LMFDB - Embedded newform 27.5.f.a.2.10

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			2.10
Character	$\chi$	$=$	27.2
Dual form			27.5.f.a.14.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.98494 + 1.05531i) q^{2} +(-1.69482 - 8.83898i) q^{3} +(19.6707 + 7.15955i) q^{4} +(10.5942 + 12.6257i) q^{5} +(-0.815584 - 54.6893i) q^{6} +(7.09675 - 2.58301i) q^{7} +(25.9633 + 14.9899i) q^{8} +(-75.2551 + 29.9610i) q^{9} +(50.0816 + 86.7438i) q^{10} +(-120.209 + 143.260i) q^{11} +(29.9447 - 186.003i) q^{12} +(-9.75217 - 55.3073i) q^{13} +(45.1995 - 7.96989i) q^{14} +(93.6426 - 115.040i) q^{15} +(-117.001 - 98.1758i) q^{16} +(396.435 - 228.882i) q^{17} +(-482.015 + 99.8976i) q^{18} +(-233.647 + 404.688i) q^{19} +(118.001 + 324.205i) q^{20} +(-34.8589 - 58.3503i) q^{21} +(-870.626 + 730.542i) q^{22} +(177.454 - 487.552i) q^{23} +(88.4924 - 254.895i) q^{24} +(61.3597 - 347.988i) q^{25} -341.302i q^{26} +(392.369 + 614.400i) q^{27} +158.091 q^{28} +(1518.15 + 267.691i) q^{29} +(681.847 - 589.685i) q^{30} +(-719.064 - 261.718i) q^{31} +(-904.971 - 1078.50i) q^{32} +(1470.00 + 819.726i) q^{33} +(2614.18 - 951.483i) q^{34} +(107.796 + 62.2363i) q^{35} +(-1694.83 + 50.5614i) q^{36} +(-254.299 - 440.459i) q^{37} +(-1825.43 + 2175.46i) q^{38} +(-472.332 + 179.935i) q^{39} +(85.8024 + 486.610i) q^{40} +(-562.688 + 99.2171i) q^{41} +(-147.051 - 386.010i) q^{42} +(850.976 + 714.053i) q^{43} +(-3390.27 + 1957.37i) q^{44} +(-1175.54 - 632.733i) q^{45} +(1576.57 - 2730.70i) q^{46} +(54.5162 + 149.782i) q^{47} +(-669.477 + 1200.56i) q^{48} +(-1795.58 + 1506.67i) q^{49} +(734.467 - 2017.93i) q^{50} +(-2694.97 - 3116.17i) q^{51} +(204.143 - 1157.75i) q^{52} -1535.13i q^{53} +(1699.92 + 4091.21i) q^{54} -3082.26 q^{55} +(222.974 + 39.3164i) q^{56} +(3973.02 + 1379.32i) q^{57} +(8803.55 + 3204.23i) q^{58} +(1352.46 + 1611.80i) q^{59} +(2665.65 - 1592.48i) q^{60} +(-1362.35 + 495.855i) q^{61} +(-4027.36 - 2325.20i) q^{62} +(-456.678 + 407.011i) q^{63} +(-3056.17 - 5293.44i) q^{64} +(594.974 - 709.063i) q^{65} +(7932.80 + 6457.31i) q^{66} +(-1241.97 - 7043.56i) q^{67} +(9436.84 - 1663.97i) q^{68} +(-4610.21 - 742.201i) q^{69} +(579.476 + 486.238i) q^{70} +(-2436.79 + 1406.88i) q^{71} +(-2402.99 - 350.182i) q^{72} +(-2132.26 + 3693.19i) q^{73} +(-1057.14 - 2904.48i) q^{74} +(-3179.85 + 47.4213i) q^{75} +(-7493.38 + 6287.69i) q^{76} +(-483.054 + 1327.18i) q^{77} +(-3016.76 + 578.447i) q^{78} +(-992.133 + 5626.67i) q^{79} -2517.31i q^{80} +(4765.67 - 4509.44i) q^{81} -3472.36 q^{82} +(4026.67 + 710.011i) q^{83} +(-267.937 - 1397.37i) q^{84} +(7089.69 + 2580.44i) q^{85} +(4339.49 + 5171.60i) q^{86} +(-206.883 - 13872.6i) q^{87} +(-5268.48 + 1917.57i) q^{88} +(5385.27 + 3109.19i) q^{89} +(-6367.83 - 5027.42i) q^{90} +(-212.068 - 367.312i) q^{91} +(6981.30 - 8319.99i) q^{92} +(-1094.63 + 6799.36i) q^{93} +(168.210 + 953.968i) q^{94} +(-7584.75 + 1337.40i) q^{95} +(-7999.10 + 9826.89i) q^{96} +(7112.63 + 5968.20i) q^{97} +(-12336.4 + 7122.44i) q^{98} +(4754.15 - 14382.6i) 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 $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	5.98494	+	1.05531i	1.49623	+	0.263826i	0.861044	−	0.508530i	$-0.169811\pi$
$2$	5.98494	+	1.05531i	1.49623	+	0.263826i	0.635189	+	0.772356i	$0.280922\pi$
$3$	−1.69482	−	8.83898i	−0.188314	−	0.982109i
$3$	−1.69482	−	8.83898i	−0.188314	−	0.982109i
$4$	19.6707	+	7.15955i	1.22942	+	0.447472i
$5$	10.5942	+	12.6257i	0.423767	+	0.505026i	0.935113	−	0.354349i	$-0.115297\pi$
$5$	10.5942	+	12.6257i	0.423767	+	0.505026i	−0.511346	+	0.859375i	$0.670853\pi$
$6$	−0.815584	−	54.6893i	−0.0226551	−	1.51915i
$7$	7.09675	−	2.58301i	0.144832	−	0.0527144i	−0.268587	−	0.963255i	$-0.586557\pi$
$7$	7.09675	−	2.58301i	0.144832	−	0.0527144i	0.413419	+	0.910541i	$0.364335\pi$
$8$	25.9633	+	14.9899i	0.405677	+	0.234218i
$9$	−75.2551	+	29.9610i	−0.929076	+	0.369889i
$10$	50.0816	+	86.7438i	0.500816	+	0.867438i
$11$	−120.209	+	143.260i	−0.993463	+	1.18396i	−0.0105406	+	0.999944i	$0.503355\pi$
$11$	−120.209	+	143.260i	−0.993463	+	1.18396i	−0.982923	+	0.184019i	$0.941089\pi$
$12$	29.9447	−	186.003i	0.207950	−	1.29169i
$13$	−9.75217	−	55.3073i	−0.0577051	−	0.327262i	0.942266	−	0.334865i	$-0.108691\pi$
$13$	−9.75217	−	55.3073i	−0.0577051	−	0.327262i	−0.999971	+	0.00760334i	$0.997580\pi$
$14$	45.1995	−	7.96989i	0.230610	−	0.0406627i
$15$	93.6426	−	115.040i	0.416189	−	0.511289i
$16$	−117.001	−	98.1758i	−0.457037	−	0.383499i
$17$	396.435	−	228.882i	1.37175	−	0.791979i	0.380599	−	0.924740i	$-0.375718\pi$
$17$	396.435	−	228.882i	1.37175	−	0.791979i	0.991148	+	0.132761i	$0.0423843\pi$
$18$	−482.015	+	99.8976i	−1.48770	+	0.308326i
$19$	−233.647	+	404.688i	−0.647221	+	1.12102i	0.336562	+	0.941661i	$0.390736\pi$
$19$	−233.647	+	404.688i	−0.647221	+	1.12102i	−0.983784	+	0.179359i	$0.942598\pi$
$20$	118.001	+	324.205i	0.295002	+	0.810512i
$21$	−34.8589	−	58.3503i	−0.0790451	−	0.132314i
$22$	−870.626	+	730.542i	−1.79881	+	1.50938i
$23$	177.454	−	487.552i	0.335452	−	0.921648i	−0.651214	−	0.758894i	$-0.725740\pi$
$23$	177.454	−	487.552i	0.335452	−	0.921648i	0.986667	−	0.162754i	$-0.0520377\pi$
$24$	88.4924	−	254.895i	0.153633	−	0.442525i
$25$	61.3597	−	347.988i	0.0981755	−	0.556781i
$26$		−	341.302i		−	0.504885i
$27$	392.369	+	614.400i	0.538229	+	0.842799i
$28$	158.091			0.201647
$29$	1518.15	+	267.691i	1.80518	+	0.318301i	0.972048	−	0.234781i	$-0.0754373\pi$
$29$	1518.15	+	267.691i	1.80518	+	0.318301i	0.833127	+	0.553082i	$0.186548\pi$
$30$	681.847	−	589.685i	0.757608	−	0.655206i
$31$	−719.064	−	261.718i	−0.748246	−	0.272339i	−0.0603785	−	0.998176i	$-0.519231\pi$
$31$	−719.064	−	261.718i	−0.748246	−	0.272339i	−0.687867	+	0.725836i	$0.741453\pi$
$32$	−904.971	−	1078.50i	−0.883761	−	1.05323i
$33$	1470.00	+	819.726i	1.34986	+	0.752733i
$34$	2614.18	−	951.483i	2.26140	−	0.823082i
$35$	107.796	+	62.2363i	0.0879971	+	0.0508051i
$36$	−1694.83	+	50.5614i	−1.30774	+	0.0390134i
$37$	−254.299	−	440.459i	−0.185755	−	0.321738i	0.758075	−	0.652167i	$-0.226140\pi$
$37$	−254.299	−	440.459i	−0.185755	−	0.321738i	−0.943831	+	0.330429i	$0.892807\pi$
$38$	−1825.43	+	2175.46i	−1.26415	+	1.50655i
$39$	−472.332	+	179.935i	−0.310540	+	0.118301i
$40$	85.8024	+	486.610i	0.0536265	+	0.304131i
$41$	−562.688	+	99.2171i	−0.334734	+	0.0590227i	−0.338489	−	0.940970i	$-0.609916\pi$
$41$	−562.688	+	99.2171i	−0.334734	+	0.0590227i	0.00375496	+	0.999993i	$0.498805\pi$
$42$	−147.051	−	386.010i	−0.0833621	−	0.218826i
$43$	850.976	+	714.053i	0.460236	+	0.386183i	0.843218	−	0.537572i	$-0.180658\pi$
$43$	850.976	+	714.053i	0.460236	+	0.386183i	−0.382982	+	0.923756i	$0.625103\pi$
$44$	−3390.27	+	1957.37i	−1.75117	+	1.01104i
$45$	−1175.54	−	632.733i	−0.580516	−	0.312461i
$46$	1576.57	−	2730.70i	0.745070	−	1.29050i
$47$	54.5162	+	149.782i	0.0246792	+	0.0678054i	0.951420	−	0.307895i	$-0.0996245\pi$
$47$	54.5162	+	149.782i	0.0246792	+	0.0678054i	−0.926741	+	0.375700i	$0.877402\pi$
$48$	−669.477	+	1200.56i	−0.290572	+	0.521078i
$49$	−1795.58	+	1506.67i	−0.747847	+	0.627518i
$50$	734.467	−	2017.93i	0.293787	−	0.807173i
$51$	−2694.97	−	3116.17i	−1.03613	−	1.19806i
$52$	204.143	−	1157.75i	0.0754968	−	0.428164i
$53$		−	1535.13i		−	0.546503i	−0.961943	−	0.273251i	$-0.911901\pi$
$53$		−	1535.13i		−	0.546503i	0.961943	−	0.273251i	$-0.0880991\pi$
$54$	1699.92	+	4091.21i	0.582964	+	1.40302i
$55$	−3082.26			−1.01893
$56$	222.974	+	39.3164i	0.0711015	+	0.0125371i
$57$	3973.02	+	1379.32i	1.22284	+	0.424538i
$58$	8803.55	+	3204.23i	2.61699	+	0.952506i
$59$	1352.46	+	1611.80i	0.388527	+	0.463028i	0.924486	−	0.381215i	$-0.124494\pi$
$59$	1352.46	+	1611.80i	0.388527	+	0.463028i	−0.535959	+	0.844244i	$0.680050\pi$
$60$	2665.65	−	1592.48i	0.740458	−	0.442355i
$61$	−1362.35	+	495.855i	−0.366124	+	0.133258i	−0.518530	−	0.855060i	$-0.673520\pi$
$61$	−1362.35	+	495.855i	−0.366124	+	0.133258i	0.152405	+	0.988318i	$0.451298\pi$
$62$	−4027.36	−	2325.20i	−1.04770	−	0.604890i
$63$	−456.678	+	407.011i	−0.115061	+	0.102547i
$64$	−3056.17	−	5293.44i	−0.746135	−	1.29234i
$65$	594.974	−	709.063i	0.140822	−	0.167826i
$66$	7932.80	+	6457.31i	1.82112	+	1.48239i
$67$	−1241.97	−	7043.56i	−0.276669	−	1.56907i	−0.733609	−	0.679572i	$-0.762165\pi$
$67$	−1241.97	−	7043.56i	−0.276669	−	1.56907i	0.456939	−	0.889498i	$-0.348946\pi$
$68$	9436.84	−	1663.97i	2.04084	−	0.359855i
$69$	−4610.21	−	742.201i	−0.968329	−	0.155892i
$70$	579.476	+	486.238i	0.118260	+	0.0992323i
$71$	−2436.79	+	1406.88i	−0.483395	+	0.279088i	−0.721830	−	0.692070i	$-0.756699\pi$
$71$	−2436.79	+	1406.88i	−0.483395	+	0.279088i	0.238435	+	0.971158i	$0.423365\pi$
$72$	−2402.99	−	350.182i	−0.463539	−	0.0675505i
$73$	−2132.26	+	3693.19i	−0.400125	+	0.693036i	−0.993741	−	0.111712i	$-0.964367\pi$
$73$	−2132.26	+	3693.19i	−0.400125	+	0.693036i	0.593616	+	0.804749i	$0.297700\pi$
$74$	−1057.14	−	2904.48i	−0.193051	−	0.530402i
$75$	−3179.85	+	47.4213i	−0.565307	+	0.00843045i
$76$	−7493.38	+	6287.69i	−1.29733	+	1.08859i
$77$	−483.054	+	1327.18i	−0.0814730	+	0.223845i
$78$	−3016.76	+	578.447i	−0.495852	+	0.0950767i
