LMFDB - Embedded newform 143.2.b.a.12.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(12,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("143.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 19x^{10} + 133x^{8} + 423x^{6} + 601x^{4} + 312x^{2} + 36 $ x^12 + 19x^10 + 133x^8 + 423x^6 + 601x^4 + 312*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			12.12
Root			$2.66546i$ of defining polynomial
Character	$\chi$	$=$	143.12
Dual form			143.2.b.a.12.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.66546i q^{2} -2.17072 q^{3} -5.10468 q^{4} -0.458686i q^{5} -5.78598i q^{6} +1.17072i q^{7} -8.27540i q^{8} +1.71204 q^{9} +O(q^{10})$	\(q+2.66546i q^{2} -2.17072 q^{3} -5.10468 q^{4} -0.458686i q^{5} -5.78598i q^{6} +1.17072i q^{7} -8.27540i q^{8} +1.71204 q^{9} +1.22261 q^{10} +1.00000i q^{11} +11.0808 q^{12} +(-3.50921 - 0.827915i) q^{13} -3.12051 q^{14} +0.995680i q^{15} +11.8484 q^{16} -6.55353 q^{17} +4.56337i q^{18} +5.85202i q^{19} +2.34145i q^{20} -2.54131i q^{21} -2.66546 q^{22} -3.16452 q^{23} +17.9636i q^{24} +4.78961 q^{25} +(2.20677 - 9.35366i) q^{26} +2.79581 q^{27} -5.97616i q^{28} -2.13998 q^{29} -2.65395 q^{30} +8.66805i q^{31} +15.0306i q^{32} -2.17072i q^{33} -17.4682i q^{34} +0.536994 q^{35} -8.73940 q^{36} -8.23483i q^{37} -15.5983 q^{38} +(7.61752 + 1.79717i) q^{39} -3.79581 q^{40} +5.38281i q^{41} +6.77377 q^{42} -3.12946 q^{43} -5.10468i q^{44} -0.785287i q^{45} -8.43490i q^{46} +10.5508i q^{47} -25.7196 q^{48} +5.62941 q^{49} +12.7665i q^{50} +14.2259 q^{51} +(17.9134 + 4.22624i) q^{52} -1.26682 q^{53} +7.45212i q^{54} +0.458686 q^{55} +9.68820 q^{56} -12.7031i q^{57} -5.70404i q^{58} +0.884643i q^{59} -5.08263i q^{60} +5.03768 q^{61} -23.1043 q^{62} +2.00432i q^{63} -16.3668 q^{64} +(-0.379753 + 1.60963i) q^{65} +5.78598 q^{66} -3.84383i q^{67} +33.4537 q^{68} +6.86929 q^{69} +1.43134i q^{70} -5.11327i q^{71} -14.1678i q^{72} +5.92140i q^{73} +21.9496 q^{74} -10.3969 q^{75} -29.8727i q^{76} -1.17072 q^{77} +(-4.79030 + 20.3042i) q^{78} +2.48143 q^{79} -5.43469i q^{80} -11.2050 q^{81} -14.3477 q^{82} -7.40248i q^{83} +12.9726i q^{84} +3.00601i q^{85} -8.34145i q^{86} +4.64531 q^{87} +8.27540 q^{88} -7.39861i q^{89} +2.09315 q^{90} +(0.969259 - 4.10831i) q^{91} +16.1539 q^{92} -18.8159i q^{93} -28.1228 q^{94} +2.68424 q^{95} -32.6273i q^{96} +14.6680i q^{97} +15.0050i q^{98} +1.71204i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} - 14 q^{4} + 12 q^{9}+O(q^{10}) $ 12 * q - 4 * q^3 - 14 * q^4 + 12 * q^9	$ 12 q - 4 q^{3} - 14 q^{4} + 12 q^{9} + 8 q^{10} - 8 q^{13} + 10 q^{16} - 12 q^{17} - 2 q^{22} - 4 q^{23} - 16 q^{25} + 10 q^{26} - 28 q^{27} + 8 q^{29} + 4 q^{30} + 16 q^{35} - 16 q^{36} + 18 q^{38} + 4 q^{39} + 16 q^{40} - 2 q^{42} + 12 q^{43} - 58 q^{48} + 32 q^{49} + 36 q^{52} - 20 q^{53} - 8 q^{55} + 22 q^{56} - 12 q^{61} - 72 q^{62} - 10 q^{64} - 20 q^{65} + 2 q^{66} + 68 q^{68} + 52 q^{69} + 20 q^{74} - 8 q^{75} + 8 q^{77} + 6 q^{78} - 48 q^{79} - 36 q^{81} - 44 q^{82} + 12 q^{87} + 30 q^{88} + 68 q^{90} - 6 q^{92} - 64 q^{94} - 4 q^{95}+O(q^{100}) $ 12 * q - 4 * q^3 - 14 * q^4 + 12 * q^9 + 8 * q^10 - 8 * q^13 + 10 * q^16 - 12 * q^17 - 2 * q^22 - 4 * q^23 - 16 * q^25 + 10 * q^26 - 28 * q^27 + 8 * q^29 + 4 * q^30 + 16 * q^35 - 16 * q^36 + 18 * q^38 + 4 * q^39 + 16 * q^40 - 2 * q^42 + 12 * q^43 - 58 * q^48 + 32 * q^49 + 36 * q^52 - 20 * q^53 - 8 * q^55 + 22 * q^56 - 12 * q^61 - 72 * q^62 - 10 * q^64 - 20 * q^65 + 2 * q^66 + 68 * q^68 + 52 * q^69 + 20 * q^74 - 8 * q^75 + 8 * q^77 + 6 * q^78 - 48 * q^79 - 36 * q^81 - 44 * q^82 + 12 * q^87 + 30 * q^88 + 68 * q^90 - 6 * q^92 - 64 * q^94 - 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$-1$	$1$

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 $

$2$			2.66546i			1.88477i	0.334537	+	0.942383i	$0.391420\pi$
$2$			2.66546i			1.88477i	−0.334537	+	0.942383i	$0.608580\pi$
$3$	−2.17072			−1.25327			−0.626634	−	0.779314i	$-0.715568\pi$
$3$	−2.17072			−1.25327			−0.626634	+	0.779314i	$0.715568\pi$
$4$	−5.10468			−2.55234
$5$		−	0.458686i		−	0.205131i	−0.994726	−	0.102565i	$-0.967295\pi$
$5$		−	0.458686i		−	0.205131i	0.994726	−	0.102565i	$-0.0327051\pi$
$6$		−	5.78598i		−	2.36211i
$7$			1.17072i			0.442492i	0.975218	+	0.221246i	$0.0710123\pi$
$7$			1.17072i			0.442492i	−0.975218	+	0.221246i	$0.928988\pi$
$8$		−	8.27540i		−	2.92580i
$9$	1.71204			0.570679
$10$	1.22261			0.386623
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	11.0808			3.19876
$13$	−3.50921	−	0.827915i	−0.973280	−	0.229622i
$13$	−3.50921	−	0.827915i	−0.973280	−	0.229622i
$14$	−3.12051			−0.833993
$15$			0.995680i			0.257083i
$16$	11.8484			2.96210
$17$	−6.55353			−1.58946			−0.794732	−	0.606960i	$-0.792389\pi$
$17$	−6.55353			−1.58946			−0.794732	+	0.606960i	$0.792389\pi$
$18$			4.56337i			1.07560i
$19$			5.85202i			1.34254i	0.741211	+	0.671272i	$0.234252\pi$
$19$			5.85202i			1.34254i	−0.741211	+	0.671272i	$0.765748\pi$
$20$			2.34145i			0.523563i
$21$		−	2.54131i		−	0.554560i
$22$	−2.66546			−0.568278
$23$	−3.16452			−0.659848			−0.329924	−	0.944008i	$-0.607023\pi$
$23$	−3.16452			−0.659848			−0.329924	+	0.944008i	$0.607023\pi$
$24$			17.9636i			3.66681i
$25$	4.78961			0.957921
$26$	2.20677	−	9.35366i	0.432784	−	1.83440i
$27$	2.79581			0.538054
$28$		−	5.97616i		−	1.12939i
$29$	−2.13998			−0.397385			−0.198692	−	0.980062i	$-0.563669\pi$
$29$	−2.13998			−0.397385			−0.198692	+	0.980062i	$0.563669\pi$
$30$	−2.65395			−0.484542
$31$			8.66805i			1.55683i	0.627752	+	0.778414i	$0.283975\pi$
$31$			8.66805i			1.55683i	−0.627752	+	0.778414i	$0.716025\pi$
$32$			15.0306i			2.65707i
$33$		−	2.17072i		−	0.377874i
$34$		−	17.4682i		−	2.99577i
$35$	0.536994			0.0907686
$36$	−8.73940			−1.45657
$37$		−	8.23483i		−	1.35380i	−0.736076	−	0.676899i	$-0.763324\pi$
$37$		−	8.23483i		−	1.35380i	0.736076	−	0.676899i	$-0.236676\pi$
$38$	−15.5983			−2.53038
$39$	7.61752	+	1.79717i	1.21978	+	0.287778i
$40$	−3.79581			−0.600170
$41$			5.38281i			0.840653i	0.907373	+	0.420327i	$0.138085\pi$
$41$			5.38281i			0.840653i	−0.907373	+	0.420327i	$0.861915\pi$
$42$	6.77377			1.04522
$43$	−3.12946			−0.477238			−0.238619	−	0.971113i	$-0.576695\pi$
$43$	−3.12946			−0.477238			−0.238619	+	0.971113i	$0.576695\pi$
$44$		−	5.10468i		−	0.769559i
$45$		−	0.785287i		−	0.117064i
$46$		−	8.43490i		−	1.24366i
$47$			10.5508i			1.53899i	0.638651	+	0.769497i	$0.279493\pi$
$47$			10.5508i			1.53899i	−0.638651	+	0.769497i	$0.720507\pi$
$48$	−25.7196			−3.71230
$49$	5.62941			0.804201
$50$			12.7665i			1.80546i
$51$	14.2259			1.99202
$52$	17.9134	+	4.22624i	2.48414	+	0.586074i
$53$	−1.26682			−0.174011			−0.0870054	−	0.996208i	$-0.527730\pi$
$53$	−1.26682			−0.174011			−0.0870054	+	0.996208i	$0.527730\pi$
$54$			7.45212i			1.01411i
