LMFDB - Embedded newform 27.5.f.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,5,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.79098900326$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.1
Character	$\chi$	$=$	27.5
Dual form			27.5.f.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.07357 - 6.04645i) q^{2} +(4.83746 + 7.58940i) q^{3} +(-8.04003 + 45.5973i) q^{4} +(2.20171 + 6.04914i) q^{5} +(21.3457 - 67.7548i) q^{6} +(3.89095 + 22.0667i) q^{7} +(207.124 - 119.583i) q^{8} +(-34.1980 + 73.4268i) q^{9} +(25.4053 - 44.0033i) q^{10} +(-28.2925 + 77.7331i) q^{11} +(-384.949 + 159.556i) q^{12} +(120.696 + 101.276i) q^{13} +(113.684 - 135.483i) q^{14} +(-35.2587 + 45.9721i) q^{15} +(-1077.77 - 392.278i) q^{16} +(33.0101 + 19.0584i) q^{17} +(617.478 - 165.760i) q^{18} +(137.485 + 238.131i) q^{19} +(-293.526 + 51.7566i) q^{20} +(-148.651 + 136.277i) q^{21} +(613.553 - 223.315i) q^{22} +(-428.407 - 75.5397i) q^{23} +(1909.51 + 993.467i) q^{24} +(447.033 - 375.105i) q^{25} -1243.61i q^{26} +(-722.697 + 95.6565i) q^{27} -1037.46 q^{28} +(-470.746 - 561.013i) q^{29} +(456.856 - 20.0529i) q^{30} +(74.5048 - 422.538i) q^{31} +(1787.49 + 4911.08i) q^{32} +(-726.812 + 161.307i) q^{33} +(-52.2436 - 296.288i) q^{34} +(-124.918 + 72.1213i) q^{35} +(-3073.11 - 2149.69i) q^{36} +(-54.4289 + 94.2735i) q^{37} +(742.306 - 2039.47i) q^{38} +(-184.762 + 1405.93i) q^{39} +(1179.40 + 989.634i) q^{40} +(1055.26 - 1257.61i) q^{41} +(1578.18 + 207.399i) q^{42} +(1379.12 + 501.958i) q^{43} +(-3316.95 - 1915.04i) q^{44} +(-519.463 - 45.2043i) q^{45} +(1716.81 + 2973.60i) q^{46} +(1303.06 - 229.765i) q^{47} +(-2236.53 - 10077.3i) q^{48} +(1784.40 - 649.470i) q^{49} +(-4536.11 - 799.839i) q^{50} +(15.0432 + 342.721i) q^{51} +(-5588.30 + 4689.14i) q^{52} +2351.34i q^{53} +(4245.04 + 3884.43i) q^{54} -532.511 q^{55} +(3444.71 + 4105.24i) q^{56} +(-1142.19 + 2195.37i) q^{57} +(-1003.77 + 5692.68i) q^{58} +(-573.291 - 1575.11i) q^{59} +(-1812.72 - 1977.32i) q^{60} +(-854.355 - 4845.29i) q^{61} +(-2932.86 + 1693.29i) q^{62} +(-1753.35 - 468.937i) q^{63} +(11450.1 - 19832.2i) q^{64} +(-346.895 + 953.086i) q^{65} +(4662.87 + 3576.23i) q^{66} +(2218.87 + 1861.85i) q^{67} +(-1134.41 + 1351.94i) q^{68} +(-1499.10 - 3616.77i) q^{69} +(1069.86 + 389.396i) q^{70} +(5708.42 + 3295.76i) q^{71} +(1697.37 + 19297.9i) q^{72} +(-1533.30 - 2655.75i) q^{73} +(846.169 - 149.202i) q^{74} +(5009.33 + 1578.16i) q^{75} +(-11963.5 + 4354.36i) q^{76} +(-1825.40 - 321.867i) q^{77} +(9438.26 - 6015.92i) q^{78} +(3255.22 - 2731.45i) q^{79} -7383.29i q^{80} +(-4221.99 - 5022.10i) q^{81} -12958.0 q^{82} +(3708.74 + 4419.90i) q^{83} +(-5018.69 - 7873.73i) q^{84} +(-42.6083 + 241.644i) q^{85} +(-3962.00 - 10885.5i) q^{86} +(1980.54 - 6286.56i) q^{87} +(3435.50 + 19483.7i) q^{88} +(-7424.17 + 4286.35i) q^{89} +(2362.21 + 3370.26i) q^{90} +(-1765.20 + 3057.42i) q^{91} +(6888.81 - 18926.8i) q^{92} +(3567.22 - 1478.56i) q^{93} +(-8000.43 - 6713.15i) q^{94} +(-1137.79 + 1355.96i) q^{95} +(-28625.3 + 37323.1i) q^{96} +(-13985.3 - 5090.22i) q^{97} +(-12980.3 - 7494.17i) q^{98} +(-4740.14 - 4735.75i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 3 q^{5} + 90 q^{6} - 6 q^{7} - 9 q^{8} - 108 q^{9} - 3 q^{10} - 492 q^{11} - 339 q^{12} - 6 q^{13} + 1137 q^{14} + 1017 q^{15} - 54 q^{16} - 9 q^{17} + 603 q^{18} - 3 q^{19}+ \cdots - 162405 q^{99}+O(q^{100}) $ 66 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 3 * q^5 + 90 * q^6 - 6 * q^7 - 9 * q^8 - 108 * q^9 - 3 * q^10 - 492 * q^11 - 339 * q^12 - 6 * q^13 + 1137 * q^14 + 1017 * q^15 - 54 * q^16 - 9 * q^17 + 603 * q^18 - 3 * q^19 - 2487 * q^20 - 2784 * q^21 + 1002 * q^22 - 2724 * q^23 - 3312 * q^24 + 435 * q^25 + 1368 * q^27 - 12 * q^28 + 5016 * q^29 + 10773 * q^30 - 1671 * q^31 + 10224 * q^32 + 2925 * q^33 - 342 * q^34 - 2682 * q^35 - 7704 * q^36 - 3 * q^37 - 6564 * q^38 - 1983 * q^39 - 1113 * q^40 + 5754 * q^41 + 8694 * q^42 - 1266 * q^43 - 4545 * q^44 - 7029 * q^45 - 3 * q^46 - 9159 * q^47 - 28383 * q^48 + 5898 * q^49 - 34977 * q^50 - 14814 * q^51 + 2871 * q^52 + 13878 * q^54 - 12 * q^55 + 39243 * q^56 + 15792 * q^57 - 12291 * q^58 + 24762 * q^59 + 50670 * q^60 - 8358 * q^61 + 38304 * q^62 + 21609 * q^63 + 6141 * q^64 + 23727 * q^65 + 11349 * q^66 + 15996 * q^67 - 43533 * q^68 - 26847 * q^69 - 7251 * q^70 - 19773 * q^71 - 77580 * q^72 + 6108 * q^73 - 74847 * q^74 - 49155 * q^75 - 28614 * q^76 - 33909 * q^77 - 9108 * q^78 - 5658 * q^79 - 12600 * q^81 - 12 * q^82 + 18813 * q^83 + 82356 * q^84 + 24219 * q^85 + 96474 * q^86 + 84555 * q^87 + 36042 * q^88 + 110232 * q^89 + 153540 * q^90 - 6042 * q^91 + 73545 * q^92 + 1293 * q^93 + 2631 * q^94 - 65163 * q^95 - 152226 * q^96 - 3696 * q^97 - 259938 * q^98 - 162405 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−5.07357	−	6.04645i	−1.26839	−	1.51161i	−0.759021	−	0.651066i	$-0.774322\pi$
$2$	−5.07357	−	6.04645i	−1.26839	−	1.51161i	−0.509372	−	0.860546i	$-0.670122\pi$
$3$	4.83746	+	7.58940i	0.537495	+	0.843267i
$3$	4.83746	+	7.58940i	0.537495	+	0.843267i
$4$	−8.04003	+	45.5973i	−0.502502	+	2.84983i
$5$	2.20171	+	6.04914i	0.0880683	+	0.241966i	0.975906	−	0.218191i	$-0.0700155\pi$
$5$	2.20171	+	6.04914i	0.0880683	+	0.241966i	−0.887838	+	0.460157i	$0.847793\pi$
$6$	21.3457	−	67.7548i	0.592937	−	1.88208i
$7$	3.89095	+	22.0667i	0.0794072	+	0.450341i	0.998424	+	0.0561220i	$0.0178736\pi$
$7$	3.89095	+	22.0667i	0.0794072	+	0.450341i	−0.919017	+	0.394219i	$0.871015\pi$
$8$	207.124	−	119.583i	3.23631	−	1.86848i
$9$	−34.1980	+	73.4268i	−0.422198	+	0.906504i
$10$	25.4053	−	44.0033i	0.254053	−	0.440033i
$11$	−28.2925	+	77.7331i	−0.233823	+	0.642422i	−1.00000		0.000206842i	$-0.999934\pi$
$11$	−28.2925	+	77.7331i	−0.233823	+	0.642422i	0.766177	+	0.642629i	$0.222156\pi$
$12$	−384.949	+	159.556i	−2.67326	+	1.10803i
$13$	120.696	+	101.276i	0.714176	+	0.599265i	0.925768	−	0.378093i	$-0.123420\pi$
$13$	120.696	+	101.276i	0.714176	+	0.599265i	−0.211591	+	0.977358i	$0.567865\pi$
$14$	113.684	−	135.483i	0.580021	−	0.691242i
$15$	−35.2587	+	45.9721i	−0.156705	+	0.204321i
$16$	−1077.77	−	392.278i	−4.21005	−	1.53233i
$17$	33.0101	+	19.0584i	0.114222	+	0.0659460i	0.556022	−	0.831167i	$-0.312327\pi$
$17$	33.0101	+	19.0584i	0.114222	+	0.0659460i	−0.441801	+	0.897113i	$0.645660\pi$
$18$	617.478	−	165.760i	1.90580	−	0.511604i
$19$	137.485	+	238.131i	0.380844	+	0.659642i	0.991183	−	0.132499i	$-0.0423000\pi$
$19$	137.485	+	238.131i	0.380844	+	0.659642i	−0.610339	+	0.792140i	$0.708967\pi$
$20$	−293.526	+	51.7566i	−0.733816	+	0.129392i
$21$	−148.651	+	136.277i	−0.337076	+	0.309017i
$22$	613.553	−	223.315i	1.26767	−	0.461395i
$23$	−428.407	−	75.5397i	−0.809843	−	0.142797i	−0.246631	−	0.969110i	$-0.579323\pi$
$23$	−428.407	−	75.5397i	−0.809843	−	0.142797i	−0.563212	+	0.826312i	$0.690435\pi$
$24$	1909.51	+	993.467i	3.31513	+	1.72477i
$25$	447.033	−	375.105i	0.715253	−	0.600169i
$26$		−	1243.61i		−	1.83966i
$27$	−722.697	+	95.6565i	−0.991354	+	0.131216i
$28$	−1037.46			−1.32330
$29$	−470.746	−	561.013i	−0.559746	−	0.667079i	0.409747	−	0.912199i	$-0.365617\pi$
$29$	−470.746	−	561.013i	−0.559746	−	0.667079i	−0.969493	+	0.245120i	$0.921173\pi$
$30$	456.856	−	20.0529i	0.507618	−	0.0222810i
$31$	74.5048	−	422.538i	0.0775284	−	0.439686i	−0.921192	−	0.389109i	$-0.872783\pi$
$31$	74.5048	−	422.538i	0.0775284	−	0.439686i	0.998720	−	0.0505766i	$-0.0161059\pi$
$32$	1787.49	+	4911.08i	1.74559	+	4.79598i
$33$	−726.812	+	161.307i	−0.667412	+	0.148124i
$34$	−52.2436	−	296.288i	−0.0451934	−	0.256304i
$35$	−124.918	+	72.1213i	−0.101974	+	0.0588746i
$36$	−3073.11	−	2149.69i	−2.37123	−	1.65871i
$37$	−54.4289	+	94.2735i	−0.0397581	+	0.0688631i	−0.885220	−	0.465173i	$-0.845992\pi$
$37$	−54.4289	+	94.2735i	−0.0397581	+	0.0688631i	0.845462	+	0.534036i	$0.179325\pi$
$38$	742.306	−	2039.47i	0.514062	−	1.41237i
$39$	−184.762	+	1405.93i	−0.121474	+	0.924343i
$40$	1179.40	+	989.634i	0.737125	+	0.618521i
$41$	1055.26	−	1257.61i	0.627758	−	0.748133i	−0.354626	−	0.935008i	$-0.615392\pi$
$41$	1055.26	−	1257.61i	0.627758	−	0.748133i	0.982384	+	0.186876i	$0.0598361\pi$
$42$	1578.18	+	207.399i	0.894660	+	0.117573i
$43$	1379.12	+	501.958i	0.745873	+	0.271476i	0.686868	−	0.726782i	$-0.258985\pi$
$43$	1379.12	+	501.958i	0.745873	+	0.271476i	0.0590049	+	0.998258i	$0.481207\pi$
$44$	−3316.95	−	1915.04i	−1.71330	−	0.989173i
$45$	−519.463	−	45.2043i	−0.256525	−	0.0223231i
$46$	1716.81	+	2973.60i	0.811345	+	1.40529i
$47$	1303.06	−	229.765i	0.589886	−	0.104013i	0.129266	−	0.991610i	$-0.458738\pi$
$47$	1303.06	−	229.765i	0.589886	−	0.104013i	0.460621	+	0.887597i	$0.347627\pi$
$48$	−2236.53	−	10077.3i	−0.970717	−	4.37382i
$49$	1784.40	−	649.470i	0.743192	−	0.270500i
$50$	−4536.11	−	799.839i	−1.81444	−	0.319935i
$51$	15.0432	+	342.721i	0.00578361	+	0.131765i
$52$	−5588.30	+	4689.14i	−2.06668	+	1.73415i
$53$			2351.34i			0.837075i	0.908199	+	0.418538i	$0.137457\pi$
$53$			2351.34i			0.837075i	−0.908199	+	0.418538i	$0.862543\pi$
$54$	4245.04	+	3884.43i	1.45577	+	1.33211i
$55$	−532.511			−0.176037
$56$	3444.71	+	4105.24i	1.09844	+	1.30907i
$57$	−1142.19	+	2195.37i	−0.351552	+	0.675708i
$58$	−1003.77	+	5692.68i	−0.298387	+	1.69224i
$59$	−573.291	−	1575.11i	−0.164692	−	0.452486i	0.829705	−	0.558202i	$-0.188509\pi$
$59$	−573.291	−	1575.11i	−0.164692	−	0.452486i	−0.994396	+	0.105716i	$0.966287\pi$
$60$	−1812.72	−	1977.32i	−0.503534	−	0.549255i
$61$	−854.355	−	4845.29i	−0.229604	−	1.30215i	−0.853686	−	0.520788i	$-0.825638\pi$