$79$	−992.133	+	5626.67i	−0.158970	+	0.901565i	0.796096	+	0.605171i	$0.206895\pi$
$79$	−992.133	+	5626.67i	−0.158970	+	0.901565i	−0.955066	+	0.296394i	$0.904216\pi$
$80$		−	2517.31i		−	0.393330i
$81$	4765.67	−	4509.44i	0.726364	−	0.687310i
$82$	−3472.36			−0.516412
$83$	4026.67	+	710.011i	0.584508	+	0.103064i	0.458079	−	0.888911i	$-0.348538\pi$
$83$	4026.67	+	710.011i	0.584508	+	0.103064i	0.126428	+	0.991976i	$0.459649\pi$
$84$	−267.937	−	1397.37i	−0.0379729	−	0.198039i
$85$	7089.69	+	2580.44i	0.981272	+	0.357154i
$86$	4339.49	+	5171.60i	0.586735	+	0.699243i
$87$	−206.883	−	13872.6i	−0.0273329	−	1.83282i
$88$	−5268.48	+	1917.57i	−0.680330	+	0.247620i
$89$	5385.27	+	3109.19i	0.679873	+	0.392525i	0.799807	−	0.600257i	$-0.204935\pi$
$89$	5385.27	+	3109.19i	0.679873	+	0.392525i	−0.119934	+	0.992782i	$0.538268\pi$
$90$	−6367.83	−	5027.42i	−0.786152	−	0.620670i
$91$	−212.068	−	367.312i	−0.0256090	−	0.0443560i
$92$	6981.30	−	8319.99i	0.824823	−	0.982986i
$93$	−1094.63	+	6799.36i	−0.126562	+	0.786144i
$94$	168.210	+	953.968i	0.0190369	+	0.107964i
$95$	−7584.75	+	1337.40i	−0.840416	+	0.148188i
$96$	−7999.10	+	9826.89i	−0.867957	+	1.06629i
$97$	7112.63	+	5968.20i	0.755939	+	0.634308i	0.937066	−	0.349152i	$-0.113530\pi$
$97$	7112.63	+	5968.20i	0.755939	+	0.634308i	−0.181127	+	0.983460i	$0.557975\pi$
$98$	−12336.4	+	7122.44i	−1.28451	+	0.741612i
$99$	4754.15	−	14382.6i	0.485068	−	1.46746i
$100$	3698.42	−	6405.86i	0.369842	−	0.640586i
$101$	6539.12	+	17966.1i	0.641027	+	1.76121i	0.648476	+	0.761235i	$0.275407\pi$
$101$	6539.12	+	17966.1i	0.641027	+	1.76121i	−0.00744872	+	0.999972i	$0.502371\pi$
$102$	−12840.7	−	21494.1i	−1.23421	−	2.06594i
$103$	−4736.32	+	3974.24i	−0.446443	+	0.374611i	−0.838114	−	0.545495i	$-0.816342\pi$
$103$	−4736.32	+	3974.24i	−0.446443	+	0.374611i	0.391671	+	0.920105i	$0.371897\pi$
$104$	575.854	−	1582.15i	0.0532409	−	0.146278i
$105$	367.410	−	1058.29i	0.0333251	−	0.0959900i
$106$	1620.03	−	9187.63i	0.144182	−	0.817696i
$107$		−	1546.43i		−	0.135072i	−0.997717	−	0.0675358i	$-0.978486\pi$
$107$		−	1546.43i		−	0.135072i	0.997717	−	0.0675358i	$-0.0215137\pi$
$108$	3319.35	+	14894.9i	0.284580	+	1.27699i
$109$	8909.57			0.749901			0.374951	−	0.927045i	$-0.377660\pi$
$109$	8909.57			0.749901			0.374951	+	0.927045i	$0.377660\pi$
$110$	−18447.1	−	3252.73i	−1.52456	−	0.268821i
$111$	−3462.22	+	2994.24i	−0.281001	+	0.243020i
$112$	−1083.92	−	394.514i	−0.0864093	−	0.0314504i
$113$	−10815.5	−	12889.4i	−0.847012	−	1.00943i	−0.999776	−	0.0211670i	$-0.993262\pi$
$113$	−10815.5	−	12889.4i	−0.847012	−	1.00943i	0.152764	−	0.988263i	$-0.451183\pi$
$114$	22322.7	+	12447.9i	1.71766	+	0.957827i
$115$	8035.64	−	2924.73i	0.607610	−	0.221152i
$116$	27946.6	+	16135.0i	2.07689	+	1.19909i
$117$	2390.96	+	3869.97i	0.174663	+	0.282707i
$118$	6393.46	+	11073.8i	0.459168	+	0.795302i
$119$	2222.20	−	2648.31i	0.156924	−	0.187015i
$120$	4155.71	−	1583.12i	0.288591	−	0.109939i
$121$	−3530.71	−	20023.6i	−0.241152	−	1.36764i
$122$	−8676.85	+	1529.96i	−0.582965	+	0.102792i
$123$	1830.64	+	4805.44i	0.121002	+	0.317631i
$124$	−12270.7	−	10296.4i	−0.798043	−	0.669638i
$125$	13964.6	−	8062.45i	0.893732	−	0.515997i
$126$	−3162.71	+	1954.00i	−0.199213	+	0.123079i
$127$	−7193.47	+	12459.5i	−0.445996	+	0.772488i	−0.998121	−	0.0612733i	$-0.980484\pi$
$127$	−7193.47	+	12459.5i	−0.445996	+	0.772488i	0.552125	+	0.833762i	$0.313817\pi$
$128$	−5000.37	−	13738.4i	−0.305198	−	0.838526i
$129$	4869.25	−	8731.95i	0.292606	−	0.524725i
$130$	4309.16	−	3615.82i	0.254980	−	0.213954i
$131$	−1057.26	+	2904.79i	−0.0616082	+	0.169267i	−0.966678	−	0.255997i	$-0.917596\pi$
$131$	−1057.26	+	2904.79i	−0.0616082	+	0.169267i	0.905069	+	0.425264i	$0.139819\pi$
$132$	23047.1	+	26649.1i	1.32272	+	1.52945i
$133$	−612.822	+	3475.48i	−0.0346442	+	0.196477i
$134$		−	43465.9i		−	2.42069i
$135$	−3600.37	+	11463.0i	−0.197551	+	0.628970i
$136$	13723.7			0.741982
$137$	−5162.83	−	910.346i	−0.275072	−	0.0485026i	0.0344104	−	0.999408i	$-0.489045\pi$
$137$	−5162.83	−	910.346i	−0.275072	−	0.0485026i	−0.309482	+	0.950905i	$0.600156\pi$
$138$	−26808.6	−	9307.21i	−1.40772	−	0.488721i
$139$	−19913.9	−	7248.08i	−1.03069	−	0.375140i	−0.229345	−	0.973345i	$-0.573659\pi$
$139$	−19913.9	−	7248.08i	−1.03069	−	0.375140i	−0.801343	+	0.598205i	$0.795881\pi$
$140$	1674.85	+	1996.01i	0.0854514	+	0.101837i
$141$	1231.53	−	735.722i	0.0619449	−	0.0370063i
$142$	−16068.7	+	5848.54i	−0.796902	+	0.290049i
$143$	9095.60	+	5251.35i	0.444794	+	0.256802i
$144$	11746.4	+	3882.75i	0.566474	+	0.187247i
$145$	12703.8	+	22003.6i	0.604224	+	1.04655i
$146$	−16658.9	+	19853.3i	−0.781521	+	0.931381i
$147$	16360.6	+	13317.6i	0.757121	+	0.616297i
$148$	−1848.75	−	10484.8i	−0.0844025	−	0.478671i
$149$	−28666.8	+	5054.73i	−1.29124	+	0.227680i	−0.776745	−	0.629815i	$-0.783131\pi$
$149$	−28666.8	+	5054.73i	−1.29124	+	0.227680i	−0.514493	+	0.857495i	$0.672020\pi$
$150$	−19081.3	−	3071.90i	−0.848056	−	0.136529i
$151$	−27382.8	−	22976.9i	−1.20095	−	1.00771i	−0.999603	−	0.0281918i	$-0.991025\pi$
$151$	−27382.8	−	22976.9i	−1.20095	−	1.00771i	−0.201343	−	0.979521i	$-0.564530\pi$
$152$	−12132.5	+	7004.70i	−0.525125	+	0.303181i
$153$	−22976.2	+	29102.1i	−0.981513	+	1.24320i
$154$	−4291.62	+	7433.31i	−0.180959	+	0.313430i
$155$	−4313.54	−	11851.3i	−0.179544	−	0.493292i
$156$	−10579.4	+	157.770i	−0.434720	+	0.00648300i
$157$	18847.0	−	15814.5i	0.764616	−	0.641589i	−0.174708	−	0.984620i	$-0.555898\pi$
$157$	18847.0	−	15814.5i	0.764616	−	0.641589i	0.939324	+	0.343031i	$0.111454\pi$
$158$	−11875.7	+	32628.2i	−0.475713	+	1.30701i
$159$	−13569.0	+	2601.77i	−0.536725	+	0.102914i
$160$	4029.37	−	22851.7i	0.157397	−	0.892644i
$161$		−	3918.40i		−	0.151167i
$162$	33281.1	−	21959.5i	1.26814	−	0.836743i
$163$	17266.5			0.649875			0.324938	−	0.945735i	$-0.394657\pi$
$163$	17266.5			0.649875			0.324938	+	0.945735i	$0.394657\pi$
$164$	−11778.8	−	2076.92i	−0.437940	−	0.0772206i
$165$	5223.89	+	27244.1i	0.191878	+	1.00070i
$166$	23350.1	+	8498.74i	0.847369	+	0.308417i
$167$	−3705.73	−	4416.31i	−0.132874	−	0.158353i	0.695505	−	0.718522i	$-0.255181\pi$
$167$	−3705.73	−	4416.31i	−0.132874	−	0.158353i	−0.828379	+	0.560168i	$0.810736\pi$
$168$	−30.3853	−	2037.50i	−0.00107658	−	0.0721904i
$169$	23874.8	−	8689.71i	0.835922	−	0.304251i
$170$	39708.2	+	22925.5i	1.37399	+	0.793271i
$171$	5458.26	−	37455.2i	0.186664	−	1.28091i
$172$	11627.0	+	20138.5i	0.393016	+	0.680724i
$173$	12635.0	−	15057.8i	0.422166	−	0.503118i	−0.512479	−	0.858700i	$-0.671273\pi$
$173$	12635.0	−	15057.8i	0.422166	−	0.503118i	0.934645	+	0.355582i	$0.115717\pi$
$174$	13401.7	−	83245.0i	0.442650	−	2.74954i
$175$	−463.401	−	2628.08i	−0.0151315	−	0.0858148i
$176$	28129.2	−	4959.95i	0.908098	−	0.160122i
$177$	11954.5	−	14686.1i	0.381579	−	0.468770i
$178$	28949.4	+	24291.4i	0.913690	+	0.766677i
$179$	−19435.1	+	11220.9i	−0.606570	+	0.350203i	−0.771622	−	0.636082i	$-0.780554\pi$
$179$	−19435.1	+	11220.9i	−0.606570	+	0.350203i	0.165052	+	0.986285i	$0.447221\pi$
$180$	−18593.7	−	20862.7i	−0.573879	−	0.643909i
$181$	13955.7	−	24172.0i	0.425985	−	0.737828i	−0.570527	−	0.821279i	$-0.693261\pi$
$181$	13955.7	−	24172.0i	0.425985	−	0.737828i	0.996512	+	0.0834510i	$0.0265942\pi$
$182$	−881.586	−	2422.14i	−0.0266147	−	0.0731233i
$183$	6691.79	+	11201.4i	0.199821	+	0.334480i
$184$	11915.7	−	9998.43i	0.351951	−	0.295322i
$185$	2866.99	−	7876.99i	0.0837689	−	0.230153i
$186$	−13726.7	+	39538.6i	−0.396772	+	1.14287i
$187$	−14865.6	+	84306.8i	−0.425107	+	2.41090i
$188$			3336.63i			0.0944045i
$189$	4371.55	+	3346.75i	0.122380	+	0.0936915i
$190$	−46805.6			−1.29655
$191$	52758.3	+	9302.72i	1.44619	+	0.255002i	0.840980	−	0.541067i	$-0.181979\pi$
$191$	52758.3	+	9302.72i	1.44619	+	0.255002i	0.605207	+	0.796068i	$0.293090\pi$
$192$	−41608.9	+	35984.8i	−1.12871	+	0.976152i
$193$	−40023.4	−	14567.3i	−1.07448	−	0.391080i	−0.256631	−	0.966509i	$-0.582613\pi$
$193$	−40023.4	−	14567.3i	−1.07448	−	0.391080i	−0.817851	+	0.575430i	$0.804835\pi$
$194$	36270.3	+	43225.3i	0.963714	+	1.14851i
$195$	−7275.77	−	4057.23i	−0.191342	−	0.106699i
$196$	−46107.4	+	16781.7i	−1.20021	+	0.436842i
$197$	−7509.39	−	4335.55i	−0.193496	−	0.111715i	0.400122	−	0.916462i	$-0.368968\pi$
$197$	−7509.39	−	4335.55i	−0.193496	−	0.111715i	−0.593618	+	0.804747i	$0.702301\pi$
$198$	43631.3	−	81061.9i	1.11293	−	2.06769i
$199$	−31430.7	−	54439.5i	−0.793684	−	1.37470i	−0.923671	−	0.383185i	$-0.874827\pi$
$199$	−31430.7	−	54439.5i	−0.793684	−	1.37470i	0.129987	−	0.991516i	$-0.458506\pi$
$200$	6809.42	−	8115.15i	0.170235	−	0.202879i
$201$	−60152.9	+	22915.3i	−1.48890	+	0.567197i
$202$	20176.5	+	114427.i	0.494473	+	2.80430i
$203$	11465.4	−	2021.66i	0.278226	−	0.0490587i
$204$	−30701.6	−	80591.9i	−0.737735	−	1.93656i
$205$	−7213.90	−	6053.18i	−0.171657	−	0.144038i
$206$	−32540.6	+	18787.3i	−0.766816	+	0.442721i
$207$	1253.20	+	42007.5i	0.0292468	+	0.980361i
$208$	−4288.82	+	7428.46i	−0.0991314	+	0.171701i
$209$	−29889.0	−	82119.3i	−0.684256	−	1.87998i
$210$	3315.74	−	5946.07i	0.0751869	−	0.134831i
