LMFDB - Embedded newform 360.4.m.c.179.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,4,Mod(179,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("360.179");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	360.m (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:	$21.2406876021$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			179.4
Character	$\chi$	$=$	360.179
Dual form			360.4.m.c.179.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.80200 + 0.385718i) q^{2} +(7.70244 - 2.16157i) q^{4} +(6.42323 - 9.15107i) q^{5} -30.0133 q^{7} +(-20.7485 + 9.02769i) q^{8} +O(q^{10})$	\(q+(-2.80200 + 0.385718i) q^{2} +(7.70244 - 2.16157i) q^{4} +(6.42323 - 9.15107i) q^{5} -30.0133 q^{7} +(-20.7485 + 9.02769i) q^{8} +(-14.4682 + 28.1189i) q^{10} +47.7066i q^{11} +12.3085 q^{13} +(84.0973 - 11.5767i) q^{14} +(54.6553 - 33.2987i) q^{16} +130.910 q^{17} -19.2759 q^{19} +(29.6939 - 84.3699i) q^{20} +(-18.4013 - 133.674i) q^{22} +58.7216i q^{23} +(-42.4842 - 117.559i) q^{25} +(-34.4885 + 4.74762i) q^{26} +(-231.176 + 64.8757i) q^{28} +176.042 q^{29} -171.697i q^{31} +(-140.300 + 114.385i) q^{32} +(-366.810 + 50.4943i) q^{34} +(-192.782 + 274.654i) q^{35} -91.9820 q^{37} +(54.0112 - 7.43508i) q^{38} +(-50.6594 + 247.858i) q^{40} -251.448i q^{41} -48.2682i q^{43} +(103.121 + 367.457i) q^{44} +(-22.6500 - 164.538i) q^{46} -501.882i q^{47} +557.797 q^{49} +(164.386 + 313.013i) q^{50} +(94.8056 - 26.6057i) q^{52} -222.896i q^{53} +(436.566 + 306.430i) q^{55} +(622.731 - 270.951i) q^{56} +(-493.271 + 67.9026i) q^{58} -348.780i q^{59} -767.157i q^{61} +(66.2267 + 481.096i) q^{62} +(349.002 - 374.622i) q^{64} +(79.0604 - 112.636i) q^{65} +176.175i q^{67} +(1008.33 - 282.971i) q^{68} +(434.237 - 843.940i) q^{70} -44.0496 q^{71} +793.199i q^{73} +(257.734 - 35.4791i) q^{74} +(-148.472 + 41.6662i) q^{76} -1431.83i q^{77} -930.985i q^{79} +(46.3446 - 714.039i) q^{80} +(96.9881 + 704.559i) q^{82} +957.629 q^{83} +(840.865 - 1197.97i) q^{85} +(18.6179 + 135.248i) q^{86} +(-430.680 - 989.840i) q^{88} +1258.94i q^{89} -369.419 q^{91} +(126.931 + 452.300i) q^{92} +(193.585 + 1406.28i) q^{94} +(-123.814 + 176.395i) q^{95} +94.5723i q^{97} +(-1562.95 + 215.153i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 76 q^{4}+O(q^{10}) $ 64 * q + 76 * q^4	$ 64 q + 76 q^{4} + 72 q^{10} - 236 q^{16} - 48 q^{19} + 1000 q^{25} - 192 q^{34} + 1284 q^{40} + 336 q^{46} + 784 q^{49} + 4228 q^{64} - 768 q^{70} + 648 q^{76} + 4304 q^{91} - 5944 q^{94}+O(q^{100}) $ 64 * q + 76 * q^4 + 72 * q^10 - 236 * q^16 - 48 * q^19 + 1000 * q^25 - 192 * q^34 + 1284 * q^40 + 336 * q^46 + 784 * q^49 + 4228 * q^64 - 768 * q^70 + 648 * q^76 + 4304 * q^91 - 5944 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−2.80200	+	0.385718i	−0.990658	+	0.136372i
$2$	−2.80200	+	0.385718i	−0.990658	+	0.136372i
$3$		0			0
$3$		0			0
$4$	7.70244	−	2.16157i	0.962805	−	0.270196i
$5$	6.42323	−	9.15107i	0.574511	−	0.818497i
$5$	6.42323	−	9.15107i	0.574511	−	0.818497i
$6$		0			0
$7$	−30.0133			−1.62057			−0.810283	−	0.586039i	$-0.800686\pi$
$7$	−30.0133			−1.62057			−0.810283	+	0.586039i	$0.800686\pi$
$8$	−20.7485	+	9.02769i	−0.916963	+	0.398971i
$9$		0			0
$10$	−14.4682	+	28.1189i	−0.457524	+	0.889197i
$11$			47.7066i			1.30764i	0.756649	+	0.653821i	$0.226835\pi$
$11$			47.7066i			1.30764i	−0.756649	+	0.653821i	$0.773165\pi$
$12$		0			0
$13$	12.3085			0.262597			0.131299	−	0.991343i	$-0.458085\pi$
$13$	12.3085			0.262597			0.131299	+	0.991343i	$0.458085\pi$
$14$	84.0973	−	11.5767i	1.60543	−	0.221000i
$15$		0			0
$16$	54.6553	−	33.2987i	0.853988	−	0.520292i
$17$	130.910			1.86767			0.933833	−	0.357709i	$-0.116442\pi$
$17$	130.910			1.86767			0.933833	+	0.357709i	$0.116442\pi$
$18$		0			0
$19$	−19.2759			−0.232748			−0.116374	−	0.993205i	$-0.537127\pi$
$19$	−19.2759			−0.232748			−0.116374	+	0.993205i	$0.537127\pi$
$20$	29.6939	−	84.3699i	0.331988	−	0.943284i
$21$		0			0
$22$	−18.4013	−	133.674i	−0.178326	−	1.29543i
$23$			58.7216i			0.532361i	0.963923	+	0.266181i	$0.0857617\pi$
$23$			58.7216i			0.532361i	−0.963923	+	0.266181i	$0.914238\pi$
$24$		0			0
$25$	−42.4842	−	117.559i	−0.339874	−	0.940471i
$26$	−34.4885	+	4.74762i	−0.260144	+	0.0358109i
$27$		0			0
$28$	−231.176	+	64.8757i	−1.56029	+	0.437870i
$29$	176.042			1.12725			0.563624	−	0.826031i	$-0.309407\pi$
$29$	176.042			1.12725			0.563624	+	0.826031i	$0.309407\pi$
$30$		0			0
$31$		−	171.697i		−	0.994766i	−0.867531	−	0.497383i	$-0.834294\pi$
$31$		−	171.697i		−	0.994766i	0.867531	−	0.497383i	$-0.165706\pi$
$32$	−140.300	+	114.385i	−0.775057	+	0.631891i
$33$		0			0
$34$	−366.810	+	50.4943i	−1.85022	+	0.254697i
$35$	−192.782	+	274.654i	−0.931033	+	1.32643i
$36$		0			0
$37$	−91.9820			−0.408696			−0.204348	−	0.978898i	$-0.565507\pi$
$37$	−91.9820			−0.408696			−0.204348	+	0.978898i	$0.565507\pi$
$38$	54.0112	−	7.43508i	0.230573	−	0.0317402i
$39$		0			0
$40$	−50.6594	+	247.858i	−0.200249	+	0.979745i
$41$		−	251.448i		−	0.957795i	−0.877871	−	0.478898i	$-0.841037\pi$
$41$		−	251.448i		−	0.957795i	0.877871	−	0.478898i	$-0.158963\pi$
$42$		0			0
$43$		−	48.2682i		−	0.171182i	−0.996330	−	0.0855911i	$-0.972722\pi$
$43$		−	48.2682i		−	0.171182i	0.996330	−	0.0855911i	$-0.0272779\pi$
$44$	103.121	+	367.457i	0.353320	+	1.25901i
$45$		0			0
$46$	−22.6500	−	164.538i	−0.0725991	−	0.527388i
$47$		−	501.882i		−	1.55760i	−0.627274	−	0.778799i	$-0.715829\pi$
$47$		−	501.882i		−	1.55760i	0.627274	−	0.778799i	$-0.284171\pi$
$48$		0			0
$49$	557.797			1.62623
$50$	164.386	+	313.013i	0.464953	+	0.885336i
$51$		0			0
$52$	94.8056	−	26.6057i	0.252830	−	0.0709527i
$53$		−	222.896i		−	0.577683i	−0.957377	−	0.288841i	$-0.906730\pi$
$53$		−	222.896i		−	0.577683i	0.957377	−	0.288841i	$-0.0932700\pi$
$54$		0			0
$55$	436.566	+	306.430i	1.07030	+	0.751255i
$56$	622.731	−	270.951i	1.48600	−	0.646559i
$57$		0			0
$58$	−493.271	+	67.9026i	−1.11672	+	0.153725i
$59$		−	348.780i		−	0.769616i	−0.922997	−	0.384808i	$-0.874268\pi$
$59$		−	348.780i		−	0.769616i	0.922997	−	0.384808i	$-0.125732\pi$
$60$		0			0
$61$		−	767.157i		−	1.61024i	−0.593115	−	0.805118i	$-0.702102\pi$
$61$		−	767.157i		−	1.61024i	0.593115	−	0.805118i	$-0.297898\pi$
$62$	66.2267	+	481.096i	0.135658	+	0.985472i
$63$		0			0
$64$	349.002	−	374.622i	0.681644	−	0.731684i
$65$	79.0604	−	112.636i	0.150865	−	0.214935i
$66$		0			0
$67$			176.175i			0.321242i	0.987016	+	0.160621i	$0.0513497\pi$
$67$			176.175i			0.321242i	−0.987016	+	0.160621i	$0.948650\pi$
$68$	1008.33	−	282.971i	1.79820	−	0.504636i
$69$		0			0
$70$	434.237	−	843.940i	0.741447	−	1.44100i
$71$	−44.0496			−0.0736299			−0.0368150	−	0.999322i	$-0.511721\pi$
$71$	−44.0496			−0.0736299			−0.0368150	+	0.999322i	$0.511721\pi$
$72$		0			0
$73$			793.199i			1.27174i	0.771797	+	0.635870i	$0.219358\pi$