$61$	−854.355	−	4845.29i	−0.229604	−	1.30215i	0.624083	−	0.781358i	$-0.285473\pi$
$62$	−2932.86	+	1693.29i	−0.762971	+	0.440501i
$63$	−1753.35	−	468.937i	−0.441761	−	0.118150i
$64$	11450.1	−	19832.2i	2.79543	−	4.84183i
$65$	−346.895	+	953.086i	−0.0821053	+	0.225583i
$66$	4662.87	+	3576.23i	1.07045	+	0.820988i
$67$	2218.87	+	1861.85i	0.494291	+	0.414759i	0.855561	−	0.517702i	$-0.173212\pi$
$67$	2218.87	+	1861.85i	0.494291	+	0.414759i	−0.361270	+	0.932461i	$0.617657\pi$
$68$	−1134.41	+	1351.94i	−0.245331	+	0.292375i
$69$	−1499.10	−	3616.77i	−0.314871	−	0.759666i
$70$	1069.86	+	389.396i	0.218338	+	0.0794687i
$71$	5708.42	+	3295.76i	1.13240	+	0.653791i	0.944537	−	0.328405i	$-0.106511\pi$
$71$	5708.42	+	3295.76i	1.13240	+	0.653791i	0.187862	+	0.982196i	$0.439844\pi$
$72$	1697.37	+	19297.9i	0.327425	+	3.72259i
$73$	−1533.30	−	2655.75i	−0.287727	−	0.498358i	0.685540	−	0.728035i	$-0.259566\pi$
$73$	−1533.30	−	2655.75i	−0.287727	−	0.498358i	−0.973267	+	0.229677i	$0.926233\pi$
$74$	846.169	−	149.202i	0.154523	−	0.0272466i
$75$	5009.33	+	1578.16i	0.890547	+	0.280561i
$76$	−11963.5	+	4354.36i	−2.07124	+	0.753870i
$77$	−1825.40	−	321.867i	−0.307876	−	0.0542868i
$78$	9438.26	−	6015.92i	1.55133	−	0.988809i
$79$	3255.22	−	2731.45i	0.521586	−	0.437663i	−0.343598	−	0.939117i	$-0.611646\pi$
$79$	3255.22	−	2731.45i	0.521586	−	0.437663i	0.865184	+	0.501454i	$0.167201\pi$
$80$		−	7383.29i		−	1.15364i
$81$	−4221.99	−	5022.10i	−0.643498	−	0.765448i
$82$	−12958.0			−1.92713
$83$	3708.74	+	4419.90i	0.538357	+	0.641589i	0.964818	−	0.262917i	$-0.0846846\pi$
$83$	3708.74	+	4419.90i	0.538357	+	0.641589i	−0.426462	+	0.904506i	$0.640240\pi$
$84$	−5018.69	−	7873.73i	−0.711265	−	1.11589i
$85$	−42.6083	+	241.644i	−0.00589735	+	0.0334455i
$86$	−3962.00	−	10885.5i	−0.535695	−	1.47181i
$87$	1980.54	−	6286.56i	0.261665	−	0.830567i
$88$	3435.50	+	19483.7i	0.443633	+	2.51597i
$89$	−7424.17	+	4286.35i	−0.937277	+	0.541137i	−0.889106	−	0.457702i	$-0.848673\pi$
$89$	−7424.17	+	4286.35i	−0.937277	+	0.541137i	−0.0481712	+	0.998839i	$0.515339\pi$
$90$	2362.21	+	3370.26i	0.291631	+	0.416081i
$91$	−1765.20	+	3057.42i	−0.213163	+	0.369208i
$92$	6888.81	−	18926.8i	0.813895	−	2.23616i
$93$	3567.22	−	1478.56i	0.412443	−	0.170952i
$94$	−8000.43	−	6713.15i	−0.905435	−	0.759750i
$95$	−1137.79	+	1355.96i	−0.126070	+	0.150245i
$96$	−28625.3	+	37323.1i	−3.10604	+	4.04981i
$97$	−13985.3	−	5090.22i	−1.48637	−	0.540995i	−0.533880	−	0.845560i	$-0.679266\pi$
$97$	−13985.3	−	5090.22i	−1.48637	−	0.540995i	−0.952491	+	0.304566i	$0.901489\pi$
$98$	−12980.3	−	7494.17i	−1.35155	−	0.780318i
$99$	−4740.14	−	4735.75i	−0.483639	−	0.483190i
$100$	13509.6	+	23399.4i	1.35096	+	2.33994i
$101$	11512.8	−	2030.01i	1.12859	−	0.199001i	0.421983	−	0.906604i	$-0.361334\pi$
$101$	11512.8	−	2030.01i	1.12859	−	0.199001i	0.706611	+	0.707602i	$0.250223\pi$
$102$	1995.92	−	1829.78i	0.191842	−	0.175873i
$103$	10815.6	−	3936.55i	1.01947	−	0.371057i	0.222409	−	0.974954i	$-0.428608\pi$
$103$	10815.6	−	3936.55i	1.01947	−	0.371057i	0.797063	+	0.603896i	$0.206386\pi$
$104$	37109.8	+	6543.46i	3.43101	+	0.604980i
$105$	−1151.64	−	599.168i	−0.104457	−	0.0543463i
$106$	14217.3	−	11929.7i	1.26533	−	1.06174i
$107$			20065.9i			1.75263i	0.481737	+	0.876316i	$0.340006\pi$
$107$			20065.9i			1.75263i	−0.481737	+	0.876316i	$0.659994\pi$
$108$	1448.83	−	33722.1i	0.124214	−	2.89113i
$109$	−17197.7			−1.44749			−0.723747	−	0.690065i	$-0.757582\pi$
$109$	−17197.7			−1.44749			−0.723747	+	0.690065i	$0.757582\pi$
$110$	2701.73	+	3219.80i	0.223284	+	0.266099i
$111$	−978.777	+	42.9618i	−0.0794397	+	0.00348688i
$112$	4462.70	−	25309.2i	0.355764	−	2.01764i
$113$	−1472.26	−	4045.00i	−0.115300	−	0.316783i	0.868598	−	0.495518i	$-0.165022\pi$
$113$	−1472.26	−	4045.00i	−0.115300	−	0.316783i	−0.983897	+	0.178735i	$0.942800\pi$
$114$	19069.2	−	4232.18i	1.46731	−	0.325653i
$115$	−486.277	−	2757.81i	−0.0367695	−	0.208530i
$116$	29365.5	−	16954.2i	2.18233	−	1.25997i
$117$	−11563.9	+	5398.87i	−0.844760	+	0.394395i
$118$	−6615.16	+	11457.8i	−0.475090	+	0.822881i
$119$	−292.115	+	802.579i	−0.0206281	+	0.0566753i
$120$	−1805.43	+	13738.3i	−0.125377	+	0.954045i
$121$	5973.69	+	5012.52i	0.408011	+	0.342362i
$122$	−24962.1	+	29748.7i	−1.67711	+	1.99870i
$123$	14649.3	+	1925.16i	0.968292	+	0.127250i
$124$	18667.6	+	6794.43i	1.21407	+	0.441886i
$125$	6737.63	+	3889.97i	0.431208	+	0.248958i
$126$	6060.34	+	12980.7i	0.381730	+	0.817632i
$127$	615.120	+	1065.42i	0.0381375	+	0.0660562i	0.884464	−	0.466608i	$-0.154524\pi$
$127$	615.120	+	1065.42i	0.0381375	+	0.0660562i	−0.846327	+	0.532664i	$0.821191\pi$
$128$	−95657.2	+	16867.0i	−5.83845	+	1.02948i
$129$	2861.87	+	12894.9i	0.171977	+	0.774887i
$130$	7522.78	−	2738.07i	0.445135	−	0.162016i
$131$	−4641.13	−	818.357i	−0.270447	−	0.0476870i	0.0367801	−	0.999323i	$-0.488290\pi$
$131$	−4641.13	−	818.357i	−0.270447	−	0.0476870i	−0.307227	+	0.951636i	$0.599401\pi$
$132$	−1511.58	−	34437.5i	−0.0867527	−	1.97644i
$133$	−4719.81	+	3960.39i	−0.266822	+	0.223890i
$134$		−	22862.6i		−	1.27325i
$135$	−2169.81	−	4161.09i	−0.119057	−	0.228318i
$136$	9116.23			0.492876
$137$	−7426.65	−	8850.74i	−0.395687	−	0.471562i	0.531013	−	0.847364i	$-0.321812\pi$
$137$	−7426.65	−	8850.74i	−0.395687	−	0.471562i	−0.926700	+	0.375802i	$0.877367\pi$
$138$	−14262.8	+	27414.2i	−0.748941	+	1.43952i
$139$	−5531.48	+	31370.6i	−0.286294	+	1.62365i	0.414334	+	0.910125i	$0.364014\pi$
$139$	−5531.48	+	31370.6i	−0.286294	+	1.62365i	−0.700628	+	0.713527i	$0.747097\pi$
$140$	−2284.19	−	6275.77i	−0.116541	−	0.320192i
$141$	8047.27	+	8777.96i	0.404772	+	0.441525i
$142$	−9034.46	−	51237.0i	−0.448049	−	2.54101i
$143$	−11287.3	+	6516.71i	−0.551972	+	0.318681i
$144$	65661.4	−	65722.4i	3.16654	−	3.16948i
$145$	2357.21	−	4082.80i	0.112114	−	0.194188i
$146$	−8278.56	+	22745.2i	−0.388373	+	1.06705i
$147$	13561.1	+	10400.8i	0.627565	+	0.481316i
$148$	−3861.01	−	3239.77i	−0.176270	−	0.147908i
$149$	13608.1	−	16217.5i	0.612949	−	0.730484i	−0.366892	−	0.930263i	$-0.619578\pi$
$149$	13608.1	−	16217.5i	0.612949	−	0.730484i	0.979841	+	0.199780i	$0.0640226\pi$
$150$	−15872.9	−	38295.6i	−0.705464	−	1.70202i
$151$	−9687.00	−	3525.78i	−0.424850	−	0.154633i	0.120742	−	0.992684i	$-0.461473\pi$
$151$	−9687.00	−	3525.78i	−0.424850	−	0.154633i	−0.545591	+	0.838051i	$0.683695\pi$
$152$	56952.7	+	32881.7i	2.46506	+	1.42320i
$153$	−2528.28	+	1772.07i	−0.108004	+	0.0757002i
$154$	7315.13	+	12670.2i	0.308447	+	0.534246i
$155$	2720.03	−	479.615i	0.113217	−	0.0199632i
$156$	−62620.9	−	19728.3i	−2.57318	−	0.810665i
$157$	31963.3	−	11633.7i	1.29674	−	0.471975i	0.400806	−	0.916163i	$-0.368730\pi$
$157$	31963.3	−	11633.7i	1.29674	−	0.471975i	0.895933	+	0.444188i	$0.146508\pi$
$158$	−33031.2	−	5824.29i	−1.32315	−	0.233307i
$159$	−17845.3	+	11374.5i	−0.705878	+	0.449924i
$160$	−25772.3	+	21625.5i	−1.00673	+	0.844747i
$161$		−	9747.44i		−	0.376044i
$162$	−8945.31	+	51008.1i	−0.340852	+	1.94361i
$163$	22115.4			0.832376			0.416188	−	0.909279i	$-0.363366\pi$
$163$	22115.4			0.832376			0.416188	+	0.909279i	$0.363366\pi$
$164$	48859.3	+	58228.3i	1.81660	+	2.16494i
$165$	−2576.00	−	4041.44i	−0.0946188	−	0.148446i
$166$	7908.16	−	44849.4i	0.286985	−	1.62757i
$167$	−9631.70	−	26462.9i	−0.345358	−	0.948865i	−0.983812	−	0.179204i	$-0.942648\pi$
$167$	−9631.70	−	26462.9i	−0.345358	−	0.948865i	0.638453	−	0.769660i	$-0.279574\pi$
$168$	−14492.7	+	46002.2i	−0.513489	+	1.62990i
$169$	−648.878	−	3679.97i	−0.0227190	−	0.128846i
$170$	1677.26	−	968.369i	0.0580368	−	0.0335076i
$171$	−22186.9	+	1951.47i	−0.758759	+	0.0667375i
$172$	−33976.1	+	58848.3i	−1.14846	+	1.98919i
$173$	7444.28	−	20453.0i	0.248731	−	0.683384i	−0.751002	−	0.660300i	$-0.770429\pi$
$173$	7444.28	−	20453.0i	0.248731	−	0.683384i	0.999734	−	0.0230839i	$-0.00734849\pi$
$174$	−48059.8	+	19920.1i	−1.58739	+	0.657949i
$175$	10016.7	+	8405.02i	0.327076	+	0.274450i
$176$	60985.9	−	72680.2i	1.96881	−	2.34634i
$177$	9180.83	−	11970.4i	0.293046	−	0.382088i
$178$	63584.2	+	23142.8i	2.00682	+	0.730425i
$179$	−29830.9	−	17222.9i	−0.931024	−	0.537527i	−0.0438887	−	0.999036i	$-0.513975\pi$
$179$	−29830.9	−	17222.9i	−0.931024	−	0.537527i	−0.887135	+	0.461509i	$0.847308\pi$
$180$	6237.70	−	23322.7i	0.192522	−	0.719836i
$181$	−11555.4	−	20014.6i	−0.352719	−	0.610927i	0.634006	−	0.773328i	$-0.281409\pi$
$181$	−11555.4	−	20014.6i	−0.352719	−	0.610927i	−0.986725	+	0.162401i	$0.948076\pi$
$182$	27442.4	−	4838.83i	0.828474	−	0.146082i
$183$	32639.9	−	29922.9i	0.974646	−	0.893514i
$184$	−97766.4	+	35584.1i	−2.88771	+	1.05104i
$185$	−690.111	−	121.685i	−0.0201639	−	0.00355545i
$186$	−27038.6	−	14067.4i	−0.781553	−	0.406620i
$187$	−2415.41	+	2026.77i	−0.0690728	+	0.0579590i
$188$			61263.3i			1.73334i
$189$	−4922.80	−	15575.3i	−0.137813	−	0.436027i
$190$	13971.4			0.387019
$191$	−41704.4	−	49701.4i	−1.14318	−	1.36239i	−0.922014	−	0.387156i	$-0.873458\pi$
$191$	−41704.4	−	49701.4i	−1.14318	−	1.36239i	−0.221168	−	0.975236i	$-0.570987\pi$
$192$	205904.	−	9037.79i	5.58549	−	0.245166i
$193$	−6465.08	+	36665.3i	−0.173564	+	0.984329i	0.766225	+	0.642573i	$0.222133\pi$
$193$	−6465.08	+	36665.3i	−0.173564	+	0.984329i	−0.939789	+	0.341756i	$0.888978\pi$
$194$	40177.5	+	110387.i	1.06753	+	2.93301i
$195$	−8911.44	+	1977.79i	−0.234357	+	0.0520128i
$196$	15267.4	+	86585.7i	0.397423	+	2.25390i
$197$	15981.5	−	9226.92i	0.411799	−	0.237752i	−0.279764	−	0.960069i	$-0.590256\pi$
