LMFDB - Embedded newform 63.4.e.d.37.4

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			37.4
Root			$-2.02770 - 3.51207i$ of defining polynomial
Character	$\chi$	$=$	63.37
Dual form			63.4.e.d.46.4

$q$-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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

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

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	−0.245323	−	0.969441i	$-0.578894\pi$
$2$	2.02770	−	3.51207i	0.716899	−	1.24171i	0.962222	−	0.272264i	$-0.0877726\pi$
$3$		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	$-0.687015\pi$
$5$	4.96020	−	8.59131i	0.443654	−	0.768430i	0.997957	+	0.0638840i	$0.0203488\pi$
$6$		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	$-0.107256\pi$
$11$	6.76980	+	11.7256i	0.185561	+	0.321401i	−0.758204	+	0.652017i	$0.773923\pi$
$12$		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	0.978331	+	0.207046i	$0.0663850\pi$
$17$	46.8551	+	81.1555i	0.668473	+	1.15783i	−0.309858	+	0.950783i	$0.600282\pi$
$18$		0			0
$19$	−65.9542	+	114.236i	−0.796365	+	1.37934i	0.125604	+	0.992080i	$0.459913\pi$
$19$	−65.9542	+	114.236i	−0.796365	+	1.37934i	−0.921969	+	0.387264i	$0.873420\pi$
$20$	−83.7899			−0.936799
$21$		0			0
$22$	54.9084			0.532115
$23$	99.1391	−	171.714i	0.898779	−	1.55673i	0.0697230	−	0.997566i	$-0.477788\pi$
$23$	99.1391	−	171.714i	0.898779	−	1.55673i	0.829056	−	0.559165i	$-0.188878\pi$
$24$		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	$-0.293950\pi$
$29$	188.358			1.20611			0.603054	+	0.797700i	$0.293950\pi$
$30$		0			0
$31$	41.9622	+	72.6807i	0.243117	+	0.421092i	0.961601	−	0.274453i	$-0.0884967\pi$
$31$	41.9622	+	72.6807i	0.243117	+	0.421092i	−0.718483	+	0.695544i	$0.755163\pi$
$32$	−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	−0.941221	−	0.337792i	$-0.890320\pi$
$37$	−40.0778	+	69.4167i	−0.178074	+	0.308434i	0.763147	+	0.646225i	$0.223653\pi$
$38$	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	$-0.762739\pi$
$41$	−385.828			−1.46967			−0.734833	+	0.678249i	$0.762739\pi$
$42$		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	$-0.972183\pi$
$47$	−136.139	+	235.799i	−0.422508	+	0.731805i	0.573676	+	0.819082i	$0.305517\pi$
$48$		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	$-0.151399\pi$
$53$	18.4998	+	32.0426i	0.0479461	+	0.0830451i	−0.841056	+	0.540948i	$0.818066\pi$
$54$		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	$-0.310494\pi$
$59$	−197.874	−	342.728i	−0.436628	−	0.756262i	−0.997427	+	0.0716901i	$0.977161\pi$
$60$		0			0
$61$	−6.73689	+	11.6686i	−0.0141405	+	0.0244921i	−0.873009	−	0.487704i	$-0.837835\pi$
$61$	−6.73689	+	11.6686i	−0.0141405	+	0.0244921i	0.858869	+	0.512196i	$0.171168\pi$
$62$	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	0.668004	−	0.744158i	$-0.267149\pi$
$67$	−170.261	−	294.901i	−0.310458	−	0.537729i	−0.978462	+	0.206429i	$0.933816\pi$
$68$	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	$-0.556466\pi$
$71$	−211.140			−0.352925			−0.176463	+	0.984307i	$0.556466\pi$
$72$		0			0
$73$	−243.062	−	420.995i	−0.389702	−	0.674983i	0.602708	−	0.797962i	$-0.294089\pi$
$73$	−243.062	−	420.995i	−0.389702	−	0.674983i	−0.992409	+	0.122979i	$0.960755\pi$
$74$	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	−0.951453	−	0.307795i	$-0.900409\pi$
$79$	−146.871	+	254.387i	−0.209168	+	0.362289i	0.742285	+	0.670084i	$0.233742\pi$
$80$	−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	$-0.299816\pi$