$73$			793.199i			1.27174i	−0.771797	+	0.635870i	$0.780642\pi$
$74$	257.734	−	35.4791i	0.404878	−	0.0557346i
$75$		0			0
$76$	−148.472	+	41.6662i	−0.224091	+	0.0628874i
$77$		−	1431.83i		−	2.11912i
$78$		0			0
$79$		−	930.985i		−	1.32587i	−0.748676	−	0.662937i	$-0.769310\pi$
$79$		−	930.985i		−	1.32587i	0.748676	−	0.662937i	$-0.230690\pi$
$80$	46.3446	−	714.039i	0.0647685	−	0.997900i
$81$		0			0
$82$	96.9881	+	704.559i	0.130616	+	0.948847i
$83$	957.629			1.26643			0.633213	−	0.773977i	$-0.281736\pi$
$83$	957.629			1.26643			0.633213	+	0.773977i	$0.281736\pi$
$84$		0			0
$85$	840.865	−	1197.97i	1.07300	−	1.52868i
$86$	18.6179	+	135.248i	0.0233445	+	0.169583i
$87$		0			0
$88$	−430.680	−	989.840i	−0.521712	−	1.19906i
$89$			1258.94i			1.49941i	0.661772	+	0.749705i	$0.269805\pi$
$89$			1258.94i			1.49941i	−0.661772	+	0.749705i	$0.730195\pi$
$90$		0			0
$91$	−369.419			−0.425556
$92$	126.931	+	452.300i	0.143842	+	0.512560i
$93$		0			0
$94$	193.585	+	1406.28i	0.212413	+	1.54305i
$95$	−123.814	+	176.395i	−0.133716	+	0.190503i
$96$		0			0
$97$			94.5723i			0.0989935i	0.998774	+	0.0494967i	$0.0157617\pi$
$97$			94.5723i			0.0989935i	−0.998774	+	0.0494967i	$0.984238\pi$
$98$	−1562.95	+	215.153i	−1.61104	+	0.221772i
$99$		0			0
$100$	−581.344	−	813.658i	−0.581344	−	0.813658i
$101$	890.691			0.877496			0.438748	−	0.898610i	$-0.355422\pi$
$101$	890.691			0.877496			0.438748	+	0.898610i	$0.355422\pi$
$102$		0			0
$103$	1588.99			1.52008			0.760038	−	0.649879i	$-0.225180\pi$
$103$	1588.99			1.52008			0.760038	+	0.649879i	$0.225180\pi$
$104$	−255.383	+	111.117i	−0.240792	+	0.104769i
$105$		0			0
$106$	85.9752	+	624.557i	0.0787797	+	0.572286i
$107$	431.860			0.390182			0.195091	−	0.980785i	$-0.437500\pi$
$107$	431.860			0.390182			0.195091	+	0.980785i	$0.437500\pi$
$108$		0			0
$109$			550.267i			0.483541i	0.970333	+	0.241771i	$0.0777282\pi$
$109$			550.267i			0.483541i	−0.970333	+	0.241771i	$0.922272\pi$
$110$	−1341.46	−	690.227i	−1.16275	−	0.598278i
$111$		0			0
$112$	−1640.38	+	999.403i	−1.38394	+	0.843167i
$113$	−1079.62			−0.898779			−0.449390	−	0.893336i	$-0.648358\pi$
$113$	−1079.62			−0.898779			−0.449390	+	0.893336i	$0.648358\pi$
$114$		0			0
$115$	537.366	+	377.182i	0.435736	+	0.305847i
$116$	1355.95	−	380.527i	1.08532	−	0.304578i
$117$		0			0
$118$	134.531	+	977.284i	0.104954	+	0.762426i
$119$	−3929.04			−3.02668
$120$		0			0
$121$	−944.915			−0.709929
$122$	295.906	+	2149.58i	0.219591	+	1.59519i
$123$		0			0
$124$	−371.135	−	1322.49i	−0.268782	−	0.957766i
$125$	−1348.68	−	366.331i	−0.965034	−	0.262125i
$126$		0			0
$127$	1084.40			0.757673			0.378837	−	0.925464i	$-0.376324\pi$
$127$	1084.40			0.757673			0.378837	+	0.925464i	$0.376324\pi$
$128$	−833.405	+	1184.31i	−0.575495	+	0.817806i
$129$		0			0
$130$	−178.082	+	346.102i	−0.120145	+	0.233501i
$131$		−	2403.66i		−	1.60312i	−0.597912	−	0.801561i	$-0.704003\pi$
$131$		−	2403.66i		−	1.60312i	0.597912	−	0.801561i	$-0.295997\pi$
$132$		0			0
$133$	578.534			0.377183
$134$	−67.9539	−	493.643i	−0.0438084	−	0.318241i
$135$		0			0
$136$	−2716.19	+	1181.81i	−1.71258	+	0.745145i
$137$	1769.34			1.10339			0.551696	−	0.834046i	$-0.313981\pi$
$137$	1769.34			1.10339			0.551696	+	0.834046i	$0.313981\pi$
$138$		0			0
$139$	1536.40			0.937525			0.468762	−	0.883324i	$-0.344700\pi$
$139$	1536.40			0.937525			0.468762	+	0.883324i	$0.344700\pi$
$140$	−891.212	+	2532.22i	−0.538008	+	1.52865i
$141$		0			0
$142$	123.427	−	16.9907i	0.0729421	−	0.0100411i
$143$			587.197i			0.343384i
$144$		0			0
$145$	1130.76	−	1610.97i	0.647617	−	0.922649i
$146$	−305.951	−	2222.55i	−0.173430	−	1.25986i
$147$		0			0
$148$	−708.486	+	198.825i	−0.393494	+	0.110428i
$149$	2159.81			1.18751			0.593755	−	0.804646i	$-0.297645\pi$
$149$	2159.81			1.18751			0.593755	+	0.804646i	$0.297645\pi$
$150$		0			0
$151$			2297.09i			1.23798i	0.785399	+	0.618990i	$0.212458\pi$
$151$			2297.09i			1.23798i	−0.785399	+	0.618990i	$0.787542\pi$
$152$	399.947	−	174.017i	0.213421	−	0.0928596i
$153$		0			0
$154$	552.283	+	4011.99i	0.288988	+	2.09932i
$155$	−1571.21	−	1102.85i	−0.814213	−	0.571504i
$156$		0			0
$157$	−583.054			−0.296387			−0.148194	−	0.988958i	$-0.547346\pi$
$157$	−583.054			−0.296387			−0.148194	+	0.988958i	$0.547346\pi$
$158$	359.098	+	2608.62i	0.180812	+	1.31349i
$159$		0			0
$160$	145.560	+	2018.62i	0.0719222	+	0.997410i
$161$		−	1762.43i		−	0.862726i
$162$		0			0
$163$		−	1935.19i		−	0.929912i	−0.885334	−	0.464956i	$-0.846070\pi$
$163$		−	1935.19i		−	0.929912i	0.885334	−	0.464956i	$-0.153930\pi$
$164$	−543.522	−	1936.77i	−0.258792	−	0.922170i
$165$		0			0
$166$	−2683.28	+	369.375i	−1.25460	+	0.172705i
$167$			3372.89i			1.56289i	0.623977	+	0.781443i	$0.285516\pi$
$167$			3372.89i			1.56289i	−0.623977	+	0.781443i	$0.714484\pi$
$168$		0			0
$169$	−2045.50			−0.931043
$170$	−1894.03	+	3681.04i	−0.854502	+	1.66072i
$171$		0			0
$172$	−104.335	−	371.783i	−0.0462527	−	0.164815i
$173$		−	3157.67i		−	1.38771i	−0.720117	−	0.693853i	$-0.755912\pi$
$173$		−	3157.67i		−	1.38771i	0.720117	−	0.693853i	$-0.244088\pi$
$174$		0			0
$175$	1275.09	+	3528.33i	0.550788	+	1.52409i
$176$	1588.57	+	2607.41i	0.680356	+	1.11671i
$177$		0			0
$178$	−485.596	−	3527.56i	−0.204477	−	1.48540i
$179$			3985.75i			1.66430i	0.554553	+	0.832149i	$0.312889\pi$
$179$			3985.75i			1.66430i	−0.554553	+	0.832149i	$0.687111\pi$
$180$		0			0
$181$		−	4404.55i		−	1.80877i	−0.426716	−	0.904386i	$-0.640330\pi$
$181$		−	4404.55i		−	1.80877i	0.426716	−	0.904386i	$-0.359670\pi$
$182$	1035.11	−	142.492i	0.421581	−	0.0580339i
$183$		0			0
$184$	−530.120	−	1218.39i	−0.212397	−	0.488156i
$185$	−590.821	+	841.734i	−0.234800	+	0.334516i
$186$		0			0
$187$			6245.26i			2.44224i
$188$	−1084.85	−	3865.72i	−0.420856	−	1.49966i
$189$		0			0
$190$	278.888	−	542.018i	0.106488	−	0.206958i
$191$	−2673.54			−1.01283			−0.506416	−	0.862289i	$-0.669030\pi$
$191$	−2673.54			−1.01283			−0.506416	+	0.862289i	$0.669030\pi$
$192$		0			0
$193$		−	2247.90i		−	0.838379i	−0.907899	−	0.419190i	$-0.862314\pi$
$193$		−	2247.90i		−	0.838379i	0.907899	−	0.419190i	$-0.137686\pi$
$194$	−36.4783	−	264.992i	−0.0134999	−	0.0980687i
$195$		0			0
$196$	4296.40	−	1205.72i	1.56574	−	0.439401i
$197$			2864.97i			1.03615i	0.855337	+	0.518073i	$0.173350\pi$
$197$			2864.97i			1.03615i	−0.855337	+	0.518073i	$0.826650\pi$
$198$		0			0
$199$		−	17.8425i		−	0.00635587i	−0.999995	−	0.00317794i	$-0.998988\pi$
$199$		−	17.8425i		−	0.00635587i	0.999995	−	0.00317794i	$-0.00101157\pi$
$200$	1942.77	+	2055.64i	0.686873	+	0.726778i
$201$		0			0
$202$	−2495.72	+	343.556i	−0.869298	+	0.119666i
$203$	−5283.60			−1.82678
$204$		0			0
$205$	−2301.02	−	1615.11i	−0.783952	−	0.550264i
$206$	−4452.35	+	612.902i	−1.50587	+	0.207296i
$207$		0			0
$208$	672.725	−	409.857i	0.224255	−	0.136627i
