LMFDB - Embedded newform 126.4.t.a.47.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,4,Mod(47,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.47"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 5])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	126.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.43424066072$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.18
Character	$\chi$	$=$	126.47
Dual form			126.4.t.a.59.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 - 1.00000i) q^{2} +(-0.660361 - 5.15402i) q^{3} +(2.00000 - 3.46410i) q^{4} -14.9619 q^{5} +(-6.29780 - 8.26666i) q^{6} +(-6.35399 + 17.3962i) q^{7} -8.00000i q^{8} +(-26.1278 + 6.80703i) q^{9} +(-25.9148 + 14.9619i) q^{10} -47.7531i q^{11} +(-19.1748 - 8.02048i) q^{12} +(-26.1335 + 15.0882i) q^{13} +(6.39074 + 36.4850i) q^{14} +(9.88027 + 77.1140i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(47.9201 + 83.0001i) q^{17} +(-38.4477 + 37.9180i) q^{18} +(-63.9852 - 36.9418i) q^{19} +(-29.9238 + 51.8296i) q^{20} +(93.8561 + 21.2608i) q^{21} +(-47.7531 - 82.7108i) q^{22} -204.225i q^{23} +(-41.2322 + 5.28289i) q^{24} +98.8591 q^{25} +(-30.1764 + 52.2671i) q^{26} +(52.3374 + 130.168i) q^{27} +(47.5541 + 56.8032i) q^{28} +(-116.156 - 67.0628i) q^{29} +(94.2272 + 123.685i) q^{30} +(-126.147 - 72.8312i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-246.121 + 31.5343i) q^{33} +(166.000 + 95.8402i) q^{34} +(95.0679 - 260.280i) q^{35} +(-28.6755 + 104.124i) q^{36} +(55.9343 - 96.8810i) q^{37} -147.767 q^{38} +(95.0225 + 124.729i) q^{39} +119.695i q^{40} +(-126.125 - 218.454i) q^{41} +(183.824 - 57.0313i) q^{42} +(33.0683 - 57.2760i) q^{43} +(-165.422 - 95.5062i) q^{44} +(390.923 - 101.846i) q^{45} +(-204.225 - 353.729i) q^{46} +(238.319 + 412.780i) q^{47} +(-66.1333 + 50.3824i) q^{48} +(-262.254 - 221.070i) q^{49} +(171.229 - 98.8591i) q^{50} +(396.140 - 301.791i) q^{51} +120.706i q^{52} +(231.396 - 133.597i) q^{53} +(220.819 + 173.121i) q^{54} +714.478i q^{55} +(139.169 + 50.8319i) q^{56} +(-148.146 + 354.176i) q^{57} -268.251 q^{58} +(406.178 - 703.520i) q^{59} +(286.891 + 120.002i) q^{60} +(-112.510 + 64.9574i) q^{61} -291.325 q^{62} +(47.5999 - 497.776i) q^{63} -64.0000 q^{64} +(391.008 - 225.749i) q^{65} +(-394.759 + 300.740i) q^{66} +(-124.586 + 215.789i) q^{67} +383.361 q^{68} +(-1052.58 + 134.862i) q^{69} +(-95.6177 - 545.886i) q^{70} +553.009i q^{71} +(54.4562 + 209.023i) q^{72} +(-193.425 + 111.674i) q^{73} -223.737i q^{74} +(-65.2827 - 509.522i) q^{75} +(-255.941 + 147.767i) q^{76} +(830.721 + 303.423i) q^{77} +(289.313 + 121.015i) q^{78} +(585.759 + 1014.56i) q^{79} +(119.695 + 207.318i) q^{80} +(636.329 - 355.706i) q^{81} +(-436.908 - 252.249i) q^{82} +(430.563 - 745.757i) q^{83} +(261.362 - 282.606i) q^{84} +(-716.977 - 1241.84i) q^{85} -132.273i q^{86} +(-268.938 + 642.957i) q^{87} -382.025 q^{88} +(-26.0013 + 45.0356i) q^{89} +(575.252 - 567.326i) q^{90} +(-96.4248 - 550.494i) q^{91} +(-707.457 - 408.451i) q^{92} +(-292.071 + 698.261i) q^{93} +(825.560 + 476.637i) q^{94} +(957.341 + 552.721i) q^{95} +(-64.1639 + 153.398i) q^{96} +(-1019.74 - 588.749i) q^{97} +(-675.307 - 120.651i) q^{98} +(325.057 + 1247.69i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 96 q^{4} - 12 q^{7} + 18 q^{9} - 72 q^{13} - 132 q^{14} + 132 q^{15} - 384 q^{16} - 144 q^{17} - 72 q^{18} + 270 q^{21} + 48 q^{24} + 1200 q^{25} - 120 q^{26} + 450 q^{27} + 48 q^{28} + 42 q^{29}+ \cdots - 5076 q^{99}+O(q^{100}) $ 48 * q + 96 * q^4 - 12 * q^7 + 18 * q^9 - 72 * q^13 - 132 * q^14 + 132 * q^15 - 384 * q^16 - 144 * q^17 - 72 * q^18 + 270 * q^21 + 48 * q^24 + 1200 * q^25 - 120 * q^26 + 450 * q^27 + 48 * q^28 + 42 * q^29 - 468 * q^30 - 90 * q^31 - 1332 * q^33 + 780 * q^35 - 240 * q^36 - 168 * q^37 + 240 * q^39 + 618 * q^41 - 252 * q^42 - 42 * q^43 - 96 * q^44 + 1038 * q^45 - 252 * q^46 + 198 * q^47 - 636 * q^49 + 1464 * q^50 + 222 * q^51 + 36 * q^53 + 180 * q^54 - 1452 * q^57 + 504 * q^58 - 1500 * q^59 - 480 * q^60 + 2466 * q^61 - 2952 * q^62 - 2988 * q^63 - 3072 * q^64 - 84 * q^65 - 384 * q^66 - 588 * q^67 - 1152 * q^68 - 1848 * q^69 + 216 * q^70 + 192 * q^72 + 2820 * q^75 + 1548 * q^77 + 2496 * q^78 + 1230 * q^79 - 4122 * q^81 + 1512 * q^84 + 720 * q^85 + 258 * q^87 + 4398 * q^89 + 6084 * q^90 - 90 * q^91 - 1632 * q^92 + 1740 * q^93 + 3246 * q^95 + 192 * q^96 - 1584 * q^97 + 1104 * q^98 - 5076 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	−0.660361	−	5.15402i	−0.127087	−	0.991892i
$3$	−0.660361	−	5.15402i	−0.127087	−	0.991892i
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	−14.9619			−1.33824			−0.669118	−	0.743157i	$-0.733328\pi$
$5$	−14.9619			−1.33824			−0.669118	+	0.743157i	$0.733328\pi$
$6$	−6.29780	−	8.26666i	−0.428511	−	0.562475i
$7$	−6.35399	+	17.3962i	−0.343083	+	0.939305i
$7$	−6.35399	+	17.3962i	−0.343083	+	0.939305i
$8$		−	8.00000i		−	0.353553i
$9$	−26.1278	+	6.80703i	−0.967698	+	0.252112i
$10$	−25.9148	+	14.9619i	−0.819498	+	0.473138i
$11$		−	47.7531i		−	1.30892i	−0.756097	−	0.654459i	$-0.772896\pi$
$11$		−	47.7531i		−	1.30892i	0.756097	−	0.654459i	$-0.227104\pi$
$12$	−19.1748	−	8.02048i	−0.461273	−	0.192943i
$13$	−26.1335	+	15.0882i	−0.557549	+	0.321901i	−0.752161	−	0.658979i	$-0.770989\pi$
$13$	−26.1335	+	15.0882i	−0.557549	+	0.321901i	0.194612	+	0.980880i	$0.437655\pi$
$14$	6.39074	+	36.4850i	0.122000	+	0.696503i
$15$	9.88027	+	77.1140i	0.170072	+	1.32738i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	47.9201	+	83.0001i	0.683667	+	1.18415i	0.973854	+	0.227176i	$0.0729492\pi$
$17$	47.9201	+	83.0001i	0.683667	+	1.18415i	−0.290187	+	0.956970i	$0.593717\pi$
$18$	−38.4477	+	37.9180i	−0.503456	+	0.496519i
$19$	−63.9852	−	36.9418i	−0.772589	−	0.446055i	0.0612081	−	0.998125i	$-0.480505\pi$
$19$	−63.9852	−	36.9418i	−0.772589	−	0.446055i	−0.833798	+	0.552070i	$0.813838\pi$
$20$	−29.9238	+	51.8296i	−0.334559	+	0.579473i
$21$	93.8561	+	21.2608i	0.975290	+	0.220928i
$22$	−47.7531	−	82.7108i	−0.462773	−	0.801546i
$23$		−	204.225i		−	1.85148i	−0.378166	−	0.925738i	$-0.623445\pi$
$23$		−	204.225i		−	1.85148i	0.378166	−	0.925738i	$-0.376555\pi$
$24$	−41.2322	+	5.28289i	−0.350687	+	0.0449319i
$25$	98.8591			0.790873
$26$	−30.1764	+	52.2671i	−0.227618	+	0.394247i
$27$	52.3374	+	130.168i	0.373049	+	0.927812i
$28$	47.5541	+	56.8032i	0.320960	+	0.383386i
$29$	−116.156	−	67.0628i	−0.743782	−	0.429423i	0.0796609	−	0.996822i	$-0.474616\pi$
$29$	−116.156	−	67.0628i	−0.743782	−	0.429423i	−0.823443	+	0.567399i	$0.807950\pi$
$30$	94.2272	+	123.685i	0.573448	+	0.752724i
$31$	−126.147	−	72.8312i	−0.730862	−	0.421964i	0.0878753	−	0.996131i	$-0.471992\pi$
$31$	−126.147	−	72.8312i	−0.730862	−	0.421964i	−0.818738	+	0.574168i	$0.805326\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	−246.121	+	31.5343i	−1.29831	+	0.166346i
$34$	166.000	+	95.8402i	0.837317	+	0.483425i
$35$	95.0679	−	260.280i	0.459126	−	1.25701i
$36$	−28.6755	+	104.124i	−0.132757	+	0.482054i
$37$	55.9343	−	96.8810i	0.248528	−	0.430463i	−0.714590	−	0.699544i	$-0.753387\pi$
$37$	55.9343	−	96.8810i	0.248528	−	0.430463i	0.963118	+	0.269081i	$0.0867199\pi$
$38$	−147.767			−0.630817
$39$	95.0225	+	124.729i	0.390148	+	0.512119i
$40$			119.695i			0.473138i
$41$	−126.125	−	218.454i	−0.480423	−	0.832117i	0.519325	−	0.854577i	$-0.326184\pi$
$41$	−126.125	−	218.454i	−0.480423	−	0.832117i	−0.999748	+	0.0224598i	$0.992850\pi$
$42$	183.824	−	57.0313i	0.675351	−	0.209527i
$43$	33.0683	−	57.2760i	0.117276	−	0.203128i	−0.801411	−	0.598114i	$-0.795917\pi$
$43$	33.0683	−	57.2760i	0.117276	−	0.203128i	0.918687	+	0.394986i	$0.129250\pi$
$44$	−165.422	−	95.5062i	−0.566778	−	0.327230i
$45$	390.923	−	101.846i	1.29501	−	0.337385i
$46$	−204.225	−	353.729i	−0.654595	−	1.13379i
$47$	238.319	+	412.780i	0.739624	+	1.28107i	0.952665	+	0.304023i	$0.0983301\pi$
$47$	238.319	+	412.780i	0.739624	+	1.28107i	−0.213040	+	0.977043i	$0.568337\pi$
$48$	−66.1333	+	50.3824i	−0.198865	+	0.151501i
$49$	−262.254	−	221.070i	−0.764588	−	0.644520i
$50$	171.229	−	98.8591i	0.484309	−	0.279616i
$51$	396.140	−	301.791i	1.08766	−	0.828612i
$52$			120.706i			0.321901i
$53$	231.396	−	133.597i	0.599712	−	0.346244i	−0.169217	−	0.985579i	$-0.554124\pi$
$53$	231.396	−	133.597i	0.599712	−	0.346244i	0.768928	+	0.639335i	$0.220790\pi$
$54$	220.819	+	173.121i	0.556476	+	0.436273i
$55$			714.478i			1.75164i
$56$	139.169	+	50.8319i	0.332094	+	0.121298i
$57$	−148.146	+	354.176i	−0.344252	+	0.823013i
$58$	−268.251			−0.607295
$59$	406.178	−	703.520i	0.896268	−	1.55238i	0.0640413	−	0.997947i	$-0.479601\pi$
$59$	406.178	−	703.520i	0.896268	−	1.55238i	0.832227	−	0.554435i	$-0.187066\pi$
$60$	286.891	+	120.002i	0.617292	+	0.258203i
$61$	−112.510	+	64.9574i	−0.236154	+	0.136343i	−0.613408	−	0.789766i	$-0.710202\pi$
$61$	−112.510	+	64.9574i	−0.236154	+	0.136343i	0.377254	+	0.926110i	$0.376868\pi$
$62$	−291.325			−0.596747
$63$	47.5999	−	497.776i	0.0951908	−	0.995459i
$64$	−64.0000			−0.125000
$65$	391.008	−	225.749i	0.746132	−	0.430779i
