LMFDB - Embedded newform 27.4.e.a.22.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,4,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.59305157015$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			22.4
Character	$\chi$	$=$	27.22
Dual form			27.4.e.a.16.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.883701 + 0.741513i) q^{2} +(-5.10626 + 0.962362i) q^{3} +(-1.15810 + 6.56791i) q^{4} +(-7.21673 + 2.62667i) q^{5} +(3.79880 - 4.63680i) q^{6} +(2.25256 + 12.7749i) q^{7} +(-8.46114 - 14.6551i) q^{8} +(25.1477 - 9.82813i) q^{9} +O(q^{10})$	\(q+(-0.883701 + 0.741513i) q^{2} +(-5.10626 + 0.962362i) q^{3} +(-1.15810 + 6.56791i) q^{4} +(-7.21673 + 2.62667i) q^{5} +(3.79880 - 4.63680i) q^{6} +(2.25256 + 12.7749i) q^{7} +(-8.46114 - 14.6551i) q^{8} +(25.1477 - 9.82813i) q^{9} +(4.42972 - 7.67249i) q^{10} +(-10.9793 - 3.99613i) q^{11} +(-0.407152 - 34.6519i) q^{12} +(54.8237 + 46.0025i) q^{13} +(-11.4633 - 9.61888i) q^{14} +(34.3227 - 20.3576i) q^{15} +(-31.7921 - 11.5714i) q^{16} +(-18.1319 + 31.4053i) q^{17} +(-14.9354 + 27.3325i) q^{18} +(-11.8561 - 20.5353i) q^{19} +(-8.89407 - 50.4408i) q^{20} +(-23.7962 - 63.0641i) q^{21} +(12.6656 - 4.60990i) q^{22} +(-34.5875 + 196.155i) q^{23} +(57.3083 + 66.6901i) q^{24} +(-50.5738 + 42.4365i) q^{25} -82.5592 q^{26} +(-118.952 + 74.3862i) q^{27} -86.5130 q^{28} +(218.552 - 183.387i) q^{29} +(-15.2356 + 43.4407i) q^{30} +(5.40959 - 30.6793i) q^{31} +(163.889 - 59.6507i) q^{32} +(59.9088 + 9.83923i) q^{33} +(-7.26431 - 41.1980i) q^{34} +(-49.8116 - 86.2762i) q^{35} +(35.4267 + 176.550i) q^{36} +(171.316 - 296.728i) q^{37} +(25.7044 + 9.35564i) q^{38} +(-324.215 - 182.141i) q^{39} +(99.5559 + 83.5374i) q^{40} +(188.628 + 158.278i) q^{41} +(67.7916 + 38.0846i) q^{42} +(-143.766 - 52.3265i) q^{43} +(38.9613 - 67.4830i) q^{44} +(-155.669 + 136.982i) q^{45} +(-114.887 - 198.990i) q^{46} +(49.8026 + 282.445i) q^{47} +(173.475 + 28.4910i) q^{48} +(164.191 - 59.7606i) q^{49} +(13.2249 - 75.0023i) q^{50} +(62.3628 - 177.813i) q^{51} +(-365.632 + 306.802i) q^{52} -321.986 q^{53} +(49.9601 - 153.940i) q^{54} +89.7310 q^{55} +(168.158 - 141.102i) q^{56} +(80.3025 + 93.4487i) q^{57} +(-57.1507 + 324.118i) q^{58} +(-382.499 + 139.218i) q^{59} +(93.9577 + 249.004i) q^{60} +(36.2242 + 205.438i) q^{61} +(17.9686 + 31.1226i) q^{62} +(182.200 + 299.121i) q^{63} +(34.7329 - 60.1591i) q^{64} +(-516.481 - 187.984i) q^{65} +(-60.2373 + 35.7282i) q^{66} +(-152.054 - 127.588i) q^{67} +(-185.269 - 155.459i) q^{68} +(-12.1599 - 1034.90i) q^{69} +(107.993 + 39.3064i) q^{70} +(-82.6900 + 143.223i) q^{71} +(-356.811 - 285.386i) q^{72} +(484.355 + 838.928i) q^{73} +(68.6357 + 389.252i) q^{74} +(217.404 - 265.362i) q^{75} +(148.605 - 54.0876i) q^{76} +(26.3187 - 149.261i) q^{77} +(421.569 - 79.4519i) q^{78} +(759.383 - 637.198i) q^{79} +259.829 q^{80} +(535.816 - 494.310i) q^{81} -284.056 q^{82} +(440.670 - 369.766i) q^{83} +(441.758 - 83.2568i) q^{84} +(48.3613 - 274.270i) q^{85} +(165.847 - 60.3633i) q^{86} +(-939.496 + 1146.74i) q^{87} +(34.3334 + 194.714i) q^{88} +(-140.691 - 243.684i) q^{89} +(35.9910 - 236.482i) q^{90} +(-464.184 + 803.990i) q^{91} +(-1248.27 - 454.335i) q^{92} +(1.90184 + 161.862i) q^{93} +(-253.447 - 212.667i) q^{94} +(139.502 + 117.056i) q^{95} +(-779.454 + 462.312i) q^{96} +(446.114 + 162.372i) q^{97} +(-100.782 + 174.560i) q^{98} +(-315.378 + 7.41226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.883701	+	0.741513i	−0.312435	+	0.262164i	−0.785498	−	0.618864i	$-0.787593\pi$
$2$	−0.883701	+	0.741513i	−0.312435	+	0.262164i	0.473062	+	0.881029i	$0.343149\pi$
$3$	−5.10626	+	0.962362i	−0.982700	+	0.185207i
$3$	−5.10626	+	0.962362i	−0.982700	+	0.185207i
$4$	−1.15810	+	6.56791i	−0.144762	+	0.820989i
$5$	−7.21673	+	2.62667i	−0.645484	+	0.234937i	−0.643957	−	0.765062i	$-0.722708\pi$
$5$	−7.21673	+	2.62667i	−0.645484	+	0.234937i	−0.00152709	+	0.999999i	$0.500486\pi$
$6$	3.79880	−	4.63680i	0.258476	−	0.315494i
$7$	2.25256	+	12.7749i	0.121627	+	0.689779i	0.983254	+	0.182238i	$0.0583342\pi$
$7$	2.25256	+	12.7749i	0.121627	+	0.689779i	−0.861628	+	0.507541i	$0.830555\pi$
$8$	−8.46114	−	14.6551i	−0.373933	−	0.647671i
$9$	25.1477	−	9.82813i	0.931397	−	0.364005i
$10$	4.42972	−	7.67249i	0.140080	−	0.242626i
$11$	−10.9793	−	3.99613i	−0.300943	−	0.109534i	0.187135	−	0.982334i	$-0.440080\pi$
$11$	−10.9793	−	3.99613i	−0.300943	−	0.109534i	−0.488078	+	0.872800i	$0.662302\pi$
$12$	−0.407152	−	34.6519i	−0.00979456	−	0.833596i
$13$	54.8237	+	46.0025i	1.16964	+	0.981447i	0.999992	−	0.00405757i	$-0.00129157\pi$
$13$	54.8237	+	46.0025i	1.16964	+	0.981447i	0.169651	+	0.985504i	$0.445736\pi$
$14$	−11.4633	−	9.61888i	−0.218836	−	0.183625i
$15$	34.3227	−	20.3576i	0.590805	−	0.350420i
$16$	−31.7921	−	11.5714i	−0.496752	−	0.180803i
$17$	−18.1319	+	31.4053i	−0.258684	+	0.448054i	−0.965890	−	0.258954i	$-0.916622\pi$
$17$	−18.1319	+	31.4053i	−0.258684	+	0.448054i	0.707206	+	0.707008i	$0.249956\pi$
$18$	−14.9354	+	27.3325i	−0.195572	+	0.357907i
$19$	−11.8561	−	20.5353i	−0.143156	−	0.247954i	0.785527	−	0.618827i	$-0.212392\pi$
$19$	−11.8561	−	20.5353i	−0.143156	−	0.247954i	−0.928684	+	0.370873i	$0.879058\pi$
$20$	−8.89407	−	50.4408i	−0.0994387	−	0.563945i
$21$	−23.7962	−	63.0641i	−0.247274	−	0.655320i
$22$	12.6656	−	4.60990i	0.122741	−	0.0446742i
$23$	−34.5875	+	196.155i	−0.313564	+	1.77831i	0.266594	+	0.963809i	$0.414102\pi$
$23$	−34.5875	+	196.155i	−0.313564	+	1.77831i	−0.580159	+	0.814504i	$0.697009\pi$
$24$	57.3083	+	66.6901i	0.487417	+	0.567211i
$25$	−50.5738	+	42.4365i	−0.404590	+	0.339492i
$26$	−82.5592			−0.622738
$27$	−118.952	+	74.3862i	−0.847867	+	0.530208i
$28$	−86.5130			−0.583908
$29$	218.552	−	183.387i	1.39945	−	1.17428i	0.438105	−	0.898924i	$-0.355650\pi$
$29$	218.552	−	183.387i	1.39945	−	1.17428i	0.961343	−	0.275353i	$-0.0887947\pi$
$30$	−15.2356	+	43.4407i	−0.0927206	+	0.264372i
$31$	5.40959	−	30.6793i	0.0313416	−	0.177747i	−0.965119	−	0.261813i	$-0.915680\pi$
$31$	5.40959	−	30.6793i	0.0313416	−	0.177747i	0.996460	+	0.0840660i	$0.0267907\pi$
$32$	163.889	−	59.6507i	0.905367	−	0.329527i
$33$	59.9088	+	9.83923i	0.316023	+	0.0519027i
$34$	−7.26431	−	41.1980i	−0.0366417	−	0.207806i
$35$	−49.8116	−	86.2762i	−0.240563	−	0.416667i
$36$	35.4267	+	176.550i	0.164013	+	0.817361i
$37$	171.316	−	296.728i	0.761195	−	1.31843i	−0.181040	−	0.983476i	$-0.557946\pi$
$37$	171.316	−	296.728i	0.761195	−	1.31843i	0.942235	−	0.334953i	$-0.108720\pi$
$38$	25.7044	+	9.35564i	0.109732	+	0.0399391i
$39$	−324.215	−	182.141i	−1.33118	−	0.747842i
$40$	99.5559	+	83.5374i	0.393529	+	0.330210i
$41$	188.628	+	158.278i	0.718507	+	0.602899i	0.926972	−	0.375131i	$-0.122402\pi$
$41$	188.628	+	158.278i	0.718507	+	0.602899i	−0.208465	+	0.978030i	$0.566847\pi$
$42$	67.7916	+	38.0846i	0.249059	+	0.139919i
$43$	−143.766	−	52.3265i	−0.509862	−	0.185575i	0.0742623	−	0.997239i	$-0.476340\pi$
$43$	−143.766	−	52.3265i	−0.509862	−	0.185575i	−0.584124	+	0.811664i	$0.698562\pi$
$44$	38.9613	−	67.4830i	0.133492	−	0.231215i
$45$	−155.669	+	136.982i	−0.515683	+	0.453779i
$46$	−114.887	−	198.990i	−0.368242	−	0.637813i
$47$	49.8026	+	282.445i	0.154563	+	0.876570i	0.959184	+	0.282782i	$0.0912573\pi$
$47$	49.8026	+	282.445i	0.154563	+	0.876570i	−0.804621	+	0.593788i	$0.797632\pi$
$48$	173.475	+	28.4910i	0.521644	+	0.0856732i
$49$	164.191	−	59.7606i	0.478690	−	0.174229i
$50$	13.2249	−	75.0023i	0.0374057	−	0.212139i
$51$	62.3628	−	177.813i	0.171226	−	0.488212i
$52$	−365.632	+	306.802i	−0.975077	+	0.818187i
$53$	−321.986			−0.834493			−0.417247	−	0.908793i	$-0.637005\pi$
$53$	−321.986			−0.834493			−0.417247	+	0.908793i	$0.637005\pi$
$54$	49.9601	−	153.940i	0.125902	−	0.387937i
$55$	89.7310			0.219988
$56$	168.158	−	141.102i	0.401270	−	0.336705i
$57$	80.3025	+	93.4487i	0.186602	+	0.217151i
$58$	−57.1507	+	324.118i	−0.129384	+	0.733771i
$59$	−382.499	+	139.218i	−0.844018	+	0.307197i	−0.727599	−	0.686003i	$-0.759364\pi$
$59$	−382.499	+	139.218i	−0.844018	+	0.307197i	−0.116419	+	0.993200i	$0.537142\pi$
$60$	93.9577	+	249.004i	0.202165	+	0.535772i
$61$	36.2242	+	205.438i	0.0760334	+	0.431207i	0.998934	+	0.0461679i	$0.0147009\pi$
$61$	36.2242	+	205.438i	0.0760334	+	0.431207i	−0.922900	+	0.385039i	$0.874188\pi$
$62$	17.9686	+	31.1226i	0.0368068	+	0.0637512i
$63$	182.200	+	299.121i	0.364366	+	0.598186i
$64$	34.7329	−	60.1591i	0.0678377	−	0.117498i
$65$	−516.481	−	187.984i	−0.985563	−	0.358716i
$66$	−60.2373	+	35.7282i	−0.112344	+	0.0666339i
$67$	−152.054	−	127.588i	−0.277258	−	0.232647i	0.493546	−	0.869720i	$-0.335701\pi$
$67$	−152.054	−	127.588i	−0.277258	−	0.232647i	−0.770804	+	0.637073i	$0.780145\pi$
$68$	−185.269	−	155.459i	−0.330399	−	0.277238i
$69$	−12.1599	−	1034.90i	−0.0212156	−	1.80562i
$70$	107.993	+	39.3064i	0.184395	+	0.0671145i
$71$	−82.6900	+	143.223i	−0.138218	+	0.239401i	−0.926822	−	0.375500i	$-0.877471\pi$
$71$	−82.6900	+	143.223i	−0.138218	+	0.239401i	0.788604	+	0.614901i	$0.210804\pi$
$72$	−356.811	−	285.386i	−0.584035	−	0.467125i
$73$	484.355	+	838.928i	0.776568	+	1.34506i	0.933909	+	0.357511i	$0.116375\pi$
$73$	484.355	+	838.928i	0.776568	+	1.34506i	−0.157341	+	0.987544i	$0.550292\pi$
$74$	68.6357	+	389.252i	0.107821	+	0.611482i
