LMFDB - Embedded newform 18.5.d.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,5,Mod(5,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("18.5");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	18.d (of order $6$, degree $2$, 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:	$1.86065933551$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.221456830464.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 38x^{6} - 100x^{5} + 449x^{4} - 736x^{3} + 1900x^{2} - 1548x + 2307 $ x^8 - 4x^7 + 38x^6 - 100x^5 + 449x^4 - 736x^3 + 1900x^2 - 1548*x + 2307
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.3
Root			$0.500000 - 2.20403i$ of defining polynomial
Character	$\chi$	$=$	18.11
Dual form			18.5.d.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44949 + 1.41421i) q^{2} +(-1.67960 + 8.84189i) q^{3} +(4.00000 + 6.92820i) q^{4} +(6.41371 - 3.70296i) q^{5} +(-16.6185 + 19.2828i) q^{6} +(30.1882 - 52.2875i) q^{7} +22.6274i q^{8} +(-75.3579 - 29.7016i) q^{9} +O(q^{10})$	\(q+(2.44949 + 1.41421i) q^{2} +(-1.67960 + 8.84189i) q^{3} +(4.00000 + 6.92820i) q^{4} +(6.41371 - 3.70296i) q^{5} +(-16.6185 + 19.2828i) q^{6} +(30.1882 - 52.2875i) q^{7} +22.6274i q^{8} +(-75.3579 - 29.7016i) q^{9} +20.9471 q^{10} +(55.2054 + 31.8729i) q^{11} +(-67.9768 + 23.7310i) q^{12} +(-144.994 - 251.137i) q^{13} +(147.892 - 85.3852i) q^{14} +(21.9687 + 62.9288i) q^{15} +(-32.0000 + 55.4256i) q^{16} +460.439i q^{17} +(-142.584 - 179.326i) q^{18} +187.741 q^{19} +(51.3097 + 29.6237i) q^{20} +(411.616 + 354.743i) q^{21} +(90.1501 + 156.144i) q^{22} +(-35.8618 + 20.7048i) q^{23} +(-200.069 - 38.0049i) q^{24} +(-285.076 + 493.766i) q^{25} -820.210i q^{26} +(389.189 - 616.419i) q^{27} +483.012 q^{28} +(-1211.49 - 699.452i) q^{29} +(-35.1827 + 185.212i) q^{30} +(-318.482 - 551.628i) q^{31} +(-156.767 + 90.5097i) q^{32} +(-374.539 + 434.586i) q^{33} +(-651.158 + 1127.84i) q^{34} -447.143i q^{35} +(-95.6529 - 640.901i) q^{36} +847.670 q^{37} +(459.869 + 265.506i) q^{38} +(2464.06 - 860.212i) q^{39} +(83.7884 + 145.126i) q^{40} +(-438.352 + 253.083i) q^{41} +(506.568 + 1451.05i) q^{42} +(-702.429 + 1216.64i) q^{43} +509.966i q^{44} +(-593.308 + 88.5497i) q^{45} -117.124 q^{46} +(2146.72 + 1239.41i) q^{47} +(-436.320 - 376.033i) q^{48} +(-622.158 - 1077.61i) q^{49} +(-1396.58 + 806.317i) q^{50} +(-4071.15 - 773.351i) q^{51} +(1159.95 - 2009.10i) q^{52} +773.208i q^{53} +(1825.06 - 959.517i) q^{54} +472.095 q^{55} +(1183.13 + 683.082i) q^{56} +(-315.329 + 1659.98i) q^{57} +(-1978.35 - 3426.60i) q^{58} +(3894.93 - 2248.74i) q^{59} +(-348.109 + 403.919i) q^{60} +(1301.48 - 2254.22i) q^{61} -1801.61i q^{62} +(-3827.95 + 3043.64i) q^{63} -512.000 q^{64} +(-1859.90 - 1073.81i) q^{65} +(-1532.03 + 534.837i) q^{66} +(1691.55 + 2929.85i) q^{67} +(-3190.01 + 1841.75i) q^{68} +(-122.836 - 351.862i) q^{69} +(632.356 - 1095.27i) q^{70} +2771.07i q^{71} +(672.070 - 1705.15i) q^{72} +3525.16 q^{73} +(2076.36 + 1198.79i) q^{74} +(-3887.01 - 3349.94i) q^{75} +(750.964 + 1300.71i) q^{76} +(3333.11 - 1924.37i) q^{77} +(7252.21 + 1377.62i) q^{78} +(-2914.90 + 5048.75i) q^{79} +473.979i q^{80} +(4796.63 + 4476.50i) q^{81} -1431.65 q^{82} +(-4438.63 - 2562.65i) q^{83} +(-811.265 + 4270.73i) q^{84} +(1704.98 + 2953.12i) q^{85} +(-3441.19 + 1986.77i) q^{86} +(8219.29 - 9537.03i) q^{87} +(-721.200 + 1249.16i) q^{88} -1221.14i q^{89} +(-1578.53 - 622.162i) q^{90} -17508.5 q^{91} +(-286.894 - 165.638i) q^{92} +(5412.35 - 1889.47i) q^{93} +(3505.58 + 6071.84i) q^{94} +(1204.12 - 695.197i) q^{95} +(-536.970 - 1538.14i) q^{96} +(7367.60 - 12761.1i) q^{97} -3519.46i q^{98} +(-3213.49 - 4041.56i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 32 q^{4} + 18 q^{5} + 48 q^{6} - 26 q^{7} - 78 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 + 32 * q^4 + 18 * q^5 + 48 * q^6 - 26 * q^7 - 78 * q^9	\( 8 q + 6 q^{3} + 32 q^{4} + 18 q^{5} + 48 q^{6} - 26 q^{7} - 78 q^{9} - 720 q^{11} - 144 q^{12} + 10 q^{13} + 288 q^{14} + 1134 q^{15} - 256 q^{16} - 384 q^{18} + 100 q^{19} + 144 q^{20} + 438 q^{21} + 336 q^{22} + 1278 q^{23} + 384 q^{24} + 794 q^{25} - 1296 q^{27} - 416 q^{28} - 1854 q^{29} - 3456 q^{30} - 1478 q^{31} - 3384 q^{33} - 96 q^{34} + 1056 q^{36} - 32 q^{37} + 6768 q^{38} + 5274 q^{39} - 36 q^{41} + 2592 q^{42} - 68 q^{43} + 3402 q^{45} + 2112 q^{46} + 2214 q^{47} - 1536 q^{48} + 2442 q^{49} - 15552 q^{50} - 12006 q^{51} - 80 q^{52} + 7056 q^{54} - 3996 q^{55} + 2304 q^{56} + 10902 q^{57} - 2400 q^{58} + 9108 q^{59} + 6480 q^{60} - 4478 q^{61} - 6654 q^{63} - 4096 q^{64} - 22554 q^{65} - 19872 q^{66} + 7504 q^{67} - 11088 q^{68} - 5994 q^{69} + 6048 q^{70} + 5376 q^{72} + 20716 q^{73} + 15264 q^{74} + 16590 q^{75} + 400 q^{76} + 34434 q^{77} + 24096 q^{78} - 6050 q^{79} - 21150 q^{81} + 1152 q^{82} - 3834 q^{83} - 9600 q^{84} - 16092 q^{85} - 12528 q^{86} + 10170 q^{87} - 2688 q^{88} + 2592 q^{90} - 45868 q^{91} + 10224 q^{92} - 10926 q^{93} + 672 q^{94} + 20880 q^{95} + 31336 q^{97} - 22338 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 + 32 * q^4 + 18 * q^5 + 48 * q^6 - 26 * q^7 - 78 * q^9 - 720 * q^11 - 144 * q^12 + 10 * q^13 + 288 * q^14 + 1134 * q^15 - 256 * q^16 - 384 * q^18 + 100 * q^19 + 144 * q^20 + 438 * q^21 + 336 * q^22 + 1278 * q^23 + 384 * q^24 + 794 * q^25 - 1296 * q^27 - 416 * q^28 - 1854 * q^29 - 3456 * q^30 - 1478 * q^31 - 3384 * q^33 - 96 * q^34 + 1056 * q^36 - 32 * q^37 + 6768 * q^38 + 5274 * q^39 - 36 * q^41 + 2592 * q^42 - 68 * q^43 + 3402 * q^45 + 2112 * q^46 + 2214 * q^47 - 1536 * q^48 + 2442 * q^49 - 15552 * q^50 - 12006 * q^51 - 80 * q^52 + 7056 * q^54 - 3996 * q^55 + 2304 * q^56 + 10902 * q^57 - 2400 * q^58 + 9108 * q^59 + 6480 * q^60 - 4478 * q^61 - 6654 * q^63 - 4096 * q^64 - 22554 * q^65 - 19872 * q^66 + 7504 * q^67 - 11088 * q^68 - 5994 * q^69 + 6048 * q^70 + 5376 * q^72 + 20716 * q^73 + 15264 * q^74 + 16590 * q^75 + 400 * q^76 + 34434 * q^77 + 24096 * q^78 - 6050 * q^79 - 21150 * q^81 + 1152 * q^82 - 3834 * q^83 - 9600 * q^84 - 16092 * q^85 - 12528 * q^86 + 10170 * q^87 - 2688 * q^88 + 2592 * q^90 - 45868 * q^91 + 10224 * q^92 - 10926 * q^93 + 672 * q^94 + 20880 * q^95 + 31336 * q^97 - 22338 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.44949	+	1.41421i	0.612372	+	0.353553i
$2$	2.44949	+	1.41421i	0.612372	+	0.353553i
$3$	−1.67960	+	8.84189i	−0.186622	+	0.982432i
$3$	−1.67960	+	8.84189i	−0.186622	+	0.982432i
$4$	4.00000	+	6.92820i	0.250000	+	0.433013i
$5$	6.41371	−	3.70296i	0.256548	−	0.148118i	−0.366211	−	0.930532i	$-0.619345\pi$
$5$	6.41371	−	3.70296i	0.256548	−	0.148118i	0.622759	+	0.782414i	$0.286012\pi$
$6$	−16.6185	+	19.2828i	−0.461624	+	0.535633i
$7$	30.1882	−	52.2875i	0.616086	−	1.06709i	−0.374107	−	0.927386i	$-0.622051\pi$
$7$	30.1882	−	52.2875i	0.616086	−	1.06709i	0.990193	−	0.139707i	$-0.0446161\pi$
$8$			22.6274i			0.353553i
$9$	−75.3579	−	29.7016i	−0.930345	−	0.366686i
$10$	20.9471			0.209471
$11$	55.2054	+	31.8729i	0.456243	+	0.263412i	0.710463	−	0.703734i	$-0.248485\pi$
$11$	55.2054	+	31.8729i	0.456243	+	0.263412i	−0.254220	+	0.967146i	$0.581819\pi$
$12$	−67.9768	+	23.7310i	−0.472061	+	0.164798i
$13$	−144.994	−	251.137i	−0.857953	−	1.48602i	−0.873878	−	0.486145i	$-0.838403\pi$
$13$	−144.994	−	251.137i	−0.857953	−	1.48602i	0.0159253	−	0.999873i	$-0.494931\pi$
$14$	147.892	−	85.3852i	0.754549	−	0.435639i
$15$	21.9687	+	62.9288i	0.0976386	+	0.279683i
$16$	−32.0000	+	55.4256i	−0.125000	+	0.216506i
$17$			460.439i			1.59321i	0.604498	+	0.796606i	$0.293374\pi$
$17$			460.439i			1.59321i	−0.604498	+	0.796606i	$0.706626\pi$
$18$	−142.584	−	179.326i	−0.440074	−	0.553475i
$19$	187.741			0.520058			0.260029	−	0.965601i	$-0.416268\pi$
$19$	187.741			0.520058			0.260029	+	0.965601i	$0.416268\pi$
$20$	51.3097	+	29.6237i	0.128274	+	0.0740592i
$21$	411.616	+	354.743i	0.933371	+	0.804406i
$22$	90.1501	+	156.144i	0.186260	+	0.322613i
$23$	−35.8618	+	20.7048i	−0.0677916	+	0.0391395i	−0.533513	−	0.845792i	$-0.679128\pi$
$23$	−35.8618	+	20.7048i	−0.0677916	+	0.0391395i	0.465721	+	0.884932i	$0.345795\pi$
$24$	−200.069	−	38.0049i	−0.347342	−	0.0659808i
$25$	−285.076	+	493.766i	−0.456122	+	0.790026i
$26$		−	820.210i		−	1.21333i
$27$	389.189	−	616.419i	0.533867	−	0.845568i
$28$	483.012			0.616086
$29$	−1211.49	−	699.452i	−1.44053	−	0.831691i	−0.442646	−	0.896696i	$-0.645960\pi$
$29$	−1211.49	−	699.452i	−1.44053	−	0.831691i	−0.997885	+	0.0650051i	$0.979294\pi$
$30$	−35.1827	+	185.212i	−0.0390918	+	0.205791i
$31$	−318.482	−	551.628i	−0.331407	−	0.574014i	0.651381	−	0.758751i	$-0.274190\pi$
$31$	−318.482	−	551.628i	−0.331407	−	0.574014i	−0.982788	+	0.184737i	$0.940857\pi$
$32$	−156.767	+	90.5097i	−0.153093	+	0.0883883i
$33$	−374.539	+	434.586i	−0.343929	+	0.399069i
$34$	−651.158	+	1127.84i	−0.563286	+	0.975640i
$35$		−	447.143i		−	0.365015i
$36$	−95.6529	−	640.901i	−0.0738063	−	0.494523i
$37$	847.670			0.619189			0.309594	−	0.950869i	$-0.399807\pi$
$37$	847.670			0.619189			0.309594	+	0.950869i	$0.399807\pi$
$38$	459.869	+	265.506i	0.318469	+	0.183868i
$39$	2464.06	−	860.212i	1.62002	−	0.565557i
$40$	83.7884	+	145.126i	0.0523677	+	0.0907036i
$41$	−438.352	+	253.083i	−0.260769	+	0.150555i	−0.624685	−	0.780877i	$-0.714773\pi$
$41$	−438.352	+	253.083i	−0.260769	+	0.150555i	0.363916	+	0.931432i	$0.381439\pi$
$42$	506.568	+	1451.05i	0.287170	+	0.822592i
$43$	−702.429	+	1216.64i	−0.379897	+	0.658001i	−0.991047	−	0.133514i	$-0.957374\pi$