$209$		−	919.589i		−	0.304351i
$210$		0			0
$211$	−2683.79			−0.875639			−0.437819	−	0.899063i	$-0.644249\pi$
$211$	−2683.79			−0.875639			−0.437819	+	0.899063i	$0.644249\pi$
$212$	−481.806	−	1716.85i	−0.156087	−	0.556196i
$213$		0			0
$214$	−1210.07	+	166.576i	−0.386537	+	0.0532099i
$215$	−441.706	−	310.038i	−0.140112	−	0.0983461i
$216$		0			0
$217$			5153.20i			1.61208i
$218$	−212.248	−	1541.85i	−0.0659415	−	0.479024i
$219$		0			0
$220$	4024.99	+	1416.59i	1.23348	+	0.434122i
$221$	1611.31			0.490444
$222$		0			0
$223$	1920.30			0.576649			0.288325	−	0.957533i	$-0.406902\pi$
$223$	1920.30			0.576649			0.288325	+	0.957533i	$0.406902\pi$
$224$	4210.87	−	3433.06i	1.25603	−	1.02402i
$225$		0			0
$226$	3025.10	−	416.429i	0.890382	−	0.122568i
$227$	2563.20			0.749452			0.374726	−	0.927136i	$-0.377737\pi$
$227$	2563.20			0.749452			0.374726	+	0.927136i	$0.377737\pi$
$228$		0			0
$229$			2500.32i			0.721510i	0.932661	+	0.360755i	$0.117481\pi$
$229$			2500.32i			0.721510i	−0.932661	+	0.360755i	$0.882519\pi$
$230$	−1651.19	−	849.595i	−0.473374	−	0.243568i
$231$		0			0
$232$	−3652.61	+	1589.25i	−1.03365	+	0.449740i
$233$	3200.11			0.899770			0.449885	−	0.893086i	$-0.351465\pi$
$233$	3200.11			0.899770			0.449885	+	0.893086i	$0.351465\pi$
$234$		0			0
$235$	−4592.76	−	3223.71i	−1.27489	−	0.894857i
$236$	−753.912	−	2686.46i	−0.207947	−	0.740990i
$237$		0			0
$238$	11009.2	−	1515.50i	2.99840	−	0.412754i
$239$	−5141.98			−1.39166			−0.695831	−	0.718206i	$-0.744964\pi$
$239$	−5141.98			−1.39166			−0.695831	+	0.718206i	$0.744964\pi$
$240$		0			0
$241$	2166.48			0.579068			0.289534	−	0.957168i	$-0.406500\pi$
$241$	2166.48			0.579068			0.289534	+	0.957168i	$0.406500\pi$
$242$	2647.66	−	364.471i	0.703296	−	0.0968144i
$243$		0			0
$244$	−1658.26	−	5908.98i	−0.435079	−	1.55034i
$245$	3582.86	−	5104.44i	0.934288	−	1.33107i
$246$		0			0
$247$	−237.258			−0.0611189
$248$	1550.03	+	3562.46i	0.396883	+	0.912164i
$249$		0			0
$250$	3920.29	+	506.253i	0.991765	+	0.128073i
$251$		−	644.051i		−	0.161961i	−0.996716	−	0.0809803i	$-0.974195\pi$
$251$		−	644.051i		−	0.161961i	0.996716	−	0.0809803i	$-0.0258051\pi$
$252$		0			0
$253$	−2801.41			−0.696138
$254$	−3038.48	+	418.271i	−0.750595	+	0.103325i
$255$		0			0
$256$	1878.39	−	3639.90i	0.458592	−	0.888647i
$257$	−833.964			−0.202417			−0.101209	−	0.994865i	$-0.532271\pi$
$257$	−833.964			−0.202417			−0.101209	+	0.994865i	$0.532271\pi$
$258$		0			0
$259$	2760.68			0.662318
$260$	365.488	−	1038.47i	0.0871792	−	0.247704i
$261$		0			0
$262$	927.137	+	6735.07i	0.218621	+	1.58815i
$263$			1387.16i			0.325232i	0.986689	+	0.162616i	$0.0519932\pi$
$263$			1387.16i			0.325232i	−0.986689	+	0.162616i	$0.948007\pi$
$264$		0			0
$265$	−2039.74	−	1431.72i	−0.472831	−	0.331885i
$266$	−1621.05	+	223.151i	−0.373659	+	0.0514371i
$267$		0			0
$268$	380.814	+	1356.98i	0.0867982	+	0.309293i
$269$	7358.13			1.66778			0.833891	−	0.551930i	$-0.186108\pi$
$269$	7358.13			1.66778			0.833891	+	0.551930i	$0.186108\pi$
$270$		0			0
$271$			931.650i			0.208833i	0.994534	+	0.104416i	$0.0332975\pi$
$271$			931.650i			0.208833i	−0.994534	+	0.104416i	$0.966703\pi$
$272$	7154.92	−	4359.13i	1.59497	−	0.971732i
$273$		0			0
$274$	−4957.69	+	682.465i	−1.09308	+	0.150472i
$275$	5608.33	−	2026.78i	1.22980	−	0.444434i
$276$		0			0
$277$	−4074.91			−0.883891			−0.441946	−	0.897042i	$-0.645712\pi$
$277$	−4074.91			−0.883891			−0.441946	+	0.897042i	$0.645712\pi$
$278$	−4305.00	+	592.618i	−0.928766	+	0.127852i
$279$		0			0
$280$	1520.46	−	7439.03i	0.324517	−	1.58774i
$281$			1403.68i			0.297995i	0.988838	+	0.148997i	$0.0476046\pi$
$281$			1403.68i			0.297995i	−0.988838	+	0.148997i	$0.952395\pi$
$282$		0			0
$283$		−	2892.07i		−	0.607476i	−0.952756	−	0.303738i	$-0.901765\pi$
$283$		−	2892.07i		−	0.607476i	0.952756	−	0.303738i	$-0.0982348\pi$
$284$	−339.289	+	95.2161i	−0.0708913	+	0.0198945i
$285$		0			0
$286$	−226.492	−	1645.33i	−0.0468279	−	0.340176i
$287$			7546.79i			1.55217i
$288$		0			0
$289$	12224.4			2.48818
$290$	−2547.01	+	4950.11i	−0.515743	+	1.00235i
$291$		0			0
$292$	1714.55	+	6109.57i	0.343619	+	1.22444i
$293$		−	672.210i		−	0.134031i	−0.997752	−	0.0670153i	$-0.978652\pi$
$293$		−	672.210i		−	0.134031i	0.997752	−	0.0670153i	$-0.0213476\pi$
$294$		0			0
$295$	−3191.71	−	2240.30i	−0.629928	−	0.442153i
$296$	1908.49	−	830.385i	0.374759	−	0.163058i
$297$		0			0
$298$	−6051.81	+	833.080i	−1.17642	+	0.161943i
$299$			722.776i			0.139797i
$300$		0			0
$301$			1448.69i			0.277412i
$302$	−886.031	−	6436.47i	−0.168826	−	1.22641i
$303$		0			0
$304$	−1053.53	+	641.863i	−0.198764	+	0.121097i
$305$	−7020.31	−	4927.63i	−1.31797	−	0.925098i
$306$		0			0
$307$		−	6301.27i		−	1.17144i	−0.810513	−	0.585721i	$-0.800812\pi$
$307$		−	6301.27i		−	1.17144i	0.810513	−	0.585721i	$-0.199188\pi$
$308$	−3095.00	−	11028.6i	−0.572577	−	2.04030i
$309$		0			0
$310$	4827.94	+	2484.15i	0.884543	+	0.455129i
$311$	3593.53			0.655211			0.327605	−	0.944815i	$-0.393758\pi$
$311$	3593.53			0.655211			0.327605	+	0.944815i	$0.393758\pi$
$312$		0			0
$313$		−	280.154i		−	0.0505917i	−0.999680	−	0.0252959i	$-0.991947\pi$
$313$		−	280.154i		−	0.0505917i	0.999680	−	0.0252959i	$-0.00805279\pi$
$314$	1633.72	−	224.895i	0.293618	−	0.0404189i
$315$		0			0
$316$	−2012.39	−	7170.86i	−0.358245	−	1.27656i
$317$		−	2309.39i		−	0.409173i	−0.978848	−	0.204587i	$-0.934415\pi$
$317$		−	2309.39i		−	0.409173i	0.978848	−	0.204587i	$-0.0655850\pi$
$318$		0			0
$319$			8398.36i			1.47404i
$320$	−1186.48	−	5600.02i	−0.207269	−	0.978284i
$321$		0			0
$322$	679.801	+	4938.33i	0.117652	+	0.854666i
$323$	−2523.41			−0.434695
$324$		0			0
$325$	−522.918	−	1446.97i	−0.0892500	−	0.246965i
$326$	746.437	+	5422.40i	0.126814	+	0.921224i
$327$		0			0
$328$	2270.00	+	5217.18i	0.382133	+	0.878263i
$329$			15063.1i			2.52419i
$330$		0			0
$331$	−645.969			−0.107268			−0.0536340	−	0.998561i	$-0.517080\pi$
$331$	−645.969			−0.107268			−0.0536340	+	0.998561i	$0.517080\pi$
$332$	7376.08	−	2069.98i	1.21932	−	0.342183i
$333$		0			0
$334$	−1300.98	−	9450.84i	−0.213134	−	1.54829i
$335$	1612.19	+	1131.61i	0.262935	+	0.184557i
$336$		0			0
$337$		−	1553.74i		−	0.251149i	−0.992084	−	0.125575i	$-0.959923\pi$
$337$		−	1553.74i		−	0.251149i	0.992084	−	0.125575i	$-0.0400775\pi$
$338$	5731.50	−	788.987i	0.922345	−	0.126968i
$339$		0			0
$340$	3887.23	−	11044.9i	0.620043	−	1.76174i
$341$	8191.09			1.30080
$342$		0			0
$343$	−6446.77			−1.01485
$344$	435.751	+	1001.49i	0.0682968	+	0.156968i
$345$		0			0
$346$	1217.97	+	8847.80i	0.189244	+	1.37474i
$347$	5377.86			0.831984			0.415992	−	0.909368i	$-0.363434\pi$
$347$	5377.86			0.831984			0.415992	+	0.909368i	$0.363434\pi$
$348$		0			0
$349$		−	6328.99i		−	0.970725i	−0.874313	−	0.485363i	$-0.838688\pi$
$349$		−	6328.99i		−	0.970725i	0.874313	−	0.485363i	$-0.161312\pi$