$55$	0.458686			0.0618492
$56$	9.68820			1.29464
$57$		−	12.7031i		−	1.68257i
$58$		−	5.70404i		−	0.748977i
$59$			0.884643i			0.115171i	0.998341	+	0.0575854i	$0.0183401\pi$
$59$			0.884643i			0.115171i	−0.998341	+	0.0575854i	$0.981660\pi$
$60$		−	5.08263i		−	0.656164i
$61$	5.03768			0.645009			0.322505	−	0.946568i	$-0.395475\pi$
$61$	5.03768			0.645009			0.322505	+	0.946568i	$0.395475\pi$
$62$	−23.1043			−2.93425
$63$			2.00432i			0.252521i
$64$	−16.3668			−2.04585
$65$	−0.379753	+	1.60963i	−0.0471026	+	0.199649i
$66$	5.78598			0.712204
$67$		−	3.84383i		−	0.469598i	−0.972044	−	0.234799i	$-0.924557\pi$
$67$		−	3.84383i		−	0.469598i	0.972044	−	0.234799i	$-0.0754432\pi$
$68$	33.4537			4.05685
$69$	6.86929			0.826966
$70$			1.43134i			0.171077i
$71$		−	5.11327i		−	0.606833i	−0.952858	−	0.303416i	$-0.901873\pi$
$71$		−	5.11327i		−	0.606833i	0.952858	−	0.303416i	$-0.0981273\pi$
$72$		−	14.1678i		−	1.66969i
$73$			5.92140i			0.693047i	0.938041	+	0.346524i	$0.112638\pi$
$73$			5.92140i			0.693047i	−0.938041	+	0.346524i	$0.887362\pi$
$74$	21.9496			2.55159
$75$	−10.3969			−1.20053
$76$		−	29.8727i		−	3.42663i
$77$	−1.17072			−0.133416
$78$	−4.79030	+	20.3042i	−0.542394	+	2.29900i
$79$	2.48143			0.279182			0.139591	−	0.990209i	$-0.455421\pi$
$79$	2.48143			0.279182			0.139591	+	0.990209i	$0.455421\pi$
$80$		−	5.43469i		−	0.607617i
$81$	−11.2050			−1.24500
$82$	−14.3477			−1.58443
$83$		−	7.40248i		−	0.812528i	−0.913756	−	0.406264i	$-0.866831\pi$
$83$		−	7.40248i		−	0.812528i	0.913756	−	0.406264i	$-0.133169\pi$
$84$			12.9726i			1.41543i
$85$			3.00601i			0.326048i
$86$		−	8.34145i		−	0.899481i
$87$	4.64531			0.498029
$88$	8.27540			0.882161
$89$		−	7.39861i		−	0.784251i	−0.919912	−	0.392125i	$-0.871740\pi$
$89$		−	7.39861i		−	0.784251i	0.919912	−	0.392125i	$-0.128260\pi$
$90$	2.09315			0.220638
$91$	0.969259	−	4.10831i	0.101606	−	0.430668i
$92$	16.1539			1.68416
$93$		−	18.8159i		−	1.95112i
$94$	−28.1228			−2.90064
$95$	2.68424			0.275397
$96$		−	32.6273i		−	3.33001i
$97$			14.6680i			1.48931i	0.667447	+	0.744657i	$0.267387\pi$
$97$			14.6680i			1.48931i	−0.667447	+	0.744657i	$0.732613\pi$
$98$			15.0050i			1.51573i
$99$			1.71204i			0.172066i
$100$	−24.4494			−2.44494
$101$	−11.6018			−1.15442			−0.577209	−	0.816596i	$-0.695858\pi$
$101$	−11.6018			−1.15442			−0.577209	+	0.816596i	$0.695858\pi$
$102$			37.9186i			3.75450i
$103$	−3.98768			−0.392918			−0.196459	−	0.980512i	$-0.562944\pi$
$103$	−3.98768			−0.392918			−0.196459	+	0.980512i	$0.562944\pi$
$104$	−6.85133	+	29.0401i	−0.671828	+	2.84762i
$105$	−1.16567			−0.113757
$106$		−	3.37665i		−	0.327970i
$107$	−13.7192			−1.32628			−0.663142	−	0.748493i	$-0.730778\pi$
$107$	−13.7192			−1.32628			−0.663142	+	0.748493i	$0.730778\pi$
$108$	−14.2717			−1.37330
$109$		−	7.12146i		−	0.682112i	−0.940043	−	0.341056i	$-0.889215\pi$
$109$		−	7.12146i		−	0.682112i	0.940043	−	0.341056i	$-0.110785\pi$
$110$			1.22261i			0.116571i
$111$			17.8755i			1.69667i
$112$			13.8712i			1.31070i
$113$	8.48050			0.797778			0.398889	−	0.916999i	$-0.369396\pi$
$113$	8.48050			0.797778			0.398889	+	0.916999i	$0.369396\pi$
$114$	33.8596			3.17125
$115$			1.45152i			0.135355i
$116$	10.9239			1.01426
$117$	−6.00790	−	1.41742i	−0.555430	−	0.131041i
$118$	−2.35798			−0.217070
$119$		−	7.67237i		−	0.703325i
$120$	8.23965			0.752174
$121$	−1.00000			−0.0909091
$122$			13.4277i			1.21569i
$123$		−	11.6846i		−	1.05356i
$124$		−	44.2476i		−	3.97355i
$125$		−	4.49036i		−	0.401630i
$126$	−5.34244			−0.475942
$127$	14.9557			1.32711			0.663553	−	0.748130i	$-0.269048\pi$
$127$	14.9557			1.32711			0.663553	+	0.748130i	$0.269048\pi$
$128$		−	13.5637i		−	1.19887i
$129$	6.79318			0.598106
$130$	−4.29039	−	1.01222i	−0.376292	−	0.0887773i
$131$	−12.1089			−1.05796			−0.528982	−	0.848633i	$-0.677426\pi$
$131$	−12.1089			−1.05796			−0.528982	+	0.848633i	$0.677426\pi$
$132$			11.0808i			0.964464i
$133$	−6.85109			−0.594065
$134$	10.2456			0.885082
$135$		−	1.28240i		−	0.110371i
$136$			54.2331i			4.65045i
$137$		−	7.58680i		−	0.648184i	−0.946026	−	0.324092i	$-0.894941\pi$
$137$		−	7.58680i		−	0.648184i	0.946026	−	0.324092i	$-0.105059\pi$
$138$			18.3098i			1.55864i
$139$	10.7464			0.911494			0.455747	−	0.890109i	$-0.349372\pi$
$139$	10.7464			0.911494			0.455747	+	0.890109i	$0.349372\pi$
$140$	−2.74118			−0.231672
$141$		−	22.9029i		−	1.92877i
$142$	13.6292			1.14374
$143$	0.827915	−	3.50921i	0.0692337	−	0.293455i
$144$	20.2849			1.69041
$145$			0.981579i			0.0815157i
$146$	−15.7833			−1.30623
$147$	−12.2199			−1.00788
$148$			42.0362i			3.45535i
$149$			11.4579i			0.938672i	0.883020	+	0.469336i	$0.155507\pi$
$149$			11.4579i			0.938672i	−0.883020	+	0.469336i	$0.844493\pi$
$150$		−	27.7126i		−	2.26272i
$151$			16.6187i			1.35241i	0.736714	+	0.676205i	$0.236376\pi$
$151$			16.6187i			1.35241i	−0.736714	+	0.676205i	$0.763624\pi$
$152$	48.4278			3.92801
$153$	−11.2199			−0.907074
$154$		−	3.12051i		−	0.251458i
$155$	3.97591			0.319353
$156$	−38.8850	−	9.17400i	−3.11329	−	0.734508i
$157$	−14.1605			−1.13013			−0.565067	−	0.825045i	$-0.691150\pi$
$157$	−14.1605			−1.13013			−0.565067	+	0.825045i	$0.691150\pi$
$158$			6.61414i			0.526193i
$159$	2.74991			0.218082
$160$	6.89434			0.545046
$161$		−	3.70477i		−	0.291977i
$162$		−	29.8666i		−	2.34654i
$163$		−	5.44196i		−	0.426247i	−0.977025	−	0.213124i	$-0.931636\pi$
$163$		−	5.44196i		−	0.426247i	0.977025	−	0.213124i	$-0.0683637\pi$
$164$		−	27.4775i		−	2.14563i
$165$	−0.995680			−0.0775136
$166$	19.7310			1.53142
$167$			0.886440i			0.0685948i	0.999412	+	0.0342974i	$0.0109193\pi$
$167$			0.886440i			0.0685948i	−0.999412	+	0.0342974i	$0.989081\pi$
$168$	−21.0304			−1.62253
$169$	11.6291	+	5.81066i	0.894547	+	0.446973i
$170$	−8.01241			−0.614524
$171$			10.0189i			0.766162i
$172$	15.9749			1.21807
$173$	6.77560			0.515140			0.257570	−	0.966260i	$-0.417078\pi$
$173$	6.77560			0.515140			0.257570	+	0.966260i	$0.417078\pi$
$174$			12.3819i			0.938668i
$175$			5.60730i			0.423872i
$176$			11.8484i			0.893107i
$177$		−	1.92032i		−	0.144340i
$178$	19.7207			1.47813
$179$	1.31745			0.0984711			0.0492356	−	0.998787i	$-0.484321\pi$
$179$	1.31745			0.0984711			0.0492356	+	0.998787i	$0.484321\pi$
$180$			4.00864i			0.298786i
$181$	11.0987			0.824961			0.412481	−	0.910966i	$-0.364662\pi$
$181$	11.0987			0.824961			0.412481	+	0.910966i	$0.364662\pi$
$182$	10.9505	+	2.58352i	0.811708	+	0.191503i
$183$	−10.9354			−0.808369
$184$			26.1877i			1.93058i
$185$	−3.77720			−0.277705
$186$	50.1531			3.67740
$187$		−	6.55353i		−	0.479242i
$188$		−	53.8585i		−	3.92803i
$189$			3.27312i			0.238084i
$190$			7.15473i			0.519059i
$191$	−19.2393			−1.39210			−0.696052	−	0.717991i	$-0.745062\pi$
$191$	−19.2393			−1.39210			−0.696052	+	0.717991i	$0.745062\pi$
$192$	35.5277			2.56399
