LMFDB - Embedded newform 72.4.l.b.11.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,4,Mod(11,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("72.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	72.l (of order $6$, degree $2$, 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:	$4.24813752041$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.30
Character	$\chi$	$=$	72.11
Dual form			72.4.l.b.59.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.78409 - 0.498867i) q^{2} +(4.10749 + 3.18254i) q^{3} +(7.50226 - 2.77778i) q^{4} +(-1.46312 - 2.53420i) q^{5} +(13.0233 + 6.81136i) q^{6} +(-4.48829 - 2.59132i) q^{7} +(19.5012 - 11.4762i) q^{8} +(6.74292 + 26.1445i) q^{9} +O(q^{10})$	\(q+(2.78409 - 0.498867i) q^{2} +(4.10749 + 3.18254i) q^{3} +(7.50226 - 2.77778i) q^{4} +(-1.46312 - 2.53420i) q^{5} +(13.0233 + 6.81136i) q^{6} +(-4.48829 - 2.59132i) q^{7} +(19.5012 - 11.4762i) q^{8} +(6.74292 + 26.1445i) q^{9} +(-5.33769 - 6.32553i) q^{10} +(-13.6440 - 7.87738i) q^{11} +(39.6558 + 12.4665i) q^{12} +(-37.3474 + 21.5625i) q^{13} +(-13.7885 - 4.97539i) q^{14} +(2.05543 - 15.0656i) q^{15} +(48.5679 - 41.6792i) q^{16} +3.31600i q^{17} +(31.8155 + 69.4246i) q^{18} -15.0818 q^{19} +(-18.0162 - 14.9480i) q^{20} +(-10.1886 - 24.9279i) q^{21} +(-41.9159 - 15.1247i) q^{22} +(-61.7219 - 106.905i) q^{23} +(116.624 + 14.9250i) q^{24} +(58.2185 - 100.837i) q^{25} +(-93.2215 + 78.6633i) q^{26} +(-55.5092 + 128.848i) q^{27} +(-40.8704 - 6.97327i) q^{28} +(11.7175 - 20.2953i) q^{29} +(-1.79325 - 42.9694i) q^{30} +(-274.752 + 158.628i) q^{31} +(114.425 - 140.267i) q^{32} +(-30.9726 - 75.7788i) q^{33} +(1.65424 + 9.23203i) q^{34} +15.1657i q^{35} +(123.211 + 177.412i) q^{36} +286.660i q^{37} +(-41.9891 + 7.52382i) q^{38} +(-222.028 - 30.2916i) q^{39} +(-57.6157 - 32.6289i) q^{40} +(284.954 - 164.518i) q^{41} +(-40.8018 - 64.3188i) q^{42} +(-175.008 + 303.123i) q^{43} +(-124.243 - 21.1982i) q^{44} +(56.3896 - 55.3405i) q^{45} +(-225.170 - 266.843i) q^{46} +(165.936 - 287.410i) q^{47} +(332.138 - 16.6277i) q^{48} +(-158.070 - 273.786i) q^{49} +(111.781 - 309.783i) q^{50} +(-10.5533 + 13.6204i) q^{51} +(-220.294 + 265.510i) q^{52} +521.214 q^{53} +(-90.2646 + 386.415i) q^{54} +46.1023i q^{55} +(-117.266 + 0.974711i) q^{56} +(-61.9484 - 47.9984i) q^{57} +(22.4979 - 62.3494i) q^{58} +(-130.749 + 75.4878i) q^{59} +(-26.4286 - 118.736i) q^{60} +(650.051 + 375.307i) q^{61} +(-685.799 + 578.699i) q^{62} +(37.4844 - 134.817i) q^{63} +(248.594 - 447.599i) q^{64} +(109.288 + 63.0972i) q^{65} +(-124.034 - 195.524i) q^{66} +(126.364 + 218.868i) q^{67} +(9.21110 + 24.8775i) q^{68} +(86.7085 - 635.545i) q^{69} +(7.56564 + 42.2225i) q^{70} +1083.28 q^{71} +(431.534 + 432.465i) q^{72} +678.405 q^{73} +(143.005 + 798.086i) q^{74} +(560.051 - 228.906i) q^{75} +(-113.148 + 41.8939i) q^{76} +(40.8256 + 70.7119i) q^{77} +(-633.255 + 26.4277i) q^{78} +(97.5980 + 56.3482i) q^{79} +(-176.684 - 62.0992i) q^{80} +(-638.066 + 352.580i) q^{81} +(711.263 - 600.187i) q^{82} +(-857.418 - 495.030i) q^{83} +(-145.682 - 158.714i) q^{84} +(8.40342 - 4.85171i) q^{85} +(-336.020 + 931.226i) q^{86} +(112.720 - 46.0714i) q^{87} +(-356.477 + 2.96304i) q^{88} +566.656i q^{89} +(129.386 - 182.204i) q^{90} +223.501 q^{91} +(-760.013 - 630.583i) q^{92} +(-1633.38 - 222.845i) q^{93} +(318.601 - 882.953i) q^{94} +(22.0666 + 38.2204i) q^{95} +(916.405 - 211.985i) q^{96} +(73.8806 - 127.965i) q^{97} +(-576.663 - 683.386i) q^{98} +(113.949 - 409.832i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 3 q^{2} + 6 q^{3} - 17 q^{4} - 3 q^{6} + 42 q^{9}+O(q^{10}) $ 64 * q - 3 * q^2 + 6 * q^3 - 17 * q^4 - 3 * q^6 + 42 * q^9	$ 64 q - 3 q^{2} + 6 q^{3} - 17 q^{4} - 3 q^{6} + 42 q^{9} + 12 q^{10} + 48 q^{11} + 318 q^{12} + 72 q^{14} + 127 q^{16} + 330 q^{18} - 220 q^{19} - 234 q^{20} - 217 q^{22} + 189 q^{24} - 902 q^{25} - 252 q^{27} - 132 q^{28} + 420 q^{30} - 693 q^{32} - 660 q^{33} + 509 q^{34} - 537 q^{36} - 1977 q^{38} - 36 q^{40} + 1620 q^{41} + 72 q^{42} - 292 q^{43} + 48 q^{46} + 765 q^{48} + 1762 q^{49} - 1227 q^{50} - 1794 q^{51} + 330 q^{52} - 645 q^{54} + 942 q^{56} - 294 q^{57} - 282 q^{58} + 5592 q^{59} + 1236 q^{60} + 1090 q^{64} - 6 q^{65} + 3522 q^{66} + 68 q^{67} - 2025 q^{68} + 600 q^{70} + 1875 q^{72} - 868 q^{73} - 420 q^{74} - 4254 q^{75} - 1471 q^{76} + 3228 q^{78} + 498 q^{81} + 362 q^{82} + 3654 q^{83} - 2028 q^{84} - 4119 q^{86} + 3155 q^{88} + 2958 q^{90} - 1380 q^{91} - 744 q^{92} - 138 q^{94} - 4782 q^{96} - 1912 q^{97} - 2118 q^{99}+O(q^{100}) $ 64 * q - 3 * q^2 + 6 * q^3 - 17 * q^4 - 3 * q^6 + 42 * q^9 + 12 * q^10 + 48 * q^11 + 318 * q^12 + 72 * q^14 + 127 * q^16 + 330 * q^18 - 220 * q^19 - 234 * q^20 - 217 * q^22 + 189 * q^24 - 902 * q^25 - 252 * q^27 - 132 * q^28 + 420 * q^30 - 693 * q^32 - 660 * q^33 + 509 * q^34 - 537 * q^36 - 1977 * q^38 - 36 * q^40 + 1620 * q^41 + 72 * q^42 - 292 * q^43 + 48 * q^46 + 765 * q^48 + 1762 * q^49 - 1227 * q^50 - 1794 * q^51 + 330 * q^52 - 645 * q^54 + 942 * q^56 - 294 * q^57 - 282 * q^58 + 5592 * q^59 + 1236 * q^60 + 1090 * q^64 - 6 * q^65 + 3522 * q^66 + 68 * q^67 - 2025 * q^68 + 600 * q^70 + 1875 * q^72 - 868 * q^73 - 420 * q^74 - 4254 * q^75 - 1471 * q^76 + 3228 * q^78 + 498 * q^81 + 362 * q^82 + 3654 * q^83 - 2028 * q^84 - 4119 * q^86 + 3155 * q^88 + 2958 * q^90 - 1380 * q^91 - 744 * q^92 - 138 * q^94 - 4782 * q^96 - 1912 * q^97 - 2118 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.78409	−	0.498867i	0.984323	−	0.176376i
$2$	2.78409	−	0.498867i	0.984323	−	0.176376i
$3$	4.10749	+	3.18254i	0.790487	+	0.612479i
$3$	4.10749	+	3.18254i	0.790487	+	0.612479i
$4$	7.50226	−	2.77778i	0.937783	−	0.347222i
$5$	−1.46312	−	2.53420i	−0.130866	−	0.226666i	0.793145	−	0.609033i	$-0.208442\pi$
$5$	−1.46312	−	2.53420i	−0.130866	−	0.226666i	−0.924011	+	0.382367i	$0.875109\pi$
$6$	13.0233	+	6.81136i	0.886121	+	0.463455i
$7$	−4.48829	−	2.59132i	−0.242345	−	0.139918i	0.373909	−	0.927465i	$-0.378017\pi$
$7$	−4.48829	−	2.59132i	−0.242345	−	0.139918i	−0.616254	+	0.787547i	$0.711351\pi$
$8$	19.5012	−	11.4762i	0.861840	−	0.507181i
$9$	6.74292	+	26.1445i	0.249738	+	0.968313i
$10$	−5.33769	−	6.32553i	−0.168793	−	0.200031i
$11$	−13.6440	−	7.87738i	−0.373984	−	0.215920i	0.301213	−	0.953557i	$-0.402608\pi$
$11$	−13.6440	−	7.87738i	−0.373984	−	0.215920i	−0.675198	+	0.737637i	$0.735942\pi$
$12$	39.6558	+	12.4665i	0.953971	+	0.299899i
$13$	−37.3474	+	21.5625i	−0.796793	+	0.460028i	−0.842348	−	0.538933i	$-0.818827\pi$
$13$	−37.3474	+	21.5625i	−0.796793	+	0.460028i	0.0455558	+	0.998962i	$0.485494\pi$
$14$	−13.7885	−	4.97539i	−0.263224	−	0.0949806i
$15$	2.05543	−	15.0656i	0.0353807	−	0.259329i
$16$	48.5679	−	41.6792i	0.758874	−	0.651238i
$17$			3.31600i			0.0473087i	0.999720	+	0.0236544i	$0.00753012\pi$
$17$			3.31600i			0.0473087i	−0.999720	+	0.0236544i	$0.992470\pi$
$18$	31.8155	+	69.4246i	0.416610	+	0.909085i
$19$	−15.0818			−0.182106			−0.0910528	−	0.995846i	$-0.529023\pi$
$19$	−15.0818			−0.182106			−0.0910528	+	0.995846i	$0.529023\pi$
$20$	−18.0162	−	14.9480i	−0.201427	−	0.167124i
$21$	−10.1886	−	24.9279i	−0.105874	−	0.259034i
$22$	−41.9159	−	15.1247i	−0.406204	−	0.146573i
$23$	−61.7219	−	106.905i	−0.559561	−	0.969188i	−0.997533	−	0.0701991i	$-0.977637\pi$
$23$	−61.7219	−	106.905i	−0.559561	−	0.969188i	0.437972	−	0.898988i	$-0.355697\pi$
$24$	116.624	+	14.9250i	0.991910	+	0.126939i
$25$	58.2185	−	100.837i	0.465748	−	0.806700i
$26$	−93.2215	+	78.6633i	−0.703163	+	0.593352i
$27$	−55.5092	+	128.848i	−0.395658	+	0.918398i
$28$	−40.8704	−	6.97327i	−0.275849	−	0.0470652i
$29$	11.7175	−	20.2953i	0.0750306	−	0.129957i	−0.826069	−	0.563569i	$-0.809428\pi$
$29$	11.7175	−	20.2953i	0.0750306	−	0.129957i	0.901100	+	0.433612i	$0.142761\pi$
$30$	−1.79325	−	42.9694i	−0.0109134	−	0.261504i
$31$	−274.752	+	158.628i	−1.59184	+	0.919048i	−0.598846	+	0.800865i	$0.704374\pi$
$31$	−274.752	+	158.628i	−1.59184	+	0.919048i	−0.992992	+	0.118183i	$0.962293\pi$
$32$	114.425	−	140.267i	0.632114	−	0.774875i
$33$	−30.9726	−	75.7788i	−0.163383	−	0.399739i
$34$	1.65424	+	9.23203i	0.00834412	+	0.0465670i
$35$			15.1657i			0.0732418i
$36$	123.211	+	177.412i	0.570420	+	0.821353i
$37$			286.660i			1.27369i	0.770991	+	0.636846i	$0.219761\pi$
$37$			286.660i			1.27369i	−0.770991	+	0.636846i	$0.780239\pi$
$38$	−41.9891	+	7.52382i	−0.179251	+	0.0321191i
$39$	−222.028	−	30.2916i	−0.911612	−	0.124373i
$40$	−57.6157	−	32.6289i	−0.227746	−	0.128977i
$41$	284.954	−	164.518i	1.08542	−	0.626669i	0.153068	−	0.988216i	$-0.451085\pi$
$41$	284.954	−	164.518i	1.08542	−	0.626669i	0.932354	+	0.361547i	$0.117751\pi$
$42$	−40.8018	−	64.3188i	−0.149901	−	0.236300i
$43$	−175.008	+	303.123i	−0.620663	+	1.07502i	0.368700	+	0.929548i	$0.379803\pi$
$43$	−175.008	+	303.123i	−0.620663	+	1.07502i	−0.989363	+	0.145471i	$0.953530\pi$
$44$	−124.243	−	21.1982i	−0.425688	−	0.0726305i
$45$	56.3896	−	55.3405i	0.186802	−	0.183326i
$46$	−225.170	−	266.843i	−0.721730	−	0.855300i
$47$	165.936	−	287.410i	0.514984	−	0.891979i	−0.484864	−	0.874589i	$-0.661131\pi$
$47$	165.936	−	287.410i	0.514984	−	0.891979i	0.999849	−	0.0173897i	$-0.00553559\pi$
$48$	332.138	−	16.6277i	0.998749	−	0.0499999i
$49$	−158.070	−	273.786i	−0.460846	−	0.798209i
$50$	111.781	−	309.783i	0.316164	−	0.876200i
$51$	−10.5533	+	13.6204i	−0.0289756	+	0.0373969i
$52$	−220.294	+	265.510i	−0.587487	+	0.708071i
$53$	521.214			1.35083			0.675417	−	0.737436i	$-0.263964\pi$
$53$	521.214			1.35083			0.675417	+	0.737436i	$0.263964\pi$
$54$	−90.2646	+	386.415i	−0.227471	+	0.973785i
$55$			46.1023i			0.113026i
