LMFDB - Embedded newform 128.4.k.a.77.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(5,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("128.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.k (of order $32$, degree $16$, 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:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$752$
Relative dimension:	$47$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			77.8
Character	$\chi$	$=$	128.77
Dual form			128.4.k.a.5.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.50388 + 1.31551i) q^{2} +(3.59854 - 1.09161i) q^{3} +(4.53886 - 6.58777i) q^{4} +(17.1492 - 1.68905i) q^{5} +(-7.57431 + 7.46718i) q^{6} +(15.6405 - 23.4076i) q^{7} +(-2.69848 + 22.4659i) q^{8} +(-10.6918 + 7.14401i) q^{9} +O(q^{10})$	\(q+(-2.50388 + 1.31551i) q^{2} +(3.59854 - 1.09161i) q^{3} +(4.53886 - 6.58777i) q^{4} +(17.1492 - 1.68905i) q^{5} +(-7.57431 + 7.46718i) q^{6} +(15.6405 - 23.4076i) q^{7} +(-2.69848 + 22.4659i) q^{8} +(-10.6918 + 7.14401i) q^{9} +(-40.7177 + 26.7892i) q^{10} +(-28.5605 - 53.4329i) q^{11} +(9.14203 - 28.6610i) q^{12} +(-0.511368 + 5.19201i) q^{13} +(-8.36893 + 79.1852i) q^{14} +(59.8685 - 24.7983i) q^{15} +(-22.7975 - 59.8020i) q^{16} +(-80.8837 - 33.5031i) q^{17} +(17.3729 - 31.9529i) q^{18} +(73.5246 + 89.5900i) q^{19} +(66.7108 - 120.642i) q^{20} +(30.7310 - 101.307i) q^{21} +(141.804 + 96.2180i) q^{22} +(2.49549 - 12.5457i) q^{23} +(14.8134 + 83.7903i) q^{24} +(168.645 - 33.5456i) q^{25} +(-5.54974 - 13.6729i) q^{26} +(-95.0880 + 115.865i) q^{27} +(-83.2143 - 209.280i) q^{28} +(137.496 + 73.4934i) q^{29} +(-117.281 + 140.850i) q^{30} +(77.9132 - 77.9132i) q^{31} +(135.752 + 119.747i) q^{32} +(-161.104 - 161.104i) q^{33} +(246.597 - 22.5155i) q^{34} +(228.686 - 427.841i) q^{35} +(-1.46531 + 102.861i) q^{36} +(63.2608 + 51.9168i) q^{37} +(-301.954 - 127.600i) q^{38} +(3.82745 + 19.2419i) q^{39} +(-8.33075 + 389.831i) q^{40} +(-43.1213 - 8.57736i) q^{41} +(56.3232 + 294.087i) q^{42} +(349.605 + 106.051i) q^{43} +(-481.636 - 54.3744i) q^{44} +(-171.289 + 140.573i) q^{45} +(10.2556 + 34.6958i) q^{46} +(-91.6496 + 221.262i) q^{47} +(-147.318 - 190.314i) q^{48} +(-172.032 - 415.323i) q^{49} +(-378.138 + 305.849i) q^{50} +(-327.636 - 32.2693i) q^{51} +(31.8828 + 26.9346i) q^{52} +(-393.285 + 210.215i) q^{53} +(85.6674 - 415.202i) q^{54} +(-580.041 - 868.092i) q^{55} +(483.669 + 414.543i) q^{56} +(362.379 + 242.134i) q^{57} +(-440.956 - 3.14067i) q^{58} +(32.0245 + 325.150i) q^{59} +(108.369 - 506.956i) q^{60} +(-97.9212 - 322.803i) q^{61} +(-92.5898 + 297.581i) q^{62} +362.005i q^{63} +(-497.436 - 121.248i) q^{64} +89.9027i q^{65} +(615.319 + 191.451i) q^{66} +(86.9480 + 286.629i) q^{67} +(-587.831 + 380.778i) q^{68} +(-4.71482 - 47.8703i) q^{69} +(-9.77267 + 1372.10i) q^{70} +(642.110 + 429.044i) q^{71} +(-131.645 - 259.478i) q^{72} +(356.730 + 533.883i) q^{73} +(-226.695 - 46.7732i) q^{74} +(570.258 - 304.809i) q^{75} +(923.917 - 77.7271i) q^{76} +(-1697.44 - 167.183i) q^{77} +(-34.8964 - 43.1444i) q^{78} +(1.24529 + 3.00640i) q^{79} +(-491.968 - 987.051i) q^{80} +(-82.8355 + 199.983i) q^{81} +(119.254 - 35.2499i) q^{82} +(1030.37 - 845.600i) q^{83} +(-527.902 - 662.266i) q^{84} +(-1443.68 - 437.936i) q^{85} +(-1014.88 + 194.369i) q^{86} +(575.013 + 114.377i) q^{87} +(1277.49 - 497.450i) q^{88} +(151.696 + 762.627i) q^{89} +(243.962 - 577.311i) q^{90} +(113.535 + 93.1755i) q^{91} +(-71.3215 - 73.3829i) q^{92} +(195.324 - 365.425i) q^{93} +(-61.5924 - 674.579i) q^{94} +(1412.21 + 1412.21i) q^{95} +(619.227 + 282.726i) q^{96} +(835.073 - 835.073i) q^{97} +(977.112 + 813.610i) q^{98} +(687.087 + 367.255i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 5696 q^{50} - 16 q^{51} + 6608 q^{52} - 16 q^{53} + 3440 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 4768 q^{58} - 16 q^{59} - 9808 q^{60} - 16 q^{61} - 5872 q^{62} - 12112 q^{64} - 10960 q^{66} - 16 q^{67} - 4144 q^{68} - 16 q^{69} - 4048 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 5248 q^{74} - 16 q^{75} + 11888 q^{76} - 16 q^{77} + 14096 q^{78} - 16 q^{79} + 10016 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 5696 * q^50 - 16 * q^51 + 6608 * q^52 - 16 * q^53 + 3440 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 4768 * q^58 - 16 * q^59 - 9808 * q^60 - 16 * q^61 - 5872 * q^62 - 12112 * q^64 - 10960 * q^66 - 16 * q^67 - 4144 * q^68 - 16 * q^69 - 4048 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 5248 * q^74 - 16 * q^75 + 11888 * q^76 - 16 * q^77 + 14096 * q^78 - 16 * q^79 + 10016 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{31}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.50388	+	1.31551i	−0.885256	+	0.465104i
$2$	−2.50388	+	1.31551i	−0.885256	+	0.465104i
$3$	3.59854	−	1.09161i	0.692540	−	0.210080i	0.0756563	−	0.997134i	$-0.475895\pi$
$3$	3.59854	−	1.09161i	0.692540	−	0.210080i	0.616884	+	0.787054i	$0.288395\pi$
$4$	4.53886	−	6.58777i	0.567357	−	0.823472i
$5$	17.1492	−	1.68905i	1.53387	−	0.151073i	0.704474	−	0.709730i	$-0.251183\pi$
$5$	17.1492	−	1.68905i	1.53387	−	0.151073i	0.829399	+	0.558656i	$0.188683\pi$
$6$	−7.57431	+	7.46718i	−0.515367	+	0.508077i
$7$	15.6405	−	23.4076i	0.844507	−	1.26389i	−0.118103	−	0.993001i	$-0.537681\pi$
$7$	15.6405	−	23.4076i	0.844507	−	1.26389i	0.962610	−	0.270893i	$-0.0873188\pi$
$8$	−2.69848	+	22.4659i	−0.119257	+	0.992863i
$9$	−10.6918	+	7.14401i	−0.395991	+	0.264593i
$10$	−40.7177	+	26.7892i	−1.28761	+	0.847149i
$11$	−28.5605	−	53.4329i	−0.782846	−	1.46460i	−0.882870	−	0.469617i	$-0.844392\pi$
$11$	−28.5605	−	53.4329i	−0.782846	−	1.46460i	0.100025	−	0.994985i	$-0.468108\pi$
$12$	9.14203	−	28.6610i	0.219923	−	0.689477i
$13$	−0.511368	+	5.19201i	−0.0109099	+	0.110770i	−0.999097	−	0.0424804i	$-0.986474\pi$
$13$	−0.511368	+	5.19201i	−0.0109099	+	0.110770i	0.988187	+	0.153250i	$0.0489740\pi$
$14$	−8.36893	+	79.1852i	−0.159764	+	1.51165i
$15$	59.8685	−	24.7983i	1.03053	−	0.426860i
$16$	−22.7975	−	59.8020i	−0.356211	−	0.934405i
$17$	−80.8837	−	33.5031i	−1.15395	−	0.477983i	−0.278095	−	0.960553i	$-0.589703\pi$
$17$	−80.8837	−	33.5031i	−1.15395	−	0.477983i	−0.875857	+	0.482571i	$0.839703\pi$
$18$	17.3729	−	31.9529i	0.227491	−	0.418409i
$19$	73.5246	+	89.5900i	0.887774	+	1.08176i	0.996152	+	0.0876458i	$0.0279344\pi$
$19$	73.5246	+	89.5900i	0.887774	+	1.08176i	−0.108378	+	0.994110i	$0.534566\pi$
$20$	66.7108	−	120.642i	0.745850	−	1.34881i
$21$	30.7310	−	101.307i	0.319336	−	1.05271i
$22$	141.804	+	96.2180i	1.37421	+	0.932443i
$23$	2.49549	−	12.5457i	0.0226238	−	0.113737i	−0.967823	−	0.251631i	$-0.919033\pi$
$23$	2.49549	−	12.5457i	0.0226238	−	0.113737i	0.990447	+	0.137893i	$0.0440332\pi$
$24$	14.8134	+	83.7903i	0.125990	+	0.712651i
$25$	168.645	−	33.5456i	1.34916	−	0.268365i
$26$	−5.54974	−	13.6729i	−0.0418613	−	0.103134i
$27$	−95.0880	+	115.865i	−0.677766	+	0.825861i
$28$	−83.2143	−	209.280i	−0.561644	−	1.41251i
$29$	137.496	+	73.4934i	0.880429	+	0.470599i	0.848686	−	0.528897i	$-0.177394\pi$
$29$	137.496	+	73.4934i	0.880429	+	0.470599i	0.0317430	+	0.999496i	$0.489894\pi$
$30$	−117.281	+	140.850i	−0.713750	+	0.857184i
$31$	77.9132	−	77.9132i	0.451407	−	0.451407i	−0.444414	−	0.895821i	$-0.646588\pi$
$31$	77.9132	−	77.9132i	0.451407	−	0.451407i	0.895821	+	0.444414i	$0.146588\pi$
$32$	135.752	+	119.747i	0.749933	+	0.661513i
$33$	−161.104	−	161.104i	−0.849835	−	0.849835i
$34$	246.597	−	22.5155i	1.24386	−	0.113570i
$35$	228.686	−	427.841i	1.10443	−	2.06624i
$36$	−1.46531	+	102.861i	−0.00678382	+	0.476206i
$37$	63.2608	+	51.9168i	0.281081	+	0.230677i	0.764361	−	0.644789i	$-0.223055\pi$
$37$	63.2608	+	51.9168i	0.281081	+	0.230677i	−0.483280	+	0.875466i	$0.660555\pi$
$38$	−301.954	−	127.600i	−1.28904	−	0.544724i
$39$	3.82745	+	19.2419i	0.0157149	+	0.0790043i
$40$	−8.33075	+	389.831i	−0.0329302	+	1.54094i
$41$	−43.1213	−	8.57736i	−0.164254	−	0.0326722i	0.112278	−	0.993677i	$-0.464185\pi$
$41$	−43.1213	−	8.57736i	−0.164254	−	0.0326722i	−0.276532	+	0.961005i	$0.589185\pi$
$42$	56.3232	+	294.087i	0.206925	+	1.08044i
$43$	349.605	+	106.051i	1.23987	+	0.376109i	0.841068	−	0.540929i	$-0.181927\pi$
$43$	349.605	+	106.051i	1.23987	+	0.376109i	0.398798	+	0.917039i	$0.369427\pi$
$44$	−481.636	−	54.3744i	−1.65021	−	0.186301i
$45$	−171.289	+	140.573i	−0.567428	+	0.465676i
$46$	10.2556	+	34.6958i	0.0328718	+	0.111209i
$47$	−91.6496	+	221.262i	−0.284435	+	0.686688i	−0.999929	−	0.0119316i	$-0.996202\pi$
$47$	−91.6496	+	221.262i	−0.284435	+	0.686688i	0.715493	+	0.698620i	$0.246202\pi$
$48$	−147.318	−	190.314i	−0.442990	−	0.572281i
$49$	−172.032	−	415.323i	−0.501552	−	1.21085i
$50$	−378.138	+	305.849i	−1.06953	+	0.865070i
$51$	−327.636	−	32.2693i	−0.899573	−	0.0886002i
$52$	31.8828	+	26.9346i	0.0850258	+	0.0718299i
$53$	−393.285	+	210.215i	−1.01928	+	0.544816i	−0.894359	−	0.447350i	$-0.852368\pi$
$53$	−393.285	+	210.215i	−1.01928	+	0.544816i	−0.124921	+	0.992167i	$0.539868\pi$
$54$	85.6674	−	415.202i	0.215886	−	1.04633i
$55$	−580.041	−	868.092i	−1.42205	−	2.12825i
$56$	483.669	+	414.543i	1.15416	+	0.989208i
$57$	362.379	+	242.134i	0.842074	+	0.562656i
$58$	−440.956	−	3.14067i	−0.998283	−	0.00711018i
$59$	32.0245	+	325.150i	0.0706650	+	0.717474i	0.963611	+	0.267309i	$0.0861346\pi$
$59$	32.0245	+	325.150i	0.0706650	+	0.717474i	−0.892946	+	0.450164i	$0.851365\pi$
$60$	108.369	−	506.956i	0.233172	−	1.09080i
$61$	−97.9212	−	322.803i	−0.205533	−	0.677552i	−0.997733	−	0.0672908i	$-0.978564\pi$
$61$	−97.9212	−	322.803i	−0.205533	−	0.677552i	0.792200	−	0.610261i	$-0.208936\pi$
