LMFDB - Embedded newform 77.4.e.c.67.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [77,4,Mod(23,77)] 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("77.23"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(77, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	77.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.54314707044$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 67 x^{18} - 2 x^{17} + 2960 x^{16} - 261 x^{15} + 74338 x^{14} - 19762 x^{13} + \cdots + 649230400 $ x^20 + 67x^18 - 2x^17 + 2960x^16 - 261x^15 + 74338x^14 - 19762x^13 + 1348686x^12 - 533131x^11 + 15140516x^10 - 9917906x^9 + 123558653x^8 - 86301269x^7 + 611013951x^6 - 481586362x^5 + 2045671324x^4 - 970096176x^3 + 1858590384x^2 + 644949760x + 649230400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.7
Root			$1.11799 - 1.93642i$ of defining polynomial
Character	$\chi$	$=$	77.67
Dual form			77.4.e.c.23.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.11799 + 1.93642i) q^{2} +(-0.448504 + 0.776832i) q^{3} +(1.50018 - 2.59839i) q^{4} +(2.13369 + 3.69565i) q^{5} -2.00570 q^{6} +(4.50836 + 17.9631i) q^{7} +24.5967 q^{8} +(13.0977 + 22.6859i) q^{9} +(-4.77090 + 8.26344i) q^{10} +(5.50000 - 9.52628i) q^{11} +(1.34567 + 2.33077i) q^{12} -30.4708 q^{13} +(-29.7439 + 28.8128i) q^{14} -3.82787 q^{15} +(15.4975 + 26.8424i) q^{16} +(7.73191 - 13.3921i) q^{17} +(-29.2863 + 50.7253i) q^{18} +(0.183360 + 0.317588i) q^{19} +12.8037 q^{20} +(-15.9764 - 4.55431i) q^{21} +24.5959 q^{22} +(-38.2422 - 66.2374i) q^{23} +(-11.0317 + 19.1075i) q^{24} +(53.3948 - 92.4824i) q^{25} +(-34.0661 - 59.0043i) q^{26} -47.7167 q^{27} +(53.4386 + 15.2335i) q^{28} -32.2465 q^{29} +(-4.27953 - 7.41237i) q^{30} +(62.7848 - 108.747i) q^{31} +(63.7345 - 110.391i) q^{32} +(4.93354 + 8.54515i) q^{33} +34.5769 q^{34} +(-56.7662 + 54.9891i) q^{35} +78.5956 q^{36} +(-33.1079 - 57.3446i) q^{37} +(-0.409990 + 0.710124i) q^{38} +(13.6663 - 23.6707i) q^{39} +(52.4816 + 90.9008i) q^{40} -384.577 q^{41} +(-9.04241 - 36.0287i) q^{42} +302.922 q^{43} +(-16.5020 - 28.5823i) q^{44} +(-55.8927 + 96.8091i) q^{45} +(85.5090 - 148.106i) q^{46} +(-260.018 - 450.365i) q^{47} -27.8027 q^{48} +(-302.349 + 161.969i) q^{49} +238.780 q^{50} +(6.93558 + 12.0128i) q^{51} +(-45.7116 + 79.1749i) q^{52} +(73.1088 - 126.628i) q^{53} +(-53.3469 - 92.3996i) q^{54} +46.9411 q^{55} +(110.891 + 441.834i) q^{56} -0.328950 q^{57} +(-36.0514 - 62.4428i) q^{58} +(-361.710 + 626.500i) q^{59} +(-5.74249 + 9.94629i) q^{60} +(82.7637 + 143.351i) q^{61} +280.772 q^{62} +(-348.460 + 337.552i) q^{63} +532.979 q^{64} +(-65.0151 - 112.609i) q^{65} +(-11.0313 + 19.1068i) q^{66} +(280.039 - 485.042i) q^{67} +(-23.1985 - 40.1810i) q^{68} +68.6071 q^{69} +(-169.946 - 48.4458i) q^{70} +108.611 q^{71} +(322.159 + 557.997i) q^{72} +(-352.012 + 609.702i) q^{73} +(74.0289 - 128.222i) q^{74} +(47.8955 + 82.9575i) q^{75} +1.10029 q^{76} +(195.918 + 55.8494i) q^{77} +61.1152 q^{78} +(243.850 + 422.360i) q^{79} +(-66.1335 + 114.547i) q^{80} +(-332.236 + 575.450i) q^{81} +(-429.955 - 744.704i) q^{82} +619.201 q^{83} +(-35.8013 + 34.6805i) q^{84} +65.9899 q^{85} +(338.665 + 586.586i) q^{86} +(14.4627 - 25.0501i) q^{87} +(135.282 - 234.315i) q^{88} +(-180.782 - 313.123i) q^{89} -249.951 q^{90} +(-137.373 - 547.351i) q^{91} -229.481 q^{92} +(56.3185 + 97.5465i) q^{93} +(581.397 - 1007.01i) q^{94} +(-0.782465 + 1.35527i) q^{95} +(57.1704 + 99.0220i) q^{96} +1511.18 q^{97} +(-651.664 - 404.396i) q^{98} +288.149 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 54 q^{4} - 10 q^{5} + 106 q^{6} - 30 q^{7} + 6 q^{8} - 76 q^{9} - 63 q^{10} + 110 q^{11} - 55 q^{12} + 324 q^{13} + 58 q^{14} + 60 q^{15} - 286 q^{16} - 200 q^{17} + 252 q^{18} - 252 q^{19} + 192 q^{20}+ \cdots - 1672 q^{99}+O(q^{100}) $ 20 * q - 54 * q^4 - 10 * q^5 + 106 * q^6 - 30 * q^7 + 6 * q^8 - 76 * q^9 - 63 * q^10 + 110 * q^11 - 55 * q^12 + 324 * q^13 + 58 * q^14 + 60 * q^15 - 286 * q^16 - 200 * q^17 + 252 * q^18 - 252 * q^19 + 192 * q^20 + 458 * q^21 - 134 * q^23 - 786 * q^24 - 86 * q^25 - 363 * q^26 + 348 * q^27 - 1057 * q^28 + 296 * q^29 + 316 * q^30 - 530 * q^31 + 731 * q^32 + 204 * q^34 - 288 * q^35 + 2574 * q^36 + 902 * q^37 - 66 * q^38 + 208 * q^39 - 2163 * q^40 + 336 * q^41 - 1482 * q^42 + 236 * q^43 + 594 * q^44 - 58 * q^45 + 210 * q^46 - 288 * q^47 - 1700 * q^48 - 1072 * q^49 + 4650 * q^50 + 1022 * q^51 - 1663 * q^52 + 608 * q^53 - 2312 * q^54 - 220 * q^55 - 4905 * q^56 + 1656 * q^57 + 1951 * q^58 + 464 * q^59 + 818 * q^60 - 3484 * q^61 - 1618 * q^62 - 3948 * q^63 + 6090 * q^64 + 1560 * q^65 + 583 * q^66 - 142 * q^67 - 1145 * q^68 + 3432 * q^69 - 4133 * q^70 + 668 * q^71 + 1176 * q^72 - 1466 * q^73 + 3460 * q^74 - 2982 * q^75 + 6774 * q^76 - 330 * q^77 + 10840 * q^78 - 578 * q^79 - 2911 * q^80 - 118 * q^81 + 307 * q^82 + 1092 * q^83 - 6786 * q^84 + 5164 * q^85 - 2597 * q^86 - 1516 * q^87 + 33 * q^88 - 3150 * q^89 - 3672 * q^90 - 3638 * q^91 + 4326 * q^92 + 1484 * q^93 - 5700 * q^94 + 1338 * q^95 - 5429 * q^96 + 3308 * q^97 - 3186 * q^98 - 1672 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.11799	+	1.93642i	0.395270	+	0.684629i	0.993136	−	0.116968i	$-0.0373175\pi$
$2$	1.11799	+	1.93642i	0.395270	+	0.684629i	−0.597865	+	0.801597i	$0.703984\pi$
$3$	−0.448504	+	0.776832i	−0.0863146	+	0.149501i	−0.905951	−	0.423383i	$-0.860842\pi$
$3$	−0.448504	+	0.776832i	−0.0863146	+	0.149501i	0.819636	+	0.572885i	$0.194176\pi$
$4$	1.50018	−	2.59839i	0.187523	−	0.324799i
$5$	2.13369	+	3.69565i	0.190843	+	0.330549i	0.945530	−	0.325536i	$-0.105545\pi$
$5$	2.13369	+	3.69565i	0.190843	+	0.330549i	−0.754687	+	0.656085i	$0.772211\pi$
$6$	−2.00570			−0.136471
$7$	4.50836	+	17.9631i	0.243429	+	0.969919i
$7$	4.50836	+	17.9631i	0.243429	+	0.969919i
$8$	24.5967			1.08703
$9$	13.0977	+	22.6859i	0.485100	+	0.840217i
$10$	−4.77090	+	8.26344i	−0.150869	+	0.261313i
$11$	5.50000	−	9.52628i	0.150756	−	0.261116i
$11$	5.50000	−	9.52628i	0.150756	−	0.261116i
$12$	1.34567	+	2.33077i	0.0323719	+	0.0560697i
$13$	−30.4708			−0.650082			−0.325041	−	0.945700i	$-0.605378\pi$
$13$	−30.4708			−0.650082			−0.325041	+	0.945700i	$0.605378\pi$
$14$	−29.7439	+	28.8128i	−0.567814	+	0.550038i
$15$	−3.82787			−0.0658901
$16$	15.4975	+	26.8424i	0.242148	+	0.419413i
$17$	7.73191	−	13.3921i	0.110310	−	0.191062i	−0.805585	−	0.592480i	$-0.798149\pi$
$17$	7.73191	−	13.3921i	0.110310	−	0.191062i	0.915895	+	0.401418i	$0.131482\pi$
$18$	−29.2863	+	50.7253i	−0.383491	+	0.664226i
$19$	0.183360	+	0.317588i	0.00221398	+	0.00383472i	0.867130	−	0.498081i	$-0.165962\pi$
$19$	0.183360	+	0.317588i	0.00221398	+	0.00383472i	−0.864916	+	0.501916i	$0.832629\pi$
$20$	12.8037			0.143149
$21$	−15.9764	−	4.55431i	−0.166016	−	0.0473253i
$22$	24.5959			0.238357
$23$	−38.2422	−	66.2374i	−0.346698	−	0.600498i	0.638963	−	0.769237i	$-0.279364\pi$
$23$	−38.2422	−	66.2374i	−0.346698	−	0.600498i	−0.985661	+	0.168740i	$0.946030\pi$
$24$	−11.0317	+	19.1075i	−0.0938265	+	0.162512i
$25$	53.3948	−	92.4824i	0.427158	−	0.739859i
$26$	−34.0661	−	59.0043i	−0.256958	−	0.445065i
$27$	−47.7167			−0.340114
$28$	53.4386	+	15.2335i	0.360677	+	0.102816i
$29$	−32.2465			−0.206484			−0.103242	−	0.994656i	$-0.532922\pi$
$29$	−32.2465			−0.206484			−0.103242	+	0.994656i	$0.532922\pi$
$30$	−4.27953	−	7.41237i	−0.0260444	−	0.0451102i
$31$	62.7848	−	108.747i	0.363758	−	0.630047i	−0.624818	−	0.780770i	$-0.714827\pi$
$31$	62.7848	−	108.747i	0.363758	−	0.630047i	0.988576	+	0.150723i	$0.0481603\pi$
$32$	63.7345	−	110.391i	0.352087	−	0.609832i
$33$	4.93354	+	8.54515i	0.0260248	+	0.0450763i
$34$	34.5769			0.174409
$35$	−56.7662	+	54.9891i	−0.274149	+	0.265567i
$36$	78.5956			0.363868
$37$	−33.1079	−	57.3446i	−0.147106	−	0.254795i	0.783051	−	0.621958i	$-0.213662\pi$
$37$	−33.1079	−	57.3446i	−0.147106	−	0.254795i	−0.930157	+	0.367163i	$0.880329\pi$
$38$	−0.409990	+	0.710124i	−0.00175024	+	0.00303151i
$39$	13.6663	−	23.6707i	0.0561116	−	0.0971882i
$40$	52.4816	+	90.9008i	0.207452	+	0.359317i
$41$	−384.577			−1.46490			−0.732450	−	0.680821i	$-0.761623\pi$
$41$	−384.577			−1.46490			−0.732450	+	0.680821i	$0.761623\pi$
$42$	−9.04241	−	36.0287i	−0.0332208	−	0.132365i
$43$	302.922			1.07431			0.537154	−	0.843484i	$-0.319499\pi$
$43$	302.922			1.07431			0.537154	+	0.843484i	$0.319499\pi$
$44$	−16.5020	−	28.5823i	−0.0565402	−	0.0979304i
$45$	−55.8927	+	96.8091i	−0.185155	+	0.320699i
$46$	85.5090	−	148.106i	0.274079	−	0.474718i
$47$	−260.018	−	450.365i	−0.806969	−	1.39771i	−0.914954	−	0.403558i	$-0.867773\pi$
$47$	−260.018	−	450.365i	−0.806969	−	1.39771i	0.107985	−	0.994153i	$-0.465560\pi$
$48$	−27.8027			−0.0836037
$49$	−302.349	+	161.969i	−0.881485	+	0.472212i
$50$	238.780			0.675372
$51$	6.93558	+	12.0128i	0.0190427	+	0.0329829i
$52$	−45.7116	+	79.1749i	−0.121905	+	0.211146i
$53$	73.1088	−	126.628i	0.189477	−	0.328183i	−0.755599	−	0.655034i	$-0.772654\pi$
