LMFDB - Embedded newform 92.5.c.a.47.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,5,Mod(47,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("92.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	92.c (of order $2$, degree $1$, 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:	$9.51003660371$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.6
Character	$\chi$	$=$	92.47
Dual form			92.5.c.a.47.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.73586 + 1.42945i) q^{2} +15.9813i q^{3} +(11.9134 - 10.6804i) q^{4} +10.8136 q^{5} +(-22.8444 - 59.7040i) q^{6} -78.4065i q^{7} +(-29.2396 + 56.9302i) q^{8} -174.403 q^{9} +(-40.3982 + 15.4575i) q^{10} -226.229i q^{11} +(170.687 + 190.391i) q^{12} -158.653 q^{13} +(112.078 + 292.916i) q^{14} +172.816i q^{15} +(27.8566 - 254.480i) q^{16} -19.7119 q^{17} +(651.544 - 249.299i) q^{18} -360.187i q^{19} +(128.826 - 115.494i) q^{20} +1253.04 q^{21} +(323.382 + 845.161i) q^{22} +110.304i q^{23} +(-909.819 - 467.288i) q^{24} -508.066 q^{25} +(592.707 - 226.786i) q^{26} -1492.70i q^{27} +(-837.415 - 934.085i) q^{28} -106.243 q^{29} +(-247.031 - 645.616i) q^{30} +78.4095i q^{31} +(259.697 + 990.522i) q^{32} +3615.44 q^{33} +(73.6410 - 28.1771i) q^{34} -847.856i q^{35} +(-2077.72 + 1862.70i) q^{36} -1232.29 q^{37} +(514.867 + 1345.61i) q^{38} -2535.49i q^{39} +(-316.186 + 615.620i) q^{40} +1831.67 q^{41} +(-4681.18 + 1791.15i) q^{42} +2735.12i q^{43} +(-2416.22 - 2695.15i) q^{44} -1885.92 q^{45} +(-157.674 - 412.081i) q^{46} +1408.79i q^{47} +(4066.92 + 445.185i) q^{48} -3746.57 q^{49} +(1898.07 - 726.253i) q^{50} -315.022i q^{51} +(-1890.10 + 1694.49i) q^{52} -1971.81 q^{53} +(2133.73 + 5576.51i) q^{54} -2446.35i q^{55} +(4463.69 + 2292.57i) q^{56} +5756.26 q^{57} +(396.908 - 151.868i) q^{58} -2430.12i q^{59} +(1845.75 + 2058.82i) q^{60} -2393.48 q^{61} +(-112.082 - 292.927i) q^{62} +13674.3i q^{63} +(-2386.09 - 3329.23i) q^{64} -1715.61 q^{65} +(-13506.8 + 5168.07i) q^{66} -4169.97i q^{67} +(-234.835 + 210.532i) q^{68} -1762.81 q^{69} +(1211.97 + 3167.48i) q^{70} -9545.49i q^{71} +(5099.46 - 9928.77i) q^{72} +3022.12 q^{73} +(4603.68 - 1761.50i) q^{74} -8119.56i q^{75} +(-3846.95 - 4291.03i) q^{76} -17737.8 q^{77} +(3624.35 + 9472.24i) q^{78} +4699.18i q^{79} +(301.230 - 2751.84i) q^{80} +9728.64 q^{81} +(-6842.88 + 2618.28i) q^{82} -4958.29i q^{83} +(14927.9 - 13383.0i) q^{84} -213.157 q^{85} +(-3909.70 - 10218.0i) q^{86} -1697.90i q^{87} +(12879.3 + 6614.85i) q^{88} +2141.67 q^{89} +(7045.54 - 2695.82i) q^{90} +12439.4i q^{91} +(1178.10 + 1314.09i) q^{92} -1253.09 q^{93} +(-2013.79 - 5263.04i) q^{94} -3894.91i q^{95} +(-15829.8 + 4150.30i) q^{96} +6854.24 q^{97} +(13996.7 - 5355.53i) q^{98} +39454.9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 24 q^{5} + 33 q^{6} - 27 q^{8} - 1300 q^{9} - 46 q^{10} + 145 q^{12} + 472 q^{13} - 264 q^{14} + 272 q^{16} - 648 q^{17} + 1313 q^{18} + 324 q^{20} - 288 q^{21} + 796 q^{22} - 1028 q^{24} + 5604 q^{25}+ \cdots + 57204 q^{98}+O(q^{100}) $ 44 * q + 24 * q^5 + 33 * q^6 - 27 * q^8 - 1300 * q^9 - 46 * q^10 + 145 * q^12 + 472 * q^13 - 264 * q^14 + 272 * q^16 - 648 * q^17 + 1313 * q^18 + 324 * q^20 - 288 * q^21 + 796 * q^22 - 1028 * q^24 + 5604 * q^25 - 3015 * q^26 - 510 * q^28 - 840 * q^29 + 1390 * q^30 + 4200 * q^32 + 320 * q^33 - 4302 * q^34 - 3741 * q^36 - 680 * q^37 + 5940 * q^38 - 626 * q^40 + 7320 * q^41 + 1320 * q^42 - 378 * q^44 - 3240 * q^45 - 8813 * q^48 - 19444 * q^49 - 6960 * q^50 + 1519 * q^52 + 4152 * q^53 - 14405 * q^54 + 13026 * q^56 + 3840 * q^57 + 6771 * q^58 - 180 * q^60 + 6360 * q^61 + 9309 * q^62 - 12765 * q^64 - 15792 * q^65 - 5610 * q^66 - 5484 * q^68 + 4236 * q^70 + 39063 * q^72 - 2888 * q^73 + 43854 * q^74 - 13712 * q^76 + 4320 * q^77 + 18907 * q^78 + 12174 * q^80 + 31628 * q^81 - 31507 * q^82 - 16642 * q^84 - 1904 * q^85 - 25470 * q^86 + 540 * q^88 - 9768 * q^89 - 42044 * q^90 - 11136 * q^93 - 2219 * q^94 + 24435 * q^96 - 3752 * q^97 + 57204 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$1$	$-1$

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 $

$2$	−3.73586	+	1.42945i	−0.933966	+	0.357362i
$2$	−3.73586	+	1.42945i	−0.933966	+	0.357362i
$3$			15.9813i			1.77570i	0.460131	+	0.887851i	$0.347802\pi$
$3$			15.9813i			1.77570i	−0.460131	+	0.887851i	$0.652198\pi$
$4$	11.9134	−	10.6804i	0.744585	−	0.667527i
$5$	10.8136			0.432544			0.216272	−	0.976333i	$-0.430610\pi$
$5$	10.8136			0.432544			0.216272	+	0.976333i	$0.430610\pi$
$6$	−22.8444	−	59.7040i	−0.634568	−	1.65845i
$7$		−	78.4065i		−	1.60013i	−0.599912	−	0.800066i	$-0.704798\pi$
$7$		−	78.4065i		−	1.60013i	0.599912	−	0.800066i	$-0.295202\pi$
$8$	−29.2396	+	56.9302i	−0.456869	+	0.889534i
$9$	−174.403			−2.15312
$10$	−40.3982	+	15.4575i	−0.403982	+	0.154575i
$11$		−	226.229i		−	1.86966i	−0.355094	−	0.934831i	$-0.615551\pi$
$11$		−	226.229i		−	1.86966i	0.355094	−	0.934831i	$-0.384449\pi$
$12$	170.687	+	190.391i	1.18533	+	1.32216i
$13$	−158.653			−0.938777			−0.469389	−	0.882992i	$-0.655526\pi$
$13$	−158.653			−0.938777			−0.469389	+	0.882992i	$0.655526\pi$
$14$	112.078	+	292.916i	0.571826	+	1.49447i
$15$			172.816i			0.768069i
$16$	27.8566	−	254.480i	0.108815	−	0.994062i
$17$	−19.7119			−0.0682073			−0.0341036	−	0.999418i	$-0.510858\pi$
$17$	−19.7119			−0.0682073			−0.0341036	+	0.999418i	$0.510858\pi$
$18$	651.544	−	249.299i	2.01094	−	0.769442i
$19$		−	360.187i		−	0.997747i	−0.866675	−	0.498873i	$-0.833747\pi$
$19$		−	360.187i		−	0.997747i	0.866675	−	0.498873i	$-0.166253\pi$
$20$	128.826	−	115.494i	0.322066	−	0.288735i
$21$	1253.04			2.84136
$22$	323.382	+	845.161i	0.668145	+	1.74620i
$23$			110.304i			0.208514i
$23$			110.304i			0.208514i
$24$	−909.819	−	467.288i	−1.57955	−	0.811263i
$25$	−508.066			−0.812906
$26$	592.707	−	226.786i	0.876786	−	0.335483i
$27$		−	1492.70i		−	2.04759i
$28$	−837.415	−	934.085i	−1.06813	−	1.19143i
$29$	−106.243			−0.126329			−0.0631645	−	0.998003i	$-0.520119\pi$
$29$	−106.243			−0.126329			−0.0631645	+	0.998003i	$0.520119\pi$
$30$	−247.031	−	645.616i	−0.274478	−	0.717351i
$31$			78.4095i			0.0815916i	0.999168	+	0.0407958i	$0.0129893\pi$
$31$			78.4095i			0.0815916i	−0.999168	+	0.0407958i	$0.987011\pi$
$32$	259.697	+	990.522i	0.253610	+	0.967306i
$33$	3615.44			3.31996
$34$	73.6410	−	28.1771i	0.0637033	−	0.0243747i
$35$		−	847.856i		−	0.692128i
$36$	−2077.72	+	1862.70i	−1.60318	+	1.43726i
$37$	−1232.29			−0.900141			−0.450071	−	0.892993i	$-0.648601\pi$
$37$	−1232.29			−0.900141			−0.450071	+	0.892993i	$0.648601\pi$
$38$	514.867	+	1345.61i	0.356556	+	0.931862i
$39$		−	2535.49i		−	1.66699i
$40$	−316.186	+	615.620i	−0.197616	+	0.384763i
$41$	1831.67			1.08963			0.544817	−	0.838555i	$-0.316599\pi$
$41$	1831.67			1.08963			0.544817	+	0.838555i	$0.316599\pi$
$42$	−4681.18	+	1791.15i	−2.65373	+	1.01539i
$43$			2735.12i			1.47924i	0.673025	+	0.739620i	$0.264995\pi$
$43$			2735.12i			1.47924i	−0.673025	+	0.739620i	$0.735005\pi$
$44$	−2416.22	−	2695.15i	−1.24805	−	1.39212i
$45$	−1885.92			−0.931318
$46$	−157.674	−	412.081i	−0.0745150	−	0.194745i
$47$			1408.79i			0.637749i	0.947797	+	0.318875i	$0.103305\pi$
$47$			1408.79i			0.637749i	−0.947797	+	0.318875i	$0.896695\pi$
$48$	4066.92	+	445.185i	1.76516	+	0.193223i
$49$	−3746.57			−1.56042
$50$	1898.07	−	726.253i	0.759226	−	0.290501i
$51$		−	315.022i		−	0.121116i
$52$	−1890.10	+	1694.49i	−0.699000	+	0.626659i
$53$	−1971.81			−0.701961			−0.350980	−	0.936383i	$-0.614152\pi$
$53$	−1971.81			−0.701961			−0.350980	+	0.936383i	$0.614152\pi$
$54$	2133.73	+	5576.51i	0.731731	+	1.91238i
$55$		−	2446.35i		−	0.808711i
$56$	4463.69	+	2292.57i	1.42337	+	0.731051i
$57$	5756.26			1.77170
$58$	396.908	−	151.868i	0.117987	−	0.0451451i
$59$		−	2430.12i		−	0.698109i	−0.937102	−	0.349055i	$-0.886503\pi$
$59$		−	2430.12i		−	0.698109i	0.937102	−	0.349055i	$-0.113497\pi$
$60$	1845.75	+	2058.82i	0.512707	+	0.571893i
