LMFDB - Embedded newform 207.4.m.a.4.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,4,Mod(4,207)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([22, 12])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("207.4"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	207.m (of order $33$, degree $20$, 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:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$1400$
Relative dimension:	$70$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			4.4
Character	$\chi$	$=$	207.4
Dual form			207.4.m.a.52.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.95477 + 4.14939i) q^{2} +(4.94560 + 1.59406i) q^{3} +(-5.87025 - 16.9610i) q^{4} +(0.0815901 - 0.0420626i) q^{5} +(-21.2275 + 15.8112i) q^{6} +(1.55780 - 1.22507i) q^{7} +(48.6222 + 14.2768i) q^{8} +(21.9180 + 15.7672i) q^{9} +(-0.0665456 + 0.462835i) q^{10} +(12.3755 - 1.18172i) q^{11} +(-1.99513 - 93.2397i) q^{12} +(-4.94929 - 3.89216i) q^{13} +(0.480347 + 10.0837i) q^{14} +(0.470563 - 0.0779656i) q^{15} +(-90.0420 + 70.8098i) q^{16} +(58.9545 + 68.0371i) q^{17} +(-130.187 + 44.3579i) q^{18} +(-75.0163 + 86.5734i) q^{19} +(-1.19238 - 1.13693i) q^{20} +(9.65710 - 3.57547i) q^{21} +(-31.6633 + 54.8424i) q^{22} +(68.5488 + 86.4180i) q^{23} +(217.708 + 148.114i) q^{24} +(-72.5022 + 101.815i) q^{25} +(30.7741 - 9.03610i) q^{26} +(83.2637 + 112.917i) q^{27} +(-29.9230 - 19.2304i) q^{28} +(18.3928 - 53.1426i) q^{29} +(-1.06689 + 2.18292i) q^{30} +(-21.6617 + 20.6544i) q^{31} +(-8.47470 - 177.906i) q^{32} +(63.0879 + 13.8830i) q^{33} +(-456.509 + 43.5914i) q^{34} +(0.0755716 - 0.165479i) q^{35} +(138.763 - 464.307i) q^{36} +(78.4595 - 50.4228i) q^{37} +(-137.571 - 567.076i) q^{38} +(-18.2729 - 27.1386i) q^{39} +(4.56761 - 0.880335i) q^{40} +(11.3103 - 5.83085i) q^{41} +(-13.6984 + 50.6358i) q^{42} +(-75.6036 - 72.0879i) q^{43} +(-92.6902 - 202.963i) q^{44} +(2.45150 + 0.364518i) q^{45} +(-561.128 + 29.0908i) q^{46} +(-5.47663 - 9.48581i) q^{47} +(-558.187 + 206.665i) q^{48} +(-79.9394 + 329.515i) q^{49} +(-208.244 - 601.680i) q^{50} +(183.110 + 430.461i) q^{51} +(-36.9613 + 106.793i) q^{52} +(-8.86736 - 61.6739i) q^{53} +(-714.560 + 11.8512i) q^{54} +(0.960011 - 0.616962i) q^{55} +(93.2338 - 37.3252i) q^{56} +(-509.004 + 308.577i) q^{57} +(166.163 + 233.343i) q^{58} +(-221.101 - 173.875i) q^{59} +(-4.08469 - 7.52352i) q^{60} +(-126.102 - 519.798i) q^{61} +(-21.6979 - 150.912i) q^{62} +(53.4597 - 2.28889i) q^{63} +(-7.67937 - 4.93523i) q^{64} +(-0.567528 - 0.109382i) q^{65} +(-244.016 + 220.756i) q^{66} +(702.598 + 67.0900i) q^{67} +(807.898 - 1399.32i) q^{68} +(201.260 + 536.660i) q^{69} +(0.463339 + 0.802527i) q^{70} +(277.972 + 608.674i) q^{71} +(840.595 + 1079.55i) q^{72} +(449.583 - 518.847i) q^{73} +(-22.6055 + 474.547i) q^{74} +(-520.866 + 387.964i) q^{75} +(1908.73 + 764.141i) q^{76} +(17.8309 - 17.0017i) q^{77} +(166.601 + 4.36682i) q^{78} +(-180.256 + 72.1638i) q^{79} +(-4.36809 + 9.56479i) q^{80} +(231.793 + 691.168i) q^{81} +(-9.22475 + 64.1596i) q^{82} +(682.168 + 351.682i) q^{83} +(-117.333 - 142.805i) q^{84} +(7.67193 + 3.07138i) q^{85} +(522.512 - 100.706i) q^{86} +(175.676 - 233.503i) q^{87} +(618.595 + 119.224i) q^{88} +(-537.902 + 157.942i) q^{89} +(-8.75613 + 9.09515i) q^{90} -12.4782 q^{91} +(1063.33 - 1669.95i) q^{92} +(-140.055 + 67.6185i) q^{93} +(55.5425 + 5.30367i) q^{94} +(-2.47908 + 10.2189i) q^{95} +(241.680 - 893.361i) q^{96} +(-84.8404 + 1781.02i) q^{97} +(-1131.08 - 1305.34i) q^{98} +(289.878 + 169.225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1400 q - 9 q^{2} - 14 q^{3} + 263 q^{4} + 19 q^{5} - 35 q^{6} - 9 q^{7} - 74 q^{8} - 78 q^{9} - 68 q^{10} + 79 q^{11} + 54 q^{12} - 9 q^{13} + 159 q^{14} - 868 q^{15} + 1031 q^{16} - 308 q^{17} - 87 q^{18}+ \cdots + 7484 q^{99}+O(q^{100}) $ 1400 * q - 9 * q^2 - 14 * q^3 + 263 * q^4 + 19 * q^5 - 35 * q^6 - 9 * q^7 - 74 * q^8 - 78 * q^9 - 68 * q^10 + 79 * q^11 + 54 * q^12 - 9 * q^13 + 159 * q^14 - 868 * q^15 + 1031 * q^16 - 308 * q^17 - 87 * q^18 - 36 * q^19 + 119 * q^20 - 660 * q^21 - 52 * q^22 - 116 * q^23 + 2420 * q^24 + 1397 * q^25 + 432 * q^26 + 274 * q^27 - 324 * q^28 - 45 * q^29 + 768 * q^30 - 45 * q^31 + 111 * q^32 - 1664 * q^33 + 403 * q^34 - 536 * q^35 - 121 * q^36 - 180 * q^37 - 117 * q^38 - 46 * q^39 - 473 * q^40 - 333 * q^41 - 332 * q^42 - 9 * q^43 - 1908 * q^44 + 1762 * q^45 + 484 * q^46 + 216 * q^47 + 1072 * q^48 + 4615 * q^49 - 105 * q^50 + 1298 * q^51 - 708 * q^52 - 1380 * q^53 + 4116 * q^54 - 1328 * q^55 - 3971 * q^56 + 2154 * q^57 - 338 * q^58 + 1917 * q^59 + 154 * q^60 + 27 * q^61 - 3854 * q^62 - 4850 * q^63 - 5854 * q^64 + 3363 * q^65 - 2017 * q^66 + 603 * q^67 - 18454 * q^68 - 4653 * q^69 + 542 * q^70 - 5296 * q^71 - 8044 * q^72 - 36 * q^73 + 3243 * q^74 + 5140 * q^75 - 1029 * q^76 - 1661 * q^77 + 14687 * q^78 - 9 * q^79 + 10312 * q^80 - 294 * q^81 - 770 * q^82 - 2735 * q^83 + 2298 * q^84 + 241 * q^85 + 10507 * q^86 - 10268 * q^87 + 2183 * q^88 - 2980 * q^89 + 33928 * q^90 - 1452 * q^91 - 1973 * q^92 - 11406 * q^93 + 2034 * q^94 - 3339 * q^95 - 4446 * q^96 - 5193 * q^97 + 14820 * q^98 + 7484 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.95477	+	4.14939i	−1.04467	+	1.46703i	−0.168090	+	0.985772i	$0.553760\pi$
$2$	−2.95477	+	4.14939i	−1.04467	+	1.46703i	−0.876578	+	0.481260i	$0.840179\pi$
$3$	4.94560	+	1.59406i	0.951781	+	0.306777i
$3$	4.94560	+	1.59406i	0.951781	+	0.306777i
$4$	−5.87025	−	16.9610i	−0.733781	−	2.12012i
$5$	0.0815901	−	0.0420626i	0.00729764	−	0.00376220i	−0.454574	−	0.890709i	$-0.650208\pi$
$5$	0.0815901	−	0.0420626i	0.00729764	−	0.00376220i	0.461871	+	0.886947i	$0.347178\pi$
$6$	−21.2275	+	15.8112i	−1.44435	+	1.07581i
$7$	1.55780	−	1.22507i	0.0841134	−	0.0661475i	−0.575217	−	0.818001i	$-0.695082\pi$
$7$	1.55780	−	1.22507i	0.0841134	−	0.0661475i	0.659330	+	0.751853i	$0.270840\pi$
$8$	48.6222	+	14.2768i	2.14882	+	0.630950i
$9$	21.9180	+	15.7672i	0.811776	+	0.583969i
$10$	−0.0665456	+	0.462835i	−0.00210436	+	0.0146361i
$11$	12.3755	−	1.18172i	0.339214	−	0.0323910i	0.0759406	−	0.997112i	$-0.475804\pi$
$11$	12.3755	−	1.18172i	0.339214	−	0.0323910i	0.263273	+	0.964721i	$0.415198\pi$
$12$	−1.99513	−	93.2397i	−0.0479953	−	2.24300i
$13$	−4.94929	−	3.89216i	−0.105591	−	0.0830379i	0.563967	−	0.825797i	$-0.309274\pi$
$13$	−4.94929	−	3.89216i	−0.105591	−	0.0830379i	−0.669559	+	0.742759i	$0.733517\pi$
$14$	0.480347	+	10.0837i	0.00916986	+	0.192499i
$15$	0.470563	−	0.0779656i	0.00809992	−	0.00134204i
$16$	−90.0420	+	70.8098i	−1.40691	+	1.10640i
$17$	58.9545	+	68.0371i	0.841092	+	0.970672i	0.999861	−	0.0166438i	$-0.00529813\pi$
$17$	58.9545	+	68.0371i	0.841092	+	0.970672i	−0.158770	+	0.987316i	$0.550753\pi$
$18$	−130.187	+	44.3579i	−1.70474	+	0.580847i
$19$	−75.0163	+	86.5734i	−0.905785	+	1.04533i	0.0929811	+	0.995668i	$0.470360\pi$
$19$	−75.0163	+	86.5734i	−0.905785	+	1.04533i	−0.998766	+	0.0496636i	$0.984185\pi$
$20$	−1.19238	−	1.13693i	−0.0133312	−	0.0127113i
$21$	9.65710	−	3.57547i	0.100350	−	0.0371539i
$22$	−31.6633	+	54.8424i	−0.306847	+	0.531475i
$23$	68.5488	+	86.4180i	0.621453	+	0.783452i
$23$	68.5488	+	86.4180i	0.621453	+	0.783452i
$24$	217.708	+	148.114i	1.85164	+	1.25973i
$25$	−72.5022	+	101.815i	−0.580018	+	0.814521i
$26$	30.7741	−	9.03610i	0.232127	−	0.0681586i
$27$	83.2637	+	112.917i	0.593485	+	0.804845i
$28$	−29.9230	−	19.2304i	−0.201961	−	0.129793i
$29$	18.3928	−	53.1426i	0.117775	−	0.340288i	−0.870670	−	0.491867i	$-0.836315\pi$
$29$	18.3928	−	53.1426i	0.117775	−	0.340288i	0.988445	+	0.151579i	$0.0484359\pi$
$30$	−1.06689	+	2.18292i	−0.00649291	+	0.0132848i
$31$	−21.6617	+	20.6544i	−0.125502	+	0.119666i	−0.750231	−	0.661176i	$-0.770058\pi$
$31$	−21.6617	+	20.6544i	−0.125502	+	0.119666i	0.624729	+	0.780841i	$0.285209\pi$
$32$	−8.47470	−	177.906i	−0.0468166	−	0.982801i
$33$	63.0879	+	13.8830i	0.332794	+	0.0732337i
$34$	−456.509	+	43.5914i	−2.30267	+	0.219878i
$35$	0.0755716	−	0.165479i	0.000364970	−	0.000799172i
$36$	138.763	−	464.307i	0.642419	−	2.14957i
$37$	78.4595	−	50.4228i	0.348612	−	0.224040i	−0.354602	−	0.935017i	$-0.615384\pi$
$37$	78.4595	−	50.4228i	0.348612	−	0.224040i	0.703215	+	0.710978i	$0.251747\pi$
$38$	−137.571	−	567.076i	−0.587289	−	2.42084i
$39$	−18.2729	−	27.1386i	−0.0750257	−	0.111427i
$40$	4.56761	−	0.880335i	0.0180551	−	0.00347983i
$41$	11.3103	−	5.83085i	0.0430821	−	0.0222104i	−0.436551	−	0.899680i	$-0.643800\pi$
$41$	11.3103	−	5.83085i	0.0430821	−	0.0222104i	0.479633	+	0.877469i	$0.340770\pi$
$42$	−13.6984	+	50.6358i	−0.0503265	+	0.186030i
$43$	−75.6036	−	72.0879i	−0.268127	−	0.255658i	0.544073	−	0.839038i	$-0.316881\pi$
$43$	−75.6036	−	72.0879i	−0.268127	−	0.255658i	−0.812200	+	0.583380i	$0.801730\pi$
$44$	−92.6902	−	202.963i	−0.317581	−	0.695406i
$45$	2.45150	+	0.364518i	0.00812106	+	0.00120754i
$46$	−561.128	+	29.0908i	−1.79856	+	0.0932435i
$47$	−5.47663	−	9.48581i	−0.0169968	−	0.0294393i	0.857402	−	0.514647i	$-0.172077\pi$
$47$	−5.47663	−	9.48581i	−0.0169968	−	0.0294393i	−0.874399	+	0.485208i	$0.838744\pi$
$48$	−558.187	+	206.665i	−1.67849	+	0.621448i
$49$	−79.9394	+	329.515i	−0.233059	+	0.960684i
$50$	−208.244	−	601.680i	−0.589002	−	1.70181i
$51$	183.110	+	430.461i	0.502756	+	1.18190i
$52$	−36.9613	+	106.793i	−0.0985695	+	0.284798i
$53$	−8.86736	−	61.6739i	−0.0229816	−	0.159841i	0.975099	−	0.221771i	$-0.0711836\pi$
$53$	−8.86736	−	61.6739i	−0.0229816	−	0.159841i	−0.998081	+	0.0619298i	$0.980274\pi$
$54$	−714.560	+	11.8512i	−1.80073	+	0.0298656i
$55$	0.960011	−	0.616962i	0.00235360	−	0.00151257i
$56$	93.2338	−	37.3252i	0.222480	−	0.0890676i
$57$	−509.004	+	308.577i	−1.18279	+	0.717053i
$58$	166.163	+	233.343i	0.376177	+	0.528267i
$59$	−221.101	−	173.875i	−0.487879	−	0.383672i	0.343699	−	0.939080i	$-0.388320\pi$