$66$	−394.759	+	300.740i	−0.736234	+	0.560886i
$67$	−124.586	+	215.789i	−0.227173	+	0.393476i	−0.956969	−	0.290189i	$-0.906282\pi$
$67$	−124.586	+	215.789i	−0.227173	+	0.393476i	0.729796	+	0.683665i	$0.239615\pi$
$68$	383.361			0.683667
$69$	−1052.58	+	134.862i	−1.83646	+	0.235298i
$70$	−95.6177	−	545.886i	−0.163264	−	0.932084i
$71$			553.009i			0.924368i	0.886784	+	0.462184i	$0.152934\pi$
$71$			553.009i			0.924368i	−0.886784	+	0.462184i	$0.847066\pi$
$72$	54.4562	+	209.023i	0.0891351	+	0.342133i
$73$	−193.425	+	111.674i	−0.310119	+	0.179047i	−0.646980	−	0.762507i	$-0.723968\pi$
$73$	−193.425	+	111.674i	−0.310119	+	0.179047i	0.336861	+	0.941555i	$0.390635\pi$
$74$		−	223.737i		−	0.351472i
$75$	−65.2827	−	509.522i	−0.100509	−	0.784460i
$76$	−255.941	+	147.767i	−0.386295	+	0.223027i
$77$	830.721	+	303.423i	1.22947	+	0.449068i
$78$	289.313	+	121.015i	0.419977	+	0.175669i
$79$	585.759	+	1014.56i	0.834215	+	1.44490i	0.894668	+	0.446732i	$0.147412\pi$
$79$	585.759	+	1014.56i	0.834215	+	1.44490i	−0.0604523	+	0.998171i	$0.519254\pi$
$80$	119.695	+	207.318i	0.167279	+	0.289736i
$81$	636.329	−	355.706i	0.872879	−	0.487937i
$82$	−436.908	−	252.249i	−0.588396	−	0.339710i
$83$	430.563	−	745.757i	0.569403	−	0.986234i	−0.427223	−	0.904146i	$-0.640508\pi$
$83$	430.563	−	745.757i	0.569403	−	0.986234i	0.996625	−	0.0820876i	$-0.0261587\pi$
$84$	261.362	−	282.606i	0.339487	−	0.367081i
$85$	−716.977	−	1241.84i	−0.914907	−	1.58467i
$86$		−	132.273i		−	0.165853i
$87$	−268.938	+	642.957i	−0.331416	+	0.792325i
$88$	−382.025			−0.462773
$89$	−26.0013	+	45.0356i	−0.0309678	+	0.0536378i	−0.881094	−	0.472941i	$-0.843192\pi$
$89$	−26.0013	+	45.0356i	−0.0309678	+	0.0536378i	0.850126	+	0.526579i	$0.176526\pi$
$90$	575.252	−	567.326i	0.673743	−	0.664460i
$91$	−96.4248	−	550.494i	−0.111078	−	0.634148i
$92$	−707.457	−	408.451i	−0.801712	−	0.462869i
$93$	−292.071	+	698.261i	−0.325659	+	0.778562i
$94$	825.560	+	476.637i	0.905851	+	0.522993i
$95$	957.341	+	552.721i	1.03391	+	0.596926i
$96$	−64.1639	+	153.398i	−0.0682156	+	0.163085i
$97$	−1019.74	−	588.749i	−1.06742	−	0.616273i	−0.139941	−	0.990160i	$-0.544691\pi$
$97$	−1019.74	−	588.749i	−1.06742	−	0.616273i	−0.927474	+	0.373887i	$0.878025\pi$
$98$	−675.307	−	120.651i	−0.696085	−	0.124363i
$99$	325.057	+	1247.69i	0.329994	+	1.26664i
$100$	197.718	−	342.458i	0.197718	−	0.342458i
$101$	−480.392			−0.473276			−0.236638	−	0.971598i	$-0.576045\pi$
$101$	−480.392			−0.473276			−0.236638	+	0.971598i	$0.576045\pi$
$102$	384.342	−	918.857i	0.373094	−	0.891965i
$103$			976.169i			0.933833i	0.884301	+	0.466917i	$0.154635\pi$
$103$			976.169i			0.933833i	−0.884301	+	0.466917i	$0.845365\pi$
$104$	120.706	+	209.068i	0.113809	+	0.197123i
$105$	−1404.27	−	318.103i	−1.30517	−	0.295654i
$106$	267.193	−	462.792i	0.244831	−	0.424060i
$107$	−674.564	−	389.459i	−0.609463	−	0.351874i	0.163292	−	0.986578i	$-0.447789\pi$
$107$	−674.564	−	389.459i	−0.609463	−	0.351874i	−0.772755	+	0.634704i	$0.781122\pi$
$108$	555.591	+	79.0347i	0.495016	+	0.0704178i
$109$	300.868	+	521.119i	0.264385	+	0.457928i	0.967402	−	0.253245i	$-0.0814977\pi$
$109$	300.868	+	521.119i	0.264385	+	0.457928i	−0.703017	+	0.711173i	$0.748164\pi$
$110$	714.478	+	1237.51i	0.619299	+	1.07266i
$111$	−536.263	−	224.310i	−0.458557	−	0.191807i
$112$	291.880	−	51.1259i	0.246251	−	0.0431334i
$113$	−880.086	+	508.118i	−0.732669	+	0.423006i	−0.819398	−	0.573225i	$-0.805692\pi$
$113$	−880.086	+	508.118i	−0.732669	+	0.423006i	0.0867290	+	0.996232i	$0.472359\pi$
$114$	97.5798	+	761.596i	0.0801683	+	0.625702i
$115$			3055.60i			2.47771i
$116$	−464.625	+	268.251i	−0.371891	+	0.214711i
$117$	580.107	−	572.114i	0.458384	−	0.452068i
$118$		−	1624.71i		−	1.26751i
$119$	−1748.37	+	306.245i	−1.34683	+	0.235911i
$120$	616.912	−	79.0422i	0.469301	−	0.0601294i
$121$	−949.360			−0.713269
$122$	−129.915	+	225.019i	−0.0964093	+	0.166986i
$123$	−1042.63	+	794.307i	−0.764315	+	0.582279i
$124$	−504.589	+	291.325i	−0.365431	+	0.210982i
$125$	391.118			0.279861
$126$	−415.331	−	909.774i	−0.293656	−	0.643247i
$127$	134.168			0.0937438			0.0468719	−	0.998901i	$-0.485075\pi$
$127$	134.168			0.0937438			0.0468719	+	0.998901i	$0.485075\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	−317.039	−	132.612i	−0.216385	−	0.0905103i
$130$	451.497	−	782.016i	0.304607	−	0.527595i
$131$	−2550.69			−1.70118			−0.850592	−	0.525827i	$-0.823756\pi$
$131$	−2550.69			−1.70118			−0.850592	+	0.525827i	$0.823756\pi$
$132$	−383.003	+	915.655i	−0.252547	+	0.603769i
$133$	1049.21	−	878.369i	0.684044	−	0.572663i
$134$			498.344i			0.321272i
$135$	−783.068	−	1947.57i	−0.499228	−	1.24163i
$136$	664.001	−	383.361i	0.418659	−	0.241713i
$137$		−	2810.14i		−	1.75246i	−0.481897	−	0.876228i	$-0.660052\pi$
$137$		−	2810.14i		−	1.75246i	0.481897	−	0.876228i	$-0.339948\pi$
$138$	−1688.26	+	1286.17i	−1.04141	+	0.793377i
$139$	−1408.55	+	813.225i	−0.859506	+	0.496236i	−0.863847	−	0.503754i	$-0.831952\pi$
$139$	−1408.55	+	813.225i	−0.859506	+	0.496236i	0.00434059	+	0.999991i	$0.498618\pi$
$140$	−711.501	−	849.885i	−0.429520	−	0.513060i
$141$	1970.10	−	1500.88i	1.17668	−	0.896433i
$142$	553.009	+	957.840i	0.326813	+	0.566058i
$143$	720.509	+	1247.96i	0.421342	+	0.729787i
$144$	303.344	+	307.582i	0.175546	+	0.177999i
$145$	1737.92	+	1003.39i	0.995355	+	0.574668i
$146$	−223.348	+	386.850i	−0.126606	+	0.219287i
$147$	−966.218	+	1497.65i	−0.542125	+	0.840298i
$148$	−223.737	−	387.524i	−0.124264	−	0.215232i
$149$			703.405i			0.386746i	0.981125	+	0.193373i	$0.0619428\pi$
$149$			703.405i			0.386746i	−0.981125	+	0.193373i	$0.938057\pi$
$150$	−622.595	−	817.235i	−0.338898	−	0.444846i
$151$	1672.60			0.901416			0.450708	−	0.892671i	$-0.351171\pi$
$151$	1672.60			0.901416			0.450708	+	0.892671i	$0.351171\pi$
$152$	−295.535	+	511.881i	−0.157704	+	0.273152i
$153$	−1817.03	−	1842.42i	−0.960121	−	0.973535i
$154$	1742.27	−	305.178i	0.911666	−	0.159688i
$155$	1887.41	+	1089.69i	0.978065	+	0.564686i
$156$	622.119	−	79.7093i	0.319291	−	0.0409093i
$157$	1.90639	+	1.10065i	0.000969085	+	0.000559501i	0.500484	−	0.865746i	$-0.333155\pi$
$157$	1.90639	+	1.10065i	0.000969085	+	0.000559501i	−0.499515	+	0.866305i	$0.666489\pi$
$158$	2029.13	+	1171.52i	1.02170	+	0.589879i
$159$	−841.365	−	1104.40i	−0.419651	−	0.550846i
$160$	414.637	+	239.391i	0.204875	+	0.118284i
$161$	3552.74	+	1297.65i	1.73910	+	0.635210i
$162$	746.448	−	1252.43i	0.362015	−	0.607408i
$163$	1487.47	−	2576.38i	0.714773	−	1.23802i	−0.248275	−	0.968690i	$-0.579864\pi$
$163$	1487.47	−	2576.38i	0.714773	−	1.23802i	0.963047	−	0.269333i	$-0.0868031\pi$
$164$	−1009.00			−0.480423
$165$	3682.44	−	471.814i	1.73744	−	0.222610i
$166$		−	1722.25i		−	0.805257i
$167$	−405.855	−	702.962i	−0.188060	−	0.325729i	0.756543	−	0.653943i	$-0.226887\pi$
$167$	−405.855	−	702.962i	−0.188060	−	0.325729i	−0.944603	+	0.328214i	$0.893553\pi$
$168$	170.087	−	750.849i	0.0781100	−	0.344817i
$169$	−643.192	+	1114.04i	−0.292759	+	0.507074i
$170$	−2483.68	−	1433.95i	−1.12053	−	0.646937i
$171$	1923.26	+	529.662i	0.860089	+	0.236867i
$172$	−132.273	−	229.104i	−0.0586380	−	0.101564i
$173$	233.703	+	404.786i	0.102706	+	0.177892i	0.912799	−	0.408410i	$-0.133917\pi$
$173$	233.703	+	404.786i	0.102706	+	0.177892i	−0.810093	+	0.586302i	$0.800583\pi$
$174$	177.143	+	1382.57i	0.0771791	+	0.602371i
$175$	−628.150	+	1719.77i	−0.271335	+	0.742871i
$176$	−661.687	+	382.025i	−0.283389	+	0.163615i
$177$	−3894.18	−	1628.87i	−1.65370	−	0.691714i
$178$			104.005i			0.0437951i
$179$	1551.29	−	895.637i	0.647758	−	0.373983i	−0.139839	−	0.990174i	$-0.544658\pi$
$179$	1551.29	−	895.637i	0.647758	−	0.373983i	0.787597	+	0.616191i	$0.211325\pi$
$180$	429.040	−	1557.89i	0.177660	−	0.645101i
$181$			127.734i			0.0524554i	0.999656	+	0.0262277i	$0.00834949\pi$
$181$			127.734i			0.0524554i	−0.999656	+	0.0262277i	$0.991651\pi$
$182$	−717.506	−	857.058i	−0.292226	−	0.349063i
$183$	409.089	+	536.981i	0.165250	+	0.216911i
$184$	−1633.80			−0.654595
$185$	−836.884	+	1449.53i	−0.332589	+	0.576061i
$186$	192.380	+	1501.49i	0.0758384	+	0.591908i
$187$	3963.51	−	2288.34i	1.54995	−	0.894864i
$188$	1906.55			0.739624
$189$	−2596.98	+	83.3814i	−0.999485	+	0.0320905i
$190$	2210.88			0.844181
$191$	−1535.66	+	886.613i	−0.581761	+	0.335880i	−0.761833	−	0.647773i	$-0.775700\pi$
$191$	−1535.66	+	886.613i	−0.581761	+	0.335880i	0.180072	+	0.983653i	$0.442367\pi$
$192$	42.2631	+	329.857i	0.0158858	+	0.123986i
$193$	1439.97	−	2494.11i	0.537055	−	0.930207i	−0.462006	−	0.886877i	$-0.652870\pi$
$193$	1439.97	−	2494.11i	0.537055	−	0.930207i	0.999061	−	0.0433299i	$-0.0137966\pi$
$194$	−2355.00			−0.871541
$195$	−1421.72	−	1866.19i	−0.522110	−	0.685336i
$196$	−1290.32	+	466.333i	−0.470232	+	0.169946i
$197$		−	1601.95i		−	0.579362i	−0.957123	−	0.289681i	$-0.906451\pi$
$197$		−	1601.95i		−	0.579362i	0.957123	−	0.289681i	$-0.0935493\pi$
$198$	1810.70	+	1836.00i	0.649904	+	0.658984i
$199$	3569.66	−	2060.95i	1.27159	−	0.734154i	0.296304	−	0.955094i	$-0.404246\pi$