$193$			19.7460i			1.42135i	0.703523	+	0.710673i	$0.251609\pi$
$193$			19.7460i			1.42135i	−0.703523	+	0.710673i	$0.748391\pi$
$194$	−39.0971			−2.80701
$195$	0.824338	−	3.49405i	0.0590321	−	0.250214i
$196$	−28.7363			−2.05260
$197$			21.0198i			1.49760i	0.662796	+	0.748800i	$0.269370\pi$
$197$			21.0198i			1.49760i	−0.662796	+	0.748800i	$0.730630\pi$
$198$	−4.56337			−0.324304
$199$	−3.72266			−0.263892			−0.131946	−	0.991257i	$-0.542123\pi$
$199$	−3.72266			−0.263892			−0.131946	+	0.991257i	$0.542123\pi$
$200$		−	39.6359i		−	2.80268i
$201$			8.34388i			0.588532i
$202$		−	30.9240i		−	2.17581i
$203$		−	2.50532i		−	0.175839i
$204$	−72.6187			−5.08432
$205$	2.46902			0.172444
$206$		−	10.6290i		−	0.740558i
$207$	−5.41777			−0.376561
$208$	−41.5785	−	9.80947i	−2.88295	−	0.680164i
$209$	−5.85202			−0.404793
$210$		−	3.10703i		−	0.214406i
$211$	−11.9327			−0.821478			−0.410739	−	0.911753i	$-0.634729\pi$
$211$	−11.9327			−0.821478			−0.410739	+	0.911753i	$0.634729\pi$
$212$	6.46670			0.444135
$213$			11.0995i			0.760524i
$214$		−	36.5680i		−	2.49974i
$215$			1.43544i			0.0978961i
$216$		−	23.1365i		−	1.57424i
$217$	−10.1479			−0.688883
$218$	18.9820			1.28562
$219$		−	12.8537i		−	0.868573i
$220$	−2.34145			−0.157860
$221$	22.9977	+	5.42577i	1.54699	+	0.364977i
$222$	−47.6465			−3.19782
$223$		−	2.88605i		−	0.193264i	−0.995320	−	0.0966320i	$-0.969193\pi$
$223$		−	2.88605i		−	0.193264i	0.995320	−	0.0966320i	$-0.0308070\pi$
$224$	−17.5967			−1.17573
$225$	8.19998			0.546666
$226$			22.6044i			1.50362i
$227$			8.00487i			0.531302i	0.964069	+	0.265651i	$0.0855868\pi$
$227$			8.00487i			0.531302i	−0.964069	+	0.265651i	$0.914413\pi$
$228$			64.8453i			4.29449i
$229$		−	26.0987i		−	1.72465i	−0.506356	−	0.862324i	$-0.669008\pi$
$229$		−	26.0987i		−	1.72465i	0.506356	−	0.862324i	$-0.330992\pi$
$230$	−3.86897			−0.255112
$231$	2.54131			0.167206
$232$			17.7092i			1.16267i
$233$	0.160396			0.0105079			0.00525394	−	0.999986i	$-0.498328\pi$
$233$	0.160396			0.0105079			0.00525394	+	0.999986i	$0.498328\pi$
$234$	3.77808	−	16.0138i	0.246981	−	1.04686i
$235$	4.83951			0.315695
$236$		−	4.51582i		−	0.293955i
$237$	−5.38649			−0.349890
$238$	20.4504			1.32560
$239$		−	9.08010i		−	0.587343i	−0.955906	−	0.293672i	$-0.905123\pi$
$239$		−	9.08010i		−	0.587343i	0.955906	−	0.293672i	$-0.0948772\pi$
$240$			11.7972i			0.761507i
$241$		−	0.132631i		−	0.00854350i	−0.999991	−	0.00427175i	$-0.998640\pi$
$241$		−	0.132631i		−	0.00854350i	0.999991	−	0.00427175i	$-0.00135974\pi$
$242$		−	2.66546i		−	0.171342i
$243$	15.9356			1.02227
$244$	−25.7158			−1.64628
$245$		−	2.58213i		−	0.164966i
$246$	31.1448			1.98572
$247$	4.84497	−	20.5360i	0.308278	−	1.30667i
$248$	71.7316			4.55496
$249$			16.0687i			1.01831i
$250$	11.9689			0.756978
$251$	27.5007			1.73583			0.867915	−	0.496713i	$-0.165460\pi$
$251$	27.5007			1.73583			0.867915	+	0.496713i	$0.165460\pi$
$252$		−	10.2314i		−	0.644518i
$253$		−	3.16452i		−	0.198952i
$254$			39.8639i			2.50128i
$255$		−	6.52522i		−	0.408625i
$256$	3.41999			0.213750
$257$	7.78887			0.485856			0.242928	−	0.970044i	$-0.421892\pi$
$257$	7.78887			0.485856			0.242928	+	0.970044i	$0.421892\pi$
$258$			18.1070i			1.12729i
$259$	9.64070			0.599044
$260$	1.93852	−	8.21662i	0.120222	−	0.509573i
$261$	−3.66373			−0.226779
$262$		−	32.2759i		−	1.99401i
$263$	7.74585			0.477629			0.238815	−	0.971065i	$-0.423241\pi$
$263$	7.74585			0.477629			0.238815	+	0.971065i	$0.423241\pi$
$264$	−17.9636			−1.10558
$265$			0.581072i			0.0356949i
$266$		−	18.2613i		−	1.11967i
$267$			16.0603i			0.982876i
$268$			19.6215i			1.19857i
$269$	−3.34660			−0.204046			−0.102023	−	0.994782i	$-0.532532\pi$
$269$	−3.34660			−0.204046			−0.102023	+	0.994782i	$0.532532\pi$
$270$	3.41819			0.208024
$271$			10.5534i			0.641075i	0.947236	+	0.320538i	$0.103864\pi$
$271$			10.5534i			0.641075i	−0.947236	+	0.320538i	$0.896136\pi$
$272$	−77.6489			−4.70815
$273$	−2.10399	+	8.91801i	−0.127339	+	0.539742i
$274$	20.2223			1.22167
$275$			4.78961i			0.288824i
$276$	−35.0655			−2.11070
$277$	10.9571			0.658348			0.329174	−	0.944269i	$-0.393230\pi$
$277$	10.9571			0.658348			0.329174	+	0.944269i	$0.393230\pi$
$278$			28.6440i			1.71795i
$279$			14.8400i			0.888448i
$280$		−	4.44384i		−	0.265570i
$281$		−	16.5005i		−	0.984338i	−0.870500	−	0.492169i	$-0.836204\pi$
$281$		−	16.5005i		−	0.984338i	0.870500	−	0.492169i	$-0.163796\pi$
$282$	61.0467			3.63528
$283$	−1.15458			−0.0686326			−0.0343163	−	0.999411i	$-0.510925\pi$
$283$	−1.15458			−0.0686326			−0.0343163	+	0.999411i	$0.510925\pi$
$284$			26.1016i			1.54884i
$285$	−5.82674			−0.345146
$286$	9.35366	+	2.20677i	0.553094	+	0.130489i
$287$	−6.30177			−0.371982
$288$			25.7330i			1.51633i
$289$	25.9488			1.52640
$290$	−2.61636			−0.153638
$291$		−	31.8403i		−	1.86651i
$292$		−	30.2268i		−	1.76889i
$293$		−	13.4247i		−	0.784281i	−0.919905	−	0.392141i	$-0.871735\pi$
$293$		−	13.4247i		−	0.784281i	0.919905	−	0.392141i	$-0.128265\pi$
$294$		−	32.5716i		−	1.89962i
$295$	0.405773			0.0236250
$296$	−68.1465			−3.96093
$297$			2.79581i			0.162229i
$298$	−30.5407			−1.76918
$299$	11.1050	+	2.61995i	0.642216	+	0.151516i
$300$	53.0729			3.06416
$301$		−	3.66373i		−	0.211174i
$302$	−44.2964			−2.54897
$303$	25.1842			1.44680
$304$			69.3370i			3.97675i
$305$		−	2.31071i		−	0.132311i
$306$		−	29.9062i		−	1.70962i
$307$			30.2535i			1.72666i	0.504643	+	0.863328i	$0.331624\pi$
$307$			30.2535i			1.72666i	−0.504643	+	0.863328i	$0.668376\pi$
$308$	5.97616			0.340524
$309$	8.65615			0.492431
$310$			10.5976i			0.601905i
$311$	−8.48341			−0.481050			−0.240525	−	0.970643i	$-0.577320\pi$
$311$	−8.48341			−0.481050			−0.240525	+	0.970643i	$0.577320\pi$
$312$	14.8723	−	63.0381i	0.841980	−	3.56883i
$313$	−10.7899			−0.609881			−0.304941	−	0.952371i	$-0.598637\pi$
$313$	−10.7899			−0.609881			−0.304941	+	0.952371i	$0.598637\pi$
$314$		−	37.7444i		−	2.13004i
$315$	0.919353			0.0517997
$316$	−12.6669			−0.712568
$317$			19.8347i			1.11403i	0.830504	+	0.557013i	$0.188053\pi$
$317$			19.8347i			1.11403i	−0.830504	+	0.557013i	$0.811947\pi$
$318$			7.32978i			0.411033i
$319$		−	2.13998i		−	0.119816i
$320$			7.50721i			0.419666i
$321$	29.7806			1.66219
$322$	9.87493			0.550308
$323$		−	38.3514i		−	2.13393i
$324$	57.1981			3.17767
$325$	−16.8077	−	3.96539i	−0.932326	−	0.219960i
$326$	14.5053			0.803376
$327$			15.4587i			0.854868i
$328$	44.5449			2.45958
$329$	−12.3521			−0.680991
$330$		−	2.65395i		−	0.146095i
$331$			3.41102i			0.187486i	0.995596	+	0.0937432i	$0.0298833\pi$
$331$			3.41102i			0.187486i	−0.995596	+	0.0937432i	$0.970117\pi$
$332$			37.7873i			2.07385i
$333$		−	14.0983i		−	0.772583i
$334$	−2.36277			−0.129285
$335$	−1.76311			−0.0963290
$336$		−	30.1105i		−	1.64266i
