LMFDB - Embedded newform 128.4.k.a.5.8

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			5.8
Character	$\chi$	$=$	128.5
Dual form			128.4.k.a.77.8

$q$-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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

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

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	0.616884	−	0.787054i	$-0.288395\pi$
$3$	3.59854	+	1.09161i	0.692540	+	0.210080i	0.0756563	+	0.997134i	$0.475895\pi$
$4$	4.53886	+	6.58777i	0.567357	+	0.823472i
$5$	17.1492	+	1.68905i	1.53387	+	0.151073i	0.829399	−	0.558656i	$-0.188683\pi$
$5$	17.1492	+	1.68905i	1.53387	+	0.151073i	0.704474	+	0.709730i	$0.251183\pi$
$6$	−7.57431	−	7.46718i	−0.515367	−	0.508077i
$7$	15.6405	+	23.4076i	0.844507	+	1.26389i	0.962610	+	0.270893i	$0.0873188\pi$
$7$	15.6405	+	23.4076i	0.844507	+	1.26389i	−0.118103	+	0.993001i	$0.537681\pi$
$8$	−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	0.100025	+	0.994985i	$0.468108\pi$
$11$	−28.5605	+	53.4329i	−0.782846	+	1.46460i	−0.882870	+	0.469617i	$0.844392\pi$
$12$	9.14203	+	28.6610i	0.219923	+	0.689477i
$13$	−0.511368	−	5.19201i	−0.0109099	−	0.110770i	0.988187	−	0.153250i	$-0.0489740\pi$
$13$	−0.511368	−	5.19201i	−0.0109099	−	0.110770i	−0.999097	+	0.0424804i	$0.986474\pi$
$14$	−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	−0.875857	−	0.482571i	$-0.839703\pi$
$17$	−80.8837	+	33.5031i	−1.15395	+	0.477983i	−0.278095	+	0.960553i	$0.589703\pi$
$18$	17.3729	+	31.9529i	0.227491	+	0.418409i
$19$	73.5246	−	89.5900i	0.887774	−	1.08176i	−0.108378	−	0.994110i	$-0.534566\pi$
$19$	73.5246	−	89.5900i	0.887774	−	1.08176i	0.996152	−	0.0876458i	$-0.0279344\pi$
$20$	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	0.990447	−	0.137893i	$-0.0440332\pi$
$23$	2.49549	+	12.5457i	0.0226238	+	0.113737i	−0.967823	+	0.251631i	$0.919033\pi$
$24$	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	0.0317430	−	0.999496i	$-0.489894\pi$
$29$	137.496	−	73.4934i	0.880429	−	0.470599i	0.848686	+	0.528897i	$0.177394\pi$
$30$	−117.281	−	140.850i	−0.713750	−	0.857184i
$31$	77.9132	+	77.9132i	0.451407	+	0.451407i	0.895821	−	0.444414i	$-0.146588\pi$
$31$	77.9132	+	77.9132i	0.451407	+	0.451407i	−0.444414	+	0.895821i	$0.646588\pi$
$32$	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	−0.483280	−	0.875466i	$-0.660555\pi$
$37$	63.2608	−	51.9168i	0.281081	−	0.230677i	0.764361	+	0.644789i	$0.223055\pi$
$38$	−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	−0.276532	−	0.961005i	$-0.589185\pi$
$41$	−43.1213	+	8.57736i	−0.164254	+	0.0326722i	0.112278	+	0.993677i	$0.464185\pi$
$42$	56.3232	−	294.087i	0.206925	−	1.08044i
$43$	349.605	−	106.051i	1.23987	−	0.376109i	0.398798	−	0.917039i	$-0.369427\pi$
$43$	349.605	−	106.051i	1.23987	−	0.376109i	0.841068	+	0.540929i	$0.181927\pi$
$44$	−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	0.715493	−	0.698620i	$-0.246202\pi$
$47$	−91.6496	−	221.262i	−0.284435	−	0.686688i	−0.999929	+	0.0119316i	$0.996202\pi$
$48$	−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	−0.124921	−	0.992167i	$-0.539868\pi$
$53$	−393.285	−	210.215i	−1.01928	−	0.544816i	−0.894359	+	0.447350i	$0.852368\pi$
$54$	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	−0.892946	−	0.450164i	$-0.851365\pi$
$59$	32.0245	−	325.150i	0.0706650	−	0.717474i	0.963611	−	0.267309i	$-0.0861346\pi$
$60$	108.369	+	506.956i	0.233172	+	1.09080i
$61$	−97.9212	+	322.803i	−0.205533	+	0.677552i	0.792200	+	0.610261i	$0.208936\pi$
$61$	−97.9212	+	322.803i	−0.205533	+	0.677552i	−0.997733	+	0.0672908i	$0.978564\pi$
$62$	−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	−0.841296	−	0.540575i	$-0.818207\pi$
$67$	86.9480	−	286.629i	0.158543	−	0.522647i	0.999839	+	0.0179277i	$0.00570687\pi$
$68$	−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	0.112293	−	0.993675i	$-0.464180\pi$