$197$	15981.5	−	9226.92i	0.411799	−	0.237752i	0.691562	+	0.722317i	$0.256923\pi$
$198$	−4584.99	+	52688.2i	−0.116952	+	1.34395i
$199$	4262.01	−	7382.03i	0.107624	−	0.186410i	−0.807183	−	0.590301i	$-0.799009\pi$
$199$	4262.01	−	7382.03i	0.107624	−	0.186410i	0.914807	+	0.403891i	$0.132342\pi$
$200$	47734.9	−	131151.i	1.19337	−	3.27877i
$201$	−3396.66	+	25846.5i	−0.0840738	+	0.639750i
$202$	−70685.3	−	59312.0i	−1.73231	−	1.45358i
$203$	10548.1	−	12570.7i	0.255965	−	0.305047i
$204$	−15748.1	−	2069.56i	−0.378414	−	0.0497299i
$205$	9930.85	+	3614.53i	0.236308	+	0.0860091i
$206$	−78675.7	−	45423.5i	−1.85399	−	1.07040i
$207$	20197.3	−	28873.2i	0.471360	−	0.673837i
$208$	−90354.6	−	156499.i	−2.08845	−	3.61730i
$209$	−22400.4	+	3949.80i	−0.512819	+	0.0904238i
$210$	2220.11	+	10003.3i	0.0503425	+	0.226832i
$211$	31636.8	−	11514.8i	0.710603	−	0.258638i	0.0386719	−	0.999252i	$-0.487687\pi$
$211$	31636.8	−	11514.8i	0.710603	−	0.258638i	0.671931	+	0.740614i	$0.265465\pi$
$212$	−107215.	−	18904.9i	−2.38552	−	0.420632i
$213$	2601.41	+	59266.6i	0.0573389	+	1.30632i
$214$	121327.	−	101806.i	2.64930	−	2.22303i
$215$			9447.66i			0.204384i
$216$	−138249.	+	106235.i	−2.96315	+	2.27698i
$217$	9613.90			0.204165
$218$	87253.7	+	103985.i	1.83599	+	2.18805i
$219$	12738.3	−	24483.9i	0.265597	−	0.510496i
$220$	4281.40	−	24281.0i	0.0884587	−	0.501674i
$221$	2054.03	+	5643.39i	0.0420554	+	0.115546i
$222$	5225.66	+	5700.16i	0.106032	+	0.115659i
$223$	10437.1	+	59191.7i	0.209879	+	1.19028i	0.889575	+	0.456790i	$0.151001\pi$
$223$	10437.1	+	59191.7i	0.209879	+	1.19028i	−0.679695	+	0.733495i	$0.737888\pi$
$224$	−101416.	+	58552.7i	−2.02121	+	1.16695i
$225$	12255.1	+	45652.1i	0.242077	+	0.901769i
$226$	−16988.3	+	29424.6i	−0.332608	+	0.576094i
$227$	−18942.4	+	52043.8i	−0.367606	+	1.00999i	0.608663	+	0.793429i	$0.291706\pi$
$227$	−18942.4	+	52043.8i	−0.367606	+	1.00999i	−0.976269	+	0.216561i	$0.930516\pi$
$228$	−90919.8	−	69731.8i	−1.74900	−	1.34141i
$229$	−52101.7	−	43718.5i	−0.993530	−	0.833671i	−0.00745522	−	0.999972i	$-0.502373\pi$
$229$	−52101.7	−	43718.5i	−0.993530	−	0.833671i	−0.986075	+	0.166301i	$0.946818\pi$
$230$	−14207.8	+	16932.2i	−0.268579	+	0.320079i
$231$	−6387.50	−	15410.7i	−0.119704	−	0.288801i
$232$	−164590.	−	59905.9i	−3.05793	−	1.11300i
$233$	77958.7	+	45009.5i	1.43599	+	0.829071i	0.997568	−	0.0696961i	$-0.0222029\pi$
$233$	77958.7	+	45009.5i	1.43599	+	0.829071i	0.438426	+	0.898767i	$0.355536\pi$
$234$	91314.4	+	42529.0i	1.66766	+	0.776701i
$235$	4258.84	+	7376.52i	0.0771179	+	0.133572i
$236$	76429.8	−	13476.6i	1.37227	−	0.241968i
$237$	36477.1	+	11491.9i	0.649416	+	0.204595i
$238$	6334.82	−	2305.68i	0.111836	−	0.0407048i
$239$	23344.1	+	4116.19i	0.408678	+	0.0720609i	0.374208	−	0.927345i	$-0.377915\pi$
$239$	23344.1	+	4116.19i	0.408678	+	0.0720609i	0.0344698	+	0.999406i	$0.489026\pi$
$240$	56034.8	−	35716.4i	0.972826	−	0.620076i
$241$	−80913.7	+	67894.7i	−1.39312	+	1.16897i	−0.429060	+	0.903276i	$0.641155\pi$
$241$	−80913.7	+	67894.7i	−1.39312	+	1.16897i	−0.964059	+	0.265690i	$0.914400\pi$
$242$		−	61551.0i		−	1.05100i
$243$	17691.1	−	56336.6i	0.299600	−	0.954065i
$244$	227801.			3.82627
$245$	7857.47	+	9364.17i	0.130903	+	0.156004i
$246$	−62683.9	−	98343.7i	−1.03582	−	1.62509i
$247$	−7523.04	+	42665.3i	−0.123310	+	0.699327i
$248$	−35096.6	−	96427.1i	−0.570639	−	1.56782i
$249$	−15603.6	+	49528.2i	−0.251666	+	0.798829i
$250$	−10663.3	−	60474.8i	−0.170613	−	0.967597i
$251$	−27670.0	+	15975.3i	−0.439200	+	0.253572i	−0.703258	−	0.710934i	$-0.748272\pi$
$251$	−27670.0	+	15975.3i	−0.439200	+	0.253572i	0.264058	+	0.964507i	$0.414939\pi$
$252$	35479.2	−	76177.7i	0.558693	−	1.19957i
$253$	17992.6	−	31164.2i	0.281096	−	0.486872i
$254$	3321.15	−	9124.78i	0.0514779	−	0.141434i
$255$	−2040.05	+	845.570i	−0.0313733	+	0.0130038i
$256$	306628.	+	257291.i	4.67877	+	3.92596i
$257$	10958.3	−	13059.6i	0.165911	−	0.197725i	−0.676683	−	0.736275i	$-0.736583\pi$
$257$	10958.3	−	13059.6i	0.165911	−	0.197725i	0.842594	+	0.538550i	$0.181028\pi$
$258$	63448.4	−	82727.3i	0.953194	−	1.24282i
$259$	−2292.08	−	834.251i	−0.0341689	−	0.0124365i
$260$	−40669.1	−	23480.3i	−0.601614	−	0.347342i
$261$	57292.0	−	15379.8i	0.841033	−	0.225772i
$262$	18599.0	+	32214.4i	0.270948	+	0.469296i
$263$	−92554.4	+	16319.8i	−1.33809	+	0.235942i	−0.796468	−	0.604680i	$-0.793301\pi$
$263$	−92554.4	+	16319.8i	−1.33809	+	0.235942i	−0.541623	+	0.840622i	$0.682190\pi$
$264$	−131250.	+	120325.i	−1.88318	+	1.72642i
$265$	−14223.6	+	5176.98i	−0.202544	+	0.0737198i
$266$	47892.6	+	8444.76i	0.676870	+	0.119350i
$267$	−68444.9	−	35610.0i	−0.960105	−	0.499516i
$268$	−102735.	+	86205.2i	−1.43038	+	1.20023i
$269$		−	59027.4i		−	0.815735i	−0.913041	−	0.407867i	$-0.866273\pi$
$269$		−	59027.4i		−	0.815735i	0.913041	−	0.407867i	$-0.133727\pi$
$270$	−14151.1	+	34231.2i	−0.194117	+	0.469564i
$271$	−32488.1			−0.442370			−0.221185	−	0.975232i	$-0.570992\pi$
$271$	−32488.1			−0.442370			−0.221185	+	0.975232i	$0.570992\pi$
$272$	−28101.2	−	33489.8i	−0.379829	−	0.452662i
$273$	−31743.0	+	1393.31i	−0.425915	+	0.0186948i
$274$	−15835.9	+	89809.8i	−0.210931	+	1.19625i
$275$	16510.4	+	45362.0i	0.218319	+	0.599827i
$276$	176968.	−	39275.9i	2.32314	−	0.515594i
$277$	−2070.19	−	11740.6i	−0.0269805	−	0.153014i	0.968341	−	0.249630i	$-0.0803091\pi$
$277$	−2070.19	−	11740.6i	−0.0269805	−	0.153014i	−0.995322	+	0.0966163i	$0.969198\pi$
$278$	217745.	−	125715.i	2.81746	−	1.62666i
$279$	28477.7	+	19920.6i	0.365844	+	0.255914i
$280$	−17249.0	+	29876.1i	−0.220012	+	0.381072i
$281$	−22709.5	+	62393.8i	−0.287604	+	0.790185i	0.708796	+	0.705413i	$0.249239\pi$
$281$	−22709.5	+	62393.8i	−0.287604	+	0.790185i	−0.996400	+	0.0847723i	$0.972984\pi$
$282$	12247.1	−	93193.0i	0.154005	−	1.17189i
$283$	−91623.7	−	76881.4i	−1.14402	−	0.959950i	−0.144461	−	0.989511i	$-0.546145\pi$
$283$	−91623.7	−	76881.4i	−1.14402	−	0.959950i	−0.999563	+	0.0295606i	$0.990589\pi$
$284$	−196174.	+	233791.i	−2.43222	+	2.89861i
$285$	−15794.9	−	2075.71i	−0.194459	−	0.0255551i
$286$	96669.8	+	35184.9i	1.18184	+	0.430154i
$287$	31857.3	+	18392.8i	0.386763	+	0.223298i
$288$	−421733.	−	36699.7i	−5.08455	−	0.442464i
$289$	−41034.1	−	71073.1i	−0.491302	−	0.850960i
$290$	−36645.9	+	6461.66i	−0.435742	+	0.0768330i
$291$	−29021.4	−	130764.i	−0.342714	−	1.54419i
$292$	133423.	−	48561.9i	1.56482	−	0.569548i
$293$	148527.	+	26189.4i	1.73010	+	0.305064i	0.948043	−	0.318142i	$-0.103059\pi$
$293$	148527.	+	26189.4i	1.73010	+	0.305064i	0.782058	+	0.623205i	$0.214170\pi$
$294$	−5915.30	−	134765.i	−0.0684356	−	1.55913i
$295$	8265.82	−	6935.85i	0.0949821	−	0.0796995i
$296$			26035.0i			0.297149i
$297$	13011.2	−	58883.8i	0.147505	−	0.667549i
$298$	−167100.			−1.88167
$299$	−44056.6	−	52504.6i	−0.492797	−	0.587293i
$300$	−112235.	+	215723.i	−1.24705	+	2.39693i
$301$	−5710.47	+	32385.7i	−0.0630288	+	0.357454i
$302$	27829.3	+	76460.3i	0.305132	+	0.838343i
$303$	71099.2	+	77555.0i	0.774425	+	0.844743i
$304$	−54764.2	−	310583.i	−0.592584	−	3.36071i
$305$	27428.8	−	15836.0i	0.294854	−	0.170234i
$306$	23542.1	+	6296.38i	0.251422	+	0.0672432i
$307$	44883.6	−	77740.7i	0.476224	−	0.824844i	−0.523405	−	0.852084i	$-0.675338\pi$
$307$	44883.6	−	77740.7i	0.476224	−	0.824844i	0.999629	+	0.0272399i	$0.00867181\pi$
$308$	29352.5	−	80645.3i	0.309417	−	0.850115i
$309$	82195.9	+	63040.8i	0.860861	+	0.660245i
$310$	−16700.2	−	14013.2i	−0.173780	−	0.145819i
$311$	−21775.1	+	25950.6i	−0.225134	+	0.268304i	−0.866773	−	0.498702i	$-0.833810\pi$
$311$	−21775.1	+	25950.6i	−0.225134	+	0.268304i	0.641640	+	0.767006i	$0.278254\pi$
$312$	129856.	+	313295.i	1.33399	+	3.21843i
$313$	−32110.5	−	11687.3i	−0.327762	−	0.119296i	0.172898	−	0.984940i	$-0.444687\pi$
$313$	−32110.5	−	11687.3i	−0.327762	−	0.119296i	−0.500660	+	0.865644i	$0.666909\pi$
$314$	−232511.	−	134240.i	−2.35822	−	1.36152i
$315$	−1023.70	−	11638.7i	−0.0103169	−	0.117296i
$316$	98374.7	+	170390.i	0.985166	+	1.70636i
$317$	−12811.0	+	2258.93i	−0.127487	+	0.0224793i	−0.237027	−	0.971503i	$-0.576173\pi$
$317$	−12811.0	+	2258.93i	−0.127487	+	0.0224793i	0.109541	+	0.993982i	$0.465062\pi$
$318$	159315.	+	50191.2i	1.57544	+	0.496333i
$319$	56927.9	−	20720.1i	0.559428	−	0.203615i
$320$	145177.	+	25598.7i	1.41775	+	0.249987i
$321$	−152288.	+	97067.9i	−1.47794	+	0.942031i
$322$	−58937.4	+	49454.4i	−0.568433	+	0.476972i
$323$			10481.0i			0.100461i
$324$	262939.	−	152133.i	2.50476	−	1.44922i
$325$	91944.1			0.870477
$326$	−112204.	−	133720.i	−1.05578	−	1.25823i
$327$	−83193.1	−	130520.i	−0.778022	−	1.22062i
$328$	68180.7	−	386672.i	0.633744	−	3.59414i
$329$	10140.3	+	27860.2i	0.0936825	+	0.257390i
$330$	−11366.8	+	36080.2i	−0.104379	+	0.331315i
$331$	11218.9	+	63625.8i	0.102399	+	0.580734i	0.992227	+	0.124438i	$0.0397129\pi$
$331$	11218.9	+	63625.8i	0.102399	+	0.580734i	−0.889828	+	0.456295i	$0.849176\pi$
$332$	−231354.	+	133572.i	−2.09894	+	1.21183i
$333$	−5060.85	−	7220.51i	−0.0456388	−	0.0651147i
$334$	−111139.	+	192499.i	−0.996265	+	1.72558i
$335$	−6377.32	+	17521.5i	−0.0568262	+	0.156129i
$336$	213670.	−	88563.1i	1.89263	−	0.784466i
$337$	−69332.0	−	58176.5i	−0.610484	−	0.512257i	0.284312	−	0.958732i	$-0.408235\pi$
$337$	−69332.0	−	58176.5i	−0.610484	−	0.512257i	−0.894796	+	0.446475i	$0.852679\pi$
$338$	−18958.6	+	22594.0i	−0.165948	+	0.197770i
$339$	23577.2	−	30741.1i	0.205160	−	0.267498i
$340$	−10675.7	−	3885.65i	−0.0923506	−	0.0336129i
$341$	30737.2	+	17746.2i	0.264336	+	0.152614i
$342$	124366.	+	124251.i	1.06329	+	1.06230i