$43$	−702.429	+	1216.64i	−0.379897	+	0.658001i	0.611150	+	0.791515i	$0.290707\pi$
$44$			509.966i			0.263412i
$45$	−593.308	+	88.5497i	−0.292991	+	0.0437282i
$46$	−117.124			−0.0553516
$47$	2146.72	+	1239.41i	0.971806	+	0.561073i	0.899786	−	0.436331i	$-0.143722\pi$
$47$	2146.72	+	1239.41i	0.971806	+	0.561073i	0.0720198	+	0.997403i	$0.477056\pi$
$48$	−436.320	−	376.033i	−0.189375	−	0.163209i
$49$	−622.158	−	1077.61i	−0.259125	−	0.448817i
$50$	−1396.58	+	806.317i	−0.558633	+	0.322527i
$51$	−4071.15	−	773.351i	−1.56522	−	0.297328i
$52$	1159.95	−	2009.10i	0.428976	−	0.743009i
$53$			773.208i			0.275261i	0.990484	+	0.137630i	$0.0439486\pi$
$53$			773.208i			0.275261i	−0.990484	+	0.137630i	$0.956051\pi$
$54$	1825.06	−	959.517i	0.625879	−	0.329052i
$55$	472.095			0.156065
$56$	1183.13	+	683.082i	0.377274	+	0.217819i
$57$	−315.329	+	1659.98i	−0.0970541	+	0.510921i
$58$	−1978.35	−	3426.60i	−0.588094	−	1.01861i
$59$	3894.93	−	2248.74i	1.11891	−	0.646004i	0.177789	−	0.984069i	$-0.443106\pi$
$59$	3894.93	−	2248.74i	1.11891	−	0.646004i	0.941123	+	0.338065i	$0.109772\pi$
$60$	−348.109	+	403.919i	−0.0966968	+	0.112200i
$61$	1301.48	−	2254.22i	0.349765	−	0.605811i	−0.636442	−	0.771324i	$-0.719595\pi$
$61$	1301.48	−	2254.22i	0.349765	−	0.605811i	0.986208	+	0.165513i	$0.0529280\pi$
$62$		−	1801.61i		−	0.468681i
$63$	−3827.95	+	3043.64i	−0.964461	+	0.766853i
$64$	−512.000			−0.125000
$65$	−1859.90	−	1073.81i	−0.440213	−	0.254157i
$66$	−1532.03	+	534.837i	−0.351705	+	0.122782i
$67$	1691.55	+	2929.85i	0.376821	+	0.652673i	0.990598	−	0.136807i	$-0.0436840\pi$
$67$	1691.55	+	2929.85i	0.376821	+	0.652673i	−0.613777	+	0.789479i	$0.710351\pi$
$68$	−3190.01	+	1841.75i	−0.689881	+	0.398303i
$69$	−122.836	−	351.862i	−0.0258005	−	0.0739050i
$70$	632.356	−	1095.27i	0.129052	−	0.223525i
$71$			2771.07i			0.549706i	0.961486	+	0.274853i	$0.0886292\pi$
$71$			2771.07i			0.549706i	−0.961486	+	0.274853i	$0.911371\pi$
$72$	672.070	−	1705.15i	0.129643	−	0.328926i
$73$	3525.16			0.661506			0.330753	−	0.943717i	$-0.392697\pi$
$73$	3525.16			0.661506			0.330753	+	0.943717i	$0.392697\pi$
$74$	2076.36	+	1198.79i	0.379174	+	0.218916i
$75$	−3887.01	−	3349.94i	−0.691025	−	0.595545i
$76$	750.964	+	1300.71i	0.130014	+	0.225192i
$77$	3333.11	−	1924.37i	0.562170	−	0.324569i
$78$	7252.21	+	1377.62i	1.19201	+	0.226434i
$79$	−2914.90	+	5048.75i	−0.467056	+	0.808964i	−0.999292	−	0.0376317i	$-0.988019\pi$
$79$	−2914.90	+	5048.75i	−0.467056	+	0.808964i	0.532236	+	0.846596i	$0.321352\pi$
$80$			473.979i			0.0740592i
$81$	4796.63	+	4476.50i	0.731082	+	0.682289i
$82$	−1431.65			−0.212917
$83$	−4438.63	−	2562.65i	−0.644307	−	0.371991i	0.141965	−	0.989872i	$-0.454658\pi$
$83$	−4438.63	−	2562.65i	−0.644307	−	0.371991i	−0.786272	+	0.617881i	$0.787991\pi$
$84$	−811.265	+	4270.73i	−0.114975	+	0.605263i
$85$	1704.98	+	2953.12i	0.235984	+	0.408736i
$86$	−3441.19	+	1986.77i	−0.465277	+	0.268628i
$87$	8219.29	−	9537.03i	1.08591	−	1.26001i
$88$	−721.200	+	1249.16i	−0.0931302	+	0.161306i
$89$		−	1221.14i		−	0.154164i	−0.997025	−	0.0770822i	$-0.975440\pi$
$89$		−	1221.14i		−	0.154164i	0.997025	−	0.0770822i	$-0.0245604\pi$
$90$	−1578.53	−	622.162i	−0.194880	−	0.0768101i
$91$	−17508.5			−2.11429
$92$	−286.894	−	165.638i	−0.0338958	−	0.0195698i
$93$	5412.35	−	1889.47i	0.625778	−	0.218461i
$94$	3505.58	+	6071.84i	0.396738	+	0.687171i
$95$	1204.12	−	695.197i	0.133420	−	0.0770301i
$96$	−536.970	−	1538.14i	−0.0582650	−	0.166899i
$97$	7367.60	−	12761.1i	0.783038	−	1.35626i	−0.147126	−	0.989118i	$-0.547002\pi$
$97$	7367.60	−	12761.1i	0.783038	−	1.35626i	0.930164	−	0.367144i	$-0.119664\pi$
$98$		−	3519.46i		−	0.366458i
$99$	−3213.49	−	4041.56i	−0.327874	−	0.412362i
$100$	−4561.22			−0.456122
$101$	−15034.0	−	8679.88i	−1.47378	−	0.850885i	−0.474213	−	0.880410i	$-0.657267\pi$
$101$	−15034.0	−	8679.88i	−1.47378	−	0.850885i	−0.999564	+	0.0295251i	$0.990601\pi$
$102$	−8878.54	−	7651.78i	−0.853378	−	0.735466i
$103$	5164.36	+	8944.94i	0.486791	+	0.843146i	0.999885	−	0.0151863i	$-0.00483414\pi$
$103$	5164.36	+	8944.94i	0.486791	+	0.843146i	−0.513094	+	0.858332i	$0.671501\pi$
$104$	5682.58	−	3280.84i	0.525387	−	0.303332i
$105$	3953.59	+	751.020i	0.358602	+	0.0681197i
$106$	−1093.48	+	1893.97i	−0.0973195	+	0.168562i
$107$			7260.47i			0.634157i	0.948399	+	0.317079i	$0.102702\pi$
$107$			7260.47i			0.634157i	−0.948399	+	0.317079i	$0.897298\pi$
$108$	5827.44	+	230.703i	0.499609	+	0.0197791i
$109$	1894.50			0.159456			0.0797280	−	0.996817i	$-0.474595\pi$
$109$	1894.50			0.159456			0.0797280	+	0.996817i	$0.474595\pi$
$110$	1156.39	+	667.644i	0.0955697	+	0.0551772i
$111$	−1423.74	+	7495.00i	−0.115554	+	0.608311i
$112$	1932.05	+	3346.40i	0.154022	+	0.266773i
$113$	−8274.94	+	4777.54i	−0.648049	+	0.374151i	−0.787708	−	0.616048i	$-0.788733\pi$
$113$	−8274.94	+	4777.54i	−0.648049	+	0.374151i	0.139659	+	0.990200i	$0.455399\pi$
$114$	−3119.97	+	3620.17i	−0.240071	+	0.278560i
$115$	−153.338	+	265.589i	−0.0115946	+	0.0200824i
$116$		−	11191.2i		−	0.831691i
$117$	3467.28	+	23231.7i	0.253289	+	1.69711i
$118$	12720.8			0.913587
$119$	24075.2	+	13899.8i	1.70011	+	0.981557i
$120$	−1423.92	+	497.095i	−0.0988830	+	0.0345205i
$121$	−5288.74	−	9160.37i	−0.361228	−	0.625666i
$122$	6375.91	−	3681.13i	0.428373	−	0.247321i
$123$	−1501.47	−	4300.94i	−0.0992448	−	0.284284i
$124$	2547.86	−	4413.02i	0.165704	−	0.287007i
$125$			8851.20i			0.566477i
$126$	−13680.9	+	2041.84i	−0.861733	+	0.128611i
$127$	7548.96			0.468037			0.234018	−	0.972232i	$-0.424812\pi$
$127$	7548.96			0.468037			0.234018	+	0.972232i	$0.424812\pi$
$128$	−1254.14	−	724.077i	−0.0765466	−	0.0441942i
$129$	−9577.62	−	8254.27i	−0.575544	−	0.496020i
$130$	−3037.20	−	5260.59i	−0.179716	−	0.311278i
$131$	−4176.24	+	2411.15i	−0.243356	+	0.140502i	−0.616718	−	0.787184i	$-0.711538\pi$
$131$	−4176.24	+	2411.15i	−0.243356	+	0.140502i	0.373362	+	0.927686i	$0.378205\pi$
$132$	−4509.06	−	856.537i	−0.258784	−	0.0491584i
$133$	5667.56	−	9816.51i	0.320400	−	0.554950i
$134$			9568.84i			0.532905i
$135$	213.571	−	5394.69i	0.0117186	−	0.296005i
$136$	−10418.5			−0.563286
$137$	9346.97	+	5396.48i	0.498001	+	0.287521i	0.727887	−	0.685697i	$-0.240502\pi$
$137$	9346.97	+	5396.48i	0.498001	+	0.287521i	−0.229887	+	0.973217i	$0.573836\pi$
$138$	196.721	−	1035.60i	0.0103298	−	0.0543792i
$139$	−14138.6	−	24488.8i	−0.731774	−	1.26747i	−0.956124	−	0.292961i	$-0.905359\pi$
$139$	−14138.6	−	24488.8i	−0.731774	−	1.26747i	0.224350	−	0.974509i	$-0.427974\pi$
$140$	3097.90	−	1788.57i	0.158056	−	0.0912537i
$141$	−14564.3	+	16899.3i	−0.732576	+	0.850025i
$142$	−3918.88	+	6787.70i	−0.194350	+	0.336625i
$143$		−	18485.5i		−	0.903981i
$144$	4057.68	−	3226.31i	0.195683	−	0.155590i
$145$	−10360.2			−0.492755
$146$	8634.85	+	4985.33i	0.405088	+	0.233878i
$147$	10573.1	−	3691.10i	0.489290	−	0.170813i
$148$	3390.68	+	5872.83i	0.154797	+	0.268117i
$149$	−8456.84	+	4882.56i	−0.380922	+	0.219925i	−0.678219	−	0.734860i	$-0.737248\pi$
$149$	−8456.84	+	4882.56i	−0.380922	+	0.219925i	0.297298	+	0.954785i	$0.403915\pi$
$150$	−4783.67	−	13702.7i	−0.212608	−	0.609009i
$151$	−383.441	+	664.140i	−0.0168169	+	0.0291277i	−0.874311	−	0.485365i	$-0.838687\pi$
$151$	−383.441	+	664.140i	−0.0168169	+	0.0291277i	0.857495	+	0.514493i	$0.172020\pi$
$152$			4248.09i			0.183868i
$153$	13675.8	−	34697.7i	0.584210	−	1.48224i
$154$	10885.9			0.459010
$155$	−4085.31	−	2358.65i	−0.170044	−	0.0981749i
$156$	15816.0	+	13630.6i	0.649899	+	0.560102i
$157$	2595.91	+	4496.26i	0.105315	+	0.182411i	0.913867	−	0.406014i	$-0.133082\pi$
$157$	2595.91	+	4496.26i	0.105315	+	0.182411i	−0.808552	+	0.588425i	$0.799748\pi$
$158$	−14280.0	+	8244.57i	−0.572024	+	0.330258i
$159$	−6836.62	−	1298.68i	−0.270425	−	0.0513697i
$160$	−670.307	+	1161.01i	−0.0261839	+	0.0453518i
$161$			2500.17i			0.0964533i
$162$	5418.57	+	17748.6i	0.206469	+	0.676292i
$163$	24180.8			0.910113			0.455057	−	0.890462i	$-0.349619\pi$
$163$	24180.8			0.910113			0.455057	+	0.890462i	$0.349619\pi$
$164$	−3506.82	−	2024.66i	−0.130384	−	0.0752775i
$165$	−792.930	+	4174.21i	−0.0291251	+	0.153323i
$166$	−7248.26	−	12554.3i	−0.263037	−	0.455594i
$167$	18849.5	−	10882.7i	0.675875	−	0.390216i	−0.122424	−	0.992478i	$-0.539067\pi$
$167$	18849.5	−	10882.7i	0.675875	−	0.390216i	0.798299	+	0.602261i	$0.205734\pi$
$168$	−8026.91	+	9313.82i	−0.284400	+	0.329996i
$169$	−27766.0	+	48092.2i	−0.972166	+	1.68384i
$170$			9644.85i			0.333732i
$171$	−14147.8	−	5576.20i	−0.483833	−	0.190698i
$172$	−11238.9			−0.379897
$173$	−20789.4	−	12002.8i	−0.694625	−	0.401042i	0.110717	−	0.993852i	$-0.464685\pi$
$173$	−20789.4	−	12002.8i	−0.694625	−	0.401042i	−0.805342	+	0.592810i	$0.798019\pi$
$174$	33620.5	−	11737.0i	1.11047	−	0.387668i
$175$	17211.9	+	29811.9i	0.562021	+	0.973449i
$176$	−3533.15	+	2039.86i	−0.114061	+	0.0658530i
$177$	13341.2	+	38215.5i	0.425841	+	1.21981i
$178$	1726.95	−	2991.16i	0.0545053	−	0.0944060i
$179$		−	41131.4i		−	1.28371i	−0.766826	−	0.641855i	$-0.778165\pi$
$179$		−	41131.4i		−	1.28371i	0.766826	−	0.641855i	$-0.221835\pi$
$180$	−2986.72	−	3756.36i	−0.0921827	−	0.115937i
$181$	32048.3			0.978246			0.489123	−	0.872215i	$-0.337317\pi$
$181$	32048.3			0.978246			0.489123	+	0.872215i	$0.337317\pi$
$182$	−42886.8	−	24760.7i	−1.29473	−	0.747515i
$183$	17745.6	+	15293.7i	0.529895	+	0.456678i
$184$	−468.496	−	811.459i	−0.0138379	−	0.0239680i
$185$	5436.71	−	3138.88i	0.158852	−	0.0917132i
