LMFDB - Embedded newform 378.3.q.a.71.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(71,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.71"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.10
Character	$\chi$	$=$	378.71
Dual form			378.3.q.a.197.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-2.30097 - 1.32846i) q^{5} +(1.32288 + 2.29129i) q^{7} -2.82843i q^{8} -3.75747 q^{10} +(2.21082 - 1.27642i) q^{11} +(9.70329 - 16.8066i) q^{13} +(3.24037 + 1.87083i) q^{14} +(-2.00000 - 3.46410i) q^{16} -28.6298i q^{17} +10.6664 q^{19} +(-4.60194 + 2.65693i) q^{20} +(1.80513 - 3.12658i) q^{22} +(-6.68464 - 3.85938i) q^{23} +(-8.97036 - 15.5371i) q^{25} -27.4451i q^{26} +5.29150 q^{28} +(1.89461 - 1.09386i) q^{29} +(-13.7932 + 23.8904i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-20.2443 - 35.0642i) q^{34} -7.02958i q^{35} -37.5014 q^{37} +(13.0636 - 7.54227i) q^{38} +(-3.75747 + 6.50812i) q^{40} +(62.6292 + 36.1590i) q^{41} +(-18.8065 - 32.5739i) q^{43} -5.10568i q^{44} -10.9160 q^{46} +(37.9709 - 21.9225i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(-21.9728 - 12.6860i) q^{50} +(-19.4066 - 33.6132i) q^{52} +24.2591i q^{53} -6.78272 q^{55} +(6.48074 - 3.74166i) q^{56} +(1.54695 - 2.67939i) q^{58} +(69.5157 + 40.1349i) q^{59} +(6.15634 + 10.6631i) q^{61} +39.0129i q^{62} -8.00000 q^{64} +(-44.6539 + 25.7810i) q^{65} +(-37.0292 + 64.1364i) q^{67} +(-49.5883 - 28.6298i) q^{68} +(-4.97066 - 8.60944i) q^{70} -98.3829i q^{71} +93.6849 q^{73} +(-45.9296 + 26.5175i) q^{74} +(10.6664 - 18.4747i) q^{76} +(5.84929 + 3.37709i) q^{77} +(47.0336 + 81.4645i) q^{79} +10.6277i q^{80} +102.273 q^{82} +(-35.7729 + 20.6535i) q^{83} +(-38.0337 + 65.8763i) q^{85} +(-46.0664 - 26.5965i) q^{86} +(-3.61026 - 6.25315i) q^{88} +75.2547i q^{89} +51.3450 q^{91} +(-13.3693 + 7.71876i) q^{92} +(31.0031 - 53.6990i) q^{94} +(-24.5430 - 14.1699i) q^{95} +(-82.0660 - 142.142i) q^{97} +9.89949i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} - 36 q^{5} - 48 q^{16} + 24 q^{19} - 72 q^{20} + 24 q^{22} + 72 q^{23} + 72 q^{25} + 108 q^{29} - 60 q^{31} - 48 q^{34} - 168 q^{37} - 144 q^{38} - 108 q^{41} + 60 q^{43} + 324 q^{47} - 84 q^{49}+ \cdots + 48 q^{97}+O(q^{100}) $ 24 * q + 24 * q^4 - 36 * q^5 - 48 * q^16 + 24 * q^19 - 72 * q^20 + 24 * q^22 + 72 * q^23 + 72 * q^25 + 108 * q^29 - 60 * q^31 - 48 * q^34 - 168 * q^37 - 144 * q^38 - 108 * q^41 + 60 * q^43 + 324 * q^47 - 84 * q^49 - 144 * q^50 + 264 * q^55 + 432 * q^59 - 192 * q^64 + 180 * q^65 + 72 * q^67 - 72 * q^68 + 24 * q^73 - 288 * q^74 + 24 * q^76 + 12 * q^79 - 288 * q^82 - 756 * q^83 - 156 * q^85 - 360 * q^86 - 48 * q^88 - 168 * q^91 + 144 * q^92 + 936 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	−2.30097	−	1.32846i	−0.460194	−	0.265693i	0.251932	−	0.967745i	$-0.418934\pi$
$5$	−2.30097	−	1.32846i	−0.460194	−	0.265693i	−0.712126	+	0.702052i	$0.752267\pi$
$6$		0			0
$7$	1.32288	+	2.29129i	0.188982	+	0.327327i
$7$	1.32288	+	2.29129i	0.188982	+	0.327327i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	−3.75747			−0.375747
$11$	2.21082	−	1.27642i	0.200984	−	0.116038i	−0.396130	−	0.918194i	$-0.629647\pi$
$11$	2.21082	−	1.27642i	0.200984	−	0.116038i	0.597114	+	0.802156i	$0.296314\pi$
$12$		0			0
$13$	9.70329	−	16.8066i	0.746407	−	1.29281i	−0.203127	−	0.979152i	$-0.565111\pi$
$13$	9.70329	−	16.8066i	0.746407	−	1.29281i	0.949534	−	0.313663i	$-0.101556\pi$
$14$	3.24037	+	1.87083i	0.231455	+	0.133631i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$		−	28.6298i		−	1.68411i	−0.539394	−	0.842053i	$-0.681347\pi$
$17$		−	28.6298i		−	1.68411i	0.539394	−	0.842053i	$-0.318653\pi$
$18$		0			0
$19$	10.6664			0.561388			0.280694	−	0.959797i	$-0.409435\pi$
$19$	10.6664			0.561388			0.280694	+	0.959797i	$0.409435\pi$
$20$	−4.60194	+	2.65693i	−0.230097	+	0.132846i
$21$		0			0
$22$	1.80513	−	3.12658i	0.0820514	−	0.142117i
$23$	−6.68464	−	3.85938i	−0.290636	−	0.167799i	0.347592	−	0.937646i	$-0.386999\pi$
$23$	−6.68464	−	3.85938i	−0.290636	−	0.167799i	−0.638229	+	0.769847i	$0.720333\pi$
$24$		0			0
$25$	−8.97036	−	15.5371i	−0.358814	−	0.621485i
$26$		−	27.4451i		−	1.05558i
$27$		0			0
$28$	5.29150			0.188982
$29$	1.89461	−	1.09386i	0.0653315	−	0.0377192i	−0.466978	−	0.884269i	$-0.654657\pi$
$29$	1.89461	−	1.09386i	0.0653315	−	0.0377192i	0.532310	+	0.846550i	$0.321324\pi$
$30$		0			0
$31$	−13.7932	+	23.8904i	−0.444940	+	0.770659i	−0.998048	−	0.0624504i	$-0.980108\pi$
$31$	−13.7932	+	23.8904i	−0.444940	+	0.770659i	0.553108	+	0.833110i	$0.313442\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−20.2443	−	35.0642i	−0.595422	−	1.03130i
$35$		−	7.02958i		−	0.200845i
$36$		0			0
$37$	−37.5014			−1.01355			−0.506775	−	0.862078i	$-0.669163\pi$
$37$	−37.5014			−1.01355			−0.506775	+	0.862078i	$0.669163\pi$
$38$	13.0636	−	7.54227i	0.343779	−	0.198481i
$39$		0			0
$40$	−3.75747	+	6.50812i	−0.0939366	+	0.162703i
$41$	62.6292	+	36.1590i	1.52754	+	0.881926i	0.999464	+	0.0327293i	$0.0104199\pi$
$41$	62.6292	+	36.1590i	1.52754	+	0.881926i	0.528077	+	0.849197i	$0.322913\pi$
$42$		0			0
$43$	−18.8065	−	32.5739i	−0.437361	−	0.757532i	0.560124	−	0.828409i	$-0.310754\pi$
$43$	−18.8065	−	32.5739i	−0.437361	−	0.757532i	−0.997485	+	0.0708769i	$0.977420\pi$
$44$		−	5.10568i		−	0.116038i
$45$		0			0
$46$	−10.9160			−0.237304
$47$	37.9709	−	21.9225i	0.807891	−	0.466436i	−0.0383316	−	0.999265i	$-0.512204\pi$
$47$	37.9709	−	21.9225i	0.807891	−	0.466436i	0.846223	+	0.532829i	$0.178871\pi$
$48$		0			0
$49$	−3.50000	+	6.06218i	−0.0714286	+	0.123718i
$50$	−21.9728	−	12.6860i	−0.439456	−	0.253720i
$51$		0			0
$52$	−19.4066	−	33.6132i	−0.373204	−	0.646407i
$53$			24.2591i			0.457718i	0.973460	+	0.228859i	$0.0734995\pi$
$53$			24.2591i			0.457718i	−0.973460	+	0.228859i	$0.926501\pi$
$54$		0			0
$55$	−6.78272			−0.123322
$56$	6.48074	−	3.74166i	0.115728	−	0.0668153i
$57$		0			0
$58$	1.54695	−	2.67939i	0.0266715	−	0.0461964i
$59$	69.5157	+	40.1349i	1.17823	+	0.680253i	0.955605	−	0.294651i	$-0.0952034\pi$
$59$	69.5157	+	40.1349i	1.17823	+	0.680253i	0.222627	+	0.974904i	$0.428537\pi$
$60$		0			0
$61$	6.15634	+	10.6631i	0.100924	+	0.174805i	0.912065	−	0.410045i	$-0.134487\pi$
$61$	6.15634	+	10.6631i	0.100924	+	0.174805i	−0.811142	+	0.584849i	$0.801154\pi$
$62$			39.0129i			0.629241i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−44.6539	+	25.7810i	−0.686984	+	0.396630i
$66$		0			0
$67$	−37.0292	+	64.1364i	−0.552675	+	0.957260i	0.445406	+	0.895329i	$0.353059\pi$
$67$	−37.0292	+	64.1364i	−0.552675	+	0.957260i	−0.998080	+	0.0619316i	$0.980274\pi$
$68$	−49.5883	−	28.6298i	−0.729240	−	0.421027i
$69$		0			0
$70$	−4.97066	−	8.60944i	−0.0710094	−	0.122992i
$71$		−	98.3829i		−	1.38567i	−0.721094	−	0.692837i	$-0.756360\pi$
$71$		−	98.3829i		−	1.38567i	0.721094	−	0.692837i	$-0.243640\pi$
$72$		0			0
$73$	93.6849			1.28336			0.641678	−	0.766974i	$-0.278239\pi$
$73$	93.6849			1.28336			0.641678	+	0.766974i	$0.278239\pi$
$74$	−45.9296	+	26.5175i	−0.620671	+	0.358344i
$75$		0			0
$76$	10.6664	−	18.4747i	0.140347	−	0.243088i
