LMFDB - Embedded newform 18.5.d.a.5.2

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			5.2
Root			$0.500000 + 3.16175i$ of defining polynomial
Character	$\chi$	$=$	18.5
Dual form			18.5.d.a.11.2

$q$-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} +(6.85811 - 5.82806i) q^{3} +(4.00000 - 6.92820i) q^{4} +(37.0033 + 21.3638i) q^{5} +(-8.55675 + 23.9746i) q^{6} +(-19.8424 - 34.3680i) q^{7} +22.6274i q^{8} +(13.0674 - 79.9390i) q^{9} -120.852 q^{10} +(-139.941 + 80.7947i) q^{11} +(-12.9455 - 70.8266i) q^{12} +(-36.6403 + 63.4629i) q^{13} +(97.2073 + 56.1227i) q^{14} +(378.282 - 69.1416i) q^{15} +(-32.0000 - 55.4256i) q^{16} +65.0171i q^{17} +(81.0423 + 214.290i) q^{18} -163.911 q^{19} +(296.026 - 170.911i) q^{20} +(-336.380 - 120.057i) q^{21} +(228.522 - 395.812i) q^{22} +(-185.421 - 107.053i) q^{23} +(131.874 + 155.181i) q^{24} +(600.327 + 1039.80i) q^{25} -207.269i q^{26} +(-376.272 - 624.388i) q^{27} -317.478 q^{28} +(-563.025 + 325.063i) q^{29} +(-828.817 + 704.334i) q^{30} +(633.812 - 1097.79i) q^{31} +(156.767 + 90.5097i) q^{32} +(-488.851 + 1369.68i) q^{33} +(-91.9481 - 159.259i) q^{34} -1695.64i q^{35} +(-501.564 - 410.290i) q^{36} +278.148 q^{37} +(401.498 - 231.805i) q^{38} +(118.582 + 648.778i) q^{39} +(-483.408 + 837.288i) q^{40} +(48.2927 + 27.8818i) q^{41} +(993.745 - 181.635i) q^{42} +(932.851 + 1615.75i) q^{43} +1292.72i q^{44} +(2191.34 - 2678.83i) q^{45} +605.581 q^{46} +(1102.58 - 636.576i) q^{47} +(-542.484 - 193.617i) q^{48} +(413.062 - 715.444i) q^{49} +(-2940.99 - 1697.98i) q^{50} +(378.924 + 445.895i) q^{51} +(293.123 + 507.703i) q^{52} +3580.69i q^{53} +(1804.69 + 997.304i) q^{54} -6904.34 q^{55} +(777.658 - 448.981i) q^{56} +(-1124.12 + 955.284i) q^{57} +(919.416 - 1592.47i) q^{58} +(2934.93 + 1694.48i) q^{59} +(1034.10 - 2897.38i) q^{60} +(-3492.55 - 6049.28i) q^{61} +3585.38i q^{62} +(-3006.63 + 1137.08i) q^{63} -512.000 q^{64} +(-2711.62 + 1565.56i) q^{65} +(-739.585 - 4046.36i) q^{66} +(-958.605 + 1660.35i) q^{67} +(450.452 + 260.069i) q^{68} +(-1895.55 + 346.464i) q^{69} +(2397.99 + 4153.44i) q^{70} -4588.94i q^{71} +(1808.81 + 295.682i) q^{72} +9910.16 q^{73} +(-681.320 + 393.360i) q^{74} +(10177.1 + 3632.30i) q^{75} +(-655.644 + 1135.61i) q^{76} +(5553.50 + 3206.31i) q^{77} +(-1207.98 - 1421.47i) q^{78} +(-974.042 - 1687.09i) q^{79} -2734.57i q^{80} +(-6219.49 - 2089.19i) q^{81} -157.723 q^{82} +(1192.14 - 688.283i) q^{83} +(-2177.30 + 1850.28i) q^{84} +(-1389.02 + 2405.85i) q^{85} +(-4570.02 - 2638.50i) q^{86} +(-1966.80 + 5510.66i) q^{87} +(-1828.18 - 3166.49i) q^{88} -13719.2i q^{89} +(-1579.22 + 9660.80i) q^{90} +2908.12 q^{91} +(-1483.37 + 856.421i) q^{92} +(-2051.26 - 11222.7i) q^{93} +(-1800.51 + 3118.57i) q^{94} +(-6065.24 - 3501.77i) q^{95} +(1602.62 - 292.924i) q^{96} +(4145.57 + 7180.34i) q^{97} +2336.63i q^{98} +(4629.99 + 12242.5i) 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} - 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}+ \cdots - 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

Character values

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

$n$	$11$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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
$3$	6.85811	−	5.82806i	0.762012	−	0.647562i
$3$	6.85811	−	5.82806i	0.762012	−	0.647562i
$4$	4.00000	−	6.92820i	0.250000	−	0.433013i
$5$	37.0033	+	21.3638i	1.48013	+	0.854553i	0.999747	−	0.0225051i	$-0.00716421\pi$
$5$	37.0033	+	21.3638i	1.48013	+	0.854553i	0.480383	+	0.877059i	$0.340498\pi$
$6$	−8.55675	+	23.9746i	−0.237688	+	0.665961i
$7$	−19.8424	−	34.3680i	−0.404946	−	0.701387i	0.589369	−	0.807864i	$-0.299376\pi$
$7$	−19.8424	−	34.3680i	−0.404946	−	0.701387i	−0.994315	+	0.106477i	$0.966043\pi$
$8$			22.6274i			0.353553i
$9$	13.0674	−	79.9390i	0.161326	−	0.986901i
$10$	−120.852			−1.20852
$11$	−139.941	+	80.7947i	−1.15653	+	0.667725i	−0.950471	−	0.310814i	$-0.899398\pi$
$11$	−139.941	+	80.7947i	−1.15653	+	0.667725i	−0.206062	+	0.978539i	$0.566065\pi$
$12$	−12.9455	−	70.8266i	−0.0898996	−	0.491852i
$13$	−36.6403	+	63.4629i	−0.216807	+	0.375520i	−0.953830	−	0.300347i	$-0.902897\pi$
$13$	−36.6403	+	63.4629i	−0.216807	+	0.375520i	0.737023	+	0.675867i	$0.236231\pi$
$14$	97.2073	+	56.1227i	0.495956	+	0.286340i
$15$	378.282	−	69.1416i	1.68125	−	0.307296i
$16$	−32.0000	−	55.4256i	−0.125000	−	0.216506i
$17$			65.0171i			0.224973i	0.993653	+	0.112486i	$0.0358815\pi$
$17$			65.0171i			0.224973i	−0.993653	+	0.112486i	$0.964119\pi$
$18$	81.0423	+	214.290i	0.250131	+	0.661388i
$19$	−163.911			−0.454047			−0.227024	−	0.973889i	$-0.572899\pi$
$19$	−163.911			−0.454047			−0.227024	+	0.973889i	$0.572899\pi$
$20$	296.026	−	170.911i	0.740065	−	0.427277i
$21$	−336.380	−	120.057i	−0.762766	−	0.272238i
$22$	228.522	−	395.812i	0.472153	−	0.817792i
$23$	−185.421	−	107.053i	−0.350512	−	0.202368i	0.314399	−	0.949291i	$-0.398197\pi$
$23$	−185.421	−	107.053i	−0.350512	−	0.202368i	−0.664911	+	0.746923i	$0.731530\pi$
$24$	131.874	+	155.181i	0.228948	+	0.269412i
$25$	600.327	+	1039.80i	0.960523	+	1.66368i
$26$		−	207.269i		−	0.306611i
$27$	−376.272	−	624.388i	−0.516148	−	0.856500i
$28$	−317.478			−0.404946
$29$	−563.025	+	325.063i	−0.669471	+	0.386519i	−0.795876	−	0.605460i	$-0.792989\pi$
$29$	−563.025	+	325.063i	−0.669471	+	0.386519i	0.126405	+	0.991979i	$0.459656\pi$
$30$	−828.817	+	704.334i	−0.920908	+	0.782593i
$31$	633.812	−	1097.79i	0.659534	−	1.14235i	−0.321203	−	0.947010i	$-0.604087\pi$
$31$	633.812	−	1097.79i	0.659534	−	1.14235i	0.980736	−	0.195336i	$-0.0625796\pi$
$32$	156.767	+	90.5097i	0.153093	+	0.0883883i
$33$	−488.851	+	1369.68i	−0.448899	+	1.25774i
$34$	−91.9481	−	159.259i	−0.0795399	−	0.137767i
$35$		−	1695.64i		−	1.38419i
$36$	−501.564	−	410.290i	−0.387009	−	0.316581i
$37$	278.148			0.203176			0.101588	−	0.994827i	$-0.467608\pi$
$37$	278.148			0.203176			0.101588	+	0.994827i	$0.467608\pi$
$38$	401.498	−	231.805i	0.278046	−	0.160530i
$39$	118.582	+	648.778i	0.0779633	+	0.426547i
$40$	−483.408	+	837.288i	−0.302130	+	0.523305i
$41$	48.2927	+	27.8818i	0.0287286	+	0.0165864i	0.514295	−	0.857613i	$-0.328053\pi$
$41$	48.2927	+	27.8818i	0.0287286	+	0.0165864i	−0.485567	+	0.874199i	$0.661387\pi$
$42$	993.745	−	181.635i	0.563347	−	0.102967i
$43$	932.851	+	1615.75i	0.504517	+	0.873849i	0.999986	+	0.00522338i	$0.00166266\pi$
$43$	932.851	+	1615.75i	0.504517	+	0.873849i	−0.495470	+	0.868625i	$0.665004\pi$
$44$			1292.72i			0.667725i
$45$	2191.34	−	2678.83i	1.08214	−	1.32288i
$46$	605.581			0.286192
$47$	1102.58	−	636.576i	0.499132	−	0.288174i	−0.229223	−	0.973374i	$-0.573619\pi$
$47$	1102.58	−	636.576i	0.499132	−	0.288174i	0.728355	+	0.685200i	$0.240285\pi$
$48$	−542.484	−	193.617i	−0.235453	−	0.0840352i
$49$	413.062	−	715.444i	0.172037	−	0.297977i
$50$	−2940.99	−	1697.98i	−1.17640	−	0.679193i
$51$	378.924	+	445.895i	0.145684	+	0.171432i
$52$	293.123	+	507.703i	0.108403	+	0.187760i
$53$			3580.69i			1.27472i	0.770566	+	0.637360i	$0.219974\pi$
$53$			3580.69i			1.27472i	−0.770566	+	0.637360i	$0.780026\pi$
$54$	1804.69	+	997.304i	0.618893	+	0.342011i
$55$	−6904.34			−2.28243
$56$	777.658	−	448.981i	0.247978	−	0.143170i
$57$	−1124.12	+	955.284i	−0.345990	+	0.294024i
$58$	919.416	−	1592.47i	0.273310	−	0.473387i
$59$	2934.93	+	1694.48i	0.843129	+	0.486781i	0.858327	−	0.513104i	$-0.171504\pi$
$59$	2934.93	+	1694.48i	0.843129	+	0.486781i	−0.0151977	+	0.999885i	$0.504838\pi$
$60$	1034.10	−	2897.38i	0.287250	−	0.804828i
$61$	−3492.55	−	6049.28i	−0.938606	−	1.62571i	−0.768073	−	0.640362i	$-0.778784\pi$
$61$	−3492.55	−	6049.28i	−0.938606	−	1.62571i	−0.170533	−	0.985352i	$-0.554549\pi$
$62$			3585.38i			0.932722i
$63$	−3006.63	+	1137.08i	−0.757528	+	0.286490i
$64$	−512.000			−0.125000
$65$	−2711.62	+	1565.56i	−0.641804	+	0.370546i
$66$	−739.585	−	4046.36i	−0.169785	−	0.928916i
$67$	−958.605	+	1660.35i	−0.213545	+	0.369871i	−0.952822	−	0.303531i	$-0.901834\pi$
$67$	−958.605	+	1660.35i	−0.213545	+	0.369871i	0.739276	+	0.673402i	$0.235168\pi$
$68$	450.452	+	260.069i	0.0974161	+	0.0562432i
$69$	−1895.55	+	346.464i	−0.398140	+	0.0727712i
$70$	2397.99	+	4153.44i	0.489386	+	0.847641i
$71$		−	4588.94i		−	0.910323i	−0.890409	−	0.455162i	$-0.849582\pi$
$71$		−	4588.94i		−	0.910323i	0.890409	−	0.455162i	$-0.150418\pi$
$72$	1808.81	+	295.682i	0.348922	+	0.0570373i
$73$	9910.16			1.85967			0.929833	−	0.367981i	$-0.119951\pi$
$73$	9910.16			1.85967			0.929833	+	0.367981i	$0.119951\pi$
$74$	−681.320	+	393.360i	−0.124419	+	0.0718335i
$75$	10177.1	+	3632.30i	1.80926	+	0.645742i
$76$	−655.644	+	1135.61i	−0.113512	+	0.196608i
$77$	5553.50	+	3206.31i	0.936667	+	0.540785i
$78$	−1207.98	−	1421.47i	−0.198550	−	0.233641i