$56$	−117.266	+	0.974711i	−0.279826	+	0.00232591i
$57$	−61.9484	−	47.9984i	−0.143952	−	0.111536i
$58$	22.4979	−	62.3494i	0.0509331	−	0.141153i
$59$	−130.749	+	75.4878i	−0.288509	+	0.166571i	−0.637269	−	0.770641i	$-0.719936\pi$
$59$	−130.749	+	75.4878i	−0.288509	+	0.166571i	0.348760	+	0.937212i	$0.386603\pi$
$60$	−26.4286	−	118.736i	−0.0568653	−	0.255479i
$61$	650.051	+	375.307i	1.36443	+	0.787756i	0.990210	−	0.139582i	$-0.0445760\pi$
$61$	650.051	+	375.307i	1.36443	+	0.787756i	0.374223	+	0.927339i	$0.377909\pi$
$62$	−685.799	+	578.699i	−1.40478	+	1.18540i
$63$	37.4844	−	134.817i	0.0749617	−	0.269609i
$64$	248.594	−	447.599i	0.485535	−	0.874217i
$65$	109.288	+	63.0972i	0.208546	+	0.120404i
$66$	−124.034	−	195.524i	−0.231326	−	0.364656i
$67$	126.364	+	218.868i	0.230415	+	0.399090i	0.957930	−	0.287001i	$-0.0926584\pi$
$67$	126.364	+	218.868i	0.230415	+	0.399090i	−0.727515	+	0.686091i	$0.759325\pi$
$68$	9.21110	+	24.8775i	0.0164266	+	0.0443653i
$69$	86.7085	−	635.545i	0.151282	−	1.10885i
$70$	7.56564	+	42.2225i	0.0129181	+	0.0720936i
$71$	1083.28			1.81072			0.905362	−	0.424640i	$-0.139599\pi$
$71$	1083.28			1.81072			0.905362	+	0.424640i	$0.139599\pi$
$72$	431.534	+	432.465i	0.706344	+	0.707869i
$73$	678.405			1.08769			0.543845	−	0.839186i	$-0.316968\pi$
$73$	678.405			1.08769			0.543845	+	0.839186i	$0.316968\pi$
$74$	143.005	+	798.086i	0.224649	+	1.25372i
$75$	560.051	−	228.906i	0.862255	−	0.352424i
$76$	−113.148	+	41.8939i	−0.170776	+	0.0632311i
$77$	40.8256	+	70.7119i	0.0604221	+	0.104654i
$78$	−633.255	+	26.4277i	−0.919257	+	0.0383635i
$79$	97.5980	+	56.3482i	0.138995	+	0.0802490i	0.567885	−	0.823108i	$-0.307762\pi$
$79$	97.5980	+	56.3482i	0.138995	+	0.0802490i	−0.428890	+	0.903357i	$0.641095\pi$
$80$	−176.684	−	62.0992i	−0.246924	−	0.0867863i
$81$	−638.066	+	352.580i	−0.875262	+	0.483649i
$82$	711.263	−	600.187i	0.957877	−	0.808287i
$83$	−857.418	−	495.030i	−1.13390	−	0.654658i	−0.188988	−	0.981979i	$-0.560521\pi$
$83$	−857.418	−	495.030i	−1.13390	−	0.654658i	−0.944913	+	0.327321i	$0.893854\pi$
$84$	−145.682	−	158.714i	−0.189229	−	0.206157i
$85$	8.40342	−	4.85171i	0.0107233	−	0.00619109i
$86$	−336.020	+	931.226i	−0.421325	+	1.16764i
$87$	112.720	−	46.0714i	0.138907	−	0.0567744i
$88$	−356.477	+	2.96304i	−0.431825	+	0.00358933i
$89$			566.656i			0.674893i	0.941345	+	0.337446i	$0.109563\pi$
$89$			566.656i			0.674893i	−0.941345	+	0.337446i	$0.890437\pi$
$90$	129.386	−	182.204i	0.151539	−	0.213399i
$91$	223.501			0.257465
$92$	−760.013	−	630.583i	−0.861270	−	0.714596i
$93$	−1633.38	−	222.845i	−1.82122	−	0.248473i
$94$	318.601	−	882.953i	0.349587	−	0.968826i
$95$	22.0666	+	38.2204i	0.0238314	+	0.0412771i
$96$	916.405	−	211.985i	0.974273	−	0.225371i
$97$	73.8806	−	127.965i	0.0773344	−	0.133947i	−0.824765	−	0.565476i	$-0.808692\pi$
$97$	73.8806	−	127.965i	0.0773344	−	0.133947i	0.902099	+	0.431529i	$0.142026\pi$
$98$	−576.663	−	683.386i	−0.594406	−	0.704413i
$99$	113.949	−	409.832i	0.115680	−	0.416057i
$100$	156.667	−	918.227i	0.156667	−	0.918227i
$101$	−733.536	+	1270.52i	−0.722669	+	1.25170i	0.237258	+	0.971447i	$0.423751\pi$
$101$	−733.536	+	1270.52i	−0.722669	+	1.25170i	−0.959926	+	0.280252i	$0.909582\pi$
$102$	−22.5865	+	43.1851i	−0.0219254	+	0.0419212i
$103$	−1005.07	+	580.278i	−0.961482	+	0.555112i	−0.896629	−	0.442783i	$-0.853991\pi$
$103$	−1005.07	+	580.278i	−0.961482	+	0.555112i	−0.0648531	+	0.997895i	$0.520658\pi$
$104$	−480.863	+	849.101i	−0.453390	+	0.800589i
$105$	−48.2652	+	62.2927i	−0.0448591	+	0.0578967i
$106$	1451.10	−	260.016i	1.32966	−	0.238255i
$107$		−	1244.09i		−	1.12402i	−0.827130	−	0.562011i	$-0.810028\pi$
$107$		−	1244.09i		−	1.12402i	0.827130	−	0.562011i	$-0.189972\pi$
$108$	−58.5349	+	1120.84i	−0.0521530	+	0.998639i
$109$		−	569.937i		−	0.500826i	−0.968139	−	0.250413i	$-0.919434\pi$
$109$		−	569.937i		−	0.500826i	0.968139	−	0.250413i	$-0.0805664\pi$
$110$	22.9989	+	128.353i	0.0199351	+	0.111254i
$111$	−912.306	+	1177.45i	−0.780110	+	1.00684i
$112$	−325.991	+	61.2135i	−0.275029	+	0.0516441i
$113$	−824.716	+	476.150i	−0.686573	+	0.396393i	−0.802327	−	0.596885i	$-0.796405\pi$
$113$	−824.716	+	476.150i	−0.686573	+	0.396393i	0.115754	+	0.993278i	$0.463072\pi$
$114$	−196.414	−	102.728i	−0.161368	−	0.0843977i
$115$	−180.613	+	312.831i	−0.146455	+	0.253667i
$116$	31.5320	−	184.809i	0.0252386	−	0.147924i
$117$	−815.571	−	831.033i	−0.644441	−	0.656658i
$118$	−326.357	+	275.391i	−0.254607	+	0.214845i
$119$	8.59280	−	14.8832i	0.00661934	−	0.0114650i
$120$	−132.813	−	317.387i	−0.101034	−	0.241444i
$121$	−541.394	−	937.722i	−0.406757	−	0.704524i
$122$	1997.02	+	720.598i	1.48198	+	0.534753i
$123$	1694.03	+	231.119i	1.24183	+	0.169426i
$124$	−1620.63	+	1953.27i	−1.17368	+	1.41459i
$125$	−706.504			−0.505533
$126$	37.1039	−	394.042i	0.0262340	−	0.278603i
$127$		−	1274.79i		−	0.890701i	−0.895356	−	0.445350i	$-0.853079\pi$
$127$		−	1274.79i		−	0.890701i	0.895356	−	0.445350i	$-0.146921\pi$
$128$	468.815	−	1370.17i	0.323732	−	0.946149i
$129$	−1683.54	+	688.104i	−1.14905	+	0.469645i
$130$	335.743	+	121.148i	0.226513	+	0.0817338i
$131$	−470.494	+	271.640i	−0.313796	+	0.181170i	−0.648624	−	0.761109i	$-0.724655\pi$
$131$	−470.494	+	271.640i	−0.313796	+	0.181170i	0.334828	+	0.942279i	$0.391322\pi$
$132$	−442.861	−	482.478i	−0.292016	−	0.318139i
$133$	67.6916	+	39.0818i	0.0441324	+	0.0254798i
$134$	460.994	+	546.310i	0.297192	+	0.352194i
$135$	407.743	−	47.8483i	0.259948	−	0.0305047i
$136$	38.0551	+	64.6660i	0.0239941	+	0.0407725i
$137$	2185.39	+	1261.73i	1.36285	+	0.786840i	0.990002	−	0.141053i	$-0.0450488\pi$
$137$	2185.39	+	1261.73i	1.36285	+	0.786840i	0.372846	+	0.927893i	$0.378382\pi$
$138$	−75.6483	−	1812.67i	−0.0466638	−	1.11815i
$139$	937.946	+	1624.57i	0.572342	+	0.991326i	0.996325	+	0.0856555i	$0.0272984\pi$
$139$	937.946	+	1624.57i	0.572342	+	0.991326i	−0.423983	+	0.905670i	$0.639368\pi$
$140$	42.1268	+	113.777i	0.0254312	+	0.0686849i
$141$	1596.27	−	652.434i	0.953407	−	0.389680i
$142$	3015.94	−	540.411i	1.78234	−	0.319368i
$143$	679.425			0.397317
$144$	1417.17	+	988.743i	0.820122	+	0.572189i
$145$	−68.5766			−0.0392757
$146$	1888.74	−	338.434i	1.07064	−	0.191842i
$147$	222.061	−	1627.64i	0.124594	−	0.913232i
$148$	796.277	+	2150.60i	0.442254	+	1.19445i
$149$	−998.646	−	1729.71i	−0.549076	−	0.951027i	−0.998338	−	0.0576270i	$-0.981647\pi$
$149$	−998.646	−	1729.71i	−0.549076	−	0.951027i	0.449263	−	0.893400i	$-0.351687\pi$
$150$	1445.04	−	916.685i	0.786578	−	0.498980i
$151$	−35.3646	−	20.4177i	−0.0190591	−	0.0110038i	0.490440	−	0.871475i	$-0.336836\pi$
$151$	−35.3646	−	20.4177i	−0.0190591	−	0.0110038i	−0.509499	+	0.860471i	$0.670169\pi$
$152$	−294.114	+	173.082i	−0.156946	+	0.0923605i
$153$	−86.6950	+	22.3595i	−0.0458097	+	0.0118148i
$154$	148.938	+	176.502i	0.0779334	+	0.0923565i
$155$	803.992	+	464.185i	0.416634	+	0.240544i
$156$	−1749.85	+	389.487i	−0.898079	+	0.199897i
$157$	1170.05	−	675.530i	0.594779	−	0.343396i	−0.172206	−	0.985061i	$-0.555089\pi$
$157$	1170.05	−	675.530i	0.594779	−	0.343396i	0.766985	+	0.641665i	$0.221756\pi$
$158$	299.831	+	108.190i	0.150970	+	0.0544755i
$159$	2140.88	+	1658.78i	1.06782	+	0.827358i
$160$	−522.884	−	84.7475i	−0.258360	−	0.0418742i
$161$			639.763i			0.313170i
$162$	−1600.54	+	1299.92i	−0.776236	+	0.630442i
$163$	−1922.43			−0.923779			−0.461890	−	0.886937i	$-0.652828\pi$
$163$	−1922.43			−0.923779			−0.461890	+	0.886937i	$0.652828\pi$
$164$	1680.80	−	2025.80i	0.800298	−	0.964562i
$165$	−146.722	+	189.365i	−0.0692261	+	0.0893455i
$166$	−2634.08	−	950.470i	−1.23159	−	0.444402i
$167$	−1311.20	−	2271.06i	−0.607566	−	1.05234i	−0.991640	−	0.129033i	$-0.958813\pi$
$167$	−1311.20	−	2271.06i	−0.607566	−	1.05234i	0.384074	−	0.923302i	$-0.374521\pi$
$168$	−484.769	−	369.198i	−0.222623	−	0.169549i
$169$	−168.615	+	292.049i	−0.0767477	+	0.132931i
$170$	20.9755	−	17.6998i	0.00946321	−	0.00798536i
$171$	−101.696	−	394.306i	−0.0454787	−	0.176335i
$172$	−470.950	+	2760.24i	−0.208777	+	1.22364i
$173$	−1385.77	+	2400.23i	−0.609008	+	1.05483i	0.382396	+	0.923998i	$0.375099\pi$
$173$	−1385.77	+	2400.23i	−0.609008	+	1.05483i	−0.991404	+	0.130834i	$0.958234\pi$
$174$	290.839	−	184.499i	0.126715	−	0.0803841i
$175$	−522.603	+	301.725i	−0.225743	+	0.130333i
$176$	−990.985	+	186.084i	−0.424422	+	0.0796966i
$177$	−777.291	−	106.047i	−0.330084	−	0.0450339i
$178$	282.686	+	1577.62i	0.119035	+	0.664312i
$179$		−	2108.40i		−	0.880389i	−0.897903	−	0.440194i	$-0.854910\pi$
$179$		−	2108.40i		−	0.880389i	0.897903	−	0.440194i	$-0.145090\pi$
$180$	269.327	−	571.817i	0.111525	−	0.236782i
$181$			583.190i			0.239493i	0.992805	+	0.119746i	$0.0382081\pi$
$181$			583.190i			0.239493i	−0.992805	+	0.119746i	$0.961792\pi$
$182$	622.247	−	111.497i	0.253429	−	0.0454106i
$183$	1475.65	+	3610.38i	0.596082	+	1.45840i
$184$	−2430.52	−	1376.45i	−0.973805	−	0.551486i
$185$	726.455	−	419.419i	0.288703	−	0.166683i
$186$	−4658.64	+	194.420i	−1.83650	+	0.0766428i
$187$	26.1214	−	45.2436i	0.0102149	−	0.0176927i
$188$	446.537	−	2617.16i	0.173229	−	1.01530i
$189$	583.027	−	434.464i	0.224386	−	0.167210i
$190$	80.5020	+	95.4006i	0.0307381	+	0.0364268i
$191$	−622.663	+	1078.48i	−0.235886	+	0.408567i	−0.959530	−	0.281607i	$-0.909133\pi$
$191$	−622.663	+	1078.48i	−0.235886	+	0.408567i	0.723644	+	0.690174i	$0.242466\pi$
$192$	2445.60	−	1047.35i	0.919249	−	0.393677i
$193$	−1316.15	−	2279.63i	−0.490872	−	0.850215i	0.509073	−	0.860723i	$-0.329988\pi$
$193$	−1316.15	−	2279.63i	−0.490872	−	0.850215i	−0.999945	+	0.0105083i	$0.996655\pi$
$194$	141.852	−	393.122i	0.0524970	−	0.145487i
