LMFDB - Embedded newform 192.4.k.a.47.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [192,4,Mod(47,192)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("192.47"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(192, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	192.k (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$11.3283667211$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.5
Character	$\chi$	$=$	192.47
Dual form			192.4.k.a.143.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.86039 + 3.47813i) q^{3} +(-13.5794 - 13.5794i) q^{5} +19.7355 q^{7} +(2.80518 - 26.8539i) q^{9} +(-20.5372 + 20.5372i) q^{11} +(36.7137 + 36.7137i) q^{13} +(99.6526 + 5.19077i) q^{15} +4.20201i q^{17} +(-38.6629 + 38.6629i) q^{19} +(-76.1866 + 68.6426i) q^{21} +69.4323i q^{23} +243.800i q^{25} +(82.5723 + 113.423i) q^{27} +(-23.0218 + 23.0218i) q^{29} +219.983i q^{31} +(7.85044 - 150.713i) q^{33} +(-267.996 - 267.996i) q^{35} +(68.0025 - 68.0025i) q^{37} +(-269.424 - 14.0339i) q^{39} +325.789 q^{41} +(36.9411 + 36.9411i) q^{43} +(-402.752 + 326.567i) q^{45} +192.724 q^{47} +46.4894 q^{49} +(-14.6152 - 16.2214i) q^{51} +(461.968 + 461.968i) q^{53} +557.767 q^{55} +(14.7791 - 283.729i) q^{57} +(0.977987 - 0.977987i) q^{59} +(216.498 + 216.498i) q^{61} +(55.3615 - 529.974i) q^{63} -997.098i q^{65} +(27.8307 - 27.8307i) q^{67} +(-241.495 - 268.036i) q^{69} +786.600i q^{71} -510.757i q^{73} +(-847.968 - 941.161i) q^{75} +(-405.313 + 405.313i) q^{77} -230.706i q^{79} +(-713.262 - 150.660i) q^{81} +(-593.835 - 593.835i) q^{83} +(57.0607 - 57.0607i) q^{85} +(8.80017 - 168.946i) q^{87} -1015.01 q^{89} +(724.562 + 724.562i) q^{91} +(-765.131 - 849.221i) q^{93} +1050.04 q^{95} +805.334 q^{97} +(493.894 + 609.115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{3} + 8 q^{7} - 4 q^{13} - 20 q^{19} - 56 q^{21} + 134 q^{27} - 4 q^{33} - 4 q^{37} - 596 q^{39} + 436 q^{43} - 252 q^{45} + 972 q^{49} + 648 q^{51} - 280 q^{55} - 916 q^{61} + 1636 q^{67} + 52 q^{69}+ \cdots - 1196 q^{99}+O(q^{100}) $ 44 * q + 2 * q^3 + 8 * q^7 - 4 * q^13 - 20 * q^19 - 56 * q^21 + 134 * q^27 - 4 * q^33 - 4 * q^37 - 596 * q^39 + 436 * q^43 - 252 * q^45 + 972 * q^49 + 648 * q^51 - 280 * q^55 - 916 * q^61 + 1636 * q^67 + 52 * q^69 - 1454 * q^75 - 4 * q^81 + 736 * q^85 - 1284 * q^87 - 424 * q^91 - 2084 * q^93 - 8 * q^97 - 1196 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.86039	+	3.47813i	−0.742932	+	0.669367i
$3$	−3.86039	+	3.47813i	−0.742932	+	0.669367i
$4$		0			0
$5$	−13.5794	−	13.5794i	−1.21458	−	1.21458i	−0.969505	−	0.245073i	$-0.921188\pi$
$5$	−13.5794	−	13.5794i	−1.21458	−	1.21458i	−0.245073	−	0.969505i	$-0.578812\pi$
$6$		0			0
$7$	19.7355			1.06562			0.532808	−	0.846236i	$-0.321137\pi$
$7$	19.7355			1.06562			0.532808	+	0.846236i	$0.321137\pi$
$8$		0			0
$9$	2.80518	−	26.8539i	0.103895	−	0.994588i
$10$		0			0
$11$	−20.5372	+	20.5372i	−0.562928	+	0.562928i	−0.930138	−	0.367210i	$-0.880313\pi$
$11$	−20.5372	+	20.5372i	−0.562928	+	0.562928i	0.367210	+	0.930138i	$0.380313\pi$
$12$		0			0
$13$	36.7137	+	36.7137i	0.783272	+	0.783272i	0.980381	−	0.197110i	$-0.0631555\pi$
$13$	36.7137	+	36.7137i	0.783272	+	0.783272i	−0.197110	+	0.980381i	$0.563155\pi$
$14$		0			0
$15$	99.6526	+	5.19077i	1.71535	+	0.0893501i
$16$		0			0
$17$			4.20201i			0.0599493i	0.999551	+	0.0299746i	$0.00954265\pi$
$17$			4.20201i			0.0599493i	−0.999551	+	0.0299746i	$0.990457\pi$
$18$		0			0
$19$	−38.6629	+	38.6629i	−0.466836	+	0.466836i	−0.900888	−	0.434052i	$-0.857083\pi$
$19$	−38.6629	+	38.6629i	−0.466836	+	0.466836i	0.434052	+	0.900888i	$0.357083\pi$
$20$		0			0
$21$	−76.1866	+	68.6426i	−0.791680	+	0.713288i
$22$		0			0
$23$			69.4323i			0.629462i	0.949181	+	0.314731i	$0.101914\pi$
$23$			69.4323i			0.629462i	−0.949181	+	0.314731i	$0.898086\pi$
$24$		0			0
$25$			243.800i			1.95040i
$26$		0			0
$27$	82.5723	+	113.423i	0.588557	+	0.808455i
$28$		0			0
$29$	−23.0218	+	23.0218i	−0.147415	+	0.147415i	−0.776962	−	0.629547i	$-0.783240\pi$
$29$	−23.0218	+	23.0218i	−0.147415	+	0.147415i	0.629547	+	0.776962i	$0.283240\pi$
$30$		0			0
$31$			219.983i			1.27452i	0.770648	+	0.637261i	$0.219933\pi$
$31$			219.983i			1.27452i	−0.770648	+	0.637261i	$0.780067\pi$
$32$		0			0
$33$	7.85044	−	150.713i	0.0414117	−	0.795023i
$34$		0			0
$35$	−267.996	−	267.996i	−1.29427	−	1.29427i
$36$		0			0
$37$	68.0025	−	68.0025i	0.302150	−	0.302150i	−0.539705	−	0.841854i	$-0.681464\pi$
$37$	68.0025	−	68.0025i	0.302150	−	0.302150i	0.841854	+	0.539705i	$0.181464\pi$
$38$		0			0
$39$	−269.424	−	14.0339i	−1.10621	−	0.0576212i
$40$		0			0
$41$	325.789			1.24097			0.620485	−	0.784219i	$-0.286936\pi$
$41$	325.789			1.24097			0.620485	+	0.784219i	$0.286936\pi$
$42$		0			0
$43$	36.9411	+	36.9411i	0.131011	+	0.131011i	0.769572	−	0.638561i	$-0.220470\pi$
$43$	36.9411	+	36.9411i	0.131011	+	0.131011i	−0.638561	+	0.769572i	$0.720470\pi$
$44$		0			0
$45$	−402.752	+	326.567i	−1.33419	+	1.08182i
$46$		0			0
$47$	192.724			0.598120			0.299060	−	0.954234i	$-0.403327\pi$
$47$	192.724			0.598120			0.299060	+	0.954234i	$0.403327\pi$
$48$		0			0
$49$	46.4894			0.135538
$50$		0			0
$51$	−14.6152	−	16.2214i	−0.0401281	−	0.0445382i
$52$		0			0
$53$	461.968	+	461.968i	1.19729	+	1.19729i	0.974976	+	0.222312i	$0.0713602\pi$
$53$	461.968	+	461.968i	1.19729	+	1.19729i	0.222312	+	0.974976i	$0.428640\pi$
$54$		0			0
$55$	557.767			1.36744
$56$		0			0
$57$	14.7791	−	283.729i	0.0343427	−	0.659312i
$58$		0			0
$59$	0.977987	−	0.977987i	0.00215802	−	0.00215802i	−0.706027	−	0.708185i	$-0.749514\pi$
$59$	0.977987	−	0.977987i	0.00215802	−	0.00215802i	0.708185	+	0.706027i	$0.249514\pi$
$60$		0			0
$61$	216.498	+	216.498i	0.454421	+	0.454421i	0.896819	−	0.442398i	$-0.145872\pi$
$61$	216.498	+	216.498i	0.454421	+	0.454421i	−0.442398	+	0.896819i	$0.645872\pi$
$62$		0			0
$63$	55.3615	−	529.974i	0.110713	−	1.05985i
$64$		0			0
$65$		−	997.098i		−	1.90269i
$66$		0			0
$67$	27.8307	−	27.8307i	0.0507472	−	0.0507472i	−0.681278	−	0.732025i	$-0.738575\pi$
$67$	27.8307	−	27.8307i	0.0507472	−	0.0507472i	0.732025	+	0.681278i	$0.238575\pi$
$68$		0			0
$69$	−241.495	−	268.036i	−0.421341	−	0.467648i
$70$		0			0
$71$			786.600i			1.31482i	0.753533	+	0.657411i	$0.228348\pi$
$71$			786.600i			1.31482i	−0.753533	+	0.657411i	$0.771652\pi$
$72$		0			0
$73$		−	510.757i		−	0.818898i	−0.912333	−	0.409449i	$-0.865721\pi$
$73$		−	510.757i		−	0.818898i	0.912333	−	0.409449i	$-0.134279\pi$