$83$	889.635			1.17651			0.588253	+	0.808677i	$0.299816\pi$
$84$		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	0.293057	+	0.956095i	$0.405327\pi$
$89$	−572.182	+	991.048i	−0.681474	+	1.18035i	−0.974531	+	0.224252i	$0.928006\pi$
$90$		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	−0.851599	−	0.524194i	$-0.824367\pi$
$101$	−892.994	−	1546.71i	−0.879765	−	1.52380i	−0.0281660	−	0.999603i	$-0.508967\pi$
$102$		0			0
$103$	−244.831	+	424.059i	−0.234212	+	0.405668i	−0.959044	−	0.283259i	$-0.908584\pi$
$103$	−244.831	+	424.059i	−0.234212	+	0.405668i	0.724831	+	0.688927i	$0.241918\pi$
$104$	−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	$-0.874004\pi$
$107$	−141.034	+	244.278i	−0.127423	+	0.220703i	0.795254	+	0.606276i	$0.207337\pi$
$108$		0			0
$109$	143.616	+	248.749i	0.126201	+	0.218586i	0.922202	−	0.386709i	$-0.126388\pi$
$109$	143.616	+	248.749i	0.126201	+	0.218586i	−0.796001	+	0.605295i	$0.793055\pi$
$110$	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	$-0.210662\pi$
$113$	1895.21			1.57776			0.788879	+	0.614548i	$0.210662\pi$
$114$		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	$-0.963295\pi$
$131$	−595.303	+	1031.10i	−0.397037	+	0.687689i	0.596322	+	0.802746i	$0.296628\pi$
$132$		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	$-0.177285\pi$
$137$	−53.4807	−	92.6313i	−0.0333516	−	0.0577666i	−0.882219	+	0.470839i	$0.843951\pi$
$138$		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	$-0.896459\pi$
$149$	−358.331	+	620.647i	−0.197018	+	0.341244i	0.750542	+	0.660822i	$0.229792\pi$
$150$		0			0
$151$	−77.1840	−	133.687i	−0.0415970	−	0.0720481i	0.844477	−	0.535591i	$-0.179911\pi$
$151$	−77.1840	−	133.687i	−0.0415970	−	0.0720481i	−0.886074	+	0.463543i	$0.846578\pi$
$152$	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	0.999295	+	0.0375459i	$0.0119541\pi$
$157$	1046.87	+	1813.24i	0.532163	+	0.921734i	−0.467132	+	0.884188i	$0.654713\pi$
$158$	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	0.237242	+	0.971451i	$0.423757\pi$
$163$	−1503.93	+	2604.88i	−0.722680	+	1.25172i	−0.959922	+	0.280268i	$0.909577\pi$
$164$	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	$-0.672860\pi$
$167$	−2230.43			−1.03351			−0.516754	+	0.856134i	$0.672860\pi$
$168$		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	$-0.793842\pi$
$173$	281.585	−	487.719i	0.123749	−	0.214339i	0.921243	+	0.388987i	$0.127175\pi$
$174$		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	$-0.292138\pi$
$179$	−919.749	−	1593.05i	−0.384052	−	0.665197i	−0.991637	+	0.129057i	$0.958805\pi$
$180$		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	−0.401553	−	0.915836i	$-0.631530\pi$
$191$	1563.64	−	2708.30i	0.592360	−	1.02600i	0.993914	−	0.110163i	$-0.0351372\pi$
$192$		0			0
$193$	1854.64	+	3212.34i	0.691711	+	1.19808i	0.971277	+	0.237952i	$0.0764761\pi$
$193$	1854.64	+	3212.34i	0.691711	+	1.19808i	−0.279566	+	0.960126i	$0.590191\pi$
$194$	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	$-0.450812\pi$
$197$	851.150			0.307827			0.153913	+	0.988084i	$0.450812\pi$
$198$		0			0
$199$	−1698.89	−	2942.57i	−0.605182	−	1.04821i	−0.992023	−	0.126060i	$-0.959767\pi$
$199$	−1698.89	−	2942.57i	−0.605182	−	1.04821i	0.386840	−	0.922147i	$-0.373566\pi$
$200$	−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	$-0.00157219\pi$
$227$	1695.40	+	2936.52i	0.495716	+	0.858606i	−0.504271	+	0.863545i	$0.668239\pi$
