LMFDB - Embedded newform 144.4.k.b.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,4,Mod(37,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("144.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	144.k (of order $4$, degree $2$, 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:	$8.49627504083$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.3
Character	$\chi$	$=$	144.37
Dual form			144.4.k.b.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.07099 + 1.92640i) q^{2} +(0.577966 - 7.97909i) q^{4} +(-0.644922 - 0.644922i) q^{5} +7.13926i q^{7} +(14.1740 + 17.6380i) q^{8} +O(q^{10})$	\(q+(-2.07099 + 1.92640i) q^{2} +(0.577966 - 7.97909i) q^{4} +(-0.644922 - 0.644922i) q^{5} +7.13926i q^{7} +(14.1740 + 17.6380i) q^{8} +(2.57800 + 0.0932465i) q^{10} +(-25.4455 - 25.4455i) q^{11} +(-14.6030 + 14.6030i) q^{13} +(-13.7531 - 14.7853i) q^{14} +(-63.3319 - 9.22328i) q^{16} -71.4024 q^{17} +(-43.6238 + 43.6238i) q^{19} +(-5.51863 + 4.77315i) q^{20} +(101.715 + 3.67906i) q^{22} -211.845i q^{23} -124.168i q^{25} +(2.11138 - 58.3737i) q^{26} +(56.9649 + 4.12625i) q^{28} +(-5.84463 + 5.84463i) q^{29} -107.807 q^{31} +(148.927 - 102.901i) q^{32} +(147.873 - 137.550i) q^{34} +(4.60426 - 4.60426i) q^{35} +(-184.865 - 184.865i) q^{37} +(6.30739 - 174.381i) q^{38} +(2.23402 - 20.5162i) q^{40} +360.146i q^{41} +(-312.475 - 312.475i) q^{43} +(-217.739 + 188.325i) q^{44} +(408.099 + 438.729i) q^{46} -343.892 q^{47} +292.031 q^{49} +(239.198 + 257.150i) q^{50} +(108.078 + 124.958i) q^{52} +(249.900 + 249.900i) q^{53} +32.8207i q^{55} +(-125.922 + 101.192i) q^{56} +(0.845051 - 23.3632i) q^{58} +(152.755 + 152.755i) q^{59} +(-525.985 + 525.985i) q^{61} +(223.267 - 207.680i) q^{62} +(-110.197 + 500.001i) q^{64} +18.8355 q^{65} +(-35.3052 + 35.3052i) q^{67} +(-41.2681 + 569.727i) q^{68} +(-0.665712 + 18.4050i) q^{70} -784.715i q^{71} +800.215i q^{73} +(738.977 + 26.7289i) q^{74} +(322.866 + 373.292i) q^{76} +(181.662 - 181.662i) q^{77} +548.062 q^{79} +(34.8958 + 46.7924i) q^{80} +(-693.784 - 745.856i) q^{82} +(-464.431 + 464.431i) q^{83} +(46.0489 + 46.0489i) q^{85} +(1249.08 + 45.1794i) q^{86} +(88.1436 - 809.471i) q^{88} +302.977i q^{89} +(-104.254 - 104.254i) q^{91} +(-1690.33 - 122.439i) q^{92} +(712.195 - 662.473i) q^{94} +56.2679 q^{95} +1567.24 q^{97} +(-604.792 + 562.568i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{4} - 84 q^{8}+O(q^{10}) $ 24 * q - 20 * q^4 - 84 * q^8	$ 24 q - 20 q^{4} - 84 q^{8} + 72 q^{10} + 40 q^{11} + 348 q^{14} - 192 q^{16} + 24 q^{19} - 80 q^{20} + 704 q^{22} + 20 q^{26} - 344 q^{28} - 400 q^{29} - 744 q^{31} + 960 q^{32} - 704 q^{34} + 456 q^{35} + 16 q^{37} - 1256 q^{38} + 1744 q^{40} + 1240 q^{43} + 200 q^{44} - 1432 q^{46} - 1176 q^{49} - 708 q^{50} + 1008 q^{52} - 752 q^{53} - 1344 q^{56} + 1936 q^{58} + 1376 q^{59} - 912 q^{61} + 996 q^{62} - 56 q^{64} - 976 q^{65} - 2256 q^{67} + 1568 q^{68} - 1760 q^{70} + 2740 q^{74} - 1880 q^{76} - 1904 q^{77} + 5992 q^{79} - 712 q^{80} - 40 q^{82} - 2680 q^{83} - 240 q^{85} + 1712 q^{86} - 3936 q^{88} - 3496 q^{91} - 5296 q^{92} + 5272 q^{94} + 7728 q^{95} - 6760 q^{98}+O(q^{100}) $ 24 * q - 20 * q^4 - 84 * q^8 + 72 * q^10 + 40 * q^11 + 348 * q^14 - 192 * q^16 + 24 * q^19 - 80 * q^20 + 704 * q^22 + 20 * q^26 - 344 * q^28 - 400 * q^29 - 744 * q^31 + 960 * q^32 - 704 * q^34 + 456 * q^35 + 16 * q^37 - 1256 * q^38 + 1744 * q^40 + 1240 * q^43 + 200 * q^44 - 1432 * q^46 - 1176 * q^49 - 708 * q^50 + 1008 * q^52 - 752 * q^53 - 1344 * q^56 + 1936 * q^58 + 1376 * q^59 - 912 * q^61 + 996 * q^62 - 56 * q^64 - 976 * q^65 - 2256 * q^67 + 1568 * q^68 - 1760 * q^70 + 2740 * q^74 - 1880 * q^76 - 1904 * q^77 + 5992 * q^79 - 712 * q^80 - 40 * q^82 - 2680 * q^83 - 240 * q^85 + 1712 * q^86 - 3936 * q^88 - 3496 * q^91 - 5296 * q^92 + 5272 * q^94 + 7728 * q^95 - 6760 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−2.07099	+	1.92640i	−0.732204	+	0.681085i
$2$	−2.07099	+	1.92640i	−0.732204	+	0.681085i
$3$		0			0
$3$		0			0
$4$	0.577966	−	7.97909i	0.0722457	−	0.997387i
$5$	−0.644922	−	0.644922i	−0.0576835	−	0.0576835i	0.677677	−	0.735360i	$-0.262987\pi$
$5$	−0.644922	−	0.644922i	−0.0576835	−	0.0576835i	−0.735360	+	0.677677i	$0.762987\pi$
$6$		0			0
$7$			7.13926i			0.385484i	0.981249	+	0.192742i	$0.0617380\pi$
$7$			7.13926i			0.385484i	−0.981249	+	0.192742i	$0.938262\pi$
$8$	14.1740	+	17.6380i	0.626407	+	0.779496i
$9$		0			0
$10$	2.57800	+	0.0932465i	0.0815235	+	0.00294871i
$11$	−25.4455	−	25.4455i	−0.697464	−	0.697464i	0.266399	−	0.963863i	$-0.414166\pi$
$11$	−25.4455	−	25.4455i	−0.697464	−	0.697464i	−0.963863	+	0.266399i	$0.914166\pi$
$12$		0			0
$13$	−14.6030	+	14.6030i	−0.311549	+	0.311549i	−0.845509	−	0.533961i	$-0.820703\pi$
$13$	−14.6030	+	14.6030i	−0.311549	+	0.311549i	0.533961	+	0.845509i	$0.320703\pi$
$14$	−13.7531	−	14.7853i	−0.262547	−	0.282253i
$15$		0			0
$16$	−63.3319	−	9.22328i	−0.989561	−	0.144114i
$17$	−71.4024			−1.01868			−0.509342	−	0.860564i	$-0.670111\pi$
$17$	−71.4024			−1.01868			−0.509342	+	0.860564i	$0.670111\pi$
$18$		0			0
$19$	−43.6238	+	43.6238i	−0.526736	+	0.526736i	−0.919598	−	0.392861i	$-0.871485\pi$
$19$	−43.6238	+	43.6238i	−0.526736	+	0.526736i	0.392861	+	0.919598i	$0.371485\pi$
$20$	−5.51863	+	4.77315i	−0.0617002	+	0.0533654i
$21$		0			0
$22$	101.715	+	3.67906i	0.985719	+	0.0356536i
$23$		−	211.845i		−	1.92056i	−0.279045	−	0.960278i	$-0.590018\pi$
$23$		−	211.845i		−	1.92056i	0.279045	−	0.960278i	$-0.409982\pi$
$24$		0			0
$25$		−	124.168i		−	0.993345i
$26$	2.11138	−	58.3737i	0.0159260	−	0.440309i
$27$		0			0
$28$	56.9649	+	4.12625i	0.384477	+	0.0278496i
$29$	−5.84463	+	5.84463i	−0.0374248	+	0.0374248i	−0.725572	−	0.688147i	$-0.758425\pi$
$29$	−5.84463	+	5.84463i	−0.0374248	+	0.0374248i	0.688147	+	0.725572i	$0.258425\pi$
$30$		0			0
$31$	−107.807			−0.624604			−0.312302	−	0.949983i	$-0.601100\pi$
$31$	−107.807			−0.624604			−0.312302	+	0.949983i	$0.601100\pi$
$32$	148.927	−	102.901i	0.822715	−	0.568455i
$33$		0			0
$34$	147.873	−	137.550i	0.745884	−	0.693811i
$35$	4.60426	−	4.60426i	0.0222361	−	0.0222361i
$36$		0			0
$37$	−184.865	−	184.865i	−0.821395	−	0.821395i	0.164913	−	0.986308i	$-0.447266\pi$
$37$	−184.865	−	184.865i	−0.821395	−	0.821395i	−0.986308	+	0.164913i	$0.947266\pi$
$38$	6.30739	−	174.381i	0.0269261	−	0.744431i
$39$		0			0
$40$	2.23402	−	20.5162i	0.00883073	−	0.0810975i
$41$			360.146i			1.37184i	0.727679	+	0.685918i	$0.240599\pi$
$41$			360.146i			1.37184i	−0.727679	+	0.685918i	$0.759401\pi$
$42$		0			0
$43$	−312.475	−	312.475i	−1.10818	−	1.10818i	−0.993389	−	0.114795i	$-0.963379\pi$
$43$	−312.475	−	312.475i	−1.10818	−	1.10818i	−0.114795	−	0.993389i	$-0.536621\pi$
$44$	−217.739	+	188.325i	−0.746030	+	0.645253i
$45$		0			0
$46$	408.099	+	438.729i	1.30806	+	1.40624i
$47$	−343.892			−1.06727			−0.533636	−	0.845715i	$-0.679175\pi$
$47$	−343.892			−1.06727			−0.533636	+	0.845715i	$0.679175\pi$
$48$		0			0
$49$	292.031			0.851402
$50$	239.198	+	257.150i	0.676553	+	0.727331i
$51$		0			0
$52$	108.078	+	124.958i	0.288227	+	0.333243i
$53$	249.900	+	249.900i	0.647667	+	0.647667i	0.952429	−	0.304762i	$-0.0985768\pi$
$53$	249.900	+	249.900i	0.647667	+	0.647667i	−0.304762	+	0.952429i	$0.598577\pi$
$54$		0			0
$55$			32.8207i			0.0804644i
$56$	−125.922	+	101.192i	−0.300483	+	0.241470i
$57$		0			0
$58$	0.845051	−	23.3632i	0.00191311	−	0.0528921i
$59$	152.755	+	152.755i	0.337067	+	0.337067i	0.855262	−	0.518195i	$-0.173396\pi$