$74$		0			0
$75$	−847.968	−	941.161i	−1.30553	−	1.44901i
$76$		0			0
$77$	−405.313	+	405.313i	−0.599866	+	0.599866i
$78$		0			0
$79$		−	230.706i		−	0.328562i	−0.986414	−	0.164281i	$-0.947470\pi$
$79$		−	230.706i		−	0.328562i	0.986414	−	0.164281i	$-0.0525304\pi$
$80$		0			0
$81$	−713.262	−	150.660i	−0.978411	−	0.206666i
$82$		0			0
$83$	−593.835	−	593.835i	−0.785323	−	0.785323i	0.195400	−	0.980724i	$-0.437399\pi$
$83$	−593.835	−	593.835i	−0.785323	−	0.785323i	−0.980724	+	0.195400i	$0.937399\pi$
$84$		0			0
$85$	57.0607	−	57.0607i	0.0728130	−	0.0728130i
$86$		0			0
$87$	8.80017	−	168.946i	0.0108446	−	0.208194i
$88$		0			0
$89$	−1015.01			−1.20889			−0.604443	−	0.796648i	$-0.706604\pi$
$89$	−1015.01			−1.20889			−0.604443	+	0.796648i	$0.706604\pi$
$90$		0			0
$91$	724.562	+	724.562i	0.834667	+	0.834667i
$92$		0			0
$93$	−765.131	−	849.221i	−0.853123	−	0.946883i
$94$		0			0
$95$	1050.04			1.13402
$96$		0			0
$97$	805.334			0.842982			0.421491	−	0.906833i	$-0.361507\pi$
$97$	805.334			0.842982			0.421491	+	0.906833i	$0.361507\pi$
$98$		0			0
$99$	493.894	+	609.115i	0.501396	+	0.618368i
$100$		0			0
$101$	−611.231	−	611.231i	−0.602176	−	0.602176i	0.338714	−	0.940889i	$-0.390008\pi$
$101$	−611.231	−	611.231i	−0.602176	−	0.602176i	−0.940889	+	0.338714i	$0.890008\pi$
$102$		0			0
$103$	−1268.38			−1.21337			−0.606685	−	0.794942i	$-0.707501\pi$
$103$	−1268.38			−1.21337			−0.606685	+	0.794942i	$0.707501\pi$
$104$		0			0
$105$	1966.69	+	102.442i	1.82790	+	0.0952129i
$106$		0			0
$107$	−153.071	+	153.071i	−0.138298	+	0.138298i	−0.772867	−	0.634568i	$-0.781178\pi$
$107$	−153.071	+	153.071i	−0.138298	+	0.138298i	0.634568	+	0.772867i	$0.281178\pi$
$108$		0			0
$109$	−119.589	−	119.589i	−0.105088	−	0.105088i	0.652608	−	0.757696i	$-0.273675\pi$
$109$	−119.589	−	119.589i	−0.105088	−	0.105088i	−0.757696	+	0.652608i	$0.773675\pi$
$110$		0			0
$111$	−25.9942	+	499.038i	−0.0222276	+	0.426726i
$112$		0			0
$113$			2097.44i			1.74611i	0.487622	+	0.873055i	$0.337865\pi$
$113$			2097.44i			1.74611i	−0.487622	+	0.873055i	$0.662135\pi$
$114$		0			0
$115$	942.848	−	942.848i	0.764531	−	0.764531i
$116$		0			0
$117$	1088.89	−	882.916i	0.860411	−	0.697655i
$118$		0			0
$119$			82.9287i			0.0638829i
$120$		0			0
$121$			487.443i			0.366223i
$122$		0			0
$123$	−1257.67	+	1133.14i	−0.921956	+	0.830664i
$124$		0			0
$125$	1613.23	−	1613.23i	1.15433	−	1.15433i
$126$		0			0
$127$		−	781.522i		−	0.546054i	−0.962006	−	0.273027i	$-0.911975\pi$
$127$		−	781.522i		−	0.546054i	0.962006	−	0.273027i	$-0.0880249\pi$
$128$		0			0
$129$	−271.093	−	14.1209i	−0.185027	−	0.00963779i
$130$		0			0
$131$	−150.465	−	150.465i	−0.100353	−	0.100353i	0.655148	−	0.755501i	$-0.272606\pi$
$131$	−150.465	−	150.465i	−0.100353	−	0.100353i	−0.755501	+	0.655148i	$0.772606\pi$
$132$		0			0
$133$	−763.032	+	763.032i	−0.497468	+	0.497468i
$134$		0			0
$135$	418.936	−	2661.50i	0.267083	−	1.69678i
$136$		0			0
$137$	−1912.58			−1.19272			−0.596361	−	0.802716i	$-0.703387\pi$
$137$	−1912.58			−1.19272			−0.596361	+	0.802716i	$0.703387\pi$
$138$		0			0
$139$	−112.824	−	112.824i	−0.0688461	−	0.0688461i	0.671845	−	0.740691i	$-0.265502\pi$
$139$	−112.824	−	112.824i	−0.0688461	−	0.0688461i	−0.740691	+	0.671845i	$0.765502\pi$
$140$		0			0
$141$	−743.988	+	670.318i	−0.444362	+	0.400362i
$142$		0			0
$143$	−1507.99			−0.881852
$144$		0			0
$145$	625.244			0.358094
$146$		0			0
$147$	−179.467	+	161.696i	−0.100695	+	0.0907244i
$148$		0			0
$149$	597.206	+	597.206i	0.328356	+	0.328356i	0.851961	−	0.523605i	$-0.175413\pi$
$149$	597.206	+	597.206i	0.328356	+	0.328356i	−0.523605	+	0.851961i	$0.675413\pi$
$150$		0			0
$151$	2256.11			1.21589			0.607946	−	0.793978i	$-0.291994\pi$
$151$	2256.11			1.21589			0.607946	+	0.793978i	$0.291994\pi$
$152$		0			0
$153$	112.840	+	11.7874i	0.0596248	+	0.00622845i
$154$		0			0
$155$	2987.24	−	2987.24i	1.54801	−	1.54801i
$156$		0			0
$157$	2287.02	+	2287.02i	1.16258	+	1.16258i	0.983910	+	0.178666i	$0.0571782\pi$
$157$	2287.02	+	2287.02i	1.16258	+	1.16258i	0.178666	+	0.983910i	$0.442822\pi$
$158$		0			0
$159$	−3390.16	−	176.589i	−1.69093	−	0.0880782i
$160$		0			0
$161$			1370.28i			0.670765i
$162$		0			0
$163$	−2602.79	+	2602.79i	−1.25071	+	1.25071i	−0.295313	+	0.955400i	$0.595424\pi$
$163$	−2602.79	+	2602.79i	−1.25071	+	1.25071i	−0.955400	+	0.295313i	$0.904576\pi$
$164$		0			0
$165$	−2153.19	+	1939.99i	−1.01592	+	0.915320i
$166$		0			0
$167$			1654.83i			0.766795i	0.923583	+	0.383397i	$0.125246\pi$
$167$			1654.83i			0.766795i	−0.923583	+	0.383397i	$0.874754\pi$
$168$		0			0
$169$			498.785i			0.227030i
$170$		0			0
$171$	929.794	+	1146.71i	0.415808	+	0.512812i
$172$		0			0
$173$	2534.53	−	2534.53i	1.11385	−	1.11385i	0.121229	−	0.992625i	$-0.461317\pi$
$173$	2534.53	−	2534.53i	1.11385	−	1.11385i	0.992625	−	0.121229i	$-0.0386835\pi$
$174$		0			0
$175$			4811.50i			2.07837i
$176$		0			0
$177$	−0.373839	+	7.17697i	−0.000158754	+	0.00304777i
$178$		0			0
$179$	3012.01	+	3012.01i	1.25770	+	1.25770i	0.952190	+	0.305508i	$0.0988262\pi$
$179$	3012.01	+	3012.01i	1.25770	+	1.25770i	0.305508	+	0.952190i	$0.401174\pi$
$180$		0			0
$181$	432.978	−	432.978i	0.177807	−	0.177807i	−0.612592	−	0.790399i	$-0.709873\pi$
$181$	432.978	−	432.978i	0.177807	−	0.177807i	0.790399	+	0.612592i	$0.209873\pi$
$182$		0			0
$183$	−1588.77	−	82.7570i	−0.641778	−	0.0334294i
$184$		0			0
$185$	−1846.87			−0.733969
$186$		0			0
$187$	−86.2977	−	86.2977i	−0.0337471	−	0.0337471i
$188$		0			0
$189$	1629.60	+	2238.46i	0.627176	+	0.861503i
$190$		0			0
$191$	−888.400			−0.336557			−0.168278	−	0.985740i	$-0.553821\pi$
$191$	−888.400			−0.336557			−0.168278	+	0.985740i	$0.553821\pi$
$192$		0			0
$193$	−2530.09			−0.943627			−0.471813	−	0.881698i	$-0.656400\pi$
$193$	−2530.09			−0.943627			−0.471813	+	0.881698i	$0.656400\pi$
$194$		0			0
$195$	3468.04	+	3849.18i	1.27360	+	1.41357i
$196$		0			0
$197$	1032.98	+	1032.98i	0.373587	+	0.373587i	0.868782	−	0.495195i	$-0.164903\pi$
$197$	1032.98	+	1032.98i	0.373587	+	0.373587i	−0.495195	+	0.868782i	$0.664903\pi$
$198$		0			0
$199$	−641.440			−0.228495			−0.114247	−	0.993452i	$-0.536446\pi$
$199$	−641.440			−0.228495			−0.114247	+	0.993452i	$0.536446\pi$
$200$		0			0
$201$	−10.6384	+	204.236i	−0.00373320	+	0.0716702i
$202$		0			0
$203$	−454.346	+	454.346i	−0.157088	+	0.157088i
$204$		0			0
$205$	−4424.02	−	4424.02i	−1.50725	−	1.50725i
$206$		0			0
