LMFDB - Embedded newform 160.4.u.a.43.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,4,Mod(43,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 6]))

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

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

chi := DirichletCharacter("160.43");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	160.u (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.44030560092$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$70$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			43.16
Character	$\chi$	$=$	160.43
Dual form			160.4.u.a.67.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96007 + 2.03915i) q^{2} +(3.68068 - 8.88596i) q^{3} +(-0.316262 - 7.99375i) q^{4} +(-6.53470 + 9.07181i) q^{5} +(10.9054 + 24.9225i) q^{6} +30.1289i q^{7} +(16.9203 + 15.0234i) q^{8} +(-46.3209 - 46.3209i) q^{9} +(-5.69033 - 31.1066i) q^{10} +(-7.33517 + 17.7087i) q^{11} +(-72.1961 - 26.6122i) q^{12} +(-3.98438 + 9.61914i) q^{13} +(-61.4374 - 59.0547i) q^{14} +(56.5596 + 91.4575i) q^{15} +(-63.8000 + 5.05624i) q^{16} +(60.6244 + 60.6244i) q^{17} +(185.247 - 3.66310i) q^{18} +(20.4129 + 49.2811i) q^{19} +(74.5844 + 49.3676i) q^{20} +(267.724 + 110.895i) q^{21} +(-21.7332 - 49.6677i) q^{22} -56.6550i q^{23} +(195.776 - 95.0571i) q^{24} +(-39.5955 - 118.563i) q^{25} +(-11.8052 - 26.9789i) q^{26} +(-342.177 + 141.734i) q^{27} +(240.843 - 9.52863i) q^{28} +(107.824 + 260.311i) q^{29} +(-297.356 - 63.9295i) q^{30} +158.843i q^{31} +(114.742 - 140.008i) q^{32} +(130.360 + 130.360i) q^{33} +(-242.450 + 4.79424i) q^{34} +(-273.324 - 196.883i) q^{35} +(-355.628 + 384.927i) q^{36} +(-65.1311 - 157.240i) q^{37} +(-140.502 - 54.9694i) q^{38} +(70.8100 + 70.8100i) q^{39} +(-246.859 + 55.3249i) q^{40} +(104.159 - 104.159i) q^{41} +(-750.889 + 328.568i) q^{42} +(-243.830 + 100.998i) q^{43} +(143.878 + 53.0349i) q^{44} +(722.907 - 117.521i) q^{45} +(115.528 + 111.048i) q^{46} +(176.983 - 176.983i) q^{47} +(-189.898 + 585.534i) q^{48} -564.751 q^{49} +(319.378 + 151.651i) q^{50} +(761.845 - 315.567i) q^{51} +(78.1530 + 28.8079i) q^{52} +(132.165 + 319.074i) q^{53} +(381.673 - 975.560i) q^{54} +(-112.717 - 182.264i) q^{55} +(-452.638 + 509.791i) q^{56} +513.043 q^{57} +(-742.155 - 290.357i) q^{58} +(-247.684 + 597.961i) q^{59} +(713.200 - 481.047i) q^{60} +(-402.040 + 166.531i) q^{61} +(-323.905 - 311.343i) q^{62} +(1395.60 - 1395.60i) q^{63} +(60.5958 + 508.402i) q^{64} +(-61.2263 - 99.0036i) q^{65} +(-521.338 + 10.3090i) q^{66} +(-330.091 - 136.728i) q^{67} +(465.443 - 503.789i) q^{68} +(-503.434 - 208.529i) q^{69} +(937.208 - 171.443i) q^{70} +(132.571 - 132.571i) q^{71} +(-87.8687 - 1479.66i) q^{72} -13.2198 q^{73} +(448.298 + 175.390i) q^{74} +(-1199.28 - 84.5491i) q^{75} +(387.485 - 178.761i) q^{76} +(-533.543 - 221.001i) q^{77} +(-283.185 + 5.59972i) q^{78} -325.998i q^{79} +(371.044 - 611.822i) q^{80} +1793.55i q^{81} +(8.23698 + 416.554i) q^{82} +(585.767 + 242.632i) q^{83} +(801.795 - 2175.19i) q^{84} +(-946.135 + 153.811i) q^{85} +(271.975 - 695.169i) q^{86} +2709.97 q^{87} +(-390.158 + 189.438i) q^{88} +(61.9317 - 61.9317i) q^{89} +(-1177.30 + 1704.47i) q^{90} +(-289.814 - 120.045i) q^{91} +(-452.886 + 17.9178i) q^{92} +(1411.47 + 584.651i) q^{93} +(13.9960 + 707.792i) q^{94} +(-580.461 - 136.855i) q^{95} +(-821.779 - 1534.92i) q^{96} +(123.993 - 123.993i) q^{97} +(1106.95 - 1151.61i) q^{98} +(1160.05 - 480.510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} + 80 q^{8} + 8 q^{10} - 8 q^{11} + 44 q^{12} - 4 q^{13} + 64 q^{14} - 8 q^{15} - 8 q^{16} + 28 q^{18} - 48 q^{19} - 312 q^{20} - 8 q^{21} - 436 q^{22} + 736 q^{24}+ \cdots + 3480 q^{98}+O(q^{100}) $ 280 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 + 80 * q^8 + 8 * q^10 - 8 * q^11 + 44 * q^12 - 4 * q^13 + 64 * q^14 - 8 * q^15 - 8 * q^16 + 28 * q^18 - 48 * q^19 - 312 * q^20 - 8 * q^21 - 436 * q^22 + 736 * q^24 - 4 * q^25 - 8 * q^26 - 112 * q^27 + 252 * q^28 - 1696 * q^30 - 344 * q^32 - 8 * q^33 + 696 * q^34 + 952 * q^35 - 8 * q^36 - 4 * q^37 - 172 * q^38 + 816 * q^40 - 8 * q^41 - 460 * q^42 + 860 * q^43 + 1232 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 + 3496 * q^48 - 11368 * q^49 - 36 * q^50 + 1480 * q^51 - 328 * q^52 - 4 * q^53 + 2968 * q^54 - 292 * q^55 - 344 * q^56 - 8 * q^57 - 2020 * q^58 + 252 * q^60 + 1816 * q^61 - 440 * q^62 + 2744 * q^63 + 816 * q^64 - 8 * q^65 + 552 * q^66 + 1844 * q^67 + 1224 * q^68 + 216 * q^69 + 1764 * q^70 - 232 * q^71 - 3432 * q^72 - 8 * q^73 + 104 * q^75 + 824 * q^76 + 1368 * q^77 - 5968 * q^78 - 1800 * q^80 + 588 * q^82 + 2676 * q^83 + 2744 * q^84 - 4 * q^85 - 1192 * q^86 + 2568 * q^87 - 5880 * q^88 - 84 * q^90 - 8 * q^91 - 3284 * q^92 + 104 * q^93 + 416 * q^94 + 6168 * q^96 - 8 * q^97 + 3480 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−1.96007	+	2.03915i	−0.692989	+	0.720948i
$2$	−1.96007	+	2.03915i	−0.692989	+	0.720948i
$3$	3.68068	−	8.88596i	0.708348	−	1.71010i	0.00425932	−	0.999991i	$-0.498644\pi$
$3$	3.68068	−	8.88596i	0.708348	−	1.71010i	0.704089	−	0.710112i	$-0.251356\pi$
$4$	−0.316262	−	7.99375i	−0.0395328	−	0.999218i
$5$	−6.53470	+	9.07181i	−0.584481	+	0.811407i
$5$	−6.53470	+	9.07181i	−0.584481	+	0.811407i
$6$	10.9054	+	24.9225i	0.742019	+	1.69576i
$7$			30.1289i			1.62681i	0.581699	+	0.813404i	$0.302388\pi$
$7$			30.1289i			1.62681i	−0.581699	+	0.813404i	$0.697612\pi$
$8$	16.9203	+	15.0234i	0.747780	+	0.663946i
$9$	−46.3209	−	46.3209i	−1.71559	−	1.71559i
$10$	−5.69033	−	31.1066i	−0.179944	−	0.983677i
$11$	−7.33517	+	17.7087i	−0.201058	+	0.485397i	−0.991961	−	0.126545i	$-0.959611\pi$
$11$	−7.33517	+	17.7087i	−0.201058	+	0.485397i	0.790903	+	0.611942i	$0.209611\pi$
$12$	−72.1961	−	26.6122i	−1.73677	−	0.640189i
$13$	−3.98438	+	9.61914i	−0.0850052	+	0.205221i	−0.960666	−	0.277706i	$-0.910426\pi$
$13$	−3.98438	+	9.61914i	−0.0850052	+	0.205221i	0.875661	+	0.482926i	$0.160426\pi$
$14$	−61.4374	−	59.0547i	−1.17284	−	1.12736i
$15$	56.5596	+	91.4575i	0.973575	+	1.57428i
$16$	−63.8000	+	5.05624i	−0.996874	+	0.0790037i
$17$	60.6244	+	60.6244i	0.864916	+	0.864916i	0.991904	−	0.126988i	$-0.0405310\pi$
$17$	60.6244	+	60.6244i	0.864916	+	0.864916i	−0.126988	+	0.991904i	$0.540531\pi$
$18$	185.247	−	3.66310i	2.42574	−	0.0479668i
$19$	20.4129	+	49.2811i	0.246476	+	0.595045i	0.997900	−	0.0647743i	$-0.0206327\pi$
$19$	20.4129	+	49.2811i	0.246476	+	0.595045i	−0.751424	+	0.659819i	$0.770633\pi$
$20$	74.5844	+	49.3676i	0.833879	+	0.551947i
$21$	267.724	+	110.895i	2.78201	+	1.15235i
$22$	−21.7332	−	49.6677i	−0.210615	−	0.481327i
$23$		−	56.6550i		−	0.513625i	−0.966461	−	0.256813i	$-0.917328\pi$
$23$		−	56.6550i		−	0.513625i	0.966461	−	0.256813i	$-0.0826724\pi$
$24$	195.776	−	95.0571i	1.66510	−	0.808477i
$25$	−39.5955	−	118.563i	−0.316764	−	0.948504i
$26$	−11.8052	−	26.9789i	−0.0890458	−	0.203500i
$27$	−342.177	+	141.734i	−2.43896	+	1.01025i
$28$	240.843	−	9.52863i	1.62554	−	0.0643122i
$29$	107.824	+	260.311i	0.690429	+	1.66684i	0.743915	+	0.668275i	$0.232967\pi$
$29$	107.824	+	260.311i	0.690429	+	1.66684i	−0.0534857	+	0.998569i	$0.517033\pi$
$30$	−297.356	−	63.9295i	−1.80965	−	0.389063i
$31$			158.843i			0.920292i	0.887843	+	0.460146i	$0.152203\pi$
$31$			158.843i			0.920292i	−0.887843	+	0.460146i	$0.847797\pi$
$32$	114.742	−	140.008i	0.633865	−	0.773444i
$33$	130.360	+	130.360i	0.687660	+	0.687660i
$34$	−242.450	+	4.79424i	−1.22294	+	0.0241825i
$35$	−273.324	−	196.883i	−1.32000	−	0.950839i
$36$	−355.628	+	384.927i	−1.64643	+	1.78207i
$37$	−65.1311	−	157.240i	−0.289391	−	0.698653i	0.710596	−	0.703600i	$-0.248425\pi$
$37$	−65.1311	−	157.240i	−0.289391	−	0.698653i	−0.999988	+	0.00494732i	$0.998425\pi$
$38$	−140.502	−	54.9694i	−0.599802	−	0.234663i
$39$	70.8100	+	70.8100i	0.290735	+	0.290735i
$40$	−246.859	+	55.3249i	−0.975794	+	0.218691i
$41$	104.159	−	104.159i	0.396753	−	0.396753i	−0.480333	−	0.877086i	$-0.659484\pi$
$41$	104.159	−	104.159i	0.396753	−	0.396753i	0.877086	+	0.480333i	$0.159484\pi$
$42$	−750.889	+	328.568i	−2.75868	+	1.20712i
$43$	−243.830	+	100.998i	−0.864739	+	0.358187i	−0.770559	−	0.637368i	$-0.780023\pi$
$43$	−243.830	+	100.998i	−0.864739	+	0.358187i	−0.0941800	+	0.995555i	$0.530023\pi$
$44$	143.878	+	53.0349i	0.492966	+	0.181712i
$45$	722.907	−	117.521i	2.39477	−	0.389313i
$46$	115.528	+	111.048i	0.370297	+	0.355937i
$47$	176.983	−	176.983i	0.549268	−	0.549268i	−0.376961	−	0.926229i	$-0.623031\pi$
$47$	176.983	−	176.983i	0.549268	−	0.549268i	0.926229	+	0.376961i	$0.123031\pi$
$48$	−189.898	+	585.534i	−0.571029	+	1.76072i
$49$	−564.751			−1.64651
$50$	319.378	+	151.651i	0.903337	+	0.428933i
$51$	761.845	−	315.567i	2.09176	−	0.866434i
$52$	78.1530	+	28.8079i	0.208421	+	0.0768258i
$53$	132.165	+	319.074i	0.342532	+	0.826946i	0.997458	+	0.0712529i	$0.0226997\pi$
$53$	132.165	+	319.074i	0.342532	+	0.826946i	−0.654926	+	0.755693i	$0.727300\pi$
$54$	381.673	−	975.560i	0.961836	−	2.45846i
$55$	−112.717	−	182.264i	−0.276340	−	0.446845i
$56$	−452.638	+	509.791i	−1.08011	+	1.21650i
$57$	513.043			1.19218
$58$	−742.155	−	290.357i	−1.68017	−	0.657340i
$59$	−247.684	+	597.961i	−0.546537	+	1.31946i	0.373503	+	0.927629i	$0.378157\pi$
$59$	−247.684	+	597.961i	−0.546537	+	1.31946i	−0.920039	+	0.391827i	$0.871843\pi$
$60$	713.200	−	481.047i	1.53456	−	1.03505i