$75$	217.404	−	265.362i	0.334715	−	0.408551i
$76$	148.605	−	54.0876i	0.224291	−	0.0816352i
$77$	26.3187	−	149.261i	0.0389518	−	0.220907i
$78$	421.569	−	79.4519i	0.611965	−	0.115335i
$79$	759.383	−	637.198i	1.08148	−	0.907473i	0.0854406	−	0.996343i	$-0.472770\pi$
$79$	759.383	−	637.198i	1.08148	−	0.907473i	0.996043	+	0.0888706i	$0.0283258\pi$
$80$	259.829			0.363123
$81$	535.816	−	494.310i	0.735001	−	0.678066i
$82$	−284.056			−0.382546
$83$	440.670	−	369.766i	0.582769	−	0.489001i	−0.303086	−	0.952963i	$-0.598017\pi$
$83$	440.670	−	369.766i	0.582769	−	0.489001i	0.885855	+	0.463962i	$0.153573\pi$
$84$	441.758	−	83.2568i	0.573806	−	0.108144i
$85$	48.3613	−	274.270i	0.0617120	−	0.349986i
$86$	165.847	−	60.3633i	0.207950	−	0.0756876i
$87$	−939.496	+	1146.74i	−1.15775	+	1.41315i
$88$	34.3334	+	194.714i	0.0415904	+	0.235871i
$89$	−140.691	−	243.684i	−0.167564	−	0.290229i	0.769999	−	0.638045i	$-0.220257\pi$
$89$	−140.691	−	243.684i	−0.167564	−	0.290229i	−0.937563	+	0.347816i	$0.886923\pi$
$90$	35.9910	−	236.482i	0.0421531	−	0.276970i
$91$	−464.184	+	803.990i	−0.534722	+	0.926165i
$92$	−1248.27	−	454.335i	−1.41458	−	0.514866i
$93$	1.90184	+	161.862i	0.00212056	+	0.180477i
$94$	−253.447	−	212.667i	−0.278097	−	0.233351i
$95$	139.502	+	117.056i	0.150659	+	0.126418i
$96$	−779.454	+	462.312i	−0.828673	+	0.491506i
$97$	446.114	+	162.372i	0.466969	+	0.169963i	0.564779	−	0.825242i	$-0.308961\pi$
$97$	446.114	+	162.372i	0.466969	+	0.169963i	−0.0978099	+	0.995205i	$0.531184\pi$
$98$	−100.782	+	174.560i	−0.103883	+	0.179931i
$99$	−315.378	+	7.41226i	−0.320169	+	0.00752485i
$100$	−220.149	−	381.310i	−0.220149	−	0.381310i
$101$	247.912	+	1405.98i	0.244240	+	1.38515i	0.822252	+	0.569124i	$0.192718\pi$
$101$	247.912	+	1405.98i	0.244240	+	1.38515i	−0.578012	+	0.816028i	$0.696171\pi$
$102$	76.7408	+	203.377i	0.0744948	+	0.197424i
$103$	−1158.18	+	421.542i	−1.10795	+	0.403260i	−0.830241	−	0.557405i	$-0.811797\pi$
$103$	−1158.18	+	421.542i	−1.10795	+	0.403260i	−0.277708	+	0.960666i	$0.589575\pi$
$104$	210.302	−	1192.68i	0.198287	−	1.12454i
$105$	337.380	+	392.611i	0.313570	+	0.364904i
$106$	284.539	−	238.757i	0.260725	−	0.218774i
$107$	1720.54			1.55449			0.777247	−	0.629196i	$-0.216616\pi$
$107$	1720.54			1.55449			0.777247	+	0.629196i	$0.216616\pi$
$108$	−350.803	−	867.416i	−0.312556	−	0.772844i
$109$	−313.942			−0.275873			−0.137937	−	0.990441i	$-0.544047\pi$
$109$	−313.942			−0.275873			−0.137937	+	0.990441i	$0.544047\pi$
$110$	−79.2954	+	66.5367i	−0.0687320	+	0.0576730i
$111$	−589.225	+	1680.04i	−0.503844	+	1.43660i
$112$	76.2096	−	432.206i	0.0642958	−	0.364640i
$113$	−500.705	+	182.242i	−0.416835	+	0.151716i	−0.541919	−	0.840431i	$-0.682302\pi$
$113$	−500.705	+	182.242i	−0.416835	+	0.151716i	0.125084	+	0.992146i	$0.460080\pi$
$114$	−140.257	−	23.0354i	−0.115230	−	0.0189251i
$115$	−265.628	−	1506.45i	−0.215390	−	1.22154i
$116$	951.362	+	1647.81i	0.761480	+	1.31892i
$117$	1830.81	+	618.044i	1.44665	+	0.488361i
$118$	234.782	−	406.655i	0.183165	−	0.317251i
$119$	−442.043	−	160.890i	−0.340521	−	0.123940i
$120$	−588.751	−	330.754i	−0.447878	−	0.251613i
$121$	−915.030	−	767.801i	−0.687475	−	0.576860i
$122$	−184.346	−	154.685i	−0.136803	−	0.114791i
$123$	−1115.51	−	626.679i	−0.817738	−	0.459397i
$124$	195.234	+	71.0594i	0.141391	+	0.0514623i
$125$	733.503	−	1270.46i	0.524852	−	0.909071i
$126$	−382.812	−	129.230i	−0.270664	−	0.0913706i
$127$	50.2066	+	86.9604i	0.0350797	+	0.0607598i	0.883032	−	0.469312i	$-0.155498\pi$
$127$	50.2066	+	86.9604i	0.0350797	+	0.0607598i	−0.847953	+	0.530072i	$0.822165\pi$
$128$	256.199	+	1452.98i	0.176914	+	1.00333i
$129$	784.462	+	128.838i	0.535411	+	0.0879343i
$130$	595.807	−	216.856i	0.401967	−	0.146304i
$131$	−31.1900	+	176.887i	−0.0208022	+	0.117975i	−0.993441	−	0.114349i	$-0.963522\pi$
$131$	−31.1900	+	176.887i	−0.0208022	+	0.117975i	0.972638	+	0.232324i	$0.0746329\pi$
$132$	−134.003	+	382.080i	−0.0883599	+	0.251938i
$133$	235.630	−	197.717i	0.153622	−	0.128904i
$134$	228.978			0.147617
$135$	663.059	−	849.274i	0.422719	−	0.541436i
$136$	613.665			0.386922
$137$	1384.41	−	1161.66i	0.863344	−	0.724431i	−0.0993420	−	0.995053i	$-0.531674\pi$
$137$	1384.41	−	1161.66i	0.863344	−	0.724431i	0.962686	+	0.270622i	$0.0872294\pi$
$138$	778.141	+	905.529i	0.479998	+	0.558578i
$139$	148.123	−	840.050i	0.0903861	−	0.512605i	−0.905678	−	0.423967i	$-0.860637\pi$
$139$	148.123	−	840.050i	0.0903861	−	0.512605i	0.996064	−	0.0886382i	$-0.0282515\pi$
$140$	624.341	−	227.241i	0.376903	−	0.137182i
$141$	−526.119	−	1394.31i	−0.314236	−	0.832779i
$142$	−33.1287	−	187.882i	−0.0195782	−	0.111033i
$143$	−418.092	−	724.157i	−0.244494	−	0.423476i
$144$	−913.225	+	21.4633i	−0.528487	+	0.0124209i
$145$	−1095.53	+	1897.51i	−0.627440	+	1.08676i
$146$	−1050.10	−	382.205i	−0.595253	−	0.216654i
$147$	−780.889	+	463.164i	−0.438140	+	0.259871i
$148$	1750.48	+	1468.83i	0.972222	+	0.815791i
$149$	−1741.89	−	1461.62i	−0.957725	−	0.803627i	0.0228566	−	0.999739i	$-0.492724\pi$
$149$	−1741.89	−	1461.62i	−0.957725	−	0.803627i	−0.980581	+	0.196112i	$0.937168\pi$
$150$	4.64947	+	395.708i	0.00253085	+	0.215396i
$151$	32.0911	+	11.6802i	0.0172950	+	0.00629485i	0.350653	−	0.936505i	$-0.385960\pi$
$151$	32.0911	+	11.6802i	0.0172950	+	0.00629485i	−0.333358	+	0.942800i	$0.608182\pi$
$152$	−200.632	+	347.504i	−0.107062	+	0.185436i
$153$	−147.320	+	967.975i	−0.0778437	+	0.511478i
$154$	87.4209	+	151.417i	0.0457440	+	0.0792309i
$155$	41.5450	+	235.613i	0.0215289	+	0.122096i
$156$	1571.76	−	1918.48i	0.806674	−	0.984623i
$157$	−1761.03	+	640.961i	−0.895192	+	0.325823i	−0.748324	−	0.663333i	$-0.769141\pi$
$157$	−1761.03	+	640.961i	−0.895192	+	0.325823i	−0.146867	+	0.989156i	$0.546919\pi$
$158$	−198.577	+	1126.18i	−0.0999868	+	0.567053i
$159$	1644.14	−	309.867i	0.820056	−	0.154554i
$160$	−1026.06	+	860.966i	−0.506982	+	0.425408i
$161$	−2583.77			−1.26478
$162$	−106.963	+	834.137i	−0.0518754	+	0.404543i
$163$	1450.53			0.697020			0.348510	−	0.937305i	$-0.386688\pi$
$163$	1450.53			0.697020			0.348510	+	0.937305i	$0.386688\pi$
$164$	−1258.01	+	1055.59i	−0.598986	+	0.502609i
$165$	−458.190	+	86.3537i	−0.216182	+	0.0407432i
$166$	−115.234	+	653.525i	−0.0538789	+	0.305563i
$167$	1758.56	−	640.064i	0.814860	−	0.296585i	0.0992302	−	0.995065i	$-0.468362\pi$
$167$	1758.56	−	640.064i	0.814860	−	0.296585i	0.715630	+	0.698480i	$0.246140\pi$
$168$	−722.869	+	882.330i	−0.331967	+	0.405198i
$169$	507.898	+	2880.43i	0.231178	+	1.31108i
$170$	160.638	+	278.234i	0.0724729	+	0.125527i
$171$	−499.977	−	399.893i	−0.223592	−	0.178834i
$172$	510.171	−	883.641i	0.226164	−	0.391727i
$173$	−797.694	−	290.337i	−0.350564	−	0.127595i	0.160736	−	0.986998i	$-0.448613\pi$
$173$	−797.694	−	290.337i	−0.350564	−	0.127595i	−0.511299	+	0.859403i	$0.670836\pi$
$174$	−20.0924	−	1710.03i	−0.00875403	−	0.745039i
$175$	−656.042	−	550.484i	−0.283383	−	0.237787i
$176$	302.814	+	254.091i	0.129690	+	0.108823i
$177$	1819.16	−	1078.99i	0.772521	−	0.458201i
$178$	305.023	+	111.019i	0.128441	+	0.0467486i
$179$	−1072.00	+	1856.77i	−0.447628	+	0.775314i	−0.998231	−	0.0594528i	$-0.981064\pi$
$179$	−1072.00	+	1856.77i	−0.447628	+	0.775314i	0.550603	+	0.834767i	$0.314398\pi$
$180$	−719.404	−	1181.06i	−0.297896	−	0.489060i
$181$	−328.190	−	568.441i	−0.134774	−	0.233436i	0.790737	−	0.612156i	$-0.209698\pi$
$181$	−328.190	−	568.441i	−0.134774	−	0.233436i	−0.925511	+	0.378720i	$0.876364\pi$
$182$	−185.969	−	1054.68i	−0.0757416	−	0.429552i
$183$	−382.676	−	1014.16i	−0.154580	−	0.409665i
$184$	3167.33	−	1152.81i	1.26901	−	0.461883i
$185$	−456.934	+	2591.40i	−0.181592	+	1.02986i
$186$	−121.704	−	141.628i	−0.0479772	−	0.0558314i
$187$	324.575	−	272.351i	0.126927	−	0.106504i
$188$	−1912.75			−0.742029
$189$	−1218.22	−	1352.05i	−0.468850	−	0.520354i
$190$	−210.076			−0.0802132
$191$	2772.47	−	2326.38i	1.05031	−	0.881314i	0.0571834	−	0.998364i	$-0.481788\pi$
$191$	2772.47	−	2326.38i	1.05031	−	0.881314i	0.993126	+	0.117049i	$0.0373436\pi$
$192$	−119.460	+	340.614i	−0.0449026	+	0.128030i
$193$	−365.157	+	2070.91i	−0.136190	+	0.772370i	0.837834	+	0.545925i	$0.183822\pi$
$193$	−365.157	+	2070.91i	−0.136190	+	0.772370i	−0.974024	+	0.226445i	$0.927290\pi$
$194$	−514.632	+	187.311i	−0.190456	+	0.0693203i
$195$	2818.19	+	462.852i	1.03495	+	0.169977i
$196$	202.353	+	1147.60i	0.0737437	+	0.418221i
$197$	−2294.50	−	3974.20i	−0.829831	−	1.43731i	−0.898171	−	0.439647i	$-0.855104\pi$
$197$	−2294.50	−	3974.20i	−0.829831	−	1.43731i	0.0683399	−	0.997662i	$-0.478230\pi$
$198$	273.204	−	240.407i	0.0980594	−	0.0862879i
$199$	983.076	−	1702.74i	0.350193	−	0.606552i	−0.636090	−	0.771615i	$-0.719449\pi$
$199$	983.076	−	1702.74i	0.350193	−	0.606552i	0.986283	+	0.165063i	$0.0527827\pi$
$200$	1049.82	+	382.104i	0.371169	+	0.135094i
$201$	899.210	+	505.167i	0.315549	+	0.177272i
$202$	−1261.63	−	1058.64i	−0.439447	−	0.368740i
$203$	2835.04	+	2378.88i	0.980202	+	0.822487i
$204$	1095.64	+	615.518i	0.376030	+	0.211250i
$205$	−1777.02	−	646.784i	−0.605428	−	0.220358i
$206$	710.904	−	1231.32i	0.240442	−	0.416458i
$207$	1058.04	+	5272.79i	0.355262	+	1.77045i
$208$	−1210.65	−	2096.91i	−0.403574	−	0.699011i
$209$	48.1093	+	272.841i	0.0159224	+	0.0903006i
$210$	−589.269	−	96.7798i	−0.193635	−	0.0318021i