$61$	−2393.48			−0.643235			−0.321618	−	0.946870i	$-0.604227\pi$
$61$	−2393.48			−0.643235			−0.321618	+	0.946870i	$0.604227\pi$
$62$	−112.082	−	292.927i	−0.0291577	−	0.0762038i
$63$			13674.3i			3.44527i
$64$	−2386.09	−	3329.23i	−0.582542	−	0.812801i
$65$	−1715.61			−0.406062
$66$	−13506.8	+	5168.07i	−3.10073	+	1.18643i
$67$		−	4169.97i		−	0.928930i	−0.885591	−	0.464465i	$-0.846247\pi$
$67$		−	4169.97i		−	0.928930i	0.885591	−	0.464465i	$-0.153753\pi$
$68$	−234.835	+	210.532i	−0.0507861	+	0.0455302i
$69$	−1762.81			−0.370259
$70$	1211.97	+	3167.48i	0.247340	+	0.646424i
$71$		−	9545.49i		−	1.89357i	−0.321867	−	0.946785i	$-0.604310\pi$
$71$		−	9545.49i		−	1.89357i	0.321867	−	0.946785i	$-0.395690\pi$
$72$	5099.46	−	9928.77i	0.983693	−	1.91527i
$73$	3022.12			0.567109			0.283555	−	0.958956i	$-0.408486\pi$
$73$	3022.12			0.567109			0.283555	+	0.958956i	$0.408486\pi$
$74$	4603.68	−	1761.50i	0.840701	−	0.321676i
$75$		−	8119.56i		−	1.44348i
$76$	−3846.95	−	4291.03i	−0.666023	−	0.742908i
$77$	−17737.8			−2.99170
$78$	3624.35	+	9472.24i	0.595718	+	1.55691i
$79$			4699.18i			0.752953i	0.926426	+	0.376477i	$0.122864\pi$
$79$			4699.18i			0.752953i	−0.926426	+	0.376477i	$0.877136\pi$
$80$	301.230	−	2751.84i	0.0470672	−	0.429976i
$81$	9728.64			1.48280
$82$	−6842.88	+	2618.28i	−1.01768	+	0.389393i
$83$		−	4958.29i		−	0.719741i	−0.933002	−	0.359870i	$-0.882821\pi$
$83$		−	4958.29i		−	0.719741i	0.933002	−	0.359870i	$-0.117179\pi$
$84$	14927.9	−	13383.0i	2.11563	−	1.89668i
$85$	−213.157			−0.0295026
$86$	−3909.70	−	10218.0i	−0.528624	−	1.38156i
$87$		−	1697.90i		−	0.224323i
$88$	12879.3	+	6614.85i	1.66313	+	0.854190i
$89$	2141.67			0.270379			0.135189	−	0.990820i	$-0.456836\pi$
$89$	2141.67			0.270379			0.135189	+	0.990820i	$0.456836\pi$
$90$	7045.54	−	2695.82i	0.869820	−	0.332817i
$91$			12439.4i			1.50217i
$92$	1178.10	+	1314.09i	0.139189	+	0.155257i
$93$	−1253.09			−0.144882
$94$	−2013.79	−	5263.04i	−0.227907	−	0.595636i
$95$		−	3894.91i		−	0.431569i
$96$	−15829.8	+	4150.30i	−1.71765	+	0.450336i
$97$	6854.24			0.728477			0.364238	−	0.931306i	$-0.381329\pi$
$97$	6854.24			0.728477			0.364238	+	0.931306i	$0.381329\pi$
$98$	13996.7	−	5355.53i	1.45738	−	0.557635i
$99$			39454.9i			4.02560i
$100$	−6052.78	+	5426.37i	−0.605278	+	0.542637i
$101$	12665.4			1.24158			0.620792	−	0.783976i	$-0.286811\pi$
$101$	12665.4			1.24158			0.620792	+	0.783976i	$0.286811\pi$
$102$	450.307	+	1176.88i	0.0432821	+	0.113118i
$103$		−	4499.74i		−	0.424144i	−0.977254	−	0.212072i	$-0.931979\pi$
$103$		−	4499.74i		−	0.424144i	0.977254	−	0.212072i	$-0.0680211\pi$
$104$	4638.96	−	9032.16i	0.428898	−	0.835074i
$105$	13549.9			1.22901
$106$	7366.41	−	2818.59i	0.655608	−	0.250854i
$107$		−	2603.43i		−	0.227393i	−0.993516	−	0.113697i	$-0.963731\pi$
$107$		−	2603.43i		−	0.227393i	0.993516	−	0.113697i	$-0.0362692\pi$
$108$	−15942.6	−	17783.0i	−1.36682	−	1.52461i
$109$	−6036.27			−0.508061			−0.254030	−	0.967196i	$-0.581756\pi$
$109$	−6036.27			−0.508061			−0.254030	+	0.967196i	$0.581756\pi$
$110$	3496.93	+	9139.23i	0.289002	+	0.755308i
$111$		−	19693.7i		−	1.59838i
$112$	−19952.9	−	2184.14i	−1.59063	−	0.174118i
$113$	20136.8			1.57700			0.788502	−	0.615032i	$-0.210857\pi$
$113$	20136.8			1.57700			0.788502	+	0.615032i	$0.210857\pi$
$114$	−21504.6	+	8228.26i	−1.65471	+	0.633138i
$115$			1192.78i			0.0901917i
$116$	−1265.71	+	1134.72i	−0.0940627	+	0.0843280i
$117$	27669.5			2.02130
$118$	3473.72	+	9078.59i	0.249477	+	0.652011i
$119$			1545.54i			0.109141i
$120$	−9838.42	−	5053.06i	−0.683224	−	0.350907i
$121$	−36538.6			−2.49563
$122$	8941.71	−	3421.35i	0.600760	−	0.229868i
$123$			29272.6i			1.93486i
$124$	837.448	+	934.121i	0.0544646	+	0.0607519i
$125$	−12252.5			−0.784162
$126$	−19546.7	−	51085.3i	−1.23121	−	3.21777i
$127$		−	4507.13i		−	0.279443i	−0.990191	−	0.139721i	$-0.955379\pi$
$127$		−	4507.13i		−	0.279443i	0.990191	−	0.139721i	$-0.0446207\pi$
$128$	13673.1	+	9026.77i	0.834538	+	0.550951i
$129$	−43710.7			−2.62669
$130$	6409.30	−	2452.38i	0.379249	−	0.145111i
$131$			23382.6i			1.36254i	0.732031	+	0.681271i	$0.238572\pi$
$131$			23382.6i			1.36254i	−0.732031	+	0.681271i	$0.761428\pi$
$132$	43072.0	−	38614.4i	2.47199	−	2.21616i
$133$	−28241.0			−1.59653
$134$	5960.74	+	15578.4i	0.331964	+	0.867589i
$135$		−	16141.4i		−	0.885674i
$136$	576.368	−	1122.20i	0.0311618	−	0.0606727i
$137$	14310.7			0.762466			0.381233	−	0.924479i	$-0.375500\pi$
$137$	14310.7			0.762466			0.381233	+	0.924479i	$0.375500\pi$
$138$	6585.60	−	2519.84i	0.345810	−	0.132317i
$139$		−	14113.5i		−	0.730477i	−0.930914	−	0.365238i	$-0.880987\pi$
$139$		−	14113.5i		−	0.730477i	0.930914	−	0.365238i	$-0.119013\pi$
$140$	−9055.47	−	10100.8i	−0.462014	−	0.515348i
$141$	−22514.3			−1.13245
$142$	13644.8	+	35660.6i	0.676689	+	1.76853i
$143$			35892.0i			1.75519i
$144$	−4858.26	+	44381.9i	−0.234291	+	2.14033i
$145$	−1148.87			−0.0546429
$146$	−11290.2	+	4319.96i	−0.529661	+	0.202663i
$147$		−	59875.2i		−	2.77084i
$148$	−14680.8	+	13161.4i	−0.670232	+	0.600869i
$149$	4087.06			0.184093			0.0920467	−	0.995755i	$-0.470659\pi$
$149$	4087.06			0.184093			0.0920467	+	0.995755i	$0.470659\pi$
$150$	11606.5	+	30333.6i	0.515844	+	1.34816i
$151$			36058.1i			1.58142i	0.612188	+	0.790712i	$0.290290\pi$
$151$			36058.1i			1.58142i	−0.612188	+	0.790712i	$0.709710\pi$
$152$	20505.5	+	10531.7i	0.887530	+	0.455839i
$153$	3437.81			0.146858
$154$	66266.1	−	25355.3i	2.79415	−	1.06912i
$155$			847.889i			0.0352920i
$156$	−27080.1	−	30206.2i	−1.11276	−	1.24122i
$157$	−1402.88			−0.0569145			−0.0284572	−	0.999595i	$-0.509059\pi$
$157$	−1402.88			−0.0569145			−0.0284572	+	0.999595i	$0.509059\pi$
$158$	−6717.23	−	17555.5i	−0.269077	−	0.703233i
$159$		−	31512.1i		−	1.24647i
$160$	2808.26	+	10711.1i	0.109698	+	0.418403i
$161$	8648.56			0.333651
$162$	−36344.9	+	13906.6i	−1.38488	+	0.529895i
$163$		−	23476.7i		−	0.883614i	−0.897110	−	0.441807i	$-0.854338\pi$
$163$		−	23476.7i		−	0.883614i	0.897110	−	0.441807i	$-0.145662\pi$
$164$	21821.4	−	19563.1i	0.811325	−	0.727360i
$165$	39095.9			1.43603
$166$	7087.61	+	18523.5i	0.257208	+	0.672213i
$167$		−	29242.4i		−	1.04853i	−0.851556	−	0.524263i	$-0.824341\pi$
$167$		−	29242.4i		−	1.04853i	0.851556	−	0.524263i	$-0.175659\pi$
$168$	−36638.4	+	71335.7i	−1.29813	+	2.52748i
$169$	−3390.12			−0.118698
$170$	796.324	−	304.696i	0.0275545	−	0.0105431i
$171$			62817.5i			2.14827i
$172$	29212.2	+	32584.4i	0.987433	+	1.10142i
$173$	20254.9			0.676765			0.338383	−	0.941009i	$-0.390120\pi$
$173$	20254.9			0.676765			0.338383	+	0.941009i	$0.390120\pi$
$174$	2427.05	+	6343.12i	0.0801643	+	0.209510i
$175$			39835.7i			1.30076i
$176$	−57570.7	−	6301.97i	−1.85856	−	0.203447i
$177$	38836.5			1.23963
$178$	−8000.99	+	3061.40i	−0.252525	+	0.0966229i
$179$		−	18207.7i		−	0.568262i	−0.958786	−	0.284131i	$-0.908295\pi$
$179$		−	18207.7i		−	0.568262i	0.958786	−	0.284131i	$-0.0917050\pi$
$180$	−22467.7	+	20142.4i	−0.693446	+	0.621680i
$181$	7316.17			0.223320			0.111660	−	0.993746i	$-0.464383\pi$
$181$	7316.17			0.223320			0.111660	+	0.993746i	$0.464383\pi$
$182$	−17781.5	−	46472.1i	−0.536817	−	1.40297i
$183$		−	38250.9i		−	1.14219i
$184$	−6279.63	−	3225.25i	−0.185481	−	0.0952638i
$185$	−13325.5			−0.389351
$186$	4681.36	−	1791.22i	0.135315	−	0.0517754i
$187$			4459.40i			0.127524i
$188$	15046.5	+	16783.4i	0.425715	+	0.474859i
$189$	−117037.			−3.27642
$190$	5567.57	+	14550.9i	0.154226	+	0.403071i
$191$			22511.7i			0.617081i	0.951211	+	0.308541i	$0.0998406\pi$
$191$			22511.7i			0.617081i	−0.951211	+	0.308541i	$0.900159\pi$
$192$	53205.5	−	38132.9i	1.44329	−	1.03442i
$193$	17916.7			0.480997			0.240499	−	0.970649i	$-0.422689\pi$
$193$	17916.7			0.480997			0.240499	+	0.970649i	$0.422689\pi$
$194$	−25606.5	+	9797.77i	−0.680373	+	0.260330i
$195$		−	27417.8i		−	0.721046i
$196$	−44634.3	+	40015.0i	−1.16187	+	1.04162i