$350$	−4933.75	−	9394.56i	−0.753486	−	1.43474i
$351$		0			0
$352$	−5456.89	−	6693.24i	−0.826288	−	1.01350i
$353$	4900.97			0.738958			0.369479	−	0.929239i	$-0.379536\pi$
$353$	4900.97			0.738958			0.369479	+	0.929239i	$0.379536\pi$
$354$		0			0
$355$	−282.941	+	403.101i	−0.0423012	+	0.0602659i
$356$	2721.28	+	9696.92i	0.405134	+	1.44364i
$357$		0			0
$358$	−1537.38	−	11168.1i	−0.226963	−	1.64875i
$359$	9040.04			1.32901			0.664506	−	0.747283i	$-0.268642\pi$
$359$	9040.04			1.32901			0.664506	+	0.747283i	$0.268642\pi$
$360$		0			0
$361$	−6487.44			−0.945829
$362$	1698.91	+	12341.6i	0.246666	+	1.79187i
$363$		0			0
$364$	−2845.43	+	798.523i	−0.409728	+	0.114984i
$365$	7258.62	+	5094.90i	1.04091	+	0.730628i
$366$		0			0
$367$	−6852.20			−0.974610			−0.487305	−	0.873232i	$-0.662020\pi$
$367$	−6852.20			−0.974610			−0.487305	+	0.873232i	$0.662020\pi$
$368$	1955.35	+	3209.45i	0.276983	+	0.454630i
$369$		0			0
$370$	1330.81	−	2586.43i	0.186988	−	0.363411i
$371$			6689.86i			0.936173i
$372$		0			0
$373$	−10739.6			−1.49082			−0.745412	−	0.666604i	$-0.767747\pi$
$373$	−10739.6			−1.49082			−0.745412	+	0.666604i	$0.767747\pi$
$374$	−2408.91	−	17499.2i	−0.333053	−	2.41942i
$375$		0			0
$376$	4530.84	+	10413.3i	0.621436	+	1.42826i
$377$	2166.82			0.296013
$378$		0			0
$379$	127.127			0.0172298			0.00861490	−	0.999963i	$-0.497258\pi$
$379$	127.127			0.0172298			0.00861490	+	0.999963i	$0.497258\pi$
$380$	−572.378	+	1626.31i	−0.0772694	+	0.219547i
$381$		0			0
$382$	7491.28	−	1031.23i	1.00337	−	0.138122i
$383$		−	53.6921i		−	0.00716329i	−0.999994	−	0.00358164i	$-0.998860\pi$
$383$		−	53.6921i		−	0.00716329i	0.999994	−	0.00358164i	$-0.00114007\pi$
$384$		0			0
$385$	−13102.8	−	9196.98i	−1.73449	−	1.21746i
$386$	867.055	+	6298.61i	0.114331	+	0.830547i
$387$		0			0
$388$	204.424	+	728.438i	0.0267476	+	0.0953115i
$389$	−12686.7			−1.65357			−0.826787	−	0.562515i	$-0.809834\pi$
$389$	−12686.7			−1.65357			−0.826787	+	0.562515i	$0.809834\pi$
$390$		0			0
$391$			7687.24i			0.994273i
$392$	−11573.5	+	5035.62i	−1.49119	+	0.648819i
$393$		0			0
$394$	−1105.07	−	8027.65i	−0.141301	−	1.02647i
$395$	−8519.51	−	5979.93i	−1.08522	−	0.761729i
$396$		0			0
$397$	−12440.9			−1.57277			−0.786386	−	0.617736i	$-0.788050\pi$
$397$	−12440.9			−1.57277			−0.786386	+	0.617736i	$0.788050\pi$
$398$	6.88216	+	49.9947i	0.000866763	+	0.00629650i
$399$		0			0
$400$	−6236.54	−	5010.54i	−0.779568	−	0.626318i
$401$			1826.48i			0.227456i	0.993512	+	0.113728i	$0.0362793\pi$
$401$			1826.48i			0.227456i	−0.993512	+	0.113728i	$0.963721\pi$
$402$		0			0
$403$		−	2113.34i		−	0.261223i
$404$	6860.50	−	1925.29i	0.844857	−	0.237096i
$405$		0			0
$406$	14804.7	−	2037.98i	1.80971	−	0.249121i
$407$		−	4388.14i		−	0.534428i
$408$		0			0
$409$	−4334.43			−0.524020			−0.262010	−	0.965065i	$-0.584385\pi$
$409$	−4334.43			−0.524020			−0.262010	+	0.965065i	$0.584385\pi$
$410$	7070.44	+	3638.00i	0.851669	+	0.438214i
$411$		0			0
$412$	12239.1	−	3434.71i	1.46354	−	0.410718i
$413$			10468.0i			1.24721i
$414$		0			0
$415$	6151.07	−	8763.33i	0.727576	−	1.03657i
$416$	−1726.89	+	1407.90i	−0.203528	+	0.165933i
$417$		0			0
$418$	354.702	+	2576.69i	0.0415049	+	0.301507i
$419$			4336.30i			0.505589i	0.967520	+	0.252795i	$0.0813497\pi$
$419$			4336.30i			0.505589i	−0.967520	+	0.252795i	$0.918650\pi$
$420$		0			0
$421$			11658.1i			1.34960i	0.738003	+	0.674798i	$0.235769\pi$
$421$			11658.1i			1.34960i	−0.738003	+	0.674798i	$0.764231\pi$
$422$	7519.99	−	1035.19i	0.867458	−	0.119413i
$423$		0			0
$424$	2012.24	+	4624.77i	0.230479	+	0.529714i
$425$	−5561.61	−	15389.6i	−0.634771	−	1.75649i
$426$		0			0
$427$			23024.9i			2.60949i
$428$	3326.38	−	933.494i	0.375669	−	0.105426i
$429$		0			0
$430$	1357.25	+	698.353i	0.152215	+	0.0783200i
$431$	−8561.67			−0.956848			−0.478424	−	0.878129i	$-0.658792\pi$
$431$	−8561.67			−0.956848			−0.478424	+	0.878129i	$0.658792\pi$
$432$		0			0
$433$			7812.50i			0.867078i	0.901135	+	0.433539i	$0.142735\pi$
$433$			7812.50i			0.867078i	−0.901135	+	0.433539i	$0.857265\pi$
$434$	−1987.68	−	14439.3i	−0.219843	−	1.59702i
$435$		0			0
$436$	1189.44	+	4238.40i	0.130651	+	0.465556i
$437$		−	1131.91i		−	0.123906i
$438$		0			0
$439$			8549.99i			0.929542i	0.885431	+	0.464771i	$0.153863\pi$
$439$			8549.99i			0.929542i	−0.885431	+	0.464771i	$0.846137\pi$
$440$	−11824.5	−	2416.79i	−1.28116	−	0.261854i
$441$		0			0
$442$	−4514.89	+	621.510i	−0.485863	+	0.0668829i
$443$	−12070.3			−1.29453			−0.647267	−	0.762263i	$-0.724088\pi$
$443$	−12070.3			−1.29453			−0.647267	+	0.762263i	$0.724088\pi$
$444$		0			0
$445$	11520.7	+	8086.47i	1.22726	+	0.861428i
$446$	−5380.68	+	740.694i	−0.571262	+	0.0786388i
$447$		0			0
$448$	−10474.7	+	11243.6i	−1.10465	+	1.18574i
$449$			3921.31i			0.412157i	0.978536	+	0.206078i	$0.0660701\pi$
$449$			3921.31i			0.412157i	−0.978536	+	0.206078i	$0.933930\pi$
$450$		0			0
$451$	11995.7			1.25245
$452$	−8315.71	+	2333.67i	−0.865349	+	0.242846i
$453$		0			0
$454$	−7182.09	+	988.673i	−0.742450	+	0.102204i
$455$	−2372.86	+	3380.58i	−0.244487	+	0.348316i
$456$		0			0
$457$		−	3943.68i		−	0.403671i	−0.979419	−	0.201836i	$-0.935309\pi$
$457$		−	3943.68i		−	0.403671i	0.979419	−	0.201836i	$-0.0646906\pi$
$458$	−964.418	−	7005.90i	−0.0983937	−	0.714769i
$459$		0			0
$460$	4954.33	+	1743.67i	0.502167	+	0.176737i
$461$	−4419.40			−0.446490			−0.223245	−	0.974762i	$-0.571665\pi$
$461$	−4419.40			−0.446490			−0.223245	+	0.974762i	$0.571665\pi$
$462$		0			0
$463$	4741.82			0.475963			0.237981	−	0.971270i	$-0.423514\pi$
$463$	4741.82			0.475963			0.237981	+	0.971270i	$0.423514\pi$
$464$	9621.63	−	5861.97i	0.962657	−	0.586498i
$465$		0			0
$466$	−8966.73	+	1234.34i	−0.891364	+	0.122703i
$467$	−1055.37			−0.104576			−0.0522878	−	0.998632i	$-0.516651\pi$
$467$	−1055.37			−0.104576			−0.0522878	+	0.998632i	$0.516651\pi$
$468$		0			0
$469$		−	5287.59i		−	0.520593i
$470$	14112.4	+	7261.32i	1.38501	+	0.712638i
$471$		0			0
$472$	3148.68	+	7236.68i	0.307055	+	0.705710i
$473$	2302.71			0.223845
$474$		0			0
$475$	818.924	+	2266.06i	0.0791048	+	0.218892i
$476$	−30263.2	+	8492.88i	−2.91410	+	0.817795i
$477$		0			0
$478$	14407.8	−	1983.36i	1.37866	−	0.189784i
$479$	6345.69			0.605307			0.302653	−	0.953101i	$-0.402128\pi$
$479$	6345.69			0.605307			0.302653	+	0.953101i	$0.402128\pi$
$480$		0			0
$481$	−1132.16			−0.107322
$482$	−6070.49	+	835.652i	−0.573659	+	0.0789687i
$483$		0			0
$484$	−7278.16	+	2042.50i	−0.683523	+	0.191820i
$485$	865.438	+	607.460i	0.0810258	+	0.0568729i
$486$		0			0
$487$	−8953.22			−0.833078			−0.416539	−	0.909118i	$-0.636757\pi$
$487$	−8953.22			−0.833078			−0.416539	+	0.909118i	$0.636757\pi$
$488$	6925.65	+	15917.4i	0.642438	+	1.47653i
$489$		0			0
$490$	−8070.31	+	15684.6i	−0.744040	+	1.44604i