$71$	642.110	−	429.044i	1.07330	−	0.717157i	0.961009	+	0.276518i	$0.0891805\pi$
$72$	−131.645	+	259.478i	−0.215480	+	0.424720i
$73$	356.730	−	533.883i	0.571946	−	0.855977i	−0.426886	−	0.904306i	$-0.640389\pi$
$73$	356.730	−	533.883i	0.571946	−	0.855977i	0.998832	+	0.0483284i	$0.0153894\pi$
$74$	−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	−0.922990	−	0.384823i	$-0.874262\pi$
$79$	1.24529	−	3.00640i	0.00177350	−	0.00428161i	0.924764	+	0.380542i	$0.124262\pi$
$80$	−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	0.981012	+	0.193948i	$0.0621292\pi$
$83$	1030.37	+	845.600i	1.36262	+	1.11827i	0.381607	+	0.924325i	$0.375371\pi$
$84$	−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	−0.778969	−	0.627063i	$-0.784257\pi$
$89$	151.696	−	762.627i	0.180671	−	0.908295i	0.959640	−	0.281232i	$-0.0907431\pi$
$90$	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	0.992918	−	0.118806i	$-0.0379066\pi$
$97$	835.073	+	835.073i	0.874112	+	0.874112i	−0.118806	+	0.992918i	$0.537907\pi$
$98$	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	−0.981280	−	0.192587i	$-0.938312\pi$
$101$	−993.446	−	1210.52i	−0.978728	−	1.19258i	0.00255158	−	0.999997i	$-0.499188\pi$
$102$	862.813	+	350.210i	0.837561	+	0.339961i
$103$	−420.442	−	83.6312i	−0.402208	−	0.0800041i	−0.0101587	−	0.999948i	$-0.503234\pi$
$103$	−420.442	−	83.6312i	−0.402208	−	0.0800041i	−0.392049	+	0.919944i	$0.628234\pi$
$104$	−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	0.888762	+	0.458369i	$0.151566\pi$
$107$	447.641	+	1475.67i	0.404440	+	1.33326i	−0.484322	+	0.874890i	$0.660934\pi$
$108$	331.702	−	1152.31i	0.295537	−	1.02668i
$109$	−454.087	+	553.307i	−0.399024	+	0.486213i	−0.933300	−	0.359098i	$-0.883084\pi$
$109$	−454.087	+	553.307i	−0.399024	+	0.486213i	0.534276	+	0.845310i	$0.320584\pi$
$110$	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	−0.207129	−	0.978314i	$-0.566412\pi$
$113$	−1255.70	−	520.127i	−1.04536	−	0.433004i	−0.838234	+	0.545310i	$0.816412\pi$
$114$	−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	−0.424397	−	0.905476i	$-0.639514\pi$
$131$	−1919.67	−	582.327i	−1.28033	−	0.388383i	−0.855929	+	0.517094i	$0.827014\pi$
$132$	−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	−0.937449	−	0.348122i	$-0.886820\pi$
$137$	−2594.24	−	1733.42i	−1.61782	−	1.08099i	−0.680369	−	0.732870i	$-0.738180\pi$
$138$	74.7793	−	113.659i	0.0461278	−	0.0701110i
$139$	−944.601	+	1767.22i	−0.576403	+	1.07837i	0.409697	+	0.912222i	$0.365634\pi$
$139$	−944.601	+	1767.22i	−0.576403	+	1.07837i	−0.986100	+	0.166153i	$0.946866\pi$
$140$	−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	0.977381	−	0.211487i	$-0.0678307\pi$
$149$	85.8869	+	283.131i	0.0472223	+	0.155671i	−0.930158	+	0.367158i	$0.880331\pi$
$150$	−1026.88	−	1513.39i	−0.558962	−	0.823783i
$151$	−282.946	−	1422.47i	−0.152489	−	0.766614i	−0.979027	−	0.203732i	$-0.934693\pi$
$151$	−282.946	−	1422.47i	−0.152489	−	0.766614i	0.826538	−	0.562881i	$-0.190307\pi$
$152$	−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	−0.206972	−	0.978347i	$-0.566361\pi$
$157$	966.892	−	516.815i	0.491506	−	0.262715i	0.698478	+	0.715632i	$0.253861\pi$
$158$	−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	0.914841	−	0.403814i	$-0.132316\pi$
$163$	147.388	+	275.743i	0.0708239	+	0.132502i	−0.844017	+	0.536316i	$0.819816\pi$
$164$	−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	−0.901795	−	0.432165i	$-0.857750\pi$
$167$	208.770	−	1049.56i	0.0967372	−	0.486331i	0.998532	−	0.0541662i	$-0.0172501\pi$
$168$	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	0.855945	−	0.517066i	$-0.172976\pi$
$173$	1173.68	+	963.218i	0.515801	+	0.423307i	−0.340144	+	0.940373i	$0.610476\pi$
$174$	−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	−0.791068	−	0.611728i	$-0.790475\pi$
$179$	−3466.78	+	341.448i	−1.44759	+	0.142576i	−0.656526	+	0.754303i	$0.727975\pi$
