LMFDB - Embedded newform 27.5.f.a.5.4

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			5.4
Character	$\chi$	$=$	27.5
Dual form			27.5.f.a.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.46212 - 2.93424i) q^{2} +(8.40252 - 3.22453i) q^{3} +(0.230635 - 1.30800i) q^{4} +(3.23200 + 8.87984i) q^{5} +(-30.1496 - 16.7158i) q^{6} +(-13.4127 - 76.0673i) q^{7} +(-57.4812 + 33.1868i) q^{8} +(60.2048 - 54.1884i) q^{9} +(18.0980 - 31.3467i) q^{10} +(-12.4441 + 34.1900i) q^{11} +(-2.27976 - 11.7342i) q^{12} +(116.163 + 97.4720i) q^{13} +(-190.176 + 226.643i) q^{14} +(55.7903 + 64.1914i) q^{15} +(218.934 + 79.6856i) q^{16} +(371.386 + 214.420i) q^{17} +(-307.233 - 43.2369i) q^{18} +(76.8422 + 133.095i) q^{19} +(12.3602 - 2.17944i) q^{20} +(-357.982 - 595.907i) q^{21} +(130.961 - 47.6658i) q^{22} +(-543.514 - 95.8361i) q^{23} +(-375.975 + 464.202i) q^{24} +(410.372 - 344.343i) q^{25} -580.837i q^{26} +(331.140 - 649.452i) q^{27} -102.589 q^{28} +(188.204 + 224.292i) q^{29} +(50.9907 - 321.749i) q^{30} +(-295.931 + 1678.31i) q^{31} +(57.9911 + 159.329i) q^{32} +(5.68458 + 327.409i) q^{33} +(-285.238 - 1617.66i) q^{34} +(632.116 - 364.952i) q^{35} +(-56.9930 - 91.2455i) q^{36} +(328.512 - 568.999i) q^{37} +(201.337 - 553.169i) q^{38} +(1290.36 + 444.441i) q^{39} +(-480.472 - 403.164i) q^{40} +(-714.418 + 851.410i) q^{41} +(-867.141 + 2517.60i) q^{42} +(-2008.45 - 731.017i) q^{43} +(41.8504 + 24.1623i) q^{44} +(675.766 + 359.472i) q^{45} +(1056.99 + 1830.76i) q^{46} +(534.052 - 94.1678i) q^{47} +(2096.55 - 36.4010i) q^{48} +(-3350.13 + 1219.35i) q^{49} +(-2020.77 - 356.317i) q^{50} +(3811.98 + 604.121i) q^{51} +(154.285 - 129.460i) q^{52} -2154.88i q^{53} +(-2720.96 + 627.385i) q^{54} -343.821 q^{55} +(3295.41 + 3927.31i) q^{56} +(1074.84 + 870.550i) q^{57} +(194.748 - 1104.47i) q^{58} +(-1344.72 - 3694.60i) q^{59} +(96.8295 - 58.1688i) q^{60} +(154.886 + 878.404i) q^{61} +(5653.19 - 3263.87i) q^{62} +(-4929.48 - 3852.80i) q^{63} +(2188.61 - 3790.78i) q^{64} +(-490.099 + 1346.54i) q^{65} +(946.700 - 822.800i) q^{66} +(-251.739 - 211.234i) q^{67} +(366.115 - 436.319i) q^{68} +(-4875.91 + 947.312i) q^{69} +(-2627.20 - 956.224i) q^{70} +(-7833.15 - 4522.47i) q^{71} +(-1662.30 + 5112.82i) q^{72} +(5045.79 + 8739.56i) q^{73} +(-2478.42 + 437.012i) q^{74} +(2337.81 - 4216.61i) q^{75} +(191.810 - 69.8132i) q^{76} +(2767.65 + 488.011i) q^{77} +(-1872.93 - 4880.50i) q^{78} +(689.267 - 578.364i) q^{79} +2201.65i q^{80} +(688.231 - 6524.80i) q^{81} +4257.23 q^{82} +(4921.00 + 5864.61i) q^{83} +(-862.009 + 330.803i) q^{84} +(-703.695 + 3990.85i) q^{85} +(2800.07 + 7693.14i) q^{86} +(2304.62 + 1277.75i) q^{87} +(-419.351 - 2378.26i) q^{88} +(-10610.2 + 6125.78i) q^{89} +(-609.041 - 2867.93i) q^{90} +(5856.38 - 10143.5i) q^{91} +(-250.707 + 688.812i) q^{92} +(2925.20 + 15056.3i) q^{93} +(-1591.21 - 1335.19i) q^{94} +(-933.505 + 1112.51i) q^{95} +(1001.03 + 1151.77i) q^{96} +(9904.15 + 3604.82i) q^{97} +(11826.3 + 6827.91i) q^{98} +(1103.50 + 2732.73i) 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 $

$2$	−2.46212	−	2.93424i	−0.615530	−	0.733561i	0.364765	−	0.931100i	$-0.381149\pi$
$2$	−2.46212	−	2.93424i	−0.615530	−	0.733561i	−0.980295	+	0.197539i	$0.936705\pi$
$3$	8.40252	−	3.22453i	0.933614	−	0.358281i
$3$	8.40252	−	3.22453i	0.933614	−	0.358281i
$4$	0.230635	−	1.30800i	0.0144147	−	0.0817499i
$5$	3.23200	+	8.87984i	0.129280	+	0.355194i	0.987398	−	0.158259i	$-0.0505882\pi$
$5$	3.23200	+	8.87984i	0.129280	+	0.355194i	−0.858118	+	0.513453i	$0.828366\pi$
$6$	−30.1496	−	16.7158i	−0.837489	−	0.464329i
$7$	−13.4127	−	76.0673i	−0.273729	−	1.55239i	−0.742971	−	0.669324i	$-0.766584\pi$
$7$	−13.4127	−	76.0673i	−0.273729	−	1.55239i	0.469242	−	0.883070i	$-0.344527\pi$
$8$	−57.4812	+	33.1868i	−0.898143	+	0.518543i
$9$	60.2048	−	54.1884i	0.743269	−	0.668993i
$10$	18.0980	−	31.3467i	0.180980	−	0.313467i
$11$	−12.4441	+	34.1900i	−0.102844	+	0.282562i	−0.980433	−	0.196852i	$-0.936928\pi$
$11$	−12.4441	+	34.1900i	−0.102844	+	0.282562i	0.877589	+	0.479413i	$0.159151\pi$
$12$	−2.27976	−	11.7342i	−0.0158317	−	0.0814874i
$13$	116.163	+	97.4720i	0.687353	+	0.576758i	0.918145	−	0.396246i	$-0.129687\pi$
$13$	116.163	+	97.4720i	0.687353	+	0.576758i	−0.230792	+	0.973003i	$0.574132\pi$
$14$	−190.176	+	226.643i	−0.970286	+	1.15634i
$15$	55.7903	+	64.1914i	0.247957	+	0.285295i
$16$	218.934	+	79.6856i	0.855212	+	0.311272i
$17$	371.386	+	214.420i	1.28507	+	0.741937i	0.977771	−	0.209676i	$-0.0672409\pi$
$17$	371.386	+	214.420i	1.28507	+	0.741937i	0.307301	+	0.951612i	$0.400574\pi$
$18$	−307.233	−	43.2369i	−0.948251	−	0.133447i
$19$	76.8422	+	133.095i	0.212859	+	0.368683i	0.952608	−	0.304200i	$-0.0983891\pi$
$19$	76.8422	+	133.095i	0.212859	+	0.368683i	−0.739749	+	0.672883i	$0.765056\pi$
$20$	12.3602	−	2.17944i	0.0309006	−	0.00544861i
$21$	−357.982	−	595.907i	−0.811751	−	1.35126i
$22$	130.961	−	47.6658i	0.270580	−	0.0984830i
$23$	−543.514	−	95.8361i	−1.02744	−	0.181165i	−0.365568	−	0.930785i	$-0.619125\pi$
$23$	−543.514	−	95.8361i	−1.02744	−	0.181165i	−0.661868	+	0.749620i	$0.730236\pi$
$24$	−375.975	+	464.202i	−0.652734	+	0.805907i
$25$	410.372	−	344.343i	0.656595	−	0.550949i
$26$		−	580.837i		−	0.859227i
$27$	331.140	−	649.452i	0.454238	−	0.890880i
$28$	−102.589			−0.130854
$29$	188.204	+	224.292i	0.223785	+	0.266697i	0.866242	−	0.499625i	$-0.166529\pi$
$29$	188.204	+	224.292i	0.223785	+	0.266697i	−0.642456	+	0.766322i	$0.722085\pi$
$30$	50.9907	−	321.749i	0.0566563	−	0.357499i
$31$	−295.931	+	1678.31i	−0.307941	+	1.74642i	0.301386	+	0.953502i	$0.402551\pi$
$31$	−295.931	+	1678.31i	−0.307941	+	1.74642i	−0.609327	+	0.792919i	$0.708560\pi$
$32$	57.9911	+	159.329i	0.0566319	+	0.155595i
$33$	5.68458	+	327.409i	0.00522000	+	0.300651i
$34$	−285.238	−	1617.66i	−0.246745	−	1.39936i
$35$	632.116	−	364.952i	0.516013	−	0.297920i
$36$	−56.9930	−	91.2455i	−0.0439761	−	0.0704055i
$37$	328.512	−	568.999i	0.239965	−	0.415631i	−0.720739	−	0.693207i	$-0.756197\pi$
$37$	328.512	−	568.999i	0.239965	−	0.415631i	0.960704	+	0.277575i	$0.0895307\pi$
$38$	201.337	−	553.169i	0.139430	−	0.383081i
$39$	1290.36	+	444.441i	0.848364	+	0.292203i
$40$	−480.472	−	403.164i	−0.300295	−	0.251978i
$41$	−714.418	+	851.410i	−0.424996	+	0.506490i	−0.935472	−	0.353402i	$-0.885025\pi$
$41$	−714.418	+	851.410i	−0.424996	+	0.506490i	0.510476	+	0.859892i	$0.329469\pi$
$42$	−867.141	+	2517.60i	−0.491577	+	1.42721i
$43$	−2008.45	−	731.017i	−1.08624	−	0.395358i	−0.264012	−	0.964519i	$-0.585046\pi$
$43$	−2008.45	−	731.017i	−1.08624	−	0.395358i	−0.822226	+	0.569161i	$0.807268\pi$
$44$	41.8504	+	24.1623i	0.0216169	+	0.0124805i
$45$	675.766	+	359.472i	0.333712	+	0.177517i
$46$	1056.99	+	1830.76i	0.499523	+	0.865199i
$47$	534.052	−	94.1678i	0.241762	−	0.0426291i	−0.0514541	−	0.998675i	$-0.516386\pi$
$47$	534.052	−	94.1678i	0.241762	−	0.0426291i	0.293216	+	0.956046i	$0.405274\pi$
$48$	2096.55	−	36.4010i	0.909961	−	0.0157990i
$49$	−3350.13	+	1219.35i	−1.39531	+	0.507850i
$50$	−2020.77	−	356.317i	−0.808309	−	0.142527i
$51$	3811.98	+	604.121i	1.46558	+	0.232265i
$52$	154.285	−	129.460i	0.0570579	−	0.0478773i
$53$		−	2154.88i		−	0.767133i	−0.923513	−	0.383567i	$-0.874696\pi$
$53$		−	2154.88i		−	0.767133i	0.923513	−	0.383567i	$-0.125304\pi$
$54$	−2720.96	+	627.385i	−0.933112	+	0.215153i
$55$	−343.821			−0.113660
$56$	3295.41	+	3927.31i	1.05083	+	1.25233i
$57$	1074.84	+	870.550i	0.330821	+	0.267944i
$58$	194.748	−	1104.47i	0.0578917	−	0.328320i
$59$	−1344.72	−	3694.60i	−0.386304	−	1.06136i	−0.968652	−	0.248422i	$-0.920088\pi$
$59$	−1344.72	−	3694.60i	−0.386304	−	1.06136i	0.582348	−	0.812940i	$-0.302134\pi$
$60$	96.8295	−	58.1688i	0.0268971	−	0.0161580i
$61$	154.886	+	878.404i	0.0416249	+	0.236067i	0.998521	−	0.0543631i	$-0.0173128\pi$
$61$	154.886	+	878.404i	0.0416249	+	0.236067i	−0.956896	+	0.290430i	$0.906202\pi$
$62$	5653.19	−	3263.87i	1.47065	−	0.849082i
$63$	−4929.48	−	3852.80i	−1.24199	−	0.970723i
$64$	2188.61	−	3790.78i	0.534329	−	0.925484i
$65$	−490.099	+	1346.54i	−0.116000	+	0.318707i
$66$	946.700	−	822.800i	0.217332	−	0.188889i
$67$	−251.739	−	211.234i	−0.0560791	−	0.0470559i	0.614317	−	0.789059i	$-0.289431\pi$
$67$	−251.739	−	211.234i	−0.0560791	−	0.0470559i	−0.670396	+	0.742003i	$0.733876\pi$
$68$	366.115	−	436.319i	0.0791772	−	0.0943597i
$69$	−4875.91	+	947.312i	−1.02414	+	0.198973i
$70$	−2627.20	−	956.224i	−0.536164	−	0.195148i
$71$	−7833.15	−	4522.47i	−1.55389	−	0.897138i	−0.997820	−	0.0660012i	$-0.978976\pi$
$71$	−7833.15	−	4522.47i	−1.55389	−	0.897138i	−0.556068	−	0.831136i	$-0.687691\pi$
$72$	−1662.30	+	5112.82i	−0.320660	+	0.986268i
$73$	5045.79	+	8739.56i	0.946854	+	1.64000i	0.751995	+	0.659169i	$0.229092\pi$
$73$	5045.79	+	8739.56i	0.946854	+	1.64000i	0.194860	+	0.980831i	$0.437575\pi$
$74$	−2478.42	+	437.012i	−0.452597	+	0.0798050i
$75$	2337.81	−	4216.61i	0.415612	−	0.749619i
$76$	191.810	−	69.8132i	0.0332081	−	0.0120868i
$77$	2767.65	+	488.011i	0.466798	+	0.0823092i
$78$	−1872.93	−	4880.50i	−0.307845	−	0.802186i
$79$	689.267	−	578.364i	0.110442	−	0.0926716i	−0.585894	−	0.810387i	$-0.699257\pi$
