LMFDB - Embedded newform 63.4.e.d.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 19x^{6} + 319x^{4} + 798x^{2} + 1764 $ x^8 + 19x^6 + 319x^4 + 798*x^2 + 1764
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.1
Root			$2.02770 - 3.51207i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.4.e.d.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.02770 - 3.51207i) q^{2} +(-4.22311 + 7.31464i) q^{4} +(-4.96020 - 8.59131i) q^{5} +(-15.3924 + 10.2992i) q^{7} +1.80961 q^{8} +O(q^{10})$	\(q+(-2.02770 - 3.51207i) q^{2} +(-4.22311 + 7.31464i) q^{4} +(-4.96020 - 8.59131i) q^{5} +(-15.3924 + 10.2992i) q^{7} +1.80961 q^{8} +(-20.1156 + 34.8412i) q^{10} +(-6.76980 + 11.7256i) q^{11} +18.5538 q^{13} +(67.3826 + 33.1758i) q^{14} +(30.1156 + 52.1617i) q^{16} +(-46.8551 + 81.1555i) q^{17} +(-65.9542 - 114.236i) q^{19} +83.7899 q^{20} +54.9084 q^{22} +(-99.1391 - 171.714i) q^{23} +(13.2929 - 23.0240i) q^{25} +(-37.6214 - 65.1622i) q^{26} +(-10.3307 - 156.085i) q^{28} -188.358 q^{29} +(41.9622 - 72.6807i) q^{31} +(129.369 - 224.073i) q^{32} +380.032 q^{34} +(164.833 + 81.1555i) q^{35} +(-40.0778 - 69.4167i) q^{37} +(-267.470 + 463.272i) q^{38} +(-8.97600 - 15.5469i) q^{40} +385.828 q^{41} -397.048 q^{43} +(-57.1793 - 99.0374i) q^{44} +(-402.048 + 696.368i) q^{46} +(136.139 + 235.799i) q^{47} +(130.855 - 317.058i) q^{49} -107.816 q^{50} +(-78.3547 + 135.714i) q^{52} +(-18.4998 + 32.0426i) q^{53} +134.318 q^{55} +(-27.8543 + 18.6374i) q^{56} +(381.932 + 661.526i) q^{58} +(197.874 - 342.728i) q^{59} +(-6.73689 - 11.6686i) q^{61} -340.347 q^{62} -567.435 q^{64} +(-92.0304 - 159.401i) q^{65} +(-170.261 + 294.901i) q^{67} +(-395.749 - 685.457i) q^{68} +(-49.2071 - 743.464i) q^{70} +211.140 q^{71} +(-243.062 + 420.995i) q^{73} +(-162.531 + 281.512i) q^{74} +1114.13 q^{76} +(-16.5604 - 250.210i) q^{77} +(-146.871 - 254.387i) q^{79} +(298.758 - 517.464i) q^{80} +(-782.343 - 1355.06i) q^{82} -889.635 q^{83} +929.643 q^{85} +(805.093 + 1394.46i) q^{86} +(-12.2507 + 21.2188i) q^{88} +(572.182 + 991.048i) q^{89} +(-285.588 + 191.088i) q^{91} +1674.70 q^{92} +(552.096 - 956.258i) q^{94} +(-654.292 + 1133.27i) q^{95} +1384.61 q^{97} +(-1378.87 + 183.327i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{4} - 12 q^{7}+O(q^{10}) $ 8 * q - 6 * q^4 - 12 * q^7	$ 8 q - 6 q^{4} - 12 q^{7} - 22 q^{10} + 204 q^{13} + 102 q^{16} - 222 q^{19} - 172 q^{22} - 366 q^{25} - 166 q^{28} - 220 q^{31} + 2040 q^{34} + 374 q^{37} - 822 q^{40} - 1676 q^{43} - 1716 q^{46} + 380 q^{49} + 40 q^{52} + 5020 q^{55} + 1694 q^{58} - 1332 q^{61} - 1372 q^{64} - 1890 q^{67} - 866 q^{70} - 1750 q^{73} + 4912 q^{76} - 8 q^{79} - 2480 q^{82} - 2232 q^{85} - 2682 q^{88} + 466 q^{91} + 1416 q^{94} + 6020 q^{97}+O(q^{100}) $ 8 * q - 6 * q^4 - 12 * q^7 - 22 * q^10 + 204 * q^13 + 102 * q^16 - 222 * q^19 - 172 * q^22 - 366 * q^25 - 166 * q^28 - 220 * q^31 + 2040 * q^34 + 374 * q^37 - 822 * q^40 - 1676 * q^43 - 1716 * q^46 + 380 * q^49 + 40 * q^52 + 5020 * q^55 + 1694 * q^58 - 1332 * q^61 - 1372 * q^64 - 1890 * q^67 - 866 * q^70 - 1750 * q^73 + 4912 * q^76 - 8 * q^79 - 2480 * q^82 - 2232 * q^85 - 2682 * q^88 + 466 * q^91 + 1416 * q^94 + 6020 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.02770	−	3.51207i	−0.716899	−	1.24171i	−0.962222	−	0.272264i	$-0.912227\pi$
$2$	−2.02770	−	3.51207i	−0.716899	−	1.24171i	0.245323	−	0.969441i	$-0.421106\pi$
$3$		0			0
$3$		0			0
$4$	−4.22311	+	7.31464i	−0.527889	+	0.914330i
$5$	−4.96020	−	8.59131i	−0.443654	−	0.768430i	0.554304	−	0.832314i	$-0.312985\pi$
$5$	−4.96020	−	8.59131i	−0.443654	−	0.768430i	−0.997957	+	0.0638840i	$0.979651\pi$
$6$		0			0
$7$	−15.3924	+	10.2992i	−0.831114	+	0.556102i
$7$	−15.3924	+	10.2992i	−0.831114	+	0.556102i
$8$	1.80961			0.0799740
$9$		0			0
$10$	−20.1156	+	34.8412i	−0.636110	+	1.10177i
$11$	−6.76980	+	11.7256i	−0.185561	+	0.321401i	−0.943765	−	0.330616i	$-0.892744\pi$
$11$	−6.76980	+	11.7256i	−0.185561	+	0.321401i	0.758204	+	0.652017i	$0.226077\pi$
$12$		0			0
$13$	18.5538			0.395838			0.197919	−	0.980218i	$-0.436582\pi$
$13$	18.5538			0.395838			0.197919	+	0.980218i	$0.436582\pi$
$14$	67.3826	+	33.1758i	1.28634	+	0.633330i
$15$		0			0
$16$	30.1156	+	52.1617i	0.470556	+	0.815026i
$17$	−46.8551	+	81.1555i	−0.668473	+	1.15783i	0.309858	+	0.950783i	$0.399718\pi$
$17$	−46.8551	+	81.1555i	−0.668473	+	1.15783i	−0.978331	+	0.207046i	$0.933615\pi$
$18$		0			0
$19$	−65.9542	−	114.236i	−0.796365	−	1.37934i	−0.921969	−	0.387264i	$-0.873420\pi$
$19$	−65.9542	−	114.236i	−0.796365	−	1.37934i	0.125604	−	0.992080i	$-0.459913\pi$
$20$	83.7899			0.936799
$21$		0			0
$22$	54.9084			0.532115
$23$	−99.1391	−	171.714i	−0.898779	−	1.55673i	−0.829056	−	0.559165i	$-0.811122\pi$
$23$	−99.1391	−	171.714i	−0.898779	−	1.55673i	−0.0697230	−	0.997566i	$-0.522212\pi$
$24$		0			0
$25$	13.2929	−	23.0240i	0.106343	−	0.184192i
$26$	−37.6214	−	65.1622i	−0.283776	−	0.491514i
$27$		0			0
$28$	−10.3307	−	156.085i	−0.0697254	−	1.05347i
$29$	−188.358			−1.20611			−0.603054	−	0.797700i	$-0.706050\pi$
$29$	−188.358			−1.20611			−0.603054	+	0.797700i	$0.706050\pi$
$30$		0			0
$31$	41.9622	−	72.6807i	0.243117	−	0.421092i	−0.718483	−	0.695544i	$-0.755163\pi$
$31$	41.9622	−	72.6807i	0.243117	−	0.421092i	0.961601	+	0.274453i	$0.0884967\pi$
$32$	129.369	−	224.073i	0.714669	−	1.23784i
$33$		0			0
$34$	380.032			1.91691
$35$	164.833	+	81.1555i	0.796053	+	0.391936i
$36$		0			0
$37$	−40.0778	−	69.4167i	−0.178074	−	0.308434i	0.763147	−	0.646225i	$-0.223653\pi$
$37$	−40.0778	−	69.4167i	−0.178074	−	0.308434i	−0.941221	+	0.337792i	$0.890320\pi$
$38$	−267.470	+	463.272i	−1.14183	+	1.97770i
$39$		0			0
$40$	−8.97600	−	15.5469i	−0.0354808	−	0.0614545i
$41$	385.828			1.46967			0.734833	−	0.678249i	$-0.237261\pi$
$41$	385.828			1.46967			0.734833	+	0.678249i	$0.237261\pi$
$42$		0			0
$43$	−397.048			−1.40812			−0.704061	−	0.710139i	$-0.748632\pi$
$43$	−397.048			−1.40812			−0.704061	+	0.710139i	$0.748632\pi$
$44$	−57.1793	−	99.0374i	−0.195911	−	0.339328i
$45$		0			0
$46$	−402.048	+	696.368i	−1.28867	+	2.23204i
$47$	136.139	+	235.799i	0.422508	+	0.731805i	0.996184	−	0.0872772i	$-0.0278166\pi$
$47$	136.139	+	235.799i	0.422508	+	0.731805i	−0.573676	+	0.819082i	$0.694483\pi$
$48$		0			0
$49$	130.855	−	317.058i	0.381500	−	0.924369i
$50$	−107.816			−0.304949
$51$		0			0
$52$	−78.3547	+	135.714i	−0.208958	+	0.361927i
$53$	−18.4998	+	32.0426i	−0.0479461	+	0.0830451i	−0.889002	−	0.457902i	$-0.848601\pi$
$53$	−18.4998	+	32.0426i	−0.0479461	+	0.0830451i	0.841056	+	0.540948i	$0.181934\pi$
$54$		0			0
$55$	134.318			0.329299
$56$	−27.8543	+	18.6374i	−0.0664675	+	0.0444738i
$57$		0			0
$58$	381.932	+	661.526i	0.864658	+	1.49763i
$59$	197.874	−	342.728i	0.436628	−	0.756262i	−0.560799	−	0.827952i	$-0.689506\pi$
$59$	197.874	−	342.728i	0.436628	−	0.756262i	0.997427	+	0.0716901i	$0.0228393\pi$
$60$		0			0
$61$	−6.73689	−	11.6686i	−0.0141405	−	0.0244921i	0.858869	−	0.512196i	$-0.171168\pi$
$61$	−6.73689	−	11.6686i	−0.0141405	−	0.0244921i	−0.873009	+	0.487704i	$0.837835\pi$
$62$	−340.347			−0.697162
$63$		0			0
$64$	−567.435			−1.10827
$65$	−92.0304	−	159.401i	−0.175615	−	0.304174i
$66$		0			0
$67$	−170.261	+	294.901i	−0.310458	+	0.537729i	−0.978462	−	0.206429i	$-0.933816\pi$