$53$	73.1088	−	126.628i	0.189477	−	0.328183i	0.945076	+	0.326851i	$0.105988\pi$
$54$	−53.3469	−	92.3996i	−0.134437	−	0.232852i
$55$	46.9411			0.115083
$56$	110.891	+	441.834i	0.264614	+	1.05433i
$57$	−0.328950			−0.000764395
$58$	−36.0514	−	62.4428i	−0.0816169	−	0.141365i
$59$	−361.710	+	626.500i	−0.798147	+	1.38243i	0.122675	+	0.992447i	$0.460853\pi$
$59$	−361.710	+	626.500i	−0.798147	+	1.38243i	−0.920822	+	0.389984i	$0.872481\pi$
$60$	−5.74249	+	9.94629i	−0.0123559	+	0.0214010i
$61$	82.7637	+	143.351i	0.173718	+	0.300889i	0.939717	−	0.341953i	$-0.111088\pi$
$61$	82.7637	+	143.351i	0.173718	+	0.300889i	−0.765999	+	0.642842i	$0.777755\pi$
$62$	280.772			0.575131
$63$	−348.460	+	337.552i	−0.696855	+	0.675040i
$64$	532.979			1.04097
$65$	−65.0151	−	112.609i	−0.124064	−	0.214884i
$66$	−11.0313	+	19.1068i	−0.0205737	+	0.0356347i
$67$	280.039	−	485.042i	0.510630	−	0.884437i	−0.489294	−	0.872119i	$-0.662745\pi$
$67$	280.039	−	485.042i	0.510630	−	0.884437i	0.999924	−	0.0123184i	$-0.00392118\pi$
$68$	−23.1985	−	40.1810i	−0.0413711	−	0.0716568i
$69$	68.6071			0.119700
$70$	−169.946	−	48.4458i	−0.290178	−	0.0827197i
$71$	108.611			0.181546			0.0907728	−	0.995872i	$-0.471066\pi$
$71$	108.611			0.181546			0.0907728	+	0.995872i	$0.471066\pi$
$72$	322.159	+	557.997i	0.527317	+	0.913341i
$73$	−352.012	+	609.702i	−0.564381	+	0.977537i	0.432725	+	0.901526i	$0.357552\pi$
$73$	−352.012	+	609.702i	−0.564381	+	0.977537i	−0.997107	+	0.0760117i	$0.975781\pi$
$74$	74.0289	−	128.222i	0.116293	−	0.201426i
$75$	47.8955	+	82.9575i	0.0737400	+	0.127721i
$76$	1.10029			0.00166068
$77$	195.918	+	55.8494i	0.289960	+	0.0826576i
$78$	61.1152			0.0887171
$79$	243.850	+	422.360i	0.347281	+	0.601509i	0.985766	−	0.168126i	$-0.0537716\pi$
$79$	243.850	+	422.360i	0.347281	+	0.601509i	−0.638484	+	0.769635i	$0.720438\pi$
$80$	−66.1335	+	114.547i	−0.0924244	+	0.160084i
$81$	−332.236	+	575.450i	−0.455743	+	0.789370i
$82$	−429.955	−	744.704i	−0.579032	−	1.00291i
$83$	619.201			0.818869			0.409434	−	0.912340i	$-0.365726\pi$
$83$	619.201			0.818869			0.409434	+	0.912340i	$0.365726\pi$
$84$	−35.8013	+	34.6805i	−0.0465029	+	0.0450471i
$85$	65.9899			0.0842072
$86$	338.665	+	586.586i	0.424642	+	0.735502i
$87$	14.4627	−	25.0501i	0.0178226	−	0.0308696i
$88$	135.282	−	234.315i	0.163876	−	0.283841i
$89$	−180.782	−	313.123i	−0.215313	−	0.372933i	0.738056	−	0.674739i	$-0.235744\pi$
$89$	−180.782	−	313.123i	−0.215313	−	0.372933i	−0.953369	+	0.301806i	$0.902410\pi$
$90$	−249.951			−0.292746
$91$	−137.373	−	547.351i	−0.158249	−	0.630527i
$92$	−229.481			−0.260054
$93$	56.3185	+	97.5465i	0.0627952	+	0.108765i
$94$	581.397	−	1007.01i	0.637942	−	1.10495i
$95$	−0.782465	+	1.35527i	−0.000845044	+	0.00146366i
$96$	57.1704	+	99.0220i	0.0607805	+	0.105275i
$97$	1511.18			1.58182			0.790911	−	0.611932i	$-0.209607\pi$
$97$	1511.18			1.58182			0.790911	+	0.611932i	$0.209607\pi$
$98$	−651.664	−	404.396i	−0.671715	−	0.416838i
$99$	288.149			0.292526
$100$	−160.204	−	277.481i	−0.160204	−	0.277481i
$101$	−270.022	+	467.692i	−0.266022	+	0.460763i	−0.967831	−	0.251602i	$-0.919043\pi$
$101$	−270.022	+	467.692i	−0.266022	+	0.460763i	0.701809	+	0.712365i	$0.252376\pi$
$102$	−15.5079	+	26.8604i	−0.0150540	+	0.0260743i
$103$	−912.265	−	1580.09i	−0.872700	−	1.51156i	−0.859193	−	0.511652i	$-0.829034\pi$
$103$	−912.265	−	1580.09i	−0.872700	−	1.51156i	−0.0135071	−	0.999909i	$-0.504300\pi$
$104$	−749.479			−0.706659
$105$	−17.2574	−	68.7606i	−0.0160395	−	0.0639080i
$106$	326.941			0.299578
$107$	−382.023	−	661.684i	−0.345155	−	0.597826i	0.640227	−	0.768186i	$-0.278840\pi$
$107$	−382.023	−	661.684i	−0.345155	−	0.597826i	−0.985382	+	0.170360i	$0.945507\pi$
$108$	−71.5836	+	123.986i	−0.0637790	+	0.110469i
$109$	4.75322	−	8.23281i	0.00417684	−	0.00723450i	−0.863929	−	0.503613i	$-0.832004\pi$
$109$	4.75322	−	8.23281i	0.00417684	−	0.00723450i	0.868106	+	0.496378i	$0.165337\pi$
$110$	52.4799	+	90.8978i	0.0454887	+	0.0787888i
$111$	59.3962			0.0507895
$112$	−412.306	+	399.399i	−0.347851	+	0.336961i
$113$	−2045.74			−1.70307			−0.851534	−	0.524300i	$-0.824327\pi$
$113$	−2045.74			−1.70307			−0.851534	+	0.524300i	$0.824327\pi$
$114$	−0.367764	−	0.636987i	−0.000302143	−	0.000523327i
$115$	163.194	−	282.660i	0.132329	−	0.229201i
$116$	−48.3756	+	83.7889i	−0.0387203	+	0.0670656i
$117$	−399.097	−	691.256i	−0.315355	−	0.546210i
$118$	−1617.56			−1.26194
$119$	275.422	+	78.5132i	0.212167	+	0.0604815i
$120$	−94.1528			−0.0716245
$121$	−60.5000	−	104.789i	−0.0454545	−	0.0787296i
$122$	−185.059	+	320.531i	−0.137331	+	0.237865i
$123$	172.484	−	298.752i	0.126442	−	0.219004i
$124$	−188.377	−	326.279i	−0.136425	−	0.236296i
$125$	989.133			0.707766
$126$	−1043.22	−	297.386i	−0.737598	−	0.210264i
$127$	2341.97			1.63635			0.818175	−	0.574970i	$-0.194986\pi$
$127$	2341.97			1.63635			0.818175	+	0.574970i	$0.194986\pi$
$128$	85.9909	+	148.941i	0.0593796	+	0.102848i
$129$	−135.862	+	235.320i	−0.0927285	+	0.160610i
$130$	145.373	−	251.793i	0.0980773	−	0.169875i
$131$	−8.41086	−	14.5680i	−0.00560962	−	0.00971614i	0.863207	−	0.504850i	$-0.168452\pi$
$131$	−8.41086	−	14.5680i	−0.00560962	−	0.00971614i	−0.868817	+	0.495134i	$0.835119\pi$
$132$	29.6048			0.0195210
$133$	−4.87824	+	4.72552i	−0.00318043	+	0.00308086i
$134$	1252.33			0.807348
$135$	−101.812	−	176.344i	−0.0649083	−	0.112424i
$136$	190.179	−	329.400i	0.119910	−	0.207690i
$137$	−409.890	+	709.951i	−0.255615	+	0.442739i	−0.965062	−	0.262020i	$-0.915611\pi$
$137$	−409.890	+	709.951i	−0.255615	+	0.442739i	0.709447	+	0.704759i	$0.248945\pi$
$138$	76.7023	+	132.852i	0.0473140	+	0.0819502i
$139$	2603.20			1.58849			0.794247	−	0.607594i	$-0.207865\pi$
$139$	2603.20			1.58849			0.794247	+	0.607594i	$0.207865\pi$
$140$	57.7235	+	229.994i	0.0348466	+	0.138843i
$141$	466.477			0.278613
$142$	121.426	+	210.317i	0.0717597	+	0.124291i
$143$	−167.589	+	290.273i	−0.0980036	+	0.169747i
$144$	−405.962	+	703.147i	−0.234932	+	0.406914i
$145$	−68.8039	−	119.172i	−0.0394059	−	0.0682530i
$146$	−1574.19			−0.892333
$147$	9.78250	−	307.518i	0.00548876	−	0.172542i
$148$	−198.672			−0.110343
$149$	1488.04	+	2577.36i	0.818153	+	1.41708i	0.907042	+	0.421040i	$0.138335\pi$
$149$	1488.04	+	2577.36i	0.818153	+	1.41708i	−0.0888892	+	0.996042i	$0.528332\pi$
$150$	−107.094	+	185.492i	−0.0582945	+	0.100969i
$151$	351.106	−	608.133i	0.189222	−	0.327743i	−0.755769	−	0.654838i	$-0.772737\pi$
$151$	351.106	−	608.133i	0.189222	−	0.327743i	0.944991	+	0.327096i	$0.106070\pi$
$152$	4.51004	+	7.81162i	0.00240666	+	0.00416846i
$153$	405.081			0.214045
$154$	110.887	+	441.819i	0.0580229	+	0.231187i
$155$	535.853			0.277682
$156$	−41.0037	−	71.0205i	−0.0210444	−	0.0364499i
$157$	−625.098	+	1082.70i	−0.317760	+	0.550376i	−0.980020	−	0.198898i	$-0.936264\pi$
$157$	−625.098	+	1082.70i	−0.317760	+	0.550376i	0.662261	+	0.749274i	$0.269597\pi$
$158$	−545.245	+	944.391i	−0.274540	+	0.475517i
$159$	65.5792	+	113.586i	0.0327092	+	0.0566540i
$160$	543.958			0.268773
$161$	1017.42	−	985.572i	0.498038	−	0.482447i
$162$	−1485.75			−0.720567
$163$	177.509	+	307.454i	0.0852979	+	0.147740i	0.905518	−	0.424308i	$-0.139482\pi$
$163$	177.509	+	307.454i	0.0852979	+	0.147740i	−0.820220	+	0.572048i	$0.806149\pi$
$164$	−576.935	+	999.281i	−0.274702	+	0.475797i
$165$	−21.0533	+	36.4653i	−0.00993331	+	0.0172050i
$166$	692.262	+	1199.03i	0.323675	+	0.560621i
$167$	1928.14			0.893438			0.446719	−	0.894674i	$-0.352592\pi$
$167$	1928.14			0.893438			0.446719	+	0.894674i	$0.352592\pi$
$168$	−392.965	−	112.021i	−0.180464	−	0.0514440i
$169$	−1268.53			−0.577393
$170$	73.7763	+	127.784i	0.0332846	+	0.0576506i
$171$	−4.80318	+	8.31935i	−0.00214800	+	0.00372045i
$172$	454.438	−	787.110i	0.201457	−	0.348934i
$173$	470.589	+	815.083i	0.206810	+	0.358206i	0.950708	−	0.310088i	$-0.100358\pi$
$173$	470.589	+	815.083i	0.206810	+	0.358206i	−0.743898	+	0.668294i	$0.767025\pi$
$174$	64.6768			0.0281789
$175$	1902.00	+	542.194i	0.821586	+	0.234206i
$176$	340.945			0.146021
$177$	−324.457	−	561.976i	−0.137783	−	0.238648i
$178$	404.226	−	700.140i	0.170214	−	0.294819i
$179$	−1775.38	+	3075.04i	−0.741329	+	1.28402i	0.210562	+	0.977581i	$0.432471\pi$
$179$	−1775.38	+	3075.04i	−0.741329	+	1.28402i	−0.951890	+	0.306439i	$0.900863\pi$
$180$	167.698	+	290.462i	0.0694417	+	0.120276i
$181$	−2171.17			−0.891611			−0.445806	−	0.895130i	$-0.647083\pi$
$181$	−2171.17			−0.891611			−0.445806	+	0.895130i	$0.647083\pi$
$182$	906.320	−	877.947i	0.369126	−	0.357570i
$183$	−148.479			−0.0599777
$184$	−940.630	−	1629.22i	−0.376870	−	0.652759i
$185$	141.284	−	244.711i	0.0561481	−	0.0972514i
$186$	−125.927	+	218.113i	−0.0496422	+	0.0859828i
$187$	−85.0510	−	147.313i	−0.0332596	−	0.0576073i
$188$	−1560.30			−0.605299
$189$	−215.124	−	857.142i	−0.0827935	−	0.329883i
$190$	−3.49916			−0.00133608
$191$	−944.933	−	1636.67i	−0.357974	−	0.620028i	0.629649	−	0.776880i	$-0.283199\pi$
