LMFDB - Embedded newform 102.5.g.d.59.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [102,5,Mod(53,102)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(102, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7]))

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

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

chi := DirichletCharacter("102.53");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 102 = 2 \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	102.g (of order $8$, degree $4$, 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:	$10.5437362346$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			59.4
Character	$\chi$	$=$	102.59
Dual form			102.5.g.d.83.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00000 + 2.00000i) q^{2} +(-6.83333 - 5.85710i) q^{3} +8.00000i q^{4} +(2.47614 - 5.97792i) q^{5} +(-1.95247 - 25.3809i) q^{6} +(-1.01811 + 0.421715i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(12.3889 + 80.0470i) q^{9} +(16.9081 - 7.00357i) q^{10} +(-97.2231 + 40.2711i) q^{11} +(46.8568 - 54.6667i) q^{12} +206.845i q^{13} +(-2.87965 - 1.19279i) q^{14} +(-51.9335 + 26.3462i) q^{15} -64.0000 q^{16} +(-288.977 - 3.63472i) q^{17} +(-135.316 + 184.872i) q^{18} +(-179.308 + 179.308i) q^{19} +(47.8234 + 19.8091i) q^{20} +(9.42711 + 3.08145i) q^{21} +(-274.989 - 113.904i) q^{22} +(-492.162 + 203.860i) q^{23} +(203.047 - 15.6198i) q^{24} +(412.337 + 412.337i) q^{25} +(-413.690 + 413.690i) q^{26} +(384.186 - 619.550i) q^{27} +(-3.37372 - 8.14488i) q^{28} +(-273.113 + 659.352i) q^{29} +(-156.559 - 51.1747i) q^{30} +(87.6713 - 211.657i) q^{31} +(-128.000 - 128.000i) q^{32} +(900.230 + 294.259i) q^{33} +(-570.685 - 585.224i) q^{34} +7.13041i q^{35} +(-640.376 + 99.1108i) q^{36} +(497.277 - 1200.53i) q^{37} -717.234 q^{38} +(1211.51 - 1413.44i) q^{39} +(56.0286 + 135.265i) q^{40} +(-416.650 - 1005.88i) q^{41} +(12.6913 + 25.0171i) q^{42} +(-384.951 - 384.951i) q^{43} +(-322.169 - 777.785i) q^{44} +(509.191 + 124.148i) q^{45} +(-1392.04 - 576.604i) q^{46} +1799.82 q^{47} +(437.333 + 374.854i) q^{48} +(-1696.90 + 1696.90i) q^{49} +1649.35i q^{50} +(1953.39 + 1717.40i) q^{51} -1654.76 q^{52} +(2130.03 + 2130.03i) q^{53} +(2007.47 - 470.729i) q^{54} +680.909i q^{55} +(9.54232 - 23.0372i) q^{56} +(2275.50 - 175.047i) q^{57} +(-1864.93 + 772.479i) q^{58} +(2899.30 - 2899.30i) q^{59} +(-210.769 - 415.468i) q^{60} +(130.265 - 53.9573i) q^{61} +(598.657 - 247.972i) q^{62} +(-46.3702 - 76.2720i) q^{63} -512.000i q^{64} +(1236.50 + 512.176i) q^{65} +(1211.94 + 2388.98i) q^{66} -6663.38 q^{67} +(29.0778 - 2311.82i) q^{68} +(4557.14 + 1489.60i) q^{69} +(-14.2608 + 14.2608i) q^{70} +(1859.82 + 770.361i) q^{71} +(-1478.97 - 1082.53i) q^{72} +(3107.20 + 1287.04i) q^{73} +(3395.62 - 1406.51i) q^{74} +(-402.539 - 5232.74i) q^{75} +(-1434.47 - 1434.47i) q^{76} +(82.0009 - 82.0009i) q^{77} +(5249.90 - 403.859i) q^{78} +(-2649.68 - 6396.88i) q^{79} +(-158.473 + 382.587i) q^{80} +(-6254.03 + 1983.38i) q^{81} +(1178.47 - 2845.07i) q^{82} +(-6187.08 - 6187.08i) q^{83} +(-24.6516 + 75.4169i) q^{84} +(-737.275 + 1718.48i) q^{85} -1539.80i q^{86} +(5728.16 - 2905.93i) q^{87} +(911.232 - 2199.91i) q^{88} +780.316 q^{89} +(770.087 + 1266.68i) q^{90} +(-87.2296 - 210.591i) q^{91} +(-1630.88 - 3937.30i) q^{92} +(-1838.78 + 932.825i) q^{93} +(3599.64 + 3599.64i) q^{94} +(627.900 + 1515.88i) q^{95} +(124.958 + 1624.37i) q^{96} +(-3230.48 - 1338.11i) q^{97} -6787.62 q^{98} +(-4428.07 - 7283.50i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 88 q^{2} - 4 q^{3} + 72 q^{5} - 40 q^{6} + 132 q^{7} - 704 q^{8} + 324 q^{9} + 384 q^{10} - 616 q^{11} - 128 q^{12} + 416 q^{14} - 908 q^{15} - 2816 q^{16} + 424 q^{17} + 1016 q^{18} + 568 q^{19}+ \cdots + 91704 q^{99}+O(q^{100}) $ 44 * q + 88 * q^2 - 4 * q^3 + 72 * q^5 - 40 * q^6 + 132 * q^7 - 704 * q^8 + 324 * q^9 + 384 * q^10 - 616 * q^11 - 128 * q^12 + 416 * q^14 - 908 * q^15 - 2816 * q^16 + 424 * q^17 + 1016 * q^18 + 568 * q^19 + 960 * q^20 + 1020 * q^21 + 424 * q^22 + 332 * q^23 - 192 * q^24 + 1888 * q^25 - 1008 * q^26 - 436 * q^27 + 608 * q^28 - 6688 * q^29 - 2000 * q^30 - 1428 * q^31 - 5632 * q^32 + 2224 * q^33 + 512 * q^34 + 1472 * q^36 + 296 * q^37 + 2272 * q^38 - 3720 * q^39 + 768 * q^40 + 4592 * q^41 + 3328 * q^42 - 228 * q^43 + 6624 * q^44 + 8228 * q^45 + 1872 * q^46 + 10712 * q^47 + 256 * q^48 + 5304 * q^49 - 3984 * q^51 - 4032 * q^52 - 5656 * q^53 - 9288 * q^54 - 896 * q^56 - 13364 * q^57 - 11472 * q^58 + 3620 * q^59 - 736 * q^60 - 10448 * q^61 - 3536 * q^62 + 28248 * q^63 - 13760 * q^65 + 12952 * q^66 - 18584 * q^67 - 1344 * q^68 + 6500 * q^69 - 9664 * q^70 + 36660 * q^71 - 2240 * q^72 + 18008 * q^73 - 144 * q^74 + 30268 * q^75 + 4544 * q^76 - 5704 * q^77 - 22576 * q^78 - 7324 * q^79 - 4608 * q^80 - 33668 * q^81 + 11160 * q^82 - 12620 * q^83 + 5152 * q^84 - 10896 * q^85 + 23860 * q^87 + 23104 * q^88 - 5040 * q^89 - 8784 * q^90 + 52368 * q^91 + 4832 * q^92 - 1304 * q^93 + 21424 * q^94 + 16032 * q^95 + 2560 * q^96 - 40164 * q^97 + 21216 * q^98 + 91704 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/102\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$3$	−6.83333	−	5.85710i	−0.759259	−	0.650788i
$3$	−6.83333	−	5.85710i	−0.759259	−	0.650788i
$4$			8.00000i			0.500000i
$5$	2.47614	−	5.97792i	0.0990455	−	0.239117i	−0.866588	−	0.499024i	$-0.833692\pi$
$5$	2.47614	−	5.97792i	0.0990455	−	0.239117i	0.965634	+	0.259907i	$0.0836919\pi$
$6$	−1.95247	−	25.3809i	−0.0542353	−	0.705024i
$7$	−1.01811	+	0.421715i	−0.0207778	+	0.00860643i	−0.393048	−	0.919518i	$-0.628579\pi$
$7$	−1.01811	+	0.421715i	−0.0207778	+	0.00860643i	0.372270	+	0.928124i	$0.378579\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$	12.3889	+	80.0470i	0.152949	+	0.988234i
$10$	16.9081	−	7.00357i	0.169081	−	0.0700357i
$11$	−97.2231	+	40.2711i	−0.803497	+	0.332819i	−0.746356	−	0.665547i	$-0.768198\pi$
$11$	−97.2231	+	40.2711i	−0.803497	+	0.332819i	−0.0571409	+	0.998366i	$0.518198\pi$
$12$	46.8568	−	54.6667i	0.325394	−	0.379630i
$13$			206.845i			1.22393i	0.790883	+	0.611967i	$0.209622\pi$
$13$			206.845i			1.22393i	−0.790883	+	0.611967i	$0.790378\pi$
$14$	−2.87965	−	1.19279i	−0.0146921	−	0.00608566i
$15$	−51.9335	+	26.3462i	−0.230816	+	0.117094i
$16$	−64.0000			−0.250000
$17$	−288.977	−	3.63472i	−0.999921	−	0.0125769i
$17$	−288.977	−	3.63472i	−0.999921	−	0.0125769i
$18$	−135.316	+	184.872i	−0.417643	+	0.570591i
$19$	−179.308	+	179.308i	−0.496699	+	0.496699i	−0.910409	−	0.413710i	$-0.864233\pi$
$19$	−179.308	+	179.308i	−0.496699	+	0.496699i	0.413710	+	0.910409i	$0.364233\pi$
$20$	47.8234	+	19.8091i	0.119558	+	0.0495227i
$21$	9.42711	+	3.08145i	0.0213767	+	0.00698741i
$22$	−274.989	−	113.904i	−0.568158	−	0.235339i
$23$	−492.162	+	203.860i	−0.930363	+	0.385369i	−0.795816	−	0.605538i	$-0.792958\pi$
$23$	−492.162	+	203.860i	−0.930363	+	0.385369i	−0.134547	+	0.990907i	$0.542958\pi$
$24$	203.047	−	15.6198i	0.352512	−	0.0271177i
$25$	412.337	+	412.337i	0.659740	+	0.659740i
$26$	−413.690	+	413.690i	−0.611967	+	0.611967i
$27$	384.186	−	619.550i	0.527004	−	0.849863i
$28$	−3.37372	−	8.14488i	−0.00430321	−	0.0103889i
$29$	−273.113	+	659.352i	−0.324747	+	0.784010i	0.674218	+	0.738532i	$0.264481\pi$
$29$	−273.113	+	659.352i	−0.324747	+	0.784010i	−0.998965	+	0.0454772i	$0.985519\pi$
$30$	−156.559	−	51.1747i	−0.173955	−	0.0568608i
$31$	87.6713	−	211.657i	0.0912293	−	0.220247i	−0.871678	−	0.490079i	$-0.836968\pi$
$31$	87.6713	−	211.657i	0.0912293	−	0.220247i	0.962908	+	0.269832i	$0.0869681\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	900.230	+	294.259i	0.826657	+	0.270210i
$34$	−570.685	−	585.224i	−0.493672	−	0.506249i
$35$			7.13041i			0.00582074i
$36$	−640.376	+	99.1108i	−0.494117	+	0.0764744i
$37$	497.277	−	1200.53i	0.363241	−	0.876941i	−0.631581	−	0.775310i	$-0.717594\pi$
$37$	497.277	−	1200.53i	0.363241	−	0.876941i	0.994822	−	0.101631i	$-0.0324062\pi$
$38$	−717.234			−0.496699
$39$	1211.51	−	1413.44i	0.796522	−	0.929283i
$40$	56.0286	+	135.265i	0.0350179	+	0.0845406i
$41$	−416.650	−	1005.88i	−0.247859	−	0.598384i	0.750163	−	0.661253i	$-0.229975\pi$
$41$	−416.650	−	1005.88i	−0.247859	−	0.598384i	−0.998022	+	0.0628690i	$0.979975\pi$
$42$	12.6913	+	25.0171i	0.00719462	+	0.0141820i
$43$	−384.951	−	384.951i	−0.208194	−	0.208194i	0.595305	−	0.803500i	$-0.297031\pi$
$43$	−384.951	−	384.951i	−0.208194	−	0.208194i	−0.803500	+	0.595305i	$0.797031\pi$
$44$	−322.169	−	777.785i	−0.166410	−	0.401749i
$45$	509.191	+	124.148i	0.251452	+	0.0613075i
$46$	−1392.04	−	576.604i	−0.657866	−	0.272497i
$47$	1799.82			0.814766			0.407383	−	0.913257i	$-0.366441\pi$
$47$	1799.82			0.814766			0.407383	+	0.913257i	$0.366441\pi$
$48$	437.333	+	374.854i	0.189815	+	0.162697i
$49$	−1696.90	+	1696.90i	−0.706749	+	0.706749i
$50$			1649.35i			0.659740i
$51$	1953.39	+	1717.40i	0.751014	+	0.660286i
$52$	−1654.76			−0.611967
$53$	2130.03	+	2130.03i	0.758287	+	0.758287i	0.976011	−	0.217723i	$-0.0698630\pi$
$53$	2130.03	+	2130.03i	0.758287	+	0.758287i	−0.217723	+	0.976011i	$0.569863\pi$
$54$	2007.47	−	470.729i	0.688433	−	0.161430i
$55$			680.909i			0.225094i
$56$	9.54232	−	23.0372i	0.00304283	−	0.00734604i
$57$	2275.50	−	175.047i	0.700370	−	0.0538773i
$58$	−1864.93	+	772.479i	−0.554379	+	0.229631i
