LMFDB - Embedded newform 128.4.k.a.101.20

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)

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);

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")

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			101.20
Character	$\chi$	$=$	128.101
Dual form			128.4.k.a.109.20

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.567432 + 2.77092i) q^{2} +(-5.84044 + 3.12178i) q^{3} +(-7.35604 - 3.14462i) q^{4} +(0.807395 + 0.983814i) q^{5} +(-5.33617 - 17.9548i) q^{6} +(-28.4348 + 18.9996i) q^{7} +(12.8876 - 18.5987i) q^{8} +(9.36483 - 14.0155i) q^{9} +(-3.18421 + 1.67898i) q^{10} +(45.4115 - 13.7754i) q^{11} +(52.7793 - 4.59798i) q^{12} +(-48.6560 - 39.9309i) q^{13} +(-36.5115 - 89.5718i) q^{14} +(-7.78679 - 3.22540i) q^{15} +(44.2227 + 46.2639i) q^{16} +(64.3737 - 26.6645i) q^{17} +(33.5219 + 33.9021i) q^{18} +(13.3540 + 135.586i) q^{19} +(-2.84551 - 9.77593i) q^{20} +(106.760 - 199.733i) q^{21} +(12.4028 + 133.649i) q^{22} +(19.8877 - 3.95592i) q^{23} +(-17.2080 + 148.857i) q^{24} +(24.0703 - 121.010i) q^{25} +(138.255 - 112.164i) q^{26} +(6.58440 - 66.8525i) q^{27} +(268.914 - 50.3448i) q^{28} +(-24.6532 + 81.2706i) q^{29} +(13.3558 - 19.7464i) q^{30} +(-73.2169 - 73.2169i) q^{31} +(-153.287 + 96.2862i) q^{32} +(-222.220 + 222.220i) q^{33} +(37.3575 + 193.505i) q^{34} +(-41.6502 - 12.6344i) q^{35} +(-112.961 + 73.6495i) q^{36} +(-127.125 - 12.5208i) q^{37} +(-383.275 - 39.9326i) q^{38} +(408.828 + 81.3209i) q^{39} +(28.7030 - 2.33753i) q^{40} +(-73.2924 - 368.466i) q^{41} +(492.867 + 409.158i) q^{42} +(-386.422 - 206.547i) q^{43} +(-377.368 - 41.4693i) q^{44} +(21.3497 - 2.10276i) q^{45} +(-0.323384 + 57.3521i) q^{46} +(-140.490 - 339.174i) q^{47} +(-402.706 - 132.148i) q^{48} +(316.297 - 763.608i) q^{49} +(321.650 + 135.362i) q^{50} +(-292.730 + 356.693i) q^{51} +(232.348 + 446.738i) q^{52} +(128.180 + 422.553i) q^{53} +(181.507 + 56.1791i) q^{54} +(50.2175 + 33.5543i) q^{55} +(-13.0889 + 773.709i) q^{56} +(-501.262 - 750.192i) q^{57} +(-211.206 - 114.428i) q^{58} +(-16.9357 + 13.8988i) q^{59} +(47.1373 + 48.2126i) q^{60} +(-136.049 - 254.530i) q^{61} +(244.424 - 161.333i) q^{62} +576.455i q^{63} +(-179.822 - 479.383i) q^{64} -80.1084i q^{65} +(-489.659 - 741.848i) q^{66} +(349.455 + 653.784i) q^{67} +(-557.385 - 6.28592i) q^{68} +(-103.804 + 85.1894i) q^{69} +(58.6427 - 108.240i) q^{70} +(32.1510 + 48.1174i) q^{71} +(-139.979 - 354.799i) q^{72} +(148.907 + 99.4963i) q^{73} +(106.829 - 345.150i) q^{74} +(237.184 + 781.891i) q^{75} +(328.133 - 1039.37i) q^{76} +(-1029.54 + 1254.50i) q^{77} +(-457.316 + 1086.69i) q^{78} +(66.9901 - 161.728i) q^{79} +(-9.80986 + 80.8602i) q^{80} +(344.410 + 831.478i) q^{81} +(1062.58 + 5.99143i) q^{82} +(-1252.13 + 123.324i) q^{83} +(-1413.41 + 1133.53i) q^{84} +(78.2079 + 41.8030i) q^{85} +(791.594 - 953.546i) q^{86} +(-109.724 - 551.618i) q^{87} +(329.039 - 1022.13i) q^{88} +(350.183 + 69.6558i) q^{89} +(-6.28791 + 60.3516i) q^{90} +(2142.20 + 210.988i) q^{91} +(-158.735 - 33.4395i) q^{92} +(656.186 + 199.052i) q^{93} +(1019.54 - 196.830i) q^{94} +(-122.609 + 122.609i) q^{95} +(594.680 - 1040.88i) q^{96} +(-533.988 - 533.988i) q^{97} +(1936.42 + 1309.73i) q^{98} +(232.202 - 765.469i) 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

)

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

$2$	−0.567432	+	2.77092i	−0.200617	+	0.979670i
$2$	−0.567432	+	2.77092i	−0.200617	+	0.979670i
$3$	−5.84044	+	3.12178i	−1.12399	+	0.600787i	−0.925285	−	0.379272i	$-0.876175\pi$
$3$	−5.84044	+	3.12178i	−1.12399	+	0.600787i	−0.198708	+	0.980059i	$0.563675\pi$
$4$	−7.35604	−	3.14462i	−0.919505	−	0.393077i
$5$	0.807395	+	0.983814i	0.0722156	+	0.0879950i	0.807865	−	0.589367i	$-0.200623\pi$
$5$	0.807395	+	0.983814i	0.0722156	+	0.0879950i	−0.735650	+	0.677362i	$0.763123\pi$
$6$	−5.33617	−	17.9548i	−0.363080	−	1.22167i
$7$	−28.4348	+	18.9996i	−1.53534	+	1.02588i	−0.554242	+	0.832356i	$0.686992\pi$
$7$	−28.4348	+	18.9996i	−1.53534	+	1.02588i	−0.981096	+	0.193524i	$0.938008\pi$
$8$	12.8876	−	18.5987i	0.569555	−	0.821953i
$9$	9.36483	−	14.0155i	0.346846	−	0.519091i
$10$	−3.18421	+	1.67898i	−0.100694	+	0.0530941i
$11$	45.4115	−	13.7754i	1.24474	−	0.377587i	0.401863	−	0.915700i	$-0.368363\pi$
$11$	45.4115	−	13.7754i	1.24474	−	0.377587i	0.842873	+	0.538113i	$0.180863\pi$
$12$	52.7793	−	4.59798i	1.26967	−	0.110610i
$13$	−48.6560	−	39.9309i	−1.03806	−	0.851911i	−0.0489044	−	0.998803i	$-0.515573\pi$
$13$	−48.6560	−	39.9309i	−1.03806	−	0.851911i	−0.989153	+	0.146892i	$0.953073\pi$
$14$	−36.5115	−	89.5718i	−0.697008	−	1.70993i
$15$	−7.78679	−	3.22540i	−0.134036	−	0.0555196i
$16$	44.2227	+	46.2639i	0.690980	+	0.722874i
$17$	64.3737	−	26.6645i	0.918407	−	0.380417i	0.127138	−	0.991885i	$-0.459421\pi$
$17$	64.3737	−	26.6645i	0.918407	−	0.380417i	0.791269	+	0.611468i	$0.209421\pi$
$18$	33.5219	+	33.9021i	0.438955	+	0.443933i
$19$	13.3540	+	135.586i	0.161243	+	1.63713i	0.646611	+	0.762820i	$0.276186\pi$
$19$	13.3540	+	135.586i	0.161243	+	1.63713i	−0.485367	+	0.874310i	$0.661314\pi$
$20$	−2.84551	−	9.77593i	−0.0318138	−	0.109298i
$21$	106.760	−	199.733i	1.10937	−	2.07549i
$22$	12.4028	+	133.649i	0.120194	+	1.29518i
$23$	19.8877	−	3.95592i	0.180299	−	0.0358637i	−0.104115	−	0.994565i	$-0.533201\pi$
$23$	19.8877	−	3.95592i	0.180299	−	0.0358637i	0.284414	+	0.958702i	$0.408201\pi$
$24$	−17.2080	+	148.857i	−0.146357	+	1.26605i
$25$	24.0703	−	121.010i	0.192562	−	0.968076i
$26$	138.255	−	112.164i	1.04284	−	0.846045i
$27$	6.58440	−	66.8525i	0.0469322	−	0.476510i
$28$	268.914	−	50.3448i	1.81500	−	0.339795i
$29$	−24.6532	+	81.2706i	−0.157861	+	0.520399i	−0.999817	−	0.0191481i	$-0.993905\pi$
$29$	−24.6532	+	81.2706i	−0.157861	+	0.520399i	0.841955	+	0.539547i	$0.181405\pi$
$30$	13.3558	−	19.7464i	0.0812808	−	0.120173i
$31$	−73.2169	−	73.2169i	−0.424198	−	0.424198i	0.462448	−	0.886646i	$-0.346971\pi$
$31$	−73.2169	−	73.2169i	−0.424198	−	0.424198i	−0.886646	+	0.462448i	$0.846971\pi$
$32$	−153.287	+	96.2862i	−0.846800	+	0.531911i
$33$	−222.220	+	222.220i	−1.17223	+	1.17223i
$34$	37.3575	+	193.505i	0.188434	+	0.976054i
$35$	−41.6502	−	12.6344i	−0.201148	−	0.0610175i
$36$	−112.961	+	73.6495i	−0.522970	+	0.340970i
$37$	−127.125	−	12.5208i	−0.564846	−	0.0556324i	−0.188436	−	0.982086i	$-0.560342\pi$
$37$	−127.125	−	12.5208i	−0.564846	−	0.0556324i	−0.376410	+	0.926453i	$0.622842\pi$
$38$	−383.275	−	39.9326i	−1.63620	−	0.170472i
$39$	408.828	+	81.3209i	1.67859	+	0.333892i
$40$	28.7030	−	2.33753i	0.113459	−	0.00923990i
$41$	−73.2924	−	368.466i	−0.279179	−	1.40353i	−0.824766	−	0.565474i	$-0.808693\pi$
$41$	−73.2924	−	368.466i	−0.279179	−	1.40353i	0.545587	−	0.838054i	$-0.316307\pi$
$42$	492.867	+	409.158i	1.81074	+	1.50320i
$43$	−386.422	−	206.547i	−1.37044	−	0.732515i	−0.388452	−	0.921469i	$-0.626990\pi$
$43$	−386.422	−	206.547i	−1.37044	−	0.732515i	−0.981986	+	0.188954i	$0.939490\pi$
$44$	−377.368	−	41.4693i	−1.29296	−	0.142085i
$45$	21.3497	−	2.10276i	0.0707251	−	0.00696581i
$46$	−0.323384	+	57.3521i	−0.00103653	+	0.183828i
$47$	−140.490	−	339.174i	−0.436013	−	1.05263i	−0.977313	−	0.211800i	$-0.932068\pi$
$47$	−140.490	−	339.174i	−0.436013	−	1.05263i	0.541300	−	0.840830i	$-0.317932\pi$
$48$	−402.706	−	132.148i	−1.21095	−	0.397373i
$49$	316.297	−	763.608i	0.922149	−	2.22626i
$50$	321.650	+	135.362i	0.909763	+	0.382860i
$51$	−292.730	+	356.693i	−0.803734	+	0.979353i
$52$	232.348	+	446.738i	0.619632	+	1.19137i
$53$	128.180	+	422.553i	0.332205	+	1.09513i	0.950899	+	0.309502i	$0.100162\pi$
$53$	128.180	+	422.553i	0.332205	+	1.09513i	−0.618694	+	0.785632i	$0.712338\pi$
$54$	181.507	+	56.1791i	0.457407	+	0.141574i
$55$	50.2175	+	33.5543i	0.123115	+	0.0822629i
$56$	−13.0889	+	773.709i	−0.0312336	+	1.84627i
$57$	−501.262	−	750.192i	−1.16480	−	1.74325i
$58$	−211.206	−	114.428i	−0.478150	−	0.259053i
$59$	−16.9357	+	13.8988i	−0.0373702	+	0.0306689i	−0.652893	−	0.757450i	$-0.726445\pi$
$59$	−16.9357	+	13.8988i	−0.0373702	+	0.0306689i	0.615523	+	0.788119i	$0.288945\pi$
$60$	47.1373	+	48.2126i	0.101423	+	0.103737i
$61$	−136.049	−	254.530i	−0.285563	−	0.534250i	0.697712	−	0.716378i	$-0.254201\pi$
$61$	−136.049	−	254.530i	−0.285563	−	0.534250i	−0.983275	+	0.182128i	$0.941701\pi$
$62$	244.424	−	161.333i	0.500676	−	0.330473i
$63$			576.455i			1.15280i
$64$	−179.822	−	479.383i	−0.351215	−	0.936295i
$65$		−	80.1084i		−	0.152865i
$66$	−489.659	−	741.848i	−0.913225	−	1.38356i
$67$	349.455	+	653.784i	0.637204	+	1.19213i	0.968598	+	0.248633i	$0.0799812\pi$
$67$	349.455	+	653.784i	0.637204	+	1.19213i	−0.331394	+	0.943493i	$0.607519\pi$
$68$	−557.385	−	6.28592i	−0.994013	−	0.0112100i
$69$	−103.804	+	85.1894i	−0.181108	+	0.148632i
$70$	58.6427	−	108.240i	0.100131	−	0.184817i
$71$	32.1510	+	48.1174i	0.0537412	+	0.0804294i	0.857367	−	0.514705i	$-0.172099\pi$
$71$	32.1510	+	48.1174i	0.0537412	+	0.0804294i	−0.803626	+	0.595135i	$0.797099\pi$