$79$	−974.042	−	1687.09i	−0.156072	−	0.270324i	0.777377	−	0.629035i	$-0.216550\pi$
$79$	−974.042	−	1687.09i	−0.156072	−	0.270324i	−0.933449	+	0.358711i	$0.883216\pi$
$80$		−	2734.57i		−	0.427277i
$81$	−6219.49	−	2089.19i	−0.947948	−	0.318426i
$82$	−157.723			−0.0234568
$83$	1192.14	−	688.283i	0.173050	−	0.0999105i	−0.410973	−	0.911647i	$-0.634811\pi$
$83$	1192.14	−	688.283i	0.173050	−	0.0999105i	0.584023	+	0.811737i	$0.301478\pi$
$84$	−2177.30	+	1850.28i	−0.308574	+	0.262228i
$85$	−1389.02	+	2405.85i	−0.192251	+	0.332989i
$86$	−4570.02	−	2638.50i	−0.617904	−	0.356747i
$87$	−1966.80	+	5510.66i	−0.259850	+	0.728056i
$88$	−1828.18	−	3166.49i	−0.236076	−	0.408896i
$89$		−	13719.2i		−	1.73200i	−0.500044	−	0.866000i	$-0.666683\pi$
$89$		−	13719.2i		−	1.73200i	0.500044	−	0.866000i	$-0.333317\pi$
$90$	−1579.22	+	9660.80i	−0.194966	+	1.19269i
$91$	2908.12			0.351180
$92$	−1483.37	+	856.421i	−0.175256	+	0.101184i
$93$	−2051.26	−	11222.7i	−0.237167	−	1.29757i
$94$	−1800.51	+	3118.57i	−0.203770	+	0.352940i
$95$	−6065.24	−	3501.77i	−0.672049	−	0.388008i
$96$	1602.62	−	292.924i	0.173896	−	0.0317843i
$97$	4145.57	+	7180.34i	0.440597	+	0.763136i	0.997734	−	0.0672848i	$-0.0214336\pi$
$97$	4145.57	+	7180.34i	0.440597	+	0.763136i	−0.557137	+	0.830420i	$0.688100\pi$
$98$			2336.63i			0.243298i
$99$	4629.99	+	12242.5i	0.472400	+	1.24911i
$100$	9605.23			0.960523
$101$	−8020.79	+	4630.80i	−0.786275	+	0.453956i	−0.838649	−	0.544672i	$-0.816654\pi$
$101$	−8020.79	+	4630.80i	−0.786275	+	0.453956i	0.0523749	+	0.998627i	$0.483321\pi$
$102$	−1558.76	−	556.335i	−0.149823	−	0.0534732i
$103$	−3969.57	+	6875.49i	−0.374170	+	0.648081i	−0.990202	−	0.139639i	$-0.955406\pi$
$103$	−3969.57	+	6875.49i	−0.374170	+	0.648081i	0.616033	+	0.787721i	$0.288739\pi$
$104$	−1436.00	−	829.076i	−0.132766	−	0.0766527i
$105$	−9882.27	−	11628.9i	−0.896351	−	1.05477i
$106$	−5063.86	−	8770.86i	−0.450682	−	0.780604i
$107$			5344.76i			0.466832i	0.972377	+	0.233416i	$0.0749905\pi$
$107$			5344.76i			0.466832i	−0.972377	+	0.233416i	$0.925010\pi$
$108$	−5830.98	+	109.334i	−0.499912	+	0.00937361i
$109$	10385.4			0.874121			0.437060	−	0.899432i	$-0.356020\pi$
$109$	10385.4			0.874121			0.437060	+	0.899432i	$0.356020\pi$
$110$	16912.1	−	9764.21i	1.39769	−	0.806959i
$111$	1907.57	−	1621.06i	0.154822	−	0.131569i
$112$	−1269.91	+	2199.55i	−0.101237	+	0.175347i
$113$	540.885	+	312.280i	0.0423593	+	0.0244561i	0.521030	−	0.853538i	$-0.325548\pi$
$113$	540.885	+	312.280i	0.0423593	+	0.0244561i	−0.478671	+	0.877994i	$0.658881\pi$
$114$	1402.55	−	3929.70i	0.107921	−	0.302378i
$115$	−4574.11	−	7922.59i	−0.345869	−	0.599062i
$116$			5201.00i			0.386519i
$117$	4594.37	+	3758.29i	0.335625	+	0.274548i
$118$	−9585.45			−0.688412
$119$	2234.51	−	1290.09i	0.157793	−	0.0911018i
$120$	1564.50	+	8559.55i	0.108646	+	0.594413i
$121$	5735.07	−	9933.43i	0.391713	−	0.678466i
$122$	17110.0	+	9878.44i	1.14955	+	0.663695i
$123$	493.694	−	90.2363i	0.0326323	−	0.00596446i
$124$	−5070.50	−	8782.36i	−0.329767	−	0.571173i
$125$			24596.4i			1.57417i
$126$	5756.64	−	7037.28i	0.362600	−	0.443265i
$127$	−9866.20			−0.611706			−0.305853	−	0.952079i	$-0.598942\pi$
$127$	−9866.20			−0.611706			−0.305853	+	0.952079i	$0.598942\pi$
$128$	1254.14	−	724.077i	0.0765466	−	0.0441942i
$129$	15814.3	+	5644.25i	0.950320	+	0.339177i
$130$	4428.06	−	7669.63i	0.262015	−	0.453824i
$131$	−3255.51	−	1879.57i	−0.189704	−	0.109526i	0.402140	−	0.915578i	$-0.368266\pi$
$131$	−3255.51	−	1879.57i	−0.189704	−	0.109526i	−0.591844	+	0.806053i	$0.701600\pi$
$132$	7534.02	+	8865.59i	0.432393	+	0.508815i
$133$	3252.38	+	5633.29i	0.183865	+	0.318463i
$134$		−	5422.69i		−	0.301999i
$135$	−583.947	−	31143.0i	−0.0320410	−	1.70881i
$136$	−1471.17			−0.0795399
$137$	−20987.5	+	12117.2i	−1.11820	+	0.645595i	−0.940941	−	0.338569i	$-0.890057\pi$
$137$	−20987.5	+	12117.2i	−1.11820	+	0.645595i	−0.177261	+	0.984164i	$0.556724\pi$
$138$	4153.14	−	3529.37i	0.218082	−	0.185327i
$139$	−13308.7	+	23051.3i	−0.688818	+	1.19307i	0.283402	+	0.959001i	$0.408537\pi$
$139$	−13308.7	+	23051.3i	−0.688818	+	1.19307i	−0.972221	+	0.234067i	$0.924797\pi$
$140$	−11747.7	−	6782.54i	−0.599373	−	0.346048i
$141$	3851.63	−	10791.6i	0.193734	−	0.542811i
$142$	6489.74	+	11240.6i	0.321848	+	0.557457i
$143$		−	11841.4i		−	0.579069i
$144$	−4848.83	+	1833.78i	−0.233836	+	0.0884346i
$145$	−27778.3			−1.32120
$146$	−24274.8	+	14015.1i	−1.13881	+	0.657492i
$147$	−1336.83	−	7313.94i	−0.0618644	−	0.338467i
$148$	1112.59	−	1927.06i	0.0507939	−	0.0879777i
$149$	5963.79	+	3443.19i	0.268627	+	0.155092i	0.628263	−	0.778001i	$-0.283766\pi$
$149$	5963.79	+	3443.19i	0.268627	+	0.155092i	−0.359637	+	0.933092i	$0.617099\pi$
$150$	−30065.6	+	5495.32i	−1.33625	+	0.244237i
$151$	−2199.51	−	3809.66i	−0.0964653	−	0.167083i	0.813754	−	0.581210i	$-0.197420\pi$
$151$	−2199.51	−	3809.66i	−0.0964653	−	0.167083i	−0.910219	+	0.414127i	$0.864087\pi$
$152$		−	3708.88i		−	0.160530i
$153$	5197.40	+	849.605i	0.222026	+	0.0362939i
$154$	−18137.7			−0.764786
$155$	46906.2	−	27081.3i	1.95239	−	1.12721i
$156$	4969.19	+	1773.55i	0.204191	+	0.0728776i
$157$	13928.3	−	24124.5i	0.565066	−	0.978723i	−0.431978	−	0.901884i	$-0.642184\pi$
$157$	13928.3	−	24124.5i	0.565066	−	0.978723i	0.997044	−	0.0768384i	$-0.0244826\pi$
$158$	4771.81	+	2755.01i	0.191148	+	0.110359i
$159$	20868.5	+	24556.8i	0.825461	+	0.971353i
$160$	3867.27	+	6698.30i	0.151065	+	0.261653i
$161$			8496.71i			0.327793i
$162$	18189.1	−	3678.23i	0.693078	−	0.140155i
$163$	33326.2			1.25433			0.627163	−	0.778888i	$-0.284216\pi$
$163$	33326.2			1.25433			0.627163	+	0.778888i	$0.284216\pi$
$164$	386.342	−	223.054i	0.0143643	−	0.00829322i
$165$	−47350.7	+	40238.9i	−1.73924	+	1.47801i
$166$	−1946.76	+	3371.89i	−0.0706474	+	0.122365i
$167$	−31413.9	−	18136.8i	−1.12639	−	0.650321i	−0.183365	−	0.983045i	$-0.558699\pi$
$167$	−31413.9	−	18136.8i	−1.12639	−	0.650321i	−0.943024	+	0.332724i	$0.892032\pi$
$168$	2716.58	−	7611.41i	0.0962506	−	0.269678i
$169$	11595.5	+	20084.0i	0.405990	+	0.703195i
$170$		−	7857.46i		−	0.271884i
$171$	−2141.89	+	13102.9i	−0.0732496	+	0.448100i
$172$	14925.6			0.504517
$173$	16944.5	−	9782.89i	0.566155	−	0.326870i	−0.189457	−	0.981889i	$-0.560673\pi$
$173$	16944.5	−	9782.89i	0.566155	−	0.326870i	0.755612	+	0.655019i	$0.227339\pi$
$174$	−2975.58	−	16279.8i	−0.0982819	−	0.537712i
$175$	23823.8	−	41264.1i	0.777920	−	1.34740i
$176$	8956.19	+	5170.86i	0.289133	+	0.166931i
$177$	30003.6	−	5484.00i	0.957696	−	0.175046i
$178$	19401.8	+	33605.0i	0.612355	+	1.06063i
$179$			11804.4i			0.368416i	0.982887	+	0.184208i	$0.0589720\pi$
$179$			11804.4i			0.368416i	−0.982887	+	0.184208i	$0.941028\pi$
$180$	−9794.14	−	25897.4i	−0.302288	−	0.799302i
$181$	−191.582			−0.00584788			−0.00292394	−	0.999996i	$-0.500931\pi$
$181$	−191.582			−0.00584788			−0.00292394	+	0.999996i	$0.500931\pi$
$182$	−7123.41	+	4112.70i	−0.215053	+	0.124161i
$183$	−59207.9	−	21131.8i	−1.76798	−	0.631008i
$184$	2422.33	−	4195.59i	0.0715479	−	0.123925i
$185$	10292.4	+	5942.30i	0.300727	+	0.173625i
$186$	20895.8	+	24589.0i	0.603995	+	0.710745i
$187$	−5253.04	−	9098.53i	−0.150220	−	0.260188i
$188$		−	10185.2i		−	0.288174i
$189$	−13992.8	+	25321.0i	−0.391726	+	0.708856i
$190$	19809.0			0.548726
$191$	−17490.1	+	10097.9i	−0.479431	+	0.276799i	−0.720179	−	0.693788i	$-0.755940\pi$
$191$	−17490.1	+	10097.9i	−0.479431	+	0.276799i	0.240749	+	0.970588i	$0.422607\pi$
$192$	−3511.35	+	2983.97i	−0.0952516	+	0.0809453i
$193$	−19464.6	+	33713.7i	−0.522555	+	0.905091i	0.477101	+	0.878848i	$0.341688\pi$
$193$	−19464.6	+	33713.7i	−0.522555	+	0.905091i	−0.999656	+	0.0262427i	$0.991646\pi$
$194$	−20309.1	−	11725.5i	−0.539618	−	0.311549i
$195$	−9472.45	+	26540.3i	−0.249111	+	0.697969i
$196$	−3304.49	−	5723.55i	−0.0860187	−	0.148989i
$197$		−	64572.8i		−	1.66386i	−0.554879	−	0.831931i	$-0.687235\pi$
$197$		−	64572.8i		−	1.66386i	0.554879	−	0.831931i	$-0.312765\pi$
$198$	−28654.6	−	23440.0i	−0.730910	−	0.597899i
$199$	−59680.7			−1.50705			−0.753525	−	0.657420i	$-0.771648\pi$
$199$	−59680.7			−1.50705			−0.753525	+	0.657420i	$0.771648\pi$
$200$	−23527.9	+	13583.9i	−0.588198	+	0.339596i
$201$	3102.42	+	16973.7i	0.0767905	+	0.420130i
$202$	13097.9	−	22686.2i	0.320995	−	0.555980i
$203$	22343.5	+	12900.0i	0.542199	+	0.313039i
$204$	4604.94	−	841.682i	0.110653	−	0.0202250i
$205$	1191.32	+	2063.43i	0.0283480	+	0.0491002i
$206$		−	22455.3i		−	0.529156i
$207$	−10980.6	+	13423.4i	−0.256264	+	0.313273i
$208$	4689.96			0.108403
$209$	22937.8	−	13243.1i	0.525121	−	0.303179i
$210$	40652.2	+	14509.1i	0.921819	+	0.329005i
$211$	8899.34	−	15414.1i	0.199891	−	0.346221i	−0.748602	−	0.663020i	$-0.769275\pi$
$211$	8899.34	−	15414.1i	0.199891	−	0.346221i	0.948493	+	0.316798i	$0.102608\pi$
