LMFDB - Embedded newform 31.5.h.a.11.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,5,Mod(3,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.3"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	31.h (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.20446885560$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	31.11
Dual form			31.5.h.a.17.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20822 - 3.71853i) q^{2} +(11.2749 - 10.1519i) q^{3} +(0.576617 - 0.418937i) q^{4} +(8.94674 + 15.4962i) q^{5} +(-51.3729 - 29.6601i) q^{6} +(4.13118 + 39.3055i) q^{7} +(-52.8652 - 38.4088i) q^{8} +(15.5941 - 148.368i) q^{9} +(46.8134 - 51.9916i) q^{10} +(-74.9869 + 168.423i) q^{11} +(2.24826 - 10.5772i) q^{12} +(-20.6573 - 97.1850i) q^{13} +(141.167 - 62.8518i) q^{14} +(258.190 + 83.8910i) q^{15} +(-75.4274 + 232.142i) q^{16} +(164.130 + 368.642i) q^{17} +(-570.550 + 121.274i) q^{18} +(-105.994 - 22.5298i) q^{19} +(11.6508 + 5.18726i) q^{20} +(445.606 + 401.226i) q^{21} +(716.888 + 75.3480i) q^{22} +(437.034 - 601.526i) q^{23} +(-985.973 + 103.630i) q^{24} +(152.412 - 263.985i) q^{25} +(-336.427 + 194.236i) q^{26} +(-608.058 - 836.920i) q^{27} +(18.8486 + 20.9335i) q^{28} +(-982.903 + 319.364i) q^{29} -1061.45i q^{30} +(314.637 - 908.033i) q^{31} -91.1615 q^{32} +(864.357 + 2660.22i) q^{33} +(1172.50 - 1055.73i) q^{34} +(-572.126 + 415.674i) q^{35} +(-53.1648 - 92.0842i) q^{36} +(349.456 + 201.758i) q^{37} +(44.2872 + 421.365i) q^{38} +(-1219.53 - 886.038i) q^{39} +(122.220 - 1162.84i) q^{40} +(-339.798 + 377.383i) q^{41} +(953.578 - 2141.77i) q^{42} +(105.859 - 498.025i) q^{43} +(27.3200 + 128.531i) q^{44} +(2438.65 - 1085.76i) q^{45} +(-2764.83 - 898.347i) q^{46} +(-1004.87 + 3092.67i) q^{47} +(1506.25 + 3383.10i) q^{48} +(820.673 - 174.439i) q^{49} +(-1165.78 - 247.795i) q^{50} +(5592.98 + 2490.16i) q^{51} +(-52.6257 - 47.3844i) q^{52} +(-4740.98 - 498.297i) q^{53} +(-2377.44 + 3272.27i) q^{54} +(-3280.81 + 344.827i) q^{55} +(1291.28 - 2236.57i) q^{56} +(-1423.80 + 822.029i) q^{57} +(2375.13 + 3269.09i) q^{58} +(-2211.04 - 2455.61i) q^{59} +(184.022 - 59.7923i) q^{60} +1086.50i q^{61} +(-3756.70 - 72.8811i) q^{62} +5896.09 q^{63} +(1316.98 + 4053.25i) q^{64} +(1321.18 - 1189.60i) q^{65} +(8847.76 - 6428.27i) q^{66} +(1163.82 + 2015.80i) q^{67} +(249.078 + 143.805i) q^{68} +(-1179.15 - 11218.9i) q^{69} +(2236.95 + 1625.24i) q^{70} +(461.964 - 4395.29i) q^{71} +(-6523.01 + 7244.54i) q^{72} +(1045.50 - 2348.23i) q^{73} +(328.024 - 1543.23i) q^{74} +(-961.536 - 4523.67i) q^{75} +(-70.5568 + 31.4139i) q^{76} +(-6929.76 - 2251.62i) q^{77} +(-1821.30 + 5605.37i) q^{78} +(-4429.54 - 9948.91i) q^{79} +(-4272.14 + 908.072i) q^{80} +(-3532.24 - 750.801i) q^{81} +(1813.86 + 807.584i) q^{82} +(8730.07 + 7860.59i) q^{83} +(425.032 + 44.6727i) q^{84} +(-4244.13 + 5841.54i) q^{85} +(-1979.82 + 208.088i) q^{86} +(-7839.94 + 13579.2i) q^{87} +(10433.2 - 6023.58i) q^{88} +(4033.32 + 5551.39i) q^{89} +(-6983.86 - 7756.36i) q^{90} +(3734.57 - 1213.44i) q^{91} -529.940i q^{92} +(-5670.81 - 13432.1i) q^{93} +12714.3 q^{94} +(-599.178 - 1844.08i) q^{95} +(-1027.83 + 925.467i) q^{96} +(-11909.1 + 8652.49i) q^{97} +(-1640.21 - 2840.93i) q^{98} +(23819.2 + 13752.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{2} - 16 q^{3} - 138 q^{4} - q^{5} - 9 q^{6} + 288 q^{7} - 221 q^{8} - 182 q^{9} + 102 q^{10} - 49 q^{11} - 159 q^{12} + 527 q^{13} - 740 q^{14} + 1060 q^{15} - 1970 q^{16} + 848 q^{17} + 3 q^{18}+ \cdots + 75228 q^{99}+O(q^{100}) $ 80 * q - 6 * q^2 - 16 * q^3 - 138 * q^4 - q^5 - 9 * q^6 + 288 * q^7 - 221 * q^8 - 182 * q^9 + 102 * q^10 - 49 * q^11 - 159 * q^12 + 527 * q^13 - 740 * q^14 + 1060 * q^15 - 1970 * q^16 + 848 * q^17 + 3 * q^18 + 1534 * q^19 + 1165 * q^20 + 1367 * q^21 + 4579 * q^22 - 1375 * q^23 - 3828 * q^24 - 5997 * q^25 - 2547 * q^26 - 3235 * q^27 - 1564 * q^28 - 1150 * q^29 - 3587 * q^31 + 15718 * q^32 - 5029 * q^33 + 5958 * q^34 + 4959 * q^35 + 13555 * q^36 + 3462 * q^37 + 6118 * q^38 - 8143 * q^39 - 13011 * q^40 - 7290 * q^41 - 24735 * q^42 + 4687 * q^43 + 17051 * q^44 - 6093 * q^45 - 16530 * q^46 - 4302 * q^47 + 40344 * q^48 + 14300 * q^49 + 30081 * q^50 + 1348 * q^51 - 14433 * q^52 + 17996 * q^53 - 42200 * q^54 - 5289 * q^55 - 32470 * q^56 - 35847 * q^57 - 38475 * q^58 + 3552 * q^59 - 26585 * q^60 - 6327 * q^62 + 35814 * q^63 + 231 * q^64 + 18280 * q^65 + 85992 * q^66 + 2185 * q^67 + 56694 * q^68 + 57836 * q^69 + 6338 * q^70 - 3708 * q^71 - 25127 * q^72 + 5344 * q^73 + 5247 * q^74 + 13921 * q^75 - 10354 * q^76 - 37000 * q^77 - 98345 * q^78 + 53300 * q^79 + 65286 * q^80 + 20439 * q^81 - 26142 * q^82 - 59542 * q^83 - 77120 * q^84 + 4525 * q^85 - 100990 * q^86 - 55761 * q^87 - 82191 * q^88 - 26395 * q^89 - 61689 * q^90 - 12450 * q^91 + 9029 * q^93 + 67112 * q^94 - 3972 * q^95 + 210490 * q^96 + 5883 * q^97 + 107722 * q^98 + 75228 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{23}{30}\right)$

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 $

$2$	−1.20822	−	3.71853i	−0.302056	−	0.929632i	−0.980759	−	0.195220i	$-0.937458\pi$
$2$	−1.20822	−	3.71853i	−0.302056	−	0.929632i	0.678704	−	0.734412i	$-0.262542\pi$
$3$	11.2749	−	10.1519i	1.25276	−	1.12799i	0.266322	−	0.963884i	$-0.414191\pi$
$3$	11.2749	−	10.1519i	1.25276	−	1.12799i	0.986442	−	0.164110i	$-0.0524752\pi$
$4$	0.576617	−	0.418937i	0.0360386	−	0.0261835i
$5$	8.94674	+	15.4962i	0.357870	+	0.619848i	0.987605	−	0.156962i	$-0.0501699\pi$
$5$	8.94674	+	15.4962i	0.357870	+	0.619848i	−0.629735	+	0.776810i	$0.716837\pi$
$6$	−51.3729	−	29.6601i	−1.42702	−	0.823893i
$7$	4.13118	+	39.3055i	0.0843098	+	0.802154i	0.952216	+	0.305426i	$0.0987988\pi$
$7$	4.13118	+	39.3055i	0.0843098	+	0.802154i	−0.867906	+	0.496728i	$0.834535\pi$
$8$	−52.8652	−	38.4088i	−0.826019	−	0.600138i
$9$	15.5941	−	148.368i	0.192519	−	1.83170i
$10$	46.8134	−	51.9916i	0.468134	−	0.519916i
$11$	−74.9869	+	168.423i	−0.619727	+	1.39193i	0.281912	+	0.959440i	$0.409031\pi$
$11$	−74.9869	+	168.423i	−0.619727	+	1.39193i	−0.901639	+	0.432489i	$0.857635\pi$
$12$	2.24826	−	10.5772i	0.0156129	−	0.0734531i
$13$	−20.6573	−	97.1850i	−0.122233	−	0.575059i	−0.996049	−	0.0888036i	$-0.971696\pi$
$13$	−20.6573	−	97.1850i	−0.122233	−	0.575059i	0.873816	−	0.486256i	$-0.161638\pi$
$14$	141.167	−	62.8518i	0.720242	−	0.320672i
$15$	258.190	+	83.8910i	1.14751	+	0.372849i
$16$	−75.4274	+	232.142i	−0.294638	+	0.906803i
$17$	164.130	+	368.642i	0.567924	+	1.27558i	0.938019	+	0.346585i	$0.112659\pi$
$17$	164.130	+	368.642i	0.567924	+	1.27558i	−0.370094	+	0.928994i	$0.620675\pi$
$18$	−570.550	+	121.274i	−1.76096	+	0.374303i
$19$	−105.994	−	22.5298i	−0.293614	−	0.0624095i	0.0587499	−	0.998273i	$-0.481289\pi$
$19$	−105.994	−	22.5298i	−0.293614	−	0.0624095i	−0.352363	+	0.935863i	$0.614622\pi$
$20$	11.6508	+	5.18726i	0.0291269	+	0.0129681i
$21$	445.606	+	401.226i	1.01045	+	0.909809i
$22$	716.888	+	75.3480i	1.48117	+	0.155678i
$23$	437.034	−	601.526i	0.826151	−	1.13710i	−0.162476	−	0.986713i	$-0.551948\pi$
$23$	437.034	−	601.526i	0.826151	−	1.13710i	0.988627	−	0.150387i	$-0.0480521\pi$
$24$	−985.973	+	103.630i	−1.71176	+	0.179913i
$25$	152.412	−	263.985i	0.243859	−	0.422376i
$26$	−336.427	+	194.236i	−0.497673	+	0.287331i
$27$	−608.058	−	836.920i	−0.834099	−	1.14804i
$28$	18.8486	+	20.9335i	0.0240416	+	0.0267009i
$29$	−982.903	+	319.364i	−1.16873	+	0.379744i	−0.828169	−	0.560478i	$-0.810617\pi$
$29$	−982.903	+	319.364i	−1.16873	+	0.379744i	−0.340562	+	0.940222i	$0.610617\pi$
$30$		−	1061.45i		−	1.17938i
$31$	314.637	−	908.033i	0.327406	−	0.944884i
$31$	314.637	−	908.033i	0.327406	−	0.944884i
$32$	−91.1615			−0.0890249
$33$	864.357	+	2660.22i	0.793716	+	2.44281i
$34$	1172.50	−	1055.73i	1.01427	−	0.913257i
$35$	−572.126	+	415.674i	−0.467042	+	0.339326i
$36$	−53.1648	−	92.0842i	−0.0410223	−	0.0710526i
$37$	349.456	+	201.758i	0.255263	+	0.147376i	0.622172	−	0.782881i	$-0.286250\pi$
$37$	349.456	+	201.758i	0.255263	+	0.147376i	−0.366909	+	0.930257i	$0.619584\pi$
$38$	44.2872	+	421.365i	0.0306698	+	0.291804i
$39$	−1219.53	−	886.038i	−0.801792	−	0.582536i
$40$	122.220	−	1162.84i	0.0763874	−	0.726778i
$41$	−339.798	+	377.383i	−0.202140	+	0.224499i	−0.835688	−	0.549204i	$-0.814931\pi$
$41$	−339.798	+	377.383i	−0.202140	+	0.224499i	0.633548	+	0.773703i	$0.281598\pi$
$42$	953.578	−	2141.77i	0.540577	−	1.21416i
$43$	105.859	−	498.025i	0.0572518	−	0.269348i	−0.940206	−	0.340606i	$-0.889368\pi$
$43$	105.859	−	498.025i	0.0572518	−	0.269348i	0.997458	+	0.0712574i	$0.0227012\pi$
$44$	27.3200	+	128.531i	0.0141116	+	0.0663898i
$45$	2438.65	−	1085.76i	1.20427	−	0.536177i
$46$	−2764.83	−	898.347i	−1.30663	−	0.424549i
$47$	−1004.87	+	3092.67i	−0.454898	+	1.40003i	0.416356	+	0.909202i	$0.363307\pi$
$47$	−1004.87	+	3092.67i	−0.454898	+	1.40003i	−0.871254	+	0.490832i	$0.836693\pi$
$48$	1506.25	+	3383.10i	0.653756	+	1.46836i
$49$	820.673	−	174.439i	0.341805	−	0.0726528i
$50$	−1165.78	−	247.795i	−0.466313	−	0.0991179i
$51$	5592.98	+	2490.16i	2.15032	+	0.957385i
$52$	−52.6257	−	47.3844i	−0.0194622	−	0.0175238i
$53$	−4740.98	−	498.297i	−1.68778	−	0.177393i	−0.788581	−	0.614931i	$-0.789184\pi$
$53$	−4740.98	−	498.297i	−1.68778	−	0.177393i	−0.899200	+	0.437538i	$0.855851\pi$
$54$	−2377.44	+	3272.27i	−0.815310	+	1.12218i
$55$	−3280.81	+	344.827i	−1.08457	+	0.113993i
$56$	1291.28	−	2236.57i	0.411762	−	0.713192i
$57$	−1423.80	+	822.029i	−0.438226	+	0.253010i
$58$	2375.13	+	3269.09i	0.706044	+	0.971786i
$59$	−2211.04	−	2455.61i	−0.635175	−	0.705434i	0.336519	−	0.941677i	$-0.390750\pi$