$180$	148.608	−	1766.45i	0.0615366	−	0.731465i
$181$	−2977.41	−	1591.46i	−1.22270	−	0.653548i	−0.271596	−	0.962411i	$-0.587551\pi$
$181$	−2977.41	−	1591.46i	−1.22270	−	0.653548i	−0.951106	+	0.308864i	$0.900051\pi$
$182$	−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	$0.119451\pi$
$191$			1934.98i			0.733040i	−0.930410	+	0.366520i	$0.880549\pi$
$192$	−1922.40	−	106.689i	−0.722591	−	0.0401022i
$193$			1920.20i			0.716161i	0.933691	+	0.358080i	$0.116569\pi$
$193$			1920.20i			0.716161i	−0.933691	+	0.358080i	$0.883431\pi$
$194$	−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	0.0929630	+	0.995670i	$0.470366\pi$
$197$	−532.155	+	5403.06i	−0.192459	+	1.95407i	−0.285422	+	0.958402i	$0.592134\pi$
$198$	−2203.51	+	15.6943i	−0.790893	+	0.00563307i
$199$	−1628.89	+	1088.39i	−0.580246	+	0.387708i	−0.810775	−	0.585357i	$-0.800954\pi$
$199$	−1628.89	+	1088.39i	−0.580246	+	0.387708i	0.230529	+	0.973065i	$0.425954\pi$
$200$	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	0.804687	−	0.593700i	$-0.202333\pi$
$211$	1162.78	+	954.273i	0.379381	+	0.311350i	−0.425306	+	0.905050i	$0.639833\pi$
$212$	−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	−0.517707	−	0.855558i	$-0.673214\pi$
$223$	1125.08	−	1125.08i	0.337852	−	0.337852i	0.855558	+	0.517707i	$0.173214\pi$
$224$	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	−0.708068	−	0.706144i	$-0.750433\pi$
$227$	−1759.00	+	940.206i	−0.514313	+	0.274906i	0.193756	+	0.981050i	$0.437933\pi$
$228$	3239.91	+	1288.26i	0.941088	+	0.374197i
$229$	−266.723	−	325.002i	−0.0769673	−	0.0937850i	0.733103	−	0.680117i	$-0.238071\pi$
$229$	−266.723	−	325.002i	−0.0769673	−	0.0937850i	−0.810071	+	0.586332i	$0.800571\pi$
$230$	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	−0.889537	−	0.456863i	$-0.848973\pi$
$233$	−862.637	−	4336.77i	−0.242546	−	1.21936i	0.646991	−	0.762498i	$-0.276027\pi$
$234$	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	−0.431937	−	0.901904i	$-0.642170\pi$
$239$	−368.079	+	152.463i	−0.0996195	+	0.0412637i	0.332317	+	0.943168i	$0.392170\pi$
$240$	−2847.84	+	3014.91i	−0.765947	+	0.810882i
$241$	−779.198	−	322.754i	−0.208268	−	0.0862674i	0.276111	−	0.961126i	$-0.410954\pi$
$241$	−779.198	−	322.754i	−0.208268	−	0.0862674i	−0.484379	+	0.874858i	$0.660954\pi$
$242$	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	−0.248103	−	0.968734i	$-0.579807\pi$
$251$	−2705.78	−	266.496i	−0.680429	−	0.0670164i	−0.432326	+	0.901717i	$0.642307\pi$
$252$	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	0.955877	−	0.293766i	$-0.0949086\pi$
$263$	1359.19	+	2034.18i	0.318675	+	0.476930i	−0.637203	+	0.770696i	$0.719909\pi$
$264$	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	−0.999710	−	0.0240611i	$-0.992340\pi$
$269$	−105.459	−	1070.75i	−0.0239032	−	0.242694i	0.975807	−	0.218633i	$-0.0701596\pi$
$270$	767.832	+	7265.09i	0.173070	+	1.63755i
$271$	790.786	+	327.554i	0.177258	+	0.0734225i	0.469547	−	0.882907i	$-0.344417\pi$
$271$	790.786	+	327.554i	0.177258	+	0.0734225i	−0.292290	+	0.956330i	$0.594417\pi$
$272$	−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	−0.876513	−	0.481377i	$-0.840137\pi$
$277$	−1913.96	−	6309.49i	−0.415158	−	1.36859i	0.461355	−	0.887215i	$-0.347363\pi$
$278$	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	0.577680	−	0.816263i	$-0.303958\pi$
$281$	3763.70	+	748.646i	0.799016	+	0.158934i	0.221336	+	0.975198i	$0.428958\pi$
$282$	−958.018	+	2360.27i	−0.202302	+	0.498411i
$283$	5290.65	+	6446.68i	1.11130	+	1.35412i	0.928658	+	0.370937i	$0.120963\pi$
$283$	5290.65	+	6446.68i	1.11130	+	1.35412i	0.182637	+	0.983180i	$0.441537\pi$
$284$	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	0.375152	−	0.926963i	$-0.377590\pi$
$293$	6808.30	−	5587.43i	1.35749	−	1.11407i	0.982340	−	0.187102i	$-0.0599095\pi$
$294$	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	0.232212	−	0.972665i	$-0.425404\pi$
