LMFDB - Embedded newform 360.4.m.c.179.1

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			179.1
Character	$\chi$	$=$	360.179
Dual form			360.4.m.c.179.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.80200 - 0.385718i) q^{2} +(7.70244 + 2.16157i) q^{4} +(-6.42323 + 9.15107i) q^{5} +30.0133 q^{7} +(-20.7485 - 9.02769i) q^{8} +O(q^{10})$	\(q+(-2.80200 - 0.385718i) q^{2} +(7.70244 + 2.16157i) q^{4} +(-6.42323 + 9.15107i) q^{5} +30.0133 q^{7} +(-20.7485 - 9.02769i) q^{8} +(21.5276 - 23.1638i) q^{10} +47.7066i q^{11} -12.3085 q^{13} +(-84.0973 - 11.5767i) q^{14} +(54.6553 + 33.2987i) q^{16} +130.910 q^{17} -19.2759 q^{19} +(-69.2552 + 56.6014i) q^{20} +(18.4013 - 133.674i) q^{22} -58.7216i q^{23} +(-42.4842 - 117.559i) q^{25} +(34.4885 + 4.74762i) q^{26} +(231.176 + 64.8757i) q^{28} -176.042 q^{29} +171.697i q^{31} +(-140.300 - 114.385i) q^{32} +(-366.810 - 50.4943i) q^{34} +(-192.782 + 274.654i) q^{35} +91.9820 q^{37} +(54.0112 + 7.43508i) q^{38} +(215.885 - 131.884i) q^{40} -251.448i q^{41} -48.2682i q^{43} +(-103.121 + 367.457i) q^{44} +(-22.6500 + 164.538i) q^{46} +501.882i q^{47} +557.797 q^{49} +(73.6964 + 345.787i) q^{50} +(-94.8056 - 26.6057i) q^{52} +222.896i q^{53} +(-436.566 - 306.430i) q^{55} +(-622.731 - 270.951i) q^{56} +(493.271 + 67.9026i) q^{58} -348.780i q^{59} +767.157i q^{61} +(66.2267 - 481.096i) q^{62} +(349.002 + 374.622i) q^{64} +(79.0604 - 112.636i) q^{65} +176.175i q^{67} +(1008.33 + 282.971i) q^{68} +(646.115 - 695.221i) q^{70} +44.0496 q^{71} +793.199i q^{73} +(-257.734 - 35.4791i) q^{74} +(-148.472 - 41.6662i) q^{76} +1431.83i q^{77} +930.985i q^{79} +(-655.782 + 286.269i) q^{80} +(-96.9881 + 704.559i) q^{82} +957.629 q^{83} +(-840.865 + 1197.97i) q^{85} +(-18.6179 + 135.248i) q^{86} +(430.680 - 989.840i) q^{88} +1258.94i q^{89} -369.419 q^{91} +(126.931 - 452.300i) q^{92} +(193.585 - 1406.28i) q^{94} +(123.814 - 176.395i) q^{95} +94.5723i q^{97} +(-1562.95 - 215.153i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.199314\pi$
$7$	30.0133			1.62057			0.810283	+	0.586039i	$0.199314\pi$
$8$	−20.7485	−	9.02769i	−0.916963	−	0.398971i
$9$		0			0
$10$	21.5276	−	23.1638i	0.680764	−	0.732503i
$11$			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	$-0.541915\pi$
$13$	−12.3085			−0.262597			−0.131299	+	0.991343i	$0.541915\pi$
$14$	−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	$0.537127\pi$
$20$	−69.2552	+	56.6014i	−0.774297	+	0.632823i
$21$		0			0
$22$	18.4013	−	133.674i	0.178326	−	1.29543i
$23$		−	58.7216i		−	0.532361i	−0.963923	−	0.266181i	$-0.914238\pi$
$23$		−	58.7216i		−	0.532361i	0.963923	−	0.266181i	$-0.0857617\pi$
$24$		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	$-0.690593\pi$
$29$	−176.042			−1.12725			−0.563624	+	0.826031i	$0.690593\pi$
$30$		0			0
$31$			171.697i			0.994766i	0.867531	+	0.497383i	$0.165706\pi$
$31$			171.697i			0.994766i	−0.867531	+	0.497383i	$0.834294\pi$
$32$	−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	$-0.434493\pi$
$37$	91.9820			0.408696			0.204348	+	0.978898i	$0.434493\pi$
$38$	54.0112	+	7.43508i	0.230573	+	0.0317402i
$39$		0			0
$40$	215.885	−	131.884i	0.853362	−	0.521318i
$41$		−	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	$0.284171\pi$
$47$			501.882i			1.55760i	−0.627274	+	0.778799i	$0.715829\pi$
$48$		0			0
$49$	557.797			1.62623
$50$	73.6964	+	345.787i	0.208445	+	0.978034i
$51$		0			0
$52$	−94.8056	−	26.6057i	−0.252830	−	0.0709527i