$211$	43363.7	−	36386.5i	0.974006	−	0.817288i	−0.00916815	−	0.999958i	$-0.502918\pi$
$211$	43363.7	−	36386.5i	0.974006	−	0.817288i	0.983174	+	0.182670i	$0.0584739\pi$
$212$	10990.8	−	30197.0i	0.244545	−	0.671881i
$213$	16565.3	+	19154.3i	0.365125	+	0.422190i
$214$	1631.96	−	9255.31i	0.0356354	−	0.202099i
$215$			18308.9i			0.396083i
$216$	977.389	+	21833.5i	0.0209488	+	0.467967i
$217$	−5779.04			−0.122726
$218$	53323.2	+	9402.32i	1.12203	+	0.197844i
$219$	36257.9	+	12587.7i	0.755986	+	0.262458i
$220$	−60630.2	−	22067.6i	−1.25269	−	0.455942i
$221$	−16524.9	−	19693.7i	−0.338342	−	0.403220i
$222$	−23881.0	+	14266.7i	−0.484558	+	0.289479i
$223$	−32580.8	+	11858.5i	−0.655168	+	0.238462i	−0.648149	−	0.761514i	$-0.724456\pi$
$223$	−32580.8	+	11858.5i	−0.655168	+	0.238462i	−0.00701901	+	0.999975i	$0.502234\pi$
$224$	−9208.14	−	5316.32i	−0.183517	−	0.105953i
$225$	5808.44	+	28026.3i	0.114735	+	0.553606i
$226$	−51127.8	−	88555.9i	−1.00101	−	1.73381i
$227$	−3339.70	+	3980.10i	−0.0648120	+	0.0772400i	−0.797476	−	0.603350i	$-0.793832\pi$
$227$	−3339.70	+	3980.10i	−0.0648120	+	0.0772400i	0.732664	+	0.680590i	$0.238277\pi$
$228$	68276.8	+	55577.3i	1.31342	+	1.06912i
$229$	7561.02	+	42880.7i	0.144182	+	0.817694i	0.968021	+	0.250870i	$0.0807168\pi$
$229$	7561.02	+	42880.7i	0.144182	+	0.817694i	−0.823839	+	0.566824i	$0.808172\pi$
$230$	51179.3	−	9024.29i	0.967472	−	0.170591i
$231$	12549.6	+	2020.37i	0.235183	+	0.0378622i
$232$	35403.6	+	29707.1i	0.657766	+	0.551931i
$233$	−81822.2	+	47240.1i	−1.50716	+	0.870159i	−0.507194	+	0.861832i	$0.669317\pi$
$233$	−81822.2	+	47240.1i	−1.50716	+	0.870159i	−0.999965	+	0.00832740i	$0.997349\pi$
$234$	10225.8	+	25684.7i	0.186751	+	0.469076i
$235$	−1313.54	+	2275.12i	−0.0237853	+	0.0411973i
$236$	15064.1	+	41388.3i	0.270470	+	0.743110i
$237$	51415.5	−	766.761i	0.915371	−	0.0136510i
$238$	16094.5	−	13504.9i	0.284134	−	0.238417i
$239$	6808.48	−	18706.1i	0.119194	−	0.327483i	−0.865720	−	0.500529i	$-0.833139\pi$
$239$	6808.48	−	18706.1i	0.119194	−	0.327483i	0.984914	+	0.173046i	$0.0553610\pi$
$240$	−22250.5	+	4266.40i	−0.386293	+	0.0740694i
$241$	5724.19	−	32463.5i	0.0985554	−	0.558935i	−0.895044	−	0.445977i	$-0.852856\pi$
$241$	5724.19	−	32463.5i	0.0985554	−	0.558935i	0.993600	−	0.112958i	$-0.0360326\pi$
$242$		−	123566.i		−	2.10993i
$243$	−47935.8	−	34481.0i	−0.811798	−	0.583939i
$244$	−30348.5			−0.509750
$245$	−38045.4	−	6708.43i	−0.633826	−	0.111761i
$246$	5885.03	+	30692.1i	0.0972476	+	0.507173i
$247$	24660.8	+	8975.79i	0.404215	+	0.147122i
$248$	−14746.2	−	17573.8i	−0.239759	−	0.285734i
$249$	−548.726	−	36795.0i	−0.00885028	−	0.593459i
$250$	92085.4	−	33516.3i	1.47337	−	0.536261i
$251$	36889.4	+	21298.1i	0.585537	+	0.338060i	0.763331	−	0.646008i	$-0.223563\pi$
$251$	36889.4	+	21298.1i	0.585537	+	0.338060i	−0.177794	+	0.984068i	$0.556896\pi$
$252$	−11897.2	+	4736.58i	−0.187345	+	0.0745870i
$253$	48514.8	+	84030.2i	0.757938	+	1.31279i
$254$	−56201.0	+	66977.8i	−0.871118	+	1.03816i
$255$	10792.6	−	67039.0i	0.165977	−	1.03097i
$256$	1553.65	+	8811.21i	0.0237069	+	0.134448i
$257$	−14099.5	+	2486.12i	−0.213470	+	0.0376406i	−0.279360	−	0.960186i	$-0.590122\pi$
$257$	−14099.5	+	2486.12i	−0.213470	+	0.0376406i	0.0658901	+	0.997827i	$0.479011\pi$
$258$	38357.0	−	47121.6i	0.576243	−	0.707914i
$259$	−2942.41	−	2468.97i	−0.0438635	−	0.0368058i
$260$	16780.1	−	9688.01i	0.248227	−	0.143314i
$261$	−122269.	+	25340.3i	−1.79488	+	0.371989i
$262$	−9393.07	+	16269.3i	−0.136837	+	0.237009i
$263$	32691.1	+	89818.0i	0.472626	+	1.29853i	0.915634	+	0.402012i	$0.131689\pi$
$263$	32691.1	+	89818.0i	0.472626	+	1.29853i	−0.443008	+	0.896518i	$0.646089\pi$
$264$	25878.5	+	43318.0i	0.371305	+	0.621528i
$265$	19382.0	−	16263.4i	0.275998	−	0.231590i
$266$	−7335.40	+	20153.8i	−0.103672	+	0.284836i
$267$	18355.0	−	52869.8i	0.257473	−	0.741627i
$268$	25998.3	−	147444.i	0.361972	−	2.05285i
$269$			18139.2i			0.250677i	0.992114	+	0.125338i	$0.0400017\pi$
$269$			18139.2i			0.250677i	−0.992114	+	0.125338i	$0.959998\pi$
$270$	−33644.9	+	64805.7i	−0.461522	+	0.888967i
$271$	128010.			1.74303			0.871513	−	0.490373i	$-0.163140\pi$
$271$	128010.			1.74303			0.871513	+	0.490373i	$0.163140\pi$
$272$	−68854.1	−	12140.8i	−0.930662	−	0.164101i
$273$	−2887.25	+	2496.99i	−0.0387399	+	0.0335037i
$274$	−29938.5	−	10896.7i	−0.398776	−	0.145143i
$275$	42476.6	+	50621.7i	0.561674	+	0.669377i
$276$	−85372.3	−	47606.7i	−1.12072	−	0.624956i
$277$	50103.9	−	18236.3i	0.652998	−	0.237672i	0.00578738	−	0.999983i	$-0.498158\pi$
$277$	50103.9	−	18236.3i	0.652998	−	0.237672i	0.647210	+	0.762312i	$0.275936\pi$
$278$	−111535.	−	64394.6i	−1.44318	−	0.833220i
$279$	61954.6	−	1848.28i	0.795913	−	0.0237442i
$280$	1865.84	+	3231.72i	0.0237989	+	0.0412209i
$281$	19299.9	−	23000.8i	0.244424	−	0.291293i	−0.629859	−	0.776709i	$-0.716887\pi$
$281$	19299.9	−	23000.8i	0.244424	−	0.291293i	0.874283	+	0.485416i	$0.161332\pi$
$282$	8147.02	−	3103.61i	0.102447	−	0.0390274i
$283$	449.898	+	2551.50i	0.00561747	+	0.0318583i	0.987488	−	0.157696i	$-0.0504067\pi$
$283$	449.898	+	2551.50i	0.00561747	+	0.0318583i	−0.981870	+	0.189555i	$0.939296\pi$
$284$	−58006.1	+	10228.0i	−0.719178	+	0.126811i
$285$	24676.0	+	64774.8i	0.303798	+	0.797474i
$286$	48894.8	+	41027.6i	0.597765	+	0.501584i
$287$	−3736.98	+	2157.55i	−0.0453688	+	0.0261937i
$288$	100417.	+	54049.0i	1.21066	+	0.651632i
$289$	63013.3	−	109142.i	0.754461	−	1.30676i
$290$	52810.9	+	145097.i	0.627953	+	1.72529i
$291$	40698.2	−	72983.4i	0.480606	−	0.861863i
$292$	−68384.7	+	57381.6i	−0.802035	+	0.672987i
$293$	16296.1	−	44773.2i	0.189823	−	0.521535i	−0.807874	−	0.589355i	$-0.799382\pi$
$293$	16296.1	−	44773.2i	0.189823	−	0.521535i	0.997698	+	0.0678198i	$0.0216043\pi$
$294$	83863.2	+	96970.2i	0.970235	+	1.12187i
$295$	−6021.82	+	34151.4i	−0.0691964	+	0.392432i
$296$		−	15247.7i		−	0.174029i
$297$	−135185.	−	17645.8i	−1.53255	−	0.200046i
$298$	−176903.			−1.99206
$299$	−28695.7	−	5059.83i	−0.320978	−	0.0565970i
$300$	−62889.4	−	21833.5i	−0.698772	−	0.242594i
$301$	7883.57	+	2869.38i	0.0870141	+	0.0316706i
$302$	−139636.	−	166412.i	−1.53103	−	1.82461i
$303$	147719.	−	88248.5i	1.60898	−	0.961218i
$304$	67067.6	−	24410.6i	0.725714	−	0.264138i
$305$	−20693.5	−	11947.4i	−0.222451	−	0.128432i
$306$	−168223.	+	149927.i	−1.79656	+	1.60117i
$307$	11346.8	+	19653.3i	0.120392	+	0.208525i	0.919922	−	0.392101i	$-0.128252\pi$
$307$	11346.8	+	19653.3i	0.120392	+	0.208525i	−0.799530	+	0.600626i	$0.794918\pi$
$308$	−19004.0	+	22648.1i	−0.200329	+	0.238743i
$309$	43155.5	+	35128.6i	0.451980	+	0.367912i
$310$	−13309.4	−	75481.6i	−0.138496	−	0.785449i
$311$	−33510.1	+	5908.73i	−0.346461	+	0.0610905i	−0.344171	−	0.938907i	$-0.611840\pi$
$311$	−33510.1	+	5908.73i	−0.346461	+	0.0610905i	−0.00229010	+	0.999997i	$0.500729\pi$
$312$	−14960.5	−	2408.50i	−0.153687	−	0.0247422i
$313$	−110952.	−	93099.5i	−1.13252	−	0.950295i	−0.133349	−	0.991069i	$-0.542573\pi$
$313$	−110952.	−	93099.5i	−1.13252	−	0.950295i	−0.999168	+	0.0407737i	$0.987018\pi$
$314$	129487.	−	74759.6i	1.31331	−	0.758242i
$315$	−9976.90	−	1453.91i	−0.100548	−	0.0146527i
$316$	−59800.3	+	103577.i	−0.598866	+	1.03727i
$317$	−10091.2	−	27725.3i	−0.100421	−	0.275904i	0.879301	−	0.476266i	$-0.158010\pi$
$317$	−10091.2	−	27725.3i	−0.100421	−	0.275904i	−0.979722	+	0.200363i	$0.935788\pi$
$318$	−83954.9	+	1252.02i	−0.830218	+	0.0123811i
$319$	−220845.	+	185311.i	−2.17023	+	1.82104i
$320$	34455.5	−	94665.7i	0.336480	−	0.924470i
$321$	−13668.9	+	2620.93i	−0.132655	+	0.0254358i
$322$	4135.11	−	23451.4i	0.0398819	−	0.226181i
$323$			213910.i			2.05034i
$324$	126030.	−	54583.8i	1.20056	−	0.519965i
$325$	−19844.7			−0.187878
$326$	103339.	+	18221.5i	0.972366	+	0.171454i
$327$	−15100.2	−	78751.6i	−0.141217	−	0.736485i
$328$	−16096.5	−	5858.65i	−0.149618	−	0.0544565i
$329$	773.777	+	922.151i	0.00714865	+	0.00851943i
$330$	2513.84	+	168567.i	0.0230840	+	1.54790i
$331$	−22731.9	+	8273.74i	−0.207482	+	0.0755172i	−0.443670	−	0.896190i	$-0.646324\pi$
$331$	−22731.9	+	8273.74i	−0.207482	+	0.0755172i	0.236189	+	0.971707i	$0.424102\pi$
$332$	74124.1	+	42795.6i	0.672486	+	0.388260i
$333$	32333.9	+	25527.7i	0.291588	+	0.230210i
$334$	−17518.0	−	30342.0i	−0.157033	−	0.271989i
$335$	75771.8	−	90301.4i	0.675178	−	0.804646i
$336$	−1650.05	+	10249.4i	−0.0146157	+	0.0907859i
$337$	7201.64	+	40842.5i	0.0634120	+	0.359627i	0.999959	+	0.00908453i	$0.00289173\pi$
$337$	7201.64	+	40842.5i	0.0634120	+	0.359627i	−0.936547	+	0.350543i	$0.885997\pi$
$338$	152059.	−	26812.1i	1.33100	−	0.234692i
$339$	−95598.9	+	117443.i	−0.831866	+	1.02195i
$340$	120984.	+	101518.i	1.04658	+	0.878183i
$341$	123932.	−	71552.0i	1.06579	−	0.615337i
$342$	72194.0	−	218407.i	0.617232	−	1.86730i
$343$	−17917.5	+	31034.0i	−0.152296	+	0.263784i
$344$	11390.5	+	31295.3i	0.0962559	+	0.264461i
$345$	−39470.7	−	66070.0i	−0.331617	−	0.555093i
$346$	91510.3	−	76786.2i	0.764395	−	0.641403i
$347$	36634.2	−	100652.i	0.304248	−	0.835916i	−0.689501	−	0.724284i	$-0.742170\pi$
$347$	36634.2	−	100652.i	0.304248	−	0.835916i	0.993750	−	0.111631i	$-0.0356075\pi$