$207$	1864.53	+	194.770i	0.626056	+	0.0653983i
$208$		0			0
$209$		−	1588.06i		−	0.525591i
$210$		0			0
$211$	2040.63	−	2040.63i	0.665796	−	0.665796i	−0.290944	−	0.956740i	$-0.593969\pi$
$211$	2040.63	−	2040.63i	0.665796	−	0.665796i	0.956740	+	0.290944i	$0.0939695\pi$
$212$		0			0
$213$	−2735.90	−	3036.58i	−0.880098	−	0.976822i
$214$		0			0
$215$		−	1003.28i		−	0.318246i
$216$		0			0
$217$			4341.48i			1.35815i
$218$		0			0
$219$	1776.48	+	1971.72i	0.548144	+	0.608386i
$220$		0			0
$221$	−154.271	+	154.271i	−0.0469566	+	0.0469566i
$222$		0			0
$223$		−	4220.28i		−	1.26731i	−0.773614	−	0.633657i	$-0.781553\pi$
$223$		−	4220.28i		−	1.26731i	0.773614	−	0.633657i	$-0.218447\pi$
$224$		0			0
$225$	6546.97	+	683.901i	1.93984	+	0.202637i
$226$		0			0
$227$	−4171.11	−	4171.11i	−1.21959	−	1.21959i	−0.967777	−	0.251810i	$-0.918974\pi$
$227$	−4171.11	−	4171.11i	−1.21959	−	1.21959i	−0.251810	−	0.967777i	$-0.581026\pi$
$228$		0			0
$229$	2178.48	−	2178.48i	0.628638	−	0.628638i	−0.319087	−	0.947725i	$-0.603376\pi$
$229$	2178.48	−	2178.48i	0.628638	−	0.628638i	0.947725	+	0.319087i	$0.103376\pi$
$230$		0			0
$231$	154.932	−	2974.39i	0.0441290	−	0.847190i
$232$		0			0
$233$	−3707.90			−1.04254			−0.521272	−	0.853391i	$-0.674542\pi$
$233$	−3707.90			−1.04254			−0.521272	+	0.853391i	$0.674542\pi$
$234$		0			0
$235$	−2617.07	−	2617.07i	−0.726463	−	0.726463i
$236$		0			0
$237$	802.425	+	890.613i	0.219929	+	0.244099i
$238$		0			0
$239$	−1721.72			−0.465979			−0.232990	−	0.972479i	$-0.574851\pi$
$239$	−1721.72			−0.465979			−0.232990	+	0.972479i	$0.574851\pi$
$240$		0			0
$241$	−3133.35			−0.837497			−0.418748	−	0.908102i	$-0.637531\pi$
$241$	−3133.35			−0.837497			−0.418748	+	0.908102i	$0.637531\pi$
$242$		0			0
$243$	3277.48	−	1899.22i	0.865229	−	0.501377i
$244$		0			0
$245$	−631.297	−	631.297i	−0.164621	−	0.164621i
$246$		0			0
$247$	−2838.92			−0.731319
$248$		0			0
$249$	4357.87	+	226.996i	1.10911	+	0.0577721i
$250$		0			0
$251$	−2709.36	+	2709.36i	−0.681327	+	0.681327i	−0.960299	−	0.278972i	$-0.910006\pi$
$251$	−2709.36	+	2709.36i	−0.681327	+	0.681327i	0.278972	+	0.960299i	$0.410006\pi$
$252$		0			0
$253$	−1425.95	−	1425.95i	−0.354342	−	0.354342i
$254$		0			0
$255$	−21.8117	+	418.741i	−0.00535647	+	0.102834i
$256$		0			0
$257$			4861.83i			1.18005i	0.807385	+	0.590025i	$0.200882\pi$
$257$			4861.83i			1.18005i	−0.807385	+	0.590025i	$0.799118\pi$
$258$		0			0
$259$	1342.06	−	1342.06i	0.321976	−	0.321976i
$260$		0			0
$261$	553.644	+	682.805i	0.131302	+	0.161933i
$262$		0			0
$263$			5128.25i			1.20236i	0.799113	+	0.601181i	$0.205303\pi$
$263$			5128.25i			1.20236i	−0.799113	+	0.601181i	$0.794697\pi$
$264$		0			0
$265$		−	12546.5i		−	2.90840i
$266$		0			0
$267$	3918.33	−	3530.34i	0.898120	−	0.809189i
$268$		0			0
$269$	2562.79	−	2562.79i	0.580877	−	0.580877i	−0.354267	−	0.935144i	$-0.615270\pi$
$269$	2562.79	−	2562.79i	0.580877	−	0.580877i	0.935144	+	0.354267i	$0.115270\pi$
$270$		0			0
$271$		−	4786.88i		−	1.07300i	−0.843901	−	0.536499i	$-0.819747\pi$
$271$		−	4786.88i		−	1.07300i	0.843901	−	0.536499i	$-0.180253\pi$
$272$		0			0
$273$	−5317.21	−	276.966i	−1.17880	−	0.0614021i
$274$		0			0
$275$	−5006.97	−	5006.97i	−1.09793	−	1.09793i
$276$		0			0
$277$	288.977	−	288.977i	0.0626821	−	0.0626821i	−0.675071	−	0.737753i	$-0.735887\pi$
$277$	288.977	−	288.977i	0.0626821	−	0.0626821i	0.737753	+	0.675071i	$0.235887\pi$
$278$		0			0
$279$	5907.41	+	617.092i	1.26762	+	0.132417i
$280$		0			0
$281$	6854.61			1.45520			0.727601	−	0.686001i	$-0.240635\pi$
$281$	6854.61			1.45520			0.727601	+	0.686001i	$0.240635\pi$
$282$		0			0
$283$	−3730.40	−	3730.40i	−0.783566	−	0.783566i	0.196865	−	0.980431i	$-0.436924\pi$
$283$	−3730.40	−	3730.40i	−0.783566	−	0.783566i	−0.980431	+	0.196865i	$0.936924\pi$
$284$		0			0
$285$	−4053.55	+	3652.17i	−0.842498	+	0.759074i
$286$		0			0
$287$	6429.61			1.32240
$288$		0			0
$289$	4895.34			0.996406
$290$		0			0
$291$	−3108.90	+	2801.06i	−0.626278	+	0.564265i
$292$		0			0
$293$	4295.66	+	4295.66i	0.856502	+	0.856502i	0.990924	−	0.134422i	$-0.0429178\pi$
$293$	4295.66	+	4295.66i	0.856502	+	0.856502i	−0.134422	+	0.990924i	$0.542918\pi$
$294$		0			0
$295$	−26.5609			−0.00524216
$296$		0			0
$297$	−4025.21	−	633.591i	−0.786418	−	0.123787i
$298$		0			0
$299$	−2549.11	+	2549.11i	−0.493040	+	0.493040i
$300$		0			0
$301$	729.051	+	729.051i	0.139607	+	0.139607i
$302$		0			0
$303$	4485.53	+	233.645i	0.850452	+	0.0442989i
$304$		0			0
$305$		−	5879.81i		−	1.10386i
$306$		0			0
$307$	−5854.72	+	5854.72i	−1.08843	+	1.08843i	−0.0927348	+	0.995691i	$0.529561\pi$
$307$	−5854.72	+	5854.72i	−1.08843	+	1.08843i	−0.995691	+	0.0927348i	$0.970439\pi$
$308$		0			0
$309$	4896.44	−	4411.59i	0.901451	−	0.812190i
$310$		0			0
$311$		−	4251.57i		−	0.775190i	−0.921830	−	0.387595i	$-0.873306\pi$
$311$		−	4251.57i		−	0.775190i	0.921830	−	0.387595i	$-0.126694\pi$
$312$		0			0
$313$			468.690i			0.0846388i	0.999104	+	0.0423194i	$0.0134747\pi$
$313$			468.690i			0.0846388i	−0.999104	+	0.0423194i	$0.986525\pi$
$314$		0			0
$315$	−7948.50	+	6444.95i	−1.42174	+	1.15280i
$316$		0			0
$317$	−4956.33	+	4956.33i	−0.878155	+	0.878155i	−0.993344	−	0.115188i	$-0.963253\pi$
$317$	−4956.33	+	4956.33i	−0.878155	+	0.878155i	0.115188	+	0.993344i	$0.463253\pi$
$318$		0			0
$319$		−	945.608i		−	0.165968i
$320$		0			0
$321$	58.5118	−	1123.31i	0.0101739	−	0.195318i
$322$		0			0
$323$	−162.462	−	162.462i	−0.0279865	−	0.0279865i
$324$		0			0
$325$	−8950.78	+	8950.78i	−1.52769	+	1.52769i
$326$		0			0
$327$	877.607	+	45.7134i	0.148415	+	0.00773075i
$328$		0			0
$329$	3803.49			0.637366
$330$		0			0
$331$	3112.74	+	3112.74i	0.516894	+	0.516894i	0.916630	−	0.399736i	$-0.130898\pi$
$331$	3112.74	+	3112.74i	0.516894	+	0.516894i	−0.399736	+	0.916630i	$0.630898\pi$
$332$		0			0
$333$	−1635.37	−	2016.89i	−0.269123	−	0.331907i
$334$		0			0
$335$	−755.848			−0.123273
$336$		0			0
$337$	−6448.09			−1.04228			−0.521142	−	0.853470i	$-0.674494\pi$
$337$	−6448.09			−1.04228			−0.521142	+	0.853470i	$0.674494\pi$
$338$		0			0
$339$	−7295.17	−	8096.92i	−1.16879	−	1.29724i
$340$		0			0
$341$	−4517.85	−	4517.85i	−0.717464	−	0.717464i
$342$		0			0
$343$	−5851.78			−0.921185
$344$		0			0
$345$	−360.407	+	6919.11i	−0.0562425	+	1.07975i
$346$		0			0
$347$	9064.25	−	9064.25i	1.40229	−	1.40229i	0.609516	−	0.792774i	$-0.291364\pi$
$347$	9064.25	−	9064.25i	1.40229	−	1.40229i	0.792774	−	0.609516i	$-0.208636\pi$
$348$		0			0