$53$			222.896i			0.577683i	0.957377	+	0.288841i	$0.0932700\pi$
$53$			222.896i			0.577683i	−0.957377	+	0.288841i	$0.906730\pi$
$54$		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	$0.297898\pi$
$61$			767.157i			1.61024i	−0.593115	+	0.805118i	$0.702102\pi$
$62$	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
$70$	646.115	−	695.221i	1.10322	−	1.18707i
$71$	44.0496			0.0736299			0.0368150	−	0.999322i	$-0.488279\pi$
$71$	44.0496			0.0736299			0.0368150	+	0.999322i	$0.488279\pi$
$72$		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	$0.230690\pi$
$79$			930.985i			1.32587i	−0.748676	+	0.662937i	$0.769310\pi$
$80$	−655.782	+	286.269i	−0.916483	+	0.400073i
$81$		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
$100$	−73.1211	−	997.323i	−0.0731211	−	0.997323i
$101$	−890.691			−0.877496			−0.438748	−	0.898610i	$-0.644578\pi$
$101$	−890.691			−0.877496			−0.438748	+	0.898610i	$0.644578\pi$
$102$		0			0
$103$	−1588.99			−1.52008			−0.760038	−	0.649879i	$-0.774820\pi$
$103$	−1588.99			−1.52008			−0.760038	+	0.649879i	$0.774820\pi$
$104$	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	$-0.922272\pi$
$109$		−	550.267i		−	0.483541i	0.970333	−	0.241771i	$-0.0777282\pi$
$110$	1105.06	+	1027.01i	0.957852	+	0.890196i
$111$		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	$-0.623676\pi$
$127$	−1084.40			−0.757673			−0.378837	+	0.925464i	$0.623676\pi$
$128$	−833.405	−	1184.31i	−0.575495	−	0.817806i
$129$		0			0
$130$	−264.973	+	285.112i	−0.178767	+	0.192353i
$131$		−	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	$0.344700\pi$
$140$	−2078.58	+	1698.79i	−1.25480	+	1.02553i
$141$		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	$-0.702355\pi$
$149$	−2159.81			−1.18751			−0.593755	+	0.804646i	$0.702355\pi$
$150$		0			0
$151$		−	2297.09i		−	1.23798i	−0.785399	−	0.618990i	$-0.787542\pi$
$151$		−	2297.09i		−	1.23798i	0.785399	−	0.618990i	$-0.212458\pi$
$152$	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	$-0.452654\pi$
$157$	583.054			0.296387			0.148194	+	0.988958i	$0.452654\pi$
$158$	359.098	−	2608.62i	0.180812	−	1.31349i
$159$		0			0
$160$	1947.92	−	549.180i	0.962480	−	0.271353i
$161$		−	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	$-0.714484\pi$
$167$		−	3372.89i		−	1.56289i	0.623977	−	0.781443i	$-0.285516\pi$
$168$		0			0
$169$	−2045.50			−0.931043
$170$	2818.18	−	3032.37i	1.27144	−	1.36807i
$171$		0			0
$172$	104.335	−	371.783i	0.0462527	−	0.164815i
$173$			3157.67i			1.38771i	0.720117	+	0.693853i	$0.244088\pi$
$173$			3157.67i			1.38771i	−0.720117	+	0.693853i	$0.755912\pi$
$174$		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	$0.359670\pi$
$181$			4404.55i			1.80877i	−0.426716	+	0.904386i	$0.640330\pi$
$182$	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
$190$	−414.966	+	446.504i	−0.158446	+	0.170488i
$191$	2673.54			1.01283			0.506416	−	0.862289i	$-0.330970\pi$
$191$	2673.54			1.01283			0.506416	+	0.862289i	$0.330970\pi$
$192$		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	$-0.826650\pi$
$197$		−	2864.97i		−	1.03615i	0.855337	−	0.518073i	$-0.173350\pi$
$198$		0			0
$199$			17.8425i			0.00635587i	0.999995	+	0.00317794i	$0.00101157\pi$
$199$			17.8425i			0.00635587i	−0.999995	+	0.00317794i	$0.998988\pi$
$200$	−179.800	+	2822.71i	−0.0635689	+	0.997977i
$201$		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
$220$	−2700.26	−	3303.93i	−0.827506	−	1.01250i
