LMFDB - Embedded newform 119.5.h.a.101.38

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [119,5,Mod(33,119)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("119.33"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(119, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	119.h (of order $6$, degree $2$, 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:	$12.3010256070$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.38
Character	$\chi$	$=$	119.101
Dual form			119.5.h.a.33.38

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.47790 + 4.29184i) q^{2} +(8.58954 - 14.8775i) q^{3} +(-4.27993 + 7.41305i) q^{4} +(4.33032 + 7.50033i) q^{5} +85.1359 q^{6} +(37.7928 + 31.1882i) q^{7} +36.8718 q^{8} +(-107.060 - 185.434i) q^{9} +(-21.4602 + 37.1701i) q^{10} +(-13.4869 - 7.78669i) q^{11} +(73.5252 + 127.349i) q^{12} -18.9206i q^{13} +(-40.2079 + 239.482i) q^{14} +148.782 q^{15} +(159.843 + 276.857i) q^{16} +(21.5325 - 288.197i) q^{17} +(530.568 - 918.971i) q^{18} +(-373.119 + 215.420i) q^{19} -74.1338 q^{20} +(788.625 - 294.372i) q^{21} -77.1784i q^{22} +(796.760 - 460.010i) q^{23} +(316.712 - 548.561i) q^{24} +(274.997 - 476.308i) q^{25} +(81.2040 - 46.8831i) q^{26} -2286.89 q^{27} +(-392.950 + 146.677i) q^{28} +1491.36i q^{29} +(368.666 + 638.548i) q^{30} +(-298.698 + 517.359i) q^{31} +(-497.175 + 861.133i) q^{32} +(-231.693 + 133.768i) q^{33} +(1290.25 - 621.707i) q^{34} +(-70.2666 + 418.514i) q^{35} +1832.84 q^{36} +(-932.297 + 538.262i) q^{37} +(-1849.10 - 1067.58i) q^{38} +(-281.491 - 162.519i) q^{39} +(159.667 + 276.551i) q^{40} +658.889 q^{41} +(3217.53 + 2655.23i) q^{42} -1193.26 q^{43} +(115.446 - 66.6530i) q^{44} +(927.211 - 1605.98i) q^{45} +(3948.58 + 2279.71i) q^{46} +(-2510.58 + 1449.48i) q^{47} +5491.92 q^{48} +(455.597 + 2357.38i) q^{49} +2725.65 q^{50} +(-4102.70 - 2795.83i) q^{51} +(140.259 + 80.9786i) q^{52} +(-449.944 + 779.325i) q^{53} +(-5666.67 - 9814.96i) q^{54} -134.876i q^{55} +(1393.49 + 1149.96i) q^{56} +7401.45i q^{57} +(-6400.69 + 3695.44i) q^{58} +(-1993.98 - 1151.23i) q^{59} +(-636.775 + 1102.93i) q^{60} +(-629.488 - 1090.30i) q^{61} -2960.57 q^{62} +(1737.23 - 10347.1i) q^{63} +187.191 q^{64} +(141.910 - 81.9321i) q^{65} +(-1148.22 - 662.927i) q^{66} +(-1588.74 + 2751.78i) q^{67} +(2044.26 + 1393.08i) q^{68} -15805.1i q^{69} +(-1970.31 + 735.460i) q^{70} +3951.85i q^{71} +(-3947.51 - 6837.28i) q^{72} +(384.449 - 665.885i) q^{73} +(-4620.27 - 2667.51i) q^{74} +(-4724.19 - 8182.53i) q^{75} -3687.94i q^{76} +(-266.857 - 714.914i) q^{77} -1610.82i q^{78} +(8176.15 - 4720.50i) q^{79} +(-1384.35 + 2397.76i) q^{80} +(-10971.4 + 19003.1i) q^{81} +(1632.66 + 2827.85i) q^{82} +6320.45i q^{83} +(-1193.07 + 7106.01i) q^{84} +(2254.81 - 1086.48i) q^{85} +(-2956.77 - 5121.27i) q^{86} +(22187.8 + 12810.1i) q^{87} +(-497.288 - 287.109i) q^{88} +(-9092.18 + 5249.37i) q^{89} +9190.12 q^{90} +(590.097 - 715.061i) q^{91} +7875.23i q^{92} +(5131.35 + 8887.76i) q^{93} +(-12441.9 - 7183.33i) q^{94} +(-3231.45 - 1865.68i) q^{95} +(8541.01 + 14793.5i) q^{96} -1222.94 q^{97} +(-8988.57 + 7796.69i) q^{98} +3334.58i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 2 q^{2} - 354 q^{4} + 56 q^{8} - 1068 q^{9} + 464 q^{15} - 3146 q^{16} + 1104 q^{17} - 906 q^{18} - 6 q^{19} - 240 q^{21} - 3106 q^{25} + 468 q^{26} + 1858 q^{30} - 1680 q^{32} - 198 q^{33} - 5318 q^{35}+ \cdots + 107386 q^{98}+O(q^{100}) $ 92 * q - 2 * q^2 - 354 * q^4 + 56 * q^8 - 1068 * q^9 + 464 * q^15 - 3146 * q^16 + 1104 * q^17 - 906 * q^18 - 6 * q^19 - 240 * q^21 - 3106 * q^25 + 468 * q^26 + 1858 * q^30 - 1680 * q^32 - 198 * q^33 - 5318 * q^35 + 17304 * q^36 - 6 * q^38 + 1888 * q^42 + 3316 * q^43 - 7242 * q^47 - 1284 * q^49 + 2136 * q^50 - 11304 * q^51 - 5202 * q^52 + 28 * q^53 - 17826 * q^59 - 3182 * q^60 + 41768 * q^64 + 5988 * q^66 + 2924 * q^67 - 22788 * q^68 + 36898 * q^70 - 23660 * q^72 - 3162 * q^77 - 6194 * q^81 + 30426 * q^84 + 46552 * q^85 + 4118 * q^86 - 7026 * q^87 + 4944 * q^89 + 11034 * q^93 - 101214 * q^94 + 107386 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/119\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.47790	+	4.29184i	0.619474	+	1.07296i	0.989582	+	0.143971i	$0.0459873\pi$
$2$	2.47790	+	4.29184i	0.619474	+	1.07296i	−0.370108	+	0.928989i	$0.620679\pi$
$3$	8.58954	−	14.8775i	0.954393	−	1.65306i	0.218642	−	0.975805i	$-0.429837\pi$
$3$	8.58954	−	14.8775i	0.954393	−	1.65306i	0.735751	−	0.677252i	$-0.236829\pi$
$4$	−4.27993	+	7.41305i	−0.267495	+	0.463316i
$5$	4.33032	+	7.50033i	0.173213	+	0.300013i	0.939541	−	0.342436i	$-0.111252\pi$
$5$	4.33032	+	7.50033i	0.173213	+	0.300013i	−0.766329	+	0.642449i	$0.777918\pi$
$6$	85.1359			2.36489
$7$	37.7928	+	31.1882i	0.771282	+	0.636493i
$7$	37.7928	+	31.1882i	0.771282	+	0.636493i
$8$	36.8718			0.576122
$9$	−107.060	−	185.434i	−1.32173	−	2.28931i
$10$	−21.4602	+	37.1701i	−0.214602	+	0.371701i
$11$	−13.4869	−	7.78669i	−0.111462	−	0.0643528i	0.443232	−	0.896407i	$-0.353832\pi$
$11$	−13.4869	−	7.78669i	−0.111462	−	0.0643528i	−0.554695	+	0.832054i	$0.687165\pi$
$12$	73.5252	+	127.349i	0.510592	+	0.884371i
$13$		−	18.9206i		−	0.111956i	−0.998432	−	0.0559780i	$-0.982172\pi$
$13$		−	18.9206i		−	0.111956i	0.998432	−	0.0559780i	$-0.0178277\pi$
$14$	−40.2079	+	239.482i	−0.205142	+	1.22185i
$15$	148.782			0.661252
$16$	159.843	+	276.857i	0.624388	+	1.08147i
$17$	21.5325	−	288.197i	0.0745070	−	0.997220i
$17$	21.5325	−	288.197i	0.0745070	−	0.997220i
$18$	530.568	−	918.971i	1.63756	−	2.83633i
$19$	−373.119	+	215.420i	−1.03357	+	0.596732i	−0.918006	−	0.396567i	$-0.870201\pi$
$19$	−373.119	+	215.420i	−1.03357	+	0.596732i	−0.115565	+	0.993300i	$0.536868\pi$
$20$	−74.1338			−0.185335
$21$	788.625	−	294.372i	1.78827	−	0.667509i
$22$		−	77.1784i		−	0.159460i
$23$	796.760	−	460.010i	1.50616	−	0.869584i	0.506189	−	0.862423i	$-0.331054\pi$
$23$	796.760	−	460.010i	1.50616	−	0.869584i	0.999974	−	0.00716101i	$-0.00227944\pi$
$24$	316.712	−	548.561i	0.549847	−	0.952362i
$25$	274.997	−	476.308i	0.439995	−	0.762093i
$26$	81.2040	−	46.8831i	0.120124	−	0.0693538i
$27$	−2286.89			−3.13702
$28$	−392.950	+	146.677i	−0.501212	+	0.187088i
$29$			1491.36i			1.77332i	0.462422	+	0.886660i	$0.346980\pi$
$29$			1491.36i			1.77332i	−0.462422	+	0.886660i	$0.653020\pi$
$30$	368.666	+	638.548i	0.409629	+	0.709497i
$31$	−298.698	+	517.359i	−0.310820	+	0.538355i	−0.978540	−	0.206057i	$-0.933937\pi$
$31$	−298.698	+	517.359i	−0.310820	+	0.538355i	0.667720	+	0.744412i	$0.267270\pi$
$32$	−497.175	+	861.133i	−0.485523	+	0.840950i
$33$	−231.693	+	133.768i	−0.212758	+	0.122836i
$34$	1290.25	−	621.707i	1.11613	−	0.537809i
$35$	−70.2666	+	418.514i	−0.0573605	+	0.341644i
$36$	1832.84			1.41423
$37$	−932.297	+	538.262i	−0.681006	+	0.393179i	−0.800234	−	0.599688i	$-0.795291\pi$
$37$	−932.297	+	538.262i	−0.681006	+	0.393179i	0.119228	+	0.992867i	$0.461958\pi$
$38$	−1849.10	−	1067.58i	−1.28054	−	0.739320i
$39$	−281.491	−	162.519i	−0.185070	−	0.106850i
$40$	159.667	+	276.551i	0.0997917	+	0.172844i
$41$	658.889			0.391963			0.195981	−	0.980608i	$-0.437211\pi$
$41$	658.889			0.391963			0.195981	+	0.980608i	$0.437211\pi$
$42$	3217.53	+	2655.23i	1.82399	+	1.50523i
$43$	−1193.26			−0.645353			−0.322676	−	0.946509i	$-0.604583\pi$
$43$	−1193.26			−0.645353			−0.322676	+	0.946509i	$0.604583\pi$
$44$	115.446	−	66.6530i	0.0596314	−	0.0344282i
$45$	927.211	−	1605.98i	0.457882	−	0.793075i
$46$	3948.58	+	2279.71i	1.86606	+	1.07737i
$47$	−2510.58	+	1449.48i	−1.13652	+	0.656171i	−0.945567	−	0.325427i	$-0.894492\pi$
$47$	−2510.58	+	1449.48i	−1.13652	+	0.656171i	−0.190955	+	0.981599i	$0.561159\pi$
$48$	5491.92			2.38365
$49$	455.597	+	2357.38i	0.189753	+	0.981832i
$50$	2725.65			1.09026
$51$	−4102.70	−	2795.83i	−1.57735	−	1.07490i
$52$	140.259	+	80.9786i	0.0518710	+	0.0299477i
$53$	−449.944	+	779.325i	−0.160179	+	0.277439i	−0.934933	−	0.354825i	$-0.884541\pi$
$53$	−449.944	+	779.325i	−0.160179	+	0.277439i	0.774754	+	0.632263i	$0.217874\pi$
$54$	−5666.67	−	9814.96i	−1.94330	−	3.36590i
$55$		−	134.876i		−	0.0445869i
$56$	1393.49	+	1149.96i	0.444353	+	0.366698i
$57$			7401.45i			2.27807i
$58$	−6400.69	+	3695.44i	−1.90270	+	1.09853i
$59$	−1993.98	−	1151.23i	−0.572819	−	0.330717i	0.185455	−	0.982653i	$-0.440624\pi$
$59$	−1993.98	−	1151.23i	−0.572819	−	0.330717i	−0.758274	+	0.651935i	$0.773957\pi$
$60$	−636.775	+	1102.93i	−0.176882	+	0.306369i
$61$	−629.488	−	1090.30i	−0.169172	−	0.293014i	0.768957	−	0.639300i	$-0.220776\pi$
$61$	−629.488	−	1090.30i	−0.169172	−	0.293014i	−0.938129	+	0.346286i	$0.887443\pi$
$62$	−2960.57			−0.770178
$63$	1737.23	−	10347.1i	0.437700	−	2.60698i
$64$	187.191			0.0457009
$65$	141.910	−	81.9321i	0.0335883	−	0.0193922i
