LMFDB - Embedded newform 128.4.k.a.101.33

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [128,4,Mod(5,128)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.55224448073$
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			101.33
Character	$\chi$	$=$	128.101
Dual form			128.4.k.a.109.33

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.66194 + 2.28866i) q^{2} +(-6.99286 + 3.73776i) q^{3} +(-2.47591 + 7.60723i) q^{4} +(-8.05192 - 9.81129i) q^{5} +(-20.1762 - 9.79232i) q^{6} +(1.10180 - 0.736202i) q^{7} +(-21.5251 + 6.97626i) q^{8} +(19.9288 - 29.8255i) q^{9} +(9.07288 - 34.7339i) q^{10} +(58.3258 - 17.6929i) q^{11} +(-11.1203 - 62.4506i) q^{12} +(-0.579028 - 0.475196i) q^{13} +(3.51605 + 1.29813i) q^{14} +(92.9782 + 38.5128i) q^{15} +(-51.7398 - 37.6695i) q^{16} +(-127.989 + 53.0148i) q^{17} +(101.381 - 3.95811i) q^{18} +(-8.92201 - 90.5867i) q^{19} +(94.5725 - 36.9609i) q^{20} +(-4.95301 + 9.26644i) q^{21} +(137.427 + 104.083i) q^{22} +(-13.7398 + 2.73302i) q^{23} +(124.447 - 129.240i) q^{24} +(-7.04178 + 35.4014i) q^{25} +(0.125251 - 2.11495i) q^{26} +(-6.89435 + 69.9995i) q^{27} +(2.87249 + 10.2044i) q^{28} +(68.9169 - 227.188i) q^{29} +(66.3816 + 276.801i) q^{30} +(-133.460 - 133.460i) q^{31} +(0.224241 - 181.019i) q^{32} +(-341.732 + 341.732i) q^{33} +(-334.043 - 204.816i) q^{34} +(-16.0947 - 4.88229i) q^{35} +(177.548 + 225.448i) q^{36} +(-264.430 - 26.0440i) q^{37} +(192.494 - 170.969i) q^{38} +(5.82523 + 1.15871i) q^{39} +(241.765 + 155.017i) q^{40} +(19.9135 + 100.112i) q^{41} +(-29.4393 + 4.06452i) q^{42} +(-87.4242 - 46.7292i) q^{43} +(-9.81500 + 487.504i) q^{44} +(-453.092 + 44.6257i) q^{45} +(-29.0897 - 26.9036i) q^{46} +(99.8337 + 241.020i) q^{47} +(502.609 + 70.0269i) q^{48} +(-130.588 + 315.268i) q^{49} +(-92.7247 + 42.7188i) q^{50} +(696.852 - 849.117i) q^{51} +(5.04855 - 3.22826i) q^{52} +(-101.853 - 335.764i) q^{53} +(-171.663 + 100.556i) q^{54} +(-643.226 - 429.790i) q^{55} +(-18.5806 + 23.5333i) q^{56} +(400.982 + 600.111i) q^{57} +(634.492 - 219.847i) q^{58} +(-461.880 + 379.055i) q^{59} +(-523.181 + 611.952i) q^{60} +(15.1123 + 28.2732i) q^{61} +(83.6416 - 527.247i) q^{62} -47.5335i q^{63} +(414.664 - 300.330i) q^{64} +9.50726i q^{65} +(-1350.05 - 214.169i) q^{66} +(301.778 + 564.587i) q^{67} +(-86.4068 - 1104.90i) q^{68} +(85.8653 - 70.4678i) q^{69} +(-15.5746 - 44.9494i) q^{70} +(281.552 + 421.372i) q^{71} +(-220.899 + 781.028i) q^{72} +(-431.979 - 288.639i) q^{73} +(-379.860 - 648.472i) q^{74} +(-83.0798 - 273.877i) q^{75} +(711.204 + 156.412i) q^{76} +(51.2381 - 62.4338i) q^{77} +(7.02930 + 15.2577i) q^{78} +(253.453 - 611.891i) q^{79} +(47.0176 + 810.947i) q^{80} +(157.204 + 379.524i) q^{81} +(-196.027 + 211.956i) q^{82} +(-103.355 + 10.1796i) q^{83} +(-58.2287 - 60.6215i) q^{84} +(1550.70 + 828.867i) q^{85} +(-38.3467 - 277.745i) q^{86} +(367.250 + 1846.29i) q^{87} +(-1132.04 + 787.739i) q^{88} +(-480.445 - 95.5665i) q^{89} +(-855.146 - 962.808i) q^{90} +(-0.987817 - 0.0972915i) q^{91} +(13.2278 - 111.289i) q^{92} +(1432.11 + 434.425i) q^{93} +(-385.694 + 629.046i) q^{94} +(-816.933 + 816.933i) q^{95} +(675.038 + 1266.68i) q^{96} +(-664.505 - 664.505i) q^{97} +(-938.572 + 225.085i) q^{98} +(634.661 - 2092.20i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18}+ \cdots - 16 q^{99}+O(q^{100})$ 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

Character values

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

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{9}{32}\right)$	$1$

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

)

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

$2$	1.66194	+	2.28866i	0.587585	+	0.809163i
$2$	1.66194	+	2.28866i	0.587585	+	0.809163i
$3$	−6.99286	+	3.73776i	−1.34578	+	0.719332i	−0.977609	−	0.210428i	$-0.932514\pi$
$3$	−6.99286	+	3.73776i	−1.34578	+	0.719332i	−0.368166	+	0.929760i	$0.620014\pi$
$4$	−2.47591	+	7.60723i	−0.309488	+	0.950903i
$5$	−8.05192	−	9.81129i	−0.720186	−	0.877549i	0.276321	−	0.961066i	$-0.410885\pi$
$5$	−8.05192	−	9.81129i	−0.720186	−	0.877549i	−0.996506	+	0.0835166i	$0.973385\pi$
$6$	−20.1762	−	9.79232i	−1.37281	−	0.666283i
$7$	1.10180	−	0.736202i	0.0594918	−	0.0397512i	−0.525469	−	0.850813i	$-0.676110\pi$
$7$	1.10180	−	0.736202i	0.0594918	−	0.0397512i	0.584961	+	0.811062i	$0.301110\pi$
$8$	−21.5251	+	6.97626i	−0.951286	+	0.308310i
$9$	19.9288	−	29.8255i	0.738103	−	1.10465i
$10$	9.07288	−	34.7339i	0.286910	−	1.09838i
$11$	58.3258	−	17.6929i	1.59872	−	0.484966i	0.639774	−	0.768563i	$-0.279028\pi$
$11$	58.3258	−	17.6929i	1.59872	−	0.484966i	0.958944	+	0.283597i	$0.0915278\pi$
$12$	−11.1203	−	62.4506i	−0.267514	−	1.50233i
$13$	−0.579028	−	0.475196i	−0.0123534	−	0.0101381i	0.628196	−	0.778055i	$-0.283793\pi$
$13$	−0.579028	−	0.475196i	−0.0123534	−	0.0101381i	−0.640550	+	0.767917i	$0.721293\pi$
$14$	3.51605	+	1.29813i	0.0671217	+	0.0247814i
$15$	92.9782	+	38.5128i	1.60046	+	0.662931i
$16$	−51.7398	−	37.6695i	−0.808434	−	0.588587i
$17$	−127.989	+	53.0148i	−1.82599	+	0.756352i	−0.854434	+	0.519560i	$0.826096\pi$
$17$	−127.989	+	53.0148i	−1.82599	+	0.756352i	−0.971560	+	0.236792i	$0.923904\pi$
$18$	101.381	−	3.95811i	1.32754	−	0.0518298i
$19$	−8.92201	−	90.5867i	−0.107729	−	1.09379i	−0.885308	−	0.465005i	$-0.846053\pi$
$19$	−8.92201	−	90.5867i	−0.107729	−	1.09379i	0.777579	−	0.628785i	$-0.216447\pi$
$20$	94.5725	−	36.9609i	1.05735	−	0.413236i
$21$	−4.95301	+	9.26644i	−0.0514684	+	0.0962906i
$22$	137.427	+	104.083i	1.33180	+	1.00866i
$23$	−13.7398	+	2.73302i	−0.124563	+	0.0247771i	−0.256978	−	0.966417i	$-0.582727\pi$
$23$	−13.7398	+	2.73302i	−0.124563	+	0.0247771i	0.132415	+	0.991194i	$0.457727\pi$
$24$	124.447	−	129.240i	1.05844	−	1.09921i
$25$	−7.04178	+	35.4014i	−0.0563342	+	0.283211i
$26$	0.125251	−	2.11495i	0.000944757	−	0.0159529i
$27$	−6.89435	+	69.9995i	−0.0491414	+	0.498941i
$28$	2.87249	+	10.2044i	0.0193875	+	0.0688735i
$29$	68.9169	−	227.188i	0.441295	−	1.45475i	−0.401171	−	0.916003i	$-0.631397\pi$
$29$	68.9169	−	227.188i	0.441295	−	1.45475i	0.842466	−	0.538750i	$-0.181103\pi$
$30$	66.3816	+	276.801i	0.403985	+	1.68456i
$31$	−133.460	−	133.460i	−0.773229	−	0.773229i	0.205440	−	0.978670i	$-0.434137\pi$
$31$	−133.460	−	133.460i	−0.773229	−	0.773229i	−0.978670	+	0.205440i	$0.934137\pi$
$32$	0.224241	−	181.019i	0.00123877	−	0.999999i
$33$	−341.732	+	341.732i	−1.80266	+	1.80266i
$34$	−334.043	−	204.816i	−1.68494	−	1.03311i
$35$	−16.0947	−	4.88229i	−0.0777288	−	0.0235788i
$36$	177.548	+	225.448i	0.821981	+	1.04374i
$37$	−264.430	−	26.0440i	−1.17492	−	0.115719i	−0.508341	−	0.861156i	$-0.669741\pi$
$37$	−264.430	−	26.0440i	−1.17492	−	0.115719i	−0.666577	+	0.745437i	$0.732241\pi$
$38$	192.494	−	170.969i	0.821754	−	0.729865i
$39$	5.82523	+	1.15871i	0.0239175	+	0.00475749i
$40$	241.765	+	155.017i	0.955660	+	0.612759i
$41$	19.9135	+	100.112i	0.0758530	+	0.381339i	1.00000		0.000698820i	$-0.000222441\pi$
$41$	19.9135	+	100.112i	0.0758530	+	0.381339i	−0.924147	+	0.382038i	$0.875222\pi$
$42$	−29.4393	+	4.06452i	−0.108157	+	0.0149326i
$43$	−87.4242	−	46.7292i	−0.310048	−	0.165724i	0.309033	−	0.951051i	$-0.399995\pi$
$43$	−87.4242	−	46.7292i	−0.310048	−	0.165724i	−0.619081	+	0.785327i	$0.712495\pi$
$44$	−9.81500	+	487.504i	−0.0336288	+	1.67032i
$45$	−453.092	+	44.6257i	−1.50096	+	0.147831i
$46$	−29.0897	−	26.9036i	−0.0932402	−	0.0862332i
$47$	99.8337	+	241.020i	0.309835	+	0.748007i	0.999710	+	0.0240792i	$0.00766538\pi$
$47$	99.8337	+	241.020i	0.309835	+	0.748007i	−0.689875	+	0.723928i	$0.742335\pi$
$48$	502.609	+	70.0269i	1.51136	+	0.210573i
$49$	−130.588	+	315.268i	−0.380724	+	0.919150i
$50$	−92.7247	+	42.7188i	−0.262265	+	0.120827i
$51$	696.852	−	849.117i	1.91331	−	2.33138i
$52$	5.04855	−	3.22826i	0.0134636	−	0.00860921i
$53$	−101.853	−	335.764i	−0.263973	−	0.870203i	−0.984290	−	0.176558i	$-0.943504\pi$
$53$	−101.853	−	335.764i	−0.263973	−	0.870203i	0.720317	−	0.693645i	$-0.243996\pi$
$54$	−171.663	+	100.556i	−0.432599	+	0.253407i
$55$	−643.226	−	429.790i	−1.57696	−	1.05369i
$56$	−18.5806	+	23.5333i	−0.0443381	+	0.0561567i
$57$	400.982	+	600.111i	0.931777	+	1.39450i
$58$	634.492	−	219.847i	1.43643	−	0.497712i
$59$	−461.880	+	379.055i	−1.01918	+	0.836419i	−0.986618	−	0.163051i	$-0.947867\pi$
$59$	−461.880	+	379.055i	−1.01918	+	0.836419i	−0.0325618	+	0.999470i	$0.510367\pi$
$60$	−523.181	+	611.952i	−1.12571	+	1.31671i
$61$	15.1123	+	28.2732i	0.0317203	+	0.0593445i	0.897282	−	0.441458i	$-0.145538\pi$
$61$	15.1123	+	28.2732i	0.0317203	+	0.0593445i	−0.865562	+	0.500802i	$0.833038\pi$
$62$	83.6416	−	527.247i	0.171330	−	1.08001i
$63$		−	47.5335i		−	0.0950581i
$64$	414.664	−	300.330i	0.809890	−	0.586582i
$65$			9.50726i			0.0181420i
$66$	−1350.05	−	214.169i	−2.51787	−	0.399430i
$67$	301.778	+	564.587i	0.550270	+	1.02948i	0.991254	+	0.131968i	$0.0421295\pi$
$67$	301.778	+	564.587i	0.550270	+	1.02948i	−0.440984	+	0.897515i	$0.645371\pi$