$199$	3569.66	−	2060.95i	1.27159	−	0.734154i	0.975287	+	0.220940i	$0.0709124\pi$
$200$		−	790.873i		−	0.279616i
$201$	1194.46	+	499.620i	0.419156	+	0.175326i
$202$	−832.064	+	480.392i	−0.289821	+	0.167328i
$203$	1904.69	−	1594.56i	0.658538	−	0.551310i
$204$	−253.157	−	1975.85i	−0.0868848	−	0.678123i
$205$	1887.07	+	3268.49i	0.642919	+	1.11357i
$206$	976.169	+	1690.77i	0.330160	+	0.571854i
$207$	1390.17	+	5335.97i	0.466779	+	1.79167i
$208$	418.137	+	241.411i	0.139387	+	0.0804753i
$209$	−1764.09	+	3055.49i	−0.583849	+	1.01126i
$210$	−2750.37	+	853.298i	−0.903778	+	0.280396i
$211$	2234.38	+	3870.05i	0.729008	+	1.26268i	0.957303	+	0.289087i	$0.0933518\pi$
$211$	2234.38	+	3870.05i	0.729008	+	1.26268i	−0.228294	+	0.973592i	$0.573315\pi$
$212$		−	1068.77i		−	0.346244i
$213$	2850.22	−	365.186i	0.916873	−	0.117475i
$214$	−1557.84			−0.497624
$215$	−494.765	+	856.959i	−0.156943	+	0.271833i
$216$	1041.35	−	418.699i	0.328031	−	0.131893i
$217$	2068.52	−	1731.71i	0.647099	−	0.541734i
$218$	1042.24	+	601.737i	0.323804	+	0.186948i
$219$	703.301	+	923.172i	0.217008	+	0.284850i
$220$	2475.03	+	1428.96i	0.758483	+	0.437910i
$221$	−2504.64	−	1446.06i	−0.762356	−	0.440146i
$222$	−1153.15	+	147.747i	−0.348622	+	0.0446673i
$223$	−3421.82	−	1975.59i	−1.02754	−	0.593251i	−0.111262	−	0.993791i	$-0.535489\pi$
$223$	−3421.82	−	1975.59i	−1.02754	−	0.593251i	−0.916279	+	0.400540i	$0.868823\pi$
$224$	454.426	−	380.433i	0.135547	−	0.113477i
$225$	−2582.98	+	672.937i	−0.765326	+	0.199389i
$226$	−1016.24	+	1760.17i	−0.299111	+	0.518075i
$227$	88.7404			0.0259467			0.0129734	−	0.999916i	$-0.495870\pi$
$227$	88.7404			0.0259467			0.0129734	+	0.999916i	$0.495870\pi$
$228$	930.609	+	1221.54i	0.270312	+	0.354819i
$229$		−	780.926i		−	0.225349i	−0.993632	−	0.112675i	$-0.964058\pi$
$229$		−	780.926i		−	0.225349i	0.993632	−	0.112675i	$-0.0359418\pi$
$230$	3055.60	+	5292.46i	0.876002	+	1.51728i
$231$	1015.27	−	4481.92i	0.289177	−	1.27658i
$232$	−536.503	+	929.250i	−0.151824	+	0.262967i
$233$	−4189.61	−	2418.87i	−1.17799	−	0.680111i	−0.222438	−	0.974947i	$-0.571402\pi$
$233$	−4189.61	−	2418.87i	−1.17799	−	0.680111i	−0.955548	+	0.294836i	$0.904735\pi$
$234$	432.661	−	1571.04i	0.120872	−	0.438897i
$235$	−3565.70	−	6175.98i	−0.989791	−	1.71437i
$236$	−1624.71	−	2814.08i	−0.448134	−	0.776191i
$237$	4842.27	−	3688.99i	1.32717	−	1.01108i
$238$	−2722.02	+	2278.80i	−0.741354	+	0.620641i
$239$	−4386.37	+	2532.47i	−1.18716	+	0.685405i	−0.957659	−	0.287904i	$-0.907042\pi$
$239$	−4386.37	+	2532.47i	−1.18716	+	0.685405i	−0.229497	+	0.973309i	$0.573708\pi$
$240$	989.481	−	753.817i	0.266128	−	0.202745i
$241$		−	3252.23i		−	0.869273i	−0.900606	−	0.434636i	$-0.856877\pi$
$241$		−	3252.23i		−	0.869273i	0.900606	−	0.434636i	$-0.143123\pi$
$242$	−1644.34	+	949.360i	−0.436786	+	0.252179i
$243$	−2253.52	−	3044.76i	−0.594912	−	0.803791i
$244$			519.659i			0.136343i
$245$	3923.82	+	3307.64i	1.02320	+	0.862519i
$246$	−1011.58	+	2418.41i	−0.262179	+	0.626797i
$247$	2229.54			0.574342
$248$	−582.650	+	1009.18i	−0.149187	+	0.258399i
$249$	−4127.97	−	1726.66i	−1.05060	−	0.439449i
$250$	677.436	−	391.118i	0.171379	−	0.0989458i
$251$	1905.25			0.479117			0.239558	−	0.970882i	$-0.422997\pi$
$251$	1905.25			0.479117			0.239558	+	0.970882i	$0.422997\pi$
$252$	−1629.15	−	1160.44i	−0.407249	−	0.290084i
$253$	−9752.40			−2.42343
$254$	232.385	−	134.168i	0.0574061	−	0.0331434i
$255$	−5927.01	+	4515.38i	−1.45554	+	1.10888i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−992.231			−0.240831			−0.120416	−	0.992724i	$-0.538423\pi$
$257$	−992.231			−0.240831			−0.120416	+	0.992724i	$0.538423\pi$
$258$	−681.739	+	87.3481i	−0.164509	+	0.0210777i
$259$	1329.95	+	1588.62i	0.319070	+	0.381128i
$260$		−	1805.99i		−	0.430779i
$261$	3491.41	+	961.529i	0.828019	+	0.228035i
$262$	−4417.93	+	2550.69i	−1.04176	+	0.601459i
$263$			38.4269i			0.00900953i	0.999990	+	0.00450477i	$0.00143392\pi$
$263$			38.4269i			0.00900953i	−0.999990	+	0.00450477i	$0.998566\pi$
$264$	252.274	+	1968.96i	0.0588122	+	0.459020i
$265$	−3462.13	+	1998.86i	−0.802555	+	0.463355i
$266$	938.912	−	2570.59i	0.216423	−	0.592529i
$267$	249.285	+	104.272i	0.0571385	+	0.0239001i
$268$	498.344	+	863.158i	0.113587	+	0.196738i
$269$	−1376.57	−	2384.29i	−0.312011	−	0.540419i	0.666787	−	0.745249i	$-0.267669\pi$
$269$	−1376.57	−	2384.29i	−0.312011	−	0.540419i	−0.978798	+	0.204830i	$0.934336\pi$
$270$	−3303.88	−	2590.22i	−0.744696	−	0.583836i
$271$	4665.04	+	2693.36i	1.04569	+	0.603727i	0.921438	−	0.388525i	$-0.127015\pi$
$271$	4665.04	+	2693.36i	1.04569	+	0.603727i	0.124247	+	0.992251i	$0.460348\pi$
$272$	766.722	−	1328.00i	0.170917	−	0.296036i
$273$	−2773.58	+	860.500i	−0.614889	+	0.190769i
$274$	−2810.14	−	4867.30i	−0.619587	−	1.07316i
$275$		−	4720.83i		−	1.03519i
$276$	−1637.99	+	3915.97i	−0.357229	+	0.854036i
$277$	−906.051			−0.196532			−0.0982659	−	0.995160i	$-0.531330\pi$
$277$	−906.051			−0.196532			−0.0982659	+	0.995160i	$0.531330\pi$
$278$	−1626.45	+	2817.09i	−0.350892	+	0.607763i
$279$	3791.72	+	1044.23i	0.813636	+	0.224074i
$280$	−2082.24	−	760.543i	−0.444420	−	0.162326i
$281$	2686.33	+	1550.95i	0.570294	+	0.329260i	0.757267	−	0.653105i	$-0.226534\pi$
$281$	2686.33	+	1550.95i	0.570294	+	0.329260i	−0.186972	+	0.982365i	$0.559868\pi$
$282$	1911.43	−	4569.70i	0.403631	−	0.964971i
$283$	−6418.55	−	3705.75i	−1.34821	−	0.778389i	−0.360213	−	0.932870i	$-0.617296\pi$
$283$	−6418.55	−	3705.75i	−1.34821	−	0.778389i	−0.987996	+	0.154481i	$0.950629\pi$
$284$	1915.68	+	1106.02i	0.400263	+	0.231092i
$285$	2216.54	−	5299.15i	0.460690	−	1.10138i
$286$	2495.92	+	1441.02i	0.516037	+	0.297934i
$287$	4601.66	−	806.029i	0.946437	−	0.165778i
$288$	832.989	+	229.404i	0.170432	+	0.0469366i
$289$	−2136.18	+	3699.97i	−0.434801	+	0.753097i
$290$	4013.56			0.812704
$291$	−2361.03	+	5644.57i	−0.475622	+	1.13708i
$292$			893.392i			0.179047i
$293$	1091.50	+	1890.53i	0.217631	+	0.376949i	0.954083	−	0.299541i	$-0.0968336\pi$
$293$	1091.50	+	1890.53i	0.217631	+	0.376949i	−0.736452	+	0.676490i	$0.763500\pi$
$294$	−175.893	+	3560.22i	−0.0348921	+	0.706245i
$295$	−6077.20	+	10526.0i	−1.19942	+	2.07745i
$296$	−775.048	−	447.474i	−0.152192	−	0.0878679i
$297$	6215.94	−	2499.27i	1.21443	−	0.488291i
$298$	703.405	+	1218.33i	0.136735	+	0.236833i
$299$	3081.39	+	5337.13i	0.595992	+	1.03229i
$300$	−1895.60	−	792.898i	−0.364809	−	0.152593i
$301$	786.267	+	939.193i	0.150564	+	0.179848i
$302$	2897.02	−	1672.60i	0.552003	−	0.318699i
$303$	317.232	+	2475.95i	0.0601469	+	0.469438i
$304$			1182.14i			0.223027i
$305$	1683.36	−	971.888i	0.316029	−	0.182460i
$306$	−4989.61	−	1374.13i	−0.932148	−	0.256712i
$307$		−	2602.62i		−	0.483841i	−0.970296	−	0.241920i	$-0.922223\pi$
$307$		−	2602.62i		−	0.483841i	0.970296	−	0.241920i	$-0.0777773\pi$
$308$	2712.53	−	2270.86i	0.501821	−	0.420111i
$309$	5031.20	−	644.624i	0.926261	−	0.118678i
$310$	4358.78			0.798587
$311$	4203.94	−	7281.44i	0.766507	−	1.32763i	−0.172939	−	0.984933i	$-0.555326\pi$
$311$	4203.94	−	7281.44i	0.766507	−	1.32763i	0.939446	−	0.342697i	$-0.111340\pi$
$312$	997.833	−	760.180i	0.181061	−	0.137938i
$313$	2427.06	−	1401.27i	0.438293	−	0.253049i	−0.264580	−	0.964364i	$-0.585233\pi$
$313$	2427.06	−	1401.27i	0.438293	−	0.253049i	0.702873	+	0.711315i	$0.251900\pi$
$314$	4.40261			0.000791254
$315$	−712.185	+	7447.69i	−0.127388	+	1.33216i
$316$	4686.07			0.834215
$317$	−4937.51	+	2850.67i	−0.874821	+	0.505078i	−0.868947	−	0.494905i	$-0.835203\pi$
$317$	−4937.51	+	2850.67i	−0.874821	+	0.505078i	−0.00587380	+	0.999983i	$0.501870\pi$
$318$	−2561.69	−	1071.51i	−0.451736	−	0.188954i
$319$	−3202.46	+	5546.82i	−0.562079	+	0.973550i
$320$	957.563			0.167279
$321$	−1561.83	+	3733.90i	−0.271566	+	0.649239i
$322$	7451.17	−	1305.15i	1.28956	−	0.225880i
$323$		−	7081.03i		−	1.21981i
$324$	40.4559	−	2915.72i	0.00693689	−	0.499952i
$325$	−2583.54	+	1491.61i	−0.440951	+	0.254583i
$326$		−	5949.89i		−	1.01084i
$327$	2487.18	−	1894.81i	0.420615	−	0.320438i
$328$	−1747.63	+	1009.00i	−0.294198	+	0.169855i
$329$	−8695.06	+	1523.03i	−1.45707	+	0.255220i
$330$	5906.35	−	4499.64i	0.985255	−	0.750597i
$331$	2016.29	+	3492.32i	0.334820	+	0.579926i	0.983450	−	0.181178i	$-0.0579910\pi$
$331$	2016.29	+	3492.32i	0.334820	+	0.579926i	−0.648630	+	0.761104i	$0.724658\pi$
$332$	−1722.25	−	2983.03i	−0.284701	−	0.493117i
$333$	−801.970	+	2912.04i	−0.131975	+	0.479215i
$334$	−1405.92	−	811.710i	−0.230326	−	0.132978i
$335$	1864.05	−	3228.63i	0.304011	−	0.526563i
$336$	−456.250	−	1470.60i	−0.0740789	−	0.238773i
$337$	−4776.54	−	8273.21i	−0.772091	−	1.33730i	−0.936415	−	0.350894i	$-0.885878\pi$
$337$	−4776.54	−	8273.21i	−0.772091	−	1.33730i	0.164324	−	0.986406i	$-0.447456\pi$
$338$			2572.77i			0.414024i
$339$	3200.03	+	4200.44i	0.512689	+	0.672970i
$340$	−5735.82			−0.914907
$341$	−3477.92	+	6023.93i	−0.552316	+	0.956639i
$342$	3860.84	−	1005.86i	0.610440	−	0.159037i
$343$	5512.13	−	3157.53i	0.867718	−	0.497057i
$344$	−458.208	−	264.546i	−0.0718166	−	0.0414633i