$59$	152.755	+	152.755i	0.337067	+	0.337067i	−0.518195	+	0.855262i	$0.673396\pi$
$60$		0			0
$61$	−525.985	+	525.985i	−1.10402	+	1.10402i	−0.110104	+	0.993920i	$0.535118\pi$
$61$	−525.985	+	525.985i	−1.10402	+	1.10402i	−0.993920	+	0.110104i	$0.964882\pi$
$62$	223.267	−	207.680i	0.457338	−	0.425409i
$63$		0			0
$64$	−110.197	+	500.001i	−0.215229	+	0.976564i
$65$	18.8355			0.0359425
$66$		0			0
$67$	−35.3052	+	35.3052i	−0.0643764	+	0.0643764i	−0.738562	−	0.674186i	$-0.764495\pi$
$67$	−35.3052	+	35.3052i	−0.0643764	+	0.0643764i	0.674186	+	0.738562i	$0.264495\pi$
$68$	−41.2681	+	569.727i	−0.0735955	+	1.01602i
$69$		0			0
$70$	−0.665712	+	18.4050i	−0.00113668	+	0.0314260i
$71$		−	784.715i		−	1.31167i	−0.754905	−	0.655834i	$-0.772317\pi$
$71$		−	784.715i		−	1.31167i	0.754905	−	0.655834i	$-0.227683\pi$
$72$		0			0
$73$			800.215i			1.28299i	0.767128	+	0.641494i	$0.221685\pi$
$73$			800.215i			1.28299i	−0.767128	+	0.641494i	$0.778315\pi$
$74$	738.977	+	26.7289i	1.16087	+	0.0419888i
$75$		0			0
$76$	322.866	+	373.292i	0.487306	+	0.563414i
$77$	181.662	−	181.662i	0.268861	−	0.268861i
$78$		0			0
$79$	548.062			0.780530			0.390265	−	0.920703i	$-0.372383\pi$
$79$	548.062			0.780530			0.390265	+	0.920703i	$0.372383\pi$
$80$	34.8958	+	46.7924i	0.0487684	+	0.0653944i
$81$		0			0
$82$	−693.784	−	745.856i	−0.934337	−	1.00446i
$83$	−464.431	+	464.431i	−0.614191	+	0.614191i	−0.944035	−	0.329844i	$-0.893004\pi$
$83$	−464.431	+	464.431i	−0.614191	+	0.614191i	0.329844	+	0.944035i	$0.393004\pi$
$84$		0			0
$85$	46.0489	+	46.0489i	0.0587613	+	0.0587613i
$86$	1249.08	+	45.1794i	1.56619	+	0.0566491i
$87$		0			0
$88$	88.1436	−	809.471i	0.106774	−	0.980567i
$89$			302.977i			0.360849i	0.983589	+	0.180424i	$0.0577471\pi$
$89$			302.977i			0.360849i	−0.983589	+	0.180424i	$0.942253\pi$
$90$		0			0
$91$	−104.254	−	104.254i	−0.120097	−	0.120097i
$92$	−1690.33	−	122.439i	−1.91554	−	0.138752i
$93$		0			0
$94$	712.195	−	662.473i	0.781460	−	0.726903i
$95$	56.2679			0.0607680
$96$		0			0
$97$	1567.24			1.64050			0.820252	−	0.572002i	$-0.193833\pi$
$97$	1567.24			1.64050			0.820252	+	0.572002i	$0.193833\pi$
$98$	−604.792	+	562.568i	−0.623400	+	0.579877i
$99$		0			0
$100$	−990.749	−	71.7649i	−0.990749	−	0.0717649i
$101$	−59.6129	−	59.6129i	−0.0587297	−	0.0587297i	0.677132	−	0.735862i	$-0.263223\pi$
$101$	−59.6129	−	59.6129i	−0.0587297	−	0.0587297i	−0.735862	+	0.677132i	$0.763223\pi$
$102$		0			0
$103$		−	1762.59i		−	1.68615i	−0.537795	−	0.843076i	$-0.680743\pi$
$103$		−	1762.59i		−	1.68615i	0.537795	−	0.843076i	$-0.319257\pi$
$104$	−464.549	−	50.5849i	−0.438007	−	0.0476948i
$105$		0			0
$106$	−998.945	−	36.1319i	−0.915341	−	0.0331080i
$107$	−656.579	−	656.579i	−0.593214	−	0.593214i	0.345284	−	0.938498i	$-0.387782\pi$
$107$	−656.579	−	656.579i	−0.593214	−	0.593214i	−0.938498	+	0.345284i	$0.887782\pi$
$108$		0			0
$109$	−327.776	+	327.776i	−0.288030	+	0.288030i	−0.836301	−	0.548271i	$-0.815286\pi$
$109$	−327.776	+	327.776i	−0.288030	+	0.288030i	0.548271	+	0.836301i	$0.315286\pi$
$110$	−63.2258	−	67.9712i	−0.0548031	−	0.0589164i
$111$		0			0
$112$	65.8475	−	452.143i	0.0555536	−	0.381460i
$113$	1349.18			1.12319			0.561593	−	0.827414i	$-0.310189\pi$
$113$	1349.18			1.12319			0.561593	+	0.827414i	$0.310189\pi$
$114$		0			0
$115$	−136.624	+	136.624i	−0.110784	+	0.110784i
$116$	43.2569	+	50.0128i	0.0346233	+	0.0400308i
$117$		0			0
$118$	−610.620	−	22.0862i	−0.476374	−	0.0172305i
$119$		−	509.761i		−	0.392686i
$120$		0			0
$121$		−	36.0534i		−	0.0270875i
$122$	76.0500	−	2102.56i	0.0564364	−	1.56031i
$123$		0			0
$124$	−62.3088	+	860.203i	−0.0451250	+	0.622972i
$125$	−160.694	+	160.694i	−0.114983	+	0.114983i
$126$		0			0
$127$	52.2111			0.0364802			0.0182401	−	0.999834i	$-0.494194\pi$
$127$	52.2111			0.0364802			0.0182401	+	0.999834i	$0.494194\pi$
$128$	−734.984	−	1247.78i	−0.507532	−	0.861633i
$129$		0			0
$130$	−39.0081	+	36.2848i	−0.0263172	+	0.0244799i
$131$	387.958	−	387.958i	0.258749	−	0.258749i	−0.565796	−	0.824545i	$-0.691431\pi$
$131$	387.958	−	387.958i	0.258749	−	0.258749i	0.824545	+	0.565796i	$0.191431\pi$
$132$		0			0
$133$	−311.442	−	311.442i	−0.203048	−	0.203048i
$134$	5.10463	−	141.128i	0.00329084	−	0.0909824i
$135$		0			0
$136$	−1012.06	−	1259.39i	−0.638111	−	0.794060i
$137$			795.048i			0.495807i	0.968785	+	0.247903i	$0.0797415\pi$
$137$			795.048i			0.495807i	−0.968785	+	0.247903i	$0.920258\pi$
$138$		0			0
$139$	1708.70	+	1708.70i	1.04266	+	1.04266i	0.999048	+	0.0436142i	$0.0138872\pi$
$139$	1708.70	+	1708.70i	1.04266	+	1.04266i	0.0436142	+	0.999048i	$0.486113\pi$
$140$	−34.0768	−	39.3990i	−0.0205715	−	0.0237844i
$141$		0			0
$142$	1511.67	+	1625.13i	0.893358	+	0.960409i
$143$	743.160			0.434588
$144$		0			0
$145$	7.53865			0.00431759
$146$	−1541.53	−	1657.23i	−0.873824	−	0.939409i
$147$		0			0
$148$	−1581.90	+	1368.21i	−0.878591	+	0.759907i
$149$	69.6301	+	69.6301i	0.0382840	+	0.0382840i	0.725990	−	0.687706i	$-0.241382\pi$
$149$	69.6301	+	69.6301i	0.0382840	+	0.0382840i	−0.687706	+	0.725990i	$0.741382\pi$
$150$		0			0
$151$		−	1567.48i		−	0.844768i	−0.906417	−	0.422384i	$-0.861193\pi$
$151$		−	1567.48i		−	0.844768i	0.906417	−	0.422384i	$-0.138807\pi$
$152$	−1387.76	−	151.114i	−0.740540	−	0.0806377i
$153$		0			0
$154$	−26.2658	+	726.174i	−0.0137439	+	0.379979i
$155$	69.5271	+	69.5271i	0.0360294	+	0.0360294i
$156$		0			0
$157$	1738.35	−	1738.35i	0.883667	−	0.883667i	−0.110238	−	0.993905i	$-0.535161\pi$
$157$	1738.35	−	1738.35i	0.883667	−	0.883667i	0.993905	+	0.110238i	$0.0351614\pi$
$158$	−1135.03	+	1055.79i	−0.571507	+	0.531607i
$159$		0			0
$160$	−162.410	−	29.6831i	−0.0802476	−	0.0146666i
$161$	1512.42			0.740344
$162$		0			0
$163$	−2685.71	+	2685.71i	−1.29056	+	1.29056i	−0.356116	+	0.934442i	$0.615899\pi$
$163$	−2685.71	+	2685.71i	−1.29056	+	1.29056i	−0.934442	+	0.356116i	$0.884101\pi$
$164$	2873.64	+	208.152i	1.36825	+	0.0991093i
$165$		0			0
$166$	67.1501	−	1856.51i	0.0313967	−	0.868030i
$167$			27.5126i			0.0127484i	0.999980	+	0.00637422i	$0.00202899\pi$
$167$			27.5126i			0.0127484i	−0.999980	+	0.00637422i	$0.997971\pi$
$168$		0			0
$169$			1770.51i			0.805875i
$170$	−184.075	−	6.65803i	−0.0830467	−	0.00300381i
$171$		0			0
$172$	−2673.86	+	2312.67i	−1.18535	+	1.02523i
$173$	−3044.87	+	3044.87i	−1.33813	+	1.33813i	−0.440267	+	0.897867i	$0.645116\pi$
$173$	−3044.87	+	3044.87i	−1.33813	+	1.33813i	−0.897867	+	0.440267i	$0.854884\pi$
$174$		0			0
$175$	886.469			0.382919
$176$	1376.82	+	1846.20i	0.589669	+	0.790698i
$177$		0			0
$178$	−583.656	−	627.462i	−0.245769	−	0.264215i
$179$	365.808	−	365.808i	0.152747	−	0.152747i	−0.626597	−	0.779344i	$-0.715553\pi$
$179$	365.808	−	365.808i	0.152747	−	0.152747i	0.779344	+	0.626597i	$0.215553\pi$
$180$		0			0
$181$	−1737.10	−	1737.10i	−0.713359	−	0.713359i	0.253877	−	0.967236i	$-0.418294\pi$
$181$	−1737.10	−	1737.10i	−0.713359	−	0.713359i	−0.967236	+	0.253877i	$0.918294\pi$
$182$	416.745	+	15.0737i	0.169732	+	0.00613922i
$183$		0			0
$184$	3736.52	−	3002.69i	1.49707	−	1.20305i
$185$			238.447i			0.0947620i
$186$		0			0
$187$	1816.87	+	1816.87i	0.710495	+	0.710495i
$188$	−198.757	+	2743.94i	−0.0771057	+	1.06448i
$189$		0			0
$190$	−116.530	+	108.394i	−0.0444946	+	0.0413882i
$191$	1709.44			0.647595			0.323798	−	0.946126i	$-0.395040\pi$
$191$	1709.44			0.647595			0.323798	+	0.946126i	$0.395040\pi$
$192$		0			0
$193$	2404.54			0.896800			0.448400	−	0.893833i	$-0.351994\pi$
$193$	2404.54			0.896800			0.448400	+	0.893833i	$0.351994\pi$
$194$	−3245.73	+	3019.13i	−1.20118	+	1.11732i
$195$		0			0