$59$	−2211.04	−	2455.61i	−0.635175	−	0.705434i	−0.971694	+	0.236243i	$0.924084\pi$
$60$	184.022	−	59.7923i	0.0511172	−	0.0166090i
$61$			1086.50i			0.291992i	0.989285	+	0.145996i	$0.0466386\pi$
$61$			1086.50i			0.291992i	−0.989285	+	0.145996i	$0.953361\pi$
$62$	−3756.70	−	72.8811i	−0.977289	−	0.0189597i
$63$	5896.09			1.48554
$64$	1316.98	+	4053.25i	0.321529	+	0.989564i
$65$	1321.18	−	1189.60i	0.312706	−	0.281562i
$66$	8847.76	−	6428.27i	2.03117	−	1.47573i
$67$	1163.82	+	2015.80i	0.259261	+	0.449053i	0.966044	−	0.258377i	$-0.0831878\pi$
$67$	1163.82	+	2015.80i	0.259261	+	0.449053i	−0.706783	+	0.707430i	$0.749854\pi$
$68$	249.078	+	143.805i	0.0538664	+	0.0310998i
$69$	−1179.15	−	11218.9i	−0.247669	−	2.35641i
$70$	2236.95	+	1625.24i	0.456521	+	0.331682i
$71$	461.964	−	4395.29i	0.0916413	−	0.871909i	−0.848057	−	0.529905i	$-0.822228\pi$
$71$	461.964	−	4395.29i	0.0916413	−	0.871909i	0.939699	−	0.342004i	$-0.111106\pi$
$72$	−6523.01	+	7244.54i	−1.25830	+	1.39748i
$73$	1045.50	−	2348.23i	0.196191	−	0.440652i	−0.788483	−	0.615056i	$-0.789133\pi$
$73$	1045.50	−	2348.23i	0.196191	−	0.440652i	0.984674	+	0.174404i	$0.0557999\pi$
$74$	328.024	−	1543.23i	0.0599020	−	0.281817i
$75$	−961.536	−	4523.67i	−0.170940	−	0.804208i
$76$	−70.5568	+	31.4139i	−0.0122155	+	0.00543869i
$77$	−6929.76	−	2251.62i	−1.16879	−	0.379763i
$78$	−1821.30	+	5605.37i	−0.299358	+	0.921330i
$79$	−4429.54	−	9948.91i	−0.709749	−	1.59412i	−0.801259	−	0.598317i	$-0.795836\pi$
$79$	−4429.54	−	9948.91i	−0.709749	−	1.59412i	0.0915107	−	0.995804i	$-0.470830\pi$
$80$	−4272.14	+	908.072i	−0.667523	+	0.141886i
$81$	−3532.24	−	750.801i	−0.538369	−	0.114434i
$82$	1813.86	+	807.584i	0.269759	+	0.120105i
$83$	8730.07	+	7860.59i	1.26725	+	1.14103i	0.983260	+	0.182207i	$0.0583240\pi$
$83$	8730.07	+	7860.59i	1.26725	+	1.14103i	0.283987	+	0.958828i	$0.408343\pi$
$84$	425.032	+	44.6727i	0.0602370	+	0.00633116i
$85$	−4244.13	+	5841.54i	−0.587423	+	0.808518i
$86$	−1979.82	+	208.088i	−0.267688	+	0.0281352i
$87$	−7839.94	+	13579.2i	−1.03580	+	1.79405i
$88$	10433.2	−	6023.58i	1.34726	−	0.777839i
$89$	4033.32	+	5551.39i	0.509194	+	0.700845i	0.983783	−	0.179362i	$-0.0574035\pi$
$89$	4033.32	+	5551.39i	0.509194	+	0.700845i	−0.474589	+	0.880207i	$0.657403\pi$
$90$	−6983.86	−	7756.36i	−0.862205	−	0.957575i
$91$	3734.57	−	1213.44i	0.450981	−	0.146533i
$92$		−	529.940i		−	0.0626110i
$93$	−5670.81	−	13432.1i	−0.655660	−	1.55303i
$94$	12714.3			1.43892
$95$	−599.178	−	1844.08i	−0.0663909	−	0.204330i
$96$	−1027.83	+	925.467i	−0.111527	+	0.100420i
$97$	−11909.1	+	8652.49i	−1.26572	+	0.919597i	−0.999023	−	0.0441843i	$-0.985931\pi$
$97$	−11909.1	+	8652.49i	−1.26572	+	0.919597i	−0.266693	+	0.963781i	$0.585931\pi$
$98$	−1640.21	−	2840.93i	−0.170784	−	0.295807i
$99$	23819.2	+	13752.0i	2.43029	+	1.40313i
$100$	−22.7098	−	216.069i	−0.00227098	−	0.0216069i
$101$	1696.78	+	1232.78i	0.166334	+	0.120849i	0.667838	−	0.744306i	$-0.267220\pi$
$101$	1696.78	+	1232.78i	0.166334	+	0.120849i	−0.501504	+	0.865155i	$0.667220\pi$
$102$	2502.15	−	23806.3i	0.240499	−	2.28819i
$103$	673.940	−	748.487i	0.0635254	−	0.0705520i	−0.710544	−	0.703652i	$-0.751551\pi$
$103$	673.940	−	748.487i	0.0635254	−	0.0705520i	0.774070	+	0.633100i	$0.218218\pi$
$104$	−2640.71	+	5931.13i	−0.244149	+	0.548367i
$105$	−2230.75	+	10494.9i	−0.202336	+	0.951916i
$106$	3875.23	+	18231.5i	0.344894	+	1.62260i
$107$	10912.6	−	4858.61i	0.953150	−	0.424370i	0.129570	−	0.991570i	$-0.458640\pi$
$107$	10912.6	−	4858.61i	0.953150	−	0.424370i	0.823580	+	0.567201i	$0.191974\pi$
$108$	−701.233	−	227.845i	−0.0601195	−	0.0195340i
$109$	−2018.19	+	6211.35i	−0.169867	+	0.522797i	−0.999362	−	0.0357175i	$-0.988628\pi$
$109$	−2018.19	+	6211.35i	−0.169867	+	0.522797i	0.829495	+	0.558514i	$0.188628\pi$
$110$	5246.21	+	11783.2i	0.433571	+	0.973816i
$111$	5988.31	−	1272.85i	0.486024	−	0.103308i
$112$	−9436.06	−	2005.70i	−0.752237	−	0.159893i
$113$	−14445.2	−	6431.42i	−1.13127	−	0.503675i	−0.246242	−	0.969208i	$-0.579196\pi$
$113$	−14445.2	−	6431.42i	−1.13127	−	0.503675i	−0.885030	+	0.465534i	$0.845862\pi$
$114$	4777.00	+	4301.23i	0.367575	+	0.330966i
$115$	13231.4	+	1390.68i	1.00048	+	0.105155i
$116$	−432.965	+	595.925i	−0.0321763	+	0.0442869i
$117$	−14741.2	+	1549.37i	−1.07687	+	0.113183i
$118$	−6459.84	+	11188.8i	−0.463935	+	0.803560i
$119$	−13811.6	+	7974.15i	−0.975329	+	0.563107i
$120$	−10427.1	−	14351.7i	−0.724105	−	0.996646i
$121$	−12946.7	−	14378.7i	−0.884275	−	0.982087i
$122$	4040.19	−	1312.74i	0.271445	−	0.0881978i
$123$			7704.56i			0.509258i
$124$	−198.983	−	655.400i	−0.0129412	−	0.0426249i
$125$	16637.8			1.06482
$126$	−7123.80	−	21924.8i	−0.448715	−	1.38100i
$127$	4170.80	−	3755.40i	0.258590	−	0.232835i	−0.529630	−	0.848229i	$-0.677669\pi$
$127$	4170.80	−	3755.40i	0.258590	−	0.232835i	0.788220	+	0.615393i	$0.211003\pi$
$128$	12300.9	−	8937.14i	0.750788	−	0.545480i
$129$	−3862.38	−	6689.84i	−0.232100	−	0.402010i
$130$	−6019.84	−	3475.56i	−0.356204	−	0.205654i
$131$	64.6504	+	615.107i	0.00376728	+	0.0358433i	0.996244	−	0.0865898i	$-0.0275970\pi$
$131$	64.6504	+	615.107i	0.00376728	+	0.0358433i	−0.992477	+	0.122433i	$0.960930\pi$
$132$	1612.87	+	1171.82i	0.0925657	+	0.0672529i
$133$	447.665	−	4259.25i	0.0253075	−	0.240785i
$134$	6089.65	−	6763.24i	0.339143	−	0.376656i
$135$	7528.95	−	16910.3i	0.413111	−	0.927863i
$136$	5482.35	−	25792.4i	0.296407	−	1.39449i
$137$	−4726.16	−	22234.8i	−0.251806	−	1.18466i	−0.904312	−	0.426872i	$-0.859615\pi$
$137$	−4726.16	−	22234.8i	−0.251806	−	1.18466i	0.652505	−	0.757784i	$-0.273718\pi$
$138$	−40293.0	+	17939.6i	−2.11579	+	0.942009i
$139$	7858.19	+	2553.28i	0.406718	+	0.132151i	0.505229	−	0.862985i	$-0.331408\pi$
$139$	7858.19	+	2553.28i	0.406718	+	0.132151i	−0.0985113	+	0.995136i	$0.531408\pi$
$140$	−155.757	+	479.369i	−0.00794676	+	0.0244576i
$141$	20066.9	+	45070.9i	1.00935	+	2.26703i
$142$	−16902.2	+	3592.67i	−0.838235	+	0.178172i
$143$	17917.3	+	3808.43i	0.876193	+	0.186241i
$144$	33266.1	+	14811.0i	1.60427	+	0.714266i
$145$	−13742.7	−	12374.0i	−0.653637	−	0.588537i
$146$	−9995.18	−	1050.54i	−0.468905	−	0.0492839i
$147$	7482.09	−	10298.2i	0.346249	−	0.476570i
$148$	286.026	−	30.0625i	0.0130582	−	0.00137247i
$149$	858.913	−	1487.68i	0.0386880	−	0.0670096i	−0.846033	−	0.533130i	$-0.821015\pi$
$149$	858.913	−	1487.68i	0.0386880	−	0.0670096i	0.884721	+	0.466121i	$0.154349\pi$
$150$	−15659.7	+	9041.11i	−0.695985	+	0.401827i
$151$	−15486.5	−	21315.3i	−0.679201	−	0.934840i	0.320723	−	0.947173i	$-0.396074\pi$
$151$	−15486.5	−	21315.3i	−0.679201	−	0.934840i	−0.999924	+	0.0123334i	$0.996074\pi$
$152$	4738.08	+	5262.17i	0.205076	+	0.227760i
$153$	57254.0	−	18603.0i	2.44581	−	0.794693i
$154$			28489.0i			1.20126i
$155$	16886.0	−	3248.25i	0.702853	−	0.135203i
$156$	−1074.39			−0.0441483
$157$	1616.58	+	4975.32i	0.0655840	+	0.201847i	0.978479	−	0.206349i	$-0.0661582\pi$
$157$	1616.58	+	4975.32i	0.0655840	+	0.201847i	−0.912895	+	0.408196i	$0.866158\pi$
$158$	−31643.4	+	28491.9i	−1.26756	+	1.14132i
$159$	−58512.6	+	42511.9i	−2.31449	+	1.68158i
$160$	−815.598	−	1412.66i	−0.0318593	−	0.0551819i
$161$	25448.8	+	14692.9i	0.981782	+	0.566832i
$162$	1475.86	+	14041.9i	0.0562361	+	0.535051i
$163$	−5106.41	−	3710.02i	−0.192194	−	0.139637i	0.487527	−	0.873108i	$-0.337899\pi$
$163$	−5106.41	−	3710.02i	−0.192194	−	0.139637i	−0.679721	+	0.733471i	$0.737899\pi$
$164$	−37.8332	+	359.959i	−0.00140665	+	0.0133834i
$165$	−33490.1	+	37194.5i	−1.23012	+	1.36619i
$166$	18682.0	−	41960.4i	0.677963	−	1.52273i
$167$	2596.54	−	12215.8i	0.0931026	−	0.438014i	−0.906763	−	0.421640i	$-0.861455\pi$
$167$	2596.54	−	12215.8i	0.0931026	−	0.438014i	0.999866	−	0.0163735i	$-0.00521207\pi$
$168$	−8146.47	−	38326.1i	−0.288636	−	1.35793i
$169$	17073.6	−	7601.64i	0.597793	−	0.266155i
$170$	26849.8	+	8724.03i	0.929059	+	0.301869i
$171$	−4995.58	+	15374.8i	−0.170842	+	0.525797i
$172$	−147.601	−	331.518i	−0.00498922	−	0.0112060i
$173$	−20002.2	+	4251.61i	−0.668323	+	0.142057i	−0.529564	−	0.848270i	$-0.677645\pi$
$173$	−20002.2	+	4251.61i	−0.668323	+	0.142057i	−0.138759	+	0.990326i	$0.544311\pi$
$174$	59966.9	+	12746.4i	1.98068	+	0.421006i
$175$	11005.7	+	4900.06i	0.359370	+	0.160002i
$176$	−33442.0	−	30111.3i	−1.07961	−	0.972086i
$177$	−49858.5	−	5240.34i	−1.59145	−	0.167268i
$178$	15769.9	−	21705.4i	0.497723	−	0.685057i
$179$	57665.8	−	6060.92i	1.79975	−	0.189161i	0.855370	−	0.518017i	$-0.173330\pi$
$179$	57665.8	−	6060.92i	1.79975	−	0.189161i	0.944380	+	0.328856i	$0.106663\pi$
$180$	951.304	−	1647.71i	0.0293612	−	0.0508551i
$181$	5496.83	−	3173.60i	0.167786	−	0.0968712i	−0.413756	−	0.910388i	$-0.635783\pi$
$181$	5496.83	−	3173.60i	0.167786	−	0.0968712i	0.581541	+	0.813517i	$0.302450\pi$
$182$	−9024.40	−	12421.0i	−0.272443	−	0.374985i
$183$	11030.1	+	12250.2i	0.329365	+	0.365797i
$184$	−46207.8	+	15013.8i	−1.36483	+	0.443461i
$185$			7220.31i			0.210966i
$186$	−43096.2	+	37316.1i	−1.24570	+	1.07862i
$187$	−74395.6			−2.12747
$188$	716.209	+	2204.26i	0.0202640	+	0.0623660i
$189$	30383.6	−	27357.5i	0.850581	−	0.765867i
$190$	−6133.33	+	4456.12i	−0.169898	+	0.123438i
$191$	−1539.19	−	2665.96i	−0.0421916	−	0.0730780i	0.844158	−	0.536094i	$-0.180101\pi$
$191$	−1539.19	−	2665.96i	−0.0421916	−	0.0730780i	−0.886350	+	0.463016i	$0.846767\pi$
$192$	55997.2	+	32330.0i	1.51902	+	0.877008i
$193$	5716.61	+	54389.9i	0.153470	+	1.46017i	0.752049	+	0.659108i	$0.229066\pi$
$193$	5716.61	+	54389.9i	0.153470	+	1.46017i	−0.598578	+	0.801064i	$0.704267\pi$
$194$	46563.4	+	33830.3i	1.23720	+	0.898882i
$195$	2819.44	−	26825.2i	0.0741470	−	0.705462i