$59$	−221.101	−	173.875i	−0.487879	−	0.383672i	−0.831578	+	0.555408i	$0.812562\pi$
$60$	−4.08469	−	7.52352i	−0.00878886	−	0.0161880i
$61$	−126.102	−	519.798i	−0.264683	−	1.09104i	−0.936597	−	0.350408i	$-0.886043\pi$
$61$	−126.102	−	519.798i	−0.264683	−	1.09104i	0.671914	−	0.740629i	$-0.265472\pi$
$62$	−21.6979	−	150.912i	−0.0444457	−	0.309127i
$63$	53.4597	−	2.28889i	0.106909	−	0.00457735i
$64$	−7.67937	−	4.93523i	−0.0149988	−	0.00963913i
$65$	−0.567528	−	0.109382i	−0.00108297	−	0.000208726i
$66$	−244.016	+	220.756i	−0.455095	+	0.411714i
$67$	702.598	+	67.0900i	1.28114	+	0.122334i	0.713329	−	0.700829i	$-0.247186\pi$
$67$	702.598	+	67.0900i	1.28114	+	0.122334i	0.567806	+	0.823162i	$0.307792\pi$
$68$	807.898	−	1399.32i	1.44076	−	2.49548i
$69$	201.260	+	536.660i	0.351142	+	0.936322i
$70$	0.463339	+	0.802527i	0.000791138	+	0.00137029i
$71$	277.972	+	608.674i	0.464637	+	1.01741i	0.986406	+	0.164326i	$0.0525450\pi$
$71$	277.972	+	608.674i	0.464637	+	1.01741i	−0.521769	+	0.853087i	$0.674728\pi$
$72$	840.595	+	1079.55i	1.37590	+	1.76703i
$73$	449.583	−	518.847i	0.720819	−	0.831869i	−0.270587	−	0.962696i	$-0.587218\pi$
$73$	449.583	−	518.847i	0.720819	−	0.831869i	0.991405	+	0.130827i	$0.0417631\pi$
$74$	−22.6055	+	474.547i	−0.0355112	+	0.745472i
$75$	−520.866	+	387.964i	−0.801926	+	0.597310i
$76$	1908.73	+	764.141i	2.88088	+	1.15333i
$77$	17.8309	−	17.0017i	0.0263898	−	0.0251626i
$78$	166.601	+	4.36682i	0.241844	+	0.00633904i
$79$	−180.256	+	72.1638i	−0.256714	+	0.102773i	−0.496450	−	0.868065i	$-0.665363\pi$
$79$	−180.256	+	72.1638i	−0.256714	+	0.102773i	0.239736	+	0.970838i	$0.422939\pi$
$80$	−4.36809	+	9.56479i	−0.00610459	+	0.0133672i
$81$	231.793	+	691.168i	0.317961	+	0.948104i
$82$	−9.22475	+	64.1596i	−0.0124232	+	0.0864053i
$83$	682.168	+	351.682i	0.902141	+	0.465086i	0.845906	−	0.533332i	$-0.179060\pi$
$83$	682.168	+	351.682i	0.902141	+	0.465086i	0.0562345	+	0.998418i	$0.482091\pi$
$84$	−117.333	−	142.805i	−0.152406	−	0.185491i
$85$	7.67193	+	3.07138i	0.00978985	+	0.00391926i
$86$	522.512	−	100.706i	0.655162	−	0.126272i
$87$	175.676	−	233.503i	0.216488	−	0.287749i
$88$	618.595	+	119.224i	0.749345	+	0.144424i
$89$	−537.902	+	157.942i	−0.640646	+	0.188111i	−0.585892	−	0.810389i	$-0.699256\pi$
$89$	−537.902	+	157.942i	−0.640646	+	0.188111i	−0.0547544	+	0.998500i	$0.517438\pi$
$90$	−8.75613	+	9.09515i	−0.0102553	+	0.0106524i
$91$	−12.4782			−0.0143744
$92$	1063.33	−	1669.95i	1.20500	−	1.89244i
$93$	−140.055	+	67.6185i	−0.156161	+	0.0753947i
$94$	55.5425	+	5.30367i	0.0609444	+	0.00581948i
$95$	−2.47908	+	10.2189i	−0.00267735	+	0.0110362i
$96$	241.680	−	893.361i	0.256941	−	0.949774i
$97$	−84.8404	+	1781.02i	−0.0888066	+	1.86428i	0.314555	+	0.949239i	$0.398145\pi$
$97$	−84.8404	+	1781.02i	−0.0888066	+	1.86428i	−0.403362	+	0.915041i	$0.632158\pi$
$98$	−1131.08	−	1305.34i	−1.16588	−	1.34550i
$99$	289.878	+	169.225i	0.294281	+	0.171796i
$100$	2152.49	+	632.028i	2.15249	+	0.632028i
$101$	1524.24	+	785.800i	1.50166	+	0.774158i	0.996066	−	0.0886145i	$-0.0282439\pi$
$101$	1524.24	+	785.800i	1.50166	+	0.774158i	0.505592	+	0.862773i	$0.331274\pi$
$102$	−2327.20	−	512.117i	−2.25909	−	0.497129i
$103$	−817.347	−	1147.80i	−0.781899	−	1.09802i	−0.992714	−	0.120498i	$-0.961551\pi$
$103$	−817.347	−	1147.80i	−0.781899	−	1.09802i	0.210814	−	0.977526i	$-0.432389\pi$
$104$	−185.078	−	259.906i	−0.174504	−	0.245056i
$105$	0.637530	−	0.697926i	0.000592539	−	0.000648673i
$106$	282.110	+	145.438i	0.258499	+	0.133266i
$107$	−1093.51	−	321.085i	−0.987981	−	0.290097i	−0.252466	−	0.967606i	$-0.581242\pi$
$107$	−1093.51	−	321.085i	−0.987981	−	0.290097i	−0.735515	+	0.677508i	$0.763060\pi$
$108$	1426.40	−	2075.08i	1.27088	−	1.84884i
$109$	−17.9825	−	20.7530i	−0.0158020	−	0.0182365i	0.747794	−	0.663931i	$-0.231113\pi$
$109$	−17.9825	−	20.7530i	−0.0158020	−	0.0182365i	−0.763596	+	0.645695i	$0.776568\pi$
$110$	−0.276595	+	5.80644i	−0.000239748	+	0.00503293i
$111$	468.406	−	124.302i	0.400533	−	0.106291i
$112$	−53.5207	+	220.615i	−0.0451538	+	0.186127i
$113$	−3.32403	−	0.317407i	−0.00276725	−	0.000264240i	0.0936723	−	0.995603i	$-0.470139\pi$
$113$	−3.32403	−	0.317407i	−0.00276725	−	0.000264240i	−0.0964396	+	0.995339i	$0.530745\pi$
$114$	223.580	−	3023.83i	0.183686	−	2.48428i
$115$	9.22787	+	4.16751i	0.00748264	+	0.00337932i
$116$	−1009.32			−0.807872
$117$	−47.1099	−	163.345i	−0.0372249	−	0.129070i
$118$	1374.78	−	403.671i	1.07253	−	0.314923i
$119$	175.189	+	33.7650i	0.134955	+	0.0260104i
$120$	23.9929	+	2.92726i	0.0182520	+	0.00222684i
$121$	−1155.19	+	222.645i	−0.867912	+	0.167276i
$122$	2529.44	+	1012.64i	1.87709	+	0.751474i
$123$	65.2308	−	10.8078i	0.0478184	−	0.00792284i
$124$	477.479	+	246.157i	0.345797	+	0.178271i
$125$	−3.26582	+	22.7143i	−0.00233683	+	0.0162530i
$126$	−148.463	+	228.588i	−0.104970	+	0.161621i
$127$	−51.5813	+	112.947i	−0.0360402	+	0.0789170i	−0.926796	−	0.375565i	$-0.877449\pi$
$127$	−51.5813	+	112.947i	−0.0360402	+	0.0789170i	0.890756	+	0.454482i	$0.150176\pi$
$128$	1365.96	−	546.850i	0.943245	−	0.377618i
$129$	−258.993	−	477.035i	−0.176768	−	0.325586i
$130$	2.13078	−	2.03170i	0.00143755	−	0.00137070i
$131$	484.228	+	193.856i	0.322956	+	0.129292i	0.527475	−	0.849571i	$-0.323139\pi$
$131$	484.228	+	193.856i	0.322956	+	0.129292i	−0.204519	+	0.978863i	$0.565563\pi$
$132$	−134.873	−	1151.53i	−0.0889336	−	0.759301i
$133$	−10.8021	+	226.764i	−0.00704257	+	0.147842i
$134$	−2354.40	+	2717.12i	−1.51783	+	1.75167i
$135$	11.5431	+	5.71059i	0.00735903	+	0.00364066i
$136$	1895.15	+	4149.79i	1.19491	+	2.61648i
$137$	−72.3650	−	125.340i	−0.0451282	−	0.0781643i	0.842579	−	0.538573i	$-0.181036\pi$
$137$	−72.3650	−	125.340i	−0.0451282	−	0.0781643i	−0.887707	+	0.460408i	$0.847703\pi$
$138$	−2821.49	−	750.599i	−1.74044	−	0.463009i
$139$	1128.31	−	1954.29i	0.688505	−	1.19253i	−0.283816	−	0.958879i	$-0.591601\pi$
$139$	1128.31	−	1954.29i	0.688505	−	1.19253i	0.972321	−	0.233647i	$-0.0750661\pi$
$140$	−3.25030	−	0.310366i	−0.00196215	−	0.000187362i
$141$	−11.9643	−	55.6431i	−0.00714594	−	0.0332340i
$142$	−3346.97	−	645.076i	−1.97797	−	0.381222i
$143$	−65.8493	−	42.3188i	−0.0385076	−	0.0247474i
$144$	−3090.01	+	132.299i	−1.78820	+	0.0765621i
$145$	−0.734645	−	5.10957i	−0.000420751	−	0.00292639i
$146$	824.484	+	3398.57i	0.467362	+	1.92649i
$147$	−920.614	+	1502.22i	−0.516537	+	0.842864i
$148$	−1315.80	−	1034.75i	−0.730796	−	0.574705i
$149$	857.649	+	1204.40i	0.471553	+	0.662203i	0.980025	−	0.198875i	$-0.0637289\pi$
$149$	857.649	+	1204.40i	0.471553	+	0.662203i	−0.508472	+	0.861078i	$0.669789\pi$
$150$	−70.7759	−	3307.62i	−0.0385255	−	1.80044i
$151$	83.9415	−	33.6051i	0.0452388	−	0.0181109i	−0.348933	−	0.937148i	$-0.613456\pi$
$151$	83.9415	−	33.6051i	0.0452388	−	0.0181109i	0.394172	+	0.919037i	$0.371032\pi$
$152$	−4883.45	+	3138.40i	−2.60592	+	1.67472i
$153$	219.410	+	2420.78i	0.115936	+	1.27914i
$154$	17.8606	+	124.223i	0.00934577	+	0.0650013i
$155$	−0.898605	+	2.59635i	−0.000465662	+	0.00134544i
$156$	−353.030	+	469.236i	−0.181186	+	0.240826i
$157$	−506.072	−	1462.20i	−0.257255	−	0.743288i	−0.997481	−	0.0709308i	$-0.977403\pi$
$157$	−506.072	−	1462.20i	−0.257255	−	0.743288i	0.740227	−	0.672357i	$-0.234718\pi$
$158$	233.180	−	961.182i	0.117410	−	0.483972i
$159$	54.4573	−	319.149i	0.0271619	−	0.159184i
$160$	−8.17464	−	14.1589i	−0.00403914	−	0.00699600i
$161$	212.653	+	50.6450i	0.104096	+	0.0247912i
$162$	−3552.82	−	1080.44i	−1.72306	−	0.523996i
$163$	−761.361	−	1667.15i	−0.365855	−	0.801111i	−0.999619	−	0.0275848i	$-0.991218\pi$
$163$	−761.361	−	1667.15i	−0.365855	−	0.801111i	0.633764	−	0.773526i	$-0.281509\pi$
$164$	−165.291	−	157.605i	−0.0787016	−	0.0750418i
$165$	5.73131	−	1.52093i	0.00270413	−	0.000717603i
$166$	−3474.92	+	1791.44i	−1.62473	+	0.837608i
$167$	−2333.52	+	449.749i	−1.08128	+	0.208399i	−0.698621	−	0.715492i	$-0.746202\pi$
$167$	−2333.52	+	449.749i	−1.08128	+	0.208399i	−0.382655	+	0.923891i	$0.624990\pi$
$168$	520.596	−	35.9753i	0.239076	−	0.0165212i
$169$	−508.616	−	2096.54i	−0.231505	−	0.954275i
$170$	−35.4131	+	22.7586i	−0.0159768	+	0.0102677i
$171$	−3009.22	+	714.718i	−1.34574	+	0.319625i
$172$	−778.869	+	1705.49i	−0.345280	+	0.756058i
$173$	2273.74	−	217.116i	0.999244	−	0.0954162i	0.417405	−	0.908720i	$-0.362940\pi$
$173$	2273.74	−	217.116i	0.999244	−	0.0954162i	0.581839	+	0.813304i	$0.302334\pi$
$174$	449.813	+	1418.90i	0.195978	+	0.618197i
$175$	11.7864	+	247.428i	0.00509127	+	0.106879i
$176$	−1030.64	+	982.710i	−0.441404	+	0.420878i
$177$	−816.308	−	1212.37i	−0.346652	−	0.514842i
$178$	934.012	−	2698.65i	0.393299	−	1.13636i
$179$	2805.60	+	1803.05i	1.17151	+	0.752883i	0.973806	−	0.227379i	$-0.0730157\pi$
$179$	2805.60	+	1803.05i	1.17151	+	0.752883i	0.197702	+	0.980262i	$0.436652\pi$
$180$	−8.20832	−	43.7196i	−0.00339896	−	0.0181037i
$181$	3538.83	−	1039.09i	1.45326	−	0.426714i	0.542639	−	0.839966i	$-0.317425\pi$
$181$	3538.83	−	1039.09i	1.45326	−	0.426714i	0.910617	+	0.413252i	$0.135607\pi$
$182$	36.8701	−	51.7768i	0.0150165	−	0.0210877i
$183$	204.940	−	2771.73i	0.0827847	−	1.11963i
$184$	2099.23	+	5180.49i	0.841070	+	2.07560i
$185$	4.28060	−	7.41422i	0.00170117	−	0.00294651i
$186$	133.254	−	780.939i	0.0525303	−	0.307856i
$187$	809.991	+	772.325i	0.316751	+	0.302021i
$188$	−128.739	+	148.573i	−0.0499430	+	0.0576373i
$189$	268.039	+	73.8979i	0.103158	+	0.0284406i
$190$	−35.0772	−	40.4812i	−0.0133935	−	0.0154569i
$191$	3227.97	−	2538.51i	1.22287	−	0.961674i	0.222955	−	0.974829i	$-0.428430\pi$
$191$	3227.97	−	2538.51i	1.22287	−	0.961674i	0.999913	+	0.0131544i	$0.00418730\pi$
$192$	−30.1121	−	36.6491i	−0.0113185	−	0.0137756i
$193$	−202.217	−	4245.05i	−0.0754190	−	1.58324i	−0.646867	−	0.762603i	$-0.723921\pi$
$193$	−202.217	−	4245.05i	−0.0754190	−	1.58324i	0.571448	−	0.820638i	$-0.306382\pi$
$194$	−7139.46	−	5614.54i	−2.64218	−	2.07784i