$196$	168.784	−	2330.14i	0.0615101	−	0.849177i
$197$	−2772.54	−	2772.54i	−1.00272	−	1.00272i	−0.999996	−	0.00271983i	$-0.999134\pi$
$197$	−2772.54	−	2772.54i	−1.00272	−	1.00272i	−0.00271983	−	0.999996i	$-0.500866\pi$
$198$		0			0
$199$		−	1506.90i		−	0.536790i	−0.963309	−	0.268395i	$-0.913507\pi$
$199$		−	1506.90i		−	0.536790i	0.963309	−	0.268395i	$-0.0864932\pi$
$200$	2190.08	−	1759.96i	0.774309	−	0.622238i
$201$		0			0
$202$	238.296	+	8.61918i	0.0830021	+	0.00300219i
$203$	−41.7263	−	41.7263i	−0.0144267	−	0.0144267i
$204$		0			0
$205$	232.266	−	232.266i	0.0791324	−	0.0791324i
$206$	3395.46	+	3650.31i	1.14841	+	1.23461i
$207$		0			0
$208$	1059.52	−	790.147i	0.353195	−	0.263398i
$209$	2220.06			0.734760
$210$		0			0
$211$	−1965.22	+	1965.22i	−0.641190	+	0.641190i	−0.950848	−	0.309658i	$-0.899785\pi$
$211$	−1965.22	+	1965.22i	−0.641190	+	0.641190i	0.309658	+	0.950848i	$0.399785\pi$
$212$	2138.41	−	1849.54i	0.692766	−	0.599183i
$213$		0			0
$214$	2624.60	+	94.9320i	0.838383	+	0.0303244i
$215$			403.043i			0.127848i
$216$		0			0
$217$		−	769.663i		−	0.240775i
$218$	47.3918	−	1310.25i	0.0147238	−	0.407070i
$219$		0			0
$220$	261.879	+	18.9692i	0.0802541	+	0.00581321i
$221$	1042.69	−	1042.69i	0.317370	−	0.317370i
$222$		0			0
$223$	85.7869			0.0257610			0.0128805	−	0.999917i	$-0.495900\pi$
$223$	85.7869			0.0257610			0.0128805	+	0.999917i	$0.495900\pi$
$224$	734.640	+	1063.23i	0.219130	+	0.317143i
$225$		0			0
$226$	−2794.13	+	2599.06i	−0.822402	+	0.764986i
$227$	−2526.02	+	2526.02i	−0.738582	+	0.738582i	−0.972304	−	0.233722i	$-0.924910\pi$
$227$	−2526.02	+	2526.02i	−0.738582	+	0.738582i	0.233722	+	0.972304i	$0.424910\pi$
$228$		0			0
$229$	−1116.65	−	1116.65i	−0.322227	−	0.322227i	0.527394	−	0.849621i	$-0.323169\pi$
$229$	−1116.65	−	1116.65i	−0.322227	−	0.322227i	−0.849621	+	0.527394i	$0.823169\pi$
$230$	19.7538	−	546.137i	0.00566317	−	0.156570i
$231$		0			0
$232$	−185.929	−	20.2459i	−0.0526157	−	0.00572934i
$233$		−	5754.25i		−	1.61791i	−0.587869	−	0.808956i	$-0.700033\pi$
$233$		−	5754.25i		−	1.61791i	0.587869	−	0.808956i	$-0.299967\pi$
$234$		0			0
$235$	221.783	+	221.783i	0.0615640	+	0.0615640i
$236$	1307.13	−	1130.56i	0.360538	−	0.311835i
$237$		0			0
$238$	982.003	+	1055.71i	0.267453	+	0.287527i
$239$	641.784			0.173697			0.0868484	−	0.996222i	$-0.472320\pi$
$239$	641.784			0.173697			0.0868484	+	0.996222i	$0.472320\pi$
$240$		0			0
$241$	−2887.45			−0.771771			−0.385885	−	0.922547i	$-0.626104\pi$
$241$	−2887.45			−0.771771			−0.385885	+	0.922547i	$0.626104\pi$
$242$	69.4533	+	74.6661i	0.0184489	+	0.0198335i
$243$		0			0
$244$	3892.88	+	4500.88i	1.02138	+	1.18090i
$245$	−188.337	−	188.337i	−0.0491119	−	0.0491119i
$246$		0			0
$247$		−	1274.07i		−	0.328208i
$248$	−1528.05	−	1901.50i	−0.391256	−	0.486877i
$249$		0			0
$250$	23.2341	−	642.356i	0.00587781	−	0.162505i
$251$	2367.55	+	2367.55i	0.595372	+	0.595372i	0.939077	−	0.343706i	$-0.111682\pi$
$251$	2367.55	+	2367.55i	0.595372	+	0.595372i	−0.343706	+	0.939077i	$0.611682\pi$
$252$		0			0
$253$	−5390.51	+	5390.51i	−1.33952	+	1.33952i
$254$	−108.129	+	100.580i	−0.0267110	+	0.0248462i
$255$		0			0
$256$	3925.86	+	1168.26i	0.958462	+	0.285219i
$257$	−5112.43			−1.24087			−0.620437	−	0.784256i	$-0.713045\pi$
$257$	−5112.43			−1.24087			−0.620437	+	0.784256i	$0.713045\pi$
$258$		0			0
$259$	1319.80	−	1319.80i	0.316635	−	0.316635i
$260$	10.8863	−	150.291i	0.00259669	−	0.0358486i
$261$		0			0
$262$	−56.0933	+	1550.82i	−0.0132269	+	0.365687i
$263$			5496.36i			1.28867i	0.764744	+	0.644334i	$0.222866\pi$
$263$			5496.36i			1.28867i	−0.764744	+	0.644334i	$0.777134\pi$
$264$		0			0
$265$		−	322.331i		−	0.0747194i
$266$	1244.95	+	45.0301i	0.286966	+	0.0103796i
$267$		0			0
$268$	261.298	+	302.109i	0.0595572	+	0.0688591i
$269$	2474.35	−	2474.35i	0.560831	−	0.560831i	−0.368712	−	0.929544i	$-0.620201\pi$
$269$	2474.35	−	2474.35i	0.560831	−	0.560831i	0.929544	+	0.368712i	$0.120201\pi$
$270$		0			0
$271$	−1718.58			−0.385226			−0.192613	−	0.981275i	$-0.561696\pi$
$271$	−1718.58			−0.385226			−0.192613	+	0.981275i	$0.561696\pi$
$272$	4522.05	+	658.565i	1.00805	+	0.146806i
$273$		0			0
$274$	−1531.58	−	1646.53i	−0.337687	−	0.363032i
$275$	−3159.52	+	3159.52i	−0.692823	+	0.692823i
$276$		0			0
$277$	−4722.69	−	4722.69i	−1.02440	−	1.02440i	−0.999695	−	0.0247055i	$-0.992135\pi$
$277$	−4722.69	−	4722.69i	−1.02440	−	1.02440i	−0.0247055	−	0.999695i	$-0.507865\pi$
$278$	−6830.34	−	247.054i	−1.47358	−	0.0532997i
$279$		0			0
$280$	146.471	+	15.9492i	0.0312618	+	0.00340411i
$281$			2543.21i			0.539911i	0.962873	+	0.269955i	$0.0870090\pi$
$281$			2543.21i			0.539911i	−0.962873	+	0.269955i	$0.912991\pi$
$282$		0			0
$283$	−3206.82	−	3206.82i	−0.673589	−	0.673589i	0.284952	−	0.958542i	$-0.408022\pi$
$283$	−3206.82	−	3206.82i	−0.673589	−	0.673589i	−0.958542	+	0.284952i	$0.908022\pi$
$284$	−6261.31	−	453.538i	−1.30824	−	0.0947624i
$285$		0			0
$286$	−1539.07	+	1431.62i	−0.318207	+	0.295992i
$287$	−2571.17			−0.528821
$288$		0			0
$289$	185.302			0.0377167
$290$	−15.6124	+	14.5225i	−0.00316136	+	0.00294065i
$291$		0			0
$292$	6384.99	+	462.497i	1.27964	+	0.0926903i
$293$	−5911.40	−	5911.40i	−1.17866	−	1.17866i	−0.980086	−	0.198575i	$-0.936369\pi$
$293$	−5911.40	−	5911.40i	−1.17866	−	1.17866i	−0.198575	−	0.980086i	$-0.563631\pi$
$294$		0			0
$295$		−	197.030i		−	0.0388865i
$296$	640.376	−	5880.92i	0.125747	−	1.15480i
$297$		0			0
$298$	−278.338	−	10.0675i	−0.0541064	−	0.00195703i
$299$	3093.57	+	3093.57i	0.598347	+	0.598347i
$300$		0			0
$301$	2230.84	−	2230.84i	0.427187	−	0.427187i
$302$	3019.60	+	3246.23i	0.575359	+	0.618542i
$303$		0			0
$304$	3165.14	−	2360.43i	0.597148	−	0.445328i
$305$	678.438			0.127368
$306$		0			0
$307$	1162.25	−	1162.25i	0.216068	−	0.216068i	−0.590771	−	0.806839i	$-0.701176\pi$
$307$	1162.25	−	1162.25i	0.216068	−	0.216068i	0.806839	+	0.590771i	$0.201176\pi$
$308$	−1344.50	−	1554.49i	−0.248735	−	0.287583i
$309$		0			0
$310$	−277.927	−	10.0526i	−0.0509199	−	0.00184178i
$311$		−	2357.28i		−	0.429805i	−0.976636	−	0.214902i	$-0.931057\pi$
$311$		−	2357.28i		−	0.429805i	0.976636	−	0.214902i	$-0.0689433\pi$
$312$		0			0
$313$		−	3785.95i		−	0.683689i	−0.939757	−	0.341844i	$-0.888948\pi$
$313$		−	3785.95i		−	0.683689i	0.939757	−	0.341844i	$-0.111052\pi$
$314$	−251.341	+	6948.87i	−0.0451720	+	1.24888i
$315$		0			0
$316$	316.761	−	4373.04i	0.0563899	−	0.778490i
$317$	3135.51	−	3135.51i	0.555545	−	0.555545i	−0.372491	−	0.928036i	$-0.621496\pi$
$317$	3135.51	−	3135.51i	0.555545	−	0.555545i	0.928036	+	0.372491i	$0.121496\pi$
$318$		0			0
$319$	297.439			0.0522050
$320$	393.530	−	251.393i	0.0687468	−	0.0439165i
$321$		0			0
$322$	−3132.20	+	2913.52i	−0.542083	+	0.504237i
$323$	3114.85	−	3114.85i	0.536578	−	0.536578i
$324$		0			0
$325$	1813.22	+	1813.22i	0.309476	+	0.309476i
$326$	388.316	−	10735.8i	0.0659718	−	1.82393i
$327$		0			0
$328$	−6352.24	+	5104.69i	−1.06934	+	0.859328i
$329$		−	2455.13i		−	0.411416i
$330$		0			0
$331$	−1734.12	−	1734.12i	−0.287963	−	0.287963i	0.548312	−	0.836274i	$-0.315271\pi$
$331$	−1734.12	−	1734.12i	−0.287963	−	0.287963i	−0.836274	+	0.548312i	$0.815271\pi$
$332$	3437.31	+	3974.16i	0.568214	+	0.656959i
$333$		0			0
$334$	−53.0003	−	56.9783i	−0.00868278	−	0.00933446i
$335$	45.5382			0.00742691
$336$		0			0
$337$	5828.89			0.942196			0.471098	−	0.882081i	$-0.343858\pi$
$337$	5828.89			0.942196			0.471098	+	0.882081i	$0.343858\pi$
$338$	−3410.70	−	3666.69i	−0.548869	−	0.590065i
$339$		0			0