$221$	−1611.31			−0.490444
$222$		0			0
$223$	−1920.30			−0.576649			−0.288325	−	0.957533i	$-0.593098\pi$
$223$	−1920.30			−0.576649			−0.288325	+	0.957533i	$0.593098\pi$
$224$	−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	$-0.882519\pi$
$229$		−	2500.32i		−	0.721510i	0.932661	−	0.360755i	$-0.117481\pi$
$230$	−1360.21	−	1264.14i	−0.389956	−	0.362412i
$231$		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	$-0.255036\pi$
$239$	5141.98			1.39166			0.695831	+	0.718206i	$0.255036\pi$
$240$		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
$250$	−3637.69	−	1546.67i	−0.920272	−	0.391280i
$251$		−	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
$260$	852.428	−	696.679i	0.203328	−	0.166178i
$261$		0			0
$262$	−927.137	+	6735.07i	−0.218621	+	1.58815i
$263$		−	1387.16i		−	0.325232i	−0.986689	−	0.162616i	$-0.948007\pi$
$263$		−	1387.16i		−	0.325232i	0.986689	−	0.162616i	$-0.0519932\pi$
$264$		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	$-0.813892\pi$
$269$	−7358.13			−1.66778			−0.833891	+	0.551930i	$0.813892\pi$
$270$		0			0
$271$		−	931.650i		−	0.208833i	−0.994534	−	0.104416i	$-0.966703\pi$
$271$		−	931.650i		−	0.208833i	0.994534	−	0.104416i	$-0.0332975\pi$
$272$	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	$-0.354288\pi$
$277$	4074.91			0.883891			0.441946	+	0.897042i	$0.354288\pi$
$278$	−4305.00	−	592.618i	−0.928766	−	0.127852i
$279$		0			0
$280$	6479.43	−	3958.28i	1.38293	−	0.844830i
$281$			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
$290$	−3789.77	+	4077.80i	−0.767390	+	0.825713i
$291$		0			0
$292$	−1714.55	+	6109.57i	−0.343619	+	1.22444i
$293$			672.210i			0.134031i	0.997752	+	0.0670153i	$0.0213476\pi$
$293$			672.210i			0.134031i	−0.997752	+	0.0670153i	$0.978652\pi$
$294$		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
$310$	3977.16	+	3696.24i	0.728669	+	0.677201i
$311$	−3593.53			−0.655211			−0.327605	−	0.944815i	$-0.606242\pi$
$311$	−3593.53			−0.655211			−0.327605	+	0.944815i	$0.606242\pi$
$312$		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	$0.0655850\pi$
$317$			2309.39i			0.409173i	−0.978848	+	0.204587i	$0.934415\pi$
$318$		0			0
$319$		−	8398.36i		−	1.47404i
$320$	−5669.91	+	787.455i	−0.990493	+	0.137563i
$321$		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
$340$	−9066.20	+	7409.68i	−1.44613	+	1.18190i
$341$	−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	$0.161312\pi$
$349$			6328.99i			0.970725i	−0.874313	+	0.485363i	$0.838688\pi$
$350$	2211.87	+	10378.2i	0.337798	+	1.58497i
$351$		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	$-0.731358\pi$
$359$	−9040.04			−1.32901			−0.664506	+	0.747283i	$0.731358\pi$
$360$		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	$-0.337980\pi$
$367$	6852.20			0.974610			0.487305	+	0.873232i	$0.337980\pi$
$368$	1955.35	−	3209.45i	0.276983	−	0.454630i
$369$		0			0
$370$	1980.16	−	2130.65i	0.278225	−	0.299371i
$371$			6689.86i			0.936173i
$372$		0			0
$373$	10739.6			1.49082			0.745412	−	0.666604i	$-0.232253\pi$
$373$	10739.6			1.49082			0.745412	+	0.666604i	$0.232253\pi$
$374$	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	$0.497258\pi$
$380$	1334.96	−	1091.04i	0.180216	−	0.147288i
$381$		0			0
$382$	−7491.28	−	1031.23i	−1.00337	−	0.138122i
$383$			53.6921i			0.00716329i	0.999994	+	0.00358164i	$0.00114007\pi$
$383$			53.6921i			0.00716329i	−0.999994	+	0.00358164i	$0.998860\pi$