$343$	48174.4	+	83440.5i	0.409476	+	0.709232i
$344$	345674.	−	60951.6i	2.92112	−	0.515072i
$345$	18577.8	−	17031.3i	0.156083	−	0.143090i
$346$	−161437.	+	58758.3i	−1.34850	+	0.490814i
$347$	12974.9	+	2287.82i	0.107757	+	0.0190004i	0.227267	−	0.973833i	$-0.427021\pi$
$347$	12974.9	+	2287.82i	0.107757	+	0.0190004i	−0.119510	+	0.992833i	$0.538132\pi$
$348$	270726.	+	140851.i	2.23549	+	1.16306i
$349$	21598.6	−	18123.4i	0.177327	−	0.148795i	−0.549804	−	0.835294i	$-0.685298\pi$
$349$	21598.6	−	18123.4i	0.177327	−	0.148795i	0.727131	+	0.686499i	$0.240853\pi$
$350$		−	103209.i		−	0.842523i
$351$	−96914.2	−	61646.4i	−0.786635	−	0.500372i
$352$	−432326.			−3.48920
$353$	70618.8	+	84160.2i	0.566723	+	0.675395i	0.970955	−	0.239262i	$-0.0769055\pi$
$353$	70618.8	+	84160.2i	0.566723	+	0.675395i	−0.404232	+	0.914657i	$0.632461\pi$
$354$	−118958.	+	5221.48i	−0.949267	+	0.0416665i
$355$	−7368.24	+	41787.4i	−0.0584665	+	0.331580i
$356$	−135755.	−	372984.i	−1.07117	−	2.94300i
$357$	−7504.18	+	1665.46i	−0.0588799	+	0.0130677i
$358$	47212.1	+	267753.i	0.368372	+	2.08914i
$359$	−81555.7	+	47086.2i	−0.632798	+	0.365346i	−0.781835	−	0.623485i	$-0.785716\pi$
$359$	−81555.7	+	47086.2i	−0.632798	+	0.365346i	0.149037	+	0.988832i	$0.452383\pi$
$360$	−112999.	+	52756.1i	−0.871905	+	0.407068i
$361$	27356.3	−	47382.6i	0.209915	−	0.363584i
$362$	−62389.8	+	171415.i	−0.476098	+	1.30807i
$363$	−9144.56	+	69584.6i	−0.0693984	+	0.528080i
$364$	−125218.	−	105070.i	−0.945067	−	0.793005i
$365$	12689.1	−	15122.3i	0.0952460	−	0.113510i
$366$	−346528.	−	45539.5i	−2.58688	−	0.339959i
$367$	101542.	+	36958.3i	0.753900	+	0.274397i	0.690246	−	0.723575i	$-0.257502\pi$
$367$	101542.	+	36958.3i	0.753900	+	0.274397i	0.0636543	+	0.997972i	$0.479724\pi$
$368$	432093.	+	249469.i	3.19067	+	1.84213i
$369$	56254.5	+	120492.i	0.413147	+	0.884925i
$370$	2765.56	+	4790.10i	0.0202013	+	0.0349898i
$371$	−51886.4	+	9148.97i	−0.376969	+	0.0664698i
$372$	38737.8	+	174543.i	0.279930	+	1.26130i
$373$	208805.	−	75998.9i	1.50080	−	0.546247i	0.544534	−	0.838739i	$-0.316706\pi$
$373$	208805.	−	75998.9i	1.50080	−	0.546247i	0.956268	+	0.292491i	$0.0944842\pi$
$374$	24509.5	+	4321.68i	0.175223	+	0.0308965i
$375$	3070.43	+	69952.1i	0.0218342	+	0.497437i
$376$	242418.	−	203413.i	1.71471	−	1.43881i
$377$		−	115387.i		−	0.811848i
$378$	−69199.3	+	108788.i	−0.484304	+	0.761373i
$379$	170172.			1.18470			0.592352	−	0.805679i	$-0.298199\pi$
$379$	170172.			1.18470			0.592352	+	0.805679i	$0.298199\pi$
$380$	−52680.3	−	62781.9i	−0.364822	−	0.434778i
$381$	−5110.28	+	9822.32i	−0.0352042	+	0.0676650i
$382$	−88926.5	+	504327.i	−0.609403	+	3.45610i
$383$	12710.5	+	34921.9i	0.0866495	+	0.238068i	0.975448	−	0.220231i	$-0.0706812\pi$
$383$	12710.5	+	34921.9i	0.0866495	+	0.238068i	−0.888798	+	0.458299i	$0.848459\pi$
$384$	−590748.	−	644388.i	−4.00626	−	4.37004i
$385$	−2071.97	−	11750.7i	−0.0139786	−	0.0792764i
$386$	254496.	−	146933.i	1.70807	−	0.986155i
$387$	−84020.3	+	84098.3i	−0.561000	+	0.561520i
$388$	344542.	−	596765.i	2.28865	−	3.96405i
$389$	71929.3	−	197624.i	0.475343	−	1.30599i	−0.438063	−	0.898944i	$-0.644335\pi$
$389$	71929.3	−	197624.i	0.475343	−	1.30599i	0.913406	−	0.407049i	$-0.133442\pi$
$390$	57171.5	+	43848.1i	0.375881	+	0.288285i
$391$	−12702.1	−	10658.3i	−0.0830848	−	0.0697164i
$392$	291927.	−	347905.i	1.89977	−	2.26406i
$393$	−16240.4	−	39182.2i	−0.105151	−	0.253690i
$394$	−136873.	−	49817.8i	−0.881712	−	0.320917i
$395$	23690.0	+	13677.4i	0.151835	+	0.0876617i
$396$	254048.	−	178062.i	1.62004	−	1.13548i
$397$	−63708.7	−	110347.i	−0.404220	−	0.700129i	0.590010	−	0.807396i	$-0.299124\pi$
$397$	−63708.7	−	110347.i	−0.404220	−	0.700129i	−0.994230	+	0.107266i	$0.965790\pi$
$398$	−66258.7	+	11683.2i	−0.418289	+	0.0737557i
$399$	−52888.9	−	16662.3i	−0.332214	−	0.104662i
$400$	−628946.	+	228918.i	−3.93091	+	1.43074i
$401$	−152127.	−	26824.2i	−0.946060	−	0.166816i	−0.320725	−	0.947172i	$-0.603927\pi$
$401$	−152127.	−	26824.2i	−0.946060	−	0.166816i	−0.625335	+	0.780356i	$0.715038\pi$
$402$	173513.	−	110597.i	1.07369	−	0.684368i
$403$	51785.3	−	43453.0i	0.318857	−	0.267553i
$404$			541273.i			3.31630i
$405$	21083.8	−	36596.6i	0.128540	−	0.223116i
$406$	−129524.			−0.785777
$407$	−5788.24	−	6898.16i	−0.0349428	−	0.0416432i
$408$	44099.4	+	69186.7i	0.264918	+	0.415626i
$409$	−15173.1	+	86050.9i	−0.0907043	+	0.514409i	0.905275	+	0.424826i	$0.139665\pi$
$409$	−15173.1	+	86050.9i	−0.0907043	+	0.514409i	−0.995979	+	0.0895835i	$0.971446\pi$
$410$	−28529.8	−	78385.0i	−0.169719	−	0.466300i
$411$	31245.7	−	99178.9i	0.184972	−	0.587132i
$412$	92538.3	+	524811.i	0.545164	+	3.09178i
$413$	32526.7	−	18779.3i	0.190695	−	0.110098i
$414$	−277053.	+	24368.5i	−1.61645	+	0.142177i
$415$	−18571.1	+	32166.0i	−0.107830	+	0.186768i
$416$	−281631.	+	773776.i	−1.62740	+	4.47124i
$417$	−264842.	+	109773.i	−1.52305	+	0.631283i
$418$	137532.	+	115403.i	0.787141	+	0.660490i
$419$	18767.9	−	22366.7i	0.106903	−	0.127401i	−0.709940	−	0.704262i	$-0.751278\pi$
$419$	18767.9	−	22366.7i	0.106903	−	0.127401i	0.816843	+	0.576861i	$0.195722\pi$
$420$	36579.7	−	47694.4i	0.207368	−	0.270377i
$421$	−107397.	−	39089.3i	−0.605937	−	0.220543i	0.0207877	−	0.999784i	$-0.493383\pi$
$421$	−107397.	−	39089.3i	−0.605937	−	0.220543i	−0.626724	+	0.779241i	$0.715605\pi$
$422$	−230135.	−	132869.i	−1.29229	−	0.746101i
$423$	−27691.2	+	103537.i	−0.154761	+	0.578648i
$424$	281181.	+	487019.i	1.56406	+	2.70903i
$425$	21905.5	−	3862.53i	0.121276	−	0.0213843i
$426$	345154.	−	316423.i	1.90193	−	1.74361i
$427$	103595.	−	37705.6i	0.568177	−	0.206800i
$428$	−914950.	−	161330.i	−4.99470	−	0.880701i
$429$	−104060.	−	54139.3i	−0.565415	−	0.294170i
$430$	57124.8	−	47933.4i	0.308950	−	0.259239i
$431$		−	102450.i		−	0.551516i	−0.961227	−	0.275758i	$-0.911071\pi$
$431$		−	102450.i		−	0.551516i	0.961227	−	0.275758i	$-0.0889289\pi$
$432$	816428.	+	180402.i	4.37472	+	0.966659i
$433$	−212538.			−1.13360			−0.566800	−	0.823855i	$-0.691819\pi$
$433$	−212538.			−1.13360			−0.566800	+	0.823855i	$0.691819\pi$
$434$	−48776.8	−	58130.0i	−0.258961	−	0.308618i
$435$	42388.9	−	1860.59i	0.224013	−	0.00983268i
$436$	138270.	−	784168.i	0.727369	−	4.12511i
$437$	−40911.1	−	112402.i	−0.214229	−	0.588590i
$438$	−212669.	+	47199.4i	−1.10855	+	0.246030i
$439$	−24162.8	−	137034.i	−0.125377	−	0.711048i	−0.981083	−	0.193586i	$-0.937988\pi$
$439$	−24162.8	−	137034.i	−0.125377	−	0.711048i	0.855706	−	0.517462i	$-0.173123\pi$
$440$	−110296.	+	63679.2i	−0.569708	+	0.328921i
$441$	−13334.6	+	153234.i	−0.0685649	+	0.787910i
$442$	23701.2	−	41051.7i	0.121318	−	0.210129i
$443$	42906.2	−	117884.i	0.218631	−	0.600685i	−0.781087	−	0.624422i	$-0.785334\pi$
$443$	42906.2	−	117884.i	0.218631	−	0.600685i	0.999718	+	0.0237377i	$0.00755667\pi$
$444$	5910.46	−	44975.0i	0.0299816	−	0.228142i
$445$	−42274.6	−	35472.6i	−0.213481	−	0.179132i
$446$	304946.	−	363421.i	1.53304	−	1.82701i
$447$	188909.	+	24825.8i	0.945450	+	0.124248i
$448$	482182.	+	175500.i	2.40245	+	0.874421i
$449$	−62243.2	−	35936.2i	−0.308745	−	0.178254i	0.337620	−	0.941283i	$-0.390378\pi$
$449$	−62243.2	−	35936.2i	−0.308745	−	0.178254i	−0.646365	+	0.763029i	$0.723711\pi$
$450$	213856.	−	305719.i	1.05608	−	1.50972i
$451$	67902.0	+	117610.i	0.333833	+	0.578216i
$452$	196278.	−	34609.1i	0.960717	−	0.169400i
$453$	−20101.9	−	90574.3i	−0.0979581	−	0.441376i
$454$	410786.	−	149514.i	1.99298	−	0.725386i
$455$	−22381.2	−	3946.41i	−0.108109	−	0.0190625i
$456$	25954.2	+	591301.i	0.124818	+	2.84367i
$457$	−14241.1	+	11949.7i	−0.0681886	+	0.0572170i	−0.676245	−	0.736677i	$-0.736394\pi$
$457$	−14241.1	+	11949.7i	−0.0681886	+	0.0572170i	0.608056	+	0.793894i	$0.291949\pi$
$458$			536840.i			2.55925i
$459$	−25679.4	−	10615.8i	−0.121887	−	0.0503881i
$460$	129658.			0.612752
$461$	177536.	+	211579.i	0.835380	+	0.995567i	0.999958	+	0.00920282i	$0.00292939\pi$
$461$	177536.	+	211579.i	0.835380	+	0.995567i	−0.164578	+	0.986364i	$0.552626\pi$
$462$	−60772.5	+	116809.i	−0.284723	+	0.547258i
$463$	−37111.6	+	210471.i	−0.173120	+	0.981814i	0.767171	+	0.641443i	$0.221664\pi$
$463$	−37111.6	+	210471.i	−0.173120	+	0.981814i	−0.940291	+	0.340371i	$0.889447\pi$
$464$	287285.	+	789309.i	1.33437	+	3.66616i
$465$	16798.0	+	18323.3i	0.0776877	+	0.0847418i
$466$	−123382.	−	699732.i	−0.568170	−	3.22225i
$467$	−255478.	+	147500.i	−1.17144	+	0.676330i	−0.954018	−	0.299749i	$-0.903097\pi$
$467$	−255478.	+	147500.i	−1.17144	+	0.676330i	−0.217419	+	0.976078i	$0.569764\pi$
$468$	−153200.	−	570690.i	−0.699466	−	2.60561i
$469$	−32451.4	+	56207.5i	−0.147533	+	0.255534i
$470$	22994.2	−	63176.1i	0.104093	−	0.285994i
$471$	242914.	+	186305.i	1.09499	+	0.839813i
$472$	−307098.	−	257686.i	−1.37846	−	1.15666i
$473$	−78037.6	+	93001.5i	−0.348804	+	0.415688i
$474$	−115584.	−	278862.i	−0.514448	−	1.24117i
$475$	150784.	+	54881.0i	0.668296	+	0.243240i
$476$	−34246.8	−	19772.4i	−0.151149	−	0.0872661i
$477$	−172652.	−	80411.3i	−0.758812	−	0.353411i
$478$	−93549.6	−	162033.i	−0.409436	−	0.709164i
$479$	144957.	−	25559.8i	0.631782	−	0.111400i	0.151418	−	0.988470i	$-0.451616\pi$
$479$	144957.	−	25559.8i	0.631782	−	0.111400i	0.480363	+	0.877070i	$0.340505\pi$
$480$	−288797.	−	90983.8i	−1.25346	−	0.394895i
$481$	−16117.0	+	5866.09i	−0.0696615	+	0.0253547i
$482$	821044.	+	144772.i	3.53405	+	0.623148i
$483$	73977.2	−	47152.8i	0.317106	−	0.202122i
$484$	−276586.	+	232083.i	−1.18070	+	0.990725i
$485$		−	95806.1i		−	0.407295i