$61$	−402.040	+	166.531i	−0.843869	+	0.349542i	−0.762378	−	0.647132i	$-0.775968\pi$
$61$	−402.040	+	166.531i	−0.843869	+	0.349542i	−0.0814909	+	0.996674i	$0.525968\pi$
$62$	−323.905	−	311.343i	−0.663483	−	0.637752i
$63$	1395.60	−	1395.60i	2.79093	−	2.79093i
$64$	60.5958	+	508.402i	0.118351	+	0.992972i
$65$	−61.2263	−	99.0036i	−0.116834	−	0.188921i
$66$	−521.338	+	10.3090i	−0.972308	+	0.0192265i
$67$	−330.091	−	136.728i	−0.601896	−	0.249313i	0.0608632	−	0.998146i	$-0.480615\pi$
$67$	−330.091	−	136.728i	−0.601896	−	0.249313i	−0.662759	+	0.748833i	$0.730615\pi$
$68$	465.443	−	503.789i	0.830048	−	0.898433i
$69$	−503.434	−	208.529i	−0.878352	−	0.363826i
$70$	937.208	−	171.443i	1.60025	−	0.292734i
$71$	132.571	−	132.571i	0.221596	−	0.221596i	−0.587574	−	0.809170i	$-0.699917\pi$
$71$	132.571	−	132.571i	0.221596	−	0.221596i	0.809170	+	0.587574i	$0.199917\pi$
$72$	−87.8687	−	1479.66i	−0.143825	−	2.42194i
$73$	−13.2198			−0.0211953			−0.0105977	−	0.999944i	$-0.503373\pi$
$73$	−13.2198			−0.0211953			−0.0105977	+	0.999944i	$0.503373\pi$
$74$	448.298	+	175.390i	0.704237	+	0.275522i
$75$	−1199.28	−	84.5491i	−1.84642	−	0.130172i
$76$	387.485	−	178.761i	0.584836	−	0.269807i
$77$	−533.543	−	221.001i	−0.789648	−	0.327083i
$78$	−283.185	+	5.59972i	−0.411081	+	0.00812877i
$79$		−	325.998i		−	0.464273i	−0.972683	−	0.232137i	$-0.925428\pi$
$79$		−	325.998i		−	0.464273i	0.972683	−	0.232137i	$-0.0745717\pi$
$80$	371.044	−	611.822i	0.518550	−	0.855047i
$81$			1793.55i			2.46028i
$82$	8.23698	+	416.554i	0.0110930	+	0.560984i
$83$	585.767	+	242.632i	0.774653	+	0.320872i	0.734756	−	0.678332i	$-0.237297\pi$
$83$	585.767	+	242.632i	0.774653	+	0.320872i	0.0398977	+	0.999204i	$0.487297\pi$
$84$	801.795	−	2175.19i	1.04146	−	2.82539i
$85$	−946.135	+	153.811i	−1.20733	+	0.196272i
$86$	271.975	−	695.169i	0.341021	−	0.871652i
$87$	2709.97			3.33954
$88$	−390.158	+	189.438i	−0.472625	+	0.229479i
$89$	61.9317	−	61.9317i	0.0737613	−	0.0737613i	−0.669264	−	0.743025i	$-0.733390\pi$
$89$	61.9317	−	61.9317i	0.0737613	−	0.0737613i	0.743025	+	0.669264i	$0.233390\pi$
$90$	−1177.30	+	1704.47i	−1.37888	+	1.99630i
$91$	−289.814	−	120.045i	−0.333855	−	0.138287i
$92$	−452.886	+	17.9178i	−0.513224	+	0.0203050i
$93$	1411.47	+	584.651i	1.57379	+	0.651887i
$94$	13.9960	+	707.792i	0.0153572	+	0.776630i
$95$	−580.461	−	136.855i	−0.626884	−	0.147800i
$96$	−821.779	−	1534.92i	−0.873671	−	1.63184i
$97$	123.993	−	123.993i	0.129790	−	0.129790i	−0.639228	−	0.769017i	$-0.720746\pi$
$97$	123.993	−	123.993i	0.129790	−	0.129790i	0.769017	+	0.639228i	$0.220746\pi$
$98$	1106.95	−	1151.61i	1.14101	−	1.18705i
$99$	1160.05	−	480.510i	1.17767	−	0.487809i
$100$	−935.240	+	354.013i	−0.935240	+	0.354013i
$101$	−516.800	+	1247.66i	−0.509144	+	1.22918i	0.435234	+	0.900317i	$0.356666\pi$
$101$	−516.800	+	1247.66i	−0.509144	+	1.22918i	−0.944377	+	0.328864i	$0.893334\pi$
$102$	−849.781	+	2172.05i	−0.824910	+	2.10848i
$103$	−2006.08			−1.91908			−0.959541	−	0.281570i	$-0.909145\pi$
$103$	−2006.08			−1.91908			−0.959541	+	0.281570i	$0.909145\pi$
$104$	−211.929	+	102.900i	−0.199821	+	0.0970211i
$105$	−2755.51	+	1704.08i	−2.56105	+	1.58382i
$106$	−909.690	−	355.903i	−0.833556	−	0.326116i
$107$	−384.040	−	927.154i	−0.346977	−	0.837676i	−0.996974	−	0.0777392i	$-0.975230\pi$
$107$	−384.040	−	927.154i	−0.346977	−	0.837676i	0.649997	−	0.759937i	$-0.274770\pi$
$108$	1241.21	+	2690.45i	1.10588	+	2.39712i
$109$	43.6848	−	18.0948i	0.0383875	−	0.0159006i	−0.363407	−	0.931630i	$-0.618387\pi$
$109$	43.6848	−	18.0948i	0.0383875	−	0.0159006i	0.401795	+	0.915730i	$0.368387\pi$
$110$	592.596	+	127.404i	0.513653	+	0.110432i
$111$	−1636.96			−1.39976
$112$	−152.339	−	1922.22i	−0.128524	−	1.62172i
$113$	1616.29	−	1616.29i	1.34556	−	1.34556i	0.455138	−	0.890421i	$-0.349590\pi$
$113$	1616.29	−	1616.29i	1.34556	−	1.34556i	0.890421	−	0.455138i	$-0.150410\pi$
$114$	−1005.60	+	1046.17i	−0.826167	+	0.859500i
$115$	513.964	+	370.223i	0.416760	+	0.300204i
$116$	2046.76	−	944.245i	1.63825	−	0.755784i
$117$	630.127	−	261.007i	0.497908	−	0.206240i
$118$	−733.855	−	1677.11i	−0.572516	−	1.30839i
$119$	−1826.55	+	1826.55i	−1.40705	+	1.40705i
$120$	−416.994	+	2397.21i	−0.317218	+	1.82362i
$121$	681.367	+	681.367i	0.511921	+	0.511921i
$122$	448.446	−	1146.23i	0.332790	−	0.850614i
$123$	−542.175	−	1308.93i	−0.397449	−	0.959527i
$124$	1269.75	−	50.2361i	0.919573	−	0.0363817i
$125$	1334.33	+	415.570i	0.954766	+	0.297358i
$126$	110.365	+	5581.30i	0.0780327	+	3.94621i
$127$	289.888	+	289.888i	0.202546	+	0.202546i	0.801090	−	0.598544i	$-0.204254\pi$
$127$	289.888	+	289.888i	0.202546	+	0.202546i	−0.598544	+	0.801090i	$0.704254\pi$
$128$	−1155.48	−	872.938i	−0.797897	−	0.602793i
$129$			2538.41i			1.73251i
$130$	321.891	+	69.2043i	0.217167	+	0.0466894i
$131$	−494.095	−	1192.85i	−0.329537	−	0.795572i	−0.998627	−	0.0523905i	$-0.983316\pi$
$131$	−494.095	−	1192.85i	−0.329537	−	0.795572i	0.669090	−	0.743181i	$-0.266684\pi$
$132$	1000.84	−	1083.29i	0.659937	−	0.714307i
$133$	−1484.79	+	615.018i	−0.968024	+	0.400969i
$134$	925.810	−	405.108i	0.596849	−	0.261164i
$135$	950.236	−	4030.36i	0.605802	−	2.56947i
$136$	115.002	+	1936.57i	0.0725097	+	1.22103i
$137$		−	19.5149i		−	0.0121698i	−0.999981	−	0.00608491i	$-0.998063\pi$
$137$		−	19.5149i		−	0.0121698i	0.999981	−	0.00608491i	$-0.00193690\pi$
$138$	1411.99	−	617.846i	0.870988	−	0.381120i
$139$	494.371	+	204.775i	0.301669	+	0.124956i	0.528384	−	0.849006i	$-0.322798\pi$
$139$	494.371	+	204.775i	0.301669	+	0.124956i	−0.226714	+	0.973961i	$0.572798\pi$
$140$	−1487.39	+	2247.15i	−0.897912	+	1.35656i
$141$	−921.243	−	2224.08i	−0.550232	−	1.32838i
$142$	10.4839	+	530.181i	0.00619567	+	0.313322i
$143$	−141.116	−	141.116i	−0.0825225	−	0.0825225i
$144$	3189.48	+	2721.06i	1.84576	+	1.57469i
$145$	−3066.09	−	722.890i	−1.75603	−	0.414019i
$146$	25.9117	−	26.9571i	0.0146881	−	0.0152807i
$147$	−2078.67	+	5018.36i	−1.16630	+	2.81569i
$148$	−1236.34	+	570.370i	−0.686666	+	0.316785i
$149$	−158.016	+	381.484i	−0.0868803	+	0.209748i	−0.961348	−	0.275336i	$-0.911211\pi$
$149$	−158.016	+	381.484i	−0.0868803	+	0.209748i	0.874468	+	0.485084i	$0.161211\pi$
$150$	2523.09	−	2279.80i	1.37340	−	1.24097i
$151$	11.1043	+	11.1043i	0.00598447	+	0.00598447i	0.710093	−	0.704108i	$-0.248653\pi$
$151$	11.1043	+	11.1043i	0.00598447	+	0.00598447i	−0.704108	+	0.710093i	$0.748653\pi$
$152$	−394.976	+	1140.52i	−0.210768	+	0.608610i
$153$		−	5616.35i		−	2.96768i
$154$	1496.43	−	654.797i	0.783027	−	0.342630i
$155$	−1440.99	−	1037.99i	−0.746732	−	0.537893i
$156$	543.643	−	588.432i	0.279014	−	0.302001i
$157$	1397.77	−	3374.51i	0.710535	−	1.71538i	0.0118762	−	0.999929i	$-0.496220\pi$
$157$	1397.77	−	3374.51i	0.710535	−	1.71538i	0.698659	−	0.715455i	$-0.253780\pi$
$158$	664.758	+	638.978i	0.334717	+	0.321736i
$159$	3321.73			1.65679
$160$	520.325	+	1955.83i	0.257096	+	0.966386i
$161$	1706.95			0.835570
$162$	−3657.31	−	3515.47i	−1.77374	−	1.70495i
$163$	416.692	−	1005.98i	0.200232	−	0.483403i	−0.791587	−	0.611057i	$-0.790745\pi$
$163$	416.692	−	1005.98i	0.200232	−	0.483403i	0.991819	+	0.127654i	$0.0407447\pi$
$164$	−865.560	−	799.677i	−0.412127	−	0.380758i
$165$	−2034.46	+	330.738i	−0.959896	+	0.156048i
$166$	−1642.91	+	718.889i	−0.768158	+	0.336124i
$167$			1169.65i			0.541976i	0.962583	+	0.270988i	$0.0873503\pi$
$167$			1169.65i			0.541976i	−0.962583	+	0.270988i	$0.912650\pi$
$168$	2863.97	+	5898.50i	1.31524	+	2.70881i
$169$	1476.86	+	1476.86i	0.672217	+	0.672217i
$170$	1540.85	−	2230.79i	0.695162	−	1.00643i
$171$	1337.20	−	3228.29i	0.598002	−	1.44370i
$172$	884.465	+	1917.18i	0.392092	+	0.849903i
$173$	−45.5774	+	110.033i	−0.0200300	+	0.0483566i	−0.933578	−	0.358374i	$-0.883331\pi$
$173$	−45.5774	+	110.033i	−0.0200300	+	0.0483566i	0.913548	+	0.406731i	$0.133331\pi$
$174$	−5311.74	+	5526.04i	−2.31426	+	2.40763i
$175$	3572.18	−	1192.97i	1.54303	−	0.515314i
$176$	378.444	−	1166.90i	0.162081	−	0.499764i
$177$	4401.81	+	4401.81i	1.86927	+	1.86927i
$178$	4.89762	+	247.679i	0.00206232	+	0.104294i
$179$	−833.817	−	2013.01i	−0.348170	−	0.840556i	−0.996836	−	0.0794833i	$-0.974673\pi$
$179$	−833.817	−	2013.01i	−0.348170	−	0.840556i	0.648666	−	0.761073i	$-0.275327\pi$
$180$	−1168.07	−	5741.57i	−0.483680	−	2.37751i
$181$	961.010	+	398.063i	0.394648	+	0.163469i	0.571177	−	0.820827i	$-0.306487\pi$
$181$	961.010	+	398.063i	0.394648	+	0.163469i	−0.176529	+	0.984295i	$0.556487\pi$
$182$	812.845	−	355.678i	0.331055	−	0.144860i
$183$			4185.46i			1.69070i
$184$	851.150	−	958.622i	0.341020	−	0.384079i
$185$	1852.07	+	436.661i	0.736036	+	0.173535i
$186$	−3958.77	+	1732.25i	−1.56060	+	0.682874i
$187$	−1518.27	+	628.887i	−0.593726	+	0.245929i
$188$	−1470.73	−	1358.78i	−0.570552	−	0.527124i
$189$	−4270.31	−	10309.4i	−1.64349	−	3.96773i
$190$	1416.81	−	915.401i	0.540980	−	0.349527i
$191$		−	2721.63i		−	1.03105i	−0.856875	−	0.515525i	$-0.827597\pi$
$191$		−	2721.63i		−	1.03105i	0.856875	−	0.515525i	$-0.172403\pi$
$192$	4740.67	+	1332.81i	1.78192	+	0.500977i
$193$	2811.73	+	2811.73i	1.04867	+	1.04867i	0.998754	+	0.0499134i	$0.0158945\pi$
$193$	2811.73	+	2811.73i	1.04867	+	1.04867i	0.0499134	+	0.998754i	$0.484105\pi$
$194$	9.80550	+	495.876i	0.00362884	+	0.183514i
$195$	−1105.10	+	179.653i	−0.405834	+	0.0659755i