$340$	394.044	−	340.814i	0.0628530	−	0.0543625i
$341$	2743.21	+	2743.21i	0.435639	+	0.435639i
$342$		0			0
$343$			4533.65i			0.713686i
$344$	1082.42	−	9940.43i	0.169651	−	1.55800i
$345$		0			0
$346$	440.245	−	12171.5i	0.0684038	−	1.89117i
$347$	716.234	+	716.234i	0.110805	+	0.110805i	0.760336	−	0.649530i	$-0.225034\pi$
$347$	716.234	+	716.234i	0.110805	+	0.110805i	−0.649530	+	0.760336i	$0.725034\pi$
$348$		0			0
$349$	−4388.39	+	4388.39i	−0.673081	+	0.673081i	−0.958425	−	0.285344i	$-0.907892\pi$
$349$	−4388.39	+	4388.39i	−0.673081	+	0.673081i	0.285344	+	0.958425i	$0.407892\pi$
$350$	−1835.87	+	1707.69i	−0.280375	+	0.260800i
$351$		0			0
$352$	−6407.90	−	1171.15i	−0.970291	−	0.177337i
$353$	−9348.76			−1.40959			−0.704794	−	0.709412i	$-0.748960\pi$
$353$	−9348.76			−1.40959			−0.704794	+	0.709412i	$0.748960\pi$
$354$		0			0
$355$	−506.079	+	506.079i	−0.0756617	+	0.0756617i
$356$	2417.49	+	175.110i	0.359906	+	0.0260698i
$357$		0			0
$358$	−52.8906	+	1462.27i	−0.00780826	+	0.215876i
$359$		−	12531.1i		−	1.84224i	−0.389275	−	0.921122i	$-0.627274\pi$
$359$		−	12531.1i		−	1.84224i	0.389275	−	0.921122i	$-0.372726\pi$
$360$		0			0
$361$			3052.92i			0.445097i
$362$	6943.88	+	251.161i	1.00818	+	0.0364661i
$363$		0			0
$364$	−892.112	+	771.601i	−0.128460	+	0.111107i
$365$	516.076	−	516.076i	0.0740073	−	0.0740073i
$366$		0			0
$367$	9276.83			1.31947			0.659736	−	0.751497i	$-0.270668\pi$
$367$	9276.83			1.31947			0.659736	+	0.751497i	$0.270668\pi$
$368$	−1953.91	+	13416.6i	−0.276779	+	1.90051i
$369$		0			0
$370$	−459.344	−	493.820i	−0.0645410	−	0.0693851i
$371$	−1784.10	+	1784.10i	−0.249665	+	0.249665i
$372$		0			0
$373$	1765.32	+	1765.32i	0.245053	+	0.245053i	0.818937	−	0.573884i	$-0.194564\pi$
$373$	1765.32	+	1765.32i	0.245053	+	0.245053i	−0.573884	+	0.818937i	$0.694564\pi$
$374$	−7262.73	−	262.694i	−1.00414	−	0.0363197i
$375$		0			0
$376$	−4874.31	−	6065.55i	−0.668546	−	0.831934i
$377$		−	170.698i		−	0.0233193i
$378$		0			0
$379$	2909.05	+	2909.05i	0.394269	+	0.394269i	0.876206	−	0.481937i	$-0.160067\pi$
$379$	2909.05	+	2909.05i	0.394269	+	0.394269i	−0.481937	+	0.876206i	$0.660067\pi$
$380$	32.5209	−	448.967i	0.00439023	−	0.0606092i
$381$		0			0
$382$	−3540.22	+	3293.06i	−0.474172	+	0.441067i
$383$	−1520.26			−0.202824			−0.101412	−	0.994845i	$-0.532336\pi$
$383$	−1520.26			−0.202824			−0.101412	+	0.994845i	$0.532336\pi$
$384$		0			0
$385$	−234.316			−0.0310177
$386$	−4979.77	+	4632.10i	−0.656641	+	0.610798i
$387$		0			0
$388$	905.810	−	12505.1i	0.118519	−	1.63622i
$389$	8093.35	+	8093.35i	1.05488	+	1.05488i	0.998404	+	0.0564785i	$0.0179872\pi$
$389$	8093.35	+	8093.35i	1.05488	+	1.05488i	0.0564785	+	0.998404i	$0.482013\pi$
$390$		0			0
$391$			15126.3i			1.95644i
$392$	4139.24	+	5150.84i	0.533324	+	0.663665i
$393$		0			0
$394$	11082.9	+	400.870i	1.41713	+	0.0512577i
$395$	−353.457	−	353.457i	−0.0450237	−	0.0450237i
$396$		0			0
$397$	8897.26	−	8897.26i	1.12479	−	1.12479i	0.133776	−	0.991012i	$-0.457290\pi$
$397$	8897.26	−	8897.26i	1.12479	−	1.12479i	0.991012	−	0.133776i	$-0.0427101\pi$
$398$	2902.89	+	3120.76i	0.365600	+	0.393040i
$399$		0			0
$400$	−1145.24	+	7863.81i	−0.143155	+	0.982976i
$401$	4199.74			0.523004			0.261502	−	0.965203i	$-0.415782\pi$
$401$	4199.74			0.523004			0.261502	+	0.965203i	$0.415782\pi$
$402$		0			0
$403$	1574.30	−	1574.30i	0.194595	−	0.194595i
$404$	−510.111	+	441.203i	−0.0628192	+	0.0543333i
$405$		0			0
$406$	166.796	+	6.03304i	0.0203891	+	0.000737475i
$407$			9407.97i			1.14579i
$408$		0			0
$409$		−	7881.87i		−	0.952894i	−0.879203	−	0.476447i	$-0.841924\pi$
$409$		−	7881.87i		−	0.952894i	0.879203	−	0.476447i	$-0.158076\pi$
$410$	−33.5823	+	928.455i	−0.00404515	+	0.111837i
$411$		0			0
$412$	−14063.9	−	1018.72i	−1.68174	−	0.121817i
$413$	−1090.56	+	1090.56i	−0.129934	+	0.129934i
$414$		0			0
$415$	599.043			0.0708575
$416$	−672.115	+	3677.44i	−0.0792143	+	0.433417i
$417$		0			0
$418$	−4597.71	+	4276.72i	−0.537994	+	0.500434i
$419$	5502.69	−	5502.69i	0.641585	−	0.641585i	−0.309360	−	0.950945i	$-0.600115\pi$
$419$	5502.69	−	5502.69i	0.641585	−	0.641585i	0.950945	+	0.309360i	$0.100115\pi$
$420$		0			0
$421$	11302.2	+	11302.2i	1.30840	+	1.30840i	0.922573	+	0.385823i	$0.126082\pi$
$421$	11302.2	+	11302.2i	1.30840	+	1.30840i	0.385823	+	0.922573i	$0.373918\pi$
$422$	284.142	−	7855.73i	0.0327769	−	0.906187i
$423$		0			0
$424$	−865.656	+	7949.79i	−0.0991509	+	0.910557i
$425$			8865.90i			1.01190i
$426$		0			0
$427$	−3755.14	−	3755.14i	−0.425584	−	0.425584i
$428$	−5618.38	+	4859.42i	−0.634521	+	0.548806i
$429$		0			0
$430$	−776.423	−	834.697i	−0.0870754	−	0.0936108i
$431$	5428.20			0.606652			0.303326	−	0.952887i	$-0.401903\pi$
$431$	5428.20			0.606652			0.303326	+	0.952887i	$0.401903\pi$
$432$		0			0
$433$	−5143.78			−0.570888			−0.285444	−	0.958395i	$-0.592141\pi$
$433$	−5143.78			−0.570888			−0.285444	+	0.958395i	$0.592141\pi$
$434$	1482.68	+	1593.96i	0.163988	+	0.176296i
$435$		0			0
$436$	2425.92	+	2804.80i	0.266469	+	0.308086i
$437$	9241.50	+	9241.50i	1.01163	+	1.01163i
$438$		0			0
$439$			2183.50i			0.237386i	0.992931	+	0.118693i	$0.0378705\pi$
$439$			2183.50i			0.237386i	−0.992931	+	0.118693i	$0.962130\pi$
$440$	−578.891	+	465.200i	−0.0627217	+	0.0504035i
$441$		0			0
$442$	−150.758	+	4168.02i	−0.0162236	+	0.448535i
$443$	−561.821	−	561.821i	−0.0602549	−	0.0602549i	0.676337	−	0.736592i	$-0.263566\pi$
$443$	−561.821	−	561.821i	−0.0602549	−	0.0602549i	−0.736592	+	0.676337i	$0.763566\pi$
$444$		0			0
$445$	195.397	−	195.397i	0.0208150	−	0.0208150i
$446$	−177.663	+	165.260i	−0.0188623	+	0.0175455i
$447$		0			0
$448$	−3569.64	−	786.726i	−0.376450	−	0.0829672i
$449$	2639.02			0.277378			0.138689	−	0.990336i	$-0.455711\pi$
$449$	2639.02			0.277378			0.138689	+	0.990336i	$0.455711\pi$
$450$		0			0
$451$	9164.08	−	9164.08i	0.956807	−	0.956807i
$452$	779.779	−	10765.2i	0.0811454	−	1.12025i
$453$		0			0
$454$	365.227	−	10097.5i	0.0377554	−	1.04383i
$455$			134.472i			0.0138552i
$456$		0			0
$457$			5546.69i			0.567753i	0.958861	+	0.283876i	$0.0916205\pi$
$457$			5546.69i			0.567753i	−0.958861	+	0.283876i	$0.908379\pi$
$458$	4463.66	+	161.451i	0.455400	+	0.0164719i
$459$		0			0
$460$	1011.17	+	1169.10i	0.102491	+	0.118499i
$461$	−8475.23	+	8475.23i	−0.856249	+	0.856249i	−0.990894	−	0.134645i	$-0.957011\pi$
$461$	−8475.23	+	8475.23i	−0.856249	+	0.856249i	0.134645	+	0.990894i	$0.457011\pi$
$462$		0			0
$463$	−16410.6			−1.64722			−0.823612	−	0.567154i	$-0.808044\pi$
$463$	−16410.6			−1.64722			−0.823612	+	0.567154i	$0.808044\pi$
$464$	424.058	−	316.245i	0.0424276	−	0.0316407i
$465$		0			0
$466$	11085.0	+	11917.0i	1.10194	+	1.18464i
$467$	6689.53	−	6689.53i	0.662858	−	0.662858i	−0.293195	−	0.956053i	$-0.594719\pi$
$467$	6689.53	−	6689.53i	0.662858	−	0.662858i	0.956053	+	0.293195i	$0.0947185\pi$
$468$		0			0
$469$	−252.053	−	252.053i	−0.0248161	−	0.0248161i
$470$	−886.553	−	32.0667i	−0.0870077	−	0.00314708i
$471$		0			0
$472$	−529.145	+	4859.43i	−0.0516014	+	0.473884i
$473$			15902.1i			1.54584i
$474$		0			0
$475$	5416.69	+	5416.69i	0.523231	+	0.523231i
$476$	−4067.43	−	294.624i	−0.391660	−	0.0283699i
$477$		0			0
$478$	−1329.13	+	1236.33i	−0.127182	+	0.118302i
$479$	−7188.55			−0.685707			−0.342853	−	0.939389i	$-0.611393\pi$
$479$	−7188.55			−0.685707			−0.342853	+	0.939389i	$0.611393\pi$
$480$		0			0
$481$	5399.16			0.511810
$482$	5979.86	−	5562.38i	0.565094	−	0.525642i
$483$		0			0
$484$	−287.674	−	20.8376i	−0.0270167	−	0.00195695i
$485$	−1010.75	−	1010.75i	−0.0946301	−	0.0946301i
