LMFDB - Embedded newform 60.4.h.c.59.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,4,Mod(59,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("60.59");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	60.h (of order $2$, degree $1$, 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:	$3.54011460034$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.2
Character	$\chi$	$=$	60.59
Dual form			60.4.h.c.59.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.76761 - 0.583363i) q^{2} +(3.16559 - 4.12057i) q^{3} +(7.31938 + 3.22905i) q^{4} +(4.82699 + 10.0847i) q^{5} +(-11.1649 + 9.55745i) q^{6} +10.1458 q^{7} +(-18.3735 - 13.2066i) q^{8} +(-6.95813 - 26.0880i) q^{9} +O(q^{10})$	\(q+(-2.76761 - 0.583363i) q^{2} +(3.16559 - 4.12057i) q^{3} +(7.31938 + 3.22905i) q^{4} +(4.82699 + 10.0847i) q^{5} +(-11.1649 + 9.55745i) q^{6} +10.1458 q^{7} +(-18.3735 - 13.2066i) q^{8} +(-6.95813 - 26.0880i) q^{9} +(-7.47622 - 30.7263i) q^{10} +60.6436 q^{11} +(36.4756 - 19.9382i) q^{12} -26.6025i q^{13} +(-28.0798 - 5.91871i) q^{14} +(56.8347 + 12.0339i) q^{15} +(43.1465 + 47.2692i) q^{16} -32.4976 q^{17} +(4.03864 + 76.2607i) q^{18} -106.833i q^{19} +(2.76672 + 89.3999i) q^{20} +(32.1176 - 41.8066i) q^{21} +(-167.838 - 35.3772i) q^{22} +88.0228i q^{23} +(-112.582 + 33.9026i) q^{24} +(-78.4004 + 97.3569i) q^{25} +(-15.5189 + 73.6255i) q^{26} +(-129.524 - 53.9124i) q^{27} +(74.2613 + 32.7614i) q^{28} +101.892i q^{29} +(-150.276 - 66.4605i) q^{30} +103.528i q^{31} +(-91.8379 - 155.993i) q^{32} +(191.973 - 249.886i) q^{33} +(89.9407 + 18.9579i) q^{34} +(48.9739 + 102.317i) q^{35} +(33.3102 - 213.416i) q^{36} +331.661i q^{37} +(-62.3225 + 295.673i) q^{38} +(-109.617 - 84.2126i) q^{39} +(44.4954 - 249.038i) q^{40} +13.7277i q^{41} +(-113.277 + 96.9685i) q^{42} +72.5383 q^{43} +(443.873 + 195.821i) q^{44} +(229.502 - 196.097i) q^{45} +(51.3492 - 243.613i) q^{46} -463.850i q^{47} +(331.360 - 28.1534i) q^{48} -240.062 q^{49} +(273.777 - 223.711i) q^{50} +(-102.874 + 133.908i) q^{51} +(85.9008 - 194.714i) q^{52} -282.917 q^{53} +(327.022 + 224.768i) q^{54} +(292.726 + 611.570i) q^{55} +(-186.415 - 133.992i) q^{56} +(-440.213 - 338.190i) q^{57} +(59.4402 - 281.999i) q^{58} -682.476 q^{59} +(377.137 + 271.603i) q^{60} +140.268 q^{61} +(60.3943 - 286.525i) q^{62} +(-70.5961 - 264.685i) q^{63} +(163.171 + 485.303i) q^{64} +(268.277 - 128.410i) q^{65} +(-677.080 + 579.598i) q^{66} -515.051 q^{67} +(-237.862 - 104.936i) q^{68} +(362.704 + 278.644i) q^{69} +(-75.8526 - 311.744i) q^{70} +38.7362 q^{71} +(-216.689 + 571.221i) q^{72} +747.691i q^{73} +(193.478 - 917.908i) q^{74} +(152.982 + 631.246i) q^{75} +(344.969 - 781.952i) q^{76} +615.281 q^{77} +(254.252 + 297.015i) q^{78} -862.927i q^{79} +(-268.426 + 663.285i) q^{80} +(-632.169 + 363.047i) q^{81} +(8.00823 - 37.9930i) q^{82} +534.332i q^{83} +(370.076 - 202.289i) q^{84} +(-156.865 - 327.727i) q^{85} +(-200.758 - 42.3161i) q^{86} +(419.854 + 322.549i) q^{87} +(-1114.24 - 800.896i) q^{88} -507.723i q^{89} +(-749.568 + 408.837i) q^{90} -269.905i q^{91} +(-284.230 + 644.272i) q^{92} +(426.594 + 327.727i) q^{93} +(-270.593 + 1283.76i) q^{94} +(1077.38 - 515.682i) q^{95} +(-933.500 - 115.385i) q^{96} -376.369i q^{97} +(664.398 + 140.043i) q^{98} +(-421.966 - 1582.07i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 56 q^{4} + 12 q^{6} + 192 q^{9}+O(q^{10}) $ 24 * q + 56 * q^4 + 12 * q^6 + 192 * q^9	$ 24 q + 56 q^{4} + 12 q^{6} + 192 q^{9} - 32 q^{10} - 240 q^{16} - 264 q^{21} + 168 q^{24} - 88 q^{25} - 252 q^{30} - 1088 q^{34} - 1104 q^{36} + 704 q^{40} + 456 q^{45} + 3368 q^{46} - 1304 q^{49} + 468 q^{54} + 2496 q^{60} + 2080 q^{61} + 1376 q^{64} - 672 q^{66} + 2568 q^{69} - 2632 q^{70} - 1536 q^{76} - 5112 q^{81} - 2328 q^{84} - 6944 q^{85} - 1152 q^{90} - 4840 q^{94} - 2832 q^{96}+O(q^{100}) $ 24 * q + 56 * q^4 + 12 * q^6 + 192 * q^9 - 32 * q^10 - 240 * q^16 - 264 * q^21 + 168 * q^24 - 88 * q^25 - 252 * q^30 - 1088 * q^34 - 1104 * q^36 + 704 * q^40 + 456 * q^45 + 3368 * q^46 - 1304 * q^49 + 468 * q^54 + 2496 * q^60 + 2080 * q^61 + 1376 * q^64 - 672 * q^66 + 2568 * q^69 - 2632 * q^70 - 1536 * q^76 - 5112 * q^81 - 2328 * q^84 - 6944 * q^85 - 1152 * q^90 - 4840 * q^94 - 2832 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−2.76761	−	0.583363i	−0.978499	−	0.206250i
$2$	−2.76761	−	0.583363i	−0.978499	−	0.206250i
$3$	3.16559	−	4.12057i	0.609217	−	0.793003i
$3$	3.16559	−	4.12057i	0.609217	−	0.793003i
$4$	7.31938	+	3.22905i	0.914922	+	0.403631i
$5$	4.82699	+	10.0847i	0.431739	+	0.901999i
$5$	4.82699	+	10.0847i	0.431739	+	0.901999i
$6$	−11.1649	+	9.55745i	−0.759676	+	0.650302i
$7$	10.1458			0.547824			0.273912	−	0.961755i	$-0.411682\pi$
$7$	10.1458			0.547824			0.273912	+	0.961755i	$0.411682\pi$
$8$	−18.3735	−	13.2066i	−0.812002	−	0.583655i
$9$	−6.95813	−	26.0880i	−0.257708	−	0.966223i
$10$	−7.47622	−	30.7263i	−0.236419	−	0.971651i
$11$	60.6436			1.66225			0.831124	−	0.556087i	$-0.187698\pi$
$11$	60.6436			1.66225			0.831124	+	0.556087i	$0.187698\pi$
$12$	36.4756	−	19.9382i	0.877467	−	0.479637i
$13$		−	26.6025i		−	0.567555i	−0.958890	−	0.283777i	$-0.908412\pi$
$13$		−	26.6025i		−	0.567555i	0.958890	−	0.283777i	$-0.0915877\pi$
$14$	−28.0798	−	5.91871i	−0.536046	−	0.112989i
$15$	56.8347	+	12.0339i	0.978311	+	0.207143i
$16$	43.1465	+	47.2692i	0.674165	+	0.738581i
$17$	−32.4976			−0.463636			−0.231818	−	0.972759i	$-0.574467\pi$
$17$	−32.4976			−0.463636			−0.231818	+	0.972759i	$0.574467\pi$
$18$	4.03864	+	76.2607i	0.0528843	+	0.998601i
$19$		−	106.833i		−	1.28996i	−0.764200	−	0.644979i	$-0.776866\pi$
$19$		−	106.833i		−	1.28996i	0.764200	−	0.644979i	$-0.223134\pi$
$20$	2.76672	+	89.3999i	0.0309329	+	0.999521i
$21$	32.1176	−	41.8066i	0.333744	−	0.434426i
$22$	−167.838	−	35.3772i	−1.62651	−	0.342838i
$23$			88.0228i			0.798001i	0.916951	+	0.399000i	$0.130643\pi$
$23$			88.0228i			0.798001i	−0.916951	+	0.399000i	$0.869357\pi$
$24$	−112.582	+	33.9026i	−0.957526	+	0.288347i
$25$	−78.4004	+	97.3569i	−0.627203	+	0.778856i
$26$	−15.5189	+	73.6255i	−0.117058	+	0.555352i
$27$	−129.524	−	53.9124i	−0.923218	−	0.384276i
$28$	74.2613	+	32.7614i	0.501217	+	0.221119i
$29$			101.892i			0.652446i	0.945293	+	0.326223i	$0.105776\pi$
$29$			101.892i			0.652446i	−0.945293	+	0.326223i	$0.894224\pi$
$30$	−150.276	−	66.4605i	−0.914553	−	0.404466i
$31$			103.528i			0.599812i	0.953969	+	0.299906i	$0.0969553\pi$
$31$			103.528i			0.599812i	−0.953969	+	0.299906i	$0.903045\pi$
$32$	−91.8379	−	155.993i	−0.507337	−	0.861748i
$33$	191.973	−	249.886i	1.01267	−	1.31817i
$34$	89.9407	+	18.9579i	0.453668	+	0.0956249i
$35$	48.9739	+	102.317i	0.236517	+	0.494137i
$36$	33.3102	−	213.416i	0.154214	−	0.988037i
$37$			331.661i			1.47364i	0.676089	+	0.736820i	$0.263673\pi$
$37$			331.661i			1.47364i	−0.676089	+	0.736820i	$0.736327\pi$
$38$	−62.3225	+	295.673i	−0.266054	+	1.26222i
$39$	−109.617	−	84.2126i	−0.450073	−	0.345764i
$40$	44.4954	−	249.038i	0.175883	−	0.984411i
$41$			13.7277i			0.0522905i	0.999658	+	0.0261452i	$0.00832323\pi$
$41$			13.7277i			0.0522905i	−0.999658	+	0.0261452i	$0.991677\pi$
$42$	−113.277	+	96.9685i	−0.416169	+	0.356251i
$43$	72.5383			0.257255			0.128628	−	0.991693i	$-0.458943\pi$
$43$	72.5383			0.257255			0.128628	+	0.991693i	$0.458943\pi$
$44$	443.873	+	195.821i	1.52083	+	0.670934i
$45$	229.502	−	196.097i	0.760269	−	0.649608i
$46$	51.3492	−	243.613i	0.164588	−	0.780843i
$47$		−	463.850i		−	1.43956i	−0.694200	−	0.719782i	$-0.744242\pi$
$47$		−	463.850i		−	1.43956i	0.694200	−	0.719782i	$-0.255758\pi$
$48$	331.360	−	28.1534i	0.996410	−	0.0846582i
$49$	−240.062			−0.699889
$50$	273.777	−	223.711i	0.774357	−	0.632749i
$51$	−102.874	+	133.908i	−0.282455	+	0.367665i
$52$	85.9008	−	194.714i	0.229083	−	0.519268i
$53$	−282.917			−0.733238			−0.366619	−	0.930371i	$-0.619485\pi$
$53$	−282.917			−0.733238			−0.366619	+	0.930371i	$0.619485\pi$
$54$	327.022	+	224.768i	0.824112	+	0.566427i
$55$	292.726	+	611.570i	0.717657	+	1.49935i
$56$	−186.415	−	133.992i	−0.444834	−	0.319740i
$57$	−440.213	−	338.190i	−1.02294	−	0.785865i
$58$	59.4402	−	281.999i	0.134567	−	0.638418i
$59$	−682.476			−1.50595			−0.752973	−	0.658051i	$-0.771381\pi$
$59$	−682.476			−1.50595			−0.752973	+	0.658051i	$0.771381\pi$
$60$	377.137	+	271.603i	0.811469	+	0.584396i
$61$	140.268			0.294418			0.147209	−	0.989105i	$-0.452971\pi$
$61$	140.268			0.294418			0.147209	+	0.989105i	$0.452971\pi$
$62$	60.3943	−	286.525i	0.123711	−	0.586915i
$63$	−70.5961	−	264.685i	−0.141179	−	0.529320i