$72$	−139.979	−	354.799i	−0.229121	−	0.580742i
$73$	148.907	+	99.4963i	0.238743	+	0.159523i	0.669186	−	0.743095i	$-0.266643\pi$
$73$	148.907	+	99.4963i	0.238743	+	0.159523i	−0.430444	+	0.902617i	$0.641643\pi$
$74$	106.829	−	345.150i	0.167819	−	0.542201i
$75$	237.184	+	781.891i	0.365169	+	1.20380i
$76$	328.133	−	1039.37i	0.495255	−	1.56873i
$77$	−1029.54	+	1254.50i	−1.52373	+	1.85667i
$78$	−457.316	+	1086.69i	−0.663857	+	1.57748i
$79$	66.9901	−	161.728i	0.0954048	−	0.230328i	−0.868971	−	0.494862i	$-0.835218\pi$
$79$	66.9901	−	161.728i	0.0954048	−	0.230328i	0.964376	+	0.264535i	$0.0852184\pi$
$80$	−9.80986	+	80.8602i	−0.0137097	+	0.113006i
$81$	344.410	+	831.478i	0.472441	+	1.14057i
$82$	1062.58	+	5.99143i	1.43100	+	0.00806881i
$83$	−1252.13	+	123.324i	−1.65590	+	0.163092i	−0.882332	−	0.470627i	$-0.844028\pi$
$83$	−1252.13	+	123.324i	−1.65590	+	0.163092i	−0.773564	+	0.633719i	$0.781528\pi$
$84$	−1413.41	+	1133.53i	−1.83590	+	1.47236i
$85$	78.2079	+	41.8030i	0.0997981	+	0.0533432i
$86$	791.594	−	953.546i	0.992556	−	1.19562i
$87$	−109.724	−	551.618i	−0.135214	−	0.679766i
$88$	329.039	−	1022.13i	0.398587	−	1.23817i
$89$	350.183	+	69.6558i	0.417071	+	0.0829606i	0.399165	−	0.916879i	$-0.369300\pi$
$89$	350.183	+	69.6558i	0.417071	+	0.0829606i	0.0179061	+	0.999840i	$0.494300\pi$
$90$	−6.28791	+	60.3516i	−0.00736448	+	0.0706847i
$91$	2142.20	+	210.988i	2.46773	+	0.243050i
$92$	−158.735	−	33.4395i	−0.179883	−	0.0378946i
$93$	656.186	+	199.052i	0.731649	+	0.221943i
$94$	1019.54	−	196.830i	1.11870	−	0.215973i
$95$	−122.609	+	122.609i	−0.132415	+	0.132415i
$96$	594.680	−	1040.88i	0.632232	−	1.10661i
$97$	−533.988	−	533.988i	−0.558951	−	0.558951i	0.370058	−	0.929009i	$-0.379338\pi$
$97$	−533.988	−	533.988i	−0.558951	−	0.558951i	−0.929009	+	0.370058i	$0.879338\pi$
$98$	1936.42	+	1309.73i	1.99600	+	1.35003i
$99$	232.202	−	765.469i	0.235729	−	0.777096i
$100$	−557.591	+	814.459i	−0.557591	+	0.814459i
$101$	105.549	−	1071.66i	0.103986	−	1.05578i	−0.791643	−	0.610983i	$-0.790774\pi$
$101$	105.549	−	1071.66i	0.103986	−	1.05578i	0.895629	−	0.444801i	$-0.146726\pi$
$102$	−822.264	−	1013.53i	−0.798199	−	0.983869i
$103$	108.646	−	546.198i	0.103934	−	0.522510i	−0.893383	−	0.449297i	$-0.851675\pi$
$103$	108.646	−	546.198i	0.103934	−	0.522510i	0.997316	−	0.0732133i	$-0.0233254\pi$
$104$	−1369.72	+	390.325i	−1.29146	+	0.368024i
$105$	282.697	−	56.2320i	0.262747	−	0.0522636i
$106$	−1243.60	+	115.407i	−1.13952	+	0.105749i
$107$	205.415	−	384.304i	0.185591	−	0.347216i	−0.771870	−	0.635781i	$-0.780678\pi$
$107$	205.415	−	384.304i	0.185591	−	0.347216i	0.957460	+	0.288565i	$0.0931782\pi$
$108$	−258.661	+	471.065i	−0.230460	+	0.419706i
$109$	34.1177	+	346.403i	0.0299806	+	0.304398i	0.998468	+	0.0553349i	$0.0176226\pi$
$109$	34.1177	+	346.403i	0.0299806	+	0.304398i	−0.968487	+	0.249063i	$0.919877\pi$
$110$	−121.471	+	120.109i	−0.105289	+	0.104109i
$111$	781.556	−	323.731i	0.668306	−	0.276821i
$112$	−2136.46	−	475.295i	−1.80247	−	0.400993i
$113$	196.721	+	81.4845i	0.163769	+	0.0678355i	0.463062	−	0.886326i	$-0.346751\pi$
$113$	196.721	+	81.4845i	0.163769	+	0.0678355i	−0.299293	+	0.954161i	$0.596751\pi$
$114$	2363.16	−	963.277i	1.94149	−	0.791396i
$115$	19.9491	+	16.3718i	0.0161762	+	0.0132755i
$116$	436.915	−	520.305i	0.349712	−	0.416458i
$117$	−1015.31	+	307.990i	−0.802265	+	0.243364i
$118$	−28.9026	−	54.8142i	−0.0225483	−	0.0427632i
$119$	−1323.84	+	1981.27i	−1.01980	+	1.52624i
$120$	−160.341	+	103.257i	−0.121975	+	0.0785500i
$121$	765.760	−	511.664i	0.575327	−	0.384421i
$122$	782.483	−	232.554i	0.580678	−	0.172577i
$123$	1578.33	+	1923.20i	1.15702	+	1.40983i
$124$	308.347	+	768.826i	0.223310	+	0.556795i
$125$	278.788	−	149.015i	0.199485	−	0.106627i
$126$	−1597.31	−	327.099i	−1.12937	−	0.231272i
$127$	−57.9733			−0.0405063			−0.0202531	−	0.999795i	$-0.506447\pi$
$127$	−57.9733			−0.0405063			−0.0202531	+	0.999795i	$0.506447\pi$
$128$	1430.37	−	226.256i	0.987720	−	0.156237i
$129$	2901.67			1.98045
$130$	221.974	+	45.4561i	0.149757	+	0.0306674i
$131$	1092.13	−	583.758i	0.728398	−	0.389337i	−0.0651248	−	0.997877i	$-0.520745\pi$
$131$	1092.13	−	583.758i	0.728398	−	0.389337i	0.793523	+	0.608540i	$0.208245\pi$
$132$	2333.45	−	935.860i	1.53864	−	0.617092i
$133$	−2955.79	−	3601.64i	−1.92706	−	2.34813i
$134$	−2009.88	+	597.335i	−1.29572	+	0.385089i
$135$	71.0866	−	47.4986i	0.0453197	−	0.0302817i
$136$	333.696	−	1540.91i	0.210398	−	0.971556i
$137$	−246.995	+	369.655i	−0.154031	+	0.230524i	−0.900457	−	0.434944i	$-0.856768\pi$
$137$	−246.995	+	369.655i	−0.154031	+	0.230524i	0.746426	+	0.665468i	$0.231768\pi$
$138$	−177.152	−	335.971i	−0.109277	−	0.207245i
$139$	331.764	−	100.640i	0.202445	−	0.0614111i	−0.187433	−	0.982277i	$-0.560017\pi$
$139$	331.764	−	100.640i	0.202445	−	0.0614111i	0.389879	+	0.920866i	$0.372517\pi$
$140$	266.650	+	223.913i	0.160972	+	0.135172i
$141$	1879.35	+	1542.34i	1.12248	+	0.921197i
$142$	−151.573	+	61.7848i	−0.0895757	+	0.0365131i
$143$	−2759.61	−	1143.07i	−1.61378	−	0.668448i
$144$	1062.55	−	186.548i	0.614901	−	0.107956i
$145$	−99.8600	+	41.3634i	−0.0571926	+	0.0236899i
$146$	−360.191	+	356.152i	−0.204176	+	0.201886i
$147$	536.504	+	5447.22i	0.301021	+	3.05632i
$148$	895.767	+	491.864i	0.497511	+	0.273182i
$149$	669.734	−	1252.98i	0.368233	−	0.688915i	−0.627754	−	0.778412i	$-0.716026\pi$
$149$	669.734	−	1252.98i	0.368233	−	0.688915i	0.995987	+	0.0894962i	$0.0285257\pi$
$150$	−2301.15	+	213.549i	−1.25259	+	0.116242i
$151$	−991.744	+	197.270i	−0.534483	+	0.106315i	−0.454950	−	0.890517i	$-0.650343\pi$
$151$	−991.744	+	197.270i	−0.534483	+	0.106315i	−0.0795330	+	0.996832i	$0.525343\pi$
$152$	2693.81	+	1499.00i	1.43748	+	0.799901i
$153$	229.134	−	1151.94i	0.121075	−	0.608683i
$154$	−2891.93	−	3564.63i	−1.51324	−	1.86523i
$155$	12.9168	−	131.147i	0.00669358	−	0.0679611i
$156$	−2751.63	−	1883.81i	−1.41222	−	0.966829i
$157$	−158.627	+	522.924i	−0.0806359	+	0.265821i	−0.987983	−	0.154561i	$-0.950604\pi$
$157$	−158.627	+	522.924i	−0.0806359	+	0.265821i	0.907347	+	0.420382i	$0.138104\pi$
$158$	410.125	+	277.394i	0.206505	+	0.139673i
$159$	−2067.75	−	2067.75i	−1.03134	−	1.03134i
$160$	−218.491	−	73.0650i	−0.107958	−	0.0361019i
$161$	−490.344	+	490.344i	−0.240028	+	0.240028i
$162$	−2499.39	+	482.526i	−1.21217	+	0.234017i
$163$	−3123.33	−	947.452i	−1.50085	−	0.455277i	−0.570296	−	0.821439i	$-0.693171\pi$
$163$	−3123.33	−	947.452i	−1.50085	−	0.455277i	−0.930551	+	0.366162i	$0.880671\pi$
$164$	−619.543	+	2940.93i	−0.294989	+	1.40029i
$165$	−398.042	−	39.2037i	−0.187803	−	0.0184970i
$166$	368.777	−	3539.54i	0.172426	−	1.65495i
$167$	−3119.87	−	620.581i	−1.44565	−	0.287557i	−0.590959	−	0.806702i	$-0.701251\pi$
$167$	−3119.87	−	620.581i	−1.44565	−	0.287557i	−0.854686	+	0.519145i	$0.826251\pi$
$168$	−2338.90	−	4559.66i	−1.07411	−	2.09396i
$169$	344.312	+	1730.97i	0.156719	+	0.787879i
$170$	−160.211	+	192.988i	−0.0722799	+	0.0870676i
$171$	2025.35	+	1082.57i	0.905747	+	0.484132i
$172$	2193.03	+	2734.52i	0.972190	+	1.21224i
$173$	−1595.00	+	157.094i	−0.700957	+	0.0690383i	−0.442216	−	0.896908i	$-0.645808\pi$
$173$	−1595.00	+	157.094i	−0.700957	+	0.0690383i	−0.258741	+	0.965947i	$0.583308\pi$
$174$	1590.75	+	8.96958i	0.693073	+	0.00390794i
$175$	1614.69	+	3898.21i	0.697481	+	1.68387i
$176$	2645.53	+	1491.73i	1.13304	+	0.638882i
$177$	55.5231	−	134.045i	0.0235784	−	0.0569232i
$178$	−391.716	+	930.806i	−0.164946	+	0.391949i
$179$	2679.60	−	3265.11i	1.11890	−	1.36338i	0.194974	−	0.980808i	$-0.437538\pi$
$179$	2679.60	−	3265.11i	1.11890	−	1.36338i	0.923925	−	0.382574i	$-0.124962\pi$
$180$	−163.662	−	51.6687i	−0.0677702	−	0.0213953i
$181$	891.108	+	2937.59i	0.365942	+	1.20635i	0.925881	+	0.377815i	$0.123325\pi$
$181$	891.108	+	2937.59i	0.365942	+	1.20635i	−0.559939	+	0.828534i	$0.689175\pi$
$182$	−1800.18	+	5816.14i	−0.733177	+	2.36880i
$183$	1589.18	+	1061.85i	0.641941	+	0.428931i
$184$	182.729	−	420.868i	0.0732119	−	0.168624i
$185$	−90.3223	−	135.177i	−0.0358953	−	0.0537211i
$186$	−923.899	+	1705.29i	−0.364213	+	0.672249i
$187$	2556.00	−	2097.65i	0.999534	−	0.820296i
$188$	−33.1194	+	2936.77i	−0.0128483	+	1.13929i
$189$	1082.94	+	2026.04i	0.416785	+	0.779751i
$190$	−270.168	−	409.313i	−0.103158	−	0.156288i
$191$			1075.40i			0.407398i	0.979034	+	0.203699i	$0.0652964\pi$
$191$			1075.40i			0.407398i	−0.979034	+	0.203699i	$0.934704\pi$
$192$	2546.77	+	2238.44i	0.957277	+	0.841384i
$193$		−	1280.11i		−	0.477430i	−0.971090	−	0.238715i	$-0.923274\pi$
$193$		−	1280.11i		−	0.477430i	0.971090	−	0.238715i	$-0.0767262\pi$
$194$	1782.64	−	1176.64i	0.659723	−	0.435452i
$195$	250.081	+	467.869i	0.0918393	+	0.171819i
$196$	−4727.95	+	4622.50i	−1.72301	+	1.68459i
$197$	−3039.67	+	2494.59i	−1.09933	+	0.902196i	−0.995720	−	0.0924226i	$-0.970539\pi$
$197$	−3039.67	+	2494.59i	−1.09933	+	0.902196i	−0.103609	+	0.994618i	$0.533039\pi$