$196$	400.135	−	444.395i	0.0104158	−	0.0115680i
$197$	−10126.3	+	22743.9i	−0.260925	+	0.586048i	−0.995738	−	0.0922217i	$-0.970603\pi$
$197$	−10126.3	+	22743.9i	−0.260925	+	0.586048i	0.734813	+	0.678270i	$0.237270\pi$
$198$	22358.4	−	105188.i	0.570309	−	2.68310i
$199$	130.105	+	612.097i	0.00328541	+	0.0154566i	0.979760	−	0.200177i	$-0.0641517\pi$
$199$	130.105	+	612.097i	0.00328541	+	0.0154566i	−0.976474	+	0.215634i	$0.930818\pi$
$200$	−18196.6	+	8101.66i	−0.454916	+	0.202542i
$201$	33586.2	+	10912.8i	0.831321	+	0.270113i
$202$	2534.05	−	7798.99i	0.0621029	−	0.191133i
$203$	−16613.3	−	37314.2i	−0.403148	−	0.905486i
$204$	4268.23	−	907.240i	0.102562	−	0.0218003i
$205$	−8888.09	−	1889.22i	−0.211495	−	0.0449547i
$206$	−3597.54	−	1601.73i	−0.0847757	−	0.0377446i
$207$	−82431.8	−	74222.0i	−1.92377	−	1.73217i
$208$	24118.8	+	2534.99i	0.557480	+	0.0585935i
$209$	11742.8	−	16162.5i	0.268830	−	0.370012i
$210$	41720.7	−	4385.03i	0.946048	−	0.0994337i
$211$	−13838.5	+	23968.9i	−0.310830	+	0.538373i	−0.978542	−	0.206046i	$-0.933940\pi$
$211$	−13838.5	+	23968.9i	−0.310830	+	0.538373i	0.667712	+	0.744419i	$0.267274\pi$
$212$	−2942.48	+	1698.84i	−0.0654700	+	0.0377991i
$213$	−39412.2	−	54246.2i	−0.868703	−	1.19567i
$214$	−31251.7	−	34708.6i	−0.682412	−	0.757895i
$215$	8664.59	−	2815.30i	0.187444	−	0.0609042i
$216$			67598.8i			1.44888i
$217$	36990.6	+	8615.74i	0.785546	+	0.182967i
$218$	25535.5			0.537318
$219$	−12051.3	−	37089.9i	−0.251272	−	0.773335i
$220$	−1747.31	+	1573.29i	−0.0361015	+	0.0325059i
$221$	32436.0	−	23566.2i	0.664115	−	0.482508i
$222$	−11968.4	−	20729.8i	−0.242845	−	0.420619i
$223$	54424.8	+	31422.2i	1.09443	+	0.631868i	0.934752	−	0.355302i	$-0.115622\pi$
$223$	54424.8	+	31422.2i	1.09443	+	0.631868i	0.159676	+	0.987170i	$0.448955\pi$
$224$	−376.605	−	3583.15i	−0.00750567	−	0.0714117i
$225$	−36790.1	−	26729.6i	−0.726718	−	0.527991i
$226$	−6462.39	+	61485.5i	−0.126525	+	1.20380i
$227$	18909.2	−	21000.8i	0.366962	−	0.407553i	−0.531179	−	0.847259i	$-0.678251\pi$
$227$	18909.2	−	21000.8i	0.366962	−	0.407553i	0.898141	+	0.439707i	$0.144918\pi$
$228$	−476.607	+	1070.48i	−0.00916834	+	0.0205924i
$229$	6177.58	−	29063.2i	0.117801	−	0.554208i	−0.879175	−	0.476498i	$-0.841906\pi$
$229$	6177.58	−	29063.2i	0.117801	−	0.554208i	0.996976	−	0.0777101i	$-0.0247608\pi$
$230$	−10815.2	−	50881.6i	−0.204446	−	0.961845i
$231$	−100990.	+	44963.9i	−1.89259	+	0.842635i
$232$	64227.8	+	20868.9i	1.19329	+	0.387724i
$233$	−22600.6	+	69557.5i	−0.416302	+	1.28125i	0.494779	+	0.869019i	$0.335249\pi$
$233$	−22600.6	+	69557.5i	−0.416302	+	1.28125i	−0.911081	+	0.412227i	$0.864751\pi$
$234$	23572.1	+	52943.8i	0.430493	+	0.966904i
$235$	−56915.0	+	12097.7i	−1.03060	+	0.219061i
$236$	−2303.67	−	489.661i	−0.0413615	−	0.00879167i
$237$	−150943.	−	67204.3i	−2.68731	−	1.19647i
$238$	46339.7	+	41724.4i	0.818086	+	0.736608i
$239$	47901.8	+	5034.68i	0.838603	+	0.0881407i	0.514085	−	0.857739i	$-0.328131\pi$
$239$	47901.8	+	5034.68i	0.838603	+	0.0881407i	0.324517	+	0.945880i	$0.394798\pi$
$240$	−38949.2	+	53609.0i	−0.676202	+	0.930712i
$241$	−10639.3	+	1118.24i	−0.183181	+	0.0192531i	−0.195675	−	0.980669i	$-0.562690\pi$
$241$	−10639.3	+	1118.24i	−0.183181	+	0.0192531i	0.0124937	+	0.999922i	$0.496023\pi$
$242$	−37825.3	+	65515.3i	−0.645879	+	1.11870i
$243$	25119.8	−	14502.9i	0.425406	−	0.245608i
$244$	455.175	+	626.495i	0.00764538	+	0.0105230i
$245$	10045.5	+	11156.7i	0.167355	+	0.185867i
$246$	28649.6	−	9308.83i	0.473422	−	0.153824i
$247$			10766.5i			0.176474i
$248$	−51509.9	+	35918.5i	−0.837504	+	0.584003i
$249$	178231.			2.87464
$250$	−20102.1	−	61868.1i	−0.321634	−	0.989889i
$251$	50055.3	−	45070.0i	0.794516	−	0.715385i	−0.168243	−	0.985745i	$-0.553809\pi$
$251$	50055.3	−	45070.0i	0.794516	−	0.715385i	0.962759	+	0.270360i	$0.0871428\pi$
$252$	3399.79	−	2470.09i	0.0535366	−	0.0388966i
$253$	68539.2	+	118713.i	1.07077	+	1.85464i
$254$	−19003.8	−	10971.9i	−0.294560	−	0.170064i
$255$	11451.0	+	108949.i	0.176101	+	1.67549i
$256$	7071.20	+	5137.53i	0.107898	+	0.0783924i
$257$	9262.32	−	88125.1i	0.140234	−	1.33424i	−0.667464	−	0.744642i	$-0.732620\pi$
$257$	9262.32	−	88125.1i	0.140234	−	1.33424i	0.807698	−	0.589596i	$-0.200713\pi$
$258$	−20209.8	+	22445.2i	−0.303614	+	0.337197i
$259$	−6486.55	+	14569.0i	−0.0966973	+	0.217186i
$260$	263.450	−	1239.44i	0.00389719	−	0.0183348i
$261$	32055.9	+	150811.i	0.470573	+	2.21387i
$262$	2209.18	−	983.591i	0.0321832	−	0.0143289i
$263$	14981.0	+	4867.62i	0.216585	+	0.0703729i	0.415300	−	0.909685i	$-0.363677\pi$
$263$	14981.0	+	4867.62i	0.216585	+	0.0703729i	−0.198714	+	0.980057i	$0.563677\pi$
$264$	56481.4	−	173832.i	0.810397	−	2.49415i
$265$	−34694.6	−	77925.3i	−0.494049	−	1.10965i
$266$	−16379.0	+	3481.47i	−0.231486	+	0.0492038i
$267$	101833.	+	21645.2i	1.42845	+	0.303626i
$268$	1515.57	+	674.776i	0.0211012	+	0.00939485i
$269$	−39146.7	−	35247.8i	−0.540991	−	0.487111i	0.352735	−	0.935723i	$-0.385252\pi$
$269$	−39146.7	−	35247.8i	−0.540991	−	0.487111i	−0.893726	+	0.448613i	$0.851918\pi$
$270$	−71978.1	−	7565.21i	−0.987354	−	0.103775i
$271$	60495.5	−	83265.0i	0.823730	−	1.13377i	−0.165328	−	0.986239i	$-0.552868\pi$
$271$	60495.5	−	83265.0i	0.823730	−	1.13377i	0.989058	−	0.147528i	$-0.0471317\pi$
$272$	−97957.2	+	10295.7i	−1.32403	+	0.139161i
$273$	29788.1	−	51594.5i	0.399685	−	0.692274i
$274$	−76970.6	+	44439.0i	−1.02524	+	0.591920i
$275$	33032.3	+	45465.1i	0.436791	+	0.601192i
$276$	−5379.92	−	5975.00i	−0.0706248	−	0.0784368i
$277$	15326.6	−	4979.92i	0.199750	−	0.0649027i	−0.207433	−	0.978249i	$-0.566511\pi$
$277$	15326.6	−	4979.92i	0.199750	−	0.0649027i	0.407183	+	0.913346i	$0.366511\pi$
$278$		−	32305.8i		−	0.418015i
$279$	−129816.	−	60841.9i	−1.66771	−	0.781618i
$280$	46211.1			0.589428
$281$	−1708.53	−	5258.33i	−0.0216377	−	0.0665940i	0.939655	−	0.342125i	$-0.111146\pi$
$281$	−1708.53	−	5258.33i	−0.0216377	−	0.0665940i	−0.961292	+	0.275531i	$0.911146\pi$
$282$	143352.	−	129075.i	1.80263	−	1.62309i
$283$	−53880.6	+	39146.6i	−0.672759	+	0.488788i	−0.870948	−	0.491376i	$-0.836494\pi$
$283$	−53880.6	+	39146.6i	−0.672759	+	0.488788i	0.198188	+	0.980164i	$0.436494\pi$
$284$	−1574.97	−	2727.93i	−0.0195270	−	0.0338218i
$285$	−25476.7	−	14709.0i	−0.313656	−	0.181089i
$286$	−7486.29	−	71227.3i	−0.0915240	−	0.870792i
$287$	−16237.0	−	11796.9i	−0.197125	−	0.143220i
$288$	−1421.58	+	13525.4i	−0.0171390	+	0.163067i
$289$	−53072.0	+	58942.4i	−0.635433	+	0.705720i
$290$	−29408.8	+	66053.2i	−0.349688	+	0.785413i
$291$	−46434.4	+	218457.i	−0.548345	+	2.57976i
$292$	−380.908	−	1792.03i	−0.00446739	−	0.0210174i
$293$	−90741.5	+	40400.7i	−1.05699	+	0.470602i	−0.860260	−	0.509856i	$-0.829699\pi$
$293$	−90741.5	+	40400.7i	−1.05699	+	0.470602i	−0.196729	+	0.980458i	$0.563032\pi$
$294$	−47334.2	−	15379.8i	−0.547622	−	0.177933i
$295$	18271.1	−	56232.5i	0.209952	−	0.646165i
$296$	−10724.7	−	24088.2i	−0.122406	−	0.274929i
$297$	186553.	−	39653.2i	2.11490	−	0.449536i
$298$	−6569.74	−	1396.44i	−0.0739803	−	0.0157250i
$299$	−67487.3	−	30047.3i	−0.754883	−	0.336095i
$300$	−2449.57	−	2205.60i	−0.0272174	−	0.0245067i
$301$	20012.5	+	2103.40i	0.220886	+	0.0232160i
$302$	−60550.4	+	83340.4i	−0.663900	+	0.913781i
$303$	31646.1	−	3326.14i	0.344695	−	0.0362289i
$304$	13225.0	−	22906.4i	0.143103	−	0.247862i
$305$	−16836.6	+	9720.64i	−0.180991	+	0.104495i
$306$	−138351.	−	190424.i	−1.47754	−	2.03367i
$307$	−11785.4	−	13089.0i	−0.125045	−	0.138877i	0.677371	−	0.735642i	$-0.263119\pi$
$307$	−11785.4	−	13089.0i	−0.125045	−	0.138877i	−0.802416	+	0.596765i	$0.796453\pi$
$308$	−4939.10	+	1604.81i	−0.0520651	+	0.0169170i
$309$		−	15280.9i		−	0.160041i
$310$	−32480.8	−	58866.6i	−0.337990	−	0.612556i
$311$	6209.19			0.0641969			0.0320985	−	0.999485i	$-0.489781\pi$
$311$	6209.19			0.0641969			0.0320985	+	0.999485i	$0.489781\pi$
$312$	30438.9	+	93681.2i	0.312694	+	0.962372i
$313$	19735.2	−	17769.6i	0.201443	−	0.181380i	−0.562235	−	0.826978i	$-0.690058\pi$
$313$	19735.2	−	17769.6i	0.201443	−	0.181380i	0.763678	+	0.645598i	$0.223392\pi$
$314$	16547.7	−	12022.6i	0.167833	−	0.121938i
$315$	52750.8	+	91367.1i	0.531628	+	0.920807i
$316$	−6722.11	−	3881.01i	−0.0673181	−	0.0388661i
$317$	−5461.57	−	51963.4i	−0.0543499	−	0.517105i	−0.987500	−	0.157618i	$-0.949618\pi$
$317$	−5461.57	−	51963.4i	−0.0543499	−	0.517105i	0.933150	−	0.359487i	$-0.117048\pi$
$318$	228778.	+	166217.i	2.26235	+	1.64369i
$319$	19916.4	−	189492.i	0.195718	−	1.86213i
$320$	−51027.4	+	56671.6i	−0.498314	+	0.553434i
$321$	73714.0	−	165564.i	0.715386	−	1.60678i
$322$	23888.0	−	112384.i	0.230392	−	1.08391i
$323$	−9091.44	−	42771.9i	−0.0871421	−	0.409971i
$324$	−2351.29	+	1046.86i	−0.0223983	+	0.00997238i
$325$	−28803.8	−	9358.92i	−0.272699	−	0.0886052i
$326$	−7626.14	+	23470.9i	−0.0717579	+	0.220848i
$327$	40302.4	+	90520.7i	0.376908	+	0.846550i
$328$	32458.3	−	6899.23i	0.301702	−	0.0641288i
$329$	−125711.	−	26720.6i	−1.16139	−	0.246862i
$330$	178772.	+	79594.6i	1.64162	+	0.730896i
$331$	85161.5	+	76679.7i	0.777297	+	0.699882i	0.958979	−	0.283476i	$-0.0914875\pi$
$331$	85161.5	+	76679.7i	0.777297	+	0.699882i	−0.181682	+	0.983357i	$0.558154\pi$
$332$	8326.99	+	875.202i	0.0755461	+	0.00794022i
$333$	35383.8	−	48701.7i	0.319092	−	0.439193i
$334$	−48561.9	+	5104.06i	−0.435314	+	0.0457533i
$335$	−20824.8	+	36069.6i	−0.185563	+	0.321405i
$336$	−126752.	+	73180.4i	−1.12273	+	0.648211i
$337$	123793.	+	170386.i	1.09002	+	1.50029i	0.847987	+	0.530017i	$0.177815\pi$
$337$	123793.	+	170386.i	1.09002	+	1.50029i	0.242034	+	0.970268i	$0.422185\pi$
$338$	−48895.6	−	54304.1i	−0.427993	−	0.475334i