$212$	24807.7	+	14322.8i	0.551970	+	0.318680i
$213$	−26744.6	−	31471.5i	−0.589491	−	0.693678i
$214$	−7558.64	−	13091.9i	−0.165050	−	0.285875i
$215$			79717.2i			1.72455i
$216$	14128.3	−	8514.06i	0.302818	−	0.182486i
$217$	−50305.3			−1.06830
$218$	−25439.0	+	14687.2i	−0.535288	+	0.309048i
$219$	67965.0	−	57757.0i	1.41709	−	1.20425i
$220$	−27617.4	+	47834.7i	−0.570607	+	0.988320i
$221$	−4126.18	−	2382.25i	−0.0844818	−	0.0487756i
$222$	−2380.04	+	6668.48i	−0.0482923	+	0.135307i
$223$	25009.9	+	43318.4i	0.502924	+	0.871090i	0.999994	+	0.00337955i	$0.00107575\pi$
$223$	25009.9	+	43318.4i	0.502924	+	0.871090i	−0.497070	+	0.867710i	$0.665591\pi$
$224$		−	7183.70i		−	0.143170i
$225$	90965.0	−	34402.1i	1.79684	−	0.679548i
$226$	−1766.52			−0.0345862
$227$	−57098.5	+	32965.8i	−1.10808	+	0.639753i	−0.938332	−	0.345734i	$-0.887630\pi$
$227$	−57098.5	+	32965.8i	−1.10808	+	0.639753i	−0.169752	+	0.985487i	$0.554297\pi$
$228$	2121.92	+	11609.3i	0.0408187	+	0.223324i
$229$	13214.2	−	22887.6i	0.251981	−	0.436445i	−0.712090	−	0.702088i	$-0.752251\pi$
$229$	13214.2	−	22887.6i	0.251981	−	0.436445i	0.964071	+	0.265644i	$0.0855845\pi$
$230$	22408.5	+	12937.5i	0.423601	+	0.244566i
$231$	56773.1	−	10376.9i	1.06394	−	0.194465i
$232$	−7355.33	−	12739.8i	−0.136655	−	0.236694i
$233$		−	31690.1i		−	0.583730i	−0.956460	−	0.291865i	$-0.905724\pi$
$233$		−	31690.1i		−	0.583730i	0.956460	−	0.291865i	$-0.0942758\pi$
$234$	−16568.9	−	2708.47i	−0.302595	−	0.0494643i
$235$	54398.8			0.985040
$236$	23479.5	−	13555.9i	0.421564	−	0.243390i
$237$	−16512.6	−	5893.48i	−0.293980	−	0.104924i
$238$	−3648.93	+	6320.14i	−0.0644187	+	0.111577i
$239$	26.2948	+	15.1813i	0.000460335	+	0.000265775i	0.500230	−	0.865892i	$-0.333249\pi$
$239$	26.2948	+	15.1813i	0.000460335	+	0.000265775i	−0.499770	+	0.866158i	$0.666582\pi$
$240$	−15937.2	−	18754.0i	−0.276688	−	0.325590i
$241$	−35876.9	−	62140.6i	−0.617705	−	1.06990i	−0.989904	−	0.141743i	$-0.954729\pi$
$241$	−35876.9	−	62140.6i	−0.617705	−	1.06990i	0.372199	−	0.928153i	$-0.378604\pi$
$242$			32442.4i			0.553965i
$243$	−54829.9	+	21919.6i	−0.928548	+	0.371211i
$244$	−55880.9			−0.938606
$245$	30569.2	−	17649.2i	0.509275	−	0.294030i
$246$	−1081.68	+	919.221i	−0.0178743	+	0.0151897i
$247$	6005.75	−	10402.3i	0.0984405	−	0.170504i
$248$	24840.3	+	14341.5i	0.403880	+	0.233180i
$249$	4164.48	−	11668.2i	0.0671680	−	0.188194i
$250$	−34784.5	−	60248.5i	−0.556552	−	0.963977i
$251$			104106.i			1.65245i	0.563338	+	0.826227i	$0.309517\pi$
$251$			104106.i			1.65245i	−0.563338	+	0.826227i	$0.690483\pi$
$252$	−4148.61	+	25378.9i	−0.0653283	+	0.399642i
$253$	34597.2			0.540505
$254$	24167.2	−	13952.9i	0.374592	−	0.216271i
$255$	4495.39	+	24594.8i	0.0691333	+	0.378236i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	−15845.4	−	9148.35i	−0.239904	−	0.138509i	0.375229	−	0.926932i	$-0.377564\pi$
$257$	−15845.4	−	9148.35i	−0.239904	−	0.138509i	−0.615133	+	0.788424i	$0.710898\pi$
$258$	−46719.1	+	8539.21i	−0.701867	+	0.128286i
$259$	−5519.10	−	9559.37i	−0.0822752	−	0.142505i
$260$			25048.9i			0.370546i
$261$	18627.9	+	49255.4i	0.273453	+	0.723057i
$262$	10632.4			0.154893
$263$	89539.9	−	51695.9i	1.29451	−	0.747385i	0.315059	−	0.949072i	$-0.397976\pi$
$263$	89539.9	−	51695.9i	1.29451	−	0.747385i	0.979450	+	0.201687i	$0.0646424\pi$
$264$	−30992.3	−	11061.4i	−0.444679	−	0.158710i
$265$	−76497.3	+	132497.i	−1.08932	+	1.88675i
$266$	−15933.4	−	9199.13i	−0.225187	−	0.130012i
$267$	−79956.2	−	94087.6i	−1.12158	−	1.31981i
$268$	7668.84	+	13282.8i	0.106773	+	0.184936i
$269$			6350.47i			0.0877609i	0.999037	+	0.0438804i	$0.0139721\pi$
$269$			6350.47i			0.0877609i	−0.999037	+	0.0438804i	$0.986028\pi$
$270$	45473.2	+	75458.6i	0.623775	+	1.03510i
$271$	111208.			1.51424			0.757122	−	0.653274i	$-0.226605\pi$
$271$	111208.			1.51424			0.757122	+	0.653274i	$0.226605\pi$
$272$	3603.61	−	2080.55i	0.0487080	−	0.0281216i
$273$	19944.2	−	16948.7i	0.267604	−	0.227411i
$274$	34272.5	−	59361.7i	0.456504	−	0.790689i
$275$	−168020.	−	97006.5i	−2.22175	−	1.28273i
$276$	−5181.81	+	14518.6i	−0.0680242	+	0.190593i
$277$	−45476.3	−	78767.3i	−0.592688	−	1.02657i	−0.993869	−	0.110566i	$-0.964734\pi$
$277$	−45476.3	−	78767.3i	−0.592688	−	1.02657i	0.401181	−	0.915999i	$-0.368600\pi$
$278$		−	75285.1i		−	0.974136i
$279$	−79474.3	−	65011.6i	−1.02098	−	0.835185i
$280$	38367.9			0.489386
$281$	−126245.	+	72887.9i	−1.59883	+	0.923087i	−0.607121	+	0.794609i	$0.707676\pi$
$281$	−126245.	+	72887.9i	−1.59883	+	0.923087i	−0.991712	+	0.128478i	$0.958991\pi$
$282$	5827.14	+	31881.0i	0.0732753	+	0.400898i
$283$	−54454.5	+	94317.9i	−0.679925	+	1.17766i	0.295079	+	0.955473i	$0.404654\pi$
$283$	−54454.5	+	94317.9i	−0.679925	+	1.17766i	−0.975003	+	0.222191i	$0.928679\pi$
$284$	−31793.1	−	18355.8i	−0.394181	−	0.227581i
$285$	−62004.6	+	11333.1i	−0.763369	+	0.139527i
$286$	16746.2	+	29005.3i	0.204732	+	0.354606i
$287$		−	2212.96i		−	0.0268665i
$288$	9283.79	−	11349.1i	0.111928	−	0.136828i
$289$	79293.8			0.949387
$290$	68042.7	−	39284.5i	0.809069	−	0.467116i
$291$	70278.3	+	25082.9i	0.829918	+	0.296205i
$292$	39640.7	−	68659.6i	0.464917	−	0.805259i
$293$	87765.8	+	50671.6i	1.02233	+	0.590241i	0.914777	−	0.403959i	$-0.132366\pi$
$293$	87765.8	+	50671.6i	1.02233	+	0.590241i	0.107550	+	0.994200i	$0.465699\pi$
$294$	13618.0	+	16024.9i	0.157550	+	0.185396i
$295$	72401.3	+	125403.i	0.831960	+	1.44100i
$296$			6293.76i			0.0718335i
$297$	103103.	+	56976.5i	1.16885	+	0.645926i
$298$	−19477.6			−0.219333
$299$	13587.7	−	7844.89i	0.151987	−	0.0877494i
$300$	65873.8	−	55979.9i	0.731931	−	0.621999i
$301$	37019.9	−	64120.4i	0.408604	−	0.707723i
$302$	10775.3	+	6221.14i	0.118145	+	0.0682113i
$303$	−28018.8	+	78504.2i	−0.305186	+	0.855082i
$304$	5245.15	+	9084.87i	0.0567559	+	0.0983041i
$305$		−	298457.i		−	3.20836i
$306$	−13932.5	+	5269.14i	−0.148794	+	0.0562726i
$307$	9427.87			0.100031			0.0500157	−	0.998748i	$-0.484073\pi$
$307$	9427.87			0.100031			0.0500157	+	0.998748i	$0.484073\pi$
$308$	44428.0	−	25650.5i	0.468334	−	0.270393i
$309$	12847.1	+	70287.8i	0.134551	+	0.736144i
$310$	−76597.5	+	132671.i	−0.797061	+	1.38055i
$311$	135532.	+	78249.3i	1.40127	+	0.809021i	0.994523	−	0.104521i	$-0.0333311\pi$
$311$	135532.	+	78249.3i	1.40127	+	0.809021i	0.406743	+	0.913543i	$0.366664\pi$
$312$	−14680.2	+	2683.21i	−0.150807	+	0.0275642i
$313$	15880.0	+	27505.0i	0.162092	+	0.280752i	0.935619	−	0.353012i	$-0.114843\pi$
$313$	15880.0	+	27505.0i	0.162092	+	0.280752i	−0.773527	+	0.633764i	$0.781509\pi$
$314$			78790.4i			0.799124i
$315$	−135547.	−	22157.6i	−1.36606	−	0.223306i
$316$	−15584.7			−0.156072
$317$	−42253.9	+	24395.3i	−0.420483	+	0.242766i	−0.695284	−	0.718735i	$-0.744721\pi$
$317$	−42253.9	+	24395.3i	−0.420483	+	0.242766i	0.274801	+	0.961501i	$0.411388\pi$
$318$	−85845.6	−	30639.1i	−0.848915	−	0.302985i
$319$	52526.7	−	90978.8i	0.516177	−	0.894044i
$320$	−18945.7	−	10938.3i	−0.185016	−	0.106819i
$321$	31149.6	+	36655.0i	0.302303	+	0.355732i
$322$	−12016.2	−	20812.6i	−0.115892	−	0.200731i
$323$		−	10657.0i		−	0.102148i
$324$	−39352.3	+	34733.1i	−0.374869	+	0.330867i
$325$	−87984.7			−0.832991
$326$	−81632.2	+	47130.4i	−0.768115	+	0.443471i
$327$	71224.5	−	60526.9i	0.666091	−	0.566048i
$328$	−630.893	+	1092.74i	−0.00586419	+	0.0101571i
$329$	−43755.7	−	25262.3i	−0.404243	−	0.233390i
$330$	59078.7	−	165529.i	0.542504	−	1.52001i
$331$	−74409.9	−	128882.i	−0.679164	−	1.17635i	−0.975233	−	0.221180i	$-0.929009\pi$
$331$	−74409.9	−	128882.i	−0.679164	−	1.17635i	0.296069	−	0.955167i	$-0.404324\pi$
$332$		−	11012.5i		−	0.0999105i
$333$	3634.67	−	22234.8i	0.0327775	−	0.200514i
$334$	102597.			0.919693
$335$	−70943.0	+	40958.9i	−0.632150	+	0.364972i
$336$	4109.92	+	22485.9i	0.0364045	+	0.199173i
$337$	−29324.5	+	50791.5i	−0.258209	+	0.447230i	−0.965762	−	0.259429i	$-0.916465\pi$
$337$	−29324.5	+	50791.5i	−0.258209	+	0.447230i	0.707554	+	0.706660i	$0.249799\pi$
$338$	−56806.0	−	32797.0i	−0.497234	−	0.287078i
$339$	5529.44	−	1010.66i	0.0481151	−	0.00879439i
$340$	11112.1	+	19246.8i	0.0961256	+	0.166494i
$341$			204835.i			1.76155i
$342$	−13283.7	−	35124.5i	−0.113571	−	0.300302i
$343$	−128067.			−1.08856
$344$	−36560.2	+	21108.0i	−0.308952	+	0.178374i
$345$	−77543.1	−	27675.8i	−0.651486	−	0.232521i
$346$	−27670.2	+	47926.2i	−0.231132	+	0.400332i
$347$	23368.5	+	13491.8i	0.194076	+	0.112050i	0.593889	−	0.804547i	$-0.297592\pi$
$347$	23368.5	+	13491.8i	0.194076	+	0.112050i	−0.399813	+	0.916597i	$0.630925\pi$
$348$	30311.7	+	35669.0i	0.250295	+	0.294532i
$349$	5578.41	+	9662.09i	0.0457994	+	0.0793268i	0.888016	−	0.459812i	$-0.152083\pi$
$349$	5578.41	+	9662.09i	0.0457994	+	0.0793268i	−0.842217	+	0.539139i	$0.818750\pi$