$186$	15929.6	+	3025.97i	0.460447	+	0.0874660i
$187$	−14675.5	+	25418.7i	−0.419671	+	0.726892i
$188$			19830.5i			0.561073i
$189$	−20482.1	−	38958.3i	−0.573392	−	1.09063i
$190$	3932.63			0.108937
$191$	11444.3	+	6607.35i	0.313705	+	0.181118i	0.648583	−	0.761144i	$-0.275362\pi$
$191$	11444.3	+	6607.35i	0.313705	+	0.181118i	−0.334878	+	0.942261i	$0.608695\pi$
$192$	859.953	−	4527.05i	0.0233277	−	0.122804i
$193$	−893.462	−	1547.52i	−0.0239862	−	0.0415453i	0.853783	−	0.520629i	$-0.174302\pi$
$193$	−893.462	−	1547.52i	−0.0239862	−	0.0415453i	−0.877769	+	0.479083i	$0.840969\pi$
$194$	36093.7	−	20838.7i	0.959022	−	0.553691i
$195$	12618.4	−	14641.5i	0.331845	−	0.385048i
$196$	4977.27	−	8620.88i	0.129562	−	0.224408i
$197$		−	17640.9i		−	0.454557i	−0.973830	−	0.227278i	$-0.927017\pi$
$197$		−	17640.9i		−	0.454557i	0.973830	−	0.227278i	$-0.0729828\pi$
$198$	−2155.78	−	14444.3i	−0.0549888	−	0.368440i
$199$	236.938			0.00598314			0.00299157	−	0.999996i	$-0.499048\pi$
$199$	236.938			0.00598314			0.00299157	+	0.999996i	$0.499048\pi$
$200$	−11172.7	−	6450.54i	−0.279316	−	0.161263i
$201$	−28746.5	+	10035.5i	−0.711529	+	0.248398i
$202$	−24550.4	−	42522.6i	−0.601667	−	1.04212i
$203$	−73145.3	+	42230.4i	−1.77498	+	1.02479i
$204$	−10926.6	−	31299.1i	−0.262559	−	0.752094i
$205$	−1874.31	+	3246.40i	−0.0445999	+	0.0772493i
$206$			29214.0i			0.688426i
$207$	3317.43	−	495.119i	0.0774215	−	0.0115550i
$208$	18559.2			0.428976
$209$	10364.3	+	5983.84i	0.237273	+	0.136990i
$210$	8622.17	+	7430.83i	0.195514	+	0.168500i
$211$	−17979.1	−	31140.8i	−0.403835	−	0.699463i	0.590350	−	0.807147i	$-0.298990\pi$
$211$	−17979.1	−	31140.8i	−0.403835	−	0.699463i	−0.994185	+	0.107684i	$0.965656\pi$
$212$	−5356.94	+	3092.83i	−0.119192	+	0.0688152i
$213$	−24501.5	−	4654.28i	−0.540049	−	0.102587i
$214$	−10267.8	+	17784.4i	−0.224208	+	0.388340i
$215$			10404.3i			0.225079i
$216$	13948.0	+	8806.34i	0.298954	+	0.188750i
$217$	−38457.7			−0.816702
$218$	4640.55	+	2679.22i	0.0976464	+	0.0563762i
$219$	−5920.85	+	31169.1i	−0.123451	+	0.649884i
$220$	1888.38	+	3270.77i	0.0390162	+	0.0675780i
$221$	115633.	−	66760.8i	2.36754	−	1.36690i
$222$	−14087.0	+	16345.4i	−0.285833	+	0.331658i
$223$	27311.5	−	47305.0i	0.549207	−	0.951255i	−0.449122	−	0.893471i	$-0.648263\pi$
$223$	27311.5	−	47305.0i	0.549207	−	0.951255i	0.998329	−	0.0577846i	$-0.0184036\pi$
$224$			10929.3i			0.217819i
$225$	36148.4	−	28742.0i	0.714043	−	0.567743i
$226$	−27025.8			−0.529130
$227$	67692.0	+	39082.0i	1.31367	+	0.758447i	0.982702	−	0.185196i	$-0.0592919\pi$
$227$	67692.0	+	39082.0i	1.31367	+	0.758447i	0.330967	+	0.943642i	$0.392625\pi$
$228$	−12762.0	+	4455.27i	−0.245499	+	0.0857047i
$229$	6019.52	+	10426.1i	0.114787	+	0.198816i	0.917694	−	0.397287i	$-0.130048\pi$
$229$	6019.52	+	10426.1i	0.114787	+	0.198816i	−0.802908	+	0.596103i	$0.796715\pi$
$230$	−751.200	+	433.706i	−0.0142004	+	0.00819859i
$231$	11416.8	+	32703.1i	0.213954	+	0.612866i
$232$	15826.8	−	27412.8i	0.294047	−	0.509305i
$233$			95396.0i			1.75719i	0.477568	+	0.878595i	$0.341518\pi$
$233$			95396.0i			1.75719i	−0.477568	+	0.878595i	$0.658482\pi$
$234$	−24361.6	+	61809.3i	−0.444911	+	1.12881i
$235$	18357.9			0.332421
$236$	31159.4	+	17989.9i	0.559456	+	0.323002i
$237$	−39744.6	−	34253.0i	−0.707590	−	0.609821i
$238$	39314.6	+	68094.9i	0.694065	+	1.20216i
$239$	−88641.6	+	51177.2i	−1.55182	+	0.895944i	−0.553827	+	0.832632i	$0.686833\pi$
$239$	−88641.6	+	51177.2i	−1.55182	+	0.895944i	−0.997994	+	0.0633127i	$0.979833\pi$
$240$	−4190.87	−	796.093i	−0.0727581	−	0.0138211i
$241$	26833.9	−	46477.6i	0.462008	−	0.800221i	−0.537053	−	0.843548i	$-0.680463\pi$
$241$	26833.9	−	46477.6i	0.462008	−	0.800221i	0.999061	+	0.0433274i	$0.0137959\pi$
$242$		−	29917.6i		−	0.510854i
$243$	−47637.1	+	34892.5i	−0.806739	+	0.590908i
$244$	20823.6			0.349765
$245$	−7980.69	−	4607.65i	−0.132956	−	0.0767622i
$246$	2404.60	−	12658.5i	0.0397349	−	0.209176i
$247$	−27221.3	−	47148.7i	−0.446185	−	0.772815i
$248$	12481.9	−	7206.43i	0.202945	−	0.117170i
$249$	30113.7	−	34941.7i	0.485698	−	0.563566i
$250$	−12517.5	+	21680.9i	−0.200280	+	0.346895i
$251$		−	99789.6i		−	1.58394i	−0.610562	−	0.791969i	$-0.709056\pi$
$251$		−	99789.6i		−	1.58394i	0.610562	−	0.791969i	$-0.290944\pi$
$252$	−36398.7	−	14346.2i	−0.573173	−	0.225910i
$253$	−2639.69			−0.0412393
$254$	18491.1	+	10675.8i	0.286613	+	0.165476i
$255$	−28974.8	+	10115.2i	−0.445595	+	0.155559i
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	−2249.40	+	1298.69i	−0.0340565	+	0.0196625i	−0.516932	−	0.856027i	$-0.672926\pi$
$257$	−2249.40	+	1298.69i	−0.0340565	+	0.0196625i	0.482875	+	0.875689i	$0.339593\pi$
$258$	−11787.0	−	33763.6i	−0.177078	−	0.507234i
$259$	25589.6	−	44322.6i	0.381474	−	0.660732i
$260$		−	17181.0i		−	0.254157i
$261$	70520.3	+	88692.4i	1.03522	+	1.30198i
$262$	−13639.5			−0.198700
$263$	−109308.	−	63109.2i	−1.58031	−	0.912392i	−0.994814	−	0.101716i	$-0.967567\pi$
$263$	−109308.	−	63109.2i	−1.58031	−	0.912392i	−0.585495	−	0.810676i	$-0.699100\pi$
$264$	−9833.57	−	8474.85i	−0.141092	−	0.121597i
$265$	2863.16	+	4959.13i	0.0407712	+	0.0706178i
$266$	27765.3	−	16030.3i	0.392409	−	0.226557i
$267$	10797.1	+	2051.01i	0.151456	+	0.0287704i
$268$	−13532.4	+	23438.8i	−0.188410	+	0.326336i
$269$			14374.7i			0.198652i	0.995055	+	0.0993262i	$0.0316687\pi$
$269$			14374.7i			0.198652i	−0.995055	+	0.0993262i	$0.968331\pi$
$270$	8152.38	−	12912.2i	0.111830	−	0.177122i
$271$	−54121.0			−0.736931			−0.368466	−	0.929641i	$-0.620117\pi$
$271$	−54121.0			−0.736931			−0.368466	+	0.929641i	$0.620117\pi$
$272$	−25520.1	−	14734.0i	−0.344941	−	0.199152i
$273$	29407.1	−	154808.i	0.394573	−	2.07715i
$274$	15263.5	+	26437.2i	0.203308	+	0.352140i
$275$	−31475.5	+	18172.4i	−0.416205	+	0.240296i
$276$	1946.42	−	2258.48i	0.0255517	−	0.0296482i
$277$	−15805.9	+	27376.6i	−0.205996	+	0.356796i	−0.950450	−	0.310878i	$-0.899377\pi$
$277$	−15805.9	+	27376.6i	−0.205996	+	0.356796i	0.744453	+	0.667674i	$0.232710\pi$
$278$		−	79980.0i		−	1.03488i
$279$	7615.94	+	51028.9i	0.0978397	+	0.655553i
$280$	10117.7			0.129052
$281$	88490.4	+	51090.0i	1.12068	+	0.647028i	0.941576	−	0.336801i	$-0.109345\pi$
$281$	88490.4	+	51090.0i	1.12068	+	0.647028i	0.179109	+	0.983829i	$0.442678\pi$
$282$	−59574.5	+	20797.7i	−0.749138	+	0.261527i
$283$	72667.1	+	125863.i	0.907329	+	1.57154i	0.817760	+	0.575560i	$0.195216\pi$
$283$	72667.1	+	125863.i	0.907329	+	1.57154i	0.0895693	+	0.995981i	$0.471451\pi$
$284$	−19198.5	+	11084.3i	−0.238030	+	0.137427i
$285$	4124.42	+	11814.3i	0.0507777	+	0.145452i
$286$	26142.4	−	45280.0i	0.319605	−	0.553573i
$287$			30560.5i			0.371019i
$288$	14501.9	−	2164.38i	0.174840	−	0.0260945i
$289$	−128483.			−1.53833
$290$	−25377.1	−	14651.5i	−0.301749	−	0.174215i
$291$	100457.	+	86576.9i	1.18630	+	1.02239i
$292$	14100.7	+	24423.1i	0.165376	+	0.286440i
$293$	−40048.4	+	23122.0i	−0.466498	+	0.269333i	−0.714773	−	0.699357i	$-0.753470\pi$
$293$	−40048.4	+	23122.0i	−0.466498	+	0.269333i	0.248274	+	0.968690i	$0.420137\pi$
$294$	31118.7	+	5911.27i	0.360020	+	0.0683890i
$295$	16654.0	−	28845.5i	0.191370	−	0.331463i
$296$			19180.6i			0.218916i
$297$	41132.4	−	21625.1i	0.466306	−	0.245158i
$298$	−27619.9			−0.311021
$299$	10399.5	+	6004.15i	0.116324	+	0.0671597i
$300$	7661.01	−	40329.8i	0.0851223	−	0.448109i
$301$	42410.2	+	73456.6i	0.468099	+	0.810770i
$302$	−1878.47	+	1084.54i	−0.0205964	+	0.0118913i
$303$	101998.	−	118350.i	1.11098	−	1.28909i
$304$	−6007.71	+	10405.7i	−0.0650072	+	0.112596i
$305$		−	19277.3i		−	0.207227i
$306$	82568.6	−	65651.2i	0.881804	−	0.701132i
$307$	−10736.4			−0.113915			−0.0569576	−	0.998377i	$-0.518140\pi$
$307$	−10736.4			−0.113915			−0.0569576	+	0.998377i	$0.518140\pi$
$308$	26664.9	+	15395.0i	0.281085	+	0.162285i
$309$	−87764.2	+	30638.8i	−0.919179	+	0.320889i
$310$	−6671.28	−	11555.0i	−0.0694202	−	0.120239i
$311$	−192.300	+	111.025i	−0.00198820	+	0.00114789i	−0.500994	−	0.865451i	$-0.667032\pi$
$311$	−192.300	+	111.025i	−0.00198820	+	0.00114789i	0.499006	+	0.866599i	$0.333699\pi$
$312$	19464.4	+	55755.2i	0.199955	+	0.572765i
$313$	−73338.2	+	127026.i	−0.748586	+	1.29659i	0.199914	+	0.979813i	$0.435934\pi$
$313$	−73338.2	+	127026.i	−0.748586	+	1.29659i	−0.948500	+	0.316776i	$0.897400\pi$
$314$			14684.7i			0.148938i
$315$	−13280.9	+	33695.8i	−0.133846	+	0.339589i
$316$	−46638.3			−0.467056
$317$	−152804.	−	88221.5i	−1.52061	−	0.877922i	−0.999705	−	0.0243045i	$-0.992263\pi$
$317$	−152804.	−	88221.5i	−1.52061	−	0.877922i	−0.520901	−	0.853617i	$-0.674404\pi$
$318$	−14909.6	−	12849.5i	−0.147439	−	0.127067i
$319$	−44587.1	−	77227.1i	−0.438155	−	0.758907i
$320$	−3283.82	+	1895.91i	−0.0320686	+	0.0185148i
$321$	−64196.2	−	12194.7i	−0.623016	−	0.118348i
$322$	−3535.77	+	6124.13i	−0.0341014	+	0.0590653i
$323$			86443.1i			0.828563i
$324$	−11827.6	+	51138.0i	−0.112669	+	0.487140i
$325$	165337.			1.56532
$326$	59230.6	+	34196.8i	0.557328	+	0.321774i
$327$	−3181.99	+	16750.9i	−0.0297580	+	0.156655i
$328$	−5726.61	−	9918.78i	−0.0532292	−	0.0921957i
$329$	129611.	−	74831.1i	1.19743	−	0.691338i
$330$	−7845.50	+	9103.32i	−0.0720432	+	0.0835934i
$331$	48118.6	−	83343.8i	0.439194	−	0.760707i	−0.558433	−	0.829549i	$-0.688597\pi$
$331$	48118.6	−	83343.8i	0.439194	−	0.760707i	0.997628	+	0.0688427i	$0.0219306\pi$
$332$		−	41002.3i		−	0.371991i
$333$	−63878.6	−	25177.1i	−0.576059	−	0.227048i
$334$	61562.1			0.551849
$335$	21698.2	+	12527.5i	0.193346	+	0.111628i