$66$	−1148.22	−	662.927i	−0.263596	−	0.152187i
$67$	−1588.74	+	2751.78i	−0.353919	+	0.613005i	−0.986932	−	0.161135i	$-0.948484\pi$
$67$	−1588.74	+	2751.78i	−0.353919	+	0.613005i	0.633013	+	0.774141i	$0.281818\pi$
$68$	2044.26	+	1393.08i	0.442098	+	0.301272i
$69$		−	15805.1i		−	3.31970i
$70$	−1970.31	+	735.460i	−0.402103	+	0.150094i
$71$			3951.85i			0.783942i	0.919978	+	0.391971i	$0.128207\pi$
$71$			3951.85i			0.783942i	−0.919978	+	0.391971i	$0.871793\pi$
$72$	−3947.51	−	6837.28i	−0.761479	−	1.31892i
$73$	384.449	−	665.885i	0.0721428	−	0.124955i	−0.827697	−	0.561175i	$-0.810350\pi$
$73$	384.449	−	665.885i	0.0721428	−	0.124955i	0.899840	+	0.436220i	$0.143683\pi$
$74$	−4620.27	−	2667.51i	−0.843730	−	0.487128i
$75$	−4724.19	−	8182.53i	−0.839856	−	1.45467i
$76$		−	3687.94i		−	0.638493i
$77$	−266.857	−	714.914i	−0.0450088	−	0.120579i
$78$		−	1610.82i		−	0.264763i
$79$	8176.15	−	4720.50i	1.31007	−	0.756370i	0.327963	−	0.944690i	$-0.393638\pi$
$79$	8176.15	−	4720.50i	1.31007	−	0.756370i	0.982108	+	0.188321i	$0.0603044\pi$
$80$	−1384.35	+	2397.76i	−0.216304	+	0.374649i
$81$	−10971.4	+	19003.1i	−1.67222	+	2.89637i
$82$	1632.66	+	2827.85i	0.242811	+	0.420560i
$83$			6320.45i			0.917470i	0.888573	+	0.458735i	$0.151697\pi$
$83$			6320.45i			0.917470i	−0.888573	+	0.458735i	$0.848303\pi$
$84$	−1193.07	+	7106.01i	−0.169086	+	1.00709i
$85$	2254.81	−	1086.48i	0.312085	−	0.150378i
$86$	−2956.77	−	5121.27i	−0.399779	−	0.692438i
$87$	22187.8	+	12810.1i	2.93140	+	1.69244i
$88$	−497.288	−	287.109i	−0.0642159	−	0.0370751i
$89$	−9092.18	+	5249.37i	−1.14786	+	0.662716i	−0.948364	−	0.317183i	$-0.897263\pi$
$89$	−9092.18	+	5249.37i	−1.14786	+	0.662716i	−0.199494	+	0.979899i	$0.563930\pi$
$90$	9190.12			1.13458
$91$	590.097	−	715.061i	0.0712592	−	0.0863496i
$92$			7875.23i			0.930439i
$93$	5131.35	+	8887.76i	0.593288	+	1.02761i
$94$	−12441.9	−	7183.33i	−1.40809	−	0.812962i
$95$	−3231.45	−	1865.68i	−0.358055	−	0.206723i
$96$	8541.01	+	14793.5i	0.926759	+	1.60519i
$97$	−1222.94			−0.129975			−0.0649875	−	0.997886i	$-0.520701\pi$
$97$	−1222.94			−0.129975			−0.0649875	+	0.997886i	$0.520701\pi$
$98$	−8988.57	+	7796.69i	−0.935919	+	0.811816i
$99$			3334.58i			0.340229i
$100$	2353.93	+	4077.13i	0.235393	+	0.407713i
$101$	−930.670	−	537.322i	−0.0912332	−	0.0526735i	0.453689	−	0.891160i	$-0.350108\pi$
$101$	−930.670	−	537.322i	−0.0912332	−	0.0526735i	−0.544922	+	0.838486i	$0.683441\pi$
$102$	1833.19	−	24535.9i	0.176201	−	2.35831i
$103$	12059.9	−	6962.76i	1.13676	−	0.656307i	0.191132	−	0.981564i	$-0.438784\pi$
$103$	12059.9	−	6962.76i	1.13676	−	0.656307i	0.945626	+	0.325257i	$0.105451\pi$
$104$		−	697.635i		−	0.0645003i
$105$	5622.89	+	4640.23i	0.510012	+	0.420883i
$106$	−4459.65			−0.396908
$107$	−8117.24	+	4686.49i	−0.708991	+	0.409336i	−0.810688	−	0.585479i	$-0.800906\pi$
$107$	−8117.24	+	4686.49i	−0.708991	+	0.409336i	0.101696	+	0.994816i	$0.467573\pi$
$108$	9787.72	−	16952.8i	0.839139	−	1.45343i
$109$	9529.19	+	5501.68i	0.802053	+	0.463065i	0.844189	−	0.536046i	$-0.180083\pi$
$109$	9529.19	+	5501.68i	0.802053	+	0.463065i	−0.0421356	+	0.999112i	$0.513416\pi$
$110$	578.864	−	334.207i	0.0478400	−	0.0276204i
$111$			18493.7i			1.50099i
$112$	−2593.72	+	15448.4i	−0.206770	+	1.23154i
$113$		−	9373.26i		−	0.734063i	−0.930208	−	0.367032i	$-0.880374\pi$
$113$		−	9373.26i		−	0.734063i	0.930208	−	0.367032i	$-0.119626\pi$
$114$	−31765.8	+	18340.0i	−2.44428	+	1.41120i
$115$	6900.45	+	3983.98i	0.521774	+	0.301246i
$116$	−11055.5	−	6382.92i	−0.821607	−	0.474355i
$117$	−3508.51	+	2025.64i	−0.256302	+	0.147976i
$118$		−	11410.5i		−	0.819483i
$119$	9802.10	−	10220.2i	0.692190	−	0.721715i
$120$	5485.85			0.380962
$121$	−7199.23	−	12469.4i	−0.491717	−	0.851680i
$122$	3119.61	−	5403.32i	0.209595	−	0.363029i
$123$	5659.55	−	9802.63i	0.374086	−	0.647937i
$124$	−2556.81	−	4428.52i	−0.166286	−	0.288015i
$125$	10176.2			0.651276
$126$	48712.7	−	18183.1i	3.06832	−	1.14532i
$127$	1690.46			0.104809			0.0524044	−	0.998626i	$-0.483312\pi$
$127$	1690.46			0.104809			0.0524044	+	0.998626i	$0.483312\pi$
$128$	8418.65	+	14581.5i	0.513833	+	0.889986i
$129$	−10249.5	+	17752.7i	−0.615920	+	1.06681i
$130$	703.279	+	406.038i	0.0416141	+	0.0240259i
$131$	−12281.1	−	21271.5i	−0.715642	−	1.23953i	−0.962711	−	0.270530i	$-0.912801\pi$
$131$	−12281.1	−	21271.5i	−0.715642	−	1.23953i	0.247070	−	0.968998i	$-0.420532\pi$
$132$		−	2290.07i		−	0.131432i
$133$	−20819.8	−	3495.55i	−1.17699	−	0.197612i
$134$	−15746.9			−0.876974
$135$	−9902.96	−	17152.4i	−0.543372	−	0.941149i
$136$	793.943	−	10626.3i	0.0429251	−	0.574520i
$137$	−12179.4	+	21095.4i	−0.648911	+	1.12395i	0.334473	+	0.942405i	$0.391442\pi$
$137$	−12179.4	+	21095.4i	−0.648911	+	1.12395i	−0.983383	+	0.181541i	$0.941892\pi$
$138$	67832.9	−	39163.3i	3.56190	−	2.05647i
$139$	8664.42			0.448446			0.224223	−	0.974538i	$-0.428016\pi$
$139$	8664.42			0.448446			0.224223	+	0.974538i	$0.428016\pi$
$140$	−2801.73	−	2312.10i	−0.142945	−	0.117964i
$141$			49801.5i			2.50498i
$142$	−16960.7	+	9792.27i	−0.841138	+	0.485631i
$143$	−147.329	+	255.181i	−0.00720468	+	0.0124789i
$144$	34225.7	−	59280.7i	1.65055	−	2.85883i
$145$	−11185.7	+	6458.07i	−0.532020	+	0.307162i
$146$	3810.50			0.178762
$147$	38985.3	+	13470.6i	1.80412	+	0.623381i
$148$		−	9214.89i		−	0.420694i
$149$	−8533.37	−	14780.2i	−0.384369	−	0.665746i	0.607313	−	0.794463i	$-0.292248\pi$
$149$	−8533.37	−	14780.2i	−0.384369	−	0.665746i	−0.991681	+	0.128717i	$0.958914\pi$
$150$	23412.1	−	40550.9i	1.04054	−	1.80226i
$151$	15912.4	−	27561.1i	0.697881	−	1.20877i	−0.271319	−	0.962489i	$-0.587460\pi$
$151$	15912.4	−	27561.1i	0.697881	−	1.20877i	0.969200	−	0.246276i	$-0.0792068\pi$
$152$	−13757.6	+	7942.94i	−0.595463	+	0.343791i
$153$	−55746.7	+	26861.6i	−2.38142	+	1.14749i
$154$	2407.05	−	2916.79i	0.101495	−	0.122988i
$155$	−5173.83			−0.215352
$156$	2409.52	−	1391.14i	0.0990106	−	0.0571638i
$157$	−20725.4	−	11965.8i	−0.840821	−	0.485448i	0.0167220	−	0.999860i	$-0.494677\pi$
$157$	−20725.4	−	11965.8i	−0.840821	−	0.485448i	−0.857543	+	0.514412i	$0.828010\pi$
$158$	40519.3	+	23393.8i	1.62311	+	0.937103i
$159$	7729.62	+	13388.1i	0.305748	+	0.529571i
$160$	−8611.71			−0.336395
$161$	44458.7	+	7464.42i	1.71516	+	0.287968i
$162$	−108744.			−4.14358
$163$	7372.73	−	4256.65i	0.277494	−	0.160211i	−0.354795	−	0.934944i	$-0.615449\pi$
$163$	7372.73	−	4256.65i	0.277494	−	0.160211i	0.632288	+	0.774733i	$0.282116\pi$
$164$	−2820.00	+	4884.38i	−0.104848	+	0.181602i
$165$	−2006.61	−	1158.52i	−0.0737048	−	0.0425535i
$166$	−27126.4	+	15661.4i	−0.984408	+	0.568348i
$167$	−34688.3			−1.24380			−0.621900	−	0.783097i	$-0.713639\pi$
$167$	−34688.3			−1.24380			−0.621900	+	0.783097i	$0.713639\pi$
$168$	29078.0	−	10854.0i	1.03026	−	0.384567i
$169$	28203.0			0.987466
$170$	10250.2	+	6985.11i	0.354678	+	0.241699i
$171$	79892.5	+	46126.0i	2.73221	+	1.57744i
$172$	5107.06	−	8845.68i	0.172629	−	0.299002i
$173$	3491.92	+	6048.19i	0.116674	+	0.202084i	0.918447	−	0.395543i	$-0.129444\pi$
$173$	3491.92	+	6048.19i	0.116674	+	0.202084i	−0.801774	+	0.597627i	$0.796110\pi$
$174$			126968.i			4.19370i
$175$	25248.1	−	9424.40i	0.824427	−	0.307735i
$176$		−	4978.60i		−	0.160725i
$177$	−34254.8	+	19777.0i	−1.09339	+	0.631268i
$178$	−45059.0	−	26014.8i	−1.42214	−	0.821071i
$179$	−9124.50	+	15804.1i	−0.284776	+	0.493246i	−0.972555	−	0.232674i	$-0.925252\pi$
$179$	−9124.50	+	15804.1i	−0.284776	+	0.493246i	0.687779	+	0.725920i	$0.258586\pi$
$180$	7936.79	+	13746.9i	0.244963	+	0.424288i
$181$	37733.2			1.15177			0.575886	−	0.817530i	$-0.304657\pi$
$181$	37733.2			1.15177			0.575886	+	0.817530i	$0.304657\pi$
$182$	4531.13	+	760.756i	0.136793	+	0.0229669i
$183$	−21628.0			−0.645825
$184$	29378.0	−	16961.4i	0.867733	−	0.500986i
$185$	−8074.29	−	4661.69i	−0.235918	−	0.136207i
$186$	−25429.9	+	44045.9i	−0.735053	+	1.27315i
$187$	−2534.51	+	3719.23i	−0.0724787	+	0.106358i
$188$		−	24814.7i		−	0.702092i
$189$	−86428.0	−	71323.9i	−2.41953	−	1.99669i
$190$		−	18491.8i		−	0.512239i
$191$	16489.4	+	28560.5i	0.452001	+	0.782888i	0.998510	−	0.0545648i	$-0.0173772\pi$
$191$	16489.4	+	28560.5i	0.452001	+	0.782888i	−0.546510	+	0.837453i	$0.684044\pi$
$192$	1607.88	−	2784.94i	0.0436166	−	0.0755462i
$193$	−14280.2	−	8244.70i	−0.383373	−	0.221340i	0.295912	−	0.955215i	$-0.404376\pi$
$193$	−14280.2	−	8244.70i	−0.383373	−	0.221340i	−0.679285	+	0.733875i	$0.737710\pi$
$194$	−3030.31	−	5248.64i	−0.0805162	−	0.139458i
$195$		−	2815.03i		−	0.0740311i
$196$	−19425.3	−	6712.04i	−0.505656	−	0.174720i
$197$		−	21547.8i		−	0.555228i	−0.960693	−	0.277614i	$-0.910456\pi$
$197$		−	21547.8i		−	0.555228i	0.960693	−	0.277614i	$-0.0895436\pi$
$198$	−14311.5	+	8262.75i	−0.365052	+	0.210763i