$195$	−2.63241	−	1.44563i	−0.000966720	−	0.000530892i
$196$	6058.15	−	578.483i	2.20778	−	0.210817i
$197$	705.939	−	4909.91i	0.255310	−	1.77572i	−0.309897	−	0.950770i	$-0.600295\pi$
$197$	705.939	−	4909.91i	0.255310	−	1.77572i	0.565207	−	0.824949i	$-0.308796\pi$
$198$	−1558.70	+	702.793i	−0.559456	+	0.252249i
$199$	3649.43	+	1071.57i	1.30001	+	0.381717i	0.857239	−	0.514919i	$-0.172178\pi$
$199$	3649.43	+	1071.57i	1.30001	+	0.381717i	0.442769	+	0.896636i	$0.353996\pi$
$200$	−4978.81	+	3915.38i	−1.76028	+	1.38430i
$201$	3367.83	+	1451.78i	1.18183	+	0.509457i
$202$	−7764.36	+	4002.81i	−2.70445	+	1.39424i
$203$	−36.4510	−	105.318i	−0.0126027	−	0.0364132i
$204$	6226.14	−	5632.64i	2.13685	−	1.93316i
$205$	0.677546	−	0.951480i	0.000230838	−	0.000324167i
$206$	7177.76			2.42766
$207$	139.884	+	2974.92i	0.0469690	+	0.998896i
$208$	721.247			0.240430
$209$	−826.058	+	1160.04i	−0.273395	+	0.383930i
$210$	1.01222	+	4.70757i	0.000332617	+	0.00154692i
$211$	−1781.82	−	5148.24i	−0.581354	−	1.67971i	−0.723884	−	0.689922i	$-0.757645\pi$
$211$	−1781.82	−	5148.24i	−0.581354	−	1.67971i	0.142530	−	0.989791i	$-0.454476\pi$
$212$	−993.995	+	512.440i	−0.322018	+	0.166012i
$213$	404.477	+	3453.36i	0.130114	+	1.11089i
$214$	4563.39	−	3588.69i	1.45769	−	1.14634i
$215$	−9.20072	−	2.70158i	−0.00291853	−	0.000856958i
$216$	2436.38	+	6678.99i	0.767475	+	2.10393i
$217$	−8.44160	+	58.7126i	−0.00264080	+	0.0183671i
$218$	139.246	−	13.2964i	0.0432613	−	0.00413095i
$219$	3050.53	−	1849.35i	0.941260	−	0.570627i
$220$	−16.0998	−	12.6610i	−0.00493385	−	0.00388002i
$221$	−26.9712	−	566.196i	−0.00820942	−	0.172337i
$222$	−868.253	+	2310.89i	−0.262493	+	0.698633i
$223$	−2647.13	+	2081.73i	−0.794910	+	0.625124i	−0.930771	−	0.365604i	$-0.880862\pi$
$223$	−2647.13	+	2081.73i	−0.794910	+	0.625124i	0.135861	+	0.990728i	$0.456620\pi$
$224$	−231.149	−	266.760i	−0.0689477	−	0.0795699i
$225$	−3194.44	+	1088.42i	−0.946500	+	0.322496i
$226$	11.1388	−	12.8549i	0.00327850	−	0.00378359i
$227$	−2425.28	−	2312.50i	−0.709126	−	0.676150i	0.247030	−	0.969008i	$-0.420545\pi$
$227$	−2425.28	−	2312.50i	−0.709126	−	0.676150i	−0.956156	+	0.292857i	$0.905394\pi$
$228$	8221.75	+	6821.77i	2.38815	+	1.98150i
$229$	−1233.83	+	2137.06i	−0.356043	+	0.616685i	−0.987296	−	0.158892i	$-0.949208\pi$
$229$	−1233.83	+	2137.06i	−0.356043	+	0.616685i	0.631253	+	0.775577i	$0.282541\pi$
$230$	−44.5589	+	25.9760i	−0.0127745	+	0.00744699i
$231$	115.286	−	55.6602i	0.0328366	−	0.0158535i
$232$	1653.01	−	2321.32i	0.467781	−	0.656906i
$233$	−4330.21	+	1271.47i	−1.21752	+	0.357496i	−0.826526	−	0.562898i	$-0.809686\pi$
$233$	−4330.21	+	1271.47i	−1.21752	+	0.357496i	−0.390992	+	0.920394i	$0.627868\pi$
$234$	816.979	+	287.168i	0.228238	+	0.0802254i
$235$	−0.845838	−	0.543587i	−0.000234793	−	0.000150892i
$236$	−1651.18	+	4770.77i	−0.455435	+	1.31589i
$237$	−1006.51	+	69.5540i	−0.275864	+	0.0190634i
$238$	−657.748	+	627.162i	−0.179141	+	0.170810i
$239$	−23.4019	−	491.266i	−0.00633365	−	0.132960i	−0.999819	−	0.0190034i	$-0.993951\pi$
$239$	−23.4019	−	491.266i	−0.00633365	−	0.132960i	0.993486	−	0.113956i	$-0.0363524\pi$
$240$	−36.8497	+	40.3406i	−0.00991098	+	0.0108499i
$241$	4266.73	−	407.424i	1.14043	−	0.108898i	0.492301	−	0.870425i	$-0.336156\pi$
$241$	4266.73	−	407.424i	1.14043	−	0.108898i	0.648133	+	0.761527i	$0.275550\pi$
$242$	2489.48	−	5451.20i	0.661281	−	1.44800i
$243$	44.5951	+	3787.73i	0.0117728	+	0.999931i
$244$	−8076.02	+	5190.15i	−2.11891	+	1.36174i
$245$	7.33799	+	30.2476i	0.00191350	+	0.00788754i
$246$	−147.896	+	302.603i	−0.0383313	+	0.0784279i
$247$	708.235	−	136.501i	0.182445	−	0.0351634i
$248$	−1348.12	+	695.004i	−0.345184	+	0.177955i
$249$	2813.13	+	2826.70i	0.715963	+	0.719416i
$250$	−84.6006	−	80.6665i	−0.0214024	−	0.0204072i
$251$	201.320	+	440.829i	0.0506263	+	0.110856i	0.933255	−	0.359215i	$-0.116956\pi$
$251$	201.320	+	440.829i	0.0506263	+	0.110856i	−0.882629	+	0.470071i	$0.844228\pi$
$252$	−352.643	−	893.291i	−0.0881525	−	0.223302i
$253$	950.446	+	988.459i	0.236182	+	0.245628i
$254$	−316.252	−	547.764i	−0.0781236	−	0.135314i
$255$	33.0463	+	27.4193i	0.00811546	+	0.00673358i
$256$	−1749.80	+	7212.77i	−0.427197	+	1.76093i
$257$	−1096.85	−	3169.13i	−0.266223	−	0.769201i	−0.996309	−	0.0858450i	$-0.972641\pi$
$257$	−1096.85	−	3169.13i	−0.266223	−	0.769201i	0.730085	−	0.683356i	$-0.239480\pi$
$258$	2744.67	+	334.864i	0.662309	+	0.0808050i
$259$	60.4528	−	174.667i	0.0145033	−	0.0419046i
$260$	1.47630	+	10.2679i	0.000352140	+	0.00244919i
$261$	1241.04	−	874.775i	0.294324	−	0.207461i
$262$	−2235.17	+	1436.45i	−0.527057	+	0.338719i
$263$	5907.81	−	2365.13i	1.38514	−	0.554525i	0.445064	−	0.895499i	$-0.353181\pi$
$263$	5907.81	−	2365.13i	1.38514	−	0.554525i	0.940073	+	0.340974i	$0.110757\pi$
$264$	2869.27	+	1575.71i	0.668907	+	0.367342i
$265$	−3.31766	−	4.65899i	−0.000769064	−	0.00108000i
$266$	−909.016	−	714.858i	−0.209531	−	0.164777i
$267$	−2912.02	−	76.3279i	−0.667463	−	0.0174951i
$268$	−2986.52	−	12310.6i	−0.680711	−	2.80593i
$269$	316.473	+	2201.12i	0.0717312	+	0.498901i	0.993739	+	0.111729i	$0.0356390\pi$
$269$	316.473	+	2201.12i	0.0717312	+	0.498901i	−0.922007	+	0.387172i	$0.873452\pi$
$270$	−57.8026	+	31.0232i	−0.0130287	+	0.00699264i
$271$	−5404.68	−	3473.38i	−1.21148	−	0.778570i	−0.230574	−	0.973055i	$-0.574060\pi$
$271$	−5404.68	−	3473.38i	−1.21148	−	0.778570i	−0.980906	+	0.194484i	$0.937697\pi$
$272$	−10126.1	−	1951.64i	−2.25729	−	0.435057i
$273$	−61.7121	−	19.8909i	−0.0136813	−	0.00440973i
$274$	733.906	+	70.0795i	0.161813	+	0.0154513i
$275$	−776.934	+	1345.69i	−0.170367	+	0.295084i
$276$	7920.82	−	6563.89i	1.72745	−	1.43152i
$277$	−2237.34	−	3875.19i	−0.485303	−	0.840569i	0.514555	−	0.857458i	$-0.327957\pi$
$277$	−2237.34	−	3875.19i	−0.485303	−	0.840569i	−0.999857	+	0.0168885i	$0.994624\pi$
$278$	4775.23	+	10456.3i	1.03021	+	2.25585i
$279$	−800.443	+	111.159i	−0.171761	+	0.0238527i
$280$	6.03696	−	6.96702i	0.00128849	−	0.00148700i
$281$	−8.21257	+	172.403i	−0.00174349	+	0.0366004i	−0.999571	−	0.0292737i	$-0.990681\pi$
$281$	−8.21257	+	172.403i	−0.00174349	+	0.0366004i	0.997828	+	0.0658741i	$0.0209836\pi$
$282$	266.237	+	114.768i	0.0562205	+	0.0242352i
$283$	2336.90	+	935.553i	0.490863	+	0.196512i	0.603871	−	0.797082i	$-0.293624\pi$
$283$	2336.90	+	935.553i	0.490863	+	0.196512i	−0.113008	+	0.993594i	$0.536049\pi$
$284$	8691.94	−	8287.74i	1.81610	−	1.73164i
$285$	−28.5501	+	46.5869i	−0.00593390	+	0.00968270i
$286$	370.166	−	148.192i	0.0765329	−	0.0306391i
$287$	10.4760	−	22.9392i	0.00215462	−	0.00471797i
$288$	2619.32	−	4032.96i	0.535920	−	0.825153i
$289$	−454.223	+	3159.19i	−0.0924534	+	0.643027i
$290$	23.3723	+	12.0493i	0.00473265	+	0.00243985i
$291$	−3258.64	+	8672.97i	−0.656442	+	1.74714i
$292$	−11439.3	−	4579.61i	−2.29259	−	0.917813i
$293$	1435.42	−	276.654i	0.286205	−	0.0551614i	−0.0441284	−	0.999026i	$-0.514051\pi$
$293$	1435.42	−	276.654i	0.286205	−	0.0551614i	0.330333	+	0.943864i	$0.392839\pi$
$294$	−3513.10	−	8258.70i	−0.696898	−	1.63829i
$295$	−25.3533	−	4.88645i	−0.00500382	−	0.000964407i
$296$	4534.75	−	1331.52i	0.890463	−	0.261463i
$297$	1163.86	+	1299.00i	0.227388	+	0.253791i
$298$	−7531.68			−1.46409
$299$	−2.91498	−	694.511i	−0.000563806	−	0.134330i
$300$	9637.87	+	6556.95i	1.85481	+	1.26189i
$301$	−206.088	−	19.6790i	−0.0394642	−	0.00376837i
$302$	−108.587	+	447.602i	−0.0206903	+	0.0852867i
$303$	6285.67	+	6315.98i	1.19176	+	1.19750i
$304$	624.369	−	13107.1i	0.117796	−	2.47285i
$305$	−32.1527	−	37.1062i	−0.00603626	−	0.00696621i
$306$	−10693.1	−	6242.42i	−1.99765	−	1.16619i
$307$	−1381.73	−	405.714i	−0.256872	−	0.0754245i	0.150761	−	0.988570i	$-0.451828\pi$
$307$	−1381.73	−	405.714i	−0.256872	−	0.0754245i	−0.407633	+	0.913146i	$0.633646\pi$
$308$	−393.037	−	202.625i	−0.0727122	−	0.0374857i
$309$	−2212.61	−	6979.48i	−0.407349	−	1.28495i
$310$	−8.11809	−	11.4003i	−0.00148734	−	0.00208868i
$311$	1008.79	+	1416.64i	0.183933	+	0.258297i	0.896239	−	0.443571i	$-0.146289\pi$
$311$	1008.79	+	1416.64i	0.183933	+	0.258297i	−0.712306	+	0.701869i	$0.752349\pi$
$312$	−501.017	−	1580.41i	−0.0909118	−	0.286774i
$313$	−2358.80	−	1216.04i	−0.425965	−	0.219600i	0.231894	−	0.972741i	$-0.425508\pi$
$313$	−2358.80	−	1216.04i	−0.425965	−	0.219600i	−0.657860	+	0.753141i	$0.728538\pi$
$314$	7562.56	+	2220.57i	1.35917	+	0.399089i
$315$	4.26550	−	2.43541i	0.000762965	−	0.000435618i
$316$	2282.12	+	2633.70i	0.406263	+	0.468853i
$317$	−417.106	+	8756.12i	−0.0739022	+	1.55140i	0.592356	+	0.805676i	$0.298198\pi$
$317$	−417.106	+	8756.12i	−0.0739022	+	1.55140i	−0.666258	+	0.745721i	$0.732105\pi$
$318$	1163.37	+	1168.98i	0.205152	+	0.206142i
$319$	164.821	−	679.401i	0.0289285	−	0.119245i
$320$	−0.834150	−	0.0796517i	−0.000145720	−	1.39146e-5i
$321$	−4896.26	−	3331.08i	−0.851347	−	0.579199i
$322$	−838.487	+	732.737i	−0.145115	+	0.126813i
$323$	−10312.7			−1.77652
$324$	10362.2	−	7988.77i	1.77678	−	1.36982i
$325$	755.116	−	221.722i	0.128881	−	0.0378428i
$326$	9167.29	+	1766.85i	1.55745	+	0.300174i
$327$	−55.8531	−	131.301i	−0.00944551	−	0.0222048i
$328$	633.176	−	122.035i	0.106589	−	0.0205434i
$329$	−20.1523	−	8.06775i	−0.00337699	−	0.00135194i
$330$	−10.6237	+	28.2754i	−0.00177217	+	0.00471670i
$331$	−8064.96	−	4157.78i	−1.33925	−	0.690429i	−0.368295	−	0.929709i	$-0.620058\pi$
$331$	−8064.96	−	4157.78i	−1.33925	−	0.690429i	−0.970951	+	0.239279i	$0.923089\pi$
$332$	1960.37	−	13634.7i	0.324065	−	2.25392i
$333$	2514.70	+	131.918i	0.413827	+	0.0217088i
$334$	5028.82	−	11011.6i	0.823847	−	1.80397i
$335$	60.1471	−	24.0793i	0.00980951	−	0.00392714i
$336$	−616.366	+	1005.76i	−0.100076	+	0.163300i
$337$	4007.53	−	3821.17i	0.647787	−	0.617663i	−0.293223	−	0.956044i	$-0.594728\pi$
$337$	4007.53	−	3821.17i	0.647787	−	0.617663i	0.941009	+	0.338381i	$0.109879\pi$
$338$	10202.2	+	4084.35i	1.64180	+	0.657277i