$79$	689.267	−	578.364i	0.110442	−	0.0926716i	0.696336	+	0.717716i	$0.254812\pi$
$80$			2201.65i			0.344007i
$81$	688.231	−	6524.80i	0.104897	−	0.994483i
$82$	4257.23			0.633139
$83$	4921.00	+	5864.61i	0.714327	+	0.851301i	0.994066	−	0.108775i	$-0.0346927\pi$
$83$	4921.00	+	5864.61i	0.714327	+	0.851301i	−0.279740	+	0.960076i	$0.590248\pi$
$84$	−862.009	+	330.803i	−0.122167	+	0.0468825i
$85$	−703.695	+	3990.85i	−0.0973972	+	0.552367i
$86$	2800.07	+	7693.14i	0.378593	+	1.04018i
$87$	2304.62	+	1277.75i	0.304482	+	0.168814i
$88$	−419.351	−	2378.26i	−0.0541518	−	0.307110i
$89$	−10610.2	+	6125.78i	−1.33950	+	0.773359i	−0.986733	−	0.162353i	$-0.948092\pi$
$89$	−10610.2	+	6125.78i	−1.33950	+	0.773359i	−0.352764	+	0.935712i	$0.614758\pi$
$90$	−609.041	−	2867.93i	−0.0751902	−	0.354065i
$91$	5856.38	−	10143.5i	0.707206	−	1.22492i
$92$	−250.707	+	688.812i	−0.0296204	+	0.0813814i
$93$	2925.20	+	15056.3i	0.338212	+	1.74081i
$94$	−1591.21	−	1335.19i	−0.180083	−	0.151107i
$95$	−933.505	+	1112.51i	−0.103436	+	0.123270i
$96$	1001.03	+	1151.77i	0.108619	+	0.124975i
$97$	9904.15	+	3604.82i	1.05263	+	0.383124i	0.809653	−	0.586909i	$-0.199655\pi$
$97$	9904.15	+	3604.82i	1.05263	+	0.383124i	0.242972	+	0.970033i	$0.421878\pi$
$98$	11826.3	+	6827.91i	1.23139	+	0.710944i
$99$	1103.50	+	2732.73i	0.112591	+	0.278821i
$100$	−355.754	−	616.184i	−0.0355754	−	0.0616184i
$101$	−11744.2	+	2070.82i	−1.15128	+	0.203001i	−0.716534	−	0.697552i	$-0.754272\pi$
$101$	−11744.2	+	2070.82i	−1.15128	+	0.203001i	−0.434745	+	0.900554i	$0.643161\pi$
$102$	−7612.92	−	12672.7i	−0.731730	−	1.21806i
$103$	2818.50	−	1025.85i	0.265670	−	0.0966961i	−0.205751	−	0.978604i	$-0.565964\pi$
$103$	2818.50	−	1025.85i	0.265670	−	0.0966961i	0.471421	+	0.881908i	$0.343741\pi$
$104$	−9911.95	−	1747.74i	−0.916415	−	0.161589i
$105$	4134.57	−	5104.80i	0.375017	−	0.463020i
$106$	−6322.93	+	5305.57i	−0.562739	+	0.472194i
$107$		−	3921.12i		−	0.342486i	−0.985229	−	0.171243i	$-0.945222\pi$
$107$		−	3921.12i		−	0.342486i	0.985229	−	0.171243i	$-0.0547784\pi$
$108$	−773.109	−	582.917i	−0.0662817	−	0.0499757i
$109$	−17641.6			−1.48486			−0.742430	−	0.669924i	$-0.766327\pi$
$109$	−17641.6			−1.48486			−0.742430	+	0.669924i	$0.766327\pi$
$110$	846.529	+	1008.85i	0.0699611	+	0.0833764i
$111$	925.572	−	5840.33i	0.0751215	−	0.474014i
$112$	3124.96	−	17722.5i	0.249120	−	1.41283i
$113$	−2014.97	−	5536.07i	−0.157801	−	0.433556i	0.835446	−	0.549573i	$-0.185209\pi$
$113$	−2014.97	−	5536.07i	−0.157801	−	0.433556i	−0.993247	+	0.116017i	$0.962987\pi$
$114$	−91.9723	−	5297.23i	−0.00707697	−	0.407605i
$115$	−905.626	−	5136.06i	−0.0684783	−	0.388360i
$116$	336.780	−	194.440i	0.0250283	−	0.0144501i
$117$	12275.4	−	426.388i	0.896735	−	0.0311482i
$118$	−7529.98	+	13042.3i	−0.540791	+	0.936678i
$119$	11329.0	−	31126.3i	0.800016	−	2.19803i
$120$	−5337.20	−	1838.30i	−0.370639	−	0.127660i
$121$	10201.6	+	8560.12i	0.696780	+	0.584668i
$122$	2196.10	−	2617.21i	0.147548	−	0.175841i
$123$	−3257.51	+	9457.66i	−0.215316	+	0.625134i
$124$	2126.98	+	774.156i	0.138331	+	0.0503483i
$125$	9498.85	+	5484.16i	0.607926	+	0.350986i
$126$	831.918	+	23950.3i	0.0524010	+	1.50859i
$127$	−5410.37	−	9371.04i	−0.335444	−	0.581006i	0.648126	−	0.761533i	$-0.275553\pi$
$127$	−5410.37	−	9371.04i	−0.335444	−	0.581006i	−0.983570	+	0.180527i	$0.942220\pi$
$128$	−13840.0	+	2440.37i	−0.844729	+	0.148949i
$129$	−19233.3	+	333.934i	−1.15578	+	0.0200670i
$130$	5157.75	−	1877.27i	0.305192	−	0.111081i
$131$	26423.9	+	4659.24i	1.53976	+	0.271502i	0.878165	−	0.478357i	$-0.158767\pi$
$131$	26423.9	+	4659.24i	1.53976	+	0.271502i	0.661598	+	0.749859i	$0.269879\pi$
$132$	429.561	+	68.0766i	0.0246534	+	0.00390706i
$133$	9093.48	−	7630.34i	0.514076	−	0.431361i
$134$			1258.75i			0.0701018i
$135$	6837.27	+	841.442i	0.375159	+	0.0461696i
$136$	−28463.6			−1.53890
$137$	−2529.41	−	3014.43i	−0.134765	−	0.160607i	0.694441	−	0.719549i	$-0.255652\pi$
$137$	−2529.41	−	3014.43i	−0.134765	−	0.160607i	−0.829206	+	0.558943i	$0.811207\pi$
$138$	14784.7	+	11974.7i	0.776346	+	0.628792i
$139$	−4483.81	+	25429.0i	−0.232069	+	1.31613i	0.616629	+	0.787254i	$0.288498\pi$
$139$	−4483.81	+	25429.0i	−0.232069	+	1.31613i	−0.848698	+	0.528877i	$0.822613\pi$
$140$	−331.569	−	910.977i	−0.0169168	−	0.0464784i
$141$	4183.74	−	2513.32i	0.210439	−	0.126418i
$142$	6016.14	+	34119.2i	0.298361	+	1.69209i
$143$	−4778.11	+	2758.64i	−0.233660	+	0.134904i
$144$	17498.9	−	7066.25i	0.843891	−	0.340772i
$145$	−1383.41	+	2396.13i	−0.0657982	+	0.113966i
$146$	13220.6	−	36323.4i	0.620222	−	1.70405i
$147$	−24217.7	+	21048.2i	−1.12072	+	0.974047i
$148$	−668.484	−	560.925i	−0.0305188	−	0.0256083i
$149$	8511.39	−	10143.5i	0.383379	−	0.456893i	−0.539499	−	0.841986i	$-0.681386\pi$
$149$	8511.39	−	10143.5i	0.383379	−	0.456893i	0.922878	+	0.385093i	$0.125831\pi$
$150$	−18128.5	+	3522.09i	−0.805713	+	0.156537i
$151$	−22439.2	−	8167.21i	−0.984133	−	0.358195i	−0.200687	−	0.979655i	$-0.564317\pi$
$151$	−22439.2	−	8167.21i	−0.984133	−	0.358195i	−0.783446	+	0.621460i	$0.786540\pi$
$152$	−8833.96	−	5100.29i	−0.382356	−	0.220754i
$153$	33978.3	−	7215.72i	1.45150	−	0.308245i
$154$	−5382.34	−	9322.49i	−0.226950	−	0.393089i
$155$	−15859.6	+	2796.47i	−0.660128	+	0.116398i
$156$	878.931	−	1585.29i	0.0361165	−	0.0651416i
$157$	6060.26	−	2205.76i	0.245862	−	0.0894866i	−0.216150	−	0.976360i	$-0.569350\pi$
$157$	6060.26	−	2205.76i	0.245862	−	0.0894866i	0.462012	+	0.886874i	$0.347128\pi$
$158$	−3394.12	−	598.475i	−0.135960	−	0.0239735i
$159$	−6948.47	−	18106.4i	−0.274850	−	0.716206i
$160$	−1227.39	+	1029.90i	−0.0479450	+	0.0402306i
$161$			42629.0i			1.64457i
$162$	−20839.9	+	14045.4i	−0.794081	+	0.535186i
$163$	18871.7			0.710291			0.355146	−	0.934811i	$-0.384431\pi$
$163$	18871.7			0.710291			0.355146	+	0.934811i	$0.384431\pi$
$164$	948.873	+	1130.82i	0.0352794	+	0.0420443i
$165$	−2888.96	+	1108.66i	−0.106114	+	0.0407222i
$166$	5092.11	−	28878.8i	0.184791	−	1.04800i
$167$	8300.39	+	22805.1i	0.297622	+	0.817711i	0.994896	+	0.100906i	$0.0321741\pi$
$167$	8300.39	+	22805.1i	0.297622	+	0.817711i	−0.697273	+	0.716805i	$0.745604\pi$
$168$	40353.5	+	22373.2i	1.42976	+	0.792701i
$169$	−966.602	−	5481.87i	−0.0338434	−	0.191936i
$170$	13442.7	−	7761.15i	0.465146	−	0.268552i
$171$	11838.5	+	3848.97i	0.404858	+	0.131629i
$172$	−1419.39	+	2458.46i	−0.0479783	+	0.0831009i
$173$	50.9868	−	140.085i	0.00170359	−	0.00468058i	−0.938838	−	0.344359i	$-0.888096\pi$
$173$	50.9868	−	140.085i	0.00170359	−	0.00468058i	0.940542	+	0.339679i	$0.110318\pi$
$174$	−1925.03	−	9908.30i	−0.0635826	−	0.327266i
$175$	−31697.4	−	26597.3i	−1.03502	−	0.868483i
$176$	−5448.90	+	6493.74i	−0.175907	+	0.209638i
$177$	−23212.4	−	26707.8i	−0.740925	−	0.852496i
$178$	44098.0	+	16050.4i	1.39181	+	0.506576i
$179$	−20505.3	−	11838.7i	−0.639971	−	0.369487i	0.144633	−	0.989485i	$-0.453800\pi$
$179$	−20505.3	−	11838.7i	−0.639971	−	0.369487i	−0.784603	+	0.619998i	$0.787133\pi$
$180$	626.045	−	800.995i	0.0193224	−	0.0247221i
$181$	−17418.5	−	30169.7i	−0.531684	−	0.920903i	−0.999316	−	0.0369802i	$-0.988226\pi$
$181$	−17418.5	−	30169.7i	−0.531684	−	0.920903i	0.467632	−	0.883923i	$-0.345107\pi$
$182$	−44182.7	+	7790.61i	−1.33386	+	0.235195i
$183$	4133.88	+	6881.38i	0.123440	+	0.205482i
$184$	34422.3	−	12528.7i	1.01673	−	0.370058i
$185$	6114.38	+	1078.13i	0.178652	+	0.0315012i
$186$	36976.6	−	45653.6i	1.06881	−	1.31962i
$187$	−11952.6	+	10029.4i	−0.341805	+	0.286808i
$188$		−	720.258i		−	0.0203785i
$189$	−53843.5	−	16478.0i	−1.50733	−	0.461297i
$190$	5562.77			0.154093
$191$	34676.2	+	41325.5i	0.950527	+	1.13279i	0.991033	+	0.133615i	$0.0426585\pi$
$191$	34676.2	+	41325.5i	0.950527	+	1.13279i	−0.0405061	+	0.999179i	$0.512897\pi$
$192$	6166.34	−	38909.4i	0.167273	−	1.05548i
$193$	1141.28	−	6472.49i	0.0306391	−	0.173763i	−0.965648	−	0.259853i	$-0.916326\pi$
$193$	1141.28	−	6472.49i	0.0306391	−	0.173763i	0.996287	+	0.0860897i	$0.0274372\pi$
$194$	−13807.8	−	37936.7i	−0.366878	−	1.00799i
$195$	223.881	+	12894.6i	0.00588773	+	0.339109i
$196$	822.246	+	4663.19i	0.0214037	+	0.121387i
$197$	−26272.1	+	15168.2i	−0.676958	+	0.390842i	−0.798708	−	0.601719i	$-0.794483\pi$
$197$	−26272.1	+	15168.2i	−0.676958	+	0.390842i	0.121750	+	0.992561i	$0.461149\pi$
$198$	5301.52	−	9966.26i	0.135229	−	0.254215i
$199$	−10896.8	+	18873.8i	−0.275164	+	0.476598i	−0.970176	−	0.242400i	$-0.922065\pi$
$199$	−10896.8	+	18873.8i	−0.275164	+	0.476598i	0.695013	+	0.718998i	$0.255399\pi$
$200$	−12161.0	+	33412.2i	−0.304026	+	0.835304i
$201$	−2796.37	−	963.159i	−0.0692155	−	0.0238400i
$202$	34991.9	+	29361.7i	0.857561	+	0.719579i
$203$	14537.0	−	17324.5i	0.352762	−	0.420406i
$204$	1669.37	−	4846.73i	0.0401136	−	0.116463i
$205$	−9869.39	−	3592.16i	−0.234846	−	0.0854768i
$206$	−9949.57	−	5744.39i	−0.234461	−	0.135366i
$207$	−37915.3	+	23682.3i	−0.884859	+	0.552693i
$208$	17664.9	+	30596.5i	0.408304	+	0.707204i
$209$	−5506.74	+	970.986i	−0.126067	+	0.0222290i
$210$	−25158.5	+	436.811i	−0.570488	+	0.00990500i
$211$	−7612.23	+	2770.63i	−0.170981	+	0.0622319i	−0.426092	−	0.904680i	$-0.640110\pi$