$211$	554.841	−	201.946i	0.181028	−	0.0658887i	−0.249916	−	0.968268i	$-0.580403\pi$
$211$	554.841	−	201.946i	0.181028	−	0.0658887i	0.430944	+	0.902379i	$0.358181\pi$
$212$	372.892	−	2114.77i	0.120803	−	0.685109i
$213$	284.404	−	810.913i	0.0914884	−	0.260858i
$214$	−1520.44	+	1275.80i	−0.485679	+	0.407533i
$215$	1174.96			0.372706
$216$	2096.61	+	1113.87i	0.660446	+	0.350877i
$217$	404.110			0.126418
$218$	277.431	−	232.792i	0.0861926	−	0.0723242i
$219$	−3280.59	−	3817.65i	−1.01225	−	1.17796i
$220$	−103.917	+	589.345i	−0.0318460	+	0.180607i
$221$	−2438.78	+	887.644i	−0.742309	+	0.270178i
$222$	−725.073	−	1921.57i	−0.219206	−	0.580934i
$223$	−745.499	−	4227.93i	−0.223867	−	1.26961i	−0.864840	−	0.502048i	$-0.832580\pi$
$223$	−745.499	−	4227.93i	−0.223867	−	1.26961i	0.640973	−	0.767563i	$-0.278531\pi$
$224$	1131.20	+	1959.30i	0.337417	+	0.584424i
$225$	−854.745	+	1564.23i	−0.253258	+	0.463475i
$226$	307.339	−	532.326i	0.0904596	−	0.156681i
$227$	4108.16	+	1495.25i	1.20118	+	0.437195i	0.863637	−	0.504114i	$-0.168181\pi$
$227$	4108.16	+	1495.25i	1.20118	+	0.437195i	0.337546	+	0.941309i	$0.390403\pi$
$228$	−706.761	+	419.197i	−0.205291	+	0.121763i
$229$	4523.97	+	3796.06i	1.30547	+	1.09542i	0.989172	+	0.146758i	$0.0468838\pi$
$229$	4523.97	+	3796.06i	1.30547	+	1.09542i	0.316296	+	0.948660i	$0.397561\pi$
$230$	1351.79	+	1134.28i	0.387540	+	0.325185i
$231$	9.25283	+	787.491i	0.00263546	+	0.224299i
$232$	−4536.75	−	1651.24i	−1.28384	−	0.467281i
$233$	−1092.56	+	1892.37i	−0.307193	+	0.532073i	−0.977747	−	0.209787i	$-0.932723\pi$
$233$	−1092.56	+	1892.37i	−0.307193	+	0.532073i	0.670554	+	0.741860i	$0.266056\pi$
$234$	−2076.18	+	811.403i	−0.580017	+	0.226680i
$235$	−1101.30	−	1907.51i	−0.305707	−	0.529499i
$236$	−471.400	−	2673.44i	−0.130024	−	0.737400i
$237$	−3264.39	+	3984.50i	−0.894704	+	1.09207i
$238$	509.936	−	185.602i	0.138883	−	0.0505494i
$239$	−217.813	+	1235.28i	−0.0589505	+	0.334325i	−0.999992	−	0.00396578i	$-0.998738\pi$
$239$	−217.813	+	1235.28i	−0.0589505	+	0.334325i	0.941042	+	0.338291i	$0.109849\pi$
$240$	−1326.76	+	250.050i	−0.356841	+	0.0672527i
$241$	−1882.83	+	1579.88i	−0.503252	+	0.422279i	−0.858747	−	0.512399i	$-0.828757\pi$
$241$	−1882.83	+	1579.88i	−0.503252	+	0.422279i	0.355495	+	0.934678i	$0.384312\pi$
$242$	1377.95			0.366024
$243$	−2260.31	+	3039.72i	−0.596703	+	0.802463i
$244$	−1391.25			−0.365023
$245$	−1027.95	+	862.551i	−0.268054	+	0.224924i
$246$	1450.46	−	273.365i	0.375928	−	0.0708501i
$247$	294.683	−	1671.23i	0.0759119	−	0.430518i
$248$	−495.380	+	180.304i	−0.126841	+	0.0461665i
$249$	−1894.33	+	2312.20i	−0.482120	+	0.588474i
$250$	293.869	+	1666.61i	0.0743436	+	0.421624i
$251$	39.4859	+	68.3916i	0.00992960	+	0.0171986i	0.870948	−	0.491376i	$-0.163506\pi$
$251$	39.4859	+	68.3916i	0.00992960	+	0.0171986i	−0.861018	+	0.508575i	$0.830173\pi$
$252$	−2175.60	+	850.262i	−0.543850	+	0.212545i
$253$	1163.61	−	2015.43i	0.289152	−	0.500825i
$254$	−108.850	−	39.6181i	−0.0268892	−	0.00978687i
$255$	17.0023	+	1447.04i	0.00417540	+	0.355360i
$256$	−878.093	−	736.808i	−0.214378	−	0.179885i
$257$	249.106	+	209.024i	0.0604622	+	0.0507338i	0.672518	−	0.740081i	$-0.265213\pi$
$257$	249.106	+	209.024i	0.0604622	+	0.0507338i	−0.612056	+	0.790815i	$0.709657\pi$
$258$	−788.764	+	467.835i	−0.190335	+	0.112892i
$259$	4176.57	+	1520.15i	1.00201	+	0.364700i
$260$	1832.80	−	3174.50i	0.437174	−	0.757208i
$261$	3693.73	−	6759.71i	0.875999	−	1.60312i
$262$	−103.602	−	179.443i	−0.0244295	−	0.0423131i
$263$	−749.827	−	4252.48i	−0.175803	−	0.997031i	−0.937212	−	0.348759i	$-0.886603\pi$
$263$	−749.827	−	4252.48i	−0.175803	−	0.997031i	0.761409	−	0.648272i	$-0.224508\pi$
$264$	−362.701	−	961.221i	−0.0845557	−	0.224087i
$265$	2323.68	−	845.751i	0.538652	−	0.196053i
$266$	−61.6166	+	349.445i	−0.0142028	+	0.0805483i
$267$	952.916	+	1108.92i	0.218418	+	0.254174i
$268$	1014.08	−	850.914i	0.231137	−	0.193947i
$269$	1591.29			0.360678			0.180339	−	0.983604i	$-0.442280\pi$
$269$	1591.29			0.360678			0.180339	+	0.983604i	$0.442280\pi$
$270$	43.8018	+	1242.17i	0.00987293	+	0.279986i
$271$	−1969.04			−0.441369			−0.220684	−	0.975345i	$-0.570829\pi$
$271$	−1969.04			−0.441369			−0.220684	+	0.975345i	$0.570829\pi$
$272$	939.855	−	788.632i	0.209511	−	0.175801i
$273$	1596.51	−	4552.09i	0.353939	−	1.00918i
$274$	−362.020	+	2053.12i	−0.0798190	+	0.452676i
$275$	724.846	−	263.822i	0.158945	−	0.0578512i
$276$	6811.24	+	1118.66i	1.48547	+	0.243968i
$277$	−313.846	−	1779.91i	−0.0680764	−	0.386081i	−0.999741	−	0.0227609i	$-0.992754\pi$
$277$	−313.846	−	1779.91i	−0.0680764	−	0.386081i	0.931665	−	0.363320i	$-0.118357\pi$
$278$	492.011	+	852.188i	0.106147	+	0.183852i
$279$	−165.481	−	824.681i	−0.0355094	−	0.176962i
$280$	−842.925	+	1459.99i	−0.179909	+	0.311611i
$281$	2764.86	+	1006.33i	0.586967	+	0.213639i	0.618395	−	0.785867i	$-0.287783\pi$
$281$	2764.86	+	1006.33i	0.586967	+	0.213639i	−0.0314277	+	0.999506i	$0.510005\pi$
$282$	1498.83	+	842.027i	0.316504	+	0.177808i
$283$	−1458.43	−	1223.76i	−0.306341	−	0.257050i	0.476637	−	0.879100i	$-0.341856\pi$
$283$	−1458.43	−	1223.76i	−0.306341	−	0.257050i	−0.782978	+	0.622050i	$0.786300\pi$
$284$	−844.914	−	708.967i	−0.176537	−	0.148132i
$285$	−824.981	−	463.466i	−0.171465	−	0.0963275i
$286$	906.441	+	329.917i	0.187409	+	0.0682113i
$287$	−1597.09	+	2766.24i	−0.328478	+	0.568940i
$288$	3535.18	−	3110.80i	0.723307	−	0.636478i
$289$	1798.97	+	3115.91i	0.366165	+	0.634217i
$290$	−438.911	−	2489.19i	−0.0888749	−	0.504034i
$291$	−2434.23	−	399.791i	−0.490368	−	0.0805366i
$292$	−6070.93	+	2209.64i	−1.21669	+	0.442840i
$293$	389.898	−	2211.22i	0.0777408	−	0.440890i	−0.920947	−	0.389687i	$-0.872583\pi$
$293$	389.898	−	2211.22i	0.0777408	−	0.440890i	0.998688	−	0.0512033i	$-0.0163056\pi$
$294$	346.630	−	988.338i	0.0687616	−	0.196058i
$295$	2394.71	−	2009.40i	0.472628	−	0.396582i
$296$	−5798.12			−1.13854
$297$	1603.27	−	341.357i	0.313236	−	0.0666921i
$298$	2623.12			0.509910
$299$	−10919.8	+	9162.84i	−2.11208	+	1.77224i
$300$	1491.10	+	1735.20i	0.286962	+	0.333940i
$301$	344.624	−	1954.46i	0.0659927	−	0.374263i
$302$	−37.0200	+	13.4742i	−0.00705385	+	0.00256739i
$303$	−2618.97	−	6940.72i	−0.496554	−	1.31595i
$304$	139.308	+	790.053i	0.0262824	+	0.149055i
$305$	−801.039	−	1387.44i	−0.150385	−	0.260474i
$306$	−587.580	−	964.640i	−0.109770	−	0.180212i
$307$	−1641.19	+	2842.62i	−0.305106	+	0.528459i	−0.977285	−	0.211930i	$-0.932025\pi$
$307$	−1641.19	+	2842.62i	−0.305106	+	0.528459i	0.672179	+	0.740389i	$0.265358\pi$
$308$	949.851	+	345.717i	0.175723	+	0.0639580i
$309$	5508.28	−	3267.09i	1.01409	−	0.601483i
$310$	−211.424	−	177.406i	−0.0387357	−	0.0325031i
$311$	−416.568	−	349.542i	−0.0759530	−	0.0637321i	0.604021	−	0.796969i	$-0.293564\pi$
$311$	−416.568	−	349.542i	−0.0759530	−	0.0637321i	−0.679974	+	0.733236i	$0.738009\pi$
$312$	73.9356	+	6292.52i	0.0134160	+	1.14181i
$313$	4550.96	+	1656.41i	0.821839	+	0.299125i	0.718505	−	0.695522i	$-0.244827\pi$
$313$	4550.96	+	1656.41i	0.821839	+	0.299125i	0.103334	+	0.994647i	$0.467049\pi$
$314$	1080.94	−	1872.24i	0.194270	−	0.336486i
$315$	−2100.58	−	1680.09i	−0.375728	−	0.300516i
$316$	3305.62	+	5725.50i	0.588467	+	1.01925i
$317$	−253.609	−	1438.29i	−0.0449340	−	0.254834i	0.954063	−	0.299605i	$-0.0968550\pi$
$317$	−253.609	−	1438.29i	−0.0449340	−	0.254834i	−0.998997	+	0.0447718i	$0.985744\pi$
$318$	−1223.16	+	1492.98i	−0.215696	+	0.263278i
$319$	−3132.38	+	1140.09i	−0.549778	+	0.200103i
$320$	−92.6394	+	525.384i	−0.0161834	+	0.0917808i
$321$	−8785.51	+	1655.78i	−1.52760	+	0.287902i
$322$	2283.28	−	1915.90i	0.395162	−	0.331581i
$323$	859.891			0.148129
$324$	2626.06	+	4091.65i	0.450284	+	0.701586i
$325$	−4724.83			−0.806419
$326$	−1281.83	+	1075.59i	−0.217774	+	0.182734i
$327$	1603.07	−	302.126i	0.271100	−	0.0510935i
$328$	723.572	−	4103.58i	0.121807	−	0.690800i
$329$	−3496.02	+	1272.45i	−0.585841	+	0.213229i
$330$	340.870	−	416.064i	0.0568615	−	0.0694048i
$331$	718.217	+	4073.21i	0.119265	+	0.676386i	0.984550	+	0.175105i	$0.0560266\pi$
$331$	718.217	+	4073.21i	0.119265	+	0.676386i	−0.865285	+	0.501281i	$0.832862\pi$
$332$	1918.25	+	3322.51i	0.317101	+	0.549236i
$333$	1391.93	−	9145.76i	0.229060	−	1.50506i
$334$	−1079.43	+	1869.62i	−0.176837	+	0.306291i
$335$	1432.46	+	521.373i	0.233623	+	0.0850318i
$336$	26.7929	+	2280.30i	0.00435022	+	0.370239i
$337$	990.666	+	831.268i	0.160134	+	0.134368i	0.719334	−	0.694665i	$-0.244447\pi$
$337$	990.666	+	831.268i	0.160134	+	0.134368i	−0.559200	+	0.829033i	$0.688892\pi$
$338$	−2584.71	−	2168.83i	−0.415946	−	0.349020i
$339$	2381.35	−	1412.43i	0.381525	−	0.226291i
$340$	1745.38	+	635.265i	0.278401	+	0.101330i
$341$	−181.992	+	315.219i	−0.0289015	+	0.0500589i
$342$	738.356	−	17.3534i	0.116742	−	0.00274376i
$343$	3357.98	+	5816.18i	0.528611	+	0.915581i
$344$	449.571	+	2549.65i	0.0704630	+	0.399615i
$345$	2806.11	+	7436.68i	0.437901	+	1.16051i
$346$	920.211	−	334.929i	0.142979	−	0.0520402i
$347$	1770.08	−	10038.6i	0.273841	−	1.55303i	−0.468777	−	0.883317i	$-0.655305\pi$
$347$	1770.08	−	10038.6i	0.273841	−	1.55303i	0.742618	−	0.669715i	$-0.233584\pi$
$348$	−6443.68	−	7498.57i	−0.992580	−	1.15507i
$349$	−1281.95	+	1075.68i	−0.196622	+	0.164986i	−0.735783	−	0.677217i	$-0.763186\pi$