$384$		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	$-0.190166\pi$
$389$	12686.7			1.65357			0.826787	+	0.562515i	$0.190166\pi$
$390$		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	$-0.211950\pi$
$397$	12440.9			1.57277			0.786386	+	0.617736i	$0.211950\pi$
$398$	6.88216	−	49.9947i	0.000866763	−	0.00629650i
$399$		0			0
$400$	1592.57	−	7839.88i	0.199071	−	0.979985i
$401$			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	$0.584385\pi$
$410$	−5824.49	−	5413.09i	−0.701588	−	0.652032i
$411$		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	$-0.764231\pi$
$421$		−	11658.1i		−	1.34960i	0.738003	−	0.674798i	$-0.235769\pi$
$422$	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
$430$	−1118.07	−	1039.10i	−0.125391	−	0.116535i
$431$	8561.67			0.956848			0.478424	−	0.878129i	$-0.341208\pi$
$431$	8561.67			0.956848			0.478424	+	0.878129i	$0.341208\pi$
$432$		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	$-0.846137\pi$
$439$		−	8549.99i		−	0.929542i	0.885431	−	0.464771i	$-0.153863\pi$
$440$	6291.74	+	10299.2i	0.681698	+	1.11589i
$441$		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
$460$	3323.72	+	4066.78i	0.336890	+	0.412205i
$461$	4419.40			0.446490			0.223245	−	0.974762i	$-0.428335\pi$
$461$	4419.40			0.446490			0.223245	+	0.974762i	$0.428335\pi$
$462$		0			0
$463$	−4741.82			−0.475963			−0.237981	−	0.971270i	$-0.576486\pi$
$463$	−4741.82			−0.475963			−0.237981	+	0.971270i	$0.576486\pi$
$464$	−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
$470$	11625.5	+	10804.3i	1.14094	+	1.06036i
$471$		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	$-0.597872\pi$
$479$	−6345.69			−0.605307			−0.302653	+	0.953101i	$0.597872\pi$
$480$		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	$-0.363243\pi$
$487$	8953.22			0.833078			0.416539	+	0.909118i	$0.363243\pi$
$488$	6925.65	−	15917.4i	0.642438	−	1.47653i
$489$		0			0
$490$	12008.1	−	12920.7i	1.10708	−	1.19122i
$491$		−	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	$0.440866\pi$
$500$	9596.25	+	5736.90i	0.858315	+	0.513124i
$501$		0			0
$502$	−248.422	+	1804.63i	−0.0220869	+	0.160448i
$503$		−	8800.34i		−	0.780095i	−0.920795	−	0.390048i	$-0.872459\pi$
$503$		−	8800.34i		−	0.780095i	0.920795	−	0.390048i	$-0.127541\pi$
$504$		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	$-0.136995\pi$
$509$	20872.7			1.81761			0.908806	+	0.417219i	$0.136995\pi$
$510$		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
$520$	−2657.23	+	1623.30i	−0.224091	+	0.136897i
$521$		−	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
$530$	5163.12	+	4798.44i	0.423154	+	0.393266i
$531$		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	$-0.991043\pi$
$541$		−	708.100i		−	0.0562728i	0.999604	−	0.0281364i	$-0.00895727\pi$
$542$	−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
$550$	−16496.3	+	3515.80i	−1.27892	+	0.272571i
$551$	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	$-0.991567\pi$
$557$		−	696.440i		−	0.0529787i	0.999649	−	0.0264893i	$-0.00843280\pi$
$558$		0			0
$559$			594.110i			0.0449520i
$560$	−19682.2	+	8591.88i	−1.48522	+	0.648345i
$561$		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
$580$	12191.8	−	9964.23i	0.872825	−	0.713348i
$581$	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
$590$	−8079.07	−	7508.42i	−0.563746	−	0.523927i
$591$		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	$-0.474231\pi$