$350$			134768.i			1.10015i
$351$	53412.2	−	1001.51i	0.433537	−	0.00812904i
$352$	−29250.8			−0.236076
$353$	109934.	−	63470.2i	0.882229	−	0.509355i	0.0108360	−	0.999941i	$-0.496551\pi$
$353$	109934.	−	63470.2i	0.882229	−	0.509355i	0.871393	+	0.490586i	$0.163217\pi$
$354$	−65738.1	+	55864.6i	−0.524578	+	0.445790i
$355$	98037.3	−	169806.i	0.777920	−	1.34740i
$356$	−95049.2	−	54876.7i	−0.749978	−	0.433000i
$357$	7805.76	−	21870.4i	0.0612461	−	0.171602i
$358$	−16694.0	−	28914.8i	−0.130255	−	0.225608i
$359$			27655.4i			0.214581i	0.994228	+	0.107290i	$0.0342175\pi$
$359$			27655.4i			0.214581i	−0.994228	+	0.107290i	$0.965783\pi$
$360$	60615.1	+	49584.4i	0.467709	+	0.382595i
$361$	−103454.			−0.793841
$362$	469.279	−	270.938i	0.00358108	−	0.00206754i
$363$	−18560.9	−	101549.i	−0.140859	−	0.770658i
$364$	11632.5	−	20148.1i	0.0877950	−	0.152065i
$365$	366708.	+	211719.i	2.75255	+	1.58918i
$366$	174914.	−	31970.4i	1.30576	−	0.238664i
$367$	−73646.3	−	127559.i	−0.546788	−	0.947064i	−0.998492	−	0.0548962i	$-0.982517\pi$
$367$	−73646.3	−	127559.i	−0.546788	−	0.947064i	0.451705	−	0.892168i	$-0.350816\pi$
$368$			13702.7i			0.101184i
$369$	2859.90	−	3496.13i	0.0210038	−	0.0256764i
$370$	−33614.7			−0.245542
$371$	123061.	−	71049.3i	0.894072	−	0.516193i
$372$	−85958.1	−	30679.2i	−0.621157	−	0.221696i
$373$	−13254.0	+	22956.7i	−0.0952644	+	0.165003i	−0.909719	−	0.415225i	$-0.863703\pi$
$373$	−13254.0	+	22956.7i	−0.0952644	+	0.165003i	0.814455	+	0.580227i	$0.197036\pi$
$374$	25734.5	+	14857.8i	0.183981	+	0.106221i
$375$	143349.	+	168685.i	1.01937	+	1.19954i
$376$	14404.1	+	24948.6i	0.101885	+	0.176470i
$377$		−	47641.6i		−	0.335200i
$378$	−1534.03	−	81812.5i	−0.0107362	−	0.572580i
$379$	−143952.			−1.00216			−0.501082	−	0.865400i	$-0.667065\pi$
$379$	−143952.			−1.00216			−0.501082	+	0.865400i	$0.667065\pi$
$380$	−48521.9	+	28014.2i	−0.336025	+	0.194004i
$381$	−67663.5	+	57500.8i	−0.466127	+	0.396117i
$382$	28561.2	−	49469.5i	0.195727	−	0.339009i
$383$	−132772.	−	76655.8i	−0.905124	−	0.522574i	−0.0262649	−	0.999655i	$-0.508361\pi$
$383$	−132772.	−	76655.8i	−0.905124	−	0.522574i	−0.878859	+	0.477081i	$0.841695\pi$
$384$	4381.06	−	12275.0i	0.0297109	−	0.0832452i
$385$	136998.	+	237288.i	0.924260	+	1.60086i
$386$		−	110109.i		−	0.739004i
$387$	141351.	−	53457.6i	0.943794	−	0.356934i
$388$	66329.2			0.440597
$389$	−220839.	+	127501.i	−1.45941	+	0.842588i	−0.998982	−	0.0451117i	$-0.985636\pi$
$389$	−220839.	+	127501.i	−1.45941	+	0.842588i	−0.460423	+	0.887700i	$0.652302\pi$
$390$	−14330.9	−	78406.2i	−0.0942203	−	0.515491i
$391$	6960.26	−	12055.5i	0.0455273	−	0.0788556i
$392$	16188.6	+	9346.52i	0.105351	+	0.0608244i
$393$	−33280.9	+	6083.01i	−0.215481	+	0.0393852i
$394$	91319.8	+	158171.i	0.588264	+	1.01890i
$395$		−	83237.1i		−	0.533486i
$396$	103338.	+	16892.4i	0.658978	+	0.107721i
$397$	14768.6			0.0937042			0.0468521	−	0.998902i	$-0.485081\pi$
$397$	14768.6			0.0937042			0.0468521	+	0.998902i	$0.485081\pi$
$398$	146187.	−	84401.2i	0.922875	−	0.532822i
$399$	55136.4	+	19678.7i	0.346332	+	0.123609i
$400$	38420.9	−	66547.0i	0.240131	−	0.415919i
$401$	−183560.	−	105979.i	−1.14154	−	0.659067i	−0.194727	−	0.980858i	$-0.562382\pi$
$401$	−183560.	−	105979.i	−1.14154	−	0.659067i	−0.946811	+	0.321791i	$0.895715\pi$
$402$	−31603.8	−	37189.4i	−0.195563	−	0.230127i
$403$	46446.1	+	80447.1i	0.285983	+	0.495336i
$404$			74092.8i			0.453956i
$405$	−185508.	−	210179.i	−1.13097	−	1.28138i
$406$	−72973.5			−0.442704
$407$	−38924.1	+	22472.9i	−0.234979	+	0.135665i
$408$	−10089.4	+	8574.07i	−0.0606104	+	0.0515070i
$409$	16193.4	−	28047.8i	0.0968035	−	0.167669i	−0.813556	−	0.581486i	$-0.802471\pi$
$409$	16193.4	−	28047.8i	0.0968035	−	0.167669i	0.910360	+	0.413817i	$0.135805\pi$
$410$	−5836.27	−	3369.57i	−0.0347191	−	0.0200451i
$411$	−73315.4	+	205418.i	−0.434022	+	1.21606i
$412$	31756.5	+	55004.0i	0.187085	+	0.324041i
$413$		−	134490.i		−	0.788480i
$414$	7913.37	−	48409.6i	0.0461701	−	0.282443i
$415$	58817.5			0.341515
$416$	−11488.0	+	6632.61i	−0.0663832	+	0.0383264i
$417$	43071.9	+	235652.i	0.247698	+	1.35519i
$418$	−37457.3	+	64877.9i	−0.214380	+	0.371316i
$419$	−72546.9	−	41885.0i	−0.413229	−	0.238578i	0.278947	−	0.960306i	$-0.410015\pi$
$419$	−72546.9	−	41885.0i	−0.413229	−	0.238578i	−0.692176	+	0.721729i	$0.743348\pi$
$420$	−120096.	+	21950.9i	−0.680817	+	0.124438i
$421$	−104651.	−	181261.i	−0.590446	−	1.02268i	−0.994172	−	0.107803i	$-0.965619\pi$
$421$	−104651.	−	181261.i	−0.590446	−	1.02268i	0.403726	−	0.914880i	$-0.367715\pi$
$422$			50342.3i			0.282688i
$423$	−36479.4	−	96457.7i	−0.203876	−	0.539084i
$424$	−81021.7			−0.450682
$425$	−67604.6	+	39031.5i	−0.374282	+	0.216092i
$426$	110018.	+	39266.4i	0.606240	+	0.216372i
$427$	−138601.	+	240064.i	−0.760170	+	1.31665i
$428$	37029.6	+	21379.1i	0.202144	+	0.116708i
$429$	−69012.3	−	81209.5i	−0.374983	−	0.441257i
$430$	−112737.	−	195266.i	−0.609719	−	1.05606i
$431$		−	80767.2i		−	0.434791i	−0.976084	−	0.217395i	$-0.930244\pi$
$431$		−	80767.2i		−	0.434791i	0.976084	−	0.217395i	$-0.0697561\pi$
$432$	−22566.4	+	40835.5i	−0.120919	+	0.218812i
$433$	237783.			1.26825			0.634124	−	0.773231i	$-0.281361\pi$
$433$	237783.			1.26825			0.634124	+	0.773231i	$0.281361\pi$
$434$	123222.	−	71142.4i	0.654199	−	0.377702i
$435$	−190507.	+	161894.i	−1.00677	+	0.855563i
$436$	41541.7	−	71952.4i	0.218530	−	0.378505i
$437$	30392.5	+	17547.1i	0.159149	+	0.0918846i
$438$	−84798.8	+	237592.i	−0.442020	+	1.23847i
$439$	130206.	+	225523.i	0.675618	+	1.17020i	0.976288	+	0.216476i	$0.0694563\pi$
$439$	130206.	+	225523.i	0.675618	+	1.17020i	−0.300670	+	0.953728i	$0.597210\pi$
$440$		−	156227.i		−	0.806959i
$441$	−51794.2	−	42368.7i	−0.266320	−	0.217855i
$442$	13476.0			0.0689791
$443$	152170.	−	87855.4i	0.775393	−	0.447673i	−0.0594024	−	0.998234i	$-0.518919\pi$
$443$	152170.	−	87855.4i	0.775393	−	0.447673i	0.834795	+	0.550561i	$0.185586\pi$
$444$	−3600.77	−	19700.3i	−0.0182654	−	0.0999323i
$445$	293094.	−	507654.i	1.48009	−	2.56359i
$446$	−122523.	−	70738.7i	−0.615953	−	0.355621i
$447$	60967.5	−	11143.5i	0.305129	−	0.0557708i
$448$	10159.3	+	17596.4i	0.0506183	+	0.0876734i
$449$			152520.i			0.756543i	0.925695	+	0.378272i	$0.123481\pi$
$449$			152520.i			0.756543i	−0.925695	+	0.378272i	$0.876519\pi$
$450$	−174166.	+	212912.i	−0.860079	+	1.05142i
$451$	−9010.81			−0.0443007
$452$	4327.08	−	2498.24i	0.0211796	−	0.0122281i
$453$	−37287.4	−	13308.2i	−0.181704	−	0.0648519i
$454$	93241.4	−	161499.i	0.452373	−	0.783534i
$455$	107610.	+	62128.6i	0.519792	+	0.300102i
$456$	−21615.6	−	25435.9i	−0.103953	−	0.122326i
$457$	144761.	+	250733.i	0.693135	+	1.20055i	0.970805	+	0.239869i	$0.0771045\pi$
$457$	144761.	+	250733.i	0.693135	+	1.20055i	−0.277670	+	0.960676i	$0.589562\pi$
$458$			74750.6i			0.356356i
$459$	40595.9	−	24464.1i	0.192689	−	0.116119i
$460$	−73185.8			−0.345869
$461$	84076.0	−	48541.3i	0.395613	−	0.228407i	−0.288977	−	0.957336i	$-0.593315\pi$
$461$	84076.0	−	48541.3i	0.395613	−	0.228407i	0.684589	+	0.728929i	$0.259982\pi$
$462$	−124390.	+	105707.i	−0.582776	+	0.495246i
$463$	−186888.	+	323699.i	−0.871804	+	1.51001i	−0.0116757	+	0.999932i	$0.503717\pi$
$463$	−186888.	+	323699.i	−0.871804	+	1.51001i	−0.860129	+	0.510077i	$0.829617\pi$
$464$	36033.6	+	20804.0i	0.167368	+	0.0966298i
$465$	163856.	−	459099.i	0.757805	−	2.12325i
$466$	44816.6	+	77624.6i	0.206380	+	0.357460i
$467$			24459.9i			0.112155i	0.998426	+	0.0560777i	$0.0178595\pi$
$467$			24459.9i			0.112155i	−0.998426	+	0.0560777i	$0.982141\pi$
$468$	44415.6	−	16797.6i	0.202789	−	0.0766928i
$469$	76083.9			0.345897
$470$	−133249.	+	76931.6i	−0.603211	+	0.348264i
$471$	−45077.4	−	246624.i	−0.203197	−	1.11171i
$472$	−38341.8	+	66409.9i	−0.172103	+	0.298091i
$473$	−261087.	−	150739.i	−1.16698	−	0.673757i
$474$	48782.0	−	8916.27i	0.217122	−	0.0396850i
$475$	−98400.3	−	170434.i	−0.436123	−	0.755387i
$476$		−	20641.5i		−	0.0911018i
$477$	286237.	+	46790.3i	1.25802	+	0.205645i
$478$	−85.8785			−0.000375862
$479$	160413.	−	92614.5i	0.699147	−	0.403653i	−0.107882	−	0.994164i	$-0.534407\pi$
$479$	160413.	−	92614.5i	0.699147	−	0.403653i	0.807030	+	0.590511i	$0.201074\pi$
$480$	65560.3	+	23399.0i	0.284550	+	0.101558i
$481$	−10191.4	+	17652.1i	−0.0440498	+	0.0762966i
$482$	175760.	+	101475.i	0.756531	+	0.436783i
$483$	49519.3	+	58271.4i	0.212266	+	0.249782i
$484$	−45880.5	−	79467.4i	−0.195856	−	0.339233i
$485$			354261.i			1.50605i
$486$	103306.	−	131233.i	0.437375	−	0.555611i
$487$	224682.			0.947349			0.473675	−	0.880700i	$-0.342927\pi$
$487$	224682.			0.947349			0.473675	+	0.880700i	$0.342927\pi$
$488$	136880.	−	79027.5i	0.574777	−	0.331848i
$489$	228555.	−	194227.i	0.955812	−	0.812255i