$349$	−1281.95	+	1075.68i	−0.196622	+	0.164986i	0.539161	+	0.842203i	$0.318741\pi$
$350$	987.936			0.150878
$351$	−9943.37	−	1393.99i	−1.51207	−	0.211982i
$352$	−2037.75			−0.308559
$353$	−5103.18	+	4282.07i	−0.769447	+	0.645643i	−0.940567	−	0.339608i	$-0.889706\pi$
$353$	−5103.18	+	4282.07i	−0.769447	+	0.645643i	0.171120	+	0.985250i	$0.445261\pi$
$354$	−807.509	+	2302.43i	−0.121239	+	0.345686i
$355$	220.550	−	1250.80i	0.0329735	−	0.187002i
$356$	1763.43	−	641.835i	0.262532	−	0.0955539i
$357$	2412.02	+	396.143i	0.357584	+	0.0587286i
$358$	−429.485	−	2435.73i	−0.0634050	−	0.359588i
$359$	2601.49	+	4505.92i	0.382455	+	0.662432i	0.991413	−	0.130771i	$-0.0417452\pi$
$359$	2601.49	+	4505.92i	0.382455	+	0.662432i	−0.608957	+	0.793203i	$0.708412\pi$
$360$	3324.62	+	1122.32i	0.486730	+	0.164310i
$361$	3148.37	−	5453.13i	0.459013	−	0.795033i
$362$	711.528	+	258.975i	0.103307	+	0.0376006i
$363$	5411.28	+	3040.00i	0.782420	+	0.439555i
$364$	−4742.96	−	3979.82i	−0.682964	−	0.573075i
$365$	−5699.05	−	4782.07i	−0.817265	−	0.685767i
$366$	1090.18	+	612.453i	0.155696	+	0.0874684i
$367$	−10308.0	−	3751.81i	−1.46614	−	0.533632i	−0.519091	−	0.854719i	$-0.673729\pi$
$367$	−10308.0	−	3751.81i	−1.46614	−	0.533632i	−0.947050	+	0.321087i	$0.895952\pi$
$368$	3369.40	−	5835.97i	0.477288	−	0.826687i
$369$	6299.15	+	2126.47i	0.888674	+	0.299998i
$370$	−1517.76	−	2628.85i	−0.213256	−	0.369371i
$371$	−725.291	−	4113.33i	−0.101497	−	0.575616i
$372$	−1065.30	−	174.962i	−0.148476	−	0.0243853i
$373$	784.003	−	285.354i	0.108831	−	0.0396114i	−0.287030	−	0.957921i	$-0.592668\pi$
$373$	784.003	−	285.354i	0.108831	−	0.0396114i	0.395862	+	0.918310i	$0.370446\pi$
$374$	−84.8756	+	481.353i	−0.0117348	+	0.0665513i
$375$	−2522.81	+	7193.22i	−0.347406	+	0.990550i
$376$	3717.88	−	3119.67i	0.509933	−	0.427885i
$377$	20418.0			2.78934
$378$	2079.10	+	291.476i	0.282904	+	0.0396611i
$379$	10439.8			1.41492			0.707459	−	0.706754i	$-0.249841\pi$
$379$	10439.8			1.41492			0.707459	+	0.706754i	$0.249841\pi$
$380$	−930.368	+	780.672i	−0.125597	+	0.105388i
$381$	−340.055	−	395.725i	−0.0457259	−	0.0532116i
$382$	−724.995	+	4111.65i	−0.0971046	+	0.550708i
$383$	9129.32	−	3322.80i	1.21798	−	0.443309i	0.348516	−	0.937303i	$-0.386686\pi$
$383$	9129.32	−	3322.80i	1.21798	−	0.443309i	0.869465	+	0.493994i	$0.164464\pi$
$384$	−2706.51	−	7172.71i	−0.359677	−	0.953206i
$385$	202.124	+	1146.30i	0.0267564	+	0.151743i
$386$	−1212.92	−	2100.83i	−0.159938	−	0.277020i
$387$	−4129.65	+	97.0582i	−0.542434	+	0.0127487i
$388$	−1583.09	+	2741.99i	−0.207137	+	0.358772i
$389$	6289.83	+	2289.31i	0.819812	+	0.298387i	0.717671	−	0.696383i	$-0.245208\pi$
$389$	6289.83	+	2289.31i	0.819812	+	0.298387i	0.102142	+	0.994770i	$0.467431\pi$
$390$	−2833.65	+	1680.71i	−0.367917	+	0.218220i
$391$	−5533.19	−	4642.89i	−0.715666	−	0.600515i
$392$	−2265.04	−	1900.59i	−0.291841	−	0.244884i
$393$	−10.9654	−	933.248i	−0.00140746	−	0.119787i
$394$	4974.58	+	1810.60i	0.636080	+	0.231514i
$395$	−3806.55	+	6593.13i	−0.484881	+	0.839839i
$396$	316.557	−	2079.96i	0.0401706	−	0.263944i
$397$	−4335.99	−	7510.15i	−0.548153	−	0.949429i	−0.998401	−	0.0565258i	$-0.981998\pi$
$397$	−4335.99	−	7510.15i	−0.548153	−	0.949429i	0.450248	−	0.892904i	$-0.351336\pi$
$398$	393.857	+	2233.67i	0.0496037	+	0.281317i
$399$	−1012.91	+	1236.35i	−0.127090	+	0.155126i
$400$	2098.90	−	763.937i	0.262362	−	0.0954921i
$401$	−1265.71	+	7178.21i	−0.157622	+	0.893921i	0.798726	+	0.601694i	$0.205507\pi$
$401$	−1265.71	+	7178.21i	−0.157622	+	0.893921i	−0.956349	+	0.292227i	$0.905604\pi$
$402$	−1169.22	+	220.360i	−0.145063	+	0.0273397i
$403$	1707.90	−	1433.10i	0.211108	−	0.177141i
$404$	−9521.47			−1.17255
$405$	−2568.44	+	4974.72i	−0.315128	+	0.610360i
$406$	−4269.30			−0.521877
$407$	−3066.69	+	2573.26i	−0.373490	+	0.313395i
$408$	−3133.53	+	590.568i	−0.380228	+	0.0716605i
$409$	732.096	−	4151.92i	0.0885081	−	0.501955i	−0.908036	−	0.418892i	$-0.862419\pi$
$409$	732.096	−	4151.92i	0.0885081	−	0.501955i	0.996544	−	0.0830628i	$-0.0264702\pi$
$410$	2049.96	−	746.123i	0.246927	−	0.0898742i
$411$	−5951.22	+	7264.02i	−0.714238	+	0.871795i
$412$	−1427.37	−	8095.00i	−0.170683	−	0.967990i
$413$	−2640.10	−	4572.78i	−0.314554	−	0.544823i
$414$	−4844.83	−	3875.01i	−0.575146	−	0.460016i
$415$	−2208.94	+	3826.00i	−0.261283	+	0.452556i
$416$	11729.1	+	4269.04i	1.38237	+	0.503141i
$417$	52.0756	+	4432.06i	0.00611548	+	0.520477i
$418$	−244.830	−	205.436i	−0.0286483	−	0.0240388i
$419$	2785.14	+	2337.01i	0.324733	+	0.272483i	0.790550	−	0.612398i	$-0.209795\pi$
$419$	2785.14	+	2337.01i	0.324733	+	0.272483i	−0.465817	+	0.884881i	$0.654239\pi$
$420$	−2969.36	+	1761.20i	−0.344976	+	0.204613i
$421$	3313.92	+	1206.17i	0.383636	+	0.139632i	0.526637	−	0.850091i	$-0.323453\pi$
$421$	3313.92	+	1206.17i	0.383636	+	0.139632i	−0.143001	+	0.989723i	$0.545675\pi$
$422$	−340.568	+	589.882i	−0.0392858	+	0.0680450i
$423$	4028.33	+	6613.38i	0.463036	+	0.760173i
$424$	2724.36	+	4718.74i	0.312044	+	0.540477i
$425$	−415.733	−	2357.74i	−0.0474495	−	0.269099i
$426$	349.974	+	927.493i	0.0398036	+	0.105486i
$427$	−2542.85	+	925.521i	−0.288190	+	0.104893i
$428$	−1992.56	+	11300.3i	−0.225032	+	1.27622i
$429$	2831.79	+	3295.38i	0.318695	+	0.370868i
$430$	−1038.32	+	871.250i	−0.116447	+	0.0977103i
$431$	−1227.61			−0.137197			−0.0685983	−	0.997644i	$-0.521853\pi$
$431$	−1227.61			−0.137197			−0.0685983	+	0.997644i	$0.521853\pi$
$432$	4642.51	−	988.450i	0.517043	−	0.110085i
$433$	−13096.8			−1.45356			−0.726781	−	0.686869i	$-0.758985\pi$
$433$	−13096.8			−1.45356			−0.726781	+	0.686869i	$0.758985\pi$
$434$	−357.112	+	299.653i	−0.0394976	+	0.0331424i
$435$	3767.96	−	10743.5i	0.415310	−	1.18416i
$436$	363.576	−	2061.94i	0.0399361	−	0.226489i
$437$	4438.18	−	1615.36i	0.485828	−	0.176827i
$438$	5729.90	+	941.062i	0.625081	+	0.102661i
$439$	275.337	+	1561.51i	0.0299342	+	0.169765i	0.996110	−	0.0881194i	$-0.0280857\pi$
$439$	275.337	+	1561.51i	0.0299342	+	0.169765i	−0.966176	+	0.257885i	$0.916975\pi$
$440$	−759.226	−	1315.02i	−0.0822607	−	0.142480i
$441$	3541.69	−	3116.53i	0.382431	−	0.336522i
$442$	1496.95	−	2592.80i	0.161092	−	0.279020i
$443$	−16704.8	−	6080.04i	−1.79157	−	0.652079i	−0.999111	−	0.0421589i	$-0.986576\pi$
$443$	−16704.8	−	6080.04i	−1.79157	−	0.652079i	−0.792463	−	0.609921i	$-0.791201\pi$
$444$	−10352.0	−	5815.63i	−1.10649	−	0.621616i
$445$	1655.41	+	1389.05i	0.176345	+	0.147971i
$446$	3793.87	+	3183.43i	0.402791	+	0.337982i
$447$	10301.1	+	5787.07i	1.08999	+	0.612347i
$448$	846.764	+	308.197i	0.0892988	+	0.0325021i
$449$	−367.697	+	636.869i	−0.0386474	+	0.0669393i	−0.884702	−	0.466157i	$-0.845638\pi$
$449$	−367.697	+	636.869i	−0.0386474	+	0.0669393i	0.846055	+	0.533096i	$0.178972\pi$
$450$	−404.556	−	2016.11i	−0.0423799	−	0.211201i
$451$	−1438.50	−	2491.56i	−0.150192	−	0.260140i
$452$	−617.081	−	3499.64i	−0.0642147	−	0.364180i
$453$	−175.106	−	28.7589i	−0.0181616	−	0.00298281i
$454$	−4739.14	+	1724.90i	−0.489909	+	0.178312i
$455$	1238.07	−	7021.44i	0.127564	−	0.723450i
$456$	690.052	−	1967.53i	0.0708654	−	0.202057i
$457$	−9890.38	+	8299.01i	−1.01237	+	0.849478i	−0.988649	−	0.150241i	$-0.951995\pi$
$457$	−9890.38	+	8299.01i	−1.01237	+	0.849478i	−0.0237189	+	0.999719i	$0.507551\pi$
$458$	−6812.67			−0.695055
$459$	−179.291	−	5084.51i	−0.0182322	−	0.517047i
$460$	10201.8			1.03405
$461$	9334.65	−	7832.70i	0.943076	−	0.791335i	−0.0350418	−	0.999386i	$-0.511156\pi$
$461$	9334.65	−	7832.70i	0.943076	−	0.791335i	0.978118	+	0.208051i	$0.0667120\pi$
$462$	−592.112	−	689.046i	−0.0596267	−	0.0693881i
$463$	−3036.40	+	17220.3i	−0.304781	+	1.72850i	0.319755	+	0.947500i	$0.396399\pi$
$463$	−3036.40	+	17220.3i	−0.304781	+	1.72850i	−0.624536	+	0.780996i	$0.714712\pi$
$464$	−9070.26	+	3301.30i	−0.907492	+	0.330300i
$465$	−438.885	−	1163.12i	−0.0437694	−	0.115997i
$466$	−437.720	−	2482.43i	−0.0435128	−	0.246774i
$467$	2497.25	+	4325.37i	0.247450	+	0.428596i	0.962818	−	0.270152i	$-0.0870741\pi$
$467$	2497.25	+	4325.37i	0.247450	+	0.428596i	−0.715368	+	0.698748i	$0.753741\pi$
$468$	−6179.52	+	11308.8i	−0.610360	+	1.11699i
$469$	1287.41	−	2229.87i	0.126753	−	0.219543i
$470$	2387.67	+	869.040i	0.234330	+	0.0852890i
$471$	8375.41	−	4967.65i	0.819360	−	0.485982i
$472$	5276.63	+	4427.62i	0.514569	+	0.431775i
$473$	1369.34	+	1149.01i	0.133113	+	0.111695i
$474$	−69.8134	−	5941.69i	−0.00676506	−	0.575761i
$475$	1471.05	+	535.419i	0.142098	+	0.0517194i
$476$	1568.64	−	2716.97i	0.151048	−	0.261622i
$477$	−8097.21	+	3164.52i	−0.777244	+	0.303760i
$478$	−723.495	−	1253.13i	−0.0692299	−	0.119910i
$479$	−2206.15	−	12511.7i	−0.210442	−	1.19348i	−0.888643	−	0.458599i	$-0.848351\pi$
$479$	−2206.15	−	12511.7i	−0.210442	−	1.19348i	0.678201	−	0.734876i	$-0.262760\pi$
$480$	4410.76	−	5383.75i	0.419422	−	0.511945i
$481$	23042.4	−	8386.76i	2.18429	−	0.795018i
$482$	492.355	−	2792.29i	0.0465273	−	0.263870i
$483$	13193.4	−	2486.52i	1.24290	−	0.234246i
$484$	6102.54	−	5120.64i	0.573116	−	0.480902i
$485$	−3645.98			−0.341351
$486$	−256.561	−	4362.25i	−0.0239461	−	0.407152i
$487$	8245.41			0.767218			0.383609	−	0.923496i	$-0.374681\pi$
$487$	8245.41			0.767218			0.383609	+	0.923496i	$0.374681\pi$