$77$	5.84929	+	3.37709i	0.0759648	+	0.0438583i
$78$		0			0
$79$	47.0336	+	81.4645i	0.595362	+	1.03120i	0.993496	+	0.113869i	$0.0363245\pi$
$79$	47.0336	+	81.4645i	0.595362	+	1.03120i	−0.398134	+	0.917327i	$0.630342\pi$
$80$			10.6277i			0.132846i
$81$		0			0
$82$	102.273			1.24723
$83$	−35.7729	+	20.6535i	−0.430999	+	0.248837i	−0.699772	−	0.714366i	$-0.746715\pi$
$83$	−35.7729	+	20.6535i	−0.430999	+	0.248837i	0.268773	+	0.963203i	$0.413382\pi$
$84$		0			0
$85$	−38.0337	+	65.8763i	−0.447455	+	0.775015i
$86$	−46.0664	−	26.5965i	−0.535656	−	0.309261i
$87$		0			0
$88$	−3.61026	−	6.25315i	−0.0410257	−	0.0710586i
$89$			75.2547i			0.845558i	0.906233	+	0.422779i	$0.138945\pi$
$89$			75.2547i			0.845558i	−0.906233	+	0.422779i	$0.861055\pi$
$90$		0			0
$91$	51.3450			0.564231
$92$	−13.3693	+	7.71876i	−0.145318	+	0.0838995i
$93$		0			0
$94$	31.0031	−	53.6990i	0.329820	−	0.571266i
$95$	−24.5430	−	14.1699i	−0.258347	−	0.149157i
$96$		0			0
$97$	−82.0660	−	142.142i	−0.846041	−	1.46539i	−0.884714	−	0.466134i	$-0.845647\pi$
$97$	−82.0660	−	142.142i	−0.846041	−	1.46539i	0.0386733	−	0.999252i	$-0.487687\pi$
$98$			9.89949i			0.101015i
$99$		0			0
$100$	−35.8814			−0.358814
$101$	−14.8067	+	8.54863i	−0.146601	+	0.0846399i	−0.571506	−	0.820598i	$-0.693641\pi$
$101$	−14.8067	+	8.54863i	−0.146601	+	0.0846399i	0.424906	+	0.905238i	$0.360307\pi$
$102$		0			0
$103$	−69.8447	+	120.975i	−0.678104	+	1.17451i	0.297448	+	0.954738i	$0.403865\pi$
$103$	−69.8447	+	120.975i	−0.678104	+	1.17451i	−0.975551	+	0.219772i	$0.929469\pi$
$104$	−47.5362	−	27.4451i	−0.457079	−	0.263895i
$105$		0			0
$106$	17.1537	+	29.7111i	0.161828	+	0.280294i
$107$			24.3628i			0.227689i	0.993499	+	0.113845i	$0.0363166\pi$
$107$			24.3628i			0.227689i	−0.993499	+	0.113845i	$0.963683\pi$
$108$		0			0
$109$	30.8295			0.282839			0.141420	−	0.989950i	$-0.454833\pi$
$109$	30.8295			0.282839			0.141420	+	0.989950i	$0.454833\pi$
$110$	−8.30710	+	4.79610i	−0.0755191	+	0.0436009i
$111$		0			0
$112$	5.29150	−	9.16515i	0.0472456	−	0.0818317i
$113$	39.6575	+	22.8963i	0.350952	+	0.202622i	0.665104	−	0.746750i	$-0.268387\pi$
$113$	39.6575	+	22.8963i	0.350952	+	0.202622i	−0.314153	+	0.949372i	$0.601720\pi$
$114$		0			0
$115$	10.2541	+	17.7606i	0.0891660	+	0.154440i
$116$		−	4.37542i		−	0.0377192i
$117$		0			0
$118$	113.519			0.962023
$119$	65.5991	−	37.8737i	0.551253	−	0.318266i
$120$		0			0
$121$	−57.2415	+	99.1452i	−0.473070	+	0.819382i
$122$	15.0799	+	8.70638i	0.123606	+	0.0713637i
$123$		0			0
$124$	27.5863	+	47.7809i	0.222470	+	0.385330i
$125$			114.090i			0.912724i
$126$		0			0
$127$	187.439			1.47590			0.737951	−	0.674855i	$-0.235794\pi$
$127$	187.439			1.47590			0.737951	+	0.674855i	$0.235794\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−36.4598	+	63.1502i	−0.280460	+	0.485771i
$131$	24.0855	+	13.9058i	0.183859	+	0.106151i	0.589104	−	0.808057i	$-0.299481\pi$
$131$	24.0855	+	13.9058i	0.183859	+	0.106151i	−0.405246	+	0.914208i	$0.632814\pi$
$132$		0			0
$133$	14.1103	+	24.4397i	0.106092	+	0.183757i
$134$			104.734i			0.781600i
$135$		0			0
$136$	−80.9773			−0.595422
$137$	−173.427	+	100.128i	−1.26589	+	0.730864i	−0.974208	−	0.225650i	$-0.927549\pi$
$137$	−173.427	+	100.128i	−1.26589	+	0.730864i	−0.291686	+	0.956514i	$0.594216\pi$
$138$		0			0
$139$	14.4841	−	25.0873i	0.104202	−	0.180484i	−0.809210	−	0.587520i	$-0.800104\pi$
$139$	14.4841	−	25.0873i	0.104202	−	0.180484i	0.913412	+	0.407036i	$0.133438\pi$
$140$	−12.1756	−	7.02958i	−0.0869684	−	0.0502113i
$141$		0			0
$142$	−69.5672	−	120.494i	−0.489910	−	0.848549i
$143$		−	49.5419i		−	0.346447i
$144$		0			0
$145$	−5.81260			−0.0400869
$146$	114.740	−	66.2453i	0.785891	−	0.453735i
$147$		0			0
$148$	−37.5014	+	64.9543i	−0.253388	+	0.438880i
$149$	−152.190	−	87.8672i	−1.02141	−	0.589713i	−0.106900	−	0.994270i	$-0.534092\pi$
$149$	−152.190	−	87.8672i	−1.02141	−	0.589713i	−0.914513	+	0.404557i	$0.867426\pi$
$150$		0			0
$151$	130.177	+	225.473i	0.862099	+	1.49320i	0.869899	+	0.493230i	$0.164184\pi$
$151$	130.177	+	225.473i	0.862099	+	1.49320i	−0.00779969	+	0.999970i	$0.502483\pi$
$152$		−	30.1691i		−	0.198481i
$153$		0			0
$154$	9.55185			0.0620250
$155$	63.4752	−	36.6474i	0.409518	−	0.236435i
$156$		0			0
$157$	141.276	−	244.697i	0.899848	−	1.55858i	0.0721601	−	0.997393i	$-0.477011\pi$
$157$	141.276	−	244.697i	0.899848	−	1.55858i	0.827688	−	0.561189i	$-0.189656\pi$
$158$	115.208	+	66.5155i	0.729166	+	0.420984i
$159$		0			0
$160$	7.51493	+	13.0162i	0.0469683	+	0.0813515i
$161$		−	20.4219i		−	0.126844i
$162$		0			0
$163$	−12.6900			−0.0778525			−0.0389262	−	0.999242i	$-0.512394\pi$
$163$	−12.6900			−0.0778525			−0.0389262	+	0.999242i	$0.512394\pi$
$164$	125.258	−	72.3179i	0.763770	−	0.440963i
$165$		0			0
$166$	−29.2084	+	50.5905i	−0.175954	+	0.304762i
$167$	183.288	+	105.822i	1.09754	+	0.633662i	0.935573	−	0.353134i	$-0.114884\pi$
$167$	183.288	+	105.822i	1.09754	+	0.633662i	0.161963	+	0.986797i	$0.448218\pi$
$168$		0			0
$169$	−103.808	−	179.800i	−0.614247	−	1.06391i
$170$			107.576i			0.632797i
$171$		0			0
$172$	−75.2262			−0.437361
$173$	−100.882	+	58.2444i	−0.583135	+	0.336673i	−0.762378	−	0.647132i	$-0.775968\pi$
$173$	−100.882	+	58.2444i	−0.583135	+	0.336673i	0.179243	+	0.983805i	$0.442635\pi$
$174$		0			0
$175$	23.7333	−	41.1074i	0.135619	−	0.234899i
$176$	−8.84330	−	5.10568i	−0.0502460	−	0.0290095i
$177$		0			0
$178$	53.2131	+	92.1678i	0.298950	+	0.517796i
$179$		−	272.774i		−	1.52388i	−0.647650	−	0.761938i	$-0.724248\pi$
$179$		−	272.774i		−	1.52388i	0.647650	−	0.761938i	$-0.275752\pi$
$180$		0			0
$181$	−27.1230			−0.149851			−0.0749255	−	0.997189i	$-0.523872\pi$
$181$	−27.1230			−0.149851			−0.0749255	+	0.997189i	$0.523872\pi$
$182$	62.8845	−	36.3064i	0.345519	−	0.199486i
$183$		0			0
$184$	−10.9160	+	18.9070i	−0.0593259	+	0.102755i
$185$	86.2895	+	49.8193i	0.466430	+	0.269293i
$186$		0			0
$187$	−36.5437	−	63.2955i	−0.195421	−	0.338479i
$188$		−	87.6900i		−	0.466436i
$189$		0			0
$190$	−40.0786			−0.210940
$191$	−196.637	+	113.528i	−1.02951	+	0.594389i	−0.916845	−	0.399244i	$-0.869273\pi$
$191$	−196.637	+	113.528i	−1.02951	+	0.594389i	−0.112667	+	0.993633i	$0.535939\pi$
$192$		0			0
$193$	−119.841	+	207.570i	−0.620937	+	1.07549i	0.368375	+	0.929677i	$0.379914\pi$
$193$	−119.841	+	207.570i	−0.620937	+	1.07549i	−0.989312	+	0.145817i	$0.953419\pi$
$194$	−201.020	−	116.059i	−1.03618	−	0.598241i
$195$		0			0
$196$	7.00000	+	12.1244i	0.0357143	+	0.0618590i
$197$			139.283i			0.707022i	0.935430	+	0.353511i	$0.115012\pi$
$197$			139.283i			0.707022i	−0.935430	+	0.353511i	$0.884988\pi$
$198$		0			0
$199$	71.5320			0.359457			0.179729	−	0.983716i	$-0.442478\pi$
$199$	71.5320			0.359457			0.179729	+	0.983716i	$0.442478\pi$
$200$	−43.9456	+	25.3720i	−0.219728	+	0.126860i
$201$		0			0
$202$	−12.0896	+	20.9398i	−0.0598494	+	0.103662i
$203$	5.01268	+	2.89407i	0.0246930	+	0.0142565i
$204$		0			0
$205$	−96.0718	−	166.401i	−0.468643	−	0.811714i
$206$			197.551i			0.958983i
$207$		0			0
$208$	−77.6263			−0.373204
$209$	23.5815	−	13.6148i	0.112830	−	0.0651425i