$195$	248.088	+	606.983i	0.0911076	+	0.222907i
$196$	−1946.40	−	1614.93i	−0.709329	−	0.588531i
$197$	−1210.94			−0.437948			−0.218974	−	0.975731i	$-0.570271\pi$
$197$	−1210.94			−0.437948			−0.218974	+	0.975731i	$0.570271\pi$
$198$	112.793	−	1197.85i	0.0404840	−	0.429938i
$199$		−	2015.72i		−	0.718043i	−0.933329	−	0.359021i	$-0.883110\pi$
$199$		−	2015.72i		−	0.718043i	0.933329	−	0.359021i	$-0.116890\pi$
$200$	−21.8986	−	2634.58i	−0.00774233	−	0.931465i
$201$	−177.519	+	1301.16i	−0.0622947	+	0.456600i
$202$	−1408.41	+	3903.18i	−0.490570	+	1.35954i
$203$	−105.183	+	60.7275i	−0.0363666	+	0.0209962i
$204$	−41.3391	+	131.499i	−0.0141878	+	0.0451311i
$205$	−833.845	−	481.421i	−0.284089	−	0.164019i
$206$	−2508.72	+	2116.94i	−0.848500	+	0.715992i
$207$	2378.80	−	2334.54i	0.798734	−	0.783873i
$208$	−915.177	+	2603.86i	−0.305077	+	0.868005i
$209$	205.777	+	118.805i	0.0681046	+	0.0393202i
$210$	−103.299	+	197.506i	−0.0339442	+	0.0649011i
$211$	−601.260	−	1041.41i	−0.196173	−	0.339781i	0.751112	−	0.660175i	$-0.229518\pi$
$211$	−601.260	−	1041.41i	−0.196173	−	0.339781i	−0.947284	+	0.320394i	$0.896185\pi$
$212$	3910.28	−	1447.81i	1.26679	−	0.469039i
$213$	4449.55	+	3447.57i	1.43135	+	1.10903i
$214$	−620.633	−	3463.64i	−0.198250	−	1.10640i
$215$	1024.23			0.324894
$216$	396.184	+	3149.72i	0.124801	+	0.992182i
$217$	1644.22			0.514365
$218$	−284.322	−	1586.75i	−0.0883337	−	0.492974i
$219$	2786.54	+	2159.05i	0.859804	+	0.666188i
$220$	128.062	+	345.872i	0.0392451	+	0.105994i
$221$	−71.5013	−	123.844i	−0.0217634	−	0.0376952i
$222$	−1952.55	+	3733.25i	−0.590299	+	1.12865i
$223$	−1135.80	−	655.752i	−0.341070	−	0.196917i	0.319675	−	0.947527i	$-0.396426\pi$
$223$	−1135.80	−	655.752i	−0.341070	−	0.196917i	−0.660745	+	0.750611i	$0.729759\pi$
$224$	−877.049	+	333.050i	−0.261609	+	0.0993430i
$225$	3028.90	+	842.153i	0.897453	+	0.249527i
$226$	−2058.54	+	1737.07i	−0.605895	+	0.511274i
$227$	−2494.70	−	1440.32i	−0.729423	−	0.421133i	0.0887881	−	0.996051i	$-0.471701\pi$
$227$	−2494.70	−	1440.32i	−0.729423	−	0.421133i	−0.818211	+	0.574918i	$0.805034\pi$
$228$	−598.082	−	188.018i	−0.173724	−	0.0546132i
$229$	3858.07	−	2227.46i	1.11331	−	0.642771i	0.173627	−	0.984812i	$-0.444451\pi$
$229$	3858.07	−	2227.46i	1.11331	−	0.642771i	0.939685	+	0.342040i	$0.111118\pi$
$230$	−346.782	+	961.051i	−0.0994178	+	0.275521i
$231$	−57.3528	+	420.377i	−0.0163357	+	0.119735i
$232$	−4.40748	−	530.256i	−0.00124727	−	0.150056i
$233$		−	1085.86i		−	0.305309i	−0.988280	−	0.152654i	$-0.951218\pi$
$233$		−	1085.86i		−	0.305309i	0.988280	−	0.152654i	$-0.0487821\pi$
$234$	−2685.20	−	1906.81i	−0.750157	−	0.532700i
$235$	−971.139			−0.269575
$236$	−771.223	+	929.520i	−0.212722	+	0.256384i
$237$	221.552	+	542.059i	0.0607231	+	0.148568i
$238$	16.4984	−	45.7227i	0.00449341	−	0.0124528i
$239$	−1617.59	−	2801.74i	−0.437795	−	0.758283i	0.559724	−	0.828679i	$-0.310907\pi$
$239$	−1617.59	−	2801.74i	−0.437795	−	0.758283i	−0.997519	+	0.0703960i	$0.977574\pi$
$240$	−528.096	−	817.376i	−0.142035	−	0.219839i
$241$	715.242	−	1238.84i	0.191173	−	0.331122i	−0.754466	−	0.656339i	$-0.772104\pi$
$241$	715.242	−	1238.84i	0.191173	−	0.331122i	0.945639	+	0.325217i	$0.105437\pi$
$242$	−1975.08	−	2340.61i	−0.524642	−	0.621737i
$243$	−3742.95	−	582.449i	−0.988108	−	0.153762i
$244$	5919.37	+	1009.96i	1.55307	+	0.264983i
$245$	−462.552	+	801.164i	−0.120618	+	0.208916i
$246$	4831.62	−	201.639i	1.25225	−	0.0522602i
$247$	563.267	−	325.202i	0.145100	−	0.0837738i
$248$	−3537.55	+	6246.55i	−0.905785	+	1.59942i
$249$	−1946.38	−	4762.09i	−0.495369	−	1.21199i
$250$	−1966.97	+	352.451i	−0.497608	+	0.0891639i
$251$			5903.80i			1.48464i	0.670046	+	0.742320i	$0.266275\pi$
$251$			5903.80i			1.48464i	−0.670046	+	0.742320i	$0.733725\pi$
$252$	−93.2738	−	1115.56i	−0.0233162	−	0.278863i
$253$			1944.83i			0.483281i
$254$	−635.948	−	3549.11i	−0.157098	−	0.876737i
$255$	49.9577	+	6.81582i	0.0122685	+	0.00167382i
$256$	621.688	−	4048.55i	0.151779	−	0.988414i
$257$	1225.66	−	707.636i	0.297489	−	0.171755i	−0.343825	−	0.939034i	$-0.611723\pi$
$257$	1225.66	−	707.636i	0.297489	−	0.171755i	0.641314	+	0.767278i	$0.278389\pi$
$258$	−4343.86	+	2755.61i	−1.04820	+	0.664948i
$259$	742.827	−	1286.61i	0.178212	−	0.308673i
$260$	995.175	+	169.796i	0.237377	+	0.0405011i
$261$	609.621	+	169.498i	0.144577	+	0.0401980i
$262$	−1174.38	+	990.981i	−0.276922	+	0.233676i
$263$	−2793.50	+	4838.48i	−0.654959	+	1.13442i	0.326945	+	0.945043i	$0.393981\pi$
$263$	−2793.50	+	4838.48i	−0.654959	+	1.13442i	−0.981904	+	0.189379i	$0.939352\pi$
$264$	−1473.66	−	1122.33i	−0.343550	−	0.261647i
$265$	−762.599	−	1320.86i	−0.176778	−	0.306188i
$266$	207.956	+	75.0379i	0.0479345	+	0.0172965i
$267$	−1803.40	+	2327.53i	−0.413358	+	0.533494i
$268$	1555.98	+	1291.00i	0.354652	+	0.294255i
$269$	5030.52			1.14021			0.570105	−	0.821572i	$-0.306903\pi$
$269$	5030.52			1.14021			0.570105	+	0.821572i	$0.306903\pi$
$270$	1111.32	−	336.623i	0.250492	−	0.0758750i
$271$		−	1317.52i		−	0.295328i	−0.989038	−	0.147664i	$-0.952825\pi$
$271$		−	1317.52i		−	0.295328i	0.989038	−	0.147664i	$-0.0471754\pi$
$272$	138.208	+	161.051i	0.0308092	+	0.0359013i
$273$	918.029	+	711.301i	0.203522	+	0.157692i
$274$	6713.74	+	2422.56i	1.48026	+	0.534131i
$275$	−1588.67	+	917.219i	−0.348365	+	0.201129i
$276$	−1114.89	−	5008.88i	−0.243147	−	1.09239i
$277$	−2626.49	−	1516.41i	−0.569714	−	0.328924i	0.187321	−	0.982299i	$-0.440019\pi$
$277$	−2626.49	−	1516.41i	−0.569714	−	0.328924i	−0.757035	+	0.653374i	$0.773353\pi$
$278$	3421.77	+	4055.03i	0.738216	+	0.874837i
$279$	−5999.88	−	6113.63i	−1.28747	−	1.31188i
$280$	174.044	+	295.748i	0.0371468	+	0.0631227i
$281$	−2118.05	−	1222.86i	−0.449653	−	0.259607i	0.258031	−	0.966137i	$-0.416926\pi$
$281$	−2118.05	−	1222.86i	−0.449653	−	0.259607i	−0.707683	+	0.706530i	$0.750260\pi$
$282$	4118.68	−	2612.76i	0.869730	−	0.551729i
$283$	4229.51	+	7325.72i	0.888403	+	1.53876i	0.841763	+	0.539847i	$0.181518\pi$
$283$	4229.51	+	7325.72i	0.888403	+	1.53876i	0.0466401	+	0.998912i	$0.485149\pi$
$284$	8127.04	−	3009.10i	1.69807	−	0.628723i
$285$	−30.9997	+	227.217i	−0.00644302	+	0.0472253i
$286$	1891.58	−	338.942i	0.391088	−	0.0700772i
$287$	−1705.27			−0.350729
$288$	4438.77	+	2045.77i	0.908185	+	0.418569i
$289$	4902.00			0.997762
$290$	−190.923	+	34.2106i	−0.0386600	+	0.00692729i
$291$	710.717	−	290.487i	0.143172	−	0.0585177i
$292$	5089.58	−	1884.46i	1.02002	−	0.377670i
$293$	−219.370	−	379.960i	−0.0437397	−	0.0757593i	0.843327	−	0.537401i	$-0.180594\pi$
$293$	−219.370	−	379.960i	−0.0437397	−	0.0757593i	−0.887066	+	0.461642i	$0.847261\pi$
$294$	−193.736	−	4642.25i	−0.0384316	−	0.920890i
$295$	382.603	+	220.896i	0.0755118	+	0.0435968i
$296$	3289.77	+	5590.22i	0.645992	+	1.09772i
$297$	1772.35	−	1320.73i	0.346270	−	0.258036i
$298$	−3643.21	−	4317.46i	−0.708206	−	0.839274i
$299$	4610.30	+	2661.76i	0.891708	+	0.514828i
$300$	3565.80	−	3273.01i	0.686239	−	0.629891i
$301$	1570.97	−	907.003i	0.300829	−	0.173684i
$302$	−108.644	−	39.2025i	−0.0207011	−	0.00746971i
$303$	−7056.47	+	2884.15i	−1.33790	+	0.546832i
$304$	−732.493	+	628.598i	−0.138195	+	0.118594i
$305$		−	2196.48i		−	0.412361i
$306$	−230.212	+	105.500i	−0.0430077	+	0.0197093i
$307$	−7875.21			−1.46405			−0.732023	−	0.681280i	$-0.761423\pi$
$307$	−7875.21			−1.46405			−0.732023	+	0.681280i	$0.761423\pi$
$308$	502.706	+	417.095i	0.0930011	+	0.0771630i
$309$	−5975.08	−	815.190i	−1.10003	−	0.150079i
$310$	2469.95	+	891.246i	0.452528	+	0.163288i
$311$	532.946	+	923.090i	0.0971724	+	0.168308i	0.910513	−	0.413480i	$-0.135687\pi$
$311$	532.946	+	923.090i	0.0971724	+	0.168308i	−0.813341	+	0.581788i	$0.802354\pi$
$312$	−4677.44	+	1957.31i	−0.848743	+	0.355163i
$313$	−4954.30	+	8581.10i	−0.894676	+	1.54962i	−0.0604700	+	0.998170i	$0.519260\pi$
$313$	−4954.30	+	8581.10i	−0.894676	+	1.54962i	−0.834206	+	0.551454i	$0.814073\pi$
$314$	2920.53	−	2464.43i	0.524888	−	0.442917i
$315$	−396.498	+	102.261i	−0.0709210	+	0.0182913i
$316$	888.729	+	151.634i	0.158212	+	0.0269939i
$317$	35.1444	−	60.8718i	0.00622683	−	0.0107852i	−0.862895	−	0.505383i	$-0.831351\pi$
$317$	35.1444	−	60.8718i	0.00622683	−	0.0107852i	0.869122	+	0.494598i	$0.164685\pi$
$318$	6787.90	+	3550.18i	1.19700	+	0.626050i
$319$	−319.748	+	184.607i	−0.0561205	+	0.0324012i
$320$	−1498.03	+	24.9050i	−0.261695	+	0.00435072i
$321$	3959.35	−	5110.07i	0.688440	−	0.888524i
$322$	319.157	+	1781.16i	0.0552357	+	0.308261i
$323$		−	50.0113i		−	0.00861518i
$324$	−3807.55	+	4417.55i	−0.652872	+	0.757468i
$325$			5021.36i			0.857030i
$326$	−5352.20	+	959.034i	−0.909297	+	0.162932i
$327$	1813.84	−	2341.01i	0.306746	−	0.395896i
$328$	3668.90	−	6478.49i	0.617626	−	1.09059i
$329$	−1489.54	+	859.986i	−0.249608	+	0.144111i
$330$	−314.019	+	600.402i	−0.0523824	+	0.100155i
$331$	4684.34	−	8113.51i	0.777868	−	1.34731i	−0.155300	−	0.987867i	$-0.549634\pi$
$331$	4684.34	−	8113.51i	0.777868	−	1.34731i	0.933168	−	0.359440i	$-0.117032\pi$
$332$	−7807.66	−	1332.13i	−1.29067	−	0.220212i
$333$	−7494.57	+	1932.93i	−1.23333	+	0.318089i
$334$	−4783.44	−	5668.71i	−0.783648	−	0.928677i
$335$	369.771	−	640.463i	0.0603067	−	0.104454i
$336$	−1533.82	−	786.044i	−0.249038	−	0.127626i
$337$	3086.72	+	5346.35i	0.498944	+	0.864197i	0.999999	−	0.00121842i	$-0.000387836\pi$
$337$	3086.72	+	5346.35i	0.498944	+	0.864197i	−0.501055	+	0.865416i	$0.667055\pi$
$338$	−323.744	+	897.206i	−0.0520987	+	0.144383i
$339$	−4902.87	−	668.908i	−0.785509	−	0.107168i
$340$	49.5677	−	59.7416i	0.00790642	−	0.00952925i
$341$	4998.30			0.793763
$342$	−479.835	−	1047.05i	−0.0758670	−	0.165550i