$488$	2704.22	−	2269.11i	0.250849	−	0.210487i
$489$	−7406.78	+	1395.93i	−0.684961	+	0.129093i
$490$	268.806	−	1524.48i	0.0247825	−	0.140548i
$491$	−15342.3	+	5584.15i	−1.41016	+	0.513257i	−0.931178	−	0.364566i	$-0.881217\pi$
$491$	−15342.3	+	5584.15i	−1.41016	+	0.513257i	−0.478985	+	0.877823i	$0.658995\pi$
$492$	5407.84	−	6600.78i	0.495537	−	0.604850i
$493$	1796.57	+	10188.8i	0.164124	+	0.930795i
$494$	978.828	+	1695.38i	0.0891489	+	0.154410i
$495$	2256.53	−	881.888i	0.204896	−	0.0800766i
$496$	−526.985	+	912.764i	−0.0477063	+	0.0826297i
$497$	−2015.93	−	733.737i	−0.181945	−	0.0662225i
$498$	−40.5127	−	3447.96i	−0.00364542	−	0.310255i
$499$	10901.6	+	9147.50i	0.977998	+	0.820638i	0.983786	−	0.179346i	$-0.0573981\pi$
$499$	10901.6	+	9147.50i	0.977998	+	0.820638i	−0.00578835	+	0.999983i	$0.501842\pi$
$500$	7494.83	+	6288.91i	0.670358	+	0.562497i
$501$	−8363.70	+	4960.71i	−0.745833	+	0.442371i
$502$	−85.6071	−	31.1584i	−0.00761121	−	0.00277026i
$503$	−112.991	+	195.706i	−0.0100159	+	0.0173481i	−0.870990	−	0.491301i	$-0.836522\pi$
$503$	−112.991	+	195.706i	−0.0100159	+	0.0173481i	0.860974	+	0.508649i	$0.169855\pi$
$504$	2842.03	−	5201.07i	0.251179	−	0.459670i
$505$	−5482.17	−	9495.40i	−0.483076	−	0.836712i
$506$	466.185	+	2643.86i	0.0409574	+	0.232281i
$507$	−5365.48	−	14219.5i	−0.469999	−	1.24558i
$508$	−629.293	+	229.044i	−0.0549613	+	0.0200043i
$509$	−725.487	+	4114.44i	−0.0631761	+	0.358290i	0.936789	+	0.349896i	$0.113783\pi$
$509$	−725.487	+	4114.44i	−0.0631761	+	0.358290i	−0.999965	+	0.00839383i	$0.997328\pi$
$510$	−1088.02	−	1266.14i	−0.0944674	−	0.109933i
$511$	−9626.17	+	8077.32i	−0.833340	+	0.699255i
$512$	−10480.8			−0.904669
$513$	2937.85	+	1560.80i	0.252845	+	0.134329i
$514$	−375.129			−0.0321911
$515$	7251.00	−	6084.31i	0.620422	−	0.520596i
$516$	−1754.68	+	5003.07i	−0.149700	+	0.426837i
$517$	581.889	−	3300.06i	0.0494999	−	0.280728i
$518$	−4818.05	+	1753.63i	−0.408674	+	0.148745i
$519$	4352.64	+	714.864i	0.368130	+	0.0604606i
$520$	1615.09	+	9159.65i	0.136205	+	0.772456i
$521$	−8636.71	−	14959.2i	−0.726259	−	1.25792i	−0.958454	−	0.285248i	$-0.907924\pi$
$521$	−8636.71	−	14959.2i	−0.726259	−	1.25792i	0.232195	−	0.972669i	$-0.425409\pi$
$522$	1748.26	+	8712.50i	0.146589	+	0.730529i
$523$	−707.631	+	1225.65i	−0.0591636	+	0.102474i	−0.894090	−	0.447887i	$-0.852177\pi$
$523$	−707.631	+	1225.65i	−0.0591636	+	0.102474i	0.834927	+	0.550361i	$0.185510\pi$
$524$	−1125.66	−	409.706i	−0.0938447	−	0.0341567i
$525$	3879.68	+	2179.56i	0.322520	+	0.181189i
$526$	3815.89	+	3201.91i	0.316313	+	0.265418i
$527$	865.408	+	726.164i	0.0715328	+	0.0600231i
$528$	−1790.77	−	1006.04i	−0.147601	−	0.0829208i
$529$	−25847.3	−	9407.66i	−2.12438	−	0.773211i
$530$	−1426.31	+	2470.43i	−0.116896	+	0.202469i
$531$	−8250.71	+	7260.26i	−0.674294	+	0.593350i
$532$	1025.70	+	1776.57i	0.0835900	+	0.144782i
$533$	3060.11	+	17354.8i	0.248683	+	1.41035i
$534$	−1664.37	−	273.351i	−0.134877	−	0.0221518i
$535$	−12416.7	+	4519.30i	−1.00340	+	0.365208i
$536$	−583.272	+	3307.90i	−0.0470029	+	0.266566i
$537$	3687.05	−	10512.8i	0.296290	−	0.844805i
$538$	−1406.22	+	1179.96i	−0.112689	+	0.0945570i
$539$	−2041.51			−0.163143
$540$	4810.07	+	5338.46i	0.383319	+	0.425427i
$541$	−1781.53			−0.141578			−0.0707892	−	0.997491i	$-0.522552\pi$
$541$	−1781.53			−0.141578			−0.0707892	+	0.997491i	$0.522552\pi$
$542$	1740.05	−	1460.07i	0.137899	−	0.115711i
$543$	2222.87	+	2586.77i	0.175676	+	0.204436i
$544$	−1098.26	+	6228.57i	−0.0865583	+	0.490897i
$545$	2265.63	−	824.623i	0.178072	−	0.0648128i
$546$	1964.60	+	5206.52i	0.153987	+	0.408093i
$547$	−1740.99	−	9873.64i	−0.136087	−	0.771785i	−0.974097	−	0.226131i	$-0.927392\pi$
$547$	−1740.99	−	9873.64i	−0.136087	−	0.771785i	0.838010	−	0.545654i	$-0.183719\pi$
$548$	6026.38	+	10438.0i	0.469770	+	0.813666i
$549$	2930.03	+	4810.28i	0.227779	+	0.373948i
$550$	−444.919	+	770.623i	−0.0344935	+	0.0597445i
$551$	−6357.06	−	2313.78i	−0.491506	−	0.178894i
$552$	−15063.8	+	8934.67i	−1.16151	+	0.688922i
$553$	9850.68	+	8265.70i	0.757493	+	0.635612i
$554$	1597.17	+	1340.19i	0.122486	+	0.102778i
$555$	−160.644	−	13672.1i	−0.0122864	−	1.04567i
$556$	5345.83	+	1945.72i	0.407758	+	0.148412i
$557$	−1468.87	+	2544.15i	−0.111738	+	0.193536i	−0.916471	−	0.400101i	$-0.868975\pi$
$557$	−1468.87	+	2544.15i	−0.111738	+	0.193536i	0.804733	+	0.593637i	$0.202308\pi$
$558$	757.748	+	606.064i	0.0574875	+	0.0459798i
$559$	−5474.62	−	9482.32i	−0.414225	−	0.717458i
$560$	585.281	+	3319.29i	0.0441654	+	0.250475i
$561$	−1395.26	+	1703.05i	−0.105005	+	0.128169i
$562$	−3189.52	+	1160.89i	−0.239398	+	0.0871337i
$563$	906.104	−	5138.77i	0.0678290	−	0.384677i	−0.931928	−	0.362643i	$-0.881875\pi$
$563$	906.104	−	5138.77i	0.0678290	−	0.384677i	0.999757	−	0.0220345i	$-0.00701436\pi$
$564$	9766.99	−	1840.76i	0.729192	−	0.137429i
$565$	3134.76	−	2630.38i	0.233417	−	0.195860i
$566$	2196.25			0.163101
$567$	7521.72	+	5731.52i	0.557112	+	0.424517i
$568$	2798.61			0.206737
$569$	6604.67	−	5541.97i	0.486612	−	0.408316i	−0.366199	−	0.930537i	$-0.619341\pi$
$569$	6604.67	−	5541.97i	0.486612	−	0.408316i	0.852810	+	0.522221i	$0.174896\pi$
$570$	1072.70	−	202.169i	0.0788255	−	0.0148560i
$571$	1857.04	−	10531.8i	0.136103	−	0.771877i	−0.837983	−	0.545697i	$-0.816265\pi$
$571$	1857.04	−	10531.8i	0.136103	−	0.771877i	0.974085	−	0.226180i	$-0.0726239\pi$
$572$	5240.39	−	1907.35i	0.383063	−	0.139423i
$573$	−11918.1	+	14547.2i	−0.868913	+	1.06059i
$574$	−639.853	−	3628.79i	−0.0465278	−	0.263872i
$575$	−6574.91	−	11388.1i	−0.476857	−	0.825941i
$576$	282.201	−	1854.22i	0.0204138	−	0.134131i
$577$	11035.7	−	19114.4i	0.796225	−	1.37910i	−0.125833	−	0.992051i	$-0.540160\pi$
$577$	11035.7	−	19114.4i	0.796225	−	1.37910i	0.922058	−	0.387051i	$-0.126506\pi$
$578$	−3900.24	−	1419.57i	−0.280672	−	0.102156i
$579$	−128.378	−	10926.0i	−0.00921452	−	0.784231i
$580$	−11194.0	−	9392.86i	−0.801387	−	0.672443i
$581$	5716.35	+	4796.59i	0.408183	+	0.342506i
$582$	2447.58	−	1451.72i	0.174322	−	0.103395i
$583$	3535.17	+	1286.70i	0.251135	+	0.0914057i
$584$	8196.39	−	14196.6i	0.580769	−	1.00592i
$585$	−14835.9	+	348.684i	−1.04853	+	0.0246432i
$586$	1295.10	+	2243.17i	0.0912967	+	0.158131i
$587$	2983.21	+	16918.6i	0.209762	+	1.18962i	0.889769	+	0.456412i	$0.150866\pi$
$587$	2983.21	+	16918.6i	0.209762	+	1.18962i	−0.680007	+	0.733205i	$0.738023\pi$
$588$	−2137.67	−	5665.20i	−0.149925	−	0.397328i
$589$	−694.145	+	252.648i	−0.0485599	+	0.0176743i
$590$	−626.210	+	3551.41i	−0.0436960	+	0.247813i
$591$	15540.9	+	18085.1i	1.08167	+	1.25875i
$592$	−8880.07	+	7451.26i	−0.616501	+	0.517306i
$593$	5277.08			0.365436			0.182718	−	0.983165i	$-0.441510\pi$
$593$	5277.08			0.365436			0.182718	+	0.983165i	$0.441510\pi$
$594$	−1163.69	+	1490.50i	−0.0803818	+	0.102956i
$595$	3612.71			0.248919
$596$	11617.1	−	9747.86i	0.798411	−	0.669946i
$597$	−3381.19	+	9640.69i	−0.231797	+	0.660917i
$598$	2855.51	−	16194.4i	0.195269	−	1.10742i
$599$	23691.1	−	8622.84i	1.61601	−	0.588180i	0.633394	−	0.773829i	$-0.281661\pi$
$599$	23691.1	−	8622.84i	1.61601	−	0.588180i	0.982616	+	0.185650i	$0.0594390\pi$
$600$	−5728.39	−	940.813i	−0.389768	−	0.0640142i
$601$	2466.89	+	13990.4i	0.167432	+	0.949555i	0.946521	+	0.322641i	$0.104571\pi$
$601$	2466.89	+	13990.4i	0.167432	+	0.949555i	−0.779089	+	0.626913i	$0.784318\pi$
$602$	1144.71	+	1982.70i	0.0775000	+	0.134234i
$603$	−5077.75	−	1714.15i	−0.342922	−	0.115764i
$604$	−113.879	+	197.245i	−0.00767167	+	0.0132877i
$605$	8620.28	+	3137.53i	0.579280	+	0.210841i
$606$	7461.02	+	4191.52i	0.500137	+	0.280972i
$607$	−11779.8	−	9884.43i	−0.787690	−	0.660950i	0.157483	−	0.987522i	$-0.449662\pi$
$607$	−11779.8	−	9884.43i	−0.787690	−	0.660950i	−0.945172	+	0.326572i	$0.894107\pi$
$608$	−3168.02	−	2658.29i	−0.211316	−	0.177315i
$609$	−16765.8	−	9418.85i	−1.11557	−	0.626718i
$610$	1736.68	+	632.101i	0.115273	+	0.0419558i
$611$	−10262.8	+	17775.7i	−0.679524	+	1.17697i
$612$	−6186.97	−	2088.59i	−0.408649	−	0.137952i
$613$	−4463.56	−	7731.11i	−0.294097	−	0.509391i	0.680677	−	0.732583i	$-0.261686\pi$
$613$	−4463.56	−	7731.11i	−0.294097	−	0.509391i	−0.974774	+	0.223192i	$0.928352\pi$
$614$	−657.521	−	3728.99i	−0.0432172	−	0.245097i
$615$	9696.38	+	1592.50i	0.635766	+	0.104416i
$616$	−2410.12	+	877.211i	−0.157640	+	0.0573764i
$617$	−776.890	+	4405.96i	−0.0506911	+	0.287484i	−0.999607	−	0.0280467i	$-0.991071\pi$
$617$	−776.890	+	4405.96i	−0.0506911	+	0.287484i	0.948916	+	0.315530i	$0.102182\pi$
$618$	−2445.08	+	6971.59i	−0.159151	+	0.453784i
$619$	16763.6	−	14066.3i	1.08851	−	0.913367i	0.0919088	−	0.995767i	$-0.470703\pi$
$619$	16763.6	−	14066.3i	1.08851	−	0.913367i	0.996599	+	0.0824007i	$0.0262587\pi$
$620$	−1595.60			−0.103356
$621$	−10477.0	−	25906.0i	−0.677015	−	1.67403i
$622$	627.311			0.0404387
$623$	2796.12	−	2346.22i	0.179814	−	0.150882i
$624$	8199.87	+	9542.25i	0.526053	+	0.612173i
$625$	−523.377	+	2968.22i	−0.0334961	+	0.189966i
$626$	−5249.94	+	1910.82i	−0.335191	+	0.122000i
$627$	−508.230	−	1346.90i	−0.0323712	−	0.0857894i
$628$	−2170.33	−	12308.6i	−0.137907	−	0.782109i
$629$	6212.57	+	10760.5i	0.393818	+	0.682113i
$630$	3102.10	−	72.9078i	0.196175	−	0.00461066i
$631$	−14486.4	+	25091.2i	−0.913939	+	1.58299i	−0.105491	+	0.994420i	$0.533641\pi$