$196$	178.609	+	4514.48i	0.0650909	+	1.64522i
$197$	788.179	+	1902.83i	0.285053	+	0.688178i	0.999939	−	0.0110627i	$-0.00352143\pi$
$197$	788.179	+	1902.83i	0.285053	+	0.688178i	−0.714886	+	0.699241i	$0.753521\pi$
$198$	−1293.95	+	3307.36i	−0.464430	+	1.18709i
$199$	−40.5365	−	40.5365i	−0.0144400	−	0.0144400i	0.699850	−	0.714290i	$-0.253250\pi$
$199$	−40.5365	−	40.5365i	−0.0144400	−	0.0144400i	−0.714290	+	0.699850i	$0.753250\pi$
$200$	1111.25	−	2600.99i	0.392886	−	0.919587i
$201$	−2429.92	+	2429.92i	−0.852703	+	0.852703i
$202$	−1531.21	−	3499.34i	−0.533345	−	1.21888i
$203$	−7842.87	+	3248.62i	−2.71163	+	1.12320i
$204$	−2763.50	−	5990.19i	−0.948450	−	2.05587i
$205$	264.263	+	1625.55i	0.0900337	+	0.553823i
$206$	3932.06	−	4090.71i	1.32990	−	1.38356i
$207$	−2624.31	+	2624.31i	−0.881170	+	0.881170i
$208$	205.566	−	633.846i	0.0685263	−	0.211295i
$209$	−1022.43			−0.338389
$210$	1926.13	−	8959.02i	0.632930	−	2.94396i
$211$	783.711	−	324.624i	0.255701	−	0.105915i	−0.251151	−	0.967948i	$-0.580809\pi$
$211$	783.711	−	324.624i	0.255701	−	0.105915i	0.506852	+	0.862033i	$0.330809\pi$
$212$	2508.79	−	1157.40i	0.812758	−	0.374956i
$213$	−690.069	−	1665.97i	−0.221985	−	0.535918i
$214$	2643.35	+	1034.17i	0.844372	+	0.330348i
$215$	677.124	−	2871.97i	0.214788	−	0.911009i
$216$	−7919.09	−	2742.47i	−2.49456	−	0.863894i
$217$	−4785.77			−1.49714
$218$	−48.7271	+	124.547i	−0.0151386	+	0.0386944i
$219$	−48.6579	+	117.470i	−0.0150137	+	0.0362462i
$220$	−1421.32	+	958.671i	−0.435571	+	0.293789i
$221$	−824.705	+	341.604i	−0.251021	+	0.103976i
$222$	3208.55	−	3338.00i	0.970016	−	1.00915i
$223$	−2155.57	+	2155.57i	−0.647298	+	0.647298i	−0.952339	−	0.305041i	$-0.901330\pi$
$223$	−2155.57	+	2155.57i	−0.647298	+	0.647298i	0.305041	+	0.952339i	$0.401330\pi$
$224$	4218.30	+	3457.05i	1.25824	+	1.03118i
$225$	−3657.85	+	7326.05i	−1.08381	+	2.17068i
$226$	127.818	+	6463.91i	0.0376210	+	1.90254i
$227$	184.374	+	76.3704i	0.0539091	+	0.0223299i	0.409475	−	0.912321i	$-0.365712\pi$
$227$	184.374	+	76.3704i	0.0539091	+	0.0223299i	−0.355566	+	0.934651i	$0.615712\pi$
$228$	−162.256	−	4101.14i	−0.0471301	−	1.19125i
$229$	939.394	+	389.110i	0.271078	+	0.112284i	0.514082	−	0.857741i	$-0.328133\pi$
$229$	939.394	+	389.110i	0.271078	+	0.112284i	−0.243004	+	0.970025i	$0.578133\pi$
$230$	−1762.34	+	322.386i	−0.505241	+	0.0924238i
$231$	−3927.61	+	3927.61i	−1.11869	+	1.11869i
$232$	−2086.32	+	6024.43i	−0.590405	+	1.70484i
$233$	6864.34			1.93003			0.965017	−	0.262186i	$-0.0844434\pi$
$233$	6864.34			1.93003			0.965017	+	0.262186i	$0.0844434\pi$
$234$	−702.859	+	1796.52i	−0.196356	+	0.501888i
$235$	449.025	+	2762.08i	0.124643	+	0.766716i
$236$	4858.28	+	1790.81i	1.34003	+	0.493948i
$237$	−2896.80	−	1199.89i	−0.793955	−	0.328867i
$238$	−144.445	−	7304.76i	−0.0393403	−	1.98948i
$239$		−	970.384i		−	0.262631i	−0.991341	−	0.131316i	$-0.958080\pi$
$239$		−	970.384i		−	0.262631i	0.991341	−	0.131316i	$-0.0419202\pi$
$240$	−4070.93	−	5549.00i	−1.09491	−	1.49244i
$241$			868.914i			0.232247i	0.993235	+	0.116124i	$0.0370469\pi$
$241$			868.914i			0.232247i	−0.993235	+	0.116124i	$0.962953\pi$
$242$	−2724.93	+	53.8832i	−0.723824	+	0.0143130i
$243$	6698.58	+	2774.64i	1.76837	+	0.732483i
$244$	1458.35	+	3161.14i	0.382629	+	0.829391i
$245$	3690.48	−	5123.32i	0.962351	−	1.33599i
$246$	3731.79	+	1460.01i	0.967197	+	0.378401i
$247$	−555.374			−0.143067
$248$	−2386.36	+	2687.68i	−0.611024	+	0.688177i
$249$	4312.04	−	4312.04i	1.09745	−	1.09745i
$250$	−3462.78	+	1906.34i	−0.876022	+	0.482271i
$251$	2902.15	+	1202.11i	0.729808	+	0.302296i	0.716473	−	0.697615i	$-0.245755\pi$
$251$	2902.15	+	1202.11i	0.729808	+	0.302296i	0.0133350	+	0.999911i	$0.495755\pi$
$252$	−11597.4	−	10714.7i	−2.89909	−	2.67842i
$253$	1003.28	+	415.574i	0.249312	+	0.103268i
$254$	−1159.32	+	22.9246i	−0.286388	+	0.00566306i
$255$	−2115.67	+	8973.44i	−0.519561	+	2.20368i
$256$	4044.87	−	645.176i	0.987517	−	0.157514i
$257$	−403.313	+	403.313i	−0.0978909	+	0.0978909i	−0.754356	−	0.656465i	$-0.772051\pi$
$257$	−403.313	+	403.313i	−0.0978909	+	0.0978909i	0.656465	+	0.754356i	$0.272051\pi$
$258$	−5176.19	−	4975.45i	−1.24905	−	1.20061i
$259$	4737.48	−	1962.33i	1.13657	−	0.470784i
$260$	−772.046	+	520.739i	−0.184155	+	0.124211i
$261$	7063.31	−	17052.3i	1.67513	−	4.04411i
$262$	3400.86	+	1330.54i	0.801931	+	0.313744i
$263$	3275.03			0.767860			0.383930	−	0.923362i	$-0.374570\pi$
$263$	3275.03			0.767860			0.383930	+	0.923362i	$0.374570\pi$
$264$	247.287	+	4164.19i	0.0576495	+	0.970787i
$265$	−3758.23	−	886.076i	−0.871194	−	0.205401i
$266$	1656.17	−	4233.18i	0.381752	−	0.975763i
$267$	−322.372	−	778.274i	−0.0738907	−	0.178388i
$268$	−988.575	+	2681.91i	−0.225324	+	0.611281i
$269$	−5865.44	+	2429.54i	−1.32945	+	0.550676i	−0.930498	−	0.366296i	$-0.880626\pi$
$269$	−5865.44	+	2429.54i	−1.32945	+	0.550676i	−0.398952	+	0.916972i	$0.630626\pi$
$270$	6355.98	+	9837.45i	1.43264	+	2.21736i
$271$	610.437			0.136832			0.0684158	−	0.997657i	$-0.478206\pi$
$271$	610.437			0.136832			0.0684158	+	0.997657i	$0.478206\pi$
$272$	−4174.37	−	3561.30i	−0.930544	−	0.793881i
$273$	−2133.43	+	2133.43i	−0.472970	+	0.472970i
$274$	39.7937	+	38.2505i	0.00877382	+	0.00843356i
$275$	2390.03	+	168.497i	0.524089	+	0.0369481i
$276$	−1507.71	+	4090.27i	−0.328817	+	0.892049i
$277$	3652.24	−	1512.81i	0.792208	−	0.328143i	0.0503770	−	0.998730i	$-0.483958\pi$
$277$	3652.24	−	1512.81i	0.792208	−	0.328143i	0.741831	+	0.670587i	$0.233958\pi$
$278$	−1386.57	+	606.724i	−0.299140	+	0.130895i
$279$	7357.76	−	7357.76i	1.57884	−	1.57884i
$280$	−1666.88	−	7437.58i	−0.355768	−	1.58743i
$281$	3322.83	+	3322.83i	0.705421	+	0.705421i	0.965569	−	0.260148i	$-0.0837713\pi$
$281$	3322.83	+	3322.83i	0.705421	+	0.705421i	−0.260148	+	0.965569i	$0.583771\pi$
$282$	6340.93	+	2480.79i	1.33900	+	0.523862i
$283$	−3387.83	−	8178.94i	−0.711610	−	1.71798i	−0.695939	−	0.718101i	$-0.745012\pi$
$283$	−3387.83	−	8178.94i	−0.711610	−	1.71798i	−0.0156704	−	0.999877i	$-0.504988\pi$
$284$	−1101.67	−	1017.81i	−0.230183	−	0.212662i
$285$	−3352.58	+	4654.23i	−0.696806	+	0.967343i
$286$	564.354	−	11.1596i	0.116682	−	0.00230728i
$287$	3138.19	+	3138.19i	0.645441	+	0.645441i
$288$	−11800.3	+	1170.36i	−2.41436	+	0.239459i
$289$			2437.64i			0.496160i
$290$	7483.82	−	4835.29i	1.51540	−	0.979097i
$291$	−645.418	−	1558.18i	−0.130017	−	0.313890i
$292$	4.18092	+	105.676i	0.000837910	+	0.0211788i
$293$	7669.43	−	3176.78i	1.52919	−	0.633411i	0.549783	−	0.835307i	$-0.314710\pi$
$293$	7669.43	−	3176.78i	1.52919	−	0.633411i	0.979407	+	0.201896i	$0.0647103\pi$
$294$	−6158.84	−	14075.0i	−1.22174	−	2.79209i
$295$	−3806.05	−	6154.43i	−0.751176	−	1.21466i
$296$	1260.24	−	3639.05i	0.247466	−	0.714579i
$297$		−	7099.15i		−	1.38699i
$298$	−468.181	−	1069.95i	−0.0910101	−	0.207989i
$299$	544.972	+	225.735i	0.105407	+	0.0436608i
$300$	−296.576	+	9613.52i	−0.0570761	+	1.85012i
$301$	−3042.96	−	7346.34i	−0.582701	−	1.40676i
$302$	−44.4085	+	0.878140i	−0.00846167	+	0.000167322i
$303$	9184.52	+	9184.52i	1.74138	+	1.74138i
$304$	−1551.52	−	3040.92i	−0.292716	−	0.573713i
$305$	1116.48	−	4735.46i	0.209604	−	0.889022i
$306$	11452.6	+	11008.4i	2.13954	+	2.05657i
$307$	−970.332	+	2342.59i	−0.180390	+	0.435500i	−0.988047	−	0.154152i	$-0.950735\pi$
$307$	−970.332	+	2342.59i	−0.180390	+	0.435500i	0.807657	+	0.589653i	$0.200735\pi$
$308$	−1597.88	+	4334.90i	−0.295610	+	0.801961i
$309$	−7383.76	+	17826.0i	−1.35938	+	3.28183i
$310$	4941.07	−	903.869i	0.905270	−	0.165601i
$311$	5391.01	+	5391.01i	0.982946	+	0.982946i	0.999857	−	0.0169108i	$-0.00538313\pi$
$311$	5391.01	+	5391.01i	0.982946	+	0.982946i	−0.0169108	+	0.999857i	$0.505383\pi$
$312$	134.323	+	2261.93i	0.0243736	+	0.410439i
$313$		−	2374.97i		−	0.428886i	−0.976737	−	0.214443i	$-0.931206\pi$
$313$		−	2374.97i		−	0.428886i	0.976737	−	0.214443i	$-0.0687936\pi$
$314$	4141.41	+	9464.53i	0.744310	+	1.70100i
$315$	3540.79	+	21780.4i	0.633337	+	3.89583i
$316$	−2605.94	+	103.101i	−0.463911	+	0.0183540i
$317$	442.424	−	1068.11i	0.0783880	−	0.189245i	−0.879827	−	0.475294i	$-0.842342\pi$
$317$	442.424	−	1068.11i	0.0783880	−	0.189245i	0.958215	+	0.286048i	$0.0923418\pi$
$318$	−6510.82	+	6773.50i	−1.14814	+	1.19446i
$319$	−5400.66			−0.947897
$320$	−5008.10	−	2772.54i	−0.874879	−	0.484342i
$321$	−9652.18			−1.67829
$322$	−3345.75	+	3480.73i	−0.579041	+	0.602403i
$323$	−1750.12	+	4225.16i	−0.301483	+	0.727845i
$324$	14337.1	−	567.231i	2.45836	−	0.0972618i
$325$	1298.24	+	91.5253i	0.221579	+	0.0156213i
$326$	1234.61	+	2821.49i	0.209750	+	0.479350i
$327$		−	454.782i		−	0.0769098i
$328$	3327.22	−	197.584i	0.560106	−	0.0332615i
$329$	5332.30	+	5332.30i	0.893553	+	0.893553i
$330$	3313.27	−	4796.85i	0.552695	−	0.800175i
$331$	684.610	−	1652.80i	0.113685	−	0.274459i	−0.856789	−	0.515668i	$-0.827544\pi$
$331$	684.610	−	1652.80i	0.113685	−	0.274459i	0.970473	+	0.241209i	$0.0775439\pi$
$332$	1754.29	−	4759.20i	0.289997	−	0.786733i
$333$	−4266.58	+	10300.4i	−0.702124	+	1.69508i
$334$	−2385.08	−	2292.59i	−0.390736	−	0.375583i
$335$	3397.42	−	2101.05i	0.554092	−	0.342664i
$336$	−17641.5	−	5721.42i	−2.86435	−	0.928955i
$337$	−5969.43	−	5969.43i	−0.964913	−	0.964913i	0.0344924	−	0.999405i	$-0.489019\pi$
$337$	−5969.43	−	5969.43i	−0.964913	−	0.964913i	−0.999405	+	0.0344924i	$0.989019\pi$