$191$	−944.933	−	1636.67i	−0.357974	−	0.620028i	−0.987622	+	0.156852i	$0.949866\pi$
$192$	−239.043	+	414.035i	−0.0898513	+	0.155627i
$193$	−1073.64	+	1859.59i	−0.400425	+	0.693556i	−0.993777	−	0.111387i	$-0.964471\pi$
$193$	−1073.64	+	1859.59i	−0.400425	+	0.693556i	0.593352	+	0.804943i	$0.297804\pi$
$194$	1689.48	+	2926.27i	0.625247	+	1.08296i
$195$	116.638			0.0428340
$196$	−32.7210	+	1028.60i	−0.0119246	+	0.374855i
$197$	−4075.83			−1.47407			−0.737033	−	0.675857i	$-0.763774\pi$
$197$	−4075.83			−1.47407			−0.737033	+	0.675857i	$0.763774\pi$
$198$	322.149	+	557.978i	0.115627	+	0.200272i
$199$	1274.53	−	2207.56i	0.454017	−	0.786380i	−0.544614	−	0.838687i	$-0.683324\pi$
$199$	1274.53	−	2207.56i	0.454017	−	0.786380i	0.998631	+	0.0523066i	$0.0166573\pi$
$200$	1313.33	−	2274.76i	0.464333	−	0.804249i
$201$	251.197	+	435.086i	0.0881497	+	0.152680i
$202$	−1207.53			−0.420602
$203$	−145.379	−	579.249i	−0.0502640	−	0.200272i
$204$	41.6185			0.0142837
$205$	−820.568	−	1421.27i	−0.279566	−	0.484222i
$206$	2039.81	−	3533.06i	0.689905	−	1.19495i
$207$	1001.77	−	1735.11i	0.336366	−	0.582602i
$208$	−472.220	−	817.909i	−0.157416	−	0.272653i
$209$	4.03391			0.00133508
$210$	113.856	−	110.292i	0.0374133	−	0.0362421i
$211$	−3183.03			−1.03853			−0.519263	−	0.854615i	$-0.673793\pi$
$211$	−3183.03			−1.03853			−0.519263	+	0.854615i	$0.673793\pi$
$212$	−219.353	−	379.930i	−0.0710623	−	0.123084i
$213$	−48.7124	+	84.3724i	−0.0156700	+	0.0271413i
$214$	854.200	−	1479.52i	0.272859	−	0.472606i
$215$	646.342	+	1119.50i	0.205024	+	0.355112i
$216$	−1173.67			−0.369714
$217$	2236.49	+	637.545i	0.699643	+	0.199444i
$218$	21.2563			0.00660393
$219$	−315.757	−	546.908i	−0.0974288	−	0.168752i
$220$	70.4201	−	121.971i	0.0215806	−	0.0373786i
$221$	−235.597	+	408.066i	−0.0717103	+	0.124206i
$222$	66.4046	+	115.016i	0.0200756	+	0.0347719i
$223$	−2852.84			−0.856684			−0.428342	−	0.903617i	$-0.640902\pi$
$223$	−2852.84			−0.856684			−0.428342	+	0.903617i	$0.640902\pi$
$224$	2270.32	+	647.188i	0.677196	+	0.193045i
$225$	2797.39			0.828857
$226$	−2287.12	−	3961.41i	−0.673172	−	1.16597i
$227$	2060.60	−	3569.06i	0.602497	−	1.04356i	−0.389945	−	0.920838i	$-0.627506\pi$
$227$	2060.60	−	3569.06i	0.602497	−	1.04356i	0.992442	−	0.122717i	$-0.0391608\pi$
$228$	−0.493485	+	0.854741i	−0.000143341	+	0.000248274i
$229$	2032.26	+	3519.98i	0.586443	+	1.01575i	0.994694	+	0.102879i	$0.0328055\pi$
$229$	2032.26	+	3519.98i	0.586443	+	1.01575i	−0.408251	+	0.912870i	$0.633861\pi$
$230$	729.798			0.209224
$231$	−131.256	+	127.147i	−0.0373852	+	0.0362149i
$232$	−793.156			−0.224454
$233$	−544.221	−	942.618i	−0.153018	−	0.265034i	0.779318	−	0.626629i	$-0.215566\pi$
$233$	−544.221	−	942.618i	−0.153018	−	0.265034i	−0.932335	+	0.361595i	$0.882232\pi$
$234$	892.375	−	1545.64i	0.249301	−	0.431802i
$235$	1109.59	−	1921.87i	0.308008	−	0.533486i
$236$	1085.26	+	1879.73i	0.299341	+	0.518474i
$237$	−437.470			−0.119902
$238$	155.885	+	621.110i	0.0424560	+	0.169162i
$239$	−1257.44			−0.340323			−0.170162	−	0.985416i	$-0.554429\pi$
$239$	−1257.44			−0.340323			−0.170162	+	0.985416i	$0.554429\pi$
$240$	−59.3223	−	102.749i	−0.0159552	−	0.0276352i
$241$	−2694.74	+	4667.43i	−0.720263	+	1.24753i	0.240631	+	0.970617i	$0.422646\pi$
$241$	−2694.74	+	4667.43i	−0.720263	+	1.24753i	−0.960894	+	0.276916i	$0.910688\pi$
$242$	135.277	−	234.307i	0.0359337	−	0.0622390i
$243$	−942.194	−	1631.93i	−0.248732	−	0.430816i
$244$	496.642			0.130304
$245$	−1243.70	−	771.788i	−0.324314	−	0.201256i
$246$	771.346			0.199916
$247$	−5.58711	−	9.67716i	−0.00143927	−	0.00249289i
$248$	1544.30	−	2674.80i	0.395415	−	0.684879i
$249$	−277.714	+	481.015i	−0.0706803	+	0.122422i
$250$	1105.84	+	1915.38i	0.279759	+	0.484557i
$251$	−4248.92			−1.06848			−0.534241	−	0.845332i	$-0.679403\pi$
$251$	−4248.92			−1.06848			−0.534241	+	0.845332i	$0.679403\pi$
$252$	354.337	+	1411.82i	0.0885760	+	0.352923i
$253$	−841.328			−0.209066
$254$	2618.31	+	4535.04i	0.646801	+	1.12029i
$255$	−29.5967	+	51.2630i	−0.00726831	+	0.0125891i
$256$	1939.64	−	3359.56i	0.473545	−	0.820204i
$257$	−550.672	−	953.791i	−0.133657	−	0.231501i	0.791426	−	0.611264i	$-0.209339\pi$
$257$	−550.672	−	953.791i	−0.133657	−	0.231501i	−0.925084	+	0.379763i	$0.876005\pi$
$258$	−607.571			−0.146611
$259$	880.828	−	853.253i	0.211320	−	0.204705i
$260$	−390.137			−0.0930588
$261$	−422.355	−	731.540i	−0.100165	−	0.173491i
$262$	18.8066	−	32.5739i	0.00443463	−	0.00768101i
$263$	300.068	−	519.732i	0.0703535	−	0.121856i	−0.828703	−	0.559689i	$-0.810921\pi$
$263$	300.068	−	519.732i	0.0703535	−	0.121856i	0.899056	+	0.437833i	$0.144254\pi$
$264$	121.349	+	210.182i	0.0282898	+	0.0489993i
$265$	623.965			0.144641
$266$	−14.6044	−	4.16322i	−0.00336637	−	0.000959637i
$267$	324.326			0.0743386
$268$	−840.218	−	1455.30i	−0.191509	−	0.331704i
$269$	1875.35	−	3248.20i	0.425063	−	0.736231i	−0.571363	−	0.820697i	$-0.693585\pi$
$269$	1875.35	−	3248.20i	0.425063	−	0.736231i	0.996426	+	0.0844664i	$0.0269186\pi$
$270$	227.651	−	394.304i	0.0513127	−	0.0888762i
$271$	410.326	+	710.706i	0.0919762	+	0.159307i	0.908343	−	0.418227i	$-0.137348\pi$
$271$	410.326	+	710.706i	0.0919762	+	0.159307i	−0.816366	+	0.577534i	$0.804015\pi$
$272$	479.300			0.106845
$273$	486.812	+	138.773i	0.107924	+	0.0307653i
$274$	−1833.02			−0.404149
$275$	−587.342	−	1017.31i	−0.128793	−	0.223076i
$276$	102.923	−	178.268i	0.0224465	−	0.0388785i
$277$	−3733.45	+	6466.53i	−0.809825	+	1.40266i	0.103160	+	0.994665i	$0.467105\pi$
$277$	−3733.45	+	6466.53i	−0.809825	+	1.40266i	−0.912985	+	0.407994i	$0.866229\pi$
$278$	2910.36	+	5040.90i	0.627885	+	1.08753i
$279$	3289.34			0.705835
$280$	−1396.26	+	1352.55i	−0.298009	+	0.288679i
$281$	−4444.03			−0.943447			−0.471724	−	0.881746i	$-0.656368\pi$
$281$	−4444.03			−0.943447			−0.471724	+	0.881746i	$0.656368\pi$
$282$	521.518	+	903.295i	0.110127	+	0.190746i
$283$	−3106.72	+	5381.00i	−0.652563	+	1.13027i	0.329936	+	0.944003i	$0.392973\pi$
$283$	−3106.72	+	5381.00i	−0.652563	+	1.13027i	−0.982499	+	0.186269i	$0.940360\pi$
$284$	162.936	−	282.213i	0.0340439	−	0.0589658i
$285$	−0.701877	−	1.21569i	−0.000145879	−	0.000252670i
$286$	−749.455			−0.154952
$287$	−1733.81	−	6908.22i	−0.356598	−	1.42083i
$288$	3339.10			0.683188
$289$	2336.94	+	4047.69i	0.475664	+	0.823873i
$290$	153.845	−	266.467i	0.0311520	−	0.0539568i
$291$	−677.768	+	1173.93i	−0.136534	+	0.236484i
$292$	1056.16	+	1829.33i	0.211668	+	0.366621i
$293$	−5710.99			−1.13870			−0.569351	−	0.822094i	$-0.692806\pi$
$293$	−5710.99			−1.13870			−0.569351	+	0.822094i	$0.692806\pi$
$294$	606.422	−	324.860i	0.120297	−	0.0644430i
$295$	−3087.10			−0.609282
$296$	−814.345	−	1410.49i	−0.159908	−	0.276969i
$297$	−262.442	+	454.562i	−0.0512741	+	0.0888094i
$298$	−3327.23	+	5762.94i	−0.646783	+	1.12026i
$299$	1165.27	+	2018.30i	0.225382	+	0.390373i
$300$	287.408			0.0553116
$301$	1365.68	+	5441.44i	0.261517	+	1.04199i
$302$	1570.14			0.299176
$303$	−242.212	−	419.524i	−0.0459232	−	0.0795413i
$304$	−5.68323	+	9.84364i	−0.00107222	+	0.00185714i
$305$	−353.184	+	611.732i	−0.0663057	+	0.114845i
$306$	452.878	+	784.407i	0.0846055	+	0.146541i
$307$	10530.9			1.95776			0.978880	−	0.204434i	$-0.0655353\pi$
$307$	10530.9			1.95776			0.978880	+	0.204434i	$0.0655353\pi$
$308$	439.031	−	425.287i	0.0812211	−	0.0786784i
$309$	1636.62			0.301307
$310$	599.080	+	1037.64i	0.109760	+	0.190109i
$311$	3760.00	−	6512.51i	0.685563	−	1.18743i	−0.287697	−	0.957722i	$-0.592889\pi$
$311$	3760.00	−	6512.51i	0.685563	−	1.18743i	0.973260	−	0.229708i	$-0.0737772\pi$
$312$	336.144	−	582.219i	0.0609950	−	0.105646i
$313$	−895.223	−	1550.57i	−0.161665	−	0.280011i	0.773801	−	0.633428i	$-0.218353\pi$
$313$	−895.223	−	1550.57i	−0.161665	−	0.280011i	−0.935466	+	0.353417i	$0.885020\pi$
$314$	−2795.42			−0.502404
$315$	−1990.98	−	567.559i	−0.356124	−	0.101519i
$316$	1463.27			0.260492
$317$	−1957.28	−	3390.11i	−0.346788	−	0.600654i	0.638889	−	0.769299i	$-0.279394\pi$
$317$	−1957.28	−	3390.11i	−0.346788	−	0.600654i	−0.985677	+	0.168645i	$0.946061\pi$
$318$	−146.634	+	253.978i	−0.0258580	+	0.0447873i
$319$	−177.356	+	307.189i	−0.0311286	+	0.0539163i
$320$	1137.21	+	1969.71i	0.198662	+	0.344093i
$321$	685.356			0.119168
$322$	3045.95	+	868.296i	0.527157	+	0.150274i
$323$	5.67088			0.000976893
$324$	996.829	+	1726.56i	0.170924	+	0.296049i
$325$	−1626.98	+	2818.01i	−0.277688	+	0.480970i
$326$	−396.907	+	687.463i	−0.0674315	+	0.116795i
$327$	4.26367	+	7.38490i	0.000721045	+	0.00124889i
$328$	−9459.32			−1.59239
$329$	6917.71	−	6701.15i	1.15923	−	1.12294i
$330$	−94.1497			−0.0157054
$331$	2855.51	+	4945.88i	0.474178	+	0.821300i	0.999563	−	0.0295644i	$-0.00941201\pi$
$331$	2855.51	+	4945.88i	0.474178	+	0.821300i	−0.525385	+	0.850865i	$0.676079\pi$
$332$	928.912	−	1608.92i	0.153556	−	0.265967i
$333$	867.275	−	1502.16i	0.142722	−	0.247202i