$631$	−14486.4	+	25091.2i	−0.913939	+	1.58299i	−0.808448	+	0.588568i	$0.799692\pi$
$632$	−15763.4	−	5737.43i	−0.992146	−	0.361112i
$633$	−2638.82	+	1565.15i	−0.165693	+	0.0982763i
$634$	1290.62	+	1082.96i	0.0808473	+	0.0678389i
$635$	−590.744	−	495.693i	−0.0369181	−	0.0309779i
$636$	131.097	+	11157.4i	0.00817349	+	0.695630i
$637$	11750.7	+	4276.90i	0.730893	+	0.266023i
$638$	1922.69	−	3330.20i	0.119310	−	0.206652i
$639$	−671.847	+	4414.43i	−0.0415929	+	0.273290i
$640$	−5665.41	−	9812.78i	−0.349914	−	0.606069i
$641$	1409.67	+	7994.62i	0.0868619	+	0.492618i	0.996939	+	0.0781800i	$0.0249109\pi$
$641$	1409.67	+	7994.62i	0.0868619	+	0.492618i	−0.910077	+	0.414438i	$0.863978\pi$
$642$	6535.98	−	7977.79i	0.401799	−	0.490433i
$643$	8064.57	−	2935.26i	0.494612	−	0.180024i	−0.0826569	−	0.996578i	$-0.526341\pi$
$643$	8064.57	−	2935.26i	0.494612	−	0.180024i	0.577269	+	0.816554i	$0.304118\pi$
$644$	2992.26	−	16970.0i	0.183093	−	1.03837i
$645$	−5999.66	+	1130.74i	−0.366258	+	0.0690276i
$646$	−759.887	+	637.621i	−0.0462807	+	0.0388341i
$647$	17695.3			1.07523			0.537616	−	0.843190i	$-0.319325\pi$
$647$	17695.3			1.07523			0.537616	+	0.843190i	$0.319325\pi$
$648$	−11777.8	−	3670.01i	−0.714005	−	0.222487i
$649$	4755.89			0.287650
$650$	4175.33	−	3503.52i	0.251954	−	0.211415i
$651$	−2063.49	+	388.900i	−0.124231	+	0.0234135i
$652$	−1679.86	+	9526.95i	−0.100902	+	0.572246i
$653$	−2354.57	+	856.993i	−0.141105	+	0.0513579i	−0.411607	−	0.911361i	$-0.635032\pi$
$653$	−2354.57	+	856.993i	−0.141105	+	0.0513579i	0.270502	+	0.962719i	$0.412810\pi$
$654$	−1192.60	+	1455.68i	−0.0713065	+	0.0870364i
$655$	−239.535	−	1358.47i	−0.0142892	−	0.0810381i
$656$	−4165.40	−	7214.69i	−0.247914	−	0.429400i
$657$	20425.5	+	16336.8i	1.21290	+	0.970106i
$658$	2145.90	−	3716.81i	0.127137	−	0.220207i
$659$	−22609.4	−	8229.15i	−1.33648	−	0.486437i	−0.427774	−	0.903886i	$-0.640702\pi$
$659$	−22609.4	−	8229.15i	−1.33648	−	0.486437i	−0.908701	+	0.417448i	$0.862924\pi$
$660$	−36.5342	−	3109.35i	−0.00215468	−	0.183381i
$661$	−14240.1	−	11948.8i	−0.837933	−	0.703109i	0.119165	−	0.992875i	$-0.461978\pi$
$661$	−14240.1	−	11948.8i	−0.837933	−	0.703109i	−0.957098	+	0.289765i	$0.906423\pi$
$662$	−3655.03	−	3066.93i	−0.214587	−	0.180060i
$663$	11598.8	−	6879.53i	0.679428	−	0.402985i
$664$	−9147.53	−	3329.43i	−0.534628	−	0.194589i
$665$	−1181.14	+	2045.79i	−0.0688761	+	0.119297i
$666$	5551.66	+	9114.25i	0.323006	+	0.530285i
$667$	28413.1	+	49212.9i	1.64941	+	2.85687i
$668$	2167.29	+	12291.3i	0.125532	+	0.711925i
$669$	7875.51	+	20871.5i	0.455134	+	1.20618i
$670$	−1652.47	+	601.451i	−0.0952844	+	0.0346807i
$671$	423.241	−	2400.32i	0.0243503	−	0.138097i
$672$	−7661.75	−	8916.05i	−0.439819	−	0.511821i
$673$	−6242.12	+	5237.76i	−0.357528	+	0.300001i	−0.803804	−	0.594894i	$-0.797194\pi$
$673$	−6242.12	+	5237.76i	−0.357528	+	0.300001i	0.446277	+	0.894895i	$0.352750\pi$
$674$	−1491.85			−0.0852580
$675$	2859.19	−	8809.92i	0.163038	−	0.502361i
$676$	−19506.6			−1.10984
$677$	−12973.4	+	10886.0i	−0.736497	+	0.617994i	−0.931894	−	0.362730i	$-0.881845\pi$
$677$	−12973.4	+	10886.0i	−0.736497	+	0.617994i	0.195397	+	0.980724i	$0.437400\pi$
$678$	−1057.06	+	3013.97i	−0.0598763	+	0.170724i
$679$	−1069.39	+	6064.81i	−0.0604409	+	0.342777i
$680$	−4428.66	+	1611.90i	−0.249752	+	0.0909022i
$681$	−22416.3	−	3681.59i	−1.26137	−	0.207164i
$682$	−72.9128	−	413.509i	−0.00409380	−	0.0232171i
$683$	4393.17	+	7609.20i	0.246120	+	0.426293i	0.962446	−	0.271473i	$-0.0875108\pi$
$683$	4393.17	+	7609.20i	0.246120	+	0.426293i	−0.716326	+	0.697766i	$0.754178\pi$
$684$	3205.49	−	2820.69i	0.179188	−	0.157678i
$685$	−6939.61	+	12019.8i	−0.387079	+	0.670440i
$686$	−7280.22	−	2649.78i	−0.405190	−	0.147477i
$687$	−26753.7	−	15030.0i	−1.48576	−	0.834686i
$688$	3965.13	+	3327.14i	0.219723	+	0.184369i
$689$	−17652.4	−	14812.2i	−0.976059	−	0.819010i
$690$	−7994.16	−	4491.04i	−0.441062	−	0.247784i
$691$	23714.3	+	8631.29i	1.30555	+	0.475181i	0.898800	−	0.438359i	$-0.144440\pi$
$691$	23714.3	+	8631.29i	1.30555	+	0.475181i	0.406749	+	0.913540i	$0.366663\pi$
$692$	2830.71	−	4902.94i	0.155502	−	0.269338i
$693$	−805.099	−	4012.23i	−0.0441316	−	0.219931i
$694$	5879.55	+	10183.7i	0.321592	+	0.557014i
$695$	1137.57	+	6451.48i	0.0620870	+	0.352113i
$696$	24754.9	+	4065.67i	1.34818	+	0.221421i
$697$	−8390.96	+	3054.06i	−0.455998	+	0.165970i
$698$	335.226	−	1901.16i	0.0181784	−	0.103095i
$699$	3757.74	−	10714.3i	0.203335	−	0.579762i
$700$	4375.29	−	3671.31i	0.236244	−	0.198232i
$701$	−1195.09			−0.0643909			−0.0321955	−	0.999482i	$-0.510250\pi$
$701$	−1195.09			−0.0643909			−0.0321955	+	0.999482i	$0.510250\pi$
$702$	9820.63	−	6141.27i	0.527999	−	0.330181i
$703$	−8124.55			−0.435879
$704$	−621.746	+	521.707i	−0.0332854	+	0.0279298i
$705$	7459.25	+	8680.39i	0.398485	+	0.463720i
$706$	1334.47	−	7568.15i	0.0711379	−	0.403443i
$707$	−17402.8	+	6334.11i	−0.925743	+	0.336943i
$708$	4979.91	+	13197.6i	0.264345	+	0.700561i
$709$	−4612.68	−	26159.8i	−0.244334	−	1.38569i	−0.822034	−	0.569439i	$-0.807161\pi$
$709$	−4612.68	−	26159.8i	−0.244334	−	1.38569i	0.577700	−	0.816249i	$-0.303951\pi$
$710$	732.586	+	1268.88i	0.0387232	+	0.0670706i
$711$	12834.3	−	23487.4i	0.676966	−	1.23888i
$712$	−2380.81	+	4123.68i	−0.125315	+	0.217053i
$713$	5830.80	+	2122.24i	0.306263	+	0.111470i
$714$	−2425.25	+	1438.47i	−0.127119	+	0.0753970i
$715$	4919.38	+	4127.85i	0.257307	+	0.215906i
$716$	−10953.6	−	9191.15i	−0.571725	−	0.479734i
$717$	−76.5764	−	6517.28i	−0.00398856	−	0.339459i
$718$	−5640.14	−	2052.84i	−0.293159	−	0.106701i
$719$	381.663	−	661.059i	0.0197964	−	0.0342884i	−0.855957	−	0.517046i	$-0.827032\pi$
$719$	381.663	−	661.059i	0.0197964	−	0.0342884i	0.875754	+	0.482758i	$0.160365\pi$
$720$	6534.12	−	2553.64i	0.338211	−	0.132178i
$721$	−7994.02	−	13846.1i	−0.412917	−	0.715193i
$722$	1261.35	+	7153.49i	0.0650176	+	0.368733i
$723$	8093.80	−	9879.25i	0.416337	−	0.508179i
$724$	4113.55	−	1497.21i	0.211158	−	0.0768554i
$725$	−3270.71	+	18549.1i	−0.167546	+	0.950202i
$726$	−7036.15	+	1326.08i	−0.359692	+	0.0677901i
$727$	26579.4	−	22302.8i	1.35595	−	1.13778i	0.378739	−	0.925503i	$-0.376358\pi$
$727$	26579.4	−	22302.8i	1.35595	−	1.13778i	0.977210	−	0.212273i	$-0.0680867\pi$
$728$	15710.1			0.799800
$729$	8616.39	−	17696.8i	0.437758	−	0.899093i
$730$	8582.22			0.435126
$731$	4250.07	−	3566.24i	0.215041	−	0.180440i
$732$	7104.08	−	1338.89i	0.358708	−	0.0676047i
$733$	−1176.42	+	6671.79i	−0.0592796	+	0.336191i	−0.999995	−	0.00300429i	$-0.999044\pi$
$733$	−1176.42	+	6671.79i	−0.0592796	+	0.336191i	0.940716	+	0.339195i	$0.110155\pi$
$734$	11891.2	−	4328.05i	0.597974	−	0.217645i
$735$	4418.88	−	5393.67i	0.221759	−	0.270678i
$736$	6032.29	+	34210.8i	0.302110	+	1.71335i
$737$	1159.58	+	2008.45i	0.0579561	+	0.100383i
$738$	−7143.37	+	2791.74i	−0.356302	+	0.139249i
$739$	14129.7	−	24473.3i	0.703340	−	1.21822i	−0.263947	−	0.964537i	$-0.585025\pi$
$739$	14129.7	−	24473.3i	0.703340	−	1.21822i	0.967287	−	0.253683i	$-0.0816421\pi$
$740$	−16490.9	−	6002.20i	−0.819213	−	0.298169i
$741$	103.601	+	8817.32i	0.00513616	+	0.437129i
$742$	3691.03	+	3097.14i	0.182617	+	0.153234i
$743$	−8665.44	−	7271.17i	−0.427866	−	0.359022i	0.403280	−	0.915077i	$-0.367870\pi$
$743$	−8665.44	−	7271.17i	−0.427866	−	0.359022i	−0.831146	+	0.556055i	$0.812315\pi$
$744$	2356.02	−	1397.41i	0.116097	−	0.0688597i
$745$	16409.9	+	5972.72i	0.806997	+	0.293723i
$746$	−481.231	+	833.516i	−0.0236181	+	0.0409078i
$747$	7447.73	−	13629.7i	0.364790	−	0.667585i
$748$	1412.88	+	2447.19i	0.0690644	+	0.119623i
$749$	3875.61	+	21979.7i	0.189068	+	1.07226i
$750$	−3104.46	−	8227.35i	−0.151145	−	0.400560i
$751$	−2748.90	+	1000.52i	−0.133567	+	0.0486144i	−0.407939	−	0.913009i	$-0.633752\pi$
$751$	−2748.90	+	1000.52i	−0.133567	+	0.0486144i	0.274372	+	0.961624i	$0.411530\pi$
$752$	1684.95	−	9555.81i	0.0817070	−	0.463384i
$753$	−267.443	−	311.226i	−0.0129431	−	0.0150620i
$754$	−18043.4	+	15140.2i	−0.871490	+	0.731267i
$755$	−262.273			−0.0126425
$756$	10290.9	−	6435.37i	0.495076	−	0.309593i
$757$	6486.15			0.311417			0.155709	−	0.987803i	$-0.450234\pi$
$757$	6486.15			0.311417			0.155709	+	0.987803i	$0.450234\pi$
$758$	−9225.62	+	7741.21i	−0.442071	+	0.370941i
$759$	−4002.11	+	11411.1i	−0.191393	+	0.545714i
$760$	535.124	−	3034.84i	0.0255408	−	0.144849i
$761$	1025.17	−	373.130i	0.0488335	−	0.0177739i	−0.317488	−	0.948262i	$-0.602839\pi$
$761$	1025.17	−	373.130i	0.0488335	−	0.0177739i	0.366321	+	0.930488i	$0.380617\pi$
$762$	593.943	+	97.5474i	0.0282366	+	0.00463749i
$763$	−707.172	−	4010.57i	−0.0335535	−	0.190292i
$764$	12068.7	+	20903.5i	0.571504	+	0.989874i
$765$	−1479.39	−	7372.58i	−0.0699183	−	0.348439i
$766$	−5603.69	+	9705.88i	−0.264321	+	0.457817i
$767$	−27374.4	−	9963.45i	−1.28870	−	0.469047i
$768$	5192.85	+	2917.29i	0.243985	+	0.137068i
$769$	−21221.6	−	17807.0i	−0.995150	−	0.835030i	−0.00884496	−	0.999961i	$-0.502815\pi$
$769$	−21221.6	−	17807.0i	−0.995150	−	0.835030i	−0.986305	+	0.164931i	$0.947260\pi$
$770$	−1028.62	−	863.112i	−0.0481413	−	0.0403953i
$771$	−1473.15	−	827.603i	−0.0688124	−	0.0386581i
$772$	−13178.7	−	4796.64i	−0.614392	−	0.223620i
$773$	17910.5	−	31021.9i	0.833371	−	1.44344i	−0.0619780	−	0.998078i	$-0.519741\pi$