$67$	−170.261	+	294.901i	−0.310458	+	0.537729i	0.668004	+	0.744158i	$0.267149\pi$
$68$	−395.749	−	685.457i	−0.705759	−	1.22241i
$69$		0			0
$70$	−49.2071	−	743.464i	−0.0840196	−	1.26944i
$71$	211.140			0.352925			0.176463	−	0.984307i	$-0.443534\pi$
$71$	211.140			0.352925			0.176463	+	0.984307i	$0.443534\pi$
$72$		0			0
$73$	−243.062	+	420.995i	−0.389702	+	0.674983i	−0.992409	−	0.122979i	$-0.960755\pi$
$73$	−243.062	+	420.995i	−0.389702	+	0.674983i	0.602708	+	0.797962i	$0.294089\pi$
$74$	−162.531	+	281.512i	−0.255323	+	0.442232i
$75$		0			0
$76$	1114.13			1.68157
$77$	−16.5604	−	250.210i	−0.0245096	−	0.370312i
$78$		0			0
$79$	−146.871	−	254.387i	−0.209168	−	0.362289i	0.742285	−	0.670084i	$-0.233742\pi$
$79$	−146.871	−	254.387i	−0.209168	−	0.362289i	−0.951453	+	0.307795i	$0.900409\pi$
$80$	298.758	−	517.464i	0.417527	−	0.723178i
$81$		0			0
$82$	−782.343	−	1355.06i	−1.05360	−	1.82489i
$83$	−889.635			−1.17651			−0.588253	−	0.808677i	$-0.700184\pi$
$83$	−889.635			−1.17651			−0.588253	+	0.808677i	$0.700184\pi$
$84$		0			0
$85$	929.643			1.18628
$86$	805.093	+	1394.46i	1.00948	+	1.74847i
$87$		0			0
$88$	−12.2507	+	21.2188i	−0.0148401	+	0.0257038i
$89$	572.182	+	991.048i	0.681474	+	1.18035i	0.974531	+	0.224252i	$0.0719939\pi$
$89$	572.182	+	991.048i	0.681474	+	1.18035i	−0.293057	+	0.956095i	$0.594673\pi$
$90$		0			0
$91$	−285.588	+	191.088i	−0.328986	+	0.220126i
$92$	1674.70			1.89782
$93$		0			0
$94$	552.096	−	956.258i	0.605791	−	1.04926i
$95$	−654.292	+	1133.27i	−0.706620	+	1.22390i
$96$		0			0
$97$	1384.61			1.44933			0.724667	−	0.689099i	$-0.241993\pi$
$97$	1384.61			1.44933			0.724667	+	0.689099i	$0.241993\pi$
$98$	−1378.87	+	183.327i	−1.42129	+	0.188968i
$99$		0			0
$100$	112.275	+	194.465i	0.112275	+	0.194465i
$101$	892.994	−	1546.71i	0.879765	−	1.52380i	0.0281660	−	0.999603i	$-0.491033\pi$
$101$	892.994	−	1546.71i	0.879765	−	1.52380i	0.851599	−	0.524194i	$-0.175633\pi$
$102$		0			0
$103$	−244.831	−	424.059i	−0.234212	−	0.405668i	0.724831	−	0.688927i	$-0.241918\pi$
$103$	−244.831	−	424.059i	−0.234212	−	0.405668i	−0.959044	+	0.283259i	$0.908584\pi$
$104$	33.5750			0.0316568
$105$		0			0
$106$	150.048			0.137490
$107$	141.034	+	244.278i	0.127423	+	0.220703i	0.922678	−	0.385573i	$-0.125996\pi$
$107$	141.034	+	244.278i	0.127423	+	0.220703i	−0.795254	+	0.606276i	$0.792663\pi$
$108$		0			0
$109$	143.616	−	248.749i	0.126201	−	0.218586i	−0.796001	−	0.605295i	$-0.793055\pi$
$109$	143.616	−	248.749i	0.126201	−	0.218586i	0.922202	+	0.386709i	$0.126388\pi$
$110$	−272.357	−	471.736i	−0.236074	−	0.408893i
$111$		0			0
$112$	−1000.77	−	492.731i	−0.844323	−	0.415702i
$113$	−1895.21			−1.57776			−0.788879	−	0.614548i	$-0.789338\pi$
$113$	−1895.21			−1.57776			−0.788879	+	0.614548i	$0.789338\pi$
$114$		0			0
$115$	−983.499	+	1703.47i	−0.797493	+	1.38130i
$116$	795.456	−	1377.77i	0.636691	−	1.10278i
$117$		0			0
$118$	−1604.92			−1.25207
$119$	−114.618	−	1731.75i	−0.0882943	−	1.33403i
$120$		0			0
$121$	573.840	+	993.919i	0.431134	+	0.746746i
$122$	−27.3208	+	47.3209i	−0.0202746	+	0.0351167i
$123$		0			0
$124$	354.422	+	613.877i	0.256678	+	0.444579i
$125$	−1503.79			−1.07603
$126$		0			0
$127$	−1222.92			−0.854463			−0.427231	−	0.904142i	$-0.640511\pi$
$127$	−1222.92			−0.854463			−0.427231	+	0.904142i	$0.640511\pi$
$128$	115.635	+	200.285i	0.0798496	+	0.138304i
$129$		0			0
$130$	−373.220	+	646.435i	−0.251796	+	0.436124i
$131$	595.303	+	1031.10i	0.397037	+	0.687689i	0.993359	−	0.115057i	$-0.0367051\pi$
$131$	595.303	+	1031.10i	0.397037	+	0.687689i	−0.596322	+	0.802746i	$0.703372\pi$
$132$		0			0
$133$	2191.73	+	1079.10i	1.42893	+	0.703532i
$134$	1380.95			0.890268
$135$		0			0
$136$	−84.7893	+	146.859i	−0.0534605	+	0.0925963i
$137$	53.4807	−	92.6313i	0.0333516	−	0.0577666i	−0.848868	−	0.528605i	$-0.822715\pi$
$137$	53.4807	−	92.6313i	0.0333516	−	0.0577666i	0.882219	+	0.470839i	$0.156049\pi$
$138$		0			0
$139$	−1096.78			−0.669262			−0.334631	−	0.942349i	$-0.608612\pi$
$139$	−1096.78			−0.669262			−0.334631	+	0.942349i	$0.608612\pi$
$140$	−1289.73	+	862.965i	−0.778587	+	0.520956i
$141$		0			0
$142$	−428.128	−	741.539i	−0.253012	−	0.438230i
$143$	−125.605	+	217.555i	−0.0734521	+	0.127223i
$144$		0			0
$145$	934.292	+	1618.24i	0.535094	+	0.926811i
$146$	1971.42			1.11751
$147$		0			0
$148$	677.012			0.376014
$149$	358.331	+	620.647i	0.197018	+	0.341244i	0.947560	−	0.319578i	$-0.103541\pi$
$149$	358.331	+	620.647i	0.197018	+	0.341244i	−0.750542	+	0.660822i	$0.770208\pi$
$150$		0			0
$151$	−77.1840	+	133.687i	−0.0415970	+	0.0720481i	−0.886074	−	0.463543i	$-0.846578\pi$
$151$	−77.1840	+	133.687i	−0.0415970	+	0.0720481i	0.844477	+	0.535591i	$0.179911\pi$
$152$	−119.351	−	206.722i	−0.0636885	−	0.110312i
$153$		0			0
$154$	−845.175	+	565.511i	−0.442248	+	0.295910i
$155$	−832.564			−0.431439
$156$		0			0
$157$	1046.87	−	1813.24i	0.532163	−	0.921734i	−0.467132	−	0.884188i	$-0.654713\pi$
$157$	1046.87	−	1813.24i	0.532163	−	0.921734i	0.999295	−	0.0375459i	$-0.0119541\pi$
$158$	−595.618	+	1031.64i	−0.299904	+	0.519449i
$159$		0			0
$160$	−2566.78			−1.26826
$161$	3294.50	+	1622.05i	1.61269	+	0.794008i
$162$		0			0
$163$	−1503.93	−	2604.88i	−0.722680	−	1.25172i	−0.959922	−	0.280268i	$-0.909577\pi$
$163$	−1503.93	−	2604.88i	−0.722680	−	1.25172i	0.237242	−	0.971451i	$-0.423757\pi$
$164$	−1629.40	+	2822.20i	−0.775820	+	1.34376i
$165$		0			0
$166$	1803.91	+	3124.46i	0.843437	+	1.46088i
$167$	2230.43			1.03351			0.516754	−	0.856134i	$-0.327140\pi$
$167$	2230.43			1.03351			0.516754	+	0.856134i	$0.327140\pi$
$168$		0			0
$169$	−1852.76			−0.843312
$170$	−1885.03	−	3264.97i	−0.850444	−	1.47301i
$171$		0			0
$172$	1676.78	−	2904.26i	0.743332	−	1.28749i
$173$	−281.585	−	487.719i	−0.123749	−	0.214339i	0.797495	−	0.603326i	$-0.206158\pi$
$173$	−281.585	−	487.719i	−0.123749	−	0.214339i	−0.921243	+	0.388987i	$0.872825\pi$
$174$		0			0
$175$	32.5174	+	491.300i	0.0140462	+	0.212222i
$176$	−815.506			−0.349267
$177$		0			0
$178$	2320.42	−	4019.09i	0.977096	−	1.69238i
$179$	919.749	−	1593.05i	0.384052	−	0.665197i	−0.607585	−	0.794254i	$-0.707862\pi$
$179$	919.749	−	1593.05i	0.384052	−	0.665197i	0.991637	+	0.129057i	$0.0411951\pi$
$180$		0			0
$181$	2324.71			0.954664			0.477332	−	0.878723i	$-0.341604\pi$
$181$	2324.71			0.954664			0.477332	+	0.878723i	$0.341604\pi$
$182$	1250.20	+	615.537i	0.509182	+	0.250696i
$183$		0			0
$184$	−179.403	−	310.735i	−0.0718790	−	0.124498i
$185$	−397.587	+	688.641i	−0.158006	+	0.273675i
$186$		0			0
$187$	−634.400	−	1098.81i	−0.248085	−	0.429696i
$188$	−2299.71			−0.892149
$189$		0			0
$190$	5306.82			2.02630
$191$	−1563.64	−	2708.30i	−0.592360	−	1.02600i	−0.993914	−	0.110163i	$-0.964863\pi$
$191$	−1563.64	−	2708.30i	−0.592360	−	1.02600i	0.401553	−	0.915836i	$-0.368470\pi$
$192$		0			0
$193$	1854.64	−	3212.34i	0.691711	−	1.19808i	−0.279566	−	0.960126i	$-0.590191\pi$
$193$	1854.64	−	3212.34i	0.691711	−	1.19808i	0.971277	−	0.237952i	$-0.0764761\pi$
$194$	−2807.56	−	4862.84i	−1.03903	−	1.79965i
$195$		0			0
$196$	1766.56	+	2296.13i	0.643788	+	0.836781i
$197$	−851.150			−0.307827			−0.153913	−	0.988084i	$-0.549188\pi$
$197$	−851.150			−0.307827			−0.153913	+	0.988084i	$0.549188\pi$
$198$		0			0
$199$	−1698.89	+	2942.57i	−0.605182	+	1.04821i	0.386840	+	0.922147i	$0.373566\pi$
