59487.0i	−0.138836	−	0.0618136i
$982$	191734.	+	172638.i	0.198827	+	0.179025i
$983$	819352.	+	86117.4i	0.847937	+	0.0891218i	0.518523	−	0.855064i	$-0.326482\pi$
$983$	819352.	+	86117.4i	0.847937	+	0.0891218i	0.329414	+	0.944186i	$0.393149\pi$
$984$	172920.	−	238004.i	0.178589	−	0.245807i
$985$	1.48617e6	−	156203.i	1.53178	−	0.160996i
$986$	−741993.	+	1.28517e6i	−0.763213	+	1.32192i
$987$	12520.3	−	7228.58i	0.0128523	−	0.00742026i
$988$	34808.4	+	47909.7i	0.0356591	+	0.0490805i
$989$	267319.	+	296888.i	0.273299	+	0.303529i
$990$	570421.	−	185341.i	0.582003	−	0.189104i
$991$		−	1.46915e6i		−	1.49595i	−0.663726	−	0.747976i	$-0.731026\pi$
$991$		−	1.46915e6i		−	1.49595i	0.663726	−	0.747976i	$-0.268974\pi$
$992$	−593323.	+	383638.i	−0.602931	+	0.389851i
$993$	112710.			0.114305
$994$	−380520.	−	1.17112e6i	−0.385128	−	1.18530i
$995$	368435.	−	331740.i	0.372147	−	0.335083i
$996$	28880.3	−	20982.8i	0.0291127	−	0.0211516i
$997$	63328.7	+	109688.i	0.0637104	+	0.110350i	0.896121	−	0.443809i	$-0.146373\pi$
$997$	63328.7	+	109688.i	0.0637104	+	0.110350i	−0.832411	+	0.554159i	$0.813040\pi$
$998$	−773629.	−	446655.i	−0.776733	−	0.448447i
$999$	83384.5	+	793351.i	0.0835515	+	0.794940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.5.h.a.11.8	✓	80
31.17	odd	30	inner	31.5.h.a.17.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.5.h.a.11.8	✓	80	1.1	even	1	trivial
31.5.h.a.17.8	yes	80	31.17	odd	30	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	31.h (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.970390 + 2.98655i) q^{2} +(3.96725 - 3.57213i) q^{3} +(4.96643 - 3.60832i) q^{4} +(13.2322 + 22.9188i) q^{5} +(14.5181 + 8.38205i) q^{6} +(-5.15690 - 49.0646i) q^{7} +(56.2440 + 40.8637i) q^{8} +(-5.48783 + 52.2132i) q^{9} +(-55.6079 + 61.7588i) q^{10} +(-55.9128 + 125.582i) q^{11} +(6.81368 - 32.0559i) q^{12} +(-55.1111 - 259.277i) q^{13} +(141.530 - 63.0131i) q^{14} +(134.364 + 43.6576i) q^{15} +(-37.1108 + 114.215i) q^{16} +(-212.733 - 477.805i) q^{17} +(-161.263 + 34.2775i) q^{18} +(-35.5978 - 7.56655i) q^{19} +(148.415 + 66.0787i) q^{20} +(-195.724 - 176.230i) q^{21} +(-429.315 - 45.1228i) q^{22} +(-279.407 + 384.571i) q^{23} +(369.105 - 38.7945i) q^{24} +(-37.6817 + 65.2666i) q^{25} +(720.866 - 416.192i) q^{26} +(418.908 + 576.578i) q^{27} +(-202.652 - 225.068i) q^{28} +(-859.313 + 279.208i) q^{29} +443.651i q^{30} +(-806.998 + 521.799i) q^{31} +735.221 q^{32} +(226.776 + 697.944i) q^{33} +(1220.56 - 1098.99i) q^{34} +(1056.27 - 767.422i) q^{35} +(161.147 + 279.115i) q^{36} +(969.351 + 559.655i) q^{37} +(-11.9459 - 113.657i) q^{38} +(-1144.81 - 831.754i) q^{39} +(-192.316 + 1829.76i) q^{40} +(530.399 - 589.067i) q^{41} +(336.393 - 755.552i) q^{42} +(174.735 - 822.062i) q^{43} +(175.454 + 825.447i) q^{44} +(-1269.28 + 565.120i) q^{45} +(-1419.68 - 461.281i) q^{46} +(-16.9627 + 52.2059i) q^{47} +(260.764 + 585.685i) q^{48} +(-32.2080 + 6.84602i) q^{49} +(-231.488 - 49.2043i) q^{50} +(-2550.75 - 1135.67i) q^{51} +(-1209.26 - 1088.82i) q^{52} +(1005.95 + 105.729i) q^{53} +(-1315.48 + 1810.60i) q^{54} +(-3618.04 + 380.272i) q^{55} +(1714.92 - 2970.32i) q^{56} +(-168.254 + 97.1416i) q^{57} +(-1667.74 - 2295.44i) q^{58} +(2048.95 + 2275.59i) q^{59} +(824.843 - 268.008i) q^{60} -3291.45i q^{61} +(-2341.48 - 1903.79i) q^{62} +2590.12 q^{63} +(1307.22 + 4023.22i) q^{64} +(5213.09 - 4693.89i) q^{65} +(-1864.39 + 1354.56i) q^{66} +(4033.66 + 6986.50i) q^{67} +(-2780.60 - 1605.38i) q^{68} +(265.259 + 2523.77i) q^{69} +(3316.94 + 2409.89i) q^{70} +(830.831 - 7904.83i) q^{71} +(-2442.28 + 2712.43i) q^{72} +(-1679.33 + 3771.83i) q^{73} +(-730.791 + 3438.10i) q^{74} +(83.6480 + 393.533i) q^{75} +(-204.097 + 90.8696i) q^{76} +(6449.97 + 2095.72i) q^{77} +(1373.16 - 4226.17i) q^{78} +(1193.65 + 2680.97i) q^{79} +(-3108.74 + 660.782i) q^{80} +(-438.112 - 93.1237i) q^{81} +(2273.97 + 1012.44i) q^{82} +(809.495 + 728.873i) q^{83} +(-1607.95 - 169.002i) q^{84} +(8135.82 - 11198.0i) q^{85} +(2624.69 - 275.866i) q^{86} +(-2411.74 + 4177.26i) q^{87} +(-8276.51 + 4778.45i) q^{88} +(-2807.44 - 3864.11i) q^{89} +(-2919.46 - 3242.39i) q^{90} +(-12437.1 + 4041.07i) q^{91} +2918.14i q^{92} +(-1337.63 + 4952.81i) q^{93} -172.376 q^{94} +(-297.621 - 915.982i) q^{95} +(2916.81 - 2626.31i) q^{96} +(6120.59 - 4446.87i) q^{97} +(-51.7003 - 89.5475i) q^{98} +(-6250.21 - 3608.56i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{2} - 16 q^{3} - 138 q^{4} - q^{5} - 9 q^{6} + 288 q^{7} - 221 q^{8} - 182 q^{9} + 102 q^{10} - 49 q^{11} - 159 q^{12} + 527 q^{13} - 740 q^{14} + 1060 q^{15} - 1970 q^{16} + 848 q^{17} + 3 q^{18}+ \cdots + 75228 q^{99}+O(q^{100}) \) 80 * q - 6 * q^2 - 16 * q^3 - 138 * q^4 - q^5 - 9 * q^6 + 288 * q^7 - 221 * q^8 - 182 * q^9 + 102 * q^10 - 49 * q^11 - 159 * q^12 + 527 * q^13 - 740 * q^14 + 1060 * q^15 - 1970 * q^16 + 848 * q^17 + 3 * q^18 + 1534 * q^19 + 1165 * q^20 + 1367 * q^21 + 4579 * q^22 - 1375 * q^23 - 3828 * q^24 - 5997 * q^25 - 2547 * q^26 - 3235 * q^27 - 1564 * q^28 - 1150 * q^29 - 3587 * q^31 + 15718 * q^32 - 5029 * q^33 + 5958 * q^34 + 4959 * q^35 + 13555 * q^36 + 3462 * q^37 + 6118 * q^38 - 8143 * q^39 - 13011 * q^40 - 7290 * q^41 - 24735 * q^42 + 4687 * q^43 + 17051 * q^44 - 6093 * q^45 - 16530 * q^46 - 4302 * q^47 + 40344 * q^48 + 14300 * q^49 + 30081 * q^50 + 1348 * q^51 - 14433 * q^52 + 17996 * q^53 - 42200 * q^54 - 5289 * q^55 - 32470 * q^56 - 35847 * q^57 - 38475 * q^58 + 3552 * q^59 - 26585 * q^60 - 6327 * q^62 + 35814 * q^63 + 231 * q^64 + 18280 * q^65 + 85992 * q^66 + 2185 * q^67 + 56694 * q^68 + 57836 * q^69 + 6338 * q^70 - 3708 * q^71 - 25127 * q^72 + 5344 * q^73 + 5247 * q^74 + 13921 * q^75 - 10354 * q^76 - 37000 * q^77 - 98345 * q^78 + 53300 * q^79 + 65286 * q^80 + 20439 * q^81 - 26142 * q^82 - 59542 * q^83 - 77120 * q^84 + 4525 * q^85 - 100990 * q^86 - 55761 * q^87 - 82191 * q^88 - 26395 * q^89 - 61689 * q^90 - 12450 * q^91 + 9029 * q^93 + 67112 * q^94 - 3972 * q^95 + 210490 * q^96 + 5883 * q^97 + 107722 * q^98 + 75228 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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