$199$	8751.27	−	15157.7i	0.220986	−	0.382759i	−0.734121	−	0.679018i	$-0.762406\pi$
$199$	8751.27	−	15157.7i	0.220986	−	0.382759i	0.955108	+	0.296259i	$0.0957391\pi$
$200$	10139.6	−	17562.3i	0.253490	−	0.439058i
$201$	27293.1	+	47273.1i	0.675555	+	1.17010i
$202$		−	5325.71i		−	0.130519i
$203$	−46512.8	+	56362.8i	−1.12871	+	1.36773i
$204$	38284.9	−	18447.6i	0.919955	−	0.443281i
$205$	2853.20	+	4941.89i	0.0678929	+	0.117594i
$206$	59766.1	+	34506.0i	1.40838	+	0.813130i
$207$	−170603.	−	98497.6i	−3.98149	−	2.29871i
$208$	5238.28	−	3024.32i	0.121077	−	0.0699039i
$209$	6709.65			0.153606
$210$	−5982.21	+	35630.5i	−0.135651	+	0.807949i
$211$		−	28754.0i		−	0.645854i	−0.946424	−	0.322927i	$-0.895333\pi$
$211$		−	28754.0i		−	0.645854i	0.946424	−	0.322927i	$-0.104667\pi$
$212$	−3851.45	−	6670.91i	−0.0856945	−	0.148427i
$213$	58793.7	+	33944.6i	1.29590	+	0.748189i
$214$	−40227.4	−	23225.3i	−0.878403	−	0.507146i
$215$	−5167.19	−	8949.83i	−0.111783	−	0.193615i
$216$	−84321.7			−1.80731
$217$	−27424.1	+	10236.7i	−0.582389	+	0.217389i
$218$			54530.4i			1.14743i
$219$	−6604.48	−	11439.3i	−0.137705	−	0.238512i
$220$	999.839	+	577.257i	0.0206578	+	0.0119268i
$221$	−5452.84	−	407.407i	−0.111645	−	0.00834150i
$222$	−79371.9	+	45825.4i	−1.61050	+	0.929823i
$223$		−	55370.3i		−	1.11344i	−0.830700	−	0.556721i	$-0.812059\pi$
$223$		−	55370.3i		−	1.11344i	0.830700	−	0.556721i	$-0.187941\pi$
$224$	−45646.8	+	17038.7i	−0.909734	+	0.339578i
$225$	−117765.			−2.32622
$226$	40228.5	−	23225.9i	0.787621	−	0.454733i
$227$	25056.1	−	43398.5i	0.486253	−	0.842215i	−0.513622	−	0.858017i	$-0.671697\pi$
$227$	25056.1	−	43398.5i	0.486253	−	0.842215i	0.999875	+	0.0158016i	$0.00503000\pi$
$228$	−54867.3	−	31677.7i	−1.05547	−	0.609373i
$229$	3747.72	−	2163.75i	0.0714654	−	0.0412606i	−0.463842	−	0.885918i	$-0.653529\pi$
$229$	3747.72	−	2163.75i	0.0714654	−	0.0412606i	0.535307	+	0.844658i	$0.320196\pi$
$230$			39487.5i			0.746456i
$231$	−12928.3	−	2170.61i	−0.242281	−	0.0406778i
$232$			54989.2i			1.02165i
$233$	48251.3	−	27857.9i	0.888786	−	0.513141i	0.0152411	−	0.999884i	$-0.495148\pi$
$233$	48251.3	−	27857.9i	0.888786	−	0.513141i	0.873545	+	0.486743i	$0.161815\pi$
$234$	−17387.4	−	10038.6i	−0.317544	−	0.183334i
$235$	−21743.2	−	12553.4i	−0.393720	−	0.227315i
$236$	17068.2	−	9854.33i	0.306453	−	0.176931i
$237$		−	162188.i		−	2.88750i
$238$	68152.1	+	16744.4i	1.20317	+	0.295608i
$239$	71978.0			1.26010			0.630048	−	0.776556i	$-0.283035\pi$
$239$	71978.0			1.26010			0.630048	+	0.776556i	$0.283035\pi$
$240$	23781.8	+	41191.2i	0.412878	+	0.715126i
$241$	28486.2	−	49339.5i	0.490456	−	0.849495i	−0.509484	−	0.860480i	$-0.670164\pi$
$241$	28486.2	−	49339.5i	0.490456	−	0.849495i	0.999940	+	0.0109857i	$0.00349694\pi$
$242$	35677.9	−	61795.9i	0.609212	−	1.05519i
$243$	95860.1	+	166035.i	1.62340	+	2.81181i
$244$	10776.7			0.181011
$245$	−15708.2	+	13625.3i	−0.261695	+	0.226994i
$246$	56095.1			0.926947
$247$	4075.87	+	7059.62i	0.0668077	+	0.115714i
$248$	−11013.5	+	19076.0i	−0.179070	+	0.310158i
$249$	94032.6	+	54289.7i	1.51663	+	0.875627i
$250$	25215.5	+	43674.6i	0.403449	+	0.698794i
$251$		−	88421.9i		−	1.40350i	−0.712423	−	0.701750i	$-0.752402\pi$
$251$		−	88421.9i		−	1.40350i	0.712423	−	0.701750i	$-0.247598\pi$
$252$	69268.3	+	57163.0i	1.09077	+	0.900147i
$253$	−14327.8			−0.223841
$254$	4188.79	+	7255.19i	0.0649263	+	0.112456i
$255$	3203.65	−	42878.4i	0.0492679	−	0.659414i
$256$	−40223.5	+	69669.2i	−0.613762	+	1.06307i
$257$	84096.8	−	48553.3i	1.27325	−	0.735110i	0.297650	−	0.954675i	$-0.403797\pi$
$257$	84096.8	−	48553.3i	1.27325	−	0.735110i	0.975598	+	0.219565i	$0.0704638\pi$
$258$	−101589.			−1.52619
$259$	−52021.5	−	8734.18i	−0.775503	−	0.130204i
$260$			1402.65i			0.0207493i
$261$	276549.	−	159666.i	4.05967	−	2.34385i
$262$	60862.7	−	105417.i	0.886643	−	1.53571i
$263$	−31053.5	+	53786.3i	−0.448951	+	0.777607i	−0.998318	−	0.0579747i	$-0.981536\pi$
$263$	−31053.5	+	53786.3i	−0.448951	+	0.777607i	0.549367	+	0.835581i	$0.314869\pi$
$264$	−8542.95	+	4932.27i	−0.122574	+	0.0707684i
$265$	−7793.60			−0.110980
$266$	−36586.9	−	98016.8i	−0.517086	−	1.38528i
$267$			180359.i			2.52997i
$268$	−13599.4	−	23554.8i	−0.189343	−	0.327952i
$269$	−42346.6	+	73346.5i	−0.585213	+	1.01362i	0.409636	+	0.912249i	$0.365656\pi$
$269$	−42346.6	+	73346.5i	−0.585213	+	1.01362i	−0.994849	+	0.101370i	$0.967678\pi$
$270$	49077.0	−	85003.9i	0.673210	−	1.16603i
$271$	−78926.1	+	45568.0i	−1.07469	+	0.620471i	−0.929458	−	0.368927i	$-0.879725\pi$
$271$	−78926.1	+	45568.0i	−1.07469	+	0.620471i	−0.145229	+	0.989398i	$0.546392\pi$
$272$	83231.0	−	40104.9i	1.12499	−	0.542075i
$273$	−5569.67	−	14921.2i	−0.0747316	−	0.200207i
$274$	−120717.			−1.60793
$275$	−7417.73	+	4282.63i	−0.0980857	+	0.0566298i
$276$	117164.	+	67644.6i	1.53807	+	0.888004i
$277$	−81205.9	−	46884.2i	−1.05835	−	0.611037i	−0.133372	−	0.991066i	$-0.542580\pi$
$277$	−81205.9	−	46884.2i	−1.05835	−	0.611037i	−0.924974	+	0.380030i	$0.875914\pi$
$278$	21469.5	+	37186.3i	0.277800	+	0.481164i
$279$	127915.			1.64328
$280$	−2590.85	+	15431.3i	−0.0330466	+	0.196828i
$281$	99830.1			1.26430			0.632148	−	0.774848i	$-0.282173\pi$
$281$	99830.1			1.26430			0.632148	+	0.774848i	$0.282173\pi$
$282$	−213740.	+	123403.i	−2.68775	+	1.55177i
$283$	−10156.1	+	17590.9i	−0.126811	+	0.219642i	−0.922439	−	0.386142i	$-0.873807\pi$
$283$	−10156.1	+	17590.9i	−0.126811	+	0.219642i	0.795629	+	0.605785i	$0.207141\pi$
$284$	−29295.3	−	16913.6i	−0.363213	−	0.209701i
$285$	−55513.3	+	32050.6i	−0.683451	+	0.394591i
$286$	−1460.26			−0.0178524
$287$	24901.3	+	20549.5i	0.302314	+	0.249481i
$288$	212911.			2.56692
$289$	−82593.7	−	12411.2i	−0.988897	−	0.148600i
$290$	−55434.0	−	32004.9i	−0.659144	−	0.380557i
$291$	−10504.5	+	18194.2i	−0.124047	+	0.214856i
$292$	3290.83	+	5699.88i	0.0385958	+	0.0668498i
$293$		−	7130.30i		−	0.0830563i	−0.999137	−	0.0415281i	$-0.986777\pi$
$293$		−	7130.30i		−	0.0830563i	0.999137	−	0.0415281i	$-0.0132226\pi$
$294$	38787.7	+	200697.i	0.448744	+	2.32192i
$295$		−	19940.7i		−	0.229138i
$296$	−34375.5	+	19846.7i	−0.392342	+	0.226519i
$297$	30843.2	+	17807.3i	0.349660	+	0.201876i
$298$	42289.6	−	73247.7i	0.476213	−	0.824825i
$299$	−8703.64	−	15075.1i	−0.0973551	−	0.168624i
$300$	80876.7			0.898630
$301$	−45096.6	−	37215.5i	−0.497749	−	0.410763i
$302$	157717.			1.72928
$303$	−15988.0	+	9230.70i	−0.174145	+	0.100542i
$304$	−119281.	−	68867.0i	−1.29070	−	0.745185i
$305$	5451.77	−	9442.74i	0.0586054	−	0.101508i
$306$	−253420.	−	172696.i	−2.70644	−	1.84433i
$307$		−	115210.i		−	1.22240i	−0.791474	−	0.611202i	$-0.790686\pi$
$307$		−	115210.i		−	1.22240i	0.791474	−	0.611202i	$-0.209314\pi$
$308$	6441.83	+	1081.55i	0.0679059	+	0.0114011i
$309$		−	239228.i		−	2.50550i
$310$	−12820.2	−	22205.2i	−0.133405	−	0.231064i
$311$	23256.3	−	40281.0i	0.240447	−	0.416466i	−0.720395	−	0.693564i	$-0.756039\pi$
$311$	23256.3	−	40281.0i	0.240447	−	0.416466i	0.960842	+	0.277098i	$0.0893727\pi$
$312$	−10379.1	−	5992.36i	−0.106623	−	0.0615586i
$313$	−14037.9	−	24314.3i	−0.143289	−	0.248184i	0.785444	−	0.618932i	$-0.212434\pi$
$313$	−14037.9	−	24314.3i	−0.143289	−	0.248184i	−0.928733	+	0.370749i	$0.879101\pi$
$314$		−	118600.i		−	1.20289i
$315$	85129.4	−	31776.4i	0.857943	−	0.320246i
$316$			80813.7i			0.809302i
$317$	−105901.	+	61142.0i	−1.05386	+	0.608445i	−0.923727	−	0.383052i	$-0.874873\pi$
$317$	−105901.	+	61142.0i	−1.05386	+	0.608445i	−0.130130	+	0.991497i	$0.541540\pi$
$318$	−38306.4	+	66348.6i	−0.378806	+	0.656111i
$319$	11612.8	−	20113.9i	0.114118	−	0.197658i
$320$	810.597	+	1404.00i	0.00791599	+	0.0137109i
$321$			161019.i			1.56267i
$322$	78127.9	+	209306.i	0.753519	+	2.01869i
$323$	54049.3	+	112170.i	0.518066	+	1.07516i
$324$	−93913.9	−	162664.i	−0.894622	−	1.54953i
$325$	−9012.01	−	5203.09i	−0.0853209	−	0.0492600i
$326$	36537.7	+	21095.1i	0.343800	+	0.198493i
$327$	163703.	−	94513.8i	1.53095	−	0.883893i
$328$	24294.4			0.225818
$329$	−140089.	−	23520.2i	−1.29423	−	0.217295i
$330$		−	11482.7i		−	0.105443i
$331$	77519.7	+	134268.i	0.707548	+	1.22551i	0.965764	+	0.259422i	$0.0835321\pi$
$331$	77519.7	+	134268.i	0.707548	+	1.22551i	−0.258216	+	0.966087i	$0.583135\pi$
$332$	−46853.8	−	27051.1i	−0.425078	−	0.245419i
$333$	199624.	+	115253.i	1.80021	+	1.03935i
$334$	−85954.0	−	148877.i	−0.770501	−	1.33455i
$335$	−27519.0			−0.245213
$336$	207555.	+	171283.i	1.83846	+	1.51717i
$337$		−	78192.1i		−	0.688499i	−0.938878	−	0.344249i	$-0.888133\pi$
$337$		−	78192.1i		−	0.688499i	0.938878	−	0.344249i	$-0.111867\pi$
$338$	69884.1	+	121043.i	0.611709	+	1.05951i
$339$	−139451.	−	80511.9i	−1.21345	−	0.700585i
$340$	−1596.29	+	21365.1i	−0.0138087	+	0.184819i
$341$	8057.04	−	4651.73i	0.0692894	−	0.0400042i