$490$	−49919.4	+	86462.9i	−0.207911	+	0.360112i
$491$	−83529.3	−	48225.7i	−0.346478	−	0.200039i	0.316655	−	0.948541i	$-0.397440\pi$
$491$	−83529.3	−	48225.7i	−0.346478	−	0.200039i	−0.663133	+	0.748502i	$0.730774\pi$
$492$	1349.60	−	3781.35i	0.00557538	−	0.0156213i
$493$	−21134.6	−	36606.3i	−0.0869563	−	0.150613i
$494$			33973.7i			0.139216i
$495$	−90221.8	+	551926.i	−0.368215	+	2.25253i
$496$	−81127.9			−0.329767
$497$	−157713.	+	91055.4i	−0.638489	+	0.368632i
$498$	6300.46	+	34470.6i	0.0254047	+	0.138992i
$499$	−20829.6	+	36077.9i	−0.0836526	+	0.144891i	−0.904816	−	0.425802i	$-0.859992\pi$
$499$	−20829.6	+	36077.9i	−0.0836526	+	0.144891i	0.821164	+	0.570693i	$0.193325\pi$
$500$	170409.	+	98385.5i	0.681634	+	0.393542i
$501$	−321142.	+	58697.7i	−1.27945	+	0.233854i
$502$	−147228.	−	255007.i	−0.584231	−	1.01192i
$503$		−	67751.0i		−	0.267781i	−0.990996	−	0.133891i	$-0.957253\pi$
$503$		−	67751.0i		−	0.267781i	0.990996	−	0.133891i	$-0.0427470\pi$
$504$	−25729.1	−	68032.3i	−0.101289	−	0.267827i
$505$	−395727.			−1.55172
$506$	−84745.4	+	48927.8i	−0.330990	+	0.191097i
$507$	196574.	+	70158.8i	0.764732	+	0.272940i
$508$	−39464.8	+	68355.0i	−0.152926	+	0.264876i
$509$	−107700.	−	62180.4i	−0.415698	−	0.240004i	0.277537	−	0.960715i	$-0.410482\pi$
$509$	−107700.	−	62180.4i	−0.415698	−	0.240004i	−0.693235	+	0.720711i	$0.743815\pi$
$510$	−45793.7	−	53887.3i	−0.176062	−	0.207179i
$511$	−196641.	−	340592.i	−0.753065	−	1.30435i
$512$		−	11585.2i		−	0.0441942i
$513$	61675.1	+	102344.i	0.234355	+	0.388891i
$514$	51750.9			0.195881
$515$	−293774.	+	169610.i	−1.10764	+	0.639496i
$516$	102362.	−	86987.5i	0.384448	−	0.326706i
$517$	−102864.	+	178166.i	−0.384842	+	0.666565i
$518$	27038.0	+	15610.4i	0.100766	+	0.0581774i
$519$	59191.7	−	165846.i	0.219749	−	0.615700i
$520$	−35424.5	−	61357.0i	−0.131008	−	0.226912i
$521$			59159.3i			0.217945i	0.994045	+	0.108973i	$0.0347561\pi$
$521$			59159.3i			0.217945i	−0.994045	+	0.108973i	$0.965244\pi$
$522$	−115286.	−	94306.7i	−0.423094	−	0.346100i
$523$	−228587.			−0.835697			−0.417848	−	0.908517i	$-0.637216\pi$
$523$	−228587.			−0.835697			−0.417848	+	0.908517i	$0.637216\pi$
$524$	−26044.1	+	15036.5i	−0.0948519	+	0.0547628i
$525$	−77103.1	−	421840.i	−0.279739	−	1.53049i
$526$	−146218.	+	253257.i	−0.528481	+	0.915356i
$527$	71375.4	+	41208.6i	0.256997	+	0.148377i
$528$	91558.7	−	16734.9i	0.328422	−	0.0600282i
$529$	−117000.	−	202650.i	−0.418094	−	0.724161i
$530$		−	432734.i		−	1.54053i
$531$	173807.	−	212473.i	0.616423	−	0.753555i
$532$	52038.1			0.183865
$533$	−3538.92	+	2043.20i	−0.0124571	+	0.00719210i
$534$	328912.	+	117392.i	1.15345	+	0.411675i
$535$	−114185.	+	197774.i	−0.398933	+	0.690973i
$536$	−37569.5	−	21690.7i	−0.130769	−	0.0754996i
$537$	68796.8	+	80956.0i	0.238572	+	0.280738i
$538$	−8980.91	−	15555.4i	−0.0310282	−	0.0537423i
$539$			133493.i			0.459494i
$540$	−218101.	−	120526.i	−0.747945	−	0.413327i
$541$	442187.			1.51082			0.755408	−	0.655255i	$-0.227439\pi$
$541$	442187.			1.51082			0.755408	+	0.655255i	$0.227439\pi$
$542$	−272402.	+	157271.i	−0.927281	+	0.535366i
$543$	−1313.89	+	1116.55i	−0.00445616	+	0.00378687i
$544$	−5884.68	+	10192.6i	−0.0198850	+	0.0344418i
$545$	384295.	+	221873.i	1.29381	+	0.746983i
$546$	−24884.1	+	69721.1i	−0.0834711	+	0.233872i
$547$	130418.	+	225891.i	0.435876	+	0.754960i	0.997367	−	0.0725231i	$-0.0231051\pi$
$547$	130418.	+	225891.i	0.435876	+	0.754960i	−0.561490	+	0.827483i	$0.689772\pi$
$548$			193875.i			0.645595i
$549$	−529212.	+	200143.i	−1.75584	+	0.664042i
$550$	548752.			1.81405
$551$	92286.0	−	53281.3i	0.303971	−	0.175498i
$552$	−7839.58	−	42891.3i	−0.0257285	−	0.140764i
$553$	−38654.6	+	66951.7i	−0.126401	+	0.218933i
$554$	222788.	+	128626.i	0.725891	+	0.419093i
$555$	105218.	−	19231.6i	0.341590	−	0.0624351i
$556$	106469.	+	184410.i	0.344409	+	0.596534i
$557$		−	161870.i		−	0.521742i	−0.965374	−	0.260871i	$-0.915990\pi$
$557$		−	161870.i		−	0.521742i	0.965374	−	0.260871i	$-0.0840098\pi$
$558$	286612.	+	46851.6i	0.920504	+	0.150472i
$559$	−136720.			−0.437530
$560$	−93981.7	+	54260.3i	−0.299686	+	0.173024i
$561$	−89052.7	−	31783.7i	−0.282958	−	0.100990i
$562$	206158.	−	357076.i	0.652721	−	1.13055i
$563$	226828.	+	130959.i	0.715617	+	0.413161i	0.813137	−	0.582072i	$-0.197758\pi$
$563$	226828.	+	130959.i	0.715617	+	0.413161i	−0.0975206	+	0.995234i	$0.531091\pi$
$564$	−59360.1	−	69851.4i	−0.186611	−	0.219592i
$565$	13343.0	+	23110.8i	0.0417981	+	0.0723965i
$566$		−	308041.i		−	0.961559i
$567$	51608.1	+	255206.i	0.160528	+	0.793824i
$568$	103836.			0.321848
$569$	248528.	−	143488.i	0.767629	−	0.443191i	−0.0643991	−	0.997924i	$-0.520513\pi$
$569$	248528.	−	143488.i	0.767629	−	0.443191i	0.832028	+	0.554733i	$0.187180\pi$
$570$	135852.	−	115448.i	0.418136	−	0.355334i
$571$	283781.	−	491522.i	0.870383	−	1.50755i	0.00878172	−	0.999961i	$-0.497205\pi$
$571$	283781.	−	491522.i	0.870383	−	1.50755i	0.861601	−	0.507586i	$-0.169462\pi$
$572$	−82039.4	−	47365.5i	−0.250744	−	0.144767i
$573$	−61097.8	+	171186.i	−0.186087	+	0.521386i
$574$	3129.60	+	5420.63i	0.00949873	+	0.0164523i
$575$		−	257066.i		−	0.777517i
$576$	−6690.51	+	40928.8i	−0.0201657	+	0.123363i
$577$	63525.8			0.190809			0.0954044	−	0.995439i	$-0.469586\pi$
$577$	63525.8			0.190809			0.0954044	+	0.995439i	$0.469586\pi$
$578$	−194229.	+	112138.i	−0.581379	+	0.335659i
$579$	62995.1	+	344654.i	0.187910	+	1.02808i
$580$	−111113.	+	192454.i	−0.330301	+	0.572098i
$581$	−47309.8	−	27314.3i	−0.140152	−	0.0809167i
$582$	−207619.	+	37948.1i	−0.612943	+	0.112032i
$583$	−289301.	−	501084.i	−0.851162	−	1.47426i
$584$			224241.i			0.657492i
$585$	89715.1	+	237222.i	0.262152	+	0.693176i
$586$	−286642.			−0.834727
$587$	404383.	−	233470.i	1.17359	−	0.677572i	0.219067	−	0.975710i	$-0.429699\pi$
$587$	404383.	−	233470.i	1.17359	−	0.677572i	0.954523	+	0.298137i	$0.0963653\pi$
$588$	−56019.8	−	19994.0i	−0.162027	−	0.0578288i
$589$	−103889.	+	179941.i	−0.299460	+	0.518679i
$590$	−354693.	−	204782.i	−1.01894	−	0.588285i
$591$	−376335.	−	442848.i	−1.07745	−	1.26788i
$592$	−8900.72	−	15416.5i	−0.0253970	−	0.0439888i
$593$			95001.6i			0.270160i	0.990835	+	0.135080i	$0.0431292\pi$
$593$			95001.6i			0.270160i	−0.990835	+	0.135080i	$0.956871\pi$
$594$	−333126.	+	6246.29i	−0.944139	+	0.0177031i
$595$	110245.			0.311406
$596$	47710.3	−	27545.5i	0.134313	−	0.0775459i
$597$	−409297.	+	347823.i	−1.14839	+	0.975908i
$598$	−22188.7	+	38431.9i	−0.0620482	+	0.107471i
$599$	−483801.	−	279323.i	−1.34838	−	0.778489i	−0.360362	−	0.932812i	$-0.617347\pi$
$599$	−483801.	−	279323.i	−1.34838	−	0.778489i	−0.988020	+	0.154323i	$0.950680\pi$
$600$	−82189.6	+	230282.i	−0.228304	+	0.639672i
$601$	−33329.2	−	57727.9i	−0.0922733	−	0.159822i	0.816194	−	0.577778i	$-0.196080\pi$
$601$	−33329.2	−	57727.9i	−0.0922733	−	0.159822i	−0.908467	+	0.417956i	$0.862747\pi$
$602$			209416.i			0.577854i
$603$	120200.	+	98326.4i	0.330576	+	0.270418i
$604$	−35192.1			−0.0964653
$605$	424432.	−	245046.i	1.15957	−	0.669479i
$606$	−42389.8	−	231920.i	−0.115429	−	0.631528i
$607$	94446.0	−	163585.i	0.256334	−	0.443983i	−0.708923	−	0.705286i	$-0.750819\pi$
$607$	94446.0	−	163585.i	0.256334	−	0.443983i	0.965257	+	0.261302i	$0.0841520\pi$
$608$	−25695.9	−	14835.5i	−0.0695115	−	0.0401325i
$609$	228416.	−	41749.4i	0.615875	−	0.112568i
$610$	422083.	+	731069.i	1.13433	+	1.96471i
$611$			93297.4i			0.249912i
$612$	26675.9	−	32610.3i	0.0712222	−	0.0870665i
$613$	689285.			1.83433			0.917165	−	0.398507i	$-0.130472\pi$
$613$	689285.			1.83433			0.917165	+	0.398507i	$0.130472\pi$
$614$	−23093.5	+	13333.0i	−0.0612565	+	0.0353665i
$615$	20196.1	+	7208.15i	0.0533969	+	0.0190578i
$616$	−72550.6	+	125661.i	−0.191196	+	0.331162i
$617$	−316147.	−	182527.i	−0.830459	−	0.479466i	0.0235507	−	0.999723i	$-0.492503\pi$
$617$	−316147.	−	182527.i	−0.830459	−	0.479466i	−0.854010	+	0.520257i	$0.825836\pi$
$618$	−130871.	−	154001.i	−0.342662	−	0.403224i
$619$	330384.	+	572241.i	0.862258	+	1.49347i	0.869744	+	0.493503i	$0.164284\pi$
$619$	330384.	+	572241.i	0.862258	+	1.49347i	−0.00748622	+	0.999972i	$0.502383\pi$
$620$		−	433301.i		−	1.12721i
$621$	2926.12	+	156055.i	0.00758767	+	0.404665i
$622$	−442645.			−1.14413
$623$	−471500.	+	272221.i	−1.21480	+	0.701367i
$624$	32164.3	−	27333.4i	0.0826047	−	0.0701979i
$625$	−150268.	+	260272.i	−0.384687	+	0.666297i
$626$	−77795.8	−	44915.4i	−0.198521	−	0.114616i
$627$	80128.1	−	224506.i	0.203821	−	0.571074i
$628$	−111426.	−	192996.i	−0.282533	−	0.489361i
$629$			18084.4i			0.0457090i
$630$	363358.	−	137418.i	0.915489	−	0.346229i
$631$	−244678.			−0.614519			−0.307260	−	0.951626i	$-0.599412\pi$
$631$	−244678.			−0.614519			−0.307260	+	0.951626i	$0.599412\pi$