$68$	−86.4068	−	1104.90i	−0.154094	−	1.97043i
$69$	85.8653	−	70.4678i	0.149811	−	0.122947i
$70$	−15.5746	−	44.9494i	−0.0265932	−	0.0767498i
$71$	281.552	+	421.372i	0.470621	+	0.704333i	0.988517	−	0.151110i	$-0.0482848\pi$
$71$	281.552	+	421.372i	0.470621	+	0.704333i	−0.517896	+	0.855443i	$0.673285\pi$
$72$	−220.899	+	781.028i	−0.361573	+	1.27840i
$73$	−431.979	−	288.639i	−0.692593	−	0.462776i	0.158795	−	0.987312i	$-0.449239\pi$
$73$	−431.979	−	288.639i	−0.692593	−	0.462776i	−0.851389	+	0.524536i	$0.824239\pi$
$74$	−379.860	−	648.472i	−0.596728	−	1.01869i
$75$	−83.0798	−	273.877i	−0.127910	−	0.421662i
$76$	711.204	+	156.412i	1.07343	+	0.236075i
$77$	51.2381	−	62.4338i	0.0758327	−	0.0924024i
$78$	7.02930	+	15.2577i	0.0102040	+	0.0221486i
$79$	253.453	−	611.891i	0.360959	−	0.871431i	−0.634202	−	0.773168i	$-0.718671\pi$
$79$	253.453	−	611.891i	0.360959	−	0.871431i	0.995160	−	0.0982637i	$-0.0313289\pi$
$80$	47.0176	+	810.947i	0.0657091	+	1.13333i
$81$	157.204	+	379.524i	0.215643	+	0.520609i
$82$	−196.027	+	211.956i	−0.263995	+	0.285446i
$83$	−103.355	+	10.1796i	−0.136683	+	0.0134621i	−0.166127	−	0.986104i	$-0.553126\pi$
$83$	−103.355	+	10.1796i	−0.136683	+	0.0134621i	0.0294442	+	0.999566i	$0.490626\pi$
$84$	−58.2287	−	60.6215i	−0.0756342	−	0.0787423i
$85$	1550.70	+	828.867i	1.97879	+	1.05769i
$86$	−38.3467	−	277.745i	−0.0480818	−	0.348256i
$87$	367.250	+	1846.29i	0.452567	+	2.27521i
$88$	−1132.04	+	787.739i	−1.37132	+	0.954242i
$89$	−480.445	−	95.5665i	−0.572214	−	0.113820i	−0.0995021	−	0.995037i	$-0.531725\pi$
$89$	−480.445	−	95.5665i	−0.572214	−	0.113820i	−0.472712	+	0.881217i	$0.656725\pi$
$90$	−855.146	−	962.808i	−1.00156	−	1.12765i
$91$	−0.987817	−	0.0972915i	−0.00113793	−	0.000112076i
$92$	13.2278	−	111.289i	0.0149902	−	0.126116i
$93$	1432.11	+	434.425i	1.59680	+	0.484385i
$94$	−385.694	+	629.046i	−0.423205	+	0.690225i
$95$	−816.933	+	816.933i	−0.882269	+	0.882269i
$96$	675.038	+	1266.68i	0.717664	+	1.34667i
$97$	−664.505	−	664.505i	−0.695570	−	0.695570i	0.267882	−	0.963452i	$-0.413676\pi$
$97$	−664.505	−	664.505i	−0.695570	−	0.695570i	−0.963452	+	0.267882i	$0.913676\pi$
$98$	−938.572	+	225.085i	−0.967449	+	0.232011i
$99$	634.661	−	2092.20i	0.644302	−	2.12398i
$100$	−251.872	−	141.219i	−0.251872	−	0.141219i
$101$	−74.1968	+	753.333i	−0.0730976	+	0.742173i	0.886862	+	0.462034i	$0.152880\pi$
$101$	−74.1968	+	753.333i	−0.0730976	+	0.742173i	−0.959960	+	0.280138i	$0.909620\pi$
$102$	3101.47	+	183.674i	3.01069	+	0.178298i
$103$	241.472	−	1213.96i	0.231000	−	1.16131i	−0.674928	−	0.737883i	$-0.735825\pi$
$103$	241.472	−	1213.96i	0.231000	−	1.16131i	0.905928	−	0.423431i	$-0.139175\pi$
$104$	15.7788	+	6.18922i	0.0148773	+	0.00583560i
$105$	130.797	−	26.0171i	0.121566	−	0.0241811i
$106$	599.176	−	791.127i	0.549029	−	0.724915i
$107$	19.4569	−	36.4014i	0.0175792	−	0.0328883i	−0.872978	−	0.487759i	$-0.837814\pi$
$107$	19.4569	−	36.4014i	0.0175792	−	0.0328883i	0.890558	+	0.454871i	$0.150314\pi$
$108$	−515.433	−	225.759i	−0.459236	−	0.201145i
$109$	−194.655	−	1976.37i	−0.171051	−	1.73671i	−0.571684	−	0.820474i	$-0.693710\pi$
$109$	−194.655	−	1976.37i	−0.171051	−	1.73671i	0.400633	−	0.916239i	$-0.368790\pi$
$110$	−85.3617	−	2186.41i	−0.0739902	−	1.89514i
$111$	1946.46	−	806.252i	1.66442	−	0.689424i
$112$	−84.7395	−	3.41354i	−0.0714923	−	0.00287990i
$113$	−1612.22	−	667.803i	−1.34217	−	0.555944i	−0.408066	−	0.912953i	$-0.633797\pi$
$113$	−1612.22	−	667.803i	−1.34217	−	0.555944i	−0.934101	+	0.357009i	$0.883797\pi$
$114$	−707.042	+	1915.06i	−0.580882	+	1.57335i
$115$	137.447	+	112.799i	0.111452	+	0.0914661i
$116$	1557.64	+	1086.76i	1.24675	+	0.869857i
$117$	−25.7123	+	7.79975i	−0.0203171	+	0.00616314i
$118$	−1635.14	−	427.117i	−1.27565	−	0.333215i
$119$	−101.989	+	152.638i	−0.0785659	+	0.117582i
$120$	−2270.04	−	180.354i	−1.72688	−	0.137200i
$121$	1982.18	−	1324.45i	1.48924	−	0.995077i
$122$	−39.5919	+	81.5754i	−0.0293810	+	0.0605368i
$123$	−513.448	−	625.638i	−0.376390	−	0.458633i
$124$	1345.69	−	684.826i	0.974572	−	0.495961i
$125$	−995.170	+	531.929i	−0.712086	+	0.380618i
$126$	108.788	−	78.9979i	0.0769175	−	0.0558547i
$127$	1327.24			0.927349			0.463675	−	0.886006i	$-0.346531\pi$
$127$	1327.24			0.927349			0.463675	+	0.886006i	$0.346531\pi$
$128$	1376.50	+	449.892i	0.950519	+	0.310666i
$129$	786.008			0.536466
$130$	−21.7589	+	15.8005i	−0.0146798	+	0.0106600i
$131$	585.068	−	312.725i	0.390211	−	0.208572i	−0.264611	−	0.964355i	$-0.585244\pi$
$131$	585.068	−	312.725i	0.390211	−	0.208572i	0.654822	+	0.755783i	$0.272744\pi$
$132$	−1753.54	−	3445.73i	−1.15626	−	2.27206i
$133$	−76.5204	−	93.2404i	−0.0498884	−	0.0607892i
$134$	−790.610	+	1628.98i	−0.509688	+	1.05017i
$135$	742.299	−	495.988i	0.473236	−	0.316206i
$136$	2385.14	−	2034.04i	1.50385	−	1.28248i
$137$	−799.879	+	1197.10i	−0.498820	+	0.746536i	−0.992385	−	0.123172i	$-0.960693\pi$
$137$	−799.879	+	1197.10i	−0.498820	+	0.746536i	0.493566	+	0.869709i	$0.335693\pi$
$138$	303.980	+	79.4029i	0.187511	+	0.0489799i
$139$	789.195	−	239.400i	0.481573	−	0.146083i	−0.0401587	−	0.999193i	$-0.512786\pi$
$139$	789.195	−	239.400i	0.481573	−	0.146083i	0.521731	+	0.853110i	$0.325286\pi$
$140$	76.9897	−	110.348i	0.0464773	−	0.0666152i
$141$	−1599.00	−	1312.26i	−0.955034	−	0.783776i
$142$	−496.454	+	1344.67i	−0.293391	+	0.794664i
$143$	−42.1799	−	17.4715i	−0.0246662	−	0.0102171i
$144$	−2154.63	+	792.459i	−1.24689	+	0.458599i
$145$	−2783.93	+	1153.14i	−1.59443	+	0.660435i
$146$	−57.3274	−	1468.35i	−0.0324962	−	0.832341i
$147$	−265.211	−	2692.73i	−0.148804	−	1.51084i
$148$	852.825	−	1947.09i	0.473661	−	1.08142i
$149$	−639.335	+	1196.11i	−0.351519	+	0.657646i	−0.994087	−	0.108582i	$-0.965369\pi$
$149$	−639.335	+	1196.11i	−0.351519	+	0.657646i	0.642568	+	0.766228i	$0.277869\pi$
$150$	488.738	−	645.309i	0.266035	−	0.351262i
$151$	−881.888	+	175.418i	−0.475279	+	0.0945388i	−0.426916	−	0.904291i	$-0.640400\pi$
$151$	−881.888	+	175.418i	−0.475279	+	0.0945388i	−0.0483621	+	0.998830i	$0.515400\pi$
$152$	824.004	+	1887.65i	0.439707	+	1.00729i
$153$	−969.472	+	4873.86i	−0.512269	+	2.57535i
$154$	228.044	+	13.5052i	0.119327	+	0.00706673i
$155$	−234.806	+	2384.02i	−0.121678	+	1.23542i
$156$	−23.2373	+	41.4450i	−0.0119261	+	0.0212709i
$157$	175.212	−	577.595i	0.0890663	−	0.293612i	−0.901079	−	0.433654i	$-0.857224\pi$
$157$	175.212	−	577.595i	0.0890663	−	0.293612i	0.990146	+	0.140042i	$0.0447239\pi$
$158$	1821.63	−	436.858i	0.917223	−	0.219966i
$159$	1967.25	+	1967.25i	0.981214	+	0.981214i
$160$	−1777.84	+	1455.35i	−0.878440	+	0.719098i
$161$	−13.1265	+	13.1265i	−0.00642557	+	0.00642557i
$162$	−607.337	+	990.532i	−0.294549	+	0.480392i
$163$	−2450.90	−	743.473i	−1.17773	−	0.357259i	−0.360048	−	0.932934i	$-0.617240\pi$
$163$	−2450.90	−	743.473i	−1.17773	−	0.357259i	−0.817679	+	0.575674i	$0.804740\pi$
$164$	−810.880	−	96.3814i	−0.386092	−	0.0458910i
$165$	6104.43	+	601.234i	2.88018	+	0.283673i
$166$	−195.068	−	219.627i	−0.0912060	−	0.102689i
$167$	4013.95	+	798.425i	1.85993	+	0.369964i	0.991950	−	0.126630i	$-0.0404160\pi$
$167$	4013.95	+	798.425i	1.85993	+	0.369964i	0.867983	+	0.496593i	$0.165416\pi$
$168$	41.9693	−	234.015i	0.0192738	−	0.107468i
$169$	−428.504	−	2154.23i	−0.195040	−	0.980535i
$170$	680.181	+	4926.55i	0.306868	+	2.22264i
$171$	−2879.60	−	1539.18i	−1.28777	−	0.688328i
$172$	571.934	−	549.359i	0.253544	−	0.243536i
$173$	−1443.30	+	142.153i	−0.634289	+	0.0624720i	−0.410051	−	0.912062i	$-0.634489\pi$
$173$	−1443.30	+	142.153i	−0.634289	+	0.0624720i	−0.224238	+	0.974534i	$0.571989\pi$
$174$	−3615.18	+	3908.94i	−1.57509	+	1.70308i
$175$	18.3039	+	44.1896i	0.00790655	+	0.0190881i
$176$	−3684.25	−	1281.68i	−1.57790	−	0.548921i
$177$	1813.04	−	4377.07i	0.769924	−	1.85876i
$178$	−579.752	−	1258.40i	−0.244125	−	0.529894i
$179$	278.616	−	339.495i	0.116339	−	0.141760i	−0.711584	−	0.702601i	$-0.752022\pi$
$179$	278.616	−	339.495i	0.116339	−	0.141760i	0.827924	+	0.560841i	$0.189522\pi$
$180$	782.336	−	3557.26i	0.323955	−	1.47302i
$181$	900.993	+	2970.18i	0.370002	+	1.21973i	0.922428	+	0.386170i	$0.126202\pi$
$181$	900.993	+	2970.18i	0.370002	+	1.21973i	−0.552426	+	0.833562i	$0.686298\pi$
$182$	−1.41903	−	2.42247i	−0.000577941	−	0.000986622i
$183$	−211.357	−	141.224i	−0.0853768	−	0.0570470i
$184$	276.686	−	154.681i	0.110856	−	0.0619742i
$185$	1873.64	+	2804.10i	0.744610	+	1.11439i
$186$	1385.83	+	3999.59i	0.546311	+	1.57669i
$187$	−6527.08	+	5356.64i	−2.55245	+	2.09474i
$188$	−2080.67	+	162.715i	−0.807173	+	0.0631235i
$189$	43.9376	+	82.2014i	0.0169100	+	0.0316364i
$190$	−3227.38	−	511.986i	−1.23231	−	0.195491i
$191$			2574.17i			0.975187i	0.873071	+	0.487594i	$0.162125\pi$
$191$			2574.17i			0.975187i	−0.873071	+	0.487594i	$0.837875\pi$
$192$	−1777.12	+	3650.08i	−0.667983	+	1.37199i
$193$			2914.97i			1.08717i	0.839354	+	0.543585i	$0.182933\pi$
$193$			2914.97i			1.08717i	−0.839354	+	0.543585i	$0.817067\pi$