$343$			3416.08i			0.537758i
$344$	65.8285	+	7919.69i	0.0103175	+	1.24128i
$345$	−1737.46	+	710.143i	−0.271136	+	0.110820i
$346$	−2660.72	+	7373.76i	−0.413413	+	1.14571i
$347$	5102.09	−	2945.69i	0.789321	−	0.455715i	−0.0504023	−	0.998729i	$-0.516050\pi$
$347$	5102.09	−	2945.69i	0.789321	−	0.455715i	0.839724	+	0.543014i	$0.182717\pi$
$348$	717.680	−	658.751i	0.110551	−	0.101473i
$349$	−8150.29	−	4705.57i	−1.25007	−	0.721729i	−0.278948	−	0.960306i	$-0.589986\pi$
$349$	−8150.29	−	4705.57i	−1.25007	−	0.721729i	−0.971123	+	0.238577i	$0.923319\pi$
$350$	−1304.45	+	1100.74i	−0.199217	+	0.168106i
$351$	−705.157	−	6009.04i	−0.107232	−	0.913787i
$352$	−2666.16	+	1012.44i	−0.403712	+	0.153305i
$353$	−6050.47	−	3493.24i	−0.912278	−	0.526704i	−0.0311148	−	0.999516i	$-0.509906\pi$
$353$	−6050.47	−	3493.24i	−0.912278	−	0.526704i	−0.881163	+	0.472812i	$0.843239\pi$
$354$	−2216.95	+	92.5203i	−0.332852	+	0.0138910i
$355$	−1584.97	−	2745.25i	−0.236962	−	0.410430i
$356$	1574.04	+	4251.21i	0.234338	+	0.632903i
$357$	82.6611	−	33.7855i	0.0122546	−	0.00500874i
$358$	−1051.81	−	5869.98i	−0.155279	−	0.866587i
$359$	3844.64			0.565215			0.282607	−	0.959236i	$-0.408801\pi$
$359$	3844.64			0.565215			0.282607	+	0.959236i	$0.408801\pi$
$360$	464.568	−	1726.34i	0.0680135	−	0.252740i
$361$	−6631.54			−0.966838
$362$	290.934	+	1623.65i	0.0422407	+	0.235738i
$363$	760.564	−	5574.69i	0.109970	−	0.806047i
$364$	1676.77	−	620.836i	0.241446	−	0.0893974i
$365$	−992.590	−	1719.22i	−0.142341	−	0.246542i
$366$	5909.43	+	9315.45i	0.843964	+	1.33040i
$367$	11663.0	+	6733.63i	1.65886	+	0.957746i	0.973240	+	0.229789i	$0.0738038\pi$
$367$	11663.0	+	6733.63i	1.65886	+	0.957746i	0.685624	+	0.727956i	$0.259530\pi$
$368$	−7453.43	−	2619.66i	−1.05581	−	0.371084i
$369$	6222.66	+	6340.63i	0.877883	+	0.894526i
$370$	1813.28	−	1530.10i	0.254778	−	0.214990i
$371$	−2339.36	−	1350.63i	−0.327368	−	0.189006i
$372$	−12873.1	+	2865.32i	−1.79419	+	0.399355i
$373$	−5361.43	+	3095.42i	−0.744248	+	0.429692i	−0.823612	−	0.567154i	$-0.808044\pi$
$373$	−5361.43	+	3095.42i	−0.744248	+	0.429692i	0.0793639	+	0.996846i	$0.474711\pi$
$374$	50.1537	−	138.993i	0.00693418	−	0.0192170i
$375$	−2901.96	−	2248.47i	−0.399617	−	0.309629i
$376$	−62.4160	−	7509.15i	−0.00856080	−	1.02993i
$377$			1010.64i			0.138065i
$378$	1406.46	−	1500.44i	0.191376	−	0.204164i
$379$	7854.31			1.06451			0.532255	−	0.846584i	$-0.321345\pi$
$379$	7854.31			1.06451			0.532255	+	0.846584i	$0.321345\pi$
$380$	271.717	+	225.444i	0.0366810	+	0.0304342i
$381$	4057.05	−	5236.17i	0.545536	−	0.704087i
$382$	−1195.53	+	3313.22i	−0.160127	+	0.443767i
$383$	5216.45	+	9035.15i	0.695948	+	1.20542i	0.969860	+	0.243662i	$0.0783489\pi$
$383$	5216.45	+	9035.15i	0.695948	+	1.20542i	−0.273912	+	0.961755i	$0.588318\pi$
$384$	6286.27	−	4135.94i	0.835403	−	0.549638i
$385$	119.466	−	206.920i	0.0158144	−	0.0273913i
$386$	−4801.50	−	5690.11i	−0.633134	−	0.750308i
$387$	−9105.06	−	2531.56i	−1.19596	−	0.332523i
$388$	198.814	−	1165.25i	0.0260135	−	0.152466i
$389$	5731.82	−	9927.81i	0.747082	−	1.29398i	−0.202133	−	0.979358i	$-0.564787\pi$
$389$	5731.82	−	9927.81i	0.747082	−	1.29398i	0.949216	−	0.314626i	$-0.101879\pi$
$390$	993.503	+	1566.13i	0.128995	+	0.203344i
$391$	354.498	−	204.670i	0.0458510	−	0.0264721i
$392$	−6224.57	−	3525.10i	−0.802011	−	0.454196i
$393$	−2797.05	−	381.606i	−0.359014	−	0.0489809i
$394$	−3371.35	+	604.096i	−0.431082	+	0.0772434i
$395$		−	329.777i		−	0.0420074i
$396$	−283.544	−	3391.19i	−0.0359814	−	0.430338i
$397$			8809.54i			1.11370i	0.830614	+	0.556849i	$0.187990\pi$
$397$			8809.54i			1.11370i	−0.830614	+	0.556849i	$0.812010\pi$
$398$	−1005.58	−	5611.93i	−0.126646	−	0.706786i
$399$	153.663	+	375.959i	0.0192802	+	0.0471716i
$400$	−1375.27	−	7323.97i	−0.171909	−	0.915496i
$401$	−6817.45	+	3936.06i	−0.848996	+	0.490168i	−0.860312	−	0.509768i	$-0.829731\pi$
$401$	−6817.45	+	3936.06i	−0.848996	+	0.490168i	0.0113159	+	0.999936i	$0.496398\pi$
$402$	154.875	+	3711.09i	0.0192151	+	0.460429i
$403$	6840.85	−	11848.7i	0.845576	−	1.46458i
$404$	−1973.96	+	11569.4i	−0.243089	+	1.42475i
$405$	1827.08	+	1101.12i	0.224169	+	0.135099i
$406$	−262.544	+	221.543i	−0.0320932	+	0.0270813i
$407$	2258.13	−	3911.20i	0.275016	−	0.476341i
$408$	−49.4912	+	386.726i	−0.00600534	+	0.0469260i
$409$	170.965	+	296.120i	0.0206691	+	0.0358000i	0.876175	−	0.481993i	$-0.160087\pi$
$409$	170.965	+	296.120i	0.0206691	+	0.0358000i	−0.855506	+	0.517793i	$0.826754\pi$
$410$	−2561.66	−	924.339i	−0.308564	−	0.111341i
$411$	4960.94	+	12137.6i	0.595389	+	1.45670i
$412$	−5928.43	+	7145.26i	−0.708914	+	0.854422i
$413$	782.451			0.0932249
$414$	5458.15	−	7686.26i	0.647956	−	0.912462i
$415$			2897.16i			0.342689i
$416$	−1248.95	+	7705.91i	−0.147199	+	0.908205i
$417$	−1317.65	+	9657.95i	−0.154738	+	1.13418i
$418$	632.168	+	228.109i	0.0739721	+	0.0266918i
$419$	1154.35	−	666.463i	0.134591	−	0.0777060i	−0.431193	−	0.902260i	$-0.641907\pi$
$419$	1154.35	−	666.463i	0.134591	−	0.0777060i	0.565784	+	0.824554i	$0.308574\pi$
$420$	−189.063	+	601.407i	−0.0219651	+	0.0698706i
$421$	−5457.42	−	3150.84i	−0.631777	−	0.364757i	0.149663	−	0.988737i	$-0.452181\pi$
$421$	−5457.42	−	3150.84i	−0.631777	−	0.364757i	−0.781440	+	0.623980i	$0.785515\pi$
$422$	−2193.49	−	2599.44i	−0.253027	−	0.299854i
$423$	8633.07	+	2400.33i	0.992326	+	0.275905i
$424$	10164.3	−	5981.55i	1.16420	−	0.685117i
$425$	334.377	+	193.053i	0.0381639	+	0.0220340i
$426$	14107.8	+	7378.60i	1.60452	+	0.839189i
$427$	−1945.08	−	3368.97i	−0.220442	−	0.381817i
$428$	−3455.79	−	9333.46i	−0.390285	−	1.05409i
$429$	2790.73	+	2162.29i	0.314074	+	0.243349i
$430$	2851.55	−	510.956i	0.319800	−	0.0573035i
$431$	1791.33			0.200198			0.100099	−	0.994977i	$-0.468084\pi$
$431$	1791.33			0.200198			0.100099	+	0.994977i	$0.468084\pi$
$432$	2674.30	+	8571.45i	0.297841	+	0.954615i
$433$	7947.77			0.882092			0.441046	−	0.897485i	$-0.354608\pi$
$433$	7947.77			0.882092			0.441046	+	0.897485i	$0.354608\pi$
$434$	4577.66	−	820.249i	0.506301	−	0.0907216i
$435$	−281.678	−	218.248i	−0.0310469	−	0.0240556i
$436$	−1583.16	−	4275.81i	−0.173898	−	0.469666i
$437$	930.878	+	1612.33i	0.101899	+	0.176495i
$438$	8835.05	+	4620.87i	0.963824	+	0.504095i
$439$	10066.8	+	5812.07i	1.09445	+	0.631879i	0.934757	−	0.355288i	$-0.115617\pi$
$439$	10066.8	+	5812.07i	1.09445	+	0.631879i	0.159690	+	0.987167i	$0.448951\pi$
$440$	529.079	+	899.050i	0.0573246	+	0.0974103i
$441$	6092.12	−	5978.77i	0.657825	−	0.645586i
$442$	−260.848	−	309.123i	−0.0280707	−	0.0332657i
$443$	12771.4	+	7373.55i	1.36972	+	0.790808i	0.990892	−	0.134660i	$-0.0429942\pi$
$443$	12771.4	+	7373.55i	1.36972	+	0.790808i	0.378827	+	0.925467i	$0.376328\pi$
$444$	−3573.66	+	11367.7i	−0.381979	+	1.21507i
$445$	1436.02	−	829.088i	0.152975	−	0.0883203i
$446$	−3489.29	−	1259.06i	−0.370454	−	0.133673i
$447$	1402.92	−	10283.0i	0.148447	−	1.08807i
$448$	−2275.63	+	1364.77i	−0.239986	+	0.143927i
$449$		−	8413.52i		−	0.884317i	−0.896937	−	0.442159i	$-0.854213\pi$
$449$		−	8413.52i		−	0.884317i	0.896937	−	0.442159i	$-0.145787\pi$
$450$	8852.85	+	833.607i	0.927394	+	0.0873258i
$451$	−5183.89			−0.541241
$452$	−4864.60	+	5863.08i	−0.506220	+	0.610124i
$453$	−80.2794	−	196.415i	−0.00832639	−	0.0203717i
$454$	−7663.98	−	2765.44i	−0.792265	−	0.285878i
$455$	−327.010	−	566.398i	−0.0336933	−	0.0583585i
$456$	−1758.91	−	225.096i	−0.180632	−	0.0231164i
$457$	−9060.70	+	15693.6i	−0.927443	+	1.60638i	−0.139860	+	0.990171i	$0.544665\pi$
$457$	−9060.70	+	15693.6i	−0.927443	+	1.60638i	−0.787584	+	0.616208i	$0.788668\pi$
$458$	9629.99	−	8126.10i	0.982489	−	0.829056i
$459$	−427.259	−	184.069i	−0.0434482	−	0.0187181i
$460$	−486.033	+	2848.65i	−0.0492639	+	0.288737i
$461$	8300.14	−	14376.3i	0.838560	−	1.45243i	−0.0525393	−	0.998619i	$-0.516731\pi$
$461$	8300.14	−	14376.3i	0.838560	−	1.45243i	0.891099	−	0.453809i	$-0.149935\pi$
$462$	50.0371	+	1198.98i	0.00503882	+	0.120739i
$463$	−9006.61	+	5199.97i	−0.904045	+	0.521950i	−0.878510	−	0.477724i	$-0.841462\pi$
$463$	−9006.61	+	5199.97i	−0.904045	+	0.521950i	−0.0255344	+	0.999674i	$0.508129\pi$
$464$	−276.798	−	1474.08i	−0.0276940	−	0.147484i
$465$	1825.10	+	4465.37i	0.182015	+	0.445326i
$466$	−541.698	−	3023.12i	−0.0538491	−	0.300522i
$467$		−	4926.33i		−	0.488144i	−0.969757	−	0.244072i	$-0.921517\pi$
$467$		−	4926.33i		−	0.488144i	0.969757	−	0.244072i	$-0.0784833\pi$
$468$	−8427.06	−	3969.16i	−0.832352	−	0.392039i
$469$		−	1309.79i		−	0.128957i
$470$	−2703.73	+	484.469i	−0.265349	+	0.0475466i
$471$	6955.87	+	949.002i	0.680488	+	0.0928401i
$472$	−1683.44	+	2972.60i	−0.164167	+	0.289884i
$473$	4775.63	−	2757.21i	0.464236	−	0.268027i
$474$	887.236	+	1398.61i	0.0859749	+	0.135528i
$475$	−878.042	+	1520.81i	−0.0848154	+	0.146905i
$476$	23.1234	−	135.526i	0.00222659	−	0.0130501i
$477$	3514.50	+	13626.9i	0.337354	+	1.30803i
$478$	−5901.20	−	6993.33i	−0.564674	−	0.669179i
$479$	934.274	−	1618.21i	0.0891191	−	0.154359i	−0.818020	−	0.575190i	$-0.804928\pi$
$479$	934.274	−	1618.21i	0.0891191	−	0.154359i	0.907139	+	0.420831i	$0.138261\pi$
$480$	−1878.03	−	2012.20i	−0.178583	−	0.191341i
$481$	−6181.12	−	10706.0i	−0.585935	−	1.01487i
$482$	1373.28	−	3805.84i	0.129774	−	0.359650i
$483$	−2036.07	+	2627.82i	−0.191810	+	0.247557i
$484$	−6666.46	−	5531.16i	−0.626076	−	0.519456i
$485$	−432.385			−0.0404817
$486$	−10711.3	+	245.645i	−0.999737	+	0.0229274i
$487$		−	3289.20i		−	0.306053i	−0.988222	−	0.153026i	$-0.951098\pi$
$487$		−	3289.20i		−	0.306053i	0.988222	−	0.153026i	$-0.0489020\pi$
$488$	16983.9	−	141.170i	1.57546	−	0.0130952i
$489$	−7896.34	−	6118.19i	−0.730235	−	0.565796i