$197$	−25465.4			−0.656172			−0.328086	−	0.944648i	$-0.606404\pi$
$197$	−25465.4			−0.656172			−0.328086	+	0.944648i	$0.606404\pi$
$198$	−56398.7	−	147398.i	−1.43859	−	3.75977i
$199$		−	18156.3i		−	0.458482i	−0.973370	−	0.229241i	$-0.926376\pi$
$199$		−	18156.3i		−	0.458482i	0.973370	−	0.229241i	$-0.0736244\pi$
$200$	14855.7	−	28924.3i	0.371391	−	0.723107i
$201$	66641.6			1.64950
$202$	−47316.2	+	18104.5i	−1.15960	+	0.443694i
$203$			8330.11i			0.202143i
$204$	−3364.57	−	3752.97i	−0.0808481	−	0.0901810i
$205$	19807.0			0.471314
$206$	6432.14	+	16810.4i	0.151573	+	0.396136i
$207$		−	19237.3i		−	0.448956i
$208$	−4419.54	+	40374.1i	−0.102153	+	0.933203i
$209$	−81484.6			−1.86545
$210$	−50620.4	+	19368.8i	−1.14786	+	0.439202i
$211$		−	67609.6i		−	1.51860i	−0.650740	−	0.759300i	$-0.725541\pi$
$211$		−	67609.6i		−	1.51860i	0.650740	−	0.759300i	$-0.274459\pi$
$212$	−23490.9	+	21059.8i	−0.522670	+	0.468578i
$213$	152549.			3.36242
$214$	3721.46	+	9726.05i	0.0812617	+	0.212378i
$215$			29576.4i			0.639837i
$216$	84979.4	+	43645.8i	1.82140	+	0.935482i
$217$	6147.81			0.130557
$218$	22550.7	−	8628.53i	0.474512	−	0.181561i
$219$			48297.5i			1.00702i
$220$	−26128.1	−	29144.3i	−0.539836	−	0.602154i
$221$	3127.36			0.0640314
$222$	28151.0	+	73572.9i	0.571200	+	1.49283i
$223$		−	8776.04i		−	0.176477i	−0.996099	−	0.0882386i	$-0.971876\pi$
$223$		−	8776.04i		−	0.176477i	0.996099	−	0.0882386i	$-0.0281238\pi$
$224$	77663.3	−	20361.9i	1.54782	−	0.405810i
$225$	88608.0			1.75028
$226$	−75228.3	+	28784.4i	−1.47287	+	0.563561i
$227$			7102.82i			0.137841i	0.997622	+	0.0689206i	$0.0219555\pi$
$227$			7102.82i			0.137841i	−0.997622	+	0.0689206i	$0.978044\pi$
$228$	68576.4	−	61479.3i	1.31918	−	1.18266i
$229$	35105.5			0.669428			0.334714	−	0.942320i	$-0.391360\pi$
$229$	35105.5			0.669428			0.334714	+	0.942320i	$0.391360\pi$
$230$	−1705.02	−	4456.08i	−0.0322310	−	0.0842360i
$231$		−	283474.i		−	5.31238i
$232$	3106.49	−	6048.41i	0.0577158	−	0.112374i
$233$	31723.1			0.584337			0.292169	−	0.956367i	$-0.405623\pi$
$233$	31723.1			0.584337			0.292169	+	0.956367i	$0.405623\pi$
$234$	−103370.	+	39552.1i	−1.88782	+	0.722334i
$235$			15234.1i			0.275855i
$236$	−25954.7	−	28950.9i	−0.466007	−	0.519802i
$237$	−75099.1			−1.33702
$238$	−2209.27	−	5773.93i	−0.0390027	−	0.101934i
$239$		−	45193.8i		−	0.791193i	−0.918424	−	0.395597i	$-0.870538\pi$
$239$		−	45193.8i		−	0.791193i	0.918424	−	0.395597i	$-0.129462\pi$
$240$	43978.1	+	4814.05i	0.763509	+	0.0835773i
$241$	−47267.8			−0.813825			−0.406913	−	0.913467i	$-0.633395\pi$
$241$	−47267.8			−0.813825			−0.406913	+	0.913467i	$0.633395\pi$
$242$	136503.	−	52229.9i	2.33084	−	0.891843i
$243$			34568.1i			0.585414i
$244$	−28514.4	+	25563.4i	−0.478943	+	0.429377i
$245$	−40514.0			−0.674951
$246$	−41843.5	−	109358.i	−0.691446	−	1.80710i
$247$			57144.8i			0.936662i
$248$	−4463.87	−	2292.66i	−0.0725785	−	0.0372767i
$249$	79240.1			1.27804
$250$	45773.8	−	17514.3i	0.732380	−	0.280229i
$251$			44053.3i			0.699247i	0.936890	+	0.349624i	$0.113691\pi$
$251$			44053.3i			0.699247i	−0.936890	+	0.349624i	$0.886309\pi$
$252$	146047.	+	162907.i	2.29981	+	2.56530i
$253$	24954.0			0.389851
$254$	6442.70	+	16838.0i	0.0998621	+	0.260990i
$255$		−	3406.52i		−	0.0523879i
$256$	−63984.0	−	14177.9i	−0.976319	−	0.216337i
$257$	−1637.35			−0.0247899			−0.0123950	−	0.999923i	$-0.503946\pi$
$257$	−1637.35			−0.0247899			−0.0123950	+	0.999923i	$0.503946\pi$
$258$	163297.	−	62482.2i	2.45324	−	0.938678i
$259$			96619.7i			1.44034i
$260$	−20438.7	+	18323.5i	−0.302348	+	0.271058i
$261$	18529.0			0.272001
$262$	−33424.1	−	87354.2i	−0.486920	−	1.27257i
$263$			124112.i			1.79433i	0.441700	+	0.897163i	$0.354376\pi$
$263$			124112.i			1.79433i	−0.441700	+	0.897163i	$0.645624\pi$
$264$	−105714.	+	205827.i	−1.51679	+	2.95322i
$265$	−21322.3			−0.303629
$266$	105504.	−	40368.9i	1.49110	−	0.570537i
$267$			34226.7i			0.480112i
$268$	−44537.1	−	49678.4i	−0.620086	−	0.691668i
$269$	−113314.			−1.56595			−0.782976	−	0.622051i	$-0.786299\pi$
$269$	−113314.			−1.56595			−0.782976	+	0.622051i	$0.786299\pi$
$270$	23073.3	+	60302.1i	0.316506	+	0.827190i
$271$		−	97762.0i		−	1.33116i	−0.746325	−	0.665582i	$-0.768184\pi$
$271$		−	97762.0i		−	1.33116i	0.746325	−	0.665582i	$-0.231816\pi$
$272$	−549.106	+	5016.28i	−0.00742196	+	0.0678023i
$273$	−198799.			−2.66740
$274$	−53463.0	+	20456.4i	−0.712118	+	0.272476i
$275$			114939.i			1.51986i
$276$	−21000.9	+	18827.5i	−0.275690	+	0.247158i
$277$	−2867.07			−0.0373662			−0.0186831	−	0.999825i	$-0.505947\pi$
$277$	−2867.07			−0.0373662			−0.0186831	+	0.999825i	$0.505947\pi$
$278$	20174.5	+	52726.3i	0.261044	+	0.682240i
$279$		−	13674.8i		−	0.175676i
$280$	48268.6	+	24791.0i	0.615671	+	0.316212i
$281$	88872.8			1.12553			0.562764	−	0.826618i	$-0.309738\pi$
$281$	88872.8			1.12553			0.562764	+	0.826618i	$0.309738\pi$
$282$	84110.3	−	32183.0i	1.05767	−	0.404695i
$283$		−	159739.i		−	1.99452i	−0.0739598	−	0.997261i	$-0.523564\pi$
$283$		−	159739.i		−	1.99452i	0.0739598	−	0.997261i	$-0.476436\pi$
$284$	−101950.	−	113719.i	−1.26401	−	1.40992i
$285$	62245.9			0.766339
$286$	−51305.7	−	134088.i	−0.627239	−	1.63929i
$287$		−	143615.i		−	1.74356i
$288$	−45291.8	−	172750.i	−0.546053	−	2.08272i
$289$	−83132.4			−0.995348
$290$	4292.01	−	1642.24i	0.0510346	−	0.0195273i
$291$			109540.i			1.29356i
$292$	36003.7	−	32277.6i	0.422261	−	0.378561i
$293$	−63118.9			−0.735231			−0.367616	−	0.929978i	$-0.619826\pi$
$293$	−63118.9			−0.735231			−0.367616	+	0.929978i	$0.619826\pi$
$294$	85588.4	+	223686.i	0.990193	+	2.58788i
$295$		−	26278.3i		−	0.301963i
$296$	36031.8	−	70154.7i	0.411246	−	0.800706i
$297$	−337691.			−3.82831
$298$	−15268.7	+	5842.23i	−0.171937	+	0.0657879i
$299$		−	17500.1i		−	0.195749i
$300$	−86720.5	−	96731.3i	−0.963561	−	1.07479i
$301$	214451.			2.36698
$302$	−51543.1	−	134708.i	−0.565140	−	1.47700i
$303$			202410.i			2.20468i
$304$	−91660.2	−	10033.6i	−0.991822	−	0.108570i
$305$	−25882.1			−0.278228
$306$	−12843.2	+	4914.16i	−0.137161	+	0.0524815i
$307$			156510.i			1.66060i	0.557315	+	0.830301i	$0.311832\pi$
$307$			156510.i			1.66060i	−0.557315	+	0.830301i	$0.688168\pi$
$308$	−211317.	+	189448.i	−2.22758	+	1.99704i
$309$	71911.8			0.753153
$310$	−1212.01	−	3167.60i	−0.0126120	−	0.0329615i
$311$		−	7020.54i		−	0.0725855i	−0.999341	−	0.0362927i	$-0.988445\pi$
$311$		−	7020.54i		−	0.0725855i	0.999341	−	0.0362927i	$-0.0115549\pi$
$312$	144346.	+	74136.7i	1.48284	+	0.761595i
$313$	−161384.			−1.64730			−0.823650	−	0.567099i	$-0.808066\pi$
$313$	−161384.			−1.64730			−0.823650	+	0.567099i	$0.808066\pi$
$314$	5240.99	−	2005.35i	0.0531562	−	0.0203390i
$315$			147868.i			1.49023i
$316$	50189.3	+	55983.1i	0.502617	+	0.560638i
$317$	−125577.			−1.24966			−0.624832	−	0.780759i	$-0.714832\pi$
$317$	−125577.			−1.24966			−0.624832	+	0.780759i	$0.714832\pi$
$318$	45044.8	+	117725.i	0.445442	+	1.16416i
$319$			24035.2i			0.236192i
$320$	−25802.2	−	36001.0i	−0.251975	−	0.351572i
$321$	41606.2			0.403783
$322$	−32309.8	+	12362.6i	−0.311618	+	0.119234i
$323$			7099.96i			0.0680536i
$324$	115901.	−	103906.i	1.10407	−	0.989808i
$325$	80606.4			0.763137
$326$	33558.7	+	87705.9i	0.315770	+	0.825265i
$327$		−	96467.6i		−	0.902165i
$328$	−53557.4	+	104277.i	−0.497819	+	0.969266i
$329$	110458.			1.02048
$330$	−146057.	+	55885.5i	−1.34120	+	0.513182i
$331$			5876.54i			0.0536371i	0.999640	+	0.0268186i	$0.00853764\pi$
$331$			5876.54i			0.0536371i	−0.999640	+	0.0268186i	$0.991462\pi$
$332$	−52956.7	−	59070.0i	−0.480446	−	0.535908i
$333$	214915.			1.93811
$334$	41800.4	+	109245.i	0.374703	+	0.979288i
$335$		−	45092.4i		−	0.401803i
$336$	34905.4	−	318873.i	0.309182	−	2.82449i
$337$	94763.5			0.834414			0.417207	−	0.908812i	$-0.363009\pi$
$337$	94763.5			0.834414			0.417207	+	0.908812i	$0.363009\pi$
$338$	12665.0	−	4846.00i	0.110860	−	0.0424180i