$632$	38174.5	−	22040.1i	0.0955739	−	0.0551796i
$633$	−28801.7	−	157578.i	−0.0718805	−	0.393267i
$634$	69000.3	−	119512.i	0.171661	−	0.297326i
$635$	−365081.	−	210780.i	−0.905404	−	0.522735i
$636$	253608.	−	46354.0i	0.626973	−	0.114597i
$637$	30269.4	+	52428.2i	0.0745977	+	0.129207i
$638$			297136.i			0.729984i
$639$	−366835.	−	59965.5i	−0.898399	−	0.146859i
$640$	61876.3			0.151065
$641$	−5356.80	+	3092.75i	−0.0130374	+	0.00752712i	−0.506505	−	0.862237i	$-0.669063\pi$
$641$	−5356.80	+	3092.75i	−0.0130374	+	0.00752712i	0.493467	+	0.869764i	$0.335729\pi$
$642$	−128139.	−	45733.8i	−0.310892	−	0.110960i
$643$	84814.1	−	146902.i	0.205138	−	0.355309i	−0.745039	−	0.667021i	$-0.767569\pi$
$643$	84814.1	−	146902.i	0.205138	−	0.355309i	0.950177	+	0.311712i	$0.100902\pi$
$644$	58866.9	+	33986.8i	0.141938	+	0.0819481i
$645$	464596.	+	546709.i	1.11675	+	1.31413i
$646$	15071.3	+	26104.3i	0.0361149	+	0.0625528i
$647$		−	315605.i		−	0.753938i	−0.926226	−	0.376969i	$-0.876966\pi$
$647$		−	315605.i		−	0.753938i	0.926226	−	0.376969i	$-0.123034\pi$
$648$	47273.0	−	140731.i	0.112580	−	0.335150i
$649$	−547621.			−1.30014
$650$	215518.	−	124429.i	0.510101	−	0.294507i
$651$	−344999.	+	293182.i	−0.814060	+	0.691793i
$652$	133305.	−	230891.i	0.313582	−	0.543139i
$653$	121196.	+	69972.5i	0.284225	+	0.164097i	0.635334	−	0.772237i	$-0.280862\pi$
$653$	121196.	+	69972.5i	0.284225	+	0.164097i	−0.351110	+	0.936334i	$0.614196\pi$
$654$	−88865.6	+	248987.i	−0.207768	+	0.582131i
$655$	−80309.6	−	139100.i	−0.187191	−	0.324224i
$656$		−	3568.87i		−	0.00829322i
$657$	129500.	−	792209.i	0.300012	−	1.83531i
$658$	142905.			0.330063
$659$	437645.	−	252674.i	1.00775	−	0.581822i	0.0972146	−	0.995263i	$-0.469007\pi$
$659$	437645.	−	252674.i	1.00775	−	0.581822i	0.910531	+	0.413441i	$0.135673\pi$
$660$	89380.4	+	489011.i	0.205189	+	1.12262i
$661$	−126095.	+	218403.i	−0.288599	+	0.499867i	−0.973475	−	0.228791i	$-0.926523\pi$
$661$	−126095.	+	218403.i	−0.288599	+	0.499867i	0.684877	+	0.728659i	$0.259856\pi$
$662$	364532.	+	210463.i	0.831802	+	0.480241i
$663$	−42181.7	+	7709.88i	−0.0959614	+	0.0175396i
$664$	15574.1	+	26975.1i	0.0353237	+	0.0611824i
$665$			277933.i			0.628489i
$666$	22541.7	+	59604.2i	0.0508205	+	0.134378i
$667$	139195.			0.312876
$668$	−251311.	+	145094.i	−0.563195	+	0.325161i
$669$	423983.	+	151323.i	0.947319	+	0.338107i
$670$	115849.	−	200657.i	0.258074	−	0.446997i
$671$	977500.	+	564360.i	2.17106	+	1.25346i
$672$	−41867.1	−	49266.6i	−0.0927115	−	0.109097i
$673$	−225789.	−	391079.i	−0.498509	−	0.863443i	0.501489	−	0.865164i	$-0.332786\pi$
$673$	−225789.	−	391079.i	−0.498509	−	0.863443i	−0.999999	+	0.00172055i	$0.999452\pi$
$674$		−	165884.i		−	0.365162i
$675$	423351.	−	766083.i	0.929165	−	1.68139i
$676$	185528.			0.405990
$677$	−136787.	+	78974.0i	−0.298447	+	0.172309i	−0.641745	−	0.766918i	$-0.721789\pi$
$677$	−136787.	+	78974.0i	−0.298447	+	0.172309i	0.343298	+	0.939227i	$0.388456\pi$
$678$	−12115.0	+	10295.4i	−0.0263551	+	0.0223967i
$679$	164516.	−	284950.i	0.356836	−	0.618058i
$680$	−54438.1	−	31429.8i	−0.117729	−	0.0679711i
$681$	−199461.	+	558857.i	−0.430094	+	1.20505i
$682$	−289680.	−	501740.i	−0.622801	−	1.07872i
$683$			769916.i			1.65045i	0.564806	+	0.825224i	$0.308951\pi$
$683$			769916.i			1.65045i	−0.564806	+	0.825224i	$0.691049\pi$
$684$	82211.9	+	67251.0i	0.175721	+	0.143743i
$685$	−1.03548e6			−2.20678
$686$	313700.	−	181115.i	0.666601	−	0.384863i
$687$	−42766.1	−	233979.i	−0.0906122	−	0.495750i
$688$	59702.5	−	103408.i	0.126129	−	0.218462i
$689$	−227241.	−	131198.i	−0.478683	−	0.276368i
$690$	229081.	−	41870.9i	0.481161	−	0.0879456i
$691$	476751.	+	825758.i	0.998472	+	1.72940i	0.547094	+	0.837071i	$0.315734\pi$
$691$	476751.	+	825758.i	0.998472	+	1.72940i	0.451378	+	0.892333i	$0.350933\pi$
$692$		−	156526.i		−	0.326870i
$693$	328879.	−	402043.i	0.684810	−	0.837155i
$694$	−76321.1			−0.158462
$695$	−984927.	+	568648.i	−2.03908	+	1.17726i
$696$	−124692.	−	44503.7i	−0.257407	−	0.0918708i
$697$	−1812.79	+	3139.85i	−0.00373150	+	0.00646314i
$698$	−27328.5	−	15778.1i	−0.0560925	−	0.0323850i
$699$	−184692.	−	217334.i	−0.378002	−	0.444810i
$700$	−190590.	−	330112.i	−0.388960	−	0.673699i
$701$			206692.i			0.420618i	0.977635	+	0.210309i	$0.0674470\pi$
$701$			206692.i			0.420618i	−0.977635	+	0.210309i	$0.932553\pi$
$702$	−129416.	+	77989.4i	−0.262612	+	0.158256i
$703$	−45591.5			−0.0922514
$704$	71649.5	−	41366.9i	0.144567	−	0.0834656i
$705$	373073.	−	317040.i	0.750613	−	0.637875i
$706$	−179521.	+	310939.i	−0.360168	+	0.623830i
$707$	318303.	+	183772.i	0.636798	+	0.367655i
$708$	82020.3	−	229807.i	0.163627	−	0.458456i
$709$	−6027.42	−	10439.8i	−0.0119905	−	0.0207682i	0.859968	−	0.510348i	$-0.170483\pi$
$709$	−6027.42	−	10439.8i	−0.0119905	−	0.0207682i	−0.871958	+	0.489580i	$0.837150\pi$
$710$			554583.i			1.10014i
$711$	−147593.	+	55818.1i	−0.291961	+	0.110417i
$712$	310429.			0.612355
$713$	−235044.	+	135703.i	−0.462349	+	0.266937i
$714$	11809.4	+	64610.4i	0.0231649	+	0.126738i
$715$	252977.	−	438169.i	0.494845	−	0.857097i
$716$	81783.4	+	47217.7i	0.159529	+	0.0921040i
$717$	268.810	−	49.1326i	0.000522887	−	9.55722e-5i
$718$	−39110.7	−	67741.6i	−0.0758658	−	0.131403i
$719$		−	446044.i		−	0.862820i	−0.902156	−	0.431410i	$-0.858016\pi$
$719$		−	446044.i		−	0.862820i	0.902156	−	0.431410i	$-0.141984\pi$
$720$	−218599.	−	35733.7i	−0.421680	−	0.0689308i
$721$	315062.			0.606075
$722$	253410.	−	146306.i	0.486126	−	0.280665i
$723$	−608207.	−	217075.i	−1.16352	−	0.415272i
$724$	−766.329	+	1327.32i	−0.00146197	+	0.00253221i
$725$	−675998.	−	390288.i	−1.28608	−	0.742521i
$726$	189076.	+	222494.i	0.358727	+	0.422129i
$727$	255195.	+	442011.i	0.482840	+	0.836304i	0.999806	−	0.0197025i	$-0.00627190\pi$
$727$	255195.	+	442011.i	0.482840	+	0.836304i	−0.516966	+	0.856006i	$0.672939\pi$
$728$			65803.3i			0.124161i
$729$	−248280.	+	469879.i	−0.467183	+	0.884161i
$730$	−1.19766e6			−2.24745
$731$	−105051.	+	60651.3i	−0.196592	+	0.113503i
$732$	−383237.	+	325677.i	−0.715230	+	0.607806i
$733$	247002.	−	427821.i	0.459720	−	0.796258i	−0.539226	−	0.842161i	$-0.681283\pi$
$733$	247002.	−	427821.i	0.459720	−	0.796258i	0.998946	+	0.0459031i	$0.0146165\pi$
$734$	360792.	+	208303.i	0.669675	+	0.386637i
$735$	106787.	−	299199.i	0.197671	−	0.553842i
$736$	−19378.6	−	33564.7i	−0.0357739	−	0.0619623i
$737$		−	309801.i		−	0.570358i
$738$	−2061.03	+	12608.2i	−0.00378418	+	0.0231495i
$739$	−464280.			−0.850141			−0.425071	−	0.905160i	$-0.639751\pi$
$739$	−464280.			−0.850141			−0.425071	+	0.905160i	$0.639751\pi$
$740$	82338.9	−	47538.4i	0.150363	−	0.0868123i
$741$	−19436.9	−	106342.i	−0.0353990	−	0.193672i
$742$	−200958.	+	348069.i	−0.365004	+	0.632205i
$743$	−104980.	−	60610.4i	−0.190165	−	0.109792i	0.401895	−	0.915686i	$-0.368352\pi$
$743$	−104980.	−	60610.4i	−0.190165	−	0.109792i	−0.592060	+	0.805894i	$0.701685\pi$
$744$	253941.	−	46414.7i	0.458761	−	0.0838513i
$745$	147120.	+	254819.i	0.265069	+	0.459112i
$746$		−	74976.2i		−	0.134724i
$747$	−39442.5	−	104293.i	−0.0706843	−	0.186901i
$748$	−84048.6			−0.150220
$749$	183689.	−	106053.i	0.327430	−	0.189042i
$750$	−589688.	−	210465.i	−1.04833	−	0.374160i
$751$	−145956.	+	252803.i	−0.258787	+	0.448232i	−0.965917	−	0.258851i	$-0.916656\pi$
$751$	−145956.	+	252803.i	−0.258787	+	0.448232i	0.707130	+	0.707083i	$0.249989\pi$
$752$	−70565.3	−	40740.9i	−0.124783	−	0.0720435i
$753$	606737.	+	713972.i	1.07007	+	1.25919i
$754$	67375.4	+	116698.i	0.118511	+	0.205267i
$755$		−	187959.i		−	0.329739i
$756$	119458.	+	198229.i	0.209012	+	0.346836i
$757$	−493650.			−0.861445			−0.430722	−	0.902485i	$-0.641741\pi$
$757$	−493650.			−0.861445			−0.430722	+	0.902485i	$0.641741\pi$
$758$	352609.	−	203579.i	0.613698	−	0.354319i
$759$	237271.	−	201634.i	0.411871	−	0.350010i
$760$	79236.0	−	137241.i	0.137181	−	0.237605i
$761$	484626.	+	279799.i	0.836831	+	0.483144i	0.856186	−	0.516668i	$-0.172828\pi$
$761$	484626.	+	279799.i	0.836831	+	0.483144i	−0.0193549	+	0.999813i	$0.506161\pi$
$762$	84422.6	−	236538.i	0.145395	−	0.407372i
$763$	−206071.	−	356926.i	−0.353972	−	0.613097i
$764$			161567.i			0.276799i
$765$	174170.	+	142475.i	0.297612	+	0.243453i
$766$	433631.			0.739031
$767$	−215074.	+	124173.i	−0.365592	+	0.211075i
$768$	6628.12	+	36263.2i	0.0112375	+	0.0614815i
$769$	267929.	−	464066.i	0.453071	−	0.784742i	−0.545504	−	0.838108i	$-0.683662\pi$
$769$	267929.	−	464066.i	0.453071	−	0.784742i	0.998575	+	0.0533663i	$0.0169951\pi$
$770$	−671152.	−	387490.i	−1.13198	−	0.653550i
$771$	−161987.	+	29607.6i	−0.272503	+	0.0498075i
$772$	155717.	+	269710.i	0.261277	+	0.452546i
$773$		−	735537.i		−	1.23097i	−0.788150	−	0.615483i	$-0.788961\pi$
$773$		−	735537.i		−	1.23097i	0.788150	−	0.615483i	$-0.211039\pi$