$349$	4033.73	+	4033.73i	0.618684	+	0.618684i	0.945194	−	0.326510i	$-0.105873\pi$
$349$	4033.73	+	4033.73i	0.618684	+	0.618684i	−0.326510	+	0.945194i	$0.605873\pi$
$350$		0			0
$351$	−1132.65	+	7195.71i	−0.172240	+	1.09424i
$352$		0			0
$353$		−	7626.45i		−	1.14990i	−0.818188	−	0.574950i	$-0.805021\pi$
$353$		−	7626.45i		−	1.14990i	0.818188	−	0.574950i	$-0.194979\pi$
$354$		0			0
$355$	10681.6	−	10681.6i	1.59695	−	1.59695i
$356$		0			0
$357$	−288.437	−	320.137i	−0.0427611	−	0.0474606i
$358$		0			0
$359$			5750.40i			0.845389i	0.906272	+	0.422694i	$0.138916\pi$
$359$			5750.40i			0.845389i	−0.906272	+	0.422694i	$0.861084\pi$
$360$		0			0
$361$			3869.35i			0.564128i
$362$		0			0
$363$	−1695.39	−	1881.72i	−0.245138	−	0.272079i
$364$		0			0
$365$	−6935.77	+	6935.77i	−0.994616	+	0.994616i
$366$		0			0
$367$		−	1897.35i		−	0.269866i	−0.990855	−	0.134933i	$-0.956918\pi$
$367$		−	1897.35i		−	0.269866i	0.990855	−	0.134933i	$-0.0430820\pi$
$368$		0			0
$369$	913.897	−	8748.71i	0.128931	−	1.23425i
$370$		0			0
$371$	9117.17	+	9117.17i	1.27585	+	1.27585i
$372$		0			0
$373$	7007.64	−	7007.64i	0.972766	−	0.972766i	−0.0268725	−	0.999639i	$-0.508555\pi$
$373$	7007.64	−	7007.64i	0.972766	−	0.972766i	0.999639	+	0.0268725i	$0.00855481\pi$
$374$		0			0
$375$	−616.662	+	11838.7i	−0.0849181	+	1.63026i
$376$		0			0
$377$	−1690.43			−0.230932
$378$		0			0
$379$	6022.88	+	6022.88i	0.816292	+	0.816292i	0.985569	−	0.169277i	$-0.0541432\pi$
$379$	6022.88	+	6022.88i	0.816292	+	0.816292i	−0.169277	+	0.985569i	$0.554143\pi$
$380$		0			0
$381$	2718.24	+	3016.98i	0.365511	+	0.405681i
$382$		0			0
$383$	5812.46			0.775464			0.387732	−	0.921772i	$-0.373259\pi$
$383$	5812.46			0.775464			0.387732	+	0.921772i	$0.373259\pi$
$384$		0			0
$385$	11007.8			1.45717
$386$		0			0
$387$	1095.64	−	888.386i	0.143913	−	0.116690i
$388$		0			0
$389$	1335.20	+	1335.20i	0.174030	+	0.174030i	0.788747	−	0.614718i	$-0.210730\pi$
$389$	1335.20	+	1335.20i	0.174030	+	0.174030i	−0.614718	+	0.788747i	$0.710730\pi$
$390$		0			0
$391$	−291.755			−0.0377358
$392$		0			0
$393$	1104.19	+	57.5158i	0.141728	+	0.00738242i
$394$		0			0
$395$	−3132.84	+	3132.84i	−0.399064	+	0.399064i
$396$		0			0
$397$	−7841.95	−	7841.95i	−0.991375	−	0.991375i	0.00858791	−	0.999963i	$-0.497266\pi$
$397$	−7841.95	−	7841.95i	−0.991375	−	0.991375i	−0.999963	+	0.00858791i	$0.997266\pi$
$398$		0			0
$399$	291.672	−	5599.53i	0.0365961	−	0.702574i
$400$		0			0
$401$		−	1006.91i		−	0.125393i	−0.998033	−	0.0626965i	$-0.980030\pi$
$401$		−	1006.91i		−	0.125393i	0.998033	−	0.0626965i	$-0.0199700\pi$
$402$		0			0
$403$	−8076.39	+	8076.39i	−0.998297	+	0.998297i
$404$		0			0
$405$	7639.79	+	11731.5i	0.937344	+	1.43937i
$406$		0			0
$407$			2793.17i			0.340178i
$408$		0			0
$409$			7577.54i			0.916100i	0.888926	+	0.458050i	$0.151452\pi$
$409$			7577.54i			0.916100i	−0.888926	+	0.458050i	$0.848548\pi$
$410$		0			0
$411$	7383.31	−	6652.22i	0.886111	−	0.798369i
$412$		0			0
$413$	19.3010	−	19.3010i	0.00229962	−	0.00229962i
$414$		0			0
$415$			16127.8i			1.90767i
$416$		0			0
$417$	827.961	+	43.1274i	0.0972313	+	0.00506465i
$418$		0			0
$419$	−5402.94	−	5402.94i	−0.629954	−	0.629954i	0.318102	−	0.948056i	$-0.396955\pi$
$419$	−5402.94	−	5402.94i	−0.629954	−	0.629954i	−0.948056	+	0.318102i	$0.896955\pi$
$420$		0			0
$421$	−1089.62	+	1089.62i	−0.126139	+	0.126139i	−0.767358	−	0.641219i	$-0.778429\pi$
$421$	−1089.62	+	1089.62i	−0.126139	+	0.126139i	0.641219	+	0.767358i	$0.278429\pi$
$422$		0			0
$423$	540.624	−	5175.38i	0.0621419	−	0.594883i
$424$		0			0
$425$	−1024.45			−0.116925
$426$		0			0
$427$	4272.68	+	4272.68i	0.484238	+	0.484238i
$428$		0			0
$429$	5821.44	−	5245.01i	0.655156	−	0.590283i
$430$		0			0
$431$	−2457.25			−0.274621			−0.137310	−	0.990528i	$-0.543846\pi$
$431$	−2457.25			−0.274621			−0.137310	+	0.990528i	$0.543846\pi$
$432$		0			0
$433$	−10663.1			−1.18346			−0.591728	−	0.806138i	$-0.701554\pi$
$433$	−10663.1			−1.18346			−0.591728	+	0.806138i	$0.701554\pi$
$434$		0			0
$435$	−2413.68	+	2174.68i	−0.266040	+	0.239696i
$436$		0			0
$437$	−2684.46	−	2684.46i	−0.293856	−	0.293856i
$438$		0			0
$439$	12250.0			1.33180			0.665900	−	0.746041i	$-0.268048\pi$
$439$	12250.0			1.33180			0.665900	+	0.746041i	$0.268048\pi$
$440$		0			0
$441$	130.411	−	1248.42i	0.0140817	−	0.134804i
$442$		0			0
$443$	−7482.50	+	7482.50i	−0.802492	+	0.802492i	−0.983485	−	0.180992i	$-0.942069\pi$
$443$	−7482.50	+	7482.50i	−0.802492	+	0.802492i	0.180992	+	0.983485i	$0.442069\pi$
$444$		0			0
$445$	13783.2	+	13783.2i	1.46829	+	1.46829i
$446$		0			0
$447$	−4382.61	−	228.284i	−0.463737	−	0.0241554i
$448$		0			0
$449$			461.956i			0.0485547i	0.999705	+	0.0242773i	$0.00772848\pi$
$449$			461.956i			0.0485547i	−0.999705	+	0.0242773i	$0.992272\pi$
$450$		0			0
$451$	−6690.82	+	6690.82i	−0.698577	+	0.698577i
$452$		0			0
$453$	−8709.46	+	7847.05i	−0.903325	+	0.813878i
$454$		0			0
$455$		−	19678.2i		−	2.02754i
$456$		0			0
$457$		−	4766.75i		−	0.487919i	−0.969785	−	0.243960i	$-0.921554\pi$
$457$		−	4766.75i		−	0.487919i	0.969785	−	0.243960i	$-0.0784464\pi$
$458$		0			0
$459$	−476.605	+	346.970i	−0.0484663	+	0.0352836i
$460$		0			0
$461$	−6786.71	+	6786.71i	−0.685658	+	0.685658i	−0.961269	−	0.275611i	$-0.911120\pi$
$461$	−6786.71	+	6786.71i	−0.685658	+	0.685658i	0.275611	+	0.961269i	$0.411120\pi$
$462$		0			0
$463$			4659.31i			0.467681i	0.972275	+	0.233841i	$0.0751294\pi$
$463$			4659.31i			0.467681i	−0.972275	+	0.233841i	$0.924871\pi$
$464$		0			0
$465$	−1141.88	+	21921.9i	−0.113879	+	2.18625i
$466$		0			0
$467$	−77.7107	−	77.7107i	−0.00770026	−	0.00770026i	0.703246	−	0.710946i	$-0.251733\pi$
$467$	−77.7107	−	77.7107i	−0.00770026	−	0.00770026i	−0.710946	+	0.703246i	$0.751733\pi$
$468$		0			0
$469$	549.252	−	549.252i	0.0540770	−	0.0540770i
$470$		0			0
$471$	−16783.4	−	874.224i	−1.64190	−	0.0855246i
$472$		0			0
$473$	−1517.34			−0.147500
$474$		0			0
$475$	−9426.01	−	9426.01i	−0.910516	−	0.910516i
$476$		0			0
$477$	13701.5	−	11109.7i	1.31520	−	1.06642i
$478$		0			0
$479$	−4315.85			−0.411683			−0.205842	−	0.978585i	$-0.565993\pi$
$479$	−4315.85			−0.411683			−0.205842	+	0.978585i	$0.565993\pi$
$480$		0			0
$481$	4993.24			0.473331
$482$		0			0
$483$	−4766.02	−	5289.81i	−0.448988	−	0.498333i
$484$		0			0
$485$	−10935.9	−	10935.9i	−1.02387	−	1.02387i
$486$		0			0
$487$	11571.8			1.07673			0.538367	−	0.842711i	$-0.319042\pi$