$342$			457181.i			3.90873i
$343$	−56304.0	+	103301.i	−0.478576	+	0.878046i
$344$	−43997.5			−0.371802
$345$	118543.	−	68441.1i	0.995954	−	0.575014i
$346$	−17305.2	+	29973.5i	−0.144552	+	0.250372i
$347$	15803.7	+	9124.27i	0.131250	+	0.0757773i	0.564187	−	0.825647i	$-0.309190\pi$
$347$	15803.7	+	9124.27i	0.131250	+	0.0757773i	−0.432937	+	0.901424i	$0.642523\pi$
$348$	−189924.	+	109653.i	−1.56827	+	0.905442i
$349$		−	48545.1i		−	0.398561i	−0.979942	−	0.199281i	$-0.936139\pi$
$349$		−	48545.1i		−	0.398561i	0.979942	−	0.199281i	$-0.0638605\pi$
$350$	103010.	+	85008.1i	0.840899	+	0.693943i
$351$			43269.2i			0.351208i
$352$	13410.8	−	7742.71i	0.108235	−	0.0624896i
$353$	−158412.	−	91459.0i	−1.27127	−	0.733968i	−0.296043	−	0.955175i	$-0.595667\pi$
$353$	−158412.	−	91459.0i	−1.27127	−	0.733968i	−0.975227	+	0.221207i	$0.929000\pi$
$354$	−169760.	−	98010.7i	−1.35465	−	0.782108i
$355$	−29640.2	+	17112.8i	−0.235193	+	0.135789i
$356$		−	89867.8i		−	0.709094i
$357$	−67855.8	−	233618.i	−0.532416	−	1.83303i
$358$	−90438.2			−0.705644
$359$	15539.6	+	26915.4i	0.120573	+	0.208839i	0.919994	−	0.391933i	$-0.128193\pi$
$359$	15539.6	+	26915.4i	0.120573	+	0.208839i	−0.799421	+	0.600772i	$0.794860\pi$
$360$	34187.9	−	59215.2i	0.263796	−	0.456908i
$361$	27651.4	−	47893.7i	0.212179	−	0.367505i
$362$	93499.0	+	161945.i	0.713493	+	1.23581i
$363$	−247352.			−1.87717
$364$	2775.21	+	7434.83i	0.0209456	+	0.0561136i
$365$	6659.15			0.0499842
$366$	−53592.0	−	92824.1i	−0.400072	−	0.692945i
$367$	27342.6	−	47358.8i	0.203006	−	0.351616i	−0.746490	−	0.665397i	$-0.768262\pi$
$367$	27342.6	−	47358.8i	0.203006	−	0.351616i	0.949495	+	0.313781i	$0.101596\pi$
$368$	254714.	+	147059.i	1.88086	+	1.08591i
$369$	−70540.9	−	122180.i	−0.518070	−	0.897323i
$370$		−	46204.7i		−	0.337507i
$371$	−41310.4	+	15420.0i	−0.300131	+	0.112031i
$372$	−87847.2			−0.634808
$373$	−14482.4	−	25084.3i	−0.104093	−	0.180295i	0.809274	−	0.587431i	$-0.199861\pi$
$373$	−14482.4	−	25084.3i	−0.104093	−	0.180295i	−0.913367	+	0.407136i	$0.866527\pi$
$374$	−22242.6	−	1661.85i	−0.159016	−	0.0118809i
$375$	87408.8	−	151396.i	0.621574	−	1.07660i
$376$	−92569.5	+	53445.0i	−0.654775	+	0.378035i
$377$	28217.4			0.198534
$378$	91951.1	−	547668.i	0.643536	−	3.83296i
$379$			230122.i			1.60206i	0.598623	+	0.801031i	$0.295715\pi$
$379$			230122.i			1.60206i	−0.598623	+	0.801031i	$0.704285\pi$
$380$	27660.8	−	15969.9i	0.191556	−	0.110595i
$381$	14520.3	−	25149.9i	0.100029	−	0.173255i
$382$	−81718.2	+	141540.i	−0.560005	+	0.969957i
$383$	148037.	−	85469.5i	1.00919	−	0.582658i	0.0982373	−	0.995163i	$-0.468680\pi$
$383$	148037.	−	85469.5i	1.00919	−	0.582658i	0.910955	+	0.412505i	$0.135346\pi$
$384$	289249.			1.96160
$385$	4206.52	−	5097.33i	0.0283793	−	0.0343891i
$386$		−	81718.1i		−	0.548458i
$387$	127751.	+	221270.i	0.852984	+	1.47741i
$388$	5234.08	−	9065.69i	0.0347678	−	0.0602195i
$389$	−139946.	+	242393.i	−0.924827	+	1.60185i	−0.132989	+	0.991118i	$0.542457\pi$
$389$	−139946.	+	242393.i	−0.924827	+	1.60185i	−0.791839	+	0.610730i	$0.790876\pi$
$390$	12081.7	−	6975.36i	0.0794325	−	0.0458603i
$391$	−115417.	−	239529.i	−0.754947	−	1.56677i
$392$	16798.7	+	86920.8i	0.109321	+	0.565655i
$393$	−421957.			−2.73201
$394$	92479.9	−	53393.3i	0.595737	−	0.343949i
$395$	70810.7	+	40882.6i	0.453842	+	0.262026i
$396$	−24719.4	−	14271.8i	−0.157633	−	0.0910097i
$397$	95773.6	+	165885.i	0.607666	+	1.05251i	0.991624	+	0.129158i	$0.0412273\pi$
$397$	95773.6	+	165885.i	0.607666	+	1.05251i	−0.383958	+	0.923350i	$0.625439\pi$
$398$	86739.0			0.547581
$399$	−230838.	+	279722.i	−1.44998	+	1.75703i
$400$	175825.			1.09891
$401$	61936.6	−	35759.1i	0.385175	−	0.222381i	−0.294892	−	0.955531i	$-0.595284\pi$
$401$	61936.6	−	35759.1i	0.385175	−	0.222381i	0.680068	+	0.733149i	$0.261950\pi$
$402$	−135259.	+	234275.i	−0.836978	+	1.44969i
$403$	9788.73	+	5651.52i	0.0602721	+	0.0347981i
$404$	7966.40	−	4599.40i	0.0488089	−	0.0281798i
$405$	−190039.			−1.15860
$406$	−357154.	−	59964.6i	−2.16672	−	0.363783i
$407$	16765.1			0.101209
$408$	−151274.	−	103087.i	−0.908748	−	0.619276i
$409$	−148727.	−	85867.5i	−0.889084	−	0.513313i	−0.0154414	−	0.999881i	$-0.504915\pi$
$409$	−148727.	−	85867.5i	−0.889084	−	0.513313i	−0.873643	+	0.486568i	$0.838249\pi$
$410$	−14139.9	+	24491.0i	−0.0841158	+	0.145693i
$411$	209231.	+	362399.i	1.23863	+	2.14537i
$412$			119200.i			0.702237i
$413$	−39453.6	−	105697.i	−0.231306	−	0.619672i
$414$		−	976267.i		−	5.69597i
$415$	−47405.5	+	27369.6i	−0.275253	+	0.158918i
$416$	16293.1	+	9406.83i	0.0941494	+	0.0543572i
$417$	74423.3	−	128905.i	0.427993	−	0.741306i
$418$	16625.8	+	28796.8i	0.0951547	+	0.164813i
$419$	218342.			1.24368			0.621841	−	0.783144i	$-0.286385\pi$
$419$	218342.			1.24368			0.621841	+	0.783144i	$0.286385\pi$
$420$	−58463.8	+	21822.9i	−0.331428	+	0.123713i
$421$	245124.			1.38300			0.691498	−	0.722378i	$-0.256951\pi$
$421$	245124.			1.38300			0.691498	+	0.722378i	$0.256951\pi$
$422$	123408.	−	71249.5i	0.692975	−	0.400089i
$423$	537566.	+	310364.i	3.00436	+	1.73457i
$424$	−16590.2	+	28735.1i	−0.0922828	+	0.159838i
$425$	−131349.	−	89509.2i	−0.727192	−	0.495553i
$426$			336444.i			1.85393i
$427$	10214.5	−	60838.3i	0.0560222	−	0.333673i
$428$		−	80231.4i		−	0.437983i
$429$	2530.97	+	4383.77i	0.0137522	+	0.0238195i
$430$	25607.5	−	44353.5i	0.138494	−	0.239878i
$431$	−140780.	−	81279.2i	−0.757854	−	0.437547i	0.0706709	−	0.997500i	$-0.477486\pi$
$431$	−140780.	−	81279.2i	−0.757854	−	0.437547i	−0.828525	+	0.559953i	$0.810819\pi$
$432$	−365544.	−	633140.i	−1.95872	−	3.39260i
$433$		−	20423.6i		−	0.108932i	−0.998516	−	0.0544661i	$-0.982654\pi$
$433$		−	20423.6i		−	0.108932i	0.998516	−	0.0544661i	$-0.0173457\pi$
$434$	−111888.	−	92334.6i	−0.594025	−	0.490213i
$435$			221887.i			1.17261i
$436$	−81568.5	+	47093.6i	−0.429091	+	0.247736i
$437$	−198191.	+	343277.i	−1.03782	+	1.79755i
$438$	32730.4	−	56690.7i	0.170610	−	0.295504i
$439$	150125.	+	260024.i	0.778974	+	1.34922i	0.932534	+	0.361083i	$0.117593\pi$
$439$	150125.	+	260024.i	0.778974	+	1.34922i	−0.153559	+	0.988139i	$0.549074\pi$
$440$		−	4973.10i		−	0.0256875i
$441$	388361.	−	336865.i	1.99691	−	1.73212i
$442$	−11763.0	−	24412.2i	−0.0602109	−	0.124958i
$443$	50601.8	+	87644.9i	0.257845	+	0.446601i	0.965664	−	0.259793i	$-0.0836543\pi$
$443$	50601.8	+	87644.9i	0.257845	+	0.446601i	−0.707819	+	0.706393i	$0.750321\pi$
$444$	−137095.	−	79151.6i	−0.695432	−	0.401508i
$445$	−78744.1	−	45462.9i	−0.397647	−	0.229582i
$446$	237641.	−	137202.i	1.19468	−	0.689748i
$447$	−293191.			−1.46736
$448$	7074.48	+	5838.14i	0.0352483	+	0.0290883i
$449$			86256.2i			0.427856i	0.976849	+	0.213928i	$0.0686258\pi$
$449$			86256.2i			0.427856i	−0.976849	+	0.213928i	$0.931374\pi$
$450$	−291809.	−	505428.i	−1.44103	−	2.49594i
$451$	−8886.40	−	5130.57i	−0.0436891	−	0.0252239i
$452$	69484.4	+	40116.9i	0.340103	+	0.196359i
$453$	−273360.	−	473473.i	−1.33211	−	2.30727i
$454$	248346.			1.20488
$455$	7918.51	+	1329.48i	0.0382491	+	0.00642185i
$456$			272905.i			1.31245i
$457$	−47826.4	−	82837.8i	−0.229000	−	0.396640i	0.728512	−	0.685033i	$-0.240212\pi$
$457$	−47826.4	−	82837.8i	−0.229000	−	0.396640i	−0.957512	+	0.288393i	$0.906879\pi$
$458$	18572.9	+	10723.1i	0.0885419	+	0.0511197i
$459$	−49242.5	+	659074.i	−0.233730	+	3.12830i
$460$	−59066.9	+	34102.3i	−0.279144	+	0.161164i
$461$			73108.0i			0.344004i	0.985097	+	0.172002i	$0.0550235\pi$
$461$			73108.0i			0.344004i	−0.985097	+	0.172002i	$0.944976\pi$
$462$	−22719.1	−	60864.9i	−0.106441	−	0.285156i
$463$	−359662.			−1.67777			−0.838884	−	0.544310i	$-0.816792\pi$
$463$	−359662.			−1.67777			−0.838884	+	0.544310i	$0.816792\pi$
$464$	−412894.	+	238384.i	−1.91779	+	1.10724i
$465$	−44440.8	+	76973.7i	−0.205530	+	0.355989i
$466$	239123.	+	138058.i	1.10116	+	0.635755i
$467$	97851.8	−	56494.7i	0.448678	−	0.259044i	−0.258594	−	0.965986i	$-0.583259\pi$
$467$	97851.8	−	56494.7i	0.448678	−	0.259044i	0.707272	+	0.706942i	$0.249926\pi$
$468$		−	34678.4i		−	0.158331i
$469$	−145866.	+	54447.7i	−0.663145	+	0.247533i
$470$		−	124425.i		−	0.563262i
$471$	−356043.	+	205562.i	−1.60495	+	0.926617i
$472$	−73521.7	−	42447.8i	−0.330013	−	0.190533i
$473$	16093.4	+	9291.53i	0.0719326	+	0.0415303i
$474$	696084.	−	401884.i	3.09817	−	1.78873i
$475$			236960.i			1.05024i
$476$	33810.7	+	116405.i	0.149224	+	0.513758i
$477$	192684.			0.846857
$478$	178354.	+	308918.i	0.780597	+	1.35203i
$479$	−58094.5	+	100623.i	−0.253200	+	0.438555i	−0.964405	−	0.264429i	$-0.914816\pi$
$479$	−58094.5	+	100623.i	−0.253200	+	0.438555i	0.711205	+	0.702985i	$0.248150\pi$
$480$	−73970.6	+	128121.i	−0.321053	+	0.556080i
$481$	10184.2	+	17639.6i	0.0440187	+	0.0762426i
$482$	282343.			1.21530