$337$	−7.64192			−0.416282			−0.208141	−	0.978099i	$-0.566741\pi$
$337$	−7.64192			−0.416282			−0.208141	+	0.978099i	$0.566741\pi$
$338$	−15.4881	+	30.9969i	−0.842440	+	1.68601i
$339$	−18.4088			−0.999829
$340$		−	15.3447i		−	0.832185i
$341$	−8.66805			−0.469401
$342$	−26.7049			−1.44404
$343$			14.7855i			0.798344i
$344$			25.8975i			1.39630i
$345$		−	3.15085i		−	0.169636i
$346$			18.0601i			0.970917i
$347$	−23.9328			−1.28478			−0.642390	−	0.766378i	$-0.722057\pi$
$347$	−23.9328			−1.28478			−0.642390	+	0.766378i	$0.722057\pi$
$348$	−23.7128			−1.27114
$349$		−	13.6173i		−	0.728917i	−0.931220	−	0.364458i	$-0.881254\pi$
$349$		−	13.6173i		−	0.728917i	0.931220	−	0.364458i	$-0.118746\pi$
$350$	−14.9460			−0.798899
$351$	−9.81109	−	2.31469i	−0.523677	−	0.123549i
$352$	−15.0306			−0.801136
$353$			3.44816i			0.183527i	0.995781	+	0.0917636i	$0.0292504\pi$
$353$			3.44816i			0.183527i	−0.995781	+	0.0917636i	$0.970750\pi$
$354$	5.11852			0.272046
$355$	−2.34538			−0.124480
$356$			37.7675i			2.00167i
$357$			16.6546i			0.881454i
$358$			3.51162i			0.185595i
$359$			20.5605i			1.08514i	0.840011	+	0.542570i	$0.182549\pi$
$359$			20.5605i			1.08514i	−0.840011	+	0.542570i	$0.817451\pi$
$360$	−6.49857			−0.342505
$361$	−15.2461			−0.802427
$362$			29.5832i			1.55486i
$363$	2.17072			0.113933
$364$	−4.94776	+	20.9716i	−0.259333	+	1.09921i
$365$	2.71606			0.142165
$366$		−	29.1479i		−	1.52359i
$367$	−33.1416			−1.72998			−0.864989	−	0.501790i	$-0.832675\pi$
$367$	−33.1416			−1.72998			−0.864989	+	0.501790i	$0.832675\pi$
$368$	−37.4945			−1.95453
$369$			9.21556i			0.479743i
$370$		−	10.0680i		−	0.523409i
$371$		−	1.48309i		−	0.0769983i
$372$			96.0493i			4.97992i
$373$	7.24503			0.375134			0.187567	−	0.982252i	$-0.439940\pi$
$373$	7.24503			0.375134			0.187567	+	0.982252i	$0.439940\pi$
$374$	17.4682			0.903258
$375$			9.74732i			0.503349i
$376$	87.3122			4.50278
$377$	7.50964	+	1.77172i	0.386766	+	0.0912484i
$378$	−8.72437			−0.448733
$379$			26.9600i			1.38484i	0.721493	+	0.692421i	$0.243456\pi$
$379$			26.9600i			1.38484i	−0.721493	+	0.692421i	$0.756544\pi$
$380$	−13.7022			−0.702907
$381$	−32.4647			−1.66322
$382$		−	51.2815i		−	2.62379i
$383$		−	16.9498i		−	0.866094i	−0.901371	−	0.433047i	$-0.857438\pi$
$383$		−	16.9498i		−	0.866094i	0.901371	−	0.433047i	$-0.142562\pi$
$384$			29.4431i			1.50251i
$385$			0.536994i			0.0273678i
$386$	−52.6321			−2.67890
$387$	−5.35775			−0.272350
$388$		−	74.8757i		−	3.80124i
$389$	2.61306			0.132488			0.0662438	−	0.997803i	$-0.478899\pi$
$389$	2.61306			0.132488			0.0662438	+	0.997803i	$0.478899\pi$
$390$	9.31325	+	2.19724i	0.471595	+	0.111262i
$391$	20.7388			1.04880
$392$		−	46.5856i		−	2.35293i
$393$	26.2852			1.32591
$394$	−56.0275			−2.82262
$395$		−	1.13820i		−	0.0572688i
$396$		−	8.73940i		−	0.439171i
$397$		−	20.0083i		−	1.00419i	−0.864813	−	0.502095i	$-0.832563\pi$
$397$		−	20.0083i		−	1.00419i	0.864813	−	0.502095i	$-0.167437\pi$
$398$		−	9.92260i		−	0.497375i
$399$	14.8718			0.744522
$400$	56.7492			2.83746
$401$			28.1352i			1.40500i	0.711682	+	0.702502i	$0.247934\pi$
$401$			28.1352i			1.40500i	−0.711682	+	0.702502i	$0.752066\pi$
$402$	−22.2403			−1.10924
$403$	7.17641	−	30.4180i	0.357482	−	1.51523i
$404$	59.2233			2.94647
$405$			5.13959i			0.255389i
$406$	6.67784			0.331416
$407$	8.23483			0.408185
$408$		−	117.725i		−	5.82826i
$409$			32.3950i			1.60183i	0.598779	+	0.800914i	$0.295653\pi$
$409$			32.3950i			1.60183i	−0.598779	+	0.800914i	$0.704347\pi$
$410$			6.58107i			0.325016i
$411$			16.4688i			0.812347i
$412$	20.3558			1.00286
$413$	−1.03567			−0.0509621
$414$		−	14.4409i		−	0.709729i
$415$	−3.39541			−0.166674
$416$	12.4441	−	52.7457i	0.610122	−	2.58607i
$417$	−23.3274			−1.14235
$418$		−	15.5983i		−	0.762939i
$419$	7.23409			0.353408			0.176704	−	0.984264i	$-0.443456\pi$
$419$	7.23409			0.353408			0.176704	+	0.984264i	$0.443456\pi$
$420$	5.95035			0.290347
$421$			6.86086i			0.334378i	0.985925	+	0.167189i	$0.0534690\pi$
$421$			6.86086i			0.334378i	−0.985925	+	0.167189i	$0.946531\pi$
$422$		−	31.8060i		−	1.54829i
$423$			18.0634i			0.878271i
$424$			10.4834i			0.509120i
$425$	−31.3888			−1.52258
$426$	−29.5852			−1.43341
$427$			5.89773i			0.285411i
$428$	70.0321			3.38513
$429$	−1.79717	+	7.61752i	−0.0867684	+	0.367777i
$430$	−3.82610			−0.184511
$431$		−	13.2631i		−	0.638863i	−0.947609	−	0.319431i	$-0.896508\pi$
$431$		−	13.2631i		−	0.638863i	0.947609	−	0.319431i	$-0.103492\pi$
$432$	33.1259			1.59377
$433$	9.73932			0.468042			0.234021	−	0.972232i	$-0.424812\pi$
$433$	9.73932			0.468042			0.234021	+	0.972232i	$0.424812\pi$
$434$		−	27.0488i		−	1.29838i
$435$		−	2.13074i		−	0.102161i
$436$			36.3528i			1.74098i
$437$		−	18.5188i		−	0.885875i
$438$	34.2611			1.63706
$439$	−11.7838			−0.562412			−0.281206	−	0.959647i	$-0.590734\pi$
$439$	−11.7838			−0.562412			−0.281206	+	0.959647i	$0.590734\pi$
$440$		−	3.79581i		−	0.180958i
$441$	9.63775			0.458941
$442$	−14.4622	+	61.2995i	−0.687895	+	2.91572i
$443$	−8.14169			−0.386823			−0.193412	−	0.981118i	$-0.561955\pi$
$443$	−8.14169			−0.386823			−0.193412	+	0.981118i	$0.561955\pi$
$444$		−	91.2488i		−	4.33048i
$445$	−3.39364			−0.160874
$446$	7.69264			0.364257
$447$		−	24.8720i		−	1.17641i
$448$		−	19.1609i		−	0.905270i
$449$			35.3317i			1.66741i	0.552211	+	0.833704i	$0.313784\pi$
$449$			35.3317i			1.66741i	−0.552211	+	0.833704i	$0.686216\pi$
$450$			21.8567i			1.03034i
$451$	−5.38281			−0.253467
$452$	−43.2902			−2.03620
$453$		−	36.0746i		−	1.69493i
$454$	−21.3367			−1.00138
$455$	−1.88443	−	0.444585i	−0.0883432	−	0.0208425i
$456$	−105.123			−4.92285
$457$		−	19.6535i		−	0.919350i	−0.888087	−	0.459675i	$-0.847966\pi$
$457$		−	19.6535i		−	0.919350i	0.888087	−	0.459675i	$-0.152034\pi$
$458$	69.5650			3.25056
$459$	−18.3224			−0.855218
$460$		−	7.40955i		−	0.345472i
$461$		−	11.8871i		−	0.553636i	−0.960922	−	0.276818i	$-0.910720\pi$
$461$		−	11.8871i		−	0.553636i	0.960922	−	0.276818i	$-0.0892799\pi$
$462$			6.77377i			0.315144i
$463$		−	33.4104i		−	1.55271i	−0.630293	−	0.776357i	$-0.717065\pi$
$463$		−	33.4104i		−	1.55271i	0.630293	−	0.776357i	$-0.282935\pi$
$464$	−25.3554			−1.17709
$465$	−8.63060			−0.400235
$466$			0.427529i			0.0198049i
$467$	7.45002			0.344746			0.172373	−	0.985032i	$-0.444857\pi$
$467$	7.45002			0.344746			0.172373	+	0.985032i	$0.444857\pi$
$468$	30.6684	+	7.23548i	1.41765	+	0.334460i
$469$	4.50005			0.207793
$470$			12.8995i			0.595010i
$471$	30.7386			1.41636
$472$	7.32078			0.336966
$473$		−	3.12946i		−	0.143893i
$474$		−	14.3575i		−	0.659461i
$475$			28.0289i			1.28605i
$476$			39.1650i			1.79512i
$477$	−2.16884			−0.0993043
$478$	24.2027			1.10700
$479$		−	22.1756i		−	1.01323i	−0.862173	−	0.506614i	$-0.830897\pi$
$479$		−	22.1756i		−	1.01323i	0.862173	−	0.506614i	$-0.169103\pi$