$487$	11571.8			1.07673			0.538367	+	0.842711i	$0.319042\pi$
$488$		0			0
$489$	994.927	−	19100.6i	0.0920085	−	1.76638i
$490$		0			0
$491$	−3134.09	+	3134.09i	−0.288064	+	0.288064i	−0.836314	−	0.548250i	$-0.815294\pi$
$491$	−3134.09	+	3134.09i	−0.288064	+	0.288064i	0.548250	+	0.836314i	$0.315294\pi$
$492$		0			0
$493$	−96.7378	−	96.7378i	−0.00883743	−	0.00883743i
$494$		0			0
$495$	1564.63	−	14978.2i	0.142071	−	1.36004i
$496$		0			0
$497$			15523.9i			1.40109i
$498$		0			0
$499$	4382.81	−	4382.81i	0.393190	−	0.393190i	−0.482633	−	0.875823i	$-0.660320\pi$
$499$	4382.81	−	4382.81i	0.393190	−	0.393190i	0.875823	+	0.482633i	$0.160320\pi$
$500$		0			0
$501$	−5755.73	−	6388.29i	−0.513267	−	0.569676i
$502$		0			0
$503$		−	11741.7i		−	1.04082i	−0.853915	−	0.520412i	$-0.825778\pi$
$503$		−	11741.7i		−	1.04082i	0.853915	−	0.520412i	$-0.174222\pi$
$504$		0			0
$505$			16600.3i			1.46278i
$506$		0			0
$507$	−1734.84	−	1925.50i	−0.151966	−	0.168668i
$508$		0			0
$509$	9177.29	−	9177.29i	0.799167	−	0.799167i	−0.183797	−	0.982964i	$-0.558839\pi$
$509$	9177.29	−	9177.29i	0.799167	−	0.799167i	0.982964	+	0.183797i	$0.0588389\pi$
$510$		0			0
$511$		−	10080.0i		−	0.872631i
$512$		0			0
$513$	−7577.76	−	1192.78i	−0.652176	−	0.102656i
$514$		0			0
$515$	17223.8	+	17223.8i	1.47373	+	1.47373i
$516$		0			0
$517$	−3958.01	+	3958.01i	−0.336699	+	0.336699i
$518$		0			0
$519$	−968.833	+	18599.7i	−0.0819404	+	1.57309i
$520$		0			0
$521$	21786.3			1.83200			0.916001	−	0.401176i	$-0.131398\pi$
$521$	21786.3			1.83200			0.916001	+	0.401176i	$0.131398\pi$
$522$		0			0
$523$	3381.21	+	3381.21i	0.282696	+	0.282696i	0.834183	−	0.551487i	$-0.185939\pi$
$523$	3381.21	+	3381.21i	0.282696	+	0.282696i	−0.551487	+	0.834183i	$0.685939\pi$
$524$		0			0
$525$	−16735.1	−	18574.3i	−1.39120	−	1.54409i
$526$		0			0
$527$	−924.372			−0.0764066
$528$		0			0
$529$	7346.16			0.603777
$530$		0			0
$531$	−23.5193	−	29.0062i	−0.00192213	−	0.00237055i
$532$		0			0
$533$	11960.9	+	11960.9i	0.972017	+	0.972017i
$534$		0			0
$535$	4157.21			0.335948
$536$		0			0
$537$	−22103.7	−	1151.35i	−1.77624	−	0.0925222i
$538$		0			0
$539$	−954.764	+	954.764i	−0.0762979	+	0.0762979i
$540$		0			0
$541$	−2531.45	−	2531.45i	−0.201175	−	0.201175i	0.599328	−	0.800503i	$-0.295434\pi$
$541$	−2531.45	−	2531.45i	−0.201175	−	0.201175i	−0.800503	+	0.599328i	$0.795434\pi$
$542$		0			0
$543$	−165.508	+	3177.42i	−0.0130803	+	0.251116i
$544$		0			0
$545$			3247.89i			0.255274i
$546$		0			0
$547$	13220.9	−	13220.9i	1.03343	−	1.03343i	0.0340067	−	0.999422i	$-0.489173\pi$
$547$	13220.9	−	13220.9i	1.03343	−	1.03343i	0.999422	−	0.0340067i	$-0.0108267\pi$
$548$		0			0
$549$	6421.11	−	5206.49i	0.499174	−	0.404749i
$550$		0			0
$551$		−	1780.18i		−	0.137637i
$552$		0			0
$553$		−	4553.09i		−	0.350121i
$554$		0			0
$555$	7129.62	−	6423.64i	0.545289	−	0.491295i
$556$		0			0
$557$	1799.67	−	1799.67i	0.136902	−	0.136902i	−0.635335	−	0.772237i	$-0.719138\pi$
$557$	1799.67	−	1799.67i	0.136902	−	0.136902i	0.772237	+	0.635335i	$0.219138\pi$
$558$		0			0
$559$			2712.49i			0.205234i
$560$		0			0
$561$	633.298	+	32.9876i	0.0476611	+	0.00248260i
$562$		0			0
$563$	9770.30	+	9770.30i	0.731384	+	0.731384i	0.970894	−	0.239510i	$-0.0769869\pi$
$563$	9770.30	+	9770.30i	0.731384	+	0.731384i	−0.239510	+	0.970894i	$0.576987\pi$
$564$		0			0
$565$	28481.9	−	28481.9i	2.12079	−	2.12079i
$566$		0			0
$567$	−14076.6	−	2973.34i	−1.04261	−	0.220227i
$568$		0			0
$569$	−10828.4			−0.797804			−0.398902	−	0.916994i	$-0.630609\pi$
$569$	−10828.4			−0.797804			−0.398902	+	0.916994i	$0.630609\pi$
$570$		0			0
$571$	−7393.50	−	7393.50i	−0.541871	−	0.541871i	0.382206	−	0.924077i	$-0.375164\pi$
$571$	−7393.50	−	7393.50i	−0.541871	−	0.541871i	−0.924077	+	0.382206i	$0.875164\pi$
$572$		0			0
$573$	3429.57	−	3089.97i	0.250039	−	0.225280i
$574$		0			0
$575$	−16927.6			−1.22770
$576$		0			0
$577$	9184.00			0.662625			0.331313	−	0.943521i	$-0.392508\pi$
$577$	9184.00			0.662625			0.331313	+	0.943521i	$0.392508\pi$
$578$		0			0
$579$	9767.13	−	8799.99i	0.701050	−	0.631633i
$580$		0			0
$581$	−11719.6	−	11719.6i	−0.836853	−	0.836853i
$582$		0			0
$583$	−18975.1			−1.34797
$584$		0			0
$585$	−26776.0	−	2797.04i	−1.89239	−	0.197681i
$586$		0			0
$587$	13196.5	−	13196.5i	0.927903	−	0.927903i	−0.0696672	−	0.997570i	$-0.522194\pi$
$587$	13196.5	−	13196.5i	0.927903	−	0.927903i	0.997570	+	0.0696672i	$0.0221937\pi$
$588$		0			0
$589$	−8505.20	−	8505.20i	−0.594993	−	0.594993i
$590$		0			0
$591$	−7580.53	−	394.860i	−0.527617	−	0.0274828i
$592$		0			0
$593$		−	6984.22i		−	0.483655i	−0.970319	−	0.241828i	$-0.922253\pi$
$593$		−	6984.22i		−	0.483655i	0.970319	−	0.241828i	$-0.0777469\pi$
$594$		0			0
$595$	1126.12	−	1126.12i	0.0775907	−	0.0775907i
$596$		0			0
$597$	2476.21	−	2231.01i	0.169756	−	0.152947i
$598$		0			0
$599$		−	6684.31i		−	0.455949i	−0.973667	−	0.227975i	$-0.926790\pi$
$599$		−	6684.31i		−	0.455949i	0.973667	−	0.227975i	$-0.0732104\pi$
$600$		0			0
$601$		−	14533.0i		−	0.986377i	−0.869923	−	0.493188i	$-0.835831\pi$
$601$		−	14533.0i		−	0.986377i	0.869923	−	0.493188i	$-0.164169\pi$
$602$		0			0
$603$	−669.292	−	825.432i	−0.0452001	−	0.0557449i
$604$		0			0
$605$	6619.18	−	6619.18i	0.444806	−	0.444806i
$606$		0			0
$607$		−	12378.6i		−	0.827733i	−0.910338	−	0.413866i	$-0.864178\pi$
$607$		−	12378.6i		−	0.827733i	0.910338	−	0.413866i	$-0.135822\pi$
$608$		0			0
$609$	173.676	−	3334.23i	0.0115561	−	0.221855i
$610$		0			0
$611$	7075.59	+	7075.59i	0.468490	+	0.468490i
$612$		0			0
$613$	−18856.7	+	18856.7i	−1.24244	+	1.24244i	−0.283455	+	0.958986i	$0.591481\pi$
$613$	−18856.7	+	18856.7i	−1.24244	+	1.24244i	−0.958986	+	0.283455i	$0.908519\pi$
$614$		0			0
$615$	32465.8	+	1691.10i	2.12869	+	0.110881i
$616$		0			0
$617$	4117.09			0.268635			0.134317	−	0.990938i	$-0.457116\pi$
$617$	4117.09			0.268635			0.134317	+	0.990938i	$0.457116\pi$
$618$		0			0
$619$	11488.2	+	11488.2i	0.745958	+	0.745958i	0.973717	−	0.227759i	$-0.0731399\pi$
$619$	11488.2	+	11488.2i	0.745958	+	0.745958i	−0.227759	+	0.973717i	$0.573140\pi$
$620$		0			0
$621$	−7875.23	+	5733.19i	−0.508892	+	0.370475i
$622$		0			0
$623$	−20031.7			−1.28821
$624$		0			0
$625$	−13338.3			−0.853652
$626$		0			0
$627$	5523.49	+	6130.53i	0.351813	+	0.390478i
$628$		0			0
$629$	285.747	+	285.747i	0.0181137	+	0.0181137i
$630$		0			0
$631$	−12047.6			−0.760077			−0.380039	−	0.924971i	$-0.624089\pi$
$631$	−12047.6			−0.760077			−0.380039	+	0.924971i	$0.624089\pi$
