LMFDB - Embedded newform 115.5.i.a.14.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,5,Mod(14,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 21]))

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

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

chi := DirichletCharacter("115.14");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	115.i (of order $22$, degree $10$, 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:	$11.8875457546$
Analytic rank:	$0$
Dimension:	$460$
Relative dimension:	$46$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			14.5
Character	$\chi$	$=$	115.14
Dual form			115.5.i.a.74.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80372 - 6.14291i) q^{2} +(-12.3789 + 10.7264i) q^{3} +(-21.0219 + 13.5100i) q^{4} +(-20.7399 + 13.9592i) q^{5} +(88.2193 + 56.6951i) q^{6} +(-35.9524 + 78.7248i) q^{7} +(43.4924 + 37.6864i) q^{8} +(26.6544 - 185.386i) q^{9} +O(q^{10})$	\(q+(-1.80372 - 6.14291i) q^{2} +(-12.3789 + 10.7264i) q^{3} +(-21.0219 + 13.5100i) q^{4} +(-20.7399 + 13.9592i) q^{5} +(88.2193 + 56.6951i) q^{6} +(-35.9524 + 78.7248i) q^{7} +(43.4924 + 37.6864i) q^{8} +(26.6544 - 185.386i) q^{9} +(123.159 + 102.225i) q^{10} +(-23.0470 + 78.4908i) q^{11} +(115.315 - 392.728i) q^{12} +(-156.294 + 71.3772i) q^{13} +(548.448 + 78.8549i) q^{14} +(107.006 - 395.262i) q^{15} +(-13.0358 + 28.5444i) q^{16} +(-62.9639 - 40.4644i) q^{17} +(-1186.89 + 170.648i) q^{18} +(-119.015 - 185.191i) q^{19} +(247.404 - 573.643i) q^{20} +(-399.381 - 1360.17i) q^{21} +523.733 q^{22} +(-374.337 + 373.782i) q^{23} -942.625 q^{24} +(235.284 - 579.022i) q^{25} +(720.376 + 831.358i) q^{26} +(941.269 + 1464.64i) q^{27} +(-307.781 - 2140.66i) q^{28} +(667.842 + 429.196i) q^{29} +(-2621.07 + 55.6180i) q^{30} +(-951.947 + 1098.61i) q^{31} +(1110.26 + 159.632i) q^{32} +(-556.625 - 1218.84i) q^{33} +(-135.000 + 459.769i) q^{34} +(-353.283 - 2134.61i) q^{35} +(1944.23 + 4257.27i) q^{36} +(117.726 - 818.806i) q^{37} +(-922.944 + 1065.13i) q^{38} +(1169.13 - 2560.04i) q^{39} +(-1428.10 - 174.493i) q^{40} +(-0.212536 - 1.47822i) q^{41} +(-7635.01 + 4906.72i) q^{42} +(829.162 + 956.904i) q^{43} +(-575.917 - 1961.39i) q^{44} +(2035.02 + 4216.95i) q^{45} +(2971.31 + 1625.32i) q^{46} -1469.07i q^{47} +(-144.809 - 493.174i) q^{48} +(-3332.70 - 3846.14i) q^{49} +(-3981.27 - 400.935i) q^{50} +(1213.46 - 174.469i) q^{51} +(2321.30 - 3612.02i) q^{52} +(534.513 - 1170.42i) q^{53} +(7299.39 - 8423.94i) q^{54} +(-617.674 - 1949.60i) q^{55} +(-4530.51 + 2069.01i) q^{56} +(3459.71 + 1015.86i) q^{57} +(1431.91 - 4876.65i) q^{58} +(2641.02 + 5783.03i) q^{59} +(3090.52 + 9754.82i) q^{60} +(123.541 + 107.049i) q^{61} +(8465.69 + 3866.15i) q^{62} +(13636.2 + 8763.43i) q^{63} +(-950.550 - 6611.22i) q^{64} +(2245.16 - 3662.09i) q^{65} +(-6483.23 + 5617.75i) q^{66} +(-3144.18 + 923.214i) q^{67} +1870.30 q^{68} +(624.557 - 8642.28i) q^{69} +(-12475.5 + 6020.43i) q^{70} +(7007.84 - 2057.69i) q^{71} +(8145.78 - 7058.36i) q^{72} +(-120.871 - 188.078i) q^{73} +(-5242.20 + 753.714i) q^{74} +(3298.25 + 9691.40i) q^{75} +(5003.86 + 2285.19i) q^{76} +(-5350.58 - 4636.30i) q^{77} +(-17834.9 - 2564.27i) q^{78} +(-1477.56 + 674.777i) q^{79} +(-128.095 - 773.975i) q^{80} +(-12806.0 - 3760.19i) q^{81} +(-8.69723 + 3.97189i) q^{82} +(-886.258 + 6164.06i) q^{83} +(26771.5 + 23197.7i) q^{84} +(1870.71 - 39.6957i) q^{85} +(4382.60 - 6819.46i) q^{86} +(-12870.9 + 1850.55i) q^{87} +(-3960.40 + 2545.19i) q^{88} +(-10641.3 + 9220.77i) q^{89} +(22233.7 - 20107.1i) q^{90} -14870.4i q^{91} +(2819.51 - 12914.9i) q^{92} -23810.5i q^{93} +(-9024.38 + 2649.80i) q^{94} +(5053.48 + 2179.49i) q^{95} +(-15456.1 + 9933.05i) q^{96} +(1362.49 + 9476.30i) q^{97} +(-17615.2 + 27409.9i) q^{98} +(13936.8 + 6364.71i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 460 q + 306 q^{4} - 11 q^{5} - 182 q^{6} + 944 q^{9}+O(q^{10}) $ 460 * q + 306 * q^4 - 11 * q^5 - 182 * q^6 + 944 * q^9	$ 460 q + 306 q^{4} - 11 q^{5} - 182 q^{6} + 944 q^{9} - 11 q^{10} - 22 q^{11} - 22 q^{14} - 1474 q^{15} - 2670 q^{16} - 22 q^{19} + 3157 q^{20} - 22 q^{21} + 3896 q^{24} - 1427 q^{25} - 3166 q^{26} - 2808 q^{29} + 1397 q^{30} + 2684 q^{31} - 12848 q^{34} + 2279 q^{35} + 1114 q^{36} + 12866 q^{39} - 11 q^{40} - 2652 q^{41} + 11110 q^{44} - 5394 q^{46} - 27026 q^{49} - 10931 q^{50} - 22 q^{51} - 51290 q^{54} - 10545 q^{55} + 25322 q^{56} + 41460 q^{59} + 49269 q^{60} - 22506 q^{61} + 68582 q^{64} + 27940 q^{65} - 24332 q^{66} + 7608 q^{69} - 15618 q^{70} + 35838 q^{71} - 59158 q^{74} + 30594 q^{75} - 58520 q^{76} - 17930 q^{79} - 63602 q^{80} + 91888 q^{81} + 92906 q^{84} - 33815 q^{85} + 101486 q^{86} - 22 q^{89} - 37598 q^{90} - 46242 q^{94} + 43336 q^{95} - 210180 q^{96} + 44528 q^{99}+O(q^{100}) $ 460 * q + 306 * q^4 - 11 * q^5 - 182 * q^6 + 944 * q^9 - 11 * q^10 - 22 * q^11 - 22 * q^14 - 1474 * q^15 - 2670 * q^16 - 22 * q^19 + 3157 * q^20 - 22 * q^21 + 3896 * q^24 - 1427 * q^25 - 3166 * q^26 - 2808 * q^29 + 1397 * q^30 + 2684 * q^31 - 12848 * q^34 + 2279 * q^35 + 1114 * q^36 + 12866 * q^39 - 11 * q^40 - 2652 * q^41 + 11110 * q^44 - 5394 * q^46 - 27026 * q^49 - 10931 * q^50 - 22 * q^51 - 51290 * q^54 - 10545 * q^55 + 25322 * q^56 + 41460 * q^59 + 49269 * q^60 - 22506 * q^61 + 68582 * q^64 + 27940 * q^65 - 24332 * q^66 + 7608 * q^69 - 15618 * q^70 + 35838 * q^71 - 59158 * q^74 + 30594 * q^75 - 58520 * q^76 - 17930 * q^79 - 63602 * q^80 + 91888 * q^81 + 92906 * q^84 - 33815 * q^85 + 101486 * q^86 - 22 * q^89 - 37598 * q^90 - 46242 * q^94 + 43336 * q^95 - 210180 * q^96 + 44528 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{21}{22}\right)$

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 $

$2$	−1.80372	−	6.14291i	−0.450931	−	1.53573i	−0.800801	−	0.598931i	$-0.795593\pi$
$2$	−1.80372	−	6.14291i	−0.450931	−	1.53573i	0.349870	−	0.936798i	$-0.386226\pi$
$3$	−12.3789	+	10.7264i	−1.37543	+	1.19182i	−0.416176	+	0.909284i	$0.636630\pi$
$3$	−12.3789	+	10.7264i	−1.37543	+	1.19182i	−0.959257	+	0.282535i	$0.908825\pi$
$4$	−21.0219	+	13.5100i	−1.31387	+	0.844373i
$5$	−20.7399	+	13.9592i	−0.829595	+	0.558366i
$5$	−20.7399	+	13.9592i	−0.829595	+	0.558366i
$6$	88.2193	+	56.6951i	2.45054	+	1.57486i
$7$	−35.9524	+	78.7248i	−0.733723	+	1.60663i	0.0598894	+	0.998205i	$0.480925\pi$
$7$	−35.9524	+	78.7248i	−0.733723	+	1.60663i	−0.793612	+	0.608424i	$0.791802\pi$
$8$	43.4924	+	37.6864i	0.679568	+	0.588849i
$9$	26.6544	−	185.386i	0.329067	−	2.28871i
$10$	123.159	+	102.225i	1.23159	+	1.02225i
$11$	−23.0470	+	78.4908i	−0.190471	+	0.648684i	0.807776	+	0.589490i	$0.200671\pi$
$11$	−23.0470	+	78.4908i	−0.190471	+	0.648684i	−0.998246	+	0.0591941i	$0.981147\pi$
$12$	115.315	−	392.728i	0.800800	−	2.72727i
$13$	−156.294	+	71.3772i	−0.924818	+	0.422350i	−0.820145	−	0.572156i	$-0.806107\pi$
$13$	−156.294	+	71.3772i	−0.924818	+	0.422350i	−0.104674	+	0.994507i	$0.533380\pi$
$14$	548.448	+	78.8549i	2.79820	+	0.402321i
$15$	107.006	−	395.262i	0.475580	−	1.75672i
$16$	−13.0358	+	28.5444i	−0.0509210	+	0.111501i
$17$	−62.9639	−	40.4644i	−0.217868	−	0.140015i	0.427155	−	0.904178i	$-0.359516\pi$
$17$	−62.9639	−	40.4644i	−0.217868	−	0.140015i	−0.645023	+	0.764163i	$0.723152\pi$
$18$	−1186.89	+	170.648i	−3.66323	+	0.526693i
$19$	−119.015	−	185.191i	−0.329682	−	0.512996i	0.636356	−	0.771396i	$-0.280441\pi$
$19$	−119.015	−	185.191i	−0.329682	−	0.512996i	−0.966038	+	0.258400i	$0.916805\pi$
$20$	247.404	−	573.643i	0.618510	−	1.43411i
$21$	−399.381	−	1360.17i	−0.905625	−	3.08427i
$22$	523.733			1.08209
$23$	−374.337	+	373.782i	−0.707632	+	0.706582i
$23$	−374.337	+	373.782i	−0.707632	+	0.706582i
$24$	−942.625			−1.63650
$25$	235.284	−	579.022i	0.376454	−	0.926435i
$26$	720.376	+	831.358i	1.06564	+	1.22982i
$27$	941.269	+	1464.64i	1.29118	+	2.00911i
$28$	−307.781	−	2140.66i	−0.392578	−	2.73044i
$29$	667.842	+	429.196i	0.794105	+	0.510340i	0.873687	−	0.486488i	$-0.161722\pi$
$29$	667.842	+	429.196i	0.794105	+	0.510340i	−0.0795824	+	0.996828i	$0.525359\pi$
$30$	−2621.07	+	55.6180i	−2.91230	+	0.0617978i
$31$	−951.947	+	1098.61i	−0.990580	+	1.14319i	−0.000884564		1.00000i	$0.500282\pi$
$31$	−951.947	+	1098.61i	−0.990580	+	1.14319i	−0.989695	+	0.143190i	$0.954264\pi$
$32$	1110.26	+	159.632i	1.08424	+	0.155891i
$33$	−556.625	−	1218.84i	−0.511134	−	1.11923i
$34$	−135.000	+	459.769i	−0.116782	+	0.397724i
$35$	−353.283	−	2134.61i	−0.288395	−	1.74254i
$36$	1944.23	+	4257.27i	1.50018	+	3.28493i
$37$	117.726	−	818.806i	0.0859945	−	0.598105i	−0.900567	−	0.434717i	$-0.856849\pi$
$37$	117.726	−	818.806i	0.0859945	−	0.598105i	0.986562	−	0.163388i	$-0.0522423\pi$
$38$	−922.944	+	1065.13i	−0.639158	+	0.737628i
$39$	1169.13	−	2560.04i	0.768660	−	1.68313i
$40$	−1428.10	−	174.493i	−0.892560	−	0.109058i
$41$	−0.212536	−	1.47822i	−0.000126434	−	0.000879370i	0.989758	−	0.142755i	$-0.0455959\pi$
$41$	−0.212536	−	1.47822i	−0.000126434	−	0.000879370i	−0.989885	+	0.141875i	$0.954687\pi$
$42$	−7635.01	+	4906.72i	−4.32824	+	2.78159i
$43$	829.162	+	956.904i	0.448438	+	0.517525i	0.934289	−	0.356517i	$-0.116036\pi$
$43$	829.162	+	956.904i	0.448438	+	0.517525i	−0.485851	+	0.874042i	$0.661490\pi$
$44$	−575.917	−	1961.39i	−0.297478	−	1.01312i
$45$	2035.02	+	4216.95i	1.00495	+	2.08244i
$46$	2971.31	+	1625.32i	1.40421	+	0.768111i
$47$		−	1469.07i		−	0.665039i	−0.943096	−	0.332519i	$-0.892101\pi$
$47$		−	1469.07i		−	0.665039i	0.943096	−	0.332519i	$-0.107899\pi$
$48$	−144.809	−	493.174i	−0.0628511	−	0.214051i
$49$	−3332.70	−	3846.14i	−1.38805	−	1.60189i
$50$	−3981.27	−	400.935i	−1.59251	−	0.160374i
$51$	1213.46	−	174.469i	0.466536	−	0.0670778i
$52$	2321.30	−	3612.02i	0.858470	−	1.33581i