$198$	1989.30	+	1077.77i	0.714006	+	0.386836i
$199$	−2215.08	−	3315.10i	−0.789059	−	1.18091i	−0.979939	−	0.199297i	$-0.936134\pi$
$199$	−2215.08	−	3315.10i	−0.789059	−	1.18091i	0.190880	−	0.981613i	$-0.438866\pi$
$200$	−1940.41	−	2007.19i	−0.686039	−	0.709650i
$201$	−4081.94	−	2727.46i	−1.43243	−	0.957117i
$202$	2909.60	+	900.564i	1.01346	+	0.313680i
$203$	−843.097	−	2779.32i	−0.291497	−	0.960935i
$204$	3275.00	−	1703.32i	1.12400	−	0.584590i
$205$	303.326	−	369.603i	0.103342	−	0.125923i
$206$	1451.83	+	610.979i	0.491036	+	0.206645i
$207$	130.801	−	315.782i	0.0439194	−	0.106031i
$208$	−304.339	−	4016.87i	−0.101452	−	1.33904i
$209$	2474.18	+	5973.20i	0.818864	+	1.97691i
$210$	−4.59679	+	815.241i	−0.00151052	+	0.267890i
$211$	−4828.88	+	475.603i	−1.57552	+	0.155175i	−0.847654	−	0.530549i	$-0.821986\pi$
$211$	−4828.88	+	475.603i	−1.57552	+	0.155175i	−0.727862	+	0.685724i	$0.759486\pi$
$212$	385.871	−	3511.39i	0.125008	−	1.13756i
$213$	−337.988	−	180.659i	−0.108726	−	0.0581151i
$214$	948.319	+	787.255i	0.302924	+	0.251475i
$215$	−108.792	−	546.933i	−0.0345094	−	0.173491i
$216$	−1158.51	−	984.027i	−0.364939	−	0.309975i
$217$	3473.00	+	690.823i	1.08646	+	0.216111i
$218$	−979.215	−	102.022i	−0.304224	−	0.0316964i
$219$	−1180.29	−	116.248i	−0.364184	−	0.0358690i
$220$	−263.887	−	404.742i	−0.0808693	−	0.124035i
$221$	−4196.90	−	1273.12i	−1.27744	−	0.387507i
$222$	453.555	+	2349.33i	0.137120	+	0.710254i
$223$	3751.99	−	3751.99i	1.12669	−	1.12669i	0.135978	−	0.990712i	$-0.456582\pi$
$223$	3751.99	−	3751.99i	1.12669	−	1.12669i	0.990712	−	0.135978i	$-0.0434178\pi$
$224$	2529.30	−	5650.27i	0.754447	−	1.68538i
$225$	−1470.59	−	1470.59i	−0.435730	−	0.435730i
$226$	−337.413	+	498.862i	−0.0993114	+	0.146831i
$227$	−665.734	+	2194.63i	−0.194653	+	0.641686i	0.804224	+	0.594326i	$0.202581\pi$
$227$	−665.734	+	2194.63i	−0.194653	+	0.641686i	−0.998878	+	0.0473606i	$0.984919\pi$
$228$	1328.24	+	7094.72i	0.385810	+	2.06079i
$229$	−290.951	+	2954.08i	−0.0839590	+	0.852450i	0.857312	+	0.514797i	$0.172133\pi$
$229$	−290.951	+	2954.08i	−0.0839590	+	0.852450i	−0.941271	+	0.337652i	$0.890367\pi$
$230$	−56.6849	+	45.9877i	−0.0162508	+	0.0131841i
$231$	2096.71	−	10540.9i	0.597200	−	3.00232i
$232$	1193.81	+	1505.90i	0.337833	+	0.426151i
$233$	2355.46	−	468.530i	0.662280	−	0.131736i	0.147505	−	0.989061i	$-0.452876\pi$
$233$	2355.46	−	468.530i	0.662280	−	0.131736i	0.514774	+	0.857326i	$0.327876\pi$
$234$	−277.299	−	2988.10i	−0.0774685	−	0.834778i
$235$	220.253	−	412.063i	0.0611391	−	0.114383i
$236$	168.286	−	48.9836i	0.0464174	−	0.0135109i
$237$	113.629	+	1153.69i	0.0311434	+	0.316204i
$238$	−4738.76	−	4792.51i	−1.29062	−	1.30526i
$239$	−3121.62	+	1293.02i	−0.844858	+	0.349952i	−0.762767	−	0.646673i	$-0.776160\pi$
$239$	−3121.62	+	1293.02i	−0.844858	+	0.349952i	−0.0820907	+	0.996625i	$0.526160\pi$
$240$	−195.134	−	502.883i	−0.0524826	−	0.135254i
$241$	−800.309	−	331.499i	−0.213911	−	0.0886046i	0.273155	−	0.961970i	$-0.411933\pi$
$241$	−800.309	−	331.499i	−0.213911	−	0.0886046i	−0.487066	+	0.873365i	$0.661933\pi$
$242$	983.267	+	2412.20i	0.261185	+	0.640751i
$243$	−3205.15	−	2630.40i	−0.846133	−	0.694403i
$244$	200.383	+	2300.16i	0.0525747	+	0.603494i
$245$	1006.63	−	305.356i	0.262494	−	0.0796265i
$246$	−6224.63	+	3282.15i	−1.61328	+	0.850658i
$247$	4764.31	−	7130.29i	1.22731	−	1.83680i
$248$	−2305.33	+	418.151i	−0.590275	+	0.107067i
$249$	6928.01	−	4629.15i	1.76323	−	1.17815i
$250$	254.717	+	857.057i	0.0644389	+	0.216820i
$251$	390.660	+	476.020i	0.0982400	+	0.119706i	0.819810	−	0.572636i	$-0.194079\pi$
$251$	390.660	+	476.020i	0.0982400	+	0.119706i	−0.721570	+	0.692342i	$0.756579\pi$
$252$	1812.73	−	4240.43i	0.453141	−	1.06001i
$253$	848.638	−	453.606i	0.210883	−	0.112719i
$254$	32.8959	−	160.640i	0.00812626	−	0.0396828i
$255$	−587.268			−0.144220
$256$	−184.700	+	4091.83i	−0.0450928	+	0.998983i
$257$	−1500.59			−0.364219			−0.182109	−	0.983278i	$-0.558293\pi$
$257$	−1500.59			−0.364219			−0.182109	+	0.983278i	$0.558293\pi$
$258$	−1646.50	+	8040.31i	−0.397312	+	1.94019i
$259$	3852.68	−	2059.30i	0.924301	−	0.494049i
$260$	−251.911	+	589.281i	−0.0600878	+	0.140560i
$261$	908.173	+	1106.61i	0.215381	+	0.262443i
$262$	997.837	+	3357.46i	0.235292	+	0.791697i
$263$	705.335	−	471.290i	0.165372	−	0.110498i	−0.470130	−	0.882597i	$-0.655793\pi$
$263$	705.335	−	471.290i	0.165372	−	0.110498i	0.635502	+	0.772099i	$0.280793\pi$
$264$	1269.12	+	6996.86i	0.295868	+	1.63116i
$265$	−312.221	+	467.272i	−0.0723759	+	0.108318i
$266$	11657.1	−	6146.58i	2.68700	−	1.41681i
$267$	−2262.67	+	686.375i	−0.518627	+	0.157324i
$268$	−514.702	−	5908.16i	−0.117315	−	1.34664i
$269$	276.948	+	227.285i	0.0627725	+	0.0515161i	0.665256	−	0.746615i	$-0.268322\pi$
$269$	276.948	+	227.285i	0.0627725	+	0.0515161i	−0.602484	+	0.798131i	$0.705822\pi$
$270$	91.2781	+	223.928i	0.0205741	+	0.0504734i
$271$	−6585.01	−	2727.60i	−1.47605	−	0.611402i	−0.507824	−	0.861461i	$-0.669550\pi$
$271$	−6585.01	−	2727.60i	−1.47605	−	0.611402i	−0.968231	+	0.250059i	$0.919550\pi$
$272$	4080.38	+	1799.00i	0.909594	+	0.401032i
$273$	−13170.0	+	5455.20i	−2.91973	+	1.20939i
$274$	−884.132	−	894.159i	−0.194936	−	0.197146i
$275$	−573.890	−	5826.81i	−0.125843	−	1.27771i
$276$	1031.47	−	300.234i	0.224954	−	0.0654781i
$277$	−556.735	+	1041.58i	−0.120762	+	0.225929i	−0.935037	−	0.354549i	$-0.884634\pi$
$277$	−556.735	+	1041.58i	−0.120762	+	0.225929i	0.814276	+	0.580478i	$0.197134\pi$
$278$	90.6112	+	976.400i	0.0195486	+	0.210650i
$279$	−1711.83	+	340.505i	−0.367329	+	0.0730663i
$280$	−771.753	+	611.811i	−0.164718	+	0.130581i
$281$	1530.83	−	7696.02i	0.324989	−	1.63383i	−0.380267	−	0.924877i	$-0.624168\pi$
$281$	1530.83	−	7696.02i	0.324989	−	1.63383i	0.705256	−	0.708953i	$-0.250832\pi$
$282$	−5340.12	+	4332.37i	−1.12766	+	0.914853i
$283$	278.728	−	2829.97i	0.0585465	−	0.594433i	−0.920493	−	0.390760i	$-0.872212\pi$
$283$	278.728	−	2829.97i	0.0585465	−	0.594433i	0.979039	−	0.203673i	$-0.0652878\pi$
$284$	−85.1934	−	455.057i	−0.0178003	−	0.0950798i
$285$	333.332	−	1098.85i	0.0692803	−	0.228387i
$286$	4733.24	−	6998.06i	0.978610	−	1.44687i
$287$	9084.74	+	9084.74i	1.86849	+	1.86849i
$288$	−86.0128	+	3050.10i	−0.0175984	+	0.624058i
$289$	−41.0342	+	41.0342i	−0.00835217	+	0.00835217i
$290$	−57.9510	−	300.175i	−0.0117345	−	0.0607824i
$291$	4785.72	+	1451.73i	0.964068	+	0.292447i
$292$	−782.486	−	1200.15i	−0.156820	−	0.240526i
$293$	−2174.52	−	214.171i	−0.433572	−	0.0427031i	−0.121123	−	0.992638i	$-0.538649\pi$
$293$	−2174.52	−	214.171i	−0.433572	−	0.0427031i	−0.312449	+	0.949934i	$0.601149\pi$
$294$	−15398.3	−	1604.31i	−3.05457	−	0.318249i
$295$	−27.3476	−	5.43978i	−0.00539742	−	0.00107361i
$296$	−1871.21	+	2203.00i	−0.367438	+	0.432591i
$297$	−621.915	−	3126.58i	−0.121506	−	0.610850i
$298$	3091.89	+	2566.76i	0.601036	+	0.498955i
$299$	−1125.62	−	601.657i	−0.217713	−	0.116370i
$300$	714.014	−	6497.48i	0.137412	−	1.25044i
$301$	14912.2	−	1468.72i	2.85556	−	0.281248i
$302$	16.1262	−	2859.98i	0.00307272	−	0.544946i
$303$	2729.04	+	6588.47i	0.517422	+	1.24917i
$304$	−5682.17	+	6613.78i	−1.07202	+	1.24778i
$305$	140.565	−	339.354i	0.0263892	−	0.0637093i
$306$	3061.91	+	1288.56i	0.572019	+	0.240725i
$307$	−2731.30	+	3328.10i	−0.507764	+	0.618712i	−0.962291	−	0.272021i	$-0.912308\pi$
$307$	−2731.30	+	3328.10i	−0.507764	+	0.618712i	0.454528	+	0.890733i	$0.349808\pi$
$308$	11518.3	−	5990.65i	2.13090	−	1.10828i
$309$	1070.57	+	3529.21i	0.197096	+	0.649740i
$310$	356.068	+	110.208i	0.0652365	+	0.0201917i
$311$	−5107.40	−	3412.66i	−0.931236	−	0.622232i	−0.00532980	−	0.999986i	$-0.501697\pi$
$311$	−5107.40	−	3412.66i	−0.931236	−	0.622232i	−0.925906	+	0.377754i	$0.876697\pi$
$312$	6781.25	−	6555.63i	1.23049	−	1.18955i
$313$	3019.22	+	4518.58i	0.545228	+	0.815992i	0.997101	−	0.0760907i	$-0.0242439\pi$
$313$	3019.22	+	4518.58i	0.545228	+	0.815992i	−0.451873	+	0.892082i	$0.649244\pi$
$314$	−1358.97	−	736.267i	−0.244240	−	0.132325i
$315$	−567.125	+	465.427i	−0.101441	+	0.0832503i
$316$	−1001.36	+	979.023i	−0.178262	+	0.174286i
$317$	3154.59	+	5901.82i	0.558925	+	1.04568i	0.989692	+	0.143212i	$0.0457431\pi$
$317$	3154.59	+	5901.82i	0.558925	+	1.04568i	−0.430767	+	0.902463i	$0.641757\pi$
$318$	6902.87	−	4556.26i	1.21728	−	0.803467i
$319$			4030.23i			0.707366i
$320$	326.436	−	563.963i	0.0570261	−	0.0985202i
$321$			2885.77i			0.501769i
$322$	−1080.47	−	1636.94i	−0.186994	−	0.283302i
$323$	4474.97	+	8372.07i	0.770879	+	1.44221i
$324$	81.1916	−	7199.43i	0.0139217	−	1.23447i
$325$	−6003.19	+	4926.69i	−1.02461	+	0.840872i
$326$	4397.59	−	8116.90i	0.747117	−	1.37900i
$327$	−1280.66	−	1916.64i	−0.216576	−	0.324129i
$328$	−7797.54	−	3385.48i	−1.31264	−	0.569914i
$329$	10439.0	+	6975.10i	1.74930	+	1.16884i
$330$	334.492	−	1080.70i	0.0557975	−	0.180274i
$331$	145.897	+	480.957i	0.0242272	+	0.0798665i	0.968220	−	0.250099i	$-0.0804630\pi$