$59$	2899.30	−	2899.30i	0.832894	−	0.832894i	−0.155018	−	0.987912i	$-0.549544\pi$
$59$	2899.30	−	2899.30i	0.832894	−	0.832894i	0.987912	+	0.155018i	$0.0495435\pi$
$60$	−210.769	−	415.468i	−0.0585470	−	0.115408i
$61$	130.265	−	53.9573i	0.0350079	−	0.0145008i	−0.365111	−	0.930964i	$-0.618969\pi$
$61$	130.265	−	53.9573i	0.0350079	−	0.0145008i	0.400119	+	0.916463i	$0.368969\pi$
$62$	598.657	−	247.972i	0.155738	−	0.0645089i
$63$	−46.3702	−	76.2720i	−0.0116831	−	0.0192169i
$64$		−	512.000i		−	0.125000i
$65$	1236.50	+	512.176i	0.292663	+	0.121225i
$66$	1211.94	+	2388.98i	0.278224	+	0.548434i
$67$	−6663.38			−1.48438			−0.742190	−	0.670189i	$-0.766213\pi$
$67$	−6663.38			−1.48438			−0.742190	+	0.670189i	$0.766213\pi$
$68$	29.0778	−	2311.82i	0.00628845	−	0.499960i
$69$	4557.14	+	1489.60i	0.957180	+	0.312875i
$70$	−14.2608	+	14.2608i	−0.00291037	+	0.00291037i
$71$	1859.82	+	770.361i	0.368938	+	0.152819i	0.559447	−	0.828866i	$-0.311014\pi$
$71$	1859.82	+	770.361i	0.368938	+	0.152819i	−0.190509	+	0.981686i	$0.561014\pi$
$72$	−1478.97	−	1082.53i	−0.285296	−	0.208821i
$73$	3107.20	+	1287.04i	0.583073	+	0.241517i	0.654667	−	0.755917i	$-0.272809\pi$
$73$	3107.20	+	1287.04i	0.583073	+	0.241517i	−0.0715943	+	0.997434i	$0.522809\pi$
$74$	3395.62	−	1406.51i	0.620091	−	0.256850i
$75$	−402.539	−	5232.74i	−0.0715624	−	0.930265i
$76$	−1434.47	−	1434.47i	−0.248350	−	0.248350i
$77$	82.0009	−	82.0009i	0.0138305	−	0.0138305i
$78$	5249.90	−	403.859i	0.862903	−	0.0663805i
$79$	−2649.68	−	6396.88i	−0.424560	−	1.02498i	−0.980986	−	0.194080i	$-0.937828\pi$
$79$	−2649.68	−	6396.88i	−0.424560	−	1.02498i	0.556426	−	0.830897i	$-0.312172\pi$
$80$	−158.473	+	382.587i	−0.0247614	+	0.0597792i
$81$	−6254.03	+	1983.38i	−0.953213	+	0.302298i
$82$	1178.47	−	2845.07i	0.175263	−	0.423121i
$83$	−6187.08	−	6187.08i	−0.898110	−	0.898110i	0.0971590	−	0.995269i	$-0.469024\pi$
$83$	−6187.08	−	6187.08i	−0.898110	−	0.898110i	−0.995269	+	0.0971590i	$0.969024\pi$
$84$	−24.6516	+	75.4169i	−0.00349371	+	0.0106883i
$85$	−737.275	+	1718.48i	−0.102045	+	0.237852i
$86$		−	1539.80i		−	0.208194i
$87$	5728.16	−	2905.93i	0.756792	−	0.383925i
$88$	911.232	−	2199.91i	0.117669	−	0.284079i
$89$	780.316			0.0985123			0.0492562	−	0.998786i	$-0.484315\pi$
$89$	780.316			0.0985123			0.0492562	+	0.998786i	$0.484315\pi$
$90$	770.087	+	1266.68i	0.0950725	+	0.156380i
$91$	−87.2296	−	210.591i	−0.0105337	−	0.0254306i
$92$	−1630.88	−	3937.30i	−0.192685	−	0.465182i
$93$	−1838.78	+	932.825i	−0.212601	+	0.107854i
$94$	3599.64	+	3599.64i	0.407383	+	0.407383i
$95$	627.900	+	1515.88i	0.0695734	+	0.167965i
$96$	124.958	+	1624.37i	0.0135588	+	0.176256i
$97$	−3230.48	−	1338.11i	−0.343339	−	0.142216i	0.204349	−	0.978898i	$-0.434492\pi$
$97$	−3230.48	−	1338.11i	−0.343339	−	0.142216i	−0.547689	+	0.836682i	$0.684492\pi$
$98$	−6787.62			−0.706749
$99$	−4428.07	−	7283.50i	−0.451797	−	0.743139i
$100$	−3298.70	+	3298.70i	−0.329870	+	0.329870i
$101$			14184.9i			1.39054i	0.718747	+	0.695272i	$0.244716\pi$
$101$			14184.9i			1.39054i	−0.718747	+	0.695272i	$0.755284\pi$
$102$	471.967	+	7341.58i	0.0453640	+	0.705650i
$103$	5997.06			0.565280			0.282640	−	0.959226i	$-0.408790\pi$
$103$	5997.06			0.565280			0.282640	+	0.959226i	$0.408790\pi$
$104$	−3309.52	−	3309.52i	−0.305984	−	0.305984i
$105$	41.7635	−	48.7244i	0.00378807	−	0.00441945i
$106$			8520.12i			0.758287i
$107$	−4496.69	+	10856.0i	−0.392759	+	0.948203i	0.596578	+	0.802555i	$0.296527\pi$
$107$	−4496.69	+	10856.0i	−0.392759	+	0.948203i	−0.989336	+	0.145648i	$0.953473\pi$
$108$	4956.40	+	3073.48i	0.424932	+	0.263502i
$109$	−17606.1	+	7292.68i	−1.48187	+	0.613810i	−0.969530	−	0.244973i	$-0.921221\pi$
$109$	−17606.1	+	7292.68i	−1.48187	+	0.613810i	−0.512339	+	0.858783i	$0.671221\pi$
$110$	−1361.82	+	1361.82i	−0.112547	+	0.112547i
$111$	−10429.7	+	5291.04i	−0.846497	+	0.429433i
$112$	65.1590	−	26.9898i	0.00519444	−	0.00215161i
$113$	13407.8	−	5553.70i	1.05003	−	0.434936i	0.210127	−	0.977674i	$-0.432612\pi$
$113$	13407.8	−	5553.70i	1.05003	−	0.434936i	0.839902	+	0.542738i	$0.182612\pi$
$114$	4901.10	+	4200.91i	0.377123	+	0.323246i
$115$			3446.89i			0.260635i
$116$	−5274.82	−	2184.90i	−0.392005	−	0.162374i
$117$	−16557.3	+	2562.57i	−1.20953	+	0.187199i
$118$	11597.2			0.832894
$119$	295.743	−	118.165i	0.0208844	−	0.00834443i
$120$	409.398	−	1252.48i	0.0284304	−	0.0869774i
$121$	−2522.18	+	2522.18i	−0.172268	+	0.172268i
$122$	368.444	+	152.614i	0.0247544	+	0.0102536i
$123$	−3044.44	+	9313.90i	−0.201232	+	0.615632i
$124$	1693.26	+	701.371i	0.110123	+	0.0456146i
$125$	7222.13	−	2991.50i	0.462216	−	0.191456i
$126$	59.8037	−	245.284i	0.00376692	−	0.0154500i
$127$	−8249.59	−	8249.59i	−0.511475	−	0.511475i	0.403503	−	0.914978i	$-0.367792\pi$
$127$	−8249.59	−	8249.59i	−0.511475	−	0.511475i	−0.914978	+	0.403503i	$0.867792\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$	375.803	+	4885.19i	0.0225830	+	0.293564i
$130$	1448.65	+	3497.36i	0.0857191	+	0.206944i
$131$	−10261.0	+	24772.2i	−0.597925	+	1.44352i	0.277768	+	0.960648i	$0.410405\pi$
$131$	−10261.0	+	24772.2i	−0.597925	+	1.44352i	−0.875692	+	0.482869i	$0.839595\pi$
$132$	−2354.07	+	7201.84i	−0.135105	+	0.413329i
$133$	106.939	−	258.173i	0.00604549	−	0.0145951i
$134$	−13326.8	−	13326.8i	−0.742190	−	0.742190i
$135$	−2752.33	−	3830.72i	−0.151019	−	0.210191i
$136$	4681.79	−	4565.48i	0.253124	−	0.246836i
$137$			2444.28i			0.130230i	0.997878	+	0.0651149i	$0.0207414\pi$
$137$			2444.28i			0.130230i	−0.997878	+	0.0651149i	$0.979259\pi$
$138$	6135.08	+	12093.5i	0.322153	+	0.635027i
$139$	9108.61	−	21990.1i	0.471436	−	1.13815i	−0.492093	−	0.870543i	$-0.663768\pi$
$139$	9108.61	−	21990.1i	0.471436	−	1.13815i	0.963529	−	0.267604i	$-0.0862320\pi$
$140$	−57.0432			−0.00291037
$141$	−12298.8	−	10541.7i	−0.618618	−	0.530240i
$142$	2178.91	+	5260.36i	0.108059	+	0.260879i
$143$	−8329.88	−	20110.1i	−0.407349	−	0.983427i
$144$	−792.887	−	5123.01i	−0.0382372	−	0.247059i
$145$	3265.29	+	3265.29i	0.155305	+	0.155305i
$146$	3640.31	+	8788.48i	0.170778	+	0.412295i
$147$	21534.4	−	1656.58i	0.996550	−	0.0766615i
$148$	9604.26	+	3978.21i	0.438471	+	0.181620i
$149$	−13938.2			−0.627817			−0.313908	−	0.949453i	$-0.601639\pi$
$149$	−13938.2			−0.627817			−0.313908	+	0.949453i	$0.601639\pi$
$150$	9660.40	−	11270.6i	0.429351	−	0.500914i
$151$	14724.1	−	14724.1i	0.645765	−	0.645765i	−0.306202	−	0.951967i	$-0.599058\pi$
$151$	14724.1	−	14724.1i	0.645765	−	0.645765i	0.951967	+	0.306202i	$0.0990582\pi$
$152$		−	5737.87i		−	0.248350i
$153$	−3289.15	−	23176.8i	−0.140508	−	0.990080i
$154$	328.004			0.0138305
$155$	−1048.19	−	1048.19i	−0.0436289	−	0.0436289i
$156$	11307.5	+	9692.08i	0.464642	+	0.398261i
$157$			32621.3i			1.32343i	0.749755	+	0.661716i	$0.230172\pi$
$157$			32621.3i			1.32343i	−0.749755	+	0.661716i	$0.769828\pi$
$158$	7494.42	−	18093.1i	0.300209	−	0.724768i
$159$	−2079.41	−	27031.0i	−0.0822519	−	1.06922i
$160$	−1082.12	+	448.229i	−0.0422703	+	0.0175089i
$161$	415.104	−	415.104i	0.0160142	−	0.0160142i
$162$	−16474.8	−	8541.31i	−0.627756	−	0.325457i
$163$	27562.0	−	11416.6i	1.03738	−	0.429695i	0.202006	−	0.979384i	$-0.435254\pi$
$163$	27562.0	−	11416.6i	1.03738	−	0.429695i	0.835369	+	0.549689i	$0.185254\pi$
$164$	8047.07	−	3333.20i	0.299192	−	0.123929i
$165$	3988.15	−	4652.88i	0.146489	−	0.170905i
$166$		−	24748.3i		−	0.898110i
$167$	33807.8	+	14003.7i	1.21223	+	0.502121i	0.894931	−	0.446205i	$-0.147225\pi$
$167$	33807.8	+	14003.7i	1.21223	+	0.502121i	0.317297	+	0.948326i	$0.397225\pi$
$168$	−200.137	+	101.531i	−0.00709102	+	0.00359731i
$169$	−14223.8			−0.498015
$170$	−4911.52	+	1962.42i	−0.169949	+	0.0679037i
$171$	−16574.5	−	12131.7i	−0.566825	−	0.414886i
$172$	3079.61	−	3079.61i	0.104097	−	0.104097i
$173$	42453.7	+	17584.9i	1.41848	+	0.587554i	0.954478	−	0.298280i	$-0.0964130\pi$
$173$	42453.7	+	17584.9i	1.41848	+	0.587554i	0.464002	+	0.885834i	$0.346413\pi$
$174$	17268.2	+	5644.46i	0.570358	+	0.186434i
$175$	−593.694	−	245.916i	−0.0193859	−	0.00802991i
$176$	6222.28	−	2577.35i	0.200874	−	0.0832048i
$177$	−36793.4	+	2830.40i	−1.17442	+	0.0903445i
$178$	1560.63	+	1560.63i	0.0492562	+	0.0492562i
$179$	−20861.5	+	20861.5i	−0.651087	+	0.651087i	−0.953255	−	0.302168i	$-0.902290\pi$
$179$	−20861.5	+	20861.5i	−0.651087	+	0.651087i	0.302168	+	0.953255i	$0.402290\pi$
$180$	−993.181	+	4073.53i	−0.0306537	+	0.125726i
$181$	−352.952	−	852.101i	−0.0107735	−	0.0260096i	0.918401	−	0.395650i	$-0.129481\pi$
$181$	−352.952	−	852.101i	−0.0107735	−	0.0260096i	−0.929175	+	0.369641i	$0.879481\pi$
$182$	246.722	−	595.641i	0.00744845	−	0.0179822i
$183$	−1206.17	−	394.264i	−0.0360170	−	0.0117729i
$184$	4612.83	−	11136.4i	0.136249	−	0.328933i
$185$	−5945.36	−	5945.36i	−0.173714	−	0.173714i
$186$	−5543.22	−	1811.92i	−0.160227	−	0.0523737i
$187$	28241.6	−	11284.1i	0.807619	−	0.322688i
$188$			14398.5i			0.407383i
$189$	−129.870	+	792.787i	−0.00363567	+	0.0221939i
$190$	−1775.97	+	4287.57i	−0.0491958	+	0.118769i
$191$	24909.5			0.682806			0.341403	−	0.939917i	$-0.389098\pi$
$191$	24909.5			0.682806			0.341403	+	0.939917i	$0.389098\pi$
$192$	−2998.83	+	3498.67i	−0.0813486	+	0.0949074i
$193$	7234.73	+	17466.2i	0.194226	+	0.468903i	0.990749	−	0.135705i	$-0.0433298\pi$
$193$	7234.73	+	17466.2i	0.194226	+	0.468903i	−0.796523	+	0.604608i	$0.793330\pi$
$194$	−3784.74	−	9137.18i	−0.100562	−	0.242778i