$348$	95252.1	−	274365.i	0.786531	−	2.26553i
$349$	−35243.1	+	199874.i	−0.289350	+	1.64098i	0.399970	+	0.916528i	$0.369020\pi$
$349$	−35243.1	+	199874.i	−0.289350	+	1.64098i	−0.689320	+	0.724457i	$0.742091\pi$
$350$		−	16217.9i		−	0.132391i
$351$	30154.4	−	27692.6i	0.244757	−	0.224776i
$352$	263292.			2.12496
$353$	−24057.6	−	4242.00i	−0.193064	−	0.0340425i	0.0762797	−	0.997086i	$-0.475696\pi$
$353$	−24057.6	−	4242.00i	−0.193064	−	0.0340425i	−0.269344	+	0.963044i	$0.586807\pi$
$354$	87045.2	−	75279.7i	0.694606	−	0.600719i
$355$	−43578.6	−	15861.3i	−0.345794	−	0.125859i
$356$	83671.7	+	99716.0i	0.660204	+	0.786801i
$357$	−27174.6	−	15153.5i	−0.213220	−	0.118899i
$358$	−128159.	+	46646.2i	−0.999963	+	0.363957i
$359$	33774.1	+	19499.5i	0.262056	+	0.151298i	0.625272	−	0.780407i	$-0.284988\pi$
$359$	33774.1	+	19499.5i	0.262056	+	0.151298i	−0.363216	+	0.931705i	$0.618321\pi$
$360$	−21036.4	−	34049.2i	−0.162318	−	0.262725i
$361$	−44021.2	−	76247.0i	−0.337791	−	0.585071i
$362$	109033.	−	129940.i	0.832032	−	0.991577i
$363$	−171005.	+	65144.4i	−1.29776	+	0.494383i
$364$	−1541.73	−	8743.60i	−0.0116361	−	0.0659914i
$365$	−69218.5	+	12205.1i	−0.519561	+	0.0916127i
$366$	28229.0	+	74101.5i	0.210734	+	0.553178i
$367$	−107689.	−	90361.5i	−0.799536	−	0.670890i	0.148550	−	0.988905i	$-0.452539\pi$
$367$	−107689.	−	90361.5i	−0.799536	−	0.670890i	−0.948086	+	0.318015i	$0.896984\pi$
$368$	−68628.2	+	39622.5i	−0.506765	+	0.292581i
$369$	39372.5	−	24325.3i	0.289162	−	0.178651i
$370$	25471.4	−	44117.7i	0.186058	−	0.322262i
$371$	−3965.24	−	10894.4i	−0.0288086	−	0.0791509i
$372$	−70212.6	+	125911.i	−0.507375	+	0.909868i
$373$	106543.	−	89399.9i	0.765783	−	0.642568i	−0.173842	−	0.984774i	$-0.555618\pi$
$373$	106543.	−	89399.9i	0.765783	−	0.642568i	0.939625	+	0.342205i	$0.111174\pi$
$374$	−177939.	+	488883.i	−1.27212	+	3.49512i
$375$	−94931.3	−	109768.i	−0.675067	−	0.780573i
$376$	−829.801	+	4706.04i	−0.00586946	+	0.0332874i
$377$		−	86575.5i		−	0.609133i
$378$	22631.6	+	24643.4i	0.158391	+	0.172472i
$379$	−205238.			−1.42883			−0.714414	−	0.699723i	$-0.753307\pi$
$379$	−205238.			−1.42883			−0.714414	+	0.699723i	$0.753307\pi$
$380$	−158772.	−	27995.9i	−1.09953	−	0.193877i
$381$	122321.	+	42466.4i	0.842655	+	0.292547i
$382$	305938.	+	111352.i	2.09656	+	0.763084i
$383$	118294.	+	140977.i	0.806428	+	0.961064i	0.999799	−	0.0200622i	$-0.00638642\pi$
$383$	118294.	+	140977.i	0.806428	+	0.961064i	−0.193371	+	0.981126i	$0.561942\pi$
$384$	−112959.	+	67482.4i	−0.766051	+	0.457644i
$385$	−21874.1	+	7961.50i	−0.147573	+	0.0537123i
$386$	−224165.	−	129421.i	−1.50450	−	0.868624i
$387$	−85434.1	−	28240.1i	−0.570439	−	0.188558i
$388$	97180.7	+	168322.i	0.645530	+	1.11809i
$389$	−82339.4	+	98128.2i	−0.544137	+	0.648477i	−0.966110	−	0.258131i	$-0.916893\pi$
$389$	−82339.4	+	98128.2i	−0.544137	+	0.648477i	0.421973	+	0.906608i	$0.361338\pi$
$390$	−39263.4	−	31960.4i	−0.258142	−	0.210128i
$391$	−41242.6	−	233899.i	−0.269770	−	1.52994i
$392$	−69204.1	+	12202.6i	−0.450360	+	0.0794106i
$393$	27467.3	+	4421.97i	0.177840	+	0.0286306i
$394$	−40367.9	−	33872.7i	−0.260042	−	0.218201i
$395$	−81551.2	+	47083.6i	−0.522680	+	0.301769i
$396$	196490.	−	248878.i	1.25300	−	1.58707i
$397$	−40759.2	+	70596.9i	−0.258609	+	0.447925i	−0.965870	−	0.259029i	$-0.916598\pi$
$397$	−40759.2	+	70596.9i	−0.258609	+	0.447925i	0.707260	+	0.706953i	$0.249931\pi$
$398$	−130660.	−	358986.i	−0.824854	−	2.26627i
$399$	31758.4	−	473.614i	0.199486	−	0.00297494i
$400$	−41343.2	+	34691.0i	−0.258395	+	0.216819i
$401$	20232.1	−	55587.3i	0.125821	−	0.345690i	−0.860749	−	0.509030i	$-0.830004\pi$
$401$	20232.1	−	55587.3i	0.125821	−	0.345690i	0.986570	+	0.163339i	$0.0522266\pi$
$402$	−384194.	+	73667.0i	−2.37738	+	0.455849i
$403$	−7462.48	+	42321.8i	−0.0459487	+	0.260588i
$404$			400222.i			2.45210i
$405$	107423.	+	12395.9i	0.654919	+	0.0755732i
$406$	70753.2			0.429234
$407$	93669.0	+	16516.4i	0.565467	+	0.0997070i
$408$	−23259.2	−	121303.i	−0.139725	−	0.728707i
$409$	273913.	+	99696.1i	1.63744	+	0.595980i	0.986589	−	0.163225i	$-0.0521897\pi$
$409$	273913.	+	99696.1i	1.63744	+	0.595980i	0.650852	+	0.759205i	$0.274412\pi$
$410$	−36786.8	−	43840.8i	−0.218839	−	0.260802i
$411$	703.553	+	47177.0i	0.00416498	+	0.279284i
$412$	−121620.	+	44266.2i	−0.716494	+	0.260782i
$413$	13761.4	+	7945.14i	0.0806793	+	0.0465802i
$414$	−36830.4	+	252735.i	−0.214885	+	1.47457i
$415$	33695.0	+	58361.4i	0.195645	+	0.338867i
$416$	−50823.6	+	60569.2i	−0.293683	+	0.349998i
$417$	−30315.0	+	188303.i	−0.174335	+	1.08289i
$418$	−92222.7	−	523021.i	−0.527819	−	2.99341i
$419$	121024.	−	21339.9i	0.689358	−	0.121552i	0.182014	−	0.983296i	$-0.441738\pi$
$419$	121024.	−	21339.9i	0.689358	−	0.121552i	0.507344	+	0.861744i	$0.330627\pi$
$420$	14804.1	−	18186.8i	0.0839234	−	0.103100i
$421$	−58336.5	−	48950.2i	−0.329137	−	0.276179i	0.463211	−	0.886248i	$-0.346697\pi$
$421$	−58336.5	−	48950.2i	−0.329137	−	0.276179i	−0.792348	+	0.610069i	$0.791142\pi$
$422$	297928.	−	172009.i	1.67296	−	0.965886i
$423$	−8590.25	−	9638.52i	−0.0480093	−	0.0538678i
$424$	23011.4	−	39857.0i	0.128001	−	0.221704i
$425$	−55323.0	−	151999.i	−0.306287	−	0.841516i
$426$	78928.8	+	132119.i	0.434927	+	0.728025i
$427$	−8387.46	+	7037.92i	−0.0460018	+	0.0386001i
$428$	11071.8	−	30419.4i	0.0604407	−	0.166059i
$429$	31001.1	−	89295.9i	0.168447	−	0.485196i
$430$	−19321.5	+	109578.i	−0.104497	+	0.592633i
$431$		−	188543.i		−	1.01497i	−0.861659	−	0.507487i	$-0.830575\pi$
$431$		−	188543.i		−	1.01497i	0.861659	−	0.507487i	$-0.169425\pi$
$432$	14411.5	−	110407.i	0.0772221	−	0.591600i
$433$	4635.55			0.0247244			0.0123622	−	0.999924i	$-0.496065\pi$
$433$	4635.55			0.0247244			0.0123622	+	0.999924i	$0.496065\pi$
$434$	−34587.2	−	6098.66i	−0.183627	−	0.0323783i
$435$	172959.	−	149581.i	0.914039	−	0.790492i
$436$	175258.	+	63788.5i	0.921942	+	0.335560i
$437$	155845.	+	185729.i	0.816074	+	0.972559i
$438$	203717.	+	113600.i	1.06189	+	0.592147i
$439$	45262.1	−	16474.0i	0.234858	−	0.0854813i	−0.221910	−	0.975067i	$-0.571229\pi$
$439$	45262.1	−	16474.0i	0.234858	−	0.0854813i	0.456768	+	0.889586i	$0.349007\pi$
$440$	−80025.7	−	46202.9i	−0.413356	−	0.238651i
$441$	89985.3	−	167182.i	0.462694	−	0.859633i
$442$	−78117.9	−	135304.i	−0.399858	−	0.692574i
$443$	8365.55	−	9969.67i	0.0426272	−	0.0508011i	−0.744310	−	0.667835i	$-0.767221\pi$
$443$	8365.55	−	9969.67i	0.0426272	−	0.0508011i	0.786937	+	0.617034i	$0.211666\pi$
$444$	−89541.6	+	34111.0i	−0.454212	+	0.173033i
$445$	17797.0	+	100932.i	0.0898725	+	0.509692i
$446$	−207508.	+	36589.3i	−1.04320	+	0.183944i
$447$	93263.7	+	244818.i	0.466764	+	1.22526i
$448$	−35361.9	−	29672.1i	−0.176189	−	0.147840i
$449$	128969.	−	74460.5i	0.639726	−	0.369346i	−0.144783	−	0.989463i	$-0.546248\pi$
$449$	128969.	−	74460.5i	0.639726	−	0.369346i	0.784509	+	0.620118i	$0.212915\pi$
$450$	5186.87	+	173865.i	0.0256142	+	0.858593i
$451$	53426.4	−	92537.3i	0.262666	−	0.454950i
$452$	−120466.	−	330978.i	−0.589641	−	1.62003i
$453$	−156683.	+	280977.i	−0.763529	+	1.36923i
$454$	−24188.1	+	20296.2i	−0.117352	+	0.0984699i
$455$	2390.87	−	6568.87i	0.0115487	−	0.0317298i
$456$	82476.8	+	95367.2i	0.396645	+	0.458637i
$457$	3815.40	−	21638.2i	0.0182687	−	0.103607i	−0.974310	−	0.225211i	$-0.927693\pi$
$457$	3815.40	−	21638.2i	0.0182687	−	0.103607i	0.992579	+	0.121604i	$0.0388039\pi$
$458$			264617.i			1.26150i
$459$	296174.	+	153764.i	1.40579	+	0.729841i
$460$	179006.			0.845966
$461$	136057.	+	23990.6i	0.640206	+	0.112886i	0.484322	−	0.874890i	$-0.339066\pi$
$461$	136057.	+	23990.6i	0.640206	+	0.112886i	0.155884	+	0.987775i	$0.450177\pi$
$462$	72976.4	+	25335.4i	0.341900	+	0.118698i
$463$	−192898.	−	70209.0i	−0.899840	−	0.327515i	−0.149651	−	0.988739i	$-0.547815\pi$
$463$	−192898.	−	70209.0i	−0.899840	−	0.327515i	−0.750189	+	0.661224i	$0.770037\pi$
$464$	−151345.	−	180366.i	−0.702963	−	0.837759i
$465$	−97443.1	+	58213.2i	−0.450656	+	0.269225i
$466$	−539553.	+	196381.i	−2.48463	+	0.904333i
$467$	−186474.	−	107661.i	−0.855035	−	0.493655i	0.00731154	−	0.999973i	$-0.497673\pi$
$467$	−186474.	−	107661.i	−0.855035	−	0.493655i	−0.862346	+	0.506319i	$0.831006\pi$
$468$	19324.7	+	93243.3i	0.0882308	+	0.425722i
$469$	−27007.5	−	46778.4i	−0.122783	−	0.212667i
$470$	−10262.4	+	12230.3i	−0.0464573	+	0.0553656i
$471$	−171727.	−	139786.i	−0.774098	−	0.630116i
$472$	10953.6	+	62121.0i	0.0491670	+	0.278840i
$473$	−204590.	+	36074.7i	−0.914454	+	0.161243i
$474$	308527.	+	49670.0i	1.37321	+	0.221074i
$475$	126490.	+	106138.i	0.560621	+	0.470417i
$476$	62672.9	−	36184.2i	0.276609	−	0.159700i
$477$	45994.0	+	115526.i	0.202145	+	0.507743i
$478$	60489.0	−	104770.i	0.264741	−	0.458544i
$479$	72574.2	+	199396.i	0.316309	+	0.869051i	0.991347	+	0.131268i	$0.0419048\pi$
$479$	72574.2	+	199396.i	0.316309	+	0.869051i	−0.675038	+	0.737783i	$0.735873\pi$
$480$	−208815.	+	3114.06i	−0.906314	+	0.0135159i
$481$	−21880.6	+	18360.0i	−0.0945735	+	0.0793566i
$482$	68517.9	−	188251.i	0.294924	−	0.810296i
$483$	−34634.7	+	6641.00i	−0.148462	+	0.0284668i
$484$	73908.7	−	419157.i	0.315504	−	1.78931i