$486$		0			0
$487$		−	11181.6i		−	1.04042i	−0.854038	−	0.520210i	$-0.825854\pi$
$487$		−	11181.6i		−	1.04042i	0.854038	−	0.520210i	$-0.174146\pi$
$488$	−16732.6	−	1822.02i	−1.55215	−	0.169014i
$489$		0			0
$490$	752.856	+	27.2309i	0.0694093	+	0.00251054i
$491$	−11679.8	−	11679.8i	−1.07353	−	1.07353i	−0.997073	−	0.0764529i	$-0.975641\pi$
$491$	−11679.8	−	11679.8i	−1.07353	−	1.07353i	−0.0764529	−	0.997073i	$-0.524359\pi$
$492$		0			0
$493$	417.321	−	417.321i	0.0381241	−	0.0381241i
$494$	2454.38	+	2638.59i	0.223538	+	0.240315i
$495$		0			0
$496$	6827.63	+	994.336i	0.618084	+	0.0900141i
$497$	5602.28			0.505627
$498$		0			0
$499$	−2094.26	+	2094.26i	−0.187880	+	0.187880i	−0.794779	−	0.606899i	$-0.792413\pi$
$499$	−2094.26	+	2094.26i	−0.187880	+	0.187880i	0.606899	+	0.794779i	$0.292413\pi$
$500$	1189.32	+	1375.07i	0.106376	+	0.122990i
$501$		0			0
$502$	−9464.00	−	342.314i	−0.841433	−	0.0304347i
$503$			4293.63i			0.380604i	0.981726	+	0.190302i	$0.0609466\pi$
$503$			4293.63i			0.380604i	−0.981726	+	0.190302i	$0.939053\pi$
$504$		0			0
$505$			76.8912i			0.00677548i
$506$	779.391	−	21547.9i	0.0684746	−	1.89313i
$507$		0			0
$508$	30.1762	−	416.598i	0.00263554	−	0.0363849i
$509$	9115.13	−	9115.13i	0.793755	−	0.793755i	−0.188348	−	0.982102i	$-0.560313\pi$
$509$	9115.13	−	9115.13i	0.793755	−	0.793755i	0.982102	+	0.188348i	$0.0603132\pi$
$510$		0			0
$511$	−5712.95			−0.494571
$512$	−10380.9	+	5143.34i	−0.896048	+	0.443956i
$513$		0			0
$514$	10587.8	−	9848.59i	0.908574	−	0.845142i
$515$	−1136.73	+	1136.73i	−0.0972631	+	0.0972631i
$516$		0			0
$517$	8750.49	+	8750.49i	0.744383	+	0.744383i
$518$	−190.825	+	5275.75i	−0.0161860	+	0.447497i
$519$		0			0
$520$	266.974	+	332.221i	0.0225146	+	0.0280170i
$521$		−	23150.3i		−	1.94671i	−0.229309	−	0.973354i	$-0.573647\pi$
$521$		−	23150.3i		−	1.94671i	0.229309	−	0.973354i	$-0.426353\pi$
$522$		0			0
$523$	−8510.52	−	8510.52i	−0.711547	−	0.711547i	0.255312	−	0.966859i	$-0.417822\pi$
$523$	−8510.52	−	8510.52i	−0.711547	−	0.711547i	−0.966859	+	0.255312i	$0.917822\pi$
$524$	−2871.33	−	3319.78i	−0.239379	−	0.276766i
$525$		0			0
$526$	−10588.2	−	11382.9i	−0.877693	−	0.943569i
$527$	7697.69			0.636274
$528$		0			0
$529$	−32711.4			−2.68854
$530$	620.939	+	667.543i	0.0508903	+	0.0547099i
$531$		0			0
$532$	−2665.03	+	2305.02i	−0.217187	+	0.187849i
$533$	−5259.19	−	5259.19i	−0.427394	−	0.427394i
$534$		0			0
$535$			846.884i			0.0684373i
$536$	−1123.13	−	122.298i	−0.0905069	−	0.00985533i
$537$		0			0
$538$	−357.756	+	9890.92i	−0.0286690	+	0.792617i
$539$	−7430.87	−	7430.87i	−0.593822	−	0.593822i
$540$		0			0
$541$	3403.84	−	3403.84i	0.270504	−	0.270504i	−0.558799	−	0.829303i	$-0.688738\pi$
$541$	3403.84	−	3403.84i	0.270504	−	0.270504i	0.829303	+	0.558799i	$0.188738\pi$
$542$	3559.15	−	3310.67i	0.282064	−	0.262372i
$543$		0			0
$544$	−10633.8	+	7347.40i	−0.838086	+	0.579076i
$545$	422.780			0.0332292
$546$		0			0
$547$	15672.4	−	15672.4i	1.22505	−	1.22505i	0.259237	−	0.965814i	$-0.416529\pi$
$547$	15672.4	−	15672.4i	1.22505	−	1.22505i	0.965814	−	0.259237i	$-0.0834710\pi$
$548$	6343.76	+	459.510i	0.494511	+	0.0358199i
$549$		0			0
$550$	456.822	−	12629.8i	0.0354163	−	0.979159i
$551$		−	509.930i		−	0.0394261i
$552$		0			0
$553$			3912.76i			0.300882i
$554$	18878.4	+	682.834i	1.44777	+	0.0523661i
$555$		0			0
$556$	14621.5	−	12646.3i	1.11527	−	0.964610i
$557$	−6285.58	+	6285.58i	−0.478149	+	0.478149i	−0.904539	−	0.426391i	$-0.859785\pi$
$557$	−6285.58	+	6285.58i	−0.478149	+	0.478149i	0.426391	+	0.904539i	$0.359785\pi$
$558$		0			0
$559$	9126.11			0.690507
$560$	−334.063	+	249.130i	−0.0252085	+	0.0187994i
$561$		0			0
$562$	−4899.23	−	5266.94i	−0.367725	−	0.395325i
$563$	1763.14	−	1763.14i	0.131985	−	0.131985i	−0.638028	−	0.770013i	$-0.720250\pi$
$563$	1763.14	−	1763.14i	0.131985	−	0.131985i	0.770013	+	0.638028i	$0.220250\pi$
$564$		0			0
$565$	−870.114	−	870.114i	−0.0647894	−	0.0647894i
$566$	12818.9	+	463.661i	0.951977	+	0.0344331i
$567$		0			0
$568$	13840.8	−	11122.5i	1.02244	−	0.821639i
$569$			1150.05i			0.0847323i	0.999102	+	0.0423662i	$0.0134896\pi$
$569$			1150.05i			0.0847323i	−0.999102	+	0.0423662i	$0.986510\pi$
$570$		0			0
$571$	−4853.30	−	4853.30i	−0.355699	−	0.355699i	0.506526	−	0.862225i	$-0.330930\pi$
$571$	−4853.30	−	4853.30i	−0.355699	−	0.355699i	−0.862225	+	0.506526i	$0.830930\pi$
$572$	429.521	−	5929.74i	0.0313971	−	0.433453i
$573$		0			0
$574$	5324.87	−	4953.11i	0.387205	−	0.360172i
$575$	−26304.4			−1.90778
$576$		0			0
$577$	−5152.84			−0.371777			−0.185889	−	0.982571i	$-0.559516\pi$
$577$	−5152.84			−0.371777			−0.185889	+	0.982571i	$0.559516\pi$
$578$	−383.759	+	356.967i	−0.0276164	+	0.0256883i
$579$		0			0
$580$	4.35708	−	60.1516i	0.000311928	−	0.00430631i
$581$	−3315.69	−	3315.69i	−0.236761	−	0.236761i
$582$		0			0
$583$		−	12717.6i		−	0.903449i
$584$	−14114.2	+	11342.2i	−1.00008	+	0.803672i
$585$		0			0
$586$	23630.1	+	854.705i	1.66579	+	0.0602517i
$587$	−12549.2	−	12549.2i	−0.882387	−	0.882387i	0.111390	−	0.993777i	$-0.464470\pi$
$587$	−12549.2	−	12549.2i	−0.882387	−	0.882387i	−0.993777	+	0.111390i	$0.964470\pi$
$588$		0			0
$589$	4702.96	−	4702.96i	0.329002	−	0.329002i
$590$	379.558	+	408.046i	0.0264850	+	0.0284728i
$591$		0			0
$592$	10002.8	+	13412.9i	0.694447	+	0.931195i
$593$	1116.75			0.0773347			0.0386674	−	0.999252i	$-0.487689\pi$
$593$	1116.75			0.0773347			0.0386674	+	0.999252i	$0.487689\pi$
$594$		0			0
$595$	−328.756	+	328.756i	−0.0226515	+	0.0226515i
$596$	595.829	−	515.341i	0.0409498	−	0.0354181i
$597$		0			0
$598$	−12366.2	−	447.286i	−0.845637	−	0.0305868i
$599$			15827.4i			1.07962i	0.841788	+	0.539808i	$0.181503\pi$
$599$			15827.4i			1.07962i	−0.841788	+	0.539808i	$0.818497\pi$
$600$		0			0
$601$			12216.9i			0.829180i	0.910008	+	0.414590i	$0.136075\pi$
$601$			12216.9i			0.829180i	−0.910008	+	0.414590i	$0.863925\pi$
$602$	−322.548	+	8917.52i	−0.0218373	+	0.603739i
$603$		0			0
$604$	−12507.1	−	905.951i	−0.842560	−	0.0610308i
$605$	−23.2516	+	23.2516i	−0.00156250	+	0.00156250i
$606$		0			0
$607$	−24175.5			−1.61656			−0.808282	−	0.588795i	$-0.799602\pi$
$607$	−24175.5			−1.61656			−0.808282	+	0.588795i	$0.799602\pi$
$608$	−2007.83	+	10985.7i	−0.133928	+	0.732780i
$609$		0			0
$610$	−1405.04	+	1306.94i	−0.0932594	+	0.0867485i
$611$	5021.84	−	5021.84i	0.332507	−	0.332507i
$612$		0			0
$613$	12893.7	+	12893.7i	0.849544	+	0.849544i	0.990076	−	0.140532i	$-0.0448812\pi$
$613$	12893.7	+	12893.7i	0.849544	+	0.849544i	−0.140532	+	0.990076i	$0.544881\pi$
$614$	−168.044	+	4645.95i	−0.0110451	+	0.305367i
$615$		0			0
$616$	5779.03	+	629.280i	0.377993	+	0.0411598i
$617$		−	13762.7i		−	0.897998i	−0.893532	−	0.448999i	$-0.851781\pi$
$617$		−	13762.7i		−	0.897998i	0.893532	−	0.448999i	$-0.148219\pi$
$618$		0			0
$619$	−326.797	−	326.797i	−0.0212199	−	0.0212199i	0.696417	−	0.717637i	$-0.254776\pi$
$619$	−326.797	−	326.797i	−0.0212199	−	0.0212199i	−0.717637	+	0.696417i	$0.754776\pi$
$620$	594.948	−	514.579i	0.0385382	−	0.0333323i
$621$		0			0
$622$	4541.07	+	4881.90i	0.292734	+	0.314705i
$623$	−2163.04			−0.139101
$624$		0			0
$625$	−15313.7			−0.980080
$626$	7293.25	+	7840.65i	0.465650	+	0.500600i
$627$		0			0
$628$	−12865.8	−	14875.2i	−0.817517	−	0.945199i
$629$	13199.8	+	13199.8i	0.836742	+	0.836742i
$630$		0			0
$631$			12260.2i			0.773487i	0.922187	+	0.386744i	$0.126400\pi$
$631$			12260.2i			0.773487i	−0.922187	+	0.386744i	$0.873600\pi$
$632$	7768.22	+	9666.72i	0.488929	+	0.608420i
$633$		0			0