$336$	−32833.6	+	11462.3i	−0.290830	+	0.101530i
$337$	−59411.3	−	102903.i	−0.523130	−	0.906087i	−0.999638	−	0.0269171i	$-0.991431\pi$
$337$	−59411.3	−	102903.i	−0.523130	−	0.906087i	0.476508	−	0.879170i	$-0.341902\pi$
$338$	−136025.	+	78534.2i	−1.19066	+	0.687426i
$339$	−28343.9	−	81190.4i	−0.246638	−	0.706489i
$340$	−13639.9	+	23625.0i	−0.117992	+	0.204368i
$341$		−	40603.8i		−	0.349187i
$342$	−26768.9	−	33666.8i	−0.228864	−	0.287839i
$343$	69836.5			0.593600
$344$	−27529.5	−	15894.2i	−0.232638	−	0.134314i
$345$	−2090.76	−	1801.88i	−0.0175658	−	0.0151387i
$346$	−33949.0	−	58801.4i	−0.283580	−	0.491174i
$347$	169009.	−	97577.4i	1.40362	−	0.810383i	0.408861	−	0.912597i	$-0.365926\pi$
$347$	169009.	−	97577.4i	1.40362	−	0.810383i	0.994762	+	0.102214i	$0.0325926\pi$
$348$	98951.6	+	18796.8i	0.817080	+	0.155212i
$349$	39097.6	−	67719.0i	0.320995	−	0.555981i	−0.659698	−	0.751531i	$-0.729316\pi$
$349$	39097.6	−	67719.0i	0.320995	−	0.555981i	0.980694	+	0.195550i	$0.0626492\pi$
$350$			97365.2i			0.794818i
$351$	−211236.	−	8362.65i	−1.71456	−	0.0678781i
$352$	−11539.2			−0.0931302
$353$	−5389.44	−	3111.59i	−0.0432508	−	0.0249708i	0.478219	−	0.878241i	$-0.341283\pi$
$353$	−5389.44	−	3111.59i	−0.0432508	−	0.0249708i	−0.521469	+	0.853270i	$0.674616\pi$
$354$	−21365.8	+	112476.i	−0.170495	+	0.897537i
$355$	10261.1	+	17772.8i	0.0814215	+	0.141026i
$356$	8460.27	−	4884.54i	0.0667551	−	0.0385411i
$357$	−163337.	+	189524.i	−1.28159	+	1.48706i
$358$	58168.6	−	100751.i	0.453860	−	0.786109i
$359$		−	126328.i		−	0.980188i	−0.871670	−	0.490094i	$-0.836962\pi$
$359$		−	126328.i		−	0.980188i	0.871670	−	0.490094i	$-0.163038\pi$
$360$	−2003.65	−	13425.0i	−0.0154603	−	0.103588i
$361$	−95074.4			−0.729540
$362$	78502.0	+	45323.2i	0.599051	+	0.345862i
$363$	89877.9	−	31376.7i	0.682087	−	0.238119i
$364$	−70033.8	−	121302.i	−0.528573	−	0.915515i
$365$	22609.4	−	13053.5i	0.169708	−	0.0979811i
$366$	21839.2	+	62557.9i	0.163033	+	0.467003i
$367$	−60152.2	+	104187.i	−0.446601	+	0.773536i	−0.998162	−	0.0605988i	$-0.980699\pi$
$367$	−60152.2	+	104187.i	−0.446601	+	0.773536i	0.551561	+	0.834134i	$0.314032\pi$
$368$		−	2650.22i		−	0.0195698i
$369$	40550.3	−	6052.03i	0.297811	−	0.0444476i
$370$	17756.2			0.129702
$371$	40429.2	+	23341.8i	0.293729	+	0.169585i
$372$	34740.0	+	29940.0i	0.251041	+	0.216354i
$373$	32755.4	+	56733.9i	0.235432	+	0.407779i	0.959398	−	0.282056i	$-0.0910163\pi$
$373$	32755.4	+	56733.9i	0.235432	+	0.407779i	−0.723966	+	0.689835i	$0.757683\pi$
$374$	−71894.9	+	41508.6i	−0.513990	+	0.296753i
$375$	−78261.3	−	14866.4i	−0.556525	−	0.105717i
$376$	−28044.6	+	48574.7i	−0.198369	+	0.343585i
$377$			405666.i			2.85421i
$378$	4924.66	−	124394.i	0.0344661	−	0.870596i
$379$	129148.			0.899106			0.449553	−	0.893254i	$-0.351583\pi$
$379$	129148.			0.899106			0.449553	+	0.893254i	$0.351583\pi$
$380$	9632.93	+	5561.57i	0.0667100	+	0.0385150i
$381$	−12679.2	+	66747.1i	−0.0873459	+	0.459814i
$382$	18688.4	+	32369.3i	0.128070	+	0.221823i
$383$	61973.9	−	35780.7i	0.422485	−	0.243922i	−0.273655	−	0.961828i	$-0.588233\pi$
$383$	61973.9	−	35780.7i	0.422485	−	0.243922i	0.696140	+	0.717906i	$0.254899\pi$
$384$	8508.66	−	9872.79i	0.0577030	−	0.0669542i
$385$	14251.7	−	24684.7i	0.0961493	−	0.166535i
$386$		−	5054.19i		−	0.0339216i
$387$	89069.9	−	70820.4i	0.594715	−	0.472864i
$388$	117882.			0.783038
$389$	−17196.4	−	9928.34i	−0.113642	−	0.0656111i	0.442102	−	0.896965i	$-0.354233\pi$
$389$	−17196.4	−	9928.34i	−0.113642	−	0.0656111i	−0.555744	+	0.831354i	$0.687566\pi$
$390$	51614.8	−	18018.9i	0.339348	−	0.118468i
$391$	−9533.29	−	16512.1i	−0.0623576	−	0.108007i
$392$	24383.5	−	14077.8i	0.158681	−	0.0916144i
$393$	−14304.7	−	40975.6i	−0.0926179	−	0.265302i
$394$	24948.0	−	43211.2i	0.160710	−	0.278358i
$395$			43174.9i			0.276718i
$396$	15146.8	−	38430.0i	0.0965896	−	0.245064i
$397$	35293.6			0.223931			0.111966	−	0.993712i	$-0.464285\pi$
$397$	35293.6			0.223931			0.111966	+	0.993712i	$0.464285\pi$
$398$	580.378	+	335.081i	0.00366391	+	0.00211536i
$399$	77277.2	+	66599.7i	0.485407	+	0.418337i
$400$	−18244.9	−	31601.1i	−0.114030	−	0.197507i
$401$	−12861.6	+	7425.63i	−0.0799844	+	0.0461790i	−0.539459	−	0.842012i	$-0.681371\pi$
$401$	−12861.6	+	7425.63i	−0.0799844	+	0.0461790i	0.459474	+	0.888191i	$0.348038\pi$
$402$	−84606.6	−	16071.8i	−0.523543	−	0.0994517i
$403$	−92356.1	+	159965.i	−0.568664	+	0.984954i
$404$		−	138878.i		−	0.850885i
$405$	47340.5	+	10949.3i	0.288618	+	0.0667536i
$406$	−238891.			−1.44927
$407$	46795.9	+	27017.7i	0.282501	+	0.163102i
$408$	17498.9	−	92119.5i	0.105121	−	0.553390i
$409$	−36029.2	−	62404.4i	−0.215381	−	0.373051i	0.738009	−	0.674791i	$-0.235766\pi$
$409$	−36029.2	−	62404.4i	−0.215381	−	0.373051i	−0.953390	+	0.301739i	$0.902433\pi$
$410$	−9182.21	+	5301.35i	−0.0546235	+	0.0315369i
$411$	−63414.2	+	73581.0i	−0.375407	+	0.435594i
$412$	−41314.9	+	71559.5i	−0.243395	+	0.421573i
$413$		−	271542.i		−	1.59198i
$414$	8826.23	+	3478.77i	0.0514961	+	0.0202967i
$415$	−37957.5			−0.220395
$416$	45460.7	+	26246.7i	0.262693	+	0.151666i
$417$	240274.	−	83880.7i	1.38177	−	0.482381i
$418$	16924.9	+	29314.7i	0.0968662	+	0.167777i
$419$	−250399.	+	144568.i	−1.42628	+	0.823462i	−0.996825	−	0.0796271i	$-0.974627\pi$
$419$	−250399.	+	144568.i	−1.42628	+	0.823462i	−0.429453	+	0.903089i	$0.641294\pi$
$420$	10611.1	+	30395.3i	0.0601538	+	0.172309i
$421$	−60963.3	+	105592.i	−0.343957	+	0.595751i	−0.985164	−	0.171617i	$-0.945101\pi$
$421$	−60963.3	+	105592.i	−0.343957	+	0.595751i	0.641207	+	0.767368i	$0.278434\pi$
$422$		−	101705.i		−	0.571109i
$423$	−124960.	−	157160.i	−0.698377	−	0.878339i
$424$	−17495.7			−0.0973195
$425$	−227349.	−	131260.i	−1.25868	−	0.726699i
$426$	−53434.0	−	46050.9i	−0.294441	−	0.253758i
$427$	−78578.6	−	136102.i	−0.430971	−	0.746464i
$428$	−50302.0	+	29041.9i	−0.274598	+	0.158539i
$429$	163447.	+	31048.2i	0.888099	+	0.168702i
$430$	−14713.9	+	25485.1i	−0.0795774	+	0.137832i
$431$		−	207467.i		−	1.11685i	−0.829555	−	0.558426i	$-0.811406\pi$
$431$		−	207467.i		−	1.11685i	0.829555	−	0.558426i	$-0.188594\pi$
$432$	21711.4	+	41296.5i	0.116338	+	0.221282i
$433$	88879.4			0.474051			0.237026	−	0.971503i	$-0.423827\pi$
$433$	88879.4			0.474051			0.237026	+	0.971503i	$0.423827\pi$
$434$	−94201.7	−	54387.4i	−0.500126	−	0.288748i
$435$	17400.9	−	91603.4i	0.0919588	−	0.484098i
$436$	7577.98	+	13125.5i	0.0398640	+	0.0690465i
$437$	−6732.72	+	3887.14i	−0.0352556	+	0.0203548i
$438$	−58582.8	+	67975.0i	−0.305367	+	0.354325i
$439$	−74141.8	+	128417.i	−0.384711	+	0.666339i	−0.991729	−	0.128349i	$-0.959032\pi$
$439$	−74141.8	+	128417.i	−0.384711	+	0.666339i	0.607018	+	0.794688i	$0.292365\pi$
$440$			10682.3i			0.0551772i
$441$	14877.8	+	99685.5i	0.0765001	+	0.512572i
$442$	377656.			1.93309
$443$	177795.	+	102650.i	0.905967	+	0.523060i	0.879131	−	0.476580i	$-0.158124\pi$
$443$	177795.	+	102650.i	0.905967	+	0.523060i	0.0268357	+	0.999640i	$0.491457\pi$
$444$	−57621.8	+	20116.0i	−0.292295	+	0.102041i
$445$	−4521.81	−	7832.01i	−0.0228346	−	0.0395506i
$446$	133799.	−	77248.7i	0.672639	−	0.388348i
$447$	−28966.9	−	82975.1i	−0.144973	−	0.415272i
$448$	−15456.4	+	26771.2i	−0.0770108	+	0.133387i
$449$			112334.i			0.557211i	0.960406	+	0.278606i	$0.0898722\pi$
$449$			112334.i			0.557211i	−0.960406	+	0.278606i	$0.910128\pi$
$450$	129192.	−	19281.7i	0.637987	−	0.0952180i
$451$	−32265.9			−0.158632
$452$	−66199.5	−	38220.3i	−0.324025	−	0.187076i
$453$	−5228.22	−	4505.83i	−0.0254776	−	0.0219573i
$454$	110541.	+	191462.i	0.536303	+	0.928904i
$455$	−112294.	+	64833.1i	−0.542418	+	0.313165i
$456$	−37561.1	−	7135.08i	−0.180638	−	0.0343138i
$457$	115511.	−	200070.i	0.553082	−	0.957967i	−0.444968	−	0.895547i	$-0.646785\pi$
$457$	115511.	−	200070.i	0.553082	−	0.957967i	0.998050	−	0.0624202i	$-0.0198819\pi$
$458$			34051.5i			0.162333i
$459$	283823.	+	179198.i	1.34717	+	0.850564i
$460$	−2453.41			−0.0115946
$461$	−186017.	−	107397.i	−0.875287	−	0.505347i	−0.00618557	−	0.999981i	$-0.501969\pi$
$461$	−186017.	−	107397.i	−0.875287	−	0.505347i	−0.869102	+	0.494634i	$0.835302\pi$
$462$	−18283.9	+	96251.7i	−0.0856613	+	0.450946i
$463$	109663.	+	189941.i	0.511561	+	0.886049i	0.999910	+	0.0134011i	$0.00426582\pi$
$463$	109663.	+	189941.i	0.511561	+	0.886049i	−0.488349	+	0.872648i	$0.662401\pi$
$464$	77535.2	−	44764.9i	0.360133	−	0.207923i
$465$	27716.6	−	32160.2i	0.128184	−	0.148735i
$466$	−134910.	+	233672.i	−0.621260	+	1.07605i
$467$		−	62261.6i		−	0.285487i	−0.989760	−	0.142744i	$-0.954408\pi$
$467$		−	62261.6i		−	0.285487i	0.989760	−	0.142744i	$-0.0455924\pi$
$468$	−147085.	+	116949.i	−0.671547	+	0.533955i
$469$	204259.			0.928616
$470$	44967.5	+	25962.0i	0.203565	+	0.117528i
$471$	−44115.5	+	15400.9i	−0.198861	+	0.0694231i
$472$	50883.2	+	88132.2i	0.228397	+	0.395595i
$473$	−77555.8	+	44776.9i	−0.346651	+	0.200139i
$474$	−48912.9	−	140110.i	−0.217704	−	0.623608i
$475$	−53520.5	+	92700.2i	−0.237210	+	0.410859i
$476$			222397.i			0.981557i
$477$	22965.5	−	58267.3i	0.100934	−	0.256088i
$478$	−289502.			−1.26706
$479$	186527.	+	107692.i	0.812964	+	0.469365i	0.847984	−	0.530022i	$-0.177816\pi$
$479$	186527.	+	107692.i	0.812964	+	0.469365i	−0.0350204	+	0.999387i	$0.511150\pi$
$480$	−9139.64	−	7876.80i	−0.0396686	−	0.0341875i
$481$	−122907.	−	212881.i	−0.531235	−	0.920126i
$482$	131459.	−	75897.7i	0.565842	−	0.326689i
$483$	−22106.2	−	4199.27i	−0.0947588	−	0.0180003i
$484$	42309.9	−	73283.0i	0.180614	−	0.312833i