$485$			153030.i			0.650568i
$486$	−250505.	−	256953.i	−1.06058	−	1.08788i
$487$	−5941.97			−0.0250537			−0.0125269	−	0.999922i	$-0.503988\pi$
$487$	−5941.97			−0.0250537			−0.0125269	+	0.999922i	$0.503988\pi$
$488$	−42803.9	−	7547.49i	−0.179740	−	0.0316930i
$489$	−29263.7	−	152619.i	−0.122380	−	0.638248i
$490$	−220620.	−	80299.1i	−0.918867	−	0.334440i
$491$	−240755.	−	286921.i	−0.998649	−	1.19014i	−0.981729	−	0.190287i	$-0.939058\pi$
$491$	−240755.	−	286921.i	−0.998649	−	1.19014i	−0.0169206	−	0.999857i	$-0.505386\pi$
$492$	1605.13	+	107633.i	0.00663103	+	0.444646i
$493$	663118.	−	241355.i	2.72833	−	0.993032i
$494$	138121.	+	79744.2i	0.565986	+	0.326772i
$495$	231956.	−	92347.7i	0.946663	−	0.376891i
$496$	58437.1	+	101216.i	0.237534	+	0.411421i
$497$	−13659.3	+	16278.6i	−0.0552989	+	0.0659027i
$498$	35545.9	−	220795.i	0.143328	−	0.890288i
$499$	−13156.0	−	74611.3i	−0.0528351	−	0.299642i	0.946927	−	0.321448i	$-0.104170\pi$
$499$	−13156.0	−	74611.3i	−0.0528351	−	0.299642i	−0.999762	+	0.0218057i	$0.993058\pi$
$500$	332416.	−	58614.0i	1.32967	−	0.234456i
$501$	−32755.1	+	40239.7i	−0.130498	+	0.160317i
$502$	198305.	+	166397.i	0.786911	+	0.660296i
$503$	88820.2	−	51280.3i	0.351055	−	0.202682i	−0.314095	−	0.949392i	$-0.601701\pi$
$503$	88820.2	−	51280.3i	0.351055	−	0.202682i	0.665150	+	0.746710i	$0.268368\pi$
$504$	−17957.9	+	3721.78i	−0.0706961	+	0.0146518i
$505$	−157557.	+	272896.i	−0.617809	+	1.07008i
$506$	201681.	+	554113.i	0.787704	+	2.16420i
$507$	−117272.	−	196301.i	−0.456223	−	0.763672i
$508$	−230705.	+	193584.i	−0.893983	+	0.750141i
$509$	−117615.	+	323146.i	−0.453972	+	1.24728i	0.475934	+	0.879481i	$0.342110\pi$
$509$	−117615.	+	323146.i	−0.453972	+	1.24728i	−0.929906	+	0.367797i	$0.880112\pi$
$510$	135340.	−	389834.i	0.520338	−	1.49879i
$511$	−5592.62	+	31717.3i	−0.0214177	+	0.121466i
$512$			288296.i			1.09976i
$513$	−340316.	+	15234.5i	−1.29315	+	0.0578886i
$514$	−87008.2			−0.329332
$515$	−100355.	−	17695.3i	−0.378376	−	0.0667179i
$516$	158298.	−	136902.i	0.594534	−	0.514174i
$517$	−28011.1	−	10195.2i	−0.104797	−	0.0381430i
$518$	−15004.6	−	17881.8i	−0.0559197	−	0.0666425i
$519$	−154510.	−	86160.2i	−0.573616	−	0.319869i
$520$	26076.3	−	9491.00i	0.0964361	−	0.0350999i
$521$	2025.59	+	1169.47i	0.00746235	+	0.00430839i	0.503727	−	0.863863i	$-0.331962\pi$
$521$	2025.59	+	1169.47i	0.00746235	+	0.00430839i	−0.496264	+	0.868172i	$0.665295\pi$
$522$	−758514.	+	22628.5i	−2.78370	+	0.0830454i
$523$	96052.9	+	166369.i	0.351162	+	0.608230i	0.986453	−	0.164042i	$-0.0524534\pi$
$523$	96052.9	+	166369.i	0.351162	+	0.608230i	−0.635291	+	0.772272i	$0.719120\pi$
$524$	−41594.0	+	49569.8i	−0.151485	+	0.180532i
$525$	−22444.1	+	8550.12i	−0.0814300	+	0.0310208i
$526$	100869.	+	572054.i	0.364573	+	2.06760i
$527$	−344965.	+	60826.6i	−1.24209	+	0.219014i
$528$	−91515.0	−	240228.i	−0.328265	−	0.861698i
$529$	8153.95	+	6841.97i	0.0291378	+	0.0244495i
$530$	133163.	−	76881.5i	0.474057	−	0.273697i
$531$	−150071.	−	80775.2i	−0.532240	−	0.286477i
$532$	−36937.5	+	63977.7i	−0.130510	+	0.226050i
$533$	10974.9	+	30153.2i	0.0386318	+	0.106140i
$534$	165647.	−	297052.i	0.580900	−	1.04172i
$535$	19524.7	−	16383.2i	0.0682146	−	0.0572389i
$536$	73336.8	−	201491.i	0.255266	−	0.701336i
$537$	132120.	+	152769.i	0.458163	+	0.529769i
$538$	−19142.4	+	108562.i	−0.0661352	+	0.375071i
$539$		−	438350.i		−	1.50884i
$540$	−152892.	+	199708.i	−0.524320	+	0.684869i
$541$	−97098.5			−0.331755			−0.165878	−	0.986146i	$-0.553046\pi$
$541$	−97098.5			−0.331755			−0.165878	+	0.986146i	$0.553046\pi$
$542$	766129.	+	135089.i	2.60797	+	0.459856i
$543$	−237308.	−	82386.9i	−0.804846	−	0.279421i
$544$	−605612.	−	220425.i	−2.04643	−	0.744839i
$545$	94389.6	+	112489.i	0.317783	+	0.378720i
$546$	−19915.1	+	11897.4i	−0.0668032	+	0.0399087i
$547$	187642.	−	68296.1i	0.627127	−	0.228256i	−0.00885339	−	0.999961i	$-0.502818\pi$
$547$	187642.	−	68296.1i	0.627127	−	0.228256i	0.635980	+	0.771705i	$0.280596\pi$
$548$	−95038.7	−	54870.6i	−0.316475	−	0.182717i
$549$	87667.5	−	78133.0i	0.290867	−	0.259233i
$550$	200799.	+	347793.i	0.663797	+	1.14973i
$551$	−463043.	+	551833.i	−1.52517	+	1.81763i
$552$	−108571.	−	88376.8i	−0.356316	−	0.290041i
$553$	7492.79	+	42493.7i	0.0245015	+	0.138955i
$554$	319113.	−	56268.3i	1.03974	−	0.183334i
$555$	−74483.6	−	11991.2i	−0.241810	−	0.0389292i
$556$	−339828.	−	285149.i	−1.09928	−	0.922408i
$557$	136110.	−	78583.1i	0.438712	−	0.253290i	−0.264339	−	0.964430i	$-0.585154\pi$
$557$	136110.	−	78583.1i	0.438712	−	0.253290i	0.703051	+	0.711139i	$0.251821\pi$
$558$	372745.	+	54319.3i	1.19714	+	0.174456i
$559$	31193.5	−	54028.7i	0.0998253	−	0.172902i
$560$	−6502.23	−	17864.7i	−0.0207342	−	0.0569666i
$561$	770381.	−	11488.7i	2.44782	−	0.0365045i
$562$	139782.	−	117291.i	0.442566	−	0.371357i
$563$	164752.	−	452653.i	0.519773	−	1.42807i	−0.350997	−	0.936376i	$-0.614157\pi$
$563$	164752.	−	452653.i	0.519773	−	1.42807i	0.870771	−	0.491689i	$-0.163620\pi$
$564$	29492.4	−	5655.00i	0.0927155	−	0.0177777i
$565$	48155.9	−	273105.i	0.150852	−	0.855526i
$566$			15745.3i			0.0491495i
$567$	22172.9	−	44312.2i	0.0689694	−	0.137834i
$568$	−84356.3			−0.261469
$569$	−431178.	−	76028.3i	−1.33178	−	0.234828i	−0.537953	−	0.842975i	$-0.680802\pi$
$569$	−431178.	−	76028.3i	−1.33178	−	0.234828i	−0.793825	+	0.608146i	$0.791913\pi$
$570$	79327.2	+	413714.i	0.244159	+	1.27336i
$571$	86789.3	+	31588.7i	0.266191	+	0.0968857i	0.471668	−	0.881776i	$-0.343652\pi$
$571$	86789.3	+	31588.7i	0.266191	+	0.0968857i	−0.205476	+	0.978662i	$0.565874\pi$
$572$	141320.	+	168418.i	0.431927	+	0.514750i
$573$	−7189.52	−	482096.i	−0.0218973	−	1.46833i
$574$	−24642.5	+	8969.12i	−0.0747929	+	0.0272224i
$575$	−158774.	−	91668.0i	−0.480223	−	0.277257i
$576$	388589.	+	306793.i	1.17124	+	0.924698i
$577$	−121423.	−	210311.i	−0.364711	−	0.631699i	0.624018	−	0.781410i	$-0.285499\pi$
$577$	−121423.	−	210311.i	−0.364711	−	0.631699i	−0.988730	+	0.149711i	$0.952166\pi$
$578$	492309.	−	586711.i	1.47361	−	1.75618i
$579$	−60927.7	+	378455.i	−0.181743	+	1.12890i
$580$	92356.6	+	523780.i	0.274544	+	1.55702i
$581$	30410.3	−	5362.15i	0.0900882	−	0.0158850i
$582$	320596.	−	393852.i	0.946481	−	1.16275i
$583$	219922.	+	184536.i	0.647039	+	0.542930i
$584$	−110721.	+	63925.0i	−0.324643	+	0.187433i
$585$	−23530.6	+	71186.7i	−0.0687578	+	0.208011i
$586$	144781.	−	250768.i	0.421614	−	0.730258i
$587$	188159.	+	516964.i	0.546072	+	1.50032i	0.838971	+	0.544177i	$0.183158\pi$
$587$	188159.	+	516964.i	0.546072	+	1.50032i	−0.292899	+	0.956144i	$0.594620\pi$
$588$	226477.	+	379100.i	0.655043	+	1.09648i
$589$	273921.	−	229847.i	0.789579	−	0.662535i
$590$	−72080.4	+	198039.i	−0.207068	+	0.568915i
$591$	−25594.7	+	73723.3i	−0.0732783	+	0.211072i
$592$	−13489.1	+	76500.3i	−0.0384892	+	0.218283i
$593$		−	265204.i		−	0.754172i	−0.926178	−	0.377086i	$-0.876926\pi$
$593$		−	265204.i		−	0.754172i	0.926178	−	0.377086i	$-0.123074\pi$
$594$	−790452.	−	248271.i	−2.24028	−	0.703643i
$595$	56979.0			0.160946
$596$	−600085.	−	105811.i	−1.68935	−	0.297878i
$597$	−427921.	+	370081.i	−1.20064	+	1.03836i
$598$	−166402.	−	60565.5i	−0.465326	−	0.169365i
$599$	96884.8	+	115463.i	0.270024	+	0.321802i	0.883968	−	0.467548i	$-0.154862\pi$
$599$	96884.8	+	115463.i	0.270024	+	0.321802i	−0.613944	+	0.789350i	$0.710418\pi$
$600$	−83270.4	−	46434.6i	−0.231307	−	0.128985i
$601$	−292365.	+	106412.i	−0.809424	+	0.294606i	−0.713386	−	0.700772i	$-0.752839\pi$
$601$	−292365.	+	106412.i	−0.809424	+	0.294606i	−0.0960378	+	0.995378i	$0.530617\pi$
$602$	44154.6	+	25492.7i	0.121838	+	0.0703432i
$603$	304497.	+	492853.i	0.837429	+	1.35545i
$604$	−374134.	−	648019.i	−1.02554	−	1.77629i
$605$	215406.	−	256711.i	0.588502	−	0.701349i
$606$	977219.	−	372272.i	2.66101	−	1.01371i
$607$	34423.9	+	195228.i	0.0934293	+	0.529864i	0.995217	+	0.0976852i	$0.0311438\pi$
$607$	34423.9	+	195228.i	0.0934293	+	0.529864i	−0.901788	+	0.432178i	$0.857745\pi$
$608$	647901.	−	114242.i	1.75268	−	0.309044i
$609$	−37301.2	−	97916.1i	−0.100575	−	0.264009i
$610$	−111241.	−	93342.2i	−0.298954	−	0.250852i
$611$	7752.39	−	4475.85i	0.0207660	−	0.0119893i
$612$	−660317.	+	407960.i	−1.76299	+	1.08922i
$613$	−312175.	+	540703.i	−0.830763	+	1.43892i	0.0666714	+	0.997775i	$0.478762\pi$
$613$	−312175.	+	540703.i	−0.830763	+	1.43892i	−0.897434	+	0.441148i	$0.854571\pi$
$614$	47169.8	+	129598.i	0.125120	+	0.343765i
$615$	−41277.7	+	74022.6i	−0.109135	+	0.195711i
$616$	−32436.0	+	27217.0i	−0.0854802	+	0.0717264i
$617$	57927.0	−	159153.i	0.152164	−	0.418066i	−0.840066	−	0.542484i	$-0.817484\pi$
$617$	57927.0	−	159153.i	0.152164	−	0.418066i	0.992230	+	0.124418i	$0.0397062\pi$
$618$	221211.	+	255785.i	0.579203	+	0.669726i
$619$	25857.6	−	146646.i	0.0674850	−	0.382726i	−0.932294	−	0.361701i	$-0.882196\pi$
$619$	25857.6	−	146646.i	0.0674850	−	0.382726i	0.999779	−	0.0210249i	$-0.00669292\pi$
$620$		−	264007.i		−	0.686803i
$621$	369179.	−	82272.3i	0.957314	−	0.213339i
$622$	−206791.			−0.534504
$623$	46249.0	+	8154.95i	0.119159	+	0.0210109i
$624$	72928.8	+	25318.9i	0.187297	+	0.0650243i