$634$	−453.350	+	12533.8i	−0.0283988	+	0.785146i
$635$	−33.6721	−	33.6721i	−0.00210431	−	0.00210431i
$636$		0			0
$637$	−4264.52	+	4264.52i	−0.265253	+	0.265253i
$638$	−615.992	+	572.986i	−0.0382247	+	0.0355560i
$639$		0			0
$640$	−330.712	+	1278.73i	−0.0204258	+	0.0789783i
$641$	−10329.4			−0.636485			−0.318242	−	0.948009i	$-0.603093\pi$
$641$	−10329.4			−0.636485			−0.318242	+	0.948009i	$0.603093\pi$
$642$		0			0
$643$	−19299.9	+	19299.9i	−1.18369	+	1.18369i	−0.204911	+	0.978781i	$0.565691\pi$
$643$	−19299.9	+	19299.9i	−1.18369	+	1.18369i	−0.978781	+	0.204911i	$0.934309\pi$
$644$	874.126	−	12067.7i	0.0534866	−	0.738409i
$645$		0			0
$646$	−450.363	+	12451.2i	−0.0274292	+	0.758340i
$647$		−	8657.07i		−	0.526035i	−0.964791	−	0.263017i	$-0.915282\pi$
$647$		−	8657.07i		−	0.526035i	0.964791	−	0.263017i	$-0.0847177\pi$
$648$		0			0
$649$		−	7773.84i		−	0.470185i
$650$	−7248.15	−	262.167i	−0.437378	−	0.0158200i
$651$		0			0
$652$	19877.3	+	22981.8i	1.19395	+	1.38042i
$653$	−5966.31	+	5966.31i	−0.357549	+	0.357549i	−0.862909	−	0.505360i	$-0.831360\pi$
$653$	−5966.31	+	5966.31i	−0.357549	+	0.357549i	0.505360	+	0.862909i	$0.331360\pi$
$654$		0			0
$655$	−500.405			−0.0298511
$656$	3321.72	−	22808.7i	0.197701	−	1.35752i
$657$		0			0
$658$	4729.57	+	5084.55i	0.280209	+	0.301240i
$659$	−7127.52	+	7127.52i	−0.421318	+	0.421318i	−0.885657	−	0.464339i	$-0.846292\pi$
$659$	−7127.52	+	7127.52i	−0.421318	+	0.421318i	0.464339	+	0.885657i	$0.346292\pi$
$660$		0			0
$661$	2386.19	+	2386.19i	0.140412	+	0.140412i	0.773819	−	0.633407i	$-0.218344\pi$
$661$	2386.19	+	2386.19i	0.140412	+	0.140412i	−0.633407	+	0.773819i	$0.718344\pi$
$662$	6931.93	+	250.729i	0.406974	+	0.0147203i
$663$		0			0
$664$	−14774.4	−	1608.80i	−0.863494	−	0.0940261i
$665$			401.711i			0.0234251i
$666$		0			0
$667$	1238.16	+	1238.16i	0.0718765	+	0.0718765i
$668$	219.526	+	15.9013i	0.0127151	+	0.000921020i
$669$		0			0
$670$	−94.3089	+	87.7247i	−0.00543802	+	0.00505836i
$671$	26767.9			1.54003
$672$		0			0
$673$	−3709.39			−0.212461			−0.106231	−	0.994342i	$-0.533878\pi$
$673$	−3709.39			−0.212461			−0.106231	+	0.994342i	$0.533878\pi$
$674$	−12071.6	+	11228.8i	−0.689880	+	0.641716i
$675$		0			0
$676$	14127.0	+	1023.29i	0.803769	+	0.0582210i
$677$	1602.20	+	1602.20i	0.0909564	+	0.0909564i	0.751121	−	0.660165i	$-0.229513\pi$
$677$	1602.20	+	1602.20i	0.0909564	+	0.0909564i	−0.660165	+	0.751121i	$0.729513\pi$
$678$		0			0
$679$			11188.9i			0.632388i
$680$	−159.514	+	1464.91i	−0.00899572	+	0.0826127i
$681$		0			0
$682$	−10965.7	−	396.629i	−0.615684	−	0.0222694i
$683$	15495.9	+	15495.9i	0.868130	+	0.868130i	0.992265	−	0.124135i	$-0.0396157\pi$
$683$	15495.9	+	15495.9i	0.868130	+	0.868130i	−0.124135	+	0.992265i	$0.539616\pi$
$684$		0			0
$685$	512.743	−	512.743i	0.0285999	−	0.0285999i
$686$	−8733.63	−	9389.13i	−0.486081	−	0.522564i
$687$		0			0
$688$	16907.6	+	22671.7i	0.936912	+	1.25632i
$689$	−7298.55			−0.403560
$690$		0			0
$691$	6337.43	−	6337.43i	0.348896	−	0.348896i	−0.510802	−	0.859698i	$-0.670652\pi$
$691$	6337.43	−	6337.43i	0.348896	−	0.348896i	0.859698	+	0.510802i	$0.170652\pi$
$692$	22535.5	+	26055.1i	1.23796	+	1.43131i
$693$		0			0
$694$	−2863.06	−	103.557i	−0.156600	−	0.00566424i
$695$		−	2203.96i		−	0.120289i
$696$		0			0
$697$		−	25715.3i		−	1.39747i
$698$	634.499	−	17542.1i	0.0344071	−	0.951258i
$699$		0			0
$700$	512.349	−	7073.22i	0.0276642	−	0.381918i
$701$	952.656	−	952.656i	0.0513285	−	0.0513285i	−0.680977	−	0.732305i	$-0.738444\pi$
$701$	952.656	−	952.656i	0.0513285	−	0.0513285i	0.732305	+	0.680977i	$0.238444\pi$
$702$		0			0
$703$	16129.0			0.865318
$704$	15526.8	−	9918.74i	0.831233	−	0.531004i
$705$		0			0
$706$	19361.1	−	18009.5i	1.03211	−	0.960049i
$707$	425.592	−	425.592i	0.0226394	−	0.0226394i
$708$		0			0
$709$	−20781.1	−	20781.1i	−1.10078	−	1.10078i	−0.994317	−	0.106461i	$-0.966048\pi$
$709$	−20781.1	−	20781.1i	−1.10078	−	1.10078i	−0.106461	−	0.994317i	$-0.533952\pi$
$710$	73.1719	−	2022.99i	0.00386774	−	0.106932i
$711$		0			0
$712$	−5343.91	+	4294.39i	−0.281280	+	0.226038i
$713$			22838.4i			1.19959i
$714$		0			0
$715$	−479.280	−	479.280i	−0.0250686	−	0.0250686i
$716$	−2707.39	−	3130.24i	−0.141313	−	0.163383i
$717$		0			0
$718$	24139.9	+	25951.7i	1.25472	+	1.34890i
$719$	1927.96			0.100001			0.0500006	−	0.998749i	$-0.484078\pi$
$719$	1927.96			0.100001			0.0500006	+	0.998749i	$0.484078\pi$
$720$		0			0
$721$	12583.6			0.649984
$722$	−5881.15	−	6322.56i	−0.303149	−	0.325902i
$723$		0			0
$724$	−14864.5	+	12856.5i	−0.763032	+	0.659958i
$725$	725.717	+	725.717i	0.0371758	+	0.0371758i
$726$		0			0
$727$			5482.27i			0.279678i	0.990174	+	0.139839i	$0.0446585\pi$
$727$			5482.27i			0.279678i	−0.990174	+	0.139839i	$0.955341\pi$
$728$	361.139	−	3316.54i	0.0183856	−	0.168845i
$729$		0			0
$730$	−74.6173	+	2062.95i	−0.00378316	+	0.104594i
$731$	22311.4	+	22311.4i	1.12889	+	1.12889i
$732$		0			0
$733$	15048.8	−	15048.8i	0.758311	−	0.758311i	−0.217704	−	0.976015i	$-0.569857\pi$
$733$	15048.8	−	15048.8i	0.758311	−	0.758311i	0.976015	+	0.217704i	$0.0698568\pi$
$734$	−19212.2	+	17870.9i	−0.966123	+	0.898673i
$735$		0			0
$736$	−21799.2	−	31549.5i	−1.09175	−	1.58007i
$737$	1796.72			0.0898004
$738$		0			0
$739$	12622.3	−	12622.3i	0.628306	−	0.628306i	−0.319335	−	0.947642i	$-0.603460\pi$
$739$	12622.3	−	12622.3i	0.628306	−	0.628306i	0.947642	+	0.319335i	$0.103460\pi$
$740$	1902.59	+	137.814i	0.0945144	+	0.00684615i
$741$		0			0
$742$	257.956	−	7131.73i	0.0127626	−	0.352849i
$743$			2335.45i			0.115315i	0.998336	+	0.0576576i	$0.0183632\pi$
$743$			2335.45i			0.115315i	−0.998336	+	0.0576576i	$0.981637\pi$
$744$		0			0
$745$		−	89.8119i		−	0.00441672i
$746$	−7056.67	−	255.241i	−0.346331	−	0.0125268i
$747$		0			0
$748$	15547.1	−	13446.9i	0.759969	−	0.657309i
$749$	4687.49	−	4687.49i	0.228674	−	0.228674i
$750$		0			0
$751$	−3513.73			−0.170729			−0.0853647	−	0.996350i	$-0.527206\pi$
$751$	−3513.73			−0.170729			−0.0853647	+	0.996350i	$0.527206\pi$
$752$	21779.3	+	3171.81i	1.05613	+	0.153809i
$753$		0			0
$754$	328.832	+	353.513i	0.0158825	+	0.0170745i
$755$	−1010.90	+	1010.90i	−0.0487292	+	0.0487292i
$756$		0			0
$757$	−10416.0	−	10416.0i	−0.500102	−	0.500102i	0.411368	−	0.911470i	$-0.365051\pi$
$757$	−10416.0	−	10416.0i	−0.500102	−	0.500102i	−0.911470	+	0.411368i	$0.865051\pi$
$758$	−11628.6	−	420.607i	−0.557215	−	0.0201545i
$759$		0			0
$760$	797.539	+	992.452i	0.0380655	+	0.0473685i
$761$			17937.9i			0.854464i	0.904142	+	0.427232i	$0.140511\pi$
$761$			17937.9i			0.854464i	−0.904142	+	0.427232i	$0.859489\pi$
$762$		0			0
$763$	−2340.08	−	2340.08i	−0.111031	−	0.111031i
$764$	987.997	−	13639.8i	0.0467860	−	0.645903i
$765$		0			0
$766$	3148.43	−	2928.62i	0.148508	−	0.138140i
$767$	−4461.34			−0.210026
$768$		0			0
$769$	32224.0			1.51109			0.755544	−	0.655097i	$-0.227372\pi$
$769$	32224.0			1.51109			0.755544	+	0.655097i	$0.227372\pi$
$770$	485.264	−	451.386i	0.0227113	−	0.0211257i
$771$		0			0
$772$	1389.74	−	19186.0i	0.0647900	−	0.894457i
$773$	−13719.5	−	13719.5i	−0.638365	−	0.638365i	0.311787	−	0.950152i	$-0.399072\pi$
$773$	−13719.5	−	13719.5i	−0.638365	−	0.638365i	−0.950152	+	0.311787i	$0.899072\pi$
$774$		0			0
$775$			13386.2i			0.620448i
$776$	22214.0	+	27642.9i	1.02762	+	1.27877i
$777$		0			0
$778$	−32352.2	−	1170.18i	−1.49085	−	0.0539243i
$779$	−15710.9	−	15710.9i	−0.722596	−	0.722596i
$780$		0			0
$781$	−19967.5	+	19967.5i	−0.914842	+	0.914842i
$782$	−29139.2	−	31326.3i	−1.33250	−	1.43251i
$783$		0			0