$486$	−430393.	+	178860.i	−1.82219	+	0.757251i
$487$	−206055.			−0.868813			−0.434406	−	0.900717i	$-0.643042\pi$
$487$	−206055.			−0.868813			−0.434406	+	0.900717i	$0.643042\pi$
$488$	−756370.	−	901407.i	−3.17610	−	3.78513i
$489$	106982.	+	167843.i	0.447398	+	0.701915i
$490$	16754.5	−	95019.6i	0.0697814	−	0.395750i
$491$	69894.1	+	192032.i	0.289919	+	0.796547i	0.996077	+	0.0884922i	$0.0282048\pi$
$491$	69894.1	+	192032.i	0.289919	+	0.796547i	−0.706157	+	0.708055i	$0.749573\pi$
$492$	−205563.	+	652490.i	−0.849209	+	2.69553i
$493$	−4847.36	−	27490.8i	−0.0199440	−	0.113108i
$494$	296142.	−	170978.i	1.21352	−	0.700625i
$495$	18210.8	−	39100.6i	0.0743223	−	0.159578i
$496$	−246052.	+	426174.i	−1.00014	+	1.73230i
$497$	−50515.3	+	138790.i	−0.204508	+	0.561881i
$498$	378636.	−	156939.i	1.52673	−	0.632808i
$499$	−42958.9	−	36046.8i	−0.172525	−	0.144766i	0.552437	−	0.833555i	$-0.313698\pi$
$499$	−42958.9	−	36046.8i	−0.172525	−	0.144766i	−0.724962	+	0.688789i	$0.758143\pi$
$500$	−231543.	+	275942.i	−0.926172	+	1.10377i
$501$	154244.	−	201112.i	0.614517	−	0.801239i
$502$	236980.	+	86253.6i	0.940381	+	0.342271i
$503$	208233.	+	120223.i	0.823025	+	0.475173i	0.851458	−	0.524422i	$-0.175719\pi$
$503$	208233.	+	120223.i	0.823025	+	0.475173i	−0.0284338	+	0.999596i	$0.509052\pi$
$504$	−419237.	+	112543.i	−1.65043	+	0.443053i
$505$	37627.6	+	65173.0i	0.147545	+	0.255555i
$506$	−279720.	+	49322.1i	−1.09250	+	0.192637i
$507$	24789.8	−	22726.3i	0.0964401	−	0.0884123i
$508$	−53525.8	+	19481.8i	−0.207413	+	0.0754922i
$509$	−431130.	−	76019.9i	−1.66407	−	0.293421i	−0.739141	−	0.673550i	$-0.764768\pi$
$509$	−431130.	−	76019.9i	−1.66407	−	0.293421i	−0.924933	+	0.380129i	$0.875880\pi$
$510$	15463.0	+	8044.99i	0.0594503	+	0.0309304i
$511$	52637.6	−	44168.2i	0.201583	−	0.169149i
$512$		−	1.60527e6i		−	6.12362i
$513$	−122139.	−	158945.i	−0.464107	−	0.603966i
$514$	−134562.			−0.509325
$515$	47625.5	+	56757.8i	0.179566	+	0.213999i
$516$	−610981.	+	26818.0i	−2.29471	+	0.100723i
$517$	−19006.5	+	107791.i	−0.0711086	+	0.403277i
$518$	6584.81	+	18091.6i	0.0245405	+	0.0674245i
$519$	191237.	−	42442.8i	0.709967	−	0.157569i
$520$	42122.6	+	238889.i	0.155779	+	0.883467i
$521$	−68925.2	+	39794.0i	−0.253923	+	0.146603i	−0.621559	−	0.783367i	$-0.713501\pi$
$521$	−68925.2	+	39794.0i	−0.253923	+	0.146603i	0.367636	+	0.929970i	$0.380167\pi$
$522$	−383669.	−	268382.i	−1.40804	−	0.984948i
$523$	−259172.	+	448900.i	−0.947514	+	1.64114i	−0.196875	+	0.980429i	$0.563079\pi$
$523$	−259172.	+	448900.i	−0.947514	+	1.64114i	−0.750639	+	0.660713i	$0.770254\pi$
$524$	74629.7	−	205043.i	0.271800	−	0.746764i
$525$	−15333.7	+	116680.i	−0.0556323	+	0.423328i
$526$	568259.	+	476826.i	2.05388	+	1.72341i
$527$	10512.3	−	12528.1i	0.0378509	−	0.0451090i
$528$	846616.	+	111259.i	3.03682	+	0.399088i
$529$	−85138.4	−	30987.8i	−0.304238	−	0.110734i
$530$	103467.	+	59736.7i	0.368341	+	0.212662i
$531$	135260.	+	11770.5i	0.479713	+	0.0417452i
$532$	−142636.	−	247052.i	−0.503970	−	0.872902i
$533$	254731.	−	44916.0i	0.896660	−	0.158105i
$534$	131946.	+	594518.i	0.462716	+	2.08489i
$535$	−121381.	+	44179.2i	−0.424077	+	0.154351i
$536$	682227.	+	120295.i	2.37465	+	0.418714i
$537$	−13594.4	−	309714.i	−0.0471423	−	1.07402i
$538$	−356906.	+	299480.i	−1.23307	+	1.03467i
$539$			157082.i			0.540692i
$540$	207180.	−	65482.1i	0.710493	−	0.224561i
$541$	−183310.			−0.626312			−0.313156	−	0.949702i	$-0.601386\pi$
$541$	−183310.			−0.626312			−0.313156	+	0.949702i	$0.601386\pi$
$542$	164831.	+	196438.i	0.561099	+	0.668692i
$543$	95999.7	−	184518.i	0.325589	−	0.625806i
$544$	−34592.1	+	196182.i	−0.116891	+	0.662920i
$545$	−37864.3	−	104031.i	−0.127478	−	0.350244i
$546$	169475.	+	184864.i	0.568487	+	0.620106i
$547$	−71918.1	−	407868.i	−0.240361	−	1.36315i	−0.831025	−	0.556236i	$-0.812245\pi$
$547$	−71918.1	−	407868.i	−0.240361	−	1.36315i	0.590664	−	0.806918i	$-0.298866\pi$
$548$	463280.	−	267475.i	1.54270	−	0.890681i
$549$	384991.	+	102967.i	1.27734	+	0.341627i
$550$	190512.	−	329976.i	0.629792	−	1.09083i
$551$	68874.1	−	189230.i	0.226857	−	0.623285i
$552$	−743003.	−	569852.i	−2.43844	−	1.87018i
$553$	72940.0	+	61203.9i	0.238515	+	0.200138i
$554$	−60485.8	+	72084.2i	−0.197076	+	0.234866i
$555$	−2414.86	−	5826.17i	−0.00783983	−	0.0189146i
$556$	−1.38594e6	−	504441.i	−4.48327	−	1.63178i
$557$	24891.2	+	14371.0i	0.0802299	+	0.0463207i	0.539578	−	0.841935i	$-0.318584\pi$
$557$	24891.2	+	14371.0i	0.0802299	+	0.0463207i	−0.459348	+	0.888256i	$0.651917\pi$
$558$	−24034.7	−	273258.i	−0.0771916	−	0.877614i
$559$	115618.	+	200256.i	0.369999	+	0.640857i
$560$	162925.	−	28728.0i	0.519531	−	0.0916073i
$561$	−27066.4	−	8527.09i	−0.0860012	−	0.0270941i
$562$	492479.	−	179248.i	1.55925	−	0.567520i
$563$	168827.	+	29768.7i	0.532629	+	0.0939169i	0.433493	−	0.901157i	$-0.357281\pi$
$563$	168827.	+	29768.7i	0.532629	+	0.0939169i	0.0991362	+	0.995074i	$0.468392\pi$
$564$	−464952.	+	296358.i	−1.46167	+	0.931664i
$565$	21227.3	−	17811.8i	0.0664964	−	0.0557971i
$566$			944062.i			2.94691i
$567$	94393.6	−	112706.i	0.293614	−	0.350575i
$568$	1.57647e6			4.88639
$569$	−27561.5	−	32846.6i	−0.0851292	−	0.101453i	0.721798	−	0.692103i	$-0.243316\pi$
$569$	−27561.5	−	32846.6i	−0.0851292	−	0.101453i	−0.806928	+	0.590650i	$0.798871\pi$
$570$	67586.0	+	106034.i	0.208021	+	0.326360i
$571$	36461.1	−	206781.i	0.111830	−	0.634218i	−0.876441	−	0.481509i	$-0.840089\pi$
$571$	36461.1	−	206781.i	0.111830	−	0.634218i	0.988271	−	0.152710i	$-0.0487999\pi$
$572$	−206394.	−	567063.i	−0.630820	−	1.73316i
$573$	175461.	−	556940.i	0.534405	−	1.69629i
$574$	−50419.1	−	285941.i	−0.153028	−	0.867865i
$575$	−219847.	+	126929.i	−0.664945	+	0.383906i
$576$	1.06464e6	+	1.51896e6i	3.20891	+	4.57828i
$577$	−59933.7	+	103808.i	−0.180020	+	0.311803i	−0.941887	−	0.335930i	$-0.890949\pi$
$577$	−59933.7	+	103808.i	−0.180020	+	0.311803i	0.761867	+	0.647733i	$0.224283\pi$
$578$	−221550.	+	608705.i	−0.663158	+	1.82201i
$579$	−309542.	+	128301.i	−0.923342	+	0.382712i
$580$	167213.	+	140308.i	0.497065	+	0.417087i
$581$	−83102.1	+	99037.2i	−0.246184	+	0.293391i
$582$	−643413.	+	838915.i	−1.89952	+	2.47669i
$583$	−182777.	−	66525.5i	−0.537756	−	0.195727i
$584$	−635165.	−	366713.i	−1.86235	−	1.07523i
$585$	−58118.9	−	58065.0i	−0.169827	−	0.169669i
$586$	−595212.	−	1.03094e6i	−1.73331	−	3.00218i
$587$	132575.	−	23376.5i	0.384755	−	0.0678426i	0.0220746	−	0.999756i	$-0.492973\pi$
$587$	132575.	−	23376.5i	0.384755	−	0.0678426i	0.362680	+	0.931914i	$0.381862\pi$
$588$	−583278.	+	534725.i	−1.68702	+	1.54659i
$589$	110863.	−	40350.7i	0.319561	−	0.116311i
$590$	−83874.5	−	14789.3i	−0.240949	−	0.0424859i
$591$	147337.	+	76655.2i	0.421828	+	0.219466i
$592$	95643.4	−	80254.4i	0.272905	−	0.228995i
$593$		−	183775.i		−	0.522610i	−0.965256	−	0.261305i	$-0.915847\pi$
$593$		−	183775.i		−	0.522610i	0.965256	−	0.261305i	$-0.0841529\pi$
$594$	−422052.	+	220080.i	−1.19617	+	0.623745i
$595$	−5498.07			−0.0155302
$596$	630063.	+	750880.i	1.77375	+	2.11387i
$597$	76642.5	−	3364.09i	0.215041	−	0.00943886i
$598$	−93942.0	+	532771.i	−0.262698	+	1.48984i
$599$	−229078.	−	629386.i	−0.638453	−	1.75414i	−0.656531	−	0.754299i	$-0.727977\pi$
$599$	−229078.	−	629386.i	−0.638453	−	1.75414i	0.0180783	−	0.999837i	$-0.494245\pi$
$600$	1.22627e6	−	272156.i	3.40631	−	0.755989i
$601$	52834.8	+	299641.i	0.146275	+	0.829569i	0.966334	+	0.257290i	$0.0828294\pi$
$601$	52834.8	+	299641.i	0.146275	+	0.829569i	−0.820059	+	0.572279i	$0.806059\pi$
$602$	224791.	−	129783.i	0.620277	−	0.358117i
$603$	−212591.	+	99252.9i	−0.584669	+	0.272966i
$604$	238650.	−	413354.i	0.654165	−	1.13305i
$605$	−17169.1	+	47171.8i	−0.0469070	+	0.128876i
$606$	108206.	−	823379.i	0.294649	−	2.24210i
$607$	−270826.	−	227250.i	−0.735042	−	0.616774i	0.196459	−	0.980512i	$-0.437056\pi$
$607$	−270826.	−	227250.i	−0.735042	−	0.616774i	−0.931501	+	0.363739i	$0.881500\pi$
$608$	−923726.	+	1.10085e6i	−2.49883	+	2.97799i
$609$	146430.	+	19243.3i	0.394816	+	0.0518853i
$610$	−234914.	−	85501.6i	−0.631319	−	0.229781i
$611$	180543.	+	104237.i	0.483614	+	0.279215i
$612$	−60474.0	−	129530.i	−0.161460	−	0.345834i
$613$	−117181.	−	202964.i	−0.311843	−	0.540129i	0.666918	−	0.745131i	$-0.267613\pi$
$613$	−117181.	−	202964.i	−0.311843	−	0.540129i	−0.978761	+	0.205002i	$0.934280\pi$
$614$	−697776.	+	123037.i	−1.85088	+	0.326361i
$615$	20607.9	+	92854.4i	0.0544859	+	0.245500i
$616$	−416573.	+	151620.i	−1.09782	+	0.399572i
$617$	−230113.	−	40575.1i	−0.604464	−	0.106583i	−0.136963	−	0.990576i	$-0.543734\pi$
$617$	−230113.	−	40575.1i	−0.604464	−	0.106583i	−0.467500	+	0.883993i	$0.654845\pi$
$618$	−35853.6	−	816836.i	−0.0938764	−	2.13874i
$619$	516508.	−	433402.i	1.34802	−	1.13112i	0.368530	−	0.929616i	$-0.379861\pi$
$619$	516508.	−	433402.i	1.34802	−	1.13112i	0.979487	−	0.201506i	$-0.0645834\pi$
$620$			127882.i			0.332680i
$621$	316834.	+	13612.4i	0.821578	+	0.0352981i
$622$	267387.			0.691129
$623$	−123473.	−	147149.i	−0.318122	−	0.379124i
$624$	750645.	−	1.44279e6i	1.92782	−	3.70540i
$625$	54637.2	−	309863.i	0.139871	−	0.793249i
$626$	92248.6	+	253451.i	0.235403	+	0.646763i
$627$	−138338.	−	150899.i	−0.351889	−	0.383841i
$628$	273479.	+	1.55098e6i	0.693433	+	3.93265i
$629$	−3593.40	+	2074.65i	−0.00908248	+	0.00524377i
$630$	−65179.2	+	65239.7i	−0.164221	+	0.164373i
$631$	−218567.	+	378569.i	−0.548940	+	0.950793i	0.449407	+	0.893327i	$0.351635\pi$
$631$	−218567.	+	378569.i	−0.548940	+	0.950793i	−0.998347	+	0.0574655i	$0.981698\pi$