$199$	−1698.89	+	2942.57i	−0.605182	+	1.04821i	−0.992023	+	0.126060i	$0.959767\pi$
$200$	24.0549	−	41.6643i	0.00850469	−	0.0147306i
$201$		0			0
$202$	−7242.89			−2.52281
$203$	2899.29	−	1939.93i	1.00241	−	0.670720i
$204$		0			0
$205$	−1913.78	−	3314.77i	−0.652022	−	1.12934i
$206$	−992.885	+	1719.73i	−0.335813	+	0.581646i
$207$		0			0
$208$	558.757	+	967.796i	0.186264	+	0.322618i
$209$	1785.99			0.591098
$210$		0			0
$211$	216.732			0.0707132			0.0353566	−	0.999375i	$-0.488743\pi$
$211$	216.732			0.0707132			0.0353566	+	0.999375i	$0.488743\pi$
$212$	−156.253	−	270.639i	−0.0506204	−	0.0876772i
$213$		0			0
$214$	571.948	−	990.644i	0.182699	−	0.316444i
$215$	1969.44	+	3411.16i	0.624718	+	1.08204i
$216$		0			0
$217$	102.649	+	1550.91i	0.0321118	+	0.485173i
$218$	−1164.84			−0.361893
$219$		0			0
$220$	−567.241	+	982.490i	−0.173833	+	0.301088i
$221$	−869.340	+	1505.74i	−0.264607	+	0.458312i
$222$		0			0
$223$	−2254.86			−0.677115			−0.338558	−	0.940946i	$-0.609939\pi$
$223$	−2254.86			−0.677115			−0.338558	+	0.940946i	$0.609939\pi$
$224$	316.465	+	4781.43i	0.0943960	+	1.42622i
$225$		0			0
$226$	3842.92	+	6656.13i	1.13109	+	1.95911i
$227$	−1695.40	+	2936.52i	−0.495716	+	0.858606i	−0.999988	−	0.00493916i	$-0.998428\pi$
$227$	−1695.40	+	2936.52i	−0.495716	+	0.858606i	0.504271	+	0.863545i	$0.331761\pi$
$228$		0			0
$229$	−1293.92	−	2241.14i	−0.373384	−	0.646720i	0.616700	−	0.787198i	$-0.288469\pi$
$229$	−1293.92	−	2241.14i	−0.373384	−	0.646720i	−0.990084	+	0.140479i	$0.955136\pi$
$230$	7976.95			2.28689
$231$		0			0
$232$	−340.853			−0.0964574
$233$	−477.210	−	826.552i	−0.134176	−	0.232400i	0.791106	−	0.611679i	$-0.209505\pi$
$233$	−477.210	−	826.552i	−0.134176	−	0.232400i	−0.925282	+	0.379279i	$0.876172\pi$
$234$		0			0
$235$	1350.55	−	2339.22i	0.374894	−	0.649336i
$236$	1671.29	+	2894.76i	0.460982	+	0.798444i
$237$		0			0
$238$	−5849.62	+	3914.01i	−1.59317	+	1.06600i
$239$	−199.504			−0.0539951			−0.0269976	−	0.999635i	$-0.508595\pi$
$239$	−199.504			−0.0539951			−0.0269976	+	0.999635i	$0.508595\pi$
$240$		0			0
$241$	−2397.21	+	4152.10i	−0.640739	+	1.10979i	0.344529	+	0.938776i	$0.388039\pi$
$241$	−2397.21	+	4152.10i	−0.640739	+	1.10979i	−0.985268	+	0.171017i	$0.945295\pi$
$242$	2327.15	−	4030.73i	0.618159	−	1.07068i
$243$		0			0
$244$	113.803			0.0298585
$245$	−3373.01	+	448.459i	−0.879567	+	0.116943i
$246$		0			0
$247$	−1223.70	−	2119.51i	−0.315231	−	0.545997i
$248$	75.9351	−	131.523i	0.0194431	−	0.0336764i
$249$		0			0
$250$	3049.23	+	5281.42i	0.771401	+	1.33611i
$251$	−6249.73			−1.57163			−0.785816	−	0.618460i	$-0.787757\pi$
$251$	−6249.73			−1.57163			−0.785816	+	0.618460i	$0.787757\pi$
$252$		0			0
$253$	2684.61			0.667114
$254$	2479.71	+	4294.99i	0.612564	+	1.06099i
$255$		0			0
$256$	−1800.79	+	3119.07i	−0.439647	+	0.761491i
$257$	−1918.93	−	3323.68i	−0.465756	−	0.806713i	0.533479	−	0.845813i	$-0.320884\pi$
$257$	−1918.93	−	3323.68i	−0.465756	−	0.806713i	−0.999235	+	0.0390999i	$0.987551\pi$
$258$		0			0
$259$	1331.83	+	655.726i	0.319521	+	0.157316i
$260$	1554.62			0.370821
$261$		0			0
$262$	2414.19	−	4181.50i	0.569271	−	0.986007i
$263$	103.602	−	179.443i	0.0242903	−	0.0420721i	−0.853625	−	0.520889i	$-0.825601\pi$
$263$	103.602	−	179.443i	0.0242903	−	0.0420721i	0.877915	+	0.478816i	$0.158934\pi$
$264$		0			0
$265$	367.051			0.0850858
$266$	−654.292	−	9885.61i	−0.150817	−	2.27867i
$267$		0			0
$268$	−1438.06	−	2490.80i	−0.327775	−	0.567722i
$269$	2402.04	−	4160.46i	0.544442	−	0.943002i	−0.454199	−	0.890900i	$-0.650075\pi$
$269$	2402.04	−	4160.46i	0.544442	−	0.943002i	0.998642	−	0.0521018i	$-0.0165920\pi$
$270$		0			0
$271$	−1607.88	−	2784.92i	−0.360411	−	0.624251i	0.627617	−	0.778522i	$-0.284030\pi$
$271$	−1607.88	−	2784.92i	−0.360411	−	0.624251i	−0.988029	+	0.154271i	$0.950697\pi$
$272$	−5644.27			−1.25821
$273$		0			0
$274$	−433.771			−0.0956388
$275$	179.980	+	311.735i	0.0394663	+	0.0683576i
$276$		0			0
$277$	−1027.20	+	1779.16i	−0.222810	+	0.385918i	−0.955660	−	0.294472i	$-0.904856\pi$
$277$	−1027.20	+	1779.16i	−0.222810	+	0.385918i	0.732850	+	0.680390i	$0.238190\pi$
$278$	2223.93	+	3851.97i	0.479794	+	0.831027i
$279$		0			0
$280$	298.283	+	146.859i	0.0636635	+	0.0313447i
$281$	−1768.61			−0.375468			−0.187734	−	0.982220i	$-0.560114\pi$
$281$	−1768.61			−0.375468			−0.187734	+	0.982220i	$0.560114\pi$
$282$		0			0
$283$	−1170.26	+	2026.96i	−0.245813	+	0.425760i	−0.962360	−	0.271779i	$-0.912388\pi$
$283$	−1170.26	+	2026.96i	−0.245813	+	0.425760i	0.716547	+	0.697539i	$0.245721\pi$
$284$	−891.668	+	1544.41i	−0.186305	+	0.322690i
$285$		0			0
$286$	1018.76			0.210631
$287$	−5938.84	+	3973.71i	−1.22146	+	0.817284i
$288$		0			0
$289$	−1934.31	−	3350.32i	−0.393712	−	0.681929i
$290$	3788.92	−	6562.60i	0.767217	−	1.32886i
$291$		0			0
$292$	−2052.95	−	3555.82i	−0.411438	−	0.712632i
$293$	3633.47			0.724470			0.362235	−	0.932087i	$-0.382014\pi$
$293$	3633.47			0.724470			0.362235	+	0.932087i	$0.382014\pi$
$294$		0			0
$295$	−3925.98			−0.774846
$296$	−72.5250	−	125.617i	−0.0142413	−	0.0246667i
$297$		0			0
$298$	1453.17	−	2516.97i	0.282483	−	0.489276i
$299$	−1839.40	−	3185.94i	−0.355771	−	0.616213i
$300$		0			0
$301$	6111.54	−	4089.26i	1.17031	−	0.783060i
$302$	626.023			0.119283
$303$		0			0
$304$	3972.50	−	6880.56i	0.749468	−	1.29812i
$305$	−66.8326	+	115.758i	−0.0125470	+	0.0217320i
$306$		0			0
$307$	5954.32			1.10694			0.553471	−	0.832868i	$-0.313303\pi$
$307$	5954.32			1.10694			0.553471	+	0.832868i	$0.313303\pi$
$308$	1900.13	+	935.529i	0.351526	+	0.173074i
$309$		0			0
$310$	1688.19	+	2924.03i	0.309299	+	0.535721i
$311$	590.047	−	1021.99i	0.107584	−	0.186340i	−0.807207	−	0.590268i	$-0.799022\pi$
$311$	590.047	−	1021.99i	0.107584	−	0.186340i	0.914791	+	0.403928i	$0.132355\pi$
$312$		0			0
$313$	4873.12	+	8440.50i	0.880017	+	1.52423i	0.851321	+	0.524646i	$0.175802\pi$
$313$	4873.12	+	8440.50i	0.880017	+	1.52423i	0.0286960	+	0.999588i	$0.490865\pi$
$314$	−8490.97			−1.52603
$315$		0			0
$316$	2481.00			0.441669
$317$	4295.96	+	7440.81i	0.761151	+	1.31835i	0.942258	+	0.334889i	$0.108699\pi$
$317$	4295.96	+	7440.81i	0.761151	+	1.31835i	−0.181106	+	0.983464i	$0.557968\pi$
$318$		0			0
$319$	1275.14	−	2208.62i	0.223807	−	0.387645i
$320$	2814.59	+	4875.01i	0.491688	+	0.851629i
$321$		0			0
$322$	−983.499	−	14859.6i	−0.170212	−	2.57171i
$323$	12361.2			2.12939
$324$		0			0
$325$	246.633	−	427.181i	0.0420946	−	0.0729100i
$326$	−6099.02	+	10563.8i	−1.03618	+	1.79471i
$327$		0			0
$328$	698.197			0.117535
$329$	−4524.04	−	2227.41i	−0.758111	−	0.373256i
$330$		0			0
$331$	2625.60	+	4547.67i	0.436000	+	0.755174i	0.997377	−	0.0723864i	$-0.0230615\pi$
$331$	2625.60	+	4547.67i	0.436000	+	0.755174i	−0.561377	+	0.827560i	$0.689728\pi$
$332$	3757.03	−	6507.36i	0.621065	−	1.07572i
$333$		0			0
$334$	−4522.64	−	7833.44i	−0.740921	−	1.28331i
$335$	3378.11			0.550943
$336$		0			0
$337$	−8496.45			−1.37339			−0.686693	−	0.726947i	$-0.740938\pi$
$337$	−8496.45			−1.37339			−0.686693	+	0.726947i	$0.740938\pi$
$338$	3756.83	+	6507.02i	0.604570	+	1.04715i
$339$		0			0
$340$	−3925.98	+	6800.00i	−0.626225	+	1.08465i
$341$	568.152	+	984.068i	0.0902263	+	0.156276i
$342$		0			0
$343$	1251.26	+	6228.00i	0.196973	+	0.980409i
$344$	−718.500			−0.112613
$345$		0			0
