LMFDB - Embedded newform 128.4.k.a.5.11

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			5.11
Character	$\chi$	$=$	128.5
Dual form			128.4.k.a.77.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.23791 - 1.72967i) q^{2} +(7.71088 + 2.33907i) q^{3} +(2.01649 + 7.74169i) q^{4} +(13.5785 + 1.33737i) q^{5} +(-13.2105 - 18.5719i) q^{6} +(-18.9453 - 28.3537i) q^{7} +(8.87784 - 20.8131i) q^{8} +(31.5368 + 21.0722i) q^{9} +O(q^{10})$	\(q+(-2.23791 - 1.72967i) q^{2} +(7.71088 + 2.33907i) q^{3} +(2.01649 + 7.74169i) q^{4} +(13.5785 + 1.33737i) q^{5} +(-13.2105 - 18.5719i) q^{6} +(-18.9453 - 28.3537i) q^{7} +(8.87784 - 20.8131i) q^{8} +(31.5368 + 21.0722i) q^{9} +(-28.0744 - 26.4793i) q^{10} +(25.4398 - 47.5946i) q^{11} +(-2.55945 + 64.4120i) q^{12} +(6.75742 + 68.6092i) q^{13} +(-6.64454 + 96.2221i) q^{14} +(101.574 + 42.0735i) q^{15} +(-55.8675 + 31.2221i) q^{16} +(48.7014 - 20.1728i) q^{17} +(-34.1286 - 101.706i) q^{18} +(26.9496 - 32.8382i) q^{19} +(17.0275 + 107.818i) q^{20} +(-79.7639 - 262.946i) q^{21} +(-139.255 + 62.5099i) q^{22} +(30.3488 + 152.574i) q^{23} +(117.139 - 139.721i) q^{24} +(59.9900 + 11.9328i) q^{25} +(103.549 - 165.229i) q^{26} +(55.8672 + 68.0744i) q^{27} +(181.302 - 203.844i) q^{28} +(-114.856 + 61.3918i) q^{29} +(-154.541 - 269.847i) q^{30} +(20.3524 + 20.3524i) q^{31} +(179.030 + 26.7601i) q^{32} +(307.491 - 307.491i) q^{33} +(-143.882 - 39.0924i) q^{34} +(-219.330 - 410.338i) q^{35} +(-99.5409 + 286.640i) q^{36} +(-3.87419 + 3.17947i) q^{37} +(-117.110 + 26.8751i) q^{38} +(-108.376 + 544.844i) q^{39} +(148.383 - 270.738i) q^{40} +(-86.0725 + 17.1209i) q^{41} +(-276.306 + 726.416i) q^{42} +(88.6468 - 26.8907i) q^{43} +(419.761 + 100.973i) q^{44} +(400.042 + 328.306i) q^{45} +(195.984 - 393.940i) q^{46} +(47.3927 + 114.416i) q^{47} +(-503.819 + 110.072i) q^{48} +(-313.745 + 757.449i) q^{49} +(-113.613 - 130.467i) q^{50} +(422.716 - 41.6339i) q^{51} +(-517.525 + 190.664i) q^{52} +(-621.359 - 332.123i) q^{53} +(-7.27966 - 248.976i) q^{54} +(409.087 - 612.242i) q^{55} +(-758.321 + 142.591i) q^{56} +(284.616 - 190.175i) q^{57} +(363.225 + 61.2734i) q^{58} +(-39.0983 + 396.972i) q^{59} +(-120.896 + 871.198i) q^{60} +(21.7196 - 71.6000i) q^{61} +(-10.3439 - 80.7496i) q^{62} -1293.40i q^{63} +(-354.368 - 369.550i) q^{64} +940.650i q^{65} +(-1219.99 + 156.279i) q^{66} +(61.7680 - 203.622i) q^{67} +(254.377 + 336.353i) q^{68} +(-122.865 + 1247.47i) q^{69} +(-218.908 + 1297.67i) q^{70} +(-593.057 + 396.268i) q^{71} +(718.556 - 469.302i) q^{72} +(78.6477 - 117.705i) q^{73} +(14.1695 - 0.414294i) q^{74} +(434.664 + 232.333i) q^{75} +(308.567 + 142.418i) q^{76} +(-1831.45 + 180.382i) q^{77} +(1184.94 - 1031.86i) q^{78} +(273.084 - 659.282i) q^{79} +(-800.355 + 349.235i) q^{80} +(-120.345 - 290.537i) q^{81} +(222.236 + 110.562i) q^{82} +(3.04169 + 2.49625i) q^{83} +(1874.81 - 1147.74i) q^{84} +(688.273 - 208.785i) q^{85} +(-244.896 - 93.1507i) q^{86} +(-1029.24 + 204.729i) q^{87} +(-764.738 - 952.018i) q^{88} +(-94.5205 + 475.187i) q^{89} +(-327.398 - 1426.66i) q^{90} +(1817.30 - 1491.42i) q^{91} +(-1119.98 + 542.615i) q^{92} +(109.329 + 204.540i) q^{93} +(91.8414 - 338.027i) q^{94} +(409.853 - 409.853i) q^{95} +(1317.89 + 625.109i) q^{96} +(450.237 + 450.237i) q^{97} +(2012.27 - 1152.43i) q^{98} +(1805.21 - 964.906i) 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 $

$2$	−2.23791	−	1.72967i	−0.791221	−	0.611530i
$2$	−2.23791	−	1.72967i	−0.791221	−	0.611530i
$3$	7.71088	+	2.33907i	1.48396	+	0.450154i	0.925298	−	0.379241i	$-0.123815\pi$
$3$	7.71088	+	2.33907i	1.48396	+	0.450154i	0.558662	+	0.829395i	$0.311315\pi$
$4$	2.01649	+	7.74169i	0.252061	+	0.967711i
$5$	13.5785	+	1.33737i	1.21450	+	0.119618i	0.684905	−	0.728632i	$-0.259844\pi$
$5$	13.5785	+	1.33737i	1.21450	+	0.119618i	0.529596	+	0.848250i	$0.322344\pi$
$6$	−13.2105	−	18.5719i	−0.898857	−	1.26366i
$7$	−18.9453	−	28.3537i	−1.02295	−	1.53095i	−0.836108	−	0.548565i	$-0.815174\pi$
$7$	−18.9453	−	28.3537i	−1.02295	−	1.53095i	−0.186843	−	0.982390i	$-0.559826\pi$
$8$	8.87784	−	20.8131i	0.392349	−	0.919817i
$9$	31.5368	+	21.0722i	1.16803	+	0.780452i
$10$	−28.0744	−	26.4793i	−0.887789	−	0.837349i
$11$	25.4398	−	47.5946i	0.697309	−	1.30457i	−0.244901	−	0.969548i	$-0.578755\pi$
$11$	25.4398	−	47.5946i	0.697309	−	1.30457i	0.942209	−	0.335024i	$-0.108745\pi$
$12$	−2.55945	+	64.4120i	−0.0615707	+	1.54951i
$13$	6.75742	+	68.6092i	0.144167	+	1.46375i	0.746435	+	0.665458i	$0.231764\pi$
$13$	6.75742	+	68.6092i	0.144167	+	1.46375i	−0.602268	+	0.798294i	$0.705736\pi$
$14$	−6.64454	+	96.2221i	−0.126845	+	1.83689i
$15$	101.574	+	42.0735i	1.74843	+	0.724221i
$16$	−55.8675	+	31.2221i	−0.872930	+	0.487845i
$17$	48.7014	−	20.1728i	0.694813	−	0.287801i	−0.00719058	−	0.999974i	$-0.502289\pi$
$17$	48.7014	−	20.1728i	0.694813	−	0.287801i	0.702004	+	0.712173i	$0.252289\pi$
$18$	−34.1286	−	101.706i	−0.446899	−	1.33180i
$19$	26.9496	−	32.8382i	0.325404	−	0.396505i	−0.584454	−	0.811427i	$-0.698691\pi$
$19$	26.9496	−	32.8382i	0.325404	−	0.396505i	0.909857	+	0.414922i	$0.136191\pi$
$20$	17.0275	+	107.818i	0.190373	+	1.20544i
$21$	−79.7639	−	262.946i	−0.828853	−	2.73236i
$22$	−139.255	+	62.5099i	−1.34951	+	0.605780i
$23$	30.3488	+	152.574i	0.275138	+	1.38321i	0.832998	+	0.553276i	$0.186622\pi$
$23$	30.3488	+	152.574i	0.275138	+	1.38321i	−0.557860	+	0.829935i	$0.688378\pi$
$24$	117.139	−	139.721i	0.996289	−	1.18835i
$25$	59.9900	+	11.9328i	0.479920	+	0.0954620i
$26$	103.549	−	165.229i	0.781061	−	1.24631i
$27$	55.8672	+	68.0744i	0.398209	+	0.485219i
$28$	181.302	−	203.844i	1.22368	−	1.37582i
$29$	−114.856	+	61.3918i	−0.735456	+	0.393109i	−0.796192	−	0.605045i	$-0.793155\pi$
$29$	−114.856	+	61.3918i	−0.735456	+	0.393109i	0.0607359	+	0.998154i	$0.480655\pi$
$30$	−154.541	−	269.847i	−0.940507	−	1.64223i
$31$	20.3524	+	20.3524i	0.117916	+	0.117916i	0.763602	−	0.645687i	$-0.223429\pi$
$31$	20.3524	+	20.3524i	0.117916	+	0.117916i	−0.645687	+	0.763602i	$0.723429\pi$
$32$	179.030	+	26.7601i	0.989013	+	0.147830i
$33$	307.491	−	307.491i	1.62204	−	1.62204i
$34$	−143.882	−	39.0924i	−0.725750	−	0.197185i
$35$	−219.330	−	410.338i	−1.05925	−	1.98171i
$36$	−99.5409	+	286.640i	−0.460838	+	1.32704i
$37$	−3.87419	+	3.17947i	−0.0172139	+	0.0141271i	−0.642961	−	0.765899i	$-0.722294\pi$
$37$	−3.87419	+	3.17947i	−0.0172139	+	0.0141271i	0.625747	+	0.780026i	$0.284794\pi$
$38$	−117.110	+	26.8751i	−0.499941	+	0.114729i
$39$	−108.376	+	544.844i	−0.444976	+	2.23705i
$40$	148.383	−	270.738i	0.586535	−	1.07019i
$41$	−86.0725	+	17.1209i	−0.327860	+	0.0652154i	−0.356276	−	0.934381i	$-0.615954\pi$
$41$	−86.0725	+	17.1209i	−0.327860	+	0.0652154i	0.0284160	+	0.999596i	$0.490954\pi$
$42$	−276.306	+	726.416i	−1.01512	+	2.66877i
$43$	88.6468	−	26.8907i	0.314384	−	0.0953674i	−0.129149	−	0.991625i	$-0.541225\pi$
$43$	88.6468	−	26.8907i	0.314384	−	0.0953674i	0.443534	+	0.896258i	$0.353725\pi$
$44$	419.761	+	100.973i	1.43821	+	0.345961i
$45$	400.042	+	328.306i	1.32522	+	1.08758i
$46$	195.984	−	393.940i	0.628181	−	1.26268i
$47$	47.3927	+	114.416i	0.147084	+	0.355092i	0.980201	−	0.198005i	$-0.0634461\pi$
$47$	47.3927	+	114.416i	0.147084	+	0.355092i	−0.833117	+	0.553096i	$0.813446\pi$
$48$	−503.819	+	110.072i	−1.51500	+	0.330989i
$49$	−313.745	+	757.449i	−0.914710	+	2.20830i
$50$	−113.613	−	130.467i	−0.321345	−	0.369017i
$51$	422.716	−	41.6339i	1.16063	−	0.114312i
$52$	−517.525	+	190.664i	−1.38015	+	0.508467i
$53$	−621.359	−	332.123i	−1.61038	−	0.860767i	−0.997506	−	0.0705882i	$-0.977512\pi$
$53$	−621.359	−	332.123i	−1.61038	−	0.860767i	−0.612876	−	0.790179i	$-0.709988\pi$
$54$	−7.27966	−	248.976i	−0.0183451	−	0.627433i
$55$	409.087	−	612.242i	1.00293	−	1.50099i
$56$	−758.321	+	142.591i	−1.80955	+	0.340259i
$57$	284.616	−	190.175i	0.661375	−	0.441916i
$58$	363.225	+	61.2734i	0.822306	+	0.138717i
$59$	−39.0983	+	396.972i	−0.0862740	+	0.875954i	0.850490	+	0.525992i	$0.176306\pi$
$59$	−39.0983	+	396.972i	−0.0862740	+	0.875954i	−0.936764	+	0.349963i	$0.886194\pi$
$60$	−120.896	+	871.198i	−0.260127	+	1.87452i
$61$	21.7196	−	71.6000i	0.0455887	−	0.150286i	−0.931191	−	0.364531i	$-0.881229\pi$
$61$	21.7196	−	71.6000i	0.0455887	−	0.150286i	0.976780	+	0.214245i	$0.0687292\pi$
$62$	−10.3439	−	80.7496i	−0.0211884	−	0.165407i
$63$		−	1293.40i		−	2.58656i
$64$	−354.368	−	369.550i	−0.692125	−	0.721778i
$65$			940.650i			1.79497i
$66$	−1219.99	+	156.279i	−2.27531	+	0.291465i
$67$	61.7680	−	203.622i	0.112629	−	0.371289i	−0.882446	−	0.470414i	$-0.844104\pi$
$67$	61.7680	−	203.622i	0.112629	−	0.371289i	0.995075	+	0.0991253i	$0.0316045\pi$
$68$	254.377	+	336.353i	0.453644	+	0.599835i
$69$	−122.865	+	1247.47i	−0.214365	+	2.17648i
$70$	−218.908	+	1297.67i	−0.373778	+	2.21573i
$71$	−593.057	+	396.268i	−0.991309	+	0.662371i	−0.941720	−	0.336398i	$-0.890791\pi$
$71$	−593.057	+	396.268i	−0.991309	+	0.662371i	−0.0495890	+	0.998770i	$0.515791\pi$
$72$	718.556	−	469.302i	1.17615	−	0.768163i
$73$	78.6477	−	117.705i	0.126096	−	0.188716i	−0.763050	−	0.646339i	$-0.776299\pi$
$73$	78.6477	−	117.705i	0.126096	−	0.188716i	0.889146	+	0.457623i	$0.151299\pi$
$74$	14.1695	−	0.414294i	0.0222591	−	0.000650820i
$75$	434.664	+	232.333i	0.669210	+	0.357700i