$228$		0			0
$229$	−1293.92	+	2241.14i	−0.373384	+	0.646720i	−0.990084	−	0.140479i	$-0.955136\pi$
$229$	−1293.92	+	2241.14i	−0.373384	+	0.646720i	0.616700	+	0.787198i	$0.288469\pi$
$230$	−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	$-0.790495\pi$
$233$	477.210	−	826.552i	0.134176	−	0.232400i	0.925282	+	0.379279i	$0.123828\pi$
$234$		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	$-0.491405\pi$
$239$	199.504			0.0539951			0.0269976	+	0.999635i	$0.491405\pi$
$240$		0			0
$241$	−2397.21	−	4152.10i	−0.640739	−	1.10979i	−0.985268	−	0.171017i	$-0.945295\pi$
$241$	−2397.21	−	4152.10i	−0.640739	−	1.10979i	0.344529	−	0.938776i	$-0.388039\pi$
$242$	−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	$-0.212243\pi$
$251$	6249.73			1.57163			0.785816	+	0.618460i	$0.212243\pi$
$252$		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	$-0.679116\pi$
$257$	1918.93	−	3323.68i	0.465756	−	0.806713i	0.999235	+	0.0390999i	$0.0124491\pi$
$258$		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	$-0.174399\pi$
$263$	−103.602	−	179.443i	−0.0242903	−	0.0420721i	−0.877915	+	0.478816i	$0.841066\pi$
$264$		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	−0.998642	−	0.0521018i	$-0.983408\pi$
$269$	−2402.04	−	4160.46i	−0.544442	−	0.943002i	0.454199	−	0.890900i	$-0.349925\pi$
$270$		0			0
$271$	−1607.88	+	2784.92i	−0.360411	+	0.624251i	−0.988029	−	0.154271i	$-0.950697\pi$
$271$	−1607.88	+	2784.92i	−0.360411	+	0.624251i	0.627617	+	0.778522i	$0.284030\pi$
$272$	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	0.732850	−	0.680390i	$-0.238190\pi$
$277$	−1027.20	−	1779.16i	−0.222810	−	0.385918i	−0.955660	+	0.294472i	$0.904856\pi$
$278$	−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	$-0.439886\pi$
$281$	1768.61			0.375468			0.187734	+	0.982220i	$0.439886\pi$
$282$		0			0
$283$	−1170.26	−	2026.96i	−0.245813	−	0.425760i	0.716547	−	0.697539i	$-0.245721\pi$
$283$	−1170.26	−	2026.96i	−0.245813	−	0.425760i	−0.962360	+	0.271779i	$0.912388\pi$
$284$	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	$-0.617986\pi$
$293$	−3633.47			−0.724470			−0.362235	+	0.932087i	$0.617986\pi$
$294$		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	$-0.200978\pi$
$311$	−590.047	−	1021.99i	−0.107584	−	0.186340i	−0.914791	+	0.403928i	$0.867645\pi$
$312$		0			0
$313$	4873.12	−	8440.50i	0.880017	−	1.52423i	0.0286960	−	0.999588i	$-0.490865\pi$
$313$	4873.12	−	8440.50i	0.880017	−	1.52423i	0.851321	−	0.524646i	$-0.175802\pi$
$314$	8490.97			1.52603
$315$		0			0
$316$	2481.00			0.441669
$317$	−4295.96	+	7440.81i	−0.761151	+	1.31835i	0.181106	+	0.983464i	$0.442032\pi$
$317$	−4295.96	+	7440.81i	−0.761151	+	1.31835i	−0.942258	+	0.334889i	$0.891301\pi$
$318$		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	−0.561377	−	0.827560i	$-0.689728\pi$
$331$	2625.60	−	4547.67i	0.436000	−	0.755174i	0.997377	+	0.0723864i	$0.0230615\pi$
$332$	−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	$-0.0177419\pi$
$347$	2915.07	+	5049.06i	0.450978	+	0.781117i	−0.547469	+	0.836826i	$0.684409\pi$
$348$		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	$-0.247385\pi$
$353$	−1663.88	−	2881.92i	−0.250876	−	0.434531i	−0.963767	+	0.266744i	$0.914052\pi$
$354$		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	$-0.812943\pi$
$359$	435.430	−	754.188i	0.0640143	−	0.110876i	0.896256	+	0.443536i	$0.146276\pi$
$360$		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	0.821227	−	0.570601i	$-0.193290\pi$