$346$	−1141.94	+	1977.89i	−0.177430	+	0.307319i
$347$	−2915.07	+	5049.06i	−0.450978	+	0.781117i	−0.998447	−	0.0557090i	$-0.982258\pi$
$347$	−2915.07	+	5049.06i	−0.450978	+	0.781117i	0.547469	+	0.836826i	$0.315591\pi$
$348$		0			0
$349$	1811.13			0.277786			0.138893	−	0.990307i	$-0.455646\pi$
$349$	1811.13			0.277786			0.138893	+	0.990307i	$0.455646\pi$
$350$	1659.55	−	1110.41i	0.253447	−	0.169583i
$351$		0			0
$352$	1751.60	+	3033.87i	0.265230	+	0.459391i
$353$	1663.88	−	2881.92i	0.250876	−	0.434531i	−0.712891	−	0.701275i	$-0.752615\pi$
$353$	1663.88	−	2881.92i	0.250876	−	0.434531i	0.963767	+	0.266744i	$0.0859479\pi$
$354$		0			0
$355$	−1047.30	−	1813.97i	−0.156577	−	0.271199i
$356$	−9665.55			−1.43897
$357$		0			0
$358$	−7459.89			−1.10131
$359$	−435.430	−	754.188i	−0.0640143	−	0.110876i	0.832242	−	0.554413i	$-0.187057\pi$
$359$	−435.430	−	754.188i	−0.0640143	−	0.110876i	−0.896256	+	0.443536i	$0.853724\pi$
$360$		0			0
$361$	−5270.42	+	9128.63i	−0.768395	+	1.33090i
$362$	−4713.80	−	8164.55i	−0.684398	−	1.18541i
$363$		0			0
$364$	−191.673	−	2895.96i	−0.0276000	−	0.417004i
$365$	4822.54			0.691570
$366$		0			0
$367$	−587.358	+	1017.33i	−0.0835418	+	0.144699i	−0.904769	−	0.425903i	$-0.859957\pi$
$367$	−587.358	+	1017.33i	−0.0835418	+	0.144699i	0.821227	+	0.570601i	$0.193290\pi$
$368$	5971.26	−	10342.5i	0.845851	−	1.46506i
$369$		0			0
$370$	3224.75			0.453099
$371$	−45.2546	−	683.746i	−0.00633289	−	0.0956829i
$372$		0			0
$373$	−1814.17	−	3142.23i	−0.251834	−	0.436189i	0.712197	−	0.701980i	$-0.247700\pi$
$373$	−1814.17	−	3142.23i	−0.251834	−	0.436189i	−0.964031	+	0.265791i	$0.914367\pi$
$374$	−2572.74	+	4456.12i	−0.355704	+	0.616097i
$375$		0			0
$376$	246.357	+	426.703i	0.0337897	+	0.0585254i
$377$	−3494.75			−0.477424
$378$		0			0
$379$	7321.99			0.992362			0.496181	−	0.868219i	$-0.334735\pi$
$379$	7321.99			0.992362			0.496181	+	0.868219i	$0.334735\pi$
$380$	−5526.29	−	9571.82i	−0.746034	−	1.29217i
$381$		0			0
$382$	−6341.17	+	10983.2i	−0.849325	+	1.47107i
$383$	−3677.45	−	6369.52i	−0.490623	−	0.849784i	0.509318	−	0.860578i	$-0.329898\pi$
$383$	−3677.45	−	6369.52i	−0.490623	−	0.849784i	−0.999942	+	0.0107937i	$0.996564\pi$
$384$		0			0
$385$	−2067.49	+	1383.36i	−0.273685	+	0.183124i
$386$	−15042.6			−1.98355
$387$		0			0
$388$	−5847.35	+	10127.9i	−0.765088	+	1.32517i
$389$	4534.81	−	7854.52i	0.591064	−	1.02375i	−0.403025	−	0.915189i	$-0.632041\pi$
$389$	4534.81	−	7854.52i	0.591064	−	1.02375i	0.994089	−	0.108564i	$-0.0346254\pi$
$390$		0			0
$391$	18580.7			2.40324
$392$	236.795	−	573.751i	0.0305101	−	0.0739255i
$393$		0			0
$394$	1725.87	+	2989.30i	0.220681	+	0.382230i
$395$	−1457.01	+	2523.62i	−0.185596	+	0.321462i
$396$		0			0
$397$	−3688.41	−	6388.52i	−0.466288	−	0.807634i	0.532971	−	0.846134i	$-0.321075\pi$
$397$	−3688.41	−	6388.52i	−0.466288	−	0.807634i	−0.999259	+	0.0384997i	$0.987742\pi$
$398$	13779.4			1.73542
$399$		0			0
$400$	1601.29			0.200161
$401$	−1426.76	−	2471.21i	−0.177678	−	0.307747i	0.763407	−	0.645918i	$-0.223525\pi$
$401$	−1426.76	−	2471.21i	−0.177678	−	0.307747i	−0.941085	+	0.338171i	$0.890192\pi$
$402$		0			0
$403$	778.558	−	1348.50i	0.0962350	−	0.166684i
$404$	7542.43	+	13063.9i	0.928836	+	1.60879i
$405$		0			0
$406$	−12692.0	−	6248.93i	−1.55147	−	0.763864i
$407$	1085.27			0.132175
$408$		0			0
$409$	−5630.03	+	9751.49i	−0.680652	+	1.17892i	0.294130	+	0.955766i	$0.404970\pi$
$409$	−5630.03	+	9751.49i	−0.680652	+	1.17892i	−0.974782	+	0.223159i	$0.928363\pi$
$410$	−7761.15	+	13442.7i	−0.934868	+	1.61924i
$411$		0			0
$412$	4135.79			0.494553
$413$	484.045	+	7313.37i	0.0576714	+	0.871350i
$414$		0			0
$415$	4412.76	+	7643.13i	0.521961	+	0.904064i
$416$	2400.28	−	4157.41i	0.282893	−	0.489985i
$417$		0			0
$418$	−3621.44	−	6272.52i	−0.423757	−	0.733969i
$419$	9221.47			1.07517			0.537587	−	0.843208i	$-0.319336\pi$
$419$	9221.47			1.07517			0.537587	+	0.843208i	$0.319336\pi$
$420$		0			0
$421$	−8520.28			−0.986349			−0.493175	−	0.869930i	$-0.664164\pi$
$421$	−8520.28			−0.986349			−0.493175	+	0.869930i	$0.664164\pi$
$422$	−439.468	−	761.181i	−0.0506942	−	0.0878049i
$423$		0			0
$424$	−33.4774	+	57.9845i	−0.00383444	+	0.00664145i
$425$	1245.68	+	2157.58i	0.142175	+	0.246254i
$426$		0			0
$427$	223.874	+	110.225i	0.0253725	+	0.0124921i
$428$	−2382.41			−0.269061
$429$		0			0
$430$	7986.84	−	13833.6i	0.895720	−	1.55143i
$431$	4581.05	−	7934.62i	0.511976	−	0.886768i	−0.487928	−	0.872884i	$-0.662247\pi$
$431$	4581.05	−	7934.62i	0.511976	−	0.886768i	0.999904	−	0.0138840i	$-0.00441955\pi$
$432$		0			0
$433$	−10976.2			−1.21820			−0.609100	−	0.793093i	$-0.708469\pi$
$433$	−10976.2			−1.21820			−0.609100	+	0.793093i	$0.708469\pi$
$434$	5238.77	−	3505.28i	0.579421	−	0.387694i
$435$		0			0
$436$	1213.01	+	2100.99i	0.133240	+	0.230778i
$437$	−13077.3	+	22650.5i	−1.43151	+	2.47945i
$438$		0			0
$439$	−1991.59	−	3449.54i	−0.216523	−	0.375028i	0.737220	−	0.675653i	$-0.236138\pi$
$439$	−1991.59	−	3449.54i	−0.216523	−	0.375028i	−0.953743	+	0.300625i	$0.902805\pi$
$440$	243.063			0.0263354
$441$		0			0
$442$	7051.03			0.758786
$443$	2262.22	+	3918.29i	0.242622	+	0.420234i	0.961460	−	0.274944i	$-0.0886592\pi$
$443$	2262.22	+	3918.29i	0.242622	+	0.420234i	−0.718838	+	0.695177i	$0.755326\pi$
$444$		0			0
$445$	5676.27	−	9831.59i	0.604676	−	1.04733i
$446$	4572.18	+	7919.24i	0.485423	+	0.840778i
$447$		0			0
$448$	8734.21	−	5844.10i	0.921099	−	0.616312i
$449$	2076.49			0.218253			0.109127	−	0.994028i	$-0.465195\pi$
$449$	2076.49			0.218253			0.109127	+	0.994028i	$0.465195\pi$
$450$		0			0
$451$	−2611.98	+	4524.09i	−0.272713	+	0.472352i
$452$	8003.70	−	13862.8i	0.832881	−	1.44259i
$453$		0			0
$454$	13751.0			1.42151
$455$	3058.27	+	1505.74i	0.315108	+	0.155143i
$456$		0			0
$457$	923.795	+	1600.06i	0.0945587	+	0.163780i	0.909424	−	0.415869i	$-0.136523\pi$
$457$	923.795	+	1600.06i	0.0945587	+	0.163780i	−0.814866	+	0.579650i	$0.803189\pi$
$458$	−5247.37	+	9088.71i	−0.535357	+	0.927266i
$459$		0			0
$460$	−8306.85	−	14387.9i	−0.841976	−	1.45834i
$461$	−876.945			−0.0885974			−0.0442987	−	0.999018i	$-0.514105\pi$
$461$	−876.945			−0.0885974			−0.0442987	+	0.999018i	$0.514105\pi$
$462$		0			0
$463$	16245.2			1.63062			0.815310	−	0.579025i	$-0.196566\pi$
$463$	16245.2			1.63062			0.815310	+	0.579025i	$0.196566\pi$
$464$	−5672.50	−	9825.05i	−0.567541	−	0.983010i
$465$		0			0
$466$	−1935.27	+	3351.99i	−0.192382	+	0.333215i
$467$	−9480.88	−	16421.4i	−0.939449	−	1.62717i	−0.766502	−	0.642242i	$-0.778004\pi$
$467$	−9480.88	−	16421.4i	−0.939449	−	1.62717i	−0.172947	−	0.984931i	$-0.555329\pi$
$468$		0			0
$469$	−416.496	−	6292.78i	−0.0410064	−	0.619560i
$470$	−10954.0			−1.07505
$471$		0			0
$472$	358.075	−	620.204i	0.0349189	−	0.0604813i
$473$	2687.94	−	4655.64i	0.261293	−	0.452572i
$474$		0			0
$475$	−3506.89			−0.338752
$476$	13151.2	+	6474.98i	1.26635	+	0.623488i
$477$		0			0
$478$	404.533	+	700.672i	0.0387090	+	0.0670460i
$479$	−4188.88	+	7255.35i	−0.399572	+	0.692078i	−0.993673	−	0.112312i	$-0.964174\pi$
$479$	−4188.88	+	7255.35i	−0.399572	+	0.692078i	0.594101	+	0.804390i	$0.297508\pi$
$480$		0			0
$481$	−743.594	−	1287.94i	−0.0704885	−	0.122090i
$482$	19443.3			1.83738
$483$		0			0
$484$	−9693.55			−0.910364
$485$	−6867.92	−	11895.6i	−0.643002	−	1.11371i