$194$	416.456	−	2625.19i	0.154123	−	0.971535i
$195$	−35.5359	−	66.4829i	−0.0130501	−	0.0244151i
$196$	−2074.99	−	1773.99i	−0.756193	−	0.646498i
$197$	3293.06	−	2702.55i	1.19097	−	0.977403i	0.190978	−	0.981594i	$-0.438834\pi$
$197$	3293.06	−	2702.55i	1.19097	−	0.977403i	0.999991	+	0.00419150i	$0.00133420\pi$
$198$	5843.10	−	2024.59i	2.09723	−	0.726672i
$199$	906.593	+	1356.81i	0.322948	+	0.483326i	0.957050	−	0.289924i	$-0.0936299\pi$
$199$	906.593	+	1356.81i	0.322948	+	0.483326i	−0.634102	+	0.773250i	$0.718630\pi$
$200$	−95.3941	−	811.145i	−0.0337269	−	0.286783i
$201$	−4220.58	−	2820.10i	−1.48108	−	0.989626i
$202$	−1847.43	+	1082.18i	−0.643490	+	0.376942i
$203$	−91.3237	−	301.054i	−0.0315747	−	0.104088i
$204$	4734.09	+	7403.45i	1.62477	+	2.54091i
$205$	821.888	−	1001.47i	0.280015	−	0.341200i
$206$	3179.66	−	1464.89i	1.07542	−	0.495454i
$207$	−192.304	+	464.264i	−0.0645704	+	0.155887i
$208$	12.0584	+	46.3983i	0.00401970	+	0.0154670i
$209$	−2123.13	−	5125.69i	−0.702679	−	1.69642i
$210$	276.921	+	256.111i	0.0909970	+	0.0841586i
$211$	−3237.29	+	318.845i	−1.05623	+	0.104029i	−0.611191	−	0.791483i	$-0.709309\pi$
$211$	−3237.29	+	318.845i	−1.05623	+	0.104029i	−0.445037	+	0.895512i	$0.646809\pi$
$212$	2806.41	+	56.5020i	0.909176	+	0.0183046i
$213$	−3543.84	−	1894.22i	−1.14000	−	0.609342i
$214$	115.647	−	15.9667i	0.0369413	−	0.00510027i
$215$	245.459	+	1234.00i	0.0778612	+	0.391435i
$216$	−339.933	−	1554.85i	−0.107081	−	0.489787i
$217$	−245.300	−	48.7933i	−0.0767376	−	0.0152641i
$218$	4199.72	−	3730.10i	1.30478	−	1.15887i
$219$	4099.63	+	403.778i	1.26496	+	0.124588i
$220$	4862.07	−	3829.04i	1.49000	−	1.17343i
$221$	99.3018	+	30.1229i	0.0302252	+	0.00916870i
$222$	5080.14	+	3114.85i	1.53584	+	0.941688i
$223$	1544.47	−	1544.47i	0.463791	−	0.463791i	−0.436105	−	0.899896i	$-0.643642\pi$
$223$	1544.47	−	1544.47i	0.463791	−	0.463791i	0.899896	+	0.436105i	$0.143642\pi$
$224$	−133.020	−	199.613i	−0.0396775	−	0.0595410i
$225$	915.532	+	915.532i	0.271269	+	0.271269i
$226$	−1151.04	−	4799.67i	−0.338788	−	1.41269i
$227$	−1072.64	+	3536.01i	−0.313627	+	1.03389i	0.648483	+	0.761229i	$0.275404\pi$
$227$	−1072.64	+	3536.01i	−0.313627	+	1.03389i	−0.962110	+	0.272661i	$0.912096\pi$
$228$	−5557.98	+	1564.54i	−1.61441	+	0.454448i
$229$	511.883	−	5197.23i	0.147712	−	1.49975i	−0.580422	−	0.814316i	$-0.697112\pi$
$229$	511.883	−	5197.23i	0.147712	−	1.49975i	0.728135	−	0.685434i	$-0.240388\pi$
$230$	−29.7313	+	502.034i	−0.00852358	+	0.143927i
$231$	−124.938	+	628.106i	−0.0355858	+	0.178902i
$232$	101.480	+	5371.05i	0.0287177	+	1.51994i
$233$	348.123	−	69.2459i	0.0978810	−	0.0194697i	−0.145907	−	0.989298i	$-0.546610\pi$
$233$	348.123	−	69.2459i	0.0978810	−	0.0194697i	0.243788	+	0.969829i	$0.421610\pi$
$234$	−60.5833	−	45.8840i	−0.0169250	−	0.0128185i
$235$	1560.86	−	2920.17i	0.433275	−	0.810600i
$236$	−1739.98	−	4452.13i	−0.479930	−	1.22800i
$237$	514.737	+	5226.21i	0.141079	+	1.43240i
$238$	−518.836	+	20.2564i	−0.141307	+	0.00551691i
$239$	−6655.84	+	2756.94i	−1.80138	+	0.746157i	−0.815491	+	0.578770i	$0.803533\pi$
$239$	−6655.84	+	2756.94i	−1.80138	+	0.746157i	−0.985891	+	0.167387i	$0.946467\pi$
$240$	−3359.91	−	5495.09i	−0.903672	−	1.47794i
$241$	1469.76	+	608.795i	0.392845	+	0.162722i	0.570357	−	0.821397i	$-0.306805\pi$
$241$	1469.76	+	608.795i	0.392845	+	0.162722i	−0.177512	+	0.984119i	$0.556805\pi$
$242$	6325.46	+	2335.37i	1.68023	+	0.620343i
$243$	−3985.92	−	3271.16i	−1.05225	−	0.863560i
$244$	−252.498	+	44.9612i	−0.0662479	+	0.0117965i
$245$	4144.68	−	1257.27i	1.08079	−	0.327854i
$246$	578.551	−	2214.88i	0.149947	−	0.574047i
$247$	−37.8804	+	56.6920i	−0.00975818	+	0.0146041i
$248$	3803.80	+	1941.69i	0.973957	+	0.497168i
$249$	684.699	−	457.501i	0.174261	−	0.116438i
$250$	−2871.32	−	1393.57i	−0.726392	−	0.352548i
$251$	−2545.89	−	3102.17i	−0.640219	−	0.780109i	0.347275	−	0.937763i	$-0.387107\pi$
$251$	−2545.89	−	3102.17i	−0.640219	−	0.780109i	−0.987494	+	0.157654i	$0.949607\pi$
$252$	361.598	+	117.689i	0.0903911	+	0.0294194i
$253$	−753.032	+	402.504i	−0.187125	+	0.100021i
$254$	2205.79	+	3037.59i	0.544896	+	0.750376i
$255$	−13941.9			−3.42384
$256$	1258.01	+	3898.03i	0.307131	+	0.951667i
$257$	1085.81			0.263544			0.131772	−	0.991280i	$-0.457933\pi$
$257$	1085.81			0.263544			0.131772	+	0.991280i	$0.457933\pi$
$258$	1306.30	+	1798.90i	0.315219	+	0.434088i
$259$	−310.523	+	165.978i	−0.0744980	+	0.0398200i
$260$	−72.3239	−	23.5391i	−0.0172513	−	0.00561474i
$261$	−5402.59	−	6583.08i	−1.28127	−	1.56123i
$262$	1688.07	+	819.289i	0.398051	+	0.193190i
$263$	−3499.50	+	2338.29i	−0.820489	+	0.548233i	−0.893482	−	0.449099i	$-0.851745\pi$
$263$	−3499.50	+	2338.29i	−0.820489	+	0.548233i	0.0729928	+	0.997332i	$0.476745\pi$
$264$	4971.82	−	9739.84i	1.15907	−	2.27063i
$265$	−2474.17	+	3702.86i	−0.573536	+	0.858357i
$266$	86.2229	−	330.089i	0.0198747	−	0.0760867i
$267$	3716.89	−	1127.51i	0.851947	−	0.258435i
$268$	−5042.12	+	897.830i	−1.14924	+	0.204641i
$269$	−212.859	−	174.689i	−0.0482462	−	0.0395946i	0.609961	−	0.792431i	$-0.291185\pi$
$269$	−212.859	−	174.689i	−0.0482462	−	0.0395946i	−0.658207	+	0.752837i	$0.728685\pi$
$270$	2368.80	+	874.565i	0.533929	+	0.197127i
$271$	−3548.65	−	1469.90i	−0.795444	−	0.329484i	−0.0523138	−	0.998631i	$-0.516660\pi$
$271$	−3548.65	−	1469.90i	−0.795444	−	0.329484i	−0.743130	+	0.669147i	$0.766660\pi$
$272$	8619.17	+	2078.32i	1.92137	+	0.463296i
$273$	7.27131	−	3.01188i	0.00161201	−	0.000667718i
$274$	−4069.11	+	158.866i	−0.897168	+	0.0350272i
$275$	215.638	+	2189.41i	0.0472852	+	0.480095i
$276$	323.470	+	827.668i	0.0705457	+	0.180506i
$277$	829.488	−	1551.86i	0.179925	−	0.336615i	−0.775750	−	0.631040i	$-0.782628\pi$
$277$	829.488	−	1551.86i	0.179925	−	0.336615i	0.955675	+	0.294425i	$0.0951282\pi$
$278$	1859.50	+	1408.33i	0.401170	+	0.303834i
$279$	−6640.21	+	1320.82i	−1.42487	+	0.283424i
$280$	380.502	−	7.18918i	0.0812119	−	0.00153441i
$281$	−1017.45	+	5115.07i	−0.216000	+	1.08591i	0.708787	+	0.705422i	$0.249243\pi$
$281$	−1017.45	+	5115.07i	−0.216000	+	1.08591i	−0.924787	+	0.380484i	$0.875757\pi$
$282$	345.882	−	5840.46i	0.0730389	−	1.23331i
$283$	29.4979	−	299.497i	0.00619599	−	0.0629089i	−0.991590	−	0.129423i	$-0.958688\pi$
$283$	29.4979	−	299.497i	0.00619599	−	0.0629089i	0.997786	+	0.0665137i	$0.0211876\pi$
$284$	−3902.57	+	1098.55i	−0.815404	+	0.229532i
$285$	2659.20	−	8766.20i	0.552692	−	1.82198i
$286$	−30.1143	−	125.572i	−0.00622620	−	0.0259623i
$287$	95.6436	+	95.6436i	0.0196713	+	0.0196713i
$288$	−5394.53	−	3614.18i	−1.10373	−	0.739471i
$289$	10096.6	−	10096.6i	2.05508	−	2.05508i
$290$	−7265.86	−	4455.00i	−1.47126	−	0.902092i
$291$	7130.55	+	2163.03i	1.43643	+	0.435735i
$292$	3265.28	−	2571.52i	0.654405	−	0.515365i
$293$	7363.11	+	725.203i	1.46811	+	0.144597i	0.800241	−	0.599678i	$-0.204705\pi$
$293$	7363.11	+	725.203i	1.46811	+	0.144597i	0.667874	+	0.744275i	$0.267205\pi$
$294$	5721.98	−	5082.14i	1.13508	−	1.00815i
$295$	7438.04	+	1479.52i	1.46800	+	0.292003i
$296$	5873.57	−	1284.13i	1.15336	−	0.252157i
$297$	836.379	+	4204.76i	0.163406	+	0.821498i
$298$	−3800.03	+	524.648i	−0.738690	+	0.101987i
$299$	9.25447	+	4.94662i	0.00178997	+	0.000956757i
$300$	2289.14	+	46.0878i	0.440546	+	0.00886959i
$301$	−130.727	+	12.8754i	−0.0250331	+	0.00246554i
$302$	−1867.12	−	1726.81i	−0.355764	−	0.329028i
$303$	−2296.93	−	5545.28i	−0.435496	−	1.05138i
$304$	−2950.74	+	5023.02i	−0.556699	+	0.947665i
$305$	155.713	−	375.925i	0.0292332	−	0.0705752i
$306$	−12765.8	+	5881.29i	−2.38488	+	1.09873i
$307$	4180.52	−	5093.98i	0.777183	−	0.947000i	−0.222427	−	0.974949i	$-0.571398\pi$
$307$	4180.52	−	5093.98i	0.777183	−	0.947000i	0.999609	+	0.0279498i	$0.00889784\pi$
$308$	348.087	+	544.360i	0.0643964	+	0.100707i
$309$	2848.92	+	9391.64i	0.524497	+	1.72903i
$310$	−5846.45	+	3424.72i	−1.07115	+	0.627454i
$311$	5620.94	+	3755.79i	1.02487	+	0.684796i	0.949953	−	0.312394i	$-0.101131\pi$
$311$	5620.94	+	3755.79i	1.02487	+	0.684796i	0.0749167	+	0.997190i	$0.476131\pi$
$312$	−133.472	+	15.6969i	−0.0242192	+	0.00284828i
$313$	2217.94	+	3319.39i	0.400529	+	0.599434i	0.975836	−	0.218503i	$-0.0701175\pi$
$313$	2217.94	+	3319.39i	0.400529	+	0.599434i	−0.575307	+	0.817937i	$0.695118\pi$
$314$	1613.11	−	558.930i	0.289914	−	0.100453i
$315$	−466.366	+	382.736i	−0.0834182	+	0.0684595i
$316$	4027.26	+	3443.06i	0.716934	+	0.612935i
$317$	1513.49	+	2831.55i	0.268159	+	0.501689i	0.979574	−	0.201082i	$-0.0644457\pi$
$317$	1513.49	+	2831.55i	0.268159	+	0.501689i	−0.711416	+	0.702771i	$0.751946\pi$
$318$	−1232.91	+	7771.81i	−0.217415	+	1.37051i
$319$		−	14470.3i		−	2.53975i
$320$	−6285.46	−	1650.15i	−1.09803	−	0.288270i
$321$			327.275i			0.0569056i
$322$	−51.8577	−	8.22663i	−0.00897490	−	0.00142376i
$323$	5944.36	+	11121.1i	1.02400	+	1.91577i
$324$	−3276.35	+	256.221i	−0.561788	+	0.0439336i
$325$	20.9000	−	17.1522i	0.00356715	−	0.00292748i
$326$	−2371.70	−	6844.88i	−0.402933	−	1.16289i