$76$	308.567	+	142.418i	0.465724	+	0.214953i
$77$	−1831.45	+	180.382i	−2.71055	+	0.266966i
$78$	1184.94	−	1031.86i	1.72010	−	1.49788i
$79$	273.084	−	659.282i	0.388915	−	0.938925i	−0.601255	−	0.799057i	$-0.705332\pi$
$79$	273.084	−	659.282i	0.388915	−	0.938925i	0.990170	−	0.139868i	$-0.0446677\pi$
$80$	−800.355	+	349.235i	−1.11853	+	0.488070i
$81$	−120.345	−	290.537i	−0.165082	−	0.398542i
$82$	222.236	+	110.562i	0.299291	+	0.148897i
$83$	3.04169	+	2.49625i	0.00402252	+	0.00330120i	0.636402	−	0.771357i	$-0.280422\pi$
$83$	3.04169	+	2.49625i	0.00402252	+	0.00330120i	−0.632380	+	0.774658i	$0.717922\pi$
$84$	1874.81	−	1147.74i	2.43522	−	1.49081i
$85$	688.273	−	208.785i	0.878278	−	0.266423i
$86$	−244.896	−	93.1507i	−0.307067	−	0.116799i
$87$	−1029.24	+	204.729i	−1.26835	+	0.252290i
$88$	−764.738	−	952.018i	−0.926379	−	1.15324i
$89$	−94.5205	+	475.187i	−0.112575	+	0.565952i	0.882789	+	0.469770i	$0.155663\pi$
$89$	−94.5205	+	475.187i	−0.112575	+	0.565952i	−0.995364	+	0.0961819i	$0.969337\pi$
$90$	−327.398	−	1426.66i	−0.383453	−	1.67092i
$91$	1817.30	−	1491.42i	2.09346	−	1.71806i
$92$	−1119.98	+	542.615i	−1.26920	+	0.614908i
$93$	109.329	+	204.540i	0.121902	+	0.228063i
$94$	91.8414	−	338.027i	0.100774	−	0.370902i
$95$	409.853	−	409.853i	0.442632	−	0.442632i
$96$	1317.89	+	625.109i	1.40111	+	0.664583i
$97$	450.237	+	450.237i	0.471285	+	0.471285i	0.902330	−	0.431045i	$-0.141855\pi$
$97$	450.237	+	450.237i	0.471285	+	0.471285i	−0.431045	+	0.902330i	$0.641855\pi$
$98$	2012.27	−	1152.43i	2.07418	−	1.18788i
$99$	1805.21	−	964.906i	1.83263	−	0.979563i
$100$	28.5895	+	488.486i	0.0285895	+	0.488486i
$101$	571.066	+	695.846i	0.562606	+	0.685538i	0.974163	−	0.225847i	$-0.0725148\pi$
$101$	571.066	+	695.846i	0.562606	+	0.685538i	−0.411557	+	0.911384i	$0.635015\pi$
$102$	−1018.01	−	637.987i	−0.988220	−	0.619315i
$103$	−1066.17	−	212.075i	−1.01993	−	0.202878i	−0.343323	−	0.939218i	$-0.611552\pi$
$103$	−1066.17	−	212.075i	−1.01993	−	0.202878i	−0.676612	+	0.736340i	$0.736552\pi$
$104$	1487.96	+	468.459i	1.40295	+	0.441694i
$105$	−731.421	−	3677.10i	−0.679804	−	3.41760i
$106$	816.083	+	1818.01i	0.747783	+	1.66585i
$107$	−25.8650	−	85.2654i	−0.0233688	−	0.0770366i	0.944480	−	0.328568i	$-0.106566\pi$
$107$	−25.8650	−	85.2654i	−0.0233688	−	0.0770366i	−0.967849	+	0.251531i	$0.919066\pi$
$108$	−414.355	+	569.778i	−0.369179	+	0.507657i
$109$	−568.530	+	692.756i	−0.499590	+	0.608752i	−0.960358	−	0.278768i	$-0.910074\pi$
$109$	−568.530	+	692.756i	−0.499590	+	0.608752i	0.460768	+	0.887520i	$0.347574\pi$
$110$	−1974.48	+	662.558i	−1.71145	+	0.574295i
$111$	−37.3104	+	15.4545i	−0.0319040	+	0.0132151i
$112$	1943.69	+	992.538i	1.63983	+	0.837375i
$113$	391.797	+	162.288i	0.326169	+	0.135104i	0.539759	−	0.841820i	$-0.318515\pi$
$113$	391.797	+	162.288i	0.326169	+	0.135104i	−0.213589	+	0.976924i	$0.568515\pi$
$114$	−965.885	−	66.6984i	−0.793539	−	0.0547972i
$115$	208.045	+	2112.32i	0.168698	+	1.71282i
$116$	−706.882	−	765.383i	−0.565796	−	0.612621i
$117$	−1232.64	+	2306.11i	−0.973997	+	1.82222i
$118$	774.128	−	820.760i	0.603934	−	0.640314i
$119$	−1494.64	−	998.684i	−1.15137	−	0.769321i
$120$	1777.44	−	1740.55i	1.35214	−	1.32408i
$121$	−878.593	−	1314.91i	−0.660100	−	0.987910i
$122$	−172.451	+	122.667i	−0.127975	+	0.0910304i
$123$	−703.742	−	69.3125i	−0.515888	−	0.0508105i
$124$	−116.521	+	198.602i	−0.0843865	+	0.143830i
$125$	−833.472	−	252.831i	−0.596384	−	0.180911i
$126$	−2237.16	+	2894.52i	−1.58176	+	2.04654i
$127$	−740.989			−0.517733			−0.258867	−	0.965913i	$-0.583349\pi$
$127$	−740.989			−0.517733			−0.258867	+	0.965913i	$0.583349\pi$
$128$	153.844	+	1439.96i	0.106235	+	0.994341i
$129$	746.445			0.509464
$130$	1627.01	−	2105.09i	1.09768	−	1.42022i
$131$	−1824.28	−	553.391i	−1.21671	−	0.369084i	−0.384278	−	0.923217i	$-0.625550\pi$
$131$	−1824.28	−	553.391i	−1.21671	−	0.369084i	−0.832428	+	0.554134i	$0.813050\pi$
$132$	3000.55	+	1760.44i	1.97852	+	1.16081i
$133$	−1441.65	−	141.990i	−0.939904	−	0.0925724i
$134$	−490.430	+	348.849i	−0.316169	+	0.224895i
$135$	667.555	+	999.066i	0.425585	+	0.636933i
$136$	12.5057	−	1192.72i	0.00788494	−	0.752019i
$137$	−700.535	−	468.082i	−0.436867	−	0.291905i	0.317623	−	0.948217i	$-0.397115\pi$
$137$	−700.535	−	468.082i	−0.436867	−	0.291905i	−0.754489	+	0.656312i	$0.772115\pi$
$138$	2432.67	−	2579.20i	1.50060	−	1.59099i
$139$	−900.722	+	1685.13i	−0.549628	+	1.02828i	0.441736	+	0.897145i	$0.354363\pi$
$139$	−900.722	+	1685.13i	−0.549628	+	1.02828i	−0.991364	+	0.131137i	$0.958137\pi$
$140$	2734.44	−	2525.43i	1.65073	−	1.52456i
$141$	97.8123	+	993.105i	0.0584204	+	0.593153i
$142$	2012.62	+	138.980i	1.18940	+	0.0821333i
$143$	3437.33	+	1423.79i	2.01010	+	0.832611i
$144$	−2419.80	−	192.608i	−1.40035	−	0.111463i
$145$	−1641.68	+	680.006i	−0.940235	+	0.389458i
$146$	−379.596	+	127.378i	−0.215176	+	0.0722046i
$147$	−4190.98	+	5106.72i	−2.35147	+	2.86528i
$148$	−32.4267	−	23.5814i	−0.0180099	−	0.0130972i
$149$	73.6711	+	242.861i	0.0405059	+	0.133530i	0.974861	−	0.222812i	$-0.0715237\pi$
$149$	73.6711	+	242.861i	0.0405059	+	0.133530i	−0.934355	+	0.356342i	$0.884024\pi$
$150$	−570.881	−	1271.77i	−0.310748	−	0.692262i
$151$	333.070	+	1674.45i	0.179502	+	0.902418i	0.960584	+	0.277990i	$0.0896681\pi$
$151$	333.070	+	1674.45i	0.179502	+	0.902418i	−0.781082	+	0.624429i	$0.785332\pi$
$152$	−444.210	−	852.437i	−0.237041	−	0.454880i
$153$	1960.97	+	390.061i	1.03618	+	0.206108i
$154$	4410.61	+	2764.12i	2.30791	+	1.44636i
$155$	249.137	+	303.574i	0.129104	+	0.157314i
$156$	−4436.55	+	259.657i	−2.27698	+	0.133264i
$157$	1827.43	−	976.783i	0.928949	−	0.496534i	0.0637522	−	0.997966i	$-0.479693\pi$
$157$	1827.43	−	976.783i	0.928949	−	0.496534i	0.865197	+	0.501432i	$0.167193\pi$
$158$	−1751.48	+	1003.07i	−0.881899	+	0.505063i
$159$	−4014.37	−	4014.37i	−2.00226	−	2.00226i
$160$	2395.18	+	602.793i	1.18347	+	0.297844i
$161$	3751.06	−	3751.06i	1.83618	−	1.83618i
$162$	−233.213	+	858.353i	−0.113105	+	0.416288i
$163$	−519.006	−	970.992i	−0.249397	−	0.466589i	0.725807	−	0.687899i	$-0.241467\pi$
$163$	−519.006	−	970.992i	−0.249397	−	0.466589i	−0.975203	+	0.221310i	$0.928967\pi$
$164$	−306.109	−	631.822i	−0.145750	−	0.300836i
$165$	4586.50	−	3764.04i	2.16399	−	1.77594i
$166$	−2.48935	−	10.8475i	−0.00116392	−	0.00507187i
$167$	612.767	−	3080.59i	0.283936	−	1.42744i	−0.530744	−	0.847532i	$-0.678087\pi$
$167$	612.767	−	3080.59i	0.283936	−	1.42744i	0.814680	−	0.579911i	$-0.196913\pi$
$168$	−6180.85	−	674.264i	−2.83847	−	0.309646i
$169$	−2506.78	+	498.630i	−1.14100	+	0.226959i
$170$	−1901.42	−	723.241i	−0.857838	−	0.326294i
$171$	1541.88	−	467.724i	0.689534	−	0.209168i
$172$	386.935	+	632.052i	0.171532	+	0.280195i
$173$	−1410.37	−	1157.46i	−0.619819	−	0.508673i	0.271268	−	0.962504i	$-0.412557\pi$
$173$	−1410.37	−	1157.46i	−0.619819	−	0.508673i	−0.891088	+	0.453831i	$0.850057\pi$
$174$	2657.46	+	1322.08i	1.15783	+	0.576016i
$175$	−798.193	−	1927.01i	−0.344787	−	0.832389i
$176$	64.7406	+	3453.27i	0.0277273	+	1.47898i
$177$	−1230.03	+	2969.55i	−0.522342	+	1.26104i
$178$	1033.44	−	899.936i	0.435168	−	0.378950i
$179$	4093.91	−	403.215i	1.70946	−	0.168367i	0.804525	−	0.593919i	$-0.202420\pi$
$179$	4093.91	−	403.215i	1.70946	−	0.168367i	0.904934	+	0.425552i	$0.139920\pi$
$180$	−1734.96	+	3759.03i	−0.718425	+	1.55656i
$181$	4029.62	+	2153.88i	1.65480	+	0.884511i	0.990573	+	0.136984i	$0.0437408\pi$
$181$	4029.62	+	2153.88i	1.65480	+	0.884511i	0.664231	+	0.747528i	$0.268759\pi$
$182$	−6646.63	+	194.337i	−2.70704	+	0.0791494i
$183$	334.955	−	501.295i	0.135304	−	0.202496i
$184$	3444.96	+	722.874i	1.38025	+	0.289625i
$185$	−56.8580	+	37.9913i	−0.0225961	+	0.0150982i
$186$	109.118	−	646.846i	0.0430158	−	0.254995i
$187$	278.840	−	2831.11i	0.109042	−	1.10712i
$188$	−790.208	+	597.619i	−0.306552	+	0.231840i
$189$	871.737	−	2873.73i	0.335500	−	1.10600i
$190$	−1626.13	+	208.305i	−0.620903	+	0.0795368i
$191$			5159.26i			1.95451i	0.212070	+	0.977254i	$0.431979\pi$
$191$			5159.26i			1.95451i	−0.212070	+	0.977254i	$0.568021\pi$
$192$	−1868.09	−	3678.45i	−0.702174	−	1.38265i
$193$		−	175.799i		−	0.0655662i	−0.999462	−	0.0327831i	$-0.989563\pi$
$193$		−	175.799i		−	0.0655662i	0.999462	−	0.0327831i	$-0.0104371\pi$
$194$	−228.829	−	1786.35i	−0.0846855	−	0.661096i
$195$	−2200.25	+	7253.25i	−0.808016	+	2.66367i
$196$	−6496.60	−	901.533i	−2.36756	−	0.328547i
$197$	52.6355	−	534.417i	0.0190361	−	0.193277i	−0.980963	−	0.194193i	$-0.937791\pi$
$197$	52.6355	−	534.417i	0.0190361	−	0.193277i	1.00000		0.000915278i	$0.000291342\pi$
$198$	−5708.87	−	963.046i	−2.04905	−	0.345660i
$199$	1835.77	−	1226.62i	0.653941	−	0.436949i	−0.183840	−	0.982956i	$-0.558853\pi$
$199$	1835.77	−	1226.62i	0.653941	−	0.436949i	0.837781	+	0.546007i	$0.183853\pi$
$200$	780.939	−	1142.64i	0.276104	−	0.403984i
$201$	952.572	−	1425.62i	0.334275	−	0.500278i
$202$	−74.4116	−	2545.00i	−0.0259187	−	0.886463i
$203$	3916.67	+	2093.50i	1.35417	+	0.723818i
$204$	1174.72	+	3188.59i	0.403171	+	1.09434i
$205$	−1191.64	+	117.366i	−0.405987	+	0.0399863i
$206$	2019.18	+	2318.73i	0.682928	+	0.784242i
$207$	−2257.96	+	5451.21i	−0.758161	+	1.83036i
$208$	−2519.64	−	3622.05i	−0.839932	−	1.20742i
$209$	−877.326	−	2118.05i	−0.290363	−	0.700999i