$486$		0			0
$487$	2279.42	−	3948.08i	0.212096	−	0.367360i	−0.740275	−	0.672305i	$-0.765304\pi$
$487$	2279.42	−	3948.08i	0.212096	−	0.367360i	0.952370	+	0.304944i	$0.0986378\pi$
$488$	−12.1911	−	21.1156i	−0.00113087	−	0.00195873i
$489$		0			0
$490$	8414.47	+	10936.9i	0.775769	+	1.00833i
$491$	−15809.9			−1.45314			−0.726570	−	0.687092i	$-0.758887\pi$
$491$	−15809.9			−1.45314			−0.726570	+	0.687092i	$0.758887\pi$
$492$		0			0
$493$	8825.53	−	15286.3i	0.806251	−	1.39647i
$494$	−4962.59	+	8595.45i	−0.451978	+	0.782849i
$495$		0			0
$496$	5054.86			0.457601
$497$	−3249.96	+	2174.56i	−0.293321	+	0.196263i
$498$		0			0
$499$	−6693.04	−	11592.7i	−0.600444	−	1.04000i	−0.992754	−	0.120167i	$-0.961657\pi$
$499$	−6693.04	−	11592.7i	−0.600444	−	1.04000i	0.392309	−	0.919833i	$-0.371676\pi$
$500$	6350.67	−	10999.7i	0.568022	−	0.983842i
$501$		0			0
$502$	12672.6	+	21949.5i	1.12670	+	1.95150i
$503$	−5720.55			−0.507091			−0.253545	−	0.967323i	$-0.581597\pi$
$503$	−5720.55			−0.507091			−0.253545	+	0.967323i	$0.581597\pi$
$504$		0			0
$505$	−17717.7			−1.56124
$506$	−5443.57	−	9428.54i	−0.478254	−	0.828359i
$507$		0			0
$508$	5164.53	−	8945.24i	0.451061	−	0.781261i
$509$	−7646.59	−	13244.3i	−0.665873	−	1.15333i	−0.979048	−	0.203630i	$-0.934726\pi$
$509$	−7646.59	−	13244.3i	−0.665873	−	1.15333i	0.313175	−	0.949695i	$-0.398607\pi$
$510$		0			0
$511$	−594.583	−	8983.48i	−0.0514732	−	0.777702i
$512$	16456.0			1.42043
$513$		0			0
$514$	−7782.00	+	13478.8i	−0.667800	+	1.15666i
$515$	−2428.82	+	4206.83i	−0.207818	+	0.359952i
$516$		0			0
$517$	−3686.53			−0.313604
$518$	−397.587	−	6007.10i	−0.0337239	−	0.509530i
$519$		0			0
$520$	−166.539	−	288.454i	−0.0140446	−	0.0243260i
$521$	2184.35	−	3783.40i	0.183681	−	0.318145i	−0.759450	−	0.650566i	$-0.774532\pi$
$521$	2184.35	−	3783.40i	0.183681	−	0.318145i	0.943131	+	0.332420i	$0.107865\pi$
$522$		0			0
$523$	1211.08	+	2097.66i	0.101256	+	0.175381i	0.912202	−	0.409740i	$-0.134381\pi$
$523$	1211.08	+	2097.66i	0.101256	+	0.175381i	−0.810946	+	0.585121i	$0.801047\pi$
$524$	−10056.1			−0.838366
$525$		0			0
$526$	−840.291			−0.0696548
$527$	3932.29	+	6810.93i	0.325035	+	0.562976i
$528$		0			0
$529$	−13573.6	+	23510.2i	−1.11561	+	1.93229i
$530$	−744.268	−	1289.11i	−0.0609980	−	0.105652i
$531$		0			0
$532$	−17149.2	+	11474.6i	−1.39758	+	0.935124i
$533$	7158.57			0.581749
$534$		0			0
$535$	1399.11	−	2423.33i	0.113063	−	0.195832i
$536$	−308.105	+	533.654i	−0.0248286	+	0.0430044i
$537$		0			0
$538$	−19482.4			−1.56124
$539$	2831.85	+	3680.78i	0.226302	+	0.294142i
$540$		0			0
$541$	−6581.27	−	11399.1i	−0.523014	−	0.905888i	−0.999641	−	0.0267819i	$-0.991474\pi$
$541$	−6581.27	−	11399.1i	−0.523014	−	0.905888i	0.476627	−	0.879106i	$-0.341859\pi$
$542$	−6520.57	+	11294.0i	−0.516757	+	0.895050i
$543$		0			0
$544$	12123.2	+	20998.0i	0.955473	+	1.65493i
$545$	−2849.45			−0.223958
$546$		0			0
$547$	12112.4			0.946778			0.473389	−	0.880853i	$-0.343031\pi$
$547$	12112.4			0.946778			0.473389	+	0.880853i	$0.343031\pi$
$548$	451.710	+	782.384i	0.0352118	+	0.0609887i
$549$		0			0
$550$	729.892	−	1264.21i	0.0565867	−	0.0980110i
$551$	12423.0	+	21517.2i	0.960503	+	1.66364i
$552$		0			0
$553$	4880.68	+	2403.00i	0.375312	+	0.184785i
$554$	8331.38			0.638928
$555$		0			0
$556$	4631.81	−	8022.54i	0.353296	−	0.611927i
$557$	−4179.82	+	7239.67i	−0.317962	+	0.550726i	−0.980063	−	0.198689i	$-0.936332\pi$
$557$	−4179.82	+	7239.67i	−0.317962	+	0.550726i	0.662101	+	0.749415i	$0.269665\pi$
$558$		0			0
$559$	−7366.74			−0.557388
$560$	730.829	+	11042.0i	0.0551485	+	0.833231i
$561$		0			0
$562$	3586.21	+	6211.50i	0.269173	+	0.466221i
$563$	6819.20	−	11811.2i	0.510471	−	0.884162i	−0.489455	−	0.872028i	$-0.662804\pi$
$563$	6819.20	−	11811.2i	0.510471	−	0.884162i	0.999926	−	0.0121334i	$-0.00386228\pi$
$564$		0			0
$565$	9400.63	+	16282.4i	0.699978	+	1.21240i
$566$	9491.76			0.704891
$567$		0			0
$568$	382.080			0.0282249
$569$	7745.67	+	13415.9i	0.570677	+	0.988442i	0.996497	+	0.0836335i	$0.0266525\pi$
$569$	7745.67	+	13415.9i	0.570677	+	0.988442i	−0.425820	+	0.904808i	$0.640014\pi$
$570$		0			0
$571$	2324.08	−	4025.42i	0.170332	−	0.295024i	−0.768204	−	0.640205i	$-0.778849\pi$
$571$	2324.08	−	4025.42i	0.170332	−	0.295024i	0.938536	+	0.345182i	$0.112183\pi$
$572$	−1060.89	−	1837.52i	−0.0775491	−	0.134319i
$573$		0			0
$574$	25998.1	+	12800.2i	1.89049	+	0.930782i
$575$	−5271.38			−0.382316
$576$		0			0
$577$	2739.53	−	4745.01i	0.197657	−	0.342352i	−0.750111	−	0.661312i	$-0.770000\pi$
$577$	2739.53	−	4745.01i	0.197657	−	0.342352i	0.947768	+	0.318959i	$0.103333\pi$
$578$	−7844.37	+	13586.8i	−0.564503	+	0.977748i
$579$		0			0
$580$	−15782.5			−1.12988
$581$	13693.6	−	9162.49i	0.977811	−	0.654258i
$582$		0			0
$583$	−250.480	−	433.844i	−0.0177939	−	0.0308199i
$584$	−439.846	+	761.836i	−0.0311660	+	0.0539811i
$585$		0			0
$586$	−7367.59	−	12761.0i	−0.519372	−	0.899579i
$587$	−4408.22			−0.309960			−0.154980	−	0.987918i	$-0.549531\pi$
$587$	−4408.22			−0.309960			−0.154980	+	0.987918i	$0.549531\pi$
$588$		0			0
$589$	−11070.3			−0.774441
$590$	7960.71	+	13788.3i	0.555487	+	0.962131i
$591$		0			0
$592$	2413.93	−	4181.05i	0.167588	−	0.290270i
$593$	1407.63	+	2438.08i	0.0974779	+	0.168837i	0.910640	−	0.413201i	$-0.135589\pi$
$593$	1407.63	+	2438.08i	0.0974779	+	0.168837i	−0.813162	+	0.582037i	$0.802256\pi$
$594$		0			0
$595$	−14309.5	+	9574.54i	−0.985935	+	0.659694i
$596$	−6053.09			−0.416014
$597$		0			0
$598$	−7459.51	+	12920.2i	−0.510104	+	0.883526i
$599$	9859.53	−	17077.2i	0.672537	−	1.16487i	−0.304646	−	0.952466i	$-0.598538\pi$
$599$	9859.53	−	17077.2i	0.672537	−	1.16487i	0.977182	−	0.212402i	$-0.0681287\pi$
$600$		0			0
$601$	−13982.8			−0.949033			−0.474517	−	0.880247i	$-0.657377\pi$
$601$	−13982.8			−0.949033			−0.474517	+	0.880247i	$0.657377\pi$
$602$	−26754.1	−	13172.4i	−1.81132	−	0.891805i
$603$		0			0
$604$	−651.913	−	1129.15i	−0.0439172	−	0.0760667i
$605$	5692.71	−	9860.07i	0.382548	−	0.662593i
$606$		0			0
$607$	−6694.14	−	11594.6i	−0.447622	−	0.775305i	0.550608	−	0.834764i	$-0.314396\pi$
$607$	−6694.14	−	11594.6i	−0.447622	−	0.775305i	−0.998231	+	0.0594590i	$0.981062\pi$
$608$	−34129.7			−2.27655
$609$		0			0
$610$	542.065			0.0359797
$611$	2525.89	+	4374.96i	0.167245	+	0.289676i
$612$		0			0
$613$	13895.9	−	24068.5i	0.915582	−	1.58583i	0.109535	−	0.993983i	$-0.465064\pi$
$613$	13895.9	−	24068.5i	0.915582	−	1.58583i	0.806047	−	0.591852i	$-0.201603\pi$
$614$	−12073.6	−	20912.0i	−0.793566	−	1.37450i
$615$		0			0
$616$	−29.9679	−	452.781i	−0.00196013	−	0.0296154i
$617$	19107.2			1.24672			0.623361	−	0.781935i	$-0.285767\pi$
$617$	19107.2			1.24672			0.623361	+	0.781935i	$0.285767\pi$
$618$		0			0
$619$	−546.469	+	946.512i	−0.0354837	+	0.0614596i	−0.883222	−	0.468955i	$-0.844631\pi$
$619$	−546.469	+	946.512i	−0.0354837	+	0.0614596i	0.847738	+	0.530415i	$0.177964\pi$
$620$	3516.01	−	6089.90i	0.227752	−	0.394478i
$621$		0			0
$622$	−4785.75			−0.308507
$623$	−19014.2	−	9361.66i	−1.22278	−	0.602034i
$624$		0			0
$625$	5797.49	+	10041.5i	0.371039	+	0.642659i
$626$	19762.4	−	34229.5i	1.26177	−	2.18544i
$627$		0			0
$628$	8842.13	+	15315.0i	0.561846	+	0.973146i
$629$	7511.40			0.476151
$630$		0			0
$631$	19235.2			1.21353			0.606767	−	0.794879i	$-0.292466\pi$