$195$	−5449.57	−	10742.2i	−0.143315	−	0.282503i
$196$	−13575.2	−	13575.2i	−0.353375	−	0.353375i
$197$	−3112.41	−	7514.03i	−0.0801982	−	0.193616i	0.878694	−	0.477385i	$-0.158415\pi$
$197$	−3112.41	−	7514.03i	−0.0801982	−	0.193616i	−0.958893	+	0.283769i	$0.908415\pi$
$198$	5710.88	−	23423.1i	0.145671	−	0.597468i
$199$	64286.6	+	26628.4i	1.62336	+	0.672416i	0.994464	−	0.105076i	$-0.0335085\pi$
$199$	64286.6	+	26628.4i	1.62336	+	0.672416i	0.628893	+	0.777492i	$0.283509\pi$
$200$	−13194.8			−0.329870
$201$	45533.1	+	39028.1i	1.12703	+	0.966018i
$202$	−28369.9	+	28369.9i	−0.695272	+	0.695272i
$203$		−	786.469i		−	0.0190849i
$204$	−13739.2	+	15627.1i	−0.330143	+	0.375507i
$205$	−7044.78			−0.167633
$206$	11994.1	+	11994.1i	0.282640	+	0.282640i
$207$	−22415.7	−	36870.5i	−0.523133	−	0.860475i
$208$		−	13238.1i		−	0.305984i
$209$	10212.0	−	24653.9i	0.233785	−	0.564408i
$210$	180.976	−	13.9219i	0.00410376	−	0.000315690i
$211$	−38208.2	+	15826.4i	−0.858207	+	0.355481i	−0.768006	−	0.640443i	$-0.778751\pi$
$211$	−38208.2	+	15826.4i	−0.858207	+	0.355481i	−0.0902009	+	0.995924i	$0.528751\pi$
$212$	−17040.2	+	17040.2i	−0.379144	+	0.379144i
$213$	−8196.66	−	16157.3i	−0.180667	−	0.356130i
$214$	−30705.4	+	12718.6i	−0.670481	+	0.277722i
$215$	−3254.40	+	1348.02i	−0.0704034	+	0.0291621i
$216$	3765.83	+	16059.8i	0.0807149	+	0.344217i
$217$			252.463i			0.00536140i
$218$	−49797.5	−	20626.8i	−1.04784	−	0.434029i
$219$	−13694.2	−	26993.9i	−0.285527	−	0.562831i
$220$	−5447.27			−0.112547
$221$	751.824	−	59773.4i	0.0153933	−	1.22384i
$222$	−31441.5	−	10277.3i	−0.637965	−	0.208532i
$223$	42896.5	−	42896.5i	0.862606	−	0.862606i	−0.129034	−	0.991640i	$-0.541188\pi$
$223$	42896.5	−	42896.5i	0.862606	−	0.862606i	0.991640	+	0.129034i	$0.0411877\pi$
$224$	184.298	+	76.3386i	0.00367302	+	0.00152142i
$225$	−27898.0	+	38114.7i	−0.551071	+	0.752884i
$226$	37923.0	+	15708.2i	0.742483	+	0.307546i
$227$	−2979.10	+	1233.98i	−0.0578140	+	0.0239474i	−0.411403	−	0.911454i	$-0.634961\pi$
$227$	−2979.10	+	1233.98i	−0.0578140	+	0.0239474i	0.353589	+	0.935401i	$0.384961\pi$
$228$	1400.38	+	18204.0i	0.0269387	+	0.350185i
$229$	62212.5	+	62212.5i	1.18633	+	1.18633i	0.978074	+	0.208260i	$0.0667799\pi$
$229$	62212.5	+	62212.5i	1.18633	+	1.18633i	0.208260	+	0.978074i	$0.433220\pi$
$230$	−6893.79	+	6893.79i	−0.130317	+	0.130317i
$231$	−1040.63	+	80.0522i	−0.0195016	+	0.00150020i
$232$	−6179.83	−	14919.4i	−0.114816	−	0.277189i
$233$	−5968.19	+	14408.5i	−0.109934	+	0.265404i	−0.969266	−	0.246013i	$-0.920879\pi$
$233$	−5968.19	+	14408.5i	−0.109934	+	0.265404i	0.859333	+	0.511417i	$0.170879\pi$
$234$	−38239.7	−	27989.5i	−0.698366	−	0.511167i
$235$	4456.60	−	10759.2i	0.0806989	−	0.194824i
$236$	23194.4	+	23194.4i	0.416447	+	0.416447i
$237$	−19361.0	+	59231.4i	−0.344693	+	1.05452i
$238$	827.817	+	355.156i	0.0146144	+	0.00626996i
$239$			34278.4i			0.600101i	0.953923	+	0.300051i	$0.0970035\pi$
$239$			34278.4i			0.600101i	−0.953923	+	0.300051i	$0.902996\pi$
$240$	3323.75	−	1686.15i	0.0577039	−	0.0292735i
$241$	−8981.44	+	21683.1i	−0.154636	+	0.373325i	−0.982144	−	0.188129i	$-0.939758\pi$
$241$	−8981.44	+	21683.1i	−0.154636	+	0.373325i	0.827508	+	0.561454i	$0.189758\pi$
$242$	−10088.7			−0.172268
$243$	54352.7	+	23077.4i	0.920468	+	0.390817i
$244$	431.659	+	1042.12i	0.00725038	+	0.0175040i
$245$	5942.20	+	14345.7i	0.0989954	+	0.238996i
$246$	−24716.7	+	12538.9i	−0.408432	+	0.207200i
$247$	−37089.0	−	37089.0i	−0.607927	−	0.607927i
$248$	1983.78	+	4789.26i	0.0322544	+	0.0778691i
$249$	6040.05	+	78516.7i	0.0974186	+	1.26638i
$250$	20427.3	+	8461.25i	0.326836	+	0.135380i
$251$	−110141.			−1.74824			−0.874122	−	0.485707i	$-0.838562\pi$
$251$	−110141.			−1.74824			−0.874122	+	0.485707i	$0.838562\pi$
$252$	610.176	−	370.962i	0.00960847	−	0.00584155i
$253$	39639.9	−	39639.9i	0.619286	−	0.619286i
$254$		−	32998.3i		−	0.511475i
$255$	15103.4	−	7424.67i	0.232270	−	0.114182i
$256$	4096.00			0.0625000
$257$	53906.8	+	53906.8i	0.816164	+	0.816164i	0.985550	−	0.169386i	$-0.0541784\pi$
$257$	53906.8	+	53906.8i	0.816164	+	0.816164i	−0.169386	+	0.985550i	$0.554178\pi$
$258$	−9018.78	+	10522.0i	−0.135490	+	0.158073i
$259$			1431.98i			0.0213471i
$260$	−4097.41	+	9892.02i	−0.0606126	+	0.146332i
$261$	−56162.7	−	13693.2i	−0.824455	−	0.201013i
$262$	−70066.4	+	29022.4i	−1.02072	+	0.422797i
$263$	24424.1	−	24424.1i	0.353107	−	0.353107i	−0.508157	−	0.861264i	$-0.669673\pi$
$263$	24424.1	−	24424.1i	0.353107	−	0.353107i	0.861264	+	0.508157i	$0.169673\pi$
$264$	−19111.8	+	9695.53i	−0.274217	+	0.139112i
$265$	18007.4	−	7458.91i	0.256424	−	0.106214i
$266$	730.223	−	302.468i	0.0103203	−	0.00427481i
$267$	−5332.16	−	4570.39i	−0.0747964	−	0.0641107i
$268$		−	53307.1i		−	0.742190i
$269$	−49361.1	−	20446.0i	−0.682150	−	0.282556i	0.0145753	−	0.999894i	$-0.495360\pi$
$269$	−49361.1	−	20446.0i	−0.682150	−	0.282556i	−0.696725	+	0.717338i	$0.745360\pi$
$270$	2156.79	−	13166.1i	0.0295856	−	0.180605i
$271$	−117703.			−1.60269			−0.801345	−	0.598203i	$-0.795882\pi$
$271$	−117703.			−1.60269			−0.801345	+	0.598203i	$0.795882\pi$
$272$	18494.5	+	232.622i	0.249980	+	0.00314422i
$273$	−637.382	+	1949.95i	−0.00855213	+	0.0261636i
$274$	−4888.57	+	4888.57i	−0.0651149	+	0.0651149i
$275$	−56694.0	−	23483.4i	−0.749673	−	0.310525i
$276$	−11916.8	+	36457.1i	−0.156437	+	0.478590i
$277$	−64692.4	−	26796.5i	−0.843129	−	0.349235i	−0.0810422	−	0.996711i	$-0.525825\pi$
$277$	−64692.4	−	26796.5i	−0.843129	−	0.349235i	−0.762086	+	0.647475i	$0.775825\pi$
$278$	62197.5	−	25763.0i	0.804791	−	0.333356i
$279$	18028.7	+	4395.63i	0.231609	+	0.0564694i
$280$	−114.086	−	114.086i	−0.00145518	−	0.00145518i
$281$	11473.3	−	11473.3i	0.145304	−	0.145304i	−0.630713	−	0.776016i	$-0.717237\pi$
$281$	11473.3	−	11473.3i	0.145304	−	0.145304i	0.776016	+	0.630713i	$0.217237\pi$
$282$	−3514.09	−	45680.9i	−0.0441891	−	0.574429i
$283$	47036.1	+	113555.i	0.587298	+	1.41786i	0.886076	+	0.463539i	$0.153421\pi$
$283$	47036.1	+	113555.i	0.587298	+	1.41786i	−0.298779	+	0.954322i	$0.596579\pi$
$284$	−6162.89	+	14878.5i	−0.0764096	+	0.184469i
$285$	4588.03	−	14036.2i	0.0564855	−	0.172807i
$286$	23560.5	−	56880.0i	0.288039	−	0.695388i
$287$	848.392	+	848.392i	0.0102999	+	0.0102999i
$288$	8660.24	−	11831.8i	0.104411	−	0.142648i
$289$	83494.6	+	2100.70i	0.999684	+	0.0251518i
$290$			13061.2i			0.155305i
$291$	14237.5	+	28065.0i	0.168131	+	0.331420i
$292$	−10296.3	+	24857.6i	−0.120758	+	0.291537i
$293$	51972.6			0.605395			0.302698	−	0.953087i	$-0.402113\pi$
$293$	51972.6			0.605395			0.302698	+	0.953087i	$0.402113\pi$
$294$	46382.1	+	39755.7i	0.536606	+	0.459944i
$295$	−10152.7	−	24510.9i	−0.116665	−	0.281653i
$296$	11252.1	+	27164.9i	0.128425	+	0.310045i
$297$	−12401.7	+	75706.2i	−0.140595	+	0.858259i
$298$	−27876.3	−	27876.3i	−0.313908	−	0.313908i
$299$	−42167.4	−	101801.i	−0.471666	−	1.13870i
$300$	41861.9	−	3220.31i	0.465132	−	0.0357812i
$301$	554.262	+	229.583i	0.00611761	+	0.00253400i
$302$	58896.4			0.645765
$303$	83082.6	−	96930.4i	0.904950	−	1.05578i
$304$	11475.7	−	11475.7i	0.124175	−	0.124175i
$305$		−	912.317i		−	0.00980723i
$306$	39775.3	−	52931.8i	0.424786	−	0.565294i
$307$	−85595.2			−0.908182			−0.454091	−	0.890955i	$-0.650036\pi$
$307$	−85595.2			−0.908182			−0.454091	+	0.890955i	$0.650036\pi$
$308$	656.007	+	656.007i	0.00691524	+	0.00691524i
$309$	−40979.9	−	35125.3i	−0.429194	−	0.367878i
$310$		−	4192.74i		−	0.0436289i
$311$	20286.0	−	48974.8i	0.209738	−	0.506352i	−0.783644	−	0.621210i	$-0.786641\pi$
$311$	20286.0	−	48974.8i	0.209738	−	0.506352i	0.993382	+	0.114858i	$0.0366414\pi$
$312$	3230.87	+	41999.2i	0.0331902	+	0.431451i
$313$	−161323.	+	66822.0i	−1.64667	+	0.682073i	−0.996946	−	0.0780962i	$-0.975116\pi$
$313$	−161323.	+	66822.0i	−1.64667	+	0.682073i	−0.649725	+	0.760169i	$0.725116\pi$
$314$	−65242.5	+	65242.5i	−0.661716	+	0.661716i
$315$	−570.767	+	88.3375i	−0.00575225	+	0.000890275i
$316$	51175.1	−	21197.4i	0.512489	−	0.212280i
$317$	−30108.1	+	12471.2i	−0.299616	+	0.124105i	−0.527427	−	0.849600i	$-0.676843\pi$
$317$	−30108.1	+	12471.2i	−0.299616	+	0.124105i	0.227811	+	0.973705i	$0.426843\pi$
$318$	49903.1	−	58220.8i	0.493485	−	0.575737i
$319$		−	75102.8i		−	0.738032i
$320$	−3060.70	−	1267.78i	−0.0298896	−	0.0123807i
$321$	94311.9	−	47844.9i	0.915285	−	0.464329i
$322$	1660.42			0.0160142
$323$	52467.8	−	51164.3i	0.502907	−	0.490413i
$324$	−15867.0	−	50032.3i	−0.151149	−	0.476607i
$325$	−85289.9	+	85289.9i	−0.807478	+	0.807478i
$326$	77957.2	+	32290.9i	0.733535	+	0.303840i
$327$	163022.	+	53287.2i	1.52458	+	0.498342i
$328$	22760.5	+	9427.72i	0.211561	+	0.0876313i
$329$	−1832.41	+	759.010i	−0.0169290	+	0.00701222i
$330$	17282.1	−	1329.46i	0.158697	−	0.0122080i
$331$	−5190.51	−	5190.51i	−0.0473755	−	0.0473755i	0.683022	−	0.730398i	$-0.260665\pi$
$331$	−5190.51	−	5190.51i	−0.0473755	−	0.0473755i	−0.730398	+	0.683022i	$0.760665\pi$
$332$	49496.6	−	49496.6i	0.449055	−	0.449055i
$333$	102260.	+	24932.3i	0.922180	+	0.224840i
$334$	39608.3	+	95622.9i	0.355053	+	0.857174i
$335$	−16499.4	+	39833.2i	−0.147021	+	0.354940i
$336$	−603.335	−	197.213i	−0.00534417	−	0.00174685i
$337$	65246.3	−	157519.i	0.574508	−	1.38699i	−0.323173	−	0.946340i	$-0.604749\pi$
$337$	65246.3	−	157519.i	0.574508	−	1.38699i	0.897681	−	0.440646i	$-0.145251\pi$
$338$	−28447.6	−	28447.6i	−0.249007	−	0.249007i