$632$		0			0
$633$	−780.039	+	14975.2i	−0.0489791	+	0.940302i
$634$		0			0
$635$	−10612.6	+	10612.6i	−0.663225	+	0.663225i
$636$		0			0
$637$	1706.80	+	1706.80i	0.106163	+	0.106163i
$638$		0			0
$639$	21123.3	+	2206.55i	1.30771	+	0.136604i
$640$		0			0
$641$		−	15280.3i		−	0.941550i	−0.882253	−	0.470775i	$-0.843974\pi$
$641$		−	15280.3i		−	0.941550i	0.882253	−	0.470775i	$-0.156026\pi$
$642$		0			0
$643$	−10573.2	+	10573.2i	−0.648468	+	0.648468i	−0.952623	−	0.304155i	$-0.901626\pi$
$643$	−10573.2	+	10573.2i	−0.648468	+	0.648468i	0.304155	+	0.952623i	$0.401626\pi$
$644$		0			0
$645$	3489.53	+	3873.03i	0.213023	+	0.236435i
$646$		0			0
$647$			4804.62i			0.291946i	0.989289	+	0.145973i	$0.0466312\pi$
$647$			4804.62i			0.291946i	−0.989289	+	0.145973i	$0.953369\pi$
$648$		0			0
$649$			40.1703i			0.00242962i
$650$		0			0
$651$	−15100.2	−	16759.8i	−0.909101	−	1.00901i
$652$		0			0
$653$	−1034.28	+	1034.28i	−0.0619823	+	0.0619823i	−0.737418	−	0.675436i	$-0.763955\pi$
$653$	−1034.28	+	1034.28i	−0.0619823	+	0.0619823i	0.675436	+	0.737418i	$0.263955\pi$
$654$		0			0
$655$			4086.45i			0.243772i
$656$		0			0
$657$	−13715.8	−	1432.76i	−0.814467	−	0.0850798i
$658$		0			0
$659$	−3161.81	−	3161.81i	−0.186899	−	0.186899i	0.607455	−	0.794354i	$-0.292191\pi$
$659$	−3161.81	−	3161.81i	−0.186899	−	0.186899i	−0.794354	+	0.607455i	$0.792191\pi$
$660$		0			0
$661$	−17535.7	+	17535.7i	−1.03186	+	1.03186i	−0.0323858	+	0.999475i	$0.510311\pi$
$661$	−17535.7	+	17535.7i	−1.03186	+	1.03186i	−0.999475	+	0.0323858i	$0.989689\pi$
$662$		0			0
$663$	58.9707	−	1132.12i	0.00345435	−	0.0663167i
$664$		0			0
$665$	20723.0			1.20843
$666$		0			0
$667$	−1598.46	−	1598.46i	−0.0927923	−	0.0927923i
$668$		0			0
$669$	14678.7	+	16291.9i	0.848298	+	0.941528i
$670$		0			0
$671$	−8892.53			−0.511613
$672$		0			0
$673$	10046.4			0.575426			0.287713	−	0.957717i	$-0.407105\pi$
$673$	10046.4			0.575426			0.287713	+	0.957717i	$0.407105\pi$
$674$		0			0
$675$	−27652.5	+	20131.1i	−1.57681	+	1.14792i
$676$		0			0
$677$	7587.41	+	7587.41i	0.430735	+	0.430735i	0.888878	−	0.458143i	$-0.151485\pi$
$677$	7587.41	+	7587.41i	0.430735	+	0.430735i	−0.458143	+	0.888878i	$0.651485\pi$
$678$		0			0
$679$	15893.7			0.898295
$680$		0			0
$681$	30609.8	+	1594.42i	1.72242	+	0.0897186i
$682$		0			0
$683$	−2298.94	+	2298.94i	−0.128795	+	0.128795i	−0.768566	−	0.639771i	$-0.779029\pi$
$683$	−2298.94	+	2298.94i	−0.128795	+	0.128795i	0.639771	+	0.768566i	$0.279029\pi$
$684$		0			0
$685$	25971.7	+	25971.7i	1.44865	+	1.44865i
$686$		0			0
$687$	−832.733	+	15986.8i	−0.0462456	+	0.887825i
$688$		0			0
$689$			33921.1i			1.87560i
$690$		0			0
$691$	−1119.72	+	1119.72i	−0.0616442	+	0.0616442i	−0.737257	−	0.675613i	$-0.763879\pi$
$691$	−1119.72	+	1119.72i	−0.0616442	+	0.0616442i	0.675613	+	0.737257i	$0.263879\pi$
$692$		0			0
$693$	9747.24	+	12021.2i	0.534296	+	0.658943i
$694$		0			0
$695$			3064.16i			0.167238i
$696$		0			0
$697$			1368.97i			0.0743952i
$698$		0			0
$699$	14313.9	−	12896.6i	0.774539	−	0.697845i
$700$		0			0
$701$	−15121.9	+	15121.9i	−0.814760	+	0.814760i	−0.985343	−	0.170583i	$-0.945435\pi$
$701$	−15121.9	+	15121.9i	−0.814760	+	0.814760i	0.170583	+	0.985343i	$0.445435\pi$
$702$		0			0
$703$			5258.35i			0.282109i
$704$		0			0
$705$	19205.4	+	1000.38i	1.02598	+	0.0534421i
$706$		0			0
$707$	−12062.9	−	12062.9i	−0.641688	−	0.641688i
$708$		0			0
$709$	−2222.19	+	2222.19i	−0.117710	+	0.117710i	−0.763508	−	0.645798i	$-0.776525\pi$
$709$	−2222.19	+	2222.19i	−0.117710	+	0.117710i	0.645798	+	0.763508i	$0.276525\pi$
$710$		0			0
$711$	−6195.34	−	647.170i	−0.326784	−	0.0341361i
$712$		0			0
$713$	−15273.9			−0.802263
$714$		0			0
$715$	20477.6	+	20477.6i	1.07108	+	1.07108i
$716$		0			0
$717$	6646.52	−	5988.38i	0.346191	−	0.311911i
$718$		0			0
$719$	27781.8			1.44101			0.720505	−	0.693450i	$-0.243910\pi$
$719$	27781.8			1.44101			0.720505	+	0.693450i	$0.243910\pi$
$720$		0			0
$721$	−25032.1			−1.29299
$722$		0			0
$723$	12095.9	−	10898.2i	0.622203	−	0.560593i
$724$		0			0
$725$	−5612.70	−	5612.70i	−0.287518	−	0.287518i
$726$		0			0
$727$	16679.8			0.850921			0.425460	−	0.904977i	$-0.360112\pi$
$727$	16679.8			0.850921			0.425460	+	0.904977i	$0.360112\pi$
$728$		0			0
$729$	−6046.63	+	18731.2i	−0.307200	+	0.951645i
$730$		0			0
$731$	−155.227	+	155.227i	−0.00785401	+	0.00785401i
$732$		0			0
$733$	−17838.8	−	17838.8i	−0.898898	−	0.898898i	0.0964409	−	0.995339i	$-0.469254\pi$
$733$	−17838.8	−	17838.8i	−0.898898	−	0.898898i	−0.995339	+	0.0964409i	$0.969254\pi$
$734$		0			0
$735$	4632.79	+	241.316i	0.232494	+	0.0121103i
$736$		0			0
$737$			1143.13i			0.0571340i
$738$		0			0
$739$	−3174.87	+	3174.87i	−0.158037	+	0.158037i	−0.781696	−	0.623659i	$-0.785645\pi$
$739$	−3174.87	+	3174.87i	−0.158037	+	0.158037i	0.623659	+	0.781696i	$0.285645\pi$
$740$		0			0
$741$	10959.3	−	9874.13i	0.543320	−	0.489521i
$742$		0			0
$743$		−	20203.2i		−	0.997555i	−0.866730	−	0.498777i	$-0.833782\pi$
$743$		−	20203.2i		−	0.997555i	0.866730	−	0.498777i	$-0.166218\pi$
$744$		0			0
$745$		−	16219.4i		−	0.797628i
$746$		0			0
$747$	−17612.6	+	14281.0i	−0.862665	+	0.699482i
$748$		0			0
$749$	−3020.92	+	3020.92i	−0.147373	+	0.147373i
$750$		0			0
$751$			7584.16i			0.368508i	0.982879	+	0.184254i	$0.0589870\pi$
$751$			7584.16i			0.368508i	−0.982879	+	0.184254i	$0.941013\pi$
$752$		0			0
$753$	1035.66	−	19882.7i	0.0501216	−	0.962237i
$754$		0			0
$755$	−30636.6	−	30636.6i	−1.47680	−	1.47680i
$756$		0			0
$757$	−1287.51	+	1287.51i	−0.0618169	+	0.0618169i	−0.737339	−	0.675522i	$-0.763918\pi$
$757$	−1287.51	+	1287.51i	−0.0618169	+	0.0618169i	0.675522	+	0.737339i	$0.263918\pi$
$758$		0			0
$759$	10464.4	+	545.074i	0.500437	+	0.0260671i
$760$		0			0
$761$	8175.32			0.389428			0.194714	−	0.980860i	$-0.437622\pi$
$761$	8175.32			0.389428			0.194714	+	0.980860i	$0.437622\pi$
$762$		0			0
$763$	−2360.15	−	2360.15i	−0.111983	−	0.111983i
$764$		0			0
$765$	−1372.24	−	1692.37i	−0.0648540	−	0.0799839i
$766$		0			0
$767$	71.8109			0.00338063
$768$		0			0
$769$	30704.5			1.43984			0.719918	−	0.694060i	$-0.244180\pi$
$769$	30704.5			1.43984			0.719918	+	0.694060i	$0.244180\pi$
$770$		0			0
$771$	−16910.1	−	18768.6i	−0.789887	−	0.876697i
$772$		0			0
$773$	9803.75	+	9803.75i	0.456166	+	0.456166i	0.897395	−	0.441229i	$-0.145457\pi$
$773$	9803.75	+	9803.75i	0.456166	+	0.456166i	−0.441229	+	0.897395i	$0.645457\pi$
$774$		0			0