$631$	19235.2			1.21353			0.606767	+	0.794879i	$0.292466\pi$
$632$	−265.778	−	460.341i	−0.0167280	−	0.0289737i
$633$		0			0
$634$	17421.8	−	30175.4i	1.09134	−	1.89025i
$635$	6065.93	+	10506.5i	0.379085	+	0.656595i
$636$		0			0
$637$	2427.85	−	5882.63i	0.151012	−	0.365900i
$638$	−10342.4			−0.641788
$639$		0			0
$640$	1147.14	−	1986.91i	0.0708511	−	0.122718i
$641$	−9975.33	+	17277.8i	−0.614667	+	1.06463i	0.375776	+	0.926711i	$0.377376\pi$
$641$	−9975.33	+	17277.8i	−0.614667	+	1.06463i	−0.990443	+	0.137924i	$0.955957\pi$
$642$		0			0
$643$	688.125			0.0422037			0.0211019	−	0.999777i	$-0.493283\pi$
$643$	688.125			0.0422037			0.0211019	+	0.999777i	$0.493283\pi$
$644$	−25777.7	+	17248.0i	−1.57731	+	1.05538i
$645$		0			0
$646$	−25064.7	−	43413.4i	−1.52656	−	2.64408i
$647$	5483.09	−	9497.00i	0.333173	−	0.577072i	−0.649959	−	0.759969i	$-0.725214\pi$
$647$	5483.09	−	9497.00i	0.333173	−	0.577072i	0.983132	+	0.182897i	$0.0585475\pi$
$648$		0			0
$649$	2679.14	+	4640.41i	0.162042	+	0.280666i
$650$	−2000.39			−0.120710
$651$		0			0
$652$	25405.0			1.52598
$653$	−6462.54	−	11193.4i	−0.387287	−	0.670802i	0.604796	−	0.796380i	$-0.293255\pi$
$653$	−6462.54	−	11193.4i	−0.387287	−	0.670802i	−0.992084	+	0.125579i	$0.959921\pi$
$654$		0			0
$655$	5905.64	−	10228.9i	0.352294	−	0.610191i
$656$	11619.4	+	20125.5i	0.691559	+	1.19782i
$657$		0			0
$658$	1350.55	+	20405.3i	0.0800150	+	1.20894i
$659$	11779.0			0.696273			0.348137	−	0.937444i	$-0.386815\pi$
$659$	11779.0			0.696273			0.348137	+	0.937444i	$0.386815\pi$
$660$		0			0
$661$	12520.0	−	21685.3i	0.736721	−	1.27604i	−0.217243	−	0.976118i	$-0.569706\pi$
$661$	12520.0	−	21685.3i	0.736721	−	1.27604i	0.953964	−	0.299921i	$-0.0969604\pi$
$662$	10647.8	−	18442.6i	0.625136	−	1.08277i
$663$		0			0
$664$	−1609.89			−0.0940900
$665$	−1600.54	−	24182.4i	−0.0933329	−	1.41016i
$666$		0			0
$667$	18673.6	+	32343.6i	1.08403	+	1.87759i
$668$	−9419.36	+	16314.8i	−0.545578	+	0.944968i
$669$		0			0
$670$	−6849.78	−	11864.2i	−0.394971	−	0.684109i
$671$	182.430			0.0104957
$672$		0			0
$673$	4104.64			0.235100			0.117550	−	0.993067i	$-0.462496\pi$
$673$	4104.64			0.235100			0.117550	+	0.993067i	$0.462496\pi$
$674$	17228.2	+	29840.2i	0.984580	+	1.70534i
$675$		0			0
$676$	7824.40	−	13552.3i	0.445175	−	0.771066i
$677$	6076.70	+	10525.1i	0.344973	+	0.597510i	0.985349	−	0.170551i	$-0.0545549\pi$
$677$	6076.70	+	10525.1i	0.344973	+	0.597510i	−0.640376	+	0.768061i	$0.721222\pi$
$678$		0			0
$679$	−21312.5	+	14260.3i	−1.20456	+	0.805978i
$680$	1682.29			0.0948717
$681$		0			0
$682$	2304.08	−	3990.78i	0.129366	−	0.224069i
$683$	−10207.0	+	17679.0i	−0.571830	+	0.990438i	0.424549	+	0.905405i	$0.360433\pi$
$683$	−10207.0	+	17679.0i	−0.571830	+	0.990438i	−0.996378	+	0.0850328i	$0.972900\pi$
$684$		0			0
$685$	−1061.10			−0.0591862
$686$	19336.0	−	17023.0i	1.07617	−	0.947437i
$687$		0			0
$688$	−11957.3	−	20710.7i	−0.662600	−	1.14766i
$689$	−343.241	+	594.511i	−0.0189789	+	0.0328724i
$690$		0			0
$691$	−8046.76	−	13937.4i	−0.443000	−	0.767299i	0.554910	−	0.831910i	$-0.312753\pi$
$691$	−8046.76	−	13937.4i	−0.443000	−	0.767299i	−0.997911	+	0.0646110i	$0.979419\pi$
$692$	4756.66			0.261302
$693$		0			0
$694$	23643.6			1.29322
$695$	5440.23	+	9422.76i	0.296921	+	0.514282i
$696$		0			0
$697$	−18078.0	+	31312.1i	−0.982431	+	1.70162i
$698$	−3672.42	−	6360.81i	−0.199145	−	0.344929i
$699$		0			0
$700$	−3731.01	−	1836.96i	−0.201456	−	0.0991867i
$701$	−20803.0			−1.12085			−0.560426	−	0.828204i	$-0.689363\pi$
$701$	−20803.0			−1.12085			−0.560426	+	0.828204i	$0.689363\pi$
$702$		0			0
$703$	−5286.60	+	9156.65i	−0.283624	+	0.491251i
$704$	3841.42	−	6653.54i	0.205652	−	0.356200i
$705$		0			0
$706$	−13495.4			−0.719412
$707$	2184.46	+	33004.8i	0.116202	+	1.75569i
$708$		0			0
$709$	−70.7460	−	122.536i	−0.00374742	−	0.00649073i	0.864146	−	0.503242i	$-0.167860\pi$
$709$	−70.7460	−	122.536i	−0.00374742	−	0.00649073i	−0.867893	+	0.496751i	$0.834526\pi$
$710$	−4247.20	+	7356.36i	−0.224499	+	0.388844i
$711$		0			0
$712$	1035.42	+	1793.41i	0.0545002	+	0.0943971i
$713$	−16640.4			−0.874035
$714$		0			0
$715$	2492.11			0.130349
$716$	7768.40	+	13455.3i	0.405473	+	0.702300i
$717$		0			0
$718$	−1765.84	+	3058.53i	−0.0917836	+	0.158974i
$719$	−3332.23	−	5771.59i	−0.172839	−	0.299366i	0.766572	−	0.642158i	$-0.221961\pi$
$719$	−3332.23	−	5771.59i	−0.172839	−	0.299366i	−0.939411	+	0.342792i	$0.888627\pi$
$720$		0			0
$721$	8135.99	+	4005.76i	0.420250	+	0.206910i
$722$	42747.2			2.20345
$723$		0			0
$724$	−9817.50	+	17004.4i	−0.503957	+	0.872878i
$725$	−2503.82	+	4336.74i	−0.128261	+	0.222155i
$726$		0			0
$727$	−4837.23			−0.246772			−0.123386	−	0.992359i	$-0.539375\pi$
$727$	−4837.23			−0.246772			−0.123386	+	0.992359i	$0.539375\pi$
$728$	−516.802	+	345.795i	−0.0263104	+	0.0176044i
$729$		0			0
$730$	−9778.65	−	16937.1i	−0.495786	−	0.858727i
$731$	18603.7	−	32222.6i	0.941291	−	1.63036i
$732$		0			0
$733$	15801.3	+	27368.6i	0.796225	+	1.37910i	0.922059	+	0.387050i	$0.126506\pi$
$733$	15801.3	+	27368.6i	0.796225	+	1.37910i	−0.125834	+	0.992051i	$0.540161\pi$
$734$	4763.93			0.239564
$735$		0			0
$736$	−51302.0			−2.56932
$737$	−2305.27	−	3992.84i	−0.115218	−	0.199563i
$738$		0			0
$739$	4113.79	−	7125.30i	0.204774	−	0.354680i	−0.745286	−	0.666744i	$-0.767687\pi$
$739$	4113.79	−	7125.30i	0.204774	−	0.354680i	0.950061	+	0.312065i	$0.101021\pi$
$740$	−3358.11	−	5816.42i	−0.166820	−	0.288940i
$741$		0			0
$742$	−2309.61	+	1545.37i	−0.114270	+	0.0764586i
$743$	−37020.3			−1.82792			−0.913959	−	0.405805i	$-0.866991\pi$
$743$	−37020.3			−1.82792			−0.913959	+	0.405805i	$0.866991\pi$
$744$		0			0
$745$	3554.78	−	6157.07i	0.174815	−	0.302789i
$746$	−7357.16	+	12743.0i	−0.361079	+	0.625407i
$747$		0			0
$748$	10716.6			0.523846
$749$	−4686.72	−	2307.50i	−0.228637	−	0.112569i
$750$		0			0
$751$	12575.0	+	21780.5i	0.611008	+	1.05830i	0.991071	+	0.133336i	$0.0425689\pi$
$751$	12575.0	+	21780.5i	0.611008	+	1.05830i	−0.380063	+	0.924960i	$0.624098\pi$
$752$	−8199.78	+	14202.4i	−0.397627	+	0.688710i
$753$		0			0
$754$	7086.29	+	12273.8i	0.342265	+	0.592820i
$755$	1531.39			0.0738186
$756$		0			0
$757$	20460.8			0.982377			0.491189	−	0.871053i	$-0.336563\pi$
$757$	20460.8			0.982377			0.491189	+	0.871053i	$0.336563\pi$
$758$	−14846.8	−	25715.4i	−0.711424	−	1.23222i
$759$		0			0
$760$	−1184.01	+	2050.77i	−0.0565113	+	0.0978804i
$761$	16329.6	+	28283.6i	0.777853	+	1.34728i	0.933177	+	0.359417i	$0.117024\pi$
$761$	16329.6	+	28283.6i	0.777853	+	1.34728i	−0.155324	+	0.987864i	$0.549642\pi$
$762$		0			0
$763$	351.316	+	5307.98i	0.0166690	+	0.251850i
$764$	26413.7			1.25080
$765$		0			0
$766$	−14913.5	+	25830.9i	−0.703455	+	1.21842i
$767$	3671.32	−	6358.91i	0.172834	−	0.299357i
$768$		0			0
$769$	−11005.3			−0.516075			−0.258037	−	0.966135i	$-0.583076\pi$
$769$	−11005.3			−0.516075			−0.258037	+	0.966135i	$0.583076\pi$
$770$	9050.72	+	4456.12i	0.423591	+	0.208555i
$771$		0			0
$772$	15664.7	+	27132.1i	0.730293	+	1.26490i
$773$	−1519.09	+	2631.14i	−0.0706829	+	0.122426i	−0.899201	−	0.437536i	$-0.855851\pi$
$773$	−1519.09	+	2631.14i	−0.0706829	+	0.122426i	0.828518	+	0.559963i	$0.189185\pi$
$774$		0			0
$775$	−1115.60	−	1932.27i	−0.0517077	−	0.0895604i
$776$	2505.59			0.115909