$327$	8748.38	+	13092.9i	1.47947	+	2.21418i
$328$	−1127.05	−	2016.01i	−0.189729	−	0.339376i
$329$	287.436	+	192.059i	0.0481668	+	0.0321840i
$330$	8769.19	+	14970.2i	1.46281	+	2.49722i
$331$	−1422.60	−	4689.70i	−0.236234	−	0.778759i	−0.992256	−	0.124212i	$-0.960360\pi$
$331$	−1422.60	−	4689.70i	−0.236234	−	0.778759i	0.756022	−	0.654547i	$-0.227140\pi$
$332$	178.459	−	811.450i	0.0295007	−	0.134139i
$333$	−6046.54	+	7367.73i	−0.995040	+	1.21246i
$334$	4843.63	+	10513.5i	0.793508	+	1.72237i
$335$	3109.44	−	7506.85i	0.507125	−	1.22431i
$336$	605.330	−	292.866i	0.0982842	−	0.0475510i
$337$	2537.26	+	6125.49i	0.410129	+	0.990138i	0.985103	+	0.171967i	$0.0550121\pi$
$337$	2537.26	+	6125.49i	0.410129	+	0.990138i	−0.574974	+	0.818172i	$0.694988\pi$
$338$	4218.16	−	4560.91i	0.678809	−	0.733967i
$339$	13770.1	−	1356.24i	2.20616	−	0.217288i
$340$	−10144.8	+	9744.34i	−1.61817	+	1.55430i
$341$	−10145.5	−	5422.86i	−1.61117	−	0.861186i
$342$	−1263.07	−	9148.45i	−0.199705	−	1.44647i
$343$	176.891	+	889.289i	0.0278461	+	0.139992i
$344$	2207.81	+	395.959i	0.346039	+	0.0620601i
$345$	−1382.76	−	275.048i	−0.215784	−	0.0429220i
$346$	−2724.02	−	3066.97i	−0.423249	−	0.476535i
$347$	2183.62	+	215.068i	0.337818	+	0.0332722i	0.265504	−	0.964110i	$-0.414462\pi$
$347$	2183.62	+	215.068i	0.337818	+	0.0332722i	0.0723140	+	0.997382i	$0.476962\pi$
$348$	−14954.4	−	1777.49i	−2.30357	−	0.273803i
$349$	−6199.03	−	1880.45i	−0.950792	−	0.288419i	−0.223466	−	0.974712i	$-0.571737\pi$
$349$	−6199.03	−	1880.45i	−0.950792	−	0.288419i	−0.727326	+	0.686292i	$0.759237\pi$
$350$	−70.7148	+	115.332i	−0.0107996	+	0.0176136i
$351$	37.2556	−	37.2556i	0.00566540	−	0.00566540i
$352$	−3189.68	−	10562.1i	−0.482985	−	1.59932i
$353$	−7903.04	−	7903.04i	−1.19160	−	1.19160i	−0.976617	−	0.214987i	$-0.931029\pi$
$353$	−7903.04	−	7903.04i	−1.19160	−	1.19160i	−0.214987	−	0.976617i	$-0.568971\pi$
$354$	13030.8	−	3125.00i	1.95644	−	0.469186i
$355$	1867.17	−	6155.24i	0.279153	−	0.920243i
$356$	1916.53	−	3418.24i	0.285326	−	0.508894i
$357$	142.673	−	1448.59i	0.0211514	−	0.214754i
$358$	1240.03	+	73.4368i	0.183066	+	0.0108415i
$359$	1418.25	−	7130.05i	0.208503	−	1.04822i	−0.724754	−	0.689008i	$-0.758047\pi$
$359$	1418.25	−	7130.05i	0.208503	−	1.04822i	0.933257	−	0.359209i	$-0.116953\pi$
$360$	9441.56	−	4121.46i	1.38226	−	0.603390i
$361$	−1399.14	+	278.306i	−0.203986	+	0.0405753i
$362$	−5300.32	+	6998.32i	−0.769554	+	1.01609i
$363$	−8910.60	+	16670.6i	−1.28839	+	2.41041i
$364$	3.18586	−	7.27366i	0.000458748	−	0.00104737i
$365$	646.337	+	6562.37i	0.0926872	+	0.941069i
$366$	−28.0489	−	718.430i	−0.00400585	−	0.102604i
$367$	−2418.85	+	1001.92i	−0.344040	+	0.142506i	−0.548012	−	0.836471i	$-0.684615\pi$
$367$	−2418.85	+	1001.92i	−0.344040	+	0.142506i	0.203971	+	0.978977i	$0.434615\pi$
$368$	813.847	+	376.167i	0.115285	+	0.0532855i
$369$	3382.75	+	1401.18i	0.477233	+	0.197677i
$370$	−3303.75	+	8948.37i	−0.464199	+	1.25731i
$371$	−359.412	−	294.962i	−0.0502959	−	0.0412767i
$372$	−6850.53	+	9818.77i	−0.954794	+	1.36849i
$373$	−2054.24	+	623.148i	−0.285160	+	0.0865024i	−0.429625	−	0.903008i	$-0.641354\pi$
$373$	−2054.24	+	623.148i	−0.285160	+	0.0865024i	0.144464	+	0.989510i	$0.453854\pi$
$374$	−23107.1	−	6035.84i	−3.19476	−	0.834507i
$375$	4970.86	−	7439.41i	0.684517	−	1.02445i
$376$	−3830.35	−	4491.52i	−0.525360	−	0.616044i
$377$	−147.864	+	98.7995i	−0.0202000	+	0.0134972i
$378$	−115.109	+	237.172i	−0.0156629	+	0.0322720i
$379$	8401.39	+	10237.1i	1.13866	+	1.38746i	0.910336	+	0.413870i	$0.135823\pi$
$379$	8401.39	+	10237.1i	1.13866	+	1.38746i	0.228320	+	0.973586i	$0.426677\pi$
$380$	−4191.95	−	8237.25i	−0.565901	−	1.11200i
$381$	−9281.19	+	4960.90i	−1.24800	+	0.667072i
$382$	−5891.40	+	4278.13i	−0.789085	+	0.573005i
$383$	463.778			0.0618745			0.0309373	−	0.999521i	$-0.490151\pi$
$383$	463.778			0.0618745			0.0309373	+	0.999521i	$0.490151\pi$
$384$	−11307.2	+	1998.99i	−1.50266	+	0.265652i
$385$	−1025.12			−0.135701
$386$	−6671.36	+	4844.50i	−0.879697	+	0.638805i
$387$	−3135.98	+	1676.22i	−0.411915	+	0.220173i
$388$	6700.29	−	3409.79i	0.876690	−	0.446149i
$389$	2708.82	+	3300.70i	0.353065	+	0.430212i	0.919011	−	0.394231i	$-0.128989\pi$
$389$	2708.82	+	3300.70i	0.353065	+	0.430212i	−0.565946	+	0.824442i	$0.691489\pi$
$390$	93.0981	−	191.820i	0.0120877	−	0.0249056i
$391$	1613.66	−	1078.21i	0.208711	−	0.139456i
$392$	611.541	−	7697.22i	0.0787946	−	0.991755i
$393$	−2922.41	+	4373.69i	−0.375104	+	0.561383i
$394$	11658.1	+	3045.22i	1.49067	+	0.389380i
$395$	−8044.23	+	2440.19i	−1.02468	+	0.310834i
$396$	14344.5	+	10008.1i	1.82029	+	1.27001i
$397$	−3918.48	−	3215.81i	−0.495372	−	0.406541i	0.353260	−	0.935525i	$-0.385073\pi$
$397$	−3918.48	−	3215.81i	−0.495372	−	0.406541i	−0.848632	+	0.528984i	$0.822573\pi$
$398$	−1598.58	+	4329.82i	−0.201330	+	0.545313i
$399$	883.607	+	366.002i	0.110866	+	0.0459223i
$400$	1697.89	−	1566.40i	0.212237	−	0.195800i
$401$	8208.15	−	3399.93i	1.02218	−	0.423402i	0.192298	−	0.981337i	$-0.438406\pi$
$401$	8208.15	−	3399.93i	1.02218	−	0.423402i	0.829885	+	0.557934i	$0.188406\pi$
$402$	−560.108	−	14346.3i	−0.0694917	−	1.77992i
$403$	13.8574	+	140.697i	0.00171287	+	0.0173911i
$404$	−5547.07	−	2429.61i	−0.683112	−	0.299203i
$405$	2457.83	−	4598.27i	0.301557	−	0.564173i
$406$	537.235	−	709.343i	0.0656712	−	0.0867096i
$407$	−15883.9	+	3159.50i	−1.93448	+	0.384792i
$408$	−9076.19	+	23138.8i	−1.10132	+	2.80770i
$409$	2094.70	−	10530.7i	0.253242	−	1.27313i	−0.619517	−	0.784983i	$-0.712672\pi$
$409$	2094.70	−	10530.7i	0.253242	−	1.27313i	0.872759	−	0.488151i	$-0.162328\pi$
$410$	3657.96	+	216.630i	0.440619	+	0.0260942i
$411$	1118.95	−	11360.9i	0.134292	−	1.36349i
$412$	8637.03	+	4842.60i	1.03281	+	0.579072i
$413$	−229.840	+	757.681i	−0.0273842	+	0.0902737i
$414$	−1382.14	+	331.460i	−0.164078	+	0.0393487i
$415$	932.083	+	932.083i	0.110251	+	0.110251i
$416$	−86.1495	+	104.709i	−0.0101534	+	0.0123408i
$417$	−4623.91	+	4623.91i	−0.543006	+	0.543006i
$418$	8202.43	−	13377.7i	0.959794	−	1.56537i
$419$	−5987.46	−	1816.28i	−0.698107	−	0.211768i	−0.0787688	−	0.996893i	$-0.525099\pi$
$419$	−5987.46	−	1816.28i	−0.698107	−	0.211768i	−0.619338	+	0.785125i	$0.712599\pi$
$420$	−125.923	+	1059.42i	−0.0146295	+	0.123082i
$421$	−803.438	−	79.1317i	−0.0930099	−	0.00916067i	0.0514051	−	0.998678i	$-0.483630\pi$
$421$	−803.438	−	79.1317i	−0.0930099	−	0.00916067i	−0.144415	+	0.989517i	$0.546130\pi$
$422$	−6109.91	−	6879.14i	−0.704800	−	0.793534i
$423$	9178.11	+	1825.64i	1.05498	+	0.209848i
$424$	4534.78	+	6516.82i	0.519406	+	0.746426i
$425$	−975.528	−	4904.31i	−0.111341	−	0.559751i
$426$	−1554.43	−	11258.7i	−0.176789	−	1.28049i
$427$	37.4657	+	20.0258i	0.00424611	+	0.00226959i
$428$	228.740	+	238.140i	0.0258331	+	0.0268947i
$429$	360.262	−	35.4828i	0.0405446	−	0.00399330i
$430$	−2416.28	+	2612.61i	−0.270984	+	0.293003i
$431$	5012.66	+	12101.6i	0.560212	+	1.35247i	0.909597	+	0.415492i	$0.136391\pi$
$431$	5012.66	+	12101.6i	0.560212	+	1.35247i	−0.349385	+	0.936979i	$0.613609\pi$
$432$	2993.56	−	3362.05i	0.333398	−	0.374437i
$433$	−1861.47	+	4493.99i	−0.206597	+	0.498770i	−0.992883	−	0.119093i	$-0.962001\pi$
$433$	−1861.47	+	4493.99i	−0.206597	+	0.498770i	0.786286	+	0.617863i	$0.212001\pi$
$434$	−296.003	−	642.500i	−0.0327388	−	0.0710622i
$435$	15157.4	−	18469.4i	1.67067	−	2.03572i
$436$	15516.6	+	3412.51i	1.70438	+	0.374839i
$437$	370.162	+	1220.26i	0.0405201	+	0.133577i
$438$	5889.23	+	10053.7i	0.642462	+	1.09677i
$439$	−3460.11	−	2311.97i	−0.376178	−	0.251354i	0.353080	−	0.935593i	$-0.385134\pi$
$439$	−3460.11	−	2311.97i	−0.376178	−	0.251354i	−0.729258	+	0.684239i	$0.760134\pi$
$440$	16843.8	+	4763.97i	1.82500	+	0.516167i
$441$	6800.58	+	10177.8i	0.734325	+	1.09899i
$442$	96.0927	+	277.330i	0.0103409	+	0.0298445i
$443$	3147.68	−	2583.23i	0.337586	−	0.277050i	−0.450291	−	0.892882i	$-0.648680\pi$
$443$	3147.68	−	2583.23i	0.337586	−	0.277050i	0.787878	+	0.615832i	$0.211180\pi$
$444$	1314.08	+	16803.4i	0.140458	+	1.79607i
$445$	2930.88	+	5483.28i	0.312218	+	0.584118i
$446$	6101.58	+	967.945i	0.647798	+	0.102766i
$447$		−	10753.9i		−	1.13790i
$448$	235.775	−	636.181i	0.0248645	−	0.0670909i
$449$			5615.06i			0.590181i	0.955469	+	0.295090i	$0.0953498\pi$
$449$			5615.06i			0.590181i	−0.955469	+	0.295090i	$0.904650\pi$
$450$	−573.779	+	3616.90i	−0.0601071	+	0.378894i
$451$	2932.75	+	5486.80i	0.306204	+	0.572867i
$452$	9071.83	−	10611.1i	0.944033	−	1.10421i
$453$	5511.25	−	4522.96i	0.571614	−	0.469111i
$454$	−9875.36	+	3421.74i	−1.02087	+	0.353723i
$455$	6.99927	+	10.4751i	0.000721166	+	0.00107930i
$456$	−12817.7	−	10120.1i	−1.31633	−	1.03930i
$457$	−2039.78	−	1362.94i	−0.208790	−	0.139509i	0.446779	−	0.894644i	$-0.352571\pi$
$457$	−2039.78	−	1362.94i	−0.208790	−	0.139509i	−0.655569	+	0.755135i	$0.727571\pi$
$458$	12745.4	−	7465.97i	1.30034	−	0.761707i
$459$	−2828.61	−	9324.68i	−0.287643	−	0.948232i