$490$	−888.111	+	2461.26i	−0.0818791	+	0.226915i
$491$	−1189.49	+	686.750i	−0.109329	+	0.0631214i	−0.553668	−	0.832738i	$-0.686772\pi$
$491$	−1189.49	+	686.750i	−0.109329	+	0.0631214i	0.444338	+	0.895859i	$0.353439\pi$
$492$	13351.1	−	2971.72i	1.22340	−	0.272307i
$493$	67.2993	+	38.8553i	0.00614809	+	0.00354960i
$494$	1405.95	−	1186.39i	0.128050	−	0.108053i
$495$	−1205.32	+	310.864i	−0.109445	+	0.0282269i
$496$	−6732.65	+	19155.7i	−0.609485	+	1.73411i
$497$	−4862.07	−	2807.11i	−0.438820	−	0.253353i
$498$	−7794.54	−	12287.1i	−0.701369	−	1.10562i
$499$	−925.039	−	1602.21i	−0.0829868	−	0.143737i	0.821545	−	0.570144i	$-0.193113\pi$
$499$	−925.039	−	1602.21i	−0.0829868	−	0.143737i	−0.904532	+	0.426407i	$0.859779\pi$
$500$	−5300.38	+	1962.51i	−0.474080	+	0.175532i
$501$	1842.00	−	13501.3i	0.164261	−	1.20398i
$502$	2945.21	+	16436.7i	0.261855	+	1.46137i
$503$	−17948.3			−1.59100			−0.795502	−	0.605951i	$-0.792793\pi$
$503$	−17948.3			−1.59100			−0.795502	+	0.605951i	$0.792793\pi$
$504$	−816.196	−	3059.27i	−0.0721354	−	0.270379i
$505$	4293.01			0.378290
$506$	970.209	+	5414.56i	0.0852392	+	0.475705i
$507$	−1622.04	+	662.966i	−0.142085	+	0.0580737i
$508$	−3541.07	−	9563.78i	−0.309271	−	0.835284i
$509$	131.163	+	227.180i	0.0114218	+	0.0197831i	0.871680	−	0.490076i	$-0.163031\pi$
$509$	131.163	+	227.180i	0.0114218	+	0.0197831i	−0.860258	+	0.509859i	$0.829698\pi$
$510$	142.487	−	5.94642i	0.0123714	−	0.000516298i
$511$	−3044.88	−	1757.96i	−0.263596	−	0.152187i
$512$	−288.853	−	11581.6i	−0.0249328	−	0.999689i
$513$	837.180	−	1943.26i	0.0720515	−	0.167245i
$514$	3059.33	−	2581.56i	0.262532	−	0.221533i
$515$	2941.09	+	1698.04i	0.251650	+	0.145290i
$516$	−10719.0	+	9838.85i	−0.914491	+	0.839401i
$517$	−4528.07	+	2614.28i	−0.385192	+	0.222391i
$518$	1426.24	−	3952.61i	0.120976	−	0.335266i
$519$	−13330.9	+	5448.64i	−1.12748	+	0.460826i
$520$	2855.36	−	23.7337i	0.240799	−	0.00200152i
$521$			938.595i			0.0789263i	0.999221	+	0.0394631i	$0.0125648\pi$
$521$			938.595i			0.0789263i	−0.999221	+	0.0394631i	$0.987435\pi$
$522$	1781.79	+	167.778i	0.149400	+	0.0140679i
$523$	−7118.07			−0.595127			−0.297563	−	0.954702i	$-0.596174\pi$
$523$	−7118.07			−0.595127			−0.297563	+	0.954702i	$0.596174\pi$
$524$	−2775.21	+	3344.84i	−0.231366	+	0.278855i
$525$	−3106.84	−	423.872i	−0.258274	−	0.0352367i
$526$	−5363.57	+	14864.3i	−0.444606	+	1.23216i
$527$	−526.011	−	911.078i	−0.0434790	−	0.0753078i
$528$	−4662.68	−	2389.51i	−0.384312	−	0.196951i
$529$	−1535.67	+	2659.87i	−0.126216	+	0.218613i
$530$	−2782.08	−	3296.95i	−0.228011	−	0.270209i
$531$	−2855.22	−	2909.35i	−0.233344	−	0.237768i
$532$	616.401	+	105.170i	0.0502337	+	0.00857083i
$533$	−7094.86	+	12288.7i	−0.576571	+	0.998650i
$534$	−3859.70	+	7379.71i	−0.312782	+	0.598036i
$535$	−3152.77	+	1820.25i	−0.254777	+	0.147096i
$536$	4976.02	+	2818.02i	0.400991	+	0.227090i
$537$	6710.07	−	8660.25i	0.539220	−	0.695935i
$538$	14005.4	−	2509.56i	1.12233	−	0.201106i
$539$			4980.71i			0.398023i
$540$	2926.08	−	1491.59i	0.233183	−	0.118866i
$541$		−	6529.45i		−	0.518896i	−0.965757	−	0.259448i	$-0.916459\pi$
$541$		−	6529.45i		−	0.518896i	0.965757	−	0.259448i	$-0.0835407\pi$
$542$	−657.269	−	3668.10i	−0.0520888	−	0.290698i
$543$	−1856.02	+	2395.45i	−0.146684	+	0.189316i
$544$	465.127	+	379.433i	0.0366583	+	0.0299045i
$545$	−1444.33	+	833.887i	−0.113520	+	0.0655409i
$546$	2910.72	+	1522.35i	0.228145	+	0.119323i
$547$	−902.529	+	1563.23i	−0.0705473	+	0.122192i	−0.899141	−	0.437658i	$-0.855808\pi$
$547$	−902.529	+	1563.23i	−0.0705473	+	0.122192i	0.828594	+	0.559850i	$0.189141\pi$
$548$	19900.2	+	3395.34i	1.55126	+	0.264675i
$549$	−5428.96	+	19525.9i	−0.422044	+	1.51793i
$550$	−3965.42	+	3346.15i	−0.307429	+	0.259419i
$551$	−176.721	+	306.090i	−0.0136635	+	0.0236659i
$552$	−5602.71	−	13389.0i	−0.432006	−	1.03238i
$553$	−292.032	−	505.814i	−0.0224565	−	0.0388959i
$554$	−8068.87	−	2911.54i	−0.618797	−	0.223284i
$555$	4318.72	+	589.210i	0.330305	+	0.0450641i
$556$	11549.4	+	9582.55i	0.880943	+	0.730919i
$557$	−25569.6			−1.94510			−0.972550	−	0.232694i	$-0.925246\pi$
$557$	−25569.6			−1.94510			−0.972550	+	0.232694i	$0.925246\pi$
$558$	−19754.1	−	14027.7i	−1.49867	−	1.06423i
$559$		−	15094.5i		−	1.14209i
$560$	632.092	+	736.564i	0.0476978	+	0.0555813i
$561$	251.283	−	102.705i	0.0189112	−	0.00772944i
$562$	−6506.88	−	2347.91i	−0.488392	−	0.176229i
$563$	−4254.07	+	2456.09i	−0.318451	+	0.183858i	−0.650702	−	0.759333i	$-0.725525\pi$
$563$	−4254.07	+	2456.09i	−0.318451	+	0.183858i	0.332251	+	0.943191i	$0.392192\pi$
$564$	10163.3	−	9328.82i	0.758783	−	0.696479i
$565$	2413.32	+	1393.33i	0.179698	+	0.103748i
$566$	15429.9	+	18285.5i	1.14588	+	1.35794i
$567$	3777.47	+	70.9477i	0.279786	+	0.00525489i
$568$	21125.2	−	12431.9i	1.56055	−	0.918365i
$569$	13142.2	+	7587.64i	0.968275	+	0.559034i	0.898710	−	0.438544i	$-0.144506\pi$
$569$	13142.2	+	7587.64i	0.968275	+	0.559034i	0.0695650	+	0.997577i	$0.477839\pi$
$570$	27.0455	+	648.057i	0.00198739	+	0.0476213i
$571$	6558.52	+	11359.7i	0.480675	+	0.832554i	0.999754	−	0.0221726i	$-0.00705833\pi$
$571$	6558.52	+	11359.7i	0.480675	+	0.832554i	−0.519079	+	0.854726i	$0.673725\pi$
$572$	5097.22	−	1887.29i	0.372597	−	0.137957i
$573$	−5989.89	+	2448.21i	−0.436704	+	0.178491i
$574$	−4747.63	+	850.705i	−0.345230	+	0.0618602i
$575$	−14373.4			−1.04246
$576$	13378.5	+	3481.23i	0.967773	+	0.251825i
$577$	9122.28			0.658173			0.329086	−	0.944300i	$-0.393259\pi$
$577$	9122.28			0.658173			0.329086	+	0.944300i	$0.393259\pi$
$578$	13647.6	−	2445.45i	0.982120	−	0.175981i
$579$	1848.96	−	13552.2i	0.132712	−	0.972733i
$580$	−514.480	+	190.490i	−0.0368321	+	0.0136374i
$581$	2565.56	+	4443.68i	0.183197	+	0.317306i
$582$	1833.78	−	1163.29i	0.130606	−	0.0828523i
$583$	−7111.45	−	4105.80i	−0.505191	−	0.291672i
$584$	13229.7	−	7785.51i	0.937414	−	0.551655i
$585$	−912.725	+	3282.73i	−0.0645069	+	0.232007i
$586$	−800.294	−	948.404i	−0.0564161	−	0.0668570i
$587$	−13405.1	−	7739.45i	−0.942570	−	0.544193i	−0.0518051	−	0.998657i	$-0.516497\pi$
$587$	−13405.1	−	7739.45i	−0.942570	−	0.544193i	−0.890765	+	0.454464i	$0.849831\pi$
$588$	−2855.24	−	12827.8i	−0.200252	−	0.899675i
$589$	4143.76	−	2392.40i	0.289883	−	0.167364i
$590$	1175.40	+	424.125i	0.0820175	+	0.0295948i
$591$	−4973.91	−	3853.85i	−0.346192	−	0.268234i
$592$	11947.8	+	13922.5i	0.829476	+	0.966572i
$593$			13499.3i			0.934824i	0.884040	+	0.467412i	$0.154813\pi$
$593$			13499.3i			0.934824i	−0.884040	+	0.467412i	$0.845187\pi$
$594$	4275.51	−	4561.20i	0.295330	−	0.315065i
$595$	−50.2893			−0.00346498
$596$	−12296.8	−	10202.7i	−0.845131	−	0.701206i
$597$	6415.10	−	8279.54i	0.439787	−	0.567603i
$598$	14163.3	+	5110.64i	0.968531	+	0.349481i
$599$	7097.54	+	12293.3i	0.484136	+	0.838548i	0.999834	−	0.0182222i	$-0.00580063\pi$
$599$	7097.54	+	12293.3i	0.484136	+	0.838548i	−0.515698	+	0.856771i	$0.672467\pi$
$600$	8294.70	−	10891.2i	0.564383	−	0.741052i
$601$	505.327	−	875.253i	0.0342974	−	0.0594048i	−0.848367	−	0.529408i	$-0.822414\pi$
$601$	505.327	−	875.253i	0.0342974	−	0.0594048i	0.882665	+	0.470003i	$0.155747\pi$
$602$	3921.25	−	3308.88i	0.265479	−	0.224020i
$603$	−4870.14	+	4779.52i	−0.328901	+	0.322782i
$604$	−322.030	−	54.9445i	−0.0216941	−	0.00370142i
$605$	−1584.25	+	2744.00i	−0.106461	+	0.184396i
$606$	−18207.0	+	11550.0i	−1.22048	+	0.774232i
$607$	7769.04	−	4485.46i	0.519498	−	0.299933i	−0.217231	−	0.976120i	$-0.569702\pi$
$607$	7769.04	−	4485.46i	0.519498	−	0.299933i	0.736729	+	0.676188i	$0.236369\pi$
$608$	−1725.74	+	2115.49i	−0.115112	+	0.141109i
$609$	−625.306	−	85.3116i	−0.0416070	−	0.00567652i
$610$	−1095.75	−	6115.19i	−0.0727306	−	0.405896i
$611$			14312.0i			0.947630i
$612$	−588.299	+	408.566i	−0.0388572	+	0.0269858i
$613$		−	14462.3i		−	0.952897i	−0.879202	−	0.476449i	$-0.841924\pi$
$613$		−	14462.3i		−	0.952897i	0.879202	−	0.476449i	$-0.158076\pi$
$614$	−21925.3	+	3928.68i	−1.44109	+	0.258222i
$615$	−1892.87	−	4631.17i	−0.124110	−	0.303653i
$616$	1607.65	+	910.446i	0.105153	+	0.0595502i
$617$	18159.9	−	10484.6i	1.18491	−	0.684108i	0.227764	−	0.973716i	$-0.426858\pi$
$617$	18159.9	−	10484.6i	1.18491	−	0.684108i	0.957145	+	0.289608i	$0.0935251\pi$
$618$	−17041.8	+	711.208i	−1.10926	+	0.0462928i
$619$	−3168.60	+	5488.18i	−0.205746	+	0.356363i	−0.950370	−	0.311121i	$-0.899295\pi$
$619$	−3168.60	+	5488.18i	−0.205746	+	0.356363i	0.744624	+	0.667484i	$0.232629\pi$
$620$	7321.17	+	1249.13i	0.474234	+	0.0809133i
$621$	17200.6	−	2018.48i	1.11149	−	0.130433i
$622$	1944.27	+	2304.09i	0.125334	+	0.148530i
$623$	1468.39	−	2543.32i	0.0944296	−	0.163557i
$624$	−12045.9	+	7782.73i	−0.772795	+	0.499293i
$625$	−6243.62	−	10814.3i	−0.399591	−	0.692113i
$626$	−9512.37	+	26362.0i	−0.607333	+	1.68313i
$627$	467.123	+	1142.88i	0.0297530	+	0.0727948i
$628$	6901.57	−	8318.14i	0.438539	−	0.528551i
$629$	−950.565			−0.0602568
$630$	−1052.87	+	482.502i	−0.0665830	+	0.0305133i
$631$		−	26190.2i		−	1.65232i	−0.563436	−	0.826160i	$-0.690521\pi$
$631$		−	26190.2i		−	1.65232i	0.563436	−	0.826160i	$-0.309479\pi$
$632$	2549.94	−	21.1951i	0.160492	−	0.00133401i
$633$	844.666	−	6191.13i	0.0530371	−	0.388744i
$634$	67.4780	−	187.005i	0.00422696	−	0.0117144i
$635$	−3230.57	+	1865.17i	−0.201892	+	0.116562i
$636$	20669.2	+	6497.74i	1.28866	+	0.405113i
$637$	11807.0	+	6816.79i	0.734397	+	0.424004i
$638$	−798.111	+	673.472i	−0.0495259	+	0.0417916i
$639$	7304.46	+	28321.7i	0.452207	+	1.75335i
$640$	−4158.22	+	816.655i	−0.256825	+	0.0504393i
$641$	−21831.2	−	12604.3i	−1.34521	−	0.776660i	−0.357647	−	0.933857i	$-0.616421\pi$