$345$	15748.6	−	2017.80i	2.45762	−	0.314883i
$346$	809.571	+	467.406i	0.125789	+	0.0726240i
$347$	8208.02	+	4738.90i	1.26983	+	0.733135i	0.974955	−	0.222402i	$-0.0713898\pi$
$347$	8208.02	+	4738.90i	1.26983	+	0.733135i	0.294872	+	0.955537i	$0.404723\pi$
$348$	1689.39	+	2217.54i	0.260233	+	0.341589i
$349$	−5142.47	−	2969.01i	−0.788740	−	0.455379i	0.0507786	−	0.998710i	$-0.483830\pi$
$349$	−5142.47	−	2969.01i	−0.788740	−	0.455379i	−0.839519	+	0.543331i	$0.817163\pi$
$350$	631.783	+	3606.88i	0.0964863	+	0.550845i
$351$	−3331.77	−	2612.08i	−0.506657	−	0.397216i
$352$	−764.050	+	1323.37i	−0.115693	+	0.200386i
$353$	−3662.83			−0.552274			−0.276137	−	0.961118i	$-0.589054\pi$
$353$	−3662.83			−0.552274			−0.276137	+	0.961118i	$0.589054\pi$
$354$	−8373.79	+	1072.90i	−1.25724	+	0.161084i
$355$		−	8274.08i		−	1.23702i
$356$	104.005	+	180.142i	0.0154839	+	0.0268189i
$357$	2732.95	+	8808.89i	0.405162	+	1.30593i
$358$	1791.27	−	3102.58i	0.264446	−	0.458034i
$359$	−7861.57	−	4538.88i	−1.15576	−	0.667278i	−0.205475	−	0.978662i	$-0.565874\pi$
$359$	−7861.57	−	4538.88i	−1.15576	−	0.667278i	−0.950284	+	0.311384i	$0.899207\pi$
$360$	−814.770	−	3127.38i	−0.119284	−	0.457854i
$361$	−700.100	−	1212.61i	−0.102070	−	0.176791i
$362$	127.734	+	221.243i	0.0185458	+	0.0321222i
$363$	626.921	+	4893.02i	0.0906468	+	0.707485i
$364$	−2099.82	−	766.962i	−0.302363	−	0.110439i
$365$	2894.01	−	1670.86i	0.415012	−	0.239607i
$366$	1245.54	+	520.990i	0.177884	+	0.0744060i
$367$		−	9421.19i		−	1.34001i	−0.742358	−	0.670003i	$-0.766293\pi$
$367$		−	9421.19i		−	1.34001i	0.742358	−	0.670003i	$-0.233707\pi$
$368$	−2829.83	+	1633.80i	−0.400856	+	0.231434i
$369$	4782.39	+	4849.20i	0.674691	+	0.684118i
$370$			3347.54i			0.470352i
$371$	853.781	+	4874.28i	0.119477	+	0.682102i
$372$	1834.70	+	2408.28i	0.255712	+	0.335655i
$373$	−3712.30			−0.515323			−0.257662	−	0.966235i	$-0.582952\pi$
$373$	−3712.30			−0.515323			−0.257662	+	0.966235i	$0.582952\pi$
$374$	4576.67	−	7927.03i	0.632765	−	1.09598i
$375$	−258.279	−	2015.83i	−0.0355666	−	0.277592i
$376$	3302.24	−	1906.55i	0.452926	−	0.261497i
$377$	4047.43			0.552927
$378$	−4414.72	+	2741.40i	−0.600711	+	0.373023i
$379$	2909.96			0.394393			0.197196	−	0.980364i	$-0.436816\pi$
$379$	2909.96			0.394393			0.197196	+	0.980364i	$0.436816\pi$
$380$	3829.36	−	2210.88i	0.516953	−	0.298463i
$381$	−88.5991	−	691.503i	−0.0119136	−	0.0929837i
$382$	−1773.23	+	3071.32i	−0.237503	+	0.411367i
$383$	528.709			0.0705372			0.0352686	−	0.999378i	$-0.488771\pi$
$383$	528.709			0.0705372			0.0352686	+	0.999378i	$0.488771\pi$
$384$	403.059	+	529.066i	0.0535639	+	0.0703094i
$385$	−12429.2	−	4539.79i	−1.64533	−	0.600959i
$386$		−	5759.90i		−	0.759511i
$387$	−474.124	+	1721.60i	−0.0622767	+	0.226133i
$388$	−4078.98	+	2355.00i	−0.533708	+	0.308136i
$389$		−	4550.81i		−	0.593150i	−0.955010	−	0.296575i	$-0.904155\pi$
$389$		−	4550.81i		−	0.593150i	0.955010	−	0.296575i	$-0.0958445\pi$
$390$	−4328.68	−	1810.61i	−0.562028	−	0.235087i
$391$	16950.7	−	9786.50i	2.19242	−	1.26579i
$392$	−1768.56	+	2098.03i	−0.227872	+	0.270323i
$393$	1684.38	+	13146.3i	0.216198	+	1.68739i
$394$	−1601.95	−	2774.66i	−0.204836	−	0.354786i
$395$	−8764.08	−	15179.8i	−1.11638	−	1.93362i
$396$	4972.23	+	1369.34i	0.630969	+	0.173768i
$397$	3240.73	+	1871.04i	0.409692	+	0.236536i	0.690657	−	0.723182i	$-0.257321\pi$
$397$	3240.73	+	1871.04i	0.409692	+	0.236536i	−0.280965	+	0.959718i	$0.590655\pi$
$398$	4121.89	−	7139.33i	0.519125	−	0.899151i
$399$	−5219.99	−	4827.60i	−0.654953	−	0.605720i
$400$	−790.873	−	1369.83i	−0.0988591	−	0.171229i
$401$		−	9776.12i		−	1.21745i	−0.793383	−	0.608723i	$-0.791682\pi$
$401$		−	9776.12i		−	1.21745i	0.793383	−	0.608723i	$-0.208318\pi$
$402$	2568.48	−	329.087i	0.318667	−	0.0408293i
$403$	4395.57			0.543322
$404$	−960.785	+	1664.13i	−0.118319	+	0.204934i
$405$	−9520.70	+	5322.04i	−1.16812	+	0.652974i
$406$	1704.47	−	4666.55i	0.208353	−	0.570436i
$407$	−4626.37	−	2671.04i	−0.563441	−	0.325303i
$408$	−2414.33	−	3169.12i	−0.292959	−	0.384546i
$409$	6630.48	+	3828.11i	0.801604	+	0.462807i	0.844032	−	0.536293i	$-0.180176\pi$
$409$	6630.48	+	3828.11i	0.801604	+	0.462807i	−0.0424275	+	0.999100i	$0.513509\pi$
$410$	6536.99	+	3774.13i	0.787412	+	0.454612i
$411$	−14483.5	+	1855.71i	−1.73825	+	0.222714i
$412$	3381.55	+	1952.34i	0.404362	+	0.233458i
$413$	9657.71	+	11536.1i	1.15067	+	1.37447i
$414$	7743.81	+	7852.00i	0.919293	+	0.932137i
$415$	−6442.05	+	11158.0i	−0.761994	+	1.31981i
$416$	965.645			0.113809
$417$	5121.53	+	6722.66i	0.601444	+	0.789472i
$418$			7056.35i			0.825688i
$419$	−5384.89	−	9326.90i	−0.627850	−	1.08747i	−0.987982	−	0.154567i	$-0.950602\pi$
$419$	−5384.89	−	9326.90i	−0.627850	−	1.08747i	0.360132	−	0.932901i	$-0.382731\pi$
$420$	−3910.48	+	4228.32i	−0.454314	+	0.491240i
$421$	7365.56	−	12757.5i	0.852673	−	1.47687i	−0.0261145	−	0.999659i	$-0.508313\pi$
$421$	7365.56	−	12757.5i	0.852673	−	1.47687i	0.878787	−	0.477214i	$-0.158353\pi$
$422$	7740.10	+	4468.75i	0.892849	+	0.515487i
$423$	−9036.56	−	9162.81i	−1.03871	−	1.05322i
$424$	−1068.77	−	1851.17i	−0.122416	−	0.212030i
$425$	4737.34	+	8205.32i	0.540694	+	0.936509i
$426$	4571.54	−	3482.74i	0.519934	−	0.396102i
$427$	−415.126	−	2369.97i	−0.0470477	−	0.268597i
$428$	−2698.25	+	1557.84i	−0.304731	+	0.175937i
$429$	5956.20	−	4537.62i	0.670322	−	0.510672i
$430$			1979.06i			0.221951i
$431$	−12525.1	+	7231.37i	−1.39980	+	0.808173i	−0.994371	−	0.105955i	$-0.966210\pi$
$431$	−12525.1	+	7231.37i	−1.39980	+	0.808173i	−0.405426	+	0.914128i	$0.632877\pi$
$432$	1384.97	−	1766.55i	0.154246	−	0.196744i
$433$			8295.44i			0.920678i	0.887743	+	0.460339i	$0.152272\pi$
$433$			8295.44i			0.920678i	−0.887743	+	0.460339i	$0.847728\pi$
$434$	1851.07	−	5067.94i	0.204734	−	0.560527i
$435$	4023.83	−	9619.88i	0.443513	−	1.06032i
$436$	2406.95			0.264385
$437$	−7544.46	+	13067.4i	−0.825859	+	1.43043i
$438$	2141.32	+	895.680i	0.233599	+	0.0977106i
$439$	−1539.61	+	888.893i	−0.167384	+	0.0966391i	−0.581352	−	0.813652i	$-0.697476\pi$
$439$	−1539.61	+	888.893i	−0.167384	+	0.0966391i	0.413968	+	0.910292i	$0.364143\pi$
$440$	5715.83			0.619299
$441$	8356.95	+	3990.92i	0.902381	+	0.430938i
$442$	−5784.23			−0.622461
$443$	−1911.30	+	1103.49i	−0.204985	+	0.118348i	−0.598979	−	0.800765i	$-0.704427\pi$
$443$	−1911.30	+	1103.49i	−0.204985	+	0.118348i	0.393994	+	0.919113i	$0.371093\pi$
$444$	−1849.56	+	1409.05i	−0.197694	+	0.150609i
$445$	389.030	−	673.819i	0.0414422	−	0.0717800i
$446$	−7902.34			−0.838984
$447$	3625.36	−	464.501i	0.383610	−	0.0491502i
$448$	406.655	−	1113.36i	0.0428854	−	0.117413i
$449$			6480.36i			0.681129i	0.940221	+	0.340565i	$0.110618\pi$
$449$			6480.36i			0.681129i	−0.940221	+	0.340565i	$0.889382\pi$
$450$	−3800.91	+	3748.54i	−0.398170	+	0.392684i
$451$	−10431.9	+	6022.84i	−1.08917	+	0.628835i
$452$			4064.94i			0.423006i
$453$	−1104.52	−	8620.59i	−0.114558	−	0.894107i
$454$	153.703	−	88.7404i	0.0158891	−	0.00917355i
$455$	1442.70	+	8236.45i	0.148648	+	0.848638i
$456$	2833.41	+	1185.17i	0.290979	+	0.121712i
$457$	9249.66	+	16020.9i	0.946785	+	1.63988i	0.752137	+	0.659007i	$0.229023\pi$
$457$	9249.66	+	16020.9i	0.946785	+	1.63988i	0.194648	+	0.980873i	$0.437643\pi$
$458$	−780.926	−	1352.60i	−0.0796730	−	0.137998i
$459$	−8295.97	+	10581.7i	−0.843623	+	1.07606i
$460$	10584.9	+	6111.21i	1.07288	+	0.619427i
$461$	−4678.44	+	8103.29i	−0.472661	+	0.818672i	−0.999510	−	0.0312862i	$-0.990040\pi$
$461$	−4678.44	+	8103.29i	−0.472661	+	0.818672i	0.526850	+	0.849958i	$0.323373\pi$
$462$	−2723.42	−	8778.19i	−0.274253	−	0.883979i
$463$	9033.99	+	15647.3i	0.906793	+	1.57061i	0.818492	+	0.574518i	$0.194810\pi$
$463$	9033.99	+	15647.3i	0.906793	+	1.57061i	0.0883011	+	0.996094i	$0.471856\pi$
$464$			2146.01i			0.214711i
$465$	4369.94	−	10447.3i	0.435809	−	1.04190i
$466$	−9675.50			−0.961822
$467$	4674.04	−	8095.67i	0.463145	−	0.802191i	−0.535971	−	0.844237i	$-0.680054\pi$
$467$	4674.04	−	8095.67i	0.463145	−	0.802191i	0.999116	+	0.0420458i	$0.0133875\pi$
$468$	−821.647	−	3153.78i	−0.0811552	−	0.311503i
$469$	−2962.29	−	3538.45i	−0.291654	−	0.348380i
$470$	−12352.0	−	7131.41i	−1.21224	−	0.699888i
$471$	4.41389	−	10.5524i	0.000431807	−	0.00103233i
$472$	−5628.16	−	3249.42i	−0.548850	−	0.316879i
$473$	−2735.11	−	1579.11i	−0.265878	−	0.153505i
$474$	4698.07	−	11231.8i	0.455252	−	1.08838i
$475$	−6325.52	−	3652.04i	−0.611020	−	0.352773i
$476$	−2435.87	+	6669.01i	−0.234555	+	0.642172i
$477$	−5136.49	+	5065.71i	−0.493047	+	0.486254i
$478$	−5064.94	+	8772.73i	−0.484655	+	0.839447i
$479$	−8691.21			−0.829042			−0.414521	−	0.910040i	$-0.636051\pi$
$479$	−8691.21			−0.829042			−0.414521	+	0.910040i	$0.636051\pi$
$480$	960.015	−	2295.13i	0.0912885	−	0.218246i
$481$			3375.79i			0.320006i
$482$	−3252.23	−	5633.03i	−0.307334	−	0.532319i
$483$	4342.00	−	19167.8i	0.409043	−	1.80573i
$484$	−1898.72	+	3288.68i	−0.178317	+	0.308854i
$485$	15257.3	+	8808.82i	1.42845	+	0.824718i
$486$	−6947.97	−	3020.15i	−0.648491	−	0.281887i