$632$	347598.	−	955016.i	0.870247	−	2.39098i
$633$	240432.	+	184402.i	0.600047	+	0.460211i
$634$	78656.1	+	66000.3i	0.195683	+	0.164198i
$635$	−5090.56	+	6066.70i	−0.0126246	+	0.0150454i
$636$	−375171.	−	905149.i	−0.927502	−	2.23772i
$637$	281145.	+	102329.i	0.692871	+	0.252184i
$638$	−414111.	−	239087.i	−1.01736	−	0.587374i
$639$	−437214.	+	306443.i	−1.07076	+	0.750495i
$640$	−312640.	−	541508.i	−0.763281	−	1.32204i
$641$	243662.	−	42964.1i	0.593022	−	0.104566i	0.130921	−	0.991393i	$-0.458207\pi$
$641$	243662.	−	42964.1i	0.593022	−	0.104566i	0.462101	+	0.886827i	$0.347096\pi$
$642$	1.35956e6	+	428321.i	3.29859	+	1.03920i
$643$	−518496.	+	188717.i	−1.25408	+	0.456446i	−0.881777	−	0.471667i	$-0.843652\pi$
$643$	−518496.	+	188717.i	−1.25408	+	0.456446i	−0.372298	+	0.928113i	$0.621430\pi$
$644$	444457.	+	78369.7i	1.07166	+	0.188963i
$645$	−71702.1	+	45702.6i	−0.172350	+	0.109856i
$646$	63372.6	−	53175.9i	0.151857	−	0.127424i
$647$		−	550163.i		−	1.31426i	−0.753776	−	0.657132i	$-0.771769\pi$
$647$		−	550163.i		−	1.31426i	0.753776	−	0.657132i	$-0.228231\pi$
$648$	−1.47503e6	−	535318.i	−3.51278	−	1.27486i
$649$	138658.			0.329196
$650$	−466485.	−	555935.i	−1.10411	−	1.31582i
$651$	46506.8	+	72963.8i	0.109737	+	0.172165i
$652$	−177809.	+	1.00840e6i	−0.418271	+	2.37213i
$653$	16849.8	+	46294.5i	0.0395156	+	0.108568i	0.957881	−	0.287165i	$-0.0927127\pi$
$653$	16849.8	+	46294.5i	0.0395156	+	0.108568i	−0.918366	+	0.395733i	$0.870491\pi$
$654$	−367097.	+	1.16523e6i	−0.858273	+	2.72430i
$655$	−5268.06	−	29876.7i	−0.0122792	−	0.0696385i
$656$	−1.63067e6	+	941465.i	−3.78929	+	2.18774i
$657$	247439.	−	21763.8i	0.573242	−	0.0504201i
$658$	117008.	−	202663.i	0.270248	−	0.468084i
$659$	−4788.00	+	13154.9i	−0.0110251	+	0.0302913i	−0.945083	−	0.326830i	$-0.894020\pi$
$659$	−4788.00	+	13154.9i	−0.0110251	+	0.0302913i	0.934058	+	0.357121i	$0.116242\pi$
$660$	204990.	−	84965.2i	0.470592	−	0.195053i
$661$	505607.	+	424255.i	1.15721	+	0.971011i	0.999863	−	0.0165336i	$-0.00526304\pi$
$661$	505607.	+	424255.i	1.15721	+	0.971011i	0.157342	+	0.987544i	$0.449707\pi$
$662$	327790.	−	390645.i	0.747962	−	0.891386i
$663$	−32893.7	+	42888.5i	−0.0748317	+	0.0975694i
$664$	1.29671e6	+	471965.i	2.94108	+	1.07047i
$665$	−34348.6	−	19831.2i	−0.0776723	−	0.0448441i
$666$	−17981.8	+	67233.9i	−0.0405402	+	0.151579i
$667$	159292.	+	275902.i	0.358049	+	0.620159i
$668$	1.28407e6	−	226417.i	2.87765	−	0.507407i
$669$	−398740.	+	365548.i	−0.890919	+	0.816757i
$670$	138299.	−	50336.7i	0.308084	−	0.112133i
$671$	400811.	+	70673.8i	0.890214	+	0.156969i
$672$	−934976.	−	486442.i	−2.07044	−	1.07719i
$673$	−36637.0	+	30742.1i	−0.0808890	+	0.0678740i	−0.682336	−	0.731039i	$-0.739036\pi$
$673$	−36637.0	+	30742.1i	−0.0808890	+	0.0678740i	0.601447	+	0.798913i	$0.294591\pi$
$674$			714375.i			1.57256i
$675$	−287188.	+	313849.i	−0.630317	+	0.688832i
$676$	173014.			0.378605
$677$	148310.	+	176749.i	0.323589	+	0.385638i	0.903175	−	0.429273i	$-0.141230\pi$
$677$	148310.	+	176749.i	0.323589	+	0.385638i	−0.579586	+	0.814911i	$0.696786\pi$
$678$	−305495.	+	13409.2i	−0.664576	+	0.0291705i
$679$	57908.3	−	328414.i	0.125603	−	0.712332i
$680$	20071.3	+	55145.4i	0.0434067	+	0.119259i
$681$	−486614.	+	107998.i	−1.04928	+	0.232875i
$682$	−48646.4	−	275888.i	−0.104588	−	0.593148i
$683$	−97471.3	+	56275.1i	−0.208947	+	0.120635i	−0.600822	−	0.799383i	$-0.705160\pi$
$683$	−97471.3	+	56275.1i	−0.208947	+	0.120635i	0.391875	+	0.920018i	$0.371827\pi$
$684$	89401.4	−	1.02735e6i	0.191087	−	2.19587i
$685$	37188.1	−	64411.7i	0.0792543	−	0.137272i
$686$	260102.	−	714625.i	0.552708	−	1.51855i
$687$	79757.7	−	606907.i	0.168989	−	1.28591i
$688$	−1.28947e6	−	1.08200e6i	−2.72417	−	2.28585i
$689$	−238134.	+	283797.i	−0.501630	+	0.597819i
$690$	−197235.	−	25919.9i	−0.414272	−	0.0544422i
$691$	193116.	+	70288.4i	0.404447	+	0.147207i	0.536230	−	0.844072i	$-0.319848\pi$
$691$	193116.	+	70288.4i	0.404447	+	0.147207i	−0.131783	+	0.991279i	$0.542070\pi$
$692$	872748.	+	503881.i	1.82254	+	1.05224i
$693$	86058.6	−	123026.i	0.179196	−	0.256171i
$694$	−51995.9	−	90059.5i	−0.107957	−	0.186987i
$695$	−201944.	+	35608.1i	−0.418082	+	0.0737191i
$696$	−341548.	−	1.53893e6i	−0.705072	−	3.17688i
$697$	58802.3	−	21402.3i	0.121040	−	0.0440549i
$698$	−219164.	−	38644.6i	−0.449841	−	0.0793191i
$699$	35526.9	+	809391.i	0.0727114	+	1.65655i
$700$	−463781.	+	389158.i	−0.946492	+	0.794201i
$701$		−	425142.i		−	0.865163i	−0.901595	−	0.432582i	$-0.857603\pi$
$701$		−	425142.i		−	0.865163i	0.901595	−	0.432582i	$-0.142397\pi$
$702$	118960.	+	898754.i	0.241393	+	1.82376i
$703$	−29932.6			−0.0605666
$704$	1.21766e6	+	1.45115e6i	2.45687	+	2.92798i
$705$	−35381.4	+	68005.6i	−0.0711864	+	0.136825i
$706$	150581.	−	853986.i	0.302107	−	1.71333i
$707$	89591.4	+	246150.i	0.179237	+	0.492449i
$708$	472006.	+	514864.i	0.941631	+	1.02713i
$709$	72444.4	+	410853.i	0.144116	+	0.817323i	0.968073	+	0.250670i	$0.0806509\pi$
$709$	72444.4	+	410853.i	0.144116	+	0.817323i	−0.823957	+	0.566653i	$0.808238\pi$
$710$	290049.	−	167460.i	0.575379	−	0.332195i
$711$	89239.8	+	332430.i	0.176530	+	0.657600i
$712$	−1.02515e6	+	1.77561e6i	−2.02221	+	3.50257i
$713$	−63836.7	+	175390.i	−0.125572	+	0.345005i
$714$	48143.2	+	36923.8i	0.0944361	+	0.0724286i
$715$	−64271.8	−	53930.4i	−0.125721	−	0.105493i
$716$	1.02516e6	−	1.22174e6i	1.99970	−	2.38315i
$717$	81686.6	+	197080.i	0.158896	+	0.383357i
$718$	698483.	+	254227.i	1.35490	+	0.493143i
$719$	−91409.9	−	52775.6i	−0.176822	−	0.102088i	0.408977	−	0.912545i	$-0.365886\pi$
$719$	−91409.9	−	52775.6i	−0.176822	−	0.102088i	−0.585799	+	0.810457i	$0.699219\pi$
$720$	542132.	+	252494.i	1.04578	+	0.487064i
$721$	128949.	+	223347.i	0.248055	+	0.429645i
$722$	−425291.	+	74990.3i	−0.815852	+	0.143857i
$723$	−906697.	−	285649.i	−1.73454	−	0.546457i
$724$	1.00552e6	−	365978.i	1.91828	−	0.698196i
$725$	−420878.	−	74212.2i	−0.800720	−	0.141188i
$726$	467135.	−	297750.i	0.886277	−	0.564910i
$727$	−124360.	+	104351.i	−0.235295	+	0.197436i	−0.752809	−	0.658239i	$-0.771302\pi$
$727$	−124360.	+	104351.i	−0.235295	+	0.197436i	0.517514	+	0.855674i	$0.326857\pi$
$728$			844351.i			1.59316i
$729$	513141.	−	138261.i	0.965565	−	0.260163i
$730$	−155816.			−0.292392
$731$	35958.3	+	42853.5i	0.0672922	+	0.0801957i
$732$	1.10198e6	+	1.72887e6i	2.05660	+	3.22657i
$733$	7187.55	−	40762.6i	0.0133774	−	0.0758672i	−0.977388	−	0.211453i	$-0.932181\pi$
$733$	7187.55	−	40762.6i	0.0133774	−	0.0758672i	0.990766	+	0.135586i	$0.0432916\pi$
$734$	−291715.	−	801480.i	−0.541460	−	1.48765i
$735$	−33058.3	+	104932.i	−0.0611935	+	0.194238i
$736$	−394790.	−	2.23897e6i	−0.728804	−	4.13325i
$737$	−207505.	+	119803.i	−0.382027	+	0.220563i
$738$	443139.	−	951467.i	0.813630	−	1.74695i
$739$	455959.	−	789743.i	0.834904	−	1.44610i	−0.0592049	−	0.998246i	$-0.518857\pi$
$739$	455959.	−	789743.i	0.834904	−	1.44610i	0.894109	−	0.447850i	$-0.147810\pi$
$740$	11097.0	−	30488.8i	0.0202648	−	0.0556772i
$741$	−360196.	+	149296.i	−0.655998	+	0.271902i
$742$	318568.	+	267310.i	0.578621	+	0.485521i
$743$	179736.	−	214201.i	0.325580	−	0.388011i	−0.578281	−	0.815838i	$-0.696276\pi$
$743$	179736.	−	214201.i	0.325580	−	0.388011i	0.903861	+	0.427827i	$0.140721\pi$
$744$	562045.	−	732824.i	1.01537	−	1.32390i
$745$	128063.	+	46611.1i	0.230733	+	0.0839801i
$746$	−1.51891e6	−	876944.i	−2.72932	−	1.57577i
$747$	−451371.	+	121169.i	−0.808895	+	0.217145i
$748$	−72995.1	−	126431.i	−0.130464	−	0.225970i
$749$	−442788.	+	78075.4i	−0.789281	+	0.139172i
$750$	407384.	−	373473.i	0.724238	−	0.663951i
$751$	−720902.	+	262387.i	−1.27819	+	0.465224i	−0.889834	−	0.456284i	$-0.849180\pi$
$751$	−720902.	+	262387.i	−1.27819	+	0.465224i	−0.388359	+	0.921508i	$0.626958\pi$
$752$	−1.49453e6	−	263527.i	−2.64284	−	0.466003i
$753$	−255096.	−	132719.i	−0.449897	−	0.234069i
$754$	−697682.	+	585425.i	−1.22720	+	1.02974i
$755$		−	66360.8i		−	0.116417i
$756$	749772.	−	99240.2i	1.31185	−	0.173638i
$757$	821137.			1.43293			0.716463	−	0.697625i	$-0.245760\pi$
$757$	821137.			1.43293			0.716463	+	0.697625i	$0.245760\pi$
$758$	−863381.	−	1.02894e6i	−1.50267	−	1.79081i
$759$	323556.	−	14202.0i	0.561650	−	0.0246527i
$760$	−73512.7	+	416911.i	−0.127273	+	0.721799i
$761$	321114.	+	882254.i	0.554485	+	1.52344i	0.827523	+	0.561432i	$0.189750\pi$
$761$	321114.	+	882254.i	0.554485	+	1.52344i	−0.273037	+	0.962003i	$0.588028\pi$
$762$	85317.5	−	18935.2i	0.146936	−	0.0326107i
$763$	−66915.4	−	379496.i	−0.114941	−	0.651866i
$764$	2.60155e6	−	1.50201e6i	4.45704	−	2.57327i
$765$	−16286.0	−	11392.3i	−0.0278286	−	0.0194666i
$766$	146666.	−	254032.i	0.249960	−	0.432944i
$767$	90326.2	−	248169.i	0.153540	−	0.421849i
$768$	−469388.	+	3.57176e6i	−0.795811	+	6.05564i
$769$	599699.	+	503208.i	1.01410	+	0.850931i	0.988875	−	0.148750i	$-0.0475251\pi$
$769$	599699.	+	503208.i	1.01410	+	0.850931i	0.0252257	+	0.999682i	$0.491970\pi$
$770$	−60538.0	+	72146.4i	−0.102105	+	0.121684i
$771$	152124.	+	19991.7i	0.255912	+	0.0336310i
$772$	−1.61986e6	−	589580.i	−2.71795	−	0.989254i
$773$	262280.	+	151428.i	0.438941	+	0.253423i	0.703148	−	0.711043i	$-0.251777\pi$
$773$	262280.	+	151428.i	0.438941	+	0.253423i	−0.264207	+	0.964466i	$0.585110\pi$
$774$	934780.	+	81345.7i	1.56037	+	0.135785i
$775$	−125190.	−	216836.i	−0.208433	−	0.361017i
$776$	−3.50538e6	+	618093.i	−5.82119	+	1.02643i
$777$	−4756.40	−	21431.2i	−0.00787837	−	0.0354980i
$778$	−1.55986e6	+	567744.i	−2.57708	+	0.937979i