$625$	42207.9	+	15362.4i	0.108052	+	0.0393278i
$626$	−565790.	−	674282.i	−1.44380	−	1.72065i
$627$	−675195.	+	403366.i	−1.71749	+	1.02604i
$628$	483959.	−	176147.i	1.22713	−	0.446638i
$629$	−201626.	−	116409.i	−0.509619	−	0.294229i
$630$	−58176.8	−	19230.2i	−0.146578	−	0.0484511i
$631$	−298176.	−	516456.i	−0.748883	−	1.29710i	−0.948359	−	0.317200i	$-0.897257\pi$
$631$	−298176.	−	516456.i	−0.748883	−	1.29710i	0.199476	−	0.979903i	$-0.436076\pi$
$632$	−110102.	+	131215.i	−0.275653	+	0.328510i
$633$	−395113.	−	321622.i	−0.986085	−	0.802674i
$634$	−31136.4	−	176583.i	−0.0774622	−	0.439310i
$635$	−233518.	+	41175.5i	−0.579125	+	0.102115i
$636$	−285538.	−	45969.0i	−0.705911	−	0.113645i
$637$	100841.	+	84615.4i	0.248518	+	0.208531i
$638$	−1.51730e6	+	876015.i	−3.72761	+	2.15214i
$639$	141230.	−	178884.i	0.345879	−	0.438096i
$640$	120482.	−	208680.i	0.294144	−	0.509473i
$641$	−50133.6	−	137741.i	−0.122015	−	0.335233i	0.863615	−	0.504152i	$-0.168195\pi$
$641$	−50133.6	−	137741.i	−0.122015	−	0.335233i	−0.985630	+	0.168918i	$0.945973\pi$
$642$	−84573.3	+	1261.25i	−0.205193	+	0.00306006i
$643$	121340.	−	101816.i	0.293482	−	0.246261i	−0.484143	−	0.874989i	$-0.660869\pi$
$643$	121340.	−	101816.i	0.293482	−	0.246261i	0.777625	+	0.628728i	$0.216424\pi$
$644$	28054.0	−	77077.7i	0.0676430	−	0.185848i
$645$	161832.	−	31030.4i	0.388997	−	0.0745878i
$646$	−225741.	+	1.28024e6i	−0.540934	+	3.06779i
$647$			428602.i			1.02387i	0.859023	+	0.511936i	$0.171072\pi$
$647$			428602.i			1.02387i	−0.859023	+	0.511936i	$0.828928\pi$
$648$	191329.	−	45643.0i	0.455649	−	0.108699i
$649$	−393484.			−0.934196
$650$	−118769.	−	20942.2i	−0.281110	−	0.0495673i
$651$	9794.46	+	51080.8i	0.0231110	+	0.120530i
$652$	339645.	+	123621.i	0.798969	+	0.290801i
$653$	472730.	+	563377.i	1.10863	+	1.32121i	0.942159	+	0.335167i	$0.108793\pi$
$653$	472730.	+	563377.i	1.10863	+	1.32121i	0.166470	+	0.986046i	$0.446763\pi$
$654$	−7266.50	−	487258.i	−0.0169891	−	1.13921i
$655$	−47875.7	+	17425.3i	−0.111592	+	0.0406161i
$656$	75576.0	+	43633.8i	0.175621	+	0.101395i
$657$	49812.1	−	341816.i	0.115400	−	0.791885i
$658$	3657.85	+	6335.59i	0.00844840	+	0.0146331i
$659$	318200.	−	379216.i	0.732706	−	0.873205i	−0.263093	−	0.964771i	$-0.584743\pi$
$659$	318200.	−	379216.i	0.732706	−	0.873205i	0.995799	+	0.0915652i	$0.0291870\pi$
$660$	−92297.6	+	573310.i	−0.211886	+	1.31614i
$661$	102468.	+	581125.i	0.234523	+	1.33005i	0.843616	+	0.536947i	$0.180423\pi$
$661$	102468.	+	581125.i	0.234523	+	1.33005i	−0.609093	+	0.793099i	$0.708466\pi$
$662$	−144780.	+	25528.7i	−0.330365	+	0.0582522i
$663$	−146065.	+	179441.i	−0.332291	+	0.408220i
$664$	93902.8	+	78793.8i	0.212982	+	0.178713i
$665$	−50372.6	+	29082.6i	−0.113907	+	0.0657643i
$666$	166577.	+	186904.i	0.375548	+	0.421376i
$667$	399916.	−	692675.i	0.898912	−	1.55696i
$668$	−41275.4	−	113403.i	−0.0924993	−	0.254140i
$669$	160035.	+	267883.i	0.357572	+	0.598540i
$670$	548785.	−	460485.i	1.22251	−	1.02581i
$671$	92730.8	−	254776.i	0.205958	−	0.565865i
$672$	−31384.7	+	90400.8i	−0.0694991	+	0.200186i
$673$	148961.	−	844798.i	0.328883	−	1.86519i	−0.151968	−	0.988385i	$-0.548561\pi$
$673$	148961.	−	844798.i	0.328883	−	1.86519i	0.480851	−	0.876802i	$-0.340328\pi$
$674$			252040.i			0.554816i
$675$	237879.	−	98840.3i	0.522095	−	0.216934i
$676$	531848.			1.16384
$677$	−264276.	−	46598.9i	−0.576607	−	0.101671i	−0.122263	−	0.992498i	$-0.539015\pi$
$677$	−264276.	−	46598.9i	−0.576607	−	0.101671i	−0.454344	+	0.890826i	$0.650126\pi$
$678$	−696092.	+	602004.i	−1.51428	+	1.30960i
$679$	65892.5	+	23982.9i	0.142921	+	0.0520190i
$680$	145391.	+	173271.i	0.314427	+	0.374720i
$681$	40840.2	+	22774.0i	0.0880630	+	0.0491071i
$682$	817232.	−	297448.i	1.75702	−	0.639503i
$683$	−165671.	−	95650.1i	−0.355144	−	0.205043i	0.311804	−	0.950146i	$-0.399067\pi$
$683$	−165671.	−	95650.1i	−0.355144	−	0.205043i	−0.666949	+	0.745104i	$0.732400\pi$
$684$	375530.	−	697691.i	0.802661	−	1.49125i
$685$	−43202.2	−	74828.4i	−0.0920714	−	0.159472i
$686$	−139985.	+	166828.i	−0.297464	+	0.354504i
$687$	366207.	−	139507.i	0.775913	−	0.295585i
$688$	−29462.5	−	167090.i	−0.0622434	−	0.353000i
$689$	−84903.7	+	14970.8i	−0.178850	+	0.0315360i
$690$	−166505.	−	437078.i	−0.349728	−	0.918039i
$691$	201952.	+	169458.i	0.422953	+	0.354900i	0.829285	−	0.558826i	$-0.188748\pi$
$691$	201952.	+	169458.i	0.422953	+	0.354900i	−0.406332	+	0.913725i	$0.633192\pi$
$692$	356346.	−	205737.i	0.744150	−	0.429635i
$693$	−3411.37	−	114350.i	−0.00710333	−	0.238105i
$694$	325472.	−	563734.i	0.675763	−	1.17046i
$695$	−119460.	−	328214.i	−0.247316	−	0.679496i
$696$	202578.	−	363280.i	0.418190	−	0.749934i
$697$	−200360.	+	168122.i	−0.412426	+	0.346067i
$698$	−421855.	+	1.15904e6i	−0.865870	+	2.37896i
$699$	556228.	+	643161.i	1.13841	+	1.31633i
$700$	9700.43	−	55013.9i	0.0197968	−	0.112273i
$701$		−	330892.i		−	0.673364i	−0.941618	−	0.336682i	$-0.890695\pi$
$701$		−	330892.i		−	0.673364i	0.941618	−	0.336682i	$-0.109305\pi$
$702$	209696.	−	133916.i	0.425516	−	0.271744i
$703$	237665.			0.480899
$704$	1.12571e6	+	198494.i	2.27134	+	0.400499i
$705$	22336.0	+	7754.45i	0.0449394	+	0.0156017i
$706$	−139506.	−	50776.2i	−0.279888	−	0.101871i
$707$	92813.0	+	110610.i	0.185682	+	0.221287i
$708$	340299.	−	203297.i	0.678882	−	0.405569i
$709$	−854464.	+	311000.i	−1.69981	+	0.618682i	−0.995804	−	0.0915085i	$-0.970831\pi$
$709$	−854464.	+	311000.i	−1.69981	+	0.618682i	−0.704010	+	0.710190i	$0.748609\pi$
$710$	−244077.	−	140918.i	−0.484183	−	0.279543i
$711$	−93917.5	−	453161.i	−0.185784	−	0.896423i
$712$	93213.0	+	161450.i	0.183872	+	0.318476i
$713$	−255202.	+	304138.i	−0.502002	+	0.598263i
$714$	−146647.	−	119371.i	−0.287658	−	0.234153i
$715$	30058.7	+	170472.i	0.0587975	+	0.333457i
$716$	−462638.	+	81575.6i	−0.902434	+	0.159123i
$717$	−176882.	−	28476.4i	−0.344070	−	0.0553920i
$718$	181558.	+	152345.i	0.352181	+	0.295515i
$719$	−534889.	+	308818.i	−1.03468	+	0.597372i	−0.918322	−	0.395835i	$-0.870455\pi$
$719$	−534889.	+	308818.i	−1.03468	+	0.597372i	−0.116358	+	0.993207i	$0.537122\pi$
$720$	75421.2	+	189441.i	0.145488	+	0.365433i
$721$	−23347.0	+	40438.2i	−0.0449118	+	0.0777895i
$722$	−183000.	−	502789.i	−0.351057	−	0.964520i
$723$	−296646.	+	4423.89i	−0.567495	+	0.00846307i
$724$	447579.	−	375563.i	0.853871	−	0.716483i
$725$	186307.	−	511873.i	0.354448	−	0.973837i
$726$	−1.09220e6	+	209423.i	−2.07218	+	0.397329i
$727$	−113322.	+	642684.i	−0.214411	+	1.21599i	0.667514	+	0.744597i	$0.267358\pi$
$727$	−113322.	+	642684.i	−0.214411	+	1.21599i	−0.881926	+	0.471389i	$0.843753\pi$
$728$		−	12715.5i		−	0.0239923i
$729$	−223534.	+	482143.i	−0.420619	+	0.907238i
$730$	−427149.			−0.801555
$731$	500790.	+	88302.9i	0.937176	+	0.165249i
$732$	51435.3	+	268249.i	0.0959928	+	0.500630i
$733$	−853703.	−	310723.i	−1.58891	−	0.578316i	−0.611792	−	0.791019i	$-0.709551\pi$
$733$	−853703.	−	310723.i	−1.58891	−	0.578316i	−0.977117	+	0.212703i	$0.931773\pi$
$734$	−549151.	−	654452.i	−1.01929	−	1.21475i
$735$	5184.55	+	347652.i	0.00959703	+	0.643532i
$736$	−686417.	+	249835.i	−1.26716	+	0.461209i
$737$	1.15835e6	+	668775.i	2.13258	+	1.23125i
$738$	261313.	−	104035.i	0.479786	−	0.191015i
$739$	346054.	+	599383.i	0.633658	+	1.09753i	0.986798	+	0.161958i	$0.0517808\pi$
$739$	346054.	+	599383.i	0.633658	+	1.09753i	−0.353139	+	0.935571i	$0.614886\pi$
$740$	112791.	−	134420.i	0.205974	−	0.245470i
$741$	37541.2	−	233189.i	0.0683709	−	0.424689i
$742$	−12234.8	−	69386.9i	−0.0222223	−	0.126029i
$743$	868910.	−	153212.i	1.57397	−	0.277534i	0.682595	−	0.730797i	$-0.260851\pi$
$743$	868910.	−	153212.i	1.57397	−	0.277534i	0.891377	+	0.453263i	$0.149740\pi$
$744$	−130342.	+	160126.i	−0.235472	+	0.289278i
$745$	−367520.	−	308386.i	−0.662169	−	0.555625i
$746$	731995.	−	422618.i	1.31532	−	0.759399i
$747$	−324301.	+	67211.3i	−0.581175	+	0.120448i
$748$	−896014.	+	1.55194e6i	−1.60144	+	2.77378i
$749$	−3994.45	−	10974.7i	−0.00712022	−	0.0195626i
$750$	−452319.	−	757137.i	−0.804122	−	1.34602i
$751$	−116154.	+	97464.8i	−0.205946	+	0.172810i	−0.739927	−	0.672687i	$-0.765140\pi$
$751$	−116154.	+	97464.8i	−0.205946	+	0.172810i	0.533981	+	0.845497i	$0.320696\pi$
$752$	8326.51	−	22876.9i	0.0147240	−	0.0404540i
$753$	125732.	−	362161.i	0.221747	−	0.638722i
$754$	91363.6	−	518149.i	0.160705	−	0.911405i
$755$		−	589146.i		−	1.03354i
$756$	62030.1	+	97131.3i	0.108532	+	0.169948i
$757$	−593090.			−1.03497			−0.517486	−	0.855692i	$-0.673132\pi$
$757$	−593090.			−1.03497			−0.517486	+	0.855692i	$0.673132\pi$
$758$	−1.22834e6	−	216589.i	−2.13786	−	0.376963i
$759$	660517.	−	571238.i	1.14657	−	0.991593i
$760$	−216973.	−	78971.6i	−0.375645	−	0.136724i
$761$	503625.	+	600197.i	0.869638	+	1.03639i	0.998996	+	0.0447960i	$0.0142638\pi$
$761$	503625.	+	600197.i	0.869638	+	1.03639i	−0.129358	+	0.991598i	$0.541292\pi$
$762$	687266.	+	383244.i	1.18363	+	0.660033i
$763$	63229.1	−	23013.5i	0.108609	−	0.0395306i
$764$	971190.	+	560717.i	1.66386	+	0.960631i
$765$	−610848.	+	18223.3i	−1.04378	+	0.0311389i
$766$	559208.	+	968577.i	0.953051	+	1.65073i
$767$	75955.0	−	90519.6i	0.129112	−	0.153869i