$483$	492932.	−	597319.i	2.11297	−	2.56042i
$484$	123249.			0.526129
$485$	−5295.70	−	9172.43i	−0.0225133	−	0.0389943i
$486$	−475062.	+	822832.i	−2.01131	+	3.48368i
$487$	96604.1	+	55774.4i	0.407322	+	0.235167i	0.689638	−	0.724154i	$-0.257770\pi$
$487$	96604.1	+	55774.4i	0.407322	+	0.235167i	−0.282317	+	0.959321i	$0.591103\pi$
$488$	−23210.3	−	40201.5i	−0.0974635	−	0.168812i
$489$		−	146251.i		−	0.611617i
$490$	−97401.1	−	33655.1i	−0.405669	−	0.140171i
$491$	−394200.			−1.63514			−0.817568	−	0.575832i	$-0.804678\pi$
$491$	−394200.			−1.63514			−0.817568	+	0.575832i	$0.804678\pi$
$492$	48445.0	+	83909.1i	0.200133	+	0.346640i
$493$	429806.	+	32112.8i	1.76839	+	0.132125i
$494$	−20199.2	+	34986.0i	−0.0827713	+	0.143364i
$495$	−25010.5	+	14439.8i	−0.102073	+	0.0589320i
$496$	−190979.			−0.776288
$497$	−123251.	+	149352.i	−0.498974	+	0.604640i
$498$			538097.i			2.16971i
$499$	214700.	−	123957.i	0.862247	−	0.497819i	−0.00251706	−	0.999997i	$-0.500801\pi$
$499$	214700.	−	123957.i	0.862247	−	0.497819i	0.864764	+	0.502178i	$0.167468\pi$
$500$	−43553.4	+	75436.7i	−0.174214	+	0.301747i
$501$	−297957.	+	516076.i	−1.18707	+	2.05607i
$502$	379493.	−	219100.i	1.50590	−	0.869431i
$503$	−372189.			−1.47105			−0.735525	−	0.677497i	$-0.763065\pi$
$503$	−372189.			−1.47105			−0.735525	+	0.677497i	$0.763065\pi$
$504$	64054.8	−	381516.i	0.252168	−	1.50194i
$505$		−	9307.11i		−	0.0364949i
$506$	−35502.8	−	61492.7i	−0.138663	−	0.240172i
$507$	242251.	−	419591.i	0.942431	−	1.63234i
$508$	−7235.06	+	12531.5i	−0.0280359	+	0.0485596i
$509$	−311404.	+	179789.i	−1.20196	+	0.693949i	−0.960990	−	0.276584i	$-0.910797\pi$
$509$	−311404.	+	179789.i	−1.20196	+	0.693949i	−0.240966	+	0.970534i	$0.577464\pi$
$510$	191966.	−	92498.7i	0.738046	−	0.355627i
$511$	35297.2	−	13175.4i	0.135176	−	0.0504572i
$512$	−129282.			−0.493171
$513$	853282.	−	492643.i	3.24233	−	1.87196i
$514$	416766.	+	240620.i	1.57749	+	0.910763i
$515$	104446.	+	60302.0i	0.393802	+	0.227362i
$516$	−87734.5	−	151961.i	−0.329512	−	0.570731i
$517$	45146.7			0.168906
$518$	−91418.2	−	244911.i	−0.340701	−	0.912742i
$519$	119976.			0.445410
$520$	5232.49	−	3020.98i	0.0193509	−	0.0111723i
$521$	−29451.7	+	51011.8i	−0.108501	+	0.187930i	−0.915163	−	0.403083i	$-0.867938\pi$
$521$	−29451.7	+	51011.8i	−0.108501	+	0.187930i	0.806662	+	0.591013i	$0.201272\pi$
$522$	1.37052e6	+	791270.i	5.02972	+	2.90391i
$523$	366422.	−	211554.i	1.33961	−	0.773424i	0.352861	−	0.935676i	$-0.385209\pi$
$523$	366422.	−	211554.i	1.33961	−	0.773424i	0.986749	+	0.162252i	$0.0518756\pi$
$524$	210249.			0.765724
$525$	76657.7	−	456580.i	0.278123	−	1.65653i
$526$	−307790.			−1.11245
$527$	142670.	+	97223.7i	0.513701	+	0.350067i
$528$	−74069.2	−	42763.9i	−0.265687	−	0.153394i
$529$	283297.	−	490686.i	1.01235	−	1.75344i
$530$	−19311.7	−	33448.9i	−0.0687495	−	0.119078i
$531$			493003.i			1.74848i
$532$	115020.	−	139378.i	0.406396	−	0.492458i
$533$		−	12466.5i		−	0.0438825i
$534$	−774071.	+	446910.i	−2.71455	+	1.56725i
$535$	−70300.5	−	40588.0i	−0.245613	−	0.141805i
$536$	−58579.7	+	101463.i	−0.203900	+	0.353166i
$537$	156750.	+	271500.i	0.543576	+	0.941501i
$538$	−419722.			−1.45010
$539$	12211.6	−	35341.4i	0.0420333	−	0.121648i
$540$	169536.			0.581399
$541$	−24681.6	+	14250.0i	−0.0843295	+	0.0486877i	−0.541572	−	0.840655i	$-0.682171\pi$
$541$	−24681.6	+	14250.0i	−0.0843295	+	0.0486877i	0.457242	+	0.889342i	$0.348837\pi$
$542$	−391141.	−	225825.i	−1.33148	−	0.768731i
$543$	324111.	−	561377.i	1.09924	−	1.90395i
$544$	237470.	+	161827.i	0.802438	+	0.546830i
$545$			95296.2i			0.320835i
$546$	50238.5	−	60877.4i	0.168520	−	0.204207i
$547$		−	212518.i		−	0.710268i	−0.934815	−	0.355134i	$-0.884435\pi$
$547$		−	212518.i		−	0.710268i	0.934815	−	0.355134i	$-0.115565\pi$
$548$	−104254.	−	180573.i	−0.347161	−	0.601301i
$549$	−134786.	+	233457.i	−0.447199	+	0.774572i
$550$	−36760.7	−	21223.8i	−0.121523	−	0.0701614i
$551$	−321270.	−	556456.i	−1.05820	−	1.83285i
$552$		−	582762.i		−	1.91255i
$553$	456224.	+	76598.0i	1.49186	+	0.250476i
$554$		−	464697.i		−	1.51408i
$555$	−138709.	+	80083.6i	−0.450317	+	0.259990i
$556$	−37083.1	+	64229.8i	−0.119957	+	0.207772i
$557$	104986.	−	181840.i	0.338391	−	0.586111i	−0.645739	−	0.763558i	$-0.723451\pi$
$557$	104986.	−	181840.i	0.338391	−	0.586111i	0.984130	+	0.177447i	$0.0567839\pi$
$558$	316959.	+	548989.i	1.01797	+	1.76317i
$559$			22577.1i			0.0722511i
$560$	−127100.	+	47442.8i	−0.405293	+	0.151285i
$561$	33562.6	+	69653.6i	0.106642	+	0.221319i
$562$	247368.	+	428455.i	0.783198	+	1.35654i
$563$	−238804.	−	137873.i	−0.753398	−	0.434974i	0.0735225	−	0.997294i	$-0.476576\pi$
$563$	−238804.	−	137873.i	−0.753398	−	0.434974i	−0.826920	+	0.562319i	$0.809909\pi$
$564$	−369181.	−	213147.i	−1.16060	−	0.670071i
$565$	70302.6	−	40589.2i	0.220229	−	0.127149i
$566$	−100663.			−0.314223
$567$	−1.00731e6	+	376001.i	−3.13327	+	1.16956i
$568$			145712.i			0.451646i
$569$	81229.1	+	140693.i	0.250892	+	0.434558i	0.963772	−	0.266729i	$-0.0859428\pi$
$569$	81229.1	+	140693.i	0.250892	+	0.434558i	−0.712880	+	0.701286i	$0.752609\pi$
$570$	−275112.	−	158836.i	−0.846760	−	0.488877i
$571$	117949.	+	68098.2i	0.361763	+	0.208864i	0.669854	−	0.742493i	$-0.266357\pi$
$571$	117949.	+	68098.2i	0.361763	+	0.208864i	−0.308091	+	0.951357i	$0.599690\pi$
$572$	−1261.11	−	2184.31i	−0.00385444	−	0.00667609i
$573$	566546.			1.72554
$574$	−26492.6	+	157792.i	−0.0804082	+	0.478918i
$575$		−	506005.i		−	1.53045i
$576$	−20040.7	−	34711.6i	−0.0604044	−	0.104623i
$577$	−369277.	−	213202.i	−1.10918	−	0.640384i	−0.170561	−	0.985347i	$-0.554558\pi$
$577$	−369277.	−	213202.i	−1.10918	−	0.640384i	−0.938616	+	0.344963i	$0.887891\pi$
$578$	−151392.	−	385233.i	−0.453154	−	1.15310i
$579$	−245321.	+	141636.i	−0.731776	+	0.422491i
$580$		−	110560.i		−	0.328657i
$581$	−197123.	+	238868.i	−0.583963	+	0.707628i
$582$	−104116.			−0.307376
$583$	12136.7	−	7007.15i	0.0357079	−	0.0206160i
$584$	14175.3	−	24552.4i	0.0415631	−	0.0719893i
$585$	−30386.0	−	17543.3i	−0.0887894	−	0.0512626i
$586$	30602.1	−	17668.1i	0.0891160	−	0.0514512i
$587$			467357.i			1.35635i	0.734900	+	0.678176i	$0.237229\pi$
$587$			467357.i			1.35635i	−0.734900	+	0.678176i	$0.762771\pi$
$588$	−266713.	+	231347.i	−0.771417	+	0.669127i
$589$		−	257382.i		−	0.741905i
$590$	85582.4	−	49411.0i	0.245856	−	0.141945i
$591$	−320578.	−	185086.i	−0.917823	−	0.529905i
$592$	−298043.	−	172075.i	−0.850423	−	0.490992i
$593$	−261149.	+	150774.i	−0.742640	+	0.428763i	−0.823028	−	0.568000i	$-0.807717\pi$
$593$	−261149.	+	150774.i	−0.742640	+	0.428763i	0.0803885	+	0.996764i	$0.474384\pi$
$594$			176499.i			0.500228i
$595$	119101.	+	29262.3i	0.336420	+	0.0826559i
$596$	146089.			0.411268
$597$	−150339.	−	260394.i	−0.421815	−	0.730606i
$598$	43133.4	−	74709.3i	0.120618	−	0.208916i
$599$	85085.7	−	147373.i	0.237139	−	0.410737i	−0.722753	−	0.691106i	$-0.757124\pi$
$599$	85085.7	−	147373.i	0.237139	−	0.410737i	0.959892	+	0.280369i	$0.0904570\pi$
$600$	−174189.	−	301705.i	−0.483859	−	0.838069i
$601$	−633204.			−1.75305			−0.876526	−	0.481355i	$-0.840145\pi$
$601$	−633204.			−1.75305			−0.876526	+	0.481355i	$0.840145\pi$
$602$	47978.4	−	285763.i	0.132389	−	0.788522i
$603$	680365.			1.87114
$604$	136208.	+	235919.i	0.373360	+	0.646678i
$605$	62350.0	−	107993.i	0.170344	−	0.295044i
$606$	−79233.4	−	45745.4i	−0.215756	−	0.124567i
$607$	104237.	+	180543.i	0.282907	+	0.490008i	0.972099	−	0.234570i	$-0.0753680\pi$
$607$	104237.	+	180543.i	0.282907	+	0.490008i	−0.689193	+	0.724578i	$0.742035\pi$
$608$		−	428407.i		−	1.15891i
$609$	439015.	+	1.17613e6i	1.18371	+	3.17117i
$610$	54035.6			0.145218
$611$	27425.0	+	47501.5i	0.0734623	+	0.127240i
$612$	39465.7	−	528219.i	0.105370	−	1.41030i
$613$	−64396.2	+	111537.i	−0.171372	+	0.296824i	−0.938900	−	0.344191i	$-0.888153\pi$
$613$	−64396.2	+	111537.i	−0.171372	+	0.296824i	0.767528	+	0.641015i	$0.221487\pi$
$614$	494465.	−	285479.i	1.31159	−	0.757248i
$615$	98030.7			0.259186
$616$	−9839.51	−	26360.2i	−0.0259306	−	0.0694683i
$617$		−	750060.i		−	1.97027i	−0.171783	−	0.985135i	$-0.554953\pi$
$617$		−	750060.i		−	1.97027i	0.171783	−	0.985135i	$-0.445047\pi$
$618$	1.02673e6	−	592781.i	2.68830	−	1.55209i
$619$	58118.2	−	100664.i	0.151681	−	0.262719i	−0.780165	−	0.625574i	$-0.784865\pi$
$619$	58118.2	−	100664.i	0.151681	−	0.262719i	0.931845	+	0.362855i	$0.118198\pi$
$620$	22143.6	−	38353.8i	0.0576056	−	0.0997759i
$621$	−1.82210e6	+	1.05199e6i	−4.72487	+	2.72790i
$622$	230506.			0.595802
$623$	−507338.	−	85179.7i	−1.30714	−	0.219462i
$624$		−	103910.i		−	0.266863i
$625$	−127807.	−	221368.i	−0.327185	−	0.566701i
$626$	69568.7	−	120497.i	0.177527	−	0.307486i
$627$	57632.8	−	99822.9i	0.146600	−	0.253919i