$367$	−587.358	−	1017.33i	−0.0835418	−	0.144699i	−0.904769	+	0.425903i	$0.859957\pi$
$368$	−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	−0.964031	−	0.265791i	$-0.914367\pi$
$373$	−1814.17	+	3142.23i	−0.251834	+	0.436189i	0.712197	+	0.701980i	$0.247700\pi$
$374$	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	$-0.670102\pi$
$383$	3677.45	−	6369.52i	0.490623	−	0.849784i	0.999942	+	0.0107937i	$0.00343580\pi$
$384$		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	−0.994089	−	0.108564i	$-0.965375\pi$
$389$	−4534.81	−	7854.52i	−0.591064	−	1.02375i	0.403025	−	0.915189i	$-0.367959\pi$
$390$		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	−0.999259	−	0.0384997i	$-0.987742\pi$
$397$	−3688.41	+	6388.52i	−0.466288	+	0.807634i	0.532971	+	0.846134i	$0.321075\pi$
$398$	−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	$-0.776475\pi$
$401$	1426.76	−	2471.21i	0.177678	−	0.307747i	0.941085	+	0.338171i	$0.109808\pi$
$402$		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	−0.974782	−	0.223159i	$-0.928363\pi$
$409$	−5630.03	−	9751.49i	−0.680652	−	1.17892i	0.294130	−	0.955766i	$-0.404970\pi$
$410$	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	$-0.680664\pi$
$419$	−9221.47			−1.07517			−0.537587	+	0.843208i	$0.680664\pi$
$420$		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	−0.999904	−	0.0138840i	$-0.995580\pi$
$431$	−4581.05	−	7934.62i	−0.511976	−	0.886768i	0.487928	−	0.872884i	$-0.337753\pi$
$432$		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	−0.953743	−	0.300625i	$-0.902805\pi$
$439$	−1991.59	+	3449.54i	−0.216523	+	0.375028i	0.737220	+	0.675653i	$0.236138\pi$
$440$	−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	$-0.911341\pi$
$443$	−2262.22	+	3918.29i	−0.242622	+	0.420234i	0.718838	+	0.695177i	$0.244674\pi$
$444$		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	$-0.534805\pi$
$449$	−2076.49			−0.218253			−0.109127	+	0.994028i	$0.534805\pi$
$450$		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	−0.814866	−	0.579650i	$-0.803189\pi$
$457$	923.795	−	1600.06i	0.0945587	−	0.163780i	0.909424	+	0.415869i	$0.136523\pi$
$458$	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	$-0.485895\pi$
$461$	876.945			0.0885974			0.0442987	+	0.999018i	$0.485895\pi$
$462$		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	0.172947	−	0.984931i	$-0.444671\pi$
$467$	9480.88	−	16421.4i	0.939449	−	1.62717i	0.766502	−	0.642242i	$-0.221996\pi$
$468$		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	$-0.0358256\pi$
$479$	4188.88	+	7255.35i	0.399572	+	0.692078i	−0.594101	+	0.804390i	$0.702492\pi$
$480$		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	0.952370	−	0.304944i	$-0.0986378\pi$
$487$	2279.42	+	3948.08i	0.212096	+	0.367360i	−0.740275	+	0.672305i	$0.765304\pi$
$488$	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	$-0.241113\pi$
$491$	15809.9			1.45314			0.726570	+	0.687092i	$0.241113\pi$
$492$		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	0.392309	+	0.919833i	$0.371676\pi$
$499$	−6693.04	+	11592.7i	−0.600444	+	1.04000i	−0.992754	+	0.120167i	$0.961657\pi$
$500$	−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	$-0.418403\pi$
$503$	5720.55			0.507091			0.253545	+	0.967323i	$0.418403\pi$
$504$		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	−0.313175	−	0.949695i	$-0.601393\pi$
$509$	7646.59	−	13244.3i	0.665873	−	1.15333i	0.979048	−	0.203630i	$-0.0652740\pi$
