LMFDB - Embedded newform 288.4.r.a.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,4,Mod(49,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("288.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	288.r (of order $6$, degree $2$, not 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:	$16.9925500817$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.5
Character	$\chi$	$=$	288.49
Dual form			288.4.r.a.241.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.64700 - 2.32494i) q^{3} +(17.5797 + 10.1497i) q^{5} +(10.6896 + 18.5150i) q^{7} +(16.1893 + 21.6080i) q^{9} +O(q^{10})$	\(q+(-4.64700 - 2.32494i) q^{3} +(17.5797 + 10.1497i) q^{5} +(10.6896 + 18.5150i) q^{7} +(16.1893 + 21.6080i) q^{9} +(-1.86021 + 1.07399i) q^{11} +(-13.7636 - 7.94640i) q^{13} +(-58.0958 - 88.0374i) q^{15} -100.066 q^{17} -2.35719i q^{19} +(-6.62852 - 110.892i) q^{21} +(-74.6153 + 129.238i) q^{23} +(143.532 + 248.604i) q^{25} +(-24.9944 - 138.052i) q^{27} +(175.273 - 101.194i) q^{29} +(-66.8886 + 115.855i) q^{31} +(11.1414 - 0.665973i) q^{33} +433.985i q^{35} -16.6443i q^{37} +(45.4845 + 68.9265i) q^{39} +(-65.4314 + 113.331i) q^{41} +(107.846 - 62.2650i) q^{43} +(65.2896 + 544.180i) q^{45} +(139.663 + 241.903i) q^{47} +(-57.0362 + 98.7895i) q^{49} +(465.006 + 232.647i) q^{51} +342.817i q^{53} -43.6028 q^{55} +(-5.48033 + 10.9539i) q^{57} +(-191.251 - 110.419i) q^{59} +(-367.557 + 212.209i) q^{61} +(-227.014 + 530.726i) q^{63} +(-161.307 - 279.391i) q^{65} +(47.7127 + 27.5469i) q^{67} +(647.207 - 427.091i) q^{69} +996.571 q^{71} -910.971 q^{73} +(-89.0025 - 1488.97i) q^{75} +(-39.7700 - 22.9612i) q^{77} +(-163.931 - 283.937i) q^{79} +(-204.813 + 699.638i) q^{81} +(147.974 - 85.4325i) q^{83} +(-1759.13 - 1015.63i) q^{85} +(-1049.77 + 62.7495i) q^{87} +850.727 q^{89} -339.776i q^{91} +(580.187 - 382.864i) q^{93} +(23.9247 - 41.4388i) q^{95} +(-24.9396 - 43.1967i) q^{97} +(-53.3225 - 22.8083i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 2 q^{7} - 4 q^{9}+O(q^{10}) $ 68 * q + 2 * q^7 - 4 * q^9	$ 68 q + 2 q^{7} - 4 q^{9} + 58 q^{15} - 8 q^{17} - 274 q^{23} + 648 q^{25} + 2 q^{31} + 174 q^{33} - 242 q^{39} - 22 q^{41} + 942 q^{47} - 1080 q^{49} + 508 q^{55} - 68 q^{57} - 722 q^{63} - 502 q^{65} + 3984 q^{71} - 8 q^{73} + 2 q^{79} + 1072 q^{81} - 3354 q^{87} - 856 q^{89} + 2792 q^{95} - 2 q^{97}+O(q^{100}) $ 68 * q + 2 * q^7 - 4 * q^9 + 58 * q^15 - 8 * q^17 - 274 * q^23 + 648 * q^25 + 2 * q^31 + 174 * q^33 - 242 * q^39 - 22 * q^41 + 942 * q^47 - 1080 * q^49 + 508 * q^55 - 68 * q^57 - 722 * q^63 - 502 * q^65 + 3984 * q^71 - 8 * q^73 + 2 * q^79 + 1072 * q^81 - 3354 * q^87 - 856 * q^89 + 2792 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−4.64700	−	2.32494i	−0.894316	−	0.447435i
$3$	−4.64700	−	2.32494i	−0.894316	−	0.447435i
$4$		0			0
$5$	17.5797	+	10.1497i	1.57238	+	0.907814i	0.995876	+	0.0907198i	$0.0289168\pi$
$5$	17.5797	+	10.1497i	1.57238	+	0.907814i	0.576504	+	0.817094i	$0.304417\pi$
$6$		0			0
$7$	10.6896	+	18.5150i	0.577185	+	0.999715i	0.995800	+	0.0915508i	$0.0291824\pi$
$7$	10.6896	+	18.5150i	0.577185	+	0.999715i	−0.418615	+	0.908164i	$0.637484\pi$
$8$		0			0
$9$	16.1893	+	21.6080i	0.599604	+	0.800297i
$10$		0			0
$11$	−1.86021	+	1.07399i	−0.0509887	+	0.0294383i	−0.525278	−	0.850931i	$-0.676039\pi$
$11$	−1.86021	+	1.07399i	−0.0509887	+	0.0294383i	0.474289	+	0.880369i	$0.342705\pi$
$12$		0			0
$13$	−13.7636	−	7.94640i	−0.293641	−	0.169534i	0.345942	−	0.938256i	$-0.387559\pi$
$13$	−13.7636	−	7.94640i	−0.293641	−	0.169534i	−0.639583	+	0.768722i	$0.720893\pi$
$14$		0			0
$15$	−58.0958	−	88.0374i	−1.00002	−	1.51541i
$16$		0			0
$17$	−100.066			−1.42762			−0.713809	−	0.700341i	$-0.753031\pi$
$17$	−100.066			−1.42762			−0.713809	+	0.700341i	$0.753031\pi$
$18$		0			0
$19$		−	2.35719i		−	0.0284619i	−0.999899	−	0.0142310i	$-0.995470\pi$
$19$		−	2.35719i		−	0.0284619i	0.999899	−	0.0142310i	$-0.00453001\pi$
$20$		0			0
$21$	−6.62852	−	110.892i	−0.0688792	−	1.15231i
$22$		0			0
$23$	−74.6153	+	129.238i	−0.676451	+	1.17165i	0.299592	+	0.954068i	$0.403150\pi$
$23$	−74.6153	+	129.238i	−0.676451	+	1.17165i	−0.976043	+	0.217580i	$0.930184\pi$
$24$		0			0
$25$	143.532	+	248.604i	1.14825	+	1.98883i
$26$		0			0
$27$	−24.9944	−	138.052i	−0.178155	−	0.984002i
$28$		0			0
$29$	175.273	−	101.194i	1.12233	−	0.647975i	0.180333	−	0.983606i	$-0.442283\pi$
$29$	175.273	−	101.194i	1.12233	−	0.647975i	0.941994	+	0.335630i	$0.108949\pi$
$30$		0			0
$31$	−66.8886	+	115.855i	−0.387534	+	0.671229i	−0.992117	−	0.125313i	$-0.960006\pi$
$31$	−66.8886	+	115.855i	−0.387534	+	0.671229i	0.604583	+	0.796542i	$0.293340\pi$
$32$		0			0
$33$	11.1414	−	0.665973i	0.0587718	−	0.00351306i
$34$		0			0
$35$			433.985i			2.09591i
$36$		0			0
$37$		−	16.6443i		−	0.0739541i	−0.999316	−	0.0369770i	$-0.988227\pi$
$37$		−	16.6443i		−	0.0739541i	0.999316	−	0.0369770i	$-0.0117728\pi$
$38$		0			0
$39$	45.4845	+	68.9265i	0.186752	+	0.283002i
$40$		0			0
$41$	−65.4314	+	113.331i	−0.249236	+	0.431689i	−0.963314	−	0.268377i	$-0.913513\pi$
$41$	−65.4314	+	113.331i	−0.249236	+	0.431689i	0.714078	+	0.700066i	$0.246846\pi$
$42$		0			0
$43$	107.846	−	62.2650i	0.382474	−	0.220821i	−0.296420	−	0.955058i	$-0.595793\pi$
$43$	107.846	−	62.2650i	0.382474	−	0.220821i	0.678894	+	0.734236i	$0.262460\pi$
$44$		0			0
$45$	65.2896	+	544.180i	0.216284	+	1.80270i
$46$		0			0
$47$	139.663	+	241.903i	0.433446	+	0.750750i	0.997167	−	0.0752150i	$-0.0239643\pi$
$47$	139.663	+	241.903i	0.433446	+	0.750750i	−0.563722	+	0.825965i	$0.690631\pi$
$48$		0			0
$49$	−57.0362	+	98.7895i	−0.166286	+	0.288016i
$50$		0			0
$51$	465.006	+	232.647i	1.27674	+	0.638766i
$52$		0			0
$53$			342.817i			0.888483i	0.895907	+	0.444241i	$0.146527\pi$
$53$			342.817i			0.888483i	−0.895907	+	0.444241i	$0.853473\pi$
$54$		0			0
$55$	−43.6028			−0.106898
$56$		0			0
$57$	−5.48033	+	10.9539i	−0.0127349	+	0.0254540i
$58$		0			0
$59$	−191.251	−	110.419i	−0.422013	−	0.243649i	0.273925	−	0.961751i	$-0.411678\pi$
$59$	−191.251	−	110.419i	−0.422013	−	0.243649i	−0.695938	+	0.718102i	$0.745011\pi$
$60$		0			0
$61$	−367.557	+	212.209i	−0.771488	+	0.445419i	−0.833405	−	0.552662i	$-0.813612\pi$
$61$	−367.557	+	212.209i	−0.771488	+	0.445419i	0.0619169	+	0.998081i	$0.480279\pi$
$62$		0			0
$63$	−227.014	+	530.726i	−0.453986	+	1.06135i
$64$		0			0
$65$	−161.307	−	279.391i	−0.307810	−	0.533142i
$66$		0			0
$67$	47.7127	+	27.5469i	0.0870005	+	0.0502298i	0.542869	−	0.839817i	$-0.317338\pi$
$67$	47.7127	+	27.5469i	0.0870005	+	0.0502298i	−0.455869	+	0.890047i	$0.650671\pi$
$68$		0			0
$69$	647.207	−	427.091i	1.12920	−	0.745156i
$70$		0			0
$71$	996.571			1.66579			0.832896	−	0.553430i	$-0.186681\pi$