$338$	−5906.29	+	116.792i	−0.950473	+	0.0187948i
$339$	−8413.25	−	20311.4i	−1.34792	−	3.25417i
$340$	1528.75	+	7514.52i	0.243848	+	1.19862i
$341$	−2812.90	−	1165.14i	−0.446707	−	0.185032i
$342$	3961.96	+	9054.42i	0.626427	+	1.43160i
$343$		−	6681.13i		−	1.05174i
$344$	−5643.02	−	1954.24i	−0.884452	−	0.306295i
$345$	5181.52	−	3204.38i	0.808591	−	0.500053i
$346$	−135.040	−	308.612i	−0.0209821	−	0.0479511i
$347$	−5334.88	+	2209.78i	−0.825335	+	0.341865i	−0.755054	−	0.655662i	$-0.772390\pi$
$347$	−5334.88	+	2209.78i	−0.825335	+	0.341865i	−0.0702809	+	0.997527i	$0.522390\pi$
$348$	−857.062	−	21662.8i	−0.132021	−	3.33693i
$349$	1684.63	+	4067.05i	0.258384	+	0.623795i	0.998832	−	0.0483192i	$-0.0153865\pi$
$349$	1684.63	+	4067.05i	0.258384	+	0.623795i	−0.740448	+	0.672114i	$0.765386\pi$
$350$	−4569.07	+	9622.50i	−0.697791	+	1.46956i
$351$		−	3856.17i		−	0.586403i
$352$	1637.71	+	3058.91i	0.247983	+	0.463183i
$353$	−6272.13	−	6272.13i	−0.945699	−	0.945699i	0.0529010	−	0.998600i	$-0.483153\pi$
$353$	−6272.13	−	6272.13i	−0.945699	−	0.945699i	−0.998600	+	0.0529010i	$0.983153\pi$
$354$	−17603.8	+	348.100i	−2.64303	+	0.0522635i
$355$	336.348	+	2068.97i	0.0502859	+	0.309323i
$356$	−514.653	−	475.480i	−0.0766196	−	0.0707876i
$357$	9507.68	+	22953.6i	1.40952	+	3.40289i
$358$	5739.17	+	2245.36i	0.847275	+	0.331484i
$359$	1190.51	+	1190.51i	0.175021	+	0.175021i	0.789181	−	0.614160i	$-0.210505\pi$
$359$	1190.51	+	1190.51i	0.175021	+	0.175021i	−0.614160	+	0.789181i	$0.710505\pi$
$360$	13997.4	+	8872.01i	2.04925	+	1.29888i
$361$	2838.11	−	2838.11i	0.413778	−	0.413778i
$362$	−2695.36	+	1179.41i	−0.391339	+	0.171239i
$363$	8562.49	−	3546.70i	1.23806	−	0.512819i
$364$	−867.951	+	2354.67i	−0.124981	+	0.339061i
$365$	86.3873	−	119.927i	0.0123883	−	0.0171980i
$366$	−8534.78	−	8203.79i	−1.21891	−	1.17164i
$367$	−835.537	+	835.537i	−0.118841	+	0.118841i	−0.764026	−	0.645185i	$-0.776780\pi$
$367$	−835.537	+	835.537i	−0.118841	+	0.118841i	0.645185	+	0.764026i	$0.276780\pi$
$368$	286.461	+	3614.59i	0.0405783	+	0.512020i
$369$	−9649.46			−1.36133
$370$	−4520.59	+	2920.75i	−0.635174	+	0.410386i
$371$	−9613.34	+	3981.98i	−1.34528	+	0.557234i
$372$	4227.16	−	11467.9i	0.589161	−	1.59834i
$373$	1097.63	+	2649.92i	0.152368	+	0.367850i	0.981571	−	0.191099i	$-0.0612051\pi$
$373$	1097.63	+	2649.92i	0.152368	+	0.367850i	−0.829203	+	0.558948i	$0.811205\pi$
$374$	1693.51	−	4328.64i	0.234143	−	0.598472i
$375$	8603.97	−	10327.2i	1.18482	−	1.42212i
$376$	5653.49	−	335.728i	0.775416	−	0.0460475i
$377$	−2933.57			−0.400761
$378$	29392.6	+	11499.4i	3.99945	+	1.56472i
$379$	−4362.77	+	10532.6i	−0.591294	+	1.42751i	0.290960	+	0.956735i	$0.406025\pi$
$379$	−4362.77	+	10532.6i	−0.591294	+	1.42751i	−0.882254	+	0.470774i	$0.843975\pi$
$380$	−910.406	+	4683.34i	−0.122902	+	0.632237i
$381$	3642.92	−	1508.95i	0.489848	−	0.202902i
$382$	5549.82	+	5334.59i	0.743334	+	0.714506i
$383$	7010.25	−	7010.25i	0.935266	−	0.935266i	−0.0627623	−	0.998029i	$-0.519991\pi$
$383$	7010.25	−	7010.25i	0.935266	−	0.935266i	0.998029	+	0.0627623i	$0.0199910\pi$
$384$	−12009.8	+	7054.53i	−1.59603	+	0.937499i
$385$	5491.42	−	3396.03i	0.726931	−	0.449552i
$386$	−11244.7	+	222.354i	−1.48275	+	0.0293201i
$387$	15972.8	+	6616.13i	2.09804	+	0.869036i
$388$	−1030.38	−	951.956i	−0.134819	−	0.124557i
$389$	2817.91	+	1167.22i	0.367285	+	0.152134i	0.558689	−	0.829377i	$-0.311304\pi$
$389$	2817.91	+	1167.22i	0.367285	+	0.152134i	−0.191405	+	0.981511i	$0.561304\pi$
$390$	1799.73	−	2605.59i	0.233673	−	0.338306i
$391$	3434.68	−	3434.68i	0.444243	−	0.444243i
$392$	−9555.79	−	8484.48i	−1.23122	−	1.09319i
$393$	−12418.2			−1.59394
$394$	−5425.04	−	2122.47i	−0.693679	−	0.271392i
$395$	2957.39	+	2130.30i	0.376715	+	0.271359i
$396$	−4207.96	−	9121.21i	−0.533984	−	1.15747i
$397$	10675.5	+	4421.92i	1.34959	+	0.559017i	0.936177	−	0.351529i	$-0.114338\pi$
$397$	10675.5	+	4421.92i	1.34959	+	0.559017i	0.413409	+	0.910546i	$0.364338\pi$
$398$	162.114	−	3.20567i	0.0204172	−	0.000403733i
$399$			15457.4i			1.93945i
$400$	3125.67	+	7364.11i	0.390709	+	0.920514i
$401$		−	6086.77i		−	0.758003i	−0.925396	−	0.379001i	$-0.876268\pi$
$401$		−	6086.77i		−	0.758003i	0.925396	−	0.379001i	$-0.123732\pi$
$402$	−192.161	−	9717.78i	−0.0238410	−	1.20567i
$403$	−1527.93	−	632.891i	−0.188863	−	0.0782296i
$404$	10137.0	+	3736.58i	1.24835	+	0.460153i
$405$	−16270.7	−	11720.3i	−1.99629	−	1.43799i
$406$	8748.14	−	22360.3i	1.06937	−	2.73331i
$407$	3262.26			0.397308
$408$	17631.6	+	6106.00i	2.13944	+	0.740912i
$409$	58.2196	−	58.2196i	0.00703857	−	0.00703857i	−0.703579	−	0.710617i	$-0.748416\pi$
$409$	58.2196	−	58.2196i	0.00703857	−	0.00703857i	0.710617	+	0.703579i	$0.248416\pi$
$410$	−3832.72	−	2647.33i	−0.461670	−	0.318883i
$411$	−173.408	−	71.8280i	−0.0208117	−	0.00862047i
$412$	634.449	+	16036.1i	0.0758666	+	1.91758i
$413$	−18015.9	−	7462.44i	−2.14650	−	0.889110i
$414$	−207.533	−	10495.2i	−0.0246369	−	1.24592i
$415$	−6028.92	+	3728.43i	−0.713128	+	0.441016i
$416$	889.583	+	1661.56i	0.104845	+	0.195829i
$417$	3639.25	−	3639.25i	0.427374	−	0.427374i
$418$	2004.04	−	2084.90i	0.234500	−	0.243961i
$419$	−6061.62	+	2510.80i	−0.706753	+	0.292747i	−0.706960	−	0.707253i	$-0.749934\pi$
$419$	−6061.62	+	2510.80i	−0.706753	+	0.292747i	0.000207258		1.00000i	$0.499934\pi$
$420$	14493.4	+	21487.9i	1.68383	+	2.49644i
$421$	2766.61	−	6679.19i	0.320276	−	0.773215i	−0.678961	−	0.734174i	$-0.737570\pi$
$421$	2766.61	−	6679.19i	0.320276	−	0.773215i	0.999238	−	0.0390413i	$-0.0124304\pi$
$422$	−874.171	+	2234.39i	−0.100839	+	0.257745i
$423$	−16396.0			−1.88464
$424$	−2557.30	+	7384.39i	−0.292909	+	0.845797i
$425$	4787.36	−	9588.27i	0.546402	−	1.09435i
$426$	4749.75	+	1858.27i	0.540202	+	0.211346i
$427$	−5017.38	−	12113.0i	−0.568638	−	1.37281i
$428$	−7289.97	+	3363.14i	−0.823304	+	0.379821i
$429$	−1773.35	+	734.547i	−0.199577	+	0.0826673i
$430$	4529.17	+	7010.02i	0.507945	+	0.786170i
$431$	−15438.9			−1.72544			−0.862722	−	0.505679i	$-0.831242\pi$
$431$	−15438.9			−1.72544			−0.862722	+	0.505679i	$0.831242\pi$
$432$	21114.3	−	10772.8i	2.35153	−	1.19978i
$433$	11059.3	−	11059.3i	1.22742	−	1.22742i	0.262488	−	0.964935i	$-0.415457\pi$
$433$	11059.3	−	11059.3i	1.22742	−	1.22742i	0.964935	−	0.262488i	$-0.0845430\pi$
$434$	9380.44	−	9758.90i	1.03750	−	1.07936i
$435$	−17708.9	+	24584.4i	−1.95190	+	2.70973i
$436$	−158.461	−	343.482i	−0.0174058	−	0.0377289i
$437$	2792.02	−	1156.49i	0.305630	−	0.126596i
$438$	−144.167	−	329.471i	−0.0157273	−	0.0359423i
$439$	5836.56	−	5836.56i	0.634541	−	0.634541i	−0.314662	−	0.949204i	$-0.601891\pi$
$439$	5836.56	−	5836.56i	0.634541	−	0.634541i	0.949204	+	0.314662i	$0.101891\pi$
$440$	831.020	−	4777.36i	0.0900394	−	0.517617i
$441$	26159.8	+	26159.8i	2.82473	+	2.82473i
$442$	919.896	−	2351.26i	0.0989932	−	0.253028i
$443$	1716.58	+	4144.20i	0.184102	+	0.444462i	0.988805	−	0.149216i	$-0.0476751\pi$
$443$	1716.58	+	4144.20i	0.184102	+	0.444462i	−0.804702	+	0.593679i	$0.797675\pi$
$444$	517.708	+	13085.4i	0.0553363	+	1.39866i
$445$	157.128	+	966.538i	0.0167384	+	0.102962i
$446$	−170.464	−	8620.58i	−0.0180980	−	0.915239i
$447$	2808.25	+	2808.25i	0.297149	+	0.297149i
$448$	−15317.6	+	1825.69i	−1.61537	+	0.192535i
$449$		−	6835.92i		−	0.718501i	−0.933241	−	0.359251i	$-0.883032\pi$
$449$		−	6835.92i		−	0.718501i	0.933241	−	0.359251i	$-0.116968\pi$
$450$	−7769.27	−	21818.5i	−0.813882	−	2.28563i
$451$	1080.49	+	2608.54i	0.112812	+	0.272353i
$452$	−13431.4	−	12409.1i	−1.39770	−	1.29131i
$453$	139.544	−	57.8009i	0.0144732	−	0.00599498i
$454$	−517.117	+	226.276i	−0.0534571	+	0.0233913i
$455$	2982.87	−	1844.68i	0.307339	−	0.190066i
$456$	8680.86	+	7707.64i	0.891488	+	0.791543i
$457$			7018.97i			0.718454i	0.933250	+	0.359227i	$0.116960\pi$
$457$			7018.97i			0.718454i	−0.933250	+	0.359227i	$0.883040\pi$
$458$	−2634.73	+	1152.88i	−0.268805	+	0.117622i
$459$	−29336.9	−	12151.7i	−2.98328	−	1.23572i
$460$	2796.92	−	4225.58i	0.283494	−	0.428302i
$461$	4688.35	+	11318.7i	0.473663	+	1.14352i	0.962533	+	0.271166i	$0.0874092\pi$
$461$	4688.35	+	11318.7i	0.473663	+	1.14352i	−0.488870	+	0.872357i	$0.662591\pi$
$462$	−310.599	−	15707.4i	−0.0312779	−	1.58176i
$463$	−850.455	−	850.455i	−0.0853650	−	0.0853650i	0.663135	−	0.748500i	$-0.269226\pi$
$463$	−850.455	−	850.455i	−0.0853650	−	0.0853650i	−0.748500	+	0.663135i	$0.769226\pi$
$464$	−8195.37	−	16062.6i	−0.819958	−	1.60709i
$465$	−14527.4	+	8984.10i	−1.44880	+	0.895973i
$466$	−13454.6	+	13997.4i	−1.33749	+	1.39146i
$467$	−2864.65	+	6915.89i	−0.283855	+	0.685287i	−0.999919	−	0.0127479i	$-0.995942\pi$
$467$	−2864.65	+	6915.89i	−0.283855	+	0.685287i	0.716063	+	0.698035i	$0.245942\pi$
$468$	−2285.71	−	4954.53i	−0.225763	−	0.489366i
$469$	4119.47	−	9945.28i	0.405585	−	0.979169i
$470$	−6512.42	−	4498.24i	−0.639139	−	0.441464i
$471$	−24841.0	−	24841.0i	−2.43018	−	2.43018i
$472$	−13174.3	+	6396.66i	−1.28474	+	0.623792i
$473$		−	5058.75i		−	0.491758i
$474$	8124.69	−	3555.14i	0.787299	−	0.344500i
$475$	5034.66	−	4371.53i	0.486328	−	0.422272i
$476$	15178.6	+	14023.3i	1.46158	+	1.35033i
$477$	8657.79	−	20901.8i	0.831055	−	2.00634i
$478$	1978.76	+	1902.02i	0.189344	+	0.182001i
$479$	−3580.44			−0.341533			−0.170766	−	0.985312i	$-0.554624\pi$
$479$	−3580.44			−0.341533			−0.170766	+	0.985312i	$0.554624\pi$