$510$		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	$-0.225468\pi$
$521$	−2184.35	−	3783.40i	−0.183681	−	0.318145i	−0.943131	+	0.332420i	$0.892135\pi$
$522$		0			0
$523$	1211.08	−	2097.66i	0.101256	−	0.175381i	−0.810946	−	0.585121i	$-0.801047\pi$
$523$	1211.08	−	2097.66i	0.101256	−	0.175381i	0.912202	+	0.409740i	$0.134381\pi$
$524$	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	0.476627	+	0.879106i	$0.341859\pi$
$541$	−6581.27	+	11399.1i	−0.523014	+	0.905888i	−0.999641	+	0.0267819i	$0.991474\pi$
$542$	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	$-0.0636682\pi$
$557$	4179.82	+	7239.67i	0.317962	+	0.550726i	−0.662101	+	0.749415i	$0.730335\pi$
$558$		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	−0.999926	−	0.0121334i	$-0.996138\pi$
$563$	−6819.20	−	11811.2i	−0.510471	−	0.884162i	0.489455	−	0.872028i	$-0.337196\pi$
$564$		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	0.425820	+	0.904808i	$0.359986\pi$
$569$	−7745.67	+	13415.9i	−0.570677	+	0.988442i	−0.996497	+	0.0836335i	$0.973348\pi$
$570$		0			0
$571$	2324.08	+	4025.42i	0.170332	+	0.295024i	0.938536	−	0.345182i	$-0.112183\pi$
$571$	2324.08	+	4025.42i	0.170332	+	0.295024i	−0.768204	+	0.640205i	$0.778849\pi$
$572$	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	0.947768	−	0.318959i	$-0.103333\pi$
$577$	2739.53	+	4745.01i	0.197657	+	0.342352i	−0.750111	+	0.661312i	$0.770000\pi$
$578$	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	$-0.450469\pi$
$587$	4408.22			0.309960			0.154980	+	0.987918i	$0.450469\pi$
$588$		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	$-0.864411\pi$
$593$	−1407.63	+	2438.08i	−0.0974779	+	0.168837i	0.813162	+	0.582037i	$0.197744\pi$
$594$		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	−0.977182	−	0.212402i	$-0.931871\pi$
$599$	−9859.53	−	17077.2i	−0.672537	−	1.16487i	0.304646	−	0.952466i	$-0.401462\pi$
$600$		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	−0.998231	−	0.0594590i	$-0.981062\pi$
$607$	−6694.14	+	11594.6i	−0.447622	+	0.775305i	0.550608	+	0.834764i	$0.314396\pi$
$608$	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	0.806047	+	0.591852i	$0.201603\pi$
$613$	13895.9	+	24068.5i	0.915582	+	1.58583i	0.109535	+	0.993983i	$0.465064\pi$
$614$	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	$-0.714233\pi$
$617$	−19107.2			−1.24672			−0.623361	+	0.781935i	$0.714233\pi$
$618$		0			0
$619$	−546.469	−	946.512i	−0.0354837	−	0.0614596i	0.847738	−	0.530415i	$-0.177964\pi$
$619$	−546.469	−	946.512i	−0.0354837	−	0.0614596i	−0.883222	+	0.468955i	$0.844631\pi$
$620$	−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	0.990443	+	0.137924i	$0.0440430\pi$
$641$	9975.33	+	17277.8i	0.614667	+	1.06463i	−0.375776	+	0.926711i	$0.622624\pi$
$642$		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	$-0.274786\pi$
$647$	−5483.09	−	9497.00i	−0.333173	−	0.577072i	−0.983132	+	0.182897i	$0.941453\pi$
$648$		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	$-0.706745\pi$
$653$	6462.54	−	11193.4i	0.387287	−	0.670802i	0.992084	+	0.125579i	$0.0400788\pi$
$654$		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	$-0.613185\pi$
$659$	−11779.0			−0.696273			−0.348137	+	0.937444i	$0.613185\pi$
$660$		0			0
$661$	12520.0	+	21685.3i	0.736721	+	1.27604i	0.953964	+	0.299921i	$0.0969604\pi$
$661$	12520.0	+	21685.3i	0.736721	+	1.27604i	−0.217243	+	0.976118i	$0.569706\pi$
$662$	−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	$-0.945445\pi$