$339$	−15.9334	−	6.86847i	−0.00255275	−	0.00110043i
$340$	7.05740	−	148.153i	0.00112571	−	0.0236315i
$341$	−243.667	+	281.207i	−0.0386959	+	0.0446574i
$342$	5925.90	−	14598.3i	0.936948	−	2.30814i
$343$	561.530	+	1229.58i	0.0883958	+	0.193560i
$344$	−2646.83	−	4584.45i	−0.414848	−	0.718538i
$345$	38.9941	+	35.3206i	0.00608514	+	0.00551188i
$346$	−5817.47	+	10076.2i	−0.903900	+	1.56560i
$347$	7123.51	+	680.213i	1.10205	+	0.105233i	0.630189	−	0.776442i	$-0.282978\pi$
$347$	7123.51	+	680.213i	1.10205	+	0.105233i	0.471858	+	0.881675i	$0.343584\pi$
$348$	−4991.70	−	1608.92i	−0.768918	−	0.247836i
$349$	−2245.07	−	432.702i	−0.344343	−	0.0663667i	0.0141477	−	0.999900i	$-0.495496\pi$
$349$	−2245.07	−	432.702i	−0.344343	−	0.0663667i	−0.358491	+	0.933533i	$0.616709\pi$
$350$	−1061.50	−	682.186i	−0.162113	−	0.104184i
$351$	27.3939	−	882.933i	0.00416575	−	0.134266i
$352$	−315.113	−	2191.66i	−0.0477147	−	0.331863i
$353$	−2673.32	−	11019.6i	−0.403078	−	1.66151i	−0.705784	−	0.708427i	$-0.749405\pi$
$353$	−2673.32	−	11019.6i	−0.403078	−	1.66151i	0.302705	−	0.953084i	$-0.402110\pi$
$354$	7442.58	+	195.080i	1.11743	+	0.0292892i
$355$	48.2822	+	37.9696i	0.00721846	+	0.00567666i
$356$	5836.48	+	8196.18i	0.868912	+	1.22022i
$357$	812.594	+	446.251i	0.120468	+	0.0661571i
$358$	−15771.4	+	6313.93i	−2.32834	+	0.932127i
$359$	−10768.1	+	6920.25i	−1.58306	+	1.01737i	−0.608416	+	0.793618i	$0.708195\pi$
$359$	−10768.1	+	6920.25i	−1.58306	+	1.01737i	−0.974646	+	0.223754i	$0.928169\pi$
$360$	113.993	+	52.7231i	0.0166888	+	0.00771876i
$361$	−891.374	−	6199.64i	−0.129957	−	0.903869i
$362$	−6144.82	+	17754.3i	−0.892167	+	2.57775i
$363$	−6068.02	−	740.330i	−0.877379	−	0.107045i
$364$	73.2500	+	211.642i	0.0105476	+	0.0304754i
$365$	14.8575	−	61.2435i	0.00213062	−	0.00878254i
$366$	10895.4	+	9040.18i	1.55605	+	1.29109i
$367$	5908.96	+	10234.6i	0.840450	+	1.45570i	0.889515	+	0.456906i	$0.151043\pi$
$367$	5908.96	+	10234.6i	0.840450	+	1.45570i	−0.0490650	+	0.998796i	$0.515624\pi$
$368$	−12291.5	−	2927.32i	−1.74114	−	0.414666i
$369$	339.834	+	50.5306i	0.0479432	+	0.00712877i
$370$	18.1163	+	39.6692i	0.00254547	+	0.00557379i
$371$	−89.3683	−	85.2125i	−0.0125061	−	0.0119246i
$372$	1969.03	+	1978.53i	0.274434	+	0.275758i
$373$	6072.91	−	3130.80i	0.843012	−	0.434603i	0.0180812	−	0.999837i	$-0.494244\pi$
$373$	6072.91	−	3130.80i	0.843012	−	0.434603i	0.824931	+	0.565234i	$0.191214\pi$
$374$	−5598.01	+	1078.93i	−0.773974	+	0.149171i
$375$	−52.3593	+	107.130i	−0.00721019	+	0.0147524i
$376$	−130.859	−	539.410i	−0.0179483	−	0.0739839i
$377$	−297.871	+	191.430i	−0.0406927	+	0.0261516i
$378$	−1098.62	+	893.847i	−0.149490	+	0.121626i
$379$	−5412.04	+	11850.7i	−0.733503	+	1.60615i	0.0604523	+	0.998171i	$0.480746\pi$
$379$	−5412.04	+	11850.7i	−0.733503	+	1.60615i	−0.793955	+	0.607976i	$0.791982\pi$
$380$	187.876	−	17.9399i	0.0253627	−	0.00242184i
$381$	−435.145	+	476.369i	−0.0585123	+	0.0640554i
$382$	995.343	+	20894.8i	0.133315	+	2.79862i
$383$	−5952.47	+	5675.67i	−0.794144	+	0.757215i	−0.974017	−	0.226475i	$-0.927280\pi$
$383$	−5952.47	+	5675.67i	−0.794144	+	0.757215i	0.179873	+	0.983690i	$0.442431\pi$
$384$	7627.23	−	527.073i	1.01361	−	0.0700445i
$385$	0.739686	−	2.13718i	9.79166e−5	−	0.000282912i
$386$	18211.9	+	11704.1i	2.40145	+	1.54332i
$387$	−520.455	−	2772.07i	−0.0683623	−	0.364115i
$388$	30705.9	−	9016.05i	4.01766	−	1.17969i
$389$	7775.65	−	10919.4i	1.01347	−	1.42322i	0.110325	−	0.993896i	$-0.464811\pi$
$389$	7775.65	−	10919.4i	1.01347	−	1.42322i	0.903148	−	0.429329i	$-0.141250\pi$
$390$	13.7766	−	6.65137i	0.00178874	−	0.000863603i
$391$	−1838.37	+	9758.59i	−0.237776	+	1.26218i
$392$	−8591.23	+	14880.5i	−1.10695	+	1.91729i
$393$	2085.78	+	1730.62i	0.267720	+	0.222133i
$394$	18287.3	+	17436.9i	2.33832	+	2.22958i
$395$	−11.6717	+	13.4699i	−0.00148676	+	0.00171581i
$396$	1168.57	−	5910.00i	0.148291	−	0.749971i
$397$	−1671.37	−	1928.87i	−0.211294	−	0.243846i	0.640203	−	0.768206i	$-0.278850\pi$
$397$	−1671.37	−	1928.87i	−0.211294	−	0.243846i	−0.851497	+	0.524359i	$0.824305\pi$
$398$	−15229.6	+	11976.7i	−1.91807	+	1.50838i
$399$	−414.898	+	1104.27i	−0.0520574	+	0.138553i
$400$	−681.265	−	14301.5i	−0.0851581	−	1.78769i
$401$	−4913.69	−	3864.17i	−0.611916	−	0.481216i	0.263453	−	0.964672i	$-0.415139\pi$
$401$	−4913.69	−	3864.17i	−0.611916	−	0.481216i	−0.875368	+	0.483457i	$0.839381\pi$
$402$	−15975.2	+	9684.75i	−1.98201	+	1.20157i
$403$	187.601	−	17.9137i	0.0231887	−	0.00221425i
$404$	4380.26	−	30465.4i	0.539422	−	3.75176i
$405$	47.9844	+	46.6426i	0.00588732	+	0.00572269i
$406$	544.710	+	159.941i	0.0665850	+	0.0195511i
$407$	911.389	−	716.724i	0.110997	−	0.0872892i
$408$	2757.63	+	23544.2i	0.334615	+	2.85689i
$409$	7306.91	−	3766.97i	0.883383	−	0.455415i	0.0440473	−	0.999029i	$-0.485975\pi$
$409$	7306.91	−	3766.97i	0.883383	−	0.455415i	0.839335	+	0.543614i	$0.182944\pi$
$410$	1.94607	+	5.62280i	0.000234414	+	0.000677294i
$411$	−158.089	−	735.235i	−0.0189732	−	0.0882396i
$412$	−14669.8	+	20600.9i	−1.75420	+	2.46343i
$413$	−557.440			−0.0664161
$414$	−12757.4	−	8209.78i	−1.51448	−	0.974610i
$415$	70.4509			0.00833325
$416$	−650.495	+	913.493i	−0.0766662	+	0.107663i
$417$	8695.44	−	7866.57i	1.02115	−	0.923807i
$418$	−2372.63	−	6855.27i	−0.277630	−	0.802159i
$419$	−8050.93	+	4150.54i	−0.938696	+	0.483932i	−0.858481	−	0.512846i	$-0.828591\pi$
$419$	−8050.93	+	4150.54i	−0.938696	+	0.483932i	−0.0802157	+	0.996778i	$0.525561\pi$
$420$	−15.5800	−	6.71612i	−0.00181006	−	0.000780270i
$421$	−1705.11	+	1340.92i	−0.197392	+	0.155231i	−0.711963	−	0.702217i	$-0.752194\pi$
$421$	−1705.11	+	1340.92i	−0.197392	+	0.155231i	0.514571	+	0.857448i	$0.327951\pi$
$422$	26626.9	+	7818.37i	3.07151	+	0.901878i
$423$	29.5277	−	294.261i	0.00339405	−	0.0338237i
$424$	449.353	−	3125.32i	0.0514682	−	0.357969i
$425$	−11201.5	+	1069.62i	−1.27848	+	0.122080i
$426$	−15524.5	−	8525.55i	−1.76564	−	0.969635i
$427$	−833.229	−	655.258i	−0.0944327	−	0.0742627i
$428$	973.291	+	20431.9i	0.109920	+	2.30751i
$429$	−258.206	−	314.259i	−0.0290590	−	0.0353673i
$430$	38.3959	−	30.1949i	0.00430608	−	0.00338634i
$431$	−2796.43	−	3227.25i	−0.312527	−	0.360676i	0.577654	−	0.816281i	$-0.303968\pi$
$431$	−2796.43	−	3227.25i	−0.312527	−	0.360676i	−0.890182	+	0.455606i	$0.849423\pi$
$432$	−15492.8	−	4271.35i	−1.72546	−	0.475707i
$433$	9998.89	−	11539.3i	1.10974	−	1.28070i	0.153487	−	0.988151i	$-0.450950\pi$
$433$	9998.89	−	11539.3i	1.10974	−	1.28070i	0.956249	−	0.292553i	$-0.0945049\pi$
$434$	−218.679	−	208.510i	−0.0241864	−	0.0230617i
$435$	4.51169	−	26.4410i	0.000497285	−	0.00291436i
$436$	−246.428	+	426.826i	−0.0270683	+	0.0468837i
$437$	−12623.8	−	548.250i	−1.38187	−	0.0600146i
$438$	−1339.95	+	18122.2i	−0.146176	+	1.97697i
$439$	10111.6	−	14199.8i	1.09932	−	1.54378i	0.289432	−	0.957199i	$-0.406534\pi$
$439$	10111.6	−	14199.8i	1.09932	−	1.54378i	0.809889	−	0.586583i	$-0.199527\pi$
$440$	55.4861	−	16.2922i	0.00601181	−	0.00176523i
$441$	−6947.62	+	5961.87i	−0.750201	+	0.643761i
$442$	2429.06	+	1561.06i	0.261400	+	0.167991i
$443$	977.674	−	2824.80i	0.104855	−	0.302958i	−0.880354	−	0.474318i	$-0.842695\pi$
$443$	977.674	−	2824.80i	0.104855	−	0.302958i	0.985209	+	0.171360i	$0.0548160\pi$
$444$	−4857.95	−	7214.94i	−0.519252	−	0.771184i
$445$	−37.2441	+	35.5121i	−0.00396750	+	0.00378300i
$446$	−816.240	−	17135.0i	−0.0866594	−	1.81920i
$447$	2321.71	+	7323.62i	0.245667	+	0.774934i
$448$	−18.0089	+	1.71964i	−0.00189920	+	0.000181352i
$449$	1019.85	−	2233.15i	0.107193	−	0.234720i	−0.848433	−	0.529303i	$-0.822454\pi$
$449$	1019.85	−	2233.15i	0.107193	−	0.234720i	0.955626	+	0.294583i	$0.0951808\pi$
$450$	4922.52	−	16471.0i	0.515666	−	1.72545i
$451$	133.080	−	85.5251i	0.0138946	−	0.00892954i
$452$	14.1294	+	58.2421i	0.00147033	+	0.00606079i
$453$	468.710	−	32.3898i	0.0486135	−	0.00335939i
$454$	16761.6	−	3230.54i	1.73274	−	0.333957i
$455$	−1.01810	+	0.524865i	−0.000104899	+	5.40792e-5i
$456$	−29154.4	+	7736.78i	−2.99403	+	0.794535i
$457$	8141.73	+	7763.12i	0.833379	+	0.794625i	0.980916	−	0.194432i	$-0.0622862\pi$
$457$	8141.73	+	7763.12i	0.833379	+	0.794625i	−0.147537	+	0.989056i	$0.547135\pi$
$458$	−5221.81	−	11434.2i	−0.532749	−	1.16656i
$459$	−2773.75	+	12322.0i	−0.282065	+	1.25303i
$460$	16.5151	−	180.978i	0.00167396	−	0.0183438i
$461$	−4610.12	−	7984.97i	−0.465759	−	0.806718i	0.533477	−	0.845815i	$-0.320885\pi$
$461$	−4610.12	−	7984.97i	−0.465759	−	0.806718i	−0.999235	+	0.0390969i	$0.987552\pi$
$462$	−109.688	+	642.830i	−0.0110457	+	0.0647341i
$463$	1694.17	−	6983.48i	0.170054	−	0.700971i	−0.821382	−	0.570378i	$-0.806797\pi$
$463$	1694.17	−	6983.48i	0.170054	−	0.700971i	0.991436	−	0.130593i	$-0.0416882\pi$
$464$	2106.89	+	6087.46i	0.210797	+	0.609059i
$465$	−8.58287	+	11.4081i	−0.000855959	+	0.00113771i
$466$	7518.97	−	21724.6i	0.747445	−	2.15960i
$467$	2477.24	+	17229.6i	0.245466	+	1.70726i	0.623797	+	0.781586i	$0.285589\pi$
$467$	2477.24	+	17229.6i	0.245466	+	1.70726i	−0.378331	+	0.925670i	$0.623502\pi$
$468$	−2493.93	+	1757.90i	−0.246329	+	0.173631i
$469$	1176.70	−	756.218i	0.115853	−	0.0744540i
$470$	4.75481	−	1.90354i	0.000466645	−	0.000186816i
$471$	−171.999	−	8038.17i	−0.0168266	−	0.786368i
$472$	−8268.02	−	11610.8i	−0.806285	−	1.13227i
$473$	−1020.82	−	802.781i	−0.0992332	−	0.0780379i
$474$	2685.40	−	4381.92i	0.260220	−	0.424616i
$475$	−3375.63	−	13914.6i	−0.326073	−	1.34409i
$476$	−455.719	−	3169.59i	−0.0438820	−	0.305206i
$477$	778.067	−	1491.58i	0.0746861	−	0.143175i
$478$	2107.60	+	1354.47i	0.201672	+	0.129607i
$479$	−2494.59	−	480.792i	−0.237955	−	0.0458621i	0.0688792	−	0.997625i	$-0.478058\pi$
$479$	−2494.59	−	480.792i	−0.237955	−	0.0458621i	−0.306835	+	0.951763i	$0.599270\pi$
$480$	−17.8584	−	83.0551i	−0.00169817	−	0.00789777i
$481$	−584.573	−	55.8199i	−0.0554142	−	0.00529141i