$53$	534.513	−	1170.42i	0.190286	−	0.416668i	−0.790310	−	0.612707i	$-0.790081\pi$
$53$	534.513	−	1170.42i	0.190286	−	0.416668i	0.980596	+	0.196039i	$0.0628080\pi$
$54$	7299.39	−	8423.94i	2.50322	−	2.88887i
$55$	−617.674	−	1949.60i	−0.204190	−	0.644497i
$56$	−4530.51	+	2069.01i	−1.44468	+	0.659762i
$57$	3459.71	+	1015.86i	1.06485	+	0.312669i
$58$	1431.91	−	4876.65i	0.425658	−	1.44966i
$59$	2641.02	+	5783.03i	0.758697	+	1.66131i	0.750076	+	0.661351i	$0.230017\pi$
$59$	2641.02	+	5783.03i	0.758697	+	1.66131i	0.00862033	+	0.999963i	$0.497256\pi$
$60$	3090.52	+	9754.82i	0.858478	+	2.70967i
$61$	123.541	+	107.049i	0.0332011	+	0.0287689i	0.671303	−	0.741183i	$-0.265735\pi$
$61$	123.541	+	107.049i	0.0332011	+	0.0287689i	−0.638102	+	0.769952i	$0.720280\pi$
$62$	8465.69	+	3866.15i	2.20231	+	1.00576i
$63$	13636.2	+	8763.43i	3.43567	+	2.20797i
$64$	−950.550	−	6611.22i	−0.232068	−	1.61407i
$65$	2245.16	−	3662.09i	0.531398	−	0.866767i
$66$	−6483.23	+	5617.75i	−1.48834	+	1.28966i
$67$	−3144.18	+	923.214i	−0.700418	+	0.205661i	−0.612505	−	0.790467i	$-0.709838\pi$
$67$	−3144.18	+	923.214i	−0.700418	+	0.205661i	−0.0879135	+	0.996128i	$0.528020\pi$
$68$	1870.30			0.404476
$69$	624.557	−	8642.28i	0.131182	−	1.81522i
$70$	−12475.5	+	6020.43i	−2.54602	+	1.22866i
$71$	7007.84	−	2057.69i	1.39017	−	0.408190i	0.500872	−	0.865521i	$-0.333013\pi$
$71$	7007.84	−	2057.69i	1.39017	−	0.408190i	0.889297	+	0.457331i	$0.151194\pi$
$72$	8145.78	−	7058.36i	1.57133	−	1.36157i
$73$	−120.871	−	188.078i	−0.0226817	−	0.0352933i	0.829728	−	0.558169i	$-0.188496\pi$
$73$	−120.871	−	188.078i	−0.0226817	−	0.0352933i	−0.852409	+	0.522875i	$0.824859\pi$
$74$	−5242.20	+	753.714i	−0.957304	+	0.137640i
$75$	3298.25	+	9691.40i	0.586355	+	1.72291i
$76$	5003.86	+	2285.19i	0.866320	+	0.395635i
$77$	−5350.58	−	4636.30i	−0.902442	−	0.781970i
$78$	−17834.9	−	2564.27i	−2.93144	−	0.421478i
$79$	−1477.56	+	674.777i	−0.236750	+	0.108120i	−0.530257	−	0.847837i	$-0.677905\pi$
$79$	−1477.56	+	674.777i	−0.236750	+	0.108120i	0.293507	+	0.955957i	$0.405177\pi$
$80$	−128.095	−	773.975i	−0.0200148	−	0.120934i
$81$	−12806.0	−	3760.19i	−1.95184	−	0.573112i
$82$	−8.69723	+	3.97189i	−0.00129346	+	0.000590704i
$83$	−886.258	+	6164.06i	−0.128648	+	0.894768i	0.818622	+	0.574333i	$0.194738\pi$
$83$	−886.258	+	6164.06i	−0.128648	+	0.894768i	−0.947270	+	0.320436i	$0.896171\pi$
$84$	26771.5	+	23197.7i	3.79415	+	3.28765i
$85$	1870.71	−	39.6957i	0.258922	−	0.00549421i
$86$	4382.60	−	6819.46i	0.592564	−	0.922047i
$87$	−12870.9	+	1850.55i	−1.70047	+	0.244491i
$88$	−3960.40	+	2545.19i	−0.511415	+	0.328667i
$89$	−10641.3	+	9220.77i	−1.34343	+	1.16409i	−0.371608	+	0.928390i	$0.621193\pi$
$89$	−10641.3	+	9220.77i	−1.34343	+	1.16409i	−0.971825	+	0.235702i	$0.924261\pi$
$90$	22233.7	−	20107.1i	2.74491	−	2.48236i
$91$		−	14870.4i		−	1.79573i
$92$	2819.51	−	12914.9i	0.333118	−	1.52586i
$93$		−	23810.5i		−	2.75297i
$94$	−9024.38	+	2649.80i	−1.02132	+	0.299886i
$95$	5053.48	+	2179.49i	0.559942	+	0.241495i
$96$	−15456.1	+	9933.05i	−1.67710	+	1.07780i
$97$	1362.49	+	9476.30i	0.144807	+	1.00715i	0.924552	+	0.381056i	$0.124439\pi$
$97$	1362.49	+	9476.30i	0.144807	+	1.00715i	−0.779745	+	0.626097i	$0.784652\pi$
$98$	−17615.2	+	27409.9i	−1.83416	+	2.85400i
$99$	13936.8	+	6364.71i	1.42197	+	0.649394i
$100$	2876.45	+	15350.8i	0.287645	+	1.53508i
$101$	−1347.72	+	9373.57i	−0.132116	+	0.918887i	0.810673	+	0.585499i	$0.199101\pi$
$101$	−1347.72	+	9373.57i	−0.132116	+	0.918887i	−0.942789	+	0.333389i	$0.891808\pi$
$102$	−3260.50	−	7139.49i	−0.313389	−	0.686225i
$103$	−5755.47	−	1689.96i	−0.542508	−	0.159295i	−0.00101418	−	0.999999i	$-0.500323\pi$
$103$	−5755.47	−	1689.96i	−0.542508	−	0.159295i	−0.541494	+	0.840705i	$0.682141\pi$
$104$	−9487.56	−	2785.80i	−0.877178	−	0.257563i
$105$	27269.9	+	22634.6i	2.47346	+	2.05303i
$106$	−8153.90	−	1172.35i	−0.725694	−	0.104339i
$107$	−1622.43	+	1872.38i	−0.141709	+	0.163541i	−0.822167	−	0.569246i	$-0.807235\pi$
$107$	−1622.43	+	1872.38i	−0.141709	+	0.163541i	0.680458	+	0.732787i	$0.261781\pi$
$108$	−39574.6	−	18073.1i	−3.39288	−	1.54948i
$109$	−849.893	+	1322.46i	−0.0715338	+	0.111309i	−0.875177	−	0.483802i	$-0.839255\pi$
$109$	−849.893	+	1322.46i	−0.0715338	+	0.111309i	0.803644	+	0.595111i	$0.202892\pi$
$110$	−10862.1	+	7310.86i	−0.897698	+	0.604204i
$111$	7325.49	+	11398.7i	0.594553	+	0.925143i
$112$	−1778.48	−	2052.48i	−0.141780	−	0.163622i
$113$	−7095.31	+	2083.37i	−0.555667	+	0.163158i	−0.547496	−	0.836808i	$-0.684419\pi$
$113$	−7095.31	+	2083.37i	−0.555667	+	0.163158i	−0.00817046	+	0.999967i	$0.502601\pi$
$114$		−	23085.0i		−	1.77632i
$115$	2546.02	−	12977.6i	0.192516	−	0.981294i
$116$	−19837.8			−1.47427
$117$	9066.38	+	30877.3i	0.662311	+	2.25563i
$118$	30761.0	−	26654.6i	2.20921	−	1.91429i
$119$	5449.26	−	3502.03i	0.384808	−	0.247301i
$120$	19549.9	−	13158.3i	1.35763	−	0.913768i
$121$	6687.15	+	4297.57i	0.456742	+	0.293530i
$122$	434.759	−	951.989i	0.0292098	−	0.0639606i
$123$	18.4869	+	16.0190i	0.00122195	+	0.00105883i
$124$	5169.63	−	35955.6i	0.336214	−	2.33842i
$125$	3202.90	+	15293.2i	0.204985	+	0.978765i
$126$	29237.2	−	99572.6i	1.84159	−	6.27189i
$127$	1994.73	−	6793.44i	0.123674	−	0.421194i	−0.874259	−	0.485460i	$-0.838652\pi$
$127$	1994.73	−	6793.44i	0.123674	−	0.421194i	0.997933	+	0.0642657i	$0.0204705\pi$
$128$	−22572.6	+	10308.5i	−1.37772	+	0.629184i
$129$	−20528.2	−	2951.51i	−1.23359	−	0.177364i
$130$	−26545.6	−	7186.42i	−1.57074	−	0.425232i
$131$	1655.97	−	3626.07i	0.0964963	−	0.211297i	−0.855228	−	0.518252i	$-0.826583\pi$
$131$	1655.97	−	3626.07i	0.0964963	−	0.211297i	0.951724	+	0.306955i	$0.0993101\pi$
$132$	28167.8	+	18102.4i	1.61661	+	1.03893i
$133$	18858.0	−	2711.38i	1.06609	−	0.153280i
$134$	11342.5	+	17649.2i	0.631680	+	0.982914i
$135$	−39967.0	−	17237.2i	−2.19297	−	0.945799i
$136$	−1213.49	−	4132.77i	−0.0656084	−	0.223442i
$137$	−25329.2			−1.34952			−0.674760	−	0.738037i	$-0.735753\pi$
$137$	−25329.2			−1.34952			−0.674760	+	0.738037i	$0.735753\pi$
$138$	−54215.3	+	11751.7i	−2.84685	+	0.617080i
$139$	−9672.83			−0.500638			−0.250319	−	0.968163i	$-0.580535\pi$
$139$	−9672.83			−0.500638			−0.250319	+	0.968163i	$0.580535\pi$
$140$	36265.2	+	40100.7i	1.85026	+	2.04595i
$141$	15757.8	+	18185.5i	0.792606	+	0.914716i
$142$	−25280.4	−	39337.1i	−1.25374	−	1.95086i
$143$	−2000.34	−	13912.7i	−0.0978211	−	0.680361i
$144$	4944.26	+	3177.48i	0.238438	+	0.153235i
$145$	−19842.2	+	421.042i	−0.943742	+	0.0200258i
$146$	−937.331	+	1081.74i	−0.0439731	+	0.0507477i
$147$	82510.3	+	11863.2i	3.81833	+	0.548993i
$148$	8587.20	+	18803.4i	0.392038	+	0.858444i
$149$	−2607.28	+	8879.57i	−0.117440	+	0.399963i	−0.997141	−	0.0755640i	$-0.975924\pi$
$149$	−2607.28	+	8879.57i	−0.117440	+	0.399963i	0.879701	+	0.475527i	$0.157742\pi$
$150$	53584.3	−	37741.4i	2.38152	−	1.67740i
$151$	−3863.48	−	8459.85i	−0.169444	−	0.371030i	0.805792	−	0.592199i	$-0.201740\pi$
$151$	−3863.48	−	8459.85i	−0.169444	−	0.371030i	−0.975235	+	0.221169i	$0.929013\pi$
$152$	1802.93	−	12539.7i	0.0780355	−	0.542749i
$153$	−9179.80	+	10594.1i	−0.392148	+	0.452563i
$154$	−18829.5	+	41230.7i	−0.793956	+	1.73852i
$155$	4407.65	−	36073.3i	0.183461	−	1.50149i
$156$	10008.7	+	69612.0i	0.411271	+	2.86045i
$157$	34650.5	−	22268.6i	1.40576	−	0.903426i	0.405814	−	0.913956i	$-0.366988\pi$
$157$	34650.5	−	22268.6i	1.40576	−	0.903426i	0.999945	+	0.0105294i	$0.00335166\pi$
$158$	6810.20	+	7859.39i	0.272801	+	0.314829i
$159$	5937.68	+	20221.9i	0.234867	+	0.799884i
$160$	−25255.1	+	12187.6i	−0.986526	+	0.476079i
$161$	−15967.6	−	42908.0i	−0.616009	−	1.65534i
$162$			85448.7i			3.25593i
$163$	−9753.61	−	33217.8i	−0.367105	−	1.25024i	−0.911460	−	0.411390i	$-0.865044\pi$
$163$	−9753.61	−	33217.8i	−0.367105	−	1.25024i	0.544355	−	0.838855i	$-0.316775\pi$
$164$	24.4387	+	28.2037i	0.000908635	+	0.00104862i
$165$	28558.3	+	17508.5i	1.04897	+	0.643106i
$166$	39463.8	−	5674.04i	1.43213	−	0.205910i
$167$	−642.744	+	1000.13i	−0.0230465	+	0.0358611i	−0.852586	−	0.522587i	$-0.824967\pi$
$167$	−642.744	+	1000.13i	−0.0230465	+	0.0358611i	0.829539	+	0.558449i	$0.188603\pi$
$168$	33889.7	−	74208.0i	1.20074	−	2.62925i
$169$	629.730	−	726.747i	0.0220486	−	0.0254454i
$170$	−3618.09	−	11420.0i	−0.125194	−	0.395157i
$171$	−37504.1	+	17127.6i	−1.28259	+	0.585738i
$172$	−30358.3	−	8914.01i	−1.02617	−	0.301312i
$173$	6162.11	−	20986.2i	0.205891	−	0.701200i	−0.790199	−	0.612851i	$-0.790023\pi$
$173$	6162.11	−	20986.2i	0.205891	−	0.701200i	0.996090	−	0.0883490i	$-0.0281591\pi$
$174$	34583.2	+	75726.7i	1.14227	+	2.50121i
$175$	37124.4	+	39339.9i	1.21222	+	1.28457i
$176$	−1940.03	−	1681.05i	−0.0626303	−	0.0542694i
$177$	−94723.9	−	43259.0i	−3.02352	−	1.38080i
$178$	75836.4	+	48737.1i	2.39352	+	1.53822i
$179$	1338.37	+	9308.59i	0.0417706	+	0.290521i	0.999990	+	0.00448658i	$0.00142813\pi$
$179$	1338.37	+	9308.59i	0.0417706	+	0.290521i	−0.958219	+	0.286035i	$0.907663\pi$
$180$	−99750.9	−	61155.3i	−3.07873	−	1.88751i
$181$	9998.86	−	8664.06i	0.305206	−	0.264463i	−0.488768	−	0.872414i	$-0.662554\pi$
$181$	9998.86	−	8664.06i	0.305206	−	0.264463i	0.793975	+	0.607951i	$0.208008\pi$
$182$	−91347.8	+	26822.1i	−2.75775	+	0.809749i
$183$	−2677.55			−0.0799531
$184$	−30367.3	+	2149.25i	−0.896954	+	0.0634822i
$185$	8988.20	+	18625.3i	0.262621	+	0.544201i
$186$	−146266.	+	42947.5i	−4.22782	+	1.24140i
$187$	4627.21	−	4009.50i	0.132323	−	0.114659i
$188$	19847.1	+	30882.7i	0.561541	+	0.873775i
$189$	−149145.	+	21443.8i	−4.17526	+	0.600312i
$190$	4273.36	−	34974.3i	0.118376	−	0.968816i
$191$	33295.1	+	15205.4i	0.912670	+	0.416802i	0.815693	−	0.578484i	$-0.196356\pi$
$191$	33295.1	+	15205.4i	0.912670	+	0.416802i	0.0969763	+	0.995287i	$0.469083\pi$