$331$	145.897	+	480.957i	0.0242272	+	0.0798665i	−0.943993	+	0.329965i	$0.892963\pi$
$332$	9598.55	+	3030.30i	1.58671	+	0.500932i
$333$	−1365.99	+	1664.47i	−0.224793	+	0.273911i
$334$	3489.89	−	8292.79i	0.571732	−	1.35857i
$335$	−361.053	+	871.660i	−0.0588849	+	0.142161i
$336$	13961.6	−	3893.63i	2.26687	−	0.632187i
$337$	−535.766	−	1293.45i	−0.0866025	−	0.209077i	0.874645	−	0.484764i	$-0.161095\pi$
$337$	−535.766	−	1293.45i	−0.0866025	−	0.209077i	−0.961247	+	0.275687i	$0.911095\pi$
$338$	−4991.76	−	28.1464i	−0.803302	−	0.00452948i
$339$	−1403.31	+	138.214i	−0.224830	+	0.0221439i
$340$	−443.846	−	553.439i	−0.0707969	−	0.0882777i
$341$	−4333.49	−	2316.30i	−0.688187	−	0.367843i
$342$	−4148.98	+	4997.82i	−0.655998	+	0.790207i
$343$	3225.95	+	16218.0i	0.507828	+	2.55303i
$344$	−8821.54	+	4525.06i	−1.38263	+	0.709229i
$345$	−167.621	−	33.3419i	−0.0261577	−	0.00520309i
$346$	469.758	−	4508.76i	0.0729895	−	0.700557i
$347$	456.312	+	44.9428i	0.0705939	+	0.00695289i	0.133252	−	0.991082i	$-0.457458\pi$
$347$	456.312	+	44.9428i	0.0705939	+	0.00695289i	−0.0626585	+	0.998035i	$0.519958\pi$
$348$	−927.497	+	4402.77i	−0.142871	+	0.678198i
$349$	−3681.90	−	1116.89i	−0.564721	−	0.171306i	−0.00500041	−	0.999987i	$-0.501592\pi$
$349$	−3681.90	−	1116.89i	−0.564721	−	0.171306i	−0.559721	+	0.828681i	$0.689092\pi$
$350$	−11717.9	+	2262.22i	−1.78956	+	0.345488i
$351$	−2989.85	+	2989.85i	−0.454663	+	0.454663i
$352$	−5634.62	+	6484.11i	−0.853200	+	0.981829i
$353$	501.031	+	501.031i	0.0755444	+	0.0755444i	0.743869	−	0.668325i	$-0.232988\pi$
$353$	501.031	+	501.031i	0.0755444	+	0.0755444i	−0.668325	+	0.743869i	$0.732988\pi$
$354$	339.922	+	229.911i	0.0510357	+	0.0345188i
$355$	−21.3800	+	70.4804i	−0.00319643	+	0.0105372i
$356$	−2356.92	−	1613.58i	−0.350889	−	0.240224i
$357$	1546.73	−	15704.3i	0.229305	−	2.32817i
$358$	7526.87	+	9277.70i	1.11119	+	1.36967i
$359$	1647.69	−	8283.50i	0.242233	−	1.21779i	−0.647770	−	0.761836i	$-0.724298\pi$
$359$	1647.69	−	8283.50i	0.242233	−	1.21779i	0.890004	−	0.455953i	$-0.150702\pi$
$360$	236.037	−	424.176i	0.0345562	−	0.0621001i
$361$	−11477.9	+	2283.10i	−1.67341	+	0.332862i
$362$	−8645.48	+	802.311i	−1.25524	+	0.116488i
$363$	−2875.07	+	5378.88i	−0.415708	+	0.777735i
$364$	−15094.6	−	8288.43i	−2.17355	−	1.19349i
$365$	22.3407	+	226.829i	0.00320375	+	0.0325282i
$366$	−3844.06	+	3800.96i	−0.548996	+	0.542839i
$367$	3758.03	−	1556.63i	0.534516	−	0.221404i	−0.0990638	−	0.995081i	$-0.531585\pi$
$367$	3758.03	−	1556.63i	0.534516	−	0.221404i	0.633580	+	0.773677i	$0.281585\pi$
$368$	1062.51	+	745.143i	0.150508	+	0.105552i
$369$	−5850.59	−	2423.39i	−0.825391	−	0.341888i
$370$	425.817	−	173.573i	0.0598302	−	0.0243881i
$371$	−11673.1	−	9579.86i	−1.63352	−	1.34060i
$372$	−4200.99	−	3527.69i	−0.585514	−	0.491673i
$373$	6995.54	−	2122.07i	0.971086	−	0.294576i	0.235400	−	0.971898i	$-0.424360\pi$
$373$	6995.54	−	2122.07i	0.971086	−	0.294576i	0.735686	+	0.677323i	$0.236860\pi$
$374$	4362.08	+	8272.74i	0.603096	+	1.14378i
$375$	−1163.05	+	1740.63i	−0.160159	+	0.239695i
$376$	−8118.76	−	1758.18i	−1.11355	−	0.241147i
$377$	4444.74	−	2969.88i	0.607203	−	0.405720i
$378$	−6228.50	+	1851.11i	−0.847513	+	0.251881i
$379$	3024.69	+	3685.60i	0.409942	+	0.499516i	0.936521	−	0.350610i	$-0.114026\pi$
$379$	3024.69	+	3685.60i	0.409942	+	0.499516i	−0.526580	+	0.850126i	$0.676526\pi$
$380$	1287.48	−	516.359i	0.173806	−	0.0697069i
$381$	338.589	−	180.980i	0.0455288	−	0.0243356i
$382$	−2979.85	−	610.215i	−0.399116	−	0.0817311i
$383$	−9144.26			−1.21997			−0.609987	−	0.792412i	$-0.708825\pi$
$383$	−9144.26			−1.21997			−0.609987	+	0.792412i	$0.708825\pi$
$384$	−7647.67	+	5786.74i	−1.01632	+	0.769019i
$385$	−2065.44			−0.273415
$386$	3547.07	+	726.372i	0.467724	+	0.0957807i
$387$	−6513.63	+	3481.61i	−0.855572	+	0.457313i
$388$	2248.85	+	5607.23i	0.294248	+	0.733670i
$389$	−2657.22	−	3237.84i	−0.346341	−	0.422018i	0.570483	−	0.821309i	$-0.306756\pi$
$389$	−2657.22	−	3237.84i	−0.346341	−	0.422018i	−0.916824	+	0.399292i	$0.869256\pi$
$390$	−1438.33	+	427.472i	−0.186751	+	0.0555023i
$391$	1174.76	−	784.953i	0.151945	−	0.101526i
$392$	−10125.8	−	15723.8i	−1.30467	−	2.02594i
$393$	−4556.18	+	6818.80i	−0.584806	+	0.875224i
$394$	−5187.53	−	9838.21i	−0.663309	−	1.25797i
$395$	213.198	−	64.6730i	0.0271574	−	0.00823810i
$396$	−4115.20	+	4900.63i	−0.522213	+	0.621884i
$397$	−3482.85	−	2858.30i	−0.440300	−	0.361345i	0.387972	−	0.921671i	$-0.373176\pi$
$397$	−3482.85	−	2858.30i	−0.440300	−	0.361345i	−0.828272	+	0.560326i	$0.810676\pi$
$398$	10442.8	−	4256.72i	1.31520	−	0.536106i
$399$	28506.6	+	11807.8i	3.57673	+	1.48153i
$400$	6662.83	−	4237.79i	0.832853	−	0.529723i
$401$	260.526	−	107.913i	0.0324440	−	0.0134388i	−0.366402	−	0.930456i	$-0.619411\pi$
$401$	260.526	−	107.913i	0.0324440	−	0.0134388i	0.398846	+	0.917018i	$0.369411\pi$
$402$	9873.82	−	9763.09i	1.22503	−	1.21129i
$403$	638.821	+	6486.06i	0.0789627	+	0.801721i
$404$	−4146.39	+	7551.27i	−0.510621	+	0.929925i
$405$	−539.945	+	1010.17i	−0.0662471	+	0.123940i
$406$	8179.68	−	759.085i	0.999878	−	0.0927900i
$407$	−5945.44	+	1182.62i	−0.724090	+	0.144030i
$408$	2861.44	+	10041.3i	0.347212	+	1.21843i
$409$	−452.237	+	2273.55i	−0.0546740	+	0.274865i	−0.998446	−	0.0557331i	$-0.982250\pi$
$409$	−452.237	+	2273.55i	−0.0546740	+	0.274865i	0.943772	+	0.330598i	$0.107250\pi$
$410$	852.027	+	1050.22i	0.102631	+	0.126504i
$411$	288.581	−	2930.01i	0.0346342	−	0.351647i
$412$	−2516.79	+	3676.21i	−0.300955	+	0.439597i
$413$	217.494	−	716.981i	0.0259132	−	0.0854245i
$414$	800.788	+	541.625i	0.0950642	+	0.0642981i
$415$	−1132.29	−	1132.29i	−0.133933	−	0.133933i
$416$	11303.1	+	1436.00i	1.33217	+	0.169244i
$417$	−1623.48	+	1623.48i	−0.190652	+	0.190652i
$418$	−17955.2	+	3466.38i	−2.10100	+	0.405613i
$419$	−6115.85	−	1855.22i	−0.713076	−	0.216309i	−0.0871541	−	0.996195i	$-0.527777\pi$
$419$	−6115.85	−	1855.22i	−0.713076	−	0.216309i	−0.625922	+	0.779886i	$0.715277\pi$
$420$	−2256.36	−	475.331i	−0.262141	−	0.0552232i
$421$	−809.007	−	79.6803i	−0.0936547	−	0.00922418i	0.0510812	−	0.998695i	$-0.483733\pi$
$421$	−809.007	−	79.6803i	−0.0936547	−	0.00922418i	−0.144736	+	0.989470i	$0.546233\pi$
$422$	1422.20	−	13650.3i	0.164056	−	1.57462i
$423$	−6069.35	−	1207.27i	−0.697640	−	0.138769i
$424$	9510.85	+	3061.69i	1.08936	+	0.350682i
$425$	−1677.16	−	8431.65i	−0.191422	−	0.962342i
$426$	692.376	−	834.029i	0.0787459	−	0.0948564i
$427$	8704.50	+	4652.65i	0.986512	+	0.527301i
$428$	−2719.53	+	2181.01i	−0.307134	+	0.246315i
$429$	19685.7	−	1938.88i	2.21547	−	0.218205i
$430$	1577.24	+	8.89339i	0.176887	+	0.000997389i
$431$	768.796	+	1856.04i	0.0859202	+	0.207430i	0.961000	−	0.276550i	$-0.0891910\pi$
$431$	768.796	+	1856.04i	0.0859202	+	0.207430i	−0.875079	+	0.483979i	$0.839191\pi$
$432$	3384.04	−	2651.78i	0.376886	−	0.295333i
$433$	4010.80	−	9682.92i	0.445142	−	1.07467i	−0.528977	−	0.848636i	$-0.677424\pi$
$433$	4010.80	−	9682.92i	0.445142	−	1.07467i	0.974120	−	0.226033i	$-0.0725757\pi$
$434$	−3884.91	+	9231.43i	−0.429681	+	1.02102i
$435$	454.099	−	553.321i	0.0500515	−	0.0609879i
$436$	838.334	−	2655.44i	0.0920847	−	0.291680i
$437$	801.946	+	2643.66i	0.0877856	+	0.289390i
$438$	991.846	−	3204.52i	0.108201	−	0.349584i
$439$	12358.5	+	8257.70i	1.34360	+	0.897764i	0.999157	−	0.0410432i	$-0.0130681\pi$
$439$	12358.5	+	8257.70i	1.34360	+	0.897764i	0.344442	+	0.938808i	$0.388068\pi$
$440$	1271.25	−	501.547i	0.137737	−	0.0543416i
$441$	−7740.26	−	11584.1i	−0.835791	−	1.25085i
$442$	5909.16	−	10906.9i	0.635906	−	1.17373i
$443$	−253.312	+	207.888i	−0.0271675	+	0.0222958i	−0.647879	−	0.761743i	$-0.724344\pi$
$443$	−253.312	+	207.888i	−0.0271675	+	0.0222958i	0.620712	+	0.784039i	$0.286844\pi$
$444$	−6767.17	−	76.3168i	−0.723323	−	0.00815728i
$445$	214.208	+	400.755i	0.0228189	+	0.0426912i
$446$	8267.49	+	12525.5i	0.877751	+	1.32982i
$447$			9408.74i			0.995566i
$448$	14221.3	+	10214.6i	1.49976	+	1.07722i
$449$			9827.26i			1.03291i	0.856314	+	0.516455i	$0.172749\pi$
$449$			9827.26i			1.03291i	−0.856314	+	0.516455i	$0.827251\pi$
$450$	4909.35	−	3240.43i	0.514287	−	0.339457i
$451$	−8404.10	−	15723.0i	−0.877458	−	1.64161i
$452$	−1190.85	−	1218.02i	−0.123922	−	0.126749i
$453$	5176.39	−	4248.15i	0.536883	−	0.440608i
$454$	−5703.40	−	3090.00i	−0.589590	−	0.319429i
$455$	1522.03	+	2277.87i	0.156821	+	0.234699i
$456$	−20412.6	−	345.323i	−2.09629	−	0.0354633i
$457$	6224.60	+	4159.15i	0.637144	+	0.425726i	0.831746	−	0.555156i	$-0.187342\pi$
$457$	6224.60	+	4159.15i	0.637144	+	0.425726i	−0.194602	+	0.980882i	$0.562342\pi$
$458$	−8020.43	−	2482.44i	−0.818276	−	0.253268i
$459$	−1358.72	−	4479.12i	−0.138170	−	0.455484i
$460$	−95.2635	−	183.164i	−0.00965583	−	0.0185654i
$461$	4335.85	−	5283.25i	0.438049	−	0.533764i	−0.506454	−	0.862267i	$-0.669044\pi$
$461$	4335.85	−	5283.25i	0.438049	−	0.533764i	0.944503	+	0.328503i	$0.106544\pi$
$462$	28018.2	+	11791.0i	2.82148	+	1.18738i