$339$			321812.i			2.80029i
$340$	−2539.41	+	2276.61i	−0.0219672	+	0.0196938i
$341$	17738.5			0.152549
$342$	−89794.2	−	234677.i	−0.767708	−	2.00641i
$343$			105502.i			0.896749i
$344$	−155711.	−	79973.7i	−1.31583	−	0.675819i
$345$	−19062.3			−0.160154
$346$	−75669.6	+	28953.3i	−0.632076	+	0.241850i
$347$			170286.i			1.41423i	0.707099	+	0.707114i	$0.250003\pi$
$347$			170286.i			1.41423i	−0.707099	+	0.707114i	$0.749997\pi$
$348$	−18134.3	−	20227.7i	−0.149741	−	0.167027i
$349$	164073.			1.34705			0.673527	−	0.739163i	$-0.264779\pi$
$349$	164073.			1.34705			0.673527	+	0.739163i	$0.264779\pi$
$350$	−56942.9	−	148821.i	−0.464840	−	1.21486i
$351$			236821.i			1.92223i
$352$	224085.	−	58751.0i	1.80854	−	0.474165i
$353$	136107.			1.09227			0.546135	−	0.837697i	$-0.316098\pi$
$353$	136107.			1.09227			0.546135	+	0.837697i	$0.316098\pi$
$354$	−145088.	+	55514.7i	−1.15778	+	0.442998i
$355$		−	103221.i		−	0.819052i
$356$	25514.5	−	22874.0i	0.201320	−	0.180485i
$357$	−24699.8			−0.193801
$358$	26026.9	+	68021.4i	0.203075	+	0.530737i
$359$			136145.i			1.05636i	0.849131	+	0.528182i	$0.177126\pi$
$359$			136145.i			1.05636i	−0.849131	+	0.528182i	$0.822874\pi$
$360$	55143.6	−	107366.i	0.425490	−	0.828439i
$361$	586.627			0.00450140
$362$	−27332.2	+	10458.1i	−0.208573	+	0.0798058i
$363$		−	583934.i		−	4.43150i
$364$	132859.	+	148196.i	1.00274	+	1.11849i
$365$	32680.1			0.245300
$366$	54677.7	+	142900.i	0.408176	+	1.06677i
$367$		−	184454.i		−	1.36948i	−0.728788	−	0.684740i	$-0.759916\pi$
$367$		−	184454.i		−	1.36948i	0.728788	−	0.684740i	$-0.240084\pi$
$368$	28070.2	+	3072.70i	0.207276	+	0.0226895i
$369$	−319448.			−2.34611
$370$	49782.4	−	19048.1i	0.363640	−	0.139139i
$371$			154602.i			1.12323i
$372$	−14928.5	+	13383.5i	−0.107877	+	0.0967129i
$373$	165450.			1.18918			0.594591	−	0.804028i	$-0.297314\pi$
$373$	165450.			1.18918			0.594591	+	0.804028i	$0.297314\pi$
$374$	−6374.48	−	16659.7i	−0.0455723	−	0.119104i
$375$		−	195811.i		−	1.39244i
$376$	−80202.6	−	41192.4i	−0.567300	−	0.291368i
$377$	16855.8			0.118595
$378$	437234.	−	167298.i	3.06006	−	1.17087i
$379$		−	77064.2i		−	0.536506i	−0.963349	−	0.268253i	$-0.913554\pi$
$379$		−	77064.2i		−	0.536506i	0.963349	−	0.268253i	$-0.0864463\pi$
$380$	−41599.4	−	46401.5i	−0.288084	−	0.321340i
$381$	72029.9			0.496207
$382$	−32179.3	−	84100.8i	−0.220521	−	0.576333i
$383$		−	56563.0i		−	0.385598i	−0.981238	−	0.192799i	$-0.938243\pi$
$383$		−	56563.0i		−	0.385598i	0.981238	−	0.192799i	$-0.0617565\pi$
$384$	−144260.	+	218514.i	−0.978324	+	1.48189i
$385$	−191810.			−1.29404
$386$	−66934.2	+	25610.9i	−0.449235	+	0.171890i
$387$		−	477011.i		−	3.18498i
$388$	81657.0	−	73206.2i	0.542413	−	0.486278i
$389$	40271.7			0.266134			0.133067	−	0.991107i	$-0.457517\pi$
$389$	40271.7			0.266134			0.133067	+	0.991107i	$0.457517\pi$
$390$	39192.2	+	102429.i	0.257674	+	0.673432i
$391$		−	2174.30i		−	0.0142222i
$392$	109548.	−	213293.i	0.712908	−	1.38805i
$393$	−373684.			−2.41947
$394$	95135.1	−	36401.4i	0.612842	−	0.234491i
$395$			50815.1i			0.325686i
$396$	421396.	+	470041.i	2.68720	+	2.99740i
$397$	−200655.			−1.27312			−0.636559	−	0.771228i	$-0.719643\pi$
$397$	−200655.			−1.27312			−0.636559	+	0.771228i	$0.719643\pi$
$398$	25953.5	+	67829.6i	0.163844	+	0.428207i
$399$		−	451328.i		−	2.83496i
$400$	−14153.0	+	129293.i	−0.0884562	+	0.808079i
$401$	122548.			0.762109			0.381055	−	0.924552i	$-0.375561\pi$
$401$	122548.			0.762109			0.381055	+	0.924552i	$0.375561\pi$
$402$	−248964.	+	95260.6i	−1.54058	+	0.589469i
$403$		−	12439.9i		−	0.0765963i
$404$	150887.	−	135272.i	0.924465	−	0.828790i
$405$	105202.			0.641375
$406$	−11907.4	−	31120.2i	−0.0722382	−	0.188795i
$407$			278780.i			1.68296i
$408$	17934.3	+	9211.13i	0.107737	+	0.0553340i
$409$	165381.			0.988642			0.494321	−	0.869280i	$-0.335417\pi$
$409$	165381.			0.988642			0.494321	+	0.869280i	$0.335417\pi$
$410$	−73996.2	+	28313.0i	−0.440192	+	0.168430i
$411$			228704.i			1.35391i
$412$	−48059.2	−	53607.1i	−0.283128	−	0.315811i
$413$	−190537.			−1.11707
$414$	27498.7	+	71868.0i	0.160440	+	0.419310i
$415$		−	53617.0i		−	0.311320i
$416$	−41201.8	−	157150.i	−0.238083	−	0.908085i
$417$	225553.			1.29711
$418$	304416.	−	116478.i	1.74227	−	0.666640i
$419$			164065.i			0.934516i	0.884121	+	0.467258i	$0.154758\pi$
$419$			164065.i			0.934516i	−0.884121	+	0.467258i	$0.845242\pi$
$420$	161424.	−	144718.i	0.915105	−	0.820399i
$421$	118558.			0.668908			0.334454	−	0.942412i	$-0.391448\pi$
$421$	118558.			0.668908			0.334454	+	0.942412i	$0.391448\pi$
$422$	96644.3	+	252580.i	0.542690	+	1.41832i
$423$		−	245696.i		−	1.37315i
$424$	57654.9	−	112255.i	0.320704	−	0.624418i
$425$	10014.9			0.0554461
$426$	−569904.	+	218061.i	−3.14038	+	1.20160i
$427$			187664.i			1.02926i
$428$	−27805.7	−	31015.6i	−0.151791	−	0.169314i
$429$	−573601.			−3.11670
$430$	−42277.9	−	110494.i	−0.228653	−	0.597586i
$431$			23423.2i			0.126093i	0.998011	+	0.0630465i	$0.0200816\pi$
$431$			23423.2i			0.126093i	−0.998011	+	0.0630465i	$0.979918\pi$
$432$	−379861.	−	41581.4i	−2.03543	−	0.222808i
$433$	−111744.			−0.596003			−0.298001	−	0.954565i	$-0.596320\pi$
$433$	−111744.			−0.596003			−0.298001	+	0.954565i	$0.596320\pi$
$434$	−22967.4	+	8787.97i	−0.121936	+	0.0466562i
$435$		−	18360.4i		−	0.0970294i
$436$	−71912.3	+	64470.0i	−0.378295	+	0.339145i
$437$	39730.1			0.208045
$438$	−69038.7	−	180433.i	−0.359869	−	0.940520i
$439$		−	50105.7i		−	0.259991i	−0.991515	−	0.129995i	$-0.958504\pi$
$439$		−	50105.7i		−	0.259991i	0.991515	−	0.129995i	$-0.0414962\pi$
$440$	139271.	+	71530.3i	0.719376	+	0.369475i
$441$	653412.			3.35977
$442$	−11683.4	+	4470.39i	−0.0598032	+	0.0228824i
$443$			25257.4i			0.128701i	0.997927	+	0.0643505i	$0.0204976\pi$
$443$			25257.4i			0.128701i	−0.997927	+	0.0643505i	$0.979502\pi$
$444$	−210337.	−	234618.i	−1.06696	−	1.19013i
$445$	23159.2			0.116951
$446$	12544.9	+	32786.1i	0.0630662	+	0.164824i
$447$			65316.6i			0.326895i
$448$	−261033.	+	187085.i	−1.30059	+	0.932143i
$449$	61017.6			0.302665			0.151332	−	0.988483i	$-0.451644\pi$
$449$	61017.6			0.302665			0.151332	+	0.988483i	$0.451644\pi$
$450$	−331027.	+	126660.i	−1.63470	+	0.625483i
$451$		−	414378.i		−	2.03724i
$452$	239897.	−	215070.i	1.17421	−	1.05269i
$453$	−576255.			−2.80814
$454$	−10153.1	−	26535.2i	−0.0492592	−	0.128739i
$455$			134515.i			0.649753i
$456$	−168311.	+	327705.i	−0.809435	+	1.57599i
$457$	149041.			0.713631			0.356816	−	0.934175i	$-0.383862\pi$
$457$	149041.			0.713631			0.356816	+	0.934175i	$0.383862\pi$
$458$	−131149.	+	50181.4i	−0.625223	+	0.239228i
$459$			29423.9i			0.139661i
$460$	12739.5	+	14210.1i	0.0602054	+	0.0671554i
$461$	118561.			0.557881			0.278941	−	0.960308i	$-0.410017\pi$
$461$	118561.			0.557881			0.278941	+	0.960308i	$0.410017\pi$
$462$	405210.	+	1.05902e6i	1.89844	+	4.96158i
$463$			44400.7i			0.207123i	0.994623	+	0.103561i	$0.0330238\pi$
$463$			44400.7i			0.207123i	−0.994623	+	0.103561i	$0.966976\pi$
$464$	−2959.56	+	27036.6i	−0.0137465	+	0.125579i
$465$	−13550.4			−0.0626680
$466$	−118513.	+	45346.5i	−0.545751	+	0.208820i
$467$			50846.5i			0.233145i	0.993182	+	0.116573i	$0.0371908\pi$
$467$			50846.5i			0.233145i	−0.993182	+	0.116573i	$0.962809\pi$
$468$	329637.	−	295523.i	1.50503	−	1.34927i
$469$	−326952.			−1.48641
$470$	−21776.3	−	56912.4i	−0.0985799	−	0.257639i
$471$		−	22420.0i		−	0.101063i
$472$	138347.	+	71055.7i	0.620992	+	0.318945i
$473$	618762.			2.76568
$474$	280560.	−	107350.i	1.24873	−	0.477800i
$475$			182999.i			0.811074i
$476$	16507.0	+	18412.6i	0.0728543	+	0.0812645i
$477$	343888.			1.51140
$478$	64602.1	+	168838.i	0.282742	+	0.738948i
$479$		−	235259.i		−	1.02536i	−0.858581	−	0.512678i	$-0.828654\pi$
$479$		−	235259.i		−	1.02536i	0.858581	−	0.512678i	$-0.171346\pi$
$480$	−171178.	+	44879.7i	−0.742959	+	0.194790i
$481$	195507.			0.845032