$71$	996.571			1.66579			0.832896	+	0.553430i	$0.186681\pi$
$72$		0			0
$73$	−910.971			−1.46056			−0.730282	−	0.683146i	$-0.760611\pi$
$73$	−910.971			−1.46056			−0.730282	+	0.683146i	$0.760611\pi$
$74$		0			0
$75$	−89.0025	−	1488.97i	−0.137028	−	2.29241i
$76$		0			0
$77$	−39.7700	−	22.9612i	−0.0588599	−	0.0339828i
$78$		0			0
$79$	−163.931	−	283.937i	−0.233464	−	0.404372i	0.725361	−	0.688369i	$-0.241673\pi$
$79$	−163.931	−	283.937i	−0.233464	−	0.404372i	−0.958825	+	0.283997i	$0.908339\pi$
$80$		0			0
$81$	−204.813	+	699.638i	−0.280950	+	0.959722i
$82$		0			0
$83$	147.974	−	85.4325i	0.195689	−	0.112981i	−0.398954	−	0.916971i	$-0.630627\pi$
$83$	147.974	−	85.4325i	0.195689	−	0.112981i	0.594643	+	0.803990i	$0.297293\pi$
$84$		0			0
$85$	−1759.13	−	1015.63i	−2.24476	−	1.29601i
$86$		0			0
$87$	−1049.77	+	62.7495i	−1.29364	+	0.0773270i
$88$		0			0
$89$	850.727			1.01322			0.506612	−	0.862174i	$-0.330898\pi$
$89$	850.727			1.01322			0.506612	+	0.862174i	$0.330898\pi$
$90$		0			0
$91$		−	339.776i		−	0.391409i
$92$		0			0
$93$	580.187	−	382.864i	0.646909	−	0.426895i
$94$		0			0
$95$	23.9247	−	41.4388i	0.0258381	−	0.0447530i
$96$		0			0
$97$	−24.9396	−	43.1967i	−0.0261055	−	0.0452161i	0.852677	−	0.522438i	$-0.174977\pi$
$97$	−24.9396	−	43.1967i	−0.0261055	−	0.0452161i	−0.878783	+	0.477222i	$0.841644\pi$
$98$		0			0
$99$	−53.3225	−	22.8083i	−0.0541324	−	0.0231548i
$100$		0			0
$101$	851.839	−	491.810i	0.839220	−	0.484524i	−0.0177792	−	0.999842i	$-0.505660\pi$
$101$	851.839	−	491.810i	0.839220	−	0.484524i	0.856999	+	0.515318i	$0.172326\pi$
$102$		0			0
$103$	270.960	−	469.316i	0.259209	−	0.448962i	−0.706822	−	0.707392i	$-0.749872\pi$
$103$	270.960	−	469.316i	0.259209	−	0.448962i	0.966030	+	0.258430i	$0.0832050\pi$
$104$		0			0
$105$	1008.99	−	2016.73i	0.937783	−	1.87441i
$106$		0			0
$107$			1655.94i			1.49613i	0.663624	+	0.748066i	$0.269017\pi$
$107$			1655.94i			1.49613i	−0.663624	+	0.748066i	$0.730983\pi$
$108$		0			0
$109$			390.839i			0.343445i	0.985145	+	0.171723i	$0.0549333\pi$
$109$			390.839i			0.343445i	−0.985145	+	0.171723i	$0.945067\pi$
$110$		0			0
$111$	−38.6969	+	77.3460i	−0.0330896	+	0.0661384i
$112$		0			0
$113$	854.064	−	1479.28i	0.711005	−	1.23150i	−0.253475	−	0.967342i	$-0.581573\pi$
$113$	854.064	−	1479.28i	0.711005	−	1.23150i	0.964480	−	0.264155i	$-0.0850932\pi$
$114$		0			0
$115$	−2623.44	+	1514.64i	−2.12728	+	1.22818i
$116$		0			0
$117$	−51.1167	−	426.050i	−0.0403909	−	0.336653i
$118$		0			0
$119$	−1069.66	−	1852.71i	−0.824000	−	1.42721i
$120$		0			0
$121$	−663.193	+	1148.68i	−0.498267	+	0.863023i
$122$		0			0
$123$	567.547	−	374.524i	0.416049	−	0.274550i
$124$		0			0
$125$			3289.78i			2.35397i
$126$		0			0
$127$	1388.03			0.969826			0.484913	−	0.874562i	$-0.338851\pi$
$127$	1388.03			0.969826			0.484913	+	0.874562i	$0.338851\pi$
$128$		0			0
$129$	−645.924	+	38.6099i	−0.440856	+	0.0263520i
$130$		0			0
$131$	1827.68	+	1055.21i	1.21897	+	0.703772i	0.964697	−	0.263361i	$-0.0848309\pi$
$131$	1827.68	+	1055.21i	1.21897	+	0.703772i	0.254272	+	0.967133i	$0.418164\pi$
$132$		0			0
$133$	43.6433	−	25.1975i	0.0284538	−	0.0164278i
$134$		0			0
$135$	961.784	−	2680.60i	0.613165	−	1.70896i
$136$		0			0
$137$	959.737	+	1662.31i	0.598510	+	1.03665i	0.993041	+	0.117767i	$0.0375736\pi$
$137$	959.737	+	1662.31i	0.598510	+	1.03665i	−0.394531	+	0.918883i	$0.629093\pi$
$138$		0			0
$139$	−679.222	−	392.149i	−0.414467	−	0.239292i	0.278241	−	0.960511i	$-0.410249\pi$
$139$	−679.222	−	392.149i	−0.414467	−	0.239292i	−0.692707	+	0.721219i	$0.743582\pi$
$140$		0			0
$141$	−86.6036	−	1448.83i	−0.0517258	−	0.865347i
$142$		0			0
$143$	34.1376			0.0199631
$144$		0			0
$145$	4108.35			2.35297
$146$		0			0
$147$	494.727	−	326.470i	0.277581	−	0.183175i
$148$		0			0
$149$	−404.617	−	233.606i	−0.222467	−	0.128441i	0.384625	−	0.923073i	$-0.374331\pi$
$149$	−404.617	−	233.606i	−0.222467	−	0.128441i	−0.607092	+	0.794632i	$0.707664\pi$
$150$		0			0
$151$	−218.102	−	377.764i	−0.117542	−	0.203589i	0.801251	−	0.598329i	$-0.204168\pi$
$151$	−218.102	−	377.764i	−0.117542	−	0.203589i	−0.918793	+	0.394739i	$0.870835\pi$
$152$		0			0
$153$	−1619.99	−	2162.22i	−0.856005	−	1.14252i
$154$		0			0
$155$	−2351.77	+	1357.80i	−1.21870	+	0.703618i
$156$		0			0
$157$	−114.915	−	66.3465i	−0.0584156	−	0.0337263i	0.470508	−	0.882396i	$-0.344071\pi$
$157$	−114.915	−	66.3465i	−0.0584156	−	0.0337263i	−0.528923	+	0.848670i	$0.677404\pi$
$158$		0			0
$159$	797.030	−	1593.07i	0.397538	−	0.794585i
$160$		0			0
$161$	−3190.44			−1.56175
$162$		0			0
$163$		−	3675.16i		−	1.76601i	−0.469359	−	0.883007i	$-0.655515\pi$
$163$		−	3675.16i		−	1.76601i	0.469359	−	0.883007i	$-0.344485\pi$
$164$		0			0
$165$	202.622	+	101.374i	0.0956008	+	0.0478300i
$166$		0			0
$167$	3.78642	−	6.55827i	0.00175450	−	0.00303889i	−0.865147	−	0.501519i	$-0.832775\pi$
$167$	3.78642	−	6.55827i	0.00175450	−	0.00303889i	0.866901	+	0.498480i	$0.166108\pi$
$168$		0			0
$169$	−972.209	−	1683.92i	−0.442517	−	0.766462i
$170$		0			0
$171$	50.9342	−	38.1613i	0.0227780	−	0.0170659i
$172$		0			0
$173$	−1208.10	+	697.499i	−0.530927	+	0.306531i	−0.741394	−	0.671070i	$-0.765835\pi$
$173$	−1208.10	+	697.499i	−0.530927	+	0.306531i	0.210467	+	0.977601i	$0.432502\pi$
$174$		0			0
$175$	−3068.60	+	5314.97i	−1.32551	+	2.29585i
$176$		0			0
$177$	632.027	+	957.763i	0.268396	+	0.406723i
$178$		0			0
$179$		−	3708.55i		−	1.54855i	−0.632852	−	0.774273i	$-0.718116\pi$
$179$		−	3708.55i		−	1.54855i	0.632852	−	0.774273i	$-0.281884\pi$
$180$		0			0
$181$		−	1909.18i		−	0.784024i	−0.919960	−	0.392012i	$-0.871779\pi$
$181$		−	1909.18i		−	0.784024i	0.919960	−	0.392012i	$-0.128221\pi$
$182$		0			0
$183$	2201.41	−	131.588i	0.889251	−	0.0531547i
$184$		0			0
$185$	168.934	−	292.602i	0.0671366	−	0.116284i
$186$		0			0
$187$	186.144	−	107.470i	0.0727923	−	0.0420267i
$188$		0			0
$189$	2288.84	−	1938.49i	0.880893	−	0.746056i
$190$		0			0
$191$	528.874	+	916.036i	0.200356	+	0.347026i	0.948643	−	0.316348i	$-0.102457\pi$
$191$	528.874	+	916.036i	0.200356	+	0.347026i	−0.748287	+	0.663375i	$0.769124\pi$
$192$		0			0
$193$	601.103	−	1041.14i	0.224188	−	0.388305i	−0.731887	−	0.681426i	$-0.761360\pi$
$193$	601.103	−	1041.14i	0.224188	−	0.388305i	0.956076	+	0.293120i	$0.0946936\pi$
$194$		0			0
$195$	100.025	+	1673.36i	0.0367329	+	0.614523i
$196$		0			0
$197$			1181.13i			0.427169i	0.976925	+	0.213584i	$0.0685138\pi$
$197$			1181.13i			0.427169i	−0.976925	+	0.213584i	$0.931486\pi$
$198$		0			0
$199$	766.932			0.273198			0.136599	−	0.990626i	$-0.456383\pi$
$199$	766.932			0.273198			0.136599	+	0.990626i	$0.456383\pi$
$200$		0			0
$201$	−157.676	−	238.940i	−0.0553314	−	0.0838484i
$202$		0			0
$203$	3747.21	+	2163.46i	1.29558	+	0.748004i