$62$	−92.5898	+	297.581i	−0.189660	+	0.609562i
$63$			362.005i			0.723942i
$64$	−497.436	−	121.248i	−0.971555	−	0.236812i
$65$			89.9027i			0.171555i
$66$	615.319	+	191.451i	1.14758	+	0.357061i
$67$	86.9480	+	286.629i	0.158543	+	0.522647i	0.999839	−	0.0179277i	$-0.00570687\pi$
$67$	86.9480	+	286.629i	0.158543	+	0.522647i	−0.841296	+	0.540575i	$0.818207\pi$
$68$	−587.831	+	380.778i	−1.04831	+	0.679060i
$69$	−4.71482	−	47.8703i	−0.00822605	−	0.0835204i
$70$	−9.77267	+	1372.10i	−0.0166865	+	2.34282i
$71$	642.110	+	429.044i	1.07330	+	0.717157i	0.961009	−	0.276518i	$-0.0891805\pi$
$71$	642.110	+	429.044i	1.07330	+	0.717157i	0.112293	+	0.993675i	$0.464180\pi$
$72$	−131.645	−	259.478i	−0.215480	−	0.424720i
$73$	356.730	+	533.883i	0.571946	+	0.855977i	0.998832	−	0.0483284i	$-0.0153894\pi$
$73$	356.730	+	533.883i	0.571946	+	0.855977i	−0.426886	+	0.904306i	$0.640389\pi$
$74$	−226.695	−	46.7732i	−0.356118	−	0.0734767i
$75$	570.258	−	304.809i	0.877969	−	0.469284i
$76$	923.917	−	77.7271i	1.39448	−	0.117315i
$77$	−1697.44	−	167.183i	−2.51222	−	0.247432i
$78$	−34.8964	−	43.1444i	−0.0506569	−	0.0626300i
$79$	1.24529	+	3.00640i	0.00177350	+	0.00428161i	0.924764	−	0.380542i	$-0.124262\pi$
$79$	1.24529	+	3.00640i	0.00177350	+	0.00428161i	−0.922990	+	0.384823i	$0.874262\pi$
$80$	−491.968	−	987.051i	−0.687547	−	1.37945i
$81$	−82.8355	+	199.983i	−0.113629	+	0.274325i
$82$	119.254	−	35.2499i	0.160603	−	0.0474719i
$83$	1030.37	−	845.600i	1.36262	−	1.11827i	0.381607	−	0.924325i	$-0.375371\pi$
$83$	1030.37	−	845.600i	1.36262	−	1.11827i	0.981012	−	0.193948i	$-0.0621292\pi$
$84$	−527.902	−	662.266i	−0.685700	−	0.860228i
$85$	−1443.68	−	437.936i	−1.84223	−	0.558834i
$86$	−1014.88	+	194.369i	−1.27253	+	0.243713i
$87$	575.013	+	114.377i	0.708596	+	0.140948i
$88$	1277.49	−	497.450i	1.54751	−	0.602595i
$89$	151.696	+	762.627i	0.180671	+	0.908295i	0.959640	+	0.281232i	$0.0907431\pi$
$89$	151.696	+	762.627i	0.180671	+	0.908295i	−0.778969	+	0.627063i	$0.784257\pi$
$90$	243.962	−	577.311i	0.285731	−	0.676155i
$91$	113.535	+	93.1755i	0.130788	+	0.107335i
$92$	−71.3215	−	73.3829i	−0.0808237	−	0.0831597i
$93$	195.324	−	365.425i	0.217786	−	0.407449i
$94$	−61.5924	−	674.579i	−0.0675827	−	0.740187i
$95$	1412.21	+	1412.21i	1.52516	+	1.52516i
$96$	619.227	+	282.726i	0.658330	+	0.300579i
$97$	835.073	−	835.073i	0.874112	−	0.874112i	−0.118806	−	0.992918i	$-0.537907\pi$
$97$	835.073	−	835.073i	0.874112	−	0.874112i	0.992918	+	0.118806i	$0.0379066\pi$
$98$	977.112	+	813.610i	1.00718	+	0.838643i
$99$	687.087	+	367.255i	0.697523	+	0.372834i
$100$	544.465	−	1263.25i	0.544465	−	1.26325i
$101$	−993.446	+	1210.52i	−0.978728	+	1.19258i	0.00255158	+	0.999997i	$0.499188\pi$
$101$	−993.446	+	1210.52i	−0.978728	+	1.19258i	−0.981280	+	0.192587i	$0.938312\pi$
$102$	862.813	−	350.210i	0.837561	−	0.339961i
$103$	−420.442	+	83.6312i	−0.402208	+	0.0800041i	−0.392049	−	0.919944i	$-0.628234\pi$
$103$	−420.442	+	83.6312i	−0.402208	+	0.0800041i	−0.0101587	+	0.999948i	$0.503234\pi$
$104$	−115.263	−	25.4989i	−0.108678	−	0.0240421i
$105$	355.902	−	1789.24i	0.330785	−	1.66297i
$106$	708.199	−	1043.72i	0.648928	−	0.956373i
$107$	447.641	−	1475.67i	0.404440	−	1.33326i	−0.484322	−	0.874890i	$-0.660934\pi$
$107$	447.641	−	1475.67i	0.404440	−	1.33326i	0.888762	−	0.458369i	$-0.151566\pi$
$108$	331.702	+	1152.31i	0.295537	+	1.02668i
$109$	−454.087	−	553.307i	−0.399024	−	0.486213i	0.534276	−	0.845310i	$-0.320584\pi$
$109$	−454.087	−	553.307i	−0.399024	−	0.486213i	−0.933300	+	0.359098i	$0.883084\pi$
$110$	2594.34	+	1410.55i	2.24873	+	1.22264i
$111$	284.319	+	117.769i	0.243121	+	0.100704i
$112$	−1756.39	−	401.696i	−1.48181	−	0.338899i
$113$	−1255.70	+	520.127i	−1.04536	+	0.433004i	−0.838234	−	0.545310i	$-0.816412\pi$
$113$	−1255.70	+	520.127i	−1.04536	+	0.433004i	−0.207129	+	0.978314i	$0.566412\pi$
$114$	−1225.88	−	129.561i	−1.00714	−	0.106443i
$115$	21.6055	−	219.364i	0.0175193	−	0.177876i
$116$	1108.23	−	572.219i	0.887043	−	0.458011i
$117$	−31.6243	−	59.1650i	−0.0249886	−	0.0467505i
$118$	−507.924	−	772.009i	−0.396256	−	0.602282i
$119$	−2049.29	+	1369.29i	−1.57864	+	1.05481i
$120$	395.564	+	1411.92i	0.300916	+	1.07408i
$121$	−1299.91	+	1945.45i	−0.976640	+	1.46165i
$122$	669.834	+	679.444i	0.497081	+	0.504213i
$123$	−164.537	+	16.2055i	−0.120616	+	0.0118797i
$124$	−159.637	−	866.911i	−0.115612	−	0.627830i
$125$	774.196	−	234.850i	0.553970	−	0.168045i
$126$	−476.221	−	906.418i	−0.336708	−	0.640874i
$127$	289.597			0.202343			0.101172	−	0.994869i	$-0.467741\pi$
$127$	289.597			0.202343			0.101172	+	0.994869i	$0.467741\pi$
$128$	1405.03	−	350.793i	0.970218	−	0.242234i
$129$	1373.84			0.937670
$130$	−118.268	−	225.106i	−0.0797907	−	0.151870i
$131$	−1919.67	+	582.327i	−1.28033	+	0.388383i	−0.855929	−	0.517094i	$-0.827014\pi$
$131$	−1919.67	+	582.327i	−1.28033	+	0.388383i	−0.424397	+	0.905476i	$0.639514\pi$
$132$	−1792.54	+	330.088i	−1.18198	+	0.217655i
$133$	3247.05	−	319.807i	2.11696	−	0.208502i
$134$	−594.772	−	603.305i	−0.383436	−	0.388937i
$135$	−1434.98	+	2147.60i	−0.914842	+	1.36916i
$136$	970.943	−	1726.72i	0.612189	−	1.08871i
$137$	−2594.24	+	1733.42i	−1.61782	+	1.08099i	−0.680369	+	0.732870i	$0.738180\pi$
$137$	−2594.24	+	1733.42i	−1.61782	+	1.08099i	−0.937449	+	0.348122i	$0.886820\pi$
$138$	74.7793	+	113.659i	0.0461278	+	0.0701110i
$139$	−944.601	−	1767.22i	−0.576403	−	1.07837i	−0.986100	−	0.166153i	$-0.946866\pi$
$139$	−944.601	−	1767.22i	−0.576403	−	1.07837i	0.409697	−	0.912222i	$-0.365634\pi$
$140$	−1780.55	−	3448.44i	−1.07488	−	2.08176i
$141$	−88.2744	+	896.265i	−0.0527237	+	0.535313i
$142$	−2172.18	−	229.573i	−1.28370	−	0.135672i
$143$	292.029	−	120.962i	0.170774	−	0.0707369i
$144$	670.971	+	476.523i	0.388294	+	0.275765i
$145$	2482.09	+	1028.12i	1.42156	+	0.588830i
$146$	−1595.54	−	867.500i	−0.904436	−	0.491745i
$147$	−1072.44	−	1306.77i	−0.601721	−	0.733199i
$148$	629.148	−	181.105i	0.349430	−	0.100586i
$149$	85.8869	−	283.131i	0.0472223	−	0.155671i	−0.930158	−	0.367158i	$-0.880331\pi$
$149$	85.8869	−	283.131i	0.0472223	−	0.155671i	0.977381	+	0.211487i	$0.0678307\pi$
$150$	−1026.88	+	1513.39i	−0.558962	+	0.823783i
$151$	−282.946	+	1422.47i	−0.152489	+	0.766614i	0.826538	+	0.562881i	$0.190307\pi$
$151$	−282.946	+	1422.47i	−0.152489	+	0.766614i	−0.979027	+	0.203732i	$0.934693\pi$
$152$	−2211.13	+	1410.04i	−1.17991	+	0.752431i
$153$	1104.14	−	219.626i	0.583426	−	0.116051i
$154$	4470.12	−	1814.39i	2.33904	−	0.949402i
$155$	1204.55	−	1467.75i	0.624206	−	0.760597i
$156$	144.133	+	62.1219i	0.0739738	+	0.0318829i
$157$	966.892	+	516.815i	0.491506	+	0.262715i	0.698478	−	0.715632i	$-0.253861\pi$
$157$	966.892	+	516.815i	0.491506	+	0.262715i	−0.206972	+	0.978347i	$0.566361\pi$
$158$	−7.07303	−	5.88949i	−0.00356139	−	0.00296546i
$159$	−1185.78	+	1185.78i	−0.591437	+	0.591437i
$160$	2530.31	+	1824.27i	1.25024	+	0.901383i
$161$	−254.634	−	254.634i	−0.124646	−	0.124646i
$162$	−55.6690	−	609.704i	−0.0269986	−	0.295697i
$163$	147.388	−	275.743i	0.0708239	−	0.132502i	−0.844017	−	0.536316i	$-0.819816\pi$
$163$	147.388	−	275.743i	0.0708239	−	0.132502i	0.914841	+	0.403814i	$0.132316\pi$
$164$	−252.227	+	245.142i	−0.120095	+	0.116722i
$165$	−3034.92	−	2490.69i	−1.43193	−	1.17515i
$166$	−1467.52	+	3472.74i	−0.686155	+	1.62372i
$167$	208.770	+	1049.56i	0.0967372	+	0.486331i	0.998532	+	0.0541662i	$0.0172501\pi$
$167$	208.770	+	1049.56i	0.0967372	+	0.486331i	−0.901795	+	0.432165i	$0.857750\pi$
$168$	2193.02	+	963.776i	1.00712	+	0.442601i
$169$	2128.09	+	423.303i	0.968634	+	0.192673i
$170$	4190.92	−	802.640i	1.89076	−	0.362116i
$171$	−1426.14	−	432.615i	−0.637776	−	0.193467i
$172$	2285.45	−	1821.77i	1.01316	−	0.807606i
$173$	1173.68	−	963.218i	0.515801	−	0.423307i	−0.340144	−	0.940373i	$-0.610476\pi$
$173$	1173.68	−	963.218i	0.515801	−	0.423307i	0.855945	+	0.517066i	$0.172976\pi$
$174$	−1590.23	+	470.049i	−0.692845	+	0.204795i
$175$	1852.47	−	4472.25i	0.800190	−	1.93183i
$176$	−2544.28	+	2926.11i	−1.08967	+	1.25320i
$177$	470.178	+	1135.11i	0.199665	+	0.482034i
$178$	−1383.07	−	1709.97i	−0.582392	−	0.720043i
$179$	−3466.78	−	341.448i	−1.44759	−	0.142576i	−0.656526	−	0.754303i	$-0.727975\pi$
$179$	−3466.78	−	341.448i	−1.44759	−	0.142576i	−0.791068	+	0.611728i	$0.790475\pi$
$180$	148.608	+	1766.45i	0.0615366	+	0.731465i
$181$	−2977.41	+	1591.46i	−1.22270	+	0.653548i	−0.951106	−	0.308864i	$-0.900051\pi$
$181$	−2977.41	+	1591.46i	−1.22270	+	0.653548i	−0.271596	+	0.962411i	$0.587551\pi$
$182$	−406.851	−	83.9444i	−0.165702	−	0.0341889i
$183$	−704.747	−	1054.73i	−0.284680	−	0.426054i
$184$	275.117	+	89.9179i	0.110228	+	0.0360263i
$185$	1172.56	+	783.482i	0.465992	+	0.311366i
$186$	−8.34698	+	1171.93i	−0.00329048	+	0.461990i
$187$	519.908	+	5278.72i	0.203313	+	2.06427i
$188$	1041.64	+	1608.04i	0.404091	+	0.623822i
$189$	1224.91	+	4037.97i	0.471422	+	1.55407i
$190$	−5393.80	−	1678.23i	−2.05951	−	0.640799i
$191$		−	1934.98i		−	0.733040i	−0.930410	−	0.366520i	$-0.880549\pi$
$191$		−	1934.98i		−	0.733040i	0.930410	−	0.366520i	$-0.119451\pi$
$192$	−1922.40	+	106.689i	−0.722591	+	0.0401022i
$193$		−	1920.20i		−	0.716161i	−0.933691	−	0.358080i	$-0.883431\pi$
$193$		−	1920.20i		−	0.716161i	0.933691	−	0.358080i	$-0.116569\pi$
$194$	−992.377	+	3189.47i	−0.367261	+	1.18037i
$195$	98.1384	+	323.519i	0.0360402	+	0.118809i
$196$	−3516.89	−	751.782i	−1.28166	−	0.273973i
$197$	−532.155	−	5403.06i	−0.192459	−	1.95407i	−0.285422	−	0.958402i	$-0.592134\pi$
$197$	−532.155	−	5403.06i	−0.192459	−	1.95407i	0.0929630	−	0.995670i	$-0.470366\pi$