$307$	3494.89	−	344.217i	0.649720	−	0.0639919i	0.417508	+	0.908673i	$0.362904\pi$
$308$	−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	−0.915163	−	0.403084i	$-0.867938\pi$
$311$	−1056.02	+	1580.44i	−0.192544	+	0.288163i	0.722619	+	0.691247i	$0.242938\pi$
$312$	−442.615	−	34.0634i	−0.0803146	−	0.00618096i
$313$	−6193.88	+	4138.62i	−1.11853	+	0.747376i	−0.970379	−	0.241589i	$-0.922331\pi$
$313$	−6193.88	+	4138.62i	−1.11853	+	0.747376i	−0.148148	+	0.988965i	$0.547331\pi$
$314$	−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	0.403200	+	0.915112i	$0.367898\pi$
$317$	−2485.95	+	8195.09i	−0.440457	+	1.45199i	−0.843657	+	0.536882i	$0.819602\pi$
$318$	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	−0.326700	−	0.945128i	$-0.605937\pi$
$331$	−7792.79	−	4165.33i	−1.29405	−	0.691684i	−0.967350	+	0.253444i	$0.918437\pi$
$332$	−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	−0.985107	−	0.171941i	$-0.944996\pi$
$337$	−2537.16	−	6125.24i	−0.410112	−	0.990098i	0.574995	−	0.818157i	$-0.305004\pi$
$338$	−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	−0.292306	−	0.956325i	$-0.594423\pi$
$347$	3804.76	−	3122.48i	0.588617	−	0.483065i	0.880923	+	0.473260i	$0.156923\pi$
$348$	3363.39	+	3268.91i	0.518094	+	0.503540i
$349$	−866.778	−	1621.63i	−0.132944	−	0.248721i	0.806637	−	0.591047i	$-0.201285\pi$
$349$	−866.778	−	1621.63i	−0.132944	−	0.248721i	−0.939581	+	0.342326i	$0.888785\pi$
$350$	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	0.846766	−	0.531966i	$-0.178547\pi$
$353$	2087.83	+	2087.83i	0.314799	+	0.314799i	−0.531966	+	0.846766i	$0.678547\pi$
$354$	−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	−0.508080	−	0.861310i	$-0.669645\pi$
$359$	−8890.96	−	1768.52i	−1.30709	−	0.259997i	−0.799014	+	0.601313i	$0.794645\pi$
$360$	−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	0.180030	−	0.983661i	$-0.442380\pi$
$367$	7050.99	−	2920.61i	1.00288	−	0.415408i	0.822854	+	0.568253i	$0.192380\pi$
$368$	−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	0.480661	+	0.876907i	$0.340397\pi$
$373$	−3713.58	+	6947.62i	−0.515501	+	0.964435i	−0.996162	+	0.0875283i	$0.972103\pi$
$374$	−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	−0.115244	−	0.993337i	$-0.536765\pi$
$379$	−3114.13	−	306.715i	−0.422064	−	0.0415697i	−0.306820	+	0.951768i	$0.599265\pi$
$380$	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	−0.778767	−	0.627313i	$-0.784155\pi$
$389$	−12774.0	−	1258.13i	−1.66495	−	0.163984i	−0.886186	+	0.463329i	$0.846655\pi$
$390$	−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	0.997240	+	0.0742508i	$0.0236565\pi$
$397$	266.156	+	2702.33i	0.0336473	+	0.341627i	−0.963592	+	0.267376i	$0.913843\pi$
$398$	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	−0.0380429	−	0.999276i	$-0.512112\pi$
$401$	5152.48	−	2134.23i	0.641652	−	0.265781i	0.679695	+	0.733495i	$0.262112\pi$
$402$	−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	0.190129	−	0.981759i	$-0.439109\pi$
$409$	−82.0355	−	16.3179i	−0.00991784	−	0.00197278i	−0.200047	+	0.979786i	$0.564109\pi$
$410$	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	0.920653	−	0.390382i	$-0.127657\pi$
$419$	725.370	+	1357.07i	0.0845744	+	0.158228i	−0.836078	+	0.548610i	$0.815157\pi$
$420$	−10171.7	+	10465.7i	−1.18173	+	1.21589i
$421$	4465.46	−	3664.71i	0.516943	−	0.424244i	−0.339407	−	0.940640i	$-0.610226\pi$
$421$	4465.46	−	3664.71i	0.516943	−	0.424244i	0.856350	+	0.516395i	$0.172726\pi$
$422$	−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	0.993188	−	0.116525i	$-0.0371755\pi$
$431$	1865.64	+	4504.04i	0.208502	+	0.503369i	−0.784685	+	0.619894i	$0.787175\pi$
$432$	9096.72	−	3045.01i	1.01312	−	0.339128i
$433$	−1003.43	+	2422.51i	−0.111367	+	0.268864i	−0.969730	−	0.244178i	$-0.921482\pi$
$433$	−1003.43	+	2422.51i	−0.111367	+	0.268864i	0.858363	+	0.513043i	$0.171482\pi$