$204$		0			0
$205$	−2300.54	+	1328.22i	−0.783788	+	0.452520i
$206$		0			0
$207$	−4000.54	+	479.976i	−1.34327	+	0.161163i
$208$		0			0
$209$	2.53161	+	4.38488i	0.000837872	+	0.00145124i
$210$		0			0
$211$	−3170.24	−	1830.34i	−1.03435	−	0.597183i	−0.116123	−	0.993235i	$-0.537047\pi$
$211$	−3170.24	−	1830.34i	−1.03435	−	0.597183i	−0.918228	+	0.396052i	$0.870380\pi$
$212$		0			0
$213$	−4631.07	−	2316.97i	−1.48974	−	0.745333i
$214$		0			0
$215$	2527.88			0.801860
$216$		0			0
$217$	−2860.06			−0.894716
$218$		0			0
$219$	4233.29	+	2117.95i	1.30621	+	0.653507i
$220$		0			0
$221$	1377.26	+	795.162i	0.419207	+	0.242029i
$222$		0			0
$223$	−497.726	−	862.086i	−0.149463	−	0.258877i	0.781566	−	0.623822i	$-0.214421\pi$
$223$	−497.726	−	862.086i	−0.149463	−	0.258877i	−0.931029	+	0.364945i	$0.881088\pi$
$224$		0			0
$225$	−3048.16	+	7126.16i	−0.903160	+	2.11146i
$226$		0			0
$227$	−73.6777	+	42.5378i	−0.0215426	+	0.0124376i	−0.510733	−	0.859740i	$-0.670626\pi$
$227$	−73.6777	+	42.5378i	−0.0215426	+	0.0124376i	0.489190	+	0.872177i	$0.337292\pi$
$228$		0			0
$229$	5136.14	+	2965.35i	1.48212	+	0.855703i	0.999794	−	0.0202888i	$-0.00645857\pi$
$229$	5136.14	+	2965.35i	1.48212	+	0.855703i	0.482326	+	0.875992i	$0.339792\pi$
$230$		0			0
$231$	131.428	+	199.164i	0.0374343	+	0.0567273i
$232$		0			0
$233$	4680.37			1.31597			0.657986	−	0.753030i	$-0.271409\pi$
$233$	4680.37			1.31597			0.657986	+	0.753030i	$0.271409\pi$
$234$		0			0
$235$			5670.13i			1.57395i
$236$		0			0
$237$	101.652	+	1700.58i	0.0278607	+	0.466096i
$238$		0			0
$239$	−1832.74	+	3174.40i	−0.496026	+	0.859142i	−0.999990	−	0.00458254i	$-0.998541\pi$
$239$	−1832.74	+	3174.40i	−0.496026	+	0.859142i	0.503963	+	0.863725i	$0.331875\pi$
$240$		0			0
$241$	−1037.00	−	1796.13i	−0.277173	−	0.480078i	0.693508	−	0.720449i	$-0.256064\pi$
$241$	−1037.00	−	1796.13i	−0.277173	−	0.480078i	−0.970681	+	0.240371i	$0.922731\pi$
$242$		0			0
$243$	2578.38	−	2775.04i	0.680672	−	0.732588i
$244$		0			0
$245$	−2005.36	+	1157.80i	−0.522930	+	0.301914i
$246$		0			0
$247$	−18.7312	+	32.4434i	−0.00482525	+	0.00835758i
$248$		0			0
$249$	−886.259	+	52.9758i	−0.225560	+	0.0134828i
$250$		0			0
$251$		−	2144.46i		−	0.539271i	−0.962963	−	0.269635i	$-0.913097\pi$
$251$		−	2144.46i		−	0.539271i	0.962963	−	0.269635i	$-0.0869031\pi$
$252$		0			0
$253$		−	320.546i		−	0.0796543i
$254$		0			0
$255$	5813.40	+	8809.53i	1.42764	+	2.16343i
$256$		0			0
$257$	1327.47	−	2299.24i	0.322199	−	0.558065i	−0.658742	−	0.752369i	$-0.728911\pi$
$257$	1327.47	−	2299.24i	0.322199	−	0.558065i	0.980941	+	0.194303i	$0.0622446\pi$
$258$		0			0
$259$	308.168	−	177.921i	0.0739330	−	0.0426852i
$260$		0			0
$261$	5024.16	+	2149.05i	1.19152	+	0.509666i
$262$		0			0
$263$	−863.016	−	1494.79i	−0.202342	−	0.350466i	0.746941	−	0.664891i	$-0.231522\pi$
$263$	−863.016	−	1494.79i	−0.202342	−	0.350466i	−0.949283	+	0.314424i	$0.898189\pi$
$264$		0			0
$265$	−3479.48	+	6026.64i	−0.806577	+	1.39703i
$266$		0			0
$267$	−3953.33	−	1977.89i	−0.906142	−	0.453352i
$268$		0			0
$269$		−	7311.35i		−	1.65718i	−0.559857	−	0.828589i	$-0.689144\pi$
$269$		−	7311.35i		−	1.65718i	0.559857	−	0.828589i	$-0.310856\pi$
$270$		0			0
$271$	474.085			0.106268			0.0531340	−	0.998587i	$-0.483079\pi$
$271$	474.085			0.106268			0.0531340	+	0.998587i	$0.483079\pi$
$272$		0			0
$273$	−789.960	+	1578.94i	−0.175130	+	0.350044i
$274$		0			0
$275$	−533.999	−	308.305i	−0.117096	−	0.0676053i
$276$		0			0
$277$	−2119.01	+	1223.41i	−0.459636	+	0.265371i	−0.711891	−	0.702290i	$-0.752161\pi$
$277$	−2119.01	+	1223.41i	−0.459636	+	0.265371i	0.252255	+	0.967661i	$0.418828\pi$
$278$		0			0
$279$	−3586.27	+	430.273i	−0.769549	+	0.0923290i
$280$		0			0
$281$	4050.94	+	7016.43i	0.859995	+	1.48956i	0.871932	+	0.489626i	$0.162867\pi$
$281$	4050.94	+	7016.43i	0.859995	+	1.48956i	−0.0119373	+	0.999929i	$0.503800\pi$
$282$		0			0
$283$	1237.85	+	714.675i	0.260010	+	0.150117i	0.624339	−	0.781153i	$-0.285368\pi$
$283$	1237.85	+	714.675i	0.260010	+	0.150117i	−0.364329	+	0.931270i	$0.618702\pi$
$284$		0			0
$285$	−207.521	+	136.943i	−0.0431315	+	0.0284624i
$286$		0			0
$287$	−2797.75			−0.575422
$288$		0			0
$289$	5100.15			1.03809
$290$		0			0
$291$	15.4648	+	258.719i	0.00311534	+	0.0521181i
$292$		0			0
$293$	4394.07	+	2536.92i	0.876123	+	0.505830i	0.869378	−	0.494147i	$-0.164520\pi$
$293$	4394.07	+	2536.92i	0.876123	+	0.505830i	0.00674493	+	0.999977i	$0.497853\pi$
$294$		0			0
$295$	−2241.43	−	3882.27i	−0.442376	−	0.766218i
$296$		0			0
$297$	194.762	+	229.962i	0.0380513	+	0.0449284i
$298$		0			0
$299$	2053.95	−	1185.85i	0.397267	−	0.229362i
$300$		0			0
$301$	2305.67	+	1331.18i	0.441517	+	0.254910i
$302$		0			0
$303$	−5101.93	+	304.966i	−0.967321	+	0.0578213i
$304$		0			0
$305$	−8615.40			−1.61743
$306$		0			0
$307$			1214.91i			0.225858i	0.993603	+	0.112929i	$0.0360233\pi$
$307$			1214.91i			0.225858i	−0.993603	+	0.112929i	$0.963977\pi$
$308$		0			0
$309$	−2350.29	+	1550.95i	−0.432696	+	0.285535i
$310$		0			0
$311$	3227.06	−	5589.44i	0.588392	−	1.01913i	−0.406051	−	0.913851i	$-0.633094\pi$
$311$	3227.06	−	5589.44i	0.588392	−	1.01913i	0.994443	−	0.105275i	$-0.0335723\pi$
$312$		0			0
$313$	−1651.53	−	2860.53i	−0.298243	−	0.516572i	0.677491	−	0.735531i	$-0.263067\pi$
$313$	−1651.53	−	2860.53i	−0.298243	−	0.516572i	−0.975734	+	0.218959i	$0.929734\pi$
$314$		0			0
$315$	−9377.55	+	7025.91i	−1.67735	+	1.25671i
$316$		0			0
$317$	385.013	−	222.288i	0.0682161	−	0.0393846i	−0.465504	−	0.885046i	$-0.654127\pi$
$317$	385.013	−	222.288i	0.0682161	−	0.0393846i	0.533720	+	0.845661i	$0.320794\pi$
$318$		0			0
$319$	−217.364	+	376.486i	−0.0381506	+	0.0660788i
$320$		0			0
$321$	3849.97	−	7695.18i	0.669422	−	1.33802i
$322$		0			0
$323$			235.874i			0.0406328i
$324$		0			0
$325$		−	4562.24i		−	0.778670i
$326$		0			0
$327$	908.676	−	1816.23i	0.153669	−	0.307149i
$328$		0			0
$329$	−2985.89	+	5171.71i	−0.500357	+	0.866644i
$330$		0			0
$331$	5662.03	−	3268.98i	0.940222	−	0.542837i	0.0501922	−	0.998740i	$-0.484017\pi$
$331$	5662.03	−	3268.98i	0.940222	−	0.542837i	0.890030	+	0.455902i	$0.150683\pi$
$332$		0			0
$333$	359.650	−	269.459i	0.0591852	−	0.0443432i
$334$		0			0
$335$	559.185	+	968.536i	0.0911986	+	0.157961i
$336$		0			0
$337$	−1151.09	+	1993.74i	−0.186065	+	0.322273i	−0.943935	−	0.330132i	$-0.892907\pi$
$337$	−1151.09	+	1993.74i	−0.186065	+	0.322273i	0.757870	+	0.652405i	$0.226240\pi$
$338$		0			0
$339$	−7408.09	+	4888.59i	−1.18688	+	0.783220i
$340$		0			0
$341$		−	287.352i		−	0.0456334i
$342$		0			0
$343$	4894.30			0.770459
$344$		0			0
$345$	15712.6	−	939.214i	2.45199	−	0.146567i
$346$		0			0
$347$	−7921.96	−	4573.75i	−1.22557	−	0.707584i	−0.259471	−	0.965751i	$-0.583548\pi$