$480$	−14.9657			−0.683088
$481$	−6.81774	+	28.8977i	−0.310862	+	1.31762i
$482$	0.353522			0.0161025
$483$			8.04204i			0.365925i
$484$	5.10468			0.232031
$485$	6.72803			0.305504
$486$			42.4757i			1.92674i
$487$		−	8.84223i		−	0.400680i	−0.979726	−	0.200340i	$-0.935795\pi$
$487$		−	8.84223i		−	0.400680i	0.979726	−	0.200340i	$-0.0642046\pi$
$488$		−	41.6888i		−	1.88717i
$489$			11.8130i			0.534201i
$490$	6.88257			0.310923
$491$	27.1206			1.22393			0.611967	−	0.790883i	$-0.290379\pi$
$491$	27.1206			1.22393			0.611967	+	0.790883i	$0.290379\pi$
$492$			59.6461i			2.68905i
$493$	14.0244			0.631629
$494$	54.7378	+	12.9141i	2.46277	+	0.581032i
$495$	0.785287			0.0352960
$496$			102.702i			4.61148i
$497$	5.98622			0.268518
$498$	−42.8306			−1.91928
$499$			27.8865i			1.24837i	0.781276	+	0.624185i	$0.214569\pi$
$499$			27.8865i			1.24837i	−0.781276	+	0.624185i	$0.785431\pi$
$500$			22.9218i			1.02510i
$501$		−	1.92422i		−	0.0859676i
$502$			73.3021i			3.27163i
$503$	−18.4384			−0.822127			−0.411064	−	0.911607i	$-0.634843\pi$
$503$	−18.4384			−0.822127			−0.411064	+	0.911607i	$0.634843\pi$
$504$	16.5866			0.738824
$505$			5.32157i			0.236807i
$506$	8.43490			0.374977
$507$	−25.2436	−	12.6133i	−1.12111	−	0.560177i
$508$	−76.3441			−3.38722
$509$		−	23.5533i		−	1.04398i	−0.852951	−	0.521992i	$-0.825189\pi$
$509$		−	23.5533i		−	1.04398i	0.852951	−	0.521992i	$-0.174811\pi$
$510$	17.3927			0.770162
$511$	−6.93231			−0.306667
$512$		−	18.0116i		−	0.796006i
$513$			16.3611i			0.722362i
$514$			20.7609i			0.915725i
$515$			1.82909i			0.0805994i
$516$	−34.6770			−1.52657
$517$	−10.5508			−0.464024
$518$			25.6969i			1.12906i
$519$	−14.7080			−0.645608
$520$	13.3203	+	3.14261i	0.584134	+	0.137813i
$521$	22.7100			0.994942			0.497471	−	0.867481i	$-0.334262\pi$
$521$	22.7100			0.994942			0.497471	+	0.867481i	$0.334262\pi$
$522$		−	9.76552i		−	0.427425i
$523$	10.4633			0.457526			0.228763	−	0.973482i	$-0.426532\pi$
$523$	10.4633			0.457526			0.228763	+	0.973482i	$0.426532\pi$
$524$	61.8123			2.70028
$525$		−	12.1719i		−	0.531225i
$526$			20.6463i			0.900219i
$527$		−	56.8063i		−	2.47452i
$528$		−	25.7196i		−	1.11930i
$529$	−12.9858			−0.564601
$530$	−1.54882			−0.0672766
$531$			1.51454i			0.0657255i
$532$	34.9726			1.51626
$533$	4.45651	−	18.8894i	0.193033	−	0.818191i
$534$	−42.8082			−1.85249
$535$			6.29280i			0.272062i
$536$	−31.8092			−1.37395
$537$	−2.85983			−0.123411
$538$		−	8.92023i		−	0.384578i
$539$			5.62941i			0.242476i
$540$			6.54624i			0.281705i
$541$		−	42.1990i		−	1.81428i	−0.420832	−	0.907139i	$-0.638262\pi$
$541$		−	42.1990i		−	1.81428i	0.420832	−	0.907139i	$-0.361738\pi$
$542$	−28.1297			−1.20828
$543$	−24.0922			−1.03390
$544$		−	98.5037i		−	4.22331i
$545$	−3.26651			−0.139922
$546$	−23.7706	−	5.60811i	−1.01729	−	0.240005i
$547$	9.87841			0.422370			0.211185	−	0.977446i	$-0.432268\pi$
$547$	9.87841			0.422370			0.211185	+	0.977446i	$0.432268\pi$
$548$			38.7282i			1.65439i
$549$	8.62470			0.368093
$550$	−12.7665			−0.544366
$551$		−	12.5232i		−	0.533507i
$552$		−	56.8462i		−	2.41953i
$553$			2.90506i			0.123536i
$554$			29.2057i			1.24083i
$555$	8.19925			0.348039
$556$	−54.8567			−2.32644
$557$			27.7902i			1.17751i	0.808312	+	0.588754i	$0.200381\pi$
$557$			27.7902i			1.17751i	−0.808312	+	0.588754i	$0.799619\pi$
$558$	−39.5555			−1.67452
$559$	10.9819	+	2.59092i	0.464486	+	0.109584i
$560$	6.36252			0.268866
$561$			14.2259i			0.600618i
$562$	43.9815			1.85525
$563$	−27.1946			−1.14612			−0.573058	−	0.819515i	$-0.694243\pi$
$563$	−27.1946			−1.14612			−0.573058	+	0.819515i	$0.694243\pi$
$564$			116.912i			4.92288i
$565$		−	3.88989i		−	0.163649i
$566$		−	3.07748i		−	0.129356i
$567$		−	13.1180i		−	0.550904i
$568$	−42.3143			−1.77547
$569$	33.0535			1.38567			0.692837	−	0.721095i	$-0.256361\pi$
$569$	33.0535			1.38567			0.692837	+	0.721095i	$0.256361\pi$
$570$		−	15.5309i		−	0.650519i
$571$	−30.0787			−1.25875			−0.629377	−	0.777100i	$-0.716690\pi$
$571$	−30.0787			−1.25875			−0.629377	+	0.777100i	$0.716690\pi$
$572$	−4.22624	+	17.9134i	−0.176708	+	0.748997i
$573$	41.7631			1.74468
$574$		−	16.7971i		−	0.701099i
$575$	−15.1568			−0.632082
$576$	−28.0205			−1.16752
$577$		−	6.67291i		−	0.277797i	−0.990307	−	0.138898i	$-0.955644\pi$
$577$		−	6.67291i		−	0.277797i	0.990307	−	0.138898i	$-0.0443561\pi$
$578$			69.1654i			2.87690i
$579$		−	42.8630i		−	1.78133i
$580$		−	5.01065i		−	0.208056i
$581$	8.66625			0.359537
$582$	84.8690			3.51793
$583$		−	1.26682i		−	0.0524662i
$584$	49.0019			2.02771
$585$	−0.650151	+	2.75574i	−0.0268804	+	0.113936i
$586$	35.7831			1.47819
$587$			16.5282i			0.682191i	0.940029	+	0.341096i	$0.110798\pi$
$587$			16.5282i			0.682191i	−0.940029	+	0.341096i	$0.889202\pi$
$588$	62.3786			2.57245
$589$	−50.7256			−2.09011
$590$			1.08157i			0.0445277i
$591$		−	45.6282i		−	1.87689i
$592$		−	97.5695i		−	4.01008i
$593$			17.3007i			0.710456i	0.934780	+	0.355228i	$0.115597\pi$
$593$			17.3007i			0.710456i	−0.934780	+	0.355228i	$0.884403\pi$
$594$	−7.45212			−0.305764
$595$	−3.51921			−0.144273
$596$		−	58.4892i		−	2.39581i
$597$	8.08086			0.330728
$598$	−6.98338	+	29.5998i	−0.285572	+	1.21043i
$599$	35.7952			1.46255			0.731276	−	0.682082i	$-0.238925\pi$
$599$	35.7952			1.46255			0.731276	+	0.682082i	$0.238925\pi$
$600$			86.0386i			3.51251i
$601$	−45.7772			−1.86729			−0.933646	−	0.358196i	$-0.883392\pi$
$601$	−45.7772			−1.86729			−0.933646	+	0.358196i	$0.883392\pi$
$602$	9.76552			0.398013
$603$		−	6.58077i		−	0.267990i
$604$		−	84.8331i		−	3.45181i
$605$			0.458686i			0.0186482i
$606$			67.1275i			2.72687i
$607$	−7.60403			−0.308638			−0.154319	−	0.988021i	$-0.549318\pi$
$607$	−7.60403			−0.308638			−0.154319	+	0.988021i	$0.549318\pi$
$608$	−87.9596			−3.56723
$609$			5.43836i			0.220374i
$610$	6.15912			0.249375
$611$	8.73517	−	37.0250i	0.353387	−	1.49787i
$612$	57.2739			2.31516
$613$			5.27304i			0.212976i	0.994314	+	0.106488i	$0.0339606\pi$
$613$			5.27304i			0.212976i	−0.994314	+	0.106488i	$0.966039\pi$
$614$	−80.6394			−3.25434
$615$	−5.35955			−0.216118
$616$			9.68820i			0.390349i
$617$			15.9614i			0.642584i	0.946980	+	0.321292i	$0.104117\pi$
$617$			15.9614i			0.642584i	−0.946980	+	0.321292i	$0.895883\pi$
$618$			23.0726i			0.928117i
$619$		−	20.0005i		−	0.803887i	−0.915665	−	0.401943i	$-0.868335\pi$
$619$		−	20.0005i		−	0.803887i	0.915665	−	0.401943i	$-0.131665\pi$
$620$	−20.2958			−0.815097
$621$	−8.84740			−0.355034
$622$		−	22.6122i		−	0.906667i
$623$	8.66172			0.347024
$624$	90.2554	+	21.2936i	3.61311	+	0.852427i
$625$	21.8884			0.875535
$626$		−	28.7601i		−	1.14948i
$627$	12.7031			0.507313
$628$	72.2850			2.88449
$629$			53.9672i			2.15181i
$630$			2.45050i			0.0976303i
$631$		−	28.7753i		−	1.14553i	−0.819721	−	0.572764i	$-0.805871\pi$