$480$	19294.6	+	2575.20i	1.83473	+	0.244877i
$481$	1772.02			0.167978
$482$	−1771.84	−	1703.13i	−0.167438	−	0.160945i
$483$	6282.76	−	15167.9i	0.591874	−	1.42891i
$484$	5231.18	−	5662.16i	0.491283	−	0.531758i
$485$	314.585	+	1935.10i	0.0294527	+	0.181172i
$486$	−18787.6	+	8220.92i	−1.75354	+	0.767301i
$487$		−	16227.9i		−	1.50997i	−0.655743	−	0.754984i	$-0.727645\pi$
$487$		−	16227.9i		−	1.50997i	0.655743	−	0.754984i	$-0.272355\pi$
$488$	−9304.51	−	3222.25i	−0.863105	−	0.298903i
$489$	−7405.41	−	7405.41i	−0.684835	−	0.684835i
$490$	3213.62	+	17567.5i	0.296279	+	1.61963i
$491$	−5147.62	+	12427.4i	−0.473134	+	1.14225i	0.489637	+	0.871927i	$0.337129\pi$
$491$	−5147.62	+	12427.4i	−0.473134	+	1.14225i	−0.962771	+	0.270320i	$0.912871\pi$
$492$	−10291.7	+	4747.97i	−0.943065	+	0.435071i
$493$	−9244.39	+	22317.9i	−0.844516	+	2.03884i
$494$	1088.57	−	1132.49i	0.0991440	−	0.103144i
$495$	−3221.50	+	13663.8i	−0.292517	+	1.24069i
$496$	−803.149	−	10134.2i	−0.0727065	−	0.917416i
$497$	3994.22	+	3994.22i	0.360494	+	0.360494i
$498$	341.001	+	17244.8i	0.0306839	+	1.55172i
$499$	−5885.54	−	14208.9i	−0.528002	−	1.27471i	−0.932830	−	0.360316i	$-0.882669\pi$
$499$	−5885.54	−	14208.9i	−0.528002	−	1.27471i	0.404828	−	0.914393i	$-0.367331\pi$
$500$	2899.97	−	10797.7i	0.259381	−	0.965775i
$501$	10393.4	+	4305.10i	0.926834	+	0.383907i
$502$	−8139.69	+	3561.70i	−0.723689	+	0.316666i
$503$			18246.9i			1.61748i	0.588169	+	0.808738i	$0.299849\pi$
$503$			18246.9i			1.61748i	−0.588169	+	0.808738i	$0.700151\pi$
$504$	44580.6	−	2647.39i	3.94004	−	0.233976i
$505$	−7941.45	−	12841.4i	−0.699782	−	1.13156i
$506$	−2813.93	+	1231.29i	−0.247222	+	0.108177i
$507$	18559.2	−	7687.46i	1.62572	−	0.673397i
$508$	2225.61	−	2408.97i	0.194381	−	0.210395i
$509$	5176.13	+	12496.3i	0.450743	+	1.08819i	0.972040	+	0.234814i	$0.0754481\pi$
$509$	5176.13	+	12496.3i	0.450743	+	1.08819i	−0.521298	+	0.853375i	$0.674552\pi$
$510$	−14151.3	−	21902.7i	−1.22869	−	1.90170i
$511$		−	398.298i		−	0.0344807i
$512$	−6612.61	+	9512.68i	−0.570779	+	0.821104i
$513$	−13969.7	−	13969.7i	−1.20229	−	1.20229i
$514$	−31.8944	−	1612.94i	−0.00273697	−	0.138412i
$515$	13109.2	−	18198.8i	1.12167	−	1.55716i
$516$	20291.4	−	802.802i	1.73116	−	0.0684911i
$517$	1835.93	+	4432.33i	0.156178	+	0.377047i
$518$	−5284.30	+	13506.7i	−0.448222	+	1.14566i
$519$	809.997	+	809.997i	0.0685066	+	0.0685066i
$520$	451.400	−	2595.00i	0.0380677	−	0.218843i
$521$	6997.41	−	6997.41i	0.588411	−	0.588411i	−0.348790	−	0.937201i	$-0.613407\pi$
$521$	6997.41	−	6997.41i	0.588411	−	0.588411i	0.937201	+	0.348790i	$0.113407\pi$
$522$	20927.7	+	47826.9i	1.75475	+	4.01020i
$523$	11345.6	−	4699.50i	0.948581	−	0.392915i	0.145884	−	0.989302i	$-0.453397\pi$
$523$	11345.6	−	4699.50i	0.948581	−	0.392915i	0.802697	+	0.596387i	$0.203397\pi$
$524$	−9379.09	+	4326.93i	−0.781923	+	0.360730i
$525$	2547.37	−	36133.1i	0.211765	−	3.00377i
$526$	−6419.29	+	6678.28i	−0.532118	+	0.553587i
$527$	−9629.77	+	9629.77i	−0.795976	+	0.795976i
$528$	−8976.10	−	7657.83i	−0.739838	−	0.631183i
$529$	8957.21			0.736189
$530$	9173.23	−	5926.82i	0.751811	−	0.485745i
$531$	39171.0	−	16225.2i	3.20128	−	1.32601i
$532$	5385.88	+	11674.5i	0.438924	+	0.951416i
$533$	586.909	+	1416.92i	0.0476958	+	0.115148i
$534$	2218.89	+	868.106i	0.179814	+	0.0703495i
$535$	10920.5	+	2574.73i	0.882498	+	0.208066i
$536$	−3531.13	−	7272.57i	−0.284555	−	0.586058i
$537$	−20956.5			−1.68406
$538$	6542.46	−	16722.6i	0.524285	−	1.34008i
$539$	4142.55	−	10001.0i	0.331043	−	0.799209i
$540$	−32518.2	−	6321.30i	−2.59141	−	0.503751i
$541$	−2064.13	+	854.992i	−0.164037	+	0.0679463i	−0.463191	−	0.886259i	$-0.653296\pi$
$541$	−2064.13	+	854.992i	−0.164037	+	0.0679463i	0.299154	+	0.954205i	$0.403296\pi$
$542$	−1196.50	+	1244.77i	−0.0948228	+	0.0986486i
$543$	7074.35	−	7074.35i	0.559096	−	0.559096i
$544$	15444.1	−	1531.76i	1.21720	−	0.120724i
$545$	−121.314	+	514.544i	−0.00953489	+	0.0404415i
$546$	−168.714	−	8532.04i	−0.0132239	−	0.668750i
$547$	−15173.1	−	6284.92i	−1.18603	−	0.491268i	−0.299567	−	0.954075i	$-0.596842\pi$
$547$	−15173.1	−	6284.92i	−1.18603	−	0.491268i	−0.886459	+	0.462807i	$0.846842\pi$
$548$	−155.997	+	6.17181i	−0.0121603	+	0.000481107i
$549$	26336.7	+	10909.0i	2.04740	+	0.848062i
$550$	−5028.22	+	4543.37i	−0.389826	+	0.352236i
$551$	−10627.4	+	10627.4i	−0.821673	+	0.821673i
$552$	−5385.46	−	11091.7i	−0.415254	−	0.855240i
$553$	9821.96			0.755284
$554$	−4073.80	+	10412.7i	−0.312417	+	0.798541i
$555$	10697.0	−	14850.2i	0.818132	−	1.13577i
$556$	1480.57	−	4016.64i	0.112932	−	0.306373i
$557$	−1640.73	−	679.612i	−0.124811	−	0.0516985i	0.319404	−	0.947619i	$-0.396517\pi$
$557$	−1640.73	−	679.612i	−0.124811	−	0.0516985i	−0.444215	+	0.895920i	$0.646517\pi$
$558$	581.859	+	29425.3i	0.0441434	+	2.23239i
$559$		−	2747.85i		−	0.207910i
$560$	18433.5	+	11179.2i	1.39100	+	0.843581i
$561$			15806.0i			1.18954i
$562$	−13288.7	+	262.773i	−0.997421	+	0.0197231i
$563$	15177.3	+	6286.63i	1.13614	+	0.470604i	0.869863	−	0.493293i	$-0.164207\pi$
$563$	15177.3	+	6286.63i	1.13614	+	0.470604i	0.266275	+	0.963897i	$0.414207\pi$
$564$	−17487.4	+	8067.58i	−1.30559	+	0.602316i
$565$	4100.72	+	25224.7i	0.305343	+	1.87825i
$566$	23318.5	+	9123.00i	1.73171	+	0.677506i
$567$	−54037.6			−4.00241
$568$	4234.81	−	251.481i	0.312832	−	0.0185773i
$569$	−4619.03	+	4619.03i	−0.340316	+	0.340316i	−0.856486	−	0.516170i	$-0.827357\pi$
$569$	−4619.03	+	4619.03i	−0.340316	+	0.340316i	0.516170	+	0.856486i	$0.327357\pi$
$570$	−2919.38	−	15959.0i	−0.214525	−	1.17272i
$571$	−19556.4	−	8100.52i	−1.43329	−	0.593689i	−0.475130	−	0.879916i	$-0.657599\pi$
$571$	−19556.4	−	8100.52i	−1.43329	−	0.593689i	−0.958162	+	0.286227i	$0.907599\pi$
$572$	−1083.42	+	1172.68i	−0.0791956	+	0.0857203i
$573$	−24184.3	−	10017.5i	−1.76320	−	0.730342i
$574$	−12550.3	+	248.171i	−0.912613	+	0.0180461i
$575$	−6717.19	+	2243.28i	−0.487176	+	0.162698i
$576$	20742.8	−	26356.5i	1.50049	−	1.90657i
$577$	16382.7	−	16382.7i	1.18201	−	1.18201i	0.202786	−	0.979223i	$-0.435000\pi$
$577$	16382.7	−	16382.7i	1.18201	−	1.18201i	0.979223	−	0.202786i	$-0.0649995\pi$
$578$	−4970.70	−	4777.93i	−0.357706	−	0.343834i
$579$	35334.0	−	14635.8i	2.53615	−	1.05051i
$580$	−4808.91	+	24738.1i	−0.344274	+	1.77103i
$581$	−7310.25	+	17648.5i	−0.521997	+	1.26021i
$582$	4442.42	+	1738.03i	0.316399	+	0.123786i
$583$	−6619.82			−0.470266
$584$	−223.683	−	198.606i	−0.0158495	−	0.0140726i
$585$	−1749.88	+	7421.99i	−0.123673	+	0.524550i
$586$	−8554.67	+	21865.8i	−0.603055	+	1.54141i
$587$	−392.268	−	947.019i	−0.0275820	−	0.0665889i	0.909488	−	0.415729i	$-0.136474\pi$
$587$	−392.268	−	947.019i	−0.0275820	−	0.0665889i	−0.937070	+	0.349140i	$0.886474\pi$
$588$	40772.9	+	15029.3i	2.85960	+	1.05407i
$589$	−7827.96	+	3242.45i	−0.547616	+	0.226830i
$590$	20009.9	+	4302.00i	1.39626	+	0.300187i
$591$	19809.5			1.37877
$592$	4950.40	+	9702.61i	0.343683	+	0.673606i
$593$	−13468.8	+	13468.8i	−0.932714	+	0.932714i	−0.997875	−	0.0651609i	$-0.979244\pi$
$593$	−13468.8	+	13468.8i	−0.932714	+	0.932714i	0.0651609	+	0.997875i	$0.479244\pi$
$594$	14476.2	+	13914.8i	0.999945	+	0.961165i
$595$	−4634.16	−	28506.0i	−0.319298	−	1.96409i
$596$	3099.46	+	1142.49i	0.213018	+	0.0785205i
$597$	−509.408	+	211.004i	−0.0349224	+	0.0144653i
$598$	−1528.49	+	668.824i	−0.104523	+	0.0457362i
$599$	−2621.74	+	2621.74i	−0.178833	+	0.178833i	−0.790847	−	0.612014i	$-0.790360\pi$
$599$	−2621.74	+	2621.74i	−0.178833	+	0.178833i	0.612014	+	0.790847i	$0.290360\pi$
$600$	−19022.1	−	19447.9i	−1.29429	−	1.32326i
$601$	−7649.13	−	7649.13i	−0.519159	−	0.519159i	0.398158	−	0.917317i	$-0.369650\pi$
$601$	−7649.13	−	7649.13i	−0.519159	−	0.519159i	−0.917317	+	0.398158i	$0.869650\pi$
$602$	20944.7	+	8194.30i	1.41801	+	0.554775i
$603$	8956.74	+	21623.5i	0.604887	+	1.46033i
$604$	85.2531	−	92.2769i	0.00574321	−	0.00621638i
$605$	−10633.8	+	1728.71i	−0.714585	+	0.116168i
$606$	−36730.9	+	726.321i	−2.46220	+	0.0486877i
$607$	9499.41	+	9499.41i	0.635205	+	0.635205i	0.949369	−	0.314164i	$-0.101724\pi$
$607$	9499.41	+	9499.41i	0.635205	+	0.635205i	−0.314164	+	0.949369i	$0.601724\pi$
$608$	9241.97	+	2796.63i	0.616466	+	0.186543i
$609$			81648.6i			5.43279i
$610$	7467.94	+	11558.5i	0.495685	+	0.767196i
$611$	997.255	+	2407.59i	0.0660305	+	0.159412i
$612$	−44895.7	+	1776.24i	−2.96536	+	0.117321i
$613$	−13290.8	+	5505.21i	−0.875708	+	0.362730i	−0.774831	−	0.632169i	$-0.782165\pi$
$613$	−13290.8	+	5505.21i	−0.875708	+	0.362730i	−0.100877	+	0.994899i	$0.532165\pi$
$614$	−2874.97	−	6570.28i	−0.188965	−	0.431849i
$615$	15417.3	+	3634.92i	1.01087	+	0.238332i
$616$	−5707.55	−	11755.0i	−0.373318	−	0.768870i
$617$			17987.3i			1.17365i	0.809713	+	0.586826i	$0.199623\pi$
$617$			17987.3i			1.17365i	−0.809713	+	0.586826i	$0.800377\pi$
$618$	−21877.2	−	49996.7i	−1.42399	−	3.25431i
$619$	22548.5	+	9339.89i	1.46414	+	0.606465i	0.965513	−	0.260354i	$-0.0838393\pi$
$619$	22548.5	+	9339.89i	1.46414	+	0.606465i	0.498623	+	0.866819i	$0.333839\pi$
$620$	−7841.71	+	11847.2i	−0.507952	+	0.767413i
$621$	8029.97	+	19386.1i	0.518891	+	1.25271i
$622$	−21559.8	+	426.327i	−1.38982	+	0.0274825i
$623$	1865.94	+	1865.94i	0.119995	+	0.119995i
$624$	−4875.71	−	4159.64i	−0.312796	−	0.266857i
$625$	−12489.4	+	9389.13i	−0.799321	+	0.600904i
$626$	4842.92	+	4655.10i	0.309204	+	0.297213i