$64$	163.171	+	485.303i	0.318694	+	0.947858i
$65$	268.277	−	128.410i	0.511934	−	0.245035i
$66$	−677.080	+	579.598i	−1.26277	+	1.08096i
$67$	−515.051			−0.939156			−0.469578	−	0.882891i	$-0.655594\pi$
$67$	−515.051			−0.939156			−0.469578	+	0.882891i	$0.655594\pi$
$68$	−237.862	−	104.936i	−0.424191	−	0.187138i
$69$	362.704	+	278.644i	0.632817	+	0.486156i
$70$	−75.8526	−	311.744i	−0.129516	−	0.532294i
$71$	38.7362			0.0647485			0.0323743	−	0.999476i	$-0.489693\pi$
$71$	38.7362			0.0647485			0.0323743	+	0.999476i	$0.489693\pi$
$72$	−216.689	+	571.221i	−0.354681	+	0.934987i
$73$			747.691i			1.19878i	0.800459	+	0.599388i	$0.204589\pi$
$73$			747.691i			1.19878i	−0.800459	+	0.599388i	$0.795411\pi$
$74$	193.478	−	917.908i	0.303938	−	1.44196i
$75$	152.982	+	631.246i	0.235532	+	0.971867i
$76$	344.969	−	781.952i	0.520667	−	1.18021i
$77$	615.281			0.910620
$78$	254.252	+	297.015i	0.369082	+	0.431158i
$79$		−	862.927i		−	1.22895i	−0.788937	−	0.614474i	$-0.789368\pi$
$79$		−	862.927i		−	1.22895i	0.788937	−	0.614474i	$-0.210632\pi$
$80$	−268.426	+	663.285i	−0.375136	+	0.926970i
$81$	−632.169	+	363.047i	−0.867173	+	0.498008i
$82$	8.00823	−	37.9930i	0.0107849	−	0.0511662i
$83$			534.332i			0.706634i	0.935504	+	0.353317i	$0.114946\pi$
$83$			534.332i			0.706634i	−0.935504	+	0.353317i	$0.885054\pi$
$84$	370.076	−	202.289i	0.480698	−	0.262757i
$85$	−156.865	−	327.727i	−0.200170	−	0.418199i
$86$	−200.758	−	42.3161i	−0.251724	−	0.0530589i
$87$	419.854	+	322.549i	0.517392	+	0.397481i
$88$	−1114.24	−	800.896i	−1.34975	−	0.970179i
$89$		−	507.723i		−	0.604703i	−0.953197	−	0.302351i	$-0.902228\pi$
$89$		−	507.723i		−	0.604703i	0.953197	−	0.302351i	$-0.0977716\pi$
$90$	−749.568	+	408.837i	−0.877904	+	0.478836i
$91$		−	269.905i		−	0.310920i
$92$	−284.230	+	644.272i	−0.322098	+	0.730109i
$93$	426.594	+	327.727i	0.475653	+	0.365416i
$94$	−270.593	+	1283.76i	−0.296910	+	1.40861i
$95$	1077.38	−	515.682i	1.16354	−	0.556925i
$96$	−933.500	−	115.385i	−0.992447	−	0.122671i
$97$		−	376.369i		−	0.393964i	−0.980407	−	0.196982i	$-0.936886\pi$
$97$		−	376.369i		−	0.393964i	0.980407	−	0.196982i	$-0.0631141\pi$
$98$	664.398	+	140.043i	0.684840	+	0.144352i
$99$	−421.966	−	1582.07i	−0.428375	−	1.60610i
$100$	−888.212	+	459.434i	−0.888212	+	0.459434i
$101$		−	423.663i		−	0.417387i	−0.977981	−	0.208694i	$-0.933079\pi$
$101$		−	423.663i		−	0.417387i	0.977981	−	0.208694i	$-0.0669211\pi$
$102$	362.832	−	310.594i	0.352213	−	0.301504i
$103$	429.791			0.411151			0.205575	−	0.978641i	$-0.434093\pi$
$103$	429.791			0.411151			0.205575	+	0.978641i	$0.434093\pi$
$104$	−351.329	+	488.782i	−0.331256	+	0.460856i
$105$	576.636	+	122.094i	0.535942	+	0.113478i
$106$	783.004	+	165.043i	0.717473	+	0.151230i
$107$			869.117i			0.785241i	0.919701	+	0.392620i	$0.128431\pi$
$107$			869.117i			0.785241i	−0.919701	+	0.392620i	$0.871569\pi$
$108$	−773.949	−	812.844i	−0.689567	−	0.724222i
$109$	−1261.98			−1.10896			−0.554478	−	0.832199i	$-0.687082\pi$
$109$	−1261.98			−1.10896			−0.554478	+	0.832199i	$0.687082\pi$
$110$	−453.385	−	1863.35i	−0.392987	−	1.61513i
$111$	1366.63	+	1049.90i	1.16860	+	0.897767i
$112$	437.758	+	479.586i	0.369324	+	0.404613i
$113$	−830.527			−0.691411			−0.345705	−	0.938343i	$-0.612360\pi$
$113$	−830.527			−0.691411			−0.345705	+	0.938343i	$0.612360\pi$
$114$	1021.05	+	1192.78i	0.838863	+	0.979950i
$115$	−887.679	+	424.885i	−0.719796	+	0.344528i
$116$	−329.015	+	745.788i	−0.263347	+	0.596937i
$117$	−694.007	+	185.104i	−0.548384	+	0.146264i
$118$	1888.83	+	398.131i	1.47357	+	0.310601i
$119$	−329.715			−0.253991
$120$	−885.326	−	971.699i	−0.673490	−	0.739196i
$121$	2346.65			1.76307
$122$	−388.209	−	81.8273i	−0.288088	−	0.0607237i
$123$	56.5659	+	43.4563i	0.0414665	+	0.0318562i
$124$	−334.296	+	757.760i	−0.242102	+	0.548781i
$125$	−1360.25	−	320.700i	−0.973315	−	0.229475i
$126$	40.9754	+	773.729i	0.0289713	+	0.547058i
$127$	2250.82			1.57266			0.786329	−	0.617807i	$-0.211979\pi$
$127$	2250.82			1.57266			0.786329	+	0.617807i	$0.211979\pi$
$128$	−168.487	−	1438.32i	−0.116346	−	0.993209i
$129$	229.626	−	298.899i	0.156724	−	0.204004i
$130$	−817.397	+	198.886i	−0.551465	+	0.134181i
$131$	919.322			0.613142			0.306571	−	0.951848i	$-0.400818\pi$
$131$	919.322			0.613142			0.306571	+	0.951848i	$0.400818\pi$
$132$	2212.01	−	1209.12i	1.45857	−	0.797276i
$133$		−	1083.91i		−	0.706671i
$134$	1425.46	+	300.461i	0.918964	+	0.193701i
$135$	−81.5221	−	1566.44i	−0.0519726	−	0.998649i
$136$	597.094	+	429.182i	0.376473	+	0.270603i
$137$	2222.33			1.38589			0.692945	−	0.720991i	$-0.256313\pi$
$137$	2222.33			1.38589			0.692945	+	0.720991i	$0.256313\pi$
$138$	−841.274	−	982.766i	−0.518942	−	0.606222i
$139$		−	701.161i		−	0.427854i	−0.976850	−	0.213927i	$-0.931375\pi$
$139$		−	701.161i		−	0.427854i	0.976850	−	0.213927i	$-0.0686255\pi$
$140$	28.0707	+	907.038i	0.0169458	+	0.547562i
$141$	−1911.33	−	1468.36i	−1.14158	−	0.877007i
$142$	−107.207	−	22.5973i	−0.0633564	−	0.0133544i
$143$		−	1613.27i		−	0.943417i
$144$	932.940	−	1454.51i	0.539896	−	0.841732i
$145$	−1027.55	+	491.833i	−0.588505	+	0.281686i
$146$	436.175	−	2069.32i	0.247247	−	1.17300i
$147$	−759.936	+	989.190i	−0.426384	+	0.555014i
$148$	−1070.95	+	2427.55i	−0.594806	+	1.34826i
$149$			2958.12i			1.62643i	0.581962	+	0.813216i	$0.302285\pi$
$149$			2958.12i			1.62643i	−0.581962	+	0.813216i	$0.697715\pi$
$150$	−55.1510	−	1836.29i	−0.0300204	−	0.999549i
$151$			653.760i			0.352333i	0.984360	+	0.176166i	$0.0563697\pi$
$151$			653.760i			0.352333i	−0.984360	+	0.176166i	$0.943630\pi$
$152$	−1410.90	+	1962.90i	−0.752891	+	1.04745i
$153$	226.122	+	847.797i	0.119483	+	0.447976i
$154$	−1702.86	−	358.932i	−0.891041	−	0.187815i
$155$	−1044.04	+	499.728i	−0.541029	+	0.258962i
$156$	−530.405	−	970.343i	−0.272220	−	0.498011i
$157$		−	1806.57i		−	0.918342i	−0.888348	−	0.459171i	$-0.848147\pi$
$157$		−	1806.57i		−	0.918342i	0.888348	−	0.459171i	$-0.151853\pi$
$158$	−503.400	+	2388.25i	−0.253470	+	1.20252i
$159$	−895.597	+	1165.78i	−0.446701	+	0.581460i
$160$	1129.83	−	1679.13i	0.558258	−	0.829667i
$161$			893.066i			0.437164i
$162$	1961.39	−	635.992i	0.951242	−	0.308446i
$163$	−3096.90			−1.48815			−0.744075	−	0.668097i	$-0.767109\pi$
$163$	−3096.90			−1.48815			−0.744075	+	0.668097i	$0.767109\pi$
$164$	−44.3274	+	100.478i	−0.0211060	+	0.0478417i
$165$	3446.66	+	729.780i	1.62620	+	0.344323i
$166$	311.710	−	1478.83i	0.145743	−	0.691441i
$167$			434.556i			0.201359i	0.994919	+	0.100679i	$0.0321017\pi$
$167$			434.556i			0.201359i	−0.994919	+	0.100679i	$0.967898\pi$
$168$	−1142.24	+	343.971i	−0.524556	+	0.157964i
$169$	1489.31			0.677882
$170$	242.959	+	998.530i	0.109612	+	0.450493i
$171$	−2787.07	+	743.359i	−1.24639	+	0.332433i
$172$	530.935	+	234.229i	0.235369	+	0.103836i
$173$	271.380			0.119264			0.0596320	−	0.998220i	$-0.481007\pi$
$173$	271.380			0.119264			0.0596320	+	0.998220i	$0.481007\pi$
$174$	−973.831	−	1137.62i	−0.424287	−	0.495647i
$175$	−795.439	+	987.769i	−0.343597	+	0.426676i
$176$	2616.56	+	2866.57i	1.12063	+	1.22771i
$177$	−2160.44	+	2812.19i	−0.917449	+	1.19422i
$178$	−296.187	+	1405.18i	−0.124720	+	0.591701i
$179$	−546.931			−0.228377			−0.114189	−	0.993459i	$-0.536427\pi$
$179$	−546.931			−0.228377			−0.114189	+	0.993459i	$0.536427\pi$
$180$	2313.02	−	694.234i	0.957789	−	0.287473i
$181$	1527.78			0.627398			0.313699	−	0.949522i	$-0.398432\pi$
$181$	1527.78			0.627398			0.313699	+	0.949522i	$0.398432\pi$
$182$	−157.453	+	746.993i	−0.0641273	+	0.304235i
$183$	444.031	−	577.985i	0.179365	−	0.233475i
$184$	1162.48	−	1617.29i	0.465757	−	0.647978i
$185$	−3344.68	+	1600.92i	−1.32922	+	0.636227i
$186$	−989.463	−	1155.88i	−0.390059	−	0.455662i
$187$	−1970.77			−0.770678
$188$	1497.79	−	3395.09i	0.581052	−	1.31709i
$189$	−1314.13	−	546.987i	−0.505761	−	0.210516i
$190$	−3282.59	+	798.709i	−1.25339	+	0.304971i
$191$	−2228.71			−0.844313			−0.422157	−	0.906523i	$-0.638727\pi$
$191$	−2228.71			−0.844313			−0.422157	+	0.906523i	$0.638727\pi$
$192$	2516.26	+	863.911i	0.945808	+	0.324726i
$193$		−	3869.72i		−	1.44326i	−0.692280	−	0.721629i	$-0.743394\pi$
$193$		−	3869.72i		−	1.44326i	0.692280	−	0.721629i	$-0.256606\pi$
$194$	−219.560	+	1041.65i	−0.0812550	+	0.385494i
$195$	320.133	−	1511.95i	0.117565	−	0.555245i
$196$	−1757.10	−	775.170i	−0.640343	−	0.282496i
$197$	537.447			0.194373			0.0971866	−	0.995266i	$-0.469016\pi$
$197$	537.447			0.194373			0.0971866	+	0.995266i	$0.469016\pi$
$198$	244.918	+	4624.72i	0.0879068	+	1.65992i
$199$			2479.16i			0.883129i	0.897230	+	0.441565i	$0.145576\pi$