$339$	−228159.	+	74133.5i	−1.98536	+	0.645082i
$340$			5146.35i			0.0445186i
$341$	129340.	+	121083.i	1.11231	+	1.04130i
$342$	63207.5			0.540401
$343$	39570.2	+	121784.i	0.336341	+	1.03515i
$344$	−24724.8	+	22262.3i	−0.208937	+	0.188128i
$345$	163300.	−	118645.i	1.37198	−	0.996805i
$346$	39976.9	+	69242.1i	0.333931	+	0.578386i
$347$	−81644.7	−	47137.6i	−0.678061	−	0.391479i	0.121063	−	0.992645i	$-0.461370\pi$
$347$	−81644.7	−	47137.6i	−0.678061	−	0.391479i	−0.799124	+	0.601166i	$0.794703\pi$
$348$	1168.17	+	11114.4i	0.00964603	+	0.0917758i
$349$	−4797.54	−	3485.62i	−0.0393884	−	0.0286173i	0.567917	−	0.823086i	$-0.307749\pi$
$349$	−4797.54	−	3485.62i	−0.0393884	−	0.0286173i	−0.607305	+	0.794469i	$0.707749\pi$
$350$	4923.65	−	46845.4i	0.0401931	−	0.382412i
$351$	−68775.3	+	76382.7i	−0.558236	+	0.619984i
$352$	6835.92	−	15353.7i	0.0551711	−	0.123916i
$353$	6386.70	−	30047.1i	0.0512539	−	0.241131i	−0.945062	−	0.326892i	$-0.893999\pi$
$353$	6386.70	−	30047.1i	0.0512539	−	0.241131i	0.996316	+	0.0857609i	$0.0273321\pi$
$354$	40753.9	+	191732.i	0.325209	+	1.52999i
$355$	72243.4	−	32164.8i	0.573247	−	0.255226i
$356$	4651.36	+	1511.32i	0.0367012	+	0.0119249i
$357$	−74771.4	+	230123.i	−0.586677	+	1.80561i
$358$	−92210.9	−	207109.i	−0.719476	−	1.61597i
$359$	−102051.	+	21691.6i	−0.791824	+	0.168307i	−0.586031	−	0.810288i	$-0.699310\pi$
$359$	−102051.	+	21691.6i	−0.791824	+	0.168307i	−0.205792	+	0.978596i	$0.565977\pi$
$360$	−170623.	−	36266.9i	−1.31653	−	0.279838i
$361$	−108327.	−	48230.3i	−0.831231	−	0.370088i
$362$	−18442.5	−	16605.7i	−0.140735	−	0.126719i
$363$	−291944.	−	30684.6i	−2.21558	−	0.232866i
$364$	1645.06	−	2264.24i	0.0124160	−	0.0170891i
$365$	45742.6	−	4807.74i	0.343348	−	0.0360873i
$366$	32225.8	−	55816.7i	0.240570	−	0.416679i
$367$	−98675.2	+	56970.2i	−0.732615	+	0.422976i	−0.819378	−	0.573253i	$-0.805681\pi$
$367$	−98675.2	+	56970.2i	−0.732615	+	0.422976i	0.0867628	+	0.996229i	$0.472348\pi$
$368$	106675.	+	146825.i	0.787710	+	1.08419i
$369$	50692.7	+	56299.9i	0.372299	+	0.413480i
$370$	26848.9	−	8723.75i	0.196121	−	0.0637235i
$371$		−	188405.i		−	1.36882i
$372$	−8897.10	−	5369.49i	−0.0642928	−	0.0388014i
$373$	−152072.			−1.09303			−0.546516	−	0.837449i	$-0.684046\pi$
$373$	−152072.			−1.09303			−0.546516	+	0.837449i	$0.684046\pi$
$374$	89886.5	+	276642.i	0.642616	+	1.97777i
$375$	187589.	−	168906.i	1.33397	−	1.20111i
$376$	171909.	−	124899.i	1.21597	−	0.883452i
$377$	51341.6	+	88926.2i	0.361232	+	0.625673i
$378$	−138440.	−	79928.4i	−0.968898	−	0.559393i
$379$	−3867.19	−	36793.9i	−0.0269226	−	0.256152i	−0.999702	−	0.0244178i	$-0.992227\pi$
$379$	−3867.19	−	36793.9i	−0.0269226	−	0.256152i	0.972779	−	0.231734i	$-0.0744399\pi$
$380$	−1118.05	−	812.310i	−0.00774272	−	0.00562542i
$381$	8900.59	−	84683.4i	0.0613153	−	0.583376i
$382$	−8053.75	+	8944.60i	−0.0551914	+	0.0612963i
$383$	82237.2	−	184708.i	0.560623	−	1.25918i	−0.381642	−	0.924310i	$-0.624641\pi$
$383$	82237.2	−	184708.i	0.560623	−	1.25918i	0.942265	−	0.334869i	$-0.108692\pi$
$384$	47962.0	−	225643.i	0.325263	−	1.53024i
$385$	−27107.3	−	127530.i	−0.182879	−	0.860379i
$386$	195344.	−	86972.6i	1.31107	−	0.583724i
$387$	−72240.1	−	23472.2i	−0.482343	−	0.156723i
$388$	−3242.16	+	9978.34i	−0.0215363	+	0.0662819i
$389$	95131.2	+	213668.i	0.628672	+	1.41202i	0.894090	+	0.447886i	$0.147823\pi$
$389$	95131.2	+	213668.i	0.628672	+	1.41202i	−0.265419	+	0.964133i	$0.585510\pi$
$390$	−103157.	+	21926.6i	−0.678216	+	0.144159i
$391$	293478.	+	62380.8i	1.91965	+	0.408035i
$392$	−50085.1	−	22299.3i	−0.325939	−	0.145117i
$393$	6973.46	+	6278.93i	0.0451506	+	0.0406538i
$394$	96808.7	+	10175.0i	0.623623	+	0.0655454i
$395$	114540.	−	157651.i	0.734116	−	1.01042i
$396$	19495.8	−	2049.09i	0.124323	−	0.0130669i
$397$	−48579.4	+	84141.9i	−0.308227	+	0.533865i	−0.977975	−	0.208724i	$-0.933069\pi$
$397$	−48579.4	+	84141.9i	−0.308227	+	0.533865i	0.669748	+	0.742589i	$0.266402\pi$
$398$	2118.91	−	1223.35i	0.0133766	−	0.00772298i
$399$	−38192.3	−	52567.2i	−0.239900	−	0.330194i
$400$	49785.9	+	55292.8i	0.311162	+	0.345580i
$401$	−198444.	+	64478.3i	−1.23410	+	0.400982i	−0.852197	−	0.523222i	$-0.824730\pi$
$401$	−198444.	+	64478.3i	−1.23410	+	0.400982i	−0.381900	+	0.924204i	$0.624730\pi$
$402$		−	138076.i		−	0.854412i
$403$	−94746.8	−	11820.5i	−0.583384	−	0.0727824i
$404$	1494.85			0.00915871
$405$	−19967.5	−	61453.6i	−0.121734	−	0.374660i
$406$	−118681.	+	106861.i	−0.719996	+	0.648287i
$407$	−60185.4	+	43727.3i	−0.363331	+	0.263975i
$408$	−200030.	−	346463.i	−1.20164	−	2.08131i
$409$	17828.2	+	10293.1i	0.106576	+	0.0615318i	0.552341	−	0.833618i	$-0.313735\pi$
$409$	17828.2	+	10293.1i	0.106576	+	0.0615318i	−0.445764	+	0.895150i	$0.647068\pi$
$410$	3713.67	+	35333.2i	0.0220920	+	0.210192i
$411$	−279013.	−	202715.i	−1.65174	−	1.20006i
$412$	75.0369	−	713.928i	0.000442059	−	0.00420591i
$413$	87385.0	−	97050.9i	0.512315	−	0.568983i
$414$	−176400.	+	396202.i	−1.02920	+	2.31162i
$415$	−43703.7	+	205610.i	−0.253759	+	1.19384i
$416$	1883.15	+	8859.53i	0.0108818	+	0.0511946i
$417$	114521.	−	50988.0i	0.658586	−	0.293222i
$418$	−74288.6	−	24137.8i	−0.425177	−	0.138148i
$419$	23849.1	−	73399.9i	0.135845	−	0.418088i	−0.859875	−	0.510504i	$-0.829459\pi$
$419$	23849.1	−	73399.9i	0.135845	−	0.418088i	0.995720	+	0.0924159i	$0.0294589\pi$
$420$	3110.40	+	6986.06i	0.0176326	+	0.0396035i
$421$	−49745.1	+	10573.6i	−0.280663	+	0.0596569i	−0.346093	−	0.938200i	$-0.612492\pi$
$421$	−49745.1	+	10573.6i	−0.280663	+	0.0596569i	0.0654291	+	0.997857i	$0.479158\pi$
$422$	105849.	+	22498.9i	0.594377	+	0.126339i
$423$	443183.	+	197318.i	2.47686	+	1.10277i
$424$	231494.	+	208438.i	1.28768	+	1.15943i
$425$	122331.	+	12857.5i	0.677267	+	0.0711836i
$426$	−154097.	+	212097.i	−0.849134	+	1.16873i
$427$	−42705.5	+	4488.53i	−0.234222	+	0.0246178i
$428$	4256.95	−	7373.25i	0.0232386	−	0.0402505i
$429$	240678.	−	138956.i	1.30774	−	0.755025i
$430$	−20937.5	−	28818.0i	−0.113237	−	0.155857i
$431$	−123041.	−	136650.i	−0.662360	−	0.735625i	0.314559	−	0.949238i	$-0.398143\pi$
$431$	−123041.	−	136650.i	−0.662360	−	0.735625i	−0.976918	+	0.213613i	$0.931477\pi$
$432$	240148.	−	78028.9i	1.28680	−	0.418108i
$433$			176500.i			0.941389i	0.882296	+	0.470695i	$0.155997\pi$
$433$			176500.i			0.941389i	−0.882296	+	0.470695i	$0.844003\pi$
$434$	−12655.0	−	147960.i	−0.0671865	−	0.785535i
$435$	−280568.			−1.48272
$436$	1438.44	+	4427.06i	0.00756691	+	0.0232886i
$437$	−59875.5	+	53912.1i	−0.313535	+	0.282308i
$438$	−123359.	+	89625.8i	−0.643019	+	0.467181i
$439$	−102437.	−	177425.i	−0.531528	−	0.920634i	−0.999323	−	0.0367965i	$-0.988285\pi$
$439$	−102437.	−	177425.i	−0.531528	−	0.920634i	0.467795	−	0.883837i	$-0.345049\pi$
$440$	186685.	+	107783.i	0.964284	+	0.556730i
$441$	−13083.5	−	124481.i	−0.0672741	−	0.640070i
$442$	−126821.	−	92141.2i	−0.649154	−	0.471638i
$443$	−30682.5	+	291924.i	−0.156345	+	1.48752i	0.582051	+	0.813152i	$0.302250\pi$
$443$	−30682.5	+	291924.i	−0.156345	+	1.48752i	−0.738396	+	0.674367i	$0.764416\pi$
$444$	2919.71	−	3242.67i	0.0148107	−	0.0164489i
$445$	−49940.4	+	112168.i	−0.252193	+	0.566434i
$446$	51086.9	−	240345.i	0.256827	−	1.20827i
$447$	−5418.72	−	25493.1i	−0.0271195	−	0.127587i
$448$	−153875.	+	68509.4i	−0.766675	+	0.341346i
$449$	74052.1	+	24061.0i	0.367320	+	0.119350i	0.486860	−	0.873480i	$-0.338142\pi$
$449$	74052.1	+	24061.0i	0.367320	+	0.119350i	−0.119540	+	0.992829i	$0.538142\pi$
$450$	−54944.0	+	169100.i	−0.271328	+	0.835063i
$451$	−38079.8	−	85528.7i	−0.187216	−	0.420493i
$452$	−11023.7	+	2343.16i	−0.0539574	+	0.0114690i
$453$	−390999.	−	83109.5i	−1.90537	−	0.404999i
$454$	−100939.	−	44940.8i	−0.489717	−	0.218036i
$455$	52215.9	+	47015.4i	0.252220	+	0.227100i
$456$	106843.	+	11229.6i	0.513824	+	0.0540051i
$457$	−40029.4	+	55095.7i	−0.191667	+	0.263807i	−0.894025	−	0.448017i	$-0.852130\pi$
$457$	−40029.4	+	55095.7i	−0.191667	+	0.263807i	0.702358	+	0.711824i	$0.252130\pi$
$458$	−115536.	+	12143.4i	−0.550792	+	0.0578906i
$459$	208724.	−	361520.i	0.990709	−	1.71596i
$460$	8212.05	−	4741.23i	0.0388093	−	0.0224066i
$461$	−62090.7	−	85460.5i	−0.292163	−	0.402127i	0.637552	−	0.770407i	$-0.279947\pi$
$461$	−62090.7	−	85460.5i	−0.292163	−	0.402127i	−0.929715	+	0.368280i	$0.879947\pi$
$462$	289218.	+	321210.i	1.35501	+	1.50489i
$463$	131992.	−	42886.8i	0.615723	−	0.200061i	0.0154827	−	0.999880i	$-0.495072\pi$
$463$	131992.	−	42886.8i	0.615723	−	0.200061i	0.600241	+	0.799820i	$0.295072\pi$
$464$		−	252262.i		−	1.17170i
$465$	157412.	−	208050.i	0.728001	−	0.962192i
$466$	285958.			1.31683
$467$	−1351.89	−	4160.70i	−0.00619882	−	0.0190780i	0.947909	−	0.318540i	$-0.103193\pi$
$467$	−1351.89	−	4160.70i	−0.00619882	−	0.0190780i	−0.954108	+	0.299462i	$0.903193\pi$
$468$	−7850.96	+	7069.04i	−0.0358452	+	0.0322752i
$469$	−74424.1	+	54072.3i	−0.338351	+	0.245827i
$470$	113752.	+	197023.i	0.514946	+	0.891913i
$471$	68735.9	+	39684.7i	0.309843	+	0.178888i
$472$	22570.1	+	214740.i	0.101309	+	0.963894i
$473$	75941.1	+	55174.5i	0.339433	+	0.246613i
$474$	−67527.9	+	642485.i	−0.300557	+	2.85961i
$475$	−22102.3	+	24547.1i	−0.0979605	+	0.108796i
$476$	−4623.36	+	10384.2i	−0.0204053	+	0.0458311i
$477$	−147862.	+	695637.i	−0.649861	+	3.05736i
$478$	−39154.5	−	184207.i	−0.171366	−	0.806215i
$479$	−55745.3	+	24819.4i	−0.242961	+	0.108173i	−0.524605	−	0.851346i	$-0.675787\pi$
$479$	−55745.3	+	24819.4i	−0.242961	+	0.108173i	0.281644	+	0.959519i	$0.409120\pi$
$480$	−23537.0	−	7647.63i	−0.102157	−	0.0331928i
$481$	12389.1	−	38129.6i	0.0535486	−	0.164806i
$482$	17012.9	+	38211.6i	0.0732292	+	0.164476i