$347$	−7921.96	−	4573.75i	−1.22557	−	0.707584i	−0.966100	+	0.258167i	$0.916882\pi$
$348$		0			0
$349$	8355.48	−	4824.04i	1.28154	−	0.739900i	0.304413	−	0.952540i	$-0.401540\pi$
$349$	8355.48	−	4824.04i	1.28154	−	0.739900i	0.977131	+	0.212640i	$0.0682063\pi$
$350$		0			0
$351$	−753.002	+	2098.70i	−0.114508	+	0.319146i
$352$		0			0
$353$	−2352.94	−	4075.41i	−0.354771	−	0.614481i	0.632308	−	0.774717i	$-0.282108\pi$
$353$	−2352.94	−	4075.41i	−0.354771	−	0.614481i	−0.987079	+	0.160236i	$0.948774\pi$
$354$		0			0
$355$	17519.5	+	10114.9i	2.61926	+	1.51223i
$356$		0			0
$357$	663.288	+	11096.5i	0.0983331	+	1.64506i
$358$		0			0
$359$	−7132.26			−1.04854			−0.524271	−	0.851552i	$-0.675662\pi$
$359$	−7132.26			−1.04854			−0.524271	+	0.851552i	$0.675662\pi$
$360$		0			0
$361$	6853.44			0.999190
$362$		0			0
$363$	5752.48	−	3796.06i	0.831755	−	0.548874i
$364$		0			0
$365$	−16014.6	−	9246.06i	−2.29656	−	1.32592i
$366$		0			0
$367$	2335.97	+	4046.02i	0.332253	+	0.575479i	0.982953	−	0.183856i	$-0.0588580\pi$
$367$	2335.97	+	4046.02i	0.332253	+	0.575479i	−0.650700	+	0.759335i	$0.725525\pi$
$368$		0			0
$369$	−3508.14	+	420.899i	−0.494923	+	0.0593798i
$370$		0			0
$371$	−6347.26	+	3664.59i	−0.888229	+	0.512819i
$372$		0			0
$373$	−5258.37	−	3035.92i	−0.729941	−	0.421432i	0.0884596	−	0.996080i	$-0.471806\pi$
$373$	−5258.37	−	3035.92i	−0.729941	−	0.421432i	−0.818401	+	0.574648i	$0.805139\pi$
$374$		0			0
$375$	7648.54	−	15287.6i	1.05325	−	2.10520i
$376$		0			0
$377$	−3216.52			−0.439414
$378$		0			0
$379$		−	7792.48i		−	1.05613i	−0.849204	−	0.528064i	$-0.822918\pi$
$379$		−	7792.48i		−	1.05613i	0.849204	−	0.528064i	$-0.177082\pi$
$380$		0			0
$381$	−6450.19	−	3227.09i	−0.867332	−	0.433934i
$382$		0			0
$383$	−6946.85	+	12032.3i	−0.926809	+	1.60528i	−0.138182	+	0.990407i	$0.544126\pi$
$383$	−6946.85	+	12032.3i	−0.926809	+	1.60528i	−0.788626	+	0.614873i	$0.789207\pi$
$384$		0			0
$385$	−466.097	−	807.304i	−0.0617001	−	0.106868i
$386$		0			0
$387$	3091.38	+	1322.31i	0.406056	+	0.173687i
$388$		0			0
$389$	11195.6	−	6463.76i	1.45922	−	0.842483i	0.460250	−	0.887790i	$-0.347760\pi$
$389$	11195.6	−	6463.76i	1.45922	−	0.842483i	0.998973	+	0.0453069i	$0.0144266\pi$
$390$		0			0
$391$	7466.44	−	12932.2i	0.965713	−	1.67266i
$392$		0			0
$393$	−6039.93	−	9152.81i	−0.775252	−	1.17480i
$394$		0			0
$395$		−	6655.38i		−	0.847768i
$396$		0			0
$397$			4139.86i			0.523359i	0.965155	+	0.261680i	$0.0842764\pi$
$397$			4139.86i			0.523359i	−0.965155	+	0.261680i	$0.915724\pi$
$398$		0			0
$399$	−261.393	+	15.6247i	−0.0327971	+	0.00196043i
$400$		0			0
$401$	1498.25	−	2595.05i	0.186581	−	0.323169i	−0.757527	−	0.652804i	$-0.773593\pi$
$401$	1498.25	−	2595.05i	0.186581	−	0.323169i	0.944108	+	0.329635i	$0.106926\pi$
$402$		0			0
$403$	1841.25	−	1063.05i	0.227591	−	0.131400i
$404$		0			0
$405$	−10701.6	+	10220.7i	−1.31301	+	1.25400i
$406$		0			0
$407$	17.8759	+	30.9619i	0.00217708	+	0.00377082i
$408$		0			0
$409$	−709.204	+	1228.38i	−0.0857405	+	0.148507i	−0.905707	−	0.423905i	$-0.860659\pi$
$409$	−709.204	+	1228.38i	−0.0857405	+	0.148507i	0.819966	+	0.572412i	$0.193992\pi$
$410$		0			0
$411$	−595.123	−	9956.11i	−0.0714240	−	1.19489i
$412$		0			0
$413$		−	4721.34i		−	0.562523i
$414$		0			0
$415$	3468.45			0.410264
$416$		0			0
$417$	2244.62	+	3401.47i	0.263596	+	0.399450i
$418$		0			0
$419$	−3590.43	−	2072.93i	−0.418625	−	0.241693i	0.275864	−	0.961197i	$-0.411036\pi$
$419$	−3590.43	−	2072.93i	−0.418625	−	0.241693i	−0.694489	+	0.719504i	$0.744369\pi$
$420$		0			0
$421$	−3018.25	+	1742.59i	−0.349408	+	0.201731i	−0.664424	−	0.747355i	$-0.731323\pi$
$421$	−3018.25	+	1742.59i	−0.349408	+	0.201731i	0.315017	+	0.949086i	$0.397990\pi$
$422$		0			0
$423$	−2966.01	+	6934.09i	−0.340927	+	0.797038i
$424$		0			0
$425$	−14362.6	−	24876.7i	−1.63927	−	2.83929i
$426$		0			0
$427$	−7858.08	−	4536.87i	−0.890584	−	0.514179i
$428$		0			0
$429$	−158.638	−	79.3678i	−0.0178534	−	0.00893220i
$430$		0			0
$431$	13182.0			1.47321			0.736606	−	0.676322i	$-0.236427\pi$
$431$	13182.0			1.47321			0.736606	+	0.676322i	$0.236427\pi$
$432$		0			0
$433$	−710.264			−0.0788293			−0.0394147	−	0.999223i	$-0.512549\pi$
$433$	−710.264			−0.0788293			−0.0394147	+	0.999223i	$0.512549\pi$
$434$		0			0
$435$	−19091.5	−	9551.67i	−2.10430	−	1.05280i
$436$		0			0
$437$	304.638	+	175.883i	0.0333473	+	0.0192531i
$438$		0			0
$439$	−8935.15	−	15476.1i	−0.971416	−	1.68254i	−0.691289	−	0.722578i	$-0.742957\pi$
$439$	−8935.15	−	15476.1i	−0.971416	−	1.68254i	−0.280126	−	0.959963i	$-0.590376\pi$
$440$		0			0
$441$	−3058.02	+	366.895i	−0.330204	+	0.0396172i
$442$		0			0
$443$	7352.63	−	4245.04i	0.788564	−	0.455278i	−0.0508927	−	0.998704i	$-0.516207\pi$
$443$	7352.63	−	4245.04i	0.788564	−	0.455278i	0.839457	+	0.543426i	$0.182873\pi$
$444$		0			0
$445$	14955.6	+	8634.60i	1.59317	+	0.919818i
$446$		0			0
$447$	1337.14	+	2026.28i	0.141486	+	0.214406i
$448$		0			0
$449$	7525.14			0.790942			0.395471	−	0.918478i	$-0.370581\pi$
$449$	7525.14			0.790942			0.395471	+	0.918478i	$0.370581\pi$
$450$		0			0
$451$		−	281.092i		−	0.0293484i
$452$		0			0
$453$	135.243	+	2262.54i	0.0140271	+	0.234666i
$454$		0			0
$455$	3448.62	−	5973.18i	0.355327	−	0.615444i
$456$		0			0
$457$	−7076.61	−	12257.0i	−0.724354	−	1.25462i	−0.959239	−	0.282595i	$-0.908805\pi$
$457$	−7076.61	−	12257.0i	−0.724354	−	1.25462i	0.234886	−	0.972023i	$-0.424528\pi$
$458$		0			0
$459$	2501.08	+	13814.2i	0.254337	+	1.40478i
$460$		0			0
$461$	1645.56	−	950.065i	0.166250	−	0.0959847i	−0.414566	−	0.910019i	$-0.636067\pi$
$461$	1645.56	−	950.065i	0.166250	−	0.0959847i	0.580817	+	0.814034i	$0.302733\pi$
$462$		0			0
$463$	−6299.69	+	10911.4i	−0.632335	+	1.09524i	0.354738	+	0.934966i	$0.384570\pi$
$463$	−6299.69	+	10911.4i	−0.632335	+	1.09524i	−0.987073	+	0.160271i	$0.948763\pi$
$464$		0			0
$465$	14085.5	−	841.955i	1.40473	−	0.0839671i
$466$		0			0
$467$			11691.5i			1.15849i	0.815152	+	0.579247i	$0.196653\pi$
$467$			11691.5i			1.15849i	−0.815152	+	0.579247i	$0.803347\pi$
$468$		0			0
$469$			1177.87i			0.115968i
$470$		0			0
$471$	379.761	+	575.484i	0.0371517	+	0.0562992i
$472$		0			0
$473$	−133.745	+	231.652i	−0.0130012	+	0.0225188i
$474$		0			0
$475$	586.007	−	338.332i	0.0566060	−	0.0326815i
$476$		0			0
$477$	−7407.61	+	5549.98i	−0.711050	+	0.532738i
$478$		0			0
$479$	645.134	+	1117.41i	0.0615385	+	0.106588i	0.895153	−	0.445758i	$-0.147066\pi$
$479$	645.134	+	1117.41i	0.0615385	+	0.106588i	−0.833615	+	0.552346i	$0.813733\pi$
$480$		0			0
$481$	−132.262	+	229.085i	−0.0125377	+	0.0217159i
$482$		0			0
$483$	14826.0	+	7417.58i	1.39670	+	0.698782i
$484$		0			0
$485$		−	1012.52i		−	0.0947959i
$486$		0			0