$628$	177406.	−	102426.i	0.449832	−	0.259711i
$629$	135051.	+	280275.i	0.341346	+	0.708407i
$630$	347321.	+	286623.i	0.875084	+	0.722154i
$631$	671659.			1.68690			0.843451	−	0.537206i	$-0.180520\pi$
$631$	671659.			1.68690			0.843451	+	0.537206i	$0.180520\pi$
$632$	301469.	−	174053.i	0.754760	−	0.435761i
$633$	−427789.	−	246984.i	−1.06763	−	0.616398i
$634$	−524823.	−	303007.i	−1.30567	−	0.753831i
$635$	7320.24	+	12679.0i	0.0181542	+	0.0314441i
$636$	−132329.			−0.327145
$637$	44602.9	−	8620.15i	0.109922	−	0.0212440i
$638$	115101.			0.282773
$639$	732807.	−	423086.i	1.79468	−	1.03616i
$640$	−72910.9	+	126285.i	−0.178005	+	0.308314i
$641$	424396.	+	245025.i	1.03289	+	0.596340i	0.917812	−	0.397016i	$-0.129954\pi$
$641$	424396.	+	245025.i	1.03289	+	0.596340i	0.115080	+	0.993356i	$0.463288\pi$
$642$	−691069.	+	398989.i	−1.67668	+	0.968034i
$643$	240195.			0.580954			0.290477	−	0.956882i	$-0.406186\pi$
$643$	240195.			0.580954			0.290477	+	0.956882i	$0.406186\pi$
$644$	−245614.	+	297627.i	−0.592218	+	0.717631i
$645$	−177535.			−0.426741
$646$	−347488.	+	509917.i	−0.832674	+	1.22190i
$647$	−259505.	−	149825.i	−0.619922	−	0.357912i	0.156917	−	0.987612i	$-0.449845\pi$
$647$	−259505.	−	149825.i	−0.619922	−	0.357912i	−0.776839	+	0.629700i	$0.783178\pi$
$648$	−404536.	+	700678.i	−0.963402	+	1.66866i
$649$	17928.5	+	31053.1i	0.0425652	+	0.0737251i
$650$		−	51570.8i		−	0.122061i
$651$	−83264.6	+	495931.i	−0.196471	+	1.17020i
$652$			72872.6i			0.171423i
$653$	−331980.	+	191669.i	−0.778548	+	0.449495i	−0.835916	−	0.548858i	$-0.815063\pi$
$653$	−331980.	+	191669.i	−0.778548	+	0.449495i	0.0573672	+	0.998353i	$0.481729\pi$
$654$	811276.	+	468391.i	1.89676	+	1.09510i
$655$	106362.	−	184225.i	0.247917	−	0.429404i
$656$	105319.	+	182418.i	0.244737	+	0.423896i
$657$	−164637.			−0.381414
$658$	−246180.	−	659518.i	−0.568591	−	1.52326i
$659$	−574078.			−1.32191			−0.660953	−	0.750428i	$-0.729848\pi$
$659$	−574078.			−1.32191			−0.660953	+	0.750428i	$0.729848\pi$
$660$	17176.3	−	9916.75i	0.0394314	−	0.0227657i
$661$	108319.	+	62538.3i	0.247916	+	0.143134i	0.618809	−	0.785541i	$-0.287615\pi$
$661$	108319.	+	62538.3i	0.247916	+	0.143134i	−0.370894	+	0.928675i	$0.620949\pi$
$662$	−384171.	+	665404.i	−0.876615	+	1.51834i
$663$	−52898.6	+	77625.3i	−0.120342	+	0.176594i
$664$			233046.i			0.528574i
$665$	−63938.6	−	171292.i	−0.144584	−	0.387342i
$666$			1.14234e6i			2.57541i
$667$	686041.	+	1.18826e6i	1.54205	+	2.67091i
$668$	148463.	−	257146.i	0.332711	−	0.576272i
$669$	−823773.	−	475606.i	−1.84058	−	1.06266i
$670$	−68189.3	−	118107.i	−0.151903	−	0.263104i
$671$			19606.5i			0.0435467i
$672$	−138592.	+	825466.i	−0.306902	+	1.82793i
$673$			825655.i			1.82292i	0.411385	+	0.911462i	$0.365045\pi$
$673$			825655.i			1.82292i	−0.411385	+	0.911462i	$0.634955\pi$
$674$	335588.	−	193752.i	0.738732	−	0.426507i
$675$	−628887.	+	1.08926e6i	−1.38027	+	2.39070i
$676$	−120707.	+	209070.i	−0.264143	+	0.457509i
$677$	41382.1	+	71675.8i	0.0902890	+	0.156385i	0.907633	−	0.419765i	$-0.137888\pi$
$677$	41382.1	+	71675.8i	0.0902890	+	0.156385i	−0.817344	+	0.576150i	$0.804554\pi$
$678$		−	798000.i		−	1.73598i
$679$	−46218.2	−	38141.1i	−0.100247	−	0.0827282i
$680$	83139.1	−	40060.6i	0.179799	−	0.0866362i
$681$	−430441.	−	745546.i	−0.928153	−	1.60761i
$682$	39929.0	+	23053.0i	0.0858459	+	0.0495632i
$683$	378056.	+	218271.i	0.810429	+	0.467901i	0.847105	−	0.531426i	$-0.178344\pi$
$683$	378056.	+	218271.i	0.810429	+	0.467901i	−0.0366758	+	0.999327i	$0.511677\pi$
$684$	−683868.	+	394832.i	−1.46171	+	0.843917i
$685$	−210963.			−0.449599
$686$	−582868.	+	14321.9i	−1.23857	+	0.0304335i
$687$		−	74342.3i		−	0.157515i
$688$	−190734.	−	330361.i	−0.402950	−	0.697931i
$689$	14745.3	+	8513.18i	0.0310609	+	0.0179330i
$690$	587476.	+	339180.i	1.23393	+	0.712413i
$691$	−18916.5	−	32764.4i	−0.0396174	−	0.0686193i	0.845537	−	0.533917i	$-0.179281\pi$
$691$	−18916.5	−	32764.4i	−0.0396174	−	0.0686193i	−0.885154	+	0.465298i	$0.845947\pi$
$692$	−59780.7			−0.124839
$693$	−104000.	+	126023.i	−0.216553	+	0.262413i
$694$			90436.0i			0.187768i
$695$	37519.7	+	64986.0i	0.0776765	+	0.134540i
$696$	818102.	+	472332.i	1.68884	+	0.975054i
$697$	14187.5	−	189890.i	0.0292040	−	0.390873i
$698$	208348.	−	120290.i	0.427640	−	0.246898i
$699$		−	957146.i		−	1.95895i
$700$	−38196.4	+	227501.i	−0.0779519	+	0.464288i
$701$	133045.			0.270747			0.135374	−	0.990795i	$-0.456777\pi$
$701$	133045.			0.270747			0.135374	+	0.990795i	$0.456777\pi$
$702$	−185705.	+	107217.i	−0.376832	+	0.217564i
$703$	231905.	−	401672.i	0.469245	−	0.812756i
$704$	−2524.64	−	1457.60i	−0.00509393	−	0.00294098i
$705$	−373528.	+	215657.i	−0.751528	+	0.433895i
$706$		−	906503.i		−	1.81870i
$707$	−18414.5	−	49332.8i	−0.0368402	−	0.0986954i
$708$		−	338577.i		−	0.675446i
$709$	−354334.	+	204575.i	−0.704888	+	0.406967i	−0.809165	−	0.587581i	$-0.800080\pi$
$709$	−354334.	+	204575.i	−0.704888	+	0.406967i	0.104277	+	0.994548i	$0.466747\pi$
$710$	−146891.	−	84807.3i	−0.291392	−	0.168235i
$711$	−1.75068e6	−	1.01076e6i	−3.46313	−	1.99944i
$712$	−335245.	+	193554.i	−0.661306	+	0.381805i
$713$			549615.i			1.08113i
$714$	834511.	−	870107.i	1.63695	−	1.70677i
$715$	−2551.92			−0.00499177
$716$	−78104.4	−	135281.i	−0.152352	−	0.263882i
$717$	618258.	−	1.07085e6i	1.20263	−	2.08301i
$718$	−77011.1	+	133387.i	−0.149384	+	0.258741i
$719$	302549.	+	524030.i	0.585245	+	1.01367i	0.994845	+	0.101409i	$0.0323352\pi$
$719$	302549.	+	524030.i	0.585245	+	1.01367i	−0.409599	+	0.912265i	$0.634332\pi$
$720$	592834.			1.14358
$721$	672932.	+	112982.i	1.29450	+	0.217340i
$722$	274069.			0.525758
$723$	−489366.	−	847607.i	−0.936175	−	1.62150i
$724$	−161496.	+	279718.i	−0.308094	+	0.533635i
$725$	710348.	+	410120.i	1.35143	+	0.780251i
$726$	−612913.	−	1.06160e6i	−1.16286	−	2.01412i
$727$			547194.i			1.03531i	0.855588	+	0.517657i	$0.173196\pi$
$727$			547194.i			1.03531i	−0.855588	+	0.517657i	$0.826804\pi$
$728$	21757.9	−	26365.6i	0.0410540	−	0.0497479i
$729$	1.51620e6			2.85300
$730$	16500.7	+	28580.0i	0.0309639	+	0.0536311i
$731$	−25693.8	+	343893.i	−0.0480833	+	0.643559i
$732$	92566.4	−	160330.i	0.172755	−	0.299221i
$733$	445486.	−	257202.i	0.829137	−	0.478703i	−0.0244198	−	0.999702i	$-0.507774\pi$
$733$	445486.	−	257202.i	0.829137	−	0.478703i	0.853557	+	0.520999i	$0.174441\pi$
$734$	271009.			0.503027
$735$	67784.5	+	350735.i	0.125475	+	0.649239i
$736$			914822.i			1.68881i
$737$	42854.6	−	24742.1i	0.0788973	−	0.0455514i
$738$	349586.	−	605500.i	0.641861	−	1.11174i
$739$	451300.	−	781674.i	0.826373	−	1.43132i	−0.0744920	−	0.997222i	$-0.523734\pi$
$739$	451300.	−	781674.i	0.826373	−	1.43132i	0.900865	−	0.434099i	$-0.142933\pi$
$740$	69114.7	−	39903.4i	0.126214	−	0.0728696i
$741$	140039.			0.255043
$742$	−168543.	−	139088.i	−0.306128	−	0.252629i
$743$		−	658706.i		−	1.19320i	−0.802538	−	0.596601i	$-0.796518\pi$
$743$		−	658706.i		−	1.19320i	0.802538	−	0.596601i	$-0.203482\pi$
$744$	189202.	+	327708.i	0.341806	+	0.592026i
$745$	73904.4	−	128006.i	0.133155	−	0.230632i
$746$	71771.8	−	124312.i	0.128966	−	0.223376i
$747$	1.17203e6	−	676669.i	2.10037	−	1.21265i
$748$	−16723.3	−	34706.5i	−0.0298895	−	0.0620308i
$749$	−452937.	−	76046.1i	−0.807372	−	0.135554i
$750$	866359.			1.54019
$751$	469886.	−	271289.i	0.833131	−	0.481008i	−0.0217928	−	0.999763i	$-0.506937\pi$
$751$	469886.	−	271289.i	0.833131	−	0.481008i	0.854923	+	0.518754i	$0.173604\pi$
$752$	−802598.	−	463380.i	−1.41926	−	0.819411i
$753$	−1.31550e6	−	759503.i	−2.32007	−	1.33949i
$754$	69919.7	+	121105.i	0.122986	+	0.213019i
$755$	275623.			0.483528
$756$	898633.	−	335434.i	1.57231	−	0.586900i
$757$	−216006.			−0.376942			−0.188471	−	0.982079i	$-0.560353\pi$
$757$	−216006.			−0.376942			−0.188471	+	0.982079i	$0.560353\pi$
$758$	−987646.	+	570218.i	−1.71895	+	0.992435i
$759$	−123069.	+	213162.i	−0.213632	+	0.370022i
$760$	−119149.	−	68790.9i	−0.206284	−	0.119098i
$761$	56116.6	−	32398.9i	0.0968995	−	0.0559450i	−0.450767	−	0.892642i	$-0.648850\pi$
$761$	56116.6	−	32398.9i	0.0968995	−	0.0559450i	0.547667	+	0.836697i	$0.315516\pi$
$762$	143919.			0.247861
$763$	188548.	+	505122.i	0.323871	+	0.867655i
$764$	−282294.			−0.483632
$765$	−442872.	−	301800.i	−0.756755	−	0.515699i
$766$	733642.	+	423569.i	1.25034	+	0.721882i
$767$	−21781.8	+	37727.3i	−0.0370258	+	0.0641305i
$768$	691003.	+	1.19685e6i	1.17154	+	2.02917i
$769$			121491.i			0.205443i	0.994710	+	0.102722i	$0.0327551\pi$
$769$			121491.i			0.205443i	−0.994710	+	0.102722i	$0.967245\pi$
$770$	32300.2	+	5423.06i	0.0544784	+	0.00914668i
$771$		−	1.66820e6i		−	2.80634i
$772$	122237.	−	70573.5i	0.205101	−	0.118415i
$773$	−518917.	−	299597.i	−0.868437	−	0.501393i	−0.00160873	−	0.999999i	$-0.500512\pi$