$773$	17910.5	−	31021.9i	0.833371	−	1.44344i	0.895349	−	0.445364i	$-0.146926\pi$
$774$	3577.41	−	3147.96i	0.166133	−	0.146190i
$775$	1028.34	+	1781.13i	0.0476632	+	0.0825551i
$776$	−1395.05	−	7911.70i	−0.0645351	−	0.365997i
$777$	−22789.6	−	3742.89i	−1.05222	−	0.172813i
$778$	−7255.88	+	2640.93i	−0.334365	+	0.121699i
$779$	1013.90	−	5750.10i	0.0466324	−	0.264465i
$780$	−6303.72	+	17973.6i	−0.289371	+	0.825075i
$781$	1480.22	−	1242.05i	0.0678185	−	0.0569065i
$782$	8332.45			0.381033
$783$	−12355.8	+	38071.5i	−0.563935	+	1.73763i
$784$	−5911.49			−0.269292
$785$	11025.2	−	9251.28i	0.501284	−	0.420627i
$786$	701.706	+	816.581i	0.0318435	+	0.0370566i
$787$	−5255.84	+	29807.4i	−0.238057	+	1.35009i	0.598023	+	0.801479i	$0.295953\pi$
$787$	−5255.84	+	29807.4i	−0.238057	+	1.35009i	−0.836080	+	0.548608i	$0.815158\pi$
$788$	28759.4	−	10467.6i	1.30014	−	0.473213i
$789$	7921.23	+	20992.6i	0.357419	+	0.947222i
$790$	−1525.05	−	8648.96i	−0.0686819	−	0.389514i
$791$	−3455.98	−	5985.94i	−0.155348	−	0.269071i
$792$	2777.09	+	4559.19i	0.124595	+	0.204550i
$793$	−7464.72	+	12929.3i	−0.334275	+	0.578981i
$794$	9400.59	+	3421.53i	0.420169	+	0.152929i
$795$	−11051.4	+	6554.85i	−0.493022	+	0.292423i
$796$	10044.9	+	8428.69i	0.447278	+	0.375311i
$797$	−8667.60	−	7272.98i	−0.385222	−	0.323240i	0.429526	−	0.903054i	$-0.358681\pi$
$797$	−8667.60	−	7272.98i	−0.385222	−	0.323240i	−0.814749	+	0.579814i	$0.803125\pi$
$798$	−21.6625	−	1843.65i	−0.000960957	−	0.0817853i
$799$	−9773.29	−	3557.19i	−0.432734	−	0.157502i
$800$	−5757.12	+	9971.63i	−0.254431	+	0.440688i
$801$	−5933.01	−	4745.36i	−0.261714	−	0.209325i
$802$	−4204.22	−	7281.93i	−0.185108	−	0.320616i
$803$	−1965.41	−	11146.4i	−0.0863732	−	0.489847i
$804$	−4359.27	+	5320.90i	−0.191218	+	0.233400i
$805$	18646.4	−	6786.72i	0.816395	−	0.297144i
$806$	−446.611	+	2532.86i	−0.0195176	+	0.110690i
$807$	−8125.52	+	1531.39i	−0.354438	+	0.0668000i
$808$	18507.2	−	15529.4i	0.805794	−	0.676141i
$809$	−19833.4			−0.861935			−0.430967	−	0.902368i	$-0.641828\pi$
$809$	−19833.4			−0.861935			−0.430967	+	0.902368i	$0.641828\pi$
$810$	−1419.08	−	6300.70i	−0.0615574	−	0.273313i
$811$	−21920.8			−0.949129			−0.474564	−	0.880221i	$-0.657394\pi$
$811$	−21920.8			−0.949129			−0.474564	+	0.880221i	$0.657394\pi$
$812$	−18907.6	+	15865.3i	−0.817149	+	0.685669i
$813$	10054.4	−	1894.93i	0.433733	−	0.0817444i
$814$	801.933	−	4547.99i	0.0345304	−	0.195832i
$815$	−10468.1	+	3810.07i	−0.449915	+	0.163756i
$816$	−4040.19	+	4931.44i	−0.173327	+	0.211562i
$817$	629.956	+	3572.66i	0.0269760	+	0.152988i
$818$	2431.75	+	4211.92i	0.103942	+	0.180032i
$819$	−3771.44	+	24780.6i	−0.160909	+	1.05727i
$820$	6305.99	−	10922.3i	0.268555	−	0.465150i
$821$	35467.4	+	12909.1i	1.50770	+	0.548758i	0.958041	−	0.286632i	$-0.0925356\pi$
$821$	35467.4	+	12909.1i	1.50770	+	0.548758i	0.549658	+	0.835389i	$0.314758\pi$
$822$	−127.275	−	10832.1i	−0.00540051	−	0.459628i
$823$	−13193.9	−	11071.0i	−0.558822	−	0.468907i	0.319093	−	0.947723i	$-0.396622\pi$
$823$	−13193.9	−	11071.0i	−0.558822	−	0.468907i	−0.877915	+	0.478816i	$0.841066\pi$
$824$	15977.3	+	13406.5i	0.675478	+	0.566794i
$825$	−3447.36	+	2044.71i	−0.145481	+	0.0862880i
$826$	5723.83	+	2083.30i	0.241111	+	0.0877572i
$827$	−12200.9	+	21132.6i	−0.513020	+	0.888577i	0.486866	+	0.873477i	$0.338140\pi$
$827$	−12200.9	+	21132.6i	−0.513020	+	0.888577i	−0.999886	+	0.0151005i	$0.995193\pi$
$828$	−35856.5	+	842.727i	−1.50495	+	0.0353705i
$829$	12405.1	+	21486.2i	0.519718	+	0.900179i	0.999737	+	0.0229206i	$0.00729649\pi$
$829$	12405.1	+	21486.2i	0.519718	+	0.900179i	−0.480019	+	0.877258i	$0.659370\pi$
$830$	−884.984	−	5018.99i	−0.0370099	−	0.209894i
$831$	3315.49	+	8786.64i	0.138403	+	0.366793i
$832$	4671.66	−	1700.34i	0.194664	−	0.0708520i
$833$	−1100.29	+	6240.04i	−0.0457655	+	0.259549i
$834$	−3332.45	−	3878.00i	−0.138361	−	0.161012i
$835$	−11009.8	+	9238.34i	−0.456300	+	0.382881i
$836$	−1847.71			−0.0764408
$837$	1638.63	+	4051.78i	0.0676696	+	0.167324i
$838$	−4194.16			−0.172893
$839$	25232.8	−	21172.9i	1.03830	−	0.871238i	0.0464853	−	0.998919i	$-0.485198\pi$
$839$	25232.8	−	21172.9i	1.03830	−	0.871238i	0.991815	+	0.127681i	$0.0407535\pi$
$840$	2899.15	−	8266.28i	0.119084	−	0.339540i
$841$	9899.06	−	56140.3i	0.405882	−	2.30187i
$842$	−3822.91	+	1391.42i	−0.156468	+	0.0569497i
$843$	−15086.5	−	2477.77i	−0.616380	−	0.101232i
$844$	683.800	+	3878.02i	0.0278879	+	0.158160i
$845$	−11231.3	−	19453.2i	−0.457242	−	0.791966i
$846$	−8463.74	−	2857.19i	−0.343959	−	0.116114i
$847$	7747.42	−	13418.9i	0.314291	−	0.544368i
$848$	10236.6	+	3725.82i	0.414536	+	0.150879i
$849$	8624.80	+	4845.32i	0.348648	+	0.195867i
$850$	2115.68	+	1775.27i	0.0853732	+	0.0716366i
$851$	52279.4	+	43867.6i	2.10589	+	1.76705i
$852$	4996.63	+	2807.06i	0.200918	+	0.112873i
$853$	−15961.4	−	5809.48i	−0.640690	−	0.233192i	0.00118739	−	0.999999i	$-0.499622\pi$
$853$	−15961.4	−	5809.48i	−0.640690	−	0.233192i	−0.641878	+	0.766807i	$0.721844\pi$
$854$	1560.83	−	2703.44i	0.0625417	−	0.108325i
$855$	4658.59	+	1572.64i	0.186339	+	0.0629044i
$856$	−14557.7	−	25214.7i	−0.581276	−	1.00680i
$857$	−1376.16	−	7804.60i	−0.0548527	−	0.311085i	0.945020	−	0.327011i	$-0.106041\pi$
$857$	−1376.16	−	7804.60i	−0.0548527	−	0.311085i	−0.999873	+	0.0159261i	$0.994930\pi$
$858$	−4946.02	−	812.319i	−0.196800	−	0.0323218i
$859$	−37994.1	+	13828.7i	−1.50913	+	0.549278i	−0.958405	−	0.285411i	$-0.907870\pi$
$859$	−37994.1	+	13828.7i	−1.50913	+	0.549278i	−0.550722	+	0.834688i	$0.685648\pi$
$860$	−1360.72	+	7717.05i	−0.0539538	+	0.305987i
$861$	5493.02	−	15662.1i	0.217423	−	0.619933i
$862$	1084.84	−	910.286i	0.0428651	−	0.0359681i
$863$	−7710.61			−0.304139			−0.152070	−	0.988370i	$-0.548594\pi$
$863$	−7710.61			−0.304139			−0.152070	+	0.988370i	$0.548594\pi$
$864$	−15057.8	+	19286.7i	−0.592913	+	0.759428i
$865$	6519.36			0.256260
$866$	11573.7	−	9711.46i	0.454145	−	0.381073i
$867$	−12184.6	−	14179.4i	−0.477292	−	0.555428i
$868$	−468.000	+	2654.16i	−0.0183006	+	0.103788i
$869$	−10883.8	+	3961.38i	−0.424865	+	0.154638i
$870$	4636.69	+	12288.0i	0.180688	+	0.478854i
$871$	−2466.76	−	13989.7i	−0.0959621	−	0.544228i
$872$	2656.31	+	4600.86i	0.103158	+	0.178675i
$873$	12814.6	−	301.177i	0.496801	−	0.0116762i
$874$	−2724.21	+	4718.47i	−0.105432	+	0.182614i
$875$	17882.3	+	6508.63i	0.690894	+	0.251465i
$876$	28873.3	−	17125.4i	1.11363	−	0.660519i
$877$	28888.1	+	24240.0i	1.11229	+	0.933326i	0.998190	−	0.0601432i	$-0.0191557\pi$
$877$	28888.1	+	24240.0i	1.11229	+	0.933326i	0.114104	+	0.993469i	$0.463600\pi$
$878$	−1401.20	−	1175.74i	−0.0538589	−	0.0451930i
$879$	137.076	+	11666.3i	0.00525990	+	0.447661i
$880$	−2852.74	−	1038.31i	−0.109279	−	0.0397744i
$881$	7285.02	−	12618.0i	0.278591	−	0.482533i	−0.692444	−	0.721472i	$-0.743466\pi$
$881$	7285.02	−	12618.0i	0.278591	−	0.482533i	0.971035	+	0.238938i	$0.0767994\pi$
$882$	−818.845	+	5380.29i	−0.0312607	+	0.205401i
$883$	−4163.74	−	7211.81i	−0.158688	−	0.274855i	0.775708	−	0.631092i	$-0.217393\pi$
$883$	−4163.74	−	7211.81i	−0.158688	−	0.274855i	−0.934396	+	0.356237i	$0.884060\pi$
$884$	−3005.61	−	17045.7i	−0.114355	−	0.648539i
$885$	−10294.2	+	12565.1i	−0.391002	+	0.477255i
$886$	19270.4	−	7013.87i	0.730703	−	0.265954i
$887$	5420.97	−	30743.8i	0.205207	−	1.16379i	−0.691907	−	0.721986i	$-0.743229\pi$
$887$	5420.97	−	30743.8i	0.205207	−	1.16379i	0.897114	−	0.441799i	$-0.145659\pi$
$888$	29606.7	−	5579.89i	1.11885	−	0.210866i
$889$	−997.817	+	837.268i	−0.0376442	+	0.0315872i
$890$	−2492.88			−0.0938894
$891$	−7858.20	+	3285.98i	−0.295465	+	0.123552i
$892$	28632.0			1.07474
$893$	5209.63	−	4371.40i	0.195222	−	0.163811i
$894$	−13394.3	+	2524.39i	−0.501088	+	0.0944386i
$895$	2859.25	−	16215.6i	0.106787	−	0.605617i
$896$	−17984.5	+	6545.83i	−0.670558	+	0.244063i
$897$	46941.6	−	57296.7i	1.74731	−	2.13275i
$898$	−147.313	−	835.454i	−0.00547428	−	0.0310462i
$899$	−4443.90	−	7697.05i	−0.164863	−	0.285552i
$900$	−9283.82	−	7425.42i	−0.343845	−	0.275015i
$901$	5838.21	−	10112.1i	0.215870	−	0.373898i
$902$	3118.73	+	1135.13i	0.115125	+	0.0419020i
$903$	121.159	+	10311.6i	0.00446503	+	0.380010i
$904$	6907.31	+	5795.92i	0.254130	+	0.213240i
$905$	3861.56	+	3240.24i	0.141837	+	0.119016i
$906$	176.067	−	104.429i	0.00645632	−	0.00382939i
$907$	−14476.0	−	5268.84i	−0.529954	−	0.192888i	0.0631638	−	0.998003i	$-0.479881\pi$
$907$	−14476.0	−	5268.84i	−0.529954	−	0.192888i	−0.593118	+	0.805116i	$0.702103\pi$
$908$	−14578.3	+	25250.4i	−0.532818	+	0.922868i
$909$	20052.6	+	32920.7i	0.731687	+	1.20122i
$910$	4112.40	+	7122.89i	0.149808	+	0.259474i
$911$	−4251.19	−	24109.7i	−0.154608	−	0.876828i	−0.959143	−	0.282922i	$-0.908696\pi$
$911$	−4251.19	−	24109.7i	−0.154608	−	0.876828i	0.804534	−	0.593906i	$-0.202415\pi$
$912$	−1471.66	−	3900.15i	−0.0534336	−	0.141608i
$913$	−6315.87	+	2298.79i	−0.228943	+	0.0833284i
$914$	2586.31	−	14667.7i	0.0935968	−	0.530814i
$915$	5425.53	+	6313.74i	0.196025	+	0.228116i
$916$	−30171.4	+	25316.8i	−1.08831	+	0.913200i
$917$	−2329.97			−0.0839067
$918$	3928.67	+	4360.24i	0.141248	+	0.156764i
$919$	−8583.14			−0.308087			−0.154043	−	0.988064i	$-0.549230\pi$
$919$	−8583.14			−0.308087			−0.154043	+	0.988064i	$0.549230\pi$