$334$	2155.65	+	3733.70i	0.353150	+	0.611673i
$335$	2390.06			0.389800
$336$	−125.345	−	499.424i	−0.0203515	−	0.0810888i
$337$	−4370.06			−0.706387			−0.353193	−	0.935550i	$-0.614904\pi$
$337$	−4370.06			−0.706387			−0.353193	+	0.935550i	$0.614904\pi$
$338$	−1418.21	−	2456.41i	−0.228226	−	0.395300i
$339$	917.521	−	1589.19i	0.147000	−	0.254611i
$340$	98.9967	−	171.467i	0.0157907	−	0.0273504i
$341$	−690.633	−	1196.21i	−0.109677	−	0.189966i
$342$	−21.4797			−0.00339617
$343$	−4272.57	−	4700.93i	−0.672586	−	0.740019i
$344$	7450.88			1.16780
$345$	146.386	+	253.548i	0.0228439	+	0.0395669i
$346$	−1052.23	+	1822.52i	−0.163492	+	0.283177i
$347$	−3770.06	+	6529.93i	−0.583248	+	1.01022i	0.411843	+	0.911255i	$0.364885\pi$
$347$	−3770.06	+	6529.93i	−0.583248	+	1.01022i	−0.995091	+	0.0989610i	$0.968448\pi$
$348$	−43.3933	−	75.1593i	−0.00668426	−	0.0115775i
$349$	9324.82			1.43022			0.715109	−	0.699013i	$-0.246377\pi$
$349$	9324.82			1.43022			0.715109	+	0.699013i	$0.246377\pi$
$350$	1076.51	+	4289.24i	0.164405	+	0.655056i
$351$	1453.96			0.221102
$352$	−701.080	−	1214.31i	−0.106158	−	0.183871i
$353$	3681.21	−	6376.04i	0.555046	−	0.961367i	−0.442854	−	0.896594i	$-0.646034\pi$
$353$	3681.21	−	6376.04i	0.555046	−	0.961367i	0.997900	−	0.0647735i	$-0.0206325\pi$
$354$	725.481	−	1256.57i	0.108923	−	0.188661i
$355$	231.742	+	401.388i	0.0346467	+	0.0600098i
$356$	−1084.82			−0.161504
$357$	−184.519	+	178.743i	−0.0273552	+	0.0264988i
$358$	−7939.44			−1.17210
$359$	−1712.42	−	2966.01i	−0.251750	−	0.436044i	0.712258	−	0.701918i	$-0.247673\pi$
$359$	−1712.42	−	2966.01i	−0.251750	−	0.436044i	−0.964008	+	0.265874i	$0.914339\pi$
$360$	−1374.78	+	2381.18i	−0.201269	+	0.348609i
$361$	3429.43	−	5939.95i	0.499990	−	0.866008i
$362$	−2427.35	−	4204.30i	−0.352428	−	0.610423i
$363$	108.538			0.0156936
$364$	−1628.31	−	464.176i	−0.234469	−	0.0668391i
$365$	−3004.33			−0.430833
$366$	−165.999	−	287.519i	−0.0237074	−	0.0410624i
$367$	−6305.51	+	10921.5i	−0.896853	+	1.55340i	−0.0653587	+	0.997862i	$0.520819\pi$
$367$	−6305.51	+	10921.5i	−0.896853	+	1.55340i	−0.831494	+	0.555533i	$0.812514\pi$
$368$	1185.31	−	2053.02i	0.167904	−	0.290819i
$369$	−5037.07	−	8724.47i	−0.710622	−	1.23083i
$370$	631.818			0.0887748
$371$	2604.24	+	742.379i	0.364435	+	0.103888i
$372$	337.951			0.0471021
$373$	−2732.39	−	4732.64i	−0.379298	−	0.656963i	0.611663	−	0.791119i	$-0.290501\pi$
$373$	−2732.39	−	4732.64i	−0.379298	−	0.656963i	−0.990960	+	0.134156i	$0.957168\pi$
$374$	190.173	−	329.389i	0.0262931	−	0.0455409i
$375$	−443.630	+	768.390i	−0.0610905	+	0.105812i
$376$	−6395.58	−	11077.5i	−0.877199	−	1.51935i
$377$	982.576			0.134231
$378$	1419.28	−	1374.85i	0.193122	−	0.187076i
$379$	3747.81			0.507947			0.253974	−	0.967211i	$-0.418262\pi$
$379$	3747.81			0.507947			0.253974	+	0.967211i	$0.418262\pi$
$380$	2.34768	+	4.06629i	0.000316930	+	0.000548938i
$381$	−1050.38	+	1819.32i	−0.141241	+	0.244636i
$382$	2112.86	−	3659.58i	0.282993	−	0.490158i
$383$	−1162.87	−	2014.16i	−0.155144	−	0.268717i	0.777968	−	0.628304i	$-0.216251\pi$
$383$	−1162.87	−	2014.16i	−0.155144	−	0.268717i	−0.933111	+	0.359587i	$0.882917\pi$
$384$	−154.269			−0.0205013
$385$	211.627	+	843.210i	0.0280144	+	0.111621i
$386$	−4801.27			−0.633104
$387$	3967.58	+	6872.06i	0.521146	+	0.902652i
$388$	2267.04	−	3926.62i	0.296627	−	0.513773i
$389$	1551.42	−	2687.13i	0.202210	−	0.350239i	−0.747030	−	0.664790i	$-0.768521\pi$
$389$	1551.42	−	2687.13i	0.202210	−	0.350239i	0.949240	+	0.314552i	$0.101854\pi$
$390$	130.401	+	225.861i	0.0169310	+	0.0293254i
$391$	−1182.74			−0.152976
$392$	−7436.79	+	3983.89i	−0.958200	+	0.513308i
$393$	15.0892			0.00193677
$394$	−4556.75	−	7892.53i	−0.582655	−	1.00919i
$395$	−1040.60	+	1802.37i	−0.132552	+	0.229587i
$396$	432.276	−	748.723i	0.0548552	−	0.0950120i
$397$	−4811.46	−	8333.69i	−0.608262	−	1.05354i	−0.991527	−	0.129903i	$-0.958534\pi$
$397$	−4811.46	−	8333.69i	−0.608262	−	1.05354i	0.383264	−	0.923639i	$-0.374800\pi$
$398$	5699.68			0.717838
$399$	−1.48303	−	5.90898i	−0.000186076	−	0.000741401i
$400$	3309.94			0.413742
$401$	5832.87	+	10102.8i	0.726383	+	1.25813i	0.958402	+	0.285421i	$0.0921333\pi$
$401$	5832.87	+	10102.8i	0.726383	+	1.25813i	−0.232020	+	0.972711i	$0.574533\pi$
$402$	−561.674	+	972.848i	−0.0696860	+	0.120700i
$403$	−1913.10	+	3313.59i	−0.236472	+	0.409582i
$404$	810.164	+	1403.24i	0.0997702	+	0.172807i
$405$	−2835.55			−0.347901
$406$	959.137	−	929.111i	0.117244	−	0.113574i
$407$	−728.375			−0.0887081
$408$	170.592	+	295.474i	0.0206999	+	0.0358533i
$409$	−4237.85	+	7340.16i	−0.512342	+	0.887403i	0.487555	+	0.873092i	$0.337889\pi$
$409$	−4237.85	+	7340.16i	−0.512342	+	0.887403i	−0.999898	+	0.0143107i	$0.995445\pi$
$410$	1834.78	−	3177.93i	0.221008	−	0.382797i
$411$	−367.675	−	636.832i	−0.0441267	−	0.0764297i
$412$	−5474.24			−0.654604
$413$	−12884.6	−	3672.96i	−1.53514	−	0.437614i
$414$	4479.88			0.531822
$415$	1321.18	+	2288.35i	0.156275	+	0.270677i
$416$	−1942.04	+	3363.71i	−0.228885	+	0.396441i
$417$	−1167.55	+	2022.25i	−0.137110	+	0.237482i
$418$	4.50989	+	7.81136i	0.000527718	+	0.000914034i
$419$	7711.25			0.899091			0.449545	−	0.893257i	$-0.351586\pi$
$419$	7711.25			0.899091			0.449545	+	0.893257i	$0.351586\pi$
$420$	−204.556	−	58.3118i	−0.0237650	−	0.00677458i
$421$	9235.54			1.06915			0.534576	−	0.845121i	$-0.320472\pi$
$421$	9235.54			1.06915			0.534576	+	0.845121i	$0.320472\pi$
$422$	−3558.61	−	6163.69i	−0.410498	−	0.711004i
$423$	6811.27	−	11797.5i	0.782920	−	1.35606i
$424$	1798.23	−	3114.63i	0.205967	−	0.356745i
$425$	−825.687	−	1430.13i	−0.0942393	−	0.163227i
$426$	−217.841			−0.0247756
$427$	−2201.91	+	2132.98i	−0.249550	+	0.241738i
$428$	−2292.42			−0.258897
$429$	−150.329	−	260.377i	−0.0169183	−	0.0293033i
$430$	−1445.21	+	2503.18i	−0.162080	+	0.280730i
$431$	−6816.59	+	11806.7i	−0.761818	+	1.31951i	0.180094	+	0.983649i	$0.442360\pi$
$431$	−6816.59	+	11806.7i	−0.761818	+	1.31951i	−0.941912	+	0.335858i	$0.890974\pi$
$432$	−739.488	−	1280.83i	−0.0823580	−	0.142648i
$433$	10405.8			1.15490			0.577449	−	0.816426i	$-0.304048\pi$
$433$	10405.8			1.15490			0.577449	+	0.816426i	$0.304048\pi$
$434$	1265.82	+	5043.55i	0.140003	+	0.557830i
$435$	123.435			0.0136052
$436$	−14.2614	−	24.7014i	−0.00156650	−	0.00271326i
$437$	14.0241	−	24.2905i	0.00153516	−	0.00265898i
$438$	706.029	−	1222.88i	0.0770214	−	0.133405i
$439$	−4707.12	−	8152.97i	−0.511751	−	0.886378i	−0.999907	−	0.0136221i	$-0.995664\pi$
$439$	−4707.12	−	8152.97i	−0.511751	−	0.886378i	0.488157	−	0.872756i	$-0.337670\pi$
$440$	1154.60			0.125098
$441$	−7634.48	−	4737.64i	−0.824369	−	0.511569i
$442$	−1053.58			−0.113380
$443$	5832.90	+	10102.9i	0.625575	+	1.08353i	0.988429	+	0.151681i	$0.0484688\pi$
$443$	5832.90	+	10102.9i	0.625575	+	1.08353i	−0.362855	+	0.931846i	$0.618198\pi$
$444$	89.1050	−	154.334i	0.00952418	−	0.0164964i
$445$	771.464	−	1336.21i	0.0821818	−	0.142343i
$446$	−3189.46	−	5524.31i	−0.338622	−	0.586510i
$447$	−2669.56			−0.282474
$448$	2402.86	+	9573.98i	0.253403	+	1.00966i
$449$	6244.13			0.656300			0.328150	−	0.944626i	$-0.393575\pi$
$449$	6244.13			0.656300			0.328150	+	0.944626i	$0.393575\pi$
$450$	3127.47	+	5416.93i	0.327623	+	0.567459i
$451$	−2115.18	+	3663.59i	−0.220842	+	0.382509i
$452$	−3068.97	+	5315.62i	−0.319363	+	0.553154i
$453$	314.945	+	545.500i	0.0326653	+	0.0565780i
$454$	9214.95			0.952597
$455$	1729.71	−	1675.56i	0.178220	−	0.172641i
$456$	−8.09108			−0.000830920
$457$	5943.16	+	10293.9i	0.608336	+	1.05367i	0.991515	+	0.129994i	$0.0414959\pi$
$457$	5943.16	+	10293.9i	0.608336	+	1.05367i	−0.383179	+	0.923674i	$0.625171\pi$
$458$	−4544.10	+	7870.62i	−0.463607	+	0.802991i
$459$	−368.941	+	639.025i	−0.0375178	+	0.0649828i
$460$	−489.640	−	848.081i	−0.0496295	−	0.0859608i
$461$	16977.9			1.71527			0.857633	−	0.514262i	$-0.171934\pi$
$461$	16977.9			1.71527			0.857633	+	0.514262i	$0.171934\pi$
$462$	−392.952	−	112.017i	−0.0395710	−	0.0112803i
$463$	5452.97			0.547346			0.273673	−	0.961823i	$-0.411761\pi$
$463$	5452.97			0.547346			0.273673	+	0.961823i	$0.411761\pi$
$464$	−499.739	−	865.574i	−0.0499996	−	0.0866019i
$465$	−240.332	+	416.267i	−0.0239680	+	0.0415138i
$466$	1216.87	−	2107.68i	0.120967	−	0.209520i
$467$	6436.77	+	11148.8i	0.637812	+	1.10472i	0.985912	+	0.167266i	$0.0534938\pi$
$467$	6436.77	+	11148.8i	0.637812	+	1.10472i	−0.348100	+	0.937458i	$0.613173\pi$
$468$	−2394.87			−0.236544
$469$	9975.40	+	2843.64i	0.982134	+	0.279972i
$470$	4962.08			0.486986
$471$	−560.718	−	971.192i	−0.0548546	−	0.0950110i
$472$	−8896.86	+	15409.8i	−0.867609	+	1.50274i
$473$	1666.07	−	2885.72i	0.161958	−	0.280520i
$474$	−489.089	−	847.127i	−0.0473937	−	0.0820882i
$475$	39.1618			0.00378288
$476$	617.190	−	597.869i	0.0594304	−	0.0575699i
$477$	3830.23			0.367660
$478$	−1405.81	−	2434.94i	−0.134520	−	0.232995i
$479$	1216.65	−	2107.30i	0.116055	−	0.201013i	−0.802146	−	0.597128i	$-0.796309\pi$