$775$	−53631.9			−2.48582
$776$		0			0
$777$	−513.009	+	9848.75i	−0.0236861	+	0.454726i
$778$		0			0
$779$	−12596.0	+	12596.0i	−0.579329	+	0.579329i
$780$		0			0
$781$	−16154.6	−	16154.6i	−0.740150	−	0.740150i
$782$		0			0
$783$	−4512.17	−	710.242i	−0.205941	−	0.0324163i
$784$		0			0
$785$		−	62112.8i		−	2.82408i
$786$		0			0
$787$	−6207.55	+	6207.55i	−0.281163	+	0.281163i	−0.833573	−	0.552410i	$-0.813708\pi$
$787$	−6207.55	+	6207.55i	−0.281163	+	0.281163i	0.552410	+	0.833573i	$0.313708\pi$
$788$		0			0
$789$	−17836.7	−	19797.0i	−0.804822	−	0.893274i
$790$		0			0
$791$			41394.0i			1.86068i
$792$		0			0
$793$			15896.8i			0.711870i
$794$		0			0
$795$	43638.4	+	48434.3i	1.94678	+	2.16074i
$796$		0			0
$797$	−16268.2	+	16268.2i	−0.723025	+	0.723025i	−0.969220	−	0.246196i	$-0.920819\pi$
$797$	−16268.2	+	16268.2i	−0.723025	+	0.723025i	0.246196	+	0.969220i	$0.420819\pi$
$798$		0			0
$799$			809.827i			0.0358568i
$800$		0			0
$801$	−2847.28	+	27257.0i	−0.125598	+	1.20234i
$802$		0			0
$803$	10489.5	+	10489.5i	0.460981	+	0.460981i
$804$		0			0
$805$	18607.6	−	18607.6i	0.814696	−	0.814696i
$806$		0			0
$807$	−979.635	+	18807.1i	−0.0427321	+	0.820372i
$808$		0			0
$809$	−22495.3			−0.977616			−0.488808	−	0.872391i	$-0.662568\pi$
$809$	−22495.3			−0.977616			−0.488808	+	0.872391i	$0.662568\pi$
$810$		0			0
$811$	−24289.2	−	24289.2i	−1.05168	−	1.05168i	−0.998590	−	0.0530865i	$-0.983094\pi$
$811$	−24289.2	−	24289.2i	−1.05168	−	1.05168i	−0.0530865	−	0.998590i	$-0.516906\pi$
$812$		0			0
$813$	16649.4	+	18479.2i	0.718229	+	0.797164i
$814$		0			0
$815$	70688.6			3.03818
$816$		0			0
$817$	−2856.51			−0.122321
$818$		0			0
$819$	21489.8	−	17424.8i	0.916868	−	0.743432i
$820$		0			0
$821$	−8033.40	−	8033.40i	−0.341495	−	0.341495i	0.515434	−	0.856929i	$-0.327631\pi$
$821$	−8033.40	−	8033.40i	−0.341495	−	0.341495i	−0.856929	+	0.515434i	$0.827631\pi$
$822$		0			0
$823$	14074.4			0.596114			0.298057	−	0.954548i	$-0.403661\pi$
$823$	14074.4			0.596114			0.298057	+	0.954548i	$0.403661\pi$
$824$		0			0
$825$	36743.8	+	1913.93i	1.55061	+	0.0807693i
$826$		0			0
$827$	6382.42	−	6382.42i	0.268366	−	0.268366i	−0.560076	−	0.828441i	$-0.689228\pi$
$827$	6382.42	−	6382.42i	0.268366	−	0.268366i	0.828441	+	0.560076i	$0.189228\pi$
$828$		0			0
$829$	8468.39	+	8468.39i	0.354788	+	0.354788i	0.861888	−	0.507099i	$-0.169282\pi$
$829$	8468.39	+	8468.39i	0.354788	+	0.354788i	−0.507099	+	0.861888i	$0.669282\pi$
$830$		0			0
$831$	−110.462	+	2120.66i	−0.00461119	+	0.0885258i
$832$		0			0
$833$			195.349i			0.00812538i
$834$		0			0
$835$	22471.6	−	22471.6i	0.931332	−	0.931332i
$836$		0			0
$837$	−24951.2	+	18164.5i	−1.03039	+	0.750129i
$838$		0			0
$839$		−	4878.66i		−	0.200751i	−0.994950	−	0.100375i	$-0.967996\pi$
$839$		−	4878.66i		−	0.200751i	0.994950	−	0.100375i	$-0.0320044\pi$
$840$		0			0
$841$			23329.0i			0.956538i
$842$		0			0
$843$	−26461.4	+	23841.2i	−1.08112	+	0.974064i
$844$		0			0
$845$	6773.19	−	6773.19i	0.275745	−	0.275745i
$846$		0			0
$847$			9619.92i			0.390253i
$848$		0			0
$849$	27375.6	+	1425.96i	1.10663	+	0.0576429i
$850$		0			0
$851$	4721.57	+	4721.57i	0.190192	+	0.190192i
$852$		0			0
$853$	−3062.44	+	3062.44i	−0.122926	+	0.122926i	−0.765894	−	0.642967i	$-0.777703\pi$
$853$	−3062.44	+	3062.44i	−0.122926	+	0.122926i	0.642967	+	0.765894i	$0.277703\pi$
$854$		0			0
$855$	2945.54	−	28197.6i	0.117819	−	1.12788i
$856$		0			0
$857$	22998.9			0.916716			0.458358	−	0.888768i	$-0.348438\pi$
$857$	22998.9			0.916716			0.458358	+	0.888768i	$0.348438\pi$
$858$		0			0
$859$	−20152.0	−	20152.0i	−0.800441	−	0.800441i	0.182723	−	0.983164i	$-0.441509\pi$
$859$	−20152.0	−	20152.0i	−0.800441	−	0.800441i	−0.983164	+	0.182723i	$0.941509\pi$
$860$		0			0
$861$	−24820.8	+	22363.0i	−0.982451	+	0.885169i
$862$		0			0
$863$	39922.6			1.57472			0.787359	−	0.616495i	$-0.211448\pi$
$863$	39922.6			1.57472			0.787359	+	0.616495i	$0.211448\pi$
$864$		0			0
$865$	−68834.7			−2.70572
$866$		0			0
$867$	−18897.9	+	17026.7i	−0.740262	+	0.666961i
$868$		0			0
$869$	4738.06	+	4738.06i	0.184957	+	0.184957i
$870$		0			0
$871$	2043.53			0.0794977
$872$		0			0
$873$	2259.10	−	21626.3i	0.0875820	−	0.838420i
$874$		0			0
$875$	31837.8	−	31837.8i	1.23007	−	1.23007i
$876$		0			0
$877$	−24622.0	−	24622.0i	−0.948035	−	0.948035i	0.0506799	−	0.998715i	$-0.483861\pi$
$877$	−24622.0	−	24622.0i	−0.948035	−	0.948035i	−0.998715	+	0.0506799i	$0.983861\pi$
$878$		0			0
$879$	−31523.8	−	1642.03i	−1.20964	−	0.0630084i
$880$		0			0
$881$			10455.7i			0.399843i	0.979812	+	0.199921i	$0.0640686\pi$
$881$			10455.7i			0.399843i	−0.979812	+	0.199921i	$0.935931\pi$
$882$		0			0
$883$	−25017.7	+	25017.7i	−0.953468	+	0.953468i	−0.998964	−	0.0454970i	$-0.985513\pi$
$883$	−25017.7	+	25017.7i	−0.953468	+	0.953468i	0.0454970	+	0.998964i	$0.485513\pi$
$884$		0			0
$885$	102.535	−	92.3824i	0.00389457	−	0.00350893i
$886$		0			0
$887$			47236.6i			1.78811i	0.447960	+	0.894054i	$0.352151\pi$
$887$			47236.6i			1.78811i	−0.447960	+	0.894054i	$0.647849\pi$
$888$		0			0
$889$		−	15423.7i		−	0.581884i
$890$		0			0
$891$	17742.6	−	11554.3i	0.667114	−	0.434437i
$892$		0			0
$893$	−7451.26	+	7451.26i	−0.279224	+	0.279224i
$894$		0			0
$895$		−	81802.4i		−	3.05514i
$896$		0			0
$897$	974.408	−	18706.7i	0.0362704	−	0.696320i
$898$		0			0
$899$	−5064.41	−	5064.41i	−0.187884	−	0.187884i
$900$		0			0
$901$	−1941.20	+	1941.20i	−0.0717765	+	0.0717765i
$902$		0			0
$903$	−5350.16	−	278.683i	−0.197167	−	0.0102702i
$904$		0			0
$905$	−11759.2			−0.431920
$906$		0			0
$907$	−31025.7	−	31025.7i	−1.13582	−	1.13582i	−0.989191	−	0.146634i	$-0.953156\pi$
$907$	−31025.7	−	31025.7i	−1.13582	−	1.13582i	−0.146634	−	0.989191i	$-0.546844\pi$
$908$		0			0
$909$	−18128.5	+	14699.3i	−0.661480	+	0.536354i
$910$		0			0
$911$	−37779.4			−1.37397			−0.686985	−	0.726672i	$-0.741066\pi$
$911$	−37779.4			−1.37397			−0.686985	+	0.726672i	$0.741066\pi$
$912$		0			0
$913$	24391.5			0.884162
$914$		0			0
$915$	20450.8	+	22698.3i	0.738887	+	0.820092i
$916$		0			0
$917$	−2969.50	−	2969.50i	−0.106937	−	0.106937i
$918$		0			0
$919$	29840.1			1.07109			0.535547	−	0.844505i	$-0.320106\pi$
$919$	29840.1			1.07109			0.535547	+	0.844505i	$0.320106\pi$
$920$		0			0
$921$	2237.99	−	42965.0i	0.0800698	−	1.53718i
$922$		0			0
$923$	−28879.0	+	28879.0i	−1.02986	+	1.02986i
$924$		0			0
$925$	16579.0	+	16579.0i	0.589312	+	0.589312i
$926$		0			0
$927$	−3558.03	+	34060.9i	−0.126064	+	1.20680i