$631$		−	28.7753i		−	1.14553i	0.819721	−	0.572764i	$-0.194129\pi$
$632$		−	20.5348i		−	0.816831i
$633$	25.9025			1.02953
$634$	−52.8686			−2.09968
$635$		−	6.85998i		−	0.272230i
$636$	−14.0374			−0.556620
$637$	−19.7548	−	4.66067i	−0.782713	−	0.184663i
$638$	5.70404			0.225825
$639$		−	8.75410i		−	0.346307i
$640$	−6.22148			−0.245926
$641$	39.5621			1.56261			0.781304	−	0.624150i	$-0.214555\pi$
$641$	39.5621			1.56261			0.781304	+	0.624150i	$0.214555\pi$
$642$			79.3789i			3.13284i
$643$			8.36156i			0.329748i	0.986315	+	0.164874i	$0.0527217\pi$
$643$			8.36156i			0.329748i	−0.986315	+	0.164874i	$0.947278\pi$
$644$			18.9117i			0.745225i
$645$		−	3.11594i		−	0.122690i
$646$	102.224			4.02195
$647$	9.64297			0.379104			0.189552	−	0.981871i	$-0.439296\pi$
$647$	9.64297			0.379104			0.189552	+	0.981871i	$0.439296\pi$
$648$			92.7262i			3.64263i
$649$	−0.884643			−0.0347253
$650$	10.5696	−	44.8004i	0.414573	−	1.75721i
$651$	22.0282			0.863354
$652$			27.7795i			1.08793i
$653$	25.0322			0.979587			0.489794	−	0.871838i	$-0.337072\pi$
$653$	25.0322			0.979587			0.489794	+	0.871838i	$0.337072\pi$
$654$	−41.2046			−1.61123
$655$			5.55420i			0.217021i
$656$			63.7777i			2.49010i
$657$			10.1376i			0.395507i
$658$		−	32.9239i		−	1.28351i
$659$	27.2819			1.06275			0.531375	−	0.847136i	$-0.321675\pi$
$659$	27.2819			1.06275			0.531375	+	0.847136i	$0.321675\pi$
$660$	5.08263			0.197841
$661$		−	1.09069i		−	0.0424229i	−0.999775	−	0.0212114i	$-0.993248\pi$
$661$		−	1.09069i		−	0.0424229i	0.999775	−	0.0212114i	$-0.00675232\pi$
$662$	−9.09193			−0.353368
$663$	−49.9217	−	11.7778i	−1.93880	−	0.457413i
$664$	−61.2585			−2.37729
$665$			3.14250i			0.121861i
$666$	37.5785			1.45614
$667$	6.77201			0.262213
$668$		−	4.52499i		−	0.175077i
$669$			6.26481i			0.242211i
$670$		−	4.69950i		−	0.181557i
$671$			5.03768i			0.194478i
$672$	38.1976			1.47350
$673$	48.0360			1.85165			0.925826	−	0.377950i	$-0.123371\pi$
$673$	48.0360			1.85165			0.925826	+	0.377950i	$0.123371\pi$
$674$		−	20.3692i		−	0.784594i
$675$	13.3908			0.515414
$676$	−59.3629	−	29.6615i	−2.28319	−	1.14083i
$677$	2.28541			0.0878355			0.0439178	−	0.999035i	$-0.486016\pi$
$677$	2.28541			0.0878355			0.0439178	+	0.999035i	$0.486016\pi$
$678$		−	49.0680i		−	1.88444i
$679$	−17.1722			−0.659009
$680$	24.8760			0.953950
$681$		−	17.3763i		−	0.665863i
$682$		−	23.1043i		−	0.884711i
$683$			35.3074i			1.35100i	0.737360	+	0.675500i	$0.236072\pi$
$683$			35.3074i			1.35100i	−0.737360	+	0.675500i	$0.763928\pi$
$684$		−	51.1431i		−	1.95551i
$685$	−3.47996			−0.132962
$686$	−39.4103			−1.50469
$687$			56.6530i			2.16145i
$688$	−37.0791			−1.41363
$689$	4.44553	+	1.04882i	0.169361	+	0.0399568i
$690$	8.39846			0.319724
$691$			31.3666i			1.19324i	0.802523	+	0.596621i	$0.203491\pi$
$691$			31.3666i			1.19324i	−0.802523	+	0.596621i	$0.796509\pi$
$692$	−34.5873			−1.31481
$693$	−2.00432			−0.0761378
$694$		−	63.7920i		−	2.42151i
$695$		−	4.92920i		−	0.186975i
$696$		−	38.4418i		−	1.45713i
$697$		−	35.2764i		−	1.33619i
$698$	36.2963			1.37384
$699$	−0.348175			−0.0131692
$700$		−	28.6235i		−	1.08187i
$701$	−21.8220			−0.824206			−0.412103	−	0.911137i	$-0.635206\pi$
$701$	−21.8220			−0.824206			−0.412103	+	0.911137i	$0.635206\pi$
$702$	6.16973	−	26.1511i	0.232861	−	0.987009i
$703$	48.1903			1.81753
$704$		−	16.3668i		−	0.616846i
$705$	−10.5052			−0.395650
$706$	−9.19094			−0.345906
$707$		−	13.5824i		−	0.510821i
$708$			9.80259i			0.368404i
$709$			36.9873i			1.38909i	0.719451	+	0.694543i	$0.244393\pi$
$709$			36.9873i			1.38909i	−0.719451	+	0.694543i	$0.755607\pi$
$710$		−	6.25153i		−	0.234616i
$711$	4.24829			0.159323
$712$	−61.2265			−2.29456
$713$		−	27.4302i		−	1.02727i
$714$	−44.3921			−1.66133
$715$	−1.60963	−	0.379753i	−0.0601966	−	0.0142020i
$716$	−6.72518			−0.251332
$717$			19.7104i			0.736098i
$718$	−54.8031			−2.04523
$719$	−11.0686			−0.412788			−0.206394	−	0.978469i	$-0.566173\pi$
$719$	−11.0686			−0.412788			−0.206394	+	0.978469i	$0.566173\pi$
$720$		−	9.30440i		−	0.346754i
$721$		−	4.66847i		−	0.173863i
$722$		−	40.6379i		−	1.51239i
$723$			0.287905i			0.0107073i
$724$	−56.6554			−2.10558
$725$	−10.2497			−0.380663
$726$			5.78598i			0.214738i
$727$	20.0495			0.743595			0.371798	−	0.928314i	$-0.378742\pi$
$727$	20.0495			0.743595			0.371798	+	0.928314i	$0.378742\pi$
$728$	−33.9979	−	8.02101i	−1.26005	−	0.297278i
$729$	−0.976648			−0.0361722
$730$			7.23956i			0.267948i
$731$	20.5090			0.758553
$732$	55.8218			2.06323
$733$		−	17.6554i		−	0.652117i	−0.945350	−	0.326059i	$-0.894279\pi$
$733$		−	17.6554i		−	0.652117i	0.945350	−	0.326059i	$-0.105721\pi$
$734$		−	88.3377i		−	3.26060i
$735$			5.60509i			0.206747i
$736$		−	47.5647i		−	1.75326i
$737$	3.84383			0.141589
$738$	−24.5637			−0.904203
$739$		−	20.1704i		−	0.741981i	−0.928637	−	0.370990i	$-0.879018\pi$
$739$		−	20.1704i		−	0.741981i	0.928637	−	0.370990i	$-0.120982\pi$
$740$	19.2814			0.708798
$741$	−10.5171	+	44.5779i	−0.386355	+	1.63761i
$742$	3.95312			0.145124
$743$		−	2.45850i		−	0.0901934i	−0.998983	−	0.0450967i	$-0.985640\pi$
$743$		−	2.45850i		−	0.0901934i	0.998983	−	0.0450967i	$-0.0143596\pi$
$744$	−155.709			−5.70858
$745$	5.25560			0.192550
$746$			19.3113i			0.707039i
$747$		−	12.6733i		−	0.463692i
$748$			33.4537i			1.22319i
$749$		−	16.0614i		−	0.586870i
$750$	−25.9811			−0.948695
$751$	−17.0807			−0.623285			−0.311642	−	0.950199i	$-0.600879\pi$
$751$	−17.0807			−0.623285			−0.311642	+	0.950199i	$0.600879\pi$
$752$			125.010i			4.55865i
$753$	−59.6964			−2.17546
$754$	−4.72246	+	20.0167i	−0.171982	+	0.728964i
$755$	7.62276			0.277421
$756$		−	16.7082i		−	0.607672i
$757$	22.8517			0.830560			0.415280	−	0.909694i	$-0.363684\pi$
$757$	22.8517			0.830560			0.415280	+	0.909694i	$0.363684\pi$
$758$	−71.8608			−2.61010
$759$			6.86929i			0.249340i
$760$		−	22.2132i		−	0.805756i
$761$			11.6590i			0.422639i	0.977417	+	0.211319i	$0.0677760\pi$
$761$			11.6590i			0.422639i	−0.977417	+	0.211319i	$0.932224\pi$
$762$		−	86.5334i		−	3.13477i
$763$	8.33725			0.301829
$764$	98.2103			3.55312
$765$			5.14640i			0.186069i
$766$	45.1790			1.63238
$767$	0.732409	−	3.10440i	0.0264458	−	0.112093i
$768$	−7.42386			−0.267885
$769$			43.9248i			1.58397i	0.610540	+	0.791985i	$0.290952\pi$
$769$			43.9248i			1.58397i	−0.610540	+	0.791985i	$0.709048\pi$
$770$	−1.43134			−0.0515818
$771$	−16.9075			−0.608908
$772$		−	100.797i		−	3.62776i
$773$			44.5121i			1.60099i	0.599341	+	0.800494i	$0.295429\pi$
$773$			44.5121i			1.60099i	−0.599341	+	0.800494i	$0.704571\pi$
$774$		−	14.2809i		−	0.513315i
$775$			41.5165i			1.49132i
$776$	121.384			4.35743
$777$	−20.9273			−0.750762
$778$			6.96502i			0.249708i
$779$	−31.5003			−1.12861
$780$	−4.20798	+	17.8360i	−0.150670	+	0.638632i