$339$	−124149.	−	40580.6i	−1.08030	−	0.353117i
$340$	−13747.9	−	5898.20i	−0.118926	−	0.0510225i
$341$			24108.6i			0.207331i
$342$	−8885.70	−	57412.4i	−0.0759696	−	0.490855i
$343$	2024.56	−	4887.73i	0.0172085	−	0.0415450i
$344$	12318.4			0.104097
$345$	20188.8	−	23553.8i	0.169618	−	0.197889i
$346$	49737.6	+	120077.i	0.415463	+	1.00302i
$347$	58615.0	+	141509.i	0.486799	+	1.17524i	0.956322	+	0.292316i	$0.0944259\pi$
$347$	58615.0	+	141509.i	0.486799	+	1.17524i	−0.469523	+	0.882920i	$0.655574\pi$
$348$	23247.4	+	45825.3i	0.191962	+	0.378396i
$349$	−160053.	−	160053.i	−1.31405	−	1.31405i	−0.918403	−	0.395647i	$-0.870520\pi$
$349$	−160053.	−	160053.i	−1.31405	−	1.31405i	−0.395647	−	0.918403i	$-0.629480\pi$
$350$	−695.555	−	1679.22i	−0.00567800	−	0.0137079i
$351$	128151.	+	79466.8i	1.04018	+	0.645018i
$352$	17599.3	+	7289.86i	0.142040	+	0.0588347i
$353$	195847.			1.57169			0.785846	−	0.618422i	$-0.212228\pi$
$353$	195847.			1.57169			0.785846	+	0.618422i	$0.212228\pi$
$354$	−79247.6	−	67926.0i	−0.632382	−	0.542038i
$355$	9210.32	−	9210.32i	0.0730833	−	0.0730833i
$356$			6242.53i			0.0492562i
$357$	−2713.02	−	924.733i	−0.0212871	−	0.00725571i
$358$	−83445.9			−0.651087
$359$	−69362.9	−	69362.9i	−0.538193	−	0.538193i	0.384805	−	0.922998i	$-0.374269\pi$
$359$	−69362.9	−	69362.9i	−0.538193	−	0.538193i	−0.922998	+	0.384805i	$0.874269\pi$
$360$	−10133.4	+	6160.69i	−0.0781900	+	0.0475362i
$361$			66018.0i			0.506580i
$362$	998.298	−	2410.10i	0.00761804	−	0.0183916i
$363$	32007.5	−	2462.24i	0.242906	−	0.0186860i
$364$	1684.73	−	697.837i	0.0127153	−	0.00526685i
$365$	15387.7	−	15387.7i	0.115502	−	0.115502i
$366$	−1623.82	−	3200.88i	−0.0121221	−	0.0238950i
$367$	−137999.	+	57161.2i	−1.02458	+	0.424394i	−0.830752	−	0.556642i	$-0.812090\pi$
$367$	−137999.	+	57161.2i	−1.02458	+	0.424394i	−0.193825	+	0.981036i	$0.562090\pi$
$368$	31498.4	−	13047.1i	0.232591	−	0.0963423i
$369$	75356.1	−	45813.3i	0.553434	−	0.336464i
$370$		−	23781.5i		−	0.173714i
$371$	−3066.87	−	1270.34i	−0.0222816	−	0.00922936i
$372$	−7462.60	−	14710.3i	−0.0539268	−	0.106300i
$373$	−192662.			−1.38478			−0.692388	−	0.721526i	$-0.743441\pi$
$373$	−192662.			−1.38478			−0.692388	+	0.721526i	$0.743441\pi$
$374$	79051.4	+	33915.2i	0.565153	+	0.242466i
$375$	−66872.7	−	21858.8i	−0.475539	−	0.155440i
$376$	−28797.1	+	28797.1i	−0.203691	+	0.203691i
$377$	−136384.	−	56491.9i	−0.959576	−	0.397469i
$378$	−1845.31	+	1325.83i	−0.0129148	+	0.00927910i
$379$	−63571.1	−	26332.0i	−0.442570	−	0.183318i	0.150260	−	0.988647i	$-0.451989\pi$
$379$	−63571.1	−	26332.0i	−0.442570	−	0.183318i	−0.592829	+	0.805328i	$0.701989\pi$
$380$	−12127.1	+	5023.20i	−0.0839825	+	0.0347867i
$381$	8053.54	+	104691.i	0.0554801	+	0.721204i
$382$	49818.9	+	49818.9i	0.341403	+	0.341403i
$383$	−84500.4	+	84500.4i	−0.576051	+	0.576051i	−0.933813	−	0.357762i	$-0.883540\pi$
$383$	−84500.4	+	84500.4i	−0.576051	+	0.576051i	0.357762	+	0.933813i	$0.383540\pi$
$384$	−12995.0	+	999.666i	−0.0881280	+	0.00677942i
$385$	−287.150	−	693.240i	−0.00193725	−	0.00467695i
$386$	−20462.9	+	49401.8i	−0.137339	+	0.331565i
$387$	26045.1	−	35583.3i	0.173902	−	0.237588i
$388$	10704.9	−	25843.8i	0.0711079	−	0.171670i
$389$	33617.2	+	33617.2i	0.222158	+	0.222158i	0.809407	−	0.587249i	$-0.199789\pi$
$389$	33617.2	+	33617.2i	0.222158	+	0.222158i	−0.587249	+	0.809407i	$0.699789\pi$
$390$	10585.2	−	32383.5i	0.0695939	−	0.212909i
$391$	142965.	−	57122.1i	0.935136	−	0.373637i
$392$		−	54300.9i		−	0.353375i
$393$	215210.	−	109177.i	1.39340	−	0.706882i
$394$	8803.23	−	21252.9i	0.0567087	−	0.136907i
$395$	−44801.0			−0.287140
$396$	58268.0	−	35424.5i	0.371569	−	0.225899i
$397$	32131.5	+	77572.4i	0.203869	+	0.492182i	0.992436	−	0.122767i	$-0.0391767\pi$
$397$	32131.5	+	77572.4i	0.203869	+	0.492182i	−0.788567	+	0.614949i	$0.789177\pi$
$398$	75316.4	+	181830.i	0.475470	+	1.14789i
$399$	−2242.89	+	1137.83i	−0.0140884	+	0.00714713i
$400$	−26389.6	−	26389.6i	−0.164935	−	0.164935i
$401$	−88729.1	−	214211.i	−0.551794	−	1.33215i	−0.916130	−	0.400882i	$-0.868704\pi$
$401$	−88729.1	−	214211.i	−0.551794	−	1.33215i	0.364335	−	0.931268i	$-0.381296\pi$
$402$	13010.1	+	169122.i	0.0805059	+	1.04652i
$403$	43780.2	+	18134.4i	0.269568	+	0.111659i
$404$	−113480.			−0.695272
$405$	−3629.35	+	42297.2i	−0.0221268	+	0.257871i
$406$	1572.94	−	1572.94i	0.00954244	−	0.00954244i
$407$			136745.i			0.825513i
$408$	−58732.7	+	3775.74i	−0.352825	+	0.0226820i
$409$	251332.			1.50245			0.751226	−	0.660045i	$-0.229463\pi$
$409$	251332.			1.50245			0.751226	+	0.660045i	$0.229463\pi$
$410$	−14089.6	−	14089.6i	−0.0838165	−	0.0838165i
$411$	14316.4	−	16702.6i	0.0847521	−	0.0988782i
$412$			47976.5i			0.282640i
$413$	−1729.13	+	4174.49i	−0.0101374	+	0.0244739i
$414$	28909.5	−	118572.i	0.168671	−	0.691804i
$415$	−52305.9	+	21665.8i	−0.303707	+	0.125800i
$416$	26476.1	−	26476.1i	0.152992	−	0.152992i
$417$	−191041.	+	96915.9i	−1.09863	+	0.557343i
$418$	69731.7	−	28883.8i	0.399096	−	0.165311i
$419$	−216957.	+	89866.4i	−1.23579	+	0.511881i	−0.902397	−	0.430906i	$-0.858194\pi$
$419$	−216957.	+	89866.4i	−1.23579	+	0.511881i	−0.333394	+	0.942788i	$0.608194\pi$
$420$	389.795	+	334.108i	0.00220972	+	0.00189403i
$421$		−	298277.i		−	1.68289i	−0.540345	−	0.841443i	$-0.681706\pi$
$421$		−	298277.i		−	1.68289i	0.540345	−	0.841443i	$-0.318294\pi$
$422$	−108069.	−	44763.7i	−0.606844	−	0.251363i
$423$	22297.7	+	144070.i	0.124617	+	0.805179i
$424$	−68160.9			−0.379144
$425$	−117657.	−	120655.i	−0.651390	−	0.667985i
$426$	15921.2	−	48707.8i	0.0877317	−	0.268398i
$427$	−109.869	+	109.869i	−0.000602587	+	0.000602587i
$428$	−86847.8	−	35973.6i	−0.474102	−	0.196379i
$429$	−60866.0	+	186208.i	−0.330720	+	1.01177i
$430$	−9204.83	−	3812.77i	−0.0497827	−	0.0206207i
$431$	−176669.	+	73178.9i	−0.951057	+	0.393941i	−0.803628	−	0.595132i	$-0.797100\pi$
$431$	−176669.	+	73178.9i	−0.951057	+	0.393941i	−0.147429	+	0.989073i	$0.547100\pi$
$432$	−24587.9	+	39651.2i	−0.131751	+	0.212466i
$433$	114214.	+	114214.i	0.609177	+	0.609177i	0.942731	−	0.333554i	$-0.108248\pi$
$433$	114214.	+	114214.i	0.609177	+	0.609177i	−0.333554	+	0.942731i	$0.608248\pi$
$434$	−504.926	+	504.926i	−0.00268070	+	0.00268070i
$435$	−3187.70	−	41438.0i	−0.0168461	−	0.218988i
$436$	−58341.4	−	140849.i	−0.306905	−	0.740934i
$437$	51695.0	−	124803.i	0.270698	−	0.653523i
$438$	26599.5	−	81376.2i	0.138652	−	0.424179i
$439$	−3268.34	+	7890.47i	−0.0169589	+	0.0409425i	−0.932132	−	0.362118i	$-0.882054\pi$
$439$	−3268.34	+	7890.47i	−0.0169589	+	0.0409425i	0.915173	+	0.403061i	$0.132054\pi$
$440$	−10894.5	−	10894.5i	−0.0562735	−	0.0562735i
$441$	−156855.	−	114809.i	−0.806530	−	0.590337i
$442$	121051.	−	118043.i	0.619615	−	0.604222i
$443$			174365.i			0.888489i	0.895906	+	0.444244i	$0.146528\pi$
$443$			174365.i			0.888489i	−0.895906	+	0.444244i	$0.853472\pi$
$444$	−42328.3	−	83437.5i	−0.214716	−	0.423249i
$445$	1932.17	−	4664.67i	0.00975720	−	0.0235560i
$446$	171586.			0.862606
$447$	95244.1	+	81637.2i	0.476676	+	0.408576i
$448$	215.918	+	521.272i	0.00107580	+	0.00259722i
$449$	−46134.4	−	111378.i	−0.228840	−	0.552469i	0.767197	−	0.641412i	$-0.221651\pi$
$449$	−46134.4	−	111378.i	−0.228840	−	0.552469i	−0.996037	+	0.0889430i	$0.971651\pi$
$450$	−132025.	+	20433.6i	−0.651977	+	0.100906i
$451$	81016.1	+	81016.1i	0.398307	+	0.398307i
$452$	44429.6	+	107263.i	0.217468	+	0.525015i
$453$	−186855.	+	14374.2i	−0.910559	+	0.0700466i
$454$	−8426.17	−	3490.23i	−0.0408807	−	0.0169333i
$455$	−1474.89			−0.00712420
$456$	−33607.3	+	39208.8i	−0.161623	+	0.188562i
$457$	99941.2	−	99941.2i	0.478533	−	0.478533i	−0.426129	−	0.904662i	$-0.640123\pi$
$457$	99941.2	−	99941.2i	0.478533	−	0.478533i	0.904662	+	0.426129i	$0.140123\pi$
$458$			248850.i			1.18633i
$459$	−113273.	+	177639.i	−0.537651	+	0.843168i
$460$	−27575.1			−0.130317
$461$	−132796.	−	132796.i	−0.624861	−	0.624861i	0.321910	−	0.946770i	$-0.395675\pi$
$461$	−132796.	−	132796.i	−0.624861	−	0.624861i	−0.946770	+	0.321910i	$0.895675\pi$
$462$	−2241.36	−	1921.15i	−0.0105009	−	0.00900071i
$463$			341742.i			1.59418i	0.603863	+	0.797088i	$0.293628\pi$
$463$			341742.i			1.59418i	−0.603863	+	0.797088i	$0.706372\pi$
$464$	17479.2	−	42198.5i	0.0811869	−	0.196002i
$465$	1023.28	+	13301.9i	0.00473246	+	0.0615189i
$466$	−40753.4	+	16880.6i	−0.187669	+	0.0777349i
$467$	224943.	−	224943.i	1.03143	−	1.03143i	0.0319382	−	0.999490i	$-0.489832\pi$
$467$	224943.	−	224943.i	1.03143	−	1.03143i	0.999490	−	0.0319382i	$-0.0101680\pi$
$468$	−20500.6	−	132458.i	−0.0935996	−	0.604767i
$469$	6784.06	−	2810.05i	0.0308421	−	0.0127752i
$470$	30431.5	−	12605.2i	0.137762	−	0.0570627i
$471$	191066.	−	222912.i	0.861274	−	1.00483i
$472$			92777.7i			0.416447i
$473$	52928.6	+	21923.7i	0.236574	+	0.0979923i
$474$	−157185.	+	79740.8i	−0.699607	+	0.354915i
$475$	−147871.			−0.655385
$476$	945.323	+	2365.95i	0.00417221	+	0.0104422i
$477$	−144114.	+	196891.i	−0.633386	+	0.865344i
$478$	−68556.7	+	68556.7i	−0.300051	+	0.300051i
$479$	−37050.1	−	15346.6i	−0.161480	−	0.0668871i	0.300479	−	0.953788i	$-0.402853\pi$
$479$	−37050.1	−	15346.6i	−0.161480	−	0.0668871i	−0.461959	+	0.886901i	$0.652853\pi$
$480$	10019.8	+	3275.18i	0.0434887	+	0.0142152i
$481$	248324.	+	102859.i	1.07332	+	0.444583i
$482$	−61329.1	+	25403.3i	−0.263981	+	0.109344i