$928$		0			0
$929$		−	5194.44i		−	0.183449i	−0.995784	−	0.0917244i	$-0.970762\pi$
$929$		−	5194.44i		−	0.183449i	0.995784	−	0.0917244i	$-0.0292379\pi$
$930$		0			0
$931$	−1797.42	+	1797.42i	−0.0632738	+	0.0632738i
$932$		0			0
$933$	14787.5	+	16412.7i	0.518887	+	0.575913i
$934$		0			0
$935$			2343.74i			0.0819770i
$936$		0			0
$937$		−	22506.4i		−	0.784687i	−0.919819	−	0.392344i	$-0.871664\pi$
$937$		−	22506.4i		−	0.784687i	0.919819	−	0.392344i	$-0.128336\pi$
$938$		0			0
$939$	−1630.17	−	1809.33i	−0.0566544	−	0.0628808i
$940$		0			0
$941$	32342.6	−	32342.6i	1.12045	−	1.12045i	0.128771	−	0.991674i	$-0.458897\pi$
$941$	32342.6	−	32342.6i	1.12045	−	1.12045i	0.991674	−	0.128771i	$-0.0411033\pi$
$942$		0			0
$943$			22620.3i			0.781144i
$944$		0			0
$945$	8267.90	−	52526.0i	0.284608	−	1.80812i
$946$		0			0
$947$	−35064.2	−	35064.2i	−1.20320	−	1.20320i	−0.973186	−	0.230018i	$-0.926122\pi$
$947$	−35064.2	−	35064.2i	−1.20320	−	1.20320i	−0.230018	−	0.973186i	$-0.573878\pi$
$948$		0			0
$949$	18751.8	−	18751.8i	0.641420	−	0.641420i
$950$		0			0
$951$	1894.58	−	36372.1i	0.0646013	−	1.24022i
$952$		0			0
$953$	−54026.3			−1.83640			−0.918198	−	0.396122i	$-0.870356\pi$
$953$	−54026.3			−1.83640			−0.918198	+	0.396122i	$0.870356\pi$
$954$		0			0
$955$	12063.9	+	12063.9i	0.408774	+	0.408774i
$956$		0			0
$957$	3288.95	+	3650.41i	0.111094	+	0.123303i
$958$		0			0
$959$	−37745.7			−1.27098
$960$		0			0
$961$	−18601.7			−0.624405
$962$		0			0
$963$	3681.15	+	4539.93i	0.123181	+	0.151918i
$964$		0			0
$965$	34357.1	+	34357.1i	1.14611	+	1.14611i
$966$		0			0
$967$	−20637.1			−0.686291			−0.343145	−	0.939282i	$-0.611492\pi$
$967$	−20637.1			−0.686291			−0.343145	+	0.939282i	$0.611492\pi$
$968$		0			0
$969$	1192.23	+	62.1018i	0.0395253	+	0.00205882i
$970$		0			0
$971$	23101.0	−	23101.0i	0.763487	−	0.763487i	−0.213464	−	0.976951i	$-0.568475\pi$
$971$	23101.0	−	23101.0i	0.763487	−	0.763487i	0.976951	+	0.213464i	$0.0684746\pi$
$972$		0			0
$973$	−2226.64	−	2226.64i	−0.0733635	−	0.0733635i
$974$		0			0
$975$	3421.47	−	65685.5i	0.112384	−	2.15756i
$976$		0			0
$977$		−	2329.22i		−	0.0762725i	−0.999273	−	0.0381362i	$-0.987858\pi$
$977$		−	2329.22i		−	0.0762725i	0.999273	−	0.0381362i	$-0.0121421\pi$
$978$		0			0
$979$	20845.5	−	20845.5i	0.680517	−	0.680517i
$980$		0			0
$981$	−3546.90	+	2875.96i	−0.115437	+	0.0936008i
$982$		0			0
$983$		−	32246.0i		−	1.04628i	−0.852248	−	0.523138i	$-0.824761\pi$
$983$		−	32246.0i		−	1.04628i	0.852248	−	0.523138i	$-0.175239\pi$
$984$		0			0
$985$		−	28054.4i		−	0.907501i
$986$		0			0
$987$	−14683.0	+	13229.1i	−0.473519	+	0.426632i
$988$		0			0
$989$	−2564.91	+	2564.91i	−0.0824664	+	0.0824664i
$990$		0			0
$991$			37641.1i			1.20657i	0.797526	+	0.603284i	$0.206142\pi$
$991$			37641.1i			1.20657i	−0.797526	+	0.603284i	$0.793858\pi$
$992$		0			0
$993$	−22842.9	−	1189.86i	−0.730009	−	0.0380252i
$994$		0			0
$995$	8710.36	+	8710.36i	0.277525	+	0.277525i
$996$		0			0
$997$	23110.9	−	23110.9i	0.734131	−	0.734131i	−0.237304	−	0.971435i	$-0.576264\pi$
$997$	23110.9	−	23110.9i	0.734131	−	0.734131i	0.971435	+	0.237304i	$0.0762638\pi$
$998$		0			0
$999$	13328.2	+	2097.94i	0.422107	+	0.0664422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.4.k.a.47.5		44
3.2	odd	2	inner	192.4.k.a.47.7		44
4.3	odd	2		48.4.k.a.35.7	yes	44
8.3	odd	2		384.4.k.b.95.5		44
8.5	even	2		384.4.k.a.95.18		44
12.11	even	2		48.4.k.a.35.16	yes	44
16.3	odd	4		384.4.k.a.287.16		44
16.5	even	4		48.4.k.a.11.16	yes	44
16.11	odd	4	inner	192.4.k.a.143.7		44
16.13	even	4		384.4.k.b.287.7		44
24.5	odd	2		384.4.k.a.95.16		44
24.11	even	2		384.4.k.b.95.7		44
48.5	odd	4		48.4.k.a.11.7	✓	44
48.11	even	4	inner	192.4.k.a.143.5		44
48.29	odd	4		384.4.k.b.287.5		44
48.35	even	4		384.4.k.a.287.18		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.k.a.11.7	✓	44	48.5	odd	4
48.4.k.a.11.16	yes	44	16.5	even	4
48.4.k.a.35.7	yes	44	4.3	odd	2
48.4.k.a.35.16	yes	44	12.11	even	2
192.4.k.a.47.5		44	1.1	even	1	trivial
192.4.k.a.47.7		44	3.2	odd	2	inner
192.4.k.a.143.5		44	48.11	even	4	inner
192.4.k.a.143.7		44	16.11	odd	4	inner
384.4.k.a.95.16		44	24.5	odd	2
384.4.k.a.95.18		44	8.5	even	2
384.4.k.a.287.16		44	16.3	odd	4
384.4.k.a.287.18		44	48.35	even	4
384.4.k.b.95.5		44	8.3	odd	2
384.4.k.b.95.7		44	24.11	even	2
384.4.k.b.287.5		44	48.29	odd	4
384.4.k.b.287.7		44	16.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	192.k (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.86039 + 3.47813i) q^{3} +(-13.5794 - 13.5794i) q^{5} +19.7355 q^{7} +(2.80518 - 26.8539i) q^{9} +(-20.5372 + 20.5372i) q^{11} +(36.7137 + 36.7137i) q^{13} +(99.6526 + 5.19077i) q^{15} +4.20201i q^{17} +(-38.6629 + 38.6629i) q^{19} +(-76.1866 + 68.6426i) q^{21} +69.4323i q^{23} +243.800i q^{25} +(82.5723 + 113.423i) q^{27} +(-23.0218 + 23.0218i) q^{29} +219.983i q^{31} +(7.85044 - 150.713i) q^{33} +(-267.996 - 267.996i) q^{35} +(68.0025 - 68.0025i) q^{37} +(-269.424 - 14.0339i) q^{39} +325.789 q^{41} +(36.9411 + 36.9411i) q^{43} +(-402.752 + 326.567i) q^{45} +192.724 q^{47} +46.4894 q^{49} +(-14.6152 - 16.2214i) q^{51} +(461.968 + 461.968i) q^{53} +557.767 q^{55} +(14.7791 - 283.729i) q^{57} +(0.977987 - 0.977987i) q^{59} +(216.498 + 216.498i) q^{61} +(55.3615 - 529.974i) q^{63} -997.098i q^{65} +(27.8307 - 27.8307i) q^{67} +(-241.495 - 268.036i) q^{69} +786.600i q^{71} -510.757i q^{73} +(-847.968 - 941.161i) q^{75} +(-405.313 + 405.313i) q^{77} -230.706i q^{79} +(-713.262 - 150.660i) q^{81} +(-593.835 - 593.835i) q^{83} +(57.0607 - 57.0607i) q^{85} +(8.80017 - 168.946i) q^{87} -1015.01 q^{89} +(724.562 + 724.562i) q^{91} +(-765.131 - 849.221i) q^{93} +1050.04 q^{95} +805.334 q^{97} +(493.894 + 609.115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{3} + 8 q^{7} - 4 q^{13} - 20 q^{19} - 56 q^{21} + 134 q^{27} - 4 q^{33} - 4 q^{37} - 596 q^{39} + 436 q^{43} - 252 q^{45} + 972 q^{49} + 648 q^{51} - 280 q^{55} - 916 q^{61} + 1636 q^{67} + 52 q^{69}+ \cdots - 1196 q^{99}+O(q^{100}) \) 44 * q + 2 * q^3 + 8 * q^7 - 4 * q^13 - 20 * q^19 - 56 * q^21 + 134 * q^27 - 4 * q^33 - 4 * q^37 - 596 * q^39 + 436 * q^43 - 252 * q^45 + 972 * q^49 + 648 * q^51 - 280 * q^55 - 916 * q^61 + 1636 * q^67 + 52 * q^69 - 1454 * q^75 - 4 * q^81 + 736 * q^85 - 1284 * q^87 - 424 * q^91 - 2084 * q^93 - 8 * q^97 - 1196 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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