$198$	−2203.51	−	15.6943i	−0.790893	−	0.00563307i
$199$	−1628.89	−	1088.39i	−0.580246	−	0.387708i	0.230529	−	0.973065i	$-0.425954\pi$
$199$	−1628.89	−	1088.39i	−0.580246	−	0.387708i	−0.810775	+	0.585357i	$0.800954\pi$
$200$	298.547	+	3879.29i	0.105552	+	1.37154i
$201$	625.773	+	936.535i	0.219595	+	0.328647i
$202$	895.023	−	4337.88i	0.311750	−	1.51095i
$203$	3870.82	−	2069.00i	1.33832	−	0.715345i
$204$	−1699.68	+	2011.93i	−0.583339	+	0.690505i
$205$	−753.985	−	74.2610i	−0.256881	−	0.0253006i
$206$	942.720	−	762.499i	0.318847	−	0.257892i
$207$	62.9453	+	151.963i	0.0211353	+	0.0510251i
$208$	322.150	−	87.7841i	0.107390	−	0.0292631i
$209$	2687.15	−	6487.36i	0.889351	−	2.14708i
$210$	1462.63	+	4948.23i	0.480623	+	1.62600i
$211$	1162.78	−	954.273i	0.379381	−	0.311350i	−0.425306	−	0.905050i	$-0.639833\pi$
$211$	1162.78	−	954.273i	0.379381	−	0.311350i	0.804687	+	0.593700i	$0.202333\pi$
$212$	−400.215	+	3545.01i	−0.129655	+	1.14845i
$213$	2779.01	+	843.003i	0.893965	+	0.271181i
$214$	820.426	+	4283.79i	0.262071	+	1.36838i
$215$	6174.58	+	1228.20i	1.95862	+	0.389593i
$216$	−2346.42	−	2448.90i	−0.739138	−	0.771419i
$217$	−605.164	−	3042.36i	−0.189314	−	0.951747i
$218$	1864.86	+	788.058i	0.579378	+	0.244835i
$219$	1866.50	+	1531.79i	0.575919	+	0.472644i
$220$	−8351.52	−	118.972i	−2.55936	−	0.0364595i
$221$	215.310	−	402.817i	0.0655354	−	0.122608i
$222$	−866.829	+	79.1457i	−0.262062	+	0.0239275i
$223$	1125.08	+	1125.08i	0.337852	+	0.337852i	0.855558	−	0.517707i	$-0.173214\pi$
$223$	1125.08	+	1125.08i	0.337852	+	0.337852i	−0.517707	+	0.855558i	$0.673214\pi$
$224$	4926.22	−	1304.75i	1.46941	−	0.389184i
$225$	−1563.46	+	1563.46i	−0.463248	+	0.463248i
$226$	2459.89	−	2954.22i	0.724023	−	0.869521i
$227$	−1759.00	−	940.206i	−0.514313	−	0.274906i	0.193756	−	0.981050i	$-0.437933\pi$
$227$	−1759.00	−	940.206i	−0.514313	−	0.274906i	−0.708068	+	0.706144i	$0.750433\pi$
$228$	3239.91	−	1288.26i	0.941088	−	0.374197i
$229$	−266.723	+	325.002i	−0.0769673	+	0.0937850i	−0.810071	−	0.586332i	$-0.800571\pi$
$229$	−266.723	+	325.002i	−0.0769673	+	0.0937850i	0.733103	+	0.680117i	$0.238071\pi$
$230$	234.478	+	577.684i	0.0672219	+	0.165615i
$231$	−6290.80	+	1251.32i	−1.79179	+	0.356410i
$232$	−2022.13	+	2890.67i	−0.572238	+	0.818024i
$233$	−862.637	+	4336.77i	−0.242546	+	1.21936i	0.646991	+	0.762498i	$0.276027\pi$
$233$	−862.637	+	4336.77i	−0.242546	+	1.21936i	−0.889537	+	0.456863i	$0.848973\pi$
$234$	157.016	+	106.540i	0.0438652	+	0.0297638i
$235$	−1198.00	+	3949.27i	−0.332548	+	1.09626i
$236$	2287.37	+	1264.84i	0.630912	+	0.348873i
$237$	7.76305	+	9.45931i	0.00212770	+	0.00259261i
$238$	3329.86	−	6124.41i	0.906904	−	1.66801i
$239$	−368.079	−	152.463i	−0.0996195	−	0.0412637i	0.332317	−	0.943168i	$-0.392170\pi$
$239$	−368.079	−	152.463i	−0.0996195	−	0.0412637i	−0.431937	+	0.901904i	$0.642170\pi$
$240$	−2847.84	−	3014.91i	−0.765947	−	0.810882i
$241$	−779.198	+	322.754i	−0.208268	+	0.0862674i	−0.484379	−	0.874858i	$-0.660954\pi$
$241$	−779.198	+	322.754i	−0.208268	+	0.0862674i	0.276111	+	0.961126i	$0.410954\pi$
$242$	695.556	−	6581.22i	0.184760	−	1.74817i
$243$	316.888	−	3217.42i	0.0836559	−	0.849373i
$244$	−2571.00	−	820.074i	−0.674556	−	0.215163i
$245$	−3651.73	−	6831.90i	−0.952246	−	1.78153i
$246$	390.663	−	257.027i	0.101251	−	0.0666156i
$247$	−502.750	+	335.927i	−0.129511	+	0.0865366i
$248$	1540.15	+	1960.64i	0.394352	+	0.502019i
$249$	2784.76	−	4167.68i	0.708742	−	1.06071i
$250$	−1629.55	+	1606.50i	−0.412247	+	0.406416i
$251$	−2705.78	+	266.496i	−0.680429	+	0.0670164i	−0.432326	−	0.901717i	$-0.642307\pi$
$251$	−2705.78	+	266.496i	−0.680429	+	0.0670164i	−0.248103	+	0.968734i	$0.579807\pi$
$252$	2384.81	+	1643.09i	0.596145	+	0.410734i
$253$	−741.625	+	224.969i	−0.184291	+	0.0559040i
$254$	−725.117	+	380.968i	−0.179126	+	0.0941105i
$255$	−5673.21			−1.39322
$256$	−3056.55	+	2726.67i	−0.746227	+	0.665691i
$257$	7568.21			1.83693			0.918467	−	0.395498i	$-0.129428\pi$
$257$	7568.21			1.83693			0.918467	+	0.395498i	$0.129428\pi$
$258$	−3439.92	+	1807.30i	−0.830078	+	0.436114i
$259$	2204.68	−	668.782i	0.528927	−	0.160448i
$260$	592.259	+	408.056i	0.141270	+	0.0973328i
$261$	−1995.12	+	196.502i	−0.473159	+	0.0466021i
$262$	4040.58	−	3983.43i	0.952778	−	0.939302i
$263$	1359.19	−	2034.18i	0.318675	−	0.476930i	−0.637203	−	0.770696i	$-0.719909\pi$
$263$	1359.19	−	2034.18i	0.318675	−	0.476930i	0.955877	+	0.293766i	$0.0949086\pi$
$264$	4054.08	−	3184.61i	0.945119	−	0.742421i
$265$	−6389.47	+	4269.31i	−1.48114	+	0.989666i
$266$	−7709.53	+	5072.29i	−1.77707	+	1.16918i
$267$	1378.37	+	2578.75i	0.315936	+	0.591076i
$268$	2282.89	+	728.176i	0.520336	+	0.165972i
$269$	−105.459	+	1070.75i	−0.0239032	+	0.242694i	0.975807	+	0.218633i	$0.0701596\pi$
$269$	−105.459	+	1070.75i	−0.0239032	+	0.242694i	−0.999710	+	0.0240611i	$0.992340\pi$
$270$	767.832	−	7265.09i	0.173070	−	1.63755i
$271$	790.786	−	327.554i	0.177258	−	0.0734225i	−0.292290	−	0.956330i	$-0.594417\pi$
$271$	790.786	−	327.554i	0.177258	−	0.0734225i	0.469547	+	0.882907i	$0.344417\pi$
$272$	−159.605	+	5600.79i	−0.0355790	+	1.24852i
$273$	510.270	+	211.361i	0.113124	+	0.0468577i
$274$	4215.35	−	7753.03i	0.929411	−	1.70941i
$275$	−6609.01	−	8053.11i	−1.44923	−	1.76589i
$276$	−336.759	−	186.217i	−0.0734438	−	0.0406120i
$277$	−1913.96	+	6309.49i	−0.415158	+	1.36859i	0.461355	+	0.887215i	$0.347363\pi$
$277$	−1913.96	+	6309.49i	−0.415158	+	1.36859i	−0.876513	+	0.481377i	$0.840137\pi$
$278$	4689.97	+	3182.29i	1.01182	+	0.686550i
$279$	−276.417	+	1389.64i	−0.0593142	+	0.298192i
$280$	8994.73	+	6292.15i	1.91978	+	1.34296i
$281$	3763.70	−	748.646i	0.799016	−	0.158934i	0.221336	−	0.975198i	$-0.428958\pi$
$281$	3763.70	−	748.646i	0.799016	−	0.158934i	0.577680	+	0.816263i	$0.303958\pi$
$282$	−958.018	−	2360.27i	−0.202302	−	0.498411i
$283$	5290.65	−	6446.68i	1.11130	−	1.35412i	0.182637	−	0.983180i	$-0.441537\pi$
$283$	5290.65	−	6446.68i	1.11130	−	1.35412i	0.928658	−	0.370937i	$-0.120963\pi$
$284$	5740.89	−	2282.70i	1.19950	−	0.476949i
$285$	6623.49	+	3540.33i	1.37664	+	0.735828i
$286$	−572.079	+	687.043i	−0.118279	+	0.142048i
$287$	−875.214	+	875.214i	−0.180008	+	0.180008i
$288$	−2306.90	−	310.487i	−0.471999	−	0.0635264i
$289$	1945.70	+	1945.70i	0.396032	+	0.396032i
$290$	−7567.36	+	690.938i	−1.53231	+	0.139908i
$291$	2093.48	−	3916.62i	0.421724	−	0.788991i
$292$	5136.25	+	73.1687i	1.02937	+	0.0146639i
$293$	6808.30	+	5587.43i	1.35749	+	1.11407i	0.982340	+	0.187102i	$0.0599095\pi$
$293$	6808.30	+	5587.43i	1.35749	+	1.11407i	0.375152	+	0.926963i	$0.377590\pi$
$294$	4404.32	+	1861.19i	0.873691	+	0.369207i
$295$	1098.39	+	5521.98i	0.216782	+	1.08984i
$296$	−1337.07	+	1281.12i	−0.262552	+	0.251565i
$297$	8906.76	+	1771.66i	1.74014	+	0.346136i
$298$	157.411	+	821.912i	0.0305993	+	0.159772i
$299$	63.8613	+	19.3721i	0.0123518	+	0.00374688i
$300$	580.306	−	5140.21i	0.111680	−	0.989235i
$301$	7950.41	−	6524.73i	1.52244	−	1.24943i
$302$	−1162.81	−	3933.91i	−0.221563	−	0.749573i
$303$	−2253.55	+	5440.55i	−0.427271	+	1.03152i
$304$	3681.48	−	6439.34i	0.694563	−	1.21487i
$305$	−2224.50	−	5370.43i	−0.417622	−	1.00823i
$306$	−2475.71	+	2002.42i	−0.462506	+	0.374088i
$307$	3494.89	+	344.217i	0.649720	+	0.0639919i	0.417508	−	0.908673i	$-0.362904\pi$
$307$	3494.89	+	344.217i	0.649720	+	0.0639919i	0.232212	+	0.972665i	$0.425404\pi$
$308$	−8805.79	+	10423.5i	−1.62908	+	1.92836i
$309$	−1421.69	+	759.908i	−0.261738	+	0.139902i
$310$	−1085.21	+	5259.68i	−0.198826	+	0.963644i
$311$	−1056.02	−	1580.44i	−0.192544	−	0.288163i	0.722619	−	0.691247i	$-0.242938\pi$
$311$	−1056.02	−	1580.44i	−0.192544	−	0.288163i	−0.915163	+	0.403084i	$0.867938\pi$
$312$	−442.615	+	34.0634i	−0.0803146	+	0.00618096i
$313$	−6193.88	−	4138.62i	−1.11853	−	0.747376i	−0.148148	−	0.988965i	$-0.547331\pi$
$313$	−6193.88	−	4138.62i	−1.11853	−	0.747376i	−0.970379	+	0.241589i	$0.922331\pi$
$314$	−3100.86	−	22.0856i	−0.557298	−	0.00396931i
$315$	611.445	+	6208.10i	0.109368	+	1.11043i
$316$	25.4577	+	5.44193i	0.00453199	+	0.000968775i
$317$	−2485.95	−	8195.09i	−0.440457	−	1.45199i	−0.843657	−	0.536882i	$-0.819602\pi$
$317$	−2485.95	−	8195.09i	−0.440457	−	1.45199i	0.403200	−	0.915112i	$-0.367898\pi$
$318$	1409.15	−	4528.96i	0.248494	−	0.798653i
$319$		−	9445.83i		−	1.65788i
$320$	−8735.44	−	1239.11i	−1.52602	−	0.216464i
$321$		−	5798.92i		−	1.00830i
$322$	972.549	+	302.600i	0.168317	+	0.0523703i
$323$	−2945.40	−	9709.68i	−0.507388	−	1.67263i
$324$	941.461	+	1453.39i	0.161430	+	0.249210i
$325$	87.9292	+	892.760i	0.0150075	+	0.152374i
$326$	−6.29848	+	884.318i	−0.00107006	+	0.150239i
$327$	−2238.05	−	1495.41i	−0.378484	−	0.252895i
$328$	309.061	−	945.615i	0.0520275	−	0.159186i
$329$	3745.77	+	5605.94i	0.627693	+	0.939409i
$330$	10875.6	+	2243.93i	1.81419	+	0.374317i
$331$	−7792.79	+	4165.33i	−1.29405	+	0.691684i	−0.967350	−	0.253444i	$-0.918437\pi$
$331$	−7792.79	+	4165.33i	−1.29405	+	0.691684i	−0.326700	+	0.945128i	$0.605937\pi$
$332$	−893.932	−	10625.9i	−0.147774	−	1.75654i
$333$	−1047.26	−	103.146i	−0.172341	−	0.0169741i
$334$	−1903.44	−	2353.33i	−0.311831	−	0.385535i
$335$	1975.22	+	4768.61i	0.322143	+	0.777723i
$336$	−6758.93	+	471.764i	−1.09741	+	0.0765977i
$337$	−2537.16	+	6125.24i	−0.410112	+	0.990098i	0.574995	+	0.818157i	$0.305004\pi$
$337$	−2537.16	+	6125.24i	−0.410112	+	0.990098i	−0.985107	+	0.171941i	$0.944996\pi$
$338$	−5885.35	+	1739.62i	−0.947103	+	0.279950i
$339$	−3950.91	+	3242.43i	−0.632991	+	0.519482i
$340$	−9437.70	+	7522.92i	−1.50538	+	1.19996i