$777$		0			0
$778$	−36780.9			−1.69493
$779$	−25447.0	−	44075.5i	−1.17039	−	2.02717i
$780$		0			0
$781$	−1429.38	+	2475.75i	−0.0654893	+	0.113431i
$782$	−37676.0	−	65256.8i	−1.72288	−	2.98411i
$783$		0			0
$784$	20479.1	−	2722.79i	0.932902	−	0.124034i
$785$	−20770.8			−0.944384
$786$		0			0
$787$	6153.38	−	10658.0i	0.278710	−	0.482739i	−0.692355	−	0.721557i	$-0.743427\pi$
$787$	6153.38	−	10658.0i	0.278710	−	0.482739i	0.971064	+	0.238818i	$0.0767600\pi$
$788$	3594.50	−	6225.86i	0.162498	−	0.281455i
$789$		0			0
$790$	11817.5			0.532214
$791$	29172.0	−	19519.1i	1.31130	−	0.877395i
$792$		0			0
$793$	−124.995	−	216.497i	−0.00559735	−	0.00969489i
$794$	−14958.0	+	25908.0i	−0.668562	+	1.15798i
$795$		0			0
$796$	−14349.2	−	24853.6i	−0.638938	−	1.10667i
$797$	−3007.06			−0.133646			−0.0668228	−	0.997765i	$-0.521286\pi$
$797$	−3007.06			−0.133646			−0.0668228	+	0.997765i	$0.521286\pi$
$798$		0			0
$799$	−25515.2			−1.12974
$800$	−3439.37	−	5957.17i	−0.152000	−	0.263272i
$801$		0			0
$802$	−5786.06	+	10021.7i	−0.254754	+	0.441247i
$803$	−3290.96	−	5700.11i	−0.144627	−	0.250501i
$804$		0			0
$805$	−2405.86	−	36349.8i	−0.105336	−	1.59150i
$806$	−6314.72			−0.275963
$807$		0			0
$808$	1615.97	−	2798.94i	0.0703584	−	0.121864i
$809$	−5292.48	+	9166.84i	−0.230005	+	0.398380i	−0.957809	−	0.287405i	$-0.907207\pi$
$809$	−5292.48	+	9166.84i	−0.230005	+	0.398380i	0.727805	+	0.685785i	$0.240541\pi$
$810$		0			0
$811$	−18217.8			−0.788796			−0.394398	−	0.918940i	$-0.629047\pi$
$811$	−18217.8			−0.788796			−0.394398	+	0.918940i	$0.629047\pi$
$812$	1945.86	+	29399.8i	0.0840965	+	1.27060i
$813$		0			0
$814$	−2200.61	−	3811.57i	−0.0947559	−	0.164122i
$815$	−14919.6	+	25841.4i	−0.641239	+	1.11066i
$816$		0			0
$817$	26187.0	+	45357.2i	1.12138	+	1.94229i
$818$	45663.9			1.95184
$819$		0			0
$820$	32328.5			1.37678
$821$	−12798.3	−	22167.2i	−0.544047	−	0.942317i	−0.998666	−	0.0516309i	$-0.983558\pi$
$821$	−12798.3	−	22167.2i	−0.544047	−	0.942317i	0.454619	−	0.890686i	$-0.349775\pi$
$822$		0			0
$823$	−21889.5	+	37913.6i	−0.927118	+	1.60582i	−0.139000	+	0.990292i	$0.544389\pi$
$823$	−21889.5	+	37913.6i	−0.927118	+	1.60582i	−0.788119	+	0.615524i	$0.788945\pi$
$824$	−443.047	−	767.380i	−0.0187309	−	0.0324429i
$825$		0			0
$826$	24703.6	−	16529.3i	1.04062	−	0.696281i
$827$	−2735.78			−0.115033			−0.0575166	−	0.998345i	$-0.518318\pi$
$827$	−2735.78			−0.115033			−0.0575166	+	0.998345i	$0.518318\pi$
$828$		0			0
$829$	15572.1	−	26971.7i	0.652402	−	1.12999i	−0.330137	−	0.943933i	$-0.607095\pi$
$829$	15572.1	−	26971.7i	0.652402	−	1.12999i	0.982538	−	0.186060i	$-0.0595719\pi$
$830$	17895.5	−	30995.9i	0.748387	−	1.29625i
$831$		0			0
$832$	−10528.1			−0.438696
$833$	19599.8	+	25475.4i	0.815238	+	1.05963i
$834$		0			0
$835$	−11063.4	−	19162.3i	−0.458520	−	0.794179i
$836$	−7542.43	+	13063.9i	−0.312034	+	0.540458i
$837$		0			0
$838$	−18698.3	−	32386.5i	−0.770792	−	1.33505i
$839$	14977.3			0.616300			0.308150	−	0.951338i	$-0.400290\pi$
$839$	14977.3			0.616300			0.308150	+	0.951338i	$0.400290\pi$
$840$		0			0
$841$	11089.6			0.454698
$842$	17276.5	+	29923.9i	0.707113	+	1.22476i
$843$		0			0
$844$	−915.285	+	1585.32i	−0.0373287	+	0.0646552i
$845$	9190.04	+	15917.6i	0.374139	+	0.648027i
$846$		0			0
$847$	−19069.3	−	9388.78i	−0.773589	−	0.380876i
$848$	−2228.53			−0.0902452
$849$		0			0
$850$	5051.72	−	8749.84i	0.203850	−	0.353079i
$851$	−7946.55	+	13763.8i	−0.320099	+	0.554427i
$852$		0			0
$853$	42861.7			1.72047			0.860233	−	0.509901i	$-0.170318\pi$
$853$	42861.7			1.72047			0.860233	+	0.509901i	$0.170318\pi$
$854$	−66.8326	−	1009.77i	−0.00267795	−	0.0404607i
$855$		0			0
$856$	255.216	+	442.047i	0.0101905	+	0.0176505i
$857$	−4695.00	+	8131.98i	−0.187139	+	0.324134i	−0.944295	−	0.329100i	$-0.893255\pi$
$857$	−4695.00	+	8131.98i	−0.187139	+	0.324134i	0.757156	+	0.653234i	$0.226588\pi$
$858$		0			0
$859$	−16780.6	−	29064.8i	−0.666526	−	1.15446i	−0.978869	−	0.204488i	$-0.934447\pi$
$859$	−16780.6	−	29064.8i	−0.666526	−	1.15446i	0.312343	−	0.949969i	$-0.398886\pi$
$860$	−33268.6			−1.31913
$861$		0			0
$862$	−37155.9			−1.46814
$863$	12845.8	+	22249.6i	0.506693	+	0.877617i	0.999970	+	0.00774521i	$0.00246540\pi$
$863$	12845.8	+	22249.6i	0.506693	+	0.877617i	−0.493277	+	0.869872i	$0.664201\pi$
$864$		0			0
$865$	−2793.43	+	4838.37i	−0.109803	+	0.190184i
$866$	22256.3	+	38549.1i	0.873327	+	1.51265i
$867$		0			0
$868$	−11777.8	−	5798.82i	−0.460560	−	0.226757i
$869$	3977.14			0.155254
$870$		0			0
$871$	−3158.98	+	5471.52i	−0.122891	+	0.212853i
$872$	259.888	−	450.138i	0.0100928	−	0.0174812i
$873$		0			0
$874$	106067.			4.10500
$875$	23147.0	−	15487.8i	0.894299	−	0.598380i
$876$		0			0
$877$	2675.76	+	4634.55i	0.103026	+	0.178447i	0.912930	−	0.408116i	$-0.133814\pi$
$877$	2675.76	+	4634.55i	0.103026	+	0.178447i	−0.809904	+	0.586563i	$0.800481\pi$
$878$	−8076.69	+	13989.2i	−0.310450	+	0.537715i
$879$		0			0
$880$	4045.07	+	7006.26i	0.154954	+	0.268388i
$881$	34212.7			1.30835			0.654174	−	0.756344i	$-0.273016\pi$
$881$	34212.7			1.30835			0.654174	+	0.756344i	$0.273016\pi$
$882$		0			0
$883$	17149.2			0.653587			0.326794	−	0.945096i	$-0.394032\pi$
$883$	17149.2			0.653587			0.326794	+	0.945096i	$0.394032\pi$
$884$	−7342.64	−	12717.8i	−0.279366	−	0.483876i
$885$		0			0
$886$	9174.21	−	15890.2i	0.347871	−	0.602530i
$887$	2010.44	+	3482.18i	0.0761035	+	0.131815i	0.901566	−	0.432642i	$-0.142419\pi$
$887$	2010.44	+	3482.18i	0.0761035	+	0.131815i	−0.825462	+	0.564458i	$0.809085\pi$
$888$		0			0
$889$	18823.8	−	12595.1i	0.710156	−	0.475169i
$890$	−46039.0			−1.73397
$891$		0			0
$892$	9522.53	−	16493.5i	0.357442	−	0.619107i
$893$	17957.8	−	31103.9i	0.672941	−	1.16557i
$894$		0			0
$895$	−18248.5			−0.681544
$896$	−3842.67	−	1891.94i	−0.143275	−	0.0705415i
$897$		0			0
$898$	−4210.50	−	7292.79i	−0.156466	−	0.271006i
$899$	−7903.91	+	13690.0i	−0.293226	+	0.507882i
$900$		0			0
$901$	−1733.62	−	3002.72i	−0.0641013	−	0.111027i
$902$	21185.2			0.782030
$903$		0			0
$904$	−3429.59			−0.126180
$905$	−11531.0	−	19972.3i	−0.423540	−	0.733593i
$906$		0			0
$907$	11483.6	−	19890.2i	0.420405	−	0.728163i	−0.575574	−	0.817750i	$-0.695221\pi$
$907$	11483.6	−	19890.2i	0.420405	−	0.728163i	0.995979	+	0.0895869i	$0.0285547\pi$
$908$	−14319.7	−	24802.5i	−0.523366	−	0.906497i
$909$		0			0
$910$	−912.978	−	13794.1i	−0.0332582	−	0.502493i
$911$	−9860.77			−0.358619			−0.179309	−	0.983793i	$-0.557386\pi$
$911$	−9860.77			−0.358619			−0.179309	+	0.983793i	$0.557386\pi$
$912$		0			0
$913$	6022.65	−	10431.5i	0.218314	−	0.378131i
$914$	3746.35	−	6488.87i	0.135578	−	0.234828i
$915$		0			0
$916$	21857.5			0.788421
$917$	−19782.6	−	9739.95i	−0.712408	−	0.350754i
$918$		0			0
$919$	2635.77	+	4565.30i	0.0946096	+	0.163869i	0.909446	−	0.415823i	$-0.136506\pi$
$919$	2635.77	+	4565.30i	0.0946096	+	0.163869i	−0.814836	+	0.579692i	$0.803173\pi$
$920$	−1779.75	+	3082.61i	−0.0637788	+	0.110468i
$921$		0			0
$922$	1778.18	+	3079.90i	0.0635154	+	0.110012i
$923$	3917.44			0.139701
$924$		0			0
$925$	−2131.00			−0.0757478
$926$	−32940.3	−	57054.3i	−1.16899	−	2.02475i
$927$		0			0
$928$	−24367.6	+	42206.0i	−0.861968	+	1.49297i
$929$	−7451.31	−	12906.0i	−0.263153	−	0.455795i	0.703925	−	0.710274i	$-0.251429\pi$