$460$	−1198.40	+	766.306i	−0.121468	+	0.0776722i
$461$	8019.96	−	9772.35i	0.810253	−	0.987296i	−0.189732	−	0.981836i	$-0.560762\pi$
$461$	8019.96	−	9772.35i	0.810253	−	0.987296i	0.999985	−	0.00546022i	$-0.00173805\pi$
$462$	−1645.16	+	757.934i	−0.165670	+	0.0763253i
$463$	2867.02	−	6921.61i	0.287779	−	0.694761i	−0.712195	−	0.701982i	$-0.752299\pi$
$463$	2867.02	−	6921.61i	0.287779	−	0.694761i	0.999974	+	0.00722126i	$0.00229862\pi$
$464$	−12123.8	+	9158.61i	−1.21301	+	0.916332i
$465$	−7268.94	−	17548.8i	−0.724923	−	1.75012i
$466$	737.039	+	681.651i	0.0732676	+	0.0677615i
$467$	−18379.6	+	1810.23i	−1.82121	+	0.179374i	−0.950150	−	0.311794i	$-0.899070\pi$
$467$	−18379.6	+	1810.23i	−1.82121	+	0.179374i	−0.871065	+	0.491168i	$0.836570\pi$
$468$	4.32684	−	214.911i	0.000427368	−	0.0212271i
$469$	748.151	+	399.895i	0.0736597	+	0.0393719i
$470$	9277.33	−	1280.87i	0.910492	−	0.125706i
$471$	933.682	+	4693.94i	0.0913414	+	0.459204i
$472$	7297.64	−	11381.4i	0.711655	−	1.10990i
$473$	−5925.87	−	1178.73i	−0.576050	−	0.114583i
$474$	−11105.5	+	9863.71i	−1.07615	+	0.955813i
$475$	3269.72	+	322.040i	0.315842	+	0.0311078i
$476$	−908.634	−	1153.77i	−0.0874941	−	0.111099i
$477$	−12044.2	−	3653.56i	−1.15611	−	0.350702i
$478$	−17371.3	−	10651.1i	−1.66223	−	1.01918i
$479$	12559.0	−	12559.0i	1.19798	−	1.19798i	0.223213	−	0.974770i	$-0.428345\pi$
$479$	12559.0	−	12559.0i	1.19798	−	1.19798i	0.974770	−	0.223213i	$-0.0716546\pi$
$480$	6992.41	−	16822.2i	0.664913	−	1.59964i
$481$	140.736	+	140.736i	0.0133410	+	0.0133410i
$482$	1049.33	+	4375.56i	0.0991613	+	0.413488i
$483$	42.7282	−	140.856i	0.00402526	−	0.0132695i
$484$	5167.69	+	18358.1i	0.485320	+	1.72409i
$485$	−1169.11	+	11870.2i	−0.109457	+	1.11134i
$486$	862.202	−	14558.9i	0.0804738	−	1.35886i
$487$	1975.41	−	9931.04i	0.183807	−	0.924063i	−0.773236	−	0.634118i	$-0.781363\pi$
$487$	1975.41	−	9931.04i	0.183807	−	0.924063i	0.957044	−	0.289944i	$-0.0936368\pi$
$488$	−522.537	−	503.157i	−0.0484716	−	0.0466739i
$489$	19917.7	−	3961.88i	1.84194	−	0.366385i
$490$	9765.68	+	7396.23i	0.900344	+	0.681893i
$491$	−3528.56	+	6601.46i	−0.324321	+	0.606762i	−0.990258	−	0.139246i	$-0.955532\pi$
$491$	−3528.56	+	6601.46i	−0.324321	+	0.606762i	0.665937	+	0.746008i	$0.268032\pi$
$492$	6030.62	−	2356.89i	0.552604	−	0.215969i
$493$	3223.75	+	32731.3i	0.294504	+	2.99015i
$494$	−192.703	+	7.52352i	−0.0175509	+	0.000685221i
$495$	−25637.4	+	10619.4i	−2.32791	+	0.964253i
$496$	1877.81	+	11932.6i	0.169992	+	1.08022i
$497$	620.430	+	256.991i	0.0559962	+	0.0231944i
$498$	2184.99	+	806.701i	0.196610	+	0.0725887i
$499$	−1143.38	−	938.351i	−0.102575	−	0.0841811i	0.581708	−	0.813398i	$-0.302385\pi$
$499$	−1143.38	−	938.351i	−0.102575	−	0.0841811i	−0.684283	+	0.729217i	$0.739885\pi$
$500$	−1582.56	−	8887.49i	−0.141548	−	0.794921i
$501$	−31053.3	+	9419.92i	−2.76918	+	0.840022i
$502$	2868.70	−	10982.3i	0.255052	−	0.976422i
$503$	10840.0	−	16223.3i	0.960902	−	1.43809i	0.0629398	−	0.998017i	$-0.479952\pi$
$503$	10840.0	−	16223.3i	0.960902	−	1.43809i	0.897962	−	0.440073i	$-0.145048\pi$
$504$	331.606	+	1023.17i	0.0293074	+	0.0904275i
$505$	7988.60	−	5337.81i	0.703937	−	0.470356i
$506$	−2172.69	−	1054.49i	−0.190885	−	0.0926442i
$507$	11048.5	+	13462.6i	0.967811	+	1.17928i
$508$	−3286.12	+	10096.6i	−0.287004	+	0.881820i
$509$	−7814.67	+	4177.03i	−0.680509	+	0.363740i	−0.775155	−	0.631771i	$-0.782328\pi$
$509$	−7814.67	+	4177.03i	−0.680509	+	0.363740i	0.0946456	+	0.995511i	$0.469828\pi$
$510$	−23170.7	−	31908.3i	−2.01179	−	2.77044i
$511$	−688.453			−0.0595995
$512$	−6830.51	+	9357.45i	−0.589588	+	0.807704i
$513$	6402.54			0.551031
$514$	1804.55	+	2485.04i	0.154855	+	0.213250i
$515$	−13854.9	+	7405.58i	−1.18547	+	0.633649i
$516$	−1946.08	+	5979.34i	−0.166030	+	0.510127i
$517$	10087.2	+	12291.3i	0.858097	+	1.04559i
$518$	−895.939	−	434.836i	−0.0759947	−	0.0368834i
$519$	9561.45	−	6388.76i	0.808673	−	0.540338i
$520$	−66.3251	−	204.645i	−0.00559336	−	0.0172582i
$521$	1389.98	−	2080.26i	0.116884	−	0.174929i	−0.768415	−	0.639952i	$-0.778954\pi$
$521$	1389.98	−	2080.26i	0.116884	−	0.174929i	0.885298	+	0.465024i	$0.153954\pi$
$522$	6087.62	−	23305.4i	0.510436	−	1.95411i
$523$	5849.77	−	1774.51i	0.489087	−	0.148363i	−0.0361027	−	0.999348i	$-0.511494\pi$
$523$	5849.77	−	1774.51i	0.489087	−	0.148363i	0.525190	+	0.850985i	$0.323994\pi$
$524$	930.400	+	5225.03i	0.0775662	+	0.435604i
$525$	−293.167	−	240.596i	−0.0243711	−	0.0200009i
$526$	−11167.5	−	4123.06i	−0.925717	−	0.341776i
$527$	24156.8	+	10006.1i	1.99675	+	0.827079i
$528$	30554.0	−	4808.25i	2.51836	−	0.396311i
$529$	−11059.5	+	4581.01i	−0.908977	+	0.376511i
$530$	−12586.5	+	491.402i	−1.03155	+	0.0402738i
$531$	2100.81	+	21329.9i	0.171690	+	1.74320i
$532$	898.758	−	351.254i	0.0732446	−	0.0286255i
$533$	36.0424	−	67.4306i	0.00292903	−	0.00547982i
$534$	8757.72	+	6632.83i	0.709707	+	0.537511i
$535$	−513.810	+	102.203i	−0.0415214	+	0.00825912i
$536$	−10434.5	−	10047.5i	−0.840864	−	0.809678i
$537$	−679.373	+	3415.44i	−0.0545943	+	0.274464i
$538$	46.0439	−	777.483i	0.00368976	−	0.0623042i
$539$	−2038.65	+	20698.8i	−0.162915	+	1.65410i
$540$	1935.23	+	6874.86i	0.154221	+	0.547864i
$541$	6408.58	−	21126.2i	0.509291	−	1.67891i	−0.204760	−	0.978812i	$-0.565641\pi$
$541$	6408.58	−	21126.2i	0.509291	−	1.67891i	0.714051	−	0.700094i	$-0.246859\pi$
$542$	−2533.55	−	10564.5i	−0.200785	−	0.837243i
$543$	−17402.3	−	17402.3i	−1.37533	−	1.37533i
$544$	9568.00	+	23180.4i	0.754089	+	1.82693i
$545$	−17823.4	+	17823.4i	−1.40086	+	1.40086i
$546$	18.9776	+	11.6360i	0.00148749	+	0.000912041i
$547$	−4472.77	−	1356.80i	−0.349620	−	0.106056i	0.110590	−	0.993866i	$-0.464726\pi$
$547$	−4472.77	−	1356.80i	−0.349620	−	0.106056i	−0.460210	+	0.887810i	$0.652226\pi$
$548$	−7126.21	−	9048.78i	−0.555505	−	0.705373i
$549$	1144.44	+	112.717i	0.0889678	+	0.00876256i
$550$	−4652.42	+	4132.18i	−0.360691	+	0.320358i
$551$	−21195.1	−	4215.97i	−1.63873	−	0.325965i
$552$	−1356.66	+	2115.85i	−0.104607	+	0.163146i
$553$	−171.219	−	860.777i	−0.0131663	−	0.0661916i
$554$	4930.24	−	680.690i	0.378097	−	0.0522017i
$555$	−23583.2	−	12605.5i	−1.80369	−	0.964093i
$556$	−132.805	+	6596.31i	−0.0101298	+	0.503140i
$557$	8640.25	−	850.991i	0.657270	−	0.0647354i	0.236116	−	0.971725i	$-0.424125\pi$
$557$	8640.25	−	850.991i	0.657270	−	0.0647354i	0.421153	+	0.906989i	$0.361625\pi$
$558$	−14058.5	−	13002.0i	−1.06657	−	0.986416i
$559$	28.4156	+	68.6012i	0.00215000	+	0.00519056i
$560$	648.825	+	858.890i	0.0489605	+	0.0648120i
$561$	25621.1	−	61854.8i	1.92821	−	4.65510i
$562$	−13397.6	+	6172.35i	−1.00559	+	0.463283i
$563$	7365.73	−	8975.17i	0.551383	−	0.671862i	−0.420509	−	0.907288i	$-0.638149\pi$
$563$	7365.73	−	8975.17i	0.551383	−	0.671862i	0.971892	+	0.235426i	$0.0756486\pi$
$564$	13941.6	−	8914.89i	1.04087	−	0.665576i
$565$	6429.45	+	21195.1i	0.478742	+	1.57820i
$566$	734.469	−	430.235i	0.0545442	−	0.0319508i
$567$	452.614	+	302.427i	0.0335238	+	0.0223999i
$568$	−9000.04	−	7105.92i	−0.664848	−	0.524925i
$569$	1204.01	+	1801.92i	0.0887076	+	0.132760i	0.873169	−	0.487417i	$-0.162061\pi$
$569$	1204.01	+	1801.92i	0.0887076	+	0.132760i	−0.784462	+	0.620177i	$0.787061\pi$
$570$	24482.3	−	8482.91i	1.79903	−	0.623351i
$571$	−3178.68	+	2608.67i	−0.232966	+	0.191190i	−0.743632	−	0.668589i	$-0.766899\pi$
$571$	−3178.68	+	2608.67i	−0.232966	+	0.191190i	0.510667	+	0.859779i	$0.329399\pi$
$572$	237.343	−	277.615i	0.0173493	−	0.0202931i
$573$	−9621.65	−	18000.8i	−0.701483	−	1.31238i
$574$	−59.9415	+	377.850i	−0.00435873	+	0.0274758i
$575$		−	505.654i		−	0.0366735i
$576$	−693.760	−	18352.8i	−0.0501852	−	1.32760i
$577$			2430.88i			0.175388i	0.996147	+	0.0876939i	$0.0279497\pi$
$577$			2430.88i			0.175388i	−0.996147	+	0.0876939i	$0.972050\pi$
$578$	39887.7	+	6327.72i	2.87043	+	0.455360i
$579$	−10895.4	−	20383.9i	−0.782036	−	1.46309i
$580$	−1879.46	−	24033.0i	−0.134552	−	1.72055i
$581$	−106.383	+	87.3062i	−0.00759640	+	0.00623420i
$582$	6900.12	+	19914.2i	0.491442	+	1.41833i
$583$	−11881.3	−	17781.6i	−0.844037	−	1.26319i
$584$	11312.0	+	3199.40i	0.801533	+	0.226699i
$585$	283.559	+	189.468i	0.0200406	+	0.0133907i
$586$	10577.3	+	18056.9i	0.745640	+	1.27291i
$587$	506.216	+	1668.77i	0.0355942	+	0.117338i	0.972937	−	0.231069i	$-0.0742225\pi$
$587$	506.216	+	1668.77i	0.0355942	+	0.117338i	−0.937343	+	0.348408i	$0.886722\pi$
$588$	21140.9	+	4649.44i	1.48271	+	0.326088i
$589$	−10899.0	+	13280.4i	−0.762452	+	0.929050i
$590$	8975.47	+	19482.0i	0.626295	+	1.35942i
$591$	−12926.4	+	31207.2i	−0.899700	+	2.17207i
$592$	12700.5	+	11308.5i	0.881733	+	0.785092i
$593$	1703.85	+	4113.45i	0.117991	+	0.284855i	0.971830	−	0.235681i	$-0.0757320\pi$
$593$	1703.85	+	4113.45i	0.117991	+	0.284855i	−0.853840	+	0.520536i	$0.825732\pi$
$594$	−8233.25	+	8902.25i	−0.568711	+	0.614922i
$595$	2318.78	−	228.380i	0.159766	−	0.0157356i
$596$	−7516.16	−	7825.02i	−0.516567	−	0.537794i
$597$	−11411.1	−	6099.37i	−0.782288	−	0.418142i