$774$	−270638.	+	330844.i	−0.451758	+	0.552258i
$775$	1.52198e6			2.53399
$776$	−162473.	+	93803.6i	−0.269809	+	0.155774i
$777$	−93563.2	−	33393.5i	−0.154976	−	0.0553121i
$778$	360628.	−	624626.i	0.595800	−	1.03196i
$779$	−7915.71	−	4570.14i	−0.0130441	−	0.00753103i
$780$	145986.	+	171788.i	0.239951	+	0.282360i
$781$	370762.	+	642178.i	0.607845	+	1.05282i
$782$			39373.2i			0.0643853i
$783$	414815.	+	229234.i	0.676599	+	0.373900i
$784$	−52871.9			−0.0860187
$785$	1.03079e6	−	595124.i	1.67274	−	0.965758i
$786$	72918.5	−	61966.5i	0.118030	−	0.100303i
$787$	−470624.	+	815144.i	−0.759844	+	1.31609i	0.183086	+	0.983097i	$0.441391\pi$
$787$	−470624.	+	815144.i	−0.759844	+	1.31609i	−0.942930	+	0.332992i	$0.891942\pi$
$788$	−447374.	−	258291.i	−0.720474	−	0.415966i
$789$	312788.	−	876380.i	0.502453	−	1.40779i
$790$	117715.	+	203889.i	0.188616	+	0.326692i
$791$		−	24785.5i		−	0.0396137i
$792$	−277016.	+	104765.i	−0.441625	+	0.167018i
$793$	511873.			0.813984
$794$	−36175.6	+	20886.0i	−0.0573819	+	0.0331294i
$795$	247575.	+	1.35451e6i	0.391717	+	2.14313i
$796$	−238723.	+	413480.i	−0.376762	+	0.652571i
$797$	−460012.	−	265588.i	−0.724191	−	0.418112i	0.0921026	−	0.995750i	$-0.470641\pi$
$797$	−460012.	−	265588.i	−0.724191	−	0.418112i	−0.816293	+	0.577638i	$0.803975\pi$
$798$	−162886.	+	29771.9i	−0.255786	+	0.0467521i
$799$	41388.4	+	71686.7i	0.0648313	+	0.112291i
$800$			217342.i			0.339596i
$801$	−1.09670e6	−	179274.i	−1.70931	−	0.279417i
$802$	599506.			0.932061
$803$	−1.38683e6	+	800689.i	−2.15077	+	1.24175i
$804$	130007.	+	46400.6i	0.201119	+	0.0717813i
$805$	−181522.	+	314406.i	−0.280116	+	0.485176i
$806$	−227539.	−	131370.i	−0.350256	−	0.202220i
$807$	37010.9	+	43552.2i	0.0568306	+	0.0668749i
$808$	−104783.	−	181490.i	−0.160498	−	0.277990i
$809$		−	999175.i		−	1.52667i	−0.646004	−	0.763334i	$-0.723561\pi$
$809$		−	999175.i		−	1.52667i	0.646004	−	0.763334i	$-0.276439\pi$
$810$	751638.	+	252483.i	1.14562	+	0.384824i
$811$	837740.			1.27370			0.636851	−	0.770987i	$-0.280237\pi$
$811$	837740.			1.27370			0.636851	+	0.770987i	$0.280237\pi$
$812$	178748.	−	103200.i	0.271100	−	0.156519i
$813$	762674.	−	648125.i	1.15387	−	0.980567i
$814$	63562.8	−	110094.i	0.0959300	−	0.166156i
$815$	1.23318e6	+	711976.i	1.85657	+	1.07189i
$816$	12588.4	−	35270.7i	0.0189056	−	0.0529705i
$817$	−152905.	−	264839.i	−0.229074	−	0.396769i
$818$			91603.6i			0.136901i
$819$	38001.6	−	232472.i	0.0566544	−	0.346580i
$820$	19061.2			0.0283480
$821$	783574.	−	452397.i	1.16250	−	0.671171i	0.210600	−	0.977572i	$-0.432458\pi$
$821$	783574.	−	452397.i	1.16250	−	0.671171i	0.951902	+	0.306402i	$0.0991250\pi$
$822$	−110919.	−	606852.i	−0.164158	−	0.898130i
$823$	−113477.	+	196547.i	−0.167535	+	0.290180i	−0.937553	−	0.347843i	$-0.886914\pi$
$823$	−113477.	+	196547.i	−0.167535	+	0.290180i	0.770017	+	0.638023i	$0.220247\pi$
$824$	−155575.	−	89821.1i	−0.229131	−	0.132289i
$825$	−1.71766e6	+	313950.i	−2.52365	+	0.461268i
$826$	190198.	+	329432.i	0.278770	+	0.482843i
$827$		−	315769.i		−	0.461699i	−0.972989	−	0.230850i	$-0.925849\pi$
$827$		−	315769.i		−	0.461699i	0.972989	−	0.230850i	$-0.0741505\pi$
$828$	49077.7	+	129770.i	0.0715853	+	0.189284i
$829$	−1.15617e6			−1.68233			−0.841166	−	0.540777i	$-0.818130\pi$
$829$	−1.15617e6			−1.68233			−0.841166	+	0.540777i	$0.818130\pi$
$830$	−144073.	+	83180.5i	−0.209135	+	0.120744i
$831$	−770943.	−	275156.i	−1.11640	−	0.398453i
$832$	18759.8	−	32493.0i	0.0271008	−	0.0469400i
$833$	46516.1	+	26856.1i	0.0670368	+	0.0387037i
$834$	−438766.	−	516314.i	−0.630814	−	0.742304i
$835$	−774944.	−	1.34224e6i	−1.11147	−	1.92512i
$836$		−	211890.i		−	0.303179i
$837$	−923935.	+	17324.3i	−1.31884	+	0.0247288i
$838$	236937.			0.337400
$839$	−789251.	+	455674.i	−1.12122	+	0.647337i	−0.941712	−	0.336420i	$-0.890784\pi$
$839$	−789251.	+	455674.i	−1.12122	+	0.647337i	−0.179508	+	0.983756i	$0.557451\pi$
$840$	263131.	−	223610.i	0.372918	−	0.316908i
$841$	−142309.	+	246487.i	−0.201206	+	0.348499i
$842$	512684.	+	295998.i	0.723146	+	0.417508i
$843$	−441011.	+	1.23564e6i	−0.620575	+	1.73875i
$844$	−71194.8	−	123313.i	−0.0999455	−	0.173111i
$845$			990895.i			1.38776i
$846$	225768.	+	184683.i	0.315443	+	0.258039i
$847$	−455189.			−0.634490
$848$	198462.	−	114582.i	0.275985	−	0.159340i
$849$	176236.	+	964207.i	0.244500	+	1.33769i
$850$	110398.	−	191215.i	0.152800	−	0.264657i
$851$	−51574.3	−	29776.4i	−0.0712155	−	0.0411163i
$852$	−325019.	+	59406.3i	−0.447744	+	0.0818377i
$853$	−519238.	−	899347.i	−0.713623	−	1.23603i	−0.963488	−	0.267751i	$-0.913720\pi$
$853$	−519238.	−	899347.i	−0.713623	−	1.23603i	0.249865	−	0.968281i	$-0.419614\pi$
$854$		−	784046.i		−	1.07504i
$855$	−359185.	+	439090.i	−0.491344	+	0.600650i
$856$	−120938.			−0.165050
$857$	−202140.	+	116706.i	−0.275227	+	0.158902i	−0.631261	−	0.775571i	$-0.717462\pi$
$857$	−202140.	+	116706.i	−0.275227	+	0.158902i	0.356034	+	0.934473i	$0.384129\pi$
$858$	283892.	+	101324.i	0.385637	+	0.137637i
$859$	253149.	−	438467.i	0.343075	−	0.594224i	−0.641927	−	0.766766i	$-0.721865\pi$
$859$	253149.	−	438467.i	0.343075	−	0.594224i	0.985002	+	0.172542i	$0.0551980\pi$
$860$	552297.	+	318869.i	0.746750	+	0.431137i
$861$	−12897.3	−	15176.7i	−0.0173977	−	0.0204726i
$862$	114222.	+	197838.i	0.153722	+	0.266254i
$863$		−	363551.i		−	0.488140i	−0.969758	−	0.244070i	$-0.921517\pi$
$863$		−	363551.i		−	0.488140i	0.969758	−	0.244070i	$-0.0784826\pi$
$864$	−2473.94	−	131940.i	−0.00331407	−	0.176746i
$865$	836000.			1.11731
$866$	−582446.	+	336275.i	−0.776640	+	0.448393i
$867$	543806.	−	462129.i	0.723445	−	0.614787i
$868$	−201221.	+	348525.i	−0.267076	+	0.462589i
$869$	272616.	+	157395.i	0.361004	+	0.208426i
$870$	237692.	−	665975.i	0.314034	−	0.879871i
$871$	−70247.2	−	121672.i	−0.0925961	−	0.160381i
$872$			234995.i			0.309048i
$873$	628161.	−	237565.i	0.824219	−	0.311712i
$874$	−99261.5			−0.129945
$875$	845327.	−	488050.i	1.10410	−	0.637453i
$876$	−128292.	−	701904.i	−0.167183	−	0.914680i
$877$	−69267.3	+	119974.i	−0.0900594	+	0.155987i	−0.907536	−	0.419974i	$-0.862039\pi$
$877$	−69267.3	+	119974.i	−0.0900594	+	0.155987i	0.817477	+	0.575962i	$0.195372\pi$
$878$	−637875.	−	368277.i	−0.827459	−	0.477734i
$879$	897225.	−	163993.i	1.16124	−	0.212250i
$880$	220939.	+	382677.i	0.285303	+	0.494160i
$881$			927282.i			1.19470i	0.801979	+	0.597352i	$0.203780\pi$
$881$			927282.i			1.19470i	−0.801979	+	0.597352i	$0.796220\pi$
$882$	186788.	+	30533.7i	0.240111	+	0.0392502i
$883$	−20106.7			−0.0257881			−0.0128941	−	0.999917i	$-0.504104\pi$
$883$	−20106.7			−0.0257881			−0.0128941	+	0.999917i	$0.504104\pi$
$884$	−33009.4	+	19058.0i	−0.0422409	+	0.0243878i
$885$	1.22739e6	+	438067.i	1.56710	+	0.559312i
$886$	−248493.	+	430402.i	−0.316553	+	0.548285i
$887$	−473446.	−	273344.i	−0.601760	−	0.347426i	0.167974	−	0.985791i	$-0.446278\pi$
$887$	−473446.	−	273344.i	−0.601760	−	0.347426i	−0.769734	+	0.638365i	$0.779611\pi$
$888$	36680.4	+	43163.3i	0.0465167	+	0.0547380i
$889$	195769.	+	339081.i	0.247708	+	0.429042i
$890$			1.65799e6i			2.09316i
$891$	1.03915e6	−	210139.i	1.30895	−	0.264699i
$892$	400158.			0.502924
$893$	−180725.	+	104342.i	−0.226629	+	0.130845i
$894$	−133580.	+	113517.i	−0.167134	+	0.142032i
$895$	−252188.	+	436802.i	−0.314831	+	0.545303i
$896$	−49770.1	−	28734.8i	−0.0619945	−	0.0357925i
$897$	47465.8	−	132991.i	0.0589924	−	0.165287i
$898$	−215696.	−	373596.i	−0.267478	−	0.463286i
$899$			824114.i			1.01969i
$900$	125515.	−	767833.i	0.154957	−	0.947942i
$901$	−232806.			−0.286777
$902$	22071.9	−	12743.2i	0.0271285	−	0.0156627i
$903$	−119811.	−	655500.i	−0.146933	−	0.803891i
$904$	−7066.10	+	12238.8i	−0.00864655	+	0.0149763i
$905$	−7089.17	−	4092.93i	−0.00865562	−	0.00499732i
$906$	110156.	−	20134.0i	0.134199	−	0.0245287i
$907$	−558994.	−	968206.i	−0.679505	−	1.17694i	−0.975130	−	0.221633i	$-0.928861\pi$
$907$	−558994.	−	968206.i	−0.679505	−	1.17694i	0.295625	−	0.955304i	$-0.404472\pi$
$908$			527453.i			0.639753i
$909$	265371.	+	701686.i	0.321163	+	0.849210i
$910$	−351453.			−0.424408
$911$	1.18288e6	−	682935.i	1.42529	−	0.822891i	0.428545	−	0.903520i	$-0.359026\pi$
$911$	1.18288e6	−	682935.i	1.42529	−	0.822891i	0.996744	+	0.0806295i	$0.0256930\pi$
$912$	88919.1	+	31736.0i	0.106907	+	0.0381560i
$913$	−111219.	+	192637.i	−0.133425	+	0.231100i
$914$	−709179.	−	409445.i	−0.848914	−	0.490121i
$915$	−1.73943e6	−	2.04685e6i	−2.07761	−	2.44481i
$916$	−105713.	−	183101.i	−0.125991	−	0.218222i
$917$			149180.i			0.177408i
$918$	−64841.8	+	117336.i	−0.0769432	+	0.139234i
$919$	90479.2			0.107132			0.0535658	−	0.998564i	$-0.482941\pi$
$919$	90479.2			0.107132			0.0535658	+	0.998564i	$0.482941\pi$