$929$	−7451.31	−	12906.0i	−0.263153	−	0.455795i	−0.967078	+	0.254480i	$0.918096\pi$
$930$		0			0
$931$	−44849.9	+	5963.02i	−1.57884	+	0.209914i
$932$	8061.24			0.283321
$933$		0			0
$934$	−38448.7	+	66595.1i	−1.34698	+	2.33304i
$935$	−6293.50	+	10900.7i	−0.220128	+	0.381272i
$936$		0			0
$937$	−21934.8			−0.764757			−0.382378	−	0.924006i	$-0.624895\pi$
$937$	−21934.8			−0.764757			−0.382378	+	0.924006i	$0.624895\pi$
$938$	−21256.2	+	14222.6i	−0.739914	+	0.495080i
$939$		0			0
$940$	11407.0	+	19757.6i	0.395805	+	0.685554i
$941$	7260.76	−	12576.0i	0.251535	−	0.435671i	−0.712414	−	0.701760i	$-0.752398\pi$
$941$	7260.76	−	12576.0i	0.251535	−	0.435671i	0.963949	+	0.266089i	$0.0857314\pi$
$942$		0			0
$943$	−38250.7	−	66252.1i	−1.32090	−	2.28787i
$944$	23836.4			0.821831
$945$		0			0
$946$	−21801.3			−0.749282
$947$	971.867	+	1683.32i	0.0333489	+	0.0577621i	0.882218	−	0.470841i	$-0.156049\pi$
$947$	971.867	+	1683.32i	0.0333489	+	0.0577621i	−0.848869	+	0.528603i	$0.822716\pi$
$948$		0			0
$949$	−4509.71	+	7811.05i	−0.154259	+	0.267184i
$950$	7110.91	+	12316.5i	0.242851	+	0.420630i
$951$		0			0
$952$	−207.413	−	3133.78i	−0.00706125	−	0.106688i
$953$	16904.1			0.574583			0.287292	−	0.957843i	$-0.407245\pi$
$953$	16904.1			0.574583			0.287292	+	0.957843i	$0.407245\pi$
$954$		0			0
$955$	−15511.9	+	26867.4i	−0.525606	+	0.910376i
$956$	842.527	−	1459.30i	0.0285034	−	0.0493694i
$957$		0			0
$958$	33975.1			1.14581
$959$	130.826	+	1976.63i	0.00440519	+	0.0665575i
$960$		0			0
$961$	11373.8	+	19700.1i	0.381788	+	0.661276i
$962$	−3015.57	+	5223.12i	−0.101066	+	0.175052i
$963$		0			0
$964$	−20247.4	−	35069.5i	−0.676478	−	1.17169i
$965$	−36797.6			−1.22752
$966$		0			0
$967$	26699.3			0.887891			0.443946	−	0.896054i	$-0.353578\pi$
$967$	26699.3			0.887891			0.443946	+	0.896054i	$0.353578\pi$
$968$	1038.42	+	1798.60i	0.0344795	+	0.0597203i
$969$		0			0
$970$	−27852.1	+	48241.3i	−0.921936	+	1.59684i
$971$	5544.74	+	9603.77i	0.183253	+	0.317404i	0.942987	−	0.332831i	$-0.108004\pi$
$971$	5544.74	+	9603.77i	0.183253	+	0.317404i	−0.759733	+	0.650235i	$0.774670\pi$
$972$		0			0
$973$	16882.1	−	11295.9i	0.556233	−	0.372178i
$974$	−18487.9			−0.608205
$975$		0			0
$976$	405.771	−	702.815i	0.0133078	−	0.0230498i
$977$	25945.9	−	44939.7i	0.849625	−	1.47159i	−0.0319179	−	0.999490i	$-0.510162\pi$
$977$	25945.9	−	44939.7i	0.849625	−	1.47159i	0.881543	−	0.472103i	$-0.156505\pi$
$978$		0			0
$979$	−15494.2			−0.505820
$980$	10964.3	−	26566.3i	0.357389	−	0.865948i
$981$		0			0
$982$	32057.7	+	55525.6i	1.04176	+	1.80437i
$983$	12280.3	−	21270.2i	0.398456	−	0.690145i	−0.595080	−	0.803666i	$-0.702880\pi$
$983$	12280.3	−	21270.2i	0.398456	−	0.690145i	0.993536	+	0.113521i	$0.0362130\pi$
$984$		0			0
$985$	4221.87	+	7312.49i	0.136569	+	0.236544i
$986$	−71582.0			−2.31200
$987$		0			0
$988$	20671.3			0.665629
$989$	39363.0	+	68178.7i	1.26559	+	2.19207i
$990$		0			0
$991$	9253.76	−	16028.0i	0.296625	−	0.513769i	−0.678737	−	0.734382i	$-0.737472\pi$
$991$	9253.76	−	16028.0i	0.296625	−	0.513769i	0.975362	+	0.220612i	$0.0708056\pi$
$992$	−10857.2	−	18805.2i	−0.347497	−	0.601882i
$993$		0			0
$994$	14227.2	+	7004.75i	0.453982	+	0.223518i
$995$	33707.4			1.07397
$996$		0			0
$997$	21483.1	−	37209.8i	0.682424	−	1.18199i	−0.291815	−	0.956475i	$-0.594259\pi$
$997$	21483.1	−	37209.8i	0.682424	−	1.18199i	0.974239	−	0.225518i	$-0.0724074\pi$
$998$	−27142.9	+	47012.9i	−0.860916	+	1.49115i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.e.d.46.1	yes	8
3.2	odd	2	inner	63.4.e.d.46.4	yes	8
7.2	even	3	inner	63.4.e.d.37.1	✓	8
7.3	odd	6		441.4.a.v.1.4		4
7.4	even	3		441.4.a.w.1.4		4
7.5	odd	6		441.4.e.x.226.1		8
7.6	odd	2		441.4.e.x.361.1		8
21.2	odd	6	inner	63.4.e.d.37.4	yes	8
21.5	even	6		441.4.e.x.226.4		8
21.11	odd	6		441.4.a.w.1.1		4
21.17	even	6		441.4.a.v.1.1		4
21.20	even	2		441.4.e.x.361.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.e.d.37.1	✓	8	7.2	even	3	inner
63.4.e.d.37.4	yes	8	21.2	odd	6	inner
63.4.e.d.46.1	yes	8	1.1	even	1	trivial
63.4.e.d.46.4	yes	8	3.2	odd	2	inner
441.4.a.v.1.1		4	21.17	even	6
441.4.a.v.1.4		4	7.3	odd	6
441.4.a.w.1.1		4	21.11	odd	6
441.4.a.w.1.4		4	7.4	even	3
441.4.e.x.226.1		8	7.5	odd	6
441.4.e.x.226.4		8	21.5	even	6
441.4.e.x.361.1		8	7.6	odd	2
441.4.e.x.361.4		8	21.20	even	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.02770 - 3.51207i) q^{2} +(-4.22311 + 7.31464i) q^{4} +(-4.96020 - 8.59131i) q^{5} +(-15.3924 + 10.2992i) q^{7} +1.80961 q^{8} +O(q^{10})\)	\(q+(-2.02770 - 3.51207i) q^{2} +(-4.22311 + 7.31464i) q^{4} +(-4.96020 - 8.59131i) q^{5} +(-15.3924 + 10.2992i) q^{7} +1.80961 q^{8} +(-20.1156 + 34.8412i) q^{10} +(-6.76980 + 11.7256i) q^{11} +18.5538 q^{13} +(67.3826 + 33.1758i) q^{14} +(30.1156 + 52.1617i) q^{16} +(-46.8551 + 81.1555i) q^{17} +(-65.9542 - 114.236i) q^{19} +83.7899 q^{20} +54.9084 q^{22} +(-99.1391 - 171.714i) q^{23} +(13.2929 - 23.0240i) q^{25} +(-37.6214 - 65.1622i) q^{26} +(-10.3307 - 156.085i) q^{28} -188.358 q^{29} +(41.9622 - 72.6807i) q^{31} +(129.369 - 224.073i) q^{32} +380.032 q^{34} +(164.833 + 81.1555i) q^{35} +(-40.0778 - 69.4167i) q^{37} +(-267.470 + 463.272i) q^{38} +(-8.97600 - 15.5469i) q^{40} +385.828 q^{41} -397.048 q^{43} +(-57.1793 - 99.0374i) q^{44} +(-402.048 + 696.368i) q^{46} +(136.139 + 235.799i) q^{47} +(130.855 - 317.058i) q^{49} -107.816 q^{50} +(-78.3547 + 135.714i) q^{52} +(-18.4998 + 32.0426i) q^{53} +134.318 q^{55} +(-27.8543 + 18.6374i) q^{56} +(381.932 + 661.526i) q^{58} +(197.874 - 342.728i) q^{59} +(-6.73689 - 11.6686i) q^{61} -340.347 q^{62} -567.435 q^{64} +(-92.0304 - 159.401i) q^{65} +(-170.261 + 294.901i) q^{67} +(-395.749 - 685.457i) q^{68} +(-49.2071 - 743.464i) q^{70} +211.140 q^{71} +(-243.062 + 420.995i) q^{73} +(-162.531 + 281.512i) q^{74} +1114.13 q^{76} +(-16.5604 - 250.210i) q^{77} +(-146.871 - 254.387i) q^{79} +(298.758 - 517.464i) q^{80} +(-782.343 - 1355.06i) q^{82} -889.635 q^{83} +929.643 q^{85} +(805.093 + 1394.46i) q^{86} +(-12.2507 + 21.2188i) q^{88} +(572.182 + 991.048i) q^{89} +(-285.588 + 191.088i) q^{91} +1674.70 q^{92} +(552.096 - 956.258i) q^{94} +(-654.292 + 1133.27i) q^{95} +1384.61 q^{97} +(-1378.87 + 183.327i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{4} - 12 q^{7}+O(q^{10}) \) 8 * q - 6 * q^4 - 12 * q^7	\( 8 q - 6 q^{4} - 12 q^{7} - 22 q^{10} + 204 q^{13} + 102 q^{16} - 222 q^{19} - 172 q^{22} - 366 q^{25} - 166 q^{28} - 220 q^{31} + 2040 q^{34} + 374 q^{37} - 822 q^{40} - 1676 q^{43} - 1716 q^{46} + 380 q^{49} + 40 q^{52} + 5020 q^{55} + 1694 q^{58} - 1332 q^{61} - 1372 q^{64} - 1890 q^{67} - 866 q^{70} - 1750 q^{73} + 4912 q^{76} - 8 q^{79} - 2480 q^{82} - 2232 q^{85} - 2682 q^{88} + 466 q^{91} + 1416 q^{94} + 6020 q^{97}+O(q^{100}) \) 8 * q - 6 * q^4 - 12 * q^7 - 22 * q^10 + 204 * q^13 + 102 * q^16 - 222 * q^19 - 172 * q^22 - 366 * q^25 - 166 * q^28 - 220 * q^31 + 2040 * q^34 + 374 * q^37 - 822 * q^40 - 1676 * q^43 - 1716 * q^46 + 380 * q^49 + 40 * q^52 + 5020 * q^55 + 1694 * q^58 - 1332 * q^61 - 1372 * q^64 - 1890 * q^67 - 866 * q^70 - 1750 * q^73 + 4912 * q^76 - 8 * q^79 - 2480 * q^82 - 2232 * q^85 - 2682 * q^88 + 466 * q^91 + 1416 * q^94 + 6020 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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