$598$	4.05927	+	29.4013i	0.000277585	+	0.00201055i
$599$	−298.052	−	1498.41i	−0.0203306	−	0.102209i	0.969288	−	0.245930i	$-0.0790933\pi$
$599$	−298.052	−	1498.41i	−0.0203306	−	0.102209i	−0.989618	+	0.143721i	$0.954093\pi$
$600$	3698.94	+	5315.66i	0.251681	+	0.361685i
$601$	−840.121	−	167.111i	−0.0570204	−	0.0113421i	0.166498	−	0.986042i	$-0.446754\pi$
$601$	−840.121	−	167.111i	−0.0570204	−	0.0113421i	−0.223518	+	0.974700i	$0.571754\pi$
$602$	−246.727	−	277.790i	−0.0167041	−	0.0188071i
$603$	22853.2	+	2250.84i	1.54337	+	0.152009i
$604$	849.024	−	7143.04i	0.0571959	−	0.481203i
$605$	−28954.9	−	8783.36i	−1.94576	−	0.590239i
$606$	8873.89	−	14472.8i	0.594846	−	0.970162i
$607$	13104.2	−	13104.2i	0.876249	−	0.876249i	−0.116895	−	0.993144i	$-0.537294\pi$
$607$	13104.2	−	13104.2i	0.876249	−	0.876249i	0.993144	+	0.116895i	$0.0372941\pi$
$608$	−16399.9	+	1594.74i	−1.09392	+	0.106374i
$609$	1763.88	+	1763.88i	0.117366	+	0.117366i
$610$	1119.15	−	268.391i	0.0742838	−	0.0178145i
$611$	56.7252	−	186.998i	0.00375590	−	0.0123815i
$612$	−34676.3	−	19442.2i	−2.29037	−	1.28416i
$613$	−1478.78	+	15014.3i	−0.0974348	+	0.989272i	0.814838	+	0.579689i	$0.196826\pi$
$613$	−1478.78	+	15014.3i	−0.0974348	+	0.989272i	−0.912273	+	0.409583i	$0.865674\pi$
$614$	18606.2	+	1101.89i	1.22294	+	0.0724244i
$615$	−2004.08	+	10075.2i	−0.131402	+	0.660602i
$616$	−667.353	+	1701.35i	−0.0436500	+	0.111281i
$617$	−22493.8	+	4474.29i	−1.46769	+	0.291942i	−0.863278	−	0.504729i	$-0.831593\pi$
$617$	−22493.8	+	4474.29i	−1.46769	+	0.291942i	−0.604414	+	0.796671i	$0.706593\pi$
$618$	−16759.5	+	22128.6i	−1.09088	+	1.44036i
$619$	−4689.25	+	8772.98i	−0.304486	+	0.569654i	−0.986904	−	0.161309i	$-0.948429\pi$
$619$	−4689.25	+	8772.98i	−0.304486	+	0.569654i	0.682418	+	0.730962i	$0.260929\pi$
$620$	−17554.5	−	7688.84i	−1.13710	−	0.498050i
$621$	−96.5830	−	980.624i	−0.00624113	−	0.0633673i
$622$	745.948	+	19106.3i	0.0480865	+	1.23166i
$623$	−599.713	+	248.409i	−0.0385666	+	0.0159748i
$624$	−257.748	−	279.385i	−0.0165356	−	0.0179237i
$625$	17400.4	+	7207.47i	1.11362	+	0.461278i
$626$	−3910.85	+	10592.7i	−0.249695	+	0.676311i
$627$	34005.3	+	27907.4i	2.16594	+	1.77754i
$628$	3960.09	+	2762.94i	0.251632	+	0.175563i
$629$	35224.8	−	10685.3i	2.23292	−	0.677348i
$630$	−1651.02	−	431.266i	−0.104410	−	0.0272731i
$631$	−15234.7	+	22800.3i	−0.961147	+	1.43846i	−0.0633795	+	0.997989i	$0.520188\pi$
$631$	−15234.7	+	22800.3i	−0.961147	+	1.43846i	−0.897768	+	0.440469i	$0.854812\pi$
$632$	−1186.91	+	14939.2i	−0.0747039	+	0.940268i
$633$	21446.1	−	14329.8i	1.34661	−	0.899779i
$634$	−3965.11	+	8169.73i	−0.248382	+	0.511769i
$635$	−10686.8	−	13021.9i	−0.667864	−	0.813794i
$636$	−19836.0	+	10094.6i	−1.23671	+	0.629365i
$637$	225.429	−	120.494i	0.0140217	−	0.00749475i
$638$	33117.6	−	24048.8i	2.05507	−	1.49232i
$639$	18178.6			1.12541
$640$	−6669.43	−	17127.7i	−0.411926	−	1.05786i
$641$	−15001.3			−0.924360			−0.462180	−	0.886786i	$-0.652933\pi$
$641$	−15001.3			−0.924360			−0.462180	+	0.886786i	$0.652933\pi$
$642$	−749.020	+	543.911i	−0.0460459	+	0.0334369i
$643$	9757.58	−	5215.54i	0.598447	−	0.319877i	−0.144212	−	0.989547i	$-0.546065\pi$
$643$	9757.58	−	5215.54i	0.598447	−	0.319877i	0.742659	+	0.669670i	$0.233565\pi$
$644$	−67.3565	−	132.357i	−0.00412146	−	0.00809873i
$645$	−6328.87	−	7711.75i	−0.386355	−	0.470775i
$646$	−15573.2	+	32087.2i	−0.948484	+	1.95426i
$647$	−17235.2	+	11516.2i	−1.04727	+	0.699766i	−0.955193	−	0.295985i	$-0.904352\pi$
$647$	−17235.2	+	11516.2i	−1.04727	+	0.699766i	−0.0920817	+	0.995751i	$0.529352\pi$
$648$	−6031.50	−	7072.61i	−0.365647	−	0.428763i
$649$	−20232.9	+	30280.7i	−1.22375	+	1.83147i
$650$	73.9901	+	19.3270i	0.00446481	+	0.00116626i
$651$	1897.73	−	575.669i	0.114252	−	0.0346578i
$652$	11724.0	−	16803.8i	0.704212	−	1.00934i
$653$	−13513.0	−	11089.8i	−0.809806	−	0.664591i	0.135499	−	0.990777i	$-0.456736\pi$
$653$	−13513.0	−	11089.8i	−0.809806	−	0.664591i	−0.945305	+	0.326187i	$0.894236\pi$
$654$	−15425.8	+	41781.6i	−0.922320	+	2.49815i
$655$	−7779.17	−	3222.24i	−0.464057	−	0.192219i
$656$	2740.86	−	5929.92i	0.163129	−	0.352933i
$657$	−17217.6	+	7131.78i	−1.02241	+	0.423496i
$658$	38.1453	+	977.034i	0.00225997	+	0.0578857i
$659$	−1776.09	−	18032.9i	−0.104987	−	1.06595i	−0.892928	−	0.450200i	$-0.851353\pi$
$659$	−1776.09	−	18032.9i	−0.104987	−	1.06595i	0.787940	−	0.615751i	$-0.211147\pi$
$660$	−19687.7	+	44949.2i	−1.16113	+	2.65098i
$661$	−708.879	+	1326.22i	−0.0417128	+	0.0780392i	−0.901914	−	0.431916i	$-0.857838\pi$
$661$	−708.879	+	1326.22i	−0.0417128	+	0.0780392i	0.860201	+	0.509955i	$0.170338\pi$
$662$	8368.83	−	11049.9i	0.491335	−	0.648739i
$663$	−806.995	+	160.521i	−0.0472716	+	0.00940291i
$664$	2153.72	−	940.150i	0.125874	−	0.0549471i
$665$	−298.673	+	1501.53i	−0.0174166	+	0.0875591i
$666$	−26911.2	−	1593.73i	−1.56575	−	0.0927262i
$667$	−325.995	+	3309.88i	−0.0189244	+	0.192143i
$668$	−16012.0	+	28558.2i	−0.927427	+	1.65412i
$669$	−5027.40	+	16573.1i	−0.290539	+	0.957778i
$670$	22348.3	−	5359.50i	1.28864	−	0.309038i
$671$	1381.68	+	1381.68i	0.0794919	+	0.0794919i
$672$	1676.29	+	898.668i	0.0962267	+	0.0515876i
$673$	−12749.7	+	12749.7i	−0.730262	+	0.730262i	−0.970672	−	0.240409i	$-0.922718\pi$
$673$	−12749.7	+	12749.7i	−0.730262	+	0.730262i	0.240409	+	0.970672i	$0.422718\pi$
$674$	−9802.37	+	15987.1i	−0.560197	+	0.913651i
$675$	−2429.53	−	736.991i	−0.138537	−	0.0420249i
$676$	17448.7	+	2073.96i	0.992756	+	0.117999i
$677$	5493.70	+	541.082i	0.311876	+	0.0307171i	0.252744	−	0.967533i	$-0.418667\pi$
$677$	5493.70	+	541.082i	0.311876	+	0.0307171i	0.0591316	+	0.998250i	$0.481167\pi$
$678$	25989.1	+	29261.1i	1.47213	+	1.65747i
$679$	−1221.36	−	242.944i	−0.0690304	−	0.0137310i
$680$	−39161.5	−	7023.39i	−2.20849	−	0.396081i
$681$	−5715.95	−	28736.0i	−0.321638	−	1.61699i
$682$	−4450.08	−	32232.0i	−0.249857	−	1.80971i
$683$	20135.6	+	10762.7i	1.12806	+	0.602962i	0.926418	−	0.376497i	$-0.122872\pi$
$683$	20135.6	+	10762.7i	1.12806	+	0.602962i	0.201644	+	0.979459i	$0.435372\pi$
$684$	18838.5	−	18094.9i	1.05308	−	1.01152i
$685$	18185.7	−	1791.14i	1.01436	−	0.0999062i
$686$	−1741.30	+	1882.79i	−0.0969140	+	0.104789i
$687$	15846.5	+	38256.8i	0.880030	+	2.12458i
$688$	2763.04	+	5710.99i	0.153110	+	0.316467i
$689$	−100.578	+	242.817i	−0.00556128	+	0.0134261i
$690$	−1668.58	−	3621.78i	−0.0920603	−	0.199824i
$691$	8530.99	−	10395.0i	0.469659	−	0.572281i	−0.483271	−	0.875471i	$-0.660552\pi$
$691$	8530.99	−	10395.0i	0.469659	−	0.572281i	0.952930	+	0.303190i	$0.0980516\pi$
$692$	2492.09	−	11331.5i	0.136900	−	0.622482i
$693$	−841.008	−	2772.43i	−0.0460999	−	0.151971i
$694$	3136.83	+	5354.99i	0.171574	+	0.292900i
$695$	−8703.35	−	5815.39i	−0.475017	−	0.317396i
$696$	−20785.3	−	37179.6i	−1.13199	−	2.02484i
$697$	−7856.14	−	11757.5i	−0.426934	−	0.638951i
$698$	−5998.70	−	17312.7i	−0.325292	−	0.938816i
$699$	−2175.55	+	1785.42i	−0.117721	+	0.0966108i
$700$	−381.479	+	29.8329i	−0.0205979	+	0.00161082i
$701$	−15380.4	−	28774.7i	−0.828688	−	1.55037i	−0.834911	−	0.550385i	$-0.814481\pi$
$701$	−15380.4	−	28774.7i	−0.828688	−	1.55037i	0.00622280	−	0.999981i	$-0.498019\pi$
$702$	147.182	+	23.3487i	0.00791313	+	0.00125533i
$703$			24186.2i			1.29758i
$704$	18871.9	−	24853.6i	1.01031	−	1.33055i
$705$			26254.5i			1.40255i
$706$	4952.97	−	31221.7i	0.264033	−	1.66437i
$707$	472.855	+	884.650i	0.0251535	+	0.0470590i
$708$	28808.4	+	24629.4i	1.52922	+	1.30739i
$709$	−2798.31	+	2296.51i	−0.148227	+	0.121646i	−0.705584	−	0.708626i	$-0.749315\pi$
$709$	−2798.31	+	2296.51i	−0.148227	+	0.121646i	0.557358	+	0.830273i	$0.311815\pi$
$710$	17190.4	−	5956.33i	0.908652	−	0.314841i
$711$	−13199.0	−	19753.6i	−0.696202	−	1.04194i
$712$	11008.3	−	1294.63i	0.579431	−	0.0681436i
$713$	2198.47	+	1468.97i	0.115474	+	0.0771575i
$714$	3552.43	−	2080.93i	0.186199	−	0.109071i
$715$	168.211	+	554.519i	0.00879826	+	0.0290040i
$716$	1892.79	+	2960.05i	0.0987944	+	0.154501i
$717$	36238.5	−	44156.8i	1.88752	−	2.29995i
$718$	18675.3	−	8603.82i	0.970691	−	0.447203i
$719$	13304.5	−	32119.9i	0.690089	−	1.66602i	−0.0545128	−	0.998513i	$-0.517361\pi$
$719$	13304.5	−	32119.9i	0.690089	−	1.66602i	0.744602	−	0.667509i	$-0.232639\pi$
$720$	25123.9	+	14758.9i	1.30044	+	0.763931i
$721$	−627.667	−	1515.32i	−0.0324210	−	0.0782713i
$722$	−2962.24	−	2739.62i	−0.152691	−	0.141216i
$723$	−12553.3	+	1236.40i	−0.645732	+	0.0635990i
$724$	−24825.6	−	499.818i	−1.27436	−	0.0256569i
$725$	7557.49	+	4039.56i	0.387142	+	0.206932i
$726$	−52962.1	+	7312.17i	−2.70745	+	0.373802i
$727$	−2549.40	−	12816.7i	−0.130058	−	0.653845i	−0.989724	−	0.142989i	$-0.954329\pi$
$727$	−2549.40	−	12816.7i	−0.130058	−	0.653845i	0.859666	−	0.510856i	$-0.170671\pi$
$728$	21.9416	−	4.79705i	0.00111705	−	0.000244218i
$729$	29221.5	+	5812.52i	1.48461	+	0.295306i
$730$	−13944.8	+	12385.5i	−0.707016	+	0.627957i
$731$	13666.7	+	1346.05i	0.691492	+	0.0681060i
$732$	1597.62	−	1258.18i	0.0806693	−	0.0635297i