$485$		−	109128.i		−	0.463929i
$486$	−166032.	+	18099.9i	−0.702942	+	0.0766307i
$487$	−387518.			−1.63393			−0.816966	−	0.576687i	$-0.804345\pi$
$487$	−387518.			−1.63393			−0.816966	+	0.576687i	$0.804345\pi$
$488$	51007.3	+	29449.1i	0.214187	+	0.123661i
$489$	−40614.0	+	213804.i	−0.169847	+	0.894124i
$490$	−13032.4	−	22572.8i	−0.0542791	−	0.0940141i
$491$	69131.7	−	39913.2i	0.286757	−	0.165559i	−0.349721	−	0.936854i	$-0.613724\pi$
$491$	69131.7	−	39913.2i	0.286757	−	0.165559i	0.636478	+	0.771295i	$0.280390\pi$
$492$	23791.9	−	27606.3i	0.0982875	−	0.114045i
$493$	322055.	−	557815.i	1.32506	−	2.29507i
$494$		−	153987.i		−	0.631001i
$495$	−35576.1	−	14022.0i	−0.145194	−	0.0572268i
$496$	40765.7			0.165704
$497$	144892.	+	83653.6i	0.586587	+	0.338666i
$498$	123178.	−	43002.0i	0.496679	−	0.173392i
$499$	−36722.7	−	63605.6i	−0.147480	−	0.255443i	0.782815	−	0.622254i	$-0.213783\pi$
$499$	−36722.7	−	63605.6i	−0.147480	−	0.255443i	−0.930296	+	0.366811i	$0.880450\pi$
$500$	−61322.9	+	35404.8i	−0.245292	+	0.141619i
$501$	64564.5	+	184943.i	0.257228	+	0.736824i
$502$	141124.	−	244434.i	0.560006	−	0.969960i
$503$			465077.i			1.83818i	0.394045	+	0.919091i	$0.371075\pi$
$503$			465077.i			1.83818i	−0.394045	+	0.919091i	$0.628925\pi$
$504$	−68869.7	−	86616.5i	−0.271124	−	0.340988i
$505$	−128565.			−0.504127
$506$	−6465.88	−	3733.08i	−0.0252538	−	0.0145803i
$507$	−378590.	−	326280.i	−1.47283	−	1.26933i
$508$	30195.9	+	52300.8i	0.117009	+	0.202666i
$509$	−82539.6	+	47654.3i	−0.318586	+	0.183936i	−0.650762	−	0.759282i	$-0.725551\pi$
$509$	−82539.6	+	47654.3i	−0.318586	+	0.183936i	0.332176	+	0.943217i	$0.392217\pi$
$510$	−85278.7	−	16199.5i	−0.327869	−	0.0622816i
$511$	106418.	−	184322.i	0.407545	−	0.705888i
$512$		−	11585.2i		−	0.0441942i
$513$	73066.7	−	115727.i	0.277642	−	0.439745i
$514$	−7346.50			−0.0278070
$515$	66245.4	+	38246.8i	0.249771	+	0.144205i
$516$	18876.8	−	99372.8i	0.0708970	−	0.373223i
$517$	79007.0	+	136844.i	0.295587	+	0.511971i
$518$	125363.	−	72378.4i	0.467208	−	0.269743i
$519$	141045.	−	163658.i	0.523629	−	0.607579i
$520$	24297.6	−	42084.7i	0.0898581	−	0.155639i
$521$			173345.i			0.638612i	0.947652	+	0.319306i	$0.103450\pi$
$521$			173345.i			0.638612i	−0.947652	+	0.319306i	$0.896550\pi$
$522$	47308.7	+	316982.i	0.173620	+	1.16330i
$523$	−403535.			−1.47529			−0.737646	−	0.675187i	$-0.764063\pi$
$523$	−403535.			−1.47529			−0.737646	+	0.675187i	$0.764063\pi$
$524$	−33409.9	−	19289.2i	−0.121678	−	0.0702509i
$525$	−292502.	+	102114.i	−1.06123	+	0.370480i
$526$	−178500.	−	309171.i	−0.645158	−	1.11745i
$527$	253991.	−	146642.i	0.914527	−	0.528002i
$528$	−12102.0	−	34665.8i	−0.0434099	−	0.124347i
$529$	−139063.	+	240864.i	−0.496936	+	0.860719i
$530$			16196.5i			0.0576592i
$531$	−360305.	+	53774.6i	−1.27785	+	0.190717i
$532$	90681.0			0.320400
$533$	127117.	+	73391.0i	0.447455	+	0.258338i
$534$	23546.9	+	20293.4i	0.0825755	+	0.0711660i
$535$	26885.2	+	46566.5i	0.0939303	+	0.162692i
$536$	−66294.9	+	38275.4i	−0.230755	+	0.133226i
$537$	363679.	+	69084.1i	1.26116	+	0.239568i
$538$	−20328.9	+	35210.6i	−0.0702342	+	0.121649i
$539$		−	79319.8i		−	0.273026i
$540$	38229.8	−	20099.1i	0.131103	−	0.0689269i
$541$	280182.			0.957295			0.478648	−	0.878007i	$-0.341127\pi$
$541$	280182.			0.957295			0.478648	+	0.878007i	$0.341127\pi$
$542$	−132569.	−	76538.6i	−0.451276	−	0.260545i
$543$	−53828.2	+	283368.i	−0.182562	+	0.961060i
$544$	−41674.1	−	72181.7i	−0.140821	−	0.243910i
$545$	12150.8	−	7015.24i	0.0409082	−	0.0236183i
$546$	290964.	−	337612.i	0.976008	−	1.13249i
$547$	48219.9	−	83519.3i	0.161158	−	0.279134i	−0.774126	−	0.633031i	$-0.781811\pi$
$547$	48219.9	−	83519.3i	0.161158	−	0.279134i	0.935284	+	0.353898i	$0.115144\pi$
$548$			86343.6i			0.287521i
$549$	−165031.	+	131218.i	−0.547545	+	0.435359i
$550$	−102799.			−0.339830
$551$	−227446.	−	131316.i	−0.749160	−	0.432528i
$552$	7961.72	−	2779.47i	0.0261293	−	0.00912186i
$553$	175991.	+	304825.i	0.575493	+	0.996784i
$554$	−77432.8	+	44705.8i	−0.252293	+	0.145661i
$555$	18622.2	+	53342.8i	0.0604567	+	0.173177i
$556$	113109.	−	195910.i	0.365887	−	0.633735i
$557$		−	403818.i		−	1.30159i	−0.759252	−	0.650797i	$-0.774435\pi$
$557$		−	403818.i		−	1.30159i	0.759252	−	0.650797i	$-0.225565\pi$
$558$	−53510.6	+	135765.i	−0.171859	+	0.436034i
$559$	407392.			1.30373
$560$	24783.2	+	14308.6i	0.0790280	+	0.0456268i
$561$	−200100.	−	172452.i	−0.635802	−	0.547953i
$562$	144504.	+	250289.i	0.457518	+	0.792444i
$563$	−12809.4	+	7395.51i	−0.0404122	+	0.0233320i	−0.520070	−	0.854124i	$-0.674094\pi$
$563$	−12809.4	+	7395.51i	−0.0404122	+	0.0233320i	0.479658	+	0.877456i	$0.340761\pi$
$564$	−175339.	−	33307.3i	−0.551216	−	0.104708i
$565$	−35382.0	+	61283.5i	−0.110837	+	0.191976i
$566$			411067.i			1.28316i
$567$	378867.	−	115666.i	1.17848	−	0.359783i
$568$	−62702.1			−0.194350
$569$	210701.	+	121648.i	0.650792	+	0.375735i	0.788760	−	0.614702i	$-0.210724\pi$
$569$	210701.	+	121648.i	0.650792	+	0.375735i	−0.137968	+	0.990437i	$0.544057\pi$
$570$	−6605.22	+	34771.8i	−0.0203300	+	0.107023i
$571$	217151.	+	376117.i	0.666025	+	1.15359i	0.979006	+	0.203829i	$0.0653388\pi$
$571$	217151.	+	376117.i	0.666025	+	1.15359i	−0.312982	+	0.949759i	$0.601328\pi$
$572$	128071.	−	73942.0i	0.391435	−	0.225995i
$573$	−77643.2	+	90091.3i	−0.236480	+	0.274393i
$574$	−43219.1	+	74857.6i	−0.131175	+	0.227202i
$575$		−	23609.8i		−	0.0714096i
$576$	38583.3	+	15207.2i	0.116293	+	0.0458358i
$577$	−404030.			−1.21356			−0.606781	−	0.794869i	$-0.707540\pi$
$577$	−404030.			−1.21356			−0.606781	+	0.794869i	$0.707540\pi$
$578$	−314717.	−	181702.i	−0.942029	−	0.543881i
$579$	15183.7	−	5300.68i	0.0452918	−	0.0158115i
$580$	−41440.7	−	71777.4i	−0.123189	−	0.213369i
$581$	−267989.	+	154723.i	−0.793898	+	0.458357i
$582$	123631.	+	354137.i	0.364990	+	1.04550i
$583$	−24644.4	+	42685.3i	−0.0725071	+	0.125586i
$584$			79765.4i			0.233878i
$585$	108264.	+	136162.i	0.316354	+	0.397874i
$586$	−130798.			−0.380894
$587$	−176946.	−	102160.i	−0.513528	−	0.296486i	0.220754	−	0.975329i	$-0.429148\pi$
$587$	−176946.	−	102160.i	−0.513528	−	0.296486i	−0.734283	+	0.678844i	$0.762481\pi$
$588$	67865.0	+	58488.0i	0.196287	+	0.169166i
$589$	−59792.1	−	103563.i	−0.172351	−	0.298521i
$590$	81587.5	−	47104.6i	0.234379	−	0.135319i
$591$	155979.	+	29629.6i	0.446571	+	0.0848302i
$592$	−27125.4	+	46982.6i	−0.0773986	+	0.134058i
$593$		−	569645.i		−	1.61993i	−0.586481	−	0.809963i	$-0.699487\pi$
$593$		−	569645.i		−	1.61993i	0.586481	−	0.809963i	$-0.300513\pi$
$594$	131336.	+	5199.48i	0.372229	+	0.0147362i
$595$	205882.			0.581546
$596$	−67654.7	−	39060.5i	−0.190461	−	0.109963i
$597$	−397.961	+	2094.98i	−0.00111658	+	0.00587803i
$598$	16982.3	+	29414.2i	0.0474891	+	0.0822535i
$599$	242136.	−	139797.i	0.674846	−	0.389623i	−0.123064	−	0.992399i	$-0.539272\pi$
$599$	242136.	−	139797.i	0.674846	−	0.389623i	0.797910	+	0.602776i	$0.205939\pi$
$600$	75800.5	−	87953.1i	0.210557	−	0.244314i
$601$	−114264.	+	197910.i	−0.316344	+	0.547923i	−0.979722	−	0.200361i	$-0.935789\pi$
$601$	−114264.	+	197910.i	−0.316344	+	0.547923i	0.663379	+	0.748284i	$0.269122\pi$
$602$			239908.i			0.661991i
$603$	−40450.4	−	271029.i	−0.111247	−	0.745385i
$604$	−6135.06			−0.0168169
$605$	−67840.9	−	39168.0i	−0.185345	−	0.107009i
$606$	417214.	−	145651.i	1.13609	−	0.396615i
$607$	95669.3	+	165704.i	0.259654	+	0.449734i	0.966149	−	0.257984i	$-0.0830581\pi$
$607$	95669.3	+	165704.i	0.259654	+	0.449734i	−0.706495	+	0.707718i	$0.749725\pi$
$608$	−29431.6	+	16992.4i	−0.0796173	+	0.0459671i
$609$	−250542.	−	717672.i	−0.675533	−	1.93505i
$610$	27262.2	−	47219.4i	0.0732657	−	0.126900i
$611$		−	718828.i		−	1.92550i
$612$	295096.	−	44042.3i	0.787880	−	0.117589i
$613$	−446105.			−1.18718			−0.593589	−	0.804768i	$-0.702290\pi$
$613$	−446105.			−1.18718			−0.593589	+	0.804768i	$0.702290\pi$
$614$	−26298.7	−	15183.6i	−0.0697585	−	0.0402751i
$615$	−25556.2	−	22025.1i	−0.0675688	−	0.0582327i
$616$	43543.5	+	75419.6i	0.114753	+	0.198757i
$617$	−283400.	+	163621.i	−0.744439	+	0.429802i	−0.823681	−	0.567053i	$-0.808083\pi$
$617$	−283400.	+	163621.i	−0.744439	+	0.429802i	0.0792421	+	0.996855i	$0.474750\pi$
$618$	−258307.	−	49067.8i	−0.676332	−	0.128475i
$619$	−55163.0	+	95545.2i	−0.143968	+	0.249360i	−0.928988	−	0.370111i	$-0.879320\pi$
$619$	−55163.0	+	95545.2i	−0.143968	+	0.249360i	0.785019	+	0.619471i	$0.212653\pi$
$620$		−	37738.5i		−	0.0981749i
$621$	−1194.17	+	30164.0i	−0.00309658	+	0.0782178i
$622$	−628.051			−0.00162336
$623$	−63850.2	−	36863.9i	−0.164508	−	0.0949785i
$624$	−31172.0	+	164099.i	−0.0800564	+	0.421440i
$625$	−145397.	−	251835.i	−0.372216	−	0.644698i
$626$	−359282.	+	207432.i	−0.916827	+	0.529330i
$627$	−70316.3	+	81589.6i	−0.178863	+	0.207539i
$628$	−20767.3	+	35970.0i	−0.0526576	+	0.0912056i
$629$			390300.i			0.986500i
$630$	−80184.3	+	63755.4i	−0.202027	+	0.160634i
$631$	321684.			0.807925			0.403962	−	0.914776i	$-0.367633\pi$
$631$	321684.			0.807925			0.403962	+	0.914776i	$0.367633\pi$
$632$	−114240.	−	65956.5i	−0.286012	−	0.165129i
$633$	305541.	−	106666.i	0.762539	−	0.266205i
$634$	−249528.	−	432195.i	−0.620784	−	1.07523i
$635$	48416.9	−	27953.5i	0.120074	−	0.0693248i
$636$	−18349.0	−	52560.2i	−0.0453626	−	0.129940i
$637$	−180418.	+	312494.i	−0.444633	+	0.770128i
$638$		−	252223.i		−	0.619645i
$639$	82305.2	−	208822.i	0.201570	−	0.511416i
$640$	−10724.9			−0.0261839