$211$	−7612.23	+	2770.63i	−0.170981	+	0.0622319i	0.255111	+	0.966912i	$0.417888\pi$
$212$	−2818.58	−	496.991i	−0.0627131	−	0.0110580i
$213$	−80401.1	−	12741.9i	−1.77216	−	0.280851i
$214$	−11505.5	+	9654.29i	−0.251234	+	0.210811i
$215$		−	20197.4i		−	0.436937i
$216$	2518.91	+	48320.7i	0.0539889	+	1.03568i
$217$	131634.			2.79542
$218$	43435.8	+	51764.8i	0.913977	+	1.08923i
$219$	70578.3	+	57164.0i	1.47158	+	1.19189i
$220$	−79.2973	+	449.717i	−0.00163837	+	0.00929168i
$221$	22241.2	+	61107.3i	0.455380	+	1.25115i
$222$	−19415.8	+	11663.7i	−0.393958	+	0.236664i
$223$	−2477.02	−	14047.9i	−0.0498103	−	0.282488i	0.949721	−	0.313097i	$-0.101367\pi$
$223$	−2477.02	−	14047.9i	−0.0498103	−	0.282488i	−0.999531	+	0.0306087i	$0.990255\pi$
$224$	11341.9	−	6548.26i	0.226043	−	0.130506i
$225$	6046.95	−	42968.5i	0.119446	−	0.848761i
$226$	−11283.1	+	19542.9i	−0.220908	+	0.382624i
$227$	26937.0	−	74008.8i	0.522754	−	1.43626i	−0.344688	−	0.938717i	$-0.612015\pi$
$227$	26937.0	−	74008.8i	0.522754	−	1.43626i	0.867442	−	0.497538i	$-0.165763\pi$
$228$	1386.57	−	1205.10i	0.0266731	−	0.0231822i
$229$	−6254.15	−	5247.86i	−0.119261	−	0.100072i	0.581207	−	0.813756i	$-0.302581\pi$
$229$	−6254.15	−	5247.86i	−0.119261	−	0.100072i	−0.700468	+	0.713684i	$0.747025\pi$
$230$	−12840.7	+	15302.9i	−0.242735	+	0.289280i
$231$	24828.8	−	4823.85i	0.465299	−	0.0904002i
$232$	−18261.7	−	6646.71i	−0.339285	−	0.123490i
$233$	20284.9	+	11711.5i	0.373647	+	0.215725i	0.675051	−	0.737771i	$-0.264122\pi$
$233$	20284.9	+	11711.5i	0.373647	+	0.215725i	−0.301403	+	0.953497i	$0.597455\pi$
$234$	−31474.7	−	34969.2i	−0.574817	−	0.638637i
$235$	2562.25	+	4437.95i	0.0463966	+	0.0803612i
$236$	−5142.67	+	906.792i	−0.0923347	+	0.0162811i
$237$	3926.63	−	7082.28i	0.0699074	−	0.126089i
$238$	−119225.	+	43394.5i	−2.10482	+	0.766092i
$239$	−882.846	−	155.670i	−0.0154557	−	0.00272526i	0.165915	−	0.986140i	$-0.446942\pi$
$239$	−882.846	−	155.670i	−0.0154557	−	0.00272526i	−0.181371	+	0.983415i	$0.558053\pi$
$240$	7099.28	+	18499.4i	0.123251	+	0.321170i
$241$	14500.9	−	12167.7i	0.249666	−	0.209495i	−0.509362	−	0.860552i	$-0.670119\pi$
$241$	14500.9	−	12167.7i	0.249666	−	0.209495i	0.759029	+	0.651057i	$0.225674\pi$
$242$		−	51009.9i		−	0.871011i
$243$	−15256.6	−	57044.0i	−0.258371	−	0.966046i
$244$	1184.67			0.0198984
$245$	−21655.2	−	25807.7i	−0.360770	−	0.429949i
$246$	35771.5	−	13727.6i	0.591107	−	0.226842i
$247$	−4046.81	+	22950.6i	−0.0663313	+	0.376184i
$248$	−38687.2	−	106292.i	−0.629019	−	1.72822i
$249$	60259.4	+	33409.6i	0.971910	+	0.538857i
$250$	−7295.46	−	41374.6i	−0.116727	−	0.661994i
$251$	−6348.71	+	3665.43i	−0.100772	+	0.0581805i	−0.549539	−	0.835468i	$-0.685197\pi$
$251$	−6348.71	+	3665.43i	−0.100772	+	0.0581805i	0.448767	+	0.893649i	$0.351863\pi$
$252$	−6176.37	+	5559.16i	−0.0972595	+	0.0875402i
$253$	10040.2	−	17390.1i	0.156856	−	0.271682i
$254$	−14175.9	+	38948.0i	−0.219727	+	0.603695i
$255$	6955.82	+	35802.3i	0.106971	+	0.550593i
$256$	−12413.8	−	10416.4i	−0.189420	−	0.158942i
$257$	−31932.1	+	38055.2i	−0.483460	+	0.576166i	−0.951542	−	0.307520i	$-0.900501\pi$
$257$	−31932.1	+	38055.2i	−0.483460	+	0.576166i	0.468081	+	0.883685i	$0.344945\pi$
$258$	48334.5	+	55612.9i	0.726135	+	0.835480i
$259$	−47688.5	−	17357.2i	−0.710909	−	0.258750i
$260$	1648.23	+	951.608i	0.0243821	+	0.0140770i
$261$	23484.8	+	3305.01i	0.344751	+	0.0485168i
$262$	−51387.5	−	89005.7i	−0.748608	−	1.29663i
$263$	32082.4	−	5657.00i	0.463827	−	0.0817852i	0.0631488	−	0.998004i	$-0.479886\pi$
$263$	32082.4	−	5657.00i	0.463827	−	0.0817852i	0.400678	+	0.916219i	$0.368775\pi$
$264$	−11192.4	−	18631.2i	−0.160589	−	0.267321i
$265$	19135.0	−	6964.56i	0.272481	−	0.0991749i
$266$	−44778.5	−	7895.66i	−0.632858	−	0.111590i
$267$	−69399.3	+	85684.8i	−0.973493	+	1.20194i
$268$	−334.354	+	280.556i	−0.00465518	+	0.00390616i
$269$		−	116785.i		−	1.61392i	−0.590604	−	0.806962i	$-0.701110\pi$
$269$		−	116785.i		−	1.61392i	0.590604	−	0.806962i	$-0.298890\pi$
$270$	−14365.2	−	22133.9i	−0.197054	−	0.303621i
$271$	−41429.0			−0.564113			−0.282056	−	0.959398i	$-0.591017\pi$
$271$	−41429.0			−0.564113			−0.282056	+	0.959398i	$0.591017\pi$
$272$	64223.0	+	76537.9i	0.868065	+	1.03452i
$273$	16500.2	−	104115.i	0.221392	−	1.39698i
$274$	−2617.36	+	14843.8i	−0.0348628	+	0.197717i
$275$	6666.35	+	18315.7i	0.0881501	+	0.242190i
$276$	114.525	+	6596.17i	0.00150343	+	0.0865912i
$277$	−13751.0	−	77985.8i	−0.179215	−	1.01638i	−0.933165	−	0.359448i	$-0.882965\pi$
$277$	−13751.0	−	77985.8i	−0.179215	−	1.01638i	0.753950	−	0.656932i	$-0.228146\pi$
$278$	85654.4	−	49452.6i	1.10831	−	0.639882i
$279$	73128.5	+	117078.i	0.939460	+	1.50407i
$280$	−24223.2	+	41955.7i	−0.308969	+	0.535150i
$281$	−2734.15	+	7512.03i	−0.0346266	+	0.0951359i	−0.955801	−	0.294014i	$-0.905009\pi$
$281$	−2734.15	+	7512.03i	−0.0346266	+	0.0951359i	0.921175	+	0.389150i	$0.127231\pi$
$282$	−17675.5	−	6088.01i	−0.222267	−	0.0765557i
$283$	−21561.4	−	18092.2i	−0.269218	−	0.225901i	0.498177	−	0.867075i	$-0.334003\pi$
$283$	−21561.4	−	18092.2i	−0.269218	−	0.225901i	−0.767395	+	0.641174i	$0.778447\pi$
$284$	−7721.99	+	9202.71i	−0.0957398	+	0.114098i
$285$	−4256.48	+	12358.0i	−0.0524036	+	0.152145i
$286$	19858.8	+	7228.02i	0.242785	+	0.0883664i
$287$	74346.8	+	42924.1i	0.902606	+	0.521120i
$288$	12125.1	+	6449.93i	0.146185	+	0.0777625i
$289$	50191.1	+	86933.5i	0.600940	+	1.04086i
$290$	10436.9	−	1840.31i	0.124102	−	0.0218825i
$291$	94843.7	−	1646.71i	1.12001	−	0.0194460i
$292$	12595.1	−	4584.23i	0.147719	−	0.0537651i
$293$	−120953.	−	21327.2i	−1.40890	−	0.248427i	−0.583105	−	0.812397i	$-0.698162\pi$
$293$	−120953.	−	21327.2i	−1.40890	−	0.248427i	−0.825795	+	0.563970i	$0.809273\pi$
$294$	121387.	+	19237.4i	1.40436	+	0.222563i
$295$	28461.3	−	23881.9i	0.327048	−	0.274426i
$296$			43609.0i			0.497729i
$297$	18084.0	+	19403.5i	0.205013	+	0.219972i
$298$	−50719.5			−0.571140
$299$	−53794.6	−	64110.0i	−0.601723	−	0.717106i
$300$	−4976.13	−	4030.36i	−0.0552904	−	0.0447818i
$301$	−28667.7	+	162582.i	−0.316417	+	1.79449i
$302$	31283.5	+	85950.7i	0.343006	+	0.942401i
$303$	−92003.4	+	55269.6i	−1.00212	+	0.602006i
$304$	6217.68	+	35262.2i	0.0672792	+	0.381560i
$305$	−7299.50	+	4214.37i	−0.0784681	+	0.0453036i
$306$	−104831.	−	81934.5i	−1.11956	−	0.875032i
$307$	−4270.01	+	7395.88i	−0.0453056	+	0.0784717i	−0.887789	−	0.460251i	$-0.847760\pi$
$307$	−4270.01	+	7395.88i	−0.0453056	+	0.0784717i	0.842483	+	0.538722i	$0.181093\pi$
$308$	1276.64	−	3507.53i	0.0134575	−	0.0369743i
$309$	20374.6	−	17708.0i	0.213389	−	0.185461i
$310$	47253.8	+	39650.6i	0.491714	+	0.412597i
$311$	4862.72	−	5795.16i	0.0502757	−	0.0599163i	−0.740321	−	0.672254i	$-0.765326\pi$
$311$	4862.72	−	5795.16i	0.0502757	−	0.0599163i	0.790596	+	0.612338i	$0.209771\pi$
$312$	−88921.0	+	17275.9i	−0.913472	+	0.177473i
$313$	−54402.3	−	19800.8i	−0.555302	−	0.202113i	0.0490988	−	0.998794i	$-0.484365\pi$
$313$	−54402.3	−	19800.8i	−0.555302	−	0.202113i	−0.604400	+	0.796681i	$0.706587\pi$
$314$	−21393.3	−	12351.4i	−0.216980	−	0.125273i
$315$	18280.2	−	56225.2i	0.184230	−	0.566644i
$316$	−597.529	−	1034.95i	−0.00598391	−	0.0103644i
$317$	39201.7	−	6912.31i	0.390109	−	0.0687867i	0.0248464	−	0.999691i	$-0.492090\pi$
$317$	39201.7	−	6912.31i	0.390109	−	0.0687867i	0.365263	+	0.930905i	$0.380979\pi$
$318$	−36020.6	+	64968.7i	−0.356202	+	0.642465i
$319$	−10010.6	+	3643.55i	−0.0983734	+	0.0358050i
$320$	40735.2	+	7182.71i	0.397804	+	0.0701436i
$321$	−12643.8	−	32947.3i	−0.122706	−	0.319750i
$322$	125084.	−	104958.i	1.20640	−	1.01229i
$323$			65905.9i			0.631712i
$324$	−8375.70	−	2405.06i	−0.0797868	−	0.0229105i
$325$	81233.7			0.769077
$326$	−46464.5	−	55374.2i	−0.437206	−	0.521042i
$327$	−148234.	+	56886.0i	−1.38629	+	0.531998i
$328$	12810.0	−	72649.3i	0.119070	−	0.675280i
$329$	−14326.2	−	39360.8i	−0.132354	−	0.363641i
$330$	10366.1	+	5747.26i	0.0951888	+	0.0527756i
$331$	−6.03385	−	34.2197i	−5.50730e−5	−	0.000312334i	0.984780	−	0.173804i	$-0.0556060\pi$
$331$	−6.03385	−	34.2197i	−5.50730e−5	−	0.000312334i	−0.984835	+	0.173492i	$0.944495\pi$
$332$	8805.86	−	5084.07i	0.0798906	−	0.0461249i
$333$	−11055.2	−	52058.0i	−0.0996960	−	0.469461i
$334$	46479.2	−	80504.4i	0.416645	−	0.721650i
$335$	1062.11	−	2918.11i	0.00946407	−	0.0260023i
$336$	−30889.4	−	158991.i	−0.273609	−	1.40829i
$337$	63759.8	+	53500.8i	0.561419	+	0.471086i	0.878786	−	0.477216i	$-0.158354\pi$
$337$	63759.8	+	53500.8i	0.561419	+	0.471086i	−0.317367	+	0.948303i	$0.602799\pi$
$338$	−13705.2	+	16333.3i	−0.119965	+	0.142968i
$339$	−34782.0	−	40019.7i	−0.302660	−	0.348236i
$340$	5057.73	+	1840.86i	0.0437520	+	0.0159244i
$341$	−53698.8	−	31003.0i	−0.461802	−	0.266621i
$342$	−17853.9	−	44213.5i	−0.152644	−	0.378010i
$343$	44959.2	+	77871.7i	0.382147	+	0.661898i
$344$	139708.	−	24634.3i	1.18061	−	0.208173i
$345$	−24170.9	−	40235.6i	−0.203074	−	0.338043i
$346$	−536.579	+	195.299i	−0.00448210	+	0.00163135i
$347$	47589.2	+	8391.25i	0.395229	+	0.0696896i	0.367731	−	0.929932i	$-0.380135\pi$
$347$	47589.2	+	8391.25i	0.395229	+	0.0696896i	0.0274984	+	0.999622i	$0.491246\pi$
$348$	2202.83	−	2719.75i	0.0181895	−	0.0224579i