$487$	9535.19			0.887230			0.443615	−	0.896218i	$-0.353696\pi$
$487$	9535.19			0.887230			0.443615	+	0.896218i	$0.353696\pi$
$488$		0			0
$489$	−8544.52	+	17078.5i	−0.790177	+	1.57938i
$490$		0			0
$491$	−7737.89	−	4467.47i	−0.711214	−	0.410620i	0.100296	−	0.994958i	$-0.468021\pi$
$491$	−7737.89	−	4467.47i	−0.711214	−	0.410620i	−0.811510	+	0.584338i	$0.801354\pi$
$492$		0			0
$493$	−17538.9	+	10126.1i	−1.60225	+	0.925061i
$494$		0			0
$495$	−705.899	−	942.170i	−0.0640965	−	0.0855503i
$496$		0			0
$497$	10653.0	+	18451.5i	0.961471	+	1.66532i
$498$		0			0
$499$	16966.8	+	9795.81i	1.52212	+	0.878799i	0.999658	+	0.0261381i	$0.00832097\pi$
$499$	16966.8	+	9795.81i	1.52212	+	0.878799i	0.522465	+	0.852660i	$0.325012\pi$
$500$		0			0
$501$	−32.8431	+	21.6731i	−0.00292879	+	0.00193270i
$502$		0			0
$503$	10902.0			0.966396			0.483198	−	0.875511i	$-0.339475\pi$
$503$	10902.0			0.966396			0.483198	+	0.875511i	$0.339475\pi$
$504$		0			0
$505$	19966.8			1.75943
$506$		0			0
$507$	602.857	+	10085.5i	0.0528083	+	0.883457i
$508$		0			0
$509$	−1301.27	−	751.291i	−0.113316	−	0.0654232i	0.442271	−	0.896882i	$-0.354173\pi$
$509$	−1301.27	−	751.291i	−0.113316	−	0.0654232i	−0.555587	+	0.831458i	$0.687506\pi$
$510$		0			0
$511$	−9737.94	−	16866.6i	−0.843016	−	1.46015i
$512$		0			0
$513$	−325.414	+	58.9166i	−0.0280066	+	0.00507063i
$514$		0			0
$515$	9526.82	−	5500.31i	0.815149	−	0.470626i
$516$		0			0
$517$	−519.606	−	299.995i	−0.0442016	−	0.0255198i
$518$		0			0
$519$	7235.71	−	432.512i	0.611970	−	0.0365803i
$520$		0			0
$521$	6339.22			0.533064			0.266532	−	0.963826i	$-0.414122\pi$
$521$	6339.22			0.533064			0.266532	+	0.963826i	$0.414122\pi$
$522$		0			0
$523$			15909.9i			1.33019i	0.746758	+	0.665096i	$0.231610\pi$
$523$			15909.9i			1.33019i	−0.746758	+	0.665096i	$0.768390\pi$
$524$		0			0
$525$	26616.8	−	17564.4i	2.21267	−	1.46014i
$526$		0			0
$527$	6693.26	−	11593.1i	0.553250	−	0.958258i
$528$		0			0
$529$	−5051.39	−	8749.27i	−0.415172	−	0.719098i
$530$		0			0
$531$	−710.288	−	5920.16i	−0.0580488	−	0.483828i
$532$		0			0
$533$	1801.14	−	1039.89i	0.146372	−	0.0845077i
$534$		0			0
$535$	−16807.3	+	29111.1i	−1.35821	+	2.35249i
$536$		0			0
$537$	−8622.15	+	17233.6i	−0.692874	+	1.38489i
$538$		0			0
$539$		−	245.026i		−	0.0195808i
$540$		0			0
$541$		−	974.163i		−	0.0774169i	−0.999251	−	0.0387085i	$-0.987676\pi$
$541$		−	974.163i		−	0.0774169i	0.999251	−	0.0387085i	$-0.0123244\pi$
$542$		0			0
$543$	−4438.73	+	8871.98i	−0.350800	+	0.701166i
$544$		0			0
$545$	−3966.88	+	6870.84i	−0.311785	+	0.540027i
$546$		0			0
$547$	−19129.5	+	11044.4i	−1.49528	+	0.863302i	−0.999985	−	0.00542137i	$-0.998274\pi$
$547$	−19129.5	+	11044.4i	−1.49528	+	0.863302i	−0.495298	+	0.868723i	$0.664941\pi$
$548$		0			0
$549$	−10535.9	−	4506.65i	−0.819055	−	0.350345i
$550$		0			0
$551$	−238.534	−	413.153i	−0.0184426	−	0.0319436i
$552$		0			0
$553$	3504.72	−	6070.35i	0.269504	−	0.466795i
$554$		0			0
$555$	−1465.32	+	966.962i	−0.112071	+	0.0739554i
$556$		0			0
$557$			2065.57i			0.157130i	0.996909	+	0.0785648i	$0.0250337\pi$
$557$			2065.57i			0.157130i	−0.996909	+	0.0785648i	$0.974966\pi$
$558$		0			0
$559$	−1979.13			−0.149747
$560$		0			0
$561$	−1114.87	+	66.6411i	−0.0839036	+	0.00501531i
$562$		0			0
$563$	−11759.3	−	6789.26i	−0.880280	−	0.508230i	−0.00952895	−	0.999955i	$-0.503033\pi$
$563$	−11759.3	−	6789.26i	−0.880280	−	0.508230i	−0.870751	+	0.491725i	$0.836367\pi$
$564$		0			0
$565$	30028.5	−	17336.9i	2.23594	−	1.29092i
$566$		0			0
$567$	−15143.1	+	3686.76i	−1.12161	+	0.273067i
$568$		0			0
$569$	−1428.57	−	2474.35i	−0.105252	−	0.182303i	0.808589	−	0.588374i	$-0.200232\pi$
$569$	−1428.57	−	2474.35i	−0.105252	−	0.182303i	−0.913841	+	0.406071i	$0.866898\pi$
$570$		0			0
$571$	−15562.8	−	8985.21i	−1.14060	−	0.658528i	−0.194024	−	0.980997i	$-0.562154\pi$
$571$	−15562.8	−	8985.21i	−1.14060	−	0.658528i	−0.946580	+	0.322469i	$0.895487\pi$
$572$		0			0
$573$	−327.949	−	5486.42i	−0.0239097	−	0.399998i
$574$		0			0
$575$	−42838.6			−3.10695
$576$		0			0
$577$	−22787.6			−1.64412			−0.822062	−	0.569398i	$-0.807176\pi$
$577$	−22787.6			−1.64412			−0.822062	+	0.569398i	$0.807176\pi$
$578$		0			0
$579$	−5213.92	+	3440.66i	−0.374237	+	0.246958i
$580$		0			0
$581$	3163.56	+	1826.48i	0.225898	+	0.130422i
$582$		0			0
$583$	−368.184	−	637.714i	−0.0261555	−	0.0453026i
$584$		0			0
$585$	3425.65	−	8008.67i	0.242108	−	0.566013i
$586$		0			0
$587$	7735.67	−	4466.19i	0.543927	−	0.314037i	−0.202742	−	0.979232i	$-0.564985\pi$
$587$	7735.67	−	4466.19i	0.543927	−	0.314037i	0.746669	+	0.665196i	$0.231652\pi$
$588$		0			0
$589$	273.091	+	157.669i	0.0191045	+	0.0110300i
$590$		0			0
$591$	2746.06	−	5488.73i	0.191130	−	0.382024i
$592$		0			0
$593$	10639.1			0.736753			0.368377	−	0.929677i	$-0.379914\pi$
$593$	10639.1			0.736753			0.368377	+	0.929677i	$0.379914\pi$
$594$		0			0
$595$		−	43427.0i		−	2.99216i
$596$		0			0
$597$	−3563.94	−	1783.07i	−0.244325	−	0.122238i
$598$		0			0
$599$	−1792.27	+	3104.30i	−0.122254	+	0.211750i	−0.920656	−	0.390374i	$-0.872346\pi$
$599$	−1792.27	+	3104.30i	−0.122254	+	0.211750i	0.798402	+	0.602125i	$0.205679\pi$
$600$		0			0
$601$	11481.4	+	19886.4i	0.779261	+	1.34972i	0.932368	+	0.361510i	$0.117739\pi$
$601$	11481.4	+	19886.4i	0.779261	+	1.34972i	−0.153107	+	0.988210i	$0.548928\pi$
$602$		0			0
$603$	177.201	+	1476.94i	0.0119671	+	0.0997442i
$604$		0			0
$605$	−23317.5	+	13462.4i	−1.56693	+	0.904667i
$606$		0			0
$607$	2226.59	−	3856.57i	0.148887	−	0.257880i	−0.781929	−	0.623367i	$-0.785764\pi$
$607$	2226.59	−	3856.57i	0.148887	−	0.257880i	0.930816	+	0.365487i	$0.119098\pi$
$608$		0			0
$609$	−12383.4	−	18765.6i	−0.823976	−	1.24864i
$610$		0			0
$611$		−	4439.27i		−	0.293934i
$612$		0			0
$613$		−	16761.2i		−	1.10437i	−0.833722	−	0.552185i	$-0.813794\pi$
$613$		−	16761.2i		−	1.10437i	0.833722	−	0.552185i	$-0.186206\pi$
$614$		0			0
$615$	13778.6	−	823.612i	0.903427	−	0.0540021i
$616$		0			0
$617$	−12004.5	+	20792.4i	−0.783278	+	1.35668i	0.146744	+	0.989174i	$0.453121\pi$
$617$	−12004.5	+	20792.4i	−0.783278	+	1.35668i	−0.930022	+	0.367503i	$0.880213\pi$
$618$		0			0
$619$	12708.3	−	7337.15i	0.825187	−	0.476422i	−0.0270152	−	0.999635i	$-0.508600\pi$
$619$	12708.3	−	7337.15i	0.825187	−	0.476422i	0.852202	+	0.523213i	$0.175267\pi$
$620$		0			0
$621$	19706.4	+	7070.56i	1.27342	+	0.456895i
$622$		0			0
$623$	9093.95	+	15751.2i	0.584818	+	1.01293i
$624$		0			0
$625$	−15448.7	+	26758.0i	−0.988718	+	1.71251i
$626$		0			0
$627$	−1.56983	−	26.2624i	−9.99885e−5	−	0.00167276i
$628$		0			0
$629$			1665.52i			0.105578i
$630$		0			0
$631$	19515.2			1.23120			0.615599	−	0.788059i	$-0.288914\pi$
$631$	19515.2			1.23120			0.615599	+	0.788059i	$0.288914\pi$