$210$	−4723.31	+	9494.14i	−1.55209	+	3.11980i
$211$	−257.838	−	211.603i	−0.0841248	−	0.0690394i	0.591391	−	0.806385i	$-0.298579\pi$
$211$	−257.838	−	211.603i	−0.0841248	−	0.0690394i	−0.675516	+	0.737346i	$0.736079\pi$
$212$	1318.23	−	5480.09i	0.427059	−	1.77535i
$213$	−5499.89	+	1668.37i	−1.76923	+	0.536691i
$214$	−89.5974	+	235.554i	−0.0286203	+	0.0752437i
$215$	1239.66	−	246.583i	0.393228	−	0.0782178i
$216$	1912.82	−	558.415i	0.602550	−	0.175904i
$217$	191.482	−	962.646i	0.0599017	−	0.301146i
$218$	2470.56	−	566.957i	0.767556	−	0.176143i
$219$	881.762	−	723.644i	0.272073	−	0.223285i
$220$	5564.71	+	1932.45i	1.70533	+	0.592207i
$221$	1713.14	+	3205.05i	0.521439	+	0.975543i
$222$	110.229	+	29.9489i	0.0333246	+	0.00905424i
$223$	3513.45	−	3513.45i	1.05506	−	1.05506i	0.0566664	−	0.998393i	$-0.481953\pi$
$223$	3513.45	−	3513.45i	1.05506	−	1.05506i	0.998393	−	0.0566664i	$-0.0180471\pi$
$224$	−2633.04	−	5583.15i	−0.785390	−	1.66536i
$225$	1640.44	+	1640.44i	0.486057	+	0.486057i
$226$	−596.102	−	1040.86i	−0.175452	−	0.306359i
$227$	3301.16	−	1764.51i	0.965225	−	0.515923i	0.0880611	−	0.996115i	$-0.471933\pi$
$227$	3301.16	−	1764.51i	0.965225	−	0.515923i	0.877164	+	0.480192i	$0.159433\pi$
$228$	2046.20	+	1819.93i	0.594354	+	0.528630i
$229$	163.855	+	199.658i	0.0472833	+	0.0576148i	0.796115	−	0.605145i	$-0.206885\pi$
$229$	163.855	+	199.658i	0.0472833	+	0.0576148i	−0.748832	+	0.662760i	$0.769385\pi$
$230$	3188.02	−	5087.03i	0.913966	−	1.45839i
$231$	−14544.0	−	2892.98i	−4.14253	−	0.824001i
$232$	258.079	+	2935.53i	0.0730333	+	0.830720i
$233$	869.393	+	4370.73i	0.244445	+	1.22891i	0.886673	+	0.462397i	$0.153010\pi$
$233$	869.393	+	4370.73i	0.244445	+	1.22891i	−0.642228	+	0.766514i	$0.721990\pi$
$234$	6747.35	−	3028.80i	1.88499	−	0.846150i
$235$	490.508	+	1616.99i	0.136158	+	0.448854i
$236$	−3152.07	+	497.802i	−0.869417	+	0.137306i
$237$	3647.82	−	4444.89i	0.999796	−	1.21826i
$238$	1617.47	+	4820.19i	0.440525	+	1.31280i
$239$	2043.83	−	846.581i	0.553156	−	0.229125i	−0.0885551	−	0.996071i	$-0.528225\pi$
$239$	2043.83	−	846.581i	0.553156	−	0.229125i	0.641711	+	0.766947i	$0.278225\pi$
$240$	−6988.33	+	820.820i	−1.87956	+	0.220766i
$241$	−2111.43	−	874.584i	−0.564354	−	0.233763i	0.0822203	−	0.996614i	$-0.473799\pi$
$241$	−2111.43	−	874.584i	−0.564354	−	0.233763i	−0.646574	+	0.762851i	$0.723799\pi$
$242$	−308.142	+	4462.32i	−0.0818517	+	1.18533i
$243$	−481.433	−	4888.07i	−0.127094	−	1.29041i
$244$	598.102	+	23.7659i	0.156924	+	0.00623548i
$245$	−5273.19	+	9865.45i	−1.37507	+	2.57257i
$246$	1455.02	+	1372.36i	0.377109	+	0.355684i
$247$	2435.11	+	1627.09i	0.627298	+	0.419147i
$248$	604.280	−	242.910i	0.154725	−	0.0621968i
$249$	17.6152	+	26.3631i	0.00448321	+	0.00670960i
$250$	1427.92	+	2007.44i	0.361239	+	0.507848i
$251$	609.219	+	60.0029i	0.153201	+	0.0150890i	0.174327	−	0.984688i	$-0.444225\pi$
$251$	609.219	+	60.0029i	0.153201	+	0.0150890i	−0.0211256	+	0.999777i	$0.506725\pi$
$252$	10013.1	−	2608.13i	2.50305	−	0.651972i
$253$	8033.75	+	2437.01i	1.99635	+	0.605588i
$254$	1658.27	+	1281.67i	0.409642	+	0.316610i
$255$	5795.55			1.42326
$256$	2146.36	−	3488.60i	0.524015	−	0.851709i
$257$	756.985			0.183733			0.0918666	−	0.995771i	$-0.470717\pi$
$257$	756.985			0.183733			0.0918666	+	0.995771i	$0.470717\pi$
$258$	−1670.48	−	1291.10i	−0.403098	−	0.311552i
$259$	163.547	+	49.6115i	0.0392368	+	0.0119024i
$260$	−7282.22	+	1896.81i	−1.73702	+	0.452443i
$261$	−4915.85	−	484.169i	−1.16584	−	0.114825i
$262$	3125.40	+	4393.85i	0.736977	+	1.03608i
$263$	−3027.56	−	4531.06i	−0.709838	−	1.06235i	−0.994603	−	0.103750i	$-0.966916\pi$
$263$	−3027.56	−	4531.06i	−0.709838	−	1.06235i	0.284765	−	0.958597i	$-0.408084\pi$
$264$	−3669.97	−	9129.67i	−0.855572	−	2.12838i
$265$	−7992.98	−	5340.74i	−1.85285	−	1.23803i
$266$	2980.70	+	2811.35i	0.687061	+	0.648025i
$267$	−1840.33	+	3443.02i	−0.421822	+	0.789174i
$268$	1700.93	+	67.5875i	0.387690	+	0.0154051i
$269$	197.032	+	2000.50i	0.0446590	+	0.453431i	0.991346	+	0.131275i	$0.0419072\pi$
$269$	197.032	+	2000.50i	0.0446590	+	0.453431i	−0.946687	+	0.322155i	$0.895593\pi$
$270$	234.126	−	3390.47i	0.0527721	−	0.764213i
$271$	−2989.65	−	1238.35i	−0.670142	−	0.277582i	0.0215572	−	0.999768i	$-0.493138\pi$
$271$	−2989.65	−	1238.35i	−0.670142	−	0.277582i	−0.691699	+	0.722186i	$0.743138\pi$
$272$	−2090.99	+	2647.56i	−0.466121	+	0.590192i
$273$	17501.6	−	7249.38i	3.88001	−	1.60715i
$274$	758.107	+	2259.22i	0.167149	+	0.498119i
$275$	2094.07	−	2551.63i	0.459190	−	0.559524i
$276$	−9905.26	+	1564.32i	−2.16024	+	0.341164i
$277$	−1751.22	−	5773.01i	−0.379858	−	1.25222i	−0.913613	−	0.406585i	$-0.866719\pi$
$277$	−1751.22	−	5773.01i	−0.379858	−	1.25222i	0.533754	−	0.845640i	$-0.320781\pi$
$278$	4930.46	−	2213.23i	1.06370	−	0.477484i
$279$	212.979	+	1070.72i	0.0457015	+	0.229757i
$280$	−10487.6	+	922.022i	−2.23840	+	0.196791i
$281$	3853.06	+	766.421i	0.817987	+	0.162708i	0.586312	−	0.810086i	$-0.300579\pi$
$281$	3853.06	+	766.421i	0.817987	+	0.162708i	0.231675	+	0.972793i	$0.425579\pi$
$282$	1498.85	−	2391.66i	0.316507	−	0.505041i
$283$	−3191.94	−	3889.38i	−0.670462	−	0.816961i	0.321038	−	0.947066i	$-0.395968\pi$
$283$	−3191.94	−	3889.38i	−0.670462	−	0.816961i	−0.991500	+	0.130106i	$0.958468\pi$
$284$	−4263.68	−	3792.19i	−0.890855	−	0.792343i
$285$	4119.01	−	2201.66i	0.856102	−	0.457596i
$286$	−5229.76	−	9131.77i	−1.08127	−	1.88802i
$287$	2116.11	+	2116.11i	0.435227	+	0.435227i
$288$	5082.15	+	4616.50i	1.03982	+	0.944547i
$289$	−1509.13	+	1509.13i	−0.307171	+	0.307171i
$290$	4850.12	+	1317.77i	0.982099	+	0.266835i
$291$	2418.59	+	4524.86i	0.487217	+	0.911520i
$292$	1069.82	+	371.516i	0.214407	+	0.0744566i
$293$	−2720.03	+	2232.27i	−0.542341	+	0.445088i	−0.865249	−	0.501343i	$-0.832840\pi$
$293$	−2720.03	+	2232.27i	−0.542341	+	0.445088i	0.322908	+	0.946430i	$0.395340\pi$
$294$	18212.0	−	4179.38i	3.61274	−	0.829070i
$295$	−1061.80	+	5338.01i	−0.209560	+	1.05353i
$296$	31.7800	+	108.861i	0.00624046	+	0.0213763i
$297$	4661.22	−	927.175i	0.910679	−	0.181145i
$298$	255.200	−	670.928i	0.0496085	−	0.130422i
$299$	−10262.9	+	3113.22i	−1.98501	+	0.602147i
$300$	−922.154	+	3833.53i	−0.177469	+	0.737764i
$301$	−2441.89	−	2004.01i	−0.467603	−	0.383752i
$302$	2150.87	−	4323.38i	0.409830	−	0.823783i
$303$	2775.79	+	6701.35i	0.526287	+	1.27057i
$304$	−480.332	+	2676.01i	−0.0906215	+	0.504868i
$305$	390.676	−	943.176i	0.0733445	−	0.177069i
$306$	−3713.80	−	4264.75i	−0.693804	−	0.796731i
$307$	5978.86	−	588.866i	1.11150	−	0.109474i	0.474442	−	0.880287i	$-0.342650\pi$
$307$	5978.86	−	588.866i	1.11150	−	0.109474i	0.637061	+	0.770813i	$0.280150\pi$
$308$	−5089.55	−	13814.8i	−0.941572	−	2.55574i
$309$	−7725.08	−	4129.14i	−1.42222	−	0.760190i
$310$	−32.4632	−	1110.30i	−0.00594770	−	0.203421i
$311$	−3256.72	+	4874.02i	−0.593799	+	0.888683i	−0.999681	−	0.0252427i	$-0.991964\pi$
$311$	−3256.72	+	4874.02i	−0.593799	+	0.888683i	0.405883	+	0.913925i	$0.366964\pi$
$312$	10377.7	+	7092.68i	1.88309	+	1.28700i
$313$	4467.77	−	2985.27i	0.806816	−	0.539097i	−0.0823920	−	0.996600i	$-0.526256\pi$
$313$	4467.77	−	2985.27i	0.806816	−	0.539097i	0.889208	+	0.457503i	$0.151256\pi$
$314$	−5779.14	−	974.901i	−1.03865	−	0.175213i
$315$	1729.76	−	17562.5i	0.309400	−	3.14139i
$316$	5654.63	+	784.694i	1.00664	+	0.139691i
$317$	819.355	−	2701.05i	0.145172	−	0.478568i	−0.853955	−	0.520347i	$-0.825803\pi$
$317$	819.355	−	2701.05i	0.145172	−	0.478568i	0.999127	+	0.0417790i	$0.0133025\pi$
$318$	2040.27	+	15927.3i	0.359788	+	2.80868i
$319$			7028.31i			1.23357i
$320$	−4317.57	−	5491.87i	−0.754249	−	0.959391i
$321$		−	717.971i		−	0.124839i
$322$	−14882.6	+	1906.45i	−2.57570	+	0.329944i
$323$	650.047	−	2142.92i	0.111980	−	0.369149i
$324$	2006.58	−	1517.54i	0.344063	−	0.260208i
$325$	−413.320	+	4196.50i	−0.0705441	+	0.716247i
$326$	−518.006	+	3070.70i	−0.0880051	+	0.521688i
$327$	−6004.27	+	4011.93i	−1.01540	+	0.678471i
$328$	−407.799	+	1943.43i	−0.0686492	+	0.327158i
$329$	2346.25	−	3511.41i	0.393170	−	0.588421i
$330$	−16774.7	+	490.466i	−2.79824	+	0.0818159i
$331$	−3304.68	−	1766.39i	−0.548767	−	0.293322i	0.173618	−	0.984813i	$-0.444454\pi$
$331$	−3304.68	−	1766.39i	−0.548767	−	0.293322i	−0.722385	+	0.691491i	$0.756954\pi$
$332$	−13.1917	+	28.5815i	−0.00218068	+	0.00472474i
$333$	−189.178	+	18.6324i	−0.0311318	+	0.00306621i
$334$	−6699.72	+	5834.20i	−1.09758	+	0.955788i
$335$	1111.04	−	2682.28i	0.181201	−	0.437459i
$336$	12665.9	+	12199.8i	2.05650	+	1.98081i
$337$	1992.68	+	4810.75i	0.322101	+	0.777621i	0.999132	+	0.0416662i	$0.0132666\pi$
$337$	1992.68	+	4810.75i	0.322101	+	0.777621i	−0.677030	+	0.735955i	$0.736733\pi$
$338$	6472.41	+	3220.01i	1.04158	+	0.518182i
$339$	2641.50	+	2167.82i	0.423205	+	0.347315i
$340$	3004.24	+	4907.38i	0.479200	+	0.782765i
$341$	1486.42	−	450.901i	0.236053	−	0.0716060i
$342$	−4259.59	−	1620.22i	−0.673487	−	0.256173i
$343$	15948.7	−	3172.39i	2.51063	−	0.499396i
$344$	227.314	−	2083.74i	0.0356277	−	0.326593i
$345$	−3336.65	+	16774.5i	−0.520693	+	2.61770i
$346$	1154.26	+	5029.78i	0.179345	+	0.781511i
$347$	−1342.65	+	1101.89i	−0.207716	+	0.170468i	−0.732499	−	0.680768i	$-0.761646\pi$
$347$	−1342.65	+	1101.89i	−0.207716	+	0.170468i	0.524783	+	0.851236i	$0.324146\pi$