$192$	82681.2	+	71643.7i	2.24287	+	1.94346i
$193$	−38492.6	−	5534.40i	−1.03339	−	0.148579i	−0.395307	−	0.918549i	$-0.629362\pi$
$193$	−38492.6	−	5534.40i	−1.03339	−	0.148579i	−0.638080	+	0.769970i	$0.720271\pi$
$194$	55754.5	−	25462.2i	1.48141	−	0.676539i
$195$	11488.4	+	69415.0i	0.302127	+	1.82551i
$196$	122021.	+	35828.6i	3.17631	+	0.932648i
$197$	54611.9	−	24940.4i	1.40720	−	0.642645i	0.440308	−	0.897847i	$-0.354869\pi$
$197$	54611.9	−	24940.4i	1.40720	−	0.642645i	0.966888	+	0.255202i	$0.0821418\pi$
$198$	13959.8	−	97092.5i	0.356081	−	2.47660i
$199$	−53552.1	−	46403.2i	−1.35229	−	1.17177i	−0.968691	−	0.248269i	$-0.920138\pi$
$199$	−53552.1	−	46403.2i	−1.35229	−	1.17177i	−0.383601	−	0.923499i	$-0.625316\pi$
$200$	32054.3	−	16316.0i	0.801357	−	0.407901i
$201$	29018.7	−	45154.0i	0.718267	−	1.11765i
$202$	60011.9	−	8628.41i	1.47074	−	0.211460i
$203$	−57798.9	+	37145.1i	−1.40258	+	0.901383i
$204$	−23152.2	+	20061.5i	−0.556329	+	0.482062i
$205$	25.0427	+	27.6913i	0.000595900	+	0.000658924i
$206$			38403.6i			0.904976i
$207$	59316.0	+	79359.7i	1.38430	+	1.85208i
$208$		−	5391.78i		−	0.124625i
$209$	17278.8	−	5073.50i	0.395567	−	0.116149i
$210$	89855.3	−	208343.i	2.03754	−	4.72433i
$211$	27533.5	−	17694.7i	0.618438	−	0.397446i	−0.193575	−	0.981086i	$-0.562008\pi$
$211$	27533.5	−	17694.7i	0.618438	−	0.397446i	0.812013	+	0.583639i	$0.198372\pi$
$212$	4575.85	+	31825.7i	0.101812	+	0.708119i
$213$	−64677.8	+	100641.i	−1.42559	+	2.21827i
$214$	14428.3	+	6589.18i	0.315056	+	0.143881i
$215$	−30554.3	−	8271.66i	−0.660990	−	0.178943i
$216$	−14259.0	+	99173.8i	−0.305621	+	2.12564i
$217$	−52262.7	−	114439.i	−1.10987	−	2.43028i
$218$	9656.72	+	2835.47i	0.203197	+	0.0596639i
$219$	3513.64	+	1031.70i	0.0732604	+	0.0215112i
$220$	39323.8	+	32639.7i	0.812475	+	0.674374i
$221$	12729.1	+	1830.17i	0.260624	+	0.0374721i
$222$	56808.0	−	65559.9i	1.15267	−	1.33025i
$223$	51896.4	+	23700.3i	1.04358	+	0.476589i	0.862064	−	0.506799i	$-0.169171\pi$
$223$	51896.4	+	23700.3i	1.04358	+	0.476589i	0.181519	+	0.983387i	$0.441899\pi$
$224$	−52483.7	+	81666.2i	−1.04599	+	1.62760i
$225$	−101071.	−	59051.8i	−1.99646	−	1.16646i
$226$	25595.9	+	39828.0i	0.501134	+	0.779780i
$227$	32728.4	+	37770.5i	0.635144	+	0.732996i	0.978508	−	0.206207i	$-0.0661119\pi$
$227$	32728.4	+	37770.5i	0.635144	+	0.732996i	−0.343364	+	0.939202i	$0.611566\pi$
$228$	−86454.0	+	25385.2i	−1.66309	+	0.488327i
$229$			7956.44i			0.151722i	0.997118	+	0.0758609i	$0.0241705\pi$
$229$			7956.44i			0.151722i	−0.997118	+	0.0758609i	$0.975830\pi$
$230$	−84312.7	+	7768.00i	−1.59381	+	0.146843i
$231$	115965.			2.17322
$232$	12871.2	+	43835.3i	0.239135	+	0.814419i
$233$	−12710.2	+	11013.4i	−0.234121	+	0.202867i	−0.764018	−	0.645195i	$-0.776776\pi$
$233$	−12710.2	+	11013.4i	−0.234121	+	0.202867i	0.529897	+	0.848062i	$0.322231\pi$
$234$	173323.	−	111388.i	3.16537	−	2.03426i
$235$	20507.0	+	30468.3i	0.371335	+	0.551713i
$236$	−133648.	−	85890.4i	−2.39960	−	1.54213i
$237$	11052.6	−	24201.8i	0.196774	−	0.430875i
$238$	−31341.6	−	27157.7i	−0.553309	−	0.479445i
$239$	6916.67	−	48106.5i	0.121088	−	0.842186i	−0.835239	−	0.549887i	$-0.814671\pi$
$239$	6916.67	−	48106.5i	0.121088	−	0.842186i	0.956327	−	0.292299i	$-0.0944201\pi$
$240$	9887.62	+	8206.96i	0.171660	+	0.142482i
$241$	−753.600	+	2566.53i	−0.0129750	+	0.0441887i	−0.965726	−	0.259563i	$-0.916421\pi$
$241$	−753.600	+	2566.53i	−0.0129750	+	0.0441887i	0.952751	+	0.303752i	$0.0982395\pi$
$242$	14337.9	−	48830.2i	0.244824	−	0.833793i
$243$	70578.7	−	32232.2i	1.19526	−	0.545855i
$244$	−4043.30	−	581.339i	−0.0679136	−	0.00976450i
$245$	122809.	+	33246.8i	2.04596	+	0.553882i
$246$	65.0581	−	142.457i	0.00107506	−	0.00235405i
$247$	31819.9	+	20449.4i	0.521560	+	0.335186i
$248$	−82804.9	+	11905.5i	−1.34633	+	0.193573i
$249$	−55147.1	−	85810.5i	−0.889455	−	1.38402i
$250$	88167.7	−	47259.8i	1.41068	−	0.756157i
$251$	−18606.6	−	63368.3i	−0.295338	−	1.00583i	−0.964800	−	0.262984i	$-0.915293\pi$
$251$	−18606.6	−	63368.3i	−0.295338	−	1.00583i	0.669462	−	0.742846i	$-0.266525\pi$
$252$	−405052.			−6.37837
$253$	−20711.1	−	37996.5i	−0.323565	−	0.593613i
$254$	−45329.4			−0.702608
$255$	−22731.6	+	20557.3i	−0.349582	+	0.316145i
$256$	34055.9	+	39302.6i	0.519652	+	0.599711i
$257$	−12690.6	−	19747.0i	−0.192140	−	0.298975i	0.731795	−	0.681524i	$-0.238683\pi$
$257$	−12690.6	−	19747.0i	−0.192140	−	0.298975i	−0.923935	+	0.382549i	$0.875046\pi$
$258$	18896.3	+	131427.i	0.283882	+	1.97444i
$259$	60227.8	+	38706.0i	0.897836	+	0.577004i
$260$	2277.20	+	107316.i	0.0336864	+	1.58752i
$261$	97367.8	−	112368.i	1.42934	−	1.64954i
$262$	−25261.6	−	3632.07i	−0.368008	−	0.0529116i
$263$	−33321.1	−	72963.0i	−0.481734	−	1.05485i	−0.981983	−	0.188969i	$-0.939485\pi$
$263$	−33321.1	−	72963.0i	−0.481734	−	1.05485i	0.500249	−	0.865882i	$-0.333242\pi$
$264$	21724.7	−	73987.4i	0.311706	−	1.06157i
$265$	5252.34	+	31735.7i	0.0747931	+	0.451914i
$266$	−50670.4	−	110953.i	−0.716129	−	1.56810i
$267$	32822.5	−	228286.i	0.460415	−	3.20226i
$268$	53624.1	−	61885.5i	0.746604	−	0.861627i
$269$	27687.8	−	60627.8i	0.382634	−	0.837852i	−0.616105	−	0.787664i	$-0.711290\pi$
$269$	27687.8	−	60627.8i	0.382634	−	0.837852i	0.998740	−	0.0501886i	$-0.0159822\pi$
$270$	−33797.2	+	276605.i	−0.463611	+	3.79430i
$271$	8867.75	+	61676.5i	0.120747	+	0.839811i	0.956714	+	0.291031i	$0.0939983\pi$
$271$	8867.75	+	61676.5i	0.120747	+	0.839811i	−0.835967	+	0.548780i	$0.815093\pi$
$272$	1975.82	−	1269.78i	0.0267060	−	0.0171629i
$273$	159506.	+	184079.i	2.14018	+	2.46990i
$274$	45686.8	+	155595.i	0.608540	+	2.07250i
$275$	40025.3	+	31812.3i	0.529260	+	0.420659i
$276$	103628.	+	190115.i	1.36037	+	2.49574i
$277$			107619.i			1.40259i	0.712872	+	0.701295i	$0.247394\pi$
$277$			107619.i			1.40259i	−0.712872	+	0.701295i	$0.752606\pi$
$278$	17447.1	+	59419.3i	0.225753	+	0.768844i
$279$	178292.	+	205760.i	2.29047	+	2.64334i
$280$	65080.4	−	106153.i	0.830108	−	1.35399i
$281$	−154497.	+	22213.3i	−1.95662	+	0.281319i	−0.999951	−	0.00986024i	$-0.996861\pi$
$281$	−154497.	+	22213.3i	−1.95662	+	0.281319i	−0.956668	+	0.291180i	$0.905952\pi$
$282$	83289.1	−	129600.i	1.04735	−	1.62970i
$283$	−17628.0	+	38599.9i	−0.220105	+	0.481963i	−0.987183	−	0.159591i	$-0.948983\pi$
$283$	−17628.0	+	38599.9i	−0.220105	+	0.481963i	0.767078	+	0.641554i	$0.221710\pi$
$284$	−119519.	+	137932.i	−1.48184	+	1.71013i
$285$	−85934.5	+	27225.8i	−1.05798	+	0.335190i
$286$	−81856.4	+	37382.6i	−1.00074	+	0.457022i
$287$	124.014	+	36.4138i	0.00150559	+	0.000442081i
$288$	59187.0	−	201572.i	0.713578	−	2.43022i
$289$	−32368.8	−	70877.8i	−0.387553	−	0.848622i
$290$	38376.2	+	121129.i	0.456316	+	1.44030i
$291$	−118512.	−	102692.i	−1.39952	−	1.21269i
$292$	5081.86	+	2320.81i	0.0596015	+	0.0272191i
$293$	6211.52	+	3991.90i	0.0723541	+	0.0464991i	0.576318	−	0.817226i	$-0.304489\pi$
$293$	6211.52	+	3991.90i	0.0723541	+	0.0464991i	−0.503964	+	0.863725i	$0.668125\pi$
$294$	−75951.1	−	528251.i	−0.878697	−	6.11148i
$295$	−135501.	−	83072.9i	−1.55703	−	0.954587i
$296$	35978.0	−	31175.1i	0.410633	−	0.355815i
$297$	−136654.	+	40125.3i	−1.54921	+	0.454889i
$298$	59249.2			0.667191
$299$	31827.3	−	85139.1i	0.356006	−	0.952328i
$300$	−200266.	−	159173.i	−2.22518	−	1.76858i
$301$	−105142.	+	30872.6i	−1.16050	+	0.340753i
$302$	−44999.5	+	38992.3i	−0.493394	+	0.427528i
$303$	−83861.1	−	130490.i	−0.913431	−	1.42133i
$304$	6837.63	−	983.102i	0.0739875	−	0.0106378i
$305$	−4056.54	−	495.652i	−0.0436070	−	0.00532816i
$306$	81636.2	+	37282.0i	0.871846	+	0.398159i
$307$	−43306.5	−	37525.3i	−0.459490	−	0.398151i	0.394123	−	0.919058i	$-0.371048\pi$
$307$	−43306.5	−	37525.3i	−0.459490	−	0.398151i	−0.853613	+	0.520907i	$0.825594\pi$
$308$	175116.	+	25177.9i	1.84597	+	0.265410i
$309$	89373.4	−	40815.5i	0.936034	−	0.427472i
$310$	−229545.	+	37990.4i	−2.38861	+	0.395322i
$311$	40256.7	+	11820.4i	0.416215	+	0.122212i	0.483133	−	0.875547i	$-0.339499\pi$
$311$	40256.7	+	11820.4i	0.416215	+	0.122212i	−0.0669187	+	0.997758i	$0.521317\pi$
$312$	147327.	−	67282.0i	1.51347	−	0.691177i
$313$	−19417.7	+	135053.i	−0.198202	+	1.37853i	0.611294	+	0.791403i	$0.290649\pi$
$313$	−19417.7	+	135053.i	−0.198202	+	1.37853i	−0.809497	+	0.587124i	$0.800260\pi$
$314$	−199294.	−	172689.i	−2.02132	−	1.75148i
$315$	−405142.	+	8596.94i	−4.08307	+	0.0866409i
$316$	21944.9	−	34146.9i	0.219765	−	0.341961i
$317$	152746.	−	21961.6i	1.52003	−	0.218547i	0.668839	−	0.743407i	$-0.266791\pi$
$317$	152746.	−	21961.6i	1.52003	−	0.218547i	0.851189	+	0.524860i	$0.175882\pi$
$318$	113511.	−	72949.3i	1.12250	−	0.721385i
$319$	−49079.7	+	42527.8i	−0.482303	+	0.417918i
$320$	112001.	+	123847.i	1.09376	+	1.20944i
$321$		−	40580.8i		−	0.393831i
$322$	−234779.	+	175482.i	−2.26437	+	1.69246i
$323$			16476.3i			0.157926i
$324$	320008.	−	93962.7i	3.04839	−	0.895087i
$325$	4555.42	+	107292.i	0.0431282	+	1.01578i
$326$	−186461.	+	119831.i	−1.75450	+	1.12755i
$327$	−3664.45	−	25486.8i	−0.0342700	−	0.238353i
$328$	46.4651	−	72.3011i	0.000431896	−	0.000672043i
$329$	115652.	+	52816.7i	1.06847	+	0.487954i
$330$	56042.3	−	207012.i	0.514621	−	1.90093i
$331$	−11.6226	+	80.8372i	−0.000106084	+	0.000737829i	−0.989874	−	0.141946i	$-0.954664\pi$
$331$	−11.6226	+	80.8372i	−0.000106084	+	0.000737829i	0.989768	+	0.142684i	$0.0455732\pi$
$332$	−64645.4	−	141554.i	−0.586491	−	1.28424i
$333$	−148657.	−	43649.6i	−1.34059	−	0.393633i
$334$	7303.04	+	2144.37i	0.0654653	+	0.0192223i
$335$	52322.6	−	63037.4i	0.466229	−	0.561706i
$336$	44031.3	+	6330.74i	0.390016	+	0.0560759i
$337$	−80119.1	+	92462.4i	−0.705466	+	0.814152i	−0.989480	−	0.144669i	$-0.953788\pi$
$337$	−80119.1	+	92462.4i	−0.705466	+	0.814152i	0.284014	+	0.958820i	$0.408334\pi$