$677$	−6076.70	+	10525.1i	−0.344973	+	0.597510i	0.640376	+	0.768061i	$0.278778\pi$
$678$		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	0.996378	+	0.0850328i	$0.0270995\pi$
$683$	10207.0	+	17679.0i	0.571830	+	0.990438i	−0.424549	+	0.905405i	$0.639567\pi$
$684$		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	−0.997911	−	0.0646110i	$-0.979419\pi$
$691$	−8046.76	+	13937.4i	−0.443000	+	0.767299i	0.554910	+	0.831910i	$0.312753\pi$
$692$	−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	$-0.310637\pi$
$701$	20803.0			1.12085			0.560426	+	0.828204i	$0.310637\pi$
$702$		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	−0.867893	−	0.496751i	$-0.834526\pi$
$709$	−70.7460	+	122.536i	−0.00374742	+	0.00649073i	0.864146	+	0.503242i	$0.167860\pi$
$710$	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	$-0.778039\pi$
$719$	3332.23	−	5771.59i	0.172839	−	0.299366i	0.939411	+	0.342792i	$0.111373\pi$
$720$		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	−0.125834	−	0.992051i	$-0.540161\pi$
$733$	15801.3	−	27368.6i	0.796225	−	1.37910i	0.922059	−	0.387050i	$-0.126506\pi$
$734$	−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	0.950061	−	0.312065i	$-0.101021\pi$
$739$	4113.79	+	7125.30i	0.204774	+	0.354680i	−0.745286	+	0.666744i	$0.767687\pi$
$740$	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	$-0.133009\pi$
$743$	37020.3			1.82792			0.913959	+	0.405805i	$0.133009\pi$
$744$		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	−0.380063	−	0.924960i	$-0.624098\pi$
$751$	12575.0	−	21780.5i	0.611008	−	1.05830i	0.991071	−	0.133336i	$-0.0425689\pi$
$752$	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	0.155324	+	0.987864i	$0.450358\pi$
$761$	−16329.6	+	28283.6i	−0.777853	+	1.34728i	−0.933177	+	0.359417i	$0.882976\pi$
$762$		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	$-0.144149\pi$
$773$	1519.09	+	2631.14i	0.0706829	+	0.122426i	−0.828518	+	0.559963i	$0.810815\pi$
$774$		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	0.971064	−	0.238818i	$-0.0767600\pi$
$787$	6153.38	+	10658.0i	0.278710	+	0.482739i	−0.692355	+	0.721557i	$0.743427\pi$
$788$	−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	$-0.478714\pi$
$797$	3007.06			0.133646			0.0668228	+	0.997765i	$0.478714\pi$
$798$		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	$-0.0927926\pi$
$809$	5292.48	+	9166.84i	0.230005	+	0.398380i	−0.727805	+	0.685785i	$0.759459\pi$
$810$		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	−0.454619	−	0.890686i	$-0.650225\pi$
$821$	12798.3	−	22167.2i	0.544047	−	0.942317i	0.998666	−	0.0516309i	$-0.0164419\pi$
$822$		0			0
$823$	−21889.5	−	37913.6i	−0.927118	−	1.60582i	−0.788119	−	0.615524i	$-0.788945\pi$
$823$	−21889.5	−	37913.6i	−0.927118	−	1.60582i	−0.139000	−	0.990292i	$-0.544389\pi$
$824$	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	$-0.481682\pi$
$827$	2735.78			0.115033			0.0575166	+	0.998345i	$0.481682\pi$
$828$		0			0
$829$	15572.1	+	26971.7i	0.652402	+	1.12999i	0.982538	+	0.186060i	$0.0595719\pi$
$829$	15572.1	+	26971.7i	0.652402	+	1.12999i	−0.330137	+	0.943933i	$0.607095\pi$
$830$	−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	$-0.599710\pi$
$839$	−14977.3			−0.616300			−0.308150	+	0.951338i	$0.599710\pi$
$840$		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	$-0.106745\pi$
$857$	4695.00	+	8131.98i	0.187139	+	0.324134i	−0.757156	+	0.653234i	$0.773412\pi$
$858$		0			0