$768$	75248.9	−	28666.2i	0.127579	−	0.0486012i
$769$	26752.7	+	151722.i	0.0452392	+	0.256564i	0.999037	−	0.0438864i	$-0.0139740\pi$
$769$	26752.7	+	151722.i	0.0452392	+	0.256564i	−0.953797	+	0.300451i	$0.902863\pi$
$770$	−139317.	+	24565.3i	−0.234975	+	0.0414324i
$771$	45870.9	+	120412.i	0.0771665	+	0.202563i
$772$	−682993.	−	573099.i	−1.14599	−	0.961601i
$773$	617858.	−	356720.i	1.03402	−	0.596992i	0.115887	−	0.993262i	$-0.463029\pi$
$773$	617858.	−	356720.i	1.03402	−	0.596992i	0.918134	+	0.396270i	$0.129696\pi$
$774$	−481515.	−	259174.i	−0.803763	−	0.432623i
$775$	−135196.	+	234167.i	−0.225093	+	0.389872i
$776$	95204.5	+	261572.i	0.158101	+	0.434378i
$777$	−16836.3	+	30192.3i	−0.0278872	+	0.0500098i
$778$	−596351.	+	500398.i	−0.985242	+	0.826716i
$779$	91318.4	−	250895.i	0.150482	−	0.413445i
$780$	−114072.	−	131900.i	−0.187494	−	0.216798i
$781$	91375.1	−	518214.i	0.149805	−	0.849585i
$782$		−	1.44339e6i		−	2.36032i
$783$	431207.	+	1.03779e6i	0.703334	+	1.69272i
$784$	358004.			0.582446
$785$	399338.	+	70414.0i	0.648039	+	0.114267i
$786$	159723.	+	55451.6i	0.258537	+	0.0897571i
$787$	118383.	+	43087.8i	0.191134	+	0.0695672i	0.435814	−	0.900037i	$-0.356461\pi$
$787$	118383.	+	43087.8i	0.191134	+	0.0695672i	−0.244680	+	0.969604i	$0.578683\pi$
$788$	−116674.	−	139047.i	−0.187898	−	0.223928i
$789$	738494.	−	441182.i	1.18630	−	0.708701i
$790$	−537766.	+	195731.i	−0.861666	+	0.313621i
$791$	−110048.	−	63536.4i	−0.175886	−	0.101548i
$792$	339028.	−	302156.i	0.540486	−	0.481704i
$793$	40710.2	+	70512.2i	0.0647377	+	0.112129i
$794$	−318442.	+	379505.i	−0.505114	+	0.601972i
$795$	−176601.	−	143753.i	−0.279421	−	0.227449i
$796$	−228501.	−	1.29589e6i	−0.360630	−	2.04523i
$797$	−989241.	+	174430.i	−1.55735	+	0.274602i	−0.884985	−	0.465620i	$-0.845831\pi$
$797$	−989241.	+	174430.i	−1.55735	+	0.274602i	−0.672362	+	0.740222i	$0.734720\pi$
$798$	190572.	+	30680.2i	0.299262	+	0.0481784i
$799$	55894.6	+	46901.1i	0.0875540	+	0.0734665i
$800$	−430835.	+	248742.i	−0.673179	+	0.388660i
$801$	−498424.	−	72634.1i	−0.776844	−	0.113208i
$802$	179750.	−	311335.i	0.279460	−	0.484038i
$803$	−272767.	−	749422.i	−0.423020	−	1.16224i
$804$	−1.34731e6	+	20092.5i	−2.08428	+	0.0310830i
$805$	49472.4	−	41512.2i	0.0763433	−	0.0640596i
$806$	−89324.9	+	245418.i	−0.137500	+	0.377778i
$807$	160332.	−	30742.8i	0.246192	−	0.0472059i
$808$	−99533.0	+	564480.i	−0.152456	+	0.864621i
$809$			583220.i			0.891118i	0.895253	+	0.445559i	$0.146995\pi$
$809$			583220.i			0.891118i	−0.895253	+	0.445559i	$0.853005\pi$
$810$	629839.	+	187553.i	0.959973	+	0.285860i
$811$	1.19604e6			1.81846			0.909228	−	0.416298i	$-0.136673\pi$
$811$	1.19604e6			1.81846			0.909228	+	0.416298i	$0.136673\pi$
$812$	240007.	+	42319.6i	0.364008	+	0.0641845i
$813$	−216954.	−	1.13147e6i	−0.328236	−	1.71184i
$814$	543173.	+	197699.i	0.819765	+	0.298370i
$815$	182925.	+	218001.i	0.275396	+	0.328204i
$816$	9382.94	+	629177.i	0.0140915	+	0.944914i
$817$	−487797.	+	177543.i	−0.730794	+	0.265987i
$818$	1.53414e6	+	885736.i	2.29276	+	1.32372i
$819$	26964.3	+	21288.4i	0.0401995	+	0.0317376i
$820$	−98564.4	−	170719.i	−0.146586	−	0.253894i
$821$	−590669.	+	703931.i	−0.876310	+	1.04435i	0.122345	+	0.992488i	$0.460959\pi$
$821$	−590669.	+	703931.i	−0.876310	+	1.04435i	−0.998654	+	0.0518575i	$0.983486\pi$
$822$	−45575.4	+	283094.i	−0.0674508	+	0.418974i
$823$	−141705.	−	803651.i	−0.209212	−	1.18650i	−0.890672	−	0.454646i	$-0.849766\pi$
$823$	−141705.	−	803651.i	−0.209212	−	1.18650i	0.681460	−	0.731855i	$-0.261345\pi$
$824$	−182544.	+	32187.5i	−0.268852	+	0.0474059i
$825$	375454.	−	461245.i	0.551631	−	0.677678i
$826$	73976.5	+	62073.6i	0.108426	+	0.0909802i
$827$	−308224.	+	177953.i	−0.450666	+	0.260192i	−0.708112	−	0.706101i	$-0.750453\pi$
$827$	−308224.	+	177953.i	−0.450666	+	0.260192i	0.257445	+	0.966293i	$0.417119\pi$
$828$	−276103.	+	835289.i	−0.402727	+	1.21836i
$829$	−224839.	+	389432.i	−0.327161	+	0.566660i	−0.981947	−	0.189154i	$-0.939425\pi$
$829$	−224839.	+	389432.i	−0.327161	+	0.566660i	0.654786	+	0.755814i	$0.272759\pi$
$830$	140073.	+	384848.i	0.203329	+	0.558641i
$831$	−246108.	−	411960.i	−0.356388	−	0.596558i
$832$	−262961.	+	220651.i	−0.379879	+	0.318756i
$833$	−366981.	+	1.00827e6i	−0.528876	+	1.45308i
$834$	−380151.	+	1.09499e6i	−0.546542	+	1.57427i
$835$	16499.7	−	93574.4i	0.0236648	−	0.134210i
$836$		−	1.82934e6i		−	2.61747i
$837$	−121339.	−	544483.i	−0.173201	−	0.777202i
$838$	746843.			1.06351
$839$	−167593.	−	29551.1i	−0.238085	−	0.0419807i	0.0533326	−	0.998577i	$-0.483016\pi$
$839$	−167593.	−	29551.1i	−0.238085	−	0.0419807i	−0.291417	+	0.956596i	$0.594127\pi$
$840$	25402.9	−	21969.3i	0.0360018	−	0.0311356i
$841$	1.56850e6	+	570888.i	2.21765	+	0.807158i
$842$	−297483.	−	354526.i	−0.419602	−	0.500063i
$843$	−236013.	−	131610.i	−0.332110	−	0.185196i
$844$	1.11351e6	−	405283.i	1.56317	−	0.568949i
$845$	362647.	+	209374.i	0.507891	+	0.293231i
$846$	−41240.5	−	66751.2i	−0.0576214	−	0.0932650i
$847$	−76777.7	−	132983.i	−0.107021	−	0.185366i
$848$	−150712.	+	179612.i	−0.209583	+	0.249772i
$849$	21790.1	−	8300.98i	0.0302304	−	0.0115163i
$850$	−170700.	−	968085.i	−0.236262	−	1.33991i
$851$	−259873.	+	45822.6i	−0.358841	+	0.0632733i
$852$	188715.	+	495380.i	0.259973	+	0.682431i
$853$	81021.3	+	67984.9i	0.111353	+	0.0934360i	0.696764	−	0.717300i	$-0.254622\pi$
$853$	81021.3	+	67984.9i	0.111353	+	0.0934360i	−0.585411	+	0.810736i	$0.699067\pi$
$854$	−57625.6	+	33270.1i	−0.0790132	+	0.0456183i
$855$	530722.	−	327893.i	0.725997	−	0.448538i
$856$	23180.9	−	40150.6i	0.0316361	−	0.0547954i
$857$	−143295.	−	393699.i	−0.195105	−	0.536047i	0.803106	−	0.595836i	$-0.203179\pi$
$857$	−143295.	−	393699.i	−0.195105	−	0.536047i	−0.998211	+	0.0597895i	$0.980957\pi$
$858$	279774.	−	501715.i	0.380043	−	0.681526i
$859$	−770583.	+	646596.i	−1.04432	+	0.876288i	−0.992485	−	0.122368i	$-0.960951\pi$
$859$	−770583.	+	646596.i	−1.04432	+	0.876288i	−0.0518343	+	0.998656i	$0.516507\pi$
$860$	−131084.	+	360149.i	−0.177236	+	0.486952i
$861$	25404.0	+	29374.4i	0.0342686	+	0.0396245i
$862$	198970.	−	1.12842e6i	0.267777	−	1.51864i
$863$			1.38007e6i			1.85302i	0.376271	+	0.926510i	$0.377206\pi$
$863$			1.38007e6i			1.85302i	−0.376271	+	0.926510i	$0.622794\pi$
$864$	307549.	−	979185.i	0.411991	−	1.31171i
$865$	323972.			0.432988
$866$	27743.5	+	4891.92i	0.0369935	+	0.00652295i
$867$	−1.07150e6	−	371997.i	−1.42546	−	0.494881i
$868$	−113678.	−	41375.3i	−0.150882	−	0.0549164i
$869$	−686810.	−	818509.i	−0.909489	−	1.08389i
$870$	1.19300e6	−	712708.i	1.57617	−	0.941614i
$871$	−377448.	+	137380.i	−0.497532	+	0.181087i
$872$	231322.	+	133554.i	0.304218	+	0.175640i
$873$	−714076.	−	236036.i	−0.936948	−	0.309707i
$874$	736721.	+	1.27604e6i	0.964451	+	1.67048i
$875$	78277.7	−	93287.8i	0.102240	−	0.121845i
$876$	623095.	+	507199.i	0.811981	+	0.660953i
$877$	38998.8	+	221173.i	0.0507051	+	0.287563i	0.999608	−	0.0280060i	$-0.00891576\pi$
$877$	38998.8	+	221173.i	0.0507051	+	0.287563i	−0.948903	+	0.315569i	$0.897805\pi$
$878$	288276.	−	50830.8i	0.373955	−	0.0659383i
$879$	−423369.	−	68158.4i	−0.547950	−	0.0882148i
$880$	360629.	+	302604.i	0.465688	+	0.390759i
$881$	−216321.	+	124893.i	−0.278707	+	0.160912i	−0.632838	−	0.774284i	$-0.718110\pi$
$881$	−216321.	+	124893.i	−0.278707	+	0.160912i	0.354131	+	0.935196i	$0.384777\pi$
$882$	714984.	−	905613.i	0.919093	−	1.16414i
$883$	564079.	−	977013.i	0.723466	−	1.25308i	−0.236136	−	0.971720i	$-0.575881\pi$
$883$	564079.	−	977013.i	0.723466	−	1.25308i	0.959602	−	0.281361i	$-0.0907857\pi$
$884$	−184059.	−	505699.i	−0.235534	−	0.647124i
$885$	312070.	−	4653.91i	0.398442	−	0.00594198i
$886$	60588.3	−	50839.6i	0.0771829	−	0.0647642i
$887$	385201.	−	1.05833e6i	0.489598	−	1.34516i	−0.411447	−	0.911434i	$-0.634976\pi$
$887$	385201.	−	1.05833e6i	0.489598	−	1.34516i	0.901045	−	0.433726i	$-0.142801\pi$
$888$	−134774.	+	25842.2i	−0.170915	+	0.0327720i
$889$	−18867.4	+	107003.i	−0.0238731	+	0.135391i
$890$			622852.i			0.786330i
$891$	73143.6	+	1.22480e6i	0.0921342	+	1.54281i
$892$	−725789.			−0.912180
$893$	−73352.6	−	12934.0i	−0.0919841	−	0.0162193i
$894$	299819.	+	1.56364e6i	0.375133	+	1.95642i
$895$	−347570.	−	126505.i	−0.433906	−	0.157929i
$896$	−70972.8	−	84582.1i	−0.0884048	−	0.105357i
$897$	3910.45	+	262217.i	0.00486006	+	0.325893i
$898$	850452.	−	309539.i	1.05462	−	0.383851i
$899$	−1.02159e6	−	589815.i	−1.26403	−	0.729788i
$900$	−86399.4	+	592882.i	−0.106666	+	0.731954i
$901$	−351363.	−	608578.i	−0.432819	−	0.749664i
$902$	417409.	−	497448.i	0.513037	−	0.611413i
$903$	12001.2	−	74545.8i	0.0147180	−	0.0914214i
$904$	−87594.9	−	496775.i	−0.107187	−	0.607887i
$905$	453036.	−	79882.5i	0.553141	−	0.0975337i
$906$	−1.23425e6	+	1.51628e6i	−1.50366	+	1.84724i
$907$	560559.	+	470365.i	0.681407	+	0.571769i	0.916417	−	0.400224i	$-0.131068\pi$
$907$	560559.	+	470365.i	0.681407	+	0.571769i	−0.235010	+	0.971993i	$0.575512\pi$
$908$	−94189.9	+	54380.6i	−0.114244	+	0.0659587i
$909$	−1.03038e6	−	1.15612e6i	−1.24701	−	1.39919i
$910$	21241.4	−	36791.2i	0.0256507	−	0.0444284i