$338$	−5600.20	−	2557.53i	−0.0490196	−	0.0223865i
$339$	65485.1	−	101897.i	0.569827	−	0.886668i
$340$	−38789.7	+	26107.8i	−0.335551	+	0.225846i
$341$	−64290.9	−	100039.i	−0.552893	−	0.860318i
$342$	172860.	+	199491.i	1.47789	+	1.70558i
$343$	223226.	−	65545.1i	1.89739	−	0.557124i
$344$			72866.1i			0.615756i
$345$	107686.	+	187958.i	0.904732	+	1.57915i
$346$	−140031.			−1.16969
$347$	65710.1	+	223788.i	0.545724	+	1.85857i	0.511733	+	0.859145i	$0.329004\pi$
$347$	65710.1	+	223788.i	0.545724	+	1.85857i	0.0339918	+	0.999422i	$0.489178\pi$
$348$	245569.	−	212787.i	2.02776	−	1.75706i
$349$	−74827.5	+	48088.7i	−0.614342	+	0.394814i	−0.810483	−	0.585762i	$-0.800795\pi$
$349$	−74827.5	+	48088.7i	−0.614342	+	0.394814i	0.196141	+	0.980576i	$0.437159\pi$
$350$	174700.	−	299010.i	1.42612	−	2.44090i
$351$	−251657.	−	161730.i	−2.04265	−	1.31273i
$352$	−38117.9	+	83466.5i	−0.307640	+	0.673639i
$353$	97512.6	+	84495.2i	0.782549	+	0.678082i	0.951537	−	0.307536i	$-0.0995044\pi$
$353$	97512.6	+	84495.2i	0.782549	+	0.678082i	−0.168988	+	0.985618i	$0.554050\pi$
$354$	−94880.5	+	659908.i	−0.757130	+	5.26595i
$355$	−116618.	+	140500.i	−0.925357	+	1.11486i
$356$	99129.0	−	337602.i	0.782170	−	2.66382i
$357$	−29891.8	+	101802.i	−0.234539	+	0.798767i
$358$	54767.8	−	25011.6i	0.427326	−	0.195153i
$359$	36880.2	+	5302.57i	0.286157	+	0.0411431i	0.283899	−	0.958854i	$-0.408372\pi$
$359$	36880.2	+	5302.57i	0.286157	+	0.0411431i	0.00225814	+	0.999997i	$0.499281\pi$
$360$	−70413.6	+	260097.i	−0.543315	+	2.00693i
$361$	34006.1	−	74462.9i	0.260941	−	0.571381i
$362$	−71257.8	−	45794.6i	−0.543770	−	0.349460i
$363$	−128877.	+	18529.7i	−0.978052	+	0.140623i
$364$	200899.	+	312605.i	1.51627	+	2.35935i
$365$	5132.25	+	2213.47i	0.0385232	+	0.0166145i
$366$	4829.56	+	16448.0i	0.0360533	+	0.122786i
$367$	91131.1			0.676604			0.338302	−	0.941038i	$-0.390147\pi$
$367$	91131.1			0.676604			0.338302	+	0.941038i	$0.390147\pi$
$368$	−5789.59	−	15557.7i	−0.0427516	−	0.114882i
$369$	−279.706			−0.00205423
$370$	98201.3	−	88808.6i	0.717321	−	0.648711i
$371$	72924.0	+	84158.8i	0.529813	+	0.611437i
$372$	321679.	+	500542.i	2.32454	+	3.61705i
$373$	−27353.6	−	190248.i	−0.196606	−	1.36742i	−0.814044	−	0.580804i	$-0.802738\pi$
$373$	−27353.6	−	190248.i	−0.196606	−	1.36742i	0.617438	−	0.786620i	$-0.288171\pi$
$374$	−32976.2	−	21192.5i	−0.235753	−	0.151510i
$375$	−203689.	−	154957.i	−1.44845	−	1.10192i
$376$	55363.9	−	63893.4i	0.391608	−	0.451939i
$377$	−135015.	−	19412.2i	−0.949945	−	0.136581i
$378$	400743.	+	877504.i	2.80467	+	6.14137i
$379$	−39923.3	+	135966.i	−0.277938	+	0.946570i	0.695674	+	0.718358i	$0.255106\pi$
$379$	−39923.3	+	135966.i	−0.277938	+	0.946570i	−0.973612	+	0.228212i	$0.926712\pi$
$380$	−135679.	+	22455.2i	−0.939603	+	0.155507i
$381$	48176.3	+	105491.i	0.331882	+	0.726720i
$382$	33350.1	−	231955.i	0.228545	−	1.58956i
$383$	−21812.3	+	25172.7i	−0.148698	+	0.171606i	−0.825212	−	0.564823i	$-0.808944\pi$
$383$	−21812.3	+	25172.7i	−0.148698	+	0.171606i	0.676514	+	0.736430i	$0.263490\pi$
$384$	168850.	−	369730.i	1.14509	−	2.50739i
$385$	175689.	+	21466.7i	1.18529	+	0.144825i
$386$	35432.6	+	246439.i	0.237809	+	1.65400i
$387$	199497.	−	128209.i	1.33203	−	0.856045i
$388$	−156667.	−	180803.i	−1.04067	−	1.20100i
$389$	40886.2	+	139246.i	0.270195	+	0.920201i	0.977080	+	0.212872i	$0.0682818\pi$
$389$	40886.2	+	139246.i	0.270195	+	0.920201i	−0.706885	+	0.707329i	$0.749900\pi$
$390$	405689.	−	195778.i	2.66725	−	1.28716i
$391$	38694.6	−	8387.41i	0.253103	−	0.0548624i
$392$		−	292875.i		−	1.90594i
$393$	18395.5	+	62649.4i	0.119104	+	0.405631i
$394$	−251711.	−	290491.i	−1.62148	−	1.87128i
$395$	21225.0	−	34620.2i	0.136036	−	0.221889i
$396$	−378965.	+	54486.9i	−2.41662	+	0.347458i
$397$	−3762.93	+	5855.24i	−0.0238751	+	0.0371504i	−0.852986	−	0.521934i	$-0.825211\pi$
$397$	−3762.93	+	5855.24i	−0.0238751	+	0.0371504i	0.829111	+	0.559084i	$0.188847\pi$
$398$	−188458.	+	412665.i	−1.18973	+	2.60514i
$399$	−204359.	+	235842.i	−1.28365	+	1.48141i
$400$	13460.7	+	14264.0i	0.0841294	+	0.0891502i
$401$	276642.	−	126338.i	1.72040	−	0.785680i	0.725119	−	0.688623i	$-0.241785\pi$
$401$	276642.	−	126338.i	1.72040	−	0.785680i	0.995279	−	0.0970562i	$-0.0309427\pi$
$402$	−329719.	−	96814.2i	−2.04029	−	0.599083i
$403$	70368.5	−	239653.i	0.433280	−	1.47561i
$404$	−98305.1	−	215258.i	−0.602300	−	1.31885i
$405$	318084.	−	100776.i	1.93924	−	0.614391i
$406$	332432.	+	288054.i	2.01675	+	1.74752i
$407$	61555.5	+	28111.4i	0.371602	+	0.169705i
$408$	59351.4	+	38142.8i	0.356542	+	0.229135i
$409$	−14630.0	−	101754.i	−0.0874574	−	0.608280i	−0.985666	−	0.168710i	$-0.946040\pi$
$409$	−14630.0	−	101754.i	−0.0874574	−	0.608280i	0.898208	−	0.439570i	$-0.144869\pi$
$410$	124.935	−	203.783i	0.000743219	−	0.00121227i
$411$	313547.	−	271690.i	1.85617	−	1.60838i
$412$	143822.	−	42230.0i	0.847289	−	0.248787i
$413$	−550219.			−3.22579
$414$	380510.	−	507516.i	2.22006	−	2.96107i
$415$	−67664.2	−	140213.i	−0.392882	−	0.814128i
$416$	−184922.	+	54298.1i	−1.06857	+	0.313760i
$417$	119739.	−	103754.i	0.688594	−	0.596670i
$418$	−62332.2	−	96990.8i	−0.356747	−	0.555108i
$419$	69737.8	−	10026.8i	0.397228	−	0.0571128i	0.0591938	−	0.998247i	$-0.481147\pi$
$419$	69737.8	−	10026.8i	0.397228	−	0.0571128i	0.338035	+	0.941134i	$0.390238\pi$
$420$	−879058.	−	107409.i	−4.98332	−	0.608892i
$421$	−134757.	−	61541.5i	−0.760304	−	0.347219i	−0.00275375	−	0.999996i	$-0.500877\pi$
$421$	−134757.	−	61541.5i	−0.760304	−	0.347219i	−0.757550	+	0.652777i	$0.773604\pi$
$422$	−158360.	−	137220.i	−0.889242	−	0.770533i
$423$	−272345.	−	39157.3i	−1.52208	−	0.218842i
$424$	67356.1	−	30760.5i	0.374667	−	0.171104i
$425$	−38244.2	+	26936.8i	−0.211733	+	0.149131i
$426$	734888.	+	215782.i	4.04950	+	1.18904i
$427$	−12869.0	+	5877.08i	−0.0705813	+	0.0322334i
$428$	8810.74	−	61280.0i	0.0480978	−	0.334527i
$429$	173995.	+	150767.i	0.945413	+	0.819205i
$430$	4299.34	+	202612.i	0.0232522	+	1.09579i
$431$	61628.8	−	95896.2i	0.331764	−	0.516234i	−0.634795	−	0.772681i	$-0.718915\pi$
$431$	61628.8	−	95896.2i	0.331764	−	0.516234i	0.966558	+	0.256446i	$0.0825517\pi$
$432$	−54077.5	+	7775.17i	−0.289767	+	0.0416622i
$433$	131496.	−	84507.1i	0.701351	−	0.450731i	−0.140754	−	0.990045i	$-0.544953\pi$
$433$	131496.	−	84507.1i	0.701351	−	0.450731i	0.842105	+	0.539314i	$0.181316\pi$
$434$	−608724.	+	527462.i	−3.23177	+	2.80035i
$435$	241108.	−	218047.i	1.27419	−	1.15231i
$436$		−	39282.7i		−	0.206646i
$437$	113773.	+	24838.3i	0.595767	+	0.130064i
$438$		−	23444.9i		−	0.122208i
$439$	−317564.	+	93245.3i	−1.64779	+	0.483836i	−0.968288	−	0.249836i	$-0.919623\pi$
$439$	−317564.	+	93245.3i	−1.64779	+	0.483836i	−0.679504	+	0.733671i	$0.737805\pi$
$440$	46609.4	−	108071.i	0.240751	−	0.558217i
$441$	−801851.	+	515318.i	−4.12303	+	2.64971i
$442$	−11717.2	−	81495.2i	−0.0599764	−	0.417145i
$443$	79383.6	−	123523.i	0.404505	−	0.629421i	−0.577917	−	0.816095i	$-0.696134\pi$
$443$	79383.6	−	123523.i	0.404505	−	0.629421i	0.982422	+	0.186674i	$0.0597708\pi$
$444$	−307992.	−	140655.i	−1.56233	−	0.713493i
$445$	91985.7	−	339782.i	0.464516	−	1.71585i
$446$	51982.1	−	361544.i	0.261327	−	1.81757i
$447$	−62970.4	−	137886.i	−0.315153	−	0.690088i
$448$	554642.	+	162858.i	2.76348	+	0.811431i
$449$	−138977.	−	40807.2i	−0.689365	−	0.202416i	−0.0817560	−	0.996652i	$-0.526053\pi$
$449$	−138977.	−	40807.2i	−0.689365	−	0.202416i	−0.607609	+	0.794237i	$0.707871\pi$
$450$	−180446.	+	727384.i	−0.891092	+	3.59202i
$451$	120.925	+	17.3864i	0.000594516	+	8.54785e-5i
$452$	121011.	−	139654.i	0.592307	−	0.683559i
$453$	138569.	+	63282.4i	0.675259	+	0.308380i
$454$	172988.	−	269175.i	0.839276	−	1.30594i
$455$	207579.	+	308411.i	1.00267	+	1.48973i
$456$	112187.	+	174566.i	0.539526	+	0.839518i
$457$	212116.	+	244795.i	1.01564	+	1.17212i	0.984994	+	0.172586i	$0.0552123\pi$
$457$	212116.	+	244795.i	1.01564	+	1.17212i	0.0306502	+	0.999530i	$0.490242\pi$
$458$	48875.7	−	14351.2i	0.233003	−	0.0684160i
$459$		−	130308.i		−	0.618506i
$460$	121805.	+	307211.i	0.575637	+	1.45185i
$461$	−13627.4			−0.0641227			−0.0320614	−	0.999486i	$-0.510207\pi$
$461$	−13627.4			−0.0641227			−0.0320614	+	0.999486i	$0.510207\pi$
$462$	−209169.	−	712363.i	−0.979969	−	3.33747i
$463$	−981.895	+	850.817i	−0.00458040	+	0.00396894i	−0.657148	−	0.753762i	$-0.728237\pi$
$463$	−981.895	+	850.817i	−0.00458040	+	0.00396894i	0.652568	+	0.757731i	$0.273692\pi$
$464$	−20957.0	+	13468.2i	−0.0973403	+	0.0625568i
$465$	332374.	+	493826.i	1.53717	+	2.28385i
$466$	90580.2	+	58212.4i	0.417121	+	0.268067i
$467$	−53314.3	+	116742.i	−0.244461	+	0.535296i	−0.991595	−	0.129378i	$-0.958702\pi$
$467$	−53314.3	+	116742.i	−0.244461	+	0.535296i	0.747134	+	0.664673i	$0.231429\pi$
$468$	−607744.	−	526613.i	−2.77478	−	2.40436i
$469$	40361.0	−	280717.i	0.183491	−	1.27621i
$470$	150175.	−	180929.i	0.679835	−	0.819054i
$471$	−190075.	+	647335.i	−0.856806	+	2.91801i
$472$	−103077.	+	351048.i	−0.462677	+	1.57573i
$473$	−94217.8	+	43027.8i	−0.421125	+	0.192321i
$474$	−168606.	−	24241.8i	−0.750438	−	0.107897i
$475$	−135232.	+	25339.9i	−0.599367	+	0.112310i
$476$	−67241.7	+	147239.i	−0.296773	+	0.649843i
$477$	−202732.	−	130288.i	−0.891015	−	0.572621i
$478$	−307990.	+	44282.2i	−1.34797	+	0.193809i
$479$	−8307.98	−	12927.5i	−0.0362096	−	0.0563433i	0.822677	−	0.568509i	$-0.192480\pi$
$479$	−8307.98	−	12927.5i	−0.0362096	−	0.0563433i	−0.858887	+	0.512166i	$0.828843\pi$
$480$	181901.	−	421764.i	0.789501	−	1.83057i
$481$	40044.1	+	136378.i	0.173081	+	0.589458i
$482$	17125.2			0.0737127
$483$	657908.	+	359879.i	2.82014	+	1.54263i
$484$	−198637.			−0.847948
$485$	−160539.	−	177518.i	−0.682490	−	0.754673i