$199$			2479.16i			0.883129i	−0.897230	+	0.441565i	$0.854424\pi$
$200$	2726.24	−	753.385i	0.963873	−	0.266362i
$201$	−1630.44	+	2122.30i	−0.572150	+	0.744754i
$202$	−247.149	+	1172.54i	−0.0860860	+	0.408413i
$203$			1033.78i			0.357426i
$204$	−1185.37	+	647.941i	−0.406825	+	0.222377i
$205$	−138.439	+	66.2635i	−0.0471659	+	0.0225758i
$206$	−1189.50	−	250.724i	−0.402311	−	0.0847998i
$207$	2296.34	−	612.474i	0.771047	−	0.205652i
$208$	1257.48	−	1147.81i	0.419185	−	0.382625i
$209$		−	6478.75i		−	2.14423i
$210$	−1524.68	−	674.298i	−0.501014	−	0.221576i
$211$		−	3488.00i		−	1.13803i	−0.822328	−	0.569013i	$-0.807325\pi$
$211$		−	3488.00i		−	1.13803i	0.822328	−	0.569013i	$-0.192675\pi$
$212$	−2070.77	−	913.551i	−0.670855	−	0.295957i
$213$	122.623	−	159.615i	0.0394459	−	0.0513458i
$214$	507.011	−	2405.38i	0.161956	−	0.768357i
$215$	350.141	+	731.523i	0.111067	+	0.232044i
$216$	1667.81	+	2701.13i	0.525370	+	0.850874i
$217$			1050.38i			0.328591i
$218$	3492.68	+	736.194i	1.08511	+	0.228722i
$219$	3080.91	+	2366.88i	0.950633	+	0.730315i
$220$	167.784	+	5421.53i	0.0514182	+	1.66145i
$221$			864.517i			0.263139i
$222$	−3169.83	−	3702.96i	−0.958311	−	1.11949i
$223$	4214.05			1.26544			0.632722	−	0.774379i	$-0.281938\pi$
$223$	4214.05			1.26544			0.632722	+	0.774379i	$0.281938\pi$
$224$	−931.773	−	1582.68i	−0.277932	−	0.472086i
$225$	3085.37	+	1367.89i	0.914184	+	0.405300i
$226$	2298.58	+	484.498i	0.676545	+	0.142603i
$227$		−	3640.30i		−	1.06438i	−0.846624	−	0.532191i	$-0.821369\pi$
$227$		−	3640.30i		−	1.06438i	0.846624	−	0.532191i	$-0.178631\pi$
$228$	−2130.06	−	3896.81i	−0.618712	−	1.13190i
$229$	1712.27			0.494105			0.247053	−	0.969002i	$-0.420538\pi$
$229$	1712.27			0.494105			0.247053	+	0.969002i	$0.420538\pi$
$230$	2704.62	−	658.078i	0.775378	−	0.188663i
$231$	1947.72	−	2535.30i	0.554766	−	0.722125i
$232$	1345.65	−	1872.12i	0.380803	−	0.529787i
$233$	1914.19			0.538208			0.269104	−	0.963111i	$-0.413272\pi$
$233$	1914.19			0.538208			0.269104	+	0.963111i	$0.413272\pi$
$234$	2028.73	−	107.438i	0.566761	−	0.0300147i
$235$	4677.77	−	2239.00i	1.29848	−	0.621515i
$236$	−4995.30	−	2203.75i	−1.37782	−	0.607846i
$237$	−3555.75	−	2731.67i	−0.974560	−	0.748696i
$238$	912.525	+	192.344i	0.248530	+	0.0523856i
$239$	5491.09			1.48615			0.743074	−	0.669210i	$-0.233367\pi$
$239$	5491.09			1.48615			0.743074	+	0.669210i	$0.233367\pi$
$240$	1883.39	+	3205.75i	0.506550	+	0.862210i
$241$	−3983.47			−1.06472			−0.532360	−	0.846518i	$-0.678695\pi$
$241$	−3983.47			−1.06472			−0.532360	+	0.846518i	$0.678695\pi$
$242$	−6494.61	−	1368.95i	−1.72516	−	0.363633i
$243$	−505.224	+	3754.15i	−0.133375	+	0.991066i
$244$	1026.68	+	452.933i	0.269370	+	0.118836i
$245$	−1158.77	−	2420.94i	−0.302169	−	0.631299i
$246$	−131.202	−	153.269i	−0.0340046	−	0.0397238i
$247$	−2842.03			−0.732122
$248$	1367.25	−	1902.17i	0.350083	−	0.487048i
$249$	2201.75	+	1691.48i	0.560363	+	0.430494i
$250$	3577.56	+	1681.09i	0.905059	+	0.425287i
$251$	2069.53			0.520429			0.260214	−	0.965551i	$-0.416207\pi$
$251$	2069.53			0.520429			0.260214	+	0.965551i	$0.416207\pi$
$252$	337.961	−	2165.29i	0.0844822	−	0.541271i
$253$			5338.02i			1.32648i
$254$	−6229.39	−	1313.04i	−1.53885	−	0.324361i
$255$	−1846.99	−	391.073i	−0.453580	−	0.0960390i
$256$	−372.754	+	4079.00i	−0.0910043	+	0.995850i
$257$	5701.62			1.38388			0.691941	−	0.721954i	$-0.256756\pi$
$257$	5701.62			1.38388			0.691941	+	0.721954i	$0.256756\pi$
$258$	−809.883	+	693.281i	−0.195431	+	0.167294i
$259$			3364.98i			0.807295i
$260$	2378.26	−	73.6018i	0.567283	−	0.0175561i
$261$	2658.17	−	708.980i	0.630408	−	0.168141i
$262$	−2544.33	−	536.298i	−0.599959	−	0.126460i
$263$		−	696.459i		−	0.163291i	−0.996661	−	0.0816454i	$-0.973982\pi$
$263$		−	696.459i		−	0.163291i	0.996661	−	0.0816454i	$-0.0260175\pi$
$264$	−6827.35	+	2055.98i	−1.59165	+	0.479305i
$265$	−1365.64	−	2853.12i	−0.316567	−	0.661380i
$266$	−632.315	+	2999.85i	−0.145751	+	0.691477i
$267$	−2092.11	−	1607.24i	−0.479531	−	0.368395i
$268$	−3769.85	−	1663.12i	−0.859255	−	0.379072i
$269$			5735.01i			1.29989i	0.759983	+	0.649943i	$0.225207\pi$
$269$			5735.01i			1.29989i	−0.759983	+	0.649943i	$0.774793\pi$
$270$	−688.180	+	4382.85i	−0.155116	+	0.987896i
$271$		−	1811.73i		−	0.406106i	−0.979168	−	0.203053i	$-0.934914\pi$
$271$		−	1811.73i		−	0.406106i	0.979168	−	0.203053i	$-0.0650864\pi$
$272$	−1402.16	−	1536.13i	−0.312567	−	0.342433i
$273$	−1112.16	−	854.408i	−0.246561	−	0.189418i
$274$	−6150.56	−	1296.43i	−1.35609	−	0.285839i
$275$	−4754.48	+	5904.07i	−1.04257	+	1.29465i
$276$	1755.01	+	3210.68i	0.382751	+	0.700219i
$277$			4779.08i			1.03663i	0.855189	+	0.518316i	$0.173441\pi$
$277$			4779.08i			1.03663i	−0.855189	+	0.518316i	$0.826559\pi$
$278$	−409.031	+	1940.54i	−0.0882449	+	0.418655i
$279$	2700.84	−	720.360i	0.579552	−	0.154577i
$280$	451.443	−	2526.71i	0.0963532	−	0.539284i
$281$		−	5577.24i		−	1.18402i	−0.805930	−	0.592011i	$-0.798334\pi$
$281$		−	5577.24i		−	1.18402i	0.805930	−	0.592011i	$-0.201666\pi$
$282$	4433.23	+	5178.84i	0.936152	+	1.09360i
$283$	2022.56			0.424836			0.212418	−	0.977179i	$-0.431866\pi$
$283$	2022.56			0.424836			0.212418	+	0.977179i	$0.431866\pi$
$284$	283.525	+	125.081i	0.0592398	+	0.0261345i
$285$	1285.62	−	6071.83i	0.267206	−	1.26198i
$286$	−941.123	+	4464.92i	−0.194580	+	0.923133i
$287$			139.279i			0.0286460i
$288$	−3430.53	+	3481.29i	−0.701895	+	0.712280i
$289$	−3856.91			−0.785042
$290$	3130.77	−	761.770i	0.633950	−	0.154251i
$291$	−1550.85	−	1191.43i	−0.312415	−	0.240010i
$292$	−2414.33	+	5472.63i	−0.483862	+	1.09679i
$293$	−5482.49			−1.09314			−0.546571	−	0.837413i	$-0.684067\pi$
$293$	−5482.49			−1.09314			−0.546571	+	0.837413i	$0.684067\pi$
$294$	2680.27	−	2294.38i	0.531688	−	0.455139i
$295$	−3294.30	−	6882.54i	−0.650175	−	1.35836i
$296$	4380.11	−	6093.77i	0.860097	−	1.19660i
$297$	−7854.80	−	3269.44i	−1.53462	−	0.638762i
$298$	1725.65	−	8186.93i	0.335451	−	1.59146i
$299$	2341.63			0.452909
$300$	−918.586	+	5114.31i	−0.176782	+	0.984250i
$301$	735.962			0.140931
$302$	381.379	−	1809.36i	0.0726686	−	0.344757i
$303$	−1745.73	−	1341.14i	−0.330989	−	0.254279i
$304$	5049.92	−	4609.48i	0.952739	−	0.869645i
$305$	677.073	+	1414.56i	0.127112	+	0.265565i
$306$	−131.246	−	2478.29i	−0.0245191	−	0.462987i
$307$	265.688			0.0493928			0.0246964	−	0.999695i	$-0.492138\pi$
$307$	265.688			0.0493928			0.0246964	+	0.999695i	$0.492138\pi$
$308$	4503.47	+	1986.77i	0.833146	+	0.367554i
$309$	1360.54	−	1770.98i	0.250480	−	0.326044i
$310$	3181.03	−	773.998i	0.582808	−	0.141807i
$311$	−3245.26			−0.591710			−0.295855	−	0.955233i	$-0.595605\pi$
$311$	−3245.26			−0.591710			−0.295855	+	0.955233i	$0.595605\pi$
$312$	901.895	+	2994.95i	0.163653	+	0.543448i
$313$			8006.59i			1.44588i	0.690913	+	0.722938i	$0.257209\pi$
$313$			8006.59i			1.44588i	−0.690913	+	0.722938i	$0.742791\pi$
$314$	−1053.88	+	4999.88i	−0.189408	+	0.898597i
$315$	2328.49	−	1989.57i	0.416494	−	0.355871i
$316$	2786.43	−	6316.09i	0.496041	−	1.12439i
$317$	3886.31			0.688571			0.344286	−	0.938865i	$-0.388121\pi$
$317$	3886.31			0.688571			0.344286	+	0.938865i	$0.388121\pi$
$318$	3158.74	−	2703.96i	0.557023	−	0.476826i
$319$			6179.11i			1.08453i
$320$	−4106.49	+	3988.08i	−0.717374	+	0.696688i
$321$	3581.26	+	2751.27i	0.622698	+	0.478382i
$322$	520.981	−	2471.66i	0.0901651	−	0.427765i
$323$			3471.82i			0.598072i
$324$	−5799.38	+	615.979i	−0.994407	+	0.105621i
$325$	2589.94	+	2085.65i	0.442043	+	0.355972i
$326$	8571.04	+	1806.62i	1.45615	+	0.306931i
$327$	−3994.92	+	5200.09i	−0.675595	+	0.879405i
$328$	181.296	−	252.226i	0.0305196	−	0.0424599i
$329$		−	4706.15i		−	0.788628i
$330$	−9113.30	−	4030.40i	−1.52021	−	0.672323i
$331$			7805.76i			1.29620i	0.761554	+	0.648102i	$0.224437\pi$
$331$			7805.76i			1.29620i	−0.761554	+	0.648102i	$0.775563\pi$
$332$	−1725.38	+	3910.98i	−0.285219	+	0.646515i
$333$	8652.36	−	2307.74i	1.42386	−	0.379769i
$334$	253.504	−	1202.68i	0.0415302	−	0.197030i
$335$	−2486.14	−	5194.11i	−0.405470	−	0.847118i
$336$	3361.93	−	285.640i	0.545858	−	0.0463778i
$337$		−	4067.26i		−	0.657441i	−0.944427	−	0.328721i	$-0.893383\pi$
$337$		−	4067.26i		−	0.657441i	0.944427	−	0.328721i	$-0.106617\pi$
$338$	−4121.82	−	868.805i	−0.663307	−	0.139813i
$339$	−2629.10	+	3422.24i	−0.421219	+	0.548291i
$340$	−89.9117	−	2905.28i	−0.0143416	−	0.463414i
$341$			6278.30i			0.997036i
$342$	8147.17	−	431.461i	1.28815	−	0.0682185i
$343$	−5915.66			−0.931240
$344$	−1332.78	−	957.984i	−0.208892	−	0.150148i
$345$	−1059.26	+	5002.75i	−0.165300	+	0.780693i