$487$	−4786.52	−	8290.50i	−0.445376	−	0.771414i	0.552702	−	0.833379i	$-0.313597\pi$
$487$	−4786.52	−	8290.50i	−0.445376	−	0.771414i	−0.998078	+	0.0619649i	$0.980263\pi$
$488$	519.659	+	900.077i	0.0482047	+	0.0834929i
$489$	−14261.0	−	5965.13i	−1.31882	−	0.551641i
$490$	10103.9	+	1805.17i	0.931525	+	0.166427i
$491$	2590.96	−	1495.89i	0.238143	−	0.137492i	−0.376180	−	0.926547i	$-0.622762\pi$
$491$	2590.96	−	1495.89i	0.238143	−	0.137492i	0.614323	+	0.789055i	$0.289429\pi$
$492$	666.302	+	5200.39i	0.0610553	+	0.476528i
$493$		−	12854.6i		−	1.17433i
$494$	3861.68	−	2229.54i	0.351711	−	0.203061i
$495$	−4863.47	−	18667.8i	−0.441610	−	1.69506i
$496$			2330.60i			0.210982i
$497$	−9620.25	−	3513.82i	−0.868264	−	0.317135i
$498$	−8876.52	+	1137.31i	−0.798727	+	0.102337i
$499$	9202.58			0.825579			0.412790	−	0.910826i	$-0.364555\pi$
$499$	9202.58			0.825579			0.412790	+	0.910826i	$0.364555\pi$
$500$	782.236	−	1354.87i	0.0699653	−	0.121183i
$501$	−3355.07	+	2555.99i	−0.299188	+	0.227931i
$502$	3299.99	−	1905.25i	0.293398	−	0.169393i
$503$	10936.9			0.969491			0.484745	−	0.874655i	$-0.338912\pi$
$503$	10936.9			0.969491			0.484745	+	0.874655i	$0.338912\pi$
$504$	−3982.21	−	380.799i	−0.351948	−	0.0336550i
$505$	7187.59			0.633354
$506$	−16891.6	+	9752.40i	−1.48404	+	0.856812i
$507$	6166.53	+	2579.36i	0.540168	+	0.225943i
$508$	268.335	−	464.771i	0.0234359	−	0.0405922i
$509$	2609.48			0.227236			0.113618	−	0.993525i	$-0.463756\pi$
$509$	2609.48			0.227236			0.113618	+	0.993525i	$0.463756\pi$
$510$	−5750.50	+	13747.9i	−0.499287	+	1.19366i
$511$	−713.680	−	4074.43i	−0.0617834	−	0.352725i
$512$			512.000i			0.0441942i
$513$	1459.84	−	10262.3i	0.125641	−	0.883218i
$514$	−1718.59	+	992.231i	−0.147478	+	0.0851467i
$515$		−	14605.4i		−	1.24969i
$516$	−1093.46	+	833.030i	−0.0932884	+	0.0710700i
$517$	19711.5	−	11380.5i	1.67681	−	0.968108i
$518$	3892.17	+	1421.62i	0.330139	+	0.120584i
$519$	1931.95	−	1471.82i	0.163397	−	0.124481i
$520$	−1805.99	−	3128.06i	−0.152304	−	0.263797i
$521$	8382.84	+	14519.5i	0.704911	+	1.22094i	0.966724	+	0.255823i	$0.0823465\pi$
$521$	8382.84	+	14519.5i	0.704911	+	1.22094i	−0.261812	+	0.965119i	$0.584320\pi$
$522$	7008.83	−	1825.99i	0.587678	−	0.153107i
$523$	1961.93	+	1132.72i	0.164033	+	0.0947045i	0.579769	−	0.814781i	$-0.303143\pi$
$523$	1961.93	+	1132.72i	0.164033	+	0.0947045i	−0.415736	+	0.909485i	$0.636476\pi$
$524$	−5101.38	+	8835.86i	−0.425296	+	0.736634i
$525$	9278.54	+	2101.83i	0.771331	+	0.174726i
$526$	38.4269	+	66.5574i	0.00318535	+	0.00551719i
$527$		−	13960.3i		−	1.15393i
$528$	2405.92	+	3158.07i	0.198303	+	0.260298i
$529$	−29541.0			−2.42796
$530$	−3997.73	+	6924.26i	−0.327642	+	0.567492i
$531$	−5823.67	+	21146.3i	−0.475943	+	1.72820i
$532$	−944.343	−	5391.30i	−0.0769595	−	0.439366i
$533$	6592.16	+	3805.99i	0.535719	+	0.309298i
$534$	536.045	−	68.6810i	0.0434400	−	0.00556577i
$535$	10092.8	+	5827.06i	0.815605	+	0.470889i
$536$	1726.32	+	996.689i	0.139115	+	0.0803179i
$537$	−5640.54	−	7403.93i	−0.453272	−	0.594978i
$538$	−4768.58	−	2753.14i	−0.382134	−	0.220625i
$539$	−10556.8	+	12523.4i	−0.843624	+	1.00078i
$540$	−8312.71	−	1182.51i	−0.662448	−	0.0942356i
$541$	1881.94	−	3259.61i	0.149558	−	0.259042i	−0.781506	−	0.623897i	$-0.785548\pi$
$541$	1881.94	−	3259.61i	0.149558	−	0.259042i	0.931064	+	0.364856i	$0.118882\pi$
$542$	10773.4			0.853799
$543$	658.346	−	84.3509i	0.0520301	−	0.00666637i
$544$		−	3066.89i		−	0.241713i
$545$	−4501.57	−	7796.95i	−0.353809	−	0.612816i
$546$	−3943.48	+	4264.01i	−0.309094	+	0.334218i
$547$	−6136.55	+	10628.8i	−0.479671	+	0.830815i	−0.999728	−	0.0233169i	$-0.992577\pi$
$547$	−6136.55	+	10628.8i	−0.479671	+	0.830815i	0.520057	+	0.854131i	$0.325911\pi$
$548$	−9734.61	−	5620.28i	−0.758836	−	0.438114i
$549$	2497.47	−	2463.05i	0.194152	−	0.191476i
$550$	−4720.83	−	8176.72i	−0.365994	−	0.633921i
$551$	4954.85	+	8582.05i	0.383092	+	0.663535i
$552$	1078.90	+	8420.65i	0.0831903	+	0.649288i
$553$	−21371.4	+	3743.43i	−1.64341	+	0.287861i
$554$	−1569.33	+	906.051i	−0.120351	+	0.0694845i
$555$	8023.53	+	3356.11i	0.613658	+	0.256683i
$556$			6505.80i			0.496236i
$557$	12642.7	−	7299.26i	0.961738	−	0.555260i	0.0650305	−	0.997883i	$-0.479286\pi$
$557$	12642.7	−	7299.26i	0.961738	−	0.555260i	0.896708	+	0.442624i	$0.145952\pi$
$558$	7611.69	−	1983.06i	0.577470	−	0.150447i
$559$			1995.77i			0.151005i
$560$	−4367.09	+	764.942i	−0.329542	+	0.0577227i
$561$	−14411.5	−	18916.9i	−1.08459	−	1.42366i
$562$	6203.80			0.465643
$563$	−11710.6	+	20283.3i	−0.876630	+	1.51837i	−0.0216135	+	0.999766i	$0.506880\pi$
$563$	−11710.6	+	20283.3i	−0.876630	+	1.51837i	−0.855016	+	0.518601i	$0.826453\pi$
$564$	−1259.01	−	9826.39i	−0.0939963	−	0.733627i
$565$	13167.8	−	7602.42i	0.980483	−	0.566082i
$566$	−14823.0			−1.10081
$567$	2144.70	+	13329.8i	0.158851	+	0.987303i
$568$	4424.08			0.326813
$569$	−5237.49	+	3023.87i	−0.385882	+	0.222789i	−0.680375	−	0.732865i	$-0.738183\pi$
$569$	−5237.49	+	3023.87i	−0.385882	+	0.222789i	0.294492	+	0.955654i	$0.404850\pi$
$570$	−1459.98	−	11394.9i	−0.107284	−	0.837336i
$571$	−3668.02	+	6353.20i	−0.268830	+	0.465627i	−0.968560	−	0.248780i	$-0.919970\pi$
$571$	−3668.02	+	6353.20i	−0.268830	+	0.465627i	0.699730	+	0.714408i	$0.253304\pi$
$572$	5764.07			0.421342
$573$	5583.71	+	7329.33i	0.407091	+	0.534358i
$574$	7164.28	−	5997.74i	0.520960	−	0.436134i
$575$		−	20189.5i		−	1.46428i
$576$	1672.18	−	435.650i	0.120962	−	0.0315140i
$577$	14135.8	−	8161.32i	1.01990	−	0.588839i	0.105824	−	0.994385i	$-0.466252\pi$
$577$	14135.8	−	8161.32i	1.01990	−	0.588839i	0.914075	+	0.405546i	$0.132919\pi$
$578$			8544.70i			0.614901i
$579$	−13805.6	−	5774.65i	−0.990917	−	0.414484i
$580$	6951.68	−	4013.56i	0.497677	−	0.287334i
$581$	10237.5	+	12228.7i	0.731022	+	0.873203i
$582$	1555.15	+	12137.7i	0.110761	+	0.864474i
$583$	−6379.66	−	11049.9i	−0.453205	−	0.784974i
$584$	893.392	+	1547.40i	0.0633028	+	0.109644i
$585$	−8679.52	+	8559.93i	−0.613426	+	0.604973i
$586$	3781.06	+	2183.00i	0.266543	+	0.153889i
$587$	6038.44	−	10458.9i	0.424588	−	0.735407i	−0.571794	−	0.820397i	$-0.693752\pi$
$587$	6038.44	−	10458.9i	0.424588	−	0.735407i	0.996382	+	0.0849898i	$0.0270858\pi$
$588$	3255.56	+	6342.37i	0.228329	+	0.444821i
$589$	5381.04	+	9320.23i	0.376438	+	0.652009i
$590$			24308.8i			1.69623i
$591$	−8256.50	+	1057.87i	−0.574665	+	0.0736292i
$592$	−1789.90			−0.124264
$593$	−5293.49	+	9168.60i	−0.366573	+	0.634923i	−0.989027	−	0.147733i	$-0.952802\pi$
$593$	−5293.49	+	9168.60i	−0.366573	+	0.634923i	0.622455	+	0.782656i	$0.286136\pi$
$594$	8267.06	−	10544.8i	0.571046	−	0.728382i
$595$	26158.9	−	4582.01i	1.80237	−	0.315705i
$596$	2436.67	+	1406.81i	0.167466	+	0.0966865i
$597$	−12979.4	−	17037.2i	−0.889803	−	1.16798i
$598$	10674.3	+	6162.79i	0.729938	+	0.421430i
$599$	676.342	+	390.486i	0.0461345	+	0.0266358i	0.522890	−	0.852400i	$-0.324854\pi$
$599$	676.342	+	390.486i	0.0461345	+	0.0266358i	−0.476755	+	0.879036i	$0.658187\pi$
$600$	−4076.18	+	522.262i	−0.277349	+	0.0355354i
$601$	4942.99	+	2853.84i	0.335489	+	0.193694i	0.658275	−	0.752777i	$-0.271286\pi$
$601$	4942.99	+	2853.84i	0.335489	+	0.193694i	−0.322787	+	0.946472i	$0.604620\pi$
$602$	2301.05	+	840.463i	0.155787	+	0.0569015i
$603$	1786.28	−	6486.18i	0.120635	−	0.438039i
$604$	3345.19	−	5794.04i	0.225354	−	0.390325i
$605$	14204.3			0.954521
$606$	3025.41	+	3971.24i	0.202804	+	0.266206i
$607$			21428.4i			1.43287i	0.697653	+	0.716436i	$0.254228\pi$
$607$			21428.4i			1.43287i	−0.697653	+	0.716436i	$0.745772\pi$
$608$	1182.14	+	2047.52i	0.0788521	+	0.136576i
$609$	−9476.17	−	8763.84i	−0.630531	−	0.583134i
$610$	1943.78	−	3366.72i	0.129018	−	0.223466i
$611$	−12456.2	−	7191.60i	−0.824754	−	0.476172i
$612$	−10016.4	+	2609.55i	−0.661583	+	0.172361i
$613$	6070.57	+	10514.5i	0.399980	+	0.692786i	0.993723	−	0.111869i	$-0.0356836\pi$
$613$	6070.57	+	10514.5i	0.399980	+	0.692786i	−0.593743	+	0.804655i	$0.702350\pi$
$614$	−2602.62	−	4507.86i	−0.171064	−	0.296291i
$615$	15599.7	−	11884.4i	1.02283	−	0.779226i
$616$	2427.38	−	6645.77i	0.158770	−	0.434685i
$617$	11439.2	−	6604.45i	0.746397	−	0.430932i	−0.0779938	−	0.996954i	$-0.524851\pi$
$617$	11439.2	−	6604.45i	0.746397	−	0.430932i	0.824390	+	0.566022i	$0.191518\pi$
$618$	8069.66	−	6147.72i	0.525258	−	0.400158i
$619$			4968.67i			0.322630i	0.986903	+	0.161315i	$0.0515734\pi$
$619$			4968.67i			0.322630i	−0.986903	+	0.161315i	$0.948427\pi$
$620$	7549.63	−	4358.78i	0.489033	−	0.282343i
$621$	26583.7	−	10688.6i	1.71782	−	0.690692i
$622$		−	16815.8i		−	1.08401i
$623$	−618.235	−	738.479i	−0.0397577	−	0.0474905i
$624$	968.117	−	2314.50i	0.0621085	−	0.148484i
$625$	−18209.3			−1.16539
$626$	2802.53	−	4854.13i	0.178932	−	0.309920i
$627$	16913.0	+	7074.42i	1.07726	+	0.450598i
$628$	7.62555	−	4.40261i	0.000484542	−	0.000279751i
$629$	10721.5			0.679641
$630$	6214.15	+	13612.0i	0.392980	+	0.860815i
$631$	−7879.82			−0.497132			−0.248566	−	0.968615i	$-0.579959\pi$
$631$	−7879.82			−0.497132			−0.248566	+	0.968615i	$0.579959\pi$