$486$	−325304.	−	375421.i	−1.37726	−	1.58945i
$487$	−172090.	−	267778.i	−0.725602	−	1.12906i	−0.986511	−	0.163696i	$-0.947659\pi$
$487$	−172090.	−	267778.i	−0.725602	−	1.12906i	0.260909	−	0.965363i	$-0.415978\pi$
$488$	1338.81	+	9311.63i	0.00562185	+	0.0391008i
$489$	477045.	+	306578.i	1.99499	+	1.28210i
$490$	−17280.6	−	814371.i	−0.0719725	−	3.39180i
$491$	140188.	−	161785.i	0.581497	−	0.671083i	−0.386429	−	0.922319i	$-0.626292\pi$
$491$	140188.	−	161785.i	0.581497	−	0.671083i	0.967926	+	0.251236i	$0.0808370\pi$
$492$	−605.047	−	86.9926i	−0.00249953	−	0.000359379i
$493$	−24682.8	−	54047.7i	−0.101555	−	0.222374i
$494$	68224.6	−	232352.i	0.279568	−	0.952121i
$495$	−377893.	+	62542.3i	−1.54226	+	0.255249i
$496$	−18949.6	−	41493.9i	−0.0770260	−	0.168663i
$497$	−89957.8	+	625670.i	−0.364188	+	2.53298i
$498$	−427657.	+	493542.i	−1.72439	+	1.99006i
$499$	−128039.	+	280366.i	−0.514211	+	1.12596i	0.457374	+	0.889274i	$0.348790\pi$
$499$	−128039.	+	280366.i	−0.514211	+	1.12596i	−0.971585	+	0.236691i	$0.923937\pi$
$500$	−273942.	−	278222.i	−1.09577	−	1.11289i
$501$	−2771.30	−	19274.8i	−0.0110410	−	0.0767918i
$502$	−355705.	+	228598.i	−1.41150	+	0.907119i
$503$	−53530.0	−	61777.0i	−0.211574	−	0.244169i	0.640037	−	0.768344i	$-0.278919\pi$
$503$	−53530.0	−	61777.0i	−0.211574	−	0.244169i	−0.851610	+	0.524175i	$0.824374\pi$
$504$	262807.	+	895040.i	1.03461	+	3.52356i
$505$	−102896.	−	213219.i	−0.403473	−	0.836073i
$506$	−196053.	+	195762.i	−0.765722	+	0.764586i
$507$			15751.0i			0.0612764i
$508$	49846.0	+	169760.i	0.193154	+	0.657821i
$509$	195296.	+	225384.i	0.753804	+	0.869936i	0.994931	−	0.100558i	$-0.0320627\pi$
$509$	195296.	+	225384.i	0.753804	+	0.869936i	−0.241128	+	0.970493i	$0.577517\pi$
$510$	167283.	+	102558.i	0.643151	+	0.394303i
$511$	19152.0	−	2753.64i	0.0733453	−	0.0105455i
$512$	−34651.1	+	53918.2i	−0.132183	+	0.205682i
$513$	159214.	−	348630.i	0.604987	−	1.32474i
$514$	−98413.9	+	113576.i	−0.372503	+	0.429892i
$515$	142958.	−	45292.0i	0.539006	−	0.170768i
$516$	471417.	−	215289.i	1.77054	−	0.808580i
$517$	115309.	+	33857.6i	0.431400	+	0.126671i
$518$	129134.	−	439789.i	0.481260	−	1.63902i
$519$	148826.	+	325883.i	0.552514	+	1.20984i
$520$	235658.	−	74661.2i	0.871517	−	0.276114i
$521$	14213.3	+	12315.9i	0.0523625	+	0.0453724i	0.680649	−	0.732610i	$-0.261698\pi$
$521$	14213.3	+	12315.9i	0.0523625	+	0.0453724i	−0.628286	+	0.777982i	$0.716243\pi$
$522$	−865894.	−	395441.i	−3.17778	−	1.45124i
$523$	181536.	+	116666.i	0.663682	+	0.426522i	0.828643	−	0.559778i	$-0.189114\pi$
$523$	181536.	+	116666.i	0.663682	+	0.426522i	−0.164961	+	0.986300i	$0.552750\pi$
$524$	14176.4	+	98599.2i	0.0516302	+	0.359096i
$525$	−881533.	−	88775.1i	−3.19831	−	0.322086i
$526$	−388103.	+	336294.i	−1.40274	+	1.21548i
$527$	104393.	−	30652.5i	0.375880	−	0.110368i
$528$	42047.0			0.150823
$529$	415.505	−	279841.i	0.00148479	−	0.999999i
$530$	185476.	−	89507.1i	0.660291	−	0.318644i
$531$	1.14249e6	−	335464.i	4.05193	−	1.18975i
$532$	−359802.	+	311770.i	−1.27128	+	1.10157i
$533$	138.730	+	215.867i	0.000488331	+	0.000759858i
$534$	−1.46154e6	+	210138.i	−5.12542	+	0.736924i
$535$	7512.08	−	61480.7i	0.0262454	−	0.214798i
$536$	−171540.	−	78339.9i	−0.597086	−	0.272680i
$537$	−116415.	−	100874.i	−0.403701	−	0.349809i
$538$	−422373.	−	60728.0i	−1.45926	−	0.209809i
$539$	378695.	−	172944.i	1.30350	−	0.595290i
$540$	1.07306e6	−	177594.i	3.67989	−	0.609032i
$541$	406219.	+	119277.i	1.38792	+	0.407531i	0.888520	−	0.458838i	$-0.151734\pi$
$541$	406219.	+	119277.i	1.38792	+	0.407531i	0.499404	+	0.866370i	$0.333553\pi$
$542$	362879.	−	165721.i	1.23527	−	0.564130i
$543$	−30840.9	+	214503.i	−0.104599	+	0.727501i
$544$	−63447.2	−	54977.3i	−0.214395	−	0.185774i
$545$	−833.746	−	39291.4i	−0.00280699	−	0.132283i
$546$	843080.	−	1.31186e6i	2.82803	−	4.40050i
$547$	−106016.	+	15242.8i	−0.354320	+	0.0509435i	−0.317177	−	0.948366i	$-0.602735\pi$
$547$	−106016.	+	15242.8i	−0.354320	+	0.0509435i	−0.0371432	+	0.999310i	$0.511826\pi$
$548$	532468.	−	342196.i	1.77310	−	1.13950i
$549$	23138.3	−	20049.4i	0.0767691	−	0.0665208i
$550$	123226.	−	303253.i	0.407358	−	1.00249i
$551$		−	174760.i		−	0.575622i
$552$	352860.	−	352336.i	1.15804	−	1.15632i
$553$		−	140580.i		−	0.459699i
$554$	661096.	−	194115.i	2.15400	−	0.632470i
$555$	−311046.	−	134150.i	−1.00981	−	0.435515i
$556$	203341.	−	130680.i	0.657774	−	0.422725i
$557$	7891.92	+	54889.5i	0.0254374	+	0.176921i	0.998579	−	0.0532849i	$-0.0169692\pi$
$557$	7891.92	+	54889.5i	0.0254374	+	0.176921i	−0.973142	+	0.230206i	$0.926060\pi$
$558$	942377.	−	1.46637e6i	3.02661	−	4.70950i
$559$	−197894.	−	90375.4i	−0.633301	−	0.289219i
$560$	65536.3	+	17742.0i	0.208981	+	0.0565753i
$561$	−14272.4	+	99266.4i	−0.0453492	+	0.315411i
$562$	415123.	+	908993.i	1.31433	+	2.87798i
$563$	357546.	+	104985.i	1.12802	+	0.331215i	0.791928	−	0.610615i	$-0.209078\pi$
$563$	357546.	+	104985.i	1.12802	+	0.331215i	0.336088	+	0.941830i	$0.390896\pi$
$564$	−576945.	−	169406.i	−1.81374	−	0.532563i
$565$	118074.	−	142253.i	0.369876	−	0.445621i
$566$	268912.	+	38663.7i	0.839417	+	0.120690i
$567$	756428.	−	872964.i	2.35289	−	2.71538i
$568$	382334.	+	174606.i	1.18508	+	0.541207i
$569$	−247631.	+	385321.i	−0.764856	+	1.19014i	0.212214	+	0.977223i	$0.431932\pi$
$569$	−247631.	+	385321.i	−0.764856	+	1.19014i	−0.977070	+	0.212916i	$0.931704\pi$
$570$	322248.	+	478781.i	0.991836	+	1.47362i
$571$	−46996.4	−	73127.8i	−0.144143	−	0.224290i	0.761674	−	0.647961i	$-0.224378\pi$
$571$	−46996.4	−	73127.8i	−0.144143	−	0.224290i	−0.905816	+	0.423670i	$0.860741\pi$
$572$	230011.	+	265447.i	0.703003	+	0.811308i
$573$	−575255.	+	168910.i	−1.75207	+	0.514454i
$574$		−	827.487i		−	0.00251153i
$575$	128352.	+	304694.i	0.388211	+	0.921571i
$576$	−1.25096e6			−3.77050
$577$	−101085.	−	344266.i	−0.303625	−	1.03405i	−0.960089	−	0.279694i	$-0.909767\pi$
$577$	−101085.	−	344266.i	−0.303625	−	1.03405i	0.656464	−	0.754357i	$-0.272051\pi$
$578$	−377012.	+	326683.i	−1.12849	+	0.977846i
$579$	535860.	−	344376.i	1.59843	−	1.02725i
$580$	411432.	−	276918.i	1.22305	−	0.823182i
$581$	−453401.	−	291383.i	−1.34317	−	0.863202i
$582$	−417062.	+	913238.i	−1.23127	+	2.69611i
$583$	79548.2	+	68928.9i	0.234042	+	0.202798i
$584$	1831.04	−	12735.1i	0.00536873	−	0.0373403i
$585$	−619056.	−	513831.i	−1.80891	−	1.50144i
$586$	13318.1	−	45357.1i	0.0387834	−	0.132084i
$587$	−46770.4	+	159285.i	−0.135736	+	0.462274i	−0.999105	−	0.0422987i	$-0.986532\pi$
$587$	−46770.4	+	159285.i	−0.135736	+	0.462274i	0.863369	+	0.504573i	$0.168350\pi$
$588$	−1.89480e6	+	865325.i	−5.48035	+	2.50279i
$589$	316749.	+	45541.6i	0.913028	+	0.131274i
$590$	−265904.	+	982210.i	−0.763873	+	2.82163i
$591$	−408515.	+	894522.i	−1.16959	+	2.56104i
$592$	21837.6	+	14034.2i	0.0623106	+	0.0400446i
$593$	135448.	−	19474.5i	0.385179	−	0.0553804i	0.0529947	−	0.998595i	$-0.483123\pi$
$593$	135448.	−	19474.5i	0.385179	−	0.0553804i	0.332185	+	0.943214i	$0.392214\pi$
$594$	492973.	+	767081.i	1.39717	+	2.17404i
$595$	−64131.6	+	148699.i	−0.181150	+	0.420023i
$596$	−65152.8	−	221890.i	−0.183417	−	0.624662i
$597$	1.16065e6			3.25652
$598$	−580410.	−	41944.8i	−1.62305	−	0.117294i
$599$	−311403.			−0.867898			−0.433949	−	0.900938i	$-0.642880\pi$
$599$	−311403.			−0.867898			−0.433949	+	0.900938i	$0.642880\pi$
$600$	−221785.	+	545801.i	−0.616069	+	1.51611i
$601$	−402179.	−	464139.i	−1.11345	−	1.28499i	−0.954668	−	0.297673i	$-0.903789\pi$
$601$	−402179.	−	464139.i	−1.11345	−	1.28499i	−0.158780	−	0.987314i	$-0.550756\pi$
$602$	379296.	+	590195.i	1.04661	+	1.62856i
$603$	87344.4	+	607494.i	0.240215	+	1.67073i
$604$	195510.	+	125647.i	0.535915	+	0.344411i
$605$	−198681.	+	4215.93i	−0.542807	+	0.0115181i
$606$	−650330.	+	750521.i	−1.77088	+	2.04370i
$607$	47270.8	+	6796.51i	0.128297	+	0.0184463i	0.206164	−	0.978517i	$-0.433902\pi$
$607$	47270.8	+	6796.51i	0.128297	+	0.0184463i	−0.0778673	+	0.996964i	$0.524811\pi$
$608$	−102576.	−	224610.i	−0.277484	−	0.607606i
$609$	317054.	−	1.07979e6i	0.854868	−	2.91141i
$610$	4272.12	+	25813.0i	0.0114811	+	0.0693711i
$611$	104858.	+	229607.i	0.280879	+	0.615040i
$612$	49851.7	−	346726.i	0.133100	−	0.925729i
$613$	−12999.6	+	15002.4i	−0.0345947	+	0.0399245i	−0.772783	−	0.634670i	$-0.781136\pi$
$613$	−12999.6	+	15002.4i	−0.0345947	+	0.0399245i	0.738189	+	0.674594i	$0.235681\pi$
$614$	−152402.	+	333713.i	−0.404253	+	0.885191i
$615$	−607.028	−	74.1703i	−0.00160494	−	0.000196101i
$616$	−57984.0	−	403288.i	−0.152808	−	1.06280i
$617$	595036.	−	382406.i	1.56305	−	1.00451i	0.581445	−	0.813586i	$-0.302488\pi$
$617$	595036.	−	382406.i	1.56305	−	1.00451i	0.981605	−	0.190925i	$-0.0611487\pi$
$618$	−411931.	−	475394.i	−1.07857	−	1.24473i
$619$	147540.	+	502476.i	0.385060	+	1.31140i	0.893021	+	0.450015i	$0.148581\pi$
$619$	147540.	+	502476.i	0.385060	+	1.31140i	−0.507960	+	0.861380i	$0.669600\pi$
$620$	394692.	+	817878.i	1.02677	+	2.12767i
$621$	−899808.	−	196441.i	−2.33328	−	0.509388i
$622$		−	268614.i		−	0.694302i
$623$	−343322.	−	1.16925e6i	−0.884555	−	3.01252i
$624$	57834.2	+	66744.3i	0.148531	+	0.171413i
$625$	−279908.	−	272469.i	−0.716564	−	0.697521i
$626$	864643.	−	124317.i	2.20642	−	0.317235i
$627$	−159472.	+	248143.i	−0.405647	+	0.631199i
$628$	−427574.	+	936256.i	−1.08416	+	2.37397i
$629$	−40545.0	+	46791.5i	−0.102479	+	0.118267i
$630$	783575.	+	2.47325e6i	1.97424	+	6.23141i
$631$	−274013.	+	125138.i	−0.688197	+	0.314289i	−0.728644	−	0.684893i	$-0.759849\pi$
$631$	−274013.	+	125138.i	−0.688197	+	0.314289i	0.0404473	+	0.999182i	$0.487122\pi$
$632$	−89692.3	−	26336.0i	−0.224554	−	0.0659351i
$633$	−151034.	+	514375.i	−0.376936	+	1.28373i
$634$	−410420.	−	898694.i	−1.02106	−	2.23580i