$482$	−10916.7	+	18908.2i	−1.03162	+	1.78681i
$483$	970.967	+	589.452i	0.0914711	+	0.0555300i
$484$	10557.5	+	18286.2i	0.991504	+	1.71733i
$485$	67.9922	+	148.882i	0.00636571	+	0.0139390i
$486$	−15848.6	−	11006.8i	−1.47923	−	1.02732i
$487$	−9739.61	+	11240.1i	−0.906250	+	1.04587i	0.0924914	+	0.995713i	$0.470517\pi$
$487$	−9739.61	+	11240.1i	−0.906250	+	1.04587i	−0.998741	+	0.0501549i	$0.984029\pi$
$488$	1289.70	−	27074.0i	0.119635	−	2.51144i
$489$	−1107.86	−	9458.70i	−0.102452	−	0.874719i
$490$	−147.191	−	58.9265i	−0.0135702	−	0.00543271i
$491$	−7468.51	+	7121.21i	−0.686454	+	0.654533i	−0.950768	−	0.309904i	$-0.899703\pi$
$491$	−7468.51	+	7121.21i	−0.686454	+	0.654533i	0.264314	+	0.964437i	$0.414855\pi$
$492$	−566.232	−	1042.93i	−0.0518856	−	0.0955672i
$493$	4700.01	−	1881.60i	0.429367	−	0.171893i
$494$	−1526.27	+	3342.07i	−0.139009	+	0.304387i
$495$	30.7692	+	1.61411i	0.00279389	+	0.000146564i
$496$	487.930	−	3393.63i	0.0441708	−	0.307215i
$497$	1178.69	+	607.658i	0.106381	+	0.0548435i
$498$	−20041.2	+	3320.55i	−1.80335	+	0.298790i
$499$	6852.07	+	2743.16i	0.614711	+	0.246093i	0.658059	−	0.752967i	$-0.271378\pi$
$499$	6852.07	+	2743.16i	0.614711	+	0.246093i	−0.0433472	+	0.999060i	$0.513802\pi$
$500$	404.427	−	77.9469i	0.0361730	−	0.00697178i
$501$	−12257.6	−	1495.49i	−1.09307	−	0.133360i
$502$	−2424.03	−	467.193i	−0.215517	−	0.0415375i
$503$	−10447.1	+	3067.54i	−0.926069	+	0.271919i	−0.709790	−	0.704413i	$-0.751210\pi$
$503$	−10447.1	+	3067.54i	−0.926069	+	0.271919i	−0.216279	+	0.976332i	$0.569392\pi$
$504$	2632.01	+	651.940i	0.232617	+	0.0576185i
$505$	157.416			0.0138711
$506$	−6909.85	+	1023.11i	−0.607076	+	0.0898865i
$507$	826.602	−	11179.4i	0.0724076	−	0.979282i
$508$	2218.49	+	211.840i	0.193759	+	0.0185018i
$509$	3663.57	−	15101.5i	0.319028	−	1.31505i	−0.556083	−	0.831127i	$-0.687696\pi$
$509$	3663.57	−	15101.5i	0.319028	−	1.31505i	0.875111	−	0.483923i	$-0.160789\pi$
$510$	−211.418	+	56.1045i	−0.0183563	+	0.00487127i
$511$	64.7386	−	1359.03i	0.00560444	−	0.117652i
$512$	−17050.0	−	19676.8i	−1.47170	−	1.69844i
$513$	−16021.7	−	1262.16i	−1.37890	−	0.108627i
$514$	16390.9	+	4812.79i	1.40656	+	0.413002i
$515$	−114.967	−	59.2697i	−0.00983701	−	0.00507133i
$516$	−6570.62	+	7193.09i	−0.560572	+	0.613678i
$517$	−78.9855	−	110.920i	−0.00671911	−	0.00943567i
$518$	546.138	+	766.943i	0.0463241	+	0.0650532i
$519$	11591.1	+	2550.71i	0.980333	+	0.215729i
$520$	−26.0328	−	13.4209i	−0.00219541	−	0.00113181i
$521$	16537.6	+	4855.89i	1.39065	+	0.408331i	0.889462	−	0.457010i	$-0.151080\pi$
$521$	16537.6	+	4855.89i	1.39065	+	0.408331i	0.501185	+	0.865340i	$0.332898\pi$
$522$	−37.2083	+	7734.33i	−0.00311985	+	0.648510i
$523$	−3207.76	−	3701.95i	−0.268194	−	0.309513i	0.605638	−	0.795740i	$-0.292918\pi$
$523$	−3207.76	−	3701.95i	−0.268194	−	0.309513i	−0.873832	+	0.486228i	$0.838373\pi$
$524$	445.441	−	9350.96i	0.0371359	−	0.779578i
$525$	−336.124	+	1242.47i	−0.0279422	+	0.103287i
$526$	−7642.35	+	31502.2i	−0.633503	+	2.61133i
$527$	−2682.32	−	256.131i	−0.221715	−	0.0211712i
$528$	−6663.61	+	3217.20i	−0.549236	+	0.265171i
$529$	−2769.12	+	11847.7i	−0.227593	+	0.973756i
$530$	29.1349			0.00238781
$531$	−2104.55	−	7297.12i	−0.171996	−	0.596362i
$532$	3909.55	−	1147.95i	0.318610	−	0.0935524i
$533$	−78.6724	−	15.1629i	−0.00639340	−	0.00123223i
$534$	8921.06	−	11857.6i	0.722944	−	0.960913i
$535$	−102.726	+	19.7987i	−0.00830134	+	0.00159995i
$536$	33204.1	+	13292.9i	2.67574	+	1.07121i
$537$	11001.2	+	13389.4i	0.884053	+	1.07597i
$538$	−10068.4	−	5190.62i	−0.806839	−	0.415955i
$539$	−599.896	+	4172.37i	−0.0479394	+	0.333426i
$540$	29.0965	−	229.304i	0.00231873	−	0.0182735i
$541$	−1853.03	+	4057.56i	−0.147260	+	0.322455i	−0.968860	−	0.247610i	$-0.920355\pi$
$541$	−1853.03	+	4057.56i	−0.147260	+	0.322455i	0.821599	+	0.570065i	$0.193082\pi$
$542$	30382.0	−	12163.1i	2.40778	−	0.963930i
$543$	19158.0	+	502.158i	1.51409	+	0.0396863i
$544$	11604.6	−	11064.9i	0.914600	−	0.872069i
$545$	−2.34012	−	0.936844i	−0.000183926	−	7.36330e-5i
$546$	264.880	−	197.294i	0.0207616	−	0.0154641i
$547$	−778.482	+	16342.3i	−0.0608510	+	1.27742i	0.737550	+	0.675293i	$0.235983\pi$
$547$	−778.482	+	16342.3i	−0.0608510	+	1.27742i	−0.798401	+	0.602126i	$0.794320\pi$
$548$	−1701.08	+	1963.16i	−0.132604	+	0.153033i
$549$	5431.85	−	13381.2i	0.422269	−	1.04024i
$550$	−3288.13	−	7200.00i	−0.254921	−	0.558198i
$551$	3220.98	+	5578.89i	0.249035	+	0.431341i
$552$	2123.93	+	28966.9i	0.163769	+	2.23354i
$553$	−192.398	+	333.243i	−0.0147949	+	0.0256256i
$554$	22690.5	+	2166.68i	1.74012	+	0.166161i
$555$	32.9889	−	29.8442i	0.00252306	−	0.00228255i
$556$	−39770.2	−	7665.08i	−3.03351	−	0.584661i
$557$	6247.23	+	4014.85i	0.475231	+	0.305413i	0.756242	−	0.654292i	$-0.227033\pi$
$557$	6247.23	+	4014.85i	0.475231	+	0.305413i	−0.281011	+	0.959705i	$0.590670\pi$
$558$	1903.88	−	3649.80i	0.144440	−	0.276897i
$559$	93.6063	+	651.046i	0.00708251	+	0.0492599i
$560$	4.91290	+	20.2512i	0.000370728	+	0.00152816i
$561$	2774.76	+	5110.78i	0.208824	+	0.384630i
$562$	−691.101	−	543.488i	−0.0518725	−	0.0407930i
$563$	−2255.51	−	3167.42i	−0.168843	−	0.237107i	0.721481	−	0.692434i	$-0.243462\pi$
$563$	−2255.51	−	3167.42i	−0.168843	−	0.237107i	−0.890324	+	0.455327i	$0.849522\pi$
$564$	−873.528	+	529.565i	−0.0652166	+	0.0395367i
$565$	−0.284559	+	0.113920i	−2.11885e−5	+	8.48260e-6i
$566$	−10787.0	+	6932.37i	−0.801078	+	0.514822i
$567$	1207.82	+	792.739i	0.0894594	+	0.0587159i
$568$	4825.72	+	33563.6i	0.356484	+	2.47940i
$569$	3005.16	−	8682.85i	0.221411	−	0.639726i	−0.778516	−	0.627625i	$-0.784027\pi$
$569$	3005.16	−	8682.85i	0.221411	−	0.639726i	0.999927	−	0.0121004i	$-0.00385177\pi$
$570$	−108.948	−	256.119i	−0.00800586	−	0.0188204i
$571$	6221.99	+	17977.3i	0.456011	+	1.31756i	0.905528	+	0.424286i	$0.139475\pi$
$571$	6221.99	+	17977.3i	0.456011	+	1.31756i	−0.449517	+	0.893272i	$0.648404\pi$
$572$	−331.216	+	1365.29i	−0.0242112	+	0.0998000i
$573$	20010.8	−	7408.86i	1.45892	−	0.540156i
$574$	64.2295	+	111.249i	0.00467054	+	0.00808961i
$575$	−13768.6	+	713.811i	−0.998592	+	0.0517704i
$576$	−90.5015	−	229.252i	−0.00654670	−	0.0165836i
$577$	5044.46	+	11045.8i	0.363958	+	0.796957i	0.999686	+	0.0250441i	$0.00797261\pi$
$577$	5044.46	+	11045.8i	0.363958	+	0.796957i	−0.635728	+	0.771913i	$0.719300\pi$
$578$	−11766.6	−	11219.4i	−0.846758	−	0.807382i
$579$	5766.78	−	21316.7i	0.413919	−	1.53004i
$580$	−82.3507	+	42.4547i	−0.00589556	+	0.00303937i
$581$	1493.52	−	287.852i	0.106646	−	0.0205544i
$582$	−26359.0	−	39148.0i	−1.87735	−	2.78821i
$583$	−182.619	−	752.765i	−0.0129731	−	0.0534757i
$584$	29267.2	−	18808.9i	2.07378	−	1.33274i
$585$	−10.7144	−	11.3457i	−0.000757241	−	0.000801860i
$586$	−3093.38	+	6773.55i	−0.218065	+	0.477497i
$587$	−13900.7	+	1327.36i	−0.977419	+	0.0933322i	−0.571522	−	0.820587i	$-0.693647\pi$
$587$	−13900.7	+	1327.36i	−0.977419	+	0.0933322i	−0.405897	+	0.913919i	$0.633041\pi$
$588$	30883.3	+	6796.10i	2.16600	+	0.476644i
$589$	−163.141	−	3424.75i	−0.0114127	−	0.239583i
$590$	95.1889	−	90.7624i	0.00664214	−	0.00633327i
$591$	11318.0	−	23157.2i	0.787749	−	1.61177i
$592$	−3494.22	+	10095.9i	−0.242587	+	0.700909i
$593$	−3758.62	−	2415.52i	−0.260283	−	0.167274i	0.403991	−	0.914763i	$-0.367623\pi$
$593$	−3758.62	−	2415.52i	−0.260283	−	0.167274i	−0.664274	+	0.747489i	$0.731259\pi$
$594$	−8829.02	+	991.071i	−0.609864	+	0.0684581i
$595$	15.7140	−	4.61404i	0.00108271	−	0.000317911i
$596$	15393.2	−	21616.7i	1.05793	−	1.48566i
$597$	16340.5	+	11117.0i	1.12022	+	0.762123i
$598$	2890.41	+	2040.02i	0.197655	+	0.139503i
$599$	311.183	−	538.985i	0.0212264	−	0.0367652i	−0.855217	−	0.518270i	$-0.826576\pi$
$599$	311.183	−	538.985i	0.0212264	−	0.0367652i	0.876443	+	0.481505i	$0.159910\pi$
$600$	−30864.6	+	11427.4i	−2.10007	+	0.777535i
$601$	4176.06	+	3981.87i	0.283436	+	0.270256i	0.818438	−	0.574595i	$-0.194841\pi$
$601$	4176.06	+	3981.87i	0.283436	+	0.270256i	−0.535002	+	0.844851i	$0.679689\pi$
$602$	690.598	−	796.993i	0.0467553	−	0.0539585i
$603$	14341.7	+	12548.5i	0.968556	+	0.847451i
$604$	−1062.73	−	1226.46i	−0.0715927	−	0.0826224i
$605$	−84.8872	+	66.7560i	−0.00570439	+	0.00448598i
$606$	−44780.2	+	7419.44i	−3.00176	+	0.497350i
$607$	−797.230	−	16735.9i	−0.0533090	−	1.11909i	−0.854086	−	0.520131i	$-0.825883\pi$
$607$	−797.230	−	16735.9i	−0.0533090	−	1.11909i	0.800777	−	0.598962i	$-0.204420\pi$
$608$	16037.7	+	12612.2i	1.06976	+	0.841267i
$609$	−12.3886	−	578.967i	−0.000824323	−	0.0385237i
$610$	248.972	−	23.7739i	0.0165255	−	0.00157800i
$611$	−9.81488	+	68.2640i	−0.000649865	+	0.00451991i
$612$	39770.8	−	17932.0i	2.62686	−	1.18441i
$613$	−5064.23	−	1486.99i	−0.333674	−	0.0979756i	0.110604	−	0.993865i	$-0.464722\pi$
$613$	−5064.23	−	1486.99i	−0.333674	−	0.0979756i	−0.444278	+	0.895889i	$0.646540\pi$
$614$	5766.17	−	4534.57i	0.378996	−	0.298046i
$615$	4.86759	−	3.62559i	0.000319155	−	0.000237720i
$616$	1109.71	−	572.093i	0.0725833	−	0.0374193i
$617$	−7610.21	−	21988.2i	−0.496556	−	1.43471i	−0.863446	−	0.504441i	$-0.831699\pi$
$617$	−7610.21	−	21988.2i	−0.496556	−	1.43471i	0.366890	−	0.930264i	$-0.380423\pi$
$618$	35498.3	+	11441.8i	2.31060	+	0.744750i
$619$	−7185.75	+	10091.0i	−0.466591	+	0.655235i	−0.979084	−	0.203456i	$-0.934783\pi$
$619$	−7185.75	+	10091.0i	−0.466591	+	0.655235i	0.512493	+	0.858691i	$0.328722\pi$
$620$	49.3116			0.00319420
$621$	−4050.40	+	14935.8i	−0.261734	+	0.965140i
$622$	−8858.94			−0.571079
$623$	−644.455	+	905.010i	−0.0414439	+	0.0581998i
$624$	3567.00	+	1149.71i	0.228837	+	0.0737584i
$625$	−5109.40	−	14762.7i	−0.327002	−	0.944810i
$626$	12015.5	−	6194.44i	0.767153	−	0.395495i
$627$	−5934.52	+	4420.29i	−0.377993	+	0.281546i
$628$	−21829.6	+	17167.0i	−1.38709	+	1.09082i
$629$	8056.16	+	2365.50i	0.510684	+	0.149950i
$630$	−2.49813	+	24.8953i	−0.000157981	+	0.00157437i