$733$	24485.7	+	7427.66i	1.23383	+	0.374280i	0.838827	−	0.544398i	$-0.183242\pi$
$733$	24485.7	+	7427.66i	1.23383	+	0.374280i	0.395008	+	0.918678i	$0.370742\pi$
$734$	−6313.03	−	3870.78i	−0.317463	−	0.194650i
$735$	−24283.8	+	24283.8i	−1.21867	+	1.21867i
$736$	491.648	+	2487.79i	0.0246228	+	0.124594i
$737$	27590.7	+	27590.7i	1.37899	+	1.37899i
$738$	2415.11	+	10070.6i	0.120463	+	0.502311i
$739$	−506.487	+	1669.66i	−0.0252116	+	0.0831117i	−0.968643	−	0.248455i	$-0.920077\pi$
$739$	−506.487	+	1669.66i	−0.0252116	+	0.0831117i	0.943432	+	0.331567i	$0.107577\pi$
$740$	−25970.4	+	7310.52i	−1.29012	+	0.363162i
$741$	52.9910	−	538.027i	0.00262709	−	0.0266733i
$742$	77.7452	−	1312.78i	0.00384652	−	0.0649511i
$743$	−637.741	+	3206.14i	−0.0314892	+	0.158307i	−0.993331	−	0.115301i	$-0.963217\pi$
$743$	−637.741	+	3206.14i	−0.0314892	+	0.158307i	0.961841	+	0.273607i	$0.0882169\pi$
$744$	−33857.0	+	639.692i	−1.66836	+	0.0315218i
$745$	16883.3	−	3358.29i	0.830275	−	0.165152i
$746$	−4840.20	−	3665.83i	−0.237550	−	0.179913i
$747$	−1756.13	+	3285.49i	−0.0860154	+	0.160923i
$748$	−24588.7	−	62915.5i	−1.20194	−	3.07543i
$749$	−5.36103	−	54.4314i	−0.000261532	−	0.00265538i
$750$	25287.5	−	987.275i	1.23116	−	0.0480669i
$751$	26279.4	−	10885.3i	1.27690	−	0.528908i	0.361843	−	0.932239i	$-0.382148\pi$
$751$	26279.4	−	10885.3i	1.27690	−	0.528908i	0.915054	+	0.403331i	$0.132148\pi$
$752$	3913.74	−	16231.0i	0.189786	−	0.787079i
$753$	29398.2	+	12177.1i	1.42275	+	0.589322i
$754$	−471.859	−	174.211i	−0.0227906	−	0.00841431i
$755$	8821.98	+	7240.01i	0.425251	+	0.348995i
$756$	−734.110	+	130.720i	−0.0353166	+	0.00628868i
$757$	−9345.24	+	2834.85i	−0.448690	+	0.136109i	−0.506540	−	0.862217i	$-0.669076\pi$
$757$	−9345.24	+	2834.85i	−0.448690	+	0.136109i	0.0578495	+	0.998325i	$0.481576\pi$
$758$	−9466.66	+	36241.4i	−0.453621	+	1.73661i
$759$	3761.38	−	5629.30i	0.179881	−	0.269210i
$760$	11885.5	−	23283.7i	0.567278	−	1.11130i
$761$	31164.9	−	20823.7i	1.48453	−	0.991929i	0.491909	−	0.870646i	$-0.336299\pi$
$761$	31164.9	−	20823.7i	1.48453	−	0.991929i	0.992618	−	0.121283i	$-0.0387008\pi$
$762$	−26778.6	−	12996.7i	−1.27308	−	0.617877i
$763$	−1669.48	−	2034.26i	−0.0792125	−	0.0965208i
$764$	−19582.3	−	6373.41i	−0.927309	−	0.301809i
$765$	55625.0	−	29732.2i	2.62892	−	1.40519i
$766$	770.771	+	1061.43i	0.0363565	+	0.0500666i
$767$	447.567			0.0210700
$768$	−23367.0	−	22556.2i	−1.09789	−	1.05980i
$769$	−28079.2			−1.31672			−0.658362	−	0.752702i	$-0.728750\pi$
$769$	−28079.2			−1.31672			−0.658362	+	0.752702i	$0.728750\pi$
$770$	−1703.69	−	2346.15i	−0.0797360	−	0.109804i
$771$	−7592.90	+	4058.49i	−0.354671	+	0.189576i
$772$	−22174.8	−	7217.18i	−1.03379	−	0.336466i
$773$	−14366.1	−	17505.1i	−0.668450	−	0.814509i	0.322805	−	0.946465i	$-0.395374\pi$
$773$	−14366.1	−	17505.1i	−0.668450	−	0.814509i	−0.991256	+	0.131957i	$0.957874\pi$
$774$	−9048.11	−	4391.42i	−0.420191	−	0.203936i
$775$	5664.46	−	3784.87i	0.262546	−	0.175428i
$776$	18939.3	+	9667.80i	0.876137	+	0.447234i
$777$	1551.06	−	2321.32i	0.0716138	−	0.107178i
$778$	−3052.29	+	11685.1i	−0.140655	+	0.538473i
$779$	8891.16	−	2697.10i	0.408933	−	0.124049i
$780$	593.734	−	105.724i	0.0272552	−	0.00485323i
$781$	23877.1	+	19595.4i	1.09397	+	0.897795i
$782$	5149.46	+	1901.19i	0.235479	+	0.0869389i
$783$	15428.0	+	6390.47i	0.704151	+	0.291669i
$784$	18632.6	−	11392.7i	0.848790	−	0.518983i
$785$	−7077.75	+	2931.70i	−0.321803	+	0.133295i
$786$	−14866.7	+	580.427i	−0.674655	+	0.0263399i
$787$	292.541	+	2970.22i	0.0132503	+	0.134532i	0.999534	−	0.0305269i	$-0.00971854\pi$
$787$	292.541	+	2970.22i	0.0132503	+	0.134532i	−0.986284	+	0.165059i	$0.947219\pi$
$788$	12405.6	+	31742.3i	0.560825	+	1.43499i
$789$	15731.5	−	29431.7i	0.709832	−	1.32800i
$790$	−18953.8	−	14355.0i	−0.853602	−	0.646492i
$791$	−2267.99	+	451.131i	−0.101947	+	0.0202786i
$792$	934.540	+	49462.4i	0.0419286	+	2.21916i
$793$	4.68485	−	23.5523i	0.000209791	−	0.00105469i
$794$	847.613	−	14312.5i	0.0378850	−	0.639714i
$795$	3461.13	−	35141.4i	0.154407	−	1.56772i
$796$	−12566.2	+	3537.32i	−0.559545	+	0.157509i
$797$	−7121.89	+	23477.7i	−0.316525	+	1.04344i	0.643948	+	0.765069i	$0.277295\pi$
$797$	−7121.89	+	23477.7i	−0.316525	+	1.04344i	−0.960473	+	0.278373i	$0.910205\pi$
$798$	630.849	+	2630.55i	0.0279847	+	0.116692i
$799$	−25555.2	−	25555.2i	−1.13151	−	1.13151i
$800$	6406.75	+	1282.64i	0.283141	+	0.0566850i
$801$	−12425.0	+	12425.0i	−0.548085	+	0.548085i
$802$	21422.7	+	13135.2i	0.943220	+	0.578328i
$803$	−30302.4	−	9192.13i	−1.33169	−	0.403964i
$804$	31902.9	−	25124.6i	1.39942	−	1.10209i
$805$	234.482	+	23.0945i	0.0102664	+	0.00101115i
$806$	−298.977	+	265.545i	−0.0130658	+	0.0116047i
$807$	2141.44	+	425.958i	0.0934103	+	0.0185805i
$808$	−3658.35	−	16733.2i	−0.159283	−	0.728555i
$809$	7808.94	+	39258.2i	0.339367	+	1.70611i	0.653662	+	0.756786i	$0.273232\pi$
$809$	7808.94	+	39258.2i	0.339367	+	1.70611i	−0.314295	+	0.949325i	$0.601768\pi$
$810$	14608.6	−	2016.93i	0.633698	−	0.0874910i
$811$	−25710.0	−	13742.3i	−1.11320	−	0.595015i	−0.190942	−	0.981601i	$-0.561154\pi$
$811$	−25710.0	−	13742.3i	−1.11320	−	0.595015i	−0.922253	+	0.386586i	$0.873654\pi$
$812$	2516.29	+	50.6610i	0.108750	+	0.00218947i
$813$	30309.3	−	2985.21i	1.30750	−	0.128777i
$814$	−33629.1	−	31101.8i	−1.44803	−	1.33921i
$815$	12440.0	+	30032.9i	0.534669	+	1.29081i
$816$	−68040.9	+	17683.0i	−2.91900	+	0.758615i
$817$	−3453.05	+	8336.39i	−0.147866	+	0.356981i
$818$	27582.5	−	12707.4i	1.17897	−	0.543160i
$819$	−22.5878	+	27.5233i	−0.000963712	+	0.00117429i
$820$	5583.52	+	8731.84i	0.237786	+	0.371865i
$821$	−8163.45	−	26911.3i	−0.347023	−	1.14398i	−0.940689	−	0.339271i	$-0.889820\pi$
$821$	−8163.45	−	26911.3i	−0.347023	−	1.14398i	0.593665	−	0.804712i	$-0.297680\pi$
$822$	27860.9	−	16320.3i	1.18219	−	0.692501i
$823$	−191.231	−	127.777i	−0.00809953	−	0.00541193i	0.551514	−	0.834166i	$-0.314050\pi$
$823$	−191.231	−	127.777i	−0.00809953	−	0.00541193i	−0.559613	+	0.828754i	$0.689050\pi$
$824$	3271.20	+	27815.3i	0.138298	+	1.17596i
$825$	−9691.39	−	14504.2i	−0.408983	−	0.612086i
$826$	−2116.05	+	733.196i	−0.0891367	+	0.0308852i
$827$	−958.892	+	786.943i	−0.0403192	+	0.0330891i	−0.654337	−	0.756203i	$-0.727052\pi$
$827$	−958.892	+	786.943i	−0.0403192	+	0.0330891i	0.614018	+	0.789292i	$0.289552\pi$
$828$	−3055.63	−	2612.38i	−0.128249	−	0.109645i
$829$	−11286.6	−	21115.8i	−0.472860	−	0.884660i	−0.999404	−	0.0345116i	$-0.989012\pi$
$829$	−11286.6	−	21115.8i	−0.472860	−	0.884660i	0.526544	−	0.850148i	$-0.323488\pi$
$830$	−584.152	+	3682.28i	−0.0244292	+	0.153993i
$831$			13952.4i			0.582434i
$832$	−382.818	−	23.1470i	−0.0159517	−	0.000964518i
$833$		−	47274.0i		−	1.96632i
$834$	−18267.2	−	2897.88i	−0.758443	−	0.120318i
$835$	−24486.4	−	45810.9i	−1.01484	−	1.89863i
$836$	44248.9	−	3460.41i	1.83060	−	0.143159i
$837$	10262.3	−	8422.01i	0.423794	−	0.347799i
$838$	−5793.97	−	16721.8i	−0.238842	−	0.689314i
$839$	23198.5	+	34719.0i	0.954589	+	1.42864i	0.902837	+	0.429983i	$0.141480\pi$
$839$	23198.5	+	34719.0i	0.954589	+	1.42864i	0.0517515	+	0.998660i	$0.483520\pi$
$840$	−2633.92	+	1472.50i	−0.108189	+	0.0604833i
$841$	−26586.4	−	17764.4i	−1.09010	−	0.728379i
$842$	−1154.16	−	1970.31i	−0.0472387	−	0.0806428i
$843$	−12004.0	−	39572.0i	−0.490439	−	1.61676i
$844$	5589.69	−	25416.2i	0.227968	−	1.03657i
$845$	−17685.6	+	21549.9i	−0.720002	+	0.877325i
$846$	11075.2	+	24039.7i	0.450087	+	0.976951i
$847$	1208.91	−	2918.56i	0.0490420	−	0.118398i
$848$	−7378.24	+	21209.1i	−0.298785	+	0.858873i
$849$	913.172	+	2204.59i	0.0369140	+	0.0891183i
$850$	9603.02	−	10383.3i	0.387507	−	0.418994i
$851$	3704.40	−	364.851i	0.149219	−	0.0146968i
$852$	23184.0	−	22268.9i	0.932242	−	0.895445i
$853$	−7673.86	−	4101.76i	−0.308028	−	0.164644i	0.310139	−	0.950691i	$-0.399624\pi$
$853$	−7673.86	−	4101.76i	−0.308028	−	0.164644i	−0.618167	+	0.786047i	$0.712124\pi$
$854$	16.4335	+	119.028i	0.000658480	+	0.00476938i
$855$	8084.99	+	40646.0i	0.323393	+	1.62581i
$856$	−164.868	+	919.281i	−0.00658303	+	0.0367061i
$857$	10752.2	+	2138.74i	0.428573	+	0.0852485i	0.404664	−	0.914466i	$-0.367389\pi$
$857$	10752.2	+	2138.74i	0.428573	+	0.0852485i	0.0239095	+	0.999714i	$0.492389\pi$
$858$	679.943	+	765.547i	0.0270546	+	0.0304608i
$859$	−24317.6	−	2395.08i	−0.965898	−	0.0951326i	−0.397247	−	0.917712i	$-0.630034\pi$
$859$	−24317.6	−	2395.08i	−0.965898	−	0.0951326i	−0.568651	+	0.822579i	$0.692534\pi$
$860$	−9995.09	−	1188.02i	−0.396314	−	0.0471059i
$861$	−1026.32	−	311.329i	−0.0406234	−	0.0123230i
$862$	−19365.7	+	31584.5i	−0.765197	+	1.24799i
$863$	26628.8	−	26628.8i	1.05035	−	1.05035i	0.0516890	−	0.998663i	$-0.483540\pi$
$863$	26628.8	−	26628.8i	1.05035	−	1.05035i	0.998663	−	0.0516890i	$-0.0164605\pi$
$864$	12669.7	+	1263.71i	0.498880	+	0.0497595i
$865$	13016.0	+	13016.0i	0.511628	+	0.511628i
$866$	−13378.9	+	3208.48i	−0.524980	+	0.125899i