$635$	53460.1	+	168740.i	0.132581	+	0.418475i
$636$	−398018.	−	344885.i	−0.983986	−	0.852629i
$637$	795409.	+	363251.i	1.96025	+	0.895216i
$638$	349771.	+	224784.i	0.859294	+	0.552235i
$639$	−194676.	−	1.35400e6i	−0.476772	−	3.31602i
$640$	324253.	−	528892.i	0.791634	−	1.29124i
$641$	−158317.	+	137182.i	−0.385311	+	0.333874i	−0.825881	−	0.563845i	$-0.809322\pi$
$641$	−158317.	+	137182.i	−0.385311	+	0.333874i	0.440570	+	0.897718i	$0.354776\pi$
$642$	−249284.	+	73196.5i	−0.604818	+	0.177591i
$643$	−379091.			−0.916898			−0.458449	−	0.888721i	$-0.651595\pi$
$643$	−379091.			−0.916898			−0.458449	+	0.888721i	$0.651595\pi$
$644$	915355.	+	686287.i	2.20708	+	1.65476i
$645$	466953.	−	225343.i	1.12242	−	0.541656i
$646$	101212.	−	29718.6i	0.242531	−	0.0712137i
$647$	369125.	−	319849.i	0.881790	−	0.764076i	−0.0909785	−	0.995853i	$-0.528999\pi$
$647$	369125.	−	319849.i	0.881790	−	0.764076i	0.972769	+	0.231777i	$0.0744540\pi$
$648$	−415257.	−	646152.i	−0.988933	−	1.53881i
$649$	−514783.	+	74014.6i	−1.22218	+	0.175723i
$650$	650867.	−	221508.i	1.54051	−	0.524280i
$651$	1.87447e6	+	856044.i	4.42301	+	2.01992i
$652$	653811.	+	566530.i	1.53800	+	1.33269i
$653$	495759.	+	71279.5i	1.16264	+	0.167162i	0.696505	−	0.717552i	$-0.254738\pi$
$653$	495759.	+	71279.5i	1.16264	+	0.167162i	0.466134	+	0.884714i	$0.345647\pi$
$654$	−149954.	+	68481.6i	−0.350592	+	0.160110i
$655$	16272.3	+	98320.2i	0.0379285	+	0.229171i
$656$	44.9655	+	13.2031i	0.000104489	+	3.06808e-5i
$657$	−38088.7	+	17394.5i	−0.0882401	+	0.0402979i
$658$	115843.	−	805709.i	0.267559	−	1.86091i
$659$	336322.	+	291424.i	0.774433	+	0.671050i	0.949592	−	0.313490i	$-0.101498\pi$
$659$	336322.	+	291424.i	0.774433	+	0.671050i	−0.175158	+	0.984540i	$0.556044\pi$
$660$	−836891.	+	17758.5i	−1.92124	+	0.0407678i
$661$	−174894.	+	272140.i	−0.400287	+	0.622859i	−0.981629	−	0.190800i	$-0.938892\pi$
$661$	−174894.	+	272140.i	−0.400287	+	0.622859i	0.581341	+	0.813660i	$0.302528\pi$
$662$	517.540	−	74.4111i	0.00118094	−	0.000169794i
$663$	−177204.	+	113882.i	−0.403131	+	0.259076i
$664$	−270846.	+	234690.i	−0.614309	+	0.532302i
$665$	−353265.	+	319476.i	−0.798835	+	0.722429i
$666$			991919.i			2.23629i
$667$	−410424.	+	88963.1i	−0.922531	+	0.199967i
$668$		−	29708.1i		−	0.0665767i
$669$	−896638.	+	263277.i	−2.00339	+	0.588247i
$670$	−481609.	−	207711.i	−1.07286	−	0.462711i
$671$	−11249.6	+	7229.69i	−0.0249858	+	0.0160574i
$672$	−226292.	−	1.57390e6i	−0.501108	−	3.48528i
$673$	−427355.	+	664977.i	−0.943536	+	1.46817i	−0.0608826	+	0.998145i	$0.519392\pi$
$673$	−427355.	+	664977.i	−0.943536	+	1.46817i	−0.882653	+	0.470025i	$0.844245\pi$
$674$	712501.	+	325388.i	1.56843	+	0.716279i
$675$	1.06953e6	−	200408.i	2.34738	−	0.439853i
$676$	−3419.80	+	23785.3i	−0.00748355	+	0.0520492i
$677$	−310162.	−	679160.i	−0.676723	−	1.48182i	−0.866078	−	0.499908i	$-0.833367\pi$
$677$	−310162.	−	679160.i	−0.676723	−	1.48182i	0.189355	−	0.981909i	$-0.439360\pi$
$678$	−744060.	−	218476.i	−1.61863	−	0.475274i
$679$	−795004.	−	233434.i	−1.72437	−	0.506320i
$680$	82857.7	+	68773.9i	0.179191	+	0.148732i
$681$	−810282.	−	116501.i	−1.74720	−	0.251209i
$682$	−498566.	+	575375.i	−1.07190	+	1.23704i
$683$	−218665.	−	99860.8i	−0.468746	−	0.214069i	0.167016	−	0.985954i	$-0.446587\pi$
$683$	−218665.	−	99860.8i	−0.468746	−	0.214069i	−0.635762	+	0.771885i	$0.719314\pi$
$684$	557016.	−	866734.i	1.19057	−	1.85257i
$685$	525323.	−	353574.i	1.11955	−	0.753527i
$686$	−805276.	−	1.25303e6i	−1.71118	−	2.66265i
$687$	−85343.7	−	98491.9i	−0.180825	−	0.208683i
$688$	−38123.0	+	11193.9i	−0.0805397	+	0.0236486i
$689$			221082.i			0.465709i
$690$	960375.	−	1.00053e6i	2.01717	−	2.10151i
$691$	384885.			0.806074			0.403037	−	0.915184i	$-0.367955\pi$
$691$	384885.			0.806074			0.403037	+	0.915184i	$0.367955\pi$
$692$	153984.	+	524420.i	0.321560	+	1.09513i
$693$	−1.00212e6	+	868343.i	−2.08667	+	1.80811i
$694$	1.25619e6	−	807304.i	2.60817	−	1.67617i
$695$	200613.	−	135024.i	0.415327	−	0.279539i
$696$	−629525.	−	404571.i	−1.29955	−	0.835173i
$697$	−46.4333	+	101.675i	−9.55794e−5	+	0.000209290i
$698$	430373.	+	372920.i	0.883353	+	0.765429i
$699$	39203.8	−	272668.i	0.0802368	−	0.558059i
$700$	−1.31191e6	−	325452.i	−2.67736	−	0.664188i
$701$	−65574.5	+	223326.i	−0.133444	+	0.454468i	−0.998919	−	0.0464837i	$-0.985198\pi$
$701$	−65574.5	+	223326.i	−0.133444	+	0.454468i	0.865475	+	0.500952i	$0.167017\pi$
$702$	−539575.	+	1.83762e6i	−1.09491	+	3.72892i
$703$	−165647.	+	75648.4i	−0.335176	+	0.153070i
$704$	540827.	+	77759.2i	1.09122	+	0.156894i
$705$	−580669.	−	157199.i	−1.16829	−	0.316279i
$706$	343161.	−	751417.i	0.688475	−	1.50755i
$707$	−689479.	−	443101.i	−1.37937	−	0.886470i
$708$	2.57571e6	−	370331.i	5.13842	−	0.738794i
$709$	−338896.	−	527333.i	−0.674178	−	1.04904i	−0.994801	−	0.101834i	$-0.967529\pi$
$709$	−338896.	−	527333.i	−0.674178	−	1.04904i	0.320624	−	0.947207i	$-0.396107\pi$
$710$	1.07342e6	+	462953.i	2.12939	+	0.918375i
$711$	85710.6	+	291904.i	0.169549	+	0.577431i
$712$	−810314.			−1.59843
$713$	−54289.5	−	767069.i	−0.106792	−	1.50888i
$714$	679278.			1.33245
$715$	235696.	+	260624.i	0.461042	+	0.509803i
$716$	−153894.	−	177603.i	−0.300190	−	0.346437i
$717$	430387.	+	669696.i	0.837184	+	1.30268i
$718$	−33948.4	−	236116.i	−0.0658521	−	0.458012i
$719$	114286.	+	73447.4i	0.221074	+	0.142075i	0.646490	−	0.762922i	$-0.276236\pi$
$719$	114286.	+	73447.4i	0.221074	+	0.142075i	−0.425417	+	0.904998i	$0.639872\pi$
$720$	−146898.	+	3117.11i	−0.283368	+	0.00601295i
$721$	339965.	−	392340.i	0.653978	−	0.754731i
$722$	−518757.	−	74586.0i	−0.995152	−	0.143081i
$723$	−18200.8	−	39854.2i	−0.0348188	−	0.0762425i
$724$	−93144.1	+	317220.i	−0.177696	+	0.605178i
$725$	405647.	−	285712.i	0.771741	−	0.543567i
$726$	346285.	+	758257.i	0.656992	+	1.43861i
$727$	−62160.0	+	432333.i	−0.117610	+	0.817992i	0.842566	+	0.538594i	$0.181044\pi$
$727$	−62160.0	+	432333.i	−0.117610	+	0.817992i	−0.960175	+	0.279399i	$0.909865\pi$
$728$	560412.	−	646750.i	1.05741	−	1.22032i
$729$	−78854.6	+	172667.i	−0.148379	+	0.324904i
$730$	4339.98	−	35519.5i	0.00814408	−	0.0666531i
$731$	−13486.7	−	93802.0i	−0.0252389	−	0.175540i
$732$	56287.3	−	36173.6i	0.105048	−	0.0675103i
$733$	−592000.	−	683205.i	−1.10183	−	1.27158i	−0.959485	−	0.281761i	$-0.909081\pi$
$733$	−592000.	−	683205.i	−1.10183	−	1.27158i	−0.142344	−	0.989817i	$-0.545464\pi$
$734$	−164375.	−	559811.i	−0.305101	−	1.03908i
$735$	−1.87685e6	+	905733.i	−3.47420	+	1.67658i
$736$	−475281.	+	355240.i	−0.877394	+	0.655793i
$737$		−	268066.i		−	0.493523i
$738$	504.512	+	1718.21i	0.000926316	+	0.00315474i
$739$	−128674.	−	148498.i	−0.235615	−	0.271914i	0.625612	−	0.780134i	$-0.284849\pi$
$739$	−128674.	−	148498.i	−0.235615	−	0.271914i	−0.861227	+	0.508220i	$0.830304\pi$
$740$	−440576.	−	270109.i	−0.804559	−	0.493260i
$741$	−613242.	+	88170.9i	−1.11685	+	0.160579i
$742$	385446.	−	599765.i	0.700092	−	1.08937i
$743$	254187.	−	556592.i	0.460443	−	1.00823i	−0.526944	−	0.849900i	$-0.676662\pi$
$743$	254187.	−	556592.i	0.460443	−	1.00823i	0.987386	−	0.158329i	$-0.0506106\pi$
$744$	897329.	−	1.03557e6i	1.62109	−	1.87083i
$745$	−69876.7	−	220556.i	−0.125898	−	0.397381i
$746$	−1.11934e6	+	511186.i	−2.01134	+	0.918546i
$747$	1.11911e6	+	328599.i	2.00553	+	0.588878i
$748$	−43104.7	+	146801.i	−0.0770409	+	0.262377i
$749$	−89072.7	−	195042.i	−0.158775	−	0.347668i
$750$	−584492.	+	1.53074e6i	−1.03910	+	2.72132i
$751$	−98886.0	−	85685.2i	−0.175329	−	0.151924i	0.562775	−	0.826610i	$-0.309734\pi$
$751$	−98886.0	−	85685.2i	−0.175329	−	0.151924i	−0.738105	+	0.674686i	$0.764279\pi$
$752$	41933.7	+	19150.5i	0.0741528	+	0.0338644i
$753$	910041.	+	584848.i	1.60499	+	1.03146i
$754$	124282.	+	864398.i	0.218607	+	1.52045i
$755$	198221.	+	121525.i	0.347740	+	0.213193i
$756$	2.84560e6	−	2.46573e6i	4.97887	−	4.31421i
$757$	−236486.	+	69438.6i	−0.412681	+	0.121174i	−0.481481	−	0.876456i	$-0.659901\pi$
$757$	−236486.	+	69438.6i	−0.412681	+	0.121174i	0.0688005	+	0.997630i	$0.478083\pi$
$758$	907240.			1.57901
$759$	663945.	+	248200.i	1.15252	+	0.430843i
$760$	137651.	+	285238.i	0.238315	+	0.493834i
$761$	−816989.	+	239890.i	−1.41074	+	0.414231i	−0.896358	−	0.443331i	$-0.853797\pi$
$761$	−816989.	+	239890.i	−1.41074	+	0.414231i	−0.514382	+	0.857561i	$0.671979\pi$
$762$	561128.	−	486220.i	0.966390	−	0.837381i
$763$	−73554.6	−	114453.i	−0.126346	−	0.196598i
$764$	−905351.	+	130170.i	−1.55107	+	0.223010i
$765$	42503.8	−	347861.i	0.0726281	−	0.594406i
$766$	193977.	+	88586.4i	0.330593	+	0.150977i
$767$	−825554.	−	715347.i	−1.40331	−	1.21598i
$768$	−843150.	−	121227.i	−1.42949	−	0.205530i
$769$	252784.	−	115443.i	0.427462	−	0.195215i	−0.190054	−	0.981774i	$-0.560866\pi$
$769$	252784.	−	115443.i	0.427462	−	0.195215i	0.617516	+	0.786558i	$0.288139\pi$
$770$	−185026.	−	1.11796e6i	−0.312070	−	1.88559i
$771$	368910.	+	108322.i	0.620600	+	0.182225i
$772$	883959.	−	403690.i	1.48319	−	0.677351i
$773$	35732.8	−	248527.i	0.0598010	−	0.415925i	−0.937828	−	0.347101i	$-0.887166\pi$
$773$	35732.8	−	248527.i	0.0598010	−	0.415925i	0.997629	−	0.0688243i	$-0.0219248\pi$
$774$	−1.14741e6	−	994240.i	−1.91531	−	1.65962i
$775$	412139.	+	809683.i	0.686183	+	1.34807i
$776$	−297869.	+	463494.i	−0.494655	+	0.769698i
$777$	−1.16073e6	+	166888.i	−1.92260	+	0.276428i
$778$	781627.	−	502321.i	1.29134	−	0.829894i
$779$	−248.459	+	215.291i	−0.000409430	+	0.000354773i
$780$	−1.17930e6	−	1.30403e6i	−1.93837	−	2.14338i
$781$			597475.i			0.979529i
$782$	−121317.	−	222569.i	−0.198385	−	0.363958i
$783$			1.38214e6i			2.25439i
$784$	153230.	−	44992.4i	0.249294	−	0.0731993i
$785$	−407798.	+	945539.i	−0.661767	+	1.53441i
$786$	351669.	−	226004.i	0.569232	−	0.365823i