$779$	444558.	+	78387.6i	0.732578	+	0.129173i
$780$	−18533.5	−	422239.i	−0.0304627	−	0.694016i
$781$	−417695.	+	350488.i	−0.684790	+	0.574607i
$782$			130878.i			0.214020i
$783$	393871.	+	360413.i	0.642437	+	0.587864i
$784$	−2.17796e6			−3.54337
$785$	140748.	+	167737.i	0.228403	+	0.272201i
$786$	−154516.	+	296991.i	−0.250109	+	0.480726i
$787$	137713.	−	781009.i	0.222344	−	1.26098i	−0.645354	−	0.763884i	$-0.723290\pi$
$787$	137713.	−	781009.i	0.222344	−	1.26098i	0.867698	−	0.497092i	$-0.165599\pi$
$788$	292231.	+	802898.i	0.470623	+	1.29303i
$789$	−571586.	−	623486.i	−0.918179	−	1.00155i
$790$	−37493.1	−	212634.i	−0.0600754	−	0.340705i
$791$	83531.3	−	48226.8i	0.133505	−	0.0770790i
$792$	−1.54811e6	−	414045.i	−2.46804	−	0.660081i
$793$	387593.	−	671331.i	0.616353	−	1.06756i
$794$	−343975.	+	945064.i	−0.545614	+	1.49906i
$795$	−108096.	−	82905.4i	−0.171032	−	0.131174i
$796$	302334.	+	253688.i	0.477156	+	0.400381i
$797$	−175666.	+	209351.i	−0.276549	+	0.329578i	−0.886384	−	0.462950i	$-0.846791\pi$
$797$	−175666.	+	209351.i	−0.276549	+	0.329578i	0.609836	+	0.792528i	$0.291235\pi$
$798$	167588.	+	404327.i	0.263170	+	0.634932i
$799$	47393.0	+	17249.7i	0.0742371	+	0.0270201i
$800$	2.64124e6	+	1.52492e6i	4.12693	+	2.38269i
$801$	−60840.8	−	691718.i	−0.0948265	−	1.07811i
$802$	609639.	+	1.05593e6i	0.947816	+	1.64166i
$803$	249821.	−	44050.1i	0.387434	−	0.0683150i
$804$	−1.15122e6	−	362686.i	−1.78093	−	0.561072i
$805$	58963.7	−	21461.0i	0.0909898	−	0.0331176i
$806$	−525473.	−	92655.0i	−0.808873	−	0.142626i
$807$	447983.	−	285542.i	0.687882	−	0.438454i
$808$	2.14181e6	−	1.79720e6i	3.28064	−	2.75279i
$809$		−	901709.i		−	1.37775i	−0.724882	−	0.688873i	$-0.758106\pi$
$809$		−	901709.i		−	1.37775i	0.724882	−	0.688873i	$-0.241894\pi$
$810$	−328250.	+	58193.4i	−0.500305	+	0.0886960i
$811$	−202036.			−0.307176			−0.153588	−	0.988135i	$-0.549083\pi$
$811$	−202036.			−0.307176			−0.153588	+	0.988135i	$0.549083\pi$
$812$	488382.	+	582031.i	0.740709	+	0.882743i
$813$	−157160.	−	246565.i	−0.237772	−	0.373036i
$814$	−12342.3	+	69996.7i	−0.0186272	+	0.105640i
$815$	48691.7	+	133779.i	0.0733060	+	0.201407i
$816$	118229.	−	375277.i	0.177559	−	0.563601i
$817$	70076.3	+	397422.i	0.104985	+	0.595399i
$818$	597284.	−	344842.i	0.892636	−	0.515364i
$819$	−164130.	−	234171.i	−0.244692	−	0.349112i
$820$	−244657.	+	423759.i	−0.363857	+	0.630218i
$821$	−323976.	+	890118.i	−0.480648	+	1.32057i	0.428291	+	0.903641i	$0.359116\pi$
$821$	−323976.	+	890118.i	−0.480648	+	1.32057i	−0.908939	+	0.416929i	$0.863107\pi$
$822$	−758208.	+	314266.i	−1.12213	+	0.465108i
$823$	−899972.	−	755166.i	−1.32871	−	1.11492i	−0.984378	−	0.176068i	$-0.943662\pi$
$823$	−899972.	−	755166.i	−1.32871	−	1.11492i	−0.344329	−	0.938849i	$-0.611893\pi$
$824$	1.76942e6	−	2.10871e6i	2.60601	−	3.10572i
$825$	−264402.	+	344741.i	−0.388469	+	0.506506i
$826$	−278575.	−	101393.i	−0.408302	−	0.148610i
$827$	512136.	+	295682.i	0.748815	+	0.432328i	0.825265	−	0.564745i	$-0.191025\pi$
$827$	512136.	+	295682.i	0.748815	+	0.432328i	−0.0764509	+	0.997073i	$0.524359\pi$
$828$	1.15415e6	+	1.15308e6i	1.68346	+	1.68190i
$829$	−316491.	−	548179.i	−0.460524	−	0.797651i	0.538463	−	0.842649i	$-0.319005\pi$
$829$	−316491.	−	548179.i	−0.460524	−	0.797651i	−0.998987	+	0.0449979i	$0.985672\pi$
$830$	288712.	−	50907.7i	0.419091	−	0.0738971i
$831$	79089.8	−	72506.2i	0.114530	−	0.104996i
$832$	3.39050e6	−	1.23404e6i	4.89798	−	1.78272i
$833$	71281.1	+	12568.8i	0.102727	+	0.0181135i
$834$	2.00743e6	+	1.04441e6i	2.88609	+	1.50155i
$835$	138872.	−	116527.i	0.199178	−	0.167130i
$836$		−	1.05316e6i		−	1.50688i
$837$	−13425.9	+	312494.i	−0.0191643	+	0.446057i
$838$	−230460.			−0.328176
$839$	−747982.	−	891410.i	−1.06259	−	1.26635i	−0.962474	−	0.271374i	$-0.912522\pi$
$839$	−747982.	−	891410.i	−1.06259	−	1.26635i	−0.100120	−	0.994975i	$-0.531923\pi$
$840$	−310183.	+	13614.9i	−0.439601	+	0.0192956i
$841$	29684.0	−	168346.i	0.0419691	−	0.238019i
$842$	308535.	+	847692.i	0.435191	+	1.19568i
$843$	−583388.	+	129476.i	−0.820923	+	0.182194i
$844$	270685.	+	1.53513e6i	0.379996	+	2.15506i
$845$	20832.0	−	12027.4i	0.0291755	−	0.0168445i
$846$	766524.	−	357869.i	1.07099	−	0.500016i
$847$	−87366.4	+	151323.i	−0.121780	+	0.210930i
$848$	922380.	−	2.53422e6i	1.28268	−	3.52413i
$849$	140258.	−	1.06728e6i	0.194587	−	1.48069i
$850$	−134494.	−	112854.i	−0.186151	−	0.156199i
$851$	30439.1	−	36275.9i	0.0420313	−	0.0500909i
$852$	−2.72331e6	−	357888.i	−3.75161	−	0.493024i
$853$	−772505.	−	281169.i	−1.06170	−	0.386429i	−0.248636	−	0.968597i	$-0.579982\pi$
$853$	−772505.	−	281169.i	−1.06170	−	0.386429i	−0.813068	+	0.582168i	$0.802204\pi$
$854$	−753582.	−	435081.i	−1.03327	−	0.596560i
$855$	−60653.8	−	129915.i	−0.0829709	−	0.177716i
$856$	2.39954e6	+	4.15612e6i	3.27476	+	5.67206i
$857$	−92965.8	+	16392.4i	−0.126579	+	0.0223193i	−0.236579	−	0.971612i	$-0.576026\pi$
$857$	−92965.8	+	16392.4i	−0.126579	+	0.0223193i	0.110000	+	0.993932i	$0.464915\pi$
$858$	200603.	+	903871.i	0.272498	+	1.22781i
$859$	−447397.	+	162839.i	−0.606327	+	0.220685i	−0.626895	−	0.779103i	$-0.715675\pi$
$859$	−447397.	+	162839.i	−0.606327	+	0.220685i	0.0205683	+	0.999788i	$0.493452\pi$
$860$	−430788.	−	75959.5i	−0.582460	−	0.102703i
$861$	14517.8	+	330752.i	0.0195837	+	0.446166i
$862$	−619460.	+	519789.i	−0.833679	+	0.699540i
$863$			285544.i			0.383399i	0.981454	+	0.191700i	$0.0613999\pi$
$863$			285544.i			0.383399i	−0.981454	+	0.191700i	$0.938600\pi$
$864$	−1.76159e6	−	3.37824e6i	−2.35981	−	4.52546i
$865$	140113.			0.187261
$866$	1.07832e6	+	1.28510e6i	1.43785	+	1.71356i
$867$	340902.	−	655237.i	0.453514	−	0.871686i
$868$	−77296.1	+	438368.i	−0.102593	+	0.581834i
$869$	120226.	+	330318.i	0.159206	+	0.437414i
$870$	−226313.	−	246862.i	−0.299000	−	0.326149i
$871$	79247.7	+	449436.i	0.104460	+	0.592423i
$872$	−3.56205e6	+	2.05655e6i	−4.68454	+	2.70462i
$873$	852027.	−	852818.i	1.11796	−	1.11899i
$874$	−472070.	+	817649.i	−0.617993	+	1.07039i
$875$	−59623.0	+	163813.i	−0.0778749	+	0.213960i
$876$	1.01398e6	+	777683.i	1.32136	+	1.01343i
$877$	531754.	+	446194.i	0.691371	+	0.580129i	0.919304	−	0.393548i	$-0.128752\pi$
$877$	531754.	+	446194.i	0.691371	+	0.580129i	−0.227933	+	0.973677i	$0.573197\pi$
$878$	−705977.	+	841351.i	−0.915802	+	1.09141i
$879$	519733.	+	1.25392e6i	0.672671	+	1.62291i
$880$	573926.	+	208892.i	0.741124	+	0.269747i
$881$	378421.	+	218482.i	0.487555	+	0.281490i	0.723560	−	0.690262i	$-0.242505\pi$
$881$	378421.	+	218482.i	0.487555	+	0.281490i	−0.236004	+	0.971752i	$0.575838\pi$
$882$	994173.	−	696815.i	1.27798	−	0.895737i
$883$	−150343.	−	260402.i	−0.192824	−	0.333981i	0.753361	−	0.657607i	$-0.228431\pi$
$883$	−150343.	−	260402.i	−0.192824	−	0.333981i	−0.946185	+	0.323626i	$0.895098\pi$
$884$	−273838.	+	48285.0i	−0.350420	+	0.0617885i
$885$	92624.5	+	29180.8i	0.118260	+	0.0372572i
$886$	−930466.	+	338662.i	−1.18531	+	0.431419i
$887$	1.46352e6	+	258059.i	1.86017	+	0.327998i	0.987164	−	0.159712i	$-0.0510564\pi$
$887$	1.46352e6	+	258059.i	1.86017	+	0.327998i	0.873006	+	0.487710i	$0.162168\pi$
$888$	−197590.	+	125943.i	−0.250576	+	0.159716i
$889$	−21116.9	+	17719.2i	−0.0267194	+	0.0224202i
$890$			435584.i			0.549910i
$891$	509834.	−	186100.i	0.642205	−	0.234419i
$892$	−2.78289e6			−3.49757
$893$	233865.	+	278709.i	0.293266	+	0.349501i
$894$	−808337.	−	1.26819e6i	−1.01139	−	1.58675i
$895$	38504.8	−	218371.i	0.0480694	−	0.272615i
$896$	−744395.	−	2.04521e6i	−0.927230	−	2.54754i
$897$	185356.	−	588351.i	0.230368	−	0.731227i
$898$	98509.5	+	558675.i	0.122159	+	0.692798i
$899$	−272122.	+	157110.i	−0.336701	+	0.194394i
$900$	−2.18014e6	+	191757.i	−2.69153	+	0.236737i
$901$	−44812.8	+	77618.1i	−0.0552017	+	0.0956122i
$902$	366615.	−	1.00727e6i	0.450607	−	1.23803i
$903$	−273412.	+	113325.i	−0.335307	+	0.138980i
$904$	−788653.	−	661759.i	−0.965049	−	0.809772i
$905$	95629.3	−	113967.i	0.116760	−	0.139149i
$906$	−445665.	+	581081.i	−0.542940	+	0.707913i
$907$	50254.6	+	18291.2i	0.0610887	+	0.0222345i	0.372384	−	0.928079i	$-0.378541\pi$
$907$	50254.6	+	18291.2i	0.0610887	+	0.0222345i	−0.311295	+	0.950313i	$0.600763\pi$
$908$	−2.22076e6	−	1.28215e6i	−2.69358	−	1.55514i
$909$	−244657.	+	914769.i	−0.296094	+	1.10709i
$910$	89690.9	+	155349.i	0.108309	+	0.187597i
$911$	152020.	−	26805.2i	0.183174	−	0.0322985i	−0.0813088	−	0.996689i	$-0.525910\pi$
$911$	152020.	−	26805.2i	0.183174	−	0.0322985i	0.264482	+	0.964391i	$0.414799\pi$
$912$	2.09222e6	−	1.91806e6i	2.51546	−	2.30607i
$913$	−448502.	+	163242.i	−0.538051	+	0.195834i
$914$	144507.	+	25480.4i	0.172980	+	0.0305010i
$915$	252872.	+	131562.i	0.302035	+	0.157141i
$916$	2.41235e6	−	2.02420e6i	2.87507	−	2.41247i
$917$		−	105599.i		−	0.125580i
$918$	66098.1	+	209129.i	0.0784339	+	0.248158i
$919$	225607.			0.267130			0.133565	−	0.991040i	$-0.457358\pi$
$919$	225607.			0.267130			0.133565	+	0.991040i	$0.457358\pi$
$920$	−430506.	−	513058.i	−0.508632	−	0.606164i
$921$	807128.	−	35427.6i	0.951532	−	0.0417659i
$922$	378560.	−	2.14692e6i	0.445321	−	2.52554i
$923$	355202.	+	975909.i	0.416938	+	1.14553i
$924$	754041.	−	167350.i	0.883184	−	0.196012i
$925$	11031.0	+	62560.0i	0.0128923	+	0.0731161i
$926$	1.46089e6	−	843444.i	1.70371	−	0.983636i
$927$	−80823.1	+	928775.i	−0.0940538	+	1.08081i
$928$	1.91373e6	−	3.31467e6i	2.22221	−	3.84897i
$929$	−284048.	+	780417.i	−0.329125	+	0.904264i	0.659209	+	0.751960i	$0.270891\pi$
$929$	−284048.	+	780417.i	−0.329125	+	0.904264i	−0.988334	+	0.152304i	$0.951331\pi$