$210$		0			0
$211$	156.271	−	270.669i	0.740619	−	1.28279i	−0.211594	−	0.977358i	$-0.567866\pi$
$211$	156.271	−	270.669i	0.740619	−	1.28279i	0.952214	−	0.305433i	$-0.0988011\pi$
$212$	42.0179	+	24.2591i	0.198198	+	0.114429i
$213$		0			0
$214$	17.2271	+	29.8382i	0.0805003	+	0.139431i
$215$			99.9353i			0.464815i
$216$		0			0
$217$	−72.9865			−0.336343
$218$	37.7583	−	21.7998i	0.173203	−	0.0999989i
$219$		0			0
$220$	−6.78272	+	11.7480i	−0.0308305	+	0.0534000i
$221$	−481.170	−	277.803i	−2.17724	−	1.25703i
$222$		0			0
$223$	−56.6245	−	98.0765i	−0.253921	−	0.439805i	0.710681	−	0.703515i	$-0.248387\pi$
$223$	−56.6245	−	98.0765i	−0.253921	−	0.439805i	−0.964602	+	0.263710i	$0.915054\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	64.7605			0.286551
$227$	224.565	−	129.652i	0.989271	−	0.571156i	0.0842147	−	0.996448i	$-0.473162\pi$
$227$	224.565	−	129.652i	0.989271	−	0.571156i	0.905056	+	0.425292i	$0.139829\pi$
$228$		0			0
$229$	−141.801	+	245.607i	−0.619219	+	1.07252i	0.370409	+	0.928869i	$0.379217\pi$
$229$	−141.801	+	245.607i	−0.619219	+	1.07252i	−0.989628	+	0.143651i	$0.954116\pi$
$230$	25.1173	+	14.5015i	0.109206	+	0.0630499i
$231$		0			0
$232$	−3.09389	−	5.35878i	−0.0133357	−	0.0230982i
$233$			122.039i			0.523773i	0.965099	+	0.261887i	$0.0843447\pi$
$233$			122.039i			0.523773i	−0.965099	+	0.261887i	$0.915655\pi$
$234$		0			0
$235$	−116.493			−0.495715
$236$	139.031	−	80.2698i	0.589116	−	0.340126i
$237$		0			0
$238$	53.5615	−	92.7712i	0.225048	−	0.389795i
$239$	96.3977	+	55.6552i	0.403338	+	0.232867i	0.687923	−	0.725784i	$-0.258523\pi$
$239$	96.3977	+	55.6552i	0.403338	+	0.232867i	−0.284585	+	0.958651i	$0.591856\pi$
$240$		0			0
$241$	51.5505	+	89.2881i	0.213902	+	0.370490i	0.952932	−	0.303183i	$-0.0980492\pi$
$241$	51.5505	+	89.2881i	0.213902	+	0.370490i	−0.739030	+	0.673672i	$0.764716\pi$
$242$			161.903i			0.669022i
$243$		0			0
$244$	24.6254			0.100924
$245$	16.1068	−	9.29925i	0.0657420	−	0.0379561i
$246$		0			0
$247$	103.499	−	179.266i	0.419024	−	0.725771i
$248$	67.5724	+	39.0129i	0.272469	+	0.157310i
$249$		0			0
$250$	80.6742	+	139.732i	0.322697	+	0.558927i
$251$		−	426.514i		−	1.69926i	−0.527380	−	0.849629i	$-0.676826\pi$
$251$		−	426.514i		−	1.69926i	0.527380	−	0.849629i	$-0.323174\pi$
$252$		0			0
$253$	−19.7047			−0.0778844
$254$	229.566	−	132.540i	0.903801	−	0.521810i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−36.9475	−	21.3317i	−0.143765	−	0.0830026i	0.426392	−	0.904538i	$-0.359784\pi$
$257$	−36.9475	−	21.3317i	−0.143765	−	0.0830026i	−0.570157	+	0.821536i	$0.693118\pi$
$258$		0			0
$259$	−49.6097	−	85.9265i	−0.191543	−	0.331762i
$260$			103.124i			0.396630i
$261$		0			0
$262$	39.3315			0.150120
$263$	−178.555	+	103.089i	−0.678916	+	0.391972i	−0.799447	−	0.600737i	$-0.794874\pi$
$263$	−178.555	+	103.089i	−0.678916	+	0.391972i	0.120530	+	0.992710i	$0.461540\pi$
$264$		0			0
$265$	32.2273	−	55.8193i	0.121612	−	0.210639i
$266$	34.5630	+	19.9550i	0.129936	+	0.0750187i
$267$		0			0
$268$	74.0584	+	128.273i	0.276337	+	0.478630i
$269$		−	452.410i		−	1.68182i	−0.541174	−	0.840910i	$-0.682020\pi$
$269$		−	452.410i		−	1.68182i	0.541174	−	0.840910i	$-0.317980\pi$
$270$		0			0
$271$	−213.136			−0.786478			−0.393239	−	0.919436i	$-0.628646\pi$
$271$	−213.136			−0.786478			−0.393239	+	0.919436i	$0.628646\pi$
$272$	−99.1766	+	57.2596i	−0.364620	+	0.210513i
$273$		0			0
$274$	−141.603	+	245.263i	−0.516799	+	0.895122i
$275$	−39.6638	−	22.8999i	−0.144232	−	0.0832724i
$276$		0			0
$277$	50.5788	+	87.6050i	0.182595	+	0.316264i	0.942763	−	0.333462i	$-0.108217\pi$
$277$	50.5788	+	87.6050i	0.182595	+	0.316264i	−0.760169	+	0.649726i	$0.774884\pi$
$278$		−	40.9673i		−	0.147365i
$279$		0			0
$280$	−19.8826			−0.0710094
$281$	245.890	−	141.965i	0.875054	−	0.505213i	0.00602973	−	0.999982i	$-0.498081\pi$
$281$	245.890	−	141.965i	0.875054	−	0.505213i	0.869025	+	0.494769i	$0.164747\pi$
$282$		0			0
$283$	180.901	−	313.329i	0.639225	−	1.10717i	−0.346378	−	0.938095i	$-0.612589\pi$
$283$	180.901	−	313.329i	0.639225	−	1.10717i	0.985603	−	0.169075i	$-0.0540781\pi$
$284$	−170.404	−	98.3829i	−0.600015	−	0.346419i
$285$		0			0
$286$	−35.0314	−	60.6762i	−0.122487	−	0.212154i
$287$			191.335i			0.666673i
$288$		0			0
$289$	−530.666			−1.83622
$290$	−7.11895	+	4.11013i	−0.0245481	+	0.0141729i
$291$		0			0
$292$	93.6849	−	162.267i	0.320839	−	0.555709i
$293$	16.2725	+	9.39495i	0.0555376	+	0.0320647i	0.527512	−	0.849548i	$-0.323125\pi$
$293$	16.2725	+	9.39495i	0.0555376	+	0.0320647i	−0.471974	+	0.881612i	$0.656458\pi$
$294$		0			0
$295$	−106.636	−	184.698i	−0.361477	−	0.626096i
$296$			106.070i			0.358344i
$297$		0			0
$298$	−248.526			−0.833980
$299$	−129.726	+	74.8973i	−0.433866	+	0.250493i
$300$		0			0
$301$	49.7574	−	86.1824i	0.165307	−	0.286320i
$302$	318.867	+	184.098i	1.05585	+	0.609596i
$303$		0			0
$304$	−21.3328	−	36.9494i	−0.0701735	−	0.121544i
$305$		−	32.7139i		−	0.107259i
$306$		0			0
$307$	158.613			0.516656			0.258328	−	0.966057i	$-0.416828\pi$
$307$	158.613			0.516656			0.258328	+	0.966057i	$0.416828\pi$
$308$	11.6986	−	6.75418i	0.0379824	−	0.0219292i
$309$		0			0
$310$	51.8273	−	89.7675i	0.167185	−	0.289573i
$311$	139.638	+	80.6198i	0.448996	+	0.259228i	0.707406	−	0.706807i	$-0.249865\pi$
$311$	139.638	+	80.6198i	0.448996	+	0.259228i	−0.258410	+	0.966035i	$0.583199\pi$
$312$		0			0
$313$	−297.789	−	515.785i	−0.951402	−	1.64788i	−0.742395	−	0.669963i	$-0.766310\pi$
$313$	−297.789	−	515.785i	−0.951402	−	1.64788i	−0.209008	−	0.977914i	$-0.567023\pi$
$314$		−	399.589i		−	1.27258i
$315$		0			0
$316$	188.134			0.595362
$317$	377.931	−	218.199i	1.19221	−	0.688324i	0.233404	−	0.972380i	$-0.425013\pi$
$317$	377.931	−	218.199i	1.19221	−	0.688324i	0.958808	+	0.284056i	$0.0916802\pi$
$318$		0			0
$319$	2.79244	−	4.83665i	0.00875373	−	0.0151619i
$320$	18.4077	+	10.6277i	0.0575242	+	0.0332116i
$321$		0			0
$322$	−14.4405	−	25.0116i	−0.0448462	−	0.0776759i
$323$		−	305.376i		−	0.945438i
$324$		0			0
$325$	−348.168			−1.07129
$326$	−15.5420	+	8.97315i	−0.0476747	+	0.0275250i
$327$		0			0
$328$	102.273	−	177.142i	0.311808	−	0.540067i
$329$	100.462	+	58.0015i	0.305354	+	0.176296i
$330$		0			0
$331$	273.895	+	474.401i	0.827478	+	1.43323i	0.900010	+	0.435868i	$0.143559\pi$
$331$	273.895	+	474.401i	0.827478	+	1.43323i	−0.0725321	+	0.997366i	$0.523108\pi$
$332$			82.6139i			0.248837i
$333$		0			0
$334$	299.309			0.896134
$335$	170.406	−	98.3840i	0.508675	−	0.293683i
$336$		0			0
$337$	311.892	−	540.213i	0.925495	−	1.60300i	0.134732	−	0.990882i	$-0.456983\pi$
$337$	311.892	−	540.213i	0.925495	−	1.60300i	0.790763	−	0.612123i	$-0.209684\pi$
$338$	−254.276	−	146.806i	−0.752296	−	0.434338i
$339$		0			0
$340$	76.0674	+	131.753i	0.223728	+	0.387508i
$341$			70.4234i			0.206520i
$342$		0			0
$343$	−18.5203			−0.0539949
$344$	−92.1328	+	53.1929i	−0.267828	+	0.154631i
$345$		0			0
$346$	−82.3700	+	142.669i	−0.238064	+	0.412338i
$347$	317.390	+	183.245i	0.914670	+	0.528085i	0.881931	−	0.471379i	$-0.156244\pi$
$347$	317.390	+	183.245i	0.914670	+	0.528085i	0.0327391	+	0.999464i	$0.489577\pi$