$349$	−92575.4	+	77680.0i	−0.760054	+	0.637761i	−0.938141	−	0.346253i	$-0.887454\pi$
$349$	−92575.4	+	77680.0i	−0.760054	+	0.637761i	0.178087	+	0.984015i	$0.443009\pi$
$350$			158494.i			1.29383i
$351$	101769.	−	43165.2i	0.826044	−	0.350364i
$352$	−6169.11			−0.0497894
$353$	−76594.7	−	91282.1i	−0.614681	−	0.732548i	0.365465	−	0.930825i	$-0.380910\pi$
$353$	−76594.7	−	91282.1i	−0.614681	−	0.732548i	−0.980146	+	0.198277i	$0.936465\pi$
$354$	−21215.5	+	133869.i	−0.169296	+	1.06825i
$355$	14842.1	−	84173.8i	0.117771	−	0.667913i
$356$	5565.43	+	15290.9i	0.0439136	+	0.120652i
$357$	−5175.19	−	298070.i	−0.0406060	−	2.33874i
$358$	15748.8	+	89315.9i	0.122880	+	0.696888i
$359$	4422.73	−	2553.47i	0.0343164	−	0.0198126i	−0.482744	−	0.875762i	$-0.660360\pi$
$359$	4422.73	−	2553.47i	0.0343164	−	0.0198126i	0.517060	+	0.855949i	$0.327026\pi$
$360$	−50773.6	+	1763.63i	−0.391771	+	0.0136082i
$361$	53351.0	−	92406.7i	0.409382	−	0.709070i
$362$	−45638.8	+	125392.i	−0.348271	+	0.956866i
$363$	113321.	+	39031.4i	0.859999	+	0.296211i
$364$	−11917.1	−	9999.59i	−0.0899427	−	0.0754709i
$365$	−61297.9	+	73052.1i	−0.460108	+	0.548336i
$366$	10013.5	−	29072.6i	0.0747522	−	0.217031i
$367$	119191.	+	43382.0i	0.884936	+	0.322090i	0.744200	−	0.667957i	$-0.232831\pi$
$367$	119191.	+	43382.0i	0.884936	+	0.322090i	0.140736	+	0.990047i	$0.455053\pi$
$368$	−111357.	−	64292.0i	−0.822285	−	0.474746i
$369$	3125.20	+	89972.2i	0.0229522	+	0.660778i
$370$	−11890.8	−	20595.6i	−0.0868579	−	0.150442i
$371$	−163916.	+	28902.8i	−1.19089	+	0.209987i
$372$	20368.3	−	353.640i	0.147186	−	0.00255550i
$373$	117915.	−	42917.4i	0.847520	−	0.308472i	0.118491	−	0.992955i	$-0.462194\pi$
$373$	117915.	−	42917.4i	0.847520	−	0.308472i	0.729029	+	0.684483i	$0.239972\pi$
$374$	58857.4	+	10378.1i	0.420783	+	0.0741953i
$375$	97498.2	+	15451.5i	0.693320	+	0.109877i
$376$	−27572.8	+	23136.3i	−0.195032	+	0.163651i
$377$			44399.0i			0.312385i
$378$	84218.9	+	198561.i	0.589421	+	1.38966i
$379$	−239132.			−1.66479			−0.832393	−	0.554185i	$-0.813030\pi$
$379$	−239132.			−1.66479			−0.832393	+	0.554185i	$0.813030\pi$
$380$	1239.86	+	1477.61i	0.00858629	+	0.0102327i
$381$	−75678.0	−	61294.5i	−0.521339	−	0.422252i
$382$	35882.0	−	203497.i	0.245895	−	1.39454i
$383$	−7249.60	−	19918.1i	−0.0494215	−	0.135785i	0.912526	−	0.409019i	$-0.134129\pi$
$383$	−7249.60	−	19918.1i	−0.0494215	−	0.135785i	−0.961948	+	0.273234i	$0.911907\pi$
$384$	−108422.	+	65133.0i	−0.735285	+	0.441711i
$385$	4611.57	+	26153.5i	0.0311120	+	0.176445i
$386$	−21801.8	+	12587.3i	−0.146325	+	0.0844807i
$387$	−160531.	+	64824.2i	−1.07186	+	0.432828i
$388$	6999.34	−	12123.2i	0.0464937	−	0.0805294i
$389$	−88135.4	+	242150.i	−0.582440	+	1.60024i	0.201557	+	0.979477i	$0.435400\pi$
$389$	−88135.4	+	242150.i	−0.582440	+	1.60024i	−0.783997	+	0.620765i	$0.786822\pi$
$390$	37284.8	−	32405.1i	0.245133	−	0.213051i
$391$	−181304.	−	152132.i	−1.18592	−	0.995102i
$392$	152103.	−	181269.i	0.989842	−	1.17965i
$393$	237051.	−	46055.3i	1.53482	−	0.298191i
$394$	109192.	+	39742.7i	0.703395	+	0.256015i
$395$	7363.49	+	4251.31i	0.0471943	+	0.0272476i
$396$	3828.91	−	813.118i	0.0244166	−	0.00518517i
$397$	−12572.3	−	21775.9i	−0.0797691	−	0.138164i	0.823381	−	0.567489i	$-0.192085\pi$
$397$	−12572.3	−	21775.9i	−0.0797691	−	0.138164i	−0.903150	+	0.429325i	$0.858752\pi$
$398$	82209.4	−	14495.7i	0.518985	−	0.0915111i
$399$	51803.9	−	93436.3i	0.325400	−	0.586908i
$400$	117284.	−	42687.8i	0.733023	−	0.266799i
$401$	200511.	+	35355.5i	1.24695	+	0.219871i	0.757892	−	0.652380i	$-0.226229\pi$
$401$	200511.	+	35355.5i	1.24695	+	0.219871i	0.489058	+	0.872251i	$0.337341\pi$
$402$	4058.87	+	10576.7i	0.0251162	+	0.0654480i
$403$	−197965.	+	166112.i	−1.21893	+	1.02280i
$404$			15839.0i			0.0970431i
$405$	60163.6	−	14976.8i	0.366795	−	0.0913079i
$406$	−86626.1			−0.525529
$407$	15366.0	+	18312.5i	0.0927626	+	0.110550i
$408$	−239166.	+	91781.7i	−1.43674	+	0.551361i
$409$	−23593.4	+	133805.i	−0.141040	+	0.799880i	0.829421	+	0.558624i	$0.188671\pi$
$409$	−23593.4	+	133805.i	−0.141040	+	0.799880i	−0.970461	+	0.241256i	$0.922441\pi$
$410$	13759.4	+	37803.5i	0.0818522	+	0.224887i
$411$	−30973.5	−	17172.7i	−0.183361	−	0.101661i
$412$	−691.764	−	3923.19i	−0.00407533	−	0.0231124i
$413$	−263002.	+	151844.i	−1.54191	+	0.890221i
$414$	162842.	+	52943.9i	0.950092	+	0.308898i
$415$	−36172.2	+	62652.1i	−0.210029	+	0.363781i
$416$	−8793.74	+	24160.6i	−0.0508144	+	0.139611i
$417$	44321.2	+	228126.i	0.254882	+	1.31190i
$418$	16407.4	+	13767.4i	0.0939045	+	0.0787952i
$419$	135633.	−	161642.i	0.772571	−	0.920715i	−0.226001	−	0.974127i	$-0.572565\pi$
$419$	135633.	−	161642.i	0.772571	−	0.920715i	0.998573	+	0.0534123i	$0.0170098\pi$
$420$	−5723.49	−	6585.35i	−0.0324461	−	0.0373319i
$421$	67045.7	+	24402.6i	0.378274	+	0.137681i	0.524158	−	0.851621i	$-0.324380\pi$
$421$	67045.7	+	24402.6i	0.378274	+	0.137681i	−0.145883	+	0.989302i	$0.546602\pi$
$422$	26871.9	+	15514.5i	0.150895	+	0.0871191i
$423$	27049.7	−	34608.8i	0.151176	−	0.193422i
$424$	71513.4	+	123865.i	0.397792	+	0.688995i
$425$	226240.	−	39892.3i	1.25254	−	0.220857i
$426$	160569.	+	267288.i	0.884797	+	1.47286i
$427$	64740.4	−	23563.6i	0.355074	−	0.129237i
$428$	−5128.83	−	904.350i	−0.0279982	−	0.00493684i
$429$	−31252.8	+	38586.7i	−0.169815	+	0.209664i
$430$	−59264.1	+	49728.4i	−0.320520	+	0.268948i
$431$		−	311727.i		−	1.67811i	−0.544046	−	0.839055i	$-0.683108\pi$
$431$		−	311727.i		−	1.67811i	0.544046	−	0.839055i	$-0.316892\pi$
$432$	124250.	−	115800.i	0.665776	−	0.620500i
$433$	−84569.4			−0.451063			−0.225532	−	0.974236i	$-0.572412\pi$
$433$	−84569.4			−0.451063			−0.225532	+	0.974236i	$0.572412\pi$
$434$	−324098.	−	386245.i	−1.72067	−	2.05061i
$435$	−3897.70	+	24594.4i	−0.0205982	+	0.129974i
$436$	−4068.78	+	23075.2i	−0.0214038	+	0.121387i
$437$	−29009.5	−	79703.0i	−0.151907	−	0.417361i
$438$	−6039.29	−	347839.i	−0.0314802	−	1.81313i
$439$	41124.9	+	233231.i	0.213391	+	1.21020i	0.883677	+	0.468098i	$0.155060\pi$
$439$	41124.9	+	233231.i	0.213391	+	1.21020i	−0.670286	+	0.742103i	$0.733828\pi$
$440$	19763.2	−	11410.3i	0.102083	−	0.0589375i
$441$	−135619.	+	254949.i	−0.697339	+	1.31092i
$442$	124543.	−	215715.i	0.637492	−	1.10417i
$443$	114294.	−	314019.i	0.582391	−	1.60010i	−0.201693	−	0.979449i	$-0.564644\pi$
$443$	114294.	−	314019.i	0.582391	−	1.60010i	0.784083	−	0.620656i	$-0.213134\pi$
$444$	−7425.67	−	2557.63i	−0.0376678	−	0.0129740i
$445$	−88687.9	−	74418.0i	−0.447862	−	0.375801i
$446$	−35121.1	+	41855.7i	−0.176563	+	0.210419i
$447$	38809.2	−	112676.i	0.194231	−	0.563919i
$448$	−317710.	−	115637.i	−1.58298	−	0.576157i
$449$	246580.	+	142363.i	1.22311	+	0.706162i	0.965579	−	0.260108i	$-0.0837582\pi$
$449$	246580.	+	142363.i	1.22311	+	0.706162i	0.257529	+	0.966270i	$0.417092\pi$
$450$	−140968.	+	88050.5i	−0.696140	+	0.434817i
$451$	−20219.4	−	35021.0i	−0.0994065	−	0.172177i
$452$	−7705.90	+	1358.76i	−0.0377178	+	0.00665067i
$453$	−214881.	+	3730.84i	−1.04713	+	0.0181807i
$454$	−283482.	+	103179.i	−1.37535	+	0.500587i
$455$	109001.	+	19219.8i	0.526511	+	0.0928380i
$456$	−90673.6	−	14369.9i	−0.436065	−	0.0691073i
$457$	59003.0	−	49509.4i	0.282515	−	0.237058i	−0.490507	−	0.871437i	$-0.663189\pi$
$457$	59003.0	−	49509.4i	0.282515	−	0.237058i	0.773022	+	0.634379i	$0.218744\pi$
$458$			31272.1i			0.149082i
$459$	262236.	−	170194.i	1.24471	−	0.807829i
$460$	−6926.83			−0.0327355
$461$	−75525.4	−	90007.7i	−0.355378	−	0.423524i	0.558504	−	0.829502i	$-0.311375\pi$
$461$	−75525.4	−	90007.7i	−0.355378	−	0.423524i	−0.913883	+	0.405978i	$0.866931\pi$
$462$	−75285.9	−	60976.9i	−0.352720	−	0.285681i
$463$	51048.9	−	289513.i	0.238136	−	1.35053i	−0.597773	−	0.801666i	$-0.703947\pi$
$463$	51048.9	−	289513.i	0.238136	−	1.35053i	0.835908	−	0.548869i	$-0.184941\pi$
$464$	23331.4	+	64102.4i	0.108369	+	0.297741i
$465$	−124243.	+	74637.2i	−0.574601	+	0.345183i
$466$	−15579.6	−	88356.1i	−0.0717436	−	0.406878i
$467$	−123548.	+	71330.2i	−0.566501	+	0.327069i	−0.755750	−	0.654860i	$-0.772728\pi$
$467$	−123548.	+	71330.2i	−0.566501	+	0.327069i	0.189250	+	0.981929i	$0.439394\pi$
$468$	2273.43	−	16154.6i	0.0103798	−	0.0737570i
$469$	−12691.5	+	21982.3i	−0.0576989	+	0.0999374i
$470$	6713.44	−	18445.0i	0.0303913	−	0.0834995i
$471$	43809.0	−	38075.4i	0.197479	−	0.171634i
$472$	199908.	+	167743.i	0.897318	+	0.752939i
$473$	49986.9	−	59572.1i	0.223426	−	0.266269i
$474$	−30449.0	+	5915.75i	−0.135524	+	0.0263301i
$475$	77364.1	+	28158.2i	0.342888	+	0.124801i
$476$	−38100.2	−	21997.2i	−0.168156	−	0.0970852i
$477$	−116769.	−	129734.i	−0.513207	−	0.570186i
$478$	1716.90	+	2973.76i	0.00751432	+	0.0130152i
$479$	316558.	−	55817.7i	1.37969	−	0.243277i	0.565920	−	0.824460i	$-0.308521\pi$
$479$	316558.	−	55817.7i	1.37969	−	0.243277i	0.813773	+	0.581183i	$0.197410\pi$
$480$	−6992.22	+	12611.5i	−0.0303482	+	0.0547376i
$481$	93622.4	−	34075.8i	0.404659	−	0.147284i
$482$	−71405.8	−	12590.8i	−0.307354	−	0.0541948i
$483$	137459.	+	358191.i	0.589221	+	1.53540i
$484$	13549.5	−	11369.4i	0.0578405	−	0.0485339i
$485$			99598.1i			0.423416i
$486$	−129817.	+	185216.i	−0.549618	+	0.784162i