$930$	25564.8	−	194533.i	0.0295581	−	0.224920i
$931$	399987.	+	335629.i	0.461473	+	0.387222i
$932$	−2.67910e6	+	3.19283e6i	−3.08430	+	3.67573i
$933$	−302286.	−	39725.4i	−0.347260	−	0.0456357i
$934$	2.18804e6	+	796380.i	2.50819	+	0.912907i
$935$	−17578.2	−	10148.8i	−0.0201072	−	0.0116089i
$936$	−1.74955e6	+	2.50108e6i	−1.99698	+	2.85480i
$937$	−88604.2	−	153467.i	−0.100919	−	0.174798i	0.811144	−	0.584846i	$-0.198845\pi$
$937$	−88604.2	−	153467.i	−0.100919	−	0.174798i	−0.912064	+	0.410048i	$0.865512\pi$
$938$	504501.	−	88957.1i	0.573398	−	0.101106i
$939$	−66633.9	−	300237.i	−0.0755726	−	0.340512i
$940$	−370590.	+	134884.i	−0.419410	+	0.152653i
$941$	−324201.	−	57165.4i	−0.366130	−	0.0645586i	−0.0124433	−	0.999923i	$-0.503961\pi$
$941$	−324201.	−	57165.4i	−0.366130	−	0.0645586i	−0.353687	+	0.935364i	$0.615072\pi$
$942$	−105958.	−	2.41400e6i	−0.119408	−	2.72042i
$943$	−547081.	+	459055.i	−0.615216	+	0.516228i
$944$			1.92250e6i			2.15736i
$945$	83378.9	−	64071.1i	0.0933668	−	0.0717461i
$946$	958258.			1.07078
$947$	−391176.	−	466186.i	−0.436187	−	0.519827i	0.502510	−	0.864571i	$-0.332410\pi$
$947$	−391176.	−	466186.i	−0.436187	−	0.519827i	−0.938697	+	0.344744i	$0.887966\pi$
$948$	−817275.	+	1.57086e6i	−0.909393	+	1.74792i
$949$	83900.6	−	475824.i	0.0931607	−	0.528341i
$950$	−433180.	−	1.19015e6i	−0.479978	−	1.31873i
$951$	−79116.6	−	86300.4i	−0.0874796	−	0.0954228i
$952$	35470.8	+	201165.i	0.0391379	+	0.221962i
$953$	686558.	−	396385.i	0.755947	−	0.436446i	−0.0718914	−	0.997412i	$-0.522903\pi$
$953$	686558.	−	396385.i	0.755947	−	0.436446i	0.827839	+	0.560966i	$0.189570\pi$
$954$	389758.	+	1.45190e6i	0.428251	+	1.59529i
$955$	208830.	−	361704.i	0.228974	−	0.396595i
$956$	−375374.	+	1.03133e6i	−0.410723	+	1.12845i
$957$	432639.	+	331816.i	0.472391	+	0.362305i
$958$	−889994.	−	746794.i	−0.969742	−	0.813710i
$959$	166410.	−	198319.i	0.180943	−	0.215639i
$960$	508011.	+	1.22564e6i	0.551227	+	1.32991i
$961$	694839.	+	252901.i	0.752380	+	0.273844i
$962$	117240.	+	67688.3i	0.126685	+	0.0731415i
$963$	−1.47337e6	−	686214.i	−1.58877	−	0.739957i
$964$	−2.44526e6	−	4.23532e6i	−2.63131	−	4.55756i
$965$	−236028.	+	41618.1i	−0.253459	+	0.0446917i
$966$	−660436.	−	208066.i	−0.707745	−	0.222971i
$967$	−1.22767e6	+	446837.i	−1.31290	+	0.477855i	−0.901175	−	0.433455i	$-0.857294\pi$
$967$	−1.22767e6	+	446837.i	−1.31290	+	0.477855i	−0.411721	+	0.911310i	$0.635072\pi$
$968$	1.83670e6	+	323860.i	1.96015	+	0.345627i
$969$	−79544.2	+	50701.2i	−0.0847151	+	0.0539971i
$970$	−579287.	+	486079.i	−0.615673	+	0.516611i
$971$			1.13384e6i			1.20258i	0.799030	+	0.601291i	$0.205347\pi$
$971$			1.13384e6i			1.20258i	−0.799030	+	0.601291i	$0.794653\pi$
$972$	2.42656e6	+	1.25961e6i	2.56837	+	1.33323i
$973$	−713767.			−0.753930
$974$	1.04544e6	+	1.24590e6i	1.10200	+	1.31331i
$975$	444776.	+	697801.i	0.467877	+	0.734044i
$976$	−979896.	+	5.55727e6i	−1.02868	+	5.83394i
$977$	−588549.	−	1.61703e6i	−0.616586	−	1.69406i	−0.715191	−	0.698929i	$-0.753660\pi$
$977$	−588549.	−	1.61703e6i	−0.616586	−	1.69406i	0.0986049	−	0.995127i	$-0.468562\pi$
$978$	472070.	−	1.49843e6i	0.493547	−	1.56660i
$979$	−123142.	−	698375.i	−0.128482	−	0.728658i
$980$	−490155.	+	282991.i	−0.510365	+	0.294660i
$981$	588127.	−	1.26277e6i	0.611129	−	1.31216i
$982$	806501.	−	1.39690e6i	0.836339	−	1.44858i
$983$	225126.	−	618528.i	0.232980	−	0.640107i	−0.767019	−	0.641624i	$-0.778261\pi$
$983$	225126.	−	618528.i	0.232980	−	0.640107i	0.999999	+	0.00151760i	$0.000483066\pi$
$984$	3.26443e6	−	1.35306e6i	3.37146	−	1.39742i
$985$	91001.6	+	76359.4i	0.0937943	+	0.0787028i
$986$	−141628.	+	168786.i	−0.145678	+	0.173613i
$987$	−162389.	+	211731.i	−0.166695	+	0.217345i
$988$	−1.88493e6	−	686060.i	−1.93100	−	0.702827i
$989$	−552906.	−	319221.i	−0.565274	−	0.326361i
$990$	−328813.	+	88268.8i	−0.335490	+	0.0900610i
$991$	329922.	+	571441.i	0.335941	+	0.581868i	0.983665	−	0.180008i	$-0.0576122\pi$
$991$	329922.	+	571441.i	0.335941	+	0.581868i	−0.647724	+	0.761875i	$0.724279\pi$
$992$	2.20829e6	−	389382.i	2.24405	−	0.395687i
$993$	−428610.	+	392932.i	−0.434674	+	0.398491i
$994$	1.09548e6	−	398721.i	1.10874	−	0.403549i
$995$	54038.7	+	9528.47i	0.0545831	+	0.00962448i
$996$	−2.13290e6	−	1.10969e6i	−2.15006	−	1.11862i
$997$	−1.09030e6	+	914868.i	−1.09687	+	0.920382i	−0.997211	−	0.0746398i	$-0.976219\pi$
$997$	−1.09030e6	+	914868.i	−1.09687	+	0.920382i	−0.0996579	+	0.995022i	$0.531775\pi$
$998$			442634.i			0.444410i
$999$	30317.7	−	73337.7i	0.0303784	−	0.0734846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.5.f.a.5.1	✓	66
3.2	odd	2		81.5.f.a.44.11		66
27.11	odd	18	inner	27.5.f.a.11.1	yes	66
27.16	even	9		81.5.f.a.35.11		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.5.1	✓	66	1.1	even	1	trivial
27.5.f.a.11.1	yes	66	27.11	odd	18	inner
81.5.f.a.35.11		66	27.16	even	9
81.5.f.a.44.11		66	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.07357 - 6.04645i) q^{2} +(4.83746 + 7.58940i) q^{3} +(-8.04003 + 45.5973i) q^{4} +(2.20171 + 6.04914i) q^{5} +(21.3457 - 67.7548i) q^{6} +(3.89095 + 22.0667i) q^{7} +(207.124 - 119.583i) q^{8} +(-34.1980 + 73.4268i) q^{9} +(25.4053 - 44.0033i) q^{10} +(-28.2925 + 77.7331i) q^{11} +(-384.949 + 159.556i) q^{12} +(120.696 + 101.276i) q^{13} +(113.684 - 135.483i) q^{14} +(-35.2587 + 45.9721i) q^{15} +(-1077.77 - 392.278i) q^{16} +(33.0101 + 19.0584i) q^{17} +(617.478 - 165.760i) q^{18} +(137.485 + 238.131i) q^{19} +(-293.526 + 51.7566i) q^{20} +(-148.651 + 136.277i) q^{21} +(613.553 - 223.315i) q^{22} +(-428.407 - 75.5397i) q^{23} +(1909.51 + 993.467i) q^{24} +(447.033 - 375.105i) q^{25} -1243.61i q^{26} +(-722.697 + 95.6565i) q^{27} -1037.46 q^{28} +(-470.746 - 561.013i) q^{29} +(456.856 - 20.0529i) q^{30} +(74.5048 - 422.538i) q^{31} +(1787.49 + 4911.08i) q^{32} +(-726.812 + 161.307i) q^{33} +(-52.2436 - 296.288i) q^{34} +(-124.918 + 72.1213i) q^{35} +(-3073.11 - 2149.69i) q^{36} +(-54.4289 + 94.2735i) q^{37} +(742.306 - 2039.47i) q^{38} +(-184.762 + 1405.93i) q^{39} +(1179.40 + 989.634i) q^{40} +(1055.26 - 1257.61i) q^{41} +(1578.18 + 207.399i) q^{42} +(1379.12 + 501.958i) q^{43} +(-3316.95 - 1915.04i) q^{44} +(-519.463 - 45.2043i) q^{45} +(1716.81 + 2973.60i) q^{46} +(1303.06 - 229.765i) q^{47} +(-2236.53 - 10077.3i) q^{48} +(1784.40 - 649.470i) q^{49} +(-4536.11 - 799.839i) q^{50} +(15.0432 + 342.721i) q^{51} +(-5588.30 + 4689.14i) q^{52} +2351.34i q^{53} +(4245.04 + 3884.43i) q^{54} -532.511 q^{55} +(3444.71 + 4105.24i) q^{56} +(-1142.19 + 2195.37i) q^{57} +(-1003.77 + 5692.68i) q^{58} +(-573.291 - 1575.11i) q^{59} +(-1812.72 - 1977.32i) q^{60} +(-854.355 - 4845.29i) q^{61} +(-2932.86 + 1693.29i) q^{62} +(-1753.35 - 468.937i) q^{63} +(11450.1 - 19832.2i) q^{64} +(-346.895 + 953.086i) q^{65} +(4662.87 + 3576.23i) q^{66} +(2218.87 + 1861.85i) q^{67} +(-1134.41 + 1351.94i) q^{68} +(-1499.10 - 3616.77i) q^{69} +(1069.86 + 389.396i) q^{70} +(5708.42 + 3295.76i) q^{71} +(1697.37 + 19297.9i) q^{72} +(-1533.30 - 2655.75i) q^{73} +(846.169 - 149.202i) q^{74} +(5009.33 + 1578.16i) q^{75} +(-11963.5 + 4354.36i) q^{76} +(-1825.40 - 321.867i) q^{77} +(9438.26 - 6015.92i) q^{78} +(3255.22 - 2731.45i) q^{79} -7383.29i q^{80} +(-4221.99 - 5022.10i) q^{81} -12958.0 q^{82} +(3708.74 + 4419.90i) q^{83} +(-5018.69 - 7873.73i) q^{84} +(-42.6083 + 241.644i) q^{85} +(-3962.00 - 10885.5i) q^{86} +(1980.54 - 6286.56i) q^{87} +(3435.50 + 19483.7i) q^{88} +(-7424.17 + 4286.35i) q^{89} +(2362.21 + 3370.26i) q^{90} +(-1765.20 + 3057.42i) q^{91} +(6888.81 - 18926.8i) q^{92} +(3567.22 - 1478.56i) q^{93} +(-8000.43 - 6713.15i) q^{94} +(-1137.79 + 1355.96i) q^{95} +(-28625.3 + 37323.1i) q^{96} +(-13985.3 - 5090.22i) q^{97} +(-12980.3 - 7494.17i) q^{98} +(-4740.14 - 4735.75i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 3 q^{5} + 90 q^{6} - 6 q^{7} - 9 q^{8} - 108 q^{9} - 3 q^{10} - 492 q^{11} - 339 q^{12} - 6 q^{13} + 1137 q^{14} + 1017 q^{15} - 54 q^{16} - 9 q^{17} + 603 q^{18} - 3 q^{19}+ \cdots - 162405 q^{99}+O(q^{100}) \) 66 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 3 * q^5 + 90 * q^6 - 6 * q^7 - 9 * q^8 - 108 * q^9 - 3 * q^10 - 492 * q^11 - 339 * q^12 - 6 * q^13 + 1137 * q^14 + 1017 * q^15 - 54 * q^16 - 9 * q^17 + 603 * q^18 - 3 * q^19 - 2487 * q^20 - 2784 * q^21 + 1002 * q^22 - 2724 * q^23 - 3312 * q^24 + 435 * q^25 + 1368 * q^27 - 12 * q^28 + 5016 * q^29 + 10773 * q^30 - 1671 * q^31 + 10224 * q^32 + 2925 * q^33 - 342 * q^34 - 2682 * q^35 - 7704 * q^36 - 3 * q^37 - 6564 * q^38 - 1983 * q^39 - 1113 * q^40 + 5754 * q^41 + 8694 * q^42 - 1266 * q^43 - 4545 * q^44 - 7029 * q^45 - 3 * q^46 - 9159 * q^47 - 28383 * q^48 + 5898 * q^49 - 34977 * q^50 - 14814 * q^51 + 2871 * q^52 + 13878 * q^54 - 12 * q^55 + 39243 * q^56 + 15792 * q^57 - 12291 * q^58 + 24762 * q^59 + 50670 * q^60 - 8358 * q^61 + 38304 * q^62 + 21609 * q^63 + 6141 * q^64 + 23727 * q^65 + 11349 * q^66 + 15996 * q^67 - 43533 * q^68 - 26847 * q^69 - 7251 * q^70 - 19773 * q^71 - 77580 * q^72 + 6108 * q^73 - 74847 * q^74 - 49155 * q^75 - 28614 * q^76 - 33909 * q^77 - 9108 * q^78 - 5658 * q^79 - 12600 * q^81 - 12 * q^82 + 18813 * q^83 + 82356 * q^84 + 24219 * q^85 + 96474 * q^86 + 84555 * q^87 + 36042 * q^88 + 110232 * q^89 + 153540 * q^90 - 6042 * q^91 + 73545 * q^92 + 1293 * q^93 + 2631 * q^94 - 65163 * q^95 - 152226 * q^96 - 3696 * q^97 - 259938 * q^98 - 162405 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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