$348$		0			0
$349$	244.644	+	423.735i	0.700985	+	1.21414i	0.968121	+	0.250482i	$0.0805892\pi$
$349$	244.644	+	423.735i	0.700985	+	1.21414i	−0.267136	+	0.963659i	$0.586077\pi$
$350$		−	67.1280i		−	0.191794i
$351$		0			0
$352$	−14.4410			−0.0410257
$353$	−304.776	+	175.963i	−0.863389	+	0.498478i	−0.865146	−	0.501521i	$-0.832774\pi$
$353$	−304.776	+	175.963i	−0.863389	+	0.498478i	0.00175684	+	0.999998i	$0.499441\pi$
$354$		0			0
$355$	−130.698	+	226.376i	−0.368164	+	0.637679i
$356$	130.345	+	75.2547i	0.366137	+	0.211390i
$357$		0			0
$358$	−192.880	−	334.078i	−0.538772	−	0.933180i
$359$		−	7.11763i		−	0.0198263i	−0.999951	−	0.00991313i	$-0.996845\pi$
$359$		−	7.11763i		−	0.0198263i	0.999951	−	0.00991313i	$-0.00315550\pi$
$360$		0			0
$361$	−247.228			−0.684843
$362$	−33.2188	+	19.1789i	−0.0917647	+	0.0529804i
$363$		0			0
$364$	51.3450	−	88.9321i	0.141058	−	0.244319i
$365$	−215.566	−	124.457i	−0.590592	−	0.340978i
$366$		0			0
$367$	−63.6226	−	110.198i	−0.173359	−	0.300266i	0.766233	−	0.642562i	$-0.222129\pi$
$367$	−63.6226	−	110.198i	−0.173359	−	0.300266i	−0.939592	+	0.342296i	$0.888795\pi$
$368$			30.8750i			0.0838995i
$369$		0			0
$370$	140.910			0.380838
$371$	−55.5845	+	32.0917i	−0.149823	+	0.0865006i
$372$		0			0
$373$	29.7402	−	51.5115i	0.0797324	−	0.138101i	−0.823402	−	0.567458i	$-0.807927\pi$
$373$	29.7402	−	51.5115i	0.0797324	−	0.138101i	0.903134	+	0.429358i	$0.141260\pi$
$374$	−89.5133	−	51.6805i	−0.239340	−	0.138183i
$375$		0			0
$376$	−62.0062	−	107.398i	−0.164910	−	0.285633i
$377$		−	42.4560i		−	0.112615i
$378$		0			0
$379$	512.562			1.35241			0.676204	−	0.736715i	$-0.263624\pi$
$379$	512.562			1.35241			0.676204	+	0.736715i	$0.263624\pi$
$380$	−49.0860	+	28.3398i	−0.129174	+	0.0745785i
$381$		0			0
$382$	−160.553	+	278.086i	−0.420296	+	0.727975i
$383$	−129.942	−	75.0220i	−0.339274	−	0.195880i	0.320677	−	0.947189i	$-0.396090\pi$
$383$	−129.942	−	75.0220i	−0.339274	−	0.195880i	−0.659951	+	0.751309i	$0.729423\pi$
$384$		0			0
$385$	−8.97269	−	15.5412i	−0.0233057	−	0.0403666i
$386$			338.961i			0.878137i
$387$		0			0
$388$	−328.264			−0.846041
$389$	−505.762	+	292.002i	−1.30016	+	0.750648i	−0.980431	−	0.196862i	$-0.936925\pi$
$389$	−505.762	+	292.002i	−1.30016	+	0.750648i	−0.319728	+	0.947509i	$0.603592\pi$
$390$		0			0
$391$	−110.493	+	191.380i	−0.282591	+	0.489463i
$392$	17.1464	+	9.89949i	0.0437409	+	0.0252538i
$393$		0			0
$394$	98.4882	+	170.586i	0.249970	+	0.432961i
$395$		−	249.930i		−	0.632733i
$396$		0			0
$397$	321.479			0.809770			0.404885	−	0.914368i	$-0.367312\pi$
$397$	321.479			0.809770			0.404885	+	0.914368i	$0.367312\pi$
$398$	87.6085	−	50.5808i	0.220122	−	0.127087i
$399$		0			0
$400$	−35.8814	+	62.1485i	−0.0897036	+	0.155371i
$401$	289.593	+	167.196i	0.722176	+	0.416949i	0.815553	−	0.578682i	$-0.196433\pi$
$401$	289.593	+	167.196i	0.722176	+	0.416949i	−0.0933768	+	0.995631i	$0.529766\pi$
$402$		0			0
$403$	267.678	+	463.632i	0.664213	+	1.15045i
$404$			34.1945i			0.0846399i
$405$		0			0
$406$	8.18567			0.0201617
$407$	−82.9090	+	47.8675i	−0.203708	+	0.117611i
$408$		0			0
$409$	23.0372	−	39.9017i	0.0563258	−	0.0975591i	−0.836488	−	0.547986i	$-0.815395\pi$
$409$	23.0372	−	39.9017i	0.0563258	−	0.0975591i	0.892813	+	0.450427i	$0.148728\pi$
$410$	−235.327	−	135.866i	−0.573968	−	0.331381i
$411$		0			0
$412$	139.689	+	241.949i	0.339052	+	0.587255i
$413$			212.374i			0.514223i
$414$		0			0
$415$	109.750			0.264457
$416$	−95.0725	+	54.8901i	−0.228540	+	0.131947i
$417$		0			0
$418$	19.2542	−	33.3493i	0.0460627	−	0.0797829i
$419$	547.560	+	316.134i	1.30683	+	0.754496i	0.981565	−	0.191128i	$-0.0612145\pi$
$419$	547.560	+	316.134i	1.30683	+	0.754496i	0.325261	+	0.945624i	$0.394548\pi$
$420$		0			0
$421$	278.114	+	481.708i	0.660604	+	1.14420i	0.980457	+	0.196732i	$0.0630329\pi$
$421$	278.114	+	481.708i	0.660604	+	1.14420i	−0.319854	+	0.947467i	$0.603634\pi$
$422$		−	442.000i		−	1.04739i
$423$		0			0
$424$	68.6150			0.161828
$425$	−444.825	+	256.820i	−1.04665	+	0.604282i
$426$		0			0
$427$	−16.2881	+	28.2119i	−0.0381455	+	0.0660700i
$428$	42.1975	+	24.3628i	0.0985923	+	0.0569223i
$429$		0			0
$430$	70.6649	+	122.395i	0.164337	+	0.284640i
$431$			374.687i			0.869344i	0.900589	+	0.434672i	$0.143136\pi$
$431$			374.687i			0.869344i	−0.900589	+	0.434672i	$0.856864\pi$
$432$		0			0
$433$	176.315			0.407195			0.203598	−	0.979055i	$-0.434737\pi$
$433$	176.315			0.407195			0.203598	+	0.979055i	$0.434737\pi$
$434$	−89.3899	+	51.6093i	−0.205967	+	0.118915i
$435$		0			0
$436$	30.8295	−	53.3983i	0.0707099	−	0.122473i
$437$	−71.3009	−	41.1656i	−0.163160	−	0.0942004i
$438$		0			0
$439$	179.794	+	311.412i	0.409554	+	0.709368i	0.994840	−	0.101459i	$-0.0323511\pi$
$439$	179.794	+	311.412i	0.409554	+	0.709368i	−0.585286	+	0.810827i	$0.699018\pi$
$440$			19.1844i			0.0436009i
$441$		0			0
$442$	−785.747			−1.77771
$443$	−243.965	+	140.853i	−0.550712	+	0.317954i	−0.749409	−	0.662107i	$-0.769662\pi$
$443$	−243.965	+	140.853i	−0.550712	+	0.317954i	0.198697	+	0.980061i	$0.436329\pi$
$444$		0			0
$445$	99.9732	−	173.159i	0.224659	−	0.389120i
$446$	−138.701	−	80.0791i	−0.310989	−	0.179550i
$447$		0			0
$448$	−10.5830	−	18.3303i	−0.0236228	−	0.0409159i
$449$		−	110.602i		−	0.246329i	−0.992386	−	0.123164i	$-0.960696\pi$
$449$		−	110.602i		−	0.246329i	0.992386	−	0.123164i	$-0.0393042\pi$
$450$		0			0
$451$	184.616			0.409348
$452$	79.3151	−	45.7926i	0.175476	−	0.101311i
$453$		0			0
$454$	183.356	−	317.582i	0.403868	−	0.699520i
$455$	−118.143	−	68.2100i	−0.259655	−	0.149912i
$456$		0			0
$457$	331.492	+	574.162i	0.725366	+	1.25637i	0.958823	+	0.284004i	$0.0916630\pi$
$457$	331.492	+	574.162i	0.725366	+	1.25637i	−0.233457	+	0.972367i	$0.575004\pi$
$458$			401.074i			0.875708i
$459$		0			0
$460$	41.0164			0.0891660
$461$	−612.243	+	353.479i	−1.32808	+	0.766765i	−0.985002	−	0.172543i	$-0.944802\pi$
$461$	−612.243	+	353.479i	−1.32808	+	0.766765i	−0.343074	+	0.939308i	$0.611468\pi$
$462$		0			0
$463$	−255.172	+	441.971i	−0.551127	+	0.954581i	0.447066	+	0.894501i	$0.352469\pi$
$463$	−255.172	+	441.971i	−0.551127	+	0.954581i	−0.998194	+	0.0600798i	$0.980864\pi$
$464$	−7.57846	−	4.37542i	−0.0163329	−	0.00942979i
$465$		0			0
$466$	86.2947	+	149.467i	0.185182	+	0.320744i
$467$			204.177i			0.437211i	0.975813	+	0.218605i	$0.0701507\pi$
$467$			204.177i			0.437211i	−0.975813	+	0.218605i	$0.929849\pi$
$468$		0			0
$469$	−195.940			−0.417783
$470$	−142.674	+	82.3731i	−0.303562	+	0.175262i
$471$		0			0
$472$	113.519	−	196.620i	0.240506	−	0.416568i
$473$	−83.1559	−	48.0101i	−0.175805	−	0.101501i
$474$		0			0
$475$	−95.6813	−	165.725i	−0.201434	−	0.348894i
$476$		−	151.495i		−	0.318266i
$477$		0			0
$478$	157.417			0.329324
$479$	−2.01637	+	1.16415i	−0.00420955	+	0.00243038i	−0.502103	−	0.864808i	$-0.667440\pi$
$479$	−2.01637	+	1.16415i	−0.00420955	+	0.00243038i	0.497894	+	0.867238i	$0.334107\pi$
$480$		0			0
$481$	−363.887	+	630.270i	−0.756521	+	1.31033i
$482$	126.272	+	72.9034i	0.261976	+	0.151252i
$483$		0			0
$484$	114.483	+	198.290i	0.236535	+	0.409691i