$641$	215079.	+	124176.i	0.523457	+	0.302218i	0.738348	−	0.674420i	$-0.235606\pi$
$641$	215079.	+	124176.i	0.523457	+	0.302218i	−0.214891	+	0.976638i	$0.568940\pi$
$642$	−140002.	−	120658.i	−0.339676	−	0.292742i
$643$	−218681.	−	378766.i	−0.528918	−	0.916113i	−0.999431	−	0.0337200i	$-0.989265\pi$
$643$	−218681.	−	378766.i	−0.528918	−	0.916113i	0.470513	−	0.882393i	$-0.344069\pi$
$644$	−17321.7	+	10000.7i	−0.0417655	+	0.0241133i
$645$	−91993.3	−	17475.0i	−0.221125	−	0.0420046i
$646$	−122249.	+	211742.i	−0.292941	+	0.507389i
$647$			721599.i			1.72380i	0.507076	+	0.861901i	$0.330726\pi$
$647$			721599.i			1.72380i	−0.507076	+	0.861901i	$0.669274\pi$
$648$	−101292.	+	108535.i	−0.241226	+	0.258477i
$649$	286695.			0.680661
$650$	404992.	+	233822.i	0.958562	+	0.553426i
$651$	64593.4	−	340038.i	0.152414	−	0.802354i
$652$	96723.2	+	167530.i	0.227528	+	0.394091i
$653$	−110385.	+	63730.7i	−0.258871	+	0.149459i	−0.623819	−	0.781569i	$-0.714420\pi$
$653$	−110385.	+	63730.7i	−0.258871	+	0.149459i	0.364949	+	0.931028i	$0.381087\pi$
$654$	−31483.6	+	36531.2i	−0.0736087	+	0.0854099i
$655$	−17856.8	+	30928.9i	−0.0416218	+	0.0720910i
$656$		−	32394.6i		−	0.0752775i
$657$	−265649.	−	104703.i	−0.615428	−	0.242565i
$658$	423309.			0.977700
$659$	137086.	+	79146.9i	0.315663	+	0.182248i	0.649458	−	0.760398i	$-0.274996\pi$
$659$	137086.	+	79146.9i	0.315663	+	0.182248i	−0.333795	+	0.942646i	$0.608329\pi$
$660$	−32091.5	+	11203.3i	−0.0736720	+	0.0257192i
$661$	285009.	+	493649.i	0.652311	+	1.12984i	0.982561	+	0.185943i	$0.0595338\pi$
$661$	285009.	+	493649.i	0.652311	+	1.12984i	−0.330249	+	0.943894i	$0.607133\pi$
$662$	235732.	−	136100.i	0.537901	−	0.310557i
$663$	396075.	+	1.13455e6i	0.901052	+	2.58104i
$664$	57986.0	−	100435.i	0.131519	−	0.227797i
$665$		−	83947.0i		−	0.189829i
$666$	−120864.	−	152009.i	−0.272489	−	0.342706i
$667$	57928.1			0.130208
$668$	150796.	+	87062.0i	0.337937	+	0.195108i
$669$	372393.	+	320939.i	0.832049	+	0.717084i
$670$	35433.0	+	61371.8i	0.0789330	+	0.136716i
$671$	143697.	−	82963.6i	0.319156	−	0.184265i
$672$	−96635.7	−	18356.8i	−0.213993	−	0.0406499i
$673$	134677.	−	233267.i	0.297347	−	0.515020i	−0.678181	−	0.734895i	$-0.737232\pi$
$673$	134677.	−	233267.i	0.297347	−	0.515020i	0.975528	+	0.219875i	$0.0705649\pi$
$674$		−	336081.i		−	0.739817i
$675$	193419.	+	367895.i	0.424513	+	0.807451i
$676$	−444257.			−0.972166
$677$	393590.	+	227240.i	0.858751	+	0.495800i	0.863594	−	0.504188i	$-0.168208\pi$
$677$	393590.	+	227240.i	0.858751	+	0.495800i	−0.00484289	+	0.999988i	$0.501542\pi$
$678$	45392.5	−	238959.i	0.0987472	−	0.519834i
$679$	−444830.	−	770468.i	−0.964838	−	1.67115i
$680$	−66821.5	+	38579.4i	−0.144510	+	0.0834329i
$681$	−459254.	+	532883.i	−0.990281	+	1.14905i
$682$	57422.4	−	99458.5i	0.123456	−	0.213832i
$683$			225234.i			0.482827i	0.970422	+	0.241414i	$0.0776110\pi$
$683$			225234.i			0.482827i	−0.970422	+	0.241414i	$0.922389\pi$
$684$	−17958.0	−	120323.i	−0.0383835	−	0.257180i
$685$	79931.7			0.170348
$686$	171064.	+	98763.7i	0.363504	+	0.209869i
$687$	−102297.	+	35712.3i	−0.216745	+	0.0756665i
$688$	−44955.5	−	77865.2i	−0.0949742	−	0.164500i
$689$	194181.	−	112111.i	0.409043	−	0.236161i
$690$	−2573.06	−	7370.48i	−0.00540446	−	0.0154809i
$691$	252440.	−	437240.i	0.528692	−	0.915722i	−0.470748	−	0.882268i	$-0.656016\pi$
$691$	252440.	−	437240.i	0.528692	−	0.915722i	0.999440	−	0.0334540i	$-0.0106507\pi$
$692$		−	192045.i		−	0.401042i
$693$	−308333.	+	46017.9i	−0.642027	+	0.0958209i
$694$	551981.			1.14605
$695$	−181362.	−	104709.i	−0.375471	−	0.216778i
$696$	215798.	+	185981.i	0.445482	+	0.383929i
$697$	−116529.	−	201834.i	−0.239866	−	0.415460i
$698$	191538.	−	110585.i	0.393138	−	0.226978i
$699$	−843481.	−	160227.i	−1.72632	−	0.327930i
$700$	−137695.	+	238495.i	−0.281010	+	0.486724i
$701$			19860.8i			0.0404166i	0.999796	+	0.0202083i	$0.00643294\pi$
$701$			19860.8i			0.0404166i	−0.999796	+	0.0202083i	$0.993567\pi$
$702$	−505593.	−	319217.i	−1.02595	−	0.647756i
$703$	159142.			0.322014
$704$	−28265.2	−	16318.9i	−0.0570304	−	0.0329265i
$705$	−30833.9	+	162319.i	−0.0620369	+	0.326580i
$706$	−8800.91	−	15243.6i	−0.0176571	−	0.0305829i
$707$	−907699.	+	524060.i	−1.81595	+	1.04844i
$708$	−211400.	+	245292.i	−0.421734	+	0.489348i
$709$	−315420.	+	546324.i	−0.627476	+	1.08682i	0.360580	+	0.932728i	$0.382579\pi$
$709$	−315420.	+	546324.i	−0.627476	+	1.08682i	−0.988056	+	0.154093i	$0.950755\pi$
$710$			58045.8i			0.115147i
$711$	369616.	−	293886.i	0.731159	−	0.581353i
$712$	27631.1			0.0545053
$713$	22842.7	+	13188.2i	0.0449333	+	0.0259422i
$714$	−668121.	+	233244.i	−1.31056	+	0.457523i
$715$	−68451.0	−	118561.i	−0.133896	−	0.231915i
$716$	284967.	−	164526.i	0.555863	−	0.320928i
$717$	−303621.	−	869716.i	−0.590601	−	1.69176i
$718$	178654.	−	309438.i	0.346549	−	0.600240i
$719$			337555.i			0.652960i	0.945204	+	0.326480i	$0.105863\pi$
$719$			337555.i			0.652960i	−0.945204	+	0.326480i	$0.894137\pi$
$720$	14077.9	−	35718.0i	0.0271565	−	0.0689005i
$721$	623612.			1.19962
$722$	−232884.	−	134455.i	−0.446750	−	0.257931i
$723$	365880.	+	315326.i	0.699942	+	0.603230i
$724$	128193.	+	222037.i	0.244561	+	0.423593i
$725$	690732.	−	398794.i	1.31412	−	0.758705i
$726$	264528.	+	50249.6i	0.501879	+	0.0953365i
$727$	257481.	−	445970.i	0.487165	−	0.843795i	−0.512726	−	0.858552i	$-0.671364\pi$
$727$	257481.	−	445970.i	0.487165	−	0.843795i	0.999891	+	0.0147576i	$0.00469766\pi$
$728$		−	396171.i		−	0.747515i
$729$	−228505.	−	479807.i	−0.429972	−	0.902842i
$730$	73841.9			0.138566
$731$	−560189.	−	323426.i	−1.04834	−	0.605257i
$732$	−34975.3	+	184120.i	−0.0652739	+	0.343621i
$733$	−508070.	−	880002.i	−0.945617	−	1.63786i	−0.754511	−	0.656287i	$-0.772126\pi$
$733$	−508070.	−	880002.i	−0.945617	−	1.63786i	−0.191106	−	0.981569i	$-0.561207\pi$
$734$	−294685.	+	170136.i	−0.546972	+	0.315795i
$735$	54144.7	−	62825.3i	0.100226	−	0.116295i
$736$	3747.97	−	6491.68i	0.00691896	−	0.0119840i
$737$			215658.i			0.397036i
$738$	107886.	+	42522.4i	0.198086	+	0.0780737i
$739$	−663801.			−1.21548			−0.607742	−	0.794135i	$-0.707924\pi$
$739$	−663801.			−1.21548			−0.607742	+	0.794135i	$0.707924\pi$
$740$	43493.7	+	25111.1i	0.0794260	+	0.0458566i
$741$	462604.	−	161497.i	0.842506	−	0.294122i
$742$	66020.5	+	114351.i	0.119914	+	0.207698i
$743$	619586.	−	357718.i	1.12234	−	0.647982i	0.180341	−	0.983604i	$-0.442280\pi$
$743$	619586.	−	357718.i	1.12234	−	0.647982i	0.941997	+	0.335622i	$0.108946\pi$
$744$	42753.9	+	122467.i	0.0772378	+	0.221246i
$745$	−36159.8	+	62630.6i	−0.0651499	+	0.112843i
$746$			185292.i			0.332950i
$747$	258371.	+	324950.i	0.463024	+	0.582338i
$748$	−234808.			−0.419671
$749$	379632.	+	219181.i	0.676705	+	0.390696i
$750$	−170676.	−	147093.i	−0.303424	−	0.261499i
$751$	221593.	+	383811.i	0.392895	+	0.680514i	0.992830	−	0.119535i	$-0.0381402\pi$
$751$	221593.	+	383811.i	0.392895	+	0.680514i	−0.599935	+	0.800049i	$0.704807\pi$
$752$	−137390.	+	79322.2i	−0.242952	+	0.140268i
$753$	882329.	+	167606.i	1.55611	+	0.295597i
$754$	−573698.	+	993674.i	−1.00911	+	1.74784i
$755$			5679.47i			0.00996355i
$756$	187983.	−	297738.i	0.328908	−	0.520943i
$757$	−270550.			−0.472123			−0.236061	−	0.971738i	$-0.575857\pi$
$757$	−270550.			−0.472123			−0.236061	+	0.971738i	$0.575857\pi$
$758$	316348.	+	182644.i	0.550588	+	0.317882i
$759$	4433.61	−	23339.8i	0.00769615	−	0.0405148i
$760$	15730.5	+	27246.0i	0.0272343	+	0.0471711i
$761$	−507749.	+	293149.i	−0.876758	+	0.506196i	−0.869588	−	0.493778i	$-0.835616\pi$
$761$	−507749.	+	293149.i	−0.876758	+	0.506196i	−0.00716962	+	0.999974i	$0.502282\pi$
$762$	−125452.	+	145565.i	−0.216057	+	0.250696i
$763$	57191.5	−	99058.5i	0.0982386	−	0.170154i
$764$			105718.i			0.181118i
$765$	−40771.7	−	273182.i	−0.0696684	−	0.466798i
$766$	202406.			0.344958
$767$	−1.12948e6	−	652108.i	−1.91995	−	1.10848i
$768$	34804.1	−	12150.3i	0.0590076	−	0.0205998i
$769$	226409.	+	392152.i	0.382861	+	0.663134i	0.991470	−	0.130336i	$-0.0416056\pi$
$769$	226409.	+	392152.i	0.382861	+	0.663134i	−0.608609	+	0.793470i	$0.708272\pi$
$770$	69818.9	−	40310.0i	0.117758	−	0.0679878i
$771$	−7704.79	−	22070.2i	−0.0129614	−	0.0371276i
$772$	7147.70	−	12380.2i	0.0119931	−	0.0207727i
$773$			217175.i			0.363455i	0.983349	+	0.181728i	$0.0581689\pi$
$773$			217175.i			0.363455i	−0.983349	+	0.181728i	$0.941831\pi$
$774$	318331.	−	47510.1i	0.531370	−	0.0793056i
$775$	363167.			0.604648
$776$	288750.	+	166710.i	0.479511	+	0.276846i
$777$	348915.	+	300705.i	0.577933	+	0.498079i
$778$	−28081.6	−	48638.7i	−0.0463941	−	0.0803569i
$779$	−82296.6	+	47514.0i	−0.135615	+	0.0782973i
$780$	151913.	+	28857.2i	0.249692	+	0.0474313i
$781$	−88321.9	+	152978.i	−0.144799	+	0.250800i
$782$		−	53928.4i		−	0.0881870i
$783$	−902653.	+	474565.i	−1.47230	+	0.774055i
$784$	79636.2			0.129562
$785$	33298.9	+	19225.1i	0.0540369	+	0.0311982i
$786$	22908.9	−	120599.i	0.0370817	−	0.195209i
$787$	23419.0	+	40562.9i	0.0378110	+	0.0654906i	0.884312	−	0.466897i	$-0.154628\pi$
$787$	23419.0	+	40562.9i	0.0378110	+	0.0654906i	−0.846501	+	0.532388i	$0.821295\pi$
$788$	122220.	−	70563.6i	0.196829	−	0.113639i
$789$	741598.	−	860494.i	1.19128	−	1.38227i
$790$	−61058.6	+	105757.i	−0.0978346	+	0.169455i
$791$			576902.i			0.922038i
$792$	91450.1	−	72713.0i	0.145792	−	0.115921i
$793$	−754826.			−1.20033
$794$	86451.3	+	49912.7i	0.137129	+	0.0791717i
$795$	−48657.0	+	16986.4i	−0.0769859	+	0.0268761i