$482$	176586.	−	67566.8i	0.760085	−	0.290830i
$483$			138215.i			0.592464i
$484$	−435297.	+	390248.i	−1.85821	+	1.66590i
$485$	74119.0			0.315098
$486$	−49413.3	−	129142.i	−0.209204	−	0.546757i
$487$		−	301207.i		−	1.27001i	−0.772509	−	0.635004i	$-0.780998\pi$
$487$		−	301207.i		−	1.27001i	0.772509	−	0.635004i	$-0.219002\pi$
$488$	69984.4	−	136261.i	0.293874	−	0.572180i
$489$	375189.			1.56904
$490$	151355.	−	57912.5i	0.630382	−	0.241202i
$491$		−	163611.i		−	0.678656i	−0.940668	−	0.339328i	$-0.889800\pi$
$491$		−	163611.i		−	0.678656i	0.940668	−	0.339328i	$-0.110200\pi$
$492$	312644.	+	348735.i	1.29157	+	1.44067i
$493$	2094.24			0.00861655
$494$	−81685.4	−	213485.i	−0.334727	−	0.874810i
$495$			426650.i			1.74125i
$496$	19953.6	+	2184.22i	0.0811071	+	0.00887837i
$497$	−748428.			−3.02996
$498$	−296030.	+	113269.i	−1.19365	+	0.456724i
$499$		−	75342.4i		−	0.302579i	−0.988490	−	0.151289i	$-0.951657\pi$
$499$		−	75342.4i		−	0.302579i	0.988490	−	0.151289i	$-0.0483425\pi$
$500$	−145969.	+	130862.i	−0.583875	+	0.523449i
$501$	467331.			1.86187
$502$	−62971.8	−	164577.i	−0.249884	−	0.653073i
$503$		−	422854.i		−	1.67130i	−0.549263	−	0.835650i	$-0.685091\pi$
$503$		−	422854.i		−	1.67130i	0.549263	−	0.835650i	$-0.314909\pi$
$504$	−778480.	−	399831.i	−3.06469	−	1.57404i
$505$	136958.			0.537039
$506$	−93224.7	+	35670.4i	−0.364108	+	0.139318i
$507$		−	54178.6i		−	0.210772i
$508$	−48138.1	−	53695.1i	−0.186536	−	0.208069i
$509$	−478320.			−1.84622			−0.923108	−	0.384541i	$-0.874360\pi$
$509$	−478320.			−1.84622			−0.923108	+	0.384541i	$0.874360\pi$
$510$	4869.44	+	12726.3i	0.0187214	+	0.0489285i
$511$		−	236954.i		−	0.907449i
$512$	259302.	−	38495.1i	0.989159	−	0.146847i
$513$	−537649.			−2.04298
$514$	6116.92	−	2340.50i	0.0231530	−	0.00885897i
$515$		−	48658.4i		−	0.183461i
$516$	−520742.	+	466850.i	−1.95579	+	1.75339i
$517$	318709.			1.19238
$518$	−138113.	−	360958.i	−0.514724	−	1.34523i
$519$			323700.i			1.20173i
$520$	50163.9	−	97670.2i	0.185517	−	0.361206i
$521$	276500.			1.01864			0.509318	−	0.860578i	$-0.329898\pi$
$521$	276500.			1.01864			0.509318	+	0.860578i	$0.329898\pi$
$522$	−69221.8	+	26486.2i	−0.254040	+	0.0972028i
$523$			128321.i			0.469130i	0.972100	+	0.234565i	$0.0753666\pi$
$523$			128321.i			0.469130i	−0.972100	+	0.234565i	$0.924633\pi$
$524$	249736.	+	278565.i	0.909534	+	1.01453i
$525$	−636626.			−2.30976
$526$	−177411.	−	463665.i	−0.641223	−	1.67584i
$527$		−	1545.60i		−	0.00556514i
$528$	100714.	−	920056.i	0.361261	−	3.30025i
$529$	−12167.0			−0.0434783
$530$	79657.4	−	30479.2i	0.283579	−	0.108505i
$531$			423819.i			1.50311i
$532$	−336445.	+	301626.i	−1.18875	+	1.06572i
$533$	−290601.			−1.02292
$534$	−48925.2	−	127866.i	−0.171574	−	0.448408i
$535$		−	28152.4i		−	0.0983577i
$536$	237397.	+	121928.i	0.826315	+	0.424399i
$537$	290983.			1.00906
$538$	423325.	−	161976.i	1.46255	−	0.559611i
$539$			847584.i			2.91746i
$540$	−172397.	−	192299.i	−0.591212	−	0.659460i
$541$	−512001.			−1.74935			−0.874674	−	0.484712i	$-0.838924\pi$
$541$	−512001.			−1.74935			−0.874674	+	0.484712i	$0.838924\pi$
$542$	139745.	+	365225.i	0.475707	+	1.24326i
$543$			116922.i			0.396549i
$544$	−5119.12	−	19525.1i	−0.0172981	−	0.0659773i
$545$	−65273.8			−0.219759
$546$	742685.	−	284172.i	2.49126	−	0.953227i
$547$			161383.i			0.539364i	0.962949	+	0.269682i	$0.0869186\pi$
$547$			161383.i			0.539364i	−0.962949	+	0.269682i	$0.913081\pi$
$548$	170489.	−	152845.i	0.567721	−	0.508967i
$549$	417429.			1.38496
$550$	−164300.	−	429397.i	−0.543139	−	1.41950i
$551$			38267.2i			0.126044i
$552$	51543.7	−	100357.i	0.169160	−	0.329358i
$553$	368446.			1.20482
$554$	10711.0	−	4098.32i	0.0348987	−	0.0133532i
$555$		−	212959.i		−	0.691371i
$556$	−150739.	−	168140.i	−0.487613	−	0.543902i
$557$	87876.0			0.283244			0.141622	−	0.989921i	$-0.454768\pi$
$557$	87876.0			0.283244			0.141622	+	0.989921i	$0.454768\pi$
$558$	19547.4	+	51087.3i	0.0627799	+	0.164076i
$559$		−	433935.i		−	1.38868i
$560$	−215762.	−	23618.4i	−0.688018	−	0.0753137i
$561$	−71267.1			−0.226445
$562$	−332017.	+	127039.i	−1.05120	+	0.402220i
$563$			382020.i			1.20523i	0.798032	+	0.602615i	$0.205874\pi$
$563$			382020.i			1.20523i	−0.798032	+	0.602615i	$0.794126\pi$
$564$	−268221.	+	240462.i	−0.843208	+	0.755943i
$565$	217751.			0.682124
$566$	228339.	+	596764.i	0.712766	+	1.86282i
$567$		−	762788.i		−	2.37267i
$568$	543426.	+	279106.i	1.68439	+	0.865113i
$569$	234061.			0.722944			0.361472	−	0.932383i	$-0.382274\pi$
$569$	234061.			0.722944			0.361472	+	0.932383i	$0.382274\pi$
$570$	−232542.	+	88977.1i	−0.715734	+	0.273860i
$571$		−	24442.3i		−	0.0749670i	−0.999297	−	0.0374835i	$-0.988066\pi$
$571$		−	24442.3i		−	0.0749670i	0.999297	−	0.0374835i	$-0.0119342\pi$
$572$	383342.	+	427594.i	1.17164	+	1.30689i
$573$	−359767.			−1.09575
$574$	205290.	+	536526.i	0.623080	+	1.62842i
$575$		−	56041.8i		−	0.169503i
$576$	416140.	+	580627.i	1.25428	+	1.75006i
$577$	84209.8			0.252936			0.126468	−	0.991971i	$-0.459636\pi$
$577$	84209.8			0.252936			0.126468	+	0.991971i	$0.459636\pi$
$578$	310572.	−	118833.i	0.929621	−	0.355699i
$579$			286332.i			0.854108i
$580$	−13686.9	+	12270.4i	−0.0406863	+	0.0364756i
$581$	−388762.			−1.15168
$582$	−156581.	−	409226.i	−0.462268	−	1.20814i
$583$			446080.i			1.31243i
$584$	−88365.7	+	172050.i	−0.259095	+	0.504463i
$585$	299207.			0.874300
$586$	235804.	−	90225.0i	0.686681	−	0.262743i
$587$		−	386265.i		−	1.12101i	−0.828151	−	0.560505i	$-0.810607\pi$
$587$		−	386265.i		−	1.12101i	0.828151	−	0.560505i	$-0.189393\pi$
$588$	−639493.	−	713315.i	−1.84961	−	2.06313i
$589$	28242.1			0.0814077
$590$	37563.5	+	98172.3i	0.107910	+	0.282023i
$591$		−	406970.i		−	1.16517i
$592$	−34327.5	+	313594.i	−0.0979487	+	0.894796i
$593$	−643367.			−1.82957			−0.914786	−	0.403939i	$-0.867641\pi$
$593$	−643367.			−1.82957			−0.914786	+	0.403939i	$0.867641\pi$
$594$	1.26157e6	−	482711.i	3.57551	−	1.36809i
$595$			16712.9i			0.0472081i
$596$	48690.6	−	43651.6i	0.137073	−	0.122887i
$597$	290162.			0.814127
$598$	25015.5	+	65378.1i	0.0699530	+	0.182823i
$599$			64233.5i			0.179023i	0.995986	+	0.0895113i	$0.0285305\pi$
$599$			64233.5i			0.179023i	−0.995986	+	0.0895113i	$0.971469\pi$
$600$	462248.	+	237413.i	1.28402	+	0.659480i
$601$	−594581.			−1.64612			−0.823061	−	0.567953i	$-0.807735\pi$
$601$	−594581.			−1.64612			−0.823061	+	0.567953i	$0.807735\pi$
$602$	−801159.	+	306546.i	−2.21068	+	0.845868i
$603$			727253.i			2.00010i
$604$	385116.	+	429573.i	1.05564	+	1.17751i
$605$	−395113.			−1.07947
$606$	−289334.	−	756175.i	−0.787868	−	2.05910i
$607$			585031.i			1.58782i	0.608035	+	0.793910i	$0.291958\pi$
$607$			585031.i			1.58782i	−0.608035	+	0.793910i	$0.708042\pi$
$608$	356773.	−	93539.3i	0.965127	−	0.253039i
$609$	−133126.			−0.358946
$610$	96692.1	−	36997.1i	0.259855	−	0.0994278i
$611$		−	223509.i		−	0.598704i
$612$	40955.8	−	36717.3i	0.109349	−	0.0980319i
$613$	−407646.			−1.08483			−0.542415	−	0.840111i	$-0.682490\pi$
$613$	−407646.			−1.08483			−0.542415	+	0.840111i	$0.682490\pi$
$614$	−223723.	−	584701.i	−0.593435	−	1.55095i
$615$			316542.i			0.836914i
$616$	518647.	−	1.00982e6i	1.36682	−	2.66122i
$617$	−336765.			−0.884620			−0.442310	−	0.896862i	$-0.645841\pi$
$617$	−336765.			−0.884620			−0.442310	+	0.896862i	$0.645841\pi$
$618$	−268653.	+	102794.i	−0.703420	+	0.269148i
$619$		−	440822.i		−	1.15049i	−0.817982	−	0.575244i	$-0.804907\pi$
$619$		−	440822.i		−	1.15049i	0.817982	−	0.575244i	$-0.195093\pi$
$620$	9055.83	+	10101.2i	0.0235583	+	0.0262779i
$621$	164650.			0.426953
$622$	10035.5	+	26227.8i	0.0259393	+	0.0677924i
$623$		−	167921.i		−	0.432642i
$624$	−645231.	−	70630.1i	−1.65709	−	0.181393i
$625$	185047.			0.473721
$626$	602910.	−	230690.i	1.53852	−	0.588681i
$627$		−	1.30223e6i		−	3.31248i
$628$	−16713.1	+	14983.4i	−0.0423777	+	0.0379920i
$629$	24290.8			0.0613962
$630$	−211370.	−	552416.i	−0.532552	−	1.39183i