$485$			436.087i			0.899148i
$486$		0			0
$487$	−700.930			−1.43928			−0.719641	−	0.694347i	$-0.755693\pi$
$487$	−700.930			−1.43928			−0.719641	+	0.694347i	$0.755693\pi$
$488$	30.1598	−	17.4128i	0.0618028	−	0.0356819i
$489$		0			0
$490$	13.1511	−	22.7784i	0.0268390	−	0.0464866i
$491$	−779.874	−	450.261i	−1.58834	−	0.917028i	−0.993581	−	0.113122i	$-0.963915\pi$
$491$	−779.874	−	450.261i	−1.58834	−	0.917028i	−0.594757	−	0.803905i	$-0.702752\pi$
$492$		0			0
$493$	−31.3169	−	54.2425i	−0.0635231	−	0.110025i
$494$		−	292.739i		−	0.592590i
$495$		0			0
$496$	110.345			0.222470
$497$	225.424	−	130.148i	0.453568	−	0.261868i
$498$		0			0
$499$	218.689	−	378.780i	0.438254	−	0.759079i	−0.559301	−	0.828965i	$-0.688930\pi$
$499$	218.689	−	378.780i	0.438254	−	0.759079i	0.997555	+	0.0698863i	$0.0222636\pi$
$500$	197.611	+	114.090i	0.395221	+	0.228181i
$501$		0			0
$502$	−301.591	−	522.371i	−0.600779	−	1.04058i
$503$			359.340i			0.714394i	0.934029	+	0.357197i	$0.116268\pi$
$503$			359.340i			0.714394i	−0.934029	+	0.357197i	$0.883732\pi$
$504$		0			0
$505$	45.4262			0.0899529
$506$	−24.1333	+	13.9334i	−0.0476942	+	0.0275363i
$507$		0			0
$508$	187.439	−	324.655i	0.368975	−	0.639084i
$509$	563.137	+	325.127i	1.10636	+	0.638757i	0.937884	−	0.346949i	$-0.112782\pi$
$509$	563.137	+	325.127i	1.10636	+	0.638757i	0.168475	+	0.985706i	$0.446116\pi$
$510$		0			0
$511$	123.934	+	214.659i	0.242531	+	0.420077i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	−60.3351			−0.117383
$515$	321.421	−	185.572i	0.624118	−	0.360335i
$516$		0			0
$517$	55.9647	−	96.9336i	0.108249	−	0.187493i
$518$	−121.518	−	70.1587i	−0.234591	−	0.135441i
$519$		0			0
$520$	72.9196	+	126.300i	0.140230	+	0.242885i
$521$			952.688i			1.82858i	0.405065	+	0.914288i	$0.367249\pi$
$521$			952.688i			1.82858i	−0.405065	+	0.914288i	$0.632751\pi$
$522$		0			0
$523$	515.678			0.985999			0.493000	−	0.870030i	$-0.335900\pi$
$523$	515.678			0.985999			0.493000	+	0.870030i	$0.335900\pi$
$524$	48.1710	−	27.8116i	0.0919294	−	0.0530755i
$525$		0			0
$526$	−145.790	+	252.515i	−0.277166	+	0.480066i
$527$	683.979	+	394.895i	1.29787	+	0.749327i
$528$		0			0
$529$	−234.710	−	406.530i	−0.443687	−	0.768488i
$530$		−	91.1526i		−	0.171986i
$531$		0			0
$532$	56.4412			0.106092
$533$	1215.42	−	701.722i	2.28033	−	1.31655i
$534$		0			0
$535$	32.3651	−	56.0579i	0.0604954	−	0.104781i
$536$	181.405	+	104.734i	0.338443	+	0.195400i
$537$		0			0
$538$	−319.902	−	554.087i	−0.594614	−	1.02990i
$539$			17.8699i			0.0331538i
$540$		0			0
$541$	−299.942			−0.554422			−0.277211	−	0.960809i	$-0.589410\pi$
$541$	−299.942			−0.554422			−0.277211	+	0.960809i	$0.589410\pi$
$542$	−261.037	+	150.710i	−0.481618	+	0.278062i
$543$		0			0
$544$	−80.9773	+	140.257i	−0.148855	+	0.257825i
$545$	−70.9377	−	40.9559i	−0.130161	−	0.0751485i
$546$		0			0
$547$	36.0805	+	62.4933i	0.0659608	+	0.114247i	0.897120	−	0.441787i	$-0.145655\pi$
$547$	36.0805	+	62.4933i	0.0659608	+	0.114247i	−0.831159	+	0.556035i	$0.812322\pi$
$548$			400.514i			0.730864i
$549$		0			0
$550$	−64.7707			−0.117765
$551$	20.2087	−	11.6675i	0.0366764	−	0.0211751i
$552$		0			0
$553$	−124.439	+	215.535i	−0.225025	+	0.389756i
$554$	123.892	+	71.5292i	0.223632	+	0.129114i
$555$		0			0
$556$	−28.9683	−	50.1745i	−0.0521012	−	0.0902420i
$557$		−	472.989i		−	0.849172i	−0.905388	−	0.424586i	$-0.860420\pi$
$557$		−	472.989i		−	0.849172i	0.905388	−	0.424586i	$-0.139580\pi$
$558$		0			0
$559$	−729.941			−1.30580
$560$	−24.3512	+	14.0592i	−0.0434842	+	0.0251056i
$561$		0			0
$562$	200.769	−	347.741i	0.357239	−	0.618757i
$563$	−188.621	−	108.901i	−0.335029	−	0.193429i	0.323042	−	0.946384i	$-0.395294\pi$
$563$	−188.621	−	108.901i	−0.335029	−	0.193429i	−0.658072	+	0.752955i	$0.728628\pi$
$564$		0			0
$565$	−60.8338	−	105.367i	−0.107671	−	0.186491i
$566$		−	511.664i		−	0.904001i
$567$		0			0
$568$	−278.269			−0.489910
$569$	421.719	−	243.479i	0.741157	−	0.427907i	−0.0813326	−	0.996687i	$-0.525918\pi$
$569$	421.719	−	243.479i	0.741157	−	0.427907i	0.822490	+	0.568780i	$0.192584\pi$
$570$		0			0
$571$	259.672	−	449.765i	0.454767	−	0.787679i	−0.543908	−	0.839145i	$-0.683056\pi$
$571$	259.672	−	449.765i	0.454767	−	0.787679i	0.998675	+	0.0514656i	$0.0163892\pi$
$572$	−85.8091	−	49.5419i	−0.150016	−	0.0866117i
$573$		0			0
$574$	135.294	+	234.337i	0.235705	+	0.408252i
$575$			138.480i			0.240835i
$576$		0			0
$577$	139.881			0.242428			0.121214	−	0.992626i	$-0.461321\pi$
$577$	139.881			0.242428			0.121214	+	0.992626i	$0.461321\pi$
$578$	−649.931	+	375.238i	−1.12445	+	0.649200i
$579$		0			0
$580$	−5.81260	+	10.0677i	−0.0100217	+	0.0173581i
$581$	−94.6462	−	54.6440i	−0.162902	−	0.0940516i
$582$		0			0
$583$	30.9647	+	53.6325i	0.0531128	+	0.0919940i
$584$		−	264.981i		−	0.453735i
$585$		0			0
$586$	26.5729			0.0453463
$587$	293.484	−	169.443i	0.499973	−	0.288660i	−0.228729	−	0.973490i	$-0.573457\pi$
$587$	293.484	−	169.443i	0.499973	−	0.288660i	0.728702	+	0.684830i	$0.240124\pi$
$588$		0			0
$589$	−147.123	+	254.825i	−0.249784	+	0.432639i
$590$	−261.203	−	150.806i	−0.442717	−	0.255603i
$591$		0			0
$592$	75.0028	+	129.909i	0.126694	+	0.219440i
$593$		−	111.970i		−	0.188820i	−0.995533	−	0.0944101i	$-0.969904\pi$
$593$		−	111.970i		−	0.188820i	0.995533	−	0.0944101i	$-0.0300965\pi$
$594$		0			0
$595$	−201.255			−0.338244
$596$	−304.381	+	175.734i	−0.510706	+	0.294856i
$597$		0			0
$598$	−105.921	+	183.460i	−0.177125	+	0.306790i
$599$	439.649	+	253.831i	0.733971	+	0.423758i	0.819873	−	0.572545i	$-0.194044\pi$
$599$	439.649	+	253.831i	0.733971	+	0.423758i	−0.0859021	+	0.996304i	$0.527377\pi$
$600$		0			0
$601$	−49.7002	−	86.0833i	−0.0826959	−	0.143233i	0.821711	−	0.569904i	$-0.193020\pi$
$601$	−49.7002	−	86.0833i	−0.0826959	−	0.143233i	−0.904407	+	0.426671i	$0.859686\pi$
$602$		−	140.735i		−	0.233779i
$603$		0			0
$604$	520.708			0.862099
$605$	263.422	−	152.087i	0.435408	−	0.251383i
$606$		0			0
$607$	−244.421	+	423.349i	−0.402670	+	0.697445i	−0.994047	−	0.108950i	$-0.965251\pi$
$607$	−244.421	+	423.349i	−0.402670	+	0.697445i	0.591377	+	0.806395i	$0.298584\pi$
$608$	−52.2544	−	30.1691i	−0.0859447	−	0.0496202i
$609$		0			0
$610$	−23.1322	−	40.0662i	−0.0379217	−	0.0656823i
$611$		−	850.882i		−	1.39261i
$612$		0			0
$613$	91.0276			0.148495			0.0742476	−	0.997240i	$-0.476344\pi$
$613$	91.0276			0.148495			0.0742476	+	0.997240i	$0.476344\pi$
$614$	194.261	−	112.157i	0.316386	−	0.182665i
$615$		0			0
$616$	9.55185	−	16.5443i	0.0155063	−	0.0268576i
$617$	−591.658	−	341.594i	−0.958927	−	0.553637i	−0.0630842	−	0.998008i	$-0.520094\pi$
$617$	−591.658	−	341.594i	−0.958927	−	0.553637i	−0.895843	+	0.444372i	$0.853427\pi$
$618$		0			0
$619$	−227.979	−	394.871i	−0.368302	−	0.637918i	0.620998	−	0.783812i	$-0.286727\pi$
$619$	−227.979	−	394.871i	−0.368302	−	0.637918i	−0.989300	+	0.145894i	$0.953394\pi$
$620$		−	146.590i		−	0.236435i
$621$		0			0
$622$	228.027			0.366603
$623$	−172.430	+	99.5526i	−0.276774	+	0.159795i
$624$		0			0
$625$	−72.6939	+	125.909i	−0.116310	+	0.201455i