$796$	947.754	+	1641.56i	0.00149579	+	0.00259078i
$797$	324494.	−	187347.i	0.510846	−	0.294937i	−0.222335	−	0.974970i	$-0.571368\pi$
$797$	324494.	−	187347.i	0.510846	−	0.294937i	0.733181	+	0.680033i	$0.238035\pi$
$798$	95103.6	+	272422.i	0.149345	+	0.427796i
$799$	−570672.	+	988433.i	−0.893908	+	1.54829i
$800$		−	103209.i		−	0.161263i
$801$	−36269.7	+	92022.2i	−0.0565300	+	0.143426i
$802$	−42005.7			−0.0653070
$803$	194608.	+	112357.i	0.301807	+	0.174249i
$804$	−184514.	−	159019.i	−0.285442	−	0.246002i
$805$	9258.01	+	16035.3i	0.0142865	+	0.0247449i
$806$	−452451.	+	261222.i	−0.696468	+	0.402106i
$807$	−127099.	−	24143.7i	−0.195162	−	0.0370729i
$808$	196403.	−	340180.i	0.300833	−	0.521059i
$809$		−	1.02586e6i		−	1.56745i	−0.621109	−	0.783724i	$-0.713318\pi$
$809$		−	1.02586e6i		−	1.56745i	0.621109	−	0.783724i	$-0.286682\pi$
$810$	100475.	+	93769.7i	0.153140	+	0.142920i
$811$	869028.			1.32127			0.660636	−	0.750707i	$-0.270287\pi$
$811$	869028.			1.32127			0.660636	+	0.750707i	$0.270287\pi$
$812$	−585162.	−	337844.i	−0.887492	−	0.512394i
$813$	90901.4	−	478532.i	0.137527	−	0.723985i
$814$	76417.5	+	132359.i	0.115330	+	0.199758i
$815$	155089.	−	89540.5i	0.233488	−	0.134804i
$816$	173140.	−	200899.i	0.260026	−	0.301715i
$817$	−131875.	+	228414.i	−0.197568	+	0.342198i
$818$		−	203812.i		−	0.304595i
$819$	1.31940e6	+	520029.i	1.96702	+	0.775282i
$820$	−29989.0			−0.0445999
$821$	−469988.	−	271348.i	−0.697269	−	0.402568i	0.109060	−	0.994035i	$-0.465216\pi$
$821$	−469988.	−	271348.i	−0.697269	−	0.402568i	−0.806329	+	0.591467i	$0.798549\pi$
$822$	−259392.	+	90554.6i	−0.383895	+	0.134019i
$823$	285782.	+	494990.i	0.421926	+	0.730797i	0.996128	−	0.0879170i	$-0.0280210\pi$
$823$	285782.	+	494990.i	0.421926	+	0.730797i	−0.574202	+	0.818713i	$0.694688\pi$
$824$	−202401.	+	116856.i	−0.298097	+	0.172106i
$825$	−107812.	−	308825.i	−0.158402	−	0.453737i
$826$	384018.	−	665139.i	0.562849	−	0.974882i
$827$		−	143023.i		−	0.209120i	−0.994519	−	0.104560i	$-0.966657\pi$
$827$		−	143023.i		−	0.209120i	0.994519	−	0.104560i	$-0.0333434\pi$
$828$	16700.0	+	21003.4i	0.0243588	+	0.0306358i
$829$	−17805.6			−0.0259087			−0.0129544	−	0.999916i	$-0.504124\pi$
$829$	−17805.6			−0.0259087			−0.0129544	+	0.999916i	$0.504124\pi$
$830$	−92976.4	−	53680.0i	−0.134964	−	0.0779213i
$831$	−215513.	−	185736.i	−0.312085	−	0.268963i
$832$	74237.0	+	128582.i	0.107244	+	0.185752i
$833$	496173.	−	286466.i	0.715061	−	0.412841i
$834$	707174.	+	134334.i	1.01670	+	0.193132i
$835$	80596.7	−	139598.i	0.115596	−	0.200219i
$836$			95741.4i			0.136990i
$837$	−463984.	−	18368.7i	−0.662296	−	0.0262197i
$838$	−817799.			−1.16455
$839$	−834828.	−	481988.i	−1.18597	−	0.684719i	−0.228580	−	0.973525i	$-0.573408\pi$
$839$	−834828.	−	481988.i	−1.18597	−	0.684719i	−0.957388	+	0.288806i	$0.906742\pi$
$840$	−16993.6	+	89459.5i	−0.0240840	+	0.126785i
$841$	624826.	+	1.08223e6i	0.883420	+	1.53013i
$842$	−298658.	+	172430.i	−0.421260	+	0.243214i
$843$	−600360.	+	696612.i	−0.844805	+	0.980247i
$844$	143833.	−	249126.i	0.201918	−	0.349731i
$845$			411266.i			0.575983i
$846$	−83829.7	−	561683.i	−0.117127	−	0.784784i
$847$	−638631.			−0.890191
$848$	−42855.5	−	24742.7i	−0.0595958	−	0.0344076i
$849$	−1.23492e6	+	431115.i	−1.71326	+	0.598105i
$850$	−371260.	−	643040.i	−0.513854	−	0.890021i
$851$	−30398.9	+	17550.8i	−0.0419758	+	0.0242348i
$852$	−65760.1	−	188368.i	−0.0905906	−	0.259495i
$853$	536801.	−	929767.i	0.737760	−	1.27784i	−0.215741	−	0.976451i	$-0.569217\pi$
$853$	536801.	−	929767.i	0.737760	−	1.27784i	0.953502	−	0.301388i	$-0.0974498\pi$
$854$		−	444508.i		−	0.609486i
$855$	−111388.	+	16624.4i	−0.152372	+	0.0227412i
$856$	−164286.			−0.224208
$857$	951017.	+	549070.i	1.29487	+	0.747595i	0.979514	−	0.201378i	$-0.0645419\pi$
$857$	951017.	+	549070.i	1.29487	+	0.747595i	0.315358	+	0.948973i	$0.397875\pi$
$858$	356452.	+	307201.i	0.484202	+	0.417299i
$859$	446.404	+	773.194i	0.000604981	+	0.00104786i	0.866328	−	0.499476i	$-0.166474\pi$
$859$	446.404	+	773.194i	0.000604981	+	0.00104786i	−0.865723	+	0.500524i	$0.833141\pi$
$860$	−72082.9	+	41617.1i	−0.0974620	+	0.0562697i
$861$	−270212.	−	51329.3i	−0.364501	−	0.0692403i
$862$	293403.	−	508189.i	0.394867	−	0.683929i
$863$		−	395494.i		−	0.531029i	−0.964107	−	0.265514i	$-0.914458\pi$
$863$		−	395494.i		−	0.531029i	0.964107	−	0.265514i	$-0.0855418\pi$
$864$	−5220.22	+	131860.i	−0.00699296	+	0.176638i
$865$	−177783.			−0.237607
$866$	217709.	+	125694.i	0.290296	+	0.167602i
$867$	215799.	−	1.13603e6i	0.287085	−	1.51130i
$868$	−153831.	−	266443.i	−0.204175	−	0.353642i
$869$	−321836.	+	185812.i	−0.426182	+	0.246056i
$870$	172170.	−	199773.i	0.227468	−	0.263936i
$871$	490529.	−	849621.i	0.646589	−	1.11992i
$872$			42867.6i			0.0563762i
$873$	−934231.	+	742818.i	−1.22582	+	0.974661i
$874$	−21989.0			−0.0287861
$875$	462807.	+	267202.i	0.604483	+	0.348999i
$876$	−239629.	+	83655.5i	−0.312271	+	0.109015i
$877$	330793.	+	572951.i	0.430088	+	0.744935i	0.996880	−	0.0789259i	$-0.0251491\pi$
$877$	330793.	+	572951.i	0.430088	+	0.744935i	−0.566792	+	0.823861i	$0.691816\pi$
$878$	−363219.	+	209705.i	−0.471173	+	0.272032i
$879$	−137177.	−	392939.i	−0.177542	−	0.508566i
$880$	−15107.1	+	26166.2i	−0.0195081	+	0.0337890i
$881$		−	419496.i		−	0.540476i	−0.962794	−	0.270238i	$-0.912898\pi$
$881$		−	419496.i		−	0.540476i	0.962794	−	0.270238i	$-0.0871024\pi$
$882$	−104534.	+	265219.i	−0.134375	+	0.340932i
$883$	−498161.			−0.638923			−0.319461	−	0.947599i	$-0.603502\pi$
$883$	−498161.			−0.638923			−0.319461	+	0.947599i	$0.603502\pi$
$884$	925065.	+	534087.i	1.18377	+	0.683451i
$885$	227077.	+	195701.i	0.289926	+	0.249866i
$886$	290338.	+	502881.i	0.369859	+	0.640615i
$887$	332952.	−	192230.i	0.423189	−	0.244328i	−0.273252	−	0.961942i	$-0.588099\pi$
$887$	332952.	−	192230.i	0.423189	−	0.244328i	0.696441	+	0.717614i	$0.254766\pi$
$888$	−169592.	−	32215.6i	−0.215070	−	0.0408546i
$889$	227890.	−	394717.i	0.288351	−	0.499439i
$890$		−	25579.2i		−	0.0322929i
$891$	122121.	+	400009.i	0.153828	+	0.503866i
$892$	436985.			0.549207
$893$	403027.	+	232688.i	0.505395	+	0.291790i
$894$	46390.3	−	244212.i	0.0580433	−	0.305557i
$895$	−152308.	−	263805.i	−0.190141	−	0.329334i
$896$	−75720.5	+	43717.2i	−0.0943186	+	0.0544548i
$897$	−70554.9	+	81866.6i	−0.0876885	+	0.101747i
$898$	−158865.	+	275162.i	−0.197004	+	0.341221i
$899$			891053.i			1.10251i
$900$	343724.	+	135476.i	0.424351	+	0.167254i
$901$	−356015.			−0.438549
$902$	−79035.0	−	45630.9i	−0.0971418	−	0.0560849i
$903$	−720727.	+	251609.i	−0.883884	+	0.308567i
$904$	−108103.	−	187240.i	−0.132282	−	0.229120i
$905$	205549.	−	118674.i	0.250967	−	0.144896i
$906$	−6434.27	−	18430.8i	−0.00783868	−	0.0224537i
$907$	−49856.1	+	86353.3i	−0.0606043	+	0.104970i	−0.894736	−	0.446596i	$-0.852636\pi$
$907$	−49856.1	+	86353.3i	−0.0606043	+	0.104970i	0.834131	+	0.551566i	$0.185969\pi$
$908$			625312.i			0.758447i
$909$	875124.	+	1.10063e6i	1.05911	+	1.33203i
$910$	−366751.			−0.442883
$911$	947426.	+	546996.i	1.14159	+	0.659095i	0.946823	−	0.321756i	$-0.104273\pi$
$911$	947426.	+	546996.i	1.14159	+	0.659095i	0.194763	+	0.980850i	$0.437606\pi$
$912$	−81915.1	−	70596.8i	−0.0984860	−	0.0848780i
$913$	−163358.	−	282944.i	−0.195974	−	0.339437i
$914$	565885.	−	326714.i	0.677385	−	0.391088i
$915$	170447.	+	32378.0i	0.203586	+	0.0386730i
$916$	−48156.2	+	83408.9i	−0.0573933	+	0.0994080i
$917$			291154.i			0.346245i
$918$	441798.	+	840329.i	0.524250	+	0.997159i
$919$	102313.			0.121143			0.0605717	−	0.998164i	$-0.480708\pi$
$919$	102313.			0.121143			0.0605717	+	0.998164i	$0.480708\pi$
$920$	−6009.60	−	3469.64i	−0.00710019	−	0.00409930i
$921$	18032.8	−	94930.0i	0.0212591	−	0.111914i
$922$	−303764.	−	526135.i	−0.357334	−	0.618922i
$923$	695918.	−	401788.i	0.816873	−	0.471622i
$924$	−180907.	+	209910.i	−0.211890	+	0.245861i
$925$	−241650.	+	418551.i	−0.282426	+	0.489176i
$926$			620346.i			0.723456i
$927$	−123497.	−	827462.i	−0.143713	−	0.962916i
$928$	253229.			0.294047
$929$	−942127.	−	543937.i	−1.09164	−	0.630256i	−0.157625	−	0.987499i	$-0.550384\pi$
$929$	−942127.	−	543937.i	−1.09164	−	0.630256i	−0.934012	+	0.357243i	$0.883717\pi$
$930$	113373.	−	39579.0i	0.131082	−	0.0457613i
$931$	−116805.	−	202311.i	−0.134760	−	0.233411i
$932$	−660923.	+	381584.i	−0.760885	+	0.439297i
$933$	−658.681	−	1886.78i	−0.000756679	−	0.00216749i
$934$	88051.2	−	152509.i	0.100935	−	0.174824i
$935$			217371.i			0.248644i
$936$	−525674.	+	78455.5i	−0.600018	+	0.0895513i
$937$	1.30162e6			1.48253			0.741265	−	0.671213i	$-0.234226\pi$
$937$	1.30162e6			1.48253			0.741265	+	0.671213i	$0.234226\pi$
$938$	500331.	+	288866.i	0.568659	+	0.328315i
$939$	−999967.	−	861800.i	−1.13411	−	0.977407i
$940$	73431.7	+	127187.i	0.0831051	+	0.143942i
$941$	−949282.	+	548068.i	−1.07205	+	0.618950i	−0.928742	−	0.370728i	$-0.879108\pi$
$941$	−949282.	+	548068.i	−1.07205	+	0.618950i	−0.143311	+	0.989678i	$0.545775\pi$
$942$	−129841.	−	24664.4i	−0.146322	−	0.0277951i
$943$	10480.1	−	18152.0i	0.0117853	−	0.0204127i
$944$			287839.i			0.323002i
$945$	−275628.	−	174023.i	−0.308645	−	0.194869i
$946$	−253296.			−0.283039
$947$	863203.	+	498371.i	0.962528	+	0.555716i	0.896950	−	0.442132i	$-0.145778\pi$
$947$	863203.	+	498371.i	0.962528	+	0.555716i	0.0655775	+	0.997847i	$0.479111\pi$
$948$	78333.6	−	412371.i	0.0871628	−	0.458850i
$949$	−511128.	−	885299.i	−0.567541	−	0.983009i
$950$	−262196.	+	151379.i	−0.290521	+	0.167733i