$483$	−5267.85	+	405.240i	−0.0225808	+	0.00173707i
$484$	−20177.4	−	20177.4i	−0.0861340	−	0.0861340i
$485$	−15998.2	+	15998.2i	−0.0680124	+	0.0680124i
$486$	62550.7	+	154860.i	0.264825	+	0.655643i
$487$	108577.	+	262127.i	0.457803	+	1.10523i	0.969285	+	0.245940i	$0.0790965\pi$
$487$	108577.	+	262127.i	0.457803	+	1.10523i	−0.511483	+	0.859294i	$0.670904\pi$
$488$	−1220.92	+	2947.55i	−0.00512679	+	0.0123772i
$489$	−255208.	−	83420.3i	−1.06728	−	0.348862i
$490$	−16807.1	+	40575.9i	−0.0700003	+	0.168996i
$491$	270837.	+	270837.i	1.12343	+	1.12343i	0.991223	+	0.132204i	$0.0422053\pi$
$491$	270837.	+	270837.i	1.12343	+	1.12343i	0.132204	+	0.991223i	$0.457795\pi$
$492$	−74511.2	−	24355.5i	−0.307816	−	0.100616i
$493$	81319.9	−	189545.i	0.334582	−	0.779863i
$494$		−	148356.i		−	0.607927i
$495$	−54504.7	+	8435.68i	−0.222446	+	0.0344279i
$496$	−5610.97	+	13546.1i	−0.0228073	+	0.0550617i
$497$	−2218.37			−0.00898093
$498$	−144953.	+	169113.i	−0.584480	+	0.681898i
$499$	170140.	+	410754.i	0.683290	+	1.64961i	0.757881	+	0.652393i	$0.226235\pi$
$499$	170140.	+	410754.i	0.683290	+	1.64961i	−0.0745912	+	0.997214i	$0.523765\pi$
$500$	23932.0	+	57777.0i	0.0957281	+	0.231108i
$501$	−148999.	−	293707.i	−0.593620	−	1.17014i
$502$	−220282.	−	220282.i	−0.874122	−	0.874122i
$503$	52601.5	+	126991.i	0.207904	+	0.501924i	0.993093	−	0.117332i	$-0.0374343\pi$
$503$	52601.5	+	126991.i	0.207904	+	0.501924i	−0.785189	+	0.619256i	$0.787434\pi$
$504$	1962.28	+	478.429i	0.00772501	+	0.00188346i
$505$	84796.5	+	35123.9i	0.332503	+	0.137727i
$506$	158559.			0.619286
$507$	97196.0	+	83310.2i	0.378122	+	0.324102i
$508$	65996.7	−	65996.7i	0.255738	−	0.255738i
$509$		−	10759.0i		−	0.0415276i	−0.999784	−	0.0207638i	$-0.993390\pi$
$509$		−	10759.0i		−	0.0415276i	0.999784	−	0.0207638i	$-0.00660980\pi$
$510$	45056.1	+	15357.4i	0.173226	+	0.0590441i
$511$	−3706.23			−0.0141935
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	42202.9	+	179978.i	0.160364	+	0.683889i
$514$			215627.i			0.816164i
$515$	14849.5	−	35849.9i	0.0559884	−	0.135168i
$516$	−39081.5	+	3006.42i	−0.146782	+	0.0112915i
$517$	−174984.	+	72480.7i	−0.654662	+	0.271170i
$518$	−2863.97	+	2863.97i	−0.0106735	+	0.0106735i
$519$	−187104.	−	368819.i	−0.694621	−	1.36924i
$520$	−27978.9	+	11589.2i	−0.103472	+	0.0428596i
$521$	321879.	−	133327.i	1.18582	−	0.491182i	0.299426	−	0.954119i	$-0.403205\pi$
$521$	321879.	−	133327.i	1.18582	−	0.491182i	0.886391	+	0.462938i	$0.153205\pi$
$522$	−84938.9	−	139712.i	−0.311721	−	0.512734i
$523$		−	173212.i		−	0.633249i	−0.948551	−	0.316624i	$-0.897451\pi$
$523$		−	173212.i		−	0.633249i	0.948551	−	0.316624i	$-0.102549\pi$
$524$	−198178.	−	82087.9i	−0.721759	−	0.298962i
$525$	2616.55	+	5157.75i	0.00949316	+	0.0187129i
$526$	97696.2			0.353107
$527$	−26104.3	+	60845.5i	−0.0939921	+	0.219082i
$528$	−57614.7	−	18832.6i	−0.206664	−	0.0675526i
$529$	2787.06	−	2787.06i	0.00995943	−	0.00995943i
$530$	50932.6	+	21097.0i	0.181319	+	0.0751049i
$531$	267999.	+	196161.i	0.950484	+	0.695704i
$532$	2065.38	+	855.509i	0.00729755	+	0.00302274i
$533$	208062.	−	86182.0i	0.732382	−	0.303363i
$534$	−1523.55	−	19805.1i	−0.00534285	−	0.0694535i
$535$	53761.8	+	53761.8i	0.187830	+	0.187830i
$536$	106614.	−	106614.i	0.371095	−	0.371095i
$537$	264741.	−	20365.7i	0.918063	−	0.0706238i
$538$	−57830.1	−	139614.i	−0.199797	−	0.482353i
$539$	96642.1	−	233315.i	0.332651	−	0.803091i
$540$	30645.8	−	22018.6i	0.105095	−	0.0755097i
$541$	174574.	−	421459.i	0.596465	−	1.43999i	−0.280696	−	0.959797i	$-0.590565\pi$
$541$	174574.	−	421459.i	0.596465	−	1.43999i	0.877161	−	0.480196i	$-0.159435\pi$
$542$	−235406.	−	235406.i	−0.801345	−	0.801345i
$543$	−2579.00	+	7889.96i	−0.00874685	+	0.0267593i
$544$	36523.8	+	37454.3i	0.123418	+	0.126562i
$545$			123305.i			0.415135i
$546$	−5174.66	+	2625.13i	−0.0173579	+	0.00880575i
$547$	152235.	−	367529.i	0.508793	−	1.22833i	−0.435786	−	0.900050i	$-0.643530\pi$
$547$	152235.	−	367529.i	0.508793	−	1.22833i	0.944579	−	0.328284i	$-0.106470\pi$
$548$	−19554.3			−0.0651149
$549$	5932.95	+	9758.81i	0.0196846	+	0.0323782i
$550$	−66421.2	−	160355.i	−0.219574	−	0.530099i
$551$	−69256.0	−	167199.i	−0.228115	−	0.550719i
$552$	−96747.7	+	49080.6i	−0.317514	+	0.161076i
$553$	5395.32	+	5395.32i	0.0176428	+	0.0176428i
$554$	−75791.9	−	182978.i	−0.246947	−	0.596182i
$555$	5804.08	+	75449.2i	0.0188429	+	0.244945i
$556$	175921.	+	72868.9i	0.569073	+	0.235718i
$557$	170122.			0.548341			0.274170	−	0.961681i	$-0.411597\pi$
$557$	170122.			0.548341			0.274170	+	0.961681i	$0.411597\pi$
$558$	27266.1	+	44848.6i	0.0875698	+	0.144039i
$559$	79625.1	−	79625.1i	0.254816	−	0.254816i
$560$		−	456.346i		−	0.00145518i
$561$	−259076.	−	88306.3i	−0.823194	−	0.280586i
$562$	45893.3			0.145304
$563$	244222.	+	244222.i	0.770493	+	0.770493i	0.978193	−	0.207700i	$-0.0665977\pi$
$563$	244222.	+	244222.i	0.770493	+	0.770493i	−0.207700	+	0.978193i	$0.566598\pi$
$564$	84333.7	−	98390.0i	0.265120	−	0.309309i
$565$		−	93902.6i		−	0.294158i
$566$	−133038.	+	321182.i	−0.415282	+	1.00258i
$567$	5530.87	−	4656.72i	0.0172039	−	0.0144848i
$568$	−42082.8	+	17431.3i	−0.130439	+	0.0540297i
$569$	310465.	−	310465.i	0.958933	−	0.958933i	−0.0402566	−	0.999189i	$-0.512818\pi$
$569$	310465.	−	310465.i	0.958933	−	0.958933i	0.999189	+	0.0402566i	$0.0128175\pi$
$570$	37248.5	−	18896.4i	0.114646	−	0.0581605i
$571$	153891.	−	63743.7i	0.471999	−	0.195508i	−0.133988	−	0.990983i	$-0.542778\pi$
$571$	153891.	−	63743.7i	0.471999	−	0.195508i	0.605987	+	0.795475i	$0.292778\pi$
$572$	160881.	−	66639.0i	0.491714	−	0.203675i
$573$	−170215.	−	145897.i	−0.518427	−	0.444363i
$574$			3393.57i			0.0102999i
$575$	−286996.	−	118878.i	−0.868041	−	0.359554i
$576$	40984.0	−	6343.09i	0.123529	−	0.0191186i
$577$	603910.			1.81393			0.906966	−	0.421205i	$-0.138393\pi$
$577$	603910.			1.81393			0.906966	+	0.421205i	$0.138393\pi$
$578$	162788.	+	171191.i	0.487266	+	0.512418i
$579$	52863.8	−	161727.i	0.157689	−	0.482419i
$580$	−26122.3	+	26122.3i	−0.0776526	+	0.0776526i
$581$	8908.31	+	3689.94i	0.0263902	+	0.0109312i
$582$	−27654.9	+	84605.0i	−0.0816444	+	0.249776i
$583$	−292867.	−	121309.i	−0.861654	−	0.356909i
$584$	−70307.8	+	29122.5i	−0.206147	+	0.0853891i
$585$	−25679.3	+	105324.i	−0.0750363	+	0.307761i
$586$	103945.	+	103945.i	0.302698	+	0.302698i
$587$	2953.03	−	2953.03i	0.00857021	−	0.00857021i	−0.702809	−	0.711379i	$-0.748071\pi$
$587$	2953.03	−	2953.03i	0.00857021	−	0.00857021i	0.711379	+	0.702809i	$0.248071\pi$
$588$	13252.6	+	172276.i	0.0383308	+	0.498275i
$589$	22231.7	+	53672.2i	0.0640830	+	0.154710i
$590$	28716.3	−	69327.2i	0.0824943	−	0.199159i
$591$	−22742.2	+	69575.6i	−0.0651116	+	0.199197i
$592$	−31825.7	+	76834.1i	−0.0908102	+	0.219235i
$593$	191665.	+	191665.i	0.545045	+	0.545045i	0.925004	−	0.379958i	$-0.124062\pi$
$593$	191665.	+	191665.i	0.545045	+	0.545045i	−0.379958	+	0.925004i	$0.624062\pi$
$594$	−176216.	+	126609.i	−0.499427	+	0.358832i
$595$	25.9170	−	2060.52i	7.32068e−5	−	0.00582028i
$596$		−	111505.i		−	0.313908i
$597$	−283326.	−	558493.i	−0.794948	−	1.56700i
$598$	119268.	−	287937.i	0.333518	−	0.805185i
$599$	−515158.			−1.43578			−0.717888	−	0.696158i	$-0.754891\pi$
$599$	−515158.			−1.43578			−0.717888	+	0.696158i	$0.754891\pi$
$600$	90164.4	+	77283.2i	0.250457	+	0.214676i
$601$	−46676.3	−	112687.i	−0.129225	−	0.311978i	0.846003	−	0.533178i	$-0.179002\pi$
$601$	−46676.3	−	112687.i	−0.129225	−	0.311978i	−0.975228	+	0.221201i	$0.929002\pi$
$602$	649.358	+	1567.69i	0.00179181	+	0.00432581i
$603$	−82551.7	−	533384.i	−0.227034	−	1.46692i
$604$	117793.	+	117793.i	0.322883	+	0.322883i
$605$	8832.12	+	21322.6i	0.0241298	+	0.0582546i
$606$	360026.	−	27695.7i	0.980367	−	0.0754166i
$607$	127962.	+	53003.8i	0.347300	+	0.143856i	0.549513	−	0.835485i	$-0.314813\pi$
$607$	127962.	+	53003.8i	0.347300	+	0.143856i	−0.202213	+	0.979342i	$0.564813\pi$
$608$	45903.0			0.124175
$609$	−4606.42	+	5374.20i	−0.0124202	+	0.0144904i
$610$	1824.63	−	1824.63i	0.00490361	−	0.00490361i
$611$			372283.i			0.997220i
$612$	185414.	−	26313.2i	0.495040	−	0.0702539i
$613$	−87101.2			−0.231794			−0.115897	−	0.993261i	$-0.536974\pi$
$613$	−87101.2			−0.231794			−0.115897	+	0.993261i	$0.536974\pi$
$614$	−171190.	−	171190.i	−0.454091	−	0.454091i
$615$	48139.3	+	41261.9i	0.127277	+	0.109094i
$616$			2624.03i			0.00691524i
$617$	227481.	−	549189.i	0.597552	−	1.44262i	−0.278517	−	0.960431i	$-0.589843\pi$
$617$	227481.	−	549189.i	0.597552	−	1.44262i	0.876069	−	0.482186i	$-0.160157\pi$
$618$	−11709.1	−	152210.i	−0.0306582	−	0.398536i
$619$	−640535.	+	265318.i	−1.67171	+	0.692445i	−0.998878	−	0.0473492i	$-0.984923\pi$
$619$	−640535.	+	265318.i	−1.67171	+	0.692445i	−0.672833	+	0.739795i	$0.734923\pi$
$620$	8385.48	−	8385.48i	0.0218145	−	0.0218145i
$621$	−62780.0	+	383239.i	−0.162794	+	0.993772i
$622$	138522.	−	57377.6i	0.358045	−	0.148307i
$623$	−794.447	+	329.071i	−0.00204686	+	0.000847839i
$624$	−77536.7	+	90460.1i	−0.199131	+	0.232321i
$625$			313878.i			0.803527i
$626$	−456289.	−	189001.i	−1.16437	−	0.482299i
$627$	−214182.	+	108656.i	−0.544813	+	0.276387i
$628$	−260970.			−0.661716
$629$	−148065.	+	345119.i	−0.374241	+	0.872303i
$630$	−1318.21	−	964.860i	−0.00332126	−	0.00243099i
$631$	−437440.	+	437440.i	−1.09865	+	1.09865i	−0.104081	+	0.994569i	$0.533190\pi$