$631$		−	597359.i		−	1.50029i	−0.661271	−	0.750147i	$-0.729983\pi$
$631$		−	597359.i		−	1.50029i	0.661271	−	0.750147i	$-0.270017\pi$
$632$	−267525.	−	137402.i	−0.669778	−	0.344001i
$633$	1.08049e6			2.69658
$634$	469140.	−	179506.i	1.16714	−	0.446582i
$635$		−	48738.3i		−	0.120871i
$636$	−336563.	−	375415.i	−0.832055	−	0.928106i
$637$	594406.			1.46489
$638$	−34357.0	−	89792.1i	−0.0844061	−	0.220596i
$639$			1.66476e6i			4.07708i
$640$	147855.	+	97611.9i	0.360974	+	0.238310i
$641$	370764.			0.902364			0.451182	−	0.892432i	$-0.351002\pi$
$641$	370764.			0.902364			0.451182	+	0.892432i	$0.351002\pi$
$642$	−155435.	+	59473.8i	−0.377120	+	0.144296i
$643$		−	486109.i		−	1.17574i	−0.808955	−	0.587870i	$-0.799967\pi$
$643$		−	486109.i		−	1.17574i	0.808955	−	0.587870i	$-0.200033\pi$
$644$	103033.	−	92370.3i	0.248431	−	0.222721i
$645$	−472671.			−1.13616
$646$	−10149.0	−	26524.5i	−0.0243197	−	0.0635597i
$647$			749289.i			1.78995i	0.446117	+	0.894975i	$0.352807\pi$
$647$			749289.i			1.78995i	−0.446117	+	0.894975i	$0.647193\pi$
$648$	−284462.	+	553853.i	−0.677444	+	1.31900i
$649$	−549763.			−1.30523
$650$	−301134.	+	115222.i	−0.712744	+	0.272716i
$651$			98250.1i			0.231831i
$652$	−250742.	−	279687.i	−0.589836	−	0.657926i
$653$	44182.2			0.103615			0.0518073	−	0.998657i	$-0.483502\pi$
$653$	44182.2			0.103615			0.0518073	+	0.998657i	$0.483502\pi$
$654$	137895.	+	360390.i	0.322399	+	0.842591i
$655$			252850.i			0.589359i
$656$	51024.2	−	466124.i	0.118568	−	1.08316i
$657$	−527066.			−1.22105
$658$	−412657.	+	157894.i	−0.953097	+	0.364681i
$659$		−	479493.i		−	1.10411i	−0.833808	−	0.552054i	$-0.813844\pi$
$659$		−	479493.i		−	1.10411i	0.833808	−	0.552054i	$-0.186156\pi$
$660$	465764.	−	417561.i	1.06925	−	0.958589i
$661$	−10966.3			−0.0250989			−0.0125495	−	0.999921i	$-0.503995\pi$
$661$	−10966.3			−0.0250989			−0.0125495	+	0.999921i	$0.503995\pi$
$662$	−8400.20	−	21954.0i	−0.0191679	−	0.0500953i
$663$			49979.3i			0.113701i
$664$	282277.	+	144979.i	0.640234	+	0.328827i
$665$	−305386.			−0.690568
$666$	−802893.	+	307210.i	−1.81013	+	0.692606i
$667$		−	11719.0i		−	0.0263414i
$668$	−312321.	−	348375.i	−0.699920	−	0.780718i
$669$	140253.			0.313371
$670$	64457.1	+	168459.i	0.143589	+	0.375271i
$671$			541474.i			1.20263i
$672$	325410.	+	1.24116e6i	0.720597	+	2.74846i
$673$	700933.			1.54756			0.773778	−	0.633456i	$-0.218364\pi$
$673$	700933.			1.54756			0.773778	+	0.633456i	$0.218364\pi$
$674$	−354024.	+	135459.i	−0.779314	+	0.298187i
$675$			758388.i			1.66450i
$676$	−40387.8	+	36208.0i	−0.0883805	+	0.0792339i
$677$	−387647.			−0.845783			−0.422892	−	0.906180i	$-0.638985\pi$
$677$	−387647.			−0.845783			−0.422892	+	0.906180i	$0.638985\pi$
$678$	−460013.	−	1.20225e6i	−1.00072	−	2.61538i
$679$		−	537417.i		−	1.16566i
$680$	6232.62	−	12135.0i	0.0134788	−	0.0262436i
$681$	−113512.			−0.244765
$682$	−66268.6	+	25356.2i	−0.142475	+	0.0545150i
$683$		−	630992.i		−	1.35264i	−0.736607	−	0.676321i	$-0.763573\pi$
$683$		−	630992.i		−	1.35264i	0.736607	−	0.676321i	$-0.236427\pi$
$684$	670918.	+	748367.i	1.43403	+	1.59957i
$685$	154751.			0.329800
$686$	−150809.	−	394140.i	−0.320464	−	0.837534i
$687$			561031.i			1.18870i
$688$	696032.	+	76191.0i	1.47046	+	0.160963i
$689$	312834.			0.658985
$690$	71214.1	−	27248.5i	0.149578	−	0.0572327i
$691$		−	23182.2i		−	0.0485511i	−0.999705	−	0.0242755i	$-0.992272\pi$
$691$		−	23182.2i		−	0.0485511i	0.999705	−	0.0242755i	$-0.00772791\pi$
$692$	241304.	−	216331.i	0.503909	−	0.451759i
$693$	3.09352e6			6.44149
$694$	−243414.	−	636165.i	−0.505391	−	1.32084i
$695$		−	152618.i		−	0.315963i
$696$	96661.6	+	49645.9i	0.199543	+	0.102486i
$697$	−36105.8			−0.0743209
$698$	−612953.	+	234533.i	−1.25810	+	0.481385i
$699$			506977.i			1.03761i
$700$	425462.	+	474577.i	0.868290	+	0.968524i
$701$	424904.			0.864678			0.432339	−	0.901711i	$-0.357688\pi$
$701$	424904.			0.864678			0.432339	+	0.901711i	$0.357688\pi$
$702$	−338523.	−	884732.i	−0.686932	−	1.79530i
$703$			443855.i			0.898113i
$704$	−753169.	+	539803.i	−1.51966	+	1.08916i
$705$	−243461.			−0.489836
$706$	−508476.	+	194557.i	−1.02014	+	0.390335i
$707$		−	993048.i		−	1.98670i
$708$	462673.	−	414791.i	0.923014	−	0.827490i
$709$	−945599.			−1.88111			−0.940556	−	0.339640i	$-0.889695\pi$
$709$	−945599.			−1.88111			−0.940556	+	0.339640i	$0.889695\pi$
$710$	147549.	+	385620.i	0.292698	+	0.764967i
$711$		−	819549.i		−	1.62120i
$712$	−62621.6	+	121926.i	−0.123528	+	0.240511i
$713$	−8648.89			−0.0170130
$714$	92275.0	−	35307.0i	0.181004	−	0.0692571i
$715$			388122.i			0.759199i
$716$	−194466.	−	216915.i	−0.379330	−	0.423119i
$717$	722256.			1.40492
$718$	−194612.	−	508620.i	−0.377504	−	0.986608i
$719$			708743.i			1.37098i	0.728082	+	0.685490i	$0.240412\pi$
$719$			708743.i			1.37098i	−0.728082	+	0.685490i	$0.759588\pi$
$720$	−52535.3	+	479929.i	−0.101341	+	0.925788i
$721$	−352809.			−0.678686
$722$	−2191.56	+	838.552i	−0.00420416	+	0.00160863i
$723$		−	755402.i		−	1.44511i
$724$	87160.2	−	78139.9i	0.166280	−	0.149072i
$725$	53978.3			0.102694
$726$	834703.	+	2.18150e6i	1.58365	+	4.13887i
$727$			576227.i			1.09025i	0.838356	+	0.545123i	$0.183517\pi$
$727$			576227.i			1.09025i	−0.838356	+	0.545123i	$0.816483\pi$
$728$	−708180.	−	363725.i	−1.33623	−	0.686293i
$729$	235576.			0.443277
$730$	−122088.	+	46714.4i	−0.229102	+	0.0876607i
$731$		−	53914.3i		−	0.100895i
$732$	−408537.	−	455697.i	−0.762446	−	0.850461i
$733$	−227718.			−0.423827			−0.211914	−	0.977288i	$-0.567970\pi$
$733$	−227718.			−0.423827			−0.211914	+	0.977288i	$0.567970\pi$
$734$	263667.	+	689095.i	0.489399	+	1.27905i
$735$		−	647466.i		−	1.19851i
$736$	−109259.	+	28645.6i	−0.201697	+	0.0528814i
$737$	−943368.			−1.73678
$738$	1.19342e6	−	456634.i	2.19119	−	0.838409i
$739$		−	577338.i		−	1.05716i	−0.848883	−	0.528581i	$-0.822724\pi$
$739$		−	577338.i		−	1.05716i	0.848883	−	0.528581i	$-0.177276\pi$
$740$	−158752.	+	142322.i	−0.289905	+	0.259902i
$741$	−913249.			−1.66323
$742$	−220996.	−	577574.i	−0.401399	−	1.04906i
$743$			650891.i			1.17905i	0.807752	+	0.589523i	$0.200684\pi$
$743$			650891.i			1.17905i	−0.807752	+	0.589523i	$0.799316\pi$
$744$	36639.8	−	71338.5i	0.0661922	−	0.128878i
$745$	44195.8			0.0796285
$746$	−618098.	+	236502.i	−1.11066	+	0.424968i
$747$			864739.i			1.54969i
$748$	47628.4	+	53126.5i	0.0851261	+	0.0949529i
$749$	−204125.			−0.363859
$750$	279902.	+	731525.i	0.497604	+	1.30049i
$751$		−	588469.i		−	1.04338i	−0.853134	−	0.521691i	$-0.825301\pi$
$751$		−	588469.i		−	1.04338i	0.853134	−	0.521691i	$-0.174699\pi$
$752$	358508.	+	39244.0i	0.633962	+	0.0693966i
$753$	−704029.			−1.24165
$754$	−62970.8	+	24094.4i	−0.110763	+	0.0423812i
$755$			389918.i			0.684036i
$756$	−1.39430e6	+	1.25001e6i	−2.43957	+	2.18710i
$757$	17544.2			0.0306156			0.0153078	−	0.999883i	$-0.495127\pi$
$757$	17544.2			0.0306156			0.0153078	+	0.999883i	$0.495127\pi$
$758$	110159.	+	287902.i	0.191727	+	0.501078i
$759$			398798.i			0.692260i
$760$	221738.	+	113886.i	0.383896	+	0.197171i
$761$	−312934.			−0.540360			−0.270180	−	0.962810i	$-0.587083\pi$
$761$	−312934.			−0.540360			−0.270180	+	0.962810i	$0.587083\pi$
$762$	−269094.	+	102963.i	−0.463440	+	0.177325i
$763$			473283.i			0.812965i
$764$	240435.	+	268191.i	0.411918	+	0.459470i
$765$	37175.1			0.0635227
$766$	80853.7	+	211312.i	0.137798	+	0.360135i
$767$			385546.i			0.655369i
$768$	226581.	−	1.02255e6i	0.384151	−	1.73365i
$769$	875598.			1.48065			0.740324	−	0.672250i	$-0.234672\pi$
$769$	875598.			1.48065			0.740324	+	0.672250i	$0.234672\pi$
$770$	716575.	−	274182.i	1.20859	−	0.462442i
$771$		−	26167.0i		−	0.0440195i
$772$	213448.	−	191358.i	0.358143	−	0.321079i
$773$	860344.			1.43984			0.719918	−	0.694059i	$-0.244179\pi$
$773$	860344.			1.43984			0.719918	+	0.694059i	$0.244179\pi$
$774$	681862.	+	1.78205e6i	1.13819	+	2.97466i
$775$		−	39837.2i		−	0.0663263i