$599$	2371.06			0.161735			0.0808673	+	0.996725i	$0.474231\pi$
$600$		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	$-0.801400\pi$
$607$	−24274.6			−1.62319			−0.811594	+	0.584222i	$0.801400\pi$
$608$	2704.42	+	2204.87i	0.180393	+	0.147071i
$609$		0			0
$610$	17770.3	+	16515.1i	1.17950	+	1.09619i
$611$		−	6177.42i		−	0.409021i
$612$		0			0
$613$	2264.69			0.149217			0.0746085	−	0.997213i	$-0.476229\pi$
$613$	2264.69			0.149217			0.0746085	+	0.997213i	$0.476229\pi$
$614$	−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	$0.290724\pi$
$620$	−9718.30	−	11890.9i	−0.629510	−	0.770244i
$621$		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	$0.184754\pi$
$631$			17384.1i			1.09675i	−0.836232	+	0.548376i	$0.815246\pi$
$632$	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
$640$	16190.8	−	19.4629i	0.999999	−	0.00120209i
$641$			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	$-0.902335\pi$
$647$		−	9941.26i		−	0.604067i	0.953297	−	0.302033i	$-0.0976654\pi$
$648$		0			0
$649$	16639.1			1.00638
$650$	−907.093	−	4256.13i	−0.0547371	−	0.256829i
$651$		0			0
$652$	4183.04	−	14905.7i	0.251258	−	0.895324i
$653$		−	4118.36i		−	0.246806i	−0.992357	−	0.123403i	$-0.960619\pi$
$653$		−	4118.36i		−	0.246806i	0.992357	−	0.123403i	$-0.0393807\pi$
$654$		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	$0.0168237\pi$
$661$			1795.57i			0.105657i	−0.998604	+	0.0528287i	$0.983176\pi$
$662$	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
$670$	4080.88	+	3792.63i	0.235311	+	0.218690i
$671$	−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	$-0.803161\pi$
$677$		−	20423.6i		−	1.15945i	0.814814	−	0.579723i	$-0.196839\pi$
$678$		0			0
$679$			2838.43i			0.160425i
$680$	28261.6	−	17265.0i	1.59380	−	0.973649i
$681$		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
$700$	−2194.60	−	29932.9i	−0.118498	−	1.61623i
$701$	−15521.8			−0.836307			−0.418154	−	0.908376i	$-0.637323\pi$
$701$	−15521.8			−0.836307			−0.418154	+	0.908376i	$0.637323\pi$
$702$		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	$-0.880393\pi$
$709$		−	13856.0i		−	0.733951i	0.930231	−	0.366976i	$-0.119607\pi$
$710$	948.284	−	1020.35i	0.0501246	−	0.0539341i
$711$		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	$-0.516578\pi$
$719$	−2007.26			−0.104114			−0.0520570	+	0.998644i	$0.516578\pi$
$720$		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	$-0.383368\pi$
$727$	14045.5			0.716533			0.358267	+	0.933619i	$0.383368\pi$
$728$	7664.89	+	3335.00i	0.390219	+	0.169785i
$729$		0			0
$730$	18373.5	+	17075.7i	0.931553	+	0.865754i
$731$		−	6318.79i		−	0.319711i
$732$		0			0
$733$	6444.43			0.324735			0.162367	−	0.986730i	$-0.448087\pi$
$733$	6444.43			0.324735			0.162367	+	0.986730i	$0.448087\pi$
$734$	−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	$0.152595\pi$
$740$	−6370.23	+	5206.31i	−0.316452	+	0.258632i
$741$		0			0
$742$	2580.40	−	18745.0i	0.127668	−	0.927427i
$743$			13569.9i			0.670028i	0.942213	+	0.335014i	$0.108741\pi$
$743$			13569.9i			0.670028i	−0.942213	+	0.335014i	$0.891259\pi$
$744$		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	$-0.949317\pi$
$751$		−	6526.25i		−	0.317105i	0.987351	−	0.158553i	$-0.0506828\pi$
$752$	−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	$-0.832684\pi$
$757$	−36032.3			−1.73001			−0.865004	+	0.501766i	$0.832684\pi$
$758$	−356.211	−	49.0353i	−0.0170688	−	0.00234966i