$911$	439260.	+	1.20686e6i	0.529279	+	1.45418i	0.859922	+	0.510426i	$0.170512\pi$
$911$	439260.	+	1.20686e6i	0.529279	+	1.45418i	−0.330642	+	0.943756i	$0.607265\pi$
$912$	−329433.	−	551437.i	−0.396075	−	0.662989i
$913$	−585759.	+	491510.i	−0.702712	+	0.589645i
$914$	45669.9	−	125477.i	0.0546685	−	0.150200i
$915$	−70530.8	+	203158.i	−0.0842436	+	0.242656i
$916$	−158276.	+	897627.i	−0.188636	+	1.06981i
$917$			23345.5i			0.0277629i
$918$	1.61031e6	+	1.23282e6i	1.91084	+	1.46290i
$919$	−321358.			−0.380503			−0.190252	−	0.981735i	$-0.560930\pi$
$919$	−321358.			−0.380503			−0.190252	+	0.981735i	$0.560930\pi$
$920$	252474.	+	44517.9i	0.298291	+	0.0525968i
$921$	154484.	−	133603.i	0.182123	−	0.157506i
$922$	788976.	+	287164.i	0.928116	+	0.337807i
$923$	101575.	+	121052.i	0.119229	+	0.142092i
$924$	232394.	+	129591.i	0.272196	+	0.151786i
$925$	−168878.	+	61466.6i	−0.197374	+	0.0718382i
$926$	−1.08039e6	−	623763.i	−1.25996	−	0.727440i
$927$	237360.	−	440987.i	0.276215	−	0.513176i
$928$	−1.08518e6	−	1.87958e6i	−1.26010	−	2.18256i
$929$	845059.	−	1.00710e6i	0.979164	−	1.16692i	−0.00680175	−	0.999977i	$-0.502165\pi$
$929$	845059.	−	1.00710e6i	0.979164	−	1.16692i	0.985966	−	0.166946i	$-0.0533905\pi$
$930$	−644623.	+	245570.i	−0.745316	+	0.283929i
$931$	−190200.	−	1.07868e6i	−0.219438	−	1.24449i
$932$	−1.94772e6	+	343435.i	−2.24230	+	0.395378i
$933$	109021.	+	286181.i	0.125241	+	0.328759i
$934$	−1.00242e6	−	841129.i	−1.14909	−	0.964204i
$935$	−1.22192e6	+	705474.i	−1.39771	+	0.806971i
$936$	4066.73	+	136318.i	0.00464188	+	0.155597i
$937$	−91197.1	+	157958.i	−0.103873	+	0.179913i	−0.913277	−	0.407339i	$-0.866457\pi$
$937$	−91197.1	+	157958.i	−0.103873	+	0.179913i	0.809404	+	0.587252i	$0.199790\pi$
$938$	−112273.	−	308467.i	−0.127605	−	0.350592i
$939$	−634861.	+	1.13849e6i	−0.720025	+	1.29121i
$940$	−42127.1	+	35348.9i	−0.0476767	+	0.0400055i
$941$	−314314.	+	863570.i	−0.354964	+	0.975255i	0.625788	+	0.779994i	$0.284778\pi$
$941$	−314314.	+	863570.i	−0.354964	+	0.975255i	−0.980751	+	0.195261i	$0.937445\pi$
$942$	−880257.	−	1.01783e6i	−0.991991	−	1.14703i
$943$	−51478.0	+	291946.i	−0.0578893	+	0.328306i
$944$		−	321362.i		−	0.360621i
$945$	4058.00	+	90649.7i	0.00454410	+	0.101509i
$946$	−1.26253e6			−1.41078
$947$	−1.27507e6	−	224828.i	−1.42178	−	0.250698i	−0.590718	−	0.806878i	$-0.701155\pi$
$947$	−1.27507e6	−	224828.i	−1.42178	−	0.250698i	−0.831062	+	0.556180i	$0.812267\pi$
$948$	1.01687e6	+	353029.i	1.13148	+	0.392820i
$949$	225055.	+	81913.2i	0.249894	+	0.0909539i
$950$	645028.	+	768714.i	0.714712	+	0.851760i
$951$	−227961.	+	136185.i	−0.252057	+	0.150581i
$952$	97393.7	−	35448.4i	0.107462	−	0.0391131i
$953$	−26148.8	−	15097.0i	−0.0287917	−	0.0166229i	0.485535	−	0.874217i	$-0.338625\pi$
$953$	−26148.8	−	15097.0i	−0.0287917	−	0.0166229i	−0.514327	+	0.857594i	$0.671958\pi$
$954$	153355.	+	739954.i	0.168501	+	0.813033i
$955$	441478.	+	764663.i	0.484064	+	0.838423i
$956$	267855.	−	319217.i	0.293079	−	0.349278i
$957$	2.01225e6	+	1.63798e6i	2.19715	+	1.78848i
$958$	223928.	+	1.26996e6i	0.243993	+	1.38375i
$959$	−38990.7	+	6875.12i	−0.0423959	+	0.00747555i
$960$	−895145.	−	144110.i	−0.971294	−	0.156369i
$961$	−258901.	−	217244.i	−0.280341	−	0.235234i
$962$	−150330.	+	86792.8i	−0.162440	+	0.0937850i
$963$	46332.7	+	116377.i	0.0499615	+	0.125492i
$964$	345023.	−	597597.i	0.371274	−	0.643065i
$965$	−240093.	−	659651.i	−0.257825	−	0.708369i
$966$	−214295.	+	3195.78i	−0.229645	+	0.00342470i
$967$	671929.	−	563815.i	0.718572	−	0.602954i	−0.208418	−	0.978040i	$-0.566831\pi$
$967$	671929.	−	563815.i	0.718572	−	0.602954i	0.926990	+	0.375086i	$0.122387\pi$
$968$	208484.	−	572805.i	0.222496	−	0.611302i
$969$	1.89075e6	−	362540.i	2.01366	−	0.386108i
$970$	−161493.	+	915874.i	−0.171637	+	0.973402i
$971$		−	552699.i		−	0.586206i	−0.956081	−	0.293103i	$-0.905312\pi$
$971$		−	552699.i		−	0.586206i	0.956081	−	0.293103i	$-0.0946879\pi$
$972$	−696063.	−	1.02146e6i	−0.736743	−	1.08116i
$973$	−160046.			−0.169052
$974$	−35562.3	−	6270.59i	−0.0374862	−	0.00660984i
$975$	33633.2	+	175407.i	0.0353801	+	0.184517i
$976$	208078.	+	75734.1i	0.218437	+	0.0795045i
$977$	661005.	+	787755.i	0.692494	+	0.825282i	0.991655	−	0.128921i	$-0.0411513\pi$
$977$	661005.	+	787755.i	0.692494	+	0.825282i	−0.299161	+	0.954203i	$0.596707\pi$
$978$	−14082.3	−	944295.i	−0.0147230	−	0.987256i
$979$	−1.09278e6	+	397739.i	−1.14016	+	0.414986i
$980$	−700350.	−	404348.i	−0.729228	−	0.421020i
$981$	−670491.	+	266940.i	−0.696715	+	0.277380i
$982$	−1.13812e6	−	1.97127e6i	−1.18022	−	2.04420i
$983$	1.15088e6	−	1.37157e6i	1.19103	−	1.41942i	0.307180	−	0.951652i	$-0.400615\pi$
$983$	1.15088e6	−	1.37157e6i	1.19103	−	1.41942i	0.883853	−	0.467765i	$-0.154941\pi$
$984$	−24503.8	+	152206.i	−0.0253071	+	0.157196i
$985$	−24816.7	−	140742.i	−0.0255783	−	0.145062i
$986$	4.22342e6	−	744704.i	4.34421	−	0.766002i
$987$	6839.46	−	8402.28i	0.00702082	−	0.00862508i
$988$	420832.	+	353120.i	0.431117	+	0.361750i
$989$	499147.	−	288183.i	0.510312	−	0.294629i
$990$	1.48570e6	−	307911.i	1.51586	−	0.314162i
$991$	219634.	−	380417.i	0.223641	−	0.387358i	−0.732270	−	0.681015i	$-0.761539\pi$
$991$	219634.	−	380417.i	0.223641	−	0.387358i	0.955911	+	0.293657i	$0.0948723\pi$
$992$	368469.	+	1.01236e6i	0.374436	+	1.02875i
$993$	111658.	+	186904.i	0.113238	+	0.189549i
$994$	−98929.1	+	83011.3i	−0.100127	+	0.0840165i
$995$	354352.	−	973575.i	0.357923	−	0.983384i
$996$	252642.	−	727713.i	0.254675	−	0.733569i
$997$	120978.	−	686100.i	0.121707	−	0.690235i	−0.861502	−	0.507754i	$-0.830476\pi$
$997$	120978.	−	686100.i	0.121707	−	0.690235i	0.983209	−	0.182481i	$-0.0584128\pi$
$998$		−	460427.i		−	0.462274i
$999$	170839.	−	329064.i	0.171181	−	0.329723i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.5.f.a.2.10	✓	66
3.2	odd	2		81.5.f.a.8.2		66
27.13	even	9		81.5.f.a.71.2		66
27.14	odd	18	inner	27.5.f.a.14.10	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.2.10	✓	66	1.1	even	1	trivial
27.5.f.a.14.10	yes	66	27.14	odd	18	inner
81.5.f.a.8.2		66	3.2	odd	2
81.5.f.a.71.2		66	27.13	even	9

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+(5.98494 + 1.05531i) q^{2} +(-1.69482 - 8.83898i) q^{3} +(19.6707 + 7.15955i) q^{4} +(10.5942 + 12.6257i) q^{5} +(-0.815584 - 54.6893i) q^{6} +(7.09675 - 2.58301i) q^{7} +(25.9633 + 14.9899i) q^{8} +(-75.2551 + 29.9610i) q^{9} +(50.0816 + 86.7438i) q^{10} +(-120.209 + 143.260i) q^{11} +(29.9447 - 186.003i) q^{12} +(-9.75217 - 55.3073i) q^{13} +(45.1995 - 7.96989i) q^{14} +(93.6426 - 115.040i) q^{15} +(-117.001 - 98.1758i) q^{16} +(396.435 - 228.882i) q^{17} +(-482.015 + 99.8976i) q^{18} +(-233.647 + 404.688i) q^{19} +(118.001 + 324.205i) q^{20} +(-34.8589 - 58.3503i) q^{21} +(-870.626 + 730.542i) q^{22} +(177.454 - 487.552i) q^{23} +(88.4924 - 254.895i) q^{24} +(61.3597 - 347.988i) q^{25} -341.302i q^{26} +(392.369 + 614.400i) q^{27} +158.091 q^{28} +(1518.15 + 267.691i) q^{29} +(681.847 - 589.685i) q^{30} +(-719.064 - 261.718i) q^{31} +(-904.971 - 1078.50i) q^{32} +(1470.00 + 819.726i) q^{33} +(2614.18 - 951.483i) q^{34} +(107.796 + 62.2363i) q^{35} +(-1694.83 + 50.5614i) q^{36} +(-254.299 - 440.459i) q^{37} +(-1825.43 + 2175.46i) q^{38} +(-472.332 + 179.935i) q^{39} +(85.8024 + 486.610i) q^{40} +(-562.688 + 99.2171i) q^{41} +(-147.051 - 386.010i) q^{42} +(850.976 + 714.053i) q^{43} +(-3390.27 + 1957.37i) q^{44} +(-1175.54 - 632.733i) q^{45} +(1576.57 - 2730.70i) q^{46} +(54.5162 + 149.782i) q^{47} +(-669.477 + 1200.56i) q^{48} +(-1795.58 + 1506.67i) q^{49} +(734.467 - 2017.93i) q^{50} +(-2694.97 - 3116.17i) q^{51} +(204.143 - 1157.75i) q^{52} -1535.13i q^{53} +(1699.92 + 4091.21i) q^{54} -3082.26 q^{55} +(222.974 + 39.3164i) q^{56} +(3973.02 + 1379.32i) q^{57} +(8803.55 + 3204.23i) q^{58} +(1352.46 + 1611.80i) q^{59} +(2665.65 - 1592.48i) q^{60} +(-1362.35 + 495.855i) q^{61} +(-4027.36 - 2325.20i) q^{62} +(-456.678 + 407.011i) q^{63} +(-3056.17 - 5293.44i) q^{64} +(594.974 - 709.063i) q^{65} +(7932.80 + 6457.31i) q^{66} +(-1241.97 - 7043.56i) q^{67} +(9436.84 - 1663.97i) q^{68} +(-4610.21 - 742.201i) q^{69} +(579.476 + 486.238i) q^{70} +(-2436.79 + 1406.88i) q^{71} +(-2402.99 - 350.182i) q^{72} +(-2132.26 + 3693.19i) q^{73} +(-1057.14 - 2904.48i) q^{74} +(-3179.85 + 47.4213i) q^{75} +(-7493.38 + 6287.69i) q^{76} +(-483.054 + 1327.18i) q^{77} +(-3016.76 + 578.447i) q^{78} +(-992.133 + 5626.67i) q^{79} -2517.31i q^{80} +(4765.67 - 4509.44i) q^{81} -3472.36 q^{82} +(4026.67 + 710.011i) q^{83} +(-267.937 - 1397.37i) q^{84} +(7089.69 + 2580.44i) q^{85} +(4339.49 + 5171.60i) q^{86} +(-206.883 - 13872.6i) q^{87} +(-5268.48 + 1917.57i) q^{88} +(5385.27 + 3109.19i) q^{89} +(-6367.83 - 5027.42i) q^{90} +(-212.068 - 367.312i) q^{91} +(6981.30 - 8319.99i) q^{92} +(-1094.63 + 6799.36i) q^{93} +(168.210 + 953.968i) q^{94} +(-7584.75 + 1337.40i) q^{95} +(-7999.10 + 9826.89i) q^{96} +(7112.63 + 5968.20i) q^{97} +(-12336.4 + 7122.44i) q^{98} +(4754.15 - 14382.6i) 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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