$348$	−3660.40	−	7555.23i	−0.563845	−	1.16380i
$349$	−4362.26	−	8161.21i	−0.669072	−	1.25175i	−0.955880	−	0.293758i	$-0.905094\pi$
$349$	−4362.26	−	8161.21i	−0.669072	−	1.25175i	0.286807	−	0.957988i	$-0.407406\pi$
$350$	−1546.80	+	5693.08i	−0.236229	+	0.869451i
$351$	−4293.02	+	4293.02i	−0.652832	+	0.652832i
$352$	5828.14	−	7840.10i	0.882502	−	1.18716i
$353$	5575.53	+	5575.53i	0.840667	+	0.840667i	0.988946	−	0.148278i	$-0.0473731\pi$
$353$	5575.53	+	5575.53i	0.840667	+	0.840667i	−0.148278	+	0.988946i	$0.547373\pi$
$354$	7889.03	−	4518.04i	1.18445	−	0.678337i
$355$	−8582.81	+	4587.61i	−1.28318	+	0.685873i
$356$	−3869.35	+	226.460i	−0.576054	+	0.0337146i
$357$	−9188.98	−	11196.8i	−1.36227	−	1.65994i
$358$	−9859.23	−	6178.75i	−1.45552	−	0.912170i
$359$	−6912.78	−	1375.04i	−1.01627	−	0.202150i	−0.341272	−	0.939965i	$-0.610858\pi$
$359$	−6912.78	−	1375.04i	−1.01627	−	0.202150i	−0.675003	+	0.737815i	$0.735858\pi$
$360$	10384.6	−	5411.46i	1.52032	−	0.792247i
$361$	986.059	+	4957.25i	0.143761	+	0.722737i
$362$	−5292.44	−	11790.1i	−0.768410	−	1.71181i
$363$	−3699.07	−	12194.2i	−0.534850	−	1.76317i
$364$	15210.7	+	11061.6i	2.19027	+	1.59281i
$365$	1225.34	−	1493.08i	0.175718	−	0.214113i
$366$	−1616.67	+	542.493i	−0.230888	+	0.0774770i
$367$	10034.6	−	4156.48i	1.42726	−	0.591189i	0.470584	−	0.882355i	$-0.344043\pi$
$367$	10034.6	−	4156.48i	1.42726	−	0.591189i	0.956672	+	0.291166i	$0.0940433\pi$
$368$	−6459.19	−	7576.37i	−0.914968	−	1.07322i
$369$	−3075.22	−	1273.80i	−0.433847	−	0.179706i
$370$	192.955	+	13.3244i	0.0271115	+	0.00187217i
$371$	2354.93	+	23910.0i	0.329547	+	3.34594i
$372$	−1363.03	+	1258.84i	−0.189972	+	0.175452i
$373$	−5296.26	+	9908.60i	−0.735200	+	1.37546i	0.184496	+	0.982833i	$0.440935\pi$
$373$	−5296.26	+	9908.60i	−0.735200	+	1.37546i	−0.919697	+	0.392630i	$0.871565\pi$
$374$	−5520.91	+	5853.48i	−0.763314	+	0.809295i
$375$	−5835.42	−	3899.10i	−0.803572	−	0.536930i
$376$	2802.10	+	29.3801i	0.384328	+	0.00402968i
$377$	−4988.17	−	7465.33i	−0.681443	−	1.01985i
$378$	−6921.48	+	4923.34i	−0.941805	+	0.669919i
$379$	−2978.41	−	293.348i	−0.403670	−	0.0397580i	−0.105855	−	0.994382i	$-0.533758\pi$
$379$	−2978.41	−	293.348i	−0.403670	−	0.0397580i	−0.297815	+	0.954624i	$0.596258\pi$
$380$	3999.42	+	2346.49i	0.539911	+	0.316770i
$381$	−5713.68	−	1733.23i	−0.768296	−	0.233060i
$382$	8923.82	−	11546.0i	1.19524	−	1.54645i
$383$	−2309.92			−0.308177			−0.154088	−	0.988057i	$-0.549244\pi$
$383$	−2309.92			−0.308177			−0.154088	+	0.988057i	$0.549244\pi$
$384$	−2181.89	+	11463.2i	−0.289959	+	1.52338i
$385$	−25109.6			−3.32391
$386$	−304.074	+	393.422i	−0.0400957	+	0.0518773i
$387$	3362.28	+	1019.94i	0.441639	+	0.133970i
$388$	−2577.70	+	4393.50i	−0.337275	+	0.574861i
$389$	13489.2	+	1328.57i	1.75817	+	0.173165i	0.925030	−	0.379895i	$-0.124040\pi$
$389$	13489.2	+	1328.57i	1.75817	+	0.173165i	0.833142	+	0.553059i	$0.186540\pi$
$390$	17469.7	−	12426.4i	2.26823	−	1.61343i
$391$	4555.87	+	6818.34i	0.589259	+	0.881888i
$392$	12979.4	+	13254.5i	1.67235	+	1.70779i
$393$	−12772.4	−	8534.26i	−1.63940	−	1.09541i
$394$	−1042.16	+	1104.94i	−0.133257	+	0.141284i
$395$	4589.78	−	8586.88i	0.584651	−	1.09380i
$396$	11110.2	+	12029.7i	1.40987	+	1.52655i
$397$	−407.978	−	4142.27i	−0.0515764	−	0.523664i	−0.985911	−	0.167268i	$-0.946505\pi$
$397$	−407.978	−	4142.27i	−0.0515764	−	0.523664i	0.934335	−	0.356396i	$-0.115995\pi$
$398$	−6229.94	−	430.203i	−0.784620	−	0.0541813i
$399$	−10784.3	−	4467.00i	−1.35311	−	0.560476i
$400$	−3724.06	+	1206.36i	−0.465507	+	0.150795i
$401$	330.412	−	136.861i	0.0411471	−	0.0170437i	−0.362015	−	0.932172i	$-0.617911\pi$
$401$	330.412	−	136.861i	0.0411471	−	0.0170437i	0.403162	+	0.915129i	$0.367911\pi$
$402$	−4597.63	+	1542.79i	−0.570420	+	0.191411i
$403$	−1258.83	+	1533.89i	−0.155600	+	0.189599i
$404$	−4235.48	+	5824.19i	−0.521591	+	0.717238i
$405$	−1245.55	−	4106.02i	−0.152819	−	0.503777i
$406$	−5144.08	−	11459.6i	−0.628809	−	1.40081i
$407$	52.7666	+	265.275i	0.00642639	+	0.0323076i
$408$	2886.28	−	9167.65i	0.350226	−	1.11242i
$409$	2512.39	+	499.746i	0.303740	+	0.0604177i	0.344608	−	0.938747i	$-0.388012\pi$
$409$	2512.39	+	499.746i	0.303740	+	0.0604177i	−0.0408670	+	0.999165i	$0.513012\pi$
$410$	2869.78	+	1798.48i	0.345679	+	0.216636i
$411$	−4306.86	−	5247.93i	−0.516890	−	0.629833i
$412$	−508.108	−	8681.64i	−0.0607590	−	1.03814i
$413$	11996.3	−	6412.17i	1.42930	−	0.763977i
$414$	14481.9	−	8293.78i	1.71919	−	0.984583i
$415$	37.9633	+	37.9633i	0.00449048	+	0.00449048i
$416$	−626.209	+	12464.0i	−0.0738039	+	1.46898i
$417$	−10887.0	+	10887.0i	−1.27851	+	1.27851i
$418$	−1700.15	+	6257.50i	−0.198941	+	0.732211i
$419$	−2017.59	−	3774.64i	−0.235240	−	0.440103i	0.736407	−	0.676539i	$-0.236521\pi$
$419$	−2017.59	−	3774.64i	−0.235240	−	0.440103i	−0.971647	+	0.236435i	$0.924021\pi$
$420$	26992.1	−	13077.3i	3.13590	−	1.51930i
$421$	1808.13	−	1483.90i	0.209318	−	0.171783i	−0.523893	−	0.851784i	$-0.675521\pi$
$421$	1808.13	−	1483.90i	0.209318	−	0.171783i	0.733211	+	0.680001i	$0.238021\pi$
$422$	211.017	+	919.523i	0.0243416	+	0.106070i
$423$	−916.387	+	4606.99i	−0.105334	+	0.529550i
$424$	−12428.8	+	9983.85i	−1.42358	+	1.14353i
$425$	3162.32	−	629.024i	0.360929	−	0.0717932i
$426$	15194.0	+	5779.32i	1.72806	+	0.657298i
$427$	−2441.61	+	740.654i	−0.276716	+	0.0839409i
$428$	607.942	−	372.175i	0.0686588	−	0.0420322i
$429$	23174.5	+	19018.8i	2.60810	+	2.14042i
$430$	−3200.75	−	1592.37i	−0.358962	−	0.178583i
$431$	−1727.21	−	4169.85i	−0.193032	−	0.466020i	0.797497	−	0.603323i	$-0.206157\pi$
$431$	−1727.21	−	4169.85i	−0.193032	−	0.466020i	−0.990529	+	0.137302i	$0.956157\pi$
$432$	−5246.59	−	2058.86i	−0.584321	−	0.229298i
$433$	−4721.74	+	11399.3i	−0.524047	+	1.26516i	0.411322	+	0.911490i	$0.365067\pi$
$433$	−4721.74	+	11399.3i	−0.524047	+	1.26516i	−0.935369	+	0.353672i	$0.884933\pi$
$434$	−2093.58	+	1823.12i	−0.231555	+	0.201641i
$435$	−14249.4	+	1403.44i	−1.57059	+	0.154689i
$436$	−6509.54	−	3004.45i	−0.715024	−	0.330016i
$437$	5828.14	+	3115.21i	0.637981	+	0.341008i
$438$	−3224.97	+	94.2929i	−0.351815	+	0.0102865i
$439$	−158.753	+	237.590i	−0.0172593	+	0.0258304i	−0.839999	−	0.542588i	$-0.817445\pi$
$439$	−158.753	+	237.590i	−0.0172593	+	0.0258304i	0.822740	+	0.568418i	$0.192445\pi$
$440$	−9110.83	−	13949.7i	−0.987140	−	1.51143i
$441$	−25855.6	+	17276.2i	−2.79188	+	1.86548i
$442$	1709.83	−	10135.8i	0.184001	−	1.09075i
$443$	−575.942	+	5847.64i	−0.0617694	+	0.627155i	0.913605	+	0.406602i	$0.133286\pi$
$443$	−575.942	+	5847.64i	−0.0617694	+	0.627155i	−0.975375	+	0.220554i	$0.929214\pi$
$444$	−194.880	−	257.682i	−0.0208302	−	0.0275429i
$445$	−1918.95	+	6325.93i	−0.204420	+	0.673883i
$446$	−13939.9	+	1785.68i	−1.47999	+	0.189584i
$447$			2045.00i			0.216387i
$448$	−3764.49	+	17048.9i	−0.396999	+	1.79796i
$449$			8594.80i			0.903371i	0.892177	+	0.451686i	$0.149177\pi$
$449$			8594.80i			0.903371i	−0.892177	+	0.451686i	$0.850823\pi$
$450$	−833.741	−	6508.59i	−0.0873399	−	0.681817i
$451$	−1374.81	+	4532.13i	−0.143541	+	0.473192i
$452$	−466.326	+	3360.42i	−0.0485268	+	0.349692i
$453$	−1348.41	+	13690.6i	−0.139854	+	1.41996i
$454$	−10439.7	−	1761.11i	−1.07921	−	0.182055i
$455$	26670.9	−	17820.9i	2.74802	−	1.83617i
$456$	−1431.34	−	7612.08i	−0.146992	−	0.781729i
$457$	7685.70	−	11502.5i	0.786700	−	1.17738i	−0.193834	−	0.981034i	$-0.562092\pi$
$457$	7685.70	−	11502.5i	0.786700	−	1.17738i	0.980535	−	0.196346i	$-0.0629076\pi$
$458$	−21.3508	−	730.233i	−0.00217830	−	0.0745012i
$459$	4094.06	+	2188.32i	0.416328	+	0.222532i
$460$	−15933.4	+	5870.09i	−1.61500	+	0.594987i
$461$	−155.826	+	15.3475i	−0.0157430	+	0.00155055i	−0.105886	−	0.994378i	$-0.533768\pi$
$461$	−155.826	+	15.3475i	−0.0157430	+	0.00155055i	0.0901426	+	0.995929i	$0.471268\pi$
$462$	27544.3	+	31630.5i	2.77376	+	3.18525i
$463$	5663.14	−	13672.0i	0.568442	−	1.37234i	−0.334426	−	0.942422i	$-0.608543\pi$
$463$	5663.14	−	13672.0i	0.568442	−	1.37234i	0.902868	−	0.429918i	$-0.141457\pi$
$464$	4499.94	−	7015.85i	0.450225	−	0.701945i
$465$	1210.98	+	2923.57i	0.120770	+	0.291564i
$466$	5614.30	−	11285.1i	0.558106	−	1.12183i
$467$	−12448.3	−	10216.1i	−1.23349	−	1.01230i	−0.999194	−	0.0401339i	$-0.987222\pi$
$467$	−12448.3	−	10216.1i	−1.23349	−	1.01230i	−0.234296	−	0.972165i	$-0.575278\pi$
$468$	−20338.8	−	4892.48i	−2.00889	−	0.483237i
$469$	−6943.64	+	2106.33i	−0.683641	+	0.207380i
$470$	1699.14	−	4467.09i	0.166756	−	0.438407i
$471$	16375.9	−	3257.37i	1.60204	−	0.318666i
$472$	7915.09	+	4338.01i	0.771868	+	0.423036i
$473$	975.307	−	4903.20i	0.0948091	−	0.476637i
$474$	−15851.7	+	3637.73i	−1.53606	+	0.352503i
$475$	2008.56	−	1648.38i	0.194019	−	0.159227i
$476$	4717.59	−	13584.9i	0.454265	−	1.30811i
$477$	−12597.1	−	23567.5i	−1.20919	−	2.26223i
$478$	−6038.21	−	1640.57i	−0.577785	−	0.156983i
$479$	−321.775	+	321.775i	−0.0306937	+	0.0306937i	−0.722287	−	0.691593i	$-0.756909\pi$
$479$	−321.775	+	321.775i	−0.0306937	+	0.0306937i	0.691593	+	0.722287i	$0.256909\pi$
$480$	17059.0	+	10250.6i	1.62215	+	0.974734i
$481$	−244.320	−	244.320i	−0.0231602	−	0.0231602i
$482$	3212.46	+	5609.32i	0.303575	+	0.530078i
$483$	37698.0	−	20150.0i	3.55138	−	1.89825i
$484$	8407.93	−	9453.29i	0.789626	−	0.887800i