$626$	−729.431	−	421.137i	−1.16522	−	0.672743i
$627$		0			0
$628$	−282.552	−	489.395i	−0.449924	−	0.779291i
$629$			1073.66i			1.70693i
$630$		0			0
$631$	857.311			1.35865			0.679327	−	0.733836i	$-0.262272\pi$
$631$	857.311			1.35865			0.679327	+	0.733836i	$0.262272\pi$
$632$	230.416	−	133.031i	0.364583	−	0.210492i
$633$		0			0
$634$	308.579	−	534.475i	0.486718	−	0.843021i
$635$	−431.292	−	249.007i	−0.679200	−	0.392137i
$636$		0			0
$637$	67.9230	+	117.646i	0.106630	+	0.184688i
$638$		−	7.89821i		−	0.0123796i
$639$		0			0
$640$	30.0597			0.0469683
$641$	869.558	−	502.040i	1.35657	−	0.783213i	0.367406	−	0.930061i	$-0.380246\pi$
$641$	869.558	−	502.040i	1.35657	−	0.783213i	0.989159	+	0.146847i	$0.0469125\pi$
$642$		0			0
$643$	−354.436	+	613.902i	−0.551223	+	0.954746i	0.446964	+	0.894552i	$0.352505\pi$
$643$	−354.436	+	613.902i	−0.551223	+	0.954746i	−0.998187	+	0.0601940i	$0.980828\pi$
$644$	−35.3718	−	20.4219i	−0.0549251	−	0.0317110i
$645$		0			0
$646$	−215.934	−	374.008i	−0.334263	−	0.578960i
$647$		−	906.254i		−	1.40070i	−0.713799	−	0.700351i	$-0.753027\pi$
$647$		−	906.254i		−	1.40070i	0.713799	−	0.700351i	$-0.246973\pi$
$648$		0			0
$649$	204.916			0.315741
$650$	−426.417	+	246.192i	−0.656026	+	0.378757i
$651$		0			0
$652$	−12.6900	+	21.9796i	−0.0194631	+	0.0337111i
$653$	−1028.26	−	593.667i	−1.57467	−	0.909138i	−0.995584	−	0.0938731i	$-0.970075\pi$
$653$	−1028.26	−	593.667i	−1.57467	−	0.909138i	−0.579089	−	0.815265i	$-0.696591\pi$
$654$		0			0
$655$	−36.9467	−	63.9935i	−0.0564071	−	0.0977000i
$656$		−	289.272i		−	0.440963i
$657$		0			0
$658$	164.053			0.249321
$659$	105.126	−	60.6946i	0.159524	−	0.0921010i	−0.418113	−	0.908395i	$-0.637308\pi$
$659$	105.126	−	60.6946i	0.159524	−	0.0921010i	0.577637	+	0.816294i	$0.303975\pi$
$660$		0			0
$661$	−235.670	+	408.193i	−0.356536	+	0.617539i	−0.987380	−	0.158372i	$-0.949376\pi$
$661$	−235.670	+	408.193i	−0.356536	+	0.617539i	0.630844	+	0.775910i	$0.282709\pi$
$662$	670.904	+	387.346i	1.01345	+	0.585116i
$663$		0			0
$664$	58.4169	+	101.181i	0.0879772	+	0.152381i
$665$		−	74.9801i		−	0.112752i
$666$		0			0
$667$	−16.8864			−0.0253170
$668$	366.577	−	211.643i	0.548768	−	0.316831i
$669$		0			0
$670$	139.136	−	240.991i	0.207666	−	0.359687i
$671$	27.2212	+	15.7161i	0.0405681	+	0.0234220i
$672$		0			0
$673$	−263.188	−	455.855i	−0.391067	−	0.677347i	0.601524	−	0.798855i	$-0.294560\pi$
$673$	−263.188	−	455.855i	−0.391067	−	0.677347i	−0.992591	+	0.121508i	$0.961227\pi$
$674$		−	882.163i		−	1.30885i
$675$		0			0
$676$	−415.231			−0.614247
$677$	571.501	−	329.956i	0.844167	−	0.487380i	−0.0145115	−	0.999895i	$-0.504619\pi$
$677$	571.501	−	329.956i	0.844167	−	0.487380i	0.858678	+	0.512515i	$0.171286\pi$
$678$		0			0
$679$	217.126	−	376.073i	0.319773	−	0.553864i
$680$	186.326	+	107.576i	0.274009	+	0.158199i
$681$		0			0
$682$	49.7969	+	86.2507i	0.0730160	+	0.126467i
$683$			412.168i			0.603467i	0.953392	+	0.301734i	$0.0975654\pi$
$683$			412.168i			0.603467i	−0.953392	+	0.301734i	$0.902435\pi$
$684$		0			0
$685$	532.068			0.776742
$686$	−22.6826	+	13.0958i	−0.0330650	+	0.0190901i
$687$		0			0
$688$	−75.2262	+	130.296i	−0.109340	+	0.189383i
$689$	407.712	+	235.393i	0.591745	+	0.341644i
$690$		0			0
$691$	−364.801	−	631.853i	−0.527931	−	0.914404i	−0.999470	−	0.0325584i	$-0.989634\pi$
$691$	−364.801	−	631.853i	−0.527931	−	0.914404i	0.471538	−	0.881845i	$-0.343699\pi$
$692$			232.978i			0.336673i
$693$		0			0
$694$	518.296			0.746825
$695$	−66.6551	+	38.4833i	−0.0959066	+	0.0553717i
$696$		0			0
$697$	1035.22	−	1793.06i	1.48526	−	2.57254i
$698$	599.252	+	345.978i	0.858527	+	0.495671i
$699$		0			0
$700$	−47.4667	−	82.2147i	−0.0678096	−	0.117450i
$701$			56.3677i			0.0804104i	0.999191	+	0.0402052i	$0.0128012\pi$
$701$			56.3677i			0.0804104i	−0.999191	+	0.0402052i	$0.987199\pi$
$702$		0			0
$703$	−400.004			−0.568996
$704$	−17.6866	+	10.2114i	−0.0251230	+	0.0145048i
$705$		0			0
$706$	−248.849	+	431.019i	−0.352477	+	0.610508i
$707$	−39.1747	−	22.6175i	−0.0554098	−	0.0319909i
$708$		0			0
$709$	−391.057	−	677.331i	−0.551561	−	0.955332i	−0.998162	−	0.0605991i	$-0.980699\pi$
$709$	−391.057	−	677.331i	−0.551561	−	0.955332i	0.446601	−	0.894733i	$-0.352634\pi$
$710$			369.670i			0.520662i
$711$		0			0
$712$	212.852			0.298950
$713$	184.404	−	106.466i	0.258632	−	0.149321i
$714$		0			0
$715$	−65.8147	+	113.994i	−0.0920485	+	0.159433i
$716$	−472.458	−	272.774i	−0.659858	−	0.380969i
$717$		0			0
$718$	−5.03292	−	8.71728i	−0.00700964	−	0.0121411i
$719$		−	131.717i		−	0.183194i	−0.995796	−	0.0915971i	$-0.970803\pi$
$719$		−	131.717i		−	0.183194i	0.995796	−	0.0915971i	$-0.0291972\pi$
$720$		0			0
$721$	−369.583			−0.512598
$722$	−302.792	+	174.817i	−0.419379	+	0.242129i
$723$		0			0
$724$	−27.1230	+	46.9785i	−0.0374628	+	0.0648874i
$725$	−33.9908	−	19.6246i	−0.0468838	−	0.0270684i
$726$		0			0
$727$	−352.691	−	610.878i	−0.485132	−	0.840273i	0.514722	−	0.857357i	$-0.327895\pi$
$727$	−352.691	−	610.878i	−0.485132	−	0.840273i	−0.999854	+	0.0170841i	$0.994562\pi$
$728$		−	145.226i		−	0.199486i
$729$		0			0
$730$	−352.018			−0.482216
$731$	−932.584	+	538.428i	−1.27576	+	0.736563i
$732$		0			0
$733$	−123.262	+	213.496i	−0.168161	+	0.291264i	−0.937773	−	0.347248i	$-0.887116\pi$
$733$	−123.262	+	213.496i	−0.168161	+	0.291264i	0.769612	+	0.638512i	$0.220450\pi$
$734$	−155.843	−	89.9760i	−0.212320	−	0.122583i
$735$		0			0
$736$	21.8319	+	37.8140i	0.0296630	+	0.0513777i
$737$			189.059i			0.256525i
$738$		0			0
$739$	573.403			0.775918			0.387959	−	0.921677i	$-0.373180\pi$
$739$	573.403			0.775918			0.387959	+	0.921677i	$0.373180\pi$
$740$	172.579	−	99.6385i	0.233215	−	0.134647i
$741$		0			0
$742$	−45.3845	+	78.6083i	−0.0611651	+	0.105941i
$743$	−245.489	−	141.733i	−0.330402	−	0.190758i	0.325618	−	0.945502i	$-0.394428\pi$
$743$	−245.489	−	141.733i	−0.330402	−	0.190758i	−0.656020	+	0.754744i	$0.727761\pi$
$744$		0			0
$745$	233.457	+	404.359i	0.313365	+	0.542764i
$746$		−	84.1180i		−	0.112759i
$747$		0			0
$748$	−146.175			−0.195421
$749$	−55.8221	+	32.2289i	−0.0745288	+	0.0430292i
$750$		0			0
$751$	−522.497	+	904.991i	−0.695735	+	1.20505i	0.274198	+	0.961673i	$0.411588\pi$
$751$	−522.497	+	904.991i	−0.695735	+	1.20505i	−0.969932	+	0.243375i	$0.921746\pi$
$752$	−151.884	−	87.6900i	−0.201973	−	0.116609i
$753$		0			0
$754$	−30.0209	−	51.9978i	−0.0398156	−	0.0689626i
$755$		−	691.742i		−	0.916215i
$756$		0			0
$757$	595.724			0.786954			0.393477	−	0.919334i	$-0.371272\pi$
$757$	595.724			0.786954			0.393477	+	0.919334i	$0.371272\pi$
$758$	627.758	−	362.436i	0.828177	−	0.478148i
$759$		0			0
$760$	−40.0786	+	69.4181i	−0.0527349	+	0.0913396i
$761$	−721.701	−	416.674i	−0.948359	−	0.547535i	−0.0557881	−	0.998443i	$-0.517767\pi$
$761$	−721.701	−	416.674i	−0.948359	−	0.547535i	−0.892571	+	0.450907i	$0.851100\pi$
$762$		0			0
$763$	40.7836	+	70.6393i	0.0534516	+	0.0925809i
$764$			454.113i			0.594389i
$765$		0			0
$766$	−212.194			−0.277016
$767$	1349.06	−	778.882i	1.75888	−	1.01549i
$768$		0			0
$769$	−158.346	+	274.264i	−0.205912	+	0.356650i	−0.950423	−	0.310960i	$-0.899349\pi$