$784$	−18494.9	−	2693.48i	−0.842514	−	0.122699i
$785$	−2242.20			−0.101946
$786$		0			0
$787$	−9919.72	+	9919.72i	−0.449301	+	0.449301i	−0.895122	−	0.445821i	$-0.852912\pi$
$787$	−9919.72	+	9919.72i	−0.449301	+	0.449301i	0.445821	+	0.895122i	$0.352912\pi$
$788$	−23724.8	+	20519.9i	−1.07254	+	0.927654i
$789$		0			0
$790$	1412.90	+	51.1049i	0.0636315	+	0.00230156i
$791$			9632.14i			0.432970i
$792$		0			0
$793$		−	15361.9i		−	0.687915i
$794$	−1286.42	+	35565.8i	−0.0574978	+	1.58965i
$795$		0			0
$796$	−12023.7	−	870.935i	−0.535387	−	0.0387807i
$797$	20018.0	−	20018.0i	0.889679	−	0.889679i	−0.104813	−	0.994492i	$-0.533424\pi$
$797$	20018.0	−	20018.0i	0.889679	−	0.889679i	0.994492	+	0.104813i	$0.0334243\pi$
$798$		0			0
$799$	24554.7			1.08721
$800$	−12777.1	−	18492.0i	−0.564672	−	0.817240i
$801$		0			0
$802$	−8697.59	+	8090.37i	−0.382946	+	0.356211i
$803$	20361.9	−	20361.9i	0.894838	−	0.894838i
$804$		0			0
$805$	−975.392	−	975.392i	−0.0427056	−	0.0427056i
$806$	−227.622	+	6293.10i	−0.00994745	+	0.275019i
$807$		0			0
$808$	206.500	−	1896.40i	0.00899089	−	0.0825683i
$809$		−	9967.99i		−	0.433196i	−0.976261	−	0.216598i	$-0.930504\pi$
$809$		−	9967.99i		−	0.433196i	0.976261	−	0.216598i	$-0.0694961\pi$
$810$		0			0
$811$	16080.2	+	16080.2i	0.696243	+	0.696243i	0.963598	−	0.267355i	$-0.0861498\pi$
$811$	16080.2	+	16080.2i	0.696243	+	0.696243i	−0.267355	+	0.963598i	$0.586150\pi$
$812$	−357.055	+	308.822i	−0.0154312	+	0.0133467i
$813$		0			0
$814$	−18123.5	−	19483.8i	−0.780379	−	0.838950i
$815$	3464.14			0.148888
$816$		0			0
$817$	27262.7			1.16744
$818$	15183.6	+	16323.3i	0.649002	+	0.697713i
$819$		0			0
$820$	−1719.03	−	1987.51i	−0.0732086	−	0.0846426i
$821$	−8235.64	−	8235.64i	−0.350092	−	0.350092i	0.510051	−	0.860144i	$-0.329626\pi$
$821$	−8235.64	−	8235.64i	−0.350092	−	0.350092i	−0.860144	+	0.510051i	$0.829626\pi$
$822$		0			0
$823$			21762.8i			0.921752i	0.887464	+	0.460876i	$0.152465\pi$
$823$			21762.8i			0.921752i	−0.887464	+	0.460876i	$0.847535\pi$
$824$	31088.6	−	24983.0i	1.31435	−	1.05622i
$825$		0			0
$826$	157.679	−	4359.37i	0.00664208	−	0.183634i
$827$	30211.4	+	30211.4i	1.27032	+	1.27032i	0.945921	+	0.324396i	$0.105161\pi$
$827$	30211.4	+	30211.4i	1.27032	+	1.27032i	0.324396	+	0.945921i	$0.394839\pi$
$828$		0			0
$829$	−16821.1	+	16821.1i	−0.704729	+	0.704729i	−0.965422	−	0.260692i	$-0.916049\pi$
$829$	−16821.1	+	16821.1i	−0.704729	+	0.704729i	0.260692	+	0.965422i	$0.416049\pi$
$830$	−1240.61	+	1154.00i	−0.0518821	+	0.0482600i
$831$		0			0
$832$	−5692.29	−	8910.70i	−0.237193	−	0.371302i
$833$	−20851.7			−0.867310
$834$		0			0
$835$	17.7435	−	17.7435i	0.000735375	−	0.000735375i
$836$	1283.12	−	17714.1i	0.0530832	−	0.732840i
$837$		0			0
$838$	−795.612	+	21996.4i	−0.0327971	+	0.906746i
$839$		−	21686.9i		−	0.892389i	−0.894936	−	0.446194i	$-0.852779\pi$
$839$		−	21686.9i		−	0.892389i	0.894936	−	0.446194i	$-0.147221\pi$
$840$		0			0
$841$			24320.7i			0.997199i
$842$	−45179.2	−	1634.14i	−1.84914	−	0.0668837i
$843$		0			0
$844$	14544.8	+	16816.5i	0.593191	+	0.685838i
$845$	1141.84	−	1141.84i	0.0464857	−	0.0464857i
$846$		0			0
$847$	257.395			0.0104418
$848$	−13521.7	−	18131.5i	−0.547568	−	0.734244i
$849$		0			0
$850$	−17079.3	−	18361.2i	−0.689193	−	0.740921i
$851$	−39162.8	+	39162.8i	−1.57754	+	1.57754i
$852$		0			0
$853$	12612.5	+	12612.5i	0.506266	+	0.506266i	0.913378	−	0.407112i	$-0.133464\pi$
$853$	12612.5	+	12612.5i	0.506266	+	0.506266i	−0.407112	+	0.913378i	$0.633464\pi$
$854$	15010.8	+	542.941i	0.601473	+	0.0217553i
$855$		0			0
$856$	2274.40	−	20887.1i	0.0908147	−	0.834001i
$857$		−	46080.3i		−	1.83672i	−0.395741	−	0.918362i	$-0.629512\pi$
$857$		−	46080.3i		−	1.83672i	0.395741	−	0.918362i	$-0.370488\pi$
$858$		0			0
$859$	8935.85	+	8935.85i	0.354933	+	0.354933i	0.861941	−	0.507008i	$-0.169249\pi$
$859$	8935.85	+	8935.85i	0.354933	+	0.354933i	−0.507008	+	0.861941i	$0.669249\pi$
$860$	3215.92	+	232.945i	0.127514	+	0.00923647i
$861$		0			0
$862$	−11241.7	+	10456.9i	−0.444193	+	0.413182i
$863$	−19360.8			−0.763674			−0.381837	−	0.924230i	$-0.624708\pi$
$863$	−19360.8			−0.763674			−0.381837	+	0.924230i	$0.624708\pi$
$864$		0			0
$865$	3927.40			0.154377
$866$	10652.7	−	9908.98i	0.418006	−	0.388823i
$867$		0			0
$868$	−6141.22	−	444.839i	−0.240146	−	0.0173950i
$869$	−13945.7	−	13945.7i	−0.544391	−	0.544391i
$870$		0			0
$871$		−	1031.12i		−	0.0401128i
$872$	−10427.2	−	1135.42i	−0.404943	−	0.0440943i
$873$		0			0
$874$	−36941.8	−	1336.19i	−1.42972	−	0.0517132i
$875$	−1147.24	−	1147.24i	−0.0443242	−	0.0443242i
$876$		0			0
$877$	19139.4	−	19139.4i	0.736933	−	0.736933i	−0.235050	−	0.971983i	$-0.575525\pi$
$877$	19139.4	−	19139.4i	0.736933	−	0.736933i	0.971983	+	0.235050i	$0.0755254\pi$
$878$	−4206.29	−	4521.99i	−0.161680	−	0.173815i
$879$		0			0
$880$	302.715	−	2078.60i	0.0115960	−	0.0796244i
$881$	−4836.79			−0.184967			−0.0924833	−	0.995714i	$-0.529480\pi$
$881$	−4836.79			−0.184967			−0.0924833	+	0.995714i	$0.529480\pi$
$882$		0			0
$883$	−7730.89	+	7730.89i	−0.294638	+	0.294638i	−0.838909	−	0.544271i	$-0.816806\pi$
$883$	−7730.89	+	7730.89i	−0.294638	+	0.294638i	0.544271	+	0.838909i	$0.316806\pi$
$884$	−7717.06	−	8922.34i	−0.293612	−	0.339469i
$885$		0			0
$886$	2245.81	+	81.2314i	0.0851576	+	0.00308016i
$887$		−	12163.5i		−	0.460442i	−0.973138	−	0.230221i	$-0.926055\pi$
$887$		−	12163.5i		−	0.460442i	0.973138	−	0.230221i	$-0.0739448\pi$
$888$		0			0
$889$			372.749i			0.0140625i
$890$	−28.2516	+	781.076i	−0.00106404	+	0.0294177i
$891$		0			0
$892$	49.5818	−	684.501i	0.00186112	−	0.0256937i
$893$	15001.9	−	15001.9i	0.562171	−	0.562171i
$894$		0			0
$895$	−471.835			−0.0176220
$896$	8908.22	−	5247.25i	0.332146	−	0.195645i
$897$		0			0
$898$	−5465.37	+	5083.80i	−0.203098	+	0.188918i
$899$	630.093	−	630.093i	0.0233757	−	0.0233757i
$900$		0			0
$901$	−17843.4	−	17843.4i	−0.659768	−	0.659768i
$902$	−1325.00	+	36632.4i	−0.0489108	+	1.35224i
$903$		0			0
$904$	19123.2	+	23796.8i	0.703572	+	0.875519i
$905$			2240.59i			0.0822981i
$906$		0			0
$907$	−8264.83	−	8264.83i	−0.302568	−	0.302568i	0.539450	−	0.842018i	$-0.318632\pi$
$907$	−8264.83	−	8264.83i	−0.302568	−	0.302568i	−0.842018	+	0.539450i	$0.818632\pi$
$908$	18695.4	+	21615.3i	0.683292	+	0.790011i
$909$		0			0
$910$	−259.047	−	278.489i	−0.00943661	−	0.0101449i
$911$	41364.8			1.50437			0.752183	−	0.658955i	$-0.229001\pi$
$911$	41364.8			1.50437			0.752183	+	0.658955i	$0.229001\pi$
$912$		0			0
$913$	23635.3			0.856753
$914$	−10685.1	−	11487.1i	−0.386688	−	0.415711i
$915$		0			0
$916$	−9555.20	+	8264.44i	−0.344665	+	0.298106i
$917$	2769.74	+	2769.74i	0.0997434	+	0.0997434i
$918$		0			0
$919$		−	36966.7i		−	1.32690i	−0.748221	−	0.663449i	$-0.769092\pi$
$919$		−	36966.7i		−	1.32690i	0.748221	−	0.663449i	$-0.230908\pi$
$920$	−4346.26	−	473.266i	−0.155752	−	0.0169599i
$921$		0			0
$922$	1225.40	−	33878.8i	0.0437704	−	1.21013i
$923$	11459.2	+	11459.2i	0.408649	+	0.408649i
$924$		0			0
$925$	−22954.4	+	22954.4i	−0.815929	+	0.815929i
$926$	33986.1	−	31613.3i	1.20610	−	1.12190i
$927$		0			0
$928$	−269.004	+	1471.84i	−0.00951563	+	0.0520643i
$929$	18882.5			0.666862			0.333431	−	0.942774i	$-0.391794\pi$
$929$	18882.5			0.666862			0.333431	+	0.942774i	$0.391794\pi$
$930$		0			0
$931$	−12739.5	+	12739.5i	−0.448464	+	0.448464i
$932$	−45913.7	−	3325.76i	−1.61368	−	0.116887i
$933$		0			0
$934$	−967.211	+	26740.6i	−0.0338845	+	0.936810i
$935$		−	2343.48i		−	0.0819678i
$936$		0			0
$937$			8581.23i			0.299185i	0.988748	+	0.149593i	$0.0477962\pi$