$434$	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	−0.820908	−	0.571060i	$-0.806532\pi$
$439$	191.599	−	286.748i	0.0208303	−	0.0311748i	0.841739	+	0.539885i	$0.181532\pi$
$440$	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	−0.997640	−	0.0686582i	$-0.978128\pi$
$443$	−53.8450	+	546.697i	−0.00577483	+	0.0586329i	0.991865	+	0.127291i	$0.0406282\pi$
$444$	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	$-0.941847\pi$
$449$		−	3457.02i		−	0.363356i	0.983358	−	0.181678i	$-0.0581528\pi$
$450$	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	−0.961659	−	0.274249i	$-0.911571\pi$
$457$	−3324.33	+	4975.21i	−0.340275	+	0.509257i	0.621384	+	0.783506i	$0.286571\pi$
$458$	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	−0.00664113	−	0.999978i	$-0.502114\pi$
$461$	1800.77	−	177.361i	0.181931	−	0.0179187i	0.188572	+	0.982059i	$0.439614\pi$
$462$	14105.3	+	11408.8i	1.42043	+	1.14888i
$463$	2186.49	−	5278.66i	0.219470	−	0.529849i	−0.775346	−	0.631537i	$-0.782424\pi$
$463$	2186.49	−	5278.66i	0.219470	−	0.529849i	0.994816	+	0.101688i	$0.0324244\pi$
$464$	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	0.172660	−	0.984981i	$-0.444764\pi$
$467$	−7666.97	−	6292.12i	−0.759711	−	0.623479i	−0.932371	+	0.361503i	$0.882264\pi$
$468$	−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	−0.0810123	+	0.996713i	$0.525815\pi$
$479$	−11298.3	+	11298.3i	−1.07773	+	1.07773i	−0.996713	+	0.0810123i	$0.974185\pi$
$480$	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	−0.483425	−	0.875386i	$-0.660607\pi$
$487$	−13595.7	−	2704.34i	−1.26505	−	0.251634i	−0.781622	+	0.623752i	$0.785607\pi$
$488$	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	0.847215	+	0.531251i	$0.178278\pi$
$491$	4764.59	+	15706.7i	0.437928	+	1.44366i	−0.409286	+	0.912406i	$0.634222\pi$
$492$	−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	0.990745	+	0.135733i	$0.0433388\pi$
$499$	507.370	+	5151.41i	0.0455170	+	0.462142i	−0.945228	+	0.326410i	$0.894161\pi$
$500$	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	0.963893	−	0.266289i	$-0.0857974\pi$
$503$	12259.6	+	8191.63i	1.08674	+	0.726137i	0.122848	+	0.992426i	$0.460797\pi$
$504$	−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	0.307013	−	0.951705i	$-0.400671\pi$
$509$	385.220	+	116.855i	0.0335453	+	0.0101759i	−0.273467	+	0.961881i	$0.588171\pi$
$510$	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	0.645410	−	0.763836i	$-0.276686\pi$
$521$	2220.32	+	1483.57i	0.186706	+	0.124753i	−0.458704	+	0.888589i	$0.651686\pi$
$522$	4737.04	+	3116.62i	0.397193	+	0.261323i
$523$	−15.0367	+	28.1316i	−0.00125718	+	0.00235202i	−0.882549	−	0.470220i	$-0.844174\pi$
$523$	−15.0367	+	28.1316i	−0.00125718	+	0.00235202i	0.881292	+	0.472572i	$0.156674\pi$
$524$	−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	−0.445899	−	0.895083i	$-0.647116\pi$
$541$	636.802	−	340.378i	0.0506068	−	0.0270499i	0.496506	+	0.868033i	$0.334616\pi$
$542$	−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	0.998222	+	0.0595974i	$0.0189817\pi$
$547$	6309.55	+	11804.3i	0.493193	+	0.922700i	−0.505029	+	0.863102i	$0.668518\pi$
$548$	−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	0.349542	−	0.936921i	$-0.386337\pi$
$557$	−6588.39	−	5406.96i	−0.501184	−	0.411311i	−0.850726	+	0.525610i	$0.823837\pi$
$558$	−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	−0.244278	−	0.969705i	$-0.578551\pi$
$563$	−3936.56	+	387.718i	−0.294683	+	0.0290237i	−0.0504044	+	0.998729i	$0.516051\pi$
$564$	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	−0.696410	−	0.717644i	$-0.745220\pi$
$569$	−4070.43	+	2719.78i	−0.299897	+	0.200385i	0.396513	+	0.918029i	$0.370220\pi$
$570$	−21241.8	+	151.293i	−1.56091	+	0.0111175i
$571$	−1130.88	+	11482.0i	−0.0828826	+	0.841521i	0.860420	+	0.509586i	$0.170202\pi$
$571$	−1130.88	+	11482.0i	−0.0828826	+	0.841521i	−0.943302	+	0.331935i	$0.892298\pi$