$769$	−158.346	+	274.264i	−0.205912	+	0.356650i	0.744511	+	0.667610i	$0.232683\pi$
$770$	−21.9785	−	12.6893i	−0.0285435	−	0.0164796i
$771$		0			0
$772$	239.682	+	415.141i	0.310468	+	0.537747i
$773$		−	367.509i		−	0.475432i	−0.971335	−	0.237716i	$-0.923601\pi$
$773$		−	367.509i		−	0.475432i	0.971335	−	0.237716i	$-0.0763987\pi$
$774$		0			0
$775$	494.918			0.638604
$776$	−402.039	+	232.118i	−0.518092	+	0.299121i
$777$		0			0
$778$	−412.953	+	715.256i	−0.530788	+	0.919352i
$779$	668.026	+	385.685i	0.857544	+	0.495103i
$780$		0			0
$781$	−125.578	−	217.507i	−0.160791	−	0.278498i
$782$			312.522i			0.399645i
$783$		0			0
$784$	28.0000			0.0357143
$785$	−650.144	+	375.361i	−0.828209	+	0.478166i
$786$		0			0
$787$	144.573	−	250.408i	0.183702	−	0.318181i	−0.759437	−	0.650581i	$-0.774525\pi$
$787$	144.573	−	250.408i	0.183702	−	0.318181i	0.943138	+	0.332401i	$0.107859\pi$
$788$	241.246	+	139.283i	0.306149	+	0.176755i
$789$		0			0
$790$	−176.727	−	306.100i	−0.223705	−	0.387469i
$791$			121.156i			0.153168i
$792$		0			0
$793$	238.947			0.301320
$794$	393.729	−	227.320i	0.495881	−	0.286297i
$795$		0			0
$796$	71.5320	−	123.897i	0.0898643	−	0.155650i
$797$	−762.615	−	440.296i	−0.956857	−	0.552442i	−0.0616529	−	0.998098i	$-0.519637\pi$
$797$	−762.615	−	440.296i	−0.956857	−	0.552442i	−0.895204	+	0.445656i	$0.852971\pi$
$798$		0			0
$799$	−627.637	−	1087.10i	−0.785529	−	1.36058i
$800$			101.488i			0.126860i
$801$		0			0
$802$	472.903			0.589655
$803$	207.121	−	119.581i	0.257934	−	0.148918i
$804$		0			0
$805$	−27.1298	+	46.9902i	−0.0337016	+	0.0583729i
$806$	655.674	+	378.554i	0.813492	+	0.469670i
$807$		0			0
$808$	24.1792	+	41.8796i	0.0299247	+	0.0518311i
$809$			776.794i			0.960190i	0.877217	+	0.480095i	$0.159398\pi$
$809$			776.794i			0.960190i	−0.877217	+	0.480095i	$0.840602\pi$
$810$		0			0
$811$	−985.397			−1.21504			−0.607520	−	0.794305i	$-0.707835\pi$
$811$	−985.397			−1.21504			−0.607520	+	0.794305i	$0.707835\pi$
$812$	10.0254	−	5.78814i	0.0123465	−	0.00712825i
$813$		0			0
$814$	−67.6949	+	117.251i	−0.0831632	+	0.144043i
$815$	29.1992	+	16.8582i	0.0358272	+	0.0206849i
$816$		0			0
$817$	−200.598	−	347.445i	−0.245530	−	0.425270i
$818$		−	65.1592i		−	0.0796567i
$819$		0			0
$820$	−384.287			−0.468643
$821$	−249.665	+	144.144i	−0.304098	+	0.175571i	−0.644282	−	0.764788i	$-0.722844\pi$
$821$	−249.665	+	144.144i	−0.304098	+	0.175571i	0.340184	+	0.940359i	$0.389511\pi$
$822$		0			0
$823$	−279.574	+	484.236i	−0.339701	+	0.588380i	−0.984376	−	0.176077i	$-0.943659\pi$
$823$	−279.574	+	484.236i	−0.339701	+	0.588380i	0.644675	+	0.764457i	$0.276993\pi$
$824$	342.168	+	197.551i	0.415252	+	0.239746i
$825$		0			0
$826$	150.171	+	260.104i	0.181805	+	0.314896i
$827$		−	402.564i		−	0.486776i	−0.969929	−	0.243388i	$-0.921741\pi$
$827$		−	402.564i		−	0.486776i	0.969929	−	0.243388i	$-0.0782589\pi$
$828$		0			0
$829$	123.079			0.148466			0.0742332	−	0.997241i	$-0.476349\pi$
$829$	123.079			0.148466			0.0742332	+	0.997241i	$0.476349\pi$
$830$	134.415	−	77.6048i	0.161946	−	0.0934997i
$831$		0			0
$832$	−77.6263	+	134.453i	−0.0933009	+	0.161602i
$833$	173.559	+	100.204i	0.208354	+	0.120293i
$834$		0			0
$835$	−281.161	−	486.984i	−0.336719	−	0.583215i
$836$		−	54.4591i		−	0.0651425i
$837$		0			0
$838$	894.162			1.06702
$839$	−1364.89	+	788.021i	−1.62681	+	0.939238i	−0.641770	+	0.766897i	$0.721800\pi$
$839$	−1364.89	+	788.021i	−1.62681	+	0.939238i	−0.985037	+	0.172341i	$0.944867\pi$
$840$		0			0
$841$	−418.107	+	724.182i	−0.497155	+	0.861097i
$842$	681.238	+	393.313i	0.809071	+	0.467117i
$843$		0			0
$844$	−312.541	−	541.338i	−0.370310	−	0.641395i
$845$			551.620i			0.652804i
$846$		0			0
$847$	−302.894			−0.357608
$848$	84.0358	−	48.5181i	0.0990988	−	0.0572147i
$849$		0			0
$850$	−363.198	+	629.078i	−0.427292	+	0.740091i
$851$	250.683	+	144.732i	0.294575	+	0.170073i
$852$		0			0
$853$	26.1971	+	45.3747i	0.0307117	+	0.0531943i	0.880973	−	0.473167i	$-0.156889\pi$
$853$	26.1971	+	45.3747i	0.0307117	+	0.0531943i	−0.850261	+	0.526361i	$0.823556\pi$
$854$			46.0698i			0.0539459i
$855$		0			0
$856$	68.9083			0.0805003
$857$	71.6612	−	41.3736i	0.0836187	−	0.0482773i	−0.457608	−	0.889154i	$-0.651294\pi$
$857$	71.6612	−	41.3736i	0.0836187	−	0.0482773i	0.541226	+	0.840877i	$0.317960\pi$
$858$		0			0
$859$	−56.9850	+	98.7008i	−0.0663387	+	0.114902i	−0.897287	−	0.441448i	$-0.854465\pi$
$859$	−56.9850	+	98.7008i	−0.0663387	+	0.114902i	0.830948	+	0.556350i	$0.187798\pi$
$860$	173.093	+	99.9353i	0.201271	+	0.116204i
$861$		0			0
$862$	264.944	+	458.896i	0.307359	+	0.532362i
$863$			864.215i			1.00141i	0.865619	+	0.500704i	$0.166925\pi$
$863$			864.215i			1.00141i	−0.865619	+	0.500704i	$0.833075\pi$
$864$		0			0
$865$	309.503			0.357807
$866$	215.941	−	124.674i	0.249355	−	0.143965i
$867$		0			0
$868$	−72.9865	+	126.416i	−0.0840858	+	0.145641i
$869$	207.966	+	120.069i	0.239316	+	0.138169i
$870$		0			0
$871$	718.610	+	1244.67i	0.825040	+	1.42901i
$872$		−	87.1990i		−	0.0999989i
$873$		0			0
$874$	−116.434			−0.133220
$875$	−261.414	+	150.928i	−0.298759	+	0.172489i
$876$		0			0
$877$	315.869	−	547.100i	0.360169	−	0.623832i	−0.627819	−	0.778359i	$-0.716052\pi$
$877$	315.869	−	547.100i	0.360169	−	0.623832i	0.987988	+	0.154528i	$0.0493856\pi$
$878$	440.404	+	254.267i	0.501599	+	0.289598i
$879$		0			0
$880$	13.5654	+	23.4960i	0.0154153	+	0.0267000i
$881$			293.562i			0.333215i	0.986023	+	0.166607i	$0.0532812\pi$
$881$			293.562i			0.333215i	−0.986023	+	0.166607i	$0.946719\pi$
$882$		0			0
$883$	−483.341			−0.547385			−0.273693	−	0.961817i	$-0.588245\pi$
$883$	−483.341			−0.547385			−0.273693	+	0.961817i	$0.588245\pi$
$884$	−962.339	+	555.607i	−1.08862	+	0.628515i
$885$		0			0
$886$	−199.197	+	345.019i	−0.224827	+	0.389412i
$887$	820.204	+	473.545i	0.924694	+	0.533872i	0.885130	−	0.465345i	$-0.154070\pi$
$887$	820.204	+	473.545i	0.924694	+	0.533872i	0.0395645	+	0.999217i	$0.487403\pi$
$888$		0			0
$889$	247.959	+	429.478i	0.278919	+	0.483102i
$890$		−	282.767i		−	0.317716i
$891$		0			0
$892$	−226.498			−0.253921
$893$	405.012	−	233.834i	0.453541	−	0.261852i
$894$		0			0
$895$	−362.371	+	627.644i	−0.404883	+	0.701278i
$896$	−25.9230	−	14.9666i	−0.0289319	−	0.0167038i
$897$		0			0
$898$	−78.2071	−	135.459i	−0.0870903	−	0.150845i
$899$			60.3509i			0.0671311i
$900$		0			0
$901$	694.532			0.770846
$902$	226.108	−	130.543i	0.250674	−	0.144727i
$903$		0			0
$904$	64.7605	−	112.168i	0.0716377	−	0.124080i
$905$	62.4093	+	36.0320i	0.0689605	+	0.0398144i
$906$		0			0
$907$	49.8208	+	86.2921i	0.0549292	+	0.0951401i	0.892183	−	0.451675i	$-0.149173\pi$
$907$	49.8208	+	86.2921i	0.0549292	+	0.0951401i	−0.837253	+	0.546815i	$0.815840\pi$
$908$		−	518.610i		−	0.571156i
$909$		0			0
$910$	−192.927			−0.212008
$911$	−1266.12	+	730.994i	−1.38981	+	0.802409i	−0.993294	−	0.115618i	$-0.963115\pi$
$911$	−1266.12	+	730.994i	−1.38981	+	0.802409i	−0.396519	+	0.918026i	$0.629782\pi$
$912$		0			0
$913$	−52.7250	+	91.3224i	−0.0577492	+	0.100025i
$914$	811.987	+	468.801i	0.888389	+	0.512911i