$632$		0			0
$633$	10476.7	+	15876.2i	0.657837	+	0.996876i
$634$		0			0
$635$	24401.3	+	14088.1i	1.52494	+	0.880422i
$636$		0			0
$637$	1570.04	−	906.465i	0.0976568	−	0.0563822i
$638$		0			0
$639$	16133.8	+	21533.9i	0.998815	+	1.33313i
$640$		0			0
$641$	8452.58	+	14640.3i	0.520837	+	0.902117i	0.999706	+	0.0242303i	$0.00771351\pi$
$641$	8452.58	+	14640.3i	0.520837	+	0.902117i	−0.478869	+	0.877886i	$0.658953\pi$
$642$		0			0
$643$	−3132.49	−	1808.54i	−0.192120	−	0.110921i	0.400854	−	0.916142i	$-0.368713\pi$
$643$	−3132.49	−	1808.54i	−0.192120	−	0.110921i	−0.592975	+	0.805221i	$0.702047\pi$
$644$		0			0
$645$	−11747.1	−	5877.16i	−0.717116	−	0.358780i
$646$		0			0
$647$	−16575.8			−1.00721			−0.503604	−	0.863935i	$-0.667993\pi$
$647$	−16575.8			−1.00721			−0.503604	+	0.863935i	$0.667993\pi$
$648$		0			0
$649$	474.357			0.0286905
$650$		0			0
$651$	13290.7	+	6649.46i	0.800159	+	0.400327i
$652$		0			0
$653$	11999.5	+	6927.91i	0.719106	+	0.415176i	0.814424	−	0.580271i	$-0.197053\pi$
$653$	11999.5	+	6927.91i	0.719106	+	0.415176i	−0.0953176	+	0.995447i	$0.530387\pi$
$654$		0			0
$655$	21420.1	+	37100.7i	1.27779	+	2.21319i
$656$		0			0
$657$	−14748.0	−	19684.3i	−0.875759	−	1.16888i
$658$		0			0
$659$	421.594	−	243.407i	0.0249210	−	0.0143882i	−0.487488	−	0.873130i	$-0.662087\pi$
$659$	421.594	−	243.407i	0.0249210	−	0.0143882i	0.512409	+	0.858742i	$0.328753\pi$
$660$		0			0
$661$	−10247.6	−	5916.48i	−0.603006	−	0.348146i	0.167217	−	0.985920i	$-0.446522\pi$
$661$	−10247.6	−	5916.48i	−0.603006	−	0.348146i	−0.770223	+	0.637774i	$0.779855\pi$
$662$		0			0
$663$	−4551.44	−	6897.18i	−0.266611	−	0.404018i
$664$		0			0
$665$	1022.99			0.0596536
$666$		0			0
$667$			30202.5i			1.75329i
$668$		0			0
$669$	308.635	+	5163.30i	0.0178363	+	0.298393i
$670$		0			0
$671$	455.822	−	789.508i	0.0262248	−	0.0454227i
$672$		0			0
$673$	242.006	+	419.167i	0.0138613	+	0.0240085i	0.872873	−	0.487948i	$-0.162254\pi$
$673$	242.006	+	419.167i	0.0138613	+	0.0240085i	−0.859012	+	0.511956i	$0.828921\pi$
$674$		0			0
$675$	30732.7	−	26028.5i	1.75245	−	1.48420i
$676$		0			0
$677$	−13099.4	+	7562.92i	−0.743648	+	0.429345i	−0.823394	−	0.567470i	$-0.807922\pi$
$677$	−13099.4	+	7562.92i	−0.743648	+	0.429345i	0.0797464	+	0.996815i	$0.474589\pi$
$678$		0			0
$679$	533.191	−	923.514i	0.0301355	−	0.0521962i
$680$		0			0
$681$	441.279	−	26.3773i	0.0248309	−	0.00148426i
$682$		0			0
$683$			23035.8i			1.29054i	0.763954	+	0.645271i	$0.223256\pi$
$683$			23035.8i			1.29054i	−0.763954	+	0.645271i	$0.776744\pi$
$684$		0			0
$685$			38964.1i			2.17334i
$686$		0			0
$687$	−16973.4	−	25721.2i	−0.942614	−	1.42842i
$688$		0			0
$689$	2724.17	−	4718.39i	0.150628	−	0.260895i
$690$		0			0
$691$	−25952.9	+	14983.9i	−1.42879	+	0.824913i	−0.997025	−	0.0770728i	$-0.975443\pi$
$691$	−25952.9	+	14983.9i	−1.42879	+	0.824913i	−0.431766	+	0.901986i	$0.642109\pi$
$692$		0			0
$693$	−147.702	−	1231.08i	−0.00809630	−	0.0674816i
$694$		0			0
$695$	−7960.37	−	13787.8i	−0.434466	−	0.752517i
$696$		0			0
$697$	6547.44	−	11340.5i	0.355814	−	0.616287i
$698$		0			0
$699$	−21749.7	−	10881.6i	−1.17690	−	0.588812i
$700$		0			0
$701$			18538.6i			0.998851i	0.866357	+	0.499425i	$0.166456\pi$
$701$			18538.6i			0.998851i	−0.866357	+	0.499425i	$0.833544\pi$
$702$		0			0
$703$	−39.2337			−0.00210488
$704$		0			0
$705$	13182.7	−	26349.1i	0.704241	−	1.40761i
$706$		0			0
$707$	18211.7	+	10514.5i	0.968771	+	0.559320i
$708$		0			0
$709$	−22910.6	+	13227.4i	−1.21358	+	0.700658i	−0.963536	−	0.267577i	$-0.913777\pi$
$709$	−22910.6	+	13227.4i	−1.21358	+	0.700658i	−0.250039	+	0.968236i	$0.580444\pi$
$710$		0			0
$711$	3481.38	−	8138.96i	0.183631	−	0.429303i
$712$		0			0
$713$	−9981.84	−	17289.0i	−0.524295	−	0.908106i
$714$		0			0
$715$	600.130	+	346.485i	0.0313896	+	0.0181228i
$716$		0			0
$717$	15897.1	−	10490.4i	0.828015	−	0.546406i
$718$		0			0
$719$	23631.1			1.22572			0.612859	−	0.790192i	$-0.290019\pi$
$719$	23631.1			1.22572			0.612859	+	0.790192i	$0.290019\pi$
$720$		0			0
$721$	11585.8			0.598446
$722$		0			0
$723$	643.030	+	10757.6i	0.0330768	+	0.553359i
$724$		0			0
$725$	50314.6	+	29049.1i	2.57743	+	1.48808i
$726$		0			0
$727$	6645.21	+	11509.8i	0.339006	+	0.587175i	0.984246	−	0.176805i	$-0.0565761\pi$
$727$	6645.21	+	11509.8i	0.339006	+	0.587175i	−0.645240	+	0.763980i	$0.723243\pi$
$728$		0			0
$729$	−18433.6	+	6901.04i	−0.936522	+	0.350609i
$730$		0			0
$731$	−10791.7	+	6230.59i	−0.546027	+	0.315249i
$732$		0			0
$733$	−1259.88	−	727.394i	−0.0634855	−	0.0366534i	0.467921	−	0.883770i	$-0.345003\pi$
$733$	−1259.88	−	727.394i	−0.0634855	−	0.0366534i	−0.531407	+	0.847117i	$0.678336\pi$
$734$		0			0
$735$	12010.7	−	717.938i	0.602752	−	0.0360293i
$736$		0			0
$737$	−118.341			−0.00591472
$738$		0			0
$739$		−	15723.2i		−	0.782662i	−0.920250	−	0.391331i	$-0.872015\pi$
$739$		−	15723.2i		−	0.782662i	0.920250	−	0.391331i	$-0.127985\pi$
$740$		0			0
$741$	162.473	−	107.216i	0.00805478	−	0.00531534i
$742$		0			0
$743$	−8319.62	+	14410.0i	−0.410790	+	0.711510i	−0.994976	−	0.100110i	$-0.968080\pi$
$743$	−8319.62	+	14410.0i	−0.410790	+	0.711510i	0.584186	+	0.811620i	$0.301414\pi$
$744$		0			0
$745$	−4742.04	−	8213.46i	−0.233201	−	0.403917i
$746$		0			0
$747$	4241.62	+	1814.32i	0.207755	+	0.0888655i
$748$		0			0
$749$	−30659.8	+	17701.4i	−1.49570	+	0.863546i
$750$		0			0
$751$	−3120.48	+	5404.83i	−0.151622	+	0.262617i	−0.931824	−	0.362911i	$-0.881783\pi$
$751$	−3120.48	+	5404.83i	−0.151622	+	0.262617i	0.780202	+	0.625528i	$0.215116\pi$
$752$		0			0
$753$	−4985.73	+	9965.30i	−0.241289	+	0.482279i
$754$		0			0
$755$		−	8854.65i		−	0.426826i
$756$		0			0
$757$		−	37281.0i		−	1.78996i	−0.446106	−	0.894980i	$-0.647189\pi$
$757$		−	37281.0i		−	1.78996i	0.446106	−	0.894980i	$-0.352811\pi$
$758$		0			0
$759$	−745.250	+	1489.58i	−0.0356401	+	0.0712362i
$760$		0			0
$761$	13119.1	−	22722.9i	0.624924	−	1.08240i	−0.363632	−	0.931543i	$-0.618463\pi$
$761$	13119.1	−	22722.9i	0.624924	−	1.08240i	0.988556	−	0.150857i	$-0.0482033\pi$
$762$		0			0
$763$	−7236.36	+	4177.92i	−0.343347	+	0.198232i
$764$		0			0
$765$	−6533.25	−	54453.7i	−0.308771	−	2.57357i
$766$		0			0
$767$	1754.86	+	3039.51i	0.0826134	+	0.143091i
$768$		0			0
$769$	4452.51	−	7711.98i	0.208793	−	0.361640i	−0.742542	−	0.669800i	$-0.766380\pi$
$769$	4452.51	−	7711.98i	0.208793	−	0.361640i	0.951335	+	0.308160i	$0.0997132\pi$
$770$		0			0
$771$	−11514.3	+	7598.30i	−0.537846	+	0.354924i
$772$		0			0
$773$		−	12743.6i		−	0.592954i	−0.955040	−	0.296477i	$-0.904188\pi$
$773$		−	12743.6i		−	0.592954i	0.955040	−	0.296477i	$-0.0958119\pi$
$774$		0			0
$775$	−38402.6			−1.77995
$776$		0			0
$777$	−1845.71	+	110.327i	−0.0852183	+	0.00509390i
$778$		0			0