$479$	1216.65	−	2107.30i	0.116055	−	0.201013i	0.918201	+	0.396115i	$0.129642\pi$
$480$	−243.967	+	422.564i	−0.0231990	+	0.0401819i
$481$	1008.82	+	1747.33i	0.0956308	+	0.165637i
$482$	−12050.8			−1.13880
$483$	309.305	+	1232.40i	0.0291385	+	0.116100i
$484$	−363.044			−0.0340950
$485$	3224.38	+	5584.78i	0.301879	+	0.522870i
$486$	2106.73	−	3648.97i	0.196632	−	0.340577i
$487$	932.957	−	1615.93i	0.0868097	−	0.150359i	−0.819351	−	0.573292i	$-0.805666\pi$
$487$	932.957	−	1615.93i	0.0868097	−	0.150359i	0.906161	+	0.422933i	$0.138999\pi$
$488$	2035.71	+	3525.96i	0.188837	+	0.327075i
$489$	−318.453			−0.0294498
$490$	104.060	−	3271.18i	0.00959378	−	0.301586i
$491$	−3508.63			−0.322489			−0.161245	−	0.986914i	$-0.551551\pi$
$491$	−3508.63			−0.322489			−0.161245	+	0.986914i	$0.551551\pi$
$492$	−517.516	−	896.363i	−0.0474216	−	0.0821365i
$493$	−249.327	+	431.847i	−0.0227771	+	0.0394511i
$494$	12.4927	−	21.6380i	0.00113780	−	0.00197073i
$495$	614.820	+	1064.90i	0.0558265	+	0.0966943i
$496$	3892.03			0.352333
$497$	489.657	+	1950.99i	0.0441934	+	0.176085i
$498$	−1241.93			−0.111751
$499$	−1672.33	−	2896.56i	−0.150027	−	0.259855i	0.781210	−	0.624268i	$-0.214603\pi$
$499$	−1672.33	−	2896.56i	−0.150027	−	0.259855i	−0.931237	+	0.364413i	$0.881270\pi$
$500$	1483.88	−	2570.15i	0.132722	−	0.229881i
$501$	−864.780	+	1497.84i	−0.0771168	+	0.133570i
$502$	−4750.26	−	8227.69i	−0.422340	−	0.731514i
$503$	−22511.5			−1.99550			−0.997752	−	0.0670100i	$-0.978654\pi$
$503$	−22511.5			−1.99550			−0.997752	+	0.0670100i	$0.978654\pi$
$504$	−8570.96	+	8302.65i	−0.757502	+	0.733788i
$505$	−2304.57			−0.203073
$506$	−940.599	−	1629.17i	−0.0826378	−	0.143133i
$507$	568.942	−	985.436i	0.0498375	−	0.0863210i
$508$	3513.38	−	6085.35i	0.306852	−	0.531484i
$509$	2410.98	+	4175.94i	0.209951	+	0.363645i	0.951699	−	0.307033i	$-0.0993363\pi$
$509$	2410.98	+	4175.94i	0.209951	+	0.363645i	−0.741748	+	0.670679i	$0.766003\pi$
$510$	−132.356			−0.0114918
$511$	−12539.2	−	3574.48i	−1.08552	−	0.309444i
$512$	10049.9			0.867473
$513$	−8.74932	−	15.1543i	−0.000753005	−	0.00130424i
$514$	1231.29	−	2132.66i	0.105662	−	0.183011i
$515$	3892.97	−	6742.83i	0.333097	−	0.576941i
$516$	407.635	+	706.044i	0.0347774	+	0.0602362i
$517$	−5720.40			−0.486621
$518$	2637.02	+	751.722i	0.223676	+	0.0637621i
$519$	−844.244			−0.0714030
$520$	−1599.15	−	2769.82i	−0.134861	−	0.233586i
$521$	−894.563	+	1549.43i	−0.0752236	+	0.130291i	−0.901184	−	0.433438i	$-0.857300\pi$
$521$	−894.563	+	1549.43i	−0.0752236	+	0.130291i	0.825960	+	0.563729i	$0.190634\pi$
$522$	944.380	−	1635.71i	0.0791846	−	0.137152i
$523$	−240.377	−	416.346i	−0.0200975	−	0.0348098i	0.855802	−	0.517304i	$-0.173064\pi$
$523$	−240.377	−	416.346i	−0.0200975	−	0.0348098i	−0.875899	+	0.482494i	$0.839731\pi$
$524$	−50.4712			−0.00420772
$525$	−1274.25	+	1234.36i	−0.105929	+	0.102613i
$526$	1341.89			0.111235
$527$	−970.893	−	1681.64i	−0.0802519	−	0.139000i
$528$	−152.915	+	264.857i	−0.0126037	+	0.0218303i
$529$	3158.57	−	5470.81i	0.259602	−	0.449643i
$530$	697.589	+	1208.26i	0.0571723	+	0.0990254i
$531$	−18950.3			−1.54872
$532$	4.96051	+	19.7647i	0.000404258	+	0.00161073i
$533$	11718.4			0.952305
$534$	362.594	+	628.031i	0.0293839	+	0.0508943i
$535$	1630.24	−	2823.65i	0.131741	−	0.228182i
$536$	6888.03	−	11930.4i	0.555070	−	0.961409i
$537$	−1592.53	−	2758.34i	−0.127975	−	0.221659i
$538$	8386.51			0.672060
$539$	−119.963	+	3771.09i	−0.00958657	+	0.301359i
$540$	−610.948			−0.0486871
$541$	−3689.76	−	6390.85i	−0.293226	−	0.507882i	0.681345	−	0.731962i	$-0.261395\pi$
$541$	−3689.76	−	6390.85i	−0.293226	−	0.507882i	−0.974571	+	0.224081i	$0.928062\pi$
$542$	−917.484	+	1589.13i	−0.0727109	+	0.125939i
$543$	973.778	−	1686.63i	0.0769591	−	0.133297i
$544$	−985.579	−	1707.07i	−0.0776771	−	0.134541i
$545$	40.5675			0.00318848
$546$	275.529	+	1097.82i	0.0215963	+	0.0860483i
$547$	15439.1			1.20682			0.603410	−	0.797431i	$-0.293808\pi$
$547$	15439.1			1.20682			0.603410	+	0.797431i	$0.293808\pi$
$548$	1229.82	+	2130.11i	0.0958673	+	0.166047i
$549$	−2168.03	+	3755.13i	−0.168541	+	0.291922i
$550$	1313.29	−	2274.69i	0.101816	−	0.176351i
$551$	−5.91271	−	10.2411i	−0.000457150	−	0.000791808i
$552$	1687.50			0.130118
$553$	−6487.55	+	6284.46i	−0.498877	+	0.483259i
$554$	−16695.9			−1.28040
$555$	126.733	+	219.508i	0.00969281	+	0.0167884i
$556$	3905.27	−	6764.13i	0.297879	−	0.515941i
$557$	5500.28	−	9526.76i	0.418410	−	0.724707i	−0.577370	−	0.816483i	$-0.695921\pi$
$557$	5500.28	−	9526.76i	0.418410	−	0.724707i	0.995780	+	0.0917757i	$0.0292543\pi$
$558$	3677.47	+	6369.56i	0.278996	+	0.483235i
$559$	−9230.28			−0.698389
$560$	−2355.77	−	671.549i	−0.177767	−	0.0506752i
$561$	152.583			0.0114832
$562$	−4968.40	−	8605.52i	−0.372917	−	0.645911i
$563$	1771.43	−	3068.20i	0.132605	−	0.229679i	−0.792075	−	0.610424i	$-0.790999\pi$
$563$	1771.43	−	3068.20i	0.132605	−	0.229679i	0.924680	+	0.380745i	$0.124332\pi$
$564$	699.799	−	1212.09i	0.0522462	−	0.0904931i
$565$	−4364.96	−	7560.33i	−0.325018	−	0.562948i
$566$	−13893.2			−1.03176
$567$	−11834.7	−	3373.68i	−0.876565	−	0.249878i
$568$	2671.47			0.197346
$569$	−8607.60	−	14908.8i	−0.634182	−	1.09843i	−0.986688	−	0.162625i	$-0.948004\pi$
$569$	−8607.60	−	14908.8i	−0.634182	−	1.09843i	0.352506	−	0.935809i	$-0.385329\pi$
$570$	1.56939	−	2.71826i	0.000115324	−	0.000199746i
$571$	−6076.83	+	10525.4i	−0.445372	+	0.771408i	−0.998078	−	0.0619690i	$-0.980262\pi$
$571$	−6076.83	+	10525.4i	−0.445372	+	0.771408i	0.552706	+	0.833376i	$0.313595\pi$
$572$	502.828	+	870.924i	0.0367558	+	0.0636628i
$573$	1695.22			0.123593
$574$	11438.8	−	11080.7i	0.831791	−	0.805751i
$575$	−8167.73			−0.592379
$576$	6980.79	+	12091.1i	0.504976	+	0.874644i
$577$	6379.60	−	11049.8i	0.460288	−	0.797242i	−0.538687	−	0.842506i	$-0.681080\pi$
$577$	6379.60	−	11049.8i	0.460288	−	0.797242i	0.998975	+	0.0452639i	$0.0144129\pi$
$578$	−5225.36	+	9050.58i	−0.376032	+	0.651306i
$579$	−963.060	−	1668.07i	−0.0691250	−	0.119728i
$580$	−412.873			−0.0295580
$581$	2791.58	+	11122.8i	0.199336	+	0.794236i
$582$	−3030.96			−0.215872
$583$	−804.197	−	1392.91i	−0.0571294	−	0.0989510i
$584$	−8658.31	+	14996.6i	−0.613499	+	1.06261i
$585$	1703.09	−	2949.85i	0.120366	−	0.208481i
$586$	−6384.86	−	11058.9i	−0.450096	−	0.779588i
$587$	9447.94			0.664324			0.332162	−	0.943222i	$-0.392222\pi$
$587$	9447.94			0.664324			0.332162	+	0.943222i	$0.392222\pi$
$588$	−784.376	−	486.751i	−0.0550121	−	0.0341382i
$589$	46.0488			0.00322141
$590$	−3451.36	−	5977.94i	−0.240831	−	0.417132i
$591$	1828.03	−	3166.24i	0.127233	−	0.220375i
$592$	1026.18	−	1777.39i	0.0712427	−	0.123396i
$593$	−10461.0	−	18119.0i	−0.724421	−	1.25473i	−0.959212	−	0.282689i	$-0.908774\pi$
$593$	−10461.0	−	18119.0i	−0.724421	−	1.25473i	0.234790	−	0.972046i	$-0.424560\pi$
$594$	−1173.63			−0.0810686
$595$	297.506	+	1185.39i	0.0204984	+	0.0816741i
$596$	8929.29			0.613688
$597$	1143.27	+	1980.20i	0.0783766	+	0.135752i
$598$	−2605.52	+	4512.90i	−0.178174	+	0.308606i
$599$	−352.376	+	610.334i	−0.0240362	+	0.0416320i	−0.877793	−	0.479040i	$-0.840985\pi$
$599$	−352.376	+	610.334i	−0.0240362	+	0.0416320i	0.853757	+	0.520672i	$0.174318\pi$
$600$	1178.07	+	2040.48i	0.0801575	+	0.138837i
$601$	22015.6			1.49423			0.747116	−	0.664694i	$-0.231438\pi$
$601$	22015.6			1.49423			0.747116	+	0.664694i	$0.231438\pi$
$602$	−9010.10	+	8728.04i	−0.610007	+	0.590911i
$603$	14671.5			0.990826
$604$	−1053.44	−	1824.62i	−0.0709669	−	0.122918i
$605$	258.176	−	447.174i	0.0173493	−	0.0300499i
$606$	541.583	−	938.049i	0.0363041	−	0.0628806i
$607$	−3358.48	−	5817.05i	−0.224574	−	0.388973i	0.731618	−	0.681715i	$-0.238766\pi$
$607$	−3358.48	−	5817.05i	−0.224574	−	0.388973i	−0.956192	+	0.292742i	$0.905432\pi$
$608$	46.7454			0.00311805
$609$	515.182	+	146.860i	0.0342795	+	0.00977190i
$610$	−1579.43			−0.104835
$611$	7922.95	+	13723.0i	0.524596	+	0.908627i
$612$	607.694	−	1052.56i	0.0401382	−	0.0695214i
$613$	14058.8	−	24350.5i	0.926311	−	1.60442i	0.136872	−	0.990589i	$-0.456295\pi$
$613$	14058.8	−	24350.5i	0.926311	−	1.60442i	0.789439	−	0.613829i	$-0.210372\pi$
$614$	11773.5	+	20392.3i	0.773845	+	1.34034i
$615$	1472.11			0.0965224
$616$	4818.93	+	1373.71i	0.315195	+	0.0898512i
$617$	3485.92			0.227452			0.113726	−	0.993512i	$-0.463721\pi$
$617$	3485.92			0.227452			0.113726	+	0.993512i	$0.463721\pi$
$618$	1829.73	+	3169.18i	0.119098	+	0.206283i
$619$	−8196.38	+	14196.5i	−0.532214	+	0.921821i	0.467079	+	0.884216i	$0.345306\pi$
$619$	−8196.38	+	14196.5i	−0.532214	+	0.921821i	−0.999293	+	0.0376055i	$0.988027\pi$
$620$	803.876	−	1392.35i	0.0520716	−	0.0901907i
$621$	1824.79	+	3160.63i	0.117917	+	0.204238i
$622$	16814.6			1.08393
$623$	4809.65	−	4659.09i	0.309301	−	0.299618i
$624$	847.170			0.0543493
$625$	−4563.85	−	7904.81i	−0.292086	−	0.505908i
$626$	2001.71	−	3467.06i	0.127802	−	0.221360i