$759$		0			0
$760$	−4161.40	+	2542.19i	−0.198618	+	0.121336i
$761$		−	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	$0.365806\pi$
$770$	33166.6	+	30823.9i	1.55226	+	1.44262i
$771$		0			0
$772$	4858.98	−	17314.3i	0.226527	−	0.807196i
$773$		−	1177.52i		−	0.0547899i	−0.999625	−	0.0273949i	$-0.991279\pi$
$773$		−	1177.52i		−	0.0547899i	0.999625	−	0.0273949i	$-0.00872117\pi$
$774$		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
$790$	21565.1	+	20041.9i	0.971206	+	0.902607i
$791$	−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	$0.297487\pi$
$797$			36196.2i			1.60870i	−0.594154	+	0.804352i	$0.702513\pi$
$798$		0			0
$799$			65701.4i			2.90907i
$800$	−7486.37	+	21353.1i	−0.330854	+	0.943682i
$801$		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
$820$	14232.3	+	17414.1i	0.606114	+	0.741618i
$821$	−8621.70			−0.366504			−0.183252	−	0.983066i	$-0.558662\pi$
$821$	−8621.70			−0.366504			−0.183252	+	0.983066i	$0.558662\pi$
$822$		0			0
$823$	36912.0			1.56339			0.781696	−	0.623659i	$-0.214355\pi$
$823$	36912.0			1.56339			0.781696	+	0.623659i	$0.214355\pi$
$824$	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	$-0.729678\pi$
$829$		−	35840.5i		−	1.50156i	0.660553	−	0.750779i	$-0.270322\pi$
$830$	20615.5	−	22182.3i	0.862138	−	0.927661i
$831$		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	$-0.520053\pi$
$839$	−3059.94			−0.125913			−0.0629564	+	0.998016i	$0.520053\pi$
$840$		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
$850$	9647.59	+	45267.0i	0.389305	+	1.82664i
$851$		−	5401.33i		−	0.217574i
$852$		0			0
$853$	−10410.6			−0.417879			−0.208940	−	0.977929i	$-0.567001\pi$
$853$	−10410.6			−0.417879			−0.208940	+	0.977929i	$0.567001\pi$
$854$	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	$0.570183\pi$
$860$	2732.05	+	3342.83i	0.108328	+	0.132546i
$861$		0			0
$862$	−23989.8	−	3302.39i	−0.947908	−	0.130487i
$863$		−	6383.87i		−	0.251807i	−0.992042	−	0.125903i	$-0.959817\pi$
$863$		−	6383.87i		−	0.251807i	0.992042	−	0.125903i	$-0.0401830\pi$
$864$		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	$-0.345303\pi$
$877$	24262.2			0.934179			0.467089	+	0.884210i	$0.345303\pi$
$878$	−3297.89	+	23957.1i	−0.126763	+	0.920858i
$879$		0			0
$880$	−13656.9	−	31285.1i	−0.523153	−	1.19843i
$881$			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	$0.0701528\pi$
$887$			11550.2i			0.437223i	−0.975812	+	0.218612i	$0.929847\pi$
$888$		0			0
$889$	−32546.3			−1.22786
$890$	29161.8	+	27102.0i	1.09832	+	1.02074i
$891$		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
$910$	−7952.72	+	8557.14i	−0.289703	+	0.311721i
$911$	28712.9			1.04424			0.522120	−	0.852872i	$-0.325141\pi$
$911$	28712.9			1.04424			0.522120	+	0.852872i	$0.325141\pi$
$912$		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	$-0.853941\pi$
$919$		−	24679.3i		−	0.885847i	0.896559	−	0.442924i	$-0.146059\pi$
$920$	−7744.46	−	12677.1i	−0.277530	−	0.454297i
$921$		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
$940$	−28407.2	−	34758.0i	−0.985683	−	1.20604i
$941$	43271.6			1.49906			0.749529	−	0.661971i	$-0.230280\pi$
$941$	43271.6			1.49906			0.749529	+	0.661971i	$0.230280\pi$
$942$		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
$950$	−1420.57	−	6665.37i	−0.0485150	−	0.227635i
$951$		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	$-0.334103\pi$
$967$	29944.3			0.995806			0.497903	+	0.867233i	$0.334103\pi$