$867$	−32865.5	+	108343.i	−1.28739	+	4.24396i
$868$	978.522	−	1745.25i	0.0382640	−	0.0682460i
$869$	3956.73	−	40173.4i	0.154457	−	1.56823i
$870$	67460.9	+	3995.15i	2.62889	+	0.155688i
$871$	93.5517	−	470.316i	0.00363935	−	0.0182963i
$872$	17977.6	+	41183.6i	0.698165	+	1.59937i
$873$	−33062.0	+	6576.44i	−1.28176	+	0.254959i
$874$	−2177.57	+	2875.18i	−0.0842763	+	0.111275i
$875$	−704.875	+	1318.73i	−0.0272333	+	0.0509499i
$876$	−13221.9	+	30187.1i	−0.509963	+	1.16430i
$877$	1169.95	+	11878.8i	0.0450474	+	0.457374i	0.991077	+	0.133293i	$0.0425551\pi$
$877$	1169.95	+	11878.8i	0.0450474	+	0.457374i	−0.946029	+	0.324081i	$0.894945\pi$
$878$	−459.187	−	11761.4i	−0.0176501	−	0.452081i
$879$	−54199.8	+	22450.3i	−2.07977	+	0.861468i
$880$	17090.4	+	46467.2i	0.654678	+	1.78001i
$881$	8752.72	+	3625.50i	0.334718	+	0.138645i	0.543711	−	0.839272i	$-0.317019\pi$
$881$	8752.72	+	3625.50i	0.334718	+	0.138645i	−0.208993	+	0.977917i	$0.567019\pi$
$882$	−11991.3	+	32479.1i	−0.457787	+	1.23994i
$883$	−4352.48	−	3571.99i	−0.165881	−	0.136135i	0.547791	−	0.836615i	$-0.315469\pi$
$883$	−4352.48	−	3571.99i	−0.165881	−	0.136135i	−0.713671	+	0.700481i	$0.752969\pi$
$884$	−475.013	+	680.830i	−0.0180729	+	0.0259036i
$885$	−57543.2	+	17455.5i	−2.18564	+	0.663007i
$886$	11143.4	+	2910.78i	0.422539	+	0.110372i
$887$	−103.391	+	154.735i	−0.00391378	+	0.00585738i	−0.833421	−	0.552638i	$-0.813621\pi$
$887$	−103.391	+	154.735i	−0.00391378	+	0.00585738i	0.829508	+	0.558495i	$0.188621\pi$
$888$	−36273.3	+	30933.7i	−1.37078	+	1.16900i
$889$	1462.36	−	977.116i	0.0551697	−	0.0368632i
$890$	−7678.41	+	15820.7i	−0.289192	+	0.595854i
$891$	15883.9	+	19354.6i	0.597230	+	0.727727i
$892$	7925.17	+	15573.1i	0.297482	+	0.584558i
$893$	20942.5	−	11194.0i	0.784785	−	0.419476i
$894$	24612.0	−	17872.4i	0.920748	−	0.668614i
$895$	−5574.28			−0.208187
$896$	1847.84	−	517.688i	0.0688975	−	0.0193022i
$897$	−83.2045			−0.00309712
$898$	−12851.0	+	9331.90i	−0.477552	+	0.346781i
$899$	−39518.2	+	21122.9i	−1.46608	+	0.783636i
$900$	−9231.43	+	4697.89i	−0.341905	+	0.173996i
$901$	30836.5	+	37574.4i	1.14019	+	1.38933i
$902$	−7683.33	+	15830.8i	−0.283622	+	0.584377i
$903$	866.027	−	578.660i	0.0319154	−	0.0213252i
$904$	39362.0	+	3127.30i	1.44819	+	0.115058i
$905$	21886.5	−	32755.5i	0.803904	−	1.20313i
$906$	19510.9	+	5096.46i	0.715459	+	0.186886i
$907$	18244.3	−	5534.34i	0.667906	−	0.202607i	0.0619185	−	0.998081i	$-0.480278\pi$
$907$	18244.3	−	5534.34i	0.667906	−	0.202607i	0.605988	+	0.795474i	$0.292778\pi$
$908$	−24243.5	−	16914.6i	−0.886065	−	0.618206i
$909$	20989.9	+	17226.0i	0.765888	+	0.628548i
$910$	−12.3416	+	33.4280i	−0.000449584	+	0.00121772i
$911$	21852.7	+	9051.69i	0.794745	+	0.329194i	0.742850	−	0.669458i	$-0.233474\pi$
$911$	21852.7	+	9051.69i	0.794745	+	0.329194i	0.0518954	+	0.998653i	$0.483474\pi$
$912$	1859.22	−	46154.4i	0.0675056	−	1.67580i
$913$	−5848.17	+	2422.39i	−0.211989	+	0.0878088i
$914$	−270.697	−	6933.49i	−0.00979635	−	0.250918i
$915$	316.237	+	3210.81i	0.0114257	+	0.116007i
$916$	38269.1	+	16761.9i	1.38040	+	0.604615i
$917$	414.402	−	775.291i	0.0149234	−	0.0279197i
$918$	16640.0	−	21970.8i	0.598259	−	0.789917i
$919$	−42612.1	+	8476.07i	−1.52953	+	0.304243i	−0.886912	−	0.461939i	$-0.847154\pi$
$919$	−42612.1	+	8476.07i	−1.52953	+	0.304243i	−0.642623	+	0.766182i	$0.722154\pi$
$920$	−3745.47	−	1469.16i	−0.134222	−	0.0526487i
$921$	−10193.7	+	51247.3i	−0.364706	+	1.83350i
$922$	35694.2	+	2113.87i	1.27498	+	0.0755062i
$923$	37.2080	−	377.779i	0.00132689	−	0.0134721i
$924$	−4468.81	−	2505.56i	−0.159105	−	0.0892067i
$925$	2784.05	−	9177.78i	0.0989610	−	0.326231i
$926$	20606.0	−	4941.67i	0.731269	−	0.175371i
$927$	−31394.9	−	31394.9i	−1.11234	−	1.11234i
$928$	−41110.0	−	12526.2i	−1.45421	−	0.443096i
$929$	−30544.1	+	30544.1i	−1.07871	+	1.07871i	−0.0820810	+	0.996626i	$0.526157\pi$
$929$	−30544.1	+	30544.1i	−1.07871	+	1.07871i	−0.996626	+	0.0820810i	$0.973843\pi$
$930$	28082.6	−	45801.2i	0.990177	−	1.61492i
$931$	29724.2	+	9016.75i	1.04637	+	0.317413i
$932$	−335.150	+	2819.69i	−0.0117792	+	0.0991010i
$933$	−53344.7	−	5253.99i	−1.87184	−	0.184360i
$934$	−34688.8	−	39056.1i	−1.21526	−	1.36826i
$935$	105111.	+	20907.9i	3.67647	+	0.731295i
$936$	499.049	−	347.267i	0.0174273	−	0.0121269i
$937$	−4002.12	−	20120.0i	−0.139534	−	0.701485i	−0.985692	−	0.168554i	$-0.946090\pi$
$937$	−4002.12	−	20120.0i	−0.139534	−	0.701485i	0.846158	−	0.532931i	$-0.178910\pi$
$938$	328.160	+	2376.86i	0.0114230	+	0.0827370i
$939$	−27916.8	−	14921.9i	−0.970214	−	0.518590i
$940$	18349.8	+	19103.9i	0.636708	+	0.662873i
$941$	−26770.2	+	2636.64i	−0.927401	+	0.0913410i	−0.550427	−	0.834883i	$-0.685535\pi$
$941$	−26770.2	+	2636.64i	−0.927401	+	0.0913410i	−0.376973	+	0.926224i	$0.623035\pi$
$942$	−9191.09	+	9937.93i	−0.317900	+	0.343732i
$943$	−547.217	−	1321.10i	−0.0188970	−	0.0456213i
$944$	38176.4	−	2213.42i	1.31624	−	0.0763141i
$945$	452.721	−	1092.96i	0.0155841	−	0.0376234i
$946$	−7150.73	−	15521.3i	−0.245762	−	0.533446i
$947$	3890.79	−	4740.95i	0.133510	−	0.162682i	−0.701964	−	0.712212i	$-0.747693\pi$
$947$	3890.79	−	4740.95i	0.133510	−	0.162682i	0.835474	+	0.549530i	$0.185193\pi$
$948$	−41031.4	−	9023.89i	−1.40574	−	0.309158i
$949$	112.968	+	372.405i	0.00386416	+	0.0127384i
$950$	4697.05	+	8018.49i	0.160413	+	0.273846i
$951$	−21167.3	−	14143.5i	−0.721763	−	0.482266i
$952$	1130.49	−	3997.05i	0.0384869	−	0.136077i
$953$	−9735.13	−	14569.7i	−0.330904	−	0.495233i	0.628291	−	0.777979i	$-0.283755\pi$
$953$	−9735.13	−	14569.7i	−0.330904	−	0.495233i	−0.959195	+	0.282745i	$0.908755\pi$
$954$	−11654.9	−	33636.9i	−0.395537	−	1.14155i
$955$	25256.0	−	20727.1i	0.855774	−	0.702316i
$956$	−4493.43	−	57458.4i	−0.152017	−	1.94387i
$957$	54086.5	+	101189.i	1.82693	+	3.41794i
$958$	49615.4	+	7870.91i	1.67328	+	0.265446i
$959$			1907.85i			0.0642415i
$960$	50121.2	−	11954.3i	1.68506	−	0.401898i
$961$			5832.11i			0.195768i
$962$	−88.2017	+	555.992i	−0.00295607	+	0.0186340i
$963$	−697.937	−	1305.75i	−0.0233548	−	0.0436938i
$964$	−8270.22	+	9673.48i	−0.276313	+	0.323197i
$965$	28599.6	−	23471.1i	0.954045	−	0.782964i
$966$	393.383	−	136.304i	0.0131024	−	0.00453987i
$967$	−11212.0	−	16780.0i	−0.372859	−	0.558023i	0.596829	−	0.802368i	$-0.296427\pi$
$967$	−11212.0	−	16780.0i	−0.372859	−	0.558023i	−0.969688	+	0.244345i	$0.921427\pi$
$968$	−33426.9	+	42337.1i	−1.10990	+	1.40575i
$969$	−83136.0	−	55549.7i	−2.75616	−	1.84160i
$970$	−29109.8	+	17051.9i	−0.963567	+	0.564435i
$971$	533.058	+	1757.26i	0.0176176	+	0.0580773i	0.965308	−	0.261112i	$-0.0840893\pi$
$971$	533.058	+	1757.26i	0.0176176	+	0.0580773i	−0.947691	+	0.319190i	$0.896589\pi$
$972$	34753.2	−	22222.7i	1.14682	−	0.733327i
$973$	693.292	−	844.778i	0.0228427	−	0.0278339i
$974$	26011.8	−	11983.8i	0.855719	−	0.394235i
$975$	−82.0400	+	198.062i	−0.00269475	+	0.00650570i
$976$	283.130	−	2032.13i	0.00928562	−	0.0666463i
$977$	−9805.89	−	23673.5i	−0.321104	−	0.775213i	−0.999190	−	0.0402308i	$-0.987191\pi$
$977$	−9805.89	−	23673.5i	−0.321104	−	0.775213i	0.678087	−	0.734982i	$-0.262809\pi$
$978$	42169.5	+	39000.4i	1.37876	+	1.27515i
$979$	−29713.2	+	2926.50i	−0.970008	+	0.0955375i
$980$	−697.462	+	34642.4i	−0.0227343	+	1.12919i
$981$	−62825.5	−	33580.9i	−2.04471	−	1.09292i
$982$	−20972.7	+	2895.59i	−0.681535	+	0.0940956i
$983$	−2873.19	−	14444.5i	−0.0932252	−	0.468675i	−0.998992	−	0.0448974i	$-0.985704\pi$
$983$	−2873.19	−	14444.5i	−0.0932252	−	0.468675i	0.905766	−	0.423777i	$-0.139296\pi$
$984$	15416.7	+	9885.00i	0.499456	+	0.320246i
$985$	−53030.9	−	10548.5i	−1.71544	−	0.341222i
$986$	−69552.9	+	61775.5i	−2.24647	+	1.99527i
$987$	−2727.87	−	268.672i	−0.0879728	−	0.00866456i
$988$	−337.481	−	428.529i	−0.0108671	−	0.0137989i
$989$	1328.91	+	403.119i	0.0427267	+	0.0129610i
$990$	−66912.0	−	41026.5i	−2.14808	−	1.31708i
$991$	−20234.0	+	20234.0i	−0.648592	+	0.648592i	−0.952653	−	0.304061i	$-0.901657\pi$
$991$	−20234.0	+	20234.0i	−0.648592	+	0.648592i	0.304061	+	0.952653i	$0.401657\pi$
$992$	−24188.7	+	24128.9i	−0.774187	+	0.772271i
$993$	27477.0	+	27477.0i	0.878104	+	0.878104i
$994$	442.955	+	1847.06i	0.0141345	+	0.0589387i
$995$	6012.27	−	19819.8i	0.191560	−	0.631487i
$996$	1785.07	+	6341.39i	0.0567891	+	0.201742i
$997$	157.819	−	1602.36i	0.00501322	−	0.0509000i	−0.992353	−	0.123435i	$-0.960609\pi$
$997$	157.819	−	1602.36i	0.00501322	−	0.0509000i	0.997366	+	0.0725351i	$0.0231089\pi$
$998$	247.328	−	4176.30i	0.00784471	−	0.132463i
$999$	3646.14	−	18330.4i	0.115474	−	0.580528i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.k.a.101.33	✓	752
128.109	even	32	inner	128.4.k.a.109.33	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.4.k.a.101.33	✓	752	1.1	even	1	trivial
128.4.k.a.109.33	yes	752	128.109	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	128.4.k.a.101.33

Level	$128$
Weight	$4$
Character	128.101
Analytic conductor	$7.552$
Analytic rank	$0$
Dimension	$752$
Inner twists	$2$