$641$	−21831.2	−	12604.3i	−1.34521	−	0.776660i	−0.987567	+	0.157197i	$0.949754\pi$
$642$	8473.92	−	16202.1i	0.520933	−	0.996019i
$643$	3931.26	+	6809.13i	0.241110	+	0.417614i	0.961031	−	0.276442i	$-0.0891553\pi$
$643$	3931.26	+	6809.13i	0.241110	+	0.417614i	−0.719921	+	0.694056i	$0.755822\pi$
$644$	1777.12	+	4799.67i	0.108740	+	0.293686i
$645$	4207.03	+	3259.66i	0.256824	+	0.198991i
$646$	−24.9490	−	139.236i	−0.00151951	−	0.00848012i
$647$	188.733			0.0114681			0.00573404	−	0.999984i	$-0.498175\pi$
$647$	188.733			0.0114681			0.00573404	+	0.999984i	$0.498175\pi$
$648$	−8396.78	+	14198.3i	−0.509038	+	0.860744i
$649$	2378.58			0.143864
$650$	2504.99	+	13979.9i	0.151160	+	0.843594i
$651$	6753.63	+	5232.80i	0.406599	+	0.315038i
$652$	−14422.5	+	5340.07i	−0.866304	+	0.320756i
$653$	15259.4	+	26430.1i	0.914468	+	1.58390i	0.807678	+	0.589623i	$0.200724\pi$
$653$	15259.4	+	26430.1i	0.914468	+	1.58390i	0.106790	+	0.994282i	$0.465943\pi$
$654$	3882.05	−	7422.43i	0.232110	−	0.443792i
$655$	1376.78	+	794.884i	0.0821301	+	0.0474178i
$656$	6982.63	−	19867.0i	0.415588	−	1.18243i
$657$	4574.44	+	17736.5i	0.271637	+	1.05322i
$658$	−3717.98	+	3137.35i	−0.220277	+	0.185877i
$659$	−16805.7	−	9702.80i	−0.993412	−	0.573547i	−0.0871197	−	0.996198i	$-0.527766\pi$
$659$	−16805.7	−	9702.80i	−0.993412	−	0.573547i	−0.906292	+	0.422651i	$0.861100\pi$
$660$	−574.736	+	1828.22i	−0.0338963	+	0.107824i
$661$	26953.4	−	15561.6i	1.58603	−	0.915696i	0.592079	−	0.805880i	$-0.298307\pi$
$661$	26953.4	−	15561.6i	1.58603	−	0.915696i	0.993952	−	0.109816i	$-0.0350262\pi$
$662$	8994.03	−	24925.6i	0.528041	−	1.46338i
$663$	100.447	−	736.243i	0.00588392	−	0.0431272i
$664$	−22401.7	+	186.203i	−1.30927	+	0.0108827i
$665$		−	228.726i		−	0.0133377i
$666$	−19901.3	+	9120.23i	−1.15790	+	0.530633i
$667$	−2892.91			−0.167937
$668$	−16145.4	−	13395.9i	−0.935159	−	0.775902i
$669$	−2578.31	−	6308.21i	−0.149004	−	0.364558i
$670$	709.969	−	1967.57i	0.0409381	−	0.113453i
$671$	−5912.87	−	10241.4i	−0.340185	−	0.589217i
$672$	−4662.41	−	1423.24i	−0.267644	−	0.0817006i
$673$	16571.1	−	28701.9i	0.949134	−	1.64395i	0.201880	−	0.979410i	$-0.435295\pi$
$673$	16571.1	−	28701.9i	0.949134	−	1.64395i	0.747254	−	0.664539i	$-0.231372\pi$
$674$	11260.8	+	13344.8i	0.643546	+	0.762647i
$675$	9761.01	+	13098.7i	0.556595	+	0.746919i
$676$	−453.745	+	2659.40i	−0.0258162	+	0.151309i
$677$	−3831.16	+	6635.77i	−0.217494	+	0.376711i	−0.954041	−	0.299675i	$-0.903122\pi$
$677$	−3831.16	+	6635.77i	−0.217494	+	0.376711i	0.736547	+	0.676386i	$0.236455\pi$
$678$	−13983.7	+	583.585i	−0.792097	+	0.0330567i
$679$	−663.195	+	382.896i	−0.0374832	+	0.0216409i
$680$	108.198	−	191.054i	0.00610174	−	0.0107744i
$681$	−5663.09	−	13855.5i	−0.318664	−	0.779656i
$682$	13915.7	−	2493.49i	0.781319	−	0.140001i
$683$		−	8233.45i		−	0.461265i	−0.973041	−	0.230633i	$-0.925920\pi$
$683$		−	8233.45i		−	0.461265i	0.973041	−	0.230633i	$-0.0740795\pi$
$684$	−1858.24	−	2675.70i	−0.103877	−	0.149573i
$685$		−	7384.28i		−	0.411882i
$686$	1704.17	+	9510.66i	0.0948477	+	0.529328i
$687$	22935.9	+	3129.19i	1.27374	+	0.173779i
$688$	4134.14	+	22016.3i	0.229088	+	1.22000i
$689$	−19466.0	+	11238.7i	−1.07633	+	0.621422i
$690$	−4482.98	+	2843.86i	−0.247339	+	0.156904i
$691$	−9201.53	+	15937.5i	−0.506574	+	0.877412i	0.493397	+	0.869804i	$0.335755\pi$
$691$	−9201.53	+	15937.5i	−0.506574	+	0.877412i	−0.999971	+	0.00760808i	$0.997578\pi$
$692$	−3729.14	+	21856.5i	−0.204856	+	1.20067i
$693$	−1573.44	+	1544.17i	−0.0862484	+	0.0846437i
$694$	12735.1	−	10746.3i	0.696570	−	0.587788i
$695$	2744.66	−	4753.89i	0.149800	−	0.259461i
$696$	1669.45	−	2192.05i	0.0909203	−	0.119381i
$697$	545.542	+	944.907i	0.0296469	+	0.0513499i
$698$	−25038.5	−	9034.80i	−1.35777	−	0.489932i
$699$	3455.78	−	4460.15i	0.186995	−	0.241342i
$700$	−3082.58	+	3715.30i	−0.166444	+	0.200607i
$701$	2617.11			0.141008			0.0705041	−	0.997511i	$-0.477539\pi$
$701$	2617.11			0.141008			0.0705041	+	0.997511i	$0.477539\pi$
$702$	−4960.93	−	16377.9i	−0.266721	−	0.880548i
$703$		−	4323.36i		−	0.231947i
$704$	−6917.73	+	4148.78i	−0.370343	+	0.222107i
$705$	−3988.94	−	3090.69i	−0.213095	−	0.165109i
$706$	−18587.7	−	6707.11i	−0.990874	−	0.357543i
$707$	6584.64	−	3801.65i	0.350270	−	0.202229i
$708$	−6126.02	+	1363.55i	−0.325184	+	0.0723803i
$709$	15311.9	+	8840.30i	0.811070	+	0.468271i	0.847327	−	0.531071i	$-0.178210\pi$
$709$	15311.9	+	8840.30i	0.811070	+	0.468271i	−0.0362573	+	0.999342i	$0.511544\pi$
$710$	−5782.20	−	6852.31i	−0.305637	−	0.362201i
$711$	−815.098	+	2931.60i	−0.0429938	+	0.154632i
$712$	6503.06	+	11050.5i	0.342293	+	0.581649i
$713$	33916.4	+	19581.7i	1.78146	+	1.02853i
$714$	213.281	−	135.299i	0.0111790	−	0.00709163i
$715$	−994.082	−	1721.80i	−0.0519952	−	0.0900583i
$716$	−5856.67	−	15817.8i	−0.305690	−	0.825613i
$717$	2272.43	−	16656.2i	0.118362	−	0.867553i
$718$	10703.8	−	1917.96i	0.556354	−	0.0996903i
$719$	7767.21			0.402876			0.201438	−	0.979501i	$-0.435438\pi$
$719$	7767.21			0.402876			0.201438	+	0.979501i	$0.435438\pi$
$720$	432.181	−	5038.05i	0.0223700	−	0.260774i
$721$	6014.74			0.310680
$722$	−18462.8	+	3308.25i	−0.951680	+	0.170527i
$723$	6880.49	−	2812.22i	0.353926	−	0.144658i
$724$	1619.97	+	4375.24i	0.0831571	+	0.224592i
$725$	−1364.35	−	2363.13i	−0.0698907	−	0.121054i
$726$	−663.550	−	15899.8i	−0.0339210	−	0.812807i
$727$	−9187.03	−	5304.13i	−0.468677	−	0.270591i	0.247009	−	0.969013i	$-0.420552\pi$
$727$	−9187.03	−	5304.13i	−0.468677	−	0.270591i	−0.715686	+	0.698423i	$0.753886\pi$
$728$	4358.54	−	2564.94i	0.221893	−	0.130581i
$729$	−13520.5	−	14304.5i	−0.686910	−	0.726742i
$730$	−3621.12	−	4291.28i	−0.183594	−	0.217572i
$731$	−1005.16	−	580.327i	−0.0508578	−	0.0293628i
$732$	21099.5	+	22987.0i	1.06538	+	1.16069i
$733$	−7738.67	+	4467.92i	−0.389951	+	0.225138i	−0.682139	−	0.731223i	$-0.738950\pi$
$733$	−7738.67	+	4467.92i	−0.389951	+	0.225138i	0.292188	+	0.956361i	$0.405617\pi$
$734$	35829.9	+	12928.7i	1.80178	+	0.650147i
$735$	−4449.66	+	1818.68i	−0.223304	+	0.0912695i
$736$	−22057.9	−	3575.07i	−1.10471	−	0.179048i
$737$		−	3981.66i		−	0.199005i
$738$	20487.6	+	14548.6i	1.02189	+	0.725665i
$739$	5767.08			0.287071			0.143535	−	0.989645i	$-0.454153\pi$
$739$	5767.08			0.287071			0.143535	+	0.989645i	$0.454153\pi$
$740$	4285.00	−	5164.52i	0.212865	−	0.256556i
$741$	3348.58	+	456.853i	0.166010	+	0.0226490i
$742$	−7186.76	−	2593.24i	−0.355572	−	0.128303i
$743$	711.865	+	1232.99i	0.0351491	+	0.0608801i	0.883065	−	0.469251i	$-0.155476\pi$
$743$	711.865	+	1232.99i	0.0351491	+	0.0608801i	−0.847916	+	0.530131i	$0.822143\pi$
$744$	−34410.3	+	14399.3i	−1.69562	+	0.709546i
$745$	−2922.28	+	5061.54i	−0.143710	+	0.248913i
$746$	−13382.5	+	11292.6i	−0.656793	+	0.554223i
$747$	7160.80	−	25754.7i	0.350736	−	1.26147i
$748$	70.2931	−	411.989i	0.00343606	−	0.0201388i
$749$	−3223.82	+	5583.82i	−0.157271	+	0.272401i
$750$	−9200.99	−	4812.26i	−0.447963	−	0.234292i
$751$	−16310.8	+	9417.02i	−0.792527	+	0.457566i	−0.840851	−	0.541266i	$-0.817945\pi$
$751$	−16310.8	+	9417.02i	−0.792527	+	0.457566i	0.0483243	+	0.998832i	$0.484612\pi$
$752$	−3919.84	−	20875.0i	−0.190082	−	1.01228i
$753$	−18789.1	+	24249.8i	−0.909311	+	1.17359i
$754$	504.173	+	2813.70i	0.0243513	+	0.135900i
$755$			119.495i			0.00576007i
$756$	3167.18	−	4878.98i	0.152367	−	0.234718i
$757$			21381.1i			1.02657i	0.858219	+	0.513283i	$0.171571\pi$
$757$			21381.1i			1.02657i	−0.858219	+	0.513283i	$0.828429\pi$
$758$	21867.1	−	3918.26i	1.04782	−	0.187754i
$759$	−6189.48	+	7988.35i	−0.296000	+	0.382027i
$760$	868.949	+	492.104i	0.0414738	+	0.0234875i
$761$	15809.6	−	9127.66i	0.753083	−	0.434793i	−0.0737237	−	0.997279i	$-0.523488\pi$
$761$	15809.6	−	9127.66i	0.753083	−	0.434793i	0.826807	+	0.562486i	$0.190155\pi$
$762$	8683.03	−	16601.9i	0.412799	−	0.789268i
$763$	−1476.89	+	2558.04i	−0.0700745	+	0.121373i
$764$	−1675.60	+	9820.68i	−0.0793467	+	0.465052i
$765$	183.509	+	186.988i	0.00867292	+	0.00883734i
$766$	19030.4	+	22552.3i	0.897644	+	1.06377i
$767$	3255.42	−	5638.55i	0.153255	−	0.265445i
$768$	15438.2	−	14650.8i	0.725363	−	0.688367i
$769$	−7996.45	−	13850.3i	−0.374980	−	0.649484i	0.615344	−	0.788259i	$-0.289017\pi$
$769$	−7996.45	−	13850.3i	−0.374980	−	0.649484i	−0.990324	+	0.138774i	$0.955684\pi$
$770$	229.377	−	635.682i	0.0107353	−	0.0297511i
$771$	7286.47	+	994.106i	0.340358	+	0.0464356i
$772$	−16206.4	−	13446.4i	−0.755545	−	0.626876i
$773$	−23733.1			−1.10429			−0.552147	−	0.833747i	$-0.686191\pi$
$773$	−23733.1			−1.10429			−0.552147	+	0.833747i	$0.686191\pi$
$774$	−26612.2	−	2505.87i	−1.23586	−	0.116371i
$775$			36940.4i			1.71218i
$776$	−27.7898	−	3343.34i	−0.00128556	−	0.154663i
$777$	7145.85	−	2920.68i	0.329930	−	0.134850i
$778$	11005.2	−	30499.3i	0.507142	−	1.40547i
$779$	−4297.62	+	2481.23i	−0.197662	+	0.114120i
$780$	3547.29	+	3864.61i	0.162838	+	0.177404i
$781$	−14780.3	−	8533.39i	−0.677182	−	0.390971i
$782$	884.851	−	746.665i	0.0404632	−	0.0341441i
$783$	1964.58	+	2636.35i	0.0896657	+	0.120326i
$784$	−19088.3	−	6708.96i	−0.869547	−	0.305619i
$785$	−3423.86	−	1976.77i	−0.155672	−	0.0898775i
$786$	−7977.60	+	332.930i	−0.362025	+	0.0151084i
$787$	3774.80	+	6538.15i	0.170975	+	0.296137i	0.938761	−	0.344569i	$-0.111975\pi$
$787$	3774.80	+	6538.15i	0.170975	+	0.296137i	−0.767786	+	0.640706i	$0.778642\pi$
$788$	−9084.77	+	3363.71i	−0.410700	+	0.152065i
$789$	−26872.9	+	10983.6i	−1.21255	+	0.495597i
$790$	−164.515	−	918.129i	−0.00740909	−	0.0413488i
$791$	4935.42			0.221850
$792$	−2481.17	−	9299.92i	−0.111319	−	0.417246i
$793$	−32370.3			−1.44956
$794$	4394.79	+	24526.5i	0.196430	+	1.09624i