$491$		−	11928.2i		−	1.09636i	−0.836362	−	0.548178i	$-0.815322\pi$
$491$		−	11928.2i		−	1.09636i	0.836362	−	0.548178i	$-0.184678\pi$
$492$		0			0
$493$	23045.7			2.10532
$494$	664.798	−	91.5147i	0.0605479	−	0.00833490i
$495$		0			0
$496$	−5717.29	−	9384.16i	−0.517569	−	0.849519i
$497$	1322.07			0.119322
$498$		0			0
$499$	4117.81			0.369416			0.184708	−	0.982793i	$-0.440866\pi$
$499$	4117.81			0.369416			0.184708	+	0.982793i	$0.440866\pi$
$500$	−11179.9	+	93.6066i	−0.999965	+	0.00837243i
$501$		0			0
$502$	248.422	+	1804.63i	0.0220869	+	0.160448i
$503$			8800.34i			0.780095i	0.920795	+	0.390048i	$0.127541\pi$
$503$			8800.34i			0.780095i	−0.920795	+	0.390048i	$0.872459\pi$
$504$		0			0
$505$	5721.11	−	8150.78i	0.504131	−	0.718227i
$506$	7849.55	−	1080.55i	0.689634	−	0.0949337i
$507$		0			0
$508$	8352.49	−	2343.99i	0.729492	−	0.204720i
$509$	−20872.7			−1.81761			−0.908806	−	0.417219i	$-0.863005\pi$
$509$	−20872.7			−1.81761			−0.908806	+	0.417219i	$0.863005\pi$
$510$		0			0
$511$		−	23806.5i		−	2.06094i
$512$	−3859.29	+	10923.5i	−0.333122	+	0.942884i
$513$		0			0
$514$	2336.77	−	321.675i	0.200526	−	0.0276040i
$515$	10206.4	−	14541.0i	0.873300	−	1.24418i
$516$		0			0
$517$	23943.1			2.03678
$518$	−7735.44	+	1064.84i	−0.656130	+	0.0903216i
$519$		0			0
$520$	−623.542	+	3050.76i	−0.0525849	+	0.257279i
$521$		−	11229.4i		−	0.944275i	−0.881525	−	0.472137i	$-0.843483\pi$
$521$		−	11229.4i		−	0.944275i	0.881525	−	0.472137i	$-0.156517\pi$
$522$		0			0
$523$		−	19234.9i		−	1.60819i	−0.594501	−	0.804095i	$-0.702650\pi$
$523$		−	19234.9i		−	1.60819i	0.594501	−	0.804095i	$-0.297350\pi$
$524$	−5195.68	−	18514.1i	−0.433157	−	1.54350i
$525$		0			0
$526$	−535.053	−	3886.83i	−0.0443525	−	0.322193i
$527$		−	22476.9i		−	1.85789i
$528$		0			0
$529$	8718.77			0.716592
$530$	6267.60	+	3224.91i	0.513674	+	0.264304i
$531$		0			0
$532$	4456.13	−	1250.54i	0.363153	−	0.101913i
$533$		−	3094.95i		−	0.251515i
$534$		0			0
$535$	2773.94	−	3951.98i	0.224164	−	0.319363i
$536$	−1590.45	−	3655.37i	−0.128166	−	0.294567i
$537$		0			0
$538$	−20617.5	+	2838.16i	−1.65220	+	0.227439i
$539$			26610.6i			2.12653i
$540$		0			0
$541$			708.100i			0.0562728i	0.999604	+	0.0281364i	$0.00895727\pi$
$541$			708.100i			0.0562728i	−0.999604	+	0.0281364i	$0.991043\pi$
$542$	−359.354	−	2610.49i	−0.0284790	−	0.206882i
$543$		0			0
$544$	−18366.7	+	14974.1i	−1.44755	+	1.18016i
$545$	5035.53	+	3534.49i	0.395777	+	0.277800i
$546$		0			0
$547$		−	19627.6i		−	1.53421i	−0.641519	−	0.767107i	$-0.721696\pi$
$547$		−	19627.6i		−	1.53421i	0.641519	−	0.767107i	$-0.278304\pi$
$548$	13628.2	−	3824.54i	1.06235	−	0.298132i
$549$		0			0
$550$	−14932.8	+	7842.27i	−1.15770	+	0.607992i
$551$	−3393.38			−0.262364
$552$		0			0
$553$			27941.9i			2.14866i
$554$	11417.9	−	1571.77i	0.875634	−	0.120538i
$555$		0			0
$556$	11834.0	−	3321.04i	0.902654	−	0.253315i
$557$			696.440i			0.0529787i	0.999649	+	0.0264893i	$0.00843280\pi$
$557$			696.440i			0.0529787i	−0.999649	+	0.0264893i	$0.991567\pi$
$558$		0			0
$559$		−	594.110i		−	0.0449520i
$560$	−1390.95	+	21430.7i	−0.104962	+	1.61716i
$561$		0			0
$562$	−541.424	−	3933.11i	−0.0406381	−	0.295211i
$563$	15372.1			1.15072			0.575360	−	0.817900i	$-0.304862\pi$
$563$	15372.1			1.15072			0.575360	+	0.817900i	$0.304862\pi$
$564$		0			0
$565$	−6934.64	+	9879.67i	−0.516359	+	0.735648i
$566$	1115.52	+	8103.59i	0.0828427	+	0.601801i
$567$		0			0
$568$	913.964	−	397.666i	0.0675159	−	0.0293762i
$569$			2009.97i			0.148088i	0.997255	+	0.0740440i	$0.0235905\pi$
$569$			2009.97i			0.148088i	−0.997255	+	0.0740440i	$0.976409\pi$
$570$		0			0
$571$	−17205.1			−1.26097			−0.630483	−	0.776203i	$-0.717143\pi$
$571$	−17205.1			−1.26097			−0.630483	+	0.776203i	$0.717143\pi$
$572$	1269.26	+	4522.85i	0.0927808	+	0.330612i
$573$		0			0
$574$	−2910.93	−	21146.1i	−0.211672	−	1.53767i
$575$	6903.25	−	2494.74i	0.500670	−	0.180936i
$576$		0			0
$577$		−	3567.94i		−	0.257427i	−0.991682	−	0.128713i	$-0.958915\pi$
$577$		−	3567.94i		−	0.257427i	0.991682	−	0.128713i	$-0.0410847\pi$
$578$	−34252.9	+	4715.18i	−2.46493	+	0.339318i
$579$		0			0
$580$	5227.38	−	14852.6i	0.374233	−	1.06331i
$581$	−28741.6			−2.05233
$582$		0			0
$583$	10633.6			0.755403
$584$	−7160.76	−	16457.7i	−0.507387	−	1.16614i
$585$		0			0
$586$	259.284	+	1883.53i	0.0182780	+	0.132778i
$587$	9766.27			0.686707			0.343354	−	0.939206i	$-0.388437\pi$
$587$	9766.27			0.686707			0.343354	+	0.939206i	$0.388437\pi$
$588$		0			0
$589$			3309.63i			0.231529i
$590$	9807.32	+	5046.22i	0.684341	+	0.352118i
$591$		0			0
$592$	−5027.30	+	3062.88i	−0.349021	+	0.212641i
$593$	−2128.52			−0.147400			−0.0736998	−	0.997280i	$-0.523481\pi$
$593$	−2128.52			−0.147400			−0.0736998	+	0.997280i	$0.523481\pi$
$594$		0			0
$595$	−25237.1	+	35954.9i	−1.73886	+	2.47732i
$596$	16635.9	−	4668.58i	1.14334	−	0.320860i
$597$		0			0
$598$	−278.788	−	2025.22i	−0.0190643	−	0.138491i
$599$	−2371.06			−0.161735			−0.0808673	−	0.996725i	$-0.525769\pi$
$599$	−2371.06			−0.161735			−0.0808673	+	0.996725i	$0.525769\pi$
$600$		0			0
$601$	18686.8			1.26830			0.634152	−	0.773208i	$-0.281349\pi$
$601$	18686.8			1.26830			0.634152	+	0.773208i	$0.281349\pi$
$602$	−558.785	−	4059.23i	−0.0378312	−	0.274820i
$603$		0			0
$604$	4965.32	+	17693.2i	0.334497	+	1.19193i
$605$	−6069.41	+	8646.99i	−0.407862	+	0.581074i
$606$		0			0
$607$	24274.6			1.62319			0.811594	−	0.584222i	$-0.198600\pi$
$607$	24274.6			1.62319			0.811594	+	0.584222i	$0.198600\pi$
$608$	2704.42	−	2204.87i	0.180393	−	0.147071i
$609$		0			0
$610$	21571.6	+	11099.4i	1.43182	+	0.736721i
$611$		−	6177.42i		−	0.409021i
$612$		0			0
$613$	−2264.69			−0.149217			−0.0746085	−	0.997213i	$-0.523771\pi$
$613$	−2264.69			−0.149217			−0.0746085	+	0.997213i	$0.523771\pi$
$614$	2430.51	+	17656.2i	0.159752	+	1.16050i
$615$		0			0
$616$	12926.1	+	29708.4i	0.845468	+	1.94316i
$617$	−17276.4			−1.12726			−0.563632	−	0.826026i	$-0.690596\pi$
$617$	−17276.4			−1.12726			−0.563632	+	0.826026i	$0.690596\pi$
$618$		0			0
$619$	18822.8			1.22222			0.611108	−	0.791547i	$-0.290724\pi$
$619$	18822.8			1.22222			0.611108	+	0.791547i	$0.290724\pi$
$620$	−14486.1	−	5098.36i	−0.938346	−	0.330250i
$621$		0			0
$622$	−10069.1	+	1386.09i	−0.649090	+	0.0893524i
$623$		−	37785.0i		−	2.42989i
$624$		0			0
$625$	−12015.2	+	9988.80i	−0.768971	+	0.639283i
$626$	108.060	+	784.991i	0.00689930	+	0.0501191i
$627$		0			0
$628$	−4490.94	+	1260.31i	−0.285363	+	0.0800826i
$629$	−12041.4			−0.763307
$630$		0			0
$631$		−	17384.1i		−	1.09675i	−0.836232	−	0.548376i	$-0.815246\pi$
$631$		−	17384.1i		−	1.09675i	0.836232	−	0.548376i	$-0.184754\pi$
$632$	8404.64	+	19316.6i	0.528985	+	1.21578i
$633$		0			0
$634$	890.772	+	6470.90i	0.0557998	+	0.405351i
$635$	6965.32	−	9923.38i	0.435292	−	0.620153i
$636$		0			0