$920$	−19829.7	+	16639.1i	−0.710614	+	0.596276i
$921$	5644.69	−	16094.6i	0.201953	−	0.575824i
$922$	−2440.99	+	13843.5i	−0.0871905	+	0.494482i
$923$	−11122.0	+	4048.08i	−0.396625	+	0.144360i
$924$	−5182.89	−	851.221i	−0.184529	−	0.0303064i
$925$	3927.99	+	22276.7i	0.139623	+	0.791843i
$926$	−10085.8	−	17469.1i	−0.357926	−	0.619946i
$927$	−24982.6	+	21983.6i	−0.885151	+	0.778894i
$928$	24879.1	−	43091.8i	0.880059	−	1.52431i
$929$	14003.0	+	5096.66i	0.494534	+	0.179996i	0.577234	−	0.816579i	$-0.304132\pi$
$929$	14003.0	+	5096.66i	0.494534	+	0.179996i	−0.0826997	+	0.996575i	$0.526354\pi$
$930$	1250.31	+	702.412i	0.0440853	+	0.0247667i
$931$	−3173.86	−	2663.18i	−0.111728	−	0.0937511i
$932$	−11163.6	−	9367.38i	−0.392356	−	0.329226i
$933$	2463.49	+	1383.96i	0.0864426	+	0.0485625i
$934$	−5414.15	−	1970.59i	−0.189675	−	0.0690360i
$935$	−1626.99	+	2818.03i	−0.0569073	+	0.0985664i
$936$	−6433.22	−	32060.1i	−0.224654	−	1.11957i
$937$	−8694.72	−	15059.7i	−0.303142	−	0.525057i	0.673704	−	0.739001i	$-0.264702\pi$
$937$	−8694.72	−	15059.7i	−0.303142	−	0.525057i	−0.976846	+	0.213944i	$0.931369\pi$
$938$	515.786	+	2925.17i	0.0179542	+	0.101823i
$939$	−24832.4	−	4078.40i	−0.863020	−	0.141740i
$940$	13803.8	−	5024.17i	0.478968	−	0.174330i
$941$	−5316.60	+	30152.0i	−0.184183	+	1.04455i	0.742817	+	0.669494i	$0.233489\pi$
$941$	−5316.60	+	30152.0i	−0.184183	+	1.04455i	−0.927000	+	0.375060i	$0.877622\pi$
$942$	−3717.78	+	10600.4i	−0.128590	+	0.366645i
$943$	−37571.2	+	31526.0i	−1.29744	+	1.08868i
$944$	13771.4			0.474810
$945$	12343.0	+	6557.47i	0.424885	+	0.225730i
$946$	−2062.10			−0.0708716
$947$	−32615.3	+	27367.5i	−1.11917	+	0.939097i	−0.998562	−	0.0536035i	$-0.982929\pi$
$947$	−32615.3	+	27367.5i	−1.11917	+	0.939097i	−0.120609	+	0.992700i	$0.538485\pi$
$948$	−22389.3	−	26054.7i	−0.767059	−	0.892633i
$949$	−12038.7	+	68274.7i	−0.411793	+	2.33539i
$950$	−1696.99	+	617.654i	−0.0579554	+	0.0210940i
$951$	2679.14	+	7100.20i	0.0913535	+	0.242103i
$952$	1382.32	+	7839.51i	0.0470600	+	0.266891i
$953$	−12976.1	−	22475.2i	−0.441066	−	0.763949i	0.556703	−	0.830712i	$-0.312066\pi$
$953$	−12976.1	−	22475.2i	−0.441066	−	0.763949i	−0.997769	+	0.0667628i	$0.978733\pi$
$954$	4808.98	−	8800.67i	0.163204	−	0.298671i
$955$	−13897.5	+	24071.2i	−0.470904	+	0.815630i
$956$	−7860.97	−	2861.16i	−0.265943	−	0.0967954i
$957$	14897.5	−	8836.08i	0.503207	−	0.298464i
$958$	11227.2	+	9420.72i	0.378637	+	0.317714i
$959$	17958.5	+	15069.0i	0.604703	+	0.507406i
$960$	−32.5691	−	2771.90i	−0.00109496	−	0.0931903i
$961$	27082.4	+	9857.20i	0.909081	+	0.330878i
$962$	−14143.7	+	24497.7i	−0.474025	+	0.821036i
$963$	43267.6	−	16909.7i	1.44785	−	0.565843i
$964$	−8196.02	−	14195.9i	−0.273834	−	0.474294i
$965$	−2804.37	−	15904.3i	−0.0935500	−	0.530548i
$966$	−9815.23	+	11980.4i	−0.326915	+	0.399031i
$967$	22892.5	−	8332.21i	0.761298	−	0.277090i	0.0679459	−	0.997689i	$-0.478355\pi$
$967$	22892.5	−	8332.21i	0.761298	−	0.277090i	0.693352	+	0.720599i	$0.256133\pi$
$968$	−3510.02	+	19906.3i	−0.116546	+	0.660965i
$969$	−4390.83	+	827.527i	−0.145566	+	0.0274345i
$970$	3221.96	−	2703.54i	0.106650	−	0.0894902i
$971$	−45135.5			−1.49173			−0.745863	−	0.666100i	$-0.767963\pi$
$971$	−45135.5			−1.49173			−0.745863	+	0.666100i	$0.767963\pi$
$972$	−17347.0	−	18365.8i	−0.572433	−	0.606053i
$973$	11065.2			0.364578
$974$	−7286.48	+	6114.08i	−0.239706	+	0.201137i
$975$	24126.2	−	4546.99i	0.792468	−	0.149354i
$976$	1225.56	−	6950.48i	0.0401938	−	0.227950i
$977$	20539.4	−	7475.72i	0.672582	−	0.244800i	0.0169227	−	0.999857i	$-0.494613\pi$
$977$	20539.4	−	7475.72i	0.672582	−	0.244800i	0.655659	+	0.755057i	$0.272391\pi$
$978$	5510.27	−	6725.81i	0.180163	−	0.219906i
$979$	570.892	+	3237.69i	0.0186372	+	0.105697i
$980$	−4474.69	−	7750.40i	−0.145856	−	0.252630i
$981$	−7894.92	+	3085.46i	−0.256947	+	0.100419i
$982$	9417.31	−	16311.3i	0.306027	−	0.530054i
$983$	27661.4	+	10067.9i	0.897521	+	0.326671i	0.749259	−	0.662277i	$-0.230410\pi$
$983$	27661.4	+	10067.9i	0.897521	+	0.326671i	0.148262	+	0.988948i	$0.452632\pi$
$984$	254.386	+	21650.3i	0.00824138	+	0.701408i
$985$	26997.7	+	22653.8i	0.873319	+	0.732802i
$986$	−9142.78	−	7671.70i	−0.295300	−	0.247786i
$987$	16627.0	−	9861.87i	0.536214	−	0.318041i
$988$	10635.2	+	3870.90i	0.342461	+	0.124646i
$989$	15236.6	−	26390.6i	0.489884	−	0.848505i
$990$	−1340.17	+	2452.57i	−0.0430235	+	0.0787352i
$991$	2399.25	+	4155.62i	0.0769068	+	0.133206i	0.901914	−	0.431916i	$-0.142162\pi$
$991$	2399.25	+	4155.62i	0.0769068	+	0.133206i	−0.825007	+	0.565122i	$0.808829\pi$
$992$	−943.470	−	5350.68i	−0.0301968	−	0.171254i
$993$	−7587.30	−	20107.7i	−0.242473	−	0.642596i
$994$	2325.55	−	846.431i	0.0742072	−	0.0270092i
$995$	−2622.06	+	14870.4i	−0.0835425	+	0.473793i
$996$	−12992.5	−	15119.5i	−0.413337	−	0.481004i
$997$	−5408.95	+	4538.65i	−0.171819	+	0.144173i	−0.724642	−	0.689125i	$-0.757995\pi$
$997$	−5408.95	+	4538.65i	−0.171819	+	0.144173i	0.552823	+	0.833299i	$0.313550\pi$
$998$	−16416.7			−0.520703
$999$	1694.00	+	48040.1i	0.0536496	+	1.52144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.e.a.22.4	yes	48
3.2	odd	2		81.4.e.a.37.5		48
9.2	odd	6		243.4.e.b.190.4		48
9.4	even	3		243.4.e.d.28.4		48
9.5	odd	6		243.4.e.a.28.5		48
9.7	even	3		243.4.e.c.190.5		48
27.2	odd	18		243.4.e.b.55.4		48
27.4	even	9		729.4.a.d.1.10		24
27.7	even	9		243.4.e.d.217.4		48
27.11	odd	18		81.4.e.a.46.5		48
27.16	even	9	inner	27.4.e.a.16.4	✓	48
27.20	odd	18		243.4.e.a.217.5		48
27.23	odd	18		729.4.a.c.1.15		24
27.25	even	9		243.4.e.c.55.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.16.4	✓	48	27.16	even	9	inner
27.4.e.a.22.4	yes	48	1.1	even	1	trivial
81.4.e.a.37.5		48	3.2	odd	2
81.4.e.a.46.5		48	27.11	odd	18
243.4.e.a.28.5		48	9.5	odd	6
243.4.e.a.217.5		48	27.20	odd	18
243.4.e.b.55.4		48	27.2	odd	18
243.4.e.b.190.4		48	9.2	odd	6
243.4.e.c.55.5		48	27.25	even	9
243.4.e.c.190.5		48	9.7	even	3
243.4.e.d.28.4		48	9.4	even	3
243.4.e.d.217.4		48	27.7	even	9
729.4.a.c.1.15		24	27.23	odd	18
729.4.a.d.1.10		24	27.4	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.883701 + 0.741513i) q^{2} +(-5.10626 + 0.962362i) q^{3} +(-1.15810 + 6.56791i) q^{4} +(-7.21673 + 2.62667i) q^{5} +(3.79880 - 4.63680i) q^{6} +(2.25256 + 12.7749i) q^{7} +(-8.46114 - 14.6551i) q^{8} +(25.1477 - 9.82813i) q^{9} +O(q^{10})\)	\(q+(-0.883701 + 0.741513i) q^{2} +(-5.10626 + 0.962362i) q^{3} +(-1.15810 + 6.56791i) q^{4} +(-7.21673 + 2.62667i) q^{5} +(3.79880 - 4.63680i) q^{6} +(2.25256 + 12.7749i) q^{7} +(-8.46114 - 14.6551i) q^{8} +(25.1477 - 9.82813i) q^{9} +(4.42972 - 7.67249i) q^{10} +(-10.9793 - 3.99613i) q^{11} +(-0.407152 - 34.6519i) q^{12} +(54.8237 + 46.0025i) q^{13} +(-11.4633 - 9.61888i) q^{14} +(34.3227 - 20.3576i) q^{15} +(-31.7921 - 11.5714i) q^{16} +(-18.1319 + 31.4053i) q^{17} +(-14.9354 + 27.3325i) q^{18} +(-11.8561 - 20.5353i) q^{19} +(-8.89407 - 50.4408i) q^{20} +(-23.7962 - 63.0641i) q^{21} +(12.6656 - 4.60990i) q^{22} +(-34.5875 + 196.155i) q^{23} +(57.3083 + 66.6901i) q^{24} +(-50.5738 + 42.4365i) q^{25} -82.5592 q^{26} +(-118.952 + 74.3862i) q^{27} -86.5130 q^{28} +(218.552 - 183.387i) q^{29} +(-15.2356 + 43.4407i) q^{30} +(5.40959 - 30.6793i) q^{31} +(163.889 - 59.6507i) q^{32} +(59.9088 + 9.83923i) q^{33} +(-7.26431 - 41.1980i) q^{34} +(-49.8116 - 86.2762i) q^{35} +(35.4267 + 176.550i) q^{36} +(171.316 - 296.728i) q^{37} +(25.7044 + 9.35564i) q^{38} +(-324.215 - 182.141i) q^{39} +(99.5559 + 83.5374i) q^{40} +(188.628 + 158.278i) q^{41} +(67.7916 + 38.0846i) q^{42} +(-143.766 - 52.3265i) q^{43} +(38.9613 - 67.4830i) q^{44} +(-155.669 + 136.982i) q^{45} +(-114.887 - 198.990i) q^{46} +(49.8026 + 282.445i) q^{47} +(173.475 + 28.4910i) q^{48} +(164.191 - 59.7606i) q^{49} +(13.2249 - 75.0023i) q^{50} +(62.3628 - 177.813i) q^{51} +(-365.632 + 306.802i) q^{52} -321.986 q^{53} +(49.9601 - 153.940i) q^{54} +89.7310 q^{55} +(168.158 - 141.102i) q^{56} +(80.3025 + 93.4487i) q^{57} +(-57.1507 + 324.118i) q^{58} +(-382.499 + 139.218i) q^{59} +(93.9577 + 249.004i) q^{60} +(36.2242 + 205.438i) q^{61} +(17.9686 + 31.1226i) q^{62} +(182.200 + 299.121i) q^{63} +(34.7329 - 60.1591i) q^{64} +(-516.481 - 187.984i) q^{65} +(-60.2373 + 35.7282i) q^{66} +(-152.054 - 127.588i) q^{67} +(-185.269 - 155.459i) q^{68} +(-12.1599 - 1034.90i) q^{69} +(107.993 + 39.3064i) q^{70} +(-82.6900 + 143.223i) q^{71} +(-356.811 - 285.386i) q^{72} +(484.355 + 838.928i) q^{73} +(68.6357 + 389.252i) q^{74} +(217.404 - 265.362i) q^{75} +(148.605 - 54.0876i) q^{76} +(26.3187 - 149.261i) q^{77} +(421.569 - 79.4519i) q^{78} +(759.383 - 637.198i) q^{79} +259.829 q^{80} +(535.816 - 494.310i) q^{81} -284.056 q^{82} +(440.670 - 369.766i) q^{83} +(441.758 - 83.2568i) q^{84} +(48.3613 - 274.270i) q^{85} +(165.847 - 60.3633i) q^{86} +(-939.496 + 1146.74i) q^{87} +(34.3334 + 194.714i) q^{88} +(-140.691 - 243.684i) q^{89} +(35.9910 - 236.482i) q^{90} +(-464.184 + 803.990i) q^{91} +(-1248.27 - 454.335i) q^{92} +(1.90184 + 161.862i) q^{93} +(-253.447 - 212.667i) q^{94} +(139.502 + 117.056i) q^{95} +(-779.454 + 462.312i) q^{96} +(446.114 + 162.372i) q^{97} +(-100.782 + 174.560i) q^{98} +(-315.378 + 7.41226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more