$341$	−6388.36	−	1937.89i	−1.01451	−	0.307749i
$342$	4140.00	−	792.886i	0.654577	−	0.125364i
$343$	−2941.77	−	585.154i	−0.463092	−	0.0921147i
$344$	−3325.95	+	7568.02i	−0.521288	+	1.18616i
$345$	−161.711	−	812.976i	−0.0252354	−	0.126867i
$346$	−1671.64	+	3955.78i	−0.259735	+	0.614636i
$347$	3804.76	+	3122.48i	0.588617	+	0.483065i	0.880923	−	0.473260i	$-0.156923\pi$
$347$	3804.76	+	3122.48i	0.588617	+	0.483065i	−0.292306	+	0.956325i	$0.594423\pi$
$348$	3363.39	−	3268.91i	0.518094	−	0.503540i
$349$	−866.778	+	1621.63i	−0.132944	+	0.248721i	−0.939581	−	0.342326i	$-0.888785\pi$
$349$	−866.778	+	1621.63i	−0.132944	+	0.248721i	0.806637	+	0.591047i	$0.201285\pi$
$350$	1244.94	+	13634.9i	0.190128	+	2.08234i
$351$	−552.947	−	552.947i	−0.0840859	−	0.0840859i
$352$	2521.26	−	10673.7i	0.381771	−	1.61622i
$353$	2087.83	−	2087.83i	0.314799	−	0.314799i	−0.531966	−	0.846766i	$-0.678547\pi$
$353$	2087.83	−	2087.83i	0.314799	−	0.314799i	0.846766	+	0.531966i	$0.178547\pi$
$354$	−2670.52	−	2223.66i	−0.400950	−	0.333859i
$355$	11736.4	+	6273.22i	1.75465	+	0.937881i
$356$	5712.54	+	2462.12i	0.850461	+	0.366550i
$357$	−5879.73	+	7164.48i	−0.871677	+	1.06214i
$358$	9129.59	−	3705.64i	1.34780	−	0.547065i
$359$	−8890.96	+	1768.52i	−1.30709	+	0.259997i	−0.799014	−	0.601313i	$-0.794645\pi$
$359$	−8890.96	+	1768.52i	−1.30709	+	0.259997i	−0.508080	+	0.861310i	$0.669645\pi$
$360$	−2695.89	−	4227.50i	−0.394683	−	0.618913i
$361$	−1282.38	+	6446.93i	−0.186962	+	0.939923i
$362$	5361.50	−	7901.64i	0.778437	−	1.14724i
$363$	−2554.11	+	8419.77i	−0.369300	+	1.21742i
$364$	1129.14	−	325.030i	0.162590	−	0.0468028i
$365$	7019.39	+	8553.15i	1.00661	+	1.22655i
$366$	3152.11	+	1713.81i	0.450174	+	0.244761i
$367$	7050.99	+	2920.61i	1.00288	+	0.415408i	0.822854	−	0.568253i	$-0.192380\pi$
$367$	7050.99	+	2920.61i	1.00288	+	0.415408i	0.180030	+	0.983661i	$0.442380\pi$
$368$	−807.148	+	136.775i	−0.114336	+	0.0193747i
$369$	522.320	−	216.352i	0.0736880	−	0.0305226i
$370$	−3966.64	−	419.226i	−0.557340	−	0.0589041i
$371$	−1230.53	+	12493.7i	−0.172199	+	1.74836i
$372$	−1520.79	−	2945.36i	−0.211960	−	0.410510i
$373$	−3713.58	−	6947.62i	−0.515501	−	0.964435i	−0.996162	−	0.0875283i	$-0.972103\pi$
$373$	−3713.58	−	6947.62i	−0.515501	−	0.964435i	0.480661	−	0.876907i	$-0.340397\pi$
$374$	−8246.00	−	12533.3i	−1.14008	−	1.73284i
$375$	2529.62	−	1690.23i	0.348343	−	0.232756i
$376$	−4723.54	−	2656.06i	−0.647866	−	0.364298i
$377$	−451.890	+	676.301i	−0.0617334	+	0.0923906i
$378$	−8379.02	−	8499.23i	−1.14013	−	1.15649i
$379$	−3114.13	+	306.715i	−0.422064	+	0.0415697i	−0.306820	−	0.951768i	$-0.599265\pi$
$379$	−3114.13	+	306.715i	−0.422064	+	0.0415697i	−0.115244	+	0.993337i	$0.536765\pi$
$380$	15713.2	−	2893.50i	2.12123	−	0.390615i
$381$	1042.13	−	316.126i	0.140131	−	0.0425082i
$382$	2545.49	+	4844.97i	0.340939	+	0.648928i
$383$	−1912.19			−0.255114			−0.127557	−	0.991831i	$-0.540714\pi$
$383$	−1912.19			−0.255114			−0.127557	+	0.991831i	$0.540714\pi$
$384$	4673.12	−	2796.08i	0.621026	−	0.371580i
$385$	−29392.1			−3.89081
$386$	2526.04	+	4807.96i	0.333089	+	0.633986i
$387$	−4495.53	+	1363.70i	−0.590492	+	0.179124i
$388$	−1710.99	−	9291.55i	−0.223872	−	1.21574i
$389$	−12774.0	+	1258.13i	−1.66495	+	0.163984i	−0.886186	−	0.463329i	$-0.846655\pi$
$389$	−12774.0	+	1258.13i	−1.66495	+	0.163984i	−0.778767	+	0.627313i	$0.784155\pi$
$390$	−671.320	−	680.951i	−0.0871631	−	0.0884136i
$391$	−622.165	+	931.136i	−0.0804712	+	0.120434i
$392$	9794.85	−	2744.13i	1.26203	−	0.353570i
$393$	−6272.36	+	4191.06i	−0.805086	+	0.537941i
$394$	8440.24	+	12828.6i	1.07922	+	1.64034i
$395$	26.4338	+	49.4541i	0.00336716	+	0.00629951i
$396$	5537.99	−	2859.45i	0.702763	−	0.362861i
$397$	266.156	−	2702.33i	0.0336473	−	0.341627i	−0.963592	−	0.267376i	$-0.913843\pi$
$397$	266.156	−	2702.33i	0.0336473	−	0.341627i	0.997240	−	0.0742508i	$-0.0236565\pi$
$398$	5510.34	+	582.377i	0.693991	+	0.0733465i
$399$	11335.6	−	4695.34i	1.42227	−	0.589125i
$400$	−5850.78	−	9320.54i	−0.731347	−	1.16507i
$401$	5152.48	+	2134.23i	0.641652	+	0.265781i	0.679695	−	0.733495i	$-0.262112\pi$
$401$	5152.48	+	2134.23i	0.641652	+	0.265781i	−0.0380429	+	0.999276i	$0.512112\pi$
$402$	−2798.88	−	1521.76i	−0.347253	−	0.188803i
$403$	364.684	+	444.368i	0.0450774	+	0.0549270i
$404$	3465.50	+	12039.0i	0.426770	+	1.48258i
$405$	−1082.78	+	3569.46i	−0.132849	+	0.437946i
$406$	−6970.29	+	10272.6i	−0.852043	+	1.25572i
$407$	967.305	−	4862.97i	0.117807	−	0.592257i
$408$	1609.08	−	7273.57i	0.195248	−	0.882587i
$409$	−82.0355	+	16.3179i	−0.00991784	+	0.00197278i	−0.200047	−	0.979786i	$-0.564109\pi$
$409$	−82.0355	+	16.3179i	−0.00991784	+	0.00197278i	0.190129	+	0.981759i	$0.439109\pi$
$410$	1985.58	−	805.935i	0.239173	−	0.0970787i
$411$	−7443.29	+	9069.67i	−0.893310	+	1.08850i
$412$	−1357.38	+	3149.37i	−0.162314	+	0.376598i
$413$	8111.88	+	4335.89i	0.966488	+	0.516598i
$414$	−357.517	−	297.693i	−0.0424421	−	0.0353402i
$415$	16241.7	−	16241.7i	1.92114	−	1.92114i
$416$	−691.146	+	643.593i	−0.0814572	+	0.0758528i
$417$	−5328.30	−	5328.30i	−0.625727	−	0.625727i
$418$	1805.88	+	19778.6i	0.211312	+	2.31436i
$419$	725.370	−	1357.07i	0.0845744	−	0.158228i	−0.836078	−	0.548610i	$-0.815157\pi$
$419$	725.370	−	1357.07i	0.0845744	−	0.158228i	0.920653	+	0.390382i	$0.127657\pi$
$420$	−10171.7	−	10465.7i	−1.18173	−	1.21589i
$421$	4465.46	+	3664.71i	0.516943	+	0.424244i	0.856350	−	0.516395i	$-0.172726\pi$
$421$	4465.46	+	3664.71i	0.516943	+	0.424244i	−0.339407	+	0.940640i	$0.610226\pi$
$422$	−1656.12	+	3919.04i	−0.191039	+	0.452076i
$423$	−600.800	−	3020.42i	−0.0690588	−	0.347182i
$424$	−3661.41	−	9402.77i	−0.419372	−	1.07698i
$425$	−14764.5	−	2936.84i	−1.68514	−	0.335195i
$426$	−8067.29	+	1545.04i	−0.917515	+	0.175721i
$427$	−9087.59	−	2756.69i	−1.02993	−	0.312425i
$428$	−7689.62	−	9646.83i	−0.868439	−	1.08948i
$429$	918.836	−	754.069i	0.103407	−	0.0848643i
$430$	−17076.1	+	5047.46i	−1.91508	+	0.566070i
$431$	1865.64	−	4504.04i	0.208502	−	0.503369i	−0.784685	−	0.619894i	$-0.787175\pi$
$431$	1865.64	−	4504.04i	0.208502	−	0.503369i	0.993188	+	0.116525i	$0.0371755\pi$
$432$	9096.72	+	3045.01i	1.01312	+	0.339128i
$433$	−1003.43	−	2422.51i	−0.111367	−	0.268864i	0.858363	−	0.513043i	$-0.171482\pi$
$433$	−1003.43	−	2422.51i	−0.111367	−	0.268864i	−0.969730	+	0.244178i	$0.921482\pi$
$434$	5517.52	+	6821.62i	0.610253	+	0.754490i
$435$	10054.2	+	990.254i	1.10819	+	0.109147i
$436$	−5706.10	+	480.041i	−0.626772	+	0.0527289i
$437$	1307.45	−	698.846i	0.143121	−	0.0764996i
$438$	−6688.58	−	1380.04i	−0.729664	−	0.150549i
$439$	191.599	+	286.748i	0.0208303	+	0.0311748i	0.841739	−	0.539885i	$-0.181532\pi$
$439$	191.599	+	286.748i	0.0208303	+	0.0311748i	−0.820908	+	0.571060i	$0.806532\pi$
$440$	21067.7	−	10688.6i	2.28265	−	1.15809i
$441$	4806.40	+	3211.54i	0.518994	+	0.346781i
$442$	−9.20108	+	1291.85i	−0.000990160	+	0.139020i
$443$	−53.8450	−	546.697i	−0.00577483	−	0.0586329i	0.991865	−	0.127291i	$-0.0406282\pi$
$443$	−53.8450	−	546.697i	−0.00577483	−	0.0586329i	−0.997640	+	0.0686582i	$0.978128\pi$
$444$	2066.32	−	1338.49i	0.220863	−	0.143068i
$445$	3889.58	+	12822.2i	0.414346	+	1.36592i
$446$	−4297.13	−	1337.01i	−0.456221	−	0.141949i
$447$		−	1112.61i		−	0.117729i
$448$	−10618.3	+	9747.44i	−1.11979	+	1.02795i
$449$			3457.02i			0.363356i	0.983358	+	0.181678i	$0.0581528\pi$
$449$			3457.02i			0.363356i	−0.983358	+	0.181678i	$0.941847\pi$
$450$	1857.97	−	5971.48i	0.194635	−	0.625552i
$451$	773.252	+	2549.07i	0.0807339	+	0.266144i
$452$	−2272.96	+	10633.0i	−0.236528	+	1.10649i
$453$	534.579	+	5427.67i	0.0554453	+	0.562945i
$454$	5641.18	+	40.1788i	0.583158	+	0.00415350i
$455$	2104.41	+	1406.12i	0.216827	+	0.144879i
$456$	−6417.63	+	7487.78i	−0.659064	+	0.768964i
$457$	−3324.33	−	4975.21i	−0.340275	−	0.509257i	0.621384	−	0.783506i	$-0.286571\pi$
$457$	−3324.33	−	4975.21i	−0.340275	−	0.509257i	−0.961659	+	0.274249i	$0.911571\pi$
$458$	240.298	−	1164.64i	0.0245161	−	0.118822i
$459$	11572.9	−	6185.85i	1.17686	−	0.629043i
$460$	−1347.06	−	1137.99i	−0.136537	−	0.115346i
$461$	1800.77	+	177.361i	0.181931	+	0.0179187i	0.188572	−	0.982059i	$-0.439614\pi$
$461$	1800.77	+	177.361i	0.181931	+	0.0179187i	−0.00664113	+	0.999978i	$0.502114\pi$
$462$	14105.3	−	11408.8i	1.42043	−	1.14888i
$463$	2186.49	+	5278.66i	0.219470	+	0.529849i	0.994816	−	0.101688i	$-0.0324244\pi$
$463$	2186.49	+	5278.66i	0.219470	+	0.529849i	−0.775346	+	0.631537i	$0.782424\pi$
$464$	1260.47	−	9898.02i	0.126112	−	0.990310i
$465$	2732.43	−	6596.66i	0.272502	−	0.657877i
$466$	−3545.13	−	11993.6i	−0.352414	−	1.19226i
$467$	−7666.97	+	6292.12i	−0.759711	+	0.623479i	−0.932371	−	0.361503i	$-0.882264\pi$
$467$	−7666.97	+	6292.12i	−0.759711	+	0.623479i	0.172660	+	0.984981i	$0.444764\pi$
$468$	−533.304	−	60.2075i	−0.0526752	−	0.00594678i
$469$	8069.23	+	2447.77i	0.794461	+	0.240997i
$470$	−2195.66	−	11464.5i	−0.215486	−	1.12514i
$471$	4043.56	+	804.314i	0.395578	+	0.0786855i
$472$	−7391.22	−	157.951i	−0.720781	−	0.0154032i
$473$	−4318.24	−	21709.3i	−0.419774	−	2.11035i
$474$	−31.8816	−	13.4726i	−0.00308939	−	0.00130552i
$475$	15404.9	+	12642.5i	1.48805	+	1.22121i
$476$	−280.855	+	19715.3i	−0.0270441	+	1.89842i
$477$	2703.13	−	5057.20i	0.259471	−	0.485437i
$478$	1122.19	−	102.462i	0.107381	−	0.00980439i
$479$	−11298.3	−	11298.3i	−1.07773	−	1.07773i	−0.996713	−	0.0810123i	$-0.974185\pi$
$479$	−11298.3	−	11298.3i	−1.07773	−	1.07773i	−0.0810123	−	0.996713i	$-0.525815\pi$
$480$	11096.8	+	3802.62i	1.05520	+	0.361594i