$487$	−257478.			−1.08563			−0.542816	−	0.839851i	$-0.682642\pi$
$487$	−257478.			−1.08563			−0.542816	+	0.839851i	$0.682642\pi$
$488$	−38054.4	−	45351.5i	−0.159796	−	0.190437i
$489$	158570.	−	60852.5i	0.663138	−	0.254484i
$490$	−22408.2	+	127083.i	−0.0933287	+	0.529293i
$491$	−19953.8	−	54822.6i	−0.0827681	−	0.227403i	0.891404	−	0.453209i	$-0.149721\pi$
$491$	−19953.8	−	54822.6i	−0.0827681	−	0.227403i	−0.974172	+	0.225805i	$0.927499\pi$
$492$	11619.3	+	6442.10i	0.0480010	+	0.0266132i
$493$	21803.4	+	123653.i	0.0897080	+	0.508759i
$494$	77306.3	−	44632.8i	0.316783	−	0.182894i
$495$	−20699.7	+	18631.1i	−0.0844798	+	0.0760376i
$496$	−198527.	+	343858.i	−0.806967	+	1.39771i
$497$	−238948.	+	656505.i	−0.967367	+	2.65782i
$498$	−50334.0	−	259074.i	−0.202957	−	1.04464i
$499$	233652.	+	196057.i	0.938357	+	0.787375i	0.977299	−	0.211867i	$-0.0679542\pi$
$499$	233652.	+	196057.i	0.938357	+	0.787375i	−0.0389417	+	0.999241i	$0.512399\pi$
$500$	9364.05	−	11159.6i	0.0374562	−	0.0446386i
$501$	143280.	+	164856.i	0.570835	+	0.656794i
$502$	26386.6	+	9603.92i	0.104707	+	0.0381102i
$503$	−50281.2	−	29029.8i	−0.198733	−	0.114738i	0.397332	−	0.917675i	$-0.369936\pi$
$503$	−50281.2	−	29029.8i	−0.198733	−	0.114738i	−0.596064	+	0.802937i	$0.703270\pi$
$504$	411214.	+	57870.1i	1.61885	+	0.227821i
$505$	−56345.7	−	97593.7i	−0.220942	−	0.382683i
$506$	−75747.0	+	13356.2i	−0.295845	+	0.0521655i
$507$	−25798.4	−	42944.7i	−0.100364	−	0.167068i
$508$	−13505.1	+	4915.47i	−0.0523325	+	0.0190475i
$509$	−285551.	−	50350.4i	−1.10217	−	0.194342i	−0.407170	−	0.913352i	$-0.633484\pi$
$509$	−285551.	−	50350.4i	−1.10217	−	0.194342i	−0.694999	+	0.719010i	$0.744595\pi$
$510$	87926.6	−	108560.i	0.338049	−	0.417377i
$511$	597117.	−	501041.i	2.28674	−	1.91881i
$512$			286928.i			1.09454i
$513$	111884.	−	5832.39i	0.425141	−	0.0221622i
$514$	190284.			0.720237
$515$	18218.7	+	21712.3i	0.0686917	+	0.0818636i
$516$	−3999.09	+	25234.1i	−0.0150197	+	0.0947738i
$517$	−3426.22	+	19431.1i	−0.0128184	+	0.0726968i
$518$	66484.7	+	182665.i	0.247778	+	0.680763i
$519$	−23.2911	−	1341.48i	−8.64681e−5	−	0.00498021i
$520$	−16515.7	−	93665.2i	−0.0610788	−	0.346395i
$521$	410300.	−	236887.i	1.51156	−	0.872700i	0.511652	−	0.859193i	$-0.329034\pi$
$521$	410300.	−	236887.i	1.51156	−	0.872700i	0.999909	−	0.0135072i	$-0.00429962\pi$
$522$	−48124.7	−	77047.4i	−0.176615	−	0.282759i
$523$	82744.6	−	143318.i	0.302508	−	0.523958i	−0.674196	−	0.738553i	$-0.735510\pi$
$523$	82744.6	−	143318.i	0.302508	−	0.523958i	0.976703	+	0.214594i	$0.0688429\pi$
$524$	12188.6	−	33487.8i	0.0443905	−	0.121962i
$525$	−352102.	−	121275.i	−1.27747	−	0.440000i
$526$	−95589.9	−	80209.4i	−0.345494	−	0.289904i
$527$	−469767.	+	559847.i	−1.69146	+	2.01580i
$528$	−24845.2	+	72134.0i	−0.0891199	+	0.258745i
$529$	23257.9	+	8465.20i	0.0831113	+	0.0302500i
$530$	−67548.3	−	38999.1i	−0.240471	−	0.138836i
$531$	−281163.	−	149564.i	−0.997171	−	0.530442i
$532$	−7883.19	−	13654.1i	−0.0278534	−	0.0482436i
$533$	−165977.	+	29266.3i	−0.584244	+	0.103018i
$534$	422289.	−	7331.93i	1.48091	−	0.0257120i
$535$	34819.0	−	12673.1i	0.121649	−	0.0442766i
$536$	21480.4	+	3787.58i	0.0747676	+	0.0131835i
$537$	−210471.	−	33355.3i	−0.729866	−	0.115669i
$538$	−342676.	+	287539.i	−1.18391	+	0.993419i
$539$		−	129715.i		−	0.446489i
$540$	2677.52	−	8749.08i	0.00918217	−	0.0300037i
$541$	136578.			0.466646			0.233323	−	0.972399i	$-0.425040\pi$
$541$	136578.			0.466646			0.233323	+	0.972399i	$0.425040\pi$
$542$	102003.	+	121563.i	0.347229	+	0.413811i
$543$	−243642.	−	197335.i	−0.826330	−	0.669275i
$544$	−12626.2	+	71607.0i	−0.0426655	+	0.241968i
$545$	−57017.7	−	156655.i	−0.191963	−	0.527413i
$546$	−346125.	+	207929.i	−1.16104	+	0.697478i
$547$	−59462.3	−	337228.i	−0.198732	−	1.12706i	−0.907003	−	0.421124i	$-0.861636\pi$
$547$	−59462.3	−	337228.i	−0.198732	−	1.12706i	0.708271	−	0.705940i	$-0.249475\pi$
$548$	−4526.24	+	2613.23i	−0.0150722	+	0.00870194i
$549$	56924.2	+	44491.1i	0.188865	+	0.147614i
$550$	37329.2	−	64656.1i	0.123402	−	0.213739i
$551$	−15390.1	+	42284.0i	−0.0506919	+	0.139275i
$552$	248835.	−	216268.i	0.816645	−	0.709765i
$553$	−53239.5	−	44673.2i	−0.174094	−	0.146082i
$554$	−194973.	+	232359.i	−0.635264	+	0.757078i
$555$	54852.7	−	10657.0i	0.178079	−	0.0345978i
$556$	32226.9	+	11729.6i	0.104248	+	0.0379433i
$557$	280441.	+	161913.i	0.903923	+	0.521880i	0.878471	−	0.477796i	$-0.158564\pi$
$557$	280441.	+	161913.i	0.903923	+	0.521880i	0.0254519	+	0.999676i	$0.491898\pi$
$558$	163485.	−	502838.i	0.525061	−	1.61495i
$559$	−162054.	−	280685.i	−0.518603	−	0.898246i
$560$	167473.	−	29530.1i	0.534035	−	0.0941647i
$561$	−68091.7	+	122814.i	−0.216356	+	0.390231i
$562$	28773.9	−	10472.9i	0.0911017	−	0.0331583i
$563$	−103951.	−	18329.4i	−0.327954	−	0.0578271i	0.00724719	−	0.999974i	$-0.497693\pi$
$563$	−103951.	−	18329.4i	−0.327954	−	0.0578271i	−0.335201	+	0.942147i	$0.608804\pi$
$564$	−2322.49	−	6051.98i	−0.00730124	−	0.0190256i
$565$	42647.1	−	35785.2i	0.133596	−	0.112100i
$566$			107812.i			0.336537i
$567$	−505555.	+	35163.5i	−1.57254	+	0.109377i
$568$	600345.			1.86082
$569$	−12779.7	−	15230.2i	−0.0394725	−	0.0470415i	0.745947	−	0.666005i	$-0.231997\pi$
$569$	−12779.7	−	15230.2i	−0.0394725	−	0.0470415i	−0.785420	+	0.618964i	$0.787553\pi$
$570$	46741.3	−	17937.3i	0.143864	−	0.0552088i
$571$	−76611.4	+	434485.i	−0.234975	+	1.33261i	0.607692	+	0.794173i	$0.292096\pi$
$571$	−76611.4	+	434485.i	−0.234975	+	1.33261i	−0.842667	+	0.538436i	$0.819015\pi$
$572$	2506.30	+	6886.00i	0.00766022	+	0.0210463i
$573$	424623.	+	235424.i	1.29328	+	0.717036i
$574$	−57101.0	−	323836.i	−0.173309	−	0.982881i
$575$	−256043.	+	147827.i	−0.774422	+	0.447113i
$576$	−73651.8	−	346821.i	−0.221993	−	1.04535i
$577$	−52486.5	+	90909.2i	−0.157651	+	0.273059i	−0.934021	−	0.357218i	$-0.883725\pi$
$577$	−52486.5	+	90909.2i	−0.157651	+	0.273059i	0.776370	+	0.630277i	$0.217059\pi$
$578$	131507.	−	361314.i	0.393636	−	1.08151i
$579$	−11281.2	−	58065.4i	−0.0336509	−	0.173205i
$580$	2815.07	+	2362.13i	0.00836823	+	0.00702178i
$581$	380101.	−	452987.i	1.12602	−	1.34194i
$582$	−238349.	−	274240.i	−0.703666	−	0.809627i
$583$	73675.2	+	26815.6i	0.216763	+	0.0788951i
$584$	−580075.	−	334907.i	−1.70082	−	0.981970i
$585$	43460.3	+	107626.i	0.126993	+	0.314488i
$586$	235221.	+	407415.i	0.684985	+	1.18643i
$587$	199920.	−	35251.3i	0.580203	−	0.102305i	0.124159	−	0.992262i	$-0.460377\pi$
$587$	199920.	−	35251.3i	0.580203	−	0.102305i	0.456045	+	0.889957i	$0.349266\pi$
$588$	21945.5	+	36531.2i	0.0634734	+	0.105660i
$589$	−246114.	+	89578.2i	−0.709424	+	0.258209i
$590$	−140150.	−	24712.3i	−0.402616	−	0.0709920i
$591$	−171841.	+	212166.i	−0.491986	+	0.607437i
$592$	117264.	−	98395.9i	0.334595	−	0.280759i
$593$		−	308327.i		−	0.876803i	−0.898779	−	0.438402i	$-0.855545\pi$
$593$		−	308327.i		−	0.876803i	0.898779	−	0.438402i	$-0.144455\pi$
$594$	12409.6	−	100837.i	0.0351712	−	0.285789i
$595$	313012.			0.884151
$596$	−11304.6	−	13472.3i	−0.0318247	−	0.0379272i
$597$	−30701.3	+	193724.i	−0.0861406	+	0.543545i
$598$	−55665.2	+	315693.i	−0.155662	+	0.882801i
$599$	18844.8	+	51775.7i	0.0525216	+	0.144302i	0.963179	−	0.268860i	$-0.0866467\pi$
$599$	18844.8	+	51775.7i	0.0525216	+	0.144302i	−0.910658	+	0.413161i	$0.864425\pi$
$600$	5555.25	+	319960.i	0.0154313	+	0.888778i
$601$	−5894.31	−	33428.3i	−0.0163186	−	0.0925476i	0.975561	−	0.219730i	$-0.0705177\pi$
$601$	−5894.31	−	33428.3i	−0.0163186	−	0.0925476i	−0.991879	+	0.127183i	$0.959407\pi$
$602$	547640.	−	316180.i	1.51113	−	0.872452i
$603$	−26602.3	+	924.036i	−0.0731619	+	0.00254129i
$604$	−15858.0	+	27466.8i	−0.0434684	+	0.0752895i
$605$	−43041.1	+	118255.i	−0.117591	+	0.323078i
$606$	388698.	+	133880.i	1.05844	+	0.364561i
$607$	−121683.	−	102104.i	−0.330257	−	0.277119i	0.462547	−	0.886595i	$-0.346936\pi$
$607$	−121683.	−	102104.i	−0.330257	−	0.277119i	−0.792805	+	0.609476i	$0.791380\pi$
$608$	−16749.7	+	19961.5i	−0.0453106	+	0.0539991i
$609$	66283.9	−	192444.i	0.178720	−	0.518885i
$610$	30338.2	+	11042.2i	0.0815325	+	0.0296754i
$611$	71215.6	+	41116.4i	0.190762	+	0.110137i
$612$	−1601.56	−	46107.7i	−0.00427602	−	0.123104i
$613$	−23153.1	−	40102.4i	−0.0616153	−	0.106721i	0.833572	−	0.552410i	$-0.186292\pi$
$613$	−23153.1	−	40102.4i	−0.0616153	−	0.106721i	−0.895188	+	0.445690i	$0.852959\pi$
$614$	32214.6	−	5680.30i	0.0854507	−	0.0150673i
$615$	−94510.8	+	1640.93i	−0.249880	+	0.00433850i
$616$	−175283.	+	63797.8i	−0.461933	+	0.168130i
$617$	−197035.	−	34742.5i	−0.517574	−	0.0912623i	−0.0912415	−	0.995829i	$-0.529084\pi$
$617$	−197035.	−	34742.5i	−0.517574	−	0.0912623i	−0.426333	+	0.904567i	$0.640195\pi$
$618$	−102124.	−	16184.6i	−0.267395	−	0.0423766i
$619$	−440177.	+	369352.i	−1.14880	+	0.963961i	−0.999691	−	0.0248591i	$-0.992086\pi$
$619$	−440177.	+	369352.i	−1.14880	+	0.963961i	−0.149113	+	0.988820i	$0.547642\pi$
$620$			21389.3i			0.0556433i
$621$	−242220.	+	321251.i	−0.628097	+	0.833030i
$622$	−28977.0			−0.0748985
$623$	608282.	+	724922.i	1.56722	+	1.86774i
$624$	247089.	+	200127.i	0.634577	+	0.513967i