$483$	436093.	−	92694.4i	1.86932	−	0.397337i
$484$	−13489.0	−	2867.19i	−0.0575825	−	0.0122395i
$485$	−240629.	−	107135.i	−1.02297	−	0.455457i
$486$	−84279.9	−	75886.0i	−0.356822	−	0.321284i
$487$	164326.	+	17271.4i	0.692866	+	0.0728232i	0.444415	−	0.895821i	$-0.353412\pi$
$487$	164326.	+	17271.4i	0.692866	+	0.0728232i	0.248451	+	0.968644i	$0.420078\pi$
$488$	41731.3	−	57438.1i	0.175235	−	0.241191i
$489$	−95238.0	+	10009.9i	−0.398284	+	0.0418613i
$490$	29349.1	−	50834.2i	0.122237	−	0.211721i
$491$	131215.	−	75757.1i	0.544278	−	0.314239i	−0.202533	−	0.979275i	$-0.564917\pi$
$491$	131215.	−	75757.1i	0.544278	−	0.314239i	0.746811	+	0.665036i	$0.231584\pi$
$492$	3227.72	+	4442.58i	0.0133342	+	0.0183529i
$493$	−279055.	−	309922.i	−1.14814	−	1.27514i
$494$	40035.5	−	13008.3i	0.164056	−	0.0533049i
$495$			492144.i			2.00854i
$496$	187060.	+	141531.i	0.760357	+	0.575292i
$497$	174668.			0.707131
$498$	−215343.	−	662756.i	−0.868303	−	2.67236i
$499$	−361822.	+	325786.i	−1.45309	+	1.30837i	−0.585916	+	0.810372i	$0.699265\pi$
$499$	−361822.	+	325786.i	−1.45309	+	1.30837i	−0.867178	+	0.497999i	$0.834068\pi$
$500$	9593.62	−	6970.17i	0.0383745	−	0.0278807i
$501$	−94738.1	−	164091.i	−0.377441	−	0.653747i
$502$	−228072.	−	131677.i	−0.905033	−	0.522521i
$503$	−3660.40	−	34826.4i	−0.0144675	−	0.137649i	0.984904	−	0.173102i	$-0.0553791\pi$
$503$	−3660.40	−	34826.4i	−0.0144675	−	0.137649i	−0.999371	+	0.0354535i	$0.988712\pi$
$504$	−311698.	−	226462.i	−1.22708	−	0.891527i
$505$	−3922.80	+	37323.0i	−0.0153820	+	0.146350i
$506$	358629.	−	398297.i	1.40070	−	1.55563i
$507$	115331.	−	259037.i	0.448673	−	1.00774i
$508$	831.676	−	3912.73i	0.00322275	−	0.0151619i
$509$	−2236.18	−	10520.4i	−0.00863120	−	0.0406066i	0.973621	−	0.228170i	$-0.0732743\pi$
$509$	−2236.18	−	10520.4i	−0.00863120	−	0.0406066i	−0.982252	+	0.187564i	$0.939941\pi$
$510$	391294.	−	174215.i	1.50440	−	0.669801i
$511$	96617.8	+	31393.0i	0.370012	+	0.120224i
$512$	85737.0	−	263871.i	0.327061	−	1.00659i
$513$	45595.2	+	102408.i	0.173254	+	0.389135i
$514$	−338887.	+	72032.6i	−1.28271	+	0.272648i
$515$	17628.3	+	3747.01i	0.0664654	+	0.0141276i
$516$	−5029.74	−	2239.38i	−0.0188906	−	0.00841064i
$517$	−445527.	−	401154.i	−1.66683	−	1.50082i
$518$	62012.6	+	6517.79i	0.231111	+	0.0242907i
$519$	−182361.	+	250998.i	−0.677013	+	0.931828i
$520$	−115536.	+	12143.3i	−0.427277	+	0.0449087i
$521$	−132584.	+	229643.i	−0.488446	+	0.846014i	−0.999912	−	0.0132899i	$-0.995770\pi$
$521$	−132584.	+	229643.i	−0.488446	+	0.846014i	0.511465	+	0.859304i	$0.329103\pi$
$522$	522065.	−	301414.i	1.91595	−	1.10617i
$523$	300249.	+	413258.i	1.09769	+	1.51084i	0.838414	+	0.545034i	$0.183483\pi$
$523$	300249.	+	413258.i	1.09769	+	1.51084i	0.259273	+	0.965804i	$0.416517\pi$
$524$	294.969	+	327.597i	0.00107427	+	0.00119310i
$525$	173833.	−	56481.8i	0.630687	−	0.204923i
$526$		−	61588.4i		−	0.222601i
$527$	386381.	−	33047.0i	1.39122	−	0.118990i
$528$	−682743.			−2.44901
$529$	−84358.9	−	259630.i	−0.301453	−	0.927777i
$530$	−247849.	+	223164.i	−0.882338	+	0.794460i
$531$	−398813.	+	289754.i	−1.41443	+	1.02764i
$532$	−1526.22	−	2643.50i	−0.00539256	−	0.00934019i
$533$	43695.3	+	25227.5i	0.153809	+	0.0888014i
$534$	−42548.3	−	404820.i	−0.149211	−	1.41964i
$535$	172922.	+	125635.i	0.604148	+	0.438939i
$536$	15898.8	−	151267.i	0.0553393	−	0.526518i
$537$	588645.	−	653756.i	2.04129	−	2.26708i
$538$	−83772.1	+	188155.i	−0.289424	+	0.650058i
$539$	−32160.1	+	151301.i	−0.110698	+	0.520793i
$540$	−2743.03	−	12904.9i	−0.00940681	−	0.0442556i
$541$	−121123.	+	53927.4i	−0.413839	+	0.184253i	−0.603086	−	0.797676i	$-0.706062\pi$
$541$	−121123.	+	53927.4i	−0.413839	+	0.184253i	0.189246	+	0.981930i	$0.439396\pi$
$542$	−382715.	−	124352.i	−1.30280	−	0.423305i
$543$	29757.9	−	91585.5i	0.100926	−	0.310618i
$544$	−14962.3	−	33606.0i	−0.0505594	−	0.113558i
$545$	−114309.	+	24297.0i	−0.384845	+	0.0818013i
$546$	−227846.	−	48430.3i	−0.764288	−	0.162454i
$547$	351851.	+	156654.i	1.17594	+	0.523561i	0.899266	−	0.437403i	$-0.144102\pi$
$547$	351851.	+	156654.i	1.17594	+	0.523561i	0.276673	+	0.960964i	$0.410768\pi$
$548$	−12040.2	−	10841.0i	−0.0400932	−	0.0361001i
$549$	161202.	+	16943.0i	0.534841	+	0.0562141i
$550$	129153.	−	177764.i	0.426952	−	0.587649i
$551$	111378.	−	11706.2i	0.366855	−	0.0385580i
$552$	−368568.	+	638378.i	−1.20959	+	2.09508i
$553$	372748.	−	215206.i	1.21889	−	0.703728i
$554$	−37035.9	−	50975.6i	−0.120671	−	0.166090i
$555$	73300.2	+	81408.1i	0.237968	+	0.264291i
$556$	5600.83	−	1819.82i	0.0181177	−	0.00588679i
$557$			359021.i			1.15720i	0.815610	+	0.578601i	$0.196401\pi$
$557$			359021.i			1.15720i	−0.815610	+	0.578601i	$0.803599\pi$
$558$	−69395.4	+	556236.i	−0.222876	+	1.78645i
$559$	−50587.4			−0.161889
$560$	−53341.3	−	164168.i	−0.170093	−	0.523494i
$561$	−838802.	+	755260.i	−2.66522	+	2.39978i
$562$	−17489.0	+	12706.5i	−0.0553721	+	0.0402302i
$563$	26590.5	+	46056.1i	0.0838899	+	0.145302i	0.904918	−	0.425587i	$-0.139932\pi$
$563$	26590.5	+	46056.1i	0.0838899	+	0.145302i	−0.821028	+	0.570888i	$0.806599\pi$
$564$	30452.7	+	17581.9i	0.0957345	+	0.0552723i
$565$	−29574.9	−	281386.i	−0.0926459	−	0.881467i
$566$	210667.	+	153059.i	0.657604	+	0.477778i
$567$	14918.3	−	141938.i	0.0464038	−	0.441503i
$568$	−193240.	+	214615.i	−0.598963	+	0.665216i
$569$	94118.2	−	211393.i	0.290703	−	0.652929i	−0.707870	−	0.706343i	$-0.750344\pi$
$569$	94118.2	−	211393.i	0.290703	−	0.652929i	0.998572	+	0.0534141i	$0.0170103\pi$
$570$	−23914.2	+	112507.i	−0.0736048	+	0.346283i
$571$	−22705.4	−	106821.i	−0.0696398	−	0.327630i	0.929513	−	0.368790i	$-0.120228\pi$
$571$	−22705.4	−	106821.i	−0.0696398	−	0.327630i	−0.999153	+	0.0411604i	$0.986895\pi$
$572$	11926.9	−	5310.19i	0.0364532	−	0.0162300i
$573$	−44418.8	−	14432.6i	−0.135288	−	0.0439576i
$574$	−24249.1	+	74631.1i	−0.0735991	+	0.226515i
$575$	−92184.6	−	207050.i	−0.278819	−	0.626238i
$576$	621909.	−	132191.i	1.87448	−	0.398434i
$577$	303409.	+	64491.6i	0.911332	+	0.193710i	0.639640	−	0.768675i	$-0.279083\pi$
$577$	303409.	+	64491.6i	0.911332	+	0.193710i	0.271692	+	0.962384i	$0.412417\pi$
$578$	283302.	+	126134.i	0.847996	+	0.377552i
$579$	616618.	+	555205.i	1.83933	+	1.65614i
$580$	−13108.2	−	1377.73i	−0.0389661	−	0.00409550i
$581$	−272899.	+	375614.i	−0.808444	+	1.11273i
$582$	868440.	−	91276.8i	2.56386	−	0.269472i
$583$	439436.	−	761126.i	1.29288	−	2.23934i
$584$	−145464.	+	83983.5i	−0.426510	+	0.246245i
$585$	−155895.	−	214572.i	−0.455535	−	0.626990i
$586$	259867.	+	288612.i	0.756756	+	0.840463i
$587$	−15894.6	+	5164.48i	−0.0461290	+	0.0149882i	−0.331991	−	0.943283i	$-0.607720\pi$
$587$	−15894.6	+	5164.48i	−0.0461290	+	0.0149882i	0.285862	+	0.958271i	$0.407720\pi$
$588$		−	9072.64i		−	0.0262409i
$589$	−53807.6	+	89157.8i	−0.155101	+	0.256997i
$590$	−231178.			−0.664113
$591$	116723.	+	359236.i	0.334181	+	1.02850i
$592$	−73195.0	+	65905.1i	−0.208852	+	0.188051i
$593$	−224807.	+	163332.i	−0.639293	+	0.464473i	−0.859607	−	0.510956i	$-0.829292\pi$
$593$	−224807.	+	163332.i	−0.639293	+	0.464473i	0.220314	+	0.975429i	$0.429292\pi$
$594$	−372850.	−	645795.i	−1.05672	−	1.83030i
$595$	−247138.	−	142685.i	−0.698081	−	0.403037i
$596$	−127.980	−	1217.65i	−0.000360289	−	0.00342792i
$597$	7680.90	+	5580.50i	0.0215508	+	0.0156576i
$598$	−30191.9	+	287257.i	−0.0844284	+	0.803283i
$599$	−138367.	+	153672.i	−0.385637	+	0.428293i	−0.904440	−	0.426601i	$-0.859711\pi$
$599$	−138367.	+	153672.i	−0.385637	+	0.428293i	0.518803	+	0.854894i	$0.326378\pi$
$600$	−122917.	+	276076.i	−0.341437	+	0.766879i
$601$	96344.0	−	453263.i	0.266732	−	1.25488i	−0.617029	−	0.786940i	$-0.711664\pi$
$601$	96344.0	−	453263.i	0.266732	−	1.25488i	0.883762	−	0.467937i	$-0.155003\pi$
$602$	−16358.0	−	76958.3i	−0.0451375	−	0.212355i
$603$	317228.	−	141239.i	0.872442	−	0.388436i
$604$	−17859.5	−	5802.90i	−0.0489548	−	0.0159064i
$605$	106985.	−	329267.i	0.292290	−	0.899575i
$606$	−50603.9	−	113658.i	−0.137797	−	0.309496i
$607$	−270073.	+	57405.8i	−0.733000	+	0.155804i	−0.559265	−	0.828989i	$-0.688917\pi$
$607$	−270073.	+	57405.8i	−0.733000	+	0.155804i	−0.173734	+	0.984793i	$0.555583\pi$
$608$	9662.62	+	2053.85i	0.0261389	+	0.00555600i
$609$	−566125.	−	252055.i	−1.52643	−	0.679612i
$610$	56488.9	+	50862.9i	0.151811	+	0.136691i
$611$	321320.	+	33772.0i	0.860706	+	0.0904638i
$612$	25220.2	−	34712.6i	0.0673357	−	0.0926796i
$613$	−49464.1	+	5198.89i	−0.131634	+	0.0138353i	−0.170117	−	0.985424i	$-0.554414\pi$
$613$	−49464.1	+	5198.89i	−0.131634	+	0.0138353i	0.0384821	+	0.999259i	$0.487748\pi$
$614$	−34432.4	+	59638.7i	−0.0913337	+	0.158195i
$615$	−119391.	+	68930.7i	−0.315662	+	0.182248i
$616$	279861.	+	385196.i	0.737533	+	1.01513i
$617$	327008.	+	363179.i	0.858990	+	0.954005i	0.999348	−	0.0360961i	$-0.0114922\pi$
$617$	327008.	+	363179.i	0.858990	+	0.954005i	−0.140359	+	0.990101i	$0.544826\pi$
$618$	−56822.5	+	18462.7i	−0.148780	+	0.0483414i
$619$		−	680850.i		−	1.77693i	−0.458944	−	0.888465i	$-0.651772\pi$
$619$		−	680850.i		−	1.77693i	0.458944	−	0.888465i	$-0.348228\pi$
$620$	8375.97	−	8947.18i	0.0217897	−	0.0232757i
$621$	−769172.			−1.99453
$622$	−7502.09	−	23089.1i	−0.0193911	−	0.0596796i
$623$	−201538.	+	181466.i	−0.519256	+	0.467540i
$624$	297672.	−	216271.i	0.764485	−	0.555431i
$625$	53596.5	+	92831.9i	0.137207	+	0.237650i
$626$	−89921.4	−	51916.1i	−0.229464	−	0.132481i
$627$	−31682.8	−	301442.i	−0.0805915	−	0.766777i
$628$	3016.49	+	2191.61i	0.00764862	+	0.00555704i
$629$	−17020.4	+	161939.i	−0.0430199	+	0.409307i
$630$	276016.	−	306547.i	0.695431	−	0.772354i