$572$	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	$0.0802207\pi$
$577$			6912.31i			0.498723i	−0.968410	+	0.249361i	$0.919779\pi$
$578$	−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	0.987005	−	0.160689i	$-0.0513717\pi$
$587$	19935.5	+	10655.7i	1.40175	+	0.749250i	0.414742	+	0.909939i	$0.363872\pi$
$588$	−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	0.970931	−	0.239359i	$-0.0769374\pi$
$593$	1662.48	+	4013.59i	0.115127	+	0.277940i	−0.855804	+	0.517299i	$0.826937\pi$
$594$	−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	−0.0803711	−	0.996765i	$-0.525611\pi$
$599$	3325.24	−	661.432i	0.226821	−	0.0451175i	0.307192	+	0.951647i	$0.400611\pi$
$600$	5308.99	−	13633.9i	0.361231	−	0.927669i
$601$	3473.39	−	17461.9i	0.235745	−	1.18517i	−0.663654	−	0.748039i	$-0.730995\pi$
$601$	3473.39	−	17461.9i	0.235745	−	1.18517i	0.899399	−	0.437129i	$-0.144005\pi$
$602$	−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	−0.888682	−	0.458523i	$-0.848379\pi$
$607$	−6432.98	+	6432.98i	−0.430159	+	0.430159i	0.458523	+	0.888682i	$0.348379\pi$
$608$	−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	0.977856	−	0.209281i	$-0.0671122\pi$
$613$	8830.47	+	10760.0i	0.581826	+	0.708957i	−0.396030	+	0.918238i	$0.629612\pi$
$614$	−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	−0.942007	−	0.335594i	$-0.891063\pi$
$617$	−3067.22	−	15420.0i	−0.200132	−	1.00613i	0.741874	−	0.670539i	$-0.233937\pi$
$618$	2560.07	+	3772.97i	0.166636	+	0.245584i
$619$	2302.14	+	7589.13i	0.149484	+	0.492783i	0.999418	−	0.0341059i	$-0.0108583\pi$
$619$	2302.14	+	7589.13i	0.149484	+	0.492783i	−0.849934	+	0.526889i	$0.823358\pi$
$620$	−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	−0.274436	−	0.961605i	$-0.588491\pi$
$631$	−20096.3	−	13427.9i	−1.26787	−	0.847160i	−0.993430	+	0.114445i	$0.963491\pi$
$632$	−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	0.783065	−	0.621940i	$-0.213655\pi$
$643$	17749.9	+	5384.38i	1.08863	+	0.330232i	0.305564	+	0.952172i	$0.401155\pi$
$644$	−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	−0.991847	−	0.127434i	$-0.959326\pi$
$647$	−12014.1	−	17980.3i	−0.730017	−	1.09255i	0.261830	−	0.965114i	$-0.415674\pi$
$648$	−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	0.989001	−	0.147907i	$-0.0472536\pi$
$653$	−164.394	−	1669.12i	−0.00985183	−	0.100027i	−0.998853	+	0.0478797i	$0.984754\pi$
$654$	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	−0.665045	−	0.746803i	$-0.731588\pi$
$659$	3335.26	−	4064.02i	0.197152	−	0.240231i	0.862197	+	0.506573i	$0.169088\pi$
$660$	−30183.2	−	8688.45i	−1.78012	−	0.512420i
$661$	−5252.77	−	17316.0i	−0.309091	−	1.01894i	−0.964593	−	0.263742i	$-0.915043\pi$
$661$	−5252.77	−	17316.0i	−0.309091	−	1.01894i	0.655503	−	0.755193i	$-0.272457\pi$
$662$	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	−0.340718	−	0.940165i	$-0.610670\pi$
$673$	10465.8	−	10465.8i	0.599447	−	0.599447i	0.940165	+	0.340718i	$0.110670\pi$
$674$	−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	−0.361462	−	0.932387i	$-0.617722\pi$
$677$	8499.09	−	6975.02i	0.482491	−	0.395970i	0.843953	+	0.536416i	$0.180222\pi$
$678$	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	−0.333396	−	0.942787i	$-0.608195\pi$
$683$	−1549.71	+	470.100i	−0.0868201	+	0.0263366i	0.246576	+	0.969124i	$0.420695\pi$
$684$	−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	−0.498288	−	0.867012i	$-0.666038\pi$
$691$	−14855.7	+	1463.16i	−0.817855	+	0.0805517i	−0.319568	+	0.947563i	$0.603538\pi$
$692$	−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	−0.798219	−	0.602367i	$-0.794224\pi$
$701$	3714.47	−	12245.0i	0.200133	−	0.659751i	0.998352	−	0.0573836i	$-0.0182758\pi$
$702$	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	−0.978299	−	0.207199i	$-0.933565\pi$
$709$	408.246	−	4144.99i	0.0216248	−	0.219560i	0.999924	−	0.0123612i	$-0.00393481\pi$