$795$	1071.32	−	7852.42i	0.0477935	−	0.350310i
$796$	−5599.21	−	15122.5i	−0.249320	−	0.673368i
$797$	−13480.4	−	23348.7i	−0.599120	−	1.03771i	−0.992951	−	0.118524i	$-0.962184\pi$
$797$	−13480.4	−	23348.7i	−0.599120	−	1.03771i	0.393831	−	0.919183i	$-0.371149\pi$
$798$	615.365	+	970.044i	0.0272979	+	0.0430316i
$799$	953.051	+	550.244i	0.0421984	+	0.0243632i
$800$	−7482.56	−	19704.5i	−0.330686	−	0.870823i
$801$	−14814.9	+	3820.92i	−0.653508	+	0.168546i
$802$	−17016.8	+	14359.3i	−0.749232	+	0.632226i
$803$	−9256.18	−	5344.06i	−0.406779	−	0.234854i
$804$	2282.53	+	10254.7i	0.100122	+	0.449821i
$805$	1621.29	−	936.052i	0.0709850	−	0.0409832i
$806$	13134.6	−	36400.5i	0.574003	−	1.59076i
$807$	20662.8	+	16009.8i	0.901320	+	0.698355i
$808$	275.916	+	33194.9i	0.0120132	+	1.44529i
$809$			33739.1i			1.46626i	0.680090	+	0.733129i	$0.261941\pi$
$809$			33739.1i			1.46626i	−0.680090	+	0.733129i	$0.738059\pi$
$810$	5636.05	+	2154.14i	0.244482	+	0.0934431i
$811$	−9809.12			−0.424716			−0.212358	−	0.977192i	$-0.568114\pi$
$811$	−9809.12			−0.424716			−0.212358	+	0.977192i	$0.568114\pi$
$812$	−620.425	+	747.769i	−0.0268136	+	0.0323172i
$813$	4193.07	−	5411.71i	0.180882	−	0.233453i
$814$	4335.66	−	12015.6i	0.186689	−	0.517379i
$815$	2812.74	+	4871.82i	0.120891	+	0.209389i
$816$	55.1373	+	1101.37i	0.00236543	+	0.0472495i
$817$	2639.44	−	4571.65i	0.113026	−	0.195767i
$818$	623.705	+	739.135i	0.0266593	+	0.0315932i
$819$	1507.05	+	5843.32i	0.0642987	+	0.249307i
$820$	−7593.00	−	1295.51i	−0.323365	−	0.0551722i
$821$	9274.38	−	16063.7i	0.394248	−	0.682858i	−0.598756	−	0.800931i	$-0.704338\pi$
$821$	9274.38	−	16063.7i	0.394248	−	0.682858i	0.993005	+	0.118073i	$0.0376716\pi$
$822$	19866.7	+	31317.3i	0.842983	+	1.32885i
$823$	−1262.62	+	728.972i	−0.0534775	+	0.0308753i	−0.526500	−	0.850175i	$-0.676496\pi$
$823$	−1262.62	+	728.972i	−0.0534775	+	0.0308753i	0.473023	+	0.881050i	$0.343163\pi$
$824$	−12940.7	+	22850.5i	−0.547101	+	0.966063i
$825$	−9444.53	−	1288.53i	−0.398565	−	0.0543769i
$826$	2178.41	−	390.339i	0.0917634	−	0.0164426i
$827$		−	42187.5i		−	1.77388i	−0.461881	−	0.886942i	$-0.652825\pi$
$827$		−	42187.5i		−	1.77388i	0.461881	−	0.886942i	$-0.347175\pi$
$828$	11361.5	−	24122.1i	0.476861	−	1.01244i
$829$			22370.3i			0.937218i	0.883406	+	0.468609i	$0.155245\pi$
$829$			22370.3i			0.937218i	−0.883406	+	0.468609i	$0.844755\pi$
$830$	1445.30	+	8065.94i	0.0604422	+	0.337317i
$831$	−5962.27	−	14587.5i	−0.248892	−	0.608948i
$832$	367.033	+	22077.0i	0.0152940	+	0.919930i
$833$	907.873	−	524.161i	0.0377622	−	0.0218020i
$834$	1149.58	+	27545.9i	0.0477297	+	1.14369i
$835$	−3836.89	+	6645.68i	−0.159019	+	0.275429i
$836$	1873.81	+	319.707i	0.0775202	+	0.0132264i
$837$	−5187.60	−	44206.5i	−0.214229	−	1.82557i
$838$	2881.32	−	2431.35i	0.118775	−	0.100226i
$839$	24035.3	−	41630.3i	0.989023	−	1.71304i	0.366548	−	0.930399i	$-0.380540\pi$
$839$	24035.3	−	41630.3i	0.989023	−	1.71304i	0.622476	−	0.782639i	$-0.286127\pi$
$840$	−226.347	+	1768.68i	−0.00929727	+	0.0726493i
$841$	11919.9	+	20645.9i	0.488741	+	0.846524i
$842$	−16765.8	−	6049.69i	−0.686207	−	0.247608i
$843$	−4808.08	−	11763.7i	−0.196440	−	0.480619i
$844$	−7403.63	−	6142.79i	−0.301947	−	0.250526i
$845$	986.816			0.0401745
$846$	25232.6	+	2375.97i	1.02543	+	0.0965573i
$847$			5611.69i			0.227650i
$848$	25314.3	−	21723.8i	1.02511	−	0.879714i
$849$	−5941.72	+	43550.9i	−0.240188	+	1.76050i
$850$	1027.24	+	370.666i	0.0414519	+	0.0149573i
$851$	30645.5	−	17693.2i	1.23445	−	0.712708i
$852$	42958.3	+	13504.7i	1.72738	+	0.543034i
$853$	−14708.0	−	8491.65i	−0.590377	−	0.340854i	0.174870	−	0.984592i	$-0.444050\pi$
$853$	−14708.0	−	8491.65i	−0.590377	−	0.340854i	−0.765246	+	0.643737i	$0.777383\pi$
$854$	−7095.93	−	8409.17i	−0.284330	−	0.336951i
$855$	−850.458	+	834.635i	−0.0340176	+	0.0333847i
$856$	−14277.4	−	24261.2i	−0.570082	−	0.968727i
$857$	22340.4	+	12898.3i	0.890473	+	0.514115i	0.874097	−	0.485751i	$-0.161454\pi$
$857$	22340.4	+	12898.3i	0.890473	+	0.514115i	0.0163755	+	0.999866i	$0.494787\pi$
$858$	8848.33	+	4627.81i	0.352071	+	0.184139i
$859$	−9914.38	−	17172.2i	−0.393800	−	0.682082i	0.599147	−	0.800639i	$-0.295506\pi$
$859$	−9914.38	−	17172.2i	−0.393800	−	0.682082i	−0.992947	+	0.118557i	$0.962173\pi$
$860$	7684.07	−	2845.09i	0.304680	−	0.112810i
$861$	−7004.40	−	5427.10i	−0.277246	−	0.214814i
$862$	4987.22	−	893.636i	0.197060	−	0.0353102i
$863$	42561.4			1.67880			0.839401	−	0.543513i	$-0.182906\pi$
$863$	42561.4			1.67880			0.839401	+	0.543513i	$0.182906\pi$
$864$	11721.5	+	22529.5i	0.461543	+	0.887118i
$865$	8110.22			0.318793
$866$	22127.3	−	3964.88i	0.868263	−	0.155580i
$867$	20134.9	+	15600.8i	0.788717	+	0.611109i
$868$	12335.4	−	4567.28i	0.482363	−	0.178599i
$869$	−887.753	−	1537.63i	−0.0346547	−	0.0600237i
$870$	−893.091	−	467.100i	−0.0348030	−	0.0182025i
$871$	−9438.71	−	5449.44i	−0.367185	−	0.211995i
$872$	−6540.70	−	11114.5i	−0.254009	−	0.431632i
$873$	3843.75	+	1068.71i	0.149016	+	0.0414323i
$874$	3395.98	+	4024.47i	0.131431	+	0.155755i
$875$	3171.00	+	1830.78i	0.122513	+	0.0707331i
$876$	26902.7	+	8457.37i	1.03762	+	0.326197i
$877$	−13338.6	+	7701.03i	−0.513582	+	0.296517i	−0.734305	−	0.678820i	$-0.762492\pi$
$877$	−13338.6	+	7701.03i	−0.513582	+	0.296517i	0.220723	+	0.975337i	$0.429158\pi$
$878$	30926.3	+	11159.3i	1.18874	+	0.428939i
$879$	308.177	−	2258.83i	0.0118254	−	0.0866764i
$880$	1921.51	+	2239.09i	0.0736068	+	0.0857725i
$881$			408.896i			0.0156368i	0.999969	+	0.00781842i	$0.00248871\pi$
$881$			408.896i			0.0156368i	−0.999969	+	0.00781842i	$0.997511\pi$
$882$	13978.4	−	19684.6i	0.533647	−	0.751490i
$883$	24945.2			0.950704			0.475352	−	0.879796i	$-0.342321\pi$
$883$	24945.2			0.950704			0.475352	+	0.879796i	$0.342321\pi$
$884$	−880.433	−	730.495i	−0.0334979	−	0.0277932i
$885$	868.527	+	2124.97i	0.0329890	+	0.0807121i
$886$	39235.0	+	14157.4i	1.48773	+	0.536824i
$887$	−5014.93	−	8686.11i	−0.189836	−	0.328806i	0.755359	−	0.655311i	$-0.227462\pi$
$887$	−5014.93	−	8686.11i	−0.189836	−	0.328806i	−0.945196	+	0.326505i	$0.894129\pi$
$888$	−4278.39	+	33431.5i	−0.161682	+	1.26339i
$889$	−3303.37	+	5721.61i	−0.124625	+	0.215857i
$890$	3584.40	−	3024.63i	0.134999	−	0.113917i
$891$	11483.2	+	215.675i	0.431764	+	0.00810929i
$892$	−10342.6	−	1764.64i	−0.388223	−	0.0662382i
$893$	−2502.62	+	4334.66i	−0.0937815	+	0.162434i
$894$	−1223.97	−	29328.5i	−0.0457894	−	1.09720i
$895$	−5343.12	+	3084.85i	−0.199554	+	0.115213i
$896$	−5654.72	+	4934.87i	−0.210838	+	0.183998i
$897$	10465.6	+	25605.6i	0.389562	+	0.953117i
$898$	−4197.22	−	23423.9i	−0.155972	−	0.870454i
$899$			7434.91i			0.275827i
$900$	25063.0	−	2095.56i	0.928258	−	0.0776134i
$901$			1728.34i			0.0639062i
$902$	−14432.4	+	2586.07i	−0.532756	+	0.0954620i
$903$	9339.33	+	1274.18i	0.344179	+	0.0469569i
$904$	−10618.6	+	18750.1i	−0.390673	+	0.689844i
$905$	1477.92	−	853.278i	0.0542848	−	0.0313413i
$906$	−321.489	−	506.787i	−0.0117889	−	0.0185837i
$907$	3767.44	−	6525.40i	0.137923	−	0.238889i	−0.788788	−	0.614666i	$-0.789291\pi$
$907$	3767.44	−	6525.40i	0.137923	−	0.238889i	0.926710	+	0.375777i	$0.122624\pi$
$908$	−22716.8	−	3875.91i	−0.830267	−	0.141659i
$909$	−38163.3	−	10610.9i	−1.39251	−	0.387173i
$910$	−1192.98	−	1413.76i	−0.0434581	−	0.0515009i
$911$	−11159.9	+	19329.6i	−0.405867	+	0.702983i	−0.994422	−	0.105475i	$-0.966364\pi$
$911$	−11159.9	+	19329.6i	−0.405867	+	0.702983i	0.588555	+	0.808457i	$0.299697\pi$
$912$	−5009.24	+	250.775i	−0.181878	+	0.00910526i
$913$	7799.08	+	13508.4i	0.282708	+	0.489664i
$914$	−17396.8	+	48212.4i	−0.629577	+	1.74477i
$915$	6990.38	−	9022.02i	0.252563	−	0.325966i
$916$	22756.9	−	27427.8i	0.820861	−	0.989346i
$917$	2815.62			0.101396
$918$	−1281.35	−	299.317i	−0.0460685	−	0.0107614i
$919$			40992.7i			1.47141i	0.677303	+	0.735704i	$0.263149\pi$
$919$			40992.7i			1.47141i	−0.677303	+	0.735704i	$0.736851\pi$
$920$	67.9368	+	8173.34i	0.00243458	+	0.292899i
$921$	−32347.3	−	25063.1i	−1.15731	−	0.896698i
$922$	15936.5	−	44165.4i	0.569240	−	1.57756i
$923$	−40457.6	+	23358.2i	−1.44277	+	0.832985i
$924$	737.438	+	3313.09i	0.0262553	+	0.117958i
$925$	28906.1	+	16688.9i	1.02749	+	0.593220i
$926$	−22481.1	+	18970.3i	−0.797812	+	0.673220i
$927$	−21948.2	−	22364.3i	−0.777641	−	0.792383i
$928$	−1506.00	−	3965.88i	−0.0532724	−	0.140287i
$929$	−20199.6	−	11662.2i	−0.713376	−	0.411868i	0.0989336	−	0.995094i	$-0.468457\pi$
$929$	−20199.6	−	11662.2i	−0.713376	−	0.411868i	−0.812310	+	0.583226i	$0.801790\pi$
$930$	7308.87	+	11521.5i	0.257707	+	0.406241i
$931$	2383.99	+	4129.18i	0.0839226	+	0.145358i
$932$	−3016.27	−	8146.39i	−0.106010	−	0.286313i
$933$	−748.697	+	5487.70i	−0.0262714	+	0.192561i
$934$	−2457.58	−	13715.3i	−0.0860969	−	0.480491i
$935$	−152.875			−0.00534712
$936$	−25441.7	−	6846.49i	−0.888449	−	0.239086i
$937$	−29355.3			−1.02348			−0.511738	−	0.859142i	$-0.670998\pi$
$937$	−29355.3			−1.02348			−0.511738	+	0.859142i	$0.670998\pi$
$938$	−653.412	−	3646.58i	−0.0227448	−	0.126935i
$939$	−47659.4	+	19479.5i	−1.65634	+	0.676986i
$940$	−7285.74	+	2697.61i	−0.252803	+	0.0936024i
$941$	−1391.16	−	2409.56i	−0.0481939	−	0.0834743i	0.840922	−	0.541156i	$-0.182013\pi$
$941$	−1391.16	−	2409.56i	−0.0481939	−	0.0834743i	−0.889116	+	0.457682i	$0.848680\pi$
$942$	19839.2	−	827.951i	0.686194	−	0.0286371i
$943$	−35175.8	−	20308.7i	−1.21472	−	0.701319i
$944$	−3203.92	+	9115.79i	−0.110465	+	0.314294i
$945$	−1954.06	−	841.833i	−0.0672651	−	0.0289787i
$946$	11920.3	−	10058.7i	0.409685	−	0.345705i
$947$	15438.1	+	8913.16i	0.529746	+	0.305849i	0.740913	−	0.671601i	$-0.234393\pi$