$968$	19605.6	+	8530.40i	0.650979	+	0.283241i
$969$		0			0
$970$	2190.65	+	2035.92i	0.0725130	+	0.0673912i
$971$			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
$980$	−38630.4	+	31572.1i	−1.25919	+	1.02912i
$981$		0			0
$982$	−4600.91	+	33422.7i	−0.149512	+	1.08611i
$983$		−	41918.2i		−	1.36010i	−0.733164	−	0.680052i	$-0.761957\pi$
$983$		−	41918.2i		−	1.36010i	0.733164	−	0.680052i	$-0.238043\pi$
$984$		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	$-0.821291\pi$
$991$		−	33218.2i		−	1.06479i	0.846495	−	0.532397i	$-0.178709\pi$
$992$	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	$-0.534467\pi$
$997$	−6804.13			−0.216137			−0.108069	+	0.994143i	$0.534467\pi$
$998$	−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.179.1	✓	64
3.2	odd	2	inner	360.4.m.c.179.64	yes	64
4.3	odd	2		1440.4.m.c.719.23		64
5.4	even	2	inner	360.4.m.c.179.63	yes	64
8.3	odd	2	inner	360.4.m.c.179.4	yes	64
8.5	even	2		1440.4.m.c.719.42		64
12.11	even	2		1440.4.m.c.719.41		64
15.14	odd	2	inner	360.4.m.c.179.2	yes	64
20.19	odd	2		1440.4.m.c.719.22		64
24.5	odd	2		1440.4.m.c.719.24		64
24.11	even	2	inner	360.4.m.c.179.61	yes	64
40.19	odd	2	inner	360.4.m.c.179.62	yes	64
40.29	even	2		1440.4.m.c.719.43		64
60.59	even	2		1440.4.m.c.719.44		64
120.29	odd	2		1440.4.m.c.719.21		64
120.59	even	2	inner	360.4.m.c.179.3	yes	64

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

\(f(q)\)	\(=\)	\(q+(-2.80200 - 0.385718i) q^{2} +(7.70244 + 2.16157i) q^{4} +(-6.42323 + 9.15107i) q^{5} +30.0133 q^{7} +(-20.7485 - 9.02769i) q^{8} +O(q^{10})\)	\(q+(-2.80200 - 0.385718i) q^{2} +(7.70244 + 2.16157i) q^{4} +(-6.42323 + 9.15107i) q^{5} +30.0133 q^{7} +(-20.7485 - 9.02769i) q^{8} +(21.5276 - 23.1638i) q^{10} +47.7066i q^{11} -12.3085 q^{13} +(-84.0973 - 11.5767i) q^{14} +(54.6553 + 33.2987i) q^{16} +130.910 q^{17} -19.2759 q^{19} +(-69.2552 + 56.6014i) q^{20} +(18.4013 - 133.674i) q^{22} -58.7216i q^{23} +(-42.4842 - 117.559i) q^{25} +(34.4885 + 4.74762i) q^{26} +(231.176 + 64.8757i) q^{28} -176.042 q^{29} +171.697i q^{31} +(-140.300 - 114.385i) q^{32} +(-366.810 - 50.4943i) q^{34} +(-192.782 + 274.654i) q^{35} +91.9820 q^{37} +(54.0112 + 7.43508i) q^{38} +(215.885 - 131.884i) q^{40} -251.448i q^{41} -48.2682i q^{43} +(-103.121 + 367.457i) q^{44} +(-22.6500 + 164.538i) q^{46} +501.882i q^{47} +557.797 q^{49} +(73.6964 + 345.787i) q^{50} +(-94.8056 - 26.6057i) q^{52} +222.896i q^{53} +(-436.566 - 306.430i) q^{55} +(-622.731 - 270.951i) q^{56} +(493.271 + 67.9026i) q^{58} -348.780i q^{59} +767.157i q^{61} +(66.2267 - 481.096i) q^{62} +(349.002 + 374.622i) q^{64} +(79.0604 - 112.636i) q^{65} +176.175i q^{67} +(1008.33 + 282.971i) q^{68} +(646.115 - 695.221i) q^{70} +44.0496 q^{71} +793.199i q^{73} +(-257.734 - 35.4791i) q^{74} +(-148.472 - 41.6662i) q^{76} +1431.83i q^{77} +930.985i q^{79} +(-655.782 + 286.269i) q^{80} +(-96.9881 + 704.559i) q^{82} +957.629 q^{83} +(-840.865 + 1197.97i) q^{85} +(-18.6179 + 135.248i) q^{86} +(430.680 - 989.840i) q^{88} +1258.94i q^{89} -369.419 q^{91} +(126.931 - 452.300i) q^{92} +(193.585 - 1406.28i) q^{94} +(123.814 - 176.395i) q^{95} +94.5723i q^{97} +(-1562.95 - 215.153i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 76 q^{4}+O(q^{10}) \) 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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Database

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