$632$	8116.51	−	4686.07i	0.510850	−	0.294940i
$633$	18470.8	−	14071.6i	1.15979	−	0.883567i
$634$	−5701.35	+	9875.02i	−0.357144	+	0.618592i
$635$	−2007.41			−0.125451
$636$	−5508.48	+	705.776i	−0.343436	+	0.0440029i
$637$	10189.2	+	1820.41i	0.633767	+	0.113230i
$638$			12809.8i			0.794900i
$639$	−3764.35	−	14448.9i	−0.233044	−	0.894509i
$640$	1658.55	−	957.563i	0.102437	−	0.0591422i
$641$		−	19452.1i		−	1.19861i	−0.800520	−	0.599306i	$-0.795443\pi$
$641$		−	19452.1i		−	1.19861i	0.800520	−	0.599306i	$-0.204557\pi$
$642$	1028.74	+	8029.13i	0.0632413	+	0.493589i
$643$	−614.956	+	355.045i	−0.0377162	+	0.0217754i	−0.518740	−	0.854932i	$-0.673599\pi$
$643$	−614.956	+	355.045i	−0.0377162	+	0.0217754i	0.481023	+	0.876708i	$0.340265\pi$
$644$	11600.7	−	9711.76i	0.709829	−	0.594250i
$645$	4743.51	+	1984.13i	0.289574	+	0.121124i
$646$	−7081.03	−	12264.7i	−0.431268	−	0.746979i
$647$	−2657.16	−	4602.33i	−0.161458	−	0.279654i	0.773934	−	0.633267i	$-0.218286\pi$
$647$	−2657.16	−	4602.33i	−0.161458	−	0.279654i	−0.935392	+	0.353613i	$0.884953\pi$
$648$	−2845.65	−	5090.63i	−0.172512	−	0.308609i
$649$	−33595.3	−	19396.3i	−2.03194	−	1.17314i
$650$	−2983.21	+	5167.08i	−0.180017	+	0.311799i
$651$	−10291.3	−	9517.65i	−0.619579	−	0.573005i
$652$	−5949.89	−	10305.5i	−0.357386	−	0.619011i
$653$			360.047i			0.0215769i	0.999942	+	0.0107885i	$0.00343414\pi$
$653$			360.047i			0.0215769i	−0.999942	+	0.0107885i	$0.996566\pi$
$654$	2413.11	−	5769.08i	0.144281	−	0.344937i
$655$	38163.3			2.27658
$656$	−2017.99	+	3495.27i	−0.120106	+	0.208029i
$657$	4293.61	−	4234.45i	0.254962	−	0.251449i
$658$	−13537.3	+	11333.0i	−0.802033	+	0.671440i
$659$	−1135.85	−	655.784i	−0.0671419	−	0.0387644i	0.466053	−	0.884757i	$-0.345676\pi$
$659$	−1135.85	−	655.784i	−0.0671419	−	0.0387644i	−0.533195	+	0.845992i	$0.679009\pi$
$660$	5730.46	−	13700.0i	0.337967	−	0.807985i
$661$	−979.289	−	565.393i	−0.0576247	−	0.0332696i	0.470911	−	0.882181i	$-0.343925\pi$
$661$	−979.289	−	565.393i	−0.0576247	−	0.0332696i	−0.528536	+	0.848911i	$0.677259\pi$
$662$	6984.65	+	4032.59i	0.410070	+	0.236754i
$663$	−5799.04	+	13863.9i	−0.339692	+	0.812111i
$664$	−5966.05	−	3444.50i	−0.348686	−	0.201314i
$665$	−15698.2	+	13142.1i	−0.915412	+	0.766358i
$666$	1522.98	+	5845.77i	0.0886103	+	0.340118i
$667$	−13695.9	+	23722.0i	−0.795065	+	1.37709i
$668$	−3246.84			−0.188060
$669$	−7922.58	+	18940.7i	−0.457854	+	1.09460i
$670$		−	7456.19i		−	0.429937i
$671$	3101.92	+	5372.68i	0.178462	+	0.309106i
$672$	−2260.84	−	2090.90i	−0.129783	−	0.120027i
$673$	−9252.40	+	16025.6i	−0.529946	+	0.917894i	0.469444	+	0.882962i	$0.344455\pi$
$673$	−9252.40	+	16025.6i	−0.529946	+	0.917894i	−0.999390	+	0.0349312i	$0.988879\pi$
$674$	−16546.4	−	9553.08i	−0.945614	−	0.545951i
$675$	5174.03	+	12868.3i	0.295035	+	0.733781i
$676$	2572.77	+	4456.17i	0.146380	+	0.253537i
$677$	−10769.3	−	18652.9i	−0.611369	−	1.05892i	−0.991010	−	0.133788i	$-0.957286\pi$
$677$	−10769.3	−	18652.9i	−0.611369	−	1.05892i	0.379641	−	0.925134i	$-0.376048\pi$
$678$	9743.05	+	4075.35i	0.551887	+	0.230845i
$679$	16721.4	−	13998.7i	0.945080	−	0.791196i
$680$	−9934.73	+	5735.82i	−0.560264	+	0.323468i
$681$	−58.6007	−	457.370i	−0.00329748	−	0.0257363i
$682$			13911.7i			0.781093i
$683$	29362.5	−	16952.4i	1.64498	−	0.949732i	0.665961	−	0.745986i	$-0.268022\pi$
$683$	29362.5	−	16952.4i	1.64498	−	0.949732i	0.979024	−	0.203746i	$-0.0653117\pi$
$684$	5681.32	−	5603.04i	0.317589	−	0.313213i
$685$			42045.1i			2.34520i
$686$	6389.76	−	10981.1i	0.355630	−	0.611169i
$687$	−4024.91	+	515.693i	−0.223522	+	0.0286389i
$688$	−1058.19			−0.0586380
$689$	−4031.47	+	6982.71i	−0.222912	+	0.386096i
$690$	25259.7	−	19243.6i	1.39365	−	1.06173i
$691$	26062.6	−	15047.3i	1.43483	−	0.828400i	0.437347	−	0.899293i	$-0.355918\pi$
$691$	26062.6	−	15047.3i	1.43483	−	0.828400i	0.997484	+	0.0708925i	$0.0225847\pi$
$692$	1869.63			0.102706
$693$	−23770.4	−	2273.04i	−1.30298	−	0.124597i
$694$	18955.6			1.03681
$695$	21074.6	−	12167.4i	1.15022	−	0.664081i
$696$	5143.66	+	2151.51i	0.280129	+	0.117173i
$697$	12087.8	−	20936.7i	0.656899	−	1.13778i
$698$	−11876.0			−0.644004
$699$	−9700.27	+	23190.7i	−0.524890	+	1.25487i
$700$	4701.16	+	5615.52i	0.253839	+	0.303209i
$701$			8290.89i			0.446708i	0.974737	+	0.223354i	$0.0717007\pi$
$701$			8290.89i			0.446708i	−0.974737	+	0.223354i	$0.928299\pi$
$702$	−8382.87	−	1192.49i	−0.450700	−	0.0641136i
$703$	−7157.93	+	4132.63i	−0.384020	+	0.221714i
$704$			3056.20i			0.163615i
$705$	−29476.5	+	22456.1i	−1.57468	+	1.19964i
$706$	−6344.20	+	3662.83i	−0.338197	+	0.195258i
$707$	3052.41	−	8356.99i	0.162373	−	0.444550i
$708$	−13430.9	+	10232.1i	−0.712946	+	0.543144i
$709$	−1049.79	−	1818.29i	−0.0556076	−	0.0963152i	0.836882	−	0.547384i	$-0.184376\pi$
$709$	−1049.79	−	1818.29i	−0.0556076	−	0.0963152i	−0.892489	+	0.451069i	$0.851043\pi$
$710$	−8274.08	−	14331.1i	−0.437353	−	0.757518i
$711$	−22210.8	−	22521.1i	−1.17155	−	1.18791i
$712$	360.285	+	208.011i	0.0189638	+	0.0109488i
$713$	−14874.0	+	25762.5i	−0.781255	+	1.35317i
$714$	13542.5	+	12524.5i	0.709825	+	0.656467i
$715$	−10780.2	−	18671.8i	−0.563855	−	0.976626i
$716$		−	7165.09i		−	0.373983i
$717$	15949.0	+	20935.1i	0.830719	+	1.09042i
$718$	−18155.5			−0.943674
$719$	−6906.63	+	11962.6i	−0.358239	+	0.620488i	−0.987667	−	0.156571i	$-0.949956\pi$
$719$	−6906.63	+	11962.6i	−0.358239	+	0.620488i	0.629428	+	0.777059i	$0.283289\pi$
$720$	−4538.61	−	4602.02i	−0.234922	−	0.238204i
$721$	−16981.6	−	6202.57i	−0.877154	−	0.320382i
$722$	−2425.22	−	1400.20i	−0.125010	−	0.0721746i
$723$	−16762.1	+	2147.65i	−0.862225	+	0.110473i
$724$	442.485	+	255.469i	0.0227139	+	0.0131138i
$725$	−11483.1	−	6629.77i	−0.588237	−	0.339619i
$726$	5978.88	+	7848.04i	0.305643	+	0.401196i
$727$	−21951.8	−	12673.9i	−1.11987	−	0.646557i	−0.178502	−	0.983940i	$-0.557125\pi$
$727$	−21951.8	−	12673.9i	−1.11987	−	0.646557i	−0.941368	+	0.337382i	$0.890458\pi$
$728$	−4403.95	+	771.398i	−0.224205	+	0.0392719i
$729$	−14204.6	+	13625.3i	−0.721668	+	0.692239i
$730$	3341.72	−	5788.02i	0.169428	−	0.293458i
$731$	6338.55			0.320711
$732$	2678.34	−	343.163i	0.135238	−	0.0173274i
$733$			30308.0i			1.52722i	0.645679	+	0.763609i	$0.276574\pi$
$733$			30308.0i			1.52722i	−0.645679	+	0.763609i	$0.723426\pi$
$734$	−9421.19	−	16318.0i	−0.473764	−	0.820583i
$735$	14456.5	−	22407.7i	0.725490	−	1.12452i
$736$	−3267.61	+	5659.66i	−0.163649	+	0.283448i
$737$	10304.6	+	5949.38i	0.515028	+	0.297352i
$738$	13132.5	+	3616.68i	0.655035	+	0.180395i
$739$	11980.1	+	20750.1i	0.596337	+	1.03289i	0.993357	+	0.115076i	$0.0367113\pi$
$739$	11980.1	+	20750.1i	0.596337	+	1.03289i	−0.397019	+	0.917810i	$0.629955\pi$
$740$	3347.54	+	5798.10i	0.166294	+	0.288030i
$741$	−1472.30	−	11491.1i	−0.0729912	−	0.569685i
$742$	6353.07	+	7588.72i	0.314324	+	0.375459i
$743$	23695.0	−	13680.3i	1.16997	−	0.675480i	0.216294	−	0.976328i	$-0.430603\pi$
$743$	23695.0	−	13680.3i	1.16997	−	0.675480i	0.953672	+	0.300848i	$0.0972698\pi$
$744$	5586.09	+	2336.57i	0.275263	+	0.115138i
$745$		−	10524.3i		−	0.517557i
$746$	−6429.89	+	3712.30i	−0.315570	+	0.182194i
$747$	−6173.29	+	22415.9i	−0.302368	+	1.09793i
$748$		−	18306.7i		−	0.894864i
$749$	11061.3	−	9260.20i	0.539613	−	0.451750i
$750$	−2463.18	−	3233.24i	−0.119924	−	0.157415i
$751$	−13573.5			−0.659527			−0.329764	−	0.944064i	$-0.606969\pi$
$751$	−13573.5			−0.659527			−0.329764	+	0.944064i	$0.606969\pi$
$752$	3813.10	−	6604.48i	0.184906	−	0.320267i
$753$	−1258.15	−	9819.69i	−0.0608893	−	0.475232i
$754$	7010.36	−	4047.43i	0.338597	−	0.195489i
$755$	−25025.2			−1.20631
$756$	−4905.12	+	9162.97i	−0.235976	+	0.440812i
$757$	−3317.64			−0.159289			−0.0796445	−	0.996823i	$-0.525379\pi$
$757$	−3317.64			−0.159289			−0.0796445	+	0.996823i	$0.525379\pi$
$758$	5040.21	−	2909.96i	0.241515	−	0.139439i
$759$	6440.10	+	50264.1i	0.307985	+	2.40378i
$760$	4421.77	−	7658.73i	0.211045	−	0.365541i
$761$	−27419.4			−1.30611			−0.653057	−	0.757309i	$-0.726514\pi$
$761$	−27419.4			−1.30611			−0.653057	+	0.757309i	$0.726514\pi$
$762$	−844.961	−	1109.12i	−0.0401702	−	0.0527285i
$763$	−10977.2	+	1922.77i	−0.520840	+	0.0912306i
$764$			7092.91i			0.335880i
$765$	27186.3	+	27566.1i	1.28487	+	1.30282i
$766$	915.751	−	528.709i	0.0431951	−	0.0249387i
$767$			24514.0i			1.15404i
$768$	1227.19	+	513.311i	0.0576592	+	0.0241179i
$769$	5499.59	−	3175.19i	0.257894	−	0.148895i	−0.365480	−	0.930819i	$-0.619095\pi$
$769$	5499.59	−	3175.19i	0.257894	−	0.148895i	0.623373	+	0.781924i	$0.285762\pi$
$770$	−26067.8	+	4566.05i	−1.22002	+	0.213700i
$771$	655.230	+	5113.98i	0.0306064	+	0.238879i
$772$	−5759.90	−	9976.44i	−0.268528	−	0.465103i
$773$	−13699.5	−	23728.3i	−0.637437	−	1.10407i	−0.985993	−	0.166785i	$-0.946661\pi$
$773$	−13699.5	−	23728.3i	−0.637437	−	1.10407i	0.348557	−	0.937288i	$-0.386672\pi$
$774$	900.388	+	3456.01i	0.0418136	+	0.160496i
$775$	−12470.8	−	7200.03i	−0.578019	−	0.333720i
$776$	−4710.00	+	8157.95i	−0.217885	+	0.377388i
$777$	7309.55	−	7903.67i	0.337488	−	0.364920i