$781$	5.11327			0.182967
$782$			55.2784i			1.97675i
$783$	−5.98298			−0.213814
$784$	66.6995			2.38212
$785$			6.49524i			0.231825i
$786$			70.0621i			2.49903i
$787$			26.3410i			0.938954i	0.882945	+	0.469477i	$0.155558\pi$
$787$			26.3410i			0.938954i	−0.882945	+	0.469477i	$0.844442\pi$
$788$		−	107.299i		−	3.82238i
$789$	−16.8141			−0.598597
$790$	3.03382			0.107938
$791$			9.92831i			0.353010i
$792$	14.1678			0.503431
$793$	−17.6783	−	4.17077i	−0.627774	−	0.148108i
$794$	53.3314			1.89266
$795$		−	1.26135i		−	0.0447353i
$796$	19.0030			0.673543
$797$	20.1094			0.712312			0.356156	−	0.934427i	$-0.384087\pi$
$797$	20.1094			0.712312			0.356156	+	0.934427i	$0.384087\pi$
$798$			39.6402i			1.40325i
$799$		−	69.1450i		−	2.44618i
$800$			71.9908i			2.54526i
$801$		−	12.6667i		−	0.447555i
$802$	−74.9932			−2.64810
$803$	−5.92140			−0.208962
$804$		−	42.5928i		−	1.50213i
$805$	−1.69933			−0.0598934
$806$	81.0780	+	19.1284i	2.85585	+	0.673770i
$807$	7.26454			0.255724
$808$			96.0093i			3.37759i
$809$	7.67428			0.269813			0.134907	−	0.990858i	$-0.456927\pi$
$809$	7.67428			0.269813			0.134907	+	0.990858i	$0.456927\pi$
$810$	−13.6994			−0.481347
$811$			4.39093i			0.154187i	0.997024	+	0.0770933i	$0.0245639\pi$
$811$			4.39093i			0.154187i	−0.997024	+	0.0770933i	$0.975436\pi$
$812$			12.7889i			0.448802i
$813$		−	22.9086i		−	0.803438i
$814$			21.9496i			0.769333i
$815$	−2.49615			−0.0874363
$816$	168.554			5.90057
$817$		−	18.3136i		−	0.640713i
$818$	−86.3475			−3.01907
$819$	1.65941	−	7.03358i	0.0579844	−	0.245773i
$820$	−12.6035			−0.440135
$821$			4.48612i			0.156567i	0.996931	+	0.0782833i	$0.0249439\pi$
$821$			4.48612i			0.156567i	−0.996931	+	0.0782833i	$0.975056\pi$
$822$	−43.8970			−1.53108
$823$	−20.7536			−0.723426			−0.361713	−	0.932289i	$-0.617808\pi$
$823$	−20.7536			−0.723426			−0.361713	+	0.932289i	$0.617808\pi$
$824$			32.9997i			1.14960i
$825$		−	10.3969i		−	0.361974i
$826$		−	2.76054i		−	0.0960516i
$827$			35.0088i			1.21737i	0.793410	+	0.608687i	$0.208303\pi$
$827$			35.0088i			1.21737i	−0.793410	+	0.608687i	$0.791697\pi$
$828$	27.6560			0.961112
$829$	48.1248			1.67144			0.835721	−	0.549154i	$-0.185050\pi$
$829$	48.1248			1.67144			0.835721	+	0.549154i	$0.185050\pi$
$830$		−	9.05034i		−	0.314142i
$831$	−23.7848			−0.825086
$832$	57.4344	+	13.5503i	1.99118	+	0.469772i
$833$	−36.8925			−1.27825
$834$		−	62.1781i		−	2.15305i
$835$	0.406598			0.0140709
$836$	29.8727			1.03317
$837$			24.2342i			0.837657i
$838$			19.2822i			0.666092i
$839$		−	15.3315i		−	0.529304i	−0.964344	−	0.264652i	$-0.914743\pi$
$839$		−	15.3315i		−	0.529304i	0.964344	−	0.264652i	$-0.0852570\pi$
$840$			9.64635i			0.332831i
$841$	−24.4205			−0.842086
$842$	−18.2874			−0.630224
$843$			35.8180i			1.23364i
$844$	60.9124			2.09669
$845$	2.66527	−	5.33411i	0.0916879	−	0.183499i
$846$	−48.1472			−1.65533
$847$		−	1.17072i		−	0.0402265i
$848$	−15.0098			−0.515437
$849$	2.50627			0.0860149
$850$		−	83.6657i		−	2.86971i
$851$			26.0593i			0.893300i
$852$		−	56.6593i		−	1.94112i
$853$			10.0332i			0.343531i	0.985138	+	0.171765i	$0.0549471\pi$
$853$			10.0332i			0.343531i	−0.985138	+	0.171765i	$0.945053\pi$
$854$	−15.7202			−0.537933
$855$	4.59551			0.157163
$856$			113.532i			3.88044i
$857$	27.6616			0.944903			0.472452	−	0.881357i	$-0.343369\pi$
$857$	27.6616			0.944903			0.472452	+	0.881357i	$0.343369\pi$
$858$	−20.3042	−	4.79030i	−0.693174	−	0.163538i
$859$	−43.3633			−1.47954			−0.739768	−	0.672862i	$-0.765065\pi$
$859$	−43.3633			−1.47954			−0.739768	+	0.672862i	$0.765065\pi$
$860$		−	7.32745i		−	0.249864i
$861$	13.6794			0.466193
$862$	35.3524			1.20411
$863$		−	38.2865i		−	1.30329i	−0.758525	−	0.651644i	$-0.774080\pi$
$863$		−	38.2865i		−	1.30329i	0.758525	−	0.651644i	$-0.225920\pi$
$864$			42.0228i			1.42965i
$865$		−	3.10787i		−	0.105671i
$866$			25.9598i			0.882149i
$867$	−56.3276			−1.91298
$868$	51.8017			1.75826
$869$			2.48143i			0.0841766i
$870$	5.67939			0.192550
$871$	−3.18236	+	13.4888i	−0.107830	+	0.457050i
$872$	−58.9329			−1.99572
$873$			25.1122i			0.849920i
$874$	49.3612			1.66967
$875$	5.25696			0.177718
$876$			65.6141i			2.21689i
$877$			4.41266i			0.149005i	0.997221	+	0.0745024i	$0.0237369\pi$
$877$			4.41266i			0.149005i	−0.997221	+	0.0745024i	$0.976263\pi$
$878$		−	31.4094i		−	1.06001i
$879$			29.1414i			0.982914i
$880$	5.43469			0.183204
$881$	−9.20818			−0.310232			−0.155116	−	0.987896i	$-0.549575\pi$
$881$	−9.20818			−0.310232			−0.155116	+	0.987896i	$0.549575\pi$
$882$			25.6891i			0.864995i
$883$	4.27713			0.143937			0.0719685	−	0.997407i	$-0.477072\pi$
$883$	4.27713			0.143937			0.0719685	+	0.997407i	$0.477072\pi$
$884$	−117.396	−	27.6968i	−3.94845	−	0.931544i
$885$	−0.880822			−0.0296085
$886$		−	21.7014i		−	0.729071i
$887$	46.4860			1.56085			0.780424	−	0.625251i	$-0.215003\pi$
$887$	46.4860			1.56085			0.780424	+	0.625251i	$0.215003\pi$
$888$	147.927			4.96411
$889$			17.5090i			0.587233i
$890$		−	9.04561i		−	0.303209i
$891$		−	11.2050i		−	0.375383i
$892$			14.7323i			0.493275i
$893$	−61.7435			−2.06617
$894$	66.2954			2.21725
$895$		−	0.604298i		−	0.0201994i
$896$	15.8793			0.530492
$897$	−24.1058	−	5.68719i	−0.804869	−	0.189890i
$898$	−94.1754			−3.14267
$899$		−	18.5495i		−	0.618659i
$900$	−41.8583			−1.39528
$901$	8.30213			0.276584
$902$		−	14.3477i		−	0.477725i
$903$			7.95293i			0.264657i
$904$		−	70.1795i		−	2.33414i
$905$		−	5.09083i		−	0.169225i
$906$	96.1553			3.19455
$907$	1.17192			0.0389129			0.0194564	−	0.999811i	$-0.493806\pi$
$907$	1.17192			0.0389129			0.0194564	+	0.999811i	$0.493806\pi$
$908$		−	40.8623i		−	1.35606i
$909$	−19.8626			−0.658802
$910$	1.18502	−	5.02286i	0.0392832	−	0.166506i
$911$	−42.8661			−1.42022			−0.710109	−	0.704091i	$-0.751355\pi$
$911$	−42.8661			−1.42022			−0.710109	+	0.704091i	$0.751355\pi$
$912$		−	150.511i		−	4.98393i
$913$	7.40248			0.244986
$914$	52.3855			1.73276
$915$			5.01592i			0.165821i
$916$			133.225i			4.40189i
$917$		−	14.1762i		−	0.468140i
$918$		−	48.8377i		−	1.61189i
$919$	24.0196			0.792333			0.396167	−	0.918179i	$-0.370340\pi$
$919$	24.0196			0.792333			0.396167	+	0.918179i	$0.370340\pi$
$920$	12.0119			0.396021
$921$		−	65.6719i		−	2.16396i
$922$	31.6845			1.04347
$923$	−4.23335	+	17.9435i	−0.139342	+	0.590618i
$924$	−12.9726			−0.426767
$925$		−	39.4416i		−	1.29683i
$926$	89.0542			2.92650
$927$	−6.82705			−0.224230
$928$		−	32.1653i		−	1.05588i
$929$			19.2035i			0.630046i	0.949084	+	0.315023i	$0.102012\pi$
$929$			19.2035i			0.630046i	−0.949084	+	0.315023i	$0.897988\pi$
$930$		−	23.0045i		−	0.754348i
$931$			32.9434i			1.07968i
$932$	−0.818770			−0.0268197
$933$	18.4151			0.602885
$934$			19.8577i			0.649765i
$935$	−3.00601			−0.0983071
$936$	−11.7297	+	49.7178i	−0.383398	+	1.62508i