$631$	−580.222	+	4035.53i	−0.0366058	+	0.254599i	−0.999904	−	0.0138335i	$-0.995597\pi$
$631$	−580.222	+	4035.53i	−0.0366058	+	0.254599i	0.963299	+	0.268432i	$0.0865056\pi$
$632$	−9794.73	+	935.284i	−0.616477	+	0.0588664i
$633$	−605.590	−	28301.5i	−0.0380253	−	1.77707i
$634$	−35100.1	−	27603.0i	−2.19874	−	1.72911i
$635$	0.542336	+	11.3850i	3.38928e−5	+	0.000711498i
$636$	−5732.76	+	949.838i	−0.357420	+	0.0592194i
$637$	1678.17	−	1319.73i	0.104382	−	0.0820870i
$638$	2332.09	+	2691.38i	0.144715	+	0.167011i
$639$	−3504.48	+	17723.7i	−0.216956	+	1.09724i
$640$	88.4473	−	102.074i	0.00546279	−	0.00630440i
$641$	6323.15	+	6029.11i	0.389625	+	0.371506i	0.859421	−	0.511268i	$-0.170824\pi$
$641$	6323.15	+	6029.11i	0.389625	+	0.371506i	−0.469796	+	0.882775i	$0.655673\pi$
$642$	28289.3	−	10473.9i	1.73908	−	0.643882i
$643$	3320.63	−	5751.50i	0.203659	−	0.352748i	−0.746046	−	0.665895i	$-0.768050\pi$
$643$	3320.63	−	5751.50i	0.203659	−	0.352748i	0.949705	+	0.313147i	$0.101383\pi$
$644$	−389.339	−	3904.11i	−0.0238232	−	0.238887i
$645$	−41.1966	−	28.0274i	−0.00251491	−	0.00171097i
$646$	30471.8	−	42791.6i	1.85588	−	2.60621i
$647$	−2505.15	+	735.577i	−0.152222	+	0.0446963i	−0.356956	−	0.934121i	$-0.616185\pi$
$647$	−2505.15	+	735.577i	−0.152222	+	0.0446963i	0.204734	+	0.978818i	$0.434367\pi$
$648$	1402.66	+	36915.4i	0.0850334	+	2.23792i
$649$	−2941.70	−	1890.52i	−0.177923	−	0.114344i
$650$	−1311.18	+	3788.41i	−0.0791211	+	0.228605i
$651$	−135.340	+	276.913i	−0.00814808	+	0.0166714i
$652$	−23807.1	+	22700.0i	−1.42999	+	1.36350i
$653$	−1233.74	−	25899.5i	−0.0739358	−	1.55210i	−0.665839	−	0.746095i	$-0.731926\pi$
$653$	−1233.74	−	25899.5i	−0.0739358	−	1.55210i	0.591903	−	0.806009i	$-0.298377\pi$
$654$	709.853	+	156.208i	0.0424426	+	0.00933979i
$655$	47.6623	−	4.55120i	0.00284324	−	0.000271496i
$656$	−605.518	+	1325.90i	−0.0360389	+	0.0789142i
$657$	18034.7	−	4283.41i	1.07093	−	0.254356i
$658$	93.0216	−	59.7813i	0.00551118	−	0.00354182i
$659$	5510.10	+	22712.9i	0.325710	+	1.34259i	0.865548	+	0.500826i	$0.166970\pi$
$659$	5510.10	+	22712.9i	0.325710	+	1.34259i	−0.539838	+	0.841769i	$0.681515\pi$
$660$	−59.4407	−	88.2803i	−0.00350565	−	0.00520652i
$661$	22602.4	−	4356.25i	1.33000	−	0.256337i	0.525756	−	0.850635i	$-0.323782\pi$
$661$	22602.4	−	4356.25i	1.33000	−	0.256337i	0.804244	+	0.594299i	$0.202570\pi$
$662$	41082.3	−	21179.4i	2.41195	−	1.24345i
$663$	769.161	−	2843.17i	0.0450554	−	0.166546i
$664$	28147.6	+	26838.7i	1.64509	+	1.56859i
$665$	8.65696	+	18.9561i	0.000504816	+	0.00110539i
$666$	−7977.72	+	10044.7i	−0.464160	+	0.584419i
$667$	5853.29	−	2053.39i	0.339790	−	0.119202i
$668$	21326.5	+	36938.6i	1.23525	+	2.13952i
$669$	−16410.0	+	6075.71i	−0.948354	+	0.351122i
$670$	−77.8064	+	320.722i	−0.00448645	+	0.0184934i
$671$	−2174.82	−	6283.73i	−0.125124	−	0.361521i
$672$	−717.939	−	1687.75i	−0.0412129	−	0.0968847i
$673$	5384.37	−	15557.1i	0.308398	−	0.891058i	−0.679186	−	0.733967i	$-0.737667\pi$
$673$	5384.37	−	15557.1i	0.308398	−	0.891058i	0.987584	−	0.157092i	$-0.0502119\pi$
$674$	4014.22	+	27919.5i	0.229409	+	1.59558i
$675$	−17533.4	+	290.797i	−0.999795	+	0.0165819i
$676$	−32573.7	+	20933.8i	−1.85331	+	1.19105i
$677$	−3004.63	+	1202.87i	−0.170572	+	0.0682867i	−0.455377	−	0.890299i	$-0.650495\pi$
$677$	−3004.63	+	1202.87i	−0.170572	+	0.0682867i	0.284805	+	0.958586i	$0.408071\pi$
$678$	75.5794	−	45.8191i	0.00428114	−	0.00259539i
$679$	2049.71	+	2878.41i	0.115848	+	0.162685i
$680$	329.177	+	258.867i	0.0185637	+	0.0145987i
$681$	−8308.22	−	15302.8i	−0.467506	−	0.861091i
$682$	−446.857	−	1841.97i	−0.0250895	−	0.103420i
$683$	−358.987	−	2496.81i	−0.0201117	−	0.139880i	0.977292	−	0.211899i	$-0.0679648\pi$
$683$	−358.987	−	2496.81i	−0.0201117	−	0.139880i	−0.997403	+	0.0720193i	$0.977056\pi$
$684$	29787.2	+	46843.7i	1.66512	+	2.61859i
$685$	−11.1764	−	7.18263i	−0.000623399	−	0.000400634i
$686$	−6761.19	−	1303.11i	−0.376303	−	0.0725264i
$687$	−9508.63	+	8602.24i	−0.528060	+	0.477723i
$688$	11912.0	+	1137.46i	0.660090	+	0.0630310i
$689$	−196.158	+	339.755i	−0.0108462	+	0.0187861i
$690$	−261.778	+	57.4377i	−0.0144431	+	0.00316901i
$691$	−3222.47	−	5581.48i	−0.177407	−	0.307279i	0.763584	−	0.645708i	$-0.223438\pi$
$691$	−3222.47	−	5581.48i	−0.177407	−	0.307279i	−0.940992	+	0.338429i	$0.890104\pi$
$692$	−17029.9	−	37290.3i	−0.935520	−	2.04850i
$693$	658.884	−	91.5002i	0.0361168	−	0.00501559i
$694$	−23870.8	+	27548.4i	−1.30565	+	1.50680i
$695$	9.85638	−	206.911i	0.000537948	−	0.0112929i
$696$	11875.4	−	8845.35i	0.646749	−	0.481727i
$697$	1063.51	+	425.763i	0.0577950	+	0.0231376i
$698$	8429.11	−	8037.14i	0.457087	−	0.435831i
$699$	−23442.3	−	614.454i	−1.26848	−	0.0332486i
$700$	4127.43	−	1652.37i	0.222860	−	0.0892198i
$701$	1907.58	−	4177.01i	0.102779	−	0.225055i	−0.851255	−	0.524752i	$-0.824158\pi$
$701$	1907.58	−	4177.01i	0.102779	−	0.225055i	0.954035	+	0.299697i	$0.0968855\pi$
$702$	3582.69	+	2722.53i	0.192621	+	0.146375i
$703$	−1520.46	+	10575.0i	−0.0815722	+	0.567347i
$704$	−100.868	−	52.0011i	−0.00540001	−	0.00278390i
$705$	−3.31667	−	4.03668i	−0.000177181	−	0.000215646i
$706$	53623.6	+	21467.7i	2.85857	+	1.14440i
$707$	3337.12	−	643.177i	0.177518	−	0.0342138i
$708$	−15771.0	+	20962.3i	−0.837161	+	1.11273i
$709$	30937.6	+	5962.73i	1.63877	+	0.315846i	0.923672	−	0.383183i	$-0.125172\pi$
$709$	30937.6	+	5962.73i	1.63877	+	0.315846i	0.715093	+	0.699029i	$0.246384\pi$
$710$	−300.213	+	88.1506i	−0.0158687	+	0.00465948i
$711$	−5088.67	−	1260.45i	−0.268411	−	0.0664846i
$712$	−28408.9			−1.49532
$713$	−3269.80	−	456.127i	−0.171746	−	0.0239581i
$714$	−4252.69	+	2053.20i	−0.222904	+	0.107618i
$715$	−7.15269	−	0.682999i	−0.000374120	−	3.57241e-5i
$716$	14111.9	−	58170.0i	0.736572	−	3.03619i
$717$	667.370	−	2466.91i	0.0347607	−	0.128491i
$718$	3102.47	−	65128.8i	0.161258	−	3.38522i
$719$	13113.6	+	15133.9i	0.680186	+	0.784976i	0.985934	−	0.167136i	$-0.0534519\pi$
$719$	13113.6	+	15133.9i	0.680186	+	0.784976i	−0.305748	+	0.952112i	$0.598906\pi$
$720$	−246.549	+	140.768i	−0.0127616	+	0.00728628i
$721$	−2679.40	−	786.744i	−0.138400	−	0.0406378i
$722$	28358.5	+	14619.8i	1.46177	+	0.753593i
$723$	21751.0	+	4786.47i	1.11885	+	0.246211i
$724$	−38397.9	−	53922.3i	−1.97106	−	2.76796i
$725$	4077.20	+	5725.63i	0.208860	+	0.293303i
$726$	21001.5	−	22991.1i	1.07361	−	1.17532i
$727$	7087.64	+	3653.93i	0.361576	+	0.186406i	0.629436	−	0.777052i	$-0.283286\pi$
$727$	7087.64	+	3653.93i	0.361576	+	0.186406i	−0.267860	+	0.963458i	$0.586316\pi$
$728$	−606.717	−	178.148i	−0.0308879	−	0.00906951i
$729$	−5817.32	+	18803.7i	−0.295550	+	0.955327i
$730$	210.223	+	242.610i	0.0106585	+	0.0123005i
$731$	447.480	−	9393.76i	0.0226411	−	0.475295i
$732$	−48214.2	+	12794.7i	−2.43449	+	0.646048i
$733$	−4603.04	+	18974.0i	−0.231947	+	0.956099i	0.730127	+	0.683311i	$0.239461\pi$
$733$	−4603.04	+	18974.0i	−0.231947	+	0.956099i	−0.962074	+	0.272787i	$0.912054\pi$
$734$	−59927.0	−	5722.34i	−3.01355	−	0.287759i
$735$	−11.9257	+	161.290i	−0.000598484	+	0.00809423i
$736$	14793.3	−	12927.6i	0.740883	−	0.647443i
$737$	8774.28			0.438541
$738$	−1213.80	+	1260.80i	−0.0605429	+	0.0628870i
$739$	−10733.3	+	3151.58i	−0.534276	+	0.156878i	−0.537731	−	0.843116i	$-0.680718\pi$
$739$	−10733.3	+	3151.58i	−0.534276	+	0.156878i	0.00345483	+	0.999994i	$0.498900\pi$
$740$	−150.881	−	29.0798i	−0.00749524	−	0.00144459i
$741$	3720.24	+	453.888i	0.184435	+	0.0225020i
$742$	617.643	−	119.041i	0.0305585	−	0.00588966i
$743$	12869.7	+	5152.24i	0.635454	+	0.254398i	0.666946	−	0.745106i	$-0.267601\pi$
$743$	12869.7	+	5152.24i	0.635454	+	0.254398i	−0.0314912	+	0.999504i	$0.510026\pi$
$744$	−7775.14	+	1288.23i	−0.383133	+	0.0634796i
$745$	120.636	+	62.1922i	0.00593256	+	0.00305845i
$746$	−4953.12	+	34449.7i	−0.243092	+	1.69074i
$747$	9406.70	+	18464.0i	0.460740	+	0.904368i
$748$	8344.53	−	18272.0i	0.407896	−	0.893167i
$749$	−2096.83	+	839.443i	−0.102292	+	0.0409514i
$750$	−289.814	−	533.803i	−0.0141100	−	0.0259890i
$751$	−17591.7	+	16773.7i	−0.854768	+	0.815020i	−0.984290	−	0.176557i	$-0.943504\pi$
$751$	−17591.7	+	16773.7i	−0.854768	+	0.815020i	0.129523	+	0.991576i	$0.458656\pi$
$752$	1164.82	+	466.322i	0.0564846	+	0.0226130i
$753$	292.940	+	2501.08i	0.0141771	+	0.121042i
$754$	85.8216	−	1801.62i	0.00414514	−	0.0870173i
$755$	5.43528	−	6.27265i	0.000262000	−	0.000302364i
$756$	−320.074	−	4980.00i	−0.0153981	−	0.239578i
$757$	3468.43	+	7594.80i	0.166529	+	0.364647i	0.974437	−	0.224661i	$-0.0721276\pi$
$757$	3468.43	+	7594.80i	0.166529	+	0.364647i	−0.807908	+	0.589308i	$0.799400\pi$
$758$	−33181.9	−	57472.7i	−1.59000	−	2.75396i
$759$	3124.87	+	6403.59i	0.149441	+	0.306239i
$760$	−266.432	+	461.473i	−0.0127164	+	0.0220255i
$761$	−30971.3	−	2957.40i	−1.47531	−	0.140875i	−0.673823	−	0.738893i	$-0.735349\pi$
$761$	−30971.3	−	2957.40i	−1.47531	−	0.140875i	−0.801483	+	0.598018i	$0.795955\pi$
$762$	−690.887	−	3213.15i	−0.0328454	−	0.152756i
$763$	−53.4370	−	10.2991i	−0.00253545	−	0.000488668i
$764$	−62004.5	−	39847.9i	−2.93618	−	1.88697i
$765$	119.726	+	188.283i	0.00565844	+	0.00889853i
$766$	−5962.41	−	41469.4i	−0.281241	−	1.95607i
$767$	417.539	+	1721.12i	0.0196564	+	0.0810248i
$768$	−20151.4	+	32882.2i	−0.946810	+	1.54497i
$769$	−20272.3	−	15942.3i	−0.950633	−	0.747586i	0.0170245	−	0.999855i	$-0.494581\pi$
$769$	−20272.3	−	15942.3i	−0.950633	−	0.747586i	−0.967657	+	0.252269i	$0.918823\pi$
$770$	6.68241	+	9.38413i	0.000312750	+	0.000439196i
$771$	−372.786	−	17421.7i	−0.0174132	−	0.813782i
$772$	−70813.1	+	28349.3i	−3.30132	+	1.32165i
$773$	−28666.8	+	18423.1i	−1.33386	+	0.857220i	−0.996454	−	0.0841386i	$-0.973186\pi$
$773$	−28666.8	+	18423.1i	−1.33386	+	0.857220i	−0.337407	+	0.941359i	$0.609550\pi$
$774$	13040.2	+	6031.27i	0.605584	+	0.280090i
$775$	−532.409	−	3702.98i	−0.0246770	−	0.171632i
$776$	−29552.3	+	85385.9i	−1.36710	+	3.94997i