$859$	−16780.6	+	29064.8i	−0.666526	+	1.15446i	0.312343	+	0.949969i	$0.398886\pi$
$859$	−16780.6	+	29064.8i	−0.666526	+	1.15446i	−0.978869	+	0.204488i	$0.934447\pi$
$860$	33268.6			1.31913
$861$		0			0
$862$	−37155.9			−1.46814
$863$	−12845.8	+	22249.6i	−0.506693	+	0.877617i	0.493277	+	0.869872i	$0.335799\pi$
$863$	−12845.8	+	22249.6i	−0.506693	+	0.877617i	−0.999970	+	0.00774521i	$0.997535\pi$
$864$		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	−0.809904	−	0.586563i	$-0.800481\pi$
$877$	2675.76	−	4634.55i	0.103026	−	0.178447i	0.912930	+	0.408116i	$0.133814\pi$
$878$	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	$-0.726984\pi$
$881$	−34212.7			−1.30835			−0.654174	+	0.756344i	$0.726984\pi$
$882$		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	$-0.857581\pi$
$887$	−2010.44	+	3482.18i	−0.0761035	+	0.131815i	0.825462	+	0.564458i	$0.190915\pi$
$888$		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	0.995979	−	0.0895869i	$-0.0285547\pi$
$907$	11483.6	+	19890.2i	0.420405	+	0.728163i	−0.575574	+	0.817750i	$0.695221\pi$
$908$	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	$-0.442614\pi$
$911$	9860.77			0.358619			0.179309	+	0.983793i	$0.442614\pi$
$912$		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	−0.814836	−	0.579692i	$-0.803173\pi$
$919$	2635.77	−	4565.30i	0.0946096	−	0.163869i	0.909446	+	0.415823i	$0.136506\pi$
$920$	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	$-0.748571\pi$
$929$	7451.31	−	12906.0i	0.263153	−	0.455795i	0.967078	+	0.254480i	$0.0819042\pi$
$930$		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	$-0.247602\pi$
$941$	−7260.76	−	12576.0i	−0.251535	−	0.435671i	−0.963949	+	0.266089i	$0.914269\pi$
$942$		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	$-0.843951\pi$
$947$	−971.867	+	1683.32i	−0.0333489	+	0.0577621i	0.848869	+	0.528603i	$0.177284\pi$
$948$		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	$-0.592755\pi$
$953$	−16904.1			−0.574583			−0.287292	+	0.957843i	$0.592755\pi$
$954$		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	$-0.891996\pi$
$971$	−5544.74	+	9603.77i	−0.183253	+	0.317404i	0.759733	+	0.650235i	$0.225330\pi$
$972$		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	−0.881543	−	0.472103i	$-0.843495\pi$
$977$	−25945.9	−	44939.7i	−0.849625	−	1.47159i	0.0319179	−	0.999490i	$-0.489838\pi$
$978$		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	$-0.297120\pi$
$983$	−12280.3	−	21270.2i	−0.398456	−	0.690145i	−0.993536	+	0.113521i	$0.963787\pi$
$984$		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	0.975362	−	0.220612i	$-0.0708056\pi$
$991$	9253.76	+	16028.0i	0.296625	+	0.513769i	−0.678737	+	0.734382i	$0.737472\pi$
$992$	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	0.974239	+	0.225518i	$0.0724074\pi$
$997$	21483.1	+	37209.8i	0.682424	+	1.18199i	−0.291815	+	0.956475i	$0.594259\pi$
$998$	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.37.4	yes	8
3.2	odd	2	inner	63.4.e.d.37.1	✓	8
7.2	even	3		441.4.a.w.1.1		4
7.3	odd	6		441.4.e.x.361.4		8
7.4	even	3	inner	63.4.e.d.46.4	yes	8
7.5	odd	6		441.4.a.v.1.1		4
7.6	odd	2		441.4.e.x.226.4		8
21.2	odd	6		441.4.a.w.1.4		4
21.5	even	6		441.4.a.v.1.4		4
21.11	odd	6	inner	63.4.e.d.46.1	yes	8
21.17	even	6		441.4.e.x.361.1		8
21.20	even	2		441.4.e.x.226.1		8

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

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

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