$485$	5511.43	+	6715.70i	0.516002	+	0.628751i
$486$	−7377.34	+	11771.8i	−0.688566	+	1.09872i
$487$	10006.5	+	1990.41i	0.931083	+	0.185204i	0.637254	−	0.770654i	$-0.280070\pi$
$487$	10006.5	+	1990.41i	0.931083	+	0.185204i	0.293829	+	0.955858i	$0.405070\pi$
$488$	−1297.39	−	1087.71i	−0.120349	−	0.100898i
$489$	−1730.78	−	8701.20i	−0.160058	−	0.804666i
$490$	28864.9	−	12957.1i	2.66119	−	1.19458i
$491$	3869.39	+	12755.7i	0.355648	+	1.17241i	0.934194	+	0.356765i	$0.116120\pi$
$491$	3869.39	+	12755.7i	0.355648	+	1.17241i	−0.578546	+	0.815650i	$0.696380\pi$
$492$	−882.492	−	5587.92i	−0.0808654	−	0.512038i
$493$	−4355.20	+	5306.83i	−0.397867	+	0.484803i
$494$	−2635.24	−	7853.23i	−0.240010	−	0.715250i
$495$	25802.6	−	10687.8i	2.34291	−	0.970465i
$496$	−1772.48	−	501.593i	−0.160457	−	0.0454077i
$497$	22471.3	+	9307.92i	2.02812	+	0.840075i
$498$	6.17805	−	89.4667i	0.000555914	−	0.00805040i
$499$	−2039.00	−	20702.4i	−0.182923	−	1.85724i	−0.449308	−	0.893377i	$-0.648329\pi$
$499$	−2039.00	−	20702.4i	−0.182923	−	1.85724i	0.266385	−	0.963867i	$-0.414171\pi$
$500$	276.652	−	6962.32i	0.0247445	−	0.622728i
$501$	11930.7	−	22320.8i	1.06392	−	1.99045i
$502$	−1259.59	−	1188.03i	−0.111989	−	0.105626i
$503$	−8849.69	−	5913.17i	−0.784469	−	0.524166i	0.0976336	−	0.995222i	$-0.468873\pi$
$503$	−8849.69	−	5913.17i	−0.784469	−	0.524166i	−0.882103	+	0.471057i	$0.843873\pi$
$504$	−26919.7	−	11482.6i	−2.37916	−	1.01484i
$505$	6823.64	+	10212.3i	0.601283	+	0.899884i
$506$	−13763.6	−	19349.6i	−1.20922	−	1.69999i
$507$	−20495.8	−	2018.66i	−1.79537	−	0.176828i
$508$	−1494.20	−	5736.51i	−0.130500	−	0.501016i
$509$	7082.49	+	2148.45i	0.616751	+	0.187089i	0.583175	−	0.812347i	$-0.301810\pi$
$509$	7082.49	+	2148.45i	0.616751	+	0.187089i	0.0335761	+	0.999436i	$0.489310\pi$
$510$	−12969.9	−	10024.4i	−1.12611	−	0.870367i
$511$	−4827.36			−0.417906
$512$	−10837.5	+	4094.68i	−0.935457	+	0.353439i
$513$	3741.04			0.321971
$514$	−1694.07	−	1309.33i	−0.145374	−	0.112358i
$515$	−14193.5	−	4305.54i	−1.21444	−	0.368398i
$516$	1505.20	+	5778.74i	0.128416	+	0.493014i
$517$	6651.25	+	655.091i	0.565806	+	0.0557270i
$518$	−280.193	−	393.909i	−0.0237663	−	0.0334119i
$519$	−8167.84	−	12224.0i	−0.690806	−	1.03386i
$520$	19577.8	+	8350.94i	1.65105	+	0.704256i
$521$	−11209.5	−	7489.97i	−0.942608	−	0.629830i	−0.0136065	−	0.999907i	$-0.504331\pi$
$521$	−11209.5	−	7489.97i	−0.942608	−	0.629830i	−0.929001	+	0.370077i	$0.879331\pi$
$522$	10163.8	+	9586.32i	0.852215	+	0.803796i
$523$	8238.09	−	15412.4i	0.688770	−	1.28860i	−0.257831	−	0.966190i	$-0.583008\pi$
$523$	8238.09	−	15412.4i	0.688770	−	1.28860i	0.946601	−	0.322407i	$-0.104492\pi$
$524$	605.528	−	15238.9i	0.0504821	−	1.27045i
$525$	−1647.36	−	16726.0i	−0.136946	−	1.39044i
$526$	−1061.83	+	15376.8i	−0.0880191	+	1.27464i
$527$	1401.75	+	580.625i	0.115866	+	0.0479932i
$528$	−7578.25	+	26779.2i	−0.624623	+	2.20723i
$529$	−11116.9	+	4604.77i	−0.913692	+	0.378464i
$530$	8649.86	+	25777.3i	0.708917	+	2.11263i
$531$	−9598.10	+	11695.3i	−0.784411	+	0.955807i
$532$	−1807.83	−	11447.2i	−0.147330	−	0.932889i
$533$	−1756.28	−	5789.67i	−0.142726	−	0.470504i
$534$	10073.8	−	4522.00i	0.816358	−	0.366454i
$535$	−237.177	−	1192.37i	−0.0191665	−	0.0963564i
$536$	−3689.63	−	3093.30i	−0.297328	−	0.249273i
$537$	32510.8	+	6466.80i	2.61256	+	0.519670i
$538$	3019.27	−	4817.75i	0.241951	−	0.386074i
$539$	28068.8	+	34201.9i	2.24306	+	2.73318i
$540$	−6388.34	+	7182.61i	−0.509094	+	0.572389i
$541$	−73.8867	+	39.4933i	−0.00587179	+	0.00313854i	−0.474330	−	0.880347i	$-0.657310\pi$
$541$	−73.8867	+	39.4933i	−0.00587179	+	0.00313854i	0.468458	+	0.883486i	$0.344810\pi$
$542$	4548.63	+	7942.44i	0.360481	+	0.629441i
$543$	26033.9	+	26033.9i	2.05750	+	2.05750i
$544$	9258.86	−	2308.29i	0.729725	−	0.181925i
$545$	−8646.28	+	8646.28i	−0.679570	+	0.679570i
$546$	−51705.9	−	14048.4i	−4.05277	−	1.10113i
$547$	6963.16	+	13027.2i	0.544284	+	1.01828i	0.992253	+	0.124235i	$0.0396476\pi$
$547$	6963.16	+	13027.2i	0.544284	+	1.01828i	−0.447969	+	0.894049i	$0.647852\pi$
$548$	2211.13	−	6367.21i	0.172363	−	0.496339i
$549$	2193.74	−	1800.35i	0.170540	−	0.139958i
$550$	−9099.82	+	2088.27i	−0.705486	+	0.161899i
$551$	−1079.33	+	5426.15i	−0.0834500	+	0.419531i
$552$	24872.9	+	13632.0i	1.91786	+	1.05112i
$553$	−23866.7	+	4747.39i	−1.83529	+	0.365062i
$554$	−6066.31	+	15948.5i	−0.465222	+	1.22308i
$555$	−527.289	+	159.951i	−0.0403283	+	0.0122334i
$556$	−14862.1	−	3575.06i	−1.13362	−	0.272691i
$557$	5497.34	+	4511.55i	0.418187	+	0.343197i	0.819838	−	0.572596i	$-0.194064\pi$
$557$	5497.34	+	4511.55i	0.418187	+	0.343197i	−0.401651	+	0.915793i	$0.631564\pi$
$558$	1375.36	−	2764.55i	0.104343	−	0.209736i
$559$	2443.98	+	5900.28i	0.184918	+	0.446432i
$560$	25065.1	+	16076.6i	1.89142	+	1.21315i
$561$	8772.28	−	21178.2i	0.660189	−	1.59384i
$562$	−7297.15	−	8379.70i	−0.547708	−	0.628962i
$563$	−17839.1	+	1757.00i	−1.33540	+	0.131525i	−0.740380	−	0.672189i	$-0.765354\pi$
$563$	−17839.1	+	1757.00i	−1.33540	+	0.131525i	−0.595016	+	0.803714i	$0.702854\pi$
$564$	−7491.07	+	2759.82i	−0.559275	+	0.206045i
$565$	5102.99	+	2727.60i	0.379972	+	0.203099i
$566$	415.918	+	14225.1i	0.0308875	+	1.05640i
$567$	−5957.84	+	8916.53i	−0.441280	+	0.660422i
$568$	2982.49	+	15861.3i	0.220321	+	1.17170i
$569$	671.244	−	448.511i	0.0494552	−	0.0330449i	−0.530597	−	0.847624i	$-0.678032\pi$
$569$	671.244	−	448.511i	0.0494552	−	0.0330449i	0.580052	+	0.814579i	$0.303032\pi$
$570$	−13026.1	−	2197.41i	−0.957199	−	0.161473i
$571$	1655.06	−	16804.2i	0.121300	−	1.23158i	−0.721140	−	0.692789i	$-0.756382\pi$
$571$	1655.06	−	16804.2i	0.121300	−	1.23158i	0.842440	−	0.538790i	$-0.181118\pi$
$572$	−4091.20	+	29481.8i	−0.299059	+	2.15507i
$573$	−12067.9	+	39782.5i	−0.879831	+	2.90041i
$574$	−1075.50	−	8395.84i	−0.0782061	−	0.610515i
$575$			9515.05i			0.690096i
$576$	−3388.39	−	19121.7i	−0.245109	−	1.38323i
$577$		−	21701.8i		−	1.56579i	−0.622157	−	0.782893i	$-0.713743\pi$
$577$		−	21701.8i		−	1.56579i	0.622157	−	0.782893i	$-0.286257\pi$
$578$	5987.59	−	767.002i	0.430884	−	0.0551957i
$579$	411.206	−	1355.56i	0.0295149	−	0.0972976i
$580$	−8574.82	−	11338.1i	−0.613880	−	0.811709i
$581$	13.1521	−	133.536i	0.000939141	−	0.00953526i
$582$	2413.93	−	14309.6i	0.171925	−	1.01916i
$583$	−31614.5	+	21124.2i	−2.24587	+	1.50064i
$584$	−1751.57	−	2681.86i	−0.124111	−	0.190028i
$585$	−19821.6	+	29665.1i	−1.40089	+	2.09658i
$586$	9948.27	−	290.871i	0.701296	−	0.0205048i
$587$	15197.5	+	8123.25i	1.06860	+	0.571180i	0.909339	−	0.416056i	$-0.136588\pi$
$587$	15197.5	+	8123.25i	1.06860	+	0.571180i	0.159263	+	0.987236i	$0.449088\pi$
$588$	−47985.7	−	22147.6i	−3.36547	−	1.55332i
$589$	1216.82	−	119.847i	0.0851245	−	0.00838403i
$590$	11609.2	−	10109.4i	0.810072	−	0.705421i
$591$	1655.90	−	3997.71i	0.115253	−	0.278247i
$592$	117.172	−	298.589i	0.00813469	−	0.0207296i
$593$	−2631.07	−	6351.97i	−0.182201	−	0.439872i	0.806218	−	0.591618i	$-0.201511\pi$
$593$	−2631.07	−	6351.97i	−0.182201	−	0.439872i	−0.988420	+	0.151746i	$0.951511\pi$
$594$	−12035.1	−	5987.44i	−0.831324	−	0.413582i
$595$	−18959.4	−	15559.6i	−1.30632	−	1.07207i
$596$	−1731.60	+	1060.07i	−0.119008	+	0.0728557i
$597$	17024.6	−	5164.34i	1.16712	−	0.354041i
$598$	28352.3	+	10784.3i	1.93881	+	0.737464i
$599$	−13054.5	+	2596.70i	−0.890472	+	0.177126i	−0.619066	−	0.785339i	$-0.712489\pi$
$599$	−13054.5	+	2596.70i	−0.890472	+	0.177126i	−0.271406	+	0.962465i	$0.587489\pi$
$600$	8694.44	−	6984.09i	0.591582	−	0.475207i
$601$	4081.66	−	20519.9i	0.277029	−	1.39272i	−0.552155	−	0.833742i	$-0.686194\pi$
$601$	4081.66	−	20519.9i	0.277029	−	1.39272i	0.829184	−	0.558976i	$-0.188806\pi$
$602$	1998.47	+	8708.47i	0.135301	+	0.589586i
$603$	6238.73	−	5119.99i	0.421328	−	0.345775i
$604$	−12291.5	+	5955.04i	−0.828035	+	0.401171i
$605$	−10171.5	−	19029.5i	−0.683521	−	1.27878i
$606$	5379.15	−	19798.2i	0.360583	−	1.32714i
$607$	17855.1	−	17855.1i	1.19393	−	1.19393i	0.217974	−	0.975955i	$-0.430055\pi$
$607$	17855.1	−	17855.1i	1.19393	−	1.19393i	0.975955	−	0.217974i	$-0.0699448\pi$
$608$	5703.56	−	5157.86i	0.380444	−	0.344044i
$609$	25304.1	+	25304.1i	1.68370	+	1.68370i
$610$	−2505.68	+	1435.00i	−0.166315	+	0.0952485i
$611$	−7529.76	+	4024.74i	−0.498562	+	0.266487i
$612$	934.543	+	15967.8i	0.0617266	+	1.05467i
$613$	10495.3	+	12788.6i	0.691519	+	0.842618i	0.993867	−	0.110579i	$-0.0352706\pi$
$613$	10495.3	+	12788.6i	0.691519	+	0.842618i	−0.302348	+	0.953197i	$0.597771\pi$
$614$	−14398.7	−	9023.62i	−0.946391	−	0.593100i
$615$	−9463.09	−	1882.32i	−0.620469	−	0.123419i
$616$	−12505.0	+	39719.4i	−0.817923	+	2.59796i
$617$	−1315.84	−	6615.18i	−0.0858570	−	0.431632i	−0.999675	−	0.0255076i	$-0.991880\pi$
$617$	−1315.84	−	6615.18i	−0.0858570	−	0.431632i	0.913818	−	0.406125i	$-0.133120\pi$
$618$	10146.0	+	22602.5i	0.660408	+	1.47121i
$619$	3313.16	+	10922.0i	0.215133	+	0.709198i	0.996383	+	0.0849797i	$0.0270825\pi$
$619$	3313.16	+	10922.0i	0.215133	+	0.709198i	−0.781250	+	0.624219i	$0.785417\pi$
$620$	−1847.79	+	2540.89i	−0.119692	+	0.164588i
$621$	−8690.87	+	10589.9i	−0.561598	+	0.684310i
$622$	15718.7	−	5274.58i	1.01328	−	0.340018i
$623$	15264.0	−	6322.56i	0.981605	−	0.406594i
$624$	−10956.4	−	33822.8i	−0.702899	−	2.16987i