$631$	−69836.0	+	156854.i	−0.175396	+	0.393947i	−0.979756	−	0.200196i	$-0.935842\pi$
$631$	−69836.0	+	156854.i	−0.175396	+	0.393947i	0.804359	+	0.594143i	$0.202509\pi$
$632$	−147957.	+	696085.i	−0.370427	+	1.74272i
$633$	87304.1	+	410734.i	0.217885	+	1.02507i
$634$	−186628.	+	83092.4i	−0.464301	+	0.206720i
$635$	95509.6	+	31032.9i	0.236864	+	0.0769618i
$636$	−15929.6	+	49026.2i	−0.0393813	+	0.121203i
$637$	−33905.8	−	76153.7i	−0.0835594	−	0.187677i
$638$	−728695.	+	154889.i	−1.79021	+	0.380521i
$639$	−644915.	−	137081.i	−1.57943	−	0.335719i
$640$	248545.	+	110659.i	0.606799	+	0.270164i
$641$	−102920.	−	92669.7i	−0.250487	−	0.225539i	0.534316	−	0.845285i	$-0.320569\pi$
$641$	−102920.	−	92669.7i	−0.250487	−	0.225539i	−0.784803	+	0.619746i	$0.787236\pi$
$642$	−704719.	−	74069.0i	−1.70980	−	0.179708i
$643$	411268.	−	566061.i	0.994724	−	1.36912i	0.0662166	−	0.997805i	$-0.478907\pi$
$643$	411268.	−	566061.i	0.994724	−	1.36912i	0.928507	−	0.371315i	$-0.121093\pi$
$644$	20829.6	−	2189.28i	0.0502237	−	0.00527872i
$645$	69111.5	−	119705.i	0.166123	−	0.287734i
$646$	−148064.	+	85484.8i	−0.354801	+	0.204844i
$647$	−215029.	−	295962.i	−0.513675	−	0.707013i	0.470858	−	0.882209i	$-0.343944\pi$
$647$	−215029.	−	295962.i	−0.513675	−	0.707013i	−0.984534	+	0.175195i	$0.943944\pi$
$648$	157895.	+	175361.i	0.376027	+	0.417621i
$649$	579383.	−	188253.i	1.37555	−	0.446943i
$650$			118415.i			0.280273i
$651$	504531.	−	278385.i	1.19049	−	0.656876i
$652$	−4498.70			−0.0105826
$653$	40157.9	+	123593.i	0.0941770	+	0.289847i	0.987038	−	0.160485i	$-0.0513057\pi$
$653$	40157.9	+	123593.i	0.0941770	+	0.289847i	−0.892861	+	0.450332i	$0.851306\pi$
$654$	287910.	−	259235.i	0.673133	−	0.606091i
$655$	−8953.42	+	6505.04i	−0.0208692	+	0.0151624i
$656$	−61976.4	−	107346.i	−0.144019	−	0.249447i
$657$	−332098.	−	191737.i	−0.769371	−	0.444197i
$658$	52525.1	+	499743.i	0.121315	+	1.15424i
$659$	−8248.25	−	5992.70i	−0.0189929	−	0.0137991i	0.578248	−	0.815861i	$-0.303736\pi$
$659$	−8248.25	−	5992.70i	−0.0189929	−	0.0137991i	−0.597241	+	0.802062i	$0.703736\pi$
$660$	−3728.81	+	35477.2i	−0.00856016	+	0.0814445i
$661$	−254427.	+	282570.i	−0.582319	+	0.646731i	−0.960263	−	0.279098i	$-0.909965\pi$
$661$	−254427.	+	282570.i	−0.582319	+	0.646731i	0.377944	+	0.925829i	$0.376631\pi$
$662$	182242.	−	409322.i	0.415845	−	0.934004i
$663$	126470.	−	594994.i	0.287714	−	1.35359i
$664$	−159601.	−	750864.i	−0.361992	−	1.70304i
$665$	70007.3	−	31169.3i	0.158307	−	0.0704828i
$666$	−223850.	−	72733.3i	−0.504672	−	0.163978i
$667$	−237456.	+	730815.i	−0.533742	+	1.64269i
$668$	−3620.42	−	8131.60i	−0.00811346	−	0.0182231i
$669$	932629.	−	198236.i	2.08380	−	0.442926i
$670$	159287.	+	33857.5i	0.354839	+	0.0754233i
$671$	−182992.	−	81473.4i	−0.406432	−	0.180955i
$672$	−40622.1	−	36576.3i	−0.0899548	−	0.0809957i
$673$	778618.	+	81836.0i	1.71907	+	0.180682i	0.912117	−	0.409930i	$-0.134447\pi$
$673$	778618.	+	81836.0i	1.71907	+	0.180682i	0.806956	+	0.590612i	$0.201114\pi$
$674$	484016.	−	666191.i	1.06547	−	1.46649i
$675$	−313610.	+	32961.7i	−0.688306	+	0.0723439i
$676$	6660.30	−	11536.0i	0.0145747	−	0.0252442i
$677$	−399226.	+	230493.i	−0.871046	+	0.502899i	−0.867696	−	0.497096i	$-0.834400\pi$
$677$	−399226.	+	230493.i	−0.871046	+	0.502899i	−0.00335053	+	0.999994i	$0.501067\pi$
$678$	551335.	+	758848.i	1.19938	+	1.65080i
$679$	−389290.	−	432350.i	−0.844371	−	0.937769i
$680$	448734.	−	145802.i	0.970445	−	0.315317i
$681$		−	428746.i		−	0.924499i
$682$	293978.	−	627251.i	0.632043	−	1.34857i
$683$	−322613.			−0.691576			−0.345788	−	0.938313i	$-0.612388\pi$
$683$	−322613.			−0.691576			−0.345788	+	0.938313i	$0.612388\pi$
$684$	3560.54	+	10958.2i	0.00761033	+	0.0234222i
$685$	302272.	−	272167.i	0.644193	−	0.580034i
$686$	405049.	−	294286.i	0.860716	−	0.625347i
$687$	−225397.	−	390399.i	−0.477567	−	0.827171i
$688$	107628.	+	62138.9i	0.227378	+	0.131276i
$689$	49508.9	+	471046.i	0.104290	+	0.992258i
$690$	−638487.	−	463888.i	−1.34108	−	0.974350i
$691$	−73319.3	+	697586.i	−0.153554	+	1.46097i	0.598104	+	0.801419i	$0.295921\pi$
$691$	−73319.3	+	697586.i	−0.153554	+	1.46097i	−0.751658	+	0.659553i	$0.770746\pi$
$692$	−9752.48	+	10831.2i	−0.0203659	+	0.0226186i
$693$	−442130.	+	993040.i	−0.920627	+	2.06776i
$694$	−76637.5	+	360551.i	−0.159119	+	0.748596i
$695$	30739.0	+	144616.i	0.0636386	+	0.299396i
$696$	936020.	−	416743.i	1.93227	−	0.860300i
$697$	−194891.	−	63323.8i	−0.401167	−	0.130347i
$698$	−7164.87	+	22051.2i	−0.0147061	+	0.0452607i
$699$	451325.	+	1.01369e6i	0.923709	+	2.07468i
$700$	8398.89	−	1785.24i	0.0171406	−	0.00364335i
$701$	64790.1	+	13771.6i	0.131848	+	0.0280251i	0.273363	−	0.961911i	$-0.411864\pi$
$701$	64790.1	+	13771.6i	0.131848	+	0.0280251i	−0.141515	+	0.989936i	$0.545197\pi$
$702$	367127.	+	163456.i	0.744976	+	0.331685i
$703$	−32494.8	−	29258.4i	−0.0657511	−	0.0592025i
$704$	−781419.	−	82130.5i	−1.57666	−	0.165714i
$705$	−518895.	+	714198.i	−1.04400	+	1.43695i
$706$	−119447.	+	12554.4i	−0.239644	+	0.0251876i
$707$	−41445.4	+	71785.6i	−0.0829159	+	0.143615i
$708$	−30944.6	+	17865.9i	−0.0617332	+	0.0356417i
$709$	−11852.7	−	16313.8i	−0.0235789	−	0.0324536i	0.797065	−	0.603894i	$-0.206385\pi$
$709$	−11852.7	−	16313.8i	−0.0235789	−	0.0324536i	−0.820644	+	0.571440i	$0.806385\pi$
$710$	−206892.	−	229777.i	−0.410419	−	0.455816i
$711$	−1.54517e6	+	502057.i	−3.05659	+	0.993147i
$712$		−	448391.i		−	0.884498i
$713$	−408698.	−	586104.i	−0.803940	−	1.15291i
$714$	946058.			1.85576
$715$	101285.	+	311723.i	0.198122	+	0.609756i
$716$	30711.9	−	27653.1i	0.0599075	−	0.0539409i
$717$	591199.	−	429531.i	1.14999	−	0.835519i
$718$	203961.	+	353271.i	0.395639	+	0.685267i
$719$	−594376.	−	343163.i	−1.14975	−	0.663808i	−0.200923	−	0.979607i	$-0.564394\pi$
$719$	−594376.	−	343163.i	−1.14975	−	0.663808i	−0.948826	+	0.315799i	$0.897728\pi$
$720$	68108.4	+	648009.i	0.131382	+	1.25002i
$721$	32203.9	+	23397.5i	0.0619494	+	0.0450089i
$722$	−48462.5	+	461090.i	−0.0929675	+	0.884527i
$723$	−108605.	+	120618.i	−0.207765	+	0.230747i
$724$	1840.03	−	4132.77i	0.00351033	−	0.00788433i
$725$	−65498.5	+	308146.i	−0.124611	+	0.586248i
$726$	238632.	+	1.12268e6i	0.452748	+	2.13001i
$727$	−714552.	+	318139.i	−1.35196	+	0.601933i	−0.949576	−	0.313537i	$-0.898486\pi$
$727$	−714552.	+	318139.i	−1.35196	+	0.601933i	−0.402387	+	0.915470i	$0.631819\pi$
$728$	−244036.	−	79292.0i	−0.460459	−	0.149612i
$729$	226378.	−	696721.i	0.425971	−	1.31100i
$730$	−73144.9	−	164286.i	−0.137258	−	0.308287i
$731$	200968.	−	42717.0i	0.376090	−	0.0799404i
$732$	11492.2	+	2442.74i	0.0214477	+	0.00455885i
$733$	478090.	+	212859.i	0.889818	+	0.396173i	0.800151	−	0.599799i	$-0.204753\pi$
$733$	478090.	+	212859.i	0.889818	+	0.396173i	0.0896677	+	0.995972i	$0.471419\pi$
$734$	331067.	+	298094.i	0.614503	+	0.553301i
$735$	226523.	+	23808.6i	0.419313	+	0.0440716i
$736$	−39840.7	+	54836.0i	−0.0735481	+	0.101230i
$737$	−426779.	+	44856.3i	−0.785721	+	0.0825826i
$738$	148105.	−	256525.i	0.271929	−	0.470996i
$739$	−288152.	+	166365.i	−0.527635	+	0.304630i	−0.740053	−	0.672549i	$-0.765199\pi$
$739$	−288152.	+	166365.i	−0.527635	+	0.304630i	0.212418	+	0.977179i	$0.431866\pi$
$740$	3024.85	+	4163.35i	0.00552384	+	0.00760291i
$741$	109301.	+	121391.i	0.199061	+	0.221080i
$742$	−700590.	+	227636.i	−1.27250	+	0.413459i
$743$		−	815092.i		−	1.47649i	−0.674535	−	0.738243i	$-0.735656\pi$
$743$		−	815092.i		−	1.47649i	0.674535	−	0.738243i	$-0.264344\pi$
$744$	−216125.	+	927902.i	−0.390444	+	1.67632i
$745$	30737.9			0.0553811
$746$	183737.	+	565486.i	0.330157	+	1.01612i
$747$	1.30239e6	−	1.17268e6i	2.33400	−	2.10155i
$748$	−42897.8	+	31167.1i	−0.0766711	+	0.0557048i
$749$	236052.	+	408854.i	0.420770	+	0.728794i
$750$	−854730.	−	493479.i	−1.51952	−	0.877296i
$751$	10127.8	+	96359.6i	0.0179571	+	0.170850i	0.999825	−	0.0187171i	$-0.00595820\pi$
$751$	10127.8	+	96359.6i	0.0179571	+	0.170850i	−0.981868	+	0.189567i	$0.939292\pi$
$752$	−642144.	−	466545.i	−1.13552	−	0.825007i
$753$	106819.	−	1.01632e6i	0.188391	−	1.79242i
$754$	268643.	−	298358.i	0.472533	−	0.524801i
$755$	191753.	−	430684.i	0.336393	−	0.755552i
$756$	6058.63	−	28503.6i	0.0106006	−	0.0498720i
$757$	90892.9	+	427617.i	0.158613	+	0.746214i	0.983499	+	0.180915i	$0.0579059\pi$
$757$	90892.9	+	427617.i	0.158613	+	0.746214i	−0.824886	+	0.565299i	$0.808761\pi$
$758$	−132147.	+	58835.5i	−0.229995	+	0.102400i
$759$	1.97794e6	+	642673.i	3.43345	+	1.11559i
$760$	−39153.3	+	120501.i	−0.0677862	+	0.208624i
$761$	−116526.	−	261723.i	−0.201213	−	0.451931i	0.784552	−	0.620063i	$-0.212893\pi$
$761$	−116526.	−	261723.i	−0.201213	−	0.451931i	−0.985764	+	0.168132i	$0.946226\pi$
$762$	−325652.	+	69219.4i	−0.560846	+	0.119211i
$763$	−252478.	−	53665.8i	−0.433685	−	0.0921826i
$764$	−2004.39	−	892.412i	−0.00343396	−	0.00152890i
$765$	800512.	+	720785.i	1.36787	+	1.23164i
$766$	−786202.	−	82633.2i	−1.33991	−	0.140831i
$767$	−192975.	+	265607.i	−0.328027	+	0.451491i
$768$	131883.	−	13861.4i	0.223597	−	0.0235010i
$769$	345062.	−	597665.i	0.583505	−	1.01066i	−0.411555	−	0.911385i	$-0.635014\pi$
$769$	345062.	−	597665.i	0.583505	−	1.01066i	0.995060	−	0.0992751i	$-0.0316524\pi$
$770$	−441471.	+	254883.i	−0.744596	+	0.429893i
$771$	−790210.	−	1.08763e6i	−1.32933	−	1.82967i
$772$	26082.2	+	28967.3i	0.0437633	+	0.0486041i
$773$	−631069.	+	205047.i	−1.05613	+	0.343158i	−0.785072	−	0.619405i	$-0.787374\pi$
$773$	−631069.	+	205047.i	−1.05613	+	0.343158i	−0.271059	+	0.962563i	$0.587374\pi$
$774$			296986.i			0.495741i
$775$	−191753.	−	221454.i	−0.319255	−	0.368707i
$776$	961911.			1.59739