$920$	179268.	−	103500.i	0.211800	−	0.122283i
$921$	64657.4	−	54946.2i	0.0762252	−	0.0647766i
$922$	−137296.	+	237803.i	−0.161508	+	0.279740i
$923$	291227.	+	168140.i	0.341845	+	0.197364i
$924$	155199.	−	434843.i	0.181780	−	0.509318i
$925$	166980.	+	289217.i	0.195155	+	0.338018i
$926$		−	1.05720e6i		−	1.23292i
$927$	497748.	+	407168.i	0.579229	+	0.473821i
$928$	−117685.			−0.136655
$929$	−49982.8	+	28857.6i	−0.0579147	+	0.0334371i	−0.528678	−	0.848823i	$-0.677312\pi$
$929$	−49982.8	+	28857.6i	−0.0579147	+	0.0334371i	0.470763	+	0.882260i	$0.343979\pi$
$930$	247899.	+	1.35629e6i	0.286622	+	1.56814i
$931$	−67705.4	+	117269.i	−0.0781131	+	0.135296i
$932$	−219556.	−	126760.i	−0.252763	−	0.145932i
$933$	1.38553e6	−	253245.i	1.59167	−	0.290923i
$934$	−34591.5	−	59914.2i	−0.0396529	−	0.0686809i
$935$		−	448900.i		−	0.513484i
$936$	−85040.3	+	103959.i	−0.0970673	+	0.118661i
$937$	−313267.			−0.356809			−0.178404	−	0.983957i	$-0.557094\pi$
$937$	−313267.			−0.356809			−0.178404	+	0.983957i	$0.557094\pi$
$938$	−186367.	+	107599.i	−0.211818	+	0.122293i
$939$	269207.	+	96082.5i	0.305320	+	0.108972i
$940$	217595.	−	376886.i	0.246260	−	0.426535i
$941$	−719464.	−	415382.i	−0.812512	−	0.469104i	0.0353157	−	0.999376i	$-0.488756\pi$
$941$	−719464.	−	415382.i	−0.812512	−	0.469104i	−0.847827	+	0.530272i	$0.822090\pi$
$942$	459195.	+	540353.i	0.517482	+	0.608942i
$943$	−5969.64	−	10339.7i	−0.00671313	−	0.0116275i
$944$		−	216894.i		−	0.243390i
$945$	−1.05873e6	+	638020.i	−1.18556	+	0.714448i
$946$	852708.			0.952836
$947$	1.19954e6	−	692554.i	1.33756	−	0.772243i	0.351118	−	0.936331i	$-0.385802\pi$
$947$	1.19954e6	−	692554.i	1.33756	−	0.772243i	0.986446	+	0.164088i	$0.0524682\pi$
$948$	−106881.	+	90828.5i	−0.118928	+	0.101066i
$949$	−363112.	+	628928.i	−0.403188	+	0.698342i
$950$	482061.	+	278318.i	0.534139	+	0.308386i
$951$	−147605.	+	413564.i	−0.163207	+	0.457279i
$952$	29191.5	+	50561.1i	0.0322094	+	0.0557883i
$953$			1.35674e6i			1.49387i	0.664898	+	0.746934i	$0.268475\pi$
$953$			1.35674e6i			1.49387i	−0.664898	+	0.746934i	$0.731525\pi$
$954$	−767305.	+	290187.i	−0.843085	+	0.318847i
$955$	−862921.			−0.946160
$956$	210.358	−	121.451i	0.000230168	−	0.000132887i
$957$	−169997.	−	930072.i	−0.185616	−	1.01553i
$958$	−261953.	+	453717.i	−0.285426	+	0.494372i
$959$	832885.	+	480866.i	0.905624	+	0.522862i
$960$	−193680.	+	35400.5i	−0.210157	+	0.0384120i
$961$	−341675.	−	591798.i	−0.369970	−	0.640806i
$962$		−	57651.4i		−	0.0622959i
$963$	427255.	+	69842.2i	0.460717	+	0.0753122i
$964$	−574031.			−0.617705
$965$	−1.44051e6	+	831679.i	−1.54690	+	0.893102i
$966$	−203705.	−	72704.2i	−0.218297	−	0.0779122i
$967$	104547.	−	181080.i	0.111804	−	0.193650i	−0.804694	−	0.593690i	$-0.797670\pi$
$967$	104547.	−	181080.i	0.111804	−	0.193650i	0.916498	+	0.400040i	$0.131004\pi$
$968$	224768.	+	129770.i	0.239874	+	0.138491i
$969$	−62109.8	−	73087.1i	−0.0661474	−	0.0778383i
$970$	−501001.	−	867760.i	−0.532470	−	0.922266i
$971$		−	1.35629e6i		−	1.43852i	−0.694742	−	0.719259i	$-0.744482\pi$
$971$		−	1.35629e6i		−	1.43852i	0.694742	−	0.719259i	$-0.255518\pi$
$972$	−67455.7	+	467551.i	−0.0713980	+	0.494876i
$973$	1.05630e6			1.11574
$974$	−550356.	+	317748.i	−0.580131	+	0.334939i
$975$	−603409.	+	512780.i	−0.634750	+	0.539414i
$976$	−223523.	+	387154.i	−0.234652	+	0.406429i
$977$	274726.	+	158613.i	0.287813	+	0.166169i	0.636955	−	0.770901i	$-0.280194\pi$
$977$	274726.	+	158613.i	0.287813	+	0.166169i	−0.349142	+	0.937070i	$0.613527\pi$
$978$	−285164.	+	798983.i	−0.298138	+	0.835333i
$979$	1.10844e6	+	1.91987e6i	1.15650	+	2.00312i
$980$		−	282387.i		−	0.294030i
$981$	135711.	−	830201.i	0.141018	−	0.862671i
$982$	272806.			0.282898
$983$	−781207.	+	451030.i	−0.808461	+	0.466765i	−0.846421	−	0.532514i	$-0.821247\pi$
$983$	−781207.	+	451030.i	−0.808461	+	0.466765i	0.0379603	+	0.999279i	$0.487914\pi$
$984$	2041.81	+	11171.0i	0.00210875	+	0.0115372i
$985$	1.37952e6	−	2.38941e6i	1.42186	−	2.46273i
$986$	103538.	+	59777.8i	0.106499	+	0.0614874i
$987$	−447312.	+	81758.7i	−0.459173	+	0.0839266i
$988$	−48046.0	−	83218.2i	−0.0492202	−	0.0852519i
$989$		−	399457.i		−	0.408392i
$990$	−559544.	−	1.47953e6i	−0.570905	−	1.50957i
$991$	−587715.			−0.598439			−0.299219	−	0.954184i	$-0.596726\pi$
$991$	−587715.			−0.598439			−0.299219	+	0.954184i	$0.596726\pi$
$992$	198722.	−	114732.i	0.201940	−	0.116590i
$993$	−1.26144e6	−	450220.i	−1.27929	−	0.456590i
$994$	257543.	−	446078.i	0.260662	−	0.451480i
$995$	−2.20838e6	−	1.27501e6i	−2.23063	−	1.28785i
$996$	−64181.7	−	75525.2i	−0.0646983	−	0.0761330i
$997$	677542.	+	1.17354e6i	0.681625	+	1.18061i	0.974485	+	0.224454i	$0.0720599\pi$
$997$	677542.	+	1.17354e6i	0.681625	+	1.18061i	−0.292859	+	0.956156i	$0.594607\pi$
$998$		−	117830.i		−	0.118303i
$999$	−104659.	−	173672.i	−0.104869	−	0.174020i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.5.d.a.5.2	✓	8
3.2	odd	2		54.5.d.a.17.3		8
4.3	odd	2		144.5.q.b.113.1		8
9.2	odd	6	inner	18.5.d.a.11.2	yes	8
9.4	even	3		162.5.b.c.161.1		8
9.5	odd	6		162.5.b.c.161.8		8
9.7	even	3		54.5.d.a.35.3		8
12.11	even	2		432.5.q.b.17.1		8
36.7	odd	6		432.5.q.b.305.1		8
36.11	even	6		144.5.q.b.65.1		8
36.23	even	6		1296.5.e.e.161.8		8
36.31	odd	6		1296.5.e.e.161.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.5.d.a.5.2	✓	8	1.1	even	1	trivial
18.5.d.a.11.2	yes	8	9.2	odd	6	inner
54.5.d.a.17.3		8	3.2	odd	2
54.5.d.a.35.3		8	9.7	even	3
144.5.q.b.65.1		8	36.11	even	6
144.5.q.b.113.1		8	4.3	odd	2
162.5.b.c.161.1		8	9.4	even	3
162.5.b.c.161.8		8	9.5	odd	6
432.5.q.b.17.1		8	12.11	even	2
432.5.q.b.305.1		8	36.7	odd	6
1296.5.e.e.161.1		8	36.31	odd	6
1296.5.e.e.161.8		8	36.23	even	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} +(6.85811 - 5.82806i) q^{3} +(4.00000 - 6.92820i) q^{4} +(37.0033 + 21.3638i) q^{5} +(-8.55675 + 23.9746i) q^{6} +(-19.8424 - 34.3680i) q^{7} +22.6274i q^{8} +(13.0674 - 79.9390i) q^{9} -120.852 q^{10} +(-139.941 + 80.7947i) q^{11} +(-12.9455 - 70.8266i) q^{12} +(-36.6403 + 63.4629i) q^{13} +(97.2073 + 56.1227i) q^{14} +(378.282 - 69.1416i) q^{15} +(-32.0000 - 55.4256i) q^{16} +65.0171i q^{17} +(81.0423 + 214.290i) q^{18} -163.911 q^{19} +(296.026 - 170.911i) q^{20} +(-336.380 - 120.057i) q^{21} +(228.522 - 395.812i) q^{22} +(-185.421 - 107.053i) q^{23} +(131.874 + 155.181i) q^{24} +(600.327 + 1039.80i) q^{25} -207.269i q^{26} +(-376.272 - 624.388i) q^{27} -317.478 q^{28} +(-563.025 + 325.063i) q^{29} +(-828.817 + 704.334i) q^{30} +(633.812 - 1097.79i) q^{31} +(156.767 + 90.5097i) q^{32} +(-488.851 + 1369.68i) q^{33} +(-91.9481 - 159.259i) q^{34} -1695.64i q^{35} +(-501.564 - 410.290i) q^{36} +278.148 q^{37} +(401.498 - 231.805i) q^{38} +(118.582 + 648.778i) q^{39} +(-483.408 + 837.288i) q^{40} +(48.2927 + 27.8818i) q^{41} +(993.745 - 181.635i) q^{42} +(932.851 + 1615.75i) q^{43} +1292.72i q^{44} +(2191.34 - 2678.83i) q^{45} +605.581 q^{46} +(1102.58 - 636.576i) q^{47} +(-542.484 - 193.617i) q^{48} +(413.062 - 715.444i) q^{49} +(-2940.99 - 1697.98i) q^{50} +(378.924 + 445.895i) q^{51} +(293.123 + 507.703i) q^{52} +3580.69i q^{53} +(1804.69 + 997.304i) q^{54} -6904.34 q^{55} +(777.658 - 448.981i) q^{56} +(-1124.12 + 955.284i) q^{57} +(919.416 - 1592.47i) q^{58} +(2934.93 + 1694.48i) q^{59} +(1034.10 - 2897.38i) q^{60} +(-3492.55 - 6049.28i) q^{61} +3585.38i q^{62} +(-3006.63 + 1137.08i) q^{63} -512.000 q^{64} +(-2711.62 + 1565.56i) q^{65} +(-739.585 - 4046.36i) q^{66} +(-958.605 + 1660.35i) q^{67} +(450.452 + 260.069i) q^{68} +(-1895.55 + 346.464i) q^{69} +(2397.99 + 4153.44i) q^{70} -4588.94i q^{71} +(1808.81 + 295.682i) q^{72} +9910.16 q^{73} +(-681.320 + 393.360i) q^{74} +(10177.1 + 3632.30i) q^{75} +(-655.644 + 1135.61i) q^{76} +(5553.50 + 3206.31i) q^{77} +(-1207.98 - 1421.47i) q^{78} +(-974.042 - 1687.09i) q^{79} -2734.57i q^{80} +(-6219.49 - 2089.19i) q^{81} -157.723 q^{82} +(1192.14 - 688.283i) q^{83} +(-2177.30 + 1850.28i) q^{84} +(-1389.02 + 2405.85i) q^{85} +(-4570.02 - 2638.50i) q^{86} +(-1966.80 + 5510.66i) q^{87} +(-1828.18 - 3166.49i) q^{88} -13719.2i q^{89} +(-1579.22 + 9660.80i) q^{90} +2908.12 q^{91} +(-1483.37 + 856.421i) q^{92} +(-2051.26 - 11222.7i) q^{93} +(-1800.51 + 3118.57i) q^{94} +(-6065.24 - 3501.77i) q^{95} +(1602.62 - 292.924i) q^{96} +(4145.57 + 7180.34i) q^{97} +2336.63i q^{98} +(4629.99 + 12242.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 32 q^{4} + 18 q^{5} + 48 q^{6} - 26 q^{7} - 78 q^{9} - 720 q^{11} - 144 q^{12} + 10 q^{13} + 288 q^{14} + 1134 q^{15} - 256 q^{16} - 384 q^{18} + 100 q^{19} + 144 q^{20} + 438 q^{21} + 336 q^{22}+ \cdots - 22338 q^{99}+O(q^{100}) \) 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

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