$627$	−1.80923	+	3.13367i	−0.000115237	+	0.000199596i
$628$	1875.52	+	3248.50i	0.119174	+	0.206416i
$629$	−1023.95			−0.0649087
$630$	−1126.87	−	4489.91i	−0.0712627	−	0.283940i
$631$	−10711.4			−0.675773			−0.337886	−	0.941187i	$-0.609712\pi$
$631$	−10711.4			−0.675773			−0.337886	+	0.941187i	$0.609712\pi$
$632$	5997.89	+	10388.6i	0.377505	+	0.653858i
$633$	1427.60	−	2472.68i	0.0896400	−	0.155261i
$634$	4376.45	−	7580.23i	0.274150	−	0.474841i
$635$	4997.03	+	8655.12i	0.312285	+	0.540894i
$636$	393.522			0.0245349
$637$	9212.82	−	4935.31i	0.573038	−	0.306977i
$638$	−793.130			−0.0492168
$639$	1422.55	+	2463.93i	0.0880677	+	0.152538i
$640$	−366.955	+	635.585i	−0.0226643	+	0.0392558i
$641$	−13356.0	+	23133.2i	−0.822977	+	1.42544i	0.0804780	+	0.996756i	$0.474355\pi$
$641$	−13356.0	+	23133.2i	−0.822977	+	1.42544i	−0.903455	+	0.428682i	$0.858978\pi$
$642$	766.224	+	1327.14i	0.0471035	+	0.0815856i
$643$	−24917.4			−1.52822			−0.764112	−	0.645084i	$-0.776823\pi$
$643$	−24917.4			−1.52822			−0.764112	+	0.645084i	$0.776823\pi$
$644$	−1034.58	−	4122.19i	−0.0633047	−	0.252232i
$645$	−1159.55			−0.0707863
$646$	6.34001	+	10.9812i	0.000386137	+	0.000668809i
$647$	9437.99	−	16347.1i	0.573486	−	0.993307i	−0.422718	−	0.906261i	$-0.638924\pi$
$647$	9437.99	−	16347.1i	0.573486	−	0.993307i	0.996204	−	0.0870459i	$-0.0277427\pi$
$648$	−8171.91	+	14154.2i	−0.495406	+	0.858068i
$649$	3978.81	+	6891.50i	0.240650	+	0.416818i
$650$	−7275.81			−0.439047
$651$	−1498.34	+	1451.43i	−0.0902066	+	0.0873826i
$652$	1065.18			0.0639811
$653$	−6129.98	−	10617.4i	−0.367358	−	0.636283i	0.621794	−	0.783181i	$-0.286404\pi$
$653$	−6129.98	−	10617.4i	−0.367358	−	0.636283i	−0.989152	+	0.146899i	$0.953071\pi$
$654$	−9.53352	+	16.5125i	−0.000570015	+	0.000987296i
$655$	35.8923	−	62.1672i	0.00214111	−	0.00370851i
$656$	−5959.98	−	10323.0i	−0.354723	−	0.614398i
$657$	−18442.2			−1.09512
$658$	20710.2	+	5903.76i	1.22700	+	0.349776i
$659$	−20163.0			−1.19186			−0.595932	−	0.803035i	$-0.703217\pi$
$659$	−20163.0			−1.19186			−0.595932	+	0.803035i	$0.703217\pi$
$660$	63.1674	+	109.409i	0.00372544	+	0.00645265i
$661$	1204.72	−	2086.64i	0.0708899	−	0.122785i	−0.828402	−	0.560135i	$-0.810749\pi$
$661$	1204.72	−	2086.64i	0.0708899	−	0.122785i	0.899292	+	0.437350i	$0.144083\pi$
$662$	−6384.88	+	11058.9i	−0.374857	+	0.649271i
$663$	−211.333	−	366.039i	−0.0123793	−	0.0214416i
$664$	15230.3			0.890134
$665$	−27.8725	−	7.94549i	−0.00162534	−	0.000463328i
$666$	3878.43			0.225655
$667$	1233.18	+	2135.92i	0.0715874	+	0.123993i
$668$	2892.56	−	5010.06i	0.167540	−	0.290187i
$669$	1279.51	−	2216.18i	0.0739444	−	0.128075i
$670$	2672.08	+	4628.17i	0.154077	+	0.266868i
$671$	1820.80			0.104756
$672$	−1521.00	+	1473.39i	−0.0873124	+	0.0845790i
$673$	−12305.9			−0.704838			−0.352419	−	0.935842i	$-0.614641\pi$
$673$	−12305.9			−0.704838			−0.352419	+	0.935842i	$0.614641\pi$
$674$	−4885.70	−	8462.28i	−0.279214	−	0.483612i
$675$	−2547.82	+	4412.95i	−0.145282	+	0.251637i
$676$	−1903.03	+	3296.14i	−0.108274	+	0.187536i
$677$	6184.40	+	10711.7i	0.351087	+	0.608101i	0.986440	−	0.164121i	$-0.0524788\pi$
$677$	6184.40	+	10711.7i	0.351087	+	0.608101i	−0.635353	+	0.772222i	$0.719145\pi$
$678$	4103.13			0.232418
$679$	6812.92	+	27145.5i	0.385060	+	1.53424i
$680$	1623.13			0.0915357
$681$	1848.37	+	3201.48i	0.104009	+	0.180148i
$682$	1544.25	−	2674.71i	0.0867042	−	0.150176i
$683$	−7831.91	+	13565.3i	−0.438770	+	0.759971i	−0.997595	−	0.0693142i	$-0.977919\pi$
$683$	−7831.91	+	13565.3i	−0.438770	+	0.759971i	0.558825	+	0.829285i	$0.311252\pi$
$684$	14.4113	+	24.9610i	0.000805597	+	0.00139534i
$685$	−3498.31			−0.195129
$686$	4326.29	−	13529.1i	0.240785	−	0.752979i
$687$	−3645.90			−0.202474
$688$	4694.53	+	8131.17i	0.260142	+	0.450579i
$689$	−2227.68	+	3858.46i	−0.123175	+	0.213346i
$690$	−327.317	+	566.930i	−0.0180591	+	0.0312792i
$691$	14821.5	+	25671.7i	0.815974	+	1.41331i	0.908626	+	0.417611i	$0.137132\pi$
$691$	14821.5	+	25671.7i	0.815974	+	1.41331i	−0.0926517	+	0.995699i	$0.529534\pi$
$692$	2823.87			0.155126
$693$	1299.08	+	5176.07i	0.0712092	+	0.283727i
$694$	−16859.6			−0.922163
$695$	5554.42	+	9620.54i	0.303153	+	0.525076i
$696$	355.734	−	616.149i	0.0193736	−	0.0335561i
$697$	−2973.52	+	5150.28i	−0.161593	+	0.279886i
$698$	10425.1	+	18056.8i	0.565323	+	0.979169i
$699$	976.341			0.0528306
$700$	4262.17	−	4128.74i	0.230136	−	0.222931i
$701$	−15209.0			−0.819453			−0.409727	−	0.912208i	$-0.634376\pi$
$701$	−15209.0			−0.819453			−0.409727	+	0.912208i	$0.634376\pi$
$702$	1625.52	+	2815.49i	0.0873951	+	0.151373i
$703$	12.1413	−	21.0294i	0.000651378	−	0.00112822i
$704$	2931.38	−	5077.30i	0.156933	−	0.271815i
$705$	995.315	+	1723.94i	0.0531713	+	0.0920953i
$706$	16462.3			0.877572
$707$	−9618.58	−	2741.92i	−0.511660	−	0.145857i
$708$	−1946.98			−0.103350
$709$	−18397.9	−	31866.0i	−0.974536	−	1.68795i	−0.681456	−	0.731859i	$-0.738653\pi$
$709$	−18397.9	−	31866.0i	−0.974536	−	1.68795i	−0.293080	−	0.956088i	$-0.594680\pi$
$710$	−518.172	+	897.499i	−0.0273896	+	0.0474402i
$711$	−6387.73	+	11063.9i	−0.336932	+	0.583583i
$712$	−4446.63	−	7701.79i	−0.234051	−	0.405389i
$713$	−9604.11			−0.504455
$714$	−552.413	−	157.474i	−0.0289545	−	0.00825394i
$715$	−1430.33			−0.0748131
$716$	5326.77	+	9226.23i	0.278032	+	0.481565i
$717$	563.969	−	976.822i	0.0293749	−	0.0508788i
$718$	3828.96	−	6631.95i	0.199019	−	0.344711i
$719$	−11482.0	−	19887.5i	−0.595560	−	1.03154i	−0.993468	−	0.114114i	$-0.963597\pi$
$719$	−11482.0	−	19887.5i	−0.595560	−	1.03154i	0.397908	−	0.917425i	$-0.369736\pi$
$720$	−3464.79			−0.179340
$721$	24270.5	−	23510.8i	1.25365	−	1.21441i
$722$	15336.3			0.790525
$723$	−2417.20	−	4186.72i	−0.124339	−	0.215361i
$724$	−3257.14	+	5641.54i	−0.167197	+	0.289594i
$725$	−1721.79	+	2982.23i	−0.0882011	+	0.152769i
$726$	121.345	+	210.175i	0.00620320	+	0.0107443i
$727$	17015.4			0.868043			0.434022	−	0.900902i	$-0.357094\pi$
$727$	17015.4			0.868043			0.434022	+	0.900902i	$0.357094\pi$
$728$	−3378.92	−	13463.0i	−0.172021	−	0.685401i
$729$	−16250.5			−0.825609
$730$	−3358.82	−	5817.65i	−0.170295	−	0.294960i
$731$	2342.17	−	4056.76i	0.118506	−	0.205259i
$732$	−222.746	+	385.807i	−0.0112472	+	0.0194807i
$733$	13873.8	+	24030.2i	0.699102	+	1.21088i	0.968778	+	0.247929i	$0.0797500\pi$
$733$	13873.8	+	24030.2i	0.699102	+	1.21088i	−0.269676	+	0.962951i	$0.586917\pi$
$734$	−28198.1			−1.41800
$735$	1157.35	−	619.995i	0.0580811	−	0.0311141i
$736$	−9749.38			−0.488270
$737$	−3080.43	−	5335.46i	−0.153961	−	0.266668i
$738$	11262.8	−	19507.8i	0.561776	−	0.973025i
$739$	−11522.5	+	19957.5i	−0.573560	+	0.993434i	0.422637	+	0.906299i	$0.361105\pi$
$739$	−11522.5	+	19957.5i	−0.573560	+	0.993434i	−0.996196	+	0.0871352i	$0.972229\pi$
$740$	−423.903	−	734.221i	−0.0210581	−	0.0364737i
$741$	10.0234			0.000496920
$742$	1473.97	+	5872.89i	0.0729259	+	0.290567i
$743$	10854.4			0.535948			0.267974	−	0.963426i	$-0.413646\pi$
$743$	10854.4			0.535948			0.267974	+	0.963426i	$0.413646\pi$
$744$	1385.25	+	2399.32i	0.0682602	+	0.118230i
$745$	−6350.01	+	10998.5i	−0.312277	+	0.540880i
$746$	6109.60	−	10582.1i	0.299850	−	0.519356i
$747$	8110.10	+	14047.1i	0.397233	+	0.688027i
$748$	−510.367			−0.0249477
$749$	10163.6	−	9845.45i	0.495822	−	0.480300i
$750$	−1983.90			−0.0965891
$751$	−4175.39	−	7231.99i	−0.202879	−	0.351397i	0.746576	−	0.665300i	$-0.231697\pi$
$751$	−4175.39	−	7231.99i	−0.202879	−	0.351397i	−0.949455	+	0.313903i	$0.898363\pi$
$752$	8059.25	−	13959.0i	0.390812	−	0.676906i
$753$	1905.66	−	3300.69i	0.0922257	−	0.159740i
$754$	1098.51	+	1902.68i	0.0530577	+	0.0918986i
$755$	2996.60			0.144447
$756$	−2549.91	−	726.891i	−0.122671	−	0.0349693i
$757$	−1224.67			−0.0587999			−0.0294000	−	0.999568i	$-0.509360\pi$
$757$	−1224.67			−0.0587999			−0.0294000	+	0.999568i	$0.509360\pi$
$758$	4190.03	+	7257.34i	0.200776	+	0.347755i
$759$	377.339	−	653.570i	0.0180455	−	0.0312557i
$760$	−19.2460	+	33.3351i	−0.000918588	+	0.00159104i
$761$	−1643.10	−	2845.92i	−0.0782683	−	0.135565i	0.824235	−	0.566248i	$-0.191606\pi$
$761$	−1643.10	−	2845.92i	−0.0782683	−	0.135565i	−0.902503	+	0.430684i	$0.858272\pi$
$762$	−4697.29			−0.223313
$763$	169.316	+	48.2662i	0.00803364	+	0.00229011i
$764$	−5670.28			−0.268512
$765$	864.315	+	1497.04i	0.0408489	+	0.0707523i
$766$	2600.17	−	4503.63i	0.122648	−	0.212432i
$767$	11021.6	−	19089.9i	0.518861	−	0.898694i
$768$	1739.87	+	3013.55i	0.0817477	+	0.141591i
$769$	27030.5			1.26755			0.633774	−	0.773519i	$-0.281505\pi$
$769$	27030.5			1.26755			0.633774	+	0.773519i	$0.281505\pi$
$770$	−1396.21	+	1352.50i	−0.0653455	+	0.0632998i
$771$	987.913			0.0461463
$772$	3221.29	+	5579.44i	0.150177	+	0.260115i
$773$	3209.83	−	5559.60i	0.149353	−	0.258687i	−0.781636	−	0.623735i	$-0.785614\pi$
$773$	3209.83	−	5559.60i	0.149353	−	0.258687i	0.930988	+	0.365049i	$0.118948\pi$
$774$	−8871.47	+	15365.8i	−0.411988	+	0.713583i