$777$	74769.0	+	230115.i	0.123845	+	0.381157i
$778$	679592.	−	611907.i	1.12277	−	1.01094i
$779$	44519.0	−	32345.0i	0.0733620	−	0.0533006i
$780$	−9612.31	−	16649.0i	−0.0157993	−	0.0273652i
$781$	705629.	+	407395.i	1.15684	+	0.667903i
$782$	−122623.	−	1.16668e6i	−0.200520	−	1.90782i
$783$	864945.	+	628419.i	1.41080	+	1.02500i
$784$	−21406.6	+	203670.i	−0.0348269	+	0.331356i
$785$	−62635.5	+	69563.8i	−0.101644	+	0.112887i
$786$	14922.9	−	33517.4i	0.0241551	−	0.0542531i
$787$	−5095.73	+	23973.5i	−0.00822729	+	0.0387063i	−0.982070	−	0.188518i	$-0.939632\pi$
$787$	−5095.73	+	23973.5i	−0.00822729	+	0.0387063i	0.973842	+	0.227224i	$0.0729650\pi$
$788$	3689.30	+	17356.8i	0.00594144	+	0.0279523i
$789$	218325.	−	97204.4i	0.350711	−	0.156146i
$790$	−724622.	−	235444.i	−1.16107	−	0.377253i
$791$	193115.	−	594346.i	0.308647	−	0.949919i
$792$	−731009.	−	1.64187e6i	−1.16539	−	2.61752i
$793$	105592.	−	22444.2i	0.167913	−	0.0356909i
$794$	371579.	+	78981.5i	0.589400	+	0.125281i
$795$	−1.18227e6	−	526381.i	−1.87061	−	0.832848i
$796$	331.451	+	298.440i	0.000523110	+	0.000471011i
$797$	1.02046e6	+	107254.i	1.60649	+	0.168849i	0.864879	−	0.501980i	$-0.167395\pi$
$797$	1.02046e6	+	107254.i	1.60649	+	0.168849i	0.741612	+	0.670829i	$0.234061\pi$
$798$	−149328.	+	205532.i	−0.234496	+	0.322755i
$799$	−1.30502e6	+	137163.i	−2.04420	+	0.214854i
$800$	−13894.1	+	24065.3i	−0.0217095	+	0.0376020i
$801$	886543.	−	511846.i	1.38177	−	0.797763i
$802$	479529.	+	660015.i	0.745532	+	1.02614i
$803$	317099.	+	352174.i	0.491772	+	0.546168i
$804$	23938.2	−	7777.98i	0.0370321	−	0.0120325i
$805$			525813.i			0.811408i
$806$	70520.4	+	366601.i	0.108554	+	0.564317i
$807$	−799208.			−1.22719
$808$	−42350.8	−	130342.i	−0.0648693	−	0.199647i
$809$	−518502.	+	466861.i	−0.792234	+	0.713331i	−0.962267	−	0.272108i	$-0.912279\pi$
$809$	−518502.	+	466861.i	−0.792234	+	0.713331i	0.170033	+	0.985438i	$0.445613\pi$
$810$	−204392.	+	148499.i	−0.311525	+	0.226336i
$811$	541573.	+	938032.i	0.823408	+	1.42619i	0.903130	+	0.429368i	$0.141264\pi$
$811$	541573.	+	938032.i	0.823408	+	1.42619i	−0.0797214	+	0.996817i	$0.525403\pi$
$812$	−25211.8	−	14556.0i	−0.0382377	−	0.0220766i
$813$	−163222.	−	1.55295e6i	−0.246943	−	2.34950i
$814$	235319.	+	170969.i	0.355146	+	0.258029i
$815$	11805.6	−	112323.i	0.0177735	−	0.169103i
$816$	−999934.	+	1.11054e6i	−1.50173	+	1.66784i
$817$	−22440.8	+	50403.0i	−0.0336198	+	0.0755113i
$818$	16734.8	−	78731.0i	0.0250100	−	0.117663i
$819$	−121797.	−	573012.i	−0.181581	−	0.854272i
$820$	−5916.49	+	2634.19i	−0.00879906	+	0.00391759i
$821$	−1.24536e6	−	404643.i	−1.84761	−	0.600324i	−0.997249	−	0.0741196i	$-0.976385\pi$
$821$	−1.24536e6	−	404643.i	−1.84761	−	0.600324i	−0.850358	−	0.526204i	$-0.823615\pi$
$822$	−416692.	+	1.28244e6i	−0.616696	+	1.89799i
$823$	37512.4	+	84254.2i	0.0553828	+	0.124392i	0.939117	−	0.343597i	$-0.111645\pi$
$823$	37512.4	+	84254.2i	0.0553828	+	0.124392i	−0.883734	+	0.467989i	$0.844979\pi$
$824$	−64376.5	+	13683.7i	−0.0948141	+	0.0201534i
$825$	833995.	+	177271.i	1.22534	+	0.260453i
$826$	−466467.	−	207685.i	−0.683693	−	0.304400i
$827$	−524279.	−	472063.i	−0.766570	−	0.690223i	0.189981	−	0.981788i	$-0.439157\pi$
$827$	−524279.	−	472063.i	−0.766570	−	0.690223i	−0.956551	+	0.291565i	$0.905824\pi$
$828$	−78625.9	−	8263.91i	−0.114685	−	0.0120538i
$829$	−100556.	+	138404.i	−0.146319	+	0.201390i	−0.875885	−	0.482519i	$-0.839722\pi$
$829$	−100556.	+	138404.i	−0.146319	+	0.201390i	0.729567	+	0.683910i	$0.239722\pi$
$830$	817369.	−	85908.9i	1.18648	−	0.124705i
$831$	122250.	−	211743.i	0.177030	−	0.306624i
$832$	366710.	−	211720.i	0.529757	−	0.305855i
$833$	199003.	+	273904.i	0.286794	+	0.394737i
$834$	−327967.	−	364244.i	−0.471518	−	0.523674i
$835$	212528.	−	69054.7i	0.304821	−	0.0990422i
$836$		−	14239.0i		−	0.0203736i
$837$	−951269.	+	288811.i	−1.35785	+	0.412252i
$838$	−301755.			−0.429701
$839$	389955.	+	1.20016e6i	0.553975	+	1.70496i	0.698634	+	0.715479i	$0.253791\pi$
$839$	389955.	+	1.20016e6i	0.553975	+	1.70496i	−0.144659	+	0.989482i	$0.546209\pi$
$840$	521025.	−	469133.i	0.738414	−	0.664871i
$841$	291902.	−	212079.i	0.412710	−	0.299851i
$842$	99421.6	+	172203.i	0.140235	+	0.242894i
$843$	−72645.8	−	41942.1i	−0.102225	−	0.0590194i
$844$	2061.97	+	19618.3i	0.00289466	+	0.0275408i
$845$	270549.	+	196566.i	0.378907	+	0.275292i
$846$	198268.	−	1.88639e6i	0.277020	−	2.63567i
$847$	511679.	−	568277.i	0.713232	−	0.792124i
$848$	473275.	−	1.06299e6i	0.658145	−	1.47822i
$849$	−210084.	+	988366.i	−0.291459	+	1.37121i
$850$	−99992.4	−	470427.i	−0.138398	−	0.651111i
$851$	274087.	−	122031.i	0.378468	−	0.168505i
$852$	−45451.4	−	14768.1i	−0.0626136	−	0.0203444i
$853$	369559.	−	1.13738e6i	0.507908	−	1.56318i	−0.287917	−	0.957655i	$-0.592963\pi$
$853$	369559.	−	1.13738e6i	0.507908	−	1.56318i	0.795826	−	0.605526i	$-0.207037\pi$
$854$	68288.6	+	153379.i	0.0936337	+	0.210305i
$855$	−282946.	+	60141.9i	−0.387053	+	0.0822707i
$856$	−763511.	−	162289.i	−1.04200	−	0.221484i
$857$	−258415.	−	115054.i	−0.351849	−	0.156653i	0.223199	−	0.974773i	$-0.428350\pi$
$857$	−258415.	−	115054.i	−0.351849	−	0.156653i	−0.575048	+	0.818120i	$0.695017\pi$
$858$	−807503.	−	727079.i	−1.09691	−	0.987659i
$859$	−824097.	−	86616.1i	−1.11684	−	0.117385i	−0.471927	−	0.881638i	$-0.656441\pi$
$859$	−824097.	−	86616.1i	−1.11684	−	0.117385i	−0.644917	+	0.764253i	$0.723108\pi$
$860$	3816.72	−	5253.26i	0.00516052	−	0.00710284i
$861$	−302832.	+	31828.9i	−0.408503	+	0.0429354i
$862$	−359478.	+	622634.i	−0.483791	+	0.837951i
$863$	−481050.	+	277735.i	−0.645905	+	0.372914i	−0.786886	−	0.617099i	$-0.788308\pi$
$863$	−481050.	+	277735.i	−0.645905	+	0.372914i	0.140980	+	0.990012i	$0.454975\pi$
$864$	55431.5	+	76294.9i	0.0742556	+	0.102204i
$865$	−244839.	−	271921.i	−0.327226	−	0.363421i
$866$	656321.	−	213252.i	0.875146	−	0.284352i
$867$			1.20335e6i			1.60087i
$868$	24938.8	−	10528.7i	0.0331007	−	0.0139745i
$869$	2.00779e6			2.65875
$870$	338988.	+	1.04330e6i	0.447864	+	1.37838i
$871$	171864.	−	154747.i	0.226542	−	0.203979i
$872$	345263.	−	250848.i	0.454064	−	0.329896i
$873$	1.09804e6	+	1.90186e6i	1.44075	+	2.49545i
$874$	272817.	+	157511.i	0.357148	+	0.206199i
$875$	68733.6	+	653957.i	0.0897746	+	0.854148i
$876$	−22487.3	−	16338.0i	−0.0293041	−	0.0212907i
$877$	15478.3	−	147266.i	0.0201244	−	0.191471i	−0.979841	−	0.199779i	$-0.935978\pi$
$877$	15478.3	−	147266.i	0.0201244	−	0.191471i	0.999965	+	0.00830755i	$0.00264441\pi$
$878$	−535995.	+	595283.i	−0.695300	+	0.772208i
$879$	−612953.	+	1.37672e6i	−0.793322	+	1.78183i
$880$	167414.	−	787623.i	0.216186	−	1.01707i
$881$	233950.	+	1.10065e6i	0.301419	+	1.41806i	0.824539	+	0.565805i	$0.191435\pi$
$881$	233950.	+	1.10065e6i	0.301419	+	1.41806i	−0.523120	+	0.852259i	$0.675232\pi$
$882$	−447080.	+	199053.i	−0.574709	+	0.255877i
$883$	−23037.4	−	7485.31i	−0.0295469	−	0.00960038i	0.294206	−	0.955742i	$-0.404945\pi$
$883$	−23037.4	−	7485.31i	−0.0295469	−	0.00960038i	−0.323753	+	0.946142i	$0.604945\pi$
$884$	8830.44	−	27177.3i	0.0113000	−	0.0347778i
$885$	−364866.	−	819502.i	−0.465851	−	1.04632i
$886$	1.12260e6	−	238616.i	1.43007	−	0.303971i
$887$	445816.	+	94761.0i	0.566641	+	0.120443i	0.482320	−	0.875995i	$-0.339794\pi$
$887$	445816.	+	94761.0i	0.566641	+	0.120443i	0.0843214	+	0.996439i	$0.473128\pi$
$888$	−365462.	−	162714.i	−0.463464	−	0.206348i
$889$	164839.	+	148421.i	0.208572	+	0.187799i
$890$	477439.	+	50180.9i	0.602751	+	0.0633517i
$891$	391325.	−	538612.i	0.492926	−	0.678454i
$892$	44546.1	−	4681.99i	0.0559861	−	0.00588438i
$893$	176188.	−	305167.i	0.220940	−	0.382679i
$894$	−88249.7	+	50951.0i	−0.110418	+	0.0637496i
$895$	609842.	+	839376.i	0.761327	+	1.04788i
$896$	402096.	+	446573.i	0.500857	+	0.556259i
$897$	−1.06595e6	+	346348.i	−1.32480	+	0.430455i
$898$		−	304436.i		−	0.377523i
$899$	−19264.3	+	992992.i	−0.0238361	+	1.22865i
$900$	−32411.8			−0.0400145
$901$	−594444.	−	1.82951e6i	−0.732253	−	2.25364i
$902$	−272032.	+	244939.i	−0.334354	+	0.301054i
$903$	246992.	−	179450.i	0.302905	−	0.220074i
$904$	516626.	+	894822.i	0.632178	+	1.09496i
$905$	98357.4	+	56786.7i	0.120091	+	0.0693345i
$906$	163370.	+	1.55436e6i	0.199028	+	1.89363i
$907$	1.03217e6	+	749918.i	1.25470	+	0.911590i	0.998485	−	0.0550311i	$-0.0175258\pi$
$907$	1.03217e6	+	749918.i	1.25470	+	0.911590i	0.256211	+	0.966621i	$0.417526\pi$
$908$	2105.36	−	20031.2i	0.00255361	−	0.0242960i
$909$	209364.	−	232523.i	0.253382	−	0.281409i
$910$	111740.	−	250971.i	0.134935	−	0.303069i
$911$	246360.	−	1.15903e6i	0.296847	−	1.39656i	−0.536545	−	0.843872i	$-0.680271\pi$
$911$	246360.	−	1.15903e6i	0.296847	−	1.39656i	0.833392	−	0.552683i	$-0.186396\pi$
$912$	−83434.0	−	392526.i	−0.100312	−	0.471931i
$913$	−1.97855e6	+	880907.i	−2.37359	+	1.05679i
$914$	253240.	+	82282.5i	0.303137	+	0.0984952i
$915$	−91147.7	+	280524.i	−0.108869	+	0.335064i
$916$	−8613.56	−	19346.4i	−0.0102658	−	0.0230573i
$917$	−23910.0	+	5082.24i	−0.0284342	+	0.00604389i
$918$	−1.59651e6	−	339348.i	−1.89446	−	0.402680i
$919$	395885.	+	176259.i	0.468746	+	0.208699i	0.627496	−	0.778620i	$-0.284080\pi$
$919$	395885.	+	176259.i	0.468746	+	0.208699i	−0.158750	+	0.987319i	$0.550746\pi$
$920$	−646067.	−	581721.i	−0.763311	−	0.687289i
$921$	−265758.	−	27932.3i	−0.313304	−	0.0329296i
$922$	−242768.	+	334142.i	−0.285581	+	0.393069i
$923$	−436699.	+	45899.0i	−0.512601	+	0.0538765i
$924$	−39395.8	+	68235.5i	−0.0461430	+	0.0799221i
$925$	106522.	−	61500.6i	0.124496	−	0.0718780i
$926$	−318952.	−	438999.i	−0.371966	−	0.511967i
$927$	−100542.	−	111663.i	−0.117000	−	0.129942i
$928$	89602.9	−	29113.7i	0.104046	−	0.0338066i