$463$	6292.53	−	15191.5i	0.631617	−	1.52486i	−0.205972	−	0.978558i	$-0.566035\pi$
$463$	6292.53	−	15191.5i	0.631617	−	1.52486i	0.837589	−	0.546301i	$-0.183965\pi$
$464$	−4850.13	+	2453.46i	−0.485262	+	0.245472i
$465$	333.971	+	806.279i	0.0333066	+	0.0804092i
$466$	−38.3009	+	6792.65i	−0.00380741	+	0.675244i
$467$	−1476.39	+	145.411i	−0.146293	+	0.0144086i	−0.170899	−	0.985289i	$-0.554667\pi$
$467$	−1476.39	+	145.411i	−0.146293	+	0.0144086i	0.0246053	+	0.999697i	$0.492167\pi$
$468$	8437.14	+	927.166i	0.833348	+	0.0915774i
$469$	−22358.3	−	11950.8i	−2.20130	−	1.17662i
$470$	1016.82	+	844.121i	0.0997922	+	0.0828434i
$471$	−706.001	−	3549.30i	−0.0690675	−	0.347226i
$472$	40.2391	+	494.103i	0.00392405	+	0.0481842i
$473$	−20393.3	−	4056.48i	−1.98242	−	0.394328i
$474$	−3261.27	−	339.785i	−0.316024	−	0.0329258i
$475$	16728.6	+	1647.62i	1.61592	+	0.159154i
$476$	15968.6	−	10411.3i	1.53765	−	1.00253i
$477$	7122.66	+	2160.63i	0.683698	+	0.207398i
$478$	−1811.55	−	9383.48i	−0.173344	−	0.897888i
$479$	−9447.61	+	9447.61i	−0.901194	+	0.901194i	−0.995540	−	0.0943451i	$-0.969924\pi$
$479$	−9447.61	+	9447.61i	−0.901194	+	0.901194i	0.0943451	+	0.995540i	$0.469924\pi$
$480$	1504.18	−	255.349i	0.143033	−	0.0242813i
$481$	5685.45	+	5685.45i	0.538948	+	0.538948i
$482$	1372.68	−	2029.49i	0.129717	−	0.191786i
$483$	1333.08	−	4394.57i	0.125584	−	0.413996i
$484$	−7241.95	+	1355.80i	−0.680123	+	0.127329i
$485$	94.2055	−	956.484i	0.00881990	−	0.0895499i
$486$	9107.33	−	7388.65i	0.850035	−	0.689621i
$487$	−3387.09	+	17028.1i	−0.315162	+	1.58442i	0.420640	+	0.907228i	$0.361806\pi$
$487$	−3387.09	+	17028.1i	−0.315162	+	1.58442i	−0.735802	+	0.677197i	$0.763194\pi$
$488$	−6487.27	−	749.936i	−0.601772	−	0.0695656i
$489$	21199.4	−	4216.81i	1.96047	−	0.389961i
$490$	274.929	+	2962.55i	0.0253469	+	0.273131i
$491$	−9858.97	+	18444.8i	−0.906169	+	1.69532i	−0.209660	+	0.977774i	$0.567236\pi$
$491$	−9858.97	+	18444.8i	−0.906169	+	1.69532i	−0.696509	+	0.717548i	$0.745264\pi$
$492$	−5562.52	−	19110.4i	−0.509711	−	1.75114i
$493$	580.021	+	5889.06i	0.0529875	+	0.537991i
$494$	17054.1	+	17247.5i	1.55324	+	1.57085i
$495$	940.557	−	389.592i	0.0854039	−	0.0353754i
$496$	149.449	−	6625.15i	0.0135292	−	0.599754i
$497$	−1828.42	−	757.357i	−0.165022	−	0.0683543i
$498$	8895.85	+	21823.7i	0.800467	+	1.96374i
$499$	5742.69	+	4712.91i	0.515187	+	0.422803i	0.855727	−	0.517427i	$-0.173110\pi$
$499$	5742.69	+	4712.91i	0.515187	+	0.422803i	−0.340541	+	0.940230i	$0.610610\pi$
$500$	−2519.37	+	219.481i	−0.225340	+	0.0196309i
$501$	20158.7	−	6115.08i	1.79766	−	0.545313i
$502$	−1540.69	+	812.380i	−0.136981	+	0.0722277i
$503$	7289.34	−	10909.3i	0.646154	−	0.967038i	−0.353348	−	0.935492i	$-0.614957\pi$
$503$	7289.34	−	10909.3i	0.646154	−	0.967038i	0.999502	−	0.0315460i	$-0.0100431\pi$
$504$	10721.3	+	7429.10i	0.947550	+	0.656584i
$505$	1139.53	−	761.413i	0.100413	−	0.0670939i
$506$	775.365	+	2608.90i	0.0681209	+	0.229209i
$507$	−7414.64	−	9034.77i	−0.649499	−	0.791417i
$508$	426.454	+	182.304i	0.0372457	+	0.0159221i
$509$	3778.66	−	2019.74i	0.329050	−	0.175881i	−0.298597	−	0.954379i	$-0.596518\pi$
$509$	3778.66	−	2019.74i	0.329050	−	0.175881i	0.627646	+	0.778499i	$0.284018\pi$
$510$	333.235	−	1627.28i	0.0289331	−	0.141288i
$511$	−6124.53			−0.530202
$512$	−11233.4	−	2833.63i	−0.969627	−	0.244589i
$513$	9152.17			0.787677
$514$	851.482	−	4158.02i	0.0730686	−	0.356814i
$515$	625.077	−	334.111i	0.0534839	−	0.0285877i
$516$	−21344.8	−	9124.65i	−1.82103	−	0.778470i
$517$	−11052.2	−	13467.1i	−0.940180	−	1.14561i
$518$	3520.03	+	11844.0i	0.298574	+	1.00462i
$519$	8825.09	−	5896.74i	0.746394	−	0.498724i
$520$	−1489.91	−	1032.40i	−0.125648	−	0.0870650i
$521$	−8522.46	+	12754.8i	−0.716652	+	1.07255i	0.277090	+	0.960844i	$0.410630\pi$
$521$	−8522.46	+	12754.8i	−0.716652	+	1.07255i	−0.993742	+	0.111702i	$0.964370\pi$
$522$	−3581.66	+	1888.55i	−0.300316	+	0.158352i
$523$	3748.09	−	1136.97i	0.313370	−	0.0950598i	−0.129682	−	0.991556i	$-0.541396\pi$
$523$	3748.09	−	1136.97i	0.313370	−	0.0950598i	0.443052	+	0.896496i	$0.353896\pi$
$524$	−9869.48	+	859.801i	−0.822806	+	0.0716805i
$525$	−21599.9	−	17726.6i	−1.79561	−	1.47362i
$526$	905.679	+	2221.85i	0.0750751	+	0.184178i
$527$	−6665.54	−	2760.96i	−0.550959	−	0.228215i
$528$	−20107.9	−	453.592i	−1.65736	−	0.0373864i
$529$	−10861.0	+	4498.76i	−0.892658	+	0.369751i
$530$	−1117.61	−	1130.29i	−0.0915962	−	0.0926350i
$531$	36.1977	+	367.522i	0.00295828	+	0.0300359i
$532$	10417.1	+	35788.6i	0.848946	+	2.91660i
$533$	−11147.1	+	20854.7i	−0.905878	+	1.69478i
$534$	−617.979	−	6659.17i	−0.0500797	−	0.539645i
$535$	543.935	−	108.195i	0.0439558	−	0.00874335i
$536$	16663.1	+	1926.28i	1.34279	+	0.155229i
$537$	−5457.12	+	27434.8i	−0.438533	+	2.20465i
$538$	−786.939	+	638.433i	−0.0630620	+	0.0511613i
$539$	3844.49	−	39033.8i	0.307224	−	3.11930i
$540$	−672.281	+	125.861i	−0.0535748	+	0.0100300i
$541$	1819.20	−	5997.10i	0.144572	−	0.476591i	−0.854509	−	0.519436i	$-0.826142\pi$
$541$	1819.20	−	5997.10i	0.144572	−	0.476591i	0.999082	+	0.0428450i	$0.0136422\pi$
$542$	11294.5	−	16698.8i	0.895094	−	1.32339i
$543$	−14375.0	−	14375.0i	−1.13608	−	1.13608i
$544$	−7300.24	+	10285.6i	−0.575359	+	0.810648i
$545$	−313.249	+	313.249i	−0.0246204	+	0.0246204i
$546$	−7642.86	−	39588.6i	−0.599056	−	3.10299i
$547$	17334.4	+	5258.33i	1.35496	+	0.411024i	0.882495	−	0.470323i	$-0.155862\pi$
$547$	17334.4	+	5258.33i	1.35496	+	0.411024i	0.472470	+	0.881347i	$0.343362\pi$
$548$	2979.33	−	1942.49i	0.232246	−	0.151422i
$549$	−4841.44	−	476.840i	−0.376371	−	0.0370693i
$550$	16471.3	+	1716.11i	1.27698	+	0.133046i
$551$	−11348.3	−	2257.33i	−0.877416	−	0.174529i
$552$	246.636	+	3028.49i	0.0190173	+	0.233517i
$553$	1167.92	+	5871.51i	0.0898098	+	0.451504i
$554$	−2570.22	−	2133.69i	−0.197109	−	0.163632i
$555$	949.515	+	507.526i	0.0726210	+	0.0388167i
$556$	−2756.95	−	302.964i	−0.210289	−	0.0231088i
$557$	−6734.39	+	663.280i	−0.512290	+	0.0504561i	−0.350860	−	0.936428i	$-0.614111\pi$
$557$	−6734.39	+	663.280i	−0.512290	+	0.0504561i	−0.161430	+	0.986884i	$0.551611\pi$
$558$	27.8352	−	4936.57i	0.00211176	−	0.374519i
$559$	10554.1	+	25479.9i	0.798556	+	1.92788i
$560$	−1257.37	−	2485.63i	−0.0948811	−	0.187566i
$561$	−8379.73	+	20230.5i	−0.630646	+	1.52251i
$562$	20456.5	+	8608.79i	1.53542	+	0.646157i
$563$	8116.18	−	9889.59i	0.607560	−	0.740314i	−0.374843	−	0.927088i	$-0.622303\pi$
$563$	8116.18	−	9889.59i	0.607560	−	0.740314i	0.982403	+	0.186775i	$0.0598034\pi$
$564$	−8974.50	−	17255.4i	−0.670026	−	1.28827i
$565$	78.6659	+	259.327i	0.00585752	+	0.0193097i
$566$	7683.48	+	2378.15i	0.570602	+	0.176610i
$567$	−25591.0	−	17099.3i	−1.89545	−	1.26650i
$568$	1309.27	+	22.1491i	0.0967178	+	0.00163619i
$569$	−12304.7	−	18415.3i	−0.906574	−	1.35678i	−0.934043	−	0.357161i	$-0.883745\pi$
$569$	−12304.7	−	18415.3i	−0.906574	−	1.35678i	0.0274693	−	0.999623i	$-0.491255\pi$
$570$	2855.68	+	1547.16i	0.209845	+	0.113690i
$571$	3534.41	−	2900.62i	0.259038	−	0.212587i	−0.495906	−	0.868376i	$-0.665164\pi$
$571$	3534.41	−	2900.62i	0.259038	−	0.212587i	0.754944	+	0.655789i	$0.227664\pi$
$572$	16705.3	+	17086.4i	1.22112	+	1.24898i
$573$	−3357.16	−	6280.80i	−0.244759	−	0.457913i
$574$	−30328.1	+	20018.2i	−2.20535	+	1.45565i
$575$		−	2501.82i		−	0.181449i
$576$	−8402.78	−	1969.06i	−0.607840	−	0.142437i
$577$			8655.14i			0.624468i	0.950005	+	0.312234i	$0.101077\pi$
$577$			8655.14i			0.624468i	−0.950005	+	0.312234i	$0.898923\pi$
$578$	−90.4186	−	136.987i	−0.00650678	−	0.00985796i
$579$	3996.21	+	7476.38i	0.286834	+	0.536628i
$580$	864.647	+	9.75106i	0.0619009	+	0.000698087i
$581$	33261.1	−	27296.7i	2.37505	−	1.94915i
$582$	−6738.21	+	12437.1i	−0.479910	+	0.885798i
$583$	11641.7	+	17423.0i	0.827016	+	1.23772i
$584$	3769.54	−	1487.20i	0.267097	−	0.105378i
$585$	−1122.76	−	750.202i	−0.0793509	−	0.0530206i
$586$	1827.34	−	5903.89i	0.128817	−	0.416190i
$587$	−6473.28	−	21339.5i	−0.455163	−	1.50047i	−0.821619	−	0.570037i	$-0.806929\pi$
$587$	−6473.28	−	21339.5i	−0.455163	−	1.50047i	0.366456	−	0.930436i	$-0.380571\pi$
$588$	13182.9	−	41757.1i	0.924580	−	2.92863i
$589$	8949.42	−	10904.9i	0.626069	−	0.762867i
$590$	30.5911	−	72.6915i	0.00213460	−	0.00507231i
$591$	9965.45	−	24058.7i	0.693610	−	1.67452i
$592$	−5042.57	−	6435.02i	−0.350082	−	0.446753i
$593$	−9720.77	−	23468.0i	−0.673160	−	1.62515i	−0.776208	−	0.630476i	$-0.782860\pi$
$593$	−9720.77	−	23468.0i	−0.673160	−	1.62515i	0.103048	−	0.994676i	$-0.467140\pi$
$594$	9016.41	+	50.8397i	0.622808	+	0.00351175i
$595$	−3018.07	+	297.254i	−0.207947	+	0.0204810i
$596$	−8866.75	+	7110.94i	−0.609389	+	0.488717i
$597$	23286.0	+	12446.7i	1.59637	+	0.853279i
$598$	2305.86	−	2777.61i	0.157681	−	0.189941i
$599$	5478.42	+	27541.9i	0.373693	+	1.87868i	0.468941	+	0.883230i	$0.344636\pi$
$599$	5478.42	+	27541.9i	0.373693	+	1.87868i	−0.0952476	+	0.995454i	$0.530364\pi$