$775$	−6704.76	−	11613.0i	−0.310764	−	0.538259i
$776$	37169.9			1.71949
$777$	267.779	+	1066.94i	0.0123636	+	0.0492617i
$778$	6937.89			0.319711
$779$	−70.5160	−	122.137i	−0.00324326	−	0.00561749i
$780$	174.978	−	303.071i	0.00803234	−	0.0139124i
$781$	597.360	−	1034.66i	0.0273690	−	0.0474046i
$782$	−1322.30	−	2290.28i	−0.0604670	−	0.104732i
$783$	1538.70			0.0702280
$784$	−9033.28	−	5605.68i	−0.411502	−	0.255361i
$785$	−5335.06			−0.242569
$786$	16.8696	+	29.2191i	0.000765547	+	0.00132597i
$787$	5425.88	−	9397.89i	0.245758	−	0.425665i	−0.716586	−	0.697498i	$-0.754296\pi$
$787$	5425.88	−	9397.89i	0.245758	−	0.425665i	0.962344	+	0.271833i	$0.0876298\pi$
$788$	−6114.48	+	10590.6i	−0.276421	+	0.478774i
$789$	269.163	+	466.204i	0.0121451	+	0.0210359i
$790$	−4653.53			−0.209576
$791$	−9222.91	−	36747.9i	−0.414575	−	1.65184i
$792$	7087.51			0.317984
$793$	−2521.87	−	4368.02i	−0.112931	−	0.195602i
$794$	10758.4	−	18634.0i	0.480856	−	0.832868i
$795$	−279.851	+	484.716i	−0.0124846	+	0.0216240i
$796$	−3824.06	−	6623.47i	−0.170277	−	0.294928i
$797$	−11082.2			−0.492535			−0.246267	−	0.969202i	$-0.579204\pi$
$797$	−11082.2			−0.492535			−0.246267	+	0.969202i	$0.579204\pi$
$798$	9.78427	−	9.47797i	0.000434034	−	0.000420447i
$799$	−8041.74			−0.356066
$800$	−6806.18	−	11788.6i	−0.300793	−	0.520989i
$801$	4735.65	−	8202.39i	0.208896	−	0.361819i
$802$	−13042.2	+	22589.8i	−0.574235	+	0.994605i
$803$	3872.13	+	6706.72i	0.170167	+	0.294739i
$804$	1507.36			0.0661202
$805$	5813.19	+	1657.14i	0.254519	+	0.0725547i
$806$	−8555.34			−0.373882
$807$	1682.20	+	2913.66i	0.0733783	+	0.127095i
$808$	−6641.65	+	11503.7i	−0.289174	+	0.500863i
$809$	−3926.46	+	6800.83i	−0.170639	+	0.295556i	−0.938643	−	0.344889i	$-0.887917\pi$
$809$	−3926.46	+	6800.83i	−0.170639	+	0.295556i	0.768004	+	0.640445i	$0.221250\pi$
$810$	−3170.13	−	5490.83i	−0.137515	−	0.238183i
$811$	−23954.3			−1.03717			−0.518587	−	0.855025i	$-0.673542\pi$
$811$	−23954.3			−1.03717			−0.518587	+	0.855025i	$0.673542\pi$
$812$	−1723.21	−	491.227i	−0.0744738	−	0.0212299i
$813$	−736.132			−0.0317556
$814$	−814.318	−	1410.44i	−0.0350637	−	0.0607321i
$815$	−757.496	+	1312.02i	−0.0325570	+	0.0563903i
$816$	−214.968	+	372.336i	−0.00922229	+	0.0159735i
$817$	55.5438	+	96.2047i	0.00237850	+	0.00411968i
$818$	−18951.5			−0.810055
$819$	10617.9	−	10285.5i	0.453013	−	0.438832i
$820$	−4924.00			−0.209699
$821$	8356.55	+	14474.0i	0.355232	+	0.615280i	0.987158	−	0.159749i	$-0.0510685\pi$
$821$	8356.55	+	14474.0i	0.355232	+	0.615280i	−0.631926	+	0.775029i	$0.717735\pi$
$822$	822.117	−	1423.95i	0.0348840	−	0.0604208i
$823$	16429.1	−	28456.1i	0.695848	−	1.20524i	−0.274046	−	0.961717i	$-0.588362\pi$
$823$	16429.1	−	28456.1i	0.695848	−	1.20524i	0.969894	−	0.243528i	$-0.0783047\pi$
$824$	−22438.7	−	38864.9i	−0.948650	−	1.64311i
$825$	1053.70			0.0444669
$826$	−7292.54	−	29056.4i	−0.307191	−	1.22397i
$827$	6260.68			0.263247			0.131624	−	0.991300i	$-0.457981\pi$
$827$	6260.68			0.263247			0.131624	+	0.991300i	$0.457981\pi$
$828$	−3005.66	−	5205.96i	−0.126152	−	0.218502i
$829$	−15607.8	+	27033.4i	−0.653896	+	1.13258i	0.328273	+	0.944583i	$0.393533\pi$
$829$	−15607.8	+	27033.4i	−0.653896	+	1.13258i	−0.982169	+	0.187999i	$0.939800\pi$
$830$	−2954.14	+	5116.73i	−0.123542	+	0.213981i
$831$	−3348.94	−	5800.53i	−0.139800	−	0.242140i
$832$	−16240.3			−0.676719
$833$	−168.644	+	5301.41i	−0.00701460	+	0.220508i
$834$	−5221.24			−0.216783
$835$	4114.05	+	7125.75i	0.170506	+	0.295325i
$836$	6.05160	−	10.4817i	0.000250358	−	0.000433632i
$837$	−2995.88	+	5189.02i	−0.123719	+	0.214288i
$838$	8621.13	+	14932.2i	0.355384	+	0.615543i
$839$	−10139.1			−0.417213			−0.208607	−	0.978000i	$-0.566893\pi$
$839$	−10139.1			−0.417213			−0.208607	+	0.978000i	$0.566893\pi$
$840$	−424.475	−	1691.28i	−0.0174354	−	0.0694699i
$841$	−23349.2			−0.957365
$842$	10325.3	+	17883.9i	0.422604	+	0.731971i
$843$	1993.17	−	3452.27i	0.0814333	−	0.141047i
$844$	−4775.12	+	8270.75i	−0.194747	+	0.337312i
$845$	−2706.65	−	4688.06i	−0.110191	−	0.190857i
$846$	30459.8			1.23786
$847$	1609.59	−	1559.20i	0.0652964	−	0.0632522i
$848$	4532.01			0.183526
$849$	−2786.75	−	4826.80i	−0.112651	−	0.195118i
$850$	1846.23	−	3197.76i	0.0745000	−	0.129038i
$851$	−2532.24	+	4385.97i	−0.102002	+	0.176673i
$852$	146.155	+	253.148i	0.00587697	+	0.0101792i
$853$	27348.5			1.09777			0.548883	−	0.835899i	$-0.315053\pi$
$853$	27348.5			1.09777			0.548883	+	0.835899i	$0.315053\pi$
$854$	−6592.06	−	1879.17i	−0.264140	−	0.0752972i
$855$	−40.9939			−0.00163972
$856$	−9396.50	−	16275.2i	−0.375194	−	0.649855i
$857$	5290.12	−	9162.76i	0.210860	−	0.365220i	−0.741124	−	0.671368i	$-0.765707\pi$
$857$	5290.12	−	9162.76i	0.210860	−	0.365220i	0.951984	+	0.306148i	$0.0990402\pi$
$858$	336.133	−	582.200i	0.0133746	−	0.0231655i
$859$	−6842.91	−	11852.3i	−0.271801	−	0.470773i	0.697522	−	0.716563i	$-0.254286\pi$
$859$	−6842.91	−	11852.3i	−0.271801	−	0.470773i	−0.969323	+	0.245790i	$0.920953\pi$
$860$	3878.52			0.153786
$861$	6144.15	+	1751.48i	0.243196	+	0.0693268i
$862$	−30483.6			−1.20450
$863$	5020.32	+	8695.45i	0.198023	+	0.342986i	0.947887	−	0.318606i	$-0.103215\pi$
$863$	5020.32	+	8695.45i	0.198023	+	0.342986i	−0.749864	+	0.661592i	$0.769881\pi$
$864$	−3041.20	+	5267.51i	−0.119750	+	0.207412i
$865$	−2008.18	+	3478.27i	−0.0789365	+	0.136722i
$866$	11633.6	+	20150.0i	0.456497	+	0.790677i
$867$	−4192.50			−0.164227
$868$	5011.72	−	4854.83i	0.195978	−	0.189843i
$869$	5364.69			0.209419
$870$	138.000	+	239.023i	0.00537774	+	0.00931453i
$871$	−8533.01	+	14779.6i	−0.331952	+	0.574957i
$872$	116.913	−	202.500i	0.00454035	−	0.00786411i
$873$	19792.9	+	34282.3i	0.767341	+	1.32907i
$874$	62.7156			0.00242722
$875$	4459.37	+	17767.9i	0.172290	+	0.686475i
$876$	−1894.77			−0.0730803
$877$	−12096.0	−	20950.8i	−0.465737	−	0.806680i	0.533498	−	0.845802i	$-0.320877\pi$
$877$	−12096.0	−	20950.8i	−0.465737	−	0.806680i	−0.999234	+	0.0391216i	$0.987544\pi$
$878$	10525.1	−	18229.9i	0.404560	−	0.700718i
$879$	2561.40	−	4436.48i	0.0982867	−	0.170238i
$880$	727.469	+	1260.01i	0.0278670	+	0.0482671i
$881$	13339.4			0.510119			0.255060	−	0.966925i	$-0.417905\pi$
$881$	13339.4			0.510119			0.255060	+	0.966925i	$0.417905\pi$
$882$	638.775	−	20080.2i	0.0243862	−	0.766594i
$883$	21849.0			0.832704			0.416352	−	0.909203i	$-0.363308\pi$
$883$	21849.0			0.832704			0.416352	+	0.909203i	$0.363308\pi$
$884$	706.876	+	1224.35i	0.0268946	+	0.0465828i
$885$	1384.58	−	2398.16i	0.0525900	−	0.0910885i
$886$	−13042.3	+	22589.9i	−0.494542	+	0.856573i
$887$	4763.99	+	8251.48i	0.180337	+	0.312353i	0.941995	−	0.335626i	$-0.108948\pi$
$887$	4763.99	+	8251.48i	0.180337	+	0.312353i	−0.761658	+	0.647979i	$0.775614\pi$
$888$	1460.95			0.0552097
$889$	10558.5	+	42069.2i	0.398334	+	1.58713i
$890$	3449.97			0.129936
$891$	3654.60	+	6329.95i	0.137412	+	0.238004i
$892$	−4279.78	+	7412.79i	−0.160648	+	0.278250i
$893$	95.3537	−	165.157i	0.00357322	−	0.00618901i
$894$	−2984.55	−	5169.40i	−0.111654	−	0.193390i
$895$	−15152.4			−0.565909
$896$	−2287.76	+	2216.14i	−0.0853000	+	0.0826297i
$897$	−2090.51			−0.0778150
$898$	6980.90	+	12091.3i	0.259416	+	0.449322i
$899$	−2024.59	+	3506.69i	−0.0751100	+	0.130094i
$900$	4196.59	−	7268.71i	0.155429	−	0.269211i
$901$	−1130.54	−	1958.16i	−0.0418022	−	0.0724036i
$902$	−9459.01			−0.349169
$903$	−4839.60	−	1379.60i	−0.178352	−	0.0508419i
$904$	−50318.3			−1.85128
$905$	−4632.59	−	8023.89i	−0.170158	−	0.294722i
$906$	−704.212	+	1219.73i	−0.0258233	+	0.0447272i
$907$	13805.0	−	23911.0i	0.505389	−	0.875359i	−0.494592	−	0.869125i	$-0.664682\pi$
$907$	13805.0	−	23911.0i	0.505389	−	0.875359i	0.999981	−	0.00623345i	$-0.00198418\pi$
$908$	−6182.54	−	10708.5i	−0.225964	−	0.391380i
$909$	−14146.7			−0.516188
$910$	5178.39	+	1476.18i	0.188640	+	0.0537746i
$911$	51523.7			1.87383			0.936913	−	0.349562i	$-0.113670\pi$
$911$	51523.7			1.87383			0.936913	+	0.349562i	$0.113670\pi$
$912$	−5.09790	−	8.82982i	−0.000185097	−	0.000320597i
$913$	3405.60	−	5898.68i	0.123449	−	0.213820i
$914$	−13288.8	+	23016.9i	−0.480914	+	0.832968i
$915$	−316.809	−	548.729i	−0.0114463	−	0.0198256i
$916$	12195.0			0.439885
$917$	223.769	−	216.763i	0.00805833	−	0.00780606i
$918$	−1649.89			−0.0593188
$919$	−20217.8	−	35018.2i	−0.725705	−	1.25696i	−0.958683	−	0.284476i	$-0.908181\pi$
$919$	−20217.8	−	35018.2i	−0.725705	−	1.25696i	0.232978	−	0.972482i	$-0.425153\pi$
$920$	4014.02	−	6952.49i	0.143846	−	0.249149i
$921$	−4723.17	+	8180.77i	−0.168983	+	0.292688i
$922$	18981.1	+	32876.3i	0.677994	+	1.17432i
$923$	−3309.46			−0.118020
$924$	133.469	+	531.796i	0.00475196	+	0.0189338i
$925$	−7071.16			−0.251350
$926$	6096.39	+	10559.2i	0.216350	+	0.374728i
$927$	23897.1	−	41391.0i	0.846693	−	1.46651i
$928$	−2055.21	+	3559.74i	−0.0727001	+	0.125920i
$929$	24090.1	+	41725.4i	0.850777	+	1.47359i	0.880508	+	0.474031i	$0.157202\pi$