$710$	−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	0.620096	+	0.784526i	$0.287094\pi$
$719$	−7193.56	+	17366.8i	−0.373122	+	0.900795i	−0.993218	+	0.116270i	$0.962906\pi$
$720$	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	−0.143746	−	0.989615i	$-0.545915\pi$
$727$	2002.54	−	398.330i	0.102160	−	0.0203208i	0.245905	+	0.969294i	$0.420915\pi$
$728$	−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	0.638227	−	0.769848i	$-0.279668\pi$
$733$	−7073.99	−	13234.5i	−0.356458	−	0.666886i	−0.994685	+	0.102962i	$0.967168\pi$
$734$	−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	−0.0208907	−	0.999782i	$-0.506650\pi$
$739$	16047.2	−	8577.42i	0.798791	−	0.426963i	0.819682	+	0.572819i	$0.194150\pi$
$740$	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	0.577348	−	0.816498i	$-0.304088\pi$
$743$	16167.5	+	3215.91i	0.798287	+	0.158789i	0.220939	+	0.975288i	$0.429088\pi$
$744$	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	0.393933	−	0.919139i	$-0.371114\pi$
$751$	27216.2	−	11273.3i	1.32242	−	0.547763i	0.928482	+	0.371376i	$0.121114\pi$
$752$	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	−0.341754	−	0.939789i	$-0.611021\pi$
$757$	13111.5	−	24530.0i	0.629520	−	1.17775i	0.971275	−	0.237961i	$-0.0764789\pi$
$758$	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	0.999991	−	0.00425970i	$-0.00135591\pi$
$761$	12876.7	+	19271.3i	0.613376	+	0.917981i	−0.386615	+	0.922241i	$0.626356\pi$
$762$	−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	−0.397874	−	0.917440i	$-0.630252\pi$
$773$	−20784.3	−	2047.07i	−0.967087	−	0.0952498i	−0.569213	+	0.822190i	$0.692752\pi$
$774$	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	−0.970610	−	0.240658i	$-0.922637\pi$
$787$	−12037.4	+	14667.6i	−0.545219	+	0.664352i	0.425391	+	0.905010i	$0.360137\pi$
$788$	−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	0.124888	−	0.992171i	$-0.460143\pi$
$797$	22933.0	−	12257.9i	1.01923	−	0.544791i	0.894344	+	0.447380i	$0.147643\pi$
$798$	−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	0.0339781	−	0.999423i	$-0.489182\pi$
$809$	10304.8	−	2049.75i	0.447832	−	0.0890794i	0.413854	+	0.910343i	$0.364182\pi$
$810$	−1984.50	+	10361.9i	−0.0860843	+	0.449483i
$811$	−31128.4	+	9442.69i	−1.34780	+	0.408850i	−0.879995	−	0.474982i	$-0.842454\pi$
$811$	−31128.4	+	9442.69i	−1.34780	+	0.408850i	−0.467803	+	0.883833i	$0.654954\pi$
$812$	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	−0.466897	−	0.884312i	$-0.654628\pi$
$821$	−34382.2	−	18377.7i	−1.46157	−	0.781225i	−0.994672	+	0.103087i	$0.967128\pi$
$822$	6705.86	+	32501.1i	0.284542	+	1.37908i
$823$	10860.0	−	16253.2i	0.459972	−	0.688397i	−0.526895	−	0.849930i	$-0.676644\pi$
$823$	10860.0	−	16253.2i	0.459972	−	0.688397i	0.986867	+	0.161533i	$0.0516439\pi$
$824$	−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	0.317935	+	0.948113i	$0.397011\pi$
$827$	−4253.71	+	43188.7i	−0.178859	+	1.81598i	−0.496793	+	0.867869i	$0.665489\pi$
$828$	1286.80	−	275.071i	0.0540090	−	0.0115452i
$829$	−10542.7	+	34754.5i	−0.441691	+	1.45606i	0.400208	+	0.916424i	$0.368938\pi$
$829$	−10542.7	+	34754.5i	−0.441691	+	1.45606i	−0.841899	+	0.539635i	$0.818562\pi$
$830$	−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	−0.874122	−	0.485706i	$-0.838563\pi$
$839$	−18467.1	+	12339.3i	−0.759901	+	0.507749i	0.114222	+	0.993455i	$0.463563\pi$
$840$	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	−0.850126	−	0.526579i	$-0.823474\pi$
$853$	−31500.5	+	9555.58i	−1.26443	+	0.383560i	−0.414302	+	0.910139i	$0.635974\pi$
$854$	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	−0.652870	−	0.757470i	$-0.726435\pi$
$857$	6025.57	−	30292.6i	0.240175	−	1.20744i	0.893044	−	0.449969i	$-0.148565\pi$
$858$	−1308.67	−	3096.84i	−0.0520714	−	0.123222i
$859$	15738.3	−	12916.1i	0.625127	−	0.513029i	−0.267656	−	0.963514i	$-0.586249\pi$