$773$	−518917.	−	299597.i	−0.868437	−	0.501393i	−0.866829	+	0.498606i	$0.833845\pi$
$774$	−633105.	+	1.09657e6i	−1.05680	+	1.83043i
$775$	164282.	+	284544.i	0.273518	+	0.473747i
$776$	−45091.8			−0.0748815
$777$	−576784.	+	698929.i	−0.955369	+	1.15769i
$778$	−1.38708e6			−2.29163
$779$	−245844.	+	141938.i	−0.405121	+	0.233897i
$780$	20868.0	+	12048.1i	0.0342998	+	0.0198030i
$781$	30771.9	−	53298.4i	0.0504489	−	0.0873800i
$782$	742028.	−	1.08888e6i	1.21341	−	1.78060i
$783$		−	3.41058e6i		−	5.56294i
$784$	−579832.	+	502946.i	−0.943344	+	0.818256i
$785$		−	207263.i		−	0.336344i
$786$	−1.04556e6	−	1.81097e6i	−1.69241	−	2.93134i
$787$	215193.	−	372726.i	0.347440	−	0.601783i	−0.638354	−	0.769743i	$-0.720384\pi$
$787$	215193.	−	372726.i	0.347440	−	0.601783i	0.985794	+	0.167959i	$0.0537178\pi$
$788$	159735.	+	92223.2i	0.257246	+	0.148521i
$789$	533471.	+	923999.i	0.856952	+	1.48429i
$790$			405211.i			0.649273i
$791$	292335.	−	354242.i	0.467226	−	0.566170i
$792$			122952.i			0.196013i
$793$	−20629.2	+	11910.3i	−0.0328047	+	0.0189398i
$794$	−474634.	+	822090.i	−0.752866	+	1.30400i
$795$	−66943.4	+	115949.i	−0.105919	+	0.183457i
$796$	74909.7	+	129747.i	0.118226	+	0.204773i
$797$			752573.i			1.18477i	0.805657	+	0.592383i	$0.201813\pi$
$797$			752573.i			1.18477i	−0.805657	+	0.592383i	$0.798187\pi$
$798$	−1.77251e6	−	297597.i	−2.78345	−	0.467329i
$799$	363677.	+	754751.i	0.569669	+	1.18225i
$800$	273443.	+	473617.i	0.427255	+	0.740027i
$801$	1.94682e6	+	1.12400e6i	3.03432	+	1.75187i
$802$	306945.	+	177215.i	0.477212	+	0.275519i
$803$	−10370.1	+	5987.18i	−0.0160824	+	0.00928519i
$804$	−467250.			−0.722832
$805$	136535.	+	365778.i	0.210694	+	0.564451i
$806$			56015.5i			0.0862260i
$807$	727475.	+	1.26002e6i	1.11705	+	1.93478i
$808$	−34315.5	−	19812.0i	−0.0525614	−	0.0303463i
$809$	392356.	+	226527.i	0.599492	+	0.346117i	0.768842	−	0.639439i	$-0.220833\pi$
$809$	392356.	+	226527.i	0.599492	+	0.346117i	−0.169350	+	0.985556i	$0.554167\pi$
$810$	−470897.	−	815618.i	−0.717722	−	1.24313i
$811$	679690.			1.03340			0.516701	−	0.856166i	$-0.327160\pi$
$811$	679690.			1.03340			0.516701	+	0.856166i	$0.327160\pi$
$812$	−218749.	−	586031.i	−0.331767	−	0.888809i
$813$			1.56563e6i			2.36869i
$814$	41542.2	+	71953.2i	0.0626961	+	0.108593i
$815$	63852.6	+	36865.3i	0.0961309	+	0.0555012i
$816$	118255.	−	1.58275e6i	0.177598	−	2.37702i
$817$	445227.	−	257052.i	0.667018	−	0.385103i
$818$		−	851083.i		−	1.27194i
$819$	−195773.	−	32869.4i	−0.291866	−	0.0490031i
$820$	−48846.0			−0.0726442
$821$	932722.	−	538507.i	1.38378	−	0.798924i	0.391172	−	0.920318i	$-0.372070\pi$
$821$	932722.	−	538507.i	1.38378	−	0.798924i	0.992604	+	0.121394i	$0.0387365\pi$
$822$	−1.03690e6	+	1.79597e6i	−1.53460	+	2.65800i
$823$	127392.	+	73549.8i	0.188080	+	0.108588i	0.591083	−	0.806610i	$-0.298700\pi$
$823$	127392.	+	73549.8i	0.188080	+	0.108588i	−0.403003	+	0.915198i	$0.632034\pi$
$824$	444668.	−	256729.i	0.654910	−	0.378113i
$825$			147143.i			0.216188i
$826$	355872.	−	431234.i	0.521595	−	0.632052i
$827$			353352.i			0.516651i	0.966058	+	0.258325i	$0.0831706\pi$
$827$			353352.i			0.516651i	−0.966058	+	0.258325i	$0.916829\pi$
$828$	1.46034e6	−	843125.i	2.13006	−	1.22979i
$829$	433140.	+	250074.i	0.630260	+	0.363881i	0.780853	−	0.624715i	$-0.214785\pi$
$829$	433140.	+	250074.i	0.630260	+	0.363881i	−0.150593	+	0.988596i	$0.548118\pi$
$830$	−234932.	−	135638.i	−0.341024	−	0.196890i
$831$	−1.39504e6	+	805428.i	−2.02016	+	1.16634i
$832$		−	3541.76i		−	0.00511649i
$833$	689199.	−	80541.3i	0.993241	−	0.116072i
$834$	737653.			1.06052
$835$	−150212.	−	260174.i	−0.215442	−	0.373156i
$836$	−28716.8	+	49739.0i	−0.0410888	+	0.0711680i
$837$	683088.	−	1.18314e6i	0.975048	−	1.68883i
$838$	541028.	+	937089.i	0.770428	+	1.33442i
$839$	770609.			1.09474			0.547369	−	0.836891i	$-0.315629\pi$
$839$	770609.			1.09474			0.547369	+	0.836891i	$0.315629\pi$
$840$	207326.	+	171094.i	0.293829	+	0.242480i
$841$	−1.51688e6			−2.14466
$842$	607390.	+	1.05203e6i	0.856730	+	1.48390i
$843$	857494.	−	1.48522e6i	1.20664	−	2.08995i
$844$	213155.	+	123065.i	0.299234	+	0.172763i
$845$	122128.	+	211532.i	0.171042	+	0.296253i
$846$			3.07620e6i			4.29807i
$847$	116819.	−	695786.i	0.162835	−	0.969860i
$848$	−287682.			−0.400056
$849$	174473.	+	302196.i	0.242054	+	0.419250i
$850$	58690.1	−	785524.i	0.0812320	−	1.08723i
$851$	−495211.	+	857731.i	−0.683804	+	1.18438i
$852$	−503266.	+	290561.i	−0.693295	+	0.400274i
$853$	−888426.			−1.22102			−0.610511	−	0.792008i	$-0.709036\pi$
$853$	−888426.			−1.22102			−0.610511	+	0.792008i	$0.709036\pi$
$854$	286419.	−	106912.i	0.392722	−	0.146592i
$855$			798961.i			1.09293i
$856$	−299297.	+	172799.i	−0.408465	+	0.235828i
$857$	50353.8	−	87215.4i	0.0685600	−	0.118749i	−0.829708	−	0.558198i	$-0.811493\pi$
$857$	50353.8	−	87215.4i	0.0685600	−	0.118749i	0.898268	+	0.439449i	$0.144826\pi$
$858$	−12542.9	+	21725.0i	−0.0170383	+	0.0295111i
$859$	−117033.	+	67569.1i	−0.158607	+	0.0915718i	−0.577203	−	0.816601i	$-0.695856\pi$
$859$	−117033.	+	67569.1i	−0.158607	+	0.0915718i	0.418596	+	0.908173i	$0.362522\pi$
$860$	88460.8			0.119606
$861$	519617.	−	193958.i	0.700933	−	0.261639i
$862$		−	805605.i		−	1.08420i
$863$	729684.	+	1.26385e6i	0.979746	+	1.69697i	0.663291	+	0.748362i	$0.269159\pi$
$863$	729684.	+	1.26385e6i	0.979746	+	1.69697i	0.316455	+	0.948608i	$0.397507\pi$
$864$	1.13698e6	−	1.96932e6i	1.52310	−	2.63808i
$865$	−30242.3	+	52381.2i	−0.0404187	+	0.0700072i
$866$	87654.8	−	50607.5i	0.116880	−	0.0674806i
$867$	−894090.	+	1.12218e6i	−1.18944	+	1.49288i
$868$	41488.4	−	247109.i	0.0550665	−	0.327981i
$869$	−147028.			−0.194698
$870$	−952306.	+	549814.i	−1.25817	+	0.726402i
$871$	52065.2	+	30059.9i	0.0686296	+	0.0396233i
$872$	351358.	+	202857.i	0.462080	+	0.266782i
$873$	130928.	+	226774.i	0.171792	+	0.297553i
$874$	−1.96439e6			−2.57160
$875$	384587.	+	317377.i	0.502318	+	0.414533i
$876$	113067.			0.147342
$877$	313526.	−	181015.i	0.407638	−	0.235350i	−0.282136	−	0.959374i	$-0.591043\pi$
$877$	313526.	−	181015.i	0.407638	−	0.235350i	0.689774	+	0.724024i	$0.257710\pi$
$878$	−743986.	+	1.28862e6i	−0.965108	+	1.67162i
$879$	−106081.	−	61245.9i	−0.137297	−	0.0792683i
$880$	37341.2	−	21558.9i	0.0482195	−	0.0278395i
$881$	−1.27731e6			−1.64567			−0.822835	−	0.568280i	$-0.807609\pi$
$881$	−1.27731e6			−1.64567			−0.822835	+	0.568280i	$0.807609\pi$
$882$	2.40809e6	+	832070.i	3.09553	+	1.06960i
$883$	−842900.			−1.08107			−0.540536	−	0.841321i	$-0.681779\pi$
$883$	−842900.			−1.08107			−0.540536	+	0.841321i	$0.681779\pi$
$884$	26357.9	−	38678.5i	0.0337292	−	0.0494955i
$885$	−296668.	−	171282.i	−0.378778	−	0.218688i
$886$	−250772.	+	434350.i	−0.319456	+	0.553315i
$887$	384324.	+	665669.i	0.488484	+	0.846080i	0.999912	−	0.0132464i	$-0.00421660\pi$
$887$	384324.	+	665669.i	0.488484	+	0.846080i	−0.511428	+	0.859326i	$0.670883\pi$
$888$			681895.i			0.864752i
$889$	63887.4	+	52722.4i	0.0808372	+	0.0667101i
$890$		−	450610.i		−	0.568880i
$891$	295942.	−	170862.i	0.372779	−	0.215224i
$892$	410463.	+	236981.i	0.515875	+	0.297841i
$893$	624496.	−	1.08166e6i	0.783118	−	1.35640i
$894$	−726496.	−	1.25833e6i	−0.908988	−	1.57441i
$895$	−158048.			−0.197307
$896$	−136606.	+	813639.i	−0.170159	+	1.01348i
$897$	−299041.			−0.371660
$898$	−370198.	+	213734.i	−0.459073	+	0.265046i
$899$	−771570.	−	445466.i	−0.954676	−	0.551183i
$900$	504025.	−	872997.i	0.622253	−	1.07777i
$901$	214911.	+	146453.i	0.264733	+	0.180405i
$902$		−	50852.0i		−	0.0625022i
$903$	−941033.	+	351261.i	−1.15406	+	0.430779i
$904$		−	345609.i		−	0.422910i
$905$	163397.	+	283012.i	0.199502	+	0.345547i
$906$	1.35471e6	−	2.34643e6i	1.65041	−	2.85859i
$907$	1.40142e6	+	809113.i	1.70355	+	0.983546i	0.942105	+	0.335318i	$0.108844\pi$
$907$	1.40142e6	+	809113.i	1.70355	+	0.983546i	0.761447	+	0.648228i	$0.224489\pi$
$908$	214477.	+	371485.i	0.260141	+	0.450577i
$909$			230104.i			0.278481i
$910$	13915.3	+	37279.3i	0.0168039	+	0.0450179i
$911$		−	1.39410e6i		−	1.67980i	−0.542742	−	0.839900i	$-0.682614\pi$
$911$		−	1.39410e6i		−	1.67980i	0.542742	−	0.839900i	$-0.317386\pi$
$912$	−2.04914e6	+	1.18307e6i	−2.46367	+	1.42240i
$913$	49215.4	−	85243.6i	0.0590418	−	0.102263i
$914$	237018.	−	410527.i	0.283719	−	0.491416i
$915$	−93656.3	−	162218.i	−0.111865	−	0.193756i
$916$			37042.7i			0.0441481i
$917$	199282.	−	1.18694e6i	0.236989	−	1.41153i
$918$	−2.95066e6	+	1.42178e6i	−3.50133	+	1.68712i
$919$	−126094.	−	218400.i	−0.149301	−	0.258596i	0.781669	−	0.623694i	$-0.214369\pi$
$919$	−126094.	−	218400.i	−0.149301	−	0.258596i	−0.930969	+	0.365098i	$0.881036\pi$
$920$	254432.	+	146896.i	0.300605	+	0.173554i
$921$	−1.71404e6	−	989604.i	−2.02070	−	1.16665i