$929$	24090.1	+	41725.4i	0.850777	+	1.47359i	−0.0297308	+	0.999558i	$0.509465\pi$
$930$	−1074.76			−0.0378954
$931$	−106.878	−	66.3241i	−0.00376239	−	0.00233479i
$932$	−3265.72			−0.114777
$933$	3372.75	+	5841.78i	0.118348	+	0.204985i
$934$	−14392.5	+	24928.6i	−0.504217	+	0.873329i
$935$	362.944	−	628.638i	0.0126947	−	0.0219879i
$936$	−9816.45	−	17002.6i	−0.342800	−	0.593747i
$937$	32499.3			1.13309			0.566545	−	0.824031i	$-0.308280\pi$
$937$	32499.3			1.13309			0.566545	+	0.824031i	$0.308280\pi$
$938$	5645.94	+	22495.7i	0.196532	+	0.783062i
$939$	1606.04			0.0558161
$940$	−3329.18	−	5766.31i	−0.115517	−	0.200081i
$941$	−16637.2	+	28816.5i	−0.576363	+	0.998290i	0.419529	+	0.907742i	$0.362195\pi$
$941$	−16637.2	+	28816.5i	−0.576363	+	0.998290i	−0.995892	+	0.0905483i	$0.971138\pi$
$942$	1253.76	−	2171.57i	0.0433648	−	0.0751101i
$943$	14707.1	+	25473.4i	0.507877	+	0.879669i
$944$	−22422.4			−0.773079
$945$	2708.69	−	2623.90i	0.0932421	−	0.0903231i
$946$	7450.64			0.256069
$947$	27500.5	+	47632.3i	0.943661	+	1.63447i	0.758410	+	0.651777i	$0.225976\pi$
$947$	27500.5	+	47632.3i	0.943661	+	1.63447i	0.185251	+	0.982691i	$0.440690\pi$
$948$	−656.284	+	1136.72i	−0.0224843	+	0.0389439i
$949$	10726.1	−	18578.1i	0.366894	−	0.635480i
$950$	43.7826	+	75.8338i	0.00149526	+	0.00258987i
$951$	3511.39			0.119731
$952$	6774.46	+	1931.16i	0.230632	+	0.0657451i
$953$	−6961.79			−0.236636			−0.118318	−	0.992976i	$-0.537750\pi$
$953$	−6961.79			−0.236636			−0.118318	+	0.992976i	$0.537750\pi$
$954$	4282.17	+	7416.93i	0.145325	+	0.251711i
$955$	4032.38	−	6984.29i	0.136633	−	0.236656i
$956$	−1886.39	+	3267.33i	−0.0638183	+	0.110537i
$957$	−159.090	−	275.551i	−0.00537370	−	0.00930753i
$958$	5440.83			0.183492
$959$	−14600.9	−	4162.21i	−0.491645	−	0.140151i
$960$	−2040.17			−0.0685899
$961$	7011.63	+	12144.5i	0.235361	+	0.407657i
$962$	−2255.72	+	3907.02i	−0.0756001	+	0.130943i
$963$	10007.2	−	17333.1i	0.334869	−	0.580010i
$964$	8085.19	+	14004.0i	0.270131	+	0.467881i
$965$	−9163.21			−0.305673
$966$	−2040.64	+	1976.76i	−0.0679675	+	0.0658398i
$967$	10554.7			0.350998			0.175499	−	0.984480i	$-0.443846\pi$
$967$	10554.7			0.350998			0.175499	+	0.984480i	$0.443846\pi$
$968$	−1488.10	−	2577.46i	−0.0494104	−	0.0855814i
$969$	−2.54341	+	4.40532i	−8.43201e−5	+	0.000146047i
$970$	−7209.66	+	12487.5i	−0.238648	+	0.413350i
$971$	8741.97	+	15141.5i	0.288922	+	0.500427i	0.973553	−	0.228463i	$-0.0733699\pi$
$971$	8741.97	+	15141.5i	0.288922	+	0.500427i	−0.684631	+	0.728890i	$0.740037\pi$
$972$	−5653.84			−0.186571
$973$	11736.2	+	46761.7i	0.386685	+	1.54071i
$974$	4172.16			0.137253
$975$	−1459.41	−	2527.78i	−0.0479371	−	0.0830294i
$976$	−2565.26	+	4443.16i	−0.0841311	+	0.145719i
$977$	23521.4	−	40740.3i	0.770233	−	1.33408i	−0.167202	−	0.985923i	$-0.553473\pi$
$977$	23521.4	−	40740.3i	0.770233	−	1.33408i	0.937435	−	0.348160i	$-0.113194\pi$
$978$	−356.029	−	616.660i	−0.0116406	−	0.0201622i
$979$	−3977.20			−0.129839
$980$	−3871.18	+	2073.79i	−0.126184	+	0.0675968i
$981$	249.025			0.00810473
$982$	−3922.62	−	6794.18i	−0.127470	−	0.220785i
$983$	25684.2	−	44486.4i	0.833368	−	1.44343i	−0.0619851	−	0.998077i	$-0.519743\pi$
$983$	25684.2	−	44486.4i	0.833368	−	1.44343i	0.895353	−	0.445358i	$-0.146924\pi$
$984$	4242.54	−	7348.30i	0.137446	−	0.238064i
$985$	−8696.55	−	15062.9i	−0.281315	−	0.487252i
$986$	−1114.98			−0.0360125
$987$	2103.04	+	8379.39i	0.0678223	+	0.270232i
$988$	−33.5267			−0.00107958
$989$	−11584.4	−	20064.8i	−0.372460	−	0.645120i
$990$	−1374.73	+	2381.10i	−0.0441331	+	0.0764408i
$991$	−4879.25	+	8451.10i	−0.156402	+	0.270896i	−0.933569	−	0.358399i	$-0.883323\pi$
$991$	−4879.25	+	8451.10i	−0.156402	+	0.270896i	0.777167	+	0.629295i	$0.216656\pi$
$992$	−8003.12	−	13861.8i	−0.256148	−	0.443662i
$993$	−5122.83			−0.163714
$994$	−3230.51	+	3129.38i	−0.103084	+	0.0998571i
$995$	10877.8			0.346583
$996$	833.242	+	1443.22i	0.0265083	+	0.0459137i
$997$	−12909.4	+	22359.7i	−0.410075	+	0.710270i	−0.994898	−	0.100891i	$-0.967831\pi$
$997$	−12909.4	+	22359.7i	−0.410075	+	0.710270i	0.584823	+	0.811161i	$0.301164\pi$
$998$	3739.30	−	6476.66i	0.118603	−	0.205426i
$999$	1579.80	+	2736.30i	0.0500327	+	0.0866592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.4.e.c.67.7	yes	20
7.2	even	3	inner	77.4.e.c.23.7	✓	20
7.3	odd	6		539.4.a.m.1.4		10
7.4	even	3		539.4.a.n.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.4.e.c.23.7	✓	20	7.2	even	3	inner
77.4.e.c.67.7	yes	20	1.1	even	1	trivial
539.4.a.m.1.4		10	7.3	odd	6
539.4.a.n.1.4		10	7.4	even	3

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	77.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11799 + 1.93642i) q^{2} +(-0.448504 + 0.776832i) q^{3} +(1.50018 - 2.59839i) q^{4} +(2.13369 + 3.69565i) q^{5} -2.00570 q^{6} +(4.50836 + 17.9631i) q^{7} +24.5967 q^{8} +(13.0977 + 22.6859i) q^{9} +(-4.77090 + 8.26344i) q^{10} +(5.50000 - 9.52628i) q^{11} +(1.34567 + 2.33077i) q^{12} -30.4708 q^{13} +(-29.7439 + 28.8128i) q^{14} -3.82787 q^{15} +(15.4975 + 26.8424i) q^{16} +(7.73191 - 13.3921i) q^{17} +(-29.2863 + 50.7253i) q^{18} +(0.183360 + 0.317588i) q^{19} +12.8037 q^{20} +(-15.9764 - 4.55431i) q^{21} +24.5959 q^{22} +(-38.2422 - 66.2374i) q^{23} +(-11.0317 + 19.1075i) q^{24} +(53.3948 - 92.4824i) q^{25} +(-34.0661 - 59.0043i) q^{26} -47.7167 q^{27} +(53.4386 + 15.2335i) q^{28} -32.2465 q^{29} +(-4.27953 - 7.41237i) q^{30} +(62.7848 - 108.747i) q^{31} +(63.7345 - 110.391i) q^{32} +(4.93354 + 8.54515i) q^{33} +34.5769 q^{34} +(-56.7662 + 54.9891i) q^{35} +78.5956 q^{36} +(-33.1079 - 57.3446i) q^{37} +(-0.409990 + 0.710124i) q^{38} +(13.6663 - 23.6707i) q^{39} +(52.4816 + 90.9008i) q^{40} -384.577 q^{41} +(-9.04241 - 36.0287i) q^{42} +302.922 q^{43} +(-16.5020 - 28.5823i) q^{44} +(-55.8927 + 96.8091i) q^{45} +(85.5090 - 148.106i) q^{46} +(-260.018 - 450.365i) q^{47} -27.8027 q^{48} +(-302.349 + 161.969i) q^{49} +238.780 q^{50} +(6.93558 + 12.0128i) q^{51} +(-45.7116 + 79.1749i) q^{52} +(73.1088 - 126.628i) q^{53} +(-53.3469 - 92.3996i) q^{54} +46.9411 q^{55} +(110.891 + 441.834i) q^{56} -0.328950 q^{57} +(-36.0514 - 62.4428i) q^{58} +(-361.710 + 626.500i) q^{59} +(-5.74249 + 9.94629i) q^{60} +(82.7637 + 143.351i) q^{61} +280.772 q^{62} +(-348.460 + 337.552i) q^{63} +532.979 q^{64} +(-65.0151 - 112.609i) q^{65} +(-11.0313 + 19.1068i) q^{66} +(280.039 - 485.042i) q^{67} +(-23.1985 - 40.1810i) q^{68} +68.6071 q^{69} +(-169.946 - 48.4458i) q^{70} +108.611 q^{71} +(322.159 + 557.997i) q^{72} +(-352.012 + 609.702i) q^{73} +(74.0289 - 128.222i) q^{74} +(47.8955 + 82.9575i) q^{75} +1.10029 q^{76} +(195.918 + 55.8494i) q^{77} +61.1152 q^{78} +(243.850 + 422.360i) q^{79} +(-66.1335 + 114.547i) q^{80} +(-332.236 + 575.450i) q^{81} +(-429.955 - 744.704i) q^{82} +619.201 q^{83} +(-35.8013 + 34.6805i) q^{84} +65.9899 q^{85} +(338.665 + 586.586i) q^{86} +(14.4627 - 25.0501i) q^{87} +(135.282 - 234.315i) q^{88} +(-180.782 - 313.123i) q^{89} -249.951 q^{90} +(-137.373 - 547.351i) q^{91} -229.481 q^{92} +(56.3185 + 97.5465i) q^{93} +(581.397 - 1007.01i) q^{94} +(-0.782465 + 1.35527i) q^{95} +(57.1704 + 99.0220i) q^{96} +1511.18 q^{97} +(-651.664 - 404.396i) q^{98} +288.149 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 54 q^{4} - 10 q^{5} + 106 q^{6} - 30 q^{7} + 6 q^{8} - 76 q^{9} - 63 q^{10} + 110 q^{11} - 55 q^{12} + 324 q^{13} + 58 q^{14} + 60 q^{15} - 286 q^{16} - 200 q^{17} + 252 q^{18} - 252 q^{19} + 192 q^{20}+ \cdots - 1672 q^{99}+O(q^{100}) \) 20 * q - 54 * q^4 - 10 * q^5 + 106 * q^6 - 30 * q^7 + 6 * q^8 - 76 * q^9 - 63 * q^10 + 110 * q^11 - 55 * q^12 + 324 * q^13 + 58 * q^14 + 60 * q^15 - 286 * q^16 - 200 * q^17 + 252 * q^18 - 252 * q^19 + 192 * q^20 + 458 * q^21 - 134 * q^23 - 786 * q^24 - 86 * q^25 - 363 * q^26 + 348 * q^27 - 1057 * q^28 + 296 * q^29 + 316 * q^30 - 530 * q^31 + 731 * q^32 + 204 * q^34 - 288 * q^35 + 2574 * q^36 + 902 * q^37 - 66 * q^38 + 208 * q^39 - 2163 * q^40 + 336 * q^41 - 1482 * q^42 + 236 * q^43 + 594 * q^44 - 58 * q^45 + 210 * q^46 - 288 * q^47 - 1700 * q^48 - 1072 * q^49 + 4650 * q^50 + 1022 * q^51 - 1663 * q^52 + 608 * q^53 - 2312 * q^54 - 220 * q^55 - 4905 * q^56 + 1656 * q^57 + 1951 * q^58 + 464 * q^59 + 818 * q^60 - 3484 * q^61 - 1618 * q^62 - 3948 * q^63 + 6090 * q^64 + 1560 * q^65 + 583 * q^66 - 142 * q^67 - 1145 * q^68 + 3432 * q^69 - 4133 * q^70 + 668 * q^71 + 1176 * q^72 - 1466 * q^73 + 3460 * q^74 - 2982 * q^75 + 6774 * q^76 - 330 * q^77 + 10840 * q^78 - 578 * q^79 - 2911 * q^80 - 118 * q^81 + 307 * q^82 + 1092 * q^83 - 6786 * q^84 + 5164 * q^85 - 2597 * q^86 - 1516 * q^87 + 33 * q^88 - 3150 * q^89 - 3672 * q^90 - 3638 * q^91 + 4326 * q^92 + 1484 * q^93 - 5700 * q^94 + 1338 * q^95 - 5429 * q^96 + 3308 * q^97 - 3186 * q^98 - 1672 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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