$625$	40141.6	−	227654.i	0.102763	−	0.582795i
$626$	75844.8	+	208382.i	0.193543	+	0.531754i
$627$	−43139.5	+	25915.4i	−0.109734	+	0.0659208i
$628$	−1487.41	−	8435.54i	−0.00377149	−	0.0213892i
$629$	244009.	−	140879.i	0.616744	−	0.356078i
$630$	−209987.	+	84794.8i	−0.529067	+	0.213643i
$631$	−227941.	+	394805.i	−0.572484	+	0.991571i	0.423826	+	0.905744i	$0.360687\pi$
$631$	−227941.	+	394805.i	−0.572484	+	0.991571i	−0.996310	+	0.0858278i	$0.972647\pi$
$632$	−20425.8	+	56119.5i	−0.0511382	+	0.140501i
$633$	−55028.0	+	47826.1i	−0.137333	+	0.119360i
$634$	−116802.	−	98008.2i	−0.290583	−	0.243828i
$635$	65727.1	−	78330.5i	0.163003	−	0.194260i
$636$	−25285.7	+	4912.61i	−0.0625117	+	0.0121450i
$637$	−508012.	−	184901.i	−1.25197	−	0.455681i
$638$	35338.3	+	20402.6i	0.0868169	+	0.0501238i
$639$	−716659.	+	152192.i	−1.75514	+	0.372725i
$640$	−66401.2	−	115010.i	−0.162112	−	0.280787i
$641$	−314799.	+	55507.6i	−0.766157	+	0.135094i	−0.543050	−	0.839700i	$-0.682731\pi$
$641$	−314799.	+	55507.6i	−0.766157	+	0.135094i	−0.223106	+	0.974794i	$0.571620\pi$
$642$	−65544.9	+	118220.i	−0.159026	+	0.286828i
$643$	93177.0	−	33913.6i	0.225365	−	0.0820262i	−0.226870	−	0.973925i	$-0.572849\pi$
$643$	93177.0	−	33913.6i	0.225365	−	0.0820262i	0.452235	+	0.891899i	$0.350627\pi$
$644$	55758.7	+	9831.77i	0.134444	+	0.0237061i
$645$	−65127.2	−	169709.i	−0.156546	−	0.407930i
$646$	193384.	−	162268.i	0.463399	−	0.388838i
$647$		−	516263.i		−	1.23328i	−0.787244	−	0.616641i	$-0.788493\pi$
$647$		−	516263.i		−	1.23328i	0.787244	−	0.616641i	$-0.211507\pi$
$648$	176977.	+	397893.i	0.421470	+	0.947582i
$649$	143052.			0.339629
$650$	−200007.	−	238359.i	−0.473390	−	0.564164i
$651$	1.10606e6	−	424457.i	2.60985	−	1.00155i
$652$	4352.49	−	24684.2i	0.0102386	−	0.0580663i
$653$	−241050.	−	662279.i	−0.565302	−	1.55315i	−0.811754	−	0.584000i	$-0.801487\pi$
$653$	−241050.	−	662279.i	−0.565302	−	1.55315i	0.246452	−	0.969155i	$-0.420735\pi$
$654$	531888.	+	294895.i	1.24355	+	0.689464i
$655$	44028.6	+	249699.i	0.102625	+	0.582014i
$656$	−224256.	+	129474.i	−0.521118	+	0.300868i
$657$	777363.	+	252740.i	1.80092	+	0.585522i
$658$	−80221.5	+	138948.i	−0.185284	+	0.320922i
$659$	−161614.	+	444030.i	−0.372141	+	1.02245i	0.602391	+	0.798201i	$0.294215\pi$
$659$	−161614.	+	444030.i	−0.372141	+	1.02245i	−0.974532	+	0.224248i	$0.928007\pi$
$660$	783.831	+	4034.46i	0.00179943	+	0.00926184i
$661$	13464.0	+	11297.6i	0.0308156	+	0.0258573i	0.658065	−	0.752961i	$-0.271375\pi$
$661$	13464.0	+	11297.6i	0.0308156	+	0.0258573i	−0.627250	+	0.778818i	$0.715819\pi$
$662$	−85.5528	+	101.958i	−0.000195217	+	0.000232651i
$663$	383925.	+	441738.i	0.873412	+	1.00493i
$664$	−477492.	−	173793.i	−1.08300	−	0.394181i
$665$	97146.3	+	56087.5i	0.219676	+	0.126830i
$666$	−125532.	+	160612.i	−0.283012	+	0.362100i
$667$	−80795.9	−	139943.i	−0.181609	−	0.314556i
$668$	31743.5	−	5597.23i	0.0711380	−	0.0125435i
$669$	−66111.0	−	110050.i	−0.147714	−	0.245889i
$670$	−11177.5	+	4068.27i	−0.0248997	+	0.00906275i
$671$	−31960.0	−	5635.42i	−0.0709843	−	0.0125164i
$672$	74185.7	−	91594.3i	0.164279	−	0.202829i
$673$	−149658.	+	125578.i	−0.330422	+	0.277257i	−0.792872	−	0.609388i	$-0.791415\pi$
$673$	−149658.	+	125578.i	−0.330422	+	0.277257i	0.462450	+	0.886646i	$0.346971\pi$
$674$		−	318812.i		−	0.701803i
$675$	−87743.7	−	380542.i	−0.192579	−	0.835210i
$676$	−7393.21			−0.0161786
$677$	371347.	+	442554.i	0.810219	+	0.965581i	0.999868	−	0.0162706i	$-0.00517933\pi$
$677$	371347.	+	442554.i	0.810219	+	0.965581i	−0.189649	+	0.981852i	$0.560735\pi$
$678$	−31789.8	+	200592.i	−0.0691557	+	0.436370i
$679$	141367.	−	801732.i	0.306626	−	1.73896i
$680$	−91994.3	−	252752.i	−0.198950	−	0.546609i
$681$	−12305.0	−	708720.i	−0.0265331	−	1.52820i
$682$	41242.6	+	233898.i	0.0886701	+	0.502873i
$683$	−549827.	+	317443.i	−1.17865	+	0.680494i	−0.955702	−	0.294337i	$-0.904901\pi$
$683$	−549827.	+	317443.i	−1.17865	+	0.680494i	−0.222948	+	0.974830i	$0.571568\pi$
$684$	7764.82	−	14597.0i	0.0165966	−	0.0311997i
$685$	18592.6	−	32203.4i	0.0396241	−	0.0686310i
$686$	117799.	−	323651.i	0.250319	−	0.687747i
$687$	−69472.5	−	23928.5i	−0.147197	−	0.0506993i
$688$	−381468.	−	320090.i	−0.805900	−	0.676230i
$689$	210040.	−	250316.i	0.442450	−	0.527291i
$690$	−58549.3	+	169988.i	−0.122977	+	0.357043i
$691$	668070.	+	243158.i	1.39915	+	0.509251i	0.927927	−	0.372761i	$-0.121589\pi$
$691$	668070.	+	243158.i	1.39915	+	0.509251i	0.471227	+	0.882012i	$0.343811\pi$
$692$	−171.472	−	98.9992i	−0.000358080	−	0.000206738i
$693$	193070.	−	120594.i	0.402021	−	0.251107i
$694$	−92548.3	−	160298.i	−0.192154	−	0.332821i
$695$	−240297.	+	42370.8i	−0.497483	+	0.0877197i
$696$	−174877.	+	3036.27i	−0.361005	+	0.00626790i
$697$	−447884.	+	163016.i	−0.921934	+	0.335557i
$698$	455864.	+	80381.1i	0.935673	+	0.164984i
$699$	208209.	+	32996.8i	0.426132	+	0.0675333i
$700$	−42099.8	+	35325.9i	−0.0859180	+	0.0720937i
$701$		−	139677.i		−	0.284243i	−0.989849	−	0.142122i	$-0.954608\pi$
$701$		−	139677.i		−	0.284243i	0.989849	−	0.142122i	$-0.0453924\pi$
$702$	−377226.	−	192338.i	−0.765468	−	0.390294i
$703$	100974.			0.204315
$704$	102371.	+	122002.i	0.206554	+	0.246161i
$705$	35839.7	+	29027.9i	0.0721084	+	0.0584033i
$706$	−79258.1	+	449495.i	−0.159014	+	0.901811i
$707$	315043.	+	865573.i	0.630276	+	1.73167i
$708$	−40287.4	+	24202.1i	−0.0803717	+	0.0482821i
$709$	−64044.2	−	363213.i	−0.127405	−	0.722551i	−0.979850	−	0.199734i	$-0.935992\pi$
$709$	−64044.2	−	363213.i	−0.127405	−	0.722551i	0.852445	−	0.522817i	$-0.175119\pi$
$710$	−283529.	+	163696.i	−0.562447	+	0.324729i
$711$	10156.6	−	72170.5i	0.0200913	−	0.142765i
$712$	406589.	−	704234.i	0.802040	−	1.38917i
$713$	321686.	−	883824.i	0.632780	−	1.73855i
$714$	−861867.	+	749070.i	−1.69061	+	1.46935i
$715$	−39939.2	−	33512.9i	−0.0781244	−	0.0655542i
$716$	−20214.3	+	24090.5i	−0.0394305	+	0.0469915i
$717$	−7920.10	+	1538.75i	−0.0154061	+	0.00299316i
$718$	−18381.8	−	6690.43i	−0.0356565	−	0.0129779i
$719$	215464.	+	124398.i	0.416789	+	0.240633i	0.693703	−	0.720262i	$-0.255978\pi$
$719$	215464.	+	124398.i	0.416789	+	0.240633i	−0.276914	+	0.960895i	$0.589312\pi$
$720$	119304.	+	132550.i	0.230138	+	0.255690i
$721$	−115837.	−	200636.i	−0.222832	−	0.385956i
$722$	−402501.	+	70971.7i	−0.772133	+	0.136148i
$723$	82608.8	−	148998.i	0.158034	−	0.285038i
$724$	−43479.3	+	15825.2i	−0.0829478	+	0.0301905i
$725$	154467.	+	27236.7i	0.293873	+	0.0518177i
$726$	−164483.	−	428612.i	−0.312067	−	0.813188i
$727$	−2756.76	+	2313.20i	−0.00521591	+	0.00437667i	−0.645392	−	0.763852i	$-0.723306\pi$
$727$	−2756.76	+	2313.20i	−0.00521591	+	0.00437667i	0.640176	+	0.768228i	$0.278861\pi$
$728$			777417.i			1.46687i
$729$	−312134.	−	430118.i	−0.587335	−	0.809344i
$730$	365275.			0.685448
$731$	−589166.	−	702141.i	−1.10256	−	1.31398i
$732$	9954.25	−	3820.02i	0.0185775	−	0.00712924i
$733$	−16936.9	+	96054.0i	−0.0315229	+	0.178775i	−0.996504	−	0.0835438i	$-0.973376\pi$
$733$	−16936.9	+	96054.0i	−0.0315229	+	0.178775i	0.964981	+	0.262319i	$0.0844873\pi$
$734$	−166170.	−	456547.i	−0.308432	−	0.847411i
$735$	−265176.	−	147022.i	−0.490863	−	0.272149i
$736$	−16249.4	−	92155.2i	−0.0299974	−	0.170123i
$737$	10354.8	−	5978.32i	0.0190636	−	0.0110064i
$738$	256306.	−	230692.i	0.470593	−	0.423566i
$739$	−309074.	+	535332.i	−0.565944	+	0.980244i	0.431017	+	0.902344i	$0.358155\pi$
$739$	−309074.	+	535332.i	−0.565944	+	0.980244i	−0.996961	+	0.0779004i	$0.975178\pi$
$740$	2820.38	−	7748.94i	0.00515045	−	0.0141507i
$741$	40001.5	+	205892.i	0.0728518	+	0.374976i
$742$	488388.	+	409806.i	0.887069	+	0.744339i
$743$	−327490.	+	390288.i	−0.593227	+	0.706980i	−0.976223	−	0.216770i	$-0.930448\pi$
$743$	−327490.	+	390288.i	−0.593227	+	0.706980i	0.382996	+	0.923750i	$0.374892\pi$
$744$	−667813.	−	768375.i	−1.20645	−	1.38812i
$745$	117581.	+	42796.1i	0.211849	+	0.0771066i
$746$	−416250.	−	240322.i	−0.747958	−	0.431834i
$747$	614062.	+	86416.8i	1.10045	+	0.154866i
$748$	10361.8	+	17947.1i	0.0185195	+	0.0320768i
$749$	−298269.	+	52592.9i	−0.531673	+	0.0937484i
$750$	−194714.	−	324127.i	−0.346158	−	0.576225i
$751$	788472.	−	286980.i	1.39800	−	0.508829i	0.470414	−	0.882446i	$-0.344105\pi$
$751$	788472.	−	286980.i	1.39800	−	0.508829i	0.927583	+	0.373616i	$0.121882\pi$
$752$	124426.	+	21939.7i	0.220027	+	0.0387967i
$753$	−41525.9	+	51270.5i	−0.0732367	+	0.0904227i
$754$	130277.	−	109316.i	0.229153	−	0.192282i
$755$		−	225653.i		−	0.395865i
$756$	−33971.4	+	66626.8i	−0.0594388	+	0.116575i
$757$	−239066.			−0.417183			−0.208591	−	0.978003i	$-0.566888\pi$
$757$	−239066.			−0.417183			−0.208591	+	0.978003i	$0.566888\pi$
$758$	588771.	+	701670.i	1.02473	+	1.22122i
$759$	28287.9	−	178496.i	0.0491041	−	0.309845i
$760$	16738.4	−	94928.3i	0.0289793	−	0.164350i
$761$	150813.	+	414356.i	0.260417	+	0.715491i	0.999139	+	0.0414804i	$0.0132074\pi$
$761$	150813.	+	414356.i	0.260417	+	0.715491i	−0.738722	+	0.674010i	$0.764570\pi$
$762$	6475.67	+	372972.i	0.0111526	+	0.642342i
$763$	236622.	+	1.34195e6i	0.406449	+	2.30509i
$764$	62051.2	−	35825.3i	0.106307	−	0.0613766i
$765$	173892.	+	278400.i	0.297137	+	0.475715i