$779$	267.142	+	154.234i	0.0122867	+	0.00709374i
$780$		0			0
$781$	−1853.83	+	1070.31i	−0.0849365	+	0.0490381i
$782$		0			0
$783$	−18350.9	−	21667.5i	−0.837557	−	0.988932i
$784$		0			0
$785$	−1346.79	−	2332.71i	−0.0612344	−	0.106061i
$786$		0			0
$787$	−18346.9	−	10592.6i	−0.831001	−	0.479779i	0.0231941	−	0.999731i	$-0.492616\pi$
$787$	−18346.9	−	10592.6i	−0.831001	−	0.479779i	−0.854195	+	0.519952i	$0.825950\pi$
$788$		0			0
$789$	535.147	+	8952.75i	0.0241467	+	0.403962i
$790$		0			0
$791$	36518.5			1.64153
$792$		0			0
$793$	6745.19			0.302054
$794$		0			0
$795$	30180.8	−	19916.2i	1.34642	−	0.888499i
$796$		0			0
$797$	−13475.6	−	7780.16i	−0.598910	−	0.345781i	0.169703	−	0.985495i	$-0.445719\pi$
$797$	−13475.6	−	7780.16i	−0.598910	−	0.345781i	−0.768613	+	0.639715i	$0.779053\pi$
$798$		0			0
$799$	−13975.5	−	24206.2i	−0.618795	−	1.07178i
$800$		0			0
$801$	13772.7	+	18382.5i	0.607533	+	0.810879i
$802$		0			0
$803$	1694.60	−	978.378i	0.0744722	−	0.0429965i
$804$		0			0
$805$	−56087.1	−	32381.9i	−2.45567	−	1.41778i
$806$		0			0
$807$	−16998.5	+	33975.9i	−0.741480	+	1.48204i
$808$		0			0
$809$	−9492.69			−0.412540			−0.206270	−	0.978495i	$-0.566133\pi$
$809$	−9492.69			−0.412540			−0.206270	+	0.978495i	$0.566133\pi$
$810$		0			0
$811$		−	17607.1i		−	0.762353i	−0.924502	−	0.381177i	$-0.875519\pi$
$811$		−	17607.1i		−	0.762353i	0.924502	−	0.381177i	$-0.124481\pi$
$812$		0			0
$813$	−2203.08	−	1102.22i	−0.0950373	−	0.0475480i
$814$		0			0
$815$	37301.6	−	64608.3i	1.60321	−	2.77685i
$816$		0			0
$817$	−146.771	−	254.214i	−0.00628501	−	0.0108860i
$818$		0			0
$819$	7341.89	−	5500.74i	0.313244	−	0.234690i
$820$		0			0
$821$	39628.7	−	22879.7i	1.68460	−	0.972601i	0.726058	−	0.687633i	$-0.241350\pi$
$821$	39628.7	−	22879.7i	1.68460	−	0.972601i	0.958537	−	0.284968i	$-0.0919830\pi$
$822$		0			0
$823$	9281.64	−	16076.3i	0.393120	−	0.680903i	−0.599739	−	0.800195i	$-0.704729\pi$
$823$	9281.64	−	16076.3i	0.393120	−	0.680903i	0.992859	+	0.119292i	$0.0380625\pi$
$824$		0			0
$825$	1764.71	+	2674.21i	0.0744718	+	0.112853i
$826$		0			0
$827$			4839.95i			0.203509i	0.994810	+	0.101754i	$0.0324455\pi$
$827$			4839.95i			0.203509i	−0.994810	+	0.101754i	$0.967554\pi$
$828$		0			0
$829$			33204.3i			1.39111i	0.718472	+	0.695556i	$0.244842\pi$
$829$			33204.3i			1.39111i	−0.718472	+	0.695556i	$0.755158\pi$
$830$		0			0
$831$	12691.4	−	758.626i	0.529796	−	0.0316684i
$832$		0			0
$833$	5707.36	−	9885.44i	0.237393	−	0.411177i
$834$		0			0
$835$	133.129	−	76.8618i	0.00551749	−	0.00318553i
$836$		0			0
$837$	17665.8	+	6338.38i	0.729532	+	0.261752i
$838$		0			0
$839$	7993.06	+	13844.4i	0.328905	+	0.569680i	0.982295	−	0.187342i	$-0.0599871\pi$
$839$	7993.06	+	13844.4i	0.328905	+	0.569680i	−0.653390	+	0.757021i	$0.726654\pi$
$840$		0			0
$841$	8286.02	−	14351.8i	0.339744	−	0.588454i
$842$		0			0
$843$	−2511.94	−	42023.6i	−0.102629	−	1.71693i
$844$		0			0
$845$		−	39470.4i		−	1.60689i
$846$		0			0
$847$	−28357.1			−1.15037
$848$		0			0
$849$	−4090.74	−	6199.04i	−0.165364	−	0.250589i
$850$		0			0
$851$	2151.06	+	1241.92i	0.0866481	+	0.0500263i
$852$		0			0
$853$	−25966.3	+	14991.7i	−1.04229	+	0.601764i	−0.920480	−	0.390790i	$-0.872202\pi$
$853$	−25966.3	+	14991.7i	−1.04229	+	0.601764i	−0.121805	+	0.992554i	$0.538868\pi$
$854$		0			0
$855$	1282.74	−	153.900i	0.0513083	−	0.00615587i
$856$		0			0
$857$	5417.14	+	9382.76i	0.215923	+	0.373990i	0.953558	−	0.301210i	$-0.0973907\pi$
$857$	5417.14	+	9382.76i	0.215923	+	0.373990i	−0.737635	+	0.675200i	$0.764057\pi$
$858$		0			0
$859$	−30072.5	−	17362.4i	−1.19448	−	0.689635i	−0.235162	−	0.971956i	$-0.575562\pi$
$859$	−30072.5	−	17362.4i	−1.19448	−	0.689635i	−0.959320	+	0.282322i	$0.908895\pi$
$860$		0			0
$861$	13001.2	+	6504.60i	0.514609	+	0.257464i
$862$		0			0
$863$	−10642.1			−0.419771			−0.209885	−	0.977726i	$-0.567309\pi$
$863$	−10642.1			−0.419771			−0.209885	+	0.977726i	$0.567309\pi$
$864$		0			0
$865$	−28317.5			−1.11309
$866$		0			0
$867$	−23700.4	−	11857.5i	−0.928383	−	0.464479i
$868$		0			0
$869$	609.893	+	352.122i	0.0238081	+	0.0137456i
$870$		0			0
$871$	−437.798	−	758.288i	−0.0170313	−	0.0294990i
$872$		0			0
$873$	529.640	−	1238.22i	0.0205333	−	0.0480039i
$874$		0			0
$875$	−60910.2	+	35166.5i	−2.35330	+	1.35868i
$876$		0			0
$877$	29723.0	+	17160.6i	1.14444	+	0.660744i	0.947527	−	0.319676i	$-0.103574\pi$
$877$	29723.0	+	17160.6i	1.14444	+	0.660744i	0.196915	+	0.980420i	$0.436908\pi$
$878$		0			0
$879$	−14521.1	−	22005.0i	−0.557205	−	0.844380i
$880$		0			0
$881$	17668.9			0.675687			0.337843	−	0.941202i	$-0.390303\pi$
$881$	17668.9			0.675687			0.337843	+	0.941202i	$0.390303\pi$
$882$		0			0
$883$			41233.2i			1.57147i	0.618563	+	0.785735i	$0.287715\pi$
$883$			41233.2i			1.57147i	−0.618563	+	0.785735i	$0.712285\pi$
$884$		0			0
$885$	1389.89	+	23252.1i	0.0527915	+	0.883176i
$886$		0			0
$887$	−5664.50	+	9811.21i	−0.214425	+	0.371396i	−0.953095	−	0.302672i	$-0.902121\pi$
$887$	−5664.50	+	9811.21i	−0.214425	+	0.371396i	0.738669	+	0.674068i	$0.235455\pi$
$888$		0			0
$889$	14837.5	+	25699.4i	0.559770	+	0.969549i
$890$		0			0
$891$	−370.411	−	1521.44i	−0.0139273	−	0.0572057i
$892$		0			0
$893$	570.213	−	329.212i	0.0213678	−	0.0123367i
$894$		0			0
$895$	37640.5	−	65195.3i	1.40579	−	2.43490i
$896$		0			0
$897$	−12301.7	+	735.331i	−0.457907	+	0.0273712i
$898$		0			0
$899$			27075.0i			1.00445i
$900$		0			0
$901$		−	34304.3i		−	1.26841i
$902$		0			0
$903$	−7619.55	−	11546.5i	−0.280800	−	0.425520i
$904$		0			0
$905$	19377.6	−	33562.9i	0.711748	−	1.23278i
$906$		0			0
$907$	39893.8	−	23032.7i	1.46048	−	0.843207i	0.461444	−	0.887169i	$-0.347332\pi$
$907$	39893.8	−	23032.7i	1.46048	−	0.843207i	0.999033	+	0.0439627i	$0.0139983\pi$
$908$		0			0
$909$	24417.7	+	10444.5i	0.890962	+	0.381103i
$910$		0			0
$911$	6966.40	+	12066.2i	0.253356	+	0.438825i	0.964448	−	0.264274i	$-0.0851323\pi$
$911$	6966.40	+	12066.2i	0.253356	+	0.438825i	−0.711092	+	0.703099i	$0.751799\pi$
$912$		0			0
$913$	−183.508	+	317.846i	−0.00665196	+	0.0115215i
$914$		0			0
$915$	40035.8	+	20030.3i	1.44650	+	0.723695i
$916$		0			0
$917$			45119.2i			1.62483i
$918$		0			0
$919$	−19716.4			−0.707709			−0.353854	−	0.935301i	$-0.615129\pi$
$919$	−19716.4			−0.707709			−0.353854	+	0.935301i	$0.615129\pi$
$920$		0			0
$921$	2824.59	−	5645.68i	0.101057	−	0.201988i
$922$		0			0
$923$	−13716.4	−	7919.15i	−0.489144	−	0.282407i
$924$		0			0
$925$	4137.83	−	2388.98i	0.147082	−	0.0849180i
$926$		0			0
$927$	14527.7	−	1743.00i	0.514726	−	0.0617557i
$928$		0			0
$929$	−11948.1	−	20694.8i	−0.421966	−	0.730866i	0.574166	−	0.818739i	$-0.305326\pi$
$929$	−11948.1	−	20694.8i	−0.421966	−	0.730866i	−0.996132	+	0.0878730i	$0.971993\pi$