$859$	15738.3	−	12916.1i	0.625127	−	0.513029i	0.892784	+	0.450486i	$0.148749\pi$
$860$	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	−0.933950	−	0.357403i	$-0.883662\pi$
$863$	−14616.8	+	14616.8i	−0.576547	+	0.576547i	0.357403	+	0.933950i	$0.383662\pi$
$864$	−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	−0.136933	+	0.990580i	$0.543725\pi$
$877$	−28095.2	+	34234.1i	−1.08177	+	1.31814i	−0.944832	+	0.327555i	$0.893775\pi$
$878$	−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	0.454626	−	0.890682i	$-0.349773\pi$
$881$	3825.36	+	1584.52i	0.146288	+	0.0605944i	−0.308338	+	0.951277i	$0.599773\pi$
$882$	−16259.5	+	1718.43i	−0.620732	+	0.0656039i
$883$	−81.6287	−	828.790i	−0.00311101	−	0.0315866i	0.993504	−	0.113798i	$-0.0363017\pi$
$883$	−81.6287	−	828.790i	−0.00311101	−	0.0315866i	−0.996615	+	0.0822115i	$0.973802\pi$
$884$	−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	0.901119	−	0.433572i	$-0.142747\pi$
$887$	22332.9	+	14922.3i	0.845394	+	0.564874i	−0.0557250	+	0.998446i	$0.517747\pi$
$888$	−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	−0.924978	−	0.380020i	$-0.875917\pi$
$907$	−2598.08	+	4860.66i	−0.0951132	+	0.177944i	0.829865	+	0.557964i	$0.188417\pi$
$908$	−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	0.668923	−	0.743332i	$-0.266756\pi$
$911$	16946.3	+	7019.39i	0.616308	+	0.255283i	−0.0526152	+	0.998615i	$0.516756\pi$
$912$	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	0.999856	−	0.0169457i	$-0.00539425\pi$
$919$	1939.71	+	9751.57i	0.0696247	+	0.350027i	−0.930232	+	0.366973i	$0.880394\pi$
$920$	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	−0.697511	−	0.716574i	$-0.745709\pi$
$929$	539.761	−	539.761i	0.0190624	−	0.0190624i	0.716574	+	0.697511i	$0.245709\pi$
$930$	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	0.511235	−	0.859441i	$-0.329188\pi$
$937$	37643.6	−	7487.78i	1.31245	−	0.261062i	0.801213	+	0.598379i	$0.204188\pi$
$938$	−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	0.760501	−	0.649336i	$-0.224953\pi$
$941$	7851.76	+	6443.77i	0.272009	+	0.223232i	−0.488493	+	0.872568i	$0.662453\pi$
$942$	−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	−0.0428536	−	0.999081i	$-0.513645\pi$
$947$	3206.46	−	315.809i	0.110027	−	0.0108367i	0.152881	+	0.988245i	$0.451145\pi$
$948$	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	−0.268341	−	0.963324i	$-0.586475\pi$
$953$	15267.8	−	10201.6i	0.518965	−	0.346761i	0.787306	+	0.616563i	$0.211475\pi$
$954$	−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	−0.760981	−	0.648774i	$-0.775282\pi$
$967$	−13616.1	+	9098.00i	−0.452808	+	0.302556i	0.308174	+	0.951330i	$0.400282\pi$
$968$	−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	0.462026	−	0.886866i	$-0.347123\pi$
$971$	−565.458	−	302.244i	−0.0186884	−	0.00998914i	−0.480714	+	0.876877i	$0.659623\pi$
$972$	−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	0.810262	−	0.586068i	$-0.199325\pi$
$977$	−5408.08	−	13056.3i	−0.177093	−	0.427540i	−0.987354	+	0.158529i	$0.949325\pi$
$978$	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	0.832198	−	0.554479i	$-0.187083\pi$
$983$	55883.7	−	11116.0i	1.81324	−	0.360675i	0.981040	+	0.193804i	$0.0620825\pi$
$984$	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	−0.655130	−	0.755516i	$-0.727386\pi$
$991$	3131.71	−	3131.71i	0.100386	−	0.100386i	0.755516	+	0.655130i	$0.227386\pi$
$992$	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	0.473510	−	0.880788i	$-0.342987\pi$
$997$	−15196.7	−	18517.2i	−0.482731	−	0.588209i	−0.956241	+	0.292579i	$0.905487\pi$
$998$	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.5.8	✓	752
128.77	even	32	inner	128.4.k.a.77.8	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.4.k.a.5.8	✓	752	1.1	even	1	trivial
128.4.k.a.77.8	yes	752	128.77	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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