$766$	−40595.2	+	70312.9i	−0.0691858	+	0.119833i
$767$	203913.	−	560248.i	0.346621	−	0.952334i
$768$	−137895.	−	47495.4i	−0.233791	−	0.0805248i
$769$	491697.	+	412583.i	0.831467	+	0.697684i	0.955627	−	0.294579i	$-0.0951793\pi$
$769$	491697.	+	412583.i	0.831467	+	0.697684i	−0.124160	+	0.992262i	$0.539624\pi$
$770$	65386.5	−	77924.7i	0.110283	−	0.131430i
$771$	−145600.	+	422725.i	−0.244936	+	0.711131i
$772$	−8202.80	−	2985.57i	−0.0137634	−	0.00500949i
$773$	863776.	+	498701.i	1.44558	+	0.834606i	0.998214	−	0.0597446i	$-0.0190286\pi$
$773$	863776.	+	498701.i	1.44558	+	0.834606i	0.447367	+	0.894351i	$0.352362\pi$
$774$	585457.	+	311432.i	0.977267	+	0.519854i
$775$	456472.	+	790634.i	0.759996	+	1.31635i
$776$	−688934.	+	121478.i	−1.14407	+	0.201731i
$777$	−456672.	+	7928.90i	−0.756419	+	0.0131332i
$778$	927527.	−	337592.i	1.53238	−	0.557742i
$779$	−168216.	−	29660.9i	−0.277199	−	0.0488776i
$780$	16917.8	+	2681.12i	0.0278070	+	0.00440685i
$781$	252100.	−	211537.i	0.413305	−	0.346804i
$782$			906558.i			1.48246i
$783$	207989.	−	47957.0i	0.339247	−	0.0782220i
$784$	−830623.			−1.35136
$785$	39173.5	+	46685.2i	0.0635702	+	0.0757600i
$786$	−718786.	−	582172.i	−1.16347	−	0.942337i
$787$	17318.9	−	98220.4i	0.0279622	−	0.158581i	−0.967629	−	0.252375i	$-0.918788\pi$
$787$	17318.9	−	98220.4i	0.0279622	−	0.158581i	0.995592	+	0.0937937i	$0.0298994\pi$
$788$	13780.7	+	37862.2i	0.0221931	+	0.0609752i
$789$	251332.	−	150984.i	0.403733	−	0.242536i
$790$	−5655.42	−	32073.5i	−0.00906173	−	0.0513916i
$791$	−394088.	+	227527.i	−0.629854	+	0.363647i
$792$	−154121.	−	120459.i	−0.245704	−	0.192038i
$793$	−67627.8	+	117135.i	−0.107542	+	0.186269i
$794$	−32941.2	+	90505.2i	−0.0522514	+	0.143560i
$795$	138325.	−	120221.i	0.218859	−	0.190216i
$796$	22173.7	+	18605.9i	0.0349954	+	0.0293647i
$797$	187577.	−	223545.i	0.295299	−	0.351924i	−0.597912	−	0.801562i	$-0.704003\pi$
$797$	187577.	−	223545.i	0.295299	−	0.351924i	0.893211	+	0.449638i	$0.148447\pi$
$798$	−401712.	+	78046.3i	−0.630826	+	0.122559i
$799$	218531.	+	79538.7i	0.342310	+	0.124590i
$800$	78661.8	+	45415.4i	0.122909	+	0.0709616i
$801$	−306836.	+	943749.i	−0.478235	+	1.47093i
$802$	−389941.	−	675397.i	−0.606247	−	1.05005i
$803$	−361596.	+	63759.1i	−0.560780	+	0.0988806i
$804$	−1904.75	+	3435.51i	−0.00294664	+	0.00531471i
$805$	−378539.	+	137777.i	−0.584143	+	0.212611i
$806$	974826.	+	171888.i	1.50057	+	0.264591i
$807$	−376577.	−	981289.i	−0.578239	−	1.50678i
$808$	606346.	−	508785.i	0.928748	−	0.779312i
$809$			369815.i			0.565050i	0.959260	+	0.282525i	$0.0911721\pi$
$809$			369815.i			0.565050i	−0.959260	+	0.282525i	$0.908828\pi$
$810$	−192076.	−	139660.i	−0.292754	−	0.212864i
$811$	−1.07237e6			−1.63043			−0.815214	−	0.579160i	$-0.803381\pi$
$811$	−1.07237e6			−1.63043			−0.815214	+	0.579160i	$0.803381\pi$
$812$	−19307.7	−	23010.0i	−0.0292832	−	0.0348983i
$813$	−348108.	+	133589.i	−0.526663	+	0.202111i
$814$	15900.3	−	90175.3i	0.0239970	−	0.136094i
$815$	60993.4	+	167578.i	0.0918264	+	0.252291i
$816$	786434.	+	436023.i	1.18109	+	0.654830i
$817$	−57039.5	−	323487.i	−0.0854539	−	0.484633i
$818$	450705.	−	260215.i	0.673575	−	0.388889i
$819$	−197081.	−	928038.i	−0.293816	−	1.38356i
$820$	−6974.78	+	12080.7i	−0.0103730	+	0.0179665i
$821$	296675.	−	815108.i	0.440144	−	1.20929i	−0.499254	−	0.866456i	$-0.666393\pi$
$821$	296675.	−	815108.i	0.440144	−	1.20929i	0.939398	−	0.342829i	$-0.111385\pi$
$822$	25871.8	+	133165.i	0.0382899	+	0.197082i
$823$	121104.	+	101618.i	0.178797	+	0.150028i	0.727794	−	0.685796i	$-0.240546\pi$
$823$	121104.	+	101618.i	0.178797	+	0.150028i	−0.548997	+	0.835824i	$0.684990\pi$
$824$	−127966.	+	152504.i	−0.188469	+	0.224608i
$825$	115074.	+	132402.i	0.169071	+	0.194530i
$826$	1.09309e6	+	397852.i	1.60212	+	0.583125i
$827$	−657032.	−	379338.i	−0.960673	−	0.554645i	−0.0642930	−	0.997931i	$-0.520479\pi$
$827$	−657032.	−	379338.i	−0.960673	−	0.554645i	−0.896380	+	0.443286i	$0.853813\pi$
$828$	22231.9	+	55055.2i	0.0324276	+	0.0803041i
$829$	−310431.	−	537683.i	−0.451707	−	0.782379i	0.546785	−	0.837273i	$-0.315851\pi$
$829$	−310431.	−	537683.i	−0.451707	−	0.782379i	−0.998492	+	0.0548937i	$0.982518\pi$
$830$	272897.	−	48119.1i	0.396134	−	0.0698491i
$831$	−367011.	−	610937.i	−0.531468	−	0.884696i
$832$	623730.	−	227019.i	0.901053	−	0.327956i
$833$	−1.50564e6	−	265485.i	−2.16986	−	0.382605i
$834$	560252.	−	691722.i	0.805473	−	0.994488i
$835$	−175679.	+	147412.i	−0.251969	+	0.211427i
$836$			7426.75i			0.0106264i
$837$	991987.	+	747948.i	1.41597	+	1.06763i
$838$	−808242.			−1.15094
$839$	−406047.	−	483908.i	−0.576836	−	0.687447i	0.396183	−	0.918172i	$-0.370335\pi$
$839$	−406047.	−	483908.i	−0.576836	−	0.687447i	−0.973019	+	0.230725i	$0.925890\pi$
$840$	−68248.0	+	430643.i	−0.0967234	+	0.610321i
$841$	107932.	−	612111.i	0.152601	−	0.865442i
$842$	−93471.4	−	256811.i	−0.131842	−	0.362234i
$843$	1248.98	+	71936.3i	0.00175752	+	0.101226i
$844$	1868.32	+	10595.8i	0.00262281	+	0.0148747i
$845$	45554.1	−	26300.7i	0.0637990	−	0.0368344i
$846$	−168150.	+	5840.72i	−0.234940	+	0.00816067i
$847$	514315.	−	890819.i	0.716906	−	1.24172i
$848$	171713.	−	471777.i	0.238787	−	0.656062i
$849$	−239509.	−	82494.5i	−0.332282	−	0.114448i
$850$	−674084.	−	565624.i	−0.932989	−	0.782871i
$851$	−233081.	+	277776.i	−0.321846	+	0.383562i
$852$	−35209.8	+	102226.i	−0.0485047	+	0.140825i
$853$	−987712.	−	359498.i	−1.35748	−	0.494081i	−0.442204	−	0.896915i	$-0.645803\pi$
$853$	−987712.	−	359498.i	−1.35748	−	0.494081i	−0.915273	+	0.402833i	$0.868025\pi$
$854$	−228540.	−	131948.i	−0.313362	−	0.180920i
$855$	4083.59	+	117564.i	0.00558611	+	0.160820i
$856$	130129.	+	225391.i	0.177594	+	0.307602i
$857$	−1.13896e6	+	200829.i	−1.55077	+	0.273442i	−0.882439	−	0.470426i	$-0.844100\pi$
$857$	−1.13896e6	+	200829.i	−1.55077	+	0.273442i	−0.668326	+	0.743868i	$0.732989\pi$
$858$	190171.	−	3301.82i	0.258327	−	0.00448516i
$859$	−290616.	+	105776.i	−0.393852	+	0.143351i	−0.531352	−	0.847151i	$-0.678316\pi$
$859$	−290616.	+	105776.i	−0.393852	+	0.143351i	0.137499	+	0.990502i	$0.456094\pi$
$860$	−26418.2	−	4658.24i	−0.0357195	−	0.00629832i
$861$	763111.	+	120937.i	1.02939	+	0.163138i
$862$	−914684.	+	767511.i	−1.23100	+	1.03293i
$863$			1.24555e6i			1.67239i	0.548431	+	0.836196i	$0.315225\pi$
$863$			1.24555e6i			1.67239i	−0.548431	+	0.836196i	$0.684775\pi$
$864$	122680.	+	15097.8i	0.164341	+	0.0202249i
$865$	1408.72			0.00188275
$866$	208220.	+	248147.i	0.277643	+	0.330882i
$867$	702052.	+	568618.i	0.933966	+	0.756454i
$868$	30359.4	−	172177.i	0.0402953	−	0.228526i
$869$	11196.9	+	30763.2i	0.0148272	+	0.0407373i
$870$	81762.5	−	49117.5i	0.108023	−	0.0648930i
$871$	−8653.25	−	49075.0i	−0.0114063	−	0.0646881i
$872$	1.01406e6	−	585468.i	1.33362	−	0.769964i
$873$	791617.	−	319663.i	1.03869	−	0.419434i
$874$	−162443.	+	281359.i	−0.212656	+	0.368331i
$875$	289760.	−	796109.i	0.378462	−	1.03982i
$876$	91048.4	−	79132.3i	0.118649	−	0.103121i
$877$	484558.	+	406593.i	0.630009	+	0.528641i	0.900932	−	0.433961i	$-0.142884\pi$
$877$	484558.	+	406593.i	0.630009	+	0.528641i	−0.270923	+	0.962601i	$0.587329\pi$
$878$	583102.	−	694914.i	0.756407	−	0.901451i
$879$	−1.08508e6	+	210813.i	−1.40438	+	0.272848i
$880$	−75274.2	−	27397.6i	−0.0972033	−	0.0353791i
$881$	134364.	+	77575.1i	0.173114	+	0.0999472i	0.584053	−	0.811715i	$-0.301466\pi$
$881$	134364.	+	77575.1i	0.173114	+	0.0999472i	−0.410940	+	0.911663i	$0.634799\pi$
$882$	1.08199e6	−	229775.i	1.39087	−	0.295369i
$883$	538530.	+	932762.i	0.690699	+	1.19633i	0.971609	+	0.236591i	$0.0760302\pi$
$883$	538530.	+	932762.i	0.690699	+	1.19633i	−0.280911	+	0.959734i	$0.590636\pi$
$884$	85057.9	−	14998.0i	0.108845	−	0.0191924i
$885$	162139.	−	292442.i	0.207015	−	0.373382i
$886$	−1.20281e6	+	437788.i	−1.53225	+	0.557694i
$887$	1.16507e6	+	205434.i	1.48083	+	0.261111i	0.854911	−	0.518775i	$-0.173612\pi$
$887$	1.16507e6	+	205434.i	1.48083	+	0.261111i	0.625922	+	0.779886i	$0.284723\pi$
$888$	140619.	+	366426.i	0.178327	+	0.464686i
$889$	−640262.	+	537244.i	−0.810129	+	0.679779i
$890$			443458.i			0.559851i
$891$	214518.	+	104726.i	0.270215	+	0.131917i
$892$	−18945.9			−0.0238114
$893$	53571.0	+	63843.4i	0.0671779	+	0.0800595i
$894$	−426172.	+	163547.i	−0.533224	+	0.204629i
$895$	38853.1	−	220347.i	0.0485042	−	0.275081i
$896$	371265.	+	1.02004e6i	0.462454	+	1.27058i
$897$	−658735.	−	365223.i	−0.818702	−	0.453913i
$898$	−189382.	−	1.07404e6i	−0.234848	−	1.33189i
$899$	−432127.	+	249489.i	−0.534678	+	0.308696i
$900$	−54808.1	−	17819.5i	−0.0676643	−	0.0219993i
$901$	462048.	−	800291.i	0.569164	−	0.985821i
$902$	−52977.5	+	145555.i	−0.0651146	+	0.178901i
$903$	283372.	+	1.45854e6i	0.347521	+	1.78873i
$904$	299547.	+	251350.i	0.366546	+	0.307568i
$905$	211606.	−	252182.i	0.258363	−	0.307905i
$906$	540011.	+	621328.i	0.657880	+	0.756946i
$907$	623357.	+	226883.i	0.757744	+	0.275796i	0.691861	−	0.722031i	$-0.256791\pi$
$907$	623357.	+	226883.i	0.757744	+	0.275796i	0.0658832	+	0.997827i	$0.479014\pi$
$908$	−90590.8	−	52302.6i	−0.109878	−	0.0634384i
$909$	−594842.	+	761072.i	−0.719903	+	0.921082i
$910$	−211978.	−	367156.i	−0.255981	−	0.443372i