$346$	−751.076	−	158.313i	−0.116700	−	0.0245982i
$347$		−	10980.5i		−	1.69874i	−0.527799	−	0.849369i	$-0.676983\pi$
$347$		−	10980.5i		−	1.69874i	0.527799	−	0.849369i	$-0.323017\pi$
$348$	2031.54	+	3716.58i	0.312937	+	0.572499i
$349$	406.843			0.0624006			0.0312003	−	0.999513i	$-0.490067\pi$
$349$	406.843			0.0624006			0.0312003	+	0.999513i	$0.490067\pi$
$350$	2777.70	−	2269.73i	0.424212	−	0.346635i
$351$	−1434.21	+	3445.66i	−0.218098	+	0.523977i
$352$	−5569.38	−	9459.97i	−0.843321	−	1.43244i
$353$	−3326.30			−0.501533			−0.250766	−	0.968048i	$-0.580683\pi$
$353$	−3326.30			−0.501533			−0.250766	+	0.968048i	$0.580683\pi$
$354$	7619.78	−	6522.73i	1.14403	−	0.979320i
$355$	186.979	+	390.641i	0.0279544	+	0.0584031i
$356$	1639.46	−	3716.22i	0.244077	−	0.553256i
$357$	−1043.74	+	1358.61i	−0.154736	+	0.201416i
$358$	1513.69	+	319.059i	0.223467	+	0.0471028i
$359$	−3871.58			−0.569177			−0.284588	−	0.958650i	$-0.591857\pi$
$359$	−3871.58			−0.569177			−0.284588	+	0.958650i	$0.591857\pi$
$360$	−6806.52	+	572.046i	−0.996487	+	0.0837486i
$361$	−4554.33			−0.663994
$362$	−4228.31	−	891.251i	−0.613909	−	0.129401i
$363$	7428.51	−	9669.51i	1.07409	−	1.39812i
$364$	871.536	−	1975.54i	0.125497	−	0.284468i
$365$	−7540.20	+	3609.09i	−1.08129	+	0.517558i
$366$	−1566.08	+	1340.61i	−0.223662	+	0.191461i
$367$	7716.60			1.09756			0.548778	−	0.835968i	$-0.315093\pi$
$367$	7716.60			1.09756			0.548778	+	0.835968i	$0.315093\pi$
$368$	−4160.77	+	3797.88i	−0.589388	+	0.537984i
$369$	358.129	−	95.5192i	0.0505242	−	0.0134757i
$370$	10190.7	−	2479.57i	1.43186	−	0.348396i
$371$	−2870.43			−0.401686
$372$	2064.15	+	3776.24i	0.287692	+	0.526315i
$373$		−	8334.91i		−	1.15701i	−0.815678	−	0.578506i	$-0.803636\pi$
$373$		−	8334.91i		−	1.15701i	0.815678	−	0.578506i	$-0.196364\pi$
$374$	5454.33	+	1149.67i	0.754108	+	0.158952i
$375$	−5627.45	+	4589.79i	−0.774934	+	0.632042i
$376$	−6125.88	+	8522.55i	−0.840208	+	1.16893i
$377$	2710.59			0.370299
$378$	3317.91	+	2280.46i	0.451468	+	0.310303i
$379$			853.055i			0.115616i	0.998328	+	0.0578080i	$0.0184111\pi$
$379$			853.055i			0.115616i	−0.998328	+	0.0578080i	$0.981589\pi$
$380$	9550.88	−	295.578i	1.28934	−	0.0399022i
$381$	7125.15	−	9274.64i	0.958091	−	1.24712i
$382$	6168.21	+	1300.15i	0.826160	+	0.174139i
$383$			2694.81i			0.359525i	0.983710	+	0.179763i	$0.0575330\pi$
$383$			2694.81i			0.359525i	−0.983710	+	0.179763i	$0.942467\pi$
$384$	−6460.05	−	3858.86i	−0.858498	−	0.512817i
$385$	2969.95	+	6204.89i	0.393150	+	0.821378i
$386$	−2257.45	+	10709.9i	−0.297672	+	1.41223i
$387$	−504.731	−	1892.38i	−0.0662969	−	0.248566i
$388$	1215.31	−	2754.79i	0.159016	−	0.360446i
$389$			4450.40i			0.580062i	0.957017	+	0.290031i	$0.0936656\pi$
$389$			4450.40i			0.580062i	−0.957017	+	0.290031i	$0.906334\pi$
$390$	−1768.02	+	3997.73i	−0.229556	+	0.519059i
$391$		−	2860.52i		−	0.369982i
$392$	4410.78	+	3170.40i	0.568311	+	0.408493i
$393$	2910.19	−	3788.13i	0.373537	−	0.486223i
$394$	−1487.45	−	313.527i	−0.190194	−	0.0400894i
$395$	8702.32	−	4165.34i	1.10851	−	0.530584i
$396$	2020.05	−	12942.3i	0.256342	−	1.64236i
$397$			4828.78i			0.610452i	0.952280	+	0.305226i	$0.0987320\pi$
$397$			4828.78i			0.610452i	−0.952280	+	0.305226i	$0.901268\pi$
$398$	1446.25	−	6861.35i	0.182145	−	0.864141i
$399$	−4466.34	−	3431.22i	−0.560392	−	0.430516i
$400$	−7984.69	+	494.689i	−0.998086	+	0.0618362i
$401$			2653.20i			0.330410i	0.986259	+	0.165205i	$0.0528286\pi$
$401$			2653.20i			0.330410i	−0.986259	+	0.165205i	$0.947171\pi$
$402$	5750.49	−	4922.57i	0.713454	−	0.610735i
$403$	2754.10			0.340426
$404$	1368.03	−	3100.95i	0.168470	−	0.381877i
$405$	−6712.68	−	4622.78i	−0.823594	−	0.567180i
$406$	603.071	−	2861.11i	0.0737190	−	0.349741i
$407$			20113.1i			2.44955i
$408$	3658.63	−	1101.75i	0.443944	−	0.133688i
$409$	9622.36			1.16331			0.581656	−	0.813435i	$-0.302405\pi$
$409$	9622.36			1.16331			0.581656	+	0.813435i	$0.302405\pi$
$410$	421.802	−	102.631i	0.0508081	−	0.0123625i
$411$	7034.99	−	9157.27i	0.844308	−	1.09901i
$412$	3145.80	+	1387.81i	0.376171	+	0.165953i
$413$	−6924.30			−0.824994
$414$	−6712.68	+	355.492i	−0.796884	+	0.0422017i
$415$	−5388.56	+	2579.21i	−0.637383	+	0.305081i
$416$	−4149.81	+	2443.12i	−0.489089	+	0.287942i
$417$	−2889.18	−	2219.59i	−0.339290	−	0.260656i
$418$	−3779.46	+	17930.7i	−0.442248	+	2.09813i
$419$	3631.36			0.423397			0.211699	−	0.977335i	$-0.432101\pi$
$419$	3631.36			0.423397			0.211699	+	0.977335i	$0.432101\pi$
$420$	3826.37	+	2755.64i	0.444542	+	0.320146i
$421$	−15559.0			−1.80118			−0.900590	−	0.434669i	$-0.856865\pi$
$421$	−15559.0			−1.80118			−0.900590	+	0.434669i	$0.856865\pi$
$422$	−2034.77	+	9653.43i	−0.234718	+	1.11356i
$423$	−12100.9	+	3227.53i	−1.39094	+	0.370988i
$424$	5198.17	+	3736.37i	0.595390	+	0.427958i
$425$	2547.82	−	3163.86i	0.290794	−	0.361106i
$426$	−432.486	+	370.220i	−0.0491879	+	0.0421061i
$427$	1423.14			0.161289
$428$	−2806.42	+	6361.40i	−0.316947	+	0.718434i
$429$	−6647.60	−	5106.95i	−0.748133	−	0.574746i
$430$	−542.312	−	2228.83i	−0.0608201	−	0.249963i
$431$	4417.12			0.493655			0.246827	−	0.969059i	$-0.420612\pi$
$431$	4417.12			0.493655			0.246827	+	0.969059i	$0.420612\pi$
$432$	−3040.11	−	8448.63i	−0.338582	−	0.940937i
$433$		−	3854.20i		−	0.427763i	−0.976860	−	0.213881i	$-0.931389\pi$
$433$		−	3854.20i		−	0.427763i	0.976860	−	0.213881i	$-0.0686106\pi$
$434$	612.752	−	2907.04i	0.0677719	−	0.321526i
$435$	−1226.16	+	5791.02i	−0.135150	+	0.638295i
$436$	−9236.93	−	4075.00i	−1.01461	−	0.447608i
$437$	9403.76			1.02939
$438$	−7146.02	−	8347.90i	−0.779566	−	0.910680i
$439$		−	16486.5i		−	1.79239i	−0.443665	−	0.896193i	$-0.646322\pi$
$439$		−	16486.5i		−	1.79239i	0.443665	−	0.896193i	$-0.353678\pi$
$440$	2698.36	−	15102.6i	0.292362	−	1.63634i
$441$	1670.38	+	6262.73i	0.180367	+	0.676248i
$442$	504.327	−	2392.65i	0.0542724	−	0.257481i
$443$		−	5122.20i		−	0.549352i	−0.961537	−	0.274676i	$-0.911429\pi$
$443$		−	5122.20i		−	0.549352i	0.961537	−	0.274676i	$-0.0885706\pi$
$444$	6612.70	+	12097.5i	0.706812	+	1.29307i
$445$	5120.21	−	2450.77i	0.545441	−	0.261074i
$446$	−11662.9	−	2458.32i	−1.23824	−	0.260998i
$447$	12189.1	+	9364.17i	1.28977	+	0.990851i
$448$	1655.51	+	4923.81i	0.174588	+	0.519259i
$449$		−	3046.09i		−	0.320165i	−0.987104	−	0.160082i	$-0.948824\pi$
$449$		−	3046.09i		−	0.320165i	0.987104	−	0.160082i	$-0.0511760\pi$
$450$	−7741.14	−	5585.68i	−0.810935	−	0.585136i
$451$			832.498i			0.0869197i
$452$	−6078.94	−	2681.81i	−0.632587	−	0.279075i
$453$	2693.86	+	2069.53i	0.279401	+	0.214647i
$454$	−2123.61	+	10074.9i	−0.219529	+	1.04150i
$455$	2721.90	−	1302.83i	0.280450	−	0.134236i
$456$	3621.92	+	12027.5i	0.371956	+	1.23517i
$457$			1758.56i			0.180005i	0.995942	+	0.0900024i	$0.0286875\pi$
$457$			1758.56i			0.180005i	−0.995942	+	0.0900024i	$0.971313\pi$
$458$	−4738.91	−	998.876i	−0.483482	−	0.101909i
$459$	4209.21	+	1752.02i	0.428037	+	0.178164i
$460$	−7869.23	+	243.535i	−0.797619	+	0.0246845i
$461$			1735.36i			0.175323i	0.996150	+	0.0876615i	$0.0279394\pi$
$461$			1735.36i			0.175323i	−0.996150	+	0.0876615i	$0.972061\pi$
$462$	−6869.55	+	5880.52i	−0.691776	+	0.592178i
$463$	−8790.53			−0.882356			−0.441178	−	0.897420i	$-0.645439\pi$
$463$	−8790.53			−0.882356			−0.441178	+	0.897420i	$0.645439\pi$
$464$	−4816.37	+	4396.30i	−0.481884	+	0.439856i
$465$	−1245.85	+	5883.98i	−0.124247	+	0.586802i
$466$	−5297.73	−	1116.66i	−0.526636	−	0.111005i
$467$		−	1018.39i		−	0.100911i	−0.998726	−	0.0504555i	$-0.983933\pi$
$467$		−	1018.39i		−	0.100911i	0.998726	−	0.0504555i	$-0.0160673\pi$
$468$	−5677.41	−	886.136i	−0.560765	−	0.0875249i
$469$	−5225.63			−0.514493
$470$	−14252.4	+	3467.85i	−1.39875	+	0.340340i
$471$	−7444.07	−	5718.84i	−0.728248	−	0.559470i
$472$	12539.5	+	9013.19i	1.22283	+	0.878953i
$473$	4398.98			0.427622
$474$	8247.39	+	9634.50i	0.799188	+	0.933602i
$475$	10401.0	+	8375.77i	1.00469	+	0.809067i
$476$	−2413.31	−	1064.67i	−0.232382	−	0.102519i
$477$	1968.57	+	7380.74i	0.188962	+	0.708471i
$478$	−15197.2	−	3203.30i	−1.45419	−	0.306518i
$479$	−5766.28			−0.550038			−0.275019	−	0.961439i	$-0.588684\pi$
$479$	−5766.28			−0.550038			−0.275019	+	0.961439i	$0.588684\pi$
$480$	−3342.37	−	9970.99i	−0.317829	−	0.948148i
$481$	8823.01			0.836371
$482$	11024.7	+	2323.81i	1.04183	+	0.219599i
$483$	3679.94	+	2827.08i	0.346673	+	0.266328i
$484$	17176.0	+	7577.43i	1.61307	+	0.711629i
$485$	3795.55	−	1816.73i	0.355355	−	0.170090i
$486$	3588.30	−	10095.3i	0.334915	−	0.942249i
$487$	−3402.19			−0.316567			−0.158283	−	0.987394i	$-0.550596\pi$