$951$	1.03669e6	−	1.20290e6i	1.14628	−	1.33005i
$952$	−314517.	+	544760.i	−0.347033	+	0.601078i
$953$		−	501410.i		−	0.552087i	−0.961145	−	0.276044i	$-0.910977\pi$
$953$		−	501410.i		−	0.552087i	0.961145	−	0.276044i	$-0.0890234\pi$
$954$	138656.	−	110247.i	0.152350	−	0.121135i
$955$	97867.0			0.107307
$956$	−709133.	−	409418.i	−0.775911	−	0.447972i
$957$	757722.	−	264524.i	0.827343	−	0.288829i
$958$	304598.	+	527579.i	0.331891	+	0.574852i
$959$	564337.	−	325820.i	0.613623	−	0.354275i
$960$	−11248.0	−	32219.5i	−0.0122048	−	0.0349604i
$961$	258899.	−	448425.i	0.280339	−	0.485561i
$962$		−	695267.i		−	0.751280i
$963$	215647.	−	547134.i	0.232537	−	0.589985i
$964$	429342.			0.462008
$965$	−11460.8	−	6616.91i	−0.0123072	−	0.00710559i
$966$	−48210.2	−	41548.9i	−0.0516636	−	0.0445252i
$967$	−105121.	−	182074.i	−0.112418	−	0.194713i	0.804327	−	0.594187i	$-0.202526\pi$
$967$	−105121.	−	182074.i	−0.112418	−	0.194713i	−0.916745	+	0.399474i	$0.869193\pi$
$968$	207275.	−	119671.i	0.221206	−	0.127713i
$969$	−764320.	−	145190.i	−0.814006	−	0.154628i
$970$	154330.	−	267307.i	0.164024	−	0.284097i
$971$		−	1.41640e6i		−	1.50227i	−0.660151	−	0.751133i	$-0.729508\pi$
$971$		−	1.41640e6i		−	1.50227i	0.660151	−	0.751133i	$-0.270492\pi$
$972$	−432291.	−	190469.i	−0.457555	−	0.201601i
$973$	−1.70728e6			−1.80334
$974$	−949221.	−	548033.i	−1.00057	−	0.577682i
$975$	−277700.	+	1.46189e6i	−0.292124	+	1.53782i
$976$	83294.5	+	144270.i	0.0874414	+	0.151453i
$977$	−1.56228e6	+	901983.i	−1.63670	+	0.944951i	−0.654745	+	0.755850i	$0.727224\pi$
$977$	−1.56228e6	+	901983.i	−1.63670	+	0.944951i	−0.981958	+	0.189101i	$0.939443\pi$
$978$	−401848.	+	466274.i	−0.420130	+	0.487487i
$979$	38921.1	−	67413.3i	0.0406087	−	0.0703364i
$980$		−	73722.4i		−	0.0767622i
$981$	−142765.	−	56269.6i	−0.148349	−	0.0584703i
$982$	225783.			0.234136
$983$	−966691.	−	558119.i	−1.00042	−	0.577590i	−0.0920447	−	0.995755i	$-0.529340\pi$
$983$	−966691.	−	558119.i	−1.00042	−	0.577590i	−0.908371	+	0.418164i	$0.862674\pi$
$984$	97319.1	−	33974.5i	0.100510	−	0.0350883i
$985$	−65323.5	−	113144.i	−0.0673282	−	0.116616i
$986$	1.57774e6	−	910908.i	1.62286	−	0.936960i
$987$	443954.	+	1.27169e6i	0.455726	+	1.30542i
$988$	217770.	−	377190.i	0.223093	−	0.386408i
$989$		−	58174.7i		−	0.0594759i
$990$	−67313.3	−	84659.0i	−0.0686800	−	0.0863779i
$991$	−888178.			−0.904383			−0.452192	−	0.891921i	$-0.649358\pi$
$991$	−888178.			−0.904383			−0.452192	+	0.891921i	$0.649358\pi$
$992$	99855.2	+	57651.5i	0.101472	+	0.0585851i
$993$	656097.	+	565443.i	0.665379	+	0.573443i
$994$	236608.	+	409817.i	0.239473	+	0.414780i
$995$	1519.65	−	877.373i	0.00153497	−	0.000886213i
$996$	362538.	+	68867.4i	0.365456	+	0.0694216i
$997$	−404840.	+	701204.i	−0.407280	+	0.705430i	−0.994584	−	0.103936i	$-0.966856\pi$
$997$	−404840.	+	701204.i	−0.407280	+	0.705430i	0.587304	+	0.809367i	$0.300190\pi$
$998$		−	207735.i		−	0.208569i
$999$	329904.	−	522520.i	0.330565	−	0.523567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.5.d.a.11.3	yes	8
3.2	odd	2		54.5.d.a.35.1		8
4.3	odd	2		144.5.q.b.65.3		8
9.2	odd	6		162.5.b.c.161.6		8
9.4	even	3		54.5.d.a.17.1		8
9.5	odd	6	inner	18.5.d.a.5.3	✓	8
9.7	even	3		162.5.b.c.161.3		8
12.11	even	2		432.5.q.b.305.2		8
36.7	odd	6		1296.5.e.e.161.6		8
36.11	even	6		1296.5.e.e.161.3		8
36.23	even	6		144.5.q.b.113.3		8
36.31	odd	6		432.5.q.b.17.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.5.d.a.5.3	✓	8	9.5	odd	6	inner
18.5.d.a.11.3	yes	8	1.1	even	1	trivial
54.5.d.a.17.1		8	9.4	even	3
54.5.d.a.35.1		8	3.2	odd	2
144.5.q.b.65.3		8	4.3	odd	2
144.5.q.b.113.3		8	36.23	even	6
162.5.b.c.161.3		8	9.7	even	3
162.5.b.c.161.6		8	9.2	odd	6
432.5.q.b.17.2		8	36.31	odd	6
432.5.q.b.305.2		8	12.11	even	2
1296.5.e.e.161.3		8	36.11	even	6
1296.5.e.e.161.6		8	36.7	odd	6

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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	18.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.44949 + 1.41421i) q^{2} +(-1.67960 + 8.84189i) q^{3} +(4.00000 + 6.92820i) q^{4} +(6.41371 - 3.70296i) q^{5} +(-16.6185 + 19.2828i) q^{6} +(30.1882 - 52.2875i) q^{7} +22.6274i q^{8} +(-75.3579 - 29.7016i) q^{9} +O(q^{10})\)	\(q+(2.44949 + 1.41421i) q^{2} +(-1.67960 + 8.84189i) q^{3} +(4.00000 + 6.92820i) q^{4} +(6.41371 - 3.70296i) q^{5} +(-16.6185 + 19.2828i) q^{6} +(30.1882 - 52.2875i) q^{7} +22.6274i q^{8} +(-75.3579 - 29.7016i) q^{9} +20.9471 q^{10} +(55.2054 + 31.8729i) q^{11} +(-67.9768 + 23.7310i) q^{12} +(-144.994 - 251.137i) q^{13} +(147.892 - 85.3852i) q^{14} +(21.9687 + 62.9288i) q^{15} +(-32.0000 + 55.4256i) q^{16} +460.439i q^{17} +(-142.584 - 179.326i) q^{18} +187.741 q^{19} +(51.3097 + 29.6237i) q^{20} +(411.616 + 354.743i) q^{21} +(90.1501 + 156.144i) q^{22} +(-35.8618 + 20.7048i) q^{23} +(-200.069 - 38.0049i) q^{24} +(-285.076 + 493.766i) q^{25} -820.210i q^{26} +(389.189 - 616.419i) q^{27} +483.012 q^{28} +(-1211.49 - 699.452i) q^{29} +(-35.1827 + 185.212i) q^{30} +(-318.482 - 551.628i) q^{31} +(-156.767 + 90.5097i) q^{32} +(-374.539 + 434.586i) q^{33} +(-651.158 + 1127.84i) q^{34} -447.143i q^{35} +(-95.6529 - 640.901i) q^{36} +847.670 q^{37} +(459.869 + 265.506i) q^{38} +(2464.06 - 860.212i) q^{39} +(83.7884 + 145.126i) q^{40} +(-438.352 + 253.083i) q^{41} +(506.568 + 1451.05i) q^{42} +(-702.429 + 1216.64i) q^{43} +509.966i q^{44} +(-593.308 + 88.5497i) q^{45} -117.124 q^{46} +(2146.72 + 1239.41i) q^{47} +(-436.320 - 376.033i) q^{48} +(-622.158 - 1077.61i) q^{49} +(-1396.58 + 806.317i) q^{50} +(-4071.15 - 773.351i) q^{51} +(1159.95 - 2009.10i) q^{52} +773.208i q^{53} +(1825.06 - 959.517i) q^{54} +472.095 q^{55} +(1183.13 + 683.082i) q^{56} +(-315.329 + 1659.98i) q^{57} +(-1978.35 - 3426.60i) q^{58} +(3894.93 - 2248.74i) q^{59} +(-348.109 + 403.919i) q^{60} +(1301.48 - 2254.22i) q^{61} -1801.61i q^{62} +(-3827.95 + 3043.64i) q^{63} -512.000 q^{64} +(-1859.90 - 1073.81i) q^{65} +(-1532.03 + 534.837i) q^{66} +(1691.55 + 2929.85i) q^{67} +(-3190.01 + 1841.75i) q^{68} +(-122.836 - 351.862i) q^{69} +(632.356 - 1095.27i) q^{70} +2771.07i q^{71} +(672.070 - 1705.15i) q^{72} +3525.16 q^{73} +(2076.36 + 1198.79i) q^{74} +(-3887.01 - 3349.94i) q^{75} +(750.964 + 1300.71i) q^{76} +(3333.11 - 1924.37i) q^{77} +(7252.21 + 1377.62i) q^{78} +(-2914.90 + 5048.75i) q^{79} +473.979i q^{80} +(4796.63 + 4476.50i) q^{81} -1431.65 q^{82} +(-4438.63 - 2562.65i) q^{83} +(-811.265 + 4270.73i) q^{84} +(1704.98 + 2953.12i) q^{85} +(-3441.19 + 1986.77i) q^{86} +(8219.29 - 9537.03i) q^{87} +(-721.200 + 1249.16i) q^{88} -1221.14i q^{89} +(-1578.53 - 622.162i) q^{90} -17508.5 q^{91} +(-286.894 - 165.638i) q^{92} +(5412.35 - 1889.47i) q^{93} +(3505.58 + 6071.84i) q^{94} +(1204.12 - 695.197i) q^{95} +(-536.970 - 1538.14i) q^{96} +(7367.60 - 12761.1i) q^{97} -3519.46i q^{98} +(-3213.49 - 4041.56i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 32 q^{4} + 18 q^{5} + 48 q^{6} - 26 q^{7} - 78 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 + 32 * q^4 + 18 * q^5 + 48 * q^6 - 26 * q^7 - 78 * q^9	\( 8 q + 6 q^{3} + 32 q^{4} + 18 q^{5} + 48 q^{6} - 26 q^{7} - 78 q^{9} - 720 q^{11} - 144 q^{12} + 10 q^{13} + 288 q^{14} + 1134 q^{15} - 256 q^{16} - 384 q^{18} + 100 q^{19} + 144 q^{20} + 438 q^{21} + 336 q^{22} + 1278 q^{23} + 384 q^{24} + 794 q^{25} - 1296 q^{27} - 416 q^{28} - 1854 q^{29} - 3456 q^{30} - 1478 q^{31} - 3384 q^{33} - 96 q^{34} + 1056 q^{36} - 32 q^{37} + 6768 q^{38} + 5274 q^{39} - 36 q^{41} + 2592 q^{42} - 68 q^{43} + 3402 q^{45} + 2112 q^{46} + 2214 q^{47} - 1536 q^{48} + 2442 q^{49} - 15552 q^{50} - 12006 q^{51} - 80 q^{52} + 7056 q^{54} - 3996 q^{55} + 2304 q^{56} + 10902 q^{57} - 2400 q^{58} + 9108 q^{59} + 6480 q^{60} - 4478 q^{61} - 6654 q^{63} - 4096 q^{64} - 22554 q^{65} - 19872 q^{66} + 7504 q^{67} - 11088 q^{68} - 5994 q^{69} + 6048 q^{70} + 5376 q^{72} + 20716 q^{73} + 15264 q^{74} + 16590 q^{75} + 400 q^{76} + 34434 q^{77} + 24096 q^{78} - 6050 q^{79} - 21150 q^{81} + 1152 q^{82} - 3834 q^{83} - 9600 q^{84} - 16092 q^{85} - 12528 q^{86} + 10170 q^{87} - 2688 q^{88} + 2592 q^{90} - 45868 q^{91} + 10224 q^{92} - 10926 q^{93} + 672 q^{94} + 20880 q^{95} + 31336 q^{97} - 22338 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 + 32 * q^4 + 18 * q^5 + 48 * q^6 - 26 * q^7 - 78 * q^9 - 720 * q^11 - 144 * q^12 + 10 * q^13 + 288 * q^14 + 1134 * q^15 - 256 * q^16 - 384 * q^18 + 100 * q^19 + 144 * q^20 + 438 * q^21 + 336 * q^22 + 1278 * q^23 + 384 * q^24 + 794 * q^25 - 1296 * q^27 - 416 * q^28 - 1854 * q^29 - 3456 * q^30 - 1478 * q^31 - 3384 * q^33 - 96 * q^34 + 1056 * q^36 - 32 * q^37 + 6768 * q^38 + 5274 * q^39 - 36 * q^41 + 2592 * q^42 - 68 * q^43 + 3402 * q^45 + 2112 * q^46 + 2214 * q^47 - 1536 * q^48 + 2442 * q^49 - 15552 * q^50 - 12006 * q^51 - 80 * q^52 + 7056 * q^54 - 3996 * q^55 + 2304 * q^56 + 10902 * q^57 - 2400 * q^58 + 9108 * q^59 + 6480 * q^60 - 4478 * q^61 - 6654 * q^63 - 4096 * q^64 - 22554 * q^65 - 19872 * q^66 + 7504 * q^67 - 11088 * q^68 - 5994 * q^69 + 6048 * q^70 + 5376 * q^72 + 20716 * q^73 + 15264 * q^74 + 16590 * q^75 + 400 * q^76 + 34434 * q^77 + 24096 * q^78 - 6050 * q^79 - 21150 * q^81 + 1152 * q^82 - 3834 * q^83 - 9600 * q^84 - 16092 * q^85 - 12528 * q^86 + 10170 * q^87 - 2688 * q^88 + 2592 * q^90 - 45868 * q^91 + 10224 * q^92 - 10926 * q^93 + 672 * q^94 + 20880 * q^95 + 31336 * q^97 - 22338 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more