$777$	577.405	−	767.468i	0.0266593	−	0.0354347i
$778$	22333.5	+	64528.4i	1.02917	+	2.97359i
$779$	−343.658	+	1416.58i	−0.0158059	+	0.0651530i
$780$	−9.06646	+	53.1344i	−0.000416194	+	0.00243912i
$781$	4159.32	+	7204.15i	0.190566	+	0.330070i
$782$	−35060.2	−	36462.5i	−1.60326	−	1.66739i
$783$	7532.14	−	2347.99i	0.343776	−	0.107165i
$784$	−16135.0	−	35330.6i	−0.735011	−	1.60945i
$785$	−102.794	−	98.0143i	−0.00467375	−	0.00445641i
$786$	−13344.0	+	3541.14i	−0.605554	+	0.160698i
$787$	−18772.8	+	9678.05i	−0.850290	+	0.438355i	−0.827554	−	0.561387i	$-0.810268\pi$
$787$	−18772.8	+	9678.05i	−0.850290	+	0.438355i	−0.0227362	+	0.999741i	$0.507238\pi$
$788$	−87420.9	+	16849.0i	−3.95208	+	0.761701i
$789$	32987.8	−	2279.59i	1.48846	−	0.102859i
$790$	−21.4046	−	88.2311i	−0.000963978	−	0.00397357i
$791$	−5.56703	+	3.57771i	−0.000250241	+	0.000160820i
$792$	11678.5	+	12366.6i	0.523961	+	0.554835i
$793$	−1399.02	+	3063.44i	−0.0626492	+	0.137183i
$794$	12942.1	−	1235.82i	0.578463	−	0.0552365i
$795$	−8.98109	−	28.3301i	−0.000400662	−	0.00126385i
$796$	−3248.21	−	68188.3i	−0.144635	−	3.03627i
$797$	6310.65	−	6017.19i	0.280470	−	0.267428i	−0.536765	−	0.843732i	$-0.680354\pi$
$797$	6310.65	−	6017.19i	0.280470	−	0.267428i	0.817236	+	0.576304i	$0.195505\pi$
$798$	−3356.10	−	4984.43i	−0.148878	−	0.221111i
$799$	322.515	−	931.845i	0.0142800	−	0.0412595i
$800$	18727.9	+	12035.7i	0.827666	+	0.531909i
$801$	−14280.0	−	5019.42i	−0.629912	−	0.221414i
$802$	30552.8	−	8971.11i	1.34521	−	0.394988i
$803$	4950.68	−	6952.26i	0.217566	−	0.305529i
$804$	4853.68	−	65643.9i	0.212906	−	2.87946i
$805$	19.4807	−	4.81263i	0.000852924	−	0.000210711i
$806$	−479.985	+	831.359i	−0.0209761	+	0.0363317i
$807$	−1943.56	+	11390.3i	−0.0847790	+	0.496851i
$808$	62893.2	+	59968.5i	2.73833	+	2.61100i
$809$	12988.7	−	14989.8i	0.564473	−	0.651437i	−0.399720	−	0.916637i	$-0.630893\pi$
$809$	12988.7	−	14989.8i	0.564473	−	0.651437i	0.964193	+	0.265200i	$0.0854381\pi$
$810$	−335.321	+	61.2878i	−0.0145457	+	0.00265856i
$811$	8752.55	+	10101.0i	0.378969	+	0.437353i	0.912905	−	0.408171i	$-0.133833\pi$
$811$	8752.55	+	10101.0i	0.378969	+	0.437353i	−0.533937	+	0.845525i	$0.679288\pi$
$812$	−1572.32	+	1236.49i	−0.0679528	+	0.0534387i
$813$	−21192.6	−	25793.3i	−0.914216	−	1.11268i
$814$	281.026	+	5899.46i	0.0121007	+	0.254025i
$815$	−132.244	−	103.998i	−0.00568382	−	0.00446980i
$816$	−46968.5	−	25793.6i	−2.01498	−	1.10656i
$817$	11912.4	−	1137.50i	0.510113	−	0.0487099i
$818$	−5959.58	+	41449.8i	−0.254733	+	1.77171i
$819$	−273.496	−	196.745i	−0.0116688	−	0.00839419i
$820$	−20.1154	−	5.90641i	−0.000856658	−	0.000251538i
$821$	−7463.06	+	5869.02i	−0.317251	+	0.249489i	−0.764067	−	0.645137i	$-0.776800\pi$
$821$	−7463.06	+	5869.02i	−0.317251	+	0.249489i	0.446816	+	0.894626i	$0.352558\pi$
$822$	3517.89	+	1516.47i	0.149271	+	0.0643468i
$823$	10519.8	−	5423.35i	0.445563	−	0.229704i	−0.220818	−	0.975315i	$-0.570873\pi$
$823$	10519.8	−	5423.35i	0.445563	−	0.229704i	0.666381	+	0.745611i	$0.267842\pi$
$824$	−23354.3	−	67477.9i	−0.987362	−	2.85279i
$825$	−5987.51	+	5416.76i	−0.252677	+	0.228591i
$826$	1647.11	−	2313.04i	0.0693828	−	0.0974345i
$827$	−10802.8			−0.454233			−0.227116	−	0.973868i	$-0.572930\pi$
$827$	−10802.8			−0.454233			−0.227116	+	0.973868i	$0.572930\pi$
$828$	49636.5	−	19836.1i	2.08332	−	0.832551i
$829$	−484.107			−0.0202819			−0.0101410	−	0.999949i	$-0.503228\pi$
$829$	−484.107			−0.0202819			−0.0101410	+	0.999949i	$0.503228\pi$
$830$	−208.166	+	292.328i	−0.00870548	+	0.0122251i
$831$	−4887.72	−	22731.6i	−0.204035	−	0.948918i
$832$	18.7987	+	54.3153i	0.000783327	+	0.00226327i
$833$	−27132.0	+	13987.5i	−1.12853	+	0.581799i
$834$	6948.44	+	59324.7i	0.288495	+	2.46312i
$835$	−171.474	+	134.849i	−0.00710673	+	0.00558879i
$836$	24524.5	+	7201.04i	1.01459	+	0.297910i
$837$	−4135.86	−	726.206i	−0.170796	−	0.0299897i
$838$	6566.41	−	45670.4i	0.270683	−	1.88264i
$839$	46078.1	−	4399.93i	1.89606	−	0.181052i	0.919034	−	0.394178i	$-0.128971\pi$
$839$	46078.1	−	4399.93i	1.89606	−	0.181052i	0.977025	+	0.213127i	$0.0683647\pi$
$840$	40.9622	−	24.8329i	0.00168254	−	0.00102002i
$841$	16685.2	+	13121.4i	0.684128	+	0.538004i
$842$	−525.770	−	11037.3i	−0.0215193	−	0.451745i
$843$	−315.437	+	839.545i	−0.0128876	+	0.0343007i
$844$	−76859.4	+	60442.9i	−3.13461	+	2.46508i
$845$	−129.684	−	149.664i	−0.00527961	−	0.00609300i
$846$	1133.75	+	991.993i	0.0460748	+	0.0403138i
$847$	−1526.80	+	1762.02i	−0.0619381	+	0.0714804i
$848$	5165.55	+	4925.34i	0.209181	+	0.199454i
$849$	10066.0	+	8352.03i	0.406909	+	0.337622i
$850$	28659.7	−	49640.0i	1.15649	−	2.00310i
$851$	9735.74	+	3323.88i	0.392170	+	0.133891i
$852$	56198.0	−	27132.4i	2.25976	−	1.09101i
$853$	2475.09	−	3475.77i	0.0993498	−	0.139517i	−0.761909	−	0.647685i	$-0.775737\pi$
$853$	2475.09	−	3475.77i	0.0993498	−	0.139517i	0.861258	+	0.508167i	$0.169677\pi$
$854$	5180.92	−	1521.26i	0.207597	−	0.0609559i
$855$	−215.460	+	184.890i	−0.00861821	+	0.00739543i
$856$	−48585.0	−	31223.7i	−1.93996	−	1.24673i
$857$	1205.74	−	3483.74i	0.0480597	−	0.138859i	−0.918417	−	0.395614i	$-0.870532\pi$
$857$	1205.74	−	3483.74i	0.0480597	−	0.138859i	0.966477	+	0.256754i	$0.0826531\pi$
$858$	2066.92	−	142.833i	0.0822419	−	0.00568326i
$859$	−6944.08	+	6621.17i	−0.275820	+	0.262994i	−0.815344	−	0.578976i	$-0.803452\pi$
$859$	−6944.08	+	6621.17i	−0.275820	+	0.262994i	0.539525	+	0.841970i	$0.318604\pi$
$860$	8.18918	+	171.912i	0.000324708	+	0.00681646i
$861$	88.3763	−	96.7487i	0.00349809	−	0.00382948i
$862$	21653.9	−	2067.70i	0.855610	−	0.0817008i
$863$	−4618.32	+	10112.7i	−0.182166	+	0.398889i	−0.978581	−	0.205862i	$-0.934000\pi$
$863$	−4618.32	+	10112.7i	−0.182166	+	0.398889i	0.796415	+	0.604751i	$0.206727\pi$
$864$	19382.9	−	15770.0i	0.763217	−	0.620958i
$865$	176.382	−	113.354i	0.00693315	−	0.00445567i
$866$	18336.8	+	75585.3i	0.719526	+	2.96593i
$867$	−7282.35	+	14900.0i	−0.285261	+	0.583659i
$868$	1045.38	−	201.480i	0.0408783	−	0.00787866i
$869$	−2145.48	+	1106.07i	−0.0837521	+	0.0431772i
$870$	96.3829	+	96.8477i	0.00375596	+	0.00377407i
$871$	−3216.24	−	3066.68i	−0.125118	−	0.119300i
$872$	−578.066	−	1265.79i	−0.0224493	−	0.0491571i
$873$	−29941.2	+	37698.6i	−1.16077	+	1.46152i
$874$	39575.2	−	50761.0i	1.53164	−	1.96455i
$875$	22.7390	+	39.3851i	0.000878536	+	0.00152167i
$876$	−49274.1	−	40883.9i	−1.90048	−	1.57687i
$877$	−3236.32	+	13340.3i	−0.124610	+	0.513649i	0.874957	+	0.484202i	$0.160890\pi$
$877$	−3236.32	+	13340.3i	−0.124610	+	0.513649i	−0.999566	+	0.0294472i	$0.990625\pi$
$878$	29043.0	+	83914.3i	1.11635	+	3.22548i
$879$	7540.00	+	919.919i	0.289327	+	0.0352993i
$880$	−42.7544	+	123.531i	−0.00163778	+	0.00473207i
$881$	4864.34	+	33832.2i	0.186020	+	1.29380i	0.842188	+	0.539184i	$0.181267\pi$
$881$	4864.34	+	33832.2i	0.186020	+	1.29380i	−0.656168	+	0.754615i	$0.727824\pi$
$882$	−4209.53	−	46444.3i	−0.160705	−	1.77309i
$883$	−18135.2	+	11654.8i	−0.691165	+	0.444185i	−0.838500	−	0.544902i	$-0.816567\pi$
$883$	−18135.2	+	11654.8i	−0.691165	+	0.444185i	0.147335	+	0.989087i	$0.452930\pi$
$884$	−9444.90	+	3781.17i	−0.359351	+	0.143863i
$885$	−117.598	−	64.5811i	−0.00446668	−	0.00245296i
$886$	8832.41	+	12403.4i	0.334910	+	0.470316i
$887$	27329.3	+	21492.0i	1.03453	+	0.813562i	0.982721	−	0.185095i	$-0.0592592\pi$
$887$	27329.3	+	21492.0i	1.03453	+	0.813562i	0.0518080	+	0.998657i	$0.483502\pi$
$888$	24549.6	+	643.477i	0.927737	+	0.0243172i
$889$	58.0148	+	239.140i	0.00218870	+	0.00902194i
$890$	−37.3062	−	259.470i	−0.00140506	−	0.00977243i
$891$	3685.32	+	8279.62i	0.138567	+	0.311311i
$892$	50847.4	+	32677.6i	1.90863	+	1.22660i
$893$	1232.06	+	237.459i	0.0461693	+	0.00889840i
$894$	−37248.7	−	12005.9i	−1.39349	−	0.449148i
$895$	304.750	+	29.1001i	0.0113817	+	0.00108683i
$896$	1457.97	−	2525.28i	0.0543610	−	0.0941560i
$897$	1092.67	−	3439.42i	0.0406726	−	0.128026i
$898$	6252.82	+	10830.2i	0.232360	+	0.402459i
$899$	699.210	+	1531.06i	0.0259399	+	0.0568004i
$900$	37212.9	+	47791.4i	1.37825	+	1.77005i
$901$	3673.34	−	4239.26i	0.135823	−	0.156748i
$902$	−38.3424	+	804.907i	−0.00141537	+	0.0297123i
$903$	−987.860	−	425.841i	−0.0364052	−	0.0156934i
$904$	−157.090	−	62.8895i	−0.00577959	−	0.00231380i
$905$	245.027	−	233.633i	0.00899996	−	0.00858145i
$906$	−1250.53	+	2040.57i	−0.0458566	+	0.0748270i
$907$	−31920.0	+	12778.9i	−1.16856	+	0.467822i	−0.873104	−	0.487533i	$-0.837897\pi$
$907$	−31920.0	+	12778.9i	−1.16856	+	0.467822i	−0.295459	+	0.955355i	$0.595473\pi$
$908$	−24985.3	+	54710.1i	−0.913178	+	1.99958i
$909$	21018.4	+	41256.0i	0.766925	+	1.50536i
$910$	0.830368	−	5.77533i	3.02488e−5	−	0.000210385i
$911$	38621.8	+	19910.9i	1.40461	+	0.724125i	0.983163	−	0.182729i	$-0.0584932\pi$
$911$	38621.8	+	19910.9i	1.40461	+	0.724125i	0.421444	+	0.906855i	$0.361524\pi$
$912$	23981.4	−	63827.4i	0.870728	−	2.31747i
$913$	8857.75	+	3546.11i	0.321083	+	0.128542i
$914$	−56269.2	+	10845.0i	−2.03634	+	0.392473i
$915$	−99.8650	−	234.766i	−0.00360813	−	0.00848210i
$916$	43489.5	+	8381.91i	1.56870	+	0.302343i
$917$	991.818	−	291.224i	0.0357172	−	0.0104875i
$918$	−42932.8	−	47917.9i	−1.54357	−	1.72280i
$919$	−2232.36			−0.0801291			−0.0400645	−	0.999197i	$-0.512756\pi$
$919$	−2232.36			−0.0801291			−0.0400645	+	0.999197i	$0.512756\pi$
$920$	389.181	+	334.378i	0.0139467	+	0.0119827i
$921$	−6186.78	−	4209.07i	−0.221348	−	0.150590i
$922$	46754.6	+	4464.52i	1.67004	+	0.159470i
$923$	993.295	−	4094.42i	0.0354222	−	0.146012i
$924$	−1620.81	−	1628.62i	−0.0577063	−	0.0579846i
$925$	−554.678	+	11644.1i	−0.0197164	+	0.413899i
$926$	23971.3	+	27664.3i	0.850697	+	0.981757i
$927$	183.026	−	38044.8i	0.00648474	−	1.34795i
$928$	−9610.27	−	2821.83i	−0.339949	−	0.0998180i
$929$	44448.5	+	22914.8i	1.56976	+	0.809268i	0.999922	−	0.0124895i	$-0.00397562\pi$