$487$	−3402.19			−0.316567			−0.158283	+	0.987394i	$0.550596\pi$
$488$	−2577.22	−	1852.47i	−0.239068	−	0.171839i
$489$	−9803.52	+	12761.0i	−0.906606	+	1.18011i
$490$	1794.76	+	7376.21i	0.165467	+	0.680048i
$491$	3300.40			0.303350			0.151675	−	0.988430i	$-0.451533\pi$
$491$	3300.40			0.303350			0.151675	+	0.988430i	$0.451533\pi$
$492$	273.705	+	500.727i	0.0250805	+	0.0458831i
$493$		−	3311.25i		−	0.302497i
$494$	7865.65	+	1657.94i	0.716381	+	0.151000i
$495$	13917.8	−	11892.0i	1.26376	−	1.07981i
$496$	−4893.68	+	4466.87i	−0.443010	+	0.404372i
$497$	393.012			0.0354708
$498$	−5106.86	−	5965.77i	−0.459525	−	0.536812i
$499$		−	16943.3i		−	1.52001i	−0.649916	−	0.760006i	$-0.725196\pi$
$499$		−	16943.3i		−	1.52001i	0.649916	−	0.760006i	$-0.274804\pi$
$500$	−8920.61	−	6739.63i	−0.797884	−	0.602811i
$501$	1790.62	+	1375.62i	0.159678	+	0.122671i
$502$	−5727.66	−	1207.29i	−0.509239	−	0.107338i
$503$			201.636i			0.0178738i	0.999960	+	0.00893689i	$0.00284474\pi$
$503$			201.636i			0.0178738i	−0.999960	+	0.00893689i	$0.997155\pi$
$504$	−2198.49	+	5795.53i	−0.194303	+	0.512209i
$505$	4272.50	−	2045.02i	0.376483	−	0.180202i
$506$	3114.00	−	14773.6i	0.273585	−	1.29796i
$507$	4714.53	−	6136.78i	0.412977	−	0.537562i
$508$	16474.6	+	7267.99i	1.43886	+	0.634773i
$509$			2473.61i			0.215404i	0.994183	+	0.107702i	$0.0343493\pi$
$509$			2473.61i			0.215404i	−0.994183	+	0.107702i	$0.965651\pi$
$510$	4883.62	+	2159.80i	0.424020	+	0.187525i
$511$			7585.96i			0.656718i
$512$	3411.18	−	11071.7i	0.294442	−	0.955669i
$513$	−5759.64	+	13837.5i	−0.495700	+	1.19091i
$514$	−15779.9	−	3326.11i	−1.35413	−	0.285425i
$515$	2074.59	+	4334.29i	0.177510	+	0.370858i
$516$	2645.88	−	1446.28i	0.225733	−	0.123389i
$517$		−	28129.5i		−	2.39291i
$518$	1963.00	−	9312.96i	0.166505	−	0.789938i
$519$	859.078	−	1118.24i	0.0726577	−	0.0945767i
$520$	−6625.05	−	1183.69i	−0.558707	−	0.0998234i
$521$		−	21437.8i		−	1.80270i	−0.433088	−	0.901352i	$-0.642576\pi$
$521$		−	21437.8i		−	1.80270i	0.433088	−	0.901352i	$-0.357424\pi$
$522$	−7770.37	+	411.506i	−0.651533	+	0.0345041i
$523$	19708.2			1.64776			0.823880	−	0.566764i	$-0.191805\pi$
$523$	19708.2			1.64776			0.823880	+	0.566764i	$0.191805\pi$
$524$	6728.87	+	2968.53i	0.560977	+	0.247483i
$525$	1552.14	+	6404.53i	0.129030	+	0.532412i
$526$	−406.288	+	1927.53i	−0.0336787	+	0.159780i
$527$		−	3364.40i		−	0.278094i
$528$	20094.9	−	1707.32i	1.65628	−	0.140723i
$529$	4418.99			0.363195
$530$	2115.15	+	8692.99i	0.173351	+	0.712451i
$531$	4748.76	+	17804.5i	0.388095	+	1.45508i
$532$	3500.01	−	7933.57i	0.285234	−	0.646549i
$533$	365.192			0.0296777
$534$	4852.54	+	5668.68i	0.393240	+	0.459378i
$535$	−8764.75	+	4195.22i	−0.708286	+	0.339019i
$536$	9463.29	+	6802.07i	0.762597	+	0.548143i
$537$	−1731.36	+	2253.66i	−0.139131	+	0.181104i
$538$	3345.59	−	15872.3i	0.268101	−	1.27194i
$539$	−14558.2			−1.16339
$540$	4461.41	−	11728.6i	0.355534	−	0.934663i
$541$	2853.73			0.226786			0.113393	−	0.993550i	$-0.463828\pi$
$541$	2853.73			0.226786			0.113393	+	0.993550i	$0.463828\pi$
$542$	−1056.89	+	5014.17i	−0.0837593	+	0.397374i
$543$	4836.32	−	6295.33i	0.382222	−	0.497529i
$544$	2984.51	+	5069.39i	0.235220	+	0.399537i
$545$	−6091.58	−	12726.7i	−0.478779	−	1.00028i
$546$	2579.61	+	3013.47i	0.202192	+	0.236199i
$547$	−14147.4			−1.10585			−0.552925	−	0.833231i	$-0.686488\pi$
$547$	−14147.4			−1.10585			−0.552925	+	0.833231i	$0.686488\pi$
$548$	16266.1	+	7176.02i	1.26798	+	0.559387i
$549$	−976.005	−	3659.32i	−0.0758741	−	0.284474i
$550$	16602.8	−	13566.6i	1.28717	−	1.05179i
$551$	10885.5			0.841628
$552$	−2984.20	−	9909.74i	−0.230101	−	0.764106i
$553$		−	8755.13i		−	0.673248i
$554$	2787.94	−	13226.6i	0.213805	−	1.01434i
$555$	−3991.18	+	18849.8i	−0.305254	+	1.44168i
$556$	2264.08	−	5132.06i	0.172695	−	0.391453i
$557$	−20821.7			−1.58392			−0.791961	−	0.610572i	$-0.790940\pi$
$557$	−20821.7			−1.58392			−0.791961	+	0.610572i	$0.790940\pi$
$558$	−7895.11	+	418.112i	−0.598972	+	0.0317206i
$559$		−	1929.70i		−	0.146007i
$560$	−2723.41	+	6729.59i	−0.205509	+	0.507817i
$561$	−6238.64	+	8120.68i	−0.469511	+	0.611150i
$562$	−3253.55	+	15435.6i	−0.244204	+	1.15857i
$563$			3815.65i			0.285632i	0.989749	+	0.142816i	$0.0456156\pi$
$563$			3815.65i			0.285632i	−0.989749	+	0.142816i	$0.954384\pi$
$564$	−9248.31	−	16919.2i	−0.690469	−	1.26317i
$565$	−4008.94	−	8375.58i	−0.298509	−	0.623652i
$566$	−5597.66	−	1179.88i	−0.415701	−	0.0876223i
$567$	−6413.89	+	3683.42i	−0.475058	+	0.272821i
$568$	−711.720	−	511.574i	−0.0525759	−	0.0377908i
$569$			5759.80i			0.424364i	0.977230	+	0.212182i	$0.0680570\pi$
$569$			5759.80i			0.424364i	−0.977230	+	0.212182i	$0.931943\pi$
$570$	−7100.19	+	16054.5i	−0.521744	+	1.17974i
$571$			12487.9i			0.915243i	0.889147	+	0.457622i	$0.151299\pi$
$571$			12487.9i			0.915243i	−0.889147	+	0.457622i	$0.848701\pi$
$572$	5209.33	−	11808.1i	0.380792	−	0.863153i
$573$	−7055.17	+	9183.55i	−0.514370	+	0.669543i
$574$	81.2503	−	385.471i	0.00590823	−	0.0280301i
$575$	−8569.63	−	6901.02i	−0.621527	−	0.500509i
$576$	11525.2	−	7633.62i	0.833712	−	0.552200i
$577$			13874.2i			1.00103i	0.865729	+	0.500513i	$0.166855\pi$
$577$			13874.2i			1.00103i	−0.865729	+	0.500513i	$0.833145\pi$
$578$	10674.4	+	2249.98i	0.768163	+	0.161915i
$579$	−15945.5	−	12249.9i	−1.14451	−	0.879258i
$580$	−9109.16	+	281.908i	−0.652133	+	0.0201820i
$581$			5421.26i			0.387111i
$582$	3597.13	+	4202.13i	0.256196	+	0.299285i
$583$	−17157.1			−1.21882
$584$	9874.46	−	13737.7i	0.699671	−	0.973408i
$585$	−5216.67	−	6105.33i	−0.368688	−	0.431494i
$586$	15173.4	+	3198.28i	1.06964	+	0.225460i
$587$		−	23978.8i		−	1.68605i	−0.537876	−	0.843024i	$-0.680773\pi$
$587$		−	23978.8i		−	1.68605i	0.537876	−	0.843024i	$-0.319227\pi$
$588$	−8756.40	+	4786.39i	−0.614129	+	0.335693i
$589$	11060.2			0.773732
$590$	5102.35	+	20970.0i	0.356034	+	1.46325i
$591$	1701.34	−	2214.59i	0.118416	−	0.154139i
$592$	−15677.3	+	14310.0i	−1.08840	+	0.993475i
$593$	13248.3			0.917444			0.458722	−	0.888580i	$-0.348307\pi$
$593$	13248.3			0.917444			0.458722	+	0.888580i	$0.348307\pi$
$594$	19831.8	+	13630.8i	1.36988	+	0.941543i
$595$	−1591.53	−	3325.06i	−0.109658	−	0.229100i
$596$	−9551.89	+	21651.6i	−0.656478	+	1.48806i
$597$	10215.5	+	7847.98i	0.700324	+	0.538018i
$598$	−6480.72	−	1366.02i	−0.443171	−	0.0934125i
$599$	−24565.3			−1.67564			−0.837821	−	0.545945i	$-0.816171\pi$
$599$	−24565.3			−1.67564			−0.837821	+	0.545945i	$0.816171\pi$
$600$	5525.79	−	13618.6i	0.375982	−	0.926627i
$601$	12505.7			0.848783			0.424391	−	0.905479i	$-0.360488\pi$
$601$	12505.7			0.848783			0.424391	+	0.905479i	$0.360488\pi$
$602$	−2036.86	−	429.333i	−0.137901	−	0.0290670i
$603$	3583.79	+	13436.7i	0.242029	+	0.907434i
$604$	−2111.02	+	4785.12i	−0.142212	+	0.322357i
$605$	11327.2	+	23665.1i	0.761185	+	1.59029i
$606$	4049.14	+	4730.16i	0.271428	+	0.317079i
$607$	11338.5			0.758178			0.379089	−	0.925360i	$-0.376237\pi$
$607$	11338.5			0.758178			0.379089	+	0.925360i	$0.376237\pi$
$608$	−16665.2	+	9811.33i	−1.11162	+	0.654444i
$609$	4259.77	+	3272.53i	0.283440	+	0.217750i
$610$	−1048.68	−	4309.93i	−0.0696061	−	0.286072i
$611$	−12339.6			−0.817031
$612$	−1082.50	+	6935.50i	−0.0714992	+	0.458090i
$613$			24675.9i			1.62586i	0.582363	+	0.812929i	$0.302128\pi$
$613$			24675.9i			1.62586i	−0.582363	+	0.812929i	$0.697872\pi$
$614$	−735.321	−	154.992i	−0.0483309	−	0.0101873i
$615$	−165.198	+	780.211i	−0.0108316	+	0.0511563i
$616$	−11304.9	−	8125.77i	−0.739425	−	0.531488i
$617$	5028.91			0.328130			0.164065	−	0.986450i	$-0.447539\pi$
$617$	5028.91			0.328130			0.164065	+	0.986450i	$0.447539\pi$
$618$	−4798.57	+	4107.70i	−0.312341	+	0.267372i
$619$			7223.88i			0.469067i	0.972108	+	0.234533i	$0.0753562\pi$
$619$			7223.88i			0.469067i	−0.972108	+	0.234533i	$0.924644\pi$
$620$	−9255.39	+	286.433i	−0.599525	+	0.0185539i
$621$	4745.52	−	11401.1i	0.306653	−	0.736729i
$622$	8981.63	+	1893.16i	0.578988	+	0.122040i
$623$		−	5151.28i		−	0.331271i
$624$	−748.952	−	8815.01i	−0.0480482	−	0.565517i
$625$	−3331.75	−	15265.7i	−0.213232	−	0.977002i
$626$	4670.74	−	22159.1i	0.298212	−	1.41479i
$627$	−26696.1	−	20509.0i	−1.70038	−	1.30630i
$628$	5833.48	−	13222.9i	0.370671	−	0.840211i
$629$		−	10778.2i		−	0.683232i
$630$	−7605.00	+	4148.00i	−0.480937	+	0.262318i
$631$			2946.15i			0.185871i	0.995672	+	0.0929353i	$0.0296250\pi$
$631$			2946.15i			0.185871i	−0.995672	+	0.0929353i	$0.970375\pi$
$632$	−11396.3	+	15855.0i	−0.717282	+	0.997908i
$633$	−14372.5	−	11041.6i	−0.902458	−	0.693305i
$634$	−10755.8	−	2267.13i	−0.673766	−	0.142018i