$637$	6865.65			0.427044
$638$	−3239.40	−	23532.2i	−0.201017	−	1.46027i
$639$		0			0
$640$	5484.54	+	15233.6i	0.338743	+	0.940879i
$641$			3085.16i			0.190104i	0.995472	+	0.0950518i	$0.0303017\pi$
$641$			3085.16i			0.190104i	−0.995472	+	0.0950518i	$0.969698\pi$
$642$		0			0
$643$		−	26407.4i		−	1.61960i	−0.586704	−	0.809801i	$-0.699575\pi$
$643$		−	26407.4i		−	1.61960i	0.586704	−	0.809801i	$-0.300425\pi$
$644$	−3809.61	−	13575.0i	−0.233105	−	0.830637i
$645$		0			0
$646$	7070.61	−	973.326i	0.430634	−	0.0592802i
$647$			9941.26i			0.604067i	0.953297	+	0.302033i	$0.0976654\pi$
$647$			9941.26i			0.604067i	−0.953297	+	0.302033i	$0.902335\pi$
$648$		0			0
$649$	16639.1			1.00638
$650$	2023.34	+	3852.73i	0.122095	+	0.232487i
$651$		0			0
$652$	−4183.04	−	14905.7i	−0.251258	−	0.895324i
$653$			4118.36i			0.246806i	0.992357	+	0.123403i	$0.0393807\pi$
$653$			4118.36i			0.246806i	−0.992357	+	0.123403i	$0.960619\pi$
$654$		0			0
$655$	−21996.1	−	15439.3i	−1.31215	−	0.921012i
$656$	−8372.89	−	13743.0i	−0.498333	−	0.817946i
$657$		0			0
$658$	−5810.13	−	42207.0i	−0.344228	−	2.50061i
$659$			19103.5i			1.12924i	0.825352	+	0.564619i	$0.190977\pi$
$659$			19103.5i			1.12924i	−0.825352	+	0.564619i	$0.809023\pi$
$660$		0			0
$661$		−	1795.57i		−	0.105657i	−0.998604	−	0.0528287i	$-0.983176\pi$
$661$		−	1795.57i		−	0.105657i	0.998604	−	0.0528287i	$-0.0168237\pi$
$662$	1810.01	−	249.162i	0.106266	−	0.0146283i
$663$		0			0
$664$	−19869.4	+	8645.18i	−1.16127	+	0.505268i
$665$	3716.06	−	5294.21i	0.216696	−	0.308723i
$666$		0			0
$667$			10337.5i			0.600103i
$668$	7290.72	+	25979.5i	0.422285	+	1.50476i
$669$		0			0
$670$	−4953.85	−	2548.93i	−0.285647	−	0.146976i
$671$	36598.4			2.10561
$672$		0			0
$673$			31751.3i			1.81861i	0.416133	+	0.909304i	$0.363385\pi$
$673$			31751.3i			1.81861i	−0.416133	+	0.909304i	$0.636615\pi$
$674$	599.304	+	4353.57i	0.0342497	+	0.248803i
$675$		0			0
$676$	−15755.4	+	4421.49i	−0.896413	+	0.251564i
$677$			20423.6i			1.15945i	0.814814	+	0.579723i	$0.196839\pi$
$677$			20423.6i			1.15945i	−0.814814	+	0.579723i	$0.803161\pi$
$678$		0			0
$679$		−	2838.43i		−	0.160425i
$680$	−6631.83	+	32447.1i	−0.373998	+	1.82984i
$681$		0			0
$682$	−22951.4	+	3159.45i	−1.28865	+	0.177392i
$683$	−12402.3			−0.694818			−0.347409	−	0.937714i	$-0.612939\pi$
$683$	−12402.3			−0.694818			−0.347409	+	0.937714i	$0.612939\pi$
$684$		0			0
$685$	11364.9	−	16191.3i	0.633910	−	0.903122i
$686$	18063.9	−	2486.64i	1.00537	−	0.138397i
$687$		0			0
$688$	−1607.27	−	2638.11i	−0.0890648	−	0.146188i
$689$		−	2743.52i		−	0.151698i
$690$		0			0
$691$	−18991.0			−1.04552			−0.522758	−	0.852481i	$-0.675097\pi$
$691$	−18991.0			−1.04552			−0.522758	+	0.852481i	$0.675097\pi$
$692$	−6825.51	−	24321.8i	−0.374952	−	1.33609i
$693$		0			0
$694$	−15068.8	+	2074.34i	−0.824212	+	0.113459i
$695$	9868.66	−	14059.7i	0.538618	−	0.767361i
$696$		0			0
$697$		−	32917.1i		−	1.78884i
$698$	2441.21	+	17733.8i	0.132380	+	0.961656i
$699$		0			0
$700$	17448.0	+	24420.6i	0.942105	+	1.31859i
$701$	15521.8			0.836307			0.418154	−	0.908376i	$-0.362677\pi$
$701$	15521.8			0.836307			0.418154	+	0.908376i	$0.362677\pi$
$702$		0			0
$703$	1773.04			0.0951229
$704$	17871.9	+	16649.7i	0.956781	+	0.891347i
$705$		0			0
$706$	−13732.5	+	1890.39i	−0.732055	+	0.100773i
$707$	−26732.6			−1.42204
$708$		0			0
$709$			13856.0i			0.733951i	0.930231	+	0.366976i	$0.119607\pi$
$709$			13856.0i			0.733951i	−0.930231	+	0.366976i	$0.880393\pi$
$710$	637.317	−	1238.63i	0.0336874	−	0.0654715i
$711$		0			0
$712$	−11365.3	−	26121.2i	−0.598221	−	1.37490i
$713$	10082.3			0.529575
$714$		0			0
$715$	5373.48	+	3771.70i	0.281058	+	0.197278i
$716$	8615.47	+	30700.0i	0.449686	+	1.60239i
$717$		0			0
$718$	−25330.2	+	3486.91i	−1.31660	+	0.181240i
$719$	2007.26			0.104114			0.0520570	−	0.998644i	$-0.483422\pi$
$719$	2007.26			0.104114			0.0520570	+	0.998644i	$0.483422\pi$
$720$		0			0
$721$	−47690.8			−2.46338
$722$	18177.8	−	2502.32i	0.936992	−	0.128984i
$723$		0			0
$724$	−9520.73	−	33925.8i	−0.488722	−	1.74149i
$725$	−7479.02	−	20695.3i	−0.383122	−	1.06014i
$726$		0			0
$727$	−14045.5			−0.716533			−0.358267	−	0.933619i	$-0.616632\pi$
$727$	−14045.5			−0.716533			−0.358267	+	0.933619i	$0.616632\pi$
$728$	7664.89	−	3335.00i	0.390219	−	0.169785i
$729$		0			0
$730$	−22303.9	−	11476.1i	−1.13083	−	0.581851i
$731$		−	6318.79i		−	0.319711i
$732$		0			0
$733$	−6444.43			−0.324735			−0.162367	−	0.986730i	$-0.551913\pi$
$733$	−6444.43			−0.324735			−0.162367	+	0.986730i	$0.551913\pi$
$734$	19199.9	−	2643.02i	0.965505	−	0.132909i
$735$		0			0
$736$	−6716.85	−	8238.66i	−0.336394	−	0.412610i
$737$	−8404.70			−0.420069
$738$		0			0
$739$	35649.6			1.77455			0.887276	−	0.461240i	$-0.152595\pi$
$739$	35649.6			1.77455			0.887276	+	0.461240i	$0.152595\pi$
$740$	−2731.30	+	7760.50i	−0.135682	+	0.385516i
$741$		0			0
$742$	−2580.40	−	18745.0i	−0.127668	−	0.927427i
$743$		−	13569.9i		−	0.670028i	−0.942213	−	0.335014i	$-0.891259\pi$
$743$		−	13569.9i		−	0.670028i	0.942213	−	0.335014i	$-0.108741\pi$
$744$		0			0
$745$	13873.0	−	19764.6i	0.682237	−	0.971973i
$746$	30092.5	−	4142.47i	1.47690	−	0.203307i
$747$		0			0
$748$	13499.6	+	48103.8i	0.659883	+	2.35140i
$749$	−12961.5			−0.632315
$750$		0			0
$751$			6526.25i			0.317105i	0.987351	+	0.158553i	$0.0506828\pi$
$751$			6526.25i			0.317105i	−0.987351	+	0.158553i	$0.949317\pi$
$752$	−16712.0	−	27430.5i	−0.810405	−	1.33017i
$753$		0			0
$754$	−6071.43	+	835.780i	−0.293247	+	0.0403678i
$755$	21020.9	+	14754.8i	1.01328	+	0.711233i
$756$		0			0
$757$	36032.3			1.73001			0.865004	−	0.501766i	$-0.167316\pi$
$757$	36032.3			1.73001			0.865004	+	0.501766i	$0.167316\pi$
$758$	−356.211	+	49.0353i	−0.0170688	+	0.00234966i
$759$		0			0
$760$	976.508	−	4777.70i	0.0466075	−	0.228033i
$761$		−	33830.5i		−	1.61150i	−0.592254	−	0.805751i	$-0.701762\pi$
$761$		−	33830.5i		−	1.61150i	0.592254	−	0.805751i	$-0.298238\pi$
$762$		0			0
$763$		−	16515.3i		−	0.783610i
$764$	−20592.8	+	5779.04i	−0.975160	+	0.273663i
$765$		0			0
$766$	20.7100	+	150.445i	0.000976871	+	0.00709636i
$767$		−	4292.97i		−	0.202099i
$768$		0			0
$769$	17452.7			0.818412			0.409206	−	0.912442i	$-0.365806\pi$
$769$	17452.7			0.818412			0.409206	+	0.912442i	$0.365806\pi$
$770$	40261.5	+	20716.0i	1.88432	+	0.969548i
$771$		0			0
$772$	−4858.98	−	17314.3i	−0.226527	−	0.807196i
$773$			1177.52i			0.0547899i	0.999625	+	0.0273949i	$0.00872117\pi$
$773$			1177.52i			0.0547899i	−0.999625	+	0.0273949i	$0.991279\pi$
$774$		0			0
$775$	−20184.5	+	7294.43i	−0.935548	+	0.338095i
$776$	−853.770	−	1962.24i	−0.0394955	−	0.0907734i
$777$		0			0
$778$	35548.1	−	4893.48i	1.63813	−	0.225501i
$779$			4846.90i			0.222924i
$780$		0			0
$781$		−	2101.45i		−	0.0962816i
$782$	−2965.11	−	21539.7i	−0.135591	−	0.984984i
$783$		0			0