$915$		0			0
$916$	283.602	+	491.214i	0.309610	+	0.536260i
$917$			73.5825i			0.0802426i
$918$		0			0
$919$	−1025.26			−1.11562			−0.557811	−	0.829968i	$-0.688359\pi$
$919$	−1025.26			−1.11562			−0.557811	+	0.829968i	$0.688359\pi$
$920$	50.2346	−	29.0030i	0.0546028	−	0.0315250i
$921$		0			0
$922$	−499.894	+	865.843i	−0.542185	+	0.939092i
$923$	−1653.48	−	954.638i	−1.79142	−	1.03428i
$924$		0			0
$925$	336.401	+	582.664i	0.363677	+	0.629907i
$926$			721.735i			0.779412i
$927$		0			0
$928$	−12.3756			−0.0133357
$929$	1015.41	−	586.248i	1.09302	−	0.631053i	0.158638	−	0.987337i	$-0.449290\pi$
$929$	1015.41	−	586.248i	1.09302	−	0.631053i	0.934378	+	0.356284i	$0.115956\pi$
$930$		0			0
$931$	−37.3323	+	64.6615i	−0.0400992	+	0.0694538i
$932$	211.378	+	122.039i	0.226800	+	0.130943i
$933$		0			0
$934$	144.375	+	250.065i	0.154577	+	0.267736i
$935$			194.188i			0.207688i
$936$		0			0
$937$	989.490			1.05602			0.528009	−	0.849239i	$-0.322939\pi$
$937$	989.490			1.05602			0.528009	+	0.849239i	$0.322939\pi$
$938$	−239.977	+	138.551i	−0.255839	+	0.147708i
$939$		0			0
$940$	−116.493	+	201.772i	−0.123929	+	0.214651i
$941$	−208.192	−	120.200i	−0.221246	−	0.127736i	0.385281	−	0.922799i	$-0.374104\pi$
$941$	−208.192	−	120.200i	−0.221246	−	0.127736i	−0.606527	+	0.795063i	$0.707438\pi$
$942$		0			0
$943$	−279.102	−	483.419i	−0.295973	−	0.512640i
$944$		−	321.079i		−	0.340126i
$945$		0			0
$946$	−135.793			−0.143544
$947$	−1035.30	+	597.728i	−1.09324	+	0.631181i	−0.934436	−	0.356130i	$-0.884096\pi$
$947$	−1035.30	+	597.728i	−1.09324	+	0.631181i	−0.158801	+	0.987311i	$0.550763\pi$
$948$		0			0
$949$	909.052	−	1574.52i	0.957905	−	1.65914i
$950$	−234.370	−	135.314i	−0.246706	−	0.142436i
$951$		0			0
$952$	−107.123	−	185.542i	−0.112524	−	0.194897i
$953$			261.104i			0.273981i	0.990572	+	0.136991i	$0.0437430\pi$
$953$			261.104i			0.273981i	−0.990572	+	0.136991i	$0.956257\pi$
$954$		0			0
$955$	603.273			0.631700
$956$	192.795	−	111.310i	0.201669	−	0.116434i
$957$		0			0
$958$	−1.64636	+	2.85158i	−0.00171854	+	0.00297660i
$959$	−458.846	−	264.915i	−0.478463	−	0.276241i
$960$		0			0
$961$	99.9978	+	173.201i	0.104056	+	0.180230i
$962$			1029.23i			1.06988i
$963$		0			0
$964$	206.202			0.213902
$965$	551.500	−	318.409i	0.571502	−	0.329957i
$966$		0			0
$967$	552.812	−	957.498i	0.571677	−	0.990174i	−0.424717	−	0.905326i	$-0.639626\pi$
$967$	552.812	−	957.498i	0.571677	−	0.990174i	0.996394	−	0.0848474i	$-0.0270403\pi$
$968$	280.425	+	161.903i	0.289695	+	0.167256i
$969$		0			0
$970$	308.360	+	534.095i	0.317897	+	0.550614i
$971$		−	139.155i		−	0.143311i	−0.997429	−	0.0716554i	$-0.977172\pi$
$971$		−	139.155i		−	0.143311i	0.997429	−	0.0716554i	$-0.0228282\pi$
$972$		0			0
$973$	76.6429			0.0787696
$974$	−858.460	+	495.632i	−0.881376	+	0.508863i
$975$		0			0
$976$	24.6254	−	42.6524i	0.0252309	−	0.0437012i
$977$	−967.481	−	558.575i	−0.990257	−	0.571725i	−0.0849057	−	0.996389i	$-0.527059\pi$
$977$	−967.481	−	558.575i	−0.990257	−	0.571725i	−0.905351	+	0.424664i	$0.860392\pi$
$978$		0			0
$979$	96.0566	+	166.375i	0.0981170	+	0.169944i
$980$		−	37.1970i		−	0.0379561i
$981$		0			0
$982$	−1273.53			−1.29687
$983$	−1611.94	+	930.655i	−1.63982	+	0.946750i	−0.658925	+	0.752209i	$0.728989\pi$
$983$	−1611.94	+	930.655i	−1.63982	+	0.946750i	−0.980894	+	0.194541i	$0.937678\pi$
$984$		0			0
$985$	185.033	−	320.486i	0.187851	−	0.325367i
$986$	−76.7104	−	44.2888i	−0.0777996	−	0.0449176i
$987$		0			0
$988$	−206.998	−	358.531i	−0.209512	−	0.362886i
$989$			290.326i			0.293555i
$990$		0			0
$991$	−73.7864			−0.0744565			−0.0372283	−	0.999307i	$-0.511853\pi$
$991$	−73.7864			−0.0744565			−0.0372283	+	0.999307i	$0.511853\pi$
$992$	135.145	−	78.0259i	0.136235	−	0.0786551i
$993$		0			0
$994$	184.058	−	318.797i	0.185169	−	0.320721i
$995$	−164.593	−	95.0277i	−0.165420	−	0.0955053i
$996$		0			0
$997$	596.044	+	1032.38i	0.597838	+	1.03549i	0.993140	+	0.116934i	$0.0373066\pi$
$997$	596.044	+	1032.38i	0.597838	+	1.03549i	−0.395302	+	0.918551i	$0.629360\pi$
$998$		−	618.545i		−	0.619785i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.q.a.71.10		24
3.2	odd	2		126.3.q.a.113.6	yes	24
9.2	odd	6	inner	378.3.q.a.197.10		24
9.4	even	3		1134.3.b.c.323.19		24
9.5	odd	6		1134.3.b.c.323.6		24
9.7	even	3		126.3.q.a.29.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.q.a.29.6	✓	24	9.7	even	3
126.3.q.a.113.6	yes	24	3.2	odd	2
378.3.q.a.71.10		24	1.1	even	1	trivial
378.3.q.a.197.10		24	9.2	odd	6	inner
1134.3.b.c.323.6		24	9.5	odd	6
1134.3.b.c.323.19		24	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-2.30097 - 1.32846i) q^{5} +(1.32288 + 2.29129i) q^{7} -2.82843i q^{8} -3.75747 q^{10} +(2.21082 - 1.27642i) q^{11} +(9.70329 - 16.8066i) q^{13} +(3.24037 + 1.87083i) q^{14} +(-2.00000 - 3.46410i) q^{16} -28.6298i q^{17} +10.6664 q^{19} +(-4.60194 + 2.65693i) q^{20} +(1.80513 - 3.12658i) q^{22} +(-6.68464 - 3.85938i) q^{23} +(-8.97036 - 15.5371i) q^{25} -27.4451i q^{26} +5.29150 q^{28} +(1.89461 - 1.09386i) q^{29} +(-13.7932 + 23.8904i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-20.2443 - 35.0642i) q^{34} -7.02958i q^{35} -37.5014 q^{37} +(13.0636 - 7.54227i) q^{38} +(-3.75747 + 6.50812i) q^{40} +(62.6292 + 36.1590i) q^{41} +(-18.8065 - 32.5739i) q^{43} -5.10568i q^{44} -10.9160 q^{46} +(37.9709 - 21.9225i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(-21.9728 - 12.6860i) q^{50} +(-19.4066 - 33.6132i) q^{52} +24.2591i q^{53} -6.78272 q^{55} +(6.48074 - 3.74166i) q^{56} +(1.54695 - 2.67939i) q^{58} +(69.5157 + 40.1349i) q^{59} +(6.15634 + 10.6631i) q^{61} +39.0129i q^{62} -8.00000 q^{64} +(-44.6539 + 25.7810i) q^{65} +(-37.0292 + 64.1364i) q^{67} +(-49.5883 - 28.6298i) q^{68} +(-4.97066 - 8.60944i) q^{70} -98.3829i q^{71} +93.6849 q^{73} +(-45.9296 + 26.5175i) q^{74} +(10.6664 - 18.4747i) q^{76} +(5.84929 + 3.37709i) q^{77} +(47.0336 + 81.4645i) q^{79} +10.6277i q^{80} +102.273 q^{82} +(-35.7729 + 20.6535i) q^{83} +(-38.0337 + 65.8763i) q^{85} +(-46.0664 - 26.5965i) q^{86} +(-3.61026 - 6.25315i) q^{88} +75.2547i q^{89} +51.3450 q^{91} +(-13.3693 + 7.71876i) q^{92} +(31.0031 - 53.6990i) q^{94} +(-24.5430 - 14.1699i) q^{95} +(-82.0660 - 142.142i) q^{97} +9.89949i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} - 36 q^{5} - 48 q^{16} + 24 q^{19} - 72 q^{20} + 24 q^{22} + 72 q^{23} + 72 q^{25} + 108 q^{29} - 60 q^{31} - 48 q^{34} - 168 q^{37} - 144 q^{38} - 108 q^{41} + 60 q^{43} + 324 q^{47} - 84 q^{49}+ \cdots + 48 q^{97}+O(q^{100}) \) 24 * q + 24 * q^4 - 36 * q^5 - 48 * q^16 + 24 * q^19 - 72 * q^20 + 24 * q^22 + 72 * q^23 + 72 * q^25 + 108 * q^29 - 60 * q^31 - 48 * q^34 - 168 * q^37 - 144 * q^38 - 108 * q^41 + 60 * q^43 + 324 * q^47 - 84 * q^49 - 144 * q^50 + 264 * q^55 + 432 * q^59 - 192 * q^64 + 180 * q^65 + 72 * q^67 - 72 * q^68 + 24 * q^73 - 288 * q^74 + 24 * q^76 + 12 * q^79 - 288 * q^82 - 756 * q^83 - 156 * q^85 - 360 * q^86 - 48 * q^88 - 168 * q^91 + 144 * q^92 + 936 * q^95 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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