$929$	44448.5	+	22914.8i	1.56976	+	0.809268i	0.569838	+	0.821757i	$0.307006\pi$
$930$	−21.9762	−	69.3219i	−0.000774867	−	0.00244425i
$931$	−22530.4	−	31639.6i	−0.793131	−	1.11380i
$932$	46984.7	+	65980.8i	1.65133	+	2.31896i
$933$	2730.85	+	8614.22i	0.0958241	+	0.302269i
$934$	−78811.8	−	40630.3i	−2.76103	−	1.42341i
$935$	98.5733	+	28.9437i	0.00344780	+	0.00101236i
$936$	41.4439	−	8614.75i	0.00144726	−	0.300835i
$937$	−9273.76	−	10702.5i	−0.323330	−	0.373143i	0.570693	−	0.821163i	$-0.306675\pi$
$937$	−9273.76	−	10702.5i	−0.323330	−	0.373143i	−0.894023	+	0.448020i	$0.852129\pi$
$938$	−339.026	+	7117.03i	−0.0118013	+	0.247739i
$939$	−9727.23	−	9774.14i	−0.338058	−	0.339688i
$940$	−4.25448	+	17.5372i	−0.000147623	+	0.000608512i
$941$	−10861.0	−	1037.10i	−0.376259	−	0.0359284i	−0.0947864	−	0.995498i	$-0.530217\pi$
$941$	−10861.0	−	1037.10i	−0.376259	−	0.0359284i	−0.281473	+	0.959569i	$0.590823\pi$
$942$	33861.7	+	23037.2i	1.17120	+	0.796808i
$943$	1279.20	+	577.713i	0.0441743	+	0.0199501i
$944$	32220.4			1.11090
$945$	24.9777	−	5.24508i	0.000859813	−	0.000180553i
$946$	6347.34	−	1863.75i	0.218150	−	0.0640546i
$947$	−26005.5	−	5012.15i	−0.892361	−	0.171988i	−0.277595	−	0.960698i	$-0.589537\pi$
$947$	−26005.5	−	5012.15i	−0.892361	−	0.171988i	−0.614766	+	0.788710i	$0.710749\pi$
$948$	7088.17	+	16663.1i	0.242841	+	0.570877i
$949$	−4244.56	+	818.071i	−0.145189	+	0.0279828i
$950$	67711.1	+	27107.5i	2.31246	+	0.925770i
$951$	−16020.6	+	42639.4i	−0.546271	+	1.45392i
$952$	8036.05	+	4142.87i	0.273582	+	0.141041i
$953$	−1398.06	+	9723.72i	−0.0475211	+	0.330516i	0.952168	+	0.305575i	$0.0988488\pi$
$953$	−1398.06	+	9723.72i	−0.0475211	+	0.330516i	−0.999689	+	0.0249408i	$0.992060\pi$
$954$	3890.13	+	7635.77i	0.132021	+	0.259138i
$955$	156.594	−	342.894i	0.00530605	−	0.0116186i
$956$	−8194.97	+	3280.77i	−0.277243	+	0.110991i
$957$	1898.14	−	3097.31i	0.0641152	−	0.104621i
$958$	9365.92	−	8930.39i	0.315866	−	0.301177i
$959$	−266.280	−	106.602i	−0.00896625	−	0.00358954i
$960$	−3.99840	−	1.72361i	−0.000134425	−	5.79472e-5i
$961$	−1374.89	+	28862.4i	−0.0461511	+	0.968831i
$962$	1958.90	−	2260.69i	0.0656521	−	0.0757666i
$963$	−18905.0	−	24279.1i	−0.632611	−	0.812444i
$964$	−31957.1	−	69976.3i	−1.06771	−	2.33795i
$965$	−195.057	−	337.849i	−0.00650684	−	0.0112702i
$966$	−5314.85	+	2287.23i	−0.177021	+	0.0761805i
$967$	20466.9	−	35449.7i	0.680632	−	1.17889i	−0.294156	−	0.955757i	$-0.595039\pi$
$967$	20466.9	−	35449.7i	0.680632	−	1.17889i	0.974788	−	0.223132i	$-0.0716281\pi$
$968$	−59346.6	−	5666.91i	−1.97053	−	0.188163i
$969$	−51002.7	−	16439.1i	−1.69086	−	0.544996i
$970$	−818.672	−	157.786i	−0.0270989	−	0.00522289i
$971$	2556.85	+	1643.19i	0.0845039	+	0.0543074i	0.582210	−	0.813038i	$-0.302188\pi$
$971$	2556.85	+	1643.19i	0.0845039	+	0.0543074i	−0.497707	+	0.867345i	$0.665824\pi$
$972$	63981.8	−	22991.3i	2.11134	−	0.758690i
$973$	−636.458	−	4426.66i	−0.0209701	−	0.145850i
$974$	−17861.3	−	73625.4i	−0.587591	−	2.42208i
$975$	4087.94	+	107.150i	0.134276	+	0.00351955i
$976$	48161.2	+	37874.4i	1.57951	+	1.24214i
$977$	13640.3	+	19155.2i	0.446666	+	0.627255i	0.975112	−	0.221712i	$-0.0711645\pi$
$977$	13640.3	+	19155.2i	0.446666	+	0.627255i	−0.528446	+	0.848967i	$0.677225\pi$
$978$	42521.3	+	23351.3i	1.39027	+	0.763491i
$979$	−6470.16	+	2590.26i	−0.211223	+	0.0845609i
$980$	469.953	−	302.020i	0.0153185	−	0.00984458i
$981$	−66.9253	−	738.396i	−0.00217814	−	0.0240318i
$982$	−7480.97	−	52031.3i	−0.243103	−	1.69082i
$983$	−1367.99	+	3952.55i	−0.0443867	+	0.128247i	−0.965016	−	0.262191i	$-0.915555\pi$
$983$	−1367.99	+	3952.55i	−0.0443867	+	0.128247i	0.920629	+	0.390438i	$0.127676\pi$
$984$	3325.97	+	405.785i	0.107752	+	0.0131463i
$985$	−148.926	−	430.294i	−0.00481744	−	0.0139191i
$986$	−6079.95	+	25061.9i	−0.196374	+	0.809466i
$987$	−86.8046	−	72.0238i	−0.00279941	−	0.00232274i
$988$	−6472.71	−	11211.1i	−0.208425	−	0.361003i
$989$	1047.15	−	11475.1i	0.0336678	−	0.368944i
$990$	−97.6135	+	122.904i	−0.00313370	+	0.00394561i
$991$	−7456.54	−	16327.5i	−0.239016	−	0.523372i	0.751670	−	0.659539i	$-0.229249\pi$
$991$	−7456.54	−	16327.5i	−0.239016	−	0.523372i	−0.990686	+	0.136168i	$0.956521\pi$
$992$	3858.12	+	3678.71i	0.123483	+	0.117741i
$993$	−33258.4	−	33418.7i	−1.06286	−	1.06799i
$994$	−6004.17	+	3095.37i	−0.191590	+	0.0987717i
$995$	342.831	−	66.0752i	0.0109231	−	0.00210525i
$996$	31429.7	−	64306.8i	0.999889	−	2.04582i
$997$	6358.68	+	26210.8i	0.201987	+	0.832603i	0.979123	+	0.203270i	$0.0651568\pi$
$997$	6358.68	+	26210.8i	0.201987	+	0.832603i	−0.777136	+	0.629333i	$0.783328\pi$
$998$	−31628.7	+	20326.5i	−1.00320	+	0.644715i
$999$	12226.4	+	4660.99i	0.387213	+	0.147615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.m.a.4.4	✓	1400
9.7	even	3	inner	207.4.m.a.142.67	yes	1400
23.6	even	11	inner	207.4.m.a.121.67	yes	1400
207.52	even	33	inner	207.4.m.a.52.4	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.m.a.4.4	✓	1400	1.1	even	1	trivial
207.4.m.a.52.4	yes	1400	207.52	even	33	inner
207.4.m.a.121.67	yes	1400	23.6	even	11	inner
207.4.m.a.142.67	yes	1400	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	207.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.95477 + 4.14939i) q^{2} +(4.94560 + 1.59406i) q^{3} +(-5.87025 - 16.9610i) q^{4} +(0.0815901 - 0.0420626i) q^{5} +(-21.2275 + 15.8112i) q^{6} +(1.55780 - 1.22507i) q^{7} +(48.6222 + 14.2768i) q^{8} +(21.9180 + 15.7672i) q^{9} +(-0.0665456 + 0.462835i) q^{10} +(12.3755 - 1.18172i) q^{11} +(-1.99513 - 93.2397i) q^{12} +(-4.94929 - 3.89216i) q^{13} +(0.480347 + 10.0837i) q^{14} +(0.470563 - 0.0779656i) q^{15} +(-90.0420 + 70.8098i) q^{16} +(58.9545 + 68.0371i) q^{17} +(-130.187 + 44.3579i) q^{18} +(-75.0163 + 86.5734i) q^{19} +(-1.19238 - 1.13693i) q^{20} +(9.65710 - 3.57547i) q^{21} +(-31.6633 + 54.8424i) q^{22} +(68.5488 + 86.4180i) q^{23} +(217.708 + 148.114i) q^{24} +(-72.5022 + 101.815i) q^{25} +(30.7741 - 9.03610i) q^{26} +(83.2637 + 112.917i) q^{27} +(-29.9230 - 19.2304i) q^{28} +(18.3928 - 53.1426i) q^{29} +(-1.06689 + 2.18292i) q^{30} +(-21.6617 + 20.6544i) q^{31} +(-8.47470 - 177.906i) q^{32} +(63.0879 + 13.8830i) q^{33} +(-456.509 + 43.5914i) q^{34} +(0.0755716 - 0.165479i) q^{35} +(138.763 - 464.307i) q^{36} +(78.4595 - 50.4228i) q^{37} +(-137.571 - 567.076i) q^{38} +(-18.2729 - 27.1386i) q^{39} +(4.56761 - 0.880335i) q^{40} +(11.3103 - 5.83085i) q^{41} +(-13.6984 + 50.6358i) q^{42} +(-75.6036 - 72.0879i) q^{43} +(-92.6902 - 202.963i) q^{44} +(2.45150 + 0.364518i) q^{45} +(-561.128 + 29.0908i) q^{46} +(-5.47663 - 9.48581i) q^{47} +(-558.187 + 206.665i) q^{48} +(-79.9394 + 329.515i) q^{49} +(-208.244 - 601.680i) q^{50} +(183.110 + 430.461i) q^{51} +(-36.9613 + 106.793i) q^{52} +(-8.86736 - 61.6739i) q^{53} +(-714.560 + 11.8512i) q^{54} +(0.960011 - 0.616962i) q^{55} +(93.2338 - 37.3252i) q^{56} +(-509.004 + 308.577i) q^{57} +(166.163 + 233.343i) q^{58} +(-221.101 - 173.875i) q^{59} +(-4.08469 - 7.52352i) q^{60} +(-126.102 - 519.798i) q^{61} +(-21.6979 - 150.912i) q^{62} +(53.4597 - 2.28889i) q^{63} +(-7.67937 - 4.93523i) q^{64} +(-0.567528 - 0.109382i) q^{65} +(-244.016 + 220.756i) q^{66} +(702.598 + 67.0900i) q^{67} +(807.898 - 1399.32i) q^{68} +(201.260 + 536.660i) q^{69} +(0.463339 + 0.802527i) q^{70} +(277.972 + 608.674i) q^{71} +(840.595 + 1079.55i) q^{72} +(449.583 - 518.847i) q^{73} +(-22.6055 + 474.547i) q^{74} +(-520.866 + 387.964i) q^{75} +(1908.73 + 764.141i) q^{76} +(17.8309 - 17.0017i) q^{77} +(166.601 + 4.36682i) q^{78} +(-180.256 + 72.1638i) q^{79} +(-4.36809 + 9.56479i) q^{80} +(231.793 + 691.168i) q^{81} +(-9.22475 + 64.1596i) q^{82} +(682.168 + 351.682i) q^{83} +(-117.333 - 142.805i) q^{84} +(7.67193 + 3.07138i) q^{85} +(522.512 - 100.706i) q^{86} +(175.676 - 233.503i) q^{87} +(618.595 + 119.224i) q^{88} +(-537.902 + 157.942i) q^{89} +(-8.75613 + 9.09515i) q^{90} -12.4782 q^{91} +(1063.33 - 1669.95i) q^{92} +(-140.055 + 67.6185i) q^{93} +(55.5425 + 5.30367i) q^{94} +(-2.47908 + 10.2189i) q^{95} +(241.680 - 893.361i) q^{96} +(-84.8404 + 1781.02i) q^{97} +(-1131.08 - 1305.34i) q^{98} +(289.878 + 169.225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1400 q - 9 q^{2} - 14 q^{3} + 263 q^{4} + 19 q^{5} - 35 q^{6} - 9 q^{7} - 74 q^{8} - 78 q^{9} - 68 q^{10} + 79 q^{11} + 54 q^{12} - 9 q^{13} + 159 q^{14} - 868 q^{15} + 1031 q^{16} - 308 q^{17} - 87 q^{18}+ \cdots + 7484 q^{99}+O(q^{100}) \) 1400 * q - 9 * q^2 - 14 * q^3 + 263 * q^4 + 19 * q^5 - 35 * q^6 - 9 * q^7 - 74 * q^8 - 78 * q^9 - 68 * q^10 + 79 * q^11 + 54 * q^12 - 9 * q^13 + 159 * q^14 - 868 * q^15 + 1031 * q^16 - 308 * q^17 - 87 * q^18 - 36 * q^19 + 119 * q^20 - 660 * q^21 - 52 * q^22 - 116 * q^23 + 2420 * q^24 + 1397 * q^25 + 432 * q^26 + 274 * q^27 - 324 * q^28 - 45 * q^29 + 768 * q^30 - 45 * q^31 + 111 * q^32 - 1664 * q^33 + 403 * q^34 - 536 * q^35 - 121 * q^36 - 180 * q^37 - 117 * q^38 - 46 * q^39 - 473 * q^40 - 333 * q^41 - 332 * q^42 - 9 * q^43 - 1908 * q^44 + 1762 * q^45 + 484 * q^46 + 216 * q^47 + 1072 * q^48 + 4615 * q^49 - 105 * q^50 + 1298 * q^51 - 708 * q^52 - 1380 * q^53 + 4116 * q^54 - 1328 * q^55 - 3971 * q^56 + 2154 * q^57 - 338 * q^58 + 1917 * q^59 + 154 * q^60 + 27 * q^61 - 3854 * q^62 - 4850 * q^63 - 5854 * q^64 + 3363 * q^65 - 2017 * q^66 + 603 * q^67 - 18454 * q^68 - 4653 * q^69 + 542 * q^70 - 5296 * q^71 - 8044 * q^72 - 36 * q^73 + 3243 * q^74 + 5140 * q^75 - 1029 * q^76 - 1661 * q^77 + 14687 * q^78 - 9 * q^79 + 10312 * q^80 - 294 * q^81 - 770 * q^82 - 2735 * q^83 + 2298 * q^84 + 241 * q^85 + 10507 * q^86 - 10268 * q^87 + 2183 * q^88 - 2980 * q^89 + 33928 * q^90 - 1452 * q^91 - 1973 * q^92 - 11406 * q^93 + 2034 * q^94 - 3339 * q^95 - 4446 * q^96 - 5193 * q^97 + 14820 * q^98 + 7484 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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