$922$	−313768.	+	181154.i	−0.369102	+	0.213101i
$923$	74771.2			0.0877669
$924$	71423.2	−	86548.4i	0.0836556	−	0.101371i
$925$			592081.i			0.691986i
$926$	−891204.	−	1.54361e6i	−1.03933	−	1.80018i
$927$	−2.58226e6	−	1.49087e6i	−3.00498	−	1.73492i
$928$	−1.28426e6	−	741468.i	−1.49127	−	0.860987i
$929$	−67573.2	−	117040.i	−0.0782966	−	0.135614i	0.824218	−	0.566272i	$-0.191615\pi$
$929$	−67573.2	−	117040.i	−0.0782966	−	0.135614i	−0.902515	+	0.430658i	$0.858281\pi$
$930$	−440478.			−0.509282
$931$	−677819.	−	781438.i	−0.782014	−	0.901561i
$932$			476919.i			0.549052i
$933$	−399521.	−	691991.i	−0.458961	−	0.794945i
$934$	484933.	+	279976.i	0.555889	+	0.320942i
$935$	−38870.7	−	2904.21i	−0.0444630	−	0.00332204i
$936$	−129365.	+	74689.0i	−0.147661	+	0.0852521i
$937$		−	132302.i		−	0.150691i	−0.997157	−	0.0753455i	$-0.975994\pi$
$937$		−	132302.i		−	0.150691i	0.997157	−	0.0753455i	$-0.0240060\pi$
$938$	−595122.	−	491118.i	−0.676394	−	0.558188i
$939$	−482315.			−0.547016
$940$	186119.	−	107456.i	0.210637	−	0.121611i
$941$	−551354.	+	954973.i	−0.622661	+	1.07848i	0.366328	+	0.930486i	$0.380615\pi$
$941$	−551354.	+	954973.i	−0.622661	+	1.07848i	−0.988988	+	0.147994i	$0.952718\pi$
$942$	−1.76448e6	−	1.01872e6i	−1.98845	−	1.14803i
$943$	524977.	−	303095.i	0.590360	−	0.340844i
$944$		−	736063.i		−	0.825983i
$945$	160692.	−	957094.i	0.179941	−	1.07174i
$946$			92093.8i			0.102908i
$947$	205197.	−	118470.i	0.228808	−	0.132102i	−0.381214	−	0.924487i	$-0.624494\pi$
$947$	205197.	−	118470.i	0.228808	−	0.132102i	0.610022	+	0.792385i	$0.291161\pi$
$948$	1.20231e6	+	694152.i	1.33782	+	0.772392i
$949$	−12598.9	−	7273.99i	−0.0139895	−	0.00807682i
$950$	−1.01699e6	+	587161.i	−1.12686	+	0.650594i
$951$			2.10073e6i			2.32278i
$952$	361421.	−	376838.i	0.398786	−	0.415796i
$953$	609551.			0.671157			0.335579	−	0.942012i	$-0.391068\pi$
$953$	609551.			0.671157			0.335579	+	0.942012i	$0.391068\pi$
$954$	477452.	+	826971.i	0.524605	+	0.908643i
$955$	−142809.	+	247353.i	−0.156585	+	0.271212i
$956$	−308061.	+	533577.i	−0.337070	+	0.583823i
$957$	−199497.	−	345539.i	−0.217827	−	0.377288i
$958$	−575808.			−0.627403
$959$	−1.11822e6	+	417400.i	−1.21588	+	0.453853i
$960$	27850.6			0.0302198
$961$	283320.	+	490725.i	0.306782	+	0.531363i
$962$	−50470.8	+	87418.0i	−0.0545369	+	0.0944606i
$963$	1.73807e6	+	1.00347e6i	1.87419	+	1.08207i
$964$	243837.	+	422339.i	0.262389	+	0.454472i
$965$		−	142809.i		−	0.153356i
$966$	3.78503e6	+	635490.i	4.05616	+	0.681011i
$967$	−352609.			−0.377086			−0.188543	−	0.982065i	$-0.560376\pi$
$967$	−352609.			−0.377086			−0.188543	+	0.982065i	$0.560376\pi$
$968$	−265449.	−	459771.i	−0.283289	−	0.490671i
$969$	2.13307e6	+	159372.i	2.27174	+	0.169732i
$970$	26244.4	−	45456.6i	0.0278929	−	0.0483118i
$971$	667009.	−	385098.i	0.707446	−	0.408444i	−0.102669	−	0.994716i	$-0.532738\pi$
$971$	667009.	−	385098.i	0.707446	−	0.408444i	0.810115	+	0.586272i	$0.199405\pi$
$972$	−1.64110e6			−1.73701
$973$	327453.	+	270227.i	0.345878	+	0.285433i
$974$			552812.i			0.582720i
$975$	−154818.	+	89384.3i	−0.162859	+	0.0940268i
$976$	201239.	−	348556.i	0.211257	−	0.365909i
$977$	477463.	−	826990.i	0.500208	−	0.866385i	−0.499792	−	0.866145i	$-0.666590\pi$
$977$	477463.	−	826990.i	0.500208	−	0.866385i	1.00000		0.000240040i	$-7.64071e-5\pi$
$978$	627684.	−	362394.i	0.656241	−	0.378881i
$979$	163501.			0.170591
$980$	−33775.1	−	174761.i	−0.0351678	−	0.181967i
$981$		−	2.35605e6i		−	2.44819i
$982$	−976786.	−	1.69184e6i	−1.01292	−	1.75444i
$983$	−242541.	+	420093.i	−0.251002	+	0.434749i	−0.963802	−	0.266619i	$-0.914094\pi$
$983$	−242541.	+	420093.i	−0.251002	+	0.434749i	0.712800	+	0.701368i	$0.247427\pi$
$984$	208678.	−	361441.i	0.215519	−	0.373290i
$985$	161616.	−	93309.0i	0.166576	−	0.0961726i
$986$	927190.	+	1.92423e6i	0.953707	+	1.97926i
$987$	−1.55322e6	+	1.88214e6i	−1.59440	+	1.93205i
$988$	−69777.8			−0.0714831
$989$	−950740.	+	548910.i	−0.972007	+	0.561188i
$990$	−123947.	−	71560.7i	−0.126463	−	0.0730137i
$991$	−753609.	−	435096.i	−0.767359	−	0.443035i	0.0645728	−	0.997913i	$-0.479432\pi$
$991$	−753609.	−	435096.i	−0.767359	−	0.443035i	−0.831932	+	0.554878i	$0.812765\pi$
$992$	−297010.	−	514437.i	−0.301820	−	0.522768i
$993$	2.66343e6			2.70112
$994$	−946396.	−	158896.i	−0.957856	−	0.160820i
$995$	151583.			0.153111
$996$	−804905.	+	464712.i	−0.811383	+	0.468452i
$997$	627890.	−	1.08754e6i	0.631675	−	1.09409i	−0.355535	−	0.934663i	$-0.615701\pi$
$997$	627890.	−	1.08754e6i	0.631675	−	1.09409i	0.987209	−	0.159429i	$-0.0509654\pi$
$998$	1.06401e6	+	614306.i	1.06828	+	0.616771i
$999$	2.13206e6	−	1.23095e6i	2.13633	−	1.23341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.5.h.a.101.38	yes	92
7.5	odd	6	inner	119.5.h.a.33.37	✓	92
17.16	even	2	inner	119.5.h.a.101.37	yes	92
119.33	odd	6	inner	119.5.h.a.33.38	yes	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.5.h.a.33.37	✓	92	7.5	odd	6	inner
119.5.h.a.33.38	yes	92	119.33	odd	6	inner
119.5.h.a.101.37	yes	92	17.16	even	2	inner
119.5.h.a.101.38	yes	92	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	119.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.47790 + 4.29184i) q^{2} +(8.58954 - 14.8775i) q^{3} +(-4.27993 + 7.41305i) q^{4} +(4.33032 + 7.50033i) q^{5} +85.1359 q^{6} +(37.7928 + 31.1882i) q^{7} +36.8718 q^{8} +(-107.060 - 185.434i) q^{9} +(-21.4602 + 37.1701i) q^{10} +(-13.4869 - 7.78669i) q^{11} +(73.5252 + 127.349i) q^{12} -18.9206i q^{13} +(-40.2079 + 239.482i) q^{14} +148.782 q^{15} +(159.843 + 276.857i) q^{16} +(21.5325 - 288.197i) q^{17} +(530.568 - 918.971i) q^{18} +(-373.119 + 215.420i) q^{19} -74.1338 q^{20} +(788.625 - 294.372i) q^{21} -77.1784i q^{22} +(796.760 - 460.010i) q^{23} +(316.712 - 548.561i) q^{24} +(274.997 - 476.308i) q^{25} +(81.2040 - 46.8831i) q^{26} -2286.89 q^{27} +(-392.950 + 146.677i) q^{28} +1491.36i q^{29} +(368.666 + 638.548i) q^{30} +(-298.698 + 517.359i) q^{31} +(-497.175 + 861.133i) q^{32} +(-231.693 + 133.768i) q^{33} +(1290.25 - 621.707i) q^{34} +(-70.2666 + 418.514i) q^{35} +1832.84 q^{36} +(-932.297 + 538.262i) q^{37} +(-1849.10 - 1067.58i) q^{38} +(-281.491 - 162.519i) q^{39} +(159.667 + 276.551i) q^{40} +658.889 q^{41} +(3217.53 + 2655.23i) q^{42} -1193.26 q^{43} +(115.446 - 66.6530i) q^{44} +(927.211 - 1605.98i) q^{45} +(3948.58 + 2279.71i) q^{46} +(-2510.58 + 1449.48i) q^{47} +5491.92 q^{48} +(455.597 + 2357.38i) q^{49} +2725.65 q^{50} +(-4102.70 - 2795.83i) q^{51} +(140.259 + 80.9786i) q^{52} +(-449.944 + 779.325i) q^{53} +(-5666.67 - 9814.96i) q^{54} -134.876i q^{55} +(1393.49 + 1149.96i) q^{56} +7401.45i q^{57} +(-6400.69 + 3695.44i) q^{58} +(-1993.98 - 1151.23i) q^{59} +(-636.775 + 1102.93i) q^{60} +(-629.488 - 1090.30i) q^{61} -2960.57 q^{62} +(1737.23 - 10347.1i) q^{63} +187.191 q^{64} +(141.910 - 81.9321i) q^{65} +(-1148.22 - 662.927i) q^{66} +(-1588.74 + 2751.78i) q^{67} +(2044.26 + 1393.08i) q^{68} -15805.1i q^{69} +(-1970.31 + 735.460i) q^{70} +3951.85i q^{71} +(-3947.51 - 6837.28i) q^{72} +(384.449 - 665.885i) q^{73} +(-4620.27 - 2667.51i) q^{74} +(-4724.19 - 8182.53i) q^{75} -3687.94i q^{76} +(-266.857 - 714.914i) q^{77} -1610.82i q^{78} +(8176.15 - 4720.50i) q^{79} +(-1384.35 + 2397.76i) q^{80} +(-10971.4 + 19003.1i) q^{81} +(1632.66 + 2827.85i) q^{82} +6320.45i q^{83} +(-1193.07 + 7106.01i) q^{84} +(2254.81 - 1086.48i) q^{85} +(-2956.77 - 5121.27i) q^{86} +(22187.8 + 12810.1i) q^{87} +(-497.288 - 287.109i) q^{88} +(-9092.18 + 5249.37i) q^{89} +9190.12 q^{90} +(590.097 - 715.061i) q^{91} +7875.23i q^{92} +(5131.35 + 8887.76i) q^{93} +(-12441.9 - 7183.33i) q^{94} +(-3231.45 - 1865.68i) q^{95} +(8541.01 + 14793.5i) q^{96} -1222.94 q^{97} +(-8988.57 + 7796.69i) q^{98} +3334.58i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 2 q^{2} - 354 q^{4} + 56 q^{8} - 1068 q^{9} + 464 q^{15} - 3146 q^{16} + 1104 q^{17} - 906 q^{18} - 6 q^{19} - 240 q^{21} - 3106 q^{25} + 468 q^{26} + 1858 q^{30} - 1680 q^{32} - 198 q^{33} - 5318 q^{35}+ \cdots + 107386 q^{98}+O(q^{100}) \) 92 * q - 2 * q^2 - 354 * q^4 + 56 * q^8 - 1068 * q^9 + 464 * q^15 - 3146 * q^16 + 1104 * q^17 - 906 * q^18 - 6 * q^19 - 240 * q^21 - 3106 * q^25 + 468 * q^26 + 1858 * q^30 - 1680 * q^32 - 198 * q^33 - 5318 * q^35 + 17304 * q^36 - 6 * q^38 + 1888 * q^42 + 3316 * q^43 - 7242 * q^47 - 1284 * q^49 + 2136 * q^50 - 11304 * q^51 - 5202 * q^52 + 28 * q^53 - 17826 * q^59 - 3182 * q^60 + 41768 * q^64 + 5988 * q^66 + 2924 * q^67 - 22788 * q^68 + 36898 * q^70 - 23660 * q^72 - 3162 * q^77 - 6194 * q^81 + 30426 * q^84 + 46552 * q^85 + 4118 * q^86 - 7026 * q^87 + 4944 * q^89 + 11034 * q^93 - 101214 * q^94 + 107386 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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