$481$	−301.902	+	301.902i	−0.0286186	+	0.0286186i
$482$	1526.43	−	1833.18i	0.144247	−	0.173235i
$483$	−1194.27	−	638.353i	−0.112508	−	0.0601367i
$484$	6916.08	+	17393.6i	0.649519	+	1.63351i
$485$	12910.4	−	15731.3i	1.20872	−	1.47283i
$486$	3439.10	+	8472.91i	0.320989	+	0.790821i
$487$	−13595.7	+	2704.34i	−1.26505	+	0.251634i	−0.781622	−	0.623752i	$-0.785607\pi$
$487$	−13595.7	+	2704.34i	−1.26505	+	0.251634i	−0.483425	+	0.875386i	$0.660607\pi$
$488$	7516.31	−	1328.81i	0.697228	−	0.123263i
$489$	229.378	−	1153.16i	0.0212124	−	0.106642i
$490$	18130.9	+	12302.4i	1.67158	+	1.13421i
$491$	4764.59	−	15706.7i	0.437928	−	1.44366i	−0.409286	−	0.912406i	$-0.634222\pi$
$491$	4764.59	−	15706.7i	0.437928	−	1.44366i	0.847215	−	0.531251i	$-0.178278\pi$
$492$	−640.053	+	1157.49i	−0.0586500	+	0.106064i
$493$	−8658.97	−	10551.0i	−0.791035	−	0.963879i
$494$	816.912	−	1502.50i	0.0744021	−	0.136843i
$495$	12403.3	+	5137.62i	1.12624	+	0.466503i
$496$	−6435.59	−	2883.13i	−0.582594	−	0.261001i
$497$	20085.8	−	8319.82i	1.81282	−	0.750895i
$498$	−1490.07	+	14098.8i	−0.134080	+	1.26864i
$499$	507.370	−	5151.41i	0.0455170	−	0.462142i	−0.945228	−	0.326410i	$-0.894161\pi$
$499$	507.370	−	5151.41i	0.0455170	−	0.462142i	0.990745	−	0.135733i	$-0.0433388\pi$
$500$	1966.83	−	6166.18i	0.175919	−	0.551520i
$501$	1896.97	+	3548.99i	0.169163	+	0.316481i
$502$	6424.39	−	4226.77i	0.571184	−	0.375796i
$503$	12259.6	−	8191.63i	1.08674	−	0.726137i	0.122848	−	0.992426i	$-0.460797\pi$
$503$	12259.6	−	8191.63i	1.08674	−	0.726137i	0.963893	+	0.266289i	$0.0857974\pi$
$504$	−8132.78	−	976.863i	−0.718775	−	0.0863352i
$505$	−14992.2	+	22437.4i	−1.32108	+	1.97713i
$506$	1560.99	−	1538.91i	0.137143	−	0.135204i
$507$	8120.11	−	799.761i	0.711295	−	0.0700564i
$508$	1314.44	−	1907.80i	0.114801	−	0.166624i
$509$	385.220	−	116.855i	0.0335453	−	0.0101759i	−0.273467	−	0.961881i	$-0.588171\pi$
$509$	385.220	−	116.855i	0.0335453	−	0.0101759i	0.307013	+	0.951705i	$0.400671\pi$
$510$	14205.0	−	7463.17i	1.23335	−	0.647990i
$511$	18076.4			1.56488
$512$	4066.27	−	10848.2i	0.350987	−	0.936380i
$513$	−17371.7			−1.49508
$514$	−18949.9	+	9956.07i	−1.62616	+	0.854365i
$515$	−7069.00	+	2144.36i	−0.604849	+	0.183479i
$516$	6235.64	−	9050.51i	0.531994	−	0.772145i
$517$	14440.2	−	1422.24i	1.22839	−	0.120986i
$518$	−4640.47	+	4574.83i	−0.393611	+	0.388043i
$519$	3172.10	−	4747.39i	0.268285	−	0.401517i
$520$	−2019.75	−	242.601i	−0.170330	−	0.0204591i
$521$	2220.32	−	1483.57i	0.186706	−	0.124753i	−0.458704	−	0.888589i	$-0.651686\pi$
$521$	2220.32	−	1483.57i	0.186706	−	0.124753i	0.645410	+	0.763836i	$0.276686\pi$
$522$	4737.04	−	3116.62i	0.397193	−	0.261323i
$523$	−15.0367	−	28.1316i	−0.00125718	−	0.00235202i	0.881292	−	0.472572i	$-0.156674\pi$
$523$	−15.0367	−	28.1316i	−0.00125718	−	0.00235202i	−0.882549	+	0.470220i	$0.844174\pi$
$524$	−4876.89	+	15289.5i	−0.406580	+	1.27466i
$525$	1784.25	−	18115.7i	0.148325	−	1.50597i
$526$	−727.278	+	6881.37i	−0.0602868	+	0.570422i
$527$	−8912.25	+	3691.57i	−0.736667	+	0.305138i
$528$	−5961.55	+	13307.1i	−0.491370	+	1.09681i
$529$	11089.7	+	4593.49i	0.911455	+	0.377537i
$530$	10382.2	−	19095.3i	0.850891	−	1.56499i
$531$	−2665.27	−	3247.65i	−0.217821	−	0.265416i
$532$	12631.1	−	22842.4i	1.02937	−	1.86155i
$533$	66.5846	−	219.500i	0.00541107	−	0.0178379i
$534$	−6843.66	−	4643.63i	−0.554596	−	0.376310i
$535$	5184.20	−	26062.7i	0.418940	−	2.10615i
$536$	−6674.02	+	1179.91i	−0.537824	+	0.0950824i
$537$	−12848.1	+	2555.64i	−1.03247	+	0.205371i
$538$	−1144.52	−	2819.76i	−0.0917172	−	0.225964i
$539$	−17278.6	+	21054.0i	−1.38078	+	1.68249i
$540$	7634.74	+	19201.0i	0.608420	+	1.53015i
$541$	636.802	+	340.378i	0.0506068	+	0.0270499i	0.496506	−	0.868033i	$-0.334616\pi$
$541$	636.802	+	340.378i	0.0506068	+	0.0270499i	−0.445899	+	0.895083i	$0.647116\pi$
$542$	−1549.13	+	1860.44i	−0.122769	+	0.147441i
$543$	−8977.09	+	8977.09i	−0.709473	+	0.709473i
$544$	−6968.28	−	14233.7i	−0.549196	−	1.12181i
$545$	−8721.81	−	8721.81i	−0.685507	−	0.685507i
$546$	−1555.71	+	142.044i	−0.121938	+	0.0111335i
$547$	6309.55	−	11804.3i	0.493193	−	0.922700i	−0.505029	−	0.863102i	$-0.668518\pi$
$547$	6309.55	−	11804.3i	0.493193	−	0.922700i	0.998222	−	0.0595974i	$-0.0189817\pi$
$548$	−355.541	+	24958.0i	−0.0277152	+	1.94554i
$549$	3353.06	+	2751.78i	0.260665	+	0.213922i
$550$	27142.2	+	11469.8i	2.10426	+	0.889226i
$551$	3525.10	+	17721.9i	0.272549	+	1.37019i
$552$	1088.17	+	23.2544i	0.0839054	+	0.00179307i
$553$	89.8498	+	17.8722i	0.00690923	+	0.00137433i
$554$	−3507.86	−	18316.1i	−0.269016	−	1.40465i
$555$	5074.77	+	1539.42i	0.388130	+	0.117738i
$556$	−15929.5	−	1798.36i	−1.21504	−	0.137172i
$557$	−6588.39	+	5406.96i	−0.501184	+	0.411311i	−0.850726	−	0.525610i	$-0.823837\pi$
$557$	−6588.39	+	5406.96i	−0.501184	+	0.411311i	0.349542	+	0.936921i	$0.386337\pi$
$558$	−1135.97	−	3843.13i	−0.0861821	−	0.291564i
$559$	−729.397	+	1760.92i	−0.0551882	+	0.133236i
$560$	−30799.2	−	3922.14i	−2.32411	−	0.295966i
$561$	7633.19	+	18428.2i	0.574463	+	1.38688i
$562$	−8439.01	+	6825.71i	−0.633413	+	0.512323i
$563$	−3936.56	−	387.718i	−0.294683	−	0.0290237i	−0.0504044	−	0.998729i	$-0.516051\pi$
$563$	−3936.56	−	387.718i	−0.294683	−	0.0290237i	−0.244278	+	0.969705i	$0.578551\pi$
$564$	5503.73	+	4649.55i	0.410902	+	0.347130i
$565$	−20655.7	+	11040.7i	−1.53804	+	0.822099i
$566$	−4766.49	+	23101.6i	−0.353976	+	1.71561i
$567$	3385.53	+	5066.81i	0.250757	+	0.375284i
$568$	−11371.6	+	13267.8i	−0.840038	+	0.980116i
$569$	−4070.43	−	2719.78i	−0.299897	−	0.200385i	0.396513	−	0.918029i	$-0.370220\pi$
$569$	−4070.43	−	2719.78i	−0.299897	−	0.200385i	−0.696410	+	0.717644i	$0.745220\pi$
$570$	−21241.8	−	151.293i	−1.56091	−	0.0111175i
$571$	−1130.88	−	11482.0i	−0.0828826	−	0.841521i	−0.943302	−	0.331935i	$-0.892298\pi$
$571$	−1130.88	−	11482.0i	−0.0828826	−	0.841521i	0.860420	−	0.509586i	$-0.170202\pi$
$572$	528.606	−	2472.85i	0.0386401	−	0.180761i
$573$	−2112.24	−	6963.13i	−0.153997	−	0.507659i
$574$	1040.08	−	3342.79i	0.0756308	−	0.243075i
$575$		−	2199.48i		−	0.159521i
$576$	6184.67	−	2257.34i	0.447386	−	0.163291i
$577$		−	6912.31i		−	0.498723i	−0.968410	−	0.249361i	$-0.919779\pi$
$577$		−	6912.31i		−	0.498723i	0.968410	−	0.249361i	$-0.0802207\pi$
$578$	−7431.41	−	2312.22i	−0.534785	−	0.166394i
$579$	−2096.10	−	6909.92i	−0.150451	−	0.495970i
$580$	18038.9	−	11685.0i	1.29142	−	0.836539i
$581$	−3678.07	−	37344.0i	−0.262637	−	2.66659i
$582$	−89.4629	+	12560.7i	−0.00637174	+	0.894604i
$583$	22464.8	+	15010.5i	1.59588	+	1.06633i
$584$	−12956.8	+	6573.59i	−0.918077	+	0.465782i
$585$	−642.266	−	961.218i	−0.0453922	−	0.0679342i
$586$	−24397.5	−	5033.87i	−1.71988	−	0.354859i
$587$	19935.5	−	10655.7i	1.40175	−	0.749250i	0.414742	−	0.909939i	$-0.363872\pi$
$587$	19935.5	−	10655.7i	1.40175	−	0.749250i	0.987005	+	0.160689i	$0.0513717\pi$
$588$	−13476.3	+	1133.73i	−0.945160	+	0.0795142i
$589$	12708.8	+	1251.71i	0.889060	+	0.0875647i
$590$	−10014.5	−	12381.5i	−0.698796	−	0.863960i
$591$	−7813.00	−	18862.2i	−0.543797	−	1.31284i
$592$	1662.54	−	4966.69i	0.115422	−	0.344814i
$593$	1662.48	−	4013.59i	0.115127	−	0.277940i	−0.855804	−	0.517299i	$-0.826937\pi$
$593$	1662.48	−	4013.59i	0.115127	−	0.277940i	0.970931	+	0.239359i	$0.0769374\pi$
$594$	−24632.1	+	7280.90i	−1.70146	+	0.502928i
$595$	−32830.9	+	26943.7i	−2.26208	+	1.85644i
$596$	−1475.37	−	1850.90i	−0.101399	−	0.127207i
$597$	−7049.73	−	2138.51i	−0.483293	−	0.146605i
$598$	−185.385	+	35.5047i	−0.0126772	+	0.00242792i
$599$	3325.24	+	661.432i	0.226821	+	0.0451175i	0.307192	−	0.951647i	$-0.400611\pi$
$599$	3325.24	+	661.432i	0.226821	+	0.0451175i	−0.0803711	+	0.996765i	$0.525611\pi$
$600$	5308.99	+	13633.9i	0.361231	+	0.927669i
$601$	3473.39	+	17461.9i	0.235745	+	1.18517i	0.899399	+	0.437129i	$0.144005\pi$
$601$	3473.39	+	17461.9i	0.235745	+	1.18517i	−0.663654	+	0.748039i	$0.730995\pi$
$602$	−11323.5	+	26796.0i	−0.766632	+	1.81416i
$603$	−2977.31	−	2443.42i	−0.201070	−	0.165014i
$604$	8086.63	+	8320.36i	0.544769	+	0.560514i
$605$	−19006.5	+	35558.6i	−1.27723	+	2.38952i
$606$	−1514.48	−	16587.1i	−0.101521	−	1.11189i
$607$	−6432.98	−	6432.98i	−0.430159	−	0.430159i	0.458523	−	0.888682i	$-0.348379\pi$
$607$	−6432.98	−	6432.98i	−0.430159	−	0.430159i	−0.888682	+	0.458523i	$0.848379\pi$
$608$	−746.960	+	20966.4i	−0.0498244	+	1.39852i
$609$	11670.8	−	11670.8i	0.776558	−	0.776558i
$610$	12634.8	+	10520.6i	0.838633	+	0.698303i
$611$	−1101.93	−	588.992i	−0.0729610	−	0.0389985i
$612$	3564.67	−	8270.66i	0.235447	−	0.546277i
$613$	8830.47	−	10760.0i	0.581826	−	0.708957i	−0.396030	−	0.918238i	$-0.629612\pi$
$613$	8830.47	−	10760.0i	0.581826	−	0.708957i	0.977856	+	0.209281i	$0.0671122\pi$
$614$	−9203.63	+	3735.69i	−0.604932	+	0.245538i
$615$	−2794.31	+	555.823i	−0.183215	+	0.0364438i
$616$	8336.42	−	37683.4i	0.545266	−	2.46478i
$617$	−3067.22	+	15420.0i	−0.200132	+	1.00613i	0.741874	+	0.670539i	$0.233937\pi$
$617$	−3067.22	+	15420.0i	−0.200132	+	1.00613i	−0.942007	+	0.335594i	$0.891063\pi$
$618$	2560.07	−	3772.97i	0.166636	−	0.245584i
$619$	2302.14	−	7589.13i	0.149484	−	0.492783i	−0.849934	−	0.526889i	$-0.823358\pi$
$619$	2302.14	−	7589.13i	0.149484	−	0.492783i	0.999418	+	0.0341059i	$0.0108583\pi$
$620$	−4201.92	−	14597.2i	−0.272182	−	0.945546i
$621$	1216.32	+	1482.09i	0.0785975	+	0.0957714i
$622$	4723.24	+	2568.04i	0.304477	+	0.165545i
$623$	20223.9	+	8377.01i	1.30057	+	0.538712i
$624$	1063.45	−	667.556i	0.0682242	−	0.0428263i
$625$	−6977.32	+	2890.10i	−0.446548	+	0.184966i
$626$	20953.2	+	2214.50i	1.33779	+	0.141388i