$911$	510712.	−	90052.3i	0.615374	−	0.108507i	0.142732	−	0.989761i	$-0.454411\pi$
$911$	510712.	−	90052.3i	0.615374	−	0.108507i	0.472643	+	0.881254i	$0.343300\pi$
$912$	165948.	+	276242.i	0.199519	+	0.332124i
$913$	−261749.	+	95268.7i	−0.314009	+	0.114290i
$914$	−290545.	−	51230.9i	−0.347793	−	0.0613253i
$915$	−47744.8	+	58948.8i	−0.0570275	+	0.0704097i
$916$	−8306.62	+	6970.08i	−0.00989996	+	0.00830705i
$917$		−	2.07249e6i		−	2.46464i
$918$	−1.14505e6	−	350424.i	−1.35875	−	0.415823i
$919$	−155260.			−0.183835			−0.0919175	−	0.995767i	$-0.529300\pi$
$919$	−155260.			−0.183835			−0.0919175	+	0.995767i	$0.529300\pi$
$920$	222506.	+	265172.i	0.262885	+	0.313294i
$921$	−12030.6	+	75912.8i	−0.0141830	+	0.0894944i
$922$	−78151.6	+	443220.i	−0.0919339	+	0.521383i
$923$	−469105.	−	1.28886e6i	−0.550639	−	1.51287i
$924$	−583.177	−	33588.6i	−0.000683056	−	0.0393413i
$925$	−61118.9	−	346622.i	−0.0714318	−	0.405110i
$926$	−975189.	+	563026.i	−1.13728	+	0.656608i
$927$	114098.	−	214491.i	0.132775	−	0.249603i
$928$	−24822.2	+	42993.3i	−0.0288233	+	0.0499234i
$929$	−94497.2	+	259629.i	−0.109493	+	0.300830i	−0.982323	−	0.187195i	$-0.940060\pi$
$929$	−94497.2	+	259629.i	−0.109493	+	0.300830i	0.872830	+	0.488025i	$0.162283\pi$
$930$	524905.	+	180794.i	0.606897	+	0.209034i
$931$	−419720.	−	352187.i	−0.484239	−	0.406325i
$932$	19997.1	−	23831.6i	0.0230215	−	0.0274360i
$933$	22172.4	−	64374.0i	0.0254712	−	0.0739515i
$934$	513489.	+	186895.i	0.588623	+	0.214241i
$935$	−127690.	−	73722.0i	−0.146061	−	0.0843284i
$936$	−691454.	+	431890.i	−0.789245	+	0.492971i
$937$	700032.	+	1.21249e6i	0.797331	+	1.38102i	0.921348	+	0.388738i	$0.127089\pi$
$937$	700032.	+	1.21249e6i	0.797331	+	1.38102i	−0.124017	+	0.992280i	$0.539578\pi$
$938$	95749.5	−	16883.2i	0.108826	−	0.0191889i
$939$	−520965.	+	9045.18i	−0.590851	+	0.0102585i
$940$	6395.78	−	2327.87i	0.00723832	−	0.00263453i
$941$	1.64688e6	+	290389.i	1.85987	+	0.327945i	0.987089	−	0.160170i	$-0.0512043\pi$
$941$	1.64688e6	+	290389.i	1.85987	+	0.327945i	0.872779	+	0.488115i	$0.162315\pi$
$942$	−219586.	−	34799.8i	−0.247458	−	0.0392170i
$943$	469892.	−	394286.i	0.528414	−	0.443392i
$944$		−	916030.i		−	1.02794i
$945$	−27700.2	−	531379.i	−0.0310184	−	0.595032i
$946$	−297873.			−0.332850
$947$	171742.	+	204674.i	0.191503	+	0.228224i	0.853249	−	0.521504i	$-0.174629\pi$
$947$	171742.	+	204674.i	0.191503	+	0.228224i	−0.661746	+	0.749728i	$0.730184\pi$
$948$	−8357.99	−	6769.45i	−0.00930005	−	0.00753246i
$949$	−265731.	+	1.50703e6i	−0.295059	+	1.67336i
$950$	−107857.	−	296334.i	−0.119509	−	0.328348i
$951$	307104.	−	184488.i	0.339566	−	0.203989i
$952$	381774.	+	2.16515e6i	0.421243	+	2.38899i
$953$	125454.	−	72431.1i	0.138134	−	0.0797516i	−0.429340	−	0.903143i	$-0.641254\pi$
$953$	125454.	−	72431.1i	0.138134	−	0.0797516i	0.567474	+	0.823391i	$0.307921\pi$
$954$	−93170.3	+	662050.i	−0.102372	+	0.727435i
$955$	−254890.	+	441483.i	−0.279477	+	0.484069i
$956$	−407.231	+	1118.86i	−0.000445580	+	0.00122422i
$957$	−72365.3	+	62894.4i	−0.0790145	+	0.0686734i
$958$	−943188.	−	791428.i	−1.02770	−	0.862344i
$959$	−195373.	+	232837.i	−0.212436	+	0.253171i
$960$	365439.	−	70999.0i	0.396527	−	0.0770388i
$961$	−1.86132e6	−	677467.i	−2.01547	−	0.733570i
$962$	−330496.	−	190812.i	−0.357122	−	0.206184i
$963$	−212480.	−	236070.i	−0.229121	−	0.254559i
$964$	−12570.9	−	21773.4i	−0.0135273	−	0.0234300i
$965$	61163.3	−	10784.7i	0.0656805	−	0.0115812i
$966$	712580.	−	1.28525e6i	0.763624	−	1.37731i
$967$	111718.	−	40662.0i	0.119473	−	0.0434846i	−0.281592	−	0.959534i	$-0.590862\pi$
$967$	111718.	−	40662.0i	0.119473	−	0.0434846i	0.401065	+	0.916050i	$0.368640\pi$
$968$	−870480.	−	153489.i	−0.928984	−	0.163805i
$969$	212516.	+	553776.i	0.226331	+	0.589775i
$970$	292245.	−	245223.i	0.310601	−	0.260626i
$971$		−	431238.i		−	0.457382i	−0.973499	−	0.228691i	$-0.926555\pi$
$971$		−	431238.i		−	0.457382i	0.973499	−	0.228691i	$-0.0734445\pi$
$972$	−78132.2	+	6799.19i	−0.0826985	+	0.00719656i
$973$	1.99445e6			2.10668
$974$	633943.	+	755504.i	0.668240	+	0.796378i
$975$	682568.	−	261941.i	0.718020	−	0.275546i
$976$	−36086.2	+	204655.i	−0.0378828	+	0.214844i
$977$	−248765.	−	683477.i	−0.260616	−	0.716036i	−0.999126	−	0.0417938i	$-0.986693\pi$
$977$	−248765.	−	683477.i	−0.260616	−	0.716036i	0.738511	−	0.674242i	$-0.235529\pi$
$978$	−568975.	−	315457.i	−0.594861	−	0.329809i
$979$	−77405.9	−	438991.i	−0.0807623	−	0.458026i
$980$	−38750.9	+	22372.8i	−0.0403487	+	0.0232953i
$981$	−1.06211e6	+	955972.i	−1.10365	+	0.993361i
$982$	−111734.	+	193529.i	−0.115868	+	0.200689i
$983$	−600688.	+	1.65038e6i	−0.621644	+	1.70795i	0.0812820	+	0.996691i	$0.474099\pi$
$983$	−600688.	+	1.65038e6i	−0.621644	+	1.70795i	−0.702926	+	0.711263i	$0.748124\pi$
$984$	−126623.	−	651744.i	−0.130775	−	0.673111i
$985$	−219602.	−	184268.i	−0.226342	−	0.189923i
$986$	309147.	−	368426.i	0.317988	−	0.378963i
$987$	−247296.	−	284535.i	−0.253854	−	0.292080i
$988$	29086.0	+	10586.4i	0.0297968	+	0.0108452i
$989$	1.02156e6	+	589800.i	1.04441	+	0.602993i
$990$	105633.	+	14865.8i	0.107778	+	0.0151676i
$991$	−133835.	−	231810.i	−0.136277	−	0.236039i	0.789807	−	0.613355i	$-0.210181\pi$
$991$	−133835.	−	231810.i	−0.136277	−	0.236039i	−0.926085	+	0.377316i	$0.876847\pi$
$992$	−284565.	+	50176.5i	−0.289173	+	0.0509891i
$993$	−161.042	−	268.075i	−0.000163321	−	0.000271868i
$994$	2.51466e6	−	915263.i	2.54511	−	0.926346i
$995$	−202814.	−	35761.6i	−0.204858	−	0.0361220i
$996$	57597.7	−	71113.8i	0.0580613	−	0.0716861i
$997$	−478061.	+	401140.i	−0.480942	+	0.403558i	−0.850767	−	0.525543i	$-0.823862\pi$
$997$	−478061.	+	401140.i	−0.480942	+	0.403558i	0.369825	+	0.929101i	$0.379418\pi$
$998$		−	1.16831e6i		−	1.17299i
$999$	−260754.	−	401771.i	−0.261277	−	0.402576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.5.f.a.5.4	✓	66
3.2	odd	2		81.5.f.a.44.8		66
27.11	odd	18	inner	27.5.f.a.11.4	yes	66
27.16	even	9		81.5.f.a.35.8		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.5.4	✓	66	1.1	even	1	trivial
27.5.f.a.11.4	yes	66	27.11	odd	18	inner
81.5.f.a.35.8		66	27.16	even	9
81.5.f.a.44.8		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+(-2.46212 - 2.93424i) q^{2} +(8.40252 - 3.22453i) q^{3} +(0.230635 - 1.30800i) q^{4} +(3.23200 + 8.87984i) q^{5} +(-30.1496 - 16.7158i) q^{6} +(-13.4127 - 76.0673i) q^{7} +(-57.4812 + 33.1868i) q^{8} +(60.2048 - 54.1884i) q^{9} +(18.0980 - 31.3467i) q^{10} +(-12.4441 + 34.1900i) q^{11} +(-2.27976 - 11.7342i) q^{12} +(116.163 + 97.4720i) q^{13} +(-190.176 + 226.643i) q^{14} +(55.7903 + 64.1914i) q^{15} +(218.934 + 79.6856i) q^{16} +(371.386 + 214.420i) q^{17} +(-307.233 - 43.2369i) q^{18} +(76.8422 + 133.095i) q^{19} +(12.3602 - 2.17944i) q^{20} +(-357.982 - 595.907i) q^{21} +(130.961 - 47.6658i) q^{22} +(-543.514 - 95.8361i) q^{23} +(-375.975 + 464.202i) q^{24} +(410.372 - 344.343i) q^{25} -580.837i q^{26} +(331.140 - 649.452i) q^{27} -102.589 q^{28} +(188.204 + 224.292i) q^{29} +(50.9907 - 321.749i) q^{30} +(-295.931 + 1678.31i) q^{31} +(57.9911 + 159.329i) q^{32} +(5.68458 + 327.409i) q^{33} +(-285.238 - 1617.66i) q^{34} +(632.116 - 364.952i) q^{35} +(-56.9930 - 91.2455i) q^{36} +(328.512 - 568.999i) q^{37} +(201.337 - 553.169i) q^{38} +(1290.36 + 444.441i) q^{39} +(-480.472 - 403.164i) q^{40} +(-714.418 + 851.410i) q^{41} +(-867.141 + 2517.60i) q^{42} +(-2008.45 - 731.017i) q^{43} +(41.8504 + 24.1623i) q^{44} +(675.766 + 359.472i) q^{45} +(1056.99 + 1830.76i) q^{46} +(534.052 - 94.1678i) q^{47} +(2096.55 - 36.4010i) q^{48} +(-3350.13 + 1219.35i) q^{49} +(-2020.77 - 356.317i) q^{50} +(3811.98 + 604.121i) q^{51} +(154.285 - 129.460i) q^{52} -2154.88i q^{53} +(-2720.96 + 627.385i) q^{54} -343.821 q^{55} +(3295.41 + 3927.31i) q^{56} +(1074.84 + 870.550i) q^{57} +(194.748 - 1104.47i) q^{58} +(-1344.72 - 3694.60i) q^{59} +(96.8295 - 58.1688i) q^{60} +(154.886 + 878.404i) q^{61} +(5653.19 - 3263.87i) q^{62} +(-4929.48 - 3852.80i) q^{63} +(2188.61 - 3790.78i) q^{64} +(-490.099 + 1346.54i) q^{65} +(946.700 - 822.800i) q^{66} +(-251.739 - 211.234i) q^{67} +(366.115 - 436.319i) q^{68} +(-4875.91 + 947.312i) q^{69} +(-2627.20 - 956.224i) q^{70} +(-7833.15 - 4522.47i) q^{71} +(-1662.30 + 5112.82i) q^{72} +(5045.79 + 8739.56i) q^{73} +(-2478.42 + 437.012i) q^{74} +(2337.81 - 4216.61i) q^{75} +(191.810 - 69.8132i) q^{76} +(2767.65 + 488.011i) q^{77} +(-1872.93 - 4880.50i) q^{78} +(689.267 - 578.364i) q^{79} +2201.65i q^{80} +(688.231 - 6524.80i) q^{81} +4257.23 q^{82} +(4921.00 + 5864.61i) q^{83} +(-862.009 + 330.803i) q^{84} +(-703.695 + 3990.85i) q^{85} +(2800.07 + 7693.14i) q^{86} +(2304.62 + 1277.75i) q^{87} +(-419.351 - 2378.26i) q^{88} +(-10610.2 + 6125.78i) q^{89} +(-609.041 - 2867.93i) q^{90} +(5856.38 - 10143.5i) q^{91} +(-250.707 + 688.812i) q^{92} +(2925.20 + 15056.3i) q^{93} +(-1591.21 - 1335.19i) q^{94} +(-933.505 + 1112.51i) q^{95} +(1001.03 + 1151.77i) q^{96} +(9904.15 + 3604.82i) q^{97} +(11826.3 + 6827.91i) q^{98} +(1103.50 + 2732.73i) 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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