$600$	17598.9	+	5665.35i	1.19745	+	0.385478i
$601$	168.047	+	33.4266i	0.0114056	+	0.00226872i	0.200790	−	0.979634i	$-0.435649\pi$
$601$	168.047	+	33.4266i	0.0114056	+	0.00226872i	−0.189384	+	0.981903i	$0.560649\pi$
$602$	−4391.92	+	42153.9i	−0.297344	+	2.85393i
$603$	12435.7	+	1224.81i	0.839833	+	0.0827164i
$604$	7915.65	+	1667.53i	0.533250	+	0.112336i
$605$	1121.65	+	340.250i	0.0753747	+	0.0228647i
$606$	−19804.7	+	3823.44i	−1.32758	+	0.256298i
$607$	−10143.0	+	10143.0i	−0.678241	+	0.678241i	−0.959602	−	0.281361i	$-0.909214\pi$
$607$	−10143.0	+	10143.0i	−0.678241	+	0.678241i	0.281361	+	0.959602i	$0.409214\pi$
$608$	−15102.0	−	19497.7i	−1.00735	−	1.30056i
$609$	13600.5	+	13600.5i	0.904957	+	0.904957i
$610$	860.562	+	582.055i	0.0571199	+	0.0386339i
$611$	−6707.83	+	22112.7i	−0.444140	+	1.46413i
$612$	−5307.92	+	7753.15i	−0.350588	+	0.512095i
$613$	1621.67	−	16465.1i	0.106849	−	1.08486i	−0.780938	−	0.624608i	$-0.785259\pi$
$613$	1621.67	−	16465.1i	0.106849	−	1.08486i	0.887788	−	0.460253i	$-0.152241\pi$
$614$	−7672.08	−	9456.69i	−0.504267	−	0.621565i
$615$	−617.735	+	3105.56i	−0.0405032	+	0.203623i
$616$	10063.8	+	35315.6i	0.658249	+	2.30991i
$617$	−9079.46	+	1806.02i	−0.592423	+	0.117840i	−0.482192	−	0.876066i	$-0.660159\pi$
$617$	−9079.46	+	1806.02i	−0.592423	+	0.117840i	−0.110231	+	0.993906i	$0.535159\pi$
$618$	−10386.6	+	963.894i	−0.676071	+	0.0627403i
$619$	−6180.76	+	11563.4i	−0.401334	+	0.750843i	−0.998692	−	0.0511315i	$-0.983717\pi$
$619$	−6180.76	+	11563.4i	−0.401334	+	0.750843i	0.597358	+	0.801975i	$0.296217\pi$
$620$	−507.424	+	924.103i	−0.0328687	+	0.0598595i
$621$	−133.514	−	1355.59i	−0.00862760	−	0.0875975i
$622$	12354.3	−	12215.8i	0.796404	−	0.787473i
$623$	−11280.8	+	4672.67i	−0.725453	+	0.300492i
$624$	14317.3	+	22510.2i	0.918508	+	1.44412i
$625$	−13876.9	−	5747.98i	−0.888119	−	0.367871i
$626$	−14233.9	+	5802.04i	−0.908785	+	0.370441i
$627$	−33097.3	−	27162.3i	−2.10810	−	1.73007i
$628$	2811.27	−	3347.83i	0.178633	−	0.212727i
$629$	−8517.40	+	2583.72i	−0.539922	+	0.163783i
$630$	−967.859	−	1835.56i	−0.0612070	−	0.116080i
$631$	−899.277	+	1345.86i	−0.0567348	+	0.0849096i	−0.858752	−	0.512391i	$-0.828760\pi$
$631$	−899.277	+	1345.86i	−0.0567348	+	0.0849096i	0.802018	+	0.597300i	$0.203760\pi$
$632$	−2144.60	−	3330.21i	−0.134980	−	0.209602i
$633$	26718.1	−	17852.4i	1.67764	−	1.12097i
$634$	−18143.5	+	5392.24i	−1.13655	+	0.337781i
$635$	−46.8073	−	57.0349i	−0.00292518	−	0.00356435i
$636$	8708.15	+	21712.7i	0.542925	+	1.35372i
$637$	−45881.3	+	24524.1i	−2.85382	+	1.52540i
$638$	−11167.5	−	2286.88i	−0.692985	−	0.141910i
$639$	975.477			0.0603901
$640$	1377.47	+	1224.54i	0.0850769	+	0.0756316i
$641$	13121.0			0.808497			0.404248	−	0.914649i	$-0.367533\pi$
$641$	13121.0			0.808497			0.404248	+	0.914649i	$0.367533\pi$
$642$	−7996.24	−	1637.47i	−0.491568	−	0.100664i
$643$	−16751.2	+	8953.71i	−1.02738	+	0.549145i	−0.896866	−	0.442302i	$-0.854162\pi$
$643$	−16751.2	+	8953.71i	−1.02738	+	0.549145i	−0.130511	+	0.991447i	$0.541662\pi$
$644$	5148.94	−	2065.05i	0.315057	−	0.126357i
$645$	2342.79	+	2854.70i	0.143019	+	0.174270i
$646$	−25737.6	+	7649.21i	−1.56754	+	0.465874i
$647$	3999.60	−	2672.45i	0.243030	−	0.162388i	−0.428090	−	0.903736i	$-0.640813\pi$
$647$	3999.60	−	2672.45i	0.243030	−	0.162388i	0.671120	+	0.741348i	$0.265813\pi$
$648$	19903.0	+	4310.16i	1.20658	+	0.261295i
$649$	−577.615	+	864.462i	−0.0349359	+	0.0522852i
$650$	−10245.1	−	19429.9i	−0.618223	−	1.17247i
$651$	−22440.5	+	6807.24i	−1.35101	+	0.409826i
$652$	19996.0	+	16791.2i	1.20108	+	1.00858i
$653$	6127.81	+	5028.97i	0.367228	+	0.301376i	0.799851	−	0.600199i	$-0.204912\pi$
$653$	6127.81	+	5028.97i	0.367228	+	0.301376i	−0.432623	+	0.901575i	$0.642412\pi$
$654$	6037.54	−	2461.04i	0.360989	−	0.147147i
$655$	1456.09	+	603.133i	0.0868614	+	0.0359792i
$656$	13805.5	−	19685.4i	0.821667	−	1.17162i
$657$	2788.97	−	1155.23i	0.165614	−	0.0685994i
$658$	−25250.9	+	24967.7i	−1.49602	+	1.47924i
$659$	1445.92	+	14680.6i	0.0854702	+	0.867794i	0.938350	+	0.345687i	$0.112354\pi$
$659$	1445.92	+	14680.6i	0.0854702	+	0.867794i	−0.852880	+	0.522107i	$0.825146\pi$
$660$	2804.73	+	1540.07i	0.165415	+	0.0908292i
$661$	9958.58	−	18631.2i	0.585997	−	1.09632i	−0.397873	−	0.917440i	$-0.630252\pi$
$661$	9958.58	−	18631.2i	0.585997	−	1.09632i	0.983870	−	0.178883i	$-0.0572483\pi$
$662$	−1415.48	+	131.359i	−0.0831032	+	0.00771208i
$663$	28486.1	−	5666.25i	1.66864	−	0.331914i
$664$	−13843.3	+	24877.4i	−0.809070	+	1.45396i
$665$	1156.85	−	5815.89i	0.0674598	−	0.339143i
$666$	−3837.00	−	4729.53i	−0.223245	−	0.275174i
$667$	−168.796	+	1713.81i	−0.00979881	+	0.0994890i
$668$	20998.4	+	14375.8i	1.21625	+	0.832661i
$669$	−10200.4	+	33626.2i	−0.589491	+	1.94329i
$670$	−2210.43	−	1495.06i	−0.127457	−	0.0862077i
$671$	−9684.47	−	9684.47i	−0.557176	−	0.557176i
$672$	2866.67	+	40896.0i	0.164560	+	2.34762i
$673$	8373.01	−	8373.01i	0.479578	−	0.479578i	−0.425419	−	0.904997i	$-0.639873\pi$
$673$	8373.01	−	8373.01i	0.479578	−	0.479578i	0.904997	+	0.425419i	$0.139873\pi$
$674$	3888.08	−	750.621i	0.222200	−	0.0428974i
$675$	−7931.30	−	2405.93i	−0.452261	−	0.137192i
$676$	2910.48	−	13815.8i	0.165594	−	0.786062i
$677$	4937.56	+	486.307i	0.280304	+	0.0276076i	0.237192	−	0.971463i	$-0.423773\pi$
$677$	4937.56	+	486.307i	0.280304	+	0.0276076i	0.0431118	+	0.999070i	$0.486273\pi$
$678$	413.303	−	3966.90i	0.0234112	−	0.224702i
$679$	25329.4	+	5038.33i	1.43160	+	0.284762i
$680$	1785.39	−	915.825i	0.100686	−	0.0516475i
$681$	−2962.98	−	14895.9i	−0.166728	−	0.838196i
$682$	8877.25	−	10693.4i	0.498427	−	0.600400i
$683$	25044.4	+	13386.5i	1.40307	+	0.749958i	0.987203	−	0.159466i	$-0.0509771\pi$
$683$	25044.4	+	13386.5i	1.40307	+	0.749958i	0.415870	+	0.909424i	$0.363477\pi$
$684$	−11494.3	−	14332.4i	−0.642538	−	0.801190i
$685$	−563.094	+	55.4599i	−0.0314083	+	0.00309345i
$686$	−46769.3	−	263.712i	−2.60300	−	0.0146772i
$687$	−7522.70	−	18161.4i	−0.417771	−	1.00859i
$688$	−7532.97	−	27011.5i	−0.417430	−	1.49681i
$689$	10636.2	−	25678.1i	0.588109	−	1.41982i
$690$	187.501	−	445.546i	0.0103450	−	0.0245821i
$691$	−1945.13	+	2370.14i	−0.107086	+	0.130484i	−0.823795	−	0.566888i	$-0.808147\pi$
$691$	−1945.13	+	2370.14i	−0.107086	+	0.130484i	0.716710	+	0.697372i	$0.245647\pi$
$692$	12226.9	+	3860.08i	0.671671	+	0.212049i
$693$	7940.93	+	26177.7i	0.435283	+	1.43493i
$694$	−383.459	+	1238.90i	−0.0209739	+	0.0677639i
$695$	366.876	+	245.138i	0.0200236	+	0.0133793i
$696$	−11673.4	−	5068.29i	−0.635748	−	0.276025i
$697$	−14543.0	−	21765.2i	−0.790326	−	1.18281i
$698$	5184.05	−	9568.51i	0.281117	−	0.518873i
$699$	−12294.3	+	10089.6i	−0.665253	+	0.545959i
$700$	380.650	−	33753.0i	0.0205532	−	1.82249i
$701$	17243.9	+	32261.1i	0.929091	+	1.73821i	0.614359	+	0.789027i	$0.289415\pi$
$701$	17243.9	+	32261.1i	0.929091	+	1.73821i	0.314732	+	0.949181i	$0.398085\pi$
$702$	−6588.12	−	9981.20i	−0.354206	−	0.536632i
$703$		−	17403.6i		−	0.933697i
$704$	−14769.7	−	19292.4i	−0.790702	−	1.03283i
$705$			3094.21i			0.165298i
$706$	−1672.62	+	1104.02i	−0.0891641	+	0.0588530i
$707$	17359.8	+	32477.9i	0.923455	+	1.72766i
$708$	−829.949	+	811.439i	−0.0440557	+	0.0430731i
$709$	−23745.7	+	19487.6i	−1.25781	+	1.03226i	−0.260034	+	0.965600i	$0.583734\pi$
$709$	−23745.7	+	19487.6i	−1.25781	+	1.03226i	−0.997776	+	0.0666581i	$0.978766\pi$
$710$	−183.164	−	99.2352i	−0.00968173	−	0.00524539i
$711$	−1639.35	−	2453.46i	−0.0864703	−	0.129412i
$712$	5808.51	−	5615.25i	0.305735	−	0.295562i
$713$	−1745.76	−	1166.48i	−0.0916959	−	0.0612692i
$714$	42637.6	+	13197.0i	2.23484	+	0.691715i
$715$	−1103.53	−	3637.85i	−0.0577198	−	0.190277i
$716$	−29978.8	+	15591.9i	−1.56475	+	0.813823i
$717$	14195.1	−	17296.8i	0.739368	−	0.900923i
$718$	22018.0	+	9265.94i	1.14443	+	0.481618i
$719$	5168.43	−	12477.7i	0.268080	−	0.647203i	−0.731313	−	0.682042i	$-0.761092\pi$
$719$	5168.43	−	12477.7i	0.268080	−	0.647203i	0.999393	+	0.0348393i	$0.0110919\pi$
$720$	1041.43	+	894.732i	0.0539050	+	0.0463121i
$721$	7288.21	+	17595.3i	0.376459	+	0.908853i
$722$	186.637	−	33100.0i	0.00962036	−	1.70617i
$723$	5709.02	−	562.290i	0.293666	−	0.0289236i
$724$	2682.57	−	24411.2i	0.137703	−	1.25309i
$725$	9241.11	+	4939.48i	0.473388	+	0.253031i
$726$	−13273.1	−	11018.7i	−0.678525	−	0.563284i
$727$	2752.00	+	13835.2i	0.140393	+	0.705804i	0.985292	+	0.170878i	$0.0546605\pi$
$727$	2752.00	+	13835.2i	0.140393	+	0.705804i	−0.844899	+	0.534926i	$0.820340\pi$
$728$	31531.8	−	37122.9i	1.60528	−	1.88993i
$729$	3098.29	+	616.287i	0.157409	+	0.0313106i
$730$	−641.204	−	66.8056i	−0.0325096	−	0.00338711i
$731$	−30382.9	−	2992.45i	−1.53728	−	0.151409i
$732$	−8350.92	−	12808.4i	−0.421665	−	0.646737i
$733$	−2293.73	−	695.795i	−0.115581	−	0.0350611i	0.231964	−	0.972724i	$-0.425485\pi$
$733$	−2293.73	−	695.795i	−0.115581	−	0.0350611i	−0.347545	+	0.937663i	$0.612985\pi$
$734$	2180.87	+	11296.5i	0.109669	+	0.568067i