$631$	−437440.	+	437440.i	−1.09865	+	1.09865i	−0.994569	+	0.104081i	$0.966810\pi$
$632$	144745.	+	59955.3i	0.362384	+	0.150104i
$633$	353786.	+	115642.i	0.882944	+	0.288609i
$634$	−85158.6	−	35273.9i	−0.211861	−	0.0877555i
$635$	−69742.5	+	28888.3i	−0.172962	+	0.0716431i
$636$	216248.	−	16635.3i	0.534611	−	0.0411260i
$637$	−350996.	−	350996.i	−0.865014	−	0.865014i
$638$	150206.	−	150206.i	0.369016	−	0.369016i
$639$	−38624.1	+	158417.i	−0.0945925	+	0.387971i
$640$	−3585.83	−	8656.96i	−0.00875447	−	0.0211351i
$641$	−206848.	+	499375.i	−0.503426	+	1.21538i	0.444181	+	0.895937i	$0.353495\pi$
$641$	−206848.	+	499375.i	−0.503426	+	1.21538i	−0.947607	+	0.319440i	$0.896505\pi$
$642$	284314.	+	92934.0i	0.689807	+	0.225478i
$643$	63978.7	−	154458.i	0.154744	−	0.373585i	−0.827427	−	0.561573i	$-0.810197\pi$
$643$	63978.7	−	154458.i	0.154744	−	0.373585i	0.982171	+	0.187988i	$0.0601965\pi$
$644$	3320.83	+	3320.83i	0.00800710	+	0.00800710i
$645$	30133.8	+	9849.88i	0.0724328	+	0.0236762i
$646$	207264.	+	2606.94i	0.496660	+	0.00624693i
$647$			539710.i			1.28929i	0.764480	+	0.644647i	$0.222996\pi$
$647$			539710.i			1.28929i	−0.764480	+	0.644647i	$0.777004\pi$
$648$	68330.4	−	131799.i	0.162729	−	0.313878i
$649$	−165121.	+	398638.i	−0.392024	+	0.946431i
$650$	−341160.			−0.807478
$651$	1478.70	−	1725.16i	0.00348913	−	0.00407069i
$652$	91332.5	+	220496.i	0.214848	+	0.518688i
$653$	169686.	+	409658.i	0.397941	+	0.960716i	0.988154	+	0.153467i	$0.0490440\pi$
$653$	169686.	+	409658.i	0.397941	+	0.960716i	−0.590212	+	0.807248i	$0.700956\pi$
$654$	219470.	+	432619.i	0.513120	+	1.01146i
$655$	122679.	+	122679.i	0.285948	+	0.285948i
$656$	26665.6	+	64376.5i	0.0619647	+	0.149596i
$657$	−64529.3	+	264667.i	−0.149495	+	0.613152i
$658$	−5182.84	−	2146.80i	−0.0119706	−	0.00495839i
$659$	−502728.			−1.15761			−0.578805	−	0.815466i	$-0.696481\pi$
$659$	−502728.			−1.15761			−0.578805	+	0.815466i	$0.696481\pi$
$660$	37223.0	+	31905.2i	0.0854523	+	0.0732443i
$661$	−119888.	+	119888.i	−0.274394	+	0.274394i	−0.830866	−	0.556473i	$-0.812154\pi$
$661$	−119888.	+	119888.i	−0.274394	+	0.274394i	0.556473	+	0.830866i	$0.312154\pi$
$662$		−	20762.0i		−	0.0473755i
$663$	−355236.	+	404048.i	−0.808147	+	0.919192i
$664$	197987.			0.449055
$665$	−1278.54	−	1278.54i	−0.00289116	−	0.00289116i
$666$	154655.	+	254384.i	0.348670	+	0.573510i
$667$		−	380185.i		−	0.854561i
$668$	−112029.	+	270462.i	−0.251061	+	0.606114i
$669$	−544375.	+	41877.1i	−1.21632	+	0.0935674i
$670$	−112665.	+	46667.5i	−0.250981	+	0.103960i
$671$	−10491.8	+	10491.8i	−0.0233026	+	0.0233026i
$672$	−812.244	−	1601.10i	−0.00179866	−	0.00354551i
$673$	14959.4	−	6196.37i	0.0330281	−	0.0136807i	−0.366108	−	0.930572i	$-0.619310\pi$
$673$	14959.4	−	6196.37i	0.0330281	−	0.0136807i	0.399136	+	0.916892i	$0.369310\pi$
$674$	445530.	−	184545.i	0.980747	−	0.406239i
$675$	413878.	−	97049.6i	0.908374	−	0.213003i
$676$		−	113790.i		−	0.249007i
$677$	−52817.2	−	21877.6i	−0.115239	−	0.0477334i	0.324319	−	0.945948i	$-0.394865\pi$
$677$	−52817.2	−	21877.6i	−0.115239	−	0.0477334i	−0.439558	+	0.898214i	$0.644865\pi$
$678$	−167136.	−	329459.i	−0.363589	−	0.716707i
$679$	3853.28			0.00835779
$680$	−15699.3	−	39292.1i	−0.0339518	−	0.0849743i
$681$	27584.7	+	9016.66i	0.0594805	+	0.0194425i
$682$	−48217.2	+	48217.2i	−0.103665	+	0.103665i
$683$	112244.	+	46493.1i	0.240615	+	0.0996661i	0.499733	−	0.866180i	$-0.333432\pi$
$683$	112244.	+	46493.1i	0.240615	+	0.0996661i	−0.259117	+	0.965846i	$0.583432\pi$
$684$	97053.4	−	132596.i	0.207443	−	0.283412i
$685$	14611.7	+	6052.38i	0.0311401	+	0.0128987i
$686$	13824.6	−	5726.33i	0.0293767	−	0.0121682i
$687$	−60734.1	−	789503.i	−0.128682	−	1.67279i
$688$	24636.9	+	24636.9i	0.0520485	+	0.0520485i
$689$	−440586.	+	440586.i	−0.928094	+	0.928094i
$690$	87485.1	−	6729.96i	0.183754	−	0.0141356i
$691$	−219298.	−	529433.i	−0.459282	−	1.10880i	−0.968689	−	0.248279i	$-0.920135\pi$
$691$	−219298.	−	529433.i	−0.459282	−	1.10880i	0.509407	−	0.860526i	$-0.329865\pi$
$692$	−140679.	+	339630.i	−0.293777	+	0.709240i
$693$	7579.82	+	5548.03i	0.0157831	+	0.0115524i
$694$	−165788.	+	400248.i	−0.344219	+	0.831017i
$695$	−108901.	−	108901.i	−0.225457	−	0.225457i
$696$	−45155.7	+	138145.i	−0.0932168	+	0.285179i
$697$	116746.	+	292192.i	0.240313	+	0.601454i
$698$		−	640210.i		−	1.31405i
$699$	125175.	−	63501.7i	0.256190	−	0.129966i
$700$	1967.33	−	4749.55i	0.00401495	−	0.00969296i
$701$	−677691.			−1.37910			−0.689550	−	0.724238i	$-0.742192\pi$
$701$	−677691.			−1.37910			−0.689550	+	0.724238i	$0.742192\pi$
$702$	97367.9	+	415235.i	0.197579	+	0.842597i
$703$	126100.	+	304432.i	0.255155	+	0.615997i
$704$	20618.8	+	49778.2i	0.0416024	+	0.100437i
$705$	−93470.9	+	47418.3i	−0.188061	+	0.0954042i
$706$	391694.	+	391694.i	0.785846	+	0.785846i
$707$	−5982.00	−	14441.8i	−0.0119676	−	0.0288924i
$708$	−22643.2	−	294347.i	−0.0451723	−	0.587210i
$709$	−607818.	−	251766.i	−1.20915	−	0.500847i	−0.315207	−	0.949023i	$-0.602074\pi$
$709$	−607818.	−	251766.i	−1.20915	−	0.500847i	−0.893946	+	0.448175i	$0.852074\pi$
$710$	36841.3			0.0730833
$711$	479225.	−	291349.i	0.947982	−	0.576333i
$712$	−12485.1	+	12485.1i	−0.0246281	+	0.0246281i
$713$			122042.i			0.240067i
$714$	−3576.57	−	7275.50i	−0.00701569	−	0.0142714i
$715$	−140843.			−0.275500
$716$	−166892.	−	166892.i	−0.325543	−	0.325543i
$717$	200772.	−	234236.i	0.390539	−	0.455632i
$718$		−	277451.i		−	0.538193i
$719$	226932.	−	547862.i	0.438973	−	1.05977i	−0.537331	−	0.843371i	$-0.680567\pi$
$719$	226932.	−	547862.i	0.438973	−	1.05977i	0.976304	−	0.216403i	$-0.0694325\pi$
$720$	−32588.2	−	7945.45i	−0.0628631	−	0.0153269i
$721$	−6105.66	+	2529.05i	−0.0117452	+	0.00486504i
$722$	−132036.	+	132036.i	−0.253290	+	0.253290i
$723$	188373.	−	95562.7i	0.360365	−	0.182815i
$724$	6816.80	−	2823.61i	0.0130048	−	0.00538676i
$725$	−384490.	+	159261.i	−0.731491	+	0.302994i
$726$	68939.5	+	59090.5i	0.130796	+	0.112110i
$727$		−	508874.i		−	0.962813i	−0.876498	−	0.481406i	$-0.840126\pi$
$727$		−	508874.i		−	0.962813i	0.876498	−	0.481406i	$-0.159874\pi$
$728$	4765.13	+	1973.78i	0.00899108	+	0.00372423i
$729$	−236244.	−	476045.i	−0.444534	−	0.895762i
$730$	61550.8			0.115502
$731$	109843.	+	112641.i	0.205559	+	0.210796i
$732$	3154.11	−	9649.39i	0.00588646	−	0.0180085i
$733$	−65147.0	+	65147.0i	−0.121251	+	0.121251i	−0.765129	−	0.643877i	$-0.777325\pi$
$733$	−65147.0	+	65147.0i	−0.121251	+	0.121251i	0.643877	+	0.765129i	$0.277325\pi$
$734$	−390321.	−	161676.i	−0.724486	−	0.300092i
$735$	43419.3	−	132833.i	0.0803727	−	0.245885i
$736$	89090.9	+	36902.6i	0.164467	+	0.0681243i
$737$	647835.	−	268342.i	1.19270	−	0.494031i
$738$	242339.	+	59085.5i	0.444949	+	0.108485i
$739$	69609.5	+	69609.5i	0.127462	+	0.127462i	0.767960	−	0.640498i	$-0.221272\pi$
$739$	69609.5	+	69609.5i	0.127462	+	0.127462i	−0.640498	+	0.767960i	$0.721272\pi$
$740$	47562.9	−	47562.9i	0.0868570	−	0.0868570i
$741$	36207.6	+	470676.i	0.0659423	+	0.857206i
$742$	−3593.06	−	8674.41i	−0.00652614	−	0.0157555i
$743$	−3893.19	+	9398.99i	−0.00705225	+	0.0170256i	−0.927366	−	0.374154i	$-0.877933\pi$
$743$	−3893.19	+	9398.99i	−0.00705225	+	0.0170256i	0.920314	+	0.391180i	$0.127933\pi$
$744$	14495.4	−	44345.8i	0.0261868	−	0.0801136i
$745$	−34512.8	+	83321.3i	−0.0621824	+	0.150122i
$746$	−385325.	−	385325.i	−0.692388	−	0.692388i
$747$	418606.	−	571908.i	0.750178	−	1.02491i
$748$	90272.5	+	225933.i	0.161344	+	0.403810i
$749$		−	12948.9i		−	0.0230818i
$750$	−90027.9	−	177463.i	−0.160050	−	0.315490i
$751$	−88533.9	+	213740.i	−0.156975	+	0.378970i	−0.982727	−	0.185063i	$-0.940751\pi$
$751$	−88533.9	+	213740.i	−0.156975	+	0.378970i	0.825752	+	0.564033i	$0.190751\pi$
$752$	−115188.			−0.203691
$753$	752631.	+	645107.i	1.32737	+	1.13774i
$754$	−159783.	−	385751.i	−0.281053	−	0.678523i
$755$	−51560.6	−	124478.i	−0.0904532	−	0.218373i
$756$	−6342.30	−	1038.96i	−0.0110969	−	0.00181783i
$757$	−415140.	−	415140.i	−0.724440	−	0.724440i	0.245066	−	0.969506i	$-0.421190\pi$
$757$	−415140.	−	415140.i	−0.724440	−	0.724440i	−0.969506	+	0.245066i	$0.921190\pi$
$758$	−74478.2	−	179806.i	−0.129626	−	0.312944i
$759$	−503047.	+	38697.9i	−0.873222	+	0.0671743i
$760$	−34300.5	−	14207.8i	−0.0593846	−	0.0245979i
$761$	184211.			0.318088			0.159044	−	0.987272i	$-0.449159\pi$
$761$	184211.			0.318088			0.159044	+	0.987272i	$0.449159\pi$
$762$	−193274.	+	225489.i	−0.332862	+	0.388342i
$763$	14849.5	−	14849.5i	0.0255072	−	0.0255072i
$764$			199276.i			0.341403i
$765$	−146693.	−	37726.6i	−0.250661	−	0.0644651i
$766$	−338002.			−0.576051
$767$	599706.	+	599706.i	1.01941	+	1.01941i
$768$	−27989.3	−	23990.7i	−0.0474537	−	0.0406743i
$769$		−	291363.i		−	0.492698i	−0.969181	−	0.246349i	$-0.920769\pi$
$769$		−	291363.i		−	0.492698i	0.969181	−	0.246349i	$-0.0792310\pi$
$770$	812.182	−	1960.78i	0.00136985	−	0.00330710i
$771$	−52625.8	−	684101.i	−0.0885299	−	1.15083i
$772$	−139729.	+	57877.8i	−0.234452	+	0.0971131i
$773$	802355.	−	802355.i	1.34279	−	1.34279i	0.449517	−	0.893272i	$-0.351596\pi$
$773$	802355.	−	802355.i	1.34279	−	1.34279i	0.893272	−	0.449517i	$-0.148404\pi$
$774$	123257.	−	19076.4i	0.205745	−	0.0318430i
$775$	123424.	−	51124.1i	0.205493	−	0.0851181i
$776$	73097.4	−	30278.0i	0.121389	−	0.0502809i
$777$	8387.26	−	9785.21i	0.0138924	−	0.0162080i
$778$			134469.i			0.222158i