$635$	10864.7	+	22698.7i	0.678978	+	1.41854i
$636$	−10319.6	+	5640.84i	−0.643392	+	0.351688i
$637$			6386.25i			0.397225i
$638$	3604.66	−	17101.4i	0.223683	−	1.06121i
$639$	−269.532	−	1010.55i	−0.0166862	−	0.0625615i
$640$	13691.7	−	8641.89i	0.845642	−	0.533751i
$641$			17750.3i			1.09375i	0.837213	+	0.546876i	$0.184183\pi$
$641$			17750.3i			1.09375i	−0.837213	+	0.546876i	$0.815817\pi$
$642$	−8306.55	−	9703.61i	−0.510644	−	0.596528i
$643$	−8831.62			−0.541656			−0.270828	−	0.962628i	$-0.587298\pi$
$643$	−8831.62			−0.541656			−0.270828	+	0.962628i	$0.587298\pi$
$644$	−2883.75	+	6536.68i	−0.176453	+	0.399971i
$645$	4122.69	+	872.920i	0.251676	+	0.0532887i
$646$	2025.33	−	9608.65i	0.123352	−	0.585213i
$647$			21358.0i			1.29779i	0.760878	+	0.648895i	$0.224768\pi$
$647$			21358.0i			1.29779i	−0.760878	+	0.648895i	$0.775232\pi$
$648$	16409.8	+	1678.35i	0.994810	+	0.101747i
$649$	−41387.8			−2.50326
$650$	−5951.27	−	7283.15i	−0.359120	−	0.439490i
$651$	4328.15	+	3325.06i	0.260574	+	0.200184i
$652$	−22667.4	−	10000.0i	−1.36154	−	0.600663i
$653$	11411.2			0.683852			0.341926	−	0.939727i	$-0.388921\pi$
$653$	11411.2			0.683852			0.341926	+	0.939727i	$0.388921\pi$
$654$	14089.9	−	12061.3i	0.842446	−	0.721156i
$655$	4437.56	+	9271.05i	0.264717	+	0.553053i
$656$	−648.898	+	592.303i	−0.0386207	+	0.0352524i
$657$	19505.8	−	5202.53i	1.15828	−	0.308934i
$658$	−2745.39	+	13024.8i	−0.162654	+	0.771672i
$659$	19101.5			1.12912			0.564558	−	0.825393i	$-0.309047\pi$
$659$	19101.5			1.12912			0.564558	+	0.825393i	$0.309047\pi$
$660$	22870.9	+	16471.0i	1.34886	+	0.971411i
$661$	−4480.69			−0.263659			−0.131830	−	0.991272i	$-0.542085\pi$
$661$	−4480.69			−0.263659			−0.131830	+	0.991272i	$0.542085\pi$
$662$	4553.59	−	21603.3i	0.267342	−	1.26833i
$663$	3562.30	+	2736.70i	0.208670	+	0.160309i
$664$	7056.72	−	9817.56i	0.412430	−	0.573788i
$665$	10930.9	−	5232.03i	0.637416	−	0.305097i
$666$	−25292.7	+	1339.46i	−1.47158	+	0.0779323i
$667$	−8968.84			−0.520652
$668$	−1403.20	+	3180.68i	−0.0812746	+	0.184228i
$669$	13340.0	−	17364.3i	0.770930	−	1.00350i
$670$	3850.64	+	15825.6i	0.222034	+	0.912532i
$671$	8506.37			0.489396
$672$	−9471.15	−	1170.68i	−0.543687	−	0.0672024i
$673$			6404.35i			0.366819i	0.983037	+	0.183410i	$0.0587135\pi$
$673$			6404.35i			0.366819i	−0.983037	+	0.183410i	$0.941287\pi$
$674$	−2372.69	+	11256.6i	−0.135597	+	0.643306i
$675$	15403.5	−	8383.30i	0.878341	−	0.478034i
$676$	10900.8	+	4809.04i	0.620209	+	0.273614i
$677$	−34201.1			−1.94159			−0.970795	−	0.239909i	$-0.922882\pi$
$677$	−34201.1			−1.94159			−0.970795	+	0.239909i	$0.922882\pi$
$678$	9272.75	−	7937.72i	0.525248	−	0.449626i
$679$		−	3818.59i		−	0.215823i
$680$	−1445.99	+	8093.14i	−0.0815459	+	0.456409i
$681$	−15000.1	−	11523.7i	−0.844059	−	0.648441i
$682$	3662.53	−	17375.9i	0.205638	−	0.975599i
$683$		−	4498.79i		−	0.252037i	−0.992028	−	0.126019i	$-0.959780\pi$
$683$		−	4498.79i		−	0.252037i	0.992028	−	0.126019i	$-0.0402199\pi$
$684$	−22799.9	−	3558.64i	−1.27453	−	0.198930i
$685$	10727.2	+	22411.5i	0.598342	+	1.25007i
$686$	16372.3	+	3450.97i	0.911218	+	0.192068i
$687$	5420.34	−	7055.53i	0.301018	−	0.391827i
$688$	3129.77	+	3428.83i	0.173432	+	0.190004i
$689$			7526.30i			0.416153i
$690$	5850.04	−	13227.7i	0.322764	−	0.729814i
$691$		−	30461.5i		−	1.67700i	−0.544899	−	0.838502i	$-0.683432\pi$
$691$		−	30461.5i		−	1.67700i	0.544899	−	0.838502i	$-0.316568\pi$
$692$	1986.34	+	876.300i	0.109117	+	0.0481386i
$693$	−4281.20	−	16051.5i	−0.234674	−	0.879862i
$694$	−6405.59	+	30389.7i	−0.350365	+	1.66221i
$695$	7070.97	−	3384.50i	0.385924	−	0.184721i
$696$	−3454.41	−	11471.2i	−0.188131	−	0.624734i
$697$		−	446.117i		−	0.0242437i
$698$	−1125.99	−	237.337i	−0.0610590	−	0.0128701i
$699$	6059.52	−	7887.53i	0.327886	−	0.426801i
$700$	−9011.67	+	4661.34i	−0.486584	+	0.251689i
$701$			4660.73i			0.251118i	0.992086	+	0.125559i	$0.0400724\pi$
$701$			4660.73i			0.251118i	−0.992086	+	0.125559i	$0.959928\pi$
$702$	5979.40	−	8699.61i	0.321479	−	0.467729i
$703$	35432.4			1.90093
$704$	9895.29	+	29430.5i	0.529748	+	1.57557i
$705$	5581.94	−	26362.8i	0.298196	−	1.40834i
$706$	9205.91	+	1940.44i	0.490749	+	0.103441i
$707$		−	4298.43i		−	0.228655i
$708$	−24893.7	+	13607.3i	−1.32142	+	0.722308i
$709$	13268.7			0.702843			0.351421	−	0.936217i	$-0.385698\pi$
$709$	13268.7			0.702843			0.351421	+	0.936217i	$0.385698\pi$
$710$	−289.601	−	1190.22i	−0.0153078	−	0.0629130i
$711$	−22512.1	+	6004.36i	−1.18744	+	0.316710i
$712$	−6705.30	+	9328.66i	−0.352938	+	0.491020i
$713$	−9112.81			−0.478650
$714$	3681.24	−	3151.24i	0.192951	−	0.165171i
$715$	16269.3	−	7787.24i	0.850961	−	0.407310i
$716$	−4003.19	−	1766.06i	−0.208947	−	0.0921801i
$717$	17382.5	−	22626.4i	0.905387	−	1.17852i
$718$	10715.1	+	2258.54i	0.556939	+	0.117393i
$719$	36947.6			1.91643			0.958215	−	0.286050i	$-0.0923422\pi$
$719$	36947.6			1.91643			0.958215	+	0.286050i	$0.0923422\pi$
$720$	19171.5	+	2387.47i	0.992335	+	0.123577i
$721$	4360.59			0.225238
$722$	12604.6	+	2656.83i	0.649718	+	0.136949i
$723$	−12610.0	+	16414.1i	−0.648646	+	0.844327i
$724$	11182.4	+	4933.28i	0.574021	+	0.253237i
$725$	−9919.92	−	7988.40i	−0.508161	−	0.409216i
$726$	−26200.1	+	22428.0i	−1.33936	+	1.14653i
$727$	22829.5			1.16465			0.582324	−	0.812957i	$-0.302144\pi$
$727$	22829.5			1.16465			0.582324	+	0.812957i	$0.302144\pi$
$728$	−3564.53	+	4959.10i	−0.181470	+	0.252468i
$729$	13869.9	+	13965.9i	0.704664	+	0.709541i
$730$	22973.8	−	5589.90i	1.16479	−	0.283413i
$731$	−2357.32			−0.119273
$732$	5116.37	−	2796.69i	0.258342	−	0.141214i
$733$		−	24153.7i		−	1.21711i	−0.793513	−	0.608553i	$-0.791750\pi$
$733$		−	24153.7i		−	1.21711i	0.793513	−	0.608553i	$-0.208250\pi$
$734$	−21356.6	−	4501.58i	−1.07396	−	0.226371i
$735$	−13643.8	−	2888.88i	−0.684708	−	0.144977i
$736$	13730.9	−	8083.82i	0.687675	−	0.404856i
$737$	−31234.5			−1.56111
$738$	−1046.88	+	55.4413i	−0.0522173	+	0.00276534i
$739$			26175.3i			1.30294i	0.758673	+	0.651472i	$0.225848\pi$
$739$			26175.3i			1.30294i	−0.758673	+	0.651472i	$0.774152\pi$
$740$	−29650.4	+	917.612i	−1.47293	+	0.0455839i
$741$	−8996.70	+	11710.8i	−0.446022	+	0.580575i
$742$	7944.24	+	1674.50i	0.393049	+	0.0828476i
$743$		−	17144.7i		−	0.846539i	−0.906004	−	0.423269i	$-0.860882\pi$
$743$		−	17144.7i		−	0.846539i	0.906004	−	0.423269i	$-0.139118\pi$
$744$	−3509.86	−	11655.3i	−0.172954	−	0.574335i
$745$	−29831.6	+	14278.8i	−1.46704	+	0.702194i
$746$	−4862.27	+	23067.8i	−0.238633	+	1.13213i
$747$	13939.7	−	3717.95i	0.682766	−	0.182105i
$748$	−14424.8	−	6363.70i	−0.705111	−	0.311069i
$749$			8817.93i			0.430174i
$750$	18252.1	−	9419.92i	0.888631	−	0.458622i
$751$		−	12945.2i		−	0.628999i	−0.949258	−	0.314500i	$-0.898163\pi$
$751$		−	12945.2i		−	0.628999i	0.949258	−	0.314500i	$-0.101837\pi$
$752$	21925.8	−	20013.5i	1.06323	−	0.970503i
$753$	6551.28	−	8527.64i	0.317054	−	0.412702i
$754$	−7501.87	−	1581.26i	−0.362337	−	0.0763740i
$755$	−6592.94	+	3155.69i	−0.317804	+	0.152116i
$756$	−7852.37	−	8246.99i	−0.377762	−	0.396746i
$757$			28324.8i			1.35995i	0.733236	+	0.679974i	$0.238009\pi$
$757$			28324.8i			1.35995i	−0.733236	+	0.679974i	$0.761991\pi$
$758$	497.640	−	2360.93i	0.0238458	−	0.113130i
$759$	21995.7	+	16898.0i	1.05190	+	0.808112i
$760$	−26605.6	−	4753.58i	−1.26985	−	0.226882i
$761$		−	22209.1i		−	1.05792i	−0.848647	−	0.528960i	$-0.822582\pi$
$761$		−	22209.1i		−	1.05792i	0.848647	−	0.528960i	$-0.177418\pi$
$762$	−25130.2	+	21512.1i	−1.19471	+	1.02270i
$763$	−12803.9			−0.607513
$764$	−16312.8	−	7196.61i	−0.772481	−	0.340791i
$765$	−7458.25	+	6372.66i	−0.352488	+	0.301182i
$766$	1572.05	−	7458.18i	0.0741520	−	0.351795i
$767$			18155.6i			0.854707i
$768$	15627.8	+	14448.4i	0.734271	+	0.678856i
$769$	5100.17			0.239164			0.119582	−	0.992824i	$-0.461845\pi$
$769$	5100.17			0.239164			0.119582	+	0.992824i	$0.461845\pi$
$770$	−4599.98	−	18905.3i	−0.215288	−	0.884805i
$771$	18049.0	−	23493.9i	0.843085	−	1.09742i
$772$	12495.5	−	28324.0i	0.582543	−	1.32047i
$773$	31697.3			1.47487			0.737433	−	0.675420i	$-0.236038\pi$
$773$	31697.3			1.47487			0.737433	+	0.675420i	$0.236038\pi$
$774$	292.956	+	5531.82i	0.0136048	+	0.256895i
$775$	−10079.2	−	8116.63i	−0.467167	−	0.376204i
$776$	−4970.56	+	6915.22i	−0.229939	+	0.319900i
$777$	13865.6	+	10652.1i	0.640188	+	0.491818i
$778$	2596.19	−	12317.0i	0.119638	−	0.567590i
$779$	1466.58			0.0674525
$780$	7225.32	−	10032.8i	0.331677	−	0.460553i
$781$	2349.10			0.107628
$782$	−1668.72	+	7916.83i	−0.0763087	+	0.362027i
$783$	5493.26	−	13197.5i	0.250719	−	0.602350i