$625$	−18042.9	−	7473.60i	−1.15474	−	0.478311i
$626$	−15162.0	−	1047.00i	−0.968044	−	0.0668475i
$627$	−1810.68	−	18384.2i	−0.115330	−	1.17096i
$628$	11247.0	+	12177.7i	0.714653	+	0.773798i
$629$	−124.540	+	232.998i	−0.00789464	+	0.0147698i
$630$	−34248.4	+	36311.5i	−2.16586	+	2.29632i
$631$	201.020	+	134.317i	0.0126822	+	0.00847399i	0.561895	−	0.827208i	$-0.310072\pi$
$631$	201.020	+	134.317i	0.0126822	+	0.00847399i	−0.549213	+	0.835682i	$0.685072\pi$
$632$	−11297.3	−	11536.7i	−0.711048	−	0.726117i
$633$	−1493.21	−	2234.74i	−0.0937594	−	0.140321i
$634$	−6505.57	+	4627.50i	−0.407522	+	0.289876i
$635$	−10061.5	−	990.976i	−0.628788	−	0.0619302i
$636$	22983.1	−	39172.9i	1.43292	−	2.44231i
$637$	−54088.1	−	16407.4i	−3.36428	−	1.02054i
$638$	12156.7	−	15728.7i	0.754368	−	0.976029i
$639$	−27053.4			−1.67483
$640$	163.222	+	19758.3i	0.0100811	+	1.22034i
$641$	2497.11			0.153869			0.0769345	−	0.997036i	$-0.475487\pi$
$641$	2497.11			0.153869			0.0769345	+	0.997036i	$0.475487\pi$
$642$	−1241.85	+	1606.76i	−0.0763427	+	0.0987750i
$643$	27321.7	+	8287.96i	1.67568	+	0.508313i	0.978090	−	0.208182i	$-0.0667547\pi$
$643$	27321.7	+	8287.96i	1.67568	+	0.508313i	0.697592	+	0.716495i	$0.254255\pi$
$644$	36603.5	+	21475.6i	2.23972	+	1.31406i
$645$	10135.6	+	998.272i	0.618744	+	0.0609410i
$646$	−5161.28	+	3671.29i	−0.314347	+	0.223599i
$647$	2949.40	+	4414.10i	0.179216	+	0.268216i	0.910191	−	0.414188i	$-0.135934\pi$
$647$	2949.40	+	4414.10i	0.179216	+	0.268216i	−0.730975	+	0.682404i	$0.760934\pi$
$648$	−7115.38	−	74.6049i	−0.431355	−	0.00452277i
$649$	17899.0	+	11959.8i	1.08259	+	0.723361i
$650$	8183.53	−	8676.49i	0.493823	−	0.523569i
$651$	3728.19	−	6974.96i	0.224454	−	0.419924i
$652$	6470.55	−	5975.98i	0.388660	−	0.358953i
$653$	2902.60	+	29470.6i	0.173947	+	1.76611i	0.545889	+	0.837858i	$0.316192\pi$
$653$	2902.60	+	29470.6i	0.173947	+	1.76611i	−0.371942	+	0.928256i	$0.621308\pi$
$654$	20376.3	+	1407.07i	1.21831	+	0.0841297i
$655$	−24031.0	−	9953.98i	−1.43354	−	0.593792i
$656$	4274.11	−	3643.86i	0.254384	−	0.216873i
$657$	4960.59	−	2054.74i	0.294568	−	0.122014i
$658$	−11324.3	+	3799.99i	−0.670921	+	0.225135i
$659$	−15836.8	+	19297.1i	−0.936134	+	1.14068i	0.0537142	+	0.998556i	$0.482894\pi$
$659$	−15836.8	+	19297.1i	−0.936134	+	1.14068i	−0.989848	+	0.142127i	$0.954606\pi$
$660$	38388.7	+	27917.1i	2.26406	+	1.64647i
$661$	−95.8335	−	315.921i	−0.00563917	−	0.0185899i	0.954076	−	0.299566i	$-0.0968418\pi$
$661$	−95.8335	−	315.921i	−0.00563917	−	0.0185899i	−0.959715	+	0.280976i	$0.909342\pi$
$662$	4340.32	+	9669.04i	0.254821	+	0.567670i
$663$	5712.95	+	28720.9i	0.334649	+	1.68240i
$664$	78.9584	−	41.1457i	0.00461473	−	0.00240476i
$665$	−19385.7	−	3856.05i	−1.13044	−	0.224859i
$666$	455.591	+	285.517i	0.0265072	+	0.0166120i
$667$	−12852.5	−	15660.8i	−0.746105	−	0.909131i
$668$	25084.6	−	1468.12i	1.45292	−	0.0850349i
$669$	35310.1	−	18873.6i	2.04061	−	1.09073i
$670$	−7125.86	+	4080.98i	−0.410890	+	0.235316i
$671$	−2855.23	−	2855.23i	−0.164269	−	0.164269i
$672$	−7243.69	−	49209.9i	−0.415820	−	2.82487i
$673$	7704.72	−	7704.72i	0.441300	−	0.441300i	−0.451149	−	0.892449i	$-0.648986\pi$
$673$	7704.72	−	7704.72i	0.441300	−	0.441300i	0.892449	+	0.451149i	$0.148986\pi$
$674$	3861.57	−	14212.7i	0.220686	−	0.812245i
$675$	2539.16	+	4750.43i	0.144789	+	0.270880i
$676$	−8915.13	−	18401.2i	−0.507233	−	1.04695i
$677$	10767.8	−	8836.91i	0.611285	−	0.501669i	−0.277055	−	0.960854i	$-0.589359\pi$
$677$	10767.8	−	8836.91i	0.611285	−	0.501669i	0.888341	+	0.459185i	$0.151859\pi$
$678$	−2161.82	−	9420.30i	−0.122455	−	0.533606i
$679$	4235.99	−	21295.8i	0.239415	−	1.20362i
$680$	1764.91	−	16178.6i	0.0995313	−	0.912385i
$681$	29582.2	−	5884.27i	1.66460	−	0.331110i
$682$	−4106.39	−	1561.94i	−0.230560	−	0.0876977i
$683$	−29133.0	+	8837.39i	−1.63213	+	0.495100i	−0.967668	−	0.252226i	$-0.918838\pi$
$683$	−29133.0	+	8837.39i	−1.63213	+	0.495100i	−0.664458	+	0.747326i	$0.731338\pi$
$684$	6730.15	+	10993.6i	0.376219	+	0.614547i
$685$	−8886.24	−	7292.75i	−0.495658	−	0.406776i
$686$	−41178.9	−	20486.4i	−2.29186	−	1.14020i
$687$	796.455	+	1922.81i	0.0442309	+	0.106783i
$688$	−4112.90	+	4270.06i	−0.227911	+	0.236620i
$689$	18587.9	−	44875.3i	1.02779	−	2.48129i
$690$	36481.4	−	31768.5i	2.01279	−	1.75276i
$691$	−9659.42	+	951.370i	−0.531782	+	0.0523760i	−0.360345	−	0.932819i	$-0.617341\pi$
$691$	−9659.42	+	951.370i	−0.531782	+	0.0523760i	−0.171437	+	0.985195i	$0.554841\pi$
$692$	6116.72	−	13252.7i	0.336016	−	0.728023i
$693$	−61559.0	−	32904.0i	−3.37436	−	1.80363i
$694$	4910.64	−	143.579i	0.268596	−	0.00785330i
$695$	−14484.1	+	21677.0i	−0.790525	+	1.18310i
$696$	−4876.40	+	23239.2i	−0.265574	+	1.26563i
$697$	−3846.47	+	2570.13i	−0.209032	+	0.139671i
$698$	−4353.85	+	25809.3i	−0.236097	+	1.39957i
$699$	−3519.67	+	35735.8i	−0.190452	+	1.93369i
$700$	13308.7	−	10065.2i	0.718605	−	0.543467i
$701$	7473.98	−	24638.4i	0.402693	−	1.32750i	−0.487978	−	0.872856i	$-0.662265\pi$
$701$	7473.98	−	24638.4i	0.402693	−	1.32750i	0.890672	−	0.454647i	$-0.150235\pi$
$702$	17032.9	−	2181.89i	0.915762	−	0.117308i
$703$			212.907i			0.0114224i
$704$	−26603.6	+	7464.69i	−1.42424	+	0.399625i
$705$			13615.7i			0.727373i
$706$	−2833.72	−	22121.4i	−0.151060	−	1.17925i
$707$	8910.77	−	29374.9i	0.474008	−	1.56260i
$708$	−25469.7	−	3534.43i	−1.35199	−	0.187616i
$709$	−1724.73	+	17511.5i	−0.0913590	+	0.927583i	0.834826	+	0.550514i	$0.185568\pi$
$709$	−1724.73	+	17511.5i	−0.0913590	+	0.927583i	−0.926185	+	0.377069i	$0.876932\pi$
$710$	27142.6	+	4578.76i	1.43471	+	0.242025i
$711$	22504.7	−	15037.2i	1.18705	−	0.793162i
$712$	9050.96	+	6185.89i	0.476403	+	0.325599i
$713$	−2487.57	+	3722.91i	−0.130659	+	0.195546i
$714$	1197.35	+	40951.3i	0.0627587	+	2.14645i
$715$	44769.8	+	23930.0i	2.34167	+	1.25165i
$716$	11376.9	+	30880.7i	0.593819	+	1.61182i
$717$	17739.9	−	1747.23i	0.924003	−	0.0910063i
$718$	13091.8	+	15034.0i	0.680477	+	0.781428i
$719$	9240.04	−	22307.4i	0.479270	−	1.15706i	−0.480682	−	0.876895i	$-0.659611\pi$
$719$	9240.04	−	22307.4i	0.479270	−	1.15706i	0.959952	−	0.280165i	$-0.0903892\pi$
$720$	−32599.8	−	5851.51i	−1.68739	−	0.302879i
$721$	14185.9	+	34247.8i	0.732747	+	1.76901i
$722$	6367.69	−	12799.4i	0.328229	−	0.659759i
$723$	−14235.3	−	11682.6i	−0.732249	−	0.600941i
$724$	−8548.97	+	35539.4i	−0.438840	+	1.82432i
$725$	−7622.78	+	2312.35i	−0.390487	+	0.118453i
$726$	−12813.7	+	33687.7i	−0.655044	+	1.72213i
$727$	−32212.3	+	6407.43i	−1.64331	+	0.326875i	−0.928185	−	0.372118i	$-0.878632\pi$
$727$	−32212.3	+	6407.43i	−1.64331	+	0.326875i	−0.715128	+	0.698994i	$0.753632\pi$
$728$	−14907.4	−	51064.3i	−0.758933	−	2.59968i
$729$	6064.79	−	30489.8i	0.308123	−	1.54904i
$730$	−5324.72	+	1221.94i	−0.269968	+	0.0619537i
$731$	3774.77	−	3097.87i	0.190991	−	0.156743i
$732$	4556.31	+	1582.26i	0.230063	+	0.0798935i
$733$	−5928.03	−	11090.6i	−0.298713	−	0.558853i	0.687128	−	0.726537i	$-0.258871\pi$
$733$	−5928.03	−	11090.6i	−0.298713	−	0.558853i	−0.985841	+	0.167684i	$0.946371\pi$
$734$	−29645.9	−	8054.75i	−1.49081	−	0.405050i
$735$	−63737.0	+	63737.0i	−3.19860	+	3.19860i
$736$	1350.47	+	28127.5i	0.0676343	+	1.40869i
$737$	−8119.93	−	8119.93i	−0.405836	−	0.405836i
$738$	4678.82	+	8169.77i	0.233374	+	0.407498i
$739$	−11676.0	+	6240.93i	−0.581200	+	0.310658i	−0.735671	−	0.677339i	$-0.763133\pi$
$739$	−11676.0	+	6240.93i	−0.581200	+	0.310658i	0.154470	+	0.987997i	$0.450633\pi$
$740$	−408.770	−	363.568i	−0.0203063	−	0.0180608i
$741$	14971.0	+	18242.2i	0.742204	+	0.904379i
$742$	36086.3	−	57581.7i	1.78540	−	2.84891i
$743$	−6766.88	−	1346.02i	−0.334122	−	0.0664611i	0.0251782	−	0.999683i	$-0.491985\pi$
$743$	−6766.88	−	1346.02i	−0.334122	−	0.0664611i	−0.359300	+	0.933222i	$0.616985\pi$
$744$	5227.72	−	459.598i	0.257604	−	0.0226474i
$745$	675.551	+	3396.23i	0.0332219	+	0.167018i
$746$	28991.1	−	13013.8i	1.42284	−	0.638698i
$747$	43.3237	+	142.819i	0.00212200	+	0.00699528i
$748$	22479.9	−	3550.22i	1.09886	−	0.173541i
$749$	−1927.57	+	2348.75i	−0.0940344	+	0.114581i
$750$	6314.99	+	18819.2i	0.307454	+	0.916239i
$751$	5272.69	−	2184.02i	0.256196	−	0.106120i	−0.250889	−	0.968016i	$-0.580723\pi$
$751$	5272.69	−	2184.02i	0.256196	−	0.106120i	0.507085	+	0.861896i	$0.330723\pi$
$752$	−6220.03	−	4912.45i	−0.301624	−	0.238216i
$753$	4557.27	+	1887.68i	0.220553	+	0.0913558i
$754$	−1749.46	+	25334.6i	−0.0844982	+	1.22365i
$755$	2283.24	+	23182.1i	0.110060	+	1.11746i
$756$	24005.4	+	953.868i	1.15485	+	0.0458887i
$757$	93.7822	−	175.454i	0.00450274	−	0.00842403i	−0.879660	−	0.475603i	$-0.842230\pi$
$757$	93.7822	−	175.454i	0.00450274	−	0.00842403i	0.884163	+	0.467179i	$0.154730\pi$
$758$	6158.03	+	5808.16i	0.295079	+	0.278314i
$759$	56247.0	+	37583.0i	2.68990	+	1.79734i
$760$	−4891.70	−	12168.9i	−0.233474	−	0.580807i
$761$	−15189.4	−	22732.6i	−0.723543	−	1.08286i	−0.992799	−	0.119790i	$-0.961778\pi$
$761$	−15189.4	−	22732.6i	−0.723543	−	1.08286i	0.269257	−	0.963068i	$-0.413222\pi$
$762$	9788.80	+	13761.6i	0.465368	+	0.654238i
$763$	30413.2	+	2995.44i	1.44303	+	0.142126i
$764$	−39941.4	+	10403.6i	−1.89140	+	0.492656i
$765$	26105.5	+	7919.01i	1.23378	+	0.374264i
$766$	5169.40	+	3995.40i	0.243836	+	0.188459i
$767$	−27500.1			−1.29462