$937$	51.2628			1.67468			0.837342	−	0.546680i	$-0.184109\pi$
$937$	51.2628			1.67468			0.837342	+	0.546680i	$0.184109\pi$
$938$			11.9947i			0.391641i
$939$	23.4219			0.764344
$940$	−24.7041			−0.805760
$941$		−	1.61030i		−	0.0524943i	−0.999655	−	0.0262471i	$-0.991644\pi$
$941$		−	1.61030i		−	0.0524943i	0.999655	−	0.0262471i	$-0.00835568\pi$
$942$			81.9326i			2.66951i
$943$		−	17.0340i		−	0.554703i
$944$			10.4816i			0.341147i
$945$	1.50133			0.0488384
$946$	8.34145			0.271204
$947$		−	11.4406i		−	0.371770i	−0.982571	−	0.185885i	$-0.940485\pi$
$947$		−	11.4406i		−	0.371770i	0.982571	−	0.185885i	$-0.0595152\pi$
$948$	27.4963			0.893038
$949$	4.90241	−	20.7794i	0.159139	−	0.674529i
$950$	−74.7098			−2.42391
$951$		−	43.0556i		−	1.39617i
$952$	−63.4919			−2.05779
$953$	16.5093			0.534789			0.267394	−	0.963587i	$-0.413837\pi$
$953$	16.5093			0.534789			0.267394	+	0.963587i	$0.413837\pi$
$954$		−	5.78095i		−	0.187165i
$955$			8.82478i			0.285563i
$956$			46.3510i			1.49910i
$957$			4.64531i			0.150161i
$958$	59.1082			1.90970
$959$	8.88203			0.286816
$960$		−	16.2961i		−	0.525953i
$961$	−44.1350			−1.42371
$962$	−77.0258	−	18.1724i	−2.48341	−	0.585902i
$963$	−23.4878			−0.756883
$964$			0.677038i			0.0218059i
$965$	9.05720			0.291561
$966$	−21.4357			−0.689683
$967$			30.8852i			0.993202i	0.867979	+	0.496601i	$0.165419\pi$
$967$			30.8852i			0.993202i	−0.867979	+	0.496601i	$0.834581\pi$
$968$			8.27540i			0.265982i
$969$			83.2502i			2.67438i
$970$			17.9333i			0.575803i
$971$	23.7146			0.761038			0.380519	−	0.924773i	$-0.375745\pi$
$971$	23.7146			0.761038			0.380519	+	0.924773i	$0.375745\pi$
$972$	−81.3461			−2.60918
$973$			12.5810i			0.403328i
$974$	23.5686			0.755187
$975$	36.4849	+	8.60776i	1.16845	+	0.275669i
$976$	59.6885			1.91058
$977$		−	52.6096i		−	1.68313i	−0.540156	−	0.841565i	$-0.681635\pi$
$977$		−	52.6096i		−	1.68313i	0.540156	−	0.841565i	$-0.318365\pi$
$978$	−31.4870			−1.00684
$979$	7.39861			0.236461
$980$			13.1810i			0.421050i
$981$		−	12.1922i		−	0.389267i
$982$			72.2888i			2.30683i
$983$			44.4857i			1.41887i	0.704769	+	0.709437i	$0.251051\pi$
$983$			44.4857i			1.41887i	−0.704769	+	0.709437i	$0.748949\pi$
$984$	−96.6946			−3.08251
$985$	9.64150			0.307204
$986$			37.3816i			1.19047i
$987$	26.8129			0.853464
$988$	−24.7320	+	104.830i	−0.786831	+	3.33507i
$989$	9.90323			0.314904
$990$			2.09315i			0.0665247i
$991$	8.68365			0.275845			0.137923	−	0.990443i	$-0.455957\pi$
$991$	8.68365			0.275845			0.137923	+	0.990443i	$0.455957\pi$
$992$	−130.286			−4.13659
$993$		−	7.40437i		−	0.234971i
$994$			15.9560i			0.506094i
$995$			1.70753i			0.0541324i
$996$		−	82.0257i		−	2.59908i
$997$	−25.3265			−0.802100			−0.401050	−	0.916056i	$-0.631355\pi$
$997$	−25.3265			−0.802100			−0.401050	+	0.916056i	$0.631355\pi$
$998$	−74.3303			−2.35289
$999$		−	23.0230i		−	0.728416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.b.a.12.12	yes	12
3.2	odd	2		1287.2.b.b.298.1		12
4.3	odd	2		2288.2.j.k.1585.9		12
13.5	odd	4		1859.2.a.n.1.6		6
13.8	odd	4		1859.2.a.j.1.1		6
13.12	even	2	inner	143.2.b.a.12.1	✓	12
39.38	odd	2		1287.2.b.b.298.12		12
52.51	odd	2		2288.2.j.k.1585.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.b.a.12.1	✓	12	13.12	even	2	inner
143.2.b.a.12.12	yes	12	1.1	even	1	trivial
1287.2.b.b.298.1		12	3.2	odd	2
1287.2.b.b.298.12		12	39.38	odd	2
1859.2.a.j.1.1		6	13.8	odd	4
1859.2.a.n.1.6		6	13.5	odd	4
2288.2.j.k.1585.9		12	4.3	odd	2
2288.2.j.k.1585.10		12	52.51	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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.66546i q^{2} -2.17072 q^{3} -5.10468 q^{4} -0.458686i q^{5} -5.78598i q^{6} +1.17072i q^{7} -8.27540i q^{8} +1.71204 q^{9} +O(q^{10})\)	\(q+2.66546i q^{2} -2.17072 q^{3} -5.10468 q^{4} -0.458686i q^{5} -5.78598i q^{6} +1.17072i q^{7} -8.27540i q^{8} +1.71204 q^{9} +1.22261 q^{10} +1.00000i q^{11} +11.0808 q^{12} +(-3.50921 - 0.827915i) q^{13} -3.12051 q^{14} +0.995680i q^{15} +11.8484 q^{16} -6.55353 q^{17} +4.56337i q^{18} +5.85202i q^{19} +2.34145i q^{20} -2.54131i q^{21} -2.66546 q^{22} -3.16452 q^{23} +17.9636i q^{24} +4.78961 q^{25} +(2.20677 - 9.35366i) q^{26} +2.79581 q^{27} -5.97616i q^{28} -2.13998 q^{29} -2.65395 q^{30} +8.66805i q^{31} +15.0306i q^{32} -2.17072i q^{33} -17.4682i q^{34} +0.536994 q^{35} -8.73940 q^{36} -8.23483i q^{37} -15.5983 q^{38} +(7.61752 + 1.79717i) q^{39} -3.79581 q^{40} +5.38281i q^{41} +6.77377 q^{42} -3.12946 q^{43} -5.10468i q^{44} -0.785287i q^{45} -8.43490i q^{46} +10.5508i q^{47} -25.7196 q^{48} +5.62941 q^{49} +12.7665i q^{50} +14.2259 q^{51} +(17.9134 + 4.22624i) q^{52} -1.26682 q^{53} +7.45212i q^{54} +0.458686 q^{55} +9.68820 q^{56} -12.7031i q^{57} -5.70404i q^{58} +0.884643i q^{59} -5.08263i q^{60} +5.03768 q^{61} -23.1043 q^{62} +2.00432i q^{63} -16.3668 q^{64} +(-0.379753 + 1.60963i) q^{65} +5.78598 q^{66} -3.84383i q^{67} +33.4537 q^{68} +6.86929 q^{69} +1.43134i q^{70} -5.11327i q^{71} -14.1678i q^{72} +5.92140i q^{73} +21.9496 q^{74} -10.3969 q^{75} -29.8727i q^{76} -1.17072 q^{77} +(-4.79030 + 20.3042i) q^{78} +2.48143 q^{79} -5.43469i q^{80} -11.2050 q^{81} -14.3477 q^{82} -7.40248i q^{83} +12.9726i q^{84} +3.00601i q^{85} -8.34145i q^{86} +4.64531 q^{87} +8.27540 q^{88} -7.39861i q^{89} +2.09315 q^{90} +(0.969259 - 4.10831i) q^{91} +16.1539 q^{92} -18.8159i q^{93} -28.1228 q^{94} +2.68424 q^{95} -32.6273i q^{96} +14.6680i q^{97} +15.0050i q^{98} +1.71204i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} - 14 q^{4} + 12 q^{9}+O(q^{10}) \) 12 * q - 4 * q^3 - 14 * q^4 + 12 * q^9	\( 12 q - 4 q^{3} - 14 q^{4} + 12 q^{9} + 8 q^{10} - 8 q^{13} + 10 q^{16} - 12 q^{17} - 2 q^{22} - 4 q^{23} - 16 q^{25} + 10 q^{26} - 28 q^{27} + 8 q^{29} + 4 q^{30} + 16 q^{35} - 16 q^{36} + 18 q^{38} + 4 q^{39} + 16 q^{40} - 2 q^{42} + 12 q^{43} - 58 q^{48} + 32 q^{49} + 36 q^{52} - 20 q^{53} - 8 q^{55} + 22 q^{56} - 12 q^{61} - 72 q^{62} - 10 q^{64} - 20 q^{65} + 2 q^{66} + 68 q^{68} + 52 q^{69} + 20 q^{74} - 8 q^{75} + 8 q^{77} + 6 q^{78} - 48 q^{79} - 36 q^{81} - 44 q^{82} + 12 q^{87} + 30 q^{88} + 68 q^{90} - 6 q^{92} - 64 q^{94} - 4 q^{95}+O(q^{100}) \) 12 * q - 4 * q^3 - 14 * q^4 + 12 * q^9 + 8 * q^10 - 8 * q^13 + 10 * q^16 - 12 * q^17 - 2 * q^22 - 4 * q^23 - 16 * q^25 + 10 * q^26 - 28 * q^27 + 8 * q^29 + 4 * q^30 + 16 * q^35 - 16 * q^36 + 18 * q^38 + 4 * q^39 + 16 * q^40 - 2 * q^42 + 12 * q^43 - 58 * q^48 + 32 * q^49 + 36 * q^52 - 20 * q^53 - 8 * q^55 + 22 * q^56 - 12 * q^61 - 72 * q^62 - 10 * q^64 - 20 * q^65 + 2 * q^66 + 68 * q^68 + 52 * q^69 + 20 * q^74 - 8 * q^75 + 8 * q^77 + 6 * q^78 - 48 * q^79 - 36 * q^81 - 44 * q^82 + 12 * q^87 + 30 * q^88 + 68 * q^90 - 6 * q^92 - 64 * q^94 - 4 * q^95

Introduction

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