$627$	2588.19	−	26278.4i	0.164853	−	1.67378i
$628$	7793.24	−	4023.92i	0.495198	−	0.255688i
$629$	−3377.39	−	6318.66i	−0.214095	−	0.400543i
$630$	−9697.82	−	14740.0i	−0.613286	−	0.932152i
$631$	−20096.3	+	13427.9i	−1.26787	+	0.847160i	−0.993430	−	0.114445i	$-0.963491\pi$
$631$	−20096.3	+	13427.9i	−1.26787	+	0.847160i	−0.274436	+	0.961605i	$0.588491\pi$
$632$	−70.9021	+	19.8640i	−0.00446255	+	0.00125023i
$633$	3142.64	−	4703.30i	0.197328	−	0.295323i
$634$	17005.3	+	17249.2i	1.06525	+	1.08053i
$635$	4966.37	−	489.144i	0.310369	−	0.0305687i
$636$	2429.56	+	13193.7i	0.151476	+	0.822588i
$637$	2244.33	−	680.811i	0.139598	−	0.0423465i
$638$	12426.1	+	23651.3i	0.771088	+	1.46765i
$639$	−9930.38			−0.614773
$640$	23502.6	−	8388.99i	1.45160	−	0.518131i
$641$	−16850.9			−1.03833			−0.519165	−	0.854674i	$-0.673757\pi$
$641$	−16850.9			−1.03833			−0.519165	+	0.854674i	$0.673757\pi$
$642$	7628.55	+	14519.8i	0.468964	+	0.892604i
$643$	17749.9	−	5384.38i	1.08863	−	0.330232i	0.305564	−	0.952172i	$-0.401155\pi$
$643$	17749.9	−	5384.38i	1.08863	−	0.330232i	0.783065	+	0.621940i	$0.213655\pi$
$644$	−2833.22	+	521.724i	−0.173361	+	0.0319236i
$645$	23560.2	−	2320.48i	1.43827	−	0.141657i
$646$	20148.1	+	20437.2i	1.22712	+	1.24472i
$647$	−12014.1	+	17980.3i	−0.730017	+	1.09255i	0.261830	+	0.965114i	$0.415674\pi$
$647$	−12014.1	+	17980.3i	−0.730017	+	1.09255i	−0.991847	+	0.127434i	$0.959326\pi$
$648$	−4269.27	−	2400.63i	−0.258816	−	0.145533i
$649$	16459.1	−	10997.6i	0.995493	−	0.665167i
$650$	−1394.60	−	2119.70i	−0.0841550	−	0.127910i
$651$	−5498.77	−	10287.5i	−0.331051	−	0.619352i
$652$	−1147.56	−	2222.51i	−0.0689293	−	0.133498i
$653$	−164.394	+	1669.12i	−0.00985183	+	0.100027i	−0.998853	−	0.0478797i	$-0.984754\pi$
$653$	−164.394	+	1669.12i	−0.00985183	+	0.100027i	0.989001	+	0.147907i	$0.0472536\pi$
$654$	7571.04	+	800.168i	0.452677	+	0.0478426i
$655$	−31937.3	+	13228.9i	−1.90518	+	0.789153i
$656$	470.116	+	2774.28i	0.0279801	+	0.165118i
$657$	−7628.14	−	3159.68i	−0.452971	−	0.187627i
$658$	−16753.6	−	9109.02i	−0.992591	−	0.539675i
$659$	3335.26	+	4064.02i	0.197152	+	0.240231i	0.862197	−	0.506573i	$-0.169088\pi$
$659$	3335.26	+	4064.02i	0.197152	+	0.240231i	−0.665045	+	0.746803i	$0.731588\pi$
$660$	−30183.2	+	8688.45i	−1.78012	+	0.512420i
$661$	−5252.77	+	17316.0i	−0.309091	+	1.01894i	0.655503	+	0.755193i	$0.272457\pi$
$661$	−5252.77	+	17316.0i	−0.309091	+	1.01894i	−0.964593	+	0.263742i	$0.915043\pi$
$662$	14032.7	−	20681.0i	0.823861	−	1.21418i
$663$	335.085	−	1684.59i	0.0196284	−	0.0986787i
$664$	16216.8	+	25430.0i	0.947790	+	1.48626i
$665$	55144.3	−	10968.9i	3.21564	−	0.639631i
$666$	2757.91	−	1119.42i	0.160461	−	0.0651301i
$667$	1265.15	−	1541.59i	0.0734433	−	0.0894909i
$668$	7861.83	+	3388.47i	0.455364	+	0.196263i
$669$	5276.80	+	2820.51i	0.304952	+	0.163000i
$670$	−11218.9	−	9341.62i	−0.646901	−	0.538654i
$671$	−14451.6	+	14451.6i	−0.831443	+	0.831443i
$672$	16303.0	−	10072.7i	0.935863	−	0.578218i
$673$	10465.8	+	10465.8i	0.599447	+	0.599447i	0.940165	−	0.340718i	$-0.110670\pi$
$673$	10465.8	+	10465.8i	0.599447	+	0.599447i	−0.340718	+	0.940165i	$0.610670\pi$
$674$	−1705.08	−	18674.5i	−0.0974438	−	1.06723i
$675$	−12149.3	+	22729.8i	−0.692783	+	1.29611i
$676$	12447.7	−	12098.1i	0.708223	−	0.688328i
$677$	8499.09	+	6975.02i	0.482491	+	0.395970i	0.843953	−	0.536416i	$-0.180222\pi$
$677$	8499.09	+	6975.02i	0.482491	+	0.395970i	−0.361462	+	0.932387i	$0.617722\pi$
$678$	5627.16	−	13316.1i	0.318746	−	0.754281i
$679$	−6486.14	−	32608.1i	−0.366591	−	1.84298i
$680$	13734.4	−	31251.9i	0.774544	−	1.76244i
$681$	−7356.18	−	1463.23i	−0.413934	−	0.0823367i
$682$	18545.0	−	3551.72i	1.04124	−	0.199417i
$683$	−1549.71	−	470.100i	−0.0868201	−	0.0263366i	0.246576	−	0.969124i	$-0.420695\pi$
$683$	−1549.71	−	470.100i	−0.0868201	−	0.0263366i	−0.333396	+	0.942787i	$0.608195\pi$
$684$	−9323.02	+	7431.51i	−0.521161	+	0.415425i
$685$	−41561.4	+	34108.6i	−2.31822	+	1.90251i
$686$	8135.62	−	2404.77i	0.452798	−	0.133841i
$687$	−605.038	+	1460.69i	−0.0336006	+	0.0811191i
$688$	−1628.04	−	23324.8i	−0.0902156	−	1.29251i
$689$	−890.326	−	2149.44i	−0.0492289	−	0.118849i
$690$	1474.38	+	1822.86i	0.0813461	+	0.100573i
$691$	−14855.7	−	1463.16i	−0.817855	−	0.0805517i	−0.319568	−	0.947563i	$-0.603538\pi$
$691$	−14855.7	−	1463.16i	−0.817855	−	0.0805517i	−0.498288	+	0.867012i	$0.666038\pi$
$692$	−1018.27	−	12103.9i	−0.0559378	−	0.664914i
$693$	19343.0	−	10339.0i	1.06029	−	0.566735i
$694$	−13634.3	−	2813.13i	−0.745752	−	0.153869i
$695$	−19184.1	−	28711.1i	−1.04704	−	1.56701i
$696$	−4121.25	+	12609.6i	−0.224448	+	0.686730i
$697$	3200.45	+	2138.47i	0.173925	+	0.116213i
$698$	37.0410	−	5200.62i	0.00200863	−	0.282015i
$699$	1629.81	+	16547.7i	0.0881902	+	0.895410i
$700$	−21054.1	−	32502.5i	−1.13681	−	1.75497i
$701$	3714.47	+	12245.0i	0.200133	+	0.659751i	0.998352	+	0.0573836i	$0.0182758\pi$
$701$	3714.47	+	12245.0i	0.200133	+	0.659751i	−0.798219	+	0.602367i	$0.794224\pi$
$702$	2111.92	+	657.107i	0.113546	+	0.0353289i
$703$			9484.69i			0.508851i
$704$	7728.40	+	30042.4i	0.413743	+	1.60833i
$705$			15519.4i			0.829068i
$706$	−2481.12	+	7974.26i	−0.132264	+	0.425092i
$707$	12797.4	+	42187.3i	0.680757	+	2.24415i
$708$	9611.91	+	2054.68i	0.510223	+	0.109067i
$709$	408.246	+	4144.99i	0.0216248	+	0.219560i	0.999924	+	0.0123612i	$0.00393481\pi$
$709$	408.246	+	4144.99i	0.0216248	+	0.219560i	−0.978299	+	0.207199i	$0.933565\pi$
$710$	−37639.0	−	268.080i	−1.98953	−	0.0141703i
$711$	−34.7922	−	23.2474i	−0.00183517	−	0.00122622i
$712$	−17542.5	+	1350.06i	−0.923359	+	0.0710611i
$713$	−783.043	−	1171.91i	−0.0411293	−	0.0615544i
$714$	5297.22	−	25673.9i	0.277652	−	1.34569i
$715$	4803.76	−	2567.66i	0.251259	−	0.134301i
$716$	−17984.6	+	21288.6i	−0.938710	+	1.11116i
$717$	−1490.98	−	146.849i	−0.0776592	−	0.00764876i
$718$	19935.4	−	16124.3i	1.03619	−	0.838098i
$719$	−7193.56	−	17366.8i	−0.373122	−	0.900795i	−0.993218	−	0.116270i	$-0.962906\pi$
$719$	−7193.56	−	17366.8i	−0.373122	−	0.900795i	0.620096	−	0.784526i	$-0.287094\pi$
$720$	12311.5	+	7038.69i	0.637254	+	0.364329i
$721$	−4618.31	+	11149.6i	−0.238551	+	0.575912i
$722$	−5270.10	−	17829.3i	−0.271652	−	0.919030i
$723$	−2451.66	+	2012.02i	−0.126111	+	0.103496i
$724$	−3029.87	+	26837.9i	−0.155531	+	1.37766i
$725$	25653.5	+	7781.89i	1.31413	+	0.398637i
$726$	−4681.12	−	24442.1i	−0.239301	−	1.24949i
$727$	2002.54	+	398.330i	0.102160	+	0.0203208i	0.245905	−	0.969294i	$-0.420915\pi$
$727$	2002.54	+	398.330i	0.102160	+	0.0203208i	−0.143746	+	0.989615i	$0.545915\pi$
$728$	−2399.65	+	2299.23i	−0.122166	+	0.117054i
$729$	−3512.01	−	17656.1i	−0.178428	−	0.897021i
$730$	−28827.5	−	12182.0i	−1.46158	−	0.617639i
$731$	−24724.3	−	20290.7i	−1.25097	−	1.02665i
$732$	−10147.1	−	144.551i	−0.512358	−	0.00729883i
$733$	−7073.99	+	13234.5i	−0.356458	+	0.666886i	−0.994685	−	0.102962i	$-0.967168\pi$
$733$	−7073.99	+	13234.5i	−0.356458	+	0.666886i	0.638227	+	0.769848i	$0.279668\pi$
$734$	−21496.9	+	1962.78i	−1.08102	+	0.0987022i
$735$	−20598.6	−	20598.6i	−1.03373	−	1.03373i
$736$	1841.07	−	1404.28i	0.0922051	−	0.0703295i
$737$	12832.2	−	12832.2i	0.641355	−	0.641355i
$738$	−1023.21	+	1228.84i	−0.0510366	+	0.0612929i
$739$	16047.2	+	8577.42i	0.798791	+	0.426963i	0.819682	−	0.572819i	$-0.194150\pi$
$739$	16047.2	+	8577.42i	0.798791	+	0.426963i	−0.0208907	+	0.999782i	$0.506650\pi$
$740$	10483.5	−	4168.47i	0.520785	−	0.207076i
$741$	−1442.47	+	1757.65i	−0.0715121	+	0.0871377i
$742$	−13354.6	−	32901.6i	−0.660730	−	1.62784i
$743$	16167.5	−	3215.91i	0.798287	−	0.158789i	0.220939	−	0.975288i	$-0.429088\pi$
$743$	16167.5	−	3215.91i	0.798287	−	0.158789i	0.577348	+	0.816498i	$0.304088\pi$
$744$	7682.53	+	5374.22i	0.378569	+	0.264823i
$745$	994.670	−	5000.55i	0.0489153	−	0.245914i
$746$	18438.0	+	12510.8i	0.904913	+	0.614011i
$747$	−4975.46	+	16401.9i	−0.243698	+	0.803365i
$748$	37134.8	+	20534.3i	1.81522	+	1.00376i
$749$	−27540.7	−	33558.5i	−1.34355	−	1.63712i
$750$	−4110.34	+	7559.89i	−0.200118	+	0.368064i
$751$	27216.2	+	11273.3i	1.32242	+	0.547763i	0.928482	−	0.371376i	$-0.121114\pi$
$751$	27216.2	+	11273.3i	1.32242	+	0.547763i	0.393933	+	0.919139i	$0.371114\pi$
$752$	15321.3	+	436.608i	0.742964	+	0.0211722i
$753$	−9445.97	+	3912.65i	−0.457145	+	0.189356i
$754$	241.798	−	2287.84i	0.0116787	−	0.110502i
$755$	−2449.69	+	24872.1i	−0.118084	+	1.19893i
$756$	32160.9	+	10258.4i	1.54720	+	0.493510i
$757$	13111.5	+	24530.0i	0.629520	+	1.17775i	0.971275	+	0.237961i	$0.0764789\pi$
$757$	13111.5	+	24530.0i	0.629520	+	1.17775i	−0.341754	+	0.939789i	$0.611021\pi$
$758$	7393.94	−	4864.66i	0.354301	−	0.233103i
$759$	−2423.19	+	1619.13i	−0.115884	+	0.0774315i
$760$	−35537.5	+	27915.8i	−1.69616	+	1.33239i
$761$	12876.7	−	19271.3i	0.613376	−	0.917981i	−0.386615	−	0.922241i	$-0.626356\pi$
$761$	12876.7	−	19271.3i	0.613376	−	0.917981i	0.999991	+	0.00425970i	$0.00135591\pi$
$762$	−2193.50	+	2162.47i	−0.104281	+	0.102806i
$763$	−20053.7	+	1975.12i	−0.951500	+	0.0937146i
$764$	−12747.2	−	8782.62i	−0.603637	−	0.415895i
$765$	18564.1	−	5631.37i	0.877369	−	0.266147i
$766$	4787.91	−	2515.51i	0.225841	−	0.118654i
$767$	−1704.56			−0.0802452
$768$	−8022.67	+	13148.6i	−0.376944	+	0.617785i
$769$	8702.49			0.408088			0.204044	−	0.978962i	$-0.434591\pi$
$769$	8702.49			0.408088			0.204044	+	0.978962i	$0.434591\pi$
$770$	73594.4	−	38665.7i	3.44436	−	1.80963i
$771$	27234.5	−	8261.51i	1.27215	−	0.385903i
$772$	−12649.8	−	8715.52i	−0.589738	−	0.406319i