$787$	23021.5	+	160118.i	0.0371693	+	0.258518i	0.999930	−	0.0118372i	$-0.00376798\pi$
$787$	23021.5	+	160118.i	0.0371693	+	0.258518i	−0.962761	+	0.270355i	$0.912859\pi$
$788$	−811103.	+	1.26210e6i	−1.30624	+	2.03255i
$789$	1.19511e6	+	545787.i	1.91978	+	0.876736i
$790$	−250953.	−	67938.1i	−0.402104	−	0.108858i
$791$	91080.5	−	633479.i	0.145570	−	1.01246i
$792$	366280.	+	802042.i	0.583933	+	1.27864i
$793$	−26949.6	−	7913.13i	−0.0428555	−	0.0125835i
$794$	42755.5	+	12554.2i	0.0678190	+	0.0199134i
$795$	−405427.	−	336514.i	−0.641473	−	0.532438i
$796$	1.75267e6	+	251997.i	2.76615	+	0.397712i
$797$	704568.	−	813115.i	1.10919	−	1.28007i	0.152712	−	0.988271i	$-0.451199\pi$
$797$	704568.	−	813115.i	1.10919	−	1.28007i	0.956478	−	0.291803i	$-0.0942553\pi$
$798$	1.81737e6	+	829963.i	2.85388	+	1.30333i
$799$	−59445.1	+	92498.4i	−0.0931157	+	0.144891i
$800$	353658.	−	605309.i	0.552591	−	0.945795i
$801$	1.42576e6	+	2.21853e6i	2.22219	+	3.45780i
$802$	−1.27507e6	−	1.47151e6i	−1.98237	−	2.28778i
$803$	17548.1	−	5152.59i	0.0272144	−	0.00799088i
$804$			1.34127e6i			2.07493i
$805$	930124.	+	667012.i	1.43532	+	1.02930i
$806$	−1.59909e6			−2.46152
$807$	307572.	+	1.04750e6i	0.472281	+	1.60844i
$808$	−411871.	+	356888.i	−0.630868	+	0.546650i
$809$	947612.	−	608993.i	1.44788	−	0.930498i	0.448559	−	0.893753i	$-0.351937\pi$
$809$	947612.	−	608993.i	1.44788	−	0.930498i	0.999325	−	0.0367449i	$-0.0116989\pi$
$810$	−1.19279e6	−	1.77219e6i	−1.81800	−	2.70110i
$811$	375385.	+	241245.i	0.570735	+	0.366789i	0.793953	−	0.607979i	$-0.208020\pi$
$811$	375385.	+	241245.i	0.570735	+	0.366789i	−0.223218	+	0.974769i	$0.571656\pi$
$812$	713215.	−	1.56172e6i	1.08170	−	2.36860i
$813$	−771338.	−	668369.i	−1.16698	−	1.01120i
$814$	61657.2	−	428835.i	0.0930540	−	0.647205i
$815$	665980.	+	552780.i	1.00264	+	0.832217i
$816$	−10838.3	+	36911.8i	−0.0162772	+	0.0554351i
$817$	78527.4	−	267440.i	0.117646	−	0.400665i
$818$	−598675.	+	273406.i	−0.894715	+	0.408603i
$819$	−2.75676e6	−	396363.i	−4.10991	−	0.590915i
$820$	−900.555	−	243.798i	−0.00133931	−	0.000362579i
$821$	267267.	−	585232.i	0.396514	−	0.868245i	−0.601098	−	0.799175i	$-0.705270\pi$
$821$	267267.	−	585232.i	0.396514	−	0.868245i	0.997612	−	0.0690692i	$-0.0220029\pi$
$822$	−2.23452e6	−	1.43604e6i	−3.30705	−	2.12531i
$823$	−884030.	+	127104.i	−1.30517	+	0.187655i	−0.759590	−	0.650402i	$-0.774600\pi$
$823$	−884030.	+	127104.i	−1.30517	+	0.187655i	−0.545582	+	0.838058i	$0.683691\pi$
$824$	−186631.	−	290403.i	−0.274871	−	0.427707i
$825$	−836700.	+	35524.8i	−1.22931	+	0.0521944i
$826$	992443.	+	3.37995e6i	1.45461	+	4.95394i
$827$	−923191.			−1.34984			−0.674918	−	0.737893i	$-0.735821\pi$
$827$	−923191.			−1.34984			−0.674918	+	0.737893i	$0.735821\pi$
$828$	−2.31908e6	−	866936.i	−3.38264	−	1.26452i
$829$	441952.			0.643081			0.321540	−	0.946896i	$-0.395799\pi$
$829$	441952.			0.643081			0.321540	+	0.946896i	$0.395799\pi$
$830$	−739270.	+	668561.i	−1.07312	+	0.970476i
$831$	−1.15436e6	−	1.33221e6i	−1.67163	−	1.92917i
$832$	620456.	+	965449.i	0.896323	+	1.39471i
$833$	54207.8	+	377024.i	0.0781218	+	0.543349i
$834$	−853330.	−	548402.i	−1.22683	−	0.788437i
$835$	−630.533	−	29714.7i	−0.000904347	−	0.0426186i
$836$	−294690.	+	340090.i	−0.421651	+	0.486611i
$837$	−2.50510e6	−	360179.i	−3.57581	−	0.514124i
$838$	−187381.	−	410308.i	−0.266832	−	0.584281i
$839$	−80781.2	+	275116.i	−0.114759	+	0.390833i	−0.996762	−	0.0804111i	$-0.974377\pi$
$839$	−80781.2	+	275116.i	−0.114759	+	0.390833i	0.882003	+	0.471244i	$0.156195\pi$
$840$	333014.	+	2.01214e6i	0.471959	+	2.85167i
$841$	−32011.3	−	70095.0i	−0.0452597	−	0.0991049i
$842$	−134980.	+	938804.i	−0.190390	+	1.32419i
$843$	1.67423e6	−	1.93216e6i	2.35592	−	2.71887i
$844$	−339752.	+	743953.i	−0.476955	+	1.04439i
$845$	−2915.74	+	23863.1i	−0.00408352	+	0.0334206i
$846$	250695.	+	1.74362e6i	0.350271	+	2.43619i
$847$	−578745.	+	371937.i	−0.806715	+	0.518444i
$848$	26441.1	+	30514.6i	0.0367695	+	0.0424343i
$849$	−195822.	−	666909.i	−0.271673	−	0.925233i
$850$	234453.	+	186344.i	0.324502	+	0.257916i
$851$	261985.	+	350513.i	0.361757	+	0.484000i
$852$		−	2.98946e6i		−	4.11825i
$853$	22032.6	+	75036.2i	0.0302808	+	0.103127i	0.973247	−	0.229762i	$-0.0737947\pi$
$853$	22032.6	+	75036.2i	0.0302808	+	0.103127i	−0.942966	+	0.332889i	$0.891977\pi$
$854$	59314.6	+	68452.6i	0.0813290	+	0.0938587i
$855$	538744.	−	878749.i	0.736971	−	1.20208i
$856$	−141127.	+	20290.9i	−0.192602	+	0.0276920i
$857$	48912.3	−	76109.1i	0.0665973	−	0.103627i	−0.806358	−	0.591428i	$-0.798564\pi$
$857$	48912.3	−	76109.1i	0.0665973	−	0.103627i	0.872955	+	0.487801i	$0.162201\pi$
$858$	612313.	−	1.34078e6i	0.831761	−	1.82130i
$859$	−410788.	+	474075.i	−0.556713	+	0.642482i	−0.962434	−	0.271516i	$-0.912475\pi$
$859$	−410788.	+	474075.i	−0.556713	+	0.642482i	0.405721	+	0.913997i	$0.367021\pi$
$860$	754060.	−	238901.i	1.01955	−	0.323014i
$861$	−1925.74	+	879.457i	−0.00259772	+	0.00118634i
$862$	−700244.	−	205610.i	−0.942398	−	0.276713i
$863$	−62573.4	+	213105.i	−0.0840172	+	0.286136i	−0.990775	−	0.135515i	$-0.956731\pi$
$863$	−62573.4	+	213105.i	−0.0840172	+	0.286136i	0.906758	+	0.421651i	$0.138549\pi$
$864$	811254.	+	1.77640e6i	1.08675	+	2.37965i
$865$	165148.	+	521269.i	0.220720	+	0.696674i
$866$	−756301.	−	655339.i	−1.00846	−	0.873837i
$867$	1.16095e6	+	530189.i	1.54446	+	0.705330i
$868$	2.64474e6	+	1.69967e6i	3.51029	+	2.25593i
$869$	−18910.6	−	131526.i	−0.0250418	−	0.174170i
$870$	−1.77433e6	−	1.08781e6i	−2.34421	−	1.43719i
$871$	425521.	−	368716.i	0.560899	−	0.486022i
$872$	−86802.5	+	25487.5i	−0.114156	+	0.0335193i
$873$	1.79309e6			2.35273
$874$	−52635.5	−	743699.i	−0.0689058	−	0.973586i
$875$	−1.31911e6	−	297680.i	−1.72291	−	0.388807i
$876$	−87801.7	+	25780.9i	−0.114418	+	0.0335962i
$877$	652081.	−	565031.i	0.847817	−	0.734637i	−0.118235	−	0.992986i	$-0.537724\pi$
$877$	652081.	−	565031.i	0.847817	−	0.734637i	0.966052	+	0.258348i	$0.0831782\pi$
$878$	1.14560e6	+	1.78258e6i	1.48608	+	2.31239i
$879$	−119710.	+	17211.8i	−0.154937	+	0.0222765i
$880$	63702.1	+	7783.50i	0.0822599	+	0.0100510i
$881$	−856077.	−	390957.i	−1.10296	−	0.503707i	−0.221119	−	0.975247i	$-0.570971\pi$
$881$	−856077.	−	390957.i	−1.10296	−	0.503707i	−0.881844	+	0.471540i	$0.843698\pi$
$882$	4.61187e6	+	3.99621e6i	5.92844	+	5.13702i
$883$	−1.29906e6	−	186776.i	−1.66612	−	0.239552i	−0.756202	−	0.654338i	$-0.772947\pi$
$883$	−1.29906e6	−	186776.i	−1.66612	−	0.239552i	−0.909919	+	0.414786i	$0.863856\pi$
$884$	−292317.	+	133497.i	−0.374067	+	0.170831i
$885$	2.56842e6	−	425081.i	3.27929	−	0.542731i
$886$	−901979.	−	264845.i	−1.14902	−	0.337384i
$887$	409888.	−	187189.i	0.520976	−	0.237922i	−0.137529	−	0.990498i	$-0.543916\pi$
$887$	409888.	−	187189.i	0.520976	−	0.237922i	0.658506	+	0.752576i	$0.271189\pi$
$888$	−110972.	+	771827.i	−0.140730	+	0.978800i
$889$	463097.	+	401275.i	0.585960	+	0.507737i
$890$	−2.25317e6	+	47811.2i	−2.84455	+	0.0603600i
$891$	590280.	−	918494.i	0.743538	−	1.15697i
$892$	−1.41115e6	+	202893.i	−1.77355	+	0.254998i
$893$	−272059.	+	174842.i	−0.341162	+	0.219252i
$894$	−733440.	+	635530.i	−0.917677	+	0.795171i
$895$	−157698.	−	174376.i	−0.196870	−	0.217691i
$896$		−	2.14764e6i		−	2.67513i
$897$	519247.	+	1.39532e6i	0.645341	+	1.73416i
$898$			927326.i			1.14995i
$899$	−1.10727e6	+	325123.i	−1.37004	+	0.402280i
$900$	2.92250e6	−	124084.i	3.60802	−	0.153190i
$901$	−81015.4	+	52065.4i	−0.0997971	+	0.0641357i
$902$	−111.312	−	774.193i	−0.000136814	−	0.000951560i
$903$	970396.	−	1.50997e6i	1.19007	−	1.85179i
$904$	−387106.	−	176786.i	−0.473689	−	0.216327i
$905$	−86432.1	+	319267.i	−0.105530	+	0.389814i
$906$	138798.	−	965363.i	0.169094	−	1.17607i
$907$	−13186.5	−	28874.5i	−0.0160293	−	0.0350994i	0.901448	−	0.432887i	$-0.142505\pi$
$907$	−13186.5	−	28874.5i	−0.0160293	−	0.0350994i	−0.917477	+	0.397788i	$0.869778\pi$
$908$	−1.19829e6	−	351850.i	−1.45342	−	0.426762i
$909$	1.70180e6	+	499694.i	2.05959	+	0.604751i
$910$	1.52013e6	−	1.83142e6i	1.83568	−	2.21160i
$911$	−286638.	−	41212.3i	−0.345380	−	0.0496581i	−0.0325578	−	0.999470i	$-0.510365\pi$
$911$	−286638.	−	41212.3i	−0.345380	−	0.0496581i	−0.312822	+	0.949812i	$0.601274\pi$
$912$	−74097.1	+	85512.7i	−0.0890865	+	0.102811i
$913$	−463396.	−	211626.i	−0.555918	−	0.253879i
$914$	1.12116e6	−	1.74456e6i	1.34207	−	2.08830i
$915$	55532.0	−	37376.3i	0.0663287	−	0.0446431i
$916$	−107491.	−	167260.i	−0.128110	−	0.199343i
$917$	225926.	+	260732.i	0.268675	+	0.310067i
$918$	−800468.	+	235039.i	−0.949858	+	0.278903i
$919$			1.56063e6i			1.84786i	0.382567	+	0.923928i	$0.375040\pi$
$919$			1.56063e6i			1.84786i	−0.382567	+	0.923928i	$0.624960\pi$
$920$	599812.	−	468477.i	0.708662	−	0.553493i
$921$	938597.			1.10652
$922$	24580.1	+	83712.1i	0.0289149	+	0.0984751i
$923$	−948414.	+	821805.i	−1.11325	+	0.964641i
$924$	−2.43781e6	+	1.56668e6i	−2.85532	+	1.83501i
$925$	−446407.	−	260818.i	−0.521732	−	0.304828i
$926$	6997.56	+	4497.06i	0.00816065	+	0.00524453i
$927$	−466703.	+	1.02194e6i	−0.543101	+	1.18923i
$928$	672968.	+	583130.i	0.781445	+	0.677126i
$929$	−70189.6	+	488179.i	−0.0813282	+	0.565650i	0.907891	+	0.419207i	$0.137692\pi$
$929$	−70189.6	+	488179.i	−0.0813282	+	0.565650i	−0.989219	+	0.146443i	$0.953217\pi$
$930$	2.43402e6	−	2.93247e6i	2.81422	−	3.39053i
$931$	−315630.	+	1.07494e6i	−0.364149	+	1.24018i
$932$	118401.	−	403238.i	0.136309	−	0.464226i
$933$	−625124.	+	285485.i	−0.718130	+	0.327959i
$934$	813301.	+	116935.i	0.932304	+	0.134045i
$935$	−39998.5	+	147749.i	−0.0457531	+	0.169005i
$936$	−769333.	+	1.68460e6i	−0.878138	+	1.92285i
$937$	49565.9	+	31854.1i	0.0564552	+	0.0362816i	0.568564	−	0.822639i	$-0.307499\pi$