$784$	30486.6	−	18573.9i	1.38878	−	0.846115i
$785$	−3745.09	+	5335.57i	−0.170278	+	0.242592i
$786$		0			0
$787$			15227.3i			0.689699i	0.938658	+	0.344850i	$0.112070\pi$
$787$			15227.3i			0.689699i	−0.938658	+	0.344850i	$0.887930\pi$
$788$	6192.82	+	22067.3i	0.279962	+	0.997606i
$789$		0			0
$790$	26178.3	+	13469.7i	1.17896	+	0.606619i
$791$	32402.9			1.45653
$792$		0			0
$793$		−	9442.56i		−	0.422844i
$794$	34859.4	−	4798.68i	1.55808	−	0.214482i
$795$		0			0
$796$	−38.5677	−	137.431i	−0.00171733	−	0.00611947i
$797$		−	36196.2i		−	1.60870i	−0.594154	−	0.804352i	$-0.702513\pi$
$797$		−	36196.2i		−	1.60870i	0.594154	−	0.804352i	$-0.297487\pi$
$798$		0			0
$799$		−	65701.4i		−	2.90907i
$800$	19407.5	+	11634.0i	0.857697	+	0.514155i
$801$		0			0
$802$	−704.506	−	5117.80i	−0.0310186	−	0.225331i
$803$	−37840.8			−1.66298
$804$		0			0
$805$	−16128.1	−	11320.5i	−0.706138	−	0.495646i
$806$	815.153	+	5921.58i	0.0356235	+	0.258783i
$807$		0			0
$808$	−18480.5	+	8040.88i	−0.804631	+	0.350095i
$809$			42473.0i			1.84582i	0.385014	+	0.922911i	$0.374197\pi$
$809$			42473.0i			1.84582i	−0.385014	+	0.922911i	$0.625803\pi$
$810$		0			0
$811$	25983.2			1.12502			0.562512	−	0.826789i	$-0.309835\pi$
$811$	25983.2			1.12502			0.562512	+	0.826789i	$0.309835\pi$
$812$	−40696.6	+	11420.9i	−1.75883	+	0.493588i
$813$		0			0
$814$	1692.59	+	12295.6i	0.0728810	+	0.529435i
$815$	−17709.0	−	12430.2i	−0.761130	−	0.534245i
$816$		0			0
$817$			930.415i			0.0398422i
$818$	12145.1	−	1671.87i	0.519124	−	0.0714616i
$819$		0			0
$820$	−21214.6	−	7466.48i	−0.903473	−	0.317977i
$821$	8621.70			0.366504			0.183252	−	0.983066i	$-0.441338\pi$
$821$	8621.70			0.366504			0.183252	+	0.983066i	$0.441338\pi$
$822$		0			0
$823$	−36912.0			−1.56339			−0.781696	−	0.623659i	$-0.785645\pi$
$823$	−36912.0			−1.56339			−0.781696	+	0.623659i	$0.785645\pi$
$824$	−32969.2	+	14344.9i	−1.39385	+	0.606466i
$825$		0			0
$826$	−4037.72	−	29331.5i	−0.170085	−	1.23556i
$827$	19778.7			0.831649			0.415825	−	0.909445i	$-0.363493\pi$
$827$	19778.7			0.831649			0.415825	+	0.909445i	$0.363493\pi$
$828$		0			0
$829$			35840.5i			1.50156i	0.660553	+	0.750779i	$0.270322\pi$
$829$			35840.5i			1.50156i	−0.660553	+	0.750779i	$0.729678\pi$
$830$	−13855.1	+	26927.5i	−0.579421	+	1.12610i
$831$		0			0
$832$	4295.69	−	4611.04i	0.178998	−	0.192138i
$833$	73021.2			3.03726
$834$		0			0
$835$	30865.5	+	21664.8i	1.27922	+	0.897895i
$836$	−1987.75	−	7083.08i	−0.0822343	−	0.293030i
$837$		0			0
$838$	−1672.59	−	12150.3i	−0.0689482	−	0.500866i
$839$	3059.94			0.125913			0.0629564	−	0.998016i	$-0.479947\pi$
$839$	3059.94			0.125913			0.0629564	+	0.998016i	$0.479947\pi$
$840$		0			0
$841$	6601.83			0.270689
$842$	−4496.73	−	32665.9i	−0.184047	−	1.33699i
$843$		0			0
$844$	−20671.7	+	5801.19i	−0.843070	+	0.236594i
$845$	−13138.7	+	18718.5i	−0.534894	+	0.762055i
$846$		0			0
$847$	28360.0			1.15049
$848$	−7422.16	−	12182.5i	−0.300564	−	0.493334i
$849$		0			0
$850$	21519.7	+	40976.6i	0.868376	+	1.65351i
$851$		−	5401.33i		−	0.217574i
$852$		0			0
$853$	10410.6			0.417879			0.208940	−	0.977929i	$-0.432999\pi$
$853$	10410.6			0.417879			0.208940	+	0.977929i	$0.432999\pi$
$854$	−8881.12	−	64515.9i	−0.355862	−	2.58511i
$855$		0			0
$856$	−8960.45	+	3898.70i	−0.357783	+	0.155671i
$857$	−16740.3			−0.667253			−0.333627	−	0.942705i	$-0.608272\pi$
$857$	−16740.3			−0.667253			−0.333627	+	0.942705i	$0.608272\pi$
$858$		0			0
$859$	−11012.3			−0.437409			−0.218705	−	0.975791i	$-0.570183\pi$
$859$	−11012.3			−0.437409			−0.218705	+	0.975791i	$0.570183\pi$
$860$	−4072.38	−	1433.27i	−0.161473	−	0.0568304i
$861$		0			0
$862$	23989.8	−	3302.39i	0.947908	−	0.130487i
$863$			6383.87i			0.251807i	0.992042	+	0.125903i	$0.0401830\pi$
$863$			6383.87i			0.251807i	−0.992042	+	0.125903i	$0.959817\pi$
$864$		0			0
$865$	−28896.1	−	20282.4i	−1.13583	−	0.797252i
$866$	−3013.42	−	21890.6i	−0.118245	−	0.858977i
$867$		0			0
$868$	11139.0	+	39692.2i	0.435578	+	1.55212i
$869$	44414.1			1.73377
$870$		0			0
$871$			2168.45i			0.0843573i
$872$	−4967.64	−	11417.2i	−0.192919	−	0.443390i
$873$		0			0
$874$	436.600	+	3171.63i	0.0168973	+	0.122748i
$875$	40478.2	+	10994.8i	1.56390	+	0.424791i
$876$		0			0
$877$	−24262.2			−0.934179			−0.467089	−	0.884210i	$-0.654697\pi$
$877$	−24262.2			−0.934179			−0.467089	+	0.884210i	$0.654697\pi$
$878$	−3297.89	−	23957.1i	−0.126763	−	0.920858i
$879$		0			0
$880$	34064.4	+	2210.94i	1.30490	+	0.0846941i
$881$			10272.6i			0.392842i	0.980520	+	0.196421i	$0.0629320\pi$
$881$			10272.6i			0.392842i	−0.980520	+	0.196421i	$0.937068\pi$
$882$		0			0
$883$			19789.1i			0.754197i	0.926173	+	0.377099i	$0.123078\pi$
$883$			19789.1i			0.754197i	−0.926173	+	0.377099i	$0.876922\pi$
$884$	12411.0	−	3482.95i	0.472202	−	0.132516i
$885$		0			0
$886$	33821.1	−	4655.74i	1.28244	−	0.176538i
$887$		−	11550.2i		−	0.437223i	−0.975812	−	0.218612i	$-0.929847\pi$
$887$		−	11550.2i		−	0.437223i	0.975812	−	0.218612i	$-0.0701528\pi$
$888$		0			0
$889$	−32546.3			−1.22786
$890$	−35400.0	−	18214.6i	−1.33327	−	0.686016i
$891$		0			0
$892$	14791.0	−	4150.85i	0.555201	−	0.155808i
$893$			9674.25i			0.362527i
$894$		0			0
$895$	36473.9	+	25601.4i	1.36222	+	0.956157i
$896$	25013.2	−	35545.0i	0.932627	−	1.32531i
$897$		0			0
$898$	−1512.52	−	10987.5i	−0.0562066	−	0.408306i
$899$		−	30226.0i		−	1.12135i
$900$		0			0
$901$		−	29179.4i		−	1.07892i
$902$	−33612.1	+	4626.97i	−1.24075	+	0.170800i
$903$		0			0
$904$	22400.5	−	9746.47i	0.824148	−	0.358587i
$905$	−40306.3	−	28291.4i	−1.48047	−	1.03916i
$906$		0			0
$907$		−	40841.0i		−	1.49515i	−0.664175	−	0.747577i	$-0.731217\pi$
$907$		−	40841.0i		−	1.49515i	0.664175	−	0.747577i	$-0.268783\pi$
$908$	19742.9	−	5540.53i	0.721576	−	0.202499i
$909$		0			0
$910$	5344.82	−	10387.6i	0.194702	−	0.378403i
$911$	−28712.9			−1.04424			−0.522120	−	0.852872i	$-0.674859\pi$
$911$	−28712.9			−1.04424			−0.522120	+	0.852872i	$0.674859\pi$
$912$		0			0
$913$			45685.2i			1.65603i
$914$	1521.15	+	11050.2i	0.0550494	+	0.399900i
$915$		0			0
$916$	5404.61	+	19258.6i	0.194949	+	0.694674i
$917$			72141.8i			2.59796i
$918$		0			0
$919$			24679.3i			0.885847i	0.896559	+	0.442924i	$0.146059\pi$
$919$			24679.3i			0.885847i	−0.896559	+	0.442924i	$0.853941\pi$
$920$	−14554.6	−	2974.80i	−0.521578	−	0.106605i
$921$		0			0
$922$	12383.2	−	1704.64i	0.442319	−	0.0608887i
$923$	−542.185			−0.0193350
$924$		0			0
$925$	3907.78	+	10813.3i	0.138905	+	0.384366i
$926$	−13286.6	+	1829.00i	−0.471516	+	0.0649080i
$927$		0			0
$928$	−24698.8	+	20136.5i	−0.873682	+	0.712298i
$929$			32611.5i			1.15172i	0.817548	+	0.575860i	$0.195333\pi$
$929$			32611.5i			1.15172i	−0.817548	+	0.575860i	$0.804667\pi$
$930$		0			0
$931$	−10752.1			−0.378501
$932$	24648.7	−	6917.26i	0.866304	−	0.243114i
$933$		0			0