$735$	−4925.88	+	4925.88i	−0.247202	+	0.247202i
$736$	−2667.63	+	2521.31i	−0.133601	+	0.126272i
$737$	24875.4	+	24875.4i	1.24328	+	1.24328i
$738$	10034.8	−	14836.4i	0.500526	−	0.740022i
$739$	5446.07	−	17953.3i	0.271092	−	0.893670i	−0.710665	−	0.703530i	$-0.751606\pi$
$739$	5446.07	−	17953.3i	0.271092	−	0.893670i	0.981757	−	0.190140i	$-0.0608941\pi$
$740$	239.335	+	1278.40i	0.0118894	+	0.0635065i
$741$	−5566.45	+	56517.2i	−0.275963	+	2.80190i
$742$	33168.8	−	26909.4i	1.64106	−	1.33137i
$743$	5263.80	−	26462.9i	0.259906	−	1.30664i	−0.601563	−	0.798825i	$-0.705455\pi$
$743$	5263.80	−	26462.9i	0.259906	−	1.30664i	0.861469	−	0.507810i	$-0.169545\pi$
$744$	12158.7	−	9638.91i	0.599141	−	0.474972i
$745$	1773.44	−	352.760i	0.0872133	−	0.0173478i
$746$	1910.62	+	20588.2i	0.0937702	+	1.01044i
$747$	−9997.56	+	18704.1i	−0.489681	+	0.916129i
$748$	−25398.3	+	7392.78i	−1.24152	+	0.361373i
$749$	1460.67	+	14830.4i	0.0712573	+	0.723487i
$750$	−4163.20	−	4210.42i	−0.202692	−	0.204990i
$751$	36092.2	−	14949.9i	1.75369	−	0.726404i	0.756302	−	0.654223i	$-0.227004\pi$
$751$	36092.2	−	14949.9i	1.75369	−	0.726404i	0.997392	−	0.0721811i	$-0.0229959\pi$
$752$	9478.64	−	21498.8i	0.459641	−	1.04253i
$753$	−3767.66	−	1560.61i	−0.182339	−	0.0755272i
$754$	5707.22	+	14001.2i	0.275656	+	0.676253i
$755$	−994.806	−	816.416i	−0.0479532	−	0.0393542i
$756$	−1595.04	−	18309.1i	−0.0767340	−	0.880814i
$757$	5217.47	−	1582.70i	0.250505	−	0.0759899i	−0.162535	−	0.986703i	$-0.551967\pi$
$757$	5217.47	−	1582.70i	0.250505	−	0.0759899i	0.413040	+	0.910713i	$0.364467\pi$
$758$	−11928.8	+	6289.87i	−0.571602	+	0.301396i
$759$	−3540.36	+	5298.52i	−0.169311	+	0.253392i
$760$	700.236	+	3860.50i	0.0334213	+	0.184257i
$761$	−27020.9	+	18054.8i	−1.28713	+	0.860035i	−0.995338	−	0.0964461i	$-0.969252\pi$
$761$	−27020.9	+	18054.8i	−1.28713	+	0.860035i	−0.291795	+	0.956481i	$0.594252\pi$
$762$	309.355	+	1040.90i	0.0147070	+	0.0494853i
$763$	−7551.63	−	9201.69i	−0.358306	−	0.436597i
$764$	3381.72	−	7910.67i	0.160139	−	0.374605i
$765$	1318.29	−	704.642i	0.0623045	−	0.0333025i
$766$	5188.74	−	25338.1i	0.244748	−	1.19517i
$767$	1379.01			0.0649196
$768$	−11695.1	−	24474.7i	−0.549492	−	1.14994i
$769$	−9728.05			−0.456180			−0.228090	−	0.973640i	$-0.573248\pi$
$769$	−9728.05			−0.456180			−0.228090	+	0.973640i	$0.573248\pi$
$770$	1172.00	−	5723.19i	0.0548518	−	0.267856i
$771$	8764.11	−	4684.51i	0.409380	−	0.218818i
$772$	−4025.44	+	9416.51i	−0.187667	+	0.438999i
$773$	1422.95	+	1733.88i	0.0662097	+	0.0806768i	0.805062	−	0.593191i	$-0.202132\pi$
$773$	1422.95	+	1733.88i	0.0662097	+	0.0806768i	−0.738852	+	0.673867i	$0.764632\pi$
$774$	−5951.23	−	20024.4i	−0.276373	−	0.929923i
$775$	−10622.3	+	7097.59i	−0.492341	+	0.328972i
$776$	−16813.3	+	3049.67i	−0.777785	+	0.141078i
$777$	−16072.7	+	24054.4i	−0.742090	+	1.11062i
$778$	10479.6	−	5525.72i	0.482920	−	0.254636i
$779$	48979.9	−	14857.9i	2.25274	−	0.683362i
$780$	−368.337	−	4228.07i	−0.0169085	−	0.194089i
$781$	2122.87	+	1742.19i	0.0972627	+	0.0798215i
$782$	1508.45	+	3700.59i	0.0689794	+	0.169224i
$783$	5270.82	+	2183.25i	0.240567	+	0.0996460i
$784$	49315.0	−	19135.7i	2.24649	−	0.871707i
$785$	−642.534	+	266.146i	−0.0292141	+	0.0121009i
$786$	−16309.1	−	16494.0i	−0.740108	−	0.748502i
$787$	−2544.91	−	25839.0i	−0.115269	−	1.17034i	−0.862599	−	0.505889i	$-0.831165\pi$
$787$	−2544.91	−	25839.0i	−0.115269	−	1.17034i	0.747330	−	0.664453i	$-0.231335\pi$
$788$	30204.5	−	8791.73i	1.36547	−	0.397452i
$789$	−2648.20	+	4954.44i	−0.119491	+	0.223552i
$790$	58.2285	+	627.453i	0.00262238	+	0.0282580i
$791$	−7141.90	+	1420.61i	−0.321032	+	0.0638573i
$792$	−11244.2	−	14183.7i	−0.504476	−	0.636357i
$793$	−3544.02	+	17817.0i	−0.158703	+	0.797856i
$794$	9896.41	−	8028.82i	0.442331	−	0.358857i
$795$	364.789	−	3703.76i	0.0162739	−	0.165231i
$796$	5869.49	+	31351.6i	0.261355	+	1.39601i
$797$	−9706.14	+	31996.9i	−0.431379	+	1.42207i	0.424753	+	0.905309i	$0.360361\pi$
$797$	−9706.14	+	31996.9i	−0.431379	+	1.42207i	−0.856132	+	0.516757i	$0.827139\pi$
$798$	−48894.1	+	72289.5i	−2.16896	+	3.20679i
$799$	−18087.8	−	18087.8i	−0.800875	−	0.800875i
$800$	7961.88	+	20866.8i	0.351869	+	0.922193i
$801$	4255.66	−	4255.66i	0.187723	−	0.187723i
$802$	151.189	+	783.132i	0.00665671	+	0.0344805i
$803$	8132.69	+	2467.02i	0.357405	+	0.108418i
$804$	21450.1	+	32899.5i	0.940903	+	1.44313i
$805$	−878.308	−	86.5058i	−0.0384550	−	0.00378749i
$806$	−18334.9	−	1910.27i	−0.801263	−	0.0834819i
$807$	−2327.03	−	462.876i	−0.101506	−	0.0201908i
$808$	−18571.2	−	15774.2i	−0.808580	−	0.686799i
$809$	5759.32	+	28954.1i	0.250293	+	1.25831i	0.877546	+	0.479492i	$0.159179\pi$
$809$	5759.32	+	28954.1i	0.250293	+	1.25831i	−0.627253	+	0.778815i	$0.715821\pi$
$810$	−2492.71	−	2069.35i	−0.108130	−	0.0897648i
$811$	−29519.8	−	15778.6i	−1.27815	−	0.683185i	−0.314222	−	0.949350i	$-0.601743\pi$
$811$	−29519.8	−	15778.6i	−1.27815	−	0.683185i	−0.963928	+	0.266165i	$0.914243\pi$
$812$	−2538.04	+	23096.0i	−0.109689	+	0.998166i
$813$	46974.3	−	4626.57i	2.02640	−	0.199583i
$814$	96.6757	−	17145.4i	0.00416276	−	0.738264i
$815$	−1589.64	−	3837.74i	−0.0683225	−	0.164945i
$816$	−29447.3	+	2231.08i	−1.26331	+	0.0957151i
$817$	22844.5	−	55151.5i	0.978248	−	2.36170i
$818$	−6043.22	−	2543.20i	−0.258308	−	0.108705i
$819$	23018.4	−	28048.0i	0.982085	−	1.19667i
$820$	−3393.54	+	1764.97i	−0.144521	+	0.0751653i
$821$	−371.866	−	1225.88i	−0.0158078	−	0.0521113i	0.948682	−	0.316233i	$-0.102418\pi$
$821$	−371.866	−	1225.88i	−0.0158078	−	0.0521113i	−0.964489	+	0.264121i	$0.914918\pi$
$822$	7955.09	+	2462.22i	0.337549	+	0.104476i
$823$	8448.65	+	5645.21i	0.357839	+	0.239100i	0.721475	−	0.692441i	$-0.243465\pi$
$823$	8448.65	+	5645.21i	0.357839	+	0.239100i	−0.363636	+	0.931541i	$0.618465\pi$
$824$	−8758.39	−	9059.83i	−0.370283	−	0.383027i
$825$	21541.8	+	32239.6i	0.909077	+	1.36053i
$826$	1863.29	+	1009.50i	0.0784891	+	0.0425240i
$827$	11760.5	−	9651.63i	0.494503	−	0.405828i	−0.353815	−	0.935316i	$-0.615116\pi$
$827$	11760.5	−	9651.63i	0.494503	−	0.405828i	0.848318	+	0.529487i	$0.177616\pi$
$828$	−1955.19	+	1911.59i	−0.0820625	+	0.0802322i
$829$	−21396.8	−	40030.6i	−0.896431	−	1.67710i	−0.721375	−	0.692545i	$-0.756489\pi$
$829$	−21396.8	−	40030.6i	−0.896431	−	1.67710i	−0.175056	−	0.984558i	$-0.556011\pi$
$830$	3780.00	−	2495.00i	0.158079	−	0.104341i
$831$		−	7821.28i		−	0.326495i
$832$	−10392.8	+	30505.3i	−0.433060	+	1.27113i
$833$		−	57590.2i		−	2.39542i
$834$	−3577.32	−	5419.74i	−0.148528	−	0.225024i
$835$	−1908.43	−	3570.42i	−0.0790946	−	0.147976i
$836$	583.266	−	51719.4i	0.0241300	−	2.13966i
$837$	−5376.83	+	4412.65i	−0.222043	+	0.182226i
$838$	8611.01	−	15893.9i	0.354967	−	0.655184i
$839$	−18677.2	−	27952.5i	−0.768546	−	1.15021i	−0.984769	−	0.173866i	$-0.944374\pi$
$839$	−18677.2	−	27952.5i	−0.768546	−	1.15021i	0.216223	−	0.976344i	$-0.430626\pi$
$840$	2597.44	−	5982.49i	0.106691	−	0.245733i
$841$	14281.6	+	9542.64i	0.585574	+	0.391268i
$842$	679.844	−	2196.49i	0.0278254	−	0.0899001i
$843$	15084.5	+	49727.1i	0.616298	+	2.03166i
$844$	37017.1	+	11686.4i	1.50969	+	0.476616i
$845$	−1424.96	+	1736.32i	−0.0580119	+	0.0706877i
$846$	6789.19	−	16132.7i	0.275907	−	0.655617i
$847$	−12052.9	+	29098.2i	−0.488951	+	1.18043i
$848$	−13880.5	+	24616.6i	−0.562096	+	0.996858i
$849$	7206.66	+	17398.4i	0.291321	+	0.703312i
$850$	24315.1	+	137.103i	0.981180	+	0.00553245i
$851$	−2577.77	+	253.888i	−0.103836	+	0.0102270i
$852$	1918.15	+	2391.78i	0.0771301	+	0.0961748i
$853$	−32975.7	−	17625.9i	−1.32364	−	0.707502i	−0.350252	−	0.936655i	$-0.613904\pi$
$853$	−32975.7	−	17625.9i	−1.32364	−	0.707502i	−0.973390	+	0.229154i	$0.926404\pi$
$854$	−17831.4	+	21479.5i	−0.714493	+	0.860670i
$855$	570.209	+	2866.64i	0.0228079	+	0.114663i
$856$	−4500.26	−	8773.19i	−0.179691	−	0.350305i
$857$	31345.8	+	6235.07i	1.24942	+	0.248525i	0.775106	−	0.631832i	$-0.217697\pi$
$857$	31345.8	+	6235.07i	1.24942	+	0.248525i	0.474313	+	0.880356i	$0.342697\pi$
$858$	−5797.83	+	55647.9i	−0.230693	+	2.21420i
$859$	−21903.1	−	2157.27i	−0.869993	−	0.0856868i	−0.346839	−	0.937925i	$-0.612745\pi$
$859$	−21903.1	−	2157.27i	−0.869993	−	0.0856868i	−0.523154	+	0.852238i	$0.675245\pi$
$860$	−919.619	+	4365.37i	−0.0364637	+	0.173090i
$861$	−81419.5	−	24698.3i	−3.22273	−	0.977604i
$862$	−5579.18	+	1077.10i	−0.220450	+	0.0425594i
$863$	9643.63	−	9643.63i	0.380386	−	0.380386i	−0.490855	−	0.871241i	$-0.663316\pi$
$863$	9643.63	−	9643.63i	0.380386	−	0.380386i	0.871241	+	0.490855i	$0.163316\pi$
$864$	5427.67	+	10881.6i	0.213719	+	0.428473i
$865$	−1442.35	−	1442.35i	−0.0566951	−	0.0566951i
$866$	24554.8	+	16608.0i	0.963517	+	0.651690i
$867$	111.558	−	367.758i	0.00436991	−	0.0144057i
$868$	−23375.2	−	16003.0i	−0.914061	−	0.625780i
$869$	814.244	−	8267.16i	0.0317852	−	0.322720i
$870$	1275.54	+	1572.25i	0.0497068	+	0.0612691i
$871$	9103.13	−	45764.5i	0.354131	−	1.78034i
$872$	6882.33	+	3829.74i	0.267276	+	0.148729i