$776$	−200415.	+	390213.i	−0.332818	+	0.648005i
$777$	−1.54411e6			−2.55762
$778$	−150449.	+	57566.2i	−0.248560	+	0.0951061i
$779$		−	659744.i		−	1.08718i
$780$	−292834.	−	326638.i	−0.481318	−	0.536880i
$781$	−2.15947e6			−3.54033
$782$	3108.05	+	8122.90i	0.00508247	+	0.0132831i
$783$			158588.i			0.258670i
$784$	−104367.	+	953428.i	−0.169797	+	1.55116i
$785$	−15170.2			−0.0246180
$786$	1.39603e6	−	534162.i	2.25970	−	0.864625i
$787$		−	209246.i		−	0.337837i	−0.985630	−	0.168919i	$-0.945972\pi$
$787$		−	209246.i		−	0.337837i	0.985630	−	0.168919i	$-0.0540275\pi$
$788$	−303378.	+	271981.i	−0.488576	+	0.438012i
$789$	−1.98347e6			−3.18619
$790$	−72637.4	−	189838.i	−0.116387	−	0.304179i
$791$		−	1.57885e6i		−	2.52342i
$792$	−2.24617e6	−	1.15365e6i	−3.58091	−	1.83917i
$793$	379733.			0.603854
$794$	749620.	−	286825.i	1.18905	−	0.454964i
$795$		−	340759.i		−	0.539155i
$796$	−193918.	−	216303.i	−0.306049	−	0.341379i
$797$	388487.			0.611589			0.305795	−	0.952097i	$-0.401078\pi$
$797$	388487.			0.611589			0.305795	+	0.952097i	$0.401078\pi$
$798$	645149.	+	1.68610e6i	1.01310	+	2.64775i
$799$		−	27769.9i		−	0.0434991i
$800$	−131943.	−	503250.i	−0.206161	−	0.786329i
$801$	−373513.			−0.582157
$802$	−457823.	+	175176.i	−0.711784	+	0.272349i
$803$		−	683692.i		−	1.06030i
$804$	793926.	−	711761.i	1.22820	−	1.10109i
$805$	93522.0			0.144319
$806$	17782.2	+	46473.9i	0.0273726	+	0.0715383i
$807$		−	1.81091e6i		−	2.78067i
$808$	−370331.	+	721043.i	−0.567241	+	1.10443i
$809$	719829.			1.09985			0.549924	−	0.835215i	$-0.314657\pi$
$809$	719829.			1.09985			0.549924	+	0.835215i	$0.314657\pi$
$810$	−393019.	+	150380.i	−0.599023	+	0.229203i
$811$		−	650174.i		−	0.988526i	−0.869312	−	0.494263i	$-0.835438\pi$
$811$		−	650174.i		−	0.988526i	0.869312	−	0.494263i	$-0.164562\pi$
$812$	88969.2	+	99239.7i	0.134936	+	0.150513i
$813$	1.56236e6			2.36375
$814$	−398502.	−	1.04149e6i	−0.601425	−	1.57183i
$815$		−	253868.i		−	0.382202i
$816$	−80166.8	−	8775.44i	−0.120397	−	0.0131792i
$817$	985152.			1.47591
$818$	−617841.	+	236403.i	−0.923358	+	0.353303i
$819$		−	2.16947e6i		−	3.23434i
$820$	235968.	−	211547.i	0.350934	−	0.314615i
$821$	461310.			0.684394			0.342197	−	0.939628i	$-0.388829\pi$
$821$	461310.			0.684394			0.342197	+	0.939628i	$0.388829\pi$
$822$	−326921.	−	854408.i	−0.483837	−	1.26451i
$823$			292392.i			0.431683i	0.976428	+	0.215842i	$0.0692495\pi$
$823$			292392.i			0.431683i	−0.976428	+	0.215842i	$0.930751\pi$
$824$	256171.	+	131571.i	0.377290	+	0.193778i
$825$	−1.83688e6			−2.69881
$826$	711821.	−	272362.i	1.04330	−	0.399197i
$827$			1.01674e6i			1.48661i	0.668952	+	0.743305i	$0.266743\pi$
$827$			1.01674e6i			1.48661i	−0.668952	+	0.743305i	$0.733257\pi$
$828$	−205463.	−	229181.i	−0.299690	−	0.334286i
$829$	1.21538e6			1.76849			0.884245	−	0.467023i	$-0.154673\pi$
$829$	1.21538e6			1.76849			0.884245	+	0.467023i	$0.154673\pi$
$830$	76642.6	+	200306.i	0.111254	+	0.290762i
$831$		−	45819.5i		−	0.0663512i
$832$	378561.	+	528194.i	0.546877	+	0.763039i
$833$	73852.1			0.106432
$834$	−842635.	+	322416.i	−1.21146	+	0.463537i
$835$		−	316215.i		−	0.453534i
$836$	−970756.	+	870291.i	−1.38899	+	1.24524i
$837$	117042.			0.167066
$838$	−234522.	−	612923.i	−0.333960	−	0.872806i
$839$		−	281848.i		−	0.400397i	−0.979755	−	0.200198i	$-0.935841\pi$
$839$		−	281848.i		−	0.400397i	0.979755	−	0.200198i	$-0.0641587\pi$
$840$	−396193.	+	771396.i	−0.561498	+	1.09325i
$841$	−695993.			−0.984041
$842$	−442916.	+	169472.i	−0.624738	+	0.239042i
$843$			1.42030e6i			1.99860i
$844$	−722100.	−	805458.i	−1.01371	−	1.13073i
$845$	−36659.4			−0.0513420
$846$	351210.	+	917888.i	0.490711	+	1.28247i
$847$			2.86486e6i			3.99334i
$848$	−54927.8	+	501785.i	−0.0763837	+	0.697793i
$849$	2.55284e6			3.54168
$850$	−37414.5	+	14315.8i	−0.0517848	+	0.0198143i
$851$		−	135927.i		−	0.187692i
$852$	1.81738e6	−	1.62929e6i	2.50361	−	2.24450i
$853$	−657320.			−0.903397			−0.451698	−	0.892171i	$-0.649182\pi$
$853$	−657320.			−0.903397			−0.451698	+	0.892171i	$0.649182\pi$
$854$	−268256.	−	701088.i	−0.367818	−	0.961295i
$855$			679283.i			0.929220i
$856$	148214.	+	76123.2i	0.202274	+	0.103889i
$857$	381565.			0.519525			0.259763	−	0.965672i	$-0.416356\pi$
$857$	381565.			0.519525			0.259763	+	0.965672i	$0.416356\pi$
$858$	2.14290e6	−	819932.i	2.91090	−	1.11379i
$859$			279276.i			0.378484i	0.981931	+	0.189242i	$0.0606030\pi$
$859$			279276.i			0.378484i	−0.981931	+	0.189242i	$0.939397\pi$
$860$	315889.	+	352355.i	0.427108	+	0.476413i
$861$	2.29516e6			3.09604
$862$	−33482.2	−	87505.8i	−0.0450608	−	0.117767i
$863$		−	926561.i		−	1.24409i	−0.782981	−	0.622046i	$-0.786302\pi$
$863$		−	926561.i		−	1.24409i	0.782981	−	0.622046i	$-0.213698\pi$
$864$	1.47855e6	−	387648.i	1.98065	−	0.519291i
$865$	219028.			0.292731
$866$	417460.	−	159732.i	0.556646	−	0.212988i
$867$		−	1.32857e6i		−	1.76744i
$868$	73241.1	−	65661.3i	0.0972110	−	0.0871505i
$869$	1.06309e6			1.40777
$870$	26245.2	+	68591.9i	0.0346746	+	0.0906222i
$871$			661579.i			0.872058i
$872$	176498.	−	343646.i	0.232117	−	0.451938i
$873$	−1.19540e6			−1.56850
$874$	−148426.	+	56792.0i	−0.194307	+	0.0743471i
$875$			960677.i			1.25476i
$876$	515839.	+	575386.i	0.672211	+	0.749810i
$877$	54005.4			0.0702163			0.0351082	−	0.999384i	$-0.488822\pi$
$877$	54005.4			0.0702163			0.0351082	+	0.999384i	$0.488822\pi$
$878$	71623.4	+	187188.i	0.0929107	+	0.242822i
$879$		−	1.00872e6i		−	1.30555i
$880$	−622547.	−	68147.0i	−0.803909	−	0.0879997i
$881$	907981.			1.16984			0.584918	−	0.811093i	$-0.301127\pi$
$881$	907981.			1.16984			0.584918	+	0.811093i	$0.301127\pi$
$882$	−2.44106e6	+	934017.i	−3.13791	+	1.20065i
$883$			1.35451e6i			1.73725i	0.495471	+	0.868624i	$0.334995\pi$
$883$			1.35451e6i			1.73725i	−0.495471	+	0.868624i	$0.665005\pi$
$884$	37257.4	−	33401.6i	0.0476769	−	0.0427427i
$885$	419962.			0.536196
$886$	−36104.2	−	94358.4i	−0.0459928	−	0.120202i
$887$		−	1.52685e6i		−	1.94066i	−0.241791	−	0.970328i	$-0.577735\pi$
$887$		−	1.52685e6i		−	1.94066i	0.241791	−	0.970328i	$-0.422265\pi$
$888$	1.12116e6	+	575835.i	1.42182	+	0.730251i
$889$	−353388.			−0.447145
$890$	−86519.5	+	33104.8i	−0.109228	+	0.0417937i
$891$		−	2.20090e6i		−	2.77233i
$892$	−93731.9	−	104552.i	−0.117803	−	0.131402i
$893$	507427.			0.636312
$894$	−93366.5	−	244014.i	−0.116820	−	0.305309i
$895$		−	196890.i		−	0.245798i
$896$	707757.	−	1.07206e6i	0.881594	−	1.33537i
$897$	279675.			0.347591
$898$	−227953.	+	87221.3i	−0.282679	+	0.108161i
$899$		−	8330.44i		−	0.0103074i
$900$	1.05562e6	−	946372.i	1.30323	−	1.16836i
$901$	38868.1			0.0478788
$902$	592330.	+	1.54806e6i	0.728033	+	1.90272i
$903$			3.42720e6i			4.20305i
$904$	−588792.	+	1.14639e6i	−0.720485	+	1.40280i
$905$	79114.2			0.0965955
$906$	2.15281e6	−	823726.i	2.62271	−	1.00352i
$907$		−	255453.i		−	0.310525i	−0.987873	−	0.155262i	$-0.950378\pi$
$907$		−	255453.i		−	0.310525i	0.987873	−	0.155262i	$-0.0496223\pi$
$908$	75861.2	+	84618.5i	0.0920128	+	0.102635i
$909$	−2.20888e6			−2.67327
$910$	−192282.	−	502531.i	−0.232197	−	0.606848i
$911$		−	1.02027e6i		−	1.22936i	−0.788777	−	0.614679i	$-0.789285\pi$
$911$		−	1.02027e6i		−	1.22936i	0.788777	−	0.614679i	$-0.210715\pi$
$912$	160350.	−	1.46485e6i	0.192787	−	1.76118i
$913$	−1.12171e6			−1.34567
$914$	−556798.	+	213046.i	−0.666507	+	0.255024i
$915$		−	413630.i		−	0.494049i
$916$	418224.	−	374942.i	0.498446	−	0.446861i
$917$	1.83335e6			2.18025
$918$	−42059.8	−	109924.i	−0.0499094	−	0.130438i
$919$			1.14150e6i			1.35159i	0.737090	+	0.675795i	$0.236200\pi$
$919$			1.14150e6i			1.35159i	−0.737090	+	0.675795i	$0.763800\pi$
$920$	−67905.5	−	34876.6i	−0.0802286	−	0.0412058i
$921$	−2.50124e6			−2.94873
$922$	−442929.	+	169477.i	−0.521042	+	0.199365i
$923$			1.51442e6i			1.77764i
$924$	−3.02762e6	−	3.37713e6i	−3.54616	−	3.95552i
$925$	626086.			0.731730
$926$	−63468.4	−	165875.i	−0.0740177	−	0.193446i