$934$	2957.16	−	407.076i	0.103599	−	0.0142612i
$935$	57150.9	+	40114.8i	1.99897	+	1.40309i
$936$		0			0
$937$		−	26119.0i		−	0.910640i	−0.890328	−	0.455320i	$-0.849525\pi$
$937$		−	26119.0i		−	0.910640i	0.890328	−	0.455320i	$-0.150475\pi$
$938$	2039.52	+	14815.8i	0.0709943	+	0.515730i
$939$		0			0
$940$	−42343.7	−	14902.8i	−1.46926	−	0.517104i
$941$	−43271.6			−1.49906			−0.749529	−	0.661971i	$-0.769720\pi$
$941$	−43271.6			−1.49906			−0.749529	+	0.661971i	$0.769720\pi$
$942$		0			0
$943$	14765.4			0.509893
$944$	−11613.9	−	19062.7i	−0.400425	−	0.657243i
$945$		0			0
$946$	−6452.20	+	888.197i	−0.221754	+	0.0305262i
$947$	7780.65			0.266987			0.133494	−	0.991050i	$-0.457380\pi$
$947$	7780.65			0.266987			0.133494	+	0.991050i	$0.457380\pi$
$948$		0			0
$949$			9763.10i			0.333955i
$950$	−3168.69	−	6033.63i	−0.108217	−	0.206060i
$951$		0			0
$952$	81521.7	−	35470.1i	2.77535	−	1.20756i
$953$	26032.0			0.884848			0.442424	−	0.896806i	$-0.354119\pi$
$953$	26032.0			0.884848			0.442424	+	0.896806i	$0.354119\pi$
$954$		0			0
$955$	−17172.8	+	24465.8i	−0.581883	+	0.828999i
$956$	−39605.8	+	11114.7i	−1.33990	+	0.376021i
$957$		0			0
$958$	−17780.6	+	2447.65i	−0.599652	+	0.0825468i
$959$	−53103.6			−1.78812
$960$		0			0
$961$	311.044			0.0104409
$962$	3172.32	−	436.695i	0.106320	−	0.0146358i
$963$		0			0
$964$	16687.2	−	4683.00i	0.557530	−	0.156462i
$965$	−20570.7	−	14438.8i	−0.686211	−	0.481658i
$966$		0			0
$967$	−29944.3			−0.995806			−0.497903	−	0.867233i	$-0.665897\pi$
$967$	−29944.3			−0.995806			−0.497903	+	0.867233i	$0.665897\pi$
$968$	19605.6	−	8530.40i	0.650979	−	0.283241i
$969$		0			0
$970$	−2659.27	−	1368.29i	−0.0880247	−	0.0452919i
$971$			3240.13i			0.107086i	0.998566	+	0.0535431i	$0.0170515\pi$
$971$			3240.13i			0.107086i	−0.998566	+	0.0535431i	$0.982949\pi$
$972$		0			0
$973$	−46112.5			−1.51932
$974$	25086.9	−	3453.42i	0.825295	−	0.113608i
$975$		0			0
$976$	−25545.3	−	41929.2i	−0.837793	−	1.37512i
$977$	−45071.3			−1.47590			−0.737952	−	0.674853i	$-0.764207\pi$
$977$	−45071.3			−1.47590			−0.737952	+	0.674853i	$0.764207\pi$
$978$		0			0
$979$	−60059.7			−1.96069
$980$	16563.2	−	47061.3i	0.539889	−	1.53400i
$981$		0			0
$982$	4600.91	+	33422.7i	0.149512	+	1.08611i
$983$			41918.2i			1.36010i	0.733164	+	0.680052i	$0.238043\pi$
$983$			41918.2i			1.36010i	−0.733164	+	0.680052i	$0.761957\pi$
$984$		0			0
$985$	26217.5	+	18402.4i	0.848082	+	0.595277i
$986$	−64574.0	+	8889.13i	−2.08566	+	0.287107i
$987$		0			0
$988$	−1827.47	+	512.849i	−0.0588456	+	0.0165141i
$989$	2834.39			0.0911308
$990$		0			0
$991$			33218.2i			1.06479i	0.846495	+	0.532397i	$0.178709\pi$
$991$			33218.2i			1.06479i	−0.846495	+	0.532397i	$0.821291\pi$
$992$	19639.5	+	24089.2i	0.628584	+	0.771000i
$993$		0			0
$994$	−3704.45	+	509.947i	−0.118207	+	0.0162722i
$995$	−163.278	−	114.606i	−0.00520226	−	0.00365152i
$996$		0			0
$997$	6804.13			0.216137			0.108069	−	0.994143i	$-0.465533\pi$
$997$	6804.13			0.216137			0.108069	+	0.994143i	$0.465533\pi$
$998$	−11538.1	+	1588.31i	−0.365964	+	0.0503779i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.4.m.c.179.4	yes	64
3.2	odd	2	inner	360.4.m.c.179.61	yes	64
4.3	odd	2		1440.4.m.c.719.42		64
5.4	even	2	inner	360.4.m.c.179.62	yes	64
8.3	odd	2	inner	360.4.m.c.179.1	✓	64
8.5	even	2		1440.4.m.c.719.23		64
12.11	even	2		1440.4.m.c.719.24		64
15.14	odd	2	inner	360.4.m.c.179.3	yes	64
20.19	odd	2		1440.4.m.c.719.43		64
24.5	odd	2		1440.4.m.c.719.41		64
24.11	even	2	inner	360.4.m.c.179.64	yes	64
40.19	odd	2	inner	360.4.m.c.179.63	yes	64
40.29	even	2		1440.4.m.c.719.22		64
60.59	even	2		1440.4.m.c.719.21		64
120.29	odd	2		1440.4.m.c.719.44		64
120.59	even	2	inner	360.4.m.c.179.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.4.m.c.179.1	✓	64	8.3	odd	2	inner
360.4.m.c.179.2	yes	64	120.59	even	2	inner
360.4.m.c.179.3	yes	64	15.14	odd	2	inner
360.4.m.c.179.4	yes	64	1.1	even	1	trivial
360.4.m.c.179.61	yes	64	3.2	odd	2	inner
360.4.m.c.179.62	yes	64	5.4	even	2	inner
360.4.m.c.179.63	yes	64	40.19	odd	2	inner
360.4.m.c.179.64	yes	64	24.11	even	2	inner
1440.4.m.c.719.21		64	60.59	even	2
1440.4.m.c.719.22		64	40.29	even	2
1440.4.m.c.719.23		64	8.5	even	2
1440.4.m.c.719.24		64	12.11	even	2
1440.4.m.c.719.41		64	24.5	odd	2
1440.4.m.c.719.42		64	4.3	odd	2
1440.4.m.c.719.43		64	20.19	odd	2
1440.4.m.c.719.44		64	120.29	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	360.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.80200 + 0.385718i) q^{2} +(7.70244 - 2.16157i) q^{4} +(6.42323 - 9.15107i) q^{5} -30.0133 q^{7} +(-20.7485 + 9.02769i) q^{8} +O(q^{10})\)	\(q+(-2.80200 + 0.385718i) q^{2} +(7.70244 - 2.16157i) q^{4} +(6.42323 - 9.15107i) q^{5} -30.0133 q^{7} +(-20.7485 + 9.02769i) q^{8} +(-14.4682 + 28.1189i) q^{10} +47.7066i q^{11} +12.3085 q^{13} +(84.0973 - 11.5767i) q^{14} +(54.6553 - 33.2987i) q^{16} +130.910 q^{17} -19.2759 q^{19} +(29.6939 - 84.3699i) q^{20} +(-18.4013 - 133.674i) q^{22} +58.7216i q^{23} +(-42.4842 - 117.559i) q^{25} +(-34.4885 + 4.74762i) q^{26} +(-231.176 + 64.8757i) q^{28} +176.042 q^{29} -171.697i q^{31} +(-140.300 + 114.385i) q^{32} +(-366.810 + 50.4943i) q^{34} +(-192.782 + 274.654i) q^{35} -91.9820 q^{37} +(54.0112 - 7.43508i) q^{38} +(-50.6594 + 247.858i) q^{40} -251.448i q^{41} -48.2682i q^{43} +(103.121 + 367.457i) q^{44} +(-22.6500 - 164.538i) q^{46} -501.882i q^{47} +557.797 q^{49} +(164.386 + 313.013i) q^{50} +(94.8056 - 26.6057i) q^{52} -222.896i q^{53} +(436.566 + 306.430i) q^{55} +(622.731 - 270.951i) q^{56} +(-493.271 + 67.9026i) q^{58} -348.780i q^{59} -767.157i q^{61} +(66.2267 + 481.096i) q^{62} +(349.002 - 374.622i) q^{64} +(79.0604 - 112.636i) q^{65} +176.175i q^{67} +(1008.33 - 282.971i) q^{68} +(434.237 - 843.940i) q^{70} -44.0496 q^{71} +793.199i q^{73} +(257.734 - 35.4791i) q^{74} +(-148.472 + 41.6662i) q^{76} -1431.83i q^{77} -930.985i q^{79} +(46.3446 - 714.039i) q^{80} +(96.9881 + 704.559i) q^{82} +957.629 q^{83} +(840.865 - 1197.97i) q^{85} +(18.6179 + 135.248i) q^{86} +(-430.680 - 989.840i) q^{88} +1258.94i q^{89} -369.419 q^{91} +(126.931 + 452.300i) q^{92} +(193.585 + 1406.28i) q^{94} +(-123.814 + 176.395i) q^{95} +94.5723i q^{97} +(-1562.95 + 215.153i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 76 q^{4}+O(q^{10}) \) 64 * q + 76 * q^4	\( 64 q + 76 q^{4} + 72 q^{10} - 236 q^{16} - 48 q^{19} + 1000 q^{25} - 192 q^{34} + 1284 q^{40} + 336 q^{46} + 784 q^{49} + 4228 q^{64} - 768 q^{70} + 648 q^{76} + 4304 q^{91} - 5944 q^{94}+O(q^{100}) \) 64 * q + 76 * q^4 + 72 * q^10 - 236 * q^16 - 48 * q^19 + 1000 * q^25 - 192 * q^34 + 1284 * q^40 + 336 * q^46 + 784 * q^49 + 4228 * q^64 - 768 * q^70 + 648 * q^76 + 4304 * q^91 - 5944 * q^94

Introduction

L-functions

Modular forms

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