$873$	−12484.8	+	2483.38i	−0.484017	+	0.0962769i
$874$	−7780.44	+	722.035i	−0.301118	+	0.0279442i
$875$	−5096.07	+	9534.08i	−0.196890	+	0.368355i
$876$	8316.68	+	4566.68i	0.320770	+	0.176134i
$877$	−1853.24	−	18816.3i	−0.0713563	−	0.724493i	−0.962592	−	0.270953i	$-0.912661\pi$
$877$	−1853.24	−	18816.3i	−0.0713563	−	0.724493i	0.891236	−	0.453540i	$-0.149839\pi$
$878$	−29894.1	+	29558.9i	−1.14906	+	1.13618i
$879$	13368.7	−	5537.51i	0.512987	−	0.212486i
$880$	668.404	+	3807.12i	0.0256044	+	0.145839i
$881$	8538.59	+	3536.80i	0.326529	+	0.135253i	0.539925	−	0.841713i	$-0.318452\pi$
$881$	8538.59	+	3536.80i	0.326529	+	0.135253i	−0.213396	+	0.976966i	$0.568452\pi$
$882$	36490.8	−	14874.5i	1.39309	−	0.567857i
$883$	15390.8	+	12630.9i	0.586571	+	0.481387i	0.880245	−	0.474519i	$-0.157378\pi$
$883$	15390.8	+	12630.9i	0.586571	+	0.481387i	−0.293674	+	0.955906i	$0.594878\pi$
$884$	26869.1	+	22562.8i	1.02229	+	0.858448i
$885$	176.704	−	53.6026i	0.00671168	−	0.00203597i
$886$	−432.304	−	819.870i	−0.0163923	−	0.0310881i
$887$	−18159.4	+	27177.4i	−0.687409	+	1.02878i	0.309553	+	0.950882i	$0.399821\pi$
$887$	−18159.4	+	27177.4i	−0.687409	+	1.02878i	−0.996961	+	0.0778974i	$0.975179\pi$
$888$	4051.37	−	18708.0i	0.153103	−	0.706981i
$889$	1648.46	−	1101.47i	0.0621908	−	0.0415546i
$890$	−1232.01	+	366.153i	−0.0464012	+	0.0137904i
$891$	27094.2	+	33014.3i	1.01873	+	1.24133i
$892$	−39398.4	+	15801.2i	−1.47887	+	0.593121i
$893$	44111.0	−	23577.8i	1.65299	−	0.883540i
$894$	−26070.9	−	5338.81i	−0.975326	−	0.199728i
$895$	5375.75			0.200773
$896$	−36373.6	+	33610.0i	−1.35620	+	1.25316i
$897$	8452.36			0.314622
$898$	−27230.6	−	5576.30i	−1.01191	−	0.207220i
$899$	7755.42	−	4145.36i	0.287717	−	0.153788i
$900$	6193.28	+	15442.2i	0.229381	+	0.571932i
$901$	19518.6	+	23783.4i	0.721707	+	0.879402i
$902$	48335.9	−	14365.4i	1.78427	−	0.530284i
$903$	−82508.6	+	55130.5i	−3.04066	+	2.03170i
$904$	4050.75	−	2608.61i	0.149033	−	0.0959748i
$905$	−2170.56	+	3248.48i	−0.0797259	+	0.119318i
$906$	8834.06	+	16753.9i	0.323942	+	0.614361i
$907$	−13868.8	+	4207.07i	−0.507726	+	0.154017i	−0.533747	−	0.845644i	$-0.679216\pi$
$907$	−13868.8	+	4207.07i	−0.507726	+	0.154017i	0.0260207	+	0.999661i	$0.491716\pi$
$908$	11798.4	−	14050.3i	0.431217	−	0.513520i
$909$	−14031.4	−	11515.3i	−0.511982	−	0.420172i
$910$	−7175.45	+	2924.88i	−0.261389	+	0.106548i
$911$	−9729.92	−	4030.26i	−0.353860	−	0.146574i	0.198670	−	0.980066i	$-0.436338\pi$
$911$	−9729.92	−	4030.26i	−0.353860	−	0.146574i	−0.552530	+	0.833493i	$0.686338\pi$
$912$	12539.6	−	56365.9i	0.455294	−	2.04656i
$913$	−55162.4	+	22849.0i	−1.99957	+	0.828250i
$914$	−15056.7	+	14887.9i	−0.544893	+	0.538782i
$915$	238.427	+	2420.79i	0.00861437	+	0.0874631i
$916$	11429.7	−	20815.4i	0.412280	−	0.750830i
$917$	−19963.5	+	37349.1i	−0.718924	+	1.34501i
$918$	13182.3	−	1223.33i	0.473943	−	0.0439825i
$919$	−12079.5	+	2402.76i	−0.433587	+	0.0862458i	−0.407058	−	0.913402i	$-0.633445\pi$
$919$	−12079.5	+	2402.76i	−0.433587	+	0.0862458i	−0.0265288	+	0.999648i	$0.508445\pi$
$920$	561.590	−	160.035i	0.0201251	−	0.00573499i
$921$	5562.40	−	27964.1i	0.199009	−	1.00049i
$922$	12179.2	+	15012.2i	0.435033	+	0.536226i
$923$	357.034	−	3625.02i	0.0127323	−	0.129273i
$924$	−48570.4	+	70945.6i	−1.72927	+	2.52591i
$925$	−4575.08	+	15082.0i	−0.162624	+	0.536101i
$926$	38524.0	+	26056.3i	1.36714	+	0.924689i
$927$	−6637.78	−	6637.78i	−0.235181	−	0.235181i
$928$	−4046.23	−	14831.5i	−0.143129	−	0.524642i
$929$	28783.0	−	28783.0i	1.01651	−	1.01651i	0.0166493	−	0.999861i	$-0.494700\pi$
$929$	28783.0	−	28783.0i	1.01651	−	1.01651i	0.999861	−	0.0166493i	$-0.00529989\pi$
$930$	−2423.64	+	467.902i	−0.0854563	+	0.0164980i
$931$	107758.	+	32688.1i	3.79337	+	1.15071i
$932$	−18800.2	−	3960.49i	−0.660752	−	0.139196i
$933$	40483.1	+	3987.23i	1.42053	+	0.139910i
$934$	434.824	−	4173.47i	0.0152333	−	0.146210i
$935$	4127.40	+	820.990i	0.144364	+	0.0287158i
$936$	−7356.61	+	22852.6i	−0.256900	+	0.798034i
$937$	6724.59	+	33806.8i	0.234453	+	1.17868i	0.901204	+	0.433395i	$0.142685\pi$
$937$	6724.59	+	33806.8i	0.234453	+	1.17868i	−0.666751	+	0.745281i	$0.732315\pi$
$938$	45801.4	−	55171.9i	1.59432	−	1.92050i
$939$	−31739.6	−	16965.2i	−1.10307	−	0.589603i
$940$	−2915.97	+	2338.55i	−0.101179	+	0.0811436i
$941$	−16523.5	+	1627.43i	−0.572425	+	0.0563790i	−0.380089	−	0.924950i	$-0.624107\pi$
$941$	−16523.5	+	1627.43i	−0.572425	+	0.0563790i	−0.192337	+	0.981329i	$0.561607\pi$
$942$	10235.5	+	57.7134i	0.354023	+	0.00199618i
$943$	−2915.24	−	7038.01i	−0.100671	−	0.243042i
$944$	−1391.96	−	168.870i	−0.0479918	−	0.00582231i
$945$	−1118.89	+	2701.23i	−0.0385157	+	0.0929852i
$946$	22812.0	−	54206.5i	0.784020	−	1.86301i
$947$	29215.2	−	35598.9i	1.00250	−	1.22155i	0.0274368	−	0.999624i	$-0.491265\pi$
$947$	29215.2	−	35598.9i	1.00250	−	1.22155i	0.975063	−	0.221926i	$-0.0712345\pi$
$948$	2792.07	−	8843.94i	0.0956563	−	0.302994i
$949$	−3272.22	−	10787.1i	−0.111929	−	0.368981i
$950$	−14057.8	+	45418.7i	−0.480099	+	1.55114i
$951$	−36848.4	−	24621.3i	−1.25646	−	0.839537i
$952$	19787.9	+	50155.5i	0.673667	+	1.70751i
$953$	−12672.0	−	18965.0i	−0.430731	−	0.644634i	0.551090	−	0.834446i	$-0.314212\pi$
$953$	−12672.0	−	18965.0i	−0.430731	−	0.644634i	−0.981820	+	0.189812i	$0.939212\pi$
$954$	−10028.6	+	18510.3i	−0.340343	+	0.628191i
$955$	−1057.99	+	868.271i	−0.0358490	+	0.0294205i
$956$	27028.8	+	304.818i	0.914409	+	0.0103123i
$957$	−12581.5	−	23538.3i	−0.424976	−	0.795075i
$958$	−20817.7	−	31539.5i	−0.702078	−	1.06367i
$959$		−	15203.9i		−	0.511949i
$960$	−145.964	+	4312.85i	−0.00490726	+	0.144997i
$961$		−	19069.6i		−	0.640112i
$962$	−18980.0	+	12527.8i	−0.636113	+	0.419869i
$963$	−3462.53	−	6477.93i	−0.115865	−	0.216769i
$964$	4844.67	+	4955.19i	0.161863	+	0.165556i
$965$	1259.38	−	1033.55i	0.0420114	−	0.0344779i
$966$	11420.6	+	6187.48i	0.380385	+	0.206086i
$967$	−22445.3	−	33591.8i	−0.746425	−	1.11710i	−0.989136	−	0.147005i	$-0.953037\pi$
$967$	−22445.3	−	33591.8i	−0.746425	−	1.11710i	0.242711	−	0.970099i	$-0.421963\pi$
$968$	352.490	−	20836.2i	0.0117040	−	0.691840i
$969$	−52271.5	−	34926.7i	−1.73292	−	1.15790i
$970$	2596.89	+	803.776i	0.0859599	+	0.0266059i
$971$	6069.97	+	20010.0i	0.200612	+	0.661331i	0.998301	+	0.0582614i	$0.0185557\pi$
$971$	6069.97	+	20010.0i	0.200612	+	0.661331i	−0.797689	+	0.603069i	$0.793944\pi$
$972$	15305.6	+	29428.3i	0.505069	+	0.971103i
$973$	−7521.56	+	9165.05i	−0.247821	+	0.301971i
$974$	−45261.5	−	19047.6i	−1.48899	−	0.626618i
$975$	19681.2	−	47514.6i	0.646465	−	1.56070i
$976$	5759.10	−	17550.2i	0.188877	−	0.575582i
$977$	664.738	+	1604.82i	0.0217675	+	0.0525514i	0.934390	−	0.356253i	$-0.115946\pi$
$977$	664.738	+	1604.82i	0.0217675	+	0.0525514i	−0.912622	+	0.408804i	$0.865946\pi$
$978$	−344.712	+	61134.6i	−0.0112706	+	1.99884i
$979$	16861.9	−	1660.75i	0.550468	−	0.0542164i
$980$	−8365.01	−	919.239i	−0.272664	−	0.0299633i
$981$	5174.50	+	2765.83i	0.168409	+	0.0900164i
$982$	−45514.9	−	37784.6i	−1.47906	−	1.22786i
$983$	8487.79	+	42671.0i	0.275400	+	1.38453i	0.832473	+	0.554066i	$0.186925\pi$
$983$	8487.79	+	42671.0i	0.275400	+	1.38453i	−0.557072	+	0.830464i	$0.688075\pi$
$984$	56109.8	−	4569.50i	1.81780	−	0.148039i
$985$	−4908.43	−	976.348i	−0.158777	−	0.0315828i
$986$	−16647.3	−	1734.44i	−0.537684	−	0.0560201i
$987$	−82742.9	−	8149.47i	−2.66843	−	0.262817i
$988$	−57468.5	+	37468.8i	−1.85052	+	1.20652i
$989$	−8502.14	−	2579.10i	−0.273359	−	0.0829227i
$990$	545.827	+	2827.28i	0.0175227	+	0.0907645i
$991$	−606.697	+	606.697i	−0.0194474	+	0.0194474i	−0.716764	−	0.697316i	$-0.754377\pi$
$991$	−606.697	+	606.697i	−0.0194474	+	0.0194474i	0.697316	+	0.716764i	$0.254377\pi$
$992$	18273.0	+	4173.43i	0.584847	+	0.133575i
$993$	−2353.55	−	2353.55i	−0.0752140	−	0.0752140i
$994$	3136.08	−	4636.67i	0.100071	−	0.147954i
$995$	1473.00	−	4855.82i	0.0469318	−	0.154713i
$996$	−65519.7	+	12266.3i	−2.08441	+	0.390232i
$997$	−2810.44	+	28534.9i	−0.0892754	+	0.906428i	0.841359	+	0.540477i	$0.181756\pi$
$997$	−2810.44	+	28534.9i	−0.0892754	+	0.906428i	−0.930634	+	0.365951i	$0.880744\pi$
$998$	−16317.7	+	13238.3i	−0.517563	+	0.419891i
$999$	−1674.09	+	8416.21i	−0.0530189	+	0.266544i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.k.a.101.20	✓	752
128.109	even	32	inner	128.4.k.a.109.20	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.4.k.a.101.20	✓	752	1.1	even	1	trivial
128.4.k.a.109.20	yes	752	128.109	even	32	inner

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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Abelian varieties over $\F_{q}$
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Newspace parameters

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$q$ -expansion

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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.101.20

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