$937$			8581.23i			0.299185i	−0.988748	+	0.149593i	$0.952204\pi$
$938$	1007.55	+	36.4433i	0.0350723	+	0.00126857i
$939$		0			0
$940$	1897.81	−	1641.45i	0.0658508	−	0.0569554i
$941$	5618.83	−	5618.83i	0.194653	−	0.194653i	−0.603050	−	0.797703i	$-0.706048\pi$
$941$	5618.83	−	5618.83i	0.194653	−	0.194653i	0.797703	+	0.603050i	$0.206048\pi$
$942$		0			0
$943$	76295.1			2.63469
$944$	−8265.35	−	11083.1i	−0.284973	−	0.382125i
$945$		0			0
$946$	−30633.9	−	32933.1i	−1.05285	−	1.13187i
$947$	−18722.7	+	18722.7i	−0.642456	+	0.642456i	−0.951159	−	0.308702i	$-0.900105\pi$
$947$	−18722.7	+	18722.7i	−0.642456	+	0.642456i	0.308702	+	0.951159i	$0.400105\pi$
$948$		0			0
$949$	−11685.5	−	11685.5i	−0.399713	−	0.399713i
$950$	−21652.6	−	783.177i	−0.739477	−	0.0267470i
$951$		0			0
$952$	8991.15	−	7225.33i	0.306098	−	0.245981i
$953$		−	17197.8i		−	0.584565i	−0.956332	−	0.292282i	$-0.905585\pi$
$953$		−	17197.8i		−	0.584565i	0.956332	−	0.292282i	$-0.0944147\pi$
$954$		0			0
$955$	−1102.45	−	1102.45i	−0.0373556	−	0.0373556i
$956$	370.929	−	5120.85i	0.0125488	−	0.173243i
$957$		0			0
$958$	14887.4	−	13848.0i	0.502077	−	0.467025i
$959$	−5676.06			−0.191126
$960$		0			0
$961$	−18168.6			−0.609870
$962$	−11181.6	+	10400.9i	−0.374749	+	0.348586i
$963$		0			0
$964$	−1668.84	+	23039.2i	−0.0557571	+	0.769754i
$965$	−1550.74	−	1550.74i	−0.0517306	−	0.0517306i
$966$		0			0
$967$		−	58259.3i		−	1.93743i	−0.248182	−	0.968713i	$-0.579833\pi$
$967$		−	58259.3i		−	1.93743i	0.248182	−	0.968713i	$-0.420167\pi$
$968$	635.909	−	511.020i	0.0211146	−	0.0169678i
$969$		0			0
$970$	4040.34	+	146.140i	0.133740	+	0.00483738i
$971$	19203.8	+	19203.8i	0.634685	+	0.634685i	0.949239	−	0.314555i	$-0.101855\pi$
$971$	19203.8	+	19203.8i	0.634685	+	0.634685i	−0.314555	+	0.949239i	$0.601855\pi$
$972$		0			0
$973$	−12198.9	+	12198.9i	−0.401930	+	0.401930i
$974$	21540.2	+	23156.9i	0.708615	+	0.761800i
$975$		0			0
$976$	38162.9	−	28460.3i	1.25160	−	0.933394i
$977$	16691.4			0.546578			0.273289	−	0.961932i	$-0.411888\pi$
$977$	16691.4			0.546578			0.273289	+	0.961932i	$0.411888\pi$
$978$		0			0
$979$	7709.41	−	7709.41i	0.251679	−	0.251679i
$980$	−1611.61	+	1393.91i	−0.0525317	+	0.0454354i
$981$		0			0
$982$	46688.6	+	1688.73i	1.51720	+	0.0548774i
$983$			36043.6i			1.16949i	0.811216	+	0.584747i	$0.198806\pi$
$983$			36043.6i			1.16949i	−0.811216	+	0.584747i	$0.801194\pi$
$984$		0			0
$985$			3576.14i			0.115680i
$986$	−60.3387	+	1668.19i	−0.00194886	+	0.0538804i
$987$		0			0
$988$	−10166.0	−	736.371i	−0.327351	−	0.0237116i
$989$	−66196.3	+	66196.3i	−2.12833	+	2.12833i
$990$		0			0
$991$	−48948.9			−1.56904			−0.784518	−	0.620107i	$-0.787089\pi$
$991$	−48948.9			−1.56904			−0.784518	+	0.620107i	$0.787089\pi$
$992$	−16055.4	+	11093.5i	−0.513871	+	0.355059i
$993$		0			0
$994$	−11602.3	+	10792.2i	−0.370222	+	0.344375i
$995$	−971.831	+	971.831i	−0.0309639	+	0.0309639i
$996$		0			0
$997$	−22542.1	−	22542.1i	−0.716062	−	0.716062i	0.251734	−	0.967796i	$-0.418999\pi$
$997$	−22542.1	−	22542.1i	−0.716062	−	0.716062i	−0.967796	+	0.251734i	$0.918999\pi$
$998$	302.800	−	8371.56i	0.00960418	−	0.265528i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.4.k.b.37.3		24
3.2	odd	2		48.4.j.a.37.10	yes	24
4.3	odd	2		576.4.k.b.433.7		24
12.11	even	2		192.4.j.a.49.3		24
16.3	odd	4		576.4.k.b.145.7		24
16.13	even	4	inner	144.4.k.b.109.3		24
24.5	odd	2		384.4.j.b.97.4		24
24.11	even	2		384.4.j.a.97.9		24
48.5	odd	4		384.4.j.b.289.4		24
48.11	even	4		384.4.j.a.289.9		24
48.29	odd	4		48.4.j.a.13.10	✓	24
48.35	even	4		192.4.j.a.145.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.10	✓	24	48.29	odd	4
48.4.j.a.37.10	yes	24	3.2	odd	2
144.4.k.b.37.3		24	1.1	even	1	trivial
144.4.k.b.109.3		24	16.13	even	4	inner
192.4.j.a.49.3		24	12.11	even	2
192.4.j.a.145.3		24	48.35	even	4
384.4.j.a.97.9		24	24.11	even	2
384.4.j.a.289.9		24	48.11	even	4
384.4.j.b.97.4		24	24.5	odd	2
384.4.j.b.289.4		24	48.5	odd	4
576.4.k.b.145.7		24	16.3	odd	4
576.4.k.b.433.7		24	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.07099 + 1.92640i) q^{2} +(0.577966 - 7.97909i) q^{4} +(-0.644922 - 0.644922i) q^{5} +7.13926i q^{7} +(14.1740 + 17.6380i) q^{8} +O(q^{10})\)	\(q+(-2.07099 + 1.92640i) q^{2} +(0.577966 - 7.97909i) q^{4} +(-0.644922 - 0.644922i) q^{5} +7.13926i q^{7} +(14.1740 + 17.6380i) q^{8} +(2.57800 + 0.0932465i) q^{10} +(-25.4455 - 25.4455i) q^{11} +(-14.6030 + 14.6030i) q^{13} +(-13.7531 - 14.7853i) q^{14} +(-63.3319 - 9.22328i) q^{16} -71.4024 q^{17} +(-43.6238 + 43.6238i) q^{19} +(-5.51863 + 4.77315i) q^{20} +(101.715 + 3.67906i) q^{22} -211.845i q^{23} -124.168i q^{25} +(2.11138 - 58.3737i) q^{26} +(56.9649 + 4.12625i) q^{28} +(-5.84463 + 5.84463i) q^{29} -107.807 q^{31} +(148.927 - 102.901i) q^{32} +(147.873 - 137.550i) q^{34} +(4.60426 - 4.60426i) q^{35} +(-184.865 - 184.865i) q^{37} +(6.30739 - 174.381i) q^{38} +(2.23402 - 20.5162i) q^{40} +360.146i q^{41} +(-312.475 - 312.475i) q^{43} +(-217.739 + 188.325i) q^{44} +(408.099 + 438.729i) q^{46} -343.892 q^{47} +292.031 q^{49} +(239.198 + 257.150i) q^{50} +(108.078 + 124.958i) q^{52} +(249.900 + 249.900i) q^{53} +32.8207i q^{55} +(-125.922 + 101.192i) q^{56} +(0.845051 - 23.3632i) q^{58} +(152.755 + 152.755i) q^{59} +(-525.985 + 525.985i) q^{61} +(223.267 - 207.680i) q^{62} +(-110.197 + 500.001i) q^{64} +18.8355 q^{65} +(-35.3052 + 35.3052i) q^{67} +(-41.2681 + 569.727i) q^{68} +(-0.665712 + 18.4050i) q^{70} -784.715i q^{71} +800.215i q^{73} +(738.977 + 26.7289i) q^{74} +(322.866 + 373.292i) q^{76} +(181.662 - 181.662i) q^{77} +548.062 q^{79} +(34.8958 + 46.7924i) q^{80} +(-693.784 - 745.856i) q^{82} +(-464.431 + 464.431i) q^{83} +(46.0489 + 46.0489i) q^{85} +(1249.08 + 45.1794i) q^{86} +(88.1436 - 809.471i) q^{88} +302.977i q^{89} +(-104.254 - 104.254i) q^{91} +(-1690.33 - 122.439i) q^{92} +(712.195 - 662.473i) q^{94} +56.2679 q^{95} +1567.24 q^{97} +(-604.792 + 562.568i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} - 84 q^{8}+O(q^{10}) \) 24 * q - 20 * q^4 - 84 * q^8	\( 24 q - 20 q^{4} - 84 q^{8} + 72 q^{10} + 40 q^{11} + 348 q^{14} - 192 q^{16} + 24 q^{19} - 80 q^{20} + 704 q^{22} + 20 q^{26} - 344 q^{28} - 400 q^{29} - 744 q^{31} + 960 q^{32} - 704 q^{34} + 456 q^{35} + 16 q^{37} - 1256 q^{38} + 1744 q^{40} + 1240 q^{43} + 200 q^{44} - 1432 q^{46} - 1176 q^{49} - 708 q^{50} + 1008 q^{52} - 752 q^{53} - 1344 q^{56} + 1936 q^{58} + 1376 q^{59} - 912 q^{61} + 996 q^{62} - 56 q^{64} - 976 q^{65} - 2256 q^{67} + 1568 q^{68} - 1760 q^{70} + 2740 q^{74} - 1880 q^{76} - 1904 q^{77} + 5992 q^{79} - 712 q^{80} - 40 q^{82} - 2680 q^{83} - 240 q^{85} + 1712 q^{86} - 3936 q^{88} - 3496 q^{91} - 5296 q^{92} + 5272 q^{94} + 7728 q^{95} - 6760 q^{98}+O(q^{100}) \) 24 * q - 20 * q^4 - 84 * q^8 + 72 * q^10 + 40 * q^11 + 348 * q^14 - 192 * q^16 + 24 * q^19 - 80 * q^20 + 704 * q^22 + 20 * q^26 - 344 * q^28 - 400 * q^29 - 744 * q^31 + 960 * q^32 - 704 * q^34 + 456 * q^35 + 16 * q^37 - 1256 * q^38 + 1744 * q^40 + 1240 * q^43 + 200 * q^44 - 1432 * q^46 - 1176 * q^49 - 708 * q^50 + 1008 * q^52 - 752 * q^53 - 1344 * q^56 + 1936 * q^58 + 1376 * q^59 - 912 * q^61 + 996 * q^62 - 56 * q^64 - 976 * q^65 - 2256 * q^67 + 1568 * q^68 - 1760 * q^70 + 2740 * q^74 - 1880 * q^76 - 1904 * q^77 + 5992 * q^79 - 712 * q^80 - 40 * q^82 - 2680 * q^83 - 240 * q^85 + 1712 * q^86 - 3936 * q^88 - 3496 * q^91 - 5296 * q^92 + 5272 * q^94 + 7728 * q^95 - 6760 * q^98

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