$937$	49565.9	+	31854.1i	0.0564552	+	0.0362816i	−0.512109	+	0.858921i	$0.671136\pi$
$938$	−1.79722e6	+	258401.i	−2.04266	+	0.293690i
$939$	−1.20826e6	−	1.88009e6i	−1.37034	−	2.13229i
$940$	−842723.	−	363454.i	−0.953738	−	0.411334i
$941$	−20689.2	−	70460.9i	−0.0233649	−	0.0795736i	0.946985	−	0.321277i	$-0.104112\pi$
$941$	−20689.2	−	70460.9i	−0.0233649	−	0.0795736i	−0.970350	+	0.241703i	$0.922294\pi$
$942$	4.31936e6			4.86763
$943$	632.092	+	473.911i	0.000710816	+	0.000532934i
$944$	−199501.			−0.223872
$945$	2.79390e6	−	2.52667e6i	3.12858	−	2.82934i
$946$	434259.	+	501162.i	0.485251	+	0.560010i
$947$	−376852.	−	586393.i	−0.420214	−	0.653866i	0.565020	−	0.825077i	$-0.308868\pi$
$947$	−376852.	−	586393.i	−0.420214	−	0.653866i	−0.985234	+	0.171211i	$0.945232\pi$
$948$	94618.9	+	658089.i	0.105284	+	0.732265i
$949$	32315.9	+	20768.2i	0.0358826	+	0.0230603i
$950$	399582.	+	785014.i	0.442750	+	0.869822i
$951$	−1.65526e6	+	1.91027e6i	−1.83023	+	2.11219i
$952$	368980.	+	53051.3i	0.407126	+	0.0585359i
$953$	200994.	+	440116.i	0.221308	+	0.484598i	0.987422	−	0.158108i	$-0.0505393\pi$
$953$	200994.	+	440116.i	0.221308	+	0.484598i	−0.766114	+	0.642705i	$0.777812\pi$
$954$	−434675.	+	1.48037e6i	−0.477604	+	1.62657i
$955$	−902790.	+	149414.i	−0.989874	+	0.163827i
$956$	504516.	+	1.10474e6i	0.552025	+	1.20877i
$957$	151383.	−	1.05289e6i	0.165293	−	1.14964i
$958$	−64427.0	+	74352.7i	−0.0702000	+	0.0810151i
$959$	910644.	−	1.99403e6i	0.990174	−	2.16818i
$960$	−2.71488e6	−	331720.i	−2.94584	−	0.359940i
$961$	−169300.	−	1.17751e6i	−0.183320	−	1.27502i
$962$	765528.	−	491975.i	0.827201	−	0.531610i
$963$	303868.	+	350682.i	0.327667	+	0.378148i
$964$	−18831.6	−	64134.5i	−0.0202643	−	0.0690140i
$965$	875587.	−	422542.i	0.940253	−	0.453748i
$966$	1.02402e6	−	4.69059e6i	1.09738	−	5.02659i
$967$			1.46177e6i			1.56324i	0.623752	+	0.781622i	$0.285608\pi$
$967$			1.46177e6i			1.56324i	−0.623752	+	0.781622i	$0.714392\pi$
$968$	128880.	+	438926.i	0.137542	+	0.468426i
$969$	−176731.	−	203958.i	−0.188219	−	0.217217i
$970$	−800910.	+	1.30637e6i	−0.851217	+	1.38843i
$971$	1.17845e6	−	169436.i	1.24989	−	0.179708i	0.514584	−	0.857440i	$-0.327946\pi$
$971$	1.17845e6	−	169436.i	1.24989	−	0.179708i	0.735309	+	0.677732i	$0.237037\pi$
$972$	−1.04824e6	+	1.63110e6i	−1.10951	+	1.72643i
$973$	347762.	−	761492.i	0.367330	−	0.804339i
$974$	−1.33453e6	+	1.54013e6i	−1.40673	+	1.62346i
$975$	−1.20724e6	−	1.27929e6i	−1.26995	−	1.34574i
$976$	−4666.10	+	2130.94i	−0.00489840	+	0.00223703i
$977$	−147595.	−	43337.8i	−0.154626	−	0.0454023i	0.203503	−	0.979074i	$-0.434767\pi$
$977$	−147595.	−	43337.8i	−0.154626	−	0.0454023i	−0.358129	+	0.933672i	$0.616585\pi$
$978$	1.02283e6	−	3.48343e6i	1.06936	−	3.64191i
$979$	−478495.	−	1.04776e6i	−0.499243	−	1.09319i
$980$	−3.03084e6	+	960230.i	−3.15581	+	0.999823i
$981$	222512.	+	192807.i	0.231214	+	0.200348i
$982$	−1.24669e6	−	569346.i	−1.29282	−	0.590409i
$983$	797695.	+	512647.i	0.825524	+	0.530532i	0.883853	−	0.467766i	$-0.154941\pi$
$983$	797695.	+	512647.i	0.825524	+	0.530532i	−0.0583288	+	0.998297i	$0.518577\pi$
$984$	200.342	+	1393.41i	0.000206910	+	0.00143909i
$985$	−784496.	+	1.27960e6i	−0.808571	+	1.31887i
$986$	−287490.	+	249111.i	−0.295712	+	0.256236i
$987$	−1.99818e6	+	586718.i	−2.05116	+	0.602276i
$988$	−945186.			−0.968285
$989$	−668059.	−	48279.1i	−0.683003	−	0.0493590i
$990$	1.06581e6	+	2.20855e6i	1.08745	+	2.25340i
$991$	255615.	−	75055.3i	0.260279	−	0.0764248i	−0.148990	−	0.988839i	$-0.547602\pi$
$991$	255615.	−	75055.3i	0.260279	−	0.0764248i	0.409269	+	0.912414i	$0.365784\pi$
$992$	−1.23229e6	+	1.06778e6i	−1.25224	+	1.08507i
$993$	−723.215	−	1125.34i	−0.000733447	−	0.00114127i
$994$	4.00570e6	−	575932.i	4.05420	−	0.582906i
$995$	1.75841e6	+	214853.i	1.77613	+	0.217018i
$996$	2.31860e6	+	1.05887e6i	2.33726	+	1.06739i
$997$	425679.	+	368853.i	0.428244	+	0.371076i	0.842149	−	0.539244i	$-0.181290\pi$
$997$	425679.	+	368853.i	0.428244	+	0.371076i	−0.413905	+	0.910320i	$0.635835\pi$
$998$	1.95321e6	+	280830.i	1.96105	+	0.281956i
$999$	1.31007e6	−	598289.i	1.31269	−	0.599487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.5.i.a.14.5	✓	460
5.4	even	2	inner	115.5.i.a.14.42	yes	460
23.5	odd	22	inner	115.5.i.a.74.42	yes	460
115.74	odd	22	inner	115.5.i.a.74.5	yes	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.5.i.a.14.5	✓	460	1.1	even	1	trivial
115.5.i.a.14.42	yes	460	5.4	even	2	inner
115.5.i.a.74.5	yes	460	115.74	odd	22	inner
115.5.i.a.74.42	yes	460	23.5	odd	22	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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	115.i (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80372 - 6.14291i) q^{2} +(-12.3789 + 10.7264i) q^{3} +(-21.0219 + 13.5100i) q^{4} +(-20.7399 + 13.9592i) q^{5} +(88.2193 + 56.6951i) q^{6} +(-35.9524 + 78.7248i) q^{7} +(43.4924 + 37.6864i) q^{8} +(26.6544 - 185.386i) q^{9} +O(q^{10})\)	\(q+(-1.80372 - 6.14291i) q^{2} +(-12.3789 + 10.7264i) q^{3} +(-21.0219 + 13.5100i) q^{4} +(-20.7399 + 13.9592i) q^{5} +(88.2193 + 56.6951i) q^{6} +(-35.9524 + 78.7248i) q^{7} +(43.4924 + 37.6864i) q^{8} +(26.6544 - 185.386i) q^{9} +(123.159 + 102.225i) q^{10} +(-23.0470 + 78.4908i) q^{11} +(115.315 - 392.728i) q^{12} +(-156.294 + 71.3772i) q^{13} +(548.448 + 78.8549i) q^{14} +(107.006 - 395.262i) q^{15} +(-13.0358 + 28.5444i) q^{16} +(-62.9639 - 40.4644i) q^{17} +(-1186.89 + 170.648i) q^{18} +(-119.015 - 185.191i) q^{19} +(247.404 - 573.643i) q^{20} +(-399.381 - 1360.17i) q^{21} +523.733 q^{22} +(-374.337 + 373.782i) q^{23} -942.625 q^{24} +(235.284 - 579.022i) q^{25} +(720.376 + 831.358i) q^{26} +(941.269 + 1464.64i) q^{27} +(-307.781 - 2140.66i) q^{28} +(667.842 + 429.196i) q^{29} +(-2621.07 + 55.6180i) q^{30} +(-951.947 + 1098.61i) q^{31} +(1110.26 + 159.632i) q^{32} +(-556.625 - 1218.84i) q^{33} +(-135.000 + 459.769i) q^{34} +(-353.283 - 2134.61i) q^{35} +(1944.23 + 4257.27i) q^{36} +(117.726 - 818.806i) q^{37} +(-922.944 + 1065.13i) q^{38} +(1169.13 - 2560.04i) q^{39} +(-1428.10 - 174.493i) q^{40} +(-0.212536 - 1.47822i) q^{41} +(-7635.01 + 4906.72i) q^{42} +(829.162 + 956.904i) q^{43} +(-575.917 - 1961.39i) q^{44} +(2035.02 + 4216.95i) q^{45} +(2971.31 + 1625.32i) q^{46} -1469.07i q^{47} +(-144.809 - 493.174i) q^{48} +(-3332.70 - 3846.14i) q^{49} +(-3981.27 - 400.935i) q^{50} +(1213.46 - 174.469i) q^{51} +(2321.30 - 3612.02i) q^{52} +(534.513 - 1170.42i) q^{53} +(7299.39 - 8423.94i) q^{54} +(-617.674 - 1949.60i) q^{55} +(-4530.51 + 2069.01i) q^{56} +(3459.71 + 1015.86i) q^{57} +(1431.91 - 4876.65i) q^{58} +(2641.02 + 5783.03i) q^{59} +(3090.52 + 9754.82i) q^{60} +(123.541 + 107.049i) q^{61} +(8465.69 + 3866.15i) q^{62} +(13636.2 + 8763.43i) q^{63} +(-950.550 - 6611.22i) q^{64} +(2245.16 - 3662.09i) q^{65} +(-6483.23 + 5617.75i) q^{66} +(-3144.18 + 923.214i) q^{67} +1870.30 q^{68} +(624.557 - 8642.28i) q^{69} +(-12475.5 + 6020.43i) q^{70} +(7007.84 - 2057.69i) q^{71} +(8145.78 - 7058.36i) q^{72} +(-120.871 - 188.078i) q^{73} +(-5242.20 + 753.714i) q^{74} +(3298.25 + 9691.40i) q^{75} +(5003.86 + 2285.19i) q^{76} +(-5350.58 - 4636.30i) q^{77} +(-17834.9 - 2564.27i) q^{78} +(-1477.56 + 674.777i) q^{79} +(-128.095 - 773.975i) q^{80} +(-12806.0 - 3760.19i) q^{81} +(-8.69723 + 3.97189i) q^{82} +(-886.258 + 6164.06i) q^{83} +(26771.5 + 23197.7i) q^{84} +(1870.71 - 39.6957i) q^{85} +(4382.60 - 6819.46i) q^{86} +(-12870.9 + 1850.55i) q^{87} +(-3960.40 + 2545.19i) q^{88} +(-10641.3 + 9220.77i) q^{89} +(22233.7 - 20107.1i) q^{90} -14870.4i q^{91} +(2819.51 - 12914.9i) q^{92} -23810.5i q^{93} +(-9024.38 + 2649.80i) q^{94} +(5053.48 + 2179.49i) q^{95} +(-15456.1 + 9933.05i) q^{96} +(1362.49 + 9476.30i) q^{97} +(-17615.2 + 27409.9i) q^{98} +(13936.8 + 6364.71i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 460 q + 306 q^{4} - 11 q^{5} - 182 q^{6} + 944 q^{9}+O(q^{10}) \) 460 * q + 306 * q^4 - 11 * q^5 - 182 * q^6 + 944 * q^9	\( 460 q + 306 q^{4} - 11 q^{5} - 182 q^{6} + 944 q^{9} - 11 q^{10} - 22 q^{11} - 22 q^{14} - 1474 q^{15} - 2670 q^{16} - 22 q^{19} + 3157 q^{20} - 22 q^{21} + 3896 q^{24} - 1427 q^{25} - 3166 q^{26} - 2808 q^{29} + 1397 q^{30} + 2684 q^{31} - 12848 q^{34} + 2279 q^{35} + 1114 q^{36} + 12866 q^{39} - 11 q^{40} - 2652 q^{41} + 11110 q^{44} - 5394 q^{46} - 27026 q^{49} - 10931 q^{50} - 22 q^{51} - 51290 q^{54} - 10545 q^{55} + 25322 q^{56} + 41460 q^{59} + 49269 q^{60} - 22506 q^{61} + 68582 q^{64} + 27940 q^{65} - 24332 q^{66} + 7608 q^{69} - 15618 q^{70} + 35838 q^{71} - 59158 q^{74} + 30594 q^{75} - 58520 q^{76} - 17930 q^{79} - 63602 q^{80} + 91888 q^{81} + 92906 q^{84} - 33815 q^{85} + 101486 q^{86} - 22 q^{89} - 37598 q^{90} - 46242 q^{94} + 43336 q^{95} - 210180 q^{96} + 44528 q^{99}+O(q^{100}) \) 460 * q + 306 * q^4 - 11 * q^5 - 182 * q^6 + 944 * q^9 - 11 * q^10 - 22 * q^11 - 22 * q^14 - 1474 * q^15 - 2670 * q^16 - 22 * q^19 + 3157 * q^20 - 22 * q^21 + 3896 * q^24 - 1427 * q^25 - 3166 * q^26 - 2808 * q^29 + 1397 * q^30 + 2684 * q^31 - 12848 * q^34 + 2279 * q^35 + 1114 * q^36 + 12866 * q^39 - 11 * q^40 - 2652 * q^41 + 11110 * q^44 - 5394 * q^46 - 27026 * q^49 - 10931 * q^50 - 22 * q^51 - 51290 * q^54 - 10545 * q^55 + 25322 * q^56 + 41460 * q^59 + 49269 * q^60 - 22506 * q^61 + 68582 * q^64 + 27940 * q^65 - 24332 * q^66 + 7608 * q^69 - 15618 * q^70 + 35838 * q^71 - 59158 * q^74 + 30594 * q^75 - 58520 * q^76 - 17930 * q^79 - 63602 * q^80 + 91888 * q^81 + 92906 * q^84 - 33815 * q^85 + 101486 * q^86 - 22 * q^89 - 37598 * q^90 - 46242 * q^94 + 43336 * q^95 - 210180 * q^96 + 44528 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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