$779$	255072.	+	105654.i	0.420328	+	0.174106i
$780$	85937.5	−	43596.5i	0.141252	−	0.0716577i
$781$	−211841.			−0.347302
$782$	400173.	+	171685.i	0.654387	+	0.280749i
$783$	303576.	+	422521.i	0.495158	+	0.689167i
$784$	108602.	−	108602.i	0.176687	−	0.176687i
$785$	195007.	+	80774.7i	0.316455	+	0.131080i
$786$	648774.	+	212066.i	1.05014	+	0.343261i
$787$	−555422.	−	230064.i	−0.896755	−	0.371448i	−0.113784	−	0.993506i	$-0.536297\pi$
$787$	−555422.	−	230064.i	−0.896755	−	0.371448i	−0.782972	+	0.622057i	$0.786297\pi$
$788$	60112.2	−	24899.3i	0.0968078	−	0.0400991i
$789$	−309952.	+	23843.6i	−0.497898	+	0.0383017i
$790$	−89602.1	−	89602.1i	−0.143570	−	0.143570i
$791$	−11308.6	+	11308.6i	−0.0180740	+	0.0180740i
$792$	187385.	+	45687.0i	0.298734	+	0.0728354i
$793$	11160.8	+	26944.6i	0.0177480	+	0.0428474i
$794$	−90881.7	+	219408.i	−0.144157	+	0.348025i
$795$	−166738.	−	54501.8i	−0.263816	−	0.0862337i
$796$	−213027.	+	514292.i	−0.336208	+	0.811678i
$797$	863713.	+	863713.i	1.35973	+	1.35973i	0.874244	+	0.485486i	$0.161357\pi$
$797$	863713.	+	863713.i	1.35973	+	1.35973i	0.485486	+	0.874244i	$0.338643\pi$
$798$	−6761.44	−	2210.12i	−0.0106178	−	0.00347064i
$799$	−520106.	−	6541.84i	−0.814701	−	0.0102472i
$800$		−	105558.i		−	0.164935i
$801$	9667.22	+	62461.9i	0.0150673	+	0.0973532i
$802$	250964.	−	605880.i	0.390178	−	0.941972i
$803$	−353922.			−0.548879
$804$	−312225.	+	364265.i	−0.483009	+	0.563515i
$805$	−1453.61	−	3509.32i	−0.00224313	−	0.00541540i
$806$	51291.7	+	123829.i	0.0789546	+	0.190613i
$807$	217546.	+	428827.i	0.334045	+	0.658468i
$808$	−226959.	−	226959.i	−0.347636	−	0.347636i
$809$	−313092.	−	755872.i	−0.478383	−	1.15492i	−0.960367	−	0.278738i	$-0.910084\pi$
$809$	−313092.	−	755872.i	−0.478383	−	1.15492i	0.481984	−	0.876180i	$-0.339916\pi$
$810$	−91853.2	+	77335.8i	−0.139999	+	0.117872i
$811$	96076.9	+	39796.3i	0.146075	+	0.0605064i	0.454523	−	0.890735i	$-0.349810\pi$
$811$	96076.9	+	39796.3i	0.146075	+	0.0605064i	−0.308448	+	0.951241i	$0.599810\pi$
$812$	6291.75			0.00954244
$813$	804305.	+	689399.i	1.21686	+	1.04301i
$814$	−273491.	+	273491.i	−0.412757	+	0.412757i
$815$		−	193033.i		−	0.290613i
$816$	−125017.	−	109914.i	−0.187754	−	0.165072i
$817$	138050.			0.206820
$818$	502663.	+	502663.i	0.751226	+	0.751226i
$819$	15776.5	−	9591.44i	0.0235203	−	0.0142993i
$820$		−	56358.2i		−	0.0838165i
$821$	359879.	−	868825.i	0.533913	−	1.28898i	−0.395000	−	0.918681i	$-0.629256\pi$
$821$	359879.	−	868825.i	0.533913	−	1.28898i	0.928913	−	0.370298i	$-0.120744\pi$
$822$	62038.0	−	4772.39i	0.0918151	−	0.00706306i
$823$	857114.	−	355028.i	1.26543	−	0.524159i	0.353859	−	0.935299i	$-0.384869\pi$
$823$	857114.	−	355028.i	1.26543	−	0.524159i	0.911572	+	0.411140i	$0.134869\pi$
$824$	−95952.9	+	95952.9i	−0.141320	+	0.141320i
$825$	249864.	+	492533.i	0.367110	+	0.723648i
$826$	−11807.2	+	4890.72i	−0.0173057	+	0.00716824i
$827$	199087.	−	82464.4i	0.291092	−	0.120574i	−0.232359	−	0.972630i	$-0.574644\pi$
$827$	199087.	−	82464.4i	0.291092	−	0.120574i	0.523451	+	0.852056i	$0.324644\pi$
$828$	294964.	−	179326.i	0.430237	−	0.261566i
$829$			1.25657e6i			1.82843i	0.405229	+	0.914215i	$0.367192\pi$
$829$			1.25657e6i			1.82843i	−0.405229	+	0.914215i	$0.632808\pi$
$830$	−147944.	−	61280.2i	−0.214753	−	0.0889537i
$831$	285115.	+	562019.i	0.412875	+	0.813858i
$832$	105905.			0.152992
$833$	496534.	−	484199.i	0.715582	−	0.697805i
$834$	−575913.	−	188249.i	−0.827989	−	0.270646i
$835$	167426.	−	167426.i	0.240131	−	0.240131i
$836$	197231.	+	81695.8i	0.282204	+	0.116893i
$837$	−97450.3	−	135633.i	−0.139102	−	0.193603i
$838$	−613646.	−	254181.i	−0.873836	−	0.361955i
$839$	−107060.	+	44345.8i	−0.152091	+	0.0629983i	−0.457431	−	0.889245i	$-0.651230\pi$
$839$	−107060.	+	44345.8i	−0.152091	+	0.0629983i	0.305339	+	0.952244i	$0.401230\pi$
$840$	111.375	+	1447.81i	0.000157845	+	0.00205188i
$841$	139968.	+	139968.i	0.197897	+	0.197897i
$842$	596553.	−	596553.i	0.841443	−	0.841443i
$843$	−145601.	+	11200.7i	−0.204885	+	0.0157612i
$844$	−126611.	−	305666.i	−0.177740	−	0.429103i
$845$	−35220.1	+	85028.8i	−0.0493261	+	0.119084i
$846$	−243545.	+	332735.i	−0.340281	+	0.464898i
$847$	1504.21	−	3631.49i	0.00209673	−	0.00506195i
$848$	−136322.	−	136322.i	−0.189572	−	0.189572i
$849$	343690.	−	1.05145e6i	0.476817	−	1.45873i
$850$	5994.93	−	476624.i	0.00829748	−	0.659688i
$851$			692231.i			0.955855i
$852$	129258.	−	65573.3i	0.178065	−	0.0903333i
$853$	−393732.	+	950553.i	−0.541131	+	1.30641i	0.382794	+	0.923834i	$0.374962\pi$
$853$	−393732.	+	950553.i	−0.541131	+	1.30641i	−0.923925	+	0.382573i	$0.875038\pi$
$854$	−439.476			−0.000602587
$855$	−113563.	+	69041.5i	−0.155348	+	0.0944448i
$856$	−101749.	−	245643.i	−0.138861	−	0.335241i
$857$	−498525.	−	1.20355e6i	−0.678774	−	1.63871i	−0.766252	−	0.642540i	$-0.777881\pi$
$857$	−498525.	−	1.20355e6i	−0.678774	−	1.63871i	0.0874777	−	0.996166i	$-0.472119\pi$
$858$	−494148.	+	250684.i	−0.671247	+	0.340527i
$859$	622079.	+	622079.i	0.843062	+	0.843062i	0.989256	−	0.146194i	$-0.0467024\pi$
$859$	622079.	+	622079.i	0.843062	+	0.843062i	−0.146194	+	0.989256i	$0.546702\pi$
$860$	−10784.1	−	26035.2i	−0.0145810	−	0.0352017i
$861$	−828.231	−	10766.5i	−0.00111724	−	0.0145233i
$862$	−499696.	−	206981.i	−0.672499	−	0.278558i
$863$	56449.5			0.0757947			0.0378973	−	0.999282i	$-0.487934\pi$
$863$	56449.5			0.0757947			0.0378973	+	0.999282i	$0.487934\pi$
$864$	−128478.	+	30126.7i	−0.172108	+	0.0403574i
$865$	210242.	−	210242.i	0.280988	−	0.280988i
$866$			456856.i			0.609177i
$867$	−558242.	−	503391.i	−0.742650	−	0.669679i
$868$	−2019.70			−0.00268070
$869$	515220.	+	515220.i	0.682265	+	0.682265i
$870$	76500.5	−	89251.3i	0.101071	−	0.117917i
$871$		−	1.37829e6i		−	1.81678i
$872$	165014.	−	398380.i	0.217015	−	0.523920i
$873$	67089.6	−	275168.i	0.0880292	−	0.361051i
$874$	352995.	−	146215.i	0.462111	−	0.191413i
$875$	−6091.36	+	6091.36i	−0.00795606	+	0.00795606i
$876$	215952.	−	109553.i	0.281416	−	0.142764i
$877$	−1.22912e6	+	509119.i	−1.59807	+	0.661942i	−0.991141	−	0.132814i	$-0.957599\pi$
$877$	−1.22912e6	+	509119.i	−1.59807	+	0.661942i	−0.606929	+	0.794756i	$0.707599\pi$
$878$	−22317.6	+	9244.27i	−0.0289507	+	0.0119918i
$879$	−355146.	−	304408.i	−0.459652	−	0.393984i
$880$		−	43578.2i		−	0.0562735i
$881$	793287.	+	328590.i	1.02207	+	0.423353i	0.829842	−	0.557998i	$-0.188430\pi$
$881$	793287.	+	328590.i	1.02207	+	0.423353i	0.192223	+	0.981351i	$0.438430\pi$
$882$	−84090.8	−	543328.i	−0.108096	−	0.698434i
$883$	1.29218e6			1.65730			0.828651	−	0.559765i	$-0.189109\pi$
$883$	1.29218e6			1.65730			0.828651	+	0.559765i	$0.189109\pi$
$884$	478188.	+	6014.59i	0.611919	+	0.00769664i
$885$	−74185.5	+	226957.i	−0.0947180	+	0.289772i
$886$	−348730.	+	348730.i	−0.444244	+	0.444244i
$887$	−1.43359e6	−	593814.i	−1.82213	−	0.754750i	−0.974584	−	0.224023i	$-0.928081\pi$
$887$	−1.43359e6	−	593814.i	−1.82213	−	0.754750i	−0.847543	−	0.530727i	$-0.821919\pi$
$888$	82218.4	−	251532.i	0.104266	−	0.318982i
$889$	11878.0	+	4920.01i	0.0150293	+	0.00622533i
$890$	13193.7	−	5465.00i	0.0166566	−	0.00689938i
$891$	528164.	−	444687.i	0.665293	−	0.560144i
$892$	343172.	+	343172.i	0.431303	+	0.431303i
$893$	−322723.	+	322723.i	−0.404694	+	0.404694i
$894$	27213.9	+	353763.i	0.0340499	+	0.442626i
$895$	73052.4	+	176364.i	0.0911987	+	0.220173i
$896$	−610.708	+	1474.38i	−0.000760708	+	0.00183651i
$897$	−308115.	+	942620.i	−0.382938	+	1.17153i
$898$	130488.	−	315025.i	0.161814	−	0.390655i
$899$	115613.	+	115613.i	0.143049	+	0.143049i
$900$	−304918.	−	223184.i	−0.376442	−	0.275536i
$901$	−607788.	−	623272.i	−0.748690	−	0.767764i
$902$			324065.i			0.398307i
$903$	−2442.77	−	4815.18i	−0.00299576	−	0.00590523i
$904$	−125666.	+	303384.i	−0.153773	+	0.371241i
$905$	−5967.75			−0.00728640
$906$	−402458.	−	344962.i	−0.490303	−	0.420256i
$907$	139027.	+	335642.i	0.169000	+	0.408001i	0.985575	−	0.169237i	$-0.0541304\pi$
$907$	139027.	+	335642.i	0.169000	+	0.408001i	−0.816576	+	0.577238i	$0.804130\pi$
$908$	−9871.87	−	23832.8i	−0.0119737	−	0.0289070i
$909$	−1.13546e6	+	175735.i	−1.37418	+	0.212682i
$910$	−2949.78	−	2949.78i	−0.00356210	−	0.00356210i
$911$	−379588.	−	916407.i	−0.457378	−	1.10421i	−0.969455	−	0.245269i	$-0.921124\pi$
$911$	−379588.	−	916407.i	−0.457378	−	1.10421i	0.512076	−	0.858940i	$-0.328876\pi$
$912$	−145632.	+	11203.0i	−0.175092	+	0.0134693i
$913$	850688.	+	352367.i	1.02054	+	0.422720i
$914$	399765.			0.478533
$915$	−5343.53	+	6234.17i	−0.00638243	+	0.00744622i
$916$	−497700.	+	497700.i	−0.593167	+	0.593167i
$917$		−	29548.0i		−	0.0351390i
$918$	−581824.	+	128733.i	−0.690409	+	0.152759i
$919$	538778.			0.637939			0.318969	−	0.947765i	$-0.396663\pi$
$919$	538778.			0.637939			0.318969	+	0.947765i	$0.396663\pi$
$920$	−55150.3	−	55150.3i	−0.0651587	−	0.0651587i
$921$	584901.	+	501339.i	0.689545	+	0.591034i
$922$		−	531184.i		−	0.624861i
$923$	−159345.	+	384694.i	−0.187041	+	0.451556i
$924$	−640.418	−	8325.01i	−0.000750101	−	0.00975082i
$925$	700070.	−	289979.i	0.818198	−	0.338909i
$926$	−683484.	+	683484.i	−0.797088	+	0.797088i
$927$	74296.7	+	480046.i	0.0864589	+	0.558629i
$928$	119355.	−	49438.7i	0.138595	−	0.0574078i
$929$	−506286.	+	209711.i	−0.586630	+	0.242990i	−0.656200	−	0.754587i	$-0.727837\pi$
$929$	−506286.	+	209711.i	−0.586630	+	0.242990i	0.0695698	+	0.997577i	$0.477837\pi$