$947$	15438.1	+	8913.16i	0.529746	+	0.305849i	−0.211167	+	0.977450i	$0.567726\pi$
$948$	3167.86	+	3451.25i	0.108531	+	0.118240i
$949$	−25336.7	+	14628.1i	−0.866663	+	0.500368i
$950$	−1685.86	+	4672.10i	−0.0575753	+	0.159561i
$951$	338.082	−	138.182i	0.0115279	−	0.00471174i
$952$	−3.23214	−	388.852i	−0.000110036	−	0.0132382i
$953$		−	21508.9i		−	0.731104i	−0.930791	−	0.365552i	$-0.880880\pi$
$953$		−	21508.9i		−	0.731104i	0.930791	−	0.365552i	$-0.119120\pi$
$954$	16582.7	+	36185.1i	0.562771	+	1.22802i
$955$	3644.13			0.123478
$956$	−19918.2	−	16526.1i	−0.673849	−	0.559093i
$957$	−1900.88	−	259.340i	−0.0642076	−	0.00875995i
$958$	1793.83	−	4971.31i	0.0604968	−	0.167657i
$959$	−6539.10	−	11326.1i	−0.220186	−	0.381374i
$960$	−6232.40	−	4665.24i	−0.209531	−	0.156844i
$961$	35430.4	−	61367.2i	1.18930	−	2.05992i
$962$	−22549.6	−	26722.9i	−0.755747	−	0.895614i
$963$	32526.0	−	8388.78i	1.08841	−	0.280711i
$964$	1924.73	−	11280.9i	0.0643064	−	0.376900i
$965$	−3851.37	+	6670.76i	−0.128477	+	0.222528i
$966$	−4357.66	+	8331.80i	−0.145140	+	0.277507i
$967$	8410.42	−	4855.76i	0.279691	−	0.161479i	−0.353593	−	0.935399i	$-0.615040\pi$
$967$	8410.42	−	4855.76i	0.279691	−	0.161479i	0.633283	+	0.773920i	$0.281707\pi$
$968$	−21319.3	−	12073.6i	−0.707881	−	0.400887i
$969$	159.163	−	205.421i	0.00527662	−	0.00681019i
$970$	−1203.80	+	215.703i	−0.0398470	+	0.00714000i
$971$		−	1908.56i		−	0.0630777i	−0.999503	−	0.0315389i	$-0.989959\pi$
$971$		−	1908.56i		−	0.0630777i	0.999503	−	0.0315389i	$-0.0100408\pi$
$972$	−29698.5	+	6027.38i	−0.980020	+	0.198898i
$973$		−	9722.06i		−	0.320324i
$974$	−1640.87	−	9157.41i	−0.0539804	−	0.301255i
$975$	−15980.6	+	20625.2i	−0.524913	+	0.677471i
$976$	47214.1	−	8865.71i	1.54845	−	0.290763i
$977$	−40899.7	+	23613.4i	−1.33930	+	0.773245i	−0.986704	−	0.162531i	$-0.948034\pi$
$977$	−40899.7	+	23613.4i	−1.33930	+	0.773245i	−0.352596	+	0.935776i	$0.614701\pi$
$978$	−25036.3	−	13094.3i	−0.818580	−	0.428130i
$979$	4463.77	−	7731.47i	0.145723	−	0.252399i
$980$	−1244.74	+	7295.41i	−0.0405731	+	0.237799i
$981$	14900.7	−	3843.04i	0.484956	−	0.125075i
$982$	−2969.03	+	2505.37i	−0.0964824	+	0.0814149i
$983$	−11777.7	+	20399.5i	−0.382146	+	0.661895i	−0.991369	−	0.131103i	$-0.958148\pi$
$983$	−11777.7	+	20399.5i	−0.382146	+	0.661895i	0.609223	+	0.792999i	$0.291481\pi$
$984$	35688.0	−	14933.9i	1.15619	−	0.483817i
$985$	1771.75	+	3068.76i	0.0573123	+	0.0992678i
$986$	206.751	+	74.6030i	0.00667777	+	0.00240958i
$987$	−8855.20	−	1208.13i	−0.285577	−	0.0389617i
$988$	3322.44	−	4004.38i	0.106985	−	0.128944i
$989$	43207.3			1.38919
$990$	−3200.63	+	1466.77i	−0.102750	+	0.0470878i
$991$			31768.2i			1.01831i	0.860673	+	0.509157i	$0.170043\pi$
$991$			31768.2i			1.01831i	−0.860673	+	0.509157i	$0.829957\pi$
$992$	−9188.12	+	56689.8i	−0.294076	+	1.81442i
$993$	45062.4	−	18418.1i	1.44009	−	0.588600i
$994$	−14936.8	−	5389.73i	−0.476626	−	0.171984i
$995$	−5108.24	+	2949.24i	−0.162756	+	0.0939672i
$996$	−27830.3	−	30319.9i	−0.885378	−	0.964581i
$997$	3600.15	+	2078.55i	0.114361	+	0.0660263i	0.556089	−	0.831122i	$-0.312301\pi$
$997$	3600.15	+	2078.55i	0.114361	+	0.0660263i	−0.441729	+	0.897149i	$0.645635\pi$
$998$	−3374.68	−	3999.23i	−0.107038	−	0.126847i
$999$	−36935.5	−	15912.3i	−1.16976	−	0.503946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.4.l.b.11.30	yes	64
3.2	odd	2		216.4.l.b.35.3		64
4.3	odd	2		288.4.p.b.47.7		64
8.3	odd	2	inner	72.4.l.b.11.20	✓	64
8.5	even	2		288.4.p.b.47.8		64
9.4	even	3		216.4.l.b.179.13		64
9.5	odd	6	inner	72.4.l.b.59.20	yes	64
12.11	even	2		864.4.p.b.143.18		64
24.5	odd	2		864.4.p.b.143.15		64
24.11	even	2		216.4.l.b.35.13		64
36.23	even	6		288.4.p.b.239.8		64
36.31	odd	6		864.4.p.b.719.15		64
72.5	odd	6		288.4.p.b.239.7		64
72.13	even	6		864.4.p.b.719.18		64
72.59	even	6	inner	72.4.l.b.59.30	yes	64
72.67	odd	6		216.4.l.b.179.3		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.l.b.11.20	✓	64	8.3	odd	2	inner
72.4.l.b.11.30	yes	64	1.1	even	1	trivial
72.4.l.b.59.20	yes	64	9.5	odd	6	inner
72.4.l.b.59.30	yes	64	72.59	even	6	inner
216.4.l.b.35.3		64	3.2	odd	2
216.4.l.b.35.13		64	24.11	even	2
216.4.l.b.179.3		64	72.67	odd	6
216.4.l.b.179.13		64	9.4	even	3
288.4.p.b.47.7		64	4.3	odd	2
288.4.p.b.47.8		64	8.5	even	2
288.4.p.b.239.7		64	72.5	odd	6
288.4.p.b.239.8		64	36.23	even	6
864.4.p.b.143.15		64	24.5	odd	2
864.4.p.b.143.18		64	12.11	even	2
864.4.p.b.719.15		64	36.31	odd	6
864.4.p.b.719.18		64	72.13	even	6

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	72.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.78409 - 0.498867i) q^{2} +(4.10749 + 3.18254i) q^{3} +(7.50226 - 2.77778i) q^{4} +(-1.46312 - 2.53420i) q^{5} +(13.0233 + 6.81136i) q^{6} +(-4.48829 - 2.59132i) q^{7} +(19.5012 - 11.4762i) q^{8} +(6.74292 + 26.1445i) q^{9} +O(q^{10})\)	\(q+(2.78409 - 0.498867i) q^{2} +(4.10749 + 3.18254i) q^{3} +(7.50226 - 2.77778i) q^{4} +(-1.46312 - 2.53420i) q^{5} +(13.0233 + 6.81136i) q^{6} +(-4.48829 - 2.59132i) q^{7} +(19.5012 - 11.4762i) q^{8} +(6.74292 + 26.1445i) q^{9} +(-5.33769 - 6.32553i) q^{10} +(-13.6440 - 7.87738i) q^{11} +(39.6558 + 12.4665i) q^{12} +(-37.3474 + 21.5625i) q^{13} +(-13.7885 - 4.97539i) q^{14} +(2.05543 - 15.0656i) q^{15} +(48.5679 - 41.6792i) q^{16} +3.31600i q^{17} +(31.8155 + 69.4246i) q^{18} -15.0818 q^{19} +(-18.0162 - 14.9480i) q^{20} +(-10.1886 - 24.9279i) q^{21} +(-41.9159 - 15.1247i) q^{22} +(-61.7219 - 106.905i) q^{23} +(116.624 + 14.9250i) q^{24} +(58.2185 - 100.837i) q^{25} +(-93.2215 + 78.6633i) q^{26} +(-55.5092 + 128.848i) q^{27} +(-40.8704 - 6.97327i) q^{28} +(11.7175 - 20.2953i) q^{29} +(-1.79325 - 42.9694i) q^{30} +(-274.752 + 158.628i) q^{31} +(114.425 - 140.267i) q^{32} +(-30.9726 - 75.7788i) q^{33} +(1.65424 + 9.23203i) q^{34} +15.1657i q^{35} +(123.211 + 177.412i) q^{36} +286.660i q^{37} +(-41.9891 + 7.52382i) q^{38} +(-222.028 - 30.2916i) q^{39} +(-57.6157 - 32.6289i) q^{40} +(284.954 - 164.518i) q^{41} +(-40.8018 - 64.3188i) q^{42} +(-175.008 + 303.123i) q^{43} +(-124.243 - 21.1982i) q^{44} +(56.3896 - 55.3405i) q^{45} +(-225.170 - 266.843i) q^{46} +(165.936 - 287.410i) q^{47} +(332.138 - 16.6277i) q^{48} +(-158.070 - 273.786i) q^{49} +(111.781 - 309.783i) q^{50} +(-10.5533 + 13.6204i) q^{51} +(-220.294 + 265.510i) q^{52} +521.214 q^{53} +(-90.2646 + 386.415i) q^{54} +46.1023i q^{55} +(-117.266 + 0.974711i) q^{56} +(-61.9484 - 47.9984i) q^{57} +(22.4979 - 62.3494i) q^{58} +(-130.749 + 75.4878i) q^{59} +(-26.4286 - 118.736i) q^{60} +(650.051 + 375.307i) q^{61} +(-685.799 + 578.699i) q^{62} +(37.4844 - 134.817i) q^{63} +(248.594 - 447.599i) q^{64} +(109.288 + 63.0972i) q^{65} +(-124.034 - 195.524i) q^{66} +(126.364 + 218.868i) q^{67} +(9.21110 + 24.8775i) q^{68} +(86.7085 - 635.545i) q^{69} +(7.56564 + 42.2225i) q^{70} +1083.28 q^{71} +(431.534 + 432.465i) q^{72} +678.405 q^{73} +(143.005 + 798.086i) q^{74} +(560.051 - 228.906i) q^{75} +(-113.148 + 41.8939i) q^{76} +(40.8256 + 70.7119i) q^{77} +(-633.255 + 26.4277i) q^{78} +(97.5980 + 56.3482i) q^{79} +(-176.684 - 62.0992i) q^{80} +(-638.066 + 352.580i) q^{81} +(711.263 - 600.187i) q^{82} +(-857.418 - 495.030i) q^{83} +(-145.682 - 158.714i) q^{84} +(8.40342 - 4.85171i) q^{85} +(-336.020 + 931.226i) q^{86} +(112.720 - 46.0714i) q^{87} +(-356.477 + 2.96304i) q^{88} +566.656i q^{89} +(129.386 - 182.204i) q^{90} +223.501 q^{91} +(-760.013 - 630.583i) q^{92} +(-1633.38 - 222.845i) q^{93} +(318.601 - 882.953i) q^{94} +(22.0666 + 38.2204i) q^{95} +(916.405 - 211.985i) q^{96} +(73.8806 - 127.965i) q^{97} +(-576.663 - 683.386i) q^{98} +(113.949 - 409.832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 3 q^{2} + 6 q^{3} - 17 q^{4} - 3 q^{6} + 42 q^{9}+O(q^{10}) \) 64 * q - 3 * q^2 + 6 * q^3 - 17 * q^4 - 3 * q^6 + 42 * q^9	\( 64 q - 3 q^{2} + 6 q^{3} - 17 q^{4} - 3 q^{6} + 42 q^{9} + 12 q^{10} + 48 q^{11} + 318 q^{12} + 72 q^{14} + 127 q^{16} + 330 q^{18} - 220 q^{19} - 234 q^{20} - 217 q^{22} + 189 q^{24} - 902 q^{25} - 252 q^{27} - 132 q^{28} + 420 q^{30} - 693 q^{32} - 660 q^{33} + 509 q^{34} - 537 q^{36} - 1977 q^{38} - 36 q^{40} + 1620 q^{41} + 72 q^{42} - 292 q^{43} + 48 q^{46} + 765 q^{48} + 1762 q^{49} - 1227 q^{50} - 1794 q^{51} + 330 q^{52} - 645 q^{54} + 942 q^{56} - 294 q^{57} - 282 q^{58} + 5592 q^{59} + 1236 q^{60} + 1090 q^{64} - 6 q^{65} + 3522 q^{66} + 68 q^{67} - 2025 q^{68} + 600 q^{70} + 1875 q^{72} - 868 q^{73} - 420 q^{74} - 4254 q^{75} - 1471 q^{76} + 3228 q^{78} + 498 q^{81} + 362 q^{82} + 3654 q^{83} - 2028 q^{84} - 4119 q^{86} + 3155 q^{88} + 2958 q^{90} - 1380 q^{91} - 744 q^{92} - 138 q^{94} - 4782 q^{96} - 1912 q^{97} - 2118 q^{99}+O(q^{100}) \) 64 * q - 3 * q^2 + 6 * q^3 - 17 * q^4 - 3 * q^6 + 42 * q^9 + 12 * q^10 + 48 * q^11 + 318 * q^12 + 72 * q^14 + 127 * q^16 + 330 * q^18 - 220 * q^19 - 234 * q^20 - 217 * q^22 + 189 * q^24 - 902 * q^25 - 252 * q^27 - 132 * q^28 + 420 * q^30 - 693 * q^32 - 660 * q^33 + 509 * q^34 - 537 * q^36 - 1977 * q^38 - 36 * q^40 + 1620 * q^41 + 72 * q^42 - 292 * q^43 + 48 * q^46 + 765 * q^48 + 1762 * q^49 - 1227 * q^50 - 1794 * q^51 + 330 * q^52 - 645 * q^54 + 942 * q^56 - 294 * q^57 - 282 * q^58 + 5592 * q^59 + 1236 * q^60 + 1090 * q^64 - 6 * q^65 + 3522 * q^66 + 68 * q^67 - 2025 * q^68 + 600 * q^70 + 1875 * q^72 - 868 * q^73 - 420 * q^74 - 4254 * q^75 - 1471 * q^76 + 3228 * q^78 + 498 * q^81 + 362 * q^82 + 3654 * q^83 - 2028 * q^84 - 4119 * q^86 + 3155 * q^88 + 2958 * q^90 - 1380 * q^91 - 744 * q^92 - 138 * q^94 - 4782 * q^96 - 1912 * q^97 - 2118 * q^99

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