$773$	−20784.3	+	2047.07i	−0.967087	+	0.0952498i	−0.569213	−	0.822190i	$-0.692752\pi$
$773$	−20784.3	+	2047.07i	−0.967087	+	0.0952498i	−0.397874	+	0.917440i	$0.630252\pi$
$774$	9462.30	−	9328.47i	0.439426	−	0.433210i
$775$	10526.0	−	15753.3i	0.487879	−	0.730162i
$776$	16507.3	+	21014.1i	0.763630	+	0.972118i
$777$	7203.58	−	4813.28i	0.332596	−	0.222234i
$778$	30329.5	−	19954.5i	1.39764	−	0.919543i
$779$	−2402.03	−	4493.89i	−0.110477	−	0.206688i
$780$	2576.70	+	821.893i	0.118283	+	0.0377288i
$781$	4586.10	−	46563.5i	0.210120	−	2.13338i
$782$	332.909	−	3149.92i	0.0152235	−	0.144042i
$783$	−21589.6	+	8942.69i	−0.985374	+	0.408155i
$784$	−20915.2	+	19756.2i	−0.952771	+	0.899973i
$785$	17454.4	+	7229.84i	0.793597	+	0.328719i
$786$	10191.9	−	18745.3i	0.462509	−	0.850664i
$787$	−12037.4	−	14667.6i	−0.545219	−	0.664352i	0.425391	−	0.905010i	$-0.360137\pi$
$787$	−12037.4	−	14667.6i	−0.545219	−	0.664352i	−0.970610	+	0.240658i	$0.922637\pi$
$788$	−38009.5	−	21018.0i	−1.71832	−	0.950172i
$789$	2670.60	−	8803.77i	0.120502	−	0.397240i
$790$	−131.245	−	89.0534i	−0.00591073	−	0.00401061i
$791$	−7464.77	+	37527.9i	−0.335546	+	1.68690i
$792$	−10104.8	+	14445.0i	−0.453358	+	0.648082i
$793$	1726.07	−	343.337i	0.0772945	−	0.0153748i
$794$	2888.52	+	7116.44i	0.129105	+	0.318077i
$795$	−18332.4	+	22338.1i	−0.817840	+	0.996540i
$796$	−14563.4	+	5790.71i	−0.648473	+	0.257847i
$797$	22933.0	+	12257.9i	1.01923	+	0.544791i	0.894344	−	0.447380i	$-0.147643\pi$
$797$	22933.0	+	12257.9i	1.01923	+	0.544791i	0.124888	+	0.992171i	$0.460143\pi$
$798$	−22206.1	+	26668.6i	−0.985073	+	1.18303i
$799$	14825.9	−	14825.9i	0.656450	−	0.656450i
$800$	26910.9	+	15640.8i	1.18931	+	0.691231i
$801$	−7070.11	−	7070.11i	−0.311873	−	0.311873i
$802$	−15708.8	+	1434.29i	−0.691642	+	0.0631503i
$803$	18338.6	−	34309.0i	0.805920	−	1.50777i
$804$	9009.98	+	128.352i	0.395221	+	0.00563013i
$805$	−4796.87	−	3936.69i	−0.210022	−	0.172360i
$806$	−1497.70	−	632.901i	−0.0654518	−	0.0276588i
$807$	789.334	+	3968.25i	0.0344311	+	0.173097i
$808$	−24514.6	−	25585.2i	−1.06735	−	1.11397i
$809$	10304.8	+	2049.75i	0.447832	+	0.0890794i	0.413854	−	0.910343i	$-0.364182\pi$
$809$	10304.8	+	2049.75i	0.447832	+	0.0890794i	0.0339781	+	0.999423i	$0.489182\pi$
$810$	−1984.50	−	10361.9i	−0.0860843	−	0.449483i
$811$	−31128.4	−	9442.69i	−1.34780	−	0.408850i	−0.467803	−	0.883833i	$-0.654954\pi$
$811$	−31128.4	−	9442.69i	−1.34780	−	0.408850i	−0.879995	+	0.474982i	$0.842454\pi$
$812$	3939.03	−	34890.9i	0.170237	−	1.50792i
$813$	2488.12	−	2041.94i	0.107333	−	0.0880862i
$814$	3975.28	+	13448.8i	0.171171	+	0.579092i
$815$	2061.84	−	4977.72i	0.0886173	−	0.213941i
$816$	5539.52	+	20328.9i	0.237649	+	0.872126i
$817$	16203.4	+	39118.5i	0.693863	+	1.67513i
$818$	183.941	−	148.777i	0.00786228	−	0.00635924i
$819$	−1879.53	−	185.118i	−0.0801907	−	0.00789809i
$820$	−3911.45	+	4630.02i	−0.166578	+	0.197180i
$821$	−34382.2	+	18377.7i	−1.46157	+	0.781225i	−0.994672	−	0.103087i	$-0.967128\pi$
$821$	−34382.2	+	18377.7i	−1.46157	+	0.781225i	−0.466897	+	0.884312i	$0.654628\pi$
$822$	6705.86	−	32501.1i	0.284542	−	1.37908i
$823$	10860.0	+	16253.2i	0.459972	+	0.688397i	0.986867	−	0.161533i	$-0.0516439\pi$
$823$	10860.0	+	16253.2i	0.459972	+	0.688397i	−0.526895	+	0.849930i	$0.676644\pi$
$824$	−744.297	−	9671.30i	−0.0314670	−	0.408878i
$825$	−32573.6	−	21765.0i	−1.37463	−	0.918498i
$826$	−26015.1	−	185.290i	−1.09586	−	0.00780518i
$827$	−4253.71	−	43188.7i	−0.178859	−	1.81598i	−0.496793	−	0.867869i	$-0.665489\pi$
$827$	−4253.71	−	43188.7i	−0.178859	−	1.81598i	0.317935	−	0.948113i	$-0.397011\pi$
$828$	1286.80	+	275.071i	0.0540090	+	0.0115452i
$829$	−10542.7	−	34754.5i	−0.441691	−	1.45606i	−0.841899	−	0.539635i	$-0.818562\pi$
$829$	−10542.7	−	34754.5i	−0.441691	−	1.45606i	0.400208	−	0.916424i	$-0.368938\pi$
$830$	−19301.2	+	62033.5i	−0.807174	+	2.59424i
$831$			24794.3i			1.03502i
$832$	883.893	−	2520.69i	0.0368311	−	0.105035i
$833$			39356.5i			1.63700i
$834$	20350.9	+	6332.00i	0.844956	+	0.262901i
$835$	5353.00	+	17646.5i	0.221854	+	0.731356i
$836$	−30540.7	−	47147.6i	−1.26348	−	1.95052i
$837$	1618.81	+	16436.0i	0.0668508	+	0.678748i
$838$	−30.9981	+	4352.18i	−0.00127782	+	0.179408i
$839$	−18467.1	−	12339.3i	−0.759901	−	0.507749i	0.114222	−	0.993455i	$-0.463563\pi$
$839$	−18467.1	−	12339.3i	−0.759901	−	0.507749i	−0.874122	+	0.485706i	$0.838563\pi$
$840$	39236.5	+	12823.9i	1.61165	+	0.526745i
$841$	−45.8114	−	68.5616i	−0.00187836	−	0.00281117i
$842$	−16001.9	−	3301.63i	−0.654945	−	0.135133i
$843$	12726.6	−	6802.51i	0.519962	−	0.277925i
$844$	−1008.82	−	11991.5i	−0.0411432	−	0.489056i
$845$	37210.1	+	3664.87i	1.51487	+	0.149202i
$846$	5477.73	+	6772.43i	0.222610	+	0.275226i
$847$	25207.2	+	60855.6i	1.02259	+	2.46874i
$848$	21537.2	+	18726.8i	0.872158	+	0.758351i
$849$	12001.4	−	28974.0i	0.485144	−	1.17124i
$850$	40832.1	−	12069.4i	1.64768	−	0.487031i
$851$	809.199	−	664.092i	0.0325957	−	0.0267506i
$852$	18167.0	−	14481.2i	0.730508	−	0.582298i
$853$	−31500.5	−	9555.58i	−1.26443	−	0.383560i	−0.414302	−	0.910139i	$-0.635974\pi$
$853$	−31500.5	−	9555.58i	−1.26443	−	0.383560i	−0.850126	+	0.526579i	$0.823474\pi$
$854$	26380.7	−	5052.40i	1.05706	−	0.202447i
$855$	−25187.9	−	5010.19i	−1.00749	−	0.200403i
$856$	31944.4	+	14038.7i	1.27551	+	0.560554i
$857$	6025.57	+	30292.6i	0.240175	+	1.20744i	0.893044	+	0.449969i	$0.148565\pi$
$857$	6025.57	+	30292.6i	0.240175	+	1.20744i	−0.652870	+	0.757470i	$0.726435\pi$
$858$	−1308.67	+	3096.84i	−0.0520714	+	0.123222i
$859$	15738.3	+	12916.1i	0.625127	+	0.513029i	0.892784	−	0.450486i	$-0.148749\pi$
$859$	15738.3	+	12916.1i	0.625127	+	0.513029i	−0.267656	+	0.963514i	$0.586249\pi$
$860$	36116.7	−	35102.1i	1.43206	−	1.39183i
$861$	−2194.11	+	4104.89i	−0.0868467	+	0.162479i
$862$	1253.79	+	13731.9i	0.0495408	+	0.542586i
$863$	−14616.8	−	14616.8i	−0.576547	−	0.576547i	0.357403	−	0.933950i	$-0.383662\pi$
$863$	−14616.8	−	14616.8i	−0.576547	−	0.576547i	−0.933950	+	0.357403i	$0.883662\pi$
$864$	−26782.9	+	4342.49i	−1.05460	+	0.170989i
$865$	18500.9	−	18500.9i	0.727223	−	0.727223i
$866$	5699.32	+	4745.64i	0.223638	+	0.186216i
$867$	9125.64	+	4877.76i	0.357466	+	0.191070i
$868$	−22789.2	−	9822.18i	−0.891146	−	0.384086i
$869$	125.075	−	152.404i	0.00488247	−	0.00594931i
$870$	−26477.3	+	10747.0i	−1.03180	+	0.418800i
$871$	−1532.64	+	304.862i	−0.0596231	+	0.0118598i
$872$	13655.9	−	8708.40i	0.530329	−	0.338192i
$873$	−2962.64	+	14894.2i	−0.114857	+	0.577424i
$874$	−2354.36	+	3469.79i	−0.0911183	+	0.134288i
$875$	6611.52	−	21795.3i	0.255440	−	0.842074i
$876$	18562.9	−	5343.46i	0.715961	−	0.206095i
$877$	−28095.2	−	34234.1i	−1.08177	−	1.31814i	−0.944832	−	0.327555i	$-0.893775\pi$
$877$	−28095.2	−	34234.1i	−1.08177	−	1.31814i	−0.136933	−	0.990580i	$-0.543725\pi$
$878$	−856.962	−	465.933i	−0.0329397	−	0.0179094i
$879$	30599.3	+	12674.6i	1.17416	+	0.486353i
$880$	−38690.1	+	54477.9i	−1.48210	+	2.08688i
$881$	3825.36	−	1584.52i	0.146288	−	0.0605944i	−0.308338	−	0.951277i	$-0.599773\pi$
$881$	3825.36	−	1584.52i	0.146288	−	0.0605944i	0.454626	+	0.890682i	$0.349773\pi$
$882$	−16259.5	−	1718.43i	−0.620732	−	0.0656039i
$883$	−81.6287	+	828.790i	−0.00311101	+	0.0315866i	−0.996615	−	0.0822115i	$-0.973802\pi$
$883$	−81.6287	+	828.790i	−0.00311101	+	0.0315866i	0.993504	+	0.113798i	$0.0363017\pi$
$884$	−1676.40	−	3246.74i	−0.0637823	−	0.123529i
$885$	9980.44	+	18672.1i	0.379083	+	0.709215i
$886$	854.008	+	1298.03i	0.0323826	+	0.0492192i
$887$	22332.9	−	14922.3i	0.845394	−	0.564874i	−0.0557250	−	0.998446i	$-0.517747\pi$
$887$	22332.9	−	14922.3i	0.845394	−	0.564874i	0.901119	+	0.433572i	$0.142747\pi$
$888$	−3413.02	+	6069.70i	−0.128979	+	0.229376i
$889$	4529.44	−	6778.79i	0.170880	−	0.255740i
$890$	−26606.9	−	26988.6i	−1.00209	−	1.01647i
$891$	13051.5	−	1285.46i	0.490730	−	0.0483327i
$892$	12518.4	−	2305.19i	0.469894	−	0.0865287i
$893$	−26561.3	+	8057.29i	−0.995343	+	0.301934i
$894$	1463.66	+	2785.86i	0.0547562	+	0.104220i
$895$	−60029.3			−2.24197
$896$	13764.0	−	38374.9i	0.513197	−	1.43082i
$897$	250.954			0.00934127
$898$	−4547.74	−	8655.96i	−0.168998	−	0.321663i
$899$	16438.9	−	4986.68i	0.609864	−	0.185000i
$900$	3203.40	+	17396.1i	0.118644	+	0.644299i
$901$	38853.2	−	3826.71i	1.43661	−	0.141494i
$902$	−5289.46	−	5365.35i	−0.195255	−	0.198056i
$903$	21487.5	−	32158.2i	0.791869	−	1.18512i
$904$	−8296.66	−	29614.0i	−0.305246	−	1.08954i
$905$	−48372.2	+	32321.3i	−1.77674	+	1.18718i
$906$	−8478.69	−	12887.0i	−0.310911	−	0.472563i
$907$	−2598.08	−	4860.66i	−0.0951132	−	0.177944i	0.829865	−	0.557964i	$-0.188417\pi$
$907$	−2598.08	−	4860.66i	−0.0951132	−	0.177944i	−0.924978	+	0.380020i	$0.875917\pi$
$908$	−14177.7	+	7320.44i	−0.518176	+	0.267552i
$909$	1973.74	−	20039.8i	0.0720186	−	0.731217i
$910$	−7118.97	−	752.389i	−0.259331	−	0.0274082i
$911$	16946.3	−	7019.39i	0.616308	−	0.255283i	−0.0526152	−	0.998615i	$-0.516756\pi$
$911$	16946.3	−	7019.39i	0.616308	−	0.255283i	0.668923	+	0.743332i	$0.266756\pi$
$912$	6218.73	−	27191.0i	0.225793	−	0.987263i
$913$	−74610.6	−	30904.7i	−2.70454	−	1.12026i
$914$	14868.7	+	8084.15i	0.538087	+	0.292560i
$915$	−13867.4	−	16897.4i	−0.501028	−	0.610505i
$916$	930.426	+	3232.25i	0.0335613	+	0.116590i
$917$	−16393.7	+	54042.9i	−0.590370	+	1.94619i
$918$	−20839.7	+	30712.9i	−0.749250	+	1.10422i
$919$	1939.71	−	9751.57i	0.0696247	−	0.350027i	−0.930232	−	0.366973i	$-0.880394\pi$
$919$	1939.71	−	9751.57i	0.0696247	−	0.350027i	0.999856	+	0.0169457i	$0.00539425\pi$
$920$	4869.91	+	1077.34i	0.174518	+	0.0386073i
$921$	12952.3	−	2576.37i	0.463401	−	0.0921761i