$778$	−4550.81	−	7882.24i	−0.209710	−	0.363229i
$779$			18637.1i			0.857180i
$780$	−9308.10	+	1192.60i	−0.427286	+	0.0547463i
$781$	26407.9			1.20992
$782$	19573.0	−	33901.4i	0.895050	−	1.55027i
$783$	2650.15	−	18629.8i	0.120956	−	0.850285i
$784$	−965.210	+	5402.45i	−0.0439691	+	0.246103i
$785$	−28.5232	−	16.4679i	−0.00129686	−	0.000748744i
$786$	16063.7	+	21085.7i	0.728976	+	0.956874i
$787$	−2447.78	−	1413.23i	−0.110869	−	0.0640104i	0.443540	−	0.896255i	$-0.353722\pi$
$787$	−2447.78	−	1413.23i	−0.110869	−	0.0640104i	−0.554409	+	0.832244i	$0.687056\pi$
$788$	−5549.33	−	3203.91i	−0.250871	−	0.144841i
$789$	198.053	−	25.3757i	0.00893648	−	0.00114499i
$790$	−30359.7	−	17528.2i	−1.36728	−	0.789397i
$791$	−3247.25	−	18538.7i	−0.145966	−	0.833326i
$792$	9981.49	−	2600.45i	0.447824	−	0.116671i
$793$	1960.18	−	3395.13i	0.0877782	−	0.152036i
$794$	7484.15			0.334512
$795$	12588.4	+	16523.9i	0.561592	+	0.737161i
$796$		−	16487.6i		−	0.734154i
$797$	542.632	+	939.866i	0.0241167	+	0.0417713i	0.877832	−	0.478969i	$-0.158989\pi$
$797$	542.632	+	939.866i	0.0241167	+	0.0417713i	−0.853715	+	0.520740i	$0.825656\pi$
$798$	−13868.9	−	3141.66i	−0.615229	−	0.139365i
$799$	−22840.5	+	39560.9i	−1.01131	+	1.75165i
$800$	−2739.66	−	1581.75i	−0.121077	−	0.0699040i
$801$	372.800	−	1353.68i	0.0164447	−	0.0597126i
$802$	−9776.12	−	16932.7i	−0.430432	−	0.745530i
$803$	5332.78	+	9236.65i	0.234359	+	0.405921i
$804$	4119.65	−	3138.47i	0.180707	−	0.137668i
$805$	−53155.8	−	19415.3i	−2.32732	−	0.850060i
$806$	7613.35	−	4395.57i	0.332716	−	0.192093i
$807$	−11379.6	+	8669.36i	−0.496384	+	0.378161i
$808$			3843.14i			0.167328i
$809$	7238.65	−	4179.24i	0.314583	−	0.181624i	−0.334393	−	0.942434i	$-0.608531\pi$
$809$	7238.65	−	4179.24i	0.314583	−	0.181624i	0.648975	+	0.760809i	$0.275198\pi$
$810$	−11168.3	+	18738.8i	−0.484462	+	0.812855i
$811$		−	13120.7i		−	0.568103i	−0.958809	−	0.284052i	$-0.908321\pi$
$811$		−	13120.7i		−	0.568103i	0.958809	−	0.284052i	$-0.0916787\pi$
$812$	−1714.32	−	9787.16i	−0.0740899	−	0.422983i
$813$	10801.0	−	25822.3i	0.465939	−	1.11393i
$814$	−10684.1			−0.460048
$815$	−22255.5	+	38547.6i	−0.956534	+	1.65676i
$816$	−7350.86	−	3074.74i	−0.315357	−	0.131909i
$817$	−4231.76	+	2443.21i	−0.181212	+	0.104623i
$818$	15312.4			0.654507
$819$	6266.60	+	13726.9i	0.267366	+	0.585659i
$820$	15096.5			0.642919
$821$	−27641.4	+	15958.8i	−1.17502	+	0.678399i	−0.954857	−	0.297064i	$-0.903992\pi$
$821$	−27641.4	+	15958.8i	−1.17502	+	0.678399i	−0.220163	+	0.975463i	$0.570659\pi$
$822$	−23230.5	+	17697.7i	−0.985713	+	0.750946i
$823$	−8.63952	+	14.9641i	−0.000365923	+	0.000633798i	−0.866208	−	0.499683i	$-0.833450\pi$
$823$	−8.63952	+	14.9641i	−0.000365923	+	0.000633798i	0.865842	+	0.500317i	$0.166783\pi$
$824$	7809.35			0.330160
$825$	−24331.3	+	3117.45i	−1.02679	+	0.131559i
$826$	28263.7	+	10323.4i	1.19058	+	0.434863i
$827$		−	9661.64i		−	0.406249i	−0.979153	−	0.203125i	$-0.934890\pi$
$827$		−	9661.64i		−	0.406249i	0.979153	−	0.203125i	$-0.0651097\pi$
$828$	21264.7	+	5856.26i	0.892510	+	0.245796i
$829$	−29889.0	+	17256.4i	−1.25222	+	0.722968i	−0.971550	−	0.236837i	$-0.923889\pi$
$829$	−29889.0	+	17256.4i	−1.25222	+	0.722968i	−0.280668	+	0.959805i	$0.590556\pi$
$830$			25768.2i			1.07762i
$831$	598.321	+	4669.80i	0.0249765	+	0.194938i
$832$	1672.55	−	965.645i	0.0696936	−	0.0402376i
$833$	5781.62	−	32360.8i	0.240482	−	1.34602i
$834$	15593.4	+	6522.46i	0.647428	+	0.270808i
$835$	6072.37	+	10517.7i	0.251668	+	0.435903i
$836$	7056.35	+	12222.0i	0.291925	+	0.505628i
$837$	2878.10	−	20232.2i	0.118855	−	0.835516i
$838$	−18653.8	−	10769.8i	−0.768956	−	0.443957i
$839$	22011.2	−	38124.6i	0.905735	−	1.56878i	0.0858083	−	0.996312i	$-0.472653\pi$
$839$	22011.2	−	38124.6i	0.905735	−	1.56878i	0.819927	−	0.572468i	$-0.194014\pi$
$840$	−2544.82	+	11234.1i	−0.104529	+	0.461446i
$841$	−3199.65	−	5541.96i	−0.131192	−	0.227232i
$842$		−	29462.2i		−	1.20586i
$843$	6219.69	−	14869.6i	0.254113	−	0.607515i
$844$	17875.0			0.729008
$845$	9623.39	−	16668.2i	0.391781	−	0.678584i
$846$	−24814.6	−	6833.89i	−1.00844	−	0.277724i
$847$	6032.23	−	16515.2i	0.244710	−	0.669977i
$848$	−3702.34	−	2137.55i	−0.149928	−	0.0865609i
$849$	−14861.0	+	35528.5i	−0.600738	+	1.43620i
$850$	16410.6	+	9474.68i	0.662212	+	0.382328i
$851$	−19785.6	−	11423.2i	−0.796992	−	0.460143i
$852$	4435.40	−	10603.8i	0.178350	−	0.426386i
$853$	7766.62	+	4484.06i	0.311752	+	0.179990i	0.647710	−	0.761887i	$-0.275727\pi$
$853$	7766.62	+	4484.06i	0.311752	+	0.179990i	−0.335958	+	0.941877i	$0.609060\pi$
$854$	−3088.99	−	3689.79i	−0.123774	−	0.147848i
$855$	−28775.6	−	7924.76i	−1.15100	−	0.316984i
$856$	−3115.68	+	5396.51i	−0.124406	+	0.215478i
$857$	12517.6			0.498943			0.249472	−	0.968382i	$-0.419743\pi$
$857$	12517.6			0.498943			0.249472	+	0.968382i	$0.419743\pi$
$858$	5778.83	−	13815.6i	0.229937	−	0.549716i
$859$			2099.71i			0.0834007i	0.999130	+	0.0417003i	$0.0132775\pi$
$859$			2099.71i			0.0834007i	−0.999130	+	0.0417003i	$0.986723\pi$
$860$	1979.06	+	3427.84i	0.0784715	+	0.135917i
$861$	−7193.05	−	23184.8i	−0.284714	−	0.917695i
$862$	−14462.7	+	25050.2i	−0.571465	+	0.989806i
$863$	29531.0	+	17049.8i	1.16483	+	0.672515i	0.952457	−	0.304674i	$-0.0985475\pi$
$863$	29531.0	+	17049.8i	1.16483	+	0.672515i	0.212373	+	0.977189i	$0.431881\pi$
$864$	632.278	−	4444.73i	0.0248964	−	0.175015i
$865$	−3496.65	−	6056.37i	−0.137445	−	0.238061i
$866$	8295.44	+	14368.1i	0.325509	+	0.563798i
$867$	20480.3	+	8566.58i	0.802248	+	0.335567i
$868$	−1861.78	−	10629.0i	−0.0728029	−	0.415636i
$869$	48448.6	−	27971.8i	1.89126	−	1.09192i
$870$	−2650.40	−	20685.9i	−0.103284	−	0.806114i
$871$		−	7519.12i		−	0.292509i
$872$	4168.95	−	2406.95i	0.161902	−	0.0934742i
$873$	30651.3	+	8441.33i	1.18831	+	0.327257i
$874$			30177.8i			1.16794i
$875$	−2485.16	+	6803.95i	−0.0960156	+	0.262875i
$876$	4604.56	−	589.962i	0.177596	−	0.0227545i
$877$	17751.1			0.683480			0.341740	−	0.939795i	$-0.388984\pi$
$877$	17751.1			0.683480			0.341740	+	0.939795i	$0.388984\pi$
$878$	−1777.79	+	3079.22i	−0.0683342	+	0.118358i
$879$	9023.05	−	6874.04i	0.346234	−	0.263772i
$880$	9900.10	−	5715.83i	0.379241	−	0.218955i
$881$	−11412.1			−0.436418			−0.218209	−	0.975902i	$-0.570021\pi$
$881$	−11412.1			−0.436418			−0.218209	+	0.975902i	$0.570021\pi$
$882$	18465.6	−	1444.48i	0.704953	−	0.0551451i
$883$	35247.9			1.34336			0.671680	−	0.740842i	$-0.265573\pi$
$883$	35247.9			1.34336			0.671680	+	0.740842i	$0.265573\pi$
$884$	−10018.6	+	5784.23i	−0.381178	+	0.220073i
$885$	58264.5	+	24371.0i	2.21304	+	0.925676i
$886$	−2206.97	+	3822.59i	−0.0836848	+	0.144946i
$887$	38654.0			1.46322			0.731609	−	0.681724i	$-0.238770\pi$
$887$	38654.0			1.46322			0.731609	+	0.681724i	$0.238770\pi$
$888$	−1794.48	+	4290.11i	−0.0678139	+	0.162125i
$889$	−852.500	+	2334.00i	−0.0321619	+	0.0880540i
$890$		−	1556.12i		−	0.0586081i
$891$	−16986.1	−	30386.7i	−0.638670	−	1.14253i
$892$	−13687.3	+	7902.34i	−0.513771	+	0.296626i
$893$		−	35215.7i		−	1.31965i
$894$	5814.81	−	4429.90i	0.217535	−	0.165725i
$895$	−23210.3	+	13400.4i	−0.866853	+	0.500478i
$896$	−409.007	−	2335.04i	−0.0152500	−	0.0870628i
$897$	25472.8	−	19406.0i	0.948176	−	0.722349i
$898$	6480.36	+	11224.3i	0.240815	+	0.417105i
$899$	9768.53	+	16919.6i	0.362401	+	0.627698i
$900$	−2834.83	+	10293.6i	−0.104994	+	0.381243i
$901$	22177.1	+	12803.9i	0.820006	+	0.473431i
$902$	−12045.7	+	20863.7i	−0.444653	+	0.770162i
$903$	4321.40	−	4672.64i	0.159255	−	0.172199i
$904$	4064.94	+	7040.69i	0.149555	+	0.259038i
$905$		−	1911.15i		−	0.0701977i
$906$	−10533.7	−	13826.8i	−0.386267	−	0.507024i
$907$	−3134.05			−0.114735			−0.0573674	−	0.998353i	$-0.518271\pi$
$907$	−3134.05			−0.114735			−0.0573674	+	0.998353i	$0.518271\pi$
$908$	177.481	−	307.406i	0.00648668	−	0.0112353i
$909$	12551.6	−	3270.04i	0.457988	−	0.119318i
$910$	10735.3	+	12823.2i	0.391067	+	0.467128i
$911$	36403.3	+	21017.5i	1.32393	+	0.764369i	0.984352	−	0.176211i	$-0.0563841\pi$
$911$	36403.3	+	21017.5i	1.32393	+	0.764369i	0.339573	+	0.940580i	$0.389717\pi$
$912$	6092.77	−	780.638i	0.221219	−	0.0283438i
$913$	−35612.2	−	20560.7i	−1.29090	−	0.745302i
$914$	32041.8	+	18499.3i	1.15957	+	0.669478i
$915$	−6120.76	−	8034.27i	−0.221143	−	0.290279i
$916$	−2705.21	−	1561.85i	−0.0975792	−	0.0563374i
$917$	16207.1	−	44372.3i	0.583647	−	1.59793i
$918$	−3787.35	+	26624.0i	−0.136167	+	0.957214i
$919$	11041.8	−	19125.0i	0.396339	−	0.686480i	−0.596932	−	0.802292i	$-0.703614\pi$
$919$	11041.8	−	19125.0i	0.396339	−	0.686480i	0.993271	+	0.115812i	$0.0369471\pi$
$920$	24444.8			0.876002
$921$	−13413.9	+	1718.67i	−0.479918	+	0.0614896i
$922$			18713.7i			0.668443i
$923$	−8343.92	−	14452.1i	−0.297555	−	0.515381i
$924$	−13495.3	−	12480.9i	−0.480479	−	0.444361i
$925$	5529.61	−	9577.57i	0.196554	−	0.340442i
$926$	31294.7	+	18068.0i	1.11059	+	0.641200i
$927$	−6644.81	−	25505.2i	−0.235431	−	0.903668i
$928$	2146.01	+	3717.00i	0.0759119	+	0.131483i
$929$	−2183.88	−	3782.59i	−0.0771267	−	0.133587i	0.824882	−	0.565304i	$-0.191241\pi$