$930$		0			0
$931$	232.866	+	134.445i	0.00819750	+	0.00473283i
$932$		0			0
$933$	−27991.3	+	18471.4i	−0.982201	+	0.648153i
$934$		0			0
$935$	4363.14			0.152610
$936$		0			0
$937$	−35884.7			−1.25112			−0.625562	−	0.780174i	$-0.715130\pi$
$937$	−35884.7			−1.25112			−0.625562	+	0.780174i	$0.715130\pi$
$938$		0			0
$939$	1024.10	+	17132.6i	0.0355912	+	0.595423i
$940$		0			0
$941$	−44632.1	−	25768.4i	−1.54619	−	0.892694i	−0.998427	−	0.0560607i	$-0.982146\pi$
$941$	−44632.1	−	25768.4i	−1.54619	−	0.892694i	−0.547764	−	0.836633i	$-0.684521\pi$
$942$		0			0
$943$	−9764.38	−	16912.4i	−0.337192	−	0.584033i
$944$		0			0
$945$	59912.3	−	10847.2i	2.06238	−	0.373396i
$946$		0			0
$947$	5450.65	−	3146.93i	0.187035	−	0.107985i	−0.403559	−	0.914954i	$-0.632227\pi$
$947$	5450.65	−	3146.93i	0.187035	−	0.107985i	0.590594	+	0.806969i	$0.298894\pi$
$948$		0			0
$949$	12538.2	+	7238.94i	0.428881	+	0.247614i
$950$		0			0
$951$	−2305.96	+	137.838i	−0.0786288	+	0.00470001i
$952$		0			0
$953$	3877.47			0.131798			0.0658991	−	0.997826i	$-0.479008\pi$
$953$	3877.47			0.131798			0.0658991	+	0.997826i	$0.479008\pi$
$954$		0			0
$955$			21471.6i			0.727543i
$956$		0			0
$957$	1885.40	−	1244.17i	0.0636847	−	0.0420255i
$958$		0			0
$959$	−20518.5	+	35539.0i	−0.690903	+	1.19668i
$960$		0			0
$961$	5947.32	+	10301.1i	0.199635	+	0.345778i
$962$		0			0
$963$	−35781.7	+	26808.6i	−1.19735	+	0.897086i
$964$		0			0
$965$	21134.5	−	12202.0i	0.705018	−	0.407043i
$966$		0			0
$967$	−5832.12	+	10101.5i	−0.193949	+	0.335929i	−0.946555	−	0.322542i	$-0.895463\pi$
$967$	−5832.12	+	10101.5i	−0.193949	+	0.335929i	0.752607	+	0.658470i	$0.228796\pi$
$968$		0			0
$969$	548.393	−	1096.11i	0.0181805	−	0.0363385i
$970$		0			0
$971$		−	10211.1i		−	0.337478i	−0.985661	−	0.168739i	$-0.946030\pi$
$971$		−	10211.1i		−	0.337478i	0.985661	−	0.168739i	$-0.0539695\pi$
$972$		0			0
$973$		−	16767.7i		−	0.552464i
$974$		0			0
$975$	−10606.9	+	21200.8i	−0.348404	+	0.696377i
$976$		0			0
$977$	−12182.5	+	21100.6i	−0.398927	+	0.690961i	−0.993594	−	0.113011i	$-0.963950\pi$
$977$	−12182.5	+	21100.6i	−0.398927	+	0.690961i	0.594667	+	0.803972i	$0.297284\pi$
$978$		0			0
$979$	−1582.53	+	913.676i	−0.0516629	+	0.0298276i
$980$		0			0
$981$	−8445.25	+	6327.40i	−0.274858	+	0.205931i
$982$		0			0
$983$	3493.53	+	6050.98i	0.113353	+	0.196334i	0.917120	−	0.398610i	$-0.130507\pi$
$983$	3493.53	+	6050.98i	0.113353	+	0.196334i	−0.803767	+	0.594944i	$0.797174\pi$
$984$		0			0
$985$	−11988.1	+	20764.0i	−0.387790	+	0.671672i
$986$		0			0
$987$	25899.4	−	17091.0i	0.835244	−	0.551177i
$988$		0			0
$989$			18583.7i			0.597500i
$990$		0			0
$991$	54914.7			1.76026			0.880132	−	0.474728i	$-0.157454\pi$
$991$	54914.7			1.76026			0.880132	+	0.474728i	$0.157454\pi$
$992$		0			0
$993$	−33911.7	+	2027.06i	−1.08374	+	0.0647802i
$994$		0			0
$995$	13482.5	+	7784.11i	0.429571	+	0.248013i
$996$		0			0
$997$	11321.2	−	6536.29i	0.359624	−	0.207629i	−0.309292	−	0.950967i	$-0.600092\pi$
$997$	11321.2	−	6536.29i	0.359624	−	0.207629i	0.668916	+	0.743338i	$0.266759\pi$
$998$		0			0
$999$	−2297.77	+	416.014i	−0.0727710	+	0.0131753i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.4.r.a.49.5		68
3.2	odd	2		864.4.r.a.145.1		68
4.3	odd	2		72.4.n.a.13.20	✓	68
8.3	odd	2		72.4.n.a.13.26	yes	68
8.5	even	2	inner	288.4.r.a.49.30		68
9.2	odd	6		864.4.r.a.721.34		68
9.7	even	3	inner	288.4.r.a.241.30		68
12.11	even	2		216.4.n.a.37.15		68
24.5	odd	2		864.4.r.a.145.34		68
24.11	even	2		216.4.n.a.37.9		68
36.7	odd	6		72.4.n.a.61.26	yes	68
36.11	even	6		216.4.n.a.181.9		68
72.11	even	6		216.4.n.a.181.15		68
72.29	odd	6		864.4.r.a.721.1		68
72.43	odd	6		72.4.n.a.61.20	yes	68
72.61	even	6	inner	288.4.r.a.241.5		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.n.a.13.20	✓	68	4.3	odd	2
72.4.n.a.13.26	yes	68	8.3	odd	2
72.4.n.a.61.20	yes	68	72.43	odd	6
72.4.n.a.61.26	yes	68	36.7	odd	6
216.4.n.a.37.9		68	24.11	even	2
216.4.n.a.37.15		68	12.11	even	2
216.4.n.a.181.9		68	36.11	even	6
216.4.n.a.181.15		68	72.11	even	6
288.4.r.a.49.5		68	1.1	even	1	trivial
288.4.r.a.49.30		68	8.5	even	2	inner
288.4.r.a.241.5		68	72.61	even	6	inner
288.4.r.a.241.30		68	9.7	even	3	inner
864.4.r.a.145.1		68	3.2	odd	2
864.4.r.a.145.34		68	24.5	odd	2
864.4.r.a.721.1		68	72.29	odd	6
864.4.r.a.721.34		68	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	288.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.64700 - 2.32494i) q^{3} +(17.5797 + 10.1497i) q^{5} +(10.6896 + 18.5150i) q^{7} +(16.1893 + 21.6080i) q^{9} +O(q^{10})\)	\(q+(-4.64700 - 2.32494i) q^{3} +(17.5797 + 10.1497i) q^{5} +(10.6896 + 18.5150i) q^{7} +(16.1893 + 21.6080i) q^{9} +(-1.86021 + 1.07399i) q^{11} +(-13.7636 - 7.94640i) q^{13} +(-58.0958 - 88.0374i) q^{15} -100.066 q^{17} -2.35719i q^{19} +(-6.62852 - 110.892i) q^{21} +(-74.6153 + 129.238i) q^{23} +(143.532 + 248.604i) q^{25} +(-24.9944 - 138.052i) q^{27} +(175.273 - 101.194i) q^{29} +(-66.8886 + 115.855i) q^{31} +(11.1414 - 0.665973i) q^{33} +433.985i q^{35} -16.6443i q^{37} +(45.4845 + 68.9265i) q^{39} +(-65.4314 + 113.331i) q^{41} +(107.846 - 62.2650i) q^{43} +(65.2896 + 544.180i) q^{45} +(139.663 + 241.903i) q^{47} +(-57.0362 + 98.7895i) q^{49} +(465.006 + 232.647i) q^{51} +342.817i q^{53} -43.6028 q^{55} +(-5.48033 + 10.9539i) q^{57} +(-191.251 - 110.419i) q^{59} +(-367.557 + 212.209i) q^{61} +(-227.014 + 530.726i) q^{63} +(-161.307 - 279.391i) q^{65} +(47.7127 + 27.5469i) q^{67} +(647.207 - 427.091i) q^{69} +996.571 q^{71} -910.971 q^{73} +(-89.0025 - 1488.97i) q^{75} +(-39.7700 - 22.9612i) q^{77} +(-163.931 - 283.937i) q^{79} +(-204.813 + 699.638i) q^{81} +(147.974 - 85.4325i) q^{83} +(-1759.13 - 1015.63i) q^{85} +(-1049.77 + 62.7495i) q^{87} +850.727 q^{89} -339.776i q^{91} +(580.187 - 382.864i) q^{93} +(23.9247 - 41.4388i) q^{95} +(-24.9396 - 43.1967i) q^{97} +(-53.3225 - 22.8083i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 2 q^{7} - 4 q^{9}+O(q^{10}) \) 68 * q + 2 * q^7 - 4 * q^9	\( 68 q + 2 q^{7} - 4 q^{9} + 58 q^{15} - 8 q^{17} - 274 q^{23} + 648 q^{25} + 2 q^{31} + 174 q^{33} - 242 q^{39} - 22 q^{41} + 942 q^{47} - 1080 q^{49} + 508 q^{55} - 68 q^{57} - 722 q^{63} - 502 q^{65} + 3984 q^{71} - 8 q^{73} + 2 q^{79} + 1072 q^{81} - 3354 q^{87} - 856 q^{89} + 2792 q^{95} - 2 q^{97}+O(q^{100}) \) 68 * q + 2 * q^7 - 4 * q^9 + 58 * q^15 - 8 * q^17 - 274 * q^23 + 648 * q^25 + 2 * q^31 + 174 * q^33 - 242 * q^39 - 22 * q^41 + 942 * q^47 - 1080 * q^49 + 508 * q^55 - 68 * q^57 - 722 * q^63 - 502 * q^65 + 3984 * q^71 - 8 * q^73 + 2 * q^79 + 1072 * q^81 - 3354 * q^87 - 856 * q^89 + 2792 * q^95 - 2 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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