$930$	−24557.3	+	28650.4i	−0.0283932	+	0.0331257i
$931$		−	608539.i		−	0.702084i
$932$	−115268.	−	47745.5i	−0.132702	−	0.0549669i
$933$	−425472.	+	215844.i	−0.488773	+	0.247957i
$934$	899772.			1.03143
$935$	2474.92	−	196767.i	0.00283098	−	0.225076i
$936$	223916.	−	305918.i	0.255584	−	0.349183i
$937$	297245.	−	297245.i	0.338560	−	0.338560i	−0.517265	−	0.855825i	$-0.673050\pi$
$937$	297245.	−	297245.i	0.338560	−	0.338560i	0.855825	+	0.517265i	$0.173050\pi$
$938$	19188.2	+	7948.02i	0.0218087	+	0.00903344i
$939$	1.49375e6	+	488265.i	1.69414	+	0.553764i
$940$	86073.4	+	35652.8i	0.0974122	+	0.0403494i
$941$	−1.30185e6	+	539244.i	−1.47022	+	0.608984i	−0.966909	−	0.255122i	$-0.917884\pi$
$941$	−1.30185e6	+	539244.i	−1.47022	+	0.608984i	−0.503309	+	0.864106i	$0.667884\pi$
$942$	827956.	−	63692.1i	0.933051	−	0.0717768i
$943$	410119.	+	410119.i	0.461197	+	0.461197i
$944$	−185555.	+	185555.i	−0.208223	+	0.208223i
$945$	4417.64	+	2739.40i	0.00494683	+	0.00306755i
$946$	62009.7	+	149705.i	0.0692910	+	0.167283i
$947$	−348785.	+	842041.i	−0.388917	+	0.938930i	0.601252	+	0.799059i	$0.294669\pi$
$947$	−348785.	+	842041.i	−0.388917	+	0.938930i	−0.990170	+	0.139870i	$0.955331\pi$
$948$	−473852.	−	154888.i	−0.527261	−	0.172346i
$949$	−266218.	+	642708.i	−0.295601	+	0.713643i
$950$	−295742.	−	295742.i	−0.327692	−	0.327692i
$951$	278784.	+	91126.4i	0.308252	+	0.100759i
$952$	−2841.25	+	6622.54i	−0.00313498	+	0.00730719i
$953$		−	965731.i		−	1.06334i	−0.846953	−	0.531668i	$-0.821565\pi$
$953$		−	965731.i		−	1.06334i	0.846953	−	0.531668i	$-0.178435\pi$
$954$	−682009.	+	105554.i	−0.749365	+	0.115979i
$955$	61679.2	−	148907.i	0.0676289	−	0.163271i
$956$	−274227.			−0.300051
$957$	−439885.	+	513203.i	−0.480302	+	0.560357i
$958$	−43406.9	−	104793.i	−0.0472963	−	0.114183i
$959$	−1030.79	−	2488.55i	−0.00112081	−	0.00270588i
$960$	13489.2	+	26590.0i	0.0146368	+	0.0288520i
$961$	615915.	+	615915.i	0.666921	+	0.666921i
$962$	290930.	+	702366.i	0.314368	+	0.758951i
$963$	−924697.	−	225454.i	−0.997119	−	0.243111i
$964$	−173465.	−	71851.5i	−0.186663	−	0.0773182i
$965$	122326.			0.131360
$966$	−11346.2	−	9725.22i	−0.0121589	−	0.0104219i
$967$	296101.	−	296101.i	0.316656	−	0.316656i	−0.530825	−	0.847481i	$-0.678118\pi$
$967$	296101.	−	296101.i	0.316656	−	0.316656i	0.847481	+	0.530825i	$0.178118\pi$
$968$		−	80709.6i		−	0.0861340i
$969$	−658204.	+	42313.9i	−0.700992	+	0.0450646i
$970$	−63992.9			−0.0680124
$971$	170099.	+	170099.i	0.180411	+	0.180411i	0.791535	−	0.611124i	$-0.209282\pi$
$971$	170099.	+	170099.i	0.180411	+	0.180411i	−0.611124	+	0.791535i	$0.709282\pi$
$972$	−184619.	+	434822.i	−0.195409	+	0.460234i
$973$			26229.6i			0.0277055i
$974$	−307101.	+	741407.i	−0.323715	+	0.781518i
$975$	1.08237e6	−	83263.1i	1.13858	−	0.0875877i
$976$	−8336.93	+	3453.27i	−0.00875198	+	0.00362519i
$977$	−955295.	+	955295.i	−1.00080	+	1.00080i	−0.000802368		1.00000i	$0.500255\pi$
$977$	−955295.	+	955295.i	−1.00080	+	1.00080i	−1.00000		0.000802368i	$0.999745\pi$
$978$	−343576.	−	677257.i	−0.359208	−	0.708070i
$979$	−75864.8	+	31424.2i	−0.0791543	+	0.0327868i
$980$	−114766.	+	47537.6i	−0.119498	+	0.0494977i
$981$	−801876.	−	1.31897e6i	−0.833238	−	1.37055i
$982$			1.08335e6i			1.12343i
$983$	178319.	+	73862.1i	0.184540	+	0.0764389i	0.473040	−	0.881041i	$-0.343157\pi$
$983$	178319.	+	73862.1i	0.184540	+	0.0764389i	−0.288500	+	0.957480i	$0.593157\pi$
$984$	−100311.	−	197733.i	−0.103600	−	0.204216i
$985$	−52625.1			−0.0542401
$986$	541730.	−	216450.i	0.557223	−	0.222641i
$987$	16967.1	+	5546.05i	0.0174170	+	0.00569311i
$988$	296712.	−	296712.i	0.303964	−	0.303964i
$989$	267934.	+	110982.i	0.273928	+	0.113465i
$990$	−125881.	−	92138.1i	−0.128437	−	0.0940088i
$991$	−970877.	−	402151.i	−0.988592	−	0.409488i	−0.170990	−	0.985273i	$-0.554697\pi$
$991$	−970877.	−	402151.i	−0.988592	−	0.409488i	−0.817602	+	0.575784i	$0.804697\pi$
$992$	−38314.1	+	15870.2i	−0.0389345	+	0.0161272i
$993$	5067.16	+	65869.8i	0.00513886	+	0.0668018i
$994$	−4436.74	−	4436.74i	−0.00449046	−	0.00449046i
$995$	318365.	−	318365.i	0.321572	−	0.321572i
$996$	−628133.	+	48320.4i	−0.633189	+	0.0487093i
$997$	−451376.	−	1.08972e6i	−0.454097	−	1.09629i	−0.970750	−	0.240092i	$-0.922822\pi$
$997$	−451376.	−	1.08972e6i	−0.454097	−	1.09629i	0.516653	−	0.856195i	$-0.327178\pi$
$998$	−481228.	+	1.16179e6i	−0.483159	+	1.16645i
$999$	−552743.	−	769315.i	−0.553851	−	0.770856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	102.5.g.d.59.4	yes	44
3.2	odd	2		102.5.g.c.59.11	✓	44
17.15	even	8		102.5.g.c.83.11	yes	44
51.32	odd	8	inner	102.5.g.d.83.4	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.5.g.c.59.11	✓	44	3.2	odd	2
102.5.g.c.83.11	yes	44	17.15	even	8
102.5.g.d.59.4	yes	44	1.1	even	1	trivial
102.5.g.d.83.4	yes	44	51.32	odd	8	inner

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:	\( N \)	\(=\)	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	102.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} +(-6.83333 - 5.85710i) q^{3} +8.00000i q^{4} +(2.47614 - 5.97792i) q^{5} +(-1.95247 - 25.3809i) q^{6} +(-1.01811 + 0.421715i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(12.3889 + 80.0470i) q^{9} +(16.9081 - 7.00357i) q^{10} +(-97.2231 + 40.2711i) q^{11} +(46.8568 - 54.6667i) q^{12} +206.845i q^{13} +(-2.87965 - 1.19279i) q^{14} +(-51.9335 + 26.3462i) q^{15} -64.0000 q^{16} +(-288.977 - 3.63472i) q^{17} +(-135.316 + 184.872i) q^{18} +(-179.308 + 179.308i) q^{19} +(47.8234 + 19.8091i) q^{20} +(9.42711 + 3.08145i) q^{21} +(-274.989 - 113.904i) q^{22} +(-492.162 + 203.860i) q^{23} +(203.047 - 15.6198i) q^{24} +(412.337 + 412.337i) q^{25} +(-413.690 + 413.690i) q^{26} +(384.186 - 619.550i) q^{27} +(-3.37372 - 8.14488i) q^{28} +(-273.113 + 659.352i) q^{29} +(-156.559 - 51.1747i) q^{30} +(87.6713 - 211.657i) q^{31} +(-128.000 - 128.000i) q^{32} +(900.230 + 294.259i) q^{33} +(-570.685 - 585.224i) q^{34} +7.13041i q^{35} +(-640.376 + 99.1108i) q^{36} +(497.277 - 1200.53i) q^{37} -717.234 q^{38} +(1211.51 - 1413.44i) q^{39} +(56.0286 + 135.265i) q^{40} +(-416.650 - 1005.88i) q^{41} +(12.6913 + 25.0171i) q^{42} +(-384.951 - 384.951i) q^{43} +(-322.169 - 777.785i) q^{44} +(509.191 + 124.148i) q^{45} +(-1392.04 - 576.604i) q^{46} +1799.82 q^{47} +(437.333 + 374.854i) q^{48} +(-1696.90 + 1696.90i) q^{49} +1649.35i q^{50} +(1953.39 + 1717.40i) q^{51} -1654.76 q^{52} +(2130.03 + 2130.03i) q^{53} +(2007.47 - 470.729i) q^{54} +680.909i q^{55} +(9.54232 - 23.0372i) q^{56} +(2275.50 - 175.047i) q^{57} +(-1864.93 + 772.479i) q^{58} +(2899.30 - 2899.30i) q^{59} +(-210.769 - 415.468i) q^{60} +(130.265 - 53.9573i) q^{61} +(598.657 - 247.972i) q^{62} +(-46.3702 - 76.2720i) q^{63} -512.000i q^{64} +(1236.50 + 512.176i) q^{65} +(1211.94 + 2388.98i) q^{66} -6663.38 q^{67} +(29.0778 - 2311.82i) q^{68} +(4557.14 + 1489.60i) q^{69} +(-14.2608 + 14.2608i) q^{70} +(1859.82 + 770.361i) q^{71} +(-1478.97 - 1082.53i) q^{72} +(3107.20 + 1287.04i) q^{73} +(3395.62 - 1406.51i) q^{74} +(-402.539 - 5232.74i) q^{75} +(-1434.47 - 1434.47i) q^{76} +(82.0009 - 82.0009i) q^{77} +(5249.90 - 403.859i) q^{78} +(-2649.68 - 6396.88i) q^{79} +(-158.473 + 382.587i) q^{80} +(-6254.03 + 1983.38i) q^{81} +(1178.47 - 2845.07i) q^{82} +(-6187.08 - 6187.08i) q^{83} +(-24.6516 + 75.4169i) q^{84} +(-737.275 + 1718.48i) q^{85} -1539.80i q^{86} +(5728.16 - 2905.93i) q^{87} +(911.232 - 2199.91i) q^{88} +780.316 q^{89} +(770.087 + 1266.68i) q^{90} +(-87.2296 - 210.591i) q^{91} +(-1630.88 - 3937.30i) q^{92} +(-1838.78 + 932.825i) q^{93} +(3599.64 + 3599.64i) q^{94} +(627.900 + 1515.88i) q^{95} +(124.958 + 1624.37i) q^{96} +(-3230.48 - 1338.11i) q^{97} -6787.62 q^{98} +(-4428.07 - 7283.50i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 88 q^{2} - 4 q^{3} + 72 q^{5} - 40 q^{6} + 132 q^{7} - 704 q^{8} + 324 q^{9} + 384 q^{10} - 616 q^{11} - 128 q^{12} + 416 q^{14} - 908 q^{15} - 2816 q^{16} + 424 q^{17} + 1016 q^{18} + 568 q^{19}+ \cdots + 91704 q^{99}+O(q^{100}) \) 44 * q + 88 * q^2 - 4 * q^3 + 72 * q^5 - 40 * q^6 + 132 * q^7 - 704 * q^8 + 324 * q^9 + 384 * q^10 - 616 * q^11 - 128 * q^12 + 416 * q^14 - 908 * q^15 - 2816 * q^16 + 424 * q^17 + 1016 * q^18 + 568 * q^19 + 960 * q^20 + 1020 * q^21 + 424 * q^22 + 332 * q^23 - 192 * q^24 + 1888 * q^25 - 1008 * q^26 - 436 * q^27 + 608 * q^28 - 6688 * q^29 - 2000 * q^30 - 1428 * q^31 - 5632 * q^32 + 2224 * q^33 + 512 * q^34 + 1472 * q^36 + 296 * q^37 + 2272 * q^38 - 3720 * q^39 + 768 * q^40 + 4592 * q^41 + 3328 * q^42 - 228 * q^43 + 6624 * q^44 + 8228 * q^45 + 1872 * q^46 + 10712 * q^47 + 256 * q^48 + 5304 * q^49 - 3984 * q^51 - 4032 * q^52 - 5656 * q^53 - 9288 * q^54 - 896 * q^56 - 13364 * q^57 - 11472 * q^58 + 3620 * q^59 - 736 * q^60 - 10448 * q^61 - 3536 * q^62 + 28248 * q^63 - 13760 * q^65 + 12952 * q^66 - 18584 * q^67 - 1344 * q^68 + 6500 * q^69 - 9664 * q^70 + 36660 * q^71 - 2240 * q^72 + 18008 * q^73 - 144 * q^74 + 30268 * q^75 + 4544 * q^76 - 5704 * q^77 - 22576 * q^78 - 7324 * q^79 - 4608 * q^80 - 33668 * q^81 + 11160 * q^82 - 12620 * q^83 + 5152 * q^84 - 10896 * q^85 + 23860 * q^87 + 23104 * q^88 - 5040 * q^89 - 8784 * q^90 + 52368 * q^91 + 4832 * q^92 - 1304 * q^93 + 21424 * q^94 + 16032 * q^95 + 2560 * q^96 - 40164 * q^97 + 21216 * q^98 + 91704 * q^99

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