$627$	−3763.26	+	9085.31i	−0.239697	+	0.578680i
$628$	−27417.0	−	10106.2i	−1.74213	−	0.642166i
$629$	5584.07	−	13481.1i	0.353977	−	0.854575i
$630$	−51353.7	−	35470.9i	−3.24759	−	2.24317i
$631$	4920.40	+	4920.40i	0.310425	+	0.310425i	0.845074	−	0.534649i	$-0.179556\pi$
$631$	4920.40	+	4920.40i	0.310425	+	0.310425i	−0.534649	+	0.845074i	$0.679556\pi$
$632$	4897.59	−	5515.99i	0.308253	−	0.347175i
$633$		−	8158.86i		−	0.512299i
$634$	1310.85	+	2995.73i	0.0821141	+	0.187659i
$635$	−4524.14	+	735.479i	−0.282732	+	0.0459631i
$636$	−1050.54	−	26553.1i	−0.0654977	−	1.65550i
$637$	2250.18	−	5432.42i	0.139961	−	0.337897i
$638$	10585.7	−	11012.8i	0.656882	−	0.683385i
$639$	−12281.6			−0.760334
$640$	15469.8	−	4777.90i	0.955467	−	0.295099i
$641$	4202.10			0.258928			0.129464	−	0.991584i	$-0.458674\pi$
$641$	4202.10			0.258928			0.129464	+	0.991584i	$0.458674\pi$
$642$	18918.9	−	19682.2i	1.16304	−	1.20996i
$643$	−6008.28	+	14505.3i	−0.368497	+	0.889631i	0.625500	+	0.780224i	$0.284895\pi$
$643$	−6008.28	+	14505.3i	−0.368497	+	0.889631i	−0.993997	+	0.109406i	$0.965105\pi$
$644$	−539.845	−	13645.0i	−0.0330324	−	0.834917i
$645$	−23027.9	−	16587.7i	−1.40577	−	1.01262i
$646$	−5185.38	−	11850.3i	−0.315814	−	0.721742i
$647$		−	32409.6i		−	1.96933i	−0.174467	−	0.984663i	$-0.555820\pi$
$647$		−	32409.6i		−	1.96933i	0.174467	−	0.984663i	$-0.444180\pi$
$648$	−26945.1	+	30347.4i	−1.63349	+	1.83975i
$649$	−8772.29	−	8772.29i	−0.530574	−	0.530574i
$650$	−2731.27	+	2467.90i	−0.164814	+	0.148922i
$651$	−17614.9	+	42526.1i	−1.06050	+	2.56026i
$652$	−8173.36	−	3012.77i	−0.490941	−	0.180965i
$653$	4683.17	−	11306.2i	0.280653	−	0.677556i	−0.719198	−	0.694805i	$-0.755491\pi$
$653$	4683.17	−	11306.2i	0.280653	−	0.677556i	0.999851	+	0.0172486i	$0.00549069\pi$
$654$	927.369	+	891.404i	0.0554480	+	0.0532976i
$655$	14050.1	+	3312.58i	0.838141	+	0.197608i
$656$	−6118.67	+	7171.98i	−0.364168	+	0.426858i
$657$	612.353	+	612.353i	0.0363625	+	0.0363625i
$658$	−21325.0	+	421.683i	−1.26343	+	0.0249832i
$659$	8129.07	+	19625.3i	0.480521	+	1.16008i	0.959362	+	0.282179i	$0.0910573\pi$
$659$	8129.07	+	19625.3i	0.480521	+	1.16008i	−0.478840	+	0.877902i	$0.658943\pi$
$660$	3287.26	+	16158.4i	0.193874	+	0.952977i
$661$	−21509.9	−	8909.68i	−1.26571	−	0.524276i	−0.354055	−	0.935225i	$-0.615197\pi$
$661$	−21509.9	−	8909.68i	−1.26571	−	0.524276i	−0.911658	+	0.410949i	$0.865197\pi$
$662$	2028.41	+	4635.61i	0.119088	+	0.272158i
$663$			8585.63i			0.502923i
$664$	6266.21	+	12905.6i	0.366229	+	0.754270i
$665$	4123.29	−	17488.7i	0.240443	−	1.01982i
$666$	−12641.3	−	28889.8i	−0.735499	−	1.68086i
$667$	14747.9	−	6108.78i	0.856133	−	0.354622i
$668$	9349.86	−	369.915i	0.541552	−	0.0214258i
$669$	11220.3	+	27088.2i	0.648434	+	1.56546i
$670$	−2374.82	+	11046.0i	−0.136936	+	0.636934i
$671$		−	8341.13i		−	0.479889i
$672$	46245.4	−	24759.3i	2.65469	−	1.42130i
$673$	20959.2	+	20959.2i	1.20047	+	1.20047i	0.974024	+	0.226446i	$0.0727105\pi$
$673$	20959.2	+	20959.2i	1.20047	+	1.20047i	0.226446	+	0.974024i	$0.427289\pi$
$674$	23873.0	−	472.068i	1.36433	−	0.0269783i
$675$	30353.2	+	34957.5i	1.73081	+	1.99336i
$676$	11338.6	−	12272.7i	0.645117	−	0.698266i
$677$	11854.9	+	28620.3i	0.673002	+	1.62477i	0.776483	+	0.630139i	$0.217002\pi$
$677$	11854.9	+	28620.3i	0.673002	+	1.62477i	−0.103481	+	0.994631i	$0.532998\pi$
$678$	57908.5	+	22655.8i	3.28018	+	1.28332i
$679$	3735.78	+	3735.78i	0.211143	+	0.211143i
$680$	−18319.7	−	11611.6i	−1.03313	−	0.654831i
$681$	1357.25	−	1357.25i	0.0763727	−	0.0763727i
$682$	7889.38	−	3452.17i	0.442962	−	0.193827i
$683$	−14291.2	+	5919.61i	−0.800640	+	0.331636i	−0.745213	−	0.666827i	$-0.767652\pi$
$683$	−14291.2	+	5919.61i	−0.800640	+	0.331636i	−0.0554275	+	0.998463i	$0.517652\pi$
$684$	−26229.0	−	9668.26i	−1.46622	−	0.540461i
$685$	177.035	+	127.524i	0.00987469	+	0.00711303i
$686$	13623.8	+	13095.5i	0.758251	+	0.728845i
$687$	6915.23	−	6915.23i	0.384035	−	0.384035i
$688$	15045.7	−	7676.52i	0.833738	−	0.425385i
$689$	−3595.81			−0.198823
$690$	−3621.93	+	16846.7i	−0.199833	+	0.929483i
$691$	12366.9	−	5122.53i	0.680837	−	0.282012i	−0.0153395	−	0.999882i	$-0.504883\pi$
$691$	12366.9	−	5122.53i	0.680837	−	0.282012i	0.696177	+	0.717870i	$0.254883\pi$
$692$	893.994	+	329.534i	0.0491106	+	0.0181026i
$693$	14477.2	+	34951.2i	0.793571	+	1.91585i
$694$	5950.66	−	15209.9i	0.325481	−	0.831933i
$695$	−5088.25	+	3146.70i	−0.277710	+	0.171743i
$696$	45853.7	+	40713.0i	2.49724	+	2.21727i
$697$	12629.1			0.686316
$698$	−11595.3	−	4536.49i	−0.628781	−	0.246001i
$699$	25265.5	−	60996.3i	1.36714	−	3.30056i
$700$	−10666.0	−	28177.8i	−0.575912	−	1.52146i
$701$	−21121.9	+	8748.98i	−1.13804	+	0.471390i	−0.870505	−	0.492160i	$-0.836208\pi$
$701$	−21121.9	+	8748.98i	−1.13804	+	0.471390i	−0.267531	+	0.963549i	$0.586208\pi$
$702$	7863.31	+	7558.36i	0.422766	+	0.406370i
$703$	6419.46	−	6419.46i	0.344402	−	0.344402i
$704$	−9447.60	−	2656.14i	−0.505781	−	0.142198i
$705$	26196.5	+	6176.33i	1.39945	+	0.329949i
$706$	25083.6	−	496.006i	1.33716	−	0.0264411i
$707$	−37590.8	−	15570.6i	−1.99964	−	0.828279i
$708$	33794.8	−	36579.1i	1.79391	−	1.94170i
$709$	−26016.4	−	10776.4i	−1.37809	−	0.570825i	−0.434122	−	0.900854i	$-0.642941\pi$
$709$	−26016.4	−	10776.4i	−1.37809	−	0.570825i	−0.943971	+	0.330029i	$0.892941\pi$
$710$	−4878.21	−	3369.46i	−0.257853	−	0.178104i
$711$	−15100.5	+	15100.5i	−0.796502	+	0.796502i
$712$	1978.33	−	117.482i	0.104131	−	0.00618373i
$713$	8999.26			0.472686
$714$	−65441.4	−	25603.0i	−3.43009	−	1.34197i
$715$	2202.33	−	358.028i	0.115192	−	0.0187265i
$716$	−15827.8	+	7301.96i	−0.826135	+	0.381127i
$717$	−8622.79	−	3571.68i	−0.449127	−	0.186034i
$718$	−4761.10	+	94.1466i	−0.247469	+	0.00489348i
$719$			30933.9i			1.60450i	0.596985	+	0.802252i	$0.296365\pi$
$719$			30933.9i			1.60450i	−0.596985	+	0.802252i	$0.703635\pi$
$720$	−45527.3	+	11153.1i	−2.35653	+	0.577292i
$721$		−	60441.1i		−	3.12198i
$722$	224.440	+	11350.2i	0.0115690	+	0.585057i
$723$	7721.13	+	3198.20i	0.397167	+	0.164512i
$724$	2878.09	−	7807.96i	0.147739	−	0.400802i
$725$	26593.9	−	23091.1i	1.36230	−	1.18287i
$726$	−9550.82	+	24412.0i	−0.488243	+	1.24795i
$727$	4017.45			0.204951			0.102475	−	0.994736i	$-0.467324\pi$
$727$	4017.45			0.204951			0.102475	+	0.994736i	$0.467324\pi$
$728$	−3100.27	−	6385.19i	−0.157835	−	0.325070i
$729$	15068.6	−	15068.6i	0.765562	−	0.765562i
$730$	75.2249	+	411.223i	0.00381397	+	0.0208494i
$731$	−20905.0	−	8659.14i	−1.05773	−	0.438125i
$732$	33457.5	−	1323.70i	1.68938	−	0.0668380i
$733$	−2342.99	−	970.498i	−0.118063	−	0.0489033i	0.322870	−	0.946443i	$-0.395352\pi$
$733$	−2342.99	−	970.498i	−0.118063	−	0.0489033i	−0.440933	+	0.897540i	$0.645352\pi$
$734$	−66.0751	−	3341.50i	−0.00332272	−	0.168034i
$735$	−31942.1	−	51650.7i	−1.60300	−	2.59206i
$736$	−7932.17	−	6500.70i	−0.397260	−	0.325569i
$737$	4842.55	−	4842.55i	0.242032	−	0.242032i
$738$	18913.6	−	19676.7i	0.943386	−	0.981448i
$739$	−5773.16	+	2391.32i	−0.287374	+	0.119034i	−0.521714	−	0.853121i	$-0.674707\pi$
$739$	−5773.16	+	2391.32i	−0.287374	+	0.119034i	0.234340	+	0.972155i	$0.424707\pi$
$740$	2904.82	−	14943.0i	0.144302	−	0.742321i
$741$	−2044.16	+	4935.03i	−0.101341	+	0.244660i
$742$	10723.0	−	27408.0i	0.530529	−	1.35604i
$743$	22010.7			1.08680			0.543402	−	0.839472i	$-0.317136\pi$
$743$	22010.7			1.08680			0.543402	+	0.839472i	$0.317136\pi$
$744$	15099.2	+	31097.6i	0.744035	+	1.53238i
$745$	−2428.17	−	3926.37i	−0.119411	−	0.193089i
$746$	−7555.03	−	2955.79i	−0.370790	−	0.145066i
$747$	−15894.3	−	38372.2i	−0.778502	−	1.87947i
$748$	5507.34	+	11937.8i	0.269209	+	0.583540i
$749$	27934.1	−	11570.7i	1.36274	−	0.564465i
$750$	4194.29	+	37786.8i	0.204205	+	1.83970i
$751$	−20000.2			−0.971794			−0.485897	−	0.874016i	$-0.661507\pi$
$751$	−20000.2			−0.971794			−0.485897	+	0.874016i	$0.661507\pi$
$752$	−10396.6	+	12186.4i	−0.504157	+	0.590945i
$753$	21363.8	−	21363.8i	1.03392	−	1.03392i
$754$	5750.01	−	5982.00i	0.277723	−	0.288928i
$755$	−173.299	+	28.1729i	−0.00835366	+	0.00135804i
$756$	−81060.4	+	37396.2i	−3.89966	+	1.79906i
$757$	−25823.8	+	10696.6i	−1.23987	+	0.513571i	−0.903674	−	0.428221i	$-0.859141\pi$
$757$	−25823.8	+	10696.6i	−1.23987	+	0.513571i	−0.336196	+	0.941792i	$0.609141\pi$
$758$	−12926.3	−	29541.0i	−0.619400	−	1.41554i
$759$	7385.55	−	7385.55i	0.353200	−	0.353200i
$760$	−7765.57	−	11036.1i	−0.370641	−	0.526740i
$761$	13074.2	+	13074.2i	0.622786	+	0.622786i	0.946243	−	0.323457i	$-0.104845\pi$
$761$	13074.2	+	13074.2i	0.622786	+	0.622786i	−0.323457	+	0.946243i	$0.604845\pi$
$762$	−4063.40	+	10386.1i	−0.193178	+	0.493764i
$763$	545.177	+	1316.17i	0.0258673	+	0.0624491i
$764$	−21756.1	+	860.750i	−1.03024	+	0.0407603i
$765$	50950.5	+	36701.2i	2.40800	+	1.73455i
$766$	554.377	+	28035.5i	0.0261494	+	1.32241i
$767$	−4765.00	−	4765.00i	−0.224321	−	0.224321i
$768$	9154.88	−	38317.2i	0.430141	−	1.80033i
$769$		−	22188.0i		−	1.04047i	−0.854024	−	0.520233i	$-0.825845\pi$
$769$		−	22188.0i		−	1.04047i	0.854024	−	0.520233i	$-0.174155\pi$
$770$	−3838.55	+	17854.3i	−0.179651	+	0.835615i
$771$	2099.35	+	5068.29i	0.0980628	+	0.236744i
$772$	21587.0	−	23365.5i	1.00639	−	1.08930i
$773$	16981.5	−	7033.95i	0.790143	−	0.327288i	0.0491420	−	0.998792i	$-0.484351\pi$
$773$	16981.5	−	7033.95i	0.790143	−	0.327288i	0.741001	+	0.671504i	$0.234351\pi$