$768$	24710.4	−	21879.7i	1.16102	−	1.02802i
$769$	−25202.8			−1.18184			−0.590921	−	0.806729i	$-0.701236\pi$
$769$	−25202.8			−1.18184			−0.590921	+	0.806729i	$0.701236\pi$
$770$	56193.1	+	43431.3i	2.62994	+	2.03267i
$771$	5837.02	+	1770.64i	0.272653	+	0.0827083i
$772$	1360.98	−	354.496i	0.0634491	−	0.0165267i
$773$	−15030.1	−	1480.33i	−0.699346	−	0.0688796i	−0.257906	−	0.966170i	$-0.583032\pi$
$773$	−15030.1	−	1480.33i	−0.699346	−	0.0688796i	−0.441441	+	0.897290i	$0.645532\pi$
$774$	−5760.34	−	8098.17i	−0.267508	−	0.376076i
$775$	978.078	+	1463.80i	0.0453337	+	0.0678467i
$776$	13368.0	−	5373.69i	0.618404	−	0.248588i
$777$	1145.05	+	765.098i	0.0528680	+	0.0353253i
$778$	−27889.6	−	26305.0i	−1.28521	−	1.21219i
$779$	−1757.40	+	3287.87i	−0.0808285	+	0.151220i
$780$	−60589.2	−	2407.55i	−2.78133	−	0.110518i
$781$	3772.94	+	38307.3i	0.172863	+	1.75511i
$782$	1597.84	−	23139.0i	0.0730675	−	1.05812i
$783$	−10595.9	−	4388.96i	−0.483610	−	0.200318i
$784$	−6120.93	−	52112.6i	−0.278832	−	2.37393i
$785$	26120.2	−	10819.3i	1.18760	−	0.491922i
$786$	13822.1	+	41191.0i	0.627249	+	1.86925i
$787$	−8648.16	+	10537.8i	−0.391707	+	0.477297i	−0.931103	−	0.364756i	$-0.881153\pi$
$787$	−8648.16	+	10537.8i	−0.391707	+	0.477297i	0.539396	+	0.842052i	$0.318653\pi$
$788$	4243.43	−	670.158i	0.191835	−	0.0302962i
$789$	−12746.7	−	42020.2i	−0.575151	−	1.89602i
$790$	−25124.0	+	11277.9i	−1.13148	+	0.507909i
$791$	−2821.27	−	14183.5i	−0.126818	−	0.637555i
$792$	−4056.28	−	46138.3i	−0.181987	−	2.07002i
$793$	5059.19	+	1006.34i	0.226554	+	0.0450643i
$794$	−6251.74	+	9975.70i	−0.279428	+	0.445874i
$795$	−49140.6	−	59877.9i	−2.19225	−	2.67126i
$796$	13197.9	+	11738.5i	0.587674	+	0.522688i
$797$	−27630.1	+	14768.6i	−1.22799	+	0.656374i	−0.952385	−	0.304898i	$-0.901378\pi$
$797$	−27630.1	+	14768.6i	−1.22799	+	0.656374i	−0.275604	+	0.961271i	$0.588878\pi$
$798$	16407.9	+	28650.0i	0.727859	+	1.27093i
$799$	4616.19	+	4616.19i	0.204392	+	0.204392i
$800$	10420.7	+	3741.67i	0.460535	+	0.165360i
$801$	−12994.1	+	12994.1i	−0.573189	+	0.573189i
$802$	−976.158	−	265.221i	−0.0429792	−	0.0116774i
$803$	−3601.31	−	6737.58i	−0.158266	−	0.296095i
$804$	12957.6	+	4499.76i	0.568382	+	0.197381i
$805$	55950.5	−	45917.4i	2.44968	−	2.01040i
$806$	5470.27	−	1255.35i	0.239060	−	0.0548607i
$807$	−3160.02	+	15886.5i	−0.137842	+	0.692976i
$808$	19552.5	−	5708.03i	0.851307	−	0.248525i
$809$	29372.3	−	5842.51i	1.27648	−	0.253908i	0.490109	−	0.871661i	$-0.336957\pi$
$809$	29372.3	−	5842.51i	1.27648	−	0.253908i	0.786372	+	0.617753i	$0.211957\pi$
$810$	−4314.63	+	11343.3i	−0.187161	+	0.492052i
$811$	−35790.0	+	10856.8i	−1.54964	+	0.470078i	−0.945177	−	0.326557i	$-0.894111\pi$
$811$	−35790.0	+	10856.8i	−1.54964	+	0.470078i	−0.604461	+	0.796635i	$0.706611\pi$
$812$	−8309.32	+	34543.1i	−0.359113	+	1.49289i
$813$	−20156.3	−	16541.8i	−0.869509	−	0.713588i
$814$	340.752	−	684.931i	0.0146724	−	0.0294924i
$815$	−5748.77	−	13878.8i	−0.247080	−	0.596505i
$816$	−22316.2	+	15524.1i	−0.957383	+	0.665994i
$817$	1505.96	−	3635.70i	0.0644880	−	0.155688i
$818$	−4758.12	−	5464.00i	−0.203379	−	0.233550i
$819$	88739.4	−	8740.07i	3.78609	−	0.372897i
$820$	−3311.53	−	8988.60i	−0.141029	−	0.382800i
$821$	30624.6	+	16369.2i	1.30183	+	0.695844i	0.968981	−	0.247136i	$-0.0794893\pi$
$821$	30624.6	+	16369.2i	1.30183	+	0.695844i	0.332851	+	0.942979i	$0.391989\pi$
$822$	561.197	+	19193.9i	0.0238126	+	0.814431i
$823$	15119.2	−	22627.5i	0.640368	−	0.958378i	−0.359315	−	0.933216i	$-0.616990\pi$
$823$	15119.2	−	22627.5i	0.640368	−	0.958378i	0.999683	−	0.0251622i	$-0.00801021\pi$
$824$	−13879.3	+	20307.6i	−0.586780	+	0.858554i
$825$	22115.6	−	14777.1i	0.933291	−	0.623605i
$826$	−37937.7	−	6399.82i	−1.59809	−	0.269586i
$827$	685.343	−	6958.40i	0.0288170	−	0.292584i	−0.969965	−	0.243245i	$-0.921788\pi$
$827$	685.343	−	6958.40i	0.0288170	−	0.292584i	0.998782	−	0.0493398i	$-0.0157117\pi$
$828$	−46754.7	−	6488.15i	−1.96237	−	0.272318i
$829$	3980.76	−	13122.8i	0.166776	−	0.549787i	−0.833219	−	0.552943i	$-0.813505\pi$
$829$	3980.76	−	13122.8i	0.166776	−	0.549787i	0.999995	+	0.00315615i	$0.00100464\pi$
$830$	−19.2946	−	150.623i	−0.000806896	−	0.00629902i
$831$		−	48611.2i		−	2.02925i
$832$	22959.9	−	26810.1i	0.956722	−	1.11716i
$833$			43217.9i			1.79761i
$834$	43195.1	−	5533.23i	1.79343	−	0.229736i
$835$	12440.4	−	41010.4i	0.515589	−	1.69967i
$836$	14628.2	−	11063.0i	0.605175	−	0.457683i
$837$	−248.445	+	2522.50i	−0.0102599	+	0.104170i
$838$	−2013.70	+	11937.1i	−0.0830096	+	0.492075i
$839$	26207.5	−	17511.3i	1.07841	−	0.720569i	0.116294	−	0.993215i	$-0.462899\pi$
$839$	26207.5	−	17511.3i	1.07841	−	0.720569i	0.962115	+	0.272645i	$0.0878986\pi$
$840$	−83025.2	−	17421.6i	−3.41029	−	0.715598i
$841$	−4126.87	+	6176.29i	−0.169210	+	0.253241i
$842$	−6613.09	+	193.356i	−0.270668	+	0.00791388i
$843$	27917.8	+	14922.4i	1.14062	+	0.609672i
$844$	1118.23	−	2422.80i	0.0456056	−	0.0988107i
$845$	−34705.3	+	3418.17i	−1.41290	+	0.139158i
$846$	10019.4	−	8724.98i	0.407178	−	0.354576i
$847$	−20637.2	+	49822.7i	−0.837195	+	2.02117i
$848$	45083.4	−	845.205i	1.82567	−	0.0342270i
$849$	−15515.1	−	37456.7i	−0.627181	−	1.51415i
$850$	−8164.98	−	4062.06i	−0.329478	−	0.163915i
$851$	−602.680	−	494.607i	−0.0242769	−	0.0199235i
$852$	−24006.5	−	39214.2i	−0.965316	−	1.57683i
$853$	14853.5	−	4505.75i	0.596217	−	0.180860i	0.0222685	−	0.999752i	$-0.492911\pi$
$853$	14853.5	−	4505.75i	0.596217	−	0.180860i	0.573948	+	0.818892i	$0.305411\pi$
$854$	6745.19	+	2565.66i	0.270276	+	0.102804i
$855$	21562.0	−	4288.94i	0.862461	−	0.171554i
$856$	−2004.26	−	218.643i	−0.0800282	−	0.00873021i
$857$	−8522.13	+	42843.6i	−0.339685	+	1.70771i	0.312722	+	0.949845i	$0.398759\pi$
$857$	−8522.13	+	42843.6i	−0.339685	+	1.70771i	−0.652407	+	0.757869i	$0.726241\pi$
$858$	−18966.2	−	82646.8i	−0.754658	−	3.28848i
$859$	−28612.9	+	23482.0i	−1.13651	+	0.932706i	−0.998334	−	0.0577020i	$-0.981623\pi$
$859$	−28612.9	+	23482.0i	−1.13651	+	0.932706i	−0.138172	+	0.990408i	$0.544123\pi$
$860$	4408.73	+	9099.81i	0.174810	+	0.360815i
$861$	11367.3	+	21266.8i	0.449940	+	0.841778i
$862$	−3347.13	+	12319.3i	−0.132255	+	0.486770i
$863$	12674.2	−	12674.2i	0.499923	−	0.499923i	−0.411491	−	0.911414i	$-0.634992\pi$
$863$	12674.2	−	12674.2i	0.499923	−	0.499923i	0.911414	+	0.411491i	$0.134992\pi$
$864$	8180.25	+	13682.4i	0.322104	+	0.538756i
$865$	−17602.9	−	17602.9i	−0.691925	−	0.691925i
$866$	30283.9	−	17343.6i	1.18832	−	0.680552i
$867$	−15166.7	+	8106.76i	−0.594103	+	0.317555i
$868$	7838.63	−	458.770i	0.306521	−	0.0179397i
$869$	−24431.1	−	29769.3i	−0.953702	−	1.16209i
$870$	34316.3	+	21505.9i	1.33728	+	0.838068i
$871$	14387.7	+	2861.90i	0.559713	+	0.111334i
$872$	9371.06	+	17983.0i	0.363927	+	0.698374i
$873$	4711.54	+	23686.5i	0.182659	+	0.918290i
$874$	−7654.59	−	17052.3i	−0.296247	−	0.659958i
$875$	8621.71	+	28422.0i	0.333105	+	1.09810i
$876$	7380.29	+	5367.11i	0.284654	+	0.207007i
$877$	−31396.8	+	38257.2i	−1.20889	+	1.47304i	−0.369740	+	0.929135i	$0.620553\pi$
$877$	−31396.8	+	38257.2i	−1.20889	+	1.47304i	−0.839149	+	0.543901i	$0.816947\pi$
$878$	766.227	−	257.116i	0.0294520	−	0.00988297i
$879$	−26195.3	+	10850.4i	−1.00517	+	0.416355i
$880$	−3739.22	+	46977.0i	−0.143238	+	1.79954i
$881$	−25948.8	−	10748.3i	−0.992322	−	0.411033i	−0.173346	−	0.984861i	$-0.555458\pi$
$881$	−25948.8	−	10748.3i	−0.992322	−	0.411033i	−0.818976	+	0.573828i	$0.805458\pi$
$882$	87744.7	+	6059.14i	3.34979	+	0.231317i
$883$	−2517.93	−	25565.0i	−0.0959627	−	0.974325i	−0.915775	−	0.401692i	$-0.868422\pi$
$883$	−2517.93	−	25565.0i	−0.0959627	−	0.974325i	0.819812	−	0.572633i	$-0.194078\pi$
$884$	−21358.0	+	19725.5i	−0.812610	+	0.750499i
$885$	−20673.4	+	38677.1i	−0.785228	+	1.46906i
$886$	11403.4	−	12090.3i	0.432398	−	0.458445i
$887$	−32176.9	−	21499.9i	−1.21803	−	0.813864i	−0.230778	−	0.973006i	$-0.574127\pi$
$887$	−32176.9	−	21499.9i	−1.21803	−	0.813864i	−0.987256	+	0.159143i	$0.949127\pi$
$888$	−9.58066	+	913.747i	−0.000362056	+	0.0345308i
$889$	14038.3	+	21009.8i	0.529616	+	0.792626i
$890$	15236.2	−	10837.7i	0.573842	−	0.408181i
$891$	−16889.5	−	1663.47i	−0.635040	−	0.0625460i
$892$	34284.9	+	20115.2i	1.28693	+	0.755053i
$893$	5034.44	+	1527.18i	0.188657	+	0.0572286i
$894$	3537.17	−	4576.52i	0.132327	−	0.171210i
$895$	56128.5			2.09628
$896$	37913.5	−	31642.6i	1.41362	−	1.17980i
$897$	−86418.0			−3.21674
$898$	14866.2	−	19234.4i	0.552439	−	0.714766i
$899$	−3587.06	−	1088.12i	−0.133076	−	0.0403681i
$900$	−9391.86	+	16007.7i	−0.347847	+	0.592879i
$901$	−36960.9	−	3640.33i	−1.36664	−	0.134603i
$902$	10915.8	−	7764.55i	0.402944	−	0.286620i
$903$	−14141.6	−	21164.5i	−0.521156	−	0.779966i
$904$	6856.01	−	6713.73i	0.252243	−	0.247008i
$905$	51835.9	+	34635.6i	1.90396	+	1.27218i
$906$	26697.8	−	28306.0i	0.979002	−	1.03797i
$907$	32.3161	−	60.4591i	0.00118306	−	0.00221335i	−0.881329	−	0.472503i	$-0.843351\pi$
$907$	32.3161	−	60.4591i	0.00118306	−	0.00221335i	0.882512	+	0.470290i	$0.155851\pi$
$908$	20317.0	+	21998.5i	0.742560	+	0.804014i
$909$	3346.58	+	33978.4i	0.122111	+	1.23982i
$910$	−90511.4	−	6250.19i	−3.29717	−	0.227683i
$911$	−31931.9	−	13226.6i	−1.16131	−	0.481029i	−0.282997	−	0.959121i	$-0.591329\pi$