$922$	−4742.24	+	1924.85i	−0.169390	+	0.0687543i
$923$	−2555.96	+	3114.44i	−0.0911488	+	0.111065i
$924$	−20309.7	+	47121.9i	−0.723094	+	1.67770i
$925$	12410.2	+	6633.38i	0.441129	+	0.235788i
$926$	−12418.8	−	10340.8i	−0.440722	−	0.366975i
$927$	3897.81	−	3897.81i	0.138102	−	0.138102i
$928$	9864.89	+	26441.6i	0.348956	+	0.935334i
$929$	539.761	+	539.761i	0.0190624	+	0.0190624i	0.716574	−	0.697511i	$-0.245709\pi$
$929$	539.761	+	539.761i	0.0190624	+	0.0190624i	−0.697511	+	0.716574i	$0.745709\pi$
$930$	1836.31	+	20111.8i	0.0647472	+	0.709131i
$931$	24560.2	−	45948.9i	0.864584	−	1.61752i
$932$	24654.2	+	25366.8i	0.866499	+	0.891543i
$933$	−5525.35	−	4534.54i	−0.193882	−	0.159115i
$934$	10919.8	−	25840.7i	0.382557	−	0.905283i
$935$	17832.0	+	89647.8i	0.623712	+	3.13561i
$936$	1414.53	−	550.815i	0.0493969	−	0.0192350i
$937$	37643.6	+	7487.78i	1.31245	+	0.261062i	0.801213	−	0.598379i	$-0.204188\pi$
$937$	37643.6	+	7487.78i	1.31245	+	0.261062i	0.511235	+	0.859441i	$0.329188\pi$
$938$	−23424.5	+	4486.22i	−0.815390	+	0.156162i
$939$	−26806.7	−	8131.72i	−0.931633	−	0.282608i
$940$	20579.3	+	25817.3i	0.714068	+	0.895817i
$941$	7851.76	−	6443.77i	0.272009	−	0.223232i	−0.488493	−	0.872568i	$-0.662453\pi$
$941$	7851.76	−	6443.77i	0.272009	−	0.223232i	0.760501	+	0.649336i	$0.224953\pi$
$942$	−11182.7	+	3305.44i	−0.386785	+	0.114328i
$943$	−215.218	+	519.582i	−0.00743209	+	0.0179427i
$944$	18714.5	−	9327.74i	0.645240	−	0.321602i
$945$	27826.5	+	67179.1i	0.957880	+	2.31253i
$946$	39371.2	+	48676.8i	1.35314	+	1.67296i
$947$	3206.46	+	315.809i	0.110027	+	0.0108367i	0.152881	−	0.988245i	$-0.451145\pi$
$947$	3206.46	+	315.809i	0.110027	+	0.0108367i	−0.0428536	+	0.999081i	$0.513645\pi$
$948$	97.5512	−	8.20677i	0.00334210	−	0.000281164i
$949$	−2954.35	+	1579.13i	−0.101056	+	0.0540156i
$950$	−55203.4	−	11390.0i	−1.88530	−	0.388988i
$951$	−17891.6	−	26776.7i	−0.610069	−	0.913033i
$952$	−25232.5	−	49734.2i	−0.859022	−	1.69317i
$953$	15267.8	+	10201.6i	0.518965	+	0.346761i	0.787306	−	0.616563i	$-0.211475\pi$
$953$	15267.8	+	10201.6i	0.518965	+	0.346761i	−0.268341	+	0.963324i	$0.586475\pi$
$954$	−115.516	+	16218.6i	−0.00392030	+	0.550417i
$955$	−3268.29	−	33183.5i	−0.110743	−	1.12439i
$956$	−2675.05	+	1732.81i	−0.0904994	+	0.0586225i
$957$	−10311.1	−	33991.2i	−0.348288	−	1.14815i
$958$	43152.5	+	13426.5i	1.45532	+	0.452809i
$959$			87836.6i			2.95766i
$960$	−32787.5	+	5076.67i	−1.10230	+	0.170676i
$961$			17650.1i			0.592463i
$962$	358.772	−	1153.08i	0.0120242	−	0.0386454i
$963$	5756.16	+	18975.5i	0.192616	+	0.634971i
$964$	−1410.44	+	6598.12i	−0.0471236	+	0.220447i
$965$	−3243.32	−	32929.9i	−0.108193	−	1.09850i
$966$	3830.08	+	27.2794i	0.127568	+	0.000908593i
$967$	−13616.1	−	9098.00i	−0.452808	−	0.302556i	0.308174	−	0.951330i	$-0.400282\pi$
$967$	−13616.1	−	9098.00i	−0.452808	−	0.302556i	−0.760981	+	0.648774i	$0.775282\pi$
$968$	−40198.6	−	34453.4i	−1.33474	−	1.14398i
$969$	−21198.3	−	31725.5i	−0.702773	−	1.05177i
$970$	−11631.3	+	56373.2i	−0.385009	+	1.86601i
$971$	−565.458	+	302.244i	−0.0186884	+	0.00998914i	−0.480714	−	0.876877i	$-0.659623\pi$
$971$	−565.458	+	302.244i	−0.0186884	+	0.00998914i	0.462026	+	0.886866i	$0.347123\pi$
$972$	−19757.3	−	16691.0i	−0.651972	−	0.550786i
$973$	−56140.6	−	5529.36i	−1.84973	−	0.182182i
$974$	30484.3	−	24656.6i	1.00286	−	0.811138i
$975$	1290.96	+	3116.65i	0.0424039	+	0.102372i
$976$	−17071.9	+	13215.0i	−0.559895	+	0.433403i
$977$	−5408.08	+	13056.3i	−0.177093	+	0.427540i	−0.987354	−	0.158529i	$-0.949325\pi$
$977$	−5408.08	+	13056.3i	−0.177093	+	0.427540i	0.810262	+	0.586068i	$0.199325\pi$
$978$	942.662	+	3189.13i	0.0308211	+	0.104271i
$979$	36416.8	−	29886.5i	1.18885	−	0.975667i
$980$	−61581.7	−	6952.29i	−2.00730	−	0.226615i
$981$	8807.82	+	2671.82i	0.286659	+	0.0869569i
$982$	8732.43	+	45595.7i	0.283771	+	1.48169i
$983$	55883.7	+	11116.0i	1.81324	+	0.360675i	0.981040	−	0.193804i	$-0.0620825\pi$
$983$	55883.7	+	11116.0i	1.81324	+	0.360675i	0.832198	+	0.554479i	$0.187083\pi$
$984$	79.9288	−	3740.21i	0.00258947	−	0.121172i
$985$	−18252.1	−	91759.5i	−0.590416	−	2.96822i
$986$	35561.0	+	15027.5i	1.14857	+	0.485367i
$987$	19598.8	+	16084.3i	0.632053	+	0.518713i
$988$	−68.9019	+	4836.73i	−0.00221869	+	0.155746i
$989$	2202.93	−	4121.39i	0.0708281	−	0.132510i
$990$	−37815.1	+	3452.70i	−1.21398	+	0.110842i
$991$	3131.71	+	3131.71i	0.100386	+	0.100386i	0.755516	−	0.655130i	$-0.227386\pi$
$991$	3131.71	+	3131.71i	0.100386	+	0.100386i	−0.655130	+	0.755516i	$0.727386\pi$
$992$	19906.8	−	1247.06i	0.637137	−	0.0399135i
$993$	−23495.8	+	23495.8i	−0.750872	+	0.750872i
$994$	−39347.7	+	47255.0i	−1.25557	+	1.50788i
$995$	−29772.6	−	15913.8i	−0.948596	−	0.507035i
$996$	−14816.1	−	37261.9i	−0.471352	−	1.18543i
$997$	−15196.7	+	18517.2i	−0.482731	+	0.588209i	−0.956241	−	0.292579i	$-0.905487\pi$
$997$	−15196.7	+	18517.2i	−0.482731	+	0.588209i	0.473510	+	0.880788i	$0.342987\pi$
$998$	5506.35	+	13566.0i	0.174650	+	0.430284i
$999$	−12030.7	+	2393.05i	−0.381015	+	0.0757885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.k.a.77.8	yes	752
128.5	even	32	inner	128.4.k.a.5.8	✓	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.4.k.a.5.8	✓	752	128.5	even	32	inner
128.4.k.a.77.8	yes	752	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.k (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.50388 + 1.31551i) q^{2} +(3.59854 - 1.09161i) q^{3} +(4.53886 - 6.58777i) q^{4} +(17.1492 - 1.68905i) q^{5} +(-7.57431 + 7.46718i) q^{6} +(15.6405 - 23.4076i) q^{7} +(-2.69848 + 22.4659i) q^{8} +(-10.6918 + 7.14401i) q^{9} +O(q^{10})\)	\(q+(-2.50388 + 1.31551i) q^{2} +(3.59854 - 1.09161i) q^{3} +(4.53886 - 6.58777i) q^{4} +(17.1492 - 1.68905i) q^{5} +(-7.57431 + 7.46718i) q^{6} +(15.6405 - 23.4076i) q^{7} +(-2.69848 + 22.4659i) q^{8} +(-10.6918 + 7.14401i) q^{9} +(-40.7177 + 26.7892i) q^{10} +(-28.5605 - 53.4329i) q^{11} +(9.14203 - 28.6610i) q^{12} +(-0.511368 + 5.19201i) q^{13} +(-8.36893 + 79.1852i) q^{14} +(59.8685 - 24.7983i) q^{15} +(-22.7975 - 59.8020i) q^{16} +(-80.8837 - 33.5031i) q^{17} +(17.3729 - 31.9529i) q^{18} +(73.5246 + 89.5900i) q^{19} +(66.7108 - 120.642i) q^{20} +(30.7310 - 101.307i) q^{21} +(141.804 + 96.2180i) q^{22} +(2.49549 - 12.5457i) q^{23} +(14.8134 + 83.7903i) q^{24} +(168.645 - 33.5456i) q^{25} +(-5.54974 - 13.6729i) q^{26} +(-95.0880 + 115.865i) q^{27} +(-83.2143 - 209.280i) q^{28} +(137.496 + 73.4934i) q^{29} +(-117.281 + 140.850i) q^{30} +(77.9132 - 77.9132i) q^{31} +(135.752 + 119.747i) q^{32} +(-161.104 - 161.104i) q^{33} +(246.597 - 22.5155i) q^{34} +(228.686 - 427.841i) q^{35} +(-1.46531 + 102.861i) q^{36} +(63.2608 + 51.9168i) q^{37} +(-301.954 - 127.600i) q^{38} +(3.82745 + 19.2419i) q^{39} +(-8.33075 + 389.831i) q^{40} +(-43.1213 - 8.57736i) q^{41} +(56.3232 + 294.087i) q^{42} +(349.605 + 106.051i) q^{43} +(-481.636 - 54.3744i) q^{44} +(-171.289 + 140.573i) q^{45} +(10.2556 + 34.6958i) q^{46} +(-91.6496 + 221.262i) q^{47} +(-147.318 - 190.314i) q^{48} +(-172.032 - 415.323i) q^{49} +(-378.138 + 305.849i) q^{50} +(-327.636 - 32.2693i) q^{51} +(31.8828 + 26.9346i) q^{52} +(-393.285 + 210.215i) q^{53} +(85.6674 - 415.202i) q^{54} +(-580.041 - 868.092i) q^{55} +(483.669 + 414.543i) q^{56} +(362.379 + 242.134i) q^{57} +(-440.956 - 3.14067i) q^{58} +(32.0245 + 325.150i) q^{59} +(108.369 - 506.956i) q^{60} +(-97.9212 - 322.803i) q^{61} +(-92.5898 + 297.581i) q^{62} +362.005i q^{63} +(-497.436 - 121.248i) q^{64} +89.9027i q^{65} +(615.319 + 191.451i) q^{66} +(86.9480 + 286.629i) q^{67} +(-587.831 + 380.778i) q^{68} +(-4.71482 - 47.8703i) q^{69} +(-9.77267 + 1372.10i) q^{70} +(642.110 + 429.044i) q^{71} +(-131.645 - 259.478i) q^{72} +(356.730 + 533.883i) q^{73} +(-226.695 - 46.7732i) q^{74} +(570.258 - 304.809i) q^{75} +(923.917 - 77.7271i) q^{76} +(-1697.44 - 167.183i) q^{77} +(-34.8964 - 43.1444i) q^{78} +(1.24529 + 3.00640i) q^{79} +(-491.968 - 987.051i) q^{80} +(-82.8355 + 199.983i) q^{81} +(119.254 - 35.2499i) q^{82} +(1030.37 - 845.600i) q^{83} +(-527.902 - 662.266i) q^{84} +(-1443.68 - 437.936i) q^{85} +(-1014.88 + 194.369i) q^{86} +(575.013 + 114.377i) q^{87} +(1277.49 - 497.450i) q^{88} +(151.696 + 762.627i) q^{89} +(243.962 - 577.311i) q^{90} +(113.535 + 93.1755i) q^{91} +(-71.3215 - 73.3829i) q^{92} +(195.324 - 365.425i) q^{93} +(-61.5924 - 674.579i) q^{94} +(1412.21 + 1412.21i) q^{95} +(619.227 + 282.726i) q^{96} +(835.073 - 835.073i) q^{97} +(977.112 + 813.610i) q^{98} +(687.087 + 367.255i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 5696 q^{50} - 16 q^{51} + 6608 q^{52} - 16 q^{53} + 3440 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 4768 q^{58} - 16 q^{59} - 9808 q^{60} - 16 q^{61} - 5872 q^{62} - 12112 q^{64} - 10960 q^{66} - 16 q^{67} - 4144 q^{68} - 16 q^{69} - 4048 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 5248 q^{74} - 16 q^{75} + 11888 q^{76} - 16 q^{77} + 14096 q^{78} - 16 q^{79} + 10016 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 5696 * q^50 - 16 * q^51 + 6608 * q^52 - 16 * q^53 + 3440 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 4768 * q^58 - 16 * q^59 - 9808 * q^60 - 16 * q^61 - 5872 * q^62 - 12112 * q^64 - 10960 * q^66 - 16 * q^67 - 4144 * q^68 - 16 * q^69 - 4048 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 5248 * q^74 - 16 * q^75 + 11888 * q^76 - 16 * q^77 + 14096 * q^78 - 16 * q^79 + 10016 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

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