$929$		−	966363.i		−	1.11972i	−0.828588	−	0.559860i	$-0.810855\pi$
$929$		−	966363.i		−	1.11972i	0.828588	−	0.559860i	$-0.189145\pi$
$930$	−963829.	−	333971.i	−1.11438	−	0.386138i
$931$	−90916.9			−0.104893
$932$	16108.3	+	49576.3i	0.0185446	+	0.0570745i
$933$	70007.9	−	63035.4i	0.0804236	−	0.0724138i
$934$	−13838.3	+	10054.1i	−0.0158631	+	0.0115252i
$935$	−665598.	−	1.15285e6i	−0.761358	−	1.31871i
$936$	838809.	+	484286.i	0.957439	+	0.552778i
$937$	40358.5	+	383986.i	0.0459681	+	0.437357i	0.993166	+	0.116708i	$0.0372342\pi$
$937$	40358.5	+	383986.i	0.0459681	+	0.437357i	−0.947198	+	0.320649i	$0.896099\pi$
$938$	290990.	+	211417.i	0.330729	+	0.240289i
$939$	42115.4	−	400701.i	0.0477649	−	0.454453i
$940$	−27750.0	+	30819.5i	−0.0314056	+	0.0348795i
$941$	393081.	−	882875.i	0.443918	−	0.997057i	−0.543570	−	0.839364i	$-0.682928\pi$
$941$	393081.	−	882875.i	0.443918	−	0.997057i	0.987488	−	0.157693i	$-0.0504057\pi$
$942$	64520.4	−	303545.i	0.0727102	−	0.342074i
$943$	78502.8	+	369326.i	0.0882798	+	0.415324i
$944$	736824.	−	328055.i	0.826837	−	0.368131i
$945$	695772.	+	226070.i	0.779118	+	0.253151i
$946$	113414.	−	349052.i	0.126731	−	0.390039i
$947$	565784.	+	1.27077e6i	0.630885	+	1.41699i	0.892157	+	0.451726i	$0.149192\pi$
$947$	565784.	+	1.27077e6i	0.630885	+	1.41699i	−0.261271	+	0.965265i	$0.584142\pi$
$948$	−115191.	+	24484.6i	−0.128174	+	0.0272443i
$949$	−249811.	−	53098.9i	−0.277382	−	0.0589594i
$950$	117984.	+	52529.8i	0.130730	+	0.0582047i
$951$	−589108.	−	530435.i	−0.651379	−	0.586504i
$952$	1.03643e6	+	108934.i	1.14358	+	0.120195i
$953$	236921.	−	326094.i	0.260866	−	0.359051i	−0.658414	−	0.752656i	$-0.728772\pi$
$953$	236921.	−	326094.i	0.260866	−	0.359051i	0.919280	+	0.393605i	$0.128772\pi$
$954$	2.76540e6	−	290655.i	3.03851	−	0.319360i
$955$	27541.5	−	47703.3i	0.0301982	−	0.0523048i
$956$	29730.2	−	17164.7i	0.0325299	−	0.0187811i
$957$	−1.69916e6	−	2.33869e6i	−1.85528	−	2.55358i
$958$	159644.	+	177303.i	0.173949	+	0.193190i
$959$	854427.	−	277620.i	0.929047	−	0.301866i
$960$			1.15699e6i			1.25542i
$961$	−725528.	−	571402.i	−0.785610	−	0.618721i
$962$	−156755.			−0.169383
$963$	−550688.	−	1.69484e6i	−0.593818	−	1.82758i
$964$	−5666.35	+	5102.01i	−0.00609747	+	0.00549019i
$965$	−791693.	+	575199.i	−0.850163	+	0.617679i
$966$	−871584.	−	1.50963e6i	−0.934018	−	1.61777i
$967$	−857422.	−	495033.i	−0.916942	−	0.529396i	−0.0342835	−	0.999412i	$-0.510915\pi$
$967$	−857422.	−	495033.i	−0.916942	−	0.529396i	−0.882658	+	0.470016i	$0.844248\pi$
$968$	132158.	+	1.25740e6i	0.141040	+	1.34191i
$969$	−536723.	−	389952.i	−0.571613	−	0.415301i
$970$	−107651.	+	1.02423e6i	−0.114412	+	1.08856i
$971$	7836.70	−	8703.53i	0.00831179	−	0.00923118i	−0.738975	−	0.673733i	$-0.764690\pi$
$971$	7836.70	−	8703.53i	0.00831179	−	0.00923118i	0.747286	+	0.664502i	$0.231356\pi$
$972$	8408.70	−	18886.2i	0.00890013	−	0.0199900i
$973$	−67894.5	+	319419.i	−0.0717148	+	0.337392i
$974$	−134319.	−	631920.i	−0.141586	−	0.666107i
$975$	−419771.	+	186894.i	−0.441573	+	0.196601i
$976$	−252222.	−	81952.0i	−0.264779	−	0.0860320i
$977$	439925.	−	1.35395e6i	0.460881	−	1.41845i	−0.403208	−	0.915108i	$-0.632105\pi$
$977$	439925.	−	1.35395e6i	0.460881	−	1.41845i	0.864089	−	0.503338i	$-0.167895\pi$
$978$	152291.	+	342051.i	0.159220	+	0.357613i
$979$	−1.23743e6	+	263024.i	−1.29109	+	0.274429i
$980$	10466.3	+	2224.69i	0.0108979	+	0.00231642i
$981$	890091.	+	396294.i	0.924904	+	0.411794i
$982$	−440242.	−	396396.i	−0.456529	−	0.411061i
$983$	−1.01043e6	−	106200.i	−1.04568	−	0.109905i	−0.433921	−	0.900951i	$-0.642870\pi$
$983$	−1.01043e6	−	106200.i	−1.04568	−	0.109905i	−0.611757	+	0.791045i	$0.709537\pi$
$984$	295923.	−	407303.i	0.305625	−	0.420657i
$985$	−443042.	+	46565.5i	−0.456638	+	0.0479946i
$986$	−815294.	+	1.41213e6i	−0.838611	+	1.45252i
$987$	−1.68864e6	+	974935.i	−1.73341	+	1.00079i
$988$	4510.48	+	6208.14i	0.00462071	+	0.00635986i
$989$	−253311.	−	281331.i	−0.258977	−	0.287624i
$990$	1.83005e6	−	594620.i	1.86721	−	0.606693i
$991$			795493.i			0.810008i	0.914315	+	0.405004i	$0.132730\pi$
$991$			795493.i			0.810008i	−0.914315	+	0.405004i	$0.867270\pi$
$992$	−28682.8	+	82777.7i	−0.0291473	+	0.0841182i
$993$	1.73863e6			1.76323
$994$	−211038.	−	649507.i	−0.213593	−	0.657372i
$995$	−8321.17	+	7492.42i	−0.00840501	+	0.00756791i
$996$	102771.	−	74667.4i	0.103598	−	0.0752683i
$997$	−864355.	−	1.49711e6i	−0.869564	−	1.50613i	−0.862443	−	0.506155i	$-0.831066\pi$
$997$	−864355.	−	1.49711e6i	−0.869564	−	1.50613i	−0.00712145	−	0.999975i	$-0.502267\pi$
$998$	1.64860e6	+	951823.i	1.65522	+	0.955641i
$999$	−43633.7	−	415147.i	−0.0437211	−	0.415979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.5.h.a.11.3	✓	80
31.17	odd	30	inner	31.5.h.a.17.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.5.h.a.11.3	✓	80	1.1	even	1	trivial
31.5.h.a.17.3	yes	80	31.17	odd	30	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	31.h (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20822 - 3.71853i) q^{2} +(11.2749 - 10.1519i) q^{3} +(0.576617 - 0.418937i) q^{4} +(8.94674 + 15.4962i) q^{5} +(-51.3729 - 29.6601i) q^{6} +(4.13118 + 39.3055i) q^{7} +(-52.8652 - 38.4088i) q^{8} +(15.5941 - 148.368i) q^{9} +(46.8134 - 51.9916i) q^{10} +(-74.9869 + 168.423i) q^{11} +(2.24826 - 10.5772i) q^{12} +(-20.6573 - 97.1850i) q^{13} +(141.167 - 62.8518i) q^{14} +(258.190 + 83.8910i) q^{15} +(-75.4274 + 232.142i) q^{16} +(164.130 + 368.642i) q^{17} +(-570.550 + 121.274i) q^{18} +(-105.994 - 22.5298i) q^{19} +(11.6508 + 5.18726i) q^{20} +(445.606 + 401.226i) q^{21} +(716.888 + 75.3480i) q^{22} +(437.034 - 601.526i) q^{23} +(-985.973 + 103.630i) q^{24} +(152.412 - 263.985i) q^{25} +(-336.427 + 194.236i) q^{26} +(-608.058 - 836.920i) q^{27} +(18.8486 + 20.9335i) q^{28} +(-982.903 + 319.364i) q^{29} -1061.45i q^{30} +(314.637 - 908.033i) q^{31} -91.1615 q^{32} +(864.357 + 2660.22i) q^{33} +(1172.50 - 1055.73i) q^{34} +(-572.126 + 415.674i) q^{35} +(-53.1648 - 92.0842i) q^{36} +(349.456 + 201.758i) q^{37} +(44.2872 + 421.365i) q^{38} +(-1219.53 - 886.038i) q^{39} +(122.220 - 1162.84i) q^{40} +(-339.798 + 377.383i) q^{41} +(953.578 - 2141.77i) q^{42} +(105.859 - 498.025i) q^{43} +(27.3200 + 128.531i) q^{44} +(2438.65 - 1085.76i) q^{45} +(-2764.83 - 898.347i) q^{46} +(-1004.87 + 3092.67i) q^{47} +(1506.25 + 3383.10i) q^{48} +(820.673 - 174.439i) q^{49} +(-1165.78 - 247.795i) q^{50} +(5592.98 + 2490.16i) q^{51} +(-52.6257 - 47.3844i) q^{52} +(-4740.98 - 498.297i) q^{53} +(-2377.44 + 3272.27i) q^{54} +(-3280.81 + 344.827i) q^{55} +(1291.28 - 2236.57i) q^{56} +(-1423.80 + 822.029i) q^{57} +(2375.13 + 3269.09i) q^{58} +(-2211.04 - 2455.61i) q^{59} +(184.022 - 59.7923i) q^{60} +1086.50i q^{61} +(-3756.70 - 72.8811i) q^{62} +5896.09 q^{63} +(1316.98 + 4053.25i) q^{64} +(1321.18 - 1189.60i) q^{65} +(8847.76 - 6428.27i) q^{66} +(1163.82 + 2015.80i) q^{67} +(249.078 + 143.805i) q^{68} +(-1179.15 - 11218.9i) q^{69} +(2236.95 + 1625.24i) q^{70} +(461.964 - 4395.29i) q^{71} +(-6523.01 + 7244.54i) q^{72} +(1045.50 - 2348.23i) q^{73} +(328.024 - 1543.23i) q^{74} +(-961.536 - 4523.67i) q^{75} +(-70.5568 + 31.4139i) q^{76} +(-6929.76 - 2251.62i) q^{77} +(-1821.30 + 5605.37i) q^{78} +(-4429.54 - 9948.91i) q^{79} +(-4272.14 + 908.072i) q^{80} +(-3532.24 - 750.801i) q^{81} +(1813.86 + 807.584i) q^{82} +(8730.07 + 7860.59i) q^{83} +(425.032 + 44.6727i) q^{84} +(-4244.13 + 5841.54i) q^{85} +(-1979.82 + 208.088i) q^{86} +(-7839.94 + 13579.2i) q^{87} +(10433.2 - 6023.58i) q^{88} +(4033.32 + 5551.39i) q^{89} +(-6983.86 - 7756.36i) q^{90} +(3734.57 - 1213.44i) q^{91} -529.940i q^{92} +(-5670.81 - 13432.1i) q^{93} +12714.3 q^{94} +(-599.178 - 1844.08i) q^{95} +(-1027.83 + 925.467i) q^{96} +(-11909.1 + 8652.49i) q^{97} +(-1640.21 - 2840.93i) q^{98} +(23819.2 + 13752.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{2} - 16 q^{3} - 138 q^{4} - q^{5} - 9 q^{6} + 288 q^{7} - 221 q^{8} - 182 q^{9} + 102 q^{10} - 49 q^{11} - 159 q^{12} + 527 q^{13} - 740 q^{14} + 1060 q^{15} - 1970 q^{16} + 848 q^{17} + 3 q^{18}+ \cdots + 75228 q^{99}+O(q^{100}) \) 80 * q - 6 * q^2 - 16 * q^3 - 138 * q^4 - q^5 - 9 * q^6 + 288 * q^7 - 221 * q^8 - 182 * q^9 + 102 * q^10 - 49 * q^11 - 159 * q^12 + 527 * q^13 - 740 * q^14 + 1060 * q^15 - 1970 * q^16 + 848 * q^17 + 3 * q^18 + 1534 * q^19 + 1165 * q^20 + 1367 * q^21 + 4579 * q^22 - 1375 * q^23 - 3828 * q^24 - 5997 * q^25 - 2547 * q^26 - 3235 * q^27 - 1564 * q^28 - 1150 * q^29 - 3587 * q^31 + 15718 * q^32 - 5029 * q^33 + 5958 * q^34 + 4959 * q^35 + 13555 * q^36 + 3462 * q^37 + 6118 * q^38 - 8143 * q^39 - 13011 * q^40 - 7290 * q^41 - 24735 * q^42 + 4687 * q^43 + 17051 * q^44 - 6093 * q^45 - 16530 * q^46 - 4302 * q^47 + 40344 * q^48 + 14300 * q^49 + 30081 * q^50 + 1348 * q^51 - 14433 * q^52 + 17996 * q^53 - 42200 * q^54 - 5289 * q^55 - 32470 * q^56 - 35847 * q^57 - 38475 * q^58 + 3552 * q^59 - 26585 * q^60 - 6327 * q^62 + 35814 * q^63 + 231 * q^64 + 18280 * q^65 + 85992 * q^66 + 2185 * q^67 + 56694 * q^68 + 57836 * q^69 + 6338 * q^70 - 3708 * q^71 - 25127 * q^72 + 5344 * q^73 + 5247 * q^74 + 13921 * q^75 - 10354 * q^76 - 37000 * q^77 - 98345 * q^78 + 53300 * q^79 + 65286 * q^80 + 20439 * q^81 - 26142 * q^82 - 59542 * q^83 - 77120 * q^84 + 4525 * q^85 - 100990 * q^86 - 55761 * q^87 - 82191 * q^88 - 26395 * q^89 - 61689 * q^90 - 12450 * q^91 + 9029 * q^93 + 67112 * q^94 - 3972 * q^95 + 210490 * q^96 + 5883 * q^97 + 107722 * q^98 + 75228 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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