$911$	−31931.9	−	13226.6i	−1.16131	−	0.481029i	−0.878310	+	0.478091i	$0.841329\pi$
$912$	−9963.17	+	19510.9i	−0.361747	+	0.708410i
$913$	196.188	−	81.2638i	0.00711159	−	0.00294572i
$914$	−37095.4	+	12447.8i	−1.34246	+	0.450477i
$915$	5218.61	−	6358.90i	0.188549	−	0.229747i
$916$	−1215.28	+	1671.13i	−0.0438363	+	0.0602790i
$917$	18871.0	+	62209.3i	0.679580	+	2.24028i
$918$	−5377.07	−	11978.6i	−0.193322	−	0.430669i
$919$	−131.942	−	663.319i	−0.00473599	−	0.0238094i	0.978345	−	0.206981i	$-0.0663637\pi$
$919$	−131.942	−	663.319i	−0.00473599	−	0.0238094i	−0.983081	+	0.183171i	$0.941364\pi$
$920$	45810.8	+	14422.8i	1.64167	+	0.516852i
$921$	47479.7	+	9444.30i	1.69871	+	0.337894i
$922$	375.270	+	235.180i	0.0134044	+	0.00840049i
$923$	−31195.2	−	38011.4i	−1.11246	−	1.35554i
$924$	−6931.25	−	118429.i	−0.246777	−	4.21647i
$925$	−270.352	+	144.506i	−0.00960988	+	0.00513659i
$926$	−36321.7	+	20801.4i	−1.28899	+	0.738205i
$927$	−29154.8	−	29154.8i	−1.03298	−	1.03298i
$928$	−22205.6	+	7917.44i	−0.785488	+	0.280067i
$929$	25145.4	−	25145.4i	0.888045	−	0.888045i	−0.106290	−	0.994335i	$-0.533897\pi$
$929$	25145.4	−	25145.4i	0.888045	−	0.888045i	0.994335	+	0.106290i	$0.0338972\pi$
$930$	2346.74	−	8637.29i	0.0827447	−	0.304546i
$931$	16417.9	+	30715.8i	0.577955	+	1.08128i
$932$	−32083.7	+	15544.1i	−1.12762	+	0.546313i
$933$	−36512.8	+	29965.3i	−1.28122	+	1.05147i
$934$	10187.8	+	44394.2i	0.356912	+	1.55527i
$935$	7572.49	−	38069.5i	0.264863	−	1.33156i
$936$	37054.0	+	46128.3i	1.29396	+	1.61084i
$937$	11598.5	−	2307.09i	0.404383	−	0.0804367i	0.0112916	−	0.999936i	$-0.496406\pi$
$937$	11598.5	−	2307.09i	0.404383	−	0.0804367i	0.393091	+	0.919500i	$0.371406\pi$
$938$	19182.5	+	7296.43i	0.667731	+	0.253984i
$939$	41433.2	−	12568.6i	1.43996	−	0.436807i
$940$	−11529.1	+	7057.99i	−0.400040	+	0.244900i
$941$	−33780.1	−	27722.6i	−1.17024	−	0.960394i	−0.170555	−	0.985348i	$-0.554556\pi$
$941$	−33780.1	−	27722.6i	−1.17024	−	0.960394i	−0.999689	+	0.0249545i	$0.992056\pi$
$942$	−42281.9	−	21035.2i	−1.46244	−	0.727561i
$943$	−5224.40	−	12612.8i	−0.180413	−	0.435556i
$944$	−10210.0	−	23398.6i	−0.352019	−	0.806735i
$945$	15680.2	−	37855.3i	0.539763	−	1.30310i
$946$	−10663.6	+	9285.97i	−0.366493	+	0.319147i
$947$	−11130.6	+	1096.27i	−0.381940	+	0.0376178i	−0.287165	−	0.957881i	$-0.592713\pi$
$947$	−11130.6	+	1096.27i	−0.381940	+	0.0376178i	−0.0947742	+	0.995499i	$0.530213\pi$
$948$	41766.7	+	19277.3i	1.43093	+	0.660439i
$949$	8607.08	+	4600.58i	0.294413	+	0.157367i
$950$	−7346.13	+	214.789i	−0.250884	+	0.00733544i
$951$	12635.9	−	18911.0i	0.430859	−	0.644826i
$952$	−34054.8	+	22241.8i	−1.15937	+	0.757208i
$953$	8154.89	−	5448.93i	0.277191	−	0.185213i	−0.409202	−	0.912444i	$-0.634193\pi$
$953$	8154.89	−	5448.93i	0.277191	−	0.185213i	0.686393	+	0.727231i	$0.259193\pi$
$954$	−12572.8	+	74530.8i	−0.426688	+	2.52937i
$955$	−6899.84	+	70055.3i	−0.233794	+	2.37375i
$956$	10675.3	+	14115.6i	0.361156	+	0.477542i
$957$	−16439.7	+	54194.5i	−0.555299	+	1.83057i
$958$	1276.67	−	163.539i	0.0430556	−	0.00551536i
$959$			28730.7i			0.967428i
$960$	−20446.4	−	52446.3i	−0.687402	−	1.76323i
$961$		−	28962.6i		−	0.972192i
$962$	124.174	+	969.360i	0.00416167	+	0.0324880i
$963$	981.031	−	3234.03i	0.0328279	−	0.108219i
$964$	2513.08	−	18109.6i	0.0839634	−	0.605054i
$965$	235.108	−	2387.09i	0.00784289	−	0.0796302i
$966$	−119218.	−	20111.2i	−3.97077	−	0.669841i
$967$	−27149.0	+	18140.4i	−0.902848	+	0.603264i	−0.917982	−	0.396622i	$-0.870182\pi$
$967$	−27149.0	+	18140.4i	−0.902848	+	0.603264i	0.0151342	+	0.999885i	$0.495182\pi$
$968$	−35167.3	+	6612.69i	−1.16768	+	0.219566i
$969$	10024.9	−	15003.3i	0.332348	−	0.497394i
$970$	−718.155	−	24562.1i	−0.0237717	−	0.813032i
$971$	−17375.5	−	9287.41i	−0.574261	−	0.306949i	0.158583	−	0.987346i	$-0.449307\pi$
$971$	−17375.5	−	9287.41i	−0.574261	−	0.306949i	−0.732844	+	0.680397i	$0.761807\pi$
$972$	36871.1	−	13583.9i	1.21671	−	0.448253i
$973$	64844.2	−	6386.60i	2.13650	−	0.210426i
$974$	−18950.9	−	21762.3i	−0.623435	−	0.715923i
$975$	−13003.0	+	31392.0i	−0.427106	+	1.03113i
$976$	1022.08	+	4678.25i	0.0335204	+	0.153429i
$977$	3190.03	+	7701.42i	0.104461	+	0.252191i	0.967464	−	0.253007i	$-0.0814196\pi$
$977$	3190.03	+	7701.42i	0.104461	+	0.252191i	−0.863004	+	0.505198i	$0.831420\pi$
$978$	−11176.9	+	22466.2i	−0.365436	+	0.734549i
$979$	20211.7	+	16587.3i	0.659826	+	0.541505i
$980$	−87008.6	−	20929.9i	−2.83611	−	0.682224i
$981$	−32527.5	+	9867.11i	−1.05864	+	0.321134i
$982$	13403.7	−	35238.8i	0.435571	−	1.14513i
$983$	20918.7	−	4160.99i	0.678742	−	0.135010i	0.156332	−	0.987705i	$-0.450033\pi$
$983$	20918.7	−	4160.99i	0.678742	−	0.135010i	0.522410	+	0.852694i	$0.325033\pi$
$984$	−7690.31	+	14031.7i	−0.249144	+	0.454587i
$985$	1429.43	−	7186.21i	0.0462389	−	0.232458i
$986$	18925.6	−	4343.15i	0.611272	−	0.140278i
$987$	26305.1	−	21588.0i	0.848329	−	0.696205i
$988$	−7686.06	+	22132.9i	−0.247496	+	0.712694i
$989$	6793.15	+	12709.1i	0.218412	+	0.408620i
$990$	−76230.2	−	20711.6i	−2.44723	−	0.664908i
$991$	−1315.15	+	1315.15i	−0.0421566	+	0.0421566i	−0.727871	−	0.685714i	$-0.759490\pi$
$991$	−1315.15	+	1315.15i	−0.0421566	+	0.0421566i	0.685714	+	0.727871i	$0.259490\pi$
$992$	3099.06	+	4188.32i	0.0991887	+	0.134052i
$993$	−21350.3	−	21350.3i	−0.682308	−	0.682308i
$994$	−34189.2	−	59698.2i	−1.09096	−	1.90494i
$995$	26567.5	−	14200.6i	0.846479	−	0.452453i
$996$	−168.574	+	189.532i	−0.00536291	+	0.00602969i
$997$	12046.1	+	14678.2i	0.382651	+	0.466262i	0.928343	−	0.371724i	$-0.121233\pi$
$997$	12046.1	+	14678.2i	0.382651	+	0.466262i	−0.545692	+	0.837986i	$0.683733\pi$
$998$	−31245.1	+	49856.8i	−0.991029	+	1.58135i
$999$	−432.880	−	86.1053i	−0.0137094	−	0.00272698i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.k.a.5.11	✓	752
128.77	even	32	inner	128.4.k.a.77.11	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.4.k.a.5.11	✓	752	1.1	even	1	trivial
128.4.k.a.77.11	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)

\(f(q)\)	\(=\)	\(q+(-2.23791 - 1.72967i) q^{2} +(7.71088 + 2.33907i) q^{3} +(2.01649 + 7.74169i) q^{4} +(13.5785 + 1.33737i) q^{5} +(-13.2105 - 18.5719i) q^{6} +(-18.9453 - 28.3537i) q^{7} +(8.87784 - 20.8131i) q^{8} +(31.5368 + 21.0722i) q^{9} +O(q^{10})\)	\(q+(-2.23791 - 1.72967i) q^{2} +(7.71088 + 2.33907i) q^{3} +(2.01649 + 7.74169i) q^{4} +(13.5785 + 1.33737i) q^{5} +(-13.2105 - 18.5719i) q^{6} +(-18.9453 - 28.3537i) q^{7} +(8.87784 - 20.8131i) q^{8} +(31.5368 + 21.0722i) q^{9} +(-28.0744 - 26.4793i) q^{10} +(25.4398 - 47.5946i) q^{11} +(-2.55945 + 64.4120i) q^{12} +(6.75742 + 68.6092i) q^{13} +(-6.64454 + 96.2221i) q^{14} +(101.574 + 42.0735i) q^{15} +(-55.8675 + 31.2221i) q^{16} +(48.7014 - 20.1728i) q^{17} +(-34.1286 - 101.706i) q^{18} +(26.9496 - 32.8382i) q^{19} +(17.0275 + 107.818i) q^{20} +(-79.7639 - 262.946i) q^{21} +(-139.255 + 62.5099i) q^{22} +(30.3488 + 152.574i) q^{23} +(117.139 - 139.721i) q^{24} +(59.9900 + 11.9328i) q^{25} +(103.549 - 165.229i) q^{26} +(55.8672 + 68.0744i) q^{27} +(181.302 - 203.844i) q^{28} +(-114.856 + 61.3918i) q^{29} +(-154.541 - 269.847i) q^{30} +(20.3524 + 20.3524i) q^{31} +(179.030 + 26.7601i) q^{32} +(307.491 - 307.491i) q^{33} +(-143.882 - 39.0924i) q^{34} +(-219.330 - 410.338i) q^{35} +(-99.5409 + 286.640i) q^{36} +(-3.87419 + 3.17947i) q^{37} +(-117.110 + 26.8751i) q^{38} +(-108.376 + 544.844i) q^{39} +(148.383 - 270.738i) q^{40} +(-86.0725 + 17.1209i) q^{41} +(-276.306 + 726.416i) q^{42} +(88.6468 - 26.8907i) q^{43} +(419.761 + 100.973i) q^{44} +(400.042 + 328.306i) q^{45} +(195.984 - 393.940i) q^{46} +(47.3927 + 114.416i) q^{47} +(-503.819 + 110.072i) q^{48} +(-313.745 + 757.449i) q^{49} +(-113.613 - 130.467i) q^{50} +(422.716 - 41.6339i) q^{51} +(-517.525 + 190.664i) q^{52} +(-621.359 - 332.123i) q^{53} +(-7.27966 - 248.976i) q^{54} +(409.087 - 612.242i) q^{55} +(-758.321 + 142.591i) q^{56} +(284.616 - 190.175i) q^{57} +(363.225 + 61.2734i) q^{58} +(-39.0983 + 396.972i) q^{59} +(-120.896 + 871.198i) q^{60} +(21.7196 - 71.6000i) q^{61} +(-10.3439 - 80.7496i) q^{62} -1293.40i q^{63} +(-354.368 - 369.550i) q^{64} +940.650i q^{65} +(-1219.99 + 156.279i) q^{66} +(61.7680 - 203.622i) q^{67} +(254.377 + 336.353i) q^{68} +(-122.865 + 1247.47i) q^{69} +(-218.908 + 1297.67i) q^{70} +(-593.057 + 396.268i) q^{71} +(718.556 - 469.302i) q^{72} +(78.6477 - 117.705i) q^{73} +(14.1695 - 0.414294i) q^{74} +(434.664 + 232.333i) q^{75} +(308.567 + 142.418i) q^{76} +(-1831.45 + 180.382i) q^{77} +(1184.94 - 1031.86i) q^{78} +(273.084 - 659.282i) q^{79} +(-800.355 + 349.235i) q^{80} +(-120.345 - 290.537i) q^{81} +(222.236 + 110.562i) q^{82} +(3.04169 + 2.49625i) q^{83} +(1874.81 - 1147.74i) q^{84} +(688.273 - 208.785i) q^{85} +(-244.896 - 93.1507i) q^{86} +(-1029.24 + 204.729i) q^{87} +(-764.738 - 952.018i) q^{88} +(-94.5205 + 475.187i) q^{89} +(-327.398 - 1426.66i) q^{90} +(1817.30 - 1491.42i) q^{91} +(-1119.98 + 542.615i) q^{92} +(109.329 + 204.540i) q^{93} +(91.8414 - 338.027i) q^{94} +(409.853 - 409.853i) q^{95} +(1317.89 + 625.109i) q^{96} +(450.237 + 450.237i) q^{97} +(2012.27 - 1152.43i) q^{98} +(1805.21 - 964.906i) 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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