$784$	−10357.8	−	11347.5i	−0.471840	−	0.516924i
$785$	18218.6	−	8720.27i	0.828343	−	0.396484i
$786$	−10264.1	+	8786.38i	−0.465789	+	0.398727i
$787$	−37233.7			−1.68645			−0.843227	−	0.537558i	$-0.819347\pi$
$787$	−37233.7			−1.68645			−0.843227	+	0.537558i	$0.819347\pi$
$788$	3933.78	+	1735.44i	0.177836	+	0.0784550i
$789$	−2869.80	−	2204.70i	−0.129490	−	0.0994796i
$790$	−26514.6	+	6451.44i	−1.19411	+	0.290547i
$791$	−8426.40			−0.378772
$792$	−13140.8	+	34640.9i	−0.589568	+	1.55418i
$793$		−	3731.49i		−	0.167099i
$794$	2816.93	−	13364.2i	0.125906	−	0.597327i
$795$	−16079.5	−	3404.60i	−0.717334	−	0.151885i
$796$	−8005.31	+	18145.9i	−0.356458	+	0.807994i
$797$	13591.9			0.604077			0.302039	−	0.953296i	$-0.402333\pi$
$797$	13591.9			0.604077			0.302039	+	0.953296i	$0.402333\pi$
$798$	10359.5	+	12101.8i	0.459550	+	0.536841i
$799$			15074.0i			0.667434i
$800$	22387.1	+	3288.86i	0.989381	+	0.145348i
$801$	−13245.5	+	3532.80i	−0.584278	+	0.155837i
$802$	1547.78	−	7343.03i	0.0681470	−	0.323306i
$803$			45342.7i			1.99266i
$804$	−18786.8	+	10269.2i	−0.824079	+	0.450454i
$805$	−9006.26	+	4310.82i	−0.394322	+	0.188741i
$806$	−7622.30	−	1606.64i	−0.333107	−	0.0702128i
$807$	23631.5	+	18154.7i	1.03081	+	0.791914i
$808$	−5595.15	+	7784.18i	−0.243610	+	0.338919i
$809$			1203.10i			0.0522853i	0.999658	+	0.0261426i	$0.00832241\pi$
$809$			1203.10i			0.0522853i	−0.999658	+	0.0261426i	$0.991678\pi$
$810$	15881.3	+	16710.0i	0.688906	+	0.724851i
$811$		−	13613.1i		−	0.589419i	−0.955587	−	0.294710i	$-0.904777\pi$
$811$		−	13613.1i		−	0.589419i	0.955587	−	0.294710i	$-0.0952229\pi$
$812$	−3338.13	+	7566.65i	−0.144268	+	0.327017i
$813$	−7465.35	−	5735.18i	−0.322043	−	0.247407i
$814$	11733.2	−	55665.3i	0.505220	−	2.39689i
$815$	−14948.7	−	31231.2i	−0.642492	−	1.34231i
$816$	−10768.4	+	914.917i	−0.461972	+	0.0392506i
$817$		−	7749.50i		−	0.331849i
$818$	−26631.0	−	5613.32i	−1.13830	−	0.239933i
$819$	−7041.29	+	1878.03i	−0.300418	+	0.0801268i
$820$	−1227.26	+	37.9808i	−0.0522654	+	0.00161749i
$821$			15331.9i			0.651748i	0.945413	+	0.325874i	$0.105659\pi$
$821$			15331.9i			0.651748i	−0.945413	+	0.325874i	$0.894341\pi$
$822$	−24812.2	+	21239.9i	−1.05283	+	0.901247i
$823$	−8285.28			−0.350920			−0.175460	−	0.984487i	$-0.556141\pi$
$823$	−8285.28			−0.350920			−0.175460	+	0.984487i	$0.556141\pi$
$824$	−7896.76	−	5676.08i	−0.333855	−	0.239970i
$825$	9277.40	+	38281.0i	0.391512	+	1.61548i
$826$	19163.8	+	4039.38i	0.807256	+	0.170155i
$827$			2390.81i			0.100528i	0.998736	+	0.0502641i	$0.0160063\pi$
$827$			2390.81i			0.100528i	−0.998736	+	0.0502641i	$0.983994\pi$
$828$	18785.5	+	2932.06i	0.788455	+	0.123063i
$829$	−19635.3			−0.822630			−0.411315	−	0.911493i	$-0.634930\pi$
$829$	−19635.3			−0.822630			−0.411315	+	0.911493i	$0.634930\pi$
$830$	16418.1	−	3994.79i	0.686602	−	0.167062i
$831$	19692.5	+	15128.6i	0.822053	+	0.631534i
$832$	12910.3	−	4340.77i	0.537961	−	0.180876i
$833$	7801.42			0.324494
$834$	6701.32	+	7828.40i	0.278235	+	0.325030i
$835$	−4382.34	+	2097.59i	−0.181625	+	0.0869344i
$836$	20920.2	−	47420.4i	0.865478	−	1.96180i
$837$	5581.44	−	13409.3i	0.230493	−	0.553757i
$838$	−10050.2	−	2118.40i	−0.414294	−	0.0873256i
$839$	−417.543			−0.0171814			−0.00859068	−	0.999963i	$-0.502735\pi$
$839$	−417.543			−0.0171814			−0.00859068	+	0.999963i	$0.502735\pi$
$840$	−8982.38	−	9858.71i	−0.368954	−	0.404950i
$841$	14007.0			0.574315
$842$	43061.2	+	9076.51i	1.76245	+	0.371493i
$843$	−22981.4	−	17655.2i	−0.938934	−	0.721327i
$844$	11262.9	−	25530.0i	0.459342	−	1.04121i
$845$	7188.86	+	15019.1i	0.292668	+	0.611448i
$846$	35373.5	−	1873.32i	1.43755	−	0.0761303i
$847$	23808.7			0.965852
$848$	−12206.9	−	13373.2i	−0.494323	−	0.541556i
$849$	6402.58	−	8334.08i	0.258817	−	0.336896i
$850$	−8897.07	+	7270.05i	−0.359020	+	0.293365i
$851$	−29193.7			−1.17597
$852$	1412.93	−	772.329i	0.0568147	−	0.0310558i
$853$			12170.1i			0.488507i	0.969711	+	0.244253i	$0.0785429\pi$
$853$			12170.1i			0.488507i	−0.969711	+	0.244253i	$0.921457\pi$
$854$	−3938.70	−	830.207i	−0.157822	−	0.0332659i
$855$	−20949.6	−	24518.4i	−0.837968	−	0.980716i
$856$	11478.1	−	15968.7i	0.458310	−	0.637617i
$857$	−1541.82			−0.0614558			−0.0307279	−	0.999528i	$-0.509783\pi$
$857$	−1541.82			−0.0614558			−0.0307279	+	0.999528i	$0.509783\pi$
$858$	15418.8	+	18012.0i	0.613506	+	0.716691i
$859$			8306.04i			0.329917i	0.986301	+	0.164958i	$0.0527490\pi$
$859$			8306.04i			0.329917i	−0.986301	+	0.164958i	$0.947251\pi$
$860$	200.693	+	6484.92i	0.00795765	+	0.257132i
$861$	573.910	+	440.901i	0.0227164	+	0.0174516i
$862$	−12224.9	−	2576.78i	−0.483041	−	0.101816i
$863$		−	41947.0i		−	1.65457i	−0.561784	−	0.827284i	$-0.689885\pi$
$863$		−	41947.0i		−	1.65457i	0.561784	−	0.827284i	$-0.310115\pi$
$864$	3485.24	+	25156.0i	0.137234	+	0.990539i
$865$	1309.95	+	2736.78i	0.0514909	+	0.107576i
$866$	−2248.40	+	10666.9i	−0.0882260	+	0.418565i
$867$	−12209.4	+	15892.6i	−0.478261	+	0.622541i
$868$	−3391.72	+	7688.11i	−0.132630	+	0.300636i
$869$		−	52331.0i		−	2.04282i
$870$	6771.81	−	15312.0i	0.263892	−	0.596696i
$871$			13701.7i			0.533023i
$872$	23187.1	+	16666.5i	0.900474	+	0.647247i
$873$	−9818.73	+	2618.83i	−0.380657	+	0.101528i
$874$	−26026.0	−	5485.80i	−1.00726	−	0.212311i
$875$	−13800.9	−	3253.78i	−0.533205	−	0.125712i
$876$	14907.6	+	27272.5i	0.574977	+	1.05189i
$877$			12604.3i			0.485312i	0.970112	+	0.242656i	$0.0780186\pi$
$877$			12604.3i			0.485312i	−0.970112	+	0.242656i	$0.921981\pi$
$878$	−9617.60	+	45628.2i	−0.369679	+	1.75385i
$879$	−17355.3	+	22591.0i	−0.665961	+	0.866865i
$880$	−16278.3	+	40224.0i	−0.623570	+	1.54085i
$881$			9360.53i			0.357962i	0.983853	+	0.178981i	$0.0572800\pi$
$881$			9360.53i			0.357962i	−0.983853	+	0.178981i	$0.942720\pi$
$882$	−969.523	−	18307.3i	−0.0370131	−	0.698909i
$883$	−8600.57			−0.327783			−0.163891	−	0.986478i	$-0.552405\pi$
$883$	−8600.57			−0.327783			−0.163891	+	0.986478i	$0.552405\pi$
$884$	−2791.56	+	6327.72i	−0.106211	+	0.240752i
$885$	−38788.3	−	8212.87i	−1.47328	−	0.311946i
$886$	−2988.10	+	14176.3i	−0.113304	+	0.537541i
$887$			5117.71i			0.193727i	0.995298	+	0.0968636i	$0.0308811\pi$
$887$			5117.71i			0.193727i	−0.995298	+	0.0968636i	$0.969119\pi$
$888$	−11244.2	−	37338.9i	−0.424920	−	1.41105i
$889$	22836.4			0.861541
$890$	−15600.5	+	3795.85i	−0.587560	+	0.142963i
$891$	−38337.0	+	22016.5i	−1.44146	+	0.827812i
$892$	30844.2	+	13607.4i	1.15778	+	0.510772i
$893$	−49554.6			−1.85698
$894$	−28272.1	−	33027.1i	−1.05767	−	1.23556i
$895$	−2640.03	−	5515.61i	−0.0985993	−	0.205996i
$896$	−1709.45	−	14593.0i	−0.0637373	−	0.544104i
$897$	7412.63	−	9648.83i	0.275920	−	0.359159i
$898$	−1776.98	+	8430.41i	−0.0660339	+	0.313281i
$899$	−10548.7			−0.391344
$900$	18166.0	+	19974.9i	0.672815	+	0.739811i
$901$	9194.10			0.339956
$902$	485.648	−	2304.03i	0.0179272	−	0.0850509i
$903$	2329.75	−	3032.58i	0.0858575	−	0.111759i
$904$	15259.7	+	10968.4i	0.561427	+	0.403545i
$905$	7374.58	+	15407.1i	0.270872	+	0.565913i
$906$	−6248.28	−	7299.17i	−0.229123	−	0.267659i
$907$	4477.83			0.163929			0.0819647	−	0.996635i	$-0.473881\pi$
$907$	4477.83			0.163929			0.0819647	+	0.996635i	$0.473881\pi$
$908$	11754.7	−	26644.7i	0.429618	−	0.973827i
$909$	−11052.5	+	2947.90i	−0.403289	+	0.107564i
$910$	−8293.19	+	2017.87i	−0.302106	+	0.0735075i
$911$	−5265.61			−0.191501			−0.0957506	−	0.995405i	$-0.530525\pi$
$911$	−5265.61			−0.191501			−0.0957506	+	0.995405i	$0.530525\pi$
$912$	−3007.72	−	35400.2i	−0.109206	−	1.28533i
$913$			32403.8i			1.17460i
$914$	1025.88	−	4867.03i	0.0371260	−	0.176135i
$915$	7972.11	+	1687.98i	0.288033	+	0.0609867i
$916$	12532.8	+	5529.00i	0.452068	+	0.199436i
$917$	9327.31			0.335894
$918$	−10627.4	−	7304.42i	−0.382088	−	0.262616i
$919$			37080.1i			1.33097i	0.746412	+	0.665484i	$0.231775\pi$
$919$			37080.1i			1.33097i	−0.746412	+	0.665484i	$0.768225\pi$
$920$	21921.1	+	3916.60i	0.785561	+	0.140355i
$921$	841.057	−	1094.78i	0.0300910	−	0.0391687i
$922$	1012.35	−	4802.81i	0.0361603	−	0.171553i
$923$		−	1030.48i		−	0.0367483i
$924$	22442.7	−	12267.6i	0.799039	−	0.436767i
$925$	−32289.5	−	26002.3i	−1.14775	−	0.924271i
$926$	24328.8	+	5128.07i	0.863385	+	0.181986i
$927$	−2990.54	−	11212.4i	−0.105957	−	0.397263i
$928$	15894.5	−	9357.57i	0.562243	−	0.331010i
$929$			24997.1i			0.882806i	0.897309	+	0.441403i	$0.145519\pi$
$929$			24997.1i			0.882806i	−0.897309	+	0.441403i	$0.854481\pi$
$930$	6880.52	−	15557.8i	0.242603	−	0.548560i
$931$			25646.6i			0.902827i
$932$	14010.6	+	6180.99i	0.492418	+	0.217237i