$927$			784766.i			0.913232i
$928$	−27590.9	−	105236.i	−0.0320383	−	0.122199i
$929$	182228.			0.211146			0.105573	−	0.994412i	$-0.466332\pi$
$929$	182228.			0.211146			0.105573	+	0.994412i	$0.466332\pi$
$930$	50622.4	−	19369.6i	0.0585298	−	0.0223951i
$931$			1.34947e6i			1.55691i
$932$	377929.	−	338816.i	0.435089	−	0.390061i
$933$	112197.			0.128890
$934$	−72682.3	−	189956.i	−0.0833172	−	0.217750i
$935$			48222.2i			0.0551600i
$936$	−809047.	+	1.57523e6i	−0.923468	+	1.79801i
$937$	1.56507e6			1.78260			0.891299	−	0.453417i	$-0.149795\pi$
$937$	1.56507e6			1.78260			0.891299	+	0.453417i	$0.149795\pi$
$938$	1.22145e6	−	467361.i	1.38826	−	0.531186i
$939$		−	2.57913e6i		−	2.92511i
$940$	162707.	+	181489.i	0.184141	+	0.205397i
$941$	−955878.			−1.07950			−0.539751	−	0.841825i	$-0.681482\pi$
$941$	−955878.			−1.07950			−0.539751	+	0.841825i	$0.681482\pi$
$942$	32048.1	+	83757.9i	0.0361161	+	0.0943896i
$943$			202041.i			0.227204i
$944$	−618416.	−	67694.8i	−0.693964	−	0.0759646i
$945$	−1.26559e6			−1.41720
$946$	−2.31161e6	+	884488.i	−2.58305	+	0.988347i
$947$		−	168701.i		−	0.188113i	−0.995567	−	0.0940565i	$-0.970017\pi$
$947$		−	168701.i		−	0.188113i	0.995567	−	0.0940565i	$-0.0299834\pi$
$948$	−894683.	+	802091.i	−0.995526	+	0.892498i
$949$	−479470.			−0.532389
$950$	−261587.	−	683658.i	−0.289847	−	0.757516i
$951$		−	2.00689e6i		−	2.21903i
$952$	−87987.9	−	45191.0i	−0.0970843	−	0.0498630i
$953$	−598059.			−0.658504			−0.329252	−	0.944242i	$-0.606797\pi$
$953$	−598059.			−0.658504			−0.329252	+	0.944242i	$0.606797\pi$
$954$	−1.28472e6	+	491570.i	−1.41160	+	0.540118i
$955$			243433.i			0.266915i
$956$	−482689.	−	538410.i	−0.528143	−	0.589111i
$957$	−384114.			−0.419407
$958$	336289.	+	878894.i	0.366423	+	0.957647i
$959$		−	1.12205e6i		−	1.22005i
$960$	575343.	−	412354.i	0.624288	−	0.447432i
$961$	917373.			0.993343
$962$	−730389.	+	279467.i	−0.789231	+	0.301982i
$963$			454044.i			0.489605i
$964$	−563118.	+	504841.i	−0.605962	+	0.543251i
$965$	193744.			0.208052
$966$	−197571.	−	516354.i	−0.211724	−	0.553341i
$967$			226129.i			0.241826i	0.992663	+	0.120913i	$0.0385822\pi$
$967$			226129.i			0.241826i	−0.992663	+	0.120913i	$0.961418\pi$
$968$	1.06837e6	−	2.08015e6i	1.14018	−	2.21995i
$969$	−113467.			−0.120843
$970$	−276899.	+	105949.i	−0.294291	+	0.112604i
$971$			471460.i			0.500042i	0.968240	+	0.250021i	$0.0804375\pi$
$971$			471460.i			0.500042i	−0.968240	+	0.250021i	$0.919563\pi$
$972$	369203.	+	411823.i	0.390780	+	0.435891i
$973$	−1.10659e6			−1.16886
$974$	430559.	+	1.12527e6i	0.453852	+	1.18614i
$975$			1.28820e6i			1.35510i
$976$	−66674.1	+	609092.i	−0.0699935	+	0.639416i
$977$	670229.			0.702156			0.351078	−	0.936346i	$-0.385815\pi$
$977$	670229.			0.702156			0.351078	+	0.936346i	$0.385815\pi$
$978$	−1.40166e6	+	536313.i	−1.46543	+	0.560713i
$979$		−	484508.i		−	0.505516i
$980$	−482658.	+	432707.i	−0.502559	+	0.450548i
$981$	1.05274e6			1.09392
$982$	233873.	+	611229.i	0.242526	+	0.633842i
$983$		−	53957.2i		−	0.0558396i	−0.999610	−	0.0279198i	$-0.991112\pi$
$983$		−	53957.2i		−	0.0558396i	0.999610	−	0.0279198i	$-0.00888830\pi$
$984$	−1.66649e6	−	855918.i	−1.72113	−	0.883979i
$985$	−275372.			−0.283823
$986$	−7823.81	+	2993.61i	−0.00804757	+	0.00307923i
$987$			1.76527e6i			1.81207i
$988$	610331.	+	680787.i	0.625247	+	0.697425i
$989$	−301694.			−0.308443
$990$	−609873.	−	1.59391e6i	−0.622256	−	1.62627i
$991$			281256.i			0.286388i	0.989695	+	0.143194i	$0.0457372\pi$
$991$			281256.i			0.286388i	−0.989695	+	0.143194i	$0.954263\pi$
$992$	−77666.3	+	20362.7i	−0.0789241	+	0.0206925i
$993$	−93914.8			−0.0952436
$994$	2.79602e6	−	1.06984e6i	2.82988	−	1.08279i
$995$		−	196335.i		−	0.198314i
$996$	944016.	−	846318.i	0.951614	−	0.853130i
$997$	−1.07803e6			−1.08452			−0.542262	−	0.840210i	$-0.682432\pi$
$997$	−1.07803e6			−1.08452			−0.542262	+	0.840210i	$0.682432\pi$
$998$	107698.	+	281469.i	0.108130	+	0.282598i
$999$			1.83944e6i			1.84312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.5.c.a.47.6	yes	44
4.3	odd	2	inner	92.5.c.a.47.5	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.5.c.a.47.5	✓	44	4.3	odd	2	inner
92.5.c.a.47.6	yes	44	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	92.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.73586 + 1.42945i) q^{2} +15.9813i q^{3} +(11.9134 - 10.6804i) q^{4} +10.8136 q^{5} +(-22.8444 - 59.7040i) q^{6} -78.4065i q^{7} +(-29.2396 + 56.9302i) q^{8} -174.403 q^{9} +(-40.3982 + 15.4575i) q^{10} -226.229i q^{11} +(170.687 + 190.391i) q^{12} -158.653 q^{13} +(112.078 + 292.916i) q^{14} +172.816i q^{15} +(27.8566 - 254.480i) q^{16} -19.7119 q^{17} +(651.544 - 249.299i) q^{18} -360.187i q^{19} +(128.826 - 115.494i) q^{20} +1253.04 q^{21} +(323.382 + 845.161i) q^{22} +110.304i q^{23} +(-909.819 - 467.288i) q^{24} -508.066 q^{25} +(592.707 - 226.786i) q^{26} -1492.70i q^{27} +(-837.415 - 934.085i) q^{28} -106.243 q^{29} +(-247.031 - 645.616i) q^{30} +78.4095i q^{31} +(259.697 + 990.522i) q^{32} +3615.44 q^{33} +(73.6410 - 28.1771i) q^{34} -847.856i q^{35} +(-2077.72 + 1862.70i) q^{36} -1232.29 q^{37} +(514.867 + 1345.61i) q^{38} -2535.49i q^{39} +(-316.186 + 615.620i) q^{40} +1831.67 q^{41} +(-4681.18 + 1791.15i) q^{42} +2735.12i q^{43} +(-2416.22 - 2695.15i) q^{44} -1885.92 q^{45} +(-157.674 - 412.081i) q^{46} +1408.79i q^{47} +(4066.92 + 445.185i) q^{48} -3746.57 q^{49} +(1898.07 - 726.253i) q^{50} -315.022i q^{51} +(-1890.10 + 1694.49i) q^{52} -1971.81 q^{53} +(2133.73 + 5576.51i) q^{54} -2446.35i q^{55} +(4463.69 + 2292.57i) q^{56} +5756.26 q^{57} +(396.908 - 151.868i) q^{58} -2430.12i q^{59} +(1845.75 + 2058.82i) q^{60} -2393.48 q^{61} +(-112.082 - 292.927i) q^{62} +13674.3i q^{63} +(-2386.09 - 3329.23i) q^{64} -1715.61 q^{65} +(-13506.8 + 5168.07i) q^{66} -4169.97i q^{67} +(-234.835 + 210.532i) q^{68} -1762.81 q^{69} +(1211.97 + 3167.48i) q^{70} -9545.49i q^{71} +(5099.46 - 9928.77i) q^{72} +3022.12 q^{73} +(4603.68 - 1761.50i) q^{74} -8119.56i q^{75} +(-3846.95 - 4291.03i) q^{76} -17737.8 q^{77} +(3624.35 + 9472.24i) q^{78} +4699.18i q^{79} +(301.230 - 2751.84i) q^{80} +9728.64 q^{81} +(-6842.88 + 2618.28i) q^{82} -4958.29i q^{83} +(14927.9 - 13383.0i) q^{84} -213.157 q^{85} +(-3909.70 - 10218.0i) q^{86} -1697.90i q^{87} +(12879.3 + 6614.85i) q^{88} +2141.67 q^{89} +(7045.54 - 2695.82i) q^{90} +12439.4i q^{91} +(1178.10 + 1314.09i) q^{92} -1253.09 q^{93} +(-2013.79 - 5263.04i) q^{94} -3894.91i q^{95} +(-15829.8 + 4150.30i) q^{96} +6854.24 q^{97} +(13996.7 - 5355.53i) q^{98} +39454.9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 24 q^{5} + 33 q^{6} - 27 q^{8} - 1300 q^{9} - 46 q^{10} + 145 q^{12} + 472 q^{13} - 264 q^{14} + 272 q^{16} - 648 q^{17} + 1313 q^{18} + 324 q^{20} - 288 q^{21} + 796 q^{22} - 1028 q^{24} + 5604 q^{25}+ \cdots + 57204 q^{98}+O(q^{100}) \) 44 * q + 24 * q^5 + 33 * q^6 - 27 * q^8 - 1300 * q^9 - 46 * q^10 + 145 * q^12 + 472 * q^13 - 264 * q^14 + 272 * q^16 - 648 * q^17 + 1313 * q^18 + 324 * q^20 - 288 * q^21 + 796 * q^22 - 1028 * q^24 + 5604 * q^25 - 3015 * q^26 - 510 * q^28 - 840 * q^29 + 1390 * q^30 + 4200 * q^32 + 320 * q^33 - 4302 * q^34 - 3741 * q^36 - 680 * q^37 + 5940 * q^38 - 626 * q^40 + 7320 * q^41 + 1320 * q^42 - 378 * q^44 - 3240 * q^45 - 8813 * q^48 - 19444 * q^49 - 6960 * q^50 + 1519 * q^52 + 4152 * q^53 - 14405 * q^54 + 13026 * q^56 + 3840 * q^57 + 6771 * q^58 - 180 * q^60 + 6360 * q^61 + 9309 * q^62 - 12765 * q^64 - 15792 * q^65 - 5610 * q^66 - 5484 * q^68 + 4236 * q^70 + 39063 * q^72 - 2888 * q^73 + 43854 * q^74 - 13712 * q^76 + 4320 * q^77 + 18907 * q^78 + 12174 * q^80 + 31628 * q^81 - 31507 * q^82 - 16642 * q^84 - 1904 * q^85 - 25470 * q^86 + 540 * q^88 - 9768 * q^89 - 42044 * q^90 - 11136 * q^93 - 2219 * q^94 + 24435 * q^96 - 3752 * q^97 + 57204 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more