$774$	−44799.0	+	19602.8i	−2.08045	+	0.910345i
$775$	18832.9	−	6289.47i	0.872901	−	0.291516i
$776$	3960.80	−	235.209i	0.183228	−	0.0108808i
$777$		−	49319.7i		−	2.27714i
$778$	−7903.42	+	3458.31i	−0.364205	+	0.159366i
$779$	7259.24	+	3006.88i	0.333876	+	0.138296i
$780$	1785.60	+	8777.04i	0.0819677	+	0.402908i
$781$	1375.23	+	3320.09i	0.0630083	+	0.152115i
$782$	271.618	+	13736.0i	0.0124207	+	0.628132i
$783$	−73790.0	−	73790.0i	−3.36786	−	3.36786i
$784$	36031.1	−	2855.52i	1.64136	−	0.130080i
$785$	21478.9	+	34731.7i	0.976581	+	1.57914i
$786$	24340.6	−	25322.6i	1.10458	−	1.14915i
$787$	−3512.29	+	8479.42i	−0.159085	+	0.384064i	−0.983244	−	0.182293i	$-0.941648\pi$
$787$	−3512.29	+	8479.42i	−0.159085	+	0.384064i	0.824160	+	0.566358i	$0.191648\pi$
$788$	14961.5	−	6902.29i	0.676371	−	0.312036i
$789$	12054.4	−	29101.8i	0.543912	−	1.31312i
$790$	−10140.7	+	1855.03i	−0.456695	+	0.0835432i
$791$	48697.2	+	48697.2i	2.18897	+	2.18897i
$792$	26847.4	+	9297.54i	1.20452	+	0.417139i
$793$		−	4530.80i		−	0.202892i
$794$	−29941.6	+	13101.6i	−1.33827	+	0.585589i
$795$	−21706.5	+	30134.1i	−0.968365	+	1.34434i
$796$	−311.219	+	336.859i	−0.0138579	+	0.0149996i
$797$	12247.8	−	29568.7i	0.544339	−	1.31415i	−0.377296	−	0.926093i	$-0.623146\pi$
$797$	12247.8	−	29568.7i	0.544339	−	1.31415i	0.921635	−	0.388058i	$-0.126854\pi$
$798$	−31520.0	−	30297.6i	−1.39824	−	1.34402i
$799$	21458.9			0.950141
$800$	−21143.1	−	8060.45i	−0.934400	−	0.356225i
$801$	−5737.47			−0.253088
$802$	12411.8	+	11930.5i	0.546481	+	0.525287i
$803$	96.9694	−	234.105i	0.00426149	−	0.0102881i
$804$	20192.7	+	18655.7i	0.885747	+	0.818327i
$805$	−11154.4	+	15485.2i	−0.488375	+	0.677988i
$806$	4285.41	−	1875.18i	0.187279	−	0.0819482i
$807$			61062.4i			2.66357i
$808$	−27488.6	+	13346.8i	−1.19684	+	0.581114i
$809$	−22938.1	−	22938.1i	−0.996860	−	0.996860i	0.00313545	−	0.999995i	$-0.499002\pi$
$809$	−22938.1	−	22938.1i	−0.996860	−	0.996860i	−0.999995	+	0.00313545i	$0.999002\pi$
$810$	55791.1	−	10205.9i	2.42012	−	0.442713i
$811$	−13162.2	+	31776.3i	−0.569897	+	1.37585i	0.331745	+	0.943369i	$0.392363\pi$
$811$	−13162.2	+	31776.3i	−0.569897	+	1.37585i	−0.901642	+	0.432484i	$0.857637\pi$
$812$	28449.1	+	61666.5i	1.22952	+	2.66511i
$813$	2246.82	−	5424.31i	0.0969244	−	0.233996i
$814$	−6394.26	+	6652.24i	−0.275330	+	0.286439i
$815$	6403.13	+	10353.9i	0.275205	+	0.445010i
$816$	−47010.1	+	23985.2i	−2.01677	+	1.02898i
$817$	−9954.57	−	9954.57i	−0.426275	−	0.426275i
$818$	4.60407	+	232.833i	0.000196794	+	0.00995210i
$819$	7863.86	+	18985.0i	0.335513	+	0.810001i
$820$	12910.7	−	2626.55i	0.549830	−	0.111857i
$821$	−18652.1	−	7725.94i	−0.792888	−	0.328425i	−0.0507842	−	0.998710i	$-0.516172\pi$
$821$	−18652.1	−	7725.94i	−0.792888	−	0.328425i	−0.742104	+	0.670285i	$0.766172\pi$
$822$	486.360	−	212.817i	0.0206372	−	0.00903024i
$823$			22231.1i			0.941587i	0.882243	+	0.470794i	$0.156032\pi$
$823$			22231.1i			0.941587i	−0.882243	+	0.470794i	$0.843968\pi$
$824$	−33943.6	−	30138.2i	−1.43505	−	1.27417i
$825$	10294.2	−	20617.6i	0.434422	−	0.870074i
$826$	50529.5	−	22110.3i	2.12850	−	0.931373i
$827$	−12643.0	+	5236.90i	−0.531608	+	0.220199i	−0.632307	−	0.774718i	$-0.717892\pi$
$827$	−12643.0	+	5236.90i	−0.531608	+	0.220199i	0.100699	+	0.994917i	$0.467892\pi$
$828$	21808.0	+	20148.1i	0.915316	+	0.845646i
$829$	−1425.10	−	3440.49i	−0.0597053	−	0.144141i	0.891212	−	0.453588i	$-0.149856\pi$
$829$	−1425.10	−	3440.49i	−0.0597053	−	0.144141i	−0.950917	+	0.309447i	$0.899856\pi$
$830$	4214.27	−	19601.9i	0.176240	−	0.819748i
$831$		−	38021.8i		−	1.58720i
$832$	−5131.82	−	1442.78i	−0.213839	−	0.0601196i
$833$	−34237.7	−	34237.7i	−1.42409	−	1.42409i
$834$	287.795	+	14554.2i	0.0119491	+	0.604280i
$835$	−10610.8	−	7643.28i	−0.439763	−	0.316774i
$836$	323.357	+	8173.09i	0.0133775	+	0.338124i
$837$	−22513.5	−	54352.5i	−0.929727	−	2.24456i
$838$	6761.28	−	17281.9i	0.278717	−	0.712402i
$839$	5475.44	+	5475.44i	0.225308	+	0.225308i	0.810729	−	0.585421i	$-0.199071\pi$
$839$	5475.44	+	5475.44i	0.225308	+	0.225308i	−0.585421	+	0.810729i	$0.699071\pi$
$840$	−72225.3	−	12563.6i	−2.96668	−	0.516053i
$841$	−38889.9	+	38889.9i	−1.59457	+	1.59457i
$842$	8197.12	+	18733.2i	0.335500	+	0.766732i
$843$	41756.8	−	17296.2i	1.70603	−	0.706659i
$844$	−2842.82	−	6162.12i	−0.115941	−	0.251314i
$845$	−23048.6	+	3746.97i	−0.938340	+	0.152544i
$846$	32137.3	−	33433.9i	1.30603	−	1.35872i
$847$	−20528.8	+	20528.8i	−0.832797	+	0.832797i
$848$	−10045.4	−	19688.6i	−0.406793	−	0.797300i
$849$	−85147.3			−3.44199
$850$	10168.4	+	28555.8i	0.410320	+	1.15230i
$851$	−8908.45	+	3690.00i	−0.358846	+	0.148639i
$852$	−13099.1	+	6043.12i	−0.526724	+	0.242997i
$853$	9519.28	+	22981.6i	0.382103	+	0.922478i	0.991559	+	0.129658i	$0.0413880\pi$
$853$	9519.28	+	22981.6i	0.382103	+	0.922478i	−0.609456	+	0.792820i	$0.708612\pi$
$854$	34534.7	+	13511.2i	1.38379	+	0.541386i
$855$	20548.2	+	33226.7i	0.821912	+	1.32904i
$856$	7430.91	−	21457.3i	0.296709	−	0.856772i
$857$	9746.28			0.388479			0.194239	−	0.980954i	$-0.437776\pi$
$857$	9746.28			0.388479			0.194239	+	0.980954i	$0.437776\pi$
$858$	1978.04	−	5055.90i	0.0787055	−	0.201172i
$859$	−7009.98	+	16923.6i	−0.278437	+	0.672207i	−0.999793	−	0.0203580i	$-0.993519\pi$
$859$	−7009.98	+	16923.6i	−0.278437	+	0.672207i	0.721356	+	0.692565i	$0.243519\pi$
$860$	−23172.0	−	4504.46i	−0.918788	−	0.178606i
$861$	39436.5	−	16335.1i	1.56097	−	0.646574i
$862$	30261.3	−	31482.2i	1.19571	−	1.24396i
$863$	−20920.0	+	20920.0i	−0.825175	+	0.825175i	−0.986845	−	0.161670i	$-0.948312\pi$
$863$	−20920.0	+	20920.0i	−0.825175	+	0.825175i	0.161670	+	0.986845i	$0.448312\pi$
$864$	−19418.1	+	64170.5i	−0.764602	+	2.52677i
$865$	−700.369	−	1132.50i	−0.0275298	−	0.0445160i
$866$	874.578	+	44228.4i	0.0343180	+	1.73550i
$867$	21660.7	+	8972.16i	0.848485	+	0.351454i
$868$	1513.56	+	38256.2i	0.0591861	+	1.49597i
$869$	5772.99	+	2391.25i	0.225357	+	0.0933459i
$870$	−15420.6	−	84298.1i	−0.600930	−	3.28503i
$871$	2630.41	−	2630.41i	0.102329	−	0.102329i
$872$	1011.01	+	350.122i	0.0392626	+	0.0135971i
$873$	−11487.0			−0.445331
$874$	−3114.29	+	7960.15i	−0.120529	+	0.308073i
$875$	−12520.7	+	40201.8i	−0.483745	+	1.55322i
$876$	954.418	+	351.807i	0.0368114	+	0.0135690i
$877$	−13144.9	−	5444.78i	−0.506124	−	0.209643i	0.114986	−	0.993367i	$-0.463318\pi$
$877$	−13144.9	−	5444.78i	−0.506124	−	0.209643i	−0.621109	+	0.783724i	$0.713318\pi$
$878$	461.561	+	23341.7i	0.0177414	+	0.897201i
$879$		−	79842.9i		−	3.06375i
$880$	8112.89	+	11058.5i	0.310779	+	0.423617i
$881$		−	10433.8i		−	0.399005i	−0.979897	−	0.199503i	$-0.936067\pi$
$881$		−	10433.8i		−	0.399005i	0.979897	−	0.199503i	$-0.0639326\pi$
$882$	−104619.	+	2068.74i	−3.99399	+	0.0789775i
$883$	37373.1	+	15480.4i	1.42435	+	0.589986i	0.955950	−	0.293529i	$-0.0948297\pi$
$883$	37373.1	+	15480.4i	1.42435	+	0.589986i	0.468403	+	0.883515i	$0.344830\pi$
$884$	2991.52	+	6484.44i	0.113819	+	0.246714i
$885$	−68696.9	+	11167.9i	−2.60929	+	0.424186i
$886$	−11815.3	−	4622.54i	−0.448015	−	0.175279i
$887$	−37227.4			−1.40921			−0.704607	−	0.709597i	$-0.748877\pi$
$887$	−37227.4			−1.40921			−0.704607	+	0.709597i	$0.748877\pi$
$888$	−27697.9	−	24592.6i	−1.04671	−	0.929364i
$889$	−8734.01	+	8734.01i	−0.329504	+	0.329504i
$890$	−2278.90	−	1574.07i	−0.0858301	−	0.0592844i
$891$	−31761.3	−	13156.0i	−1.19421	−	0.494659i
$892$	17912.8	+	16549.3i	0.672381	+	0.621202i
$893$	12334.6	+	5109.17i	0.462220	+	0.191458i
$894$	−11230.8	+	222.079i	−0.420149	+	0.00830808i
$895$	23710.4	+	5590.19i	0.885532	+	0.208782i
$896$	26300.7	−	34813.3i	0.980629	−	1.29803i
$897$	4011.74	−	4011.74i	0.149329	−	0.149329i
$898$	13939.5	+	13398.9i	0.518002	+	0.497913i
$899$	−41348.5	+	17127.1i	−1.53398	+	0.635397i
$900$	59719.4	+	26923.0i	2.21183	+	0.997147i
$901$	−11331.2	+	27356.0i	−0.418977	+	1.01150i
$902$	−7437.03	−	2909.63i	−0.274530	−	0.107406i
$903$	−76479.4			−2.81847
$904$	51630.5	−	3066.04i	1.89956	−	0.112804i
$905$	−9891.07	+	6116.88i	−0.363304	+	0.224676i
$906$	−155.651	+	397.845i	−0.00570767	+	0.0145889i
$907$	−2619.47	−	6323.97i	−0.0958965	−	0.231515i	0.868651	−	0.495425i	$-0.164988\pi$
$907$	−2619.47	−	6323.97i	−0.0958965	−	0.231515i	−0.964547	+	0.263910i	$0.914988\pi$
$908$	552.175	−	1497.99i	0.0201812	−	0.0547497i
$909$	81731.6	−	33854.3i	2.98225	−	1.23529i
$910$	−2085.05	+	9698.22i	−0.0759547	+	0.353289i
$911$	38175.4			1.38837			0.694186	−	0.719796i	$-0.255765\pi$
$911$	38175.4			1.38837			0.694186	+	0.719796i	$0.255765\pi$
$912$	−32732.1	+	2594.07i	−1.18845	+	0.0941866i
$913$	−8593.40	+	8593.40i	−0.311500	+	0.311500i
$914$	−14312.7	−	13757.7i	−0.517968	−	0.497881i
$915$	−37969.7	−	27350.7i	−1.37185	−	0.988182i
$916$	2813.35	−	7632.34i	0.101480	−	0.275305i
$917$	35939.3	−	14886.6i	1.29424	−	0.536093i
$918$	82281.4	−	36004.0i	2.95827	−	1.29446i
$919$	2573.23	−	2573.23i	0.0923647	−	0.0923647i	−0.659415	−	0.751779i	$-0.729196\pi$
$919$	2573.23	−	2573.23i	0.0923647	−	0.0923647i	0.751779	+	0.659415i	$0.229196\pi$
$920$	3134.43	+	13985.8i	0.112325	+	0.501193i
$921$	17244.7	+	17244.7i	0.616971	+	0.616971i
$922$	−32270.0	−	12625.2i	−1.15266	−	0.450962i
$923$	747.006	+	1803.43i	0.0266392	+	0.0643128i
$924$	32638.4	+	30154.1i	1.16204	+	1.07359i
$925$	−16064.0	+	13948.1i	−0.571006	+	0.495797i