$933$	−10273.2	+	13372.3i	−0.360480	+	0.469228i
$934$	−594.091	+	2818.51i	−0.0208129	+	0.0987414i
$935$	−9512.87	−	19874.5i	−0.332732	−	0.695151i
$936$	15195.9	+	5764.47i	0.530657	+	0.201301i
$937$		−	45349.3i		−	1.58111i	−0.612393	−	0.790554i	$-0.709793\pi$
$937$		−	45349.3i		−	1.58111i	0.612393	−	0.790554i	$-0.290207\pi$
$938$	14462.5	+	3048.44i	0.503431	+	0.106114i
$939$	32991.7	+	25345.5i	1.14658	+	0.880853i
$940$	41468.2	−	1283.34i	1.43887	−	0.0445299i
$941$		−	31446.5i		−	1.08940i	−0.838631	−	0.544700i	$-0.816643\pi$
$941$		−	31446.5i		−	1.08940i	0.838631	−	0.544700i	$-0.183357\pi$
$942$	17266.2	+	20170.1i	0.597200	+	0.697642i
$943$	−1208.35			−0.0417278
$944$	−29446.5	−	32260.1i	−1.01526	−	1.11226i
$945$	−827.111	−	15892.8i	−0.0284719	−	0.547084i
$946$	−12174.7	−	2566.20i	−0.418428	−	0.0881971i
$947$			876.054i			0.0300612i	0.999887	+	0.0150306i	$0.00478456\pi$
$947$			876.054i			0.0300612i	−0.999887	+	0.0150306i	$0.995215\pi$
$948$	−17205.2	−	31475.8i	−0.589449	−	1.07836i
$949$	19890.5			0.680371
$950$	−23899.7	−	29248.4i	−0.816220	−	0.998889i
$951$	12302.5	−	16013.8i	0.419489	−	0.546039i
$952$	6058.02	+	4354.42i	0.206241	+	0.148243i
$953$	7224.06			0.245551			0.122776	−	0.992434i	$-0.460820\pi$
$953$	7224.06			0.245551			0.122776	+	0.992434i	$0.460820\pi$
$954$	−1142.60	−	21575.4i	−0.0387767	−	0.732212i
$955$	−10758.0	−	22475.8i	−0.364523	−	0.761569i
$956$	40191.4	+	17731.0i	1.35971	+	0.599855i
$957$	25461.4	+	19560.5i	0.860033	+	0.660712i
$958$	15958.9	+	3363.84i	0.538212	+	0.113445i
$959$	22547.5			0.759224
$960$	3433.69	+	29545.7i	0.115440	+	0.993315i
$961$	19073.0			0.640226
$962$	−24418.7	−	5147.01i	−0.818389	−	0.172501i
$963$	22673.5	−	6047.43i	0.758717	−	0.202363i
$964$	−29156.5	−	12862.8i	−0.974137	−	0.429754i
$965$	39024.8	−	18679.1i	1.30182	−	0.623111i
$966$	−8535.43	−	9971.00i	−0.284289	−	0.332103i
$967$	47806.0			1.58980			0.794900	−	0.606740i	$-0.207523\pi$
$967$	47806.0			1.58980			0.794900	+	0.606740i	$0.207523\pi$
$968$	−43116.1	−	30991.2i	−1.43162	−	1.02902i
$969$	14305.9	+	10990.3i	0.474273	+	0.364356i
$970$	−11564.4	+	2813.82i	−0.382796	+	0.0931406i
$971$	36858.7			1.21818			0.609090	−	0.793101i	$-0.291535\pi$
$971$	36858.7			1.21818			0.609090	+	0.793101i	$0.291535\pi$
$972$	−15820.3	+	25846.7i	−0.522052	+	0.852913i
$973$		−	7113.88i		−	0.234389i
$974$	9415.95	+	1984.71i	0.309760	+	0.0652919i
$975$	16792.7	−	4069.72i	0.551588	−	0.133677i
$976$	6052.09	+	6630.37i	0.198486	+	0.217452i
$977$	−36840.0			−1.20636			−0.603181	−	0.797604i	$-0.706100\pi$
$977$	−36840.0			−1.20636			−0.603181	+	0.797604i	$0.706100\pi$
$978$	34576.6	−	29598.5i	1.13051	−	0.967747i
$979$		−	30790.2i		−	1.00517i
$980$	−664.184	−	21461.5i	−0.0216496	−	0.699554i
$981$	8781.04	+	32922.6i	0.285787	+	1.07150i
$982$	−9134.23	−	1925.33i	−0.296828	−	0.0625659i
$983$		−	925.863i		−	0.0300411i	−0.999887	−	0.0150206i	$-0.995219\pi$
$983$		−	925.863i		−	0.0300411i	0.999887	−	0.0150206i	$-0.00478138\pi$
$984$	−465.405	−	1545.49i	−0.0150778	−	0.0500695i
$985$	2594.25	+	5419.97i	0.0839184	+	0.175324i
$986$	−1931.66	+	9164.26i	−0.0623900	+	0.295993i
$987$	−19392.0	−	14897.7i	−0.625385	−	0.480446i
$988$	−20801.9	−	9177.05i	−0.669835	−	0.295507i
$989$			6385.02i			0.205290i
$990$	−45456.5	+	24793.4i	−1.45929	+	0.795945i
$991$		−	16089.2i		−	0.515732i	−0.966181	−	0.257866i	$-0.916981\pi$
$991$		−	16089.2i		−	0.515732i	0.966181	−	0.257866i	$-0.0830194\pi$
$992$	16149.6	−	9507.78i	0.516886	−	0.304307i
$993$	32164.2	+	24709.8i	1.02789	+	0.789670i
$994$	−1087.71	−	229.268i	−0.0347082	−	0.00731585i
$995$	−25001.4	+	11966.8i	−0.796581	+	0.381281i
$996$	10653.6	+	19490.1i	0.338928	+	0.620048i
$997$		−	20261.1i		−	0.643606i	−0.946807	−	0.321803i	$-0.895711\pi$
$997$		−	20261.1i		−	0.643606i	0.946807	−	0.321803i	$-0.104289\pi$
$998$	−9884.09	+	46892.5i	−0.313502	+	1.48733i
$999$	17880.6	−	42958.0i	0.566284	−	1.36049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.4.h.c.59.2	yes	24
3.2	odd	2	inner	60.4.h.c.59.24	yes	24
4.3	odd	2	inner	60.4.h.c.59.3	yes	24
5.4	even	2	inner	60.4.h.c.59.23	yes	24
12.11	even	2	inner	60.4.h.c.59.21	yes	24
15.14	odd	2	inner	60.4.h.c.59.1	✓	24
20.19	odd	2	inner	60.4.h.c.59.22	yes	24
60.59	even	2	inner	60.4.h.c.59.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.4.h.c.59.1	✓	24	15.14	odd	2	inner
60.4.h.c.59.2	yes	24	1.1	even	1	trivial
60.4.h.c.59.3	yes	24	4.3	odd	2	inner
60.4.h.c.59.4	yes	24	60.59	even	2	inner
60.4.h.c.59.21	yes	24	12.11	even	2	inner
60.4.h.c.59.22	yes	24	20.19	odd	2	inner
60.4.h.c.59.23	yes	24	5.4	even	2	inner
60.4.h.c.59.24	yes	24	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	60.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.76761 - 0.583363i) q^{2} +(3.16559 - 4.12057i) q^{3} +(7.31938 + 3.22905i) q^{4} +(4.82699 + 10.0847i) q^{5} +(-11.1649 + 9.55745i) q^{6} +10.1458 q^{7} +(-18.3735 - 13.2066i) q^{8} +(-6.95813 - 26.0880i) q^{9} +O(q^{10})\)	\(q+(-2.76761 - 0.583363i) q^{2} +(3.16559 - 4.12057i) q^{3} +(7.31938 + 3.22905i) q^{4} +(4.82699 + 10.0847i) q^{5} +(-11.1649 + 9.55745i) q^{6} +10.1458 q^{7} +(-18.3735 - 13.2066i) q^{8} +(-6.95813 - 26.0880i) q^{9} +(-7.47622 - 30.7263i) q^{10} +60.6436 q^{11} +(36.4756 - 19.9382i) q^{12} -26.6025i q^{13} +(-28.0798 - 5.91871i) q^{14} +(56.8347 + 12.0339i) q^{15} +(43.1465 + 47.2692i) q^{16} -32.4976 q^{17} +(4.03864 + 76.2607i) q^{18} -106.833i q^{19} +(2.76672 + 89.3999i) q^{20} +(32.1176 - 41.8066i) q^{21} +(-167.838 - 35.3772i) q^{22} +88.0228i q^{23} +(-112.582 + 33.9026i) q^{24} +(-78.4004 + 97.3569i) q^{25} +(-15.5189 + 73.6255i) q^{26} +(-129.524 - 53.9124i) q^{27} +(74.2613 + 32.7614i) q^{28} +101.892i q^{29} +(-150.276 - 66.4605i) q^{30} +103.528i q^{31} +(-91.8379 - 155.993i) q^{32} +(191.973 - 249.886i) q^{33} +(89.9407 + 18.9579i) q^{34} +(48.9739 + 102.317i) q^{35} +(33.3102 - 213.416i) q^{36} +331.661i q^{37} +(-62.3225 + 295.673i) q^{38} +(-109.617 - 84.2126i) q^{39} +(44.4954 - 249.038i) q^{40} +13.7277i q^{41} +(-113.277 + 96.9685i) q^{42} +72.5383 q^{43} +(443.873 + 195.821i) q^{44} +(229.502 - 196.097i) q^{45} +(51.3492 - 243.613i) q^{46} -463.850i q^{47} +(331.360 - 28.1534i) q^{48} -240.062 q^{49} +(273.777 - 223.711i) q^{50} +(-102.874 + 133.908i) q^{51} +(85.9008 - 194.714i) q^{52} -282.917 q^{53} +(327.022 + 224.768i) q^{54} +(292.726 + 611.570i) q^{55} +(-186.415 - 133.992i) q^{56} +(-440.213 - 338.190i) q^{57} +(59.4402 - 281.999i) q^{58} -682.476 q^{59} +(377.137 + 271.603i) q^{60} +140.268 q^{61} +(60.3943 - 286.525i) q^{62} +(-70.5961 - 264.685i) q^{63} +(163.171 + 485.303i) q^{64} +(268.277 - 128.410i) q^{65} +(-677.080 + 579.598i) q^{66} -515.051 q^{67} +(-237.862 - 104.936i) q^{68} +(362.704 + 278.644i) q^{69} +(-75.8526 - 311.744i) q^{70} +38.7362 q^{71} +(-216.689 + 571.221i) q^{72} +747.691i q^{73} +(193.478 - 917.908i) q^{74} +(152.982 + 631.246i) q^{75} +(344.969 - 781.952i) q^{76} +615.281 q^{77} +(254.252 + 297.015i) q^{78} -862.927i q^{79} +(-268.426 + 663.285i) q^{80} +(-632.169 + 363.047i) q^{81} +(8.00823 - 37.9930i) q^{82} +534.332i q^{83} +(370.076 - 202.289i) q^{84} +(-156.865 - 327.727i) q^{85} +(-200.758 - 42.3161i) q^{86} +(419.854 + 322.549i) q^{87} +(-1114.24 - 800.896i) q^{88} -507.723i q^{89} +(-749.568 + 408.837i) q^{90} -269.905i q^{91} +(-284.230 + 644.272i) q^{92} +(426.594 + 327.727i) q^{93} +(-270.593 + 1283.76i) q^{94} +(1077.38 - 515.682i) q^{95} +(-933.500 - 115.385i) q^{96} -376.369i q^{97} +(664.398 + 140.043i) q^{98} +(-421.966 - 1582.07i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 56 q^{4} + 12 q^{6} + 192 q^{9}+O(q^{10}) \) 24 * q + 56 * q^4 + 12 * q^6 + 192 * q^9	\( 24 q + 56 q^{4} + 12 q^{6} + 192 q^{9} - 32 q^{10} - 240 q^{16} - 264 q^{21} + 168 q^{24} - 88 q^{25} - 252 q^{30} - 1088 q^{34} - 1104 q^{36} + 704 q^{40} + 456 q^{45} + 3368 q^{46} - 1304 q^{49} + 468 q^{54} + 2496 q^{60} + 2080 q^{61} + 1376 q^{64} - 672 q^{66} + 2568 q^{69} - 2632 q^{70} - 1536 q^{76} - 5112 q^{81} - 2328 q^{84} - 6944 q^{85} - 1152 q^{90} - 4840 q^{94} - 2832 q^{96}+O(q^{100}) \) 24 * q + 56 * q^4 + 12 * q^6 + 192 * q^9 - 32 * q^10 - 240 * q^16 - 264 * q^21 + 168 * q^24 - 88 * q^25 - 252 * q^30 - 1088 * q^34 - 1104 * q^36 + 704 * q^40 + 456 * q^45 + 3368 * q^46 - 1304 * q^49 + 468 * q^54 + 2496 * q^60 + 2080 * q^61 + 1376 * q^64 - 672 * q^66 + 2568 * q^69 - 2632 * q^70 - 1536 * q^76 - 5112 * q^81 - 2328 * q^84 - 6944 * q^85 - 1152 * q^90 - 4840 * q^94 - 2832 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more