$929$	−2183.88	−	3782.59i	−0.0771267	−	0.133587i	−0.902009	+	0.431717i	$0.857908\pi$
$930$	−2878.37	−	22465.2i	−0.101490	−	0.792112i
$931$	8613.60	+	23833.3i	0.303221	+	0.838997i
$932$	−16758.5	+	9675.50i	−0.588993	+	0.340055i
$933$	−40304.8	−	16858.8i	−1.41428	−	0.591568i
$934$		−	18696.2i		−	0.654986i
$935$	−59301.8	+	34237.9i	−2.07420	+	1.19754i
$936$	−4576.91	−	4640.86i	−0.159830	−	0.162063i
$937$		−	19193.7i		−	0.669192i	−0.942362	−	0.334596i	$-0.891400\pi$
$937$		−	19193.7i		−	0.669192i	0.942362	−	0.334596i	$-0.108600\pi$
$938$	−8669.29	−	3166.48i	−0.301772	−	0.110223i
$939$	−8824.89	−	11583.8i	−0.306698	−	0.402580i
$940$	−28525.6			−0.989791
$941$	5113.50	−	8856.84i	0.177147	−	0.306828i	−0.763755	−	0.645506i	$-0.776647\pi$
$941$	5113.50	−	8856.84i	0.177147	−	0.306828i	0.940902	+	0.338678i	$0.109980\pi$
$942$	−2.90731	−	22.6912i	−0.000100558	−	0.000784838i
$943$	−44613.9	+	25757.8i	−1.54064	+	0.889492i
$944$	−12997.7			−0.448134
$945$	38855.8	−	1247.55i	1.33755	−	0.0429447i
$946$	−6316.46			−0.217089
$947$	8897.92	−	5137.22i	0.305326	−	0.176280i	−0.339507	−	0.940603i	$-0.610260\pi$
$947$	8897.92	−	5137.22i	0.305326	−	0.176280i	0.644833	+	0.764324i	$0.276927\pi$
$948$	−3094.50	−	24152.1i	−0.106018	−	0.827451i
$949$	3369.92	−	5836.88i	0.115271	−	0.199655i
$950$	−14608.2			−0.498896
$951$	17953.0	+	23565.6i	0.612161	+	0.803539i
$952$	2449.96	+	13986.9i	0.0834072	+	0.476176i
$953$			11903.0i			0.404593i	0.979324	+	0.202297i	$0.0648405\pi$
$953$			11903.0i			0.404593i	−0.979324	+	0.202297i	$0.935160\pi$
$954$	−3830.95	+	13910.6i	−0.130012	+	0.472087i
$955$	22976.4	−	13265.4i	0.778533	−	0.449486i
$956$			20259.8i			0.685405i
$957$	30703.2	+	12842.6i	1.03709	+	0.433797i
$958$	−15053.6	+	8691.21i	−0.507683	+	0.293111i
$959$	48885.7	+	17855.6i	1.64609	+	0.601238i
$960$	−632.337	−	4935.30i	−0.0212590	−	0.165923i
$961$	−4286.73	−	7424.84i	−0.143894	−	0.249231i
$962$	3375.79	+	5847.04i	0.113139	+	0.195963i
$963$	20276.0	+	5583.96i	0.678488	+	0.186854i
$964$	−11266.1	−	6504.47i	−0.376406	−	0.217318i
$965$	−21544.8	+	37316.7i	−0.718706	+	1.24484i
$966$	−11647.2	−	37541.6i	−0.387933	−	1.25040i
$967$	−15431.1	−	26727.4i	−0.513165	−	0.888827i	−0.999883	−	0.0152685i	$-0.995140\pi$
$967$	−15431.1	−	26727.4i	−0.513165	−	0.888827i	0.486719	−	0.873559i	$-0.338194\pi$
$968$			7594.88i			0.252179i
$969$	−36495.8	+	4676.04i	−1.20992	+	0.155022i
$970$	35235.3			1.16633
$971$	−12653.5	+	21916.5i	−0.418198	+	0.724341i	−0.995758	−	0.0920074i	$-0.970672\pi$
$971$	−12653.5	+	21916.5i	−0.418198	+	0.724341i	0.577560	+	0.816348i	$0.304005\pi$
$972$	−15054.4	+	1716.92i	−0.496780	+	0.0566565i
$973$	−5197.11	−	29670.5i	−0.171235	−	0.977589i
$974$	−16581.0	−	9573.05i	−0.545472	−	0.314928i
$975$	9393.84	+	12330.6i	0.308558	+	0.405021i
$976$	1800.15	+	1039.32i	0.0590384	+	0.0340858i
$977$	−4863.70	−	2808.06i	−0.159267	−	0.0919527i	0.418248	−	0.908333i	$-0.362644\pi$
$977$	−4863.70	−	2808.06i	−0.159267	−	0.0919527i	−0.577515	+	0.816380i	$0.695978\pi$
$978$	−30665.9	+	3929.08i	−1.00264	+	0.128464i
$979$	2150.59	+	1241.64i	0.0702075	+	0.0405343i
$980$	19305.6	−	6977.23i	0.629281	−	0.227428i
$981$	−11408.3	−	11567.7i	−0.371294	−	0.376482i
$982$	2991.78	−	5181.92i	0.0972216	−	0.168393i
$983$	28269.6			0.917252			0.458626	−	0.888629i	$-0.348342\pi$
$983$	28269.6			0.917252			0.458626	+	0.888629i	$0.348342\pi$
$984$	6354.46	+	8341.04i	0.205867	+	0.270226i
$985$			23968.3i			0.775323i
$986$	−12854.6	−	22264.9i	−0.415188	−	0.719126i
$987$	13591.6	+	43808.8i	0.438324	+	1.41282i
$988$	4459.09	−	7723.37i	0.143586	−	0.248697i
$989$	−11697.2	−	6753.39i	−0.376087	−	0.217134i
$990$	−27091.6	−	27470.1i	−0.869724	−	0.881875i
$991$	−2105.15	−	3646.23i	−0.0674797	−	0.116878i	0.830312	−	0.557299i	$-0.188162\pi$
$991$	−2105.15	−	3646.23i	−0.0674797	−	0.116878i	−0.897791	+	0.440421i	$0.854829\pi$
$992$	2330.60	+	4036.71i	0.0745933	+	0.129199i
$993$	16668.0	−	12698.2i	0.532672	−	0.405806i
$994$	−20176.6	+	3534.14i	−0.643825	+	0.112773i
$995$	−53409.0	+	30835.7i	−1.70169	+	0.982471i
$996$	−14237.3	+	10846.4i	−0.452937	+	0.345061i
$997$			26010.8i			0.826250i	0.910674	+	0.413125i	$0.135563\pi$
$997$			26010.8i			0.826250i	−0.910674	+	0.413125i	$0.864437\pi$
$998$	15939.3	−	9202.58i	0.505562	−	0.291886i
$999$	15538.3	+	2210.38i	0.492102	+	0.0700032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.t.a.47.18	yes	48
3.2	odd	2		378.4.t.a.89.9		48
7.3	odd	6		126.4.l.a.101.21	yes	48
9.4	even	3		378.4.l.a.341.19		48
9.5	odd	6		126.4.l.a.5.9	✓	48
21.17	even	6		378.4.l.a.143.19		48
63.31	odd	6		378.4.t.a.17.9		48
63.59	even	6	inner	126.4.t.a.59.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.l.a.5.9	✓	48	9.5	odd	6
126.4.l.a.101.21	yes	48	7.3	odd	6
126.4.t.a.47.18	yes	48	1.1	even	1	trivial
126.4.t.a.59.18	yes	48	63.59	even	6	inner
378.4.l.a.143.19		48	21.17	even	6
378.4.l.a.341.19		48	9.4	even	3
378.4.t.a.17.9		48	63.31	odd	6
378.4.t.a.89.9		48	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(-0.660361 - 5.15402i) q^{3} +(2.00000 - 3.46410i) q^{4} -14.9619 q^{5} +(-6.29780 - 8.26666i) q^{6} +(-6.35399 + 17.3962i) q^{7} -8.00000i q^{8} +(-26.1278 + 6.80703i) q^{9} +(-25.9148 + 14.9619i) q^{10} -47.7531i q^{11} +(-19.1748 - 8.02048i) q^{12} +(-26.1335 + 15.0882i) q^{13} +(6.39074 + 36.4850i) q^{14} +(9.88027 + 77.1140i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(47.9201 + 83.0001i) q^{17} +(-38.4477 + 37.9180i) q^{18} +(-63.9852 - 36.9418i) q^{19} +(-29.9238 + 51.8296i) q^{20} +(93.8561 + 21.2608i) q^{21} +(-47.7531 - 82.7108i) q^{22} -204.225i q^{23} +(-41.2322 + 5.28289i) q^{24} +98.8591 q^{25} +(-30.1764 + 52.2671i) q^{26} +(52.3374 + 130.168i) q^{27} +(47.5541 + 56.8032i) q^{28} +(-116.156 - 67.0628i) q^{29} +(94.2272 + 123.685i) q^{30} +(-126.147 - 72.8312i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-246.121 + 31.5343i) q^{33} +(166.000 + 95.8402i) q^{34} +(95.0679 - 260.280i) q^{35} +(-28.6755 + 104.124i) q^{36} +(55.9343 - 96.8810i) q^{37} -147.767 q^{38} +(95.0225 + 124.729i) q^{39} +119.695i q^{40} +(-126.125 - 218.454i) q^{41} +(183.824 - 57.0313i) q^{42} +(33.0683 - 57.2760i) q^{43} +(-165.422 - 95.5062i) q^{44} +(390.923 - 101.846i) q^{45} +(-204.225 - 353.729i) q^{46} +(238.319 + 412.780i) q^{47} +(-66.1333 + 50.3824i) q^{48} +(-262.254 - 221.070i) q^{49} +(171.229 - 98.8591i) q^{50} +(396.140 - 301.791i) q^{51} +120.706i q^{52} +(231.396 - 133.597i) q^{53} +(220.819 + 173.121i) q^{54} +714.478i q^{55} +(139.169 + 50.8319i) q^{56} +(-148.146 + 354.176i) q^{57} -268.251 q^{58} +(406.178 - 703.520i) q^{59} +(286.891 + 120.002i) q^{60} +(-112.510 + 64.9574i) q^{61} -291.325 q^{62} +(47.5999 - 497.776i) q^{63} -64.0000 q^{64} +(391.008 - 225.749i) q^{65} +(-394.759 + 300.740i) q^{66} +(-124.586 + 215.789i) q^{67} +383.361 q^{68} +(-1052.58 + 134.862i) q^{69} +(-95.6177 - 545.886i) q^{70} +553.009i q^{71} +(54.4562 + 209.023i) q^{72} +(-193.425 + 111.674i) q^{73} -223.737i q^{74} +(-65.2827 - 509.522i) q^{75} +(-255.941 + 147.767i) q^{76} +(830.721 + 303.423i) q^{77} +(289.313 + 121.015i) q^{78} +(585.759 + 1014.56i) q^{79} +(119.695 + 207.318i) q^{80} +(636.329 - 355.706i) q^{81} +(-436.908 - 252.249i) q^{82} +(430.563 - 745.757i) q^{83} +(261.362 - 282.606i) q^{84} +(-716.977 - 1241.84i) q^{85} -132.273i q^{86} +(-268.938 + 642.957i) q^{87} -382.025 q^{88} +(-26.0013 + 45.0356i) q^{89} +(575.252 - 567.326i) q^{90} +(-96.4248 - 550.494i) q^{91} +(-707.457 - 408.451i) q^{92} +(-292.071 + 698.261i) q^{93} +(825.560 + 476.637i) q^{94} +(957.341 + 552.721i) q^{95} +(-64.1639 + 153.398i) q^{96} +(-1019.74 - 588.749i) q^{97} +(-675.307 - 120.651i) q^{98} +(325.057 + 1247.69i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 96 q^{4} - 12 q^{7} + 18 q^{9} - 72 q^{13} - 132 q^{14} + 132 q^{15} - 384 q^{16} - 144 q^{17} - 72 q^{18} + 270 q^{21} + 48 q^{24} + 1200 q^{25} - 120 q^{26} + 450 q^{27} + 48 q^{28} + 42 q^{29}+ \cdots - 5076 q^{99}+O(q^{100}) \) 48 * q + 96 * q^4 - 12 * q^7 + 18 * q^9 - 72 * q^13 - 132 * q^14 + 132 * q^15 - 384 * q^16 - 144 * q^17 - 72 * q^18 + 270 * q^21 + 48 * q^24 + 1200 * q^25 - 120 * q^26 + 450 * q^27 + 48 * q^28 + 42 * q^29 - 468 * q^30 - 90 * q^31 - 1332 * q^33 + 780 * q^35 - 240 * q^36 - 168 * q^37 + 240 * q^39 + 618 * q^41 - 252 * q^42 - 42 * q^43 - 96 * q^44 + 1038 * q^45 - 252 * q^46 + 198 * q^47 - 636 * q^49 + 1464 * q^50 + 222 * q^51 + 36 * q^53 + 180 * q^54 - 1452 * q^57 + 504 * q^58 - 1500 * q^59 - 480 * q^60 + 2466 * q^61 - 2952 * q^62 - 2988 * q^63 - 3072 * q^64 - 84 * q^65 - 384 * q^66 - 588 * q^67 - 1152 * q^68 - 1848 * q^69 + 216 * q^70 + 192 * q^72 + 2820 * q^75 + 1548 * q^77 + 2496 * q^78 + 1230 * q^79 - 4122 * q^81 + 1512 * q^84 + 720 * q^85 + 258 * q^87 + 4398 * q^89 + 6084 * q^90 - 90 * q^91 - 1632 * q^92 + 1740 * q^93 + 3246 * q^95 + 192 * q^96 - 1584 * q^97 + 1104 * q^98 - 5076 * q^99

Introduction

L-functions

Modular forms

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