$926$	3401.15	−	67.2548i	0.120701	−	0.00238675i
$927$	92923.6	+	92923.6i	3.29235	+	3.29235i
$928$	48817.6	+	14772.2i	1.72685	+	0.522546i
$929$			4844.91i			0.171105i	0.996334	+	0.0855523i	$0.0272655\pi$
$929$			4844.91i			0.171105i	−0.996334	+	0.0855523i	$0.972735\pi$
$930$	10154.8	−	47233.0i	0.358051	−	1.66541i
$931$	−11528.2	−	27831.6i	−0.405824	−	0.979745i
$932$	−2170.93	−	54871.8i	−0.0762996	−	1.92853i
$933$	67746.9	−	28061.7i	2.37721	−	0.984671i
$934$	−8487.61	−	19397.1i	−0.297348	−	0.679541i
$935$	4216.27	−	17883.0i	0.147473	−	0.625495i
$936$	14583.2	+	5050.31i	0.509258	+	0.176362i
$937$			3390.41i			0.118207i	0.998252	+	0.0591035i	$0.0188242\pi$
$937$			3390.41i			0.118207i	−0.998252	+	0.0591035i	$0.981176\pi$
$938$	12205.5	+	27893.7i	0.424864	+	0.970959i
$939$	−21103.9	−	8741.51i	−0.733439	−	0.303800i
$940$	21937.4	−	4462.94i	0.761189	−	0.154856i
$941$	−9245.57	−	22320.8i	−0.320294	−	0.773259i	−0.999237	−	0.0390672i	$-0.987561\pi$
$941$	−9245.57	−	22320.8i	−0.320294	−	0.773259i	0.678942	−	0.734192i	$-0.262439\pi$
$942$	99344.6	−	1964.45i	3.43612	−	0.0679462i
$943$	−5901.11	−	5901.11i	−0.203782	−	0.203782i
$944$	12778.8	−	39402.2i	0.440586	−	1.35851i
$945$	121430.	+	28629.6i	4.18003	+	0.985524i
$946$	10315.5	+	9915.50i	0.354532	+	0.340783i
$947$	20613.3	−	49764.8i	0.707330	−	1.70765i	0.000762109	−	1.00000i	$-0.499757\pi$
$947$	20613.3	−	49764.8i	0.707330	−	1.70765i	0.706568	−	0.707645i	$-0.250243\pi$
$948$	−8675.50	+	23535.8i	−0.297223	+	0.806336i
$949$	52.6726	−	127.163i	0.00180171	−	0.00434972i
$950$	−954.081	+	18834.9i	−0.0325836	+	0.643248i
$951$	−7862.72	−	7862.72i	−0.268103	−	0.268103i
$952$	−58346.7	+	3464.88i	−1.98637	+	0.117959i
$953$		−	5358.06i		−	0.182124i	−0.995845	−	0.0910622i	$-0.970974\pi$
$953$		−	5358.06i		−	0.182124i	0.995845	−	0.0910622i	$-0.0290262\pi$
$954$	25651.9	+	58623.4i	0.870558	+	1.98952i
$955$	24690.2	+	17785.1i	0.836602	+	0.602629i
$956$	−7757.00	+	306.896i	−0.262426	+	0.0103825i
$957$	−19878.1	+	47990.1i	−0.671441	+	1.62100i
$958$	7017.90	−	7301.04i	0.236679	−	0.246228i
$959$	587.961			0.0197980
$960$	−43069.9	+	34296.9i	−1.44799	+	1.15305i
$961$	4559.87			0.153062
$962$	−3473.29	+	3613.42i	−0.116407	+	0.121103i
$963$	−25157.5	+	60735.7i	−0.841838	+	2.03238i
$964$	6945.87	−	274.804i	0.232066	−	0.00918139i
$965$	−43881.3	+	7133.68i	−1.46382	+	0.237970i
$966$	18615.0	+	42541.6i	0.620009	+	1.41693i
$967$		−	20041.1i		−	0.666470i	−0.942844	−	0.333235i	$-0.891860\pi$
$967$		−	20041.1i		−	0.666470i	0.942844	−	0.333235i	$-0.108140\pi$
$968$	1292.52	+	21765.4i	0.0429166	+	0.722692i
$969$	31102.9	+	31102.9i	1.03114	+	1.03114i
$970$	−4562.57	−	3151.44i	−0.151026	−	0.104316i
$971$	11907.8	−	28747.9i	0.393552	−	0.950118i	−0.595608	−	0.803275i	$-0.703089\pi$
$971$	11907.8	−	28747.9i	0.393552	−	0.950118i	0.989160	−	0.146843i	$-0.0469111\pi$
$972$	20061.3	−	54424.3i	0.662002	−	1.79595i
$973$	−6169.66	+	14894.9i	−0.203279	+	0.490758i
$974$	33091.0	+	31807.7i	1.08861	+	1.04639i
$975$	5591.69	−	11199.2i	0.183669	−	0.367858i
$976$	24808.1	−	12657.5i	0.813616	−	0.415118i
$977$	−31401.8	−	31401.8i	−1.02828	−	1.02828i	−0.999588	−	0.0286948i	$-0.990865\pi$
$977$	−31401.8	−	31401.8i	−1.02828	−	1.02828i	−0.0286948	−	0.999588i	$-0.509135\pi$
$978$	29615.9	−	585.627i	0.968313	−	0.0191475i
$979$	642.449	+	1551.01i	0.0209732	+	0.0506338i
$980$	−42121.7	−	27880.4i	−1.37299	−	0.908784i
$981$	−2861.69	−	1185.35i	−0.0931362	−	0.0385783i
$982$	−15251.7	−	34855.4i	−0.495624	−	1.13267i
$983$		−	13597.1i		−	0.441181i	−0.975367	−	0.220590i	$-0.929202\pi$
$983$		−	13597.1i		−	0.441181i	0.975367	−	0.220590i	$-0.0707984\pi$
$984$	10490.7	−	30292.8i	0.339870	−	0.981400i
$985$	−22412.6	−	5284.22i	−0.725001	−	0.170933i
$986$	−27390.0	−	62595.4i	−0.884660	−	2.02175i
$987$	67009.0	−	27756.1i	2.16101	−	0.895122i
$988$	175.644	+	4439.52i	0.00565584	+	0.142955i
$989$	5722.03	+	13814.2i	0.183974	+	0.444152i
$990$	−21548.1	−	33351.1i	−0.691762	−	1.07067i
$991$			6363.22i			0.203970i	0.994786	+	0.101985i	$0.0325194\pi$
$991$			6363.22i			0.203970i	−0.994786	+	0.101985i	$0.967481\pi$
$992$	22239.3	+	18226.0i	0.711794	+	0.583341i
$993$	−12166.8	−	12166.8i	−0.388825	−	0.388825i
$994$	−15973.8	+	315.867i	−0.509715	+	0.0100792i
$995$	632.634	−	102.846i	0.0201566	−	0.00327682i
$996$	−35833.1	−	33105.6i	−1.13998	−	1.05321i
$997$	−998.318	−	2410.15i	−0.0317122	−	0.0765600i	0.907230	−	0.420635i	$-0.138193\pi$
$997$	−998.318	−	2410.15i	−0.0317122	−	0.0765600i	−0.938942	+	0.344075i	$0.888193\pi$
$998$	40510.2	+	15849.0i	1.28490	+	0.502697i
$999$	44572.7	+	44572.7i	1.41163	+	1.41163i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.4.u.a.43.16	✓	280
5.2	odd	4		160.4.ba.a.107.19	yes	280
32.3	odd	8		160.4.ba.a.3.19	yes	280
160.67	even	8	inner	160.4.u.a.67.16	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.4.u.a.43.16	✓	280	1.1	even	1	trivial
160.4.u.a.67.16	yes	280	160.67	even	8	inner
160.4.ba.a.3.19	yes	280	32.3	odd	8
160.4.ba.a.107.19	yes	280	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	160.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96007 + 2.03915i) q^{2} +(3.68068 - 8.88596i) q^{3} +(-0.316262 - 7.99375i) q^{4} +(-6.53470 + 9.07181i) q^{5} +(10.9054 + 24.9225i) q^{6} +30.1289i q^{7} +(16.9203 + 15.0234i) q^{8} +(-46.3209 - 46.3209i) q^{9} +(-5.69033 - 31.1066i) q^{10} +(-7.33517 + 17.7087i) q^{11} +(-72.1961 - 26.6122i) q^{12} +(-3.98438 + 9.61914i) q^{13} +(-61.4374 - 59.0547i) q^{14} +(56.5596 + 91.4575i) q^{15} +(-63.8000 + 5.05624i) q^{16} +(60.6244 + 60.6244i) q^{17} +(185.247 - 3.66310i) q^{18} +(20.4129 + 49.2811i) q^{19} +(74.5844 + 49.3676i) q^{20} +(267.724 + 110.895i) q^{21} +(-21.7332 - 49.6677i) q^{22} -56.6550i q^{23} +(195.776 - 95.0571i) q^{24} +(-39.5955 - 118.563i) q^{25} +(-11.8052 - 26.9789i) q^{26} +(-342.177 + 141.734i) q^{27} +(240.843 - 9.52863i) q^{28} +(107.824 + 260.311i) q^{29} +(-297.356 - 63.9295i) q^{30} +158.843i q^{31} +(114.742 - 140.008i) q^{32} +(130.360 + 130.360i) q^{33} +(-242.450 + 4.79424i) q^{34} +(-273.324 - 196.883i) q^{35} +(-355.628 + 384.927i) q^{36} +(-65.1311 - 157.240i) q^{37} +(-140.502 - 54.9694i) q^{38} +(70.8100 + 70.8100i) q^{39} +(-246.859 + 55.3249i) q^{40} +(104.159 - 104.159i) q^{41} +(-750.889 + 328.568i) q^{42} +(-243.830 + 100.998i) q^{43} +(143.878 + 53.0349i) q^{44} +(722.907 - 117.521i) q^{45} +(115.528 + 111.048i) q^{46} +(176.983 - 176.983i) q^{47} +(-189.898 + 585.534i) q^{48} -564.751 q^{49} +(319.378 + 151.651i) q^{50} +(761.845 - 315.567i) q^{51} +(78.1530 + 28.8079i) q^{52} +(132.165 + 319.074i) q^{53} +(381.673 - 975.560i) q^{54} +(-112.717 - 182.264i) q^{55} +(-452.638 + 509.791i) q^{56} +513.043 q^{57} +(-742.155 - 290.357i) q^{58} +(-247.684 + 597.961i) q^{59} +(713.200 - 481.047i) q^{60} +(-402.040 + 166.531i) q^{61} +(-323.905 - 311.343i) q^{62} +(1395.60 - 1395.60i) q^{63} +(60.5958 + 508.402i) q^{64} +(-61.2263 - 99.0036i) q^{65} +(-521.338 + 10.3090i) q^{66} +(-330.091 - 136.728i) q^{67} +(465.443 - 503.789i) q^{68} +(-503.434 - 208.529i) q^{69} +(937.208 - 171.443i) q^{70} +(132.571 - 132.571i) q^{71} +(-87.8687 - 1479.66i) q^{72} -13.2198 q^{73} +(448.298 + 175.390i) q^{74} +(-1199.28 - 84.5491i) q^{75} +(387.485 - 178.761i) q^{76} +(-533.543 - 221.001i) q^{77} +(-283.185 + 5.59972i) q^{78} -325.998i q^{79} +(371.044 - 611.822i) q^{80} +1793.55i q^{81} +(8.23698 + 416.554i) q^{82} +(585.767 + 242.632i) q^{83} +(801.795 - 2175.19i) q^{84} +(-946.135 + 153.811i) q^{85} +(271.975 - 695.169i) q^{86} +2709.97 q^{87} +(-390.158 + 189.438i) q^{88} +(61.9317 - 61.9317i) q^{89} +(-1177.30 + 1704.47i) q^{90} +(-289.814 - 120.045i) q^{91} +(-452.886 + 17.9178i) q^{92} +(1411.47 + 584.651i) q^{93} +(13.9960 + 707.792i) q^{94} +(-580.461 - 136.855i) q^{95} +(-821.779 - 1534.92i) q^{96} +(123.993 - 123.993i) q^{97} +(1106.95 - 1151.61i) q^{98} +(1160.05 - 480.510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} + 80 q^{8} + 8 q^{10} - 8 q^{11} + 44 q^{12} - 4 q^{13} + 64 q^{14} - 8 q^{15} - 8 q^{16} + 28 q^{18} - 48 q^{19} - 312 q^{20} - 8 q^{21} - 436 q^{22} + 736 q^{24}+ \cdots + 3480 q^{98}+O(q^{100}) \) 280 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 + 80 * q^8 + 8 * q^10 - 8 * q^11 + 44 * q^12 - 4 * q^13 + 64 * q^14 - 8 * q^15 - 8 * q^16 + 28 * q^18 - 48 * q^19 - 312 * q^20 - 8 * q^21 - 436 * q^22 + 736 * q^24 - 4 * q^25 - 8 * q^26 - 112 * q^27 + 252 * q^28 - 1696 * q^30 - 344 * q^32 - 8 * q^33 + 696 * q^34 + 952 * q^35 - 8 * q^36 - 4 * q^37 - 172 * q^38 + 816 * q^40 - 8 * q^41 - 460 * q^42 + 860 * q^43 + 1232 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 + 3496 * q^48 - 11368 * q^49 - 36 * q^50 + 1480 * q^51 - 328 * q^52 - 4 * q^53 + 2968 * q^54 - 292 * q^55 - 344 * q^56 - 8 * q^57 - 2020 * q^58 + 252 * q^60 + 1816 * q^61 - 440 * q^62 + 2744 * q^63 + 816 * q^64 - 8 * q^65 + 552 * q^66 + 1844 * q^67 + 1224 * q^68 + 216 * q^69 + 1764 * q^70 - 232 * q^71 - 3432 * q^72 - 8 * q^73 + 104 * q^75 + 824 * q^76 + 1368 * q^77 - 5968 * q^78 - 1800 * q^80 + 588 * q^82 + 2676 * q^83 + 2744 * q^84 - 4 * q^85 - 1192 * q^86 + 2568 * q^87 - 5880 * q^88 - 84 * q^90 - 8 * q^91 - 3284 * q^92 + 104 * q^93 + 416 * q^94 + 6168 * q^96 - 8 * q^97 + 3480 * q^98

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